[{"data":1,"prerenderedAt":101348},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-lagrangeova-metoda":1626,"course-stats-imek":3305,"course-topics-imek":3309,"backlinks-lagrangeova-metoda":101319,"related-lagrangeova-metoda":101345},{"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":3304},{"id":1628,"title":1629,"body":1630,"course":659,"courses":3292,"created":1129,"description":3293,"extension":661,"meta":3294,"navigation":664,"path":3295,"seo":3296,"sources":3297,"stem":3298,"tags":3299,"type":3302,"updated":677,"__hash__":3303},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":1631,"toc":3280},[1632,1635,1753,1762,1783,1787,1794,1861,1883,1887,1890,2030,2034,2247,2284,2426,2430,2495,2511,2539,2543,2641,2645,2649,2705,2811,3030,3034,3077,3183,3235,3239],[12,1633,1629],{"id":1634},"lagrangeova-metoda-vázané-extrémy",[724,1636,1637,1638,1671,1672,1709,1710,1713,1714,1745,1746,1752],{},"Hledáme extrém funkce ",[883,1639,1641],{"className":1640},[886],[888,1642,1643],{"xmlns":890},[892,1644,1645,1668],{},[895,1646,1647,1650,1655,1658,1662,1665],{},[898,1648,1649],{},"f",[1651,1652,1654],"mo",{"stretchy":1653},"false","(",[898,1656,1657],{},"x",[1651,1659,1661],{"separator":1660},"true",",",[898,1663,1664],{},"y",[1651,1666,1667],{"stretchy":1653},")",[902,1669,1670],{"encoding":904},"f(x, y)"," (resp. ",[883,1673,1675],{"className":1674},[886],[888,1676,1677],{"xmlns":890},[892,1678,1679,1706],{},[895,1680,1681,1683,1685,1695,1697,1704],{},[898,1682,900],{},[1651,1684,1654],{"stretchy":1653},[1686,1687,1688,1691],"msub",{},[898,1689,1690],{},"Q",[1692,1693,1694],"mn",{},"1",[1651,1696,1661],{"separator":1660},[1686,1698,1699,1701],{},[898,1700,1690],{},[1692,1702,1703],{},"2",[1651,1705,1667],{"stretchy":1653},[902,1707,1708],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,1711,1712],{},"podmíněný"," rovnicí ",[883,1715,1717],{"className":1716},[886],[888,1718,1719],{"xmlns":890},[892,1720,1721,1742],{},[895,1722,1723,1726,1728,1730,1732,1734,1736,1739],{},[898,1724,1725],{},"g",[1651,1727,1654],{"stretchy":1653},[898,1729,1657],{},[1651,1731,1661],{"separator":1660},[898,1733,1664],{},[1651,1735,1667],{"stretchy":1653},[1651,1737,1738],{},"=",[1692,1740,1741],{},"0",[902,1743,1744],{"encoding":904},"g(x, y) = 0",". V ",[207,1747,1751],{"className":1748,"dataFsResolvedFilePath":1749,"href":1750},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","matematické ekonomii"," se používá pro:",[724,1754,1755],{},[1756,1757],"img",{"alt":1758,"className":1759,"src":1761},"imek-lagrange-tecnost",[210,1760],"wikilink-broken","\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,1763,1764,1774,1780],{},[123,1765,1766,1769,1770,1667],{},[38,1767,1768],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,1771,1773],{"className":1772,"dataFsResolvedFilePath":878,"href":879},[210],"uzitecnost",[123,1775,1776,1779],{},[38,1777,1778],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,1781,1782],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,1784,1786],{"id":1785},"princip","Princip",[724,1788,1789,1790,1793],{},"Definujeme ",[38,1791,1792],{},"Lagrangeovu funkci",":",[724,1795,1796],{},[883,1797,1799],{"className":1798},[886],[888,1800,1801],{"xmlns":890},[892,1802,1803,1858],{},[895,1804,1805,1808,1810,1812,1814,1816,1818,1821,1823,1825,1827,1829,1831,1833,1835,1837,1840,1842,1846,1848,1850,1852,1854,1856],{},[898,1806,1807],{},"L",[1651,1809,1654],{"stretchy":1653},[898,1811,1657],{},[1651,1813,1661],{"separator":1660},[898,1815,1664],{},[1651,1817,1661],{"separator":1660},[898,1819,1820],{},"λ",[1651,1822,1667],{"stretchy":1653},[1651,1824,1738],{},[898,1826,1649],{},[1651,1828,1654],{"stretchy":1653},[898,1830,1657],{},[1651,1832,1661],{"separator":1660},[898,1834,1664],{},[1651,1836,1667],{"stretchy":1653},[1651,1838,1839],{},"+",[898,1841,1820],{},[1843,1844,1845],"mtext",{}," ",[898,1847,1725],{},[1651,1849,1654],{"stretchy":1653},[898,1851,1657],{},[1651,1853,1661],{"separator":1660},[898,1855,1664],{},[1651,1857,1667],{"stretchy":1653},[902,1859,1860],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,1862,1863,1864,1878,1879,1882],{},"kde ",[883,1865,1867],{"className":1866},[886],[888,1868,1869],{"xmlns":890},[892,1870,1871,1875],{},[895,1872,1873],{},[898,1874,1820],{},[902,1876,1877],{"encoding":904},"\\lambda"," je ",[38,1880,1881],{},"Lagrangeův multiplikátor",".",[115,1884,1886],{"id":1885},"nutná-podmínka","Nutná podmínka",[724,1888,1889],{},"Řešíme soustavu:",[724,1891,1892,1944,1992],{},[883,1893,1895],{"className":1894},[886],[888,1896,1897],{"xmlns":890},[892,1898,1899,1941],{},[895,1900,1901,1913,1915,1923,1925,1927,1929,1937,1939],{},[1902,1903,1904,1906,1908],"msubsup",{},[898,1905,1807],{},[898,1907,1657],{},[1651,1909,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},"normal","0em","′",[1651,1914,1738],{},[1902,1916,1917,1919,1921],{},[898,1918,1649],{},[898,1920,1657],{},[1651,1922,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,1924,1839],{},[898,1926,1820],{},[1843,1928,1845],{},[1902,1930,1931,1933,1935],{},[898,1932,1725],{},[898,1934,1657],{},[1651,1936,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,1938,1738],{},[1692,1940,1741],{},[902,1942,1943],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,1945,1947],{"className":1946},[886],[888,1948,1949],{"xmlns":890},[892,1950,1951,1989],{},[895,1952,1953,1961,1963,1971,1973,1975,1977,1985,1987],{},[1902,1954,1955,1957,1959],{},[898,1956,1807],{},[898,1958,1664],{},[1651,1960,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,1962,1738],{},[1902,1964,1965,1967,1969],{},[898,1966,1649],{},[898,1968,1664],{},[1651,1970,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,1972,1839],{},[898,1974,1820],{},[1843,1976,1845],{},[1902,1978,1979,1981,1983],{},[898,1980,1725],{},[898,1982,1664],{},[1651,1984,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,1986,1738],{},[1692,1988,1741],{},[902,1990,1991],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,1993,1995],{"className":1994},[886],[888,1996,1997],{"xmlns":890},[892,1998,1999,2027],{},[895,2000,2001,2009,2011,2013,2015,2017,2019,2021,2023,2025],{},[1902,2002,2003,2005,2007],{},[898,2004,1807],{},[898,2006,1820],{},[1651,2008,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,2010,1738],{},[898,2012,1725],{},[1651,2014,1654],{"stretchy":1653},[898,2016,1657],{},[1651,2018,1661],{"separator":1660},[898,2020,1664],{},[1651,2022,1667],{"stretchy":1653},[1651,2024,1738],{},[1692,2026,1741],{},[902,2028,2029],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,2031,2033],{"id":2032},"postačující-podmínka","Postačující podmínka",[724,2035,2036],{},[883,2037,2039],{"className":2038},[886],[888,2040,2041],{"xmlns":890},[892,2042,2043,2244],{},[895,2044,2045,2048,2050,2052,2054,2056,2058,2060,2062,2064,2066,2082,2084,2086,2102,2104,2106,2114,2121,2123,2125,2141,2143,2145,2161,2163,2165,2173,2179,2182,2184,2186,2202,2204,2206,2222,2224,2226,2234,2236],{},[898,2046,2047],{},"D",[1651,2049,1654],{"stretchy":1653},[898,2051,1657],{},[1651,2053,1661],{"separator":1660},[898,2055,1664],{},[1651,2057,1661],{"separator":1660},[898,2059,1820],{},[1651,2061,1667],{"stretchy":1653},[1651,2063,1738],{},[1651,2065,1654],{"stretchy":1653},[1902,2067,2068,2070,2076],{},[898,2069,1649],{},[895,2071,2072,2074],{},[898,2073,1657],{},[898,2075,1657],{},[895,2077,2078,2080],{},[1651,2079,1912],{"mathvariant":1910},[1651,2081,1912],{"mathvariant":1910},[1651,2083,1839],{},[898,2085,1820],{},[1902,2087,2088,2090,2096],{},[898,2089,1725],{},[895,2091,2092,2094],{},[898,2093,1657],{},[898,2095,1657],{},[895,2097,2098,2100],{},[1651,2099,1912],{"mathvariant":1910},[1651,2101,1912],{"mathvariant":1910},[1651,2103,1667],{"stretchy":1653},[1651,2105,1654],{"stretchy":1653},[1902,2107,2108,2110,2112],{},[898,2109,1725],{},[898,2111,1664],{},[1651,2113,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[2115,2116,2117,2119],"msup",{},[1651,2118,1667],{"stretchy":1653},[1692,2120,1703],{},[1651,2122,1839],{},[1651,2124,1654],{"stretchy":1653},[1902,2126,2127,2129,2135],{},[898,2128,1649],{},[895,2130,2131,2133],{},[898,2132,1664],{},[898,2134,1664],{},[895,2136,2137,2139],{},[1651,2138,1912],{"mathvariant":1910},[1651,2140,1912],{"mathvariant":1910},[1651,2142,1839],{},[898,2144,1820],{},[1902,2146,2147,2149,2155],{},[898,2148,1725],{},[895,2150,2151,2153],{},[898,2152,1664],{},[898,2154,1664],{},[895,2156,2157,2159],{},[1651,2158,1912],{"mathvariant":1910},[1651,2160,1912],{"mathvariant":1910},[1651,2162,1667],{"stretchy":1653},[1651,2164,1654],{"stretchy":1653},[1902,2166,2167,2169,2171],{},[898,2168,1725],{},[898,2170,1657],{},[1651,2172,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[2115,2174,2175,2177],{},[1651,2176,1667],{"stretchy":1653},[1692,2178,1703],{},[1651,2180,2181],{},"−",[1692,2183,1703],{},[1651,2185,1654],{"stretchy":1653},[1902,2187,2188,2190,2196],{},[898,2189,1649],{},[895,2191,2192,2194],{},[898,2193,1657],{},[898,2195,1664],{},[895,2197,2198,2200],{},[1651,2199,1912],{"mathvariant":1910},[1651,2201,1912],{"mathvariant":1910},[1651,2203,1839],{},[898,2205,1820],{},[1902,2207,2208,2210,2216],{},[898,2209,1725],{},[895,2211,2212,2214],{},[898,2213,1657],{},[898,2215,1664],{},[895,2217,2218,2220],{},[1651,2219,1912],{"mathvariant":1910},[1651,2221,1912],{"mathvariant":1910},[1651,2223,1667],{"stretchy":1653},[1843,2225,1845],{},[1902,2227,2228,2230,2232],{},[898,2229,1725],{},[898,2231,1657],{},[1651,2233,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1843,2235,1845],{},[1902,2237,2238,2240,2242],{},[898,2239,1725],{},[898,2241,1664],{},[1651,2243,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,2245,2246],{"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",[724,2248,2249,2250,2283],{},"Je-li ",[883,2251,2253],{"className":2252},[886],[888,2254,2255],{"xmlns":890},[892,2256,2257,2280],{},[895,2258,2259,2262,2264,2266,2269,2271,2277],{},[1651,2260,2261],{"stretchy":1653},"[",[898,2263,207],{},[1651,2265,1661],{"separator":1660},[898,2267,2268],{},"b",[1651,2270,1661],{"separator":1660},[1686,2272,2273,2275],{},[898,2274,1820],{},[1692,2276,1741],{},[1651,2278,2279],{"stretchy":1653},"]",[902,2281,2282],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,2285,2286,2357],{},[123,2287,2288,2325,2326,2329,2330],{},[883,2289,2291],{"className":2290},[886],[888,2292,2293],{"xmlns":890},[892,2294,2295,2322],{},[895,2296,2297,2299,2301,2303,2305,2307,2309,2315,2317,2320],{},[898,2298,2047],{},[1651,2300,1654],{"stretchy":1653},[898,2302,207],{},[1651,2304,1661],{"separator":1660},[898,2306,2268],{},[1651,2308,1661],{"separator":1660},[1686,2310,2311,2313],{},[898,2312,1820],{},[1692,2314,1741],{},[1651,2316,1667],{"stretchy":1653},[1651,2318,2319],{},"\u003C",[1692,2321,1741],{},[902,2323,2324],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0"," ⇒ ",[38,2327,2328],{},"maximum"," vázané podmínkou ",[883,2331,2333],{"className":2332},[886],[888,2334,2335],{"xmlns":890},[892,2336,2337,2355],{},[895,2338,2339,2341,2343,2345,2347,2349,2351,2353],{},[898,2340,1725],{},[1651,2342,1654],{"stretchy":1653},[898,2344,1657],{},[1651,2346,1661],{"separator":1660},[898,2348,1664],{},[1651,2350,1667],{"stretchy":1653},[1651,2352,1738],{},[1692,2354,1741],{},[902,2356,1744],{"encoding":904},[123,2358,2359,2325,2396,2329,2399],{},[883,2360,2362],{"className":2361},[886],[888,2363,2364],{"xmlns":890},[892,2365,2366,2393],{},[895,2367,2368,2370,2372,2374,2376,2378,2380,2386,2388,2391],{},[898,2369,2047],{},[1651,2371,1654],{"stretchy":1653},[898,2373,207],{},[1651,2375,1661],{"separator":1660},[898,2377,2268],{},[1651,2379,1661],{"separator":1660},[1686,2381,2382,2384],{},[898,2383,1820],{},[1692,2385,1741],{},[1651,2387,1667],{"stretchy":1653},[1651,2389,2390],{},">",[1692,2392,1741],{},[902,2394,2395],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,2397,2398],{},"minimum",[883,2400,2402],{"className":2401},[886],[888,2403,2404],{"xmlns":890},[892,2405,2406,2424],{},[895,2407,2408,2410,2412,2414,2416,2418,2420,2422],{},[898,2409,1725],{},[1651,2411,1654],{"stretchy":1653},[898,2413,1657],{},[1651,2415,1661],{"separator":1660},[898,2417,1664],{},[1651,2419,1667],{"stretchy":1653},[1651,2421,1738],{},[1692,2423,1741],{},[902,2425,1744],{"encoding":904},[115,2427,2429],{"id":2428},"význam-multiplikátoru","Význam multiplikátoru",[724,2431,2432],{},[883,2433,2435],{"className":2434},[886],[888,2436,2437],{"xmlns":890},[892,2438,2439,2492],{},[895,2440,2441,2443,2445,2468,2470],{},[898,2442,1820],{},[1651,2444,1738],{},[2446,2447,2448,2456],"mfrac",{},[1902,2449,2450,2452,2454],{},[898,2451,1649],{},[898,2453,1657],{},[1651,2455,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[895,2457,2458,2460],{},[1651,2459,2181],{},[1902,2461,2462,2464,2466],{},[898,2463,1725],{},[898,2465,1657],{},[1651,2467,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,2469,1738],{},[2446,2471,2472,2480],{},[1902,2473,2474,2476,2478],{},[898,2475,1649],{},[898,2477,1664],{},[1651,2479,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[895,2481,2482,2484],{},[1651,2483,2181],{},[1902,2485,2486,2488,2490],{},[898,2487,1725],{},[898,2489,1664],{},[1651,2491,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,2493,2494],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,2496,2497,2510],{},[883,2498,2500],{"className":2499},[886],[888,2501,2502],{"xmlns":890},[892,2503,2504,2508],{},[895,2505,2506],{},[898,2507,1820],{},[902,2509,1877],{"encoding":904}," udává:",[120,2512,2513,2519],{},[123,2514,2515,2516],{},"konstantní ",[38,2517,2518],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,2520,2521,2524,2525,2538],{},[38,2522,2523],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,2526,2528],{"className":2527},[886],[888,2529,2530],{"xmlns":890},[892,2531,2532,2536],{},[895,2533,2534],{},[898,2535,1649],{},[902,2537,1649],{"encoding":904},", uvolní-li se omezení o jednotku",[115,2540,2542],{"id":2541},"alternativní-postup","Alternativní postup",[724,2544,2545,2546,2573,2574,2598,2599,2623,2624,2637,2638,1882],{},"Lze-li z ",[883,2547,2549],{"className":2548},[886],[888,2550,2551],{"xmlns":890},[892,2552,2553,2571],{},[895,2554,2555,2557,2559,2561,2563,2565,2567,2569],{},[898,2556,1725],{},[1651,2558,1654],{"stretchy":1653},[898,2560,1657],{},[1651,2562,1661],{"separator":1660},[898,2564,1664],{},[1651,2566,1667],{"stretchy":1653},[1651,2568,1738],{},[1692,2570,1741],{},[902,2572,1744],{"encoding":904}," vyjádřit ",[883,2575,2577],{"className":2576},[886],[888,2578,2579],{"xmlns":890},[892,2580,2581,2595],{},[895,2582,2583,2585,2587,2589,2591,2593],{},[898,2584,1664],{},[1651,2586,1738],{},[898,2588,1664],{},[1651,2590,1654],{"stretchy":1653},[898,2592,1657],{},[1651,2594,1667],{"stretchy":1653},[902,2596,2597],{"encoding":904},"y = y(x)"," (nebo ",[883,2600,2602],{"className":2601},[886],[888,2603,2604],{"xmlns":890},[892,2605,2606,2620],{},[895,2607,2608,2610,2612,2614,2616,2618],{},[898,2609,1657],{},[1651,2611,1738],{},[898,2613,1657],{},[1651,2615,1654],{"stretchy":1653},[898,2617,1664],{},[1651,2619,1667],{"stretchy":1653},[902,2621,2622],{"encoding":904},"x = x(y)","), dosadíme do ",[883,2625,2627],{"className":2626},[886],[888,2628,2629],{"xmlns":890},[892,2630,2631,2635],{},[895,2632,2633],{},[898,2634,1649],{},[902,2636,1649],{"encoding":904}," a převedeme na ",[38,2639,2640],{},"extrém funkce jedné proměnné",[115,2642,2644],{"id":2643},"použití-v-imek","Použití v ImeK",[198,2646,2648],{"id":2647},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,2650,2651,2652,1882],{},"Rozpočtové omezení: ",[883,2653,2655],{"className":2654},[886],[888,2656,2657],{"xmlns":890},[892,2658,2659,2702],{},[895,2660,2661,2669,2671,2680,2686,2688,2696],{},[2115,2662,2663,2666],{},[898,2664,2665],{},"Y",[1651,2667,2668],{},"∗",[1651,2670,1738],{},[1902,2672,2673,2676,2678],{},[898,2674,2675],{},"P",[1692,2677,1694],{},[1651,2679,2668],{},[1686,2681,2682,2684],{},[898,2683,1690],{},[1692,2685,1694],{},[1651,2687,1839],{},[1902,2689,2690,2692,2694],{},[898,2691,2675],{},[1692,2693,1703],{},[1651,2695,2668],{},[1686,2697,2698,2700],{},[898,2699,1690],{},[1692,2701,1703],{},[902,2703,2704],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,2706,2707],{},[883,2708,2710],{"className":2709},[886],[888,2711,2712],{"xmlns":890},[892,2713,2714,2808],{},[895,2715,2716,2718,2720,2726,2728,2734,2736,2738,2740,2742,2744,2746,2752,2754,2760,2762,2764,2766,2768,2774,2776,2784,2790,2792,2800,2806],{},[898,2717,1807],{},[1651,2719,1654],{"stretchy":1653},[1686,2721,2722,2724],{},[898,2723,1690],{},[1692,2725,1694],{},[1651,2727,1661],{"separator":1660},[1686,2729,2730,2732],{},[898,2731,1690],{},[1692,2733,1703],{},[1651,2735,1661],{"separator":1660},[898,2737,1820],{},[1651,2739,1667],{"stretchy":1653},[1651,2741,1738],{},[898,2743,900],{},[1651,2745,1654],{"stretchy":1653},[1686,2747,2748,2750],{},[898,2749,1690],{},[1692,2751,1694],{},[1651,2753,1661],{"separator":1660},[1686,2755,2756,2758],{},[898,2757,1690],{},[1692,2759,1703],{},[1651,2761,1667],{"stretchy":1653},[1651,2763,1839],{},[898,2765,1820],{},[1651,2767,1654],{"stretchy":1653},[2115,2769,2770,2772],{},[898,2771,2665],{},[1651,2773,2668],{},[1651,2775,2181],{},[1902,2777,2778,2780,2782],{},[898,2779,2675],{},[1692,2781,1694],{},[1651,2783,2668],{},[1686,2785,2786,2788],{},[898,2787,1690],{},[1692,2789,1694],{},[1651,2791,2181],{},[1902,2793,2794,2796,2798],{},[898,2795,2675],{},[1692,2797,1703],{},[1651,2799,2668],{},[1686,2801,2802,2804],{},[898,2803,1690],{},[1692,2805,1703],{},[1651,2807,1667],{"stretchy":1653},[902,2809,2810],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,2812,2813,2814,1343,2846,1343,2878,2927,2928,2983,2984,1882],{},"Soustava: ",[883,2815,2817],{"className":2816},[886],[888,2818,2819],{"xmlns":890},[892,2820,2821,2843],{},[895,2822,2823,2831,2833,2835],{},[1902,2824,2825,2827,2829],{},[898,2826,900],{},[1692,2828,1694],{},[1651,2830,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,2832,1738],{},[898,2834,1820],{},[1902,2836,2837,2839,2841],{},[898,2838,2675],{},[1692,2840,1694],{},[1651,2842,2668],{},[902,2844,2845],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,2847,2849],{"className":2848},[886],[888,2850,2851],{"xmlns":890},[892,2852,2853,2875],{},[895,2854,2855,2863,2865,2867],{},[1902,2856,2857,2859,2861],{},[898,2858,900],{},[1692,2860,1703],{},[1651,2862,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,2864,1738],{},[898,2866,1820],{},[1902,2868,2869,2871,2873],{},[898,2870,2675],{},[1692,2872,1703],{},[1651,2874,2668],{},[902,2876,2877],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,2879,2881],{"className":2880},[886],[888,2882,2883],{"xmlns":890},[892,2884,2885,2925],{},[895,2886,2887,2893,2895,2903,2909,2911,2919],{},[2115,2888,2889,2891],{},[898,2890,2665],{},[1651,2892,2668],{},[1651,2894,1738],{},[1902,2896,2897,2899,2901],{},[898,2898,2675],{},[1692,2900,1694],{},[1651,2902,2668],{},[1686,2904,2905,2907],{},[898,2906,1690],{},[1692,2908,1694],{},[1651,2910,1839],{},[1902,2912,2913,2915,2917],{},[898,2914,2675],{},[1692,2916,1703],{},[1651,2918,2668],{},[1686,2920,2921,2923],{},[898,2922,1690],{},[1692,2924,1703],{},[902,2926,2704],{"encoding":904},". Z prvních dvou: ",[883,2929,2931],{"className":2930},[886],[888,2932,2933],{"xmlns":890},[892,2934,2935,2980],{},[895,2936,2937,2958,2960],{},[2938,2939,2940],"mstyle",{"scriptlevel":1741,"displaystyle":1653},[2446,2941,2942,2950],{},[1902,2943,2944,2946,2948],{},[898,2945,900],{},[1692,2947,1694],{},[1651,2949,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1902,2951,2952,2954,2956],{},[898,2953,900],{},[1692,2955,1703],{},[1651,2957,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,2959,1738],{},[2938,2961,2962],{"scriptlevel":1741,"displaystyle":1653},[2446,2963,2964,2972],{},[1902,2965,2966,2968,2970],{},[898,2967,2675],{},[1692,2969,1694],{},[1651,2971,2668],{},[1902,2973,2974,2976,2978],{},[898,2975,2675],{},[1692,2977,1703],{},[1651,2979,2668],{},[902,2981,2982],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,2985,2987],{"className":2986},[886],[888,2988,2989],{"xmlns":890},[892,2990,2991,3027],{},[895,2992,2993,2996,2999,3002,3005,3007],{},[898,2994,2995],{},"M",[898,2997,2998],{},"R",[898,3000,3001],{},"C",[898,3003,3004],{},"S",[1651,3006,1738],{},[2938,3008,3009],{"scriptlevel":1741,"displaystyle":1653},[2446,3010,3011,3019],{},[1902,3012,3013,3015,3017],{},[898,3014,2675],{},[1692,3016,1694],{},[1651,3018,2668],{},[1902,3020,3021,3023,3025],{},[898,3022,2675],{},[1692,3024,1703],{},[1651,3026,2668],{},[902,3028,3029],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,3031,3033],{"id":3032},"minimalizace-výdajů","Minimalizace výdajů",[724,3035,3036,3037,1882],{},"Podmínka dané užitečnosti ",[883,3038,3040],{"className":3039},[886],[888,3041,3042],{"xmlns":890},[892,3043,3044,3074],{},[895,3045,3046,3052,3054,3056,3058,3064,3066,3072],{},[2115,3047,3048,3050],{},[898,3049,900],{},[1651,3051,2668],{},[1651,3053,1738],{},[898,3055,900],{},[1651,3057,1654],{"stretchy":1653},[1686,3059,3060,3062],{},[898,3061,1690],{},[1692,3063,1694],{},[1651,3065,1661],{"separator":1660},[1686,3067,3068,3070],{},[898,3069,1690],{},[1692,3071,1703],{},[1651,3073,1667],{"stretchy":1653},[902,3075,3076],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,3078,3079],{},[883,3080,3082],{"className":3081},[886],[888,3083,3084],{"xmlns":890},[892,3085,3086,3180],{},[895,3087,3088,3090,3092,3098,3100,3106,3108,3110,3112,3114,3122,3128,3130,3138,3144,3146,3148,3150,3156,3158,3160,3162,3168,3170,3176,3178],{},[898,3089,1807],{},[1651,3091,1654],{"stretchy":1653},[1686,3093,3094,3096],{},[898,3095,1690],{},[1692,3097,1694],{},[1651,3099,1661],{"separator":1660},[1686,3101,3102,3104],{},[898,3103,1690],{},[1692,3105,1703],{},[1651,3107,1661],{"separator":1660},[898,3109,1820],{},[1651,3111,1667],{"stretchy":1653},[1651,3113,1738],{},[1902,3115,3116,3118,3120],{},[898,3117,2675],{},[1692,3119,1694],{},[1651,3121,2668],{},[1686,3123,3124,3126],{},[898,3125,1690],{},[1692,3127,1694],{},[1651,3129,1839],{},[1902,3131,3132,3134,3136],{},[898,3133,2675],{},[1692,3135,1703],{},[1651,3137,2668],{},[1686,3139,3140,3142],{},[898,3141,1690],{},[1692,3143,1703],{},[1651,3145,1839],{},[898,3147,1820],{},[1651,3149,1654],{"stretchy":1653},[2115,3151,3152,3154],{},[898,3153,900],{},[1651,3155,2668],{},[1651,3157,2181],{},[898,3159,900],{},[1651,3161,1654],{"stretchy":1653},[1686,3163,3164,3166],{},[898,3165,1690],{},[1692,3167,1694],{},[1651,3169,1661],{"separator":1660},[1686,3171,3172,3174],{},[898,3173,1690],{},[1692,3175,1703],{},[1651,3177,1667],{"stretchy":1653},[1651,3179,1667],{"stretchy":1653},[902,3181,3182],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,3184,3185,3186,1882],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,3187,3189],{"className":3188},[886],[888,3190,3191],{"xmlns":890},[892,3192,3193,3232],{},[895,3194,3195,3202,3204,3210,3212,3218,3220,3226,3228,3230],{},[1686,3196,3197,3199],{},[898,3198,1690],{},[898,3200,3201],{},"i",[1651,3203,1738],{},[1686,3205,3206,3208],{},[898,3207,2047],{},[898,3209,3201],{},[1651,3211,1654],{"stretchy":1653},[1686,3213,3214,3216],{},[898,3215,2675],{},[1692,3217,1694],{},[1651,3219,1661],{"separator":1660},[1686,3221,3222,3224],{},[898,3223,2675],{},[1692,3225,1703],{},[1651,3227,1661],{"separator":1660},[898,3229,900],{},[1651,3231,1667],{"stretchy":1653},[902,3233,3234],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,3236,3238],{"id":3237},"navigace","Navigace",[120,3240,3241,3250,3259,3268],{},[123,3242,3243,3246,3247],{},[38,3244,3245],{},"Předchozí:"," ",[207,3248,784],{"className":3249,"dataFsResolvedFilePath":782,"href":783},[210],[123,3251,3252,3246,3255],{},[38,3253,3254],{},"Navazující:",[207,3256,3258],{"className":3257,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka",[123,3260,3261,3246,3264,3267],{},[38,3262,3263],{},"Aplikace v kurzu:",[207,3265,880],{"className":3266,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,3269,3270,3246,3273,1343,3276,3279],{},[38,3271,3272],{},"Souvislosti:",[207,3274,936],{"className":3275,"dataFsResolvedFilePath":934,"href":935},[210],[207,3277,1400],{"className":3278,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":3281},[3282,3283,3284,3285,3286,3287,3291],{"id":1785,"depth":642,"text":1786},{"id":1885,"depth":642,"text":1886},{"id":2032,"depth":642,"text":2033},{"id":2428,"depth":642,"text":2429},{"id":2541,"depth":642,"text":2542},{"id":2643,"depth":642,"text":2644,"children":3288},[3289,3290],{"id":2647,"depth":649,"text":2648},{"id":3032,"depth":649,"text":3033},{"id":3237,"depth":642,"text":3238},[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":1629,"description":3293},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,3300,3301],"vazane-extremy","multiplikator","topic","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow","topics",{"zapisku":1625,"topics":3306,"summaries":3307,"outputs":3308},15,5,1,[3310,5170,10871,12422,13293,17577,19098,28978,37972,52039,56331,75675,87787,96746,97034],{"id":3311,"title":3312,"body":3313,"course":1128,"courses":659,"created":1129,"description":5159,"extension":661,"meta":5160,"navigation":664,"path":5161,"seo":5162,"sources":5163,"stem":5164,"tags":5165,"type":3302,"updated":677,"__hash__":5169},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":3314,"toc":5142},[3315,3318,3337,3341,3417,3420,3546,3693,3696,3776,3780,3839,3889,3896,3900,4035,4086,4090,4132,4200,4271,4279,4283,4321,4393,4397,4478,4527,4571,4575,4577,4647,4649,4699,4775,4782,4785,4838,5106,5108],[12,3316,3312],{"id":3317},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,3319,3320,3321,3325,3326,3329,3330,3333,3334,1882],{},"Matematický aparát kurzu ",[207,3322,3324],{"className":3323,"dataFsResolvedFilePath":1749,"href":1750},[210],"ImeK",". Bez derivace se neobejdou ",[38,3327,3328],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,3331,3332],{},"maximalizace zisku"," ani ",[38,3335,3336],{},"minimalizace nákladů",[115,3338,3340],{"id":3339},"funkce-a-polynomy","Funkce a polynomy",[724,3342,3343,3344,3368,3369,3382,3383,3396,3397,1882],{},"Funkce jedné proměnné ",[883,3345,3347],{"className":3346},[886],[888,3348,3349],{"xmlns":890},[892,3350,3351,3365],{},[895,3352,3353,3355,3357,3359,3361,3363],{},[898,3354,1664],{},[1651,3356,1738],{},[898,3358,1649],{},[1651,3360,1654],{"stretchy":1653},[898,3362,1657],{},[1651,3364,1667],{"stretchy":1653},[902,3366,3367],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,3370,3372],{"className":3371},[886],[888,3373,3374],{"xmlns":890},[892,3375,3376,3380],{},[895,3377,3378],{},[898,3379,1657],{},[902,3381,1657],{"encoding":904}," (nezávislá) → ",[883,3384,3386],{"className":3385},[886],[888,3387,3388],{"xmlns":890},[892,3389,3390,3394],{},[895,3391,3392],{},[898,3393,1664],{},[902,3395,1664],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,3398,3400],{"className":3399},[886],[888,3401,3402],{"xmlns":890},[892,3403,3404,3414],{},[895,3405,3406,3408,3410,3412],{},[898,3407,1649],{},[1651,3409,1654],{"stretchy":1653},[898,3411,207],{},[1651,3413,1667],{"stretchy":1653},[902,3415,3416],{"encoding":904},"f(a)",[724,3418,3419],{},"Polynomy:",[120,3421,3422,3453,3494],{},[123,3423,3424],{},[152,3425,3426],{},[123,3427,3428,3429],{},"stupně: ",[883,3430,3432],{"className":3431},[886],[888,3433,3434],{"xmlns":890},[892,3435,3436,3450],{},[895,3437,3438,3440,3442,3444,3446,3448],{},[898,3439,1664],{},[1651,3441,1738],{},[898,3443,207],{},[898,3445,1657],{},[1651,3447,1839],{},[898,3449,2268],{},[902,3451,3452],{"encoding":904},"y = ax + b",[123,3454,3455],{},[152,3456,3457],{"start":642},[123,3458,3428,3459],{},[883,3460,3462],{"className":3461},[886],[888,3463,3464],{"xmlns":890},[892,3465,3466,3491],{},[895,3467,3468,3470,3472,3474,3480,3482,3484,3486,3488],{},[898,3469,1664],{},[1651,3471,1738],{},[898,3473,207],{},[2115,3475,3476,3478],{},[898,3477,1657],{},[1692,3479,1703],{},[1651,3481,1839],{},[898,3483,2268],{},[898,3485,1657],{},[1651,3487,1839],{},[898,3489,3490],{},"c",[902,3492,3493],{"encoding":904},"y = ax^2 + bx + c",[123,3495,3496],{},[152,3497,3498],{"start":649},[123,3499,3428,3500],{},[883,3501,3503],{"className":3502},[886],[888,3504,3505],{"xmlns":890},[892,3506,3507,3543],{},[895,3508,3509,3511,3513,3515,3522,3524,3526,3532,3534,3536,3538,3540],{},[898,3510,1664],{},[1651,3512,1738],{},[898,3514,207],{},[2115,3516,3517,3519],{},[898,3518,1657],{},[1692,3520,3521],{},"3",[1651,3523,1839],{},[898,3525,2268],{},[2115,3527,3528,3530],{},[898,3529,1657],{},[1692,3531,1703],{},[1651,3533,1839],{},[898,3535,3490],{},[898,3537,1657],{},[1651,3539,1839],{},[898,3541,3542],{},"d",[902,3544,3545],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,3547,3548,3246,3551,3607,3608,3645,3646,1882],{},[38,3549,3550],{},"Příklad rozkladu:",[883,3552,3554],{"className":3553},[886],[888,3555,3556],{"xmlns":890},[892,3557,3558,3604],{},[895,3559,3560,3562,3564,3570,3572,3575,3577,3579,3582,3584,3586,3588,3590,3592,3594,3596,3598,3600,3602],{},[898,3561,1664],{},[1651,3563,1738],{},[2115,3565,3566,3568],{},[898,3567,1657],{},[1692,3569,1703],{},[1651,3571,2181],{},[1692,3573,3574],{},"5",[898,3576,1657],{},[1651,3578,1839],{},[1692,3580,3581],{},"6",[1651,3583,1738],{},[1651,3585,1654],{"stretchy":1653},[898,3587,1657],{},[1651,3589,2181],{},[1692,3591,1703],{},[1651,3593,1667],{"stretchy":1653},[1651,3595,1654],{"stretchy":1653},[898,3597,1657],{},[1651,3599,2181],{},[1692,3601,3521],{},[1651,3603,1667],{"stretchy":1653},[902,3605,3606],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,3609,3611],{"className":3610},[886],[888,3612,3613],{"xmlns":890},[892,3614,3615,3642],{},[895,3616,3617,3623,3625,3627,3629,3632,3638,3640],{},[1686,3618,3619,3621],{},[898,3620,1657],{},[1692,3622,1694],{},[1651,3624,1738],{},[1692,3626,1703],{},[1651,3628,1661],{"separator":1660},[1843,3630,3631],{}," ",[1686,3633,3634,3636],{},[898,3635,1657],{},[1692,3637,1703],{},[1651,3639,1738],{},[1692,3641,3521],{},[902,3643,3644],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,3647,3649],{"className":3648},[886],[888,3650,3651],{"xmlns":890},[892,3652,3653,3690],{},[895,3654,3655,3657,3659,3661,3663,3665,3673,3679,3681],{},[898,3656,1664],{},[1651,3658,1738],{},[1651,3660,1654],{"stretchy":1653},[898,3662,1657],{},[1651,3664,2181],{},[2938,3666,3667],{"scriptlevel":1741,"displaystyle":1653},[2446,3668,3669,3671],{},[1692,3670,3574],{},[1692,3672,1703],{},[2115,3674,3675,3677],{},[1651,3676,1667],{"stretchy":1653},[1692,3678,1703],{},[1651,3680,2181],{},[2938,3682,3683],{"scriptlevel":1741,"displaystyle":1653},[2446,3684,3685,3687],{},[1692,3686,1694],{},[1692,3688,3689],{},"4",[902,3691,3692],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,3694,3695],{"id":1145},"Derivace",[724,3697,3698,3699,1348,3723,3751,3752,1882],{},"Označení ",[883,3700,3702],{"className":3701},[886],[888,3703,3704],{"xmlns":890},[892,3705,3706,3720],{},[895,3707,3708,3714,3716,3718],{},[2115,3709,3710,3712],{},[898,3711,1649],{},[1651,3713,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,3715,1654],{"stretchy":1653},[898,3717,1657],{},[1651,3719,1667],{"stretchy":1653},[902,3721,3722],{"encoding":904},"f'(x)",[883,3724,3726],{"className":3725},[886],[888,3727,3728],{"xmlns":890},[892,3729,3730,3748],{},[895,3731,3732],{},[2938,3733,3734],{"scriptlevel":1741,"displaystyle":1660},[2446,3735,3736,3742],{},[895,3737,3738,3740],{},[898,3739,3542],{},[898,3741,1664],{},[895,3743,3744,3746],{},[898,3745,3542],{},[898,3747,1657],{},[902,3749,3750],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,3753,3755],{"className":3754},[886],[888,3756,3757],{"xmlns":890},[892,3758,3759,3773],{},[895,3760,3761,3767,3769,3771],{},[2115,3762,3763,3765],{},[898,3764,1649],{},[1651,3766,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,3768,1654],{"stretchy":1653},[898,3770,207],{},[1651,3772,1667],{"stretchy":1653},[902,3774,3775],{"encoding":904},"f'(a)",[198,3777,3779],{"id":3778},"geometrická-interpretace","Geometrická interpretace",[724,3781,3782,3805,3806,3809,3810,3838],{},[883,3783,3785],{"className":3784},[886],[888,3786,3787],{"xmlns":890},[892,3788,3789,3803],{},[895,3790,3791,3797,3799,3801],{},[2115,3792,3793,3795],{},[898,3794,1649],{},[1651,3796,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,3798,1654],{"stretchy":1653},[898,3800,207],{},[1651,3802,1667],{"stretchy":1653},[902,3804,3775],{"encoding":904}," = ",[38,3807,3808],{},"sklon tečny"," ke grafu funkce v bodě ",[883,3811,3813],{"className":3812},[886],[888,3814,3815],{"xmlns":890},[892,3816,3817,3835],{},[895,3818,3819,3821,3823,3825,3827,3829,3831,3833],{},[1651,3820,2261],{"stretchy":1653},[898,3822,207],{},[1651,3824,1661],{"separator":1660},[898,3826,1649],{},[1651,3828,1654],{"stretchy":1653},[898,3830,207],{},[1651,3832,1667],{"stretchy":1653},[1651,3834,2279],{"stretchy":1653},[902,3836,3837],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,3840,3841],{},[883,3842,3844],{"className":3843},[886],[888,3845,3846],{"xmlns":890},[892,3847,3848,3886],{},[895,3849,3850,3852,3854,3856,3858,3860,3862,3864,3870,3872,3874,3876,3878,3880,3882,3884],{},[898,3851,1664],{},[1651,3853,2181],{},[898,3855,1649],{},[1651,3857,1654],{"stretchy":1653},[898,3859,207],{},[1651,3861,1667],{"stretchy":1653},[1651,3863,1738],{},[2115,3865,3866,3868],{},[898,3867,1649],{},[1651,3869,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,3871,1654],{"stretchy":1653},[898,3873,207],{},[1651,3875,1667],{"stretchy":1653},[1651,3877,1654],{"stretchy":1653},[898,3879,1657],{},[1651,3881,2181],{},[898,3883,207],{},[1651,3885,1667],{"stretchy":1653},[902,3887,3888],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,3890,3891],{},[1756,3892],{"alt":3893,"className":3894,"src":3895},"imek-derivace-tecna",[210,1760],"\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,3897,3899],{"id":3898},"inženýrská-interpretace","Inženýrská interpretace",[724,3901,3902,3805,3925,3246,3928,3941,3942,3955,3956,3974,3975,3988,3989,4002,4003,4016,4017,1793],{},[883,3903,3905],{"className":3904},[886],[888,3906,3907],{"xmlns":890},[892,3908,3909,3923],{},[895,3910,3911,3917,3919,3921],{},[2115,3912,3913,3915],{},[898,3914,1649],{},[1651,3916,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,3918,1654],{"stretchy":1653},[898,3920,207],{},[1651,3922,1667],{"stretchy":1653},[902,3924,3775],{"encoding":904},[38,3926,3927],{},"rychlost změny",[883,3929,3931],{"className":3930},[886],[888,3932,3933],{"xmlns":890},[892,3934,3935,3939],{},[895,3936,3937],{},[898,3938,1664],{},[902,3940,1664],{"encoding":904}," vzhledem k ",[883,3943,3945],{"className":3944},[886],[888,3946,3947],{"xmlns":890},[892,3948,3949,3953],{},[895,3950,3951],{},[898,3952,1657],{},[902,3954,1657],{"encoding":904}," v bodě ",[883,3957,3959],{"className":3958},[886],[888,3960,3961],{"xmlns":890},[892,3962,3963,3971],{},[895,3964,3965,3967,3969],{},[898,3966,1657],{},[1651,3968,1738],{},[898,3970,207],{},[902,3972,3973],{"encoding":904},"x = a","; přibližná změna ",[883,3976,3978],{"className":3977},[886],[888,3979,3980],{"xmlns":890},[892,3981,3982,3986],{},[895,3983,3984],{},[898,3985,1664],{},[902,3987,1664],{"encoding":904}," při změně ",[883,3990,3992],{"className":3991},[886],[888,3993,3994],{"xmlns":890},[892,3995,3996,4000],{},[895,3997,3998],{},[898,3999,1657],{},[902,4001,1657],{"encoding":904}," z ",[883,4004,4006],{"className":4005},[886],[888,4007,4008],{"xmlns":890},[892,4009,4010,4014],{},[895,4011,4012],{},[898,4013,207],{},[902,4015,207],{"encoding":904}," na ",[883,4018,4020],{"className":4019},[886],[888,4021,4022],{"xmlns":890},[892,4023,4024,4032],{},[895,4025,4026,4028,4030],{},[898,4027,207],{},[1651,4029,1839],{},[1692,4031,1694],{},[902,4033,4034],{"encoding":904},"a+1",[724,4036,4037],{},[883,4038,4040],{"className":4039},[886],[888,4041,4042],{"xmlns":890},[892,4043,4044,4083],{},[895,4045,4046,4048,4050,4052,4054,4056,4058,4061,4063,4065,4067,4069,4071,4077,4079,4081],{},[898,4047,1649],{},[1651,4049,1654],{"stretchy":1653},[898,4051,207],{},[1651,4053,1839],{},[1692,4055,1694],{},[1651,4057,1667],{"stretchy":1653},[1651,4059,4060],{},"≈",[898,4062,1649],{},[1651,4064,1654],{"stretchy":1653},[898,4066,207],{},[1651,4068,1667],{"stretchy":1653},[1651,4070,1839],{},[2115,4072,4073,4075],{},[898,4074,1649],{},[1651,4076,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,4078,1654],{"stretchy":1653},[898,4080,207],{},[1651,4082,1667],{"stretchy":1653},[902,4084,4085],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,4087,4089],{"id":4088},"příklad-mezní-náklady","Příklad — mezní náklady",[724,4091,4092,4093,1882],{},"Celkové náklady ",[883,4094,4096],{"className":4095},[886],[888,4097,4098],{"xmlns":890},[892,4099,4100,4129],{},[895,4101,4102,4105,4107,4109,4112,4114,4116,4118,4120,4123],{},[898,4103,4104],{},"T",[898,4106,3001],{},[1651,4108,1738],{},[1692,4110,4111],{},"1000",[1651,4113,1839],{},[1692,4115,1703],{},[898,4117,1690],{},[1651,4119,1839],{},[1692,4121,4122],{},"0,1",[2115,4124,4125,4127],{},[898,4126,1690],{},[1692,4128,1703],{},[902,4130,4131],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,4133,4134,4135,4172,4173,1882],{},"Mezní náklady: ",[883,4136,4138],{"className":4137},[886],[888,4139,4140],{"xmlns":890},[892,4141,4142,4169],{},[895,4143,4144,4146,4148,4150,4152,4158,4160,4162,4164,4167],{},[898,4145,2995],{},[898,4147,3001],{},[1651,4149,1738],{},[898,4151,4104],{},[2115,4153,4154,4156],{},[898,4155,3001],{},[1651,4157,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,4159,1738],{},[1692,4161,1703],{},[1651,4163,1839],{},[1692,4165,4166],{},"0,2",[898,4168,1690],{},[902,4170,4171],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,4174,4176],{"className":4175},[886],[888,4177,4178],{"xmlns":890},[892,4179,4180,4197],{},[895,4181,4182,4184,4186,4188,4191,4193,4195],{},[898,4183,2995],{},[898,4185,3001],{},[1651,4187,1654],{"stretchy":1653},[1692,4189,4190],{},"10",[1651,4192,1667],{"stretchy":1653},[1651,4194,1738],{},[1692,4196,3689],{},[902,4198,4199],{"encoding":904},"MC(10) = 4",[724,4201,4202,3246,4205,4254,4255,3246,4258,1882],{},[38,4203,4204],{},"Skutečný přírůstek:",[883,4206,4208],{"className":4207},[886],[888,4209,4210],{"xmlns":890},[892,4211,4212,4251],{},[895,4213,4214,4217,4219,4221,4223,4225,4227,4229,4232,4234,4236,4238,4240,4242,4244,4246,4248],{},[898,4215,4216],{"mathvariant":1910},"Δ",[898,4218,4104],{},[898,4220,3001],{},[1651,4222,1738],{},[898,4224,4104],{},[898,4226,3001],{},[1651,4228,1654],{"stretchy":1653},[1692,4230,4231],{},"11",[1651,4233,1667],{"stretchy":1653},[1651,4235,2181],{},[898,4237,4104],{},[898,4239,3001],{},[1651,4241,1654],{"stretchy":1653},[1692,4243,4190],{},[1651,4245,1667],{"stretchy":1653},[1651,4247,1738],{},[1692,4249,4250],{},"4,2",[902,4252,4253],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",". ",[38,4256,4257],{},"Přibližný (lineární):",[883,4259,4261],{"className":4260},[886],[888,4262,4263],{"xmlns":890},[892,4264,4265,4269],{},[895,4266,4267],{},[1692,4268,3689],{},[902,4270,3689],{"encoding":904},[724,4272,4273,4274,4278],{},"(Viz aplikace v ",[207,4275,4277],{"className":4276,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk",".)",[115,4280,4282],{"id":4281},"diferenciál","Diferenciál",[724,4284,4285],{},[883,4286,4288],{"className":4287},[886],[888,4289,4290],{"xmlns":890},[892,4291,4292,4318],{},[895,4293,4294,4296,4298,4300,4306,4308,4310,4312,4314,4316],{},[898,4295,3542],{},[898,4297,1649],{},[1651,4299,1738],{},[2115,4301,4302,4304],{},[898,4303,1649],{},[1651,4305,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,4307,1654],{"stretchy":1653},[898,4309,1657],{},[1651,4311,1667],{"stretchy":1653},[1843,4313,1845],{},[898,4315,3542],{},[898,4317,1657],{},[902,4319,4320],{"encoding":904},"df = f'(x)\\, dx",[724,4322,4323,4324,4340,4341,4389,4390,1882],{},"Pro malá ",[883,4325,4327],{"className":4326},[886],[888,4328,4329],{"xmlns":890},[892,4330,4331,4337],{},[895,4332,4333,4335],{},[898,4334,3542],{},[898,4336,1657],{},[902,4338,4339],{"encoding":904},"dx"," platí: ",[883,4342,4344],{"className":4343},[886],[888,4345,4346],{"xmlns":890},[892,4347,4348,4386],{},[895,4349,4350,4352,4354,4356,4358,4360,4362,4364,4366,4368,4370,4372,4374,4376,4378,4380,4382,4384],{},[898,4351,4216],{"mathvariant":1910},[898,4353,1649],{},[1651,4355,1738],{},[898,4357,1649],{},[1651,4359,1654],{"stretchy":1653},[898,4361,1657],{},[1651,4363,1839],{},[898,4365,3542],{},[898,4367,1657],{},[1651,4369,1667],{"stretchy":1653},[1651,4371,2181],{},[898,4373,1649],{},[1651,4375,1654],{"stretchy":1653},[898,4377,1657],{},[1651,4379,1667],{"stretchy":1653},[1651,4381,4060],{},[898,4383,3542],{},[898,4385,1649],{},[902,4387,4388],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,4391,4392],{},"lineární odhad přírůstku",[198,4394,4396],{"id":4395},"příklad","Příklad",[724,4398,4399,4430,4431,4456,4457,4477],{},[883,4400,4402],{"className":4401},[886],[888,4403,4404],{"xmlns":890},[892,4405,4406,4427],{},[895,4407,4408,4410,4412,4414,4417,4419,4421],{},[898,4409,4104],{},[898,4411,3001],{},[1651,4413,1738],{},[1692,4415,4416],{},"100",[1651,4418,1839],{},[1692,4420,4122],{},[2115,4422,4423,4425],{},[898,4424,1690],{},[1692,4426,1703],{},[902,4428,4429],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,4432,4434],{"className":4433},[886],[888,4435,4436],{"xmlns":890},[892,4437,4438,4453],{},[895,4439,4440,4442,4444,4447,4450],{},[898,4441,1690],{},[1651,4443,1793],{},[1692,4445,4446],{},"50",[1651,4448,4449],{},"→",[1692,4451,4452],{},"60",[902,4454,4455],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,4458,4460],{"className":4459},[886],[888,4461,4462],{"xmlns":890},[892,4463,4464,4474],{},[895,4465,4466,4468,4470,4472],{},[898,4467,3542],{},[898,4469,1690],{},[1651,4471,1738],{},[1692,4473,4190],{},[902,4475,4476],{"encoding":904},"dQ = 10","):",[724,4479,4480],{},[883,4481,4483],{"className":4482},[886],[888,4484,4485],{"xmlns":890},[892,4486,4487,4524],{},[895,4488,4489,4491,4493,4495,4497,4499,4501,4504,4506,4508,4510,4512,4514,4516,4518,4520,4522],{},[898,4490,3542],{},[898,4492,4104],{},[898,4494,3001],{},[1651,4496,1738],{},[1692,4498,4166],{},[898,4500,1690],{},[1651,4502,4503],{},"⋅",[898,4505,3542],{},[898,4507,1690],{},[1651,4509,1738],{},[1692,4511,4166],{},[1651,4513,4503],{},[1692,4515,4446],{},[1651,4517,4503],{},[1692,4519,4190],{},[1651,4521,1738],{},[1692,4523,4416],{},[902,4525,4526],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,4528,4529,4530,4553,4554,4570],{},"Přesná změna: ",[883,4531,4533],{"className":4532},[886],[888,4534,4535],{"xmlns":890},[892,4536,4537,4550],{},[895,4538,4539,4541,4543,4545,4547],{},[898,4540,4216],{"mathvariant":1910},[898,4542,4104],{},[898,4544,3001],{},[1651,4546,1738],{},[1692,4548,4549],{},"110",[902,4551,4552],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,4555,4557],{"className":4556},[886],[888,4558,4559],{"xmlns":890},[892,4560,4561,4567],{},[895,4562,4563,4565],{},[898,4564,4104],{},[898,4566,3001],{},[902,4568,4569],{"encoding":904},"TC"," je konvexní.",[115,4572,4574],{"id":4573},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,4576,1886],{"id":1885},[724,4578,4579,4580,3955,4600,4613,4614,4642,4643,4646],{},"Má-li ",[883,4581,4583],{"className":4582},[886],[888,4584,4585],{"xmlns":890},[892,4586,4587,4597],{},[895,4588,4589,4591,4593,4595],{},[898,4590,1649],{},[1651,4592,1654],{"stretchy":1653},[898,4594,1657],{},[1651,4596,1667],{"stretchy":1653},[902,4598,4599],{"encoding":904},"f(x)",[883,4601,4603],{"className":4602},[886],[888,4604,4605],{"xmlns":890},[892,4606,4607,4611],{},[895,4608,4609],{},[898,4610,207],{},[902,4612,207],{"encoding":904}," extrém, pak ",[883,4615,4617],{"className":4616},[886],[888,4618,4619],{"xmlns":890},[892,4620,4621,4639],{},[895,4622,4623,4629,4631,4633,4635,4637],{},[2115,4624,4625,4627],{},[898,4626,1649],{},[1651,4628,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,4630,1654],{"stretchy":1653},[898,4632,207],{},[1651,4634,1667],{"stretchy":1653},[1651,4636,1738],{},[1692,4638,1741],{},[902,4640,4641],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,4644,4645],{},"stacionární"," (podezřelé) body.",[198,4648,2033],{"id":2032},[724,4650,4651,4652,4665,4666,1793],{},"Pro stacionární bod ",[883,4653,4655],{"className":4654},[886],[888,4656,4657],{"xmlns":890},[892,4658,4659,4663],{},[895,4660,4661],{},[898,4662,207],{},[902,4664,207],{"encoding":904},", je-li ",[883,4667,4669],{"className":4668},[886],[888,4670,4671],{"xmlns":890},[892,4672,4673,4696],{},[895,4674,4675,4685,4687,4689,4691,4694],{},[2115,4676,4677,4679],{},[898,4678,1649],{},[895,4680,4681,4683],{},[1651,4682,1912],{"mathvariant":1910},[1651,4684,1912],{"mathvariant":1910},[1651,4686,1654],{"stretchy":1653},[898,4688,207],{},[1651,4690,1667],{"stretchy":1653},[1651,4692,4693],{"mathvariant":1910},"≠",[1692,4695,1741],{},[902,4697,4698],{"encoding":904},"f''(a) \\neq 0",[120,4700,4701,4738],{},[123,4702,4703,2325,4735],{},[883,4704,4706],{"className":4705},[886],[888,4707,4708],{"xmlns":890},[892,4709,4710,4732],{},[895,4711,4712,4722,4724,4726,4728,4730],{},[2115,4713,4714,4716],{},[898,4715,1649],{},[895,4717,4718,4720],{},[1651,4719,1912],{"mathvariant":1910},[1651,4721,1912],{"mathvariant":1910},[1651,4723,1654],{"stretchy":1653},[898,4725,207],{},[1651,4727,1667],{"stretchy":1653},[1651,4729,2390],{},[1692,4731,1741],{},[902,4733,4734],{"encoding":904},"f''(a) > 0",[38,4736,4737],{},"lokální minimum",[123,4739,4740,2325,4772],{},[883,4741,4743],{"className":4742},[886],[888,4744,4745],{"xmlns":890},[892,4746,4747,4769],{},[895,4748,4749,4759,4761,4763,4765,4767],{},[2115,4750,4751,4753],{},[898,4752,1649],{},[895,4754,4755,4757],{},[1651,4756,1912],{"mathvariant":1910},[1651,4758,1912],{"mathvariant":1910},[1651,4760,1654],{"stretchy":1653},[898,4762,207],{},[1651,4764,1667],{"stretchy":1653},[1651,4766,2319],{},[1692,4768,1741],{},[902,4770,4771],{"encoding":904},"f''(a) \u003C 0",[38,4773,4774],{},"lokální maximum",[724,4776,4777],{},[1756,4778],{"alt":4779,"className":4780,"src":4781},"imek-extremy-1d",[210,1760],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,4783,4396],{"id":4784},"příklad-1",[724,4786,4787],{},[883,4788,4790],{"className":4789},[886],[888,4791,4792],{"xmlns":890},[892,4793,4794,4835],{},[895,4795,4796,4798,4800,4802,4804,4806,4808,4814,4816,4818,4824,4826,4829,4831,4833],{},[898,4797,1649],{},[1651,4799,1654],{"stretchy":1653},[898,4801,1657],{},[1651,4803,1667],{"stretchy":1653},[1651,4805,1738],{},[1692,4807,1703],{},[2115,4809,4810,4812],{},[898,4811,1657],{},[1692,4813,3521],{},[1651,4815,2181],{},[1692,4817,3521],{},[2115,4819,4820,4822],{},[898,4821,1657],{},[1692,4823,1703],{},[1651,4825,2181],{},[1692,4827,4828],{},"12",[898,4830,1657],{},[1651,4832,1839],{},[1692,4834,3521],{},[902,4836,4837],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,4839,4840,4951,4991,5053],{},[123,4841,4842,4914,4915],{},[883,4843,4845],{"className":4844},[886],[888,4846,4847],{"xmlns":890},[892,4848,4849,4911],{},[895,4850,4851,4857,4859,4861,4863,4865,4867,4873,4875,4877,4879,4881,4883,4885,4887,4889,4891,4893,4895,4897,4899,4901,4903,4905,4907,4909],{},[2115,4852,4853,4855],{},[898,4854,1649],{},[1651,4856,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,4858,1654],{"stretchy":1653},[898,4860,1657],{},[1651,4862,1667],{"stretchy":1653},[1651,4864,1738],{},[1692,4866,3581],{},[2115,4868,4869,4871],{},[898,4870,1657],{},[1692,4872,1703],{},[1651,4874,2181],{},[1692,4876,3581],{},[898,4878,1657],{},[1651,4880,2181],{},[1692,4882,4828],{},[1651,4884,1738],{},[1692,4886,3581],{},[1651,4888,1654],{"stretchy":1653},[898,4890,1657],{},[1651,4892,1839],{},[1692,4894,1694],{},[1651,4896,1667],{"stretchy":1653},[1651,4898,1654],{"stretchy":1653},[898,4900,1657],{},[1651,4902,2181],{},[1692,4904,1703],{},[1651,4906,1667],{"stretchy":1653},[1651,4908,1738],{},[1692,4910,1741],{},[902,4912,4913],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,4916,4918],{"className":4917},[886],[888,4919,4920],{"xmlns":890},[892,4921,4922,4948],{},[895,4923,4924,4930,4932,4934,4936,4938,4944,4946],{},[1686,4925,4926,4928],{},[898,4927,1657],{},[1692,4929,1694],{},[1651,4931,1738],{},[1651,4933,2181],{},[1692,4935,1694],{},[1651,4937,1661],{"separator":1660},[1686,4939,4940,4942],{},[898,4941,1657],{},[1692,4943,1703],{},[1651,4945,1738],{},[1692,4947,1703],{},[902,4949,4950],{"encoding":904},"x_1 = -1, x_2 = 2",[123,4952,4953],{},[883,4954,4956],{"className":4955},[886],[888,4957,4958],{"xmlns":890},[892,4959,4960,4988],{},[895,4961,4962,4972,4974,4976,4978,4980,4982,4984,4986],{},[2115,4963,4964,4966],{},[898,4965,1649],{},[895,4967,4968,4970],{},[1651,4969,1912],{"mathvariant":1910},[1651,4971,1912],{"mathvariant":1910},[1651,4973,1654],{"stretchy":1653},[898,4975,1657],{},[1651,4977,1667],{"stretchy":1653},[1651,4979,1738],{},[1692,4981,4828],{},[898,4983,1657],{},[1651,4985,2181],{},[1692,4987,3581],{},[902,4989,4990],{"encoding":904},"f''(x) = 12x - 6",[123,4992,4993,2325,5034,5036,5037],{},[883,4994,4996],{"className":4995},[886],[888,4997,4998],{"xmlns":890},[892,4999,5000,5031],{},[895,5001,5002,5012,5014,5016,5018,5020,5022,5024,5027,5029],{},[2115,5003,5004,5006],{},[898,5005,1649],{},[895,5007,5008,5010],{},[1651,5009,1912],{"mathvariant":1910},[1651,5011,1912],{"mathvariant":1910},[1651,5013,1654],{"stretchy":1653},[1651,5015,2181],{},[1692,5017,1694],{},[1651,5019,1667],{"stretchy":1653},[1651,5021,1738],{},[1651,5023,2181],{},[1692,5025,5026],{},"18",[1651,5028,2319],{},[1692,5030,1741],{},[902,5032,5033],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,5035,2328],{}," v ",[883,5038,5040],{"className":5039},[886],[888,5041,5042],{"xmlns":890},[892,5043,5044,5050],{},[895,5045,5046,5048],{},[1651,5047,2181],{},[1692,5049,1694],{},[902,5051,5052],{"encoding":904},"-1",[123,5054,5055,2325,5091,5036,5093],{},[883,5056,5058],{"className":5057},[886],[888,5059,5060],{"xmlns":890},[892,5061,5062,5088],{},[895,5063,5064,5074,5076,5078,5080,5082,5084,5086],{},[2115,5065,5066,5068],{},[898,5067,1649],{},[895,5069,5070,5072],{},[1651,5071,1912],{"mathvariant":1910},[1651,5073,1912],{"mathvariant":1910},[1651,5075,1654],{"stretchy":1653},[1692,5077,1703],{},[1651,5079,1667],{"stretchy":1653},[1651,5081,1738],{},[1692,5083,5026],{},[1651,5085,2390],{},[1692,5087,1741],{},[902,5089,5090],{"encoding":904},"f''(2) = 18 > 0",[38,5092,2398],{},[883,5094,5096],{"className":5095},[886],[888,5097,5098],{"xmlns":890},[892,5099,5100,5104],{},[895,5101,5102],{},[1692,5103,1703],{},[902,5105,1703],{"encoding":904},[115,5107,3238],{"id":3237},[120,5109,5110,5117,5124],{},[123,5111,5112,3246,5114],{},[38,5113,3245],{},[207,5115,757],{"className":5116,"dataFsResolvedFilePath":755,"href":756},[210],[123,5118,5119,3246,5121],{},[38,5120,3254],{},[207,5122,775],{"className":5123,"dataFsResolvedFilePath":773,"href":774},[210],[123,5125,5126,3246,5128,5131,5132,5136,5137,5141],{},[38,5127,3272],{},[207,5129,784],{"className":5130,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,5133,5135],{"className":5134,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk"," (aplikace mezních veličin), ",[207,5138,5140],{"className":5139,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita"," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":5143},[5144,5145,5150,5153,5158],{"id":3339,"depth":642,"text":3340},{"id":1145,"depth":642,"text":3695,"children":5146},[5147,5148,5149],{"id":3778,"depth":649,"text":3779},{"id":3898,"depth":649,"text":3899},{"id":4088,"depth":649,"text":4089},{"id":4281,"depth":642,"text":4282,"children":5151},[5152],{"id":4395,"depth":649,"text":4396},{"id":4573,"depth":642,"text":4574,"children":5154},[5155,5156,5157],{"id":1885,"depth":649,"text":1886},{"id":2032,"depth":649,"text":2033},{"id":4784,"depth":649,"text":4396},{"id":3237,"depth":642,"text":3238},"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":3312,"description":5159},[1135],"topics\u002Fderivace",[1128,1145,5166,5167,5168],"diferencial","extremy","mezni-naklady","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":5171,"title":5172,"body":5173,"course":1128,"courses":659,"created":10859,"description":641,"extension":661,"meta":10860,"navigation":664,"path":10861,"seo":10862,"sources":10863,"stem":10864,"tags":10865,"type":3302,"updated":677,"__hash__":10870},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":9,"value":5174,"toc":10832},[5175,5178,5201,5205,5231,5235,5276,5366,5410,5414,5438,5445,5449,5459,5471,5475,5503,5512,5569,5575,5578,5584,5611,5617,5713,5873,6164,6168,6248,6254,6258,6356,6422,6590,6594,6672,6703,6730,6736,6768,6846,6933,6937,7000,7006,7009,7015,7129,7214,7258,7262,7308,7315,7632,7637,7661,7690,7757,7854,7858,7865,7872,7943,8063,8147,8150,8156,8483,8487,8650,8658,8794,8802,9040,9048,9051,9056,9312,9316,9489,9623,9660,9704,9707,9837,9927,9945,9949,9956,9962,10022,10025,10049,10052,10058,10061,10067,10070,10074,10112,10170,10359,10363,10435,10441,10448,10452,10458,10599,10603,10609,10645,10650,10827],[12,5176,5172],{"id":5177},"elasticita-poptávky-a-nabídky",[5179,5180,5181],"blockquote",{},[724,5182,5183,5186,5187,5189,5190,5193,5194,5197,5198,1882],{},[883,5184,5185],{},"!abstract"," TL;DR\n",[38,5188,5140],{}," 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: ",[38,5191,5192],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,5195,5196],{},"křížově-cenovou elasticitu"," a ",[38,5199,5200],{},"důchodovou elasticitu",[115,5202,5204],{"id":5203},"úvod-motivace","Úvod — motivace",[724,5206,5207,5208,5211,5212,5215,5216,5219,5220,1671,5223,5226,5227,5230],{},"Termín ",[614,5209,5210],{},"elasticita"," (alternativně ",[614,5213,5214],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,5217,5218],{},"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 ",[614,5221,5222],{},"cenové elasticity poptávky",[614,5224,5225],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,5228,3695],{"className":5229,"dataFsResolvedFilePath":764,"href":765},[210],").",[198,5232,5234],{"id":5233},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,5236,5237,5238,5256,5257,5275],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,5239,5241],{"className":5240},[886],[888,5242,5243],{"xmlns":890},[892,5244,5245,5253],{},[895,5246,5247,5249,5251],{},[898,5248,2675],{},[1651,5250,1738],{},[1692,5252,4190],{},[902,5254,5255],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,5258,5260],{"className":5259},[886],[888,5261,5262],{"xmlns":890},[892,5263,5264,5272],{},[895,5265,5266,5268,5270],{},[898,5267,1690],{},[1651,5269,1738],{},[1692,5271,4416],{},[902,5273,5274],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,5277,5278,5323],{},[123,5279,5280,5283,5284,5322],{},[38,5281,5282],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,5285,5287],{"className":5286},[886],[888,5288,5289],{"xmlns":890},[892,5290,5291,5319],{},[895,5292,5293,5296,5299,5301,5303,5305,5307,5310,5312,5314,5316],{},[1843,5294,5295],{},"  ",[1651,5297,5298],{},"⇒",[1843,5300,5295],{},[898,5302,4104],{},[898,5304,2998],{},[1651,5306,1738],{},[1692,5308,5309],{},"9",[1651,5311,4503],{},[1692,5313,4549],{},[1651,5315,1738],{},[1692,5317,5318],{},"990",[902,5320,5321],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,5324,5325,5328,5329,5365],{},[38,5326,5327],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,5330,5332],{"className":5331},[886],[888,5333,5334],{"xmlns":890},[892,5335,5336,5362],{},[895,5337,5338,5340,5342,5344,5346,5348,5350,5352,5354,5357,5359],{},[1843,5339,5295],{},[1651,5341,5298],{},[1843,5343,5295],{},[898,5345,4104],{},[898,5347,2998],{},[1651,5349,1738],{},[1692,5351,5309],{},[1651,5353,4503],{},[1692,5355,5356],{},"120",[1651,5358,1738],{},[1692,5360,5361],{},"1080",[902,5363,5364],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,5367,5368,5369,5372,5373,5376,5377,5380,5381,5384,5385,5388,5389,5405,5406,5409],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,5370,5371],{},"nerozumné",", na Trhu 2 ",[38,5374,5375],{},"rozumné",". Trh 2 je ",[38,5378,5379],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,5382,5383],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,5386,5387],{},"neelastická"," a vyššího ",[883,5390,5392],{"className":5391},[886],[888,5393,5394],{"xmlns":890},[892,5395,5396,5402],{},[895,5397,5398,5400],{},[898,5399,4104],{},[898,5401,2998],{},[902,5403,5404],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,5407,5408],{},"zvýšením"," ceny.",[198,5411,5413],{"id":5412},"hypotéza-41","Hypotéza 4.1",[5179,5415,5416],{},[724,5417,5418,5419],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,5420,5422],{"className":5421},[886],[888,5423,5424],{"xmlns":890},[892,5425,5426,5435],{},[895,5427,5428,5430,5433],{},[1651,5429,1654],{"stretchy":1653},[1692,5431,5432],{},"4.1",[1651,5434,1667],{"stretchy":1653},[902,5436,5437],{"encoding":904},"(4.1)",[724,5439,5440,5441,5444],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,5442,5443],{},"procentní změny"," obou faktorů.",[115,5446,5448],{"id":5447},"pojem-elasticity","Pojem elasticity",[724,5450,5451,5452,5454,5455,5458],{},"Obecně ",[38,5453,5210],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,5456,5457],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[5179,5460,5461],{},[724,5462,5463,5466,5467,5470],{},[883,5464,5465],{},"!info"," Intuice\nElasticitu lze číst jako ",[38,5468,5469],{},"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.",[115,5472,5474],{"id":5473},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,5476,5477,5478,5502],{},"Nechť ",[883,5479,5481],{"className":5480},[886],[888,5482,5483],{"xmlns":890},[892,5484,5485,5499],{},[895,5486,5487,5489,5491,5493,5495,5497],{},[898,5488,1690],{},[1651,5490,1738],{},[898,5492,2047],{},[1651,5494,1654],{"stretchy":1653},[898,5496,2675],{},[1651,5498,1667],{"stretchy":1653},[902,5500,5501],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,5504,5505],{},[883,5506,5511],{"className":5507,"title":5509,"style":5510},[5508],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,5513,5514,5515,5197,5531,5547,5548,5568],{},"Znaménko minus je korekce: změny ",[883,5516,5518],{"className":5517},[886],[888,5519,5520],{"xmlns":890},[892,5521,5522,5528],{},[895,5523,5524,5526],{},[898,5525,4216],{"mathvariant":1910},[898,5527,1690],{},[902,5529,5530],{"encoding":904},"\\Delta Q",[883,5532,5534],{"className":5533},[886],[888,5535,5536],{"xmlns":890},[892,5537,5538,5544],{},[895,5539,5540,5542],{},[898,5541,4216],{"mathvariant":1910},[898,5543,2675],{},[902,5545,5546],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,5549,5551],{"className":5550},[886],[888,5552,5553],{"xmlns":890},[892,5554,5555,5565],{},[895,5556,5557],{},[2115,5558,5559,5562],{},[898,5560,5561],{},"E",[898,5563,5564],{},"A",[902,5566,5567],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,5570,5571],{},[883,5572,5574],{"className":5573,"title":5509,"style":5510},[5508],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,5576,5577],{},"Po dosazení:",[724,5579,5580],{},[883,5581,5583],{"className":5582,"title":5509,"style":5510},[5508],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,5585,5586,5587,5607,5608,5610],{},"Limitním přechodem ",[883,5588,5590],{"className":5589},[886],[888,5591,5592],{"xmlns":890},[892,5593,5594,5604],{},[895,5595,5596,5598,5600,5602],{},[898,5597,4216],{"mathvariant":1910},[898,5599,2675],{},[1651,5601,4449],{},[1692,5603,1741],{},[902,5605,5606],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,5609,5222],{}," (price elasticity of demand):",[724,5612,5613],{},[883,5614,5616],{"className":5615,"title":5509,"style":5510},[5508],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,5618,1863,5619,5642,5643,5665,5666,5690,5691,5712],{},[883,5620,5622],{"className":5621},[886],[888,5623,5624],{"xmlns":890},[892,5625,5626,5640],{},[895,5627,5628,5630,5632,5634,5636,5638],{},[898,5629,1690],{},[1651,5631,1738],{},[898,5633,2047],{},[1651,5635,1654],{"stretchy":1653},[898,5637,2675],{},[1651,5639,1667],{"stretchy":1653},[902,5641,5501],{"encoding":904},". Pro pevnou cenu ",[883,5644,5646],{"className":5645},[886],[888,5647,5648],{"xmlns":890},[892,5649,5650,5662],{},[895,5651,5652,5654,5656],{},[898,5653,2675],{},[1651,5655,1738],{},[2115,5657,5658,5660],{},[898,5659,2675],{},[1651,5661,2668],{},[902,5663,5664],{"encoding":904},"P = P^*"," se ",[883,5667,5669],{"className":5668},[886],[888,5670,5671],{"xmlns":890},[892,5672,5673,5687],{},[895,5674,5675,5677,5679,5685],{},[898,5676,5561],{},[1651,5678,1654],{"stretchy":1653},[2115,5680,5681,5683],{},[898,5682,2675],{},[1651,5684,2668],{},[1651,5686,1667],{"stretchy":1653},[902,5688,5689],{"encoding":904},"E(P^*)"," nazývá ",[614,5692,5693,5694],{},"elasticita poptávky při ceně ",[883,5695,5697],{"className":5696},[886],[888,5698,5699],{"xmlns":890},[892,5700,5701,5709],{},[895,5702,5703],{},[2115,5704,5705,5707],{},[898,5706,2675],{},[1651,5708,2668],{},[902,5710,5711],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[5179,5714,5715],{},[724,5716,5717,5720,5721,5739,5740,5768,5769,5798,5799,1343,5817,1343,5835,5853,5854,5869,5870,1882],{},[883,5718,5719],{},"!warning"," Pozor na znaménko\nV (4.5) je ",[38,5722,5723,5724],{},"explicitní ",[883,5725,5727],{"className":5726},[886],[888,5728,5729],{"xmlns":890},[892,5730,5731,5737],{},[895,5732,5733,5735],{},[1651,5734,2181],{},[1692,5736,1694],{},[902,5738,5052],{"encoding":904}," právě proto, že ",[883,5741,5743],{"className":5742},[886],[888,5744,5745],{"xmlns":890},[892,5746,5747,5765],{},[895,5748,5749,5755,5757,5759,5761,5763],{},[2115,5750,5751,5753],{},[898,5752,1690],{},[1651,5754,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,5756,1654],{"stretchy":1653},[898,5758,2675],{},[1651,5760,1667],{"stretchy":1653},[1651,5762,2319],{},[1692,5764,1741],{},[902,5766,5767],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,5770,5772],{"className":5771},[886],[888,5773,5774],{"xmlns":890},[892,5775,5776,5795],{},[895,5777,5778,5780,5782,5788,5790,5793],{},[898,5779,5561],{},[1651,5781,1654],{"stretchy":1653},[2115,5783,5784,5786],{},[898,5785,2675],{},[1651,5787,2668],{},[1651,5789,1667],{"stretchy":1653},[1651,5791,5792],{},"≥",[1692,5794,1741],{},[902,5796,5797],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,5800,5802],{"className":5801},[886],[888,5803,5804],{"xmlns":890},[892,5805,5806,5814],{},[895,5807,5808,5810,5812],{},[898,5809,5561],{},[1651,5811,2390],{},[1692,5813,1694],{},[902,5815,5816],{"encoding":904},"E > 1",[883,5818,5820],{"className":5819},[886],[888,5821,5822],{"xmlns":890},[892,5823,5824,5832],{},[895,5825,5826,5828,5830],{},[898,5827,5561],{},[1651,5829,2319],{},[1692,5831,1694],{},[902,5833,5834],{"encoding":904},"E \u003C 1",[883,5836,5838],{"className":5837},[886],[888,5839,5840],{"xmlns":890},[892,5841,5842,5850],{},[895,5843,5844,5846,5848],{},[898,5845,5561],{},[1651,5847,1738],{},[1692,5849,1694],{},[902,5851,5852],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,5855,5857],{"className":5856},[886],[888,5858,5859],{"xmlns":890},[892,5860,5861,5867],{},[895,5862,5863,5865],{},[1651,5864,2181],{},[1692,5866,1694],{},[902,5868,5052],{"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 ",[38,5871,5872],{},"absolutní hodnotou",[5179,5874,5875,5895],{},[724,5876,5877,5880,5881,5894],{},[883,5878,5879],{},"!tip"," Postup: jak spočítat ",[883,5882,5884],{"className":5883},[886],[888,5885,5886],{"xmlns":890},[892,5887,5888,5892],{},[895,5889,5890],{},[898,5891,5561],{},[902,5893,5561],{"encoding":904}," v bodě",[152,5896,5897,5949,5989,6042,6107],{},[123,5898,5899,5900,5923,5924,5948],{},"Zapište ",[883,5901,5903],{"className":5902},[886],[888,5904,5905],{"xmlns":890},[892,5906,5907,5921],{},[895,5908,5909,5911,5913,5915,5917,5919],{},[898,5910,1690],{},[1651,5912,1738],{},[898,5914,2047],{},[1651,5916,1654],{"stretchy":1653},[898,5918,2675],{},[1651,5920,1667],{"stretchy":1653},[902,5922,5501],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,5925,5927],{"className":5926},[886],[888,5928,5929],{"xmlns":890},[892,5930,5931,5945],{},[895,5932,5933,5935,5937,5939,5941,5943],{},[898,5934,2675],{},[1651,5936,1738],{},[898,5938,2047],{},[1651,5940,1654],{"stretchy":1653},[898,5942,1690],{},[1651,5944,1667],{"stretchy":1653},[902,5946,5947],{"encoding":904},"P = D(Q)",", použijte vztah (4.9).",[123,5950,5951,5952,1882],{},"Spočítejte derivaci ",[883,5953,5955],{"className":5954},[886],[888,5956,5957],{"xmlns":890},[892,5958,5959,5986],{},[895,5960,5961,5967,5969,5971,5973,5975,5977,5979,5982,5984],{},[2115,5962,5963,5965],{},[898,5964,1690],{},[1651,5966,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,5968,1654],{"stretchy":1653},[898,5970,2675],{},[1651,5972,1667],{"stretchy":1653},[1651,5974,1738],{},[898,5976,3542],{"mathvariant":1910},[898,5978,1690],{},[898,5980,5981],{"mathvariant":1910},"\u002F",[898,5983,3542],{"mathvariant":1910},[898,5985,2675],{},[902,5987,5988],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,5990,5991,5992,6009,6010,1882],{},"Dosaďte zadanou cenu ",[883,5993,5995],{"className":5994},[886],[888,5996,5997],{"xmlns":890},[892,5998,5999,6007],{},[895,6000,6001],{},[2115,6002,6003,6005],{},[898,6004,2675],{},[1651,6006,2668],{},[902,6008,5711],{"encoding":904}," a dopočítejte odpovídající ",[883,6011,6013],{"className":6012},[886],[888,6014,6015],{"xmlns":890},[892,6016,6017,6039],{},[895,6018,6019,6025,6027,6029,6031,6037],{},[2115,6020,6021,6023],{},[898,6022,1690],{},[1651,6024,2668],{},[1651,6026,1738],{},[898,6028,2047],{},[1651,6030,1654],{"stretchy":1653},[2115,6032,6033,6035],{},[898,6034,2675],{},[1651,6036,2668],{},[1651,6038,1667],{"stretchy":1653},[902,6040,6041],{"encoding":904},"Q^* = D(P^*)",[123,6043,6044,6045,1882],{},"Dosaďte do (4.5): ",[883,6046,6048],{"className":6047},[886],[888,6049,6050],{"xmlns":890},[892,6051,6052,6104],{},[895,6053,6054,6056,6058,6064,6066,6068,6070,6086,6088,6094,6096,6102],{},[898,6055,5561],{},[1651,6057,1654],{"stretchy":1653},[2115,6059,6060,6062],{},[898,6061,2675],{},[1651,6063,2668],{},[1651,6065,1667],{"stretchy":1653},[1651,6067,1738],{},[1651,6069,2181],{},[2938,6071,6072],{"scriptlevel":1741,"displaystyle":1660},[2446,6073,6074,6080],{},[2115,6075,6076,6078],{},[898,6077,2675],{},[1651,6079,2668],{},[2115,6081,6082,6084],{},[898,6083,1690],{},[1651,6085,2668],{},[1843,6087,1845],{},[2115,6089,6090,6092],{},[898,6091,1690],{},[1651,6093,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,6095,1654],{"stretchy":1653},[2115,6097,6098,6100],{},[898,6099,2675],{},[1651,6101,2668],{},[1651,6103,1667],{"stretchy":1653},[902,6105,6106],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,6108,6109,6110,6127,6128,6145,6146,6163],{},"Klasifikujte: ",[883,6111,6113],{"className":6112},[886],[888,6114,6115],{"xmlns":890},[892,6116,6117,6125],{},[895,6118,6119,6121,6123],{},[898,6120,5561],{},[1651,6122,2390],{},[1692,6124,1694],{},[902,6126,5816],{"encoding":904}," elastická, ",[883,6129,6131],{"className":6130},[886],[888,6132,6133],{"xmlns":890},[892,6134,6135,6143],{},[895,6136,6137,6139,6141],{},[898,6138,5561],{},[1651,6140,1738],{},[1692,6142,1694],{},[902,6144,5852],{"encoding":904}," jednotková, ",[883,6147,6149],{"className":6148},[886],[888,6150,6151],{"xmlns":890},[892,6152,6153,6161],{},[895,6154,6155,6157,6159],{},[898,6156,5561],{},[1651,6158,2319],{},[1692,6160,1694],{},[902,6162,5834],{"encoding":904}," neelastická.",[198,6165,6167],{"id":6166},"interpretace-46","Interpretace (4.6)",[5179,6169,6170],{},[724,6171,6172,6173,6196,6197,6210,6211,6228,6229],{},"Číslo ",[883,6174,6176],{"className":6175},[886],[888,6177,6178],{"xmlns":890},[892,6179,6180,6194],{},[895,6181,6182,6184,6186,6192],{},[898,6183,5561],{},[1651,6185,1654],{"stretchy":1653},[2115,6187,6188,6190],{},[898,6189,2675],{},[1651,6191,2668],{},[1651,6193,1667],{"stretchy":1653},[902,6195,5689],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,6198,6200],{"className":6199},[886],[888,6201,6202],{"xmlns":890},[892,6203,6204,6208],{},[895,6205,6206],{},[898,6207,1690],{},[902,6209,1690],{"encoding":904},", jestliže se cena ",[883,6212,6214],{"className":6213},[886],[888,6215,6216],{"xmlns":890},[892,6217,6218,6226],{},[895,6219,6220],{},[2115,6221,6222,6224],{},[898,6223,2675],{},[1651,6225,2668],{},[902,6227,5711],{"encoding":904}," změní o 1 %. ",[883,6230,6232],{"className":6231},[886],[888,6233,6234],{"xmlns":890},[892,6235,6236,6245],{},[895,6237,6238,6240,6243],{},[1651,6239,1654],{"stretchy":1653},[1692,6241,6242],{},"4.6",[1651,6244,1667],{"stretchy":1653},[902,6246,6247],{"encoding":904},"(4.6)",[724,6249,6250,6253],{},[38,6251,6252],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,6255,6257],{"id":6256},"příklad-41","Příklad 4.1",[724,6259,6260,6261,6295,6296,1343,6322,1793],{},"Poptávka ",[883,6262,6264],{"className":6263},[886],[888,6265,6266],{"xmlns":890},[892,6267,6268,6292],{},[895,6269,6270,6272,6274,6276,6278,6280,6282,6284,6286,6288,6290],{},[898,6271,2675],{},[1651,6273,1738],{},[898,6275,2047],{},[1651,6277,1654],{"stretchy":1653},[898,6279,1690],{},[1651,6281,1667],{"stretchy":1653},[1651,6283,1738],{},[1692,6285,4446],{},[1651,6287,2181],{},[1692,6289,1703],{},[898,6291,1690],{},[902,6293,6294],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,6297,6299],{"className":6298},[886],[888,6300,6301],{"xmlns":890},[892,6302,6303,6319],{},[895,6304,6305,6307,6309,6312,6314,6317],{},[898,6306,1690],{},[1651,6308,1738],{},[1692,6310,6311],{},"25",[1651,6313,2181],{},[1692,6315,6316],{},"0,5",[898,6318,2675],{},[902,6320,6321],{"encoding":904},"Q = 25 - 0{,}5P",[883,6323,6325],{"className":6324},[886],[888,6326,6327],{"xmlns":890},[892,6328,6329,6353],{},[895,6330,6331,6347,6349,6351],{},[2938,6332,6333],{"scriptlevel":1741,"displaystyle":1660},[2446,6334,6335,6341],{},[895,6336,6337,6339],{},[898,6338,3542],{"mathvariant":1910},[898,6340,1690],{},[895,6342,6343,6345],{},[898,6344,3542],{"mathvariant":1910},[898,6346,2675],{},[1651,6348,1738],{},[1651,6350,2181],{},[1692,6352,6316],{},[902,6354,6355],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,6357,6358],{},[883,6359,6361],{"className":6360},[886],[888,6362,6363],{"xmlns":890},[892,6364,6365,6419],{},[895,6366,6367,6369,6371,6373,6387,6389,6391,6393,6395,6397,6399,6417],{},[898,6368,5561],{},[1651,6370,1738],{},[1651,6372,2181],{},[2446,6374,6375,6377],{},[898,6376,2675],{},[895,6378,6379,6381,6383,6385],{},[1692,6380,6311],{},[1651,6382,2181],{},[1692,6384,6316],{},[898,6386,2675],{},[1651,6388,4503],{},[1651,6390,1654],{"stretchy":1653},[1651,6392,2181],{},[1692,6394,6316],{},[1651,6396,1667],{"stretchy":1653},[1651,6398,1738],{},[2446,6400,6401,6407],{},[895,6402,6403,6405],{},[1692,6404,6316],{},[898,6406,2675],{},[895,6408,6409,6411,6413,6415],{},[1692,6410,6311],{},[1651,6412,2181],{},[1692,6414,6316],{},[898,6416,2675],{},[898,6418,1882],{"mathvariant":1910},[902,6420,6421],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,6423,6424,6425,1343,6449,1343,6479,1343,6503,6528,6529,6552,6553,4016,6571,5230],{},"Potom ",[883,6426,6428],{"className":6427},[886],[888,6429,6430],{"xmlns":890},[892,6431,6432,6446],{},[895,6433,6434,6436,6438,6440,6442,6444],{},[898,6435,5561],{},[1651,6437,1654],{"stretchy":1653},[1692,6439,1741],{},[1651,6441,1667],{"stretchy":1653},[1651,6443,1738],{},[1692,6445,1741],{},[902,6447,6448],{"encoding":904},"E(0)=0",[883,6450,6452],{"className":6451},[886],[888,6453,6454],{"xmlns":890},[892,6455,6456,6476],{},[895,6457,6458,6460,6462,6464,6466,6468],{},[898,6459,5561],{},[1651,6461,1654],{"stretchy":1653},[1692,6463,4190],{},[1651,6465,1667],{"stretchy":1653},[1651,6467,1738],{},[2938,6469,6470],{"scriptlevel":1741,"displaystyle":1653},[2446,6471,6472,6474],{},[1692,6473,1694],{},[1692,6475,3689],{},[902,6477,6478],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,6480,6482],{"className":6481},[886],[888,6483,6484],{"xmlns":890},[892,6485,6486,6500],{},[895,6487,6488,6490,6492,6494,6496,6498],{},[898,6489,5561],{},[1651,6491,1654],{"stretchy":1653},[1692,6493,6311],{},[1651,6495,1667],{"stretchy":1653},[1651,6497,1738],{},[1692,6499,1694],{},[902,6501,6502],{"encoding":904},"E(25)=1",[883,6504,6506],{"className":6505},[886],[888,6507,6508],{"xmlns":890},[892,6509,6510,6525],{},[895,6511,6512,6514,6516,6519,6521,6523],{},[898,6513,5561],{},[1651,6515,1654],{"stretchy":1653},[1692,6517,6518],{},"40",[1651,6520,1667],{"stretchy":1653},[1651,6522,1738],{},[1692,6524,3689],{},[902,6526,6527],{"encoding":904},"E(40)=4",". Např. ",[883,6530,6532],{"className":6531},[886],[888,6533,6534],{"xmlns":890},[892,6535,6536,6550],{},[895,6537,6538,6540,6542,6544,6546,6548],{},[898,6539,5561],{},[1651,6541,1654],{"stretchy":1653},[1692,6543,6518],{},[1651,6545,1667],{"stretchy":1653},[1651,6547,1738],{},[1692,6549,3689],{},[902,6551,6527],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,6554,6556],{"className":6555},[886],[888,6557,6558],{"xmlns":890},[892,6559,6560,6568],{},[895,6561,6562,6564,6566],{},[898,6563,1690],{},[1651,6565,1738],{},[1692,6567,3574],{},[902,6569,6570],{"encoding":904},"Q=5",[883,6572,6574],{"className":6573},[886],[888,6575,6576],{"xmlns":890},[892,6577,6578,6587],{},[895,6579,6580,6582,6584],{},[898,6581,1690],{},[1651,6583,1738],{},[1692,6585,6586],{},"4,8",[902,6588,6589],{"encoding":904},"Q=4{,}8",[198,6591,6593],{"id":6592},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,6595,6596,6652],{},[123,6597,6598,6601,6602,6619,6620,1882],{},[38,6599,6600],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,6603,6605],{"className":6604},[886],[888,6606,6607],{"xmlns":890},[892,6608,6609,6617],{},[895,6610,6611],{},[2115,6612,6613,6615],{},[898,6614,5561],{},[898,6616,5564],{},[902,6618,5567],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,6621,6623],{"className":6622},[886],[888,6624,6625],{"xmlns":890},[892,6626,6627,6649],{},[895,6628,6629,6632,6634,6636,6638,6640,6642,6644,6646],{},[1651,6630,6631],{"stretchy":1653},"⟨",[898,6633,2675],{},[1651,6635,1661],{"separator":1660},[1843,6637,1845],{},[898,6639,2675],{},[1651,6641,1839],{},[898,6643,4216],{"mathvariant":1910},[898,6645,2675],{},[1651,6647,6648],{"stretchy":1653},"⟩",[902,6650,6651],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,6653,6654,6657,6658,6671],{},[38,6655,6656],{},"Bodová"," (okamžitá) elasticita: ",[883,6659,6661],{"className":6660},[886],[888,6662,6663],{"xmlns":890},[892,6664,6665,6669],{},[895,6666,6667],{},[898,6668,5561],{},[902,6670,5561],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,6673,6675,6676,6689,6690],{"id":6674},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,6677,6679],{"className":6678},[886],[888,6680,6681],{"xmlns":890},[892,6682,6683,6687],{},[895,6684,6685],{},[898,6686,2675],{},[902,6688,2675],{"encoding":904}," jako funkce ",[883,6691,6693],{"className":6692},[886],[888,6694,6695],{"xmlns":890},[892,6696,6697,6701],{},[895,6698,6699],{},[898,6700,1690],{},[902,6702,1690],{"encoding":904},[724,6704,6705,6706,6729],{},"Pokud je poptávka zadaná ve tvaru ",[883,6707,6709],{"className":6708},[886],[888,6710,6711],{"xmlns":890},[892,6712,6713,6727],{},[895,6714,6715,6717,6719,6721,6723,6725],{},[898,6716,2675],{},[1651,6718,1738],{},[898,6720,2047],{},[1651,6722,1654],{"stretchy":1653},[898,6724,1690],{},[1651,6726,1667],{"stretchy":1653},[902,6728,5947],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,6731,6732],{},[883,6733,6735],{"className":6734,"title":5509,"style":5510},[5508],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,6737,6738,3246,6741,6767],{},[38,6739,6740],{},"Příklad 4.3.",[883,6742,6744],{"className":6743},[886],[888,6745,6746],{"xmlns":890},[892,6747,6748,6764],{},[895,6749,6750,6752,6754,6756,6758],{},[898,6751,2675],{},[1651,6753,1738],{},[1692,6755,4416],{},[1651,6757,2181],{},[2115,6759,6760,6762],{},[898,6761,1690],{},[1692,6763,1703],{},[902,6765,6766],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,6769,6770],{},[883,6771,6773],{"className":6772},[886],[888,6774,6775],{"xmlns":890},[892,6776,6777,6843],{},[895,6778,6779,6781,6783,6785,6801,6803,6815,6817,6841],{},[898,6780,5561],{},[1651,6782,1738],{},[1651,6784,2181],{},[2446,6786,6787,6799],{},[895,6788,6789,6791,6793],{},[1692,6790,4416],{},[1651,6792,2181],{},[2115,6794,6795,6797],{},[898,6796,1690],{},[1692,6798,1703],{},[898,6800,1690],{},[1651,6802,4503],{},[2446,6804,6805,6807],{},[1692,6806,1694],{},[895,6808,6809,6811,6813],{},[1651,6810,2181],{},[1692,6812,1703],{},[898,6814,1690],{},[1651,6816,1738],{},[2446,6818,6819,6831],{},[895,6820,6821,6823,6825],{},[1692,6822,4416],{},[1651,6824,2181],{},[2115,6826,6827,6829],{},[898,6828,1690],{},[1692,6830,1703],{},[895,6832,6833,6835],{},[1692,6834,1703],{},[2115,6836,6837,6839],{},[898,6838,1690],{},[1692,6840,1703],{},[898,6842,1882],{"mathvariant":1910},[902,6844,6845],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,6847,6848,6849,6876,6877,6896,6897,1882],{},"Z rovnice ",[883,6850,6852],{"className":6851},[886],[888,6853,6854],{"xmlns":890},[892,6855,6856,6873],{},[895,6857,6858,6860,6862,6868,6870],{},[1692,6859,4416],{},[1651,6861,2181],{},[2115,6863,6864,6866],{},[898,6865,1690],{},[1692,6867,1703],{},[1651,6869,1738],{},[1692,6871,6872],{},"36",[902,6874,6875],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,6878,6880],{"className":6879},[886],[888,6881,6882],{"xmlns":890},[892,6883,6884,6893],{},[895,6885,6886,6888,6890],{},[898,6887,1690],{},[1651,6889,1738],{},[1692,6891,6892],{},"8",[902,6894,6895],{"encoding":904},"Q = 8",", tedy ",[883,6898,6900],{"className":6899},[886],[888,6901,6902],{"xmlns":890},[892,6903,6904,6930],{},[895,6905,6906,6908,6910,6912,6914,6916,6925,6927],{},[898,6907,5561],{},[1651,6909,1654],{"stretchy":1653},[1692,6911,6892],{},[1651,6913,1667],{"stretchy":1653},[1651,6915,1738],{},[2938,6917,6918],{"scriptlevel":1741,"displaystyle":1653},[2446,6919,6920,6922],{},[1692,6921,6872],{},[1692,6923,6924],{},"128",[1651,6926,1738],{},[1692,6928,6929],{},"0,281",[902,6931,6932],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,6934,6936],{"id":6935},"přibližné-změny","Přibližné změny",[724,6938,6939,6940,6976,6977,6999],{},"Diferenciál ",[883,6941,6943],{"className":6942},[886],[888,6944,6945],{"xmlns":890},[892,6946,6947,6973],{},[895,6948,6949,6951,6953,6955,6961,6963,6965,6967,6969,6971],{},[898,6950,3542],{"mathvariant":1910},[898,6952,1690],{},[1651,6954,1738],{},[2115,6956,6957,6959],{},[898,6958,1690],{},[1651,6960,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,6962,1654],{"stretchy":1653},[898,6964,2675],{},[1651,6966,1667],{"stretchy":1653},[1843,6968,1845],{},[898,6970,3542],{"mathvariant":1910},[898,6972,2675],{},[902,6974,6975],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[883,6978,6980],{"className":6979},[886],[888,6981,6982],{"xmlns":890},[892,6983,6984,6996],{},[895,6985,6986,6988,6990,6992,6994],{},[898,6987,3542],{"mathvariant":1910},[898,6989,2675],{},[1651,6991,1738],{},[898,6993,4216],{"mathvariant":1910},[898,6995,2675],{},[902,6997,6998],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,7001,7002],{},[883,7003,7005],{"className":7004,"title":5509,"style":5510},[5508],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,7007,7008],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,7010,7011],{},[883,7012,7014],{"className":7013,"title":5509,"style":5510},[5508],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,7016,7017,3246,7020,7055,7056,7075,7076,7110,7111,7128],{},[38,7018,7019],{},"Příklad 4.5.",[883,7021,7023],{"className":7022},[886],[888,7024,7025],{"xmlns":890},[892,7026,7027,7052],{},[895,7028,7029,7031,7033,7035,7041,7043,7045,7047,7049],{},[898,7030,2675],{},[1651,7032,1738],{},[1651,7034,2181],{},[2115,7036,7037,7039],{},[898,7038,1690],{},[1692,7040,1703],{},[1651,7042,2181],{},[1692,7044,3689],{},[898,7046,1690],{},[1651,7048,1839],{},[1692,7050,7051],{},"96",[902,7053,7054],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,7057,7059],{"className":7058},[886],[888,7060,7061],{"xmlns":890},[892,7062,7063,7072],{},[895,7064,7065,7067,7069],{},[898,7066,2675],{},[1651,7068,1738],{},[1692,7070,7071],{},"51",[902,7073,7074],{"encoding":904},"P=51",". Z rovnice ",[883,7077,7079],{"className":7078},[886],[888,7080,7081],{"xmlns":890},[892,7082,7083,7107],{},[895,7084,7085,7087,7089,7091,7097,7099,7101,7103,7105],{},[1692,7086,7071],{},[1651,7088,1738],{},[1651,7090,2181],{},[2115,7092,7093,7095],{},[898,7094,1690],{},[1692,7096,1703],{},[1651,7098,2181],{},[1692,7100,3689],{},[898,7102,1690],{},[1651,7104,1839],{},[1692,7106,7051],{},[902,7108,7109],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,7112,7114],{"className":7113},[886],[888,7115,7116],{"xmlns":890},[892,7117,7118,7126],{},[895,7119,7120,7122,7124],{},[898,7121,1690],{},[1651,7123,1738],{},[1692,7125,3574],{},[902,7127,6570],{"encoding":904},". Elasticita:",[724,7130,7131],{},[883,7132,7134],{"className":7133},[886],[888,7135,7136],{"xmlns":890},[892,7137,7138,7211],{},[895,7139,7140,7142,7144,7182,7184,7188,7190,7192,7194,7196,7198,7205,7208],{},[898,7141,5561],{},[1651,7143,1738],{},[2446,7145,7146,7166],{},[895,7147,7148,7150,7156,7158,7160,7162,7164],{},[1651,7149,2181],{},[2115,7151,7152,7154],{},[898,7153,1690],{},[1692,7155,1703],{},[1651,7157,2181],{},[1692,7159,3689],{},[898,7161,1690],{},[1651,7163,1839],{},[1692,7165,7051],{},[895,7167,7168,7170,7172,7174,7176,7178,7180],{},[898,7169,1690],{},[1651,7171,1654],{"stretchy":1653},[1692,7173,1703],{},[898,7175,1690],{},[1651,7177,1839],{},[1692,7179,3689],{},[1651,7181,1667],{"stretchy":1653},[1651,7183,1661],{"separator":1660},[7185,7186],"mspace",{"width":7187},"2em",[898,7189,5561],{},[1651,7191,1654],{"stretchy":1653},[1692,7193,3574],{},[1651,7195,1667],{"stretchy":1653},[1651,7197,1738],{},[2446,7199,7200,7202],{},[1692,7201,7071],{},[1692,7203,7204],{},"70",[1651,7206,7207],{},"≐",[1692,7209,7210],{},"0,728.",[902,7212,7213],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,7215,7216,7217,1882],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,7218,7220],{"className":7219},[886],[888,7221,7222],{"xmlns":890},[892,7223,7224,7255],{},[895,7225,7226,7228,7230,7233,7235,7237,7240,7242,7244,7246,7248,7251,7253],{},[898,7227,4216],{"mathvariant":1910},[898,7229,1690],{},[898,7231,7232],{"mathvariant":1910},"%",[1651,7234,4060],{},[1651,7236,2181],{},[1692,7238,7239],{},"0,728",[1651,7241,4503],{},[1692,7243,1703],{},[1651,7245,1738],{},[1651,7247,2181],{},[1692,7249,7250],{},"1,456",[1843,7252,1845],{},[898,7254,7232],{"mathvariant":1910},[902,7256,7257],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,7259,7261],{"id":7260},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,7263,7264,7265,7288,7289,1793],{},"V závislosti na hodnotě ",[883,7266,7268],{"className":7267},[886],[888,7269,7270],{"xmlns":890},[892,7271,7272,7286],{},[895,7273,7274,7276,7278,7284],{},[898,7275,5561],{},[1651,7277,1654],{"stretchy":1653},[2115,7279,7280,7282],{},[898,7281,2675],{},[1651,7283,2668],{},[1651,7285,1667],{"stretchy":1653},[902,7287,5689],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,7290,7292],{"className":7291},[886],[888,7293,7294],{"xmlns":890},[892,7295,7296,7305],{},[895,7297,7298,7300,7303],{},[1651,7299,1654],{"stretchy":1653},[1692,7301,7302],{},"4.7",[1651,7304,1667],{"stretchy":1653},[902,7306,7307],{"encoding":904},"(4.7)",[724,7309,7310],{},[1756,7311],{"alt":7312,"className":7313,"src":7314},"imek-typy-elasticity-5panelu",[210,1760],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,7316,7317,7356],{},[19,7318,7319],{},[22,7320,7321,7347,7350,7353],{},[25,7322,7323,7324],{},"Hodnota ",[883,7325,7327],{"className":7326},[886],[888,7328,7329],{"xmlns":890},[892,7330,7331,7345],{},[895,7332,7333,7335,7337,7343],{},[898,7334,5561],{},[1651,7336,1654],{"stretchy":1653},[2115,7338,7339,7341],{},[898,7340,2675],{},[1651,7342,2668],{},[1651,7344,1667],{"stretchy":1653},[902,7346,5689],{"encoding":904},[25,7348,7349],{},"Typ poptávky",[25,7351,7352],{},"Termín",[25,7354,7355],{},"Význam",[30,7357,7358,7391,7453,7528,7585],{},[22,7359,7360,7380,7385,7388],{},[35,7361,7362],{},[883,7363,7365],{"className":7364},[886],[888,7366,7367],{"xmlns":890},[892,7368,7369,7377],{},[895,7370,7371,7373,7375],{},[898,7372,5561],{},[1651,7374,1738],{},[1692,7376,1741],{},[902,7378,7379],{"encoding":904},"E = 0",[35,7381,7382],{},[38,7383,7384],{},"dokonale neelastická",[35,7386,7387],{},"perfectly inelastic",[35,7389,7390],{},"množství se nemění bez ohledu na cenu",[22,7392,7393,7417,7421,7424],{},[35,7394,7395],{},[883,7396,7398],{"className":7397},[886],[888,7399,7400],{"xmlns":890},[892,7401,7402,7414],{},[895,7403,7404,7406,7408,7410,7412],{},[1692,7405,1741],{},[1651,7407,2319],{},[898,7409,5561],{},[1651,7411,2319],{},[1692,7413,1694],{},[902,7415,7416],{"encoding":904},"0 \u003C E \u003C 1",[35,7418,7419],{},[38,7420,5387],{},[35,7422,7423],{},"inelastic",[35,7425,7426,7439,7440],{},[883,7427,7429],{"className":7428},[886],[888,7430,7431],{"xmlns":890},[892,7432,7433,7437],{},[895,7434,7435],{},[898,7436,1690],{},[902,7438,1690],{"encoding":904}," se mění pomaleji než ",[883,7441,7443],{"className":7442},[886],[888,7444,7445],{"xmlns":890},[892,7446,7447,7451],{},[895,7448,7449],{},[898,7450,2675],{},[902,7452,2675],{"encoding":904},[22,7454,7455,7474,7479,7482],{},[35,7456,7457],{},[883,7458,7460],{"className":7459},[886],[888,7461,7462],{"xmlns":890},[892,7463,7464,7472],{},[895,7465,7466,7468,7470],{},[898,7467,5561],{},[1651,7469,1738],{},[1692,7471,1694],{},[902,7473,5852],{"encoding":904},[35,7475,7476],{},[38,7477,7478],{},"jednotkově elastická",[35,7480,7481],{},"unit elastic",[35,7483,7484,7497,7498,7511,7512,7527],{},[883,7485,7487],{"className":7486},[886],[888,7488,7489],{"xmlns":890},[892,7490,7491,7495],{},[895,7492,7493],{},[898,7494,1690],{},[902,7496,1690],{"encoding":904}," i ",[883,7499,7501],{"className":7500},[886],[888,7502,7503],{"xmlns":890},[892,7504,7505,7509],{},[895,7506,7507],{},[898,7508,2675],{},[902,7510,2675],{"encoding":904}," se mění stejně rychle; ",[883,7513,7515],{"className":7514},[886],[888,7516,7517],{"xmlns":890},[892,7518,7519,7525],{},[895,7520,7521,7523],{},[898,7522,4104],{},[898,7524,2998],{},[902,7526,5404],{"encoding":904}," má maximum",[22,7529,7530,7549,7553,7556],{},[35,7531,7532],{},[883,7533,7535],{"className":7534},[886],[888,7536,7537],{"xmlns":890},[892,7538,7539,7547],{},[895,7540,7541,7543,7545],{},[898,7542,5561],{},[1651,7544,2390],{},[1692,7546,1694],{},[902,7548,5816],{"encoding":904},[35,7550,7551],{},[38,7552,5383],{},[35,7554,7555],{},"elastic",[35,7557,7558,7571,7572],{},[883,7559,7561],{"className":7560},[886],[888,7562,7563],{"xmlns":890},[892,7564,7565,7569],{},[895,7566,7567],{},[898,7568,1690],{},[902,7570,1690],{"encoding":904}," se mění rychleji než ",[883,7573,7575],{"className":7574},[886],[888,7576,7577],{"xmlns":890},[892,7578,7579,7583],{},[895,7580,7581],{},[898,7582,2675],{},[902,7584,2675],{"encoding":904},[22,7586,7587,7608,7613,7616],{},[35,7588,7589],{},[883,7590,7592],{"className":7591},[886],[888,7593,7594],{"xmlns":890},[892,7595,7596,7605],{},[895,7597,7598,7600,7602],{},[898,7599,5561],{},[1651,7601,4449],{},[898,7603,7604],{"mathvariant":1910},"∞",[902,7606,7607],{"encoding":904},"E \\to \\infty",[35,7609,7610],{},[38,7611,7612],{},"dokonale elastická",[35,7614,7615],{},"perfectly elastic",[35,7617,7618,7619],{},"sebemenší změna ceny úplně mění ",[883,7620,7622],{"className":7621},[886],[888,7623,7624],{"xmlns":890},[892,7625,7626,7630],{},[895,7627,7628],{},[898,7629,1690],{},[902,7631,1690],{"encoding":904},[724,7633,7634],{},[38,7635,7636],{},"Pravidlo růstu elasticity s cenou:",[5179,7638,7639],{},[724,7640,7641,7642],{},"S rostoucí cenou elasticita poptávky roste. ",[883,7643,7645],{"className":7644},[886],[888,7646,7647],{"xmlns":890},[892,7648,7649,7658],{},[895,7650,7651,7653,7656],{},[1651,7652,1654],{"stretchy":1653},[1692,7654,7655],{},"4.8",[1651,7657,1667],{"stretchy":1653},[902,7659,7660],{"encoding":904},"(4.8)",[724,7662,7663,7664,7667,7668,7671,7672,7689],{},"Z toho plyne, že při ",[614,7665,7666],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,7669,7670],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,7673,7675],{"className":7674},[886],[888,7676,7677],{"xmlns":890},[892,7678,7679,7687],{},[895,7680,7681],{},[2115,7682,7683,7685],{},[898,7684,2675],{},[1651,7686,2668],{},[902,7688,5711],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[5179,7691,7692,7697],{},[724,7693,7694,7696],{},[883,7695,5879],{}," Postup: jak klasifikovat poptávku",[152,7698,7699,7726,7729],{},[123,7700,7701,7702,7725],{},"Spočítejte ",[883,7703,7705],{"className":7704},[886],[888,7706,7707],{"xmlns":890},[892,7708,7709,7723],{},[895,7710,7711,7713,7715,7721],{},[898,7712,5561],{},[1651,7714,1654],{"stretchy":1653},[2115,7716,7717,7719],{},[898,7718,2675],{},[1651,7720,2668],{},[1651,7722,1667],{"stretchy":1653},[902,7724,5689],{"encoding":904}," dle (4.5).",[123,7727,7728],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,7730,7731,7732,7756],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,7733,7735],{"className":7734},[886],[888,7736,7737],{"xmlns":890},[892,7738,7739,7753],{},[895,7740,7741,7743,7745,7747,7749,7751],{},[898,7742,5561],{},[1651,7744,1654],{"stretchy":1653},[898,7746,2675],{},[1651,7748,1667],{"stretchy":1653},[1651,7750,1738],{},[1692,7752,1694],{},[902,7754,7755],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,7758,7759,7762,7763,7780,7781,7799,7800,7827,7828,1882],{},[38,7760,7761],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,7764,7766],{"className":7765},[886],[888,7767,7768],{"xmlns":890},[892,7769,7770,7778],{},[895,7771,7772,7774,7776],{},[898,7773,5561],{},[1651,7775,1738],{},[1692,7777,1694],{},[902,7779,5852],{"encoding":904}," pro ",[883,7782,7784],{"className":7783},[886],[888,7785,7786],{"xmlns":890},[892,7787,7788,7796],{},[895,7789,7790,7792,7794],{},[898,7791,2675],{},[1651,7793,1738],{},[1692,7795,6311],{},[902,7797,7798],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,7801,7803],{"className":7802},[886],[888,7804,7805],{"xmlns":890},[892,7806,7807,7824],{},[895,7808,7809,7811,7814,7816,7818,7820,7822],{},[898,7810,2675],{},[1651,7812,7813],{},"∈",[1651,7815,6631],{"stretchy":1653},[1692,7817,1741],{},[1651,7819,1661],{"separator":1660},[1692,7821,6311],{},[1651,7823,1667],{"stretchy":1653},[902,7825,7826],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,7829,7831],{"className":7830},[886],[888,7832,7833],{"xmlns":890},[892,7834,7835,7851],{},[895,7836,7837,7839,7841,7843,7845,7847,7849],{},[898,7838,2675],{},[1651,7840,7813],{},[1651,7842,1654],{"stretchy":1653},[1692,7844,6311],{},[1651,7846,1661],{"separator":1660},[1692,7848,4446],{},[1651,7850,6648],{"stretchy":1653},[902,7852,7853],{"encoding":904},"P \\in (25, 50\\rangle",[115,7855,7857],{"id":7856},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,7859,7860],{},[1756,7861],{"alt":7862,"className":7863,"src":7864},"imek-elasticita-tr",[210,1760],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,7866,7867],{},[1756,7868],{"alt":7869,"className":7870,"src":7871},"imek-elasticita-podel-linearni-poptavky",[210,1760],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,7873,7874,7875,7925,7926,7942],{},"Pro celkový příjem platí ",[883,7876,7878],{"className":7877},[886],[888,7879,7880],{"xmlns":890},[892,7881,7882,7922],{},[895,7883,7884,7886,7888,7890,7892,7894,7896,7898,7900,7902,7904,7906,7908,7910,7912,7914,7916,7918,7920],{},[898,7885,4104],{},[898,7887,2998],{},[1651,7889,1738],{},[898,7891,4104],{},[898,7893,2998],{},[1651,7895,1654],{"stretchy":1653},[898,7897,1690],{},[1651,7899,1667],{"stretchy":1653},[1651,7901,1738],{},[898,7903,2675],{},[1651,7905,4503],{},[898,7907,1690],{},[1651,7909,1738],{},[898,7911,1690],{},[1651,7913,4503],{},[898,7915,2047],{},[1651,7917,1654],{"stretchy":1653},[898,7919,1690],{},[1651,7921,1667],{"stretchy":1653},[902,7923,7924],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,7927,7929],{"className":7928},[886],[888,7930,7931],{"xmlns":890},[892,7932,7933,7939],{},[895,7934,7935,7937],{},[898,7936,2995],{},[898,7938,2998],{},[902,7940,7941],{"encoding":904},"MR"," odvodíme:",[724,7944,7945],{},[883,7946,7948],{"className":7947},[886],[888,7949,7950],{"xmlns":890},[892,7951,7952,8060],{},[895,7953,7954,7956,7958,7960,7962,7968,7970,7972,7974,7976,7978,7980,7982,7984,7986,7988,7990,7996,7998,8000,8002,8004,8006,8008,8010,8024,8026,8028],{},[898,7955,2995],{},[898,7957,2998],{},[1651,7959,1738],{},[898,7961,4104],{},[2115,7963,7964,7966],{},[898,7965,2998],{},[1651,7967,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,7969,1654],{"stretchy":1653},[898,7971,1690],{},[1651,7973,1667],{"stretchy":1653},[1651,7975,1738],{},[898,7977,2047],{},[1651,7979,1654],{"stretchy":1653},[898,7981,1690],{},[1651,7983,1667],{"stretchy":1653},[1651,7985,1839],{},[898,7987,1690],{},[1843,7989,1845],{},[2115,7991,7992,7994],{},[898,7993,2047],{},[1651,7995,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,7997,1654],{"stretchy":1653},[898,7999,1690],{},[1651,8001,1667],{"stretchy":1653},[1651,8003,1738],{},[898,8005,2675],{},[1651,8007,1839],{},[898,8009,1690],{},[2446,8011,8012,8018],{},[895,8013,8014,8016],{},[898,8015,3542],{"mathvariant":1910},[898,8017,2675],{},[895,8019,8020,8022],{},[898,8021,3542],{"mathvariant":1910},[898,8023,1690],{},[1651,8025,1738],{},[898,8027,2675],{},[895,8029,8030,8032,8034,8036,8042,8044,8058],{},[1651,8031,1654],{"fence":1660},[1692,8033,1694],{},[1651,8035,1839],{},[2446,8037,8038,8040],{},[898,8039,1690],{},[898,8041,2675],{},[1651,8043,4503],{},[2446,8045,8046,8052],{},[895,8047,8048,8050],{},[898,8049,3542],{"mathvariant":1910},[898,8051,2675],{},[895,8053,8054,8056],{},[898,8055,3542],{"mathvariant":1910},[898,8057,1690],{},[1651,8059,1667],{"fence":1660},[902,8061,8062],{"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)",[724,8064,8065],{},[883,8066,8068],{"className":8067},[886],[888,8069,8070],{"xmlns":890},[892,8071,8072,8144],{},[895,8073,8074,8076,8078,8120,8122,8124],{},[1651,8075,1738],{},[898,8077,2675],{},[895,8079,8080,8082,8084,8086,8118],{},[1651,8081,1654],{"fence":1660},[1692,8083,1694],{},[1651,8085,1839],{},[2446,8087,8088,8090],{},[1692,8089,1694],{},[895,8091,8092,8100,8102],{},[2938,8093,8094],{"scriptlevel":1741,"displaystyle":1653},[2446,8095,8096,8098],{},[898,8097,2675],{},[898,8099,1690],{},[1651,8101,4503],{},[2938,8103,8104],{"scriptlevel":1741,"displaystyle":1653},[2446,8105,8106,8112],{},[895,8107,8108,8110],{},[898,8109,3542],{"mathvariant":1910},[898,8111,1690],{},[895,8113,8114,8116],{},[898,8115,3542],{"mathvariant":1910},[898,8117,2675],{},[1651,8119,1667],{"fence":1660},[1651,8121,1738],{},[898,8123,2675],{},[895,8125,8126,8128,8130,8132,8142],{},[1651,8127,1654],{"fence":1660},[1692,8129,1694],{},[1651,8131,1839],{},[2446,8133,8134,8136],{},[1692,8135,1694],{},[895,8137,8138,8140],{},[1651,8139,2181],{},[898,8141,5561],{},[1651,8143,1667],{"fence":1660},[902,8145,8146],{"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)",[724,8148,8149],{},"a tedy",[724,8151,8152],{},[883,8153,8155],{"className":8154,"title":5509,"style":5510},[5508],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[5179,8157,8158,8227,8477],{},[724,8159,8160,8162,8163,8197,8198,8213,8214,1793],{},[883,8161,5465],{}," Intuice: vztah ",[883,8164,8166],{"className":8165},[886],[888,8167,8168],{"xmlns":890},[892,8169,8170,8194],{},[895,8171,8172,8174,8176,8178,8180,8182,8184,8186,8188,8190,8192],{},[898,8173,2995],{},[898,8175,2998],{},[1651,8177,1738],{},[898,8179,2675],{},[1651,8181,1654],{"stretchy":1653},[1692,8183,1694],{},[1651,8185,2181],{},[1692,8187,1694],{},[898,8189,5981],{"mathvariant":1910},[898,8191,5561],{},[1651,8193,1667],{"stretchy":1653},[902,8195,8196],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,8199,8201],{"className":8200},[886],[888,8202,8203],{"xmlns":890},[892,8204,8205,8211],{},[895,8206,8207,8209],{},[898,8208,2995],{},[898,8210,2998],{},[902,8212,7941],{"encoding":904}," jednoznačně určuje hodnota ",[883,8215,8217],{"className":8216},[886],[888,8218,8219],{"xmlns":890},[892,8220,8221,8225],{},[895,8222,8223],{},[898,8224,5561],{},[902,8226,5561],{"encoding":904},[120,8228,8229,8339,8408],{},[123,8230,8231,8248,8249,3246,8263,3246,8289,3246,8302,8322,8323,8338],{},[883,8232,8234],{"className":8233},[886],[888,8235,8236],{"xmlns":890},[892,8237,8238,8246],{},[895,8239,8240,8242,8244],{},[898,8241,5561],{},[1651,8243,2390],{},[1692,8245,1694],{},[902,8247,5816],{"encoding":904}," (elastická) ",[883,8250,8252],{"className":8251},[886],[888,8253,8254],{"xmlns":890},[892,8255,8256,8260],{},[895,8257,8258],{},[1651,8259,5298],{},[902,8261,8262],{"encoding":904},"\\Rightarrow",[883,8264,8266],{"className":8265},[886],[888,8267,8268],{"xmlns":890},[892,8269,8270,8286],{},[895,8271,8272,8274,8276,8278,8280,8282,8284],{},[1692,8273,1694],{},[1651,8275,2181],{},[1692,8277,1694],{},[898,8279,5981],{"mathvariant":1910},[898,8281,5561],{},[1651,8283,2390],{},[1692,8285,1741],{},[902,8287,8288],{"encoding":904},"1 - 1\u002FE > 0",[883,8290,8292],{"className":8291},[886],[888,8293,8294],{"xmlns":890},[892,8295,8296,8300],{},[895,8297,8298],{},[1651,8299,5298],{},[902,8301,8262],{"encoding":904},[883,8303,8305],{"className":8304},[886],[888,8306,8307],{"xmlns":890},[892,8308,8309,8319],{},[895,8310,8311,8313,8315,8317],{},[898,8312,2995],{},[898,8314,2998],{},[1651,8316,2390],{},[1692,8318,1741],{},[902,8320,8321],{"encoding":904},"MR > 0"," — ",[883,8324,8326],{"className":8325},[886],[888,8327,8328],{"xmlns":890},[892,8329,8330,8336],{},[895,8331,8332,8334],{},[898,8333,4104],{},[898,8335,2998],{},[902,8337,5404],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,8340,8341,8358,8359,3246,8372,8322,8392,8407],{},[883,8342,8344],{"className":8343},[886],[888,8345,8346],{"xmlns":890},[892,8347,8348,8356],{},[895,8349,8350,8352,8354],{},[898,8351,5561],{},[1651,8353,1738],{},[1692,8355,1694],{},[902,8357,5852],{"encoding":904}," (jednotková) ",[883,8360,8362],{"className":8361},[886],[888,8363,8364],{"xmlns":890},[892,8365,8366,8370],{},[895,8367,8368],{},[1651,8369,5298],{},[902,8371,8262],{"encoding":904},[883,8373,8375],{"className":8374},[886],[888,8376,8377],{"xmlns":890},[892,8378,8379,8389],{},[895,8380,8381,8383,8385,8387],{},[898,8382,2995],{},[898,8384,2998],{},[1651,8386,1738],{},[1692,8388,1741],{},[902,8390,8391],{"encoding":904},"MR = 0",[883,8393,8395],{"className":8394},[886],[888,8396,8397],{"xmlns":890},[892,8398,8399,8405],{},[895,8400,8401,8403],{},[898,8402,4104],{},[898,8404,2998],{},[902,8406,5404],{"encoding":904}," je extrém (maximum).",[123,8409,8410,8427,8428,3246,8441,8322,8461,8476],{},[883,8411,8413],{"className":8412},[886],[888,8414,8415],{"xmlns":890},[892,8416,8417,8425],{},[895,8418,8419,8421,8423],{},[898,8420,5561],{},[1651,8422,2319],{},[1692,8424,1694],{},[902,8426,5834],{"encoding":904}," (neelastická) ",[883,8429,8431],{"className":8430},[886],[888,8432,8433],{"xmlns":890},[892,8434,8435,8439],{},[895,8436,8437],{},[1651,8438,5298],{},[902,8440,8262],{"encoding":904},[883,8442,8444],{"className":8443},[886],[888,8445,8446],{"xmlns":890},[892,8447,8448,8458],{},[895,8449,8450,8452,8454,8456],{},[898,8451,2995],{},[898,8453,2998],{},[1651,8455,2319],{},[1692,8457,1741],{},[902,8459,8460],{"encoding":904},"MR \u003C 0",[883,8462,8464],{"className":8463},[886],[888,8465,8466],{"xmlns":890},[892,8467,8468,8474],{},[895,8469,8470,8472],{},[898,8471,4104],{},[898,8473,2998],{},[902,8475,5404],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,8478,8479,8480,1882],{},"Viz také ",[207,8481,5135],{"className":8482,"dataFsResolvedFilePath":827,"href":828},[210],[198,8484,8486],{"id":8485},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,8488,8489,8509,8510,8536,8537,8552,8553,8566,8567,8580,8581,8594,8595,8611,8612,3246,8627,8630,8631,8611,8647,1882],{},[38,8490,8491,8492,5230],{},"(a) Poptávka elastická (",[883,8493,8495],{"className":8494},[886],[888,8496,8497],{"xmlns":890},[892,8498,8499,8507],{},[895,8500,8501,8503,8505],{},[898,8502,5561],{},[1651,8504,2390],{},[1692,8506,1694],{},[902,8508,5816],{"encoding":904}," Z (4.12) plyne ",[883,8511,8513],{"className":8512},[886],[888,8514,8515],{"xmlns":890},[892,8516,8517,8533],{},[895,8518,8519,8521,8523,8525,8527,8529,8531],{},[898,8520,2995],{},[898,8522,2998],{},[1651,8524,1654],{"stretchy":1653},[898,8526,1690],{},[1651,8528,1667],{"stretchy":1653},[1651,8530,2390],{},[1692,8532,1741],{},[902,8534,8535],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,8538,8540],{"className":8539},[886],[888,8541,8542],{"xmlns":890},[892,8543,8544,8550],{},[895,8545,8546,8548],{},[898,8547,4104],{},[898,8549,2998],{},[902,8551,5404],{"encoding":904}," je rostoucí funkcí ",[883,8554,8556],{"className":8555},[886],[888,8557,8558],{"xmlns":890},[892,8559,8560,8564],{},[895,8561,8562],{},[898,8563,1690],{},[902,8565,1690],{"encoding":904},". Avšak růst ",[883,8568,8570],{"className":8569},[886],[888,8571,8572],{"xmlns":890},[892,8573,8574,8578],{},[895,8575,8576],{},[898,8577,1690],{},[902,8579,1690],{"encoding":904}," je odezvou na pokles ceny ",[883,8582,8584],{"className":8583},[886],[888,8585,8586],{"xmlns":890},[892,8587,8588,8592],{},[895,8589,8590],{},[898,8591,2675],{},[902,8593,2675],{"encoding":904},". Tudíž s ",[614,8596,8597,8598],{},"poklesem ceny ",[883,8599,8601],{"className":8600},[886],[888,8602,8603],{"xmlns":890},[892,8604,8605,8609],{},[895,8606,8607],{},[898,8608,2675],{},[902,8610,2675],{"encoding":904}," celkový příjem ",[883,8613,8615],{"className":8614},[886],[888,8616,8617],{"xmlns":890},[892,8618,8619,8625],{},[895,8620,8621,8623],{},[898,8622,4104],{},[898,8624,2998],{},[902,8626,5404],{"encoding":904},[614,8628,8629],{},"roste"," a s ",[614,8632,8633,8634],{},"růstem ceny ",[883,8635,8637],{"className":8636},[886],[888,8638,8639],{"xmlns":890},[892,8640,8641,8645],{},[895,8642,8643],{},[898,8644,2675],{},[902,8646,2675],{"encoding":904},[614,8648,8649],{},"klesá",[5179,8651,8652],{},[724,8653,8654,8657],{},[38,8655,8656],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,8659,8660,8509,8680,1343,8706,8721,8722,8735,8736,8749,8750,8763,8764,8611,8777,3246,8792,1882],{},[38,8661,8662,8663,5230],{},"(b) Poptávka neelastická (",[883,8664,8666],{"className":8665},[886],[888,8667,8668],{"xmlns":890},[892,8669,8670,8678],{},[895,8671,8672,8674,8676],{},[898,8673,5561],{},[1651,8675,2319],{},[1692,8677,1694],{},[902,8679,5834],{"encoding":904},[883,8681,8683],{"className":8682},[886],[888,8684,8685],{"xmlns":890},[892,8686,8687,8703],{},[895,8688,8689,8691,8693,8695,8697,8699,8701],{},[898,8690,2995],{},[898,8692,2998],{},[1651,8694,1654],{"stretchy":1653},[898,8696,1690],{},[1651,8698,1667],{"stretchy":1653},[1651,8700,2319],{},[1692,8702,1741],{},[902,8704,8705],{"encoding":904},"MR(Q) \u003C 0",[883,8707,8709],{"className":8708},[886],[888,8710,8711],{"xmlns":890},[892,8712,8713,8719],{},[895,8714,8715,8717],{},[898,8716,4104],{},[898,8718,2998],{},[902,8720,5404],{"encoding":904}," je klesající funkce ",[883,8723,8725],{"className":8724},[886],[888,8726,8727],{"xmlns":890},[892,8728,8729,8733],{},[895,8730,8731],{},[898,8732,1690],{},[902,8734,1690],{"encoding":904},", tj. s růstem ",[883,8737,8739],{"className":8738},[886],[888,8740,8741],{"xmlns":890},[892,8742,8743,8747],{},[895,8744,8745],{},[898,8746,1690],{},[902,8748,1690],{"encoding":904}," (s poklesem ceny ",[883,8751,8753],{"className":8752},[886],[888,8754,8755],{"xmlns":890},[892,8756,8757,8761],{},[895,8758,8759],{},[898,8760,2675],{},[902,8762,2675],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,8765,8767],{"className":8766},[886],[888,8768,8769],{"xmlns":890},[892,8770,8771,8775],{},[895,8772,8773],{},[898,8774,2675],{},[902,8776,2675],{"encoding":904},[883,8778,8780],{"className":8779},[886],[888,8781,8782],{"xmlns":890},[892,8783,8784,8790],{},[895,8785,8786,8788],{},[898,8787,4104],{},[898,8789,2998],{},[902,8791,5404],{"encoding":904},[614,8793,8629],{},[5179,8795,8796],{},[724,8797,8798,8801],{},[38,8799,8800],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,8803,8804,8509,8824,8843,8844,8859,8860,8930,8931,5197,8959,8992,8993,6896,9021,9036,9037,1882],{},[38,8805,8806,8807,5230],{},"(c) Jednotková elasticita (",[883,8808,8810],{"className":8809},[886],[888,8811,8812],{"xmlns":890},[892,8813,8814,8822],{},[895,8815,8816,8818,8820],{},[898,8817,5561],{},[1651,8819,1738],{},[1692,8821,1694],{},[902,8823,5852],{"encoding":904},[883,8825,8827],{"className":8826},[886],[888,8828,8829],{"xmlns":890},[892,8830,8831,8841],{},[895,8832,8833,8835,8837,8839],{},[898,8834,2995],{},[898,8836,2998],{},[1651,8838,1738],{},[1692,8840,1741],{},[902,8842,8391],{"encoding":904}," — nutná podmínka extrému ",[883,8845,8847],{"className":8846},[886],[888,8848,8849],{"xmlns":890},[892,8850,8851,8857],{},[895,8852,8853,8855],{},[898,8854,4104],{},[898,8856,2998],{},[902,8858,5404],{"encoding":904},". Dále ",[883,8861,8863],{"className":8862},[886],[888,8864,8865],{"xmlns":890},[892,8866,8867,8927],{},[895,8868,8869,8871,8881,8883,8885,8891,8893,8899,8901,8903,8905,8907,8909,8911,8921,8923,8925],{},[898,8870,4104],{},[2115,8872,8873,8875],{},[898,8874,2998],{},[895,8876,8877,8879],{},[1651,8878,1912],{"mathvariant":1910},[1651,8880,1912],{"mathvariant":1910},[1651,8882,1738],{},[898,8884,2995],{},[2115,8886,8887,8889],{},[898,8888,2998],{},[1651,8890,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,8892,1738],{},[2115,8894,8895,8897],{},[898,8896,2047],{},[1651,8898,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,8900,1654],{"stretchy":1653},[898,8902,1690],{},[1651,8904,1667],{"stretchy":1653},[1651,8906,1839],{},[898,8908,1690],{},[1843,8910,1845],{},[2115,8912,8913,8915],{},[898,8914,2047],{},[895,8916,8917,8919],{},[1651,8918,1912],{"mathvariant":1910},[1651,8920,1912],{"mathvariant":1910},[1651,8922,1654],{"stretchy":1653},[898,8924,1690],{},[1651,8926,1667],{"stretchy":1653},[902,8928,8929],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,8932,8934],{"className":8933},[886],[888,8935,8936],{"xmlns":890},[892,8937,8938,8956],{},[895,8939,8940,8946,8948,8950,8952,8954],{},[2115,8941,8942,8944],{},[898,8943,2047],{},[1651,8945,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,8947,1654],{"stretchy":1653},[898,8949,1690],{},[1651,8951,1667],{"stretchy":1653},[1651,8953,2319],{},[1692,8955,1741],{},[902,8957,8958],{"encoding":904},"D'(Q) \u003C 0",[883,8960,8962],{"className":8961},[886],[888,8963,8964],{"xmlns":890},[892,8965,8966,8989],{},[895,8967,8968,8978,8980,8982,8984,8987],{},[2115,8969,8970,8972],{},[898,8971,2047],{},[895,8973,8974,8976],{},[1651,8975,1912],{"mathvariant":1910},[1651,8977,1912],{"mathvariant":1910},[1651,8979,1654],{"stretchy":1653},[898,8981,1690],{},[1651,8983,1667],{"stretchy":1653},[1651,8985,8986],{},"≤",[1692,8988,1741],{},[902,8990,8991],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,8994,8996],{"className":8995},[886],[888,8997,8998],{"xmlns":890},[892,8999,9000,9018],{},[895,9001,9002,9004,9014,9016],{},[898,9003,4104],{},[2115,9005,9006,9008],{},[898,9007,2998],{},[895,9009,9010,9012],{},[1651,9011,1912],{"mathvariant":1910},[1651,9013,1912],{"mathvariant":1910},[1651,9015,2319],{},[1692,9017,1741],{},[902,9019,9020],{"encoding":904},"TR'' \u003C 0",[883,9022,9024],{"className":9023},[886],[888,9025,9026],{"xmlns":890},[892,9027,9028,9034],{},[895,9029,9030,9032],{},[898,9031,4104],{},[898,9033,2998],{},[902,9035,5404],{"encoding":904}," nabývá ",[38,9038,9039],{},"maxima",[5179,9041,9042],{},[724,9043,9044,9047],{},[38,9045,9046],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,9049,9050],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,9052,9053],{},[38,9054,9055],{},"Souhrnná tabulka Pravidel 1–3:",[16,9057,9058,9162],{},[19,9059,9060],{},[22,9061,9062,9065,9080,9097,9128,9159],{},[25,9063,9064],{},"Charakter poptávky",[25,9066,9067],{},[883,9068,9070],{"className":9069},[886],[888,9071,9072],{"xmlns":890},[892,9073,9074,9078],{},[895,9075,9076],{},[898,9077,5561],{},[902,9079,5561],{"encoding":904},[25,9081,9082],{},[883,9083,9085],{"className":9084},[886],[888,9086,9087],{"xmlns":890},[892,9088,9089,9095],{},[895,9090,9091,9093],{},[898,9092,2995],{},[898,9094,2998],{},[902,9096,7941],{"encoding":904},[25,9098,9099,9100,3246,9113],{},"Pokles ceny ",[883,9101,9103],{"className":9102},[886],[888,9104,9105],{"xmlns":890},[892,9106,9107,9111],{},[895,9108,9109],{},[1651,9110,5298],{},[902,9112,8262],{"encoding":904},[883,9114,9116],{"className":9115},[886],[888,9117,9118],{"xmlns":890},[892,9119,9120,9126],{},[895,9121,9122,9124],{},[898,9123,4104],{},[898,9125,2998],{},[902,9127,5404],{"encoding":904},[25,9129,9130,9131,3246,9144],{},"Růst ceny ",[883,9132,9134],{"className":9133},[886],[888,9135,9136],{"xmlns":890},[892,9137,9138,9142],{},[895,9139,9140],{},[1651,9141,5298],{},[902,9143,8262],{"encoding":904},[883,9145,9147],{"className":9146},[886],[888,9148,9149],{"xmlns":890},[892,9150,9151,9157],{},[895,9152,9153,9155],{},[898,9154,4104],{},[898,9156,2998],{},[902,9158,5404],{"encoding":904},[25,9160,9161],{},"Doporučení",[30,9163,9164,9213,9263],{},[22,9165,9166,9168,9186,9204,9206,9208],{},[35,9167,5383],{},[35,9169,9170],{},[883,9171,9173],{"className":9172},[886],[888,9174,9175],{"xmlns":890},[892,9176,9177,9183],{},[895,9178,9179,9181],{},[1651,9180,2390],{},[1692,9182,1694],{},[902,9184,9185],{"encoding":904},"> 1",[35,9187,9188],{},[883,9189,9191],{"className":9190},[886],[888,9192,9193],{"xmlns":890},[892,9194,9195,9201],{},[895,9196,9197,9199],{},[1651,9198,2390],{},[1692,9200,1741],{},[902,9202,9203],{"encoding":904},"> 0",[35,9205,8629],{},[35,9207,8649],{},[35,9209,9210],{},[38,9211,9212],{},"snížit cenu",[22,9214,9215,9218,9236,9254,9256,9258],{},[35,9216,9217],{},"jednotková",[35,9219,9220],{},[883,9221,9223],{"className":9222},[886],[888,9224,9225],{"xmlns":890},[892,9226,9227,9233],{},[895,9228,9229,9231],{},[1651,9230,1738],{},[1692,9232,1694],{},[902,9234,9235],{"encoding":904},"= 1",[35,9237,9238],{},[883,9239,9241],{"className":9240},[886],[888,9242,9243],{"xmlns":890},[892,9244,9245,9251],{},[895,9246,9247,9249],{},[1651,9248,1738],{},[1692,9250,1741],{},[902,9252,9253],{"encoding":904},"= 0",[35,9255,2328],{},[35,9257,2328],{},[35,9259,9260],{},[38,9261,9262],{},"držet cenu",[22,9264,9265,9267,9285,9303,9305,9307],{},[35,9266,5387],{},[35,9268,9269],{},[883,9270,9272],{"className":9271},[886],[888,9273,9274],{"xmlns":890},[892,9275,9276,9282],{},[895,9277,9278,9280],{},[1651,9279,2319],{},[1692,9281,1694],{},[902,9283,9284],{"encoding":904},"\u003C 1",[35,9286,9287],{},[883,9288,9290],{"className":9289},[886],[888,9291,9292],{"xmlns":890},[892,9293,9294,9300],{},[895,9295,9296,9298],{},[1651,9297,2319],{},[1692,9299,1741],{},[902,9301,9302],{"encoding":904},"\u003C 0",[35,9304,8649],{},[35,9306,8629],{},[35,9308,9309],{},[38,9310,9311],{},"zvýšit cenu",[198,9313,9315],{"id":9314},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,9317,9318,9319,9344,9345,9367,9368,9381,9382,9395,9396,1878,9409,6896,9436,9488],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,9320,9322],{"className":9321},[886],[888,9323,9324],{"xmlns":890},[892,9325,9326,9342],{},[895,9327,9328,9330,9332,9334,9336],{},[898,9329,2675],{},[1651,9331,1738],{},[1692,9333,4416],{},[1651,9335,2181],{},[2115,9337,9338,9340],{},[898,9339,1690],{},[1692,9341,1703],{},[902,9343,6766],{"encoding":904},". Reálné cenové rozpětí je ",[883,9346,9348],{"className":9347},[886],[888,9349,9350],{"xmlns":890},[892,9351,9352,9364],{},[895,9353,9354,9356,9358,9360,9362],{},[1651,9355,6631],{"stretchy":1653},[1692,9357,1694],{},[1651,9359,1661],{"separator":1660},[1692,9361,4416],{},[1651,9363,6648],{"stretchy":1653},[902,9365,9366],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,9369,9371],{"className":9370},[886],[888,9372,9373],{"xmlns":890},[892,9374,9375,9379],{},[895,9376,9377],{},[898,9378,1690],{},[902,9380,1690],{"encoding":904}," jako funkci ",[883,9383,9385],{"className":9384},[886],[888,9386,9387],{"xmlns":890},[892,9388,9389,9393],{},[895,9390,9391],{},[898,9392,2675],{},[902,9394,2675],{"encoding":904},"; pro nezáporné ",[883,9397,9399],{"className":9398},[886],[888,9400,9401],{"xmlns":890},[892,9402,9403,9407],{},[895,9404,9405],{},[898,9406,1690],{},[902,9408,1690],{"encoding":904},[883,9410,9412],{"className":9411},[886],[888,9413,9414],{"xmlns":890},[892,9415,9416,9433],{},[895,9417,9418,9420,9422],{},[898,9419,1690],{},[1651,9421,1738],{},[9423,9424,9425],"msqrt",{},[895,9426,9427,9429,9431],{},[1692,9428,4416],{},[1651,9430,2181],{},[898,9432,2675],{},[902,9434,9435],{"encoding":904},"Q = \\sqrt{100 - P}",[883,9437,9439],{"className":9438},[886],[888,9440,9441],{"xmlns":890},[892,9442,9443,9485],{},[895,9444,9445,9461,9463,9465],{},[2938,9446,9447],{"scriptlevel":1741,"displaystyle":1660},[2446,9448,9449,9455],{},[895,9450,9451,9453],{},[898,9452,3542],{"mathvariant":1910},[898,9454,1690],{},[895,9456,9457,9459],{},[898,9458,3542],{"mathvariant":1910},[898,9460,2675],{},[1651,9462,1738],{},[1651,9464,2181],{},[2938,9466,9467],{"scriptlevel":1741,"displaystyle":1660},[2446,9468,9469,9471],{},[1692,9470,1694],{},[895,9472,9473,9475],{},[1692,9474,1703],{},[9423,9476,9477],{},[895,9478,9479,9481,9483],{},[1692,9480,4416],{},[1651,9482,2181],{},[898,9484,2675],{},[902,9486,9487],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,9490,9491],{},[883,9492,9494],{"className":9493},[886],[888,9495,9496],{"xmlns":890},[892,9497,9498,9620],{},[895,9499,9500,9502,9504,9506,9508,9510,9512,9518,9520,9534,9536,9538,9552,9554,9580,9582,9600,9602,9618],{},[898,9501,5561],{},[1651,9503,1654],{"stretchy":1653},[898,9505,2675],{},[1651,9507,1667],{"stretchy":1653},[1651,9509,1738],{},[1651,9511,2181],{},[2446,9513,9514,9516],{},[898,9515,2675],{},[898,9517,1690],{},[1651,9519,4503],{},[2446,9521,9522,9528],{},[895,9523,9524,9526],{},[898,9525,3542],{"mathvariant":1910},[898,9527,1690],{},[895,9529,9530,9532],{},[898,9531,3542],{"mathvariant":1910},[898,9533,2675],{},[1651,9535,1738],{},[1651,9537,2181],{},[2446,9539,9540,9542],{},[898,9541,2675],{},[9423,9543,9544],{},[895,9545,9546,9548,9550],{},[1692,9547,4416],{},[1651,9549,2181],{},[898,9551,2675],{},[1651,9553,4503],{},[895,9555,9556,9558,9560,9578],{},[1651,9557,1654],{"fence":1660},[1651,9559,2181],{},[2446,9561,9562,9564],{},[1692,9563,1694],{},[895,9565,9566,9568],{},[1692,9567,1703],{},[9423,9569,9570],{},[895,9571,9572,9574,9576],{},[1692,9573,4416],{},[1651,9575,2181],{},[898,9577,2675],{},[1651,9579,1667],{"fence":1660},[1651,9581,1738],{},[2446,9583,9584,9586],{},[898,9585,2675],{},[895,9587,9588,9590,9592,9594,9596,9598],{},[1692,9589,1703],{},[1651,9591,1654],{"stretchy":1653},[1692,9593,4416],{},[1651,9595,2181],{},[898,9597,2675],{},[1651,9599,1667],{"stretchy":1653},[1651,9601,1738],{},[2446,9603,9604,9610],{},[895,9605,9606,9608],{},[1692,9607,6316],{},[898,9609,2675],{},[895,9611,9612,9614,9616],{},[1692,9613,4416],{},[1651,9615,2181],{},[898,9617,2675],{},[898,9619,1882],{"mathvariant":1910},[902,9621,9622],{"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}.",[724,9624,9625,9626,1793],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,9627,9629],{"className":9628},[886],[888,9630,9631],{"xmlns":890},[892,9632,9633,9657],{},[895,9634,9635,9653,9655],{},[2938,9636,9637],{"scriptlevel":1741,"displaystyle":1660},[2446,9638,9639,9645],{},[895,9640,9641,9643],{},[1692,9642,6316],{},[898,9644,2675],{},[895,9646,9647,9649,9651],{},[1692,9648,4416],{},[1651,9650,2181],{},[898,9652,2675],{},[1651,9654,1738],{},[1692,9656,1694],{},[902,9658,9659],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,9661,9662],{},[883,9663,9665],{"className":9664},[886],[888,9666,9667],{"xmlns":890},[892,9668,9669,9701],{},[895,9670,9671,9677,9679,9686,9688,9691,9699],{},[2115,9672,9673,9675],{},[898,9674,2675],{},[1651,9676,2668],{},[1651,9678,1738],{},[2446,9680,9681,9684],{},[1692,9682,9683],{},"200",[1692,9685,3521],{},[1651,9687,7207],{},[1692,9689,9690],{},"66,",[9692,9693,9694,9696],"mover",{"accent":1660},[1692,9695,3581],{},[1651,9697,9698],{"stretchy":1660},"‾",[898,9700,1882],{"mathvariant":1910},[902,9702,9703],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,9705,9706],{},"S využitím vlastnosti (4.8):",[120,9708,9709,9755,9797],{},[123,9710,9711,9712,9747,9748,9750,9751,9754],{},"Při cenách ",[883,9713,9715],{"className":9714},[886],[888,9716,9717],{"xmlns":890},[892,9718,9719,9744],{},[895,9720,9721,9723,9725,9727,9729,9732,9734,9736,9742],{},[898,9722,2675],{},[1651,9724,7813],{},[1651,9726,6631],{"stretchy":1653},[1692,9728,1694],{},[1651,9730,9731],{"separator":1660},";",[1843,9733,1845],{},[1692,9735,9690],{},[9692,9737,9738,9740],{"accent":1660},[1692,9739,3581],{},[1651,9741,9698],{"stretchy":1660},[1651,9743,1667],{"stretchy":1653},[902,9745,9746],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,9749,5387],{}," — dle ",[614,9752,9753],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,9756,9711,9757,9747,9791,9750,9793,9796],{},[883,9758,9760],{"className":9759},[886],[888,9761,9762],{"xmlns":890},[892,9763,9764,9788],{},[895,9765,9766,9768,9770,9772,9774,9780,9782,9784,9786],{},[898,9767,2675],{},[1651,9769,7813],{},[1651,9771,1654],{"stretchy":1653},[1692,9773,9690],{},[9692,9775,9776,9778],{"accent":1660},[1692,9777,3581],{},[1651,9779,9698],{"stretchy":1660},[1651,9781,9731],{"separator":1660},[1843,9783,1845],{},[1692,9785,4416],{},[1651,9787,6648],{"stretchy":1653},[902,9789,9790],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,9792,5383],{},[614,9794,9795],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,9798,9799,9800,9803,9804,9832,9833,9836],{},"Dle ",[614,9801,9802],{},"Pravidla 3"," je při ceně ",[883,9805,9807],{"className":9806},[886],[888,9808,9809],{"xmlns":890},[892,9810,9811,9829],{},[895,9812,9813,9819,9821,9823],{},[2115,9814,9815,9817],{},[898,9816,2675],{},[1651,9818,2668],{},[1651,9820,1738],{},[1692,9822,9690],{},[9692,9824,9825,9827],{"accent":1660},[1692,9826,3581],{},[1651,9828,9698],{"stretchy":1660},[902,9830,9831],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,9834,9835],{},"maxima celkového příjmu"," ve výši",[724,9838,9839],{},[883,9840,9842],{"className":9841},[886],[888,9843,9844],{"xmlns":890},[892,9845,9846,9924],{},[895,9847,9848,9850,9852,9854,9860,9862,9864,9870,9872,9886,9888,9894,9896,9904,9906,9919,9921],{},[898,9849,4104],{},[898,9851,2998],{},[1651,9853,1654],{"stretchy":1653},[2115,9855,9856,9858],{},[898,9857,2675],{},[1651,9859,2668],{},[1651,9861,1667],{"stretchy":1653},[1651,9863,1738],{},[2115,9865,9866,9868],{},[898,9867,2675],{},[1651,9869,2668],{},[1651,9871,4503],{},[9423,9873,9874],{},[895,9875,9876,9878,9880],{},[1692,9877,4416],{},[1651,9879,2181],{},[2115,9881,9882,9884],{},[898,9883,2675],{},[1651,9885,2668],{},[1651,9887,1738],{},[2446,9889,9890,9892],{},[1692,9891,9683],{},[1692,9893,3521],{},[1651,9895,4503],{},[9423,9897,9898],{},[2446,9899,9900,9902],{},[1692,9901,4416],{},[1692,9903,3521],{},[1651,9905,1738],{},[2446,9907,9908,9911],{},[1692,9909,9910],{},"2000",[895,9912,9913,9915],{},[1692,9914,3521],{},[9423,9916,9917],{},[1692,9918,3521],{},[1651,9920,7207],{},[1692,9922,9923],{},"384,9.",[902,9925,9926],{"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.",[724,9928,9929,9930,1882],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,9931,9933],{"className":9932},[886],[888,9934,9935],{"xmlns":890},[892,9936,9937,9943],{},[895,9938,9939,9941],{},[898,9940,4104],{},[898,9942,2998],{},[902,9944,5404],{"encoding":904},[115,9946,9948],{"id":9947},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,9950,9951,9952,9955],{},"Analogicky se definuje ",[38,9953,9954],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,9957,9958],{},[883,9959,9961],{"className":9960,"title":5509,"style":5510},[5508],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,9963,1863,9964,9988,9989,10021],{},[883,9965,9967],{"className":9966},[886],[888,9968,9969],{"xmlns":890},[892,9970,9971,9985],{},[895,9972,9973,9975,9977,9979,9981,9983],{},[898,9974,1690],{},[1651,9976,1738],{},[898,9978,3004],{},[1651,9980,1654],{"stretchy":1653},[898,9982,2675],{},[1651,9984,1667],{"stretchy":1653},[902,9986,9987],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,9990,9992],{"className":9991},[886],[888,9993,9994],{"xmlns":890},[892,9995,9996,10018],{},[895,9997,9998,10014,10016],{},[2938,9999,10000],{"scriptlevel":1741,"displaystyle":1660},[2446,10001,10002,10008],{},[895,10003,10004,10006],{},[898,10005,3542],{"mathvariant":1910},[898,10007,1690],{},[895,10009,10010,10012],{},[898,10011,3542],{"mathvariant":1910},[898,10013,2675],{},[1651,10015,2390],{},[1692,10017,1741],{},[902,10019,10020],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,10023,10024],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[5179,10026,10027],{},[724,10028,10029,10030],{},"S rostoucí cenou elasticita nabídky roste. ",[883,10031,10033],{"className":10032},[886],[888,10034,10035],{"xmlns":890},[892,10036,10037,10046],{},[895,10038,10039,10041,10044],{},[1651,10040,1654],{"stretchy":1653},[1692,10042,10043],{},"4.14",[1651,10045,1667],{"stretchy":1653},[902,10047,10048],{"encoding":904},"(4.14)",[724,10050,10051],{},"Pro nominální změny platí",[724,10053,10054],{},[883,10055,10057],{"className":10056,"title":5509,"style":5510},[5508],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,10059,10060],{},"a pro procentní změny",[724,10062,10063],{},[883,10064,10066],{"className":10065,"title":5509,"style":5510},[5508],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,10068,10069],{},"(bez znaménka minus).",[198,10071,10073],{"id":10072},"příklad-47","Příklad 4.7",[724,10075,10076,10077,1793],{},"Nabídka ",[883,10078,10080],{"className":10079},[886],[888,10081,10082],{"xmlns":890},[892,10083,10084,10109],{},[895,10085,10086,10088,10090,10092,10098,10100,10102,10104,10106],{},[898,10087,1690],{},[1651,10089,1738],{},[1692,10091,4122],{},[2115,10093,10094,10096],{},[898,10095,2675],{},[1692,10097,1703],{},[1651,10099,1839],{},[1692,10101,3574],{},[898,10103,2675],{},[1651,10105,1839],{},[1692,10107,10108],{},"150",[902,10110,10111],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,10113,10114],{},[883,10115,10117],{"className":10116},[886],[888,10118,10119],{"xmlns":890},[892,10120,10121,10167],{},[895,10122,10123,10125,10127,10151,10153,10155,10157,10159,10161,10163,10165],{},[898,10124,5561],{},[1651,10126,1738],{},[2446,10128,10129,10131],{},[898,10130,2675],{},[895,10132,10133,10135,10141,10143,10145,10147,10149],{},[1692,10134,4122],{},[2115,10136,10137,10139],{},[898,10138,2675],{},[1692,10140,1703],{},[1651,10142,1839],{},[1692,10144,3574],{},[898,10146,2675],{},[1651,10148,1839],{},[1692,10150,10108],{},[1843,10152,1845],{},[1651,10154,1654],{"stretchy":1653},[1692,10156,4166],{},[898,10158,2675],{},[1651,10160,1839],{},[1692,10162,3574],{},[1651,10164,1667],{"stretchy":1653},[898,10166,1882],{"mathvariant":1910},[902,10168,10169],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,10171,6424,10172,1343,10202,1343,10229,10265,10266,10291,10292,10310,10311,1882],{},[883,10173,10175],{"className":10174},[886],[888,10176,10177],{"xmlns":890},[892,10178,10179,10199],{},[895,10180,10181,10183,10185,10187,10189,10191],{},[898,10182,5561],{},[1651,10184,1654],{"stretchy":1653},[1692,10186,4190],{},[1651,10188,1667],{"stretchy":1653},[1651,10190,1738],{},[2938,10192,10193],{"scriptlevel":1741,"displaystyle":1653},[2446,10194,10195,10197],{},[1692,10196,1694],{},[1692,10198,3521],{},[902,10200,10201],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,10203,10205],{"className":10204},[886],[888,10206,10207],{"xmlns":890},[892,10208,10209,10226],{},[895,10210,10211,10213,10215,10220,10222,10224],{},[898,10212,5561],{},[1651,10214,1654],{"stretchy":1653},[9423,10216,10217],{},[1692,10218,10219],{},"1500",[1651,10221,1667],{"stretchy":1653},[1651,10223,1738],{},[1692,10225,1694],{},[902,10227,10228],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,10230,10232],{"className":10231},[886],[888,10233,10234],{"xmlns":890},[892,10235,10236,10262],{},[895,10237,10238,10240,10242,10244,10246,10248,10257,10259],{},[898,10239,5561],{},[1651,10241,1654],{"stretchy":1653},[1692,10243,4416],{},[1651,10245,1667],{"stretchy":1653},[1651,10247,1738],{},[2938,10249,10250],{"scriptlevel":1741,"displaystyle":1653},[2446,10251,10252,10254],{},[1692,10253,4446],{},[1692,10255,10256],{},"33",[1651,10258,7207],{},[1692,10260,10261],{},"1,515",[902,10263,10264],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,10267,10269],{"className":10268},[886],[888,10270,10271],{"xmlns":890},[892,10272,10273,10288],{},[895,10274,10275,10277,10279,10283,10285],{},[898,10276,2675],{},[1651,10278,2390],{},[9423,10280,10281],{},[1692,10282,10219],{},[1651,10284,4060],{},[1692,10286,10287],{},"38,7",[902,10289,10290],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,10293,10295],{"className":10294},[886],[888,10296,10297],{"xmlns":890},[892,10298,10299,10307],{},[895,10300,10301,10303,10305],{},[898,10302,2675],{},[1651,10304,2319],{},[1692,10306,10287],{},[902,10308,10309],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,10312,10314],{"className":10313},[886],[888,10315,10316],{"xmlns":890},[892,10317,10318,10356],{},[895,10319,10320,10322,10324,10326,10328,10336,10338,10341,10343,10346,10352,10354],{},[898,10321,4216],{"mathvariant":1910},[898,10323,1690],{},[898,10325,7232],{"mathvariant":1910},[1651,10327,4060],{},[2938,10329,10330],{"scriptlevel":1741,"displaystyle":1653},[2446,10331,10332,10334],{},[1692,10333,1694],{},[1692,10335,3521],{},[1651,10337,4503],{},[1692,10339,10340],{},"20",[1651,10342,1738],{},[1692,10344,10345],{},"6,",[9692,10347,10348,10350],{"accent":1660},[1692,10349,3581],{},[1651,10351,9698],{"stretchy":1660},[1843,10353,1845],{},[898,10355,7232],{"mathvariant":1910},[902,10357,10358],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,10360,10362],{"id":10361},"vícefaktorový-model","Vícefaktorový model",[724,10364,10365,10366,10379,10380,3246,10383,10396,10397,3246,10400,10418,10419,3246,10422,1793],{},"Předpokládejme, že poptávané množství ",[883,10367,10369],{"className":10368},[886],[888,10370,10371],{"xmlns":890},[892,10372,10373,10377],{},[895,10374,10375],{},[898,10376,1690],{},[902,10378,1690],{"encoding":904}," závisí na ",[38,10381,10382],{},"ceně základního zboží",[883,10384,10386],{"className":10385},[886],[888,10387,10388],{"xmlns":890},[892,10389,10390,10394],{},[895,10391,10392],{},[898,10393,2675],{},[902,10395,2675],{"encoding":904},", na ",[38,10398,10399],{},"ceně alternativního zboží",[883,10401,10403],{"className":10402},[886],[888,10404,10405],{"xmlns":890},[892,10406,10407,10415],{},[895,10408,10409],{},[1686,10410,10411,10413],{},[898,10412,2675],{},[898,10414,5564],{},[902,10416,10417],{"encoding":904},"P_A"," a na ",[38,10420,10421],{},"důchodu",[883,10423,10425],{"className":10424},[886],[888,10426,10427],{"xmlns":890},[892,10428,10429,10433],{},[895,10430,10431],{},[898,10432,2665],{},[902,10434,2665],{"encoding":904},[724,10436,10437],{},[883,10438,10440],{"className":10439,"title":5509,"style":5510},[5508],"Q = D(P, P_A, Y). \\tag{4.17}",[724,10442,10443,10444,10447],{},"V analogii jednofaktorového modelu pracujeme s ",[38,10445,10446],{},"parciálními derivacemi"," funkce poptávky.",[198,10449,10451],{"id":10450},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,10453,10454],{},[883,10455,10457],{"className":10456,"title":5509,"style":5510},[5508],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,10459,1863,10460,10480,10481,10494,10495,4254,10517,3246,10520,10566,10567,10580,10581,10598],{},[883,10461,10463],{"className":10462},[886],[888,10464,10465],{"xmlns":890},[892,10466,10467,10477],{},[895,10468,10469],{},[1902,10470,10471,10473,10475],{},[898,10472,1690],{},[898,10474,2675],{},[1651,10476,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,10478,10479],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,10482,10484],{"className":10483},[886],[888,10485,10486],{"xmlns":890},[892,10487,10488,10492],{},[895,10489,10490],{},[898,10491,2675],{},[902,10493,2675],{"encoding":904},". Vždy ",[883,10496,10498],{"className":10497},[886],[888,10499,10500],{"xmlns":890},[892,10501,10502,10514],{},[895,10503,10504,10510,10512],{},[1686,10505,10506,10508],{},[898,10507,5561],{},[898,10509,2675],{},[1651,10511,5792],{},[1692,10513,1741],{},[902,10515,10516],{"encoding":904},"E_P \\ge 0",[614,10518,10519],{},"Interpretace:",[883,10521,10523],{"className":10522},[886],[888,10524,10525],{"xmlns":890},[892,10526,10527,10563],{},[895,10528,10529,10535,10537,10543,10545,10553,10555,10561],{},[1686,10530,10531,10533],{},[898,10532,5561],{},[898,10534,2675],{},[1651,10536,1654],{"stretchy":1653},[2115,10538,10539,10541],{},[898,10540,2675],{},[1651,10542,2668],{},[1651,10544,1661],{"separator":1660},[1902,10546,10547,10549,10551],{},[898,10548,2675],{},[898,10550,5564],{},[1651,10552,2668],{},[1651,10554,1661],{"separator":1660},[2115,10556,10557,10559],{},[898,10558,2665],{},[1651,10560,2668],{},[1651,10562,1667],{"stretchy":1653},[902,10564,10565],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,10568,10570],{"className":10569},[886],[888,10571,10572],{"xmlns":890},[892,10573,10574,10578],{},[895,10575,10576],{},[898,10577,1690],{},[902,10579,1690],{"encoding":904}," při 1% změně ",[883,10582,10584],{"className":10583},[886],[888,10585,10586],{"xmlns":890},[892,10587,10588,10596],{},[895,10589,10590],{},[2115,10591,10592,10594],{},[898,10593,2675],{},[1651,10595,2668],{},[902,10597,5711],{"encoding":904},", ceteris paribus.",[198,10600,10602],{"id":10601},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,10604,10605],{},[883,10606,10608],{"className":10607,"title":5509,"style":5510},[5508],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,10610,10611,10566,10613,10626,10627,10644],{},[614,10612,10519],{},[883,10614,10616],{"className":10615},[886],[888,10617,10618],{"xmlns":890},[892,10619,10620,10624],{},[895,10621,10622],{},[898,10623,1690],{},[902,10625,1690],{"encoding":904}," základního zboží při 1% změně ceny ",[883,10628,10630],{"className":10629},[886],[888,10631,10632],{"xmlns":890},[892,10633,10634,10642],{},[895,10635,10636],{},[1686,10637,10638,10640],{},[898,10639,2675],{},[898,10641,5564],{},[902,10643,10417],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,10646,10647],{},[38,10648,10649],{},"Znaménko závisí na povaze alternativního zboží:",[120,10651,10652,10740],{},[123,10653,10654,10655,10658,10659,10676,10677,3246,10690,1882],{},"Je-li alternativní zboží ",[38,10656,10657],{},"komplement",", růst ",[883,10660,10662],{"className":10661},[886],[888,10663,10664],{"xmlns":890},[892,10665,10666,10674],{},[895,10667,10668],{},[1686,10669,10670,10672],{},[898,10671,2675],{},[898,10673,5564],{},[902,10675,10417],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,10678,10680],{"className":10679},[886],[888,10681,10682],{"xmlns":890},[892,10683,10684,10688],{},[895,10685,10686],{},[898,10687,1690],{},[902,10689,1690],{"encoding":904},[883,10691,10693],{"className":10692},[886],[888,10694,10695],{"xmlns":890},[892,10696,10697,10737],{},[895,10698,10699,10701,10703,10715,10717,10719,10721,10723,10733,10735],{},[1651,10700,5298],{},[1843,10702,5295],{},[1902,10704,10705,10707,10713],{},[898,10706,1690],{},[1686,10708,10709,10711],{},[898,10710,2675],{},[898,10712,5564],{},[1651,10714,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,10716,2319],{},[1692,10718,1741],{},[1651,10720,1661],{"separator":1660},[1843,10722,5295],{},[1686,10724,10725,10727],{},[898,10726,5561],{},[1686,10728,10729,10731],{},[898,10730,2675],{},[898,10732,5564],{},[1651,10734,2319],{},[1692,10736,1741],{},[902,10738,10739],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,10741,10654,10742,10658,10745,10762,10763,10776,10777,1882],{},[38,10743,10744],{},"substitut",[883,10746,10748],{"className":10747},[886],[888,10749,10750],{"xmlns":890},[892,10751,10752,10760],{},[895,10753,10754],{},[1686,10755,10756,10758],{},[898,10757,2675],{},[898,10759,5564],{},[902,10761,10417],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,10764,10766],{"className":10765},[886],[888,10767,10768],{"xmlns":890},[892,10769,10770,10774],{},[895,10771,10772],{},[898,10773,1690],{},[902,10775,1690],{"encoding":904}," roste ",[883,10778,10780],{"className":10779},[886],[888,10781,10782],{"xmlns":890},[892,10783,10784,10824],{},[895,10785,10786,10788,10790,10802,10804,10806,10808,10810,10820,10822],{},[1651,10787,5298],{},[1843,10789,5295],{},[1902,10791,10792,10794,10800],{},[898,10793,1690],{},[1686,10795,10796,10798],{},[898,10797,2675],{},[898,10799,5564],{},[1651,10801,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,10803,2390],{},[1692,10805,1741],{},[1651,10807,1661],{"separator":1660},[1843,10809,5295],{},[1686,10811,10812,10814],{},[898,10813,5561],{},[1686,10815,10816,10818],{},[898,10817,2675],{},[898,10819,5564],{},[1651,10821,2390],{},[1692,10823,1741],{},[902,10825,10826],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,10828,10831],{"className":10829,"title":10830,"style":5510},[5508],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":10833},[10834,10838,10839,10847,10848,10852,10855],{"id":5203,"depth":642,"text":5204,"children":10835},[10836,10837],{"id":5233,"depth":649,"text":5234},{"id":5412,"depth":649,"text":5413},{"id":5447,"depth":642,"text":5448},{"id":5473,"depth":642,"text":5474,"children":10840},[10841,10842,10843,10844,10846],{"id":6166,"depth":649,"text":6167},{"id":6256,"depth":649,"text":6257},{"id":6592,"depth":649,"text":6593},{"id":6674,"depth":649,"text":10845},"Výpočet, je-li dáno PP jako funkce QQ",{"id":6935,"depth":649,"text":6936},{"id":7260,"depth":642,"text":7261},{"id":7856,"depth":642,"text":7857,"children":10849},[10850,10851],{"id":8485,"depth":649,"text":8486},{"id":9314,"depth":649,"text":9315},{"id":9947,"depth":642,"text":9948,"children":10853},[10854],{"id":10072,"depth":649,"text":10073},{"id":10361,"depth":642,"text":10362,"children":10856},[10857,10858],{"id":10450,"depth":649,"text":10451},{"id":10601,"depth":649,"text":10602},"2026-04-22",{},"\u002Ftopics\u002Felasticita",{"title":5172,"description":641},[1138,1136],"topics\u002Felasticita",[1128,5210,10866,10867,10868,10869],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":10872,"title":10873,"body":10874,"course":1128,"courses":659,"created":1129,"description":12410,"extension":661,"meta":12411,"navigation":664,"path":12412,"seo":12413,"sources":12414,"stem":12415,"tags":12416,"type":3302,"updated":677,"__hash__":12421},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":10875,"toc":12395},[10876,10879,10953,10960,10964,11028,11115,11119,11145,11212,11267,11271,11298,11391,11393,11425,11596,11600,11670,11718,11722,11783,11889,11904,11908,11910,11938,12003,12005,12011,12099,12124,12322,12326,12360,12362],[12,10877,10873],{"id":10878},"kalkul-funkcí-více-proměnných",[724,10880,10881,10882,10885,10886,1343,10915,1882],{},"Většina ekonomických veličin závisí na ",[38,10883,10884],{},"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 ",[883,10887,10889],{"className":10888},[886],[888,10890,10891],{"xmlns":890},[892,10892,10893,10912],{},[895,10894,10895,10898,10900,10902,10904,10906,10908,10910],{},[898,10896,10897],{},"z",[1651,10899,1738],{},[898,10901,1649],{},[1651,10903,1654],{"stretchy":1653},[898,10905,1657],{},[1651,10907,1661],{"separator":1660},[898,10909,1664],{},[1651,10911,1667],{"stretchy":1653},[902,10913,10914],{"encoding":904},"z = f(x, y)",[883,10916,10918],{"className":10917},[886],[888,10919,10920],{"xmlns":890},[892,10921,10922,10950],{},[895,10923,10924,10927,10929,10931,10933,10935,10937,10939,10941,10943,10945,10947],{},[898,10925,10926],{},"w",[1651,10928,1738],{},[898,10930,1649],{},[1651,10932,1654],{"stretchy":1653},[898,10934,1657],{},[1651,10936,1661],{"separator":1660},[898,10938,1664],{},[1651,10940,1661],{"separator":1660},[898,10942,10897],{},[1651,10944,1667],{"stretchy":1653},[1651,10946,1661],{"separator":1660},[1651,10948,10949],{},"…",[902,10951,10952],{"encoding":904},"w = f(x, y, z), \\ldots",[724,10954,10955],{},[1756,10956],{"alt":10957,"className":10958,"src":10959},"imek-funkce-2d-vrstevnice",[210,1760],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,10961,10963],{"id":10962},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,10965,10966,10967,10994,10995,11023,11024,11027],{},"Pro ",[883,10968,10970],{"className":10969},[886],[888,10971,10972],{"xmlns":890},[892,10973,10974,10992],{},[895,10975,10976,10978,10980,10982,10984,10986,10988,10990],{},[898,10977,10897],{},[1651,10979,1738],{},[898,10981,1649],{},[1651,10983,1654],{"stretchy":1653},[898,10985,1657],{},[1651,10987,1661],{"separator":1660},[898,10989,1664],{},[1651,10991,1667],{"stretchy":1653},[902,10993,10914],{"encoding":904}," se křivkou s předpisem ",[883,10996,10998],{"className":10997},[886],[888,10999,11000],{"xmlns":890},[892,11001,11002,11020],{},[895,11003,11004,11006,11008,11010,11012,11014,11016,11018],{},[898,11005,1649],{},[1651,11007,1654],{"stretchy":1653},[898,11009,1657],{},[1651,11011,1661],{"separator":1660},[898,11013,1664],{},[1651,11015,1667],{"stretchy":1653},[1651,11017,1738],{},[898,11019,3490],{},[902,11021,11022],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,11025,11026],{},"vrstevnice"," funkce. V ekonomii:",[120,11029,11030,11076],{},[123,11031,11032,11035,11036,11072,11073,1882],{},[38,11033,11034],{},"Indiferenční křivky"," užitečnosti ",[883,11037,11039],{"className":11038},[886],[888,11040,11041],{"xmlns":890},[892,11042,11043,11069],{},[895,11044,11045,11047,11049,11055,11057,11063,11065,11067],{},[898,11046,900],{},[1651,11048,1654],{"stretchy":1653},[1686,11050,11051,11053],{},[898,11052,1690],{},[1692,11054,1694],{},[1651,11056,1661],{"separator":1660},[1686,11058,11059,11061],{},[898,11060,1690],{},[1692,11062,1703],{},[1651,11064,1667],{"stretchy":1653},[1651,11066,1738],{},[898,11068,3490],{},[902,11070,11071],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,11074,1773],{"className":11075,"dataFsResolvedFilePath":878,"href":879},[210],[123,11077,11078,11081,11082,11072,11111,1882],{},[38,11079,11080],{},"Izokvanty"," produkce ",[883,11083,11085],{"className":11084},[886],[888,11086,11087],{"xmlns":890},[892,11088,11089,11108],{},[895,11090,11091,11093,11095,11097,11099,11102,11104,11106],{},[898,11092,1690],{},[1651,11094,1654],{"stretchy":1653},[898,11096,1807],{},[1651,11098,1661],{"separator":1660},[898,11100,11101],{},"K",[1651,11103,1667],{"stretchy":1653},[1651,11105,1738],{},[898,11107,3490],{},[902,11109,11110],{"encoding":904},"Q(L, K) = c",[207,11112,11114],{"className":11113,"dataFsResolvedFilePath":857,"href":858},[210],"produkce",[115,11116,11118],{"id":11117},"parciální-derivace","Parciální derivace",[724,11120,10966,11121,11144],{},[883,11122,11124],{"className":11123},[886],[888,11125,11126],{"xmlns":890},[892,11127,11128,11142],{},[895,11129,11130,11132,11134,11136,11138,11140],{},[898,11131,1649],{},[1651,11133,1654],{"stretchy":1653},[898,11135,1657],{},[1651,11137,1661],{"separator":1660},[898,11139,1664],{},[1651,11141,1667],{"stretchy":1653},[902,11143,1670],{"encoding":904}," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,11146,11147],{},[883,11148,11150],{"className":11149},[886],[888,11151,11152],{"xmlns":890},[892,11153,11154,11209],{},[895,11155,11156,11164,11166,11181,11183,11185,11193,11195],{},[1902,11157,11158,11160,11162],{},[898,11159,1649],{},[898,11161,1657],{},[1651,11163,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,11165,1738],{},[2446,11167,11168,11175],{},[895,11169,11170,11173],{},[898,11171,11172],{"mathvariant":1910},"∂",[898,11174,1649],{},[895,11176,11177,11179],{},[898,11178,11172],{"mathvariant":1910},[898,11180,1657],{},[1651,11182,1661],{"separator":1660},[7185,11184],{"width":7187},[1902,11186,11187,11189,11191],{},[898,11188,1649],{},[898,11190,1664],{},[1651,11192,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,11194,1738],{},[2446,11196,11197,11203],{},[895,11198,11199,11201],{},[898,11200,11172],{"mathvariant":1910},[898,11202,1649],{},[895,11204,11205,11207],{},[898,11206,11172],{"mathvariant":1910},[898,11208,1664],{},[902,11210,11211],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,11213,11214,11215,1882],{},"Hodnoty v bodě: ",[883,11216,11218],{"className":11217},[886],[888,11219,11220],{"xmlns":890},[892,11221,11222,11264],{},[895,11223,11224,11232,11234,11236,11238,11240,11242,11244,11246,11254,11256,11258,11260,11262],{},[1902,11225,11226,11228,11230],{},[898,11227,1649],{},[898,11229,1657],{},[1651,11231,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,11233,1654],{"stretchy":1653},[898,11235,207],{},[1651,11237,1661],{"separator":1660},[898,11239,2268],{},[1651,11241,1667],{"stretchy":1653},[1651,11243,1661],{"separator":1660},[1843,11245,3631],{},[1902,11247,11248,11250,11252],{},[898,11249,1649],{},[898,11251,1664],{},[1651,11253,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,11255,1654],{"stretchy":1653},[898,11257,207],{},[1651,11259,1661],{"separator":1660},[898,11261,2268],{},[1651,11263,1667],{"stretchy":1653},[902,11265,11266],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,11268,11270],{"id":11269},"ekonomické-značení","Ekonomické značení",[724,11272,11273,11274,1793],{},"Pro produkční funkci ",[883,11275,11277],{"className":11276},[886],[888,11278,11279],{"xmlns":890},[892,11280,11281,11295],{},[895,11282,11283,11285,11287,11289,11291,11293],{},[898,11284,1690],{},[1651,11286,1654],{"stretchy":1653},[898,11288,1807],{},[1651,11290,1661],{"separator":1660},[898,11292,11101],{},[1651,11294,1667],{"stretchy":1653},[902,11296,11297],{"encoding":904},"Q(L, K)",[120,11299,11300,11346],{},[123,11301,11302,3805,11322,11325,11326,1667],{},[883,11303,11305],{"className":11304},[886],[888,11306,11307],{"xmlns":890},[892,11308,11309,11319],{},[895,11310,11311],{},[1902,11312,11313,11315,11317],{},[898,11314,1690],{},[898,11316,1807],{},[1651,11318,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,11320,11321],{"encoding":904},"Q'_L",[38,11323,11324],{},"mezní produkt práce"," (",[883,11327,11329],{"className":11328},[886],[888,11330,11331],{"xmlns":890},[892,11332,11333,11343],{},[895,11334,11335,11337],{},[898,11336,2995],{},[1686,11338,11339,11341],{},[898,11340,2675],{},[898,11342,1807],{},[902,11344,11345],{"encoding":904},"MP_L",[123,11347,11348,3805,11368,11325,11371,1667],{},[883,11349,11351],{"className":11350},[886],[888,11352,11353],{"xmlns":890},[892,11354,11355,11365],{},[895,11356,11357],{},[1902,11358,11359,11361,11363],{},[898,11360,1690],{},[898,11362,11101],{},[1651,11364,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,11366,11367],{"encoding":904},"Q'_K",[38,11369,11370],{},"mezní produkt kapitálu",[883,11372,11374],{"className":11373},[886],[888,11375,11376],{"xmlns":890},[892,11377,11378,11388],{},[895,11379,11380,11382],{},[898,11381,2995],{},[1686,11383,11384,11386],{},[898,11385,2675],{},[898,11387,11101],{},[902,11389,11390],{"encoding":904},"MP_K",[198,11392,3899],{"id":3898},[724,11394,11395,1793],{},[883,11396,11398],{"className":11397},[886],[888,11399,11400],{"xmlns":890},[892,11401,11402,11422],{},[895,11403,11404,11412,11414,11416,11418,11420],{},[1902,11405,11406,11408,11410],{},[898,11407,1649],{},[898,11409,1657],{},[1651,11411,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,11413,1654],{"stretchy":1653},[898,11415,207],{},[1651,11417,1661],{"separator":1660},[898,11419,2268],{},[1651,11421,1667],{"stretchy":1653},[902,11423,11424],{"encoding":904},"f'_x(a, b)",[120,11426,11427,11485],{},[123,11428,11429,11430,11443,11444,11457,11458,11484],{},"rychlost změny ",[883,11431,11433],{"className":11432},[886],[888,11434,11435],{"xmlns":890},[892,11436,11437,11441],{},[895,11438,11439],{},[898,11440,1649],{},[902,11442,1649],{"encoding":904}," vůči ",[883,11445,11447],{"className":11446},[886],[888,11448,11449],{"xmlns":890},[892,11450,11451,11455],{},[895,11452,11453],{},[898,11454,1657],{},[902,11456,1657],{"encoding":904}," při ",[883,11459,11461],{"className":11460},[886],[888,11462,11463],{"xmlns":890},[892,11464,11465,11481],{},[895,11466,11467,11469,11471,11473,11475,11477,11479],{},[898,11468,1657],{},[1651,11470,1738],{},[898,11472,207],{},[1651,11474,1661],{"separator":1660},[898,11476,1664],{},[1651,11478,1738],{},[898,11480,2268],{},[902,11482,11483],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,11486,11487,11488,3988,11501,11514,11515,11533,11534,1882],{},"přibližná změna ",[883,11489,11491],{"className":11490},[886],[888,11492,11493],{"xmlns":890},[892,11494,11495,11499],{},[895,11496,11497],{},[898,11498,1649],{},[902,11500,1649],{"encoding":904},[883,11502,11504],{"className":11503},[886],[888,11505,11506],{"xmlns":890},[892,11507,11508,11512],{},[895,11509,11510],{},[898,11511,1657],{},[902,11513,1657],{"encoding":904}," o 1 (a pevném ",[883,11516,11518],{"className":11517},[886],[888,11519,11520],{"xmlns":890},[892,11521,11522,11530],{},[895,11523,11524,11526,11528],{},[898,11525,1664],{},[1651,11527,1738],{},[898,11529,2268],{},[902,11531,11532],{"encoding":904},"y = b","): ",[883,11535,11537],{"className":11536},[886],[888,11538,11539],{"xmlns":890},[892,11540,11541,11593],{},[895,11542,11543,11545,11547,11549,11551,11553,11555,11557,11559,11561,11563,11565,11567,11569,11571,11573,11575,11583,11585,11587,11589,11591],{},[898,11544,1649],{},[1651,11546,1654],{"stretchy":1653},[898,11548,207],{},[1651,11550,1839],{},[1692,11552,1694],{},[1651,11554,1661],{"separator":1660},[898,11556,2268],{},[1651,11558,1667],{"stretchy":1653},[1651,11560,4060],{},[898,11562,1649],{},[1651,11564,1654],{"stretchy":1653},[898,11566,207],{},[1651,11568,1661],{"separator":1660},[898,11570,2268],{},[1651,11572,1667],{"stretchy":1653},[1651,11574,1839],{},[1902,11576,11577,11579,11581],{},[898,11578,1649],{},[898,11580,1657],{},[1651,11582,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,11584,1654],{"stretchy":1653},[898,11586,207],{},[1651,11588,1661],{"separator":1660},[898,11590,2268],{},[1651,11592,1667],{"stretchy":1653},[902,11594,11595],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,11597,11599],{"id":11598},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,11601,11602],{},[883,11603,11605],{"className":11604},[886],[888,11606,11607],{"xmlns":890},[892,11608,11609,11667],{},[895,11610,11611,11613,11615,11617,11625,11627,11629,11631,11633,11635,11637,11639,11641,11643,11651,11653,11655,11657,11659,11661,11663,11665],{},[898,11612,3542],{},[898,11614,1649],{},[1651,11616,1738],{},[1902,11618,11619,11621,11623],{},[898,11620,1649],{},[898,11622,1657],{},[1651,11624,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,11626,1654],{"stretchy":1653},[898,11628,1657],{},[1651,11630,1661],{"separator":1660},[898,11632,1664],{},[1651,11634,1667],{"stretchy":1653},[1843,11636,1845],{},[898,11638,3542],{},[898,11640,1657],{},[1651,11642,1839],{},[1902,11644,11645,11647,11649],{},[898,11646,1649],{},[898,11648,1664],{},[1651,11650,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,11652,1654],{"stretchy":1653},[898,11654,1657],{},[1651,11656,1661],{"separator":1660},[898,11658,1664],{},[1651,11660,1667],{"stretchy":1653},[1843,11662,1845],{},[898,11664,3542],{},[898,11666,1664],{},[902,11668,11669],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,11671,4323,11672,11694,11695,11717],{},[883,11673,11675],{"className":11674},[886],[888,11676,11677],{"xmlns":890},[892,11678,11679,11691],{},[895,11680,11681,11683,11685,11687,11689],{},[898,11682,3542],{},[898,11684,1657],{},[1651,11686,1661],{"separator":1660},[898,11688,3542],{},[898,11690,1664],{},[902,11692,11693],{"encoding":904},"dx, dy"," platí ",[883,11696,11698],{"className":11697},[886],[888,11699,11700],{"xmlns":890},[892,11701,11702,11714],{},[895,11703,11704,11706,11708,11710,11712],{},[898,11705,4216],{"mathvariant":1910},[898,11707,1649],{},[1651,11709,4060],{},[898,11711,3542],{},[898,11713,1649],{},[902,11715,11716],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,11719,11721],{"id":11720},"implicitní-funkce","Implicitní funkce",[724,11723,11724,11725,11754,11755,11768,11769,11782],{},"Je-li vztah dán rovnicí ",[883,11726,11728],{"className":11727},[886],[888,11729,11730],{"xmlns":890},[892,11731,11732,11751],{},[895,11733,11734,11737,11739,11741,11743,11745,11747,11749],{},[898,11735,11736],{},"F",[1651,11738,1654],{"stretchy":1653},[898,11740,1657],{},[1651,11742,1661],{"separator":1660},[898,11744,1664],{},[1651,11746,1667],{"stretchy":1653},[1651,11748,1738],{},[1692,11750,1741],{},[902,11752,11753],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,11756,11758],{"className":11757},[886],[888,11759,11760],{"xmlns":890},[892,11761,11762,11766],{},[895,11763,11764],{},[898,11765,1664],{},[902,11767,1664],{"encoding":904}," podle ",[883,11770,11772],{"className":11771},[886],[888,11773,11774],{"xmlns":890},[892,11775,11776,11780],{},[895,11777,11778],{},[898,11779,1657],{},[902,11781,1657],{"encoding":904}," (nebo naopak):",[724,11784,11785],{},[883,11786,11788],{"className":11787},[886],[888,11789,11790],{"xmlns":890},[892,11791,11792,11886],{},[895,11793,11794,11800,11802,11816,11818,11820,11838,11840,11842,11848,11850,11864,11866,11868],{},[2115,11795,11796,11798],{},[898,11797,1664],{},[1651,11799,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,11801,1738],{},[2446,11803,11804,11810],{},[895,11805,11806,11808],{},[898,11807,3542],{},[898,11809,1664],{},[895,11811,11812,11814],{},[898,11813,3542],{},[898,11815,1657],{},[1651,11817,1738],{},[1651,11819,2181],{},[2446,11821,11822,11830],{},[1902,11823,11824,11826,11828],{},[898,11825,11736],{},[898,11827,1657],{},[1651,11829,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1902,11831,11832,11834,11836],{},[898,11833,11736],{},[898,11835,1664],{},[1651,11837,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,11839,1661],{"separator":1660},[7185,11841],{"width":7187},[2115,11843,11844,11846],{},[898,11845,1657],{},[1651,11847,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,11849,1738],{},[2446,11851,11852,11858],{},[895,11853,11854,11856],{},[898,11855,3542],{},[898,11857,1657],{},[895,11859,11860,11862],{},[898,11861,3542],{},[898,11863,1664],{},[1651,11865,1738],{},[1651,11867,2181],{},[2446,11869,11870,11878],{},[1902,11871,11872,11874,11876],{},[898,11873,11736],{},[898,11875,1664],{},[1651,11877,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1902,11879,11880,11882,11884],{},[898,11881,11736],{},[898,11883,1657],{},[1651,11885,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,11887,11888],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,11890,11891,11892,11895,11896,5197,11900,1882],{},"Tato vzorec dává ",[38,11893,11894],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,11897,11899],{"className":11898,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS",[207,11901,11903],{"className":11902,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS",[115,11905,11907],{"id":11906},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,11909,1886],{"id":1885},[724,11911,11912,11913,11937],{},"V bodě extrému ",[883,11914,11916],{"className":11915},[886],[888,11917,11918],{"xmlns":890},[892,11919,11920,11934],{},[895,11921,11922,11924,11926,11928,11930,11932],{},[898,11923,5564],{},[1651,11925,2261],{"stretchy":1653},[898,11927,207],{},[1651,11929,1661],{"separator":1660},[898,11931,2268],{},[1651,11933,2279],{"stretchy":1653},[902,11935,11936],{"encoding":904},"A[a, b]"," musí platit současně:",[724,11939,11940],{},[883,11941,11943],{"className":11942},[886],[888,11944,11945],{"xmlns":890},[892,11946,11947,12000],{},[895,11948,11949,11957,11959,11961,11963,11965,11967,11969,11971,11973,11976,11978,11986,11988,11990,11992,11994,11996,11998],{},[1902,11950,11951,11953,11955],{},[898,11952,1649],{},[898,11954,1657],{},[1651,11956,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,11958,1654],{"stretchy":1653},[898,11960,207],{},[1651,11962,1661],{"separator":1660},[898,11964,2268],{},[1651,11966,1667],{"stretchy":1653},[1651,11968,1738],{},[1692,11970,1741],{},[1843,11972,5295],{},[1651,11974,11975],{},"∧",[1843,11977,5295],{},[1902,11979,11980,11982,11984],{},[898,11981,1649],{},[898,11983,1664],{},[1651,11985,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,11987,1654],{"stretchy":1653},[898,11989,207],{},[1651,11991,1661],{"separator":1660},[898,11993,2268],{},[1651,11995,1667],{"stretchy":1653},[1651,11997,1738],{},[1692,11999,1741],{},[902,12001,12002],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,12004,2033],{"id":2032},[724,12006,1789,12007,12010],{},[38,12008,12009],{},"diskriminant"," (Hessián zjednodušeně):",[724,12012,12013],{},[883,12014,12016],{"className":12015},[886],[888,12017,12018],{"xmlns":890},[892,12019,12020,12096],{},[895,12021,12022,12024,12026,12028,12030,12032,12034,12036,12052,12054,12070,12072,12074,12090],{},[898,12023,2047],{},[1651,12025,1654],{"stretchy":1653},[898,12027,1657],{},[1651,12029,1661],{"separator":1660},[898,12031,1664],{},[1651,12033,1667],{"stretchy":1653},[1651,12035,1738],{},[1902,12037,12038,12040,12046],{},[898,12039,1649],{},[895,12041,12042,12044],{},[898,12043,1657],{},[898,12045,1657],{},[895,12047,12048,12050],{},[1651,12049,1912],{"mathvariant":1910},[1651,12051,1912],{"mathvariant":1910},[1651,12053,4503],{},[1902,12055,12056,12058,12064],{},[898,12057,1649],{},[895,12059,12060,12062],{},[898,12061,1664],{},[898,12063,1664],{},[895,12065,12066,12068],{},[1651,12067,1912],{"mathvariant":1910},[1651,12069,1912],{"mathvariant":1910},[1651,12071,2181],{},[1651,12073,1654],{"stretchy":1653},[1902,12075,12076,12078,12084],{},[898,12077,1649],{},[895,12079,12080,12082],{},[898,12081,1657],{},[898,12083,1664],{},[895,12085,12086,12088],{},[1651,12087,1912],{"mathvariant":1910},[1651,12089,1912],{"mathvariant":1910},[2115,12091,12092,12094],{},[1651,12093,1667],{"stretchy":1653},[1692,12095,1703],{},[902,12097,12098],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,12100,12101,12102,1793],{},"V podezřelém bodě ",[883,12103,12105],{"className":12104},[886],[888,12106,12107],{"xmlns":890},[892,12108,12109,12121],{},[895,12110,12111,12113,12115,12117,12119],{},[1651,12112,2261],{"stretchy":1653},[898,12114,207],{},[1651,12116,1661],{"separator":1660},[898,12118,2268],{},[1651,12120,2279],{"stretchy":1653},[902,12122,12123],{"encoding":904},"[a, b]",[152,12125,12126,12253,12289],{},[123,12127,12128,12158,12159],{},[38,12129,12130,1793],{},[883,12131,12133],{"className":12132},[886],[888,12134,12135],{"xmlns":890},[892,12136,12137,12155],{},[895,12138,12139,12141,12143,12145,12147,12149,12151,12153],{},[898,12140,2047],{},[1651,12142,1654],{"stretchy":1653},[898,12144,207],{},[1651,12146,1661],{"separator":1660},[898,12148,2268],{},[1651,12150,1667],{"stretchy":1653},[1651,12152,2390],{},[1692,12154,1741],{},[902,12156,12157],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,12160,12161,12207],{},[123,12162,12163,2325,12205],{},[883,12164,12166],{"className":12165},[886],[888,12167,12168],{"xmlns":890},[892,12169,12170,12202],{},[895,12171,12172,12188,12190,12192,12194,12196,12198,12200],{},[1902,12173,12174,12176,12182],{},[898,12175,1649],{},[895,12177,12178,12180],{},[898,12179,1657],{},[898,12181,1657],{},[895,12183,12184,12186],{},[1651,12185,1912],{"mathvariant":1910},[1651,12187,1912],{"mathvariant":1910},[1651,12189,1654],{"stretchy":1653},[898,12191,207],{},[1651,12193,1661],{"separator":1660},[898,12195,2268],{},[1651,12197,1667],{"stretchy":1653},[1651,12199,2390],{},[1692,12201,1741],{},[902,12203,12204],{"encoding":904},"f''_{xx}(a, b) > 0",[38,12206,2398],{},[123,12208,12209,2325,12251],{},[883,12210,12212],{"className":12211},[886],[888,12213,12214],{"xmlns":890},[892,12215,12216,12248],{},[895,12217,12218,12234,12236,12238,12240,12242,12244,12246],{},[1902,12219,12220,12222,12228],{},[898,12221,1649],{},[895,12223,12224,12226],{},[898,12225,1657],{},[898,12227,1657],{},[895,12229,12230,12232],{},[1651,12231,1912],{"mathvariant":1910},[1651,12233,1912],{"mathvariant":1910},[1651,12235,1654],{"stretchy":1653},[898,12237,207],{},[1651,12239,1661],{"separator":1660},[898,12241,2268],{},[1651,12243,1667],{"stretchy":1653},[1651,12245,2319],{},[1692,12247,1741],{},[902,12249,12250],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,12252,2328],{},[123,12254,12255,3246,12285,12288],{},[38,12256,12257,1793],{},[883,12258,12260],{"className":12259},[886],[888,12261,12262],{"xmlns":890},[892,12263,12264,12282],{},[895,12265,12266,12268,12270,12272,12274,12276,12278,12280],{},[898,12267,2047],{},[1651,12269,1654],{"stretchy":1653},[898,12271,207],{},[1651,12273,1661],{"separator":1660},[898,12275,2268],{},[1651,12277,1667],{"stretchy":1653},[1651,12279,2319],{},[1692,12281,1741],{},[902,12283,12284],{"encoding":904},"D(a, b) \u003C 0",[38,12286,12287],{},"sedlo"," (v daném bodě extrém není).",[123,12290,12291,12321],{},[38,12292,12293,1793],{},[883,12294,12296],{"className":12295},[886],[888,12297,12298],{"xmlns":890},[892,12299,12300,12318],{},[895,12301,12302,12304,12306,12308,12310,12312,12314,12316],{},[898,12303,2047],{},[1651,12305,1654],{"stretchy":1653},[898,12307,207],{},[1651,12309,1661],{"separator":1660},[898,12311,2268],{},[1651,12313,1667],{"stretchy":1653},[1651,12315,1738],{},[1692,12317,1741],{},[902,12319,12320],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,12323,12325],{"id":12324},"vázané-extrémy","Vázané extrémy",[724,12327,12328,12329,12356,12357,1882],{},"Pro extrémy s omezující podmínkou ",[883,12330,12332],{"className":12331},[886],[888,12333,12334],{"xmlns":890},[892,12335,12336,12354],{},[895,12337,12338,12340,12342,12344,12346,12348,12350,12352],{},[898,12339,1725],{},[1651,12341,1654],{"stretchy":1653},[898,12343,1657],{},[1651,12345,1661],{"separator":1660},[898,12347,1664],{},[1651,12349,1667],{"stretchy":1653},[1651,12351,1738],{},[1692,12353,1741],{},[902,12355,1744],{"encoding":904}," se používá ",[207,12358,793],{"className":12359,"dataFsResolvedFilePath":791,"href":792},[210],[115,12361,3238],{"id":3237},[120,12363,12364,12371,12378],{},[123,12365,12366,3246,12368],{},[38,12367,3245],{},[207,12369,775],{"className":12370,"dataFsResolvedFilePath":773,"href":774},[210],[123,12372,12373,3246,12375],{},[38,12374,3254],{},[207,12376,793],{"className":12377,"dataFsResolvedFilePath":791,"href":792},[210],[123,12379,12380,3246,12382,12386,12387,12390,12391,12394],{},[38,12381,3272],{},[207,12383,12385],{"className":12384,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (parciální derivace = mezní produkty), ",[207,12388,880],{"className":12389,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,12392,5140],{"className":12393,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":12396},[12397,12398,12402,12403,12404,12408,12409],{"id":10962,"depth":642,"text":10963},{"id":11117,"depth":642,"text":11118,"children":12399},[12400,12401],{"id":11269,"depth":649,"text":11270},{"id":3898,"depth":649,"text":3899},{"id":11598,"depth":642,"text":11599},{"id":11720,"depth":642,"text":11721},{"id":11906,"depth":642,"text":11907,"children":12405},[12406,12407],{"id":1885,"depth":649,"text":1886},{"id":2032,"depth":649,"text":2033},{"id":12324,"depth":642,"text":12325},{"id":3237,"depth":642,"text":3238},"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":10873,"description":12410},[1135],"topics\u002Ffunkce-vice-promennych",[1128,12417,5166,12418,12419,12420],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":12423,"title":775,"body":12424,"course":1128,"courses":659,"created":1129,"description":13279,"extension":661,"meta":13280,"navigation":664,"path":13281,"seo":13282,"sources":13283,"stem":13284,"tags":13285,"type":3302,"updated":677,"__hash__":13292},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":12425,"toc":13269},[12426,12429,12440,12444,12489,12569,12573,12649,12691,12698,12702,12706,12735,12793,12840,12878,12882,12932,12984,13036,13080,13083,13086,13158,13161,13233,13239,13241],[12,12427,775],{"id":12428},"integrál",[724,12430,12431,12432,12435,12436,12439],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,12433,12434],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,12437,12438],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,12441,12443],{"id":12442},"neurčitý-integrál","Neurčitý integrál",[724,12445,12446],{},[883,12447,12449],{"className":12448},[886],[888,12450,12451],{"xmlns":890},[892,12452,12453,12486],{},[895,12454,12455,12457,12459,12461,12463,12465,12468,12470,12472,12474,12476,12478,12480,12482,12484],{},[898,12456,11736],{},[1651,12458,1654],{"stretchy":1653},[898,12460,1657],{},[1651,12462,1667],{"stretchy":1653},[1651,12464,1738],{},[1651,12466,12467],{},"∫",[898,12469,1649],{},[1651,12471,1654],{"stretchy":1653},[898,12473,1657],{},[1651,12475,1667],{"stretchy":1653},[1843,12477,1845],{},[898,12479,3542],{},[898,12481,1657],{},[1651,12483,1839],{},[898,12485,3001],{},[902,12487,12488],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,12490,1863,12491,4254,12525,1878,12538,12541,12542,1343,12555,12568],{},[883,12492,12494],{"className":12493},[886],[888,12495,12496],{"xmlns":890},[892,12497,12498,12522],{},[895,12499,12500,12506,12508,12510,12512,12514,12516,12518,12520],{},[2115,12501,12502,12504],{},[898,12503,11736],{},[1651,12505,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,12507,1654],{"stretchy":1653},[898,12509,1657],{},[1651,12511,1667],{"stretchy":1653},[1651,12513,1738],{},[898,12515,1649],{},[1651,12517,1654],{"stretchy":1653},[898,12519,1657],{},[1651,12521,1667],{"stretchy":1653},[902,12523,12524],{"encoding":904},"F'(x) = f(x)",[883,12526,12528],{"className":12527},[886],[888,12529,12530],{"xmlns":890},[892,12531,12532,12536],{},[895,12533,12534],{},[898,12535,11736],{},[902,12537,11736],{"encoding":904},[38,12539,12540],{},"primitivní funkce"," k ",[883,12543,12545],{"className":12544},[886],[888,12546,12547],{"xmlns":890},[892,12548,12549,12553],{},[895,12550,12551],{},[898,12552,1649],{},[902,12554,1649],{"encoding":904},[883,12556,12558],{"className":12557},[886],[888,12559,12560],{"xmlns":890},[892,12561,12562,12566],{},[895,12563,12564],{},[898,12565,3001],{},[902,12567,3001],{"encoding":904}," konstanta.",[115,12570,12572],{"id":12571},"určitý-integrál","Určitý integrál",[724,12574,12575],{},[883,12576,12578],{"className":12577},[886],[888,12579,12580],{"xmlns":890},[892,12581,12582,12646],{},[895,12583,12584,12592,12594,12596,12598,12600,12602,12604,12606,12608,12610,12612,12614,12616,12618,12626,12628,12630,12632,12634,12636,12638,12640,12642,12644],{},[1902,12585,12586,12588,12590],{},[1651,12587,12467],{},[898,12589,207],{},[898,12591,2268],{},[898,12593,1649],{},[1651,12595,1654],{"stretchy":1653},[898,12597,1657],{},[1651,12599,1667],{"stretchy":1653},[1843,12601,1845],{},[898,12603,3542],{},[898,12605,1657],{},[1651,12607,1738],{},[1651,12609,2261],{"stretchy":1653},[898,12611,11736],{},[1651,12613,1654],{"stretchy":1653},[898,12615,1657],{},[1651,12617,1667],{"stretchy":1653},[1902,12619,12620,12622,12624],{},[1651,12621,2279],{"stretchy":1653},[898,12623,207],{},[898,12625,2268],{},[1651,12627,1738],{},[898,12629,11736],{},[1651,12631,1654],{"stretchy":1653},[898,12633,2268],{},[1651,12635,1667],{"stretchy":1653},[1651,12637,2181],{},[898,12639,11736],{},[1651,12641,1654],{"stretchy":1653},[898,12643,207],{},[1651,12645,1667],{"stretchy":1653},[902,12647,12648],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,12650,12651,12652,3246,12655,12668,12669,12690],{},"Geometricky ",[38,12653,12654],{},"plocha pod grafem",[883,12656,12658],{"className":12657},[886],[888,12659,12660],{"xmlns":890},[892,12661,12662,12666],{},[895,12663,12664],{},[898,12665,1649],{},[902,12667,1649],{"encoding":904}," na intervalu ",[883,12670,12672],{"className":12671},[886],[888,12673,12674],{"xmlns":890},[892,12675,12676,12688],{},[895,12677,12678,12680,12682,12684,12686],{},[1651,12679,2261],{"stretchy":1653},[898,12681,207],{},[1651,12683,1661],{"separator":1660},[898,12685,2268],{},[1651,12687,2279],{"stretchy":1653},[902,12689,12123],{"encoding":904}," (orientovaná).",[724,12692,12693],{},[1756,12694],{"alt":12695,"className":12696,"src":12697},"imek-integral-plocha",[210,1760],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,12699,12701],{"id":12700},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,12703,12705],{"id":12704},"příklad-tr-z-mr","Příklad — TR z MR",[724,12707,12708,12709,1882],{},"Mezní příjem ",[883,12710,12712],{"className":12711},[886],[888,12713,12714],{"xmlns":890},[892,12715,12716,12732],{},[895,12717,12718,12720,12722,12724,12726,12728,12730],{},[898,12719,2995],{},[898,12721,2998],{},[1651,12723,1738],{},[1692,12725,4416],{},[1651,12727,2181],{},[1692,12729,1703],{},[898,12731,1690],{},[902,12733,12734],{"encoding":904},"MR = 100 - 2Q",[724,12736,12737],{},[883,12738,12740],{"className":12739},[886],[888,12741,12742],{"xmlns":890},[892,12743,12744,12790],{},[895,12745,12746,12748,12750,12752,12754,12756,12758,12760,12762,12764,12766,12768,12770,12772,12774,12776,12778,12780,12786,12788],{},[898,12747,4104],{},[898,12749,2998],{},[1651,12751,1738],{},[1651,12753,12467],{},[1651,12755,1654],{"stretchy":1653},[1692,12757,4416],{},[1651,12759,2181],{},[1692,12761,1703],{},[898,12763,1690],{},[1651,12765,1667],{"stretchy":1653},[1843,12767,1845],{},[898,12769,3542],{},[898,12771,1690],{},[1651,12773,1738],{},[1692,12775,4416],{},[898,12777,1690],{},[1651,12779,2181],{},[2115,12781,12782,12784],{},[898,12783,1690],{},[1692,12785,1703],{},[1651,12787,1839],{},[898,12789,3490],{},[902,12791,12792],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,12794,12795,12796,2325,12822,1793],{},"Okrajová podmínka ",[883,12797,12799],{"className":12798},[886],[888,12800,12801],{"xmlns":890},[892,12802,12803,12819],{},[895,12804,12805,12807,12809,12811,12813,12815,12817],{},[898,12806,4104],{},[898,12808,2998],{},[1651,12810,1654],{"stretchy":1653},[1692,12812,1741],{},[1651,12814,1667],{"stretchy":1653},[1651,12816,1738],{},[1692,12818,1741],{},[902,12820,12821],{"encoding":904},"TR(0) = 0",[883,12823,12825],{"className":12824},[886],[888,12826,12827],{"xmlns":890},[892,12828,12829,12837],{},[895,12830,12831,12833,12835],{},[898,12832,3490],{},[1651,12834,1738],{},[1692,12836,1741],{},[902,12838,12839],{"encoding":904},"c = 0",[724,12841,12842],{},[883,12843,12845],{"className":12844},[886],[888,12846,12847],{"xmlns":890},[892,12848,12849,12875],{},[895,12850,12851,12853,12855,12857,12859,12861,12863,12865,12867,12869],{},[898,12852,4104],{},[898,12854,2998],{},[1651,12856,1654],{"stretchy":1653},[898,12858,1690],{},[1651,12860,1667],{"stretchy":1653},[1651,12862,1738],{},[1692,12864,4416],{},[898,12866,1690],{},[1651,12868,2181],{},[2115,12870,12871,12873],{},[898,12872,1690],{},[1692,12874,1703],{},[902,12876,12877],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,12879,12881],{"id":12880},"příklad-tc-z-mc","Příklad — TC z MC",[724,12883,12884,12885,12911,12912,1882],{},"Mezní náklady ",[883,12886,12888],{"className":12887},[886],[888,12889,12890],{"xmlns":890},[892,12891,12892,12908],{},[895,12893,12894,12896,12898,12900,12902,12904,12906],{},[898,12895,2995],{},[898,12897,3001],{},[1651,12899,1738],{},[1692,12901,1703],{},[1651,12903,1839],{},[1692,12905,4166],{},[898,12907,1690],{},[902,12909,12910],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,12913,12915],{"className":12914},[886],[888,12916,12917],{"xmlns":890},[892,12918,12919,12929],{},[895,12920,12921,12923,12925,12927],{},[898,12922,11736],{},[898,12924,3001],{},[1651,12926,1738],{},[1692,12928,4416],{},[902,12930,12931],{"encoding":904},"FC = 100",[724,12933,12934],{},[883,12935,12937],{"className":12936},[886],[888,12938,12939],{"xmlns":890},[892,12940,12941,12981],{},[895,12942,12943,12945,12947,12949,12951,12953,12955,12957,12959,12961,12963,12965,12967,12969,12971,12977,12979],{},[898,12944,4104],{},[898,12946,3001],{},[1651,12948,1738],{},[1651,12950,12467],{},[898,12952,2995],{},[898,12954,3001],{},[1843,12956,1845],{},[898,12958,3542],{},[898,12960,1690],{},[1651,12962,1738],{},[1692,12964,1703],{},[898,12966,1690],{},[1651,12968,1839],{},[1692,12970,4122],{},[2115,12972,12973,12975],{},[898,12974,1690],{},[1692,12976,1703],{},[1651,12978,1839],{},[898,12980,3490],{},[902,12982,12983],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,12985,12795,12986,2325,13018,1793],{},[883,12987,12989],{"className":12988},[886],[888,12990,12991],{"xmlns":890},[892,12992,12993,13015],{},[895,12994,12995,12997,12999,13001,13003,13005,13007,13009,13011,13013],{},[898,12996,4104],{},[898,12998,3001],{},[1651,13000,1654],{"stretchy":1653},[1692,13002,1741],{},[1651,13004,1667],{"stretchy":1653},[1651,13006,1738],{},[898,13008,11736],{},[898,13010,3001],{},[1651,13012,1738],{},[1692,13014,4416],{},[902,13016,13017],{"encoding":904},"TC(0) = FC = 100",[883,13019,13021],{"className":13020},[886],[888,13022,13023],{"xmlns":890},[892,13024,13025,13033],{},[895,13026,13027,13029,13031],{},[898,13028,3490],{},[1651,13030,1738],{},[1692,13032,4416],{},[902,13034,13035],{"encoding":904},"c = 100",[724,13037,13038],{},[883,13039,13041],{"className":13040},[886],[888,13042,13043],{"xmlns":890},[892,13044,13045,13077],{},[895,13046,13047,13049,13051,13053,13055,13057,13059,13061,13063,13065,13067,13069,13071],{},[898,13048,4104],{},[898,13050,3001],{},[1651,13052,1654],{"stretchy":1653},[898,13054,1690],{},[1651,13056,1667],{"stretchy":1653},[1651,13058,1738],{},[1692,13060,4416],{},[1651,13062,1839],{},[1692,13064,1703],{},[898,13066,1690],{},[1651,13068,1839],{},[1692,13070,4122],{},[2115,13072,13073,13075],{},[898,13074,1690],{},[1692,13076,1703],{},[902,13078,13079],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,13081,820],{"id":13082},"přebytek-spotřebitele-a-výrobce",[724,13084,13085],{},"Přebytek spotřebitele:",[724,13087,13088],{},[883,13089,13091],{"className":13090},[886],[888,13092,13093],{"xmlns":890},[892,13094,13095,13155],{},[895,13096,13097,13099,13101,13103,13109,13111,13113,13125,13127,13129,13131,13133,13135,13137,13139,13141,13147,13149],{},[898,13098,3001],{},[898,13100,3004],{},[1651,13102,1654],{"stretchy":1653},[1686,13104,13105,13107],{},[898,13106,1690],{},[1692,13108,1741],{},[1651,13110,1667],{"stretchy":1653},[1651,13112,1738],{},[1902,13114,13115,13117,13119],{},[1651,13116,12467],{},[1692,13118,1741],{},[1686,13120,13121,13123],{},[898,13122,1690],{},[1692,13124,1741],{},[898,13126,2047],{},[1651,13128,1654],{"stretchy":1653},[898,13130,1690],{},[1651,13132,1667],{"stretchy":1653},[1843,13134,1845],{},[898,13136,3542],{},[898,13138,1690],{},[1651,13140,2181],{},[1686,13142,13143,13145],{},[898,13144,2675],{},[1692,13146,1741],{},[1843,13148,1845],{},[1686,13150,13151,13153],{},[898,13152,1690],{},[1692,13154,1741],{},[902,13156,13157],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,13159,13160],{},"Přebytek výrobce:",[724,13162,13163],{},[883,13164,13166],{"className":13165},[886],[888,13167,13168],{"xmlns":890},[892,13169,13170,13230],{},[895,13171,13172,13174,13176,13178,13184,13186,13188,13194,13196,13202,13204,13216,13218,13220,13222,13224,13226,13228],{},[898,13173,2675],{},[898,13175,3004],{},[1651,13177,1654],{"stretchy":1653},[1686,13179,13180,13182],{},[898,13181,1690],{},[1692,13183,1741],{},[1651,13185,1667],{"stretchy":1653},[1651,13187,1738],{},[1686,13189,13190,13192],{},[898,13191,2675],{},[1692,13193,1741],{},[1843,13195,1845],{},[1686,13197,13198,13200],{},[898,13199,1690],{},[1692,13201,1741],{},[1651,13203,2181],{},[1902,13205,13206,13208,13210],{},[1651,13207,12467],{},[1692,13209,1741],{},[1686,13211,13212,13214],{},[898,13213,1690],{},[1692,13215,1741],{},[898,13217,3004],{},[1651,13219,1654],{"stretchy":1653},[898,13221,1690],{},[1651,13223,1667],{"stretchy":1653},[1843,13225,1845],{},[898,13227,3542],{},[898,13229,1690],{},[902,13231,13232],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,13234,13235,13236,1882],{},"Detailně viz ",[207,13237,3258],{"className":13238,"dataFsResolvedFilePath":800,"href":801},[210],[115,13240,3238],{"id":3237},[120,13242,13243,13250,13257],{},[123,13244,13245,3246,13247],{},[38,13246,3245],{},[207,13248,766],{"className":13249,"dataFsResolvedFilePath":764,"href":765},[210],[123,13251,13252,3246,13254],{},[38,13253,3254],{},[207,13255,784],{"className":13256,"dataFsResolvedFilePath":782,"href":783},[210],[123,13258,13259,3246,13261,13264,13265,13268],{},[38,13260,3272],{},[207,13262,5135],{"className":13263,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,13266,3258],{"className":13267,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":13270},[13271,13272,13273,13278],{"id":12442,"depth":642,"text":12443},{"id":12571,"depth":642,"text":12572},{"id":12700,"depth":642,"text":12701,"children":13274},[13275,13276,13277],{"id":12704,"depth":649,"text":12705},{"id":12880,"depth":649,"text":12881},{"id":13082,"depth":649,"text":820},{"id":3237,"depth":642,"text":3238},"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":13279},[1135],"topics\u002Fintegral",[1128,13286,13287,13288,13289,13290,13291],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":13294,"title":13295,"body":13296,"course":1128,"courses":659,"created":10859,"description":641,"extension":661,"meta":17565,"navigation":664,"path":17566,"seo":17567,"sources":17568,"stem":17569,"tags":17570,"type":3302,"updated":677,"__hash__":17576},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":13297,"toc":17553},[13298,13301,13305,13449,13456,13460,13530,13568,13671,13675,13705,13771,13818,13821,13890,13893,13928,13964,13968,14016,14023,14069,14115,14118,14197,14294,14377,14381,14425,14455,14461,14490,14512,14562,14615,14681,14684,14750,14779,14838,14854,14941,15039,15170,15174,15331,15480,15860,15864,15867,15926,15929,16015,16043,16081,16084,16121,16161,16195,16197,16234,16266,16364,16369,16493,16545,16627,16766,16770,16890,16897,17008,17015,17019,17494,17496],[12,13299,13295],{"id":13300},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,13302,13304],{"id":13303},"tldr","TL;DR",[724,13306,13307,13310,13311,11325,13314,13327,13328,13342,13343,13346,13347,1343,13350,13353,13354,1343,13357,13360,13361,3246,13364,13394,13395,13398,13399,1343,13413,13426,13427,13430,13431,5230],{},[38,13308,13309],{},"IS-LM"," je makroekonomický model se ",[38,13312,13313],{},"dvěma neznámými",[883,13315,13317],{"className":13316},[886],[888,13318,13319],{"xmlns":890},[892,13320,13321,13325],{},[895,13322,13323],{},[898,13324,2665],{},[902,13326,2665],{"encoding":904}," — národní důchod a ",[883,13329,13331],{"className":13330},[886],[888,13332,13333],{"xmlns":890},[892,13334,13335,13340],{},[895,13336,13337],{},[898,13338,13339],{},"r",[902,13341,13339],{"encoding":904}," — úroková míra) a ",[38,13344,13345],{},"dvěma trhy",": trhem zboží (křivka ",[38,13348,13349],{},"IS",[614,13351,13352],{},"Investment = Savings",") a trhem peněz (křivka ",[38,13355,13356],{},"LM",[614,13358,13359],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,13362,13363],{},"simultánní rovnováhu",[883,13365,13367],{"className":13366},[886],[888,13368,13369],{"xmlns":890},[892,13370,13371,13391],{},[895,13372,13373,13375,13381,13383,13389],{},[1651,13374,1654],{"stretchy":1653},[2115,13376,13377,13379],{},[898,13378,2665],{},[898,13380,5561],{},[1651,13382,1661],{"separator":1660},[2115,13384,13385,13387],{},[898,13386,13339],{},[898,13388,5561],{},[1651,13390,1667],{"stretchy":1653},[902,13392,13393],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,13396,13397],{},"fiskální politiky"," (posun IS změnou ",[883,13400,13402],{"className":13401},[886],[888,13403,13404],{"xmlns":890},[892,13405,13406,13411],{},[895,13407,13408],{},[898,13409,13410],{},"G",[902,13412,13410],{"encoding":904},[883,13414,13416],{"className":13415},[886],[888,13417,13418],{"xmlns":890},[892,13419,13420,13424],{},[895,13421,13422],{},[898,13423,4104],{},[902,13425,4104],{"encoding":904},") a ",[38,13428,13429],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,13432,13434],{"className":13433},[886],[888,13435,13436],{"xmlns":890},[892,13437,13438,13446],{},[895,13439,13440],{},[2115,13441,13442,13444],{},[898,13443,2995],{},[1651,13445,2668],{},[902,13447,13448],{"encoding":904},"M^*",[724,13450,13451],{},[1756,13452],{"alt":13453,"className":13454,"src":13455},"imek-is-lm-model",[210,1760],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,13457,13459],{"id":13458},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,13461,13462,13463,13467,13468,11325,13471,13494,13495,13498,13499,13515,13516,13529],{},"V modelech ",[207,13464,13466],{"className":13465,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,13469,13470],{},"investice pokládány za konstantní",[883,13472,13474],{"className":13473},[886],[888,13475,13476],{"xmlns":890},[892,13477,13478,13491],{},[895,13479,13480,13483,13485],{},[898,13481,13482],{},"I",[1651,13484,1738],{},[2115,13486,13487,13489],{},[898,13488,13482],{},[1651,13490,2668],{},[902,13492,13493],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,13496,13497],{},"ceně peněz",", tedy na ",[38,13500,13501,13502],{},"úrokové míře ",[883,13503,13505],{"className":13504},[886],[888,13506,13507],{"xmlns":890},[892,13508,13509,13513],{},[895,13510,13511],{},[898,13512,13339],{},[902,13514,13339],{"encoding":904},": čím vyšší ",[883,13517,13519],{"className":13518},[886],[888,13520,13521],{"xmlns":890},[892,13522,13523,13527],{},[895,13524,13525],{},[898,13526,13339],{},[902,13528,13339],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,13531,13532,13562],{},[123,13533,13534,3246,13537,13561],{},[38,13535,13536],{},"funkci investic",[883,13538,13540],{"className":13539},[886],[888,13541,13542],{"xmlns":890},[892,13543,13544,13558],{},[895,13545,13546,13548,13550,13552,13554,13556],{},[898,13547,13482],{},[1651,13549,1738],{},[898,13551,13482],{},[1651,13553,1654],{"stretchy":1653},[898,13555,13339],{},[1651,13557,1667],{"stretchy":1653},[902,13559,13560],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,13563,13564,13567],{},[38,13565,13566],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[5179,13569,13570],{},[724,13571,13572,13574,13575,13594,13595,13622,13623,13636,13637,13666,13667,13670],{},[883,13573,5719],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,13576,13578],{"className":13577},[886],[888,13579,13580],{"xmlns":890},[892,13581,13582,13591],{},[895,13583,13584,13586,13589],{},[898,13585,3001],{},[1843,13587,13588],{},"-",[898,13590,13482],{},[902,13592,13593],{"encoding":904},"C\\text{-}I"," až ",[883,13596,13598],{"className":13597},[886],[888,13599,13600],{"xmlns":890},[892,13601,13602,13619],{},[895,13603,13604,13606,13608,13610,13612,13614,13616],{},[898,13605,3001],{},[1843,13607,13588],{},[898,13609,13482],{},[1843,13611,13588],{},[898,13613,13410],{},[1843,13615,13588],{},[898,13617,13618],{},"X",[902,13620,13621],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,13624,13626],{"className":13625},[886],[888,13627,13628],{"xmlns":890},[892,13629,13630,13634],{},[895,13631,13632],{},[898,13633,2665],{},[902,13635,2665],{"encoding":904},". V IS-LM jsou ",[38,13638,13639,13640,5197,13653],{},"dvě neznámé ",[883,13641,13643],{"className":13642},[886],[888,13644,13645],{"xmlns":890},[892,13646,13647,13651],{},[895,13648,13649],{},[898,13650,2665],{},[902,13652,2665],{"encoding":904},[883,13654,13656],{"className":13655},[886],[888,13657,13658],{"xmlns":890},[892,13659,13660,13664],{},[895,13661,13662],{},[898,13663,13339],{},[902,13665,13339],{"encoding":904},", a proto potřebujeme ",[38,13668,13669],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,13672,13674],{"id":13673},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,13676,13677,13678,13691,13692,1793],{},"Lineární závislost investic ",[883,13679,13681],{"className":13680},[886],[888,13682,13683],{"xmlns":890},[892,13684,13685,13689],{},[895,13686,13687],{},[898,13688,13482],{},[902,13690,13482],{"encoding":904}," na úrokové míře ",[883,13693,13695],{"className":13694},[886],[888,13696,13697],{"xmlns":890},[892,13698,13699,13703],{},[895,13700,13701],{},[898,13702,13339],{},[902,13704,13339],{"encoding":904},[724,13706,13707],{},[883,13708,13710],{"className":13709},[886],[888,13711,13712],{"xmlns":890},[892,13713,13714,13768],{},[895,13715,13716,13718,13720,13722,13724,13726,13728,13730,13732,13734,13736,13738,13740,13742,13744,13746,13748,13750,13752,13754,13756,13759,13761,13763,13766],{},[898,13717,13482],{},[1651,13719,1738],{},[898,13721,13482],{},[1651,13723,1654],{"stretchy":1653},[898,13725,13339],{},[1651,13727,1667],{"stretchy":1653},[1651,13729,1738],{},[898,13731,3490],{},[898,13733,13339],{},[1651,13735,1839],{},[898,13737,3542],{},[1651,13739,1661],{"separator":1660},[7185,13741],{"width":7187},[898,13743,3490],{},[1651,13745,2319],{},[1692,13747,1741],{},[1651,13749,1661],{"separator":1660},[1843,13751,3631],{},[898,13753,3542],{},[1651,13755,2390],{},[1692,13757,13758],{},"0.",[7185,13760],{"width":7187},[1651,13762,1654],{"stretchy":1653},[1692,13764,13765],{},"7.11",[1651,13767,1667],{"stretchy":1653},[902,13769,13770],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,13772,13773,13794],{},[123,13774,13775,13793],{},[883,13776,13778],{"className":13777},[886],[888,13779,13780],{"xmlns":890},[892,13781,13782,13790],{},[895,13783,13784,13786,13788],{},[898,13785,3542],{},[1651,13787,2390],{},[1692,13789,1741],{},[902,13791,13792],{"encoding":904},"d > 0"," zřejmé,",[123,13795,13796,13814,13815,1882],{},[883,13797,13799],{"className":13798},[886],[888,13800,13801],{"xmlns":890},[892,13802,13803,13811],{},[895,13804,13805,13807,13809],{},[898,13806,3490],{},[1651,13808,2319],{},[1692,13810,1741],{},[902,13812,13813],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,13816,13817],{},"klesající",[724,13819,13820],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,13822,13823],{},[883,13824,13826],{"className":13825},[886],[888,13827,13828],{"xmlns":890},[892,13829,13830,13887],{},[895,13831,13832,13834,13836,13838,13840,13842,13844,13846,13848,13850,13852,13854,13856,13858,13860,13862,13864,13866,13868,13870,13872,13874,13876,13878,13880,13882,13885],{},[898,13833,3001],{},[1651,13835,1738],{},[898,13837,3001],{},[1651,13839,1654],{"stretchy":1653},[898,13841,2665],{},[1651,13843,1667],{"stretchy":1653},[1651,13845,1738],{},[898,13847,207],{},[898,13849,2665],{},[1651,13851,1839],{},[898,13853,2268],{},[1651,13855,1661],{"separator":1660},[7185,13857],{"width":7187},[1692,13859,1741],{},[1651,13861,2319],{},[898,13863,207],{},[1651,13865,2319],{},[1692,13867,1694],{},[1651,13869,1661],{"separator":1660},[1843,13871,3631],{},[898,13873,2268],{},[1651,13875,2390],{},[1692,13877,13758],{},[7185,13879],{"width":7187},[1651,13881,1654],{"stretchy":1653},[1692,13883,13884],{},"7.12",[1651,13886,1667],{"stretchy":1653},[902,13888,13889],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,13891,13892],{},"Podmínka rovnováhy na trhu zboží:",[724,13894,13895],{},[883,13896,13898],{"className":13897},[886],[888,13899,13900],{"xmlns":890},[892,13901,13902,13925],{},[895,13903,13904,13906,13908,13910,13912,13914,13916,13918,13920,13923],{},[898,13905,2665],{},[1651,13907,1738],{},[898,13909,3001],{},[1651,13911,1839],{},[898,13913,13482],{},[898,13915,1882],{"mathvariant":1910},[7185,13917],{"width":7187},[1651,13919,1654],{"stretchy":1653},[1692,13921,13922],{},"7.13",[1651,13924,1667],{"stretchy":1653},[902,13926,13927],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,13929,13930,13931,3246,13934,13960,13961,1882],{},"To dává ",[38,13932,13933],{},"tři rovnice o čtyřech neznámých",[883,13935,13937],{"className":13936},[886],[888,13938,13939],{"xmlns":890},[892,13940,13941,13957],{},[895,13942,13943,13945,13947,13949,13951,13953,13955],{},[898,13944,2665],{},[1651,13946,1661],{"separator":1660},[898,13948,3001],{},[1651,13950,1661],{"separator":1660},[898,13952,13482],{},[1651,13954,1661],{"separator":1660},[898,13956,13339],{},[902,13958,13959],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,13962,13963],{},"rovnováhy na trhu peněz",[115,13965,13967],{"id":13966},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,13969,13970,13971,6876,13993,14011,14012,14015],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,13972,13974],{"className":13973},[886],[888,13975,13976],{"xmlns":890},[892,13977,13978,13990],{},[895,13979,13980,13982,13984,13986,13988],{},[898,13981,2665],{},[1651,13983,1738],{},[898,13985,3001],{},[1651,13987,1839],{},[898,13989,3004],{},[902,13991,13992],{"encoding":904},"Y = C + S",[883,13994,13996],{"className":13995},[886],[888,13997,13998],{"xmlns":890},[892,13999,14000,14008],{},[895,14001,14002,14004,14006],{},[898,14003,13482],{},[1651,14005,1738],{},[898,14007,3004],{},[902,14009,14010],{"encoding":904},"I = S"," (plánované ",[38,14013,14014],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,14017,14018],{},[1756,14019],{"alt":14020,"className":14021,"src":14022},"imek-odvozeni-is-4panelu",[210,1760],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,14024,14025],{},[883,14026,14028],{"className":14027},[886],[888,14029,14030],{"xmlns":890},[892,14031,14032,14066],{},[895,14033,14034,14036,14038,14040,14042,14044,14046,14048,14050,14052,14054,14056,14058,14060,14062,14064],{},[898,14035,2665],{},[1651,14037,1738],{},[1651,14039,1654],{"stretchy":1653},[898,14041,207],{},[898,14043,2665],{},[1651,14045,1839],{},[898,14047,2268],{},[1651,14049,1667],{"stretchy":1653},[1651,14051,1839],{},[1651,14053,1654],{"stretchy":1653},[898,14055,3490],{},[898,14057,13339],{},[1651,14059,1839],{},[898,14061,3542],{},[1651,14063,1667],{"stretchy":1653},[1651,14065,1661],{"separator":1660},[902,14067,14068],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,14070,14071],{},[883,14072,14074],{"className":14073},[886],[888,14075,14076],{"xmlns":890},[892,14077,14078,14112],{},[895,14079,14080,14082,14084,14086,14088,14090,14092,14094,14096,14098,14100,14102,14104,14106,14108,14110],{},[1651,14081,1654],{"stretchy":1653},[1692,14083,1694],{},[1651,14085,2181],{},[898,14087,207],{},[1651,14089,1667],{"stretchy":1653},[898,14091,2665],{},[1651,14093,2181],{},[898,14095,3490],{},[898,14097,13339],{},[1651,14099,2181],{},[898,14101,2268],{},[1651,14103,2181],{},[898,14105,3542],{},[1651,14107,1738],{},[1692,14109,1741],{},[1651,14111,1661],{"separator":1660},[902,14113,14114],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,14116,14117],{},"odkud",[724,14119,14120],{},[883,14121,14123],{"className":14122},[886],[888,14124,14125],{"xmlns":890},[892,14126,14127,14194],{},[895,14128,14129,14185,14187,14189,14192],{},[14130,14131,14133],"menclose",{"notation":14132},"box",[2938,14134,14135],{"scriptlevel":1741,"displaystyle":1653},[2938,14136,14137],{"scriptlevel":1741,"displaystyle":1653},[2938,14138,14139],{"scriptlevel":1741,"displaystyle":1660},[895,14140,14141,14143,14145,14147,14159,14161,14163,14165,14183],{},[1843,14142,1845],{},[898,14144,2665],{},[1651,14146,1738],{},[2446,14148,14149,14151],{},[898,14150,3490],{},[895,14152,14153,14155,14157],{},[1692,14154,1694],{},[1651,14156,2181],{},[898,14158,207],{},[1843,14160,1845],{},[898,14162,13339],{},[1651,14164,1839],{},[2446,14166,14167,14175],{},[895,14168,14169,14171,14173],{},[898,14170,2268],{},[1651,14172,1839],{},[898,14174,3542],{},[895,14176,14177,14179,14181],{},[1692,14178,1694],{},[1651,14180,2181],{},[898,14182,207],{},[1843,14184,1845],{},[7185,14186],{"width":7187},[1651,14188,1654],{"stretchy":1653},[1692,14190,14191],{},"7.14",[1651,14193,1667],{"stretchy":1653},[902,14195,14196],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,14198,14199,14200,11325,14203,14206,14207,14210,14211,14213,14214,14236,14237,14265,14266,14287,14288,14290,14291,14293],{},"Tento vztah se nazývá ",[38,14201,14202],{},"funkce IS",[614,14204,14205],{},"IS schedule",") a její graf ",[38,14208,14209],{},"křivka IS",". Křivka je ",[38,14212,13817],{}," přímka v rovině ",[883,14215,14217],{"className":14216},[886],[888,14218,14219],{"xmlns":890},[892,14220,14221,14233],{},[895,14222,14223,14225,14227,14229,14231],{},[1651,14224,1654],{"stretchy":1653},[898,14226,13339],{},[1651,14228,1661],{"separator":1660},[898,14230,2665],{},[1651,14232,1667],{"stretchy":1653},[902,14234,14235],{"encoding":904},"(r, Y)",", neboť ",[883,14238,14240],{"className":14239},[886],[888,14241,14242],{"xmlns":890},[892,14243,14244,14262],{},[895,14245,14246,14258,14260],{},[2446,14247,14248,14250],{},[898,14249,3490],{},[895,14251,14252,14254,14256],{},[1692,14253,1694],{},[1651,14255,2181],{},[898,14257,207],{},[1651,14259,2319],{},[1692,14261,1741],{},[902,14263,14264],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,14267,14269],{"className":14268},[886],[888,14270,14271],{"xmlns":890},[892,14272,14273,14285],{},[895,14274,14275,14277,14279,14281,14283],{},[1651,14276,1654],{"stretchy":1653},[898,14278,13339],{},[1651,14280,1661],{"separator":1660},[898,14282,2665],{},[1651,14284,1667],{"stretchy":1653},[902,14286,14235],{"encoding":904},", pro které plánované ",[38,14289,13482],{},"nvestment = ",[38,14292,3004],{},"avings.",[5179,14295,14296],{},[724,14297,14298,14300,14301,14314,14315,3246,14318,14331,14332,14345,14346,5197,14359,14372,14373,14376],{},[883,14299,5465],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,14302,14304],{"className":14303},[886],[888,14305,14306],{"xmlns":890},[892,14307,14308,14312],{},[895,14309,14310],{},[898,14311,13339],{},[902,14313,13339],{"encoding":904}," → levnější úvěr → ",[38,14316,14317],{},"více investic",[883,14319,14321],{"className":14320},[886],[888,14322,14323],{"xmlns":890},[892,14324,14325,14329],{},[895,14326,14327],{},[898,14328,13482],{},[902,14330,13482],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,14333,14335],{"className":14334},[886],[888,14336,14337],{"xmlns":890},[892,14338,14339,14343],{},[895,14340,14341],{},[898,14342,2665],{},[902,14344,2665],{"encoding":904},". Vztah mezi ",[883,14347,14349],{"className":14348},[886],[888,14350,14351],{"xmlns":890},[892,14352,14353,14357],{},[895,14354,14355],{},[898,14356,13339],{},[902,14358,13339],{"encoding":904},[883,14360,14362],{"className":14361},[886],[888,14363,14364],{"xmlns":890},[892,14365,14366,14370],{},[895,14367,14368],{},[898,14369,2665],{},[902,14371,2665],{"encoding":904}," na trhu zboží je proto ",[38,14374,14375],{},"nepřímý"," (klesající křivka).",[115,14378,14380],{"id":14379},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,14382,14383,14384,14402,14403,4254,14421,14424],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,14385,14387],{"className":14386},[886],[888,14388,14389],{"xmlns":890},[892,14390,14391,14399],{},[895,14392,14393],{},[2115,14394,14395,14397],{},[898,14396,2995],{},[898,14398,2047],{},[902,14400,14401],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,14404,14406],{"className":14405},[886],[888,14407,14408],{"xmlns":890},[892,14409,14410,14418],{},[895,14411,14412],{},[2115,14413,14414,14416],{},[898,14415,2995],{},[898,14417,3004],{},[902,14419,14420],{"encoding":904},"M^S",[38,14422,14423],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,14426,14427],{},[883,14428,14430],{"className":14429},[886],[888,14431,14432],{"xmlns":890},[892,14433,14434,14452],{},[895,14435,14436,14442,14444,14450],{},[2115,14437,14438,14440],{},[898,14439,2995],{},[898,14441,3004],{},[1651,14443,1738],{},[2115,14445,14446,14448],{},[898,14447,2995],{},[1651,14449,2668],{},[898,14451,1882],{"mathvariant":1910},[902,14453,14454],{"encoding":904},"M^S = M^*.",[724,14456,14457,14460],{},[38,14458,14459],{},"Poptávka"," po penězích má tři zdroje:",[120,14462,14463,14472,14481],{},[123,14464,14465,11325,14468,14471],{},[38,14466,14467],{},"transakční poptávka",[614,14469,14470],{},"transactions demand",") — peníze pro nákup zboží,",[123,14473,14474,11325,14477,14480],{},[38,14475,14476],{},"opatrnostní poptávka",[614,14478,14479],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,14482,14483,11325,14486,14489],{},[38,14484,14485],{},"spekulační poptávka",[614,14487,14488],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,14491,14492,14493,14511],{},"Součet transakční a opatrnostní poptávky ",[883,14494,14496],{"className":14495},[886],[888,14497,14498],{"xmlns":890},[892,14499,14500,14508],{},[895,14501,14502],{},[1686,14503,14504,14506],{},[898,14505,1807],{},[1692,14507,1694],{},[902,14509,14510],{"encoding":904},"L_1"," je úměrný důchodu:",[724,14513,14514],{},[883,14515,14517],{"className":14516},[886],[888,14518,14519],{"xmlns":890},[892,14520,14521,14559],{},[895,14522,14523,14529,14531,14538,14540,14542,14544,14546,14548,14554,14556],{},[1686,14524,14525,14527],{},[898,14526,1807],{},[1692,14528,1694],{},[1651,14530,1738],{},[1686,14532,14533,14536],{},[898,14534,14535],{},"k",[1692,14537,1694],{},[898,14539,2665],{},[1651,14541,1661],{"separator":1660},[7185,14543],{"width":7187},[1692,14545,1741],{},[1651,14547,2319],{},[1686,14549,14550,14552],{},[898,14551,14535],{},[1692,14553,1694],{},[1651,14555,2319],{},[1692,14557,14558],{},"1.",[902,14560,14561],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,14563,14564,14565,14583,14584,1343,14597,14614],{},"Spekulační poptávka ",[883,14566,14568],{"className":14567},[886],[888,14569,14570],{"xmlns":890},[892,14571,14572,14580],{},[895,14573,14574],{},[1686,14575,14576,14578],{},[898,14577,1807],{},[1692,14579,1703],{},[902,14581,14582],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,14585,14587],{"className":14586},[886],[888,14588,14589],{"xmlns":890},[892,14590,14591,14595],{},[895,14592,14593],{},[898,14594,13339],{},[902,14596,13339],{"encoding":904},[883,14598,14600],{"className":14599},[886],[888,14601,14602],{"xmlns":890},[892,14603,14604,14612],{},[895,14605,14606],{},[1686,14607,14608,14610],{},[898,14609,1807],{},[1692,14611,1703],{},[902,14613,14582],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,14616,14617],{},[883,14618,14620],{"className":14619},[886],[888,14621,14622],{"xmlns":890},[892,14623,14624,14678],{},[895,14625,14626,14632,14634,14640,14642,14644,14650,14652,14654,14660,14662,14664,14666,14668,14674,14676],{},[1686,14627,14628,14630],{},[898,14629,1807],{},[1692,14631,1703],{},[1651,14633,1738],{},[1686,14635,14636,14638],{},[898,14637,14535],{},[1692,14639,1703],{},[898,14641,13339],{},[1651,14643,1839],{},[1686,14645,14646,14648],{},[898,14647,14535],{},[1692,14649,3521],{},[1651,14651,1661],{"separator":1660},[7185,14653],{"width":7187},[1686,14655,14656,14658],{},[898,14657,14535],{},[1692,14659,1703],{},[1651,14661,2319],{},[1692,14663,1741],{},[1651,14665,1661],{"separator":1660},[1843,14667,3631],{},[1686,14669,14670,14672],{},[898,14671,14535],{},[1692,14673,3521],{},[1651,14675,2390],{},[1692,14677,13758],{},[902,14679,14680],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,14682,14683],{},"Celková poptávka po penězích:",[724,14685,14686],{},[883,14687,14689],{"className":14688},[886],[888,14690,14691],{"xmlns":890},[892,14692,14693,14747],{},[895,14694,14695,14701,14703,14709,14711,14717,14719,14725,14727,14729,14735,14737,14739,14745],{},[2115,14696,14697,14699],{},[898,14698,2995],{},[898,14700,2047],{},[1651,14702,1738],{},[1686,14704,14705,14707],{},[898,14706,1807],{},[1692,14708,1694],{},[1651,14710,1839],{},[1686,14712,14713,14715],{},[898,14714,1807],{},[1692,14716,1703],{},[1651,14718,1738],{},[1686,14720,14721,14723],{},[898,14722,14535],{},[1692,14724,1694],{},[898,14726,2665],{},[1651,14728,1839],{},[1686,14730,14731,14733],{},[898,14732,14535],{},[1692,14734,1703],{},[898,14736,13339],{},[1651,14738,1839],{},[1686,14740,14741,14743],{},[898,14742,14535],{},[1692,14744,3521],{},[898,14746,1882],{"mathvariant":1910},[902,14748,14749],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,14751,14752,14753,1793],{},"Podmínka rovnováhy na trhu peněz ",[883,14754,14756],{"className":14755},[886],[888,14757,14758],{"xmlns":890},[892,14759,14760,14776],{},[895,14761,14762,14768,14770],{},[2115,14763,14764,14766],{},[898,14765,2995],{},[898,14767,2047],{},[1651,14769,1738],{},[2115,14771,14772,14774],{},[898,14773,2995],{},[1651,14775,2668],{},[902,14777,14778],{"encoding":904},"M^D = M^*",[724,14780,14781],{},[883,14782,14784],{"className":14783},[886],[888,14785,14786],{"xmlns":890},[892,14787,14788,14835],{},[895,14789,14790,14796,14798,14804,14806,14808,14814,14816,14818,14824,14826,14828,14830,14833],{},[2115,14791,14792,14794],{},[898,14793,2995],{},[1651,14795,2668],{},[1651,14797,1738],{},[1686,14799,14800,14802],{},[898,14801,14535],{},[1692,14803,1694],{},[898,14805,2665],{},[1651,14807,1839],{},[1686,14809,14810,14812],{},[898,14811,14535],{},[1692,14813,1703],{},[898,14815,13339],{},[1651,14817,1839],{},[1686,14819,14820,14822],{},[898,14821,14535],{},[1692,14823,3521],{},[1651,14825,1661],{"separator":1660},[7185,14827],{"width":7187},[1651,14829,1654],{"stretchy":1653},[1692,14831,14832],{},"7.15",[1651,14834,1667],{"stretchy":1653},[902,14836,14837],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,14839,14840,14841,4477],{},"po úpravě (vyjádření ",[883,14842,14844],{"className":14843},[886],[888,14845,14846],{"xmlns":890},[892,14847,14848,14852],{},[895,14849,14850],{},[898,14851,2665],{},[902,14853,2665],{"encoding":904},[724,14855,14856],{},[883,14857,14859],{"className":14858},[886],[888,14860,14861],{"xmlns":890},[892,14862,14863,14938],{},[895,14864,14865,14929,14931,14933,14936],{},[14130,14866,14867],{"notation":14132},[2938,14868,14869],{"scriptlevel":1741,"displaystyle":1653},[2938,14870,14871],{"scriptlevel":1741,"displaystyle":1653},[2938,14872,14873],{"scriptlevel":1741,"displaystyle":1660},[895,14874,14875,14877,14879,14881,14883,14897,14899,14901,14903,14927],{},[1843,14876,1845],{},[898,14878,2665],{},[1651,14880,1738],{},[1651,14882,2181],{},[2446,14884,14885,14891],{},[1686,14886,14887,14889],{},[898,14888,14535],{},[1692,14890,1703],{},[1686,14892,14893,14895],{},[898,14894,14535],{},[1692,14896,1694],{},[1843,14898,1845],{},[898,14900,13339],{},[1651,14902,1839],{},[2446,14904,14905,14921],{},[895,14906,14907,14913,14915],{},[2115,14908,14909,14911],{},[898,14910,2995],{},[1651,14912,2668],{},[1651,14914,2181],{},[1686,14916,14917,14919],{},[898,14918,14535],{},[1692,14920,3521],{},[1686,14922,14923,14925],{},[898,14924,14535],{},[1692,14926,1694],{},[1843,14928,1845],{},[7185,14930],{"width":7187},[1651,14932,1654],{"stretchy":1653},[1692,14934,14935],{},"7.16",[1651,14937,1667],{"stretchy":1653},[902,14939,14940],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,14942,14199,14943,11325,14946,14949,14950,14210,14953,14213,14956,14236,14977,15009,15010,15032,15033,15035,15036,15038],{},[38,14944,14945],{},"funkce LM",[614,14947,14948],{},"LM schedule","), její graf ",[38,14951,14952],{},"křivka LM",[38,14954,14955],{},"rostoucí",[883,14957,14959],{"className":14958},[886],[888,14960,14961],{"xmlns":890},[892,14962,14963,14975],{},[895,14964,14965,14967,14969,14971,14973],{},[1651,14966,1654],{"stretchy":1653},[898,14968,13339],{},[1651,14970,1661],{"separator":1660},[898,14972,2665],{},[1651,14974,1667],{"stretchy":1653},[902,14976,14235],{"encoding":904},[883,14978,14980],{"className":14979},[886],[888,14981,14982],{"xmlns":890},[892,14983,14984,15006],{},[895,14985,14986,14988,15002,15004],{},[1651,14987,2181],{},[2446,14989,14990,14996],{},[1686,14991,14992,14994],{},[898,14993,14535],{},[1692,14995,1703],{},[1686,14997,14998,15000],{},[898,14999,14535],{},[1692,15001,1694],{},[1651,15003,2390],{},[1692,15005,1741],{},[902,15007,15008],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,15011,15013],{"className":15012},[886],[888,15014,15015],{"xmlns":890},[892,15016,15017,15029],{},[895,15018,15019,15025,15027],{},[1686,15020,15021,15023],{},[898,15022,14535],{},[1692,15024,1703],{},[1651,15026,2319],{},[1692,15028,1741],{},[902,15030,15031],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,15034,1807],{},"iquidity of ",[38,15037,2995],{},"oney.",[5179,15040,15041],{},[724,15042,15043,15045,15046,15059,15060,15088,15089,15106,15107,15120,15121,15138,15139,5197,15152,15165,15166,15169],{},[883,15044,5465],{}," Intuice — proč LM roste\nVyšší důchod ",[883,15047,15049],{"className":15048},[886],[888,15050,15051],{"xmlns":890},[892,15052,15053,15057],{},[895,15054,15055],{},[898,15056,2665],{},[902,15058,2665],{"encoding":904}," → větší transakční poptávka po penězích ",[883,15061,15063],{"className":15062},[886],[888,15064,15065],{"xmlns":890},[892,15066,15067,15085],{},[895,15068,15069,15075,15077,15083],{},[1686,15070,15071,15073],{},[898,15072,1807],{},[1692,15074,1694],{},[1651,15076,1738],{},[1686,15078,15079,15081],{},[898,15080,14535],{},[1692,15082,1694],{},[898,15084,2665],{},[902,15086,15087],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,15090,15092],{"className":15091},[886],[888,15093,15094],{"xmlns":890},[892,15095,15096,15104],{},[895,15097,15098],{},[2115,15099,15100,15102],{},[898,15101,2995],{},[1651,15103,2668],{},[902,15105,13448],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,15108,15110],{"className":15109},[886],[888,15111,15112],{"xmlns":890},[892,15113,15114,15118],{},[895,15115,15116],{},[898,15117,13339],{},[902,15119,13339],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,15122,15124],{"className":15123},[886],[888,15125,15126],{"xmlns":890},[892,15127,15128,15136],{},[895,15129,15130],{},[1686,15131,15132,15134],{},[898,15133,1807],{},[1692,15135,1703],{},[902,15137,14582],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,15140,15142],{"className":15141},[886],[888,15143,15144],{"xmlns":890},[892,15145,15146,15150],{},[895,15147,15148],{},[898,15149,2665],{},[902,15151,2665],{"encoding":904},[883,15153,15155],{"className":15154},[886],[888,15156,15157],{"xmlns":890},[892,15158,15159,15163],{},[895,15160,15161],{},[898,15162,13339],{},[902,15164,13339],{"encoding":904}," na trhu peněz je proto ",[38,15167,15168],{},"přímý"," (rostoucí křivka).",[115,15171,15173],{"id":15172},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,15175,15176,15177,15180,15181,3246,15184,5197,15202,3246,15205,15223,15224,15242,15243,15261,15262,15278,15279,5197,15294,15309,15310,1882],{},"Řešením ",[38,15178,15179],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,15182,15183],{},"rovnovážný důchod",[883,15185,15187],{"className":15186},[886],[888,15188,15189],{"xmlns":890},[892,15190,15191,15199],{},[895,15192,15193],{},[2115,15194,15195,15197],{},[898,15196,2665],{},[898,15198,5561],{},[902,15200,15201],{"encoding":904},"Y^E",[38,15203,15204],{},"rovnovážnou úrokovou míru",[883,15206,15208],{"className":15207},[886],[888,15209,15210],{"xmlns":890},[892,15211,15212,15220],{},[895,15213,15214],{},[2115,15215,15216,15218],{},[898,15217,13339],{},[898,15219,5561],{},[902,15221,15222],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,15225,15227],{"className":15226},[886],[888,15228,15229],{"xmlns":890},[892,15230,15231,15239],{},[895,15232,15233],{},[2115,15234,15235,15237],{},[898,15236,13482],{},[898,15238,5561],{},[902,15240,15241],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,15244,15246],{"className":15245},[886],[888,15247,15248],{"xmlns":890},[892,15249,15250,15258],{},[895,15251,15252],{},[2115,15253,15254,15256],{},[898,15255,3001],{},[898,15257,5561],{},[902,15259,15260],{"encoding":904},"C^E",". Graficky jde o ",[38,15263,15264,15265],{},"průsečík ",[883,15266,15268],{"className":15267},[886],[888,15269,15270],{"xmlns":890},[892,15271,15272,15276],{},[895,15273,15274],{},[898,15275,5561],{},[902,15277,5561],{"encoding":904}," křivek ",[883,15280,15282],{"className":15281},[886],[888,15283,15284],{"xmlns":890},[892,15285,15286,15292],{},[895,15287,15288,15290],{},[898,15289,13482],{},[898,15291,3004],{},[902,15293,13349],{"encoding":904},[883,15295,15297],{"className":15296},[886],[888,15298,15299],{"xmlns":890},[892,15300,15301,15307],{},[895,15302,15303,15305],{},[898,15304,1807],{},[898,15306,2995],{},[902,15308,13356],{"encoding":904}," v rovině ",[883,15311,15313],{"className":15312},[886],[888,15314,15315],{"xmlns":890},[892,15316,15317,15329],{},[895,15318,15319,15321,15323,15325,15327],{},[1651,15320,1654],{"stretchy":1653},[898,15322,13339],{},[1651,15324,1661],{"separator":1660},[898,15326,2665],{},[1651,15328,1667],{"stretchy":1653},[902,15330,14235],{"encoding":904},[724,15332,15333],{},[614,15334,15335,15336,15357,15358,15373,15374,15389,15390,15403,15404,15421,15422,13426,15435,15421,15452,15465,15466,15479],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,15337,15339],{"className":15338},[886],[888,15340,15341],{"xmlns":890},[892,15342,15343,15355],{},[895,15344,15345,15347,15349,15351,15353],{},[1651,15346,1654],{"stretchy":1653},[898,15348,13339],{},[1651,15350,1661],{"separator":1660},[898,15352,2665],{},[1651,15354,1667],{"stretchy":1653},[902,15356,14235],{"encoding":904},". Rostoucí přímka ",[883,15359,15361],{"className":15360},[886],[888,15362,15363],{"xmlns":890},[892,15364,15365,15371],{},[895,15366,15367,15369],{},[898,15368,1807],{},[898,15370,2995],{},[902,15372,13356],{"encoding":904}," a klesající přímka ",[883,15375,15377],{"className":15376},[886],[888,15378,15379],{"xmlns":890},[892,15380,15381,15387],{},[895,15382,15383,15385],{},[898,15384,13482],{},[898,15386,3004],{},[902,15388,13349],{"encoding":904}," se protínají v bodě ",[883,15391,15393],{"className":15392},[886],[888,15394,15395],{"xmlns":890},[892,15396,15397,15401],{},[895,15398,15399],{},[898,15400,5561],{},[902,15402,5561],{"encoding":904}," se souřadnicemi ",[883,15405,15407],{"className":15406},[886],[888,15408,15409],{"xmlns":890},[892,15410,15411,15419],{},[895,15412,15413],{},[2115,15414,15415,15417],{},[898,15416,13339],{},[898,15418,5561],{},[902,15420,15222],{"encoding":904}," (na ose ",[883,15423,15425],{"className":15424},[886],[888,15426,15427],{"xmlns":890},[892,15428,15429,15433],{},[895,15430,15431],{},[898,15432,13339],{},[902,15434,13339],{"encoding":904},[883,15436,15438],{"className":15437},[886],[888,15439,15440],{"xmlns":890},[892,15441,15442,15450],{},[895,15443,15444],{},[2115,15445,15446,15448],{},[898,15447,2665],{},[898,15449,5561],{},[902,15451,15201],{"encoding":904},[883,15453,15455],{"className":15454},[886],[888,15456,15457],{"xmlns":890},[892,15458,15459,15463],{},[895,15460,15461],{},[898,15462,2665],{},[902,15464,2665],{"encoding":904},"); tečkované čáry z ",[883,15467,15469],{"className":15468},[886],[888,15470,15471],{"xmlns":890},[892,15472,15473,15477],{},[895,15474,15475],{},[898,15476,5561],{},[902,15478,5561],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[5179,15481,15482,15487],{},[724,15483,15484,15486],{},[883,15485,5879],{}," Postup — jak najít IS-LM rovnováhu",[152,15488,15489,15565,15633,15691,15764],{},[123,15490,15491,15494,15495,5197,15515,15535,15536,5197,15549,15562,15563,1882],{},[38,15492,15493],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,15496,15498],{"className":15497},[886],[888,15499,15500],{"xmlns":890},[892,15501,15502,15512],{},[895,15503,15504,15506,15508,15510],{},[898,15505,3001],{},[1651,15507,1654],{"stretchy":1653},[898,15509,2665],{},[1651,15511,1667],{"stretchy":1653},[902,15513,15514],{"encoding":904},"C(Y)",[883,15516,15518],{"className":15517},[886],[888,15519,15520],{"xmlns":890},[892,15521,15522,15532],{},[895,15523,15524,15526,15528,15530],{},[898,15525,13482],{},[1651,15527,1654],{"stretchy":1653},[898,15529,13339],{},[1651,15531,1667],{"stretchy":1653},[902,15533,15534],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,15537,15539],{"className":15538},[886],[888,15540,15541],{"xmlns":890},[892,15542,15543,15547],{},[895,15544,15545],{},[898,15546,2665],{},[902,15548,2665],{"encoding":904},[883,15550,15552],{"className":15551},[886],[888,15553,15554],{"xmlns":890},[892,15555,15556,15560],{},[895,15557,15558],{},[898,15559,13339],{},[902,15561,13339],{"encoding":904}," — dostaneš rovnici ",[38,15564,13349],{},[123,15566,15567,15570,15571,5197,15588,15605,15606,15562,15631,1882],{},[38,15568,15569],{},"Z trhu peněz (7.15)"," dosaď ",[883,15572,15574],{"className":15573},[886],[888,15575,15576],{"xmlns":890},[892,15577,15578,15586],{},[895,15579,15580],{},[1686,15581,15582,15584],{},[898,15583,1807],{},[1692,15585,1694],{},[902,15587,14510],{"encoding":904},[883,15589,15591],{"className":15590},[886],[888,15592,15593],{"xmlns":890},[892,15594,15595,15603],{},[895,15596,15597],{},[1686,15598,15599,15601],{},[898,15600,1807],{},[1692,15602,1703],{},[902,15604,14582],{"encoding":904}," a vztah ",[883,15607,15609],{"className":15608},[886],[888,15610,15611],{"xmlns":890},[892,15612,15613,15629],{},[895,15614,15615,15621,15623],{},[2115,15616,15617,15619],{},[898,15618,2995],{},[898,15620,2047],{},[1651,15622,1738],{},[2115,15624,15625,15627],{},[898,15626,2995],{},[1651,15628,2668],{},[902,15630,14778],{"encoding":904},[38,15632,13356],{},[123,15634,15635,15638,15639,5197,15652,15665,15666,15690],{},[38,15636,15637],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,15640,15642],{"className":15641},[886],[888,15643,15644],{"xmlns":890},[892,15645,15646,15650],{},[895,15647,15648],{},[898,15649,2665],{},[902,15651,2665],{"encoding":904},[883,15653,15655],{"className":15654},[886],[888,15656,15657],{"xmlns":890},[892,15658,15659,15663],{},[895,15660,15661],{},[898,15662,13339],{},[902,15664,13339],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,15667,15669],{"className":15668},[886],[888,15670,15671],{"xmlns":890},[892,15672,15673,15687],{},[895,15674,15675,15677,15679,15681,15683,15685],{},[898,15676,2665],{},[1651,15678,1738],{},[898,15680,1649],{},[1651,15682,1654],{"stretchy":1653},[898,15684,13339],{},[1651,15686,1667],{"stretchy":1653},[902,15688,15689],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,15692,15693,3246,15696,5197,15730,1882],{},[38,15694,15695],{},"Zpětně dopočítej",[883,15697,15699],{"className":15698},[886],[888,15700,15701],{"xmlns":890},[892,15702,15703,15727],{},[895,15704,15705,15711,15713,15715,15717,15723,15725],{},[2115,15706,15707,15709],{},[898,15708,3001],{},[898,15710,5561],{},[1651,15712,1738],{},[898,15714,207],{},[1843,15716,1845],{},[2115,15718,15719,15721],{},[898,15720,2665],{},[898,15722,5561],{},[1651,15724,1839],{},[898,15726,2268],{},[902,15728,15729],{"encoding":904},"C^E = a\\,Y^E + b",[883,15731,15733],{"className":15732},[886],[888,15734,15735],{"xmlns":890},[892,15736,15737,15761],{},[895,15738,15739,15745,15747,15749,15751,15757,15759],{},[2115,15740,15741,15743],{},[898,15742,13482],{},[898,15744,5561],{},[1651,15746,1738],{},[898,15748,3490],{},[1843,15750,1845],{},[2115,15752,15753,15755],{},[898,15754,13339],{},[898,15756,5561],{},[1651,15758,1839],{},[898,15760,3542],{},[902,15762,15763],{"encoding":904},"I^E = c\\,r^E + d",[123,15765,15766,15769,15770,15804,15805,15859],{},[38,15767,15768],{},"Ověř:"," musí platit ",[883,15771,15773],{"className":15772},[886],[888,15774,15775],{"xmlns":890},[892,15776,15777,15801],{},[895,15778,15779,15785,15787,15793,15795],{},[2115,15780,15781,15783],{},[898,15782,2665],{},[898,15784,5561],{},[1651,15786,1738],{},[2115,15788,15789,15791],{},[898,15790,3001],{},[898,15792,5561],{},[1651,15794,1839],{},[2115,15796,15797,15799],{},[898,15798,13482],{},[898,15800,5561],{},[902,15802,15803],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,15806,15808],{"className":15807},[886],[888,15809,15810],{"xmlns":890},[892,15811,15812,15856],{},[895,15813,15814,15820,15822,15828,15834,15836,15842,15848,15850],{},[2115,15815,15816,15818],{},[898,15817,2995],{},[1651,15819,2668],{},[1651,15821,1738],{},[1686,15823,15824,15826],{},[898,15825,14535],{},[1692,15827,1694],{},[2115,15829,15830,15832],{},[898,15831,2665],{},[898,15833,5561],{},[1651,15835,1839],{},[1686,15837,15838,15840],{},[898,15839,14535],{},[1692,15841,1703],{},[2115,15843,15844,15846],{},[898,15845,13339],{},[898,15847,5561],{},[1651,15849,1839],{},[1686,15851,15852,15854],{},[898,15853,14535],{},[1692,15855,3521],{},[902,15857,15858],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,15861,15863],{"id":15862},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,15865,15866],{},"Pro trh zboží jsou dány:",[120,15868,15869,15897],{},[123,15870,15871,15872,1661],{},"spotřeba ",[883,15873,15875],{"className":15874},[886],[888,15876,15877],{"xmlns":890},[892,15878,15879,15894],{},[895,15880,15881,15883,15885,15888,15890,15892],{},[898,15882,3001],{},[1651,15884,1738],{},[1692,15886,15887],{},"0,8",[898,15889,2665],{},[1651,15891,1839],{},[1692,15893,4416],{},[902,15895,15896],{"encoding":904},"C = 0{,}8Y + 100",[123,15898,15899,15900,1882],{},"investice ",[883,15901,15903],{"className":15902},[886],[888,15904,15905],{"xmlns":890},[892,15906,15907,15923],{},[895,15908,15909,15911,15913,15915,15917,15919,15921],{},[898,15910,13482],{},[1651,15912,1738],{},[1651,15914,2181],{},[1692,15916,10340],{},[898,15918,13339],{},[1651,15920,1839],{},[1692,15922,4111],{},[902,15924,15925],{"encoding":904},"I = -20r + 1000",[724,15927,15928],{},"Pro trh peněz:",[120,15930,15931,15957,15989],{},[123,15932,15933,1661],{},[883,15934,15936],{"className":15935},[886],[888,15937,15938],{"xmlns":890},[892,15939,15940,15954],{},[895,15941,15942,15948,15950,15952],{},[1686,15943,15944,15946],{},[898,15945,1807],{},[1692,15947,1694],{},[1651,15949,1738],{},[1692,15951,4122],{},[898,15953,2665],{},[902,15955,15956],{"encoding":904},"L_1 = 0{,}1Y",[123,15958,15959,1661],{},[883,15960,15962],{"className":15961},[886],[888,15963,15964],{"xmlns":890},[892,15965,15966,15986],{},[895,15967,15968,15974,15976,15978,15980,15982,15984],{},[1686,15969,15970,15972],{},[898,15971,1807],{},[1692,15973,1703],{},[1651,15975,1738],{},[1651,15977,2181],{},[1692,15979,6311],{},[898,15981,13339],{},[1651,15983,1839],{},[1692,15985,9910],{},[902,15987,15988],{"encoding":904},"L_2 = -25r + 2000",[123,15990,15991,15992,1882],{},"nabídka peněz ",[883,15993,15995],{"className":15994},[886],[888,15996,15997],{"xmlns":890},[892,15998,15999,16012],{},[895,16000,16001,16007,16009],{},[2115,16002,16003,16005],{},[898,16004,2995],{},[1651,16006,2668],{},[1651,16008,1738],{},[1692,16010,16011],{},"2375",[902,16013,16014],{"encoding":904},"M^* = 2375",[724,16016,16017,16020,16021,1793],{},[38,16018,16019],{},"Funkce IS"," — dosazením do (7.13) ",[883,16022,16024],{"className":16023},[886],[888,16025,16026],{"xmlns":890},[892,16027,16028,16040],{},[895,16029,16030,16032,16034,16036,16038],{},[898,16031,2665],{},[1651,16033,1738],{},[898,16035,3001],{},[1651,16037,1839],{},[898,16039,13482],{},[902,16041,16042],{"encoding":904},"Y = C + I",[724,16044,16045],{},[883,16046,16048],{"className":16047},[886],[888,16049,16050],{"xmlns":890},[892,16051,16052,16078],{},[895,16053,16054,16056,16058,16060,16062,16064,16066,16068,16070,16072,16074,16076],{},[898,16055,2665],{},[1651,16057,1738],{},[1692,16059,15887],{},[898,16061,2665],{},[1651,16063,1839],{},[1692,16065,4416],{},[1651,16067,2181],{},[1692,16069,10340],{},[898,16071,13339],{},[1651,16073,1839],{},[1692,16075,4111],{},[1651,16077,1661],{"separator":1660},[902,16079,16080],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,16082,16083],{},"tj.",[724,16085,16086],{},[883,16087,16089],{"className":16088},[886],[888,16090,16091],{"xmlns":890},[892,16092,16093,16118],{},[895,16094,16095,16097,16099,16101,16103,16105,16107,16110,16112,16114,16116],{},[1692,16096,4166],{},[898,16098,2665],{},[1651,16100,1839],{},[1692,16102,10340],{},[898,16104,13339],{},[1651,16106,1738],{},[1692,16108,16109],{},"1100.",[7185,16111],{"width":7187},[1651,16113,1654],{"stretchy":1653},[1843,16115,13349],{},[1651,16117,1667],{"stretchy":1653},[902,16119,16120],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,16122,16123,16126,16127,1793],{},[38,16124,16125],{},"Funkce LM"," — dosazením do (7.15) ",[883,16128,16130],{"className":16129},[886],[888,16131,16132],{"xmlns":890},[892,16133,16134,16158],{},[895,16135,16136,16142,16144,16150,16152],{},[2115,16137,16138,16140],{},[898,16139,2995],{},[1651,16141,2668],{},[1651,16143,1738],{},[1686,16145,16146,16148],{},[898,16147,1807],{},[1692,16149,1694],{},[1651,16151,1839],{},[1686,16153,16154,16156],{},[898,16155,1807],{},[1692,16157,1703],{},[902,16159,16160],{"encoding":904},"M^* = L_1 + L_2",[724,16162,16163],{},[883,16164,16166],{"className":16165},[886],[888,16167,16168],{"xmlns":890},[892,16169,16170,16192],{},[895,16171,16172,16174,16176,16178,16180,16182,16184,16186,16188,16190],{},[1692,16173,16011],{},[1651,16175,1738],{},[1692,16177,4122],{},[898,16179,2665],{},[1651,16181,2181],{},[1692,16183,6311],{},[898,16185,13339],{},[1651,16187,1839],{},[1692,16189,9910],{},[1651,16191,1661],{"separator":1660},[902,16193,16194],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,16196,16083],{},[724,16198,16199],{},[883,16200,16202],{"className":16201},[886],[888,16203,16204],{"xmlns":890},[892,16205,16206,16231],{},[895,16207,16208,16210,16212,16214,16216,16218,16220,16223,16225,16227,16229],{},[1692,16209,4122],{},[898,16211,2665],{},[1651,16213,2181],{},[1692,16215,6311],{},[898,16217,13339],{},[1651,16219,1738],{},[1692,16221,16222],{},"375.",[7185,16224],{"width":7187},[1651,16226,1654],{"stretchy":1653},[1843,16228,13356],{},[1651,16230,1667],{"stretchy":1653},[902,16232,16233],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,16235,16236,16239,16240,16265],{},[38,16237,16238],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,16241,16243],{"className":16242},[886],[888,16244,16245],{"xmlns":890},[892,16246,16247,16262],{},[895,16248,16249,16251,16253,16256,16258,16260],{},[898,16250,2665],{},[1651,16252,1738],{},[1692,16254,16255],{},"5500",[1651,16257,2181],{},[1692,16259,4416],{},[898,16261,13339],{},[902,16263,16264],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,16267,16268],{},[883,16269,16271],{"className":16270},[886],[888,16272,16273],{"xmlns":890},[892,16274,16275,16361],{},[895,16276,16277,16279,16281,16283,16285,16287,16289,16291,16293,16295,16297,16299,16302,16304,16307,16309,16312,16314,16316,16318,16320,16322,16324,16326,16328,16330,16332,16334,16337,16339,16341,16344,16346,16348,16350,16356,16358],{},[1692,16278,4122],{},[1651,16280,1654],{"stretchy":1653},[1692,16282,16255],{},[1651,16284,2181],{},[1692,16286,4416],{},[898,16288,13339],{},[1651,16290,1667],{"stretchy":1653},[1651,16292,2181],{},[1692,16294,6311],{},[898,16296,13339],{},[1651,16298,1738],{},[1692,16300,16301],{},"375",[1843,16303,5295],{},[1651,16305,16306],{},"⟹",[1843,16308,5295],{},[1692,16310,16311],{},"550",[1651,16313,2181],{},[1692,16315,4190],{},[898,16317,13339],{},[1651,16319,2181],{},[1692,16321,6311],{},[898,16323,13339],{},[1651,16325,1738],{},[1692,16327,16301],{},[1843,16329,5295],{},[1651,16331,16306],{},[1843,16333,5295],{},[1692,16335,16336],{},"35",[898,16338,13339],{},[1651,16340,1738],{},[1692,16342,16343],{},"175",[1843,16345,5295],{},[1651,16347,16306],{},[1843,16349,5295],{},[2115,16351,16352,16354],{},[898,16353,13339],{},[898,16355,5561],{},[1651,16357,1738],{},[1692,16359,16360],{},"5.",[902,16362,16363],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,16365,16366],{},[38,16367,16368],{},"Zpětné dosazení:",[120,16370,16371,16417,16454],{},[123,16372,16373,1661],{},[883,16374,16376],{"className":16375},[886],[888,16377,16378],{"xmlns":890},[892,16379,16380,16414],{},[895,16381,16382,16388,16390,16392,16394,16396,16398,16400,16402,16404,16406,16409,16411],{},[2115,16383,16384,16386],{},[898,16385,2665],{},[898,16387,5561],{},[1651,16389,1738],{},[1692,16391,16255],{},[1651,16393,2181],{},[1692,16395,4416],{},[1651,16397,4503],{},[1692,16399,3574],{},[1651,16401,1738],{},[1692,16403,16255],{},[1651,16405,2181],{},[1692,16407,16408],{},"500",[1651,16410,1738],{},[1692,16412,16413],{},"5000",[902,16415,16416],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,16418,16419,1661],{},[883,16420,16422],{"className":16421},[886],[888,16423,16424],{"xmlns":890},[892,16425,16426,16451],{},[895,16427,16428,16434,16436,16438,16440,16442,16444,16446,16448],{},[2115,16429,16430,16432],{},[898,16431,3001],{},[898,16433,5561],{},[1651,16435,1738],{},[1692,16437,15887],{},[1651,16439,4503],{},[1692,16441,16413],{},[1651,16443,1839],{},[1692,16445,4416],{},[1651,16447,1738],{},[1692,16449,16450],{},"4100",[902,16452,16453],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,16455,16456,1882],{},[883,16457,16459],{"className":16458},[886],[888,16460,16461],{"xmlns":890},[892,16462,16463,16490],{},[895,16464,16465,16471,16473,16475,16477,16479,16481,16483,16485,16487],{},[2115,16466,16467,16469],{},[898,16468,13482],{},[898,16470,5561],{},[1651,16472,1738],{},[1651,16474,2181],{},[1692,16476,10340],{},[1651,16478,4503],{},[1692,16480,3574],{},[1651,16482,1839],{},[1692,16484,4111],{},[1651,16486,1738],{},[1692,16488,16489],{},"900",[902,16491,16492],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,16494,16495,3246,16498,16544],{},[38,16496,16497],{},"Ověření:",[883,16499,16501],{"className":16500},[886],[888,16502,16503],{"xmlns":890},[892,16504,16505,16541],{},[895,16506,16507,16513,16515,16521,16523,16525,16527,16529,16531,16533,16535],{},[2115,16508,16509,16511],{},[898,16510,3001],{},[898,16512,5561],{},[1651,16514,1839],{},[2115,16516,16517,16519],{},[898,16518,13482],{},[898,16520,5561],{},[1651,16522,1738],{},[1692,16524,16450],{},[1651,16526,1839],{},[1692,16528,16489],{},[1651,16530,1738],{},[1692,16532,16413],{},[1651,16534,1738],{},[2115,16536,16537,16539],{},[898,16538,2665],{},[898,16540,5561],{},[902,16542,16543],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,16546,16547],{},[883,16548,16550],{"className":16549},[886],[888,16551,16552],{"xmlns":890},[892,16553,16554,16624],{},[895,16555,16556],{},[14130,16557,16558],{"notation":14132},[2938,16559,16560],{"scriptlevel":1741,"displaystyle":1653},[2938,16561,16562],{"scriptlevel":1741,"displaystyle":1653},[2938,16563,16564],{"scriptlevel":1741,"displaystyle":1660},[895,16565,16566,16568,16574,16576,16578,16580,16583,16589,16591,16593,16595,16597,16603,16605,16607,16609,16611,16617,16619,16622],{},[1843,16567,1845],{},[2115,16569,16570,16572],{},[898,16571,2665],{},[898,16573,5561],{},[1651,16575,1738],{},[1692,16577,16413],{},[1651,16579,1661],{"separator":1660},[7185,16581],{"width":16582},"1em",[2115,16584,16585,16587],{},[898,16586,13339],{},[898,16588,5561],{},[1651,16590,1738],{},[1692,16592,3574],{},[1651,16594,1661],{"separator":1660},[7185,16596],{"width":16582},[2115,16598,16599,16601],{},[898,16600,3001],{},[898,16602,5561],{},[1651,16604,1738],{},[1692,16606,16450],{},[1651,16608,1661],{"separator":1660},[7185,16610],{"width":16582},[2115,16612,16613,16615],{},[898,16614,13482],{},[898,16616,5561],{},[1651,16618,1738],{},[1692,16620,16621],{},"900.",[1843,16623,1845],{},[902,16625,16626],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,16628,16629],{},[614,16630,16631,16632,16645,16646,16659,16660,16675,16676,16689,16690,16705,16706,16719,16720,16733,16734,1882],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,16633,16635],{"className":16634},[886],[888,16636,16637],{"xmlns":890},[892,16638,16639,16643],{},[895,16640,16641],{},[898,16642,2665],{},[902,16644,2665],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,16647,16649],{"className":16648},[886],[888,16650,16651],{"xmlns":890},[892,16652,16653,16657],{},[895,16654,16655],{},[898,16656,13339],{},[902,16658,13339],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,16661,16663],{"className":16662},[886],[888,16664,16665],{"xmlns":890},[892,16666,16667,16673],{},[895,16668,16669,16671],{},[898,16670,1807],{},[898,16672,2995],{},[902,16674,13356],{"encoding":904}," stoupá z oblasti nízkých ",[883,16677,16679],{"className":16678},[886],[888,16680,16681],{"xmlns":890},[892,16682,16683,16687],{},[895,16684,16685],{},[898,16686,13339],{},[902,16688,13339],{"encoding":904},", přímka ",[883,16691,16693],{"className":16692},[886],[888,16694,16695],{"xmlns":890},[892,16696,16697,16703],{},[895,16698,16699,16701],{},[898,16700,13482],{},[898,16702,3004],{},[902,16704,13349],{"encoding":904}," klesá a protíná osu ",[883,16707,16709],{"className":16708},[886],[888,16710,16711],{"xmlns":890},[892,16712,16713,16717],{},[895,16714,16715],{},[898,16716,13339],{},[902,16718,13339],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,16721,16723],{"className":16722},[886],[888,16724,16725],{"xmlns":890},[892,16726,16727,16731],{},[895,16728,16729],{},[898,16730,5561],{},[902,16732,5561],{"encoding":904}," leží v bodě ",[883,16735,16737],{"className":16736},[886],[888,16738,16739],{"xmlns":890},[892,16740,16741,16763],{},[895,16742,16743,16745,16747,16749,16751,16753,16755,16757,16759,16761],{},[1651,16744,2261],{"stretchy":1653},[898,16746,13339],{},[1651,16748,1738],{},[1692,16750,3574],{},[1651,16752,1661],{"separator":1660},[1843,16754,3631],{},[898,16756,2665],{},[1651,16758,1738],{},[1692,16760,16413],{},[1651,16762,2279],{"stretchy":1653},[902,16764,16765],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,16767,16769],{"id":16768},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,16771,16772,16775,16776,16789,16790,8322,16803,16806,16807,16825,16826,16843,16844,16861,16862,16875,16876,16889],{},[38,16773,16774],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,16777,16779],{"className":16778},[886],[888,16780,16781],{"xmlns":890},[892,16782,16783,16787],{},[895,16784,16785],{},[898,16786,13410],{},[902,16788,13410],{"encoding":904}," nebo snížení daní ",[883,16791,16793],{"className":16792},[886],[888,16794,16795],{"xmlns":890},[892,16796,16797,16801],{},[895,16798,16799],{},[898,16800,4104],{},[902,16802,4104],{"encoding":904},[38,16804,16805],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,16808,16810],{"className":16809},[886],[888,16811,16812],{"xmlns":890},[892,16813,16814,16822],{},[895,16815,16816],{},[2115,16817,16818,16820],{},[898,16819,5561],{},[1651,16821,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,16823,16824],{"encoding":904},"E'"," má vyšší ",[883,16827,16829],{"className":16828},[886],[888,16830,16831],{"xmlns":890},[892,16832,16833,16841],{},[895,16834,16835],{},[2115,16836,16837,16839],{},[898,16838,2665],{},[898,16840,5561],{},[902,16842,15201],{"encoding":904}," i vyšší ",[883,16845,16847],{"className":16846},[886],[888,16848,16849],{"xmlns":890},[892,16850,16851,16859],{},[895,16852,16853],{},[2115,16854,16855,16857],{},[898,16856,13339],{},[898,16858,5561],{},[902,16860,15222],{"encoding":904}," (vyšší ",[883,16863,16865],{"className":16864},[886],[888,16866,16867],{"xmlns":890},[892,16868,16869,16873],{},[895,16870,16871],{},[898,16872,2665],{},[902,16874,2665],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,16877,16879],{"className":16878},[886],[888,16880,16881],{"xmlns":890},[892,16882,16883,16887],{},[895,16884,16885],{},[898,16886,13339],{},[902,16888,13339],{"encoding":904}," nahoru).",[724,16891,16892],{},[1756,16893],{"alt":16894,"className":16895,"src":16896},"imek-posun-is-lm-politiky",[210,1760],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,16898,16899,16902,16903,16920,16921,16924,16925,16942,16943,16960,16961,16974,16975,16994,16995,5230],{},[38,16900,16901],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,16904,16906],{"className":16905},[886],[888,16907,16908],{"xmlns":890},[892,16909,16910,16918],{},[895,16911,16912],{},[2115,16913,16914,16916],{},[898,16915,2995],{},[1651,16917,2668],{},[902,16919,13448],{"encoding":904}," národní bankou — ",[38,16922,16923],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,16926,16928],{"className":16927},[886],[888,16929,16930],{"xmlns":890},[892,16931,16932,16940],{},[895,16933,16934],{},[2115,16935,16936,16938],{},[898,16937,13339],{},[898,16939,5561],{},[902,16941,15222],{"encoding":904}," a vyšší ",[883,16944,16946],{"className":16945},[886],[888,16947,16948],{"xmlns":890},[892,16949,16950,16958],{},[895,16951,16952],{},[2115,16953,16954,16956],{},[898,16955,2665],{},[898,16957,5561],{},[902,16959,15201],{"encoding":904}," (nižší ",[883,16962,16964],{"className":16963},[886],[888,16965,16966],{"xmlns":890},[892,16967,16968,16972],{},[895,16969,16970],{},[898,16971,13339],{},[902,16973,13339],{"encoding":904}," povzbuzuje investice ",[883,16976,16978],{"className":16977},[886],[888,16979,16980],{"xmlns":890},[892,16981,16982,16992],{},[895,16983,16984,16986,16988,16990],{},[898,16985,13482],{},[1651,16987,1654],{"stretchy":1653},[898,16989,13339],{},[1651,16991,1667],{"stretchy":1653},[902,16993,15534],{"encoding":904},", ty zvedají ",[883,16996,16998],{"className":16997},[886],[888,16999,17000],{"xmlns":890},[892,17001,17002,17006],{},[895,17003,17004],{},[898,17005,2665],{},[902,17007,2665],{"encoding":904},[724,17009,17010,17011,17014],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,17012,17013],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,17016,17018],{"id":17017},"klíčové-pojmy","Klíčové pojmy",[120,17020,17021,17094,17140,17222,17272,17339,17396,17437,17470],{},[123,17022,17023,8322,17056,1343,17073,17090,17091,17093],{},[38,17024,17025,17026],{},"Funkce investic ",[883,17027,17029],{"className":17028},[886],[888,17030,17031],{"xmlns":890},[892,17032,17033,17053],{},[895,17034,17035,17037,17039,17041,17043,17045,17047,17049,17051],{},[898,17036,13482],{},[1651,17038,1654],{"stretchy":1653},[898,17040,13339],{},[1651,17042,1667],{"stretchy":1653},[1651,17044,1738],{},[898,17046,3490],{},[898,17048,13339],{},[1651,17050,1839],{},[898,17052,3542],{},[902,17054,17055],{"encoding":904},"I(r) = cr + d",[883,17057,17059],{"className":17058},[886],[888,17060,17061],{"xmlns":890},[892,17062,17063,17071],{},[895,17064,17065,17067,17069],{},[898,17066,3490],{},[1651,17068,2319],{},[1692,17070,1741],{},[902,17072,13813],{"encoding":904},[883,17074,17076],{"className":17075},[886],[888,17077,17078],{"xmlns":890},[892,17079,17080,17088],{},[895,17081,17082,17084,17086],{},[898,17083,3542],{},[1651,17085,2390],{},[1692,17087,1741],{},[902,17089,13792],{"encoding":904},"; ",[38,17092,13817],{}," funkce úrokové míry.",[123,17095,17096,17099,17100,17121,17122,17139],{},[38,17097,17098],{},"Trh zboží"," — rovnováha ",[883,17101,17103],{"className":17102},[886],[888,17104,17105],{"xmlns":890},[892,17106,17107,17119],{},[895,17108,17109,17111,17113,17115,17117],{},[898,17110,2665],{},[1651,17112,1738],{},[898,17114,3001],{},[1651,17116,1839],{},[898,17118,13482],{},[902,17120,16042],{"encoding":904},", ekvivalentně ",[883,17123,17125],{"className":17124},[886],[888,17126,17127],{"xmlns":890},[892,17128,17129,17137],{},[895,17130,17131,17133,17135],{},[898,17132,13482],{},[1651,17134,1738],{},[898,17136,3004],{},[902,17138,14010],{"encoding":904}," (investice = úspory).",[123,17141,17142,11325,17145,17147,17148,17198,17199,14213,17201,1882],{},[38,17143,17144],{},"Křivka IS",[614,17146,13352],{},") — ",[883,17149,17151],{"className":17150},[886],[888,17152,17153],{"xmlns":890},[892,17154,17155,17195],{},[895,17156,17157,17159,17161,17173,17175,17177],{},[898,17158,2665],{},[1651,17160,1738],{},[2446,17162,17163,17165],{},[898,17164,3490],{},[895,17166,17167,17169,17171],{},[1692,17168,1694],{},[1651,17170,2181],{},[898,17172,207],{},[898,17174,13339],{},[1651,17176,1839],{},[2446,17178,17179,17187],{},[895,17180,17181,17183,17185],{},[898,17182,2268],{},[1651,17184,1839],{},[898,17186,3542],{},[895,17188,17189,17191,17193],{},[1692,17190,1694],{},[1651,17192,2181],{},[898,17194,207],{},[902,17196,17197],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,17200,13817],{},[883,17202,17204],{"className":17203},[886],[888,17205,17206],{"xmlns":890},[892,17207,17208,17220],{},[895,17209,17210,17212,17214,17216,17218],{},[1651,17211,1654],{"stretchy":1653},[898,17213,13339],{},[1651,17215,1661],{"separator":1660},[898,17217,2665],{},[1651,17219,1667],{"stretchy":1653},[902,17221,14235],{"encoding":904},[123,17223,17224,17099,17227,17253,17254,1882],{},[38,17225,17226],{},"Trh peněz",[883,17228,17230],{"className":17229},[886],[888,17231,17232],{"xmlns":890},[892,17233,17234,17250],{},[895,17235,17236,17242,17244],{},[2115,17237,17238,17240],{},[898,17239,2995],{},[898,17241,2047],{},[1651,17243,1738],{},[2115,17245,17246,17248],{},[898,17247,2995],{},[898,17249,3004],{},[902,17251,17252],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,17255,17257],{"className":17256},[886],[888,17258,17259],{"xmlns":890},[892,17260,17261,17269],{},[895,17262,17263],{},[2115,17264,17265,17267],{},[898,17266,2995],{},[1651,17268,2668],{},[902,17270,17271],{"encoding":904},"M^* ",[123,17273,17274,8322,17277,1882],{},[38,17275,17276],{},"Transakční, opatrnostní, spekulační poptávka",[883,17278,17280],{"className":17279},[886],[888,17281,17282],{"xmlns":890},[892,17283,17284,17336],{},[895,17285,17286,17292,17294,17300,17302,17308,17310,17316,17318,17320,17326,17328,17330],{},[2115,17287,17288,17290],{},[898,17289,2995],{},[898,17291,2047],{},[1651,17293,1738],{},[1686,17295,17296,17298],{},[898,17297,1807],{},[1692,17299,1694],{},[1651,17301,1839],{},[1686,17303,17304,17306],{},[898,17305,1807],{},[1692,17307,1703],{},[1651,17309,1738],{},[1686,17311,17312,17314],{},[898,17313,14535],{},[1692,17315,1694],{},[898,17317,2665],{},[1651,17319,1839],{},[1686,17321,17322,17324],{},[898,17323,14535],{},[1692,17325,1703],{},[898,17327,13339],{},[1651,17329,1839],{},[1686,17331,17332,17334],{},[898,17333,14535],{},[1692,17335,3521],{},[902,17337,17338],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,17340,17341,11325,17344,17147,17346,17392,17393,17395],{},[38,17342,17343],{},"Křivka LM",[614,17345,13359],{},[883,17347,17349],{"className":17348},[886],[888,17350,17351],{"xmlns":890},[892,17352,17353,17389],{},[895,17354,17355,17361,17363,17369,17371,17373,17379,17381,17383],{},[2115,17356,17357,17359],{},[898,17358,2995],{},[1651,17360,2668],{},[1651,17362,1738],{},[1686,17364,17365,17367],{},[898,17366,14535],{},[1692,17368,1694],{},[898,17370,2665],{},[1651,17372,1839],{},[1686,17374,17375,17377],{},[898,17376,14535],{},[1692,17378,1703],{},[898,17380,13339],{},[1651,17382,1839],{},[1686,17384,17385,17387],{},[898,17386,14535],{},[1692,17388,3521],{},[902,17390,17391],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,17394,14955],{}," přímka.",[123,17397,17398,17401,17402,17436],{},[38,17399,17400],{},"Simultánní rovnováha"," — průsečík ",[883,17403,17405],{"className":17404},[886],[888,17406,17407],{"xmlns":890},[892,17408,17409,17433],{},[895,17410,17411,17413,17415,17417,17423,17425,17431],{},[898,17412,5561],{},[1651,17414,1738],{},[1651,17416,1654],{"stretchy":1653},[2115,17418,17419,17421],{},[898,17420,13339],{},[898,17422,5561],{},[1651,17424,1661],{"separator":1660},[2115,17426,17427,17429],{},[898,17428,2665],{},[898,17430,5561],{},[1651,17432,1667],{"stretchy":1653},[902,17434,17435],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,17438,17439,17442,17443,1343,17456,17469],{},[38,17440,17441],{},"Fiskální politika"," — nástroje ",[883,17444,17446],{"className":17445},[886],[888,17447,17448],{"xmlns":890},[892,17449,17450,17454],{},[895,17451,17452],{},[898,17453,13410],{},[902,17455,13410],{"encoding":904},[883,17457,17459],{"className":17458},[886],[888,17460,17461],{"xmlns":890},[892,17462,17463,17467],{},[895,17464,17465],{},[898,17466,4104],{},[902,17468,4104],{"encoding":904}," posouvající křivku IS.",[123,17471,17472,17475,17476,17493],{},[38,17473,17474],{},"Monetární politika"," — nástroj ",[883,17477,17479],{"className":17478},[886],[888,17480,17481],{"xmlns":890},[892,17482,17483,17491],{},[895,17484,17485],{},[2115,17486,17487,17489],{},[898,17488,2995],{},[1651,17490,2668],{},[902,17492,13448],{"encoding":904}," posouvající křivku LM.",[115,17495,3238],{"id":3237},[120,17497,17498,17507,17516,17526],{},[123,17499,17500,3246,17503],{},[38,17501,17502],{},"Kurz:",[207,17504,17506],{"className":17505,"dataFsResolvedFilePath":1749,"href":1750},[210],"Matematická ekonomie",[123,17508,17509,3246,17512],{},[38,17510,17511],{},"Přednáška:",[207,17513,17515],{"className":17514,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,17517,17518,3246,17521,17525],{},[38,17519,17520],{},"Nadřazené téma:",[207,17522,17524],{"className":17523,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,17527,17528,17531],{},[38,17529,17530],{},"Související:",[120,17532,17533,17540,17546],{},[123,17534,17535,17539],{},[207,17536,17538],{"className":17537,"dataFsResolvedFilePath":800,"href":801},[210],"poptavka-nabidka"," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,17541,17542,17545],{},[207,17543,1145],{"className":17544,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,17547,17548,17552],{},[207,17549,17551],{"className":17550,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":17554},[17555,17556,17557,17558,17559,17560,17561,17562,17563,17564],{"id":13303,"depth":642,"text":13304},{"id":13458,"depth":642,"text":13459},{"id":13673,"depth":642,"text":13674},{"id":13966,"depth":642,"text":13967},{"id":14379,"depth":642,"text":14380},{"id":15172,"depth":642,"text":15173},{"id":15862,"depth":642,"text":15863},{"id":16768,"depth":642,"text":16769},{"id":17017,"depth":642,"text":17018},{"id":3237,"depth":642,"text":3238},{},"\u002Ftopics\u002Fis-lm",{"title":13295,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,17571,1143,17572,17573,17574,17575,17524],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":1628,"title":1629,"body":17578,"course":659,"courses":19093,"created":1129,"description":3293,"extension":661,"meta":19094,"navigation":664,"path":3295,"seo":19095,"sources":19096,"stem":3298,"tags":19097,"type":3302,"updated":677,"__hash__":3303},{"type":9,"value":17579,"toc":19081},[17580,17582,17670,17675,17690,17692,17696,17757,17774,17776,17778,17911,17913,18122,18153,18287,18289,18352,18367,18390,18392,18482,18484,18486,18537,18642,18849,18851,18892,18997,19046,19048],[12,17581,1629],{"id":1634},[724,17583,1637,17584,1671,17607,1709,17638,1713,17640,1745,17667,1752],{},[883,17585,17587],{"className":17586},[886],[888,17588,17589],{"xmlns":890},[892,17590,17591,17605],{},[895,17592,17593,17595,17597,17599,17601,17603],{},[898,17594,1649],{},[1651,17596,1654],{"stretchy":1653},[898,17598,1657],{},[1651,17600,1661],{"separator":1660},[898,17602,1664],{},[1651,17604,1667],{"stretchy":1653},[902,17606,1670],{"encoding":904},[883,17608,17610],{"className":17609},[886],[888,17611,17612],{"xmlns":890},[892,17613,17614,17636],{},[895,17615,17616,17618,17620,17626,17628,17634],{},[898,17617,900],{},[1651,17619,1654],{"stretchy":1653},[1686,17621,17622,17624],{},[898,17623,1690],{},[1692,17625,1694],{},[1651,17627,1661],{"separator":1660},[1686,17629,17630,17632],{},[898,17631,1690],{},[1692,17633,1703],{},[1651,17635,1667],{"stretchy":1653},[902,17637,1708],{"encoding":904},[38,17639,1712],{},[883,17641,17643],{"className":17642},[886],[888,17644,17645],{"xmlns":890},[892,17646,17647,17665],{},[895,17648,17649,17651,17653,17655,17657,17659,17661,17663],{},[898,17650,1725],{},[1651,17652,1654],{"stretchy":1653},[898,17654,1657],{},[1651,17656,1661],{"separator":1660},[898,17658,1664],{},[1651,17660,1667],{"stretchy":1653},[1651,17662,1738],{},[1692,17664,1741],{},[902,17666,1744],{"encoding":904},[207,17668,1751],{"className":17669,"dataFsResolvedFilePath":1749,"href":1750},[210],[724,17671,17672],{},[1756,17673],{"alt":1758,"className":17674,"src":1761},[210,1760],[120,17676,17677,17684,17688],{},[123,17678,17679,1769,17681,1667],{},[38,17680,1768],{},[207,17682,1773],{"className":17683,"dataFsResolvedFilePath":878,"href":879},[210],[123,17685,17686,1779],{},[38,17687,1778],{},[123,17689,1782],{},[115,17691,1786],{"id":1785},[724,17693,1789,17694,1793],{},[38,17695,1792],{},[724,17697,17698],{},[883,17699,17701],{"className":17700},[886],[888,17702,17703],{"xmlns":890},[892,17704,17705,17755],{},[895,17706,17707,17709,17711,17713,17715,17717,17719,17721,17723,17725,17727,17729,17731,17733,17735,17737,17739,17741,17743,17745,17747,17749,17751,17753],{},[898,17708,1807],{},[1651,17710,1654],{"stretchy":1653},[898,17712,1657],{},[1651,17714,1661],{"separator":1660},[898,17716,1664],{},[1651,17718,1661],{"separator":1660},[898,17720,1820],{},[1651,17722,1667],{"stretchy":1653},[1651,17724,1738],{},[898,17726,1649],{},[1651,17728,1654],{"stretchy":1653},[898,17730,1657],{},[1651,17732,1661],{"separator":1660},[898,17734,1664],{},[1651,17736,1667],{"stretchy":1653},[1651,17738,1839],{},[898,17740,1820],{},[1843,17742,1845],{},[898,17744,1725],{},[1651,17746,1654],{"stretchy":1653},[898,17748,1657],{},[1651,17750,1661],{"separator":1660},[898,17752,1664],{},[1651,17754,1667],{"stretchy":1653},[902,17756,1860],{"encoding":904},[724,17758,1863,17759,1878,17772,1882],{},[883,17760,17762],{"className":17761},[886],[888,17763,17764],{"xmlns":890},[892,17765,17766,17770],{},[895,17767,17768],{},[898,17769,1820],{},[902,17771,1877],{"encoding":904},[38,17773,1881],{},[115,17775,1886],{"id":1885},[724,17777,1889],{},[724,17779,17780,17827,17874],{},[883,17781,17783],{"className":17782},[886],[888,17784,17785],{"xmlns":890},[892,17786,17787,17825],{},[895,17788,17789,17797,17799,17807,17809,17811,17813,17821,17823],{},[1902,17790,17791,17793,17795],{},[898,17792,1807],{},[898,17794,1657],{},[1651,17796,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,17798,1738],{},[1902,17800,17801,17803,17805],{},[898,17802,1649],{},[898,17804,1657],{},[1651,17806,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,17808,1839],{},[898,17810,1820],{},[1843,17812,1845],{},[1902,17814,17815,17817,17819],{},[898,17816,1725],{},[898,17818,1657],{},[1651,17820,1912],{"mathvariant"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7 ",[207,19111,19113],{"className":19112,"dataFsResolvedFilePath":1749,"href":1750},[210],"Matematické ekonomie",[38,19115,19116],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,19119,19120],{},"národním důchodem",[883,19122,19124],{"className":19123},[886],[888,19125,19126],{"xmlns":890},[892,19127,19128,19132],{},[895,19129,19130],{},[898,19131,2665],{},[902,19133,2665],{"encoding":904},". Budují se postupně bohatší modely — ",[38,19136,19137],{},"C-I"," (jen spotřeba a investice) → ",[38,19140,19141],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,19144,19145],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,19148,13309],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,19151,15183],{},[883,19153,19155],{"className":19154},[886],[888,19156,19157],{"xmlns":890},[892,19158,19159,19167],{},[895,19160,19161],{},[2115,19162,19163,19165],{},[898,19164,2665],{},[898,19166,5561],{},[902,19168,15201],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,19171,19173],{"className":19172},[886],[888,19174,19175],{"xmlns":890},[892,19176,19177,19185],{},[895,19178,19179],{},[2115,19180,19181,19183],{},[898,19182,2665],{},[898,19184,5561],{},[902,19186,15201],{"encoding":904}," na exogenní veličiny popisují ",[38,19189,19190],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,19193,19195],{"className":19194},[886],[888,19196,19197],{"xmlns":890},[892,19198,19199,19227],{},[895,19200,19201,19203,19205,19207,19209,19211,19213,19215,19217,19219,19221,19223,19225],{},[1692,19202,1694],{},[898,19204,5981],{"mathvariant":1910},[1651,19206,1654],{"stretchy":1653},[1692,19208,1694],{},[1651,19210,2181],{},[898,19212,207],{},[1651,19214,1667],{"stretchy":1653},[1651,19216,1738],{},[1692,19218,1694],{},[898,19220,5981],{"mathvariant":1910},[898,19222,2995],{},[898,19224,2675],{},[898,19226,3004],{},[902,19228,19229],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[5179,19231,19232],{},[724,19233,19234,19236,19237,19240,19241,19259,19260,19290,19291,19338,19339,19341,19342,19364],{},[883,19235,5465],{}," Intuice\n",[38,19238,19239],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,19242,19244],{"className":19243},[886],[888,19245,19246],{"xmlns":890},[892,19247,19248,19256],{},[895,19249,19250,19252,19254],{},[898,19251,2995],{},[898,19253,2675],{},[898,19255,3001],{},[902,19257,19258],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,19261,19263],{"className":19262},[886],[888,19264,19265],{"xmlns":890},[892,19266,19267,19287],{},[895,19268,19269,19271,19273,19275,19277,19279,19281,19283,19285],{},[898,19270,2995],{},[898,19272,2675],{},[898,19274,3004],{},[1651,19276,1738],{},[1692,19278,1694],{},[1651,19280,2181],{},[898,19282,2995],{},[898,19284,2675],{},[898,19286,3001],{},[902,19288,19289],{"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 ",[883,19292,19294],{"className":19293},[886],[888,19295,19296],{"xmlns":890},[892,19297,19298,19335],{},[895,19299,19300,19302,19304,19306,19308,19314,19316,19319,19321,19323,19325,19327,19329,19331,19333],{},[1692,19301,1694],{},[1651,19303,1839],{},[898,19305,207],{},[1651,19307,1839],{},[2115,19309,19310,19312],{},[898,19311,207],{},[1692,19313,1703],{},[1651,19315,1839],{},[1651,19317,19318],{},"⋯",[1651,19320,1738],{},[1692,19322,1694],{},[898,19324,5981],{"mathvariant":1910},[1651,19326,1654],{"stretchy":1653},[1692,19328,1694],{},[1651,19330,2181],{},[898,19332,207],{},[1651,19334,1667],{"stretchy":1653},[902,19336,19337],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,19340,13309],{}," 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 ",[883,19343,19345],{"className":19344},[886],[888,19346,19347],{"xmlns":890},[892,19348,19349,19361],{},[895,19350,19351,19353,19355,19357,19359],{},[1651,19352,1654],{"stretchy":1653},[898,19354,2665],{},[1651,19356,1661],{"separator":1660},[898,19358,13339],{},[1651,19360,1667],{"stretchy":1653},[902,19362,19363],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,19366,19368],{"id":19367},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,19370,19371],{},"Po prostudování kapitoly by čtenář měl umět:",[120,19373,19374,19377,19380,19383,19386,19389,19392,19482],{},[123,19375,19376],{},"popsat zjednodušený model národní ekonomiky,",[123,19378,19379],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,19381,19382],{},"popsat lineární model spotřeby a úspor,",[123,19384,19385],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,19387,19388],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,19390,19391],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,19393,19394,19395,1343,19412,1343,19434,5197,19459,19481],{},"popsat modely ",[883,19396,19398],{"className":19397},[886],[888,19399,19400],{"xmlns":890},[892,19401,19402,19410],{},[895,19403,19404,19406,19408],{},[898,19405,3001],{},[1843,19407,13588],{},[898,19409,13482],{},[902,19411,13593],{"encoding":904},[883,19413,19415],{"className":19414},[886],[888,19416,19417],{"xmlns":890},[892,19418,19419,19431],{},[895,19420,19421,19423,19425,19427,19429],{},[898,19422,3001],{},[1843,19424,13588],{},[898,19426,13482],{},[1843,19428,13588],{},[898,19430,13410],{},[902,19432,19433],{"encoding":904},"C\\text{-}I\\text{-}G",[883,19435,19437],{"className":19436},[886],[888,19438,19439],{"xmlns":890},[892,19440,19441,19457],{},[895,19442,19443,19445,19447,19449,19451,19453,19455],{},[898,19444,3001],{},[1843,19446,13588],{},[898,19448,13482],{},[1843,19450,13588],{},[898,19452,13410],{},[1843,19454,13588],{},[898,19456,13618],{},[902,19458,13621],{"encoding":904},[883,19460,19462],{"className":19461},[886],[888,19463,19464],{"xmlns":890},[892,19465,19466,19478],{},[895,19467,19468,19470,19472,19474,19476],{},[898,19469,13482],{},[898,19471,3004],{},[1843,19473,13588],{},[898,19475,1807],{},[898,19477,2995],{},[902,19479,19480],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,19483,19484],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,19486,19488],{"id":19487},"gnp-a-národní-důchod","GNP a národní důchod",[724,19490,19491,3246,19494,11325,19513,19516],{},[38,19492,19493],{},"Hrubý národní produkt",[883,19495,19497],{"className":19496},[886],[888,19498,19499],{"xmlns":890},[892,19500,19501,19510],{},[895,19502,19503,19505,19508],{},[898,19504,13410],{},[898,19506,19507],{},"N",[898,19509,2675],{},[902,19511,19512],{"encoding":904},"GNP",[614,19514,19515],{},"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:",[724,19518,19519],{},[883,19520,19522],{"className":19521},[886],[888,19523,19524],{"xmlns":890},[892,19525,19526,19561],{},[895,19527,19528,19530,19532,19534,19536,19538,19540,19542,19544,19546,19548,19550,19552,19554,19556,19559],{},[898,19529,13410],{},[898,19531,19507],{},[898,19533,2675],{},[1651,19535,1738],{},[898,19537,3001],{},[1651,19539,1839],{},[898,19541,13482],{},[1651,19543,1839],{},[898,19545,13410],{},[1651,19547,1839],{},[898,19549,13618],{},[1651,19551,1661],{"separator":1660},[7185,19553],{"width":7187},[1651,19555,1654],{"stretchy":1653},[1692,19557,19558],{},"7.1",[1651,19560,1667],{"stretchy":1653},[902,19562,19563],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,19565,19566],{},"kde",[120,19568,19569,19585,19601,19617],{},[123,19570,19571,19584],{},[883,19572,19574],{"className":19573},[886],[888,19575,19576],{"xmlns":890},[892,19577,19578,19582],{},[895,19579,19580],{},[898,19581,3001],{},[902,19583,3001],{"encoding":904}," — výdaje domácností na spotřebu,",[123,19586,19587,19600],{},[883,19588,19590],{"className":19589},[886],[888,19591,19592],{"xmlns":890},[892,19593,19594,19598],{},[895,19595,19596],{},[898,19597,13482],{},[902,19599,13482],{"encoding":904}," — hrubé domácí investice,",[123,19602,19603,19616],{},[883,19604,19606],{"className":19605},[886],[888,19607,19608],{"xmlns":890},[892,19609,19610,19614],{},[895,19611,19612],{},[898,19613,13410],{},[902,19615,13410],{"encoding":904}," — vládní výdaje,",[123,19618,19619,19632],{},[883,19620,19622],{"className":19621},[886],[888,19623,19624],{"xmlns":890},[892,19625,19626,19630],{},[895,19627,19628],{},[898,19629,13618],{},[902,19631,13618],{"encoding":904}," — čistý export.",[724,19634,19635,19636,19653,19654,19657,19658,3246,19661,11325,19674,19677],{},"K měření ",[883,19637,19639],{"className":19638},[886],[888,19640,19641],{"xmlns":890},[892,19642,19643,19651],{},[895,19644,19645,19647,19649],{},[898,19646,13410],{},[898,19648,19507],{},[898,19650,2675],{},[902,19652,19512],{"encoding":904}," se užívá ",[38,19655,19656],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,19659,19660],{},"národní důchod",[883,19662,19664],{"className":19663},[886],[888,19665,19666],{"xmlns":890},[892,19667,19668,19672],{},[895,19669,19670],{},[898,19671,2665],{},[902,19673,2665],{"encoding":904},[614,19675,19676],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,19679,19680],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,19682,19683],{},[883,19684,19686],{"className":19685},[886],[888,19687,19688],{"xmlns":890},[892,19689,19690,19704],{},[895,19691,19692,19694,19696,19698,19700,19702],{},[898,19693,13410],{},[898,19695,19507],{},[898,19697,2675],{},[1651,19699,4060],{},[898,19701,2665],{},[1651,19703,1661],{"separator":1660},[902,19705,19706],{"encoding":904},"GNP \\approx Y,",[724,19708,19709,19710,11325,19713,19716,19717,19730,19731,19734,19735,1882],{},"a užívá se společného názvu ",[38,19711,19712],{},"důchod",[614,19714,19715],{},"income",") s označením ",[883,19718,19720],{"className":19719},[886],[888,19721,19722],{"xmlns":890},[892,19723,19724,19728],{},[895,19725,19726],{},[898,19727,2665],{},[902,19729,2665],{"encoding":904},". Domácnosti důchod použijí ke ",[38,19732,19733],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,19736,19737],{},"úspor",[115,19739,19741],{"id":19740},"spotřeba-a-úspory","Spotřeba a úspory",[198,19743,19745],{"id":19744},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,19747,19748,19749,19762,19763,19776,19777,1793],{},"Jak spotřeba ",[883,19750,19752],{"className":19751},[886],[888,19753,19754],{"xmlns":890},[892,19755,19756,19760],{},[895,19757,19758],{},[898,19759,3001],{},[902,19761,3001],{"encoding":904},", tak úspory ",[883,19764,19766],{"className":19765},[886],[888,19767,19768],{"xmlns":890},[892,19769,19770,19774],{},[895,19771,19772],{},[898,19773,3004],{},[902,19775,3004],{"encoding":904}," závisejí na důchodu ",[883,19778,19780],{"className":19779},[886],[888,19781,19782],{"xmlns":890},[892,19783,19784,19788],{},[895,19785,19786],{},[898,19787,2665],{},[902,19789,2665],{"encoding":904},[724,19791,19792],{},[883,19793,19795],{"className":19794},[886],[888,19796,19797],{"xmlns":890},[892,19798,19799,19831],{},[895,19800,19801,19803,19805,19807,19809,19811,19813,19815,19817,19819,19821,19823,19825,19827,19829],{},[898,19802,3001],{},[1651,19804,1738],{},[898,19806,3001],{},[1651,19808,1654],{"stretchy":1653},[898,19810,2665],{},[1651,19812,1667],{"stretchy":1653},[1651,19814,1661],{"separator":1660},[7185,19816],{"width":7187},[898,19818,3004],{},[1651,19820,1738],{},[898,19822,3004],{},[1651,19824,1654],{"stretchy":1653},[898,19826,2665],{},[1651,19828,1667],{"stretchy":1653},[898,19830,1882],{"mathvariant":1910},[902,19832,19833],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,19835,19836,1878,19855,11325,19858,19861,19862,1878,19882,11325,19885,19888,19889,5197,19892,19895],{},[883,19837,19839],{"className":19838},[886],[888,19840,19841],{"xmlns":890},[892,19842,19843,19853],{},[895,19844,19845,19847,19849,19851],{},[898,19846,3001],{},[1651,19848,1654],{"stretchy":1653},[898,19850,2665],{},[1651,19852,1667],{"stretchy":1653},[902,19854,15514],{"encoding":904},[38,19856,19857],{},"funkce spotřeby",[614,19859,19860],{},"consumption function","), ",[883,19863,19865],{"className":19864},[886],[888,19866,19867],{"xmlns":890},[892,19868,19869,19879],{},[895,19870,19871,19873,19875,19877],{},[898,19872,3004],{},[1651,19874,1654],{"stretchy":1653},[898,19876,2665],{},[1651,19878,1667],{"stretchy":1653},[902,19880,19881],{"encoding":904},"S(Y)",[38,19883,19884],{},"funkce úspor",[614,19886,19887],{},"savings function","); jejich grafy se nazývají ",[38,19890,19891],{},"křivka spotřeby",[38,19893,19894],{},"křivka úspor",". Platí základní identita",[724,19897,19898],{},[883,19899,19901],{"className":19900},[886],[888,19902,19903],{"xmlns":890},[892,19904,19905,19948],{},[895,19906,19907,19909,19911,19913,19915,19917,19919,19921,19923,19925,19927,19929,19931,19933,19935,19937,19939,19941,19943,19946],{},[898,19908,2665],{},[1651,19910,1738],{},[898,19912,3001],{},[1651,19914,1839],{},[898,19916,3004],{},[1651,19918,1738],{},[898,19920,3001],{},[1651,19922,1654],{"stretchy":1653},[898,19924,2665],{},[1651,19926,1667],{"stretchy":1653},[1651,19928,1839],{},[898,19930,3004],{},[1651,19932,1654],{"stretchy":1653},[898,19934,2665],{},[1651,19936,1667],{"stretchy":1653},[898,19938,1882],{"mathvariant":1910},[7185,19940],{"width":7187},[1651,19942,1654],{"stretchy":1653},[1692,19944,19945],{},"7.2",[1651,19947,1667],{"stretchy":1653},[902,19949,19950],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,19952,19953],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,19955,19957],{"id":19956},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,19959,19960],{},"Nejjednodušší model předpokládá lineární tvar",[724,19962,19963],{},[883,19964,19966],{"className":19965},[886],[888,19967,19968],{"xmlns":890},[892,19969,19970,20005],{},[895,19971,19972,19974,19976,19978,19980,19982,19984,19986,19988,19990,19992,19994,19996,19998,20000,20003],{},[898,19973,3001],{},[1651,19975,1738],{},[898,19977,3001],{},[1651,19979,1654],{"stretchy":1653},[898,19981,2665],{},[1651,19983,1667],{"stretchy":1653},[1651,19985,1738],{},[898,19987,207],{},[898,19989,2665],{},[1651,19991,1839],{},[898,19993,2268],{},[1651,19995,1661],{"separator":1660},[7185,19997],{"width":7187},[1651,19999,1654],{"stretchy":1653},[1692,20001,20002],{},"7.3",[1651,20004,1667],{"stretchy":1653},[902,20006,20007],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,20009,1863,20010,5197,20028,20050,20051,20091,20092,1882],{},[883,20011,20013],{"className":20012},[886],[888,20014,20015],{"xmlns":890},[892,20016,20017,20025],{},[895,20018,20019,20021,20023],{},[898,20020,2268],{},[1651,20022,2390],{},[1692,20024,1741],{},[902,20026,20027],{"encoding":904},"b > 0",[883,20029,20031],{"className":20030},[886],[888,20032,20033],{"xmlns":890},[892,20034,20035,20047],{},[895,20036,20037,20039,20041,20043,20045],{},[1692,20038,1741],{},[1651,20040,2319],{},[898,20042,207],{},[1651,20044,2319],{},[1692,20046,1694],{},[902,20048,20049],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,20052,20054],{"className":20053},[886],[888,20055,20056],{"xmlns":890},[892,20057,20058,20088],{},[895,20059,20060,20062,20064,20071,20073,20076,20078,20080,20082,20084,20086],{},[898,20061,207],{},[1651,20063,1738],{},[895,20065,20066,20069],{},[898,20067,20068],{"mathvariant":1910},"t",[898,20070,1725],{"mathvariant":1910},[1843,20072,1845],{},[898,20074,20075],{},"α",[1651,20077,1738],{},[898,20079,4216],{"mathvariant":1910},[898,20081,3001],{},[898,20083,5981],{"mathvariant":1910},[898,20085,4216],{"mathvariant":1910},[898,20087,2665],{},[902,20089,20090],{"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 ",[883,20093,20095],{"className":20094},[886],[888,20096,20097],{"xmlns":890},[892,20098,20099,20103],{},[895,20100,20101],{},[898,20102,2665],{},[902,20104,2665],{"encoding":904},[724,20106,20107],{},[614,20108,20109,20110,20134,20135,20173,20174,20190,20191,1882],{},"Obrázek 7.1 — Přímka spotřeby ",[883,20111,20113],{"className":20112},[886],[888,20114,20115],{"xmlns":890},[892,20116,20117,20131],{},[895,20118,20119,20121,20123,20125,20127,20129],{},[898,20120,3001],{},[1651,20122,1738],{},[898,20124,207],{},[898,20126,2665],{},[1651,20128,1839],{},[898,20130,2268],{},[902,20132,20133],{"encoding":904},"C = aY + b"," se směrnicí ",[883,20136,20138],{"className":20137},[886],[888,20139,20140],{"xmlns":890},[892,20141,20142,20170],{},[895,20143,20144,20146,20148,20154,20156,20158,20160,20162,20164,20166,20168],{},[898,20145,207],{},[1651,20147,1738],{},[895,20149,20150,20152],{},[898,20151,20068],{"mathvariant":1910},[898,20153,1725],{"mathvariant":1910},[1843,20155,1845],{},[898,20157,20075],{},[1651,20159,1738],{},[898,20161,4216],{"mathvariant":1910},[898,20163,3001],{},[898,20165,5981],{"mathvariant":1910},[898,20167,4216],{"mathvariant":1910},[898,20169,2665],{},[902,20171,20172],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,20175,20177],{"className":20176},[886],[888,20178,20179],{"xmlns":890},[892,20180,20181,20187],{},[895,20182,20183,20185],{},[898,20184,4216],{"mathvariant":1910},[898,20186,3001],{},[902,20188,20189],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,20192,20194],{"className":20193},[886],[888,20195,20196],{"xmlns":890},[892,20197,20198,20208],{},[895,20199,20200,20202,20204,20206],{},[898,20201,4216],{"mathvariant":1910},[898,20203,2665],{},[1651,20205,1738],{},[1692,20207,1694],{},[902,20209,20210],{"encoding":904},"\\Delta Y = 1",[724,20212,20213,20214,1793],{},"Dosazením do (7.2) plyne ",[38,20215,20216],{},"lineární model úspor",[724,20218,20219],{},[883,20220,20222],{"className":20221},[886],[888,20223,20224],{"xmlns":890},[892,20225,20226,20291],{},[895,20227,20228,20230,20232,20234,20236,20238,20240,20242,20244,20246,20248,20250,20252,20254,20256,20258,20260,20262,20264,20266,20268,20270,20272,20274,20276,20278,20280,20282,20284,20286,20289],{},[898,20229,3004],{},[1651,20231,1738],{},[898,20233,2665],{},[1651,20235,2181],{},[898,20237,3001],{},[1651,20239,1654],{"stretchy":1653},[898,20241,2665],{},[1651,20243,1667],{"stretchy":1653},[1651,20245,1738],{},[898,20247,2665],{},[1651,20249,2181],{},[1651,20251,1654],{"stretchy":1653},[898,20253,207],{},[898,20255,2665],{},[1651,20257,1839],{},[898,20259,2268],{},[1651,20261,1667],{"stretchy":1653},[1651,20263,1738],{},[1651,20265,1654],{"stretchy":1653},[1692,20267,1694],{},[1651,20269,2181],{},[898,20271,207],{},[1651,20273,1667],{"stretchy":1653},[898,20275,2665],{},[1651,20277,2181],{},[898,20279,2268],{},[898,20281,1882],{"mathvariant":1910},[7185,20283],{"width":7187},[1651,20285,1654],{"stretchy":1653},[1692,20287,20288],{},"7.4",[1651,20290,1667],{"stretchy":1653},[902,20292,20293],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,20295,20296,20297,5230],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,20298,20300],{"className":20299},[886],[888,20301,20302],{"xmlns":890},[892,20303,20304,20320],{},[895,20305,20306,20308,20310,20312,20314,20316,20318],{},[1692,20307,1741],{},[1651,20309,2319],{},[1692,20311,1694],{},[1651,20313,2181],{},[898,20315,207],{},[1651,20317,2319],{},[1692,20319,1694],{},[902,20321,20322],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,20324,20325],{},[614,20326,20327,20328,5197,20351,20383,20384,3955,20397,20427,20428,3955,20446,1882],{},"Obrázek 7.2 — Přímky ",[883,20329,20331],{"className":20330},[886],[888,20332,20333],{"xmlns":890},[892,20334,20335,20349],{},[895,20336,20337,20339,20341,20343,20345,20347],{},[898,20338,3001],{},[1651,20340,1738],{},[898,20342,207],{},[898,20344,2665],{},[1651,20346,1839],{},[898,20348,2268],{},[902,20350,20133],{"encoding":904},[883,20352,20354],{"className":20353},[886],[888,20355,20356],{"xmlns":890},[892,20357,20358,20380],{},[895,20359,20360,20362,20364,20366,20368,20370,20372,20374,20376,20378],{},[898,20361,3004],{},[1651,20363,1738],{},[1651,20365,1654],{"stretchy":1653},[1692,20367,1694],{},[1651,20369,2181],{},[898,20371,207],{},[1651,20373,1667],{"stretchy":1653},[898,20375,2665],{},[1651,20377,2181],{},[898,20379,2268],{},[902,20381,20382],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,20385,20387],{"className":20386},[886],[888,20388,20389],{"xmlns":890},[892,20390,20391,20395],{},[895,20392,20393],{},[898,20394,2665],{},[902,20396,2665],{"encoding":904},[883,20398,20400],{"className":20399},[886],[888,20401,20402],{"xmlns":890},[892,20403,20404,20424],{},[895,20405,20406,20408,20410,20412,20414,20416,20418,20420,20422],{},[898,20407,2665],{},[1651,20409,1738],{},[898,20411,2268],{},[898,20413,5981],{"mathvariant":1910},[1651,20415,1654],{"stretchy":1653},[1692,20417,1694],{},[1651,20419,2181],{},[898,20421,207],{},[1651,20423,1667],{"stretchy":1653},[902,20425,20426],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,20429,20431],{"className":20430},[886],[888,20432,20433],{"xmlns":890},[892,20434,20435,20443],{},[895,20436,20437,20439,20441],{},[898,20438,3001],{},[1651,20440,1661],{"separator":1660},[898,20442,3004],{},[902,20444,20445],{"encoding":904},"C, S",[883,20447,20449],{"className":20448},[886],[888,20450,20451],{"xmlns":890},[892,20452,20453,20459],{},[895,20454,20455,20457],{},[1651,20456,2181],{},[898,20458,2268],{},[902,20460,20461],{"encoding":904},"-b",[198,20463,20465],{"id":20464},"příklad-71","Příklad 7.1",[724,20467,20468,20469,20494],{},"Pro spotřebu ",[883,20470,20472],{"className":20471},[886],[888,20473,20474],{"xmlns":890},[892,20475,20476,20491],{},[895,20477,20478,20480,20482,20485,20487,20489],{},[898,20479,3001],{},[1651,20481,1738],{},[1692,20483,20484],{},"0,4",[898,20486,2665],{},[1651,20488,1839],{},[1692,20490,4190],{},[902,20492,20493],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,20496,20497],{},[883,20498,20500],{"className":20499},[886],[888,20501,20502],{"xmlns":890},[892,20503,20504,20542],{},[895,20505,20506,20508,20510,20512,20514,20516,20518,20520,20522,20524,20526,20528,20530,20532,20535,20537,20539],{},[898,20507,3004],{},[1651,20509,1738],{},[898,20511,2665],{},[1651,20513,2181],{},[898,20515,3001],{},[1651,20517,1738],{},[898,20519,2665],{},[1651,20521,2181],{},[1692,20523,20484],{},[898,20525,2665],{},[1651,20527,2181],{},[1692,20529,4190],{},[1651,20531,1738],{},[1692,20533,20534],{},"0,6",[898,20536,2665],{},[1651,20538,2181],{},[1692,20540,20541],{},"10.",[902,20543,20544],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,20546,20547],{},[614,20548,20549,20550,5197,20573,20597,20598,1878,20611,20635,20636,1878,20653,20669,20670,1882],{},"Obrázek 7.3 — Přímky ",[883,20551,20553],{"className":20552},[886],[888,20554,20555],{"xmlns":890},[892,20556,20557,20571],{},[895,20558,20559,20561,20563,20565,20567,20569],{},[898,20560,3001],{},[1651,20562,1738],{},[1692,20564,20484],{},[898,20566,2665],{},[1651,20568,1839],{},[1692,20570,4190],{},[902,20572,20493],{"encoding":904},[883,20574,20576],{"className":20575},[886],[888,20577,20578],{"xmlns":890},[892,20579,20580,20594],{},[895,20581,20582,20584,20586,20588,20590,20592],{},[898,20583,3004],{},[1651,20585,1738],{},[1692,20587,20534],{},[898,20589,2665],{},[1651,20591,2181],{},[1692,20593,4190],{},[902,20595,20596],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,20599,20601],{"className":20600},[886],[888,20602,20603],{"xmlns":890},[892,20604,20605,20609],{},[895,20606,20607],{},[898,20608,2665],{},[902,20610,2665],{"encoding":904},[883,20612,20614],{"className":20613},[886],[888,20615,20616],{"xmlns":890},[892,20617,20618,20632],{},[895,20619,20620,20622,20625],{},[1651,20621,4060],{},[1692,20623,20624],{},"16,",[9692,20626,20627,20629],{"accent":1660},[1692,20628,3581],{},[1651,20630,20631],{},"ˉ",[902,20633,20634],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,20637,20639],{"className":20638},[886],[888,20640,20641],{"xmlns":890},[892,20642,20643,20651],{},[895,20644,20645,20647,20649],{},[898,20646,3001],{},[1651,20648,1661],{"separator":1660},[898,20650,3004],{},[902,20652,20445],{"encoding":904},[883,20654,20656],{"className":20655},[886],[888,20657,20658],{"xmlns":890},[892,20659,20660,20666],{},[895,20661,20662,20664],{},[1651,20663,2181],{},[1692,20665,4190],{},[902,20667,20668],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,20671,20673],{"className":20672},[886],[888,20674,20675],{"xmlns":890},[892,20676,20677,20689],{},[895,20678,20679,20681,20683,20685,20687],{},[1651,20680,1654],{"stretchy":1653},[1692,20682,1741],{},[1651,20684,1661],{"separator":1660},[1692,20686,4190],{},[1651,20688,1667],{"stretchy":1653},[902,20690,20691],{"encoding":904},"(0, 10)",[724,20693,20694,20695,1878,20713,20743,20744,11325,20747,20750,20751,1878,20775,11325,20778,20781],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,20696,20698],{"className":20697},[886],[888,20699,20700],{"xmlns":890},[892,20701,20702,20710],{},[895,20703,20704,20706,20708],{},[898,20705,2665],{},[1651,20707,1738],{},[1692,20709,1741],{},[902,20711,20712],{"encoding":904},"Y = 0",[883,20714,20716],{"className":20715},[886],[888,20717,20718],{"xmlns":890},[892,20719,20720,20740],{},[895,20721,20722,20724,20726,20728,20730,20732,20734,20736,20738],{},[898,20723,3004],{},[1651,20725,1654],{"stretchy":1653},[1692,20727,1741],{},[1651,20729,1667],{"stretchy":1653},[1651,20731,1738],{},[1651,20733,2181],{},[898,20735,2268],{},[1651,20737,2319],{},[1692,20739,1741],{},[902,20741,20742],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,20745,20746],{},"autonomních úsporách",[614,20748,20749],{},"autonomous savings","). Analogicky ",[883,20752,20754],{"className":20753},[886],[888,20755,20756],{"xmlns":890},[892,20757,20758,20772],{},[895,20759,20760,20762,20764,20766,20768,20770],{},[898,20761,3001],{},[1651,20763,1654],{"stretchy":1653},[1692,20765,1741],{},[1651,20767,1667],{"stretchy":1653},[1651,20769,1738],{},[898,20771,2268],{},[902,20773,20774],{"encoding":904},"C(0) = b",[38,20776,20777],{},"autonomní spotřeba",[614,20779,20780],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,20783,20785],{"id":20784},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,20787,20788,3246,20791,11325,20808,20811],{},[38,20789,20790],{},"Mezní sklon ke spotřebě",[883,20792,20794],{"className":20793},[886],[888,20795,20796],{"xmlns":890},[892,20797,20798,20806],{},[895,20799,20800,20802,20804],{},[898,20801,2995],{},[898,20803,2675],{},[898,20805,3001],{},[902,20807,19258],{"encoding":904},[614,20809,20810],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,20813,20814],{},[883,20815,20817],{"className":20816},[886],[888,20818,20819],{"xmlns":890},[892,20820,20821,20847],{},[895,20822,20823,20825,20827,20829,20831,20845],{},[898,20824,2995],{},[898,20826,2675],{},[898,20828,3001],{},[1651,20830,1738],{},[2446,20832,20833,20839],{},[895,20834,20835,20837],{},[898,20836,3542],{"mathvariant":1910},[898,20838,3001],{},[895,20840,20841,20843],{},[898,20842,3542],{"mathvariant":1910},[898,20844,2665],{},[898,20846,1882],{"mathvariant":1910},[902,20848,20849],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,20851,20852,3246,20855,11325,20873,20876],{},[38,20853,20854],{},"Mezní sklon k úsporám",[883,20856,20858],{"className":20857},[886],[888,20859,20860],{"xmlns":890},[892,20861,20862,20870],{},[895,20863,20864,20866,20868],{},[898,20865,2995],{},[898,20867,2675],{},[898,20869,3004],{},[902,20871,20872],{"encoding":904},"MPS",[614,20874,20875],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,20878,20879],{},[883,20880,20882],{"className":20881},[886],[888,20883,20884],{"xmlns":890},[892,20885,20886,20912],{},[895,20887,20888,20890,20892,20894,20896,20910],{},[898,20889,2995],{},[898,20891,2675],{},[898,20893,3004],{},[1651,20895,1738],{},[2446,20897,20898,20904],{},[895,20899,20900,20902],{},[898,20901,3542],{"mathvariant":1910},[898,20903,3004],{},[895,20905,20906,20908],{},[898,20907,3542],{"mathvariant":1910},[898,20909,2665],{},[898,20911,1882],{"mathvariant":1910},[902,20913,20914],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,20916,20917,20918,20976],{},"Z (7.2) plyne ",[883,20919,20921],{"className":20920},[886],[888,20922,20923],{"xmlns":890},[892,20924,20925,20973],{},[895,20926,20927,20941,20943,20957,20959],{},[2446,20928,20929,20935],{},[895,20930,20931,20933],{},[898,20932,3542],{"mathvariant":1910},[898,20934,2665],{},[895,20936,20937,20939],{},[898,20938,3542],{"mathvariant":1910},[898,20940,2665],{},[1651,20942,1738],{},[2446,20944,20945,20951],{},[895,20946,20947,20949],{},[898,20948,3542],{"mathvariant":1910},[898,20950,3001],{},[895,20952,20953,20955],{},[898,20954,3542],{"mathvariant":1910},[898,20956,2665],{},[1651,20958,1839],{},[2446,20960,20961,20967],{},[895,20962,20963,20965],{},[898,20964,3542],{"mathvariant":1910},[898,20966,3004],{},[895,20968,20969,20971],{},[898,20970,3542],{"mathvariant":1910},[898,20972,2665],{},[902,20974,20975],{"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",[724,20978,20979],{},[883,20980,20982],{"className":20981},[886],[888,20983,20984],{"xmlns":890},[892,20985,20986,21049],{},[895,20987,20988,21040,21042,21044,21047],{},[14130,20989,20990],{"notation":14132},[2938,20991,20992],{"scriptlevel":1741,"displaystyle":1653},[2938,20993,20994],{"scriptlevel":1741,"displaystyle":1653},[2938,20995,20996],{"scriptlevel":1741,"displaystyle":1660},[895,20997,20998,21000,21002,21004,21006,21008,21010,21012,21014,21016,21018,21020,21022,21024,21026,21028,21030,21032,21034,21036,21038],{},[898,20999,2995],{},[898,21001,2675],{},[898,21003,3001],{},[1651,21005,1839],{},[898,21007,2995],{},[898,21009,2675],{},[898,21011,3004],{},[1651,21013,1738],{},[1692,21015,1694],{},[1651,21017,1661],{"separator":1660},[7185,21019],{"width":7187},[898,21021,2995],{},[898,21023,2675],{},[898,21025,3004],{},[1651,21027,1738],{},[1692,21029,1694],{},[1651,21031,2181],{},[898,21033,2995],{},[898,21035,2675],{},[898,21037,3001],{},[898,21039,1882],{"mathvariant":1910},[7185,21041],{"width":7187},[1651,21043,1654],{"stretchy":1653},[1692,21045,21046],{},"7.5",[1651,21048,1667],{"stretchy":1653},[902,21050,21051],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,21053,21054,3246,21057,21080,21081,5197,21103,21129],{},[38,21055,21056],{},"Pro lineární model",[883,21058,21060],{"className":21059},[886],[888,21061,21062],{"xmlns":890},[892,21063,21064,21078],{},[895,21065,21066,21068,21070,21072,21074,21076],{},[898,21067,3001],{},[1651,21069,1738],{},[898,21071,207],{},[898,21073,2665],{},[1651,21075,1839],{},[898,21077,2268],{},[902,21079,20133],{"encoding":904}," vychází ",[883,21082,21084],{"className":21083},[886],[888,21085,21086],{"xmlns":890},[892,21087,21088,21100],{},[895,21089,21090,21092,21094,21096,21098],{},[898,21091,2995],{},[898,21093,2675],{},[898,21095,3001],{},[1651,21097,1738],{},[898,21099,207],{},[902,21101,21102],{"encoding":904},"MPC = a",[883,21104,21106],{"className":21105},[886],[888,21107,21108],{"xmlns":890},[892,21109,21110,21126],{},[895,21111,21112,21114,21116,21118,21120,21122,21124],{},[898,21113,2995],{},[898,21115,2675],{},[898,21117,3004],{},[1651,21119,1738],{},[1692,21121,1694],{},[1651,21123,2181],{},[898,21125,207],{},[902,21127,21128],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,21131,21132,21135,21136,21158,21159,21187],{},[38,21133,21134],{},"Interpretace diferenciálem."," Pro pevné ",[883,21137,21139],{"className":21138},[886],[888,21140,21141],{"xmlns":890},[892,21142,21143,21155],{},[895,21144,21145,21147,21149],{},[898,21146,2665],{},[1651,21148,1738],{},[2115,21150,21151,21153],{},[898,21152,2665],{},[1651,21154,2668],{},[902,21156,21157],{"encoding":904},"Y = Y^*"," udává ",[883,21160,21162],{"className":21161},[886],[888,21163,21164],{"xmlns":890},[892,21165,21166,21184],{},[895,21167,21168,21170,21172,21174,21176,21182],{},[898,21169,2995],{},[898,21171,2675],{},[898,21173,3001],{},[1651,21175,1654],{"stretchy":1653},[2115,21177,21178,21180],{},[898,21179,2665],{},[1651,21181,2668],{},[1651,21183,1667],{"stretchy":1653},[902,21185,21186],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,21189,21190],{},[883,21191,21193],{"className":21192},[886],[888,21194,21195],{"xmlns":890},[892,21196,21197,21251],{},[895,21198,21199,21201,21203,21205,21207,21209,21211,21217,21219,21221,21223,21225,21227,21229,21231,21233,21235,21237,21239,21241,21243,21245,21247,21249],{},[898,21200,4216],{"mathvariant":1910},[898,21202,3001],{},[1651,21204,4060],{},[898,21206,3542],{"mathvariant":1910},[898,21208,3001],{},[1651,21210,1738],{},[2115,21212,21213,21215],{},[898,21214,3001],{},[1651,21216,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,21218,1654],{"stretchy":1653},[898,21220,2665],{},[1651,21222,1667],{"stretchy":1653},[1843,21224,1845],{},[898,21226,3542],{"mathvariant":1910},[898,21228,2665],{},[1651,21230,1738],{},[898,21232,2995],{},[898,21234,2675],{},[898,21236,3001],{},[1651,21238,1654],{"stretchy":1653},[898,21240,2665],{},[1651,21242,1667],{"stretchy":1653},[1843,21244,1845],{},[898,21246,3542],{"mathvariant":1910},[898,21248,2665],{},[898,21250,1882],{"mathvariant":1910},[902,21252,21253],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,21255,21256,21257,21293,21294,21297],{},"Analogicky ",[883,21258,21260],{"className":21259},[886],[888,21261,21262],{"xmlns":890},[892,21263,21264,21290],{},[895,21265,21266,21268,21270,21272,21274,21276,21278,21280,21282,21284,21286,21288],{},[898,21267,4216],{"mathvariant":1910},[898,21269,3004],{},[1651,21271,4060],{},[898,21273,2995],{},[898,21275,2675],{},[898,21277,3004],{},[1651,21279,1654],{"stretchy":1653},[898,21281,2665],{},[1651,21283,1667],{"stretchy":1653},[1843,21285,1845],{},[898,21287,3542],{"mathvariant":1910},[898,21289,2665],{},[902,21291,21292],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,21295,1145],{"className":21296,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,21299,21301],{"id":21300},"příklad-72","Příklad 7.2",[724,21303,20468,21304,21339,21340,21359],{},[883,21305,21307],{"className":21306},[886],[888,21308,21309],{"xmlns":890},[892,21310,21311,21336],{},[895,21312,21313,21315,21317,21320,21326,21328,21330,21332,21334],{},[898,21314,3001],{},[1651,21316,1738],{},[1692,21318,21319],{},"0,001",[2115,21321,21322,21324],{},[898,21323,2665],{},[1692,21325,1703],{},[1651,21327,1839],{},[1692,21329,4166],{},[898,21331,2665],{},[1651,21333,1839],{},[1692,21335,4446],{},[902,21337,21338],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,21341,21343],{"className":21342},[886],[888,21344,21345],{"xmlns":890},[892,21346,21347,21356],{},[895,21348,21349,21351,21353],{},[898,21350,2665],{},[1651,21352,2319],{},[1692,21354,21355],{},"400",[902,21357,21358],{"encoding":904},"Y \u003C 400",") platí",[724,21361,21362],{},[883,21363,21365],{"className":21364},[886],[888,21366,21367],{"xmlns":890},[892,21368,21369,21406],{},[895,21370,21371,21373,21375,21377,21379,21393,21395,21398,21400,21402,21404],{},[898,21372,2995],{},[898,21374,2675],{},[898,21376,3001],{},[1651,21378,1738],{},[2446,21380,21381,21387],{},[895,21382,21383,21385],{},[898,21384,3542],{"mathvariant":1910},[898,21386,3001],{},[895,21388,21389,21391],{},[898,21390,3542],{"mathvariant":1910},[898,21392,2665],{},[1651,21394,1738],{},[1692,21396,21397],{},"0,002",[898,21399,2665],{},[1651,21401,1839],{},[1692,21403,4166],{},[1651,21405,1661],{"separator":1660},[902,21407,21408],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,21410,21411],{},[883,21412,21414],{"className":21413},[886],[888,21415,21416],{"xmlns":890},[892,21417,21418,21451],{},[895,21419,21420,21422,21424,21426,21428,21430,21432,21434,21436,21438,21440,21442,21444,21446,21448],{},[898,21421,2995],{},[898,21423,2675],{},[898,21425,3004],{},[1651,21427,1738],{},[1692,21429,1694],{},[1651,21431,2181],{},[898,21433,2995],{},[898,21435,2675],{},[898,21437,3001],{},[1651,21439,1738],{},[1651,21441,2181],{},[1692,21443,21397],{},[898,21445,2665],{},[1651,21447,1839],{},[1692,21449,21450],{},"0,8.",[902,21452,21453],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,21455,21456,21536,21615],{},[123,21457,21458,1343,21486,21514,21515,1878,21533,1882],{},[883,21459,21461],{"className":21460},[886],[888,21462,21463],{"xmlns":890},[892,21464,21465,21483],{},[895,21466,21467,21469,21471,21473,21475,21477,21479,21481],{},[898,21468,2995],{},[898,21470,2675],{},[898,21472,3001],{},[1651,21474,1654],{"stretchy":1653},[1692,21476,4416],{},[1651,21478,1667],{"stretchy":1653},[1651,21480,1738],{},[1692,21482,20484],{},[902,21484,21485],{"encoding":904},"MPC(100) = 0{,}4",[883,21487,21489],{"className":21488},[886],[888,21490,21491],{"xmlns":890},[892,21492,21493,21511],{},[895,21494,21495,21497,21499,21501,21503,21505,21507,21509],{},[898,21496,2995],{},[898,21498,2675],{},[898,21500,3004],{},[1651,21502,1654],{"stretchy":1653},[1692,21504,4416],{},[1651,21506,1667],{"stretchy":1653},[1651,21508,1738],{},[1692,21510,20534],{},[902,21512,21513],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,21516,21518],{"className":21517},[886],[888,21519,21520],{"xmlns":890},[892,21521,21522,21530],{},[895,21523,21524,21526,21528],{},[898,21525,2665],{},[1651,21527,1738],{},[1692,21529,4416],{},[902,21531,21532],{"encoding":904},"Y = 100",[38,21534,21535],{},"větší sklon k úsporám",[123,21537,21538,1343,21566,21514,21594,1878,21612,1882],{},[883,21539,21541],{"className":21540},[886],[888,21542,21543],{"xmlns":890},[892,21544,21545,21563],{},[895,21546,21547,21549,21551,21553,21555,21557,21559,21561],{},[898,21548,2995],{},[898,21550,2675],{},[898,21552,3001],{},[1651,21554,1654],{"stretchy":1653},[1692,21556,9683],{},[1651,21558,1667],{"stretchy":1653},[1651,21560,1738],{},[1692,21562,20534],{},[902,21564,21565],{"encoding":904},"MPC(200) = 0{,}6",[883,21567,21569],{"className":21568},[886],[888,21570,21571],{"xmlns":890},[892,21572,21573,21591],{},[895,21574,21575,21577,21579,21581,21583,21585,21587,21589],{},[898,21576,2995],{},[898,21578,2675],{},[898,21580,3004],{},[1651,21582,1654],{"stretchy":1653},[1692,21584,9683],{},[1651,21586,1667],{"stretchy":1653},[1651,21588,1738],{},[1692,21590,20484],{},[902,21592,21593],{"encoding":904},"MPS(200) = 0{,}4",[883,21595,21597],{"className":21596},[886],[888,21598,21599],{"xmlns":890},[892,21600,21601,21609],{},[895,21602,21603,21605,21607],{},[898,21604,2665],{},[1651,21606,1738],{},[1692,21608,9683],{},[902,21610,21611],{"encoding":904},"Y = 200",[38,21613,21614],{},"větší sklon ke spotřebě",[123,21616,21617,21618,21636,21637,5230],{},"Přesně při ",[883,21619,21621],{"className":21620},[886],[888,21622,21623],{"xmlns":890},[892,21624,21625,21633],{},[895,21626,21627,21629,21631],{},[898,21628,2665],{},[1651,21630,1738],{},[1692,21632,10108],{},[902,21634,21635],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,21638,21640],{"className":21639},[886],[888,21641,21642],{"xmlns":890},[892,21643,21644,21664],{},[895,21645,21646,21648,21650,21652,21654,21656,21658,21660,21662],{},[898,21647,2995],{},[898,21649,2675],{},[898,21651,3001],{},[1651,21653,1738],{},[898,21655,2995],{},[898,21657,2675],{},[898,21659,3004],{},[1651,21661,1738],{},[1692,21663,6316],{},[902,21665,21666],{"encoding":904},"MPC = MPS = 0{,}5",[724,21668,21669,21670,21687,21688,21702,21703,4016,21716,21730,21731,21744,21745,21786],{},"Interpretace: při ",[883,21671,21673],{"className":21672},[886],[888,21674,21675],{"xmlns":890},[892,21676,21677,21685],{},[895,21678,21679,21681,21683],{},[898,21680,2665],{},[1651,21682,1738],{},[1692,21684,4416],{},[902,21686,21532],{"encoding":904}," se spotřeba mění ",[883,21689,21691],{"className":21690},[886],[888,21692,21693],{"xmlns":890},[892,21694,21695,21699],{},[895,21696,21697],{},[1692,21698,20484],{},[902,21700,21701],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,21704,21706],{"className":21705},[886],[888,21707,21708],{"xmlns":890},[892,21709,21710,21714],{},[895,21711,21712],{},[1692,21713,4416],{},[902,21715,4416],{"encoding":904},[883,21717,21719],{"className":21718},[886],[888,21720,21721],{"xmlns":890},[892,21722,21723,21728],{},[895,21724,21725],{},[1692,21726,21727],{},"101",[902,21729,21727],{"encoding":904},", změní se spotřeba přibližně o ",[883,21732,21734],{"className":21733},[886],[888,21735,21736],{"xmlns":890},[892,21737,21738,21742],{},[895,21739,21740],{},[1692,21741,20484],{},[902,21743,21701],{"encoding":904},". Skutečná změna ",[883,21746,21748],{"className":21747},[886],[888,21749,21750],{"xmlns":890},[892,21751,21752,21783],{},[895,21753,21754,21756,21758,21760,21762,21764,21766,21768,21770,21772,21774,21776,21778,21780],{},[898,21755,4216],{"mathvariant":1910},[898,21757,3001],{},[1651,21759,1738],{},[898,21761,3001],{},[1651,21763,1654],{"stretchy":1653},[1692,21765,21727],{},[1651,21767,1667],{"stretchy":1653},[1651,21769,2181],{},[898,21771,3001],{},[1651,21773,1654],{"stretchy":1653},[1692,21775,4416],{},[1651,21777,1667],{"stretchy":1653},[1651,21779,1738],{},[1692,21781,21782],{},"0,401",[902,21784,21785],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,21788,21789,21790],{},"Obecný trend: ",[38,21791,21792],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,21794,21796],{"id":21795},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,21798,21799,21800,11325,21803,21806,21807,11325,21810,13426,21813,11325,21816,21819],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,21801,21802],{},"makroekonomická rovnováha",[614,21804,21805],{},"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 ",[38,21808,21809],{},"agregátní poptávky",[614,21811,21812],{},"aggregate demand",[38,21814,21815],{},"agregátní nabídky",[614,21817,21818],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,21821,21823],{"id":21822},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,21825,21826],{},[1756,21827],{"alt":21828,"className":21829,"src":21830},"imek-keynesian-kriz",[210,1760],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,21832,21834],{"id":21833},"zadání-modelu","Zadání modelu",[724,21836,21837,21838,21851,21852,21865],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,21839,21841],{"className":21840},[886],[888,21842,21843],{"xmlns":890},[892,21844,21845,21849],{},[895,21846,21847],{},[898,21848,3001],{},[902,21850,3001],{"encoding":904}," a investice ",[883,21853,21855],{"className":21854},[886],[888,21856,21857],{"xmlns":890},[892,21858,21859,21863],{},[895,21860,21861],{},[898,21862,13482],{},[902,21864,13482],{"encoding":904},". Podmínka rovnováhy:",[724,21867,21868],{},[883,21869,21871],{"className":21870},[886],[888,21872,21873],{"xmlns":890},[892,21874,21875,21898],{},[895,21876,21877,21879,21881,21883,21885,21887,21889,21891,21893,21896],{},[898,21878,2665],{},[1651,21880,1738],{},[898,21882,3001],{},[1651,21884,1839],{},[898,21886,13482],{},[898,21888,1882],{"mathvariant":1910},[7185,21890],{"width":7187},[1651,21892,1654],{"stretchy":1653},[1692,21894,21895],{},"7.6",[1651,21897,1667],{"stretchy":1653},[902,21899,21900],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,21902,21904],{"id":21903},"soustava-rovnic","Soustava rovnic",[724,21906,21907,21908,21929,21930,21954],{},"Pro pevně zadané (plánované) investice ",[883,21909,21911],{"className":21910},[886],[888,21912,21913],{"xmlns":890},[892,21914,21915,21927],{},[895,21916,21917,21919,21921],{},[898,21918,13482],{},[1651,21920,1738],{},[2115,21922,21923,21925],{},[898,21924,13482],{},[1651,21926,2668],{},[902,21928,13493],{"encoding":904}," a funkci spotřeby ",[883,21931,21933],{"className":21932},[886],[888,21934,21935],{"xmlns":890},[892,21936,21937,21951],{},[895,21938,21939,21941,21943,21945,21947,21949],{},[898,21940,3001],{},[1651,21942,1738],{},[898,21944,3001],{},[1651,21946,1654],{"stretchy":1653},[898,21948,2665],{},[1651,21950,1667],{"stretchy":1653},[902,21952,21953],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,21956,21957],{},[883,21958,21960],{"className":21959},[886],[888,21961,21962],{"xmlns":890},[892,21963,21964,22040],{},[895,21965,21966,22031,22033,22035,22038],{},[21967,21968,21971,22003],"mtable",{"rowspacing":21969,"columnalign":21970,"columnspacing":1911},"0.25em","right left",[21972,21973,21974,21981],"mtr",{},[21975,21976,21977],"mtd",{},[2938,21978,21979],{"scriptlevel":1741,"displaystyle":1660},[898,21980,2665],{},[21975,21982,21983],{},[2938,21984,21985],{"scriptlevel":1741,"displaystyle":1660},[895,21986,21987,21989,21991,21993,21995,22001],{},[895,21988],{},[1651,21990,1738],{},[898,21992,3001],{},[1651,21994,1839],{},[2115,21996,21997,21999],{},[898,21998,13482],{},[1651,22000,2668],{},[1651,22002,1661],{"separator":1660},[21972,22004,22005,22011],{},[21975,22006,22007],{},[2938,22008,22009],{"scriptlevel":1741,"displaystyle":1660},[898,22010,3001],{},[21975,22012,22013],{},[2938,22014,22015],{"scriptlevel":1741,"displaystyle":1660},[895,22016,22017,22019,22021,22023,22025,22027,22029],{},[895,22018],{},[1651,22020,1738],{},[898,22022,3001],{},[1651,22024,1654],{"stretchy":1653},[898,22026,2665],{},[1651,22028,1667],{"stretchy":1653},[1651,22030,1661],{"separator":1660},[7185,22032],{"width":7187},[1651,22034,1654],{"stretchy":1653},[1692,22036,22037],{},"7.7",[1651,22039,1667],{"stretchy":1653},[902,22041,22042],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,22044,22045,22046,3246,22048,5197,22065,3246,22068,1882],{},"jejímž řešením jsou ",[38,22047,15183],{},[883,22049,22051],{"className":22050},[886],[888,22052,22053],{"xmlns":890},[892,22054,22055,22063],{},[895,22056,22057],{},[2115,22058,22059,22061],{},[898,22060,2665],{},[898,22062,5561],{},[902,22064,15201],{"encoding":904},[38,22066,22067],{},"rovnovážná spotřeba",[883,22069,22071],{"className":22070},[886],[888,22072,22073],{"xmlns":890},[892,22074,22075,22083],{},[895,22076,22077],{},[2115,22078,22079,22081],{},[898,22080,3001],{},[898,22082,5561],{},[902,22084,15260],{"encoding":904},[198,22086,22088,22089],{"id":22087},"výpočet-yeye","Výpočet ",[883,22090,22092],{"className":22091},[886],[888,22093,22094],{"xmlns":890},[892,22095,22096,22104],{},[895,22097,22098],{},[2115,22099,22100,22102],{},[898,22101,2665],{},[898,22103,5561],{},[902,22105,15201],{"encoding":904},[724,22107,22108,22109,22132,22133,8992,22165],{},"Pro lineární spotřebu ",[883,22110,22112],{"className":22111},[886],[888,22113,22114],{"xmlns":890},[892,22115,22116,22130],{},[895,22117,22118,22120,22122,22124,22126,22128],{},[898,22119,3001],{},[1651,22121,1738],{},[898,22123,207],{},[898,22125,2665],{},[1651,22127,1839],{},[898,22129,2268],{},[902,22131,20133],{"encoding":904}," plyne z (7.7) rovnice ",[883,22134,22136],{"className":22135},[886],[888,22137,22138],{"xmlns":890},[892,22139,22140,22162],{},[895,22141,22142,22144,22146,22148,22150,22152,22154,22156],{},[898,22143,2665],{},[1651,22145,1738],{},[898,22147,207],{},[898,22149,2665],{},[1651,22151,1839],{},[898,22153,2268],{},[1651,22155,1839],{},[2115,22157,22158,22160],{},[898,22159,13482],{},[1651,22161,2668],{},[902,22163,22164],{"encoding":904},"Y = aY + b + I^*",[38,22166,22167],{},"redukovaný tvar",[724,22169,22170],{},[883,22171,22173],{"className":22172},[886],[888,22174,22175],{"xmlns":890},[892,22176,22177,22225],{},[895,22178,22179],{},[14130,22180,22181],{"notation":14132},[2938,22182,22183],{"scriptlevel":1741,"displaystyle":1653},[2938,22184,22185],{"scriptlevel":1741,"displaystyle":1653},[2938,22186,22187],{"scriptlevel":1741,"displaystyle":1660},[895,22188,22189,22191,22197,22199,22221,22223],{},[1843,22190,1845],{},[2115,22192,22193,22195],{},[898,22194,2665],{},[898,22196,5561],{},[1651,22198,1738],{},[2446,22200,22201,22213],{},[895,22202,22203,22205,22207],{},[898,22204,2268],{},[1651,22206,1839],{},[2115,22208,22209,22211],{},[898,22210,13482],{},[1651,22212,2668],{},[895,22214,22215,22217,22219],{},[1692,22216,1694],{},[1651,22218,2181],{},[898,22220,207],{},[898,22222,1882],{"mathvariant":1910},[1843,22224,1845],{},[902,22226,22227],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,22229,22231],{"id":22230},"příklad-73","Příklad 7.3",[724,22233,22234,22235,1878,22252,5197,22276,22302],{},"V modelu ",[883,22236,22238],{"className":22237},[886],[888,22239,22240],{"xmlns":890},[892,22241,22242,22250],{},[895,22243,22244,22246,22248],{},[898,22245,3001],{},[1843,22247,13588],{},[898,22249,13482],{},[902,22251,13593],{"encoding":904},[883,22253,22255],{"className":22254},[886],[888,22256,22257],{"xmlns":890},[892,22258,22259,22273],{},[895,22260,22261,22263,22265,22267,22269,22271],{},[898,22262,3001],{},[1651,22264,1738],{},[1692,22266,20534],{},[898,22268,2665],{},[1651,22270,1839],{},[1692,22272,4190],{},[902,22274,22275],{"encoding":904},"C = 0{,}6Y + 10",[883,22277,22279],{"className":22278},[886],[888,22280,22281],{"xmlns":890},[892,22282,22283,22299],{},[895,22284,22285,22287,22289,22291,22293],{},[898,22286,13482],{},[1651,22288,1738],{},[1692,22290,4828],{},[1651,22292,1738],{},[2115,22294,22295,22297],{},[898,22296,13482],{},[1651,22298,2668],{},[902,22300,22301],{"encoding":904},"I = 12 = I^*",". Soustava",[724,22304,22305],{},[883,22306,22308],{"className":22307},[886],[888,22309,22310],{"xmlns":890},[892,22311,22312,22368],{},[21967,22313,22314,22340],{"rowspacing":21969,"columnalign":21970,"columnspacing":1911},[21972,22315,22316,22322],{},[21975,22317,22318],{},[2938,22319,22320],{"scriptlevel":1741,"displaystyle":1660},[898,22321,2665],{},[21975,22323,22324],{},[2938,22325,22326],{"scriptlevel":1741,"displaystyle":1660},[895,22327,22328,22330,22332,22334,22336,22338],{},[895,22329],{},[1651,22331,1738],{},[898,22333,3001],{},[1651,22335,1839],{},[1692,22337,4828],{},[1651,22339,1661],{"separator":1660},[21972,22341,22342,22348],{},[21975,22343,22344],{},[2938,22345,22346],{"scriptlevel":1741,"displaystyle":1660},[898,22347,3001],{},[21975,22349,22350],{},[2938,22351,22352],{"scriptlevel":1741,"displaystyle":1660},[895,22353,22354,22356,22358,22360,22362,22364,22366],{},[895,22355],{},[1651,22357,1738],{},[1692,22359,20534],{},[898,22361,2665],{},[1651,22363,1839],{},[1692,22365,4190],{},[1651,22367,1661],{"separator":1660},[902,22369,22370],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,22372,22373,22374,1343,22397,22420,22421,5230],{},"má řešení ",[883,22375,22377],{"className":22376},[886],[888,22378,22379],{"xmlns":890},[892,22380,22381,22394],{},[895,22382,22383,22389,22391],{},[2115,22384,22385,22387],{},[898,22386,2665],{},[898,22388,5561],{},[1651,22390,1738],{},[1692,22392,22393],{},"55",[902,22395,22396],{"encoding":904},"Y^E = 55",[883,22398,22400],{"className":22399},[886],[888,22401,22402],{"xmlns":890},[892,22403,22404,22417],{},[895,22405,22406,22412,22414],{},[2115,22407,22408,22410],{},[898,22409,3001],{},[898,22411,5561],{},[1651,22413,1738],{},[1692,22415,22416],{},"43",[902,22418,22419],{"encoding":904},"C^E = 43"," (a ",[883,22422,22424],{"className":22423},[886],[888,22425,22426],{"xmlns":890},[892,22427,22428,22440],{},[895,22429,22430,22436,22438],{},[2115,22431,22432,22434],{},[898,22433,3004],{},[898,22435,5561],{},[1651,22437,1738],{},[1692,22439,4828],{},[902,22441,22442],{"encoding":904},"S^E = 12",[724,22444,22445],{},[614,22446,22447,22448,22470,22471,13426,22492,22515,22516,1882],{},"Obrázek 7.5 — Přímky ",[883,22449,22451],{"className":22450},[886],[888,22452,22453],{"xmlns":890},[892,22454,22455,22467],{},[895,22456,22457,22459,22461,22463,22465],{},[898,22458,3001],{},[1651,22460,1738],{},[898,22462,2665],{},[1651,22464,2181],{},[1692,22466,4828],{},[902,22468,22469],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,22472,22474],{"className":22473},[886],[888,22475,22476],{"xmlns":890},[892,22477,22478,22490],{},[895,22479,22480,22482,22484,22486,22488],{},[898,22481,2665],{},[1651,22483,1738],{},[898,22485,3001],{},[1651,22487,1839],{},[898,22489,13482],{},[902,22491,16042],{"encoding":904},[883,22493,22495],{"className":22494},[886],[888,22496,22497],{"xmlns":890},[892,22498,22499,22513],{},[895,22500,22501,22503,22505,22507,22509,22511],{},[898,22502,3001],{},[1651,22504,1738],{},[1692,22506,20534],{},[898,22508,2665],{},[1651,22510,1839],{},[1692,22512,4190],{},[902,22514,22275],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,22517,22519],{"className":22518},[886],[888,22520,22521],{"xmlns":890},[892,22522,22523,22555],{},[895,22524,22525,22527,22533,22535,22541,22543,22545,22547,22549,22551,22553],{},[1651,22526,2261],{"stretchy":1653},[2115,22528,22529,22531],{},[898,22530,2665],{},[898,22532,5561],{},[1651,22534,1661],{"separator":1660},[2115,22536,22537,22539],{},[898,22538,3001],{},[898,22540,5561],{},[1651,22542,2279],{"stretchy":1653},[1651,22544,1738],{},[1651,22546,2261],{"stretchy":1653},[1692,22548,22393],{},[1651,22550,1661],{"separator":1660},[1692,22552,22416],{},[1651,22554,2279],{"stretchy":1653},[902,22556,22557],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,22559,22560,22563,22564,22581,22582,1882],{},[38,22561,22562],{},"Komentář k přechodu."," Model ",[883,22565,22567],{"className":22566},[886],[888,22568,22569],{"xmlns":890},[892,22570,22571,22579],{},[895,22572,22573,22575,22577],{},[898,22574,3001],{},[1843,22576,13588],{},[898,22578,13482],{},[902,22580,13593],{"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 ",[38,22583,22584,22585],{},"model ",[883,22586,22588],{"className":22587},[886],[888,22589,22590],{"xmlns":890},[892,22591,22592,22604],{},[895,22593,22594,22596,22598,22600,22602],{},[898,22595,3001],{},[1843,22597,13588],{},[898,22599,13482],{},[1843,22601,13588],{},[898,22603,13410],{},[902,22605,19433],{"encoding":904},[115,22607,22609],{"id":22608},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,22611,21834],{"id":22612},"zadání-modelu-1",[724,22614,22615,22616,22633,22634,3246,22637,11325,22650,22653],{},"Rozšíření modelu ",[883,22617,22619],{"className":22618},[886],[888,22620,22621],{"xmlns":890},[892,22622,22623,22631],{},[895,22624,22625,22627,22629],{},[898,22626,3001],{},[1843,22628,13588],{},[898,22630,13482],{},[902,22632,13593],{"encoding":904}," o ",[38,22635,22636],{},"vládní výdaje",[883,22638,22640],{"className":22639},[886],[888,22641,22642],{"xmlns":890},[892,22643,22644,22648],{},[895,22645,22646],{},[898,22647,13410],{},[902,22649,13410],{"encoding":904},[614,22651,22652],{},"government expenditure","). Podmínka rovnováhy:",[724,22655,22656],{},[883,22657,22659],{"className":22658},[886],[888,22660,22661],{"xmlns":890},[892,22662,22663,22690],{},[895,22664,22665,22667,22669,22671,22673,22675,22677,22679,22681,22683,22685,22688],{},[898,22666,2665],{},[1651,22668,1738],{},[898,22670,3001],{},[1651,22672,1839],{},[898,22674,13482],{},[1651,22676,1839],{},[898,22678,13410],{},[898,22680,1882],{"mathvariant":1910},[7185,22682],{"width":7187},[1651,22684,1654],{"stretchy":1653},[1692,22686,22687],{},"7.8",[1651,22689,1667],{"stretchy":1653},[902,22691,22692],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,22694,22695,22696,3246,22699,11325,22712,22715],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,22697,22698],{},"zdaněním domácností",[883,22700,22702],{"className":22701},[886],[888,22703,22704],{"xmlns":890},[892,22705,22706,22710],{},[895,22707,22708],{},[898,22709,4104],{},[902,22711,4104],{"encoding":904},[614,22713,22714],{},"taxation","). Zdanění bývá:",[120,22717,22718,22751,22776],{},[123,22719,22720,22721,1661],{},"úměrné důchodu: ",[883,22722,22724],{"className":22723},[886],[888,22725,22726],{"xmlns":890},[892,22727,22728,22748],{},[895,22729,22730,22732,22734,22736,22738,22740,22742,22744,22746],{},[898,22731,4104],{},[1651,22733,1738],{},[898,22735,4104],{},[1651,22737,1654],{"stretchy":1653},[898,22739,2665],{},[1651,22741,1667],{"stretchy":1653},[1651,22743,1738],{},[898,22745,20068],{},[898,22747,2665],{},[902,22749,22750],{"encoding":904},"T = T(Y) = tY",[123,22752,22753,22754,1661],{},"fixní: ",[883,22755,22757],{"className":22756},[886],[888,22758,22759],{"xmlns":890},[892,22760,22761,22773],{},[895,22762,22763,22765,22767],{},[898,22764,4104],{},[1651,22766,1738],{},[2115,22768,22769,22771],{},[898,22770,4104],{},[1651,22772,2668],{},[902,22774,22775],{"encoding":904},"T = T^*",[123,22777,22778,22779,22807,22808,1882],{},"kombinované: ",[883,22780,22782],{"className":22781},[886],[888,22783,22784],{"xmlns":890},[892,22785,22786,22804],{},[895,22787,22788,22790,22792,22798,22800,22802],{},[898,22789,4104],{},[1651,22791,1738],{},[2115,22793,22794,22796],{},[898,22795,4104],{},[1651,22797,2668],{},[1651,22799,1839],{},[898,22801,20068],{},[898,22803,2665],{},[902,22805,22806],{"encoding":904},"T = T^* + tY",", kde ",[883,22809,22811],{"className":22810},[886],[888,22812,22813],{"xmlns":890},[892,22814,22815,22827],{},[895,22816,22817,22819,22821,22823,22825],{},[1692,22818,1741],{},[1651,22820,8986],{},[898,22822,20068],{},[1651,22824,2319],{},[1692,22826,1694],{},[902,22828,22829],{"encoding":904},"0 \\le t \u003C 1",[5179,22831,22832],{},[724,22833,22834,22836,22837,22858,22859,22862,22863,22876,22877,13426,22903,3246,22906,22932,22933,22961,22962,5197,22975,22993],{},[883,22835,5719],{}," Pozor na disponibilní důchod\nV modelu ",[883,22838,22840],{"className":22839},[886],[888,22841,22842],{"xmlns":890},[892,22843,22844,22856],{},[895,22845,22846,22848,22850,22852,22854],{},[898,22847,3001],{},[1843,22849,13588],{},[898,22851,13482],{},[1843,22853,13588],{},[898,22855,13410],{},[902,22857,19433],{"encoding":904}," je nutné ",[38,22860,22861],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,22864,22866],{"className":22865},[886],[888,22867,22868],{"xmlns":890},[892,22869,22870,22874],{},[895,22871,22872],{},[898,22873,2665],{},[902,22875,2665],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,22878,22880],{"className":22879},[886],[888,22881,22882],{"xmlns":890},[892,22883,22884,22900],{},[895,22885,22886,22888,22890,22892,22894,22896,22898],{},[898,22887,2665],{},[1651,22889,1738],{},[898,22891,3001],{},[1651,22893,1839],{},[898,22895,13482],{},[1651,22897,1839],{},[898,22899,13410],{},[902,22901,22902],{"encoding":904},"Y = C + I + G",[38,22904,22905],{},"disponibilní důchod",[883,22907,22909],{"className":22908},[886],[888,22910,22911],{"xmlns":890},[892,22912,22913,22929],{},[895,22914,22915,22921,22923,22925,22927],{},[1686,22916,22917,22919],{},[898,22918,2665],{},[898,22920,2047],{},[1651,22922,1738],{},[898,22924,2665],{},[1651,22926,2181],{},[898,22928,4104],{},[902,22930,22931],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,22934,22936],{"className":22935},[886],[888,22937,22938],{"xmlns":890},[892,22939,22940,22958],{},[895,22941,22942,22944,22946,22948,22950,22956],{},[898,22943,3001],{},[1651,22945,1738],{},[898,22947,3001],{},[1651,22949,1654],{"stretchy":1653},[1686,22951,22952,22954],{},[898,22953,2665],{},[898,22955,2047],{},[1651,22957,1667],{"stretchy":1653},[902,22959,22960],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,22963,22965],{"className":22964},[886],[888,22966,22967],{"xmlns":890},[892,22968,22969,22973],{},[895,22970,22971],{},[898,22972,2665],{},[902,22974,2665],{"encoding":904},[883,22976,22978],{"className":22977},[886],[888,22979,22980],{"xmlns":890},[892,22981,22982,22990],{},[895,22983,22984],{},[1686,22985,22986,22988],{},[898,22987,2665],{},[898,22989,2047],{},[902,22991,22992],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,22995,22996,11325,22999,1667],{},[38,22997,22998],{},"Disponibilní důchod",[614,23000,23001],{},"disposable income",[724,23003,23004],{},[883,23005,23007],{"className":23006},[886],[888,23008,23009],{"xmlns":890},[892,23010,23011,23027],{},[895,23012,23013,23019,23021,23023,23025],{},[1686,23014,23015,23017],{},[898,23016,2665],{},[898,23018,2047],{},[1651,23020,1738],{},[898,23022,2665],{},[1651,23024,2181],{},[898,23026,4104],{},[902,23028,22931],{"encoding":904},[724,23030,23031,23032,1882],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,23033,23035],{"className":23034},[886],[888,23036,23037],{"xmlns":890},[892,23038,23039,23057],{},[895,23040,23041,23043,23045,23047,23049,23055],{},[898,23042,3001],{},[1651,23044,1738],{},[898,23046,3001],{},[1651,23048,1654],{"stretchy":1653},[1686,23050,23051,23053],{},[898,23052,2665],{},[898,23054,2047],{},[1651,23056,1667],{"stretchy":1653},[902,23058,22960],{"encoding":904},[198,23060,21904],{"id":23061},"soustava-rovnic-1",[724,23063,23064,23065,1343,23086,23108,23109,1793],{},"Pro pevně zadané ",[883,23066,23068],{"className":23067},[886],[888,23069,23070],{"xmlns":890},[892,23071,23072,23084],{},[895,23073,23074,23076,23078],{},[898,23075,13482],{},[1651,23077,1738],{},[2115,23079,23080,23082],{},[898,23081,13482],{},[1651,23083,2668],{},[902,23085,13493],{"encoding":904},[883,23087,23089],{"className":23088},[886],[888,23090,23091],{"xmlns":890},[892,23092,23093,23105],{},[895,23094,23095,23097,23099],{},[898,23096,13410],{},[1651,23098,1738],{},[2115,23100,23101,23103],{},[898,23102,13410],{},[1651,23104,2668],{},[902,23106,23107],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,23110,23112],{"className":23111},[886],[888,23113,23114],{"xmlns":890},[892,23115,23116,23136],{},[895,23117,23118,23120,23122,23124,23126,23132,23134],{},[898,23119,2665],{},[1651,23121,1661],{"separator":1660},[898,23123,3001],{},[1651,23125,1661],{"separator":1660},[1686,23127,23128,23130],{},[898,23129,2665],{},[898,23131,2047],{},[1651,23133,1661],{"separator":1660},[898,23135,4104],{},[902,23137,23138],{"encoding":904},"Y, C, Y_D, T",[724,23140,23141],{},[883,23142,23144],{"className":23143},[886],[888,23145,23146],{"xmlns":890},[892,23147,23148,23289],{},[895,23149,23150,23280,23282,23284,23287],{},[21967,23151,23152,23190,23218,23250],{"rowspacing":21969,"columnalign":21970,"columnspacing":1911},[21972,23153,23154,23160],{},[21975,23155,23156],{},[2938,23157,23158],{"scriptlevel":1741,"displaystyle":1660},[898,23159,2665],{},[21975,23161,23162],{},[2938,23163,23164],{"scriptlevel":1741,"displaystyle":1660},[895,23165,23166,23168,23170,23172,23174,23180,23182,23188],{},[895,23167],{},[1651,23169,1738],{},[898,23171,3001],{},[1651,23173,1839],{},[2115,23175,23176,23178],{},[898,23177,13482],{},[1651,23179,2668],{},[1651,23181,1839],{},[2115,23183,23184,23186],{},[898,23185,13410],{},[1651,23187,2668],{},[1651,23189,1661],{"separator":1660},[21972,23191,23192,23198],{},[21975,23193,23194],{},[2938,23195,23196],{"scriptlevel":1741,"displaystyle":1660},[898,23197,4104],{},[21975,23199,23200],{},[2938,23201,23202],{"scriptlevel":1741,"displaystyle":1660},[895,23203,23204,23206,23208,23210,23212,23214,23216],{},[895,23205],{},[1651,23207,1738],{},[898,23209,4104],{},[1651,23211,1654],{"stretchy":1653},[898,23213,2665],{},[1651,23215,1667],{"stretchy":1653},[1651,23217,1661],{"separator":1660},[21972,23219,23220,23226],{},[21975,23221,23222],{},[2938,23223,23224],{"scriptlevel":1741,"displaystyle":1660},[898,23225,3001],{},[21975,23227,23228],{},[2938,23229,23230],{"scriptlevel":1741,"displaystyle":1660},[895,23231,23232,23234,23236,23238,23240,23246,23248],{},[895,23233],{},[1651,23235,1738],{},[898,23237,3001],{},[1651,23239,1654],{"stretchy":1653},[1686,23241,23242,23244],{},[898,23243,2665],{},[898,23245,2047],{},[1651,23247,1667],{"stretchy":1653},[1651,23249,1661],{"separator":1660},[21972,23251,23252,23262],{},[21975,23253,23254],{},[2938,23255,23256],{"scriptlevel":1741,"displaystyle":1660},[1686,23257,23258,23260],{},[898,23259,2665],{},[898,23261,2047],{},[21975,23263,23264],{},[2938,23265,23266],{"scriptlevel":1741,"displaystyle":1660},[895,23267,23268,23270,23272,23274,23276,23278],{},[895,23269],{},[1651,23271,1738],{},[898,23273,2665],{},[1651,23275,2181],{},[898,23277,4104],{},[1651,23279,1661],{"separator":1660},[7185,23281],{"width":7187},[1651,23283,1654],{"stretchy":1653},[1692,23285,23286],{},"7.9",[1651,23288,1667],{"stretchy":1653},[902,23290,23291],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,23293,23294,23295,23339,23340,1882],{},"s řešeními ",[883,23296,23298],{"className":23297},[886],[888,23299,23300],{"xmlns":890},[892,23301,23302,23336],{},[895,23303,23304,23310,23312,23318,23320,23326,23328],{},[2115,23305,23306,23308],{},[898,23307,2665],{},[898,23309,5561],{},[1651,23311,1661],{"separator":1660},[2115,23313,23314,23316],{},[898,23315,3001],{},[898,23317,5561],{},[1651,23319,1661],{"separator":1660},[2115,23321,23322,23324],{},[898,23323,4104],{},[898,23325,5561],{},[1651,23327,1661],{"separator":1660},[1902,23329,23330,23332,23334],{},[898,23331,2665],{},[898,23333,2047],{},[898,23335,5561],{},[902,23337,23338],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,23341,23343],{"className":23342},[886],[888,23344,23345],{"xmlns":890},[892,23346,23347,23373],{},[895,23348,23349,23355,23357,23365,23367],{},[2115,23350,23351,23353],{},[898,23352,3004],{},[898,23354,5561],{},[1651,23356,1738],{},[1902,23358,23359,23361,23363],{},[898,23360,2665],{},[898,23362,2047],{},[898,23364,5561],{},[1651,23366,2181],{},[2115,23368,23369,23371],{},[898,23370,3001],{},[898,23372,5561],{},[902,23374,23375],{"encoding":904},"S^E = Y_D^E - C^E",[5179,23377,23378,23383],{},[724,23379,23380,23382],{},[883,23381,5879],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,23384,23385,23408,23491,23546,23636],{},[123,23386,23387,23390,23391,1882],{},[38,23388,23389],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,23392,23394],{"className":23393},[886],[888,23395,23396],{"xmlns":890},[892,23397,23398,23406],{},[895,23399,23400],{},[1686,23401,23402,23404],{},[898,23403,2665],{},[898,23405,2047],{},[902,23407,22992],{"encoding":904},[123,23409,23410,23459,23460,23477,23478,1882],{},[38,23411,23412,23413,23433,23434],{},"Dosaď ",[883,23414,23416],{"className":23415},[886],[888,23417,23418],{"xmlns":890},[892,23419,23420,23430],{},[895,23421,23422,23424,23426,23428],{},[898,23423,4104],{},[1651,23425,1654],{"stretchy":1653},[898,23427,2665],{},[1651,23429,1667],{"stretchy":1653},[902,23431,23432],{"encoding":904},"T(Y)"," do ",[883,23435,23437],{"className":23436},[886],[888,23438,23439],{"xmlns":890},[892,23440,23441,23457],{},[895,23442,23443,23449,23451,23453,23455],{},[1686,23444,23445,23447],{},[898,23446,2665],{},[898,23448,2047],{},[1651,23450,1738],{},[898,23452,2665],{},[1651,23454,2181],{},[898,23456,4104],{},[902,23458,22931],{"encoding":904}," — dostaneš ",[883,23461,23463],{"className":23462},[886],[888,23464,23465],{"xmlns":890},[892,23466,23467,23475],{},[895,23468,23469],{},[1686,23470,23471,23473],{},[898,23472,2665],{},[898,23474,2047],{},[902,23476,22992],{"encoding":904}," jako lineární funkci ",[883,23479,23481],{"className":23480},[886],[888,23482,23483],{"xmlns":890},[892,23484,23485,23489],{},[895,23486,23487],{},[898,23488,2665],{},[902,23490,2665],{"encoding":904},[123,23492,23493,23459,23520,23477,23533,1882],{},[38,23494,23412,23495,23519],{},[883,23496,23498],{"className":23497},[886],[888,23499,23500],{"xmlns":890},[892,23501,23502,23516],{},[895,23503,23504,23510,23512,23514],{},[1686,23505,23506,23508],{},[898,23507,2665],{},[898,23509,2047],{},[1651,23511,1654],{"stretchy":1653},[898,23513,2665],{},[1651,23515,1667],{"stretchy":1653},[902,23517,23518],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,23521,23523],{"className":23522},[886],[888,23524,23525],{"xmlns":890},[892,23526,23527,23531],{},[895,23528,23529],{},[898,23530,3001],{},[902,23532,3001],{"encoding":904},[883,23534,23536],{"className":23535},[886],[888,23537,23538],{"xmlns":890},[892,23539,23540,23544],{},[895,23541,23542],{},[898,23543,2665],{},[902,23545,2665],{"encoding":904},[123,23547,23548,3246,23570,23604,23605,23618,23619,1882],{},[38,23549,23412,23550,23569],{},[883,23551,23553],{"className":23552},[886],[888,23554,23555],{"xmlns":890},[892,23556,23557,23567],{},[895,23558,23559,23561,23563,23565],{},[898,23560,3001],{},[1651,23562,1654],{"stretchy":1653},[898,23564,2665],{},[1651,23566,1667],{"stretchy":1653},[902,23568,15514],{"encoding":904}," do podmínky rovnováhy",[883,23571,23573],{"className":23572},[886],[888,23574,23575],{"xmlns":890},[892,23576,23577,23601],{},[895,23578,23579,23581,23583,23585,23587,23593,23595],{},[898,23580,2665],{},[1651,23582,1738],{},[898,23584,3001],{},[1651,23586,1839],{},[2115,23588,23589,23591],{},[898,23590,13482],{},[1651,23592,2668],{},[1651,23594,1839],{},[2115,23596,23597,23599],{},[898,23598,13410],{},[1651,23600,2668],{},[902,23602,23603],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,23606,23608],{"className":23607},[886],[888,23609,23610],{"xmlns":890},[892,23611,23612,23616],{},[895,23613,23614],{},[898,23615,2665],{},[902,23617,2665],{"encoding":904},", odtud ",[883,23620,23622],{"className":23621},[886],[888,23623,23624],{"xmlns":890},[892,23625,23626,23634],{},[895,23627,23628],{},[2115,23629,23630,23632],{},[898,23631,2665],{},[898,23633,5561],{},[902,23635,15201],{"encoding":904},[123,23637,23638,23641,23642,1343,23660,1343,23680,1343,23697,1882],{},[38,23639,23640],{},"Zpětným dosazením"," dopočítej ",[883,23643,23645],{"className":23644},[886],[888,23646,23647],{"xmlns":890},[892,23648,23649,23657],{},[895,23650,23651],{},[2115,23652,23653,23655],{},[898,23654,4104],{},[898,23656,5561],{},[902,23658,23659],{"encoding":904},"T^E",[883,23661,23663],{"className":23662},[886],[888,23664,23665],{"xmlns":890},[892,23666,23667,23677],{},[895,23668,23669],{},[1902,23670,23671,23673,23675],{},[898,23672,2665],{},[898,23674,2047],{},[898,23676,5561],{},[902,23678,23679],{"encoding":904},"Y_D^E",[883,23681,23683],{"className":23682},[886],[888,23684,23685],{"xmlns":890},[892,23686,23687,23695],{},[895,23688,23689],{},[2115,23690,23691,23693],{},[898,23692,3001],{},[898,23694,5561],{},[902,23696,15260],{"encoding":904},[883,23698,23700],{"className":23699},[886],[888,23701,23702],{"xmlns":890},[892,23703,23704,23712],{},[895,23705,23706],{},[2115,23707,23708,23710],{},[898,23709,3004],{},[898,23711,5561],{},[902,23713,23714],{"encoding":904},"S^E",[198,23716,23718],{"id":23717},"příklad-74","Příklad 7.4",[724,23720,22234,23721,23742,23743,1343,23774,1343,23798,1343,23820,23842],{},[883,23722,23724],{"className":23723},[886],[888,23725,23726],{"xmlns":890},[892,23727,23728,23740],{},[895,23729,23730,23732,23734,23736,23738],{},[898,23731,3001],{},[1843,23733,13588],{},[898,23735,13482],{},[1843,23737,13588],{},[898,23739,13410],{},[902,23741,19433],{"encoding":904}," jsou dány ",[883,23744,23746],{"className":23745},[886],[888,23747,23748],{"xmlns":890},[892,23749,23750,23771],{},[895,23751,23752,23754,23756,23759,23761,23767,23769],{},[898,23753,3001],{},[1651,23755,1738],{},[1692,23757,23758],{},"0,9",[1843,23760,1845],{},[1686,23762,23763,23765],{},[898,23764,2665],{},[898,23766,2047],{},[1651,23768,1839],{},[1692,23770,7204],{},[902,23772,23773],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,23775,23777],{"className":23776},[886],[888,23778,23779],{"xmlns":890},[892,23780,23781,23795],{},[895,23782,23783,23785,23787,23789,23791,23793],{},[898,23784,4104],{},[1651,23786,1738],{},[1692,23788,4166],{},[898,23790,2665],{},[1651,23792,1839],{},[1692,23794,6311],{},[902,23796,23797],{"encoding":904},"T = 0{,}2Y + 25",[883,23799,23801],{"className":23800},[886],[888,23802,23803],{"xmlns":890},[892,23804,23805,23817],{},[895,23806,23807,23813,23815],{},[2115,23808,23809,23811],{},[898,23810,13482],{},[1651,23812,2668],{},[1651,23814,1738],{},[1692,23816,16336],{},[902,23818,23819],{"encoding":904},"I^* = 35",[883,23821,23823],{"className":23822},[886],[888,23824,23825],{"xmlns":890},[892,23826,23827,23839],{},[895,23828,23829,23835,23837],{},[2115,23830,23831,23833],{},[898,23832,13410],{},[1651,23834,2668],{},[1651,23836,1738],{},[1692,23838,10340],{},[902,23840,23841],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,23844,23845],{},[883,23846,23848],{"className":23847},[886],[888,23849,23850],{"xmlns":890},[892,23851,23852,23976],{},[21967,23853,23854,23884,23912,23946],{"rowspacing":21969,"columnalign":21970,"columnspacing":1911},[21972,23855,23856,23862],{},[21975,23857,23858],{},[2938,23859,23860],{"scriptlevel":1741,"displaystyle":1660},[898,23861,2665],{},[21975,23863,23864],{},[2938,23865,23866],{"scriptlevel":1741,"displaystyle":1660},[895,23867,23868,23870,23872,23874,23876,23878,23880,23882],{},[895,23869],{},[1651,23871,1738],{},[898,23873,3001],{},[1651,23875,1839],{},[1692,23877,16336],{},[1651,23879,1839],{},[1692,23881,10340],{},[1651,23883,1661],{"separator":1660},[21972,23885,23886,23892],{},[21975,23887,23888],{},[2938,23889,23890],{"scriptlevel":1741,"displaystyle":1660},[898,23891,4104],{},[21975,23893,23894],{},[2938,23895,23896],{"scriptlevel":1741,"displaystyle":1660},[895,23897,23898,23900,23902,23904,23906,23908,23910],{},[895,23899],{},[1651,23901,1738],{},[1692,23903,4166],{},[898,23905,2665],{},[1651,23907,1839],{},[1692,23909,6311],{},[1651,23911,1661],{"separator":1660},[21972,23913,23914,23920],{},[21975,23915,23916],{},[2938,23917,23918],{"scriptlevel":1741,"displaystyle":1660},[898,23919,3001],{},[21975,23921,23922],{},[2938,23923,23924],{"scriptlevel":1741,"displaystyle":1660},[895,23925,23926,23928,23930,23932,23934,23940,23942,23944],{},[895,23927],{},[1651,23929,1738],{},[1692,23931,23758],{},[1843,23933,1845],{},[1686,23935,23936,23938],{},[898,23937,2665],{},[898,23939,2047],{},[1651,23941,1839],{},[1692,23943,7204],{},[1651,23945,1661],{"separator":1660},[21972,23947,23948,23958],{},[21975,23949,23950],{},[2938,23951,23952],{"scriptlevel":1741,"displaystyle":1660},[1686,23953,23954,23956],{},[898,23955,2665],{},[898,23957,2047],{},[21975,23959,23960],{},[2938,23961,23962],{"scriptlevel":1741,"displaystyle":1660},[895,23963,23964,23966,23968,23970,23972,23974],{},[895,23965],{},[1651,23967,1738],{},[898,23969,2665],{},[1651,23971,2181],{},[898,23973,4104],{},[898,23975,1882],{"mathvariant":1910},[902,23977,23978],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,23980,23981,23984,23985,24039,24040,24086,24087,1793],{},[38,23982,23983],{},"Řešení."," Z definice ",[883,23986,23988],{"className":23987},[886],[888,23989,23990],{"xmlns":890},[892,23991,23992,24036],{},[895,23993,23994,24000,24002,24004,24006,24008,24010,24012,24014,24016,24018,24020,24022,24024,24026,24028,24030,24032,24034],{},[1686,23995,23996,23998],{},[898,23997,2665],{},[898,23999,2047],{},[1651,24001,1738],{},[898,24003,2665],{},[1651,24005,2181],{},[898,24007,4104],{},[1651,24009,1738],{},[898,24011,2665],{},[1651,24013,2181],{},[1651,24015,1654],{"stretchy":1653},[1692,24017,4166],{},[898,24019,2665],{},[1651,24021,1839],{},[1692,24023,6311],{},[1651,24025,1667],{"stretchy":1653},[1651,24027,1738],{},[1692,24029,15887],{},[898,24031,2665],{},[1651,24033,2181],{},[1692,24035,6311],{},[902,24037,24038],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,24041,24043],{"className":24042},[886],[888,24044,24045],{"xmlns":890},[892,24046,24047,24083],{},[895,24048,24049,24051,24053,24055,24057,24059,24061,24063,24065,24067,24069,24071,24073,24076,24078,24080],{},[898,24050,3001],{},[1651,24052,1738],{},[1692,24054,23758],{},[1651,24056,1654],{"stretchy":1653},[1692,24058,15887],{},[898,24060,2665],{},[1651,24062,2181],{},[1692,24064,6311],{},[1651,24066,1667],{"stretchy":1653},[1651,24068,1839],{},[1692,24070,7204],{},[1651,24072,1738],{},[1692,24074,24075],{},"0,72",[898,24077,2665],{},[1651,24079,1839],{},[1692,24081,24082],{},"47,5",[902,24084,24085],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,24088,24090],{"className":24089},[886],[888,24091,24092],{"xmlns":890},[892,24093,24094,24112],{},[895,24095,24096,24098,24100,24102,24104,24106,24108,24110],{},[898,24097,2665],{},[1651,24099,1738],{},[1692,24101,24075],{},[898,24103,2665],{},[1651,24105,1839],{},[1692,24107,24082],{},[1651,24109,1839],{},[1692,24111,22393],{},[902,24113,24114],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,24116,24117],{},[883,24118,24120],{"className":24119},[886],[888,24121,24122],{"xmlns":890},[892,24123,24124,24165],{},[895,24125,24126,24129,24131,24133,24136,24138,24140,24142,24148,24150,24160,24162],{},[1692,24127,24128],{},"0,28",[898,24130,2665],{},[1651,24132,1738],{},[1692,24134,24135],{},"102,5",[1843,24137,5295],{},[1651,24139,16306],{},[1843,24141,5295],{},[2115,24143,24144,24146],{},[898,24145,2665],{},[898,24147,5561],{},[1651,24149,1738],{},[2938,24151,24152],{"scriptlevel":1741,"displaystyle":1653},[2446,24153,24154,24157],{},[1692,24155,24156],{},"5125",[1692,24158,24159],{},"14",[1651,24161,7207],{},[1692,24163,24164],{},"366,071.",[902,24166,24167],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,24169,24170],{},"Rovnovážné veličiny:",[120,24172,24173,24208,24260,24314,24362],{},[123,24174,24175,1661],{},[883,24176,24178],{"className":24177},[886],[888,24179,24180],{"xmlns":890},[892,24181,24182,24205],{},[895,24183,24184,24190,24192,24200,24202],{},[2115,24185,24186,24188],{},[898,24187,2665],{},[898,24189,5561],{},[1651,24191,1738],{},[2938,24193,24194],{"scriptlevel":1741,"displaystyle":1653},[2446,24195,24196,24198],{},[1692,24197,24156],{},[1692,24199,24159],{},[1651,24201,7207],{},[1692,24203,24204],{},"366,071",[902,24206,24207],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,24209,24210,1661],{},[883,24211,24213],{"className":24212},[886],[888,24214,24215],{"xmlns":890},[892,24216,24217,24257],{},[895,24218,24219,24225,24227,24229,24231,24237,24239,24241,24243,24252,24254],{},[2115,24220,24221,24223],{},[898,24222,4104],{},[898,24224,5561],{},[1651,24226,1738],{},[1692,24228,4166],{},[1843,24230,1845],{},[2115,24232,24233,24235],{},[898,24234,2665],{},[898,24236,5561],{},[1651,24238,1839],{},[1692,24240,6311],{},[1651,24242,1738],{},[2938,24244,24245],{"scriptlevel":1741,"displaystyle":1653},[2446,24246,24247,24250],{},[1692,24248,24249],{},"1375",[1692,24251,24159],{},[1651,24253,7207],{},[1692,24255,24256],{},"98,214",[902,24258,24259],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,24261,24262,1661],{},[883,24263,24265],{"className":24264},[886],[888,24266,24267],{"xmlns":890},[892,24268,24269,24311],{},[895,24270,24271,24279,24281,24287,24289,24295,24297,24306,24308],{},[1902,24272,24273,24275,24277],{},[898,24274,2665],{},[898,24276,2047],{},[898,24278,5561],{},[1651,24280,1738],{},[2115,24282,24283,24285],{},[898,24284,2665],{},[898,24286,5561],{},[1651,24288,2181],{},[2115,24290,24291,24293],{},[898,24292,4104],{},[898,24294,5561],{},[1651,24296,1738],{},[2938,24298,24299],{"scriptlevel":1741,"displaystyle":1653},[2446,24300,24301,24304],{},[1692,24302,24303],{},"3750",[1692,24305,24159],{},[1651,24307,7207],{},[1692,24309,24310],{},"267,857",[902,24312,24313],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,24315,24316,1661],{},[883,24317,24319],{"className":24318},[886],[888,24320,24321],{"xmlns":890},[892,24322,24323,24359],{},[895,24324,24325,24331,24333,24339,24341,24343,24345,24354,24356],{},[2115,24326,24327,24329],{},[898,24328,3001],{},[898,24330,5561],{},[1651,24332,1738],{},[2115,24334,24335,24337],{},[898,24336,2665],{},[898,24338,5561],{},[1651,24340,2181],{},[1692,24342,22393],{},[1651,24344,1738],{},[2938,24346,24347],{"scriptlevel":1741,"displaystyle":1653},[2446,24348,24349,24352],{},[1692,24350,24351],{},"4355",[1692,24353,24159],{},[1651,24355,7207],{},[1692,24357,24358],{},"311,071",[902,24360,24361],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,24363,24364,24420],{},[883,24365,24367],{"className":24366},[886],[888,24368,24369],{"xmlns":890},[892,24370,24371,24417],{},[895,24372,24373,24379,24381,24389,24391,24397,24399,24401,24410,24412,24414],{},[2115,24374,24375,24377],{},[898,24376,3004],{},[898,24378,5561],{},[1651,24380,1738],{},[1902,24382,24383,24385,24387],{},[898,24384,2665],{},[898,24386,2047],{},[898,24388,5561],{},[1651,24390,2181],{},[2115,24392,24393,24395],{},[898,24394,3001],{},[898,24396,5561],{},[1651,24398,1738],{},[1651,24400,2181],{},[2938,24402,24403],{"scriptlevel":1741,"displaystyle":1653},[2446,24404,24405,24408],{},[1692,24406,24407],{},"605",[1692,24409,24159],{},[1651,24411,7207],{},[1651,24413,2181],{},[1692,24415,24416],{},"43,214",[902,24418,24419],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,24422,24423,22563,24425,24446,24447,24450,24451,24474,24475,1882],{},[38,24424,22562],{},[883,24426,24428],{"className":24427},[886],[888,24429,24430],{"xmlns":890},[892,24431,24432,24444],{},[895,24433,24434,24436,24438,24440,24442],{},[898,24435,3001],{},[1843,24437,13588],{},[898,24439,13482],{},[1843,24441,13588],{},[898,24443,13410],{},[902,24445,19433],{"encoding":904}," stále uvažuje ",[38,24448,24449],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,24452,24454],{"className":24453},[886],[888,24455,24456],{"xmlns":890},[892,24457,24458,24471],{},[895,24459,24460,24462,24464,24467,24469],{},[898,24461,13618],{},[1651,24463,1738],{},[898,24465,24466],{},"B",[1651,24468,2181],{},[898,24470,2995],{},[902,24472,24473],{"encoding":904},"X = B - M"," dává ",[38,24476,22584,24477],{},[883,24478,24480],{"className":24479},[886],[888,24481,24482],{"xmlns":890},[892,24483,24484,24500],{},[895,24485,24486,24488,24490,24492,24494,24496,24498],{},[898,24487,3001],{},[1843,24489,13588],{},[898,24491,13482],{},[1843,24493,13588],{},[898,24495,13410],{},[1843,24497,13588],{},[898,24499,13618],{},[902,24501,13621],{"encoding":904},[115,24503,24505],{"id":24504},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,24507,21834],{"id":24508},"zadání-modelu-2",[724,24510,24511,24512,3246,24515,22807,24536,24549,24550,13426,24553,24566],{},"Rozšíření o ",[38,24513,24514],{},"čistý export",[883,24516,24518],{"className":24517},[886],[888,24519,24520],{"xmlns":890},[892,24521,24522,24534],{},[895,24523,24524,24526,24528,24530,24532],{},[898,24525,13618],{},[1651,24527,1738],{},[898,24529,24466],{},[1651,24531,2181],{},[898,24533,2995],{},[902,24535,24473],{"encoding":904},[883,24537,24539],{"className":24538},[886],[888,24540,24541],{"xmlns":890},[892,24542,24543,24547],{},[895,24544,24545],{},[898,24546,24466],{},[902,24548,24466],{"encoding":904}," je hrubý export (",[614,24551,24552],{},"brutto export",[883,24554,24556],{"className":24555},[886],[888,24557,24558],{"xmlns":890},[892,24559,24560,24564],{},[895,24561,24562],{},[898,24563,2995],{},[902,24565,2995],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,24568,24569],{},[883,24570,24572],{"className":24571},[886],[888,24573,24574],{"xmlns":890},[892,24575,24576,24596],{},[895,24577,24578,24580,24582,24584,24586,24592,24594],{},[898,24579,2995],{},[1651,24581,1738],{},[898,24583,2995],{},[1651,24585,1654],{"stretchy":1653},[1686,24587,24588,24590],{},[898,24589,2665],{},[898,24591,2047],{},[1651,24593,1667],{"stretchy":1653},[898,24595,1882],{"mathvariant":1910},[902,24597,24598],{"encoding":904},"M = M(Y_D).",[724,24600,24601],{},"Podmínka rovnováhy:",[724,24603,24604],{},[883,24605,24607],{"className":24606},[886],[888,24608,24609],{"xmlns":890},[892,24610,24611,24648],{},[895,24612,24613,24615,24617,24619,24621,24623,24625,24627,24629,24631,24633,24635,24637,24639,24641,24644,24646],{},[898,24614,2665],{},[1651,24616,1738],{},[898,24618,3001],{},[1651,24620,1839],{},[898,24622,13482],{},[1651,24624,1839],{},[898,24626,13410],{},[1651,24628,1839],{},[898,24630,24466],{},[1651,24632,2181],{},[898,24634,2995],{},[898,24636,1882],{"mathvariant":1910},[7185,24638],{"width":7187},[1651,24640,1654],{"stretchy":1653},[1692,24642,24643],{},"7.10",[1843,24645,207],{},[1651,24647,1667],{"stretchy":1653},[902,24649,24650],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,24652,21904],{"id":24653},"soustava-rovnic-2",[724,24655,23064,24656,24690,24691,1793],{},[883,24657,24659],{"className":24658},[886],[888,24660,24661],{"xmlns":890},[892,24662,24663,24687],{},[895,24664,24665,24671,24673,24679,24681],{},[2115,24666,24667,24669],{},[898,24668,13482],{},[1651,24670,2668],{},[1651,24672,1661],{"separator":1660},[2115,24674,24675,24677],{},[898,24676,13410],{},[1651,24678,2668],{},[1651,24680,1661],{"separator":1660},[2115,24682,24683,24685],{},[898,24684,24466],{},[1651,24686,2668],{},[902,24688,24689],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,24692,24694],{"className":24693},[886],[888,24695,24696],{"xmlns":890},[892,24697,24698,24722],{},[895,24699,24700,24702,24704,24706,24708,24710,24712,24718,24720],{},[898,24701,2665],{},[1651,24703,1661],{"separator":1660},[898,24705,3001],{},[1651,24707,1661],{"separator":1660},[898,24709,4104],{},[1651,24711,1661],{"separator":1660},[1686,24713,24714,24716],{},[898,24715,2665],{},[898,24717,2047],{},[1651,24719,1661],{"separator":1660},[898,24721,2995],{},[902,24723,24724],{"encoding":904},"Y, C, T, Y_D, M",[724,24726,24727],{},[883,24728,24730],{"className":24729},[886],[888,24731,24732],{"xmlns":890},[892,24733,24734,24918],{},[895,24735,24736,24910,24912,24914,24916],{},[21967,24737,24738,24770,24800,24828,24860],{"rowspacing":21969,"columnalign":21970,"columnspacing":1911},[21972,24739,24740,24746],{},[21975,24741,24742],{},[2938,24743,24744],{"scriptlevel":1741,"displaystyle":1660},[898,24745,3001],{},[21975,24747,24748],{},[2938,24749,24750],{"scriptlevel":1741,"displaystyle":1660},[895,24751,24752,24754,24756,24758,24760,24766,24768],{},[895,24753],{},[1651,24755,1738],{},[898,24757,3001],{},[1651,24759,1654],{"stretchy":1653},[1686,24761,24762,24764],{},[898,24763,2665],{},[898,24765,2047],{},[1651,24767,1667],{"stretchy":1653},[1651,24769,1661],{"separator":1660},[21972,24771,24772,24782],{},[21975,24773,24774],{},[2938,24775,24776],{"scriptlevel":1741,"displaystyle":1660},[1686,24777,24778,24780],{},[898,24779,2665],{},[898,24781,2047],{},[21975,24783,24784],{},[2938,24785,24786],{"scriptlevel":1741,"displaystyle":1660},[895,24787,24788,24790,24792,24794,24796,24798],{},[895,24789],{},[1651,24791,1738],{},[898,24793,2665],{},[1651,24795,2181],{},[898,24797,4104],{},[1651,24799,1661],{"separator":1660},[21972,24801,24802,24808],{},[21975,24803,24804],{},[2938,24805,24806],{"scriptlevel":1741,"displaystyle":1660},[898,24807,4104],{},[21975,24809,24810],{},[2938,24811,24812],{"scriptlevel":1741,"displaystyle":1660},[895,24813,24814,24816,24818,24820,24822,24824,24826],{},[895,24815],{},[1651,24817,1738],{},[898,24819,4104],{},[1651,24821,1654],{"stretchy":1653},[898,24823,2665],{},[1651,24825,1667],{"stretchy":1653},[1651,24827,1661],{"separator":1660},[21972,24829,24830,24836],{},[21975,24831,24832],{},[2938,24833,24834],{"scriptlevel":1741,"displaystyle":1660},[898,24835,2995],{},[21975,24837,24838],{},[2938,24839,24840],{"scriptlevel":1741,"displaystyle":1660},[895,24841,24842,24844,24846,24848,24850,24856,24858],{},[895,24843],{},[1651,24845,1738],{},[898,24847,2995],{},[1651,24849,1654],{"stretchy":1653},[1686,24851,24852,24854],{},[898,24853,2665],{},[898,24855,2047],{},[1651,24857,1667],{"stretchy":1653},[1651,24859,1661],{"separator":1660},[21972,24861,24862,24868],{},[21975,24863,24864],{},[2938,24865,24866],{"scriptlevel":1741,"displaystyle":1660},[898,24867,2665],{},[21975,24869,24870],{},[2938,24871,24872],{"scriptlevel":1741,"displaystyle":1660},[895,24873,24874,24876,24878,24880,24882,24888,24890,24896,24898,24904,24906,24908],{},[895,24875],{},[1651,24877,1738],{},[898,24879,3001],{},[1651,24881,1839],{},[2115,24883,24884,24886],{},[898,24885,13482],{},[1651,24887,2668],{},[1651,24889,1839],{},[2115,24891,24892,24894],{},[898,24893,13410],{},[1651,24895,2668],{},[1651,24897,1839],{},[2115,24899,24900,24902],{},[898,24901,24466],{},[1651,24903,2668],{},[1651,24905,2181],{},[898,24907,2995],{},[898,24909,1882],{"mathvariant":1910},[7185,24911],{"width":7187},[1651,24913,1654],{"stretchy":1653},[1692,24915,24643],{},[1651,24917,1667],{"stretchy":1653},[902,24919,24920],{"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)",[198,24922,24924],{"id":24923},"příklad-75","Příklad 7.5",[724,24926,24927,24928,1343,24960,1343,24987,1343,25008,1343,25030,1343,25052,25075],{},"Dáno: ",[883,24929,24931],{"className":24930},[886],[888,24932,24933],{"xmlns":890},[892,24934,24935,24957],{},[895,24936,24937,24939,24941,24944,24946,24952,24954],{},[898,24938,3001],{},[1651,24940,1738],{},[1692,24942,24943],{},"0,75",[1843,24945,1845],{},[1686,24947,24948,24950],{},[898,24949,2665],{},[898,24951,2047],{},[1651,24953,1839],{},[1692,24955,24956],{},"750",[902,24958,24959],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,24961,24963],{"className":24962},[886],[888,24964,24965],{"xmlns":890},[892,24966,24967,24984],{},[895,24968,24969,24971,24973,24976,24978],{},[898,24970,2995],{},[1651,24972,1738],{},[1692,24974,24975],{},"0,15",[1843,24977,1845],{},[1686,24979,24980,24982],{},[898,24981,2665],{},[898,24983,2047],{},[902,24985,24986],{"encoding":904},"M = 0{,}15\\,Y_D",[883,24988,24990],{"className":24989},[886],[888,24991,24992],{"xmlns":890},[892,24993,24994,25005],{},[895,24995,24996,24998,25000,25003],{},[898,24997,4104],{},[1651,24999,1738],{},[1692,25001,25002],{},"0,25",[898,25004,2665],{},[902,25006,25007],{"encoding":904},"T = 0{,}25Y",[883,25009,25011],{"className":25010},[886],[888,25012,25013],{"xmlns":890},[892,25014,25015,25027],{},[895,25016,25017,25023,25025],{},[2115,25018,25019,25021],{},[898,25020,13482],{},[1651,25022,2668],{},[1651,25024,1738],{},[1692,25026,16408],{},[902,25028,25029],{"encoding":904},"I^* = 500",[883,25031,25033],{"className":25032},[886],[888,25034,25035],{"xmlns":890},[892,25036,25037,25049],{},[895,25038,25039,25045,25047],{},[2115,25040,25041,25043],{},[898,25042,13410],{},[1651,25044,2668],{},[1651,25046,1738],{},[1692,25048,10108],{},[902,25050,25051],{"encoding":904},"G^* = 150",[883,25053,25055],{"className":25054},[886],[888,25056,25057],{"xmlns":890},[892,25058,25059,25072],{},[895,25060,25061,25067,25069],{},[2115,25062,25063,25065],{},[898,25064,24466],{},[1651,25066,2668],{},[1651,25068,1738],{},[1692,25070,25071],{},"800",[902,25073,25074],{"encoding":904},"B^* = 800",". Soustava:",[724,25077,25078],{},[883,25079,25081],{"className":25080},[886],[888,25082,25083],{"xmlns":890},[892,25084,25085,25303],{},[21967,25086,25087,25133,25175,25211,25253],{"rowspacing":21969,"columnalign":21970,"columnspacing":1911},[21972,25088,25089,25105],{},[21975,25090,25091],{},[2938,25092,25093],{"scriptlevel":1741,"displaystyle":1660},[895,25094,25095,25097,25099,25101,25103],{},[1651,25096,1654],{"stretchy":1653},[898,25098,13339],{},[1692,25100,1694],{},[1651,25102,1667],{"stretchy":1653},[1843,25104,3631],{},[21975,25106,25107],{},[2938,25108,25109],{"scriptlevel":1741,"displaystyle":1660},[895,25110,25111,25113,25115,25117,25119,25121,25127,25129,25131],{},[895,25112],{},[898,25114,3001],{},[1651,25116,1738],{},[1692,25118,24943],{},[1843,25120,1845],{},[1686,25122,25123,25125],{},[898,25124,2665],{},[898,25126,2047],{},[1651,25128,1839],{},[1692,25130,24956],{},[1651,25132,1661],{"separator":1660},[21972,25134,25135,25151],{},[21975,25136,25137],{},[2938,25138,25139],{"scriptlevel":1741,"displaystyle":1660},[895,25140,25141,25143,25145,25147,25149],{},[1651,25142,1654],{"stretchy":1653},[898,25144,13339],{},[1692,25146,1703],{},[1651,25148,1667],{"stretchy":1653},[1843,25150,3631],{},[21975,25152,25153],{},[2938,25154,25155],{"scriptlevel":1741,"displaystyle":1660},[895,25156,25157,25159,25165,25167,25169,25171,25173],{},[895,25158],{},[1686,25160,25161,25163],{},[898,25162,2665],{},[898,25164,2047],{},[1651,25166,1738],{},[898,25168,2665],{},[1651,25170,2181],{},[898,25172,4104],{},[1651,25174,1661],{"separator":1660},[21972,25176,25177,25193],{},[21975,25178,25179],{},[2938,25180,25181],{"scriptlevel":1741,"displaystyle":1660},[895,25182,25183,25185,25187,25189,25191],{},[1651,25184,1654],{"stretchy":1653},[898,25186,13339],{},[1692,25188,3521],{},[1651,25190,1667],{"stretchy":1653},[1843,25192,3631],{},[21975,25194,25195],{},[2938,25196,25197],{"scriptlevel":1741,"displaystyle":1660},[895,25198,25199,25201,25203,25205,25207,25209],{},[895,25200],{},[898,25202,4104],{},[1651,25204,1738],{},[1692,25206,25002],{},[898,25208,2665],{},[1651,25210,1661],{"separator":1660},[21972,25212,25213,25229],{},[21975,25214,25215],{},[2938,25216,25217],{"scriptlevel":1741,"displaystyle":1660},[895,25218,25219,25221,25223,25225,25227],{},[1651,25220,1654],{"stretchy":1653},[898,25222,13339],{},[1692,25224,3689],{},[1651,25226,1667],{"stretchy":1653},[1843,25228,3631],{},[21975,25230,25231],{},[2938,25232,25233],{"scriptlevel":1741,"displaystyle":1660},[895,25234,25235,25237,25239,25241,25243,25245,25251],{},[895,25236],{},[898,25238,2995],{},[1651,25240,1738],{},[1692,25242,24975],{},[1843,25244,1845],{},[1686,25246,25247,25249],{},[898,25248,2665],{},[898,25250,2047],{},[1651,25252,1661],{"separator":1660},[21972,25254,25255,25271],{},[21975,25256,25257],{},[2938,25258,25259],{"scriptlevel":1741,"displaystyle":1660},[895,25260,25261,25263,25265,25267,25269],{},[1651,25262,1654],{"stretchy":1653},[898,25264,13339],{},[1692,25266,3574],{},[1651,25268,1667],{"stretchy":1653},[1843,25270,3631],{},[21975,25272,25273],{},[2938,25274,25275],{"scriptlevel":1741,"displaystyle":1660},[895,25276,25277,25279,25281,25283,25285,25287,25289,25291,25293,25295,25297,25299,25301],{},[895,25278],{},[898,25280,2665],{},[1651,25282,1738],{},[898,25284,3001],{},[1651,25286,1839],{},[1692,25288,16408],{},[1651,25290,1839],{},[1692,25292,10108],{},[1651,25294,1839],{},[1692,25296,25071],{},[1651,25298,2181],{},[898,25300,2995],{},[898,25302,1882],{"mathvariant":1910},[902,25304,25305],{"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}",[724,25307,25308,25309,25343],{},"Postupná substituce — z (r3) do (r2): ",[883,25310,25312],{"className":25311},[886],[888,25313,25314],{"xmlns":890},[892,25315,25316,25340],{},[895,25317,25318,25324,25326,25328,25330,25332,25334,25336,25338],{},[1686,25319,25320,25322],{},[898,25321,2665],{},[898,25323,2047],{},[1651,25325,1738],{},[898,25327,2665],{},[1651,25329,2181],{},[1692,25331,25002],{},[898,25333,2665],{},[1651,25335,1738],{},[1692,25337,24943],{},[898,25339,2665],{},[902,25341,25342],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,25345,25346],{},[883,25347,25349],{"className":25348},[886],[888,25350,25351],{"xmlns":890},[892,25352,25353,25394],{},[895,25354,25355,25357,25359,25361,25363,25365,25367,25369,25371,25373,25375,25377,25379,25381,25383,25386,25388,25390,25392],{},[1651,25356,1654],{"stretchy":1653},[898,25358,13339],{},[1692,25360,3581],{},[1651,25362,1667],{"stretchy":1653},[1843,25364,3631],{},[898,25366,3001],{},[1651,25368,1738],{},[1692,25370,24943],{},[1651,25372,4503],{},[1692,25374,24943],{},[898,25376,2665],{},[1651,25378,1839],{},[1692,25380,24956],{},[1651,25382,1738],{},[1692,25384,25385],{},"0,5625",[898,25387,2665],{},[1651,25389,1839],{},[1692,25391,24956],{},[1651,25393,1661],{"separator":1660},[902,25395,25396],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,25398,25399],{},[883,25400,25402],{"className":25401},[886],[888,25403,25404],{"xmlns":890},[892,25405,25406,25440],{},[895,25407,25408,25410,25412,25415,25417,25419,25421,25423,25425,25427,25429,25431,25433,25436,25438],{},[1651,25409,1654],{"stretchy":1653},[898,25411,13339],{},[1692,25413,25414],{},"7",[1651,25416,1667],{"stretchy":1653},[1843,25418,3631],{},[898,25420,2995],{},[1651,25422,1738],{},[1692,25424,24975],{},[1651,25426,4503],{},[1692,25428,24943],{},[898,25430,2665],{},[1651,25432,1738],{},[1692,25434,25435],{},"0,1125",[898,25437,2665],{},[898,25439,1882],{"mathvariant":1910},[902,25441,25442],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,25444,25445],{},"Dosazením do (r5):",[724,25447,25448],{},[883,25449,25451],{"className":25450},[886],[888,25452,25453],{"xmlns":890},[892,25454,25455,25499],{},[895,25456,25457,25459,25461,25463,25465,25467,25469,25471,25473,25475,25477,25479,25481,25483,25485,25487,25489,25492,25494,25496],{},[898,25458,2665],{},[1651,25460,1738],{},[1692,25462,25385],{},[898,25464,2665],{},[1651,25466,1839],{},[1692,25468,24956],{},[1651,25470,1839],{},[1692,25472,16408],{},[1651,25474,1839],{},[1692,25476,10108],{},[1651,25478,1839],{},[1692,25480,25071],{},[1651,25482,2181],{},[1692,25484,25435],{},[898,25486,2665],{},[1651,25488,1738],{},[1692,25490,25491],{},"0,45",[898,25493,2665],{},[1651,25495,1839],{},[1692,25497,25498],{},"2200.",[902,25500,25501],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,25503,25504,25505,6896,25527,25550],{},"Odtud ",[883,25506,25508],{"className":25507},[886],[888,25509,25510],{"xmlns":890},[892,25511,25512,25524],{},[895,25513,25514,25517,25519,25521],{},[1692,25515,25516],{},"0,55",[898,25518,2665],{},[1651,25520,1738],{},[1692,25522,25523],{},"2200",[902,25525,25526],{"encoding":904},"0{,}55Y = 2200",[883,25528,25530],{"className":25529},[886],[888,25531,25532],{"xmlns":890},[892,25533,25534,25547],{},[895,25535,25536,25542,25544],{},[2115,25537,25538,25540],{},[898,25539,2665],{},[898,25541,5561],{},[1651,25543,1738],{},[1692,25545,25546],{},"4000",[902,25548,25549],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,25552,25553,25576,25608,25643,25676,25712],{},[123,25554,25555,1661],{},[883,25556,25558],{"className":25557},[886],[888,25559,25560],{"xmlns":890},[892,25561,25562,25574],{},[895,25563,25564,25570,25572],{},[2115,25565,25566,25568],{},[898,25567,2665],{},[898,25569,5561],{},[1651,25571,1738],{},[1692,25573,25546],{},[902,25575,25549],{"encoding":904},[123,25577,25578,1661],{},[883,25579,25581],{"className":25580},[886],[888,25582,25583],{"xmlns":890},[892,25584,25585,25605],{},[895,25586,25587,25593,25595,25597,25599,25601,25603],{},[2115,25588,25589,25591],{},[898,25590,4104],{},[898,25592,5561],{},[1651,25594,1738],{},[1692,25596,25002],{},[1651,25598,4503],{},[1692,25600,25546],{},[1651,25602,1738],{},[1692,25604,4111],{},[902,25606,25607],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,25609,25610,1661],{},[883,25611,25613],{"className":25612},[886],[888,25614,25615],{"xmlns":890},[892,25616,25617,25640],{},[895,25618,25619,25627,25629,25631,25633,25635,25637],{},[1902,25620,25621,25623,25625],{},[898,25622,2665],{},[898,25624,2047],{},[898,25626,5561],{},[1651,25628,1738],{},[1692,25630,24943],{},[1651,25632,4503],{},[1692,25634,25546],{},[1651,25636,1738],{},[1692,25638,25639],{},"3000",[902,25641,25642],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,25644,25645,1661],{},[883,25646,25648],{"className":25647},[886],[888,25649,25650],{"xmlns":890},[892,25651,25652,25673],{},[895,25653,25654,25660,25662,25664,25666,25668,25670],{},[2115,25655,25656,25658],{},[898,25657,2995],{},[898,25659,5561],{},[1651,25661,1738],{},[1692,25663,24975],{},[1651,25665,4503],{},[1692,25667,25639],{},[1651,25669,1738],{},[1692,25671,25672],{},"450",[902,25674,25675],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,25677,25678,1661],{},[883,25679,25681],{"className":25680},[886],[888,25682,25683],{"xmlns":890},[892,25684,25685,25709],{},[895,25686,25687,25693,25695,25697,25699,25701,25703,25705,25707],{},[2115,25688,25689,25691],{},[898,25690,3001],{},[898,25692,5561],{},[1651,25694,1738],{},[1692,25696,24943],{},[1651,25698,4503],{},[1692,25700,25639],{},[1651,25702,1839],{},[1692,25704,24956],{},[1651,25706,1738],{},[1692,25708,25639],{},[902,25710,25711],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,25713,25714,25754],{},[883,25715,25717],{"className":25716},[886],[888,25718,25719],{"xmlns":890},[892,25720,25721,25751],{},[895,25722,25723,25729,25731,25739,25741,25747,25749],{},[2115,25724,25725,25727],{},[898,25726,3004],{},[898,25728,5561],{},[1651,25730,1738],{},[1902,25732,25733,25735,25737],{},[898,25734,2665],{},[898,25736,2047],{},[898,25738,5561],{},[1651,25740,2181],{},[2115,25742,25743,25745],{},[898,25744,3001],{},[898,25746,5561],{},[1651,25748,1738],{},[1692,25750,1741],{},[902,25752,25753],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,25756,25757,25759,25760,1343,25777,5197,25798,25823,25824,25827,25828,25841,25842,1882],{},[38,25758,22562],{}," Modely ",[883,25761,25763],{"className":25762},[886],[888,25764,25765],{"xmlns":890},[892,25766,25767,25775],{},[895,25768,25769,25771,25773],{},[898,25770,3001],{},[1843,25772,13588],{},[898,25774,13482],{},[902,25776,13593],{"encoding":904},[883,25778,25780],{"className":25779},[886],[888,25781,25782],{"xmlns":890},[892,25783,25784,25796],{},[895,25785,25786,25788,25790,25792,25794],{},[898,25787,3001],{},[1843,25789,13588],{},[898,25791,13482],{},[1843,25793,13588],{},[898,25795,13410],{},[902,25797,19433],{"encoding":904},[883,25799,25801],{"className":25800},[886],[888,25802,25803],{"xmlns":890},[892,25804,25805,25821],{},[895,25806,25807,25809,25811,25813,25815,25817,25819],{},[898,25808,3001],{},[1843,25810,13588],{},[898,25812,13482],{},[1843,25814,13588],{},[898,25816,13410],{},[1843,25818,13588],{},[898,25820,13618],{},[902,25822,13621],{"encoding":904}," pokládají investice za ",[38,25825,25826],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,25829,25831],{"className":25830},[886],[888,25832,25833],{"xmlns":890},[892,25834,25835,25839],{},[895,25836,25837],{},[898,25838,13339],{},[902,25840,13339],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,25843,25844],{},"model IS-LM",[115,25846,25848],{"id":25847},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,25850,25851,25852,25856,25857,25860,25861,25864],{},"V článku ",[207,25853,25855],{"className":25854,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,25858,25859],{},"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 ",[38,25862,25863],{},"výraznější"," než v mikroekonomických modelech.",[724,25866,25867],{},[1756,25868],{"alt":25869,"className":25870,"src":25871},"imek-multiplikatorovy-efekt-chain",[210,1760],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,25873,13462,25874,1343,25891,1343,25912,25937,25938,25941,25942,25960,25961,25979,25980,25998,25999,26002,26003,1343,26020,26037,26038,26040],{},[883,25875,25877],{"className":25876},[886],[888,25878,25879],{"xmlns":890},[892,25880,25881,25889],{},[895,25882,25883,25885,25887],{},[898,25884,3001],{},[1843,25886,13588],{},[898,25888,13482],{},[902,25890,13593],{"encoding":904},[883,25892,25894],{"className":25893},[886],[888,25895,25896],{"xmlns":890},[892,25897,25898,25910],{},[895,25899,25900,25902,25904,25906,25908],{},[898,25901,3001],{},[1843,25903,13588],{},[898,25905,13482],{},[1843,25907,13588],{},[898,25909,13410],{},[902,25911,19433],{"encoding":904},[883,25913,25915],{"className":25914},[886],[888,25916,25917],{"xmlns":890},[892,25918,25919,25935],{},[895,25920,25921,25923,25925,25927,25929,25931,25933],{},[898,25922,3001],{},[1843,25924,13588],{},[898,25926,13482],{},[1843,25928,13588],{},[898,25930,13410],{},[1843,25932,13588],{},[898,25934,13618],{},[902,25936,13621],{"encoding":904}," se vyšetřuje vliv změn ",[38,25939,25940],{},"exogenních"," veličin (plánovaných investic ",[883,25943,25945],{"className":25944},[886],[888,25946,25947],{"xmlns":890},[892,25948,25949,25957],{},[895,25950,25951],{},[2115,25952,25953,25955],{},[898,25954,13482],{},[1651,25956,2668],{},[902,25958,25959],{"encoding":904},"I^*",", vládních výdajů ",[883,25962,25964],{"className":25963},[886],[888,25965,25966],{"xmlns":890},[892,25967,25968,25976],{},[895,25969,25970],{},[2115,25971,25972,25974],{},[898,25973,13410],{},[1651,25975,2668],{},[902,25977,25978],{"encoding":904},"G^*",", exportu ",[883,25981,25983],{"className":25982},[886],[888,25984,25985],{"xmlns":890},[892,25986,25987,25995],{},[895,25988,25989],{},[2115,25990,25991,25993],{},[898,25992,24466],{},[1651,25994,2668],{},[902,25996,25997],{"encoding":904},"B^*",") na změny ",[38,26000,26001],{},"endogenních"," rovnovážných veličin (",[883,26004,26006],{"className":26005},[886],[888,26007,26008],{"xmlns":890},[892,26009,26010,26018],{},[895,26011,26012],{},[2115,26013,26014,26016],{},[898,26015,2665],{},[898,26017,5561],{},[902,26019,15201],{"encoding":904},[883,26021,26023],{"className":26022},[886],[888,26024,26025],{"xmlns":890},[892,26026,26027,26035],{},[895,26028,26029],{},[2115,26030,26031,26033],{},[898,26032,3001],{},[898,26034,5561],{},[902,26036,15260],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,26039,19190],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,26042,26044],{"id":26043},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,26046,22108,26047,26070,26071,26115],{},[883,26048,26050],{"className":26049},[886],[888,26051,26052],{"xmlns":890},[892,26053,26054,26068],{},[895,26055,26056,26058,26060,26062,26064,26066],{},[898,26057,3001],{},[1651,26059,1738],{},[898,26061,207],{},[898,26063,2665],{},[1651,26065,1839],{},[898,26067,2268],{},[902,26069,20133],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,26072,26074],{"className":26073},[886],[888,26075,26076],{"xmlns":890},[892,26077,26078,26112],{},[895,26079,26080,26086,26088],{},[2115,26081,26082,26084],{},[898,26083,2665],{},[898,26085,5561],{},[1651,26087,1738],{},[2938,26089,26090],{"scriptlevel":1741,"displaystyle":1660},[2446,26091,26092,26104],{},[895,26093,26094,26096,26098],{},[898,26095,2268],{},[1651,26097,1839],{},[2115,26099,26100,26102],{},[898,26101,13482],{},[1651,26103,2668],{},[895,26105,26106,26108,26110],{},[1692,26107,1694],{},[1651,26109,2181],{},[898,26111,207],{},[902,26113,26114],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,26117,26118],{},[883,26119,26121],{"className":26120},[886],[888,26122,26123],{"xmlns":890},[892,26124,26125,26194],{},[895,26126,26127,26145,26147,26177,26179],{},[2446,26128,26129,26139],{},[895,26130,26131,26133],{},[898,26132,11172],{"mathvariant":1910},[2115,26134,26135,26137],{},[898,26136,2665],{},[898,26138,5561],{},[895,26140,26141,26143],{},[898,26142,11172],{"mathvariant":1910},[898,26144,207],{},[1651,26146,1738],{},[2446,26148,26149,26161],{},[895,26150,26151,26153,26155],{},[898,26152,2268],{},[1651,26154,1839],{},[2115,26156,26157,26159],{},[898,26158,13482],{},[1651,26160,2668],{},[895,26162,26163,26165,26167,26169,26171],{},[1651,26164,1654],{"stretchy":1653},[1692,26166,1694],{},[1651,26168,2181],{},[898,26170,207],{},[2115,26172,26173,26175],{},[1651,26174,1667],{"stretchy":1653},[1692,26176,1703],{},[7185,26178],{"width":7187},[895,26180,26181,26184,26191],{},[1843,26182,26183],{},"(multiplik",[9692,26185,26186,26188],{"accent":1660},[1843,26187,207],{},[1651,26189,26190],{},"ˊ",[1843,26192,26193],{},"tor MPC)",[902,26195,26196],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,26198,26199],{},[883,26200,26202],{"className":26201},[886],[888,26203,26204],{"xmlns":890},[892,26205,26206,26275],{},[895,26207,26208,26226,26228,26240,26242],{},[2446,26209,26210,26220],{},[895,26211,26212,26214],{},[898,26213,11172],{"mathvariant":1910},[2115,26215,26216,26218],{},[898,26217,2665],{},[898,26219,5561],{},[895,26221,26222,26224],{},[898,26223,11172],{"mathvariant":1910},[898,26225,2268],{},[1651,26227,1738],{},[2446,26229,26230,26232],{},[1692,26231,1694],{},[895,26233,26234,26236,26238],{},[1692,26235,1694],{},[1651,26237,2181],{},[898,26239,207],{},[7185,26241],{"width":7187},[895,26243,26244,26246,26252,26255,26262,26265,26272],{},[1843,26245,26183],{},[9692,26247,26248,26250],{"accent":1660},[1843,26249,207],{},[1651,26251,26190],{},[1843,26253,26254],{},"tor autonomn",[9692,26256,26257,26260],{"accent":1660},[1843,26258,26259],{},"ı",[1651,26261,26190],{},[1843,26263,26264],{}," spot",[9692,26266,26267,26269],{"accent":1660},[1843,26268,13339],{},[1651,26270,26271],{},"ˇ",[1843,26273,26274],{},"eby)",[902,26276,26277],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,26279,26280],{},[883,26281,26283],{"className":26282},[886],[888,26284,26285],{"xmlns":890},[892,26286,26287,26354],{},[895,26288,26289,26311,26313,26325,26327,26339,26341],{},[2446,26290,26291,26301],{},[895,26292,26293,26295],{},[898,26294,11172],{"mathvariant":1910},[2115,26296,26297,26299],{},[898,26298,2665],{},[898,26300,5561],{},[895,26302,26303,26305],{},[898,26304,11172],{"mathvariant":1910},[2115,26306,26307,26309],{},[898,26308,13482],{},[1651,26310,2668],{},[1651,26312,1738],{},[2446,26314,26315,26317],{},[1692,26316,1694],{},[895,26318,26319,26321,26323],{},[1692,26320,1694],{},[1651,26322,2181],{},[898,26324,207],{},[1651,26326,1738],{},[2446,26328,26329,26331],{},[1692,26330,1694],{},[895,26332,26333,26335,26337],{},[898,26334,2995],{},[898,26336,2675],{},[898,26338,3004],{},[7185,26340],{"width":7187},[895,26342,26343,26345,26351],{},[1843,26344,26183],{},[9692,26346,26347,26349],{"accent":1660},[1843,26348,207],{},[1651,26350,26190],{},[1843,26352,26353],{},"tor investic)",[902,26355,26356],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[5179,26358,26359],{},[724,26360,26361,26363,26364,26367,26368,26381,26382,26399,26400,26418,26419,26463,26464,22633,26481,26484,26485,26502],{},[883,26362,5465],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,26365,26366],{},"důchodem","; z něj se utratí ",[883,26369,26371],{"className":26370},[886],[888,26372,26373],{"xmlns":890},[892,26374,26375,26379],{},[895,26376,26377],{},[898,26378,207],{},[902,26380,207],{"encoding":904}," Kč (= ",[883,26383,26385],{"className":26384},[886],[888,26386,26387],{"xmlns":890},[892,26388,26389,26397],{},[895,26390,26391,26393,26395],{},[898,26392,2995],{},[898,26394,2675],{},[898,26396,3001],{},[902,26398,19258],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,26401,26403],{"className":26402},[886],[888,26404,26405],{"xmlns":890},[892,26406,26407,26415],{},[895,26408,26409],{},[2115,26410,26411,26413],{},[898,26412,207],{},[1692,26414,1703],{},[902,26416,26417],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,26420,26422],{"className":26421},[886],[888,26423,26424],{"xmlns":890},[892,26425,26426,26460],{},[895,26427,26428,26430,26432,26434,26436,26442,26444,26446,26448],{},[1692,26429,1694],{},[1651,26431,1839],{},[898,26433,207],{},[1651,26435,1839],{},[2115,26437,26438,26440],{},[898,26439,207],{},[1692,26441,1703],{},[1651,26443,1839],{},[1651,26445,19318],{},[1651,26447,1738],{},[2446,26449,26450,26452],{},[1692,26451,1694],{},[895,26453,26454,26456,26458],{},[1692,26455,1694],{},[1651,26457,2181],{},[898,26459,207],{},[902,26461,26462],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,26465,26467],{"className":26466},[886],[888,26468,26469],{"xmlns":890},[892,26470,26471,26479],{},[895,26472,26473],{},[2115,26474,26475,26477],{},[898,26476,2665],{},[898,26478,5561],{},[902,26480,15201],{"encoding":904},[38,26482,26483],{},"více"," než korunu — čím vyšší ",[883,26486,26488],{"className":26487},[886],[888,26489,26490],{"xmlns":890},[892,26491,26492,26500],{},[895,26493,26494,26496,26498],{},[898,26495,2995],{},[898,26497,2675],{},[898,26499,3001],{},[902,26501,19258],{"encoding":904},", tím silnější multiplikační efekt.",[724,26504,26505,26508,26509,26535,26536,26539,26540,5197,26561,26586,26587,1882],{},[38,26506,26507],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,26510,26512],{"className":26511},[886],[888,26513,26514],{"xmlns":890},[892,26515,26516,26532],{},[895,26517,26518],{},[2938,26519,26520],{"scriptlevel":1741,"displaystyle":1653},[2446,26521,26522,26524],{},[1692,26523,1694],{},[895,26525,26526,26528,26530],{},[1692,26527,1694],{},[1651,26529,2181],{},[898,26531,207],{},[902,26533,26534],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,26537,26538],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,26541,26543],{"className":26542},[886],[888,26544,26545],{"xmlns":890},[892,26546,26547,26559],{},[895,26548,26549,26551,26553,26555,26557],{},[898,26550,3001],{},[1843,26552,13588],{},[898,26554,13482],{},[1843,26556,13588],{},[898,26558,13410],{},[902,26560,19433],{"encoding":904},[883,26562,26564],{"className":26563},[886],[888,26565,26566],{"xmlns":890},[892,26567,26568,26584],{},[895,26569,26570,26572,26574,26576,26578,26580,26582],{},[898,26571,3001],{},[1843,26573,13588],{},[898,26575,13482],{},[1843,26577,13588],{},[898,26579,13410],{},[1843,26581,13588],{},[898,26583,13618],{},[902,26585,13621],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,26588,26590],{"className":26589,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,26592,26594],{"id":26593},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,26596,13462,26597,1343,26614,5197,26635,13467,26660,11325,26663,26684,26685,3246,26688,26701,26702,6976,26731,26748,26749,26752,26753,26755,26756,26777],{},[883,26598,26600],{"className":26599},[886],[888,26601,26602],{"xmlns":890},[892,26603,26604,26612],{},[895,26605,26606,26608,26610],{},[898,26607,3001],{},[1843,26609,13588],{},[898,26611,13482],{},[902,26613,13593],{"encoding":904},[883,26615,26617],{"className":26616},[886],[888,26618,26619],{"xmlns":890},[892,26620,26621,26633],{},[895,26622,26623,26625,26627,26629,26631],{},[898,26624,3001],{},[1843,26626,13588],{},[898,26628,13482],{},[1843,26630,13588],{},[898,26632,13410],{},[902,26634,19433],{"encoding":904},[883,26636,26638],{"className":26637},[886],[888,26639,26640],{"xmlns":890},[892,26641,26642,26658],{},[895,26643,26644,26646,26648,26650,26652,26654,26656],{},[898,26645,3001],{},[1843,26647,13588],{},[898,26649,13482],{},[1843,26651,13588],{},[898,26653,13410],{},[1843,26655,13588],{},[898,26657,13618],{},[902,26659,13621],{"encoding":904},[38,26661,26662],{},"investice konstantní",[883,26664,26666],{"className":26665},[886],[888,26667,26668],{"xmlns":890},[892,26669,26670,26682],{},[895,26671,26672,26674,26676],{},[898,26673,13482],{},[1651,26675,1738],{},[2115,26677,26678,26680],{},[898,26679,13482],{},[1651,26681,2668],{},[902,26683,13493],{"encoding":904},"). Reálnější je předpoklad, že ",[38,26686,26687],{},"investice závisejí na úrokové míře",[883,26689,26691],{"className":26690},[886],[888,26692,26693],{"xmlns":890},[892,26694,26695,26699],{},[895,26696,26697],{},[898,26698,13339],{},[902,26700,13339],{"encoding":904}," — klesající funkce ",[883,26703,26705],{"className":26704},[886],[888,26706,26707],{"xmlns":890},[892,26708,26709,26729],{},[895,26710,26711,26713,26715,26717,26719,26721,26723,26725,26727],{},[898,26712,13482],{},[1651,26714,1654],{"stretchy":1653},[898,26716,13339],{},[1651,26718,1667],{"stretchy":1653},[1651,26720,1738],{},[898,26722,3490],{},[898,26724,13339],{},[1651,26726,1839],{},[898,26728,3542],{},[902,26730,17055],{"encoding":904},[883,26732,26734],{"className":26733},[886],[888,26735,26736],{"xmlns":890},[892,26737,26738,26746],{},[895,26739,26740,26742,26744],{},[898,26741,3490],{},[1651,26743,2319],{},[1692,26745,1741],{},[902,26747,13813],{"encoding":904},". Přidáním ",[38,26750,26751],{},"trhu peněz"," k trhu zboží vzniká model ",[38,26754,13309],{}," se dvěma neznámými ",[883,26757,26759],{"className":26758},[886],[888,26760,26761],{"xmlns":890},[892,26762,26763,26775],{},[895,26764,26765,26767,26769,26771,26773],{},[1651,26766,1654],{"stretchy":1653},[898,26768,2665],{},[1651,26770,1661],{"separator":1660},[898,26772,13339],{},[1651,26774,1667],{"stretchy":1653},[902,26776,19363],{"encoding":904}," a dvěma rovnicemi:",[120,26779,26780,26830],{},[123,26781,26782,11325,26784,26786,26787,26808,26809,1882],{},[38,26783,17144],{},[614,26785,13352],{},") — klesající přímka v rovině ",[883,26788,26790],{"className":26789},[886],[888,26791,26792],{"xmlns":890},[892,26793,26794,26806],{},[895,26795,26796,26798,26800,26802,26804],{},[1651,26797,1654],{"stretchy":1653},[898,26799,13339],{},[1651,26801,1661],{"separator":1660},[898,26803,2665],{},[1651,26805,1667],{"stretchy":1653},[902,26807,14235],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,26810,26812],{"className":26811},[886],[888,26813,26814],{"xmlns":890},[892,26815,26816,26828],{},[895,26817,26818,26820,26822,26824,26826],{},[898,26819,2665],{},[1651,26821,1738],{},[898,26823,3001],{},[1651,26825,1839],{},[898,26827,13482],{},[902,26829,16042],{"encoding":904},[123,26831,26832,11325,26834,26836,26837,22807,26862,26908],{},[38,26833,17343],{},[614,26835,13359],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,26838,26840],{"className":26839},[886],[888,26841,26842],{"xmlns":890},[892,26843,26844,26860],{},[895,26845,26846,26852,26854],{},[2115,26847,26848,26850],{},[898,26849,2995],{},[898,26851,2047],{},[1651,26853,1738],{},[2115,26855,26856,26858],{},[898,26857,2995],{},[1651,26859,2668],{},[902,26861,14778],{"encoding":904},[883,26863,26865],{"className":26864},[886],[888,26866,26867],{"xmlns":890},[892,26868,26869,26905],{},[895,26870,26871,26877,26879,26885,26887,26889,26895,26897,26899],{},[2115,26872,26873,26875],{},[898,26874,2995],{},[898,26876,2047],{},[1651,26878,1738],{},[1686,26880,26881,26883],{},[898,26882,14535],{},[1692,26884,1694],{},[898,26886,2665],{},[1651,26888,1839],{},[1686,26890,26891,26893],{},[898,26892,14535],{},[1692,26894,1703],{},[898,26896,13339],{},[1651,26898,1839],{},[1686,26900,26901,26903],{},[898,26902,14535],{},[1692,26904,3521],{},[902,26906,26907],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,26910,26911,3246,26914,26947,26948,26950,26951,26953],{},[38,26912,26913],{},"Simultánní rovnovážný bod",[883,26915,26917],{"className":26916},[886],[888,26918,26919],{"xmlns":890},[892,26920,26921,26945],{},[895,26922,26923,26925,26927,26929,26935,26937,26943],{},[898,26924,5561],{},[1651,26926,1738],{},[1651,26928,1654],{"stretchy":1653},[2115,26930,26931,26933],{},[898,26932,13339],{},[898,26934,5561],{},[1651,26936,1661],{"separator":1660},[2115,26938,26939,26941],{},[898,26940,2665],{},[898,26942,5561],{},[1651,26944,1667],{"stretchy":1653},[902,26946,17435],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,26949,13397],{}," (posun IS) a ",[38,26952,13429],{}," (posun LM).",[724,26955,26956],{},[38,26957,26958,26959,1343,26981,1343,27003,1343,27025,27047,27048,1882],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,26960,26962],{"className":26961},[886],[888,26963,26964],{"xmlns":890},[892,26965,26966,26978],{},[895,26967,26968,26974,26976],{},[2115,26969,26970,26972],{},[898,26971,2665],{},[898,26973,5561],{},[1651,26975,1738],{},[1692,26977,16413],{},[902,26979,26980],{"encoding":904},"Y^E = 5000",[883,26982,26984],{"className":26983},[886],[888,26985,26986],{"xmlns":890},[892,26987,26988,27000],{},[895,26989,26990,26996,26998],{},[2115,26991,26992,26994],{},[898,26993,13339],{},[898,26995,5561],{},[1651,26997,1738],{},[1692,26999,3574],{},[902,27001,27002],{"encoding":904},"r^E = 5",[883,27004,27006],{"className":27005},[886],[888,27007,27008],{"xmlns":890},[892,27009,27010,27022],{},[895,27011,27012,27018,27020],{},[2115,27013,27014,27016],{},[898,27015,3001],{},[898,27017,5561],{},[1651,27019,1738],{},[1692,27021,16450],{},[902,27023,27024],{"encoding":904},"C^E = 4100",[883,27026,27028],{"className":27027},[886],[888,27029,27030],{"xmlns":890},[892,27031,27032,27044],{},[895,27033,27034,27040,27042],{},[2115,27035,27036,27038],{},[898,27037,13482],{},[898,27039,5561],{},[1651,27041,1738],{},[1692,27043,16489],{},[902,27045,27046],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,27049,945],{"className":27050,"dataFsResolvedFilePath":943,"href":944},[210],[115,27052,27054],{"id":27053},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,27056,27057,27121,27232,27375,27617,27685],{},[123,27058,27059,27062,27063,27085,27086,27120],{},[38,27060,27061],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,27064,27066],{"className":27065},[886],[888,27067,27068],{"xmlns":890},[892,27069,27070,27082],{},[895,27071,27072,27074,27076,27078,27080],{},[898,27073,13410],{},[898,27075,19507],{},[898,27077,2675],{},[1651,27079,4060],{},[898,27081,2665],{},[902,27083,27084],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,27087,27089],{"className":27088},[886],[888,27090,27091],{"xmlns":890},[892,27092,27093,27117],{},[895,27094,27095,27097,27099,27101,27103,27105,27107,27109,27111,27113,27115],{},[898,27096,13410],{},[898,27098,19507],{},[898,27100,2675],{},[1651,27102,1738],{},[898,27104,3001],{},[1651,27106,1839],{},[898,27108,13482],{},[1651,27110,1839],{},[898,27112,13410],{},[1651,27114,1839],{},[898,27116,13618],{},[902,27118,27119],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,27122,27123,27125,27126,27147,27148,1343,27171,27202,27203,27216,27217,1882],{},[38,27124,19741],{}," splňují ",[883,27127,27129],{"className":27128},[886],[888,27130,27131],{"xmlns":890},[892,27132,27133,27145],{},[895,27134,27135,27137,27139,27141,27143],{},[898,27136,2665],{},[1651,27138,1738],{},[898,27140,3001],{},[1651,27142,1839],{},[898,27144,3004],{},[902,27146,13992],{"encoding":904}," (7.2); lineární model ",[883,27149,27151],{"className":27150},[886],[888,27152,27153],{"xmlns":890},[892,27154,27155,27169],{},[895,27156,27157,27159,27161,27163,27165,27167],{},[898,27158,3001],{},[1651,27160,1738],{},[898,27162,207],{},[898,27164,2665],{},[1651,27166,1839],{},[898,27168,2268],{},[902,27170,20133],{"encoding":904},[883,27172,27174],{"className":27173},[886],[888,27175,27176],{"xmlns":890},[892,27177,27178,27200],{},[895,27179,27180,27182,27184,27186,27188,27190,27192,27194,27196,27198],{},[898,27181,3004],{},[1651,27183,1738],{},[1651,27185,1654],{"stretchy":1653},[1692,27187,1694],{},[1651,27189,2181],{},[898,27191,207],{},[1651,27193,1667],{"stretchy":1653},[898,27195,2665],{},[1651,27197,2181],{},[898,27199,2268],{},[902,27201,20382],{"encoding":904}," s autonomní spotřebou ",[883,27204,27206],{"className":27205},[886],[888,27207,27208],{"xmlns":890},[892,27209,27210,27214],{},[895,27211,27212],{},[898,27213,2268],{},[902,27215,2268],{"encoding":904}," a autonomními úsporami ",[883,27218,27220],{"className":27219},[886],[888,27221,27222],{"xmlns":890},[892,27223,27224,27230],{},[895,27225,27226,27228],{},[1651,27227,2181],{},[898,27229,2268],{},[902,27231,20461],{"encoding":904},[123,27233,27234,3246,27237,1343,27267,27297,27298,27328,27329,1343,27350,1882],{},[38,27235,27236],{},"Mezní sklony",[883,27238,27240],{"className":27239},[886],[888,27241,27242],{"xmlns":890},[892,27243,27244,27264],{},[895,27245,27246,27248,27250,27252,27254,27256,27258,27260,27262],{},[898,27247,2995],{},[898,27249,2675],{},[898,27251,3001],{},[1651,27253,1738],{},[898,27255,3542],{"mathvariant":1910},[898,27257,3001],{},[898,27259,5981],{"mathvariant":1910},[898,27261,3542],{"mathvariant":1910},[898,27263,2665],{},[902,27265,27266],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,27268,27270],{"className":27269},[886],[888,27271,27272],{"xmlns":890},[892,27273,27274,27294],{},[895,27275,27276,27278,27280,27282,27284,27286,27288,27290,27292],{},[898,27277,2995],{},[898,27279,2675],{},[898,27281,3004],{},[1651,27283,1738],{},[898,27285,3542],{"mathvariant":1910},[898,27287,3004],{},[898,27289,5981],{"mathvariant":1910},[898,27291,3542],{"mathvariant":1910},[898,27293,2665],{},[902,27295,27296],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,27299,27301],{"className":27300},[886],[888,27302,27303],{"xmlns":890},[892,27304,27305,27325],{},[895,27306,27307,27309,27311,27313,27315,27317,27319,27321,27323],{},[898,27308,2995],{},[898,27310,2675],{},[898,27312,3001],{},[1651,27314,1839],{},[898,27316,2995],{},[898,27318,2675],{},[898,27320,3004],{},[1651,27322,1738],{},[1692,27324,1694],{},[902,27326,27327],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,27330,27332],{"className":27331},[886],[888,27333,27334],{"xmlns":890},[892,27335,27336,27348],{},[895,27337,27338,27340,27342,27344,27346],{},[898,27339,2995],{},[898,27341,2675],{},[898,27343,3001],{},[1651,27345,1738],{},[898,27347,207],{},[902,27349,21102],{"encoding":904},[883,27351,27353],{"className":27352},[886],[888,27354,27355],{"xmlns":890},[892,27356,27357,27373],{},[895,27358,27359,27361,27363,27365,27367,27369,27371],{},[898,27360,2995],{},[898,27362,2675],{},[898,27364,3004],{},[1651,27366,1738],{},[1692,27368,1694],{},[1651,27370,2181],{},[898,27372,207],{},[902,27374,21128],{"encoding":904},[123,27376,27377,27380,27381],{},[38,27378,27379],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,27382,27383,27471,27540],{},[123,27384,27385,27402,27403,27424,27425,1661],{},[883,27386,27388],{"className":27387},[886],[888,27389,27390],{"xmlns":890},[892,27391,27392,27400],{},[895,27393,27394,27396,27398],{},[898,27395,3001],{},[1843,27397,13588],{},[898,27399,13482],{},[902,27401,13593],{"encoding":904},": ",[883,27404,27406],{"className":27405},[886],[888,27407,27408],{"xmlns":890},[892,27409,27410,27422],{},[895,27411,27412,27414,27416,27418,27420],{},[898,27413,2665],{},[1651,27415,1738],{},[898,27417,3001],{},[1651,27419,1839],{},[898,27421,13482],{},[902,27423,16042],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,27426,27428],{"className":27427},[886],[888,27429,27430],{"xmlns":890},[892,27431,27432,27468],{},[895,27433,27434,27440,27442,27444,27446,27448,27454,27456,27458,27460,27462,27464,27466],{},[2115,27435,27436,27438],{},[898,27437,2665],{},[898,27439,5561],{},[1651,27441,1738],{},[1651,27443,1654],{"stretchy":1653},[898,27445,2268],{},[1651,27447,1839],{},[2115,27449,27450,27452],{},[898,27451,13482],{},[1651,27453,2668],{},[1651,27455,1667],{"stretchy":1653},[898,27457,5981],{"mathvariant":1910},[1651,27459,1654],{"stretchy":1653},[1692,27461,1694],{},[1651,27463,2181],{},[898,27465,207],{},[1651,27467,1667],{"stretchy":1653},[902,27469,27470],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,27472,27473,27494,27495,27514,27515,1661],{},[883,27474,27476],{"className":27475},[886],[888,27477,27478],{"xmlns":890},[892,27479,27480,27492],{},[895,27481,27482,27484,27486,27488,27490],{},[898,27483,3001],{},[1843,27485,13588],{},[898,27487,13482],{},[1843,27489,13588],{},[898,27491,13410],{},[902,27493,19433],{"encoding":904},": přidává vládu, zdanění ",[883,27496,27498],{"className":27497},[886],[888,27499,27500],{"xmlns":890},[892,27501,27502,27512],{},[895,27503,27504,27506,27508,27510],{},[898,27505,4104],{},[1651,27507,1654],{"stretchy":1653},[898,27509,2665],{},[1651,27511,1667],{"stretchy":1653},[902,27513,23432],{"encoding":904}," a disponibilní důchod ",[883,27516,27518],{"className":27517},[886],[888,27519,27520],{"xmlns":890},[892,27521,27522,27538],{},[895,27523,27524,27530,27532,27534,27536],{},[1686,27525,27526,27528],{},[898,27527,2665],{},[898,27529,2047],{},[1651,27531,1738],{},[898,27533,2665],{},[1651,27535,2181],{},[898,27537,4104],{},[902,27539,22931],{"encoding":904},[123,27541,27542,27567,27568,22807,27589,1882],{},[883,27543,27545],{"className":27544},[886],[888,27546,27547],{"xmlns":890},[892,27548,27549,27565],{},[895,27550,27551,27553,27555,27557,27559,27561,27563],{},[898,27552,3001],{},[1843,27554,13588],{},[898,27556,13482],{},[1843,27558,13588],{},[898,27560,13410],{},[1843,27562,13588],{},[898,27564,13618],{},[902,27566,13621],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,27569,27571],{"className":27570},[886],[888,27572,27573],{"xmlns":890},[892,27574,27575,27587],{},[895,27576,27577,27579,27581,27583,27585],{},[898,27578,13618],{},[1651,27580,1738],{},[898,27582,24466],{},[1651,27584,2181],{},[898,27586,2995],{},[902,27588,24473],{"encoding":904},[883,27590,27592],{"className":27591},[886],[888,27593,27594],{"xmlns":890},[892,27595,27596,27614],{},[895,27597,27598,27600,27602,27604,27606,27612],{},[898,27599,2995],{},[1651,27601,1738],{},[898,27603,2995],{},[1651,27605,1654],{"stretchy":1653},[1686,27607,27608,27610],{},[898,27609,2665],{},[898,27611,2047],{},[1651,27613,1667],{"stretchy":1653},[902,27615,27616],{"encoding":904},"M = M(Y_D)",[123,27618,27619,27622,27623,3246,27626,27684],{},[38,27620,27621],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,27624,27625],{},"multiplikátor investic",[883,27627,27629],{"className":27628},[886],[888,27630,27631],{"xmlns":890},[892,27632,27633,27681],{},[895,27634,27635,27637,27643,27645,27647,27653,27655,27657,27659,27661,27663,27665,27667,27669,27671,27673,27675,27677,27679],{},[898,27636,11172],{"mathvariant":1910},[2115,27638,27639,27641],{},[898,27640,2665],{},[898,27642,5561],{},[898,27644,5981],{"mathvariant":1910},[898,27646,11172],{"mathvariant":1910},[2115,27648,27649,27651],{},[898,27650,13482],{},[1651,27652,2668],{},[1651,27654,1738],{},[1692,27656,1694],{},[898,27658,5981],{"mathvariant":1910},[1651,27660,1654],{"stretchy":1653},[1692,27662,1694],{},[1651,27664,2181],{},[898,27666,207],{},[1651,27668,1667],{"stretchy":1653},[1651,27670,1738],{},[1692,27672,1694],{},[898,27674,5981],{"mathvariant":1910},[898,27676,2995],{},[898,27678,2675],{},[898,27680,3004],{},[902,27682,27683],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,27686,27687,27689,27690,27705,27706,19861,27723,27738,27739,27764,27765,1882],{},[38,27688,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,27691,27693],{"className":27692},[886],[888,27694,27695],{"xmlns":890},[892,27696,27697,27703],{},[895,27698,27699,27701],{},[898,27700,13482],{},[898,27702,3004],{},[902,27704,13349],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,27707,27709],{"className":27708},[886],[888,27710,27711],{"xmlns":890},[892,27712,27713,27721],{},[895,27714,27715,27717,27719],{},[898,27716,13482],{},[1651,27718,1738],{},[898,27720,3004],{},[902,27722,14010],{"encoding":904},[883,27724,27726],{"className":27725},[886],[888,27727,27728],{"xmlns":890},[892,27729,27730,27736],{},[895,27731,27732,27734],{},[898,27733,1807],{},[898,27735,2995],{},[902,27737,13356],{"encoding":904}," rovnováhu trhu peněz (",[883,27740,27742],{"className":27741},[886],[888,27743,27744],{"xmlns":890},[892,27745,27746,27762],{},[895,27747,27748,27754,27756],{},[2115,27749,27750,27752],{},[898,27751,2995],{},[898,27753,2047],{},[1651,27755,1738],{},[2115,27757,27758,27760],{},[898,27759,2995],{},[1651,27761,2668],{},[902,27763,14778],{"encoding":904},"); průsečík dává ",[883,27766,27768],{"className":27767},[886],[888,27769,27770],{"xmlns":890},[892,27771,27772,27792],{},[895,27773,27774,27776,27782,27784,27790],{},[1651,27775,1654],{"stretchy":1653},[2115,27777,27778,27780],{},[898,27779,2665],{},[898,27781,5561],{},[1651,27783,1661],{"separator":1660},[2115,27785,27786,27788],{},[898,27787,13339],{},[898,27789,5561],{},[1651,27791,1667],{"stretchy":1653},[902,27793,13393],{"encoding":904},[115,27795,17018],{"id":17017},[120,27797,27798,27836,27876,27966,28048,28102,28158,28217,28252,28257,28329,28404,28490,28552,28620,28678,28731,28770],{},[123,27799,27800,8322,27803,27120],{},[38,27801,27802],{},"Hrubý národní produkt (GNP)",[883,27804,27806],{"className":27805},[886],[888,27807,27808],{"xmlns":890},[892,27809,27810,27834],{},[895,27811,27812,27814,27816,27818,27820,27822,27824,27826,27828,27830,27832],{},[898,27813,13410],{},[898,27815,19507],{},[898,27817,2675],{},[1651,27819,1738],{},[898,27821,3001],{},[1651,27823,1839],{},[898,27825,13482],{},[1651,27827,1839],{},[898,27829,13410],{},[1651,27831,1839],{},[898,27833,13618],{},[902,27835,27119],{"encoding":904},[123,27837,27838,27854,27855,1882],{},[38,27839,27840,27841],{},"Národní důchod ",[883,27842,27844],{"className":27843},[886],[888,27845,27846],{"xmlns":890},[892,27847,27848,27852],{},[895,27849,27850],{},[898,27851,2665],{},[902,27853,2665],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,27856,27858],{"className":27857},[886],[888,27859,27860],{"xmlns":890},[892,27861,27862,27874],{},[895,27863,27864,27866,27868,27870,27872],{},[898,27865,13410],{},[898,27867,19507],{},[898,27869,2675],{},[1651,27871,4060],{},[898,27873,2665],{},[902,27875,27084],{"encoding":904},[123,27877,27878,27904,27905,1343,27928,1343,27949,1882],{},[38,27879,27880,27881],{},"Funkce spotřeby ",[883,27882,27884],{"className":27883},[886],[888,27885,27886],{"xmlns":890},[892,27887,27888,27902],{},[895,27889,27890,27892,27894,27896,27898,27900],{},[898,27891,3001],{},[1651,27893,1738],{},[898,27895,3001],{},[1651,27897,1654],{"stretchy":1653},[898,27899,2665],{},[1651,27901,1667],{"stretchy":1653},[902,27903,21953],{"encoding":904}," — lineární model ",[883,27906,27908],{"className":27907},[886],[888,27909,27910],{"xmlns":890},[892,27911,27912,27926],{},[895,27913,27914,27916,27918,27920,27922,27924],{},[898,27915,3001],{},[1651,27917,1738],{},[898,27919,207],{},[898,27921,2665],{},[1651,27923,1839],{},[898,27925,2268],{},[902,27927,20133],{"encoding":904},[883,27929,27931],{"className":27930},[886],[888,27932,27933],{"xmlns":890},[892,27934,27935,27947],{},[895,27936,27937,27939,27941,27943,27945],{},[1692,27938,1741],{},[1651,27940,2319],{},[898,27942,207],{},[1651,27944,2319],{},[1692,27946,1694],{},[902,27948,20049],{"encoding":904},[883,27950,27952],{"className":27951},[886],[888,27953,27954],{"xmlns":890},[892,27955,27956,27964],{},[895,27957,27958,27960,27962],{},[898,27959,2268],{},[1651,27961,2390],{},[1692,27963,1741],{},[902,27965,20027],{"encoding":904},[123,27967,27968,8322,27995,28016,28017,1882],{},[38,27969,27970,27971],{},"Funkce úspor ",[883,27972,27974],{"className":27973},[886],[888,27975,27976],{"xmlns":890},[892,27977,27978,27992],{},[895,27979,27980,27982,27984,27986,27988,27990],{},[898,27981,3004],{},[1651,27983,1738],{},[898,27985,3004],{},[1651,27987,1654],{"stretchy":1653},[898,27989,2665],{},[1651,27991,1667],{"stretchy":1653},[902,27993,27994],{"encoding":904},"S = S(Y)",[883,27996,27998],{"className":27997},[886],[888,27999,28000],{"xmlns":890},[892,28001,28002,28014],{},[895,28003,28004,28006,28008,28010,28012],{},[898,28005,2665],{},[1651,28007,1738],{},[898,28009,3001],{},[1651,28011,1839],{},[898,28013,3004],{},[902,28015,13992],{"encoding":904},"; lineární ",[883,28018,28020],{"className":28019},[886],[888,28021,28022],{"xmlns":890},[892,28023,28024,28046],{},[895,28025,28026,28028,28030,28032,28034,28036,28038,28040,28042,28044],{},[898,28027,3004],{},[1651,28029,1738],{},[1651,28031,1654],{"stretchy":1653},[1692,28033,1694],{},[1651,28035,2181],{},[898,28037,207],{},[1651,28039,1667],{"stretchy":1653},[898,28041,2665],{},[1651,28043,2181],{},[898,28045,2268],{},[902,28047,20382],{"encoding":904},[123,28049,28050,8322,28053,1343,28076,1882],{},[38,28051,28052],{},"Autonomní spotřeba\u002Fúspory",[883,28054,28056],{"className":28055},[886],[888,28057,28058],{"xmlns":890},[892,28059,28060,28074],{},[895,28061,28062,28064,28066,28068,28070,28072],{},[898,28063,3001],{},[1651,28065,1654],{"stretchy":1653},[1692,28067,1741],{},[1651,28069,1667],{"stretchy":1653},[1651,28071,1738],{},[898,28073,2268],{},[902,28075,20774],{"encoding":904},[883,28077,28079],{"className":28078},[886],[888,28080,28081],{"xmlns":890},[892,28082,28083,28099],{},[895,28084,28085,28087,28089,28091,28093,28095,28097],{},[898,28086,3004],{},[1651,28088,1654],{"stretchy":1653},[1692,28090,1741],{},[1651,28092,1667],{"stretchy":1653},[1651,28094,1738],{},[1651,28096,2181],{},[898,28098,2268],{},[902,28100,28101],{"encoding":904},"S(0) = -b",[123,28103,28104,28136,28137,5230],{},[38,28105,28106,28107],{},"Mezní sklon ke spotřebě ",[883,28108,28110],{"className":28109},[886],[888,28111,28112],{"xmlns":890},[892,28113,28114,28134],{},[895,28115,28116,28118,28120,28122,28124,28126,28128,28130,28132],{},[898,28117,2995],{},[898,28119,2675],{},[898,28121,3001],{},[1651,28123,1738],{},[898,28125,3542],{"mathvariant":1910},[898,28127,3001],{},[898,28129,5981],{"mathvariant":1910},[898,28131,3542],{"mathvariant":1910},[898,28133,2665],{},[902,28135,27266],{"encoding":904}," (v lineárním modelu ",[883,28138,28140],{"className":28139},[886],[888,28141,28142],{"xmlns":890},[892,28143,28144,28156],{},[895,28145,28146,28148,28150,28152,28154],{},[898,28147,2995],{},[898,28149,2675],{},[898,28151,3001],{},[1651,28153,1738],{},[898,28155,207],{},[902,28157,21102],{"encoding":904},[123,28159,28160,28136,28192,5230],{},[38,28161,28162,28163],{},"Mezní sklon k úsporám ",[883,28164,28166],{"className":28165},[886],[888,28167,28168],{"xmlns":890},[892,28169,28170,28190],{},[895,28171,28172,28174,28176,28178,28180,28182,28184,28186,28188],{},[898,28173,2995],{},[898,28175,2675],{},[898,28177,3004],{},[1651,28179,1738],{},[898,28181,3542],{"mathvariant":1910},[898,28183,3004],{},[898,28185,5981],{"mathvariant":1910},[898,28187,3542],{"mathvariant":1910},[898,28189,2665],{},[902,28191,27296],{"encoding":904},[883,28193,28195],{"className":28194},[886],[888,28196,28197],{"xmlns":890},[892,28198,28199,28215],{},[895,28200,28201,28203,28205,28207,28209,28211,28213],{},[898,28202,2995],{},[898,28204,2675],{},[898,28206,3004],{},[1651,28208,1738],{},[1692,28210,1694],{},[1651,28212,2181],{},[898,28214,207],{},[902,28216,21128],{"encoding":904},[123,28218,28219,3246,28222,28251],{},[38,28220,28221],{},"Vztah",[883,28223,28225],{"className":28224},[886],[888,28226,28227],{"xmlns":890},[892,28228,28229,28249],{},[895,28230,28231,28233,28235,28237,28239,28241,28243,28245,28247],{},[898,28232,2995],{},[898,28234,2675],{},[898,28236,3001],{},[1651,28238,1839],{},[898,28240,2995],{},[898,28242,2675],{},[898,28244,3004],{},[1651,28246,1738],{},[1692,28248,1694],{},[902,28250,27327],{"encoding":904}," (7.5).",[123,28253,28254,28256],{},[38,28255,21796],{}," — rovnováha agregátní poptávky a nabídky.",[123,28258,28259,28262,28263,17090,28284,1882],{},[38,28260,28261],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,28264,28266],{"className":28265},[886],[888,28267,28268],{"xmlns":890},[892,28269,28270,28282],{},[895,28271,28272,28274,28276,28278,28280],{},[898,28273,2665],{},[1651,28275,1738],{},[898,28277,3001],{},[1651,28279,1839],{},[898,28281,13482],{},[902,28283,16042],{"encoding":904},[883,28285,28287],{"className":28286},[886],[888,28288,28289],{"xmlns":890},[892,28290,28291,28327],{},[895,28292,28293,28299,28301,28303,28305,28307,28313,28315,28317,28319,28321,28323,28325],{},[2115,28294,28295,28297],{},[898,28296,2665],{},[898,28298,5561],{},[1651,28300,1738],{},[1651,28302,1654],{"stretchy":1653},[898,28304,2268],{},[1651,28306,1839],{},[2115,28308,28309,28311],{},[898,28310,13482],{},[1651,28312,2668],{},[1651,28314,1667],{"stretchy":1653},[898,28316,5981],{"mathvariant":1910},[1651,28318,1654],{"stretchy":1653},[1692,28320,1694],{},[1651,28322,2181],{},[898,28324,207],{},[1651,28326,1667],{"stretchy":1653},[902,28328,27470],{"encoding":904},[123,28330,28331,28334,28335,1343,28354,17090,28379,1882],{},[38,28332,28333],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,28336,28338],{"className":28337},[886],[888,28339,28340],{"xmlns":890},[892,28341,28342,28352],{},[895,28343,28344,28346,28348,28350],{},[898,28345,4104],{},[1651,28347,1654],{"stretchy":1653},[898,28349,2665],{},[1651,28351,1667],{"stretchy":1653},[902,28353,23432],{"encoding":904},[883,28355,28357],{"className":28356},[886],[888,28358,28359],{"xmlns":890},[892,28360,28361,28377],{},[895,28362,28363,28369,28371,28373,28375],{},[1686,28364,28365,28367],{},[898,28366,2665],{},[898,28368,2047],{},[1651,28370,1738],{},[898,28372,2665],{},[1651,28374,2181],{},[898,28376,4104],{},[902,28378,22931],{"encoding":904},[883,28380,28382],{"className":28381},[886],[888,28383,28384],{"xmlns":890},[892,28385,28386,28402],{},[895,28387,28388,28390,28392,28394,28396,28398,28400],{},[898,28389,2665],{},[1651,28391,1738],{},[898,28393,3001],{},[1651,28395,1839],{},[898,28397,13482],{},[1651,28399,1839],{},[898,28401,13410],{},[902,28403,22902],{"encoding":904},[123,28405,28406,28409,28410,28431,28432,17090,28456,1882],{},[38,28407,28408],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,28411,28413],{"className":28412},[886],[888,28414,28415],{"xmlns":890},[892,28416,28417,28429],{},[895,28418,28419,28421,28423,28425,28427],{},[898,28420,13618],{},[1651,28422,1738],{},[898,28424,24466],{},[1651,28426,2181],{},[898,28428,2995],{},[902,28430,24473],{"encoding":904},", importem ",[883,28433,28435],{"className":28434},[886],[888,28436,28437],{"xmlns":890},[892,28438,28439,28453],{},[895,28440,28441,28443,28445,28451],{},[898,28442,2995],{},[1651,28444,1654],{"stretchy":1653},[1686,28446,28447,28449],{},[898,28448,2665],{},[898,28450,2047],{},[1651,28452,1667],{"stretchy":1653},[902,28454,28455],{"encoding":904},"M(Y_D)",[883,28457,28459],{"className":28458},[886],[888,28460,28461],{"xmlns":890},[892,28462,28463,28487],{},[895,28464,28465,28467,28469,28471,28473,28475,28477,28479,28481,28483,28485],{},[898,28466,2665],{},[1651,28468,1738],{},[898,28470,3001],{},[1651,28472,1839],{},[898,28474,13482],{},[1651,28476,1839],{},[898,28478,13410],{},[1651,28480,1839],{},[898,28482,24466],{},[1651,28484,2181],{},[898,28486,2995],{},[902,28488,28489],{"encoding":904},"Y = C + I + G + B - M",[123,28491,28492,8322,28495,27684],{},[38,28493,28494],{},"Multiplikátor investic",[883,28496,28498],{"className":28497},[886],[888,28499,28500],{"xmlns":890},[892,28501,28502,28550],{},[895,28503,28504,28506,28512,28514,28516,28522,28524,28526,28528,28530,28532,28534,28536,28538,28540,28542,28544,28546,28548],{},[898,28505,11172],{"mathvariant":1910},[2115,28507,28508,28510],{},[898,28509,2665],{},[898,28511,5561],{},[898,28513,5981],{"mathvariant":1910},[898,28515,11172],{"mathvariant":1910},[2115,28517,28518,28520],{},[898,28519,13482],{},[1651,28521,2668],{},[1651,28523,1738],{},[1692,28525,1694],{},[898,28527,5981],{"mathvariant":1910},[1651,28529,1654],{"stretchy":1653},[1692,28531,1694],{},[1651,28533,2181],{},[898,28535,207],{},[1651,28537,1667],{"stretchy":1653},[1651,28539,1738],{},[1692,28541,1694],{},[898,28543,5981],{"mathvariant":1910},[898,28545,2995],{},[898,28547,2675],{},[898,28549,3004],{},[902,28551,27683],{"encoding":904},[123,28553,28554,8322,28585,1343,28602,28619],{},[38,28555,17025,28556],{},[883,28557,28559],{"className":28558},[886],[888,28560,28561],{"xmlns":890},[892,28562,28563,28583],{},[895,28564,28565,28567,28569,28571,28573,28575,28577,28579,28581],{},[898,28566,13482],{},[1651,28568,1654],{"stretchy":1653},[898,28570,13339],{},[1651,28572,1667],{"stretchy":1653},[1651,28574,1738],{},[898,28576,3490],{},[898,28578,13339],{},[1651,28580,1839],{},[898,28582,3542],{},[902,28584,17055],{"encoding":904},[883,28586,28588],{"className":28587},[886],[888,28589,28590],{"xmlns":890},[892,28591,28592,28600],{},[895,28593,28594,28596,28598],{},[898,28595,3490],{},[1651,28597,2319],{},[1692,28599,1741],{},[902,28601,13813],{"encoding":904},[883,28603,28605],{"className":28604},[886],[888,28606,28607],{"xmlns":890},[892,28608,28609,28617],{},[895,28610,28611,28613,28615],{},[898,28612,3542],{},[1651,28614,2390],{},[1692,28616,1741],{},[902,28618,13792],{"encoding":904},"; klesající.",[123,28621,28622,28624,28625,28627,28628,28677],{},[38,28623,17144],{}," — rovnováha na trhu zboží (",[614,28626,13352],{},"); ",[883,28629,28631],{"className":28630},[886],[888,28632,28633],{"xmlns":890},[892,28634,28635,28675],{},[895,28636,28637,28639,28641,28653,28655,28657],{},[898,28638,2665],{},[1651,28640,1738],{},[2446,28642,28643,28645],{},[898,28644,3490],{},[895,28646,28647,28649,28651],{},[1692,28648,1694],{},[1651,28650,2181],{},[898,28652,207],{},[898,28654,13339],{},[1651,28656,1839],{},[2446,28658,28659,28667],{},[895,28660,28661,28663,28665],{},[898,28662,2268],{},[1651,28664,1839],{},[898,28666,3542],{},[895,28668,28669,28671,28673],{},[1692,28670,1694],{},[1651,28672,2181],{},[898,28674,207],{},[902,28676,17197],{"encoding":904}," (7.14); klesající.",[123,28679,28680,28682,28683,28627,28685,28730],{},[38,28681,17343],{}," — rovnováha na trhu peněz (",[614,28684,13359],{},[883,28686,28688],{"className":28687},[886],[888,28689,28690],{"xmlns":890},[892,28691,28692,28728],{},[895,28693,28694,28700,28702,28708,28710,28712,28718,28720,28722],{},[2115,28695,28696,28698],{},[898,28697,2995],{},[1651,28699,2668],{},[1651,28701,1738],{},[1686,28703,28704,28706],{},[898,28705,14535],{},[1692,28707,1694],{},[898,28709,2665],{},[1651,28711,1839],{},[1686,28713,28714,28716],{},[898,28715,14535],{},[1692,28717,1703],{},[898,28719,13339],{},[1651,28721,1839],{},[1686,28723,28724,28726],{},[898,28725,14535],{},[1692,28727,3521],{},[902,28729,17391],{"encoding":904}," (7.15); rostoucí.",[123,28732,28733,8322,28736,1882],{},[38,28734,28735],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,28737,28739],{"className":28738},[886],[888,28740,28741],{"xmlns":890},[892,28742,28743,28767],{},[895,28744,28745,28751,28753,28759,28761],{},[2115,28746,28747,28749],{},[898,28748,2995],{},[898,28750,2047],{},[1651,28752,1738],{},[1686,28754,28755,28757],{},[898,28756,1807],{},[1692,28758,1694],{},[1651,28760,1839],{},[1686,28762,28763,28765],{},[898,28764,1807],{},[1692,28766,1703],{},[902,28768,28769],{"encoding":904},"M^D = L_1 + L_2",[123,28771,28772,17401,28774,15278,28787,5197,28802,28817,28818,1882],{},[38,28773,945],{},[883,28775,28777],{"className":28776},[886],[888,28778,28779],{"xmlns":890},[892,28780,28781,28785],{},[895,28782,28783],{},[898,28784,5561],{},[902,28786,5561],{"encoding":904},[883,28788,28790],{"className":28789},[886],[888,28791,28792],{"xmlns":890},[892,28793,28794,28800],{},[895,28795,28796,28798],{},[898,28797,13482],{},[898,28799,3004],{},[902,28801,13349],{"encoding":904},[883,28803,28805],{"className":28804},[886],[888,28806,28807],{"xmlns":890},[892,28808,28809,28815],{},[895,28810,28811,28813],{},[898,28812,1807],{},[898,28814,2995],{},[902,28816,13356],{"encoding":904}," určuje ",[883,28819,28821],{"className":28820},[886],[888,28822,28823],{"xmlns":890},[892,28824,28825,28845],{},[895,28826,28827,28829,28835,28837,28843],{},[1651,28828,1654],{"stretchy":1653},[2115,28830,28831,28833],{},[898,28832,2665],{},[898,28834,5561],{},[1651,28836,1661],{"separator":1660},[2115,28838,28839,28841],{},[898,28840,13339],{},[898,28842,5561],{},[1651,28844,1667],{"stretchy":1653},[902,28846,13393],{"encoding":904},[115,28848,3238],{"id":3237},[120,28850,28851,28858,28865],{},[123,28852,28853,3246,28855],{},[38,28854,17502],{},[207,28856,17506],{"className":28857,"dataFsResolvedFilePath":1749,"href":1750},[210],[123,28859,28860,3246,28862],{},[38,28861,17511],{},[207,28863,17515],{"className":28864,"dataFsResolvedFilePath":868,"href":869},[210],[123,28866,28867,28869],{},[38,28868,17530],{},[120,28870,28871,28877,28883,28889],{},[123,28872,28873,28876],{},[207,28874,17571],{"className":28875,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,28878,28879,28882],{},[207,28880,17538],{"className":28881,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,28884,28885,28888],{},[207,28886,4277],{"className":28887,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,28890,28891,28894,28895,1343,28912,28929],{},[207,28892,1145],{"className":28893,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,28896,28898],{"className":28897},[886],[888,28899,28900],{"xmlns":890},[892,28901,28902,28910],{},[895,28903,28904,28906,28908],{},[898,28905,2995],{},[898,28907,2675],{},[898,28909,3001],{},[902,28911,19258],{"encoding":904},[883,28913,28915],{"className":28914},[886],[888,28916,28917],{"xmlns":890},[892,28918,28919,28927],{},[895,28920,28921,28923,28925],{},[898,28922,2995],{},[898,28924,2675],{},[898,28926,3004],{},[902,28928,20872],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":28931},[28932,28933,28934,28935,28940,28943,28944,28951,28956,28961,28964,28965,28966,28967],{"id":13303,"depth":642,"text":13304},{"id":19367,"depth":642,"text":19368},{"id":19487,"depth":642,"text":19488},{"id":19740,"depth":642,"text":19741,"children":28936},[28937,28938,28939],{"id":19744,"depth":649,"text":19745},{"id":19956,"depth":649,"text":19957},{"id":20464,"depth":649,"text":20465},{"id":20784,"depth":642,"text":20785,"children":28941},[28942],{"id":21300,"depth":649,"text":21301},{"id":21795,"depth":642,"text":21796},{"id":21822,"depth":642,"text":21823,"children":28945},[28946,28947,28948,28950],{"id":21833,"depth":649,"text":21834},{"id":21903,"depth":649,"text":21904},{"id":22087,"depth":649,"text":28949},"Výpočet YEY^E",{"id":22230,"depth":649,"text":22231},{"id":22608,"depth":642,"text":22609,"children":28952},[28953,28954,28955],{"id":22612,"depth":649,"text":21834},{"id":23061,"depth":649,"text":21904},{"id":23717,"depth":649,"text":23718},{"id":24504,"depth":642,"text":24505,"children":28957},[28958,28959,28960],{"id":24508,"depth":649,"text":21834},{"id":24653,"depth":649,"text":21904},{"id":24923,"depth":649,"text":24924},{"id":25847,"depth":642,"text":25848,"children":28962},[28963],{"id":26043,"depth":649,"text":26044},{"id":26593,"depth":642,"text":26594},{"id":27053,"depth":642,"text":27054},{"id":17017,"depth":642,"text":17018},{"id":3237,"depth":642,"text":3238},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,17524,1143,28974,28975,28976,17571,3301],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":28979,"title":28980,"body":28981,"course":1128,"courses":659,"created":10859,"description":641,"extension":661,"meta":37961,"navigation":664,"path":37962,"seo":37963,"sources":37964,"stem":37965,"tags":37966,"type":3302,"updated":677,"__hash__":37971},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":28982,"toc":37930},[28983,28986,28988,29217,29221,29274,29344,29456,29615,29619,29735,29739,29742,29864,29867,30060,30084,30152,30316,30334,30400,30778,30782,30789,31033,31089,31093,31158,31276,31408,31440,31560,31642,31645,31767,31960,32181,32185,32225,32330,32387,32487,32664,32794,32847,32850,32937,32941,33117,33121,33124,33209,33212,33269,33374,33378,33499,33502,33685,33688,33796,34005,34325,34373,34446,34520,34522,34746,34981,35249,35253,35256,35361,35418,35452,35499,35532,35616,35618,35850,35983,36060,36182,36337,36341,36482,36489,36713,36724,36728,36732,36837,36979,37089,37188,37192,37351,37461,37463,37856,37858],[12,28984,28980],{"id":28985},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,28987,13304],{"id":13303},[724,28989,28990,28992,28993,29027,29028,29031,29032,29063,29064,29110,29111,29114,29115,29157,29158,29176,29177,29181,29182,29212,29213,29216],{},[38,28991,913],{}," řeší, jaký svazek zboží ",[883,28994,28996],{"className":28995},[886],[888,28997,28998],{"xmlns":890},[892,28999,29000,29024],{},[895,29001,29002,29004,29012,29014,29022],{},[1651,29003,2261],{"stretchy":1653},[1902,29005,29006,29008,29010],{},[898,29007,1690],{},[1692,29009,1694],{},[1651,29011,2668],{},[1651,29013,1661],{"separator":1660},[1902,29015,29016,29018,29020],{},[898,29017,1690],{},[1692,29019,1703],{},[1651,29021,2668],{},[1651,29023,2279],{"stretchy":1653},[902,29025,29026],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,29029,29030],{},"primární úloha"," — maximalizace užitečnosti ",[883,29033,29035],{"className":29034},[886],[888,29036,29037],{"xmlns":890},[892,29038,29039,29061],{},[895,29040,29041,29043,29045,29051,29053,29059],{},[898,29042,900],{},[1651,29044,1654],{"stretchy":1653},[1686,29046,29047,29049],{},[898,29048,1690],{},[1692,29050,1694],{},[1651,29052,1661],{"separator":1660},[1686,29054,29055,29057],{},[898,29056,1690],{},[1692,29058,1703],{},[1651,29060,1667],{"stretchy":1653},[902,29062,1708],{"encoding":904}," při rozpočtovém omezení ",[883,29065,29067],{"className":29066},[886],[888,29068,29069],{"xmlns":890},[892,29070,29071,29107],{},[895,29072,29073,29079,29081,29087,29093,29095,29101],{},[2115,29074,29075,29077],{},[898,29076,2665],{},[1651,29078,2668],{},[1651,29080,1738],{},[1686,29082,29083,29085],{},[898,29084,2675],{},[1692,29086,1694],{},[1686,29088,29089,29091],{},[898,29090,1690],{},[1692,29092,1694],{},[1651,29094,1839],{},[1686,29096,29097,29099],{},[898,29098,2675],{},[1692,29100,1703],{},[1686,29102,29103,29105],{},[898,29104,1690],{},[1692,29106,1703],{},[902,29108,29109],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,29112,29113],{},"duální úloha"," — minimalizace výdajů ",[883,29116,29118],{"className":29117},[886],[888,29119,29120],{"xmlns":890},[892,29121,29122,29154],{},[895,29123,29124,29126,29128,29134,29140,29142,29148],{},[898,29125,5561],{},[1651,29127,1738],{},[1686,29129,29130,29132],{},[898,29131,2675],{},[1692,29133,1694],{},[1686,29135,29136,29138],{},[898,29137,1690],{},[1692,29139,1694],{},[1651,29141,1839],{},[1686,29143,29144,29146],{},[898,29145,2675],{},[1692,29147,1703],{},[1686,29149,29150,29152],{},[898,29151,1690],{},[1692,29153,1703],{},[902,29155,29156],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,29159,29161],{"className":29160},[886],[888,29162,29163],{"xmlns":890},[892,29164,29165,29173],{},[895,29166,29167],{},[2115,29168,29169,29171],{},[898,29170,900],{},[1651,29172,2668],{},[902,29174,29175],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,29178,29180],{"className":29179,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,29183,29185],{"className":29184},[886],[888,29186,29187],{"xmlns":890},[892,29188,29189,29209],{},[895,29190,29191,29193,29195,29201,29203],{},[1843,29192,11903],{},[1651,29194,1738],{},[1686,29196,29197,29199],{},[898,29198,2675],{},[1692,29200,1694],{},[898,29202,5981],{"mathvariant":1910},[1686,29204,29205,29207],{},[898,29206,2675],{},[1692,29208,1703],{},[902,29210,29211],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,29214,29215],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,29218,29220],{"id":29219},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,29222,29223,29224,29242,29243,29273],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,29225,29227],{"className":29226},[886],[888,29228,29229],{"xmlns":890},[892,29230,29231,29239],{},[895,29232,29233],{},[2115,29234,29235,29237],{},[898,29236,2665],{},[1651,29238,2668],{},[902,29240,29241],{"encoding":904},"Y^*"," a ceny ",[883,29244,29246],{"className":29245},[886],[888,29247,29248],{"xmlns":890},[892,29249,29250,29270],{},[895,29251,29252,29260,29262],{},[1902,29253,29254,29256,29258],{},[898,29255,2675],{},[1692,29257,1694],{},[1651,29259,2668],{},[1651,29261,1661],{"separator":1660},[1902,29263,29264,29266,29268],{},[898,29265,2675],{},[1692,29267,1703],{},[1651,29269,2668],{},[902,29271,29272],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,29275,29277],{"className":29276},[886],[888,29278,29280],{"xmlns":890,"display":29279},"block",[892,29281,29282,29341],{},[21967,29283,29285],{"width":29284},"100%",[21972,29286,29287,29290,29334,29336],{},[21975,29288],{"width":29289},"50%",[21975,29291,29292],{},[895,29293,29294,29300,29302,29310,29316,29318,29326,29332],{},[2115,29295,29296,29298],{},[898,29297,2665],{},[1651,29299,2668],{},[1651,29301,1738],{},[1902,29303,29304,29306,29308],{},[898,29305,2675],{},[1692,29307,1694],{},[1651,29309,2668],{},[1686,29311,29312,29314],{},[898,29313,1690],{},[1692,29315,1694],{},[1651,29317,1839],{},[1902,29319,29320,29322,29324],{},[898,29321,2675],{},[1692,29323,1703],{},[1651,29325,2668],{},[1686,29327,29328,29330],{},[898,29329,1690],{},[1692,29331,1703],{},[1651,29333,1661],{"separator":1660},[21975,29335],{"width":29289},[21975,29337,29338],{},[1843,29339,29340],{},"(6.12)",[902,29342,29343],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,29345,29346,29347,29350,29351,5197,29387,29423,29424,29437,29438,29452,29453,1882],{},"geometricky ",[38,29348,29349],{},"rozpočtová přímka (budget line)"," procházející body ",[883,29352,29354],{"className":29353},[886],[888,29355,29356],{"xmlns":890},[892,29357,29358,29384],{},[895,29359,29360,29362,29368,29370,29378,29380,29382],{},[1651,29361,2261],{"stretchy":1653},[2115,29363,29364,29366],{},[898,29365,2665],{},[1651,29367,2668],{},[898,29369,5981],{"mathvariant":1910},[1902,29371,29372,29374,29376],{},[898,29373,2675],{},[1692,29375,1694],{},[1651,29377,2668],{},[1651,29379,1661],{"separator":1660},[1692,29381,1741],{},[1651,29383,2279],{"stretchy":1653},[902,29385,29386],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,29388,29390],{"className":29389},[886],[888,29391,29392],{"xmlns":890},[892,29393,29394,29420],{},[895,29395,29396,29398,29400,29402,29408,29410,29418],{},[1651,29397,2261],{"stretchy":1653},[1692,29399,1741],{},[1651,29401,1661],{"separator":1660},[2115,29403,29404,29406],{},[898,29405,2665],{},[1651,29407,2668],{},[898,29409,5981],{"mathvariant":1910},[1902,29411,29412,29414,29416],{},[898,29413,2675],{},[1692,29415,1703],{},[1651,29417,2668],{},[1651,29419,2279],{"stretchy":1653},[902,29421,29422],{"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 ",[883,29425,29427],{"className":29426},[886],[888,29428,29429],{"xmlns":890},[892,29430,29431,29435],{},[895,29432,29433],{},[898,29434,900],{},[902,29436,900],{"encoding":904},", indiferenční křivky a ",[883,29439,29441],{"className":29440},[886],[888,29442,29443],{"xmlns":890},[892,29444,29445,29449],{},[895,29446,29447],{},[1843,29448,11903],{},[902,29450,29451],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,29454,880],{"className":29455,"dataFsResolvedFilePath":878,"href":879},[210],[5179,29457,29458],{},[724,29459,29460,29462,29463,29466,29467,29480,29481,29483,29484,29497,29498,3246,29501,29541,29542,29559,29560,29577,29578,29595,29596,29614],{},[883,29461,5719],{}," Pozor — dvě úlohy, totéž řešení\n",[38,29464,29465],{},"Primární úloha"," (max ",[883,29468,29470],{"className":29469},[886],[888,29471,29472],{"xmlns":890},[892,29473,29474,29478],{},[895,29475,29476],{},[898,29477,900],{},[902,29479,900],{"encoding":904}," při pevném rozpočtu) a ",[38,29482,29113],{}," (min ",[883,29485,29487],{"className":29486},[886],[888,29488,29489],{"xmlns":890},[892,29490,29491,29495],{},[895,29492,29493],{},[898,29494,5561],{},[902,29496,5561],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,29499,29500],{},"tentýž bod",[883,29502,29504],{"className":29503},[886],[888,29505,29506],{"xmlns":890},[892,29507,29508,29538],{},[895,29509,29510,29516,29518,29526,29528,29536],{},[2115,29511,29512,29514],{},[898,29513,1690],{},[1651,29515,2668],{},[1651,29517,2261],{"stretchy":1653},[1902,29519,29520,29522,29524],{},[898,29521,1690],{},[1692,29523,1694],{},[1651,29525,2668],{},[1651,29527,1661],{"separator":1660},[1902,29529,29530,29532,29534],{},[898,29531,1690],{},[1692,29533,1703],{},[1651,29535,2668],{},[1651,29537,2279],{"stretchy":1653},[902,29539,29540],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,29543,29545],{"className":29544},[886],[888,29546,29547],{"xmlns":890},[892,29548,29549,29557],{},[895,29550,29551],{},[2115,29552,29553,29555],{},[898,29554,2665],{},[1651,29556,2668],{},[902,29558,29241],{"encoding":904}," a hledáme maximální ",[883,29561,29563],{"className":29562},[886],[888,29564,29565],{"xmlns":890},[892,29566,29567,29575],{},[895,29568,29569],{},[2115,29570,29571,29573],{},[898,29572,900],{},[1651,29574,2668],{},[902,29576,29175],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,29579,29581],{"className":29580},[886],[888,29582,29583],{"xmlns":890},[892,29584,29585,29593],{},[895,29586,29587],{},[2115,29588,29589,29591],{},[898,29590,900],{},[1651,29592,2668],{},[902,29594,29175],{"encoding":904}," a hledáme minimální ",[883,29597,29599],{"className":29598},[886],[888,29600,29601],{"xmlns":890},[892,29602,29603,29611],{},[895,29604,29605],{},[2115,29606,29607,29609],{},[898,29608,5561],{},[1651,29610,2668],{},[902,29612,29613],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,29616,29618],{"id":29617},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,29620,29621,29622,29653,29654,29730,29731,1882],{},"Úlohou je najít maximum ",[883,29623,29625],{"className":29624},[886],[888,29626,29627],{"xmlns":890},[892,29628,29629,29651],{},[895,29630,29631,29633,29635,29641,29643,29649],{},[898,29632,900],{},[1651,29634,1654],{"stretchy":1653},[1686,29636,29637,29639],{},[898,29638,1690],{},[1692,29640,1694],{},[1651,29642,1661],{"separator":1660},[1686,29644,29645,29647],{},[898,29646,1690],{},[1692,29648,1703],{},[1651,29650,1667],{"stretchy":1653},[902,29652,1708],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,29655,29657],{"className":29656},[886],[888,29658,29659],{"xmlns":890},[892,29660,29661,29727],{},[895,29662,29663,29665,29667,29673,29675,29681,29683,29685,29691,29693,29701,29707,29709,29717,29723,29725],{},[898,29664,1725],{},[1651,29666,1654],{"stretchy":1653},[1686,29668,29669,29671],{},[898,29670,1690],{},[1692,29672,1694],{},[1651,29674,1661],{"separator":1660},[1686,29676,29677,29679],{},[898,29678,1690],{},[1692,29680,1703],{},[1651,29682,1667],{"stretchy":1653},[1651,29684,1738],{},[2115,29686,29687,29689],{},[898,29688,2665],{},[1651,29690,2668],{},[1651,29692,2181],{},[1902,29694,29695,29697,29699],{},[898,29696,2675],{},[1692,29698,1694],{},[1651,29700,2668],{},[1686,29702,29703,29705],{},[898,29704,1690],{},[1692,29706,1694],{},[1651,29708,2181],{},[1902,29710,29711,29713,29715],{},[898,29712,2675],{},[1692,29714,1703],{},[1651,29716,2668],{},[1686,29718,29719,29721],{},[898,29720,1690],{},[1692,29722,1703],{},[1651,29724,1738],{},[1692,29726,1741],{},[902,29728,29729],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,29732,29734],{"className":29733,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,29736,29738],{"id":29737},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,29740,29741],{},"Sestavíme",[883,29743,29745],{"className":29744},[886],[888,29746,29747],{"xmlns":890,"display":29279},[892,29748,29749,29861],{},[21967,29750,29751],{"width":29284},[21972,29752,29753,29755,29854,29856],{},[21975,29754],{"width":29289},[21975,29756,29757],{},[895,29758,29759,29762,29764,29770,29772,29778,29780,29782,29784,29786,29788,29790,29796,29798,29804,29806,29808,29810,29812,29818,29820,29828,29834,29836,29844,29850,29852],{},[898,29760,1807],{"mathvariant":29761},"script",[1651,29763,1654],{"stretchy":1653},[1686,29765,29766,29768],{},[898,29767,1690],{},[1692,29769,1694],{},[1651,29771,1661],{"separator":1660},[1686,29773,29774,29776],{},[898,29775,1690],{},[1692,29777,1703],{},[1651,29779,1661],{"separator":1660},[898,29781,1820],{},[1651,29783,1667],{"stretchy":1653},[1651,29785,1738],{},[898,29787,900],{},[1651,29789,1654],{"stretchy":1653},[1686,29791,29792,29794],{},[898,29793,1690],{},[1692,29795,1694],{},[1651,29797,1661],{"separator":1660},[1686,29799,29800,29802],{},[898,29801,1690],{},[1692,29803,1703],{},[1651,29805,1667],{"stretchy":1653},[1651,29807,1839],{},[898,29809,1820],{},[1651,29811,1654],{"stretchy":1653},[2115,29813,29814,29816],{},[898,29815,2665],{},[1651,29817,2668],{},[1651,29819,2181],{},[1902,29821,29822,29824,29826],{},[898,29823,2675],{},[1692,29825,1694],{},[1651,29827,2668],{},[1686,29829,29830,29832],{},[898,29831,1690],{},[1692,29833,1694],{},[1651,29835,2181],{},[1902,29837,29838,29840,29842],{},[898,29839,2675],{},[1692,29841,1703],{},[1651,29843,2668],{},[1686,29845,29846,29848],{},[898,29847,1690],{},[1692,29849,1703],{},[1651,29851,1667],{"stretchy":1653},[898,29853,1882],{"mathvariant":1910},[21975,29855],{"width":29289},[21975,29857,29858],{},[1843,29859,29860],{},"(6.13)",[902,29862,29863],{"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}",[724,29865,29866],{},"Soustava prvního řádu:",[883,29868,29870],{"className":29869},[886],[888,29871,29872],{"xmlns":890,"display":29279},[892,29873,29874,30057],{},[21967,29875,29876],{"width":29284},[21972,29877,29878,29880,30050,30052],{},[21975,29879],{"width":29289},[21975,29881,29882],{},[21967,29883,29884,29934,29984],{"rowspacing":21969,"columnalign":21970,"columnspacing":1911},[21972,29885,29886,29898],{},[21975,29887,29888],{},[2938,29889,29890],{"scriptlevel":1741,"displaystyle":1660},[1902,29891,29892,29894,29896],{},[898,29893,1807],{"mathvariant":29761},[1692,29895,1694],{},[1651,29897,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[21975,29899,29900],{},[2938,29901,29902],{"scriptlevel":1741,"displaystyle":1660},[895,29903,29904,29906,29908,29916,29918,29920,29928,29930,29932],{},[895,29905],{},[1651,29907,1738],{},[1902,29909,29910,29912,29914],{},[898,29911,900],{},[1692,29913,1694],{},[1651,29915,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,29917,2181],{},[898,29919,1820],{},[1902,29921,29922,29924,29926],{},[898,29923,2675],{},[1692,29925,1694],{},[1651,29927,2668],{},[1651,29929,1738],{},[1692,29931,1741],{},[1651,29933,1661],{"separator":1660},[21972,29935,29936,29948],{},[21975,29937,29938],{},[2938,29939,29940],{"scriptlevel":1741,"displaystyle":1660},[1902,29941,29942,29944,29946],{},[898,29943,1807],{"mathvariant":29761},[1692,29945,1703],{},[1651,29947,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[21975,29949,29950],{},[2938,29951,29952],{"scriptlevel":1741,"displaystyle":1660},[895,29953,29954,29956,29958,29966,29968,29970,29978,29980,29982],{},[895,29955],{},[1651,29957,1738],{},[1902,29959,29960,29962,29964],{},[898,29961,900],{},[1692,29963,1703],{},[1651,29965,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,29967,2181],{},[898,29969,1820],{},[1902,29971,29972,29974,29976],{},[898,29973,2675],{},[1692,29975,1703],{},[1651,29977,2668],{},[1651,29979,1738],{},[1692,29981,1741],{},[1651,29983,1661],{"separator":1660},[21972,29985,29986,29998],{},[21975,29987,29988],{},[2938,29989,29990],{"scriptlevel":1741,"displaystyle":1660},[1902,29991,29992,29994,29996],{},[898,29993,1807],{"mathvariant":29761},[898,29995,1820],{},[1651,29997,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[21975,29999,30000],{},[2938,30001,30002],{"scriptlevel":1741,"displaystyle":1660},[895,30003,30004,30006,30008,30014,30016,30024,30030,30032,30040,30046,30048],{},[895,30005],{},[1651,30007,1738],{},[2115,30009,30010,30012],{},[898,30011,2665],{},[1651,30013,2668],{},[1651,30015,2181],{},[1902,30017,30018,30020,30022],{},[898,30019,2675],{},[1692,30021,1694],{},[1651,30023,2668],{},[1686,30025,30026,30028],{},[898,30027,1690],{},[1692,30029,1694],{},[1651,30031,2181],{},[1902,30033,30034,30036,30038],{},[898,30035,2675],{},[1692,30037,1703],{},[1651,30039,2668],{},[1686,30041,30042,30044],{},[898,30043,1690],{},[1692,30045,1703],{},[1651,30047,1738],{},[1692,30049,13758],{},[21975,30051],{"width":29289},[21975,30053,30054],{},[1843,30055,30056],{},"(6.14)",[902,30058,30059],{"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}",[724,30061,30062,30063,30066,30067,30080,30081,1793],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,30064,30065],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,30068,30070],{"className":30069},[886],[888,30071,30072],{"xmlns":890},[892,30073,30074,30078],{},[895,30075,30076],{},[898,30077,1820],{},[902,30079,1877],{"encoding":904}," dostáváme ",[38,30082,30083],{},"podmínku optimality",[883,30085,30087],{"className":30086},[886],[888,30088,30089],{"xmlns":890,"display":29279},[892,30090,30091,30149],{},[895,30092,30093],{},[14130,30094,30095],{"notation":14132},[2938,30096,30097],{"scriptlevel":1741,"displaystyle":1653},[2938,30098,30099],{"scriptlevel":1741,"displaystyle":1653},[2938,30100,30101],{"scriptlevel":1741,"displaystyle":1660},[895,30102,30103,30105,30107,30109,30127,30129,30147],{},[1843,30104,5295],{},[1843,30106,11903],{},[1651,30108,1738],{},[2446,30110,30111,30119],{},[1902,30112,30113,30115,30117],{},[898,30114,900],{},[1692,30116,1694],{},[1651,30118,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1902,30120,30121,30123,30125],{},[898,30122,900],{},[1692,30124,1703],{},[1651,30126,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,30128,1738],{},[2446,30130,30131,30139],{},[1902,30132,30133,30135,30137],{},[898,30134,2675],{},[1692,30136,1694],{},[1651,30138,2668],{},[1902,30140,30141,30143,30145],{},[898,30142,2675],{},[1692,30144,1703],{},[1651,30146,2668],{},[1843,30148,5295],{},[902,30150,30151],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[5179,30153,30154],{},[724,30155,30156,30158,30159,30193,30194,30197,30198,30216,30217,30235,30236,30266,30267,30284,30285,30315],{},[883,30157,5465],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,30160,30162],{"className":30161},[886],[888,30163,30164],{"xmlns":890},[892,30165,30166,30190],{},[895,30167,30168,30170,30172,30180,30182],{},[1843,30169,11903],{},[1651,30171,1738],{},[1902,30173,30174,30176,30178],{},[898,30175,2675],{},[1692,30177,1694],{},[1651,30179,2668],{},[898,30181,5981],{"mathvariant":1910},[1902,30183,30184,30186,30188],{},[898,30185,2675],{},[1692,30187,1703],{},[1651,30189,2668],{},[902,30191,30192],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,30195,30196],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,30199,30201],{"className":30200},[886],[888,30202,30203],{"xmlns":890},[892,30204,30205,30213],{},[895,30206,30207],{},[1686,30208,30209,30211],{},[898,30210,1690],{},[1692,30212,1694],{},[902,30214,30215],{"encoding":904},"Q_1"," za ",[883,30218,30220],{"className":30219},[886],[888,30221,30222],{"xmlns":890},[892,30223,30224,30232],{},[895,30225,30226],{},[1686,30227,30228,30230],{},[898,30229,1690],{},[1692,30231,1703],{},[902,30233,30234],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,30237,30239],{"className":30238},[886],[888,30240,30241],{"xmlns":890},[892,30242,30243,30263],{},[895,30244,30245,30247,30249,30255,30257],{},[1843,30246,11903],{},[1651,30248,2390],{},[1686,30250,30251,30253],{},[898,30252,2675],{},[1692,30254,1694],{},[898,30256,5981],{"mathvariant":1910},[1686,30258,30259,30261],{},[898,30260,2675],{},[1692,30262,1703],{},[902,30264,30265],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,30268,30270],{"className":30269},[886],[888,30271,30272],{"xmlns":890},[892,30273,30274,30282],{},[895,30275,30276],{},[1686,30277,30278,30280],{},[898,30279,1690],{},[1692,30281,1694],{},[902,30283,30215],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,30286,30288],{"className":30287},[886],[888,30289,30290],{"xmlns":890},[892,30291,30292,30312],{},[895,30293,30294,30296,30298,30304,30306],{},[1843,30295,11903],{},[1651,30297,2319],{},[1686,30299,30300,30302],{},[898,30301,2675],{},[1692,30303,1694],{},[898,30305,5981],{"mathvariant":1910},[1686,30307,30308,30310],{},[898,30309,2675],{},[1692,30311,1703],{},[902,30313,30314],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,30317,30319,30320,30333],{"id":30318},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,30321,30323],{"className":30322},[886],[888,30324,30325],{"xmlns":890},[892,30326,30327,30331],{},[895,30328,30329],{},[898,30330,1820],{},[902,30332,1877],{"encoding":904}," — mezní užitečnost důchodu",[724,30335,30336,30337,30355,30356,30359,30360,30377,30378,30395,30396,30399],{},"Lagrangeův multiplikátor ",[883,30338,30340],{"className":30339},[886],[888,30341,30342],{"xmlns":890},[892,30343,30344,30352],{},[895,30345,30346],{},[2115,30347,30348,30350],{},[898,30349,1820],{},[1651,30351,2668],{},[902,30353,30354],{"encoding":904},"\\lambda^*"," představuje ",[38,30357,30358],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,30361,30363],{"className":30362},[886],[888,30364,30365],{"xmlns":890},[892,30366,30367,30375],{},[895,30368,30369],{},[2115,30370,30371,30373],{},[898,30372,900],{},[1651,30374,2668],{},[902,30376,29175],{"encoding":904}," při jednotkové změně důchodu ",[883,30379,30381],{"className":30380},[886],[888,30382,30383],{"xmlns":890},[892,30384,30385,30393],{},[895,30386,30387],{},[2115,30388,30389,30391],{},[898,30390,2665],{},[1651,30392,2668],{},[902,30394,29241],{"encoding":904},". Je to ",[38,30397,30398],{},"stínová cena"," rozpočtového omezení.",[5179,30401,30402,30407],{},[724,30403,30404,30406],{},[883,30405,5879],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,30408,30409,30469,30556,30592,30679],{},[123,30410,30411,30414,30415,1882],{},[38,30412,30413],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,30416,30418],{"className":30417},[886],[888,30419,30420],{"xmlns":890},[892,30421,30422,30466],{},[895,30423,30424,30430,30432,30440,30446,30448,30456,30462,30464],{},[2115,30425,30426,30428],{},[898,30427,2665],{},[1651,30429,2668],{},[1651,30431,2181],{},[1902,30433,30434,30436,30438],{},[898,30435,2675],{},[1692,30437,1694],{},[1651,30439,2668],{},[1686,30441,30442,30444],{},[898,30443,1690],{},[1692,30445,1694],{},[1651,30447,2181],{},[1902,30449,30450,30452,30454],{},[898,30451,2675],{},[1692,30453,1703],{},[1651,30455,2668],{},[1686,30457,30458,30460],{},[898,30459,1690],{},[1692,30461,1703],{},[1651,30463,1738],{},[1692,30465,1741],{},[902,30467,30468],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,30470,30471,3246,30474,1882],{},[38,30472,30473],{},"Sestav Lagrangeovu funkci",[883,30475,30477],{"className":30476},[886],[888,30478,30479],{"xmlns":890},[892,30480,30481,30553],{},[895,30482,30483,30485,30487,30489,30491,30497,30499,30505,30507,30509,30511,30513,30519,30521,30529,30535,30537,30545,30551],{},[898,30484,1807],{"mathvariant":29761},[1651,30486,1738],{},[898,30488,900],{},[1651,30490,1654],{"stretchy":1653},[1686,30492,30493,30495],{},[898,30494,1690],{},[1692,30496,1694],{},[1651,30498,1661],{"separator":1660},[1686,30500,30501,30503],{},[898,30502,1690],{},[1692,30504,1703],{},[1651,30506,1667],{"stretchy":1653},[1651,30508,1839],{},[898,30510,1820],{},[1651,30512,1654],{"stretchy":1653},[2115,30514,30515,30517],{},[898,30516,2665],{},[1651,30518,2668],{},[1651,30520,2181],{},[1902,30522,30523,30525,30527],{},[898,30524,2675],{},[1692,30526,1694],{},[1651,30528,2668],{},[1686,30530,30531,30533],{},[898,30532,1690],{},[1692,30534,1694],{},[1651,30536,2181],{},[1902,30538,30539,30541,30543],{},[898,30540,2675],{},[1692,30542,1703],{},[1651,30544,2668],{},[1686,30546,30547,30549],{},[898,30548,1690],{},[1692,30550,1703],{},[1651,30552,1667],{"stretchy":1653},[902,30554,30555],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,30557,30558,11768,30561,30591],{},[38,30559,30560],{},"Spočítej parciální derivace",[883,30562,30564],{"className":30563},[886],[888,30565,30566],{"xmlns":890},[892,30567,30568,30588],{},[895,30569,30570,30576,30578,30584,30586],{},[1686,30571,30572,30574],{},[898,30573,1690],{},[1692,30575,1694],{},[1651,30577,1661],{"separator":1660},[1686,30579,30580,30582],{},[898,30581,1690],{},[1692,30583,1703],{},[1651,30585,1661],{"separator":1660},[898,30587,1820],{},[902,30589,30590],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,30593,30594,30610,30611,30644,30645,5197,30662,1882],{},[38,30595,30596,30597],{},"Vyluč ",[883,30598,30600],{"className":30599},[886],[888,30601,30602],{"xmlns":890},[892,30603,30604,30608],{},[895,30605,30606],{},[898,30607,1820],{},[902,30609,1877],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,30612,30614],{"className":30613},[886],[888,30615,30616],{"xmlns":890},[892,30617,30618,30642],{},[895,30619,30620,30622,30624,30632,30634],{},[1843,30621,11903],{},[1651,30623,1738],{},[1902,30625,30626,30628,30630],{},[898,30627,2675],{},[1692,30629,1694],{},[1651,30631,2668],{},[898,30633,5981],{"mathvariant":1910},[1902,30635,30636,30638,30640],{},[898,30637,2675],{},[1692,30639,1703],{},[1651,30641,2668],{},[902,30643,30192],{"encoding":904},", která dá vztah mezi ",[883,30646,30648],{"className":30647},[886],[888,30649,30650],{"xmlns":890},[892,30651,30652,30660],{},[895,30653,30654],{},[1686,30655,30656,30658],{},[898,30657,1690],{},[1692,30659,1694],{},[902,30661,30215],{"encoding":904},[883,30663,30665],{"className":30664},[886],[888,30666,30667],{"xmlns":890},[892,30668,30669,30677],{},[895,30670,30671],{},[1686,30672,30673,30675],{},[898,30674,1690],{},[1692,30676,1703],{},[902,30678,30234],{"encoding":904},[123,30680,30681,30684,30685,30715,30716,30733,30734,1882],{},[38,30682,30683],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,30686,30688],{"className":30687},[886],[888,30689,30690],{"xmlns":890},[892,30691,30692,30712],{},[895,30693,30694,30702,30704],{},[1902,30695,30696,30698,30700],{},[898,30697,1690],{},[1692,30699,1694],{},[1651,30701,2668],{},[1651,30703,1661],{"separator":1660},[1902,30705,30706,30708,30710],{},[898,30707,1690],{},[1692,30709,1703],{},[1651,30711,2668],{},[902,30713,30714],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,30717,30719],{"className":30718},[886],[888,30720,30721],{"xmlns":890},[892,30722,30723,30731],{},[895,30724,30725],{},[2115,30726,30727,30729],{},[898,30728,1820],{},[1651,30730,2668],{},[902,30732,30354],{"encoding":904}," a maximální užitečnost ",[883,30735,30737],{"className":30736},[886],[888,30738,30739],{"xmlns":890},[892,30740,30741,30775],{},[895,30742,30743,30749,30751,30753,30755,30763,30765,30773],{},[2115,30744,30745,30747],{},[898,30746,900],{},[1651,30748,2668],{},[1651,30750,1738],{},[898,30752,900],{},[1651,30754,1654],{"stretchy":1653},[1902,30756,30757,30759,30761],{},[898,30758,1690],{},[1692,30760,1694],{},[1651,30762,2668],{},[1651,30764,1661],{"separator":1660},[1902,30766,30767,30769,30771],{},[898,30768,1690],{},[1692,30770,1703],{},[1651,30772,2668],{},[1651,30774,1667],{"stretchy":1653},[902,30776,30777],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,30779,30781],{"id":30780},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,30783,30784],{},[1756,30785],{"alt":30786,"className":30787,"src":30788},"imek-uzitecnost-optimum",[210,1760],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,30790,30791],{},[614,30792,30793,30794,30843,30844,5197,30872,30900,30901,30935,30936,30975,30976,30994,30995,31013,31014,31032],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,30795,30797],{"className":30796},[886],[888,30798,30799],{"xmlns":890},[892,30800,30801,30841],{},[895,30802,30803,30809,30811,30819,30825,30827,30835],{},[2115,30804,30805,30807],{},[898,30806,2665],{},[1651,30808,2668],{},[1651,30810,1738],{},[1902,30812,30813,30815,30817],{},[898,30814,2675],{},[1692,30816,1694],{},[1651,30818,2668],{},[1686,30820,30821,30823],{},[898,30822,1690],{},[1692,30824,1694],{},[1651,30826,1839],{},[1902,30828,30829,30831,30833],{},[898,30830,2675],{},[1692,30832,1703],{},[1651,30834,2668],{},[1686,30836,30837,30839],{},[898,30838,1690],{},[1692,30840,1703],{},[902,30842,2704],{"encoding":904}," protíná osy v ",[883,30845,30847],{"className":30846},[886],[888,30848,30849],{"xmlns":890},[892,30850,30851,30869],{},[895,30852,30853,30859,30861],{},[2115,30854,30855,30857],{},[898,30856,2665],{},[1651,30858,2668],{},[898,30860,5981],{"mathvariant":1910},[1902,30862,30863,30865,30867],{},[898,30864,2675],{},[1692,30866,1694],{},[1651,30868,2668],{},[902,30870,30871],{"encoding":904},"Y^*\u002FP_1^*",[883,30873,30875],{"className":30874},[886],[888,30876,30877],{"xmlns":890},[892,30878,30879,30897],{},[895,30880,30881,30887,30889],{},[2115,30882,30883,30885],{},[898,30884,2665],{},[1651,30886,2668],{},[898,30888,5981],{"mathvariant":1910},[1902,30890,30891,30893,30895],{},[898,30892,2675],{},[1692,30894,1703],{},[1651,30896,2668],{},[902,30898,30899],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,30902,30904],{"className":30903},[886],[888,30905,30906],{"xmlns":890},[892,30907,30908,30932],{},[895,30909,30910,30916,30918,30924,30926],{},[1686,30911,30912,30914],{},[898,30913,3490],{},[1692,30915,1694],{},[1651,30917,2319],{},[2115,30919,30920,30922],{},[898,30921,3490],{},[1651,30923,2668],{},[1651,30925,2319],{},[1686,30927,30928,30930],{},[898,30929,3490],{},[1692,30931,1703],{},[902,30933,30934],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,30937,30939],{"className":30938},[886],[888,30940,30941],{"xmlns":890},[892,30942,30943,30973],{},[895,30944,30945,30951,30953,30961,30963,30971],{},[2115,30946,30947,30949],{},[898,30948,1690],{},[1651,30950,2668],{},[1651,30952,2261],{"stretchy":1653},[1902,30954,30955,30957,30959],{},[898,30956,1690],{},[1692,30958,1694],{},[1651,30960,2668],{},[1651,30962,1661],{"separator":1660},[1902,30964,30965,30967,30969],{},[898,30966,1690],{},[1692,30968,1703],{},[1651,30970,2668],{},[1651,30972,2279],{"stretchy":1653},[902,30974,29540],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,30977,30979],{"className":30978},[886],[888,30980,30981],{"xmlns":890},[892,30982,30983,30991],{},[895,30984,30985],{},[2115,30986,30987,30989],{},[898,30988,3490],{},[1651,30990,2668],{},[902,30992,30993],{"encoding":904},"c^*",". Křivka ",[883,30996,30998],{"className":30997},[886],[888,30999,31000],{"xmlns":890},[892,31001,31002,31010],{},[895,31003,31004],{},[1686,31005,31006,31008],{},[898,31007,3490],{},[1692,31009,1694],{},[902,31011,31012],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,31015,31017],{"className":31016},[886],[888,31018,31019],{"xmlns":890},[892,31020,31021,31029],{},[895,31022,31023],{},[1686,31024,31025,31027],{},[898,31026,3490],{},[1692,31028,1703],{},[902,31030,31031],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,31034,31035,31036,31039,31040,31058,31059,31088],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,31037,31038],{},"dotýkají",", tj. mají v bodě ",[883,31041,31043],{"className":31042},[886],[888,31044,31045],{"xmlns":890},[892,31046,31047,31055],{},[895,31048,31049],{},[2115,31050,31051,31053],{},[898,31052,1690],{},[1651,31054,2668],{},[902,31056,31057],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,31060,31062],{"className":31061},[886],[888,31063,31064],{"xmlns":890},[892,31065,31066,31086],{},[895,31067,31068,31070,31072,31078,31080],{},[1843,31069,11903],{},[1651,31071,1738],{},[1686,31073,31074,31076],{},[898,31075,2675],{},[1692,31077,1694],{},[898,31079,5981],{"mathvariant":1910},[1686,31081,31082,31084],{},[898,31083,2675],{},[1692,31085,1703],{},[902,31087,29211],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,31090,31092],{"id":31091},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,31094,10966,31095,31157],{},[883,31096,31098],{"className":31097},[886],[888,31099,31100],{"xmlns":890},[892,31101,31102,31154],{},[895,31103,31104,31106,31108,31114,31116,31122,31124,31126,31140],{},[898,31105,900],{},[1651,31107,1654],{"stretchy":1653},[1686,31109,31110,31112],{},[898,31111,1690],{},[1692,31113,1694],{},[1651,31115,1661],{"separator":1660},[1686,31117,31118,31120],{},[898,31119,1690],{},[1692,31121,1703],{},[1651,31123,1667],{"stretchy":1653},[1651,31125,1738],{},[1902,31127,31128,31130,31132],{},[898,31129,1690],{},[1692,31131,1694],{},[895,31133,31134,31136,31138],{},[1692,31135,1694],{},[898,31137,5981],{"mathvariant":1910},[1692,31139,1703],{},[1902,31141,31142,31144,31146],{},[898,31143,1690],{},[1692,31145,1703],{},[895,31147,31148,31150,31152],{},[1692,31149,1694],{},[898,31151,5981],{"mathvariant":1910},[1692,31153,1703],{},[902,31155,31156],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[724,31159,31160],{},[883,31161,31163],{"className":31162},[886],[888,31164,31165],{"xmlns":890},[892,31166,31167,31273],{},[895,31168,31169,31171,31173,31255,31257,31271],{},[1843,31170,11903],{},[1651,31172,1738],{},[2446,31174,31175,31215],{},[895,31176,31177,31185,31201],{},[2938,31178,31179],{"scriptlevel":1741,"displaystyle":1653},[2446,31180,31181,31183],{},[1692,31182,1694],{},[1692,31184,1703],{},[1902,31186,31187,31189,31191],{},[898,31188,1690],{},[1692,31190,1694],{},[895,31192,31193,31195,31197,31199],{},[1651,31194,2181],{},[1692,31196,1694],{},[898,31198,5981],{"mathvariant":1910},[1692,31200,1703],{},[1902,31202,31203,31205,31207],{},[898,31204,1690],{},[1692,31206,1703],{},[895,31208,31209,31211,31213],{},[1692,31210,1694],{},[898,31212,5981],{"mathvariant":1910},[1692,31214,1703],{},[895,31216,31217,31225,31239],{},[2938,31218,31219],{"scriptlevel":1741,"displaystyle":1653},[2446,31220,31221,31223],{},[1692,31222,1694],{},[1692,31224,1703],{},[1902,31226,31227,31229,31231],{},[898,31228,1690],{},[1692,31230,1694],{},[895,31232,31233,31235,31237],{},[1692,31234,1694],{},[898,31236,5981],{"mathvariant":1910},[1692,31238,1703],{},[1902,31240,31241,31243,31245],{},[898,31242,1690],{},[1692,31244,1703],{},[895,31246,31247,31249,31251,31253],{},[1651,31248,2181],{},[1692,31250,1694],{},[898,31252,5981],{"mathvariant":1910},[1692,31254,1703],{},[1651,31256,1738],{},[2446,31258,31259,31265],{},[1686,31260,31261,31263],{},[898,31262,1690],{},[1692,31264,1703],{},[1686,31266,31267,31269],{},[898,31268,1690],{},[1692,31270,1694],{},[898,31272,1882],{"mathvariant":1910},[902,31274,31275],{"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}.",[724,31277,31278,31279,4254,31324,31326,31327,31347,31348,31378,31379,1882],{},"Tedy ",[883,31280,31282],{"className":31281},[886],[888,31283,31284],{"xmlns":890},[892,31285,31286,31321],{},[895,31287,31288,31290,31292,31295,31297,31299,31301,31303,31311,31313],{},[1843,31289,11903],{},[1651,31291,1654],{"stretchy":1653},[1692,31293,31294],{},"300",[1651,31296,1661],{"separator":1660},[1692,31298,16408],{},[1651,31300,1667],{"stretchy":1653},[1651,31302,1738],{},[2938,31304,31305],{"scriptlevel":1741,"displaystyle":1653},[2446,31306,31307,31309],{},[1692,31308,16408],{},[1692,31310,31294],{},[1651,31312,1738],{},[2938,31314,31315],{"scriptlevel":1741,"displaystyle":1653},[2446,31316,31317,31319],{},[1692,31318,3574],{},[1692,31320,3521],{},[902,31322,31323],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,31325,10519],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,31328,31330],{"className":31329},[886],[888,31331,31332],{"xmlns":890},[892,31333,31334,31344],{},[895,31335,31336],{},[2938,31337,31338],{"scriptlevel":1741,"displaystyle":1653},[2446,31339,31340,31342],{},[1692,31341,3574],{},[1692,31343,3521],{},[902,31345,31346],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,31349,31351],{"className":31350},[886],[888,31352,31353],{"xmlns":890},[892,31354,31355,31375],{},[895,31356,31357,31359,31361,31367,31369],{},[1843,31358,11903],{},[1651,31360,1738],{},[1686,31362,31363,31365],{},[898,31364,1690],{},[1692,31366,1703],{},[898,31368,5981],{"mathvariant":1910},[1686,31370,31371,31373],{},[898,31372,1690],{},[1692,31374,1694],{},[902,31376,31377],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,31380,31382],{"className":31381},[886],[888,31383,31384],{"xmlns":890},[892,31385,31386,31406],{},[895,31387,31388,31390,31392,31398,31400],{},[1843,31389,11903],{},[1651,31391,1738],{},[1686,31393,31394,31396],{},[898,31395,2675],{},[1692,31397,1694],{},[898,31399,5981],{"mathvariant":1910},[1686,31401,31402,31404],{},[898,31403,2675],{},[1692,31405,1703],{},[902,31407,29211],{"encoding":904},[115,31409,31411,31412],{"id":31410},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,31413,31415],{"className":31414},[886],[888,31416,31417],{"xmlns":890},[892,31418,31419,31437],{},[895,31420,31421,31423,31425,31431],{},[898,31422,900],{},[1651,31424,1738],{},[1686,31426,31427,31429],{},[898,31428,1690],{},[1692,31430,1694],{},[1686,31432,31433,31435],{},[898,31434,1690],{},[1692,31436,1703],{},[902,31438,31439],{"encoding":904},"U = Q_1 Q_2",[724,31441,31442,31443,1343,31489,1343,31513,1343,31537,31559],{},"Je dána ",[883,31444,31446],{"className":31445},[886],[888,31447,31448],{"xmlns":890},[892,31449,31450,31486],{},[895,31451,31452,31454,31456,31462,31464,31470,31472,31474,31480],{},[898,31453,900],{},[1651,31455,1654],{"stretchy":1653},[1686,31457,31458,31460],{},[898,31459,1690],{},[1692,31461,1694],{},[1651,31463,1661],{"separator":1660},[1686,31465,31466,31468],{},[898,31467,1690],{},[1692,31469,1703],{},[1651,31471,1667],{"stretchy":1653},[1651,31473,1738],{},[1686,31475,31476,31478],{},[898,31477,1690],{},[1692,31479,1694],{},[1686,31481,31482,31484],{},[898,31483,1690],{},[1692,31485,1703],{},[902,31487,31488],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,31490,31492],{"className":31491},[886],[888,31493,31494],{"xmlns":890},[892,31495,31496,31510],{},[895,31497,31498,31506,31508],{},[1902,31499,31500,31502,31504],{},[898,31501,2675],{},[1692,31503,1694],{},[1651,31505,2668],{},[1651,31507,1738],{},[1692,31509,1703],{},[902,31511,31512],{"encoding":904},"P_1^* = 2",[883,31514,31516],{"className":31515},[886],[888,31517,31518],{"xmlns":890},[892,31519,31520,31534],{},[895,31521,31522,31530,31532],{},[1902,31523,31524,31526,31528],{},[898,31525,2675],{},[1692,31527,1703],{},[1651,31529,2668],{},[1651,31531,1738],{},[1692,31533,3574],{},[902,31535,31536],{"encoding":904},"P_2^* = 5",[883,31538,31540],{"className":31539},[886],[888,31541,31542],{"xmlns":890},[892,31543,31544,31556],{},[895,31545,31546,31552,31554],{},[2115,31547,31548,31550],{},[898,31549,2665],{},[1651,31551,2668],{},[1651,31553,1738],{},[1692,31555,4416],{},[902,31557,31558],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,31561,31563],{"className":31562},[886],[888,31564,31565],{"xmlns":890,"display":29279},[892,31566,31567,31639],{},[895,31568,31569,31571,31573,31579,31581,31587,31589,31591,31593,31595,31601,31607,31609,31611,31613,31615,31617,31619,31625,31627,31629,31635,31637],{},[898,31570,1807],{"mathvariant":29761},[1651,31572,1654],{"stretchy":1653},[1686,31574,31575,31577],{},[898,31576,1690],{},[1692,31578,1694],{},[1651,31580,1661],{"separator":1660},[1686,31582,31583,31585],{},[898,31584,1690],{},[1692,31586,1703],{},[1651,31588,1661],{"separator":1660},[898,31590,1820],{},[1651,31592,1667],{"stretchy":1653},[1651,31594,1738],{},[1686,31596,31597,31599],{},[898,31598,1690],{},[1692,31600,1694],{},[1686,31602,31603,31605],{},[898,31604,1690],{},[1692,31606,1703],{},[1651,31608,1839],{},[898,31610,1820],{},[1651,31612,1654],{"stretchy":1653},[1692,31614,4416],{},[1651,31616,2181],{},[1692,31618,1703],{},[1686,31620,31621,31623],{},[898,31622,1690],{},[1692,31624,1694],{},[1651,31626,2181],{},[1692,31628,3574],{},[1686,31630,31631,31633],{},[898,31632,1690],{},[1692,31634,1703],{},[1651,31636,1667],{"stretchy":1653},[898,31638,1882],{"mathvariant":1910},[902,31640,31641],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,31643,31644],{},"Soustava:",[883,31646,31648],{"className":31647},[886],[888,31649,31650],{"xmlns":890,"display":29279},[892,31651,31652,31764],{},[21967,31653,31654,31688,31722],{"rowspacing":21969,"columnalign":21970,"columnspacing":1911},[21972,31655,31656,31674],{},[21975,31657,31658],{},[2938,31659,31660],{"scriptlevel":1741,"displaystyle":1660},[895,31661,31662,31668,31670,31672],{},[1686,31663,31664,31666],{},[898,31665,1690],{},[1692,31667,1703],{},[1651,31669,2181],{},[1692,31671,1703],{},[898,31673,1820],{},[21975,31675,31676],{},[2938,31677,31678],{"scriptlevel":1741,"displaystyle":1660},[895,31679,31680,31682,31684,31686],{},[895,31681],{},[1651,31683,1738],{},[1692,31685,1741],{},[1651,31687,1661],{"separator":1660},[21972,31689,31690,31708],{},[21975,31691,31692],{},[2938,31693,31694],{"scriptlevel":1741,"displaystyle":1660},[895,31695,31696,31702,31704,31706],{},[1686,31697,31698,31700],{},[898,31699,1690],{},[1692,31701,1694],{},[1651,31703,2181],{},[1692,31705,3574],{},[898,31707,1820],{},[21975,31709,31710],{},[2938,31711,31712],{"scriptlevel":1741,"displaystyle":1660},[895,31713,31714,31716,31718,31720],{},[895,31715],{},[1651,31717,1738],{},[1692,31719,1741],{},[1651,31721,1661],{"separator":1660},[21972,31723,31724,31752],{},[21975,31725,31726],{},[2938,31727,31728],{"scriptlevel":1741,"displaystyle":1660},[895,31729,31730,31732,31734,31736,31742,31744,31746],{},[1692,31731,4416],{},[1651,31733,2181],{},[1692,31735,1703],{},[1686,31737,31738,31740],{},[898,31739,1690],{},[1692,31741,1694],{},[1651,31743,2181],{},[1692,31745,3574],{},[1686,31747,31748,31750],{},[898,31749,1690],{},[1692,31751,1703],{},[21975,31753,31754],{},[2938,31755,31756],{"scriptlevel":1741,"displaystyle":1660},[895,31757,31758,31760,31762],{},[895,31759],{},[1651,31761,1738],{},[1692,31763,13758],{},[902,31765,31766],{"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}",[724,31768,31769,31770,1343,31794,31818,31819,6896,31859,31877,31878,31928,31929,1882],{},"Z prvních dvou rovnic ",[883,31771,31773],{"className":31772},[886],[888,31774,31775],{"xmlns":890},[892,31776,31777,31791],{},[895,31778,31779,31785,31787,31789],{},[1686,31780,31781,31783],{},[898,31782,1690],{},[1692,31784,1703],{},[1651,31786,1738],{},[1692,31788,1703],{},[898,31790,1820],{},[902,31792,31793],{"encoding":904},"Q_2 = 2\\lambda",[883,31795,31797],{"className":31796},[886],[888,31798,31799],{"xmlns":890},[892,31800,31801,31815],{},[895,31802,31803,31809,31811,31813],{},[1686,31804,31805,31807],{},[898,31806,1690],{},[1692,31808,1694],{},[1651,31810,1738],{},[1692,31812,3574],{},[898,31814,1820],{},[902,31816,31817],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,31820,31822],{"className":31821},[886],[888,31823,31824],{"xmlns":890},[892,31825,31826,31856],{},[895,31827,31828,31830,31832,31834,31836,31838,31840,31842,31844,31846,31848,31850,31852,31854],{},[1692,31829,4416],{},[1651,31831,1738],{},[1692,31833,1703],{},[1651,31835,4503],{},[1692,31837,3574],{},[898,31839,1820],{},[1651,31841,1839],{},[1692,31843,3574],{},[1651,31845,4503],{},[1692,31847,1703],{},[898,31849,1820],{},[1651,31851,1738],{},[1692,31853,10340],{},[898,31855,1820],{},[902,31857,31858],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,31860,31862],{"className":31861},[886],[888,31863,31864],{"xmlns":890},[892,31865,31866,31874],{},[895,31867,31868,31870,31872],{},[898,31869,1820],{},[1651,31871,1738],{},[1692,31873,3574],{},[902,31875,31876],{"encoding":904},"\\lambda = 5",". Odtud ",[38,31879,31880,1343,31904],{},[883,31881,31883],{"className":31882},[886],[888,31884,31885],{"xmlns":890},[892,31886,31887,31901],{},[895,31888,31889,31897,31899],{},[1902,31890,31891,31893,31895],{},[898,31892,1690],{},[1692,31894,1694],{},[1651,31896,2668],{},[1651,31898,1738],{},[1692,31900,6311],{},[902,31902,31903],{"encoding":904},"Q_1^* = 25",[883,31905,31907],{"className":31906},[886],[888,31908,31909],{"xmlns":890},[892,31910,31911,31925],{},[895,31912,31913,31921,31923],{},[1902,31914,31915,31917,31919],{},[898,31916,1690],{},[1692,31918,1703],{},[1651,31920,2668],{},[1651,31922,1738],{},[1692,31924,4190],{},[902,31926,31927],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,31930,31932],{"className":31931},[886],[888,31933,31934],{"xmlns":890},[892,31935,31936,31957],{},[895,31937,31938,31944,31946,31948,31950,31952,31954],{},[2115,31939,31940,31942],{},[898,31941,900],{},[1651,31943,2668],{},[1651,31945,1738],{},[1692,31947,6311],{},[1651,31949,4503],{},[1692,31951,4190],{},[1651,31953,1738],{},[1692,31955,31956],{},"250",[902,31958,31959],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,31961,31962],{},[614,31963,31964,31965,29350,32003,5197,32027,32051,32052,32082,32083,32107,32108,32130,32131,1882],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,31966,31968],{"className":31967},[886],[888,31969,31970],{"xmlns":890},[892,31971,31972,32000],{},[895,31973,31974,31976,31978,31980,31986,31988,31990,31996,31998],{},[1692,31975,4416],{},[1651,31977,2181],{},[1692,31979,1703],{},[1686,31981,31982,31984],{},[898,31983,1690],{},[1692,31985,1694],{},[1651,31987,2181],{},[1692,31989,3574],{},[1686,31991,31992,31994],{},[898,31993,1690],{},[1692,31995,1703],{},[1651,31997,1738],{},[1692,31999,1741],{},[902,32001,32002],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,32004,32006],{"className":32005},[886],[888,32007,32008],{"xmlns":890},[892,32009,32010,32024],{},[895,32011,32012,32014,32016,32018,32020,32022],{},[898,32013,5564],{},[1651,32015,2261],{"stretchy":1653},[1692,32017,1741],{},[1651,32019,1661],{"separator":1660},[1692,32021,10340],{},[1651,32023,2279],{"stretchy":1653},[902,32025,32026],{"encoding":904},"A[0, 20]",[883,32028,32030],{"className":32029},[886],[888,32031,32032],{"xmlns":890},[892,32033,32034,32048],{},[895,32035,32036,32038,32040,32042,32044,32046],{},[898,32037,24466],{},[1651,32039,2261],{"stretchy":1653},[1692,32041,4446],{},[1651,32043,1661],{"separator":1660},[1692,32045,1741],{},[1651,32047,2279],{"stretchy":1653},[902,32049,32050],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,32053,32055],{"className":32054},[886],[888,32056,32057],{"xmlns":890},[892,32058,32059,32079],{},[895,32060,32061,32067,32069,32071,32073],{},[1686,32062,32063,32065],{},[898,32064,1690],{},[1692,32066,1703],{},[1651,32068,1738],{},[1692,32070,31956],{},[898,32072,5981],{"mathvariant":1910},[1686,32074,32075,32077],{},[898,32076,1690],{},[1692,32078,1694],{},[902,32080,32081],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,32084,32086],{"className":32085},[886],[888,32087,32088],{"xmlns":890},[892,32089,32090,32104],{},[895,32091,32092,32094,32096,32098,32100,32102],{},[898,32093,5561],{},[1651,32095,2261],{"stretchy":1653},[1692,32097,6311],{},[1651,32099,1661],{"separator":1660},[1692,32101,4190],{},[1651,32103,2279],{"stretchy":1653},[902,32105,32106],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,32109,32111],{"className":32110},[886],[888,32112,32113],{"xmlns":890},[892,32114,32115,32127],{},[895,32116,32117,32119],{},[1651,32118,2181],{},[2938,32120,32121],{"scriptlevel":1741,"displaystyle":1653},[2446,32122,32123,32125],{},[1692,32124,1703],{},[1692,32126,3574],{},[902,32128,32129],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,32132,32134],{"className":32133},[886],[888,32135,32136],{"xmlns":890},[892,32137,32138,32178],{},[895,32139,32140,32142,32144,32146,32148,32150,32152,32154,32156,32158,32166,32168,32170],{},[1651,32141,2181],{},[1843,32143,11903],{},[1651,32145,1654],{"stretchy":1653},[1692,32147,6311],{},[1651,32149,1661],{"separator":1660},[1692,32151,4190],{},[1651,32153,1667],{"stretchy":1653},[1651,32155,1738],{},[1651,32157,2181],{},[2938,32159,32160],{"scriptlevel":1741,"displaystyle":1653},[2446,32161,32162,32164],{},[1692,32163,4190],{},[1692,32165,6311],{},[1651,32167,1738],{},[1651,32169,2181],{},[2938,32171,32172],{"scriptlevel":1741,"displaystyle":1653},[2446,32173,32174,32176],{},[1692,32175,1703],{},[1692,32177,3574],{},[902,32179,32180],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,32182,32184],{"id":32183},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,32186,32187,32188,30216,32218,32221,32222,1793],{},"Považujeme-li v úloze ",[883,32189,32191],{"className":32190},[886],[888,32192,32193],{"xmlns":890},[892,32194,32195,32215],{},[895,32196,32197,32203,32205,32211,32213],{},[1686,32198,32199,32201],{},[898,32200,2675],{},[1692,32202,1694],{},[1651,32204,1661],{"separator":1660},[1686,32206,32207,32209],{},[898,32208,2675],{},[1692,32210,1703],{},[1651,32212,1661],{"separator":1660},[898,32214,2665],{},[902,32216,32217],{"encoding":904},"P_1, P_2, Y",[38,32219,32220],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,32223,32224],{},"Marshallovy poptávkové funkce",[883,32226,32228],{"className":32227},[886],[888,32229,32230],{"xmlns":890,"display":29279},[892,32231,32232,32327],{},[21967,32233,32234],{"width":29284},[21972,32235,32236,32238,32320,32322],{},[21975,32237],{"width":29289},[21975,32239,32240],{},[895,32241,32242,32248,32250,32256,32258,32264,32266,32272,32274,32276,32278,32280,32282,32288,32290,32296,32298,32304,32306,32312,32314,32316,32318],{},[1686,32243,32244,32246],{},[898,32245,1690],{},[1692,32247,1694],{},[1651,32249,1738],{},[1686,32251,32252,32254],{},[898,32253,2047],{},[1692,32255,1694],{},[1651,32257,1654],{"stretchy":1653},[1686,32259,32260,32262],{},[898,32261,2675],{},[1692,32263,1694],{},[1651,32265,1661],{"separator":1660},[1686,32267,32268,32270],{},[898,32269,2675],{},[1692,32271,1703],{},[1651,32273,1661],{"separator":1660},[898,32275,2665],{},[1651,32277,1667],{"stretchy":1653},[1651,32279,1661],{"separator":1660},[7185,32281],{"width":16582},[1686,32283,32284,32286],{},[898,32285,1690],{},[1692,32287,1703],{},[1651,32289,1738],{},[1686,32291,32292,32294],{},[898,32293,2047],{},[1692,32295,1703],{},[1651,32297,1654],{"stretchy":1653},[1686,32299,32300,32302],{},[898,32301,2675],{},[1692,32303,1694],{},[1651,32305,1661],{"separator":1660},[1686,32307,32308,32310],{},[898,32309,2675],{},[1692,32311,1703],{},[1651,32313,1661],{"separator":1660},[898,32315,2665],{},[1651,32317,1667],{"stretchy":1653},[1651,32319,1661],{"separator":1660},[21975,32321],{"width":29289},[21975,32323,32324],{},[1843,32325,32326],{},"(6.15)",[902,32328,32329],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,32331,32333],{"className":32332},[886],[888,32334,32335],{"xmlns":890,"display":29279},[892,32336,32337,32384],{},[21967,32338,32339],{"width":29284},[21972,32340,32341,32343,32377,32379],{},[21975,32342],{"width":29289},[21975,32344,32345],{},[895,32346,32347,32349,32351,32353,32355,32361,32363,32369,32371,32373,32375],{},[898,32348,1820],{},[1651,32350,1738],{},[898,32352,1820],{},[1651,32354,1654],{"stretchy":1653},[1686,32356,32357,32359],{},[898,32358,2675],{},[1692,32360,1694],{},[1651,32362,1661],{"separator":1660},[1686,32364,32365,32367],{},[898,32366,2675],{},[1692,32368,1703],{},[1651,32370,1661],{"separator":1660},[898,32372,2665],{},[1651,32374,1667],{"stretchy":1653},[898,32376,1882],{"mathvariant":1910},[21975,32378],{"width":29289},[21975,32380,32381],{},[1843,32382,32383],{},"(6.16)",[902,32385,32386],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,32388,32389,32419,32420,32486],{},[38,32390,32391,32392,1882],{},"Odvození pro ",[883,32393,32395],{"className":32394},[886],[888,32396,32397],{"xmlns":890},[892,32398,32399,32417],{},[895,32400,32401,32403,32405,32411],{},[898,32402,900],{},[1651,32404,1738],{},[1686,32406,32407,32409],{},[898,32408,1690],{},[1692,32410,1694],{},[1686,32412,32413,32415],{},[898,32414,1690],{},[1692,32416,1703],{},[902,32418,31439],{"encoding":904}," Lagrangeova funkce ",[883,32421,32423],{"className":32422},[886],[888,32424,32425],{"xmlns":890},[892,32426,32427,32483],{},[895,32428,32429,32431,32433,32439,32445,32447,32449,32451,32453,32455,32461,32467,32469,32475,32481],{},[898,32430,1807],{"mathvariant":29761},[1651,32432,1738],{},[1686,32434,32435,32437],{},[898,32436,1690],{},[1692,32438,1694],{},[1686,32440,32441,32443],{},[898,32442,1690],{},[1692,32444,1703],{},[1651,32446,1839],{},[898,32448,1820],{},[1651,32450,1654],{"stretchy":1653},[898,32452,2665],{},[1651,32454,2181],{},[1686,32456,32457,32459],{},[898,32458,2675],{},[1692,32460,1694],{},[1686,32462,32463,32465],{},[898,32464,1690],{},[1692,32466,1694],{},[1651,32468,2181],{},[1686,32470,32471,32473],{},[898,32472,2675],{},[1692,32474,1703],{},[1686,32476,32477,32479],{},[898,32478,1690],{},[1692,32480,1703],{},[1651,32482,1667],{"stretchy":1653},[902,32484,32485],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,32488,32490],{"className":32489},[886],[888,32491,32492],{"xmlns":890,"display":29279},[892,32493,32494,32661],{},[21967,32495,32496],{"width":29284},[21972,32497,32498,32500,32654,32656],{},[21975,32499],{"width":29289},[21975,32501,32502],{},[21967,32503,32504,32550,32596],{"rowspacing":21969,"columnalign":21970,"columnspacing":1911},[21972,32505,32506,32518],{},[21975,32507,32508],{},[2938,32509,32510],{"scriptlevel":1741,"displaystyle":1660},[1902,32511,32512,32514,32516],{},[898,32513,1807],{"mathvariant":29761},[1692,32515,1694],{},[1651,32517,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[21975,32519,32520],{},[2938,32521,32522],{"scriptlevel":1741,"displaystyle":1660},[895,32523,32524,32526,32528,32534,32536,32538,32544,32546,32548],{},[895,32525],{},[1651,32527,1738],{},[1686,32529,32530,32532],{},[898,32531,1690],{},[1692,32533,1703],{},[1651,32535,2181],{},[898,32537,1820],{},[1686,32539,32540,32542],{},[898,32541,2675],{},[1692,32543,1694],{},[1651,32545,1738],{},[1692,32547,1741],{},[1651,32549,1661],{"separator":1660},[21972,32551,32552,32564],{},[21975,32553,32554],{},[2938,32555,32556],{"scriptlevel":1741,"displaystyle":1660},[1902,32557,32558,32560,32562],{},[898,32559,1807],{"mathvariant":29761},[1692,32561,1703],{},[1651,32563,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[21975,32565,32566],{},[2938,32567,32568],{"scriptlevel":1741,"displaystyle":1660},[895,32569,32570,32572,32574,32580,32582,32584,32590,32592,32594],{},[895,32571],{},[1651,32573,1738],{},[1686,32575,32576,32578],{},[898,32577,1690],{},[1692,32579,1694],{},[1651,32581,2181],{},[898,32583,1820],{},[1686,32585,32586,32588],{},[898,32587,2675],{},[1692,32589,1703],{},[1651,32591,1738],{},[1692,32593,1741],{},[1651,32595,1661],{"separator":1660},[21972,32597,32598,32610],{},[21975,32599,32600],{},[2938,32601,32602],{"scriptlevel":1741,"displaystyle":1660},[1902,32603,32604,32606,32608],{},[898,32605,1807],{"mathvariant":29761},[898,32607,1820],{},[1651,32609,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[21975,32611,32612],{},[2938,32613,32614],{"scriptlevel":1741,"displaystyle":1660},[895,32615,32616,32618,32620,32622,32624,32630,32636,32638,32644,32650,32652],{},[895,32617],{},[1651,32619,1738],{},[898,32621,2665],{},[1651,32623,2181],{},[1686,32625,32626,32628],{},[898,32627,2675],{},[1692,32629,1694],{},[1686,32631,32632,32634],{},[898,32633,1690],{},[1692,32635,1694],{},[1651,32637,2181],{},[1686,32639,32640,32642],{},[898,32641,2675],{},[1692,32643,1703],{},[1686,32645,32646,32648],{},[898,32647,1690],{},[1692,32649,1703],{},[1651,32651,1738],{},[1692,32653,13758],{},[21975,32655],{"width":29289},[21975,32657,32658],{},[1843,32659,32660],{},"(6.17)",[902,32662,32663],{"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}",[724,32665,32666,32667,32695,32696,32724,32725,32793],{},"Z prvních dvou: ",[883,32668,32670],{"className":32669},[886],[888,32671,32672],{"xmlns":890},[892,32673,32674,32692],{},[895,32675,32676,32682,32684,32690],{},[1686,32677,32678,32680],{},[898,32679,1690],{},[1692,32681,1703],{},[1651,32683,1738],{},[1686,32685,32686,32688],{},[898,32687,2675],{},[1692,32689,1694],{},[898,32691,1820],{},[902,32693,32694],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,32697,32699],{"className":32698},[886],[888,32700,32701],{"xmlns":890},[892,32702,32703,32721],{},[895,32704,32705,32711,32713,32719],{},[1686,32706,32707,32709],{},[898,32708,1690],{},[1692,32710,1694],{},[1651,32712,1738],{},[1686,32714,32715,32717],{},[898,32716,2675],{},[1692,32718,1703],{},[898,32720,1820],{},[902,32722,32723],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,32726,32728],{"className":32727},[886],[888,32729,32730],{"xmlns":890},[892,32731,32732,32790],{},[895,32733,32734,32736,32738,32744,32746,32752,32754,32756,32762,32764,32770,32772,32774,32776,32782,32788],{},[898,32735,2665],{},[1651,32737,1738],{},[1686,32739,32740,32742],{},[898,32741,2675],{},[1692,32743,1694],{},[1651,32745,4503],{},[1686,32747,32748,32750],{},[898,32749,2675],{},[1692,32751,1703],{},[898,32753,1820],{},[1651,32755,1839],{},[1686,32757,32758,32760],{},[898,32759,2675],{},[1692,32761,1703],{},[1651,32763,4503],{},[1686,32765,32766,32768],{},[898,32767,2675],{},[1692,32769,1694],{},[898,32771,1820],{},[1651,32773,1738],{},[1692,32775,1703],{},[1686,32777,32778,32780],{},[898,32779,2675],{},[1692,32781,1694],{},[1686,32783,32784,32786],{},[898,32785,2675],{},[1692,32787,1703],{},[898,32789,1820],{},[902,32791,32792],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,32795,32797],{"className":32796},[886],[888,32798,32799],{"xmlns":890,"display":29279},[892,32800,32801,32844],{},[21967,32802,32803],{"width":29284},[21972,32804,32805,32807,32837,32839],{},[21975,32806],{"width":29289},[21975,32808,32809],{},[895,32810,32811,32813,32815,32835],{},[898,32812,1820],{},[1651,32814,1738],{},[2446,32816,32817,32819],{},[898,32818,2665],{},[895,32820,32821,32823,32829],{},[1692,32822,1703],{},[1686,32824,32825,32827],{},[898,32826,2675],{},[1692,32828,1694],{},[1686,32830,32831,32833],{},[898,32832,2675],{},[1692,32834,1703],{},[898,32836,1882],{"mathvariant":1910},[21975,32838],{"width":29289},[21975,32840,32841],{},[1843,32842,32843],{},"(6.20)",[902,32845,32846],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,32848,32849],{},"Zpětně:",[883,32851,32853],{"className":32852},[886],[888,32854,32855],{"xmlns":890,"display":29279},[892,32856,32857,32934],{},[21967,32858,32859],{"width":29284},[21972,32860,32861,32863,32927,32929],{},[21975,32862],{"width":29289},[21975,32864,32865],{},[14130,32866,32867],{"notation":14132},[2938,32868,32869],{"scriptlevel":1741,"displaystyle":1653},[2938,32870,32871],{"scriptlevel":1741,"displaystyle":1653},[2938,32872,32873],{"scriptlevel":1741,"displaystyle":1660},[895,32874,32875,32877,32883,32885,32899,32901,32903,32909,32911,32925],{},[1843,32876,5295],{},[1686,32878,32879,32881],{},[898,32880,1690],{},[1692,32882,1694],{},[1651,32884,1738],{},[2446,32886,32887,32889],{},[898,32888,2665],{},[895,32890,32891,32893],{},[1692,32892,1703],{},[1686,32894,32895,32897],{},[898,32896,2675],{},[1692,32898,1694],{},[1651,32900,1661],{"separator":1660},[7185,32902],{"width":16582},[1686,32904,32905,32907],{},[898,32906,1690],{},[1692,32908,1703],{},[1651,32910,1738],{},[2446,32912,32913,32915],{},[898,32914,2665],{},[895,32916,32917,32919],{},[1692,32918,1703],{},[1686,32920,32921,32923],{},[898,32922,2675],{},[1692,32924,1703],{},[1843,32926,5295],{},[21975,32928],{"width":29289},[21975,32930,32931],{},[1843,32932,32933],{},"(6.21)",[902,32935,32936],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,32938,32940],{"id":32939},"engelova-funkce","Engelova funkce",[724,32942,10966,32943,32946,32947,32950,32951,21080,32968,1343,32998,33028,33029,33063,33064,1343,33090,33116],{},[38,32944,32945],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,32948,32949],{},"Engelovou funkcí",": pro ",[883,32952,32954],{"className":32953},[886],[888,32955,32956],{"xmlns":890},[892,32957,32958,32966],{},[895,32959,32960,32962,32964],{},[898,32961,2665],{},[1651,32963,1738],{},[1692,32965,4416],{},[902,32967,21532],{"encoding":904},[883,32969,32971],{"className":32970},[886],[888,32972,32973],{"xmlns":890},[892,32974,32975,32995],{},[895,32976,32977,32983,32985,32987,32989],{},[1686,32978,32979,32981],{},[898,32980,1690],{},[1692,32982,1694],{},[1651,32984,1738],{},[1692,32986,4446],{},[898,32988,5981],{"mathvariant":1910},[1686,32990,32991,32993],{},[898,32992,2675],{},[1692,32994,1694],{},[902,32996,32997],{"encoding":904},"Q_1 = 50\u002FP_1",[883,32999,33001],{"className":33000},[886],[888,33002,33003],{"xmlns":890},[892,33004,33005,33025],{},[895,33006,33007,33013,33015,33017,33019],{},[1686,33008,33009,33011],{},[898,33010,1690],{},[1692,33012,1703],{},[1651,33014,1738],{},[1692,33016,4446],{},[898,33018,5981],{"mathvariant":1910},[1686,33020,33021,33023],{},[898,33022,2675],{},[1692,33024,1703],{},[902,33026,33027],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,33030,33032],{"className":33031},[886],[888,33033,33034],{"xmlns":890},[892,33035,33036,33060],{},[895,33037,33038,33044,33046,33048,33050,33056,33058],{},[1686,33039,33040,33042],{},[898,33041,2675],{},[1692,33043,1694],{},[1651,33045,1738],{},[1692,33047,4190],{},[1651,33049,1661],{"separator":1660},[1686,33051,33052,33054],{},[898,33053,2675],{},[1692,33055,1703],{},[1651,33057,1738],{},[1692,33059,10340],{},[902,33061,33062],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,33065,33067],{"className":33066},[886],[888,33068,33069],{"xmlns":890},[892,33070,33071,33087],{},[895,33072,33073,33079,33081,33083,33085],{},[1686,33074,33075,33077],{},[898,33076,1690],{},[1692,33078,1694],{},[1651,33080,1738],{},[898,33082,2665],{},[898,33084,5981],{"mathvariant":1910},[1692,33086,10340],{},[902,33088,33089],{"encoding":904},"Q_1 = Y\u002F20",[883,33091,33093],{"className":33092},[886],[888,33094,33095],{"xmlns":890},[892,33096,33097,33113],{},[895,33098,33099,33105,33107,33109,33111],{},[1686,33100,33101,33103],{},[898,33102,1690],{},[1692,33104,1703],{},[1651,33106,1738],{},[898,33108,2665],{},[898,33110,5981],{"mathvariant":1910},[1692,33112,6518],{},[902,33114,33115],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,33118,33120],{"id":33119},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,33122,33123],{},"Výdaje spotřebitele jsou",[883,33125,33127],{"className":33126},[886],[888,33128,33129],{"xmlns":890,"display":29279},[892,33130,33131,33206],{},[21967,33132,33133],{"width":29284},[21972,33134,33135,33137,33199,33201],{},[21975,33136],{"width":29289},[21975,33138,33139],{},[895,33140,33141,33143,33145,33147,33149,33155,33157,33163,33165,33167,33175,33181,33183,33191,33197],{},[898,33142,5561],{},[1651,33144,1738],{},[898,33146,5561],{},[1651,33148,1654],{"stretchy":1653},[1686,33150,33151,33153],{},[898,33152,1690],{},[1692,33154,1694],{},[1651,33156,1661],{"separator":1660},[1686,33158,33159,33161],{},[898,33160,1690],{},[1692,33162,1703],{},[1651,33164,1667],{"stretchy":1653},[1651,33166,1738],{},[1902,33168,33169,33171,33173],{},[898,33170,2675],{},[1692,33172,1694],{},[1651,33174,2668],{},[1686,33176,33177,33179],{},[898,33178,1690],{},[1692,33180,1694],{},[1651,33182,1839],{},[1902,33184,33185,33187,33189],{},[898,33186,2675],{},[1692,33188,1703],{},[1651,33190,2668],{},[1686,33192,33193,33195],{},[898,33194,1690],{},[1692,33196,1703],{},[1651,33198,1661],{"separator":1660},[21975,33200],{"width":29289},[21975,33202,33203],{},[1843,33204,33205],{},"(6.22)",[902,33207,33208],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,33210,33211],{},"a je pevně zadána hladina užitečnosti",[883,33213,33215],{"className":33214},[886],[888,33216,33217],{"xmlns":890,"display":29279},[892,33218,33219,33266],{},[21967,33220,33221],{"width":29284},[21972,33222,33223,33225,33259,33261],{},[21975,33224],{"width":29289},[21975,33226,33227],{},[895,33228,33229,33235,33237,33239,33241,33247,33249,33255,33257],{},[2115,33230,33231,33233],{},[898,33232,900],{},[1651,33234,2668],{},[1651,33236,1738],{},[898,33238,900],{},[1651,33240,1654],{"stretchy":1653},[1686,33242,33243,33245],{},[898,33244,1690],{},[1692,33246,1694],{},[1651,33248,1661],{"separator":1660},[1686,33250,33251,33253],{},[898,33252,1690],{},[1692,33254,1703],{},[1651,33256,1667],{"stretchy":1653},[898,33258,1882],{"mathvariant":1910},[21975,33260],{"width":29289},[21975,33262,33263],{},[1843,33264,33265],{},"(6.23)",[902,33267,33268],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,33270,33271,33274,33275,33307,33308,1882],{},[38,33272,33273],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,33276,33278],{"className":33277},[886],[888,33279,33280],{"xmlns":890},[892,33281,33282,33304],{},[895,33283,33284,33286,33288,33294,33296,33302],{},[898,33285,5561],{},[1651,33287,1654],{"stretchy":1653},[1686,33289,33290,33292],{},[898,33291,1690],{},[1692,33293,1694],{},[1651,33295,1661],{"separator":1660},[1686,33297,33298,33300],{},[898,33299,1690],{},[1692,33301,1703],{},[1651,33303,1667],{"stretchy":1653},[902,33305,33306],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,33309,33311],{"className":33310},[886],[888,33312,33313],{"xmlns":890},[892,33314,33315,33371],{},[895,33316,33317,33319,33321,33327,33329,33335,33337,33339,33345,33347,33349,33351,33357,33359,33365,33367,33369],{},[898,33318,1725],{},[1651,33320,1654],{"stretchy":1653},[1686,33322,33323,33325],{},[898,33324,1690],{},[1692,33326,1694],{},[1651,33328,1661],{"separator":1660},[1686,33330,33331,33333],{},[898,33332,1690],{},[1692,33334,1703],{},[1651,33336,1667],{"stretchy":1653},[1651,33338,1738],{},[2115,33340,33341,33343],{},[898,33342,900],{},[1651,33344,2668],{},[1651,33346,2181],{},[898,33348,900],{},[1651,33350,1654],{"stretchy":1653},[1686,33352,33353,33355],{},[898,33354,1690],{},[1692,33356,1694],{},[1651,33358,1661],{"separator":1660},[1686,33360,33361,33363],{},[898,33362,1690],{},[1692,33364,1703],{},[1651,33366,1667],{"stretchy":1653},[1651,33368,1738],{},[1692,33370,1741],{},[902,33372,33373],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,33375,33377],{"id":33376},"lagrangeova-funkce","Lagrangeova funkce",[883,33379,33381],{"className":33380},[886],[888,33382,33383],{"xmlns":890,"display":29279},[892,33384,33385,33496],{},[21967,33386,33387],{"width":29284},[21972,33388,33389,33391,33489,33491],{},[21975,33390],{"width":29289},[21975,33392,33393],{},[895,33394,33395,33397,33399,33405,33407,33413,33415,33417,33419,33421,33429,33435,33437,33445,33451,33453,33455,33457,33463,33465,33467,33469,33475,33477,33483,33485,33487],{},[898,33396,1807],{"mathvariant":29761},[1651,33398,1654],{"stretchy":1653},[1686,33400,33401,33403],{},[898,33402,1690],{},[1692,33404,1694],{},[1651,33406,1661],{"separator":1660},[1686,33408,33409,33411],{},[898,33410,1690],{},[1692,33412,1703],{},[1651,33414,1661],{"separator":1660},[898,33416,1820],{},[1651,33418,1667],{"stretchy":1653},[1651,33420,1738],{},[1902,33422,33423,33425,33427],{},[898,33424,2675],{},[1692,33426,1694],{},[1651,33428,2668],{},[1686,33430,33431,33433],{},[898,33432,1690],{},[1692,33434,1694],{},[1651,33436,1839],{},[1902,33438,33439,33441,33443],{},[898,33440,2675],{},[1692,33442,1703],{},[1651,33444,2668],{},[1686,33446,33447,33449],{},[898,33448,1690],{},[1692,33450,1703],{},[1651,33452,1839],{},[898,33454,1820],{},[1651,33456,1654],{"stretchy":1653},[2115,33458,33459,33461],{},[898,33460,900],{},[1651,33462,2668],{},[1651,33464,2181],{},[898,33466,900],{},[1651,33468,1654],{"stretchy":1653},[1686,33470,33471,33473],{},[898,33472,1690],{},[1692,33474,1694],{},[1651,33476,1661],{"separator":1660},[1686,33478,33479,33481],{},[898,33480,1690],{},[1692,33482,1703],{},[1651,33484,1667],{"stretchy":1653},[1651,33486,1667],{"stretchy":1653},[898,33488,1882],{"mathvariant":1910},[21975,33490],{"width":29289},[21975,33492,33493],{},[1843,33494,33495],{},"(6.24)",[902,33497,33498],{"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}",[724,33500,33501],{},"Soustava podmínek prvního řádu:",[883,33503,33505],{"className":33504},[886],[888,33506,33507],{"xmlns":890,"display":29279},[892,33508,33509,33682],{},[21967,33510,33511],{"width":29284},[21972,33512,33513,33515,33675,33677],{},[21975,33514],{"width":29289},[21975,33516,33517],{},[21967,33518,33519,33569,33619],{"rowspacing":21969,"columnalign":21970,"columnspacing":1911},[21972,33520,33521,33533],{},[21975,33522,33523],{},[2938,33524,33525],{"scriptlevel":1741,"displaystyle":1660},[1902,33526,33527,33529,33531],{},[898,33528,1807],{"mathvariant":29761},[1692,33530,1694],{},[1651,33532,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[21975,33534,33535],{},[2938,33536,33537],{"scriptlevel":1741,"displaystyle":1660},[895,33538,33539,33541,33543,33551,33553,33555,33563,33565,33567],{},[895,33540],{},[1651,33542,1738],{},[1902,33544,33545,33547,33549],{},[898,33546,2675],{},[1692,33548,1694],{},[1651,33550,2668],{},[1651,33552,2181],{},[898,33554,1820],{},[1902,33556,33557,33559,33561],{},[898,33558,900],{},[1692,33560,1694],{},[1651,33562,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,33564,1738],{},[1692,33566,1741],{},[1651,33568,1661],{"separator":1660},[21972,33570,33571,33583],{},[21975,33572,33573],{},[2938,33574,33575],{"scriptlevel":1741,"displaystyle":1660},[1902,33576,33577,33579,33581],{},[898,33578,1807],{"mathvariant":29761},[1692,33580,1703],{},[1651,33582,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[21975,33584,33585],{},[2938,33586,33587],{"scriptlevel":1741,"displaystyle":1660},[895,33588,33589,33591,33593,33601,33603,33605,33613,33615,33617],{},[895,33590],{},[1651,33592,1738],{},[1902,33594,33595,33597,33599],{},[898,33596,2675],{},[1692,33598,1703],{},[1651,33600,2668],{},[1651,33602,2181],{},[898,33604,1820],{},[1902,33606,33607,33609,33611],{},[898,33608,900],{},[1692,33610,1703],{},[1651,33612,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,33614,1738],{},[1692,33616,1741],{},[1651,33618,1661],{"separator":1660},[21972,33620,33621,33633],{},[21975,33622,33623],{},[2938,33624,33625],{"scriptlevel":1741,"displaystyle":1660},[1902,33626,33627,33629,33631],{},[898,33628,1807],{"mathvariant":29761},[898,33630,1820],{},[1651,33632,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[21975,33634,33635],{},[2938,33636,33637],{"scriptlevel":1741,"displaystyle":1660},[895,33638,33639,33641,33643,33649,33651,33653,33655,33661,33663,33669,33671,33673],{},[895,33640],{},[1651,33642,1738],{},[2115,33644,33645,33647],{},[898,33646,900],{},[1651,33648,2668],{},[1651,33650,2181],{},[898,33652,900],{},[1651,33654,1654],{"stretchy":1653},[1686,33656,33657,33659],{},[898,33658,1690],{},[1692,33660,1694],{},[1651,33662,1661],{"separator":1660},[1686,33664,33665,33667],{},[898,33666,1690],{},[1692,33668,1703],{},[1651,33670,1667],{"stretchy":1653},[1651,33672,1738],{},[1692,33674,13758],{},[21975,33676],{"width":29289},[21975,33678,33679],{},[1843,33680,33681],{},"(6.25)",[902,33683,33684],{"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}",[724,33686,33687],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,33689,33691],{"className":33690},[886],[888,33692,33693],{"xmlns":890,"display":29279},[892,33694,33695,33793],{},[21967,33696,33697],{"width":29284},[21972,33698,33699,33701,33786,33788],{},[21975,33700],{"width":29289},[21975,33702,33703],{},[895,33704,33705,33707,33709,33715,33717,33723,33725,33727,33729,33731,33733,33735,33784],{},[898,33706,2047],{},[1651,33708,1654],{"stretchy":1653},[1686,33710,33711,33713],{},[898,33712,1690],{},[1692,33714,1694],{},[1651,33716,1661],{"separator":1660},[1686,33718,33719,33721],{},[898,33720,1690],{},[1692,33722,1703],{},[1651,33724,1661],{"separator":1660},[898,33726,1820],{},[1651,33728,1667],{"stretchy":1653},[1651,33730,1738],{},[1651,33732,2181],{},[898,33734,1820],{},[895,33736,33737,33739,33751,33753,33766,33768,33770,33782],{},[1651,33738,1654],{"fence":1660},[1902,33740,33741,33743,33745],{},[898,33742,900],{},[1692,33744,4231],{},[895,33746,33747,33749],{},[1651,33748,1912],{"mathvariant":1910},[1651,33750,1912],{"mathvariant":1910},[1651,33752,1839],{},[1902,33754,33755,33757,33760],{},[898,33756,900],{},[1692,33758,33759],{},"22",[895,33761,33762,33764],{},[1651,33763,1912],{"mathvariant":1910},[1651,33765,1912],{"mathvariant":1910},[1651,33767,1839],{},[1692,33769,1703],{},[1902,33771,33772,33774,33776],{},[898,33773,900],{},[1692,33775,4828],{},[895,33777,33778,33780],{},[1651,33779,1912],{"mathvariant":1910},[1651,33781,1912],{"mathvariant":1910},[1651,33783,1667],{"fence":1660},[898,33785,1882],{"mathvariant":1910},[21975,33787],{"width":29289},[21975,33789,33790],{},[1843,33791,33792],{},"(6.26)",[902,33794,33795],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,33797,33798,33801,33802,33841,33842,33881,33882,33932,33933,33959,33960,33977,33978,34004],{},[38,33799,33800],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,33803,33805],{"className":33804},[886],[888,33806,33807],{"xmlns":890},[892,33808,33809,33839],{},[895,33810,33811,33817,33819,33827,33829,33837],{},[2115,33812,33813,33815],{},[898,33814,1690],{},[1651,33816,2668],{},[1651,33818,2261],{"stretchy":1653},[1902,33820,33821,33823,33825],{},[898,33822,1690],{},[1692,33824,1694],{},[1651,33826,2668],{},[1651,33828,1661],{"separator":1660},[1902,33830,33831,33833,33835],{},[898,33832,1690],{},[1692,33834,1703],{},[1651,33836,2668],{},[1651,33838,2279],{"stretchy":1653},[902,33840,29540],{"encoding":904}," dotyku křivky užitečnosti ",[883,33843,33845],{"className":33844},[886],[888,33846,33847],{"xmlns":890},[892,33848,33849,33879],{},[895,33850,33851,33857,33859,33861,33863,33869,33871,33877],{},[2115,33852,33853,33855],{},[898,33854,900],{},[1651,33856,2668],{},[1651,33858,1738],{},[898,33860,900],{},[1651,33862,1654],{"stretchy":1653},[1686,33864,33865,33867],{},[898,33866,1690],{},[1692,33868,1694],{},[1651,33870,1661],{"separator":1660},[1686,33872,33873,33875],{},[898,33874,1690],{},[1692,33876,1703],{},[1651,33878,1667],{"stretchy":1653},[902,33880,3076],{"encoding":904}," s přímkou výdajů ",[883,33883,33885],{"className":33884},[886],[888,33886,33887],{"xmlns":890},[892,33888,33889,33929],{},[895,33890,33891,33897,33899,33907,33913,33915,33923],{},[2115,33892,33893,33895],{},[898,33894,5561],{},[1651,33896,2668],{},[1651,33898,1738],{},[1902,33900,33901,33903,33905],{},[898,33902,2675],{},[1692,33904,1694],{},[1651,33906,2668],{},[1686,33908,33909,33911],{},[898,33910,1690],{},[1692,33912,1694],{},[1651,33914,1839],{},[1902,33916,33917,33919,33921],{},[898,33918,2675],{},[1692,33920,1703],{},[1651,33922,2668],{},[1686,33924,33925,33927],{},[898,33926,1690],{},[1692,33928,1703],{},[902,33930,33931],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,33934,33936],{"className":33935},[886],[888,33937,33938],{"xmlns":890},[892,33939,33940,33956],{},[895,33941,33942,33948,33950],{},[1686,33943,33944,33946],{},[898,33945,5561],{},[1692,33947,1741],{},[1651,33949,2319],{},[2115,33951,33952,33954],{},[898,33953,5561],{},[1651,33955,2668],{},[902,33957,33958],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,33961,33963],{"className":33962},[886],[888,33964,33965],{"xmlns":890},[892,33966,33967,33975],{},[895,33968,33969],{},[2115,33970,33971,33973],{},[898,33972,900],{},[1651,33974,2668],{},[902,33976,29175],{"encoding":904},", hladina ",[883,33979,33981],{"className":33980},[886],[888,33982,33983],{"xmlns":890},[892,33984,33985,34001],{},[895,33986,33987,33993,33995],{},[1686,33988,33989,33991],{},[898,33990,5561],{},[1692,33992,1694],{},[1651,33994,2390],{},[2115,33996,33997,33999],{},[898,33998,5561],{},[1651,34000,2668],{},[902,34002,34003],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[5179,34006,34007,34012],{},[724,34008,34009,34011],{},[883,34010,5879],{}," Postup — duální úloha (minimalizace výdajů)",[152,34013,34014,34064,34150,34190,34265],{},[123,34015,34016,3246,34019,34063],{},[38,34017,34018],{},"Zapiš vazbu",[883,34020,34022],{"className":34021},[886],[888,34023,34024],{"xmlns":890},[892,34025,34026,34060],{},[895,34027,34028,34034,34036,34038,34040,34046,34048,34054,34056,34058],{},[2115,34029,34030,34032],{},[898,34031,900],{},[1651,34033,2668],{},[1651,34035,2181],{},[898,34037,900],{},[1651,34039,1654],{"stretchy":1653},[1686,34041,34042,34044],{},[898,34043,1690],{},[1692,34045,1694],{},[1651,34047,1661],{"separator":1660},[1686,34049,34050,34052],{},[898,34051,1690],{},[1692,34053,1703],{},[1651,34055,1667],{"stretchy":1653},[1651,34057,1738],{},[1692,34059,1741],{},[902,34061,34062],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,34065,34066,3246,34068,1882],{},[38,34067,30473],{},[883,34069,34071],{"className":34070},[886],[888,34072,34073],{"xmlns":890},[892,34074,34075,34147],{},[895,34076,34077,34079,34081,34089,34095,34097,34105,34111,34113,34115,34117,34123,34125,34127,34129,34135,34137,34143,34145],{},[898,34078,1807],{"mathvariant":29761},[1651,34080,1738],{},[1902,34082,34083,34085,34087],{},[898,34084,2675],{},[1692,34086,1694],{},[1651,34088,2668],{},[1686,34090,34091,34093],{},[898,34092,1690],{},[1692,34094,1694],{},[1651,34096,1839],{},[1902,34098,34099,34101,34103],{},[898,34100,2675],{},[1692,34102,1703],{},[1651,34104,2668],{},[1686,34106,34107,34109],{},[898,34108,1690],{},[1692,34110,1703],{},[1651,34112,1839],{},[898,34114,1820],{},[1651,34116,1654],{"stretchy":1653},[2115,34118,34119,34121],{},[898,34120,900],{},[1651,34122,2668],{},[1651,34124,2181],{},[898,34126,900],{},[1651,34128,1654],{"stretchy":1653},[1686,34130,34131,34133],{},[898,34132,1690],{},[1692,34134,1694],{},[1651,34136,1661],{"separator":1660},[1686,34138,34139,34141],{},[898,34140,1690],{},[1692,34142,1703],{},[1651,34144,1667],{"stretchy":1653},[1651,34146,1667],{"stretchy":1653},[902,34148,34149],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,34151,34152,34155,34156,34189],{},[38,34153,34154],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,34157,34159],{"className":34158},[886],[888,34160,34161],{"xmlns":890},[892,34162,34163,34187],{},[895,34164,34165,34167,34169,34177,34179],{},[1843,34166,11903],{},[1651,34168,1738],{},[1902,34170,34171,34173,34175],{},[898,34172,2675],{},[1692,34174,1694],{},[1651,34176,2668],{},[898,34178,5981],{"mathvariant":1910},[1902,34180,34181,34183,34185],{},[898,34182,2675],{},[1692,34184,1703],{},[1651,34186,2668],{},[902,34188,30192],{"encoding":904}," (stejná jako u maximalizace!).",[123,34191,34192,3246,34195,34235,34236,1882],{},[38,34193,34194],{},"Dosaď do vazby",[883,34196,34198],{"className":34197},[886],[888,34199,34200],{"xmlns":890},[892,34201,34202,34232],{},[895,34203,34204,34206,34208,34214,34216,34222,34224,34226],{},[898,34205,900],{},[1651,34207,1654],{"stretchy":1653},[1686,34209,34210,34212],{},[898,34211,1690],{},[1692,34213,1694],{},[1651,34215,1661],{"separator":1660},[1686,34217,34218,34220],{},[898,34219,1690],{},[1692,34221,1703],{},[1651,34223,1667],{"stretchy":1653},[1651,34225,1738],{},[2115,34227,34228,34230],{},[898,34229,900],{},[1651,34231,2668],{},[902,34233,34234],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,34237,34239],{"className":34238},[886],[888,34240,34241],{"xmlns":890},[892,34242,34243,34263],{},[895,34244,34245,34253,34255],{},[1902,34246,34247,34249,34251],{},[898,34248,1690],{},[1692,34250,1694],{},[1651,34252,2668],{},[1651,34254,1661],{"separator":1660},[1902,34256,34257,34259,34261],{},[898,34258,1690],{},[1692,34260,1703],{},[1651,34262,2668],{},[902,34264,30714],{"encoding":904},[123,34266,34267,3246,34270,34324],{},[38,34268,34269],{},"Vypočítej minimální výdaje",[883,34271,34273],{"className":34272},[886],[888,34274,34275],{"xmlns":890},[892,34276,34277,34321],{},[895,34278,34279,34285,34287,34295,34303,34305,34313],{},[2115,34280,34281,34283],{},[898,34282,5561],{},[1651,34284,2668],{},[1651,34286,1738],{},[1902,34288,34289,34291,34293],{},[898,34290,2675],{},[1692,34292,1694],{},[1651,34294,2668],{},[1902,34296,34297,34299,34301],{},[898,34298,1690],{},[1692,34300,1694],{},[1651,34302,2668],{},[1651,34304,1839],{},[1902,34306,34307,34309,34311],{},[898,34308,2675],{},[1692,34310,1703],{},[1651,34312,2668],{},[1902,34314,34315,34317,34319],{},[898,34316,1690],{},[1692,34318,1703],{},[1651,34320,2668],{},[902,34322,34323],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,34326,34328,34329],{"id":34327},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,34330,34332],{"className":34331},[886],[888,34333,34334],{"xmlns":890},[892,34335,34336,34370],{},[895,34337,34338,34340,34342,34356],{},[898,34339,900],{},[1651,34341,1738],{},[1902,34343,34344,34346,34348],{},[898,34345,1690],{},[1692,34347,1694],{},[895,34349,34350,34352,34354],{},[1692,34351,1694],{},[898,34353,5981],{"mathvariant":1910},[1692,34355,1703],{},[1902,34357,34358,34360,34362],{},[898,34359,1690],{},[1692,34361,1703],{},[895,34363,34364,34366,34368],{},[1692,34365,1694],{},[898,34367,5981],{"mathvariant":1910},[1692,34369,1703],{},[902,34371,34372],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,34374,34375,34376,1343,34398,1343,34422,31559],{},"Dáno ",[883,34377,34379],{"className":34378},[886],[888,34380,34381],{"xmlns":890},[892,34382,34383,34395],{},[895,34384,34385,34391,34393],{},[2115,34386,34387,34389],{},[898,34388,900],{},[1651,34390,2668],{},[1651,34392,1738],{},[1692,34394,1703],{},[902,34396,34397],{"encoding":904},"U^* = 2",[883,34399,34401],{"className":34400},[886],[888,34402,34403],{"xmlns":890},[892,34404,34405,34419],{},[895,34406,34407,34415,34417],{},[1902,34408,34409,34411,34413],{},[898,34410,2675],{},[1692,34412,1694],{},[1651,34414,2668],{},[1651,34416,1738],{},[1692,34418,25002],{},[902,34420,34421],{"encoding":904},"P_1^* = 0{,}25",[883,34423,34425],{"className":34424},[886],[888,34426,34427],{"xmlns":890},[892,34428,34429,34443],{},[895,34430,34431,34439,34441],{},[1902,34432,34433,34435,34437],{},[898,34434,2675],{},[1692,34436,1703],{},[1651,34438,2668],{},[1651,34440,1738],{},[1692,34442,1694],{},[902,34444,34445],{"encoding":904},"P_2^* = 1",[883,34447,34449],{"className":34448},[886],[888,34450,34451],{"xmlns":890,"display":29279},[892,34452,34453,34517],{},[895,34454,34455,34457,34459,34461,34467,34469,34475,34477,34479,34481,34483,34485,34499,34513,34515],{},[898,34456,1807],{"mathvariant":29761},[1651,34458,1738],{},[1692,34460,25002],{},[1686,34462,34463,34465],{},[898,34464,1690],{},[1692,34466,1694],{},[1651,34468,1839],{},[1686,34470,34471,34473],{},[898,34472,1690],{},[1692,34474,1703],{},[1651,34476,1839],{},[898,34478,1820],{},[1651,34480,1654],{"stretchy":1653},[1692,34482,1703],{},[1651,34484,2181],{},[1902,34486,34487,34489,34491],{},[898,34488,1690],{},[1692,34490,1694],{},[895,34492,34493,34495,34497],{},[1692,34494,1694],{},[898,34496,5981],{"mathvariant":1910},[1692,34498,1703],{},[1902,34500,34501,34503,34505],{},[898,34502,1690],{},[1692,34504,1703],{},[895,34506,34507,34509,34511],{},[1692,34508,1694],{},[898,34510,5981],{"mathvariant":1910},[1692,34512,1703],{},[1651,34514,1667],{"stretchy":1653},[898,34516,1882],{"mathvariant":1910},[902,34518,34519],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,34521,31644],{},[883,34523,34525],{"className":34524},[886],[888,34526,34527],{"xmlns":890,"display":29279},[892,34528,34529,34743],{},[21967,34530,34531,34607,34683],{"rowspacing":21969,"columnalign":21970,"columnspacing":1911},[21972,34532,34533,34545],{},[21975,34534,34535],{},[2938,34536,34537],{"scriptlevel":1741,"displaystyle":1660},[1902,34538,34539,34541,34543],{},[898,34540,1807],{"mathvariant":29761},[1692,34542,1694],{},[1651,34544,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[21975,34546,34547],{},[2938,34548,34549],{"scriptlevel":1741,"displaystyle":1660},[895,34550,34551,34553,34555,34557,34559,34561,34563,34571,34587,34601,34603,34605],{},[895,34552],{},[1651,34554,1738],{},[1692,34556,25002],{},[1651,34558,2181],{},[898,34560,1820],{},[1651,34562,4503],{},[2938,34564,34565],{"scriptlevel":1741,"displaystyle":1653},[2446,34566,34567,34569],{},[1692,34568,1694],{},[1692,34570,1703],{},[1902,34572,34573,34575,34577],{},[898,34574,1690],{},[1692,34576,1694],{},[895,34578,34579,34581,34583,34585],{},[1651,34580,2181],{},[1692,34582,1694],{},[898,34584,5981],{"mathvariant":1910},[1692,34586,1703],{},[1902,34588,34589,34591,34593],{},[898,34590,1690],{},[1692,34592,1703],{},[895,34594,34595,34597,34599],{},[1692,34596,1694],{},[898,34598,5981],{"mathvariant":1910},[1692,34600,1703],{},[1651,34602,1738],{},[1692,34604,1741],{},[1651,34606,1661],{"separator":1660},[21972,34608,34609,34621],{},[21975,34610,34611],{},[2938,34612,34613],{"scriptlevel":1741,"displaystyle":1660},[1902,34614,34615,34617,34619],{},[898,34616,1807],{"mathvariant":29761},[1692,34618,1703],{},[1651,34620,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[21975,34622,34623],{},[2938,34624,34625],{"scriptlevel":1741,"displaystyle":1660},[895,34626,34627,34629,34631,34633,34635,34637,34639,34647,34661,34677,34679,34681],{},[895,34628],{},[1651,34630,1738],{},[1692,34632,1694],{},[1651,34634,2181],{},[898,34636,1820],{},[1651,34638,4503],{},[2938,34640,34641],{"scriptlevel":1741,"displaystyle":1653},[2446,34642,34643,34645],{},[1692,34644,1694],{},[1692,34646,1703],{},[1902,34648,34649,34651,34653],{},[898,34650,1690],{},[1692,34652,1694],{},[895,34654,34655,34657,34659],{},[1692,34656,1694],{},[898,34658,5981],{"mathvariant":1910},[1692,34660,1703],{},[1902,34662,34663,34665,34667],{},[898,34664,1690],{},[1692,34666,1703],{},[895,34668,34669,34671,34673,34675],{},[1651,34670,2181],{},[1692,34672,1694],{},[898,34674,5981],{"mathvariant":1910},[1692,34676,1703],{},[1651,34678,1738],{},[1692,34680,1741],{},[1651,34682,1661],{"separator":1660},[21972,34684,34685,34697],{},[21975,34686,34687],{},[2938,34688,34689],{"scriptlevel":1741,"displaystyle":1660},[1902,34690,34691,34693,34695],{},[898,34692,1807],{"mathvariant":29761},[898,34694,1820],{},[1651,34696,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[21975,34698,34699],{},[2938,34700,34701],{"scriptlevel":1741,"displaystyle":1660},[895,34702,34703,34705,34707,34709,34711,34725,34739,34741],{},[895,34704],{},[1651,34706,1738],{},[1692,34708,1703],{},[1651,34710,2181],{},[1902,34712,34713,34715,34717],{},[898,34714,1690],{},[1692,34716,1694],{},[895,34718,34719,34721,34723],{},[1692,34720,1694],{},[898,34722,5981],{"mathvariant":1910},[1692,34724,1703],{},[1902,34726,34727,34729,34731],{},[898,34728,1690],{},[1692,34730,1703],{},[895,34732,34733,34735,34737],{},[1692,34734,1694],{},[898,34736,5981],{"mathvariant":1910},[1692,34738,1703],{},[1651,34740,1738],{},[1692,34742,13758],{},[902,34744,34745],{"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}",[724,34747,34748,34749,2983,34779,34807,34808,6896,34870,1343,34920,34942,34943,1882],{},"Podílem prvních dvou rovnic: ",[883,34750,34752],{"className":34751},[886],[888,34753,34754],{"xmlns":890},[892,34755,34756,34776],{},[895,34757,34758,34760,34762,34768,34770],{},[1692,34759,25002],{},[1651,34761,1738],{},[1686,34763,34764,34766],{},[898,34765,1690],{},[1692,34767,1703],{},[898,34769,5981],{"mathvariant":1910},[1686,34771,34772,34774],{},[898,34773,1690],{},[1692,34775,1694],{},[902,34777,34778],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,34780,34782],{"className":34781},[886],[888,34783,34784],{"xmlns":890},[892,34785,34786,34804],{},[895,34787,34788,34794,34796,34798],{},[1686,34789,34790,34792],{},[898,34791,1690],{},[1692,34793,1703],{},[1651,34795,1738],{},[1692,34797,25002],{},[1686,34799,34800,34802],{},[898,34801,1690],{},[1692,34803,1694],{},[902,34805,34806],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,34809,34811],{"className":34810},[886],[888,34812,34813],{"xmlns":890},[892,34814,34815,34867],{},[895,34816,34817,34831,34833,34835,34841,34853,34855,34857,34863,34865],{},[1902,34818,34819,34821,34823],{},[898,34820,1690],{},[1692,34822,1694],{},[895,34824,34825,34827,34829],{},[1692,34826,1694],{},[898,34828,5981],{"mathvariant":1910},[1692,34830,1703],{},[1651,34832,1654],{"stretchy":1653},[1692,34834,25002],{},[1686,34836,34837,34839],{},[898,34838,1690],{},[1692,34840,1694],{},[2115,34842,34843,34845],{},[1651,34844,1667],{"stretchy":1653},[895,34846,34847,34849,34851],{},[1692,34848,1694],{},[898,34850,5981],{"mathvariant":1910},[1692,34852,1703],{},[1651,34854,1738],{},[1692,34856,6316],{},[1686,34858,34859,34861],{},[898,34860,1690],{},[1692,34862,1694],{},[1651,34864,1738],{},[1692,34866,1703],{},[902,34868,34869],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,34871,34872,1343,34896],{},[883,34873,34875],{"className":34874},[886],[888,34876,34877],{"xmlns":890},[892,34878,34879,34893],{},[895,34880,34881,34889,34891],{},[1902,34882,34883,34885,34887],{},[898,34884,1690],{},[1692,34886,1694],{},[1651,34888,2668],{},[1651,34890,1738],{},[1692,34892,3689],{},[902,34894,34895],{"encoding":904},"Q_1^* = 4",[883,34897,34899],{"className":34898},[886],[888,34900,34901],{"xmlns":890},[892,34902,34903,34917],{},[895,34904,34905,34913,34915],{},[1902,34906,34907,34909,34911],{},[898,34908,1690],{},[1692,34910,1703],{},[1651,34912,2668],{},[1651,34914,1738],{},[1692,34916,1694],{},[902,34918,34919],{"encoding":904},"Q_2^* = 1",[883,34921,34923],{"className":34922},[886],[888,34924,34925],{"xmlns":890},[892,34926,34927,34939],{},[895,34928,34929,34935,34937],{},[2115,34930,34931,34933],{},[898,34932,1820],{},[1651,34934,2668],{},[1651,34936,1738],{},[1692,34938,1694],{},[902,34940,34941],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,34944,34946],{"className":34945},[886],[888,34947,34948],{"xmlns":890},[892,34949,34950,34978],{},[895,34951,34952,34958,34960,34962,34964,34966,34968,34970,34972,34974,34976],{},[2115,34953,34954,34956],{},[898,34955,5561],{},[1651,34957,2668],{},[1651,34959,1738],{},[1692,34961,25002],{},[1651,34963,4503],{},[1692,34965,3689],{},[1651,34967,1839],{},[1692,34969,1694],{},[1651,34971,4503],{},[1692,34973,1694],{},[1651,34975,1738],{},[1692,34977,1703],{},[902,34979,34980],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,34982,34983,34986,34987,1343,35053,1343,35119,35185,35186,35223,35224,35246,35247,1882],{},[614,34984,34985],{},"Ověření postačující podmínky"," (6.26): ",[883,34988,34990],{"className":34989},[886],[888,34991,34992],{"xmlns":890},[892,34993,34994,35050],{},[895,34995,34996,35008,35010,35012,35020,35036],{},[1902,34997,34998,35000,35002],{},[898,34999,900],{},[1692,35001,4231],{},[895,35003,35004,35006],{},[1651,35005,1912],{"mathvariant":1910},[1651,35007,1912],{"mathvariant":1910},[1651,35009,1738],{},[1651,35011,2181],{},[2938,35013,35014],{"scriptlevel":1741,"displaystyle":1653},[2446,35015,35016,35018],{},[1692,35017,1694],{},[1692,35019,3689],{},[1902,35021,35022,35024,35026],{},[898,35023,1690],{},[1692,35025,1694],{},[895,35027,35028,35030,35032,35034],{},[1651,35029,2181],{},[1692,35031,3521],{},[898,35033,5981],{"mathvariant":1910},[1692,35035,1703],{},[1902,35037,35038,35040,35042],{},[898,35039,1690],{},[1692,35041,1703],{},[895,35043,35044,35046,35048],{},[1692,35045,1694],{},[898,35047,5981],{"mathvariant":1910},[1692,35049,1703],{},[902,35051,35052],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,35054,35056],{"className":35055},[886],[888,35057,35058],{"xmlns":890},[892,35059,35060,35116],{},[895,35061,35062,35074,35076,35078,35086,35100],{},[1902,35063,35064,35066,35068],{},[898,35065,900],{},[1692,35067,33759],{},[895,35069,35070,35072],{},[1651,35071,1912],{"mathvariant":1910},[1651,35073,1912],{"mathvariant":1910},[1651,35075,1738],{},[1651,35077,2181],{},[2938,35079,35080],{"scriptlevel":1741,"displaystyle":1653},[2446,35081,35082,35084],{},[1692,35083,1694],{},[1692,35085,3689],{},[1902,35087,35088,35090,35092],{},[898,35089,1690],{},[1692,35091,1694],{},[895,35093,35094,35096,35098],{},[1692,35095,1694],{},[898,35097,5981],{"mathvariant":1910},[1692,35099,1703],{},[1902,35101,35102,35104,35106],{},[898,35103,1690],{},[1692,35105,1703],{},[895,35107,35108,35110,35112,35114],{},[1651,35109,2181],{},[1692,35111,3521],{},[898,35113,5981],{"mathvariant":1910},[1692,35115,1703],{},[902,35117,35118],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,35120,35122],{"className":35121},[886],[888,35123,35124],{"xmlns":890},[892,35125,35126,35182],{},[895,35127,35128,35140,35142,35150,35166],{},[1902,35129,35130,35132,35134],{},[898,35131,900],{},[1692,35133,4828],{},[895,35135,35136,35138],{},[1651,35137,1912],{"mathvariant":1910},[1651,35139,1912],{"mathvariant":1910},[1651,35141,1738],{},[2938,35143,35144],{"scriptlevel":1741,"displaystyle":1653},[2446,35145,35146,35148],{},[1692,35147,1694],{},[1692,35149,3689],{},[1902,35151,35152,35154,35156],{},[898,35153,1690],{},[1692,35155,1694],{},[895,35157,35158,35160,35162,35164],{},[1651,35159,2181],{},[1692,35161,1694],{},[898,35163,5981],{"mathvariant":1910},[1692,35165,1703],{},[1902,35167,35168,35170,35172],{},[898,35169,1690],{},[1692,35171,1703],{},[895,35173,35174,35176,35178,35180],{},[1651,35175,2181],{},[1692,35177,1694],{},[898,35179,5981],{"mathvariant":1910},[1692,35181,1703],{},[902,35183,35184],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,35187,35189],{"className":35188},[886],[888,35190,35191],{"xmlns":890},[892,35192,35193,35220],{},[895,35194,35195,35197,35199,35201,35203,35205,35207,35209,35211,35213,35216,35218],{},[898,35196,2047],{},[1651,35198,1654],{"stretchy":1653},[1692,35200,3689],{},[1651,35202,1661],{"separator":1660},[1692,35204,1694],{},[1651,35206,1661],{"separator":1660},[1692,35208,1694],{},[1651,35210,1667],{"stretchy":1653},[1651,35212,1738],{},[1692,35214,35215],{},"0,28125",[1651,35217,2390],{},[1692,35219,1741],{},[902,35221,35222],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,35225,35227],{"className":35226},[886],[888,35228,35229],{"xmlns":890},[892,35230,35231,35243],{},[895,35232,35233,35235,35237,35239,35241],{},[1651,35234,2261],{"stretchy":1653},[1692,35236,3689],{},[1651,35238,1661],{"separator":1660},[1692,35240,1694],{},[1651,35242,2279],{"stretchy":1653},[902,35244,35245],{"encoding":904},"[4, 1]"," je vázané ",[38,35248,2398],{},[115,35250,35252],{"id":35251},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,35254,35255],{},"Obecně:",[883,35257,35259],{"className":35258},[886],[888,35260,35261],{"xmlns":890,"display":29279},[892,35262,35263,35358],{},[21967,35264,35265],{"width":29284},[21972,35266,35267,35269,35351,35353],{},[21975,35268],{"width":29289},[21975,35270,35271],{},[895,35272,35273,35279,35281,35287,35289,35295,35297,35303,35305,35307,35309,35311,35313,35319,35321,35327,35329,35335,35337,35343,35345,35347,35349],{},[1686,35274,35275,35277],{},[898,35276,1690],{},[1692,35278,1694],{},[1651,35280,1738],{},[1686,35282,35283,35285],{},[898,35284,2047],{},[1692,35286,1694],{},[1651,35288,1654],{"stretchy":1653},[1686,35290,35291,35293],{},[898,35292,2675],{},[1692,35294,1694],{},[1651,35296,1661],{"separator":1660},[1686,35298,35299,35301],{},[898,35300,2675],{},[1692,35302,1703],{},[1651,35304,1661],{"separator":1660},[898,35306,900],{},[1651,35308,1667],{"stretchy":1653},[1651,35310,1661],{"separator":1660},[7185,35312],{"width":16582},[1686,35314,35315,35317],{},[898,35316,1690],{},[1692,35318,1703],{},[1651,35320,1738],{},[1686,35322,35323,35325],{},[898,35324,2047],{},[1692,35326,1703],{},[1651,35328,1654],{"stretchy":1653},[1686,35330,35331,35333],{},[898,35332,2675],{},[1692,35334,1694],{},[1651,35336,1661],{"separator":1660},[1686,35338,35339,35341],{},[898,35340,2675],{},[1692,35342,1703],{},[1651,35344,1661],{"separator":1660},[898,35346,900],{},[1651,35348,1667],{"stretchy":1653},[1651,35350,1661],{"separator":1660},[21975,35352],{"width":29289},[21975,35354,35355],{},[1843,35356,35357],{},"(6.27)",[902,35359,35360],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,35362,35364],{"className":35363},[886],[888,35365,35366],{"xmlns":890,"display":29279},[892,35367,35368,35415],{},[21967,35369,35370],{"width":29284},[21972,35371,35372,35374,35408,35410],{},[21975,35373],{"width":29289},[21975,35375,35376],{},[895,35377,35378,35380,35382,35384,35386,35392,35394,35400,35402,35404,35406],{},[898,35379,1820],{},[1651,35381,1738],{},[898,35383,1820],{},[1651,35385,1654],{"stretchy":1653},[1686,35387,35388,35390],{},[898,35389,2675],{},[1692,35391,1694],{},[1651,35393,1661],{"separator":1660},[1686,35395,35396,35398],{},[898,35397,2675],{},[1692,35399,1703],{},[1651,35401,1661],{"separator":1660},[898,35403,900],{},[1651,35405,1667],{"stretchy":1653},[898,35407,1882],{"mathvariant":1910},[21975,35409],{"width":29289},[21975,35411,35412],{},[1843,35413,35414],{},"(6.28)",[902,35416,35417],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,35419,35420,35421,3246,35424,35437,35438,35451],{},"Hicksova poptávka závisí na ",[38,35422,35423],{},"hladině užitečnosti",[883,35425,35427],{"className":35426},[886],[888,35428,35429],{"xmlns":890},[892,35430,35431,35435],{},[895,35432,35433],{},[898,35434,900],{},[902,35436,900],{"encoding":904}," (nikoli na důchodu ",[883,35439,35441],{"className":35440},[886],[888,35442,35443],{"xmlns":890},[892,35444,35445,35449],{},[895,35446,35447],{},[898,35448,2665],{},[902,35450,2665],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,35453,35455,35456],{"id":35454},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,35457,35459],{"className":35458},[886],[888,35460,35461],{"xmlns":890},[892,35462,35463,35497],{},[895,35464,35465,35467,35469,35483],{},[898,35466,900],{},[1651,35468,1738],{},[1902,35470,35471,35473,35475],{},[898,35472,1690],{},[1692,35474,1694],{},[895,35476,35477,35479,35481],{},[1692,35478,1694],{},[898,35480,5981],{"mathvariant":1910},[1692,35482,1703],{},[1902,35484,35485,35487,35489],{},[898,35486,1690],{},[1692,35488,1703],{},[895,35490,35491,35493,35495],{},[1692,35492,1694],{},[898,35494,5981],{"mathvariant":1910},[1692,35496,1703],{},[902,35498,34372],{"encoding":904},[724,35500,35501,35531],{},[883,35502,35504],{"className":35503},[886],[888,35505,35506],{"xmlns":890},[892,35507,35508,35528],{},[895,35509,35510,35516,35518,35524,35526],{},[1686,35511,35512,35514],{},[898,35513,2675],{},[1692,35515,1694],{},[1651,35517,1661],{"separator":1660},[1686,35519,35520,35522],{},[898,35521,2675],{},[1692,35523,1703],{},[1651,35525,1661],{"separator":1660},[898,35527,900],{},[902,35529,35530],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,35533,35535],{"className":35534},[886],[888,35536,35537],{"xmlns":890,"display":29279},[892,35538,35539,35613],{},[895,35540,35541,35543,35545,35551,35557,35559,35565,35571,35573,35575,35577,35579,35581,35595,35609,35611],{},[898,35542,1807],{"mathvariant":29761},[1651,35544,1738],{},[1686,35546,35547,35549],{},[898,35548,2675],{},[1692,35550,1694],{},[1686,35552,35553,35555],{},[898,35554,1690],{},[1692,35556,1694],{},[1651,35558,1839],{},[1686,35560,35561,35563],{},[898,35562,2675],{},[1692,35564,1703],{},[1686,35566,35567,35569],{},[898,35568,1690],{},[1692,35570,1703],{},[1651,35572,1839],{},[898,35574,1820],{},[1651,35576,1654],{"stretchy":1653},[898,35578,900],{},[1651,35580,2181],{},[1902,35582,35583,35585,35587],{},[898,35584,1690],{},[1692,35586,1694],{},[895,35588,35589,35591,35593],{},[1692,35590,1694],{},[898,35592,5981],{"mathvariant":1910},[1692,35594,1703],{},[1902,35596,35597,35599,35601],{},[898,35598,1690],{},[1692,35600,1703],{},[895,35602,35603,35605,35607],{},[1692,35604,1694],{},[898,35606,5981],{"mathvariant":1910},[1692,35608,1703],{},[1651,35610,1667],{"stretchy":1653},[898,35612,1882],{"mathvariant":1910},[902,35614,35615],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,35617,31644],{},[883,35619,35621],{"className":35620},[886],[888,35622,35623],{"xmlns":890,"display":29279},[892,35624,35625,35847],{},[21967,35626,35627,35707,35787],{"rowspacing":21969,"columnalign":21970,"columnspacing":1911},[21972,35628,35629,35641],{},[21975,35630,35631],{},[2938,35632,35633],{"scriptlevel":1741,"displaystyle":1660},[1902,35634,35635,35637,35639],{},[898,35636,1807],{"mathvariant":29761},[1692,35638,1694],{},[1651,35640,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[21975,35642,35643],{},[2938,35644,35645],{"scriptlevel":1741,"displaystyle":1660},[895,35646,35647,35649,35651,35657,35659,35661,35663,35671,35687,35701,35703,35705],{},[895,35648],{},[1651,35650,1738],{},[1686,35652,35653,35655],{},[898,35654,2675],{},[1692,35656,1694],{},[1651,35658,2181],{},[898,35660,1820],{},[1651,35662,4503],{},[2938,35664,35665],{"scriptlevel":1741,"displaystyle":1653},[2446,35666,35667,35669],{},[1692,35668,1694],{},[1692,35670,1703],{},[1902,35672,35673,35675,35677],{},[898,35674,1690],{},[1692,35676,1694],{},[895,35678,35679,35681,35683,35685],{},[1651,35680,2181],{},[1692,35682,1694],{},[898,35684,5981],{"mathvariant":1910},[1692,35686,1703],{},[1902,35688,35689,35691,35693],{},[898,35690,1690],{},[1692,35692,1703],{},[895,35694,35695,35697,35699],{},[1692,35696,1694],{},[898,35698,5981],{"mathvariant":1910},[1692,35700,1703],{},[1651,35702,1738],{},[1692,35704,1741],{},[1651,35706,1661],{"separator":1660},[21972,35708,35709,35721],{},[21975,35710,35711],{},[2938,35712,35713],{"scriptlevel":1741,"displaystyle":1660},[1902,35714,35715,35717,35719],{},[898,35716,1807],{"mathvariant":29761},[1692,35718,1703],{},[1651,35720,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[21975,35722,35723],{},[2938,35724,35725],{"scriptlevel":1741,"displaystyle":1660},[895,35726,35727,35729,35731,35737,35739,35741,35743,35751,35765,35781,35783,35785],{},[895,35728],{},[1651,35730,1738],{},[1686,35732,35733,35735],{},[898,35734,2675],{},[1692,35736,1703],{},[1651,35738,2181],{},[898,35740,1820],{},[1651,35742,4503],{},[2938,35744,35745],{"scriptlevel":1741,"displaystyle":1653},[2446,35746,35747,35749],{},[1692,35748,1694],{},[1692,35750,1703],{},[1902,35752,35753,35755,35757],{},[898,35754,1690],{},[1692,35756,1694],{},[895,35758,35759,35761,35763],{},[1692,35760,1694],{},[898,35762,5981],{"mathvariant":1910},[1692,35764,1703],{},[1902,35766,35767,35769,35771],{},[898,35768,1690],{},[1692,35770,1703],{},[895,35772,35773,35775,35777,35779],{},[1651,35774,2181],{},[1692,35776,1694],{},[898,35778,5981],{"mathvariant":1910},[1692,35780,1703],{},[1651,35782,1738],{},[1692,35784,1741],{},[1651,35786,1661],{"separator":1660},[21972,35788,35789,35801],{},[21975,35790,35791],{},[2938,35792,35793],{"scriptlevel":1741,"displaystyle":1660},[1902,35794,35795,35797,35799],{},[898,35796,1807],{"mathvariant":29761},[898,35798,1820],{},[1651,35800,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[21975,35802,35803],{},[2938,35804,35805],{"scriptlevel":1741,"displaystyle":1660},[895,35806,35807,35809,35811,35813,35815,35829,35843,35845],{},[895,35808],{},[1651,35810,1738],{},[898,35812,900],{},[1651,35814,2181],{},[1902,35816,35817,35819,35821],{},[898,35818,1690],{},[1692,35820,1694],{},[895,35822,35823,35825,35827],{},[1692,35824,1694],{},[898,35826,5981],{"mathvariant":1910},[1692,35828,1703],{},[1902,35830,35831,35833,35835],{},[898,35832,1690],{},[1692,35834,1703],{},[895,35836,35837,35839,35841],{},[1692,35838,1694],{},[898,35840,5981],{"mathvariant":1910},[1692,35842,1703],{},[1651,35844,1738],{},[1692,35846,13758],{},[902,35848,35849],{"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}",[724,35851,35852,35853,35923,35924,35982],{},"Podílem rovnic: ",[883,35854,35856],{"className":35855},[886],[888,35857,35858],{"xmlns":890},[892,35859,35860,35920],{},[895,35861,35862,35868,35870,35876,35878,35884,35886,35892,35894,35900,35906,35908,35914],{},[1686,35863,35864,35866],{},[898,35865,2675],{},[1692,35867,1694],{},[898,35869,5981],{"mathvariant":1910},[1686,35871,35872,35874],{},[898,35873,2675],{},[1692,35875,1703],{},[1651,35877,1738],{},[1686,35879,35880,35882],{},[898,35881,1690],{},[1692,35883,1703],{},[898,35885,5981],{"mathvariant":1910},[1686,35887,35888,35890],{},[898,35889,1690],{},[1692,35891,1694],{},[1651,35893,5298],{},[1686,35895,35896,35898],{},[898,35897,2675],{},[1692,35899,1694],{},[1686,35901,35902,35904],{},[898,35903,1690],{},[1692,35905,1694],{},[1651,35907,1738],{},[1686,35909,35910,35912],{},[898,35911,2675],{},[1692,35913,1703],{},[1686,35915,35916,35918],{},[898,35917,1690],{},[1692,35919,1703],{},[902,35921,35922],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,35925,35927],{"className":35926},[886],[888,35928,35929],{"xmlns":890},[892,35930,35931,35979],{},[895,35932,35933,35935,35937,35943,35949,35951,35957,35963,35965,35967,35973],{},[898,35934,5561],{},[1651,35936,1738],{},[1686,35938,35939,35941],{},[898,35940,2675],{},[1692,35942,1694],{},[1686,35944,35945,35947],{},[898,35946,1690],{},[1692,35948,1694],{},[1651,35950,1839],{},[1686,35952,35953,35955],{},[898,35954,2675],{},[1692,35956,1703],{},[1686,35958,35959,35961],{},[898,35960,1690],{},[1692,35962,1703],{},[1651,35964,1738],{},[1692,35966,1703],{},[1686,35968,35969,35971],{},[898,35970,2675],{},[1692,35972,1694],{},[1686,35974,35975,35977],{},[898,35976,1690],{},[1692,35978,1694],{},[902,35980,35981],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,35984,35986],{"className":35985},[886],[888,35987,35988],{"xmlns":890,"display":29279},[892,35989,35990,36057],{},[21967,35991,35992],{"width":29284},[21972,35993,35994,35996,36050,36052],{},[21975,35995],{"width":29289},[21975,35997,35998],{},[895,35999,36000,36006,36008,36022,36024,36026,36032,36034,36048],{},[1686,36001,36002,36004],{},[898,36003,1690],{},[1692,36005,1694],{},[1651,36007,1738],{},[2446,36009,36010,36012],{},[898,36011,5561],{},[895,36013,36014,36016],{},[1692,36015,1703],{},[1686,36017,36018,36020],{},[898,36019,2675],{},[1692,36021,1694],{},[1651,36023,1661],{"separator":1660},[7185,36025],{"width":16582},[1686,36027,36028,36030],{},[898,36029,1690],{},[1692,36031,1703],{},[1651,36033,1738],{},[2446,36035,36036,36038],{},[898,36037,5561],{},[895,36039,36040,36042],{},[1692,36041,1703],{},[1686,36043,36044,36046],{},[898,36045,2675],{},[1692,36047,1703],{},[898,36049,1882],{"mathvariant":1910},[21975,36051],{"width":29289},[21975,36053,36054],{},[1843,36055,36056],{},"(6.29)",[902,36058,36059],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,36061,36062,36063,2983,36145,36181],{},"Ze třetí rovnice ",[883,36064,36066],{"className":36065},[886],[888,36067,36068],{"xmlns":890},[892,36069,36070,36142],{},[895,36071,36072,36074,36076,36114,36116],{},[898,36073,900],{},[1651,36075,1738],{},[9423,36077,36078],{},[895,36079,36080,36096,36098],{},[2938,36081,36082],{"scriptlevel":1741,"displaystyle":1653},[2446,36083,36084,36086],{},[898,36085,5561],{},[895,36087,36088,36090],{},[1692,36089,1703],{},[1686,36091,36092,36094],{},[898,36093,2675],{},[1692,36095,1694],{},[1651,36097,4503],{},[2938,36099,36100],{"scriptlevel":1741,"displaystyle":1653},[2446,36101,36102,36104],{},[898,36103,5561],{},[895,36105,36106,36108],{},[1692,36107,1703],{},[1686,36109,36110,36112],{},[898,36111,2675],{},[1692,36113,1703],{},[1651,36115,1738],{},[2938,36117,36118],{"scriptlevel":1741,"displaystyle":1653},[2446,36119,36120,36122],{},[898,36121,5561],{},[895,36123,36124,36126],{},[1692,36125,1703],{},[9423,36127,36128],{},[895,36129,36130,36136],{},[1686,36131,36132,36134],{},[898,36133,2675],{},[1692,36135,1694],{},[1686,36137,36138,36140],{},[898,36139,2675],{},[1692,36141,1703],{},[902,36143,36144],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,36146,36148],{"className":36147},[886],[888,36149,36150],{"xmlns":890},[892,36151,36152,36178],{},[895,36153,36154,36156,36158,36160,36162],{},[898,36155,5561],{},[1651,36157,1738],{},[1692,36159,1703],{},[898,36161,900],{},[9423,36163,36164],{},[895,36165,36166,36172],{},[1686,36167,36168,36170],{},[898,36169,2675],{},[1692,36171,1694],{},[1686,36173,36174,36176],{},[898,36175,2675],{},[1692,36177,1703],{},[902,36179,36180],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,36183,36185],{"className":36184},[886],[888,36186,36187],{"xmlns":890,"display":29279},[892,36188,36189,36334],{},[21967,36190,36191],{"width":29284},[21972,36192,36193,36195,36327,36329],{},[21975,36194],{"width":29289},[21975,36196,36197],{},[14130,36198,36199],{"notation":14132},[2938,36200,36201],{"scriptlevel":1741,"displaystyle":1653},[2938,36202,36203],{"scriptlevel":1741,"displaystyle":1653},[2938,36204,36205],{"scriptlevel":1741,"displaystyle":1660},[895,36206,36207,36209,36215,36217,36219,36235,36237,36243,36245,36251,36253,36259,36261,36263,36265,36267,36269,36275,36277,36279,36295,36297,36303,36305,36311,36313,36319,36321,36323,36325],{},[1843,36208,5295],{},[1686,36210,36211,36213],{},[898,36212,1690],{},[1692,36214,1694],{},[1651,36216,1738],{},[898,36218,900],{},[9423,36220,36221],{},[2446,36222,36223,36229],{},[1686,36224,36225,36227],{},[898,36226,2675],{},[1692,36228,1703],{},[1686,36230,36231,36233],{},[898,36232,2675],{},[1692,36234,1694],{},[1651,36236,1738],{},[1686,36238,36239,36241],{},[898,36240,2047],{},[1692,36242,1694],{},[1651,36244,1654],{"stretchy":1653},[1686,36246,36247,36249],{},[898,36248,2675],{},[1692,36250,1694],{},[1651,36252,1661],{"separator":1660},[1686,36254,36255,36257],{},[898,36256,2675],{},[1692,36258,1703],{},[1651,36260,1661],{"separator":1660},[898,36262,900],{},[1651,36264,1667],{"stretchy":1653},[1651,36266,1661],{"separator":1660},[7185,36268],{"width":16582},[1686,36270,36271,36273],{},[898,36272,1690],{},[1692,36274,1703],{},[1651,36276,1738],{},[898,36278,900],{},[9423,36280,36281],{},[2446,36282,36283,36289],{},[1686,36284,36285,36287],{},[898,36286,2675],{},[1692,36288,1694],{},[1686,36290,36291,36293],{},[898,36292,2675],{},[1692,36294,1703],{},[1651,36296,1738],{},[1686,36298,36299,36301],{},[898,36300,2047],{},[1692,36302,1703],{},[1651,36304,1654],{"stretchy":1653},[1686,36306,36307,36309],{},[898,36308,2675],{},[1692,36310,1694],{},[1651,36312,1661],{"separator":1660},[1686,36314,36315,36317],{},[898,36316,2675],{},[1692,36318,1703],{},[1651,36320,1661],{"separator":1660},[898,36322,900],{},[1651,36324,1667],{"stretchy":1653},[1843,36326,5295],{},[21975,36328],{"width":29289},[21975,36330,36331],{},[1843,36332,36333],{},"(6.30)",[902,36335,36336],{"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}",[115,36338,36340],{"id":36339},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,36342,36343,36344,36357,36358,36375,36376,36389,36390,36407,36408,36411,36412,36451,36452,36481],{},"Primární (max ",[883,36345,36347],{"className":36346},[886],[888,36348,36349],{"xmlns":890},[892,36350,36351,36355],{},[895,36352,36353],{},[898,36354,900],{},[902,36356,900],{"encoding":904}," při rozpočtu ",[883,36359,36361],{"className":36360},[886],[888,36362,36363],{"xmlns":890},[892,36364,36365,36373],{},[895,36366,36367],{},[2115,36368,36369,36371],{},[898,36370,2665],{},[1651,36372,2668],{},[902,36374,29241],{"encoding":904},") a duální (min ",[883,36377,36379],{"className":36378},[886],[888,36380,36381],{"xmlns":890},[892,36382,36383,36387],{},[895,36384,36385],{},[898,36386,5561],{},[902,36388,5561],{"encoding":904}," při užitečnosti ",[883,36391,36393],{"className":36392},[886],[888,36394,36395],{"xmlns":890},[892,36396,36397,36405],{},[895,36398,36399],{},[2115,36400,36401,36403],{},[898,36402,900],{},[1651,36404,2668],{},[902,36406,29175],{"encoding":904},") úloha jsou ",[38,36409,36410],{},"ekvivalentní",": mají tentýž bod optima ",[883,36413,36415],{"className":36414},[886],[888,36416,36417],{"xmlns":890},[892,36418,36419,36449],{},[895,36420,36421,36427,36429,36437,36439,36447],{},[2115,36422,36423,36425],{},[898,36424,1690],{},[1651,36426,2668],{},[1651,36428,2261],{"stretchy":1653},[1902,36430,36431,36433,36435],{},[898,36432,1690],{},[1692,36434,1694],{},[1651,36436,2668],{},[1651,36438,1661],{"separator":1660},[1902,36440,36441,36443,36445],{},[898,36442,1690],{},[1692,36444,1703],{},[1651,36446,2668],{},[1651,36448,2279],{"stretchy":1653},[902,36450,29540],{"encoding":904}," a v obou platí ",[883,36453,36455],{"className":36454},[886],[888,36456,36457],{"xmlns":890},[892,36458,36459,36479],{},[895,36460,36461,36463,36465,36471,36473],{},[1843,36462,11903],{},[1651,36464,1738],{},[1686,36466,36467,36469],{},[898,36468,2675],{},[1692,36470,1694],{},[898,36472,5981],{"mathvariant":1910},[1686,36474,36475,36477],{},[898,36476,2675],{},[1692,36478,1703],{},[902,36480,29211],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,36483,36484],{},[1756,36485],{"alt":36486,"className":36487,"src":36488},"imek-primarni-vs-dualni",[210,1760],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,36490,36491,36602],{},[123,36492,36493,36496,36497,36510,36511,36551,36552,1882],{},[38,36494,36495],{},"Primární"," (Marshall): zadáno ",[883,36498,36500],{"className":36499},[886],[888,36501,36502],{"xmlns":890},[892,36503,36504,36508],{},[895,36505,36506],{},[898,36507,2665],{},[902,36509,2665],{"encoding":904},", hledáme maximální ",[883,36512,36514],{"className":36513},[886],[888,36515,36516],{"xmlns":890},[892,36517,36518,36548],{},[895,36519,36520,36526,36528,36534,36536,36542,36544,36546],{},[2115,36521,36522,36524],{},[898,36523,900],{},[1651,36525,2668],{},[1651,36527,1654],{"stretchy":1653},[1686,36529,36530,36532],{},[898,36531,2675],{},[1692,36533,1694],{},[1651,36535,1661],{"separator":1660},[1686,36537,36538,36540],{},[898,36539,2675],{},[1692,36541,1703],{},[1651,36543,1661],{"separator":1660},[898,36545,2665],{},[1651,36547,1667],{"stretchy":1653},[902,36549,36550],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,36553,36555],{"className":36554},[886],[888,36556,36557],{"xmlns":890},[892,36558,36559,36599],{},[895,36560,36561,36567,36569,36577,36579,36585,36587,36593,36595,36597],{},[1686,36562,36563,36565],{},[898,36564,1690],{},[898,36566,3201],{},[1651,36568,1738],{},[1902,36570,36571,36573,36575],{},[898,36572,2047],{},[898,36574,3201],{},[898,36576,2995],{},[1651,36578,1654],{"stretchy":1653},[1686,36580,36581,36583],{},[898,36582,2675],{},[1692,36584,1694],{},[1651,36586,1661],{"separator":1660},[1686,36588,36589,36591],{},[898,36590,2675],{},[1692,36592,1703],{},[1651,36594,1661],{"separator":1660},[898,36596,2665],{},[1651,36598,1667],{"stretchy":1653},[902,36600,36601],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,36603,36604,36607,36608,36621,36622,36551,36662,1882],{},[38,36605,36606],{},"Duální"," (Hicks): zadáno ",[883,36609,36611],{"className":36610},[886],[888,36612,36613],{"xmlns":890},[892,36614,36615,36619],{},[895,36616,36617],{},[898,36618,900],{},[902,36620,900],{"encoding":904},", hledáme minimální ",[883,36623,36625],{"className":36624},[886],[888,36626,36627],{"xmlns":890},[892,36628,36629,36659],{},[895,36630,36631,36637,36639,36645,36647,36653,36655,36657],{},[2115,36632,36633,36635],{},[898,36634,5561],{},[1651,36636,2668],{},[1651,36638,1654],{"stretchy":1653},[1686,36640,36641,36643],{},[898,36642,2675],{},[1692,36644,1694],{},[1651,36646,1661],{"separator":1660},[1686,36648,36649,36651],{},[898,36650,2675],{},[1692,36652,1703],{},[1651,36654,1661],{"separator":1660},[898,36656,900],{},[1651,36658,1667],{"stretchy":1653},[902,36660,36661],{"encoding":904},"E^*(P_1, P_2, U)",[883,36663,36665],{"className":36664},[886],[888,36666,36667],{"xmlns":890},[892,36668,36669,36710],{},[895,36670,36671,36677,36679,36688,36690,36696,36698,36704,36706,36708],{},[1686,36672,36673,36675],{},[898,36674,1690],{},[898,36676,3201],{},[1651,36678,1738],{},[1902,36680,36681,36683,36685],{},[898,36682,2047],{},[898,36684,3201],{},[898,36686,36687],{},"H",[1651,36689,1654],{"stretchy":1653},[1686,36691,36692,36694],{},[898,36693,2675],{},[1692,36695,1694],{},[1651,36697,1661],{"separator":1660},[1686,36699,36700,36702],{},[898,36701,2675],{},[1692,36703,1703],{},[1651,36705,1661],{"separator":1660},[898,36707,900],{},[1651,36709,1667],{"stretchy":1653},[902,36711,36712],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,36714,36715,36716,36719,36720,36723],{},"Proč se studují obě? Marshallova poptávka je ",[38,36717,36718],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,36721,36722],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,36725,36727],{"id":36726},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,36729,36731],{"id":36730},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,36733,36734,36737,36738,36770,36771,36809,36810,36836],{},[38,36735,36736],{},"6.8"," Jsou dány užitečnost ",[883,36739,36741],{"className":36740},[886],[888,36742,36743],{"xmlns":890},[892,36744,36745,36767],{},[895,36746,36747,36749,36751,36759],{},[898,36748,900],{},[1651,36750,1738],{},[1902,36752,36753,36755,36757],{},[898,36754,1690],{},[1692,36756,1694],{},[1692,36758,6316],{},[1902,36760,36761,36763,36765],{},[898,36762,1690],{},[1692,36764,1703],{},[1692,36766,6316],{},[902,36768,36769],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,36772,36774],{"className":36773},[886],[888,36775,36776],{"xmlns":890},[892,36777,36778,36806],{},[895,36779,36780,36788,36790,36792,36794,36802,36804],{},[1902,36781,36782,36784,36786],{},[898,36783,2675],{},[1692,36785,1694],{},[1651,36787,2668],{},[1651,36789,1738],{},[1692,36791,3689],{},[1651,36793,1661],{"separator":1660},[1902,36795,36796,36798,36800],{},[898,36797,2675],{},[1692,36799,1703],{},[1651,36801,2668],{},[1651,36803,1738],{},[1692,36805,4190],{},[902,36807,36808],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,36811,36813],{"className":36812},[886],[888,36814,36815],{"xmlns":890},[892,36816,36817,36833],{},[895,36818,36819,36825,36827],{},[1686,36820,36821,36823],{},[898,36822,1690],{},[1692,36824,1694],{},[1651,36826,1661],{"separator":1660},[1686,36828,36829,36831],{},[898,36830,1690],{},[1692,36832,1703],{},[902,36834,36835],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,36838,36839,36842,36843,36885,36886,36917,36918,36940,36941,1882],{},[38,36840,36841],{},"6.9"," Jsou dány rozpočtové omezení ",[883,36844,36846],{"className":36845},[886],[888,36847,36848],{"xmlns":890},[892,36849,36850,36882],{},[895,36851,36852,36854,36856,36862,36868,36870,36876],{},[898,36853,2665],{},[1651,36855,1738],{},[1686,36857,36858,36860],{},[898,36859,2675],{},[1692,36861,1694],{},[1686,36863,36864,36866],{},[898,36865,1690],{},[1692,36867,1694],{},[1651,36869,1839],{},[1686,36871,36872,36874],{},[898,36873,2675],{},[1692,36875,1703],{},[1686,36877,36878,36880],{},[898,36879,1690],{},[1692,36881,1703],{},[902,36883,36884],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,36887,36889],{"className":36888},[886],[888,36890,36891],{"xmlns":890},[892,36892,36893,36915],{},[895,36894,36895,36897,36899,36907],{},[898,36896,900],{},[1651,36898,1738],{},[1902,36900,36901,36903,36905],{},[898,36902,1690],{},[1692,36904,1694],{},[1692,36906,6316],{},[1902,36908,36909,36911,36913],{},[898,36910,1690],{},[1692,36912,1703],{},[1692,36914,6316],{},[902,36916,36769],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,36919,36921],{"className":36920},[886],[888,36922,36923],{"xmlns":890},[892,36924,36925,36937],{},[895,36926,36927,36933,36935],{},[2115,36928,36929,36931],{},[898,36930,2665],{},[1651,36932,2668],{},[1651,36934,1738],{},[1692,36936,16408],{},[902,36938,36939],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,36942,36944],{"className":36943},[886],[888,36945,36946],{"xmlns":890},[892,36947,36948,36976],{},[895,36949,36950,36958,36960,36962,36964,36972,36974],{},[1902,36951,36952,36954,36956],{},[898,36953,2675],{},[1692,36955,1694],{},[1651,36957,2668],{},[1651,36959,1738],{},[1692,36961,3574],{},[1651,36963,1661],{"separator":1660},[1902,36965,36966,36968,36970],{},[898,36967,2675],{},[1692,36969,1703],{},[1651,36971,2668],{},[1651,36973,1738],{},[1692,36975,4190],{},[902,36977,36978],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,36980,36981,36984,36985,22807,37017,37047,37048,1882],{},[38,36982,36983],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,36986,36988],{"className":36987},[886],[888,36989,36990],{"xmlns":890},[892,36991,36992,37014],{},[895,36993,36994,36996,36998,37006],{},[898,36995,900],{},[1651,36997,1738],{},[1902,36999,37000,37002,37004],{},[898,37001,1690],{},[1692,37003,1694],{},[898,37005,207],{},[1902,37007,37008,37010,37012],{},[898,37009,1690],{},[1692,37011,1703],{},[898,37013,2268],{},[902,37015,37016],{"encoding":904},"U = Q_1^a Q_2^b",[883,37018,37020],{"className":37019},[886],[888,37021,37022],{"xmlns":890},[892,37023,37024,37044],{},[895,37025,37026,37028,37030,37032,37034,37036,37038,37040,37042],{},[898,37027,207],{},[1651,37029,1661],{"separator":1660},[898,37031,2268],{},[1651,37033,7813],{},[1651,37035,6631],{"stretchy":1653},[1692,37037,1741],{},[1651,37039,1661],{"separator":1660},[1692,37041,1694],{},[1651,37043,6648],{"stretchy":1653},[902,37045,37046],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,37049,37051],{"className":37050},[886],[888,37052,37053],{"xmlns":890},[892,37054,37055,37087],{},[895,37056,37057,37059,37061,37067,37073,37075,37081],{},[898,37058,2665],{},[1651,37060,1738],{},[1686,37062,37063,37065],{},[898,37064,2675],{},[1692,37066,1694],{},[1686,37068,37069,37071],{},[898,37070,1690],{},[1692,37072,1694],{},[1651,37074,1839],{},[1686,37076,37077,37079],{},[898,37078,2675],{},[1692,37080,1703],{},[1686,37082,37083,37085],{},[898,37084,1690],{},[1692,37086,1703],{},[902,37088,36884],{"encoding":904},[724,37090,37091,37094,37095,22807,37129,37047,37147,1882],{},[38,37092,37093],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,37096,37098],{"className":37097},[886],[888,37099,37100],{"xmlns":890},[892,37101,37102,37126],{},[895,37103,37104,37106,37108,37116,37118],{},[898,37105,900],{},[1651,37107,1738],{},[1902,37109,37110,37112,37114],{},[898,37111,1690],{},[1692,37113,1694],{},[898,37115,207],{},[1651,37117,1839],{},[1902,37119,37120,37122,37124],{},[898,37121,1690],{},[1692,37123,1703],{},[898,37125,207],{},[902,37127,37128],{"encoding":904},"U = Q_1^a + Q_2^a",[883,37130,37132],{"className":37131},[886],[888,37133,37134],{"xmlns":890},[892,37135,37136,37144],{},[895,37137,37138,37140,37142],{},[898,37139,207],{},[1651,37141,4693],{"mathvariant":1910},[1692,37143,1741],{},[902,37145,37146],{"encoding":904},"a \\neq 0",[883,37148,37150],{"className":37149},[886],[888,37151,37152],{"xmlns":890},[892,37153,37154,37186],{},[895,37155,37156,37158,37160,37166,37172,37174,37180],{},[898,37157,2665],{},[1651,37159,1738],{},[1686,37161,37162,37164],{},[898,37163,2675],{},[1692,37165,1694],{},[1686,37167,37168,37170],{},[898,37169,1690],{},[1692,37171,1694],{},[1651,37173,1839],{},[1686,37175,37176,37178],{},[898,37177,2675],{},[1692,37179,1703],{},[1686,37181,37182,37184],{},[898,37183,1690],{},[1692,37185,1703],{},[902,37187,36884],{"encoding":904},[198,37189,37191],{"id":37190},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,37193,37194,36737,37197,1343,37224,37246,37247,1343,37270,37294,37295,37320,37321,1882],{},[38,37195,37196],{},"6.12",[883,37198,37200],{"className":37199},[886],[888,37201,37202],{"xmlns":890},[892,37203,37204,37222],{},[895,37205,37206,37208,37210,37216],{},[898,37207,900],{},[1651,37209,1738],{},[1686,37211,37212,37214],{},[898,37213,1690],{},[1692,37215,1694],{},[1686,37217,37218,37220],{},[898,37219,1690],{},[1692,37221,1703],{},[902,37223,31439],{"encoding":904},[883,37225,37227],{"className":37226},[886],[888,37228,37229],{"xmlns":890},[892,37230,37231,37243],{},[895,37232,37233,37239,37241],{},[2115,37234,37235,37237],{},[898,37236,900],{},[1651,37238,2668],{},[1651,37240,1738],{},[1692,37242,4190],{},[902,37244,37245],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,37248,37250],{"className":37249},[886],[888,37251,37252],{"xmlns":890},[892,37253,37254,37268],{},[895,37255,37256,37264,37266],{},[1902,37257,37258,37260,37262],{},[898,37259,2675],{},[1692,37261,1694],{},[1651,37263,2668],{},[1651,37265,1738],{},[1692,37267,1703],{},[902,37269,31512],{"encoding":904},[883,37271,37273],{"className":37272},[886],[888,37274,37275],{"xmlns":890},[892,37276,37277,37291],{},[895,37278,37279,37287,37289],{},[1902,37280,37281,37283,37285],{},[898,37282,2675],{},[1692,37284,1703],{},[1651,37286,2668],{},[1651,37288,1738],{},[1692,37290,3689],{},[902,37292,37293],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,37296,37298],{"className":37297},[886],[888,37299,37300],{"xmlns":890},[892,37301,37302,37318],{},[895,37303,37304,37310,37312],{},[1686,37305,37306,37308],{},[898,37307,1690],{},[1692,37309,1694],{},[1651,37311,1661],{"separator":1660},[1686,37313,37314,37316],{},[898,37315,1690],{},[1692,37317,1703],{},[902,37319,36835],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,37322,37324],{"className":37323},[886],[888,37325,37326],{"xmlns":890},[892,37327,37328,37348],{},[895,37329,37330,37332,37334,37340,37342],{},[898,37331,900],{},[1651,37333,1738],{},[1686,37335,37336,37338],{},[898,37337,1690],{},[1692,37339,1694],{},[1651,37341,4503],{},[1686,37343,37344,37346],{},[898,37345,1690],{},[1692,37347,1703],{},[902,37349,37350],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,37352,37353,37356,37357,37398,37399,37421,37422,1882],{},[38,37354,37355],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,37358,37360],{"className":37359},[886],[888,37361,37362],{"xmlns":890},[892,37363,37364,37396],{},[895,37365,37366,37368,37370,37376,37382,37384,37390],{},[898,37367,5561],{},[1651,37369,1738],{},[1686,37371,37372,37374],{},[898,37373,2675],{},[1692,37375,1694],{},[1686,37377,37378,37380],{},[898,37379,1690],{},[1692,37381,1694],{},[1651,37383,1839],{},[1686,37385,37386,37388],{},[898,37387,2675],{},[1692,37389,1703],{},[1686,37391,37392,37394],{},[898,37393,1690],{},[1692,37395,1703],{},[902,37397,29156],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,37400,37402],{"className":37401},[886],[888,37403,37404],{"xmlns":890},[892,37405,37406,37418],{},[895,37407,37408,37414,37416],{},[2115,37409,37410,37412],{},[898,37411,900],{},[1651,37413,2668],{},[1651,37415,1738],{},[1692,37417,6311],{},[902,37419,37420],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,37423,37425],{"className":37424},[886],[888,37426,37427],{"xmlns":890},[892,37428,37429,37458],{},[895,37430,37431,37439,37441,37443,37445,37453,37455],{},[1902,37432,37433,37435,37437],{},[898,37434,2675],{},[1692,37436,1694],{},[1651,37438,2668],{},[1651,37440,1738],{},[1692,37442,10340],{},[1651,37444,1661],{"separator":1660},[1902,37446,37447,37449,37451],{},[898,37448,2675],{},[1692,37450,1703],{},[1651,37452,2668],{},[1651,37454,1738],{},[1692,37456,37457],{},"15",[902,37459,37460],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,37462,17018],{"id":17017},[120,37464,37465,37522,37561,37581,37616,37670,37675,37681,37777,37822],{},[123,37466,37467,3246,37470,37519,37520,1882],{},[38,37468,37469],{},"Rozpočtové omezení (budget constraint)",[883,37471,37473],{"className":37472},[886],[888,37474,37475],{"xmlns":890},[892,37476,37477,37517],{},[895,37478,37479,37485,37487,37495,37501,37503,37511],{},[2115,37480,37481,37483],{},[898,37482,2665],{},[1651,37484,2668],{},[1651,37486,1738],{},[1902,37488,37489,37491,37493],{},[898,37490,2675],{},[1692,37492,1694],{},[1651,37494,2668],{},[1686,37496,37497,37499],{},[898,37498,1690],{},[1692,37500,1694],{},[1651,37502,1839],{},[1902,37504,37505,37507,37509],{},[898,37506,2675],{},[1692,37508,1703],{},[1651,37510,2668],{},[1686,37512,37513,37515],{},[898,37514,1690],{},[1692,37516,1703],{},[902,37518,2704],{"encoding":904}," — (6.12); ",[38,37521,29349],{},[123,37523,37524,37527,37528,1882],{},[38,37525,37526],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,37529,37531],{"className":37530},[886],[888,37532,37533],{"xmlns":890},[892,37534,37535,37559],{},[895,37536,37537,37539,37541,37549,37551],{},[1843,37538,11903],{},[1651,37540,1738],{},[1902,37542,37543,37545,37547],{},[898,37544,2675],{},[1692,37546,1694],{},[1651,37548,2668],{},[898,37550,5981],{"mathvariant":1910},[1902,37552,37553,37555,37557],{},[898,37554,2675],{},[1692,37556,1703],{},[1651,37558,2668],{},[902,37560,30192],{"encoding":904},[123,37562,37563,37578,37579,1882],{},[38,37564,30336,37565],{},[883,37566,37568],{"className":37567},[886],[888,37569,37570],{"xmlns":890},[892,37571,37572,37576],{},[895,37573,37574],{},[898,37575,1820],{},[902,37577,1877],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,37580,30358],{},[123,37582,37583,37586,37587,1882],{},[38,37584,37585],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,37588,37590],{"className":37589},[886],[888,37591,37592],{"xmlns":890},[892,37593,37594,37614],{},[895,37595,37596,37598,37600,37606,37608],{},[1843,37597,11903],{},[1651,37599,1738],{},[1686,37601,37602,37604],{},[898,37603,2675],{},[1692,37605,1694],{},[898,37607,5981],{"mathvariant":1910},[1686,37609,37610,37612],{},[898,37611,2675],{},[1692,37613,1703],{},[902,37615,29211],{"encoding":904},[123,37617,37618,8322,37621,37669],{},[38,37619,37620],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,37622,37624],{"className":37623},[886],[888,37625,37626],{"xmlns":890},[892,37627,37628,37666],{},[895,37629,37630,37636,37638,37644,37646,37652,37654,37660,37662,37664],{},[1686,37631,37632,37634],{},[898,37633,1690],{},[898,37635,3201],{},[1651,37637,1738],{},[1686,37639,37640,37642],{},[898,37641,2047],{},[898,37643,3201],{},[1651,37645,1654],{"stretchy":1653},[1686,37647,37648,37650],{},[898,37649,2675],{},[1692,37651,1694],{},[1651,37653,1661],{"separator":1660},[1686,37655,37656,37658],{},[898,37657,2675],{},[1692,37659,1703],{},[1651,37661,1661],{"separator":1660},[898,37663,2665],{},[1651,37665,1667],{"stretchy":1653},[902,37667,37668],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,37671,37672,37674],{},[38,37673,32940],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,37676,37677,37680],{},[38,37678,37679],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,37682,37683,8322,37685,37732,37733,37776],{},[38,37684,35252],{},[883,37686,37688],{"className":37687},[886],[888,37689,37690],{"xmlns":890},[892,37691,37692,37730],{},[895,37693,37694,37700,37702,37708,37710,37716,37718,37724,37726,37728],{},[1686,37695,37696,37698],{},[898,37697,1690],{},[898,37699,3201],{},[1651,37701,1738],{},[1686,37703,37704,37706],{},[898,37705,2047],{},[898,37707,3201],{},[1651,37709,1654],{"stretchy":1653},[1686,37711,37712,37714],{},[898,37713,2675],{},[1692,37715,1694],{},[1651,37717,1661],{"separator":1660},[1686,37719,37720,37722],{},[898,37721,2675],{},[1692,37723,1703],{},[1651,37725,1661],{"separator":1660},[898,37727,900],{},[1651,37729,1667],{"stretchy":1653},[902,37731,3234],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,37734,37736],{"className":37735},[886],[888,37737,37738],{"xmlns":890},[892,37739,37740,37774],{},[895,37741,37742,37744,37746,37760],{},[898,37743,900],{},[1651,37745,1738],{},[1902,37747,37748,37750,37752],{},[898,37749,1690],{},[1692,37751,1694],{},[895,37753,37754,37756,37758],{},[1692,37755,1694],{},[898,37757,5981],{"mathvariant":1910},[1692,37759,1703],{},[1902,37761,37762,37764,37766],{},[898,37763,1690],{},[1692,37765,1703],{},[895,37767,37768,37770,37772],{},[1692,37769,1694],{},[898,37771,5981],{"mathvariant":1910},[1692,37773,1703],{},[902,37775,34372],{"encoding":904},": (6.30).",[123,37778,37779,37821],{},[38,37780,37781,37782],{},"Bod dotyku ",[883,37783,37785],{"className":37784},[886],[888,37786,37787],{"xmlns":890},[892,37788,37789,37819],{},[895,37790,37791,37797,37799,37807,37809,37817],{},[2115,37792,37793,37795],{},[898,37794,1690],{},[1651,37796,2668],{},[1651,37798,2261],{"stretchy":1653},[1902,37800,37801,37803,37805],{},[898,37802,1690],{},[1692,37804,1694],{},[1651,37806,2668],{},[1651,37808,1661],{"separator":1660},[1902,37810,37811,37813,37815],{},[898,37812,1690],{},[1692,37814,1703],{},[1651,37816,2668],{},[1651,37818,2279],{"stretchy":1653},[902,37820,29540],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,37823,37824,37827,37828,37841,37842,37855],{},[38,37825,37826],{},"Dualita"," — ekvivalence max ",[883,37829,37831],{"className":37830},[886],[888,37832,37833],{"xmlns":890},[892,37834,37835,37839],{},[895,37836,37837],{},[898,37838,900],{},[902,37840,900],{"encoding":904}," a min ",[883,37843,37845],{"className":37844},[886],[888,37846,37847],{"xmlns":890},[892,37848,37849,37853],{},[895,37850,37851],{},[898,37852,5561],{},[902,37854,5561],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,37857,3238],{"id":3237},[120,37859,37860,37883,37899,37912,37923],{},[123,37861,37862,3246,37865,37868,37869,37882],{},[38,37863,37864],{},"Teorie před optimalizací:",[207,37866,880],{"className":37867,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,37870,37872],{"className":37871},[886],[888,37873,37874],{"xmlns":890},[892,37875,37876,37880],{},[895,37877,37878],{},[898,37879,900],{},[902,37881,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,37884,37885,3246,37888,37891,37892,37895,37896,1882],{},[38,37886,37887],{},"Matematický aparát:",[207,37889,793],{"className":37890,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,37893,784],{"className":37894,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,37897,3695],{"className":37898,"dataFsResolvedFilePath":764,"href":765},[210],[123,37900,37901,3246,37904,37907,37908,37911],{},[38,37902,37903],{},"Paralely:",[207,37905,12385],{"className":37906,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,37909,3258],{"className":37910,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,37913,37914,3246,37917,1343,37920],{},[38,37915,37916],{},"Přednášky:",[207,37918,1094],{"className":37919,"dataFsResolvedFilePath":838,"href":839},[210],[207,37921,1101],{"className":37922,"dataFsResolvedFilePath":868,"href":869},[210],[123,37924,37925,3246,37927],{},[38,37926,17502],{},[207,37928,17506],{"className":37929,"dataFsResolvedFilePath":1749,"href":1750},[210],{"title":641,"searchDepth":642,"depth":642,"links":37931},[37932,37933,37934,37939,37940,37941,37943,37946,37949,37951,37952,37954,37955,37959,37960],{"id":13303,"depth":642,"text":13304},{"id":29219,"depth":642,"text":29220},{"id":29617,"depth":642,"text":29618,"children":37935},[37936,37937],{"id":29737,"depth":649,"text":29738},{"id":30318,"depth":649,"text":37938},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":30780,"depth":642,"text":30781},{"id":31091,"depth":642,"text":31092},{"id":31410,"depth":642,"text":37942},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":32183,"depth":642,"text":32184,"children":37944},[37945],{"id":32939,"depth":649,"text":32940},{"id":33119,"depth":642,"text":33120,"children":37947},[37948],{"id":33376,"depth":649,"text":33377},{"id":34327,"depth":642,"text":37950},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":35251,"depth":642,"text":35252},{"id":35454,"depth":642,"text":37953},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":36339,"depth":642,"text":36340},{"id":36726,"depth":642,"text":36727,"children":37956},[37957,37958],{"id":36730,"depth":649,"text":36731},{"id":37190,"depth":649,"text":37191},{"id":17017,"depth":642,"text":17018},{"id":3237,"depth":642,"text":3238},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":28980,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,37967,1144,1773,37968,37969,37970],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":37973,"title":802,"body":37974,"course":1128,"courses":659,"created":10859,"description":641,"extension":661,"meta":52027,"navigation":664,"path":52028,"seo":52029,"sources":52030,"stem":52031,"tags":52032,"type":3302,"updated":677,"__hash__":52038},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":37975,"toc":51983},[37976,37979,38005,38009,38016,38168,38182,38185,38187,38274,38278,38314,38387,38408,38533,38543,38556,38560,38565,38595,38657,38666,38670,38732,38739,38760,38878,38956,38960,38963,39022,39137,39142,39174,39236,39284,39339,39343,39364,39388,39436,39440,39452,39456,39566,39570,39586,39627,39638,39797,39807,39812,39816,39938,39948,39955,39959,40037,40048,40128,40134,40141,40280,40287,40290,40347,40351,40429,40475,40519,40525,40638,40642,40645,40840,40844,41081,41084,41238,41391,41393,41395,41475,41478,41583,41652,41661,41665,41668,41729,41738,41742,41775,41853,41892,41896,41945,41999,42003,42032,42061,42113,42120,42174,42252,42256,42299,42366,42410,42514,42533,42535,42539,42647,42651,42719,42768,42775,42860,42864,42936,42941,42989,43178,43182,43187,43363,43368,43427,43532,43536,43563,43567,43574,43738,43825,43830,43832,43835,43935,44085,44157,44231,44233,44237,44251,44255,44388,44443,44555,44632,44636,44693,44796,44855,45016,45020,45095,45167,45265,45323,45417,45470,45491,45545,45550,45628,45676,45763,45801,45889,46042,46078,46132,46135,46137,46139,46188,46195,46203,46290,46299,46386,46393,46395,46399,46624,46626,46630,46634,46703,46754,46957,46963,46974,47042,47048,47470,47474,47538,47562,47758,47764,47778,47846,47849,47889,48113,48181,48483,48892,48969,49135,49141,49144,49219,49672,49723,50129,50234,50897,50900,50977,50985,51059,51090,51092,51096,51140,51142,51144,51148,51378,51382,51473,51478,51572,51577,51750,51754,51872,51877,51926,51928,51930],[12,37977,802],{"id":37978},"poptávka-nabídka-a-tržní-rovnováha",[5179,37980,37981],{},[724,37982,37983,37985,37986,37989,37990,37993,37994,37997,37998,38000,38001,38004],{},[883,37984,5465],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,37987,37988],{},"poptávka",") a výrobce (",[38,37991,37992],{},"nabídka","), jejich interakci v ",[38,37995,37996],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,37999,19190],{},"). Uzavírá ji pojem ",[38,38002,38003],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,38006,38008],{"id":38007},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,38010,38011,38012,38015],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,38013,38014],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,38017,38018,38035,38077,38093],{},[123,38019,38020,38021,38034],{},"cena ",[883,38022,38024],{"className":38023},[886],[888,38025,38026],{"xmlns":890},[892,38027,38028,38032],{},[895,38029,38030],{},[898,38031,2675],{},[902,38033,2675],{"encoding":904}," zkoumaného zboží,",[123,38036,38037,38038,1661],{},"ceny alternativních zboží ",[883,38039,38041],{"className":38040},[886],[888,38042,38043],{"xmlns":890},[892,38044,38045,38074],{},[895,38046,38047,38053,38055,38061,38063,38065,38067],{},[1686,38048,38049,38051],{},[898,38050,2675],{},[1692,38052,1694],{},[1651,38054,1661],{"separator":1660},[1686,38056,38057,38059],{},[898,38058,2675],{},[1692,38060,1703],{},[1651,38062,1661],{"separator":1660},[1651,38064,10949],{},[1651,38066,1661],{"separator":1660},[1686,38068,38069,38071],{},[898,38070,2675],{},[898,38072,38073],{},"n",[902,38075,38076],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,38078,38079,38080,1661],{},"důchod ",[883,38081,38083],{"className":38082},[886],[888,38084,38085],{"xmlns":890},[892,38086,38087,38091],{},[895,38088,38089],{},[898,38090,2665],{},[902,38092,2665],{"encoding":904},[123,38094,38095,38096,38109,38110,38123,38124,38137,38138,38152,38153,38167],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,38097,38099],{"className":38098},[886],[888,38100,38101],{"xmlns":890},[892,38102,38103,38107],{},[895,38104,38105],{},[898,38106,1807],{},[902,38108,1807],{"encoding":904},", kapitál ",[883,38111,38113],{"className":38112},[886],[888,38114,38115],{"xmlns":890},[892,38116,38117,38121],{},[895,38118,38119],{},[898,38120,11101],{},[902,38122,11101],{"encoding":904},", půda ",[883,38125,38127],{"className":38126},[886],[888,38128,38129],{"xmlns":890},[892,38130,38131,38135],{},[895,38132,38133],{},[898,38134,5561],{},[902,38136,5561],{"encoding":904},"), technologie, počet výrobců ",[883,38139,38141],{"className":38140},[886],[888,38142,38143],{"xmlns":890},[892,38144,38145,38150],{},[895,38146,38147],{},[898,38148,38149],{},"O",[902,38151,38149],{"encoding":904},", počasí ",[883,38154,38156],{"className":38155},[886],[888,38157,38158],{"xmlns":890},[892,38159,38160,38165],{},[895,38161,38162],{},[898,38163,38164],{},"W",[902,38166,38164],{"encoding":904}," atd.",[724,38169,38170,38171,38174,38175,38178,38179,1882],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,38172,38173],{},"ceteris paribus","), hovoříme o ",[38,38176,38177],{},"jednofaktorovém modelu","; jinak jde o model ",[38,38180,38181],{},"vícefaktorový",[38183,38184],"hr",{},[115,38186,14459],{"id":37988},[5179,38188,38189],{},[724,38190,38191,38193,38194,38207,38208,38221,38222,38225,38226,38249,38250,1882],{},[883,38192,5465],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,38195,38197],{"className":38196},[886],[888,38198,38199],{"xmlns":890},[892,38200,38201,38205],{},[895,38202,38203],{},[898,38204,1690],{},[902,38206,1690],{"encoding":904}," na ceně ",[883,38209,38211],{"className":38210},[886],[888,38212,38213],{"xmlns":890},[892,38214,38215,38219],{},[895,38216,38217],{},[898,38218,2675],{},[902,38220,2675],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,38223,38224],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,38227,38229],{"className":38228},[886],[888,38230,38231],{"xmlns":890},[892,38232,38233,38247],{},[895,38234,38235,38237,38239,38241,38243,38245],{},[898,38236,1690],{},[1651,38238,1738],{},[898,38240,2047],{},[1651,38242,1654],{"stretchy":1653},[898,38244,2675],{},[1651,38246,1667],{"stretchy":1653},[902,38248,5501],{"encoding":904}," a jeho lineární verzí ",[883,38251,38253],{"className":38252},[886],[888,38254,38255],{"xmlns":890},[892,38256,38257,38271],{},[895,38258,38259,38261,38263,38265,38267,38269],{},[898,38260,2675],{},[1651,38262,1738],{},[898,38264,207],{},[898,38266,1690],{},[1651,38268,1839],{},[898,38270,2268],{},[902,38272,38273],{"encoding":904},"P = aQ + b",[198,38275,38277],{"id":38276},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,38279,38280,38281,38294,38295,38308,38309,11325,38311,4477],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,38282,38284],{"className":38283},[886],[888,38285,38286],{"xmlns":890},[892,38287,38288,38292],{},[895,38289,38290],{},[898,38291,1690],{},[902,38293,1690],{"encoding":904}," závisí na ceně ",[883,38296,38298],{"className":38297},[886],[888,38299,38300],{"xmlns":890},[892,38301,38302,38306],{},[895,38303,38304],{},[898,38305,2675],{},[902,38307,2675],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,38310,29215],{},[614,38312,38313],{},"demand function",[883,38315,38317],{"className":38316},[886],[888,38318,38319],{"xmlns":890,"display":29279},[892,38320,38321,38384],{},[21967,38322,38323],{"width":29284},[21972,38324,38325,38327,38377,38379],{},[21975,38326],{"width":29289},[21975,38328,38329],{},[895,38330,38331,38333,38335,38337,38339,38341,38343,38349,38351,38357,38359,38361,38363,38369,38371,38373,38375],{},[898,38332,1690],{},[1651,38334,1738],{},[898,38336,2047],{},[1651,38338,1654],{"stretchy":1653},[898,38340,2675],{},[1651,38342,1661],{"separator":1660},[1686,38344,38345,38347],{},[898,38346,2675],{},[1692,38348,1694],{},[1651,38350,1661],{"separator":1660},[1686,38352,38353,38355],{},[898,38354,2675],{},[1692,38356,1703],{},[1651,38358,1661],{"separator":1660},[1651,38360,10949],{},[1651,38362,1661],{"separator":1660},[1686,38364,38365,38367],{},[898,38366,2675],{},[898,38368,38073],{},[1651,38370,1661],{"separator":1660},[898,38372,2665],{},[1651,38374,1667],{"stretchy":1653},[898,38376,1882],{"mathvariant":1910},[21975,38378],{"width":29289},[21975,38380,38381],{},[1843,38382,38383],{},"(2.1)",[902,38385,38386],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,38388,38389,38390,38393,38394,38407],{},"Důležitou vlastností je ",[38,38391,38392],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,38395,38397],{"className":38396},[886],[888,38398,38399],{"xmlns":890},[892,38400,38401,38405],{},[895,38402,38403],{},[898,38404,13339],{},[902,38406,13339],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,38409,38411],{"className":38410},[886],[888,38412,38413],{"xmlns":890,"display":29279},[892,38414,38415,38530],{},[21967,38416,38417],{"width":29284},[21972,38418,38419,38421,38523,38525],{},[21975,38420],{"width":29289},[21975,38422,38423],{},[895,38424,38425,38427,38429,38431,38433,38435,38437,38439,38441,38447,38449,38451,38457,38459,38461,38463,38465,38471,38473,38475,38477,38479,38481,38483,38485,38487,38489,38495,38497,38503,38505,38507,38509,38515,38517,38519,38521],{},[898,38426,1690],{},[1651,38428,1738],{},[898,38430,2047],{},[1651,38432,1654],{"stretchy":1653},[898,38434,13339],{},[898,38436,2675],{},[1651,38438,1661],{"separator":1660},[898,38440,13339],{},[1686,38442,38443,38445],{},[898,38444,2675],{},[1692,38446,1694],{},[1651,38448,1661],{"separator":1660},[898,38450,13339],{},[1686,38452,38453,38455],{},[898,38454,2675],{},[1692,38456,1703],{},[1651,38458,1661],{"separator":1660},[1651,38460,10949],{},[1651,38462,1661],{"separator":1660},[898,38464,13339],{},[1686,38466,38467,38469],{},[898,38468,2675],{},[898,38470,38073],{},[1651,38472,1661],{"separator":1660},[898,38474,13339],{},[898,38476,2665],{},[1651,38478,1667],{"stretchy":1653},[1651,38480,1738],{},[898,38482,2047],{},[1651,38484,1654],{"stretchy":1653},[898,38486,2675],{},[1651,38488,1661],{"separator":1660},[1686,38490,38491,38493],{},[898,38492,2675],{},[1692,38494,1694],{},[1651,38496,1661],{"separator":1660},[1686,38498,38499,38501],{},[898,38500,2675],{},[1692,38502,1703],{},[1651,38504,1661],{"separator":1660},[1651,38506,10949],{},[1651,38508,1661],{"separator":1660},[1686,38510,38511,38513],{},[898,38512,2675],{},[898,38514,38073],{},[1651,38516,1661],{"separator":1660},[898,38518,2665],{},[1651,38520,1667],{"stretchy":1653},[898,38522,1882],{"mathvariant":1910},[21975,38524],{"width":29289},[21975,38526,38527],{},[1843,38528,38529],{},"(2.2)",[902,38531,38532],{"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}",[5179,38534,38535],{},[724,38536,38537,38539,38540,1882],{},[883,38538,5719],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,38541,38542],{},"v jednofaktorových modelech neplatí",[724,38544,38545,38546,1343,38549,5197,38552,38555],{},"Rozlišuje se poptávka ",[38,38547,38548],{},"individuální",[38,38550,38551],{},"tržní",[38,38553,38554],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,38557,38559],{"id":38558},"jednofaktorové-modely","Jednofaktorové modely",[38561,38562,38564],"h4",{"id":38563},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,38566,38567,38568,38581,38582,1793],{},"Poptávané množství ",[883,38569,38571],{"className":38570},[886],[888,38572,38573],{"xmlns":890},[892,38574,38575,38579],{},[895,38576,38577],{},[898,38578,1690],{},[902,38580,1690],{"encoding":904}," závisí pouze na ceně ",[883,38583,38585],{"className":38584},[886],[888,38586,38587],{"xmlns":890},[892,38588,38589,38593],{},[895,38590,38591],{},[898,38592,2675],{},[902,38594,2675],{"encoding":904},[883,38596,38598],{"className":38597},[886],[888,38599,38600],{"xmlns":890,"display":29279},[892,38601,38602,38654],{},[21967,38603,38604],{"width":29284},[21972,38605,38606,38608,38647,38649],{},[21975,38607],{"width":29289},[21975,38609,38610],{},[895,38611,38612,38614,38616,38618,38620,38622,38624,38626,38628,38631,38633,38635,38637,38639,38641,38643,38645],{},[898,38613,1690],{},[1651,38615,1738],{},[898,38617,2047],{},[1651,38619,1654],{"stretchy":1653},[898,38621,2675],{},[1651,38623,1667],{"stretchy":1653},[1651,38625,1661],{"separator":1660},[7185,38627],{"width":7187},[1843,38629,38630],{},"resp.",[7185,38632],{"width":7187},[898,38634,2675],{},[1651,38636,1738],{},[898,38638,2047],{},[1651,38640,1654],{"stretchy":1653},[898,38642,1690],{},[1651,38644,1667],{"stretchy":1653},[898,38646,1882],{"mathvariant":1910},[21975,38648],{"width":29289},[21975,38650,38651],{},[1843,38652,38653],{},"(2.3)",[902,38655,38656],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,38658,38659,38660,11325,38663,5230],{},"Graf této funkce se nazývá ",[38,38661,38662],{},"křivka poptávky",[614,38664,38665],{},"demand curve",[38561,38667,38669],{"id":38668},"zákon-klesající-poptávky","Zákon klesající poptávky",[5179,38671,38672],{},[724,38673,38674],{},[38,38675,38676,38677,38690,38691,38704,38705,38690,38718,38731],{},"Roste-li cena ",[883,38678,38680],{"className":38679},[886],[888,38681,38682],{"xmlns":890},[892,38683,38684,38688],{},[895,38685,38686],{},[898,38687,2675],{},[902,38689,2675],{"encoding":904},", pak množství ",[883,38692,38694],{"className":38693},[886],[888,38695,38696],{"xmlns":890},[892,38697,38698,38702],{},[895,38699,38700],{},[898,38701,1690],{},[902,38703,1690],{"encoding":904}," klesá; klesá-li cena ",[883,38706,38708],{"className":38707},[886],[888,38709,38710],{"xmlns":890},[892,38711,38712,38716],{},[895,38713,38714],{},[898,38715,2675],{},[902,38717,2675],{"encoding":904},[883,38719,38721],{"className":38720},[886],[888,38722,38723],{"xmlns":890},[892,38724,38725,38729],{},[895,38726,38727],{},[898,38728,1690],{},[902,38730,1690],{"encoding":904}," roste.",[724,38733,38734,38735,38738],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,38736,38737],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[5179,38740,38741,38746],{},[724,38742,38743,38745],{},[883,38744,5465],{}," Intuice — proč zákon platí",[120,38747,38748,38754],{},[123,38749,38750,38753],{},[38,38751,38752],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,38755,38756,38759],{},[38,38757,38758],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,38761,38762,38763,38776,38777,38790,38791,38817,38818,38844,38845,1878,38871,38874,38875,1882],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,38764,38766],{"className":38765},[886],[888,38767,38768],{"xmlns":890},[892,38769,38770,38774],{},[895,38771,38772],{},[898,38773,2675],{},[902,38775,2675],{"encoding":904}," se vynáší na svislou osu, množství ",[883,38778,38780],{"className":38779},[886],[888,38781,38782],{"xmlns":890},[892,38783,38784,38788],{},[895,38785,38786],{},[898,38787,1690],{},[902,38789,1690],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,38792,38794],{"className":38793},[886],[888,38795,38796],{"xmlns":890},[892,38797,38798,38814],{},[895,38799,38800,38802,38804,38806,38812],{},[1651,38801,2261],{"stretchy":1653},[1692,38803,1741],{},[1651,38805,1661],{"separator":1660},[1686,38807,38808,38810],{},[898,38809,2675],{},[1692,38811,1741],{},[1651,38813,2279],{"stretchy":1653},[902,38815,38816],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,38819,38821],{"className":38820},[886],[888,38822,38823],{"xmlns":890},[892,38824,38825,38841],{},[895,38826,38827,38829,38835,38837,38839],{},[1651,38828,2261],{"stretchy":1653},[1686,38830,38831,38833],{},[898,38832,1690],{},[1692,38834,1741],{},[1651,38836,1661],{"separator":1660},[1692,38838,1741],{},[1651,38840,2279],{"stretchy":1653},[902,38842,38843],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,38846,38848],{"className":38847},[886],[888,38849,38850],{"xmlns":890},[892,38851,38852,38868],{},[895,38853,38854,38856,38858,38860,38866],{},[1651,38855,1654],{"stretchy":1653},[1692,38857,1741],{},[1651,38859,1661],{"separator":1660},[1686,38861,38862,38864],{},[898,38863,2675],{},[1692,38865,1741],{},[1651,38867,1667],{"stretchy":1653},[902,38869,38870],{"encoding":904},"(0, P_0)",[38,38872,38873],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,38876,38877],{},"konvexní",[724,38879,38880],{},[614,38881,38882,38883,38905,38906,5197,38931,1882],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,38884,38886],{"className":38885},[886],[888,38887,38888],{"xmlns":890},[892,38889,38890,38902],{},[895,38891,38892,38894,38896,38898,38900],{},[1651,38893,1654],{"stretchy":1653},[898,38895,1690],{},[1651,38897,1661],{"separator":1660},[898,38899,2675],{},[1651,38901,1667],{"stretchy":1653},[902,38903,38904],{"encoding":904},"(Q, P)"," — klesající, konvexní, procházející body ",[883,38907,38909],{"className":38908},[886],[888,38910,38911],{"xmlns":890},[892,38912,38913,38929],{},[895,38914,38915,38917,38919,38921,38927],{},[1651,38916,2261],{"stretchy":1653},[1692,38918,1741],{},[1651,38920,1661],{"separator":1660},[1686,38922,38923,38925],{},[898,38924,2675],{},[1692,38926,1741],{},[1651,38928,2279],{"stretchy":1653},[902,38930,38816],{"encoding":904},[883,38932,38934],{"className":38933},[886],[888,38935,38936],{"xmlns":890},[892,38937,38938,38954],{},[895,38939,38940,38942,38948,38950,38952],{},[1651,38941,2261],{"stretchy":1653},[1686,38943,38944,38946],{},[898,38945,1690],{},[1692,38947,1741],{},[1651,38949,1661],{"separator":1660},[1692,38951,1741],{},[1651,38953,2279],{"stretchy":1653},[902,38955,38843],{"encoding":904},[38561,38957,38959],{"id":38958},"lineární-model-poptávky","Lineární model poptávky",[724,38961,38962],{},"Nejjednodušší závislostí je",[883,38964,38966],{"className":38965},[886],[888,38967,38968],{"xmlns":890,"display":29279},[892,38969,38970,39019],{},[21967,38971,38972],{"width":29284},[21972,38973,38974,38976,39012,39014],{},[21975,38975],{"width":29289},[21975,38977,38978],{},[895,38979,38980,38982,38984,38986,38988,38990,38992,38994,38996,38998,39000,39002,39004,39006,39008,39010],{},[898,38981,2675],{},[1651,38983,1738],{},[898,38985,207],{},[898,38987,1690],{},[1651,38989,1839],{},[898,38991,2268],{},[1651,38993,1661],{"separator":1660},[7185,38995],{"width":7187},[898,38997,207],{},[1651,38999,2319],{},[1692,39001,1741],{},[1651,39003,1661],{"separator":1660},[1843,39005,3631],{},[898,39007,2268],{},[1651,39009,2390],{},[1692,39011,13758],{},[21975,39013],{"width":29289},[21975,39015,39016],{},[1843,39017,39018],{},"(2.4)",[902,39020,39021],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,39023,39024,39025,22807,39061,5197,39085,9344,39111,39133,39134,1882],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,39026,39028],{"className":39027},[886],[888,39029,39030],{"xmlns":890},[892,39031,39032,39058],{},[895,39033,39034,39036,39038,39046,39048,39050],{},[898,39035,1690],{},[1651,39037,1738],{},[2938,39039,39040],{"scriptlevel":1741,"displaystyle":1653},[2446,39041,39042,39044],{},[1692,39043,1694],{},[898,39045,207],{},[898,39047,2675],{},[1651,39049,2181],{},[2938,39051,39052],{"scriptlevel":1741,"displaystyle":1653},[2446,39053,39054,39056],{},[898,39055,2268],{},[898,39057,207],{},[902,39059,39060],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,39062,39064],{"className":39063},[886],[888,39065,39066],{"xmlns":890},[892,39067,39068,39082],{},[895,39069,39070,39078,39080],{},[2938,39071,39072],{"scriptlevel":1741,"displaystyle":1653},[2446,39073,39074,39076],{},[1692,39075,1694],{},[898,39077,207],{},[1651,39079,2319],{},[1692,39081,1741],{},[902,39083,39084],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,39086,39088],{"className":39087},[886],[888,39089,39090],{"xmlns":890},[892,39091,39092,39108],{},[895,39093,39094,39096,39104,39106],{},[1651,39095,2181],{},[2938,39097,39098],{"scriptlevel":1741,"displaystyle":1653},[2446,39099,39100,39102],{},[898,39101,2268],{},[898,39103,207],{},[1651,39105,2390],{},[1692,39107,1741],{},[902,39109,39110],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,39112,39114],{"className":39113},[886],[888,39115,39116],{"xmlns":890},[892,39117,39118,39130],{},[895,39119,39120,39122,39124,39126,39128],{},[1651,39121,1654],{"stretchy":1653},[1692,39123,1741],{},[1651,39125,1661],{"separator":1660},[898,39127,2268],{},[1651,39129,1667],{"stretchy":1653},[902,39131,39132],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,39135,39136],{},"nedokonalé konkurenci",[39138,39139,39141],"h5",{"id":39140},"příklad-21","Příklad 2.1",[724,39143,39144,39147,39148,1882],{},[38,39145,39146],{},"Zadání:"," Lineární poptávka ",[883,39149,39151],{"className":39150},[886],[888,39152,39153],{"xmlns":890},[892,39154,39155,39171],{},[895,39156,39157,39159,39161,39163,39165,39167,39169],{},[898,39158,2675],{},[1651,39160,1738],{},[1651,39162,2181],{},[1692,39164,1703],{},[898,39166,1690],{},[1651,39168,1839],{},[1692,39170,4452],{},[902,39172,39173],{"encoding":904},"P = -2Q + 60",[724,39175,39176,39179,39180,39202,39203,1882],{},[38,39177,39178],{},"Řešení:"," Reálné cenové rozpětí je ",[883,39181,39183],{"className":39182},[886],[888,39184,39185],{"xmlns":890},[892,39186,39187,39199],{},[895,39188,39189,39191,39193,39195,39197],{},[1651,39190,1654],{"stretchy":1653},[1692,39192,1741],{},[1651,39194,1661],{"separator":1660},[1692,39196,4452],{},[1651,39198,1667],{"stretchy":1653},[902,39200,39201],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,39204,39206],{"className":39205},[886],[888,39207,39208],{"xmlns":890},[892,39209,39210,39233],{},[895,39211,39212,39214,39216,39218,39226,39228,39230],{},[898,39213,1690],{},[1651,39215,1738],{},[1651,39217,2181],{},[2938,39219,39220],{"scriptlevel":1741,"displaystyle":1653},[2446,39221,39222,39224],{},[1692,39223,1694],{},[1692,39225,1703],{},[898,39227,2675],{},[1651,39229,1839],{},[1692,39231,39232],{},"30",[902,39234,39235],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,39237,39238,39261],{},[19,39239,39240],{},[22,39241,39242,39257,39259],{},[25,39243,39244],{},[883,39245,39247],{"className":39246},[886],[888,39248,39249],{"xmlns":890},[892,39250,39251,39255],{},[895,39252,39253],{},[898,39254,2675],{},[902,39256,2675],{"encoding":904},[25,39258,6518],{},[25,39260,10340],{},[30,39262,39263],{},[22,39264,39265,39280,39282],{},[35,39266,39267],{},[883,39268,39270],{"className":39269},[886],[888,39271,39272],{"xmlns":890},[892,39273,39274,39278],{},[895,39275,39276],{},[898,39277,1690],{},[902,39279,1690],{"encoding":904},[35,39281,4190],{},[35,39283,10340],{},[724,39285,39286],{},[614,39287,39288,39289,5197,39311,1882],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,39290,39292],{"className":39291},[886],[888,39293,39294],{"xmlns":890},[892,39295,39296,39308],{},[895,39297,39298,39300,39302,39304,39306],{},[1651,39299,2261],{"stretchy":1653},[1692,39301,1741],{},[1651,39303,1661],{"separator":1660},[898,39305,2268],{},[1651,39307,2279],{"stretchy":1653},[902,39309,39310],{"encoding":904},"[0, b]",[883,39312,39314],{"className":39313},[886],[888,39315,39316],{"xmlns":890},[892,39317,39318,39336],{},[895,39319,39320,39322,39324,39326,39328,39330,39332,39334],{},[1651,39321,2261],{"stretchy":1653},[1651,39323,2181],{},[898,39325,2268],{},[898,39327,5981],{"mathvariant":1910},[898,39329,207],{},[1651,39331,1661],{"separator":1660},[1692,39333,1741],{},[1651,39335,2279],{"stretchy":1653},[902,39337,39338],{"encoding":904},"[-b\u002Fa, 0]",[38561,39340,39342],{"id":39341},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,39344,39345,39346,39363],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,39347,39349],{"className":39348},[886],[888,39350,39351],{"xmlns":890},[892,39352,39353,39361],{},[895,39354,39355],{},[2115,39356,39357,39359],{},[898,39358,2675],{},[1651,39360,2668],{},[902,39362,5711],{"encoding":904},", je funkce poptávky konstantní:",[883,39365,39367],{"className":39366},[886],[888,39368,39369],{"xmlns":890,"display":29279},[892,39370,39371,39385],{},[895,39372,39373,39375,39377,39383],{},[898,39374,2675],{},[1651,39376,1738],{},[2115,39378,39379,39381],{},[898,39380,2675],{},[1651,39382,2668],{},[898,39384,1882],{"mathvariant":1910},[902,39386,39387],{"encoding":904},"P = P^*.",[724,39389,39390],{},[614,39391,39392,39393,39414,39415,1882],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,39394,39396],{"className":39395},[886],[888,39397,39398],{"xmlns":890},[892,39399,39400,39412],{},[895,39401,39402,39404,39406,39408,39410],{},[1651,39403,1654],{"stretchy":1653},[898,39405,1690],{},[1651,39407,1661],{"separator":1660},[898,39409,2675],{},[1651,39411,1667],{"stretchy":1653},[902,39413,38904],{"encoding":904}," na úrovni ",[883,39416,39418],{"className":39417},[886],[888,39419,39420],{"xmlns":890},[892,39421,39422,39434],{},[895,39423,39424,39426,39428],{},[898,39425,2675],{},[1651,39427,1738],{},[2115,39429,39430,39432],{},[898,39431,2675],{},[1651,39433,2668],{},[902,39435,5664],{"encoding":904},[38561,39437,39439],{"id":39438},"giffenův-statek","Giffenův statek",[724,39441,39442,39443,39445,39446,39448,39449,1882],{},"Existují zboží, u nichž je křivka poptávky ",[38,39444,14955],{}," — tzv. ",[38,39447,39439],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,39450,39451],{},"podřadnému zboží",[39138,39453,39455],{"id":39454},"příklad-22","Příklad 2.2",[724,39457,39458,39461,39462,39480,39481,39503,39504,39522,39523,39541,39542,39565],{},[38,39459,39460],{},"Zadání a popis:"," Křivka ",[883,39463,39465],{"className":39464},[886],[888,39466,39467],{"xmlns":890},[892,39468,39469,39477],{},[895,39470,39471],{},[1686,39472,39473,39475],{},[898,39474,2047],{},[1692,39476,1694],{},[902,39478,39479],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,39482,39484],{"className":39483},[886],[888,39485,39486],{"xmlns":890},[892,39487,39488,39500],{},[895,39489,39490,39492,39494,39496,39498],{},[1651,39491,1654],{"stretchy":1653},[1692,39493,1741],{},[1651,39495,1661],{"separator":1660},[1692,39497,37457],{},[1651,39499,1667],{"stretchy":1653},[902,39501,39502],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,39505,39507],{"className":39506},[886],[888,39508,39509],{"xmlns":890},[892,39510,39511,39519],{},[895,39512,39513],{},[1686,39514,39515,39517],{},[898,39516,1690],{},[1692,39518,1741],{},[902,39520,39521],{"encoding":904},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[883,39524,39526],{"className":39525},[886],[888,39527,39528],{"xmlns":890},[892,39529,39530,39538],{},[895,39531,39532],{},[1686,39533,39534,39536],{},[898,39535,2047],{},[1692,39537,1703],{},[902,39539,39540],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,39543,39545],{"className":39544},[886],[888,39546,39547],{"xmlns":890},[892,39548,39549,39562],{},[895,39550,39551,39553,39555,39557,39560],{},[1651,39552,2261],{"stretchy":1653},[1692,39554,1741],{},[1651,39556,1661],{"separator":1660},[1692,39558,39559],{},"21",[1651,39561,2279],{"stretchy":1653},[902,39563,39564],{"encoding":904},"[0, 21]"," centů.",[198,39567,39569],{"id":39568},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,39571,39572,39573,1793],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,39574,39576],{"className":39575},[886],[888,39577,39578],{"xmlns":890},[892,39579,39580,39584],{},[895,39581,39582],{},[898,39583,2665],{},[902,39585,2665],{"encoding":904},[883,39587,39589],{"className":39588},[886],[888,39590,39591],{"xmlns":890,"display":29279},[892,39592,39593,39624],{},[21967,39594,39595],{"width":29284},[21972,39596,39597,39599,39617,39619],{},[21975,39598],{"width":29289},[21975,39600,39601],{},[895,39602,39603,39605,39607,39609,39611,39613,39615],{},[898,39604,1690],{},[1651,39606,1738],{},[898,39608,5561],{},[1651,39610,1654],{"stretchy":1653},[898,39612,2665],{},[1651,39614,1667],{"stretchy":1653},[898,39616,1882],{"mathvariant":1910},[21975,39618],{"width":29289},[21975,39620,39621],{},[1843,39622,39623],{},"(2.5)",[902,39625,39626],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,39628,39629,39630,39633,39634,39637],{},"Funkce se nazývá ",[38,39631,39632],{},"Engelova",", její graf ",[38,39635,39636],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,39639,39640,39772],{},[123,39641,39642,8322,39645,39658,39659,39672,39673,39690,39691],{},[38,39643,39644],{},"Normální (superior) zboží",[883,39646,39648],{"className":39647},[886],[888,39649,39650],{"xmlns":890},[892,39651,39652,39656],{},[895,39653,39654],{},[898,39655,1690],{},[902,39657,1690],{"encoding":904}," roste s ",[883,39660,39662],{"className":39661},[886],[888,39663,39664],{"xmlns":890},[892,39665,39666,39670],{},[895,39667,39668],{},[898,39669,2665],{},[902,39671,2665],{"encoding":904},", nepřesáhne hodnotu ",[883,39674,39676],{"className":39675},[886],[888,39677,39678],{"xmlns":890},[892,39679,39680,39688],{},[895,39681,39682],{},[1686,39683,39684,39686],{},[898,39685,1690],{},[1692,39687,1741],{},[902,39689,39521],{"encoding":904},":\n",[120,39692,39693,39725],{},[123,39694,39695,39698,39699,39702,39703,1882],{},[38,39696,39697],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,39700,39701],{},"konkávní"," křivka, autonomní spotřeba ",[883,39704,39706],{"className":39705},[886],[888,39707,39708],{"xmlns":890},[892,39709,39710,39722],{},[895,39711,39712,39718,39720],{},[1686,39713,39714,39716],{},[898,39715,1690],{},[1692,39717,1694],{},[1651,39719,2390],{},[1692,39721,1741],{},[902,39723,39724],{"encoding":904},"Q_1 > 0",[123,39726,39727,39730,39731,39749,39750,39752,39753,3246,39770,1882],{},[38,39728,39729],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,39732,39734],{"className":39733},[886],[888,39735,39736],{"xmlns":890},[892,39737,39738,39746],{},[895,39739,39740],{},[1686,39741,39742,39744],{},[898,39743,2665],{},[1692,39745,1694],{},[902,39747,39748],{"encoding":904},"Y_1",", křivka je nejprve ",[38,39751,38877],{}," a od ",[883,39754,39756],{"className":39755},[886],[888,39757,39758],{"xmlns":890},[892,39759,39760,39768],{},[895,39761,39762],{},[1686,39763,39764,39766],{},[898,39765,2665],{},[1692,39767,1694],{},[902,39769,39748],{"encoding":904},[38,39771,39701],{},[123,39773,39774,39777,39778,39796],{},[38,39775,39776],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,39779,39781],{"className":39780},[886],[888,39782,39783],{"xmlns":890},[892,39784,39785,39793],{},[895,39786,39787],{},[1686,39788,39789,39791],{},[898,39790,2665],{},[1692,39792,1741],{},[902,39794,39795],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,39798,39799,39800,39803,39804,5230],{},"Mírou citlivosti je ",[614,39801,39802],{},"důchodová elasticita"," (viz ",[207,39805,5210],{"className":39806,"dataFsResolvedFilePath":848,"href":849},[210],[724,39808,39809],{},[614,39810,39811],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[38561,39813,39815],{"id":39814},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[5179,39817,39818,39889,39932],{},[724,39819,39820,39822,39823,3246,39826,3246,39839,6976,39841,39854,39855,39858,39859,1882],{},[883,39821,5719],{}," Pozor — nezbytné ≠ podřadné\n",[38,39824,39825],{},"Nezbytné zboží:",[883,39827,39829],{"className":39828},[886],[888,39830,39831],{"xmlns":890},[892,39832,39833,39837],{},[895,39834,39835],{},[898,39836,1690],{},[902,39838,1690],{"encoding":904},[38,39840,8629],{},[883,39842,39844],{"className":39843},[886],[888,39845,39846],{"xmlns":890},[892,39847,39848,39852],{},[895,39849,39850],{},[898,39851,2665],{},[902,39853,2665],{"encoding":904},", ale ",[38,39856,39857],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,39860,39862],{"className":39861},[886],[888,39863,39864],{"xmlns":890},[892,39865,39866,39886],{},[895,39867,39868,39874,39876,39878,39880,39882,39884],{},[1686,39869,39870,39872],{},[898,39871,5561],{},[898,39873,2665],{},[1651,39875,7813],{},[1651,39877,1654],{"stretchy":1653},[1692,39879,1741],{},[1651,39881,1661],{"separator":1660},[1692,39883,1694],{},[1651,39885,1667],{"stretchy":1653},[902,39887,39888],{"encoding":904},"E_Y \\in (0, 1)",[724,39890,39891,3246,39894,3246,39907,39909,39910,1882],{},[38,39892,39893],{},"Podřadné zboží:",[883,39895,39897],{"className":39896},[886],[888,39898,39899],{"xmlns":890},[892,39900,39901,39905],{},[895,39902,39903],{},[898,39904,1690],{},[902,39906,1690],{"encoding":904},[38,39908,8649],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,39911,39913],{"className":39912},[886],[888,39914,39915],{"xmlns":890},[892,39916,39917,39929],{},[895,39918,39919,39925,39927],{},[1686,39920,39921,39923],{},[898,39922,5561],{},[898,39924,2665],{},[1651,39926,2319],{},[1692,39928,1741],{},[902,39930,39931],{"encoding":904},"E_Y \u003C 0",[724,39933,39934,39935,1882],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,39936,39937],{},"méně kusů, ne jen proporčně méně",[724,39939,39940,39943,39944,39947],{},[38,39941,39942],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,39945,39946],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,39949,39950],{},[1756,39951],{"alt":39952,"className":39953,"src":39954},"imek-engelovy-krivky-3typy",[210,1760],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[39138,39956,39958],{"id":39957},"české-příklady","České příklady",[16,39960,39961,39971],{},[19,39962,39963],{},[22,39964,39965,39968],{},[25,39966,39967],{},"Podřadné",[25,39969,39970],{},"Nahradí se za",[30,39972,39973,39981,39989,39997,40005,40013,40021,40029],{},[22,39974,39975,39978],{},[35,39976,39977],{},"Instantní polévky, ramen",[35,39979,39980],{},"Čerstvé jídlo, restaurace",[22,39982,39983,39986],{},[35,39984,39985],{},"MHD (autobus, tramvaj)",[35,39987,39988],{},"Vlastní auto, Uber, taxi",[22,39990,39991,39994],{},[35,39992,39993],{},"Mražené polotovary, pizza z mrazáku",[35,39995,39996],{},"Čerstvé suroviny, hotovky",[22,39998,39999,40002],{},[35,40000,40001],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,40003,40004],{},"Značkové produkty",[22,40006,40007,40010],{},[35,40008,40009],{},"Paštika Májka, obyčejný měkký salám",[35,40011,40012],{},"Kvalitní uzeniny, šunka od kosti",[22,40014,40015,40018],{},[35,40016,40017],{},"Second hand oblečení",[35,40019,40020],{},"Nové oblečení, značky",[22,40022,40023,40026],{},[35,40024,40025],{},"Krabicové víno, nejlevnější pivo",[35,40027,40028],{},"Lahvové víno, řemeslná piva",[22,40030,40031,40034],{},[35,40032,40033],{},"Ojetá auta nižších tříd",[35,40035,40036],{},"Nová auta, prémiové značky",[5179,40038,40039],{},[724,40040,40041,40043,40044,40047],{},[883,40042,5879],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,40045,40046],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,40049,40050,40053,40054,11325,40057,40079,40080,11325,40083,40104,40105,40123,40124,40127],{},[38,40051,40052],{},"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 ",[38,40055,40056],{},"luxus",[883,40058,40060],{"className":40059},[886],[888,40061,40062],{"xmlns":890},[892,40063,40064,40076],{},[895,40065,40066,40072,40074],{},[1686,40067,40068,40070],{},[898,40069,5561],{},[898,40071,2665],{},[1651,40073,2390],{},[1692,40075,1694],{},[902,40077,40078],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,40081,40082],{},"podřadné",[883,40084,40086],{"className":40085},[886],[888,40087,40088],{"xmlns":890},[892,40089,40090,40102],{},[895,40091,40092,40098,40100],{},[1686,40093,40094,40096],{},[898,40095,5561],{},[898,40097,2665],{},[1651,40099,2319],{},[1692,40101,1741],{},[902,40103,39931],{"encoding":904},"). Proto je ",[883,40106,40108],{"className":40107},[886],[888,40109,40110],{"xmlns":890},[892,40111,40112,40120],{},[895,40113,40114],{},[1686,40115,40116,40118],{},[898,40117,5561],{},[898,40119,2665],{},[902,40121,40122],{"encoding":904},"E_Y"," vždy ",[38,40125,40126],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,40129,40130,40131,40133],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,40132,39439],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,40135,40137,40138,1667],{"id":40136},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,40139,40140],{},"shift of demand",[724,40142,40143,40144,40162,40163,40180,40181,40194,40195,4016,40208,40230,40231,40248,40249,40275,40276,40279],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,40145,40147],{"className":40146},[886],[888,40148,40149],{"xmlns":890},[892,40150,40151,40159],{},[895,40152,40153],{},[1686,40154,40155,40157],{},[898,40156,2675],{},[1692,40158,1741],{},[902,40160,40161],{"encoding":904},"P_0"," odpovídá množství ",[883,40164,40166],{"className":40165},[886],[888,40167,40168],{"xmlns":890},[892,40169,40170,40178],{},[895,40171,40172],{},[1686,40173,40174,40176],{},[898,40175,1690],{},[1692,40177,1741],{},[902,40179,39521],{"encoding":904}," na křivce ",[883,40182,40184],{"className":40183},[886],[888,40185,40186],{"xmlns":890},[892,40187,40188,40192],{},[895,40189,40190],{},[898,40191,2047],{},[902,40193,2047],{"encoding":904},"; vzroste-li důchod z ",[883,40196,40198],{"className":40197},[886],[888,40199,40200],{"xmlns":890},[892,40201,40202,40206],{},[895,40203,40204],{},[898,40205,2665],{},[902,40207,2665],{"encoding":904},[883,40209,40211],{"className":40210},[886],[888,40212,40213],{"xmlns":890},[892,40214,40215,40227],{},[895,40216,40217,40223,40225],{},[1686,40218,40219,40221],{},[898,40220,2665],{},[1692,40222,1694],{},[1651,40224,2390],{},[898,40226,2665],{},[902,40228,40229],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,40232,40234],{"className":40233},[886],[888,40235,40236],{"xmlns":890},[892,40237,40238,40246],{},[895,40239,40240],{},[1686,40241,40242,40244],{},[898,40243,2675],{},[1692,40245,1741],{},[902,40247,40161],{"encoding":904}," odpovídá vyšší ",[883,40250,40252],{"className":40251},[886],[888,40253,40254],{"xmlns":890},[892,40255,40256,40272],{},[895,40257,40258,40264,40266],{},[1686,40259,40260,40262],{},[898,40261,1690],{},[1692,40263,1694],{},[1651,40265,2390],{},[1686,40267,40268,40270],{},[898,40269,1690],{},[1692,40271,1741],{},[902,40273,40274],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,40277,40278],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,40281,40282],{},[1756,40283],{"alt":40284,"className":40285,"src":40286},"imek-posun-vs-pohyb-po-krivce",[210,1760],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,40288,40289],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,40291,40292],{},[614,40293,40294,40295,15309,40325,40346],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,40296,40298],{"className":40297},[886],[888,40299,40300],{"xmlns":890},[892,40301,40302,40322],{},[895,40303,40304,40310,40312,40314,40316],{},[1686,40305,40306,40308],{},[898,40307,2047],{},[1692,40309,1703],{},[1651,40311,1661],{"separator":1660},[898,40313,2047],{},[1651,40315,1661],{"separator":1660},[1686,40317,40318,40320],{},[898,40319,2047],{},[1692,40321,1694],{},[902,40323,40324],{"encoding":904},"D_2, D, D_1",[883,40326,40328],{"className":40327},[886],[888,40329,40330],{"xmlns":890},[892,40331,40332,40344],{},[895,40333,40334,40336,40338,40340,40342],{},[1651,40335,1654],{"stretchy":1653},[898,40337,1690],{},[1651,40339,1661],{"separator":1660},[898,40341,2675],{},[1651,40343,1667],{"stretchy":1653},[902,40345,38904],{"encoding":904},", šipky naznačují posuny.",[39138,40348,40350],{"id":40349},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,40352,40353,40355,40356,40379,40380,40397,40398,40415,40416,1882],{},[38,40354,39146],{}," Poptávce ",[883,40357,40359],{"className":40358},[886],[888,40360,40361],{"xmlns":890},[892,40362,40363,40377],{},[895,40364,40365,40367,40369,40371,40373,40375],{},[898,40366,2675],{},[1651,40368,1738],{},[898,40370,2047],{},[1651,40372,1654],{"stretchy":1653},[898,40374,1690],{},[1651,40376,1667],{"stretchy":1653},[902,40378,5947],{"encoding":904}," odpovídá ceně ",[883,40381,40383],{"className":40382},[886],[888,40384,40385],{"xmlns":890},[892,40386,40387,40395],{},[895,40388,40389],{},[1686,40390,40391,40393],{},[898,40392,2675],{},[1692,40394,1741],{},[902,40396,40161],{"encoding":904}," množství ",[883,40399,40401],{"className":40400},[886],[888,40402,40403],{"xmlns":890},[892,40404,40405,40413],{},[895,40406,40407],{},[1686,40408,40409,40411],{},[898,40410,1690],{},[1692,40412,1741],{},[902,40414,39521],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,40417,40419],{"className":40418},[886],[888,40420,40421],{"xmlns":890},[892,40422,40423,40427],{},[895,40424,40425],{},[898,40426,4104],{},[902,40428,4104],{"encoding":904},[724,40430,40431,40433,40434,40451,40452,40474],{},[38,40432,39178],{}," Kupující nakupuje množství ",[883,40435,40437],{"className":40436},[886],[888,40438,40439],{"xmlns":890},[892,40440,40441,40449],{},[895,40442,40443],{},[1686,40444,40445,40447],{},[898,40446,1690],{},[1692,40448,1694],{},[902,40450,30215],{"encoding":904},", které odpovídá ceně ",[883,40453,40455],{"className":40454},[886],[888,40456,40457],{"xmlns":890},[892,40458,40459,40471],{},[895,40460,40461,40467,40469],{},[1686,40462,40463,40465],{},[898,40464,2675],{},[1692,40466,1741],{},[1651,40468,1839],{},[898,40470,4104],{},[902,40472,40473],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,40476,40478],{"className":40477},[886],[888,40479,40480],{"xmlns":890,"display":29279},[892,40481,40482,40516],{},[895,40483,40484,40486,40488,40494,40496,40498,40500,40502,40504,40506,40508,40510,40512,40514],{},[898,40485,2675],{},[1651,40487,1738],{},[1686,40489,40490,40492],{},[898,40491,2047],{},[1692,40493,1694],{},[1651,40495,1654],{"stretchy":1653},[898,40497,1690],{},[1651,40499,1667],{"stretchy":1653},[1651,40501,1738],{},[898,40503,2047],{},[1651,40505,1654],{"stretchy":1653},[898,40507,1690],{},[1651,40509,1667],{"stretchy":1653},[1651,40511,2181],{},[898,40513,4104],{},[1651,40515,1661],{"separator":1660},[902,40517,40518],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,40520,40521,40522,1882],{},"tj. dojde k ",[38,40523,40524],{},"posunu poptávky doleva",[724,40526,40527],{},[614,40528,40529,40530,40551,40552,1343,40569,1343,40582,40603,40604,5197,40621,1882],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,40531,40533],{"className":40532},[886],[888,40534,40535],{"xmlns":890},[892,40536,40537,40549],{},[895,40538,40539,40541,40543,40545,40547],{},[1651,40540,1654],{"stretchy":1653},[898,40542,1690],{},[1651,40544,1661],{"separator":1660},[898,40546,2675],{},[1651,40548,1667],{"stretchy":1653},[902,40550,38904],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,40553,40555],{"className":40554},[886],[888,40556,40557],{"xmlns":890},[892,40558,40559,40567],{},[895,40560,40561],{},[1686,40562,40563,40565],{},[898,40564,2675],{},[1692,40566,1741],{},[902,40568,40161],{"encoding":904},[883,40570,40572],{"className":40571},[886],[888,40573,40574],{"xmlns":890},[892,40575,40576,40580],{},[895,40577,40578],{},[898,40579,4104],{},[902,40581,4104],{"encoding":904},[883,40583,40585],{"className":40584},[886],[888,40586,40587],{"xmlns":890},[892,40588,40589,40601],{},[895,40590,40591,40597,40599],{},[1686,40592,40593,40595],{},[898,40594,2675],{},[1692,40596,1741],{},[1651,40598,1839],{},[898,40600,4104],{},[902,40602,40473],{"encoding":904},"; na vodorovné ",[883,40605,40607],{"className":40606},[886],[888,40608,40609],{"xmlns":890},[892,40610,40611,40619],{},[895,40612,40613],{},[1686,40614,40615,40617],{},[898,40616,1690],{},[1692,40618,1694],{},[902,40620,30215],{"encoding":904},[883,40622,40624],{"className":40623},[886],[888,40625,40626],{"xmlns":890},[892,40627,40628,40636],{},[895,40629,40630],{},[1686,40631,40632,40634],{},[898,40633,1690],{},[1692,40635,1741],{},[902,40637,39521],{"encoding":904},[198,40639,40641],{"id":40640},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,40643,40644],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,40646,40648],{"className":40647},[886],[888,40649,40650],{"xmlns":890,"display":29279},[892,40651,40652,40837],{},[21967,40653,40654],{"width":29284},[21972,40655,40656,40658,40830,40832],{},[21975,40657],{"width":29289},[21975,40659,40660],{},[21967,40661,40662,40746],{"rowspacing":21969,"columnalign":21970,"columnspacing":1911},[21972,40663,40664,40674],{},[21975,40665,40666],{},[2938,40667,40668],{"scriptlevel":1741,"displaystyle":1660},[1686,40669,40670,40672],{},[898,40671,1690],{},[1692,40673,1694],{},[21975,40675,40676],{},[2938,40677,40678],{"scriptlevel":1741,"displaystyle":1660},[895,40679,40680,40682,40684,40690,40692,40698,40700,40706,40708,40710,40716,40718,40724,40730,40732,40738,40744],{},[895,40681],{},[1651,40683,1738],{},[1686,40685,40686,40688],{},[898,40687,2047],{},[1692,40689,1694],{},[1651,40691,1654],{"stretchy":1653},[1686,40693,40694,40696],{},[898,40695,2675],{},[1692,40697,1694],{},[1651,40699,1661],{"separator":1660},[1686,40701,40702,40704],{},[898,40703,2675],{},[1692,40705,1703],{},[1651,40707,1667],{"stretchy":1653},[1651,40709,1738],{},[1686,40711,40712,40714],{},[898,40713,207],{},[1692,40715,1694],{},[1651,40717,1839],{},[1686,40719,40720,40722],{},[898,40721,2268],{},[1692,40723,1694],{},[1686,40725,40726,40728],{},[898,40727,2675],{},[1692,40729,1694],{},[1651,40731,1839],{},[1686,40733,40734,40736],{},[898,40735,3490],{},[1692,40737,1694],{},[1686,40739,40740,40742],{},[898,40741,2675],{},[1692,40743,1703],{},[1651,40745,1661],{"separator":1660},[21972,40747,40748,40758],{},[21975,40749,40750],{},[2938,40751,40752],{"scriptlevel":1741,"displaystyle":1660},[1686,40753,40754,40756],{},[898,40755,1690],{},[1692,40757,1703],{},[21975,40759,40760],{},[2938,40761,40762],{"scriptlevel":1741,"displaystyle":1660},[895,40763,40764,40766,40768,40774,40776,40782,40784,40790,40792,40794,40800,40802,40808,40814,40816,40822,40828],{},[895,40765],{},[1651,40767,1738],{},[1686,40769,40770,40772],{},[898,40771,2047],{},[1692,40773,1703],{},[1651,40775,1654],{"stretchy":1653},[1686,40777,40778,40780],{},[898,40779,2675],{},[1692,40781,1694],{},[1651,40783,1661],{"separator":1660},[1686,40785,40786,40788],{},[898,40787,2675],{},[1692,40789,1703],{},[1651,40791,1667],{"stretchy":1653},[1651,40793,1738],{},[1686,40795,40796,40798],{},[898,40797,207],{},[1692,40799,1703],{},[1651,40801,1839],{},[1686,40803,40804,40806],{},[898,40805,2268],{},[1692,40807,1703],{},[1686,40809,40810,40812],{},[898,40811,2675],{},[1692,40813,1694],{},[1651,40815,1839],{},[1686,40817,40818,40820],{},[898,40819,3490],{},[1692,40821,1703],{},[1686,40823,40824,40826],{},[898,40825,2675],{},[1692,40827,1703],{},[898,40829,1882],{"mathvariant":1910},[21975,40831],{"width":29289},[21975,40833,40834],{},[1843,40835,40836],{},"(2.6)",[902,40838,40839],{"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}",[38561,40841,40843],{"id":40842},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,40845,40846,40893,40940],{},[123,40847,40848,1343,40870,40892],{},[883,40849,40851],{"className":40850},[886],[888,40852,40853],{"xmlns":890},[892,40854,40855,40867],{},[895,40856,40857,40863,40865],{},[1686,40858,40859,40861],{},[898,40860,207],{},[1692,40862,1694],{},[1651,40864,2390],{},[1692,40866,1741],{},[902,40868,40869],{"encoding":904},"a_1 > 0",[883,40871,40873],{"className":40872},[886],[888,40874,40875],{"xmlns":890},[892,40876,40877,40889],{},[895,40878,40879,40885,40887],{},[1686,40880,40881,40883],{},[898,40882,207],{},[1692,40884,1703],{},[1651,40886,2390],{},[1692,40888,1741],{},[902,40890,40891],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,40894,40895,1343,40917,40939],{},[883,40896,40898],{"className":40897},[886],[888,40899,40900],{"xmlns":890},[892,40901,40902,40914],{},[895,40903,40904,40910,40912],{},[1686,40905,40906,40908],{},[898,40907,2268],{},[1692,40909,1694],{},[1651,40911,2319],{},[1692,40913,1741],{},[902,40915,40916],{"encoding":904},"b_1 \u003C 0",[883,40918,40920],{"className":40919},[886],[888,40921,40922],{"xmlns":890},[892,40923,40924,40936],{},[895,40925,40926,40932,40934],{},[1686,40927,40928,40930],{},[898,40929,3490],{},[1692,40931,1703],{},[1651,40933,2319],{},[1692,40935,1741],{},[902,40937,40938],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,40941,40942,40943,1343,40960,40978,40979],{},"zkřížené koeficienty ",[883,40944,40946],{"className":40945},[886],[888,40947,40948],{"xmlns":890},[892,40949,40950,40958],{},[895,40951,40952],{},[1686,40953,40954,40956],{},[898,40955,3490],{},[1692,40957,1694],{},[902,40959,31012],{"encoding":904},[883,40961,40963],{"className":40962},[886],[888,40964,40965],{"xmlns":890},[892,40966,40967,40975],{},[895,40968,40969],{},[1686,40970,40971,40973],{},[898,40972,2268],{},[1692,40974,1703],{},[902,40976,40977],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,40980,40981,41031],{},[123,40982,40983,40986,40987,1343,41009,1661],{},[38,40984,40985],{},"substituty"," (máslo vs. margarín): ",[883,40988,40990],{"className":40989},[886],[888,40991,40992],{"xmlns":890},[892,40993,40994,41006],{},[895,40995,40996,41002,41004],{},[1686,40997,40998,41000],{},[898,40999,3490],{},[1692,41001,1694],{},[1651,41003,2390],{},[1692,41005,1741],{},[902,41007,41008],{"encoding":904},"c_1 > 0",[883,41010,41012],{"className":41011},[886],[888,41013,41014],{"xmlns":890},[892,41015,41016,41028],{},[895,41017,41018,41024,41026],{},[1686,41019,41020,41022],{},[898,41021,2268],{},[1692,41023,1703],{},[1651,41025,2390],{},[1692,41027,1741],{},[902,41029,41030],{"encoding":904},"b_2 > 0",[123,41032,41033,41036,41037,1343,41059,1882],{},[38,41034,41035],{},"komplementy"," (auto vs. benzín): ",[883,41038,41040],{"className":41039},[886],[888,41041,41042],{"xmlns":890},[892,41043,41044,41056],{},[895,41045,41046,41052,41054],{},[1686,41047,41048,41050],{},[898,41049,3490],{},[1692,41051,1694],{},[1651,41053,2319],{},[1692,41055,1741],{},[902,41057,41058],{"encoding":904},"c_1 \u003C 0",[883,41060,41062],{"className":41061},[886],[888,41063,41064],{"xmlns":890},[892,41065,41066,41078],{},[895,41067,41068,41074,41076],{},[1686,41069,41070,41072],{},[898,41071,2268],{},[1692,41073,1703],{},[1651,41075,2319],{},[1692,41077,1741],{},[902,41079,41080],{"encoding":904},"b_2 \u003C 0",[724,41082,41083],{},"Schematicky:",[724,41085,41086,41089],{},[38,41087,41088],{},"Substituty",[883,41090,41092],{"className":41091},[886],[888,41093,41094],{"xmlns":890},[892,41095,41096,41235],{},[895,41097,41098,41104,41106,41121,41123,41143,41145,41165,41167,41169,41175,41177,41191,41193,41213,41215],{},[1686,41099,41100,41102],{},[898,41101,1690],{},[1692,41103,1694],{},[1651,41105,1738],{},[898,41107,41108],{},[41109,41110,41111,41119],"munder",{},[1651,41112,41113],{},[1686,41114,41115,41117],{},[898,41116,207],{},[1692,41118,1694],{},[1651,41120,1839],{"lspace":1911,"rspace":1911},[1651,41122,1839],{},[898,41124,41125],{},[41109,41126,41127,41141],{},[1651,41128,41129,41135],{},[1686,41130,41131,41133],{},[898,41132,2268],{},[1692,41134,1694],{},[1686,41136,41137,41139],{},[898,41138,2675],{},[1692,41140,1694],{},[1651,41142,2181],{"lspace":1911,"rspace":1911},[1651,41144,1839],{},[898,41146,41147],{},[41109,41148,41149,41163],{},[1651,41150,41151,41157],{},[1686,41152,41153,41155],{},[898,41154,3490],{},[1692,41156,1694],{},[1686,41158,41159,41161],{},[898,41160,2675],{},[1692,41162,1703],{},[1651,41164,1839],{"lspace":1911,"rspace":1911},[1651,41166,1661],{"separator":1660},[7185,41168],{"width":7187},[1686,41170,41171,41173],{},[898,41172,1690],{},[1692,41174,1703],{},[1651,41176,1738],{},[898,41178,41179],{},[41109,41180,41181,41189],{},[1651,41182,41183],{},[1686,41184,41185,41187],{},[898,41186,207],{},[1692,41188,1703],{},[1651,41190,1839],{"lspace":1911,"rspace":1911},[1651,41192,1839],{},[898,41194,41195],{},[41109,41196,41197,41211],{},[1651,41198,41199,41205],{},[1686,41200,41201,41203],{},[898,41202,2268],{},[1692,41204,1703],{},[1686,41206,41207,41209],{},[898,41208,2675],{},[1692,41210,1694],{},[1651,41212,1839],{"lspace":1911,"rspace":1911},[1651,41214,1839],{},[898,41216,41217],{},[41109,41218,41219,41233],{},[1651,41220,41221,41227],{},[1686,41222,41223,41225],{},[898,41224,3490],{},[1692,41226,1703],{},[1686,41228,41229,41231],{},[898,41230,2675],{},[1692,41232,1703],{},[1651,41234,2181],{"lspace":1911,"rspace":1911},[902,41236,41237],{"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}",[724,41239,41240,41243],{},[38,41241,41242],{},"Komplementy",[883,41244,41246],{"className":41245},[886],[888,41247,41248],{"xmlns":890},[892,41249,41250,41388],{},[895,41251,41252,41258,41260,41274,41276,41296,41298,41318,41320,41322,41328,41330,41344,41346,41366,41368],{},[1686,41253,41254,41256],{},[898,41255,1690],{},[1692,41257,1694],{},[1651,41259,1738],{},[898,41261,41262],{},[41109,41263,41264,41272],{},[1651,41265,41266],{},[1686,41267,41268,41270],{},[898,41269,207],{},[1692,41271,1694],{},[1651,41273,1839],{"lspace":1911,"rspace":1911},[1651,41275,1839],{},[898,41277,41278],{},[41109,41279,41280,41294],{},[1651,41281,41282,41288],{},[1686,41283,41284,41286],{},[898,41285,2268],{},[1692,41287,1694],{},[1686,41289,41290,41292],{},[898,41291,2675],{},[1692,41293,1694],{},[1651,41295,2181],{"lspace":1911,"rspace":1911},[1651,41297,1839],{},[898,41299,41300],{},[41109,41301,41302,41316],{},[1651,41303,41304,41310],{},[1686,41305,41306,41308],{},[898,41307,3490],{},[1692,41309,1694],{},[1686,41311,41312,41314],{},[898,41313,2675],{},[1692,41315,1703],{},[1651,41317,2181],{"lspace":1911,"rspace":1911},[1651,41319,1661],{"separator":1660},[7185,41321],{"width":7187},[1686,41323,41324,41326],{},[898,41325,1690],{},[1692,41327,1703],{},[1651,41329,1738],{},[898,41331,41332],{},[41109,41333,41334,41342],{},[1651,41335,41336],{},[1686,41337,41338,41340],{},[898,41339,207],{},[1692,41341,1703],{},[1651,41343,1839],{"lspace":1911,"rspace":1911},[1651,41345,1839],{},[898,41347,41348],{},[41109,41349,41350,41364],{},[1651,41351,41352,41358],{},[1686,41353,41354,41356],{},[898,41355,2268],{},[1692,41357,1703],{},[1686,41359,41360,41362],{},[898,41361,2675],{},[1692,41363,1694],{},[1651,41365,2181],{"lspace":1911,"rspace":1911},[1651,41367,1839],{},[898,41369,41370],{},[41109,41371,41372,41386],{},[1651,41373,41374,41380],{},[1686,41375,41376,41378],{},[898,41377,3490],{},[1692,41379,1703],{},[1686,41381,41382,41384],{},[898,41383,2675],{},[1692,41385,1703],{},[1651,41387,2181],{"lspace":1911,"rspace":1911},[902,41389,41390],{"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}",[38183,41392],{},[115,41394,14423],{"id":37992},[5179,41396,41397],{},[724,41398,41399,41401,41402,38207,41415,38221,41428,41431,41432,6976,41456,41474],{},[883,41400,5465],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,41403,41405],{"className":41404},[886],[888,41406,41407],{"xmlns":890},[892,41408,41409,41413],{},[895,41410,41411],{},[898,41412,1690],{},[902,41414,1690],{"encoding":904},[883,41416,41418],{"className":41417},[886],[888,41419,41420],{"xmlns":890},[892,41421,41422,41426],{},[895,41423,41424],{},[898,41425,2675],{},[902,41427,2675],{"encoding":904},[38,41429,41430],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,41433,41435],{"className":41434},[886],[888,41436,41437],{"xmlns":890},[892,41438,41439,41453],{},[895,41440,41441,41443,41445,41447,41449,41451],{},[898,41442,2675],{},[1651,41444,1738],{},[898,41446,3490],{},[898,41448,1690],{},[1651,41450,1839],{},[898,41452,3542],{},[902,41454,41455],{"encoding":904},"P = cQ + d",[883,41457,41459],{"className":41458},[886],[888,41460,41461],{"xmlns":890},[892,41462,41463,41471],{},[895,41464,41465,41467,41469],{},[898,41466,3490],{},[1651,41468,2390],{},[1692,41470,1741],{},[902,41472,41473],{"encoding":904},"c > 0"," je standardní aproximací.",[198,41476,38277],{"id":41477},"obecný-vícefaktorový-model-1",[724,41479,41480,11325,41483,41486,41487,41500,41501,38109,41514,38123,41527,41540,41541,41555,41556,38152,41569,41582],{},[38,41481,41482],{},"Nabízené množství",[614,41484,41485],{},"quantity supplied",") závisí na ceně ",[883,41488,41490],{"className":41489},[886],[888,41491,41492],{"xmlns":890},[892,41493,41494,41498],{},[895,41495,41496],{},[898,41497,2675],{},[902,41499,2675],{"encoding":904},", cenách výrobních faktorů (práce ",[883,41502,41504],{"className":41503},[886],[888,41505,41506],{"xmlns":890},[892,41507,41508,41512],{},[895,41509,41510],{},[898,41511,1807],{},[902,41513,1807],{"encoding":904},[883,41515,41517],{"className":41516},[886],[888,41518,41519],{"xmlns":890},[892,41520,41521,41525],{},[895,41522,41523],{},[898,41524,11101],{},[902,41526,11101],{"encoding":904},[883,41528,41530],{"className":41529},[886],[888,41531,41532],{"xmlns":890},[892,41533,41534,41538],{},[895,41535,41536],{},[898,41537,5561],{},[902,41539,5561],{"encoding":904},"), očekávání ",[883,41542,41544],{"className":41543},[886],[888,41545,41546],{"xmlns":890},[892,41547,41548,41553],{},[895,41549,41550],{},[898,41551,41552],{},"V",[902,41554,41552],{"encoding":904},", počtu výrobců ",[883,41557,41559],{"className":41558},[886],[888,41560,41561],{"xmlns":890},[892,41562,41563,41567],{},[895,41564,41565],{},[898,41566,38149],{},[902,41568,38149],{"encoding":904},[883,41570,41572],{"className":41571},[886],[888,41573,41574],{"xmlns":890},[892,41575,41576,41580],{},[895,41577,41578],{},[898,41579,38164],{},[902,41581,38164],{"encoding":904}," a dalších:",[883,41584,41586],{"className":41585},[886],[888,41587,41588],{"xmlns":890,"display":29279},[892,41589,41590,41649],{},[21967,41591,41592],{"width":29284},[21972,41593,41594,41596,41642,41644],{},[21975,41595],{"width":29289},[21975,41597,41598],{},[895,41599,41600,41602,41604,41606,41608,41610,41612,41614,41616,41618,41620,41622,41624,41626,41628,41630,41632,41634,41636,41638,41640],{},[898,41601,1690],{},[1651,41603,1738],{},[898,41605,3004],{},[1651,41607,1654],{"stretchy":1653},[898,41609,2675],{},[1651,41611,1661],{"separator":1660},[898,41613,1807],{},[1651,41615,1661],{"separator":1660},[898,41617,11101],{},[1651,41619,1661],{"separator":1660},[898,41621,5561],{},[1651,41623,1661],{"separator":1660},[898,41625,41552],{},[1651,41627,1661],{"separator":1660},[898,41629,38149],{},[1651,41631,1661],{"separator":1660},[898,41633,38164],{},[1651,41635,1661],{"separator":1660},[1651,41637,10949],{},[1651,41639,1667],{"stretchy":1653},[898,41641,1882],{"mathvariant":1910},[21975,41643],{"width":29289},[21975,41645,41646],{},[1843,41647,41648],{},"(2.7)",[902,41650,41651],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,41653,39629,41654,11325,41657,41660],{},[38,41655,41656],{},"funkce nabídky",[614,41658,41659],{},"supply function",") v širším slova smyslu.",[198,41662,41664],{"id":41663},"jednofaktorový-model","Jednofaktorový model",[724,41666,41667],{},"V nejpřirozenějším jednofaktorovém modelu",[883,41669,41671],{"className":41670},[886],[888,41672,41673],{"xmlns":890,"display":29279},[892,41674,41675,41726],{},[21967,41676,41677],{"width":29284},[21972,41678,41679,41681,41719,41721],{},[21975,41680],{"width":29289},[21975,41682,41683],{},[895,41684,41685,41687,41689,41691,41693,41695,41697,41699,41701,41703,41705,41707,41709,41711,41713,41715,41717],{},[898,41686,1690],{},[1651,41688,1738],{},[898,41690,3004],{},[1651,41692,1654],{"stretchy":1653},[898,41694,2675],{},[1651,41696,1667],{"stretchy":1653},[1651,41698,1661],{"separator":1660},[7185,41700],{"width":7187},[1843,41702,38630],{},[7185,41704],{"width":7187},[898,41706,2675],{},[1651,41708,1738],{},[898,41710,3004],{},[1651,41712,1654],{"stretchy":1653},[898,41714,1690],{},[1651,41716,1667],{"stretchy":1653},[898,41718,1882],{"mathvariant":1910},[21975,41720],{"width":29289},[21975,41722,41723],{},[1843,41724,41725],{},"(2.8)",[902,41727,41728],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,41730,41731,41732,11325,41735,5230],{},"Graf je ",[38,41733,41734],{},"křivka nabídky",[614,41736,41737],{},"supply curve",[38561,41739,41741],{"id":41740},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[5179,41743,41744],{},[724,41745,41746],{},[38,41747,38676,41748,41761,41762,38731],{},[883,41749,41751],{"className":41750},[886],[888,41752,41753],{"xmlns":890},[892,41754,41755,41759],{},[895,41756,41757],{},[898,41758,2675],{},[902,41760,2675],{"encoding":904},", pak nabízené množství ",[883,41763,41765],{"className":41764},[886],[888,41766,41767],{"xmlns":890},[892,41768,41769,41773],{},[895,41770,41771],{},[898,41772,1690],{},[902,41774,1690],{"encoding":904},[724,41776,41777,41778,41803,41804,41834,41835,41852],{},"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 ",[883,41779,41781],{"className":41780},[886],[888,41782,41783],{"xmlns":890},[892,41784,41785,41801],{},[895,41786,41787,41789,41791,41793,41799],{},[1651,41788,2261],{"stretchy":1653},[1692,41790,1741],{},[1651,41792,1661],{"separator":1660},[1686,41794,41795,41797],{},[898,41796,2675],{},[1692,41798,1741],{},[1651,41800,2279],{"stretchy":1653},[902,41802,38816],{"encoding":904}," na svislé ose (případně z ",[883,41805,41807],{"className":41806},[886],[888,41808,41809],{"xmlns":890},[892,41810,41811,41831],{},[895,41812,41813,41815,41821,41823,41829],{},[1651,41814,2261],{"stretchy":1653},[1686,41816,41817,41819],{},[898,41818,1690],{},[1692,41820,1694],{},[1651,41822,1661],{"separator":1660},[1686,41824,41825,41827],{},[898,41826,2675],{},[1692,41828,1694],{},[1651,41830,2279],{"stretchy":1653},[902,41832,41833],{"encoding":904},"[Q_1, P_1]","), kde ",[883,41836,41838],{"className":41837},[886],[888,41839,41840],{"xmlns":890},[892,41841,41842,41850],{},[895,41843,41844],{},[1686,41845,41846,41848],{},[898,41847,2675],{},[1692,41849,1741],{},[902,41851,40161],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,41854,41855],{},[614,41856,41857,41858,5036,41871,1882],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,41859,41861],{"className":41860},[886],[888,41862,41863],{"xmlns":890},[892,41864,41865,41869],{},[895,41866,41867],{},[898,41868,3004],{},[902,41870,3004],{"encoding":904},[883,41872,41874],{"className":41873},[886],[888,41875,41876],{"xmlns":890},[892,41877,41878,41890],{},[895,41879,41880,41882,41884,41886,41888],{},[1651,41881,1654],{"stretchy":1653},[898,41883,1690],{},[1651,41885,1661],{"separator":1660},[898,41887,2675],{},[1651,41889,1667],{"stretchy":1653},[902,41891,38904],{"encoding":904},[38561,41893,41895],{"id":41894},"lineární-model-nabídky","Lineární model nabídky",[883,41897,41899],{"className":41898},[886],[888,41900,41901],{"xmlns":890,"display":29279},[892,41902,41903,41942],{},[21967,41904,41905],{"width":29284},[21972,41906,41907,41909,41935,41937],{},[21975,41908],{"width":29289},[21975,41910,41911],{},[895,41912,41913,41915,41917,41919,41921,41923,41925,41927,41929,41931,41933],{},[898,41914,2675],{},[1651,41916,1738],{},[898,41918,3490],{},[898,41920,1690],{},[1651,41922,1839],{},[898,41924,3542],{},[1651,41926,1661],{"separator":1660},[7185,41928],{"width":7187},[898,41930,3490],{},[1651,41932,2390],{},[1692,41934,13758],{},[21975,41936],{"width":29289},[21975,41938,41939],{},[1843,41940,41941],{},"(2.9)",[902,41943,41944],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,41946,41947,41948,41984,41985,41998],{},"Alternativně ",[883,41949,41951],{"className":41950},[886],[888,41952,41953],{"xmlns":890},[892,41954,41955,41981],{},[895,41956,41957,41959,41961,41969,41971,41973],{},[898,41958,1690],{},[1651,41960,1738],{},[2938,41962,41963],{"scriptlevel":1741,"displaystyle":1653},[2446,41964,41965,41967],{},[1692,41966,1694],{},[898,41968,3490],{},[898,41970,2675],{},[1651,41972,2181],{},[2938,41974,41975],{"scriptlevel":1741,"displaystyle":1653},[2446,41976,41977,41979],{},[898,41978,3542],{},[898,41980,3490],{},[902,41982,41983],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,41986,41988],{"className":41987},[886],[888,41989,41990],{"xmlns":890},[892,41991,41992,41996],{},[895,41993,41994],{},[898,41995,2675],{},[902,41997,2675],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[39138,42000,42002],{"id":42001},"příklad-25","Příklad 2.5",[724,42004,42005,42007,42008,1882],{},[38,42006,39146],{}," Lineární nabídka ",[883,42009,42011],{"className":42010},[886],[888,42012,42013],{"xmlns":890},[892,42014,42015,42029],{},[895,42016,42017,42019,42021,42023,42025,42027],{},[898,42018,2675],{},[1651,42020,1738],{},[1692,42022,6316],{},[898,42024,1690],{},[1651,42026,1839],{},[1692,42028,6311],{},[902,42030,42031],{"encoding":904},"P = 0{,}5Q + 25",[724,42033,42034,42036,42037,1882],{},[38,42035,39178],{}," Alternativní tvar ",[883,42038,42040],{"className":42039},[886],[888,42041,42042],{"xmlns":890},[892,42043,42044,42058],{},[895,42045,42046,42048,42050,42052,42054,42056],{},[898,42047,1690],{},[1651,42049,1738],{},[1692,42051,1703],{},[898,42053,2675],{},[1651,42055,2181],{},[1692,42057,4446],{},[902,42059,42060],{"encoding":904},"Q = 2P - 50",[16,42062,42063,42088],{},[19,42064,42065],{},[22,42066,42067,42082,42084,42086],{},[25,42068,42069],{},[883,42070,42072],{"className":42071},[886],[888,42073,42074],{"xmlns":890},[892,42075,42076,42080],{},[895,42077,42078],{},[898,42079,2675],{},[902,42081,2675],{"encoding":904},[25,42083,39232],{},[25,42085,16336],{},[25,42087,6518],{},[30,42089,42090],{},[22,42091,42092,42107,42109,42111],{},[35,42093,42094],{},[883,42095,42097],{"className":42096},[886],[888,42098,42099],{"xmlns":890},[892,42100,42101,42105],{},[895,42102,42103],{},[898,42104,1690],{},[902,42106,1690],{"encoding":904},[35,42108,4190],{},[35,42110,10340],{},[35,42112,39232],{},[198,42114,42116,42117,1667],{"id":42115},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,42118,42119],{},"shift of supply",[724,42121,42122,42123,42126,42127,42144,42145,42170,42171,1882],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,42124,42125],{},"doprava",": při stejné ceně ",[883,42128,42130],{"className":42129},[886],[888,42131,42132],{"xmlns":890},[892,42133,42134,42142],{},[895,42135,42136],{},[1686,42137,42138,42140],{},[898,42139,2675],{},[1692,42141,1741],{},[902,42143,40161],{"encoding":904}," vyrobí výrobce větší ",[883,42146,42148],{"className":42147},[886],[888,42149,42150],{"xmlns":890},[892,42151,42152,42168],{},[895,42153,42154,42160,42162],{},[1686,42155,42156,42158],{},[898,42157,1690],{},[1692,42159,1694],{},[1651,42161,2390],{},[1686,42163,42164,42166],{},[898,42165,1690],{},[1692,42167,1741],{},[902,42169,40274],{"encoding":904},"); zdražení vstupů posune křivku ",[38,42172,42173],{},"doleva",[724,42175,42176],{},[614,42177,42178,42179,42192,42193,42211,42212,42230,42231,1882],{},"Obrázek 2.11: Původní ",[883,42180,42182],{"className":42181},[886],[888,42183,42184],{"xmlns":890},[892,42185,42186,42190],{},[895,42187,42188],{},[898,42189,3004],{},[902,42191,3004],{"encoding":904},", posunuté ",[883,42194,42196],{"className":42195},[886],[888,42197,42198],{"xmlns":890},[892,42199,42200,42208],{},[895,42201,42202],{},[1686,42203,42204,42206],{},[898,42205,3004],{},[1692,42207,1694],{},[902,42209,42210],{"encoding":904},"S_1"," (doprava) a ",[883,42213,42215],{"className":42214},[886],[888,42216,42217],{"xmlns":890},[892,42218,42219,42227],{},[895,42220,42221],{},[1686,42222,42223,42225],{},[898,42224,3004],{},[1692,42226,1703],{},[902,42228,42229],{"encoding":904},"S_2"," (doleva) v ",[883,42232,42234],{"className":42233},[886],[888,42235,42236],{"xmlns":890},[892,42237,42238,42250],{},[895,42239,42240,42242,42244,42246,42248],{},[1651,42241,1654],{"stretchy":1653},[898,42243,1690],{},[1651,42245,1661],{"separator":1660},[898,42247,2675],{},[1651,42249,1667],{"stretchy":1653},[902,42251,38904],{"encoding":904},[39138,42253,42255],{"id":42254},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,42257,42258,42260,42261,42285,42286,1882],{},[38,42259,39146],{}," Nabídka ",[883,42262,42264],{"className":42263},[886],[888,42265,42266],{"xmlns":890},[892,42267,42268,42282],{},[895,42269,42270,42272,42274,42276,42278,42280],{},[898,42271,2675],{},[1651,42273,1738],{},[898,42275,3004],{},[1651,42277,1654],{"stretchy":1653},[898,42279,1690],{},[1651,42281,1667],{"stretchy":1653},[902,42283,42284],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,42287,42289],{"className":42288},[886],[888,42290,42291],{"xmlns":890},[892,42292,42293,42297],{},[895,42294,42295],{},[898,42296,4104],{},[902,42298,4104],{"encoding":904},[724,42300,42301,42303,42304,42317,42318,42336,42337,42365],{},[38,42302,39178],{}," Spotřebitel zaplatí ",[883,42305,42307],{"className":42306},[886],[888,42308,42309],{"xmlns":890},[892,42310,42311,42315],{},[895,42312,42313],{},[898,42314,2675],{},[902,42316,2675],{"encoding":904},", výrobce obdrží ",[883,42319,42321],{"className":42320},[886],[888,42322,42323],{"xmlns":890},[892,42324,42325,42333],{},[895,42326,42327,42329,42331],{},[898,42328,2675],{},[1651,42330,2181],{},[898,42332,4104],{},[902,42334,42335],{"encoding":904},"P - T",". Z podmínky ",[883,42338,42340],{"className":42339},[886],[888,42341,42342],{"xmlns":890},[892,42343,42344,42362],{},[895,42345,42346,42348,42350,42352,42354,42356,42358,42360],{},[898,42347,2675],{},[1651,42349,2181],{},[898,42351,4104],{},[1651,42353,1738],{},[898,42355,3004],{},[1651,42357,1654],{"stretchy":1653},[898,42359,1690],{},[1651,42361,1667],{"stretchy":1653},[902,42363,42364],{"encoding":904},"P - T = S(Q)"," plyne",[883,42367,42369],{"className":42368},[886],[888,42370,42371],{"xmlns":890,"display":29279},[892,42372,42373,42407],{},[895,42374,42375,42377,42379,42385,42387,42389,42391,42393,42395,42397,42399,42401,42403,42405],{},[898,42376,2675],{},[1651,42378,1738],{},[1686,42380,42381,42383],{},[898,42382,3004],{},[1692,42384,1694],{},[1651,42386,1654],{"stretchy":1653},[898,42388,1690],{},[1651,42390,1667],{"stretchy":1653},[1651,42392,1738],{},[898,42394,3004],{},[1651,42396,1654],{"stretchy":1653},[898,42398,1690],{},[1651,42400,1667],{"stretchy":1653},[1651,42402,1839],{},[898,42404,4104],{},[898,42406,1882],{"mathvariant":1910},[902,42408,42409],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,42411,42412,42413,42426,42427,3246,42440,42443,42444,5197,42464,1878,42482,1882],{},"Křivka ",[883,42414,42416],{"className":42415},[886],[888,42417,42418],{"xmlns":890},[892,42419,42420,42424],{},[895,42421,42422],{},[898,42423,3004],{},[902,42425,3004],{"encoding":904}," se tedy posune o ",[883,42428,42430],{"className":42429},[886],[888,42431,42432],{"xmlns":890},[892,42433,42434,42438],{},[895,42435,42436],{},[898,42437,4104],{},[902,42439,4104],{"encoding":904},[38,42441,42442],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,42445,42447],{"className":42446},[886],[888,42448,42449],{"xmlns":890},[892,42450,42451,42461],{},[895,42452,42453,42455,42457,42459],{},[898,42454,2675],{},[1651,42456,1738],{},[1692,42458,1703],{},[898,42460,1690],{},[902,42462,42463],{"encoding":904},"P = 2Q",[883,42465,42467],{"className":42466},[886],[888,42468,42469],{"xmlns":890},[892,42470,42471,42479],{},[895,42472,42473,42475,42477],{},[898,42474,4104],{},[1651,42476,1738],{},[1692,42478,3581],{},[902,42480,42481],{"encoding":904},"T = 6",[883,42483,42485],{"className":42484},[886],[888,42486,42487],{"xmlns":890},[892,42488,42489,42511],{},[895,42490,42491,42497,42499,42501,42503,42505,42507,42509],{},[1686,42492,42493,42495],{},[898,42494,3004],{},[1692,42496,1694],{},[1651,42498,1793],{},[898,42500,2675],{},[1651,42502,1738],{},[1692,42504,1703],{},[898,42506,1690],{},[1651,42508,1839],{},[1692,42510,3581],{},[902,42512,42513],{"encoding":904},"S_1: P = 2Q + 6",[724,42515,42516],{},[614,42517,42518,42519,42532],{},"Obrázek 2.12: Posun nabídky o ",[883,42520,42522],{"className":42521},[886],[888,42523,42524],{"xmlns":890},[892,42525,42526,42530],{},[895,42527,42528],{},[898,42529,4104],{},[902,42531,4104],{"encoding":904}," svisle nahoru.",[38183,42534],{},[115,42536,42538],{"id":42537},"tržní-rovnováha","Tržní rovnováha",[5179,42540,42541],{},[724,42542,42543,42545,42546,3246,42549,42581,42582,1343,42605,42628,42629,42632,42633,42646],{},[883,42544,5465],{}," TL;DR\nV ",[38,42547,42548],{},"rovnovážném bodě",[883,42550,42552],{"className":42551},[886],[888,42553,42554],{"xmlns":890},[892,42555,42556,42578],{},[895,42557,42558,42560,42562,42568,42570,42576],{},[898,42559,5561],{},[1651,42561,2261],{"stretchy":1653},[2115,42563,42564,42566],{},[898,42565,1690],{},[898,42567,5561],{},[1651,42569,1661],{"separator":1660},[2115,42571,42572,42574],{},[898,42573,2675],{},[898,42575,5561],{},[1651,42577,2279],{"stretchy":1653},[902,42579,42580],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,42583,42585],{"className":42584},[886],[888,42586,42587],{"xmlns":890},[892,42588,42589,42603],{},[895,42590,42591,42593,42595,42597,42599,42601],{},[898,42592,2675],{},[1651,42594,1738],{},[898,42596,2047],{},[1651,42598,1654],{"stretchy":1653},[898,42600,1690],{},[1651,42602,1667],{"stretchy":1653},[902,42604,5947],{"encoding":904},[883,42606,42608],{"className":42607},[886],[888,42609,42610],{"xmlns":890},[892,42611,42612,42626],{},[895,42613,42614,42616,42618,42620,42622,42624],{},[898,42615,2675],{},[1651,42617,1738],{},[898,42619,3004],{},[1651,42621,1654],{"stretchy":1653},[898,42623,1690],{},[1651,42625,1667],{"stretchy":1653},[902,42627,42284],{"encoding":904},". Čtyři ",[38,42630,42631],{},"pravidla komparativní statiky"," popisují, jak se ",[883,42634,42636],{"className":42635},[886],[888,42637,42638],{"xmlns":890},[892,42639,42640,42644],{},[895,42641,42642],{},[898,42643,5561],{},[902,42645,5561],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,42648,42650],{"id":42649},"definice","Definice",[724,42652,42653,11325,42655,42658,42659,3246,42662,42680,42681,42712,42713,11325,42716,5230],{},[38,42654,42538],{},[614,42656,42657],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,42660,42661],{},"rovnovážné ceně",[883,42663,42665],{"className":42664},[886],[888,42666,42667],{"xmlns":890},[892,42668,42669,42677],{},[895,42670,42671],{},[2115,42672,42673,42675],{},[898,42674,2675],{},[898,42676,5561],{},[902,42678,42679],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,42682,42684],{"className":42683},[886],[888,42685,42686],{"xmlns":890},[892,42687,42688,42710],{},[895,42689,42690,42692,42694,42700,42702,42708],{},[898,42691,5561],{},[1651,42693,2261],{"stretchy":1653},[2115,42695,42696,42698],{},[898,42697,1690],{},[898,42699,5561],{},[1651,42701,1661],{"separator":1660},[2115,42703,42704,42706],{},[898,42705,2675],{},[898,42707,5561],{},[1651,42709,2279],{"stretchy":1653},[902,42711,42580],{"encoding":904}," se nazývá ",[38,42714,42715],{},"rovnovážný bod",[614,42717,42718],{},"equilibrium point",[724,42720,42721,42722,1343,42745,1882],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,42723,42725],{"className":42724},[886],[888,42726,42727],{"xmlns":890},[892,42728,42729,42743],{},[895,42730,42731,42733,42735,42737,42739,42741],{},[898,42732,2675],{},[1651,42734,1738],{},[898,42736,2047],{},[1651,42738,1654],{"stretchy":1653},[898,42740,1690],{},[1651,42742,1667],{"stretchy":1653},[902,42744,5947],{"encoding":904},[883,42746,42748],{"className":42747},[886],[888,42749,42750],{"xmlns":890},[892,42751,42752,42766],{},[895,42753,42754,42756,42758,42760,42762,42764],{},[898,42755,2675],{},[1651,42757,1738],{},[898,42759,3004],{},[1651,42761,1654],{"stretchy":1653},[898,42763,1690],{},[1651,42765,1667],{"stretchy":1653},[902,42767,42284],{"encoding":904},[724,42769,42770],{},[1756,42771],{"alt":42772,"className":42773,"src":42774},"imek-poptavka-nabidka-rovnovaha",[210,1760],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,42776,42777],{},[614,42778,42779,42780,42793,42794,15309,42807,42828,42829,1882],{},"Obrázek 2.13: Klesající ",[883,42781,42783],{"className":42782},[886],[888,42784,42785],{"xmlns":890},[892,42786,42787,42791],{},[895,42788,42789],{},[898,42790,2047],{},[902,42792,2047],{"encoding":904}," a rostoucí ",[883,42795,42797],{"className":42796},[886],[888,42798,42799],{"xmlns":890},[892,42800,42801,42805],{},[895,42802,42803],{},[898,42804,3004],{},[902,42806,3004],{"encoding":904},[883,42808,42810],{"className":42809},[886],[888,42811,42812],{"xmlns":890},[892,42813,42814,42826],{},[895,42815,42816,42818,42820,42822,42824],{},[1651,42817,1654],{"stretchy":1653},[898,42819,1690],{},[1651,42821,1661],{"separator":1660},[898,42823,2675],{},[1651,42825,1667],{"stretchy":1653},[902,42827,38904],{"encoding":904}," protínající se v ",[883,42830,42832],{"className":42831},[886],[888,42833,42834],{"xmlns":890},[892,42835,42836,42858],{},[895,42837,42838,42840,42842,42848,42850,42856],{},[898,42839,5561],{},[1651,42841,2261],{"stretchy":1653},[2115,42843,42844,42846],{},[898,42845,1690],{},[898,42847,5561],{},[1651,42849,1661],{"separator":1660},[2115,42851,42852,42854],{},[898,42853,2675],{},[898,42855,5561],{},[1651,42857,2279],{"stretchy":1653},[902,42859,42580],{"encoding":904},[198,42861,42863],{"id":42862},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,42865,42866,42868,42869,42903,42904,1882],{},[38,42867,39146],{}," Poptávka ",[883,42870,42872],{"className":42871},[886],[888,42873,42874],{"xmlns":890},[892,42875,42876,42900],{},[895,42877,42878,42880,42882,42884,42890,42892,42894,42896,42898],{},[898,42879,2675],{},[1651,42881,1738],{},[1651,42883,2181],{},[2115,42885,42886,42888],{},[898,42887,1690],{},[1692,42889,1703],{},[1651,42891,2181],{},[1692,42893,4190],{},[898,42895,1690],{},[1651,42897,1839],{},[1692,42899,10108],{},[902,42901,42902],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,42905,42907],{"className":42906},[886],[888,42908,42909],{"xmlns":890},[892,42910,42911,42933],{},[895,42912,42913,42915,42917,42923,42925,42927,42929,42931],{},[898,42914,2675],{},[1651,42916,1738],{},[2115,42918,42919,42921],{},[898,42920,1690],{},[1692,42922,1703],{},[1651,42924,1839],{},[1692,42926,24159],{},[898,42928,1690],{},[1651,42930,1839],{},[1692,42932,33759],{},[902,42934,42935],{"encoding":904},"P = Q^2 + 14Q + 22",[724,42937,42938,42940],{},[38,42939,39178],{}," Z rovnosti",[883,42942,42944],{"className":42943},[886],[888,42945,42946],{"xmlns":890,"display":29279},[892,42947,42948,42986],{},[895,42949,42950,42952,42958,42960,42962,42964,42966,42968,42970,42976,42978,42980,42982,42984],{},[1651,42951,2181],{},[2115,42953,42954,42956],{},[898,42955,1690],{},[1692,42957,1703],{},[1651,42959,2181],{},[1692,42961,4190],{},[898,42963,1690],{},[1651,42965,1839],{},[1692,42967,10108],{},[1651,42969,1738],{},[2115,42971,42972,42974],{},[898,42973,1690],{},[1692,42975,1703],{},[1651,42977,1839],{},[1692,42979,24159],{},[898,42981,1690],{},[1651,42983,1839],{},[1692,42985,33759],{},[902,42987,42988],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,42990,42991,42992,43027,43028,43061,43062,43079,43080,43093,43094,1343,43116,43153,43154,1882],{},"dostaneme ",[883,42993,42995],{"className":42994},[886],[888,42996,42997],{"xmlns":890},[892,42998,42999,43024],{},[895,43000,43001,43003,43009,43011,43014,43016,43018,43020,43022],{},[1692,43002,1703],{},[2115,43004,43005,43007],{},[898,43006,1690],{},[1692,43008,1703],{},[1651,43010,1839],{},[1692,43012,43013],{},"24",[898,43015,1690],{},[1651,43017,2181],{},[1692,43019,6924],{},[1651,43021,1738],{},[1692,43023,1741],{},[902,43025,43026],{"encoding":904},"2Q^2 + 24Q - 128 = 0",", resp. ",[883,43029,43031],{"className":43030},[886],[888,43032,43033],{"xmlns":890},[892,43034,43035,43058],{},[895,43036,43037,43043,43045,43047,43049,43051,43054,43056],{},[2115,43038,43039,43041],{},[898,43040,1690],{},[1692,43042,1703],{},[1651,43044,1839],{},[1692,43046,4828],{},[898,43048,1690],{},[1651,43050,2181],{},[1692,43052,43053],{},"64",[1651,43055,1738],{},[1692,43057,1741],{},[902,43059,43060],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,43063,43065],{"className":43064},[886],[888,43066,43067],{"xmlns":890},[892,43068,43069,43076],{},[895,43070,43071,43073],{},[1651,43072,2181],{},[1692,43074,43075],{},"16",[902,43077,43078],{"encoding":904},"-16"," (nevyhovuje) a ",[883,43081,43083],{"className":43082},[886],[888,43084,43085],{"xmlns":890},[892,43086,43087,43091],{},[895,43088,43089],{},[1692,43090,3689],{},[902,43092,3689],{"encoding":904},". Tedy ",[883,43095,43097],{"className":43096},[886],[888,43098,43099],{"xmlns":890},[892,43100,43101,43113],{},[895,43102,43103,43109,43111],{},[2115,43104,43105,43107],{},[898,43106,1690],{},[898,43108,5561],{},[1651,43110,1738],{},[1692,43112,3689],{},[902,43114,43115],{"encoding":904},"Q^E = 4",[883,43117,43119],{"className":43118},[886],[888,43120,43121],{"xmlns":890},[892,43122,43123,43150],{},[895,43124,43125,43131,43133,43135,43137,43139,43141,43143,43145,43147],{},[2115,43126,43127,43129],{},[898,43128,2675],{},[898,43130,5561],{},[1651,43132,1738],{},[1651,43134,2181],{},[1692,43136,43075],{},[1651,43138,2181],{},[1692,43140,6518],{},[1651,43142,1839],{},[1692,43144,10108],{},[1651,43146,1738],{},[1692,43148,43149],{},"94",[902,43151,43152],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,43155,43157],{"className":43156},[886],[888,43158,43159],{"xmlns":890},[892,43160,43161,43175],{},[895,43162,43163,43165,43167,43169,43171,43173],{},[898,43164,5561],{},[1651,43166,2261],{"stretchy":1653},[1692,43168,3689],{},[1651,43170,1661],{"separator":1660},[1692,43172,43149],{},[1651,43174,2279],{"stretchy":1653},[902,43176,43177],{"encoding":904},"E[4, 94]",[198,43179,43181],{"id":43180},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,43183,43184,43186],{},[38,43185,39146],{}," Poptávky a nabídky dvou zboží",[883,43188,43190],{"className":43189},[886],[888,43191,43192],{"xmlns":890,"display":29279},[892,43193,43194,43360],{},[21967,43195,43198,43286],{"rowspacing":21969,"columnalign":43196,"columnspacing":43197},"right left right left","0em 1em 0em",[21972,43199,43200,43210,43242,43252],{},[21975,43201,43202],{},[2938,43203,43204],{"scriptlevel":1741,"displaystyle":1660},[1686,43205,43206,43208],{},[898,43207,1690],{},[1692,43209,1694],{},[21975,43211,43212],{},[2938,43213,43214],{"scriptlevel":1741,"displaystyle":1660},[895,43215,43216,43218,43220,43222,43224,43226,43232,43234,43240],{},[895,43217],{},[1651,43219,1738],{},[1692,43221,6518],{},[1651,43223,2181],{},[1692,43225,3574],{},[1686,43227,43228,43230],{},[898,43229,2675],{},[1692,43231,1694],{},[1651,43233,2181],{},[1686,43235,43236,43238],{},[898,43237,2675],{},[1692,43239,1703],{},[1651,43241,1661],{"separator":1660},[21975,43243,43244],{},[2938,43245,43246],{"scriptlevel":1741,"displaystyle":1660},[1686,43247,43248,43250],{},[898,43249,1690],{},[1692,43251,1703],{},[21975,43253,43254],{},[2938,43255,43256],{"scriptlevel":1741,"displaystyle":1660},[895,43257,43258,43260,43262,43264,43266,43268,43274,43276,43278,43284],{},[895,43259],{},[1651,43261,1738],{},[1692,43263,4446],{},[1651,43265,2181],{},[1692,43267,1703],{},[1686,43269,43270,43272],{},[898,43271,2675],{},[1692,43273,1694],{},[1651,43275,2181],{},[1692,43277,3689],{},[1686,43279,43280,43282],{},[898,43281,2675],{},[1692,43283,1703],{},[1651,43285,1661],{"separator":1660},[21972,43287,43288,43298,43324,43334],{},[21975,43289,43290],{},[2938,43291,43292],{"scriptlevel":1741,"displaystyle":1660},[1686,43293,43294,43296],{},[898,43295,1690],{},[1692,43297,1694],{},[21975,43299,43300],{},[2938,43301,43302],{"scriptlevel":1741,"displaystyle":1660},[895,43303,43304,43306,43308,43310,43312,43314,43316,43322],{},[895,43305],{},[1651,43307,1738],{},[1651,43309,2181],{},[1692,43311,3521],{},[1651,43313,1839],{},[1692,43315,3689],{},[1686,43317,43318,43320],{},[898,43319,2675],{},[1692,43321,1694],{},[1651,43323,1661],{"separator":1660},[21975,43325,43326],{},[2938,43327,43328],{"scriptlevel":1741,"displaystyle":1660},[1686,43329,43330,43332],{},[898,43331,1690],{},[1692,43333,1703],{},[21975,43335,43336],{},[2938,43337,43338],{"scriptlevel":1741,"displaystyle":1660},[895,43339,43340,43342,43344,43346,43348,43350,43352,43358],{},[895,43341],{},[1651,43343,1738],{},[1651,43345,2181],{},[1692,43347,25414],{},[1651,43349,1839],{},[1692,43351,3521],{},[1686,43353,43354,43356],{},[898,43355,2675],{},[1692,43357,1703],{},[898,43359,1882],{"mathvariant":1910},[902,43361,43362],{"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}",[724,43364,43365,43367],{},[38,43366,39178],{}," Z rovností poptávek a nabídek dostaneme",[883,43369,43371],{"className":43370},[886],[888,43372,43373],{"xmlns":890,"display":29279},[892,43374,43375,43424],{},[895,43376,43377,43379,43385,43387,43393,43395,43397,43399,43401,43403,43409,43411,43413,43419,43421],{},[1692,43378,5309],{},[1686,43380,43381,43383],{},[898,43382,2675],{},[1692,43384,1694],{},[1651,43386,1839],{},[1686,43388,43389,43391],{},[898,43390,2675],{},[1692,43392,1703],{},[1651,43394,1738],{},[1692,43396,22416],{},[1651,43398,1661],{"separator":1660},[7185,43400],{"width":7187},[1692,43402,1703],{},[1686,43404,43405,43407],{},[898,43406,2675],{},[1692,43408,1694],{},[1651,43410,1839],{},[1692,43412,25414],{},[1686,43414,43415,43417],{},[898,43416,2675],{},[1692,43418,1703],{},[1651,43420,1738],{},[1692,43422,43423],{},"57.",[902,43425,43426],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,43428,43429,43430,1343,43454,43478,43479,1343,43504,43528,43529,43531],{},"Řešením je ",[883,43431,43433],{"className":43432},[886],[888,43434,43435],{"xmlns":890},[892,43436,43437,43451],{},[895,43438,43439,43447,43449],{},[1902,43440,43441,43443,43445],{},[898,43442,2675],{},[1692,43444,1694],{},[898,43446,5561],{},[1651,43448,1738],{},[1692,43450,3689],{},[902,43452,43453],{"encoding":904},"P_1^E = 4",[883,43455,43457],{"className":43456},[886],[888,43458,43459],{"xmlns":890},[892,43460,43461,43475],{},[895,43462,43463,43471,43473],{},[1902,43464,43465,43467,43469],{},[898,43466,2675],{},[1692,43468,1703],{},[898,43470,5561],{},[1651,43472,1738],{},[1692,43474,25414],{},[902,43476,43477],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,43480,43482],{"className":43481},[886],[888,43483,43484],{"xmlns":890},[892,43485,43486,43501],{},[895,43487,43488,43496,43498],{},[1902,43489,43490,43492,43494],{},[898,43491,1690],{},[1692,43493,1694],{},[898,43495,5561],{},[1651,43497,1738],{},[1692,43499,43500],{},"13",[902,43502,43503],{"encoding":904},"Q_1^E = 13",[883,43505,43507],{"className":43506},[886],[888,43508,43509],{"xmlns":890},[892,43510,43511,43525],{},[895,43512,43513,43521,43523],{},[1902,43514,43515,43517,43519],{},[898,43516,1690],{},[1692,43518,1703],{},[898,43520,5561],{},[1651,43522,1738],{},[1692,43524,24159],{},[902,43526,43527],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,43530,41035],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,43533,43535],{"id":43534},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,43537,43538,43539,43556,43557,11325,43560,5230],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,43540,43542],{"className":43541},[886],[888,43543,43544],{"xmlns":890},[892,43545,43546,43554],{},[895,43547,43548],{},[2115,43549,43550,43552],{},[898,43551,2675],{},[898,43553,5561],{},[902,43555,42679],{"encoding":904},"; mechanismus popisuje ",[38,43558,43559],{},"teorém pavučiny",[614,43561,43562],{},"cobweb model",[198,43564,43566],{"id":43565},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,43568,43569],{},[1756,43570],{"alt":43571,"className":43572,"src":43573},"imek-komparativni-statika-4pripady",[210,1760],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[5179,43575,43576,43617,43657,43697],{},[724,43577,43578,43581,43582,7497,43599,1882],{},[38,43579,43580],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,43583,43585],{"className":43584},[886],[888,43586,43587],{"xmlns":890},[892,43588,43589,43597],{},[895,43590,43591],{},[2115,43592,43593,43595],{},[898,43594,2675],{},[898,43596,5561],{},[902,43598,42679],{"encoding":904},[883,43600,43602],{"className":43601},[886],[888,43603,43604],{"xmlns":890},[892,43605,43606,43614],{},[895,43607,43608],{},[2115,43609,43610,43612],{},[898,43611,1690],{},[898,43613,5561],{},[902,43615,43616],{"encoding":904},"Q^E",[724,43618,43619,43622,43623,7497,43640,1882],{},[38,43620,43621],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,43624,43626],{"className":43625},[886],[888,43627,43628],{"xmlns":890},[892,43629,43630,43638],{},[895,43631,43632],{},[2115,43633,43634,43636],{},[898,43635,2675],{},[898,43637,5561],{},[902,43639,42679],{"encoding":904},[883,43641,43643],{"className":43642},[886],[888,43644,43645],{"xmlns":890},[892,43646,43647,43655],{},[895,43648,43649],{},[2115,43650,43651,43653],{},[898,43652,1690],{},[898,43654,5561],{},[902,43656,43616],{"encoding":904},[724,43658,43659,43662,43663,10658,43680,1882],{},[38,43660,43661],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,43664,43666],{"className":43665},[886],[888,43667,43668],{"xmlns":890},[892,43669,43670,43678],{},[895,43671,43672],{},[2115,43673,43674,43676],{},[898,43675,2675],{},[898,43677,5561],{},[902,43679,42679],{"encoding":904},[883,43681,43683],{"className":43682},[886],[888,43684,43685],{"xmlns":890},[892,43686,43687,43695],{},[895,43688,43689],{},[2115,43690,43691,43693],{},[898,43692,1690],{},[898,43694,5561],{},[902,43696,43616],{"encoding":904},[724,43698,43699,43702,43703,43720,43721,1882],{},[38,43700,43701],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,43704,43706],{"className":43705},[886],[888,43707,43708],{"xmlns":890},[892,43709,43710,43718],{},[895,43711,43712],{},[2115,43713,43714,43716],{},[898,43715,2675],{},[898,43717,5561],{},[902,43719,42679],{"encoding":904},", pokles ",[883,43722,43724],{"className":43723},[886],[888,43725,43726],{"xmlns":890},[892,43727,43728,43736],{},[895,43729,43730],{},[2115,43731,43732,43734],{},[898,43733,1690],{},[898,43735,5561],{},[902,43737,43616],{"encoding":904},[16,43739,43740,43785],{},[19,43741,43742],{},[22,43743,43744,43747,43766],{},[25,43745,43746],{},"Změna",[25,43748,43749],{},[883,43750,43752],{"className":43751},[886],[888,43753,43754],{"xmlns":890},[892,43755,43756,43764],{},[895,43757,43758],{},[2115,43759,43760,43762],{},[898,43761,2675],{},[898,43763,5561],{},[902,43765,42679],{"encoding":904},[25,43767,43768],{},[883,43769,43771],{"className":43770},[886],[888,43772,43773],{"xmlns":890},[892,43774,43775,43783],{},[895,43776,43777],{},[2115,43778,43779,43781],{},[898,43780,1690],{},[898,43782,5561],{},[902,43784,43616],{"encoding":904},[30,43786,43787,43797,43807,43816],{},[22,43788,43789,43792,43795],{},[35,43790,43791],{},"Růst poptávky",[35,43793,43794],{},"↑",[35,43796,43794],{},[22,43798,43799,43802,43805],{},[35,43800,43801],{},"Pokles poptávky",[35,43803,43804],{},"↓",[35,43806,43804],{},[22,43808,43809,43812,43814],{},[35,43810,43811],{},"Růst nabídky",[35,43813,43804],{},[35,43815,43794],{},[22,43817,43818,43821,43823],{},[35,43819,43820],{},"Pokles nabídky",[35,43822,43794],{},[35,43824,43804],{},[724,43826,43827],{},[614,43828,43829],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[38183,43831],{},[115,43833,811],{"id":43834},"zdanění-trhu",[5179,43836,43837,43926],{},[724,43838,43839,43841,43842,43855,43856,4254,43869,43872,43873,37989,43896,43921,43922,43925],{},[883,43840,5465],{}," TL;DR\nJednotková daň ",[883,43843,43845],{"className":43844},[886],[888,43846,43847],{"xmlns":890},[892,43848,43849,43853],{},[895,43850,43851],{},[898,43852,4104],{},[902,43854,4104],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,43857,43859],{"className":43858},[886],[888,43860,43861],{"xmlns":890},[892,43862,43863,43867],{},[895,43864,43865],{},[898,43866,4104],{},[902,43868,4104],{"encoding":904},[38,43870,43871],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,43874,43876],{"className":43875},[886],[888,43877,43878],{"xmlns":890},[892,43879,43880,43893],{},[895,43881,43882],{},[1686,43883,43884,43886],{},[898,43885,4104],{},[895,43887,43888,43891],{},[898,43889,43890],{},"s",[898,43892,724],{},[902,43894,43895],{"encoding":904},"T_{sp}",[883,43897,43899],{"className":43898},[886],[888,43900,43901],{"xmlns":890},[892,43902,43903,43918],{},[895,43904,43905],{},[1686,43906,43907,43909],{},[898,43908,4104],{},[895,43910,43911,43914,43916],{},[898,43912,43913],{},"v",[898,43915,1664],{},[898,43917,13339],{},[902,43919,43920],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,43923,43924],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,43927,43928],{},[614,43929,43930,43931,1882],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,43932,43934],{"className":43933,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,43936,43937,43938,43941,43942,43968,43969,43972,43973,43999,44000,44017,44018,44058,44059,5197,44072,1882],{},"Existují dvě formy zdanění — daň uložená ",[38,43939,43940],{},"výrobci"," (posun nabídky ",[883,43943,43945],{"className":43944},[886],[888,43946,43947],{"xmlns":890},[892,43948,43949,43965],{},[895,43950,43951,43957,43959,43961,43963],{},[1686,43952,43953,43955],{},[898,43954,3004],{},[1692,43956,1694],{},[1651,43958,1738],{},[898,43960,3004],{},[1651,43962,1839],{},[898,43964,4104],{},[902,43966,43967],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,43970,43971],{},"spotřebiteli"," (posun poptávky ",[883,43974,43976],{"className":43975},[886],[888,43977,43978],{"xmlns":890},[892,43979,43980,43996],{},[895,43981,43982,43988,43990,43992,43994],{},[1686,43983,43984,43986],{},[898,43985,2047],{},[1692,43987,1703],{},[1651,43989,1738],{},[898,43991,2047],{},[1651,43993,2181],{},[898,43995,4104],{},[902,43997,43998],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,44001,44003],{"className":44002},[886],[888,44004,44005],{"xmlns":890},[892,44006,44007,44015],{},[895,44008,44009],{},[2115,44010,44011,44013],{},[898,44012,1690],{},[898,44014,5561],{},[902,44016,43616],{"encoding":904}," klesá a vzniká rozklad daně ",[883,44019,44021],{"className":44020},[886],[888,44022,44023],{"xmlns":890},[892,44024,44025,44055],{},[895,44026,44027,44029,44031,44041,44043],{},[898,44028,4104],{},[1651,44030,1738],{},[1686,44032,44033,44035],{},[898,44034,4104],{},[895,44036,44037,44039],{},[898,44038,43890],{},[898,44040,724],{},[1651,44042,1839],{},[1686,44044,44045,44047],{},[898,44046,4104],{},[895,44048,44049,44051,44053],{},[898,44050,43913],{},[898,44052,1664],{},[898,44054,13339],{},[902,44056,44057],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,44060,44062],{"className":44061},[886],[888,44063,44064],{"xmlns":890},[892,44065,44066,44070],{},[895,44067,44068],{},[898,44069,2047],{},[902,44071,2047],{"encoding":904},[883,44073,44075],{"className":44074},[886],[888,44076,44077],{"xmlns":890},[892,44078,44079,44083],{},[895,44080,44081],{},[898,44082,3004],{},[902,44084,3004],{"encoding":904},[724,44086,44087,44088,44091,44092,5197,44122,44156],{},"Zásadním výsledkem kapitoly je ",[38,44089,44090],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,44093,44095],{"className":44094},[886],[888,44096,44097],{"xmlns":890},[892,44098,44099,44119],{},[895,44100,44101,44109,44111],{},[1902,44102,44103,44105,44107],{},[898,44104,1690],{},[1692,44106,1694],{},[898,44108,5561],{},[1651,44110,1738],{},[1902,44112,44113,44115,44117],{},[898,44114,1690],{},[1692,44116,1703],{},[898,44118,5561],{},[902,44120,44121],{"encoding":904},"Q_1^E = Q_2^E",[883,44123,44125],{"className":44124},[886],[888,44126,44127],{"xmlns":890},[892,44128,44129,44153],{},[895,44130,44131,44139,44141,44143,44145],{},[1902,44132,44133,44135,44137],{},[898,44134,2675],{},[1692,44136,1694],{},[898,44138,5561],{},[1651,44140,2181],{},[898,44142,4104],{},[1651,44144,1738],{},[1902,44146,44147,44149,44151],{},[898,44148,2675],{},[1692,44150,1703],{},[898,44152,5561],{},[902,44154,44155],{"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.",[724,44158,44159,44160,44163,44164,44190,44191,44219,44220,44223,44224,44227,44228,1882],{},"Podrobný výklad, Příklady ",[38,44161,44162],{},"2.9"," (daň výrobci, ",[883,44165,44167],{"className":44166},[886],[888,44168,44169],{"xmlns":890},[892,44170,44171,44187],{},[895,44172,44173,44183,44185],{},[1686,44174,44175,44177],{},[898,44176,4104],{},[895,44178,44179,44181],{},[898,44180,43890],{},[898,44182,724],{},[1651,44184,1738],{},[1692,44186,1703],{},[902,44188,44189],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,44192,44194],{"className":44193},[886],[888,44195,44196],{"xmlns":890},[892,44197,44198,44216],{},[895,44199,44200,44212,44214],{},[1686,44201,44202,44204],{},[898,44203,4104],{},[895,44205,44206,44208,44210],{},[898,44207,43913],{},[898,44209,1664],{},[898,44211,13339],{},[1651,44213,1738],{},[1692,44215,3689],{},[902,44217,44218],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,44221,44222],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,44225,44226],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,44229,43934],{"className":44230,"dataFsResolvedFilePath":809,"href":810},[210],[38183,44232],{},[115,44234,44236],{"id":44235},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[5179,44238,44239],{},[724,44240,44241,44243,44244,44247,44248,44250],{},[883,44242,5465],{}," TL;DR\nMultiplikátory jsou ",[38,44245,44246],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,44249,38173],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,44252,44254],{"id":44253},"redukovaný-tvar","Redukovaný tvar",[724,44256,44257,44258,11325,44281,1343,44299,13426,44316,11325,44339,44356,44357,44387],{},"Pro lineární model ",[883,44259,44261],{"className":44260},[886],[888,44262,44263],{"xmlns":890},[892,44264,44265,44279],{},[895,44266,44267,44269,44271,44273,44275,44277],{},[898,44268,2675],{},[1651,44270,1738],{},[898,44272,207],{},[898,44274,1690],{},[1651,44276,1839],{},[898,44278,2268],{},[902,44280,38273],{"encoding":904},[883,44282,44284],{"className":44283},[886],[888,44285,44286],{"xmlns":890},[892,44287,44288,44296],{},[895,44289,44290,44292,44294],{},[898,44291,207],{},[1651,44293,2319],{},[1692,44295,1741],{},[902,44297,44298],{"encoding":904},"a \u003C 0",[883,44300,44302],{"className":44301},[886],[888,44303,44304],{"xmlns":890},[892,44305,44306,44314],{},[895,44307,44308,44310,44312],{},[898,44309,2268],{},[1651,44311,2390],{},[1692,44313,1741],{},[902,44315,20027],{"encoding":904},[883,44317,44319],{"className":44318},[886],[888,44320,44321],{"xmlns":890},[892,44322,44323,44337],{},[895,44324,44325,44327,44329,44331,44333,44335],{},[898,44326,2675],{},[1651,44328,1738],{},[898,44330,3490],{},[898,44332,1690],{},[1651,44334,1839],{},[898,44336,3542],{},[902,44338,41455],{"encoding":904},[883,44340,44342],{"className":44341},[886],[888,44343,44344],{"xmlns":890},[892,44345,44346,44354],{},[895,44347,44348,44350,44352],{},[898,44349,3490],{},[1651,44351,2390],{},[1692,44353,1741],{},[902,44355,41473],{"encoding":904},") dává podmínka rovnováhy ",[883,44358,44360],{"className":44359},[886],[888,44361,44362],{"xmlns":890},[892,44363,44364,44384],{},[895,44365,44366,44368,44370,44372,44374,44376,44378,44380,44382],{},[898,44367,207],{},[898,44369,1690],{},[1651,44371,1839],{},[898,44373,2268],{},[1651,44375,1738],{},[898,44377,3490],{},[898,44379,1690],{},[1651,44381,1839],{},[898,44383,3542],{},[902,44385,44386],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,44389,44391],{"className":44390},[886],[888,44392,44393],{"xmlns":890,"display":29279},[892,44394,44395,44440],{},[21967,44396,44397],{"width":29284},[21972,44398,44399,44401,44433,44435],{},[21975,44400],{"width":29289},[21975,44402,44403],{},[895,44404,44405,44411,44413,44431],{},[2115,44406,44407,44409],{},[898,44408,1690],{},[898,44410,5561],{},[1651,44412,1738],{},[2446,44414,44415,44423],{},[895,44416,44417,44419,44421],{},[898,44418,2268],{},[1651,44420,2181],{},[898,44422,3542],{},[895,44424,44425,44427,44429],{},[898,44426,3490],{},[1651,44428,2181],{},[898,44430,207],{},[898,44432,1882],{"mathvariant":1910},[21975,44434],{"width":29289},[21975,44436,44437],{},[1843,44438,44439],{},"(2.10)",[902,44441,44442],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,44444,44445,44446,11325,44448,44451,44452,44469,44470,3246,44473,44499,44500,44513,44514,44532,44533,5230],{},"Vztah (2.10) je ",[38,44447,22167],{},[614,44449,44450],{},"reduced form",") pro ",[883,44453,44455],{"className":44454},[886],[888,44456,44457],{"xmlns":890},[892,44458,44459,44467],{},[895,44460,44461],{},[2115,44462,44463,44465],{},[898,44464,1690],{},[898,44466,5561],{},[902,44468,43616],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,44471,44472],{},"parametrů",[883,44474,44476],{"className":44475},[886],[888,44477,44478],{"xmlns":890},[892,44479,44480,44496],{},[895,44481,44482,44484,44486,44488,44490,44492,44494],{},[898,44483,207],{},[1651,44485,1661],{"separator":1660},[898,44487,2268],{},[1651,44489,1661],{"separator":1660},[898,44491,3490],{},[1651,44493,1661],{"separator":1660},[898,44495,3542],{},[902,44497,44498],{"encoding":904},"a, b, c, d",". Aby ",[883,44501,44503],{"className":44502},[886],[888,44504,44505],{"xmlns":890},[892,44506,44507,44511],{},[895,44508,44509],{},[898,44510,5561],{},[902,44512,5561],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,44515,44517],{"className":44516},[886],[888,44518,44519],{"xmlns":890},[892,44520,44521,44529],{},[895,44522,44523,44525,44527],{},[898,44524,2268],{},[1651,44526,2390],{},[898,44528,3542],{},[902,44530,44531],{"encoding":904},"b > d"," (neboť ",[883,44534,44536],{"className":44535},[886],[888,44537,44538],{"xmlns":890},[892,44539,44540,44552],{},[895,44541,44542,44544,44546,44548,44550],{},[898,44543,3490],{},[1651,44545,2181],{},[898,44547,207],{},[1651,44549,2390],{},[1692,44551,1741],{},[902,44553,44554],{"encoding":904},"c - a > 0",[724,44556,44557],{},[614,44558,44559,44560,44573,44574,44587,44588,19861,44601,43153,44618,44631],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,44561,44563],{"className":44562},[886],[888,44564,44565],{"xmlns":890},[892,44566,44567,44571],{},[895,44568,44569],{},[898,44570,2268],{},[902,44572,2268],{"encoding":904}," na ose ",[883,44575,44577],{"className":44576},[886],[888,44578,44579],{"xmlns":890},[892,44580,44581,44585],{},[895,44582,44583],{},[898,44584,2675],{},[902,44586,2675],{"encoding":904},") a nabídka (úsek ",[883,44589,44591],{"className":44590},[886],[888,44592,44593],{"xmlns":890},[892,44594,44595,44599],{},[895,44596,44597],{},[898,44598,3542],{},[902,44600,3542],{"encoding":904},[883,44602,44604],{"className":44603},[886],[888,44605,44606],{"xmlns":890},[892,44607,44608,44616],{},[895,44609,44610,44612,44614],{},[898,44611,2268],{},[1651,44613,2390],{},[898,44615,3542],{},[902,44617,44531],{"encoding":904},[883,44619,44621],{"className":44620},[886],[888,44622,44623],{"xmlns":890},[892,44624,44625,44629],{},[895,44626,44627],{},[898,44628,5561],{},[902,44630,5561],{"encoding":904}," v 1. kvadrantu.",[198,44633,44635],{"id":44634},"definice-multiplikátorů","Definice multiplikátorů",[724,44637,44638,44639,44664,44665,44678,44679,44692],{},"V komparativní statice jsou ",[883,44640,44642],{"className":44641},[886],[888,44643,44644],{"xmlns":890},[892,44645,44646,44662],{},[895,44647,44648,44650,44652,44654,44656,44658,44660],{},[898,44649,207],{},[1651,44651,1661],{"separator":1660},[898,44653,2268],{},[1651,44655,1661],{"separator":1660},[898,44657,3490],{},[1651,44659,1661],{"separator":1660},[898,44661,3542],{},[902,44663,44498],{"encoding":904}," exogenní proměnné a ",[883,44666,44668],{"className":44667},[886],[888,44669,44670],{"xmlns":890},[892,44671,44672,44676],{},[895,44673,44674],{},[898,44675,1690],{},[902,44677,1690],{"encoding":904}," endogenní. Přibližná změna ",[883,44680,44682],{"className":44681},[886],[888,44683,44684],{"xmlns":890},[892,44685,44686,44690],{},[895,44687,44688],{},[898,44689,1690],{},[902,44691,1690],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,44694,44696],{"className":44695},[886],[888,44697,44698],{"xmlns":890,"display":29279},[892,44699,44700,44793],{},[21967,44701,44702],{"width":29284},[21972,44703,44704,44706,44786,44788],{},[21975,44705],{"width":29289},[21975,44707,44708],{},[895,44709,44710,44712,44714,44716,44718,44720,44722,44730,44732,44734,44736,44738,44746,44748,44750,44752,44754,44762,44764,44766,44768,44770,44778,44780,44782,44784],{},[898,44711,4216],{"mathvariant":1910},[898,44713,1690],{},[1651,44715,4060],{},[898,44717,3542],{},[898,44719,1690],{},[1651,44721,1738],{},[1902,44723,44724,44726,44728],{},[898,44725,1690],{},[898,44727,207],{},[1651,44729,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1843,44731,1845],{},[898,44733,3542],{},[898,44735,207],{},[1651,44737,1839],{},[1902,44739,44740,44742,44744],{},[898,44741,1690],{},[898,44743,2268],{},[1651,44745,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1843,44747,1845],{},[898,44749,3542],{},[898,44751,2268],{},[1651,44753,1839],{},[1902,44755,44756,44758,44760],{},[898,44757,1690],{},[898,44759,3490],{},[1651,44761,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1843,44763,1845],{},[898,44765,3542],{},[898,44767,3490],{},[1651,44769,1839],{},[1902,44771,44772,44774,44776],{},[898,44773,1690],{},[898,44775,3542],{},[1651,44777,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1843,44779,1845],{},[898,44781,3542],{},[898,44783,3542],{},[898,44785,1882],{"mathvariant":1910},[21975,44787],{"width":29289},[21975,44789,44790],{},[1843,44791,44792],{},"(2.11)",[902,44794,44795],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,44797,44798,44799,44849,44850,11325,44852,4477],{},"Parciální derivace ",[883,44800,44802],{"className":44801},[886],[888,44803,44804],{"xmlns":890},[892,44805,44806,44846],{},[895,44807,44808,44816,44818,44826,44828,44836,44838],{},[1902,44809,44810,44812,44814],{},[898,44811,1690],{},[898,44813,207],{},[1651,44815,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,44817,1661],{"separator":1660},[1902,44819,44820,44822,44824],{},[898,44821,1690],{},[898,44823,2268],{},[1651,44825,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,44827,1661],{"separator":1660},[1902,44829,44830,44832,44834],{},[898,44831,1690],{},[898,44833,3490],{},[1651,44835,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,44837,1661],{"separator":1660},[1902,44839,44840,44842,44844],{},[898,44841,1690],{},[898,44843,3542],{},[1651,44845,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,44847,44848],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,44851,19190],{},[614,44853,44854],{},"multipliers",[883,44856,44858],{"className":44857},[886],[888,44859,44860],{"xmlns":890,"display":29279},[892,44861,44862,45013],{},[21967,44863,44864],{"width":29284},[21972,44865,44866,44868,45006,45008],{},[21975,44867],{"width":29289},[21975,44869,44870],{},[895,44871,44872,44880,44882,44908,44910,44912,44920,44922,44934,44936,44938,44946,44948,44950,44976,44978,44980,44988,44990,44992,45004],{},[1902,44873,44874,44876,44878],{},[898,44875,1690],{},[898,44877,207],{},[1651,44879,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,44881,1738],{},[2446,44883,44884,44892],{},[895,44885,44886,44888,44890],{},[898,44887,2268],{},[1651,44889,2181],{},[898,44891,3542],{},[895,44893,44894,44896,44898,44900,44902],{},[1651,44895,1654],{"stretchy":1653},[898,44897,3490],{},[1651,44899,2181],{},[898,44901,207],{},[2115,44903,44904,44906],{},[1651,44905,1667],{"stretchy":1653},[1692,44907,1703],{},[1651,44909,1661],{"separator":1660},[7185,44911],{"width":16582},[1902,44913,44914,44916,44918],{},[898,44915,1690],{},[898,44917,2268],{},[1651,44919,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,44921,1738],{},[2446,44923,44924,44926],{},[1692,44925,1694],{},[895,44927,44928,44930,44932],{},[898,44929,3490],{},[1651,44931,2181],{},[898,44933,207],{},[1651,44935,1661],{"separator":1660},[7185,44937],{"width":16582},[1902,44939,44940,44942,44944],{},[898,44941,1690],{},[898,44943,3490],{},[1651,44945,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,44947,1738],{},[1651,44949,2181],{},[2446,44951,44952,44960],{},[895,44953,44954,44956,44958],{},[898,44955,2268],{},[1651,44957,2181],{},[898,44959,3542],{},[895,44961,44962,44964,44966,44968,44970],{},[1651,44963,1654],{"stretchy":1653},[898,44965,3490],{},[1651,44967,2181],{},[898,44969,207],{},[2115,44971,44972,44974],{},[1651,44973,1667],{"stretchy":1653},[1692,44975,1703],{},[1651,44977,1661],{"separator":1660},[7185,44979],{"width":16582},[1902,44981,44982,44984,44986],{},[898,44983,1690],{},[898,44985,3542],{},[1651,44987,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,44989,1738],{},[1651,44991,2181],{},[2446,44993,44994,44996],{},[1692,44995,1694],{},[895,44997,44998,45000,45002],{},[898,44999,3490],{},[1651,45001,2181],{},[898,45003,207],{},[898,45005,1882],{"mathvariant":1910},[21975,45007],{"width":29289},[21975,45009,45010],{},[1843,45011,45012],{},"(2.12)",[902,45014,45015],{"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}",[198,45017,45019],{"id":45018},"znaménka-a-interpretace","Znaménka a interpretace",[724,45021,45022,45023,1343,45040,1343,45057,1343,45074,45091,45092,4477],{},"Za podmínek ",[883,45024,45026],{"className":45025},[886],[888,45027,45028],{"xmlns":890},[892,45029,45030,45038],{},[895,45031,45032,45034,45036],{},[898,45033,207],{},[1651,45035,2319],{},[1692,45037,1741],{},[902,45039,44298],{"encoding":904},[883,45041,45043],{"className":45042},[886],[888,45044,45045],{"xmlns":890},[892,45046,45047,45055],{},[895,45048,45049,45051,45053],{},[898,45050,2268],{},[1651,45052,2390],{},[1692,45054,1741],{},[902,45056,20027],{"encoding":904},[883,45058,45060],{"className":45059},[886],[888,45061,45062],{"xmlns":890},[892,45063,45064,45072],{},[895,45065,45066,45068,45070],{},[898,45067,3490],{},[1651,45069,2390],{},[1692,45071,1741],{},[902,45073,41473],{"encoding":904},[883,45075,45077],{"className":45076},[886],[888,45078,45079],{"xmlns":890},[892,45080,45081,45089],{},[895,45082,45083,45085,45087],{},[898,45084,2268],{},[1651,45086,2390],{},[898,45088,3542],{},[902,45090,44531],{"encoding":904}," platí (znaménka se ",[38,45093,45094],{},"nemění",[883,45096,45098],{"className":45097},[886],[888,45099,45100],{"xmlns":890,"display":29279},[892,45101,45102,45164],{},[895,45103,45104,45112,45114,45116,45118,45120,45128,45130,45132,45134,45136,45144,45146,45148,45150,45152,45160,45162],{},[1902,45105,45106,45108,45110],{},[898,45107,1690],{},[898,45109,207],{},[1651,45111,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,45113,2390],{},[1692,45115,1741],{},[1651,45117,1661],{"separator":1660},[7185,45119],{"width":7187},[1902,45121,45122,45124,45126],{},[898,45123,1690],{},[898,45125,2268],{},[1651,45127,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,45129,2390],{},[1692,45131,1741],{},[1651,45133,1661],{"separator":1660},[7185,45135],{"width":7187},[1902,45137,45138,45140,45142],{},[898,45139,1690],{},[898,45141,3490],{},[1651,45143,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,45145,2319],{},[1692,45147,1741],{},[1651,45149,1661],{"separator":1660},[7185,45151],{"width":7187},[1902,45153,45154,45156,45158],{},[898,45155,1690],{},[898,45157,3542],{},[1651,45159,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,45161,2319],{},[1692,45163,13758],{},[902,45165,45166],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,45168,45169,45228],{},[123,45170,45171,3246,45174,45194,45195,45212,45213,1343,45226,1882],{},[38,45172,45173],{},"Kvantitativní smysl:",[883,45175,45177],{"className":45176},[886],[888,45178,45179],{"xmlns":890},[892,45180,45181,45191],{},[895,45182,45183],{},[1902,45184,45185,45187,45189],{},[898,45186,1690],{},[898,45188,1657],{},[1651,45190,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,45192,45193],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,45196,45198],{"className":45197},[886],[888,45199,45200],{"xmlns":890},[892,45201,45202,45210],{},[895,45203,45204],{},[2115,45205,45206,45208],{},[898,45207,1690],{},[898,45209,5561],{},[902,45211,43616],{"encoding":904}," při jednotkové změně parametru ",[883,45214,45216],{"className":45215},[886],[888,45217,45218],{"xmlns":890},[892,45219,45220,45224],{},[895,45221,45222],{},[898,45223,1657],{},[902,45225,1657],{"encoding":904},[614,45227,38173],{},[123,45229,45230,45233,45234,45251,45252,1882],{},[38,45231,45232],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,45235,45237],{"className":45236},[886],[888,45238,45239],{"xmlns":890},[892,45240,45241,45249],{},[895,45242,45243],{},[2115,45244,45245,45247],{},[898,45246,1690],{},[898,45248,5561],{},[902,45250,43616],{"encoding":904}," na růst ",[883,45253,45255],{"className":45254},[886],[888,45256,45257],{"xmlns":890},[892,45258,45259,45263],{},[895,45260,45261],{},[898,45262,1657],{},[902,45264,1657],{"encoding":904},[724,45266,45267,45268,45281,45282,44532,45299,5230],{},"Např. růst ",[883,45269,45271],{"className":45270},[886],[888,45272,45273],{"xmlns":890},[892,45274,45275,45279],{},[895,45276,45277],{},[898,45278,3490],{},[902,45280,3490],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,45283,45285],{"className":45284},[886],[888,45286,45287],{"xmlns":890},[892,45288,45289,45297],{},[895,45290,45291],{},[2115,45292,45293,45295],{},[898,45294,1690],{},[898,45296,5561],{},[902,45298,43616],{"encoding":904},[883,45300,45302],{"className":45301},[886],[888,45303,45304],{"xmlns":890},[892,45305,45306,45320],{},[895,45307,45308,45316,45318],{},[1902,45309,45310,45312,45314],{},[898,45311,1690],{},[898,45313,3490],{},[1651,45315,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,45317,2319],{},[1692,45319,1741],{},[902,45321,45322],{"encoding":904},"Q'_c \u003C 0",[724,45324,45325],{},[614,45326,45327,45328,45348,45349,45373,45374,45396,45397,1882],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,45329,45331],{"className":45330},[886],[888,45332,45333],{"xmlns":890},[892,45334,45335,45345],{},[895,45336,45337,45339,45341,45343],{},[898,45338,3490],{},[898,45340,1690],{},[1651,45342,1839],{},[898,45344,3542],{},[902,45346,45347],{"encoding":904},"cQ + d"," na strmější ",[883,45350,45352],{"className":45351},[886],[888,45353,45354],{"xmlns":890},[892,45355,45356,45370],{},[895,45357,45358,45364,45366,45368],{},[1686,45359,45360,45362],{},[898,45361,3490],{},[1692,45363,1694],{},[898,45365,1690],{},[1651,45367,1839],{},[898,45369,3542],{},[902,45371,45372],{"encoding":904},"c_1 Q + d"," (při ",[883,45375,45377],{"className":45376},[886],[888,45378,45379],{"xmlns":890},[892,45380,45381,45393],{},[895,45382,45383,45389,45391],{},[1686,45384,45385,45387],{},[898,45386,3490],{},[1692,45388,1694],{},[1651,45390,2390],{},[898,45392,3490],{},[902,45394,45395],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,45398,45400],{"className":45399},[886],[888,45401,45402],{"xmlns":890},[892,45403,45404,45414],{},[895,45405,45406,45412],{},[2115,45407,45408,45410],{},[898,45409,1690],{},[898,45411,5561],{},[1651,45413,43804],{},[902,45415,45416],{"encoding":904},"Q^E \\downarrow",[724,45418,45419,45420,45452,45453,1882],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,45421,45423],{"className":45422},[886],[888,45424,45425],{"xmlns":890},[892,45426,45427,45449],{},[895,45428,45429,45431,45433,45435,45443,45445,45447],{},[898,45430,4216],{"mathvariant":1910},[898,45432,1690],{},[1651,45434,4060],{},[1902,45436,45437,45439,45441],{},[898,45438,1690],{},[898,45440,2268],{},[1651,45442,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1843,45444,1845],{},[898,45446,3542],{},[898,45448,2268],{},[902,45450,45451],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,45454,45456],{"className":45455},[886],[888,45457,45458],{"xmlns":890},[892,45459,45460,45468],{},[895,45461,45462],{},[2115,45463,45464,45466],{},[898,45465,2675],{},[898,45467,5561],{},[902,45469,42679],{"encoding":904},[198,45471,45473,45474],{"id":45472},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,45475,45477],{"className":45476},[886],[888,45478,45479],{"xmlns":890},[892,45480,45481,45489],{},[895,45482,45483],{},[2115,45484,45485,45487],{},[898,45486,1690],{},[898,45488,5561],{},[902,45490,43616],{"encoding":904},[724,45492,45493,42868,45495,42903,45521,1882],{},[38,45494,39146],{},[883,45496,45498],{"className":45497},[886],[888,45499,45500],{"xmlns":890},[892,45501,45502,45518],{},[895,45503,45504,45506,45508,45510,45512,45514,45516],{},[898,45505,2675],{},[1651,45507,1738],{},[1651,45509,2181],{},[1692,45511,3521],{},[898,45513,1690],{},[1651,45515,1839],{},[1692,45517,6518],{},[902,45519,45520],{"encoding":904},"P = -3Q + 40",[883,45522,45524],{"className":45523},[886],[888,45525,45526],{"xmlns":890},[892,45527,45528,45542],{},[895,45529,45530,45532,45534,45536,45538,45540],{},[898,45531,2675],{},[1651,45533,1738],{},[1692,45535,6316],{},[898,45537,1690],{},[1651,45539,1839],{},[1692,45541,4190],{},[902,45543,45544],{"encoding":904},"P = 0{,}5Q + 10",[724,45546,45547,45549],{},[38,45548,39178],{}," Rovnovážné množství",[883,45551,45553],{"className":45552},[886],[888,45554,45555],{"xmlns":890,"display":29279},[892,45556,45557,45625],{},[895,45558,45559,45565,45567,45585,45587,45611,45613,45620,45622],{},[2115,45560,45561,45563],{},[898,45562,1690],{},[898,45564,5561],{},[1651,45566,1738],{},[2446,45568,45569,45577],{},[895,45570,45571,45573,45575],{},[898,45572,2268],{},[1651,45574,2181],{},[898,45576,3542],{},[895,45578,45579,45581,45583],{},[898,45580,3490],{},[1651,45582,2181],{},[898,45584,207],{},[1651,45586,1738],{},[2446,45588,45589,45597],{},[895,45590,45591,45593,45595],{},[1692,45592,6518],{},[1651,45594,2181],{},[1692,45596,4190],{},[895,45598,45599,45601,45603,45605,45607,45609],{},[1692,45600,6316],{},[1651,45602,2181],{},[1651,45604,1654],{"stretchy":1653},[1651,45606,2181],{},[1692,45608,3521],{},[1651,45610,1667],{"stretchy":1653},[1651,45612,1738],{},[2446,45614,45615,45617],{},[1692,45616,39232],{},[1692,45618,45619],{},"3,5",[1651,45621,4060],{},[1692,45623,45624],{},"8,571.",[902,45626,45627],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,45629,45630,45675],{},[38,45631,45632,45633,4002,45646,4016,45660,45674],{},"(a) Změna ",[883,45634,45636],{"className":45635},[886],[888,45637,45638],{"xmlns":890},[892,45639,45640,45644],{},[895,45641,45642],{},[898,45643,3490],{},[902,45645,3490],{"encoding":904},[883,45647,45649],{"className":45648},[886],[888,45650,45651],{"xmlns":890},[892,45652,45653,45657],{},[895,45654,45655],{},[1692,45656,6316],{},[902,45658,45659],{"encoding":904},"0{,}5",[883,45661,45663],{"className":45662},[886],[888,45664,45665],{"xmlns":890},[892,45666,45667,45671],{},[895,45668,45669],{},[1692,45670,20534],{},[902,45672,45673],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,45677,45679],{"className":45678},[886],[888,45680,45681],{"xmlns":890,"display":29279},[892,45682,45683,45760],{},[895,45684,45685,45693,45695,45697,45699,45701,45703,45729,45731,45733,45735,45737,45739,45749,45751,45753,45755,45757],{},[1902,45686,45687,45689,45691],{},[898,45688,1690],{},[898,45690,3490],{},[1651,45692,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1843,45694,1845],{},[898,45696,3542],{},[898,45698,3490],{},[1651,45700,1738],{},[1651,45702,2181],{},[2446,45704,45705,45713],{},[895,45706,45707,45709,45711],{},[898,45708,2268],{},[1651,45710,2181],{},[898,45712,3542],{},[895,45714,45715,45717,45719,45721,45723],{},[1651,45716,1654],{"stretchy":1653},[898,45718,3490],{},[1651,45720,2181],{},[898,45722,207],{},[2115,45724,45725,45727],{},[1651,45726,1667],{"stretchy":1653},[1692,45728,1703],{},[1843,45730,1845],{},[898,45732,3542],{},[898,45734,3490],{},[1651,45736,1738],{},[1651,45738,2181],{},[2446,45740,45741,45743],{},[1692,45742,39232],{},[2115,45744,45745,45747],{},[1692,45746,45619],{},[1692,45748,1703],{},[1651,45750,4503],{},[1692,45752,4122],{},[1651,45754,4060],{},[1651,45756,2181],{},[1692,45758,45759],{},"0,245.",[902,45761,45762],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,45764,45765,45766,1882],{},"Nové rovnovážné množství ",[883,45767,45769],{"className":45768},[886],[888,45770,45771],{"xmlns":890},[892,45772,45773,45798],{},[895,45774,45775,45783,45785,45788,45790,45793,45795],{},[1902,45776,45777,45779,45781],{},[898,45778,1690],{},[1692,45780,1694],{},[898,45782,5561],{},[1651,45784,4060],{},[1692,45786,45787],{},"8,571",[1651,45789,2181],{},[1692,45791,45792],{},"0,245",[1651,45794,1738],{},[1692,45796,45797],{},"8,326",[902,45799,45800],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,45802,45803,45888],{},[38,45804,45805,45806,1343,45826,1343,45848,1343,45868,1882],{},"(b) Současné změny ",[883,45807,45809],{"className":45808},[886],[888,45810,45811],{"xmlns":890},[892,45812,45813,45823],{},[895,45814,45815,45817,45819,45821],{},[898,45816,3542],{},[898,45818,207],{},[1651,45820,1738],{},[1692,45822,6316],{},[902,45824,45825],{"encoding":904},"da = 0{,}5",[883,45827,45829],{"className":45828},[886],[888,45830,45831],{"xmlns":890},[892,45832,45833,45845],{},[895,45834,45835,45837,45839,45841,45843],{},[898,45836,3542],{},[898,45838,2268],{},[1651,45840,1738],{},[1651,45842,2181],{},[1692,45844,3574],{},[902,45846,45847],{"encoding":904},"db = -5",[883,45849,45851],{"className":45850},[886],[888,45852,45853],{"xmlns":890},[892,45854,45855,45865],{},[895,45856,45857,45859,45861,45863],{},[898,45858,3542],{},[898,45860,3490],{},[1651,45862,1738],{},[1692,45864,4122],{},[902,45866,45867],{"encoding":904},"dc = 0{,}1",[883,45869,45871],{"className":45870},[886],[888,45872,45873],{"xmlns":890},[892,45874,45875,45885],{},[895,45876,45877,45879,45881,45883],{},[898,45878,3542],{},[898,45880,3542],{},[1651,45882,1738],{},[1692,45884,1694],{},[902,45886,45887],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,45890,45892],{"className":45891},[886],[888,45893,45894],{"xmlns":890,"display":29279},[892,45895,45896,46039],{},[21967,45897,45898,45980,46016],{"rowspacing":21969,"columnalign":21970,"columnspacing":1911},[21972,45899,45900,45910],{},[21975,45901,45902],{},[2938,45903,45904],{"scriptlevel":1741,"displaystyle":1660},[895,45905,45906,45908],{},[898,45907,4216],{"mathvariant":1910},[898,45909,1690],{},[21975,45911,45912],{},[2938,45913,45914],{"scriptlevel":1741,"displaystyle":1660},[895,45915,45916,45918,45920,45930,45932,45934,45936,45942,45944,45946,45948,45950,45952,45954,45964,45966,45968,45970,45976,45978],{},[895,45917],{},[1651,45919,4060],{},[2446,45921,45922,45924],{},[1692,45923,39232],{},[2115,45925,45926,45928],{},[1692,45927,45619],{},[1692,45929,1703],{},[1651,45931,4503],{},[1692,45933,6316],{},[1651,45935,1839],{},[2446,45937,45938,45940],{},[1692,45939,1694],{},[1692,45941,45619],{},[1651,45943,4503],{},[1651,45945,1654],{"stretchy":1653},[1651,45947,2181],{},[1692,45949,3574],{},[1651,45951,1667],{"stretchy":1653},[1651,45953,2181],{},[2446,45955,45956,45958],{},[1692,45957,39232],{},[2115,45959,45960,45962],{},[1692,45961,45619],{},[1692,45963,1703],{},[1651,45965,4503],{},[1692,45967,4122],{},[1651,45969,2181],{},[2446,45971,45972,45974],{},[1692,45973,1694],{},[1692,45975,45619],{},[1651,45977,4503],{},[1692,45979,1694],{},[21972,45981,45982,45988],{},[21975,45983,45984],{},[2938,45985,45986],{"scriptlevel":1741,"displaystyle":1660},[895,45987],{},[21975,45989,45990],{},[2938,45991,45992],{"scriptlevel":1741,"displaystyle":1660},[895,45993,45994,45996,45998,46001,46003,46006,46008,46011,46013],{},[895,45995],{},[1651,45997,1738],{},[1692,45999,46000],{},"1,2245",[1651,46002,2181],{},[1692,46004,46005],{},"1,4286",[1651,46007,2181],{},[1692,46009,46010],{},"0,2449",[1651,46012,2181],{},[1692,46014,46015],{},"0,2857",[21972,46017,46018,46024],{},[21975,46019,46020],{},[2938,46021,46022],{"scriptlevel":1741,"displaystyle":1660},[895,46023],{},[21975,46025,46026],{},[2938,46027,46028],{"scriptlevel":1741,"displaystyle":1660},[895,46029,46030,46032,46034,46036],{},[895,46031],{},[1651,46033,4060],{},[1651,46035,2181],{},[1692,46037,46038],{},"0,735.",[902,46040,46041],{"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}",[724,46043,31278,46044,1882],{},[883,46045,46047],{"className":46046},[886],[888,46048,46049],{"xmlns":890},[892,46050,46051,46075],{},[895,46052,46053,46061,46063,46065,46067,46070,46072],{},[1902,46054,46055,46057,46059],{},[898,46056,1690],{},[1692,46058,1694],{},[898,46060,5561],{},[1651,46062,4060],{},[1692,46064,45787],{},[1651,46066,2181],{},[1692,46068,46069],{},"0,735",[1651,46071,1738],{},[1692,46073,46074],{},"7,836",[902,46076,46077],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[5179,46079,46080],{},[724,46081,46082,46084,46085,46108,46109,46131],{},[883,46083,5719],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,46086,46088],{"className":46087},[886],[888,46089,46090],{"xmlns":890},[892,46091,46092,46105],{},[895,46093,46094,46096,46098,46100,46102],{},[898,46095,4216],{"mathvariant":1910},[898,46097,1690],{},[1651,46099,4060],{},[1651,46101,2181],{},[1692,46103,46104],{},"2,69",[902,46106,46107],{"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 ",[883,46110,46112],{"className":46111},[886],[888,46113,46114],{"xmlns":890},[892,46115,46116,46128],{},[895,46117,46118,46120,46122,46124,46126],{},[898,46119,4216],{"mathvariant":1910},[898,46121,1690],{},[1651,46123,4060],{},[1651,46125,2181],{},[1692,46127,46069],{},[902,46129,46130],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,46133,46134],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[38183,46136],{},[115,46138,820],{"id":13082},[5179,46140,46141],{},[724,46142,46143,5186,46145,11325,46148,13426,46164,11325,46167,46183,46184,1882],{},[883,46144,5465],{},[38,46146,46147],{},"Přebytek spotřebitele",[883,46149,46151],{"className":46150},[886],[888,46152,46153],{"xmlns":890},[892,46154,46155,46161],{},[895,46156,46157,46159],{},[898,46158,3001],{},[898,46160,3004],{},[902,46162,46163],{"encoding":904},"CS",[38,46165,46166],{},"přebytek výrobce",[883,46168,46170],{"className":46169},[886],[888,46171,46172],{"xmlns":890},[892,46173,46174,46180],{},[895,46175,46176,46178],{},[898,46177,2675],{},[898,46179,3004],{},[902,46181,46182],{"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 ",[207,46185,46187],{"className":46186,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,46189,46190],{},[1756,46191],{"alt":46192,"className":46193,"src":46194},"imek-prebytky-cs-ps",[210,1760],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,46196,46197,11325,46199,46202],{},[38,46198,46147],{},[614,46200,46201],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,46204,46206],{"className":46205},[886],[888,46207,46208],{"xmlns":890,"display":29279},[892,46209,46210,46287],{},[21967,46211,46212],{"width":29284},[21972,46213,46214,46216,46280,46282],{},[21975,46215],{"width":29289},[21975,46217,46218],{},[895,46219,46220,46222,46224,46226,46232,46234,46236,46248,46250,46252,46254,46256,46258,46260,46262,46264,46270,46272,46278],{},[898,46221,3001],{},[898,46223,3004],{},[1651,46225,1654],{"stretchy":1653},[1686,46227,46228,46230],{},[898,46229,1690],{},[1692,46231,1741],{},[1651,46233,1667],{"stretchy":1653},[1651,46235,1738],{},[1902,46237,46238,46240,46242],{},[1651,46239,12467],{},[1692,46241,1741],{},[1686,46243,46244,46246],{},[898,46245,1690],{},[1692,46247,1741],{},[898,46249,2047],{},[1651,46251,1654],{"stretchy":1653},[898,46253,1690],{},[1651,46255,1667],{"stretchy":1653},[1843,46257,1845],{},[898,46259,3542],{},[898,46261,1690],{},[1651,46263,2181],{},[1686,46265,46266,46268],{},[898,46267,2675],{},[1692,46269,1741],{},[1843,46271,1845],{},[1686,46273,46274,46276],{},[898,46275,1690],{},[1692,46277,1741],{},[898,46279,1882],{"mathvariant":1910},[21975,46281],{"width":29289},[21975,46283,46284],{},[1843,46285,46286],{},"(2.14)",[902,46288,46289],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,46291,46292,11325,46295,46298],{},[38,46293,46294],{},"Přebytek výrobce",[614,46296,46297],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,46300,46302],{"className":46301},[886],[888,46303,46304],{"xmlns":890,"display":29279},[892,46305,46306,46383],{},[21967,46307,46308],{"width":29284},[21972,46309,46310,46312,46376,46378],{},[21975,46311],{"width":29289},[21975,46313,46314],{},[895,46315,46316,46318,46320,46322,46328,46330,46332,46338,46340,46346,46348,46360,46362,46364,46366,46368,46370,46372,46374],{},[898,46317,2675],{},[898,46319,3004],{},[1651,46321,1654],{"stretchy":1653},[1686,46323,46324,46326],{},[898,46325,1690],{},[1692,46327,1741],{},[1651,46329,1667],{"stretchy":1653},[1651,46331,1738],{},[1686,46333,46334,46336],{},[898,46335,2675],{},[1692,46337,1741],{},[1843,46339,1845],{},[1686,46341,46342,46344],{},[898,46343,1690],{},[1692,46345,1741],{},[1651,46347,2181],{},[1902,46349,46350,46352,46354],{},[1651,46351,12467],{},[1692,46353,1741],{},[1686,46355,46356,46358],{},[898,46357,1690],{},[1692,46359,1741],{},[898,46361,3004],{},[1651,46363,1654],{"stretchy":1653},[898,46365,1690],{},[1651,46367,1667],{"stretchy":1653},[1843,46369,1845],{},[898,46371,3542],{},[898,46373,1690],{},[898,46375,1882],{"mathvariant":1910},[21975,46377],{"width":29289},[21975,46379,46380],{},[1843,46381,46382],{},"(2.15)",[902,46384,46385],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,46387,46388,46389,1882],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,46390,46392],{"className":46391,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[38183,46394],{},[115,46396,46398],{"id":46397},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,46400,46401,46432,46437,46443,46471,46477,46506,46512,46592,46618],{},[123,46402,46403,46405,46406,46431],{},[38,46404,39141],{}," — lineární poptávka ",[883,46407,46409],{"className":46408},[886],[888,46410,46411],{"xmlns":890},[892,46412,46413,46429],{},[895,46414,46415,46417,46419,46421,46423,46425,46427],{},[898,46416,2675],{},[1651,46418,1738],{},[1651,46420,2181],{},[1692,46422,1703],{},[898,46424,1690],{},[1651,46426,1839],{},[1692,46428,4452],{},[902,46430,39173],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,46433,46434,46436],{},[38,46435,39455],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,46438,46439,46442],{},[38,46440,46441],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,46444,46445,46447,46448,1882],{},[38,46446,42002],{}," — lineární nabídka ",[883,46449,46451],{"className":46450},[886],[888,46452,46453],{"xmlns":890},[892,46454,46455,46469],{},[895,46456,46457,46459,46461,46463,46465,46467],{},[898,46458,2675],{},[1651,46460,1738],{},[1692,46462,6316],{},[898,46464,1690],{},[1651,46466,1839],{},[1692,46468,6311],{},[902,46470,42031],{"encoding":904},[123,46472,46473,46476],{},[38,46474,46475],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,46478,46479,46482,46483,1882],{},[38,46480,46481],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,46484,46486],{"className":46485},[886],[888,46487,46488],{"xmlns":890},[892,46489,46490,46504],{},[895,46491,46492,46494,46496,46498,46500,46502],{},[898,46493,5561],{},[1651,46495,2261],{"stretchy":1653},[1692,46497,3689],{},[1651,46499,1661],{"separator":1660},[1692,46501,43149],{},[1651,46503,2279],{"stretchy":1653},[902,46505,43177],{"encoding":904},[123,46507,46508,46511],{},[38,46509,46510],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,46513,46514,46517,46518,46535,46536,1343,46561,46588,46589,4278],{},[38,46515,46516],{},"Příklad 2.9"," — daň ",[883,46519,46521],{"className":46520},[886],[888,46522,46523],{"xmlns":890},[892,46524,46525,46533],{},[895,46526,46527,46529,46531],{},[898,46528,4104],{},[1651,46530,1738],{},[1692,46532,3581],{},[902,46534,42481],{"encoding":904}," na výrobce; rozklad ",[883,46537,46539],{"className":46538},[886],[888,46540,46541],{"xmlns":890},[892,46542,46543,46559],{},[895,46544,46545,46555,46557],{},[1686,46546,46547,46549],{},[898,46548,4104],{},[895,46550,46551,46553],{},[898,46552,43890],{},[898,46554,724],{},[1651,46556,1738],{},[1692,46558,1703],{},[902,46560,44189],{"encoding":904},[883,46562,46564],{"className":46563},[886],[888,46565,46566],{"xmlns":890},[892,46567,46568,46586],{},[895,46569,46570,46582,46584],{},[1686,46571,46572,46574],{},[898,46573,4104],{},[895,46575,46576,46578,46580],{},[898,46577,43913],{},[898,46579,1664],{},[898,46581,13339],{},[1651,46583,1738],{},[1692,46585,3689],{},[902,46587,44218],{"encoding":904},". (Viz ",[207,46590,43934],{"className":46591,"dataFsResolvedFilePath":809,"href":810},[210],[123,46593,46594,46517,46597,46614,46615,4278],{},[38,46595,46596],{},"Příklad 2.10",[883,46598,46600],{"className":46599},[886],[888,46601,46602],{"xmlns":890},[892,46603,46604,46612],{},[895,46605,46606,46608,46610],{},[898,46607,4104],{},[1651,46609,1738],{},[1692,46611,3581],{},[902,46613,42481],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,46616,43934],{"className":46617,"dataFsResolvedFilePath":809,"href":810},[210],[123,46619,46620,46623],{},[38,46621,46622],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[38183,46625],{},[115,46627,46629],{"id":46628},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,46631,46633],{"id":46632},"základní-analýza-poptávky","Základní analýza poptávky",[724,46635,46636,46639,46640,46675,46676,46702],{},[38,46637,46638],{},"2.1"," Je dána poptávka ",[883,46641,46643],{"className":46642},[886],[888,46644,46645],{"xmlns":890},[892,46646,46647,46672],{},[895,46648,46649,46651,46653,46655,46657,46659,46661,46663,46666,46668,46670],{},[898,46650,1690],{},[1651,46652,1738],{},[898,46654,2047],{},[1651,46656,1654],{"stretchy":1653},[898,46658,2675],{},[1651,46660,1667],{"stretchy":1653},[1651,46662,1738],{},[1692,46664,46665],{},"75",[1651,46667,2181],{},[1692,46669,3574],{},[898,46671,2675],{},[902,46673,46674],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,46677,46679],{"className":46678},[886],[888,46680,46681],{"xmlns":890},[892,46682,46683,46699],{},[895,46684,46685,46687,46689,46691,46693,46695,46697],{},[1692,46686,1741],{},[1651,46688,1661],{"separator":1660},[1692,46690,3574],{},[1651,46692,1661],{"separator":1660},[1692,46694,4190],{},[1651,46696,1661],{"separator":1660},[1692,46698,37457],{},[902,46700,46701],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,46704,46705,46708,46709,46727,46728,4477],{},[38,46706,46707],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,46710,46712],{"className":46711},[886],[888,46713,46714],{"xmlns":890},[892,46715,46716,46724],{},[895,46717,46718,46720,46722],{},[898,46719,2675],{},[1651,46721,1661],{"separator":1660},[898,46723,1690],{},[902,46725,46726],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,46729,46731],{"className":46730},[886],[888,46732,46733],{"xmlns":890},[892,46734,46735,46751],{},[895,46736,46737,46739,46741,46743,46745,46747,46749],{},[898,46738,207],{},[1651,46740,1661],{"separator":1660},[898,46742,2268],{},[1651,46744,1661],{"separator":1660},[898,46746,3490],{},[1651,46748,2390],{},[1692,46750,1741],{},[902,46752,46753],{"encoding":904},"a, b, c > 0",[120,46755,46756,46789,46820,46855,46886,46921],{},[123,46757,46758,46759],{},"(a) ",[883,46760,46762],{"className":46761},[886],[888,46763,46764],{"xmlns":890},[892,46765,46766,46786],{},[895,46767,46768,46770,46772],{},[898,46769,1690],{},[1651,46771,1738],{},[2938,46773,46774],{"scriptlevel":1741,"displaystyle":1660},[2446,46775,46776,46778],{},[898,46777,207],{},[895,46779,46780,46782,46784],{},[898,46781,2675],{},[1651,46783,1839],{},[898,46785,3490],{},[902,46787,46788],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,46790,46791,46792],{},"(b) ",[883,46793,46795],{"className":46794},[886],[888,46796,46797],{"xmlns":890},[892,46798,46799,46817],{},[895,46800,46801,46803,46805],{},[898,46802,1690],{},[1651,46804,1738],{},[9423,46806,46807],{},[895,46808,46809,46811,46813,46815],{},[898,46810,207],{},[1651,46812,2181],{},[898,46814,2268],{},[898,46816,1690],{},[902,46818,46819],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,46821,46822,46823],{},"(c) ",[883,46824,46826],{"className":46825},[886],[888,46827,46828],{"xmlns":890},[892,46829,46830,46852],{},[895,46831,46832,46834,46836],{},[898,46833,1690],{},[1651,46835,1738],{},[2938,46837,46838],{"scriptlevel":1741,"displaystyle":1660},[2446,46839,46840,46850],{},[895,46841,46842,46844,46846],{},[898,46843,207],{},[1651,46845,2181],{},[9423,46847,46848],{},[898,46849,2675],{},[898,46851,2268],{},[902,46853,46854],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,46856,46857,46858],{},"(d) ",[883,46859,46861],{"className":46860},[886],[888,46862,46863],{"xmlns":890},[892,46864,46865,46883],{},[895,46866,46867,46869,46871,46873,46875,46877],{},[898,46868,2675],{},[1651,46870,1738],{},[898,46872,207],{},[1651,46874,2181],{},[898,46876,2268],{},[2115,46878,46879,46881],{},[898,46880,1690],{},[1692,46882,1703],{},[902,46884,46885],{"encoding":904},"P = a - bQ^2",[123,46887,46888,46889],{},"(e) ",[883,46890,46892],{"className":46891},[886],[888,46893,46894],{"xmlns":890},[892,46895,46896,46918],{},[895,46897,46898,46900,46902,46904,46914,46916],{},[898,46899,1690],{},[1651,46901,1738],{},[898,46903,2268],{},[2115,46905,46906,46908],{},[898,46907,2675],{},[895,46909,46910,46912],{},[1651,46911,2181],{},[898,46913,207],{},[1651,46915,1839],{},[898,46917,3490],{},[902,46919,46920],{"encoding":904},"Q = bP^{-a} + c",[123,46922,46923,46924],{},"(f) ",[883,46925,46927],{"className":46926},[886],[888,46928,46929],{"xmlns":890},[892,46930,46931,46954],{},[895,46932,46933,46935,46937,46939,46941],{},[898,46934,1690],{},[1651,46936,1738],{},[898,46938,207],{},[1651,46940,4503],{},[2115,46942,46943,46946],{},[898,46944,46945],{},"e",[895,46947,46948,46950,46952],{},[1651,46949,2181],{},[898,46951,2268],{},[898,46953,2675],{},[902,46955,46956],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,46958,46959,46962],{},[38,46960,46961],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,46964,46965,46968,46971],{},[123,46966,46967],{},"(a) Cena substitutu.",[123,46969,46970],{},"(b) Cena komplementu.",[123,46972,46973],{},"(c) Výdaje na reklamu.",[724,46975,46976,46639,46978,47012,47013,47041],{},[38,46977,25855],{},[883,46979,46981],{"className":46980},[886],[888,46982,46983],{"xmlns":890},[892,46984,46985,47009],{},[895,46986,46987,46989,46991,46993,46995,46997,46999,47001,47003,47005,47007],{},[898,46988,2675],{},[1651,46990,1738],{},[898,46992,2047],{},[1651,46994,1654],{"stretchy":1653},[898,46996,1690],{},[1651,46998,1667],{"stretchy":1653},[1651,47000,1738],{},[1692,47002,4828],{},[1651,47004,2181],{},[1692,47006,1703],{},[898,47008,1690],{},[902,47010,47011],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,47014,47016],{"className":47015},[886],[888,47017,47018],{"xmlns":890},[892,47019,47020,47038],{},[895,47021,47022,47024,47026,47032,47034,47036],{},[898,47023,2675],{},[1651,47025,1738],{},[2115,47027,47028,47030],{},[898,47029,2047],{},[1651,47031,2668],{},[1651,47033,1654],{"stretchy":1653},[898,47035,1690],{},[1651,47037,1667],{"stretchy":1653},[902,47039,47040],{"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.",[724,47043,47044,47047],{},[38,47045,47046],{},"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:",[120,47049,47050,47134,47210,47296,47384],{},[123,47051,46758,47052,1343,47092,1882],{},[883,47053,47055],{"className":47054},[886],[888,47056,47057],{"xmlns":890},[892,47058,47059,47089],{},[895,47060,47061,47067,47069,47071,47073,47075,47081,47083],{},[1686,47062,47063,47065],{},[898,47064,24466],{},[1692,47066,1694],{},[1651,47068,1738],{},[1692,47070,10340],{},[1651,47072,2181],{},[1692,47074,3689],{},[1686,47076,47077,47079],{},[898,47078,5564],{},[1692,47080,1694],{},[1651,47082,1839],{},[1686,47084,47085,47087],{},[898,47086,5564],{},[1692,47088,1703],{},[902,47090,47091],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,47093,47095],{"className":47094},[886],[888,47096,47097],{"xmlns":890},[892,47098,47099,47131],{},[895,47100,47101,47107,47109,47111,47113,47115,47121,47123,47125],{},[1686,47102,47103,47105],{},[898,47104,24466],{},[1692,47106,1703],{},[1651,47108,1738],{},[1692,47110,4190],{},[1651,47112,1839],{},[1692,47114,1703],{},[1686,47116,47117,47119],{},[898,47118,5564],{},[1692,47120,1694],{},[1651,47122,2181],{},[1692,47124,3689],{},[1686,47126,47127,47129],{},[898,47128,5564],{},[1692,47130,1703],{},[902,47132,47133],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,47135,46791,47136,1343,47178,1882],{},[883,47137,47139],{"className":47138},[886],[888,47140,47141],{"xmlns":890},[892,47142,47143,47175],{},[895,47144,47145,47151,47153,47155,47157,47159,47165,47167,47169],{},[1686,47146,47147,47149],{},[898,47148,24466],{},[1692,47150,1694],{},[1651,47152,1738],{},[1692,47154,4446],{},[1651,47156,2181],{},[1692,47158,4190],{},[1686,47160,47161,47163],{},[898,47162,5564],{},[1692,47164,1694],{},[1651,47166,2181],{},[1692,47168,3581],{},[1686,47170,47171,47173],{},[898,47172,5564],{},[1692,47174,1703],{},[902,47176,47177],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,47179,47181],{"className":47180},[886],[888,47182,47183],{"xmlns":890},[892,47184,47185,47207],{},[895,47186,47187,47193,47195,47197,47199,47201],{},[1686,47188,47189,47191],{},[898,47190,24466],{},[1692,47192,1703],{},[1651,47194,1738],{},[1692,47196,37457],{},[1651,47198,2181],{},[1692,47200,4190],{},[1686,47202,47203,47205],{},[898,47204,5564],{},[1692,47206,1703],{},[902,47208,47209],{"encoding":904},"B_2 = 15 - 10A_2",[123,47211,46822,47212,1343,47254,1882],{},[883,47213,47215],{"className":47214},[886],[888,47216,47217],{"xmlns":890},[892,47218,47219,47251],{},[895,47220,47221,47227,47229,47231,47233,47235,47241,47243,47245],{},[1686,47222,47223,47225],{},[898,47224,24466],{},[1692,47226,1694],{},[1651,47228,1738],{},[1692,47230,39232],{},[1651,47232,2181],{},[1692,47234,1703],{},[1686,47236,47237,47239],{},[898,47238,5564],{},[1692,47240,1694],{},[1651,47242,2181],{},[1692,47244,3689],{},[1686,47246,47247,47249],{},[898,47248,5564],{},[1692,47250,1703],{},[902,47252,47253],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,47255,47257],{"className":47256},[886],[888,47258,47259],{"xmlns":890},[892,47260,47261,47293],{},[895,47262,47263,47269,47271,47273,47275,47277,47283,47285,47287],{},[1686,47264,47265,47267],{},[898,47266,24466],{},[1692,47268,1703],{},[1651,47270,1738],{},[1692,47272,37457],{},[1651,47274,1839],{},[1692,47276,1703],{},[1686,47278,47279,47281],{},[898,47280,5564],{},[1692,47282,1694],{},[1651,47284,2181],{},[1692,47286,1703],{},[1686,47288,47289,47291],{},[898,47290,5564],{},[1692,47292,1703],{},[902,47294,47295],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,47297,46857,47298,1343,47342,1882],{},[883,47299,47301],{"className":47300},[886],[888,47302,47303],{"xmlns":890},[892,47304,47305,47339],{},[895,47306,47307,47313,47315,47317,47319,47321,47323,47329,47331,47333],{},[1686,47308,47309,47311],{},[898,47310,24466],{},[1692,47312,1694],{},[1651,47314,1738],{},[1651,47316,2181],{},[1692,47318,10340],{},[1651,47320,2181],{},[1692,47322,1703],{},[1686,47324,47325,47327],{},[898,47326,5564],{},[1692,47328,1694],{},[1651,47330,1839],{},[1692,47332,3521],{},[1686,47334,47335,47337],{},[898,47336,5564],{},[1692,47338,1703],{},[902,47340,47341],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,47343,47345],{"className":47344},[886],[888,47346,47347],{"xmlns":890},[892,47348,47349,47381],{},[895,47350,47351,47357,47359,47361,47363,47365,47371,47373,47375],{},[1686,47352,47353,47355],{},[898,47354,24466],{},[1692,47356,1703],{},[1651,47358,1738],{},[1692,47360,4190],{},[1651,47362,1839],{},[1692,47364,1703],{},[1686,47366,47367,47369],{},[898,47368,5564],{},[1692,47370,1694],{},[1651,47372,2181],{},[1692,47374,1703],{},[1686,47376,47377,47379],{},[898,47378,5564],{},[1692,47380,1703],{},[902,47382,47383],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,47385,46888,47386,1343,47428,1882],{},[883,47387,47389],{"className":47388},[886],[888,47390,47391],{"xmlns":890},[892,47392,47393,47425],{},[895,47394,47395,47401,47403,47405,47407,47409,47415,47417,47419],{},[1686,47396,47397,47399],{},[898,47398,24466],{},[1692,47400,1694],{},[1651,47402,1738],{},[1692,47404,10340],{},[1651,47406,1839],{},[1692,47408,1703],{},[1686,47410,47411,47413],{},[898,47412,5564],{},[1692,47414,1694],{},[1651,47416,1839],{},[1692,47418,3689],{},[1686,47420,47421,47423],{},[898,47422,5564],{},[1692,47424,1703],{},[902,47426,47427],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,47429,47431],{"className":47430},[886],[888,47432,47433],{"xmlns":890},[892,47434,47435,47467],{},[895,47436,47437,47443,47445,47447,47449,47451,47457,47459,47461],{},[1686,47438,47439,47441],{},[898,47440,24466],{},[1692,47442,1703],{},[1651,47444,1738],{},[1692,47446,6518],{},[1651,47448,2181],{},[1692,47450,3521],{},[1686,47452,47453,47455],{},[898,47454,5564],{},[1692,47456,1694],{},[1651,47458,1839],{},[1692,47460,3574],{},[1686,47462,47463,47465],{},[898,47464,5564],{},[1692,47466,1703],{},[902,47468,47469],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,47471,47473],{"id":47472},"základní-analýza-nabídky","Základní analýza nabídky",[724,47475,47476,47479,47480,47514,47515,47537],{},[38,47477,47478],{},"2.6"," Je dána nabídka ",[883,47481,47483],{"className":47482},[886],[888,47484,47485],{"xmlns":890},[892,47486,47487,47511],{},[895,47488,47489,47491,47493,47495,47497,47499,47501,47503,47505,47507,47509],{},[898,47490,2675],{},[1651,47492,1738],{},[898,47494,3004],{},[1651,47496,1654],{"stretchy":1653},[898,47498,1690],{},[1651,47500,1667],{"stretchy":1653},[1651,47502,1738],{},[1692,47504,10340],{},[1651,47506,1839],{},[1692,47508,4166],{},[898,47510,1690],{},[902,47512,47513],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,47516,47518],{"className":47517},[886],[888,47519,47520],{"xmlns":890},[892,47521,47522,47534],{},[895,47523,47524,47526,47528,47530,47532],{},[1692,47525,6311],{},[1651,47527,1661],{"separator":1660},[1692,47529,39232],{},[1651,47531,1661],{"separator":1660},[1692,47533,16336],{},[902,47535,47536],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,47539,47540,47543,47544,47561],{},[38,47541,47542],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,47545,47547],{"className":47546},[886],[888,47548,47549],{"xmlns":890},[892,47550,47551,47559],{},[895,47552,47553,47555,47557],{},[898,47554,2675],{},[1651,47556,1661],{"separator":1660},[898,47558,1690],{},[902,47560,46726],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,47563,47564,47590,47618,47651,47685,47721],{},[123,47565,46758,47566],{},[883,47567,47569],{"className":47568},[886],[888,47570,47571],{"xmlns":890},[892,47572,47573,47587],{},[895,47574,47575,47577,47579,47581,47583,47585],{},[898,47576,2675],{},[1651,47578,1738],{},[1692,47580,39232],{},[1651,47582,1839],{},[1692,47584,1703],{},[898,47586,1690],{},[902,47588,47589],{"encoding":904},"P = 30 + 2Q",[123,47591,46791,47592],{},[883,47593,47595],{"className":47594},[886],[888,47596,47597],{"xmlns":890},[892,47598,47599,47615],{},[895,47600,47601,47603,47605,47607,47609,47611,47613],{},[898,47602,1690],{},[1651,47604,1738],{},[1651,47606,2181],{},[1692,47608,3521],{},[1651,47610,1839],{},[1692,47612,4828],{},[898,47614,2675],{},[902,47616,47617],{"encoding":904},"Q = -3 + 12P",[123,47619,46822,47620],{},[883,47621,47623],{"className":47622},[886],[888,47624,47625],{"xmlns":890},[892,47626,47627,47649],{},[895,47628,47629,47631,47633,47639,47641,47643,47645,47647],{},[898,47630,2675],{},[1651,47632,1738],{},[2115,47634,47635,47637],{},[898,47636,1690],{},[1692,47638,1703],{},[1651,47640,1839],{},[1692,47642,24159],{},[898,47644,1690],{},[1651,47646,1839],{},[1692,47648,33759],{},[902,47650,42935],{"encoding":904},[123,47652,46857,47653],{},[883,47654,47656],{"className":47655},[886],[888,47657,47658],{"xmlns":890},[892,47659,47660,47682],{},[895,47661,47662,47664,47666,47672,47674,47676,47678,47680],{},[898,47663,2675],{},[1651,47665,1738],{},[2115,47667,47668,47670],{},[898,47669,1690],{},[1692,47671,1703],{},[1651,47673,1839],{},[1692,47675,1703],{},[898,47677,1690],{},[1651,47679,1839],{},[1692,47681,4828],{},[902,47683,47684],{"encoding":904},"P = Q^2 + 2Q + 12",[123,47686,46888,47687],{},[883,47688,47690],{"className":47689},[886],[888,47691,47692],{"xmlns":890},[892,47693,47694,47718],{},[895,47695,47696,47698,47700,47702,47704,47706,47708,47710,47712],{},[898,47697,1690],{},[1651,47699,1738],{},[1692,47701,10108],{},[1651,47703,1839],{},[1692,47705,3574],{},[898,47707,2675],{},[1651,47709,1839],{},[1692,47711,4122],{},[2115,47713,47714,47716],{},[898,47715,2675],{},[1692,47717,1703],{},[902,47719,47720],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,47722,46923,47723],{},[883,47724,47726],{"className":47725},[886],[888,47727,47728],{"xmlns":890},[892,47729,47730,47755],{},[895,47731,47732,47734,47736,47738,47740,47742,47744,47746,47749],{},[898,47733,1690],{},[1651,47735,1738],{},[1692,47737,25414],{},[1651,47739,1839],{},[1692,47741,4122],{},[898,47743,2675],{},[1651,47745,1839],{},[1692,47747,47748],{},"0,004",[2115,47750,47751,47753],{},[898,47752,2675],{},[1692,47754,1703],{},[902,47756,47757],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,47759,47760,47763],{},[38,47761,47762],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,47765,47766,47769,47772,47775],{},[123,47767,47768],{},"(a) Sníží ceny surovin — vstupů.",[123,47770,47771],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,47773,47774],{},"(c) Zvýší ceny všech energií.",[123,47776,47777],{},"(d) Sníží daňové odvody státu.",[724,47779,47780,47479,47782,47816,47817,47845],{},[38,47781,44162],{},[883,47783,47785],{"className":47784},[886],[888,47786,47787],{"xmlns":890},[892,47788,47789,47813],{},[895,47790,47791,47793,47795,47797,47799,47801,47803,47805,47807,47809,47811],{},[898,47792,2675],{},[1651,47794,1738],{},[898,47796,3004],{},[1651,47798,1654],{"stretchy":1653},[898,47800,1690],{},[1651,47802,1667],{"stretchy":1653},[1651,47804,1738],{},[1692,47806,6316],{},[898,47808,1690],{},[1651,47810,1839],{},[1692,47812,37457],{},[902,47814,47815],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,47818,47820],{"className":47819},[886],[888,47821,47822],{"xmlns":890},[892,47823,47824,47842],{},[895,47825,47826,47828,47830,47836,47838,47840],{},[898,47827,2675],{},[1651,47829,1738],{},[2115,47831,47832,47834],{},[898,47833,3004],{},[1651,47835,2668],{},[1651,47837,1654],{"stretchy":1653},[898,47839,1690],{},[1651,47841,1667],{"stretchy":1653},[902,47843,47844],{"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.",[198,47847,42538],{"id":47848},"tržní-rovnováha-1",[724,47850,47851,47853,47854,47871,47872,1793],{},[38,47852,44222],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,47855,47857],{"className":47856},[886],[888,47858,47859],{"xmlns":890},[892,47860,47861,47869],{},[895,47862,47863],{},[2115,47864,47865,47867],{},[898,47866,1690],{},[898,47868,5561],{},[902,47870,43616],{"encoding":904}," a rovnovážnou cenu ",[883,47873,47875],{"className":47874},[886],[888,47876,47877],{"xmlns":890},[892,47878,47879,47887],{},[895,47880,47881],{},[2115,47882,47883,47885],{},[898,47884,2675],{},[898,47886,5561],{},[902,47888,42679],{"encoding":904},[120,47890,47891,47944,47995,48054],{},[123,47892,46758,47893,1343,47920,1882],{},[883,47894,47896],{"className":47895},[886],[888,47897,47898],{"xmlns":890},[892,47899,47900,47917],{},[895,47901,47902,47904,47906,47908,47910,47912,47914],{},[898,47903,2675],{},[1651,47905,1738],{},[1651,47907,2181],{},[1692,47909,3574],{},[898,47911,1690],{},[1651,47913,1839],{},[1692,47915,47916],{},"80",[902,47918,47919],{"encoding":904},"P = -5Q + 80",[883,47921,47923],{"className":47922},[886],[888,47924,47925],{"xmlns":890},[892,47926,47927,47941],{},[895,47928,47929,47931,47933,47935,47937,47939],{},[898,47930,2675],{},[1651,47932,1738],{},[1692,47934,1703],{},[898,47936,1690],{},[1651,47938,1839],{},[1692,47940,4190],{},[902,47942,47943],{"encoding":904},"P = 2Q + 10",[123,47945,46791,47946,1343,47972,1882],{},[883,47947,47949],{"className":47948},[886],[888,47950,47951],{"xmlns":890},[892,47952,47953,47969],{},[895,47954,47955,47957,47959,47961,47963,47965,47967],{},[898,47956,1690],{},[1651,47958,1738],{},[1651,47960,2181],{},[1692,47962,6316],{},[898,47964,2675],{},[1651,47966,1839],{},[1692,47968,6311],{},[902,47970,47971],{"encoding":904},"Q = -0{,}5P + 25",[883,47973,47975],{"className":47974},[886],[888,47976,47977],{"xmlns":890},[892,47978,47979,47993],{},[895,47980,47981,47983,47985,47987,47989,47991],{},[898,47982,1690],{},[1651,47984,1738],{},[1692,47986,1703],{},[898,47988,2675],{},[1651,47990,2181],{},[1692,47992,4446],{},[902,47994,42060],{"encoding":904},[123,47996,46822,47997,1343,48023,1882],{},[883,47998,48000],{"className":47999},[886],[888,48001,48002],{"xmlns":890},[892,48003,48004,48020],{},[895,48005,48006,48008,48010,48012,48014,48016,48018],{},[898,48007,2675],{},[1651,48009,1738],{},[1651,48011,2181],{},[1692,48013,3689],{},[898,48015,1690],{},[1651,48017,1839],{},[1692,48019,5356],{},[902,48021,48022],{"encoding":904},"P = -4Q + 120",[883,48024,48026],{"className":48025},[886],[888,48027,48028],{"xmlns":890},[892,48029,48030,48051],{},[895,48031,48032,48034,48036,48044,48046,48048],{},[898,48033,2675],{},[1651,48035,1738],{},[2938,48037,48038],{"scriptlevel":1741,"displaystyle":1653},[2446,48039,48040,48042],{},[1692,48041,1694],{},[1692,48043,3521],{},[898,48045,1690],{},[1651,48047,1839],{},[1692,48049,48050],{},"29",[902,48052,48053],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,48055,46857,48056,1343,48085,1882],{},[883,48057,48059],{"className":48058},[886],[888,48060,48061],{"xmlns":890},[892,48062,48063,48082],{},[895,48064,48065,48067,48069,48071,48077,48079],{},[898,48066,2675],{},[1651,48068,1738],{},[1651,48070,2181],{},[2115,48072,48073,48075],{},[898,48074,1690],{},[1692,48076,1703],{},[1651,48078,1839],{},[1692,48080,48081],{},"52",[902,48083,48084],{"encoding":904},"P = -Q^2 + 52",[883,48086,48088],{"className":48087},[886],[888,48089,48090],{"xmlns":890},[892,48091,48092,48110],{},[895,48093,48094,48096,48098,48100,48106,48108],{},[898,48095,2675],{},[1651,48097,1738],{},[1692,48099,1703],{},[2115,48101,48102,48104],{},[898,48103,1690],{},[1692,48105,1703],{},[1651,48107,1839],{},[1692,48109,4190],{},[902,48111,48112],{"encoding":904},"P = 2Q^2 + 10",[724,48114,48115,48118,48119,48149,48150,48180],{},[38,48116,48117],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,48120,48122],{"className":48121},[886],[888,48123,48124],{"xmlns":890},[892,48125,48126,48146],{},[895,48127,48128,48136,48138],{},[1902,48129,48130,48132,48134],{},[898,48131,1690],{},[1692,48133,1694],{},[898,48135,5561],{},[1651,48137,1661],{"separator":1660},[1902,48139,48140,48142,48144],{},[898,48141,1690],{},[1692,48143,1703],{},[898,48145,5561],{},[902,48147,48148],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,48151,48153],{"className":48152},[886],[888,48154,48155],{"xmlns":890},[892,48156,48157,48177],{},[895,48158,48159,48167,48169],{},[1902,48160,48161,48163,48165],{},[898,48162,2675],{},[1692,48164,1694],{},[898,48166,5561],{},[1651,48168,1661],{"separator":1660},[1902,48170,48171,48173,48175],{},[898,48172,2675],{},[1692,48174,1703],{},[898,48176,5561],{},[902,48178,48179],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,48182,48183,48335],{},[123,48184,46758,48185,1343,48225,1343,48267,1343,48301,1882],{},[883,48186,48188],{"className":48187},[886],[888,48189,48190],{"xmlns":890},[892,48191,48192,48222],{},[895,48193,48194,48200,48202,48204,48206,48208,48214,48216],{},[1686,48195,48196,48198],{},[898,48197,1690],{},[1692,48199,1694],{},[1651,48201,1738],{},[1692,48203,4190],{},[1651,48205,2181],{},[1692,48207,1703],{},[1686,48209,48210,48212],{},[898,48211,2675],{},[1692,48213,1694],{},[1651,48215,1839],{},[1686,48217,48218,48220],{},[898,48219,2675],{},[1692,48221,1703],{},[902,48223,48224],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,48226,48228],{"className":48227},[886],[888,48229,48230],{"xmlns":890},[892,48231,48232,48264],{},[895,48233,48234,48240,48242,48244,48246,48248,48254,48256,48258],{},[1686,48235,48236,48238],{},[898,48237,1690],{},[1692,48239,1703],{},[1651,48241,1738],{},[1692,48243,3574],{},[1651,48245,1839],{},[1692,48247,1703],{},[1686,48249,48250,48252],{},[898,48251,2675],{},[1692,48253,1694],{},[1651,48255,2181],{},[1692,48257,1703],{},[1686,48259,48260,48262],{},[898,48261,2675],{},[1692,48263,1703],{},[902,48265,48266],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,48268,48270],{"className":48269},[886],[888,48271,48272],{"xmlns":890},[892,48273,48274,48298],{},[895,48275,48276,48282,48284,48286,48288,48290,48292],{},[1686,48277,48278,48280],{},[898,48279,1690],{},[1692,48281,1694],{},[1651,48283,1738],{},[1651,48285,2181],{},[1692,48287,3521],{},[1651,48289,1839],{},[1692,48291,1703],{},[1686,48293,48294,48296],{},[898,48295,2675],{},[1692,48297,1694],{},[902,48299,48300],{"encoding":904},"Q_1 = -3 + 2P_1",[883,48302,48304],{"className":48303},[886],[888,48305,48306],{"xmlns":890},[892,48307,48308,48332],{},[895,48309,48310,48316,48318,48320,48322,48324,48326],{},[1686,48311,48312,48314],{},[898,48313,1690],{},[1692,48315,1703],{},[1651,48317,1738],{},[1651,48319,2181],{},[1692,48321,1703],{},[1651,48323,1839],{},[1692,48325,3521],{},[1686,48327,48328,48330],{},[898,48329,2675],{},[1692,48331,1703],{},[902,48333,48334],{"encoding":904},"Q_2 = -2 + 3P_2",[123,48336,46791,48337,1343,48377,1343,48419,1343,48451,1882],{},[883,48338,48340],{"className":48339},[886],[888,48341,48342],{"xmlns":890},[892,48343,48344,48374],{},[895,48345,48346,48352,48354,48356,48358,48360,48366,48368],{},[1686,48347,48348,48350],{},[898,48349,1690],{},[1692,48351,1694],{},[1651,48353,1738],{},[1692,48355,4416],{},[1651,48357,2181],{},[1692,48359,1703],{},[1686,48361,48362,48364],{},[898,48363,2675],{},[1692,48365,1694],{},[1651,48367,1839],{},[1686,48369,48370,48372],{},[898,48371,2675],{},[1692,48373,1703],{},[902,48375,48376],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,48378,48380],{"className":48379},[886],[888,48381,48382],{"xmlns":890},[892,48383,48384,48416],{},[895,48385,48386,48392,48394,48396,48398,48400,48406,48408,48410],{},[1686,48387,48388,48390],{},[898,48389,1690],{},[1692,48391,1703],{},[1651,48393,1738],{},[1692,48395,3574],{},[1651,48397,1839],{},[1692,48399,1703],{},[1686,48401,48402,48404],{},[898,48403,2675],{},[1692,48405,1694],{},[1651,48407,2181],{},[1692,48409,3521],{},[1686,48411,48412,48414],{},[898,48413,2675],{},[1692,48415,1703],{},[902,48417,48418],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,48420,48422],{"className":48421},[886],[888,48423,48424],{"xmlns":890},[892,48425,48426,48448],{},[895,48427,48428,48434,48436,48438,48440,48442],{},[1686,48429,48430,48432],{},[898,48431,1690],{},[1692,48433,1694],{},[1651,48435,1738],{},[1651,48437,2181],{},[1692,48439,4190],{},[1651,48441,1839],{},[1686,48443,48444,48446],{},[898,48445,2675],{},[1692,48447,1694],{},[902,48449,48450],{"encoding":904},"Q_1 = -10 + P_1",[883,48452,48454],{"className":48453},[886],[888,48455,48456],{"xmlns":890},[892,48457,48458,48480],{},[895,48459,48460,48466,48468,48470,48472,48474],{},[1686,48461,48462,48464],{},[898,48463,1690],{},[1692,48465,1703],{},[1651,48467,1738],{},[1692,48469,3574],{},[1651,48471,1839],{},[1692,48473,3581],{},[1686,48475,48476,48478],{},[898,48477,2675],{},[1692,48479,1703],{},[902,48481,48482],{"encoding":904},"Q_2 = 5 + 6P_2",[724,48484,48485,48488,48489,1343,48537,1343,48583,48633,48634,1343,48666,1343,48700,22807,48734,5197,48752,48770,48771,48784,48785,48811,48812,48149,48852,1882],{},[38,48486,48487],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,48490,48492],{"className":48491},[886],[888,48493,48494],{"xmlns":890},[892,48495,48496,48534],{},[895,48497,48498,48504,48506,48508,48510,48516,48518,48520,48526,48528],{},[1686,48499,48500,48502],{},[898,48501,1690],{},[1692,48503,1694],{},[1651,48505,1738],{},[1692,48507,37457],{},[1651,48509,2181],{},[1686,48511,48512,48514],{},[898,48513,2675],{},[1692,48515,1694],{},[1651,48517,1839],{},[1692,48519,1703],{},[1686,48521,48522,48524],{},[898,48523,2675],{},[1692,48525,1703],{},[1651,48527,1839],{},[1686,48529,48530,48532],{},[898,48531,2675],{},[1692,48533,3521],{},[902,48535,48536],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,48538,48540],{"className":48539},[886],[888,48541,48542],{"xmlns":890},[892,48543,48544,48580],{},[895,48545,48546,48552,48554,48556,48558,48564,48566,48572,48574],{},[1686,48547,48548,48550],{},[898,48549,1690],{},[1692,48551,1703],{},[1651,48553,1738],{},[1692,48555,5309],{},[1651,48557,1839],{},[1686,48559,48560,48562],{},[898,48561,2675],{},[1692,48563,1694],{},[1651,48565,2181],{},[1686,48567,48568,48570],{},[898,48569,2675],{},[1692,48571,1703],{},[1651,48573,2181],{},[1686,48575,48576,48578],{},[898,48577,2675],{},[1692,48579,3521],{},[902,48581,48582],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,48584,48586],{"className":48585},[886],[888,48587,48588],{"xmlns":890},[892,48589,48590,48630],{},[895,48591,48592,48598,48600,48602,48604,48606,48612,48614,48620,48622,48624],{},[1686,48593,48594,48596],{},[898,48595,1690],{},[1692,48597,3521],{},[1651,48599,1738],{},[1692,48601,6892],{},[1651,48603,1839],{},[1692,48605,1703],{},[1686,48607,48608,48610],{},[898,48609,2675],{},[1692,48611,1694],{},[1651,48613,2181],{},[1686,48615,48616,48618],{},[898,48617,2675],{},[1692,48619,1703],{},[1651,48621,2181],{},[1692,48623,3689],{},[1686,48625,48626,48628],{},[898,48627,2675],{},[1692,48629,3521],{},[902,48631,48632],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,48635,48637],{"className":48636},[886],[888,48638,48639],{"xmlns":890},[892,48640,48641,48663],{},[895,48642,48643,48649,48651,48653,48655,48657],{},[1686,48644,48645,48647],{},[898,48646,1690],{},[1692,48648,1694],{},[1651,48650,1738],{},[1651,48652,2181],{},[1692,48654,25414],{},[1651,48656,1839],{},[1686,48658,48659,48661],{},[898,48660,2675],{},[1692,48662,1694],{},[902,48664,48665],{"encoding":904},"Q_1 = -7 + P_1",[883,48667,48669],{"className":48668},[886],[888,48670,48671],{"xmlns":890},[892,48672,48673,48697],{},[895,48674,48675,48681,48683,48685,48687,48689,48691],{},[1686,48676,48677,48679],{},[898,48678,1690],{},[1692,48680,1703],{},[1651,48682,1738],{},[1651,48684,2181],{},[1692,48686,3689],{},[1651,48688,1839],{},[1692,48690,3689],{},[1686,48692,48693,48695],{},[898,48694,2675],{},[1692,48696,1703],{},[902,48698,48699],{"encoding":904},"Q_2 = -4 + 4P_2",[883,48701,48703],{"className":48702},[886],[888,48704,48705],{"xmlns":890},[892,48706,48707,48731],{},[895,48708,48709,48715,48717,48719,48721,48723,48725],{},[1686,48710,48711,48713],{},[898,48712,1690],{},[1692,48714,3521],{},[1651,48716,1738],{},[1651,48718,2181],{},[1692,48720,3574],{},[1651,48722,1839],{},[1692,48724,1703],{},[1686,48726,48727,48729],{},[898,48728,2675],{},[1692,48730,3521],{},[902,48732,48733],{"encoding":904},"Q_3 = -5 + 2P_3",[883,48735,48737],{"className":48736},[886],[888,48738,48739],{"xmlns":890},[892,48740,48741,48749],{},[895,48742,48743],{},[1686,48744,48745,48747],{},[898,48746,1690],{},[898,48748,3201],{},[902,48750,48751],{"encoding":904},"Q_i",[883,48753,48755],{"className":48754},[886],[888,48756,48757],{"xmlns":890},[892,48758,48759,48767],{},[895,48760,48761],{},[1686,48762,48763,48765],{},[898,48764,2675],{},[898,48766,3201],{},[902,48768,48769],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,48772,48774],{"className":48773},[886],[888,48775,48776],{"xmlns":890},[892,48777,48778,48782],{},[895,48779,48780],{},[898,48781,3201],{},[902,48783,3201],{"encoding":904},"-tého zboží, ",[883,48786,48788],{"className":48787},[886],[888,48789,48790],{"xmlns":890},[892,48791,48792,48808],{},[895,48793,48794,48796,48798,48800,48802,48804,48806],{},[898,48795,3201],{},[1651,48797,1738],{},[1692,48799,1694],{},[1651,48801,1661],{"separator":1660},[1692,48803,1703],{},[1651,48805,1661],{"separator":1660},[1692,48807,3521],{},[902,48809,48810],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,48813,48815],{"className":48814},[886],[888,48816,48817],{"xmlns":890},[892,48818,48819,48849],{},[895,48820,48821,48829,48831,48839,48841],{},[1902,48822,48823,48825,48827],{},[898,48824,1690],{},[1692,48826,1694],{},[898,48828,5561],{},[1651,48830,1661],{"separator":1660},[1902,48832,48833,48835,48837],{},[898,48834,1690],{},[1692,48836,1703],{},[898,48838,5561],{},[1651,48840,1661],{"separator":1660},[1902,48842,48843,48845,48847],{},[898,48844,1690],{},[1692,48846,3521],{},[898,48848,5561],{},[902,48850,48851],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,48853,48855],{"className":48854},[886],[888,48856,48857],{"xmlns":890},[892,48858,48859,48889],{},[895,48860,48861,48869,48871,48879,48881],{},[1902,48862,48863,48865,48867],{},[898,48864,2675],{},[1692,48866,1694],{},[898,48868,5561],{},[1651,48870,1661],{"separator":1660},[1902,48872,48873,48875,48877],{},[898,48874,2675],{},[1692,48876,1703],{},[898,48878,5561],{},[1651,48880,1661],{"separator":1660},[1902,48882,48883,48885,48887],{},[898,48884,2675],{},[1692,48886,3521],{},[898,48888,5561],{},[902,48890,48891],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,48893,48894,48897,48898,48934,48935,1882],{},[38,48895,48896],{},"2.13"," Jsou dány poptávka ",[883,48899,48901],{"className":48900},[886],[888,48902,48903],{"xmlns":890},[892,48904,48905,48931],{},[895,48906,48907,48909,48911,48913,48915,48917,48919,48921,48923,48925,48927,48929],{},[898,48908,2675],{},[1651,48910,1738],{},[898,48912,2047],{},[1651,48914,1654],{"stretchy":1653},[898,48916,1690],{},[1651,48918,1667],{"stretchy":1653},[1651,48920,1738],{},[1651,48922,2181],{},[1692,48924,3689],{},[898,48926,1690],{},[1651,48928,1839],{},[1692,48930,47916],{},[902,48932,48933],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,48936,48938],{"className":48937},[886],[888,48939,48940],{"xmlns":890},[892,48941,48942,48966],{},[895,48943,48944,48946,48948,48950,48952,48954,48956,48958,48960,48962,48964],{},[898,48945,2675],{},[1651,48947,1738],{},[898,48949,3004],{},[1651,48951,1654],{"stretchy":1653},[898,48953,1690],{},[1651,48955,1667],{"stretchy":1653},[1651,48957,1738],{},[1692,48959,3521],{},[898,48961,1690],{},[1651,48963,1839],{},[1692,48965,4190],{},[902,48967,48968],{"encoding":904},"P = S(Q) = 3Q + 10",[120,48970,48971,49008,49072,49132],{},[123,48972,48973,48974,47871,48991,1882],{},"(a) Určete rovnovážné množství ",[883,48975,48977],{"className":48976},[886],[888,48978,48979],{"xmlns":890},[892,48980,48981,48989],{},[895,48982,48983],{},[2115,48984,48985,48987],{},[898,48986,1690],{},[898,48988,5561],{},[902,48990,43616],{"encoding":904},[883,48992,48994],{"className":48993},[886],[888,48995,48996],{"xmlns":890},[892,48997,48998,49006],{},[895,48999,49000],{},[2115,49001,49002,49004],{},[898,49003,2675],{},[898,49005,5561],{},[902,49007,42679],{"encoding":904},[123,49009,49010,49011,49029,49030,49050,49051,49071],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,49012,49014],{"className":49013},[886],[888,49015,49016],{"xmlns":890},[892,49017,49018,49026],{},[895,49019,49020,49022,49024],{},[898,49021,4104],{},[1651,49023,1738],{},[1692,49025,25414],{},[902,49027,49028],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,49031,49033],{"className":49032},[886],[888,49034,49035],{"xmlns":890},[892,49036,49037,49047],{},[895,49038,49039],{},[1902,49040,49041,49043,49045],{},[898,49042,1690],{},[1692,49044,1694],{},[898,49046,5561],{},[902,49048,49049],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,49052,49054],{"className":49053},[886],[888,49055,49056],{"xmlns":890},[892,49057,49058,49068],{},[895,49059,49060],{},[1902,49061,49062,49064,49066],{},[898,49063,2675],{},[1692,49065,1694],{},[898,49067,5561],{},[902,49069,49070],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,49073,49074,49075,49029,49092,49050,49112,49071],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,49076,49078],{"className":49077},[886],[888,49079,49080],{"xmlns":890},[892,49081,49082,49090],{},[895,49083,49084,49086,49088],{},[898,49085,4104],{},[1651,49087,1738],{},[1692,49089,25414],{},[902,49091,49028],{"encoding":904},[883,49093,49095],{"className":49094},[886],[888,49096,49097],{"xmlns":890},[892,49098,49099,49109],{},[895,49100,49101],{},[1902,49102,49103,49105,49107],{},[898,49104,1690],{},[1692,49106,1703],{},[898,49108,5561],{},[902,49110,49111],{"encoding":904},"Q_2^E",[883,49113,49115],{"className":49114},[886],[888,49116,49117],{"xmlns":890},[892,49118,49119,49129],{},[895,49120,49121],{},[1902,49122,49123,49125,49127],{},[898,49124,2675],{},[1692,49126,1703],{},[898,49128,5561],{},[902,49130,49131],{"encoding":904},"P_2^E",[123,49133,49134],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,49136,49137,49138,1882],{},"Viz též ",[207,49139,43934],{"className":49140,"dataFsResolvedFilePath":809,"href":810},[210],[198,49142,44236],{"id":49143},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,49145,49146,48897,49149,48934,49185,1882],{},[38,49147,49148],{},"2.14",[883,49150,49152],{"className":49151},[886],[888,49153,49154],{"xmlns":890},[892,49155,49156,49182],{},[895,49157,49158,49160,49162,49164,49166,49168,49170,49172,49174,49176,49178,49180],{},[898,49159,2675],{},[1651,49161,1738],{},[898,49163,207],{},[898,49165,1690],{},[1651,49167,1839],{},[898,49169,2268],{},[1651,49171,1738],{},[1651,49173,2181],{},[1692,49175,1703],{},[898,49177,1690],{},[1651,49179,1839],{},[1692,49181,4446],{},[902,49183,49184],{"encoding":904},"P = aQ + b = -2Q + 50",[883,49186,49188],{"className":49187},[886],[888,49189,49190],{"xmlns":890},[892,49191,49192,49216],{},[895,49193,49194,49196,49198,49200,49202,49204,49206,49208,49210,49212,49214],{},[898,49195,2675],{},[1651,49197,1738],{},[898,49199,3490],{},[898,49201,1690],{},[1651,49203,1839],{},[898,49205,3542],{},[1651,49207,1738],{},[1692,49209,20534],{},[898,49211,1690],{},[1651,49213,1839],{},[1692,49215,10340],{},[902,49217,49218],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,49220,49221,49257,49260,49346,49399,49479,49533],{},[123,49222,48973,49223,47871,49240,1882],{},[883,49224,49226],{"className":49225},[886],[888,49227,49228],{"xmlns":890},[892,49229,49230,49238],{},[895,49231,49232],{},[2115,49233,49234,49236],{},[898,49235,1690],{},[898,49237,5561],{},[902,49239,43616],{"encoding":904},[883,49241,49243],{"className":49242},[886],[888,49244,49245],{"xmlns":890},[892,49246,49247,49255],{},[895,49248,49249],{},[2115,49250,49251,49253],{},[898,49252,2675],{},[898,49254,5561],{},[902,49256,42679],{"encoding":904},[123,49258,49259],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,49261,49262,49263,49280,49281,4002,49294,4016,49310,49326,49327,1882],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,49264,49266],{"className":49265},[886],[888,49267,49268],{"xmlns":890},[892,49269,49270,49278],{},[895,49271,49272],{},[2115,49273,49274,49276],{},[898,49275,1690],{},[898,49277,5561],{},[902,49279,43616],{"encoding":904}," odpovídající změně ",[883,49282,49284],{"className":49283},[886],[888,49285,49286],{"xmlns":890},[892,49287,49288,49292],{},[895,49289,49290],{},[898,49291,207],{},[902,49293,207],{"encoding":904},[883,49295,49297],{"className":49296},[886],[888,49298,49299],{"xmlns":890},[892,49300,49301,49307],{},[895,49302,49303,49305],{},[1651,49304,2181],{},[1692,49306,1703],{},[902,49308,49309],{"encoding":904},"-2",[883,49311,49313],{"className":49312},[886],[888,49314,49315],{"xmlns":890},[892,49316,49317,49323],{},[895,49318,49319,49321],{},[1651,49320,2181],{},[1692,49322,3521],{},[902,49324,49325],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49328,49330],{"className":49329},[886],[888,49331,49332],{"xmlns":890},[892,49333,49334,49344],{},[895,49335,49336],{},[1902,49337,49338,49340,49342],{},[898,49339,1690],{},[1692,49341,1694],{},[898,49343,5561],{},[902,49345,49049],{"encoding":904},[123,49347,49348,49349,49280,49366,49379,49380,1882],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,49350,49352],{"className":49351},[886],[888,49353,49354],{"xmlns":890},[892,49355,49356,49364],{},[895,49357,49358],{},[2115,49359,49360,49362],{},[898,49361,1690],{},[898,49363,5561],{},[902,49365,43616],{"encoding":904},[883,49367,49369],{"className":49368},[886],[888,49370,49371],{"xmlns":890},[892,49372,49373,49377],{},[895,49374,49375],{},[898,49376,2268],{},[902,49378,2268],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49381,49383],{"className":49382},[886],[888,49384,49385],{"xmlns":890},[892,49386,49387,49397],{},[895,49388,49389],{},[1902,49390,49391,49393,49395],{},[898,49392,1690],{},[1692,49394,1703],{},[898,49396,5561],{},[902,49398,49111],{"encoding":904},[123,49400,49401,49402,49280,49419,4002,49432,4016,49445,49326,49459,1882],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,49403,49405],{"className":49404},[886],[888,49406,49407],{"xmlns":890},[892,49408,49409,49417],{},[895,49410,49411],{},[2115,49412,49413,49415],{},[898,49414,1690],{},[898,49416,5561],{},[902,49418,43616],{"encoding":904},[883,49420,49422],{"className":49421},[886],[888,49423,49424],{"xmlns":890},[892,49425,49426,49430],{},[895,49427,49428],{},[898,49429,3490],{},[902,49431,3490],{"encoding":904},[883,49433,49435],{"className":49434},[886],[888,49436,49437],{"xmlns":890},[892,49438,49439,49443],{},[895,49440,49441],{},[1692,49442,20534],{},[902,49444,45673],{"encoding":904},[883,49446,49448],{"className":49447},[886],[888,49449,49450],{"xmlns":890},[892,49451,49452,49456],{},[895,49453,49454],{},[1692,49455,15887],{},[902,49457,49458],{"encoding":904},"0{,}8",[883,49460,49462],{"className":49461},[886],[888,49463,49464],{"xmlns":890},[892,49465,49466,49476],{},[895,49467,49468],{},[1902,49469,49470,49472,49474],{},[898,49471,1690],{},[1692,49473,3521],{},[898,49475,5561],{},[902,49477,49478],{"encoding":904},"Q_3^E",[123,49480,49481,49482,49280,49499,49512,49513,1882],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,49483,49485],{"className":49484},[886],[888,49486,49487],{"xmlns":890},[892,49488,49489,49497],{},[895,49490,49491],{},[2115,49492,49493,49495],{},[898,49494,1690],{},[898,49496,5561],{},[902,49498,43616],{"encoding":904},[883,49500,49502],{"className":49501},[886],[888,49503,49504],{"xmlns":890},[892,49505,49506,49510],{},[895,49507,49508],{},[898,49509,3542],{},[902,49511,3542],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49514,49516],{"className":49515},[886],[888,49517,49518],{"xmlns":890},[892,49519,49520,49530],{},[895,49521,49522],{},[1902,49523,49524,49526,49528],{},[898,49525,1690],{},[1692,49527,3689],{},[898,49529,5561],{},[902,49531,49532],{"encoding":904},"Q_4^E",[123,49534,49535,49536,49553,49554,49567,49568,22633,49581,1343,49596,22633,49609,5197,49623,22633,49636,49651,49652,1882],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,49537,49539],{"className":49538},[886],[888,49540,49541],{"xmlns":890},[892,49542,49543,49551],{},[895,49544,49545],{},[2115,49546,49547,49549],{},[898,49548,1690],{},[898,49550,5561],{},[902,49552,43616],{"encoding":904}," odpovídající změnám ",[883,49555,49557],{"className":49556},[886],[888,49558,49559],{"xmlns":890},[892,49560,49561,49565],{},[895,49562,49563],{},[898,49564,207],{},[902,49566,207],{"encoding":904}," o 1, ",[883,49569,49571],{"className":49570},[886],[888,49572,49573],{"xmlns":890},[892,49574,49575,49579],{},[895,49576,49577],{},[898,49578,2268],{},[902,49580,2268],{"encoding":904},[883,49582,49584],{"className":49583},[886],[888,49585,49586],{"xmlns":890},[892,49587,49588,49594],{},[895,49589,49590,49592],{},[1651,49591,2181],{},[1692,49593,4190],{},[902,49595,20668],{"encoding":904},[883,49597,49599],{"className":49598},[886],[888,49600,49601],{"xmlns":890},[892,49602,49603,49607],{},[895,49604,49605],{},[898,49606,3490],{},[902,49608,3490],{"encoding":904},[883,49610,49612],{"className":49611},[886],[888,49613,49614],{"xmlns":890},[892,49615,49616,49620],{},[895,49617,49618],{},[1692,49619,4122],{},[902,49621,49622],{"encoding":904},"0{,}1",[883,49624,49626],{"className":49625},[886],[888,49627,49628],{"xmlns":890},[892,49629,49630,49634],{},[895,49631,49632],{},[898,49633,3542],{},[902,49635,3542],{"encoding":904},[883,49637,49639],{"className":49638},[886],[888,49640,49641],{"xmlns":890},[892,49642,49643,49649],{},[895,49644,49645,49647],{},[1651,49646,2181],{},[1692,49648,4190],{},[902,49650,20668],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,49653,49655],{"className":49654},[886],[888,49656,49657],{"xmlns":890},[892,49658,49659,49669],{},[895,49660,49661],{},[1902,49662,49663,49665,49667],{},[898,49664,1690],{},[1692,49666,3574],{},[898,49668,5561],{},[902,49670,49671],{"encoding":904},"Q_5^E",[724,49673,49674,48897,49677,48934,49700,1882],{},[38,49675,49676],{},"2.15",[883,49678,49680],{"className":49679},[886],[888,49681,49682],{"xmlns":890},[892,49683,49684,49698],{},[895,49685,49686,49688,49690,49692,49694,49696],{},[898,49687,2675],{},[1651,49689,1738],{},[898,49691,207],{},[898,49693,1690],{},[1651,49695,1839],{},[898,49697,2268],{},[902,49699,38273],{"encoding":904},[883,49701,49703],{"className":49702},[886],[888,49704,49705],{"xmlns":890},[892,49706,49707,49721],{},[895,49708,49709,49711,49713,49715,49717,49719],{},[898,49710,2675],{},[1651,49712,1738],{},[898,49714,3490],{},[898,49716,1690],{},[1651,49718,1839],{},[898,49720,3542],{},[902,49722,41455],{"encoding":904},[120,49724,49725,49800,49817,49926,49979,50033],{},[123,49726,49727,49728,49741,49742,49767,49768,49799],{},"(a) Odvoďte redukovaný tvar pro ",[883,49729,49731],{"className":49730},[886],[888,49732,49733],{"xmlns":890},[892,49734,49735,49739],{},[895,49736,49737],{},[898,49738,2675],{},[902,49740,2675],{"encoding":904},". Stanovte podmínky pro ",[883,49743,49745],{"className":49744},[886],[888,49746,49747],{"xmlns":890},[892,49748,49749,49765],{},[895,49750,49751,49753,49755,49757,49759,49761,49763],{},[898,49752,207],{},[1651,49754,1661],{"separator":1660},[898,49756,2268],{},[1651,49758,1661],{"separator":1660},[898,49760,3490],{},[1651,49762,1661],{"separator":1660},[898,49764,3542],{},[902,49766,44498],{"encoding":904}," tak, aby rovnovážný bod ",[883,49769,49771],{"className":49770},[886],[888,49772,49773],{"xmlns":890},[892,49774,49775,49797],{},[895,49776,49777,49779,49781,49787,49789,49795],{},[898,49778,5561],{},[1651,49780,2261],{"stretchy":1653},[2115,49782,49783,49785],{},[898,49784,1690],{},[898,49786,5561],{},[1651,49788,1661],{"separator":1660},[2115,49790,49791,49793],{},[898,49792,2675],{},[898,49794,5561],{},[1651,49796,2279],{"stretchy":1653},[902,49798,42580],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,49801,49802,49803,49816],{},"(b) Vypočtěte multiplikátory pro ",[883,49804,49806],{"className":49805},[886],[888,49807,49808],{"xmlns":890},[892,49809,49810,49814],{},[895,49811,49812],{},[898,49813,2675],{},[902,49815,2675],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,49818,49819,49820,1343,49840,1343,49858,1343,49876,49894,49895,49912,49913,1882],{},"(c) Pro hodnoty parametrů ",[883,49821,49823],{"className":49822},[886],[888,49824,49825],{"xmlns":890},[892,49826,49827,49837],{},[895,49828,49829,49831,49833,49835],{},[898,49830,207],{},[1651,49832,1738],{},[1651,49834,2181],{},[1692,49836,1703],{},[902,49838,49839],{"encoding":904},"a = -2",[883,49841,49843],{"className":49842},[886],[888,49844,49845],{"xmlns":890},[892,49846,49847,49855],{},[895,49848,49849,49851,49853],{},[898,49850,2268],{},[1651,49852,1738],{},[1692,49854,6518],{},[902,49856,49857],{"encoding":904},"b = 40",[883,49859,49861],{"className":49860},[886],[888,49862,49863],{"xmlns":890},[892,49864,49865,49873],{},[895,49866,49867,49869,49871],{},[898,49868,3490],{},[1651,49870,1738],{},[1692,49872,6316],{},[902,49874,49875],{"encoding":904},"c = 0{,}5",[883,49877,49879],{"className":49878},[886],[888,49880,49881],{"xmlns":890},[892,49882,49883,49891],{},[895,49884,49885,49887,49889],{},[898,49886,3542],{},[1651,49888,1738],{},[1692,49890,4190],{},[902,49892,49893],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,49896,49898],{"className":49897},[886],[888,49899,49900],{"xmlns":890},[892,49901,49902,49910],{},[895,49903,49904],{},[2115,49905,49906,49908],{},[898,49907,2675],{},[898,49909,5561],{},[902,49911,42679],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,49914,49916],{"className":49915},[886],[888,49917,49918],{"xmlns":890},[892,49919,49920,49924],{},[895,49921,49922],{},[898,49923,2675],{},[902,49925,2675],{"encoding":904},[123,49927,49928,49929,49280,49946,49959,49960,1882],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,49930,49932],{"className":49931},[886],[888,49933,49934],{"xmlns":890},[892,49935,49936,49944],{},[895,49937,49938],{},[2115,49939,49940,49942],{},[898,49941,2675],{},[898,49943,5561],{},[902,49945,42679],{"encoding":904},[883,49947,49949],{"className":49948},[886],[888,49950,49951],{"xmlns":890},[892,49952,49953,49957],{},[895,49954,49955],{},[898,49956,207],{},[902,49958,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,49961,49963],{"className":49962},[886],[888,49964,49965],{"xmlns":890},[892,49966,49967,49977],{},[895,49968,49969],{},[1902,49970,49971,49973,49975],{},[898,49972,2675],{},[1692,49974,1694],{},[898,49976,5561],{},[902,49978,49070],{"encoding":904},[123,49980,49981,49982,49999,50000,50013,50014,1882],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,49983,49985],{"className":49984},[886],[888,49986,49987],{"xmlns":890},[892,49988,49989,49997],{},[895,49990,49991],{},[2115,49992,49993,49995],{},[898,49994,2675],{},[898,49996,5561],{},[902,49998,42679],{"encoding":904}," odpovídající poklesu ",[883,50001,50003],{"className":50002},[886],[888,50004,50005],{"xmlns":890},[892,50006,50007,50011],{},[895,50008,50009],{},[898,50010,207],{},[902,50012,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,50015,50017],{"className":50016},[886],[888,50018,50019],{"xmlns":890},[892,50020,50021,50031],{},[895,50022,50023],{},[1902,50024,50025,50027,50029],{},[898,50026,2675],{},[1692,50028,1703],{},[898,50030,5561],{},[902,50032,49131],{"encoding":904},[123,50034,50035,50036,49553,50053,50066,50067,4016,50080,5197,50095,50108,50109,1882],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,50037,50039],{"className":50038},[886],[888,50040,50041],{"xmlns":890},[892,50042,50043,50051],{},[895,50044,50045],{},[2115,50046,50047,50049],{},[898,50048,2675],{},[898,50050,5561],{},[902,50052,42679],{"encoding":904},[883,50054,50056],{"className":50055},[886],[888,50057,50058],{"xmlns":890},[892,50059,50060,50064],{},[895,50061,50062],{},[898,50063,207],{},[902,50065,207],{"encoding":904}," na 35, ",[883,50068,50070],{"className":50069},[886],[888,50071,50072],{"xmlns":890},[892,50073,50074,50078],{},[895,50075,50076],{},[898,50077,3490],{},[902,50079,3490],{"encoding":904},[883,50081,50083],{"className":50082},[886],[888,50084,50085],{"xmlns":890},[892,50086,50087,50092],{},[895,50088,50089],{},[1692,50090,50091],{},"0,7",[902,50093,50094],{"encoding":904},"0{,}7",[883,50096,50098],{"className":50097},[886],[888,50099,50100],{"xmlns":890},[892,50101,50102,50106],{},[895,50103,50104],{},[898,50105,3542],{},[902,50107,3542],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,50110,50112],{"className":50111},[886],[888,50113,50114],{"xmlns":890},[892,50115,50116,50126],{},[895,50117,50118],{},[1902,50119,50120,50122,50124],{},[898,50121,2675],{},[1692,50123,3521],{},[898,50125,5561],{},[902,50127,50128],{"encoding":904},"P_3^E",[724,50130,50131,48897,50134,48934,50162,22807,50190,5197,50216,1882],{},[38,50132,50133],{},"2.16",[883,50135,50137],{"className":50136},[886],[888,50138,50139],{"xmlns":890},[892,50140,50141,50159],{},[895,50142,50143,50145,50147,50149,50151,50153],{},[898,50144,2675],{},[1651,50146,1738],{},[898,50148,207],{},[1651,50150,1839],{},[898,50152,2268],{},[2115,50154,50155,50157],{},[898,50156,1690],{},[1692,50158,1703],{},[902,50160,50161],{"encoding":904},"P = a + bQ^2",[883,50163,50165],{"className":50164},[886],[888,50166,50167],{"xmlns":890},[892,50168,50169,50187],{},[895,50170,50171,50173,50175,50177,50179,50181],{},[898,50172,2675],{},[1651,50174,1738],{},[898,50176,3490],{},[1651,50178,1839],{},[898,50180,3542],{},[2115,50182,50183,50185],{},[898,50184,1690],{},[1692,50186,1703],{},[902,50188,50189],{"encoding":904},"P = c + dQ^2",[883,50191,50193],{"className":50192},[886],[888,50194,50195],{"xmlns":890},[892,50196,50197,50213],{},[895,50198,50199,50201,50203,50205,50207,50209,50211],{},[898,50200,207],{},[1651,50202,1661],{"separator":1660},[898,50204,3490],{},[1651,50206,1661],{"separator":1660},[898,50208,3542],{},[1651,50210,2390],{},[1692,50212,1741],{},[902,50214,50215],{"encoding":904},"a, c, d > 0",[883,50217,50219],{"className":50218},[886],[888,50220,50221],{"xmlns":890},[892,50222,50223,50231],{},[895,50224,50225,50227,50229],{},[898,50226,2268],{},[1651,50228,2319],{},[1692,50230,1741],{},[902,50232,50233],{"encoding":904},"b \u003C 0",[120,50235,50236,50284,50300,50407,50459,50511,50620,50636,50735,50788],{},[123,50237,49727,50238,50251,50252,50283],{},[883,50239,50241],{"className":50240},[886],[888,50242,50243],{"xmlns":890},[892,50244,50245,50249],{},[895,50246,50247],{},[898,50248,1690],{},[902,50250,1690],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,50253,50255],{"className":50254},[886],[888,50256,50257],{"xmlns":890},[892,50258,50259,50281],{},[895,50260,50261,50263,50265,50271,50273,50279],{},[898,50262,5561],{},[1651,50264,2261],{"stretchy":1653},[2115,50266,50267,50269],{},[898,50268,1690],{},[898,50270,5561],{},[1651,50272,1661],{"separator":1660},[2115,50274,50275,50277],{},[898,50276,2675],{},[898,50278,5561],{},[1651,50280,2279],{"stretchy":1653},[902,50282,42580],{"encoding":904}," patřil do 1. kvadrantu.",[123,50285,49802,50286,50299],{},[883,50287,50289],{"className":50288},[886],[888,50290,50291],{"xmlns":890},[892,50292,50293,50297],{},[895,50294,50295],{},[898,50296,1690],{},[902,50298,1690],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,50301,49819,50302,1343,50320,1343,50340,1343,50358,50376,50377,49912,50394,1882],{},[883,50303,50305],{"className":50304},[886],[888,50306,50307],{"xmlns":890},[892,50308,50309,50317],{},[895,50310,50311,50313,50315],{},[898,50312,207],{},[1651,50314,1738],{},[1692,50316,4416],{},[902,50318,50319],{"encoding":904},"a = 100",[883,50321,50323],{"className":50322},[886],[888,50324,50325],{"xmlns":890},[892,50326,50327,50337],{},[895,50328,50329,50331,50333,50335],{},[898,50330,2268],{},[1651,50332,1738],{},[1651,50334,2181],{},[1692,50336,1694],{},[902,50338,50339],{"encoding":904},"b = -1",[883,50341,50343],{"className":50342},[886],[888,50344,50345],{"xmlns":890},[892,50346,50347,50355],{},[895,50348,50349,50351,50353],{},[898,50350,3490],{},[1651,50352,1738],{},[1692,50354,10340],{},[902,50356,50357],{"encoding":904},"c = 20",[883,50359,50361],{"className":50360},[886],[888,50362,50363],{"xmlns":890},[892,50364,50365,50373],{},[895,50366,50367,50369,50371],{},[898,50368,3542],{},[1651,50370,1738],{},[1692,50372,1694],{},[902,50374,50375],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,50378,50380],{"className":50379},[886],[888,50381,50382],{"xmlns":890},[892,50383,50384,50392],{},[895,50385,50386],{},[2115,50387,50388,50390],{},[898,50389,1690],{},[898,50391,5561],{},[902,50393,43616],{"encoding":904},[883,50395,50397],{"className":50396},[886],[888,50398,50399],{"xmlns":890},[892,50400,50401,50405],{},[895,50402,50403],{},[898,50404,1690],{},[902,50406,1690],{"encoding":904},[123,50408,49348,50409,49280,50426,50439,50440,1882],{},[883,50410,50412],{"className":50411},[886],[888,50413,50414],{"xmlns":890},[892,50415,50416,50424],{},[895,50417,50418],{},[2115,50419,50420,50422],{},[898,50421,1690],{},[898,50423,5561],{},[902,50425,43616],{"encoding":904},[883,50427,50429],{"className":50428},[886],[888,50430,50431],{"xmlns":890},[892,50432,50433,50437],{},[895,50434,50435],{},[898,50436,207],{},[902,50438,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,50441,50443],{"className":50442},[886],[888,50444,50445],{"xmlns":890},[892,50446,50447,50457],{},[895,50448,50449],{},[1902,50450,50451,50453,50455],{},[898,50452,1690],{},[1692,50454,1694],{},[898,50456,5561],{},[902,50458,49049],{"encoding":904},[123,50460,49401,50461,49280,50478,50491,50492,1882],{},[883,50462,50464],{"className":50463},[886],[888,50465,50466],{"xmlns":890},[892,50467,50468,50476],{},[895,50469,50470],{},[2115,50471,50472,50474],{},[898,50473,1690],{},[898,50475,5561],{},[902,50477,43616],{"encoding":904},[883,50479,50481],{"className":50480},[886],[888,50482,50483],{"xmlns":890},[892,50484,50485,50489],{},[895,50486,50487],{},[898,50488,3490],{},[902,50490,3490],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,50493,50495],{"className":50494},[886],[888,50496,50497],{"xmlns":890},[892,50498,50499,50509],{},[895,50500,50501],{},[1902,50502,50503,50505,50507],{},[898,50504,1690],{},[1692,50506,1703],{},[898,50508,5561],{},[902,50510,49111],{"encoding":904},[123,50512,49481,50513,49553,50530,50543,50544,4016,50557,50572,50573,50586,50587,50600,50601,1882],{},[883,50514,50516],{"className":50515},[886],[888,50517,50518],{"xmlns":890},[892,50519,50520,50528],{},[895,50521,50522],{},[2115,50523,50524,50526],{},[898,50525,1690],{},[898,50527,5561],{},[902,50529,43616],{"encoding":904},[883,50531,50533],{"className":50532},[886],[888,50534,50535],{"xmlns":890},[892,50536,50537,50541],{},[895,50538,50539],{},[898,50540,207],{},[902,50542,207],{"encoding":904}," na 110, poklesu ",[883,50545,50547],{"className":50546},[886],[888,50548,50549],{"xmlns":890},[892,50550,50551,50555],{},[895,50552,50553],{},[898,50554,2268],{},[902,50556,2268],{"encoding":904},[883,50558,50560],{"className":50559},[886],[888,50561,50562],{"xmlns":890},[892,50563,50564,50570],{},[895,50565,50566,50568],{},[1651,50567,2181],{},[1692,50569,1703],{},[902,50571,49309],{"encoding":904},", růstu ",[883,50574,50576],{"className":50575},[886],[888,50577,50578],{"xmlns":890},[892,50579,50580,50584],{},[895,50581,50582],{},[898,50583,3490],{},[902,50585,3490],{"encoding":904}," na 25 a růstu ",[883,50588,50590],{"className":50589},[886],[888,50591,50592],{"xmlns":890},[892,50593,50594,50598],{},[895,50595,50596],{},[898,50597,3542],{},[902,50599,3542],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,50602,50604],{"className":50603},[886],[888,50605,50606],{"xmlns":890},[892,50607,50608,50618],{},[895,50609,50610],{},[1902,50611,50612,50614,50616],{},[898,50613,1690],{},[1692,50615,3521],{},[898,50617,5561],{},[902,50619,49478],{"encoding":904},[123,50621,50622,50623,50299],{},"(i) Vypočtěte multiplikátory pro ",[883,50624,50626],{"className":50625},[886],[888,50627,50628],{"xmlns":890},[892,50629,50630,50634],{},[895,50631,50632],{},[898,50633,2675],{},[902,50635,2675],{"encoding":904},[123,50637,50638,50639,49912,50656,50669,50670,49280,50687,4016,50700,50715,50716,1882],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,50640,50642],{"className":50641},[886],[888,50643,50644],{"xmlns":890},[892,50645,50646,50654],{},[895,50647,50648],{},[2115,50649,50650,50652],{},[898,50651,2675],{},[898,50653,5561],{},[902,50655,42679],{"encoding":904},[883,50657,50659],{"className":50658},[886],[888,50660,50661],{"xmlns":890},[892,50662,50663,50667],{},[895,50664,50665],{},[898,50666,2675],{},[902,50668,2675],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,50671,50673],{"className":50672},[886],[888,50674,50675],{"xmlns":890},[892,50676,50677,50685],{},[895,50678,50679],{},[2115,50680,50681,50683],{},[898,50682,2675],{},[898,50684,5561],{},[902,50686,42679],{"encoding":904},[883,50688,50690],{"className":50689},[886],[888,50691,50692],{"xmlns":890},[892,50693,50694,50698],{},[895,50695,50696],{},[898,50697,207],{},[902,50699,207],{"encoding":904},[883,50701,50703],{"className":50702},[886],[888,50704,50705],{"xmlns":890},[892,50706,50707,50713],{},[895,50708,50709,50711],{},[1651,50710,2181],{},[1692,50712,3521],{},[902,50714,49325],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,50717,50719],{"className":50718},[886],[888,50720,50721],{"xmlns":890},[892,50722,50723,50733],{},[895,50724,50725],{},[1902,50726,50727,50729,50731],{},[898,50728,2675],{},[1692,50730,1694],{},[898,50732,5561],{},[902,50734,49070],{"encoding":904},[123,50736,50737,50738,49280,50755,50768,50769,1882],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,50739,50741],{"className":50740},[886],[888,50742,50743],{"xmlns":890},[892,50744,50745,50753],{},[895,50746,50747],{},[2115,50748,50749,50751],{},[898,50750,2675],{},[898,50752,5561],{},[902,50754,42679],{"encoding":904},[883,50756,50758],{"className":50757},[886],[888,50759,50760],{"xmlns":890},[892,50761,50762,50766],{},[895,50763,50764],{},[898,50765,207],{},[902,50767,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,50770,50772],{"className":50771},[886],[888,50773,50774],{"xmlns":890},[892,50775,50776,50786],{},[895,50777,50778],{},[1902,50779,50780,50782,50784],{},[898,50781,2675],{},[1692,50783,1703],{},[898,50785,5561],{},[902,50787,49131],{"encoding":904},[123,50789,50790,50791,49999,50808,50821,50822,4016,50835,50572,50850,50863,50864,50877,50878,1882],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,50792,50794],{"className":50793},[886],[888,50795,50796],{"xmlns":890},[892,50797,50798,50806],{},[895,50799,50800],{},[2115,50801,50802,50804],{},[898,50803,2675],{},[898,50805,5561],{},[902,50807,42679],{"encoding":904},[883,50809,50811],{"className":50810},[886],[888,50812,50813],{"xmlns":890},[892,50814,50815,50819],{},[895,50816,50817],{},[898,50818,207],{},[902,50820,207],{"encoding":904}," na 90, poklesu ",[883,50823,50825],{"className":50824},[886],[888,50826,50827],{"xmlns":890},[892,50828,50829,50833],{},[895,50830,50831],{},[898,50832,2268],{},[902,50834,2268],{"encoding":904},[883,50836,50838],{"className":50837},[886],[888,50839,50840],{"xmlns":890},[892,50841,50842,50848],{},[895,50843,50844,50846],{},[1651,50845,2181],{},[1692,50847,3521],{},[902,50849,49325],{"encoding":904},[883,50851,50853],{"className":50852},[886],[888,50854,50855],{"xmlns":890},[892,50856,50857,50861],{},[895,50858,50859],{},[898,50860,3490],{},[902,50862,3490],{"encoding":904}," na 30 a růstu ",[883,50865,50867],{"className":50866},[886],[888,50868,50869],{"xmlns":890},[892,50870,50871,50875],{},[895,50872,50873],{},[898,50874,3542],{},[902,50876,3542],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,50879,50881],{"className":50880},[886],[888,50882,50883],{"xmlns":890},[892,50884,50885,50895],{},[895,50886,50887],{},[1902,50888,50889,50891,50893],{},[898,50890,2675],{},[1692,50892,3521],{},[898,50894,5561],{},[902,50896,50128],{"encoding":904},[198,50898,820],{"id":50899},"přebytek-spotřebitele-a-výrobce-1",[724,50901,50902,48897,50905,48934,50941,1882],{},[38,50903,50904],{},"2.17",[883,50906,50908],{"className":50907},[886],[888,50909,50910],{"xmlns":890},[892,50911,50912,50938],{},[895,50913,50914,50916,50918,50920,50922,50924,50926,50928,50930,50932],{},[898,50915,2675],{},[1651,50917,1738],{},[898,50919,2047],{},[1651,50921,1654],{"stretchy":1653},[898,50923,1690],{},[1651,50925,1667],{"stretchy":1653},[1651,50927,1738],{},[1692,50929,16336],{},[1651,50931,2181],{},[2115,50933,50934,50936],{},[898,50935,1690],{},[1692,50937,1703],{},[902,50939,50940],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,50942,50944],{"className":50943},[886],[888,50945,50946],{"xmlns":890},[892,50947,50948,50974],{},[895,50949,50950,50952,50954,50956,50958,50960,50962,50964,50966,50968],{},[898,50951,2675],{},[1651,50953,1738],{},[898,50955,3004],{},[1651,50957,1654],{"stretchy":1653},[898,50959,1690],{},[1651,50961,1667],{"stretchy":1653},[1651,50963,1738],{},[1692,50965,3521],{},[1651,50967,1839],{},[2115,50969,50970,50972],{},[898,50971,1690],{},[1692,50973,1703],{},[902,50975,50976],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,50978,50979,50982],{},[123,50980,50981],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,50983,50984],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,50986,50987,48897,50990,48934,51024,1882],{},[38,50988,50989],{},"2.18",[883,50991,50993],{"className":50992},[886],[888,50994,50995],{"xmlns":890},[892,50996,50997,51021],{},[895,50998,50999,51001,51003,51005,51007,51009,51011,51013,51015,51017,51019],{},[898,51000,2675],{},[1651,51002,1738],{},[898,51004,2047],{},[1651,51006,1654],{"stretchy":1653},[898,51008,1690],{},[1651,51010,1667],{"stretchy":1653},[1651,51012,1738],{},[1692,51014,5026],{},[1651,51016,2181],{},[1692,51018,1703],{},[898,51020,1690],{},[902,51022,51023],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,51025,51027],{"className":51026},[886],[888,51028,51029],{"xmlns":890},[892,51030,51031,51057],{},[895,51032,51033,51035,51037,51039,51041,51043,51045,51047,51049,51051],{},[898,51034,2675],{},[1651,51036,1738],{},[898,51038,3004],{},[1651,51040,1654],{"stretchy":1653},[898,51042,1690],{},[1651,51044,1667],{"stretchy":1653},[1651,51046,1738],{},[1692,51048,3521],{},[1651,51050,1839],{},[2115,51052,51053,51055],{},[898,51054,1690],{},[1692,51056,1703],{},[902,51058,50976],{"encoding":904},[120,51060,51061,51081,51084,51087],{},[123,51062,51063,51064,1882],{},"(a) Vypočtěte rovnovážné množství ",[883,51065,51067],{"className":51066},[886],[888,51068,51069],{"xmlns":890},[892,51070,51071,51079],{},[895,51072,51073],{},[2115,51074,51075,51077],{},[898,51076,1690],{},[898,51078,5561],{},[902,51080,43616],{"encoding":904},[123,51082,51083],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,51085,51086],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,51088,51089],{},"(c) Graficky interpretujte.",[38183,51091],{},[115,51093,51095],{"id":51094},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,51097,51098,51101,51104,51107,51110,51113,51116,51119,51122,51125,51128,51131,51134,51137],{},[123,51099,51100],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,51102,51103],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,51105,51106],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,51108,51109],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,51111,51112],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,51114,51115],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,51117,51118],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,51120,51121],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,51123,51124],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,51126,51127],{},"K čemu slouží multiplikátory?",[123,51129,51130],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,51132,51133],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,51135,51136],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,51138,51139],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[38183,51141],{},[115,51143,17018],{"id":17017},[724,51145,51146],{},[38,51147,14459],{},[120,51149,51150,51185,51190,51220,51225,51288,51314,51319,51349,51358,51365,51371],{},[123,51151,51152,11325,51155,19861,51158,3246,51160,1343,51183],{},[38,51153,51154],{},"Poptávané množství",[614,51156,51157],{},"quantity demanded",[38,51159,29215],{},[883,51161,51163],{"className":51162},[886],[888,51164,51165],{"xmlns":890},[892,51166,51167,51181],{},[895,51168,51169,51171,51173,51175,51177,51179],{},[898,51170,1690],{},[1651,51172,1738],{},[898,51174,2047],{},[1651,51176,1654],{"stretchy":1653},[898,51178,2675],{},[1651,51180,1667],{"stretchy":1653},[902,51182,5501],{"encoding":904},[38,51184,38662],{},[123,51186,51187,51189],{},[38,51188,38669],{}," — substituční + důchodový efekt",[123,51191,51192,3246,51195],{},[38,51193,51194],{},"Reálné cenové rozpětí",[883,51196,51198],{"className":51197},[886],[888,51199,51200],{"xmlns":890},[892,51201,51202,51218],{},[895,51203,51204,51206,51208,51210,51216],{},[1651,51205,1654],{"stretchy":1653},[1692,51207,1741],{},[1651,51209,1661],{"separator":1660},[1686,51211,51212,51214],{},[898,51213,2675],{},[1692,51215,1741],{},[1651,51217,1667],{"stretchy":1653},[902,51219,38870],{"encoding":904},[123,51221,51222,12394],{},[38,51223,51224],{},"Homogenita poptávky",[123,51226,51227,3246,51230,1343,51253,1343,51270,51287],{},[38,51228,51229],{},"Lineární poptávka",[883,51231,51233],{"className":51232},[886],[888,51234,51235],{"xmlns":890},[892,51236,51237,51251],{},[895,51238,51239,51241,51243,51245,51247,51249],{},[898,51240,2675],{},[1651,51242,1738],{},[898,51244,207],{},[898,51246,1690],{},[1651,51248,1839],{},[898,51250,2268],{},[902,51252,38273],{"encoding":904},[883,51254,51256],{"className":51255},[886],[888,51257,51258],{"xmlns":890},[892,51259,51260,51268],{},[895,51261,51262,51264,51266],{},[898,51263,207],{},[1651,51265,2319],{},[1692,51267,1741],{},[902,51269,44298],{"encoding":904},[883,51271,51273],{"className":51272},[886],[888,51274,51275],{"xmlns":890},[892,51276,51277,51285],{},[895,51278,51279,51281,51283],{},[898,51280,2268],{},[1651,51282,2390],{},[1692,51284,1741],{},[902,51286,20027],{"encoding":904}," — nedokonalá konkurence",[123,51289,51290,8322,51293],{},[38,51291,51292],{},"Dokonalá konkurence",[883,51294,51296],{"className":51295},[886],[888,51297,51298],{"xmlns":890},[892,51299,51300,51312],{},[895,51301,51302,51304,51306],{},[898,51303,2675],{},[1651,51305,1738],{},[2115,51307,51308,51310],{},[898,51309,2675],{},[1651,51311,2668],{},[902,51313,5664],{"encoding":904},[123,51315,51316,51318],{},[38,51317,39439],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,51320,51321,3246,51323,1343,51347],{},[38,51322,32940],{},[883,51324,51326],{"className":51325},[886],[888,51327,51328],{"xmlns":890},[892,51329,51330,51344],{},[895,51331,51332,51334,51336,51338,51340,51342],{},[898,51333,1690],{},[1651,51335,1738],{},[898,51337,5561],{},[1651,51339,1654],{"stretchy":1653},[898,51341,2665],{},[1651,51343,1667],{"stretchy":1653},[902,51345,51346],{"encoding":904},"Q = E(Y)",[38,51348,39636],{},[123,51350,51351,51354,51355,51357],{},[38,51352,51353],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,51356,40082],{}," zboží",[123,51359,51360,5197,51362,51364],{},[38,51361,41088],{},[38,51363,41035],{}," — znaménka zkřížených koeficientů",[123,51366,51367,51370],{},[38,51368,51369],{},"Dvoukomoditní trh"," (2.6)",[123,51372,51373,11325,51376,1667],{},[38,51374,51375],{},"Posun poptávky",[614,51377,40140],{},[724,51379,51380],{},[38,51381,14423],{},[120,51383,51384,51417,51421,51466],{},[123,51385,51386,11325,51388,19861,51390,3246,51392,1343,51415],{},[38,51387,41482],{},[614,51389,41485],{},[38,51391,41656],{},[883,51393,51395],{"className":51394},[886],[888,51396,51397],{"xmlns":890},[892,51398,51399,51413],{},[895,51400,51401,51403,51405,51407,51409,51411],{},[898,51402,1690],{},[1651,51404,1738],{},[898,51406,3004],{},[1651,51408,1654],{"stretchy":1653},[898,51410,2675],{},[1651,51412,1667],{"stretchy":1653},[902,51414,9987],{"encoding":904},[38,51416,41734],{},[123,51418,51419],{},[38,51420,41741],{},[123,51422,51423,3246,51426,1343,51449],{},[38,51424,51425],{},"Lineární nabídka",[883,51427,51429],{"className":51428},[886],[888,51430,51431],{"xmlns":890},[892,51432,51433,51447],{},[895,51434,51435,51437,51439,51441,51443,51445],{},[898,51436,2675],{},[1651,51438,1738],{},[898,51440,3490],{},[898,51442,1690],{},[1651,51444,1839],{},[898,51446,3542],{},[902,51448,41455],{"encoding":904},[883,51450,51452],{"className":51451},[886],[888,51453,51454],{"xmlns":890},[892,51455,51456,51464],{},[895,51457,51458,51460,51462],{},[898,51459,3490],{},[1651,51461,2390],{},[1692,51463,1741],{},[902,51465,41473],{"encoding":904},[123,51467,51468,11325,51471,1667],{},[38,51469,51470],{},"Posun nabídky",[614,51472,42119],{},[724,51474,51475],{},[38,51476,51477],{},"Rovnováha a komparativní statika",[120,51479,51480,51559,51565],{},[123,51481,51482,11325,51484,19861,51486,3246,51489,1343,51506,3246,51509,1343,51526,3246,51528],{},[38,51483,42538],{},[614,51485,42657],{},[38,51487,51488],{},"rovnovážná cena",[883,51490,51492],{"className":51491},[886],[888,51493,51494],{"xmlns":890},[892,51495,51496,51504],{},[895,51497,51498],{},[2115,51499,51500,51502],{},[898,51501,2675],{},[898,51503,5561],{},[902,51505,42679],{"encoding":904},[38,51507,51508],{},"rovnovážné množství",[883,51510,51512],{"className":51511},[886],[888,51513,51514],{"xmlns":890},[892,51515,51516,51524],{},[895,51517,51518],{},[2115,51519,51520,51522],{},[898,51521,1690],{},[898,51523,5561],{},[902,51525,43616],{"encoding":904},[38,51527,42715],{},[883,51529,51531],{"className":51530},[886],[888,51532,51533],{"xmlns":890},[892,51534,51535,51557],{},[895,51536,51537,51539,51541,51547,51549,51555],{},[898,51538,5561],{},[1651,51540,2261],{"stretchy":1653},[2115,51542,51543,51545],{},[898,51544,1690],{},[898,51546,5561],{},[1651,51548,1661],{"separator":1660},[2115,51550,51551,51553],{},[898,51552,2675],{},[898,51554,5561],{},[1651,51556,2279],{"stretchy":1653},[902,51558,42580],{"encoding":904},[123,51560,51561,51564],{},[38,51562,51563],{},"Pravidla 1–4"," komparativní statiky",[123,51566,51567,11325,51570,1667],{},[38,51568,51569],{},"Teorém pavučiny",[614,51571,43562],{},[724,51573,51574],{},[38,51575,51576],{},"Zdanění",[120,51578,51579,51635,51683],{},[123,51580,51581,51583,51584,51609,51610,1667],{},[38,51582,51576],{}," — daň výrobci (",[883,51585,51587],{"className":51586},[886],[888,51588,51589],{"xmlns":890},[892,51590,51591,51607],{},[895,51592,51593,51599,51601,51603,51605],{},[1686,51594,51595,51597],{},[898,51596,3004],{},[1692,51598,1694],{},[1651,51600,1738],{},[898,51602,3004],{},[1651,51604,1839],{},[898,51606,4104],{},[902,51608,43967],{"encoding":904},") vs. daň spotřebiteli (",[883,51611,51613],{"className":51612},[886],[888,51614,51615],{"xmlns":890},[892,51616,51617,51633],{},[895,51618,51619,51625,51627,51629,51631],{},[1686,51620,51621,51623],{},[898,51622,2047],{},[1692,51624,1703],{},[1651,51626,1738],{},[898,51628,2047],{},[1651,51630,2181],{},[898,51632,4104],{},[902,51634,43998],{"encoding":904},[123,51636,51637,3246,51639,1343,51660],{},[38,51638,43871],{},[883,51640,51642],{"className":51641},[886],[888,51643,51644],{"xmlns":890},[892,51645,51646,51658],{},[895,51647,51648],{},[1686,51649,51650,51652],{},[898,51651,4104],{},[895,51653,51654,51656],{},[898,51655,43890],{},[898,51657,724],{},[902,51659,43895],{"encoding":904},[883,51661,51663],{"className":51662},[886],[888,51664,51665],{"xmlns":890},[892,51666,51667,51681],{},[895,51668,51669],{},[1686,51670,51671,51673],{},[898,51672,4104],{},[895,51674,51675,51677,51679],{},[898,51676,43913],{},[898,51678,1664],{},[898,51680,13339],{},[902,51682,43920],{"encoding":904},[123,51684,51685,3246,51688,1343,51717],{},[38,51686,51687],{},"Ekvivalence zdanění",[883,51689,51691],{"className":51690},[886],[888,51692,51693],{"xmlns":890},[892,51694,51695,51715],{},[895,51696,51697,51705,51707],{},[1902,51698,51699,51701,51703],{},[898,51700,1690],{},[1692,51702,1694],{},[898,51704,5561],{},[1651,51706,1738],{},[1902,51708,51709,51711,51713],{},[898,51710,1690],{},[1692,51712,1703],{},[898,51714,5561],{},[902,51716,44121],{"encoding":904},[883,51718,51720],{"className":51719},[886],[888,51721,51722],{"xmlns":890},[892,51723,51724,51748],{},[895,51725,51726,51734,51736,51738,51740],{},[1902,51727,51728,51730,51732],{},[898,51729,2675],{},[1692,51731,1694],{},[898,51733,5561],{},[1651,51735,2181],{},[898,51737,4104],{},[1651,51739,1738],{},[1902,51741,51742,51744,51746],{},[898,51743,2675],{},[1692,51745,1703],{},[898,51747,5561],{},[902,51749,44155],{"encoding":904},[724,51751,51752],{},[38,51753,27621],{},[120,51755,51756,51802,51833,51838,51844,51851],{},[123,51757,51758,3246,51760],{},[38,51759,44254],{},[883,51761,51763],{"className":51762},[886],[888,51764,51765],{"xmlns":890},[892,51766,51767,51799],{},[895,51768,51769,51775,51777,51779,51781,51783,51785,51787,51789,51791,51793,51795,51797],{},[2115,51770,51771,51773],{},[898,51772,1690],{},[898,51774,5561],{},[1651,51776,1738],{},[1651,51778,1654],{"stretchy":1653},[898,51780,2268],{},[1651,51782,2181],{},[898,51784,3542],{},[1651,51786,1667],{"stretchy":1653},[898,51788,5981],{"mathvariant":1910},[1651,51790,1654],{"stretchy":1653},[898,51792,3490],{},[1651,51794,2181],{},[898,51796,207],{},[1651,51798,1667],{"stretchy":1653},[902,51800,51801],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,51803,51804,3246,51807,51832],{},[38,51805,51806],{},"Parametry",[883,51808,51810],{"className":51809},[886],[888,51811,51812],{"xmlns":890},[892,51813,51814,51830],{},[895,51815,51816,51818,51820,51822,51824,51826,51828],{},[898,51817,207],{},[1651,51819,1661],{"separator":1660},[898,51821,2268],{},[1651,51823,1661],{"separator":1660},[898,51825,3490],{},[1651,51827,1661],{"separator":1660},[898,51829,3542],{},[902,51831,44498],{"encoding":904}," — exogenní proměnné",[123,51834,51835],{},[38,51836,51837],{},"Endogenní \u002F exogenní proměnná",[123,51839,51840,51843],{},[38,51841,51842],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,51845,51846,1343,51849],{},[38,51847,51848],{},"Komparativní statika",[38,51850,38173],{},[123,51852,51853,3246,51855,51871],{},[38,51854,4282],{},[883,51856,51858],{"className":51857},[886],[888,51859,51860],{"xmlns":890},[892,51861,51862,51868],{},[895,51863,51864,51866],{},[898,51865,3542],{},[898,51867,1690],{},[902,51869,51870],{"encoding":904},"dQ"," (2.11)",[724,51873,51874],{},[38,51875,51876],{},"Přebytky a ostatní",[120,51878,51879,51917],{},[123,51880,51881,3246,51883,51898,51899,3246,51901,51916],{},[38,51882,46147],{},[883,51884,51886],{"className":51885},[886],[888,51887,51888],{"xmlns":890},[892,51889,51890,51896],{},[895,51891,51892,51894],{},[898,51893,3001],{},[898,51895,3004],{},[902,51897,46163],{"encoding":904}," (2.14), ",[38,51900,46166],{},[883,51902,51904],{"className":51903},[886],[888,51905,51906],{"xmlns":890},[892,51907,51908,51914],{},[895,51909,51910,51912],{},[898,51911,2675],{},[898,51913,3004],{},[902,51915,46182],{"encoding":904}," (2.15)",[123,51918,51919,1343,51922,51925],{},[38,51920,51921],{},"Homo economicus",[38,51923,51924],{},"Marshallova formulace"," (1890)",[38183,51927],{},[115,51929,3238],{"id":3237},[120,51931,51932,51967,51976],{},[123,51933,51934,3246,51937,51940,51941,1343,51944,51947,51948,51951,51952,51955,51956,51959,51960,51963,51964],{},[38,51935,51936],{},"Související témata:",[207,51938,811],{"className":51939,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,51942,820],{"className":51943,"dataFsResolvedFilePath":818,"href":819},[210],[207,51945,3695],{"className":51946,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,51949,775],{"className":51950,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,51953,784],{"className":51954,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,51957,793],{"className":51958,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,51961,5140],{"className":51962,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,51965,5135],{"className":51966,"dataFsResolvedFilePath":827,"href":828},[210],[123,51968,51969,3246,51972],{},[38,51970,51971],{},"Shrnutí přednášek:",[207,51973,51975],{"className":51974,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,51977,51978,3246,51980],{},[38,51979,17502],{},[207,51981,17506],{"className":51982,"dataFsResolvedFilePath":1749,"href":1750},[210],{"title":641,"searchDepth":642,"depth":642,"links":51984},[51985,51986,51994,52000,52007,52008,52015,52016,52017,52024,52025,52026],{"id":38007,"depth":642,"text":38008},{"id":37988,"depth":642,"text":14459,"children":51987},[51988,51989,51990,51991,51993],{"id":38276,"depth":649,"text":38277},{"id":38558,"depth":649,"text":38559},{"id":39568,"depth":649,"text":39569},{"id":40136,"depth":649,"text":51992},"Posun poptávky (shift of demand)",{"id":40640,"depth":649,"text":40641},{"id":37992,"depth":642,"text":14423,"children":51995},[51996,51997,51998],{"id":41477,"depth":649,"text":38277},{"id":41663,"depth":649,"text":41664},{"id":42115,"depth":649,"text":51999},"Posun nabídky (shift of supply)",{"id":42537,"depth":642,"text":42538,"children":52001},[52002,52003,52004,52005,52006],{"id":42649,"depth":649,"text":42650},{"id":42862,"depth":649,"text":42863},{"id":43180,"depth":649,"text":43181},{"id":43534,"depth":649,"text":43535},{"id":43565,"depth":649,"text":43566},{"id":43834,"depth":642,"text":811},{"id":44235,"depth":642,"text":44236,"children":52009},[52010,52011,52012,52013],{"id":44253,"depth":649,"text":44254},{"id":44634,"depth":649,"text":44635},{"id":45018,"depth":649,"text":45019},{"id":45472,"depth":649,"text":52014},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":13082,"depth":642,"text":820},{"id":46397,"depth":642,"text":46398},{"id":46628,"depth":642,"text":46629,"children":52018},[52019,52020,52021,52022,52023],{"id":46632,"depth":649,"text":46633},{"id":47472,"depth":649,"text":47473},{"id":47848,"depth":649,"text":42538},{"id":49143,"depth":649,"text":44236},{"id":50899,"depth":649,"text":820},{"id":51094,"depth":642,"text":51095},{"id":17017,"depth":642,"text":17018},{"id":3237,"depth":642,"text":3238},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,52033,52034,52035,3301,52036,52037],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":52040,"title":820,"body":52041,"course":1128,"courses":659,"created":10859,"description":641,"extension":661,"meta":56320,"navigation":664,"path":56321,"seo":56322,"sources":56323,"stem":56324,"tags":56325,"type":3302,"updated":677,"__hash__":56330},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":52042,"toc":56298},[52043,52045,52113,52163,52165,52168,52426,52502,52507,52509,52528,52532,52608,52693,52695,53009,53102,53104,53123,53127,53201,53286,53289,53465,53470,53472,53892,53894,53898,53902,54138,54182,54282,54348,54351,54384,54560,54622,54752,54830,54941,54975,55173,55192,55211,55276,55280,55283,55328,55331,55449,55495,55497,55501,55849,55851,55853,56131,56133,56137,56172,56179,56252,56254,56256],[12,52044,820],{"id":13082},[5179,52046,52047],{},[724,52048,52049,5186,52051,11325,52053,52068,52069,11325,52071,52086,52087,52109,52110,1882],{},[883,52050,5185],{},[38,52052,46147],{},[883,52054,52056],{"className":52055},[886],[888,52057,52058],{"xmlns":890},[892,52059,52060,52066],{},[895,52061,52062,52064],{},[898,52063,3001],{},[898,52065,3004],{},[902,52067,46163],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,52070,46294],{},[883,52072,52074],{"className":52073},[886],[888,52075,52076],{"xmlns":890},[892,52077,52078,52084],{},[895,52079,52080,52082],{},[898,52081,2675],{},[898,52083,3004],{},[902,52085,46182],{"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 ",[883,52088,52090],{"className":52089},[886],[888,52091,52092],{"xmlns":890},[892,52093,52094,52106],{},[895,52095,52096,52098,52100,52102,52104],{},[898,52097,3001],{},[898,52099,3004],{},[1651,52101,1839],{},[898,52103,2675],{},[898,52105,3004],{},[902,52107,52108],{"encoding":904},"CS + PS"," měří ",[38,52111,52112],{},"celkový blahobyt trhu",[724,52114,52115,11325,52117,1343,52119,13426,52134,11325,52136,1343,52138,52153,52154,52158,52159,1882],{},[38,52116,46147],{},[614,52118,46201],{},[883,52120,52122],{"className":52121},[886],[888,52123,52124],{"xmlns":890},[892,52125,52126,52132],{},[895,52127,52128,52130],{},[898,52129,3001],{},[898,52131,3004],{},[902,52133,46163],{"encoding":904},[38,52135,46166],{},[614,52137,46297],{},[883,52139,52141],{"className":52140},[886],[888,52142,52143],{"xmlns":890},[892,52144,52145,52151],{},[895,52146,52147,52149],{},[898,52148,2675],{},[898,52150,3004],{},[902,52152,46182],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,52155,52157],{"className":52156,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,52160,52162],{"className":52161,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[38183,52164],{},[115,52166,1241],{"id":52167},"úvod",[724,52169,52170,52171,52194,52195,52218,52219,52236,52237,1671,52269,52301,52302,52328,52329,52332,52333,52336,52337,15309,52371,22807,52392,1882],{},"Je dána funkce poptávky ",[883,52172,52174],{"className":52173},[886],[888,52175,52176],{"xmlns":890},[892,52177,52178,52192],{},[895,52179,52180,52182,52184,52186,52188,52190],{},[898,52181,2675],{},[1651,52183,1738],{},[898,52185,2047],{},[1651,52187,1654],{"stretchy":1653},[898,52189,1690],{},[1651,52191,1667],{"stretchy":1653},[902,52193,5947],{"encoding":904},", resp. funkce nabídky ",[883,52196,52198],{"className":52197},[886],[888,52199,52200],{"xmlns":890},[892,52201,52202,52216],{},[895,52203,52204,52206,52208,52210,52212,52214],{},[898,52205,2675],{},[1651,52207,1738],{},[898,52209,3004],{},[1651,52211,1654],{"stretchy":1653},[898,52213,1690],{},[1651,52215,1667],{"stretchy":1653},[902,52217,42284],{"encoding":904},". Pro pevně zadané množství ",[883,52220,52222],{"className":52221},[886],[888,52223,52224],{"xmlns":890},[892,52225,52226,52234],{},[895,52227,52228],{},[1686,52229,52230,52232],{},[898,52231,1690],{},[1692,52233,1741],{},[902,52235,39521],{"encoding":904}," je odpovídající cena ",[883,52238,52240],{"className":52239},[886],[888,52241,52242],{"xmlns":890},[892,52243,52244,52266],{},[895,52245,52246,52252,52254,52256,52258,52264],{},[1686,52247,52248,52250],{},[898,52249,2675],{},[1692,52251,1741],{},[1651,52253,1738],{},[898,52255,2047],{},[1651,52257,1654],{"stretchy":1653},[1686,52259,52260,52262],{},[898,52261,1690],{},[1692,52263,1741],{},[1651,52265,1667],{"stretchy":1653},[902,52267,52268],{"encoding":904},"P_0 = D(Q_0)",[883,52270,52272],{"className":52271},[886],[888,52273,52274],{"xmlns":890},[892,52275,52276,52298],{},[895,52277,52278,52284,52286,52288,52290,52296],{},[1686,52279,52280,52282],{},[898,52281,2675],{},[1692,52283,1741],{},[1651,52285,1738],{},[898,52287,3004],{},[1651,52289,1654],{"stretchy":1653},[1686,52291,52292,52294],{},[898,52293,1690],{},[1692,52295,1741],{},[1651,52297,1667],{"stretchy":1653},[902,52299,52300],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,52303,52305],{"className":52304},[886],[888,52306,52307],{"xmlns":890},[892,52308,52309,52325],{},[895,52310,52311,52317,52319],{},[1686,52312,52313,52315],{},[898,52314,2675],{},[1692,52316,1741],{},[1843,52318,1845],{},[1686,52320,52321,52323],{},[898,52322,1690],{},[1692,52324,1741],{},[902,52326,52327],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,52330,52331],{},"výdaje spotřebitele",", nebo ",[38,52334,52335],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,52338,52340],{"className":52339},[886],[888,52341,52342],{"xmlns":890},[892,52343,52344,52368],{},[895,52345,52346,52348,52350,52356,52358,52360,52362],{},[1692,52347,1741],{},[1843,52349,1845],{},[1686,52351,52352,52354],{},[898,52353,1690],{},[1692,52355,1741],{},[1843,52357,1845],{},[898,52359,5564],{},[1843,52361,1845],{},[1686,52363,52364,52366],{},[898,52365,2675],{},[1692,52367,1741],{},[902,52369,52370],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,52372,52374],{"className":52373},[886],[888,52375,52376],{"xmlns":890},[892,52377,52378,52390],{},[895,52379,52380,52382,52384,52386,52388],{},[1651,52381,1654],{"stretchy":1653},[898,52383,1690],{},[1651,52385,1661],{"separator":1660},[898,52387,2675],{},[1651,52389,1667],{"stretchy":1653},[902,52391,38904],{"encoding":904},[883,52393,52395],{"className":52394},[886],[888,52396,52397],{"xmlns":890},[892,52398,52399,52423],{},[895,52400,52401,52403,52405,52407,52413,52415,52421],{},[898,52402,5564],{},[1651,52404,1738],{},[1651,52406,2261],{"stretchy":1653},[1686,52408,52409,52411],{},[898,52410,1690],{},[1692,52412,1741],{},[1651,52414,1661],{"separator":1660},[1686,52416,52417,52419],{},[898,52418,2675],{},[1692,52420,1741],{},[1651,52422,2279],{"stretchy":1653},[902,52424,52425],{"encoding":904},"A = [Q_0, P_0]",[5179,52427,52428,52433,52491],{},[724,52429,52430,52432],{},[883,52431,5465],{}," Intuice",[120,52434,52435,52463],{},[123,52436,52437,52438,52441,52442,52444,52445,52462],{},"Za jednotky zboží nakoupené ",[38,52439,52440],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,52443,26483],{}," než ",[883,52446,52448],{"className":52447},[886],[888,52449,52450],{"xmlns":890},[892,52451,52452,52460],{},[895,52453,52454],{},[1686,52455,52456,52458],{},[898,52457,2675],{},[1692,52459,1741],{},[902,52461,40161],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,52464,52465,52466,52468,52469,52472,52473,52490],{},"Za jednotky zboží prodané ",[38,52467,52440],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,52470,52471],{},"nižší"," cenu než ",[883,52474,52476],{"className":52475},[886],[888,52477,52478],{"xmlns":890},[892,52479,52480,52488],{},[895,52481,52482],{},[1686,52483,52484,52486],{},[898,52485,2675],{},[1692,52487,1741],{},[902,52489,40161],{"encoding":904}," — rozdíl je jeho přebytek.",[724,52492,52493,52494,52497,52498,52501],{},"Přebytek je tedy rozdíl mezi ",[614,52495,52496],{},"ochotou"," (platit \u002F prodávat) a ",[614,52499,52500],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,52503,52504],{},[1756,52505],{"alt":46192,"className":52506,"src":46194},[210,1760],[38183,52508],{},[115,52510,52512,52513,1667],{"id":52511},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,52514,52516],{"className":52515},[886],[888,52517,52518],{"xmlns":890},[892,52519,52520,52526],{},[895,52521,52522,52524],{},[898,52523,3001],{},[898,52525,3004],{},[902,52527,46163],{"encoding":904},[198,52529,52531],{"id":52530},"definice-vzorec-214","Definice (vzorec 2.14)",[724,52533,52534,52535,52558,52559,52576,52577,1793],{},"Pro poptávku ",[883,52536,52538],{"className":52537},[886],[888,52539,52540],{"xmlns":890},[892,52541,52542,52556],{},[895,52543,52544,52546,52548,52550,52552,52554],{},[898,52545,2675],{},[1651,52547,1738],{},[898,52549,2047],{},[1651,52551,1654],{"stretchy":1653},[898,52553,1690],{},[1651,52555,1667],{"stretchy":1653},[902,52557,5947],{"encoding":904}," a pevně zadané ",[883,52560,52562],{"className":52561},[886],[888,52563,52564],{"xmlns":890},[892,52565,52566,52574],{},[895,52567,52568],{},[1686,52569,52570,52572],{},[898,52571,1690],{},[1692,52573,1741],{},[902,52575,39521],{"encoding":904}," s cenou ",[883,52578,52580],{"className":52579},[886],[888,52581,52582],{"xmlns":890},[892,52583,52584,52606],{},[895,52585,52586,52592,52594,52596,52598,52604],{},[1686,52587,52588,52590],{},[898,52589,2675],{},[1692,52591,1741],{},[1651,52593,1738],{},[898,52595,2047],{},[1651,52597,1654],{"stretchy":1653},[1686,52599,52600,52602],{},[898,52601,1690],{},[1692,52603,1741],{},[1651,52605,1667],{"stretchy":1653},[902,52607,52268],{"encoding":904},[883,52609,52611],{"className":52610},[886],[888,52612,52613],{"xmlns":890,"display":29279},[892,52614,52615,52691],{},[21967,52616,52617],{"width":29284},[21972,52618,52619,52621,52685,52687],{},[21975,52620],{"width":29289},[21975,52622,52623],{},[895,52624,52625,52627,52629,52631,52637,52639,52641,52653,52655,52657,52659,52661,52663,52665,52667,52669,52675,52677,52683],{},[898,52626,3001],{},[898,52628,3004],{},[1651,52630,1654],{"stretchy":1653},[1686,52632,52633,52635],{},[898,52634,1690],{},[1692,52636,1741],{},[1651,52638,1667],{"stretchy":1653},[1651,52640,1738],{},[1902,52642,52643,52645,52647],{},[1651,52644,12467],{},[1692,52646,1741],{},[1686,52648,52649,52651],{},[898,52650,1690],{},[1692,52652,1741],{},[898,52654,2047],{},[1651,52656,1654],{"stretchy":1653},[898,52658,1690],{},[1651,52660,1667],{"stretchy":1653},[1843,52662,1845],{},[898,52664,3542],{},[898,52666,1690],{},[1651,52668,2181],{},[1686,52670,52671,52673],{},[898,52672,2675],{},[1692,52674,1741],{},[1843,52676,1845],{},[1686,52678,52679,52681],{},[898,52680,1690],{},[1692,52682,1741],{},[898,52684,1882],{"mathvariant":1910},[21975,52686],{"width":29289},[21975,52688,52689],{},[1843,52690,46286],{},[902,52692,46289],{"encoding":904},[198,52694,3779],{"id":3778},[120,52696,52697,52789,52851],{},[123,52698,52699,52739,52740,52766,52767,52770,52771,52788],{},[883,52700,52702],{"className":52701},[886],[888,52703,52704],{"xmlns":890},[892,52705,52706,52736],{},[895,52707,52708],{},[2938,52709,52710,52722,52724,52726,52728,52730,52732,52734],{"scriptlevel":1741,"displaystyle":1660},[1902,52711,52712,52714,52716],{},[1651,52713,12467],{},[1692,52715,1741],{},[1686,52717,52718,52720],{},[898,52719,1690],{},[1692,52721,1741],{},[898,52723,2047],{},[1651,52725,1654],{"stretchy":1653},[898,52727,1690],{},[1651,52729,1667],{"stretchy":1653},[1843,52731,1845],{},[898,52733,3542],{},[898,52735,1690],{},[902,52737,52738],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,52741,52743],{"className":52742},[886],[888,52744,52745],{"xmlns":890},[892,52746,52747,52763],{},[895,52748,52749,52751,52753,52755,52761],{},[1651,52750,2261],{"stretchy":1653},[1692,52752,1741],{},[1651,52754,1661],{"separator":1660},[1686,52756,52757,52759],{},[898,52758,1690],{},[1692,52760,1741],{},[1651,52762,2279],{"stretchy":1653},[902,52764,52765],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,52768,52769],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,52772,52774],{"className":52773},[886],[888,52775,52776],{"xmlns":890},[892,52777,52778,52786],{},[895,52779,52780],{},[1686,52781,52782,52784],{},[898,52783,1690],{},[1692,52785,1741],{},[902,52787,39521],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,52790,52791,52817,52818,5230],{},[883,52792,52794],{"className":52793},[886],[888,52795,52796],{"xmlns":890},[892,52797,52798,52814],{},[895,52799,52800,52806,52808],{},[1686,52801,52802,52804],{},[898,52803,2675],{},[1692,52805,1741],{},[1843,52807,1845],{},[1686,52809,52810,52812],{},[898,52811,1690],{},[1692,52813,1741],{},[902,52815,52816],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,52819,52821],{"className":52820},[886],[888,52822,52823],{"xmlns":890},[892,52824,52825,52849],{},[895,52826,52827,52829,52831,52837,52839,52841,52843],{},[1692,52828,1741],{},[1843,52830,1845],{},[1686,52832,52833,52835],{},[898,52834,1690],{},[1692,52836,1741],{},[1843,52838,1845],{},[898,52840,5564],{},[1843,52842,1845],{},[1686,52844,52845,52847],{},[898,52846,2675],{},[1692,52848,1741],{},[902,52850,52370],{"encoding":904},[123,52852,52853,52868,52869,52891,52892,52917,52918,22807,52944,5197,52976,1882],{},[883,52854,52856],{"className":52855},[886],[888,52857,52858],{"xmlns":890},[892,52859,52860,52866],{},[895,52861,52862,52864],{},[898,52863,3001],{},[898,52865,3004],{},[902,52867,46163],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,52870,52872],{"className":52871},[886],[888,52873,52874],{"xmlns":890},[892,52875,52876,52888],{},[895,52877,52878,52880,52882],{},[898,52879,2675],{},[1651,52881,1738],{},[1686,52883,52884,52886],{},[898,52885,2675],{},[1692,52887,1741],{},[902,52889,52890],{"encoding":904},"P = P_0"," v pásu ",[883,52893,52895],{"className":52894},[886],[888,52896,52897],{"xmlns":890},[892,52898,52899,52915],{},[895,52900,52901,52903,52905,52907,52913],{},[1651,52902,2261],{"stretchy":1653},[1692,52904,1741],{},[1651,52906,1661],{"separator":1660},[1686,52908,52909,52911],{},[898,52910,1690],{},[1692,52912,1741],{},[1651,52914,2279],{"stretchy":1653},[902,52916,52765],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,52919,52921],{"className":52920},[886],[888,52922,52923],{"xmlns":890},[892,52924,52925,52941],{},[895,52926,52927,52933,52935,52937,52939],{},[1686,52928,52929,52931],{},[898,52930,2675],{},[1692,52932,1741],{},[1843,52934,1845],{},[898,52936,24466],{},[1843,52938,1845],{},[898,52940,5564],{},[902,52942,52943],{"encoding":904},"P_0\\,B\\,A",[883,52945,52947],{"className":52946},[886],[888,52948,52949],{"xmlns":890},[892,52950,52951,52973],{},[895,52952,52953,52955,52957,52959,52961,52963,52965,52967,52969,52971],{},[898,52954,24466],{},[1651,52956,1738],{},[1651,52958,2261],{"stretchy":1653},[1692,52960,1741],{},[1651,52962,1661],{"separator":1660},[898,52964,2047],{},[1651,52966,1654],{"stretchy":1653},[1692,52968,1741],{},[1651,52970,1667],{"stretchy":1653},[1651,52972,2279],{"stretchy":1653},[902,52974,52975],{"encoding":904},"B = [0, D(0)]",[883,52977,52979],{"className":52978},[886],[888,52980,52981],{"xmlns":890},[892,52982,52983,53007],{},[895,52984,52985,52987,52989,52991,52997,52999,53005],{},[898,52986,5564],{},[1651,52988,1738],{},[1651,52990,2261],{"stretchy":1653},[1686,52992,52993,52995],{},[898,52994,1690],{},[1692,52996,1741],{},[1651,52998,1661],{"separator":1660},[1686,53000,53001,53003],{},[898,53002,2675],{},[1692,53004,1741],{},[1651,53006,2279],{"stretchy":1653},[902,53008,52425],{"encoding":904},[724,53010,53011],{},[614,53012,53013,53014,53027,53028,53061,53062,30355,53087,1882],{},"Obrázek 2.24: Křivka poptávky ",[883,53015,53017],{"className":53016},[886],[888,53018,53019],{"xmlns":890},[892,53020,53021,53025],{},[895,53022,53023],{},[898,53024,2047],{},[902,53026,2047],{"encoding":904},", bod ",[883,53029,53031],{"className":53030},[886],[888,53032,53033],{"xmlns":890},[892,53034,53035,53059],{},[895,53036,53037,53039,53041,53043,53049,53051,53057],{},[898,53038,5564],{},[1651,53040,1738],{},[1651,53042,2261],{"stretchy":1653},[1686,53044,53045,53047],{},[898,53046,1690],{},[1692,53048,1741],{},[1651,53050,1661],{"separator":1660},[1686,53052,53053,53055],{},[898,53054,2675],{},[1692,53056,1741],{},[1651,53058,2279],{"stretchy":1653},[902,53060,52425],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,53063,53065],{"className":53064},[886],[888,53066,53067],{"xmlns":890},[892,53068,53069,53085],{},[895,53070,53071,53077,53079,53081,53083],{},[1686,53072,53073,53075],{},[898,53074,2675],{},[1692,53076,1741],{},[1843,53078,1845],{},[898,53080,24466],{},[1843,53082,1845],{},[898,53084,5564],{},[902,53086,52943],{"encoding":904},[883,53088,53090],{"className":53089},[886],[888,53091,53092],{"xmlns":890},[892,53093,53094,53100],{},[895,53095,53096,53098],{},[898,53097,3001],{},[898,53099,3004],{},[902,53101,46163],{"encoding":904},[38183,53103],{},[115,53105,53107,53108,1667],{"id":53106},"přebytek-výrobce-psps","Přebytek výrobce (",[883,53109,53111],{"className":53110},[886],[888,53112,53113],{"xmlns":890},[892,53114,53115,53121],{},[895,53116,53117,53119],{},[898,53118,2675],{},[898,53120,3004],{},[902,53122,46182],{"encoding":904},[198,53124,53126],{"id":53125},"definice-vzorec-215","Definice (vzorec 2.15)",[724,53128,53129,53130,52558,53153,52576,53170,1793],{},"Analogicky — pro nabídku ",[883,53131,53133],{"className":53132},[886],[888,53134,53135],{"xmlns":890},[892,53136,53137,53151],{},[895,53138,53139,53141,53143,53145,53147,53149],{},[898,53140,2675],{},[1651,53142,1738],{},[898,53144,3004],{},[1651,53146,1654],{"stretchy":1653},[898,53148,1690],{},[1651,53150,1667],{"stretchy":1653},[902,53152,42284],{"encoding":904},[883,53154,53156],{"className":53155},[886],[888,53157,53158],{"xmlns":890},[892,53159,53160,53168],{},[895,53161,53162],{},[1686,53163,53164,53166],{},[898,53165,1690],{},[1692,53167,1741],{},[902,53169,39521],{"encoding":904},[883,53171,53173],{"className":53172},[886],[888,53174,53175],{"xmlns":890},[892,53176,53177,53199],{},[895,53178,53179,53185,53187,53189,53191,53197],{},[1686,53180,53181,53183],{},[898,53182,2675],{},[1692,53184,1741],{},[1651,53186,1738],{},[898,53188,3004],{},[1651,53190,1654],{"stretchy":1653},[1686,53192,53193,53195],{},[898,53194,1690],{},[1692,53196,1741],{},[1651,53198,1667],{"stretchy":1653},[902,53200,52300],{"encoding":904},[883,53202,53204],{"className":53203},[886],[888,53205,53206],{"xmlns":890,"display":29279},[892,53207,53208,53284],{},[21967,53209,53210],{"width":29284},[21972,53211,53212,53214,53278,53280],{},[21975,53213],{"width":29289},[21975,53215,53216],{},[895,53217,53218,53220,53222,53224,53230,53232,53234,53240,53242,53248,53250,53262,53264,53266,53268,53270,53272,53274,53276],{},[898,53219,2675],{},[898,53221,3004],{},[1651,53223,1654],{"stretchy":1653},[1686,53225,53226,53228],{},[898,53227,1690],{},[1692,53229,1741],{},[1651,53231,1667],{"stretchy":1653},[1651,53233,1738],{},[1686,53235,53236,53238],{},[898,53237,2675],{},[1692,53239,1741],{},[1843,53241,1845],{},[1686,53243,53244,53246],{},[898,53245,1690],{},[1692,53247,1741],{},[1651,53249,2181],{},[1902,53251,53252,53254,53256],{},[1651,53253,12467],{},[1692,53255,1741],{},[1686,53257,53258,53260],{},[898,53259,1690],{},[1692,53261,1741],{},[898,53263,3004],{},[1651,53265,1654],{"stretchy":1653},[898,53267,1690],{},[1651,53269,1667],{"stretchy":1653},[1843,53271,1845],{},[898,53273,3542],{},[898,53275,1690],{},[898,53277,1882],{"mathvariant":1910},[21975,53279],{"width":29289},[21975,53281,53282],{},[1843,53283,46382],{},[902,53285,46385],{"encoding":904},[198,53287,3779],{"id":53288},"geometrická-interpretace-1",[120,53290,53291,53339,53400],{},[123,53292,53293,8322,53318,53321,53322,1882],{},[883,53294,53296],{"className":53295},[886],[888,53297,53298],{"xmlns":890},[892,53299,53300,53316],{},[895,53301,53302,53308,53310],{},[1686,53303,53304,53306],{},[898,53305,2675],{},[1692,53307,1741],{},[1843,53309,1845],{},[1686,53311,53312,53314],{},[898,53313,1690],{},[1692,53315,1741],{},[902,53317,52816],{"encoding":904},[38,53319,53320],{},"tržba"," výrobce za prodané množství ",[883,53323,53325],{"className":53324},[886],[888,53326,53327],{"xmlns":890},[892,53328,53329,53337],{},[895,53330,53331],{},[1686,53332,53333,53335],{},[898,53334,1690],{},[1692,53336,1741],{},[902,53338,39521],{"encoding":904},[123,53340,53341,53381,53382,53399],{},[883,53342,53344],{"className":53343},[886],[888,53345,53346],{"xmlns":890},[892,53347,53348,53378],{},[895,53349,53350],{},[2938,53351,53352,53364,53366,53368,53370,53372,53374,53376],{"scriptlevel":1741,"displaystyle":1660},[1902,53353,53354,53356,53358],{},[1651,53355,12467],{},[1692,53357,1741],{},[1686,53359,53360,53362],{},[898,53361,1690],{},[1692,53363,1741],{},[898,53365,3004],{},[1651,53367,1654],{"stretchy":1653},[898,53369,1690],{},[1651,53371,1667],{"stretchy":1653},[1843,53373,1845],{},[898,53375,3542],{},[898,53377,1690],{},[902,53379,53380],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,53383,53385],{"className":53384},[886],[888,53386,53387],{"xmlns":890},[892,53388,53389,53397],{},[895,53390,53391],{},[1686,53392,53393,53395],{},[898,53394,1690],{},[1692,53396,1741],{},[902,53398,39521],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,53401,53402,53417,53418,53439,53440,1882],{},[883,53403,53405],{"className":53404},[886],[888,53406,53407],{"xmlns":890},[892,53408,53409,53415],{},[895,53410,53411,53413],{},[898,53412,2675],{},[898,53414,3004],{},[902,53416,46182],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,53419,53421],{"className":53420},[886],[888,53422,53423],{"xmlns":890},[892,53424,53425,53437],{},[895,53426,53427,53429,53431],{},[898,53428,2675],{},[1651,53430,1738],{},[1686,53432,53433,53435],{},[898,53434,2675],{},[1692,53436,1741],{},[902,53438,52890],{"encoding":904}," a křivkou nabídky v pásu ",[883,53441,53443],{"className":53442},[886],[888,53444,53445],{"xmlns":890},[892,53446,53447,53463],{},[895,53448,53449,53451,53453,53455,53461],{},[1651,53450,2261],{"stretchy":1653},[1692,53452,1741],{},[1651,53454,1661],{"separator":1660},[1686,53456,53457,53459],{},[898,53458,1690],{},[1692,53460,1741],{},[1651,53462,2279],{"stretchy":1653},[902,53464,52765],{"encoding":904},[724,53466,53467],{},[614,53468,53469],{},"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.",[38183,53471],{},[5179,53473,53474,53479],{},[724,53475,53476,53478],{},[883,53477,5879],{}," Postup výpočtu CS a PS",[152,53480,53481,53612,53722,53751,53885],{},[123,53482,53483,53484,53501,53502,53533,53534,53565,53566,1882],{},"Zjisti (nebo si zvol) množství ",[883,53485,53487],{"className":53486},[886],[888,53488,53489],{"xmlns":890},[892,53490,53491,53499],{},[895,53492,53493],{},[1686,53494,53495,53497],{},[898,53496,1690],{},[1692,53498,1741],{},[902,53500,39521],{"encoding":904}," a odpovídající cenu ",[883,53503,53505],{"className":53504},[886],[888,53506,53507],{"xmlns":890},[892,53508,53509,53531],{},[895,53510,53511,53517,53519,53521,53523,53529],{},[1686,53512,53513,53515],{},[898,53514,2675],{},[1692,53516,1741],{},[1651,53518,1738],{},[898,53520,2047],{},[1651,53522,1654],{"stretchy":1653},[1686,53524,53525,53527],{},[898,53526,1690],{},[1692,53528,1741],{},[1651,53530,1667],{"stretchy":1653},[902,53532,52268],{"encoding":904}," resp. ",[883,53535,53537],{"className":53536},[886],[888,53538,53539],{"xmlns":890},[892,53540,53541,53563],{},[895,53542,53543,53549,53551,53553,53555,53561],{},[1686,53544,53545,53547],{},[898,53546,2675],{},[1692,53548,1741],{},[1651,53550,1738],{},[898,53552,3004],{},[1651,53554,1654],{"stretchy":1653},[1686,53556,53557,53559],{},[898,53558,1690],{},[1692,53560,1741],{},[1651,53562,1667],{"stretchy":1653},[902,53564,52300],{"encoding":904},". V rovnováze platí ",[883,53567,53569],{"className":53568},[886],[888,53570,53571],{"xmlns":890},[892,53572,53573,53609],{},[895,53574,53575,53577,53579,53585,53587,53589,53591,53593,53599,53601,53603],{},[898,53576,2047],{},[1651,53578,1654],{"stretchy":1653},[2115,53580,53581,53583],{},[898,53582,1690],{},[898,53584,5561],{},[1651,53586,1667],{"stretchy":1653},[1651,53588,1738],{},[898,53590,3004],{},[1651,53592,1654],{"stretchy":1653},[2115,53594,53595,53597],{},[898,53596,1690],{},[898,53598,5561],{},[1651,53600,1667],{"stretchy":1653},[1651,53602,1738],{},[2115,53604,53605,53607],{},[898,53606,2675],{},[898,53608,5561],{},[902,53610,53611],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,53613,53614,53615,21339,53653,53668,53669,21339,53707,5230],{},"Spočti určitý integrál ",[883,53616,53618],{"className":53617},[886],[888,53619,53620],{"xmlns":890},[892,53621,53622,53650],{},[895,53623,53624,53636,53638,53640,53642,53644,53646,53648],{},[1902,53625,53626,53628,53630],{},[1651,53627,12467],{},[1692,53629,1741],{},[1686,53631,53632,53634],{},[898,53633,1690],{},[1692,53635,1741],{},[898,53637,2047],{},[1651,53639,1654],{"stretchy":1653},[898,53641,1690],{},[1651,53643,1667],{"stretchy":1653},[1843,53645,1845],{},[898,53647,3542],{},[898,53649,1690],{},[902,53651,53652],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,53654,53656],{"className":53655},[886],[888,53657,53658],{"xmlns":890},[892,53659,53660,53666],{},[895,53661,53662,53664],{},[898,53663,3001],{},[898,53665,3004],{},[902,53667,46163],{"encoding":904},") nebo ",[883,53670,53672],{"className":53671},[886],[888,53673,53674],{"xmlns":890},[892,53675,53676,53704],{},[895,53677,53678,53690,53692,53694,53696,53698,53700,53702],{},[1902,53679,53680,53682,53684],{},[1651,53681,12467],{},[1692,53683,1741],{},[1686,53685,53686,53688],{},[898,53687,1690],{},[1692,53689,1741],{},[898,53691,3004],{},[1651,53693,1654],{"stretchy":1653},[898,53695,1690],{},[1651,53697,1667],{"stretchy":1653},[1843,53699,1845],{},[898,53701,3542],{},[898,53703,1690],{},[902,53705,53706],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,53708,53710],{"className":53709},[886],[888,53711,53712],{"xmlns":890},[892,53713,53714,53720],{},[895,53715,53716,53718],{},[898,53717,2675],{},[898,53719,3004],{},[902,53721,46182],{"encoding":904},[123,53723,53724,53725,1882],{},"Sestav obdélník ",[883,53726,53728],{"className":53727},[886],[888,53729,53730],{"xmlns":890},[892,53731,53732,53748],{},[895,53733,53734,53740,53742],{},[1686,53735,53736,53738],{},[898,53737,2675],{},[1692,53739,1741],{},[1651,53741,4503],{},[1686,53743,53744,53746],{},[898,53745,1690],{},[1692,53747,1741],{},[902,53749,53750],{"encoding":904},"P_0 \\cdot Q_0",[123,53752,53753,53754],{},"Dosaď:\n",[120,53755,53756,53821],{},[123,53757,53758,53816,53817,53820],{},[883,53759,53761],{"className":53760},[886],[888,53762,53763],{"xmlns":890},[892,53764,53765,53813],{},[895,53766,53767,53769,53771,53773,53785,53787,53789,53791,53793,53795,53797,53799,53801,53807],{},[898,53768,3001],{},[898,53770,3004],{},[1651,53772,1738],{},[1902,53774,53775,53777,53779],{},[1651,53776,12467],{},[1692,53778,1741],{},[1686,53780,53781,53783],{},[898,53782,1690],{},[1692,53784,1741],{},[898,53786,2047],{},[1651,53788,1654],{"stretchy":1653},[898,53790,1690],{},[1651,53792,1667],{"stretchy":1653},[1843,53794,1845],{},[898,53796,3542],{},[898,53798,1690],{},[1651,53800,2181],{},[1686,53802,53803,53805],{},[898,53804,2675],{},[1692,53806,1741],{},[1686,53808,53809,53811],{},[898,53810,1690],{},[1692,53812,1741],{},[902,53814,53815],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,53818,53819],{},"mínus"," obdélník)",[123,53822,53823,53881,53882,53884],{},[883,53824,53826],{"className":53825},[886],[888,53827,53828],{"xmlns":890},[892,53829,53830,53878],{},[895,53831,53832,53834,53836,53838,53844,53850,53852,53864,53866,53868,53870,53872,53874,53876],{},[898,53833,2675],{},[898,53835,3004],{},[1651,53837,1738],{},[1686,53839,53840,53842],{},[898,53841,2675],{},[1692,53843,1741],{},[1686,53845,53846,53848],{},[898,53847,1690],{},[1692,53849,1741],{},[1651,53851,2181],{},[1902,53853,53854,53856,53858],{},[1651,53855,12467],{},[1692,53857,1741],{},[1686,53859,53860,53862],{},[898,53861,1690],{},[1692,53863,1741],{},[898,53865,3004],{},[1651,53867,1654],{"stretchy":1653},[898,53869,1690],{},[1651,53871,1667],{"stretchy":1653},[1843,53873,1845],{},[898,53875,3542],{},[898,53877,1690],{},[902,53879,53880],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,53883,53819],{}," integrál)",[123,53886,53887,53888,53891],{},"Kontrola znaménka: obě hodnoty musí být ",[38,53889,53890],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[38183,53893],{},[115,53895,53897],{"id":53896},"příklady","Příklady",[198,53899,53901],{"id":53900},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[5179,53903,53904],{},[724,53905,53906,53909,53910,48934,53933,53956,53957,1343,53977,1343,53994,1343,54011,54028,54029,54105,54106,54123,54124,54137],{},[883,53907,53908],{},"!example"," Zadání\nJsou dány poptávka ",[883,53911,53913],{"className":53912},[886],[888,53914,53915],{"xmlns":890},[892,53916,53917,53931],{},[895,53918,53919,53921,53923,53925,53927,53929],{},[898,53920,2675],{},[1651,53922,1738],{},[898,53924,207],{},[898,53926,1690],{},[1651,53928,1839],{},[898,53930,2268],{},[902,53932,38273],{"encoding":904},[883,53934,53936],{"className":53935},[886],[888,53937,53938],{"xmlns":890},[892,53939,53940,53954],{},[895,53941,53942,53944,53946,53948,53950,53952],{},[898,53943,2675],{},[1651,53945,1738],{},[898,53947,3490],{},[898,53949,1690],{},[1651,53951,1839],{},[898,53953,3542],{},[902,53955,41455],{"encoding":904}," s hodnotami ",[883,53958,53960],{"className":53959},[886],[888,53961,53962],{"xmlns":890},[892,53963,53964,53974],{},[895,53965,53966,53968,53970,53972],{},[898,53967,207],{},[1651,53969,1738],{},[1651,53971,2181],{},[1692,53973,3521],{},[902,53975,53976],{"encoding":904},"a = -3",[883,53978,53980],{"className":53979},[886],[888,53981,53982],{"xmlns":890},[892,53983,53984,53992],{},[895,53985,53986,53988,53990],{},[898,53987,2268],{},[1651,53989,1738],{},[1692,53991,6518],{},[902,53993,49857],{"encoding":904},[883,53995,53997],{"className":53996},[886],[888,53998,53999],{"xmlns":890},[892,54000,54001,54009],{},[895,54002,54003,54005,54007],{},[898,54004,3490],{},[1651,54006,1738],{},[1692,54008,6316],{},[902,54010,49875],{"encoding":904},[883,54012,54014],{"className":54013},[886],[888,54015,54016],{"xmlns":890},[892,54017,54018,54026],{},[895,54019,54020,54022,54024],{},[898,54021,3542],{},[1651,54023,1738],{},[1692,54025,4190],{},[902,54027,49893],{"encoding":904},".\nRovnovážné množství:\n",[883,54030,54032],{"className":54031},[886],[888,54033,54034],{"xmlns":890},[892,54035,54036,54102],{},[895,54037,54038,54044,54046,54064,54066,54090,54092,54098,54100],{},[2115,54039,54040,54042],{},[898,54041,1690],{},[898,54043,5561],{},[1651,54045,1738],{},[2446,54047,54048,54056],{},[895,54049,54050,54052,54054],{},[898,54051,2268],{},[1651,54053,2181],{},[898,54055,3542],{},[895,54057,54058,54060,54062],{},[898,54059,3490],{},[1651,54061,2181],{},[898,54063,207],{},[1651,54065,1738],{},[2446,54067,54068,54076],{},[895,54069,54070,54072,54074],{},[1692,54071,6518],{},[1651,54073,2181],{},[1692,54075,4190],{},[895,54077,54078,54080,54082,54084,54086,54088],{},[1692,54079,6316],{},[1651,54081,2181],{},[1651,54083,1654],{"stretchy":1653},[1651,54085,2181],{},[1692,54087,3521],{},[1651,54089,1667],{"stretchy":1653},[1651,54091,1738],{},[2446,54093,54094,54096],{},[1692,54095,39232],{},[1692,54097,45619],{},[1651,54099,7207],{},[1692,54101,45624],{},[902,54103,54104],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,54107,54109],{"className":54108},[886],[888,54110,54111],{"xmlns":890},[892,54112,54113,54121],{},[895,54114,54115],{},[2115,54116,54117,54119],{},[898,54118,1690],{},[898,54120,5561],{},[902,54122,43616],{"encoding":904}," (a) při změně samotného parametru ",[883,54125,54127],{"className":54126},[886],[888,54128,54129],{"xmlns":890},[892,54130,54131,54135],{},[895,54132,54133],{},[898,54134,3490],{},[902,54136,3490],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,54139,54140],{},[38,54141,54142,54143,4002,54156,4016,54169,10598],{},"Řešení (a) — změna ",[883,54144,54146],{"className":54145},[886],[888,54147,54148],{"xmlns":890},[892,54149,54150,54154],{},[895,54151,54152],{},[898,54153,3490],{},[902,54155,3490],{"encoding":904},[883,54157,54159],{"className":54158},[886],[888,54160,54161],{"xmlns":890},[892,54162,54163,54167],{},[895,54164,54165],{},[1692,54166,6316],{},[902,54168,45659],{"encoding":904},[883,54170,54172],{"className":54171},[886],[888,54173,54174],{"xmlns":890},[892,54175,54176,54180],{},[895,54177,54178],{},[1692,54179,20534],{},[902,54181,45673],{"encoding":904},[724,54183,54184,54185,54249,54250,1793],{},"Pomocí vzorce (2.13) pro ",[883,54186,54188],{"className":54187},[886],[888,54189,54190],{"xmlns":890},[892,54191,54192,54246],{},[895,54193,54194,54214,54216,54218],{},[2938,54195,54196],{"scriptlevel":1741,"displaystyle":1660},[2446,54197,54198,54208],{},[895,54199,54200,54202],{},[898,54201,11172],{"mathvariant":1910},[2115,54203,54204,54206],{},[898,54205,1690],{},[898,54207,5561],{},[895,54209,54210,54212],{},[898,54211,11172],{"mathvariant":1910},[898,54213,3490],{},[1651,54215,1738],{},[1651,54217,2181],{},[2938,54219,54220],{"scriptlevel":1741,"displaystyle":1660},[2446,54221,54222,54230],{},[895,54223,54224,54226,54228],{},[898,54225,2268],{},[1651,54227,2181],{},[898,54229,3542],{},[895,54231,54232,54234,54236,54238,54240],{},[1651,54233,1654],{"stretchy":1653},[898,54235,3490],{},[1651,54237,2181],{},[898,54239,207],{},[2115,54241,54242,54244],{},[1651,54243,1667],{"stretchy":1653},[1692,54245,1703],{},[902,54247,54248],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,54251,54253],{"className":54252},[886],[888,54254,54255],{"xmlns":890},[892,54256,54257,54279],{},[895,54258,54259,54261],{},[1651,54260,2181],{},[2938,54262,54263],{"scriptlevel":1741,"displaystyle":1660},[2446,54264,54265,54271],{},[2115,54266,54267,54269],{},[898,54268,1690],{},[898,54270,5561],{},[895,54272,54273,54275,54277],{},[898,54274,3490],{},[1651,54276,2181],{},[898,54278,207],{},[902,54280,54281],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,54283,54285],{"className":54284},[886],[888,54286,54287],{"xmlns":890,"display":29279},[892,54288,54289,54345],{},[895,54290,54291,54293,54299,54301,54303,54319,54321,54323,54325,54327,54329,54335,54337,54339,54341,54343],{},[898,54292,3542],{},[2115,54294,54295,54297],{},[898,54296,1690],{},[898,54298,5561],{},[1651,54300,1738],{},[1651,54302,2181],{},[2446,54304,54305,54311],{},[2115,54306,54307,54309],{},[898,54308,1690],{},[898,54310,5561],{},[895,54312,54313,54315,54317],{},[898,54314,3490],{},[1651,54316,2181],{},[898,54318,207],{},[1843,54320,1845],{},[898,54322,3542],{},[898,54324,3490],{},[1651,54326,1738],{},[1651,54328,2181],{},[2446,54330,54331,54333],{},[1692,54332,45787],{},[1692,54334,45619],{},[1651,54336,4503],{},[1692,54338,4122],{},[1651,54340,7207],{},[1651,54342,2181],{},[1692,54344,45759],{},[902,54346,54347],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,54349,54350],{},"Nové rovnovážné množství:",[883,54352,54354],{"className":54353},[886],[888,54355,54356],{"xmlns":890,"display":29279},[892,54357,54358,54381],{},[895,54359,54360,54368,54370,54372,54374,54376,54378],{},[1902,54361,54362,54364,54366],{},[898,54363,1690],{},[1692,54365,1694],{},[898,54367,5561],{},[1651,54369,4060],{},[1692,54371,45787],{},[1651,54373,2181],{},[1692,54375,45792],{},[1651,54377,1738],{},[1692,54379,54380],{},"8,326.",[902,54382,54383],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,54385,54386,3246,54389,1343,54416,1343,54438,1343,54460,6896,54482,1343,54501,1343,54522,1343,54541,1882],{},[38,54387,54388],{},"Řešení (b) — současná změna všech parametrů:",[883,54390,54392],{"className":54391},[886],[888,54393,54394],{"xmlns":890},[892,54395,54396,54413],{},[895,54397,54398,54400,54402,54404,54406,54408,54410],{},[898,54399,207],{},[1651,54401,1793],{},[1651,54403,2181],{},[1692,54405,3521],{},[1651,54407,4449],{},[1651,54409,2181],{},[1692,54411,54412],{},"2,5",[902,54414,54415],{"encoding":904},"a: -3 \\to -2{,}5",[883,54417,54419],{"className":54418},[886],[888,54420,54421],{"xmlns":890},[892,54422,54423,54435],{},[895,54424,54425,54427,54429,54431,54433],{},[898,54426,2268],{},[1651,54428,1793],{},[1692,54430,6518],{},[1651,54432,4449],{},[1692,54434,16336],{},[902,54436,54437],{"encoding":904},"b: 40 \\to 35",[883,54439,54441],{"className":54440},[886],[888,54442,54443],{"xmlns":890},[892,54444,54445,54457],{},[895,54446,54447,54449,54451,54453,54455],{},[898,54448,3490],{},[1651,54450,1793],{},[1692,54452,6316],{},[1651,54454,4449],{},[1692,54456,20534],{},[902,54458,54459],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,54461,54463],{"className":54462},[886],[888,54464,54465],{"xmlns":890},[892,54466,54467,54479],{},[895,54468,54469,54471,54473,54475,54477],{},[898,54470,3542],{},[1651,54472,1793],{},[1692,54474,4190],{},[1651,54476,4449],{},[1692,54478,4231],{},[902,54480,54481],{"encoding":904},"d: 10 \\to 11",[883,54483,54485],{"className":54484},[886],[888,54486,54487],{"xmlns":890},[892,54488,54489,54499],{},[895,54490,54491,54493,54495,54497],{},[898,54492,3542],{},[898,54494,207],{},[1651,54496,1738],{},[1692,54498,6316],{},[902,54500,45825],{"encoding":904},[883,54502,54504],{"className":54503},[886],[888,54505,54506],{"xmlns":890},[892,54507,54508,54520],{},[895,54509,54510,54512,54514,54516,54518],{},[898,54511,3542],{},[898,54513,2268],{},[1651,54515,1738],{},[1651,54517,2181],{},[1692,54519,3574],{},[902,54521,45847],{"encoding":904},[883,54523,54525],{"className":54524},[886],[888,54526,54527],{"xmlns":890},[892,54528,54529,54539],{},[895,54530,54531,54533,54535,54537],{},[898,54532,3542],{},[898,54534,3490],{},[1651,54536,1738],{},[1692,54538,4122],{},[902,54540,45867],{"encoding":904},[883,54542,54544],{"className":54543},[886],[888,54545,54546],{"xmlns":890},[892,54547,54548,54558],{},[895,54549,54550,54552,54554,54556],{},[898,54551,3542],{},[898,54553,3542],{},[1651,54555,1738],{},[1692,54557,1694],{},[902,54559,45887],{"encoding":904},[724,54561,54562,54563,54621],{},"Totální diferenciál ",[883,54564,54566],{"className":54565},[886],[888,54567,54568],{"xmlns":890},[892,54569,54570,54618],{},[895,54571,54572,54578,54580,54582,54584,54586,54588,54590,54592,54594,54596,54598],{},[2115,54573,54574,54576],{},[898,54575,1690],{},[898,54577,5561],{},[1651,54579,1654],{"stretchy":1653},[898,54581,207],{},[1651,54583,1661],{"separator":1660},[898,54585,2268],{},[1651,54587,1661],{"separator":1660},[898,54589,3490],{},[1651,54591,1661],{"separator":1660},[898,54593,3542],{},[1651,54595,1667],{"stretchy":1653},[1651,54597,1738],{},[2938,54599,54600],{"scriptlevel":1741,"displaystyle":1660},[2446,54601,54602,54610],{},[895,54603,54604,54606,54608],{},[898,54605,2268],{},[1651,54607,2181],{},[898,54609,3542],{},[895,54611,54612,54614,54616],{},[898,54613,3490],{},[1651,54615,2181],{},[898,54617,207],{},[902,54619,54620],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,54623,54625],{"className":54624},[886],[888,54626,54627],{"xmlns":890,"display":29279},[892,54628,54629,54749],{},[895,54630,54631,54633,54639,54641,54667,54669,54671,54673,54675,54687,54689,54691,54693,54695,54721,54723,54725,54727,54729,54741,54743,54745,54747],{},[898,54632,3542],{},[2115,54634,54635,54637],{},[898,54636,1690],{},[898,54638,5561],{},[1651,54640,1738],{},[2446,54642,54643,54651],{},[895,54644,54645,54647,54649],{},[898,54646,2268],{},[1651,54648,2181],{},[898,54650,3542],{},[895,54652,54653,54655,54657,54659,54661],{},[1651,54654,1654],{"stretchy":1653},[898,54656,3490],{},[1651,54658,2181],{},[898,54660,207],{},[2115,54662,54663,54665],{},[1651,54664,1667],{"stretchy":1653},[1692,54666,1703],{},[1843,54668,1845],{},[898,54670,3542],{},[898,54672,207],{},[1651,54674,1839],{},[2446,54676,54677,54679],{},[1692,54678,1694],{},[895,54680,54681,54683,54685],{},[898,54682,3490],{},[1651,54684,2181],{},[898,54686,207],{},[1843,54688,1845],{},[898,54690,3542],{},[898,54692,2268],{},[1651,54694,2181],{},[2446,54696,54697,54705],{},[895,54698,54699,54701,54703],{},[898,54700,2268],{},[1651,54702,2181],{},[898,54704,3542],{},[895,54706,54707,54709,54711,54713,54715],{},[1651,54708,1654],{"stretchy":1653},[898,54710,3490],{},[1651,54712,2181],{},[898,54714,207],{},[2115,54716,54717,54719],{},[1651,54718,1667],{"stretchy":1653},[1692,54720,1703],{},[1843,54722,1845],{},[898,54724,3542],{},[898,54726,3490],{},[1651,54728,2181],{},[2446,54730,54731,54733],{},[1692,54732,1694],{},[895,54734,54735,54737,54739],{},[898,54736,3490],{},[1651,54738,2181],{},[898,54740,207],{},[1843,54742,1845],{},[898,54744,3542],{},[898,54746,3542],{},[898,54748,1882],{"mathvariant":1910},[902,54750,54751],{"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.",[724,54753,54754,54755,1343,54777,1343,54808,4477],{},"Dosazením číselných hodnot (",[883,54756,54758],{"className":54757},[886],[888,54759,54760],{"xmlns":890},[892,54761,54762,54774],{},[895,54763,54764,54766,54768,54770,54772],{},[898,54765,3490],{},[1651,54767,2181],{},[898,54769,207],{},[1651,54771,1738],{},[1692,54773,45619],{},[902,54775,54776],{"encoding":904},"c - a = 3{,}5",[883,54778,54780],{"className":54779},[886],[888,54781,54782],{"xmlns":890},[892,54783,54784,54805],{},[895,54785,54786,54788,54790,54792,54794,54800,54802],{},[1651,54787,1654],{"stretchy":1653},[898,54789,3490],{},[1651,54791,2181],{},[898,54793,207],{},[2115,54795,54796,54798],{},[1651,54797,1667],{"stretchy":1653},[1692,54799,1703],{},[1651,54801,1738],{},[1692,54803,54804],{},"12,25",[902,54806,54807],{"encoding":904},"(c-a)^2 = 12{,}25",[883,54809,54811],{"className":54810},[886],[888,54812,54813],{"xmlns":890},[892,54814,54815,54827],{},[895,54816,54817,54819,54821,54823,54825],{},[898,54818,2268],{},[1651,54820,2181],{},[898,54822,3542],{},[1651,54824,1738],{},[1692,54826,39232],{},[902,54828,54829],{"encoding":904},"b - d = 30",[883,54831,54833],{"className":54832},[886],[888,54834,54835],{"xmlns":890,"display":29279},[892,54836,54837,54938],{},[895,54838,54839,54841,54847,54849,54857,54859,54861,54863,54865,54873,54875,54877,54879,54881,54883,54891,54893,54895,54897,54899,54907,54909,54911,54913,54915,54918,54920,54923,54925,54927,54929,54932,54934,54936],{},[898,54840,3542],{},[2115,54842,54843,54845],{},[898,54844,1690],{},[898,54846,5561],{},[1651,54848,4060],{},[2938,54850,54851],{"scriptlevel":1741,"displaystyle":1653},[2446,54852,54853,54855],{},[1692,54854,39232],{},[1692,54856,54804],{},[1651,54858,1654],{"stretchy":1653},[1692,54860,6316],{},[1651,54862,1667],{"stretchy":1653},[1651,54864,1839],{},[2938,54866,54867],{"scriptlevel":1741,"displaystyle":1653},[2446,54868,54869,54871],{},[1692,54870,1694],{},[1692,54872,45619],{},[1651,54874,1654],{"stretchy":1653},[1651,54876,2181],{},[1692,54878,3574],{},[1651,54880,1667],{"stretchy":1653},[1651,54882,2181],{},[2938,54884,54885],{"scriptlevel":1741,"displaystyle":1653},[2446,54886,54887,54889],{},[1692,54888,39232],{},[1692,54890,54804],{},[1651,54892,1654],{"stretchy":1653},[1692,54894,4122],{},[1651,54896,1667],{"stretchy":1653},[1651,54898,2181],{},[2938,54900,54901],{"scriptlevel":1741,"displaystyle":1653},[2446,54902,54903,54905],{},[1692,54904,1694],{},[1692,54906,45619],{},[1651,54908,1654],{"stretchy":1653},[1692,54910,1694],{},[1651,54912,1667],{"stretchy":1653},[1651,54914,7207],{},[1692,54916,54917],{},"1,224",[1651,54919,2181],{},[1692,54921,54922],{},"1,429",[1651,54924,2181],{},[1692,54926,45792],{},[1651,54928,2181],{},[1692,54930,54931],{},"0,286",[1651,54933,7207],{},[1651,54935,2181],{},[1692,54937,46038],{},[902,54939,54940],{"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.",[724,54942,31278,54943,1882],{},[883,54944,54946],{"className":54945},[886],[888,54947,54948],{"xmlns":890},[892,54949,54950,54972],{},[895,54951,54952,54960,54962,54964,54966,54968,54970],{},[1902,54953,54954,54956,54958],{},[898,54955,1690],{},[1692,54957,1694],{},[898,54959,5561],{},[1651,54961,4060],{},[1692,54963,45787],{},[1651,54965,2181],{},[1692,54967,46069],{},[1651,54969,7207],{},[1692,54971,46074],{},[902,54973,54974],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[5179,54976,54977],{},[724,54978,54979,54981,54982,55003,55004,55030,55031,55034,55035,55131,55132,55155,55156,55172],{},[883,54980,5719],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,54983,54985],{"className":54984},[886],[888,54986,54987],{"xmlns":890},[892,54988,54989,55001],{},[895,54990,54991,54993,54995,54997,54999],{},[898,54992,4216],{"mathvariant":1910},[898,54994,1690],{},[1651,54996,4060],{},[1651,54998,2181],{},[1692,55000,46104],{},[902,55002,46107],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,55005,55007],{"className":55006},[886],[888,55008,55009],{"xmlns":890},[892,55010,55011,55027],{},[895,55012,55013,55015,55021,55023,55025],{},[898,55014,3542],{},[2115,55016,55017,55019],{},[898,55018,1690],{},[898,55020,5561],{},[1651,55022,7207],{},[1651,55024,2181],{},[1692,55026,46069],{},[902,55028,55029],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,55032,55033],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,55036,55038],{"className":55037},[886],[888,55039,55040],{"xmlns":890},[892,55041,55042,55128],{},[895,55043,55044,55052,55054,55088,55090,55114,55116,55123,55125],{},[1902,55045,55046,55048,55050],{},[898,55047,1690],{},[1692,55049,1694],{},[898,55051,5561],{},[1651,55053,1738],{},[2446,55055,55056,55072],{},[895,55057,55058,55064,55066],{},[2115,55059,55060,55062],{},[898,55061,2268],{},[1651,55063,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,55065,2181],{},[2115,55067,55068,55070],{},[898,55069,3542],{},[1651,55071,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[895,55073,55074,55080,55082],{},[2115,55075,55076,55078],{},[898,55077,3490],{},[1651,55079,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,55081,2181],{},[2115,55083,55084,55086],{},[898,55085,207],{},[1651,55087,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,55089,1738],{},[2446,55091,55092,55100],{},[895,55093,55094,55096,55098],{},[1692,55095,16336],{},[1651,55097,2181],{},[1692,55099,4231],{},[895,55101,55102,55104,55106,55108,55110,55112],{},[1692,55103,20534],{},[1651,55105,2181],{},[1651,55107,1654],{"stretchy":1653},[1651,55109,2181],{},[1692,55111,54412],{},[1651,55113,1667],{"stretchy":1653},[1651,55115,1738],{},[2446,55117,55118,55120],{},[1692,55119,43013],{},[1692,55121,55122],{},"3,1",[1651,55124,7207],{},[1692,55126,55127],{},"7,742",[902,55129,55130],{"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 ",[883,55133,55135],{"className":55134},[886],[888,55136,55137],{"xmlns":890},[892,55138,55139,55152],{},[895,55140,55141,55143,55145,55147,55149],{},[898,55142,4216],{"mathvariant":1910},[898,55144,1690],{},[1651,55146,7207],{},[1651,55148,2181],{},[1692,55150,55151],{},"0,829",[902,55153,55154],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,55157,55159],{"className":55158},[886],[888,55160,55161],{"xmlns":890},[892,55162,55163,55169],{},[895,55164,55165,55167],{},[1651,55166,2181],{},[1692,55168,46104],{},[902,55170,55171],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,55174,55175],{},[614,55176,55177,55178,55191],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,55179,55181],{"className":55180},[886],[888,55182,55183],{"xmlns":890},[892,55184,55185,55189],{},[895,55186,55187],{},[898,55188,1690],{},[902,55190,1690],{"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.",[198,55193,55195,55196],{"id":55194},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,55197,55199],{"className":55198},[886],[888,55200,55201],{"xmlns":890},[892,55202,55203,55209],{},[895,55204,55205,55207],{},[898,55206,2675],{},[898,55208,3004],{},[902,55210,46182],{"encoding":904},[5179,55212,55213],{},[724,55214,55215,55217,55218,55252,55253,55275],{},[883,55216,53908],{}," Zadání\nPro nabídku ",[883,55219,55221],{"className":55220},[886],[888,55222,55223],{"xmlns":890},[892,55224,55225,55249],{},[895,55226,55227,55229,55231,55233,55235,55237,55239,55241,55243,55245,55247],{},[898,55228,2675],{},[1651,55230,1738],{},[898,55232,3004],{},[1651,55234,1654],{"stretchy":1653},[898,55236,1690],{},[1651,55238,1667],{"stretchy":1653},[1651,55240,1738],{},[1692,55242,4190],{},[1651,55244,1839],{},[1692,55246,1703],{},[898,55248,1690],{},[902,55250,55251],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,55254,55256],{"className":55255},[886],[888,55257,55258],{"xmlns":890},[892,55259,55260,55272],{},[895,55261,55262,55268,55270],{},[1686,55263,55264,55266],{},[898,55265,1690],{},[1692,55267,1741],{},[1651,55269,1738],{},[1692,55271,4190],{},[902,55273,55274],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,55277,55278],{},[38,55279,23983],{},[724,55281,55282],{},"Odpovídající cena:",[883,55284,55286],{"className":55285},[886],[888,55287,55288],{"xmlns":890,"display":29279},[892,55289,55290,55325],{},[895,55291,55292,55298,55300,55302,55304,55306,55308,55310,55312,55314,55316,55318,55320,55322],{},[1686,55293,55294,55296],{},[898,55295,2675],{},[1692,55297,1741],{},[1651,55299,1738],{},[898,55301,3004],{},[1651,55303,1654],{"stretchy":1653},[1692,55305,4190],{},[1651,55307,1667],{"stretchy":1653},[1651,55309,1738],{},[1692,55311,4190],{},[1651,55313,1839],{},[1692,55315,1703],{},[1651,55317,4503],{},[1692,55319,4190],{},[1651,55321,1738],{},[1692,55323,55324],{},"30.",[902,55326,55327],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,55329,55330],{},"Dle vzorce (2.15):",[883,55332,55334],{"className":55333},[886],[888,55335,55336],{"xmlns":890,"display":29279},[892,55337,55338,55446],{},[895,55339,55340,55342,55344,55346,55348,55350,55352,55358,55364,55366,55374,55376,55378,55380,55382,55384,55386,55388,55390,55392,55394,55396,55398,55400,55402,55405,55407,55409,55411,55417,55425,55427,55429,55431,55433,55435,55437,55439,55441,55443],{},[898,55341,2675],{},[898,55343,3004],{},[1651,55345,1654],{"stretchy":1653},[1692,55347,4190],{},[1651,55349,1667],{"stretchy":1653},[1651,55351,1738],{},[1686,55353,55354,55356],{},[898,55355,2675],{},[1692,55357,1741],{},[1686,55359,55360,55362],{},[898,55361,1690],{},[1692,55363,1741],{},[1651,55365,2181],{},[1902,55367,55368,55370,55372],{},[1651,55369,12467],{},[1692,55371,1741],{},[1692,55373,4190],{},[1651,55375,1654],{"stretchy":1653},[1692,55377,4190],{},[1651,55379,1839],{},[1692,55381,1703],{},[898,55383,1690],{},[1651,55385,1667],{"stretchy":1653},[1843,55387,1845],{},[898,55389,3542],{},[898,55391,1690],{},[1651,55393,1738],{},[1692,55395,4190],{},[1651,55397,4503],{},[1692,55399,39232],{},[1651,55401,2181],{},[1651,55403,2261],{"fence":1653,"stretchy":1660,"minsize":55404,"maxsize":55404},"1.8em",[1692,55406,4190],{},[898,55408,1690],{},[1651,55410,1839],{},[2115,55412,55413,55415],{},[898,55414,1690],{},[1692,55416,1703],{},[1902,55418,55419,55421,55423],{},[1651,55420,2279],{"fence":1653,"stretchy":1660,"minsize":55404,"maxsize":55404},[1692,55422,1741],{},[1692,55424,4190],{},[1651,55426,1738],{},[1692,55428,31294],{},[1651,55430,2181],{},[1651,55432,1654],{"stretchy":1653},[1692,55434,4416],{},[1651,55436,1839],{},[1692,55438,4416],{},[1651,55440,1667],{"stretchy":1653},[1651,55442,1738],{},[1692,55444,55445],{},"100.",[902,55447,55448],{"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.",[724,55450,55451,55452,55473,55474,55494],{},"Přebytek výrobce při množství ",[883,55453,55455],{"className":55454},[886],[888,55456,55457],{"xmlns":890},[892,55458,55459,55471],{},[895,55460,55461,55467,55469],{},[1686,55462,55463,55465],{},[898,55464,1690],{},[1692,55466,1741],{},[1651,55468,1738],{},[1692,55470,4190],{},[902,55472,55274],{"encoding":904}," je tedy ",[883,55475,55477],{"className":55476},[886],[888,55478,55479],{"xmlns":890},[892,55480,55481,55491],{},[895,55482,55483,55485,55487,55489],{},[898,55484,2675],{},[898,55486,3004],{},[1651,55488,1738],{},[1692,55490,4416],{},[902,55492,55493],{"encoding":904},"PS = 100"," (peněžních jednotek).",[38183,55496],{},[115,55498,55500],{"id":55499},"cheat-sheet","Cheat sheet",[16,55502,55503,55516],{},[19,55504,55505],{},[22,55506,55507,55510,55513],{},[25,55508,55509],{},"Veličina",[25,55511,55512],{},"Vzorec",[25,55514,55515],{},"Geometrie",[30,55517,55518,55636,55750,55818],{},[22,55519,55520,55548,55604],{},[35,55521,55522],{},[883,55523,55525],{"className":55524},[886],[888,55526,55527],{"xmlns":890},[892,55528,55529,55545],{},[895,55530,55531,55533,55535,55537,55543],{},[898,55532,3001],{},[898,55534,3004],{},[1651,55536,1654],{"stretchy":1653},[1686,55538,55539,55541],{},[898,55540,1690],{},[1692,55542,1741],{},[1651,55544,1667],{"stretchy":1653},[902,55546,55547],{"encoding":904},"CS(Q_0)",[35,55549,55550],{},[883,55551,55553],{"className":55552},[886],[888,55554,55555],{"xmlns":890},[892,55556,55557,55601],{},[895,55558,55559],{},[2938,55560,55561,55573,55575,55577,55579,55581,55583,55585,55587,55589,55595],{"scriptlevel":1741,"displaystyle":1660},[1902,55562,55563,55565,55567],{},[1651,55564,12467],{},[1692,55566,1741],{},[1686,55568,55569,55571],{},[898,55570,1690],{},[1692,55572,1741],{},[898,55574,2047],{},[1651,55576,1654],{"stretchy":1653},[898,55578,1690],{},[1651,55580,1667],{"stretchy":1653},[1843,55582,1845],{},[898,55584,3542],{},[898,55586,1690],{},[1651,55588,2181],{},[1686,55590,55591,55593],{},[898,55592,2675],{},[1692,55594,1741],{},[1686,55596,55597,55599],{},[898,55598,1690],{},[1692,55600,1741],{},[902,55602,55603],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,55605,55606,55607,55610,55611,55614,55615],{},"plocha ",[38,55608,55609],{},"pod"," křivkou poptávky, ",[38,55612,55613],{},"nad"," čárou ",[883,55616,55618],{"className":55617},[886],[888,55619,55620],{"xmlns":890},[892,55621,55622,55634],{},[895,55623,55624,55626,55628],{},[898,55625,2675],{},[1651,55627,1738],{},[1686,55629,55630,55632],{},[898,55631,2675],{},[1692,55633,1741],{},[902,55635,52890],{"encoding":904},[22,55637,55638,55666,55722],{},[35,55639,55640],{},[883,55641,55643],{"className":55642},[886],[888,55644,55645],{"xmlns":890},[892,55646,55647,55663],{},[895,55648,55649,55651,55653,55655,55661],{},[898,55650,2675],{},[898,55652,3004],{},[1651,55654,1654],{"stretchy":1653},[1686,55656,55657,55659],{},[898,55658,1690],{},[1692,55660,1741],{},[1651,55662,1667],{"stretchy":1653},[902,55664,55665],{"encoding":904},"PS(Q_0)",[35,55667,55668],{},[883,55669,55671],{"className":55670},[886],[888,55672,55673],{"xmlns":890},[892,55674,55675,55719],{},[895,55676,55677],{},[2938,55678,55679,55685,55691,55693,55705,55707,55709,55711,55713,55715,55717],{"scriptlevel":1741,"displaystyle":1660},[1686,55680,55681,55683],{},[898,55682,2675],{},[1692,55684,1741],{},[1686,55686,55687,55689],{},[898,55688,1690],{},[1692,55690,1741],{},[1651,55692,2181],{},[1902,55694,55695,55697,55699],{},[1651,55696,12467],{},[1692,55698,1741],{},[1686,55700,55701,55703],{},[898,55702,1690],{},[1692,55704,1741],{},[898,55706,3004],{},[1651,55708,1654],{"stretchy":1653},[898,55710,1690],{},[1651,55712,1667],{"stretchy":1653},[1843,55714,1845],{},[898,55716,3542],{},[898,55718,1690],{},[902,55720,55721],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,55723,55606,55724,55726,55727,55614,55729],{},[38,55725,55613],{}," křivkou nabídky, ",[38,55728,55609],{},[883,55730,55732],{"className":55731},[886],[888,55733,55734],{"xmlns":890},[892,55735,55736,55748],{},[895,55737,55738,55740,55742],{},[898,55739,2675],{},[1651,55741,1738],{},[1686,55743,55744,55746],{},[898,55745,2675],{},[1692,55747,1741],{},[902,55749,52890],{"encoding":904},[22,55751,55752,55755,55782],{},[35,55753,55754],{},"Výdaje \u002F tržby",[35,55756,55757],{},[883,55758,55760],{"className":55759},[886],[888,55761,55762],{"xmlns":890},[892,55763,55764,55780],{},[895,55765,55766,55772,55774],{},[1686,55767,55768,55770],{},[898,55769,2675],{},[1692,55771,1741],{},[1651,55773,4503],{},[1686,55775,55776,55778],{},[898,55777,1690],{},[1692,55779,1741],{},[902,55781,53750],{"encoding":904},[35,55783,55784,55785],{},"obdélník ",[883,55786,55788],{"className":55787},[886],[888,55789,55790],{"xmlns":890},[892,55791,55792,55816],{},[895,55793,55794,55796,55798,55804,55806,55808,55810],{},[1692,55795,1741],{},[1843,55797,1845],{},[1686,55799,55800,55802],{},[898,55801,1690],{},[1692,55803,1741],{},[1843,55805,1845],{},[898,55807,5564],{},[1843,55809,1845],{},[1686,55811,55812,55814],{},[898,55813,2675],{},[1692,55815,1741],{},[902,55817,52370],{"encoding":904},[22,55819,55820,55823,55846],{},[35,55821,55822],{},"Celkový přebytek",[35,55824,55825],{},[883,55826,55828],{"className":55827},[886],[888,55829,55830],{"xmlns":890},[892,55831,55832,55844],{},[895,55833,55834,55836,55838,55840,55842],{},[898,55835,3001],{},[898,55837,3004],{},[1651,55839,1839],{},[898,55841,2675],{},[898,55843,3004],{},[902,55845,52108],{"encoding":904},[35,55847,55848],{},"součet obou ploch v rovnováze",[38183,55850],{},[115,55852,17018],{"id":17017},[120,55854,55855,55877,55899,55943,55987,56050,56078],{},[123,55856,55857,11325,55859,1343,55874,55876],{},[38,55858,46147],{},[883,55860,55862],{"className":55861},[886],[888,55863,55864],{"xmlns":890},[892,55865,55866,55872],{},[895,55867,55868,55870],{},[898,55869,3001],{},[898,55871,3004],{},[902,55873,46163],{"encoding":904},[614,55875,46201],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,55878,55879,11325,55881,1343,55896,55898],{},[38,55880,46294],{},[883,55882,55884],{"className":55883},[886],[888,55885,55886],{"xmlns":890},[892,55887,55888,55894],{},[895,55889,55890,55892],{},[898,55891,2675],{},[898,55893,3004],{},[902,55895,46182],{"encoding":904},[614,55897,46297],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,55900,55901,8322,55904,1882],{},[38,55902,55903],{},"Ochota platit",[883,55905,55907],{"className":55906},[886],[888,55908,55909],{"xmlns":890},[892,55910,55911,55941],{},[895,55912,55913],{},[2938,55914,55915,55927,55929,55931,55933,55935,55937,55939],{"scriptlevel":1741,"displaystyle":1660},[1902,55916,55917,55919,55921],{},[1651,55918,12467],{},[1692,55920,1741],{},[1686,55922,55923,55925],{},[898,55924,1690],{},[1692,55926,1741],{},[898,55928,2047],{},[1651,55930,1654],{"stretchy":1653},[898,55932,1690],{},[1651,55934,1667],{"stretchy":1653},[1843,55936,1845],{},[898,55938,3542],{},[898,55940,1690],{},[902,55942,52738],{"encoding":904},[123,55944,55945,8322,55948,1882],{},[38,55946,55947],{},"Minimální cena výrobce",[883,55949,55951],{"className":55950},[886],[888,55952,55953],{"xmlns":890},[892,55954,55955,55985],{},[895,55956,55957],{},[2938,55958,55959,55971,55973,55975,55977,55979,55981,55983],{"scriptlevel":1741,"displaystyle":1660},[1902,55960,55961,55963,55965],{},[1651,55962,12467],{},[1692,55964,1741],{},[1686,55966,55967,55969],{},[898,55968,1690],{},[1692,55970,1741],{},[898,55972,3004],{},[1651,55974,1654],{"stretchy":1653},[898,55976,1690],{},[1651,55978,1667],{"stretchy":1653},[1843,55980,1845],{},[898,55982,3542],{},[898,55984,1690],{},[902,55986,53380],{"encoding":904},[123,55988,55989,8322,55992,53881,56017,5230],{},[38,55990,55991],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,55993,55995],{"className":55994},[886],[888,55996,55997],{"xmlns":890},[892,55998,55999,56015],{},[895,56000,56001,56007,56009],{},[1686,56002,56003,56005],{},[898,56004,2675],{},[1692,56006,1741],{},[1843,56008,1845],{},[1686,56010,56011,56013],{},[898,56012,1690],{},[1692,56014,1741],{},[902,56016,52816],{"encoding":904},[883,56018,56020],{"className":56019},[886],[888,56021,56022],{"xmlns":890},[892,56023,56024,56048],{},[895,56025,56026,56028,56030,56036,56038,56040,56042],{},[1692,56027,1741],{},[1843,56029,1845],{},[1686,56031,56032,56034],{},[898,56033,1690],{},[1692,56035,1741],{},[1843,56037,1845],{},[898,56039,5564],{},[1843,56041,1845],{},[1686,56043,56044,56046],{},[898,56045,2675],{},[1692,56047,1741],{},[902,56049,52370],{"encoding":904},[123,56051,56052,56055,56056,56077],{},[38,56053,56054],{},"Celkový přebytek trhu"," — součet ",[883,56057,56059],{"className":56058},[886],[888,56060,56061],{"xmlns":890},[892,56062,56063,56075],{},[895,56064,56065,56067,56069,56071,56073],{},[898,56066,3001],{},[898,56068,3004],{},[1651,56070,1839],{},[898,56072,2675],{},[898,56074,3004],{},[902,56076,52108],{"encoding":904}," v rovnovážném bodě.",[123,56079,56080,56082,56083,1343,56096,56109,56110,1882],{},[38,56081,3779],{}," — plochy ohraničené křivkami ",[883,56084,56086],{"className":56085},[886],[888,56087,56088],{"xmlns":890},[892,56089,56090,56094],{},[895,56091,56092],{},[898,56093,2047],{},[902,56095,2047],{"encoding":904},[883,56097,56099],{"className":56098},[886],[888,56100,56101],{"xmlns":890},[892,56102,56103,56107],{},[895,56104,56105],{},[898,56106,3004],{},[902,56108,3004],{"encoding":904}," a přímkou ",[883,56111,56113],{"className":56112},[886],[888,56114,56115],{"xmlns":890},[892,56116,56117,56129],{},[895,56118,56119,56121,56123],{},[898,56120,2675],{},[1651,56122,1738],{},[1686,56124,56125,56127],{},[898,56126,2675],{},[1692,56128,1741],{},[902,56130,52890],{"encoding":904},[38183,56132],{},[115,56134,56136],{"id":56135},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,56138,56139,56140,56153,56154,56171],{},"Uvalení jednotkové daně ",[883,56141,56143],{"className":56142},[886],[888,56144,56145],{"xmlns":890},[892,56146,56147,56151],{},[895,56148,56149],{},[898,56150,4104],{},[902,56152,4104],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,56155,56157],{"className":56156},[886],[888,56158,56159],{"xmlns":890},[892,56160,56161,56169],{},[895,56162,56163],{},[2115,56164,56165,56167],{},[898,56166,1690],{},[898,56168,5561],{},[902,56170,43616],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,56173,56174],{},[1756,56175],{"alt":56176,"className":56177,"src":56178},"imek-prebytky-s-dani-deadweight",[210,1760],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,56180,56181,56182,56197,56198,56213,56214,53881,56217,56241,56242,11325,56245,56248,56249,1882],{},"Přebytek spotřebitele ",[883,56183,56185],{"className":56184},[886],[888,56186,56187],{"xmlns":890},[892,56188,56189,56195],{},[895,56190,56191,56193],{},[898,56192,3001],{},[898,56194,3004],{},[902,56196,46163],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,56199,56201],{"className":56200},[886],[888,56202,56203],{"xmlns":890},[892,56204,56205,56211],{},[895,56206,56207,56209],{},[898,56208,2675],{},[898,56210,3004],{},[902,56212,46182],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,56215,56216],{},"daňový příjem",[883,56218,56220],{"className":56219},[886],[888,56221,56222],{"xmlns":890},[892,56223,56224,56238],{},[895,56225,56226,56228,56230],{},[898,56227,4104],{},[1651,56229,4503],{},[1902,56231,56232,56234,56236],{},[898,56233,1690],{},[1692,56235,1694],{},[898,56237,5561],{},[902,56239,56240],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,56243,56244],{},"mrtvá ztráta",[614,56246,56247],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,56250,811],{"className":56251,"dataFsResolvedFilePath":809,"href":810},[210],[38183,56253],{},[115,56255,3238],{"id":3237},[120,56257,56258,56265,56277,56284,56291],{},[123,56259,56260,3246,56262],{},[38,56261,17520],{},[207,56263,802],{"className":56264,"dataFsResolvedFilePath":800,"href":801},[210],[123,56266,56267,3246,56269,56272,56273,56276],{},[38,56268,37887],{},[207,56270,775],{"className":56271,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,56274,3695],{"className":56275,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,56278,56279,3246,56281],{},[38,56280,17530],{},[207,56282,5135],{"className":56283,"dataFsResolvedFilePath":827,"href":828},[210],[123,56285,56286,3246,56288],{},[38,56287,51971],{},[207,56289,51975],{"className":56290,"dataFsResolvedFilePath":745,"href":746},[210],[123,56292,56293,3246,56295],{},[38,56294,17502],{},[207,56296,17506],{"className":56297,"dataFsResolvedFilePath":1749,"href":1750},[210],{"title":641,"searchDepth":642,"depth":642,"links":56299},[56300,56301,56306,56311,56316,56317,56318,56319],{"id":52167,"depth":642,"text":1241},{"id":52511,"depth":642,"text":56302,"children":56303},"Přebytek spotřebitele (CSCS)",[56304,56305],{"id":52530,"depth":649,"text":52531},{"id":3778,"depth":649,"text":3779},{"id":53106,"depth":642,"text":56307,"children":56308},"Přebytek výrobce (PSPS)",[56309,56310],{"id":53125,"depth":649,"text":53126},{"id":53288,"depth":649,"text":3779},{"id":53896,"depth":642,"text":53897,"children":56312},[56313,56314],{"id":53900,"depth":649,"text":53901},{"id":55194,"depth":649,"text":56315},"Příklad 2.13 — numerický výpočet PSPS",{"id":55499,"depth":642,"text":55500},{"id":17017,"depth":642,"text":17018},{"id":56135,"depth":642,"text":56136},{"id":3237,"depth":642,"text":3238},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,52037,56326,56327,13286,17538,56328,56329],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":56332,"title":56333,"body":56334,"course":1128,"courses":659,"created":10859,"description":641,"extension":661,"meta":75663,"navigation":664,"path":75664,"seo":75665,"sources":75666,"stem":75667,"tags":75668,"type":3302,"updated":677,"__hash__":75674},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":56335,"toc":75627},[56336,56339,56525,56527,56618,56623,56949,56953,56960,56964,57009,57076,57107,57157,57192,57196,57255,57260,57326,57444,57546,57550,57573,57651,57694,57698,57727,57794,57800,57914,57918,57998,58035,58087,58285,58349,58436,58440,58443,58522,58525,58643,58662,58727,58731,58823,58891,58932,58986,59054,59091,59095,59153,59183,59394,59466,59518,59684,59777,59812,59816,59820,59857,59922,59977,59981,60004,60093,60197,60266,60270,60367,60480,60536,60590,60648,60709,60712,60748,60813,60843,61072,61130,61164,61168,61195,61274,61388,61409,61488,61490,61598,61602,61740,62062,62066,62069,62073,62122,62126,62380,62532,62539,62612,62796,62801,63144,63148,63171,63173,63194,63253,63263,63312,63454,63528,63623,63738,63836,63954,63958,64027,64032,64144,64289,64340,64452,64494,64498,64518,64579,64606,64668,64672,64694,64763,65043,65050,65080,65087,65280,65284,65362,65367,65443,65446,65534,65610,65677,65726,65829,65902,66023,66374,66487,66589,66593,66596,66603,66606,66642,66701,66710,66859,67083,67087,67150,67329,67421,67476,67480,67536,67606,67658,67679,67760,67763,67838,67882,67886,67927,67970,67996,68000,68071,68167,68229,68281,68384,68462,68485,68514,68518,68684,68801,68873,69188,69348,69352,69403,69465,69500,69530,69630,69672,69841,69846,69942,69980,69984,70103,70404,70406,70441,70445,70449,70577,70709,71031,71219,71297,71301,71606,71719,71865,72050,72156,72388,72503,72585,72704,72802,72843,72847,72902,73046,73200,73360,73453,73647,73959,74090,74219,74223,74295,74337,74388,74390,75585,75587],[12,56337,56333],{"id":56338},"příjem-náklady-zisk-a-nabídka-firmy",[5179,56340,56341],{},[724,56342,56343,5186,56345,3246,56348,56363,56364,3246,56367,56382,56383,3246,56386,56414,56415,56437,56438,56462,56463,56485,56486,56489,56490,56506,56507,1882],{},[883,56344,5185],{},[38,56346,56347],{},"Příjem",[883,56349,56351],{"className":56350},[886],[888,56352,56353],{"xmlns":890},[892,56354,56355,56361],{},[895,56356,56357,56359],{},[898,56358,4104],{},[898,56360,2998],{},[902,56362,5404],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,56365,56366],{},"náklady",[883,56368,56370],{"className":56369},[886],[888,56371,56372],{"xmlns":890},[892,56373,56374,56380],{},[895,56375,56376,56378],{},[898,56377,4104],{},[898,56379,3001],{},[902,56381,4569],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,56384,56385],{},"zisk",[883,56387,56389],{"className":56388},[886],[888,56390,56391],{"xmlns":890},[892,56392,56393,56411],{},[895,56394,56395,56397,56399,56401,56403,56405,56407,56409],{},[898,56396,2675],{},[898,56398,2998],{},[1651,56400,1738],{},[898,56402,4104],{},[898,56404,2998],{},[1651,56406,2181],{},[898,56408,4104],{},[898,56410,3001],{},[902,56412,56413],{"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: ",[883,56416,56418],{"className":56417},[886],[888,56419,56420],{"xmlns":890},[892,56421,56422,56434],{},[895,56423,56424,56426,56428,56430,56432],{},[898,56425,5564],{},[898,56427,3001],{},[1651,56429,1738],{},[898,56431,2995],{},[898,56433,3001],{},[902,56435,56436],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,56439,56441],{"className":56440},[886],[888,56442,56443],{"xmlns":890},[892,56444,56445,56459],{},[895,56446,56447,56449,56451,56453,56455,56457],{},[898,56448,5564],{},[898,56450,41552],{},[898,56452,3001],{},[1651,56454,1738],{},[898,56456,2995],{},[898,56458,3001],{},[902,56460,56461],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,56464,56466],{"className":56465},[886],[888,56467,56468],{"xmlns":890},[892,56469,56470,56482],{},[895,56471,56472,56474,56476,56478,56480],{},[898,56473,2995],{},[898,56475,2998],{},[1651,56477,1738],{},[898,56479,2995],{},[898,56481,3001],{},[902,56483,56484],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,56487,56488],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,56491,56493],{"className":56492},[886],[888,56494,56495],{"xmlns":890},[892,56496,56497,56503],{},[895,56498,56499,56501],{},[898,56500,2995],{},[898,56502,3001],{},[902,56504,56505],{"encoding":904},"MC"," nad bodem minima ",[883,56508,56510],{"className":56509},[886],[888,56511,56512],{"xmlns":890},[892,56513,56514,56522],{},[895,56515,56516,56518,56520],{},[898,56517,5564],{},[898,56519,41552],{},[898,56521,3001],{},[902,56523,56524],{"encoding":904},"AVC",[115,56526,1241],{"id":52167},[724,56528,56529,56530,56533,56534,56536,56537,1343,56540,1343,56543,56545,56546,56549,56550,56553,56554,56557,56558,4002,56573,1348,56588,4002,56603,5230],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,56531,56532],{},"příjmem"," (revenue) a ",[38,56535,56366],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,56538,56539],{},"zisku",[38,56541,56542],{},"bodů zvratu",[38,56544,3332],{}," a konstrukcí ",[38,56547,56548],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,56551,1145],{"className":56552,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,56555,12428],{"className":56556,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,56559,56561],{"className":56560},[886],[888,56562,56563],{"xmlns":890},[892,56564,56565,56571],{},[895,56566,56567,56569],{},[898,56568,4104],{},[898,56570,2998],{},[902,56572,5404],{"encoding":904},[883,56574,56576],{"className":56575},[886],[888,56577,56578],{"xmlns":890},[892,56579,56580,56586],{},[895,56581,56582,56584],{},[898,56583,2995],{},[898,56585,2998],{},[902,56587,7941],{"encoding":904},[883,56589,56591],{"className":56590},[886],[888,56592,56593],{"xmlns":890},[892,56594,56595,56601],{},[895,56596,56597,56599],{},[898,56598,4104],{},[898,56600,3001],{},[902,56602,4569],{"encoding":904},[883,56604,56606],{"className":56605},[886],[888,56607,56608],{"xmlns":890},[892,56609,56610,56616],{},[895,56611,56612,56614],{},[898,56613,2995],{},[898,56615,3001],{},[902,56617,56505],{"encoding":904},[724,56619,56620],{},[38,56621,56622],{},"Cílové znalosti:",[120,56624,56625,56789,56792,56795,56888,56935,56942],{},[123,56626,56627,56628,1343,56643,1343,56659,5197,56674,1343,56689,1343,56705,1343,56723,1343,56741,1343,56758,1343,56774,9731],{},"odvodit a interpretovat funkce ",[883,56629,56631],{"className":56630},[886],[888,56632,56633],{"xmlns":890},[892,56634,56635,56641],{},[895,56636,56637,56639],{},[898,56638,4104],{},[898,56640,2998],{},[902,56642,5404],{"encoding":904},[883,56644,56646],{"className":56645},[886],[888,56647,56648],{"xmlns":890},[892,56649,56650,56656],{},[895,56651,56652,56654],{},[898,56653,5564],{},[898,56655,2998],{},[902,56657,56658],{"encoding":904},"AR",[883,56660,56662],{"className":56661},[886],[888,56663,56664],{"xmlns":890},[892,56665,56666,56672],{},[895,56667,56668,56670],{},[898,56669,2995],{},[898,56671,2998],{},[902,56673,7941],{"encoding":904},[883,56675,56677],{"className":56676},[886],[888,56678,56679],{"xmlns":890},[892,56680,56681,56687],{},[895,56682,56683,56685],{},[898,56684,4104],{},[898,56686,3001],{},[902,56688,4569],{"encoding":904},[883,56690,56692],{"className":56691},[886],[888,56693,56694],{"xmlns":890},[892,56695,56696,56702],{},[895,56697,56698,56700],{},[898,56699,11736],{},[898,56701,3001],{},[902,56703,56704],{"encoding":904},"FC",[883,56706,56708],{"className":56707},[886],[888,56709,56710],{"xmlns":890},[892,56711,56712,56720],{},[895,56713,56714,56716,56718],{},[898,56715,4104],{},[898,56717,41552],{},[898,56719,3001],{},[902,56721,56722],{"encoding":904},"TVC",[883,56724,56726],{"className":56725},[886],[888,56727,56728],{"xmlns":890},[892,56729,56730,56738],{},[895,56731,56732,56734,56736],{},[898,56733,5564],{},[898,56735,11736],{},[898,56737,3001],{},[902,56739,56740],{"encoding":904},"AFC",[883,56742,56744],{"className":56743},[886],[888,56745,56746],{"xmlns":890},[892,56747,56748,56756],{},[895,56749,56750,56752,56754],{},[898,56751,5564],{},[898,56753,41552],{},[898,56755,3001],{},[902,56757,56524],{"encoding":904},[883,56759,56761],{"className":56760},[886],[888,56762,56763],{"xmlns":890},[892,56764,56765,56771],{},[895,56766,56767,56769],{},[898,56768,5564],{},[898,56770,3001],{},[902,56772,56773],{"encoding":904},"AC",[883,56775,56777],{"className":56776},[886],[888,56778,56779],{"xmlns":890},[892,56780,56781,56787],{},[895,56782,56783,56785],{},[898,56784,2995],{},[898,56786,3001],{},[902,56788,56505],{"encoding":904},[123,56790,56791],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,56793,56794],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,56796,56797,56798,56801,56802,43027,56844,9731],{},"osvojit si ",[38,56799,56800],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,56803,56805],{"className":56804},[886],[888,56806,56807],{"xmlns":890},[892,56808,56809,56841],{},[895,56810,56811,56813,56815,56817,56823,56825,56827,56829,56831,56833,56839],{},[898,56812,5564],{},[898,56814,3001],{},[1651,56816,1654],{"stretchy":1653},[1686,56818,56819,56821],{},[898,56820,1690],{},[1692,56822,1741],{},[1651,56824,1667],{"stretchy":1653},[1651,56826,1738],{},[898,56828,2995],{},[898,56830,3001],{},[1651,56832,1654],{"stretchy":1653},[1686,56834,56835,56837],{},[898,56836,1690],{},[1692,56838,1741],{},[1651,56840,1667],{"stretchy":1653},[902,56842,56843],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,56845,56847],{"className":56846},[886],[888,56848,56849],{"xmlns":890},[892,56850,56851,56885],{},[895,56852,56853,56855,56857,56859,56861,56867,56869,56871,56873,56875,56877,56883],{},[898,56854,5564],{},[898,56856,41552],{},[898,56858,3001],{},[1651,56860,1654],{"stretchy":1653},[1686,56862,56863,56865],{},[898,56864,1690],{},[1692,56866,1741],{},[1651,56868,1667],{"stretchy":1653},[1651,56870,1738],{},[898,56872,2995],{},[898,56874,3001],{},[1651,56876,1654],{"stretchy":1653},[1686,56878,56879,56881],{},[898,56880,1690],{},[1692,56882,1741],{},[1651,56884,1667],{"stretchy":1653},[902,56886,56887],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,56889,56797,56890,56801,56893,9731],{},[38,56891,56892],{},"princip maximalizace zisku",[883,56894,56896],{"className":56895},[886],[888,56897,56898],{"xmlns":890},[892,56899,56900,56932],{},[895,56901,56902,56904,56906,56908,56914,56916,56918,56920,56922,56924,56930],{},[898,56903,2995],{},[898,56905,2998],{},[1651,56907,1654],{"stretchy":1653},[1686,56909,56910,56912],{},[898,56911,1690],{},[1692,56913,1741],{},[1651,56915,1667],{"stretchy":1653},[1651,56917,1738],{},[898,56919,2995],{},[898,56921,3001],{},[1651,56923,1654],{"stretchy":1653},[1686,56925,56926,56928],{},[898,56927,1690],{},[1692,56929,1741],{},[1651,56931,1667],{"stretchy":1653},[902,56933,56934],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,56936,56937,56938,56941],{},"stanovit ",[38,56939,56940],{},"body zvratu"," a interval zisku;",[123,56943,56944,56945,56948],{},"zkonstruovat ",[38,56946,56947],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,56950,56952],{"id":56951},"příjem-firmy","Příjem firmy",[724,56954,56955],{},[1756,56956],{"alt":56957,"className":56958,"src":56959},"imek-ar-mr-dvojnasobny-sklon",[210,1760],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,56961,56963],{"id":56962},"celkový-příjem","Celkový příjem",[724,56965,56966,56967,11325,56982,56985,56986,31157],{},"Celkový příjem ",[883,56968,56970],{"className":56969},[886],[888,56971,56972],{"xmlns":890},[892,56973,56974,56980],{},[895,56975,56976,56978],{},[898,56977,4104],{},[898,56979,2998],{},[902,56981,5404],{"encoding":904},[38,56983,56984],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,56987,56989],{"className":56988},[886],[888,56990,56991],{"xmlns":890},[892,56992,56993,57007],{},[895,56994,56995,56997,56999,57001,57003,57005],{},[898,56996,2675],{},[1651,56998,1738],{},[898,57000,2047],{},[1651,57002,1654],{"stretchy":1653},[898,57004,1690],{},[1651,57006,1667],{"stretchy":1653},[902,57008,5947],{"encoding":904},[883,57010,57012],{"className":57011},[886],[888,57013,57014],{"xmlns":890,"display":29279},[892,57015,57016,57073],{},[21967,57017,57018],{"width":29284},[21972,57019,57020,57022,57066,57068],{},[21975,57021],{"width":29289},[21975,57023,57024],{},[895,57025,57026,57028,57030,57032,57034,57036,57038,57040,57042,57044,57046,57048,57050,57052,57054,57056,57058,57060,57062,57064],{},[898,57027,4104],{},[898,57029,2998],{},[1651,57031,1738],{},[898,57033,4104],{},[898,57035,2998],{},[1651,57037,1654],{"stretchy":1653},[898,57039,1690],{},[1651,57041,1667],{"stretchy":1653},[1651,57043,1738],{},[898,57045,2675],{},[1651,57047,4503],{},[898,57049,1690],{},[1651,57051,1738],{},[898,57053,2047],{},[1651,57055,1654],{"stretchy":1653},[898,57057,1690],{},[1651,57059,1667],{"stretchy":1653},[1651,57061,4503],{},[898,57063,1690],{},[898,57065,1882],{"mathvariant":1910},[21975,57067],{"width":29289},[21975,57069,57070],{},[1843,57071,57072],{},"(3.1)",[902,57074,57075],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,57077,57078,57079,57082,57083,57106],{},"Graf funkce se nazývá ",[38,57080,57081],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,57084,57086],{"className":57085},[886],[888,57087,57088],{"xmlns":890},[892,57089,57090,57104],{},[895,57091,57092,57094,57096,57098,57100,57102],{},[898,57093,2675],{},[1651,57095,1738],{},[898,57097,207],{},[898,57099,1690],{},[1651,57101,1839],{},[898,57103,2268],{},[902,57105,38273],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,57108,57110],{"className":57109},[886],[888,57111,57112],{"xmlns":890,"display":29279},[892,57113,57114,57154],{},[895,57115,57116,57118,57120,57122,57124,57126,57128,57130,57132,57134,57136,57138,57140,57146,57148,57150,57152],{},[898,57117,4104],{},[898,57119,2998],{},[1651,57121,1738],{},[898,57123,1690],{},[1651,57125,1654],{"stretchy":1653},[898,57127,207],{},[898,57129,1690],{},[1651,57131,1839],{},[898,57133,2268],{},[1651,57135,1667],{"stretchy":1653},[1651,57137,1738],{},[898,57139,207],{},[2115,57141,57142,57144],{},[898,57143,1690],{},[1692,57145,1703],{},[1651,57147,1839],{},[898,57149,2268],{},[898,57151,1690],{},[1651,57153,1661],{"separator":1660},[902,57155,57156],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,57158,57159,57160,57173,57174,57191],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,57161,57163],{"className":57162},[886],[888,57164,57165],{"xmlns":890},[892,57166,57167,57171],{},[895,57168,57169],{},[898,57170,900],{},[902,57172,900],{"encoding":904}," (jelikož ",[883,57175,57177],{"className":57176},[886],[888,57178,57179],{"xmlns":890},[892,57180,57181,57189],{},[895,57182,57183,57185,57187],{},[898,57184,207],{},[1651,57186,2319],{},[1692,57188,1741],{},[902,57190,44298],{"encoding":904},") procházející počátkem.",[38561,57193,57195],{"id":57194},"příklad-31","Příklad 3.1",[724,57197,57198,57201,57202,57238,57239,57254],{},[38,57199,57200],{},"Zadání."," Pro poptávku ",[883,57203,57205],{"className":57204},[886],[888,57206,57207],{"xmlns":890},[892,57208,57209,57235],{},[895,57210,57211,57213,57215,57217,57219,57221,57223,57225,57227,57229,57231,57233],{},[898,57212,2675],{},[1651,57214,1738],{},[898,57216,2047],{},[1651,57218,1654],{"stretchy":1653},[898,57220,1690],{},[1651,57222,1667],{"stretchy":1653},[1651,57224,1738],{},[1651,57226,2181],{},[1692,57228,1703],{},[898,57230,1690],{},[1651,57232,1839],{},[1692,57234,4416],{},[902,57236,57237],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,57240,57242],{"className":57241},[886],[888,57243,57244],{"xmlns":890},[892,57245,57246,57252],{},[895,57247,57248,57250],{},[898,57249,4104],{},[898,57251,2998],{},[902,57253,5404],{"encoding":904}," a charakterizujte jeho křivku.",[724,57256,57257,57259],{},[38,57258,23983],{}," Celkový příjem je",[883,57261,57263],{"className":57262},[886],[888,57264,57265],{"xmlns":890,"display":29279},[892,57266,57267,57323],{},[895,57268,57269,57271,57273,57275,57277,57279,57281,57283,57285,57287,57289,57291,57293,57295,57297,57299,57301,57303,57305,57307,57309,57315,57317,57319,57321],{},[898,57270,4104],{},[898,57272,2998],{},[1651,57274,1738],{},[898,57276,4104],{},[898,57278,2998],{},[1651,57280,1654],{"stretchy":1653},[898,57282,1690],{},[1651,57284,1667],{"stretchy":1653},[1651,57286,1738],{},[898,57288,1690],{},[1651,57290,1654],{"stretchy":1653},[1651,57292,2181],{},[1692,57294,1703],{},[898,57296,1690],{},[1651,57298,1839],{},[1692,57300,4416],{},[1651,57302,1667],{"stretchy":1653},[1651,57304,1738],{},[1651,57306,2181],{},[1692,57308,1703],{},[2115,57310,57311,57313],{},[898,57312,1690],{},[1692,57314,1703],{},[1651,57316,1839],{},[1692,57318,4416],{},[898,57320,1690],{},[898,57322,1882],{"mathvariant":1910},[902,57324,57325],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,57327,57328,57329,5197,57351,57373,57374,57392,57393,1882],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,57330,57332],{"className":57331},[886],[888,57333,57334],{"xmlns":890},[892,57335,57336,57348],{},[895,57337,57338,57344,57346],{},[1686,57339,57340,57342],{},[898,57341,1690],{},[1692,57343,1694],{},[1651,57345,1738],{},[1692,57347,1741],{},[902,57349,57350],{"encoding":904},"Q_1 = 0",[883,57352,57354],{"className":57353},[886],[888,57355,57356],{"xmlns":890},[892,57357,57358,57370],{},[895,57359,57360,57366,57368],{},[1686,57361,57362,57364],{},[898,57363,1690],{},[1692,57365,1703],{},[1651,57367,1738],{},[1692,57369,4446],{},[902,57371,57372],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,57375,57377],{"className":57376},[886],[888,57378,57379],{"xmlns":890},[892,57380,57381,57389],{},[895,57382,57383,57385,57387],{},[898,57384,1690],{},[1651,57386,1738],{},[1692,57388,6311],{},[902,57390,57391],{"encoding":904},"Q = 25"," ve výši ",[883,57394,57396],{"className":57395},[886],[888,57397,57398],{"xmlns":890},[892,57399,57400,57441],{},[895,57401,57402,57404,57414,57416,57418,57420,57422,57425,57427,57429,57431,57433,57435,57437,57439],{},[898,57403,4104],{},[1686,57405,57406,57408,57411],{},[898,57407,2998],{},[898,57409,57410],{},"max",[1651,57412,57413],{},"⁡",[1651,57415,1738],{},[1651,57417,2181],{},[1692,57419,1703],{},[1651,57421,4503],{},[1692,57423,57424],{},"625",[1651,57426,1839],{},[1692,57428,4416],{},[1651,57430,4503],{},[1692,57432,6311],{},[1651,57434,1738],{},[1692,57436,1694],{},[1843,57438,1845],{},[1692,57440,31956],{},[902,57442,57443],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,57445,57446],{},[614,57447,57448,57449,57483,57484,5197,57497,57510,57511,3955,57529,1882],{},"Obrázek 3.1: Parabola ",[883,57450,57452],{"className":57451},[886],[888,57453,57454],{"xmlns":890},[892,57455,57456,57480],{},[895,57457,57458,57460,57462,57464,57466,57468,57474,57476,57478],{},[898,57459,4104],{},[898,57461,2998],{},[1651,57463,1738],{},[1651,57465,2181],{},[1692,57467,1703],{},[2115,57469,57470,57472],{},[898,57471,1690],{},[1692,57473,1703],{},[1651,57475,1839],{},[1692,57477,4416],{},[898,57479,1690],{},[902,57481,57482],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,57485,57487],{"className":57486},[886],[888,57488,57489],{"xmlns":890},[892,57490,57491,57495],{},[895,57492,57493],{},[1692,57494,1741],{},[902,57496,1741],{"encoding":904},[883,57498,57500],{"className":57499},[886],[888,57501,57502],{"xmlns":890},[892,57503,57504,57508],{},[895,57505,57506],{},[1692,57507,4446],{},[902,57509,4446],{"encoding":904}," a maximem ",[883,57512,57514],{"className":57513},[886],[888,57515,57516],{"xmlns":890},[892,57517,57518,57526],{},[895,57519,57520,57522,57524],{},[1692,57521,1694],{},[1843,57523,1845],{},[1692,57525,31956],{},[902,57527,57528],{"encoding":904},"1\\,250",[883,57530,57532],{"className":57531},[886],[888,57533,57534],{"xmlns":890},[892,57535,57536,57544],{},[895,57537,57538,57540,57542],{},[898,57539,1690],{},[1651,57541,1738],{},[1692,57543,6311],{},[902,57545,57391],{"encoding":904},[198,57547,57549],{"id":57548},"průměrný-příjem","Průměrný příjem",[724,57551,57552,3246,57554,11325,57569,57572],{},[38,57553,57549],{},[883,57555,57557],{"className":57556},[886],[888,57558,57559],{"xmlns":890},[892,57560,57561,57567],{},[895,57562,57563,57565],{},[898,57564,5564],{},[898,57566,2998],{},[902,57568,56658],{"encoding":904},[38,57570,57571],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,57574,57576],{"className":57575},[886],[888,57577,57578],{"xmlns":890,"display":29279},[892,57579,57580,57648],{},[895,57581,57582,57584,57586,57588,57590,57592,57594,57596,57598,57600,57616,57618,57636,57638,57640,57642,57644,57646],{},[898,57583,5564],{},[898,57585,2998],{},[1651,57587,1738],{},[898,57589,5564],{},[898,57591,2998],{},[1651,57593,1654],{"stretchy":1653},[898,57595,1690],{},[1651,57597,1667],{"stretchy":1653},[1651,57599,1738],{},[2446,57601,57602,57614],{},[895,57603,57604,57606,57608,57610,57612],{},[898,57605,4104],{},[898,57607,2998],{},[1651,57609,1654],{"stretchy":1653},[898,57611,1690],{},[1651,57613,1667],{"stretchy":1653},[898,57615,1690],{},[1651,57617,1738],{},[2446,57619,57620,57634],{},[895,57621,57622,57624,57626,57628,57630,57632],{},[898,57623,1690],{},[1843,57625,1845],{},[898,57627,2047],{},[1651,57629,1654],{"stretchy":1653},[898,57631,1690],{},[1651,57633,1667],{"stretchy":1653},[898,57635,1690],{},[1651,57637,1738],{},[898,57639,2047],{},[1651,57641,1654],{"stretchy":1653},[898,57643,1690],{},[1651,57645,1667],{"stretchy":1653},[898,57647,1882],{"mathvariant":1910},[902,57649,57650],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[5179,57652,57653],{},[724,57654,57655,57658,57659,1343,57662,1882],{},[883,57656,57657],{},"!note"," Klíčové pozorování\n",[38,57660,57661],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,57663,57665],{"className":57664},[886],[888,57666,57667],{"xmlns":890},[892,57668,57669,57691],{},[895,57670,57671,57673,57675,57677,57679,57681,57683,57685,57687,57689],{},[898,57672,5564],{},[898,57674,2998],{},[1651,57676,1654],{"stretchy":1653},[898,57678,1690],{},[1651,57680,1667],{"stretchy":1653},[1651,57682,1738],{},[898,57684,2047],{},[1651,57686,1654],{"stretchy":1653},[898,57688,1690],{},[1651,57690,1667],{"stretchy":1653},[902,57692,57693],{"encoding":904},"AR(Q) = D(Q)",[198,57695,57697],{"id":57696},"mezní-příjem","Mezní příjem",[724,57699,57700,57701,3246,57704,11325,57719,57722,57723,57726],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,57702,57703],{},"mezní příjem",[883,57705,57707],{"className":57706},[886],[888,57708,57709],{"xmlns":890},[892,57710,57711,57717],{},[895,57712,57713,57715],{},[898,57714,2995],{},[898,57716,2998],{},[902,57718,7941],{"encoding":904},[38,57720,57721],{},"marginal revenue","), definovaný jako ",[207,57724,1145],{"className":57725,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,57728,57730],{"className":57729},[886],[888,57731,57732],{"xmlns":890,"display":29279},[892,57733,57734,57791],{},[21967,57735,57736],{"width":29284},[21972,57737,57738,57740,57784,57786],{},[21975,57739],{"width":29289},[21975,57741,57742],{},[895,57743,57744,57746,57748,57750,57766,57768,57770,57776,57778,57780,57782],{},[898,57745,2995],{},[898,57747,2998],{},[1651,57749,1738],{},[2446,57751,57752,57760],{},[895,57753,57754,57756,57758],{},[898,57755,3542],{"mathvariant":1910},[898,57757,4104],{},[898,57759,2998],{},[895,57761,57762,57764],{},[898,57763,3542],{"mathvariant":1910},[898,57765,1690],{},[1651,57767,1738],{},[898,57769,4104],{},[2115,57771,57772,57774],{},[898,57773,2998],{},[1651,57775,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,57777,1654],{"stretchy":1653},[898,57779,1690],{},[1651,57781,1667],{"stretchy":1653},[898,57783,1882],{"mathvariant":1910},[21975,57785],{"width":29289},[21975,57787,57788],{},[1843,57789,57790],{},"(3.2)",[902,57792,57793],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,57795,57796,57797,57799],{},"Mezní příjem udává ",[38,57798,3927],{}," celkového příjmu vzhledem k množství.",[5179,57801,57802],{},[724,57803,57804,57806,57807,57833,57834,57851,57852,1882],{},[883,57805,5465],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,57808,57810],{"className":57809},[886],[888,57811,57812],{"xmlns":890},[892,57813,57814,57830],{},[895,57815,57816,57818,57820,57822,57828],{},[898,57817,2995],{},[898,57819,2998],{},[1651,57821,1654],{"stretchy":1653},[2115,57823,57824,57826],{},[898,57825,1690],{},[1651,57827,2668],{},[1651,57829,1667],{"stretchy":1653},[902,57831,57832],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,57835,57837],{"className":57836},[886],[888,57838,57839],{"xmlns":890},[892,57840,57841,57849],{},[895,57842,57843],{},[2115,57844,57845,57847],{},[898,57846,1690],{},[1651,57848,2668],{},[902,57850,31057],{"encoding":904},". Jinak řečeno: ",[883,57853,57855],{"className":57854},[886],[888,57856,57857],{"xmlns":890},[892,57858,57859,57911],{},[895,57860,57861,57863,57865,57867,57873,57875,57877,57879,57881,57883,57889,57891,57893,57895,57897,57899,57901,57903,57909],{},[898,57862,2995],{},[898,57864,2998],{},[1651,57866,1654],{"stretchy":1653},[2115,57868,57869,57871],{},[898,57870,1690],{},[1651,57872,2668],{},[1651,57874,1667],{"stretchy":1653},[1651,57876,4060],{},[898,57878,4104],{},[898,57880,2998],{},[1651,57882,1654],{"stretchy":1653},[2115,57884,57885,57887],{},[898,57886,1690],{},[1651,57888,2668],{},[1651,57890,1839],{},[1692,57892,1694],{},[1651,57894,1667],{"stretchy":1653},[1651,57896,2181],{},[898,57898,4104],{},[898,57900,2998],{},[1651,57902,1654],{"stretchy":1653},[2115,57904,57905,57907],{},[898,57906,1690],{},[1651,57908,2668],{},[1651,57910,1667],{"stretchy":1653},[902,57912,57913],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[38561,57915,57917],{"id":57916},"příklad-32","Příklad 3.2",[724,57919,57920,57201,57922,57238,57956,57971,57972,1882],{},[38,57921,57200],{},[883,57923,57925],{"className":57924},[886],[888,57926,57927],{"xmlns":890},[892,57928,57929,57953],{},[895,57930,57931,57933,57935,57937,57939,57941,57943,57945,57947,57949,57951],{},[898,57932,2675],{},[1651,57934,1738],{},[898,57936,2047],{},[1651,57938,1654],{"stretchy":1653},[898,57940,1690],{},[1651,57942,1667],{"stretchy":1653},[1651,57944,1738],{},[1692,57946,4416],{},[1651,57948,2181],{},[1692,57950,1703],{},[898,57952,1690],{},[902,57954,57955],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,57957,57959],{"className":57958},[886],[888,57960,57961],{"xmlns":890},[892,57962,57963,57969],{},[895,57964,57965,57967],{},[898,57966,2995],{},[898,57968,2998],{},[902,57970,7941],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,57973,57975],{"className":57974},[886],[888,57976,57977],{"xmlns":890},[892,57978,57979,57995],{},[895,57980,57981,57983,57985,57987,57989,57991,57993],{},[898,57982,1690],{},[1651,57984,1738],{},[1692,57986,37457],{},[1651,57988,1661],{"separator":1660},[1692,57990,43075],{},[1651,57992,1661],{"separator":1660},[1692,57994,10340],{},[902,57996,57997],{"encoding":904},"Q = 15, 16, 20",[724,57999,58000,3246,58002,58034],{},[38,58001,23983],{},[883,58003,58005],{"className":58004},[886],[888,58006,58007],{"xmlns":890},[892,58008,58009,58031],{},[895,58010,58011,58013,58015,58017,58019,58021,58023,58025],{},[898,58012,4104],{},[898,58014,2998],{},[1651,58016,1738],{},[1692,58018,4416],{},[898,58020,1690],{},[1651,58022,2181],{},[1692,58024,1703],{},[2115,58026,58027,58029],{},[898,58028,1690],{},[1692,58030,1703],{},[902,58032,58033],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,58036,58038],{"className":58037},[886],[888,58039,58040],{"xmlns":890,"display":29279},[892,58041,58042,58084],{},[895,58043,58044,58046,58048,58050,58052,58054,58056,58058,58060,58066,58072,58074,58076,58078,58080,58082],{},[898,58045,2995],{},[898,58047,2998],{},[1651,58049,1738],{},[1651,58051,1654],{"stretchy":1653},[1692,58053,4416],{},[898,58055,1690],{},[1651,58057,2181],{},[1692,58059,1703],{},[2115,58061,58062,58064],{},[898,58063,1690],{},[1692,58065,1703],{},[2115,58067,58068,58070],{},[1651,58069,1667],{"stretchy":1653},[1651,58071,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,58073,1738],{},[1692,58075,4416],{},[1651,58077,2181],{},[1692,58079,3689],{},[898,58081,1690],{},[898,58083,1882],{"mathvariant":1910},[902,58085,58086],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,58088,10966,58089,1878,58107,58133,58134,5665,58147,58162,58163,58176,58177,22633,58190,5665,58203,58218,58219,58232,58233,58264,58265,58284],{},[883,58090,58092],{"className":58091},[886],[888,58093,58094],{"xmlns":890},[892,58095,58096,58104],{},[895,58097,58098,58100,58102],{},[898,58099,1690],{},[1651,58101,1738],{},[1692,58103,37457],{},[902,58105,58106],{"encoding":904},"Q = 15",[883,58108,58110],{"className":58109},[886],[888,58111,58112],{"xmlns":890},[892,58113,58114,58130],{},[895,58115,58116,58118,58120,58122,58124,58126,58128],{},[898,58117,2995],{},[898,58119,2998],{},[1651,58121,1654],{"stretchy":1653},[1692,58123,37457],{},[1651,58125,1667],{"stretchy":1653},[1651,58127,1738],{},[1692,58129,6518],{},[902,58131,58132],{"encoding":904},"MR(15) = 40",": při množství ",[883,58135,58137],{"className":58136},[886],[888,58138,58139],{"xmlns":890},[892,58140,58141,58145],{},[895,58142,58143],{},[1692,58144,37457],{},[902,58146,37457],{"encoding":904},[883,58148,58150],{"className":58149},[886],[888,58151,58152],{"xmlns":890},[892,58153,58154,58160],{},[895,58155,58156,58158],{},[898,58157,4104],{},[898,58159,2998],{},[902,58161,5404],{"encoding":904}," mění asi ",[883,58164,58166],{"className":58165},[886],[888,58167,58168],{"xmlns":890},[892,58169,58170,58174],{},[895,58171,58172],{},[1692,58173,6518],{},[902,58175,6518],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,58178,58180],{"className":58179},[886],[888,58181,58182],{"xmlns":890},[892,58183,58184,58188],{},[895,58185,58186],{},[898,58187,1690],{},[902,58189,1690],{"encoding":904},[883,58191,58193],{"className":58192},[886],[888,58194,58195],{"xmlns":890},[892,58196,58197,58201],{},[895,58198,58199],{},[1692,58200,1694],{},[902,58202,1694],{"encoding":904},[883,58204,58206],{"className":58205},[886],[888,58207,58208],{"xmlns":890},[892,58209,58210,58216],{},[895,58211,58212,58214],{},[898,58213,4104],{},[898,58215,2998],{},[902,58217,5404],{"encoding":904}," zvýší přibližně o ",[883,58220,58222],{"className":58221},[886],[888,58223,58224],{"xmlns":890},[892,58225,58226,58230],{},[895,58227,58228],{},[1692,58229,6518],{},[902,58231,6518],{"encoding":904},", tj. ze skutečné hodnoty ",[883,58234,58236],{"className":58235},[886],[888,58237,58238],{"xmlns":890},[892,58239,58240,58261],{},[895,58241,58242,58244,58246,58248,58250,58252,58254,58256,58258],{},[898,58243,4104],{},[898,58245,2998],{},[1651,58247,1654],{"stretchy":1653},[1692,58249,37457],{},[1651,58251,1667],{"stretchy":1653},[1651,58253,1738],{},[1692,58255,1694],{},[1843,58257,1845],{},[1692,58259,58260],{},"050",[902,58262,58263],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,58266,58268],{"className":58267},[886],[888,58269,58270],{"xmlns":890},[892,58271,58272,58281],{},[895,58273,58274,58276,58278],{},[1692,58275,1694],{},[1843,58277,1845],{},[1692,58279,58280],{},"090",[902,58282,58283],{"encoding":904},"1\\,090",". Skutečná změna je",[883,58286,58288],{"className":58287},[886],[888,58289,58290],{"xmlns":890,"display":29279},[892,58291,58292,58346],{},[895,58293,58294,58296,58298,58300,58302,58304,58306,58308,58310,58312,58314,58316,58318,58320,58322,58324,58326,58328,58330,58333,58335,58337,58339,58341,58343],{},[898,58295,4216],{"mathvariant":1910},[898,58297,4104],{},[898,58299,2998],{},[1651,58301,1738],{},[898,58303,4104],{},[898,58305,2998],{},[1651,58307,1654],{"stretchy":1653},[1692,58309,43075],{},[1651,58311,1667],{"stretchy":1653},[1651,58313,2181],{},[898,58315,4104],{},[898,58317,2998],{},[1651,58319,1654],{"stretchy":1653},[1692,58321,37457],{},[1651,58323,1667],{"stretchy":1653},[1651,58325,1738],{},[1692,58327,1694],{},[1843,58329,1845],{},[1692,58331,58332],{},"088",[1651,58334,2181],{},[1692,58336,1694],{},[1843,58338,1845],{},[1692,58340,58260],{},[1651,58342,1738],{},[1692,58344,58345],{},"38.",[902,58347,58348],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,58350,58351,58352,1343,58378,4254,58404,58419,58420,58435],{},"Podobně ",[883,58353,58355],{"className":58354},[886],[888,58356,58357],{"xmlns":890},[892,58358,58359,58375],{},[895,58360,58361,58363,58365,58367,58369,58371,58373],{},[898,58362,2995],{},[898,58364,2998],{},[1651,58366,1654],{"stretchy":1653},[1692,58368,43075],{},[1651,58370,1667],{"stretchy":1653},[1651,58372,1738],{},[1692,58374,6872],{},[902,58376,58377],{"encoding":904},"MR(16) = 36",[883,58379,58381],{"className":58380},[886],[888,58382,58383],{"xmlns":890},[892,58384,58385,58401],{},[895,58386,58387,58389,58391,58393,58395,58397,58399],{},[898,58388,2995],{},[898,58390,2998],{},[1651,58392,1654],{"stretchy":1653},[1692,58394,10340],{},[1651,58396,1667],{"stretchy":1653},[1651,58398,1738],{},[1692,58400,10340],{},[902,58402,58403],{"encoding":904},"MR(20) = 20",[883,58405,58407],{"className":58406},[886],[888,58408,58409],{"xmlns":890},[892,58410,58411,58417],{},[895,58412,58413,58415],{},[898,58414,2995],{},[898,58416,2998],{},[902,58418,7941],{"encoding":904}," je klesající funkce — rychlost změny ",[883,58421,58423],{"className":58422},[886],[888,58424,58425],{"xmlns":890},[892,58426,58427,58433],{},[895,58428,58429,58431],{},[898,58430,4104],{},[898,58432,2998],{},[902,58434,5404],{"encoding":904}," s růstem množství klesá.",[198,58437,58439],{"id":58438},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,58441,58442],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,58444,58446],{"className":58445},[886],[888,58447,58448],{"xmlns":890,"display":29279},[892,58449,58450,58519],{},[21967,58451,58452],{"width":29284},[21972,58453,58454,58456,58512,58514],{},[21975,58455],{"width":29289},[21975,58457,58458],{},[895,58459,58460,58462,58464,58466,58468,58470,58472,58474,58476,58478,58480,58482,58484,58486,58492,58494,58496,58498,58500,58502,58504,58506,58508,58510],{},[898,58461,4216],{"mathvariant":1910},[898,58463,4104],{},[898,58465,2998],{},[1843,58467,5295],{},[1651,58469,4060],{},[1843,58471,5295],{},[898,58473,3542],{"mathvariant":1910},[898,58475,4104],{},[898,58477,2998],{},[1651,58479,1738],{},[1651,58481,1654],{"stretchy":1653},[898,58483,4104],{},[898,58485,2998],{},[2115,58487,58488,58490],{},[1651,58489,1667],{"stretchy":1653},[1651,58491,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1843,58493,1845],{},[898,58495,3542],{"mathvariant":1910},[898,58497,1690],{},[1651,58499,1738],{},[898,58501,2995],{},[898,58503,2998],{},[1843,58505,1845],{},[898,58507,3542],{"mathvariant":1910},[898,58509,1690],{},[1651,58511,1661],{"separator":1660},[21975,58513],{"width":29289},[21975,58515,58516],{},[1843,58517,58518],{},"(3.3)",[902,58520,58521],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,58523,58524],{},"schematicky:",[883,58526,58528],{"className":58527},[886],[888,58529,58530],{"xmlns":890,"display":29279},[892,58531,58532,58640],{},[895,58533,58534,58572,58574,58576,58578,58607,58610,58638],{},[895,58535,58536,58539,58545,58548,58554,58557,58563,58569],{},[1843,58537,58538],{},"zm",[9692,58540,58541,58543],{"accent":1660},[1843,58542,46945],{},[1651,58544,26271],{},[1843,58546,58547],{},"na celkov",[9692,58549,58550,58552],{"accent":1660},[1843,58551,46945],{},[1651,58553,26190],{},[1843,58555,58556],{},"ho p",[9692,58558,58559,58561],{"accent":1660},[1843,58560,13339],{},[1651,58562,26271],{},[9692,58564,58565,58567],{"accent":1660},[1843,58566,26259],{},[1651,58568,26190],{},[1843,58570,58571],{},"jmu",[1843,58573,5295],{},[1651,58575,4060],{},[1843,58577,5295],{},[895,58579,58580,58583,58589,58592,58598,58604],{},[1843,58581,58582],{},"mezn",[9692,58584,58585,58587],{"accent":1660},[1843,58586,26259],{},[1651,58588,26190],{},[1843,58590,58591],{}," p",[9692,58593,58594,58596],{"accent":1660},[1843,58595,13339],{},[1651,58597,26271],{},[9692,58599,58600,58602],{"accent":1660},[1843,58601,26259],{},[1651,58603,26190],{},[1843,58605,58606],{},"jem",[1651,58608,58609],{},"×",[895,58611,58612,58614,58620,58623,58629,58632],{},[1843,58613,58538],{},[9692,58615,58616,58618],{"accent":1660},[1843,58617,46945],{},[1651,58619,26271],{},[1843,58621,58622],{},"na mno",[9692,58624,58625,58627],{"accent":1660},[1843,58626,10897],{},[1651,58628,26271],{},[1843,58630,58631],{},"stv",[9692,58633,58634,58636],{"accent":1660},[1843,58635,26259],{},[1651,58637,26190],{},[898,58639,1882],{"mathvariant":1910},[902,58641,58642],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,58644,58645,58646,58661],{},"Pro porovnání skutečná změna ",[883,58647,58649],{"className":58648},[886],[888,58650,58651],{"xmlns":890},[892,58652,58653,58659],{},[895,58654,58655,58657],{},[898,58656,4104],{},[898,58658,2998],{},[902,58660,5404],{"encoding":904}," je",[883,58663,58665],{"className":58664},[886],[888,58666,58667],{"xmlns":890,"display":29279},[892,58668,58669,58724],{},[21967,58670,58671],{"width":29284},[21972,58672,58673,58675,58717,58719],{},[21975,58674],{"width":29289},[21975,58676,58677],{},[895,58678,58679,58681,58683,58685,58687,58689,58691,58693,58695,58697,58699,58701,58703,58705,58707,58709,58711,58713,58715],{},[898,58680,4216],{"mathvariant":1910},[898,58682,4104],{},[898,58684,2998],{},[1651,58686,1738],{},[898,58688,4104],{},[898,58690,2998],{},[1651,58692,1654],{"stretchy":1653},[898,58694,1690],{},[1651,58696,1839],{},[898,58698,3542],{"mathvariant":1910},[898,58700,1690],{},[1651,58702,1667],{"stretchy":1653},[1651,58704,2181],{},[898,58706,4104],{},[898,58708,2998],{},[1651,58710,1654],{"stretchy":1653},[898,58712,1690],{},[1651,58714,1667],{"stretchy":1653},[898,58716,1882],{"mathvariant":1910},[21975,58718],{"width":29289},[21975,58720,58721],{},[1843,58722,58723],{},"(3.4)",[902,58725,58726],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[38561,58728,58730],{"id":58729},"příklad-33","Příklad 3.3",[724,58732,58733,58735,58736,58766,58767,3988,58782,4002,58795,4016,58808,58822],{},[38,58734,57200],{}," Pro ",[883,58737,58739],{"className":58738},[886],[888,58740,58741],{"xmlns":890},[892,58742,58743,58763],{},[895,58744,58745,58747,58749,58751,58753,58755,58757],{},[898,58746,4104],{},[898,58748,2998],{},[1651,58750,1738],{},[1692,58752,4416],{},[898,58754,1690],{},[1651,58756,2181],{},[2115,58758,58759,58761],{},[898,58760,1690],{},[1692,58762,1703],{},[902,58764,58765],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,58768,58770],{"className":58769},[886],[888,58771,58772],{"xmlns":890},[892,58773,58774,58780],{},[895,58775,58776,58778],{},[898,58777,4104],{},[898,58779,2998],{},[902,58781,5404],{"encoding":904},[883,58783,58785],{"className":58784},[886],[888,58786,58787],{"xmlns":890},[892,58788,58789,58793],{},[895,58790,58791],{},[898,58792,1690],{},[902,58794,1690],{"encoding":904},[883,58796,58798],{"className":58797},[886],[888,58799,58800],{"xmlns":890},[892,58801,58802,58806],{},[895,58803,58804],{},[1692,58805,4452],{},[902,58807,4452],{"encoding":904},[883,58809,58811],{"className":58810},[886],[888,58812,58813],{"xmlns":890},[892,58814,58815,58820],{},[895,58816,58817],{},[1692,58818,58819],{},"63",[902,58821,58819],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,58824,58825,3246,58827,58852,58853,1343,58871,1793],{},[38,58826,23983],{},[883,58828,58830],{"className":58829},[886],[888,58831,58832],{"xmlns":890},[892,58833,58834,58850],{},[895,58835,58836,58838,58840,58842,58844,58846,58848],{},[898,58837,2995],{},[898,58839,2998],{},[1651,58841,1738],{},[1692,58843,4416],{},[1651,58845,2181],{},[1692,58847,1703],{},[898,58849,1690],{},[902,58851,12734],{"encoding":904},", tedy při ",[883,58854,58856],{"className":58855},[886],[888,58857,58858],{"xmlns":890},[892,58859,58860,58868],{},[895,58861,58862,58864,58866],{},[898,58863,1690],{},[1651,58865,1738],{},[1692,58867,4452],{},[902,58869,58870],{"encoding":904},"Q = 60",[883,58872,58874],{"className":58873},[886],[888,58875,58876],{"xmlns":890},[892,58877,58878,58888],{},[895,58879,58880,58882,58884,58886],{},[898,58881,3542],{"mathvariant":1910},[898,58883,1690],{},[1651,58885,1738],{},[1692,58887,3521],{},[902,58889,58890],{"encoding":904},"\\mathrm{d}Q = 3",[883,58892,58894],{"className":58893},[886],[888,58895,58896],{"xmlns":890,"display":29279},[892,58897,58898,58929],{},[895,58899,58900,58902,58904,58906,58908,58910,58912,58914,58916,58918,58920,58922,58924,58926],{},[898,58901,3542],{"mathvariant":1910},[898,58903,4104],{},[898,58905,2998],{},[1651,58907,1738],{},[1651,58909,1654],{"stretchy":1653},[1692,58911,4416],{},[1651,58913,2181],{},[1692,58915,5356],{},[1651,58917,1667],{"stretchy":1653},[1651,58919,4503],{},[1692,58921,3521],{},[1651,58923,1738],{},[1651,58925,2181],{},[1692,58927,58928],{},"60.",[902,58930,58931],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,58933,58934,58935,58965,58966,58985],{},"Celkový příjem klesne z ",[883,58936,58938],{"className":58937},[886],[888,58939,58940],{"xmlns":890},[892,58941,58942,58962],{},[895,58943,58944,58946,58948,58950,58952,58954,58956,58958,58960],{},[898,58945,4104],{},[898,58947,2998],{},[1651,58949,1654],{"stretchy":1653},[1692,58951,4452],{},[1651,58953,1667],{"stretchy":1653},[1651,58955,1738],{},[1692,58957,1703],{},[1843,58959,1845],{},[1692,58961,21355],{},[902,58963,58964],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,58967,58969],{"className":58968},[886],[888,58970,58971],{"xmlns":890},[892,58972,58973,58982],{},[895,58974,58975,58977,58979],{},[1692,58976,1703],{},[1843,58978,1845],{},[1692,58980,58981],{},"340",[902,58983,58984],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,58987,58989],{"className":58988},[886],[888,58990,58991],{"xmlns":890,"display":29279},[892,58992,58993,59051],{},[895,58994,58995,58997,58999,59001,59003,59005,59007,59009,59011,59013,59015,59017,59019,59021,59023,59025,59027,59029,59031,59034,59036,59038,59040,59042,59044,59046,59049],{},[898,58996,4216],{"mathvariant":1910},[898,58998,4104],{},[898,59000,2998],{},[1651,59002,1738],{},[898,59004,4104],{},[898,59006,2998],{},[1651,59008,1654],{"stretchy":1653},[1692,59010,58819],{},[1651,59012,1667],{"stretchy":1653},[1651,59014,2181],{},[898,59016,4104],{},[898,59018,2998],{},[1651,59020,1654],{"stretchy":1653},[1692,59022,4452],{},[1651,59024,1667],{"stretchy":1653},[1651,59026,1738],{},[1692,59028,1703],{},[1843,59030,1845],{},[1692,59032,59033],{},"331",[1651,59035,2181],{},[1692,59037,1703],{},[1843,59039,1845],{},[1692,59041,21355],{},[1651,59043,1738],{},[1651,59045,2181],{},[1692,59047,59048],{},"69",[1651,59050,1661],{"separator":1660},[902,59052,59053],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,59055,59056,59057,59072,59073,1882],{},"tj. ",[883,59058,59060],{"className":59059},[886],[888,59061,59062],{"xmlns":890},[892,59063,59064,59070],{},[895,59065,59066,59068],{},[898,59067,4104],{},[898,59069,2998],{},[902,59071,5404],{"encoding":904}," klesne na ",[883,59074,59076],{"className":59075},[886],[888,59077,59078],{"xmlns":890},[892,59079,59080,59088],{},[895,59081,59082,59084,59086],{},[1692,59083,1703],{},[1843,59085,1845],{},[1692,59087,59033],{},[902,59089,59090],{"encoding":904},"2\\,331",[198,59092,59094],{"id":59093},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,59096,59097,59098,11694,59121,32793],{},"Obecně pro lineární poptávku ",[883,59099,59101],{"className":59100},[886],[888,59102,59103],{"xmlns":890},[892,59104,59105,59119],{},[895,59106,59107,59109,59111,59113,59115,59117],{},[898,59108,2675],{},[1651,59110,1738],{},[898,59112,207],{},[898,59114,1690],{},[1651,59116,1839],{},[898,59118,2268],{},[902,59120,38273],{"encoding":904},[883,59122,59124],{"className":59123},[886],[888,59125,59126],{"xmlns":890},[892,59127,59128,59150],{},[895,59129,59130,59132,59134,59136,59138,59144,59146,59148],{},[898,59131,4104],{},[898,59133,2998],{},[1651,59135,1738],{},[898,59137,207],{},[2115,59139,59140,59142],{},[898,59141,1690],{},[1692,59143,1703],{},[1651,59145,1839],{},[898,59147,2268],{},[898,59149,1690],{},[902,59151,59152],{"encoding":904},"TR = aQ^2 + bQ",[883,59154,59156],{"className":59155},[886],[888,59157,59158],{"xmlns":890,"display":29279},[892,59159,59160,59180],{},[895,59161,59162,59164,59166,59168,59170,59172,59174,59176,59178],{},[898,59163,2995],{},[898,59165,2998],{},[1651,59167,1738],{},[1692,59169,1703],{},[898,59171,207],{},[898,59173,1690],{},[1651,59175,1839],{},[898,59177,2268],{},[898,59179,1882],{"mathvariant":1910},[902,59181,59182],{"encoding":904},"MR = 2aQ + b.",[724,59184,59185,59186,59201,59202,59217,59218,59231,59232,11325,59235,59251,59252,59265,59266,59281,59282,59297,59298,59313,59314,3955,59327,59357,59358,59377,59378,59393],{},"Křivky ",[883,59187,59189],{"className":59188},[886],[888,59190,59191],{"xmlns":890},[892,59192,59193,59199],{},[895,59194,59195,59197],{},[898,59196,2995],{},[898,59198,2998],{},[902,59200,7941],{"encoding":904}," a poptávky (resp. ",[883,59203,59205],{"className":59204},[886],[888,59206,59207],{"xmlns":890},[892,59208,59209,59215],{},[895,59210,59211,59213],{},[898,59212,5564],{},[898,59214,2998],{},[902,59216,56658],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,59219,59221],{"className":59220},[886],[888,59222,59223],{"xmlns":890},[892,59224,59225,59229],{},[895,59226,59227],{},[898,59228,2268],{},[902,59230,2268],{"encoding":904},", přičemž ",[38,59233,59234],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,59236,59238],{"className":59237},[886],[888,59239,59240],{"xmlns":890},[892,59241,59242,59248],{},[895,59243,59244,59246],{},[1692,59245,1703],{},[898,59247,207],{},[902,59249,59250],{"encoding":904},"2a"," vs. ",[883,59253,59255],{"className":59254},[886],[888,59256,59257],{"xmlns":890},[892,59258,59259,59263],{},[895,59260,59261],{},[898,59262,207],{},[902,59264,207],{"encoding":904},", obrázek 3.2). ",[883,59267,59269],{"className":59268},[886],[888,59270,59271],{"xmlns":890},[892,59272,59273,59279],{},[895,59274,59275,59277],{},[898,59276,2995],{},[898,59278,2998],{},[902,59280,7941],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,59283,59285],{"className":59284},[886],[888,59286,59287],{"xmlns":890},[892,59288,59289,59295],{},[895,59290,59291,59293],{},[898,59292,4104],{},[898,59294,2998],{},[902,59296,5404],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,59299,59301],{"className":59300},[886],[888,59302,59303],{"xmlns":890},[892,59304,59305,59311],{},[895,59306,59307,59309],{},[898,59308,2995],{},[898,59310,2998],{},[902,59312,7941],{"encoding":904}," osu ",[883,59315,59317],{"className":59316},[886],[888,59318,59319],{"xmlns":890},[892,59320,59321,59325],{},[895,59322,59323],{},[898,59324,1690],{},[902,59326,1690],{"encoding":904},[883,59328,59330],{"className":59329},[886],[888,59331,59332],{"xmlns":890},[892,59333,59334,59354],{},[895,59335,59336,59338,59340,59342],{},[898,59337,1690],{},[1651,59339,1738],{},[1651,59341,2181],{},[2938,59343,59344],{"scriptlevel":1741,"displaystyle":1653},[2446,59345,59346,59348],{},[898,59347,2268],{},[895,59349,59350,59352],{},[1692,59351,1703],{},[898,59353,207],{},[902,59355,59356],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,59359,59361],{"className":59360},[886],[888,59362,59363],{"xmlns":890},[892,59364,59365,59375],{},[895,59366,59367,59369,59371,59373],{},[898,59368,2995],{},[898,59370,2998],{},[1651,59372,1738],{},[1692,59374,1741],{},[902,59376,8391],{"encoding":904},", a dále ",[883,59379,59381],{"className":59380},[886],[888,59382,59383],{"xmlns":890},[892,59384,59385,59391],{},[895,59386,59387,59389],{},[898,59388,4104],{},[898,59390,2998],{},[902,59392,5404],{"encoding":904}," klesá.",[724,59395,59396,59397,59403,59404,59436,59437,59465],{},"V případě ",[38,59398,59399],{},[207,59400,59402],{"className":59401,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,59405,59407],{"className":59406},[886],[888,59408,59409],{"xmlns":890},[892,59410,59411,59433],{},[895,59412,59413,59415,59417,59419,59421,59423,59425,59427],{},[898,59414,2675],{},[1651,59416,1738],{},[898,59418,2047],{},[1651,59420,1654],{"stretchy":1653},[898,59422,1690],{},[1651,59424,1667],{"stretchy":1653},[1651,59426,1738],{},[2115,59428,59429,59431],{},[898,59430,2675],{},[1651,59432,2668],{},[902,59434,59435],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,59438,59440],{"className":59439},[886],[888,59441,59442],{"xmlns":890},[892,59443,59444,59462],{},[895,59445,59446,59448,59450,59452,59454,59456],{},[898,59447,4104],{},[898,59449,2998],{},[1651,59451,1738],{},[898,59453,1690],{},[1651,59455,4503],{},[2115,59457,59458,59460],{},[898,59459,2675],{},[1651,59461,2668],{},[902,59463,59464],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,59467,59469],{"className":59468},[886],[888,59470,59471],{"xmlns":890,"display":29279},[892,59472,59473,59515],{},[895,59474,59475,59477,59479,59481,59483,59485,59487,59493,59495,59497,59511,59513],{},[898,59476,2995],{},[898,59478,2998],{},[1651,59480,1738],{},[898,59482,5564],{},[898,59484,2998],{},[1651,59486,1738],{},[2115,59488,59489,59491],{},[898,59490,2675],{},[1651,59492,2668],{},[7185,59494],{"width":16582},[1651,59496,1654],{"stretchy":1653},[895,59498,59499,59502,59508],{},[1843,59500,59501],{},"obr",[9692,59503,59504,59506],{"accent":1660},[1843,59505,207],{},[1651,59507,26190],{},[1843,59509,59510],{},"zek 3.4",[1651,59512,1667],{"stretchy":1653},[898,59514,1882],{"mathvariant":1910},[902,59516,59517],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,59519,59520],{},[614,59521,59522,59523,5197,59549,59577,59578,59591,59592,59607,59608,5036,59621,1343,59647,5036,59662,1882],{},"Obrázek 3.2: Přímky ",[883,59524,59526],{"className":59525},[886],[888,59527,59528],{"xmlns":890},[892,59529,59530,59546],{},[895,59531,59532,59534,59536,59538,59540,59542,59544],{},[898,59533,5564],{},[898,59535,2998],{},[1651,59537,1738],{},[898,59539,207],{},[898,59541,1690],{},[1651,59543,1839],{},[898,59545,2268],{},[902,59547,59548],{"encoding":904},"AR = aQ + b",[883,59550,59552],{"className":59551},[886],[888,59553,59554],{"xmlns":890},[892,59555,59556,59574],{},[895,59557,59558,59560,59562,59564,59566,59568,59570,59572],{},[898,59559,2995],{},[898,59561,2998],{},[1651,59563,1738],{},[1692,59565,1703],{},[898,59567,207],{},[898,59569,1690],{},[1651,59571,1839],{},[898,59573,2268],{},[902,59575,59576],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,59579,59581],{"className":59580},[886],[888,59582,59583],{"xmlns":890},[892,59584,59585,59589],{},[895,59586,59587],{},[898,59588,2268],{},[902,59590,2268],{"encoding":904}," se svislou osou, ",[883,59593,59595],{"className":59594},[886],[888,59596,59597],{"xmlns":890},[892,59598,59599,59605],{},[895,59600,59601,59603],{},[898,59602,2995],{},[898,59604,2998],{},[902,59606,7941],{"encoding":904}," protíná osu ",[883,59609,59611],{"className":59610},[886],[888,59612,59613],{"xmlns":890},[892,59614,59615,59619],{},[895,59616,59617],{},[898,59618,1690],{},[902,59620,1690],{"encoding":904},[883,59622,59624],{"className":59623},[886],[888,59625,59626],{"xmlns":890},[892,59627,59628,59644],{},[895,59629,59630,59632],{},[1651,59631,2181],{},[2938,59633,59634],{"scriptlevel":1741,"displaystyle":1653},[2446,59635,59636,59638],{},[898,59637,2268],{},[895,59639,59640,59642],{},[1692,59641,1703],{},[898,59643,207],{},[902,59645,59646],{"encoding":904},"-\\tfrac{b}{2a}",[883,59648,59650],{"className":59649},[886],[888,59651,59652],{"xmlns":890},[892,59653,59654,59660],{},[895,59655,59656,59658],{},[898,59657,5564],{},[898,59659,2998],{},[902,59661,56658],{"encoding":904},[883,59663,59665],{"className":59664},[886],[888,59666,59667],{"xmlns":890},[892,59668,59669,59681],{},[895,59670,59671,59673],{},[1651,59672,2181],{},[2938,59674,59675],{"scriptlevel":1741,"displaystyle":1653},[2446,59676,59677,59679],{},[898,59678,2268],{},[898,59680,207],{},[902,59682,59683],{"encoding":904},"-\\tfrac{b}{a}",[724,59685,59686],{},[614,59687,59688,59689,59720,59721,59750,59751,1882],{},"Obrázek 3.3: Parabola ",[883,59690,59692],{"className":59691},[886],[888,59693,59694],{"xmlns":890},[892,59695,59696,59718],{},[895,59697,59698,59700,59702,59704,59706,59712,59714,59716],{},[898,59699,4104],{},[898,59701,2998],{},[1651,59703,1738],{},[898,59705,207],{},[2115,59707,59708,59710],{},[898,59709,1690],{},[1692,59711,1703],{},[1651,59713,1839],{},[898,59715,2268],{},[898,59717,1690],{},[902,59719,59152],{"encoding":904}," s maximem v ",[883,59722,59724],{"className":59723},[886],[888,59725,59726],{"xmlns":890},[892,59727,59728,59748],{},[895,59729,59730,59732,59734,59736],{},[898,59731,1690],{},[1651,59733,1738],{},[1651,59735,2181],{},[2938,59737,59738],{"scriptlevel":1741,"displaystyle":1653},[2446,59739,59740,59742],{},[898,59741,2268],{},[895,59743,59744,59746],{},[1692,59745,1703],{},[898,59747,207],{},[902,59749,59356],{"encoding":904}," a nulou v ",[883,59752,59754],{"className":59753},[886],[888,59755,59756],{"xmlns":890},[892,59757,59758,59774],{},[895,59759,59760,59762,59764,59766],{},[898,59761,1690],{},[1651,59763,1738],{},[1651,59765,2181],{},[2938,59767,59768],{"scriptlevel":1741,"displaystyle":1653},[2446,59769,59770,59772],{},[898,59771,2268],{},[898,59773,207],{},[902,59775,59776],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,59778,59779],{},[614,59780,59781,59782,1882],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,59783,59785],{"className":59784},[886],[888,59786,59787],{"xmlns":890},[892,59788,59789,59809],{},[895,59790,59791,59793,59795,59797,59799,59801,59803],{},[898,59792,5564],{},[898,59794,2998],{},[1651,59796,1738],{},[898,59798,2995],{},[898,59800,2998],{},[1651,59802,1738],{},[2115,59804,59805,59807],{},[898,59806,2675],{},[1651,59808,2668],{},[902,59810,59811],{"encoding":904},"AR = MR = P^*",[115,59813,59815],{"id":59814},"náklady-firmy","Náklady firmy",[198,59817,59819],{"id":59818},"celkové-náklady","Celkové náklady",[724,59821,59822,3246,59824,11325,59839,59842,59843,59856],{},[38,59823,59819],{},[883,59825,59827],{"className":59826},[886],[888,59828,59829],{"xmlns":890},[892,59830,59831,59837],{},[895,59832,59833,59835],{},[898,59834,4104],{},[898,59836,3001],{},[902,59838,4569],{"encoding":904},[38,59840,59841],{},"total cost",") jsou veškeré náklady na realizaci ",[883,59844,59846],{"className":59845},[886],[888,59847,59848],{"xmlns":890},[892,59849,59850,59854],{},[895,59851,59852],{},[898,59853,1690],{},[902,59855,1690],{"encoding":904}," jednotek produkce:",[883,59858,59860],{"className":59859},[886],[888,59861,59862],{"xmlns":890,"display":29279},[892,59863,59864,59919],{},[21967,59865,59866],{"width":29284},[21972,59867,59868,59870,59912,59914],{},[21975,59869],{"width":29289},[21975,59871,59872],{},[895,59873,59874,59876,59878,59880,59882,59884,59886,59888,59890,59892,59894,59896,59898,59900,59902,59904,59906,59908,59910],{},[898,59875,4104],{},[898,59877,3001],{},[1651,59879,1738],{},[898,59881,4104],{},[898,59883,3001],{},[1651,59885,1654],{"stretchy":1653},[898,59887,1690],{},[1651,59889,1667],{"stretchy":1653},[1651,59891,1738],{},[898,59893,11736],{},[898,59895,3001],{},[1651,59897,1839],{},[898,59899,4104],{},[898,59901,41552],{},[898,59903,3001],{},[1651,59905,1654],{"stretchy":1653},[898,59907,1690],{},[1651,59909,1667],{"stretchy":1653},[1651,59911,1661],{"separator":1660},[21975,59913],{"width":29289},[21975,59915,59916],{},[1843,59917,59918],{},"(3.5)",[902,59920,59921],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,59923,1863,59924,59939,59940,11325,59943,13426,59946,59939,59970,11325,59973,59976],{},[883,59925,59927],{"className":59926},[886],[888,59928,59929],{"xmlns":890},[892,59930,59931,59937],{},[895,59932,59933,59935],{},[898,59934,11736],{},[898,59936,3001],{},[902,59938,56704],{"encoding":904}," jsou ",[38,59941,59942],{},"fixní náklady",[38,59944,59945],{},"fixed cost",[883,59947,59949],{"className":59948},[886],[888,59950,59951],{"xmlns":890},[892,59952,59953,59967],{},[895,59954,59955,59957,59959,59961,59963,59965],{},[898,59956,4104],{},[898,59958,41552],{},[898,59960,3001],{},[1651,59962,1654],{"stretchy":1653},[898,59964,1690],{},[1651,59966,1667],{"stretchy":1653},[902,59968,59969],{"encoding":904},"TVC(Q)",[38,59971,59972],{},"celkové variabilní náklady",[38,59974,59975],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,59978,59980],{"id":59979},"průměrné-náklady","Průměrné náklady",[724,59982,59983,3246,59985,11325,60000,60003],{},[38,59984,59980],{},[883,59986,59988],{"className":59987},[886],[888,59989,59990],{"xmlns":890},[892,59991,59992,59998],{},[895,59993,59994,59996],{},[898,59995,5564],{},[898,59997,3001],{},[902,59999,56773],{"encoding":904},[38,60001,60002],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,60005,60007],{"className":60006},[886],[888,60008,60009],{"xmlns":890,"display":29279},[892,60010,60011,60090],{},[21967,60012,60013],{"width":29284},[21972,60014,60015,60017,60083,60085],{},[21975,60016],{"width":29289},[21975,60018,60019],{},[895,60020,60021,60023,60025,60027,60029,60031,60033,60035,60037,60039,60049,60051,60061,60063,60081],{},[898,60022,5564],{},[898,60024,3001],{},[1651,60026,1738],{},[898,60028,5564],{},[898,60030,3001],{},[1651,60032,1654],{"stretchy":1653},[898,60034,1690],{},[1651,60036,1667],{"stretchy":1653},[1651,60038,1738],{},[2446,60040,60041,60047],{},[895,60042,60043,60045],{},[898,60044,4104],{},[898,60046,3001],{},[898,60048,1690],{},[1651,60050,1738],{},[2446,60052,60053,60059],{},[895,60054,60055,60057],{},[898,60056,11736],{},[898,60058,3001],{},[898,60060,1690],{},[1651,60062,1839],{},[2446,60064,60065,60079],{},[895,60066,60067,60069,60071,60073,60075,60077],{},[898,60068,4104],{},[898,60070,41552],{},[898,60072,3001],{},[1651,60074,1654],{"stretchy":1653},[898,60076,1690],{},[1651,60078,1667],{"stretchy":1653},[898,60080,1690],{},[1651,60082,1661],{"separator":1660},[21975,60084],{"width":29289},[21975,60086,60087],{},[1843,60088,60089],{},"(3.6)",[902,60091,60092],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,60094,1863,60095,59939,60119,3246,60122,11325,60139,13426,60142,59939,60174,3246,60177,11325,60194,4477],{},[883,60096,60098],{"className":60097},[886],[888,60099,60100],{"xmlns":890},[892,60101,60102,60116],{},[895,60103,60104],{},[2938,60105,60106],{"scriptlevel":1741,"displaystyle":1653},[2446,60107,60108,60114],{},[895,60109,60110,60112],{},[898,60111,11736],{},[898,60113,3001],{},[898,60115,1690],{},[902,60117,60118],{"encoding":904},"\\tfrac{FC}{Q}",[38,60120,60121],{},"průměrné fixní náklady",[883,60123,60125],{"className":60124},[886],[888,60126,60127],{"xmlns":890},[892,60128,60129,60137],{},[895,60130,60131,60133,60135],{},[898,60132,5564],{},[898,60134,11736],{},[898,60136,3001],{},[902,60138,56740],{"encoding":904},[38,60140,60141],{},"average fixed cost",[883,60143,60145],{"className":60144},[886],[888,60146,60147],{"xmlns":890},[892,60148,60149,60171],{},[895,60150,60151],{},[2938,60152,60153],{"scriptlevel":1741,"displaystyle":1653},[2446,60154,60155,60169],{},[895,60156,60157,60159,60161,60163,60165,60167],{},[898,60158,4104],{},[898,60160,41552],{},[898,60162,3001],{},[1651,60164,1654],{"stretchy":1653},[898,60166,1690],{},[1651,60168,1667],{"stretchy":1653},[898,60170,1690],{},[902,60172,60173],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,60175,60176],{},"průměrné variabilní náklady",[883,60178,60180],{"className":60179},[886],[888,60181,60182],{"xmlns":890},[892,60183,60184,60192],{},[895,60185,60186,60188,60190],{},[898,60187,5564],{},[898,60189,41552],{},[898,60191,3001],{},[902,60193,56524],{"encoding":904},[38,60195,60196],{},"average variable cost",[883,60198,60200],{"className":60199},[886],[888,60201,60202],{"xmlns":890,"display":29279},[892,60203,60204,60263],{},[21967,60205,60206],{"width":29284},[21972,60207,60208,60210,60256,60258],{},[21975,60209],{"width":29289},[21975,60211,60212],{},[895,60213,60214,60216,60218,60220,60222,60224,60226,60228,60230,60232,60234,60236,60254],{},[898,60215,5564],{},[898,60217,41552],{},[898,60219,3001],{},[1651,60221,1738],{},[898,60223,5564],{},[898,60225,41552],{},[898,60227,3001],{},[1651,60229,1654],{"stretchy":1653},[898,60231,1690],{},[1651,60233,1667],{"stretchy":1653},[1651,60235,1738],{},[2446,60237,60238,60252],{},[895,60239,60240,60242,60244,60246,60248,60250],{},[898,60241,4104],{},[898,60243,41552],{},[898,60245,3001],{},[1651,60247,1654],{"stretchy":1653},[898,60249,1690],{},[1651,60251,1667],{"stretchy":1653},[898,60253,1690],{},[898,60255,1882],{"mathvariant":1910},[21975,60257],{"width":29289},[21975,60259,60260],{},[1843,60261,60262],{},"(3.7)",[902,60264,60265],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[38561,60267,60269],{"id":60268},"příklad-34","Příklad 3.4",[724,60271,60272,58735,60274,5197,60299,57238,60323,5197,60338,60353,60354,1882],{},[38,60273,57200],{},[883,60275,60277],{"className":60276},[886],[888,60278,60279],{"xmlns":890},[892,60280,60281,60296],{},[895,60282,60283,60285,60287,60289,60291,60293],{},[898,60284,11736],{},[898,60286,3001],{},[1651,60288,1738],{},[1692,60290,1694],{},[1843,60292,1845],{},[1692,60294,60295],{},"000",[902,60297,60298],{"encoding":904},"FC = 1\\,000",[883,60300,60302],{"className":60301},[886],[888,60303,60304],{"xmlns":890},[892,60305,60306,60320],{},[895,60307,60308,60310,60312,60314,60316,60318],{},[898,60309,4104],{},[898,60311,41552],{},[898,60313,3001],{},[1651,60315,1738],{},[1692,60317,3689],{},[898,60319,1690],{},[902,60321,60322],{"encoding":904},"TVC = 4Q",[883,60324,60326],{"className":60325},[886],[888,60327,60328],{"xmlns":890},[892,60329,60330,60336],{},[895,60331,60332,60334],{},[898,60333,4104],{},[898,60335,3001],{},[902,60337,4569],{"encoding":904},[883,60339,60341],{"className":60340},[886],[888,60342,60343],{"xmlns":890},[892,60344,60345,60351],{},[895,60346,60347,60349],{},[898,60348,5564],{},[898,60350,3001],{},[902,60352,56773],{"encoding":904}," a jejich chování s rostoucím ",[883,60355,60357],{"className":60356},[886],[888,60358,60359],{"xmlns":890},[892,60360,60361,60365],{},[895,60362,60363],{},[898,60364,1690],{},[902,60366,1690],{"encoding":904},[724,60368,60369,3246,60371,5197,60401,60437,60438,5665,60451,60466,60467,1793],{},[38,60370,23983],{},[883,60372,60374],{"className":60373},[886],[888,60375,60376],{"xmlns":890},[892,60377,60378,60398],{},[895,60379,60380,60382,60384,60386,60388,60390,60392,60394,60396],{},[898,60381,4104],{},[898,60383,3001],{},[1651,60385,1738],{},[1692,60387,1694],{},[1843,60389,1845],{},[1692,60391,60295],{},[1651,60393,1839],{},[1692,60395,3689],{},[898,60397,1690],{},[902,60399,60400],{"encoding":904},"TC = 1\\,000 + 4Q",[883,60402,60404],{"className":60403},[886],[888,60405,60406],{"xmlns":890},[892,60407,60408,60434],{},[895,60409,60410,60412,60414,60416,60430,60432],{},[898,60411,5564],{},[898,60413,3001],{},[1651,60415,1738],{},[2938,60417,60418],{"scriptlevel":1741,"displaystyle":1653},[2446,60419,60420,60428],{},[895,60421,60422,60424,60426],{},[1692,60423,1694],{},[1843,60425,1845],{},[1692,60427,60295],{},[898,60429,1690],{},[1651,60431,1839],{},[1692,60433,3689],{},[902,60435,60436],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,60439,60441],{"className":60440},[886],[888,60442,60443],{"xmlns":890},[892,60444,60445,60449],{},[895,60446,60447],{},[898,60448,1690],{},[902,60450,1690],{"encoding":904},[883,60452,60454],{"className":60453},[886],[888,60455,60456],{"xmlns":890},[892,60457,60458,60464],{},[895,60459,60460,60462],{},[898,60461,5564],{},[898,60463,3001],{},[902,60465,56773],{"encoding":904}," blíží ",[883,60468,60470],{"className":60469},[886],[888,60471,60472],{"xmlns":890},[892,60473,60474,60478],{},[895,60475,60476],{},[1692,60477,3689],{},[902,60479,3689],{"encoding":904},[883,60481,60483],{"className":60482},[886],[888,60484,60485],{"xmlns":890,"display":29279},[892,60486,60487,60533],{},[895,60488,60489,60506,60528,60530],{},[41109,60490,60491,60498],{},[895,60492,60493,60496],{},[898,60494,60495],{},"lim",[1651,60497,57413],{},[895,60499,60500,60502,60504],{},[898,60501,1690],{},[1651,60503,4449],{},[898,60505,7604],{"mathvariant":1910},[895,60507,60508,60510,60522,60524,60526],{},[1651,60509,1654],{"fence":1660},[2446,60511,60512,60520],{},[895,60513,60514,60516,60518],{},[1692,60515,1694],{},[1843,60517,1845],{},[1692,60519,60295],{},[898,60521,1690],{},[1651,60523,1839],{},[1692,60525,3689],{},[1651,60527,1667],{"fence":1660},[1651,60529,1738],{},[1692,60531,60532],{},"4.",[902,60534,60535],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,60537,60538,60576,60577,1882],{},[883,60539,60541],{"className":60540},[886],[888,60542,60543],{"xmlns":890},[892,60544,60545,60573],{},[895,60546,60547,60549,60551,60553,60555,60569,60571],{},[898,60548,5564],{},[898,60550,11736],{},[898,60552,3001],{},[1651,60554,1738],{},[2938,60556,60557],{"scriptlevel":1741,"displaystyle":1653},[2446,60558,60559,60567],{},[895,60560,60561,60563,60565],{},[1692,60562,1694],{},[1843,60564,1845],{},[1692,60566,60295],{},[898,60568,1690],{},[1651,60570,4449],{},[1692,60572,1741],{},[902,60574,60575],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,60578,60580],{"className":60579},[886],[888,60581,60582],{"xmlns":890},[892,60583,60584,60588],{},[895,60585,60586],{},[898,60587,1690],{},[902,60589,1690],{"encoding":904},[724,60591,60592],{},[614,60593,60594,60595,60624,60625,1882],{},"Obrázek 3.5: Přímka ",[883,60596,60598],{"className":60597},[886],[888,60599,60600],{"xmlns":890},[892,60601,60602,60622],{},[895,60603,60604,60606,60608,60610,60612,60614,60616,60618,60620],{},[898,60605,4104],{},[898,60607,3001],{},[1651,60609,1738],{},[1692,60611,1694],{},[1843,60613,1845],{},[1692,60615,60295],{},[1651,60617,1839],{},[1692,60619,3689],{},[898,60621,1690],{},[902,60623,60400],{"encoding":904}," protínající svislou osu ve výši ",[883,60626,60628],{"className":60627},[886],[888,60629,60630],{"xmlns":890},[892,60631,60632,60646],{},[895,60633,60634,60636,60638,60640,60642,60644],{},[898,60635,11736],{},[898,60637,3001],{},[1651,60639,1738],{},[1692,60641,1694],{},[1843,60643,1845],{},[1692,60645,60295],{},[902,60647,60298],{"encoding":904},[724,60649,60650],{},[614,60651,60652,60653,60688,60689,1882],{},"Obrázek 3.6: Hyperbola ",[883,60654,60656],{"className":60655},[886],[888,60657,60658],{"xmlns":890},[892,60659,60660,60686],{},[895,60661,60662,60664,60666,60668,60682,60684],{},[898,60663,5564],{},[898,60665,3001],{},[1651,60667,1738],{},[2938,60669,60670],{"scriptlevel":1741,"displaystyle":1653},[2446,60671,60672,60680],{},[895,60673,60674,60676,60678],{},[1692,60675,1694],{},[1843,60677,1845],{},[1692,60679,60295],{},[898,60681,1690],{},[1651,60683,1839],{},[1692,60685,3689],{},[902,60687,60436],{"encoding":904}," s vodorovnou asymptotou ",[883,60690,60692],{"className":60691},[886],[888,60693,60694],{"xmlns":890},[892,60695,60696,60706],{},[895,60697,60698,60700,60702,60704],{},[898,60699,5564],{},[898,60701,3001],{},[1651,60703,1738],{},[1692,60705,3689],{},[902,60707,60708],{"encoding":904},"AC = 4",[724,60710,60711],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,60713,60715],{"className":60714},[886],[888,60716,60717],{"xmlns":890,"display":29279},[892,60718,60719,60745],{},[895,60720,60721,60723,60725,60727,60729,60731,60733,60735,60737,60739,60741,60743],{},[898,60722,4104],{},[898,60724,41552],{},[898,60726,3001],{},[1651,60728,1738],{},[898,60730,1690],{},[1651,60732,4503],{},[898,60734,41552],{},[898,60736,3001],{},[1651,60738,1654],{"stretchy":1653},[898,60740,1690],{},[1651,60742,1667],{"stretchy":1653},[1651,60744,1661],{"separator":1660},[902,60746,60747],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,60749,1863,60750,59939,60778,60781,60782,60812],{},[883,60751,60753],{"className":60752},[886],[888,60754,60755],{"xmlns":890},[892,60756,60757,60775],{},[895,60758,60759,60761,60763,60765,60767,60769,60771,60773],{},[898,60760,41552],{},[898,60762,3001],{},[1651,60764,1738],{},[898,60766,41552],{},[898,60768,3001],{},[1651,60770,1654],{"stretchy":1653},[898,60772,1690],{},[1651,60774,1667],{"stretchy":1653},[902,60776,60777],{"encoding":904},"VC = VC(Q)",[38,60779,60780],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,60783,60785],{"className":60784},[886],[888,60786,60787],{"xmlns":890},[892,60788,60789,60809],{},[895,60790,60791,60793,60795,60797,60799,60801,60803,60805,60807],{},[898,60792,4104],{},[898,60794,41552],{},[898,60796,3001],{},[1651,60798,1654],{"stretchy":1653},[898,60800,1690],{},[1651,60802,1667],{"stretchy":1653},[1651,60804,1738],{},[898,60806,207],{},[898,60808,1690],{},[902,60810,60811],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,60814,60816],{"className":60815},[886],[888,60817,60818],{"xmlns":890,"display":29279},[892,60819,60820,60840],{},[895,60821,60822,60824,60826,60828,60830,60832,60834,60836,60838],{},[898,60823,4104],{},[898,60825,3001],{},[1651,60827,1738],{},[898,60829,11736],{},[898,60831,3001],{},[1651,60833,1839],{},[898,60835,207],{},[898,60837,1690],{},[898,60839,1882],{"mathvariant":1910},[902,60841,60842],{"encoding":904},"TC = FC + aQ.",[724,60844,60845,60846,60861,60862,60877,60878,60901,60902,60936,60937,60688,60950,60963,60964,5197,61012,61056,61057,1882],{},"Křivkou ",[883,60847,60849],{"className":60848},[886],[888,60850,60851],{"xmlns":890},[892,60852,60853,60859],{},[895,60854,60855,60857],{},[898,60856,4104],{},[898,60858,3001],{},[902,60860,4569],{"encoding":904}," je přímka se svislým průsečíkem ",[883,60863,60865],{"className":60864},[886],[888,60866,60867],{"xmlns":890},[892,60868,60869,60875],{},[895,60870,60871,60873],{},[898,60872,11736],{},[898,60874,3001],{},[902,60876,56704],{"encoding":904}," a sklonem ",[883,60879,60881],{"className":60880},[886],[888,60882,60883],{"xmlns":890},[892,60884,60885,60898],{},[895,60886,60887,60890,60892,60894,60896],{},[898,60888,60889],{},"tan",[1651,60891,57413],{},[898,60893,20075],{},[1651,60895,1738],{},[898,60897,207],{},[902,60899,60900],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,60903,60905],{"className":60904},[886],[888,60906,60907],{"xmlns":890},[892,60908,60909,60933],{},[895,60910,60911,60913,60915,60917,60929,60931],{},[898,60912,5564],{},[898,60914,3001],{},[1651,60916,1738],{},[2938,60918,60919],{"scriptlevel":1741,"displaystyle":1653},[2446,60920,60921,60927],{},[895,60922,60923,60925],{},[898,60924,11736],{},[898,60926,3001],{},[898,60928,1690],{},[1651,60930,1839],{},[898,60932,207],{},[902,60934,60935],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,60938,60940],{"className":60939},[886],[888,60941,60942],{"xmlns":890},[892,60943,60944,60948],{},[895,60945,60946],{},[898,60947,1807],{},[902,60949,1807],{"encoding":904},[883,60951,60953],{"className":60952},[886],[888,60954,60955],{"xmlns":890},[892,60956,60957,60961],{},[895,60958,60959],{},[898,60960,207],{},[902,60962,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,60965,60967],{"className":60966},[886],[888,60968,60969],{"xmlns":890},[892,60970,60971,61009],{},[895,60972,60973,60993,61005,61007],{},[1686,60974,60975,60981],{},[895,60976,60977,60979],{},[898,60978,60495],{},[1651,60980,57413],{},[895,60982,60983,60985,60987],{},[898,60984,1690],{},[1651,60986,4449],{},[2115,60988,60989,60991],{},[1692,60990,1741],{},[1651,60992,1839],{},[2938,60994,60995],{"scriptlevel":1741,"displaystyle":1653},[2446,60996,60997,61003],{},[895,60998,60999,61001],{},[898,61000,11736],{},[898,61002,3001],{},[898,61004,1690],{},[1651,61006,1738],{},[898,61008,7604],{"mathvariant":1910},[902,61010,61011],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,61013,61015],{"className":61014},[886],[888,61016,61017],{"xmlns":890},[892,61018,61019,61053],{},[895,61020,61021,61037,61049,61051],{},[1686,61022,61023,61029],{},[895,61024,61025,61027],{},[898,61026,60495],{},[1651,61028,57413],{},[895,61030,61031,61033,61035],{},[898,61032,1690],{},[1651,61034,4449],{},[898,61036,7604],{"mathvariant":1910},[2938,61038,61039],{"scriptlevel":1741,"displaystyle":1653},[2446,61040,61041,61047],{},[895,61042,61043,61045],{},[898,61044,11736],{},[898,61046,3001],{},[898,61048,1690],{},[1651,61050,1738],{},[1692,61052,1741],{},[902,61054,61055],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,61058,61060],{"className":61059},[886],[888,61061,61062],{"xmlns":890},[892,61063,61064,61070],{},[895,61065,61066,61068],{},[898,61067,5564],{},[898,61069,3001],{},[902,61071,56773],{"encoding":904},[724,61073,61074],{},[614,61075,61076,61077,61092,61093,61108,61109,1882],{},"Obrázek 3.7: Přímka ",[883,61078,61080],{"className":61079},[886],[888,61081,61082],{"xmlns":890},[892,61083,61084,61090],{},[895,61085,61086,61088],{},[898,61087,4104],{},[898,61089,3001],{},[902,61091,4569],{"encoding":904}," s osovým průsečíkem ve výši ",[883,61094,61096],{"className":61095},[886],[888,61097,61098],{"xmlns":890},[892,61099,61100,61106],{},[895,61101,61102,61104],{},[898,61103,11736],{},[898,61105,3001],{},[902,61107,56704],{"encoding":904}," a se sklonem ",[883,61110,61112],{"className":61111},[886],[888,61113,61114],{"xmlns":890},[892,61115,61116,61128],{},[895,61117,61118,61120,61122,61124,61126],{},[898,61119,60889],{},[1651,61121,57413],{},[898,61123,20075],{},[1651,61125,1738],{},[898,61127,207],{},[902,61129,60900],{"encoding":904},[724,61131,61132],{},[614,61133,61134,61135,61150,61151,1882],{},"Obrázek 3.8: Klesající hyperbola ",[883,61136,61138],{"className":61137},[886],[888,61139,61140],{"xmlns":890},[892,61141,61142,61148],{},[895,61143,61144,61146],{},[898,61145,5564],{},[898,61147,3001],{},[902,61149,56773],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,61152,61154],{"className":61153},[886],[888,61155,61156],{"xmlns":890},[892,61157,61158,61162],{},[895,61159,61160],{},[898,61161,207],{},[902,61163,207],{"encoding":904},[198,61165,61167],{"id":61166},"mezní-náklady","Mezní náklady",[724,61169,61170,3246,61172,11325,61187,61190,61191,61194],{},[38,61171,61167],{},[883,61173,61175],{"className":61174},[886],[888,61176,61177],{"xmlns":890},[892,61178,61179,61185],{},[895,61180,61181,61183],{},[898,61182,2995],{},[898,61184,3001],{},[902,61186,56505],{"encoding":904},[38,61188,61189],{},"marginal cost",") jsou ",[207,61192,1145],{"className":61193,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,61196,61198],{"className":61197},[886],[888,61199,61200],{"xmlns":890,"display":29279},[892,61201,61202,61271],{},[21967,61203,61204],{"width":29284},[21972,61205,61206,61208,61264,61266],{},[21975,61207],{"width":29289},[21975,61209,61210],{},[895,61211,61212,61214,61216,61218,61220,61222,61224,61226,61228,61230,61246,61248,61250,61256,61258,61260,61262],{},[898,61213,2995],{},[898,61215,3001],{},[1651,61217,1738],{},[898,61219,2995],{},[898,61221,3001],{},[1651,61223,1654],{"stretchy":1653},[898,61225,1690],{},[1651,61227,1667],{"stretchy":1653},[1651,61229,1738],{},[2446,61231,61232,61240],{},[895,61233,61234,61236,61238],{},[898,61235,3542],{"mathvariant":1910},[898,61237,4104],{},[898,61239,3001],{},[895,61241,61242,61244],{},[898,61243,3542],{"mathvariant":1910},[898,61245,1690],{},[1651,61247,1738],{},[898,61249,4104],{},[2115,61251,61252,61254],{},[898,61253,3001],{},[1651,61255,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,61257,1654],{"stretchy":1653},[898,61259,1690],{},[1651,61261,1667],{"stretchy":1653},[898,61263,1882],{"mathvariant":1910},[21975,61265],{"width":29289},[21975,61267,61268],{},[1843,61269,61270],{},"(3.8)",[902,61272,61273],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[5179,61275,61276],{},[724,61277,61278,61280,61281,61307,61308,61325,61326,1882],{},[883,61279,5465],{}," Intuice — „kolik stojí další kus\"\n",[883,61282,61284],{"className":61283},[886],[888,61285,61286],{"xmlns":890},[892,61287,61288,61304],{},[895,61289,61290,61292,61294,61296,61302],{},[898,61291,2995],{},[898,61293,3001],{},[1651,61295,1654],{"stretchy":1653},[2115,61297,61298,61300],{},[898,61299,1690],{},[1651,61301,2668],{},[1651,61303,1667],{"stretchy":1653},[902,61305,61306],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,61309,61311],{"className":61310},[886],[888,61312,61313],{"xmlns":890},[892,61314,61315,61323],{},[895,61316,61317],{},[2115,61318,61319,61321],{},[898,61320,1690],{},[1651,61322,2668],{},[902,61324,31057],{"encoding":904},". Formálně ",[883,61327,61329],{"className":61328},[886],[888,61330,61331],{"xmlns":890},[892,61332,61333,61385],{},[895,61334,61335,61337,61339,61341,61347,61349,61351,61353,61355,61357,61363,61365,61367,61369,61371,61373,61375,61377,61383],{},[898,61336,2995],{},[898,61338,3001],{},[1651,61340,1654],{"stretchy":1653},[2115,61342,61343,61345],{},[898,61344,1690],{},[1651,61346,2668],{},[1651,61348,1667],{"stretchy":1653},[1651,61350,4060],{},[898,61352,4104],{},[898,61354,3001],{},[1651,61356,1654],{"stretchy":1653},[2115,61358,61359,61361],{},[898,61360,1690],{},[1651,61362,2668],{},[1651,61364,1839],{},[1692,61366,1694],{},[1651,61368,1667],{"stretchy":1653},[1651,61370,2181],{},[898,61372,4104],{},[898,61374,3001],{},[1651,61376,1654],{"stretchy":1653},[2115,61378,61379,61381],{},[898,61380,1690],{},[1651,61382,2668],{},[1651,61384,1667],{"stretchy":1653},[902,61386,61387],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,61389,61390,61391,1793],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,61392,61394],{"className":61393},[886],[888,61395,61396],{"xmlns":890},[892,61397,61398,61406],{},[895,61399,61400,61402,61404],{},[898,61401,4216],{"mathvariant":1910},[898,61403,4104],{},[898,61405,3001],{},[902,61407,61408],{"encoding":904},"\\Delta TC",[883,61410,61412],{"className":61411},[886],[888,61413,61414],{"xmlns":890,"display":29279},[892,61415,61416,61485],{},[21967,61417,61418],{"width":29284},[21972,61419,61420,61422,61478,61480],{},[21975,61421],{"width":29289},[21975,61423,61424],{},[895,61425,61426,61428,61430,61432,61434,61436,61438,61440,61442,61444,61446,61448,61450,61452,61458,61460,61462,61464,61466,61468,61470,61472,61474,61476],{},[898,61427,4216],{"mathvariant":1910},[898,61429,4104],{},[898,61431,3001],{},[1843,61433,5295],{},[1651,61435,4060],{},[1843,61437,5295],{},[898,61439,3542],{"mathvariant":1910},[898,61441,4104],{},[898,61443,3001],{},[1651,61445,1738],{},[1651,61447,1654],{"stretchy":1653},[898,61449,4104],{},[898,61451,3001],{},[2115,61453,61454,61456],{},[1651,61455,1667],{"stretchy":1653},[1651,61457,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1843,61459,1845],{},[898,61461,3542],{"mathvariant":1910},[898,61463,1690],{},[1651,61465,1738],{},[898,61467,2995],{},[898,61469,3001],{},[1843,61471,1845],{},[898,61473,3542],{"mathvariant":1910},[898,61475,1690],{},[1651,61477,1661],{"separator":1660},[21975,61479],{"width":29289},[21975,61481,61482],{},[1843,61483,61484],{},"(3.9)",[902,61486,61487],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,61489,58524],{},[883,61491,61493],{"className":61492},[886],[888,61494,61495],{"xmlns":890,"display":29279},[892,61496,61497,61595],{},[895,61498,61499,61537,61539,61541,61543,61565,61567,61593],{},[895,61500,61501,61503,61509,61511,61517,61520,61526,61529],{},[1843,61502,58538],{},[9692,61504,61505,61507],{"accent":1660},[1843,61506,46945],{},[1651,61508,26271],{},[1843,61510,58547],{},[9692,61512,61513,61515],{"accent":1660},[1843,61514,1664],{},[1651,61516,26190],{},[1843,61518,61519],{},"ch n",[9692,61521,61522,61524],{"accent":1660},[1843,61523,207],{},[1651,61525,26190],{},[1843,61527,61528],{},"klad",[9692,61530,61531,61534],{"accent":1660},[1843,61532,61533],{},"u",[1651,61535,61536],{},"˚",[1843,61538,5295],{},[1651,61540,4060],{},[1843,61542,5295],{},[895,61544,61545,61547,61553,61556,61562],{},[1843,61546,58582],{},[9692,61548,61549,61551],{"accent":1660},[1843,61550,26259],{},[1651,61552,26190],{},[1843,61554,61555],{}," n",[9692,61557,61558,61560],{"accent":1660},[1843,61559,207],{},[1651,61561,26190],{},[1843,61563,61564],{},"klady",[1651,61566,58609],{},[895,61568,61569,61571,61577,61579,61585,61587],{},[1843,61570,58538],{},[9692,61572,61573,61575],{"accent":1660},[1843,61574,46945],{},[1651,61576,26271],{},[1843,61578,58622],{},[9692,61580,61581,61583],{"accent":1660},[1843,61582,10897],{},[1651,61584,26271],{},[1843,61586,58631],{},[9692,61588,61589,61591],{"accent":1660},[1843,61590,26259],{},[1651,61592,26190],{},[898,61594,1882],{"mathvariant":1910},[902,61596,61597],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[38561,61599,61601],{"id":61600},"příklad-35","Příklad 3.5",[724,61603,61604,58735,61606,57238,61642,61657,61658,61673,61674,4002,61687,4016,61700,61713,61714,4016,61727,1882],{},[38,61605,57200],{},[883,61607,61609],{"className":61608},[886],[888,61610,61611],{"xmlns":890},[892,61612,61613,61639],{},[895,61614,61615,61617,61619,61621,61623,61625,61627,61629,61631,61633],{},[898,61616,4104],{},[898,61618,3001],{},[1651,61620,1738],{},[1692,61622,9683],{},[1651,61624,1839],{},[1692,61626,3581],{},[898,61628,1690],{},[1651,61630,1839],{},[1692,61632,1703],{},[2115,61634,61635,61637],{},[898,61636,1690],{},[1692,61638,1703],{},[902,61640,61641],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,61643,61645],{"className":61644},[886],[888,61646,61647],{"xmlns":890},[892,61648,61649,61655],{},[895,61650,61651,61653],{},[898,61652,2995],{},[898,61654,3001],{},[902,61656,56505],{"encoding":904}," a odhadněte změny ",[883,61659,61661],{"className":61660},[886],[888,61662,61663],{"xmlns":890},[892,61664,61665,61671],{},[895,61666,61667,61669],{},[898,61668,4104],{},[898,61670,3001],{},[902,61672,4569],{"encoding":904}," při změnách ",[883,61675,61677],{"className":61676},[886],[888,61678,61679],{"xmlns":890},[892,61680,61681,61685],{},[895,61682,61683],{},[898,61684,1690],{},[902,61686,1690],{"encoding":904},[883,61688,61690],{"className":61689},[886],[888,61691,61692],{"xmlns":890},[892,61693,61694,61698],{},[895,61695,61696],{},[1692,61697,37457],{},[902,61699,37457],{"encoding":904},[883,61701,61703],{"className":61702},[886],[888,61704,61705],{"xmlns":890},[892,61706,61707,61711],{},[895,61708,61709],{},[1692,61710,43075],{},[902,61712,43075],{"encoding":904}," a z ",[883,61715,61717],{"className":61716},[886],[888,61718,61719],{"xmlns":890},[892,61720,61721,61725],{},[895,61722,61723],{},[1692,61724,37457],{},[902,61726,37457],{"encoding":904},[883,61728,61730],{"className":61729},[886],[888,61731,61732],{"xmlns":890},[892,61733,61734,61738],{},[895,61735,61736],{},[1692,61737,4828],{},[902,61739,4828],{"encoding":904},[724,61741,61742,3246,61744,4254,61770,1343,61797,61824,61825,61840,61841,61856,61857,61884,61885,61905,61906,21744,61927,61983,61984,4002,61997,4016,62010,1878,62023,1882],{},[38,61743,23983],{},[883,61745,61747],{"className":61746},[886],[888,61748,61749],{"xmlns":890},[892,61750,61751,61767],{},[895,61752,61753,61755,61757,61759,61761,61763,61765],{},[898,61754,2995],{},[898,61756,3001],{},[1651,61758,1738],{},[1692,61760,3581],{},[1651,61762,1839],{},[1692,61764,3689],{},[898,61766,1690],{},[902,61768,61769],{"encoding":904},"MC = 6 + 4Q",[883,61771,61773],{"className":61772},[886],[888,61774,61775],{"xmlns":890},[892,61776,61777,61794],{},[895,61778,61779,61781,61783,61785,61787,61789,61791],{},[898,61780,2995],{},[898,61782,3001],{},[1651,61784,1654],{"stretchy":1653},[1692,61786,37457],{},[1651,61788,1667],{"stretchy":1653},[1651,61790,1738],{},[1692,61792,61793],{},"66",[902,61795,61796],{"encoding":904},"MC(15) = 66",[883,61798,61800],{"className":61799},[886],[888,61801,61802],{"xmlns":890},[892,61803,61804,61821],{},[895,61805,61806,61808,61810,61812,61814,61816,61818],{},[898,61807,2995],{},[898,61809,3001],{},[1651,61811,1654],{"stretchy":1653},[1692,61813,10340],{},[1651,61815,1667],{"stretchy":1653},[1651,61817,1738],{},[1692,61819,61820],{},"86",[902,61822,61823],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,61826,61828],{"className":61827},[886],[888,61829,61830],{"xmlns":890},[892,61831,61832,61838],{},[895,61833,61834,61836],{},[898,61835,4104],{},[898,61837,3001],{},[902,61839,4569],{"encoding":904}," zvyšuje (",[883,61842,61844],{"className":61843},[886],[888,61845,61846],{"xmlns":890},[892,61847,61848,61854],{},[895,61849,61850,61852],{},[898,61851,2995],{},[898,61853,3001],{},[902,61855,56505],{"encoding":904}," je rostoucí). Z ",[883,61858,61860],{"className":61859},[886],[888,61861,61862],{"xmlns":890},[892,61863,61864,61881],{},[895,61865,61866,61868,61870,61872,61874,61876,61878],{},[898,61867,4104],{},[898,61869,3001],{},[1651,61871,1654],{"stretchy":1653},[1692,61873,37457],{},[1651,61875,1667],{"stretchy":1653},[1651,61877,1738],{},[1692,61879,61880],{},"740",[902,61882,61883],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,61886,61888],{"className":61887},[886],[888,61889,61890],{"xmlns":890},[892,61891,61892,61902],{},[895,61893,61894,61896,61898,61900],{},[898,61895,3542],{"mathvariant":1910},[898,61897,1690],{},[1651,61899,1738],{},[1692,61901,1694],{},[902,61903,61904],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,61907,61909],{"className":61908},[886],[888,61910,61911],{"xmlns":890},[892,61912,61913,61924],{},[895,61914,61915,61917,61919,61921],{},[898,61916,4104],{},[898,61918,3001],{},[1651,61920,4060],{},[1692,61922,61923],{},"806",[902,61925,61926],{"encoding":904},"TC \\approx 806",[883,61928,61930],{"className":61929},[886],[888,61931,61932],{"xmlns":890},[892,61933,61934,61980],{},[895,61935,61936,61938,61940,61942,61944,61946,61948,61950,61952,61954,61956,61958,61960,61962,61964,61966,61968,61971,61973,61975,61977],{},[898,61937,4216],{"mathvariant":1910},[898,61939,4104],{},[898,61941,3001],{},[1651,61943,1738],{},[898,61945,4104],{},[898,61947,3001],{},[1651,61949,1654],{"stretchy":1653},[1692,61951,43075],{},[1651,61953,1667],{"stretchy":1653},[1651,61955,2181],{},[898,61957,4104],{},[898,61959,3001],{},[1651,61961,1654],{"stretchy":1653},[1692,61963,37457],{},[1651,61965,1667],{"stretchy":1653},[1651,61967,1738],{},[1692,61969,61970],{},"808",[1651,61972,2181],{},[1692,61974,61880],{},[1651,61976,1738],{},[1692,61978,61979],{},"68",[902,61981,61982],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,61985,61987],{"className":61986},[886],[888,61988,61989],{"xmlns":890},[892,61990,61991,61995],{},[895,61992,61993],{},[898,61994,1690],{},[902,61996,1690],{"encoding":904},[883,61998,62000],{"className":61999},[886],[888,62001,62002],{"xmlns":890},[892,62003,62004,62008],{},[895,62005,62006],{},[1692,62007,37457],{},[902,62009,37457],{"encoding":904},[883,62011,62013],{"className":62012},[886],[888,62014,62015],{"xmlns":890},[892,62016,62017,62021],{},[895,62018,62019],{},[1692,62020,4828],{},[902,62022,4828],{"encoding":904},[883,62024,62026],{"className":62025},[886],[888,62027,62028],{"xmlns":890},[892,62029,62030,62059],{},[895,62031,62032,62034,62036,62038,62040,62042,62044,62046,62048,62050,62052,62054,62056],{},[898,62033,4216],{"mathvariant":1910},[898,62035,4104],{},[898,62037,3001],{},[1651,62039,4060],{},[1692,62041,61793],{},[1651,62043,4503],{},[1651,62045,1654],{"stretchy":1653},[1651,62047,2181],{},[1692,62049,3521],{},[1651,62051,1667],{"stretchy":1653},[1651,62053,1738],{},[1651,62055,2181],{},[1692,62057,62058],{},"198",[902,62060,62061],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,62063,62065],{"id":62064},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,62067,62068],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[38561,62070,62072],{"id":62071},"příklad-36","Příklad 3.6",[724,62074,62075,58735,62077,62121],{},[38,62076,57200],{},[883,62078,62080],{"className":62079},[886],[888,62081,62082],{"xmlns":890},[892,62083,62084,62118],{},[895,62085,62086,62088,62090,62092,62094,62096,62098,62100,62102,62104,62110,62112],{},[898,62087,4104],{},[898,62089,3001],{},[1651,62091,1738],{},[1692,62093,4416],{},[1651,62095,1839],{},[1692,62097,6311],{},[898,62099,1690],{},[1651,62101,2181],{},[1692,62103,3574],{},[2115,62105,62106,62108],{},[898,62107,1690],{},[1692,62109,1703],{},[1651,62111,1839],{},[2115,62113,62114,62116],{},[898,62115,1690],{},[1692,62117,3521],{},[902,62119,62120],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,62123,62124],{},[38,62125,23983],{},[883,62127,62129],{"className":62128},[886],[888,62130,62131],{"xmlns":890,"display":29279},[892,62132,62133,62377],{},[21967,62134,62135,62161,62209,62243,62285,62335],{"rowspacing":21969,"columnalign":21970,"columnspacing":1911},[21972,62136,62137,62147],{},[21975,62138,62139],{},[2938,62140,62141],{"scriptlevel":1741,"displaystyle":1660},[895,62142,62143,62145],{},[898,62144,11736],{},[898,62146,3001],{},[21975,62148,62149],{},[2938,62150,62151],{"scriptlevel":1741,"displaystyle":1660},[895,62152,62153,62155,62157,62159],{},[895,62154],{},[1651,62156,1738],{},[1692,62158,4416],{},[1651,62160,1661],{"separator":1660},[21972,62162,62163,62175],{},[21975,62164,62165],{},[2938,62166,62167],{"scriptlevel":1741,"displaystyle":1660},[895,62168,62169,62171,62173],{},[898,62170,4104],{},[898,62172,41552],{},[898,62174,3001],{},[21975,62176,62177],{},[2938,62178,62179],{"scriptlevel":1741,"displaystyle":1660},[895,62180,62181,62183,62185,62187,62189,62191,62193,62199,62201,62207],{},[895,62182],{},[1651,62184,1738],{},[1692,62186,6311],{},[898,62188,1690],{},[1651,62190,2181],{},[1692,62192,3574],{},[2115,62194,62195,62197],{},[898,62196,1690],{},[1692,62198,1703],{},[1651,62200,1839],{},[2115,62202,62203,62205],{},[898,62204,1690],{},[1692,62206,3521],{},[1651,62208,1661],{"separator":1660},[21972,62210,62211,62223],{},[21975,62212,62213],{},[2938,62214,62215],{"scriptlevel":1741,"displaystyle":1660},[895,62216,62217,62219,62221],{},[898,62218,5564],{},[898,62220,11736],{},[898,62222,3001],{},[21975,62224,62225],{},[2938,62226,62227],{"scriptlevel":1741,"displaystyle":1660},[895,62228,62229,62231,62233,62241],{},[895,62230],{},[1651,62232,1738],{},[2938,62234,62235],{"scriptlevel":1741,"displaystyle":1653},[2446,62236,62237,62239],{},[1692,62238,4416],{},[898,62240,1690],{},[1651,62242,1661],{"separator":1660},[21972,62244,62245,62257],{},[21975,62246,62247],{},[2938,62248,62249],{"scriptlevel":1741,"displaystyle":1660},[895,62250,62251,62253,62255],{},[898,62252,5564],{},[898,62254,41552],{},[898,62256,3001],{},[21975,62258,62259],{},[2938,62260,62261],{"scriptlevel":1741,"displaystyle":1660},[895,62262,62263,62265,62267,62269,62271,62273,62275,62277,62283],{},[895,62264],{},[1651,62266,1738],{},[1692,62268,6311],{},[1651,62270,2181],{},[1692,62272,3574],{},[898,62274,1690],{},[1651,62276,1839],{},[2115,62278,62279,62281],{},[898,62280,1690],{},[1692,62282,1703],{},[1651,62284,1661],{"separator":1660},[21972,62286,62287,62297],{},[21975,62288,62289],{},[2938,62290,62291],{"scriptlevel":1741,"displaystyle":1660},[895,62292,62293,62295],{},[898,62294,5564],{},[898,62296,3001],{},[21975,62298,62299],{},[2938,62300,62301],{"scriptlevel":1741,"displaystyle":1660},[895,62302,62303,62305,62307,62315,62317,62319,62321,62323,62325,62327,62333],{},[895,62304],{},[1651,62306,1738],{},[2938,62308,62309],{"scriptlevel":1741,"displaystyle":1653},[2446,62310,62311,62313],{},[1692,62312,4416],{},[898,62314,1690],{},[1651,62316,1839],{},[1692,62318,6311],{},[1651,62320,2181],{},[1692,62322,3574],{},[898,62324,1690],{},[1651,62326,1839],{},[2115,62328,62329,62331],{},[898,62330,1690],{},[1692,62332,1703],{},[1651,62334,1661],{"separator":1660},[21972,62336,62337,62347],{},[21975,62338,62339],{},[2938,62340,62341],{"scriptlevel":1741,"displaystyle":1660},[895,62342,62343,62345],{},[898,62344,2995],{},[898,62346,3001],{},[21975,62348,62349],{},[2938,62350,62351],{"scriptlevel":1741,"displaystyle":1660},[895,62352,62353,62355,62357,62359,62361,62363,62365,62367,62369,62375],{},[895,62354],{},[1651,62356,1738],{},[1692,62358,6311],{},[1651,62360,2181],{},[1692,62362,4190],{},[898,62364,1690],{},[1651,62366,1839],{},[1692,62368,3521],{},[2115,62370,62371,62373],{},[898,62372,1690],{},[1692,62374,1703],{},[898,62376,1882],{"mathvariant":1910},[902,62378,62379],{"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}",[724,62381,62382,62383,17090,62398,17090,62413,62428,62429,62444,62445,1343,62463,62444,62480,1343,62498,62444,62513,62531],{},"Význačné body ",[883,62384,62386],{"className":62385},[886],[888,62387,62388],{"xmlns":890},[892,62389,62390,62395],{},[895,62391,62392],{},[1692,62393,62394],{},"1,67",[902,62396,62397],{"encoding":904},"1{,}67",[883,62399,62401],{"className":62400},[886],[888,62402,62403],{"xmlns":890},[892,62404,62405,62410],{},[895,62406,62407],{},[1692,62408,62409],{},"2,50",[902,62411,62412],{"encoding":904},"2{,}50",[883,62414,62416],{"className":62415},[886],[888,62417,62418],{"xmlns":890},[892,62419,62420,62425],{},[895,62421,62422],{},[1692,62423,62424],{},"4,73",[902,62426,62427],{"encoding":904},"4{,}73"," odpovídají: ",[883,62430,62432],{"className":62431},[886],[888,62433,62434],{"xmlns":890},[892,62435,62436,62442],{},[895,62437,62438,62440],{},[898,62439,2995],{},[898,62441,3001],{},[902,62443,56505],{"encoding":904}," minimum v ",[883,62446,62448],{"className":62447},[886],[888,62449,62450],{"xmlns":890},[892,62451,62452,62460],{},[895,62453,62454,62456,62458],{},[898,62455,1690],{},[1651,62457,7207],{},[1692,62459,62394],{},[902,62461,62462],{"encoding":904},"Q \\doteq 1{,}67",[883,62464,62466],{"className":62465},[886],[888,62467,62468],{"xmlns":890},[892,62469,62470,62478],{},[895,62471,62472,62474,62476],{},[898,62473,5564],{},[898,62475,41552],{},[898,62477,3001],{},[902,62479,56524],{"encoding":904},[883,62481,62483],{"className":62482},[886],[888,62484,62485],{"xmlns":890},[892,62486,62487,62495],{},[895,62488,62489,62491,62493],{},[898,62490,1690],{},[1651,62492,1738],{},[1692,62494,62409],{},[902,62496,62497],{"encoding":904},"Q = 2{,}50",[883,62499,62501],{"className":62500},[886],[888,62502,62503],{"xmlns":890},[892,62504,62505,62511],{},[895,62506,62507,62509],{},[898,62508,5564],{},[898,62510,3001],{},[902,62512,56773],{"encoding":904},[883,62514,62516],{"className":62515},[886],[888,62517,62518],{"xmlns":890},[892,62519,62520,62528],{},[895,62521,62522,62524,62526],{},[898,62523,1690],{},[1651,62525,7207],{},[1692,62527,62424],{},[902,62529,62530],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,62533,62534],{},[1756,62535],{"alt":62536,"className":62537,"src":62538},"imek-ac-avc-mc",[210,1760],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,62540,62541],{},[614,62542,62543,62544,5197,62559,62576,62577,17090,62596,62611],{},"Obrázek 3.9: Kubické křivky ",[883,62545,62547],{"className":62546},[886],[888,62548,62549],{"xmlns":890},[892,62550,62551,62557],{},[895,62552,62553,62555],{},[898,62554,4104],{},[898,62556,3001],{},[902,62558,4569],{"encoding":904},[883,62560,62562],{"className":62561},[886],[888,62563,62564],{"xmlns":890},[892,62565,62566,62574],{},[895,62567,62568,62570,62572],{},[898,62569,4104],{},[898,62571,41552],{},[898,62573,3001],{},[902,62575,56722],{"encoding":904}," rostoucí od bodu ",[883,62578,62580],{"className":62579},[886],[888,62581,62582],{"xmlns":890},[892,62583,62584,62594],{},[895,62585,62586,62588,62590,62592],{},[898,62587,11736],{},[898,62589,3001],{},[1651,62591,1738],{},[1692,62593,4416],{},[902,62595,12931],{"encoding":904},[883,62597,62599],{"className":62598},[886],[888,62600,62601],{"xmlns":890},[892,62602,62603,62609],{},[895,62604,62605,62607],{},[898,62606,11736],{},[898,62608,3001],{},[902,62610,56704],{"encoding":904}," je vodorovná přímka.",[724,62613,62614],{},[614,62615,62616,62617,1343,62632,1343,62649,30414,62664,62677,62678,4254,62695,62710,62711,7497,62728,62743,62744,27402,62757,1343,62770,1343,62783,1882],{},"Obrázek 3.10: Křivky ",[883,62618,62620],{"className":62619},[886],[888,62621,62622],{"xmlns":890},[892,62623,62624,62630],{},[895,62625,62626,62628],{},[898,62627,5564],{},[898,62629,3001],{},[902,62631,56773],{"encoding":904},[883,62633,62635],{"className":62634},[886],[888,62636,62637],{"xmlns":890},[892,62638,62639,62647],{},[895,62640,62641,62643,62645],{},[898,62642,5564],{},[898,62644,41552],{},[898,62646,3001],{},[902,62648,56524],{"encoding":904},[883,62650,62652],{"className":62651},[886],[888,62653,62654],{"xmlns":890},[892,62655,62656,62662],{},[895,62657,62658,62660],{},[898,62659,2995],{},[898,62661,3001],{},[902,62663,56505],{"encoding":904},[883,62665,62667],{"className":62666},[886],[888,62668,62669],{"xmlns":890},[892,62670,62671,62675],{},[895,62672,62673],{},[898,62674,900],{},[902,62676,900],{"encoding":904}," a klesající hyperbola ",[883,62679,62681],{"className":62680},[886],[888,62682,62683],{"xmlns":890},[892,62684,62685,62693],{},[895,62686,62687,62689,62691],{},[898,62688,5564],{},[898,62690,11736],{},[898,62692,3001],{},[902,62694,56740],{"encoding":904},[883,62696,62698],{"className":62697},[886],[888,62699,62700],{"xmlns":890},[892,62701,62702,62708],{},[895,62703,62704,62706],{},[898,62705,2995],{},[898,62707,3001],{},[902,62709,56505],{"encoding":904}," protíná ",[883,62712,62714],{"className":62713},[886],[888,62715,62716],{"xmlns":890},[892,62717,62718,62726],{},[895,62719,62720,62722,62724],{},[898,62721,5564],{},[898,62723,41552],{},[898,62725,3001],{},[902,62727,56524],{"encoding":904},[883,62729,62731],{"className":62730},[886],[888,62732,62733],{"xmlns":890},[892,62734,62735,62741],{},[895,62736,62737,62739],{},[898,62738,5564],{},[898,62740,3001],{},[902,62742,56773],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,62745,62747],{"className":62746},[886],[888,62748,62749],{"xmlns":890},[892,62750,62751,62755],{},[895,62752,62753],{},[898,62754,1690],{},[902,62756,1690],{"encoding":904},[883,62758,62760],{"className":62759},[886],[888,62761,62762],{"xmlns":890},[892,62763,62764,62768],{},[895,62765,62766],{},[1692,62767,62394],{},[902,62769,62397],{"encoding":904},[883,62771,62773],{"className":62772},[886],[888,62774,62775],{"xmlns":890},[892,62776,62777,62781],{},[895,62778,62779],{},[1692,62780,62409],{},[902,62782,62412],{"encoding":904},[883,62784,62786],{"className":62785},[886],[888,62787,62788],{"xmlns":890},[892,62789,62790,62794],{},[895,62791,62792],{},[1692,62793,62424],{},[902,62795,62427],{"encoding":904},[724,62797,62798],{},[38,62799,62800],{},"Standardní vlastnosti:",[120,62802,62803,62838,62902,62970,63020,63040],{},[123,62804,62805,5197,62820,62837],{},[883,62806,62808],{"className":62807},[886],[888,62809,62810],{"xmlns":890},[892,62811,62812,62818],{},[895,62813,62814,62816],{},[898,62815,4104],{},[898,62817,3001],{},[902,62819,4569],{"encoding":904},[883,62821,62823],{"className":62822},[886],[888,62824,62825],{"xmlns":890},[892,62826,62827,62835],{},[895,62828,62829,62831,62833],{},[898,62830,4104],{},[898,62832,41552],{},[898,62834,3001],{},[902,62836,56722],{"encoding":904}," jsou kubické funkce;",[123,62839,62840,1343,62855,1343,62872,62887,62888,62901],{},[883,62841,62843],{"className":62842},[886],[888,62844,62845],{"xmlns":890},[892,62846,62847,62853],{},[895,62848,62849,62851],{},[898,62850,5564],{},[898,62852,3001],{},[902,62854,56773],{"encoding":904},[883,62856,62858],{"className":62857},[886],[888,62859,62860],{"xmlns":890},[892,62861,62862,62870],{},[895,62863,62864,62866,62868],{},[898,62865,5564],{},[898,62867,41552],{},[898,62869,3001],{},[902,62871,56524],{"encoding":904},[883,62873,62875],{"className":62874},[886],[888,62876,62877],{"xmlns":890},[892,62878,62879,62885],{},[895,62880,62881,62883],{},[898,62882,2995],{},[898,62884,3001],{},[902,62886,56505],{"encoding":904}," jsou křivky tvaru ",[883,62889,62891],{"className":62890},[886],[888,62892,62893],{"xmlns":890},[892,62894,62895,62899],{},[895,62896,62897],{},[898,62898,900],{},[902,62900,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,62903,62904,62919,62920,1343,62937,62954,62955,9731],{},[883,62905,62907],{"className":62906},[886],[888,62908,62909],{"xmlns":890},[892,62910,62911,62917],{},[895,62912,62913,62915],{},[898,62914,2995],{},[898,62916,3001],{},[902,62918,56505],{"encoding":904}," nabývá minima před ",[883,62921,62923],{"className":62922},[886],[888,62924,62925],{"xmlns":890},[892,62926,62927,62935],{},[895,62928,62929,62931,62933],{},[898,62930,5564],{},[898,62932,41552],{},[898,62934,3001],{},[902,62936,56524],{"encoding":904},[883,62938,62940],{"className":62939},[886],[888,62941,62942],{"xmlns":890},[892,62943,62944,62952],{},[895,62945,62946,62948,62950],{},[898,62947,5564],{},[898,62949,41552],{},[898,62951,3001],{},[902,62953,56524],{"encoding":904}," před ",[883,62956,62958],{"className":62957},[886],[888,62959,62960],{"xmlns":890},[892,62961,62962,62968],{},[895,62963,62964,62966],{},[898,62965,5564],{},[898,62967,3001],{},[902,62969,56773],{"encoding":904},[123,62971,62972,62710,62987,5197,63002,63019],{},[883,62973,62975],{"className":62974},[886],[888,62976,62977],{"xmlns":890},[892,62978,62979,62985],{},[895,62980,62981,62983],{},[898,62982,2995],{},[898,62984,3001],{},[902,62986,56505],{"encoding":904},[883,62988,62990],{"className":62989},[886],[888,62991,62992],{"xmlns":890},[892,62993,62994,63000],{},[895,62995,62996,62998],{},[898,62997,5564],{},[898,62999,3001],{},[902,63001,56773],{"encoding":904},[883,63003,63005],{"className":63004},[886],[888,63006,63007],{"xmlns":890},[892,63008,63009,63017],{},[895,63010,63011,63013,63015],{},[898,63012,5564],{},[898,63014,41552],{},[898,63016,3001],{},[902,63018,56524],{"encoding":904}," zdola právě v jejich minimech;",[123,63021,63022,63039],{},[883,63023,63025],{"className":63024},[886],[888,63026,63027],{"xmlns":890},[892,63028,63029,63037],{},[895,63030,63031,63033,63035],{},[898,63032,5564],{},[898,63034,11736],{},[898,63036,3001],{},[902,63038,56740],{"encoding":904}," je hyperbola, stále klesající;",[123,63041,63042,63074,63075,5197,63090,63107,63108,63121,63122,5230],{},[883,63043,63045],{"className":63044},[886],[888,63046,63047],{"xmlns":890},[892,63048,63049,63071],{},[895,63050,63051,63053,63055,63057,63059,63061,63063,63065,63067,63069],{},[898,63052,5564],{},[898,63054,3001],{},[1651,63056,1738],{},[898,63058,5564],{},[898,63060,11736],{},[898,63062,3001],{},[1651,63064,1839],{},[898,63066,5564],{},[898,63068,41552],{},[898,63070,3001],{},[902,63072,63073],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,63076,63078],{"className":63077},[886],[888,63079,63080],{"xmlns":890},[892,63081,63082,63088],{},[895,63083,63084,63086],{},[898,63085,5564],{},[898,63087,3001],{},[902,63089,56773],{"encoding":904},[883,63091,63093],{"className":63092},[886],[888,63094,63095],{"xmlns":890},[892,63096,63097,63105],{},[895,63098,63099,63101,63103],{},[898,63100,5564],{},[898,63102,41552],{},[898,63104,3001],{},[902,63106,56524],{"encoding":904}," klesá s rostoucím ",[883,63109,63111],{"className":63110},[886],[888,63112,63113],{"xmlns":890},[892,63114,63115,63119],{},[895,63116,63117],{},[898,63118,1690],{},[902,63120,1690],{"encoding":904}," (protože ",[883,63123,63125],{"className":63124},[886],[888,63126,63127],{"xmlns":890},[892,63128,63129,63141],{},[895,63130,63131,63133,63135,63137,63139],{},[898,63132,5564],{},[898,63134,11736],{},[898,63136,3001],{},[1651,63138,4449],{},[1692,63140,1741],{},[902,63142,63143],{"encoding":904},"AFC \\to 0",[115,63145,63147],{"id":63146},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,63149,63150,63151,63154,63155,63170],{},"Častou optimalizační úlohou je ",[38,63152,63153],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,63156,63158],{"className":63157},[886],[888,63159,63160],{"xmlns":890},[892,63161,63162,63168],{},[895,63163,63164,63166],{},[898,63165,5564],{},[898,63167,3001],{},[902,63169,56773],{"encoding":904}," minimální.",[198,63172,1786],{"id":1785},[724,63174,63175,63176,63193],{},"Mají-li průměrné náklady minimum v bodě ",[883,63177,63179],{"className":63178},[886],[888,63180,63181],{"xmlns":890},[892,63182,63183,63191],{},[895,63184,63185],{},[1686,63186,63187,63189],{},[898,63188,1690],{},[1692,63190,1741],{},[902,63192,39521],{"encoding":904},", pak platí",[883,63195,63197],{"className":63196},[886],[888,63198,63199],{"xmlns":890,"display":29279},[892,63200,63201,63250],{},[21967,63202,63203],{"width":29284},[21972,63204,63205,63207,63243,63245],{},[21975,63206],{"width":29289},[21975,63208,63209],{},[895,63210,63211,63213,63215,63217,63223,63225,63227,63229,63231,63233,63239,63241],{},[898,63212,5564],{},[898,63214,3001],{},[1651,63216,1654],{"stretchy":1653},[1686,63218,63219,63221],{},[898,63220,1690],{},[1692,63222,1741],{},[1651,63224,1667],{"stretchy":1653},[1651,63226,1738],{},[898,63228,2995],{},[898,63230,3001],{},[1651,63232,1654],{"stretchy":1653},[1686,63234,63235,63237],{},[898,63236,1690],{},[1692,63238,1741],{},[1651,63240,1667],{"stretchy":1653},[898,63242,1882],{"mathvariant":1910},[21975,63244],{"width":29289},[21975,63246,63247],{},[1843,63248,63249],{},"(3.10)",[902,63251,63252],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[5179,63254,63255],{},[724,63256,63257,63259,63260],{},[883,63258,57657],{}," Princip\n",[38,63261,63262],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,63264,63265,63268,63269,63311],{},[38,63266,63267],{},"Odvození."," Z ",[883,63270,63272],{"className":63271},[886],[888,63273,63274],{"xmlns":890},[892,63275,63276,63308],{},[895,63277,63278,63280,63282,63284,63286,63288,63290],{},[898,63279,5564],{},[898,63281,3001],{},[1651,63283,1654],{"stretchy":1653},[898,63285,1690],{},[1651,63287,1667],{"stretchy":1653},[1651,63289,1738],{},[2938,63291,63292],{"scriptlevel":1741,"displaystyle":1653},[2446,63293,63294,63306],{},[895,63295,63296,63298,63300,63302,63304],{},[898,63297,4104],{},[898,63299,3001],{},[1651,63301,1654],{"stretchy":1653},[898,63303,1690],{},[1651,63305,1667],{"stretchy":1653},[898,63307,1690],{},[902,63309,63310],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,63313,63315],{"className":63314},[886],[888,63316,63317],{"xmlns":890,"display":29279},[892,63318,63319,63451],{},[895,63320,63321,63323,63329,63331,63333,63335,63337,63377,63379,63419,63421,63449],{},[898,63322,5564],{},[2115,63324,63325,63327],{},[898,63326,3001],{},[1651,63328,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,63330,1654],{"stretchy":1653},[898,63332,1690],{},[1651,63334,1667],{"stretchy":1653},[1651,63336,1738],{},[2446,63338,63339,63371],{},[895,63340,63341,63343,63349,63351,63353,63355,63357,63359,63361,63363,63365,63367,63369],{},[898,63342,4104],{},[2115,63344,63345,63347],{},[898,63346,3001],{},[1651,63348,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,63350,1654],{"stretchy":1653},[898,63352,1690],{},[1651,63354,1667],{"stretchy":1653},[1651,63356,4503],{},[898,63358,1690],{},[1651,63360,2181],{},[898,63362,4104],{},[898,63364,3001],{},[1651,63366,1654],{"stretchy":1653},[898,63368,1690],{},[1651,63370,1667],{"stretchy":1653},[2115,63372,63373,63375],{},[898,63374,1690],{},[1692,63376,1703],{},[1651,63378,1738],{},[2446,63380,63381,63413],{},[895,63382,63383,63385,63387,63389,63391,63393,63395,63397,63399,63401,63403,63405,63407,63409,63411],{},[898,63384,2995],{},[898,63386,3001],{},[1651,63388,1654],{"stretchy":1653},[898,63390,1690],{},[1651,63392,1667],{"stretchy":1653},[1651,63394,4503],{},[898,63396,1690],{},[1651,63398,2181],{},[898,63400,5564],{},[898,63402,3001],{},[1651,63404,1654],{"stretchy":1653},[898,63406,1690],{},[1651,63408,1667],{"stretchy":1653},[1651,63410,4503],{},[898,63412,1690],{},[2115,63414,63415,63417],{},[898,63416,1690],{},[1692,63418,1703],{},[1651,63420,1738],{},[2446,63422,63423,63447],{},[895,63424,63425,63427,63429,63431,63433,63435,63437,63439,63441,63443,63445],{},[898,63426,2995],{},[898,63428,3001],{},[1651,63430,1654],{"stretchy":1653},[898,63432,1690],{},[1651,63434,1667],{"stretchy":1653},[1651,63436,2181],{},[898,63438,5564],{},[898,63440,3001],{},[1651,63442,1654],{"stretchy":1653},[898,63444,1690],{},[1651,63446,1667],{"stretchy":1653},[898,63448,1690],{},[898,63450,1882],{"mathvariant":1910},[902,63452,63453],{"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}.",[724,63455,63456,63457,3955,63472,1878,63494,58034],{},"Nutnou podmínkou minima ",[883,63458,63460],{"className":63459},[886],[888,63461,63462],{"xmlns":890},[892,63463,63464,63470],{},[895,63465,63466,63468],{},[898,63467,5564],{},[898,63469,3001],{},[902,63471,56773],{"encoding":904},[883,63473,63475],{"className":63474},[886],[888,63476,63477],{"xmlns":890},[892,63478,63479,63491],{},[895,63480,63481,63487,63489],{},[1686,63482,63483,63485],{},[898,63484,1690],{},[1692,63486,1741],{},[1651,63488,2390],{},[1692,63490,1741],{},[902,63492,63493],{"encoding":904},"Q_0 > 0",[883,63495,63497],{"className":63496},[886],[888,63498,63499],{"xmlns":890},[892,63500,63501,63525],{},[895,63502,63503,63505,63511,63513,63519,63521,63523],{},[898,63504,5564],{},[2115,63506,63507,63509],{},[898,63508,3001],{},[1651,63510,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,63512,1654],{"stretchy":1653},[1686,63514,63515,63517],{},[898,63516,1690],{},[1692,63518,1741],{},[1651,63520,1667],{"stretchy":1653},[1651,63522,1738],{},[1692,63524,1741],{},[902,63526,63527],{"encoding":904},"AC'(Q_0) = 0",[883,63529,63531],{"className":63530},[886],[888,63532,63533],{"xmlns":890,"display":29279},[892,63534,63535,63620],{},[895,63536,63537,63577,63579,63581,63583,63586,63588,63590,63592,63594,63600,63602,63604,63606,63608,63610,63616,63618],{},[2446,63538,63539,63571],{},[895,63540,63541,63543,63545,63547,63553,63555,63557,63559,63561,63563,63569],{},[898,63542,2995],{},[898,63544,3001],{},[1651,63546,1654],{"stretchy":1653},[1686,63548,63549,63551],{},[898,63550,1690],{},[1692,63552,1741],{},[1651,63554,1667],{"stretchy":1653},[1651,63556,2181],{},[898,63558,5564],{},[898,63560,3001],{},[1651,63562,1654],{"stretchy":1653},[1686,63564,63565,63567],{},[898,63566,1690],{},[1692,63568,1741],{},[1651,63570,1667],{"stretchy":1653},[1686,63572,63573,63575],{},[898,63574,1690],{},[1692,63576,1741],{},[1651,63578,1738],{},[1692,63580,1741],{},[7185,63582],{"width":16582},[1651,63584,63585],{},"⟺",[7185,63587],{"width":16582},[898,63589,2995],{},[898,63591,3001],{},[1651,63593,1654],{"stretchy":1653},[1686,63595,63596,63598],{},[898,63597,1690],{},[1692,63599,1741],{},[1651,63601,1667],{"stretchy":1653},[1651,63603,1738],{},[898,63605,5564],{},[898,63607,3001],{},[1651,63609,1654],{"stretchy":1653},[1686,63611,63612,63614],{},[898,63613,1690],{},[1692,63615,1741],{},[1651,63617,1667],{"stretchy":1653},[898,63619,1882],{"mathvariant":1910},[902,63621,63622],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,63624,63625,3246,63628,62710,63643,63658,63659,63674,63675,1878,63692,63714,63715,63737],{},[38,63626,63627],{},"Geometrická interpretace.",[883,63629,63631],{"className":63630},[886],[888,63632,63633],{"xmlns":890},[892,63634,63635,63641],{},[895,63636,63637,63639],{},[898,63638,2995],{},[898,63640,3001],{},[902,63642,56505],{"encoding":904},[883,63644,63646],{"className":63645},[886],[888,63647,63648],{"xmlns":890},[892,63649,63650,63656],{},[895,63651,63652,63654],{},[898,63653,5564],{},[898,63655,3001],{},[902,63657,56773],{"encoding":904}," právě v bodě minima ",[883,63660,63662],{"className":63661},[886],[888,63663,63664],{"xmlns":890},[892,63665,63666,63672],{},[895,63667,63668,63670],{},[898,63669,5564],{},[898,63671,3001],{},[902,63673,56773],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,63676,63678],{"className":63677},[886],[888,63679,63680],{"xmlns":890},[892,63681,63682,63690],{},[895,63683,63684],{},[1686,63685,63686,63688],{},[898,63687,1690],{},[1692,63689,1741],{},[902,63691,39521],{"encoding":904},[883,63693,63695],{"className":63694},[886],[888,63696,63697],{"xmlns":890},[892,63698,63699,63711],{},[895,63700,63701,63703,63705,63707,63709],{},[898,63702,2995],{},[898,63704,3001],{},[1651,63706,2319],{},[898,63708,5564],{},[898,63710,3001],{},[902,63712,63713],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,63716,63718],{"className":63717},[886],[888,63719,63720],{"xmlns":890},[892,63721,63722,63734],{},[895,63723,63724,63726,63728,63730,63732],{},[898,63725,2995],{},[898,63727,3001],{},[1651,63729,2390],{},[898,63731,5564],{},[898,63733,3001],{},[902,63735,63736],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,63739,63740,63741,63783,63784,63801,63802,1882],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,63742,63744],{"className":63743},[886],[888,63745,63746],{"xmlns":890},[892,63747,63748,63780],{},[895,63749,63750,63752,63754,63756,63762,63764,63766,63768,63770,63772,63778],{},[898,63751,5564],{},[898,63753,3001],{},[1651,63755,1654],{"stretchy":1653},[1686,63757,63758,63760],{},[898,63759,1690],{},[1692,63761,1741],{},[1651,63763,1667],{"stretchy":1653},[1651,63765,1738],{},[898,63767,2995],{},[898,63769,3001],{},[1651,63771,1654],{"stretchy":1653},[1686,63773,63774,63776],{},[898,63775,1690],{},[1692,63777,1741],{},[1651,63779,1667],{"stretchy":1653},[902,63781,63782],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,63785,63787],{"className":63786},[886],[888,63788,63789],{"xmlns":890},[892,63790,63791,63799],{},[895,63792,63793],{},[1686,63794,63795,63797],{},[898,63796,1690],{},[1692,63798,1741],{},[902,63800,39521],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,63803,63805],{"className":63804},[886],[888,63806,63807],{"xmlns":890},[892,63808,63809,63833],{},[895,63810,63811,63813,63815,63817,63819,63821,63823,63825,63827,63829,63831],{},[898,63812,5564],{},[898,63814,3001],{},[1651,63816,1654],{"stretchy":1653},[898,63818,1690],{},[1651,63820,1667],{"stretchy":1653},[1651,63822,1738],{},[898,63824,2995],{},[898,63826,3001],{},[1651,63828,1654],{"stretchy":1653},[898,63830,1690],{},[1651,63832,1667],{"stretchy":1653},[902,63834,63835],{"encoding":904},"AC(Q) = MC(Q)",[5179,63837,63838],{},[724,63839,63840,63842,63843,11694,63861,63882,63883,11694,63886,63907,63908,63923,63924,59251,63939,5230],{},[883,63841,5719],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,63844,63845,63846],{},"minimum ",[883,63847,63849],{"className":63848},[886],[888,63850,63851],{"xmlns":890},[892,63852,63853,63859],{},[895,63854,63855,63857],{},[898,63856,5564],{},[898,63858,3001],{},[902,63860,56773],{"encoding":904},[883,63862,63864],{"className":63863},[886],[888,63865,63866],{"xmlns":890},[892,63867,63868,63880],{},[895,63869,63870,63872,63874,63876,63878],{},[898,63871,5564],{},[898,63873,3001],{},[1651,63875,1738],{},[898,63877,2995],{},[898,63879,3001],{},[902,63881,56436],{"encoding":904},", pro ",[38,63884,63885],{},"maximum zisku",[883,63887,63889],{"className":63888},[886],[888,63890,63891],{"xmlns":890},[892,63892,63893,63905],{},[895,63894,63895,63897,63899,63901,63903],{},[898,63896,2995],{},[898,63898,2998],{},[1651,63900,1738],{},[898,63902,2995],{},[898,63904,3001],{},[902,63906,56484],{"encoding":904},". Obě podmínky využívají ",[883,63909,63911],{"className":63910},[886],[888,63912,63913],{"xmlns":890},[892,63914,63915,63921],{},[895,63916,63917,63919],{},[898,63918,2995],{},[898,63920,3001],{},[902,63922,56505],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,63925,63927],{"className":63926},[886],[888,63928,63929],{"xmlns":890},[892,63930,63931,63937],{},[895,63932,63933,63935],{},[898,63934,5564],{},[898,63936,3001],{},[902,63938,56773],{"encoding":904},[883,63940,63942],{"className":63941},[886],[888,63943,63944],{"xmlns":890},[892,63945,63946,63952],{},[895,63947,63948,63950],{},[898,63949,2995],{},[898,63951,2998],{},[902,63953,7941],{"encoding":904},[38561,63955,63957],{"id":63956},"příklad-37","Příklad 3.7",[724,63959,63960,58735,63962,63996,63997,64010,64011,64026],{},[38,63961,57200],{},[883,63963,63965],{"className":63964},[886],[888,63966,63967],{"xmlns":890},[892,63968,63969,63993],{},[895,63970,63971,63973,63975,63977,63983,63985,63987,63989,63991],{},[898,63972,4104],{},[898,63974,3001],{},[1651,63976,1738],{},[2115,63978,63979,63981],{},[898,63980,1690],{},[1692,63982,1703],{},[1651,63984,1839],{},[1692,63986,3521],{},[898,63988,1690],{},[1651,63990,1839],{},[1692,63992,6872],{},[902,63994,63995],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,63998,64000],{"className":63999},[886],[888,64001,64002],{"xmlns":890},[892,64003,64004,64008],{},[895,64005,64006],{},[898,64007,1690],{},[902,64009,1690],{"encoding":904}," minimalizující ",[883,64012,64014],{"className":64013},[886],[888,64015,64016],{"xmlns":890},[892,64017,64018,64024],{},[895,64019,64020,64022],{},[898,64021,5564],{},[898,64023,3001],{},[902,64025,56773],{"encoding":904}," a ověřte princip (3.10).",[724,64028,64029,64031],{},[38,64030,23983],{}," Přímý výpočet:",[883,64033,64035],{"className":64034},[886],[888,64036,64037],{"xmlns":890,"display":29279},[892,64038,64039,64141],{},[895,64040,64041,64043,64045,64047,64069,64071,64073,64075,64077,64079,64085,64087,64089,64091,64093,64095,64101,64103,64105,64107,64117,64119,64139],{},[898,64042,5564],{},[898,64044,3001],{},[1651,64046,1738],{},[2446,64048,64049,64067],{},[895,64050,64051,64057,64059,64061,64063,64065],{},[2115,64052,64053,64055],{},[898,64054,1690],{},[1692,64056,1703],{},[1651,64058,1839],{},[1692,64060,3521],{},[898,64062,1690],{},[1651,64064,1839],{},[1692,64066,6872],{},[898,64068,1690],{},[1651,64070,1738],{},[898,64072,1690],{},[1651,64074,1839],{},[1692,64076,3521],{},[1651,64078,1839],{},[2446,64080,64081,64083],{},[1692,64082,6872],{},[898,64084,1690],{},[1651,64086,1661],{"separator":1660},[7185,64088],{"width":7187},[1651,64090,1654],{"stretchy":1653},[898,64092,5564],{},[898,64094,3001],{},[2115,64096,64097,64099],{},[1651,64098,1667],{"stretchy":1653},[1651,64100,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,64102,1738],{},[1692,64104,1694],{},[1651,64106,2181],{},[2446,64108,64109,64111],{},[1692,64110,6872],{},[2115,64112,64113,64115],{},[898,64114,1690],{},[1692,64116,1703],{},[1651,64118,1738],{},[2446,64120,64121,64133],{},[895,64122,64123,64129,64131],{},[2115,64124,64125,64127],{},[898,64126,1690],{},[1692,64128,1703],{},[1651,64130,2181],{},[1692,64132,6872],{},[2115,64134,64135,64137],{},[898,64136,1690],{},[1692,64138,1703],{},[898,64140,1882],{"mathvariant":1910},[902,64142,64143],{"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}.",[724,64145,64146,64186,64187,64211,64212,64262,64263,1882],{},[883,64147,64149],{"className":64148},[886],[888,64150,64151],{"xmlns":890},[892,64152,64153,64183],{},[895,64154,64155,64157,64159,64161,64167,64169,64171,64173,64179,64181],{},[1651,64156,1654],{"stretchy":1653},[898,64158,5564],{},[898,64160,3001],{},[2115,64162,64163,64165],{},[1651,64164,1667],{"stretchy":1653},[1651,64166,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,64168,1738],{},[1692,64170,1741],{},[1651,64172,5298],{},[1686,64174,64175,64177],{},[898,64176,1690],{},[1692,64178,1694],{},[1651,64180,1738],{},[1692,64182,3581],{},[902,64184,64185],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,64188,64190],{"className":64189},[886],[888,64191,64192],{"xmlns":890},[892,64193,64194,64208],{},[895,64195,64196,64202,64204,64206],{},[1686,64197,64198,64200],{},[898,64199,1690],{},[1692,64201,1703],{},[1651,64203,1738],{},[1651,64205,2181],{},[1692,64207,3581],{},[902,64209,64210],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,64213,64215],{"className":64214},[886],[888,64216,64217],{"xmlns":890},[892,64218,64219,64259],{},[895,64220,64221,64223,64225,64227,64237,64239,64241,64243,64245,64253,64255,64257],{},[1651,64222,1654],{"stretchy":1653},[898,64224,5564],{},[898,64226,3001],{},[2115,64228,64229,64231],{},[1651,64230,1667],{"stretchy":1653},[895,64232,64233,64235],{},[1651,64234,1912],{"mathvariant":1910},[1651,64236,1912],{"mathvariant":1910},[1651,64238,1654],{"stretchy":1653},[1692,64240,3581],{},[1651,64242,1667],{"stretchy":1653},[1651,64244,1738],{},[2938,64246,64247],{"scriptlevel":1741,"displaystyle":1653},[2446,64248,64249,64251],{},[1692,64250,1694],{},[1692,64252,3521],{},[1651,64254,2390],{},[1692,64256,1741],{},[1651,64258,5298],{},[902,64260,64261],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,64264,64266],{"className":64265},[886],[888,64267,64268],{"xmlns":890},[892,64269,64270,64286],{},[895,64271,64272,64274,64276,64278,64280,64282,64284],{},[898,64273,5564],{},[898,64275,3001],{},[1651,64277,1654],{"stretchy":1653},[1692,64279,3581],{},[1651,64281,1667],{"stretchy":1653},[1651,64283,1738],{},[1692,64285,37457],{},[902,64287,64288],{"encoding":904},"AC(6) = 15",[724,64290,64291,64292,64318,64319,1793],{},"Pomocí principu: ",[883,64293,64295],{"className":64294},[886],[888,64296,64297],{"xmlns":890},[892,64298,64299,64315],{},[895,64300,64301,64303,64305,64307,64309,64311,64313],{},[898,64302,2995],{},[898,64304,3001],{},[1651,64306,1738],{},[1692,64308,1703],{},[898,64310,1690],{},[1651,64312,1839],{},[1692,64314,3521],{},[902,64316,64317],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,64320,64322],{"className":64321},[886],[888,64323,64324],{"xmlns":890},[892,64325,64326,64338],{},[895,64327,64328,64330,64332,64334,64336],{},[898,64329,5564],{},[898,64331,3001],{},[1651,64333,1738],{},[898,64335,2995],{},[898,64337,3001],{},[902,64339,56436],{"encoding":904},[883,64341,64343],{"className":64342},[886],[888,64344,64345],{"xmlns":890,"display":29279},[892,64346,64347,64449],{},[895,64348,64349,64371,64373,64375,64377,64379,64381,64383,64385,64387,64393,64395,64397,64399,64401,64403,64405,64407,64413,64415,64417,64419,64421,64423,64425,64431,64433,64435,64437,64439,64441,64443,64445,64447],{},[2446,64350,64351,64369],{},[895,64352,64353,64359,64361,64363,64365,64367],{},[2115,64354,64355,64357],{},[898,64356,1690],{},[1692,64358,1703],{},[1651,64360,1839],{},[1692,64362,3521],{},[898,64364,1690],{},[1651,64366,1839],{},[1692,64368,6872],{},[898,64370,1690],{},[1651,64372,1738],{},[1692,64374,1703],{},[898,64376,1690],{},[1651,64378,1839],{},[1692,64380,3521],{},[1843,64382,5295],{},[1651,64384,5298],{},[1843,64386,5295],{},[2115,64388,64389,64391],{},[898,64390,1690],{},[1692,64392,1703],{},[1651,64394,1839],{},[1692,64396,3521],{},[898,64398,1690],{},[1651,64400,1839],{},[1692,64402,6872],{},[1651,64404,1738],{},[1692,64406,1703],{},[2115,64408,64409,64411],{},[898,64410,1690],{},[1692,64412,1703],{},[1651,64414,1839],{},[1692,64416,3521],{},[898,64418,1690],{},[1843,64420,5295],{},[1651,64422,5298],{},[1843,64424,5295],{},[2115,64426,64427,64429],{},[898,64428,1690],{},[1692,64430,1703],{},[1651,64432,1738],{},[1692,64434,6872],{},[1843,64436,5295],{},[1651,64438,5298],{},[1843,64440,5295],{},[898,64442,1690],{},[1651,64444,1738],{},[1692,64446,3581],{},[1651,64448,1661],{"separator":1660},[902,64450,64451],{"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,",[724,64453,64454,64455,64493],{},"a ",[883,64456,64458],{"className":64457},[886],[888,64459,64460],{"xmlns":890},[892,64461,64462,64490],{},[895,64463,64464,64466,64468,64470,64472,64474,64476,64478,64480,64482,64484,64486,64488],{},[898,64465,5564],{},[898,64467,3001],{},[1651,64469,1654],{"stretchy":1653},[1692,64471,3581],{},[1651,64473,1667],{"stretchy":1653},[1651,64475,1738],{},[898,64477,2995],{},[898,64479,3001],{},[1651,64481,1654],{"stretchy":1653},[1692,64483,3581],{},[1651,64485,1667],{"stretchy":1653},[1651,64487,1738],{},[1692,64489,37457],{},[902,64491,64492],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,64495,64497],{"id":64496},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,64499,64500,64501,1793],{},"Analogicky pro ",[883,64502,64504],{"className":64503},[886],[888,64505,64506],{"xmlns":890},[892,64507,64508,64516],{},[895,64509,64510,64512,64514],{},[898,64511,5564],{},[898,64513,41552],{},[898,64515,3001],{},[902,64517,56524],{"encoding":904},[883,64519,64521],{"className":64520},[886],[888,64522,64523],{"xmlns":890,"display":29279},[892,64524,64525,64576],{},[21967,64526,64527],{"width":29284},[21972,64528,64529,64531,64569,64571],{},[21975,64530],{"width":29289},[21975,64532,64533],{},[895,64534,64535,64537,64539,64541,64543,64549,64551,64553,64555,64557,64559,64565,64567],{},[898,64536,5564],{},[898,64538,41552],{},[898,64540,3001],{},[1651,64542,1654],{"stretchy":1653},[1686,64544,64545,64547],{},[898,64546,1690],{},[1692,64548,1741],{},[1651,64550,1667],{"stretchy":1653},[1651,64552,1738],{},[898,64554,2995],{},[898,64556,3001],{},[1651,64558,1654],{"stretchy":1653},[1686,64560,64561,64563],{},[898,64562,1690],{},[1692,64564,1741],{},[1651,64566,1667],{"stretchy":1653},[898,64568,1882],{"mathvariant":1910},[21975,64570],{"width":29289},[21975,64572,64573],{},[1843,64574,64575],{},"(3.11)",[902,64577,64578],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[5179,64580,64581],{},[724,64582,64583,63259,64585],{},[883,64584,57657],{},[38,64586,64587,64588,64605],{},"V bodě minima průměrných variabilních nákladů se ",[883,64589,64591],{"className":64590},[886],[888,64592,64593],{"xmlns":890},[892,64594,64595,64603],{},[895,64596,64597,64599,64601],{},[898,64598,5564],{},[898,64600,41552],{},[898,64602,3001],{},[902,64604,56524],{"encoding":904}," rovnají mezním nákladům.",[724,64607,64608,64609,64631,64632,1882],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,64610,64612],{"className":64611},[886],[888,64613,64614],{"xmlns":890},[892,64615,64616,64628],{},[895,64617,64618,64624,64626],{},[1686,64619,64620,64622],{},[898,64621,1690],{},[1692,64623,1741],{},[1651,64625,1738],{},[1692,64627,54412],{},[902,64629,64630],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,64633,64635],{"className":64634},[886],[888,64636,64637],{"xmlns":890},[892,64638,64639,64665],{},[895,64640,64641,64643,64645,64647,64649,64651,64653,64655,64657,64659,64661,64663],{},[898,64642,5564],{},[898,64644,41552],{},[898,64646,3001],{},[1651,64648,1654],{"stretchy":1653},[898,64650,1690],{},[1651,64652,1667],{"stretchy":1653},[1651,64654,1738],{},[898,64656,2995],{},[898,64658,3001],{},[1651,64660,1654],{"stretchy":1653},[898,64662,1690],{},[1651,64664,1667],{"stretchy":1653},[902,64666,64667],{"encoding":904},"AVC(Q) = MC(Q)",[115,64669,64671],{"id":64670},"zisk-a-body-zvratu","Zisk a body zvratu",[724,64673,64674,3246,64677,64693],{},[38,64675,64676],{},"Zisk",[883,64678,64680],{"className":64679},[886],[888,64681,64682],{"xmlns":890},[892,64683,64684,64690],{},[895,64685,64686,64688],{},[898,64687,2675],{},[898,64689,2998],{},[902,64691,64692],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,64695,64697],{"className":64696},[886],[888,64698,64699],{"xmlns":890,"display":29279},[892,64700,64701,64760],{},[21967,64702,64703],{"width":29284},[21972,64704,64705,64707,64753,64755],{},[21975,64706],{"width":29289},[21975,64708,64709],{},[895,64710,64711,64713,64715,64717,64719,64721,64723,64725,64727,64729,64731,64733,64735,64737,64739,64741,64743,64745,64747,64749,64751],{},[898,64712,2675],{},[898,64714,2998],{},[1651,64716,1738],{},[898,64718,2675],{},[898,64720,2998],{},[1651,64722,1654],{"stretchy":1653},[898,64724,1690],{},[1651,64726,1667],{"stretchy":1653},[1651,64728,1738],{},[898,64730,4104],{},[898,64732,2998],{},[1651,64734,1654],{"stretchy":1653},[898,64736,1690],{},[1651,64738,1667],{"stretchy":1653},[1651,64740,2181],{},[898,64742,4104],{},[898,64744,3001],{},[1651,64746,1654],{"stretchy":1653},[898,64748,1690],{},[1651,64750,1667],{"stretchy":1653},[898,64752,1882],{"mathvariant":1910},[21975,64754],{"width":29289},[21975,64756,64757],{},[1843,64758,64759],{},"(3.12)",[902,64761,64762],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,64764,64765,64766,5197,64781,44849,64796,64798,64799,64802,64803,64819,64820,64835,64836,64851,64852,1343,64865,64878,64879,1343,64897,64915,64916,11325,64919,64922,64923,1348,64945,1878,64967,64989,64990,1878,65020,65042],{},"Body rovnosti ",[883,64767,64769],{"className":64768},[886],[888,64770,64771],{"xmlns":890},[892,64772,64773,64779],{},[895,64774,64775,64777],{},[898,64776,4104],{},[898,64778,2998],{},[902,64780,5404],{"encoding":904},[883,64782,64784],{"className":64783},[886],[888,64785,64786],{"xmlns":890},[892,64787,64788,64794],{},[895,64789,64790,64792],{},[898,64791,4104],{},[898,64793,3001],{},[902,64795,4569],{"encoding":904},[38,64797,56940],{}," (též vyrovnání, ",[614,64800,64801],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,64804,64806],{"className":64805},[886],[888,64807,64808],{"xmlns":890},[892,64809,64810,64816],{},[895,64811,64812,64814],{},[898,64813,41552],{},[898,64815,3001],{},[902,64817,64818],{"encoding":904},"VC",") je ",[883,64821,64823],{"className":64822},[886],[888,64824,64825],{"xmlns":890},[892,64826,64827,64833],{},[895,64828,64829,64831],{},[898,64830,4104],{},[898,64832,2998],{},[902,64834,5404],{"encoding":904}," kvadratická a ",[883,64837,64839],{"className":64838},[886],[888,64840,64841],{"xmlns":890},[892,64842,64843,64849],{},[895,64844,64845,64847],{},[898,64846,4104],{},[898,64848,3001],{},[902,64850,4569],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,64853,64855],{"className":64854},[886],[888,64856,64857],{"xmlns":890},[892,64858,64859,64863],{},[895,64860,64861],{},[898,64862,5564],{},[902,64864,5564],{"encoding":904},[883,64866,64868],{"className":64867},[886],[888,64869,64870],{"xmlns":890},[892,64871,64872,64876],{},[895,64873,64874],{},[898,64875,24466],{},[902,64877,24466],{"encoding":904}," odpovídajících množstvím ",[883,64880,64882],{"className":64881},[886],[888,64883,64884],{"xmlns":890},[892,64885,64886,64894],{},[895,64887,64888],{},[1686,64889,64890,64892],{},[898,64891,1690],{},[898,64893,5564],{},[902,64895,64896],{"encoding":904},"Q_A",[883,64898,64900],{"className":64899},[886],[888,64901,64902],{"xmlns":890},[892,64903,64904,64912],{},[895,64905,64906],{},[1686,64907,64908,64910],{},[898,64909,1690],{},[898,64911,24466],{},[902,64913,64914],{"encoding":904},"Q_B"," — firma je na ",[38,64917,64918],{},"prahu rentability",[614,64920,64921],{},"break even","). Pro ",[883,64924,64926],{"className":64925},[886],[888,64927,64928],{"xmlns":890},[892,64929,64930,64942],{},[895,64931,64932,64934,64936],{},[898,64933,1690],{},[1651,64935,2319],{},[1686,64937,64938,64940],{},[898,64939,1690],{},[898,64941,5564],{},[902,64943,64944],{"encoding":904},"Q \u003C Q_A",[883,64946,64948],{"className":64947},[886],[888,64949,64950],{"xmlns":890},[892,64951,64952,64964],{},[895,64953,64954,64956,64958],{},[898,64955,1690],{},[1651,64957,2390],{},[1686,64959,64960,64962],{},[898,64961,1690],{},[898,64963,24466],{},[902,64965,64966],{"encoding":904},"Q > Q_B",[883,64968,64970],{"className":64969},[886],[888,64971,64972],{"xmlns":890},[892,64973,64974,64986],{},[895,64975,64976,64978,64980,64982,64984],{},[898,64977,4104],{},[898,64979,3001],{},[1651,64981,2390],{},[898,64983,4104],{},[898,64985,2998],{},[902,64987,64988],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,64991,64993],{"className":64992},[886],[888,64994,64995],{"xmlns":890},[892,64996,64997,65017],{},[895,64998,64999,65005,65007,65009,65011],{},[1686,65000,65001,65003],{},[898,65002,1690],{},[898,65004,5564],{},[1651,65006,2319],{},[898,65008,1690],{},[1651,65010,2319],{},[1686,65012,65013,65015],{},[898,65014,1690],{},[898,65016,24466],{},[902,65018,65019],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,65021,65023],{"className":65022},[886],[888,65024,65025],{"xmlns":890},[892,65026,65027,65039],{},[895,65028,65029,65031,65033,65035,65037],{},[898,65030,4104],{},[898,65032,2998],{},[1651,65034,2390],{},[898,65036,4104],{},[898,65038,3001],{},[902,65040,65041],{"encoding":904},"TR > TC"," (zisk).",[5179,65044,65045],{},[724,65046,65047,65049],{},[883,65048,5465],{}," 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.",[724,65051,65052,65053,65079],{},"Body zvratu jsou řešení rovnice ",[883,65054,65056],{"className":65055},[886],[888,65057,65058],{"xmlns":890},[892,65059,65060,65076],{},[895,65061,65062,65064,65066,65068,65070,65072,65074],{},[898,65063,2675],{},[898,65065,2998],{},[1651,65067,1654],{"stretchy":1653},[898,65069,1690],{},[1651,65071,1667],{"stretchy":1653},[1651,65073,1738],{},[1692,65075,1741],{},[902,65077,65078],{"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.",[724,65081,65082],{},[1756,65083],{"alt":65084,"className":65085,"src":65086},"imek-tr-tc-body-zvratu",[210,1760],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,65088,65089],{},[614,65090,65091,65092,65107,65108,65123,65124,5197,65137,44573,65150,65163,65164,5197,65181,65198,65199,65219,65220,5197,65235,7780,65250,65279],{},"Obrázek 3.11: Body zvratu — křivky ",[883,65093,65095],{"className":65094},[886],[888,65096,65097],{"xmlns":890},[892,65098,65099,65105],{},[895,65100,65101,65103],{},[898,65102,4104],{},[898,65104,2998],{},[902,65106,5404],{"encoding":904}," (obrácená parabola) a ",[883,65109,65111],{"className":65110},[886],[888,65112,65113],{"xmlns":890},[892,65114,65115,65121],{},[895,65116,65117,65119],{},[898,65118,4104],{},[898,65120,3001],{},[902,65122,4569],{"encoding":904}," (přímka) se protínají v bodech ",[883,65125,65127],{"className":65126},[886],[888,65128,65129],{"xmlns":890},[892,65130,65131,65135],{},[895,65132,65133],{},[898,65134,5564],{},[902,65136,5564],{"encoding":904},[883,65138,65140],{"className":65139},[886],[888,65141,65142],{"xmlns":890},[892,65143,65144,65148],{},[895,65145,65146],{},[898,65147,24466],{},[902,65149,24466],{"encoding":904},[883,65151,65153],{"className":65152},[886],[888,65154,65155],{"xmlns":890},[892,65156,65157,65161],{},[895,65158,65159],{},[898,65160,1690],{},[902,65162,1690],{"encoding":904}," v hodnotách ",[883,65165,65167],{"className":65166},[886],[888,65168,65169],{"xmlns":890},[892,65170,65171,65179],{},[895,65172,65173],{},[1686,65174,65175,65177],{},[898,65176,1690],{},[898,65178,5564],{},[902,65180,64896],{"encoding":904},[883,65182,65184],{"className":65183},[886],[888,65185,65186],{"xmlns":890},[892,65187,65188,65196],{},[895,65189,65190],{},[1686,65191,65192,65194],{},[898,65193,1690],{},[898,65195,24466],{},[902,65197,64914],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,65200,65202],{"className":65201},[886],[888,65203,65204],{"xmlns":890},[892,65205,65206,65216],{},[895,65207,65208],{},[1686,65209,65210,65212,65214],{},[898,65211,1690],{},[898,65213,57410],{},[1651,65215,57413],{},[902,65217,65218],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,65221,65223],{"className":65222},[886],[888,65224,65225],{"xmlns":890},[892,65226,65227,65233],{},[895,65228,65229,65231],{},[898,65230,4104],{},[898,65232,2998],{},[902,65234,5404],{"encoding":904},[883,65236,65238],{"className":65237},[886],[888,65239,65240],{"xmlns":890},[892,65241,65242,65248],{},[895,65243,65244,65246],{},[898,65245,4104],{},[898,65247,3001],{},[902,65249,4569],{"encoding":904},[883,65251,65253],{"className":65252},[886],[888,65254,65255],{"xmlns":890},[892,65256,65257,65277],{},[895,65258,65259,65265,65267,65269,65271],{},[1686,65260,65261,65263],{},[898,65262,1690],{},[898,65264,5564],{},[1651,65266,2319],{},[898,65268,1690],{},[1651,65270,2319],{},[1686,65272,65273,65275],{},[898,65274,1690],{},[898,65276,24466],{},[902,65278,65019],{"encoding":904}," vyznačuje zisk.",[38561,65281,65283],{"id":65282},"příklad-38","Příklad 3.8",[724,65285,65286,65288,65289,1343,65309,1343,65335,65361],{},[38,65287,57200],{}," Dáno ",[883,65290,65292],{"className":65291},[886],[888,65293,65294],{"xmlns":890},[892,65295,65296,65306],{},[895,65297,65298,65300,65302,65304],{},[898,65299,11736],{},[898,65301,3001],{},[1651,65303,1738],{},[1692,65305,3689],{},[902,65307,65308],{"encoding":904},"FC = 4",[883,65310,65312],{"className":65311},[886],[888,65313,65314],{"xmlns":890},[892,65315,65316,65332],{},[895,65317,65318,65320,65322,65324,65326],{},[898,65319,4104],{},[898,65321,41552],{},[898,65323,3001],{},[1651,65325,1738],{},[2115,65327,65328,65330],{},[898,65329,1690],{},[1692,65331,1703],{},[902,65333,65334],{"encoding":904},"TVC = Q^2",[883,65336,65338],{"className":65337},[886],[888,65339,65340],{"xmlns":890},[892,65341,65342,65358],{},[895,65343,65344,65346,65348,65350,65352,65354,65356],{},[898,65345,2675],{},[1651,65347,1738],{},[1651,65349,2181],{},[1692,65351,1703],{},[898,65353,1690],{},[1651,65355,1839],{},[1692,65357,5309],{},[902,65359,65360],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,65363,65364,65366],{},[38,65365,23983],{}," Celkové náklady a příjem:",[883,65368,65370],{"className":65369},[886],[888,65371,65372],{"xmlns":890,"display":29279},[892,65373,65374,65440],{},[895,65375,65376,65378,65380,65382,65384,65386,65392,65394,65396,65398,65400,65402,65404,65406,65408,65410,65412,65414,65416,65418,65420,65422,65424,65426,65432,65434,65436,65438],{},[898,65377,4104],{},[898,65379,3001],{},[1651,65381,1738],{},[1692,65383,3689],{},[1651,65385,1839],{},[2115,65387,65388,65390],{},[898,65389,1690],{},[1692,65391,1703],{},[1651,65393,1661],{"separator":1660},[7185,65395],{"width":7187},[898,65397,4104],{},[898,65399,2998],{},[1651,65401,1738],{},[898,65403,1690],{},[1651,65405,4503],{},[1651,65407,1654],{"stretchy":1653},[1651,65409,2181],{},[1692,65411,1703],{},[898,65413,1690],{},[1651,65415,1839],{},[1692,65417,5309],{},[1651,65419,1667],{"stretchy":1653},[1651,65421,1738],{},[1651,65423,2181],{},[1692,65425,1703],{},[2115,65427,65428,65430],{},[898,65429,1690],{},[1692,65431,1703],{},[1651,65433,1839],{},[1692,65435,5309],{},[898,65437,1690],{},[898,65439,1882],{"mathvariant":1910},[902,65441,65442],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,65444,65445],{},"Zisk dle (3.12):",[883,65447,65449],{"className":65448},[886],[888,65450,65451],{"xmlns":890,"display":29279},[892,65452,65453,65531],{},[895,65454,65455,65457,65459,65461,65463,65465,65467,65469,65471,65473,65475,65477,65479,65485,65487,65489,65491,65493,65495,65497,65499,65501,65507,65509,65511,65513,65515,65521,65523,65525,65527,65529],{},[898,65456,2675],{},[898,65458,2998],{},[1651,65460,1738],{},[898,65462,4104],{},[898,65464,2998],{},[1651,65466,2181],{},[898,65468,4104],{},[898,65470,3001],{},[1651,65472,1738],{},[1651,65474,1654],{"stretchy":1653},[1651,65476,2181],{},[1692,65478,1703],{},[2115,65480,65481,65483],{},[898,65482,1690],{},[1692,65484,1703],{},[1651,65486,1839],{},[1692,65488,5309],{},[898,65490,1690],{},[1651,65492,1667],{"stretchy":1653},[1651,65494,2181],{},[1651,65496,1654],{"stretchy":1653},[1692,65498,3689],{},[1651,65500,1839],{},[2115,65502,65503,65505],{},[898,65504,1690],{},[1692,65506,1703],{},[1651,65508,1667],{"stretchy":1653},[1651,65510,1738],{},[1651,65512,2181],{},[1692,65514,3521],{},[2115,65516,65517,65519],{},[898,65518,1690],{},[1692,65520,1703],{},[1651,65522,1839],{},[1692,65524,5309],{},[898,65526,1690],{},[1651,65528,2181],{},[1692,65530,60532],{},[902,65532,65533],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,65535,65536,65539,65540,2983,65576,1793],{},[38,65537,65538],{},"Body zvratu"," jsou kořeny rovnice ",[883,65541,65543],{"className":65542},[886],[888,65544,65545],{"xmlns":890},[892,65546,65547,65573],{},[895,65548,65549,65551,65553,65559,65561,65563,65565,65567,65569,65571],{},[1651,65550,2181],{},[1692,65552,3521],{},[2115,65554,65555,65557],{},[898,65556,1690],{},[1692,65558,1703],{},[1651,65560,1839],{},[1692,65562,5309],{},[898,65564,1690],{},[1651,65566,2181],{},[1692,65568,3689],{},[1651,65570,1738],{},[1692,65572,1741],{},[902,65574,65575],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,65577,65579],{"className":65578},[886],[888,65580,65581],{"xmlns":890},[892,65582,65583,65607],{},[895,65584,65585,65587,65593,65595,65597,65599,65601,65603,65605],{},[1692,65586,3521],{},[2115,65588,65589,65591],{},[898,65590,1690],{},[1692,65592,1703],{},[1651,65594,2181],{},[1692,65596,5309],{},[898,65598,1690],{},[1651,65600,1839],{},[1692,65602,3689],{},[1651,65604,1738],{},[1692,65606,1741],{},[902,65608,65609],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,65611,65613],{"className":65612},[886],[888,65614,65615],{"xmlns":890,"display":29279},[892,65616,65617,65674],{},[895,65618,65619,65631,65633,65656,65658,65672],{},[1686,65620,65621,65623],{},[898,65622,1690],{},[895,65624,65625,65627,65629],{},[1692,65626,1694],{},[1651,65628,1661],{"separator":1660},[1692,65630,1703],{},[1651,65632,1738],{},[2446,65634,65635,65654],{},[895,65636,65637,65639,65642],{},[1692,65638,5309],{},[1651,65640,65641],{},"±",[9423,65643,65644],{},[895,65645,65646,65649,65651],{},[1692,65647,65648],{},"81",[1651,65650,2181],{},[1692,65652,65653],{},"48",[1692,65655,3581],{},[1651,65657,1738],{},[2446,65659,65660,65670],{},[895,65661,65662,65664,65666],{},[1692,65663,5309],{},[1651,65665,65641],{},[9423,65667,65668],{},[1692,65669,10256],{},[1692,65671,3581],{},[1651,65673,1661],{"separator":1660},[902,65675,65676],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,65678,65679,65680,5197,65703,1882],{},"numericky ",[883,65681,65683],{"className":65682},[886],[888,65684,65685],{"xmlns":890},[892,65686,65687,65700],{},[895,65688,65689,65695,65697],{},[1686,65690,65691,65693],{},[898,65692,1690],{},[1692,65694,1694],{},[1651,65696,7207],{},[1692,65698,65699],{},"0,543",[902,65701,65702],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,65704,65706],{"className":65705},[886],[888,65707,65708],{"xmlns":890},[892,65709,65710,65723],{},[895,65711,65712,65718,65720],{},[1686,65713,65714,65716],{},[898,65715,1690],{},[1692,65717,1703],{},[1651,65719,7207],{},[1692,65721,65722],{},"2,457",[902,65724,65725],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,65727,65728,3246,65731,8859,65776,2983,65810,65828],{},[38,65729,65730],{},"Maximum zisku.",[883,65732,65734],{"className":65733},[886],[888,65735,65736],{"xmlns":890},[892,65737,65738,65773],{},[895,65739,65740,65742,65748,65750,65752,65754,65756,65758,65760,65762,65764,65766,65768,65770],{},[898,65741,2675],{},[2115,65743,65744,65746],{},[898,65745,2998],{},[1651,65747,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,65749,1738],{},[1651,65751,2181],{},[1692,65753,3581],{},[898,65755,1690],{},[1651,65757,1839],{},[1692,65759,5309],{},[1651,65761,1738],{},[1692,65763,1741],{},[1651,65765,5298],{},[898,65767,1690],{},[1651,65769,1738],{},[1692,65771,65772],{},"1,5",[902,65774,65775],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,65777,65779],{"className":65778},[886],[888,65780,65781],{"xmlns":890},[892,65782,65783,65807],{},[895,65784,65785,65787,65797,65799,65801,65803,65805],{},[898,65786,2675],{},[2115,65788,65789,65791],{},[898,65790,2998],{},[895,65792,65793,65795],{},[1651,65794,1912],{"mathvariant":1910},[1651,65796,1912],{"mathvariant":1910},[1651,65798,1738],{},[1651,65800,2181],{},[1692,65802,3581],{},[1651,65804,2319],{},[1692,65806,1741],{},[902,65808,65809],{"encoding":904},"PR'' = -6 \u003C 0",[883,65811,65813],{"className":65812},[886],[888,65814,65815],{"xmlns":890},[892,65816,65817,65825],{},[895,65818,65819,65821,65823],{},[898,65820,1690],{},[1651,65822,1738],{},[1692,65824,65772],{},[902,65826,65827],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,65830,65832],{"className":65831},[886],[888,65833,65834],{"xmlns":890,"display":29279},[892,65835,65836,65899],{},[895,65837,65838,65840,65842,65844,65846,65848,65850,65852,65854,65856,65858,65860,65866,65868,65870,65872,65874,65876,65878,65880,65882,65885,65887,65890,65892,65894,65896],{},[898,65839,2675],{},[898,65841,2998],{},[1651,65843,1654],{"stretchy":1653},[1692,65845,65772],{},[1651,65847,1667],{"stretchy":1653},[1651,65849,1738],{},[1651,65851,2181],{},[1692,65853,3521],{},[1651,65855,4503],{},[1651,65857,1654],{"stretchy":1653},[1692,65859,65772],{},[2115,65861,65862,65864],{},[1651,65863,1667],{"stretchy":1653},[1692,65865,1703],{},[1651,65867,1839],{},[1692,65869,5309],{},[1651,65871,4503],{},[1692,65873,65772],{},[1651,65875,2181],{},[1692,65877,3689],{},[1651,65879,1738],{},[1651,65881,2181],{},[1692,65883,65884],{},"6,75",[1651,65886,1839],{},[1692,65888,65889],{},"13,5",[1651,65891,2181],{},[1692,65893,3689],{},[1651,65895,1738],{},[1692,65897,65898],{},"2,75.",[902,65900,65901],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,65903,65904,65905,1343,65950,66003,66004,66022],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,65906,65908],{"className":65907},[886],[888,65909,65910],{"xmlns":890},[892,65911,65912,65947],{},[895,65913,65914,65916,65922,65924,65926,65928,65930,65932,65934,65936,65938,65940,65942,65944],{},[898,65915,4104],{},[2115,65917,65918,65920],{},[898,65919,2998],{},[1651,65921,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,65923,1738],{},[1651,65925,2181],{},[1692,65927,3689],{},[898,65929,1690],{},[1651,65931,1839],{},[1692,65933,5309],{},[1651,65935,1738],{},[1692,65937,1741],{},[1651,65939,5298],{},[898,65941,1690],{},[1651,65943,1738],{},[1692,65945,65946],{},"2,25",[902,65948,65949],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,65951,65953],{"className":65952},[886],[888,65954,65955],{"xmlns":890},[892,65956,65957,66000],{},[895,65958,65959,65961,65969,65971,65973,65975,65977,65979,65981,65987,65989,65991,65993,65995,65997],{},[898,65960,4104],{},[1686,65962,65963,65965,65967],{},[898,65964,2998],{},[898,65966,57410],{},[1651,65968,57413],{},[1651,65970,1738],{},[1651,65972,2181],{},[1692,65974,1703],{},[1651,65976,4503],{},[1651,65978,1654],{"stretchy":1653},[1692,65980,65946],{},[2115,65982,65983,65985],{},[1651,65984,1667],{"stretchy":1653},[1692,65986,1703],{},[1651,65988,1839],{},[1692,65990,5309],{},[1651,65992,4503],{},[1692,65994,65946],{},[1651,65996,1738],{},[1692,65998,65999],{},"10,125",[902,66001,66002],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,66005,66007],{"className":66006},[886],[888,66008,66009],{"xmlns":890},[892,66010,66011,66019],{},[895,66012,66013,66015,66017],{},[898,66014,1690],{},[1651,66016,1738],{},[1692,66018,65946],{},[902,66020,66021],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[5179,66024,66025],{},[724,66026,66027,66029,66030,1343,66052,66074,66075,1343,66092,66113,66114,66146,66147,66185,66186,4002,66204,66221,66222,5197,66250,66284,66285,8992,66323,5197,66347,1882],{},[883,66028,5719],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,66031,66033],{"className":66032},[886],[888,66034,66035],{"xmlns":890},[892,66036,66037,66049],{},[895,66038,66039,66045,66047],{},[1686,66040,66041,66043],{},[898,66042,1690],{},[1692,66044,1694],{},[1651,66046,1738],{},[1692,66048,6316],{},[902,66050,66051],{"encoding":904},"Q_1 = 0{,}5",[883,66053,66055],{"className":66054},[886],[888,66056,66057],{"xmlns":890},[892,66058,66059,66071],{},[895,66060,66061,66067,66069],{},[1686,66062,66063,66065],{},[898,66064,1690],{},[1692,66066,1703],{},[1651,66068,1738],{},[1692,66070,3689],{},[902,66072,66073],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,66076,66078],{"className":66077},[886],[888,66079,66080],{"xmlns":890},[892,66081,66082,66090],{},[895,66083,66084,66086,66088],{},[898,66085,1690],{},[1651,66087,1738],{},[1692,66089,65946],{},[902,66091,66021],{"encoding":904},[883,66093,66095],{"className":66094},[886],[888,66096,66097],{"xmlns":890},[892,66098,66099,66110],{},[895,66100,66101,66103,66105,66107],{},[898,66102,2675],{},[898,66104,2998],{},[1651,66106,1738],{},[1692,66108,66109],{},"6,125",[902,66111,66112],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,66115,66117],{"className":66116},[886],[888,66118,66119],{"xmlns":890},[892,66120,66121,66143],{},[895,66122,66123,66125,66131,66133,66135,66137,66139,66141],{},[898,66124,2675],{},[2115,66126,66127,66129],{},[898,66128,2998],{},[1651,66130,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,66132,1738],{},[1651,66134,2181],{},[1692,66136,3689],{},[898,66138,1690],{},[1651,66140,1839],{},[1692,66142,5309],{},[902,66144,66145],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,66148,66150],{"className":66149},[886],[888,66151,66152],{"xmlns":890},[892,66153,66154,66182],{},[895,66155,66156,66158,66160,66162,66164,66166,66172,66174,66176,66178,66180],{},[898,66157,2675],{},[898,66159,2998],{},[1651,66161,1738],{},[1651,66163,2181],{},[1692,66165,1703],{},[2115,66167,66168,66170],{},[898,66169,1690],{},[1692,66171,1703],{},[1651,66173,1839],{},[1692,66175,5309],{},[898,66177,1690],{},[1651,66179,2181],{},[1692,66181,3689],{},[902,66183,66184],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,66187,66189],{"className":66188},[886],[888,66190,66191],{"xmlns":890},[892,66192,66193,66201],{},[895,66194,66195],{},[2115,66196,66197,66199],{},[898,66198,1690],{},[1692,66200,1703],{},[902,66202,66203],{"encoding":904},"Q^2",[883,66205,66207],{"className":66206},[886],[888,66208,66209],{"xmlns":890},[892,66210,66211,66219],{},[895,66212,66213,66215,66217],{},[898,66214,4104],{},[898,66216,41552],{},[898,66218,3001],{},[902,66220,56722],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,66223,66225],{"className":66224},[886],[888,66226,66227],{"xmlns":890},[892,66228,66229,66247],{},[895,66230,66231,66233,66235,66237,66239,66241],{},[898,66232,4104],{},[898,66234,3001],{},[1651,66236,1738],{},[1692,66238,3689],{},[1651,66240,1839],{},[2115,66242,66243,66245],{},[898,66244,1690],{},[1692,66246,1703],{},[902,66248,66249],{"encoding":904},"TC = 4 + Q^2",[883,66251,66253],{"className":66252},[886],[888,66254,66255],{"xmlns":890},[892,66256,66257,66281],{},[895,66258,66259,66261,66263,66265,66267,66269,66275,66277,66279],{},[898,66260,4104],{},[898,66262,2998],{},[1651,66264,1738],{},[1651,66266,2181],{},[1692,66268,1703],{},[2115,66270,66271,66273],{},[898,66272,1690],{},[1692,66274,1703],{},[1651,66276,1839],{},[1692,66278,5309],{},[898,66280,1690],{},[902,66282,66283],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,66286,66288],{"className":66287},[886],[888,66289,66290],{"xmlns":890},[892,66291,66292,66320],{},[895,66293,66294,66296,66298,66300,66302,66304,66310,66312,66314,66316,66318],{},[898,66295,2675],{},[898,66297,2998],{},[1651,66299,1738],{},[1651,66301,2181],{},[1692,66303,3521],{},[2115,66305,66306,66308],{},[898,66307,1690],{},[1692,66309,1703],{},[1651,66311,1839],{},[1692,66313,5309],{},[898,66315,1690],{},[1651,66317,2181],{},[1692,66319,3689],{},[902,66321,66322],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,66324,66326],{"className":66325},[886],[888,66327,66328],{"xmlns":890},[892,66329,66330,66344],{},[895,66331,66332,66340,66342],{},[1686,66333,66334,66336,66338],{},[898,66335,1690],{},[898,66337,57410],{},[1651,66339,57413],{},[1651,66341,1738],{},[1692,66343,65772],{},[902,66345,66346],{"encoding":904},"Q_{\\max} = 1{,}5",[883,66348,66350],{"className":66349},[886],[888,66351,66352],{"xmlns":890},[892,66353,66354,66371],{},[895,66355,66356,66358,66366,66368],{},[898,66357,2675],{},[1686,66359,66360,66362,66364],{},[898,66361,2998],{},[898,66363,57410],{},[1651,66365,57413],{},[1651,66367,1738],{},[1692,66369,66370],{},"2,75",[902,66372,66373],{"encoding":904},"PR_{\\max} = 2{,}75",[724,66375,66376],{},[614,66377,66378,66379,66406,66407,66440,66441,1343,66464,1882],{},"Obrázek 3.12: Graf ",[883,66380,66382],{"className":66381},[886],[888,66383,66384],{"xmlns":890},[892,66385,66386,66404],{},[895,66387,66388,66390,66392,66394,66396,66398],{},[898,66389,4104],{},[898,66391,3001],{},[1651,66393,1738],{},[1692,66395,3689],{},[1651,66397,1839],{},[2115,66399,66400,66402],{},[898,66401,1690],{},[1692,66403,1703],{},[902,66405,66249],{"encoding":904}," (parabola) a ",[883,66408,66410],{"className":66409},[886],[888,66411,66412],{"xmlns":890},[892,66413,66414,66438],{},[895,66415,66416,66418,66420,66422,66424,66426,66432,66434,66436],{},[898,66417,4104],{},[898,66419,2998],{},[1651,66421,1738],{},[1651,66423,2181],{},[1692,66425,1703],{},[2115,66427,66428,66430],{},[898,66429,1690],{},[1692,66431,1703],{},[1651,66433,1839],{},[1692,66435,5309],{},[898,66437,1690],{},[902,66439,66283],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,66442,66444],{"className":66443},[886],[888,66445,66446],{"xmlns":890},[892,66447,66448,66461],{},[895,66449,66450,66456,66458],{},[1686,66451,66452,66454],{},[898,66453,1690],{},[1692,66455,1694],{},[1651,66457,7207],{},[1692,66459,66460],{},"0,54",[902,66462,66463],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,66465,66467],{"className":66466},[886],[888,66468,66469],{"xmlns":890},[892,66470,66471,66484],{},[895,66472,66473,66479,66481],{},[1686,66474,66475,66477],{},[898,66476,1690],{},[1692,66478,1703],{},[1651,66480,7207],{},[1692,66482,66483],{},"2,46",[902,66485,66486],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,66488,66489],{},[614,66490,66491,66492,59720,66529,66546,66547,1343,66568,1882],{},"Obrázek 3.13: Graf zisku ",[883,66493,66495],{"className":66494},[886],[888,66496,66497],{"xmlns":890},[892,66498,66499,66527],{},[895,66500,66501,66503,66505,66507,66509,66511,66517,66519,66521,66523,66525],{},[898,66502,2675],{},[898,66504,2998],{},[1651,66506,1738],{},[1651,66508,2181],{},[1692,66510,3521],{},[2115,66512,66513,66515],{},[898,66514,1690],{},[1692,66516,1703],{},[1651,66518,1839],{},[1692,66520,5309],{},[898,66522,1690],{},[1651,66524,2181],{},[1692,66526,3689],{},[902,66528,66322],{"encoding":904},[883,66530,66532],{"className":66531},[886],[888,66533,66534],{"xmlns":890},[892,66535,66536,66544],{},[895,66537,66538,66540,66542],{},[898,66539,1690],{},[1651,66541,1738],{},[1692,66543,65772],{},[902,66545,65827],{"encoding":904}," a nulami ",[883,66548,66550],{"className":66549},[886],[888,66551,66552],{"xmlns":890},[892,66553,66554,66566],{},[895,66555,66556,66562,66564],{},[1686,66557,66558,66560],{},[898,66559,1690],{},[1692,66561,1694],{},[1651,66563,7207],{},[1692,66565,66460],{},[902,66567,66463],{"encoding":904},[883,66569,66571],{"className":66570},[886],[888,66572,66573],{"xmlns":890},[892,66574,66575,66587],{},[895,66576,66577,66583,66585],{},[1686,66578,66579,66581],{},[898,66580,1690],{},[1692,66582,1703],{},[1651,66584,7207],{},[1692,66586,66483],{},[902,66588,66486],{"encoding":904},[115,66590,66592],{"id":66591},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,66594,66595],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,66597,66598],{},[1756,66599],{"alt":66600,"className":66601,"src":66602},"imek-max-zisku-dva-pohledy",[210,1760],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,66604,1786],{"id":66605},"princip-1",[724,66607,66608,66609,3955,66624,66641],{},"Má-li zisk ",[883,66610,66612],{"className":66611},[886],[888,66613,66614],{"xmlns":890},[892,66615,66616,66622],{},[895,66617,66618,66620],{},[898,66619,2675],{},[898,66621,2998],{},[902,66623,64692],{"encoding":904},[883,66625,66627],{"className":66626},[886],[888,66628,66629],{"xmlns":890},[892,66630,66631,66639],{},[895,66632,66633],{},[1686,66634,66635,66637],{},[898,66636,1690],{},[1692,66638,1741],{},[902,66640,39521],{"encoding":904}," maximum, pak platí",[883,66643,66645],{"className":66644},[886],[888,66646,66647],{"xmlns":890,"display":29279},[892,66648,66649,66698],{},[21967,66650,66651],{"width":29284},[21972,66652,66653,66655,66691,66693],{},[21975,66654],{"width":29289},[21975,66656,66657],{},[895,66658,66659,66661,66663,66665,66671,66673,66675,66677,66679,66681,66687,66689],{},[898,66660,2995],{},[898,66662,2998],{},[1651,66664,1654],{"stretchy":1653},[1686,66666,66667,66669],{},[898,66668,1690],{},[1692,66670,1741],{},[1651,66672,1667],{"stretchy":1653},[1651,66674,1738],{},[898,66676,2995],{},[898,66678,3001],{},[1651,66680,1654],{"stretchy":1653},[1686,66682,66683,66685],{},[898,66684,1690],{},[1692,66686,1741],{},[1651,66688,1667],{"stretchy":1653},[898,66690,1882],{"mathvariant":1910},[21975,66692],{"width":29289},[21975,66694,66695],{},[1843,66696,66697],{},"(3.13)",[902,66699,66700],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[5179,66702,66703],{},[724,66704,66705,63259,66707],{},[883,66706,57657],{},[38,66708,66709],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,66711,66712,66715,66716,1878,66743,2983,66817,1882],{},[38,66713,66714],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,66717,66719],{"className":66718},[886],[888,66720,66721],{"xmlns":890},[892,66722,66723,66741],{},[895,66724,66725,66727,66729,66731,66733,66735,66737,66739],{},[898,66726,2675],{},[898,66728,2998],{},[1651,66730,1738],{},[898,66732,4104],{},[898,66734,2998],{},[1651,66736,2181],{},[898,66738,4104],{},[898,66740,3001],{},[902,66742,56413],{"encoding":904},[883,66744,66746],{"className":66745},[886],[888,66747,66748],{"xmlns":890},[892,66749,66750,66814],{},[895,66751,66752,66754,66760,66762,66768,66770,66772,66774,66780,66782,66788,66790,66792,66794,66800,66802,66808,66810,66812],{},[898,66753,2675],{},[2115,66755,66756,66758],{},[898,66757,2998],{},[1651,66759,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,66761,1654],{"stretchy":1653},[1686,66763,66764,66766],{},[898,66765,1690],{},[1692,66767,1741],{},[1651,66769,1667],{"stretchy":1653},[1651,66771,1738],{},[898,66773,4104],{},[2115,66775,66776,66778],{},[898,66777,2998],{},[1651,66779,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,66781,1654],{"stretchy":1653},[1686,66783,66784,66786],{},[898,66785,1690],{},[1692,66787,1741],{},[1651,66789,1667],{"stretchy":1653},[1651,66791,2181],{},[898,66793,4104],{},[2115,66795,66796,66798],{},[898,66797,3001],{},[1651,66799,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,66801,1654],{"stretchy":1653},[1686,66803,66804,66806],{},[898,66805,1690],{},[1692,66807,1741],{},[1651,66809,1667],{"stretchy":1653},[1651,66811,1738],{},[1692,66813,1741],{},[902,66815,66816],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,66818,66820],{"className":66819},[886],[888,66821,66822],{"xmlns":890},[892,66823,66824,66856],{},[895,66825,66826,66828,66830,66832,66838,66840,66842,66844,66846,66848,66854],{},[898,66827,2995],{},[898,66829,2998],{},[1651,66831,1654],{"stretchy":1653},[1686,66833,66834,66836],{},[898,66835,1690],{},[1692,66837,1741],{},[1651,66839,1667],{"stretchy":1653},[1651,66841,1738],{},[898,66843,2995],{},[898,66845,3001],{},[1651,66847,1654],{"stretchy":1653},[1686,66849,66850,66852],{},[898,66851,1690],{},[1692,66853,1741],{},[1651,66855,1667],{"stretchy":1653},[902,66857,66858],{"encoding":904},"MR(Q_0) = MC(Q_0)",[5179,66860,66861,66866],{},[724,66862,66863,66865],{},[883,66864,5879],{}," Postup — jak najít maximum zisku",[152,66867,66868,66932,66987,67024,67052],{},[123,66869,66870,66871,5197,66886,66901,66902,5230],{},"Sestavte ",[883,66872,66874],{"className":66873},[886],[888,66875,66876],{"xmlns":890},[892,66877,66878,66884],{},[895,66879,66880,66882],{},[898,66881,4104],{},[898,66883,2998],{},[902,66885,5404],{"encoding":904},[883,66887,66889],{"className":66888},[886],[888,66890,66891],{"xmlns":890},[892,66892,66893,66899],{},[895,66894,66895,66897],{},[898,66896,4104],{},[898,66898,3001],{},[902,66900,4569],{"encoding":904}," ze zadání (typicky ",[883,66903,66905],{"className":66904},[886],[888,66906,66907],{"xmlns":890},[892,66908,66909,66929],{},[895,66910,66911,66913,66915,66917,66919,66921,66923,66925,66927],{},[898,66912,4104],{},[898,66914,2998],{},[1651,66916,1738],{},[898,66918,2675],{},[1651,66920,1654],{"stretchy":1653},[898,66922,1690],{},[1651,66924,1667],{"stretchy":1653},[1651,66926,4503],{},[898,66928,1690],{},[902,66930,66931],{"encoding":904},"TR = P(Q) \\cdot Q",[123,66933,66934,66935,5197,66961,1882],{},"Vypočtěte ",[883,66936,66938],{"className":66937},[886],[888,66939,66940],{"xmlns":890},[892,66941,66942,66958],{},[895,66943,66944,66946,66948,66950,66952],{},[898,66945,2995],{},[898,66947,2998],{},[1651,66949,1738],{},[898,66951,4104],{},[2115,66953,66954,66956],{},[898,66955,2998],{},[1651,66957,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,66959,66960],{"encoding":904},"MR = TR'",[883,66962,66964],{"className":66963},[886],[888,66965,66966],{"xmlns":890},[892,66967,66968,66984],{},[895,66969,66970,66972,66974,66976,66978],{},[898,66971,2995],{},[898,66973,3001],{},[1651,66975,1738],{},[898,66977,4104],{},[2115,66979,66980,66982],{},[898,66981,3001],{},[1651,66983,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,66985,66986],{"encoding":904},"MC = TC'",[123,66988,66989,66990,1882],{},"Řešte rovnici ",[883,66991,66993],{"className":66992},[886],[888,66994,66995],{"xmlns":890},[892,66996,66997,67021],{},[895,66998,66999,67001,67003,67005,67007,67009,67011,67013,67015,67017,67019],{},[898,67000,2995],{},[898,67002,2998],{},[1651,67004,1654],{"stretchy":1653},[898,67006,1690],{},[1651,67008,1667],{"stretchy":1653},[1651,67010,1738],{},[898,67012,2995],{},[898,67014,3001],{},[1651,67016,1654],{"stretchy":1653},[898,67018,1690],{},[1651,67020,1667],{"stretchy":1653},[902,67022,67023],{"encoding":904},"MR(Q) = MC(Q)",[123,67025,67026,67027,67051],{},"Ověřte druhou derivaci ",[883,67028,67030],{"className":67029},[886],[888,67031,67032],{"xmlns":890},[892,67033,67034,67048],{},[895,67035,67036,67038],{},[898,67037,2675],{},[2115,67039,67040,67042],{},[898,67041,2998],{},[895,67043,67044,67046],{},[1651,67045,1912],{"mathvariant":1910},[1651,67047,1912],{"mathvariant":1910},[902,67049,67050],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,67053,67054,67055,67082],{},"Dosaďte do ",[883,67056,67058],{"className":67057},[886],[888,67059,67060],{"xmlns":890},[892,67061,67062,67080],{},[895,67063,67064,67066,67068,67070,67072,67074,67076,67078],{},[898,67065,2675],{},[898,67067,2998],{},[1651,67069,1738],{},[898,67071,4104],{},[898,67073,2998],{},[1651,67075,2181],{},[898,67077,4104],{},[898,67079,3001],{},[902,67081,56413],{"encoding":904}," pro hodnotu maxima.",[38561,67084,67086],{"id":67085},"příklad-39","Příklad 3.9",[724,67088,67089,57201,67091,5197,67113,67149],{},[38,67090,57200],{},[883,67092,67094],{"className":67093},[886],[888,67095,67096],{"xmlns":890},[892,67097,67098,67110],{},[895,67099,67100,67102,67104,67106,67108],{},[898,67101,2675],{},[1651,67103,1738],{},[1692,67105,39232],{},[1651,67107,2181],{},[898,67109,1690],{},[902,67111,67112],{"encoding":904},"P = 30 - Q",[883,67114,67116],{"className":67115},[886],[888,67117,67118],{"xmlns":890},[892,67119,67120,67146],{},[895,67121,67122,67124,67126,67128,67130,67136,67138,67140,67142,67144],{},[898,67123,4104],{},[898,67125,3001],{},[1651,67127,1738],{},[1692,67129,6316],{},[2115,67131,67132,67134],{},[898,67133,1690],{},[1692,67135,1703],{},[1651,67137,1839],{},[1692,67139,3581],{},[898,67141,1690],{},[1651,67143,1839],{},[1692,67145,25414],{},[902,67147,67148],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,67151,67152,3246,67154,1343,67184,67222,67223,17090,67267,67301,67302,1882],{},[38,67153,23983],{},[883,67155,67157],{"className":67156},[886],[888,67158,67159],{"xmlns":890},[892,67160,67161,67181],{},[895,67162,67163,67165,67167,67169,67171,67173,67175],{},[898,67164,4104],{},[898,67166,2998],{},[1651,67168,1738],{},[1692,67170,39232],{},[898,67172,1690],{},[1651,67174,2181],{},[2115,67176,67177,67179],{},[898,67178,1690],{},[1692,67180,1703],{},[902,67182,67183],{"encoding":904},"TR = 30Q - Q^2",[883,67185,67187],{"className":67186},[886],[888,67188,67189],{"xmlns":890},[892,67190,67191,67219],{},[895,67192,67193,67195,67197,67199,67201,67203,67209,67211,67213,67215,67217],{},[898,67194,2675],{},[898,67196,2998],{},[1651,67198,1738],{},[1651,67200,2181],{},[1692,67202,65772],{},[2115,67204,67205,67207],{},[898,67206,1690],{},[1692,67208,1703],{},[1651,67210,1839],{},[1692,67212,43013],{},[898,67214,1690],{},[1651,67216,2181],{},[1692,67218,25414],{},[902,67220,67221],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,67224,67226],{"className":67225},[886],[888,67227,67228],{"xmlns":890},[892,67229,67230,67264],{},[895,67231,67232,67234,67240,67242,67244,67246,67248,67250,67252,67254,67256,67258,67260,67262],{},[898,67233,2675],{},[2115,67235,67236,67238],{},[898,67237,2998],{},[1651,67239,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,67241,1738],{},[1651,67243,2181],{},[1692,67245,3521],{},[898,67247,1690],{},[1651,67249,1839],{},[1692,67251,43013],{},[1651,67253,1738],{},[1692,67255,1741],{},[1651,67257,5298],{},[898,67259,1690],{},[1651,67261,1738],{},[1692,67263,6892],{},[902,67265,67266],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,67268,67270],{"className":67269},[886],[888,67271,67272],{"xmlns":890},[892,67273,67274,67298],{},[895,67275,67276,67278,67288,67290,67292,67294,67296],{},[898,67277,2675],{},[2115,67279,67280,67282],{},[898,67281,2998],{},[895,67283,67284,67286],{},[1651,67285,1912],{"mathvariant":1910},[1651,67287,1912],{"mathvariant":1910},[1651,67289,1738],{},[1651,67291,2181],{},[1692,67293,3521],{},[1651,67295,2319],{},[1692,67297,1741],{},[902,67299,67300],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,67303,67305],{"className":67304},[886],[888,67306,67307],{"xmlns":890},[892,67308,67309,67326],{},[895,67310,67311,67313,67315,67317,67319,67321,67323],{},[898,67312,2675],{},[898,67314,2998],{},[1651,67316,1654],{"stretchy":1653},[1692,67318,6892],{},[1651,67320,1667],{"stretchy":1653},[1651,67322,1738],{},[1692,67324,67325],{},"89",[902,67327,67328],{"encoding":904},"PR(8) = 89",[724,67330,67331,67332,1343,67358,17090,67382,67420],{},"Ověření principu: ",[883,67333,67335],{"className":67334},[886],[888,67336,67337],{"xmlns":890},[892,67338,67339,67355],{},[895,67340,67341,67343,67345,67347,67349,67351,67353],{},[898,67342,2995],{},[898,67344,2998],{},[1651,67346,1738],{},[1692,67348,39232],{},[1651,67350,2181],{},[1692,67352,1703],{},[898,67354,1690],{},[902,67356,67357],{"encoding":904},"MR = 30 - 2Q",[883,67359,67361],{"className":67360},[886],[888,67362,67363],{"xmlns":890},[892,67364,67365,67379],{},[895,67366,67367,67369,67371,67373,67375,67377],{},[898,67368,2995],{},[898,67370,3001],{},[1651,67372,1738],{},[898,67374,1690],{},[1651,67376,1839],{},[1692,67378,3581],{},[902,67380,67381],{"encoding":904},"MC = Q + 6",[883,67383,67385],{"className":67384},[886],[888,67386,67387],{"xmlns":890},[892,67388,67389,67417],{},[895,67390,67391,67393,67395,67397,67399,67401,67403,67405,67407,67409,67411,67413,67415],{},[898,67392,2995],{},[898,67394,2998],{},[1651,67396,1654],{"stretchy":1653},[1692,67398,6892],{},[1651,67400,1667],{"stretchy":1653},[1651,67402,1738],{},[1692,67404,24159],{},[1651,67406,1738],{},[898,67408,2995],{},[898,67410,3001],{},[1651,67412,1654],{"stretchy":1653},[1692,67414,6892],{},[1651,67416,1667],{"stretchy":1653},[902,67418,67419],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,67422,67423,67424,67457,67458,67475],{},"V řadě případů — má-li rovnice ",[883,67425,67427],{"className":67426},[886],[888,67428,67429],{"xmlns":890},[892,67430,67431,67455],{},[895,67432,67433,67435,67437,67439,67441,67443,67445,67447,67449,67451,67453],{},[898,67434,2995],{},[898,67436,2998],{},[1651,67438,1654],{"stretchy":1653},[898,67440,1690],{},[1651,67442,1667],{"stretchy":1653},[1651,67444,1738],{},[898,67446,2995],{},[898,67448,3001],{},[1651,67450,1654],{"stretchy":1653},[898,67452,1690],{},[1651,67454,1667],{"stretchy":1653},[902,67456,67023],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,67459,67461],{"className":67460},[886],[888,67462,67463],{"xmlns":890},[892,67464,67465,67473],{},[895,67466,67467],{},[1686,67468,67469,67471],{},[898,67470,1690],{},[1692,67472,1741],{},[902,67474,39521],{"encoding":904}," — není třeba provádět test druhé derivace.",[38561,67477,67479],{"id":67478},"příklad-310","Příklad 3.10",[724,67481,67482,67484,67485,67489,67490,67503,67504,67535],{},[38,67483,57200],{}," Firma vyrábí minipočítače v ",[207,67486,67488],{"className":67487,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,67491,67493],{"className":67492},[886],[888,67494,67495],{"xmlns":890},[892,67496,67497,67501],{},[895,67498,67499],{},[1692,67500,16489],{},[902,67502,16489],{"encoding":904}," EUR\u002Fks. ",[883,67505,67507],{"className":67506},[886],[888,67508,67509],{"xmlns":890},[892,67510,67511,67532],{},[895,67512,67513,67515,67517,67519,67521,67523,67526],{},[898,67514,4104],{},[898,67516,3001],{},[1651,67518,1738],{},[1692,67520,4446],{},[1651,67522,1839],{},[1692,67524,67525],{},"28",[2115,67527,67528,67530],{},[898,67529,1690],{},[1692,67531,1703],{},[902,67533,67534],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,67537,67538,3246,67540,1343,67562,1343,67582,67605],{},[38,67539,23983],{},[883,67541,67543],{"className":67542},[886],[888,67544,67545],{"xmlns":890},[892,67546,67547,67559],{},[895,67548,67549,67551,67553,67555,67557],{},[898,67550,4104],{},[898,67552,2998],{},[1651,67554,1738],{},[1692,67556,16489],{},[898,67558,1690],{},[902,67560,67561],{"encoding":904},"TR = 900Q",[883,67563,67565],{"className":67564},[886],[888,67566,67567],{"xmlns":890},[892,67568,67569,67579],{},[895,67570,67571,67573,67575,67577],{},[898,67572,2995],{},[898,67574,2998],{},[1651,67576,1738],{},[1692,67578,16489],{},[902,67580,67581],{"encoding":904},"MR = 900",[883,67583,67585],{"className":67584},[886],[888,67586,67587],{"xmlns":890},[892,67588,67589,67602],{},[895,67590,67591,67593,67595,67597,67600],{},[898,67592,2995],{},[898,67594,3001],{},[1651,67596,1738],{},[1692,67598,67599],{},"56",[898,67601,1690],{},[902,67603,67604],{"encoding":904},"MC = 56Q",". Z principu:",[883,67607,67609],{"className":67608},[886],[888,67610,67611],{"xmlns":890,"display":29279},[892,67612,67613,67655],{},[895,67614,67615,67617,67619,67621,67623,67625,67627,67629,67631,67633,67641,67643,67646,67648,67650,67652],{},[1692,67616,16489],{},[1651,67618,1738],{},[1692,67620,67599],{},[898,67622,1690],{},[1843,67624,5295],{},[1651,67626,5298],{},[1843,67628,5295],{},[898,67630,1690],{},[1651,67632,1738],{},[2938,67634,67635],{"scriptlevel":1741,"displaystyle":1653},[2446,67636,67637,67639],{},[1692,67638,16489],{},[1692,67640,67599],{},[1651,67642,7207],{},[1692,67644,67645],{},"16,07",[1843,67647,5295],{},[1651,67649,4060],{},[1843,67651,5295],{},[1692,67653,67654],{},"16.",[902,67656,67657],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,67659,67660,67661,1793],{},"Zisk při ",[883,67662,67664],{"className":67663},[886],[888,67665,67666],{"xmlns":890},[892,67667,67668,67676],{},[895,67669,67670,67672,67674],{},[898,67671,1690],{},[1651,67673,1738],{},[1692,67675,43075],{},[902,67677,67678],{"encoding":904},"Q = 16",[883,67680,67682],{"className":67681},[886],[888,67683,67684],{"xmlns":890,"display":29279},[892,67685,67686,67757],{},[895,67687,67688,67690,67692,67694,67696,67698,67700,67702,67704,67706,67708,67710,67712,67714,67716,67718,67724,67726,67728,67730,67732,67734,67736,67738,67740,67743,67745,67747,67749,67752,67755],{},[898,67689,2675],{},[898,67691,2998],{},[1651,67693,1654],{"stretchy":1653},[1692,67695,43075],{},[1651,67697,1667],{"stretchy":1653},[1651,67699,1738],{},[1692,67701,16489],{},[1651,67703,4503],{},[1692,67705,43075],{},[1651,67707,2181],{},[1651,67709,1654],{"stretchy":1653},[1692,67711,4446],{},[1651,67713,1839],{},[1692,67715,67525],{},[1651,67717,4503],{},[2115,67719,67720,67722],{},[1692,67721,43075],{},[1692,67723,1703],{},[1651,67725,1667],{"stretchy":1653},[1651,67727,1738],{},[1692,67729,24159],{},[1843,67731,1845],{},[1692,67733,21355],{},[1651,67735,2181],{},[1692,67737,25414],{},[1843,67739,1845],{},[1692,67741,67742],{},"218",[1651,67744,1738],{},[1692,67746,25414],{},[1843,67748,1845],{},[1692,67750,67751],{},"182",[1843,67753,67754],{}," EUR",[898,67756,1882],{"mathvariant":1910},[902,67758,67759],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,67761,67762],{},"Pro srovnání při původních 30 ks:",[883,67764,67766],{"className":67765},[886],[888,67767,67768],{"xmlns":890,"display":29279},[892,67769,67770,67835],{},[895,67771,67772,67774,67776,67778,67780,67782,67784,67786,67788,67790,67792,67794,67796,67798,67800,67802,67804,67806,67808,67811,67813,67815,67817,67819,67821,67823,67825,67827,67829,67831,67833],{},[898,67773,2675],{},[898,67775,2998],{},[1651,67777,1654],{"stretchy":1653},[1692,67779,39232],{},[1651,67781,1667],{"stretchy":1653},[1651,67783,1738],{},[1692,67785,16489],{},[1651,67787,4503],{},[1692,67789,39232],{},[1651,67791,2181],{},[1651,67793,1654],{"stretchy":1653},[1692,67795,4446],{},[1651,67797,1839],{},[1692,67799,67525],{},[1651,67801,4503],{},[1692,67803,16489],{},[1651,67805,1667],{"stretchy":1653},[1651,67807,1738],{},[1692,67809,67810],{},"27",[1843,67812,1845],{},[1692,67814,60295],{},[1651,67816,2181],{},[1692,67818,6311],{},[1843,67820,1845],{},[1692,67822,31956],{},[1651,67824,1738],{},[1692,67826,1694],{},[1843,67828,1845],{},[1692,67830,24956],{},[1843,67832,67754],{},[898,67834,1882],{"mathvariant":1910},[902,67836,67837],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,67839,67840,67843,67844,67862,67863,67881],{},[38,67841,67842],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,67845,67847],{"className":67846},[886],[888,67848,67849],{"xmlns":890},[892,67850,67851,67859],{},[895,67852,67853,67855,67857],{},[1692,67854,25414],{},[1843,67856,1845],{},[1692,67858,67751],{},[902,67860,67861],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,67864,67866],{"className":67865},[886],[888,67867,67868],{"xmlns":890},[892,67869,67870,67878],{},[895,67871,67872,67874,67876],{},[1692,67873,1694],{},[1843,67875,1845],{},[1692,67877,24956],{},[902,67879,67880],{"encoding":904},"1\\,750"," EUR.",[198,67883,67885],{"id":67884},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,67887,67888,67889,63783,67902,67926],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,67890,67892],{"className":67891},[886],[888,67893,67894],{"xmlns":890},[892,67895,67896,67900],{},[895,67897,67898],{},[898,67899,2675],{},[902,67901,2675],{"encoding":904},[883,67903,67905],{"className":67904},[886],[888,67906,67907],{"xmlns":890},[892,67908,67909,67923],{},[895,67910,67911,67913,67915,67917,67919,67921],{},[898,67912,4104],{},[898,67914,2998],{},[1651,67916,1738],{},[898,67918,2675],{},[1651,67920,4503],{},[898,67922,1690],{},[902,67924,67925],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,67928,67930],{"className":67929},[886],[888,67931,67932],{"xmlns":890,"display":29279},[892,67933,67934,67967],{},[21967,67935,67936],{"width":29284},[21972,67937,67938,67940,67960,67962],{},[21975,67939],{"width":29289},[21975,67941,67942],{},[895,67943,67944,67946,67948,67950,67952,67954,67956,67958],{},[898,67945,2675],{},[1651,67947,1738],{},[898,67949,2995],{},[898,67951,3001],{},[1651,67953,1654],{"stretchy":1653},[898,67955,1690],{},[1651,67957,1667],{"stretchy":1653},[898,67959,1882],{"mathvariant":1910},[21975,67961],{"width":29289},[21975,67963,67964],{},[1843,67965,67966],{},"(3.14)",[902,67968,67969],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,67971,67972,67973,1882],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,67974,67976],{"className":67975},[886],[888,67977,67978],{"xmlns":890},[892,67979,67980,67994],{},[895,67981,67982,67984],{},[898,67983,2675],{},[2115,67985,67986,67988],{},[898,67987,2998],{},[895,67989,67990,67992],{},[1651,67991,1912],{"mathvariant":1910},[1651,67993,1912],{"mathvariant":1910},[902,67995,67050],{"encoding":904},[38561,67997,67999],{"id":67998},"příklad-311","Příklad 3.11",[724,68001,68002,58735,68004,68051,68052,68070],{},[38,68003,57200],{},[883,68005,68007],{"className":68006},[886],[888,68008,68009],{"xmlns":890},[892,68010,68011,68048],{},[895,68012,68013,68015,68017,68019,68022,68028,68030,68032,68038,68040,68042,68044,68046],{},[898,68014,4104],{},[898,68016,3001],{},[1651,68018,1738],{},[1692,68020,68021],{},"0,04",[2115,68023,68024,68026],{},[898,68025,1690],{},[1692,68027,3521],{},[1651,68029,2181],{},[1692,68031,23758],{},[2115,68033,68034,68036],{},[898,68035,1690],{},[1692,68037,1703],{},[1651,68039,1839],{},[1692,68041,4190],{},[898,68043,1690],{},[1651,68045,1839],{},[1692,68047,3574],{},[902,68049,68050],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,68053,68055],{"className":68054},[886],[888,68056,68057],{"xmlns":890},[892,68058,68059,68067],{},[895,68060,68061,68063,68065],{},[898,68062,2675],{},[1651,68064,1738],{},[1692,68066,3689],{},[902,68068,68069],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,68072,68073,68075,68076,2983,68118,68152,68153,1793],{},[38,68074,23983],{}," Z (3.14): ",[883,68077,68079],{"className":68078},[886],[888,68080,68081],{"xmlns":890},[892,68082,68083,68115],{},[895,68084,68085,68087,68089,68091,68094,68100,68102,68105,68107,68109,68111,68113],{},[898,68086,2995],{},[898,68088,3001],{},[1651,68090,1738],{},[1692,68092,68093],{},"0,12",[2115,68095,68096,68098],{},[898,68097,1690],{},[1692,68099,1703],{},[1651,68101,2181],{},[1692,68103,68104],{},"1,8",[898,68106,1690],{},[1651,68108,1839],{},[1692,68110,4190],{},[1651,68112,1738],{},[1692,68114,3689],{},[902,68116,68117],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,68119,68121],{"className":68120},[886],[888,68122,68123],{"xmlns":890},[892,68124,68125,68149],{},[895,68126,68127,68129,68135,68137,68139,68141,68143,68145,68147],{},[1692,68128,68093],{},[2115,68130,68131,68133],{},[898,68132,1690],{},[1692,68134,1703],{},[1651,68136,2181],{},[1692,68138,68104],{},[898,68140,1690],{},[1651,68142,1839],{},[1692,68144,3581],{},[1651,68146,1738],{},[1692,68148,1741],{},[902,68150,68151],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,68154,68156],{"className":68155},[886],[888,68157,68158],{"xmlns":890},[892,68159,68160,68164],{},[895,68161,68162],{},[1692,68163,68093],{},[902,68165,68166],{"encoding":904},"0{,}12",[883,68168,68170],{"className":68169},[886],[888,68171,68172],{"xmlns":890,"display":29279},[892,68173,68174,68226],{},[895,68175,68176,68182,68184,68186,68188,68190,68192,68194,68196,68198,68200,68202,68208,68210,68212,68214,68216,68222,68224],{},[2115,68177,68178,68180],{},[898,68179,1690],{},[1692,68181,1703],{},[1651,68183,2181],{},[1692,68185,37457],{},[898,68187,1690],{},[1651,68189,1839],{},[1692,68191,4446],{},[1651,68193,1738],{},[1692,68195,1741],{},[1843,68197,5295],{},[1651,68199,5298],{},[1843,68201,5295],{},[1686,68203,68204,68206],{},[898,68205,1690],{},[1692,68207,1694],{},[1651,68209,1738],{},[1692,68211,3574],{},[1651,68213,1661],{"separator":1660},[1843,68215,5295],{},[1686,68217,68218,68220],{},[898,68219,1690],{},[1692,68221,1703],{},[1651,68223,1738],{},[1692,68225,20541],{},[902,68227,68228],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,68230,68231,68232,1793],{},"Dále ",[883,68233,68235],{"className":68234},[886],[888,68236,68237],{"xmlns":890},[892,68238,68239,68278],{},[895,68240,68241,68243,68253,68255,68257,68259,68265,68267,68269,68272,68274,68276],{},[898,68242,2675],{},[2115,68244,68245,68247],{},[898,68246,2998],{},[895,68248,68249,68251],{},[1651,68250,1912],{"mathvariant":1910},[1651,68252,1912],{"mathvariant":1910},[1651,68254,1738],{},[1651,68256,2181],{},[898,68258,2995],{},[2115,68260,68261,68263],{},[898,68262,3001],{},[1651,68264,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,68266,1738],{},[1651,68268,2181],{},[1692,68270,68271],{},"0,24",[898,68273,1690],{},[1651,68275,1839],{},[1692,68277,68104],{},[902,68279,68280],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,68282,68283,68333],{},[123,68284,68285,68329,68330,68332],{},[883,68286,68288],{"className":68287},[886],[888,68289,68290],{"xmlns":890},[892,68291,68292,68326],{},[895,68293,68294,68296,68306,68308,68310,68312,68314,68316,68318,68320,68322,68324],{},[898,68295,2675],{},[2115,68297,68298,68300],{},[898,68299,2998],{},[895,68301,68302,68304],{},[1651,68303,1912],{"mathvariant":1910},[1651,68305,1912],{"mathvariant":1910},[1651,68307,1654],{"stretchy":1653},[1692,68309,3574],{},[1651,68311,1667],{"stretchy":1653},[1651,68313,1738],{},[1692,68315,20534],{},[1651,68317,2390],{},[1692,68319,1741],{},[1843,68321,5295],{},[1651,68323,5298],{},[1843,68325,5295],{},[902,68327,68328],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,68331,2398],{}," zisku (minimalizace ztráty);",[123,68334,68335,68329,68381,68383],{},[883,68336,68338],{"className":68337},[886],[888,68339,68340],{"xmlns":890},[892,68341,68342,68378],{},[895,68343,68344,68346,68356,68358,68360,68362,68364,68366,68368,68370,68372,68374,68376],{},[898,68345,2675],{},[2115,68347,68348,68350],{},[898,68349,2998],{},[895,68351,68352,68354],{},[1651,68353,1912],{"mathvariant":1910},[1651,68355,1912],{"mathvariant":1910},[1651,68357,1654],{"stretchy":1653},[1692,68359,4190],{},[1651,68361,1667],{"stretchy":1653},[1651,68363,1738],{},[1651,68365,2181],{},[1692,68367,20534],{},[1651,68369,2319],{},[1692,68371,1741],{},[1843,68373,5295],{},[1651,68375,5298],{},[1843,68377,5295],{},[902,68379,68380],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,68382,2328],{}," zisku, avšak",[883,68385,68387],{"className":68386},[886],[888,68388,68389],{"xmlns":890,"display":29279},[892,68390,68391,68459],{},[895,68392,68393,68395,68397,68399,68401,68403,68405,68407,68409,68411,68413,68415,68417,68419,68421,68423,68425,68427,68429,68431,68433,68435,68437,68439,68441,68443,68445,68447,68449,68451,68453,68455,68457],{},[898,68394,2675],{},[898,68396,2998],{},[1651,68398,1654],{"stretchy":1653},[1692,68400,4190],{},[1651,68402,1667],{"stretchy":1653},[1651,68404,1738],{},[1692,68406,3689],{},[1651,68408,4503],{},[1692,68410,4190],{},[1651,68412,2181],{},[1651,68414,1654],{"stretchy":1653},[1692,68416,68021],{},[1651,68418,4503],{},[1692,68420,1694],{},[1843,68422,1845],{},[1692,68424,60295],{},[1651,68426,2181],{},[1692,68428,23758],{},[1651,68430,4503],{},[1692,68432,4416],{},[1651,68434,1839],{},[1692,68436,4416],{},[1651,68438,1839],{},[1692,68440,3574],{},[1651,68442,1667],{"stretchy":1653},[1651,68444,1738],{},[1692,68446,6518],{},[1651,68448,2181],{},[1692,68450,22393],{},[1651,68452,1738],{},[1651,68454,2181],{},[1692,68456,37457],{},[1651,68458,1661],{"separator":1660},[902,68460,68461],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,68463,68464,68465,1882],{},"tj. ztráta větší než ",[883,68466,68468],{"className":68467},[886],[888,68469,68470],{"xmlns":890},[892,68471,68472,68482],{},[895,68473,68474,68476,68478,68480],{},[898,68475,11736],{},[898,68477,3001],{},[1651,68479,1738],{},[1692,68481,3574],{},[902,68483,68484],{"encoding":904},"FC = 5",[724,68486,68487,68490,68491,68494,68495,1882],{},[38,68488,68489],{},"Závěr:"," firma by měla ",[38,68492,68493],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,68496,68498],{"className":68497},[886],[888,68499,68500],{"xmlns":890},[892,68501,68502,68512],{},[895,68503,68504,68506,68508,68510],{},[898,68505,11736],{},[898,68507,3001],{},[1651,68509,1738],{},[1692,68511,3574],{},[902,68513,68484],{"encoding":904},[115,68515,68517],{"id":68516},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,68519,68520,68521,68523,68524,68539,68540,68553,68554,68580,68581,68594,68595,68612,68613,3955,68630,68633,68634,68654,68655,68670,68671,1793],{},"Důležitým završením analýzy je konstrukce ",[38,68522,56488],{},". S nabízeným množstvím rostou mezní náklady ",[883,68525,68527],{"className":68526},[886],[888,68528,68529],{"xmlns":890},[892,68530,68531,68537],{},[895,68532,68533,68535],{},[898,68534,2995],{},[898,68536,3001],{},[902,68538,56505],{"encoding":904}," a tyto určují cenu ",[883,68541,68543],{"className":68542},[886],[888,68544,68545],{"xmlns":890},[892,68546,68547,68551],{},[895,68548,68549],{},[898,68550,2675],{},[902,68552,2675],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,68555,68557],{"className":68556},[886],[888,68558,68559],{"xmlns":890},[892,68560,68561,68577],{},[895,68562,68563,68565,68567,68569,68571,68573,68575],{},[898,68564,2675],{},[1651,68566,1738],{},[898,68568,2995],{},[898,68570,3001],{},[1651,68572,1654],{"stretchy":1653},[898,68574,1690],{},[1651,68576,1667],{"stretchy":1653},[902,68578,68579],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,68582,68584],{"className":68583},[886],[888,68585,68586],{"xmlns":890},[892,68587,68588,68592],{},[895,68589,68590],{},[898,68591,2675],{},[902,68593,2675],{"encoding":904}," však nemůže být nižší než ",[883,68596,68598],{"className":68597},[886],[888,68599,68600],{"xmlns":890},[892,68601,68602,68610],{},[895,68603,68604],{},[2115,68605,68606,68608],{},[898,68607,2675],{},[1651,68609,2668],{},[902,68611,5711],{"encoding":904}," odpovídající množství ",[883,68614,68616],{"className":68615},[886],[888,68617,68618],{"xmlns":890},[892,68619,68620,68628],{},[895,68621,68622],{},[2115,68623,68624,68626],{},[898,68625,1690],{},[1651,68627,2668],{},[902,68629,31057],{"encoding":904},[38,68631,68632],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,68635,68637],{"className":68636},[886],[888,68638,68639],{"xmlns":890},[892,68640,68641,68651],{},[895,68642,68643,68645],{},[1692,68644,1741],{},[2115,68646,68647,68649],{},[898,68648,1690],{},[1651,68650,2668],{},[902,68652,68653],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,68656,68658],{"className":68657},[886],[888,68659,68660],{"xmlns":890},[892,68661,68662,68668],{},[895,68663,68664,68666],{},[898,68665,2995],{},[898,68667,3001],{},[902,68669,56505],{"encoding":904}," nad bodem ",[883,68672,68674],{"className":68673},[886],[888,68675,68676],{"xmlns":890},[892,68677,68678,68682],{},[895,68679,68680],{},[898,68681,5564],{},[902,68683,5564],{"encoding":904},[883,68685,68687],{"className":68686},[886],[888,68688,68689],{"xmlns":890,"display":29279},[892,68690,68691,68798],{},[21967,68692,68693],{"width":29284},[21972,68694,68695,68697,68791,68793],{},[21975,68696],{"width":29289},[21975,68698,68699],{},[895,68700,68701,68703,68705,68707,68709,68711,68713,68715],{},[898,68702,2675],{},[1651,68704,1738],{},[898,68706,3004],{},[1651,68708,1654],{"stretchy":1653},[898,68710,1690],{},[1651,68712,1667],{"stretchy":1653},[1651,68714,1738],{},[895,68716,68717,68720],{},[1651,68718,68719],{"fence":1660},"{",[21967,68721,68724,68763],{"rowspacing":68722,"columnalign":68723,"columnspacing":16582},"0.36em","left left",[21972,68725,68726,68742],{},[21975,68727,68728],{},[2938,68729,68730],{"scriptlevel":1741,"displaystyle":1653},[895,68731,68732,68734,68736,68738,68740],{},[898,68733,2995],{},[898,68735,3001],{},[1651,68737,1654],{"stretchy":1653},[898,68739,1690],{},[1651,68741,1667],{"stretchy":1653},[21975,68743,68744],{},[2938,68745,68746],{"scriptlevel":1741,"displaystyle":1653},[895,68747,68748,68751,68753,68755,68761],{},[1843,68749,68750],{},"pro ",[898,68752,1690],{},[1651,68754,5792],{},[2115,68756,68757,68759],{},[898,68758,1690],{},[1651,68760,2668],{},[1651,68762,1661],{"separator":1660},[21972,68764,68765,68771],{},[21975,68766,68767],{},[2938,68768,68769],{"scriptlevel":1741,"displaystyle":1653},[1692,68770,1741],{},[21975,68772,68773],{},[2938,68774,68775],{"scriptlevel":1741,"displaystyle":1653},[895,68776,68777,68779,68781,68783,68789],{},[1843,68778,68750],{},[898,68780,1690],{},[1651,68782,2319],{},[2115,68784,68785,68787],{},[898,68786,1690],{},[1651,68788,2668],{},[1651,68790,1661],{"separator":1660},[21975,68792],{"width":29289},[21975,68794,68795],{},[1843,68796,68797],{},"(3.15)",[902,68799,68800],{"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}",[724,68802,1863,68803,68820,68821,68838,68839,42712,68869,68872],{},[883,68804,68806],{"className":68805},[886],[888,68807,68808],{"xmlns":890},[892,68809,68810,68818],{},[895,68811,68812],{},[2115,68813,68814,68816],{},[898,68815,1690],{},[1651,68817,2668],{},[902,68819,31057],{"encoding":904}," je bod minima ",[883,68822,68824],{"className":68823},[886],[888,68825,68826],{"xmlns":890},[892,68827,68828,68836],{},[895,68829,68830,68832,68834],{},[898,68831,5564],{},[898,68833,41552],{},[898,68835,3001],{},[902,68837,56524],{"encoding":904},". Bod ",[883,68840,68842],{"className":68841},[886],[888,68843,68844],{"xmlns":890},[892,68845,68846,68866],{},[895,68847,68848,68850,68856,68858,68864],{},[1651,68849,1654],{"stretchy":1653},[2115,68851,68852,68854],{},[898,68853,1690],{},[1651,68855,2668],{},[1651,68857,1661],{"separator":1660},[2115,68859,68860,68862],{},[898,68861,2675],{},[1651,68863,2668],{},[1651,68865,1667],{"stretchy":1653},[902,68867,68868],{"encoding":904},"(Q^*, P^*)",[38,68870,68871],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[5179,68874,68875,68880],{},[724,68876,68877,68879],{},[883,68878,5879],{}," Postup — jak odvodit nabídku firmy",[152,68881,68882,68931,69026,69081,69152],{},[123,68883,68884,68885,5197,68907,1882],{},"Ze zadaných nákladů určete ",[883,68886,68888],{"className":68887},[886],[888,68889,68890],{"xmlns":890},[892,68891,68892,68904],{},[895,68893,68894,68896,68898,68900,68902],{},[898,68895,2995],{},[898,68897,3001],{},[1651,68899,1654],{"stretchy":1653},[898,68901,1690],{},[1651,68903,1667],{"stretchy":1653},[902,68905,68906],{"encoding":904},"MC(Q)",[883,68908,68910],{"className":68909},[886],[888,68911,68912],{"xmlns":890},[892,68913,68914,68928],{},[895,68915,68916,68918,68920,68922,68924,68926],{},[898,68917,5564],{},[898,68919,41552],{},[898,68921,3001],{},[1651,68923,1654],{"stretchy":1653},[898,68925,1690],{},[1651,68927,1667],{"stretchy":1653},[902,68929,68930],{"encoding":904},"AVC(Q)",[123,68932,68933,68934,68951,68952,68969,68970,69002,69003,5230],{},"Najděte ",[883,68935,68937],{"className":68936},[886],[888,68938,68939],{"xmlns":890},[892,68940,68941,68949],{},[895,68942,68943],{},[2115,68944,68945,68947],{},[898,68946,1690],{},[1651,68948,2668],{},[902,68950,31057],{"encoding":904}," jako bod minima ",[883,68953,68955],{"className":68954},[886],[888,68956,68957],{"xmlns":890},[892,68958,68959,68967],{},[895,68960,68961,68963,68965],{},[898,68962,5564],{},[898,68964,41552],{},[898,68966,3001],{},[902,68968,56524],{"encoding":904}," (řešením ",[883,68971,68973],{"className":68972},[886],[888,68974,68975],{"xmlns":890},[892,68976,68977,68999],{},[895,68978,68979,68981,68983,68989,68991,68993,68995,68997],{},[898,68980,5564],{},[898,68982,41552],{},[2115,68984,68985,68987],{},[898,68986,3001],{},[1651,68988,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,68990,1654],{"stretchy":1653},[898,68992,1690],{},[1651,68994,1667],{"stretchy":1653},[1651,68996,1738],{},[1692,68998,1741],{},[902,69000,69001],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,69004,69006],{"className":69005},[886],[888,69007,69008],{"xmlns":890},[892,69009,69010,69024],{},[895,69011,69012,69014,69016,69018,69020,69022],{},[898,69013,5564],{},[898,69015,41552],{},[898,69017,3001],{},[1651,69019,1738],{},[898,69021,2995],{},[898,69023,3001],{},[902,69025,56461],{"encoding":904},[123,69027,66934,69028,69080],{},[883,69029,69031],{"className":69030},[886],[888,69032,69033],{"xmlns":890},[892,69034,69035,69077],{},[895,69036,69037,69043,69045,69047,69049,69051,69057,69059,69061,69063,69065,69067,69069,69075],{},[2115,69038,69039,69041],{},[898,69040,2675],{},[1651,69042,2668],{},[1651,69044,1738],{},[898,69046,2995],{},[898,69048,3001],{},[1651,69050,1654],{"stretchy":1653},[2115,69052,69053,69055],{},[898,69054,1690],{},[1651,69056,2668],{},[1651,69058,1667],{"stretchy":1653},[1651,69060,1738],{},[898,69062,5564],{},[898,69064,41552],{},[898,69066,3001],{},[1651,69068,1654],{"stretchy":1653},[2115,69070,69071,69073],{},[898,69072,1690],{},[1651,69074,2668],{},[1651,69076,1667],{"stretchy":1653},[902,69078,69079],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,69082,69083,69084,7780,69116,69138,69139,1882],{},"Zapište nabídku: ",[883,69085,69087],{"className":69086},[886],[888,69088,69089],{"xmlns":890},[892,69090,69091,69113],{},[895,69092,69093,69095,69097,69099,69101,69103,69105,69107,69109,69111],{},[898,69094,3004],{},[1651,69096,1654],{"stretchy":1653},[898,69098,1690],{},[1651,69100,1667],{"stretchy":1653},[1651,69102,1738],{},[898,69104,2995],{},[898,69106,3001],{},[1651,69108,1654],{"stretchy":1653},[898,69110,1690],{},[1651,69112,1667],{"stretchy":1653},[902,69114,69115],{"encoding":904},"S(Q) = MC(Q)",[883,69117,69119],{"className":69118},[886],[888,69120,69121],{"xmlns":890},[892,69122,69123,69135],{},[895,69124,69125,69127,69129],{},[898,69126,1690],{},[1651,69128,5792],{},[2115,69130,69131,69133],{},[898,69132,1690],{},[1651,69134,2668],{},[902,69136,69137],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,69140,69142],{"className":69141},[886],[888,69143,69144],{"xmlns":890},[892,69145,69146,69150],{},[895,69147,69148],{},[1692,69149,1741],{},[902,69151,1741],{"encoding":904},[123,69153,69154,69155,69187],{},"V případě potřeby vyjádřete inverzi ",[883,69156,69158],{"className":69157},[886],[888,69159,69160],{"xmlns":890},[892,69161,69162,69184],{},[895,69163,69164,69166,69168,69178,69180,69182],{},[898,69165,1690],{},[1651,69167,1738],{},[2115,69169,69170,69172],{},[898,69171,3004],{},[895,69173,69174,69176],{},[1651,69175,2181],{},[1692,69177,1694],{},[1651,69179,1654],{"stretchy":1653},[898,69181,2675],{},[1651,69183,1667],{"stretchy":1653},[902,69185,69186],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,69189,69190],{},[614,69191,69192,69193,1343,69208,5197,69225,30414,69240,69253,69254,69279,69280,69293,69294,69311,69312,69329,69330,69347],{},"Obrázek 3.14: Křivky ",[883,69194,69196],{"className":69195},[886],[888,69197,69198],{"xmlns":890},[892,69199,69200,69206],{},[895,69201,69202,69204],{},[898,69203,5564],{},[898,69205,3001],{},[902,69207,56773],{"encoding":904},[883,69209,69211],{"className":69210},[886],[888,69212,69213],{"xmlns":890},[892,69214,69215,69223],{},[895,69216,69217,69219,69221],{},[898,69218,5564],{},[898,69220,41552],{},[898,69222,3001],{},[902,69224,56524],{"encoding":904},[883,69226,69228],{"className":69227},[886],[888,69229,69230],{"xmlns":890},[892,69231,69232,69238],{},[895,69233,69234,69236],{},[898,69235,2995],{},[898,69237,3001],{},[902,69239,56505],{"encoding":904},[883,69241,69243],{"className":69242},[886],[888,69244,69245],{"xmlns":890},[892,69246,69247,69251],{},[895,69248,69249],{},[898,69250,900],{},[902,69252,900],{"encoding":904},"; křivka nabídky ",[883,69255,69257],{"className":69256},[886],[888,69258,69259],{"xmlns":890},[892,69260,69261,69277],{},[895,69262,69263,69265,69267,69269,69271,69273,69275],{},[898,69264,2675],{},[1651,69266,1738],{},[898,69268,2995],{},[898,69270,3001],{},[1651,69272,1654],{"stretchy":1653},[898,69274,1690],{},[1651,69276,1667],{"stretchy":1653},[902,69278,68579],{"encoding":904}," začíná v bodě ",[883,69281,69283],{"className":69282},[886],[888,69284,69285],{"xmlns":890},[892,69286,69287,69291],{},[895,69288,69289],{},[898,69290,5564],{},[902,69292,5564],{"encoding":904}," odpovídajícím minimu ",[883,69295,69297],{"className":69296},[886],[888,69298,69299],{"xmlns":890},[892,69300,69301,69309],{},[895,69302,69303,69305,69307],{},[898,69304,5564],{},[898,69306,41552],{},[898,69308,3001],{},[902,69310,56524],{"encoding":904}," při ceně ",[883,69313,69315],{"className":69314},[886],[888,69316,69317],{"xmlns":890},[892,69318,69319,69327],{},[895,69320,69321],{},[2115,69322,69323,69325],{},[898,69324,2675],{},[1651,69326,2668],{},[902,69328,5711],{"encoding":904}," (minimální cena nabídky); pod ",[883,69331,69333],{"className":69332},[886],[888,69334,69335],{"xmlns":890},[892,69336,69337,69345],{},[895,69338,69339],{},[2115,69340,69341,69343],{},[898,69342,1690],{},[1651,69344,2668],{},[902,69346,31057],{"encoding":904}," je nabídka nulová.",[38561,69349,69351],{"id":69350},"příklad-312","Příklad 3.12",[724,69353,69354,58735,69356,69402],{},[38,69355,57200],{},[883,69357,69359],{"className":69358},[886],[888,69360,69361],{"xmlns":890},[892,69362,69363,69399],{},[895,69364,69365,69367,69369,69371,69373,69379,69381,69383,69389,69391,69393,69395,69397],{},[898,69366,4104],{},[898,69368,3001],{},[1651,69370,1738],{},[1692,69372,4122],{},[2115,69374,69375,69377],{},[898,69376,1690],{},[1692,69378,3521],{},[1651,69380,2181],{},[1692,69382,1703],{},[2115,69384,69385,69387],{},[898,69386,1690],{},[1692,69388,1703],{},[1651,69390,1839],{},[1692,69392,37457],{},[898,69394,1690],{},[1651,69396,1839],{},[1692,69398,4190],{},[902,69400,69401],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,69404,69405,3246,69407,69444,69445,1793],{},[38,69406,23983],{},[883,69408,69410],{"className":69409},[886],[888,69411,69412],{"xmlns":890},[892,69413,69414,69441],{},[895,69415,69416,69418,69420,69422,69425,69431,69433,69435,69437,69439],{},[898,69417,2995],{},[898,69419,3001],{},[1651,69421,1738],{},[1692,69423,69424],{},"0,3",[2115,69426,69427,69429],{},[898,69428,1690],{},[1692,69430,1703],{},[1651,69432,2181],{},[1692,69434,3689],{},[898,69436,1690],{},[1651,69438,1839],{},[1692,69440,37457],{},[902,69442,69443],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,69446,69448],{"className":69447},[886],[888,69449,69450],{"xmlns":890},[892,69451,69452,69462],{},[895,69453,69454,69456,69458,69460],{},[898,69455,2675],{},[1651,69457,1738],{},[898,69459,2995],{},[898,69461,3001],{},[902,69463,69464],{"encoding":904},"P = MC",[883,69466,69468],{"className":69467},[886],[888,69469,69470],{"xmlns":890,"display":29279},[892,69471,69472,69497],{},[895,69473,69474,69476,69478,69480,69486,69488,69490,69492,69494],{},[898,69475,2675],{},[1651,69477,1738],{},[1692,69479,69424],{},[2115,69481,69482,69484],{},[898,69483,1690],{},[1692,69485,1703],{},[1651,69487,2181],{},[1692,69489,3689],{},[898,69491,1690],{},[1651,69493,1839],{},[1692,69495,69496],{},"15.",[902,69498,69499],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,69501,69502,69503,6689,69516,69529],{},"Vyjádření ",[883,69504,69506],{"className":69505},[886],[888,69507,69508],{"xmlns":890},[892,69509,69510,69514],{},[895,69511,69512],{},[898,69513,1690],{},[902,69515,1690],{"encoding":904},[883,69517,69519],{"className":69518},[886],[888,69520,69521],{"xmlns":890},[892,69522,69523,69527],{},[895,69524,69525],{},[898,69526,2675],{},[902,69528,2675],{"encoding":904}," doplněním na čtverec:",[883,69531,69533],{"className":69532},[886],[888,69534,69535],{"xmlns":890,"display":29279},[892,69536,69537,69627],{},[895,69538,69539,69541,69543,69545,69583,69585,69587,69609,69611,69625],{},[898,69540,2675],{},[1651,69542,1738],{},[1692,69544,69424],{},[895,69546,69547,69549,69571,69573,69581],{},[1651,69548,1654],{"fence":1660},[2115,69550,69551,69569],{},[895,69552,69553,69555,69557,69559,69567],{},[1651,69554,1654],{"fence":1660},[898,69556,1690],{},[1651,69558,2181],{},[2938,69560,69561],{"scriptlevel":1741,"displaystyle":1653},[2446,69562,69563,69565],{},[1692,69564,10340],{},[1692,69566,3521],{},[1651,69568,1667],{"fence":1660},[1692,69570,1703],{},[1651,69572,1839],{},[2938,69574,69575],{"scriptlevel":1741,"displaystyle":1653},[2446,69576,69577,69579],{},[1692,69578,4446],{},[1692,69580,5309],{},[1651,69582,1667],{"fence":1660},[1651,69584,1661],{"separator":1660},[7185,69586],{"width":7187},[2115,69588,69589,69607],{},[895,69590,69591,69593,69595,69597,69605],{},[1651,69592,1654],{"fence":1660},[898,69594,1690],{},[1651,69596,2181],{},[2938,69598,69599],{"scriptlevel":1741,"displaystyle":1653},[2446,69600,69601,69603],{},[1692,69602,10340],{},[1692,69604,3521],{},[1651,69606,1667],{"fence":1660},[1692,69608,1703],{},[1651,69610,1738],{},[2446,69612,69613,69623],{},[895,69614,69615,69617,69619,69621],{},[1692,69616,39232],{},[898,69618,2675],{},[1651,69620,2181],{},[1692,69622,4446],{},[1692,69624,5309],{},[1651,69626,1661],{"separator":1660},[902,69628,69629],{"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},",[883,69631,69633],{"className":69632},[886],[888,69634,69635],{"xmlns":890,"display":29279},[892,69636,69637,69669],{},[895,69638,69639,69641,69643,69649,69651,69667],{},[898,69640,1690],{},[1651,69642,1738],{},[2446,69644,69645,69647],{},[1692,69646,10340],{},[1692,69648,3521],{},[1651,69650,1839],{},[2446,69652,69653,69665],{},[9423,69654,69655],{},[895,69656,69657,69659,69661,69663],{},[1692,69658,39232],{},[898,69660,2675],{},[1651,69662,2181],{},[1692,69664,4446],{},[1692,69666,3521],{},[898,69668,1882],{"mathvariant":1910},[902,69670,69671],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,69673,68231,69674,1343,69712,1343,69760,69794,69795,1882],{},[883,69675,69677],{"className":69676},[886],[888,69678,69679],{"xmlns":890},[892,69680,69681,69709],{},[895,69682,69683,69685,69687,69689,69691,69693,69699,69701,69703,69705,69707],{},[898,69684,5564],{},[898,69686,41552],{},[898,69688,3001],{},[1651,69690,1738],{},[1692,69692,4122],{},[2115,69694,69695,69697],{},[898,69696,1690],{},[1692,69698,1703],{},[1651,69700,2181],{},[1692,69702,1703],{},[898,69704,1690],{},[1651,69706,1839],{},[1692,69708,37457],{},[902,69710,69711],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,69713,69715],{"className":69714},[886],[888,69716,69717],{"xmlns":890},[892,69718,69719,69757],{},[895,69720,69721,69723,69725,69731,69733,69735,69737,69739,69741,69743,69745,69747,69753,69755],{},[898,69722,5564],{},[898,69724,41552],{},[2115,69726,69727,69729],{},[898,69728,3001],{},[1651,69730,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,69732,1738],{},[1692,69734,4166],{},[898,69736,1690],{},[1651,69738,2181],{},[1692,69740,1703],{},[1651,69742,1738],{},[1692,69744,1741],{},[1651,69746,5298],{},[2115,69748,69749,69751],{},[898,69750,1690],{},[1651,69752,2668],{},[1651,69754,1738],{},[1692,69756,4190],{},[902,69758,69759],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,69761,69763],{"className":69762},[886],[888,69764,69765],{"xmlns":890},[892,69766,69767,69791],{},[895,69768,69769,69771,69773,69783,69785,69787,69789],{},[898,69770,5564],{},[898,69772,41552],{},[2115,69774,69775,69777],{},[898,69776,3001],{},[895,69778,69779,69781],{},[1651,69780,1912],{"mathvariant":1910},[1651,69782,1912],{"mathvariant":1910},[1651,69784,1738],{},[1692,69786,4166],{},[1651,69788,2390],{},[1692,69790,1741],{},[902,69792,69793],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,69796,69798],{"className":69797},[886],[888,69799,69800],{"xmlns":890},[892,69801,69802,69838],{},[895,69803,69804,69810,69812,69814,69816,69818,69820,69822,69824,69826,69828,69830,69832,69834,69836],{},[2115,69805,69806,69808],{},[898,69807,2675],{},[1651,69809,2668],{},[1651,69811,1738],{},[898,69813,2995],{},[898,69815,3001],{},[1651,69817,1654],{"stretchy":1653},[1692,69819,4190],{},[1651,69821,1667],{"stretchy":1653},[1651,69823,1738],{},[1692,69825,39232],{},[1651,69827,2181],{},[1692,69829,6518],{},[1651,69831,1839],{},[1692,69833,37457],{},[1651,69835,1738],{},[1692,69837,3574],{},[902,69839,69840],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,69842,69843],{},[38,69844,69845],{},"Závěr.",[883,69847,69849],{"className":69848},[886],[888,69850,69851],{"xmlns":890,"display":29279},[892,69852,69853,69939],{},[895,69854,69855,69857,69859,69861,69863,69865,69867,69869],{},[898,69856,2675],{},[1651,69858,1738],{},[898,69860,3004],{},[1651,69862,1654],{"stretchy":1653},[898,69864,1690],{},[1651,69866,1667],{"stretchy":1653},[1651,69868,1738],{},[895,69870,69871,69873],{},[1651,69872,68719],{"fence":1660},[21967,69874,69875,69917],{"rowspacing":68722,"columnalign":68723,"columnspacing":16582},[21972,69876,69877,69901],{},[21975,69878,69879],{},[2938,69880,69881],{"scriptlevel":1741,"displaystyle":1653},[895,69882,69883,69885,69891,69893,69895,69897,69899],{},[1692,69884,69424],{},[2115,69886,69887,69889],{},[898,69888,1690],{},[1692,69890,1703],{},[1651,69892,2181],{},[1692,69894,3689],{},[898,69896,1690],{},[1651,69898,1839],{},[1692,69900,37457],{},[21975,69902,69903],{},[2938,69904,69905],{"scriptlevel":1741,"displaystyle":1653},[895,69906,69907,69909,69911,69913,69915],{},[1843,69908,68750],{},[898,69910,1690],{},[1651,69912,5792],{},[1692,69914,4190],{},[1651,69916,1661],{"separator":1660},[21972,69918,69919,69925],{},[21975,69920,69921],{},[2938,69922,69923],{"scriptlevel":1741,"displaystyle":1653},[1692,69924,1741],{},[21975,69926,69927],{},[2938,69928,69929],{"scriptlevel":1741,"displaystyle":1653},[895,69930,69931,69933,69935,69937],{},[1843,69932,68750],{},[898,69934,1690],{},[1651,69936,2319],{},[1692,69938,20541],{},[902,69940,69941],{"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}",[724,69943,69944],{},[614,69945,69946,69947,69962,69963,1882],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,69948,69950],{"className":69949},[886],[888,69951,69952],{"xmlns":890},[892,69953,69954,69960],{},[895,69955,69956,69958],{},[898,69957,2995],{},[898,69959,3001],{},[902,69961,56505],{"encoding":904}," ležící nad minimem ",[883,69964,69966],{"className":69965},[886],[888,69967,69968],{"xmlns":890},[892,69969,69970,69978],{},[895,69971,69972,69974,69976],{},[898,69973,5564],{},[898,69975,41552],{},[898,69977,3001],{},[902,69979,56524],{"encoding":904},[115,69981,69983],{"id":69982},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,69985,69986,69987,69991,69992,70007,70008,70028,70029,5197,70032,70035,70036,70038,70039,21158,70061,70063,70064,5197,70066,59939,70069,3246,70072,43027,70087,70102],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,69988,69990],{"className":69989,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,69993,69995],{"className":69994},[886],[888,69996,69997],{"xmlns":890},[892,69998,69999,70005],{},[895,70000,70001,70003],{},[898,70002,4104],{},[898,70004,2998],{},[902,70006,5404],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,70009,70011],{"className":70010},[886],[888,70012,70013],{"xmlns":890},[892,70014,70015,70025],{},[895,70016,70017,70019,70021,70023],{},[898,70018,4104],{},[898,70020,2998],{},[898,70022,5981],{"mathvariant":1910},[898,70024,1690],{},[902,70026,70027],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,70030,70031],{},"fixních",[38,70033,70034],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,70037,65538],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,70040,70042],{"className":70041},[886],[888,70043,70044],{"xmlns":890},[892,70045,70046,70058],{},[895,70047,70048,70050,70052,70054,70056],{},[898,70049,4104],{},[898,70051,2998],{},[1651,70053,2181],{},[898,70055,4104],{},[898,70057,3001],{},[902,70059,70060],{"encoding":904},"TR - TC",[38,70062,56385],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,70065,57697],{},[38,70067,70068],{},"mezní náklady",[207,70070,1145],{"className":70071,"dataFsResolvedFilePath":764,"href":765},[210],[883,70073,70075],{"className":70074},[886],[888,70076,70077],{"xmlns":890},[892,70078,70079,70085],{},[895,70080,70081,70083],{},[898,70082,4104],{},[898,70084,2998],{},[902,70086,5404],{"encoding":904},[883,70088,70090],{"className":70089},[886],[888,70091,70092],{"xmlns":890},[892,70093,70094,70100],{},[895,70095,70096,70098],{},[898,70097,4104],{},[898,70099,3001],{},[902,70101,4569],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,70104,70105,70167,70233,70295],{},[123,70106,70107,70110,70111,11694,70126,1882],{},[38,70108,70109],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,70112,70114],{"className":70113},[886],[888,70115,70116],{"xmlns":890},[892,70117,70118,70124],{},[895,70119,70120,70122],{},[898,70121,5564],{},[898,70123,3001],{},[902,70125,56773],{"encoding":904},[883,70127,70129],{"className":70128},[886],[888,70130,70131],{"xmlns":890},[892,70132,70133,70165],{},[895,70134,70135,70137,70139,70141,70147,70149,70151,70153,70155,70157,70163],{},[898,70136,5564],{},[898,70138,3001],{},[1651,70140,1654],{"stretchy":1653},[1686,70142,70143,70145],{},[898,70144,1690],{},[1692,70146,1741],{},[1651,70148,1667],{"stretchy":1653},[1651,70150,1738],{},[898,70152,2995],{},[898,70154,3001],{},[1651,70156,1654],{"stretchy":1653},[1686,70158,70159,70161],{},[898,70160,1690],{},[1692,70162,1741],{},[1651,70164,1667],{"stretchy":1653},[902,70166,63782],{"encoding":904},[123,70168,70169,70110,70172,11694,70189,1882],{},[38,70170,70171],{},"Princip minimalizace průměrných variabilních nákladů:",[883,70173,70175],{"className":70174},[886],[888,70176,70177],{"xmlns":890},[892,70178,70179,70187],{},[895,70180,70181,70183,70185],{},[898,70182,5564],{},[898,70184,41552],{},[898,70186,3001],{},[902,70188,56524],{"encoding":904},[883,70190,70192],{"className":70191},[886],[888,70193,70194],{"xmlns":890},[892,70195,70196,70230],{},[895,70197,70198,70200,70202,70204,70206,70212,70214,70216,70218,70220,70222,70228],{},[898,70199,5564],{},[898,70201,41552],{},[898,70203,3001],{},[1651,70205,1654],{"stretchy":1653},[1686,70207,70208,70210],{},[898,70209,1690],{},[1692,70211,1741],{},[1651,70213,1667],{"stretchy":1653},[1651,70215,1738],{},[898,70217,2995],{},[898,70219,3001],{},[1651,70221,1654],{"stretchy":1653},[1686,70223,70224,70226],{},[898,70225,1690],{},[1692,70227,1741],{},[1651,70229,1667],{"stretchy":1653},[902,70231,70232],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,70234,70235,70238,70239,11694,70254,1882],{},[38,70236,70237],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,70240,70242],{"className":70241},[886],[888,70243,70244],{"xmlns":890},[892,70245,70246,70252],{},[895,70247,70248,70250],{},[898,70249,2675],{},[898,70251,2998],{},[902,70253,64692],{"encoding":904},[883,70255,70257],{"className":70256},[886],[888,70258,70259],{"xmlns":890},[892,70260,70261,70293],{},[895,70262,70263,70265,70267,70269,70275,70277,70279,70281,70283,70285,70291],{},[898,70264,2995],{},[898,70266,2998],{},[1651,70268,1654],{"stretchy":1653},[1686,70270,70271,70273],{},[898,70272,1690],{},[1692,70274,1741],{},[1651,70276,1667],{"stretchy":1653},[1651,70278,1738],{},[898,70280,2995],{},[898,70282,3001],{},[1651,70284,1654],{"stretchy":1653},[1686,70286,70287,70289],{},[898,70288,1690],{},[1692,70290,1741],{},[1651,70292,1667],{"stretchy":1653},[902,70294,66858],{"encoding":904},[123,70296,70297,3246,70300,7780,70336,69138,70357,22807,70370,68820,70387,1882],{},[38,70298,70299],{},"Funkce nabídky firmy:",[883,70301,70303],{"className":70302},[886],[888,70304,70305],{"xmlns":890},[892,70306,70307,70333],{},[895,70308,70309,70311,70313,70315,70317,70319,70321,70323,70325,70327,70329,70331],{},[898,70310,2675],{},[1651,70312,1738],{},[898,70314,3004],{},[1651,70316,1654],{"stretchy":1653},[898,70318,1690],{},[1651,70320,1667],{"stretchy":1653},[1651,70322,1738],{},[898,70324,2995],{},[898,70326,3001],{},[1651,70328,1654],{"stretchy":1653},[898,70330,1690],{},[1651,70332,1667],{"stretchy":1653},[902,70334,70335],{"encoding":904},"P = S(Q) = MC(Q)",[883,70337,70339],{"className":70338},[886],[888,70340,70341],{"xmlns":890},[892,70342,70343,70355],{},[895,70344,70345,70347,70349],{},[898,70346,1690],{},[1651,70348,5792],{},[2115,70350,70351,70353],{},[898,70352,1690],{},[1651,70354,2668],{},[902,70356,69137],{"encoding":904},[883,70358,70360],{"className":70359},[886],[888,70361,70362],{"xmlns":890},[892,70363,70364,70368],{},[895,70365,70366],{},[1692,70367,1741],{},[902,70369,1741],{"encoding":904},[883,70371,70373],{"className":70372},[886],[888,70374,70375],{"xmlns":890},[892,70376,70377,70385],{},[895,70378,70379],{},[2115,70380,70381,70383],{},[898,70382,1690],{},[1651,70384,2668],{},[902,70386,31057],{"encoding":904},[883,70388,70390],{"className":70389},[886],[888,70391,70392],{"xmlns":890},[892,70393,70394,70402],{},[895,70395,70396,70398,70400],{},[898,70397,5564],{},[898,70399,41552],{},[898,70401,3001],{},[902,70403,56524],{"encoding":904},[115,70405,51095],{"id":51094},[152,70407,70408,70411,70414,70417,70420,70423,70426,70429,70432,70435,70438],{},[123,70409,70410],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,70412,70413],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,70415,70416],{},"Jak se vypočte mezní příjem a co udává?",[123,70418,70419],{},"Z jakých složek se skládají celkové náklady?",[123,70421,70422],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,70424,70425],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,70427,70428],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,70430,70431],{},"Jak se vypočte zisk?",[123,70433,70434],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,70436,70437],{},"Co jsou body zvratu? Jak se najdou?",[123,70439,70440],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,70442,70444],{"id":70443},"úlohy-31328","Úlohy 3.1–3.28",[198,70446,70448],{"id":70447},"příjem-3135","Příjem (3.1–3.5)",[724,70450,70451,46639,70454,70482,70483,70498,70499,70514,70515,70530,70531,1343,70546,1343,70561,70576],{},[38,70452,70453],{},"3.1",[883,70455,70457],{"className":70456},[886],[888,70458,70459],{"xmlns":890},[892,70460,70461,70479],{},[895,70462,70463,70465,70467,70469,70471,70473,70475,70477],{},[898,70464,2675],{},[1651,70466,1738],{},[898,70468,2047],{},[1651,70470,1654],{"stretchy":1653},[898,70472,1690],{},[1651,70474,1667],{"stretchy":1653},[1651,70476,1738],{},[1692,70478,4416],{},[902,70480,70481],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,70484,70486],{"className":70485},[886],[888,70487,70488],{"xmlns":890},[892,70489,70490,70496],{},[895,70491,70492,70494],{},[898,70493,4104],{},[898,70495,2998],{},[902,70497,5404],{"encoding":904},", průměrný příjem ",[883,70500,70502],{"className":70501},[886],[888,70503,70504],{"xmlns":890},[892,70505,70506,70512],{},[895,70507,70508,70510],{},[898,70509,5564],{},[898,70511,2998],{},[902,70513,56658],{"encoding":904}," a mezní příjem ",[883,70516,70518],{"className":70517},[886],[888,70519,70520],{"xmlns":890},[892,70521,70522,70528],{},[895,70523,70524,70526],{},[898,70525,2995],{},[898,70527,2998],{},[902,70529,7941],{"encoding":904},". (c) Vypočtěte ",[883,70532,70534],{"className":70533},[886],[888,70535,70536],{"xmlns":890},[892,70537,70538,70544],{},[895,70539,70540,70542],{},[898,70541,4104],{},[898,70543,2998],{},[902,70545,5404],{"encoding":904},[883,70547,70549],{"className":70548},[886],[888,70550,70551],{"xmlns":890},[892,70552,70553,70559],{},[895,70554,70555,70557],{},[898,70556,5564],{},[898,70558,2998],{},[902,70560,56658],{"encoding":904},[883,70562,70564],{"className":70563},[886],[888,70565,70566],{"xmlns":890},[892,70567,70568,70574],{},[895,70569,70570,70572],{},[898,70571,2995],{},[898,70573,2998],{},[902,70575,7941],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,70578,70579,46639,70582,70482,70618,70498,70633,70514,70648,70530,70663,1343,70678,1343,70693,70708],{},[38,70580,70581],{},"3.2",[883,70583,70585],{"className":70584},[886],[888,70586,70587],{"xmlns":890},[892,70588,70589,70615],{},[895,70590,70591,70593,70595,70597,70599,70601,70603,70605,70607,70609,70611,70613],{},[898,70592,2675],{},[1651,70594,1738],{},[898,70596,2047],{},[1651,70598,1654],{"stretchy":1653},[898,70600,1690],{},[1651,70602,1667],{"stretchy":1653},[1651,70604,1738],{},[1651,70606,2181],{},[1692,70608,6316],{},[898,70610,1690],{},[1651,70612,1839],{},[1692,70614,10340],{},[902,70616,70617],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,70619,70621],{"className":70620},[886],[888,70622,70623],{"xmlns":890},[892,70624,70625,70631],{},[895,70626,70627,70629],{},[898,70628,4104],{},[898,70630,2998],{},[902,70632,5404],{"encoding":904},[883,70634,70636],{"className":70635},[886],[888,70637,70638],{"xmlns":890},[892,70639,70640,70646],{},[895,70641,70642,70644],{},[898,70643,5564],{},[898,70645,2998],{},[902,70647,56658],{"encoding":904},[883,70649,70651],{"className":70650},[886],[888,70652,70653],{"xmlns":890},[892,70654,70655,70661],{},[895,70656,70657,70659],{},[898,70658,2995],{},[898,70660,2998],{},[902,70662,7941],{"encoding":904},[883,70664,70666],{"className":70665},[886],[888,70667,70668],{"xmlns":890},[892,70669,70670,70676],{},[895,70671,70672,70674],{},[898,70673,4104],{},[898,70675,2998],{},[902,70677,5404],{"encoding":904},[883,70679,70681],{"className":70680},[886],[888,70682,70683],{"xmlns":890},[892,70684,70685,70691],{},[895,70686,70687,70689],{},[898,70688,5564],{},[898,70690,2998],{},[902,70692,56658],{"encoding":904},[883,70694,70696],{"className":70695},[886],[888,70697,70698],{"xmlns":890},[892,70699,70700,70706],{},[895,70701,70702,70704],{},[898,70703,2995],{},[898,70705,2998],{},[902,70707,7941],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,70710,70711,46639,70714,70751,70752,70498,70767,70514,70782,70797,70798,7780,70813,70839,70840,70855,70856,1343,70871,7780,70886,70839,70911,70926,70927,70940,70941,70956,70957,70972,70973,1343,70986,1343,71001,1343,71016,1882],{},[38,70712,70713],{},"3.3",[883,70715,70717],{"className":70716},[886],[888,70718,70719],{"xmlns":890},[892,70720,70721,70748],{},[895,70722,70723,70725,70727,70729,70731,70733,70735,70737,70740,70742],{},[898,70724,2675],{},[1651,70726,1738],{},[898,70728,2047],{},[1651,70730,1654],{"stretchy":1653},[898,70732,1690],{},[1651,70734,1667],{"stretchy":1653},[1651,70736,1738],{},[1692,70738,70739],{},"1200",[1651,70741,2181],{},[2115,70743,70744,70746],{},[898,70745,1690],{},[1692,70747,1703],{},[902,70749,70750],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,70753,70755],{"className":70754},[886],[888,70756,70757],{"xmlns":890},[892,70758,70759,70765],{},[895,70760,70761,70763],{},[898,70762,4104],{},[898,70764,2998],{},[902,70766,5404],{"encoding":904},[883,70768,70770],{"className":70769},[886],[888,70771,70772],{"xmlns":890},[892,70773,70774,70780],{},[895,70775,70776,70778],{},[898,70777,5564],{},[898,70779,2998],{},[902,70781,56658],{"encoding":904},[883,70783,70785],{"className":70784},[886],[888,70786,70787],{"xmlns":890},[892,70788,70789,70795],{},[895,70790,70791,70793],{},[898,70792,2995],{},[898,70794,2998],{},[902,70796,7941],{"encoding":904},". (b) Vypočtěte ",[883,70799,70801],{"className":70800},[886],[888,70802,70803],{"xmlns":890},[892,70804,70805,70811],{},[895,70806,70807,70809],{},[898,70808,4104],{},[898,70810,2998],{},[902,70812,5404],{"encoding":904},[883,70814,70816],{"className":70815},[886],[888,70817,70818],{"xmlns":890},[892,70819,70820,70836],{},[895,70821,70822,70824,70826,70828,70830,70832,70834],{},[898,70823,1690],{},[1651,70825,1738],{},[1692,70827,4190],{},[1651,70829,1661],{"separator":1660},[1692,70831,10340],{},[1651,70833,1661],{"separator":1660},[1692,70835,39232],{},[902,70837,70838],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,70841,70843],{"className":70842},[886],[888,70844,70845],{"xmlns":890},[892,70846,70847,70853],{},[895,70848,70849,70851],{},[898,70850,4104],{},[898,70852,2998],{},[902,70854,5404],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,70857,70859],{"className":70858},[886],[888,70860,70861],{"xmlns":890},[892,70862,70863,70869],{},[895,70864,70865,70867],{},[898,70866,5564],{},[898,70868,2998],{},[902,70870,56658],{"encoding":904},[883,70872,70874],{"className":70873},[886],[888,70875,70876],{"xmlns":890},[892,70877,70878,70884],{},[895,70879,70880,70882],{},[898,70881,2995],{},[898,70883,2998],{},[902,70885,7941],{"encoding":904},[883,70887,70889],{"className":70888},[886],[888,70890,70891],{"xmlns":890},[892,70892,70893,70909],{},[895,70894,70895,70897,70899,70901,70903,70905,70907],{},[898,70896,1690],{},[1651,70898,1738],{},[1692,70900,4190],{},[1651,70902,1661],{"separator":1660},[1692,70904,10340],{},[1651,70906,1661],{"separator":1660},[1692,70908,39232],{},[902,70910,70838],{"encoding":904},[883,70912,70914],{"className":70913},[886],[888,70915,70916],{"xmlns":890},[892,70917,70918,70924],{},[895,70919,70920,70922],{},[898,70921,2995],{},[898,70923,2998],{},[902,70925,7941],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,70928,70930],{"className":70929},[886],[888,70931,70932],{"xmlns":890},[892,70933,70934,70938],{},[895,70935,70936],{},[898,70937,1690],{},[902,70939,1690],{"encoding":904},", které maximalizuje ",[883,70942,70944],{"className":70943},[886],[888,70945,70946],{"xmlns":890},[892,70947,70948,70954],{},[895,70949,70950,70952],{},[898,70951,4104],{},[898,70953,2998],{},[902,70955,5404],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,70958,70960],{"className":70959},[886],[888,70961,70962],{"xmlns":890},[892,70963,70964,70970],{},[895,70965,70966,70968],{},[898,70967,4104],{},[898,70969,2998],{},[902,70971,5404],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,70974,70976],{"className":70975},[886],[888,70977,70978],{"xmlns":890},[892,70979,70980,70984],{},[895,70981,70982],{},[898,70983,2047],{},[902,70985,2047],{"encoding":904},[883,70987,70989],{"className":70988},[886],[888,70990,70991],{"xmlns":890},[892,70992,70993,70999],{},[895,70994,70995,70997],{},[898,70996,4104],{},[898,70998,2998],{},[902,71000,5404],{"encoding":904},[883,71002,71004],{"className":71003},[886],[888,71005,71006],{"xmlns":890},[892,71007,71008,71014],{},[895,71009,71010,71012],{},[898,71011,5564],{},[898,71013,2998],{},[902,71015,56658],{"encoding":904},[883,71017,71019],{"className":71018},[886],[888,71020,71021],{"xmlns":890},[892,71022,71023,71029],{},[895,71024,71025,71027],{},[898,71026,2995],{},[898,71028,2998],{},[902,71030,7941],{"encoding":904},[724,71032,71033,71036,71037,71067,71068,71083,71084,11457,71097,1343,71115,1343,71132,71150,71151,71173,71174,71189,71190,71203,71204,1882],{},[38,71034,71035],{},"3.4"," Je dán celkový příjem ",[883,71038,71040],{"className":71039},[886],[888,71041,71042],{"xmlns":890},[892,71043,71044,71064],{},[895,71045,71046,71048,71050,71052,71054,71056,71058],{},[898,71047,4104],{},[898,71049,2998],{},[1651,71051,1738],{},[1692,71053,70739],{},[898,71055,1690],{},[1651,71057,2181],{},[2115,71059,71060,71062],{},[898,71061,1690],{},[1692,71063,3521],{},[902,71065,71066],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,71069,71071],{"className":71070},[886],[888,71072,71073],{"xmlns":890},[892,71074,71075,71081],{},[895,71076,71077,71079],{},[898,71078,4104],{},[898,71080,2998],{},[902,71082,5404],{"encoding":904}," vzhledem ke ",[883,71085,71087],{"className":71086},[886],[888,71088,71089],{"xmlns":890},[892,71090,71091,71095],{},[895,71092,71093],{},[898,71094,1690],{},[902,71096,1690],{"encoding":904},[883,71098,71100],{"className":71099},[886],[888,71101,71102],{"xmlns":890},[892,71103,71104,71112],{},[895,71105,71106,71108,71110],{},[898,71107,1690],{},[1651,71109,1738],{},[1692,71111,3574],{},[902,71113,71114],{"encoding":904},"Q = 5",[883,71116,71118],{"className":71117},[886],[888,71119,71120],{"xmlns":890},[892,71121,71122,71130],{},[895,71123,71124,71126,71128],{},[898,71125,1690],{},[1651,71127,1738],{},[1692,71129,6892],{},[902,71131,6895],{"encoding":904},[883,71133,71135],{"className":71134},[886],[888,71136,71137],{"xmlns":890},[892,71138,71139,71147],{},[895,71140,71141,71143,71145],{},[898,71142,1690],{},[1651,71144,1738],{},[1692,71146,4828],{},[902,71148,71149],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,71152,71154],{"className":71153},[886],[888,71155,71156],{"xmlns":890},[892,71157,71158,71170],{},[895,71159,71160,71162,71164,71166,71168],{},[898,71161,2995],{},[898,71163,2998],{},[1651,71165,1654],{"stretchy":1653},[1692,71167,4190],{},[1651,71169,1667],{"stretchy":1653},[902,71171,71172],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,71175,71177],{"className":71176},[886],[888,71178,71179],{"xmlns":890},[892,71180,71181,71187],{},[895,71182,71183,71185],{},[898,71184,4104],{},[898,71186,2998],{},[902,71188,5404],{"encoding":904},", jestliže se ",[883,71191,71193],{"className":71192},[886],[888,71194,71195],{"xmlns":890},[892,71196,71197,71201],{},[895,71198,71199],{},[898,71200,1690],{},[902,71202,1690],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,71205,71207],{"className":71206},[886],[888,71208,71209],{"xmlns":890},[892,71210,71211,71217],{},[895,71212,71213,71215],{},[898,71214,4104],{},[898,71216,2998],{},[902,71218,5404],{"encoding":904},[724,71220,71221,71224,71225,71251,71252,71267,71268,71189,71283,71296],{},[38,71222,71223],{},"3.5"," Je dán mezní příjem ",[883,71226,71228],{"className":71227},[886],[888,71229,71230],{"xmlns":890},[892,71231,71232,71248],{},[895,71233,71234,71236,71238,71240,71242,71244,71246],{},[898,71235,2995],{},[898,71237,2998],{},[1651,71239,1738],{},[1651,71241,2181],{},[898,71243,1690],{},[1651,71245,1839],{},[1692,71247,10340],{},[902,71249,71250],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,71253,71255],{"className":71254},[886],[888,71256,71257],{"xmlns":890},[892,71258,71259,71265],{},[895,71260,71261,71263],{},[898,71262,4104],{},[898,71264,2998],{},[902,71266,5404],{"encoding":904},". (b) Vypočtěte změnu ",[883,71269,71271],{"className":71270},[886],[888,71272,71273],{"xmlns":890},[892,71274,71275,71281],{},[895,71276,71277,71279],{},[898,71278,4104],{},[898,71280,2998],{},[902,71282,5404],{"encoding":904},[883,71284,71286],{"className":71285},[886],[888,71287,71288],{"xmlns":890},[892,71289,71290,71294],{},[895,71291,71292],{},[898,71293,1690],{},[902,71295,1690],{"encoding":904}," změní z 8 na 12.",[198,71298,71300],{"id":71299},"náklady-36316","Náklady (3.6–3.16)",[724,71302,71303,71306,71307,71347,71348,71363,71364,71381,71382,71399,71400,71415,71416,71431,71432,70797,71447,1343,71462,1343,71479,1343,71496,1343,71511,1343,71526,7780,71541,71559,71560,1343,71575,1343,71590,71605],{},[38,71304,71305],{},"3.6"," Jsou dány celkové náklady ",[883,71308,71310],{"className":71309},[886],[888,71311,71312],{"xmlns":890},[892,71313,71314,71344],{},[895,71315,71316,71318,71320,71322,71324,71326,71328,71330,71332],{},[898,71317,4104],{},[898,71319,3001],{},[1651,71321,1738],{},[1692,71323,4416],{},[1651,71325,1839],{},[1692,71327,1703],{},[898,71329,1690],{},[1651,71331,1839],{},[2938,71333,71334],{"scriptlevel":1741,"displaystyle":1653},[2446,71335,71336,71342],{},[2115,71337,71338,71340],{},[898,71339,1690],{},[1692,71341,1703],{},[1692,71343,4190],{},[902,71345,71346],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,71349,71351],{"className":71350},[886],[888,71352,71353],{"xmlns":890},[892,71354,71355,71361],{},[895,71356,71357,71359],{},[898,71358,11736],{},[898,71360,3001],{},[902,71362,56704],{"encoding":904},", celkové variabilní náklady ",[883,71365,71367],{"className":71366},[886],[888,71368,71369],{"xmlns":890},[892,71370,71371,71379],{},[895,71372,71373,71375,71377],{},[898,71374,4104],{},[898,71376,41552],{},[898,71378,3001],{},[902,71380,56722],{"encoding":904},", průměrné variabilní náklady ",[883,71383,71385],{"className":71384},[886],[888,71386,71387],{"xmlns":890},[892,71388,71389,71397],{},[895,71390,71391,71393,71395],{},[898,71392,5564],{},[898,71394,41552],{},[898,71396,3001],{},[902,71398,56524],{"encoding":904},", variabilní náklady na jednotku ",[883,71401,71403],{"className":71402},[886],[888,71404,71405],{"xmlns":890},[892,71406,71407,71413],{},[895,71408,71409,71411],{},[898,71410,41552],{},[898,71412,3001],{},[902,71414,64818],{"encoding":904},", průměrné náklady ",[883,71417,71419],{"className":71418},[886],[888,71420,71421],{"xmlns":890},[892,71422,71423,71429],{},[895,71424,71425,71427],{},[898,71426,5564],{},[898,71428,3001],{},[902,71430,56773],{"encoding":904}," a mezní náklady ",[883,71433,71435],{"className":71434},[886],[888,71436,71437],{"xmlns":890},[892,71438,71439,71445],{},[895,71440,71441,71443],{},[898,71442,2995],{},[898,71444,3001],{},[902,71446,56505],{"encoding":904},[883,71448,71450],{"className":71449},[886],[888,71451,71452],{"xmlns":890},[892,71453,71454,71460],{},[895,71455,71456,71458],{},[898,71457,4104],{},[898,71459,3001],{},[902,71461,4569],{"encoding":904},[883,71463,71465],{"className":71464},[886],[888,71466,71467],{"xmlns":890},[892,71468,71469,71477],{},[895,71470,71471,71473,71475],{},[898,71472,4104],{},[898,71474,41552],{},[898,71476,3001],{},[902,71478,56722],{"encoding":904},[883,71480,71482],{"className":71481},[886],[888,71483,71484],{"xmlns":890},[892,71485,71486,71494],{},[895,71487,71488,71490,71492],{},[898,71489,5564],{},[898,71491,41552],{},[898,71493,3001],{},[902,71495,56524],{"encoding":904},[883,71497,71499],{"className":71498},[886],[888,71500,71501],{"xmlns":890},[892,71502,71503,71509],{},[895,71504,71505,71507],{},[898,71506,41552],{},[898,71508,3001],{},[902,71510,64818],{"encoding":904},[883,71512,71514],{"className":71513},[886],[888,71515,71516],{"xmlns":890},[892,71517,71518,71524],{},[895,71519,71520,71522],{},[898,71521,5564],{},[898,71523,3001],{},[902,71525,56773],{"encoding":904},[883,71527,71529],{"className":71528},[886],[888,71530,71531],{"xmlns":890},[892,71532,71533,71539],{},[895,71534,71535,71537],{},[898,71536,2995],{},[898,71538,3001],{},[902,71540,56505],{"encoding":904},[883,71542,71544],{"className":71543},[886],[888,71545,71546],{"xmlns":890},[892,71547,71548,71556],{},[895,71549,71550,71552,71554],{},[898,71551,1690],{},[1651,71553,1738],{},[1692,71555,4446],{},[902,71557,71558],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,71561,71563],{"className":71562},[886],[888,71564,71565],{"xmlns":890},[892,71566,71567,71573],{},[895,71568,71569,71571],{},[898,71570,4104],{},[898,71572,3001],{},[902,71574,4569],{"encoding":904},[883,71576,71578],{"className":71577},[886],[888,71579,71580],{"xmlns":890},[892,71581,71582,71588],{},[895,71583,71584,71586],{},[898,71585,5564],{},[898,71587,3001],{},[902,71589,56773],{"encoding":904},[883,71591,71593],{"className":71592},[886],[888,71594,71595],{"xmlns":890},[892,71596,71597,71603],{},[895,71598,71599,71601],{},[898,71600,2995],{},[898,71602,3001],{},[902,71604,56505],{"encoding":904}," rostou, resp. klesají.",[724,71607,71608,71611,71612,71431,71642,71657,71658,71673,71674,1343,71689,1343,71704,1882],{},[38,71609,71610],{},"3.7"," Jsou dány průměrné náklady ",[883,71613,71615],{"className":71614},[886],[888,71616,71617],{"xmlns":890},[892,71618,71619,71639],{},[895,71620,71621,71623,71625,71627,71635,71637],{},[898,71622,5564],{},[898,71624,3001],{},[1651,71626,1738],{},[2938,71628,71629],{"scriptlevel":1741,"displaystyle":1653},[2446,71630,71631,71633],{},[1692,71632,4416],{},[898,71634,1690],{},[1651,71636,1839],{},[1692,71638,10340],{},[902,71640,71641],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,71643,71645],{"className":71644},[886],[888,71646,71647],{"xmlns":890},[892,71648,71649,71655],{},[895,71650,71651,71653],{},[898,71652,2995],{},[898,71654,3001],{},[902,71656,56505],{"encoding":904},". (a) Určete celkové náklady ",[883,71659,71661],{"className":71660},[886],[888,71662,71663],{"xmlns":890},[892,71664,71665,71671],{},[895,71666,71667,71669],{},[898,71668,4104],{},[898,71670,3001],{},[902,71672,4569],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,71675,71677],{"className":71676},[886],[888,71678,71679],{"xmlns":890},[892,71680,71681,71687],{},[895,71682,71683,71685],{},[898,71684,5564],{},[898,71686,3001],{},[902,71688,56773],{"encoding":904},[883,71690,71692],{"className":71691},[886],[888,71693,71694],{"xmlns":890},[892,71695,71696,71702],{},[895,71697,71698,71700],{},[898,71699,4104],{},[898,71701,3001],{},[902,71703,4569],{"encoding":904},[883,71705,71707],{"className":71706},[886],[888,71708,71709],{"xmlns":890},[892,71710,71711,71717],{},[895,71712,71713,71715],{},[898,71714,2995],{},[898,71716,3001],{},[902,71718,56505],{"encoding":904},[724,71720,71721,71306,71724,71768,71769,1343,71786,1343,71801,1343,71818,1343,71833,1343,71850,1882],{},[38,71722,71723],{},"3.8",[883,71725,71727],{"className":71726},[886],[888,71728,71729],{"xmlns":890},[892,71730,71731,71765],{},[895,71732,71733,71735,71737,71739,71741,71743,71745,71747,71749,71751,71757,71759],{},[898,71734,4104],{},[898,71736,3001],{},[1651,71738,1738],{},[1692,71740,47916],{},[1651,71742,1839],{},[1692,71744,39232],{},[898,71746,1690],{},[1651,71748,2181],{},[1692,71750,3581],{},[2115,71752,71753,71755],{},[898,71754,1690],{},[1692,71756,1703],{},[1651,71758,1839],{},[2115,71760,71761,71763],{},[898,71762,1690],{},[1692,71764,3521],{},[902,71766,71767],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,71770,71772],{"className":71771},[886],[888,71773,71774],{"xmlns":890},[892,71775,71776,71784],{},[895,71777,71778,71780,71782],{},[898,71779,4104],{},[898,71781,41552],{},[898,71783,3001],{},[902,71785,56722],{"encoding":904},[883,71787,71789],{"className":71788},[886],[888,71790,71791],{"xmlns":890},[892,71792,71793,71799],{},[895,71794,71795,71797],{},[898,71796,11736],{},[898,71798,3001],{},[902,71800,56704],{"encoding":904},[883,71802,71804],{"className":71803},[886],[888,71805,71806],{"xmlns":890},[892,71807,71808,71816],{},[895,71809,71810,71812,71814],{},[898,71811,5564],{},[898,71813,41552],{},[898,71815,3001],{},[902,71817,56524],{"encoding":904},[883,71819,71821],{"className":71820},[886],[888,71822,71823],{"xmlns":890},[892,71824,71825,71831],{},[895,71826,71827,71829],{},[898,71828,5564],{},[898,71830,3001],{},[902,71832,56773],{"encoding":904},[883,71834,71836],{"className":71835},[886],[888,71837,71838],{"xmlns":890},[892,71839,71840,71848],{},[895,71841,71842,71844,71846],{},[898,71843,5564],{},[898,71845,11736],{},[898,71847,3001],{},[902,71849,56740],{"encoding":904},[883,71851,71853],{"className":71852},[886],[888,71854,71855],{"xmlns":890},[892,71856,71857,71863],{},[895,71858,71859,71861],{},[898,71860,2995],{},[898,71862,3001],{},[902,71864,56505],{"encoding":904},[724,71866,71867,71306,71870,71900,71901,71083,71916,7780,71929,1343,71947,1343,71965,71150,71983,71173,72005,72020,72021,72034,72035,1882],{},[38,71868,71869],{},"3.9",[883,71871,71873],{"className":71872},[886],[888,71874,71875],{"xmlns":890},[892,71876,71877,71897],{},[895,71878,71879,71881,71883,71885,71887,71889,71891],{},[898,71880,4104],{},[898,71882,3001],{},[1651,71884,1738],{},[1692,71886,16408],{},[1651,71888,1839],{},[1692,71890,20534],{},[2115,71892,71893,71895],{},[898,71894,1690],{},[1692,71896,1703],{},[902,71898,71899],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,71902,71904],{"className":71903},[886],[888,71905,71906],{"xmlns":890},[892,71907,71908,71914],{},[895,71909,71910,71912],{},[898,71911,4104],{},[898,71913,3001],{},[902,71915,4569],{"encoding":904},[883,71917,71919],{"className":71918},[886],[888,71920,71921],{"xmlns":890},[892,71922,71923,71927],{},[895,71924,71925],{},[898,71926,1690],{},[902,71928,1690],{"encoding":904},[883,71930,71932],{"className":71931},[886],[888,71933,71934],{"xmlns":890},[892,71935,71936,71944],{},[895,71937,71938,71940,71942],{},[898,71939,1690],{},[1651,71941,1738],{},[1692,71943,4190],{},[902,71945,71946],{"encoding":904},"Q = 10",[883,71948,71950],{"className":71949},[886],[888,71951,71952],{"xmlns":890},[892,71953,71954,71962],{},[895,71955,71956,71958,71960],{},[898,71957,1690],{},[1651,71959,1738],{},[1692,71961,10340],{},[902,71963,71964],{"encoding":904},"Q = 20",[883,71966,71968],{"className":71967},[886],[888,71969,71970],{"xmlns":890},[892,71971,71972,71980],{},[895,71973,71974,71976,71978],{},[898,71975,1690],{},[1651,71977,1738],{},[1692,71979,39232],{},[902,71981,71982],{"encoding":904},"Q = 30",[883,71984,71986],{"className":71985},[886],[888,71987,71988],{"xmlns":890},[892,71989,71990,72002],{},[895,71991,71992,71994,71996,71998,72000],{},[898,71993,2995],{},[898,71995,3001],{},[1651,71997,1654],{"stretchy":1653},[1692,71999,37457],{},[1651,72001,1667],{"stretchy":1653},[902,72003,72004],{"encoding":904},"MC(15)",[883,72006,72008],{"className":72007},[886],[888,72009,72010],{"xmlns":890},[892,72011,72012,72018],{},[895,72013,72014,72016],{},[898,72015,4104],{},[898,72017,3001],{},[902,72019,4569],{"encoding":904}," v důsledku změny ",[883,72022,72024],{"className":72023},[886],[888,72025,72026],{"xmlns":890},[892,72027,72028,72032],{},[895,72029,72030],{},[898,72031,1690],{},[902,72033,1690],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,72036,72038],{"className":72037},[886],[888,72039,72040],{"xmlns":890},[892,72041,72042,72048],{},[895,72043,72044,72046],{},[898,72045,4104],{},[898,72047,3001],{},[902,72049,4569],{"encoding":904},[724,72051,72052,72055,72056,71657,72092,72107,72108,71267,72127,72020,72142,72155],{},[38,72053,72054],{},"3.10"," Jsou dány mezní náklady ",[883,72057,72059],{"className":72058},[886],[888,72060,72061],{"xmlns":890},[892,72062,72063,72089],{},[895,72064,72065,72067,72069,72071,72073,72075,72077,72079,72081,72083],{},[898,72066,2995],{},[898,72068,3001],{},[1651,72070,1738],{},[1692,72072,4452],{},[1651,72074,2181],{},[1692,72076,43075],{},[898,72078,1690],{},[1651,72080,1839],{},[1692,72082,65772],{},[2115,72084,72085,72087],{},[898,72086,1690],{},[1692,72088,1703],{},[902,72090,72091],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,72093,72095],{"className":72094},[886],[888,72096,72097],{"xmlns":890},[892,72098,72099,72105],{},[895,72100,72101,72103],{},[898,72102,4104],{},[898,72104,3001],{},[902,72106,4569],{"encoding":904},", jestliže fixní náklady ",[883,72109,72111],{"className":72110},[886],[888,72112,72113],{"xmlns":890},[892,72114,72115,72125],{},[895,72116,72117,72119,72121,72123],{},[898,72118,11736],{},[898,72120,3001],{},[1651,72122,1738],{},[1692,72124,4416],{},[902,72126,12931],{"encoding":904},[883,72128,72130],{"className":72129},[886],[888,72131,72132],{"xmlns":890},[892,72133,72134,72140],{},[895,72135,72136,72138],{},[898,72137,4104],{},[898,72139,3001],{},[902,72141,4569],{"encoding":904},[883,72143,72145],{"className":72144},[886],[888,72146,72147],{"xmlns":890},[892,72148,72149,72153],{},[895,72150,72151],{},[898,72152,1690],{},[902,72154,1690],{"encoding":904}," z 15 na 20.",[724,72157,72158,71306,72161,72204,72205,72218,72219,72234,72235,72250,72251,72218,72264,72234,72281,72298,72299,72218,72312,72234,72327,72342,72343,72363,72364,72387],{},[38,72159,72160],{},"3.11",[883,72162,72164],{"className":72163},[886],[888,72165,72166],{"xmlns":890},[892,72167,72168,72202],{},[895,72169,72170,72172,72174,72176,72178,72180,72182,72184,72186,72188,72194,72196],{},[898,72171,4104],{},[898,72173,3001],{},[1651,72175,1738],{},[1692,72177,4416],{},[1651,72179,1839],{},[1692,72181,6311],{},[898,72183,1690],{},[1651,72185,2181],{},[1692,72187,3574],{},[2115,72189,72190,72192],{},[898,72191,1690],{},[1692,72193,1703],{},[1651,72195,1839],{},[2115,72197,72198,72200],{},[898,72199,1690],{},[1692,72201,3521],{},[902,72203,62120],{"encoding":904},". (a) Určete ",[883,72206,72208],{"className":72207},[886],[888,72209,72210],{"xmlns":890},[892,72211,72212,72216],{},[895,72213,72214],{},[898,72215,1690],{},[902,72217,1690],{"encoding":904},", které minimalizuje ",[883,72220,72222],{"className":72221},[886],[888,72223,72224],{"xmlns":890},[892,72225,72226,72232],{},[895,72227,72228,72230],{},[898,72229,2995],{},[898,72231,3001],{},[902,72233,56505],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,72236,72238],{"className":72237},[886],[888,72239,72240],{"xmlns":890},[892,72241,72242,72248],{},[895,72243,72244,72246],{},[898,72245,2995],{},[898,72247,3001],{},[902,72249,56505],{"encoding":904},". (b) Určete ",[883,72252,72254],{"className":72253},[886],[888,72255,72256],{"xmlns":890},[892,72257,72258,72262],{},[895,72259,72260],{},[898,72261,1690],{},[902,72263,1690],{"encoding":904},[883,72265,72267],{"className":72266},[886],[888,72268,72269],{"xmlns":890},[892,72270,72271,72279],{},[895,72272,72273,72275,72277],{},[898,72274,5564],{},[898,72276,41552],{},[898,72278,3001],{},[902,72280,56524],{"encoding":904},[883,72282,72284],{"className":72283},[886],[888,72285,72286],{"xmlns":890},[892,72287,72288,72296],{},[895,72289,72290,72292,72294],{},[898,72291,5564],{},[898,72293,41552],{},[898,72295,3001],{},[902,72297,56524],{"encoding":904},". (c) Určete ",[883,72300,72302],{"className":72301},[886],[888,72303,72304],{"xmlns":890},[892,72305,72306,72310],{},[895,72307,72308],{},[898,72309,1690],{},[902,72311,1690],{"encoding":904},[883,72313,72315],{"className":72314},[886],[888,72316,72317],{"xmlns":890},[892,72318,72319,72325],{},[895,72320,72321,72323],{},[898,72322,5564],{},[898,72324,3001],{},[902,72326,56773],{"encoding":904},[883,72328,72330],{"className":72329},[886],[888,72331,72332],{"xmlns":890},[892,72333,72334,72340],{},[895,72335,72336,72338],{},[898,72337,5564],{},[898,72339,3001],{},[902,72341,56773],{"encoding":904}," (rada: hledaný kořen ",[883,72344,72346],{"className":72345},[886],[888,72347,72348],{"xmlns":890},[892,72349,72350,72360],{},[895,72351,72352,72354],{},[898,72353,5564],{},[2115,72355,72356,72358],{},[898,72357,3001],{},[1651,72359,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,72361,72362],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,72365,72367],{"className":72366},[886],[888,72368,72369],{"xmlns":890},[892,72370,72371,72384],{},[895,72372,72373,72375,72378,72380,72382],{},[1651,72374,1654],{"stretchy":1653},[1692,72376,72377],{},"4,7",[1651,72379,9731],{"separator":1660},[1692,72381,6586],{},[1651,72383,1667],{"stretchy":1653},[902,72385,72386],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,72389,72390,72393,72394,3955,72422,72439,72440,22807,72481,72502],{},[38,72391,72392],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,72395,72397],{"className":72396},[886],[888,72398,72399],{"xmlns":890},[892,72400,72401,72419],{},[895,72402,72403,72405,72407,72409,72411,72413,72415,72417],{},[898,72404,5564],{},[898,72406,3001],{},[1651,72408,1738],{},[898,72410,5564],{},[898,72412,3001],{},[1651,72414,1654],{"stretchy":1653},[898,72416,1690],{},[1651,72418,1667],{"stretchy":1653},[902,72420,72421],{"encoding":904},"AC = AC(Q)",[883,72423,72425],{"className":72424},[886],[888,72426,72427],{"xmlns":890},[892,72428,72429,72437],{},[895,72430,72431],{},[1686,72432,72433,72435],{},[898,72434,1690],{},[1692,72436,1741],{},[902,72438,39521],{"encoding":904}," minimum, pak platí ",[883,72441,72443],{"className":72442},[886],[888,72444,72445],{"xmlns":890},[892,72446,72447,72479],{},[895,72448,72449,72451,72453,72455,72461,72463,72465,72467,72469,72471,72477],{},[898,72450,5564],{},[898,72452,3001],{},[1651,72454,1654],{"stretchy":1653},[1686,72456,72457,72459],{},[898,72458,1690],{},[1692,72460,1741],{},[1651,72462,1667],{"stretchy":1653},[1651,72464,1738],{},[898,72466,2995],{},[898,72468,3001],{},[1651,72470,1654],{"stretchy":1653},[1686,72472,72473,72475],{},[898,72474,1690],{},[1692,72476,1741],{},[1651,72478,1667],{"stretchy":1653},[902,72480,63782],{"encoding":904},[883,72482,72484],{"className":72483},[886],[888,72485,72486],{"xmlns":890},[892,72487,72488,72500],{},[895,72489,72490,72492,72494,72496,72498],{},[898,72491,2995],{},[898,72493,3001],{},[1651,72495,1654],{"stretchy":1653},[898,72497,1690],{},[1651,72499,1667],{"stretchy":1653},[902,72501,68906],{"encoding":904}," jsou mezní náklady.",[724,72504,72505,71306,72508,71768,72542,72218,72555,72234,72570,1882],{},[38,72506,72507],{},"3.13",[883,72509,72511],{"className":72510},[886],[888,72512,72513],{"xmlns":890},[892,72514,72515,72539],{},[895,72516,72517,72519,72521,72523,72529,72531,72533,72535,72537],{},[898,72518,4104],{},[898,72520,3001],{},[1651,72522,1738],{},[2115,72524,72525,72527],{},[898,72526,1690],{},[1692,72528,1703],{},[1651,72530,1839],{},[1692,72532,1703],{},[898,72534,1690],{},[1651,72536,1839],{},[1692,72538,6311],{},[902,72540,72541],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,72543,72545],{"className":72544},[886],[888,72546,72547],{"xmlns":890},[892,72548,72549,72553],{},[895,72550,72551],{},[898,72552,1690],{},[902,72554,1690],{"encoding":904},[883,72556,72558],{"className":72557},[886],[888,72559,72560],{"xmlns":890},[892,72561,72562,72568],{},[895,72563,72564,72566],{},[898,72565,5564],{},[898,72567,3001],{},[902,72569,56773],{"encoding":904},[883,72571,72573],{"className":72572},[886],[888,72574,72575],{"xmlns":890},[892,72576,72577,72583],{},[895,72578,72579,72581],{},[898,72580,5564],{},[898,72582,3001],{},[902,72584,56773],{"encoding":904},[724,72586,72587,72590,72591,3955,72623,72439,72640,22807,72683,72502],{},[38,72588,72589],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,72592,72594],{"className":72593},[886],[888,72595,72596],{"xmlns":890},[892,72597,72598,72620],{},[895,72599,72600,72602,72604,72606,72608,72610,72612,72614,72616,72618],{},[898,72601,5564],{},[898,72603,41552],{},[898,72605,3001],{},[1651,72607,1738],{},[898,72609,5564],{},[898,72611,41552],{},[898,72613,3001],{},[1651,72615,1654],{"stretchy":1653},[898,72617,1690],{},[1651,72619,1667],{"stretchy":1653},[902,72621,72622],{"encoding":904},"AVC = AVC(Q)",[883,72624,72626],{"className":72625},[886],[888,72627,72628],{"xmlns":890},[892,72629,72630,72638],{},[895,72631,72632],{},[1686,72633,72634,72636],{},[898,72635,1690],{},[1692,72637,1741],{},[902,72639,39521],{"encoding":904},[883,72641,72643],{"className":72642},[886],[888,72644,72645],{"xmlns":890},[892,72646,72647,72681],{},[895,72648,72649,72651,72653,72655,72657,72663,72665,72667,72669,72671,72673,72679],{},[898,72650,5564],{},[898,72652,41552],{},[898,72654,3001],{},[1651,72656,1654],{"stretchy":1653},[1686,72658,72659,72661],{},[898,72660,1690],{},[1692,72662,1741],{},[1651,72664,1667],{"stretchy":1653},[1651,72666,1738],{},[898,72668,2995],{},[898,72670,3001],{},[1651,72672,1654],{"stretchy":1653},[1686,72674,72675,72677],{},[898,72676,1690],{},[1692,72678,1741],{},[1651,72680,1667],{"stretchy":1653},[902,72682,70232],{"encoding":904},[883,72684,72686],{"className":72685},[886],[888,72687,72688],{"xmlns":890},[892,72689,72690,72702],{},[895,72691,72692,72694,72696,72698,72700],{},[898,72693,2995],{},[898,72695,3001],{},[1651,72697,1654],{"stretchy":1653},[898,72699,1690],{},[1651,72701,1667],{"stretchy":1653},[902,72703,68906],{"encoding":904},[724,72705,72706,71306,72709,71768,72755,72218,72768,72234,72785,1882],{},[38,72707,72708],{},"3.15",[883,72710,72712],{"className":72711},[886],[888,72713,72714],{"xmlns":890},[892,72715,72716,72752],{},[895,72717,72718,72720,72722,72724,72726,72728,72730,72732,72734,72736,72742,72744,72746],{},[898,72719,4104],{},[898,72721,3001],{},[1651,72723,1738],{},[1692,72725,4446],{},[1651,72727,1839],{},[1692,72729,37457],{},[898,72731,1690],{},[1651,72733,2181],{},[1692,72735,1703],{},[2115,72737,72738,72740],{},[898,72739,1690],{},[1692,72741,1703],{},[1651,72743,1839],{},[1692,72745,4166],{},[2115,72747,72748,72750],{},[898,72749,1690],{},[1692,72751,3521],{},[902,72753,72754],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,72756,72758],{"className":72757},[886],[888,72759,72760],{"xmlns":890},[892,72761,72762,72766],{},[895,72763,72764],{},[898,72765,1690],{},[902,72767,1690],{"encoding":904},[883,72769,72771],{"className":72770},[886],[888,72772,72773],{"xmlns":890},[892,72774,72775,72783],{},[895,72776,72777,72779,72781],{},[898,72778,5564],{},[898,72780,41552],{},[898,72782,3001],{},[902,72784,56524],{"encoding":904},[883,72786,72788],{"className":72787},[886],[888,72789,72790],{"xmlns":890},[892,72791,72792,72800],{},[895,72793,72794,72796,72798],{},[898,72795,5564],{},[898,72797,41552],{},[898,72799,3001],{},[902,72801,56524],{"encoding":904},[724,72803,72804,72807,72808,72821,72822,72842],{},[38,72805,72806],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,72809,72811],{"className":72810},[886],[888,72812,72813],{"xmlns":890},[892,72814,72815,72819],{},[895,72816,72817],{},[898,72818,1657],{},[902,72820,1657],{"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 ",[883,72823,72825],{"className":72824},[886],[888,72826,72827],{"xmlns":890},[892,72828,72829,72839],{},[895,72830,72831,72833,72835,72837],{},[1692,72832,4190],{},[1843,72834,1845],{},[1692,72836,60295],{},[898,72838,1657],{},[902,72840,72841],{"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.",[198,72844,72846],{"id":72845},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,72848,72849,72852,72853,5197,72875,72901],{},[38,72850,72851],{},"3.17"," Jsou dány ",[883,72854,72856],{"className":72855},[886],[888,72857,72858],{"xmlns":890},[892,72859,72860,72872],{},[895,72861,72862,72864,72866,72868,72870],{},[898,72863,4104],{},[898,72865,2998],{},[1651,72867,1738],{},[1692,72869,4190],{},[898,72871,1690],{},[902,72873,72874],{"encoding":904},"TR = 10Q",[883,72876,72878],{"className":72877},[886],[888,72879,72880],{"xmlns":890},[892,72881,72882,72898],{},[895,72883,72884,72886,72888,72890,72892,72894,72896],{},[898,72885,4104],{},[898,72887,3001],{},[1651,72889,1738],{},[1692,72891,4416],{},[1651,72893,1839],{},[1692,72895,3574],{},[898,72897,1690],{},[902,72899,72900],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,72903,72904,72907,72908,7497,72923,72938,72939,1343,72961,22807,72988,73010,73011,73045],{},[38,72905,72906],{},"3.18"," Odvoďte, že jestliže ",[883,72909,72911],{"className":72910},[886],[888,72912,72913],{"xmlns":890},[892,72914,72915,72921],{},[895,72916,72917,72919],{},[898,72918,4104],{},[898,72920,2998],{},[902,72922,5404],{"encoding":904},[883,72924,72926],{"className":72925},[886],[888,72927,72928],{"xmlns":890},[892,72929,72930,72936],{},[895,72931,72932,72934],{},[898,72933,4104],{},[898,72935,3001],{},[902,72937,4569],{"encoding":904}," jsou lineární tvaru ",[883,72940,72942],{"className":72941},[886],[888,72943,72944],{"xmlns":890},[892,72945,72946,72958],{},[895,72947,72948,72950,72952,72954,72956],{},[898,72949,4104],{},[898,72951,2998],{},[1651,72953,1738],{},[898,72955,724],{},[898,72957,1690],{},[902,72959,72960],{"encoding":904},"TR = pQ",[883,72962,72964],{"className":72963},[886],[888,72965,72966],{"xmlns":890},[892,72967,72968,72985],{},[895,72969,72970,72972,72974,72976,72979,72981,72983],{},[898,72971,4104],{},[898,72973,3001],{},[1651,72975,1738],{},[898,72977,72978],{},"m",[1651,72980,1839],{},[898,72982,38073],{},[898,72984,1690],{},[902,72986,72987],{"encoding":904},"TC = m + nQ",[883,72989,72991],{"className":72990},[886],[888,72992,72993],{"xmlns":890},[892,72994,72995,73007],{},[895,72996,72997,72999,73001,73003,73005],{},[898,72998,72978],{},[1651,73000,1661],{"separator":1660},[898,73002,38073],{},[1651,73004,1661],{"separator":1660},[898,73006,724],{},[902,73008,73009],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,73012,73014],{"className":73013},[886],[888,73015,73016],{"xmlns":890},[892,73017,73018,73042],{},[895,73019,73020,73026,73028],{},[2115,73021,73022,73024],{},[898,73023,1690],{},[1651,73025,2668],{},[1651,73027,1738],{},[2938,73029,73030],{"scriptlevel":1741,"displaystyle":1653},[2446,73031,73032,73034],{},[898,73033,72978],{},[895,73035,73036,73038,73040],{},[898,73037,724],{},[1651,73039,2181],{},[898,73041,38073],{},[902,73043,73044],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,73047,73048,72852,73051,5197,73085,72204,73111,73124,73125,70956,73140,73155,73156,70940,73169,70956,73184,73199],{},[38,73049,73050],{},"3.19",[883,73052,73054],{"className":73053},[886],[888,73055,73056],{"xmlns":890},[892,73057,73058,73082],{},[895,73059,73060,73062,73064,73066,73068,73070,73076,73078,73080],{},[898,73061,4104],{},[898,73063,2998],{},[1651,73065,1738],{},[1651,73067,2181],{},[1692,73069,1703],{},[2115,73071,73072,73074],{},[898,73073,1690],{},[1692,73075,1703],{},[1651,73077,1839],{},[1692,73079,24159],{},[898,73081,1690],{},[902,73083,73084],{"encoding":904},"TR = -2Q^2 + 14Q",[883,73086,73088],{"className":73087},[886],[888,73089,73090],{"xmlns":890},[892,73091,73092,73108],{},[895,73093,73094,73096,73098,73100,73102,73104,73106],{},[898,73095,4104],{},[898,73097,3001],{},[1651,73099,1738],{},[1692,73101,1703],{},[898,73103,1690],{},[1651,73105,1839],{},[1692,73107,4190],{},[902,73109,73110],{"encoding":904},"TC = 2Q + 10",[883,73112,73114],{"className":73113},[886],[888,73115,73116],{"xmlns":890},[892,73117,73118,73122],{},[895,73119,73120],{},[898,73121,1690],{},[902,73123,1690],{"encoding":904},", které maximalizuje zisk ",[883,73126,73128],{"className":73127},[886],[888,73129,73130],{"xmlns":890},[892,73131,73132,73138],{},[895,73133,73134,73136],{},[898,73135,2675],{},[898,73137,2998],{},[902,73139,64692],{"encoding":904},[883,73141,73143],{"className":73142},[886],[888,73144,73145],{"xmlns":890},[892,73146,73147,73153],{},[895,73148,73149,73151],{},[898,73150,2675],{},[898,73152,2998],{},[902,73154,64692],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,73157,73159],{"className":73158},[886],[888,73160,73161],{"xmlns":890},[892,73162,73163,73167],{},[895,73164,73165],{},[898,73166,1690],{},[902,73168,1690],{"encoding":904},[883,73170,73172],{"className":73171},[886],[888,73173,73174],{"xmlns":890},[892,73175,73176,73182],{},[895,73177,73178,73180],{},[898,73179,4104],{},[898,73181,2998],{},[902,73183,5404],{"encoding":904},[883,73185,73187],{"className":73186},[886],[888,73188,73189],{"xmlns":890},[892,73190,73191,73197],{},[895,73192,73193,73195],{},[898,73194,4104],{},[898,73196,2998],{},[902,73198,5404],{"encoding":904},". (d) Graficky interpretujte.",[724,73201,73202,48897,73205,1343,73231,1343,73250,72204,73270,73124,73283,70956,73298,73313,73314,73336,73337,72387],{},[38,73203,73204],{},"3.20",[883,73206,73208],{"className":73207},[886],[888,73209,73210],{"xmlns":890},[892,73211,73212,73228],{},[895,73213,73214,73216,73218,73220,73222],{},[898,73215,2675],{},[1651,73217,1738],{},[1692,73219,21355],{},[1651,73221,2181],{},[2115,73223,73224,73226],{},[898,73225,1690],{},[1692,73227,1703],{},[902,73229,73230],{"encoding":904},"P = 400 - Q^2",[883,73232,73234],{"className":73233},[886],[888,73235,73236],{"xmlns":890},[892,73237,73238,73248],{},[895,73239,73240,73242,73244,73246],{},[898,73241,11736],{},[898,73243,3001],{},[1651,73245,1738],{},[1692,73247,4416],{},[902,73249,12931],{"encoding":904},[883,73251,73253],{"className":73252},[886],[888,73254,73255],{"xmlns":890},[892,73256,73257,73267],{},[895,73258,73259,73261,73263,73265],{},[898,73260,2995],{},[898,73262,3001],{},[1651,73264,1738],{},[1692,73266,10340],{},[902,73268,73269],{"encoding":904},"MC = 20",[883,73271,73273],{"className":73272},[886],[888,73274,73275],{"xmlns":890},[892,73276,73277,73281],{},[895,73278,73279],{},[898,73280,1690],{},[902,73282,1690],{"encoding":904},[883,73284,73286],{"className":73285},[886],[888,73287,73288],{"xmlns":890},[892,73289,73290,73296],{},[895,73291,73292,73294],{},[898,73293,2675],{},[898,73295,2998],{},[902,73297,64692],{"encoding":904},[883,73299,73301],{"className":73300},[886],[888,73302,73303],{"xmlns":890},[892,73304,73305,73311],{},[895,73306,73307,73309],{},[898,73308,2675],{},[898,73310,2998],{},[902,73312,64692],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,73315,73317],{"className":73316},[886],[888,73318,73319],{"xmlns":890},[892,73320,73321,73333],{},[895,73322,73323,73325,73327,73329,73331],{},[1651,73324,1654],{"stretchy":1653},[1692,73326,1741],{},[1651,73328,1661],{"separator":1660},[1692,73330,1694],{},[1651,73332,1667],{"stretchy":1653},[902,73334,73335],{"encoding":904},"(0, 1)",", druhý do ",[883,73338,73340],{"className":73339},[886],[888,73341,73342],{"xmlns":890},[892,73343,73344,73357],{},[895,73345,73346,73348,73351,73353,73355],{},[1651,73347,1654],{"stretchy":1653},[1692,73349,73350],{},"19",[1651,73352,1661],{"separator":1660},[1692,73354,10340],{},[1651,73356,1667],{"stretchy":1653},[902,73358,73359],{"encoding":904},"(19, 20)",[724,73361,73362,73365,73366,3955,73394,73411,73412,1882],{},[38,73363,73364],{},"3.21"," Dokažte, že má-li zisk ",[883,73367,73369],{"className":73368},[886],[888,73370,73371],{"xmlns":890},[892,73372,73373,73391],{},[895,73374,73375,73377,73379,73381,73383,73385,73387,73389],{},[898,73376,2675],{},[898,73378,2998],{},[1651,73380,1738],{},[898,73382,2675],{},[898,73384,2998],{},[1651,73386,1654],{"stretchy":1653},[898,73388,1690],{},[1651,73390,1667],{"stretchy":1653},[902,73392,73393],{"encoding":904},"PR = PR(Q)",[883,73395,73397],{"className":73396},[886],[888,73398,73399],{"xmlns":890},[892,73400,73401,73409],{},[895,73402,73403],{},[1686,73404,73405,73407],{},[898,73406,1690],{},[1692,73408,1741],{},[902,73410,39521],{"encoding":904}," maximum, pak platí ",[883,73413,73415],{"className":73414},[886],[888,73416,73417],{"xmlns":890},[892,73418,73419,73451],{},[895,73420,73421,73423,73425,73427,73433,73435,73437,73439,73441,73443,73449],{},[898,73422,2995],{},[898,73424,2998],{},[1651,73426,1654],{"stretchy":1653},[1686,73428,73429,73431],{},[898,73430,1690],{},[1692,73432,1741],{},[1651,73434,1667],{"stretchy":1653},[1651,73436,1738],{},[898,73438,2995],{},[898,73440,3001],{},[1651,73442,1654],{"stretchy":1653},[1686,73444,73445,73447],{},[898,73446,1690],{},[1692,73448,1741],{},[1651,73450,1667],{"stretchy":1653},[902,73452,66858],{"encoding":904},[724,73454,73455,73458,73459,5197,73474,57238,73489,73124,73502,73517,73518,1343,73545,73582,73583,1343,73610,1882],{},[38,73456,73457],{},"3.22"," Pro zadané ",[883,73460,73462],{"className":73461},[886],[888,73463,73464],{"xmlns":890},[892,73465,73466,73472],{},[895,73467,73468,73470],{},[898,73469,2995],{},[898,73471,2998],{},[902,73473,7941],{"encoding":904},[883,73475,73477],{"className":73476},[886],[888,73478,73479],{"xmlns":890},[892,73480,73481,73487],{},[895,73482,73483,73485],{},[898,73484,2995],{},[898,73486,3001],{},[902,73488,56505],{"encoding":904},[883,73490,73492],{"className":73491},[886],[888,73493,73494],{"xmlns":890},[892,73495,73496,73500],{},[895,73497,73498],{},[898,73499,1690],{},[902,73501,1690],{"encoding":904},[883,73503,73505],{"className":73504},[886],[888,73506,73507],{"xmlns":890},[892,73508,73509,73515],{},[895,73510,73511,73513],{},[898,73512,2675],{},[898,73514,2998],{},[902,73516,64692],{"encoding":904},". (a) ",[883,73519,73521],{"className":73520},[886],[888,73522,73523],{"xmlns":890},[892,73524,73525,73542],{},[895,73526,73527,73529,73531,73533,73536,73538,73540],{},[898,73528,2995],{},[898,73530,2998],{},[1651,73532,1738],{},[1692,73534,73535],{},"236",[1651,73537,2181],{},[1692,73539,43075],{},[898,73541,1690],{},[902,73543,73544],{"encoding":904},"MR = 236 - 16Q",[883,73546,73548],{"className":73547},[886],[888,73549,73550],{"xmlns":890},[892,73551,73552,73579],{},[895,73553,73554,73556,73558,73560,73562,73568,73570,73573,73575,73577],{},[898,73555,2995],{},[898,73557,3001],{},[1651,73559,1738],{},[1692,73561,3521],{},[2115,73563,73564,73566],{},[898,73565,1690],{},[1692,73567,1703],{},[1651,73569,2181],{},[1692,73571,73572],{},"32",[898,73574,1690],{},[1651,73576,1839],{},[1692,73578,7051],{},[902,73580,73581],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,73584,73586],{"className":73585},[886],[888,73587,73588],{"xmlns":890},[892,73589,73590,73607],{},[895,73591,73592,73594,73596,73598,73601,73603,73605],{},[898,73593,2995],{},[898,73595,2998],{},[1651,73597,1738],{},[1692,73599,73600],{},"280",[1651,73602,2181],{},[1692,73604,10340],{},[898,73606,1690],{},[902,73608,73609],{"encoding":904},"MR = 280 - 20Q",[883,73611,73613],{"className":73612},[886],[888,73614,73615],{"xmlns":890},[892,73616,73617,73644],{},[895,73618,73619,73621,73623,73625,73628,73634,73636,73638,73640,73642],{},[898,73620,2995],{},[898,73622,3001],{},[1651,73624,1738],{},[1692,73626,73627],{},"1,6",[2115,73629,73630,73632],{},[898,73631,1690],{},[1692,73633,1703],{},[1651,73635,2181],{},[1692,73637,37457],{},[898,73639,1690],{},[1651,73641,1839],{},[1692,73643,4452],{},[902,73645,73646],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,73648,73649,73458,73652,5197,73667,57238,73682,70940,73695,70956,73710,73517,73725,1343,73756,73582,73792,1343,73824,73868,73869,1343,73901,1882],{},[38,73650,73651],{},"3.23",[883,73653,73655],{"className":73654},[886],[888,73656,73657],{"xmlns":890},[892,73658,73659,73665],{},[895,73660,73661,73663],{},[898,73662,4104],{},[898,73664,2998],{},[902,73666,5404],{"encoding":904},[883,73668,73670],{"className":73669},[886],[888,73671,73672],{"xmlns":890},[892,73673,73674,73680],{},[895,73675,73676,73678],{},[898,73677,4104],{},[898,73679,3001],{},[902,73681,4569],{"encoding":904},[883,73683,73685],{"className":73684},[886],[888,73686,73687],{"xmlns":890},[892,73688,73689,73693],{},[895,73690,73691],{},[898,73692,1690],{},[902,73694,1690],{"encoding":904},[883,73696,73698],{"className":73697},[886],[888,73699,73700],{"xmlns":890},[892,73701,73702,73708],{},[895,73703,73704,73706],{},[898,73705,2675],{},[898,73707,2998],{},[902,73709,64692],{"encoding":904},[883,73711,73713],{"className":73712},[886],[888,73714,73715],{"xmlns":890},[892,73716,73717,73723],{},[895,73718,73719,73721],{},[898,73720,2675],{},[898,73722,2998],{},[902,73724,64692],{"encoding":904},[883,73726,73728],{"className":73727},[886],[888,73729,73730],{"xmlns":890},[892,73731,73732,73753],{},[895,73733,73734,73736,73738,73740,73743,73745,73747],{},[898,73735,4104],{},[898,73737,2998],{},[1651,73739,1738],{},[1692,73741,73742],{},"125",[898,73744,1690],{},[1651,73746,2181],{},[2115,73748,73749,73751],{},[898,73750,1690],{},[1692,73752,1703],{},[902,73754,73755],{"encoding":904},"TR = 125Q - Q^2",[883,73757,73759],{"className":73758},[886],[888,73760,73761],{"xmlns":890},[892,73762,73763,73789],{},[895,73764,73765,73767,73769,73771,73773,73775,73777,73779,73781,73783],{},[898,73766,4104],{},[898,73768,3001],{},[1651,73770,1738],{},[1692,73772,16408],{},[1651,73774,1839],{},[1692,73776,3574],{},[898,73778,1690],{},[1651,73780,1839],{},[1692,73782,6316],{},[2115,73784,73785,73787],{},[898,73786,1690],{},[1692,73788,1703],{},[902,73790,73791],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,73793,73795],{"className":73794},[886],[888,73796,73797],{"xmlns":890},[892,73798,73799,73821],{},[895,73800,73801,73803,73805,73807,73809,73811,73813,73815],{},[898,73802,4104],{},[898,73804,2998],{},[1651,73806,1738],{},[1692,73808,10340],{},[898,73810,1690],{},[1651,73812,2181],{},[1692,73814,1703],{},[2115,73816,73817,73819],{},[898,73818,1690],{},[1692,73820,1703],{},[902,73822,73823],{"encoding":904},"TR = 20Q - 2Q^2",[883,73825,73827],{"className":73826},[886],[888,73828,73829],{"xmlns":890},[892,73830,73831,73865],{},[895,73832,73833,73835,73837,73839,73841,73843,73845,73847,73849,73851,73857,73859],{},[898,73834,4104],{},[898,73836,3001],{},[1651,73838,1738],{},[1692,73840,1703],{},[1651,73842,1839],{},[1692,73844,10340],{},[898,73846,1690],{},[1651,73848,2181],{},[1692,73850,6892],{},[2115,73852,73853,73855],{},[898,73854,1690],{},[1692,73856,1703],{},[1651,73858,1839],{},[2115,73860,73861,73863],{},[898,73862,1690],{},[1692,73864,3521],{},[902,73866,73867],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,73870,73872],{"className":73871},[886],[888,73873,73874],{"xmlns":890},[892,73875,73876,73898],{},[895,73877,73878,73880,73882,73884,73886,73888,73890,73892],{},[898,73879,4104],{},[898,73881,2998],{},[1651,73883,1738],{},[1692,73885,3689],{},[898,73887,1690],{},[1651,73889,2181],{},[1692,73891,25002],{},[2115,73893,73894,73896],{},[898,73895,1690],{},[1692,73897,1703],{},[902,73899,73900],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,73902,73904],{"className":73903},[886],[888,73905,73906],{"xmlns":890},[892,73907,73908,73956],{},[895,73909,73910,73912,73914,73916,73918,73920,73922,73924,73926,73942,73944],{},[898,73911,4104],{},[898,73913,3001],{},[1651,73915,1738],{},[1692,73917,3689],{},[1651,73919,1839],{},[1692,73921,1703],{},[898,73923,1690],{},[1651,73925,2181],{},[2938,73927,73928],{"scriptlevel":1741,"displaystyle":1653},[2446,73929,73930,73940],{},[895,73931,73932,73934],{},[1692,73933,3521],{},[2115,73935,73936,73938],{},[898,73937,1690],{},[1692,73939,1703],{},[1692,73941,4190],{},[1651,73943,1839],{},[2938,73945,73946],{"scriptlevel":1741,"displaystyle":1653},[2446,73947,73948,73954],{},[2115,73949,73950,73952],{},[898,73951,1690],{},[1692,73953,3521],{},[1692,73955,10340],{},[902,73957,73958],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,73960,73961,73964,73965,73995,73996,74028,74029,22807,74059,74089],{},[38,73962,73963],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,73966,73968],{"className":73967},[886],[888,73969,73970],{"xmlns":890},[892,73971,73972,73992],{},[895,73973,73974,73980,73982,73984,73986],{},[1686,73975,73976,73978],{},[898,73977,2675],{},[1692,73979,1694],{},[1651,73981,1738],{},[1692,73983,16408],{},[1651,73985,2181],{},[1686,73987,73988,73990],{},[898,73989,1690],{},[1692,73991,1694],{},[902,73993,73994],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,73997,73999],{"className":73998},[886],[888,74000,74001],{"xmlns":890},[892,74002,74003,74025],{},[895,74004,74005,74011,74013,74015,74017,74019],{},[1686,74006,74007,74009],{},[898,74008,2675],{},[1692,74010,1703],{},[1651,74012,1738],{},[1692,74014,31294],{},[1651,74016,2181],{},[1692,74018,65772],{},[1686,74020,74021,74023],{},[898,74022,1690],{},[1692,74024,1703],{},[902,74026,74027],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,74030,74032],{"className":74031},[886],[888,74033,74034],{"xmlns":890},[892,74035,74036,74056],{},[895,74037,74038,74040,74042,74044,74046,74048,74050,74052,74054],{},[898,74039,4104],{},[898,74041,3001],{},[1651,74043,1738],{},[1692,74045,4446],{},[1843,74047,1845],{},[1692,74049,60295],{},[1651,74051,1839],{},[1692,74053,10340],{},[898,74055,1690],{},[902,74057,74058],{"encoding":904},"TC = 50\\,000 + 20Q",[883,74060,74062],{"className":74061},[886],[888,74063,74064],{"xmlns":890},[892,74065,74066,74086],{},[895,74067,74068,74070,74072,74078,74080],{},[898,74069,1690],{},[1651,74071,1738],{},[1686,74073,74074,74076],{},[898,74075,1690],{},[1692,74077,1694],{},[1651,74079,1839],{},[1686,74081,74082,74084],{},[898,74083,1690],{},[1692,74085,1703],{},[902,74087,74088],{"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.",[724,74091,74092,74095,74096,74126,74127,74028,74159,22807,74189,74218],{},[38,74093,74094],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,74097,74099],{"className":74098},[886],[888,74100,74101],{"xmlns":890},[892,74102,74103,74123],{},[895,74104,74105,74111,74113,74115,74117],{},[1686,74106,74107,74109],{},[898,74108,2675],{},[1692,74110,1694],{},[1651,74112,1738],{},[1692,74114,31294],{},[1651,74116,2181],{},[1686,74118,74119,74121],{},[898,74120,1690],{},[1692,74122,1694],{},[902,74124,74125],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,74128,74130],{"className":74129},[886],[888,74131,74132],{"xmlns":890},[892,74133,74134,74156],{},[895,74135,74136,74142,74144,74146,74148,74150],{},[1686,74137,74138,74140],{},[898,74139,2675],{},[1692,74141,1703],{},[1651,74143,1738],{},[1692,74145,9683],{},[1651,74147,2181],{},[1692,74149,6316],{},[1686,74151,74152,74154],{},[898,74153,1690],{},[1692,74155,1703],{},[902,74157,74158],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,74160,74162],{"className":74161},[886],[888,74163,74164],{"xmlns":890},[892,74165,74166,74186],{},[895,74167,74168,74170,74172,74174,74176,74178,74180,74182,74184],{},[898,74169,4104],{},[898,74171,3001],{},[1651,74173,1738],{},[1692,74175,3574],{},[1843,74177,1845],{},[1692,74179,60295],{},[1651,74181,1839],{},[1692,74183,4416],{},[898,74185,1690],{},[902,74187,74188],{"encoding":904},"TC = 5\\,000 + 100Q",[883,74190,74192],{"className":74191},[886],[888,74193,74194],{"xmlns":890},[892,74195,74196,74216],{},[895,74197,74198,74200,74202,74208,74210],{},[898,74199,1690],{},[1651,74201,1738],{},[1686,74203,74204,74206],{},[898,74205,1690],{},[1692,74207,1694],{},[1651,74209,1839],{},[1686,74211,74212,74214],{},[898,74213,1690],{},[1692,74215,1703],{},[902,74217,74088],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,74220,74222],{"id":74221},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,74224,74225,74228,74229,74276,74277,74294],{},[38,74226,74227],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,74230,74232],{"className":74231},[886],[888,74233,74234],{"xmlns":890},[892,74235,74236,74273],{},[895,74237,74238,74240,74242,74244,74246,74249,74255,74257,74260,74266,74268,74271],{},[898,74239,4104],{},[898,74241,41552],{},[898,74243,3001],{},[1651,74245,1738],{},[1692,74247,74248],{},"0,85",[2115,74250,74251,74253],{},[898,74252,1690],{},[1692,74254,3521],{},[1651,74256,2181],{},[1692,74258,74259],{},"11,9",[2115,74261,74262,74264],{},[898,74263,1690],{},[1692,74265,1703],{},[1651,74267,1839],{},[1692,74269,74270],{},"102",[898,74272,1690],{},[902,74274,74275],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,74278,74280],{"className":74279},[886],[888,74281,74282],{"xmlns":890},[892,74283,74284,74292],{},[895,74285,74286],{},[2115,74287,74288,74290],{},[898,74289,2675],{},[1651,74291,2668],{},[902,74293,5711],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,74296,74297,72055,74300,74336],{},[38,74298,74299],{},"3.27",[883,74301,74303],{"className":74302},[886],[888,74304,74305],{"xmlns":890},[892,74306,74307,74333],{},[895,74308,74309,74311,74313,74315,74317,74323,74325,74327,74329,74331],{},[898,74310,2995],{},[898,74312,3001],{},[1651,74314,1738],{},[1692,74316,4250],{},[2115,74318,74319,74321],{},[898,74320,1690],{},[1692,74322,1703],{},[1651,74324,2181],{},[1692,74326,65653],{},[898,74328,1690],{},[1651,74330,1839],{},[1692,74332,31956],{},[902,74334,74335],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,74338,74339,71306,74342,74336],{},[38,74340,74341],{},"3.28",[883,74343,74345],{"className":74344},[886],[888,74346,74347],{"xmlns":890},[892,74348,74349,74385],{},[895,74350,74351,74353,74355,74357,74359,74365,74367,74369,74375,74377,74379,74381,74383],{},[898,74352,4104],{},[898,74354,3001],{},[1651,74356,1738],{},[1692,74358,6316],{},[2115,74360,74361,74363],{},[898,74362,1690],{},[1692,74364,3521],{},[1651,74366,2181],{},[1692,74368,25414],{},[2115,74370,74371,74373],{},[898,74372,1690],{},[1692,74374,1703],{},[1651,74376,1839],{},[1692,74378,4452],{},[898,74380,1690],{},[1651,74382,1839],{},[1692,74384,16408],{},[902,74386,74387],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,74389,17018],{"id":17017},[120,74391,74392,74420,74465,74537,74602,74642,74734,74840,74880,74994,75087,75151,75183,75243,75249,75313,75362,75416,75524,75579],{},[123,74393,74394,3246,74396,74419],{},[38,74395,56963],{},[883,74397,74399],{"className":74398},[886],[888,74400,74401],{"xmlns":890},[892,74402,74403,74417],{},[895,74404,74405,74407,74409,74411,74413,74415],{},[898,74406,4104],{},[898,74408,2998],{},[1651,74410,1738],{},[898,74412,2675],{},[1651,74414,4503],{},[898,74416,1690],{},[902,74418,67925],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,74421,74422,3246,74424,74464],{},[38,74423,57549],{},[883,74425,74427],{"className":74426},[886],[888,74428,74429],{"xmlns":890},[892,74430,74431,74461],{},[895,74432,74433,74435,74437,74439,74451,74453,74455,74457,74459],{},[898,74434,5564],{},[898,74436,2998],{},[1651,74438,1738],{},[2938,74440,74441],{"scriptlevel":1741,"displaystyle":1653},[2446,74442,74443,74449],{},[895,74444,74445,74447],{},[898,74446,4104],{},[898,74448,2998],{},[898,74450,1690],{},[1651,74452,1738],{},[898,74454,2047],{},[1651,74456,1654],{"stretchy":1653},[898,74458,1690],{},[1651,74460,1667],{"stretchy":1653},[902,74462,74463],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,74466,74467,3246,74469,74505,74506,74521,74522,1882],{},[38,74468,57697],{},[883,74470,74472],{"className":74471},[886],[888,74473,74474],{"xmlns":890},[892,74475,74476,74502],{},[895,74477,74478,74480,74482,74484],{},[898,74479,2995],{},[898,74481,2998],{},[1651,74483,1738],{},[2938,74485,74486],{"scriptlevel":1741,"displaystyle":1653},[2446,74487,74488,74496],{},[895,74489,74490,74492,74494],{},[898,74491,3542],{"mathvariant":1910},[898,74493,4104],{},[898,74495,2998],{},[895,74497,74498,74500],{},[898,74499,3542],{"mathvariant":1910},[898,74501,1690],{},[902,74503,74504],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,74507,74509],{"className":74508},[886],[888,74510,74511],{"xmlns":890},[892,74512,74513,74519],{},[895,74514,74515,74517],{},[898,74516,4104],{},[898,74518,2998],{},[902,74520,5404],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,74523,74525],{"className":74524},[886],[888,74526,74527],{"xmlns":890},[892,74528,74529,74535],{},[895,74530,74531,74533],{},[898,74532,5564],{},[898,74534,2998],{},[902,74536,56658],{"encoding":904},[123,74538,74539,3246,74542,1343,74572,1882],{},[38,74540,74541],{},"Diferenciál příjmu\u002Fnákladů",[883,74543,74545],{"className":74544},[886],[888,74546,74547],{"xmlns":890},[892,74548,74549,74569],{},[895,74550,74551,74553,74555,74557,74559,74561,74563,74565,74567],{},[898,74552,4216],{"mathvariant":1910},[898,74554,4104],{},[898,74556,2998],{},[1651,74558,4060],{},[898,74560,2995],{},[898,74562,2998],{},[1843,74564,1845],{},[898,74566,3542],{"mathvariant":1910},[898,74568,1690],{},[902,74570,74571],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,74573,74575],{"className":74574},[886],[888,74576,74577],{"xmlns":890},[892,74578,74579,74599],{},[895,74580,74581,74583,74585,74587,74589,74591,74593,74595,74597],{},[898,74582,4216],{"mathvariant":1910},[898,74584,4104],{},[898,74586,3001],{},[1651,74588,4060],{},[898,74590,2995],{},[898,74592,3001],{},[1843,74594,1845],{},[898,74596,3542],{"mathvariant":1910},[898,74598,1690],{},[902,74600,74601],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,74603,74604,3246,74606,1882],{},[38,74605,59819],{},[883,74607,74609],{"className":74608},[886],[888,74610,74611],{"xmlns":890},[892,74612,74613,74639],{},[895,74614,74615,74617,74619,74621,74623,74625,74627,74629,74631,74633,74635,74637],{},[898,74616,4104],{},[898,74618,3001],{},[1651,74620,1738],{},[898,74622,11736],{},[898,74624,3001],{},[1651,74626,1839],{},[898,74628,4104],{},[898,74630,41552],{},[898,74632,3001],{},[1651,74634,1654],{"stretchy":1653},[898,74636,1690],{},[1651,74638,1667],{"stretchy":1653},[902,74640,74641],{"encoding":904},"TC = FC + TVC(Q)",[123,74643,74644,3246,74647,1343,74662,3246,74664,1343,74687,3246,74690,1882],{},[38,74645,74646],{},"Fixní náklady",[883,74648,74650],{"className":74649},[886],[888,74651,74652],{"xmlns":890},[892,74653,74654,74660],{},[895,74655,74656,74658],{},[898,74657,11736],{},[898,74659,3001],{},[902,74661,56704],{"encoding":904},[38,74663,59972],{},[883,74665,74667],{"className":74666},[886],[888,74668,74669],{"xmlns":890},[892,74670,74671,74685],{},[895,74672,74673,74675,74677,74679,74681,74683],{},[898,74674,4104],{},[898,74676,41552],{},[898,74678,3001],{},[1651,74680,1654],{"stretchy":1653},[898,74682,1690],{},[1651,74684,1667],{"stretchy":1653},[902,74686,59969],{"encoding":904},[38,74688,74689],{},"variabilní náklady na jednotku",[883,74691,74693],{"className":74692},[886],[888,74694,74695],{"xmlns":890},[892,74696,74697,74731],{},[895,74698,74699,74701,74703,74705,74707,74709,74711],{},[898,74700,41552],{},[898,74702,3001],{},[1651,74704,1654],{"stretchy":1653},[898,74706,1690],{},[1651,74708,1667],{"stretchy":1653},[1651,74710,1738],{},[2938,74712,74713],{"scriptlevel":1741,"displaystyle":1653},[2446,74714,74715,74729],{},[895,74716,74717,74719,74721,74723,74725,74727],{},[898,74718,4104],{},[898,74720,41552],{},[898,74722,3001],{},[1651,74724,1654],{"stretchy":1653},[898,74726,1690],{},[1651,74728,1667],{"stretchy":1653},[898,74730,1690],{},[902,74732,74733],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,74735,74736,3246,74738,1343,74768,3246,74771,1343,74803,3246,74806,1882],{},[38,74737,59980],{},[883,74739,74741],{"className":74740},[886],[888,74742,74743],{"xmlns":890},[892,74744,74745,74765],{},[895,74746,74747,74749,74751,74753],{},[898,74748,5564],{},[898,74750,3001],{},[1651,74752,1738],{},[2938,74754,74755],{"scriptlevel":1741,"displaystyle":1653},[2446,74756,74757,74763],{},[895,74758,74759,74761],{},[898,74760,4104],{},[898,74762,3001],{},[898,74764,1690],{},[902,74766,74767],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,74769,74770],{},"průměrné fixní",[883,74772,74774],{"className":74773},[886],[888,74775,74776],{"xmlns":890},[892,74777,74778,74800],{},[895,74779,74780,74782,74784,74786,74788],{},[898,74781,5564],{},[898,74783,11736],{},[898,74785,3001],{},[1651,74787,1738],{},[2938,74789,74790],{"scriptlevel":1741,"displaystyle":1653},[2446,74791,74792,74798],{},[895,74793,74794,74796],{},[898,74795,11736],{},[898,74797,3001],{},[898,74799,1690],{},[902,74801,74802],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,74804,74805],{},"průměrné variabilní",[883,74807,74809],{"className":74808},[886],[888,74810,74811],{"xmlns":890},[892,74812,74813,74837],{},[895,74814,74815,74817,74819,74821,74823],{},[898,74816,5564],{},[898,74818,41552],{},[898,74820,3001],{},[1651,74822,1738],{},[2938,74824,74825],{"scriptlevel":1741,"displaystyle":1653},[2446,74826,74827,74835],{},[895,74828,74829,74831,74833],{},[898,74830,4104],{},[898,74832,41552],{},[898,74834,3001],{},[898,74836,1690],{},[902,74838,74839],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,74841,74842,3246,74844,1882],{},[38,74843,61167],{},[883,74845,74847],{"className":74846},[886],[888,74848,74849],{"xmlns":890},[892,74850,74851,74877],{},[895,74852,74853,74855,74857,74859],{},[898,74854,2995],{},[898,74856,3001],{},[1651,74858,1738],{},[2938,74860,74861],{"scriptlevel":1741,"displaystyle":1653},[2446,74862,74863,74871],{},[895,74864,74865,74867,74869],{},[898,74866,3542],{"mathvariant":1910},[898,74868,4104],{},[898,74870,3001],{},[895,74872,74873,74875],{},[898,74874,3542],{"mathvariant":1910},[898,74876,1690],{},[902,74878,74879],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,74881,74882,3246,74884,74932,74933,74946,74947,1343,74962,1343,74979,1882],{},[38,74883,62065],{},[883,74885,74887],{"className":74886},[886],[888,74888,74889],{"xmlns":890},[892,74890,74891,74929],{},[895,74892,74893,74895,74897,74899,74901,74903,74905,74907,74909,74911,74913,74919,74921,74923],{},[898,74894,4104],{},[898,74896,3001],{},[1651,74898,1738],{},[898,74900,11736],{},[898,74902,3001],{},[1651,74904,1839],{},[898,74906,207],{},[898,74908,1690],{},[1651,74910,1839],{},[898,74912,2268],{},[2115,74914,74915,74917],{},[898,74916,1690],{},[1692,74918,1703],{},[1651,74920,1839],{},[898,74922,3490],{},[2115,74924,74925,74927],{},[898,74926,1690],{},[1692,74928,3521],{},[902,74930,74931],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,74934,74936],{"className":74935},[886],[888,74937,74938],{"xmlns":890},[892,74939,74940,74944],{},[895,74941,74942],{},[898,74943,900],{},[902,74945,900],{"encoding":904},"-průběhem ",[883,74948,74950],{"className":74949},[886],[888,74951,74952],{"xmlns":890},[892,74953,74954,74960],{},[895,74955,74956,74958],{},[898,74957,5564],{},[898,74959,3001],{},[902,74961,56773],{"encoding":904},[883,74963,74965],{"className":74964},[886],[888,74966,74967],{"xmlns":890},[892,74968,74969,74977],{},[895,74970,74971,74973,74975],{},[898,74972,5564],{},[898,74974,41552],{},[898,74976,3001],{},[902,74978,56524],{"encoding":904},[883,74980,74982],{"className":74981},[886],[888,74983,74984],{"xmlns":890},[892,74985,74986,74992],{},[895,74987,74988,74990],{},[898,74989,2995],{},[898,74991,3001],{},[902,74993,56505],{"encoding":904},[123,74995,74996,74998,74999,11694,75014,75055,75056,62710,75071,75086],{},[38,74997,63147],{},": v bodě minima ",[883,75000,75002],{"className":75001},[886],[888,75003,75004],{"xmlns":890},[892,75005,75006,75012],{},[895,75007,75008,75010],{},[898,75009,5564],{},[898,75011,3001],{},[902,75013,56773],{"encoding":904},[883,75015,75017],{"className":75016},[886],[888,75018,75019],{"xmlns":890},[892,75020,75021,75053],{},[895,75022,75023,75025,75027,75029,75035,75037,75039,75041,75043,75045,75051],{},[898,75024,5564],{},[898,75026,3001],{},[1651,75028,1654],{"stretchy":1653},[1686,75030,75031,75033],{},[898,75032,1690],{},[1692,75034,1741],{},[1651,75036,1667],{"stretchy":1653},[1651,75038,1738],{},[898,75040,2995],{},[898,75042,3001],{},[1651,75044,1654],{"stretchy":1653},[1686,75046,75047,75049],{},[898,75048,1690],{},[1692,75050,1741],{},[1651,75052,1667],{"stretchy":1653},[902,75054,63782],{"encoding":904},"; geometricky ",[883,75057,75059],{"className":75058},[886],[888,75060,75061],{"xmlns":890},[892,75062,75063,75069],{},[895,75064,75065,75067],{},[898,75066,2995],{},[898,75068,3001],{},[902,75070,56505],{"encoding":904},[883,75072,75074],{"className":75073},[886],[888,75075,75076],{"xmlns":890},[892,75077,75078,75084],{},[895,75079,75080,75082],{},[898,75081,5564],{},[898,75083,3001],{},[902,75085,56773],{"encoding":904}," v jejím minimu.",[123,75088,75089,74998,75091,11694,75108,1882],{},[38,75090,64497],{},[883,75092,75094],{"className":75093},[886],[888,75095,75096],{"xmlns":890},[892,75097,75098,75106],{},[895,75099,75100,75102,75104],{},[898,75101,5564],{},[898,75103,41552],{},[898,75105,3001],{},[902,75107,56524],{"encoding":904},[883,75109,75111],{"className":75110},[886],[888,75112,75113],{"xmlns":890},[892,75114,75115,75149],{},[895,75116,75117,75119,75121,75123,75125,75131,75133,75135,75137,75139,75141,75147],{},[898,75118,5564],{},[898,75120,41552],{},[898,75122,3001],{},[1651,75124,1654],{"stretchy":1653},[1686,75126,75127,75129],{},[898,75128,1690],{},[1692,75130,1741],{},[1651,75132,1667],{"stretchy":1653},[1651,75134,1738],{},[898,75136,2995],{},[898,75138,3001],{},[1651,75140,1654],{"stretchy":1653},[1686,75142,75143,75145],{},[898,75144,1690],{},[1692,75146,1741],{},[1651,75148,1667],{"stretchy":1653},[902,75150,70232],{"encoding":904},[123,75152,75153,3246,75155,75182],{},[38,75154,64676],{},[883,75156,75158],{"className":75157},[886],[888,75159,75160],{"xmlns":890},[892,75161,75162,75180],{},[895,75163,75164,75166,75168,75170,75172,75174,75176,75178],{},[898,75165,2675],{},[898,75167,2998],{},[1651,75169,1738],{},[898,75171,4104],{},[898,75173,2998],{},[1651,75175,2181],{},[898,75177,4104],{},[898,75179,3001],{},[902,75181,56413],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,75184,75185,11325,75187,75189,75190,75216,75217,75242],{},[38,75186,65538],{},[614,75188,64801],{},") — hodnoty ",[883,75191,75193],{"className":75192},[886],[888,75194,75195],{"xmlns":890},[892,75196,75197,75213],{},[895,75198,75199,75205,75207],{},[1686,75200,75201,75203],{},[898,75202,1690],{},[898,75204,5564],{},[1651,75206,1661],{"separator":1660},[1686,75208,75209,75211],{},[898,75210,1690],{},[898,75212,24466],{},[902,75214,75215],{"encoding":904},"Q_A, Q_B"," splňující ",[883,75218,75220],{"className":75219},[886],[888,75221,75222],{"xmlns":890},[892,75223,75224,75240],{},[895,75225,75226,75228,75230,75232,75234,75236,75238],{},[898,75227,2675],{},[898,75229,2998],{},[1651,75231,1654],{"stretchy":1653},[898,75233,1690],{},[1651,75235,1667],{"stretchy":1653},[1651,75237,1738],{},[1692,75239,1741],{},[902,75241,65078],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,75244,75245,75248],{},[38,75246,75247],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,75250,75251,75253,75254,11694,75271,75312],{},[38,75252,66592],{}," — v bodě maxima zisku ",[883,75255,75257],{"className":75256},[886],[888,75258,75259],{"xmlns":890},[892,75260,75261,75269],{},[895,75262,75263],{},[1686,75264,75265,75267],{},[898,75266,1690],{},[1692,75268,1741],{},[902,75270,39521],{"encoding":904},[883,75272,75274],{"className":75273},[886],[888,75275,75276],{"xmlns":890},[892,75277,75278,75310],{},[895,75279,75280,75282,75284,75286,75292,75294,75296,75298,75300,75302,75308],{},[898,75281,2995],{},[898,75283,2998],{},[1651,75285,1654],{"stretchy":1653},[1686,75287,75288,75290],{},[898,75289,1690],{},[1692,75291,1741],{},[1651,75293,1667],{"stretchy":1653},[1651,75295,1738],{},[898,75297,2995],{},[898,75299,3001],{},[1651,75301,1654],{"stretchy":1653},[1686,75303,75304,75306],{},[898,75305,1690],{},[1692,75307,1741],{},[1651,75309,1667],{"stretchy":1653},[902,75311,66858],{"encoding":904}," (3.13).",[123,75314,75315,21514,75317,11694,75336,75361],{},[38,75316,67885],{},[883,75318,75320],{"className":75319},[886],[888,75321,75322],{"xmlns":890},[892,75323,75324,75333],{},[895,75325,75326,75328,75330],{},[898,75327,2675],{},[1651,75329,1738],{},[1843,75331,75332],{},"konst",[902,75334,75335],{"encoding":904},"P = \\text{konst}",[883,75337,75339],{"className":75338},[886],[888,75340,75341],{"xmlns":890},[892,75342,75343,75359],{},[895,75344,75345,75347,75349,75351,75353,75355,75357],{},[898,75346,2675],{},[1651,75348,1738],{},[898,75350,2995],{},[898,75352,3001],{},[1651,75354,1654],{"stretchy":1653},[898,75356,1690],{},[1651,75358,1667],{"stretchy":1653},[902,75360,68579],{"encoding":904}," (3.14).",[123,75363,75364,75367,75368,75397,75398,75415],{},[38,75365,75366],{},"Shutdown point"," — bod ",[883,75369,75371],{"className":75370},[886],[888,75372,75373],{"xmlns":890},[892,75374,75375,75395],{},[895,75376,75377,75379,75385,75387,75393],{},[1651,75378,1654],{"stretchy":1653},[2115,75380,75381,75383],{},[898,75382,1690],{},[1651,75384,2668],{},[1651,75386,1661],{"separator":1660},[2115,75388,75389,75391],{},[898,75390,2675],{},[1651,75392,2668],{},[1651,75394,1667],{"stretchy":1653},[902,75396,68868],{"encoding":904}," v minimu ",[883,75399,75401],{"className":75400},[886],[888,75402,75403],{"xmlns":890},[892,75404,75405,75413],{},[895,75406,75407,75409,75411],{},[898,75408,5564],{},[898,75410,41552],{},[898,75412,3001],{},[902,75414,56524],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,75417,75418,3246,75421,7780,75456,69138,75477,75490,75491,75506,75507,1882],{},[38,75419,75420],{},"Funkce nabídky firmy",[883,75422,75424],{"className":75423},[886],[888,75425,75426],{"xmlns":890},[892,75427,75428,75454],{},[895,75429,75430,75432,75434,75436,75438,75440,75442,75444,75446,75448,75450,75452],{},[898,75431,2675],{},[1651,75433,1738],{},[898,75435,3004],{},[1651,75437,1654],{"stretchy":1653},[898,75439,1690],{},[1651,75441,1667],{"stretchy":1653},[1651,75443,1738],{},[898,75445,2995],{},[898,75447,3001],{},[1651,75449,1654],{"stretchy":1653},[898,75451,1690],{},[1651,75453,1667],{"stretchy":1653},[902,75455,70335],{"encoding":904},[883,75457,75459],{"className":75458},[886],[888,75460,75461],{"xmlns":890},[892,75462,75463,75475],{},[895,75464,75465,75467,75469],{},[898,75466,1690],{},[1651,75468,5792],{},[2115,75470,75471,75473],{},[898,75472,1690],{},[1651,75474,2668],{},[902,75476,69137],{"encoding":904},[883,75478,75480],{"className":75479},[886],[888,75481,75482],{"xmlns":890},[892,75483,75484,75488],{},[895,75485,75486],{},[1692,75487,1741],{},[902,75489,1741],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,75492,75494],{"className":75493},[886],[888,75495,75496],{"xmlns":890},[892,75497,75498,75504],{},[895,75499,75500,75502],{},[898,75501,2995],{},[898,75503,3001],{},[902,75505,56505],{"encoding":904}," nad minimem ",[883,75508,75510],{"className":75509},[886],[888,75511,75512],{"xmlns":890},[892,75513,75514,75522],{},[895,75515,75516,75518,75520],{},[898,75517,5564],{},[898,75519,41552],{},[898,75521,3001],{},[902,75523,56524],{"encoding":904},[123,75525,75526,8322,75528,75549,75550,1882],{},[38,75527,51292],{},[883,75529,75531],{"className":75530},[886],[888,75532,75533],{"xmlns":890},[892,75534,75535,75547],{},[895,75536,75537,75539,75541],{},[898,75538,2675],{},[1651,75540,1738],{},[2115,75542,75543,75545],{},[898,75544,2675],{},[1651,75546,2668],{},[902,75548,5664],{"encoding":904}," konstantní ⇒ ",[883,75551,75553],{"className":75552},[886],[888,75554,75555],{"xmlns":890},[892,75556,75557,75577],{},[895,75558,75559,75561,75563,75565,75567,75569,75571],{},[898,75560,5564],{},[898,75562,2998],{},[1651,75564,1738],{},[898,75566,2995],{},[898,75568,2998],{},[1651,75570,1738],{},[2115,75572,75573,75575],{},[898,75574,2675],{},[1651,75576,2668],{},[902,75578,59811],{"encoding":904},[123,75580,75581,75584],{},[38,75582,75583],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,75586,3238],{"id":3237},[120,75588,75589,75608,75620],{},[123,75590,75591,3246,75593,1343,75596,1343,75599,1343,75602,1343,75605],{},[38,75592,51936],{},[207,75594,3258],{"className":75595,"dataFsResolvedFilePath":800,"href":801},[210],[207,75597,5140],{"className":75598,"dataFsResolvedFilePath":848,"href":849},[210],[207,75600,3695],{"className":75601,"dataFsResolvedFilePath":764,"href":765},[210],[207,75603,775],{"className":75604,"dataFsResolvedFilePath":773,"href":774},[210],[207,75606,859],{"className":75607,"dataFsResolvedFilePath":857,"href":858},[210],[123,75609,75610,3246,75612,1343,75616],{},[38,75611,37916],{},[207,75613,75615],{"className":75614,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,75617,75619],{"className":75618,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,75621,75622,3246,75624],{},[38,75623,17502],{},[207,75625,17506],{"className":75626,"dataFsResolvedFilePath":1749,"href":1750},[210],{"title":641,"searchDepth":642,"depth":642,"links":75628},[75629,75630,75637,75643,75647,75648,75652,75653,75654,75655,75661,75662],{"id":52167,"depth":642,"text":1241},{"id":56951,"depth":642,"text":56952,"children":75631},[75632,75633,75634,75635,75636],{"id":56962,"depth":649,"text":56963},{"id":57548,"depth":649,"text":57549},{"id":57696,"depth":649,"text":57697},{"id":58438,"depth":649,"text":58439},{"id":59093,"depth":649,"text":59094},{"id":59814,"depth":642,"text":59815,"children":75638},[75639,75640,75641,75642],{"id":59818,"depth":649,"text":59819},{"id":59979,"depth":649,"text":59980},{"id":61166,"depth":649,"text":61167},{"id":62064,"depth":649,"text":62065},{"id":63146,"depth":642,"text":63147,"children":75644},[75645,75646],{"id":1785,"depth":649,"text":1786},{"id":64496,"depth":649,"text":64497},{"id":64670,"depth":642,"text":64671},{"id":66591,"depth":642,"text":66592,"children":75649},[75650,75651],{"id":66605,"depth":649,"text":1786},{"id":67884,"depth":649,"text":67885},{"id":68516,"depth":642,"text":68517},{"id":69982,"depth":642,"text":69983},{"id":51094,"depth":642,"text":51095},{"id":70443,"depth":642,"text":70444,"children":75656},[75657,75658,75659,75660],{"id":70447,"depth":649,"text":70448},{"id":71299,"depth":649,"text":71300},{"id":72845,"depth":649,"text":72846},{"id":74221,"depth":649,"text":74222},{"id":17017,"depth":642,"text":17018},{"id":3237,"depth":642,"text":3238},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":56333,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,75669,75670,56385,75671,75672,75673],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":75676,"title":75677,"body":75678,"course":1128,"courses":659,"created":10859,"description":641,"extension":661,"meta":87775,"navigation":664,"path":87776,"seo":87777,"sources":87778,"stem":87779,"tags":87780,"type":3302,"updated":677,"__hash__":87786},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":75679,"toc":87732},[75680,75683,76039,76043,76046,76114,76166,76176,76180,76214,76255,76279,76302,76331,76398,76505,76548,76605,76680,76725,76729,76737,76745,76748,77013,77064,77144,77214,77237,77265,77310,77332,77336,77343,77392,77418,77569,77572,77609,77772,77880,77884,77921,77996,78065,78184,78306,78387,78393,78434,78507,78600,78604,78640,78728,78842,78947,79032,79172,79176,79224,79269,79275,79279,79282,79333,79383,79390,79456,79589,79634,79638,79659,80038,80133,80150,80204,80208,80290,80374,80544,80547,80590,80657,80731,80735,80740,80809,80817,80826,80904,80970,80975,81070,81113,81118,81166,81171,81219,81337,81420,81458,81561,81620,81761,81765,81808,81881,81905,81959,81966,81968,82013,82058,82069,82074,82110,82172,82195,82204,82305,82372,82445,82452,82543,82605,82641,82698,82757,82942,83038,83042,83046,83125,83130,83254,83340,83346,83456,83493,83584,83682,83685,83689,83755,83792,83914,83966,83970,83998,84050,84124,84229,84253,84312,84316,84334,84477,84625,84627,84662,84666,84668,84758,84888,85014,85106,85181,85185,85301,85405,85595,85631,85725,85731,85844,86147,86153,86271,86370,86446,86448,87610,87612],[12,75681,75677],{"id":75682},"produkce-produkční-funkce-cobb-douglas-mrts",[5179,75684,75685],{},[724,75686,75687,5186,75689,75691,75692,38109,75705,75718,75719,1745,75732,11325,75734,75758,75759,3246,75761,5197,75795,3246,75798,75826,75827,11694,75847,75877,75878,11325,75881,75909,75910,75913,75914,75944,75945,75975,75976,3246,75979,76019,76020,76038],{},[883,75688,5185],{},[38,75690,859],{}," popisuje vztah mezi vstupy (práce ",[883,75693,75695],{"className":75694},[886],[888,75696,75697],{"xmlns":890},[892,75698,75699,75703],{},[895,75700,75701],{},[898,75702,1807],{},[902,75704,1807],{"encoding":904},[883,75706,75708],{"className":75707},[886],[888,75709,75710],{"xmlns":890},[892,75711,75712,75716],{},[895,75713,75714],{},[898,75715,11101],{},[902,75717,11101],{"encoding":904},") a výstupem ",[883,75720,75722],{"className":75721},[886],[888,75723,75724],{"xmlns":890},[892,75725,75726,75730],{},[895,75727,75728],{},[898,75729,1690],{},[902,75731,1690],{"encoding":904},[38,75733,38177],{},[883,75735,75737],{"className":75736},[886],[888,75738,75739],{"xmlns":890},[892,75740,75741,75755],{},[895,75742,75743,75745,75747,75749,75751,75753],{},[898,75744,1690],{},[1651,75746,1738],{},[898,75748,1690],{},[1651,75750,1654],{"stretchy":1653},[898,75752,1807],{},[1651,75754,1667],{"stretchy":1653},[902,75756,75757],{"encoding":904},"Q = Q(L)",") studujeme ",[614,75760,11324],{},[883,75762,75764],{"className":75763},[886],[888,75765,75766],{"xmlns":890},[892,75767,75768,75792],{},[895,75769,75770,75772,75778,75780,75786,75788,75790],{},[898,75771,2995],{},[1686,75773,75774,75776],{},[898,75775,2675],{},[898,75777,1807],{},[1651,75779,1738],{},[2115,75781,75782,75784],{},[898,75783,1690],{},[1651,75785,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,75787,1654],{"stretchy":1653},[898,75789,1807],{},[1651,75791,1667],{"stretchy":1653},[902,75793,75794],{"encoding":904},"MP_L = Q'(L)",[614,75796,75797],{},"průměrný produkt",[883,75799,75801],{"className":75800},[886],[888,75802,75803],{"xmlns":890},[892,75804,75805,75823],{},[895,75806,75807,75809,75815,75817,75819,75821],{},[898,75808,5564],{},[1686,75810,75811,75813],{},[898,75812,2675],{},[898,75814,1807],{},[1651,75816,1738],{},[898,75818,1690],{},[898,75820,5981],{"mathvariant":1910},[898,75822,1807],{},[902,75824,75825],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,75828,75830],{"className":75829},[886],[888,75831,75832],{"xmlns":890},[892,75833,75834,75844],{},[895,75835,75836,75838],{},[898,75837,5564],{},[1686,75839,75840,75842],{},[898,75841,2675],{},[898,75843,1807],{},[902,75845,75846],{"encoding":904},"AP_L",[883,75848,75850],{"className":75849},[886],[888,75851,75852],{"xmlns":890},[892,75853,75854,75874],{},[895,75855,75856,75858,75864,75866,75868],{},[898,75857,2995],{},[1686,75859,75860,75862],{},[898,75861,2675],{},[898,75863,1807],{},[1651,75865,1738],{},[898,75867,5564],{},[1686,75869,75870,75872],{},[898,75871,2675],{},[898,75873,1807],{},[902,75875,75876],{"encoding":904},"MP_L = AP_L",". Ve ",[38,75879,75880],{},"dvoufaktorovém modelu",[883,75882,75884],{"className":75883},[886],[888,75885,75886],{"xmlns":890},[892,75887,75888,75906],{},[895,75889,75890,75892,75894,75896,75898,75900,75902,75904],{},[898,75891,1690],{},[1651,75893,1738],{},[898,75895,1690],{},[1651,75897,1654],{"stretchy":1653},[898,75899,1807],{},[1651,75901,1661],{"separator":1660},[898,75903,11101],{},[1651,75905,1667],{"stretchy":1653},[902,75907,75908],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,75911,75912],{},"Cobb-Douglasovy"," funkce ",[883,75915,75917],{"className":75916},[886],[888,75918,75919],{"xmlns":890},[892,75920,75921,75941],{},[895,75922,75923,75925,75927,75929,75935],{},[898,75924,1690],{},[1651,75926,1738],{},[898,75928,5564],{},[2115,75930,75931,75933],{},[898,75932,1807],{},[898,75934,207],{},[2115,75936,75937,75939],{},[898,75938,11101],{},[898,75940,2268],{},[902,75942,75943],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,75946,75948],{"className":75947},[886],[888,75949,75950],{"xmlns":890},[892,75951,75952,75972],{},[895,75953,75954,75956,75962,75964,75966],{},[898,75955,2995],{},[1686,75957,75958,75960],{},[898,75959,2675],{},[898,75961,1807],{},[1651,75963,1661],{"separator":1660},[898,75965,2995],{},[1686,75967,75968,75970],{},[898,75969,2675],{},[898,75971,11101],{},[902,75973,75974],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,75977,75978],{},"mezní míru technické substituce",[883,75980,75982],{"className":75981},[886],[888,75983,75984],{"xmlns":890},[892,75985,75986,76016],{},[895,75987,75988,75990,75992,75994,75996,75998,76000,76006,76008,76010],{},[898,75989,2995],{},[898,75991,2998],{},[898,75993,4104],{},[898,75995,3004],{},[1651,75997,1738],{},[898,75999,2995],{},[1686,76001,76002,76004],{},[898,76003,2675],{},[898,76005,1807],{},[898,76007,5981],{"mathvariant":1910},[898,76009,2995],{},[1686,76011,76012,76014],{},[898,76013,2675],{},[898,76015,11101],{},[902,76017,76018],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,76021,76023],{"className":76022},[886],[888,76024,76025],{"xmlns":890},[892,76026,76027,76035],{},[895,76028,76029,76031,76033],{},[898,76030,207],{},[1651,76032,1839],{},[898,76034,2268],{},[902,76036,76037],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,76040,76042],{"id":76041},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,76044,76045],{},"Po prostudování kapitoly 5 student umí:",[120,76047,76048,76054,76064,76070,76076,76081,76087,76097,76102,76108],{},[123,76049,76050,76051,1661],{},"popsat ",[38,76052,76053],{},"jednofaktorový model produkce",[123,76055,76056,76057,5197,76060,76063],{},"vypočítat ",[38,76058,76059],{},"mezní",[38,76061,76062],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,76065,76066,76067,1661],{},"charakterizovat průběh ",[38,76068,76069],{},"křivky produkce",[123,76071,76072,76073,1661],{},"formulovat ",[38,76074,76075],{},"princip maximalizace průměrného produktu práce",[123,76077,76050,76078,1661],{},[38,76079,76080],{},"dvoufaktorový model produkce",[123,76082,76083,76084,1661],{},"uvést tvar ",[38,76085,76086],{},"Cobb–Douglasových produkčních funkcí",[123,76088,76089,76090,1343,76092,1343,76094,1661],{},"vyložit, co jsou ",[38,76091,25826],{},[38,76093,14955],{},[38,76095,76096],{},"klesající výnosy z rozsahu",[123,76098,76056,76099,76063],{},[38,76100,76101],{},"mezní produkty práce a kapitálu",[123,76103,76104,76105,1661],{},"najít ",[38,76106,76107],{},"izokvanty",[123,76109,76056,76110,76113],{},[38,76111,76112],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,76115,76116,76117,76120,76121,76124,76125,3246,76128,1343,76141,3246,76144,5197,76157,76160,76161,76163,76164,1882],{},"Každý proces produkce je určován ",[38,76118,76119],{},"faktory"," (též ",[38,76122,76123],{},"vstupy",") produkce. K hlavním patří ",[38,76126,76127],{},"práce",[883,76129,76131],{"className":76130},[886],[888,76132,76133],{"xmlns":890},[892,76134,76135,76139],{},[895,76136,76137],{},[898,76138,1807],{},[902,76140,1807],{"encoding":904},[38,76142,76143],{},"kapitál",[883,76145,76147],{"className":76146},[886],[888,76148,76149],{"xmlns":890},[892,76150,76151,76155],{},[895,76152,76153],{},[898,76154,11101],{},[902,76156,11101],{"encoding":904},[38,76158,76159],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,76162,38177],{}," (produkce závisí jen na práci); v opačném případě o ",[38,76165,75880],{},[724,76167,76168,76169,1343,76172,76175],{},"Související matematický aparát: ",[207,76170,3695],{"className":76171,"dataFsResolvedFilePath":764,"href":765},[210],[207,76173,784],{"className":76174,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,76177,76179],{"id":76178},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,76181,76182,76183,76196,76197,76210,76211],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,76184,76186],{"className":76185},[886],[888,76187,76188],{"xmlns":890},[892,76189,76190,76194],{},[895,76191,76192],{},[898,76193,1690],{},[902,76195,1690],{"encoding":904}," na práci ",[883,76198,76200],{"className":76199},[886],[888,76201,76202],{"xmlns":890},[892,76203,76204,76208],{},[895,76205,76206],{},[898,76207,1807],{},[902,76209,1807],{"encoding":904}," vyjadřuje ",[38,76212,76213],{},"produkční funkce",[883,76215,76217],{"className":76216},[886],[888,76218,76219],{"xmlns":890,"display":29279},[892,76220,76221,76252],{},[21967,76222,76223],{"width":29284},[21972,76224,76225,76227,76245,76247],{},[21975,76226],{"width":29289},[21975,76228,76229],{},[895,76230,76231,76233,76235,76237,76239,76241,76243],{},[898,76232,1690],{},[1651,76234,1738],{},[898,76236,1690],{},[1651,76238,1654],{"stretchy":1653},[898,76240,1807],{},[1651,76242,1667],{"stretchy":1653},[1651,76244,1661],{"separator":1660},[21975,76246],{"width":29289},[21975,76248,76249],{},[1843,76250,76251],{},"(5.1)",[902,76253,76254],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,76256,76257,76258,11325,76261,76264,76265,76278],{},"jejíž graf se nazývá ",[38,76259,76260],{},"křivka produkce",[614,76262,76263],{},"production curve","). Práce ",[883,76266,76268],{"className":76267},[886],[888,76269,76270],{"xmlns":890},[892,76271,76272,76276],{},[895,76273,76274],{},[898,76275,1807],{},[902,76277,1807],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,76280,76282,76283,1667],{"id":76281},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,76284,76286],{"className":76285},[886],[888,76287,76288],{"xmlns":890},[892,76289,76290,76300],{},[895,76291,76292,76294],{},[898,76293,2995],{},[1686,76295,76296,76298],{},[898,76297,2675],{},[898,76299,1807],{},[902,76301,11345],{"encoding":904},[724,76303,76304,11325,76307,76310,76311,76330],{},[38,76305,76306],{},"Mezní produkt práce",[614,76308,76309],{},"marginal product of labour",") ",[883,76312,76314],{"className":76313},[886],[888,76315,76316],{"xmlns":890},[892,76317,76318,76328],{},[895,76319,76320,76322],{},[898,76321,2995],{},[1686,76323,76324,76326],{},[898,76325,2675],{},[898,76327,1807],{},[902,76329,11345],{"encoding":904}," je derivace produkce podle práce:",[883,76332,76334],{"className":76333},[886],[888,76335,76336],{"xmlns":890,"display":29279},[892,76337,76338,76395],{},[21967,76339,76340],{"width":29284},[21972,76341,76342,76344,76388,76390],{},[21975,76343],{"width":29289},[21975,76345,76346],{},[895,76347,76348,76350,76356,76358,76372,76374,76380,76382,76384,76386],{},[898,76349,2995],{},[1686,76351,76352,76354],{},[898,76353,2675],{},[898,76355,1807],{},[1651,76357,1738],{},[2446,76359,76360,76366],{},[895,76361,76362,76364],{},[898,76363,3542],{},[898,76365,1690],{},[895,76367,76368,76370],{},[898,76369,3542],{},[898,76371,1807],{},[1651,76373,1738],{},[2115,76375,76376,76378],{},[898,76377,1690],{},[1651,76379,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,76381,1654],{"stretchy":1653},[898,76383,1807],{},[1651,76385,1667],{"stretchy":1653},[898,76387,1882],{"mathvariant":1910},[21975,76389],{"width":29289},[21975,76391,76392],{},[1843,76393,76394],{},"(5.2)",[902,76396,76397],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,76399,76400,76401,21158,76419,76447,76448,76465,76466,4016,76483,5230],{},"Pro pevnou hodnotu ",[883,76402,76404],{"className":76403},[886],[888,76405,76406],{"xmlns":890},[892,76407,76408,76416],{},[895,76409,76410],{},[2115,76411,76412,76414],{},[898,76413,1807],{},[1651,76415,2668],{},[902,76417,76418],{"encoding":904},"L^*",[883,76420,76422],{"className":76421},[886],[888,76423,76424],{"xmlns":890},[892,76425,76426,76444],{},[895,76427,76428,76434,76436,76442],{},[2115,76429,76430,76432],{},[898,76431,1690],{},[1651,76433,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,76435,1654],{"stretchy":1653},[2115,76437,76438,76440],{},[898,76439,1807],{},[1651,76441,2668],{},[1651,76443,1667],{"stretchy":1653},[902,76445,76446],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,76449,76451],{"className":76450},[886],[888,76452,76453],{"xmlns":890},[892,76454,76455,76463],{},[895,76456,76457],{},[2115,76458,76459,76461],{},[898,76460,1807],{},[1651,76462,2668],{},[902,76464,76418],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,76467,76469],{"className":76468},[886],[888,76470,76471],{"xmlns":890},[892,76472,76473,76481],{},[895,76474,76475],{},[2115,76476,76477,76479],{},[898,76478,1807],{},[1651,76480,2668],{},[902,76482,76418],{"encoding":904},[883,76484,76486],{"className":76485},[886],[888,76487,76488],{"xmlns":890},[892,76489,76490,76502],{},[895,76491,76492,76498,76500],{},[2115,76493,76494,76496],{},[898,76495,1807],{},[1651,76497,2668],{},[1651,76499,1839],{},[1692,76501,1694],{},[902,76503,76504],{"encoding":904},"L^*+1",[5179,76506,76507],{},[724,76508,76509,19236,76511,76530,76531,76534,76535,1882],{},[883,76510,5465],{},[883,76512,76514],{"className":76513},[886],[888,76515,76516],{"xmlns":890},[892,76517,76518,76528],{},[895,76519,76520,76522],{},[898,76521,2995],{},[1686,76523,76524,76526],{},[898,76525,2675],{},[898,76527,1807],{},[902,76529,11345],{"encoding":904}," odpovídá na otázku „",[38,76532,76533],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,76536,76538],{"className":76537},[886],[888,76539,76540],{"xmlns":890},[892,76541,76542,76546],{},[895,76543,76544],{},[898,76545,1807],{},[902,76547,1807],{"encoding":904},[724,76549,76550,76553,76554,76570,76571,4016,76584,76604],{},[38,76551,76552],{},"Přibližná změna produkce"," pro změnu práce o ",[883,76555,76557],{"className":76556},[886],[888,76558,76559],{"xmlns":890},[892,76560,76561,76567],{},[895,76562,76563,76565],{},[898,76564,3542],{},[898,76566,1807],{},[902,76568,76569],{"encoding":904},"dL"," (z ",[883,76572,76574],{"className":76573},[886],[888,76575,76576],{"xmlns":890},[892,76577,76578,76582],{},[895,76579,76580],{},[898,76581,1807],{},[902,76583,1807],{"encoding":904},[883,76585,76587],{"className":76586},[886],[888,76588,76589],{"xmlns":890},[892,76590,76591,76601],{},[895,76592,76593,76595,76597,76599],{},[898,76594,1807],{},[1651,76596,1839],{},[898,76598,3542],{},[898,76600,1807],{},[902,76602,76603],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,76606,76608],{"className":76607},[886],[888,76609,76610],{"xmlns":890,"display":29279},[892,76611,76612,76677],{},[21967,76613,76614],{"width":29284},[21972,76615,76616,76618,76670,76672],{},[21975,76617],{"width":29289},[21975,76619,76620],{},[895,76621,76622,76624,76626,76628,76630,76632,76634,76640,76642,76644,76646,76648,76650,76652,76654,76656,76662,76664,76666,76668],{},[898,76623,4216],{"mathvariant":1910},[898,76625,1690],{},[1651,76627,4060],{},[898,76629,3542],{},[898,76631,1690],{},[1651,76633,1738],{},[2115,76635,76636,76638],{},[898,76637,1690],{},[1651,76639,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,76641,1654],{"stretchy":1653},[898,76643,1807],{},[1651,76645,1667],{"stretchy":1653},[1843,76647,1845],{},[898,76649,3542],{},[898,76651,1807],{},[1651,76653,1738],{},[898,76655,2995],{},[1686,76657,76658,76660],{},[898,76659,2675],{},[898,76661,1807],{},[1843,76663,1845],{},[898,76665,3542],{},[898,76667,1807],{},[898,76669,1882],{"mathvariant":1910},[21975,76671],{"width":29289},[21975,76673,76674],{},[1843,76675,76676],{},"(5.3)",[902,76678,76679],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,76681,76682,76683,1882],{},"Skutečná změna je ",[883,76684,76686],{"className":76685},[886],[888,76687,76688],{"xmlns":890},[892,76689,76690,76722],{},[895,76691,76692,76694,76696,76698,76700,76702,76704,76706,76708,76710,76712,76714,76716,76718,76720],{},[898,76693,4216],{"mathvariant":1910},[898,76695,1690],{},[1651,76697,1738],{},[898,76699,1690],{},[1651,76701,1654],{"stretchy":1653},[898,76703,1807],{},[1651,76705,1839],{},[898,76707,3542],{},[898,76709,1807],{},[1651,76711,1667],{"stretchy":1653},[1651,76713,2181],{},[898,76715,1690],{},[1651,76717,1654],{"stretchy":1653},[898,76719,1807],{},[1651,76721,1667],{"stretchy":1653},[902,76723,76724],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,76726,76728],{"id":76727},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,76730,76731,11325,76734,4477],{},[38,76732,76733],{},"Zákon klesajících výnosů",[614,76735,76736],{},"law of diminishing marginal productivity",[5179,76738,76739],{},[724,76740,76741,76742,76744],{},"Roste-li postupně některý ze vstupů (",[614,76743,38173],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,76746,76747],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,76749,76750,76751,3246,76772,76791,76792,76842,76843,76845,76846,3246,76866,76885,76886,76842,76918,4254,76920,76939,76940,22807,76957,76991,76992,1878,77009,77012],{},"1° ",[38,76752,76753,76754,1793],{},"Do bodu ",[883,76755,76757],{"className":76756},[886],[888,76758,76759],{"xmlns":890},[892,76760,76761,76769],{},[895,76762,76763],{},[1686,76764,76765,76767],{},[898,76766,1807],{},[1692,76768,1741],{},[902,76770,76771],{"encoding":904},"L_0",[883,76773,76775],{"className":76774},[886],[888,76776,76777],{"xmlns":890},[892,76778,76779,76789],{},[895,76780,76781,76783],{},[898,76782,2995],{},[1686,76784,76785,76787],{},[898,76786,2675],{},[898,76788,1807],{},[902,76790,11345],{"encoding":904}," roste, tj. ",[883,76793,76795],{"className":76794},[886],[888,76796,76797],{"xmlns":890},[892,76798,76799,76839],{},[895,76800,76801,76803,76805,76811,76817,76819,76829,76831,76833,76835,76837],{},[1651,76802,1654],{"stretchy":1653},[898,76804,2995],{},[1686,76806,76807,76809],{},[898,76808,2675],{},[898,76810,1807],{},[2115,76812,76813,76815],{},[1651,76814,1667],{"stretchy":1653},[1651,76816,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,76818,1738],{},[2115,76820,76821,76823],{},[898,76822,1690],{},[895,76824,76825,76827],{},[1651,76826,1912],{"mathvariant":1910},[1651,76828,1912],{"mathvariant":1910},[1651,76830,1654],{"stretchy":1653},[898,76832,1807],{},[1651,76834,1667],{"stretchy":1653},[1651,76836,2390],{},[1692,76838,1741],{},[902,76840,76841],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,76844,38877],{},".\n2° ",[38,76847,76848,76849,1793],{},"Od bodu ",[883,76850,76852],{"className":76851},[886],[888,76853,76854],{"xmlns":890},[892,76855,76856,76864],{},[895,76857,76858],{},[1686,76859,76860,76862],{},[898,76861,1807],{},[1692,76863,1741],{},[902,76865,76771],{"encoding":904},[883,76867,76869],{"className":76868},[886],[888,76870,76871],{"xmlns":890},[892,76872,76873,76883],{},[895,76874,76875,76877],{},[898,76876,2995],{},[1686,76878,76879,76881],{},[898,76880,2675],{},[898,76882,1807],{},[902,76884,11345],{"encoding":904}," klesá, ",[883,76887,76889],{"className":76888},[886],[888,76890,76891],{"xmlns":890},[892,76892,76893,76915],{},[895,76894,76895,76905,76907,76909,76911,76913],{},[2115,76896,76897,76899],{},[898,76898,1690],{},[895,76900,76901,76903],{},[1651,76902,1912],{"mathvariant":1910},[1651,76904,1912],{"mathvariant":1910},[1651,76906,1654],{"stretchy":1653},[898,76908,1807],{},[1651,76910,1667],{"stretchy":1653},[1651,76912,2319],{},[1692,76914,1741],{},[902,76916,76917],{"encoding":904},"Q''(L) \u003C 0",[38,76919,39701],{},[883,76921,76923],{"className":76922},[886],[888,76924,76925],{"xmlns":890},[892,76926,76927,76937],{},[895,76928,76929,76931],{},[898,76930,2995],{},[1686,76932,76933,76935],{},[898,76934,2675],{},[898,76936,1807],{},[902,76938,11345],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,76941,76943],{"className":76942},[886],[888,76944,76945],{"xmlns":890},[892,76946,76947,76955],{},[895,76948,76949],{},[1686,76950,76951,76953],{},[898,76952,1807],{},[1692,76954,1694],{},[902,76956,14510],{"encoding":904},[883,76958,76960],{"className":76959},[886],[888,76961,76962],{"xmlns":890},[892,76963,76964,76988],{},[895,76965,76966,76968,76974,76976,76982,76984,76986],{},[898,76967,2995],{},[1686,76969,76970,76972],{},[898,76971,2675],{},[898,76973,1807],{},[1651,76975,1654],{"stretchy":1653},[1686,76977,76978,76980],{},[898,76979,1807],{},[1692,76981,1694],{},[1651,76983,1667],{"stretchy":1653},[1651,76985,1738],{},[1692,76987,1741],{},[902,76989,76990],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,76993,76995],{"className":76994},[886],[888,76996,76997],{"xmlns":890},[892,76998,76999,77007],{},[895,77000,77001],{},[1686,77002,77003,77005],{},[898,77004,1807],{},[1692,77006,1741],{},[902,77008,76771],{"encoding":904},[38,77010,77011],{},"inflexním bodem"," produkční funkce.",[724,77014,77015,77016,11694,77033,1882],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,77017,77019],{"className":77018},[886],[888,77020,77021],{"xmlns":890},[892,77022,77023,77031],{},[895,77024,77025],{},[1686,77026,77027,77029],{},[898,77028,1807],{},[1692,77030,1741],{},[902,77032,76771],{"encoding":904},[883,77034,77036],{"className":77035},[886],[888,77037,77038],{"xmlns":890},[892,77039,77040,77062],{},[895,77041,77042,77052,77054,77056,77058,77060],{},[2115,77043,77044,77046],{},[898,77045,1690],{},[895,77047,77048,77050],{},[1651,77049,1912],{"mathvariant":1910},[1651,77051,1912],{"mathvariant":1910},[1651,77053,1654],{"stretchy":1653},[898,77055,1807],{},[1651,77057,1667],{"stretchy":1653},[1651,77059,2319],{},[1692,77061,1741],{},[902,77063,76917],{"encoding":904},[724,77065,77066,3246,77069,6976,77109,1343,77126,77143],{},[38,77067,77068],{},"Typický polynom třetího stupně:",[883,77070,77072],{"className":77071},[886],[888,77073,77074],{"xmlns":890},[892,77075,77076,77106],{},[895,77077,77078,77080,77082,77084,77086,77088,77090,77096,77098,77100],{},[898,77079,1690],{},[1651,77081,1654],{"stretchy":1653},[898,77083,1807],{},[1651,77085,1667],{"stretchy":1653},[1651,77087,1738],{},[898,77089,207],{},[2115,77091,77092,77094],{},[898,77093,1807],{},[1692,77095,3521],{},[1651,77097,1839],{},[898,77099,2268],{},[2115,77101,77102,77104],{},[898,77103,1807],{},[1692,77105,1703],{},[902,77107,77108],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,77110,77112],{"className":77111},[886],[888,77113,77114],{"xmlns":890},[892,77115,77116,77124],{},[895,77117,77118,77120,77122],{},[898,77119,207],{},[1651,77121,2319],{},[1692,77123,1741],{},[902,77125,44298],{"encoding":904},[883,77127,77129],{"className":77128},[886],[888,77130,77131],{"xmlns":890},[892,77132,77133,77141],{},[895,77134,77135,77137,77139],{},[898,77136,2268],{},[1651,77138,2390],{},[1692,77140,1741],{},[902,77142,20027],{"encoding":904},". Pak",[883,77145,77147],{"className":77146},[886],[888,77148,77149],{"xmlns":890,"display":29279},[892,77150,77151,77211],{},[895,77152,77153,77159,77161,77163,77171,77179,77181,77183,77189,77191,77193,77201,77209],{},[1686,77154,77155,77157],{},[898,77156,1807],{},[1692,77158,1741],{},[1651,77160,1738],{},[1651,77162,2181],{},[2938,77164,77165],{"scriptlevel":1741,"displaystyle":1653},[2446,77166,77167,77169],{},[1692,77168,1694],{},[1692,77170,3521],{},[2938,77172,77173],{"scriptlevel":1741,"displaystyle":1653},[2446,77174,77175,77177],{},[898,77176,2268],{},[898,77178,207],{},[1651,77180,1661],{"separator":1660},[7185,77182],{"width":7187},[1686,77184,77185,77187],{},[898,77186,1807],{},[1692,77188,1694],{},[1651,77190,1738],{},[1651,77192,2181],{},[2938,77194,77195],{"scriptlevel":1741,"displaystyle":1653},[2446,77196,77197,77199],{},[1692,77198,1703],{},[1692,77200,3521],{},[2938,77202,77203],{"scriptlevel":1741,"displaystyle":1653},[2446,77204,77205,77207],{},[898,77206,2268],{},[898,77208,207],{},[898,77210,1882],{"mathvariant":1910},[902,77212,77213],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,77215,77217,77218,1667],{"id":77216},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,77219,77221],{"className":77220},[886],[888,77222,77223],{"xmlns":890},[892,77224,77225,77235],{},[895,77226,77227,77229],{},[898,77228,5564],{},[1686,77230,77231,77233],{},[898,77232,2675],{},[898,77234,1807],{},[902,77236,75846],{"encoding":904},[724,77238,77239,11325,77242,76310,77245,77264],{},[38,77240,77241],{},"Průměrný produkt práce",[614,77243,77244],{},"average product of labour",[883,77246,77248],{"className":77247},[886],[888,77249,77250],{"xmlns":890},[892,77251,77252,77262],{},[895,77253,77254,77256],{},[898,77255,5564],{},[1686,77257,77258,77260],{},[898,77259,2675],{},[898,77261,1807],{},[902,77263,75846],{"encoding":904}," je podíl produkce a práce:",[883,77266,77268],{"className":77267},[886],[888,77269,77270],{"xmlns":890,"display":29279},[892,77271,77272,77307],{},[21967,77273,77274],{"width":29284},[21972,77275,77276,77278,77300,77302],{},[21975,77277],{"width":29289},[21975,77279,77280],{},[895,77281,77282,77284,77290,77292,77298],{},[898,77283,5564],{},[1686,77285,77286,77288],{},[898,77287,2675],{},[898,77289,1807],{},[1651,77291,1738],{},[2446,77293,77294,77296],{},[898,77295,1690],{},[898,77297,1807],{},[898,77299,1882],{"mathvariant":1910},[21975,77301],{"width":29289},[21975,77303,77304],{},[1843,77305,77306],{},"(5.4)",[902,77308,77309],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,77311,77312,77313,1882],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,77314,77316],{"className":77315},[886],[888,77317,77318],{"xmlns":890},[892,77319,77320,77330],{},[895,77321,77322,77324],{},[898,77323,5564],{},[1686,77325,77326,77328],{},[898,77327,2675],{},[898,77329,1807],{},[902,77331,75846],{"encoding":904},[115,77333,77335],{"id":77334},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,77337,77338],{},[1756,77339],{"alt":77340,"className":77341,"src":77342},"imek-q-mpl-apl-tripanel",[210,1760],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[5179,77344,77345],{},[724,77346,77347,77350,77351,3955,77370,77387,77388],{},[38,77348,77349],{},"Princip:"," Má-li ",[883,77352,77354],{"className":77353},[886],[888,77355,77356],{"xmlns":890},[892,77357,77358,77368],{},[895,77359,77360,77362],{},[898,77361,5564],{},[1686,77363,77364,77366],{},[898,77365,2675],{},[898,77367,1807],{},[902,77369,75846],{"encoding":904},[883,77371,77373],{"className":77372},[886],[888,77374,77375],{"xmlns":890},[892,77376,77377,77385],{},[895,77378,77379],{},[1686,77380,77381,77383],{},[898,77382,1807],{},[1692,77384,1741],{},[902,77386,76771],{"encoding":904}," maximum, pak platí\n",[883,77389,77391],{"className":77390,"title":5509,"style":5510},[5508],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,77393,77394,77395,77398,77399,3246,77403,1882],{},"Slovně: ",[38,77396,77397],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,77400,77402],{"className":77401,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,77404,77406],{"className":77405},[886],[888,77407,77408],{"xmlns":890},[892,77409,77410,77416],{},[895,77411,77412,77414],{},[898,77413,5564],{},[898,77415,3001],{},[902,77417,56773],{"encoding":904},[5179,77419,77420,77444],{},[724,77421,77422,77424,77425],{},[883,77423,5879],{}," Postup — jak najít max ",[883,77426,77428],{"className":77427},[886],[888,77429,77430],{"xmlns":890},[892,77431,77432,77442],{},[895,77433,77434,77436],{},[898,77435,5564],{},[1686,77437,77438,77440],{},[898,77439,2675],{},[898,77441,1807],{},[902,77443,75846],{"encoding":904},[152,77445,77446,77484,77566],{},[123,77447,77448,77449,77483],{},"Napište ",[883,77450,77452],{"className":77451},[886],[888,77453,77454],{"xmlns":890},[892,77455,77456,77480],{},[895,77457,77458,77460,77466,77468,77470,77472,77474,77476,77478],{},[898,77459,5564],{},[1686,77461,77462,77464],{},[898,77463,2675],{},[898,77465,1807],{},[1651,77467,1738],{},[898,77469,1690],{},[1651,77471,1654],{"stretchy":1653},[898,77473,1807],{},[1651,77475,1667],{"stretchy":1653},[898,77477,5981],{"mathvariant":1910},[898,77479,1807],{},[902,77481,77482],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,77485,77486,77487,77519,77520,77523,77524,1882],{},"Položte ",[883,77488,77490],{"className":77489},[886],[888,77491,77492],{"xmlns":890},[892,77493,77494,77516],{},[895,77495,77496,77498,77500,77506,77512,77514],{},[1651,77497,1654],{"stretchy":1653},[898,77499,5564],{},[1686,77501,77502,77504],{},[898,77503,2675],{},[898,77505,1807],{},[2115,77507,77508,77510],{},[1651,77509,1667],{"stretchy":1653},[1651,77511,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,77513,1738],{},[1692,77515,1741],{},[902,77517,77518],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,77521,77522],{},"Zkratka:"," můžete rovnou řešit ",[883,77525,77527],{"className":77526},[886],[888,77528,77529],{"xmlns":890},[892,77530,77531,77563],{},[895,77532,77533,77535,77541,77543,77545,77547,77549,77551,77557,77559,77561],{},[898,77534,2995],{},[1686,77536,77537,77539],{},[898,77538,2675],{},[898,77540,1807],{},[1651,77542,1654],{"stretchy":1653},[898,77544,1807],{},[1651,77546,1667],{"stretchy":1653},[1651,77548,1738],{},[898,77550,5564],{},[1686,77552,77553,77555],{},[898,77554,2675],{},[898,77556,1807],{},[1651,77558,1654],{"stretchy":1653},[898,77560,1807],{},[1651,77562,1667],{"stretchy":1653},[902,77564,77565],{"encoding":904},"MP_L(L) = AP_L(L)",[123,77567,77568],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,77570,66714],{"id":77571},"odvození",[724,77573,77574,77575,77608],{},"Z ",[883,77576,77578],{"className":77577},[886],[888,77579,77580],{"xmlns":890},[892,77581,77582,77606],{},[895,77583,77584,77586,77592,77594,77596,77598,77600,77602,77604],{},[898,77585,5564],{},[1686,77587,77588,77590],{},[898,77589,2675],{},[898,77591,1807],{},[1651,77593,1738],{},[898,77595,1690],{},[1651,77597,1654],{"stretchy":1653},[898,77599,1807],{},[1651,77601,1667],{"stretchy":1653},[898,77603,5981],{"mathvariant":1910},[898,77605,1807],{},[902,77607,77482],{"encoding":904}," a derivace podílu:",[883,77610,77612],{"className":77611},[886],[888,77613,77614],{"xmlns":890,"display":29279},[892,77615,77616,77769],{},[895,77617,77618,77620,77622,77628,77634,77636,77638,77640,77642,77682,77684,77690,77724,77726,77732,77735,77737,77743,77745,77747,77749,77751,77753,77759,77761,77763,77765,77767],{},[1651,77619,1654],{"stretchy":1653},[898,77621,5564],{},[1686,77623,77624,77626],{},[898,77625,2675],{},[898,77627,1807],{},[2115,77629,77630,77632],{},[1651,77631,1667],{"stretchy":1653},[1651,77633,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,77635,1654],{"stretchy":1653},[898,77637,1807],{},[1651,77639,1667],{"stretchy":1653},[1651,77641,1738],{},[2446,77643,77644,77676],{},[895,77645,77646,77652,77654,77656,77658,77660,77662,77664,77666,77668,77670,77672,77674],{},[2115,77647,77648,77650],{},[898,77649,1690],{},[1651,77651,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,77653,1654],{"stretchy":1653},[898,77655,1807],{},[1651,77657,1667],{"stretchy":1653},[1651,77659,4503],{},[898,77661,1807],{},[1651,77663,2181],{},[898,77665,1690],{},[1651,77667,1654],{"stretchy":1653},[898,77669,1807],{},[1651,77671,1667],{"stretchy":1653},[1651,77673,4503],{},[1692,77675,1694],{},[2115,77677,77678,77680],{},[898,77679,1807],{},[1692,77681,1703],{},[1651,77683,1738],{},[2446,77685,77686,77688],{},[1692,77687,1694],{},[898,77689,1807],{},[895,77691,77692,77694,77700,77702,77704,77706,77708,77722],{},[1651,77693,1654],{"fence":1660},[2115,77695,77696,77698],{},[898,77697,1690],{},[1651,77699,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,77701,1654],{"stretchy":1653},[898,77703,1807],{},[1651,77705,1667],{"stretchy":1653},[1651,77707,2181],{},[2446,77709,77710,77720],{},[895,77711,77712,77714,77716,77718],{},[898,77713,1690],{},[1651,77715,1654],{"stretchy":1653},[898,77717,1807],{},[1651,77719,1667],{"stretchy":1653},[898,77721,1807],{},[1651,77723,1667],{"fence":1660},[1651,77725,1738],{},[2446,77727,77728,77730],{},[1692,77729,1694],{},[898,77731,1807],{},[1651,77733,1654],{"fence":1660,"stretchy":1660,"minsize":77734,"maxsize":77734},"1.2em",[898,77736,2995],{},[1686,77738,77739,77741],{},[898,77740,2675],{},[898,77742,1807],{},[1651,77744,1654],{"stretchy":1653},[898,77746,1807],{},[1651,77748,1667],{"stretchy":1653},[1651,77750,2181],{},[898,77752,5564],{},[1686,77754,77755,77757],{},[898,77756,2675],{},[898,77758,1807],{},[1651,77760,1654],{"stretchy":1653},[898,77762,1807],{},[1651,77764,1667],{"stretchy":1653},[1651,77766,1667],{"fence":1660,"stretchy":1660,"minsize":77734,"maxsize":77734},[898,77768,1882],{"mathvariant":1910},[902,77770,77771],{"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).",[724,77773,10966,77774,1878,77796,77879],{},[883,77775,77777],{"className":77776},[886],[888,77778,77779],{"xmlns":890},[892,77780,77781,77793],{},[895,77782,77783,77789,77791],{},[1686,77784,77785,77787],{},[898,77786,1807],{},[1692,77788,1741],{},[1651,77790,2390],{},[1692,77792,1741],{},[902,77794,77795],{"encoding":904},"L_0 > 0",[883,77797,77799],{"className":77798},[886],[888,77800,77801],{"xmlns":890},[892,77802,77803,77876],{},[895,77804,77805,77807,77809,77815,77821,77823,77829,77831,77833,77835,77838,77840,77846,77848,77854,77856,77858,77860,77866,77868,77874],{},[1651,77806,1654],{"stretchy":1653},[898,77808,5564],{},[1686,77810,77811,77813],{},[898,77812,2675],{},[898,77814,1807],{},[2115,77816,77817,77819],{},[1651,77818,1667],{"stretchy":1653},[1651,77820,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,77822,1654],{"stretchy":1653},[1686,77824,77825,77827],{},[898,77826,1807],{},[1692,77828,1741],{},[1651,77830,1667],{"stretchy":1653},[1651,77832,1738],{},[1692,77834,1741],{},[1651,77836,77837],{},"⇔",[898,77839,2995],{},[1686,77841,77842,77844],{},[898,77843,2675],{},[898,77845,1807],{},[1651,77847,1654],{"stretchy":1653},[1686,77849,77850,77852],{},[898,77851,1807],{},[1692,77853,1741],{},[1651,77855,1667],{"stretchy":1653},[1651,77857,1738],{},[898,77859,5564],{},[1686,77861,77862,77864],{},[898,77863,2675],{},[898,77865,1807],{},[1651,77867,1654],{"stretchy":1653},[1686,77869,77870,77872],{},[898,77871,1807],{},[1692,77873,1741],{},[1651,77875,1667],{"stretchy":1653},[902,77877,77878],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,77881,77883],{"id":77882},"příklad-51","Příklad 5.1",[724,77885,77886,77887,1882],{},"Je dána produkce ",[883,77888,77890],{"className":77889},[886],[888,77891,77892],{"xmlns":890},[892,77893,77894,77918],{},[895,77895,77896,77898,77900,77902,77908,77910,77912],{},[898,77897,1690],{},[1651,77899,1738],{},[1692,77901,3581],{},[2115,77903,77904,77906],{},[898,77905,1807],{},[1692,77907,1703],{},[1651,77909,2181],{},[1692,77911,4166],{},[2115,77913,77914,77916],{},[898,77915,1807],{},[1692,77917,3521],{},[902,77919,77920],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,77922,77923,58735,77926,77976,77977,1882],{},[38,77924,77925],{},"(a)",[883,77927,77929],{"className":77928},[886],[888,77930,77931],{"xmlns":890},[892,77932,77933,77973],{},[895,77934,77935,77937,77939,77941,77943,77945,77947,77949,77951,77953,77955,77957,77959,77961,77963,77965,77967,77969,77971],{},[898,77936,1807],{},[1651,77938,1738],{},[1692,77940,1703],{},[1651,77942,1661],{"separator":1660},[1692,77944,3574],{},[1651,77946,1661],{"separator":1660},[1692,77948,6892],{},[1651,77950,1661],{"separator":1660},[1692,77952,4190],{},[1651,77954,1661],{"separator":1660},[1692,77956,24159],{},[1651,77958,1661],{"separator":1660},[1692,77960,5026],{},[1651,77962,1661],{"separator":1660},[1692,77964,10340],{},[1651,77966,1661],{"separator":1660},[1692,77968,39559],{},[1651,77970,1661],{"separator":1660},[1692,77972,6311],{},[902,77974,77975],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,77978,77980],{"className":77979},[886],[888,77981,77982],{"xmlns":890},[892,77983,77984,77994],{},[895,77985,77986,77988],{},[898,77987,2995],{},[1686,77989,77990,77992],{},[898,77991,2675],{},[898,77993,1807],{},[902,77995,11345],{"encoding":904},[724,77997,77998,77999,36181],{},"Podle (5.2): ",[883,78000,78002],{"className":78001},[886],[888,78003,78004],{"xmlns":890},[892,78005,78006,78062],{},[895,78007,78008,78010,78016,78018,78024,78026,78028,78030,78032,78034,78036,78038,78040,78046,78048,78050,78052,78054,78056,78058,78060],{},[898,78009,2995],{},[1686,78011,78012,78014],{},[898,78013,2675],{},[898,78015,1807],{},[1651,78017,1738],{},[2115,78019,78020,78022],{},[898,78021,1690],{},[1651,78023,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,78025,1654],{"stretchy":1653},[898,78027,1807],{},[1651,78029,1667],{"stretchy":1653},[1651,78031,1738],{},[1692,78033,4828],{},[898,78035,1807],{},[1651,78037,2181],{},[1692,78039,20534],{},[2115,78041,78042,78044],{},[898,78043,1807],{},[1692,78045,1703],{},[1651,78047,1738],{},[898,78049,1807],{},[1651,78051,1654],{"stretchy":1653},[1692,78053,4828],{},[1651,78055,2181],{},[1692,78057,20534],{},[898,78059,1807],{},[1651,78061,1667],{"stretchy":1653},[902,78063,78064],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,78066,78067,78104],{},[19,78068,78069],{},[22,78070,78071,78086,78088,78090,78092,78094,78096,78098,78100,78102],{},[25,78072,78073],{},[883,78074,78076],{"className":78075},[886],[888,78077,78078],{"xmlns":890},[892,78079,78080,78084],{},[895,78081,78082],{},[898,78083,1807],{},[902,78085,1807],{"encoding":904},[25,78087,1703],{},[25,78089,3574],{},[25,78091,6892],{},[25,78093,4190],{},[25,78095,24159],{},[25,78097,5026],{},[25,78099,10340],{},[25,78101,39559],{},[25,78103,6311],{},[30,78105,78106],{},[22,78107,78108,78129,78132,78135,78138,78140,78143,78145,78147,78166],{},[35,78109,78110],{},[883,78111,78113],{"className":78112},[886],[888,78114,78115],{"xmlns":890},[892,78116,78117,78127],{},[895,78118,78119,78121],{},[898,78120,2995],{},[1686,78122,78123,78125],{},[898,78124,2675],{},[898,78126,1807],{},[902,78128,11345],{"encoding":904},[35,78130,78131],{},"21,6",[35,78133,78134],{},"45",[35,78136,78137],{},"57,6",[35,78139,4452],{},[35,78141,78142],{},"50,4",[35,78144,78131],{},[35,78146,1741],{},[35,78148,78149],{},[883,78150,78152],{"className":78151},[886],[888,78153,78154],{"xmlns":890},[892,78155,78156,78163],{},[895,78157,78158,78160],{},[1651,78159,2181],{},[1692,78161,78162],{},"12,6",[902,78164,78165],{"encoding":904},"-12{,}6",[35,78167,78168],{},[883,78169,78171],{"className":78170},[886],[888,78172,78173],{"xmlns":890},[892,78174,78175,78181],{},[895,78176,78177,78179],{},[1651,78178,2181],{},[1692,78180,46665],{},[902,78182,78183],{"encoding":904},"-75",[724,78185,78186,78205,78206,78224,78225,78242,78243,78261,78262,78286,78287,78305],{},[883,78187,78189],{"className":78188},[886],[888,78190,78191],{"xmlns":890},[892,78192,78193,78203],{},[895,78194,78195,78197],{},[898,78196,2995],{},[1686,78198,78199,78201],{},[898,78200,2675],{},[898,78202,1807],{},[902,78204,11345],{"encoding":904}," nabývá maxima pro ",[883,78207,78209],{"className":78208},[886],[888,78210,78211],{"xmlns":890},[892,78212,78213,78221],{},[895,78214,78215,78217,78219],{},[898,78216,1807],{},[1651,78218,1738],{},[1692,78220,4190],{},[902,78222,78223],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,78226,78228],{"className":78227},[886],[888,78229,78230],{"xmlns":890},[892,78231,78232,78240],{},[895,78233,78234,78236,78238],{},[898,78235,1807],{},[1651,78237,1738],{},[1692,78239,4190],{},[902,78241,78223],{"encoding":904}," přírůstky klesají, v ",[883,78244,78246],{"className":78245},[886],[888,78247,78248],{"xmlns":890},[892,78249,78250,78258],{},[895,78251,78252,78254,78256],{},[898,78253,1807],{},[1651,78255,1738],{},[1692,78257,10340],{},[902,78259,78260],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,78263,78265],{"className":78264},[886],[888,78266,78267],{"xmlns":890},[892,78268,78269,78283],{},[895,78270,78271,78273,78275,78277,78279,78281],{},[898,78272,1690],{},[1651,78274,1654],{"stretchy":1653},[1692,78276,10340],{},[1651,78278,1667],{"stretchy":1653},[1651,78280,1738],{},[1692,78282,25071],{},[902,78284,78285],{"encoding":904},"Q(20) = 800","), od ",[883,78288,78290],{"className":78289},[886],[888,78291,78292],{"xmlns":890},[892,78293,78294,78302],{},[895,78295,78296,78298,78300],{},[898,78297,1807],{},[1651,78299,2390],{},[1692,78301,10340],{},[902,78303,78304],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,78307,78308],{},[614,78309,78310,78311,78351,78352,3955,78370,1882],{},"Obrázek 5.1 — graf produkce ",[883,78312,78314],{"className":78313},[886],[888,78315,78316],{"xmlns":890},[892,78317,78318,78348],{},[895,78319,78320,78322,78324,78326,78328,78330,78332,78338,78340,78342],{},[898,78321,1690],{},[1651,78323,1654],{"stretchy":1653},[898,78325,1807],{},[1651,78327,1667],{"stretchy":1653},[1651,78329,1738],{},[1692,78331,3581],{},[2115,78333,78334,78336],{},[898,78335,1807],{},[1692,78337,1703],{},[1651,78339,2181],{},[1692,78341,4166],{},[2115,78343,78344,78346],{},[898,78345,1807],{},[1692,78347,3521],{},[902,78349,78350],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,78353,78355],{"className":78354},[886],[888,78356,78357],{"xmlns":890},[892,78358,78359,78367],{},[895,78360,78361,78363,78365],{},[898,78362,1690],{},[1651,78364,1738],{},[1692,78366,25071],{},[902,78368,78369],{"encoding":904},"Q = 800",[883,78371,78373],{"className":78372},[886],[888,78374,78375],{"xmlns":890},[892,78376,78377,78385],{},[895,78378,78379,78381,78383],{},[898,78380,1807],{},[1651,78382,1738],{},[1692,78384,10340],{},[902,78386,78260],{"encoding":904},[724,78388,78389,78392],{},[38,78390,78391],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,78394,78395,78396,1343,78414,1793],{},"Podle (5.3) s ",[883,78397,78399],{"className":78398},[886],[888,78400,78401],{"xmlns":890},[892,78402,78403,78411],{},[895,78404,78405,78407,78409],{},[898,78406,1807],{},[1651,78408,1738],{},[1692,78410,3581],{},[902,78412,78413],{"encoding":904},"L = 6",[883,78415,78417],{"className":78416},[886],[888,78418,78419],{"xmlns":890},[892,78420,78421,78431],{},[895,78422,78423,78425,78427,78429],{},[898,78424,3542],{},[898,78426,1807],{},[1651,78428,1738],{},[1692,78430,3521],{},[902,78432,78433],{"encoding":904},"dL = 3",[883,78435,78437],{"className":78436},[886],[888,78438,78439],{"xmlns":890,"display":29279},[892,78440,78441,78504],{},[895,78442,78443,78445,78447,78449,78451,78457,78459,78461,78463,78465,78467,78469,78471,78473,78475,78477,78479,78481,78483,78485,78487,78489,78491,78493,78495,78497,78499,78501],{},[898,78444,3542],{},[898,78446,1690],{},[1651,78448,1738],{},[898,78450,2995],{},[1686,78452,78453,78455],{},[898,78454,2675],{},[898,78456,1807],{},[1651,78458,1654],{"stretchy":1653},[1692,78460,3581],{},[1651,78462,1667],{"stretchy":1653},[1651,78464,4503],{},[1692,78466,3521],{},[1651,78468,1738],{},[1651,78470,1654],{"stretchy":1653},[1692,78472,4828],{},[1651,78474,4503],{},[1692,78476,3581],{},[1651,78478,2181],{},[1692,78480,20534],{},[1651,78482,4503],{},[1692,78484,6872],{},[1651,78486,1667],{"stretchy":1653},[1651,78488,4503],{},[1692,78490,3521],{},[1651,78492,1738],{},[1692,78494,78142],{},[1651,78496,4503],{},[1692,78498,3521],{},[1651,78500,1738],{},[1692,78502,78503],{},"151,2.",[902,78505,78506],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,78508,78509,78510,58965,78535,78549,78550,1882],{},"Produkce vzroste z ",[883,78511,78513],{"className":78512},[886],[888,78514,78515],{"xmlns":890},[892,78516,78517,78532],{},[895,78518,78519,78521,78523,78525,78527,78529],{},[898,78520,1690],{},[1651,78522,1654],{"stretchy":1653},[1692,78524,3581],{},[1651,78526,1667],{"stretchy":1653},[1651,78528,1738],{},[1692,78530,78531],{},"172,8",[902,78533,78534],{"encoding":904},"Q(6) = 172{,}8",[883,78536,78538],{"className":78537},[886],[888,78539,78540],{"xmlns":890},[892,78541,78542,78547],{},[895,78543,78544],{},[1692,78545,78546],{},"324",[902,78548,78546],{"encoding":904},". Skutečná hodnota: ",[883,78551,78553],{"className":78552},[886],[888,78554,78555],{"xmlns":890},[892,78556,78557,78597],{},[895,78558,78559,78561,78563,78565,78567,78569,78571,78573,78575,78577,78579,78581,78583,78585,78588,78590,78592,78594],{},[898,78560,4216],{"mathvariant":1910},[898,78562,1690],{},[1651,78564,1738],{},[898,78566,1690],{},[1651,78568,1654],{"stretchy":1653},[1692,78570,5309],{},[1651,78572,1667],{"stretchy":1653},[1651,78574,2181],{},[898,78576,1690],{},[1651,78578,1654],{"stretchy":1653},[1692,78580,3581],{},[1651,78582,1667],{"stretchy":1653},[1651,78584,1738],{},[1692,78586,78587],{},"340,2",[1651,78589,2181],{},[1692,78591,78531],{},[1651,78593,1738],{},[1692,78595,78596],{},"167,4",[902,78598,78599],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,78601,78603],{"id":78602},"příklad-52","Příklad 5.2",[724,78605,78606,78607,1882],{},"Ověříme princip (5.5) pro ",[883,78608,78610],{"className":78609},[886],[888,78611,78612],{"xmlns":890},[892,78613,78614,78638],{},[895,78615,78616,78618,78620,78622,78628,78630,78632],{},[898,78617,1690],{},[1651,78619,1738],{},[1692,78621,3581],{},[2115,78623,78624,78626],{},[898,78625,1807],{},[1692,78627,1703],{},[1651,78629,2181],{},[1692,78631,4166],{},[2115,78633,78634,78636],{},[898,78635,1807],{},[1692,78637,3521],{},[902,78639,77920],{"encoding":904},[883,78641,78643],{"className":78642},[886],[888,78644,78645],{"xmlns":890,"display":29279},[892,78646,78647,78725],{},[895,78648,78649,78651,78657,78659,78665,78667,78669,78671,78673,78675,78681,78683,78685,78687,78695,78697,78699,78701,78703,78705,78707,78709,78711,78713,78715,78721,78723],{},[898,78650,5564],{},[1686,78652,78653,78655],{},[898,78654,2675],{},[898,78656,1807],{},[1651,78658,1738],{},[2446,78660,78661,78663],{},[898,78662,1690],{},[898,78664,1807],{},[1651,78666,1738],{},[1692,78668,3581],{},[898,78670,1807],{},[1651,78672,2181],{},[1692,78674,4166],{},[2115,78676,78677,78679],{},[898,78678,1807],{},[1692,78680,1703],{},[1651,78682,1661],{"separator":1660},[7185,78684],{"width":16582},[898,78686,5564],{},[1902,78688,78689,78691,78693],{},[898,78690,2675],{},[898,78692,1807],{},[1651,78694,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,78696,1738],{},[1692,78698,3581],{},[1651,78700,2181],{},[1692,78702,20484],{},[898,78704,1807],{},[1651,78706,1738],{},[1692,78708,1741],{},[1843,78710,5295],{},[1651,78712,5298],{},[1843,78714,5295],{},[1686,78716,78717,78719],{},[898,78718,1807],{},[1692,78720,1741],{},[1651,78722,1738],{},[1692,78724,69496],{},[902,78726,78727],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,78729,78730,78766,78767,78785,78786,1882],{},[883,78731,78733],{"className":78732},[886],[888,78734,78735],{"xmlns":890},[892,78736,78737,78763],{},[895,78738,78739,78741,78753,78755,78757,78759,78761],{},[898,78740,5564],{},[1902,78742,78743,78745,78747],{},[898,78744,2675],{},[898,78746,1807],{},[895,78748,78749,78751],{},[1651,78750,1912],{"mathvariant":1910},[1651,78752,1912],{"mathvariant":1910},[1651,78754,1738],{},[1651,78756,2181],{},[1692,78758,20484],{},[1651,78760,2319],{},[1692,78762,1741],{},[902,78764,78765],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,78768,78770],{"className":78769},[886],[888,78771,78772],{"xmlns":890},[892,78773,78774,78782],{},[895,78775,78776,78778,78780],{},[898,78777,1807],{},[1651,78779,1738],{},[1692,78781,37457],{},[902,78783,78784],{"encoding":904},"L = 15"," je maximum, ",[883,78787,78789],{"className":78788},[886],[888,78790,78791],{"xmlns":890},[892,78792,78793,78839],{},[895,78794,78795,78797,78803,78805,78807,78809,78811,78813,78815,78817,78819,78821,78823,78826,78828,78831,78833,78835,78837],{},[898,78796,5564],{},[1686,78798,78799,78801],{},[898,78800,2675],{},[898,78802,1807],{},[1651,78804,1654],{"stretchy":1653},[1692,78806,37457],{},[1651,78808,1667],{"stretchy":1653},[1651,78810,1738],{},[1692,78812,3581],{},[1651,78814,4503],{},[1692,78816,37457],{},[1651,78818,2181],{},[1692,78820,4166],{},[1651,78822,4503],{},[1692,78824,78825],{},"225",[1651,78827,1738],{},[1692,78829,78830],{},"90",[1651,78832,2181],{},[1692,78834,78134],{},[1651,78836,1738],{},[1692,78838,78134],{},[902,78840,78841],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,78843,78844,43093,78900,78946],{},[883,78845,78847],{"className":78846},[886],[888,78848,78849],{"xmlns":890},[892,78850,78851,78897],{},[895,78852,78853,78855,78861,78863,78865,78867,78869,78871,78873,78875,78877,78879,78881,78883,78885,78888,78890,78893,78895],{},[898,78854,2995],{},[1686,78856,78857,78859],{},[898,78858,2675],{},[898,78860,1807],{},[1651,78862,1654],{"stretchy":1653},[1692,78864,37457],{},[1651,78866,1667],{"stretchy":1653},[1651,78868,1738],{},[1692,78870,4828],{},[1651,78872,4503],{},[1692,78874,37457],{},[1651,78876,2181],{},[1692,78878,20534],{},[1651,78880,4503],{},[1692,78882,78825],{},[1651,78884,1738],{},[1692,78886,78887],{},"180",[1651,78889,2181],{},[1692,78891,78892],{},"135",[1651,78894,1738],{},[1692,78896,78134],{},[902,78898,78899],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,78901,78903],{"className":78902},[886],[888,78904,78905],{"xmlns":890},[892,78906,78907,78943],{},[895,78908,78909,78911,78917,78919,78921,78923,78925,78927,78933,78935,78937,78939,78941],{},[898,78910,2995],{},[1686,78912,78913,78915],{},[898,78914,2675],{},[898,78916,1807],{},[1651,78918,1654],{"stretchy":1653},[1692,78920,37457],{},[1651,78922,1667],{"stretchy":1653},[1651,78924,1738],{},[898,78926,5564],{},[1686,78928,78929,78931],{},[898,78930,2675],{},[898,78932,1807],{},[1651,78934,1654],{"stretchy":1653},[1692,78936,37457],{},[1651,78938,1667],{"stretchy":1653},[1651,78940,1738],{},[1692,78942,78134],{},[902,78944,78945],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,78948,78949,78952,78953,2983,78982,1882],{},[38,78950,78951],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,78954,78956],{"className":78955},[886],[888,78957,78958],{"xmlns":890},[892,78959,78960,78980],{},[895,78961,78962,78964,78970,78972,78974],{},[898,78963,2995],{},[1686,78965,78966,78968],{},[898,78967,2675],{},[898,78969,1807],{},[1651,78971,1738],{},[898,78973,5564],{},[1686,78975,78976,78978],{},[898,78977,2675],{},[898,78979,1807],{},[902,78981,75876],{"encoding":904},[883,78983,78985],{"className":78984},[886],[888,78986,78987],{"xmlns":890},[892,78988,78989,79029],{},[895,78990,78991,78993,78995,78997,78999,79005,79007,79009,79011,79013,79015,79021,79023,79025,79027],{},[1692,78992,4828],{},[898,78994,1807],{},[1651,78996,2181],{},[1692,78998,20534],{},[2115,79000,79001,79003],{},[898,79002,1807],{},[1692,79004,1703],{},[1651,79006,1738],{},[1692,79008,3581],{},[898,79010,1807],{},[1651,79012,2181],{},[1692,79014,4166],{},[2115,79016,79017,79019],{},[898,79018,1807],{},[1692,79020,1703],{},[1651,79022,5298],{},[898,79024,1807],{},[1651,79026,1738],{},[1692,79028,37457],{},[902,79030,79031],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,79033,79034],{},[614,79035,79036,79037,79056,79057,13426,79075,79094,79095,79113,79114,79131,79132,79151,79152,79171],{},"Obrázek 5.3 — křivky ",[883,79038,79040],{"className":79039},[886],[888,79041,79042],{"xmlns":890},[892,79043,79044,79054],{},[895,79045,79046,79048],{},[898,79047,2995],{},[1686,79049,79050,79052],{},[898,79051,2675],{},[898,79053,1807],{},[902,79055,11345],{"encoding":904}," (max 60 při ",[883,79058,79060],{"className":79059},[886],[888,79061,79062],{"xmlns":890},[892,79063,79064,79072],{},[895,79065,79066,79068,79070],{},[898,79067,1807],{},[1651,79069,1738],{},[1692,79071,4190],{},[902,79073,79074],{"encoding":904},"L=10",[883,79076,79078],{"className":79077},[886],[888,79079,79080],{"xmlns":890},[892,79081,79082,79092],{},[895,79083,79084,79086],{},[898,79085,5564],{},[1686,79087,79088,79090],{},[898,79089,2675],{},[898,79091,1807],{},[902,79093,75846],{"encoding":904}," (max 45 při ",[883,79096,79098],{"className":79097},[886],[888,79099,79100],{"xmlns":890},[892,79101,79102,79110],{},[895,79103,79104,79106,79108],{},[898,79105,1807],{},[1651,79107,1738],{},[1692,79109,37457],{},[902,79111,79112],{"encoding":904},"L=15","), průsečík v ",[883,79115,79117],{"className":79116},[886],[888,79118,79119],{"xmlns":890},[892,79120,79121,79129],{},[895,79122,79123,79125,79127],{},[898,79124,1807],{},[1651,79126,1738],{},[1692,79128,37457],{},[902,79130,78784],{"encoding":904},". Nalevo od 15 leží ",[883,79133,79135],{"className":79134},[886],[888,79136,79137],{"xmlns":890},[892,79138,79139,79149],{},[895,79140,79141,79143],{},[898,79142,2995],{},[1686,79144,79145,79147],{},[898,79146,2675],{},[898,79148,1807],{},[902,79150,11345],{"encoding":904}," nad ",[883,79153,79155],{"className":79154},[886],[888,79156,79157],{"xmlns":890},[892,79158,79159,79169],{},[895,79160,79161,79163],{},[898,79162,5564],{},[1686,79164,79165,79167],{},[898,79166,2675],{},[898,79168,1807],{},[902,79170,75846],{"encoding":904},", napravo pod ní.",[115,79173,79175],{"id":79174},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,79177,79178,79179,4016,79192,3246,79195,7497,79208,3246,79211,1793],{},"V dvoufaktorovém modelu závisí produkce ",[883,79180,79182],{"className":79181},[886],[888,79183,79184],{"xmlns":890},[892,79185,79186,79190],{},[895,79187,79188],{},[898,79189,1690],{},[902,79191,1690],{"encoding":904},[38,79193,79194],{},"práci",[883,79196,79198],{"className":79197},[886],[888,79199,79200],{"xmlns":890},[892,79201,79202,79206],{},[895,79203,79204],{},[898,79205,1807],{},[902,79207,1807],{"encoding":904},[38,79209,79210],{},"kapitálu",[883,79212,79214],{"className":79213},[886],[888,79215,79216],{"xmlns":890},[892,79217,79218,79222],{},[895,79219,79220],{},[898,79221,11101],{},[902,79223,11101],{"encoding":904},[883,79225,79227],{"className":79226},[886],[888,79228,79229],{"xmlns":890,"display":29279},[892,79230,79231,79266],{},[21967,79232,79233],{"width":29284},[21972,79234,79235,79237,79259,79261],{},[21975,79236],{"width":29289},[21975,79238,79239],{},[895,79240,79241,79243,79245,79247,79249,79251,79253,79255,79257],{},[898,79242,1690],{},[1651,79244,1738],{},[898,79246,1690],{},[1651,79248,1654],{"stretchy":1653},[898,79250,1807],{},[1651,79252,1661],{"separator":1660},[898,79254,11101],{},[1651,79256,1667],{"stretchy":1653},[898,79258,1882],{"mathvariant":1910},[21975,79260],{"width":29289},[21975,79262,79263],{},[1843,79264,79265],{},"(5.6)",[902,79267,79268],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,79270,79271,79272,79274],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,79273,76213],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,79276,79278],{"id":79277},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,79280,79281],{},"Široce používané produkční funkce mají tvar",[883,79283,79285],{"className":79284},[886],[888,79286,79287],{"xmlns":890,"display":29279},[892,79288,79289,79330],{},[21967,79290,79291],{"width":29284},[21972,79292,79293,79295,79323,79325],{},[21975,79294],{"width":29289},[21975,79296,79297],{},[895,79298,79299,79301,79303,79305,79307,79313,79315,79321],{},[898,79300,1690],{},[1651,79302,1738],{},[898,79304,5564],{},[1843,79306,1845],{},[2115,79308,79309,79311],{},[898,79310,1807],{},[898,79312,207],{},[1843,79314,1845],{},[2115,79316,79317,79319],{},[898,79318,11101],{},[898,79320,2268],{},[1651,79322,1661],{"separator":1660},[21975,79324],{"width":29289},[21975,79326,79327],{},[1843,79328,79329],{},"(5.7)",[902,79331,79332],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,79334,1863,79335,79357,79358,79360,79361,1882],{},[883,79336,79338],{"className":79337},[886],[888,79339,79340],{"xmlns":890},[892,79341,79342,79354],{},[895,79343,79344,79346,79348,79350,79352],{},[898,79345,5564],{},[1651,79347,1661],{"separator":1660},[898,79349,207],{},[1651,79351,1661],{"separator":1660},[898,79353,2268],{},[902,79355,79356],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,79359,75912],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,79362,79364],{"className":79363},[886],[888,79365,79366],{"xmlns":890},[892,79367,79368,79380],{},[895,79369,79370,79372,79374,79376,79378],{},[898,79371,207],{},[1651,79373,1661],{"separator":1660},[898,79375,2268],{},[1651,79377,2319],{},[1692,79379,1694],{},[902,79381,79382],{"encoding":904},"a, b \u003C 1",[724,79384,79385],{},[1756,79386],{"alt":79387,"className":79388,"src":79389},"imek-vynosy-z-rozsahu-3typy",[210,1760],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,79391,79392,79393,79396,79397,4016,79410,79426,79427,4016,79440,1793],{},"Reflektují ekonomickou zákonitost, že ",[38,79394,79395],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,79398,79400],{"className":79399},[886],[888,79401,79402],{"xmlns":890},[892,79403,79404,79408],{},[895,79405,79406],{},[898,79407,1807],{},[902,79409,1807],{"encoding":904},[883,79411,79413],{"className":79412},[886],[888,79414,79415],{"xmlns":890},[892,79416,79417,79423],{},[895,79418,79419,79421],{},[898,79420,13339],{},[898,79422,1807],{},[902,79424,79425],{"encoding":904},"rL"," a kapitál z ",[883,79428,79430],{"className":79429},[886],[888,79431,79432],{"xmlns":890},[892,79433,79434,79438],{},[895,79435,79436],{},[898,79437,11101],{},[902,79439,11101],{"encoding":904},[883,79441,79443],{"className":79442},[886],[888,79444,79445],{"xmlns":890},[892,79446,79447,79453],{},[895,79448,79449,79451],{},[898,79450,13339],{},[898,79452,11101],{},[902,79454,79455],{"encoding":904},"rK",[883,79457,79459],{"className":79458},[886],[888,79460,79461],{"xmlns":890,"display":29279},[892,79462,79463,79586],{},[21967,79464,79465],{"width":29284},[21972,79466,79467,79469,79579,79581],{},[21975,79468],{"width":29289},[21975,79470,79471],{},[895,79472,79473,79475,79477,79479,79481,79483,79485,79487,79489,79491,79493,79495,79497,79499,79505,79507,79509,79511,79517,79519,79521,79523,79535,79537,79543,79549,79551,79563,79565,79567,79569,79571,79573,79575,79577],{},[898,79474,1690],{},[1651,79476,1654],{"stretchy":1653},[898,79478,13339],{},[898,79480,1807],{},[1651,79482,1661],{"separator":1660},[898,79484,13339],{},[898,79486,11101],{},[1651,79488,1667],{"stretchy":1653},[1651,79490,1738],{},[898,79492,5564],{},[1651,79494,1654],{"stretchy":1653},[898,79496,13339],{},[898,79498,1807],{},[2115,79500,79501,79503],{},[1651,79502,1667],{"stretchy":1653},[898,79504,207],{},[1651,79506,1654],{"stretchy":1653},[898,79508,13339],{},[898,79510,11101],{},[2115,79512,79513,79515],{},[1651,79514,1667],{"stretchy":1653},[898,79516,2268],{},[1651,79518,1738],{},[898,79520,5564],{},[1843,79522,1845],{},[2115,79524,79525,79527],{},[898,79526,13339],{},[895,79528,79529,79531,79533],{},[898,79530,207],{},[1651,79532,1839],{},[898,79534,2268],{},[1843,79536,1845],{},[2115,79538,79539,79541],{},[898,79540,1807],{},[898,79542,207],{},[2115,79544,79545,79547],{},[898,79546,11101],{},[898,79548,2268],{},[1651,79550,1738],{},[2115,79552,79553,79555],{},[898,79554,13339],{},[895,79556,79557,79559,79561],{},[898,79558,207],{},[1651,79560,1839],{},[898,79562,2268],{},[1843,79564,1845],{},[898,79566,1690],{},[1651,79568,1654],{"stretchy":1653},[898,79570,1807],{},[1651,79572,1661],{"separator":1660},[898,79574,11101],{},[1651,79576,1667],{"stretchy":1653},[898,79578,1882],{"mathvariant":1910},[21975,79580],{"width":29289},[21975,79582,79583],{},[1843,79584,79585],{},"(5.8)",[902,79587,79588],{"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}",[724,79590,79591,79592],{},"Volně: ",[38,79593,79594,79595,79608,79609,79633],{},"změní-li se vstupy ",[883,79596,79598],{"className":79597},[886],[888,79599,79600],{"xmlns":890},[892,79601,79602,79606],{},[895,79603,79604],{},[898,79605,13339],{},[902,79607,13339],{"encoding":904},"-krát, změní se výstup ",[883,79610,79612],{"className":79611},[886],[888,79613,79614],{"xmlns":890},[892,79615,79616,79630],{},[895,79617,79618],{},[2115,79619,79620,79622],{},[898,79621,13339],{},[895,79623,79624,79626,79628],{},[898,79625,207],{},[1651,79627,1839],{},[898,79629,2268],{},[902,79631,79632],{"encoding":904},"r^{a+b}","-krát.",[198,79635,79637],{"id":79636},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,79639,79640,79641,79658],{},"Součet exponentů ",[883,79642,79644],{"className":79643},[886],[888,79645,79646],{"xmlns":890},[892,79647,79648,79656],{},[895,79649,79650,79652,79654],{},[898,79651,207],{},[1651,79653,1839],{},[898,79655,2268],{},[902,79657,76037],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,79660,79661,79690],{},[19,79662,79663],{},[22,79664,79665,79668,79671,79688],{},[25,79666,79667],{},"Typ",[25,79669,79670],{},"Podmínka",[25,79672,79673,79674,79687],{},"Chování produkce při ",[883,79675,79677],{"className":79676},[886],[888,79678,79679],{"xmlns":890},[892,79680,79681,79685],{},[895,79682,79683],{},[898,79684,13339],{},[902,79686,13339],{"encoding":904},"-násobném zvýšení vstupů",[25,79689,4396],{},[30,79691,79692,79803,79918],{},[22,79693,79694,79702,79726,79759],{},[35,79695,76750,79696,11325,79699,1667],{},[38,79697,79698],{},"Konstantní",[614,79700,79701],{},"constant returns",[35,79703,79704],{},[883,79705,79707],{"className":79706},[886],[888,79708,79709],{"xmlns":890},[892,79710,79711,79723],{},[895,79712,79713,79715,79717,79719,79721],{},[898,79714,207],{},[1651,79716,1839],{},[898,79718,2268],{},[1651,79720,1738],{},[1692,79722,1694],{},[902,79724,79725],{"encoding":904},"a+b = 1",[35,79727,79728,79741,79742,3246,79745,79758],{},[883,79729,79731],{"className":79730},[886],[888,79732,79733],{"xmlns":890},[892,79734,79735,79739],{},[895,79736,79737],{},[898,79738,1690],{},[902,79740,1690],{"encoding":904}," vzroste ",[38,79743,79744],{},"přesně",[883,79746,79748],{"className":79747},[886],[888,79749,79750],{"xmlns":890},[892,79751,79752,79756],{},[895,79753,79754],{},[898,79755,13339],{},[902,79757,13339],{"encoding":904},"-krát",[35,79760,79761],{},[883,79762,79764],{"className":79763},[886],[888,79765,79766],{"xmlns":890},[892,79767,79768,79800],{},[895,79769,79770,79772,79774,79776,79788],{},[898,79771,1690],{},[1651,79773,1738],{},[1692,79775,1703],{},[2115,79777,79778,79780],{},[898,79779,1807],{},[895,79781,79782,79784,79786],{},[1692,79783,1694],{},[898,79785,5981],{"mathvariant":1910},[1692,79787,3689],{},[2115,79789,79790,79792],{},[898,79791,11101],{},[895,79793,79794,79796,79798],{},[1692,79795,3521],{},[898,79797,5981],{"mathvariant":1910},[1692,79799,3689],{},[902,79801,79802],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,79804,79805,79814,79838,79868],{},[35,79806,79807,79808,11325,79811,1667],{},"2° ",[38,79809,79810],{},"Rostoucí",[614,79812,79813],{},"increasing returns",[35,79815,79816],{},[883,79817,79819],{"className":79818},[886],[888,79820,79821],{"xmlns":890},[892,79822,79823,79835],{},[895,79824,79825,79827,79829,79831,79833],{},[898,79826,207],{},[1651,79828,1839],{},[898,79830,2268],{},[1651,79832,2390],{},[1692,79834,1694],{},[902,79836,79837],{"encoding":904},"a+b > 1",[35,79839,79840,79741,79853,52444,79855,79758],{},[883,79841,79843],{"className":79842},[886],[888,79844,79845],{"xmlns":890},[892,79846,79847,79851],{},[895,79848,79849],{},[898,79850,1690],{},[902,79852,1690],{"encoding":904},[38,79854,26483],{},[883,79856,79858],{"className":79857},[886],[888,79859,79860],{"xmlns":890},[892,79861,79862,79866],{},[895,79863,79864],{},[898,79865,13339],{},[902,79867,13339],{"encoding":904},[35,79869,79870,11325,79896,1667],{},[883,79871,79873],{"className":79872},[886],[888,79874,79875],{"xmlns":890},[892,79876,79877,79893],{},[895,79878,79879,79881,79883,79885,79887],{},[898,79880,1690],{},[1651,79882,1738],{},[1692,79884,25414],{},[898,79886,1807],{},[2115,79888,79889,79891],{},[898,79890,11101],{},[1692,79892,1703],{},[902,79894,79895],{"encoding":904},"Q = 7LK^2",[883,79897,79899],{"className":79898},[886],[888,79900,79901],{"xmlns":890},[892,79902,79903,79915],{},[895,79904,79905,79907,79909,79911,79913],{},[898,79906,207],{},[1651,79908,1839],{},[898,79910,2268],{},[1651,79912,1738],{},[1692,79914,3521],{},[902,79916,79917],{"encoding":904},"a+b = 3",[22,79919,79920,79929,79953,79984],{},[35,79921,79922,79923,11325,79926,1667],{},"3° ",[38,79924,79925],{},"Klesající",[614,79927,79928],{},"decreasing returns",[35,79930,79931],{},[883,79932,79934],{"className":79933},[886],[888,79935,79936],{"xmlns":890},[892,79937,79938,79950],{},[895,79939,79940,79942,79944,79946,79948],{},[898,79941,207],{},[1651,79943,1839],{},[898,79945,2268],{},[1651,79947,2319],{},[1692,79949,1694],{},[902,79951,79952],{"encoding":904},"a+b \u003C 1",[35,79954,79955,79741,79968,52444,79971,79758],{},[883,79956,79958],{"className":79957},[886],[888,79959,79960],{"xmlns":890},[892,79961,79962,79966],{},[895,79963,79964],{},[898,79965,1690],{},[902,79967,1690],{"encoding":904},[38,79969,79970],{},"méně",[883,79972,79974],{"className":79973},[886],[888,79975,79976],{"xmlns":890},[892,79977,79978,79982],{},[895,79979,79980],{},[898,79981,13339],{},[902,79983,13339],{"encoding":904},[35,79985,79986,11325,80016,1667],{},[883,79987,79989],{"className":79988},[886],[888,79990,79991],{"xmlns":890},[892,79992,79993,80013],{},[895,79994,79995,79997,79999,80001,80007],{},[898,79996,1690],{},[1651,79998,1738],{},[1692,80000,4190],{},[2115,80002,80003,80005],{},[898,80004,1807],{},[1692,80006,69424],{},[2115,80008,80009,80011],{},[898,80010,11101],{},[1692,80012,6316],{},[902,80014,80015],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,80017,80019],{"className":80018},[886],[888,80020,80021],{"xmlns":890},[892,80022,80023,80035],{},[895,80024,80025,80027,80029,80031,80033],{},[898,80026,207],{},[1651,80028,1839],{},[898,80030,2268],{},[1651,80032,1738],{},[1692,80034,15887],{},[902,80036,80037],{"encoding":904},"a+b = 0{,}8",[5179,80039,80040],{},[724,80041,80042,80044,80045,80062,80063,80066,80067,3246,80070,80106,80107,80129,80130,1882],{},[883,80043,5719],{}," Pozor\nSoučet ",[883,80046,80048],{"className":80047},[886],[888,80049,80050],{"xmlns":890},[892,80051,80052,80060],{},[895,80053,80054,80056,80058],{},[898,80055,207],{},[1651,80057,1839],{},[898,80059,2268],{},[902,80061,76037],{"encoding":904}," neudává velikost produkce, ale ",[38,80064,80065],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,80068,80069],{},"ryzí Cobb-Douglas",[883,80071,80073],{"className":80072},[886],[888,80074,80075],{"xmlns":890},[892,80076,80077,80103],{},[895,80078,80079,80081,80083,80085,80091],{},[898,80080,1690],{},[1651,80082,1738],{},[898,80084,5564],{},[2115,80086,80087,80089],{},[898,80088,1807],{},[898,80090,207],{},[2115,80092,80093,80095],{},[898,80094,11101],{},[895,80096,80097,80099,80101],{},[1692,80098,1694],{},[1651,80100,2181],{},[898,80102,207],{},[902,80104,80105],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,80108,80110],{"className":80109},[886],[888,80111,80112],{"xmlns":890},[892,80113,80114,80126],{},[895,80115,80116,80118,80120,80122,80124],{},[898,80117,2268],{},[1651,80119,1738],{},[1692,80121,1694],{},[1651,80123,2181],{},[898,80125,207],{},[902,80127,80128],{"encoding":904},"b = 1-a",", tedy vždy ",[38,80131,80132],{},"konstantní výnosy z rozsahu",[198,80134,80136,80137],{"id":80135},"parametr-efektivity-aa","Parametr efektivity ",[883,80138,80140],{"className":80139},[886],[888,80141,80142],{"xmlns":890},[892,80143,80144,80148],{},[895,80145,80146],{},[898,80147,5564],{},[902,80149,5564],{"encoding":904},[724,80151,80152,80153,80166,80167,80180,80181,80199,80200,80203],{},"Konstanta ",[883,80154,80156],{"className":80155},[886],[888,80157,80158],{"xmlns":890},[892,80159,80160,80164],{},[895,80161,80162],{},[898,80163,5564],{},[902,80165,5564],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,80168,80170],{"className":80169},[886],[888,80171,80172],{"xmlns":890},[892,80173,80174,80178],{},[895,80175,80176],{},[898,80177,1690],{},[902,80179,1690],{"encoding":904}," při pevně zadaných ",[883,80182,80184],{"className":80183},[886],[888,80185,80186],{"xmlns":890},[892,80187,80188,80196],{},[895,80189,80190,80192,80194],{},[898,80191,1807],{},[1651,80193,1661],{"separator":1660},[898,80195,11101],{},[902,80197,80198],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,80201,80202],{},"parametr efektivity"," — indikátor stavu technologie.",[198,80205,80207],{"id":80206},"příklad-53","Příklad 5.3",[724,80209,80210,80211,80106,80253,80255,80256,1882],{},"Produkční funkce ",[883,80212,80214],{"className":80213},[886],[888,80215,80216],{"xmlns":890},[892,80217,80218,80250],{},[895,80219,80220,80222,80224,80226,80238],{},[898,80221,1690],{},[1651,80223,1738],{},[1692,80225,1703],{},[2115,80227,80228,80230],{},[898,80229,1807],{},[895,80231,80232,80234,80236],{},[1692,80233,1694],{},[898,80235,5981],{"mathvariant":1910},[1692,80237,3689],{},[2115,80239,80240,80242],{},[898,80241,11101],{},[895,80243,80244,80246,80248],{},[1692,80245,3521],{},[898,80247,5981],{"mathvariant":1910},[1692,80249,3689],{},[902,80251,80252],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,80254,25826],{}," výnosy z rozsahu, neboť ",[883,80257,80259],{"className":80258},[886],[888,80260,80261],{"xmlns":890},[892,80262,80263,80287],{},[895,80264,80265,80273,80275,80283,80285],{},[2938,80266,80267],{"scriptlevel":1741,"displaystyle":1653},[2446,80268,80269,80271],{},[1692,80270,1694],{},[1692,80272,3689],{},[1651,80274,1839],{},[2938,80276,80277],{"scriptlevel":1741,"displaystyle":1653},[2446,80278,80279,80281],{},[1692,80280,3521],{},[1692,80282,3689],{},[1651,80284,1738],{},[1692,80286,1694],{},[902,80288,80289],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,80291,80292,80293,7497,80306,80319,80320,3246,80333,80373],{},"Změní-li se ",[883,80294,80296],{"className":80295},[886],[888,80297,80298],{"xmlns":890},[892,80299,80300,80304],{},[895,80301,80302],{},[898,80303,1807],{},[902,80305,1807],{"encoding":904},[883,80307,80309],{"className":80308},[886],[888,80310,80311],{"xmlns":890},[892,80312,80313,80317],{},[895,80314,80315],{},[898,80316,11101],{},[902,80318,11101],{"encoding":904}," čtyřnásobně, změní se ",[883,80321,80323],{"className":80322},[886],[888,80324,80325],{"xmlns":890},[892,80326,80327,80331],{},[895,80328,80329],{},[898,80330,1690],{},[902,80332,1690],{"encoding":904},[883,80334,80336],{"className":80335},[886],[888,80337,80338],{"xmlns":890},[892,80339,80340,80370],{},[895,80341,80342,80362,80364],{},[2115,80343,80344,80346],{},[1692,80345,3689],{},[895,80347,80348,80350,80352,80354,80356,80358,80360],{},[1692,80349,1694],{},[898,80351,5981],{"mathvariant":1910},[1692,80353,3689],{},[1651,80355,1839],{},[1692,80357,3521],{},[898,80359,5981],{"mathvariant":1910},[1692,80361,3689],{},[1651,80363,1738],{},[2115,80365,80366,80368],{},[1692,80367,3689],{},[1692,80369,1694],{},[902,80371,80372],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,80375,80377],{"className":80376},[886],[888,80378,80379],{"xmlns":890,"display":29279},[892,80380,80381,80541],{},[895,80382,80383,80385,80387,80389,80391,80393,80395,80397,80399,80401,80403,80405,80407,80409,80421,80423,80425,80427,80439,80441,80443,80445,80465,80477,80489,80491,80493,80495,80497,80509,80521,80523,80525,80527,80529,80531,80533,80535,80537,80539],{},[898,80384,1690],{},[1651,80386,1654],{"stretchy":1653},[1692,80388,3689],{},[898,80390,1807],{},[1651,80392,1661],{"separator":1660},[1692,80394,3689],{},[898,80396,11101],{},[1651,80398,1667],{"stretchy":1653},[1651,80400,1738],{},[1692,80402,1703],{},[1651,80404,1654],{"stretchy":1653},[1692,80406,3689],{},[898,80408,1807],{},[2115,80410,80411,80413],{},[1651,80412,1667],{"stretchy":1653},[895,80414,80415,80417,80419],{},[1692,80416,1694],{},[898,80418,5981],{"mathvariant":1910},[1692,80420,3689],{},[1651,80422,1654],{"stretchy":1653},[1692,80424,3689],{},[898,80426,11101],{},[2115,80428,80429,80431],{},[1651,80430,1667],{"stretchy":1653},[895,80432,80433,80435,80437],{},[1692,80434,3521],{},[898,80436,5981],{"mathvariant":1910},[1692,80438,3689],{},[1651,80440,1738],{},[1692,80442,1703],{},[1651,80444,4503],{},[2115,80446,80447,80449],{},[1692,80448,3689],{},[895,80450,80451,80453,80455,80457,80459,80461,80463],{},[1692,80452,1694],{},[898,80454,5981],{"mathvariant":1910},[1692,80456,3689],{},[1651,80458,1839],{},[1692,80460,3521],{},[898,80462,5981],{"mathvariant":1910},[1692,80464,3689],{},[2115,80466,80467,80469],{},[898,80468,1807],{},[895,80470,80471,80473,80475],{},[1692,80472,1694],{},[898,80474,5981],{"mathvariant":1910},[1692,80476,3689],{},[2115,80478,80479,80481],{},[898,80480,11101],{},[895,80482,80483,80485,80487],{},[1692,80484,3521],{},[898,80486,5981],{"mathvariant":1910},[1692,80488,3689],{},[1651,80490,1738],{},[1692,80492,3689],{},[1651,80494,4503],{},[1692,80496,1703],{},[2115,80498,80499,80501],{},[898,80500,1807],{},[895,80502,80503,80505,80507],{},[1692,80504,1694],{},[898,80506,5981],{"mathvariant":1910},[1692,80508,3689],{},[2115,80510,80511,80513],{},[898,80512,11101],{},[895,80514,80515,80517,80519],{},[1692,80516,3521],{},[898,80518,5981],{"mathvariant":1910},[1692,80520,3689],{},[1651,80522,1738],{},[1692,80524,3689],{},[1843,80526,1845],{},[898,80528,1690],{},[1651,80530,1654],{"stretchy":1653},[898,80532,1807],{},[1651,80534,1661],{"separator":1660},[898,80536,11101],{},[1651,80538,1667],{"stretchy":1653},[898,80540,1882],{"mathvariant":1910},[902,80542,80543],{"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).",[198,80545,80546],{"id":38392},"Homogenita",[724,80548,80549,80550,1878,80573,80589],{},"Funkce ",[883,80551,80553],{"className":80552},[886],[888,80554,80555],{"xmlns":890},[892,80556,80557,80571],{},[895,80558,80559,80561,80563,80565,80567,80569],{},[898,80560,1690],{},[1651,80562,1654],{"stretchy":1653},[898,80564,1807],{},[1651,80566,1661],{"separator":1660},[898,80568,11101],{},[1651,80570,1667],{"stretchy":1653},[902,80572,11297],{"encoding":904},[38,80574,80575,80576],{},"homogenní stupně ",[883,80577,80579],{"className":80578},[886],[888,80580,80581],{"xmlns":890},[892,80582,80583,80587],{},[895,80584,80585],{},[898,80586,38073],{},[902,80588,38073],{"encoding":904},", jestliže",[883,80591,80593],{"className":80592},[886],[888,80594,80595],{"xmlns":890,"display":29279},[892,80596,80597,80654],{},[21967,80598,80599],{"width":29284},[21972,80600,80601,80603,80647,80649],{},[21975,80602],{"width":29289},[21975,80604,80605],{},[895,80606,80607,80609,80611,80613,80615,80617,80619,80621,80623,80625,80631,80633,80635,80637,80639,80641,80643,80645],{},[898,80608,1690],{},[1651,80610,1654],{"stretchy":1653},[898,80612,13339],{},[898,80614,1807],{},[1651,80616,1661],{"separator":1660},[898,80618,13339],{},[898,80620,11101],{},[1651,80622,1667],{"stretchy":1653},[1651,80624,1738],{},[2115,80626,80627,80629],{},[898,80628,13339],{},[898,80630,38073],{},[1843,80632,1845],{},[898,80634,1690],{},[1651,80636,1654],{"stretchy":1653},[898,80638,1807],{},[1651,80640,1661],{"separator":1660},[898,80642,11101],{},[1651,80644,1667],{"stretchy":1653},[1651,80646,1661],{"separator":1660},[21975,80648],{"width":29289},[21975,80650,80651],{},[1843,80652,80653],{},"(5.10)",[902,80655,80656],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,80658,1863,80659,80677,80678,80696,80697,44849,80710,80713,80714,1882],{},[883,80660,80662],{"className":80661},[886],[888,80663,80664],{"xmlns":890},[892,80665,80666,80674],{},[895,80667,80668,80670,80672],{},[898,80669,38073],{},[1651,80671,5792],{},[1692,80673,1741],{},[902,80675,80676],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,80679,80681],{"className":80680},[886],[888,80682,80683],{"xmlns":890},[892,80684,80685,80693],{},[895,80686,80687,80689,80691],{},[898,80688,13339],{},[1651,80690,2390],{},[1692,80692,1741],{},[902,80694,80695],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,80698,80700],{"className":80699},[886],[888,80701,80702],{"xmlns":890},[892,80703,80704,80708],{},[895,80705,80706],{},[1692,80707,1694],{},[902,80709,1694],{"encoding":904},[38,80711,80712],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,80715,80717],{"className":80716},[886],[888,80718,80719],{"xmlns":890},[892,80720,80721,80729],{},[895,80722,80723,80725,80727],{},[898,80724,207],{},[1651,80726,1839],{},[898,80728,2268],{},[902,80730,76037],{"encoding":904},[115,80732,80734],{"id":80733},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,80736,80737],{},[38,80738,80739],{},"Ryzí Cobb-Douglasovy funkce:",[883,80741,80743],{"className":80742},[886],[888,80744,80745],{"xmlns":890,"display":29279},[892,80746,80747,80806],{},[21967,80748,80749],{"width":29284},[21972,80750,80751,80753,80799,80801],{},[21975,80752],{"width":29289},[21975,80754,80755],{},[895,80756,80757,80759,80761,80763,80765,80771,80773,80785,80787,80789,80791,80793,80795,80797],{},[898,80758,1690],{},[1651,80760,1738],{},[898,80762,5564],{},[1843,80764,1845],{},[2115,80766,80767,80769],{},[898,80768,1807],{},[898,80770,207],{},[1843,80772,1845],{},[2115,80774,80775,80777],{},[898,80776,11101],{},[895,80778,80779,80781,80783],{},[1692,80780,1694],{},[1651,80782,2181],{},[898,80784,207],{},[1651,80786,1661],{"separator":1660},[7185,80788],{"width":16582},[1692,80790,1741],{},[1651,80792,2319],{},[898,80794,207],{},[1651,80796,2319],{},[1692,80798,14558],{},[21975,80800],{"width":29289},[21975,80802,80803],{},[1843,80804,80805],{},"(5.9)",[902,80807,80808],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,80810,80811,80812,80814,80815,1882],{},"Mají vždy ",[38,80813,80132],{}," a jsou ",[38,80816,80712],{},[724,80818,80819,11325,80822,80825],{},[38,80820,80821],{},"CES produkční funkce",[614,80823,80824],{},"Constant Elasticity of Substitution",", 1961):",[883,80827,80829],{"className":80828},[886],[888,80830,80831],{"xmlns":890,"display":29279},[892,80832,80833,80901],{},[895,80834,80835,80837,80839,80841,80899],{},[898,80836,1690],{},[1651,80838,1738],{},[898,80840,5564],{},[2115,80842,80843,80887],{},[895,80844,80845,80847,80849,80851,80853,80855,80857,80859,80869,80871,80873,80875,80885],{},[1651,80846,2261],{"fence":1660},[1651,80848,1654],{"stretchy":1653},[1692,80850,1694],{},[1651,80852,2181],{},[898,80854,207],{},[1651,80856,1667],{"stretchy":1653},[1843,80858,1845],{},[2115,80860,80861,80863],{},[898,80862,1807],{},[895,80864,80865,80867],{},[1651,80866,2181],{},[898,80868,2268],{},[1651,80870,1839],{},[898,80872,207],{},[1843,80874,1845],{},[2115,80876,80877,80879],{},[898,80878,11101],{},[895,80880,80881,80883],{},[1651,80882,2181],{},[898,80884,2268],{},[1651,80886,2279],{"fence":1660},[895,80888,80889,80891],{},[1651,80890,2181],{},[2938,80892,80893],{"scriptlevel":1741,"displaystyle":1653},[2446,80894,80895,80897],{},[1692,80896,1694],{},[898,80898,2268],{},[1651,80900,1661],{"separator":1660},[902,80902,80903],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,80905,1863,80906,1343,80924,1343,80945,80969],{},[883,80907,80909],{"className":80908},[886],[888,80910,80911],{"xmlns":890},[892,80912,80913,80921],{},[895,80914,80915,80917,80919],{},[898,80916,5564],{},[1651,80918,2390],{},[1692,80920,1741],{},[902,80922,80923],{"encoding":904},"A > 0",[883,80925,80927],{"className":80926},[886],[888,80928,80929],{"xmlns":890},[892,80930,80931,80943],{},[895,80932,80933,80935,80937,80939,80941],{},[1692,80934,1741],{},[1651,80936,2319],{},[898,80938,207],{},[1651,80940,2319],{},[1692,80942,1694],{},[902,80944,20049],{"encoding":904},[883,80946,80948],{"className":80947},[886],[888,80949,80950],{"xmlns":890},[892,80951,80952,80966],{},[895,80953,80954,80956,80958,80960,80962,80964],{},[1651,80955,2181],{},[1692,80957,1694],{},[1651,80959,2319],{},[898,80961,2268],{},[1651,80963,4693],{"mathvariant":1910},[1692,80965,1741],{},[902,80967,80968],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,80971,80972],{},[38,80973,80974],{},"Další typy:",[120,80976,80977,81019],{},[123,80978,80979,3246,80982,81018],{},[38,80980,80981],{},"Lineární:",[883,80983,80985],{"className":80984},[886],[888,80986,80987],{"xmlns":890},[892,80988,80989,81015],{},[895,80990,80991,80993,80995,80997,80999,81001,81003,81005,81007,81009,81011,81013],{},[898,80992,1690],{},[1651,80994,1654],{"stretchy":1653},[898,80996,1807],{},[1651,80998,1661],{"separator":1660},[898,81000,11101],{},[1651,81002,1667],{"stretchy":1653},[1651,81004,1738],{},[898,81006,207],{},[898,81008,1807],{},[1651,81010,1839],{},[898,81012,2268],{},[898,81014,11101],{},[902,81016,81017],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,81020,81021,3246,81024,81069],{},[38,81022,81023],{},"Leontiefova:",[883,81025,81027],{"className":81026},[886],[888,81028,81029],{"xmlns":890},[892,81030,81031,81066],{},[895,81032,81033,81035,81037,81039,81041,81043,81045,81047,81050,81052,81054,81056,81058,81060,81062,81064],{},[898,81034,1690],{},[1651,81036,1654],{"stretchy":1653},[898,81038,1807],{},[1651,81040,1661],{"separator":1660},[898,81042,11101],{},[1651,81044,1667],{"stretchy":1653},[1651,81046,1738],{},[898,81048,81049],{},"min",[1651,81051,57413],{},[1651,81053,1654],{"stretchy":1653},[898,81055,207],{},[898,81057,1807],{},[1651,81059,1661],{"separator":1660},[898,81061,2268],{},[898,81063,11101],{},[1651,81065,1667],{"stretchy":1653},[902,81067,81068],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,81071,81073,81074,1343,81093,81112],{"id":81072},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,81075,81077],{"className":81076},[886],[888,81078,81079],{"xmlns":890},[892,81080,81081,81091],{},[895,81082,81083,81085],{},[898,81084,2995],{},[1686,81086,81087,81089],{},[898,81088,2675],{},[898,81090,1807],{},[902,81092,11345],{"encoding":904},[883,81094,81096],{"className":81095},[886],[888,81097,81098],{"xmlns":890},[892,81099,81100,81110],{},[895,81101,81102,81104],{},[898,81103,2995],{},[1686,81105,81106,81108],{},[898,81107,2675],{},[898,81109,11101],{},[902,81111,11390],{"encoding":904}," a totální diferenciál",[724,81114,81115],{},[38,81116,81117],{},"Mezní produkt práce:",[883,81119,81121],{"className":81120},[886],[888,81122,81123],{"xmlns":890,"display":29279},[892,81124,81125,81163],{},[895,81126,81127,81129,81135,81137,81145,81147,81161],{},[898,81128,2995],{},[1686,81130,81131,81133],{},[898,81132,2675],{},[898,81134,1807],{},[1651,81136,1738],{},[1902,81138,81139,81141,81143],{},[898,81140,1690],{},[898,81142,1807],{},[1651,81144,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,81146,1738],{},[2446,81148,81149,81155],{},[895,81150,81151,81153],{},[898,81152,11172],{"mathvariant":1910},[898,81154,1690],{},[895,81156,81157,81159],{},[898,81158,11172],{"mathvariant":1910},[898,81160,1807],{},[898,81162,1882],{"mathvariant":1910},[902,81164,81165],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,81167,81168],{},[38,81169,81170],{},"Mezní produkt kapitálu:",[883,81172,81174],{"className":81173},[886],[888,81175,81176],{"xmlns":890,"display":29279},[892,81177,81178,81216],{},[895,81179,81180,81182,81188,81190,81198,81200,81214],{},[898,81181,2995],{},[1686,81183,81184,81186],{},[898,81185,2675],{},[898,81187,11101],{},[1651,81189,1738],{},[1902,81191,81192,81194,81196],{},[898,81193,1690],{},[898,81195,11101],{},[1651,81197,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,81199,1738],{},[2446,81201,81202,81208],{},[895,81203,81204,81206],{},[898,81205,11172],{"mathvariant":1910},[898,81207,1690],{},[895,81209,81210,81212],{},[898,81211,11172],{"mathvariant":1910},[898,81213,11101],{},[898,81215,1882],{"mathvariant":1910},[902,81217,81218],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,81220,81221,81251,81252,81273,81274,81292,81293,81306,81307,1882],{},[883,81222,81224],{"className":81223},[886],[888,81225,81226],{"xmlns":890},[892,81227,81228,81248],{},[895,81229,81230,81232,81238,81240,81242,81244,81246],{},[898,81231,2995],{},[1686,81233,81234,81236],{},[898,81235,2675],{},[898,81237,1807],{},[1651,81239,1654],{"stretchy":1653},[898,81241,207],{},[1651,81243,1661],{"separator":1660},[898,81245,2268],{},[1651,81247,1667],{"stretchy":1653},[902,81249,81250],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,81253,81255],{"className":81254},[886],[888,81256,81257],{"xmlns":890},[892,81258,81259,81271],{},[895,81260,81261,81263,81265,81267,81269],{},[1651,81262,2261],{"stretchy":1653},[898,81264,207],{},[1651,81266,1661],{"separator":1660},[898,81268,2268],{},[1651,81270,2279],{"stretchy":1653},[902,81272,12123],{"encoding":904}," (na hladině ",[883,81275,81277],{"className":81276},[886],[888,81278,81279],{"xmlns":890},[892,81280,81281,81289],{},[895,81282,81283,81285,81287],{},[898,81284,11101],{},[1651,81286,1738],{},[898,81288,2268],{},[902,81290,81291],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,81294,81296],{"className":81295},[886],[888,81297,81298],{"xmlns":890},[892,81299,81300,81304],{},[895,81301,81302],{},[898,81303,1807],{},[902,81305,1807],{"encoding":904},". Analogicky ",[883,81308,81310],{"className":81309},[886],[888,81311,81312],{"xmlns":890},[892,81313,81314,81334],{},[895,81315,81316,81318,81324,81326,81328,81330,81332],{},[898,81317,2995],{},[1686,81319,81320,81322],{},[898,81321,2675],{},[898,81323,11101],{},[1651,81325,1654],{"stretchy":1653},[898,81327,207],{},[1651,81329,1661],{"separator":1660},[898,81331,2268],{},[1651,81333,1667],{"stretchy":1653},[902,81335,81336],{"encoding":904},"MP_K(a, b)",[5179,81338,81339,81343],{},[724,81340,81341,52432],{},[883,81342,5465],{},[120,81344,81345,81383],{},[123,81346,81347,27402,81366],{},[883,81348,81350],{"className":81349},[886],[888,81351,81352],{"xmlns":890},[892,81353,81354,81364],{},[895,81355,81356,81358],{},[898,81357,2995],{},[1686,81359,81360,81362],{},[898,81361,2675],{},[898,81363,1807],{},[902,81365,11345],{"encoding":904},[614,81367,81368,81369,81382],{},"„o kolik vzroste ",[883,81370,81372],{"className":81371},[886],[888,81373,81374],{"xmlns":890},[892,81375,81376,81380],{},[895,81377,81378],{},[898,81379,1690],{},[902,81381,1690],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,81384,81385,27402,81404],{},[883,81386,81388],{"className":81387},[886],[888,81389,81390],{"xmlns":890},[892,81391,81392,81402],{},[895,81393,81394,81396],{},[898,81395,2995],{},[1686,81397,81398,81400],{},[898,81399,2675],{},[898,81401,11101],{},[902,81403,11390],{"encoding":904},[614,81405,81368,81406,81419],{},[883,81407,81409],{"className":81408},[886],[888,81410,81411],{"xmlns":890},[892,81412,81413,81417],{},[895,81414,81415],{},[898,81416,1690],{},[902,81418,1690],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,81421,81422,81425,81426,81441,81442,1793],{},[38,81423,81424],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,81427,81429],{"className":81428},[886],[888,81430,81431],{"xmlns":890},[892,81432,81433,81439],{},[895,81434,81435,81437],{},[898,81436,3542],{},[898,81438,1807],{},[902,81440,76569],{"encoding":904}," a kapitálu o ",[883,81443,81445],{"className":81444},[886],[888,81446,81447],{"xmlns":890},[892,81448,81449,81455],{},[895,81450,81451,81453],{},[898,81452,3542],{},[898,81454,11101],{},[902,81456,81457],{"encoding":904},"dK",[883,81459,81461],{"className":81460},[886],[888,81462,81463],{"xmlns":890,"display":29279},[892,81464,81465,81558],{},[21967,81466,81467],{"width":29284},[21972,81468,81469,81471,81551,81553],{},[21975,81470],{"width":29289},[21975,81472,81473],{},[895,81474,81475,81477,81479,81481,81483,81485,81487,81495,81497,81499,81501,81503,81511,81513,81515,81517,81519,81521,81527,81529,81531,81533,81535,81537,81543,81545,81547,81549],{},[898,81476,4216],{"mathvariant":1910},[898,81478,1690],{},[1651,81480,4060],{},[898,81482,3542],{},[898,81484,1690],{},[1651,81486,1738],{},[1902,81488,81489,81491,81493],{},[898,81490,1690],{},[898,81492,1807],{},[1651,81494,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1843,81496,1845],{},[898,81498,3542],{},[898,81500,1807],{},[1651,81502,1839],{},[1902,81504,81505,81507,81509],{},[898,81506,1690],{},[898,81508,11101],{},[1651,81510,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1843,81512,1845],{},[898,81514,3542],{},[898,81516,11101],{},[1651,81518,1738],{},[898,81520,2995],{},[1686,81522,81523,81525],{},[898,81524,2675],{},[898,81526,1807],{},[1843,81528,1845],{},[898,81530,3542],{},[898,81532,1807],{},[1651,81534,1839],{},[898,81536,2995],{},[1686,81538,81539,81541],{},[898,81540,2675],{},[898,81542,11101],{},[1843,81544,1845],{},[898,81546,3542],{},[898,81548,11101],{},[898,81550,1882],{"mathvariant":1910},[21975,81552],{"width":29289},[21975,81554,81555],{},[1843,81556,81557],{},"(5.11)",[902,81559,81560],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,81562,81563,81564,1882],{},"Skutečná změna: ",[883,81565,81567],{"className":81566},[886],[888,81568,81569],{"xmlns":890},[892,81570,81571,81617],{},[895,81572,81573,81575,81577,81579,81581,81583,81585,81587,81589,81591,81593,81595,81597,81599,81601,81603,81605,81607,81609,81611,81613,81615],{},[898,81574,4216],{"mathvariant":1910},[898,81576,1690],{},[1651,81578,1738],{},[898,81580,1690],{},[1651,81582,1654],{"stretchy":1653},[898,81584,1807],{},[1651,81586,1839],{},[898,81588,3542],{},[898,81590,1807],{},[1651,81592,1661],{"separator":1660},[898,81594,11101],{},[1651,81596,1839],{},[898,81598,3542],{},[898,81600,11101],{},[1651,81602,1667],{"stretchy":1653},[1651,81604,2181],{},[898,81606,1690],{},[1651,81608,1654],{"stretchy":1653},[898,81610,1807],{},[1651,81612,1661],{"separator":1660},[898,81614,11101],{},[1651,81616,1667],{"stretchy":1653},[902,81618,81619],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,81621,81622,81624,81625,81643,81644,81657,81658,81677,81678,81710,81711,81743,81744,1882],{},[38,81623,76733],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,81626,81628],{"className":81627},[886],[888,81629,81630],{"xmlns":890},[892,81631,81632,81640],{},[895,81633,81634],{},[1686,81635,81636,81638],{},[898,81637,11101],{},[1692,81639,1741],{},[902,81641,81642],{"encoding":904},"K_0"," se od jistého ",[883,81645,81647],{"className":81646},[886],[888,81648,81649],{"xmlns":890},[892,81650,81651,81655],{},[895,81652,81653],{},[898,81654,1807],{},[902,81656,1807],{"encoding":904}," stane ",[883,81659,81661],{"className":81660},[886],[888,81662,81663],{"xmlns":890},[892,81664,81665,81675],{},[895,81666,81667,81669],{},[898,81668,2995],{},[1686,81670,81671,81673],{},[898,81672,2675],{},[898,81674,1807],{},[902,81676,11345],{"encoding":904}," klesající (",[883,81679,81681],{"className":81680},[886],[888,81682,81683],{"xmlns":890},[892,81684,81685,81707],{},[895,81686,81687,81703,81705],{},[1902,81688,81689,81691,81697],{},[898,81690,1690],{},[895,81692,81693,81695],{},[898,81694,1807],{},[898,81696,1807],{},[895,81698,81699,81701],{},[1651,81700,1912],{"mathvariant":1910},[1651,81702,1912],{"mathvariant":1910},[1651,81704,2319],{},[1692,81706,1741],{},[902,81708,81709],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,81712,81714],{"className":81713},[886],[888,81715,81716],{"xmlns":890},[892,81717,81718,81740],{},[895,81719,81720,81736,81738],{},[1902,81721,81722,81724,81730],{},[898,81723,1690],{},[895,81725,81726,81728],{},[898,81727,11101],{},[898,81729,11101],{},[895,81731,81732,81734],{},[1651,81733,1912],{"mathvariant":1910},[1651,81735,1912],{"mathvariant":1910},[1651,81737,2319],{},[1692,81739,1741],{},[902,81741,81742],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,81745,81747],{"className":81746},[886],[888,81748,81749],{"xmlns":890},[892,81750,81751,81759],{},[895,81752,81753],{},[1686,81754,81755,81757],{},[898,81756,1807],{},[1692,81758,1741],{},[902,81760,76771],{"encoding":904},[115,81762,81764],{"id":81763},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,81766,81767,81770,81771,81794,81795,31157],{},[38,81768,81769],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,81772,81774],{"className":81773},[886],[888,81775,81776],{"xmlns":890},[892,81777,81778,81792],{},[895,81779,81780,81782,81784,81786,81788,81790],{},[898,81781,1690],{},[1651,81783,1654],{"stretchy":1653},[898,81785,1807],{},[1651,81787,1661],{"separator":1660},[898,81789,11101],{},[1651,81791,1667],{"stretchy":1653},[902,81793,11297],{"encoding":904}," stupně ",[883,81796,81798],{"className":81797},[886],[888,81799,81800],{"xmlns":890},[892,81801,81802,81806],{},[895,81803,81804],{},[898,81805,38073],{},[902,81807,38073],{"encoding":904},[883,81809,81811],{"className":81810},[886],[888,81812,81813],{"xmlns":890,"display":29279},[892,81814,81815,81878],{},[21967,81816,81817],{"width":29284},[21972,81818,81819,81821,81871,81873],{},[21975,81820],{"width":29289},[21975,81822,81823],{},[895,81824,81825,81827,81829,81837,81839,81841,81843,81851,81853,81855,81857,81859,81861,81863,81865,81867,81869],{},[898,81826,1807],{},[1843,81828,1845],{},[1902,81830,81831,81833,81835],{},[898,81832,1690],{},[898,81834,1807],{},[1651,81836,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,81838,1839],{},[898,81840,11101],{},[1843,81842,1845],{},[1902,81844,81845,81847,81849],{},[898,81846,1690],{},[898,81848,11101],{},[1651,81850,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,81852,1738],{},[898,81854,38073],{},[1843,81856,1845],{},[898,81858,1690],{},[1651,81860,1654],{"stretchy":1653},[898,81862,1807],{},[1651,81864,1661],{"separator":1660},[898,81866,11101],{},[1651,81868,1667],{"stretchy":1653},[898,81870,1882],{"mathvariant":1910},[21975,81872],{"width":29289},[21975,81874,81875],{},[1843,81876,81877],{},"(5.12)",[902,81879,81880],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,81882,81883,81904],{},[38,81884,81885,81886],{},"Speciální případ ",[883,81887,81889],{"className":81888},[886],[888,81890,81891],{"xmlns":890},[892,81892,81893,81901],{},[895,81894,81895,81897,81899],{},[898,81896,38073],{},[1651,81898,1738],{},[1692,81900,1694],{},[902,81902,81903],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,81906,81908],{"className":81907},[886],[888,81909,81910],{"xmlns":890,"display":29279},[892,81911,81912,81956],{},[895,81913,81914,81916,81918,81920,81926,81928,81930,81932,81934,81940,81942,81944,81946,81948,81950,81952,81954],{},[898,81915,1807],{},[1651,81917,4503],{},[898,81919,2995],{},[1686,81921,81922,81924],{},[898,81923,2675],{},[898,81925,1807],{},[1651,81927,1839],{},[898,81929,11101],{},[1651,81931,4503],{},[898,81933,2995],{},[1686,81935,81936,81938],{},[898,81937,2675],{},[898,81939,11101],{},[1651,81941,1738],{},[898,81943,1690],{},[1651,81945,1654],{"stretchy":1653},[898,81947,1807],{},[1651,81949,1661],{"separator":1660},[898,81951,11101],{},[1651,81953,1667],{"stretchy":1653},[898,81955,1882],{"mathvariant":1910},[902,81957,81958],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,81960,81961,81962,81965],{},"Slovně — ",[38,81963,81964],{},"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).",[115,81967,11080],{"id":76107},[724,81969,81970,11325,81972,81975,81976,81998,81999,1793],{},[38,81971,11080],{},[614,81973,81974],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,81977,81979],{"className":81978},[886],[888,81980,81981],{"xmlns":890},[892,81982,81983,81995],{},[895,81984,81985,81987,81989,81991,81993],{},[1651,81986,2261],{"stretchy":1653},[898,81988,1807],{},[1651,81990,1661],{"separator":1660},[898,81992,11101],{},[1651,81994,2279],{"stretchy":1653},[902,81996,81997],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,82000,82002],{"className":82001},[886],[888,82003,82004],{"xmlns":890},[892,82005,82006,82011],{},[895,82007,82008],{},[898,82009,82010],{},"q",[902,82012,82010],{"encoding":904},[883,82014,82016],{"className":82015},[886],[888,82017,82018],{"xmlns":890,"display":29279},[892,82019,82020,82055],{},[21967,82021,82022],{"width":29284},[21972,82023,82024,82026,82048,82050],{},[21975,82025],{"width":29289},[21975,82027,82028],{},[895,82029,82030,82032,82034,82036,82038,82040,82042,82044,82046],{},[898,82031,1690],{},[1651,82033,1654],{"stretchy":1653},[898,82035,1807],{},[1651,82037,1661],{"separator":1660},[898,82039,11101],{},[1651,82041,1667],{"stretchy":1653},[1651,82043,1738],{},[898,82045,82010],{},[898,82047,1882],{"mathvariant":1910},[21975,82049],{"width":29289},[21975,82051,82052],{},[1843,82053,82054],{},"(5.13)",[902,82056,82057],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,82059,82060,82061,82064,82065,5230],{},"Jsou to ",[38,82062,82063],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,82066,82068],{"className":82067,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,82070,82071],{},[38,82072,82073],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,82075,82076,82081,82086,82091],{},[123,82077,82078,82080],{},[38,82079,13817],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,82082,82083,82085],{},[38,82084,38877],{}," (úloha 5.14);",[123,82087,82088,9731],{},[38,82089,82090],{},"neprotínají se",[123,82092,82093,82094,5665,82107,1882],{},"s rostoucím ",[883,82095,82097],{"className":82096},[886],[888,82098,82099],{"xmlns":890},[892,82100,82101,82105],{},[895,82102,82103],{},[898,82104,82010],{},[902,82106,82010],{"encoding":904},[38,82108,82109],{},"vzdalují od počátku",[724,82111,82112],{},[614,82113,82114,82115,82137,82138,1882],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,82116,82118],{"className":82117},[886],[888,82119,82120],{"xmlns":890},[892,82121,82122,82134],{},[895,82123,82124,82126,82128,82130,82132],{},[1651,82125,1654],{"stretchy":1653},[898,82127,1807],{},[1651,82129,1661],{"separator":1660},[898,82131,11101],{},[1651,82133,1667],{"stretchy":1653},[902,82135,82136],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,82139,82141],{"className":82140},[886],[888,82142,82143],{"xmlns":890},[892,82144,82145,82169],{},[895,82146,82147,82153,82155,82161,82163],{},[1686,82148,82149,82151],{},[898,82150,82010],{},[1692,82152,1694],{},[1651,82154,2319],{},[1686,82156,82157,82159],{},[898,82158,82010],{},[1692,82160,1741],{},[1651,82162,2319],{},[1686,82164,82165,82167],{},[898,82166,82010],{},[1692,82168,1703],{},[902,82170,82171],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,82173,82175,82176,1667],{"id":82174},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,82177,82179],{"className":82178},[886],[888,82180,82181],{"xmlns":890},[892,82182,82183,82193],{},[895,82184,82185,82187,82189,82191],{},[898,82186,2995],{},[898,82188,2998],{},[898,82190,4104],{},[898,82192,3004],{},[902,82194,11899],{"encoding":904},[724,82196,82197,11325,82200,82203],{},[38,82198,82199],{},"Mezní míra technické substituce",[614,82201,82202],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,82205,82207],{"className":82206},[886],[888,82208,82209],{"xmlns":890,"display":29279},[892,82210,82211,82302],{},[21967,82212,82213],{"width":29284},[21972,82214,82215,82217,82295,82297],{},[21975,82216],{"width":29289},[21975,82218,82219],{},[895,82220,82221,82223,82225,82227,82229,82231,82233,82235,82237,82239,82241,82243,82245,82247,82249,82251,82273,82275,82293],{},[898,82222,2995],{},[898,82224,2998],{},[898,82226,4104],{},[898,82228,3004],{},[1651,82230,1738],{},[898,82232,2995],{},[898,82234,2998],{},[898,82236,4104],{},[898,82238,3004],{},[1651,82240,1654],{"stretchy":1653},[898,82242,1807],{},[1651,82244,1661],{"separator":1660},[898,82246,11101],{},[1651,82248,1667],{"stretchy":1653},[1651,82250,1738],{},[2446,82252,82253,82263],{},[895,82254,82255,82257],{},[898,82256,2995],{},[1686,82258,82259,82261],{},[898,82260,2675],{},[898,82262,1807],{},[895,82264,82265,82267],{},[898,82266,2995],{},[1686,82268,82269,82271],{},[898,82270,2675],{},[898,82272,11101],{},[1651,82274,1738],{},[2446,82276,82277,82285],{},[1902,82278,82279,82281,82283],{},[898,82280,1690],{},[898,82282,1807],{},[1651,82284,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1902,82286,82287,82289,82291],{},[898,82288,1690],{},[898,82290,11101],{},[1651,82292,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[898,82294,1882],{"mathvariant":1910},[21975,82296],{"width":29289},[21975,82298,82299],{},[1843,82300,82301],{},"(5.14)",[902,82303,82304],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,82306,82307,3246,82309,82339,82340,82371],{},[38,82308,10519],{},[883,82310,82312],{"className":82311},[886],[888,82313,82314],{"xmlns":890},[892,82315,82316,82336],{},[895,82317,82318,82320,82322,82324,82326,82328,82330,82332,82334],{},[898,82319,2995],{},[898,82321,2998],{},[898,82323,4104],{},[898,82325,3004],{},[1651,82327,1654],{"stretchy":1653},[898,82329,1807],{},[1651,82331,1661],{"separator":1660},[898,82333,11101],{},[1651,82335,1667],{"stretchy":1653},[902,82337,82338],{"encoding":904},"MRTS(L, K)"," udává, ",[38,82341,82342,82343,82356,82357,82370],{},"o kolik se musí přibližně změnit kapitál ",[883,82344,82346],{"className":82345},[886],[888,82347,82348],{"xmlns":890},[892,82349,82350,82354],{},[895,82351,82352],{},[898,82353,11101],{},[902,82355,11101],{"encoding":904},", jestliže se práce ",[883,82358,82360],{"className":82359},[886],[888,82361,82362],{"xmlns":890},[892,82363,82364,82368],{},[895,82365,82366],{},[898,82367,1807],{},[902,82369,1807],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[5179,82373,82374],{},[724,82375,82376,19236,82378,82397,82398,82435,82436,82439,82440,82444],{},[883,82377,5465],{},[883,82379,82381],{"className":82380},[886],[888,82382,82383],{"xmlns":890},[892,82384,82385,82395],{},[895,82386,82387,82389,82391,82393],{},[898,82388,2995],{},[898,82390,2998],{},[898,82392,4104],{},[898,82394,3004],{},[902,82396,11899],{"encoding":904}," říká: ",[614,82399,82400,82401,82420,82421,82434],{},"„jednu jednotku práce musím nahradit přibližně ",[883,82402,82404],{"className":82403},[886],[888,82405,82406],{"xmlns":890},[892,82407,82408,82418],{},[895,82409,82410,82412,82414,82416],{},[898,82411,2995],{},[898,82413,2998],{},[898,82415,4104],{},[898,82417,3004],{},[902,82419,11899],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,82422,82424],{"className":82423},[886],[888,82425,82426],{"xmlns":890},[892,82427,82428,82432],{},[895,82429,82430],{},[898,82431,1690],{},[902,82433,1690],{"encoding":904}," zůstala stejná.\""," Je to ",[38,82437,82438],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,82441,82443],{"className":82442,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,82446,82447],{},[1756,82448],{"alt":82449,"className":82450,"src":82451},"imek-izokvanty-mrts",[210,1760],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,82453,82454,82457,82458,1878,82488,82510,82511,4477],{},[38,82455,82456],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,82459,82461],{"className":82460},[886],[888,82462,82463],{"xmlns":890},[892,82464,82465,82485],{},[895,82466,82467,82469,82475,82477,82483],{},[1651,82468,2261],{"stretchy":1653},[1686,82470,82471,82473],{},[898,82472,1807],{},[1692,82474,1741],{},[1651,82476,1661],{"separator":1660},[1686,82478,82479,82481],{},[898,82480,11101],{},[1692,82482,1741],{},[1651,82484,2279],{"stretchy":1653},[902,82486,82487],{"encoding":904},"[L_0, K_0]",[883,82489,82491],{"className":82490},[886],[888,82492,82493],{"xmlns":890},[892,82494,82495,82507],{},[895,82496,82497,82499,82501,82503,82505],{},[1651,82498,2181],{},[898,82500,2995],{},[898,82502,2998],{},[898,82504,4104],{},[898,82506,3004],{},[902,82508,82509],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,82512,82514],{"className":82513},[886],[888,82515,82516],{"xmlns":890},[892,82517,82518,82540],{},[895,82519,82520,82522,82524,82526,82528,82530,82532,82534],{},[898,82521,1690],{},[1651,82523,1654],{"stretchy":1653},[898,82525,1807],{},[1651,82527,1661],{"separator":1660},[898,82529,11101],{},[1651,82531,1667],{"stretchy":1653},[1651,82533,1738],{},[1686,82535,82536,82538],{},[898,82537,82010],{},[1692,82539,1741],{},[902,82541,82542],{"encoding":904},"Q(L,K) = q_0",[883,82544,82546],{"className":82545},[886],[888,82547,82548],{"xmlns":890,"display":29279},[892,82549,82550,82602],{},[895,82551,82552,82566,82568,82570,82588,82590,82592,82594,82596,82598,82600],{},[2446,82553,82554,82560],{},[895,82555,82556,82558],{},[898,82557,3542],{},[898,82559,11101],{},[895,82561,82562,82564],{},[898,82563,3542],{},[898,82565,1807],{},[1651,82567,1738],{},[1651,82569,2181],{},[2446,82571,82572,82580],{},[1902,82573,82574,82576,82578],{},[898,82575,1690],{},[898,82577,1807],{},[1651,82579,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1902,82581,82582,82584,82586],{},[898,82583,1690],{},[898,82585,11101],{},[1651,82587,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,82589,1738],{},[1651,82591,2181],{},[898,82593,2995],{},[898,82595,2998],{},[898,82597,4104],{},[898,82599,3004],{},[898,82601,1882],{"mathvariant":1910},[902,82603,82604],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,82606,82607,82608,82623,82624,82640],{},"Změní-li se práce o ",[883,82609,82611],{"className":82610},[886],[888,82612,82613],{"xmlns":890},[892,82614,82615,82621],{},[895,82616,82617,82619],{},[898,82618,3542],{},[898,82620,1807],{},[902,82622,76569],{"encoding":904},", lze pro odhad změny kapitálu ",[883,82625,82627],{"className":82626},[886],[888,82628,82629],{"xmlns":890},[892,82630,82631,82637],{},[895,82632,82633,82635],{},[898,82634,4216],{"mathvariant":1910},[898,82636,11101],{},[902,82638,82639],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,82642,82644],{"className":82643},[886],[888,82645,82646],{"xmlns":890,"display":29279},[892,82647,82648,82695],{},[21967,82649,82650],{"width":29284},[21972,82651,82652,82654,82688,82690],{},[21975,82653],{"width":29289},[21975,82655,82656],{},[895,82657,82658,82660,82662,82664,82666,82668,82670,82672,82674,82676,82678,82680,82682,82684,82686],{},[898,82659,4216],{"mathvariant":1910},[898,82661,11101],{},[1651,82663,4060],{},[898,82665,3542],{},[898,82667,11101],{},[1651,82669,1738],{},[1651,82671,2181],{},[898,82673,2995],{},[898,82675,2998],{},[898,82677,4104],{},[898,82679,3004],{},[1843,82681,1845],{},[898,82683,3542],{},[898,82685,1807],{},[1651,82687,1661],{"separator":1660},[21975,82689],{"width":29289},[21975,82691,82692],{},[1843,82693,82694],{},"(5.15)",[902,82696,82697],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,82699,82701],{"className":82700},[886],[888,82702,82703],{"xmlns":890,"display":29279},[892,82704,82705,82754],{},[21967,82706,82707],{"width":29284},[21972,82708,82709,82711,82747,82749],{},[21975,82710],{"width":29289},[21975,82712,82713],{},[895,82714,82715,82717,82719,82721,82739,82741,82743,82745],{},[898,82716,3542],{},[898,82718,1807],{},[1651,82720,1738],{},[2446,82722,82723,82729],{},[895,82724,82725,82727],{},[1651,82726,2181],{},[1692,82728,1694],{},[895,82730,82731,82733,82735,82737],{},[898,82732,2995],{},[898,82734,2998],{},[898,82736,4104],{},[898,82738,3004],{},[1843,82740,1845],{},[898,82742,3542],{},[898,82744,11101],{},[898,82746,1882],{"mathvariant":1910},[21975,82748],{"width":29289},[21975,82750,82751],{},[1843,82752,82753],{},"(5.16)",[902,82755,82756],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[5179,82758,82759,82783],{},[724,82760,82761,82763,82764],{},[883,82762,5879],{}," Postup — jak spočítat ",[883,82765,82767],{"className":82766},[886],[888,82768,82769],{"xmlns":890},[892,82770,82771,82781],{},[895,82772,82773,82775,82777,82779],{},[898,82774,2995],{},[898,82776,2998],{},[898,82778,4104],{},[898,82780,3004],{},[902,82782,11899],{"encoding":904},[152,82784,82785,82826,82869,82901],{},[123,82786,82787,82788,5197,82807,1882],{},"Vypočtěte parciální derivace ",[883,82789,82791],{"className":82790},[886],[888,82792,82793],{"xmlns":890},[892,82794,82795,82805],{},[895,82796,82797],{},[1902,82798,82799,82801,82803],{},[898,82800,1690],{},[898,82802,1807],{},[1651,82804,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,82806,11321],{"encoding":904},[883,82808,82810],{"className":82809},[886],[888,82811,82812],{"xmlns":890},[892,82813,82814,82824],{},[895,82815,82816],{},[1902,82817,82818,82820,82822],{},[898,82819,1690],{},[898,82821,11101],{},[1651,82823,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,82825,11367],{"encoding":904},[123,82827,67054,82828,82868],{},[883,82829,82831],{"className":82830},[886],[888,82832,82833],{"xmlns":890},[892,82834,82835,82865],{},[895,82836,82837,82839,82841,82843,82845,82847,82855,82857],{},[898,82838,2995],{},[898,82840,2998],{},[898,82842,4104],{},[898,82844,3004],{},[1651,82846,1738],{},[1902,82848,82849,82851,82853],{},[898,82850,1690],{},[898,82852,1807],{},[1651,82854,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[898,82856,5981],{"mathvariant":1910},[1902,82858,82859,82861,82863],{},[898,82860,1690],{},[898,82862,11101],{},[1651,82864,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,82866,82867],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,82870,82871,82872,1882],{},"Případně dosaďte konkrétní ",[883,82873,82875],{"className":82874},[886],[888,82876,82877],{"xmlns":890},[892,82878,82879,82899],{},[895,82880,82881,82883,82889,82891,82897],{},[1651,82882,2261],{"stretchy":1653},[1686,82884,82885,82887],{},[898,82886,1807],{},[1692,82888,1741],{},[1651,82890,1661],{"separator":1660},[1686,82892,82893,82895],{},[898,82894,11101],{},[1692,82896,1741],{},[1651,82898,2279],{"stretchy":1653},[902,82900,82487],{"encoding":904},[123,82902,82903,82904,82938,82939,82941],{},"Pro odhad substituce použijte ",[883,82905,82907],{"className":82906},[886],[888,82908,82909],{"xmlns":890},[892,82910,82911,82935],{},[895,82912,82913,82915,82917,82919,82921,82923,82925,82927,82929,82931,82933],{},[898,82914,4216],{"mathvariant":1910},[898,82916,11101],{},[1651,82918,4060],{},[1651,82920,2181],{},[898,82922,2995],{},[898,82924,2998],{},[898,82926,4104],{},[898,82928,3004],{},[1651,82930,4503],{},[898,82932,4216],{"mathvariant":1910},[898,82934,1807],{},[902,82936,82937],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,82940,53819],{}," — substituce, ne doplnění).",[724,82943,82944],{},[614,82945,82946,82947,82979,82980,3955,82993,17090,83022,83037],{},"Obrázek 5.7 — izokvanta ",[883,82948,82950],{"className":82949},[886],[888,82951,82952],{"xmlns":890},[892,82953,82954,82976],{},[895,82955,82956,82962,82964,82966,82968,82970,82972,82974],{},[1686,82957,82958,82960],{},[898,82959,82010],{},[1692,82961,1741],{},[1651,82963,1738],{},[898,82965,1690],{},[1651,82967,1654],{"stretchy":1653},[898,82969,1807],{},[1651,82971,1661],{"separator":1660},[898,82973,11101],{},[1651,82975,1667],{"stretchy":1653},[902,82977,82978],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,82981,82983],{"className":82982},[886],[888,82984,82985],{"xmlns":890},[892,82986,82987,82991],{},[895,82988,82989],{},[898,82990,20068],{},[902,82992,20068],{"encoding":904},[883,82994,82996],{"className":82995},[886],[888,82997,82998],{"xmlns":890},[892,82999,83000,83020],{},[895,83001,83002,83004,83010,83012,83018],{},[1651,83003,2261],{"stretchy":1653},[1686,83005,83006,83008],{},[898,83007,1807],{},[1692,83009,1741],{},[1651,83011,1661],{"separator":1660},[1686,83013,83014,83016],{},[898,83015,11101],{},[1692,83017,1741],{},[1651,83019,2279],{"stretchy":1653},[902,83021,82487],{"encoding":904},[883,83023,83025],{"className":83024},[886],[888,83026,83027],{"xmlns":890},[892,83028,83029,83035],{},[895,83030,83031,83033],{},[898,83032,4216],{"mathvariant":1910},[898,83034,11101],{},[902,83036,82639],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,83039,83041],{"id":83040},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,83043,83045],{"id":83044},"příklad-54","Příklad 5.4",[724,83047,77886,83048,1343,83090,1343,83107,1882],{},[883,83049,83051],{"className":83050},[886],[888,83052,83053],{"xmlns":890},[892,83054,83055,83087],{},[895,83056,83057,83059,83061,83063,83075],{},[898,83058,1690],{},[1651,83060,1738],{},[1692,83062,37457],{},[2115,83064,83065,83067],{},[898,83066,1807],{},[895,83068,83069,83071,83073],{},[1692,83070,1694],{},[898,83072,5981],{"mathvariant":1910},[1692,83074,1703],{},[2115,83076,83077,83079],{},[898,83078,11101],{},[895,83080,83081,83083,83085],{},[1692,83082,1694],{},[898,83084,5981],{"mathvariant":1910},[1692,83086,3521],{},[902,83088,83089],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,83091,83093],{"className":83092},[886],[888,83094,83095],{"xmlns":890},[892,83096,83097,83105],{},[895,83098,83099,83101,83103],{},[898,83100,1807],{},[1651,83102,1738],{},[1692,83104,10340],{},[902,83106,78260],{"encoding":904},[883,83108,83110],{"className":83109},[886],[888,83111,83112],{"xmlns":890},[892,83113,83114,83122],{},[895,83115,83116,83118,83120],{},[898,83117,11101],{},[1651,83119,1738],{},[1692,83121,4416],{},[902,83123,83124],{"encoding":904},"K = 100",[724,83126,83127],{},[38,83128,83129],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,83131,83133],{"className":83132},[886],[888,83134,83135],{"xmlns":890,"display":29279},[892,83136,83137,83251],{},[895,83138,83139,83141,83147,83149,83157,83159,83167,83181,83193,83195,83197,83199,83205,83207,83209,83211,83213,83215,83217,83225,83227,83237,83239,83246,83248],{},[898,83140,2995],{},[1686,83142,83143,83145],{},[898,83144,2675],{},[898,83146,1807],{},[1651,83148,1738],{},[1902,83150,83151,83153,83155],{},[898,83152,1690],{},[898,83154,1807],{},[1651,83156,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,83158,1738],{},[2938,83160,83161],{"scriptlevel":1741,"displaystyle":1653},[2446,83162,83163,83165],{},[1692,83164,37457],{},[1692,83166,1703],{},[2115,83168,83169,83171],{},[898,83170,1807],{},[895,83172,83173,83175,83177,83179],{},[1651,83174,2181],{},[1692,83176,1694],{},[898,83178,5981],{"mathvariant":1910},[1692,83180,1703],{},[2115,83182,83183,83185],{},[898,83184,11101],{},[895,83186,83187,83189,83191],{},[1692,83188,1694],{},[898,83190,5981],{"mathvariant":1910},[1692,83192,3521],{},[1651,83194,1661],{"separator":1660},[7185,83196],{"width":16582},[898,83198,2995],{},[1686,83200,83201,83203],{},[898,83202,2675],{},[898,83204,1807],{},[1651,83206,1654],{"stretchy":1653},[1692,83208,10340],{},[1651,83210,1661],{"separator":1660},[1692,83212,4416],{},[1651,83214,1667],{"stretchy":1653},[1651,83216,1738],{},[2938,83218,83219],{"scriptlevel":1741,"displaystyle":1653},[2446,83220,83221,83223],{},[1692,83222,37457],{},[1692,83224,1703],{},[1651,83226,4503],{},[2938,83228,83229],{"scriptlevel":1741,"displaystyle":1653},[2446,83230,83231,83233],{},[1692,83232,1694],{},[9423,83234,83235],{},[1692,83236,10340],{},[1651,83238,4503],{},[83240,83241,83242,83244],"mroot",{},[1692,83243,4416],{},[1692,83245,3521],{},[1651,83247,4060],{},[1692,83249,83250],{},"7,153.",[902,83252,83253],{"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.",[724,83255,83256,83257,45373,83279,11533,83296,83317,83318,83339],{},"Přibližná změna při ",[883,83258,83260],{"className":83259},[886],[888,83261,83262],{"xmlns":890},[892,83263,83264,83276],{},[895,83265,83266,83268,83270,83272,83274],{},[898,83267,1807],{},[1651,83269,1793],{},[1692,83271,10340],{},[1651,83273,4449],{},[1692,83275,39559],{},[902,83277,83278],{"encoding":904},"L: 20 \\to 21",[883,83280,83282],{"className":83281},[886],[888,83283,83284],{"xmlns":890},[892,83285,83286,83294],{},[895,83287,83288,83290,83292],{},[898,83289,11101],{},[1651,83291,1738],{},[1692,83293,4416],{},[902,83295,83124],{"encoding":904},[883,83297,83299],{"className":83298},[886],[888,83300,83301],{"xmlns":890},[892,83302,83303,83314],{},[895,83304,83305,83307,83309,83311],{},[898,83306,4216],{"mathvariant":1910},[898,83308,1690],{},[1651,83310,4060],{},[1692,83312,83313],{},"7,153",[902,83315,83316],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,83319,83321],{"className":83320},[886],[888,83322,83323],{"xmlns":890},[892,83324,83325,83336],{},[895,83326,83327,83329,83331,83333],{},[898,83328,4216],{"mathvariant":1910},[898,83330,1690],{},[1651,83332,4060],{},[1692,83334,83335],{},"26,888",[902,83337,83338],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,83341,83342,83345],{},[38,83343,83344],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,83347,83349],{"className":83348},[886],[888,83350,83351],{"xmlns":890,"display":29279},[892,83352,83353,83453],{},[895,83354,83355,83357,83363,83365,83373,83375,83377,83389,83403,83405,83407,83409,83415,83417,83419,83421,83423,83425,83427,83429,83433,83435,83448,83450],{},[898,83356,2995],{},[1686,83358,83359,83361],{},[898,83360,2675],{},[898,83362,11101],{},[1651,83364,1738],{},[1902,83366,83367,83369,83371],{},[898,83368,1690],{},[898,83370,11101],{},[1651,83372,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,83374,1738],{},[1692,83376,3574],{},[2115,83378,83379,83381],{},[898,83380,1807],{},[895,83382,83383,83385,83387],{},[1692,83384,1694],{},[898,83386,5981],{"mathvariant":1910},[1692,83388,1703],{},[2115,83390,83391,83393],{},[898,83392,11101],{},[895,83394,83395,83397,83399,83401],{},[1651,83396,2181],{},[1692,83398,1703],{},[898,83400,5981],{"mathvariant":1910},[1692,83402,3521],{},[1651,83404,1661],{"separator":1660},[7185,83406],{"width":16582},[898,83408,2995],{},[1686,83410,83411,83413],{},[898,83412,2675],{},[898,83414,11101],{},[1651,83416,1654],{"stretchy":1653},[1692,83418,10340],{},[1651,83420,1661],{"separator":1660},[1692,83422,4416],{},[1651,83424,1667],{"stretchy":1653},[1651,83426,1738],{},[1692,83428,3574],{},[9423,83430,83431],{},[1692,83432,10340],{},[1651,83434,4503],{},[2938,83436,83437],{"scriptlevel":1741,"displaystyle":1653},[2446,83438,83439,83441],{},[1692,83440,1694],{},[83240,83442,83443,83446],{},[1692,83444,83445],{},"10000",[1692,83447,3521],{},[1651,83449,4060],{},[1692,83451,83452],{},"4,525.",[902,83454,83455],{"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.",[724,83457,83458,83459,4016,83476,5230],{},"Produkce poklesne přibližně o 4,525 (z ",[883,83460,83462],{"className":83461},[886],[888,83463,83464],{"xmlns":890},[892,83465,83466,83473],{},[895,83467,83468,83470],{},[1651,83469,4060],{},[1692,83471,83472],{},"905,126",[902,83474,83475],{"encoding":904},"\\approx 905{,}126",[883,83477,83479],{"className":83478},[886],[888,83480,83481],{"xmlns":890},[892,83482,83483,83490],{},[895,83484,83485,83487],{},[1651,83486,4060],{},[1692,83488,83489],{},"900,601",[902,83491,83492],{"encoding":904},"\\approx 900{,}601",[724,83494,83495,4456,83542,1343,83564,5230],{},[38,83496,83497,83498,5197,83520],{},"(c) Změna ",[883,83499,83501],{"className":83500},[886],[888,83502,83503],{"xmlns":890},[892,83504,83505,83517],{},[895,83506,83507,83509,83511,83513,83515],{},[898,83508,1807],{},[1651,83510,1793],{},[1692,83512,10340],{},[1651,83514,4449],{},[1692,83516,37457],{},[902,83518,83519],{"encoding":904},"L: 20 \\to 15",[883,83521,83523],{"className":83522},[886],[888,83524,83525],{"xmlns":890},[892,83526,83527,83539],{},[895,83528,83529,83531,83533,83535,83537],{},[898,83530,11101],{},[1651,83532,1793],{},[1692,83534,4416],{},[1651,83536,4449],{},[1692,83538,10108],{},[902,83540,83541],{"encoding":904},"K: 100 \\to 150",[883,83543,83545],{"className":83544},[886],[888,83546,83547],{"xmlns":890},[892,83548,83549,83561],{},[895,83550,83551,83553,83555,83557,83559],{},[898,83552,3542],{},[898,83554,1807],{},[1651,83556,1738],{},[1651,83558,2181],{},[1692,83560,3574],{},[902,83562,83563],{"encoding":904},"dL = -5",[883,83565,83567],{"className":83566},[886],[888,83568,83569],{"xmlns":890},[892,83570,83571,83581],{},[895,83572,83573,83575,83577,83579],{},[898,83574,3542],{},[898,83576,11101],{},[1651,83578,1738],{},[1692,83580,4446],{},[902,83582,83583],{"encoding":904},"dK = 50",[883,83585,83587],{"className":83586},[886],[888,83588,83589],{"xmlns":890,"display":29279},[892,83590,83591,83679],{},[895,83592,83593,83595,83597,83599,83601,83607,83609,83611,83613,83615,83617,83619,83621,83623,83625,83627,83629,83631,83637,83639,83641,83643,83645,83647,83649,83651,83653,83655,83657,83659,83661,83663,83665,83667,83670,83672,83674,83676],{},[898,83594,3542],{},[898,83596,1690],{},[1651,83598,1738],{},[898,83600,2995],{},[1686,83602,83603,83605],{},[898,83604,2675],{},[898,83606,1807],{},[1651,83608,1654],{"stretchy":1653},[1692,83610,10340],{},[1651,83612,1661],{"separator":1660},[1692,83614,4416],{},[1651,83616,1667],{"stretchy":1653},[1651,83618,4503],{},[1651,83620,1654],{"stretchy":1653},[1651,83622,2181],{},[1692,83624,3574],{},[1651,83626,1667],{"stretchy":1653},[1651,83628,1839],{},[898,83630,2995],{},[1686,83632,83633,83635],{},[898,83634,2675],{},[898,83636,11101],{},[1651,83638,1654],{"stretchy":1653},[1692,83640,10340],{},[1651,83642,1661],{"separator":1660},[1692,83644,4416],{},[1651,83646,1667],{"stretchy":1653},[1651,83648,4503],{},[1692,83650,4446],{},[1651,83652,1738],{},[1692,83654,83313],{},[1651,83656,4503],{},[1651,83658,1654],{"stretchy":1653},[1651,83660,2181],{},[1692,83662,3574],{},[1651,83664,1667],{"stretchy":1653},[1651,83666,1839],{},[1692,83668,83669],{},"4,525",[1651,83671,4503],{},[1692,83673,4446],{},[1651,83675,4060],{},[1692,83677,83678],{},"190,485.",[902,83680,83681],{"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.",[724,83683,83684],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,83686,83688],{"id":83687},"příklad-55","Příklad 5.5",[724,83690,83691,83692,83728,83729,1882],{},"Pro produkci ",[883,83693,83695],{"className":83694},[886],[888,83696,83697],{"xmlns":890},[892,83698,83699,83725],{},[895,83700,83701,83703,83705,83707,83709,83711,83713,83715,83721],{},[898,83702,1690],{},[1651,83704,1654],{"stretchy":1653},[898,83706,1807],{},[1651,83708,1661],{"separator":1660},[898,83710,11101],{},[1651,83712,1667],{"stretchy":1653},[1651,83714,1738],{},[83240,83716,83717,83719],{},[898,83718,1807],{},[1692,83720,3521],{},[9423,83722,83723],{},[898,83724,11101],{},[902,83726,83727],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,83730,83732],{"className":83731},[886],[888,83733,83734],{"xmlns":890},[892,83735,83736,83752],{},[895,83737,83738,83744,83748,83750],{},[83240,83739,83740,83742],{},[898,83741,1807],{},[1692,83743,3521],{},[9423,83745,83746],{},[898,83747,11101],{},[1651,83749,1738],{},[898,83751,82010],{},[902,83753,83754],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,83756,83757,83758,1882],{},"Umocněním na druhou: ",[883,83759,83761],{"className":83760},[886],[888,83762,83763],{"xmlns":890},[892,83764,83765,83789],{},[895,83766,83767,83769,83771,83777,83779],{},[898,83768,11101],{},[1651,83770,1738],{},[2115,83772,83773,83775],{},[898,83774,82010],{},[1692,83776,1703],{},[898,83778,5981],{"mathvariant":1910},[83240,83780,83781,83787],{},[2115,83782,83783,83785],{},[898,83784,1807],{},[1692,83786,1703],{},[1692,83788,3521],{},[902,83790,83791],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,83793,83794,83834,83874],{},[123,83795,83796],{},[883,83797,83799],{"className":83798},[886],[888,83800,83801],{"xmlns":890},[892,83802,83803,83831],{},[895,83804,83805,83807,83809,83811,83813,83815,83817,83819,83821],{},[898,83806,82010],{},[1651,83808,1738],{},[1692,83810,1694],{},[1651,83812,5298],{},[898,83814,11101],{},[1651,83816,1738],{},[1692,83818,1694],{},[898,83820,5981],{"mathvariant":1910},[83240,83822,83823,83829],{},[2115,83824,83825,83827],{},[898,83826,1807],{},[1692,83828,1703],{},[1692,83830,3521],{},[902,83832,83833],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,83835,83836],{},[883,83837,83839],{"className":83838},[886],[888,83840,83841],{"xmlns":890},[892,83842,83843,83871],{},[895,83844,83845,83847,83849,83851,83853,83855,83857,83859,83861],{},[898,83846,82010],{},[1651,83848,1738],{},[1692,83850,1703],{},[1651,83852,5298],{},[898,83854,11101],{},[1651,83856,1738],{},[1692,83858,3689],{},[898,83860,5981],{"mathvariant":1910},[83240,83862,83863,83869],{},[2115,83864,83865,83867],{},[898,83866,1807],{},[1692,83868,1703],{},[1692,83870,3521],{},[902,83872,83873],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,83875,83876],{},[883,83877,83879],{"className":83878},[886],[888,83880,83881],{"xmlns":890},[892,83882,83883,83911],{},[895,83884,83885,83887,83889,83891,83893,83895,83897,83899,83901],{},[898,83886,82010],{},[1651,83888,1738],{},[1692,83890,3521],{},[1651,83892,5298],{},[898,83894,11101],{},[1651,83896,1738],{},[1692,83898,5309],{},[898,83900,5981],{"mathvariant":1910},[83240,83902,83903,83909],{},[2115,83904,83905,83907],{},[898,83906,1807],{},[1692,83908,1703],{},[1692,83910,3521],{},[902,83912,83913],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,83915,83916],{},[614,83917,83918,83919,7780,83940,1882],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,83920,83922],{"className":83921},[886],[888,83923,83924],{"xmlns":890},[892,83925,83926,83938],{},[895,83927,83928,83930,83932,83934,83936],{},[1651,83929,1654],{"stretchy":1653},[898,83931,1807],{},[1651,83933,1661],{"separator":1660},[898,83935,11101],{},[1651,83937,1667],{"stretchy":1653},[902,83939,82136],{"encoding":904},[883,83941,83943],{"className":83942},[886],[888,83944,83945],{"xmlns":890},[892,83946,83947,83963],{},[895,83948,83949,83951,83953,83955,83957,83959,83961],{},[898,83950,82010],{},[1651,83952,1738],{},[1692,83954,1694],{},[1651,83956,1661],{"separator":1660},[1692,83958,1703],{},[1651,83960,1661],{"separator":1660},[1692,83962,3521],{},[902,83964,83965],{"encoding":904},"q = 1, 2, 3",[198,83967,83969],{"id":83968},"příklad-56","Příklad 5.6",[724,83971,77886,83972,1882],{},[883,83973,83975],{"className":83974},[886],[888,83976,83977],{"xmlns":890},[892,83978,83979,83995],{},[895,83980,83981,83983,83985,83987,83989,83991],{},[898,83982,1690],{},[1651,83984,1738],{},[1692,83986,1703],{},[898,83988,1807],{},[1651,83990,1839],{},[9423,83992,83993],{},[898,83994,11101],{},[902,83996,83997],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,83999,84001],{"className":84000},[886],[888,84002,84003],{"xmlns":890,"display":29279},[892,84004,84005,84047],{},[895,84006,84007,84009,84015,84017,84019,84021,84023,84025,84031,84033,84045],{},[898,84008,2995],{},[1686,84010,84011,84013],{},[898,84012,2675],{},[898,84014,1807],{},[1651,84016,1738],{},[1692,84018,1703],{},[1651,84020,1661],{"separator":1660},[7185,84022],{"width":7187},[898,84024,2995],{},[1686,84026,84027,84029],{},[898,84028,2675],{},[898,84030,11101],{},[1651,84032,1738],{},[2446,84034,84035,84037],{},[1692,84036,1694],{},[895,84038,84039,84041],{},[1692,84040,1703],{},[9423,84042,84043],{},[898,84044,11101],{},[898,84046,1882],{"mathvariant":1910},[902,84048,84049],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,84051,84053],{"className":84052},[886],[888,84054,84055],{"xmlns":890,"display":29279},[892,84056,84057,84121],{},[895,84058,84059,84061,84063,84065,84067,84069,84091,84093,84111,84113,84115,84119],{},[898,84060,2995],{},[898,84062,2998],{},[898,84064,4104],{},[898,84066,3004],{},[1651,84068,1738],{},[2446,84070,84071,84081],{},[895,84072,84073,84075],{},[898,84074,2995],{},[1686,84076,84077,84079],{},[898,84078,2675],{},[898,84080,1807],{},[895,84082,84083,84085],{},[898,84084,2995],{},[1686,84086,84087,84089],{},[898,84088,2675],{},[898,84090,11101],{},[1651,84092,1738],{},[2446,84094,84095,84097],{},[1692,84096,1703],{},[2938,84098,84099],{"scriptlevel":1741,"displaystyle":1653},[2446,84100,84101,84103],{},[1692,84102,1694],{},[895,84104,84105,84107],{},[1692,84106,1703],{},[9423,84108,84109],{},[898,84110,11101],{},[1651,84112,1738],{},[1692,84114,3689],{},[9423,84116,84117],{},[898,84118,11101],{},[898,84120,1882],{"mathvariant":1910},[902,84122,84123],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,84125,84126,84127,84170,84171,84210,84211,1882],{},"Například ",[883,84128,84130],{"className":84129},[886],[888,84131,84132],{"xmlns":890},[892,84133,84134,84167],{},[895,84135,84136,84138,84140,84142,84144,84146,84148,84150,84152,84154,84156,84158,84162,84164],{},[898,84137,2995],{},[898,84139,2998],{},[898,84141,4104],{},[898,84143,3004],{},[1651,84145,1654],{"stretchy":1653},[1692,84147,3689],{},[1651,84149,1661],{"separator":1660},[1692,84151,25414],{},[1651,84153,1667],{"stretchy":1653},[1651,84155,1738],{},[1692,84157,3689],{},[9423,84159,84160],{},[1692,84161,25414],{},[1651,84163,4060],{},[1692,84165,84166],{},"10,58",[902,84168,84169],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,84172,84174],{"className":84173},[886],[888,84175,84176],{"xmlns":890},[892,84177,84178,84207],{},[895,84179,84180,84182,84184,84186,84188,84190,84192,84194,84196,84198,84202,84204],{},[898,84181,1690],{},[1651,84183,1654],{"stretchy":1653},[1692,84185,3689],{},[1651,84187,1661],{"separator":1660},[1692,84189,25414],{},[1651,84191,1667],{"stretchy":1653},[1651,84193,1738],{},[1692,84195,6892],{},[1651,84197,1839],{},[9423,84199,84200],{},[1692,84201,25414],{},[1651,84203,4060],{},[1692,84205,84206],{},"10,646",[902,84208,84209],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,84212,84214],{"className":84213},[886],[888,84215,84216],{"xmlns":890},[892,84217,84218,84226],{},[895,84219,84220,84222],{},[1692,84221,3689],{},[9423,84223,84224],{},[1692,84225,25414],{},[902,84227,84228],{"encoding":904},"4\\sqrt{7}",[724,84230,84231,84232,84252],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,84233,84235],{"className":84234},[886],[888,84236,84237],{"xmlns":890},[892,84238,84239,84249],{},[895,84240,84241,84243,84245,84247],{},[898,84242,3542],{},[898,84244,1807],{},[1651,84246,1738],{},[1692,84248,1703],{},[902,84250,84251],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,84254,84256],{"className":84255},[886],[888,84257,84258],{"xmlns":890,"display":29279},[892,84259,84260,84309],{},[895,84261,84262,84264,84266,84268,84270,84272,84274,84276,84278,84280,84282,84284,84286,84288,84290,84292,84294,84296,84298,84302,84304,84306],{},[898,84263,3542],{},[898,84265,11101],{},[1651,84267,1738],{},[1651,84269,2181],{},[898,84271,2995],{},[898,84273,2998],{},[898,84275,4104],{},[898,84277,3004],{},[1651,84279,1654],{"stretchy":1653},[1692,84281,3689],{},[1651,84283,1661],{"separator":1660},[1692,84285,25414],{},[1651,84287,1667],{"stretchy":1653},[1651,84289,4503],{},[1692,84291,1703],{},[1651,84293,1738],{},[1651,84295,2181],{},[1692,84297,6892],{},[9423,84299,84300],{},[1692,84301,25414],{},[1651,84303,4060],{},[1651,84305,2181],{},[1692,84307,84308],{},"21,17.",[902,84310,84311],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,84313,84315],{"id":84314},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,84317,84318,84319,1343,84321,5197,84323,84325,84326,84329,84330,84333],{},"Hlavními faktory produkce jsou ",[38,84320,76127],{},[38,84322,76143],{},[38,84324,76159],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,84327,84328],{},"jednofaktorový"," (pouze práce) a ",[38,84331,84332],{},"dvoufaktorový"," (práce + kapitál) model.",[724,84335,84336,84337,84340,84341,84343,84344,84346,84347,27402,84350,84369,84370,84387,84388,84405,84406,84428,84429,5665,84448,1882],{},"V ",[38,84338,84339],{},"1F modelu"," se definuje ",[38,84342,11324],{}," (derivace produkce podle práce) a ",[38,84345,76062],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,84348,84349],{},"zákonu klesajících výnosů",[883,84351,84353],{"className":84352},[886],[888,84354,84355],{"xmlns":890},[892,84356,84357,84367],{},[895,84358,84359,84361],{},[898,84360,2995],{},[1686,84362,84363,84365],{},[898,84364,2675],{},[898,84366,1807],{},[902,84368,11345],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,84371,84373],{"className":84372},[886],[888,84374,84375],{"xmlns":890},[892,84376,84377,84385],{},[895,84378,84379],{},[1686,84380,84381,84383],{},[898,84382,1807],{},[1692,84384,1741],{},[902,84386,76771],{"encoding":904}," klesá a v bodě ",[883,84389,84391],{"className":84390},[886],[888,84392,84393],{"xmlns":890},[892,84394,84395,84403],{},[895,84396,84397],{},[1686,84398,84399,84401],{},[898,84400,1807],{},[1692,84402,1694],{},[902,84404,14510],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,84407,84408,84409],{},"princip maximalizace ",[883,84410,84412],{"className":84411},[886],[888,84413,84414],{"xmlns":890},[892,84415,84416,84426],{},[895,84417,84418,84420],{},[898,84419,5564],{},[1686,84421,84422,84424],{},[898,84423,2675],{},[898,84425,1807],{},[902,84427,75846],{"encoding":904},": v bodě maxima ",[883,84430,84432],{"className":84431},[886],[888,84433,84434],{"xmlns":890},[892,84435,84436,84446],{},[895,84437,84438,84440],{},[898,84439,5564],{},[1686,84441,84442,84444],{},[898,84443,2675],{},[898,84445,1807],{},[902,84447,75846],{"encoding":904},[883,84449,84451],{"className":84450},[886],[888,84452,84453],{"xmlns":890},[892,84454,84455,84475],{},[895,84456,84457,84459,84465,84467,84469],{},[898,84458,2995],{},[1686,84460,84461,84463],{},[898,84462,2675],{},[898,84464,1807],{},[1651,84466,1738],{},[898,84468,5564],{},[1686,84470,84471,84473],{},[898,84472,2675],{},[898,84474,1807],{},[902,84476,75876],{"encoding":904},[724,84478,84479,84480,84483,84484,3246,84487,84516,84517,84534,84535,84538,84539,84568,84569,84571,84572,1878,84602,84624],{},"Ve ",[38,84481,84482],{},"2F modelu"," se obvykle používají ",[38,84485,84486],{},"Cobb-Douglasovy funkce",[883,84488,84490],{"className":84489},[886],[888,84491,84492],{"xmlns":890},[892,84493,84494,84514],{},[895,84495,84496,84498,84500,84502,84508],{},[898,84497,1690],{},[1651,84499,1738],{},[898,84501,5564],{},[2115,84503,84504,84506],{},[898,84505,1807],{},[898,84507,207],{},[2115,84509,84510,84512],{},[898,84511,11101],{},[898,84513,2268],{},[902,84515,75943],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,84518,84520],{"className":84519},[886],[888,84521,84522],{"xmlns":890},[892,84523,84524,84532],{},[895,84525,84526,84528,84530],{},[898,84527,207],{},[1651,84529,1839],{},[898,84531,2268],{},[902,84533,76037],{"encoding":904}," rozlišujeme ",[38,84536,84537],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,84540,84542],{"className":84541},[886],[888,84543,84544],{"xmlns":890},[892,84545,84546,84566],{},[895,84547,84548,84550,84556,84558,84560],{},[898,84549,2995],{},[1686,84551,84552,84554],{},[898,84553,2675],{},[898,84555,1807],{},[1651,84557,1661],{"separator":1660},[898,84559,2995],{},[1686,84561,84562,84564],{},[898,84563,2675],{},[898,84565,11101],{},[902,84567,75974],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,84570,11080],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,84573,84575],{"className":84574},[886],[888,84576,84577],{"xmlns":890},[892,84578,84579,84599],{},[895,84580,84581,84583,84589,84591,84593],{},[898,84582,2995],{},[1686,84584,84585,84587],{},[898,84586,2675],{},[898,84588,1807],{},[898,84590,5981],{"mathvariant":1910},[898,84592,2995],{},[1686,84594,84595,84597],{},[898,84596,2675],{},[898,84598,11101],{},[902,84600,84601],{"encoding":904},"MP_L\u002FMP_K",[38,84603,84604,84605,1667],{},"mezní míra technické substituce (",[883,84606,84608],{"className":84607},[886],[888,84609,84610],{"xmlns":890},[892,84611,84612,84622],{},[895,84613,84614,84616,84618,84620],{},[898,84615,2995],{},[898,84617,2998],{},[898,84619,4104],{},[898,84621,3004],{},[902,84623,11899],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,84626,51095],{"id":51094},[152,84628,84629,84632,84635,84638,84641,84644,84647,84650,84653,84656,84659],{},[123,84630,84631],{},"Jaké jsou faktory produkce?",[123,84633,84634],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,84636,84637],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,84639,84640],{},"Co udává mezní produkt práce?",[123,84642,84643],{},"Co musí respektovat průběh křivky produkce?",[123,84645,84646],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,84648,84649],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,84651,84652],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,84654,84655],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,84657,84658],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,84660,84661],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,84663,84665],{"id":84664},"úlohy-51517","Úlohy 5.1–5.17",[198,84667,41664],{"id":41663},[724,84669,84670,84673,84674,84696,84697,1343,84717,1343,84737,84757],{},[38,84671,84672],{},"5.1"," Je dána produkce ",[883,84675,84677],{"className":84676},[886],[888,84678,84679],{"xmlns":890},[892,84680,84681,84693],{},[895,84682,84683,84685,84687,84689],{},[898,84684,1690],{},[1651,84686,1738],{},[1692,84688,4190],{},[9423,84690,84691],{},[898,84692,1807],{},[902,84694,84695],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,84698,84700],{"className":84699},[886],[888,84701,84702],{"xmlns":890},[892,84703,84704,84714],{},[895,84705,84706,84708,84710,84712],{},[898,84707,1690],{},[1651,84709,1654],{"stretchy":1653},[1692,84711,1694],{},[1651,84713,1667],{"stretchy":1653},[902,84715,84716],{"encoding":904},"Q(1)",[883,84718,84720],{"className":84719},[886],[888,84721,84722],{"xmlns":890},[892,84723,84724,84734],{},[895,84725,84726,84728,84730,84732],{},[898,84727,1690],{},[1651,84729,1654],{"stretchy":1653},[1692,84731,3689],{},[1651,84733,1667],{"stretchy":1653},[902,84735,84736],{"encoding":904},"Q(4)",[883,84738,84740],{"className":84739},[886],[888,84741,84742],{"xmlns":890},[892,84743,84744,84754],{},[895,84745,84746,84748,84750,84752],{},[898,84747,1690],{},[1651,84749,1654],{"stretchy":1653},[1692,84751,5309],{},[1651,84753,1667],{"stretchy":1653},[902,84755,84756],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,84759,84760,84673,84763,84799,84800,84813,84814,84833,84834,84860,84861,4016,84874,84887],{},[38,84761,84762],{},"5.2",[883,84764,84766],{"className":84765},[886],[888,84767,84768],{"xmlns":890},[892,84769,84770,84796],{},[895,84771,84772,84774,84776,84778,84780,84786,84788,84790],{},[898,84773,1690],{},[1651,84775,1738],{},[1651,84777,2181],{},[1692,84779,4122],{},[2115,84781,84782,84784],{},[898,84783,1807],{},[1692,84785,3521],{},[1651,84787,1839],{},[1692,84789,5309],{},[2115,84791,84792,84794],{},[898,84793,1807],{},[1692,84795,1703],{},[902,84797,84798],{"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 ",[883,84801,84803],{"className":84802},[886],[888,84804,84805],{"xmlns":890},[892,84806,84807,84811],{},[895,84808,84809],{},[898,84810,1807],{},[902,84812,1807],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,84815,84817],{"className":84816},[886],[888,84818,84819],{"xmlns":890},[892,84820,84821,84831],{},[895,84822,84823,84825],{},[898,84824,2995],{},[1686,84826,84827,84829],{},[898,84828,2675],{},[898,84830,1807],{},[902,84832,11345],{"encoding":904},". (f) Vypočtěte ",[883,84835,84837],{"className":84836},[886],[888,84838,84839],{"xmlns":890},[892,84840,84841,84857],{},[895,84842,84843,84845,84851,84853,84855],{},[898,84844,2995],{},[1686,84846,84847,84849],{},[898,84848,2675],{},[898,84850,1807],{},[1651,84852,1654],{"stretchy":1653},[1692,84854,4190],{},[1651,84856,1667],{"stretchy":1653},[902,84858,84859],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,84862,84864],{"className":84863},[886],[888,84865,84866],{"xmlns":890},[892,84867,84868,84872],{},[895,84869,84870],{},[1692,84871,4190],{},[902,84873,4190],{"encoding":904},[883,84875,84877],{"className":84876},[886],[888,84878,84879],{"xmlns":890},[892,84880,84881,84885],{},[895,84882,84883],{},[1692,84884,43500],{},[902,84886,43500],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,84889,84890,84893,84894,84916,84917,84945,84946,84977,84978,1882],{},[38,84891,84892],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,84895,84897],{"className":84896},[886],[888,84898,84899],{"xmlns":890},[892,84900,84901,84913],{},[895,84902,84903,84905,84907,84909],{},[898,84904,1690],{},[1651,84906,1738],{},[1692,84908,16408],{},[9423,84910,84911],{},[898,84912,1807],{},[902,84914,84915],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,84918,84920],{"className":84919},[886],[888,84921,84922],{"xmlns":890},[892,84923,84924,84942],{},[895,84925,84926,84928,84930,84932,84936,84938,84940],{},[898,84927,1690],{},[1651,84929,1738],{},[1692,84931,31294],{},[9423,84933,84934],{},[898,84935,1807],{},[1651,84937,2181],{},[1692,84939,3689],{},[898,84941,1807],{},[902,84943,84944],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,84947,84949],{"className":84948},[886],[888,84950,84951],{"xmlns":890},[892,84952,84953,84974],{},[895,84954,84955,84957,84959,84961,84963,84965,84968],{},[898,84956,1690],{},[1651,84958,1738],{},[1692,84960,4446],{},[898,84962,1807],{},[1651,84964,2181],{},[1692,84966,84967],{},"0,01",[2115,84969,84970,84972],{},[898,84971,1807],{},[1692,84973,1703],{},[902,84975,84976],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,84979,84981],{"className":84980},[886],[888,84982,84983],{"xmlns":890},[892,84984,84985,85011],{},[895,84986,84987,84989,84991,84993,84995,85001,85003,85005],{},[898,84988,1690],{},[1651,84990,1738],{},[1651,84992,2181],{},[1692,84994,69424],{},[2115,84996,84997,84999],{},[898,84998,1807],{},[1692,85000,3521],{},[1651,85002,1839],{},[1692,85004,5309],{},[2115,85006,85007,85009],{},[898,85008,1807],{},[1692,85010,1703],{},[902,85012,85013],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,85015,85016,85019,85020,3955,85039,73411,85056,1882],{},[38,85017,85018],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,85021,85023],{"className":85022},[886],[888,85024,85025],{"xmlns":890},[892,85026,85027,85037],{},[895,85028,85029,85031],{},[898,85030,5564],{},[1686,85032,85033,85035],{},[898,85034,2675],{},[898,85036,1807],{},[902,85038,75846],{"encoding":904},[883,85040,85042],{"className":85041},[886],[888,85043,85044],{"xmlns":890},[892,85045,85046,85054],{},[895,85047,85048],{},[1686,85049,85050,85052],{},[898,85051,1807],{},[1692,85053,1741],{},[902,85055,76771],{"encoding":904},[883,85057,85059],{"className":85058},[886],[888,85060,85061],{"xmlns":890},[892,85062,85063,85103],{},[895,85064,85065,85067,85073,85075,85081,85083,85085,85087,85093,85095,85101],{},[898,85066,5564],{},[1686,85068,85069,85071],{},[898,85070,2675],{},[898,85072,1807],{},[1651,85074,1654],{"stretchy":1653},[1686,85076,85077,85079],{},[898,85078,1807],{},[1692,85080,1741],{},[1651,85082,1667],{"stretchy":1653},[1651,85084,1738],{},[898,85086,2995],{},[1686,85088,85089,85091],{},[898,85090,2675],{},[898,85092,1807],{},[1651,85094,1654],{"stretchy":1653},[1686,85096,85097,85099],{},[898,85098,1807],{},[1692,85100,1741],{},[1651,85102,1667],{"stretchy":1653},[902,85104,85105],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,85107,85108,84673,85111,22807,85147,85160,85161,85180],{},[38,85109,85110],{},"5.5",[883,85112,85114],{"className":85113},[886],[888,85115,85116],{"xmlns":890},[892,85117,85118,85144],{},[895,85119,85120,85122,85124,85126,85128,85134,85136,85138],{},[898,85121,1690],{},[1651,85123,1738],{},[1651,85125,2181],{},[1692,85127,4166],{},[2115,85129,85130,85132],{},[898,85131,1807],{},[1692,85133,3521],{},[1651,85135,1839],{},[1692,85137,4828],{},[2115,85139,85140,85142],{},[898,85141,1807],{},[1692,85143,1703],{},[902,85145,85146],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,85148,85150],{"className":85149},[886],[888,85151,85152],{"xmlns":890},[892,85153,85154,85158],{},[895,85155,85156],{},[898,85157,1807],{},[902,85159,1807],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,85162,85164],{"className":85163},[886],[888,85165,85166],{"xmlns":890},[892,85167,85168,85178],{},[895,85169,85170,85172],{},[898,85171,5564],{},[1686,85173,85174,85176],{},[898,85175,2675],{},[898,85177,1807],{},[902,85179,75846],{"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.",[198,85182,85184],{"id":85183},"dvoufaktorový-model","Dvoufaktorový model",[724,85186,85187,85190,85191,84916,85217,84945,85259,1882],{},[38,85188,85189],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,85192,85194],{"className":85193},[886],[888,85195,85196],{"xmlns":890},[892,85197,85198,85214],{},[895,85199,85200,85202,85204,85206,85208],{},[898,85201,1690],{},[1651,85203,1738],{},[1692,85205,25414],{},[898,85207,1807],{},[2115,85209,85210,85212],{},[898,85211,11101],{},[1692,85213,1703],{},[902,85215,85216],{"encoding":904},"Q = 7 L K^{2}",[883,85218,85220],{"className":85219},[886],[888,85221,85222],{"xmlns":890},[892,85223,85224,85256],{},[895,85225,85226,85228,85230,85232,85244],{},[898,85227,1690],{},[1651,85229,1738],{},[1692,85231,4446],{},[2115,85233,85234,85236],{},[898,85235,1807],{},[895,85237,85238,85240,85242],{},[1692,85239,1703],{},[898,85241,5981],{"mathvariant":1910},[1692,85243,3521],{},[2115,85245,85246,85248],{},[898,85247,11101],{},[895,85249,85250,85252,85254],{},[1692,85251,1694],{},[898,85253,5981],{"mathvariant":1910},[1692,85255,3521],{},[902,85257,85258],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,85260,85262],{"className":85261},[886],[888,85263,85264],{"xmlns":890},[892,85265,85266,85298],{},[895,85267,85268,85270,85272,85274,85286],{},[898,85269,1690],{},[1651,85271,1738],{},[1692,85273,5026],{},[2115,85275,85276,85278],{},[898,85277,1807],{},[895,85279,85280,85282,85284],{},[1692,85281,3521],{},[898,85283,5981],{"mathvariant":1910},[1692,85285,3574],{},[2115,85287,85288,85290],{},[898,85289,11101],{},[895,85291,85292,85294,85296],{},[1692,85293,1703],{},[898,85295,5981],{"mathvariant":1910},[1692,85297,3574],{},[902,85299,85300],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,85302,85303,84673,85306,85348,85349,1343,85367,85386,85387,85404],{},[38,85304,85305],{},"5.7",[883,85307,85309],{"className":85308},[886],[888,85310,85311],{"xmlns":890},[892,85312,85313,85345],{},[895,85314,85315,85317,85319,85321,85333],{},[898,85316,1690],{},[1651,85318,1738],{},[1692,85320,4190],{},[2115,85322,85323,85325],{},[898,85324,1807],{},[895,85326,85327,85329,85331],{},[1692,85328,1694],{},[898,85330,5981],{"mathvariant":1910},[1692,85332,1703],{},[2115,85334,85335,85337],{},[898,85336,11101],{},[895,85338,85339,85341,85343],{},[1692,85340,1694],{},[898,85342,5981],{"mathvariant":1910},[1692,85344,1703],{},[902,85346,85347],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,85350,85352],{"className":85351},[886],[888,85353,85354],{"xmlns":890},[892,85355,85356,85364],{},[895,85357,85358,85360,85362],{},[898,85359,1807],{},[1651,85361,1738],{},[1692,85363,21355],{},[902,85365,85366],{"encoding":904},"L = 400",[883,85368,85370],{"className":85369},[886],[888,85371,85372],{"xmlns":890},[892,85373,85374,85383],{},[895,85375,85376,85378,85380],{},[898,85377,11101],{},[1651,85379,1738],{},[1692,85381,85382],{},"17576",[902,85384,85385],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,85388,85390],{"className":85389},[886],[888,85391,85392],{"xmlns":890},[892,85393,85394,85402],{},[895,85395,85396,85398,85400],{},[898,85397,1807],{},[1651,85399,1661],{"separator":1660},[898,85401,11101],{},[902,85403,80198],{"encoding":904}," zdvojnásobí.",[724,85406,85407,85410,85411,85348,85442,1343,85460,70797,85478,85508,85509,85539,85540,4016,85553,85567,85568,4016,85581,85594],{},[38,85408,85409],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,85412,85414],{"className":85413},[886],[888,85415,85416],{"xmlns":890},[892,85417,85418,85439],{},[895,85419,85420,85422,85424,85427,85433],{},[898,85421,1690],{},[1651,85423,1738],{},[1692,85425,85426],{},"1,01",[2115,85428,85429,85431],{},[898,85430,1807],{},[1692,85432,24943],{},[2115,85434,85435,85437],{},[898,85436,11101],{},[1692,85438,25002],{},[902,85440,85441],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,85443,85445],{"className":85444},[886],[888,85446,85447],{"xmlns":890},[892,85448,85449,85457],{},[895,85450,85451,85453,85455],{},[898,85452,1807],{},[1651,85454,1738],{},[1692,85456,31956],{},[902,85458,85459],{"encoding":904},"L = 250",[883,85461,85463],{"className":85462},[886],[888,85464,85465],{"xmlns":890},[892,85466,85467,85475],{},[895,85468,85469,85471,85473],{},[898,85470,11101],{},[1651,85472,1738],{},[1692,85474,4111],{},[902,85476,85477],{"encoding":904},"K = 1000",[883,85479,85481],{"className":85480},[886],[888,85482,85483],{"xmlns":890},[892,85484,85485,85505],{},[895,85486,85487,85489,85495,85497,85499,85501,85503],{},[898,85488,2995],{},[1686,85490,85491,85493],{},[898,85492,2675],{},[898,85494,1807],{},[1651,85496,1654],{"stretchy":1653},[1692,85498,31956],{},[1651,85500,1661],{"separator":1660},[1692,85502,4111],{},[1651,85504,1667],{"stretchy":1653},[902,85506,85507],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,85510,85512],{"className":85511},[886],[888,85513,85514],{"xmlns":890},[892,85515,85516,85536],{},[895,85517,85518,85520,85526,85528,85530,85532,85534],{},[898,85519,2995],{},[1686,85521,85522,85524],{},[898,85523,2675],{},[898,85525,11101],{},[1651,85527,1654],{"stretchy":1653},[1692,85529,31956],{},[1651,85531,1661],{"separator":1660},[1692,85533,4111],{},[1651,85535,1667],{"stretchy":1653},[902,85537,85538],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,85541,85543],{"className":85542},[886],[888,85544,85545],{"xmlns":890},[892,85546,85547,85551],{},[895,85548,85549],{},[898,85550,1807],{},[902,85552,1807],{"encoding":904},[883,85554,85556],{"className":85555},[886],[888,85557,85558],{"xmlns":890},[892,85559,85560,85565],{},[895,85561,85562],{},[1692,85563,85564],{},"260",[902,85566,85564],{"encoding":904}," a současném poklesu ",[883,85569,85571],{"className":85570},[886],[888,85572,85573],{"xmlns":890},[892,85574,85575,85579],{},[895,85576,85577],{},[898,85578,11101],{},[902,85580,11101],{"encoding":904},[883,85582,85584],{"className":85583},[886],[888,85585,85586],{"xmlns":890},[892,85587,85588,85592],{},[895,85589,85590],{},[1692,85591,16489],{},[902,85593,16489],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,85596,85597,85600,85601,1882],{},[38,85598,85599],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,85602,85604],{"className":85603},[886],[888,85605,85606],{"xmlns":890},[892,85607,85608,85628],{},[895,85609,85610,85612,85614,85616,85622],{},[898,85611,1690],{},[1651,85613,1738],{},[1692,85615,4190],{},[2115,85617,85618,85620],{},[898,85619,1807],{},[1692,85621,69424],{},[2115,85623,85624,85626],{},[898,85625,11101],{},[1692,85627,6316],{},[902,85629,85630],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,85632,85633,85636,85637,81794,85660,11694,85673,11325,85723,5230],{},[38,85634,85635],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,85638,85640],{"className":85639},[886],[888,85641,85642],{"xmlns":890},[892,85643,85644,85658],{},[895,85645,85646,85648,85650,85652,85654,85656],{},[898,85647,1690],{},[1651,85649,1654],{"stretchy":1653},[898,85651,1807],{},[1651,85653,1661],{"separator":1660},[898,85655,11101],{},[1651,85657,1667],{"stretchy":1653},[902,85659,11297],{"encoding":904},[883,85661,85663],{"className":85662},[886],[888,85664,85665],{"xmlns":890},[892,85666,85667,85671],{},[895,85668,85669],{},[898,85670,38073],{},[902,85672,38073],{"encoding":904},[883,85674,85676],{"className":85675},[886],[888,85677,85678],{"xmlns":890},[892,85679,85680,85720],{},[895,85681,85682,85684,85692,85694,85696,85704,85706,85708,85710,85712,85714,85716,85718],{},[898,85683,1807],{},[1902,85685,85686,85688,85690],{},[898,85687,1690],{},[898,85689,1807],{},[1651,85691,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,85693,1839],{},[898,85695,11101],{},[1902,85697,85698,85700,85702],{},[898,85699,1690],{},[898,85701,11101],{},[1651,85703,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,85705,1738],{},[898,85707,38073],{},[898,85709,1690],{},[1651,85711,1654],{"stretchy":1653},[898,85713,1807],{},[1651,85715,1661],{"separator":1660},[898,85717,11101],{},[1651,85719,1667],{"stretchy":1653},[902,85721,85722],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,85724,81769],{},[724,85726,85727,85730],{},[38,85728,85729],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,85732,85733,84673,85736,85776,85777,1343,85799,1343,85821,85843],{},[38,85734,85735],{},"5.12",[883,85737,85739],{"className":85738},[886],[888,85740,85741],{"xmlns":890},[892,85742,85743,85773],{},[895,85744,85745,85747,85749,85761],{},[898,85746,1690],{},[1651,85748,1738],{},[2115,85750,85751,85753],{},[898,85752,1807],{},[895,85754,85755,85757,85759],{},[1692,85756,1694],{},[898,85758,5981],{"mathvariant":1910},[1692,85760,3521],{},[2115,85762,85763,85765],{},[898,85764,11101],{},[895,85766,85767,85769,85771],{},[1692,85768,1694],{},[898,85770,5981],{"mathvariant":1910},[1692,85772,3689],{},[902,85774,85775],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,85778,85780],{"className":85779},[886],[888,85781,85782],{"xmlns":890},[892,85783,85784,85796],{},[895,85785,85786,85792,85794],{},[1686,85787,85788,85790],{},[898,85789,82010],{},[1692,85791,1741],{},[1651,85793,1738],{},[1692,85795,1694],{},[902,85797,85798],{"encoding":904},"q_0 = 1",[883,85800,85802],{"className":85801},[886],[888,85803,85804],{"xmlns":890},[892,85805,85806,85818],{},[895,85807,85808,85814,85816],{},[1686,85809,85810,85812],{},[898,85811,82010],{},[1692,85813,1694],{},[1651,85815,1738],{},[1692,85817,1703],{},[902,85819,85820],{"encoding":904},"q_1 = 2",[883,85822,85824],{"className":85823},[886],[888,85825,85826],{"xmlns":890},[892,85827,85828,85840],{},[895,85829,85830,85836,85838],{},[1686,85831,85832,85834],{},[898,85833,82010],{},[1692,85835,1703],{},[1651,85837,1738],{},[1692,85839,3521],{},[902,85841,85842],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,85845,85846,84673,85849,85889,85890,1343,85918,1343,85946,1343,85974,1343,86003,1343,86032,1343,86061,1343,86090,1343,86119,1882],{},[38,85847,85848],{},"5.13",[883,85850,85852],{"className":85851},[886],[888,85853,85854],{"xmlns":890},[892,85855,85856,85886],{},[895,85857,85858,85860,85862,85874],{},[898,85859,1690],{},[1651,85861,1738],{},[2115,85863,85864,85866],{},[898,85865,1807],{},[895,85867,85868,85870,85872],{},[1692,85869,1694],{},[898,85871,5981],{"mathvariant":1910},[1692,85873,3521],{},[2115,85875,85876,85878],{},[898,85877,11101],{},[895,85879,85880,85882,85884],{},[1692,85881,1694],{},[898,85883,5981],{"mathvariant":1910},[1692,85885,1703],{},[902,85887,85888],{"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): ",[883,85891,85893],{"className":85892},[886],[888,85894,85895],{"xmlns":890},[892,85896,85897,85915],{},[895,85898,85899,85905,85907,85909,85911,85913],{},[1686,85900,85901,85903],{},[898,85902,5564],{},[1692,85904,1694],{},[1651,85906,2261],{"stretchy":1653},[1692,85908,1694],{},[1651,85910,9731],{"separator":1660},[1692,85912,1694],{},[1651,85914,2279],{"stretchy":1653},[902,85916,85917],{"encoding":904},"A_1[1; 1]",[883,85919,85921],{"className":85920},[886],[888,85922,85923],{"xmlns":890},[892,85924,85925,85943],{},[895,85926,85927,85933,85935,85937,85939,85941],{},[1686,85928,85929,85931],{},[898,85930,5564],{},[1692,85932,1703],{},[1651,85934,2261],{"stretchy":1653},[1692,85936,1694],{},[1651,85938,9731],{"separator":1660},[1692,85940,6892],{},[1651,85942,2279],{"stretchy":1653},[902,85944,85945],{"encoding":904},"A_2[1; 8]",[883,85947,85949],{"className":85948},[886],[888,85950,85951],{"xmlns":890},[892,85952,85953,85971],{},[895,85954,85955,85961,85963,85965,85967,85969],{},[1686,85956,85957,85959],{},[898,85958,5564],{},[1692,85960,3521],{},[1651,85962,2261],{"stretchy":1653},[1692,85964,1694],{},[1651,85966,9731],{"separator":1660},[1692,85968,67810],{},[1651,85970,2279],{"stretchy":1653},[902,85972,85973],{"encoding":904},"A_3[1; 27]",[883,85975,85977],{"className":85976},[886],[888,85978,85979],{"xmlns":890},[892,85980,85981,86000],{},[895,85982,85983,85989,85991,85993,85995,85998],{},[1686,85984,85985,85987],{},[898,85986,5564],{},[1692,85988,3689],{},[1651,85990,2261],{"stretchy":1653},[1692,85992,1703],{},[1651,85994,9731],{"separator":1660},[1692,85996,85997],{},"0,353",[1651,85999,2279],{"stretchy":1653},[902,86001,86002],{"encoding":904},"A_4[2; 0{,}353]",[883,86004,86006],{"className":86005},[886],[888,86007,86008],{"xmlns":890},[892,86009,86010,86029],{},[895,86011,86012,86018,86020,86022,86024,86027],{},[1686,86013,86014,86016],{},[898,86015,5564],{},[1692,86017,3574],{},[1651,86019,2261],{"stretchy":1653},[1692,86021,1703],{},[1651,86023,9731],{"separator":1660},[1692,86025,86026],{},"2,828",[1651,86028,2279],{"stretchy":1653},[902,86030,86031],{"encoding":904},"A_5[2; 2{,}828]",[883,86033,86035],{"className":86034},[886],[888,86036,86037],{"xmlns":890},[892,86038,86039,86058],{},[895,86040,86041,86047,86049,86051,86053,86056],{},[1686,86042,86043,86045],{},[898,86044,5564],{},[1692,86046,3581],{},[1651,86048,2261],{"stretchy":1653},[1692,86050,1703],{},[1651,86052,9731],{"separator":1660},[1692,86054,86055],{},"9,545",[1651,86057,2279],{"stretchy":1653},[902,86059,86060],{"encoding":904},"A_6[2; 9{,}545]",[883,86062,86064],{"className":86063},[886],[888,86065,86066],{"xmlns":890},[892,86067,86068,86087],{},[895,86069,86070,86076,86078,86080,86082,86085],{},[1686,86071,86072,86074],{},[898,86073,5564],{},[1692,86075,25414],{},[1651,86077,2261],{"stretchy":1653},[1692,86079,65772],{},[1651,86081,9731],{"separator":1660},[1692,86083,86084],{},"0,544",[1651,86086,2279],{"stretchy":1653},[902,86088,86089],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,86091,86093],{"className":86092},[886],[888,86094,86095],{"xmlns":890},[892,86096,86097,86116],{},[895,86098,86099,86105,86107,86109,86111,86114],{},[1686,86100,86101,86103],{},[898,86102,5564],{},[1692,86104,6892],{},[1651,86106,2261],{"stretchy":1653},[1692,86108,65772],{},[1651,86110,9731],{"separator":1660},[1692,86112,86113],{},"14,696",[1651,86115,2279],{"stretchy":1653},[902,86117,86118],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,86120,86122],{"className":86121},[886],[888,86123,86124],{"xmlns":890},[892,86125,86126,86144],{},[895,86127,86128,86134,86136,86138,86140,86142],{},[1686,86129,86130,86132],{},[898,86131,5564],{},[1692,86133,5309],{},[1651,86135,2261],{"stretchy":1653},[1692,86137,1703],{},[1651,86139,9731],{"separator":1660},[1692,86141,3574],{},[1651,86143,2279],{"stretchy":1653},[902,86145,86146],{"encoding":904},"A_9[2; 5]",[724,86148,86149,86152],{},[38,86150,86151],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,86154,86155,86158,86159,86189,86190,86203,86204,86217,86218,70530,86237,86256,86257,1882],{},[38,86156,86157],{},"5.15"," Produkce firmy je dána vztahem ",[883,86160,86162],{"className":86161},[886],[888,86163,86164],{"xmlns":890},[892,86165,86166,86186],{},[895,86167,86168,86170,86172,86174,86180],{},[898,86169,1690],{},[1651,86171,1738],{},[1692,86173,1703],{},[2115,86175,86176,86178],{},[898,86177,1807],{},[1692,86179,6316],{},[2115,86181,86182,86184],{},[898,86183,11101],{},[1692,86185,25002],{},[902,86187,86188],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,86191,86193],{"className":86192},[886],[888,86194,86195],{"xmlns":890},[892,86196,86197,86201],{},[895,86198,86199],{},[1692,86200,4416],{},[902,86202,4416],{"encoding":904}," pracovníků a disponuje-li ",[883,86205,86207],{"className":86206},[886],[888,86208,86209],{"xmlns":890},[892,86210,86211,86215],{},[895,86212,86213],{},[1692,86214,65648],{},[902,86216,65648],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,86219,86221],{"className":86220},[886],[888,86222,86223],{"xmlns":890},[892,86224,86225,86235],{},[895,86226,86227,86229,86231,86233],{},[898,86228,2995],{},[898,86230,2998],{},[898,86232,4104],{},[898,86234,3004],{},[902,86236,11899],{"encoding":904},[883,86238,86240],{"className":86239},[886],[888,86241,86242],{"xmlns":890},[892,86243,86244,86254],{},[895,86245,86246,86248,86250,86252],{},[898,86247,2995],{},[898,86249,2998],{},[898,86251,4104],{},[898,86253,3004],{},[902,86255,11899],{"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 ",[883,86258,86260],{"className":86259},[886],[888,86261,86262],{"xmlns":890},[892,86263,86264,86269],{},[895,86265,86266],{},[1692,86267,86268],{},"95",[902,86270,86268],{"encoding":904},[724,86272,86273,84673,86276,72204,86308,86327,86328,86341,86342,86355,86356,86369],{},[38,86274,86275],{},"5.16",[883,86277,86279],{"className":86278},[886],[888,86280,86281],{"xmlns":890},[892,86282,86283,86305],{},[895,86284,86285,86287,86289,86295,86297,86299],{},[898,86286,1690],{},[1651,86288,1738],{},[2115,86290,86291,86293],{},[898,86292,11101],{},[1692,86294,1703],{},[1651,86296,1839],{},[1692,86298,1703],{},[2115,86300,86301,86303],{},[898,86302,1807],{},[1692,86304,1703],{},[902,86306,86307],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,86309,86311],{"className":86310},[886],[888,86312,86313],{"xmlns":890},[892,86314,86315,86325],{},[895,86316,86317,86319,86321,86323],{},[898,86318,2995],{},[898,86320,2998],{},[898,86322,4104],{},[898,86324,3004],{},[902,86326,11899],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,86329,86331],{"className":86330},[886],[888,86332,86333],{"xmlns":890},[892,86334,86335,86339],{},[895,86336,86337],{},[1692,86338,4446],{},[902,86340,4446],{"encoding":904}," pracovníky a ",[883,86343,86345],{"className":86344},[886],[888,86346,86347],{"xmlns":890},[892,86348,86349,86353],{},[895,86350,86351],{},[1692,86352,78830],{},[902,86354,78830],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,86357,86359],{"className":86358},[886],[888,86360,86361],{"xmlns":890},[892,86362,86363,86367],{},[895,86364,86365],{},[1692,86366,47916],{},[902,86368,47916],{"encoding":904}," jednotek.",[724,86371,86372,86375,86376,11694,86406,1882],{},[38,86373,86374],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,86377,86379],{"className":86378},[886],[888,86380,86381],{"xmlns":890},[892,86382,86383,86403],{},[895,86384,86385,86387,86389,86391,86397],{},[898,86386,1690],{},[1651,86388,1738],{},[898,86390,5564],{},[2115,86392,86393,86395],{},[898,86394,1807],{},[898,86396,207],{},[2115,86398,86399,86401],{},[898,86400,11101],{},[898,86402,2268],{},[902,86404,86405],{"encoding":904},"Q = A L^{a} K^{b}",[883,86407,86409],{"className":86408},[886],[888,86410,86411],{"xmlns":890},[892,86412,86413,86443],{},[895,86414,86415,86417,86419,86421,86423,86425,86433,86435],{},[898,86416,2995],{},[898,86418,2998],{},[898,86420,4104],{},[898,86422,3004],{},[1651,86424,1738],{},[2938,86426,86427],{"scriptlevel":1741,"displaystyle":1653},[2446,86428,86429,86431],{},[898,86430,207],{},[898,86432,2268],{},[1651,86434,4503],{},[2938,86436,86437],{"scriptlevel":1741,"displaystyle":1653},[2446,86438,86439,86441],{},[898,86440,11101],{},[898,86442,1807],{},[902,86444,86445],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,86447,17018],{"id":17017},[120,86449,86450,86483,86510,86519,86569,86600,86653,86676,86731,86804,86882,86925,86957,86990,87031,87103,87164,87230,87247,87320,87386,87438,87494,87528,87571],{},[123,86451,86452,86455,86456,38109,86469,86482],{},[38,86453,86454],{},"Faktory (vstupy) produkce:"," práce ",[883,86457,86459],{"className":86458},[886],[888,86460,86461],{"xmlns":890},[892,86462,86463,86467],{},[895,86464,86465],{},[898,86466,1807],{},[902,86468,1807],{"encoding":904},[883,86470,86472],{"className":86471},[886],[888,86473,86474],{"xmlns":890},[892,86475,86476,86480],{},[895,86477,86478],{},[898,86479,11101],{},[902,86481,11101],{"encoding":904},", půda.",[123,86484,86485,8322,86487,1882],{},[38,86486,41664],{},[883,86488,86490],{"className":86489},[886],[888,86491,86492],{"xmlns":890},[892,86493,86494,86508],{},[895,86495,86496,86498,86500,86502,86504,86506],{},[898,86497,1690],{},[1651,86499,1738],{},[898,86501,1690],{},[1651,86503,1654],{"stretchy":1653},[898,86505,1807],{},[1651,86507,1667],{"stretchy":1653},[902,86509,75757],{"encoding":904},[123,86511,86512,11325,86514,13426,86517,1882],{},[38,86513,859],{},[614,86515,86516],{},"production function",[38,86518,76260],{},[123,86520,86521,3246,86523,1882],{},[38,86522,76306],{},[883,86524,86526],{"className":86525},[886],[888,86527,86528],{"xmlns":890},[892,86529,86530,86566],{},[895,86531,86532,86534,86540,86542,86544,86546,86548,86550,86552,86554,86560,86562,86564],{},[898,86533,2995],{},[1686,86535,86536,86538],{},[898,86537,2675],{},[898,86539,1807],{},[1651,86541,1738],{},[898,86543,3542],{},[898,86545,1690],{},[898,86547,5981],{"mathvariant":1910},[898,86549,3542],{},[898,86551,1807],{},[1651,86553,1738],{},[2115,86555,86556,86558],{},[898,86557,1690],{},[1651,86559,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,86561,1654],{"stretchy":1653},[898,86563,1807],{},[1651,86565,1667],{"stretchy":1653},[902,86567,86568],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,86570,86571,3246,86573,1882],{},[38,86572,77241],{},[883,86574,86576],{"className":86575},[886],[888,86577,86578],{"xmlns":890},[892,86579,86580,86598],{},[895,86581,86582,86584,86590,86592,86594,86596],{},[898,86583,5564],{},[1686,86585,86586,86588],{},[898,86587,2675],{},[898,86589,1807],{},[1651,86591,1738],{},[898,86593,1690],{},[898,86595,5981],{"mathvariant":1910},[898,86597,1807],{},[902,86599,75825],{"encoding":904},[123,86601,86602,86604,86605,11694,86622,1882],{},[38,86603,76728],{}," — od určitého ",[883,86606,86608],{"className":86607},[886],[888,86609,86610],{"xmlns":890},[892,86611,86612,86620],{},[895,86613,86614],{},[1686,86615,86616,86618],{},[898,86617,1807],{},[1692,86619,1741],{},[902,86621,76771],{"encoding":904},[883,86623,86625],{"className":86624},[886],[888,86626,86627],{"xmlns":890},[892,86628,86629,86651],{},[895,86630,86631,86641,86643,86645,86647,86649],{},[2115,86632,86633,86635],{},[898,86634,1690],{},[895,86636,86637,86639],{},[1651,86638,1912],{"mathvariant":1910},[1651,86640,1912],{"mathvariant":1910},[1651,86642,1654],{"stretchy":1653},[898,86644,1807],{},[1651,86646,1667],{"stretchy":1653},[1651,86648,2319],{},[1692,86650,1741],{},[902,86652,76917],{"encoding":904},[123,86654,86655,3246,86658,86675],{},[38,86656,86657],{},"Inflexní bod",[883,86659,86661],{"className":86660},[886],[888,86662,86663],{"xmlns":890},[892,86664,86665,86673],{},[895,86666,86667],{},[1686,86668,86669,86671],{},[898,86670,1807],{},[1692,86672,1741],{},[902,86674,76771],{"encoding":904}," — přechod z konvexity do konkavity.",[123,86677,86678,3246,86681,8322,86698,1882],{},[38,86679,86680],{},"Bod maxima produkce",[883,86682,86684],{"className":86683},[886],[888,86685,86686],{"xmlns":890},[892,86687,86688,86696],{},[895,86689,86690],{},[1686,86691,86692,86694],{},[898,86693,1807],{},[1692,86695,1694],{},[902,86697,14510],{"encoding":904},[883,86699,86701],{"className":86700},[886],[888,86702,86703],{"xmlns":890},[892,86704,86705,86729],{},[895,86706,86707,86709,86715,86717,86723,86725,86727],{},[898,86708,2995],{},[1686,86710,86711,86713],{},[898,86712,2675],{},[898,86714,1807],{},[1651,86716,1654],{"stretchy":1653},[1686,86718,86719,86721],{},[898,86720,1807],{},[1692,86722,1694],{},[1651,86724,1667],{"stretchy":1653},[1651,86726,1738],{},[1692,86728,1741],{},[902,86730,76990],{"encoding":904},[123,86732,86733,86755,86756,11694,86775,1882],{},[38,86734,86735,86736],{},"Princip maximalizace ",[883,86737,86739],{"className":86738},[886],[888,86740,86741],{"xmlns":890},[892,86742,86743,86753],{},[895,86744,86745,86747],{},[898,86746,5564],{},[1686,86748,86749,86751],{},[898,86750,2675],{},[898,86752,1807],{},[902,86754,75846],{"encoding":904}," — v bodě maxima ",[883,86757,86759],{"className":86758},[886],[888,86760,86761],{"xmlns":890},[892,86762,86763,86773],{},[895,86764,86765,86767],{},[898,86766,5564],{},[1686,86768,86769,86771],{},[898,86770,2675],{},[898,86772,1807],{},[902,86774,75846],{"encoding":904},[883,86776,86778],{"className":86777},[886],[888,86779,86780],{"xmlns":890},[892,86781,86782,86802],{},[895,86783,86784,86786,86792,86794,86796],{},[898,86785,2995],{},[1686,86787,86788,86790],{},[898,86789,2675],{},[898,86791,1807],{},[1651,86793,1738],{},[898,86795,5564],{},[1686,86797,86798,86800],{},[898,86799,2675],{},[898,86801,1807],{},[902,86803,75876],{"encoding":904},[123,86805,86806,3246,86809,1343,86848,1343,86865,1882],{},[38,86807,86808],{},"Polynomiální produkční funkce",[883,86810,86812],{"className":86811},[886],[888,86813,86814],{"xmlns":890},[892,86815,86816,86846],{},[895,86817,86818,86820,86822,86824,86826,86828,86830,86836,86838,86840],{},[898,86819,1690],{},[1651,86821,1654],{"stretchy":1653},[898,86823,1807],{},[1651,86825,1667],{"stretchy":1653},[1651,86827,1738],{},[898,86829,207],{},[2115,86831,86832,86834],{},[898,86833,1807],{},[1692,86835,3521],{},[1651,86837,1839],{},[898,86839,2268],{},[2115,86841,86842,86844],{},[898,86843,1807],{},[1692,86845,1703],{},[902,86847,77108],{"encoding":904},[883,86849,86851],{"className":86850},[886],[888,86852,86853],{"xmlns":890},[892,86854,86855,86863],{},[895,86856,86857,86859,86861],{},[898,86858,207],{},[1651,86860,2319],{},[1692,86862,1741],{},[902,86864,44298],{"encoding":904},[883,86866,86868],{"className":86867},[886],[888,86869,86870],{"xmlns":890},[892,86871,86872,86880],{},[895,86873,86874,86876,86878],{},[898,86875,2268],{},[1651,86877,2390],{},[1692,86879,1741],{},[902,86881,20027],{"encoding":904},[123,86883,86884,3246,86887,1882],{},[38,86885,86886],{},"Diferenciál produkce",[883,86888,86890],{"className":86889},[886],[888,86891,86892],{"xmlns":890},[892,86893,86894,86922],{},[895,86895,86896,86898,86900,86902,86904,86906,86908,86910,86916,86918,86920],{},[898,86897,4216],{"mathvariant":1910},[898,86899,1690],{},[1651,86901,4060],{},[898,86903,3542],{},[898,86905,1690],{},[1651,86907,1738],{},[898,86909,2995],{},[1686,86911,86912,86914],{},[898,86913,2675],{},[898,86915,1807],{},[1843,86917,1845],{},[898,86919,3542],{},[898,86921,1807],{},[902,86923,86924],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,86926,86927,8322,86929,1882],{},[38,86928,85184],{},[883,86930,86932],{"className":86931},[886],[888,86933,86934],{"xmlns":890},[892,86935,86936,86954],{},[895,86937,86938,86940,86942,86944,86946,86948,86950,86952],{},[898,86939,1690],{},[1651,86941,1738],{},[898,86943,1690],{},[1651,86945,1654],{"stretchy":1653},[898,86947,1807],{},[1651,86949,1661],{"separator":1660},[898,86951,11101],{},[1651,86953,1667],{"stretchy":1653},[902,86955,86956],{"encoding":904},"Q = Q(L, K)",[123,86958,86959,8322,86961,1882],{},[38,86960,79278],{},[883,86962,86964],{"className":86963},[886],[888,86965,86966],{"xmlns":890},[892,86967,86968,86988],{},[895,86969,86970,86972,86974,86976,86982],{},[898,86971,1690],{},[1651,86973,1738],{},[898,86975,5564],{},[2115,86977,86978,86980],{},[898,86979,1807],{},[898,86981,207],{},[2115,86983,86984,86986],{},[898,86985,11101],{},[898,86987,2268],{},[902,86989,75943],{"encoding":904},[123,86991,86992,8322,86995,87030],{},[38,86993,86994],{},"Ryzí Cobb-Douglas",[883,86996,86998],{"className":86997},[886],[888,86999,87000],{"xmlns":890},[892,87001,87002,87028],{},[895,87003,87004,87006,87008,87010,87016],{},[898,87005,1690],{},[1651,87007,1738],{},[898,87009,5564],{},[2115,87011,87012,87014],{},[898,87013,1807],{},[898,87015,207],{},[2115,87017,87018,87020],{},[898,87019,11101],{},[895,87021,87022,87024,87026],{},[1692,87023,1694],{},[1651,87025,2181],{},[898,87027,207],{},[902,87029,80105],{"encoding":904}," (konstantní výnosy).",[123,87032,87033,8322,87035,1882],{},[38,87034,80821],{},[883,87036,87038],{"className":87037},[886],[888,87039,87040],{"xmlns":890},[892,87041,87042,87100],{},[895,87043,87044,87046,87048,87050,87052,87054,87056,87058,87060,87062,87072,87074,87076,87086],{},[898,87045,1690],{},[1651,87047,1738],{},[898,87049,5564],{},[1651,87051,2261],{"stretchy":1653},[1651,87053,1654],{"stretchy":1653},[1692,87055,1694],{},[1651,87057,2181],{},[898,87059,207],{},[1651,87061,1667],{"stretchy":1653},[2115,87063,87064,87066],{},[898,87065,1807],{},[895,87067,87068,87070],{},[1651,87069,2181],{},[898,87071,2268],{},[1651,87073,1839],{},[898,87075,207],{},[2115,87077,87078,87080],{},[898,87079,11101],{},[895,87081,87082,87084],{},[1651,87083,2181],{},[898,87085,2268],{},[2115,87087,87088,87090],{},[1651,87089,2279],{"stretchy":1653},[895,87091,87092,87094,87096,87098],{},[1651,87093,2181],{},[1692,87095,1694],{},[898,87097,5981],{"mathvariant":1910},[898,87099,2268],{},[902,87101,87102],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,87104,87105,11325,87108,13426,87130,11325,87133,87163],{},[38,87106,87107],{},"Lineární",[883,87109,87111],{"className":87110},[886],[888,87112,87113],{"xmlns":890},[892,87114,87115,87127],{},[895,87116,87117,87119,87121,87123,87125],{},[898,87118,207],{},[898,87120,1807],{},[1651,87122,1839],{},[898,87124,2268],{},[898,87126,11101],{},[902,87128,87129],{"encoding":904},"aL + bK",[38,87131,87132],{},"Leontiefova",[883,87134,87136],{"className":87135},[886],[888,87137,87138],{"xmlns":890},[892,87139,87140,87160],{},[895,87141,87142,87144,87146,87148,87150,87152,87154,87156,87158],{},[898,87143,81049],{},[1651,87145,57413],{},[1651,87147,1654],{"stretchy":1653},[898,87149,207],{},[898,87151,1807],{},[1651,87153,1661],{"separator":1660},[898,87155,2268],{},[898,87157,11101],{},[1651,87159,1667],{"stretchy":1653},[902,87161,87162],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,87165,87166,8322,87182,1882],{},[38,87167,87168,87169],{},"Homogenita stupně ",[883,87170,87172],{"className":87171},[886],[888,87173,87174],{"xmlns":890},[892,87175,87176,87180],{},[895,87177,87178],{},[898,87179,38073],{},[902,87181,38073],{"encoding":904},[883,87183,87185],{"className":87184},[886],[888,87186,87187],{"xmlns":890},[892,87188,87189,87227],{},[895,87190,87191,87193,87195,87197,87199,87201,87203,87205,87207,87209,87215,87217,87219,87221,87223,87225],{},[898,87192,1690],{},[1651,87194,1654],{"stretchy":1653},[898,87196,13339],{},[898,87198,1807],{},[1651,87200,1661],{"separator":1660},[898,87202,13339],{},[898,87204,11101],{},[1651,87206,1667],{"stretchy":1653},[1651,87208,1738],{},[2115,87210,87211,87213],{},[898,87212,13339],{},[898,87214,38073],{},[898,87216,1690],{},[1651,87218,1654],{"stretchy":1653},[898,87220,1807],{},[1651,87222,1661],{"separator":1660},[898,87224,11101],{},[1651,87226,1667],{"stretchy":1653},[902,87228,87229],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,87231,87232,80203],{},[38,87233,80136,87234],{},[883,87235,87237],{"className":87236},[886],[888,87238,87239],{"xmlns":890},[892,87240,87241,87245],{},[895,87242,87243],{},[898,87244,5564],{},[902,87246,5564],{"encoding":904},[123,87248,87249,87251,87252,87274,87275,87297,87298,5230],{},[38,87250,79637],{}," — konstantní (",[883,87253,87255],{"className":87254},[886],[888,87256,87257],{"xmlns":890},[892,87258,87259,87271],{},[895,87260,87261,87263,87265,87267,87269],{},[898,87262,207],{},[1651,87264,1839],{},[898,87266,2268],{},[1651,87268,1738],{},[1692,87270,1694],{},[902,87272,87273],{"encoding":904},"a+b=1","), rostoucí (",[883,87276,87278],{"className":87277},[886],[888,87279,87280],{"xmlns":890},[892,87281,87282,87294],{},[895,87283,87284,87286,87288,87290,87292],{},[898,87285,207],{},[1651,87287,1839],{},[898,87289,2268],{},[1651,87291,2390],{},[1692,87293,1694],{},[902,87295,87296],{"encoding":904},"a+b>1","), klesající (",[883,87299,87301],{"className":87300},[886],[888,87302,87303],{"xmlns":890},[892,87304,87305,87317],{},[895,87306,87307,87309,87311,87313,87315],{},[898,87308,207],{},[1651,87310,1839],{},[898,87312,2268],{},[1651,87314,2319],{},[1692,87316,1694],{},[902,87318,87319],{"encoding":904},"a+b\u003C1",[123,87321,87322,3246,87324,1343,87354,3246,87356,1882],{},[38,87323,76306],{},[883,87325,87327],{"className":87326},[886],[888,87328,87329],{"xmlns":890},[892,87330,87331,87351],{},[895,87332,87333,87335,87341,87343],{},[898,87334,2995],{},[1686,87336,87337,87339],{},[898,87338,2675],{},[898,87340,1807],{},[1651,87342,1738],{},[1902,87344,87345,87347,87349],{},[898,87346,1690],{},[898,87348,1807],{},[1651,87350,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,87352,87353],{"encoding":904},"MP_L = Q'_L",[38,87355,79210],{},[883,87357,87359],{"className":87358},[886],[888,87360,87361],{"xmlns":890},[892,87362,87363,87383],{},[895,87364,87365,87367,87373,87375],{},[898,87366,2995],{},[1686,87368,87369,87371],{},[898,87370,2675],{},[898,87372,11101],{},[1651,87374,1738],{},[1902,87376,87377,87379,87381],{},[898,87378,1690],{},[898,87380,11101],{},[1651,87382,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,87384,87385],{"encoding":904},"MP_K = Q'_K",[123,87387,87388,3246,87390,1882],{},[38,87389,81424],{},[883,87391,87393],{"className":87392},[886],[888,87394,87395],{"xmlns":890},[892,87396,87397,87435],{},[895,87398,87399,87401,87403,87405,87407,87413,87415,87417,87419,87421,87423,87429,87431,87433],{},[898,87400,3542],{},[898,87402,1690],{},[1651,87404,1738],{},[898,87406,2995],{},[1686,87408,87409,87411],{},[898,87410,2675],{},[898,87412,1807],{},[1843,87414,1845],{},[898,87416,3542],{},[898,87418,1807],{},[1651,87420,1839],{},[898,87422,2995],{},[1686,87424,87425,87427],{},[898,87426,2675],{},[898,87428,11101],{},[1843,87430,1845],{},[898,87432,3542],{},[898,87434,11101],{},[902,87436,87437],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,87439,87440,8322,87442,1882],{},[38,87441,81769],{},[883,87443,87445],{"className":87444},[886],[888,87446,87447],{"xmlns":890},[892,87448,87449,87491],{},[895,87450,87451,87453,87461,87463,87465,87473,87475,87477,87479,87481,87483,87485,87487,87489],{},[898,87452,1807],{},[1902,87454,87455,87457,87459],{},[898,87456,1690],{},[898,87458,1807],{},[1651,87460,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,87462,1839],{},[898,87464,11101],{},[1902,87466,87467,87469,87471],{},[898,87468,1690],{},[898,87470,11101],{},[1651,87472,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,87474,1738],{},[898,87476,38073],{},[1843,87478,1845],{},[898,87480,1690],{},[1651,87482,1654],{"stretchy":1653},[898,87484,1807],{},[1651,87486,1661],{"separator":1660},[898,87488,11101],{},[1651,87490,1667],{"stretchy":1653},[902,87492,87493],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,87495,87496,87499,87500,1882],{},[38,87497,87498],{},"Izokvanta"," — křivka ",[883,87501,87503],{"className":87502},[886],[888,87504,87505],{"xmlns":890},[892,87506,87507,87525],{},[895,87508,87509,87511,87513,87515,87517,87519,87521,87523],{},[898,87510,1690],{},[1651,87512,1654],{"stretchy":1653},[898,87514,1807],{},[1651,87516,1661],{"separator":1660},[898,87518,11101],{},[1651,87520,1667],{"stretchy":1653},[1651,87522,1738],{},[898,87524,82010],{},[902,87526,87527],{"encoding":904},"Q(L, K) = q",[123,87529,87530,3246,87532,1882],{},[38,87531,82199],{},[883,87533,87535],{"className":87534},[886],[888,87536,87537],{"xmlns":890},[892,87538,87539,87569],{},[895,87540,87541,87543,87545,87547,87549,87551,87553,87559,87561,87563],{},[898,87542,2995],{},[898,87544,2998],{},[898,87546,4104],{},[898,87548,3004],{},[1651,87550,1738],{},[898,87552,2995],{},[1686,87554,87555,87557],{},[898,87556,2675],{},[898,87558,1807],{},[898,87560,5981],{"mathvariant":1910},[898,87562,2995],{},[1686,87564,87565,87567],{},[898,87566,2675],{},[898,87568,11101],{},[902,87570,76018],{"encoding":904},[123,87572,87573,3246,87576,1882],{},[38,87574,87575],{},"Substituční vztah",[883,87577,87579],{"className":87578},[886],[888,87580,87581],{"xmlns":890},[892,87582,87583,87607],{},[895,87584,87585,87587,87589,87591,87593,87595,87597,87599,87601,87603,87605],{},[898,87586,4216],{"mathvariant":1910},[898,87588,11101],{},[1651,87590,4060],{},[1651,87592,2181],{},[898,87594,2995],{},[898,87596,2998],{},[898,87598,4104],{},[898,87600,3004],{},[1843,87602,1845],{},[898,87604,3542],{},[898,87606,1807],{},[902,87608,87609],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,87611,3238],{"id":3237},[120,87613,87614,87711,87718,87725],{},[123,87615,87616,3246,87618,87621,87622,1343,87625,87628,87629,87632,87633,87652,87653,19861,87672,87675,87676,87695,87696,5230],{},[38,87617,51936],{},[207,87619,784],{"className":87620,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,87623,3695],{"className":87624,"dataFsResolvedFilePath":764,"href":765},[210],[207,87626,793],{"className":87627,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,87630,880],{"className":87631,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,87634,87636],{"className":87635},[886],[888,87637,87638],{"xmlns":890},[892,87639,87640,87650],{},[895,87641,87642,87644,87646,87648],{},[898,87643,2995],{},[898,87645,2998],{},[898,87647,4104],{},[898,87649,3004],{},[902,87651,11899],{"encoding":904}," ↔ ",[883,87654,87656],{"className":87655},[886],[888,87657,87658],{"xmlns":890},[892,87659,87660,87670],{},[895,87661,87662,87664,87666,87668],{},[898,87663,2995],{},[898,87665,2998],{},[898,87667,3001],{},[898,87669,3004],{},[902,87671,11903],{"encoding":904},[207,87673,5135],{"className":87674,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,87677,87679],{"className":87678},[886],[888,87680,87681],{"xmlns":890},[892,87682,87683,87693],{},[895,87684,87685,87687],{},[898,87686,5564],{},[1686,87688,87689,87691],{},[898,87690,2675],{},[898,87692,1807],{},[902,87694,75846],{"encoding":904}," ↔ min ",[883,87697,87699],{"className":87698},[886],[888,87700,87701],{"xmlns":890},[892,87702,87703,87709],{},[895,87704,87705,87707],{},[898,87706,5564],{},[898,87708,3001],{},[902,87710,56773],{"encoding":904},[123,87712,87713,3246,87715,1882],{},[38,87714,3245],{},[207,87716,5140],{"className":87717,"dataFsResolvedFilePath":848,"href":849},[210],[123,87719,87720,3246,87722,1882],{},[38,87721,17511],{},[207,87723,1094],{"className":87724,"dataFsResolvedFilePath":838,"href":839},[210],[123,87726,87727,3246,87729,1882],{},[38,87728,17502],{},[207,87730,17506],{"className":87731,"dataFsResolvedFilePath":1749,"href":1750},[210],{"title":641,"searchDepth":642,"depth":642,"links":87733},[87734,87735,87736,87740,87742,87747,87748,87755,87756,87758,87759,87760,87762,87767,87768,87769,87773,87774],{"id":76041,"depth":642,"text":76042},{"id":76178,"depth":642,"text":76179},{"id":76281,"depth":642,"text":87737,"children":87738},"Mezní produkt práce (MPLMP_L)",[87739],{"id":76727,"depth":649,"text":76728},{"id":77216,"depth":642,"text":87741},"Průměrný produkt práce (APLAP_L)",{"id":77334,"depth":642,"text":77335,"children":87743},[87744,87745,87746],{"id":77571,"depth":649,"text":66714},{"id":77882,"depth":649,"text":77883},{"id":78602,"depth":649,"text":78603},{"id":79174,"depth":642,"text":79175},{"id":79277,"depth":642,"text":79278,"children":87749},[87750,87751,87753,87754],{"id":79636,"depth":649,"text":79637},{"id":80135,"depth":649,"text":87752},"Parametr efektivity AA",{"id":80206,"depth":649,"text":80207},{"id":38392,"depth":649,"text":80546},{"id":80733,"depth":642,"text":80734},{"id":81072,"depth":642,"text":87757},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":81763,"depth":642,"text":81764},{"id":76107,"depth":642,"text":11080},{"id":82174,"depth":642,"text":87761},"Mezní míra technické substituce (MRTSMRTS)",{"id":83040,"depth":642,"text":83041,"children":87763},[87764,87765,87766],{"id":83044,"depth":649,"text":83045},{"id":83687,"depth":649,"text":83688},{"id":83968,"depth":649,"text":83969},{"id":84314,"depth":642,"text":84315},{"id":51094,"depth":642,"text":51095},{"id":84664,"depth":642,"text":84665,"children":87770},[87771,87772],{"id":41663,"depth":649,"text":41664},{"id":85183,"depth":649,"text":85184},{"id":17017,"depth":642,"text":17018},{"id":3237,"depth":642,"text":3238},{},"\u002Ftopics\u002Fprodukce",{"title":75677,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,11114,87781,87782,87783,76107,87784,87785],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":87788,"title":87789,"body":87790,"course":1128,"courses":659,"created":10859,"description":641,"extension":661,"meta":96737,"navigation":664,"path":96738,"seo":96739,"sources":96740,"stem":96741,"tags":96742,"type":3302,"updated":677,"__hash__":96745},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":87791,"toc":96711},[87792,87795,87797,87994,88003,88007,88010,88063,88067,88079,88083,88086,88103,88226,88232,88376,88386,88390,88425,88463,88511,88568,88628,88670,89246,89250,89333,89442,89535,89793,89796,89849,89960,90042,90046,90057,90290,90345,90351,90391,90454,90465,90656,90762,90915,90963,90968,91082,91120,91246,91292,91319,91396,91471,91551,91681,91742,91830,91834,91837,91906,91989,91996,92056,92366,92370,92376,92429,92445,92496,92634,92710,92823,93140,93144,93151,93311,93370,93374,93396,93493,93614,93728,93751,93814,93871,94123,94131,94135,94142,94396,94446,94502,94505,94669,94673,94771,94773,94805,94809,94942,95184,95368,95536,95843,95976,96163,96175,96177,96612,96614],[12,87793,87789],{"id":87794},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,87796,13304],{"id":13303},[724,87798,87799,3246,87801,87832,87833,87836,87837,87867,87868,87886,87887,87927,87928,87931,87932,87945,87946,29466,87949,87962,87963,87976,87977,87990,87991,1882],{},[38,87800,880],{},[883,87802,87804],{"className":87803},[886],[888,87805,87806],{"xmlns":890},[892,87807,87808,87830],{},[895,87809,87810,87812,87814,87820,87822,87828],{},[898,87811,900],{},[1651,87813,1654],{"stretchy":1653},[1686,87815,87816,87818],{},[898,87817,1690],{},[1692,87819,1694],{},[1651,87821,1661],{"separator":1660},[1686,87823,87824,87826],{},[898,87825,1690],{},[1692,87827,1703],{},[1651,87829,1667],{"stretchy":1653},[902,87831,1708],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,87834,87835],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,87838,87840],{"className":87839},[886],[888,87841,87842],{"xmlns":890},[892,87843,87844,87864],{},[895,87845,87846,87848,87854,87856],{},[898,87847,2995],{},[1686,87849,87850,87852],{},[898,87851,900],{},[898,87853,3201],{},[1651,87855,1738],{},[1902,87857,87858,87860,87862],{},[898,87859,900],{},[898,87861,3201],{},[1651,87863,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,87865,87866],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,87869,87871],{"className":87870},[886],[888,87872,87873],{"xmlns":890},[892,87874,87875,87883],{},[895,87876,87877,87879,87881],{},[898,87878,900],{},[1651,87880,1738],{},[898,87882,3490],{},[902,87884,87885],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,87888,87890],{"className":87889},[886],[888,87891,87892],{"xmlns":890},[892,87893,87894,87924],{},[895,87895,87896,87898,87900,87902,87904,87906,87908,87914,87916,87918],{},[898,87897,2995],{},[898,87899,2998],{},[898,87901,3001],{},[898,87903,3004],{},[1651,87905,1738],{},[898,87907,2995],{},[1686,87909,87910,87912],{},[898,87911,900],{},[1692,87913,1694],{},[898,87915,5981],{"mathvariant":1910},[898,87917,2995],{},[1686,87919,87920,87922],{},[898,87921,900],{},[1692,87923,1703],{},[902,87925,87926],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,87929,87930],{},"teorii užitečnosti"," — funkce ",[883,87933,87935],{"className":87934},[886],[888,87936,87937],{"xmlns":890},[892,87938,87939,87943],{},[895,87940,87941],{},[898,87942,900],{},[902,87944,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,87947,87948],{},"Optimalizaci spotřebitele",[883,87950,87952],{"className":87951},[886],[888,87953,87954],{"xmlns":890},[892,87955,87956,87960],{},[895,87957,87958],{},[898,87959,900],{},[902,87961,900],{"encoding":904}," při rozpočtu, min ",[883,87964,87966],{"className":87965},[886],[888,87967,87968],{"xmlns":890},[892,87969,87970,87974],{},[895,87971,87972],{},[898,87973,5561],{},[902,87975,5561],{"encoding":904}," při dané ",[883,87978,87980],{"className":87979},[886],[888,87981,87982],{"xmlns":890},[892,87983,87984,87988],{},[895,87985,87986],{},[898,87987,900],{},[902,87989,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,87992,913],{"className":87993,"dataFsResolvedFilePath":911,"href":912},[210],[724,87995,87996,87997,87999,88000,1882],{},"Kapitola 6 knihy ",[614,87998,17506],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,88001,37967],{"className":88002,"dataFsResolvedFilePath":911,"href":912},[210],[115,88004,88006],{"id":88005},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,88008,88009],{},"Po prostudování této kapitoly byste měli umět:",[120,88011,88012,88018,88027,88032,88035,88041,88047,88050,88056],{},[123,88013,88014,88015,1661],{},"vyložit, co se rozumí termínem ",[38,88016,88017],{},"užitečnost",[123,88019,88020,88021,5197,88024,1661],{},"definovat pojmy ",[38,88022,88023],{},"svazek zboží",[38,88025,88026],{},"funkce užitečnosti",[123,88028,76056,88029,76063],{},[38,88030,88031],{},"mezní užitečnosti",[123,88033,88034],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,88036,76083,88037,88040],{},[38,88038,88039],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,88042,76104,88043,88046],{},[38,88044,88045],{},"křivky užitečnosti"," (indiferenční křivky),",[123,88048,88049],{},"vyjmenovat jejich základní vlastnosti,",[123,88051,76056,88052,88055],{},[38,88053,88054],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,88057,88058,88059,88062],{},"řešit ",[38,88060,88061],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,88064,88066],{"id":88065},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,88068,88069,88070,88074,88075,88078],{},"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 ",[207,88071,88073],{"className":88072,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,88076,88077],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,88080,88082],{"id":88081},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,88084,88085],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,88087,88088,88094],{},[123,88089,88090,88093],{},[38,88091,88092],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,88095,88096,88099,88100,88102],{},[38,88097,88098],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,88101,87835],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[5179,88104,88105],{},[724,88106,88107,88109,88110,88113,88114,3246,88127,88130,88131,5197,88144,88163,88164,1343,88190,88217,88218,88221,88222,88225],{},[883,88108,5719],{}," Pozor — ordinalisté užitečnost ",[38,88111,88112],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,88115,88117],{"className":88116},[886],[888,88118,88119],{"xmlns":890},[892,88120,88121,88125],{},[895,88122,88123],{},[898,88124,900],{},[902,88126,900],{"encoding":904},[38,88128,88129],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,88132,88134],{"className":88133},[886],[888,88135,88136],{"xmlns":890},[892,88137,88138,88142],{},[895,88139,88140],{},[898,88141,900],{},[902,88143,900],{"encoding":904},[883,88145,88147],{"className":88146},[886],[888,88148,88149],{"xmlns":890},[892,88150,88151,88160],{},[895,88152,88153],{},[9692,88154,88155,88157],{"accent":1660},[898,88156,900],{},[1651,88158,88159],{},"~",[902,88161,88162],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,88165,88167],{"className":88166},[886],[888,88168,88169],{"xmlns":890},[892,88170,88171,88187],{},[895,88172,88173,88179,88181],{},[9692,88174,88175,88177],{"accent":1660},[898,88176,900],{},[1651,88178,88159],{},[1651,88180,1738],{},[2115,88182,88183,88185],{},[898,88184,900],{},[1692,88186,1703],{},[902,88188,88189],{"encoding":904},"\\tilde U = U^2",[883,88191,88193],{"className":88192},[886],[888,88194,88195],{"xmlns":890},[892,88196,88197,88214],{},[895,88198,88199,88205,88207,88210,88212],{},[9692,88200,88201,88203],{"accent":1660},[898,88202,900],{},[1651,88204,88159],{},[1651,88206,1738],{},[898,88208,88209],{},"ln",[1651,88211,57413],{},[898,88213,900],{},[902,88215,88216],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,88219,88220],{},"porovnání"," mezi svazky a ",[38,88223,88224],{},"poměry"," mezních veličin.",[724,88227,88228,88229,1793],{},"Ordinalistický přístup vychází z ",[38,88230,88231],{},"pěti hlavních předpokladů",[152,88233,88234,88240,88246,88364,88370],{},[123,88235,88236,88239],{},[38,88237,88238],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,88241,88242,88245],{},[38,88243,88244],{},"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.",[123,88247,88248,88251,88252,62954,88265,88278,88279,62954,88292,4254,88305,88308,88309,5197,88328,63783,88346,1882],{},[38,88249,88250],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,88253,88255],{"className":88254},[886],[888,88256,88257],{"xmlns":890},[892,88258,88259,88263],{},[895,88260,88261],{},[898,88262,5564],{},[902,88264,5564],{"encoding":904},[883,88266,88268],{"className":88267},[886],[888,88269,88270],{"xmlns":890},[892,88271,88272,88276],{},[895,88273,88274],{},[898,88275,24466],{},[902,88277,24466],{"encoding":904},", nebude jindy preferovat ",[883,88280,88282],{"className":88281},[886],[888,88283,88284],{"xmlns":890},[892,88285,88286,88290],{},[895,88287,88288],{},[898,88289,24466],{},[902,88291,24466],{"encoding":904},[883,88293,88295],{"className":88294},[886],[888,88296,88297],{"xmlns":890},[892,88298,88299,88303],{},[895,88300,88301],{},[898,88302,5564],{},[902,88304,5564],{"encoding":904},[38,88306,88307],{},"Tranzitivita",": pokud ",[883,88310,88312],{"className":88311},[886],[888,88313,88314],{"xmlns":890},[892,88315,88316,88325],{},[895,88317,88318,88320,88323],{},[898,88319,5564],{},[1651,88321,88322],{},"≻",[898,88324,24466],{},[902,88326,88327],{"encoding":904},"A \\succ B",[883,88329,88331],{"className":88330},[886],[888,88332,88333],{"xmlns":890},[892,88334,88335,88343],{},[895,88336,88337,88339,88341],{},[898,88338,24466],{},[1651,88340,88322],{},[898,88342,3001],{},[902,88344,88345],{"encoding":904},"B \\succ C",[883,88347,88349],{"className":88348},[886],[888,88350,88351],{"xmlns":890},[892,88352,88353,88361],{},[895,88354,88355,88357,88359],{},[898,88356,5564],{},[1651,88358,88322],{},[898,88360,3001],{},[902,88362,88363],{"encoding":904},"A \\succ C",[123,88365,88366,88369],{},[38,88367,88368],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,88371,88372,88375],{},[38,88373,88374],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,88377,88378,88379,88382,88383,1882],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,88380,88381],{},"preference"," a na příbuzné ",[614,88384,88385],{},"funkci užitečnosti",[115,88387,88389],{"id":88388},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,88391,88392,88393,88406,88407,88410,88411,88424],{},"Uvažujme ",[883,88394,88396],{"className":88395},[886],[888,88397,88398],{"xmlns":890},[892,88399,88400,88404],{},[895,88401,88402],{},[898,88403,38073],{},[902,88405,38073],{"encoding":904}," různých zboží. ",[38,88408,88409],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,88412,88414],{"className":88413},[886],[888,88415,88416],{"xmlns":890},[892,88417,88418,88422],{},[895,88419,88420],{},[898,88421,38073],{},[902,88423,38073],{"encoding":904},"-tice",[724,88426,88427],{},[883,88428,88430],{"className":88429},[886],[888,88431,88432],{"xmlns":890},[892,88433,88434,88460],{},[895,88435,88436,88438,88444,88446,88448,88450,88456,88458],{},[1651,88437,1654],{"stretchy":1653},[1686,88439,88440,88442],{},[898,88441,1690],{},[1692,88443,1694],{},[1651,88445,1661],{"separator":1660},[1651,88447,10949],{},[1651,88449,1661],{"separator":1660},[1686,88451,88452,88454],{},[898,88453,1690],{},[898,88455,38073],{},[1651,88457,1667],{"stretchy":1653},[1651,88459,1661],{"separator":1660},[902,88461,88462],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,88464,1863,88465,88482,88483,88496,88497,88500,88501,88504,88505,88508,88509,1793],{},[883,88466,88468],{"className":88467},[886],[888,88469,88470],{"xmlns":890},[892,88471,88472,88480],{},[895,88473,88474],{},[1686,88475,88476,88478],{},[898,88477,1690],{},[898,88479,3201],{},[902,88481,48751],{"encoding":904}," značí množství ",[883,88484,88486],{"className":88485},[886],[888,88487,88488],{"xmlns":890},[892,88489,88490,88494],{},[895,88491,88492],{},[898,88493,3201],{},[902,88495,3201],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,88498,88499],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,88502,88503],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,88506,88507],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,88510,88385],{},[883,88512,88514],{"className":88513},[886],[888,88515,88516],{"xmlns":890,"display":29279},[892,88517,88518,88565],{},[21967,88519,88520],{"width":29284},[21972,88521,88522,88524,88558,88560],{},[21975,88523],{"width":29289},[21975,88525,88526],{},[895,88527,88528,88530,88532,88534,88536,88542,88544,88546,88548,88554,88556],{},[898,88529,900],{},[1651,88531,1738],{},[898,88533,900],{},[1651,88535,1654],{"stretchy":1653},[1686,88537,88538,88540],{},[898,88539,1690],{},[1692,88541,1694],{},[1651,88543,1661],{"separator":1660},[1651,88545,10949],{},[1651,88547,1661],{"separator":1660},[1686,88549,88550,88552],{},[898,88551,1690],{},[898,88553,38073],{},[1651,88555,1667],{"stretchy":1653},[1651,88557,1661],{"separator":1660},[21975,88559],{"width":29289},[21975,88561,88562],{},[1843,88563,88564],{},"(6.1)",[902,88566,88567],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,88569,1863,88570,88600,88601,88623,88624,88627],{},[883,88571,88573],{"className":88572},[886],[888,88574,88575],{"xmlns":890},[892,88576,88577,88597],{},[895,88578,88579,88585,88587,88589,88591],{},[1686,88580,88581,88583],{},[898,88582,1690],{},[1692,88584,1694],{},[1651,88586,1661],{"separator":1660},[1651,88588,10949],{},[1651,88590,1661],{"separator":1660},[1686,88592,88593,88595],{},[898,88594,1690],{},[898,88596,38073],{},[902,88598,88599],{"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 ",[883,88602,88604],{"className":88603},[886],[888,88605,88606],{"xmlns":890},[892,88607,88608,88620],{},[895,88609,88610,88612,88614],{},[898,88611,900],{},[1651,88613,1661],{"separator":1660},[9692,88615,88616,88618],{"accent":1660},[898,88617,900],{},[1651,88619,88159],{},[902,88621,88622],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,88625,88626],{},"monotónní transformace"," zachovávající pořadí.",[724,88629,88630,88631,8322,88634,1882],{},"Dále se omezíme na funkce pro ",[38,88632,88633],{},"dvě zboží",[883,88635,88637],{"className":88636},[886],[888,88638,88639],{"xmlns":890},[892,88640,88641,88667],{},[895,88642,88643,88645,88647,88649,88651,88657,88659,88665],{},[898,88644,900],{},[1651,88646,1738],{},[898,88648,900],{},[1651,88650,1654],{"stretchy":1653},[1686,88652,88653,88655],{},[898,88654,1690],{},[1692,88656,1694],{},[1651,88658,1661],{"separator":1660},[1686,88660,88661,88663],{},[898,88662,1690],{},[1692,88664,1703],{},[1651,88666,1667],{"stretchy":1653},[902,88668,88669],{"encoding":904},"U = U(Q_1, Q_2)",[5179,88671,88672,88747],{},[724,88673,88674,88676,88677,1793],{},[883,88675,53908],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,88678,88680],{"className":88679},[886],[888,88681,88682],{"xmlns":890},[892,88683,88684,88744],{},[895,88685,88686,88688,88690,88692,88694,88700,88702,88708,88710,88716,88718,88720,88722],{},[898,88687,900],{},[1651,88689,1738],{},[898,88691,900],{},[1651,88693,1654],{"stretchy":1653},[1686,88695,88696,88698],{},[898,88697,1690],{},[1692,88699,1694],{},[1651,88701,1661],{"separator":1660},[1686,88703,88704,88706],{},[898,88705,1690],{},[1692,88707,1703],{},[1651,88709,1661],{"separator":1660},[1686,88711,88712,88714],{},[898,88713,1690],{},[1692,88715,3521],{},[1651,88717,1667],{"stretchy":1653},[1651,88719,1738],{},[1692,88721,1703],{},[9423,88723,88724],{},[895,88725,88726,88732,88738],{},[1686,88727,88728,88730],{},[898,88729,1690],{},[1692,88731,1694],{},[1686,88733,88734,88736],{},[898,88735,1690],{},[1692,88737,1703],{},[1686,88739,88740,88742],{},[898,88741,1690],{},[1692,88743,3521],{},[902,88745,88746],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,88748,88749,88942],{},[123,88750,88751,88752,88778,88779,14236,88805,5197,88864,6896,88924,9731],{},"svazek ",[883,88753,88755],{"className":88754},[886],[888,88756,88757],{"xmlns":890},[892,88758,88759,88775],{},[895,88760,88761,88763,88765,88767,88769,88771,88773],{},[1651,88762,1654],{"stretchy":1653},[1692,88764,43075],{},[1651,88766,1661],{"separator":1660},[1692,88768,3689],{},[1651,88770,1661],{"separator":1660},[1692,88772,43053],{},[1651,88774,1667],{"stretchy":1653},[902,88776,88777],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,88780,88782],{"className":88781},[886],[888,88783,88784],{"xmlns":890},[892,88785,88786,88802],{},[895,88787,88788,88790,88792,88794,88796,88798,88800],{},[1651,88789,1654],{"stretchy":1653},[1692,88791,5309],{},[1651,88793,1661],{"separator":1660},[1692,88795,5309],{},[1651,88797,1661],{"separator":1660},[1692,88799,67810],{},[1651,88801,1667],{"stretchy":1653},[902,88803,88804],{"encoding":904},"(9, 9, 27)",[883,88806,88808],{"className":88807},[886],[888,88809,88810],{"xmlns":890},[892,88811,88812,88861],{},[895,88813,88814,88816,88818,88820,88822,88824,88826,88828,88830,88832,88834,88848,88850,88852,88857,88859],{},[898,88815,900],{},[1651,88817,1654],{"stretchy":1653},[1692,88819,43075],{},[1651,88821,1661],{"separator":1660},[1692,88823,3689],{},[1651,88825,1661],{"separator":1660},[1692,88827,43053],{},[1651,88829,1667],{"stretchy":1653},[1651,88831,1738],{},[1692,88833,1703],{},[9423,88835,88836],{},[895,88837,88838,88840,88842,88844,88846],{},[1692,88839,43075],{},[1651,88841,4503],{},[1692,88843,3689],{},[1651,88845,4503],{},[1692,88847,43053],{},[1651,88849,1738],{},[1692,88851,1703],{},[9423,88853,88854],{},[1692,88855,88856],{},"4096",[1651,88858,1738],{},[1692,88860,6924],{},[902,88862,88863],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,88865,88867],{"className":88866},[886],[888,88868,88869],{"xmlns":890},[892,88870,88871,88921],{},[895,88872,88873,88875,88877,88879,88881,88883,88885,88887,88889,88891,88893,88907,88909,88911,88916,88918],{},[898,88874,900],{},[1651,88876,1654],{"stretchy":1653},[1692,88878,5309],{},[1651,88880,1661],{"separator":1660},[1692,88882,5309],{},[1651,88884,1661],{"separator":1660},[1692,88886,67810],{},[1651,88888,1667],{"stretchy":1653},[1651,88890,1738],{},[1692,88892,1703],{},[9423,88894,88895],{},[895,88896,88897,88899,88901,88903,88905],{},[1692,88898,5309],{},[1651,88900,4503],{},[1692,88902,5309],{},[1651,88904,4503],{},[1692,88906,67810],{},[1651,88908,1738],{},[1692,88910,1703],{},[9423,88912,88913],{},[1692,88914,88915],{},"2187",[1651,88917,7207],{},[1692,88919,88920],{},"93,53",[902,88922,88923],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,88925,88927],{"className":88926},[886],[888,88928,88929],{"xmlns":890},[892,88930,88931,88939],{},[895,88932,88933,88935,88937],{},[1692,88934,6924],{},[1651,88936,2390],{},[1692,88938,88920],{},[902,88940,88941],{"encoding":904},"128 > 93{,}53",[123,88943,88944,88945,5197,88971,88997,88998,5197,89038,89079,89080,89126,89127,5197,89153,4172,89179,5197,89197,89215,89216,1882],{},"svazky ",[883,88946,88948],{"className":88947},[886],[888,88949,88950],{"xmlns":890},[892,88951,88952,88968],{},[895,88953,88954,88956,88958,88960,88962,88964,88966],{},[1651,88955,1654],{"stretchy":1653},[1692,88957,3689],{},[1651,88959,1661],{"separator":1660},[1692,88961,6892],{},[1651,88963,1661],{"separator":1660},[1692,88965,1703],{},[1651,88967,1667],{"stretchy":1653},[902,88969,88970],{"encoding":904},"(4, 8, 2)",[883,88972,88974],{"className":88973},[886],[888,88975,88976],{"xmlns":890},[892,88977,88978,88994],{},[895,88979,88980,88982,88984,88986,88988,88990,88992],{},[1651,88981,1654],{"stretchy":1653},[1692,88983,43053],{},[1651,88985,1661],{"separator":1660},[1692,88987,1694],{},[1651,88989,1661],{"separator":1660},[1692,88991,3689],{},[1651,88993,1667],{"stretchy":1653},[902,88995,88996],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,88999,89001],{"className":89000},[886],[888,89002,89003],{"xmlns":890},[892,89004,89005,89035],{},[895,89006,89007,89009,89011,89013,89015,89017,89019,89021,89023,89025,89027,89031,89033],{},[898,89008,900],{},[1651,89010,1654],{"stretchy":1653},[1692,89012,3689],{},[1651,89014,1661],{"separator":1660},[1692,89016,6892],{},[1651,89018,1661],{"separator":1660},[1692,89020,1703],{},[1651,89022,1667],{"stretchy":1653},[1651,89024,1738],{},[1692,89026,1703],{},[9423,89028,89029],{},[1692,89030,43053],{},[1651,89032,1738],{},[1692,89034,43075],{},[902,89036,89037],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,89039,89041],{"className":89040},[886],[888,89042,89043],{"xmlns":890},[892,89044,89045,89076],{},[895,89046,89047,89049,89051,89053,89055,89057,89059,89061,89063,89065,89067,89072,89074],{},[898,89048,900],{},[1651,89050,1654],{"stretchy":1653},[1692,89052,43053],{},[1651,89054,1661],{"separator":1660},[1692,89056,1694],{},[1651,89058,1661],{"separator":1660},[1692,89060,3689],{},[1651,89062,1667],{"stretchy":1653},[1651,89064,1738],{},[1692,89066,1703],{},[9423,89068,89069],{},[1692,89070,89071],{},"256",[1651,89073,1738],{},[1692,89075,73572],{},[902,89077,89078],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,89081,89083],{"className":89082},[886],[888,89084,89085],{"xmlns":890},[892,89086,89087,89123],{},[895,89088,89089,89091,89093,89095,89097,89099,89101,89103,89105,89107,89109,89111,89113,89115,89117,89119,89121],{},[898,89090,900],{},[1651,89092,1654],{"stretchy":1653},[1692,89094,3689],{},[1651,89096,1661],{"separator":1660},[1692,89098,6892],{},[1651,89100,1661],{"separator":1660},[1692,89102,1703],{},[1651,89104,1667],{"stretchy":1653},[1651,89106,1738],{},[898,89108,900],{},[1651,89110,1654],{"stretchy":1653},[1692,89112,43053],{},[1651,89114,1661],{"separator":1660},[1692,89116,1694],{},[1651,89118,1661],{"separator":1660},[1692,89120,3689],{},[1651,89122,1667],{"stretchy":1653},[902,89124,89125],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,89128,89130],{"className":89129},[886],[888,89131,89132],{"xmlns":890},[892,89133,89134,89150],{},[895,89135,89136,89138,89140,89142,89144,89146,89148],{},[1692,89137,3689],{},[1651,89139,4503],{},[1692,89141,6892],{},[1651,89143,4503],{},[1692,89145,1703],{},[1651,89147,1738],{},[1692,89149,43053],{},[902,89151,89152],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,89154,89156],{"className":89155},[886],[888,89157,89158],{"xmlns":890},[892,89159,89160,89176],{},[895,89161,89162,89164,89166,89168,89170,89172,89174],{},[1692,89163,43053],{},[1651,89165,4503],{},[1692,89167,1694],{},[1651,89169,4503],{},[1692,89171,3689],{},[1651,89173,1738],{},[1692,89175,89071],{},[902,89177,89178],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,89180,89182],{"className":89181},[886],[888,89183,89184],{"xmlns":890},[892,89185,89186,89194],{},[895,89187,89188,89190,89192],{},[898,89189,900],{},[1651,89191,1738],{},[1692,89193,43075],{},[902,89195,89196],{"encoding":904},"U = 16",[883,89198,89200],{"className":89199},[886],[888,89201,89202],{"xmlns":890},[892,89203,89204,89212],{},[895,89205,89206,89208,89210],{},[898,89207,900],{},[1651,89209,1738],{},[1692,89211,73572],{},[902,89213,89214],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,89217,89219],{"className":89218},[886],[888,89220,89221],{"xmlns":890},[892,89222,89223,89243],{},[895,89224,89225,89231,89237],{},[1686,89226,89227,89229],{},[898,89228,1690],{},[1692,89230,1694],{},[1686,89232,89233,89235],{},[898,89234,1690],{},[1692,89236,1703],{},[1686,89238,89239,89241],{},[898,89240,1690],{},[1692,89242,3521],{},[902,89244,89245],{"encoding":904},"Q_1 Q_2 Q_3",[115,89247,89249],{"id":89248},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,89251,89252,89253,1878,89288,3246,89291,43027,89308,11325,89325,89328,89329,89332],{},"Pro funkci užitečnosti ",[883,89254,89256],{"className":89255},[886],[888,89257,89258],{"xmlns":890},[892,89259,89260,89286],{},[895,89261,89262,89264,89266,89268,89270,89276,89278,89284],{},[898,89263,900],{},[1651,89265,1738],{},[898,89267,900],{},[1651,89269,1654],{"stretchy":1653},[1686,89271,89272,89274],{},[898,89273,1690],{},[1692,89275,1694],{},[1651,89277,1661],{"separator":1660},[1686,89279,89280,89282],{},[898,89281,1690],{},[1692,89283,1703],{},[1651,89285,1667],{"stretchy":1653},[902,89287,88669],{"encoding":904},[38,89289,89290],{},"mezní užitečnost",[883,89292,89294],{"className":89293},[886],[888,89295,89296],{"xmlns":890},[892,89297,89298,89306],{},[895,89299,89300],{},[1686,89301,89302,89304],{},[898,89303,1690],{},[1692,89305,1694],{},[902,89307,30215],{"encoding":904},[883,89309,89311],{"className":89310},[886],[888,89312,89313],{"xmlns":890},[892,89314,89315,89323],{},[895,89316,89317],{},[1686,89318,89319,89321],{},[898,89320,1690],{},[1692,89322,1703],{},[902,89324,30234],{"encoding":904},[38,89326,89327],{},"marginal utility",") parciální ",[207,89330,1145],{"className":89331,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,89334,89336],{"className":89335},[886],[888,89337,89338],{"xmlns":890,"display":29279},[892,89339,89340,89439],{},[21967,89341,89342],{"width":29284},[21972,89343,89344,89346,89432,89434],{},[21975,89345],{"width":29289},[21975,89347,89348],{},[895,89349,89350,89352,89358,89360,89368,89370,89388,89390,89392,89394,89400,89402,89410,89412,89430],{},[898,89351,2995],{},[1686,89353,89354,89356],{},[898,89355,900],{},[1692,89357,1694],{},[1651,89359,1738],{},[1902,89361,89362,89364,89366],{},[898,89363,900],{},[1692,89365,1694],{},[1651,89367,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,89369,1738],{},[2446,89371,89372,89378],{},[895,89373,89374,89376],{},[898,89375,11172],{"mathvariant":1910},[898,89377,900],{},[895,89379,89380,89382],{},[898,89381,11172],{"mathvariant":1910},[1686,89383,89384,89386],{},[898,89385,1690],{},[1692,89387,1694],{},[1651,89389,1661],{"separator":1660},[7185,89391],{"width":16582},[898,89393,2995],{},[1686,89395,89396,89398],{},[898,89397,900],{},[1692,89399,1703],{},[1651,89401,1738],{},[1902,89403,89404,89406,89408],{},[898,89405,900],{},[1692,89407,1703],{},[1651,89409,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,89411,1738],{},[2446,89413,89414,89420],{},[895,89415,89416,89418],{},[898,89417,11172],{"mathvariant":1910},[898,89419,900],{},[895,89421,89422,89424],{},[898,89423,11172],{"mathvariant":1910},[1686,89425,89426,89428],{},[898,89427,1690],{},[1692,89429,1703],{},[898,89431,1882],{"mathvariant":1910},[21975,89433],{"width":29289},[21975,89435,89436],{},[1843,89437,89438],{},"(6.2)",[902,89440,89441],{"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}",[724,89443,89444,89445,89479,89480,89510,89511,3246,89514,1882],{},"Pro pevné ",[883,89446,89448],{"className":89447},[886],[888,89449,89450],{"xmlns":890},[892,89451,89452,89476],{},[895,89453,89454,89460,89462,89464,89466,89472,89474],{},[1686,89455,89456,89458],{},[898,89457,1690],{},[1692,89459,1694],{},[1651,89461,1738],{},[898,89463,207],{},[1651,89465,1661],{"separator":1660},[1686,89467,89468,89470],{},[898,89469,1690],{},[1692,89471,1703],{},[1651,89473,1738],{},[898,89475,2268],{},[902,89477,89478],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,89481,89483],{"className":89482},[886],[888,89484,89485],{"xmlns":890},[892,89486,89487,89507],{},[895,89488,89489,89491,89497,89499,89501,89503,89505],{},[898,89490,2995],{},[1686,89492,89493,89495],{},[898,89494,900],{},[1692,89496,1694],{},[1651,89498,1654],{"stretchy":1653},[898,89500,207],{},[1651,89502,1661],{"separator":1660},[898,89504,2268],{},[1651,89506,1667],{"stretchy":1653},[902,89508,89509],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,89512,89513],{},"v bodě (na hladině)",[883,89515,89517],{"className":89516},[886],[888,89518,89519],{"xmlns":890},[892,89520,89521,89533],{},[895,89522,89523,89525,89527,89529,89531],{},[1651,89524,2261],{"stretchy":1653},[898,89526,207],{},[1651,89528,1661],{"separator":1660},[898,89530,2268],{},[1651,89532,2279],{"stretchy":1653},[902,89534,12123],{"encoding":904},[5179,89536,89537],{},[724,89538,89539,89541,89542,89572,89601,89602,3941,89615,3955,89632,89653,89654,4002,89671,4016,89684,89701,89702,89724,89725,89754,89755,7780,89775,89792],{},[883,89540,5465],{}," Intuice — co říká ",[883,89543,89545],{"className":89544},[886],[888,89546,89547],{"xmlns":890},[892,89548,89549,89569],{},[895,89550,89551,89553,89559,89561,89563,89565,89567],{},[898,89552,2995],{},[1686,89554,89555,89557],{},[898,89556,900],{},[1692,89558,1694],{},[1651,89560,1654],{"stretchy":1653},[898,89562,207],{},[1651,89564,1661],{"separator":1660},[898,89566,2268],{},[1651,89568,1667],{"stretchy":1653},[902,89570,89571],{"encoding":904},"MU_1(a,b)",[883,89573,89575],{"className":89574},[886],[888,89576,89577],{"xmlns":890},[892,89578,89579,89599],{},[895,89580,89581,89583,89589,89591,89593,89595,89597],{},[898,89582,2995],{},[1686,89584,89585,89587],{},[898,89586,900],{},[1692,89588,1694],{},[1651,89590,1654],{"stretchy":1653},[898,89592,207],{},[1651,89594,1661],{"separator":1660},[898,89596,2268],{},[1651,89598,1667],{"stretchy":1653},[902,89600,89509],{"encoding":904}," je rychlost změny ",[883,89603,89605],{"className":89604},[886],[888,89606,89607],{"xmlns":890},[892,89608,89609,89613],{},[895,89610,89611],{},[898,89612,900],{},[902,89614,900],{"encoding":904},[883,89616,89618],{"className":89617},[886],[888,89619,89620],{"xmlns":890},[892,89621,89622,89630],{},[895,89623,89624],{},[1686,89625,89626,89628],{},[898,89627,1690],{},[1692,89629,1694],{},[902,89631,30215],{"encoding":904},[883,89633,89635],{"className":89634},[886],[888,89636,89637],{"xmlns":890},[892,89638,89639,89651],{},[895,89640,89641,89643,89645,89647,89649],{},[1651,89642,2261],{"stretchy":1653},[898,89644,207],{},[1651,89646,1661],{"separator":1660},[898,89648,2268],{},[1651,89650,2279],{"stretchy":1653},[902,89652,12123],{"encoding":904},". Přibližně: změní-li se ",[883,89655,89657],{"className":89656},[886],[888,89658,89659],{"xmlns":890},[892,89660,89661,89669],{},[895,89662,89663],{},[1686,89664,89665,89667],{},[898,89666,1690],{},[1692,89668,1694],{},[902,89670,30215],{"encoding":904},[883,89672,89674],{"className":89673},[886],[888,89675,89676],{"xmlns":890},[892,89677,89678,89682],{},[895,89679,89680],{},[898,89681,207],{},[902,89683,207],{"encoding":904},[883,89685,89687],{"className":89686},[886],[888,89688,89689],{"xmlns":890},[892,89690,89691,89699],{},[895,89692,89693,89695,89697],{},[898,89694,207],{},[1651,89696,1839],{},[1692,89698,1694],{},[902,89700,4034],{"encoding":904}," při pevném ",[883,89703,89705],{"className":89704},[886],[888,89706,89707],{"xmlns":890},[892,89708,89709,89721],{},[895,89710,89711,89717,89719],{},[1686,89712,89713,89715],{},[898,89714,1690],{},[1692,89716,1703],{},[1651,89718,1738],{},[898,89720,2268],{},[902,89722,89723],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,89726,89728],{"className":89727},[886],[888,89729,89730],{"xmlns":890},[892,89731,89732,89752],{},[895,89733,89734,89736,89742,89744,89746,89748,89750],{},[898,89735,2995],{},[1686,89737,89738,89740],{},[898,89739,900],{},[1692,89741,1694],{},[1651,89743,1654],{"stretchy":1653},[898,89745,207],{},[1651,89747,1661],{"separator":1660},[898,89749,2268],{},[1651,89751,1667],{"stretchy":1653},[902,89753,89509],{"encoding":904},". Stejně tak ",[883,89756,89758],{"className":89757},[886],[888,89759,89760],{"xmlns":890},[892,89761,89762,89772],{},[895,89763,89764,89766],{},[898,89765,2995],{},[1686,89767,89768,89770],{},[898,89769,900],{},[1692,89771,1703],{},[902,89773,89774],{"encoding":904},"MU_2",[883,89776,89778],{"className":89777},[886],[888,89779,89780],{"xmlns":890},[892,89781,89782,89790],{},[895,89783,89784],{},[1686,89785,89786,89788],{},[898,89787,1690],{},[1692,89789,1703],{},[902,89791,30234],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,89794,81424],{"id":89795},"totální-diferenciál",[724,89797,89798,89799,49553,89815,89845,89846,1793],{},"Přibližnou změnu užitečnosti ",[883,89800,89802],{"className":89801},[886],[888,89803,89804],{"xmlns":890},[892,89805,89806,89812],{},[895,89807,89808,89810],{},[898,89809,4216],{"mathvariant":1910},[898,89811,900],{},[902,89813,89814],{"encoding":904},"\\Delta U",[883,89816,89818],{"className":89817},[886],[888,89819,89820],{"xmlns":890},[892,89821,89822,89842],{},[895,89823,89824,89826,89832,89834,89836],{},[898,89825,3542],{"mathvariant":1910},[1686,89827,89828,89830],{},[898,89829,1690],{},[1692,89831,1694],{},[1651,89833,1661],{"separator":1660},[898,89835,3542],{"mathvariant":1910},[1686,89837,89838,89840],{},[898,89839,1690],{},[1692,89841,1703],{},[902,89843,89844],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,89847,89848],{},"totálního diferenciálu",[883,89850,89852],{"className":89851},[886],[888,89853,89854],{"xmlns":890,"display":29279},[892,89855,89856,89957],{},[21967,89857,89858],{"width":29284},[21972,89859,89860,89862,89950,89952],{},[21975,89861],{"width":29289},[21975,89863,89864],{},[895,89865,89866,89868,89870,89872,89874,89876,89878,89886,89888,89894,89896,89904,89906,89912,89914,89916,89922,89924,89930,89932,89934,89940,89942,89948],{},[898,89867,4216],{"mathvariant":1910},[898,89869,900],{},[1651,89871,4060],{},[898,89873,3542],{"mathvariant":1910},[898,89875,900],{},[1651,89877,1738],{},[1902,89879,89880,89882,89884],{},[898,89881,900],{},[1692,89883,1694],{},[1651,89885,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[898,89887,3542],{"mathvariant":1910},[1686,89889,89890,89892],{},[898,89891,1690],{},[1692,89893,1694],{},[1651,89895,1839],{},[1902,89897,89898,89900,89902],{},[898,89899,900],{},[1692,89901,1703],{},[1651,89903,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[898,89905,3542],{"mathvariant":1910},[1686,89907,89908,89910],{},[898,89909,1690],{},[1692,89911,1703],{},[1651,89913,1738],{},[898,89915,2995],{},[1686,89917,89918,89920],{},[898,89919,900],{},[1692,89921,1694],{},[898,89923,3542],{"mathvariant":1910},[1686,89925,89926,89928],{},[898,89927,1690],{},[1692,89929,1694],{},[1651,89931,1839],{},[898,89933,2995],{},[1686,89935,89936,89938],{},[898,89937,900],{},[1692,89939,1703],{},[898,89941,3542],{"mathvariant":1910},[1686,89943,89944,89946],{},[898,89945,1690],{},[1692,89947,1703],{},[898,89949,1882],{"mathvariant":1910},[21975,89951],{"width":29289},[21975,89953,89954],{},[1843,89955,89956],{},"(6.3)",[902,89958,89959],{"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}",[724,89961,76682,89962,1882],{},[883,89963,89965],{"className":89964},[886],[888,89966,89967],{"xmlns":890},[892,89968,89969,90039],{},[895,89970,89971,89973,89975,89977,89979,89981,89987,89989,89991,89997,89999,90005,90007,90009,90015,90017,90019,90021,90023,90029,90031,90037],{},[898,89972,4216],{"mathvariant":1910},[898,89974,900],{},[1651,89976,1738],{},[898,89978,900],{},[1651,89980,1654],{"stretchy":1653},[1686,89982,89983,89985],{},[898,89984,1690],{},[1692,89986,1694],{},[1651,89988,1839],{},[898,89990,3542],{"mathvariant":1910},[1686,89992,89993,89995],{},[898,89994,1690],{},[1692,89996,1694],{},[1651,89998,1661],{"separator":1660},[1686,90000,90001,90003],{},[898,90002,1690],{},[1692,90004,1703],{},[1651,90006,1839],{},[898,90008,3542],{"mathvariant":1910},[1686,90010,90011,90013],{},[898,90012,1690],{},[1692,90014,1703],{},[1651,90016,1667],{"stretchy":1653},[1651,90018,2181],{},[898,90020,900],{},[1651,90022,1654],{"stretchy":1653},[1686,90024,90025,90027],{},[898,90026,1690],{},[1692,90028,1694],{},[1651,90030,1661],{"separator":1660},[1686,90032,90033,90035],{},[898,90034,1690],{},[1692,90036,1703],{},[1651,90038,1667],{"stretchy":1653},[902,90040,90041],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,90043,90045],{"id":90044},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,90047,90048,90049,90052,90053,90056],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,90050,90051],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,90054,90055],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,90058,90059,90062,90063,43027,90089,90115,90116,1343,90148,90180,90181,5197,90235,90289],{},[38,90060,90061],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,90064,90066],{"className":90065},[886],[888,90067,90068],{"xmlns":890},[892,90069,90070,90086],{},[895,90071,90072,90078,90080],{},[1686,90073,90074,90076],{},[898,90075,1690],{},[1692,90077,1703],{},[1651,90079,1738],{},[1686,90081,90082,90084],{},[898,90083,207],{},[1692,90085,1741],{},[902,90087,90088],{"encoding":904},"Q_2 = a_0",[883,90090,90092],{"className":90091},[886],[888,90093,90094],{"xmlns":890},[892,90095,90096,90112],{},[895,90097,90098,90104,90106],{},[1686,90099,90100,90102],{},[898,90101,1690],{},[1692,90103,1694],{},[1651,90105,1738],{},[1686,90107,90108,90110],{},[898,90109,2268],{},[1692,90111,1741],{},[902,90113,90114],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,90117,90119],{"className":90118},[886],[888,90120,90121],{"xmlns":890},[892,90122,90123,90145],{},[895,90124,90125,90127,90129,90135,90137,90143],{},[898,90126,900],{},[1651,90128,1654],{"stretchy":1653},[1686,90130,90131,90133],{},[898,90132,1690],{},[1692,90134,1694],{},[1651,90136,1661],{"separator":1660},[1686,90138,90139,90141],{},[898,90140,207],{},[1692,90142,1741],{},[1651,90144,1667],{"stretchy":1653},[902,90146,90147],{"encoding":904},"U(Q_1, a_0)",[883,90149,90151],{"className":90150},[886],[888,90152,90153],{"xmlns":890},[892,90154,90155,90177],{},[895,90156,90157,90159,90161,90167,90169,90175],{},[898,90158,900],{},[1651,90160,1654],{"stretchy":1653},[1686,90162,90163,90165],{},[898,90164,2268],{},[1692,90166,1741],{},[1651,90168,1661],{"separator":1660},[1686,90170,90171,90173],{},[898,90172,1690],{},[1692,90174,1703],{},[1651,90176,1667],{"stretchy":1653},[902,90178,90179],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,90182,90184],{"className":90183},[886],[888,90185,90186],{"xmlns":890},[892,90187,90188,90232],{},[895,90189,90190,90228,90230],{},[2938,90191,90192],{"scriptlevel":1741,"displaystyle":1660},[2446,90193,90194,90218],{},[895,90195,90196,90198,90200,90202,90208,90210,90216],{},[898,90197,3542],{"mathvariant":1910},[898,90199,900],{},[1651,90201,1654],{"stretchy":1653},[1686,90203,90204,90206],{},[898,90205,1690],{},[1692,90207,1694],{},[1651,90209,1661],{"separator":1660},[1686,90211,90212,90214],{},[898,90213,207],{},[1692,90215,1741],{},[1651,90217,1667],{"stretchy":1653},[895,90219,90220,90222],{},[898,90221,3542],{"mathvariant":1910},[1686,90223,90224,90226],{},[898,90225,1690],{},[1692,90227,1694],{},[1651,90229,2390],{},[1692,90231,1741],{},[902,90233,90234],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,90236,90238],{"className":90237},[886],[888,90239,90240],{"xmlns":890},[892,90241,90242,90286],{},[895,90243,90244,90282,90284],{},[2938,90245,90246],{"scriptlevel":1741,"displaystyle":1660},[2446,90247,90248,90272],{},[895,90249,90250,90252,90254,90256,90262,90264,90270],{},[898,90251,3542],{"mathvariant":1910},[898,90253,900],{},[1651,90255,1654],{"stretchy":1653},[1686,90257,90258,90260],{},[898,90259,2268],{},[1692,90261,1741],{},[1651,90263,1661],{"separator":1660},[1686,90265,90266,90268],{},[898,90267,1690],{},[1692,90269,1703],{},[1651,90271,1667],{"stretchy":1653},[895,90273,90274,90276],{},[898,90275,3542],{"mathvariant":1910},[1686,90277,90278,90280],{},[898,90279,1690],{},[1692,90281,1703],{},[1651,90283,2390],{},[1692,90285,1741],{},[902,90287,90288],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,90291,90293],{"className":90292},[886],[888,90294,90295],{"xmlns":890,"display":29279},[892,90296,90297,90342],{},[21967,90298,90299],{"width":29284},[21972,90300,90301,90303,90335,90337],{},[21975,90302],{"width":29289},[21975,90304,90305],{},[895,90306,90307,90315,90317,90319,90321,90323,90331,90333],{},[1902,90308,90309,90311,90313],{},[898,90310,900],{},[1692,90312,1694],{},[1651,90314,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,90316,2390],{},[1692,90318,1741],{},[1651,90320,1661],{"separator":1660},[7185,90322],{"width":16582},[1902,90324,90325,90327,90329],{},[898,90326,900],{},[1692,90328,1703],{},[1651,90330,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,90332,2390],{},[1692,90334,13758],{},[21975,90336],{"width":29289},[21975,90338,90339],{},[1843,90340,90341],{},"(6.4)",[902,90343,90344],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,90346,90347,90348,90350],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,90349,53890],{}," — užitečnost roste s množstvím každého zboží.",[724,90352,90353,90356,90357,90387,90388,1793],{},[38,90354,90355],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,90358,90360],{"className":90359},[886],[888,90361,90362],{"xmlns":890},[892,90363,90364,90384],{},[895,90365,90366,90374,90376],{},[1902,90367,90368,90370,90372],{},[898,90369,900],{},[1692,90371,1694],{},[1651,90373,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,90375,1661],{"separator":1660},[1902,90377,90378,90380,90382],{},[898,90379,900],{},[1692,90381,1703],{},[1651,90383,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,90385,90386],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,90389,90390],{},"záporné",[883,90392,90394],{"className":90393},[886],[888,90395,90396],{"xmlns":890,"display":29279},[892,90397,90398,90451],{},[21967,90399,90400],{"width":29284},[21972,90401,90402,90404,90444,90446],{},[21975,90403],{"width":29289},[21975,90405,90406],{},[895,90407,90408,90420,90422,90424,90426,90428,90440,90442],{},[1902,90409,90410,90412,90414],{},[898,90411,900],{},[1692,90413,4231],{},[895,90415,90416,90418],{},[1651,90417,1912],{"mathvariant":1910},[1651,90419,1912],{"mathvariant":1910},[1651,90421,2319],{},[1692,90423,1741],{},[1651,90425,1661],{"separator":1660},[7185,90427],{"width":16582},[1902,90429,90430,90432,90434],{},[898,90431,900],{},[1692,90433,33759],{},[895,90435,90436,90438],{},[1651,90437,1912],{"mathvariant":1910},[1651,90439,1912],{"mathvariant":1910},[1651,90441,2319],{},[1692,90443,13758],{},[21975,90445],{"width":29289},[21975,90447,90448],{},[1843,90449,90450],{},"(6.5)",[902,90452,90453],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,90455,90456,90457,90460,90461,1882],{},"Podmínka (6.5) je známa jako ",[38,90458,90459],{},"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 ",[207,90462,90464],{"className":90463,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,90466,90467,90468,5197,90500,90532,90533,5197,90559,90585,90586,90614,90615,5197,90617,90619,90620,90655],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,90469,90471],{"className":90470},[886],[888,90472,90473],{"xmlns":890},[892,90474,90475,90497],{},[895,90476,90477,90479,90481,90487,90489,90495],{},[898,90478,900],{},[1651,90480,1654],{"stretchy":1653},[1686,90482,90483,90485],{},[898,90484,1690],{},[1692,90486,1694],{},[1651,90488,1661],{"separator":1660},[1686,90490,90491,90493],{},[898,90492,2268],{},[1692,90494,1741],{},[1651,90496,1667],{"stretchy":1653},[902,90498,90499],{"encoding":904},"U(Q_1, b_0)",[883,90501,90503],{"className":90502},[886],[888,90504,90505],{"xmlns":890},[892,90506,90507,90529],{},[895,90508,90509,90511,90513,90519,90521,90527],{},[898,90510,900],{},[1651,90512,1654],{"stretchy":1653},[1686,90514,90515,90517],{},[898,90516,207],{},[1692,90518,1741],{},[1651,90520,1661],{"separator":1660},[1686,90522,90523,90525],{},[898,90524,1690],{},[1692,90526,1703],{},[1651,90528,1667],{"stretchy":1653},[902,90530,90531],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,90534,90536],{"className":90535},[886],[888,90537,90538],{"xmlns":890},[892,90539,90540,90556],{},[895,90541,90542,90544,90546,90548,90554],{},[1651,90543,1654],{"stretchy":1653},[898,90545,900],{},[1651,90547,1661],{"separator":1660},[1686,90549,90550,90552],{},[898,90551,1690],{},[1692,90553,1694],{},[1651,90555,1667],{"stretchy":1653},[902,90557,90558],{"encoding":904},"(U, Q_1)",[883,90560,90562],{"className":90561},[886],[888,90563,90564],{"xmlns":890},[892,90565,90566,90582],{},[895,90567,90568,90570,90572,90574,90580],{},[1651,90569,1654],{"stretchy":1653},[898,90571,900],{},[1651,90573,1661],{"separator":1660},[1686,90575,90576,90578],{},[898,90577,1690],{},[1692,90579,1703],{},[1651,90581,1667],{"stretchy":1653},[902,90583,90584],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,90587,90589],{"className":90588},[886],[888,90590,90591],{"xmlns":890},[892,90592,90593,90611],{},[895,90594,90595,90597,90599,90601,90603,90605,90607,90609],{},[898,90596,900],{},[1651,90598,1654],{"stretchy":1653},[1692,90600,1741],{},[1651,90602,1661],{"separator":1660},[1692,90604,1741],{},[1651,90606,1667],{"stretchy":1653},[1651,90608,1738],{},[1692,90610,1741],{},[902,90612,90613],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,90616,14955],{},[38,90618,39701],{},". Typický tvar grafu ",[883,90621,90623],{"className":90622},[886],[888,90624,90625],{"xmlns":890},[892,90626,90627,90653],{},[895,90628,90629,90631,90633,90635,90637,90643,90645,90651],{},[898,90630,900],{},[1651,90632,1738],{},[898,90634,900],{},[1651,90636,1654],{"stretchy":1653},[1686,90638,90639,90641],{},[898,90640,1690],{},[1692,90642,1694],{},[1651,90644,1661],{"separator":1660},[1686,90646,90647,90649],{},[898,90648,1690],{},[1692,90650,1703],{},[1651,90652,1667],{"stretchy":1653},[902,90654,88669],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,90657,90658],{},[614,90659,90660,90661,89701,90689,90710,90711,89701,90739,90761],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,90662,90664],{"className":90663},[886],[888,90665,90666],{"xmlns":890},[892,90667,90668,90686],{},[895,90669,90670,90672,90674,90680,90682,90684],{},[898,90671,900],{},[1651,90673,1654],{"stretchy":1653},[1686,90675,90676,90678],{},[898,90677,1690],{},[1692,90679,1694],{},[1651,90681,1661],{"separator":1660},[898,90683,2268],{},[1651,90685,1667],{"stretchy":1653},[902,90687,90688],{"encoding":904},"U(Q_1, b)",[883,90690,90692],{"className":90691},[886],[888,90693,90694],{"xmlns":890},[892,90695,90696,90708],{},[895,90697,90698,90704,90706],{},[1686,90699,90700,90702],{},[898,90701,1690],{},[1692,90703,1703],{},[1651,90705,1738],{},[898,90707,2268],{},[902,90709,89723],{"encoding":904}," (vlevo) a ",[883,90712,90714],{"className":90713},[886],[888,90715,90716],{"xmlns":890},[892,90717,90718,90736],{},[895,90719,90720,90722,90724,90726,90728,90734],{},[898,90721,900],{},[1651,90723,1654],{"stretchy":1653},[898,90725,207],{},[1651,90727,1661],{"separator":1660},[1686,90729,90730,90732],{},[898,90731,1690],{},[1692,90733,1703],{},[1651,90735,1667],{"stretchy":1653},[902,90737,90738],{"encoding":904},"U(a, Q_2)",[883,90740,90742],{"className":90741},[886],[888,90743,90744],{"xmlns":890},[892,90745,90746,90758],{},[895,90747,90748,90754,90756],{},[1686,90749,90750,90752],{},[898,90751,1690],{},[1692,90753,1694],{},[1651,90755,1738],{},[898,90757,207],{},[902,90759,90760],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,90763,90764],{},[614,90765,90766,90767,90802,90803,90833,90834,5197,90857,90879,90880,1882],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,90768,90770],{"className":90769},[886],[888,90771,90772],{"xmlns":890},[892,90773,90774,90800],{},[895,90775,90776,90778,90780,90782,90784,90790,90792,90798],{},[898,90777,900],{},[1651,90779,1738],{},[898,90781,900],{},[1651,90783,1654],{"stretchy":1653},[1686,90785,90786,90788],{},[898,90787,1690],{},[1692,90789,1694],{},[1651,90791,1661],{"separator":1660},[1686,90793,90794,90796],{},[898,90795,1690],{},[1692,90797,1703],{},[1651,90799,1667],{"stretchy":1653},[902,90801,88669],{"encoding":904}," nad rovinou ",[883,90804,90806],{"className":90805},[886],[888,90807,90808],{"xmlns":890},[892,90809,90810,90830],{},[895,90811,90812,90814,90820,90822,90828],{},[1651,90813,1654],{"stretchy":1653},[1686,90815,90816,90818],{},[898,90817,1690],{},[1692,90819,1694],{},[1651,90821,1661],{"separator":1660},[1686,90823,90824,90826],{},[898,90825,1690],{},[1692,90827,1703],{},[1651,90829,1667],{"stretchy":1653},[902,90831,90832],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,90835,90837],{"className":90836},[886],[888,90838,90839],{"xmlns":890},[892,90840,90841,90854],{},[895,90842,90843,90849,90851],{},[1686,90844,90845,90847],{},[898,90846,1690],{},[1692,90848,1694],{},[1651,90850,1738],{},[1843,90852,90853],{},"const",[902,90855,90856],{"encoding":904},"Q_1 = \\text{const}",[883,90858,90860],{"className":90859},[886],[888,90861,90862],{"xmlns":890},[892,90863,90864,90876],{},[895,90865,90866,90872,90874],{},[1686,90867,90868,90870],{},[898,90869,1690],{},[1692,90871,1703],{},[1651,90873,1738],{},[1843,90875,90853],{},[902,90877,90878],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,90881,90883],{"className":90882},[886],[888,90884,90885],{"xmlns":890},[892,90886,90887,90913],{},[895,90888,90889,90891,90893,90899,90901,90907,90909,90911],{},[898,90890,900],{},[1651,90892,1654],{"stretchy":1653},[1686,90894,90895,90897],{},[898,90896,1690],{},[1692,90898,1694],{},[1651,90900,1661],{"separator":1660},[1686,90902,90903,90905],{},[898,90904,1690],{},[1692,90906,1703],{},[1651,90908,1667],{"stretchy":1653},[1651,90910,1738],{},[898,90912,3490],{},[902,90914,11071],{"encoding":904},[198,90916,90918,90919],{"id":90917},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,90920,90922],{"className":90921},[886],[888,90923,90924],{"xmlns":890},[892,90925,90926,90960],{},[895,90927,90928,90930,90932,90946],{},[898,90929,900],{},[1651,90931,1738],{},[1902,90933,90934,90936,90938],{},[898,90935,1690],{},[1692,90937,1694],{},[895,90939,90940,90942,90944],{},[1692,90941,1694],{},[898,90943,5981],{"mathvariant":1910},[1692,90945,1703],{},[1902,90947,90948,90950,90952],{},[898,90949,1690],{},[1692,90951,1703],{},[895,90953,90954,90956,90958],{},[1692,90955,1694],{},[898,90957,5981],{"mathvariant":1910},[1692,90959,3521],{},[902,90961,90962],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,90964,90965],{},[38,90966,90967],{},"Ověření (6.4) a (6.5).",[883,90969,90971],{"className":90970},[886],[888,90972,90973],{"xmlns":890,"display":29279},[892,90974,90975,91079],{},[895,90976,90977,90985,90987,90995,91011,91025,91027,91029,91037,91039,91047,91061,91077],{},[1902,90978,90979,90981,90983],{},[898,90980,900],{},[1692,90982,1694],{},[1651,90984,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,90986,1738],{},[2938,90988,90989],{"scriptlevel":1741,"displaystyle":1653},[2446,90990,90991,90993],{},[1692,90992,1694],{},[1692,90994,1703],{},[1902,90996,90997,90999,91001],{},[898,90998,1690],{},[1692,91000,1694],{},[895,91002,91003,91005,91007,91009],{},[1651,91004,2181],{},[1692,91006,1694],{},[898,91008,5981],{"mathvariant":1910},[1692,91010,1703],{},[1902,91012,91013,91015,91017],{},[898,91014,1690],{},[1692,91016,1703],{},[895,91018,91019,91021,91023],{},[1692,91020,1694],{},[898,91022,5981],{"mathvariant":1910},[1692,91024,3521],{},[1651,91026,1661],{"separator":1660},[7185,91028],{"width":16582},[1902,91030,91031,91033,91035],{},[898,91032,900],{},[1692,91034,1703],{},[1651,91036,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,91038,1738],{},[2938,91040,91041],{"scriptlevel":1741,"displaystyle":1653},[2446,91042,91043,91045],{},[1692,91044,1694],{},[1692,91046,3521],{},[1902,91048,91049,91051,91053],{},[898,91050,1690],{},[1692,91052,1694],{},[895,91054,91055,91057,91059],{},[1692,91056,1694],{},[898,91058,5981],{"mathvariant":1910},[1692,91060,1703],{},[1902,91062,91063,91065,91067],{},[898,91064,1690],{},[1692,91066,1703],{},[895,91068,91069,91071,91073,91075],{},[1651,91070,2181],{},[1692,91072,1703],{},[898,91074,5981],{"mathvariant":1910},[1692,91076,3521],{},[1651,91078,1661],{"separator":1660},[902,91080,91081],{"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},",[724,91083,91084,91085,91119],{},"zřejmě ",[883,91086,91088],{"className":91087},[886],[888,91089,91090],{"xmlns":890},[892,91091,91092,91116],{},[895,91093,91094,91102,91104,91112,91114],{},[1902,91095,91096,91098,91100],{},[898,91097,900],{},[1692,91099,1694],{},[1651,91101,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,91103,1661],{"separator":1660},[1902,91105,91106,91108,91110],{},[898,91107,900],{},[1692,91109,1703],{},[1651,91111,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,91113,2390],{},[1692,91115,1741],{},[902,91117,91118],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,91121,91123],{"className":91122},[886],[888,91124,91125],{"xmlns":890,"display":29279},[892,91126,91127,91243],{},[895,91128,91129,91141,91143,91145,91153,91169,91183,91185,91187,91199,91201,91203,91211,91225,91241],{},[1902,91130,91131,91133,91135],{},[898,91132,900],{},[1692,91134,4231],{},[895,91136,91137,91139],{},[1651,91138,1912],{"mathvariant":1910},[1651,91140,1912],{"mathvariant":1910},[1651,91142,1738],{},[1651,91144,2181],{},[2938,91146,91147],{"scriptlevel":1741,"displaystyle":1653},[2446,91148,91149,91151],{},[1692,91150,1694],{},[1692,91152,3689],{},[1902,91154,91155,91157,91159],{},[898,91156,1690],{},[1692,91158,1694],{},[895,91160,91161,91163,91165,91167],{},[1651,91162,2181],{},[1692,91164,3521],{},[898,91166,5981],{"mathvariant":1910},[1692,91168,1703],{},[1902,91170,91171,91173,91175],{},[898,91172,1690],{},[1692,91174,1703],{},[895,91176,91177,91179,91181],{},[1692,91178,1694],{},[898,91180,5981],{"mathvariant":1910},[1692,91182,3521],{},[1651,91184,1661],{"separator":1660},[7185,91186],{"width":16582},[1902,91188,91189,91191,91193],{},[898,91190,900],{},[1692,91192,33759],{},[895,91194,91195,91197],{},[1651,91196,1912],{"mathvariant":1910},[1651,91198,1912],{"mathvariant":1910},[1651,91200,1738],{},[1651,91202,2181],{},[2938,91204,91205],{"scriptlevel":1741,"displaystyle":1653},[2446,91206,91207,91209],{},[1692,91208,1703],{},[1692,91210,5309],{},[1902,91212,91213,91215,91217],{},[898,91214,1690],{},[1692,91216,1694],{},[895,91218,91219,91221,91223],{},[1692,91220,1694],{},[898,91222,5981],{"mathvariant":1910},[1692,91224,1703],{},[1902,91226,91227,91229,91231],{},[898,91228,1690],{},[1692,91230,1703],{},[895,91232,91233,91235,91237,91239],{},[1651,91234,2181],{},[1692,91236,3574],{},[898,91238,5981],{"mathvariant":1910},[1692,91240,3521],{},[1651,91242,1661],{"separator":1660},[902,91244,91245],{"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},",[724,91247,91248,91249,91291],{},"opět ",[883,91250,91252],{"className":91251},[886],[888,91253,91254],{"xmlns":890},[892,91255,91256,91288],{},[895,91257,91258,91270,91272,91284,91286],{},[1902,91259,91260,91262,91264],{},[898,91261,900],{},[1692,91263,4231],{},[895,91265,91266,91268],{},[1651,91267,1912],{"mathvariant":1910},[1651,91269,1912],{"mathvariant":1910},[1651,91271,1661],{"separator":1660},[1902,91273,91274,91276,91278],{},[898,91275,900],{},[1692,91277,33759],{},[895,91279,91280,91282],{},[1651,91281,1912],{"mathvariant":1910},[1651,91283,1912],{"mathvariant":1910},[1651,91285,2319],{},[1692,91287,1741],{},[902,91289,91290],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,91293,91294],{},[38,91295,91296,91297,1882],{},"(a) Mezní užitečnosti v bodě ",[883,91298,91300],{"className":91299},[886],[888,91301,91302],{"xmlns":890},[892,91303,91304,91316],{},[895,91305,91306,91308,91310,91312,91314],{},[1651,91307,2261],{"stretchy":1653},[1692,91309,4416],{},[1651,91311,1661],{"separator":1660},[1692,91313,9683],{},[1651,91315,2279],{"stretchy":1653},[902,91317,91318],{"encoding":904},"[100, 200]",[883,91320,91322],{"className":91321},[886],[888,91323,91324],{"xmlns":890,"display":29279},[892,91325,91326,91393],{},[895,91327,91328,91330,91336,91338,91340,91342,91344,91346,91348,91356,91358,91372,91374,91386,91388,91391],{},[898,91329,2995],{},[1686,91331,91332,91334],{},[898,91333,900],{},[1692,91335,1694],{},[1651,91337,1654],{"stretchy":1653},[1692,91339,4416],{},[1651,91341,1661],{"separator":1660},[1692,91343,9683],{},[1651,91345,1667],{"stretchy":1653},[1651,91347,1738],{},[2938,91349,91350],{"scriptlevel":1741,"displaystyle":1653},[2446,91351,91352,91354],{},[1692,91353,1694],{},[1692,91355,1703],{},[1651,91357,4503],{},[2115,91359,91360,91362],{},[1692,91361,4416],{},[895,91363,91364,91366,91368,91370],{},[1651,91365,2181],{},[1692,91367,1694],{},[898,91369,5981],{"mathvariant":1910},[1692,91371,1703],{},[1651,91373,4503],{},[2115,91375,91376,91378],{},[1692,91377,9683],{},[895,91379,91380,91382,91384],{},[1692,91381,1694],{},[898,91383,5981],{"mathvariant":1910},[1692,91385,3521],{},[1651,91387,7207],{},[1692,91389,91390],{},"0,4204",[1651,91392,1661],{"separator":1660},[902,91394,91395],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,91397,91399],{"className":91398},[886],[888,91400,91401],{"xmlns":890,"display":29279},[892,91402,91403,91468],{},[895,91404,91405,91407,91413,91415,91417,91419,91421,91423,91425,91433,91435,91447,91449,91463,91465],{},[898,91406,2995],{},[1686,91408,91409,91411],{},[898,91410,900],{},[1692,91412,1703],{},[1651,91414,1654],{"stretchy":1653},[1692,91416,4416],{},[1651,91418,1661],{"separator":1660},[1692,91420,9683],{},[1651,91422,1667],{"stretchy":1653},[1651,91424,1738],{},[2938,91426,91427],{"scriptlevel":1741,"displaystyle":1653},[2446,91428,91429,91431],{},[1692,91430,1694],{},[1692,91432,3521],{},[1651,91434,4503],{},[2115,91436,91437,91439],{},[1692,91438,4416],{},[895,91440,91441,91443,91445],{},[1692,91442,1694],{},[898,91444,5981],{"mathvariant":1910},[1692,91446,1703],{},[1651,91448,4503],{},[2115,91450,91451,91453],{},[1692,91452,9683],{},[895,91454,91455,91457,91459,91461],{},[1651,91456,2181],{},[1692,91458,1703],{},[898,91460,5981],{"mathvariant":1910},[1692,91462,3521],{},[1651,91464,7207],{},[1692,91466,91467],{},"0,63067.",[902,91469,91470],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,91472,91473,3246,91475,91510,91511,91532,91533,91550],{},[614,91474,10519],{},[883,91476,91478],{"className":91477},[886],[888,91479,91480],{"xmlns":890},[892,91481,91482,91507],{},[895,91483,91484,91486,91492,91494,91496,91498,91500,91502,91504],{},[898,91485,2995],{},[1686,91487,91488,91490],{},[898,91489,900],{},[1692,91491,1703],{},[1651,91493,1654],{"stretchy":1653},[1692,91495,4416],{},[1651,91497,1661],{"separator":1660},[1692,91499,9683],{},[1651,91501,1667],{"stretchy":1653},[1651,91503,7207],{},[1692,91505,91506],{},"0,63067",[902,91508,91509],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,91512,91514],{"className":91513},[886],[888,91515,91516],{"xmlns":890},[892,91517,91518,91530],{},[895,91519,91520,91522,91524,91526,91528],{},[1651,91521,2261],{"stretchy":1653},[1692,91523,4416],{},[1651,91525,1661],{"separator":1660},[1692,91527,9683],{},[1651,91529,2279],{"stretchy":1653},[902,91531,91318],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,91534,91536],{"className":91535},[886],[888,91537,91538],{"xmlns":890},[892,91539,91540,91548],{},[895,91541,91542],{},[1686,91543,91544,91546],{},[898,91545,1690],{},[1692,91547,1703],{},[902,91549,30234],{"encoding":904}," přibližně o 0,63067.",[724,91552,91553,91572,91573,40397,91594,91611,91612,91638,91639,91656,91657,4477],{},[38,91554,91555,91556,91571],{},"(b) Odhad změny ",[883,91557,91559],{"className":91558},[886],[888,91560,91561],{"xmlns":890},[892,91562,91563,91569],{},[895,91564,91565,91567],{},[898,91566,4216],{"mathvariant":1910},[898,91568,900],{},[902,91570,89814],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,91574,91576],{"className":91575},[886],[888,91577,91578],{"xmlns":890},[892,91579,91580,91592],{},[895,91581,91582,91584,91586,91588,91590],{},[1651,91583,2261],{"stretchy":1653},[1692,91585,4416],{},[1651,91587,1661],{"separator":1660},[1692,91589,9683],{},[1651,91591,2279],{"stretchy":1653},[902,91593,91318],{"encoding":904},[883,91595,91597],{"className":91596},[886],[888,91598,91599],{"xmlns":890},[892,91600,91601,91609],{},[895,91602,91603],{},[1686,91604,91605,91607],{},[898,91606,1690],{},[1692,91608,1694],{},[902,91610,30215],{"encoding":904}," na 98 (tj. ",[883,91613,91615],{"className":91614},[886],[888,91616,91617],{"xmlns":890},[892,91618,91619,91635],{},[895,91620,91621,91623,91629,91631,91633],{},[898,91622,3542],{"mathvariant":1910},[1686,91624,91625,91627],{},[898,91626,1690],{},[1692,91628,1694],{},[1651,91630,1738],{},[1651,91632,2181],{},[1692,91634,1703],{},[902,91636,91637],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,91640,91642],{"className":91641},[886],[888,91643,91644],{"xmlns":890},[892,91645,91646,91654],{},[895,91647,91648],{},[1686,91649,91650,91652],{},[898,91651,1690],{},[1692,91653,1703],{},[902,91655,30234],{"encoding":904}," o 3 (tj. ",[883,91658,91660],{"className":91659},[886],[888,91661,91662],{"xmlns":890},[892,91663,91664,91678],{},[895,91665,91666,91668,91674,91676],{},[898,91667,3542],{"mathvariant":1910},[1686,91669,91670,91672],{},[898,91671,1690],{},[1692,91673,1703],{},[1651,91675,1738],{},[1692,91677,3521],{},[902,91679,91680],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,91682,91684],{"className":91683},[886],[888,91685,91686],{"xmlns":890,"display":29279},[892,91687,91688,91739],{},[895,91689,91690,91692,91694,91696,91698,91700,91702,91704,91706,91708,91710,91712,91714,91716,91718,91720,91722,91724,91726,91729,91731,91734,91736],{},[898,91691,4216],{"mathvariant":1910},[898,91693,900],{},[1651,91695,4060],{},[898,91697,3542],{"mathvariant":1910},[898,91699,900],{},[1651,91701,1738],{},[1692,91703,91390],{},[1651,91705,4503],{},[1651,91707,1654],{"stretchy":1653},[1651,91709,2181],{},[1692,91711,1703],{},[1651,91713,1667],{"stretchy":1653},[1651,91715,1839],{},[1692,91717,91506],{},[1651,91719,4503],{},[1692,91721,3521],{},[1651,91723,1738],{},[1651,91725,2181],{},[1692,91727,91728],{},"0,8408",[1651,91730,1839],{},[1692,91732,91733],{},"1,89201",[1651,91735,7207],{},[1692,91737,91738],{},"1,05.",[902,91740,91741],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,91743,91744,91745,91748,91749,91800,91801,1882],{},"Užitečnost se tedy zvýší přibližně o ",[38,91746,91747],{},"1,05",". Skutečná změna je ",[883,91750,91752],{"className":91751},[886],[888,91753,91754],{"xmlns":890},[892,91755,91756,91797],{},[895,91757,91758,91760,91762,91764,91766,91768,91771,91773,91776,91778,91780,91782,91784,91786,91788,91790,91792,91794],{},[898,91759,4216],{"mathvariant":1910},[898,91761,900],{},[1651,91763,1738],{},[898,91765,900],{},[1651,91767,1654],{"stretchy":1653},[1692,91769,91770],{},"98",[1651,91772,1661],{"separator":1660},[1692,91774,91775],{},"203",[1651,91777,1667],{"stretchy":1653},[1651,91779,2181],{},[898,91781,900],{},[1651,91783,1654],{"stretchy":1653},[1692,91785,4416],{},[1651,91787,1661],{"separator":1660},[1692,91789,9683],{},[1651,91791,1667],{"stretchy":1653},[1651,91793,7207],{},[1692,91795,91796],{},"1,031",[902,91798,91799],{"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 ",[883,91802,91804],{"className":91803},[886],[888,91805,91806],{"xmlns":890},[892,91807,91808,91828],{},[895,91809,91810,91812,91818,91820,91822],{},[898,91811,3542],{"mathvariant":1910},[1686,91813,91814,91816],{},[898,91815,1690],{},[1692,91817,1694],{},[1651,91819,1661],{"separator":1660},[898,91821,3542],{"mathvariant":1910},[1686,91823,91824,91826],{},[898,91825,1690],{},[1692,91827,1703],{},[902,91829,89844],{"encoding":904},[115,91831,91833],{"id":91832},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,91835,91836],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,91838,91840],{"className":91839},[886],[888,91841,91842],{"xmlns":890,"display":29279},[892,91843,91844,91903],{},[21967,91845,91846],{"width":29284},[21972,91847,91848,91850,91896,91898],{},[21975,91849],{"width":29289},[21975,91851,91852],{},[895,91853,91854,91856,91858,91864,91866,91872,91874,91876,91884,91886,91894],{},[898,91855,900],{},[1651,91857,1654],{"stretchy":1653},[1686,91859,91860,91862],{},[898,91861,1690],{},[1692,91863,1694],{},[1651,91865,1661],{"separator":1660},[1686,91867,91868,91870],{},[898,91869,1690],{},[1692,91871,1703],{},[1651,91873,1667],{"stretchy":1653},[1651,91875,1738],{},[1902,91877,91878,91880,91882],{},[898,91879,1690],{},[1692,91881,1694],{},[898,91883,207],{},[1651,91885,4503],{},[1902,91887,91888,91890,91892],{},[898,91889,1690],{},[1692,91891,1703],{},[898,91893,2268],{},[1651,91895,1661],{"separator":1660},[21975,91897],{"width":29289},[21975,91899,91900],{},[1843,91901,91902],{},"(6.6)",[902,91904,91905],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,91907,1863,91908,91926,91927,91929,91930,91934,91935,91965,91966,91988],{},[883,91909,91911],{"className":91910},[886],[888,91912,91913],{"xmlns":890},[892,91914,91915,91923],{},[895,91916,91917,91919,91921],{},[898,91918,207],{},[1651,91920,1661],{"separator":1660},[898,91922,2268],{},[902,91924,91925],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,91928,75912],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,91931,91933],{"className":91932,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,91936,91938],{"className":91937},[886],[888,91939,91940],{"xmlns":890},[892,91941,91942,91962],{},[895,91943,91944,91946,91948,91950,91952,91954,91956,91958,91960],{},[898,91945,207],{},[1651,91947,1661],{"separator":1660},[898,91949,2268],{},[1651,91951,7813],{},[1651,91953,1654],{"stretchy":1653},[1692,91955,1741],{},[1651,91957,1661],{"separator":1660},[1692,91959,1694],{},[1651,91961,1667],{"stretchy":1653},[902,91963,91964],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,91967,91969],{"className":91968},[886],[888,91970,91971],{"xmlns":890},[892,91972,91973,91985],{},[895,91974,91975,91977,91979,91981,91983],{},[898,91976,2268],{},[1651,91978,1738],{},[1692,91980,1694],{},[1651,91982,2181],{},[898,91984,207],{},[902,91986,91987],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,91990,91991],{},[1756,91992],{"alt":91993,"className":91994,"src":91995},"imek-cobb-douglas-3d-plus-ic",[210,1760],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,91997,91999],{"className":91998},[886],[888,92000,92001],{"xmlns":890,"display":29279},[892,92002,92003,92053],{},[895,92004,92005,92007,92009,92015,92017,92023,92025,92027,92035,92037,92051],{},[898,92006,900],{},[1651,92008,1654],{"stretchy":1653},[1686,92010,92011,92013],{},[898,92012,1690],{},[1692,92014,1694],{},[1651,92016,1661],{"separator":1660},[1686,92018,92019,92021],{},[898,92020,1690],{},[1692,92022,1703],{},[1651,92024,1667],{"stretchy":1653},[1651,92026,1738],{},[1902,92028,92029,92031,92033],{},[898,92030,1690],{},[1692,92032,1694],{},[898,92034,207],{},[1651,92036,4503],{},[1902,92038,92039,92041,92043],{},[898,92040,1690],{},[1692,92042,1703],{},[895,92044,92045,92047,92049],{},[1692,92046,1694],{},[1651,92048,2181],{},[898,92050,207],{},[898,92052,1882],{"mathvariant":1910},[902,92054,92055],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[5179,92057,92058,92107,92229,92363],{},[724,92059,92060,92062,92063],{},[883,92061,53908],{}," Příklad 6.3 — ověření vlastností pro ",[883,92064,92066],{"className":92065},[886],[888,92067,92068],{"xmlns":890},[892,92069,92070,92104],{},[895,92071,92072,92074,92076,92090],{},[898,92073,900],{},[1651,92075,1738],{},[1902,92077,92078,92080,92082],{},[898,92079,1690],{},[1692,92081,1694],{},[895,92083,92084,92086,92088],{},[1692,92085,1694],{},[898,92087,5981],{"mathvariant":1910},[1692,92089,3689],{},[1902,92091,92092,92094,92096],{},[898,92093,1690],{},[1692,92095,1703],{},[895,92097,92098,92100,92102],{},[1692,92099,3521],{},[898,92101,5981],{"mathvariant":1910},[1692,92103,3689],{},[902,92105,92106],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,92108,92110],{"className":92109},[886],[888,92111,92112],{"xmlns":890,"display":29279},[892,92113,92114,92226],{},[895,92115,92116,92124,92126,92134,92150,92164,92166,92168,92170,92172,92180,92182,92190,92204,92220,92222,92224],{},[1902,92117,92118,92120,92122],{},[898,92119,900],{},[1692,92121,1694],{},[1651,92123,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,92125,1738],{},[2938,92127,92128],{"scriptlevel":1741,"displaystyle":1653},[2446,92129,92130,92132],{},[1692,92131,1694],{},[1692,92133,3689],{},[1902,92135,92136,92138,92140],{},[898,92137,1690],{},[1692,92139,1694],{},[895,92141,92142,92144,92146,92148],{},[1651,92143,2181],{},[1692,92145,3521],{},[898,92147,5981],{"mathvariant":1910},[1692,92149,3689],{},[1902,92151,92152,92154,92156],{},[898,92153,1690],{},[1692,92155,1703],{},[895,92157,92158,92160,92162],{},[1692,92159,3521],{},[898,92161,5981],{"mathvariant":1910},[1692,92163,3689],{},[1651,92165,2390],{},[1692,92167,1741],{},[1651,92169,1661],{"separator":1660},[7185,92171],{"width":16582},[1902,92173,92174,92176,92178],{},[898,92175,900],{},[1692,92177,1703],{},[1651,92179,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,92181,1738],{},[2938,92183,92184],{"scriptlevel":1741,"displaystyle":1653},[2446,92185,92186,92188],{},[1692,92187,3521],{},[1692,92189,3689],{},[1902,92191,92192,92194,92196],{},[898,92193,1690],{},[1692,92195,1694],{},[895,92197,92198,92200,92202],{},[1692,92199,1694],{},[898,92201,5981],{"mathvariant":1910},[1692,92203,3689],{},[1902,92205,92206,92208,92210],{},[898,92207,1690],{},[1692,92209,1703],{},[895,92211,92212,92214,92216,92218],{},[1651,92213,2181],{},[1692,92215,1694],{},[898,92217,5981],{"mathvariant":1910},[1692,92219,3689],{},[1651,92221,2390],{},[1692,92223,1741],{},[1651,92225,1661],{"separator":1660},[902,92227,92228],{"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,",[883,92230,92232],{"className":92231},[886],[888,92233,92234],{"xmlns":890,"display":29279},[892,92235,92236,92360],{},[895,92237,92238,92250,92252,92254,92262,92278,92292,92294,92296,92298,92300,92312,92314,92316,92324,92338,92354,92356,92358],{},[1902,92239,92240,92242,92244],{},[898,92241,900],{},[1692,92243,4231],{},[895,92245,92246,92248],{},[1651,92247,1912],{"mathvariant":1910},[1651,92249,1912],{"mathvariant":1910},[1651,92251,1738],{},[1651,92253,2181],{},[2938,92255,92256],{"scriptlevel":1741,"displaystyle":1653},[2446,92257,92258,92260],{},[1692,92259,3521],{},[1692,92261,43075],{},[1902,92263,92264,92266,92268],{},[898,92265,1690],{},[1692,92267,1694],{},[895,92269,92270,92272,92274,92276],{},[1651,92271,2181],{},[1692,92273,25414],{},[898,92275,5981],{"mathvariant":1910},[1692,92277,3689],{},[1902,92279,92280,92282,92284],{},[898,92281,1690],{},[1692,92283,1703],{},[895,92285,92286,92288,92290],{},[1692,92287,3521],{},[898,92289,5981],{"mathvariant":1910},[1692,92291,3689],{},[1651,92293,2319],{},[1692,92295,1741],{},[1651,92297,1661],{"separator":1660},[7185,92299],{"width":16582},[1902,92301,92302,92304,92306],{},[898,92303,900],{},[1692,92305,33759],{},[895,92307,92308,92310],{},[1651,92309,1912],{"mathvariant":1910},[1651,92311,1912],{"mathvariant":1910},[1651,92313,1738],{},[1651,92315,2181],{},[2938,92317,92318],{"scriptlevel":1741,"displaystyle":1653},[2446,92319,92320,92322],{},[1692,92321,3521],{},[1692,92323,43075],{},[1902,92325,92326,92328,92330],{},[898,92327,1690],{},[1692,92329,1694],{},[895,92331,92332,92334,92336],{},[1692,92333,1694],{},[898,92335,5981],{"mathvariant":1910},[1692,92337,3689],{},[1902,92339,92340,92342,92344],{},[898,92341,1690],{},[1692,92343,1703],{},[895,92345,92346,92348,92350,92352],{},[1651,92347,2181],{},[1692,92349,3574],{},[898,92351,5981],{"mathvariant":1910},[1692,92353,3689],{},[1651,92355,2319],{},[1692,92357,1741],{},[1651,92359,1661],{"separator":1660},[902,92361,92362],{"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,",[724,92364,92365],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,92367,92369],{"id":92368},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,92371,92372,92375],{},[38,92373,92374],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,92377,92379],{"className":92378},[886],[888,92380,92381],{"xmlns":890,"display":29279},[892,92382,92383,92426],{},[21967,92384,92385],{"width":29284},[21972,92386,92387,92389,92419,92421],{},[21975,92388],{"width":29289},[21975,92390,92391],{},[895,92392,92393,92395,92397,92403,92405,92411,92413,92415,92417],{},[898,92394,900],{},[1651,92396,1654],{"stretchy":1653},[1686,92398,92399,92401],{},[898,92400,1690],{},[1692,92402,1694],{},[1651,92404,1661],{"separator":1660},[1686,92406,92407,92409],{},[898,92408,1690],{},[1692,92410,1703],{},[1651,92412,1667],{"stretchy":1653},[1651,92414,1738],{},[898,92416,3490],{},[1651,92418,1661],{"separator":1660},[21975,92420],{"width":29289},[21975,92422,92423],{},[1843,92424,92425],{},"(6.7)",[902,92427,92428],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,92430,1863,92431,92444],{},[883,92432,92434],{"className":92433},[886],[888,92435,92436],{"xmlns":890},[892,92437,92438,92442],{},[895,92439,92440],{},[898,92441,3490],{},[902,92443,3490],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,92446,92448],{"className":92447},[886],[888,92449,92450],{"xmlns":890,"display":29279},[892,92451,92452,92493],{},[21967,92453,92454],{"width":29284},[21972,92455,92456,92458,92486,92488],{},[21975,92457],{"width":29289},[21975,92459,92460],{},[895,92461,92462,92470,92472,92480,92482,92484],{},[1902,92463,92464,92466,92468],{},[898,92465,1690],{},[1692,92467,1694],{},[898,92469,207],{},[1651,92471,4503],{},[1902,92473,92474,92476,92478],{},[898,92475,1690],{},[1692,92477,1703],{},[898,92479,2268],{},[1651,92481,1738],{},[898,92483,3490],{},[898,92485,1882],{"mathvariant":1910},[21975,92487],{"width":29289},[21975,92489,92490],{},[1843,92491,92492],{},"(6.8)",[902,92494,92495],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,92497,92498,92499,5665,92529,3246,92532,92545,92546,92581,92582,92599,92600,92629,92630,92633],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,92500,92502],{"className":92501},[886],[888,92503,92504],{"xmlns":890},[892,92505,92506,92526],{},[895,92507,92508,92510,92516,92518,92524],{},[1651,92509,2261],{"stretchy":1653},[1686,92511,92512,92514],{},[898,92513,1690],{},[1692,92515,1694],{},[1651,92517,1661],{"separator":1660},[1686,92519,92520,92522],{},[898,92521,1690],{},[1692,92523,1703],{},[1651,92525,2279],{"stretchy":1653},[902,92527,92528],{"encoding":904},"[Q_1, Q_2]",[38,92530,92531],{},"stejnou úrovní uspokojení",[883,92533,92535],{"className":92534},[886],[888,92536,92537],{"xmlns":890},[892,92538,92539,92543],{},[895,92540,92541],{},[898,92542,3490],{},[902,92544,3490],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,92547,92549],{"className":92548},[886],[888,92550,92551],{"xmlns":890},[892,92552,92553,92579],{},[895,92554,92555,92557,92559,92561,92563,92569,92571,92577],{},[898,92556,900],{},[1651,92558,1738],{},[898,92560,900],{},[1651,92562,1654],{"stretchy":1653},[1686,92564,92565,92567],{},[898,92566,1690],{},[1692,92568,1694],{},[1651,92570,1661],{"separator":1660},[1686,92572,92573,92575],{},[898,92574,1690],{},[1692,92576,1703],{},[1651,92578,1667],{"stretchy":1653},[902,92580,88669],{"encoding":904}," s rovinami ",[883,92583,92585],{"className":92584},[886],[888,92586,92587],{"xmlns":890},[892,92588,92589,92597],{},[895,92590,92591,92593,92595],{},[898,92592,900],{},[1651,92594,1738],{},[898,92596,3490],{},[902,92598,87885],{"encoding":904}," rovnoběžnými s rovinou ",[883,92601,92603],{"className":92602},[886],[888,92604,92605],{"xmlns":890},[892,92606,92607,92627],{},[895,92608,92609,92611,92617,92619,92625],{},[1651,92610,1654],{"stretchy":1653},[1686,92612,92613,92615],{},[898,92614,1690],{},[1692,92616,1694],{},[1651,92618,1661],{"separator":1660},[1686,92620,92621,92623],{},[898,92622,1690],{},[1692,92624,1703],{},[1651,92626,1667],{"stretchy":1653},[902,92628,90832],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,92631,92632],{},"izokvantami"," produkčních funkcí.",[724,92635,92636],{},[614,92637,92638,92639,90710,92657,92675,92676,1882],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,92640,92642],{"className":92641},[886],[888,92643,92644],{"xmlns":890},[892,92645,92646,92654],{},[895,92647,92648,92650,92652],{},[898,92649,207],{},[1651,92651,2319],{},[898,92653,2268],{},[902,92655,92656],{"encoding":904},"a \u003C b",[883,92658,92660],{"className":92659},[886],[888,92661,92662],{"xmlns":890},[892,92663,92664,92672],{},[895,92665,92666,92668,92670],{},[898,92667,207],{},[1651,92669,2390],{},[898,92671,2268],{},[902,92673,92674],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,92677,92679],{"className":92678},[886],[888,92680,92681],{"xmlns":890},[892,92682,92683,92707],{},[895,92684,92685,92691,92693,92699,92701],{},[1686,92686,92687,92689],{},[898,92688,3490],{},[1692,92690,1741],{},[1651,92692,2319],{},[1686,92694,92695,92697],{},[898,92696,3490],{},[1692,92698,1694],{},[1651,92700,2319],{},[1686,92702,92703,92705],{},[898,92704,3490],{},[1692,92706,1703],{},[902,92708,92709],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,92711,92712],{},[614,92713,92714,92715,92744,92745,92803,92804,92822],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,92716,92718],{"className":92717},[886],[888,92719,92720],{"xmlns":890},[892,92721,92722,92742],{},[895,92723,92724,92726,92732,92734,92740],{},[1651,92725,1654],{"stretchy":1653},[1686,92727,92728,92730],{},[898,92729,1690],{},[1692,92731,1694],{},[1651,92733,1661],{"separator":1660},[1686,92735,92736,92738],{},[898,92737,1690],{},[1692,92739,1703],{},[1651,92741,1667],{"stretchy":1653},[902,92743,90832],{"encoding":904},"; body ",[883,92746,92748],{"className":92747},[886],[888,92749,92750],{"xmlns":890},[892,92751,92752,92800],{},[895,92753,92754,92756,92758,92760,92766,92768,92774,92776,92778,92780,92782,92784,92790,92792,92798],{},[898,92755,5564],{},[1651,92757,1738],{},[1651,92759,2261],{"stretchy":1653},[1686,92761,92762,92764],{},[898,92763,207],{},[1692,92765,1694],{},[1651,92767,1661],{"separator":1660},[1686,92769,92770,92772],{},[898,92771,207],{},[1692,92773,1703],{},[1651,92775,2279],{"stretchy":1653},[1651,92777,1661],{"separator":1660},[898,92779,24466],{},[1651,92781,1738],{},[1651,92783,2261],{"stretchy":1653},[1686,92785,92786,92788],{},[898,92787,2268],{},[1692,92789,1694],{},[1651,92791,1661],{"separator":1660},[1686,92793,92794,92796],{},[898,92795,2268],{},[1692,92797,1703],{},[1651,92799,2279],{"stretchy":1653},[902,92801,92802],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,92805,92807],{"className":92806},[886],[888,92808,92809],{"xmlns":890},[892,92810,92811,92819],{},[895,92812,92813,92815,92817],{},[898,92814,3001],{},[1651,92816,1661],{"separator":1660},[898,92818,2047],{},[902,92820,92821],{"encoding":904},"C, D"," na vyšší hladině.",[5179,92824,92825],{},[724,92826,92827,92829,92830,92892,92893,92937,92938,92972,92973,27402,92991,92972,93045,27402,93063,93139],{},[883,92828,53908],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,92831,92833],{"className":92832},[886],[888,92834,92835],{"xmlns":890},[892,92836,92837,92889],{},[895,92838,92839,92841,92843,92849,92851,92857,92859,92861,92875],{},[898,92840,900],{},[1651,92842,1654],{"stretchy":1653},[1686,92844,92845,92847],{},[898,92846,1690],{},[1692,92848,1694],{},[1651,92850,1661],{"separator":1660},[1686,92852,92853,92855],{},[898,92854,1690],{},[1692,92856,1703],{},[1651,92858,1667],{"stretchy":1653},[1651,92860,1738],{},[1902,92862,92863,92865,92867],{},[898,92864,1690],{},[1692,92866,1694],{},[895,92868,92869,92871,92873],{},[1692,92870,1694],{},[898,92872,5981],{"mathvariant":1910},[1692,92874,3689],{},[1902,92876,92877,92879,92881],{},[898,92878,1690],{},[1692,92880,1703],{},[895,92882,92883,92885,92887],{},[1692,92884,3521],{},[898,92886,5981],{"mathvariant":1910},[1692,92888,3689],{},[902,92890,92891],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,92894,92896],{"className":92895},[886],[888,92897,92898],{"xmlns":890},[892,92899,92900,92934],{},[895,92901,92902,92916,92930,92932],{},[1902,92903,92904,92906,92908],{},[898,92905,1690],{},[1692,92907,1694],{},[895,92909,92910,92912,92914],{},[1692,92911,1694],{},[898,92913,5981],{"mathvariant":1910},[1692,92915,3689],{},[1902,92917,92918,92920,92922],{},[898,92919,1690],{},[1692,92921,1703],{},[895,92923,92924,92926,92928],{},[1692,92925,3521],{},[898,92927,5981],{"mathvariant":1910},[1692,92929,3689],{},[1651,92931,1738],{},[898,92933,3490],{},[902,92935,92936],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,92939,92941],{"className":92940},[886],[888,92942,92943],{"xmlns":890},[892,92944,92945,92969],{},[895,92946,92947,92953,92961,92963],{},[1686,92948,92949,92951],{},[898,92950,1690],{},[1692,92952,1694],{},[1902,92954,92955,92957,92959],{},[898,92956,1690],{},[1692,92958,1703],{},[1692,92960,3521],{},[1651,92962,1738],{},[2115,92964,92965,92967],{},[898,92966,3490],{},[1692,92968,3689],{},[902,92970,92971],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,92974,92976],{"className":92975},[886],[888,92977,92978],{"xmlns":890},[892,92979,92980,92988],{},[895,92981,92982,92984,92986],{},[898,92983,3490],{},[1651,92985,1738],{},[1692,92987,1694],{},[902,92989,92990],{"encoding":904},"c = 1",[883,92992,92994],{"className":92993},[886],[888,92995,92996],{"xmlns":890},[892,92997,92998,93042],{},[895,92999,93000,93006,93008,93024,93026],{},[1686,93001,93002,93004],{},[898,93003,1690],{},[1692,93005,1703],{},[1651,93007,1738],{},[1902,93009,93010,93012,93014],{},[898,93011,1690],{},[1692,93013,1694],{},[895,93015,93016,93018,93020,93022],{},[1651,93017,2181],{},[1692,93019,1694],{},[898,93021,5981],{"mathvariant":1910},[1692,93023,3521],{},[1651,93025,1738],{},[2938,93027,93028],{"scriptlevel":1741,"displaystyle":1660},[2446,93029,93030,93032],{},[1692,93031,1694],{},[83240,93033,93034,93040],{},[1686,93035,93036,93038],{},[898,93037,1690],{},[1692,93039,1694],{},[1692,93041,3521],{},[902,93043,93044],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,93046,93048],{"className":93047},[886],[888,93049,93050],{"xmlns":890},[892,93051,93052,93060],{},[895,93053,93054,93056,93058],{},[898,93055,3490],{},[1651,93057,1738],{},[1692,93059,1703],{},[902,93061,93062],{"encoding":904},"c = 2",[883,93064,93066],{"className":93065},[886],[888,93067,93068],{"xmlns":890},[892,93069,93070,93136],{},[895,93071,93072,93078,93080,93092,93094,93110,93112],{},[1686,93073,93074,93076],{},[898,93075,1690],{},[1692,93077,1703],{},[1651,93079,1738],{},[2115,93081,93082,93084],{},[1692,93083,1703],{},[895,93085,93086,93088,93090],{},[1692,93087,3689],{},[898,93089,5981],{"mathvariant":1910},[1692,93091,3521],{},[1651,93093,4503],{},[1902,93095,93096,93098,93100],{},[898,93097,1690],{},[1692,93099,1694],{},[895,93101,93102,93104,93106,93108],{},[1651,93103,2181],{},[1692,93105,1694],{},[898,93107,5981],{"mathvariant":1910},[1692,93109,3521],{},[1651,93111,1738],{},[2938,93113,93114],{"scriptlevel":1741,"displaystyle":1660},[2446,93115,93116,93126],{},[895,93117,93118,93120],{},[1692,93119,1703],{},[83240,93121,93122,93124],{},[1692,93123,1703],{},[1692,93125,3521],{},[83240,93127,93128,93134],{},[1686,93129,93130,93132],{},[898,93131,1690],{},[1692,93133,1694],{},[1692,93135,3521],{},[902,93137,93138],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,93141,93143],{"id":93142},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,93145,93146],{},[1756,93147],{"alt":93148,"className":93149,"src":93150},"imek-ic-4vlastnosti-anotovane",[210,1760],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[5179,93152,93153,93162,93209,93253,93259,93265],{},[724,93154,93155,93157,93158,93161],{},[883,93156,5719],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,93159,93160],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,93163,93164],{},[883,93165,93167],{"className":93166},[886],[888,93168,93169],{"xmlns":890},[892,93170,93171,93206],{},[895,93172,93173,93176,93178,93180,93182,93184,93202,93204],{},[898,93174,93175],{"mathvariant":1910},"tg",[1651,93177,57413],{},[898,93179,20075],{},[1651,93181,1738],{},[1651,93183,2181],{},[2446,93185,93186,93194],{},[1902,93187,93188,93190,93192],{},[898,93189,900],{},[1692,93191,1694],{},[1651,93193,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1902,93195,93196,93198,93200],{},[898,93197,900],{},[1692,93199,1703],{},[1651,93201,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,93203,2319],{},[1692,93205,1741],{},[902,93207,93208],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,93210,93211,93212,93252],{},"(derivace implicitně zadané funkce ",[883,93213,93215],{"className":93214},[886],[888,93216,93217],{"xmlns":890},[892,93218,93219,93249],{},[895,93220,93221,93223,93225,93231,93233,93239,93241,93243,93245,93247],{},[898,93222,900],{},[1651,93224,1654],{"stretchy":1653},[1686,93226,93227,93229],{},[898,93228,1690],{},[1692,93230,1694],{},[1651,93232,1661],{"separator":1660},[1686,93234,93235,93237],{},[898,93236,1690],{},[1692,93238,1703],{},[1651,93240,1667],{"stretchy":1653},[1651,93242,2181],{},[898,93244,3490],{},[1651,93246,1738],{},[1692,93248,1741],{},[902,93250,93251],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,93254,93255,93258],{},[38,93256,93257],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,93260,93261,93264],{},[38,93262,93263],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,93266,93267,93270,93271,93289,93290,93306,93307,93310],{},[38,93268,93269],{},"4° Konvexní."," Pro každé dva body ",[883,93272,93274],{"className":93273},[886],[888,93275,93276],{"xmlns":890},[892,93277,93278,93286],{},[895,93279,93280,93282,93284],{},[898,93281,5564],{},[1651,93283,1661],{"separator":1660},[898,93285,24466],{},[902,93287,93288],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,93291,93293],{"className":93292},[886],[888,93294,93295],{"xmlns":890},[892,93296,93297,93303],{},[895,93298,93299,93301],{},[898,93300,5564],{},[898,93302,24466],{},[902,93304,93305],{"encoding":904},"AB"," ve ",[38,93308,93309],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,93312,93313],{},[614,93314,93315,93316,93351,93352,1882],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,93317,93319],{"className":93318},[886],[888,93320,93321],{"xmlns":890},[892,93322,93323,93349],{},[895,93324,93325,93327,93329,93335,93337,93343,93345,93347],{},[898,93326,900],{},[1651,93328,1654],{"stretchy":1653},[1686,93330,93331,93333],{},[898,93332,1690],{},[1692,93334,1694],{},[1651,93336,1661],{"separator":1660},[1686,93338,93339,93341],{},[898,93340,1690],{},[1692,93342,1703],{},[1651,93344,1667],{"stretchy":1653},[1651,93346,1738],{},[898,93348,3490],{},[902,93350,11071],{"encoding":904}," s tečnou se sklonem ",[883,93353,93355],{"className":93354},[886],[888,93356,93357],{"xmlns":890},[892,93358,93359,93367],{},[895,93360,93361,93363,93365],{},[898,93362,93175],{"mathvariant":1910},[1651,93364,57413],{},[898,93366,20075],{},[902,93368,93369],{"encoding":904},"\\operatorname{tg}\\alpha",[115,93371,93373],{"id":93372},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,93375,93376,3246,93379,11325,93392,93395],{},[38,93377,93378],{},"Mezní míra komoditní substituce",[883,93380,93382],{"className":93381},[886],[888,93383,93384],{"xmlns":890},[892,93385,93386,93390],{},[895,93387,93388],{},[1843,93389,11903],{},[902,93391,29451],{"encoding":904},[38,93393,93394],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,93397,93399],{"className":93398},[886],[888,93400,93401],{"xmlns":890,"display":29279},[892,93402,93403,93490],{},[21967,93404,93405],{"width":29284},[21972,93406,93407,93409,93483,93485],{},[21975,93408],{"width":29289},[21975,93410,93411],{},[895,93412,93413,93415,93417,93419,93421,93427,93429,93435,93437,93439,93461,93463,93481],{},[1843,93414,11903],{},[1651,93416,1738],{},[1843,93418,11903],{},[1651,93420,1654],{"stretchy":1653},[1686,93422,93423,93425],{},[898,93424,1690],{},[1692,93426,1694],{},[1651,93428,1661],{"separator":1660},[1686,93430,93431,93433],{},[898,93432,1690],{},[1692,93434,1703],{},[1651,93436,1667],{"stretchy":1653},[1651,93438,1738],{},[2446,93440,93441,93451],{},[895,93442,93443,93445],{},[898,93444,2995],{},[1686,93446,93447,93449],{},[898,93448,900],{},[1692,93450,1694],{},[895,93452,93453,93455],{},[898,93454,2995],{},[1686,93456,93457,93459],{},[898,93458,900],{},[1692,93460,1703],{},[1651,93462,1738],{},[2446,93464,93465,93473],{},[1902,93466,93467,93469,93471],{},[898,93468,900],{},[1692,93470,1694],{},[1651,93472,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1902,93474,93475,93477,93479],{},[898,93476,900],{},[1692,93478,1703],{},[1651,93480,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[898,93482,1882],{"mathvariant":1910},[21975,93484],{"width":29289},[21975,93486,93487],{},[1843,93488,93489],{},"(6.9)",[902,93491,93492],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,93494,93495,93496,93530,93531,93563,93564,93599,93600,93613],{},"Geometricky: ",[883,93497,93499],{"className":93498},[886],[888,93500,93501],{"xmlns":890},[892,93502,93503,93527],{},[895,93504,93505,93507],{},[1651,93506,2181],{},[2938,93508,93509],{"scriptlevel":1741,"displaystyle":1653},[2446,93510,93511,93519],{},[1902,93512,93513,93515,93517],{},[898,93514,900],{},[1692,93516,1694],{},[1651,93518,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1902,93520,93521,93523,93525],{},[898,93522,900],{},[1692,93524,1703],{},[1651,93526,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,93528,93529],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,93532,93534],{"className":93533},[886],[888,93535,93536],{"xmlns":890},[892,93537,93538,93560],{},[895,93539,93540,93546,93548,93550,93552,93558],{},[1686,93541,93542,93544],{},[898,93543,1690],{},[1692,93545,1703],{},[1651,93547,1738],{},[898,93549,1649],{},[1651,93551,1654],{"stretchy":1653},[1686,93553,93554,93556],{},[898,93555,1690],{},[1692,93557,1694],{},[1651,93559,1667],{"stretchy":1653},[902,93561,93562],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,93565,93567],{"className":93566},[886],[888,93568,93569],{"xmlns":890},[892,93570,93571,93597],{},[895,93572,93573,93575,93577,93583,93585,93591,93593,93595],{},[898,93574,900],{},[1651,93576,1654],{"stretchy":1653},[1686,93578,93579,93581],{},[898,93580,1690],{},[1692,93582,1694],{},[1651,93584,1661],{"separator":1660},[1686,93586,93587,93589],{},[898,93588,1690],{},[1692,93590,1703],{},[1651,93592,1667],{"stretchy":1653},[1651,93594,1738],{},[898,93596,3490],{},[902,93598,11071],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,93601,93603],{"className":93602},[886],[888,93604,93605],{"xmlns":890},[892,93606,93607,93611],{},[895,93608,93609],{},[1843,93610,11903],{},[902,93612,29451],{"encoding":904}," chápeme jako velikost kompenzace.",[5179,93615,93616],{},[724,93617,93618,93620,93621,1878,93653,93691,93692,93709,93710,93727],{},[883,93619,5465],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,93622,93624],{"className":93623},[886],[888,93625,93626],{"xmlns":890},[892,93627,93628,93650],{},[895,93629,93630,93632,93634,93640,93642,93648],{},[1843,93631,11903],{},[1651,93633,1654],{"stretchy":1653},[1686,93635,93636,93638],{},[898,93637,1690],{},[1692,93639,1694],{},[1651,93641,1661],{"separator":1660},[1686,93643,93644,93646],{},[898,93645,1690],{},[1692,93647,1703],{},[1651,93649,1667],{"stretchy":1653},[902,93651,93652],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,93654,93655,93656,30216,93673,93690],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,93657,93659],{"className":93658},[886],[888,93660,93661],{"xmlns":890},[892,93662,93663,93671],{},[895,93664,93665],{},[1686,93666,93667,93669],{},[898,93668,1690],{},[1692,93670,1694],{},[902,93672,30215],{"encoding":904},[883,93674,93676],{"className":93675},[886],[888,93677,93678],{"xmlns":890},[892,93679,93680,93688],{},[895,93681,93682],{},[1686,93683,93684,93686],{},[898,93685,1690],{},[1692,93687,1703],{},[902,93689,30234],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,93693,93695],{"className":93694},[886],[888,93696,93697],{"xmlns":890},[892,93698,93699,93707],{},[895,93700,93701],{},[1686,93702,93703,93705],{},[898,93704,1690],{},[1692,93706,1703],{},[902,93708,30234],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,93711,93713],{"className":93712},[886],[888,93714,93715],{"xmlns":890},[892,93716,93717,93725],{},[895,93718,93719],{},[1686,93720,93721,93723],{},[898,93722,1690],{},[1692,93724,1694],{},[902,93726,30215],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,93729,93730,93731,31157],{},"Pro obecnou změnu ",[883,93732,93734],{"className":93733},[886],[888,93735,93736],{"xmlns":890},[892,93737,93738,93748],{},[895,93739,93740,93742],{},[898,93741,3542],{"mathvariant":1910},[1686,93743,93744,93746],{},[898,93745,1690],{},[1692,93747,1694],{},[902,93749,93750],{"encoding":904},"\\mathrm{d} Q_1",[883,93752,93754],{"className":93753},[886],[888,93755,93756],{"xmlns":890,"display":29279},[892,93757,93758,93811],{},[21967,93759,93760],{"width":29284},[21972,93761,93762,93764,93804,93806],{},[21975,93763],{"width":29289},[21975,93765,93766],{},[895,93767,93768,93770,93776,93778,93780,93786,93788,93790,93792,93794,93796,93802],{},[898,93769,4216],{"mathvariant":1910},[1686,93771,93772,93774],{},[898,93773,1690],{},[1692,93775,1703],{},[1651,93777,4060],{},[898,93779,3542],{"mathvariant":1910},[1686,93781,93782,93784],{},[898,93783,1690],{},[1692,93785,1703],{},[1651,93787,1738],{},[1651,93789,2181],{},[1843,93791,11903],{},[1651,93793,4503],{},[898,93795,3542],{"mathvariant":1910},[1686,93797,93798,93800],{},[898,93799,1690],{},[1692,93801,1694],{},[1651,93803,1661],{"separator":1660},[21975,93805],{"width":29289},[21975,93807,93808],{},[1843,93809,93810],{},"(6.10)",[902,93812,93813],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,93815,93817],{"className":93816},[886],[888,93818,93819],{"xmlns":890,"display":29279},[892,93820,93821,93868],{},[21967,93822,93823],{"width":29284},[21972,93824,93825,93827,93861,93863],{},[21975,93826],{"width":29289},[21975,93828,93829],{},[895,93830,93831,93833,93839,93841,93843,93849,93851,93853,93859],{},[898,93832,3542],{"mathvariant":1910},[1686,93834,93835,93837],{},[898,93836,1690],{},[1692,93838,1694],{},[1651,93840,1738],{},[1651,93842,2181],{},[2446,93844,93845,93847],{},[1692,93846,1694],{},[1843,93848,11903],{},[1843,93850,1845],{},[898,93852,3542],{"mathvariant":1910},[1686,93854,93855,93857],{},[898,93856,1690],{},[1692,93858,1703],{},[898,93860,1882],{"mathvariant":1910},[21975,93862],{"width":29289},[21975,93864,93865],{},[1843,93866,93867],{},"(6.11)",[902,93869,93870],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[5179,93872,93873,93939,94056],{},[724,93874,93875,93877,93878,31157],{},[883,93876,53908],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,93879,93881],{"className":93880},[886],[888,93882,93883],{"xmlns":890},[892,93884,93885,93937],{},[895,93886,93887,93889,93891,93897,93899,93905,93907,93909,93923],{},[898,93888,900],{},[1651,93890,1654],{"stretchy":1653},[1686,93892,93893,93895],{},[898,93894,1690],{},[1692,93896,1694],{},[1651,93898,1661],{"separator":1660},[1686,93900,93901,93903],{},[898,93902,1690],{},[1692,93904,1703],{},[1651,93906,1667],{"stretchy":1653},[1651,93908,1738],{},[1902,93910,93911,93913,93915],{},[898,93912,1690],{},[1692,93914,1694],{},[895,93916,93917,93919,93921],{},[1692,93918,1694],{},[898,93920,5981],{"mathvariant":1910},[1692,93922,1703],{},[1902,93924,93925,93927,93929],{},[898,93926,1690],{},[1692,93928,1703],{},[895,93930,93931,93933,93935],{},[1692,93932,1694],{},[898,93934,5981],{"mathvariant":1910},[1692,93936,1703],{},[902,93938,31156],{"encoding":904},[724,93940,93941],{},[883,93942,93944],{"className":93943},[886],[888,93945,93946],{"xmlns":890},[892,93947,93948,94054],{},[895,93949,93950,93952,93954,94036,94038,94052],{},[1843,93951,11903],{},[1651,93953,1738],{},[2446,93955,93956,93996],{},[895,93957,93958,93966,93982],{},[2938,93959,93960],{"scriptlevel":1741,"displaystyle":1653},[2446,93961,93962,93964],{},[1692,93963,1694],{},[1692,93965,1703],{},[1902,93967,93968,93970,93972],{},[898,93969,1690],{},[1692,93971,1694],{},[895,93973,93974,93976,93978,93980],{},[1651,93975,2181],{},[1692,93977,1694],{},[898,93979,5981],{"mathvariant":1910},[1692,93981,1703],{},[1902,93983,93984,93986,93988],{},[898,93985,1690],{},[1692,93987,1703],{},[895,93989,93990,93992,93994],{},[1692,93991,1694],{},[898,93993,5981],{"mathvariant":1910},[1692,93995,1703],{},[895,93997,93998,94006,94020],{},[2938,93999,94000],{"scriptlevel":1741,"displaystyle":1653},[2446,94001,94002,94004],{},[1692,94003,1694],{},[1692,94005,1703],{},[1902,94007,94008,94010,94012],{},[898,94009,1690],{},[1692,94011,1694],{},[895,94013,94014,94016,94018],{},[1692,94015,1694],{},[898,94017,5981],{"mathvariant":1910},[1692,94019,1703],{},[1902,94021,94022,94024,94026],{},[898,94023,1690],{},[1692,94025,1703],{},[895,94027,94028,94030,94032,94034],{},[1651,94029,2181],{},[1692,94031,1694],{},[898,94033,5981],{"mathvariant":1910},[1692,94035,1703],{},[1651,94037,1738],{},[2446,94039,94040,94046],{},[1686,94041,94042,94044],{},[898,94043,1690],{},[1692,94045,1703],{},[1686,94047,94048,94050],{},[898,94049,1690],{},[1692,94051,1694],{},[898,94053,1882],{"mathvariant":1910},[902,94055,31275],{"encoding":904},[724,94057,31278,94058,4254,94101,31326,94103,94122],{},[883,94059,94061],{"className":94060},[886],[888,94062,94063],{"xmlns":890},[892,94064,94065,94099],{},[895,94066,94067,94069,94071,94073,94075,94077,94079,94081,94089,94091],{},[1843,94068,11903],{},[1651,94070,1654],{"stretchy":1653},[1692,94072,31294],{},[1651,94074,1661],{"separator":1660},[1692,94076,16408],{},[1651,94078,1667],{"stretchy":1653},[1651,94080,1738],{},[2938,94082,94083],{"scriptlevel":1741,"displaystyle":1653},[2446,94084,94085,94087],{},[1692,94086,16408],{},[1692,94088,31294],{},[1651,94090,1738],{},[2938,94092,94093],{"scriptlevel":1741,"displaystyle":1653},[2446,94094,94095,94097],{},[1692,94096,3574],{},[1692,94098,3521],{},[902,94100,31323],{"encoding":904},[614,94102,10519],{},[883,94104,94106],{"className":94105},[886],[888,94107,94108],{"xmlns":890},[892,94109,94110,94120],{},[895,94111,94112],{},[2938,94113,94114],{"scriptlevel":1741,"displaystyle":1653},[2446,94115,94116,94118],{},[1692,94117,3574],{},[1692,94119,3521],{},[902,94121,31346],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,94124,94125,94126,94130],{},"(Paralelou je ",[207,94127,94129],{"className":94128,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,94132,94134],{"id":94133},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,94136,94137,94138,94141],{},"Rámcově se v kapitole 6 studují ",[38,94139,94140],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,94143,94144,94280],{},[123,94145,94146,94148,94149,11457,94180,3246,94183,94232,94233,1882],{},[38,94147,29465],{}," — maximalizace ",[883,94150,94152],{"className":94151},[886],[888,94153,94154],{"xmlns":890},[892,94155,94156,94178],{},[895,94157,94158,94160,94162,94168,94170,94176],{},[898,94159,900],{},[1651,94161,1654],{"stretchy":1653},[1686,94163,94164,94166],{},[898,94165,1690],{},[1692,94167,1694],{},[1651,94169,1661],{"separator":1660},[1686,94171,94172,94174],{},[898,94173,1690],{},[1692,94175,1703],{},[1651,94177,1667],{"stretchy":1653},[902,94179,1708],{"encoding":904},[38,94181,94182],{},"rozpočtovém omezení",[883,94184,94186],{"className":94185},[886],[888,94187,94188],{"xmlns":890},[892,94189,94190,94230],{},[895,94191,94192,94198,94200,94208,94214,94216,94224],{},[2115,94193,94194,94196],{},[898,94195,2665],{},[1651,94197,2668],{},[1651,94199,1738],{},[1902,94201,94202,94204,94206],{},[898,94203,2675],{},[1692,94205,1694],{},[1651,94207,2668],{},[1686,94209,94210,94212],{},[898,94211,1690],{},[1692,94213,1694],{},[1651,94215,1839],{},[1902,94217,94218,94220,94222],{},[898,94219,2675],{},[1692,94221,1703],{},[1651,94223,2668],{},[1686,94225,94226,94228],{},[898,94227,1690],{},[1692,94229,1703],{},[902,94231,2704],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,94234,94236],{"className":94235},[886],[888,94237,94238],{"xmlns":890},[892,94239,94240,94278],{},[895,94241,94242,94248,94250,94256,94258,94264,94266,94272,94274,94276],{},[1686,94243,94244,94246],{},[898,94245,1690],{},[898,94247,3201],{},[1651,94249,1738],{},[1686,94251,94252,94254],{},[898,94253,2047],{},[898,94255,3201],{},[1651,94257,1654],{"stretchy":1653},[1686,94259,94260,94262],{},[898,94261,2675],{},[1692,94263,1694],{},[1651,94265,1661],{"separator":1660},[1686,94267,94268,94270],{},[898,94269,2675],{},[1692,94271,1703],{},[1651,94273,1661],{"separator":1660},[898,94275,2665],{},[1651,94277,1667],{"stretchy":1653},[902,94279,37668],{"encoding":904},[123,94281,94282,29114,94285,29157,94331,94348,94349,1882],{},[38,94283,94284],{},"Duální úloha",[883,94286,94288],{"className":94287},[886],[888,94289,94290],{"xmlns":890},[892,94291,94292,94328],{},[895,94293,94294,94296,94298,94306,94312,94314,94322],{},[898,94295,5561],{},[1651,94297,1738],{},[1902,94299,94300,94302,94304],{},[898,94301,2675],{},[1692,94303,1694],{},[1651,94305,2668],{},[1686,94307,94308,94310],{},[898,94309,1690],{},[1692,94311,1694],{},[1651,94313,1839],{},[1902,94315,94316,94318,94320],{},[898,94317,2675],{},[1692,94319,1703],{},[1651,94321,2668],{},[1686,94323,94324,94326],{},[898,94325,1690],{},[1692,94327,1703],{},[902,94329,94330],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,94332,94334],{"className":94333},[886],[888,94335,94336],{"xmlns":890},[892,94337,94338,94346],{},[895,94339,94340],{},[2115,94341,94342,94344],{},[898,94343,900],{},[1651,94345,2668],{},[902,94347,29175],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,94350,94352],{"className":94351},[886],[888,94353,94354],{"xmlns":890},[892,94355,94356,94394],{},[895,94357,94358,94364,94366,94372,94374,94380,94382,94388,94390,94392],{},[1686,94359,94360,94362],{},[898,94361,1690],{},[898,94363,3201],{},[1651,94365,1738],{},[1686,94367,94368,94370],{},[898,94369,2047],{},[898,94371,3201],{},[1651,94373,1654],{"stretchy":1653},[1686,94375,94376,94378],{},[898,94377,2675],{},[1692,94379,1694],{},[1651,94381,1661],{"separator":1660},[1686,94383,94384,94386],{},[898,94385,2675],{},[1692,94387,1703],{},[1651,94389,1661],{"separator":1660},[898,94391,900],{},[1651,94393,1667],{"stretchy":1653},[902,94395,3234],{"encoding":904},[724,94397,94398,94399,94402,94403,3246,94406,94445],{},"Obě úlohy se řeší ",[207,94400,29180],{"className":94401,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,94404,94405],{},"tentýž bod dotyku",[883,94407,94409],{"className":94408},[886],[888,94410,94411],{"xmlns":890},[892,94412,94413,94443],{},[895,94414,94415,94421,94423,94431,94433,94441],{},[2115,94416,94417,94419],{},[898,94418,1690],{},[1651,94420,2668],{},[1651,94422,2261],{"stretchy":1653},[1902,94424,94425,94427,94429],{},[898,94426,1690],{},[1692,94428,1694],{},[1651,94430,2668],{},[1651,94432,1661],{"separator":1660},[1902,94434,94435,94437,94439],{},[898,94436,1690],{},[1692,94438,1703],{},[1651,94440,2668],{},[1651,94442,2279],{"stretchy":1653},[902,94444,29540],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,94447,94449],{"className":94448},[886],[888,94450,94451],{"xmlns":890,"display":29279},[892,94452,94453,94499],{},[895,94454,94455,94457,94459,94477,94479,94497],{},[1843,94456,11903],{},[1651,94458,1738],{},[2446,94460,94461,94469],{},[1902,94462,94463,94465,94467],{},[898,94464,900],{},[1692,94466,1694],{},[1651,94468,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1902,94470,94471,94473,94475],{},[898,94472,900],{},[1692,94474,1703],{},[1651,94476,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,94478,1738],{},[2446,94480,94481,94489],{},[1902,94482,94483,94485,94487],{},[898,94484,2675],{},[1692,94486,1694],{},[1651,94488,2668],{},[1902,94490,94491,94493,94495],{},[898,94492,2675],{},[1692,94494,1703],{},[1651,94496,2668],{},[898,94498,1882],{"mathvariant":1910},[902,94500,94501],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,94503,94504],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[5179,94506,94507],{},[724,94508,94509,94511,94512,94515,94516,94519,94520,94547,94548,94582,94583,94617,94618,94661,94662,94665,94666,1882],{},[883,94510,5465],{}," Pro detailní postup viz ",[207,94513,37967],{"className":94514,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,94517,94518],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,94521,94523],{"className":94522},[886],[888,94524,94525],{"xmlns":890},[892,94526,94527,94545],{},[895,94528,94529,94531,94533,94539],{},[898,94530,900],{},[1651,94532,1738],{},[1686,94534,94535,94537],{},[898,94536,1690],{},[1692,94538,1694],{},[1686,94540,94541,94543],{},[898,94542,1690],{},[1692,94544,1703],{},[902,94546,31439],{"encoding":904}," s výsledkem ",[883,94549,94551],{"className":94550},[886],[888,94552,94553],{"xmlns":890},[892,94554,94555,94579],{},[895,94556,94557,94563,94565,94567,94569,94575,94577],{},[1686,94558,94559,94561],{},[898,94560,1690],{},[1692,94562,1694],{},[1651,94564,1738],{},[1692,94566,6311],{},[1651,94568,1661],{"separator":1660},[1686,94570,94571,94573],{},[898,94572,1690],{},[1692,94574,1703],{},[1651,94576,1738],{},[1692,94578,4190],{},[902,94580,94581],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,94584,94586],{"className":94585},[886],[888,94587,94588],{"xmlns":890},[892,94589,94590,94614],{},[895,94591,94592,94598,94600,94602,94604,94610,94612],{},[1686,94593,94594,94596],{},[898,94595,1690],{},[1692,94597,1694],{},[1651,94599,1738],{},[1692,94601,3689],{},[1651,94603,1661],{"separator":1660},[1686,94605,94606,94608],{},[898,94607,1690],{},[1692,94609,1703],{},[1651,94611,1738],{},[1692,94613,1694],{},[902,94615,94616],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,94619,94621],{"className":94620},[886],[888,94622,94623],{"xmlns":890},[892,94624,94625,94659],{},[895,94626,94627,94629,94631,94645],{},[898,94628,900],{},[1651,94630,1738],{},[1902,94632,94633,94635,94637],{},[898,94634,1690],{},[1692,94636,1694],{},[895,94638,94639,94641,94643],{},[1692,94640,1694],{},[898,94642,5981],{"mathvariant":1910},[1692,94644,1703],{},[1902,94646,94647,94649,94651],{},[898,94648,1690],{},[1692,94650,1703],{},[895,94652,94653,94655,94657],{},[1692,94654,1694],{},[898,94656,5981],{"mathvariant":1910},[1692,94658,1703],{},[902,94660,34372],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,94663,94664],{},"6.8–6.13"," jsou na stránce ",[207,94667,28980],{"className":94668,"dataFsResolvedFilePath":911,"href":912},[210],[115,94670,94672],{"id":94671},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,94674,94675,94676,94689,94690,94692,94693,94695,94696,94698,94699,94701,94702,94704,94705,94707,94708,3246,94710,94745,94746,94759,94760,94763,94764,94767,94768,1882],{},"Každá ",[883,94677,94679],{"className":94678},[886],[888,94680,94681],{"xmlns":890},[892,94682,94683,94687],{},[895,94684,94685],{},[898,94686,38073],{},[902,94688,38073],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,94691,88023],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,94694,88507],{}," a současně ",[38,94697,88026],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,94700,88031],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,94703,53890],{}," (6.4) a druhé parciální derivace ",[38,94706,90390],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,94709,11034],{},[883,94711,94713],{"className":94712},[886],[888,94714,94715],{"xmlns":890},[892,94716,94717,94743],{},[895,94718,94719,94721,94723,94729,94731,94737,94739,94741],{},[898,94720,900],{},[1651,94722,1654],{"stretchy":1653},[1686,94724,94725,94727],{},[898,94726,1690],{},[1692,94728,1694],{},[1651,94730,1661],{"separator":1660},[1686,94732,94733,94735],{},[898,94734,1690],{},[1692,94736,1703],{},[1651,94738,1667],{"stretchy":1653},[1651,94740,1738],{},[898,94742,3490],{},[902,94744,11071],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,94747,94749],{"className":94748},[886],[888,94750,94751],{"xmlns":890},[892,94752,94753,94757],{},[895,94754,94755],{},[1843,94756,11903],{},[902,94758,29451],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,94761,94762],{},"maximalizace užitečnosti"," a duální ",[38,94765,94766],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,94769,37967],{"className":94770,"dataFsResolvedFilePath":911,"href":912},[210],[115,94772,51095],{"id":51094},[152,94774,94775,94778,94781,94784,94787,94790,94793,94796,94799,94802],{},[123,94776,94777],{},"Co se zahrnuje pod termín užitečnost?",[123,94779,94780],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,94782,94783],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,94785,94786],{},"Jak se vypočítá mezní užitečnost?",[123,94788,94789],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,94791,94792],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,94794,94795],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,94797,94798],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,94800,94801],{},"Proč mají křivky užitečnosti záporný sklon?",[123,94803,94804],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,94806,94808],{"id":94807},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,94810,94811,94814,94815,84696,94857,1343,94885,1343,94913,94941],{},[38,94812,94813],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,94816,94818],{"className":94817},[886],[888,94819,94820],{"xmlns":890},[892,94821,94822,94854],{},[895,94823,94824,94826,94828,94834,94836,94838,94844,94846,94848],{},[898,94825,900],{},[1651,94827,1738],{},[1686,94829,94830,94832],{},[898,94831,1690],{},[1692,94833,1694],{},[1651,94835,1839],{},[1692,94837,65772],{},[1686,94839,94840,94842],{},[898,94841,1690],{},[1692,94843,1703],{},[1651,94845,1839],{},[1692,94847,1703],{},[1686,94849,94850,94852],{},[898,94851,1690],{},[1692,94853,3521],{},[902,94855,94856],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,94858,94860],{"className":94859},[886],[888,94861,94862],{"xmlns":890},[892,94863,94864,94882],{},[895,94865,94866,94868,94870,94872,94874,94876,94878,94880],{},[898,94867,900],{},[1651,94869,1654],{"stretchy":1653},[1692,94871,3689],{},[1651,94873,1661],{"separator":1660},[1692,94875,1703],{},[1651,94877,1661],{"separator":1660},[1692,94879,1703],{},[1651,94881,1667],{"stretchy":1653},[902,94883,94884],{"encoding":904},"U(4, 2, 2)",[883,94886,94888],{"className":94887},[886],[888,94889,94890],{"xmlns":890},[892,94891,94892,94910],{},[895,94893,94894,94896,94898,94900,94902,94904,94906,94908],{},[898,94895,900],{},[1651,94897,1654],{"stretchy":1653},[1692,94899,1694],{},[1651,94901,1661],{"separator":1660},[1692,94903,3689],{},[1651,94905,1661],{"separator":1660},[1692,94907,1703],{},[1651,94909,1667],{"stretchy":1653},[902,94911,94912],{"encoding":904},"U(1, 4, 2)",[883,94914,94916],{"className":94915},[886],[888,94917,94918],{"xmlns":890},[892,94919,94920,94938],{},[895,94921,94922,94924,94926,94928,94930,94932,94934,94936],{},[898,94923,900],{},[1651,94925,1654],{"stretchy":1653},[1692,94927,1703],{},[1651,94929,1661],{"separator":1660},[1692,94931,3521],{},[1651,94933,1661],{"separator":1660},[1692,94935,1694],{},[1651,94937,1667],{"stretchy":1653},[902,94939,94940],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,94943,94944,94947,94948,95000,95001,1343,95027,1343,95053,1343,95079,1343,95105,1343,95131,1343,95157,95183],{},[38,94945,94946],{},"6.2"," Je dána užitečnost ",[883,94949,94951],{"className":94950},[886],[888,94952,94953],{"xmlns":890},[892,94954,94955,94997],{},[895,94956,94957,94959,94961,94963,94977,94991],{},[898,94958,900],{},[1651,94960,1738],{},[1692,94962,1703],{},[1902,94964,94965,94967,94969],{},[898,94966,1690],{},[1692,94968,1694],{},[895,94970,94971,94973,94975],{},[1692,94972,1694],{},[898,94974,5981],{"mathvariant":1910},[1692,94976,3521],{},[1902,94978,94979,94981,94983],{},[898,94980,1690],{},[1692,94982,1703],{},[895,94984,94985,94987,94989],{},[1692,94986,1694],{},[898,94988,5981],{"mathvariant":1910},[1692,94990,1703],{},[1686,94992,94993,94995],{},[898,94994,1690],{},[1692,94996,3521],{},[902,94998,94999],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,95002,95004],{"className":95003},[886],[888,95005,95006],{"xmlns":890},[892,95007,95008,95024],{},[895,95009,95010,95012,95014,95016,95018,95020,95022],{},[1651,95011,1654],{"stretchy":1653},[1692,95013,6872],{},[1651,95015,1661],{"separator":1660},[1692,95017,67810],{},[1651,95019,1661],{"separator":1660},[1692,95021,4190],{},[1651,95023,1667],{"stretchy":1653},[902,95025,95026],{"encoding":904},"(36, 27, 10)",[883,95028,95030],{"className":95029},[886],[888,95031,95032],{"xmlns":890},[892,95033,95034,95050],{},[895,95035,95036,95038,95040,95042,95044,95046,95048],{},[1651,95037,1654],{"stretchy":1653},[1692,95039,43053],{},[1651,95041,1661],{"separator":1660},[1692,95043,6892],{},[1651,95045,1661],{"separator":1660},[1692,95047,10340],{},[1651,95049,1667],{"stretchy":1653},[902,95051,95052],{"encoding":904},"(64, 8, 20)",[883,95054,95056],{"className":95055},[886],[888,95057,95058],{"xmlns":890},[892,95059,95060,95076],{},[895,95061,95062,95064,95066,95068,95070,95072,95074],{},[1651,95063,1654],{"stretchy":1653},[1692,95065,6311],{},[1651,95067,1661],{"separator":1660},[1692,95069,43053],{},[1651,95071,1661],{"separator":1660},[1692,95073,6892],{},[1651,95075,1667],{"stretchy":1653},[902,95077,95078],{"encoding":904},"(25, 64, 8)",[883,95080,95082],{"className":95081},[886],[888,95083,95084],{"xmlns":890},[892,95085,95086,95102],{},[895,95087,95088,95090,95092,95094,95096,95098,95100],{},[1651,95089,1654],{"stretchy":1653},[1692,95091,3689],{},[1651,95093,1661],{"separator":1660},[1692,95095,73742],{},[1651,95097,1661],{"separator":1660},[1692,95099,3581],{},[1651,95101,1667],{"stretchy":1653},[902,95103,95104],{"encoding":904},"(4, 125, 6)",[883,95106,95108],{"className":95107},[886],[888,95109,95110],{"xmlns":890},[892,95111,95112,95128],{},[895,95113,95114,95116,95118,95120,95122,95124,95126],{},[1651,95115,1654],{"stretchy":1653},[1692,95117,5309],{},[1651,95119,1661],{"separator":1660},[1692,95121,6518],{},[1651,95123,1661],{"separator":1660},[1692,95125,4828],{},[1651,95127,1667],{"stretchy":1653},[902,95129,95130],{"encoding":904},"(9, 40, 12)",[883,95132,95134],{"className":95133},[886],[888,95135,95136],{"xmlns":890},[892,95137,95138,95154],{},[895,95139,95140,95142,95144,95146,95148,95150,95152],{},[1651,95141,1654],{"stretchy":1653},[1692,95143,5309],{},[1651,95145,1661],{"separator":1660},[1692,95147,43053],{},[1651,95149,1661],{"separator":1660},[1692,95151,3574],{},[1651,95153,1667],{"stretchy":1653},[902,95155,95156],{"encoding":904},"(9, 64, 5)",[883,95158,95160],{"className":95159},[886],[888,95161,95162],{"xmlns":890},[892,95163,95164,95180],{},[895,95165,95166,95168,95170,95172,95174,95176,95178],{},[1651,95167,1654],{"stretchy":1653},[1692,95169,43053],{},[1651,95171,1661],{"separator":1660},[1692,95173,6892],{},[1651,95175,1661],{"separator":1660},[1692,95177,4190],{},[1651,95179,1667],{"stretchy":1653},[902,95181,95182],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,95185,95186,94947,95189,95232,95233,95267,95268,7780,95298,95331,95332,95349,95350,95367],{},[38,95187,95188],{},"6.3",[883,95190,95192],{"className":95191},[886],[888,95193,95194],{"xmlns":890},[892,95195,95196,95230],{},[895,95197,95198,95200,95202,95216],{},[898,95199,900],{},[1651,95201,1738],{},[1902,95203,95204,95206,95208],{},[898,95205,1690],{},[1692,95207,1694],{},[895,95209,95210,95212,95214],{},[1692,95211,1694],{},[898,95213,5981],{"mathvariant":1910},[1692,95215,1703],{},[1902,95217,95218,95220,95222],{},[898,95219,1690],{},[1692,95221,1703],{},[895,95223,95224,95226,95228],{},[1692,95225,1694],{},[898,95227,5981],{"mathvariant":1910},[1692,95229,1703],{},[902,95231,34372],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,95234,95236],{"className":95235},[886],[888,95237,95238],{"xmlns":890},[892,95239,95240,95264],{},[895,95241,95242,95248,95250,95252,95254,95260,95262],{},[1686,95243,95244,95246],{},[898,95245,1690],{},[1692,95247,1694],{},[1651,95249,1738],{},[1692,95251,4446],{},[1651,95253,1661],{"separator":1660},[1686,95255,95256,95258],{},[898,95257,1690],{},[1692,95259,1703],{},[1651,95261,1738],{},[1692,95263,47916],{},[902,95265,95266],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,95269,95271],{"className":95270},[886],[888,95272,95273],{"xmlns":890},[892,95274,95275,95295],{},[895,95276,95277,95279,95285,95287,95289],{},[898,95278,2995],{},[1686,95280,95281,95283],{},[898,95282,900],{},[1692,95284,1694],{},[1651,95286,1661],{"separator":1660},[898,95288,2995],{},[1686,95290,95291,95293],{},[898,95292,900],{},[1692,95294,1703],{},[902,95296,95297],{"encoding":904},"MU_1, MU_2",[883,95299,95301],{"className":95300},[886],[888,95302,95303],{"xmlns":890},[892,95304,95305,95329],{},[895,95306,95307,95313,95315,95317,95319,95325,95327],{},[1686,95308,95309,95311],{},[898,95310,1690],{},[1692,95312,1694],{},[1651,95314,1738],{},[1692,95316,4446],{},[1651,95318,1661],{"separator":1660},[1686,95320,95321,95323],{},[898,95322,1690],{},[1692,95324,1703],{},[1651,95326,1738],{},[1692,95328,47916],{},[902,95330,95266],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,95333,95335],{"className":95334},[886],[888,95336,95337],{"xmlns":890},[892,95338,95339,95347],{},[895,95340,95341],{},[1686,95342,95343,95345],{},[898,95344,1690],{},[1692,95346,1694],{},[902,95348,30215],{"encoding":904}," na 60 a poklesu ",[883,95351,95353],{"className":95352},[886],[888,95354,95355],{"xmlns":890},[892,95356,95357,95365],{},[895,95358,95359],{},[1686,95360,95361,95363],{},[898,95362,1690],{},[1692,95364,1703],{},[902,95366,30234],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,95369,95370,95373,95374,95435,95436,1882],{},[38,95371,95372],{},"6.4"," Je dána funkce ",[883,95375,95377],{"className":95376},[886],[888,95378,95379],{"xmlns":890},[892,95380,95381,95433],{},[895,95382,95383,95385,95387,95393,95395,95401,95403,95405,95419],{},[898,95384,900],{},[1651,95386,1654],{"stretchy":1653},[1686,95388,95389,95391],{},[898,95390,1690],{},[1692,95392,1694],{},[1651,95394,1661],{"separator":1660},[1686,95396,95397,95399],{},[898,95398,1690],{},[1692,95400,1703],{},[1651,95402,1667],{"stretchy":1653},[1651,95404,1738],{},[1902,95406,95407,95409,95411],{},[898,95408,1690],{},[1692,95410,1694],{},[895,95412,95413,95415,95417],{},[1692,95414,1694],{},[898,95416,5981],{"mathvariant":1910},[1692,95418,1703],{},[1902,95420,95421,95423,95425],{},[898,95422,1690],{},[1692,95424,1703],{},[895,95426,95427,95429,95431],{},[1692,95428,1694],{},[898,95430,5981],{"mathvariant":1910},[1692,95432,1703],{},[902,95434,31156],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,95437,95439],{"className":95438},[886],[888,95440,95441],{"xmlns":890},[892,95442,95443,95533],{},[895,95444,95445,95447,95449,95455,95457,95459,95461,95463,95465,95467,95473,95475,95477,95479,95481,95483,95485,95487,95489,95495,95497,95499,95501,95503,95505,95507,95513,95515,95517,95519,95521,95523,95525,95531],{},[898,95446,900],{},[1651,95448,1654],{"stretchy":1653},[1686,95450,95451,95453],{},[898,95452,1690],{},[1692,95454,1694],{},[1651,95456,1661],{"separator":1660},[1692,95458,1694],{},[1651,95460,1667],{"stretchy":1653},[1651,95462,1661],{"separator":1660},[898,95464,900],{},[1651,95466,1654],{"stretchy":1653},[1686,95468,95469,95471],{},[898,95470,1690],{},[1692,95472,1694],{},[1651,95474,1661],{"separator":1660},[1692,95476,1703],{},[1651,95478,1667],{"stretchy":1653},[1651,95480,1661],{"separator":1660},[898,95482,900],{},[1651,95484,1654],{"stretchy":1653},[1692,95486,1694],{},[1651,95488,1661],{"separator":1660},[1686,95490,95491,95493],{},[898,95492,1690],{},[1692,95494,1703],{},[1651,95496,1667],{"stretchy":1653},[1651,95498,1661],{"separator":1660},[898,95500,900],{},[1651,95502,1654],{"stretchy":1653},[1692,95504,1703],{},[1651,95506,1661],{"separator":1660},[1686,95508,95509,95511],{},[898,95510,1690],{},[1692,95512,1703],{},[1651,95514,1667],{"stretchy":1653},[1651,95516,1661],{"separator":1660},[898,95518,900],{},[1651,95520,1654],{"stretchy":1653},[1692,95522,3521],{},[1651,95524,1661],{"separator":1660},[1686,95526,95527,95529],{},[898,95528,1690],{},[1692,95530,1703],{},[1651,95532,1667],{"stretchy":1653},[902,95534,95535],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,95537,95538,94947,95541,95585,95586,95694,95695,1343,95720,1343,95745,95787,95788,1343,95817,95842],{},[38,95539,95540],{},"6.5",[883,95542,95544],{"className":95543},[886],[888,95545,95546],{"xmlns":890},[892,95547,95548,95582],{},[895,95549,95550,95552,95554,95568],{},[898,95551,900],{},[1651,95553,1738],{},[1902,95555,95556,95558,95560],{},[898,95557,1690],{},[1692,95559,1694],{},[895,95561,95562,95564,95566],{},[1692,95563,1703],{},[898,95565,5981],{"mathvariant":1910},[1692,95567,3521],{},[1902,95569,95570,95572,95574],{},[898,95571,1690],{},[1692,95573,1703],{},[895,95575,95576,95578,95580],{},[1692,95577,1694],{},[898,95579,5981],{"mathvariant":1910},[1692,95581,3521],{},[902,95583,95584],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,95587,95589],{"className":95588},[886],[888,95590,95591],{"xmlns":890},[892,95592,95593,95691],{},[895,95594,95595,95597,95599,95605,95607,95613,95615,95617,95619,95621,95623,95625,95631,95633,95635,95637,95639,95641,95643,95649,95651,95653,95655,95657,95659,95661,95663,95665,95671,95673,95675,95677,95679,95681,95683,95689],{},[898,95596,900],{},[1651,95598,1654],{"stretchy":1653},[1686,95600,95601,95603],{},[898,95602,1690],{},[1692,95604,1694],{},[1651,95606,1661],{"separator":1660},[1686,95608,95609,95611],{},[898,95610,1690],{},[1692,95612,1703],{},[1651,95614,1667],{"stretchy":1653},[1651,95616,1738],{},[1692,95618,1703],{},[1651,95620,1661],{"separator":1660},[898,95622,900],{},[1651,95624,1654],{"stretchy":1653},[1686,95626,95627,95629],{},[898,95628,1690],{},[1692,95630,1694],{},[1651,95632,1661],{"separator":1660},[1692,95634,3521],{},[1651,95636,1667],{"stretchy":1653},[1651,95638,1661],{"separator":1660},[898,95640,900],{},[1651,95642,1654],{"stretchy":1653},[1686,95644,95645,95647],{},[898,95646,1690],{},[1692,95648,1694],{},[1651,95650,1661],{"separator":1660},[1692,95652,1703],{},[1651,95654,1667],{"stretchy":1653},[1651,95656,1661],{"separator":1660},[898,95658,900],{},[1651,95660,1654],{"stretchy":1653},[1692,95662,1703],{},[1651,95664,1661],{"separator":1660},[1686,95666,95667,95669],{},[898,95668,1690],{},[1692,95670,1703],{},[1651,95672,1667],{"stretchy":1653},[1651,95674,1661],{"separator":1660},[898,95676,900],{},[1651,95678,1654],{"stretchy":1653},[1692,95680,3521],{},[1651,95682,1661],{"separator":1660},[1686,95684,95685,95687],{},[898,95686,1690],{},[1692,95688,1703],{},[1651,95690,1667],{"stretchy":1653},[902,95692,95693],{"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 ",[883,95696,95698],{"className":95697},[886],[888,95699,95700],{"xmlns":890},[892,95701,95702,95717],{},[895,95703,95704,95706,95708,95710,95712,95715],{},[898,95705,5564],{},[1651,95707,2261],{"stretchy":1653},[1692,95709,65772],{},[1651,95711,9731],{"separator":1660},[1692,95713,95714],{},"3,555",[1651,95716,2279],{"stretchy":1653},[902,95718,95719],{"encoding":904},"A[1{,}5; 3{,}555]",[883,95721,95723],{"className":95722},[886],[888,95724,95725],{"xmlns":890},[892,95726,95727,95742],{},[895,95728,95729,95731,95733,95735,95737,95740],{},[898,95730,24466],{},[1651,95732,2261],{"stretchy":1653},[1692,95734,54412],{},[1651,95736,9731],{"separator":1660},[1692,95738,95739],{},"1,28",[1651,95741,2279],{"stretchy":1653},[902,95743,95744],{"encoding":904},"B[2{,}5; 1{,}28]",[883,95746,95748],{"className":95747},[886],[888,95749,95750],{"xmlns":890},[892,95751,95752,95784],{},[895,95753,95754,95756,95758,95760,95762,95764,95766,95772,95774,95776,95778,95780,95782],{},[898,95755,3001],{},[1651,95757,2261],{"stretchy":1653},[1692,95759,1703],{},[1651,95761,9731],{"separator":1660},[898,95763,900],{},[1651,95765,1654],{"stretchy":1653},[1686,95767,95768,95770],{},[898,95769,1690],{},[1692,95771,1694],{},[1651,95773,1661],{"separator":1660},[1692,95775,3521],{},[1651,95777,1667],{"stretchy":1653},[1651,95779,1738],{},[1692,95781,3521],{},[1651,95783,2279],{"stretchy":1653},[902,95785,95786],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,95789,95791],{"className":95790},[886],[888,95792,95793],{"xmlns":890},[892,95794,95795,95814],{},[895,95796,95797,95799,95801,95803,95805,95807,95809,95812],{},[898,95798,2047],{},[1651,95800,2261],{"stretchy":1653},[1692,95802,3521],{},[1651,95804,9731],{"separator":1660},[1692,95806,1694],{},[1651,95808,9731],{"separator":1660},[1692,95810,95811],{},"0,832",[1651,95813,2279],{"stretchy":1653},[902,95815,95816],{"encoding":904},"D[3; 1; 0{,}832]",[883,95818,95820],{"className":95819},[886],[888,95821,95822],{"xmlns":890},[892,95823,95824,95839],{},[895,95825,95826,95828,95830,95832,95834,95837],{},[898,95827,5561],{},[1651,95829,2261],{"stretchy":1653},[1692,95831,54412],{},[1651,95833,9731],{"separator":1660},[1692,95835,95836],{},"4,32",[1651,95838,2279],{"stretchy":1653},[902,95840,95841],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,95844,95845,94947,95848,95891,95892,7780,95905,95939,95940,95957,95958,95975],{},[38,95846,95847],{},"6.6",[883,95849,95851],{"className":95850},[886],[888,95852,95853],{"xmlns":890},[892,95854,95855,95889],{},[895,95856,95857,95859,95861,95875],{},[898,95858,900],{},[1651,95860,1738],{},[1902,95862,95863,95865,95867],{},[898,95864,1690],{},[1692,95866,1694],{},[895,95868,95869,95871,95873],{},[1692,95870,1703],{},[898,95872,5981],{"mathvariant":1910},[1692,95874,3521],{},[1902,95876,95877,95879,95881],{},[898,95878,1690],{},[1692,95880,1703],{},[895,95882,95883,95885,95887],{},[1692,95884,1694],{},[898,95886,5981],{"mathvariant":1910},[1692,95888,3521],{},[902,95890,95584],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,95893,95895],{"className":95894},[886],[888,95896,95897],{"xmlns":890},[892,95898,95899,95903],{},[895,95900,95901],{},[1843,95902,11903],{},[902,95904,29451],{"encoding":904},[883,95906,95908],{"className":95907},[886],[888,95909,95910],{"xmlns":890},[892,95911,95912,95936],{},[895,95913,95914,95920,95922,95924,95926,95932,95934],{},[1686,95915,95916,95918],{},[898,95917,1690],{},[1692,95919,1694],{},[1651,95921,1738],{},[1692,95923,4416],{},[1651,95925,1661],{"separator":1660},[1686,95927,95928,95930],{},[898,95929,1690],{},[1692,95931,1703],{},[1651,95933,1738],{},[1692,95935,9683],{},[902,95937,95938],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,95941,95943],{"className":95942},[886],[888,95944,95945],{"xmlns":890},[892,95946,95947,95955],{},[895,95948,95949],{},[1686,95950,95951,95953],{},[898,95952,1690],{},[1692,95954,1694],{},[902,95956,30215],{"encoding":904},", poklesne-li ",[883,95959,95961],{"className":95960},[886],[888,95962,95963],{"xmlns":890},[892,95964,95965,95973],{},[895,95966,95967],{},[1686,95968,95969,95971],{},[898,95970,1690],{},[1692,95972,1703],{},[902,95974,30234],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,95977,95978,95981,95982,95999,96000,96017,96018,96050,96051,96076,96077,96090,96091,1343,96115,1343,96139,1882],{},[38,95979,95980],{},"6.7"," Míra uspokojení z nákupu množství ",[883,95983,95985],{"className":95984},[886],[888,95986,95987],{"xmlns":890},[892,95988,95989,95997],{},[895,95990,95991],{},[1686,95992,95993,95995],{},[898,95994,1690],{},[1692,95996,1694],{},[902,95998,30215],{"encoding":904}," nealko nápojů a množství ",[883,96001,96003],{"className":96002},[886],[888,96004,96005],{"xmlns":890},[892,96006,96007,96015],{},[895,96008,96009],{},[1686,96010,96011,96013],{},[898,96012,1690],{},[1692,96014,1703],{},[902,96016,30234],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,96019,96021],{"className":96020},[886],[888,96022,96023],{"xmlns":890},[892,96024,96025,96047],{},[895,96026,96027,96029,96031],{},[898,96028,900],{},[1651,96030,1738],{},[9423,96032,96033],{},[895,96034,96035,96041],{},[1686,96036,96037,96039],{},[898,96038,1690],{},[1692,96040,1694],{},[1686,96042,96043,96045],{},[898,96044,1690],{},[1692,96046,1703],{},[902,96048,96049],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,96052,96054],{"className":96053},[886],[888,96055,96056],{"xmlns":890},[892,96057,96058,96074],{},[895,96059,96060,96066,96068],{},[1686,96061,96062,96064],{},[898,96063,1690],{},[1692,96065,1694],{},[1651,96067,1661],{"separator":1660},[1686,96069,96070,96072],{},[898,96071,1690],{},[1692,96073,1703],{},[902,96075,36835],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,96078,96080],{"className":96079},[886],[888,96081,96082],{"xmlns":890},[892,96083,96084,96088],{},[895,96085,96086],{},[1843,96087,11903],{},[902,96089,29451],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,96092,96094],{"className":96093},[886],[888,96095,96096],{"xmlns":890},[892,96097,96098,96112],{},[895,96099,96100,96102,96104,96106,96108,96110],{},[1843,96101,11903],{},[1651,96103,1654],{"stretchy":1653},[1692,96105,3574],{},[1651,96107,1661],{"separator":1660},[1692,96109,10340],{},[1651,96111,1667],{"stretchy":1653},[902,96113,96114],{"encoding":904},"\\text{MRCS}(5, 20)",[883,96116,96118],{"className":96117},[886],[888,96119,96120],{"xmlns":890},[892,96121,96122,96136],{},[895,96123,96124,96126,96128,96130,96132,96134],{},[1843,96125,11903],{},[1651,96127,1654],{"stretchy":1653},[1692,96129,10340],{},[1651,96131,1661],{"separator":1660},[1692,96133,3574],{},[1651,96135,1667],{"stretchy":1653},[902,96137,96138],{"encoding":904},"\\text{MRCS}(20, 5)",[883,96140,96142],{"className":96141},[886],[888,96143,96144],{"xmlns":890},[892,96145,96146,96160],{},[895,96147,96148,96150,96152,96154,96156,96158],{},[1843,96149,11903],{},[1651,96151,1654],{"stretchy":1653},[1692,96153,1703],{},[1651,96155,1661],{"separator":1660},[1692,96157,4446],{},[1651,96159,1667],{"stretchy":1653},[902,96161,96162],{"encoding":904},"\\text{MRCS}(2, 50)",[5179,96164,96165],{},[724,96166,96167,96169,96170,1882],{},[883,96168,5879],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,96171,96174],{"className":96172,"dataFsResolvedFilePath":911,"href":96173},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,96176,17018],{"id":17017},[120,96178,96179,96185,96190,96196,96249,96259,96305,96360,96423,96480,96535,96574],{},[123,96180,96181,96184],{},[38,96182,96183],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,96186,96187,96189],{},[38,96188,88082],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,96191,96192,96195],{},[38,96193,96194],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,96197,96198,96200,96201,96214,96215,1882],{},[38,96199,88409],{}," — uspořádaná ",[883,96202,96204],{"className":96203},[886],[888,96205,96206],{"xmlns":890},[892,96207,96208,96212],{},[895,96209,96210],{},[898,96211,38073],{},[902,96213,38073],{"encoding":904},"-tice ",[883,96216,96218],{"className":96217},[886],[888,96219,96220],{"xmlns":890},[892,96221,96222,96246],{},[895,96223,96224,96226,96232,96234,96236,96238,96244],{},[1651,96225,1654],{"stretchy":1653},[1686,96227,96228,96230],{},[898,96229,1690],{},[1692,96231,1694],{},[1651,96233,1661],{"separator":1660},[1651,96235,10949],{},[1651,96237,1661],{"separator":1660},[1686,96239,96240,96242],{},[898,96241,1690],{},[898,96243,38073],{},[1651,96245,1667],{"stretchy":1653},[902,96247,96248],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,96250,96251,96254,96255,96258],{},[38,96252,96253],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,96256,96257],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,96260,96261,3246,96264,96304],{},[38,96262,96263],{},"Funkce užitečnosti",[883,96265,96267],{"className":96266},[886],[888,96268,96269],{"xmlns":890},[892,96270,96271,96301],{},[895,96272,96273,96275,96277,96279,96281,96287,96289,96291,96293,96299],{},[898,96274,900],{},[1651,96276,1738],{},[898,96278,900],{},[1651,96280,1654],{"stretchy":1653},[1686,96282,96283,96285],{},[898,96284,1690],{},[1692,96286,1694],{},[1651,96288,1661],{"separator":1660},[1651,96290,10949],{},[1651,96292,1661],{"separator":1660},[1686,96294,96295,96297],{},[898,96296,1690],{},[898,96298,38073],{},[1651,96300,1667],{"stretchy":1653},[902,96302,96303],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,96306,96307,3246,96310,96339,96340,3246,96343,96359],{},[38,96308,96309],{},"Mezní užitečnost",[883,96311,96313],{"className":96312},[886],[888,96314,96315],{"xmlns":890},[892,96316,96317,96337],{},[895,96318,96319,96321,96327,96329],{},[898,96320,2995],{},[1686,96322,96323,96325],{},[898,96324,900],{},[898,96326,3201],{},[1651,96328,1738],{},[1902,96330,96331,96333,96335],{},[898,96332,900],{},[898,96334,3201],{},[1651,96336,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[902,96338,87866],{"encoding":904}," — vzorec (6.2); ",[38,96341,96342],{},"totální diferenciál",[883,96344,96346],{"className":96345},[886],[888,96347,96348],{"xmlns":890},[892,96349,96350,96356],{},[895,96351,96352,96354],{},[898,96353,3542],{"mathvariant":1910},[898,96355,900],{},[902,96357,96358],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,96361,96362,96364,96365,96389,96390,96422],{},[38,96363,90045],{}," — (6.4) ",[883,96366,96368],{"className":96367},[886],[888,96369,96370],{"xmlns":890},[892,96371,96372,96386],{},[895,96373,96374,96382,96384],{},[1902,96375,96376,96378,96380],{},[898,96377,900],{},[898,96379,3201],{},[1651,96381,1912],{"mathvariant":1910,"lspace":1911,"rspace":1911},[1651,96383,2390],{},[1692,96385,1741],{},[902,96387,96388],{"encoding":904},"U'_i > 0",", (6.5) ",[883,96391,96393],{"className":96392},[886],[888,96394,96395],{"xmlns":890},[892,96396,96397,96419],{},[895,96398,96399,96415,96417],{},[1902,96400,96401,96403,96409],{},[898,96402,900],{},[895,96404,96405,96407],{},[898,96406,3201],{},[898,96408,3201],{},[895,96410,96411,96413],{},[1651,96412,1912],{"mathvariant":1910},[1651,96414,1912],{"mathvariant":1910},[1651,96416,2319],{},[1692,96418,1741],{},[902,96420,96421],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,96424,96425,3246,96427,96458,96459,1882],{},[38,96426,91833],{},[883,96428,96430],{"className":96429},[886],[888,96431,96432],{"xmlns":890},[892,96433,96434,96456],{},[895,96435,96436,96438,96440,96448],{},[898,96437,900],{},[1651,96439,1738],{},[1902,96441,96442,96444,96446],{},[898,96443,1690],{},[1692,96445,1694],{},[898,96447,207],{},[1902,96449,96450,96452,96454],{},[898,96451,1690],{},[1692,96453,1703],{},[898,96455,2268],{},[902,96457,37016],{"encoding":904}," — (6.6), speciálně ",[883,96460,96462],{"className":96461},[886],[888,96463,96464],{"xmlns":890},[892,96465,96466,96478],{},[895,96467,96468,96470,96472,96474,96476],{},[898,96469,2268],{},[1651,96471,1738],{},[1692,96473,1694],{},[1651,96475,2181],{},[898,96477,207],{},[902,96479,91987],{"encoding":904},[123,96481,96482,3246,96485,96520,96521,96534],{},[38,96483,96484],{},"Křivky užitečnosti (indiferenční)",[883,96486,96488],{"className":96487},[886],[888,96489,96490],{"xmlns":890},[892,96491,96492,96518],{},[895,96493,96494,96496,96498,96504,96506,96512,96514,96516],{},[898,96495,900],{},[1651,96497,1654],{"stretchy":1653},[1686,96499,96500,96502],{},[898,96501,1690],{},[1692,96503,1694],{},[1651,96505,1661],{"separator":1660},[1686,96507,96508,96510],{},[898,96509,1690],{},[1692,96511,1703],{},[1651,96513,1667],{"stretchy":1653},[1651,96515,1738],{},[898,96517,3490],{},[902,96519,11071],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,96522,96524],{"className":96523},[886],[888,96525,96526],{"xmlns":890},[892,96527,96528,96532],{},[895,96529,96530],{},[898,96531,900],{},[902,96533,900],{"encoding":904},", konvexní.",[123,96536,96537,3246,96539,96573],{},[38,96538,93378],{},[883,96540,96542],{"className":96541},[886],[888,96543,96544],{"xmlns":890},[892,96545,96546,96570],{},[895,96547,96548,96550,96552,96554,96560,96562,96564],{},[1843,96549,11903],{},[1651,96551,1738],{},[898,96553,2995],{},[1686,96555,96556,96558],{},[898,96557,900],{},[1692,96559,1694],{},[898,96561,5981],{"mathvariant":1910},[898,96563,2995],{},[1686,96565,96566,96568],{},[898,96567,900],{},[1692,96569,1703],{},[902,96571,96572],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,96575,96576,3246,96579,11072,96608,96611],{},[38,96577,96578],{},"Podmínka optimality",[883,96580,96582],{"className":96581},[886],[888,96583,96584],{"xmlns":890},[892,96585,96586,96606],{},[895,96587,96588,96590,96592,96598,96600],{},[1843,96589,11903],{},[1651,96591,1738],{},[1686,96593,96594,96596],{},[898,96595,2675],{},[1692,96597,1694],{},[898,96599,5981],{"mathvariant":1910},[1686,96601,96602,96604],{},[898,96603,2675],{},[1692,96605,1703],{},[902,96607,29211],{"encoding":904},[207,96609,37967],{"className":96610,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,96613,3238],{"id":3237},[120,96615,96616,96653,96694,96704],{},[123,96617,96618,3246,96621,96624,96625,96638,96639,96652],{},[38,96619,96620],{},"Navazující téma:",[207,96622,913],{"className":96623,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,96626,96628],{"className":96627},[886],[888,96629,96630],{"xmlns":890},[892,96631,96632,96636],{},[895,96633,96634],{},[898,96635,900],{},[902,96637,900],{"encoding":904},", min ",[883,96640,96642],{"className":96641},[886],[888,96643,96644],{"xmlns":890},[892,96645,96646,96650],{},[895,96647,96648],{},[898,96649,5561],{},[902,96651,5561],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,96654,96655,3246,96658,12390,96661,87621,96664,96667,96668,96671,96672,19861,96690,96693],{},[38,96656,96657],{},"Související pojmy:",[207,96659,784],{"className":96660,"dataFsResolvedFilePath":782,"href":783},[210],[207,96662,3695],{"className":96663,"dataFsResolvedFilePath":764,"href":765},[210],[207,96665,12385],{"className":96666,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,96669,3258],{"className":96670,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,96673,96675],{"className":96674},[886],[888,96676,96677],{"xmlns":890},[892,96678,96679,96687],{},[895,96680,96681],{},[1686,96682,96683,96685],{},[898,96684,2047],{},[898,96686,3201],{},[902,96688,96689],{"encoding":904},"D_i",[207,96691,793],{"className":96692,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,96695,96696,3246,96698,1343,96701],{},[38,96697,37916],{},[207,96699,1094],{"className":96700,"dataFsResolvedFilePath":838,"href":839},[210],[207,96702,1101],{"className":96703,"dataFsResolvedFilePath":868,"href":869},[210],[123,96705,96706,3246,96708],{},[38,96707,17502],{},[207,96709,17506],{"className":96710,"dataFsResolvedFilePath":1749,"href":1750},[210],{"title":641,"searchDepth":642,"depth":642,"links":96712},[96713,96714,96715,96718,96719,96722,96726,96727,96730,96731,96732,96733,96734,96735,96736],{"id":13303,"depth":642,"text":13304},{"id":88005,"depth":642,"text":88006},{"id":88065,"depth":642,"text":88066,"children":96716},[96717],{"id":88081,"depth":649,"text":88082},{"id":88388,"depth":642,"text":88389},{"id":89248,"depth":642,"text":89249,"children":96720},[96721],{"id":89795,"depth":649,"text":81424},{"id":90044,"depth":642,"text":90045,"children":96723},[96724],{"id":90917,"depth":649,"text":96725},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":91832,"depth":642,"text":91833},{"id":92368,"depth":642,"text":92369,"children":96728},[96729],{"id":93142,"depth":649,"text":93143},{"id":93372,"depth":642,"text":93373},{"id":94133,"depth":642,"text":94134},{"id":94671,"depth":642,"text":94672},{"id":51094,"depth":642,"text":51095},{"id":94807,"depth":642,"text":94808},{"id":17017,"depth":642,"text":17018},{"id":3237,"depth":642,"text":3238},{},"\u002Ftopics\u002Fuzitecnost",{"title":87789,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,1773,96743,87783,12420,96744],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":96747,"title":757,"body":96748,"course":1128,"courses":659,"created":1129,"description":97021,"extension":661,"meta":97022,"navigation":664,"path":97023,"seo":97024,"sources":97025,"stem":97026,"tags":97027,"type":3302,"updated":677,"__hash__":97033},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":96749,"toc":97013},[96750,96753,96760,96767,96771,96781,96783,96817,96821,96864,96867,96925,96929,96959,96963,96984,96986],[12,96751,757],{"id":96752},"základy-matematické-ekonomie",[724,96754,96755,96756,96759],{},"Úvodní pojmy a princip modelování v ",[207,96757,1751],{"className":96758,"dataFsResolvedFilePath":1749,"href":1750},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,96761,96762],{},[1756,96763],{"alt":96764,"className":96765,"src":96766},"imek-model-promenne",[210,1760],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,96768,96770],{"id":96769},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,96772,96773,96776,96777,96780],{},[38,96774,96775],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,96778,96779],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,96782,17018],{"id":17017},[120,96784,96785,96791,96797,96803,96812],{},[123,96786,96787,96790],{},[38,96788,96789],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,96792,96793,96796],{},[38,96794,96795],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,96798,96799,96802],{},[38,96800,96801],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,96804,96805,8322,96808,96811],{},[38,96806,96807],{},"Ceteris paribus",[614,96809,96810],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,96813,96814,96816],{},[38,96815,51848],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,96818,96820],{"id":96819},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,96822,96823,96863],{},[883,96824,96826],{"className":96825},[886],[888,96827,96828],{"xmlns":890},[892,96829,96830,96860],{},[895,96831,96832,96834,96836,96838,96840,96842,96844,96846,96848,96850,96852,96854,96856,96858],{},[898,96833,1690],{},[1651,96835,1738],{},[898,96837,2047],{},[1651,96839,1654],{"stretchy":1653},[898,96841,2675],{},[1651,96843,1661],{"separator":1660},[898,96845,2665],{},[1651,96847,1661],{"separator":1660},[898,96849,19507],{},[1651,96851,1661],{"separator":1660},[898,96853,900],{},[1651,96855,1661],{"separator":1660},[1651,96857,10949],{},[1651,96859,1667],{"stretchy":1653},[902,96861,96862],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,96865,96866],{},"Zjednodušení:",[120,96868,96869,96897],{},[123,96870,96871,3246,96874],{},[38,96872,96873],{},"Jednofaktorový model:",[883,96875,96877],{"className":96876},[886],[888,96878,96879],{"xmlns":890},[892,96880,96881,96895],{},[895,96882,96883,96885,96887,96889,96891,96893],{},[898,96884,1690],{},[1651,96886,1738],{},[898,96888,2047],{},[1651,96890,1654],{"stretchy":1653},[898,96892,2675],{},[1651,96894,1667],{"stretchy":1653},[902,96896,5501],{"encoding":904},[123,96898,96899,3246,96902],{},[38,96900,96901],{},"Inverzní zápis:",[883,96903,96905],{"className":96904},[886],[888,96906,96907],{"xmlns":890},[892,96908,96909,96923],{},[895,96910,96911,96913,96915,96917,96919,96921],{},[898,96912,2675],{},[1651,96914,1738],{},[898,96916,2047],{},[1651,96918,1654],{"stretchy":1653},[898,96920,1690],{},[1651,96922,1667],{"stretchy":1653},[902,96924,5947],{"encoding":904},[115,96926,96928],{"id":96927},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,96930,96931,96940],{},[123,96932,96933,96936,96937,5230],{},[38,96934,96935],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,96938,17538],{"className":96939,"dataFsResolvedFilePath":800,"href":801},[210],[123,96941,96942,96945,96946,96949,96950,96953,96954,96958],{},[38,96943,96944],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,96947,1145],{"className":96948,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,96951,17551],{"className":96952,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,96955,96957],{"className":96956,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,96960,96962],{"id":96961},"konvence-z-přednášek","Konvence z přednášek",[120,96964,96965,96972,96978],{},[123,96966,96967,96968,96971],{},"Symbol ",[96969,96970,4060],"code",{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,96973,96974,96975,1882],{},"Numerické výsledky ",[38,96976,96977],{},"na 3 desetinná místa",[123,96979,5207,96980,96983],{},[614,96981,96982],{},"jednotková změna"," má standardní význam (změna o 1).",[115,96985,3238],{"id":3237},[120,96987,96988,96993,97001],{},[123,96989,96990,96992],{},[38,96991,3245],{}," —",[123,96994,96995,3246,96997],{},[38,96996,3254],{},[207,96998,97000],{"className":96999,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,97002,97003,3246,97005,1343,97009],{},[38,97004,3272],{},[207,97006,97008],{"className":97007,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,97010,97012],{"className":97011,"dataFsResolvedFilePath":1749,"href":1750},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":97014},[97015,97016,97017,97018,97019,97020],{"id":96769,"depth":642,"text":96770},{"id":17017,"depth":642,"text":17018},{"id":96819,"depth":642,"text":96820},{"id":96927,"depth":642,"text":96928},{"id":96961,"depth":642,"text":96962},{"id":3237,"depth":642,"text":3238},"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":97021},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,97028,97029,97030,97031,97032],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":97035,"title":97036,"body":97037,"course":1128,"courses":659,"created":10859,"description":641,"extension":661,"meta":101309,"navigation":664,"path":101310,"seo":101311,"sources":101312,"stem":101313,"tags":101314,"type":3302,"updated":677,"__hash__":101318},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":97038,"toc":101292},[97039,97042,97136,97140,97162,97176,97228,97230,97234,97297,97340,97359,97522,97621,97624,97691,97695,97824,97863,97893,98005,98050,98116,98169,98245,98301,98303,98307,98371,98415,98435,98596,98599,98683,98780,98783,98849,98853,98902,98928,99033,99097,99102,99198,99245,99247,99250,99272,99314,99321,99354,99356,99427,99481,99590,99594,99683,99759,100023,100061,100063,100067,100070,100077,100388,100391,100449,100629,100658,100660,100664,100670,100808,100817,100819,100821,101246,101248,101250],[12,97040,97036],{"id":97041},"zdanění-trhu-dopady-daně-na-rovnováhu",[5179,97043,97044],{},[724,97045,97046,43841,97048,97061,97062,97065,97066,97068,97069,97072,97073,97094,97095,97118,97119,97122,97123,1882],{},[883,97047,5465],{},[883,97049,97051],{"className":97050},[886],[888,97052,97053],{"xmlns":890},[892,97054,97055,97059],{},[895,97056,97057],{},[898,97058,4104],{},[902,97060,4104],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,97063,97064],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,97067,88073],{}," (je-li uložena spotřebiteli). Výsledné ",[38,97070,97071],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,97074,97076],{"className":97075},[886],[888,97077,97078],{"xmlns":890},[892,97079,97080,97092],{},[895,97081,97082],{},[1686,97083,97084,97086],{},[898,97085,4104],{},[895,97087,97088,97090],{},[898,97089,43890],{},[898,97091,724],{},[902,97093,43895],{"encoding":904}," (spotřebitel) a ",[883,97096,97098],{"className":97097},[886],[888,97099,97100],{"xmlns":890},[892,97101,97102,97116],{},[895,97103,97104],{},[1686,97105,97106,97108],{},[898,97107,4104],{},[895,97109,97110,97112,97114],{},[898,97111,43913],{},[898,97113,1664],{},[898,97115,13339],{},[902,97117,43920],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,97120,97121],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,97124,97126],{"className":97125},[886],[888,97127,97128],{"xmlns":890},[892,97129,97130,97134],{},[895,97131,97132],{},[898,97133,4104],{},[902,97135,4104],{"encoding":904},[115,97137,97139],{"id":97138},"dvě-formy-zdanění","Dvě formy zdanění",[724,97141,97142,97143,97161],{},"Uvažujme jednotkovou daň ",[883,97144,97146],{"className":97145},[886],[888,97147,97148],{"xmlns":890},[892,97149,97150,97158],{},[895,97151,97152,97154,97156],{},[898,97153,4104],{},[1651,97155,2390],{},[1692,97157,1741],{},[902,97159,97160],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,97163,97164,97170],{},[123,97165,97166,97169],{},[38,97167,97168],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,97171,97172,97175],{},[38,97173,97174],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,97177,97178,97179,97192,97193,97196,97197,1882],{},"V obou případech dochází k posunu jedné z křivek o ",[883,97180,97182],{"className":97181},[886],[888,97183,97184],{"xmlns":890},[892,97185,97186,97190],{},[895,97187,97188],{},[898,97189,4104],{},[902,97191,4104],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,97194,97195],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,97198,97200],{"className":97199},[886],[888,97201,97202],{"xmlns":890},[892,97203,97204,97226],{},[895,97205,97206,97208,97210,97216,97218,97224],{},[898,97207,5561],{},[1651,97209,2261],{"stretchy":1653},[2115,97211,97212,97214],{},[898,97213,1690],{},[898,97215,5561],{},[1651,97217,1661],{"separator":1660},[2115,97219,97220,97222],{},[898,97221,2675],{},[898,97223,5561],{},[1651,97225,2279],{"stretchy":1653},[902,97227,42580],{"encoding":904},[38183,97229],{},[115,97231,97233],{"id":97232},"daň-uložená-výrobci","Daň uložená výrobci",[724,97235,97236,97237,97250,97251,97268,97269,97296],{},"Je-li daň ",[883,97238,97240],{"className":97239},[886],[888,97241,97242],{"xmlns":890},[892,97243,97244,97248],{},[895,97245,97246],{},[898,97247,4104],{},[902,97249,4104],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,97252,97254],{"className":97253},[886],[888,97255,97256],{"xmlns":890},[892,97257,97258,97266],{},[895,97259,97260,97262,97264],{},[898,97261,2675],{},[1651,97263,2181],{},[898,97265,4104],{},[902,97267,42335],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,97270,97272],{"className":97271},[886],[888,97273,97274],{"xmlns":890},[892,97275,97276,97294],{},[895,97277,97278,97280,97282,97284,97286,97288,97290,97292],{},[898,97279,2675],{},[1651,97281,2181],{},[898,97283,4104],{},[1651,97285,1738],{},[898,97287,3004],{},[1651,97289,1654],{"stretchy":1653},[898,97291,1690],{},[1651,97293,1667],{"stretchy":1653},[902,97295,42364],{"encoding":904}," nová funkce nabídky:",[883,97298,97300],{"className":97299},[886],[888,97301,97302],{"xmlns":890,"display":29279},[892,97303,97304,97338],{},[895,97305,97306,97308,97310,97316,97318,97320,97322,97324,97326,97328,97330,97332,97334,97336],{},[898,97307,2675],{},[1651,97309,1738],{},[1686,97311,97312,97314],{},[898,97313,3004],{},[1692,97315,1694],{},[1651,97317,1654],{"stretchy":1653},[898,97319,1690],{},[1651,97321,1667],{"stretchy":1653},[1651,97323,1738],{},[898,97325,3004],{},[1651,97327,1654],{"stretchy":1653},[898,97329,1690],{},[1651,97331,1667],{"stretchy":1653},[1651,97333,1839],{},[898,97335,4104],{},[898,97337,1882],{"mathvariant":1910},[902,97339,42409],{"encoding":904},[724,97341,97342,97343,3246,97356,97358],{},"Nabídka se tedy posouvá o ",[883,97344,97346],{"className":97345},[886],[888,97347,97348],{"xmlns":890},[892,97349,97350,97354],{},[895,97351,97352],{},[898,97353,4104],{},[902,97355,4104],{"encoding":904},[38,97357,42442],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,97360,97361,97362,97402,97403,5197,97431,97459,97460,97479,97480,97504,97505,5230],{},"Nový rovnovážný bod ",[883,97363,97365],{"className":97364},[886],[888,97366,97367],{"xmlns":890},[892,97368,97369,97399],{},[895,97370,97371,97377,97379,97387,97389,97397],{},[1686,97372,97373,97375],{},[898,97374,5561],{},[1692,97376,1694],{},[1651,97378,2261],{"stretchy":1653},[1902,97380,97381,97383,97385],{},[898,97382,1690],{},[1692,97384,1694],{},[898,97386,5561],{},[1651,97388,1661],{"separator":1660},[1902,97390,97391,97393,97395],{},[898,97392,2675],{},[1692,97394,1694],{},[898,97396,5561],{},[1651,97398,2279],{"stretchy":1653},[902,97400,97401],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,97404,97406],{"className":97405},[886],[888,97407,97408],{"xmlns":890},[892,97409,97410,97428],{},[895,97411,97412,97420,97422],{},[1902,97413,97414,97416,97418],{},[898,97415,1690],{},[1692,97417,1694],{},[898,97419,5561],{},[1651,97421,2319],{},[2115,97423,97424,97426],{},[898,97425,1690],{},[898,97427,5561],{},[902,97429,97430],{"encoding":904},"Q_1^E \u003C Q^E",[883,97432,97434],{"className":97433},[886],[888,97435,97436],{"xmlns":890},[892,97437,97438,97456],{},[895,97439,97440,97448,97450],{},[1902,97441,97442,97444,97446],{},[898,97443,2675],{},[1692,97445,1694],{},[898,97447,5561],{},[1651,97449,2390],{},[2115,97451,97452,97454],{},[898,97453,2675],{},[898,97455,5561],{},[902,97457,97458],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,97461,97463],{"className":97462},[886],[888,97464,97465],{"xmlns":890},[892,97466,97467,97477],{},[895,97468,97469],{},[1902,97470,97471,97473,97475],{},[898,97472,2675],{},[1692,97474,1694],{},[898,97476,5561],{},[902,97478,49070],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,97481,97483],{"className":97482},[886],[888,97484,97485],{"xmlns":890},[892,97486,97487,97501],{},[895,97488,97489,97497,97499],{},[1902,97490,97491,97493,97495],{},[898,97492,2675],{},[1692,97494,1694],{},[898,97496,5561],{},[1651,97498,2181],{},[898,97500,4104],{},[902,97502,97503],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,97506,97508],{"className":97507},[886],[888,97509,97510],{"xmlns":890},[892,97511,97512,97520],{},[895,97513,97514],{},[2115,97515,97516,97518],{},[898,97517,2675],{},[898,97519,5561],{},[902,97521,42679],{"encoding":904},[724,97523,97524],{},[614,97525,97526,97527,97557,97558,97571,97572,6976,97589,97602,97603,1882],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,97528,97530],{"className":97529},[886],[888,97531,97532],{"xmlns":890},[892,97533,97534,97554],{},[895,97535,97536,97538,97540,97546,97548,97550,97552],{},[898,97537,3004],{},[1651,97539,4449],{},[1686,97541,97542,97544],{},[898,97543,3004],{},[1692,97545,1694],{},[1651,97547,1738],{},[898,97549,3004],{},[1651,97551,1839],{},[898,97553,4104],{},[902,97555,97556],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,97559,97561],{"className":97560},[886],[888,97562,97563],{"xmlns":890},[892,97564,97565,97569],{},[895,97566,97567],{},[898,97568,4104],{},[902,97570,4104],{"encoding":904},". Průsečík ",[883,97573,97575],{"className":97574},[886],[888,97576,97577],{"xmlns":890},[892,97578,97579,97587],{},[895,97580,97581],{},[1686,97582,97583,97585],{},[898,97584,3004],{},[1692,97586,1694],{},[902,97588,42210],{"encoding":904},[883,97590,97592],{"className":97591},[886],[888,97593,97594],{"xmlns":890},[892,97595,97596,97600],{},[895,97597,97598],{},[898,97599,2047],{},[902,97601,2047],{"encoding":904}," je nový rovnovážný bod ",[883,97604,97606],{"className":97605},[886],[888,97607,97608],{"xmlns":890},[892,97609,97610,97618],{},[895,97611,97612],{},[1686,97613,97614,97616],{},[898,97615,5561],{},[1692,97617,1694],{},[902,97619,97620],{"encoding":904},"E_1",[198,97622,46516],{"id":97623},"příklad-29",[724,97625,97626,42868,97628,42903,97652,97672,97673,97690],{},[38,97627,39146],{},[883,97629,97631],{"className":97630},[886],[888,97632,97633],{"xmlns":890},[892,97634,97635,97649],{},[895,97636,97637,97639,97641,97643,97645,97647],{},[898,97638,2675],{},[1651,97640,1738],{},[1692,97642,4828],{},[1651,97644,2181],{},[1692,97646,1703],{},[898,97648,1690],{},[902,97650,97651],{"encoding":904},"P = 12 - 2Q",[883,97653,97655],{"className":97654},[886],[888,97656,97657],{"xmlns":890},[892,97658,97659,97669],{},[895,97660,97661,97663,97665,97667],{},[898,97662,2675],{},[1651,97664,1738],{},[1692,97666,3689],{},[898,97668,1690],{},[902,97670,97671],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,97674,97676],{"className":97675},[886],[888,97677,97678],{"xmlns":890},[892,97679,97680,97688],{},[895,97681,97682,97684,97686],{},[898,97683,4104],{},[1651,97685,1738],{},[1692,97687,3581],{},[902,97689,42481],{"encoding":904}," Kč.",[724,97692,97693],{},[38,97694,39178],{},[724,97696,97697,97700,97701,6876,97727,6896,97747,1343,97769,97799,97800,1882],{},[614,97698,97699],{},"Bez daně."," Z rovnosti ",[883,97702,97704],{"className":97703},[886],[888,97705,97706],{"xmlns":890},[892,97707,97708,97724],{},[895,97709,97710,97712,97714,97716,97718,97720,97722],{},[1692,97711,4828],{},[1651,97713,2181],{},[1692,97715,1703],{},[898,97717,1690],{},[1651,97719,1738],{},[1692,97721,3689],{},[898,97723,1690],{},[902,97725,97726],{"encoding":904},"12 - 2Q = 4Q",[883,97728,97730],{"className":97729},[886],[888,97731,97732],{"xmlns":890},[892,97733,97734,97744],{},[895,97735,97736,97738,97740,97742],{},[1692,97737,3581],{},[898,97739,1690],{},[1651,97741,1738],{},[1692,97743,4828],{},[902,97745,97746],{"encoding":904},"6Q = 12",[883,97748,97750],{"className":97749},[886],[888,97751,97752],{"xmlns":890},[892,97753,97754,97766],{},[895,97755,97756,97762,97764],{},[2115,97757,97758,97760],{},[898,97759,1690],{},[898,97761,5561],{},[1651,97763,1738],{},[1692,97765,1703],{},[902,97767,97768],{"encoding":904},"Q^E = 2",[883,97770,97772],{"className":97771},[886],[888,97773,97774],{"xmlns":890},[892,97775,97776,97796],{},[895,97777,97778,97784,97786,97788,97790,97792,97794],{},[2115,97779,97780,97782],{},[898,97781,2675],{},[898,97783,5561],{},[1651,97785,1738],{},[1692,97787,3689],{},[1651,97789,4503],{},[1692,97791,1703],{},[1651,97793,1738],{},[1692,97795,6892],{},[902,97797,97798],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,97801,97803],{"className":97802},[886],[888,97804,97805],{"xmlns":890},[892,97806,97807,97821],{},[895,97808,97809,97811,97813,97815,97817,97819],{},[898,97810,5561],{},[1651,97812,2261],{"stretchy":1653},[1692,97814,1703],{},[1651,97816,1661],{"separator":1660},[1692,97818,6892],{},[1651,97820,2279],{"stretchy":1653},[902,97822,97823],{"encoding":904},"E[2, 8]",[724,97825,97826,97829,97830,97862],{},[614,97827,97828],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,97831,97833],{"className":97832},[886],[888,97834,97835],{"xmlns":890},[892,97836,97837,97859],{},[895,97838,97839,97845,97847,97849,97851,97853,97855,97857],{},[1686,97840,97841,97843],{},[898,97842,3004],{},[1692,97844,1694],{},[1651,97846,1793],{},[898,97848,2675],{},[1651,97850,1738],{},[1692,97852,3689],{},[898,97854,1690],{},[1651,97856,1839],{},[1692,97858,3581],{},[902,97860,97861],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,97864,97866],{"className":97865},[886],[888,97867,97868],{"xmlns":890,"display":29279},[892,97869,97870,97890],{},[895,97871,97872,97874,97876,97878,97880,97882,97884,97886,97888],{},[1692,97873,4828],{},[1651,97875,2181],{},[1692,97877,1703],{},[898,97879,1690],{},[1651,97881,1738],{},[1692,97883,3689],{},[898,97885,1690],{},[1651,97887,1839],{},[1692,97889,3581],{},[902,97891,97892],{"encoding":904},"12 - 2Q = 4Q + 6",[724,97894,97895,97896,6896,97916,1343,97940,97976,97977,1882],{},"plyne ",[883,97897,97899],{"className":97898},[886],[888,97900,97901],{"xmlns":890},[892,97902,97903,97913],{},[895,97904,97905,97907,97909,97911],{},[1692,97906,3581],{},[898,97908,1690],{},[1651,97910,1738],{},[1692,97912,3581],{},[902,97914,97915],{"encoding":904},"6Q = 6",[883,97917,97919],{"className":97918},[886],[888,97920,97921],{"xmlns":890},[892,97922,97923,97937],{},[895,97924,97925,97933,97935],{},[1902,97926,97927,97929,97931],{},[898,97928,1690],{},[1692,97930,1694],{},[898,97932,5561],{},[1651,97934,1738],{},[1692,97936,1694],{},[902,97938,97939],{"encoding":904},"Q_1^E = 1",[883,97941,97943],{"className":97942},[886],[888,97944,97945],{"xmlns":890},[892,97946,97947,97973],{},[895,97948,97949,97957,97959,97961,97963,97965,97967,97969,97971],{},[1902,97950,97951,97953,97955],{},[898,97952,2675],{},[1692,97954,1694],{},[898,97956,5561],{},[1651,97958,1738],{},[1692,97960,3689],{},[1651,97962,4503],{},[1692,97964,1694],{},[1651,97966,1839],{},[1692,97968,3581],{},[1651,97970,1738],{},[1692,97972,4190],{},[902,97974,97975],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,97978,97980],{"className":97979},[886],[888,97981,97982],{"xmlns":890},[892,97983,97984,98002],{},[895,97985,97986,97992,97994,97996,97998,98000],{},[1686,97987,97988,97990],{},[898,97989,5561],{},[1692,97991,1694],{},[1651,97993,2261],{"stretchy":1653},[1692,97995,1694],{},[1651,97997,1661],{"separator":1660},[1692,97999,4190],{},[1651,98001,2279],{"stretchy":1653},[902,98003,98004],{"encoding":904},"E_1[1, 10]",[724,98006,98007,98010,98011,98035,98036,98049],{},[614,98008,98009],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,98012,98014],{"className":98013},[886],[888,98015,98016],{"xmlns":890},[892,98017,98018,98032],{},[895,98019,98020,98028,98030],{},[1902,98021,98022,98024,98026],{},[898,98023,2675],{},[1692,98025,1694],{},[898,98027,5561],{},[1651,98029,1738],{},[1692,98031,4190],{},[902,98033,98034],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,98037,98039],{"className":98038},[886],[888,98040,98041],{"xmlns":890},[892,98042,98043,98047],{},[895,98044,98045],{},[1692,98046,6892],{},[902,98048,6892],{"encoding":904},", navýšení je",[883,98051,98053],{"className":98052},[886],[888,98054,98055],{"xmlns":890,"display":29279},[892,98056,98057,98113],{},[895,98058,98059,98069,98071,98079,98081,98087,98089,98091,98093,98095,98097,98099,98101,98111],{},[1686,98060,98061,98063],{},[898,98062,4104],{},[895,98064,98065,98067],{},[898,98066,43890],{},[898,98068,724],{},[1651,98070,1738],{},[1902,98072,98073,98075,98077],{},[898,98074,2675],{},[1692,98076,1694],{},[898,98078,5561],{},[1651,98080,2181],{},[2115,98082,98083,98085],{},[898,98084,2675],{},[898,98086,5561],{},[1651,98088,1738],{},[1692,98090,4190],{},[1651,98092,2181],{},[1692,98094,6892],{},[1651,98096,1738],{},[1692,98098,1703],{},[1843,98100,3631],{},[895,98102,98103,98105],{},[1843,98104,11101],{},[9692,98106,98107,98109],{"accent":1660},[1843,98108,3490],{},[1651,98110,26271],{},[898,98112,1882],{"mathvariant":1910},[902,98114,98115],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,98117,98118,98119,98035,98155,98168],{},"Výrobci zůstává čistá cena ",[883,98120,98122],{"className":98121},[886],[888,98123,98124],{"xmlns":890},[892,98125,98126,98152],{},[895,98127,98128,98136,98138,98140,98142,98144,98146,98148,98150],{},[1902,98129,98130,98132,98134],{},[898,98131,2675],{},[1692,98133,1694],{},[898,98135,5561],{},[1651,98137,2181],{},[898,98139,4104],{},[1651,98141,1738],{},[1692,98143,4190],{},[1651,98145,2181],{},[1692,98147,3581],{},[1651,98149,1738],{},[1692,98151,3689],{},[902,98153,98154],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,98156,98158],{"className":98157},[886],[888,98159,98160],{"xmlns":890},[892,98161,98162,98166],{},[895,98163,98164],{},[1692,98165,6892],{},[902,98167,6892],{"encoding":904},", pokles je",[883,98170,98172],{"className":98171},[886],[888,98173,98174],{"xmlns":890,"display":29279},[892,98175,98176,98242],{},[895,98177,98178,98190,98192,98198,98200,98202,98210,98212,98214,98216,98218,98220,98222,98224,98226,98228,98230,98240],{},[1686,98179,98180,98182],{},[898,98181,4104],{},[895,98183,98184,98186,98188],{},[898,98185,43913],{},[898,98187,1664],{},[898,98189,13339],{},[1651,98191,1738],{},[2115,98193,98194,98196],{},[898,98195,2675],{},[898,98197,5561],{},[1651,98199,2181],{},[1651,98201,1654],{"stretchy":1653},[1902,98203,98204,98206,98208],{},[898,98205,2675],{},[1692,98207,1694],{},[898,98209,5561],{},[1651,98211,2181],{},[898,98213,4104],{},[1651,98215,1667],{"stretchy":1653},[1651,98217,1738],{},[1692,98219,6892],{},[1651,98221,2181],{},[1692,98223,3689],{},[1651,98225,1738],{},[1692,98227,3689],{},[1843,98229,3631],{},[895,98231,98232,98234],{},[1843,98233,11101],{},[9692,98235,98236,98238],{"accent":1660},[1843,98237,3490],{},[1651,98239,26271],{},[898,98241,1882],{"mathvariant":1910},[902,98243,98244],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,98246,98247,98248,98300],{},"Kontrola: ",[883,98249,98251],{"className":98250},[886],[888,98252,98253],{"xmlns":890},[892,98254,98255,98297],{},[895,98256,98257,98267,98269,98281,98283,98285,98287,98289,98291,98293,98295],{},[1686,98258,98259,98261],{},[898,98260,4104],{},[895,98262,98263,98265],{},[898,98264,43890],{},[898,98266,724],{},[1651,98268,1839],{},[1686,98270,98271,98273],{},[898,98272,4104],{},[895,98274,98275,98277,98279],{},[898,98276,43913],{},[898,98278,1664],{},[898,98280,13339],{},[1651,98282,1738],{},[1692,98284,1703],{},[1651,98286,1839],{},[1692,98288,3689],{},[1651,98290,1738],{},[1692,98292,3581],{},[1651,98294,1738],{},[898,98296,4104],{},[902,98298,98299],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[38183,98302],{},[115,98304,98306],{"id":98305},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,98308,97236,98309,98322,98323,98341,98342,98370],{},[883,98310,98312],{"className":98311},[886],[888,98313,98314],{"xmlns":890},[892,98315,98316,98320],{},[895,98317,98318],{},[898,98319,4104],{},[902,98321,4104],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,98324,98326],{"className":98325},[886],[888,98327,98328],{"xmlns":890},[892,98329,98330,98338],{},[895,98331,98332,98334,98336],{},[898,98333,2675],{},[1651,98335,1839],{},[898,98337,4104],{},[902,98339,98340],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,98343,98345],{"className":98344},[886],[888,98346,98347],{"xmlns":890},[892,98348,98349,98367],{},[895,98350,98351,98353,98355,98357,98359,98361,98363,98365],{},[898,98352,2675],{},[1651,98354,1839],{},[898,98356,4104],{},[1651,98358,1738],{},[898,98360,2047],{},[1651,98362,1654],{"stretchy":1653},[898,98364,1690],{},[1651,98366,1667],{"stretchy":1653},[902,98368,98369],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,98372,98374],{"className":98373},[886],[888,98375,98376],{"xmlns":890,"display":29279},[892,98377,98378,98412],{},[895,98379,98380,98382,98384,98390,98392,98394,98396,98398,98400,98402,98404,98406,98408,98410],{},[898,98381,2675],{},[1651,98383,1738],{},[1686,98385,98386,98388],{},[898,98387,2047],{},[1692,98389,1703],{},[1651,98391,1654],{"stretchy":1653},[898,98393,1690],{},[1651,98395,1667],{"stretchy":1653},[1651,98397,1738],{},[898,98399,2047],{},[1651,98401,1654],{"stretchy":1653},[898,98403,1690],{},[1651,98405,1667],{"stretchy":1653},[1651,98407,2181],{},[898,98409,4104],{},[898,98411,1882],{"mathvariant":1910},[902,98413,98414],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,98416,98417,98418,3246,98431,98434],{},"Poptávka se tedy posouvá o ",[883,98419,98421],{"className":98420},[886],[888,98422,98423],{"xmlns":890},[892,98424,98425,98429],{},[895,98426,98427],{},[898,98428,4104],{},[902,98430,4104],{"encoding":904},[38,98432,98433],{},"svisle dolů",". Nabídka se nemění.",[724,98436,97361,98437,97402,98477,5197,98505,98533,98534,98553,98554,98578,98579,5230],{},[883,98438,98440],{"className":98439},[886],[888,98441,98442],{"xmlns":890},[892,98443,98444,98474],{},[895,98445,98446,98452,98454,98462,98464,98472],{},[1686,98447,98448,98450],{},[898,98449,5561],{},[1692,98451,1703],{},[1651,98453,2261],{"stretchy":1653},[1902,98455,98456,98458,98460],{},[898,98457,1690],{},[1692,98459,1703],{},[898,98461,5561],{},[1651,98463,1661],{"separator":1660},[1902,98465,98466,98468,98470],{},[898,98467,2675],{},[1692,98469,1703],{},[898,98471,5561],{},[1651,98473,2279],{"stretchy":1653},[902,98475,98476],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,98478,98480],{"className":98479},[886],[888,98481,98482],{"xmlns":890},[892,98483,98484,98502],{},[895,98485,98486,98494,98496],{},[1902,98487,98488,98490,98492],{},[898,98489,1690],{},[1692,98491,1703],{},[898,98493,5561],{},[1651,98495,2319],{},[2115,98497,98498,98500],{},[898,98499,1690],{},[898,98501,5561],{},[902,98503,98504],{"encoding":904},"Q_2^E \u003C Q^E",[883,98506,98508],{"className":98507},[886],[888,98509,98510],{"xmlns":890},[892,98511,98512,98530],{},[895,98513,98514,98522,98524],{},[1902,98515,98516,98518,98520],{},[898,98517,2675],{},[1692,98519,1703],{},[898,98521,5561],{},[1651,98523,2319],{},[2115,98525,98526,98528],{},[898,98527,2675],{},[898,98529,5561],{},[902,98531,98532],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,98535,98537],{"className":98536},[886],[888,98538,98539],{"xmlns":890},[892,98540,98541,98551],{},[895,98542,98543],{},[1902,98544,98545,98547,98549],{},[898,98546,2675],{},[1692,98548,1703],{},[898,98550,5561],{},[902,98552,49131],{"encoding":904},", spotřebitel platí celkem ",[883,98555,98557],{"className":98556},[886],[888,98558,98559],{"xmlns":890},[892,98560,98561,98575],{},[895,98562,98563,98571,98573],{},[1902,98564,98565,98567,98569],{},[898,98566,2675],{},[1692,98568,1703],{},[898,98570,5561],{},[1651,98572,1839],{},[898,98574,4104],{},[902,98576,98577],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,98580,98582],{"className":98581},[886],[888,98583,98584],{"xmlns":890},[892,98585,98586,98594],{},[895,98587,98588],{},[2115,98589,98590,98592],{},[898,98591,2675],{},[898,98593,5561],{},[902,98595,42679],{"encoding":904},[724,98597,98598],{},"Daňové břemeno:",[883,98600,98602],{"className":98601},[886],[888,98603,98604],{"xmlns":890,"display":29279},[892,98605,98606,98680],{},[895,98607,98608,98618,98620,98622,98630,98632,98634,98636,98638,98644,98646,98648,98660,98662,98668,98670,98678],{},[1686,98609,98610,98612],{},[898,98611,4104],{},[895,98613,98614,98616],{},[898,98615,43890],{},[898,98617,724],{},[1651,98619,1738],{},[1651,98621,1654],{"stretchy":1653},[1902,98623,98624,98626,98628],{},[898,98625,2675],{},[1692,98627,1703],{},[898,98629,5561],{},[1651,98631,1839],{},[898,98633,4104],{},[1651,98635,1667],{"stretchy":1653},[1651,98637,2181],{},[2115,98639,98640,98642],{},[898,98641,2675],{},[898,98643,5561],{},[1651,98645,1661],{"separator":1660},[7185,98647],{"width":7187},[1686,98649,98650,98652],{},[898,98651,4104],{},[895,98653,98654,98656,98658],{},[898,98655,43913],{},[898,98657,1664],{},[898,98659,13339],{},[1651,98661,1738],{},[2115,98663,98664,98666],{},[898,98665,2675],{},[898,98667,5561],{},[1651,98669,2181],{},[1902,98671,98672,98674,98676],{},[898,98673,2675],{},[1692,98675,1703],{},[898,98677,5561],{},[898,98679,1882],{"mathvariant":1910},[902,98681,98682],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,98684,98685],{},[614,98686,98687,98688,98718,98719,97571,98732,6976,98749,97602,98762,1882],{},"Obrázek 2.19: Posun ",[883,98689,98691],{"className":98690},[886],[888,98692,98693],{"xmlns":890},[892,98694,98695,98715],{},[895,98696,98697,98699,98701,98707,98709,98711,98713],{},[898,98698,2047],{},[1651,98700,4449],{},[1686,98702,98703,98705],{},[898,98704,2047],{},[1692,98706,1703],{},[1651,98708,1738],{},[898,98710,2047],{},[1651,98712,2181],{},[898,98714,4104],{},[902,98716,98717],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,98720,98722],{"className":98721},[886],[888,98723,98724],{"xmlns":890},[892,98725,98726,98730],{},[895,98727,98728],{},[898,98729,4104],{},[902,98731,4104],{"encoding":904},[883,98733,98735],{"className":98734},[886],[888,98736,98737],{"xmlns":890},[892,98738,98739,98747],{},[895,98740,98741],{},[1686,98742,98743,98745],{},[898,98744,2047],{},[1692,98746,1703],{},[902,98748,39540],{"encoding":904},[883,98750,98752],{"className":98751},[886],[888,98753,98754],{"xmlns":890},[892,98755,98756,98760],{},[895,98757,98758],{},[898,98759,3004],{},[902,98761,3004],{"encoding":904},[883,98763,98765],{"className":98764},[886],[888,98766,98767],{"xmlns":890},[892,98768,98769,98777],{},[895,98770,98771],{},[1686,98772,98773,98775],{},[898,98774,5561],{},[1692,98776,1703],{},[902,98778,98779],{"encoding":904},"E_2",[198,98781,46596],{"id":98782},"příklad-210",[724,98784,98785,98787,98788,42903,98811,98830,98831,98848],{},[38,98786,39146],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,98789,98791],{"className":98790},[886],[888,98792,98793],{"xmlns":890},[892,98794,98795,98809],{},[895,98796,98797,98799,98801,98803,98805,98807],{},[898,98798,2675],{},[1651,98800,1738],{},[1692,98802,4828],{},[1651,98804,2181],{},[1692,98806,1703],{},[898,98808,1690],{},[902,98810,97651],{"encoding":904},[883,98812,98814],{"className":98813},[886],[888,98815,98816],{"xmlns":890},[892,98817,98818,98828],{},[895,98819,98820,98822,98824,98826],{},[898,98821,2675],{},[1651,98823,1738],{},[1692,98825,3689],{},[898,98827,1690],{},[902,98829,97671],{"encoding":904},". Daň ",[883,98832,98834],{"className":98833},[886],[888,98835,98836],{"xmlns":890},[892,98837,98838,98846],{},[895,98839,98840,98842,98844],{},[898,98841,4104],{},[1651,98843,1738],{},[1692,98845,3581],{},[902,98847,42481],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,98850,98851],{},[38,98852,39178],{},[724,98854,98855,98856,97862],{},"Nová poptávka je ",[883,98857,98859],{"className":98858},[886],[888,98860,98861],{"xmlns":890},[892,98862,98863,98899],{},[895,98864,98865,98871,98873,98875,98877,98879,98881,98883,98885,98887,98889,98891,98893,98895,98897],{},[1686,98866,98867,98869],{},[898,98868,2047],{},[1692,98870,1703],{},[1651,98872,1793],{},[898,98874,2675],{},[1651,98876,1738],{},[1692,98878,4828],{},[1651,98880,2181],{},[1692,98882,1703],{},[898,98884,1690],{},[1651,98886,2181],{},[1692,98888,3581],{},[1651,98890,1738],{},[1692,98892,3581],{},[1651,98894,2181],{},[1692,98896,1703],{},[898,98898,1690],{},[902,98900,98901],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,98903,98905],{"className":98904},[886],[888,98906,98907],{"xmlns":890,"display":29279},[892,98908,98909,98925],{},[895,98910,98911,98913,98915,98917,98919,98921,98923],{},[1692,98912,3581],{},[1651,98914,2181],{},[1692,98916,1703],{},[898,98918,1690],{},[1651,98920,1738],{},[1692,98922,3689],{},[898,98924,1690],{},[902,98926,98927],{"encoding":904},"6 - 2Q = 4Q",[724,98929,97895,98930,6896,98949,1343,98973,97976,99005,1882],{},[883,98931,98933],{"className":98932},[886],[888,98934,98935],{"xmlns":890},[892,98936,98937,98947],{},[895,98938,98939,98941,98943,98945],{},[1692,98940,3581],{},[898,98942,1690],{},[1651,98944,1738],{},[1692,98946,3581],{},[902,98948,97915],{"encoding":904},[883,98950,98952],{"className":98951},[886],[888,98953,98954],{"xmlns":890},[892,98955,98956,98970],{},[895,98957,98958,98966,98968],{},[1902,98959,98960,98962,98964],{},[898,98961,1690],{},[1692,98963,1703],{},[898,98965,5561],{},[1651,98967,1738],{},[1692,98969,1694],{},[902,98971,98972],{"encoding":904},"Q_2^E = 1",[883,98974,98976],{"className":98975},[886],[888,98977,98978],{"xmlns":890},[892,98979,98980,99002],{},[895,98981,98982,98990,98992,98994,98996,98998,99000],{},[1902,98983,98984,98986,98988],{},[898,98985,2675],{},[1692,98987,1703],{},[898,98989,5561],{},[1651,98991,1738],{},[1692,98993,3689],{},[1651,98995,4503],{},[1692,98997,1694],{},[1651,98999,1738],{},[1692,99001,3689],{},[902,99003,99004],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,99006,99008],{"className":99007},[886],[888,99009,99010],{"xmlns":890},[892,99011,99012,99030],{},[895,99013,99014,99020,99022,99024,99026,99028],{},[1686,99015,99016,99018],{},[898,99017,5561],{},[1692,99019,1703],{},[1651,99021,2261],{"stretchy":1653},[1692,99023,1694],{},[1651,99025,1661],{"separator":1660},[1692,99027,3689],{},[1651,99029,2279],{"stretchy":1653},[902,99031,99032],{"encoding":904},"E_2[1, 4]",[724,99034,99035,99036,99072,99073,97690],{},"Spotřebitel platí celkem ",[883,99037,99039],{"className":99038},[886],[888,99040,99041],{"xmlns":890},[892,99042,99043,99069],{},[895,99044,99045,99053,99055,99057,99059,99061,99063,99065,99067],{},[1902,99046,99047,99049,99051],{},[898,99048,2675],{},[1692,99050,1703],{},[898,99052,5561],{},[1651,99054,1839],{},[898,99056,4104],{},[1651,99058,1738],{},[1692,99060,3689],{},[1651,99062,1839],{},[1692,99064,3581],{},[1651,99066,1738],{},[1692,99068,4190],{},[902,99070,99071],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,99074,99076],{"className":99075},[886],[888,99077,99078],{"xmlns":890},[892,99079,99080,99094],{},[895,99081,99082,99090,99092],{},[1902,99083,99084,99086,99088],{},[898,99085,2675],{},[1692,99087,1703],{},[898,99089,5561],{},[1651,99091,1738],{},[1692,99093,3689],{},[902,99095,99096],{"encoding":904},"P_2^E = 4",[724,99098,99099],{},[614,99100,99101],{},"Rozklad daňového břemene:",[883,99103,99105],{"className":99104},[886],[888,99106,99107],{"xmlns":890,"display":29279},[892,99108,99109,99195],{},[895,99110,99111,99121,99123,99125,99127,99129,99131,99133,99135,99137,99139,99141,99143,99153,99155,99157,99169,99171,99173,99175,99177,99179,99181,99183,99193],{},[1686,99112,99113,99115],{},[898,99114,4104],{},[895,99116,99117,99119],{},[898,99118,43890],{},[898,99120,724],{},[1651,99122,1738],{},[1651,99124,1654],{"stretchy":1653},[1692,99126,3689],{},[1651,99128,1839],{},[1692,99130,3581],{},[1651,99132,1667],{"stretchy":1653},[1651,99134,2181],{},[1692,99136,6892],{},[1651,99138,1738],{},[1692,99140,1703],{},[1843,99142,3631],{},[895,99144,99145,99147],{},[1843,99146,11101],{},[9692,99148,99149,99151],{"accent":1660},[1843,99150,3490],{},[1651,99152,26271],{},[1651,99154,1661],{"separator":1660},[7185,99156],{"width":7187},[1686,99158,99159,99161],{},[898,99160,4104],{},[895,99162,99163,99165,99167],{},[898,99164,43913],{},[898,99166,1664],{},[898,99168,13339],{},[1651,99170,1738],{},[1692,99172,6892],{},[1651,99174,2181],{},[1692,99176,3689],{},[1651,99178,1738],{},[1692,99180,3689],{},[1843,99182,3631],{},[895,99184,99185,99187],{},[1843,99186,11101],{},[9692,99188,99189,99191],{"accent":1660},[1843,99190,3490],{},[1651,99192,26271],{},[898,99194,1882],{"mathvariant":1910},[902,99196,99197],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,99199,99200,99201,1882],{},"Opět ",[883,99202,99204],{"className":99203},[886],[888,99205,99206],{"xmlns":890},[892,99207,99208,99242],{},[895,99209,99210,99220,99222,99234,99236,99238,99240],{},[1686,99211,99212,99214],{},[898,99213,4104],{},[895,99215,99216,99218],{},[898,99217,43890],{},[898,99219,724],{},[1651,99221,1839],{},[1686,99223,99224,99226],{},[898,99225,4104],{},[895,99227,99228,99230,99232],{},[898,99229,43913],{},[898,99231,1664],{},[898,99233,13339],{},[1651,99235,1738],{},[1692,99237,3581],{},[1651,99239,1738],{},[898,99241,4104],{},[902,99243,99244],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[38183,99246],{},[115,99248,43871],{"id":99249},"daňové-břemeno",[724,99251,99252,11325,99254,99257,99258,99271],{},[38,99253,43871],{},[614,99255,99256],{},"tax burden",") je rozdělení zaplacené daně ",[883,99259,99261],{"className":99260},[886],[888,99262,99263],{"xmlns":890},[892,99264,99265,99269],{},[895,99266,99267],{},[898,99268,4104],{},[902,99270,4104],{"encoding":904}," mezi spotřebitele a výrobce:",[883,99273,99275],{"className":99274},[886],[888,99276,99277],{"xmlns":890,"display":29279},[892,99278,99279,99311],{},[895,99280,99281,99283,99285,99295,99297,99309],{},[898,99282,4104],{},[1651,99284,1738],{},[1686,99286,99287,99289],{},[898,99288,4104],{},[895,99290,99291,99293],{},[898,99292,43890],{},[898,99294,724],{},[1651,99296,1839],{},[1686,99298,99299,99301],{},[898,99300,4104],{},[895,99302,99303,99305,99307],{},[898,99304,43913],{},[898,99306,1664],{},[898,99308,13339],{},[898,99310,1882],{"mathvariant":1910},[902,99312,99313],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,99315,99316],{},[1756,99317],{"alt":99318,"className":99319,"src":99320},"imek-dan-rozklad-bremene-sklony",[210,1760],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[5179,99322,99323],{},[724,99324,99325,99327,99328,5197,99341,1882],{},[883,99326,5465],{}," 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 ",[883,99329,99331],{"className":99330},[886],[888,99332,99333],{"xmlns":890},[892,99334,99335,99339],{},[895,99336,99337],{},[898,99338,2047],{},[902,99340,2047],{"encoding":904},[883,99342,99344],{"className":99343},[886],[888,99345,99346],{"xmlns":890},[892,99347,99348,99352],{},[895,99349,99350],{},[898,99351,3004],{},[902,99353,3004],{"encoding":904},[198,99355,3779],{"id":3778},[724,99357,99358,99359,99380,99381,99394,99395,99412,99413,99426],{},"V grafu ",[883,99360,99362],{"className":99361},[886],[888,99363,99364],{"xmlns":890},[892,99365,99366,99378],{},[895,99367,99368,99370,99372,99374,99376],{},[1651,99369,1654],{"stretchy":1653},[898,99371,1690],{},[1651,99373,1661],{"separator":1660},[898,99375,2675],{},[1651,99377,1667],{"stretchy":1653},[902,99379,38904],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,99382,99384],{"className":99383},[886],[888,99385,99386],{"xmlns":890},[892,99387,99388,99392],{},[895,99389,99390],{},[898,99391,4104],{},[902,99393,4104],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,99396,99398],{"className":99397},[886],[888,99399,99400],{"xmlns":890},[892,99401,99402,99410],{},[895,99403,99404],{},[2115,99405,99406,99408],{},[898,99407,2675],{},[898,99409,5561],{},[902,99411,42679],{"encoding":904},", rozdělí se úsečka ",[883,99414,99416],{"className":99415},[886],[888,99417,99418],{"xmlns":890},[892,99419,99420,99424],{},[895,99421,99422],{},[898,99423,4104],{},[902,99425,4104],{"encoding":904}," na dvě části:",[120,99428,99429,99454],{},[123,99430,99431,99432,99453],{},"horní část odpovídá ",[883,99433,99435],{"className":99434},[886],[888,99436,99437],{"xmlns":890},[892,99438,99439,99451],{},[895,99440,99441],{},[1686,99442,99443,99445],{},[898,99444,4104],{},[895,99446,99447,99449],{},[898,99448,43890],{},[898,99450,724],{},[902,99452,43895],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,99455,99456,99457,99480],{},"dolní část odpovídá ",[883,99458,99460],{"className":99459},[886],[888,99461,99462],{"xmlns":890},[892,99463,99464,99478],{},[895,99465,99466],{},[1686,99467,99468,99470],{},[898,99469,4104],{},[895,99471,99472,99474,99476],{},[898,99473,43913],{},[898,99475,1664],{},[898,99477,13339],{},[902,99479,43920],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,99482,99483],{},[614,99484,99485,99486,4016,99499,99520,99521,99544,99545,5197,99566,99589],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,99487,99489],{"className":99488},[886],[888,99490,99491],{"xmlns":890},[892,99492,99493,99497],{},[895,99494,99495],{},[898,99496,4104],{},[902,99498,4104],{"encoding":904},[883,99500,99502],{"className":99501},[886],[888,99503,99504],{"xmlns":890},[892,99505,99506,99518],{},[895,99507,99508],{},[1686,99509,99510,99512],{},[898,99511,4104],{},[895,99513,99514,99516],{},[898,99515,43890],{},[898,99517,724],{},[902,99519,43895],{"encoding":904}," (nahoře) a ",[883,99522,99524],{"className":99523},[886],[888,99525,99526],{"xmlns":890},[892,99527,99528,99542],{},[895,99529,99530],{},[1686,99531,99532,99534],{},[898,99533,4104],{},[895,99535,99536,99538,99540],{},[898,99537,43913],{},[898,99539,1664],{},[898,99541,13339],{},[902,99543,43920],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,99546,99548],{"className":99547},[886],[888,99549,99550],{"xmlns":890},[892,99551,99552,99564],{},[895,99553,99554],{},[1686,99555,99556,99558],{},[898,99557,4104],{},[895,99559,99560,99562],{},[898,99561,43890],{},[898,99563,724],{},[902,99565,43895],{"encoding":904},[883,99567,99569],{"className":99568},[886],[888,99570,99571],{"xmlns":890},[892,99572,99573,99587],{},[895,99574,99575],{},[1686,99576,99577,99579],{},[898,99578,4104],{},[895,99580,99581,99583,99585],{},[898,99582,43913],{},[898,99584,1664],{},[898,99586,13339],{},[902,99588,43920],{"encoding":904}," je v obou případech stejná.",[198,99591,99593],{"id":99592},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,99595,99596,99597,99600,99601,11325,99624,99641,99642,11325,99665,99682],{},"Platí obecně: ",[38,99598,99599],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,99602,99604],{"className":99603},[886],[888,99605,99606],{"xmlns":890},[892,99607,99608,99622],{},[895,99609,99610,99612,99614,99616,99618,99620],{},[898,99611,2675],{},[1651,99613,1738],{},[898,99615,207],{},[898,99617,1690],{},[1651,99619,1839],{},[898,99621,2268],{},[902,99623,38273],{"encoding":904},[883,99625,99627],{"className":99626},[886],[888,99628,99629],{"xmlns":890},[892,99630,99631,99639],{},[895,99632,99633,99635,99637],{},[898,99634,207],{},[1651,99636,2319],{},[1692,99638,1741],{},[902,99640,44298],{"encoding":904},") a lineární nabídku ",[883,99643,99645],{"className":99644},[886],[888,99646,99647],{"xmlns":890},[892,99648,99649,99663],{},[895,99650,99651,99653,99655,99657,99659,99661],{},[898,99652,2675],{},[1651,99654,1738],{},[898,99656,3490],{},[898,99658,1690],{},[1651,99660,1839],{},[898,99662,3542],{},[902,99664,41455],{"encoding":904},[883,99666,99668],{"className":99667},[886],[888,99669,99670],{"xmlns":890},[892,99671,99672,99680],{},[895,99673,99674,99676,99678],{},[898,99675,3490],{},[1651,99677,2390],{},[1692,99679,1741],{},[902,99681,41473],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,99684,99686],{"className":99685},[886],[888,99687,99688],{"xmlns":890,"display":29279},[892,99689,99690,99756],{},[895,99691,99692,99716,99718,99728,99730,99754],{},[2446,99693,99694,99704],{},[1686,99695,99696,99698],{},[898,99697,4104],{},[895,99699,99700,99702],{},[898,99701,43890],{},[898,99703,724],{},[1686,99705,99706,99708],{},[898,99707,4104],{},[895,99709,99710,99712,99714],{},[898,99711,43913],{},[898,99713,1664],{},[898,99715,13339],{},[1651,99717,1738],{},[2446,99719,99720,99722],{},[898,99721,3490],{},[895,99723,99724,99726],{},[1651,99725,2181],{},[898,99727,207],{},[1651,99729,1738],{},[2446,99731,99732,99744],{},[895,99733,99734,99737,99740,99742],{},[898,99735,99736],{"mathvariant":1910},"∣",[1843,99738,99739],{},"sklon ",[898,99741,3004],{},[898,99743,99736],{"mathvariant":1910},[895,99745,99746,99748,99750,99752],{},[898,99747,99736],{"mathvariant":1910},[1843,99749,99739],{},[898,99751,2047],{},[898,99753,99736],{"mathvariant":1910},[898,99755,1882],{"mathvariant":1910},[902,99757,99758],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[5179,99760,99761,99766],{},[724,99762,99763,99765],{},[883,99764,5879],{}," Postup výpočtu rozkladu",[152,99767,99768,99803,99856,99935],{},[123,99769,99770,99771,99802],{},"Spočti rovnovážný bod ",[883,99772,99774],{"className":99773},[886],[888,99775,99776],{"xmlns":890},[892,99777,99778,99800],{},[895,99779,99780,99782,99784,99790,99792,99798],{},[898,99781,5561],{},[1651,99783,2261],{"stretchy":1653},[2115,99785,99786,99788],{},[898,99787,1690],{},[898,99789,5561],{},[1651,99791,1661],{"separator":1660},[2115,99793,99794,99796],{},[898,99795,2675],{},[898,99797,5561],{},[1651,99799,2279],{"stretchy":1653},[902,99801,42580],{"encoding":904}," bez daně.",[123,99804,99805,99806,1348,99831,5230],{},"Urči posunutou křivku (",[883,99807,99809],{"className":99808},[886],[888,99810,99811],{"xmlns":890},[892,99812,99813,99829],{},[895,99814,99815,99821,99823,99825,99827],{},[1686,99816,99817,99819],{},[898,99818,3004],{},[1692,99820,1694],{},[1651,99822,1738],{},[898,99824,3004],{},[1651,99826,1839],{},[898,99828,4104],{},[902,99830,43967],{"encoding":904},[883,99832,99834],{"className":99833},[886],[888,99835,99836],{"xmlns":890},[892,99837,99838,99854],{},[895,99839,99840,99846,99848,99850,99852],{},[1686,99841,99842,99844],{},[898,99843,2047],{},[1692,99845,1703],{},[1651,99847,1738],{},[898,99849,2047],{},[1651,99851,2181],{},[898,99853,4104],{},[902,99855,43998],{"encoding":904},[123,99857,99858,99859,1671,99878,13426,99897,1671,99916,5230],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,99860,99862],{"className":99861},[886],[888,99863,99864],{"xmlns":890},[892,99865,99866,99876],{},[895,99867,99868],{},[1902,99869,99870,99872,99874],{},[898,99871,1690],{},[1692,99873,1694],{},[898,99875,5561],{},[902,99877,49049],{"encoding":904},[883,99879,99881],{"className":99880},[886],[888,99882,99883],{"xmlns":890},[892,99884,99885,99895],{},[895,99886,99887],{},[1902,99888,99889,99891,99893],{},[898,99890,1690],{},[1692,99892,1703],{},[898,99894,5561],{},[902,99896,49111],{"encoding":904},[883,99898,99900],{"className":99899},[886],[888,99901,99902],{"xmlns":890},[892,99903,99904,99914],{},[895,99905,99906],{},[1902,99907,99908,99910,99912],{},[898,99909,2675],{},[1692,99911,1694],{},[898,99913,5561],{},[902,99915,49070],{"encoding":904},[883,99917,99919],{"className":99918},[886],[888,99920,99921],{"xmlns":890},[892,99922,99923,99933],{},[895,99924,99925],{},[1902,99926,99927,99929,99931],{},[898,99928,2675],{},[1692,99930,1703],{},[898,99932,5561],{},[902,99934,49131],{"encoding":904},[123,99936,99937,99938,5197,99959,99982,99983,1882],{},"Dopočítej ",[883,99939,99941],{"className":99940},[886],[888,99942,99943],{"xmlns":890},[892,99944,99945,99957],{},[895,99946,99947],{},[1686,99948,99949,99951],{},[898,99950,4104],{},[895,99952,99953,99955],{},[898,99954,43890],{},[898,99956,724],{},[902,99958,43895],{"encoding":904},[883,99960,99962],{"className":99961},[886],[888,99963,99964],{"xmlns":890},[892,99965,99966,99980],{},[895,99967,99968],{},[1686,99969,99970,99972],{},[898,99971,4104],{},[895,99973,99974,99976,99978],{},[898,99975,43913],{},[898,99977,1664],{},[898,99979,13339],{},[902,99981,43920],{"encoding":904}," z definice, vždy ověř ",[883,99984,99986],{"className":99985},[886],[888,99987,99988],{"xmlns":890},[892,99989,99990,100020],{},[895,99991,99992,100002,100004,100016,100018],{},[1686,99993,99994,99996],{},[898,99995,4104],{},[895,99997,99998,100000],{},[898,99999,43890],{},[898,100001,724],{},[1651,100003,1839],{},[1686,100005,100006,100008],{},[898,100007,4104],{},[895,100009,100010,100012,100014],{},[898,100011,43913],{},[898,100013,1664],{},[898,100015,13339],{},[1651,100017,1738],{},[898,100019,4104],{},[902,100021,100022],{"encoding":904},"T_{sp} + T_{vyr} = T",[5179,100024,100025],{},[724,100026,100027,100029,100030,100033,100034,5197,100047,100060],{},[883,100028,5719],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,100031,100032],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,100035,100037],{"className":100036},[886],[888,100038,100039],{"xmlns":890},[892,100040,100041,100045],{},[895,100042,100043],{},[898,100044,2047],{},[902,100046,2047],{"encoding":904},[883,100048,100050],{"className":100049},[886],[888,100051,100052],{"xmlns":890},[892,100053,100054,100058],{},[895,100055,100056],{},[898,100057,3004],{},[902,100059,3004],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[38183,100062],{},[115,100064,100066],{"id":100065},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,100068,100069],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,100071,100072],{},[1756,100073],{"alt":100074,"className":100075,"src":100076},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,1760],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,100078,100079,100091],{},[19,100080,100081],{},[22,100082,100083,100085,100088],{},[25,100084,55509],{},[25,100086,100087],{},"(a) daň výrobci",[25,100089,100090],{},"(b) daň spotřebiteli",[30,100092,100093,100148,100215,100275],{},[22,100094,100095,100098,100123],{},[35,100096,100097],{},"Rovnovážné množství",[35,100099,100100],{},[883,100101,100103],{"className":100102},[886],[888,100104,100105],{"xmlns":890},[892,100106,100107,100121],{},[895,100108,100109,100117,100119],{},[1902,100110,100111,100113,100115],{},[898,100112,1690],{},[1692,100114,1694],{},[898,100116,5561],{},[1651,100118,1738],{},[1692,100120,1694],{},[902,100122,97939],{"encoding":904},[35,100124,100125],{},[883,100126,100128],{"className":100127},[886],[888,100129,100130],{"xmlns":890},[892,100131,100132,100146],{},[895,100133,100134,100142,100144],{},[1902,100135,100136,100138,100140],{},[898,100137,1690],{},[1692,100139,1703],{},[898,100141,5561],{},[1651,100143,1738],{},[1692,100145,1694],{},[902,100147,98972],{"encoding":904},[22,100149,100150,100153,100178],{},[35,100151,100152],{},"Cena placená spotřebitelem",[35,100154,100155],{},[883,100156,100158],{"className":100157},[886],[888,100159,100160],{"xmlns":890},[892,100161,100162,100176],{},[895,100163,100164,100172,100174],{},[1902,100165,100166,100168,100170],{},[898,100167,2675],{},[1692,100169,1694],{},[898,100171,5561],{},[1651,100173,1738],{},[1692,100175,4190],{},[902,100177,98034],{"encoding":904},[35,100179,100180],{},[883,100181,100183],{"className":100182},[886],[888,100184,100185],{"xmlns":890},[892,100186,100187,100213],{},[895,100188,100189,100197,100199,100201,100203,100205,100207,100209,100211],{},[1902,100190,100191,100193,100195],{},[898,100192,2675],{},[1692,100194,1703],{},[898,100196,5561],{},[1651,100198,1839],{},[898,100200,4104],{},[1651,100202,1738],{},[1692,100204,3689],{},[1651,100206,1839],{},[1692,100208,3581],{},[1651,100210,1738],{},[1692,100212,4190],{},[902,100214,99071],{"encoding":904},[22,100216,100217,100220,100250],{},[35,100218,100219],{},"Cena přijímaná výrobcem",[35,100221,100222],{},[883,100223,100225],{"className":100224},[886],[888,100226,100227],{"xmlns":890},[892,100228,100229,100247],{},[895,100230,100231,100239,100241,100243,100245],{},[1902,100232,100233,100235,100237],{},[898,100234,2675],{},[1692,100236,1694],{},[898,100238,5561],{},[1651,100240,2181],{},[898,100242,4104],{},[1651,100244,1738],{},[1692,100246,3689],{},[902,100248,100249],{"encoding":904},"P_1^E - T = 4",[35,100251,100252],{},[883,100253,100255],{"className":100254},[886],[888,100256,100257],{"xmlns":890},[892,100258,100259,100273],{},[895,100260,100261,100269,100271],{},[1902,100262,100263,100265,100267],{},[898,100264,2675],{},[1692,100266,1703],{},[898,100268,5561],{},[1651,100270,1738],{},[1692,100272,3689],{},[902,100274,99096],{"encoding":904},[22,100276,100277,100280,100334],{},[35,100278,100279],{},"Rozklad břemene",[35,100281,100282,1343,100307],{},[883,100283,100285],{"className":100284},[886],[888,100286,100287],{"xmlns":890},[892,100288,100289,100305],{},[895,100290,100291,100301,100303],{},[1686,100292,100293,100295],{},[898,100294,4104],{},[895,100296,100297,100299],{},[898,100298,43890],{},[898,100300,724],{},[1651,100302,1738],{},[1692,100304,1703],{},[902,100306,44189],{"encoding":904},[883,100308,100310],{"className":100309},[886],[888,100311,100312],{"xmlns":890},[892,100313,100314,100332],{},[895,100315,100316,100328,100330],{},[1686,100317,100318,100320],{},[898,100319,4104],{},[895,100321,100322,100324,100326],{},[898,100323,43913],{},[898,100325,1664],{},[898,100327,13339],{},[1651,100329,1738],{},[1692,100331,3689],{},[902,100333,44218],{"encoding":904},[35,100335,100336,1343,100361],{},[883,100337,100339],{"className":100338},[886],[888,100340,100341],{"xmlns":890},[892,100342,100343,100359],{},[895,100344,100345,100355,100357],{},[1686,100346,100347,100349],{},[898,100348,4104],{},[895,100350,100351,100353],{},[898,100352,43890],{},[898,100354,724],{},[1651,100356,1738],{},[1692,100358,1703],{},[902,100360,44189],{"encoding":904},[883,100362,100364],{"className":100363},[886],[888,100365,100366],{"xmlns":890},[892,100367,100368,100386],{},[895,100369,100370,100382,100384],{},[1686,100371,100372,100374],{},[898,100373,4104],{},[895,100375,100376,100378,100380],{},[898,100377,43913],{},[898,100379,1664],{},[898,100381,13339],{},[1651,100383,1738],{},[1692,100385,3689],{},[902,100387,44218],{"encoding":904},[724,100389,100390],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,100392,100394],{"className":100393},[886],[888,100395,100396],{"xmlns":890,"display":29279},[892,100397,100398,100446],{},[895,100399,100400,100408,100410,100418,100420,100422,100430,100432,100434,100436,100444],{},[1902,100401,100402,100404,100406],{},[898,100403,1690],{},[1692,100405,1694],{},[898,100407,5561],{},[1651,100409,1738],{},[1902,100411,100412,100414,100416],{},[898,100413,1690],{},[1692,100415,1703],{},[898,100417,5561],{},[1651,100419,1661],{"separator":1660},[7185,100421],{"width":7187},[1902,100423,100424,100426,100428],{},[898,100425,2675],{},[1692,100427,1694],{},[898,100429,5561],{},[1651,100431,2181],{},[898,100433,4104],{},[1651,100435,1738],{},[1902,100437,100438,100440,100442],{},[898,100439,2675],{},[1692,100441,1703],{},[898,100443,5561],{},[898,100445,1882],{"mathvariant":1910},[902,100447,100448],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[5179,100450,100451,100470,100624],{},[724,100452,100453,100455,100456,100469],{},[883,100454,5879],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,100457,100459],{"className":100458},[886],[888,100460,100461],{"xmlns":890},[892,100462,100463,100467],{},[895,100464,100465],{},[898,100466,4104],{},[902,100468,4104],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,100471,100472,100504,100540,100577],{},[123,100473,100474,100475,1661],{},"rovnovážná množství obou režimů, ",[883,100476,100478],{"className":100477},[886],[888,100479,100480],{"xmlns":890},[892,100481,100482,100502],{},[895,100483,100484,100492,100494],{},[1902,100485,100486,100488,100490],{},[898,100487,1690],{},[1692,100489,1694],{},[898,100491,5561],{},[1651,100493,1738],{},[1902,100495,100496,100498,100500],{},[898,100497,1690],{},[1692,100499,1703],{},[898,100501,5561],{},[902,100503,44121],{"encoding":904},[123,100505,100506,100507,1661],{},"čistá cena přijímaná výrobcem, ",[883,100508,100510],{"className":100509},[886],[888,100511,100512],{"xmlns":890},[892,100513,100514,100538],{},[895,100515,100516,100524,100526,100528,100530],{},[1902,100517,100518,100520,100522],{},[898,100519,2675],{},[1692,100521,1694],{},[898,100523,5561],{},[1651,100525,2181],{},[898,100527,4104],{},[1651,100529,1738],{},[1902,100531,100532,100534,100536],{},[898,100533,2675],{},[1692,100535,1703],{},[898,100537,5561],{},[902,100539,44155],{"encoding":904},[123,100541,100542,100543,1661],{},"celková cena placená spotřebitelem, ",[883,100544,100546],{"className":100545},[886],[888,100547,100548],{"xmlns":890},[892,100549,100550,100574],{},[895,100551,100552,100560,100562,100570,100572],{},[1902,100553,100554,100556,100558],{},[898,100555,2675],{},[1692,100557,1694],{},[898,100559,5561],{},[1651,100561,1738],{},[1902,100563,100564,100566,100568],{},[898,100565,2675],{},[1692,100567,1703],{},[898,100569,5561],{},[1651,100571,1839],{},[898,100573,4104],{},[902,100575,100576],{"encoding":904},"P_1^E = P_2^E + T",[123,100578,100579,100580,5197,100601,1882],{},"rozklad daňového břemene ",[883,100581,100583],{"className":100582},[886],[888,100584,100585],{"xmlns":890},[892,100586,100587,100599],{},[895,100588,100589],{},[1686,100590,100591,100593],{},[898,100592,4104],{},[895,100594,100595,100597],{},[898,100596,43890],{},[898,100598,724],{},[902,100600,43895],{"encoding":904},[883,100602,100604],{"className":100603},[886],[888,100605,100606],{"xmlns":890},[892,100607,100608,100622],{},[895,100609,100610],{},[1686,100611,100612,100614],{},[898,100613,4104],{},[895,100615,100616,100618,100620],{},[898,100617,43913],{},[898,100619,1664],{},[898,100621,13339],{},[902,100623,43920],{"encoding":904},[724,100625,100626,100627,1882],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,100628,36410],{},[724,100630,100631,100632,5197,100645,5230],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,100633,100635],{"className":100634},[886],[888,100636,100637],{"xmlns":890},[892,100638,100639,100643],{},[895,100640,100641],{},[898,100642,2047],{},[902,100644,2047],{"encoding":904},[883,100646,100648],{"className":100647},[886],[888,100649,100650],{"xmlns":890},[892,100651,100652,100656],{},[895,100653,100654],{},[898,100655,3004],{},[902,100657,3004],{"encoding":904},[38183,100659],{},[115,100661,100663],{"id":100662},"úlohy","Úlohy",[724,100665,100666,100667,4477],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,100668,17538],{"className":100669,"dataFsResolvedFilePath":800,"href":801},[210],[120,100671,100672,100702,100733],{},[123,100673,100674,100677,100678,100701],{},[38,100675,100676],{},"Úloha 2.4"," — Poptávka ",[883,100679,100681],{"className":100680},[886],[888,100682,100683],{"xmlns":890},[892,100684,100685,100699],{},[895,100686,100687,100689,100691,100693,100695,100697],{},[898,100688,2675],{},[1651,100690,1738],{},[1692,100692,4828],{},[1651,100694,2181],{},[1692,100696,1703],{},[898,100698,1690],{},[902,100700,97651],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,100703,100704,100707,100708,100732],{},[38,100705,100706],{},"Úloha 2.9"," — Nabídka ",[883,100709,100711],{"className":100710},[886],[888,100712,100713],{"xmlns":890},[892,100714,100715,100729],{},[895,100716,100717,100719,100721,100723,100725,100727],{},[898,100718,2675],{},[1651,100720,1738],{},[1692,100722,6316],{},[898,100724,1690],{},[1651,100726,1839],{},[1692,100728,37457],{},[902,100730,100731],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,100734,100735,100738,100739,5197,100765,100789,100790,100807],{},[38,100736,100737],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,100740,100742],{"className":100741},[886],[888,100743,100744],{"xmlns":890},[892,100745,100746,100762],{},[895,100747,100748,100750,100752,100754,100756,100758,100760],{},[898,100749,2675],{},[1651,100751,1738],{},[1651,100753,2181],{},[1692,100755,3689],{},[898,100757,1690],{},[1651,100759,1839],{},[1692,100761,47916],{},[902,100763,100764],{"encoding":904},"P = -4Q + 80",[883,100766,100768],{"className":100767},[886],[888,100769,100770],{"xmlns":890},[892,100771,100772,100786],{},[895,100773,100774,100776,100778,100780,100782,100784],{},[898,100775,2675],{},[1651,100777,1738],{},[1692,100779,3521],{},[898,100781,1690],{},[1651,100783,1839],{},[1692,100785,4190],{},[902,100787,100788],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,100791,100793],{"className":100792},[886],[888,100794,100795],{"xmlns":890},[892,100796,100797,100805],{},[895,100798,100799,100801,100803],{},[898,100800,4104],{},[1651,100802,1738],{},[1692,100804,25414],{},[902,100806,49028],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,100809,100810,100811,100813,100814,100816],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,100812,46441],{}," (posun poptávky při zdanění kupujícího) a ",[38,100815,46475],{}," (posun nabídky při zdanění výrobce).",[38183,100818],{},[115,100820,17018],{"id":17017},[120,100822,100823,100842,100900,100957,101040,101086,101129,101174,101240],{},[123,100824,100825,3246,100828,100841],{},[38,100826,100827],{},"Jednotková daň",[883,100829,100831],{"className":100830},[886],[888,100832,100833],{"xmlns":890},[892,100834,100835,100839],{},[895,100836,100837],{},[898,100838,4104],{},[902,100840,4104],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,100843,100844,100846,100847,100885,100886,100899],{},[38,100845,97233],{}," — posun nabídky ",[883,100848,100850],{"className":100849},[886],[888,100851,100852],{"xmlns":890},[892,100853,100854,100882],{},[895,100855,100856,100862,100864,100866,100868,100870,100872,100874,100876,100878,100880],{},[1686,100857,100858,100860],{},[898,100859,3004],{},[1692,100861,1694],{},[1651,100863,1654],{"stretchy":1653},[898,100865,1690],{},[1651,100867,1667],{"stretchy":1653},[1651,100869,1738],{},[898,100871,3004],{},[1651,100873,1654],{"stretchy":1653},[898,100875,1690],{},[1651,100877,1667],{"stretchy":1653},[1651,100879,1839],{},[898,100881,4104],{},[902,100883,100884],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,100887,100889],{"className":100888},[886],[888,100890,100891],{"xmlns":890},[892,100892,100893,100897],{},[895,100894,100895],{},[898,100896,4104],{},[902,100898,4104],{"encoding":904}," svisle nahoru)",[123,100901,100902,100904,100905,100885,100943,100956],{},[38,100903,98306],{}," — posun poptávky ",[883,100906,100908],{"className":100907},[886],[888,100909,100910],{"xmlns":890},[892,100911,100912,100940],{},[895,100913,100914,100920,100922,100924,100926,100928,100930,100932,100934,100936,100938],{},[1686,100915,100916,100918],{},[898,100917,2047],{},[1692,100919,1703],{},[1651,100921,1654],{"stretchy":1653},[898,100923,1690],{},[1651,100925,1667],{"stretchy":1653},[1651,100927,1738],{},[898,100929,2047],{},[1651,100931,1654],{"stretchy":1653},[898,100933,1690],{},[1651,100935,1667],{"stretchy":1653},[1651,100937,2181],{},[898,100939,4104],{},[902,100941,100942],{"encoding":904},"D_2(Q) = D(Q) - T",[883,100944,100946],{"className":100945},[886],[888,100947,100948],{"xmlns":890},[892,100949,100950,100954],{},[895,100951,100952],{},[898,100953,4104],{},[902,100955,4104],{"encoding":904}," svisle dolů)",[123,100958,100959,8322,100962,43027,101001],{},[38,100960,100961],{},"Rovnovážný bod s daní",[883,100963,100965],{"className":100964},[886],[888,100966,100967],{"xmlns":890},[892,100968,100969,100999],{},[895,100970,100971,100977,100979,100987,100989,100997],{},[1686,100972,100973,100975],{},[898,100974,5561],{},[1692,100976,1694],{},[1651,100978,2261],{"stretchy":1653},[1902,100980,100981,100983,100985],{},[898,100982,1690],{},[1692,100984,1694],{},[898,100986,5561],{},[1651,100988,1661],{"separator":1660},[1902,100990,100991,100993,100995],{},[898,100992,2675],{},[1692,100994,1694],{},[898,100996,5561],{},[1651,100998,2279],{"stretchy":1653},[902,101000,97401],{"encoding":904},[883,101002,101004],{"className":101003},[886],[888,101005,101006],{"xmlns":890},[892,101007,101008,101038],{},[895,101009,101010,101016,101018,101026,101028,101036],{},[1686,101011,101012,101014],{},[898,101013,5561],{},[1692,101015,1703],{},[1651,101017,2261],{"stretchy":1653},[1902,101019,101020,101022,101024],{},[898,101021,1690],{},[1692,101023,1703],{},[898,101025,5561],{},[1651,101027,1661],{"separator":1660},[1902,101029,101030,101032,101034],{},[898,101031,2675],{},[1692,101033,1703],{},[898,101035,5561],{},[1651,101037,2279],{"stretchy":1653},[902,101039,98476],{"encoding":904},[123,101041,101042,11325,101044,101046,101047],{},[38,101043,43871],{},[614,101045,99256],{},") — rozklad ",[883,101048,101050],{"className":101049},[886],[888,101051,101052],{"xmlns":890},[892,101053,101054,101084],{},[895,101055,101056,101058,101060,101070,101072],{},[898,101057,4104],{},[1651,101059,1738],{},[1686,101061,101062,101064],{},[898,101063,4104],{},[895,101065,101066,101068],{},[898,101067,43890],{},[898,101069,724],{},[1651,101071,1839],{},[1686,101073,101074,101076],{},[898,101075,4104],{},[895,101077,101078,101080,101082],{},[898,101079,43913],{},[898,101081,1664],{},[898,101083,13339],{},[902,101085,44057],{"encoding":904},[123,101087,101088,101111,101112,1667],{},[38,101089,101090],{},[883,101091,101093],{"className":101092},[886],[888,101094,101095],{"xmlns":890},[892,101096,101097,101109],{},[895,101098,101099],{},[1686,101100,101101,101103],{},[898,101102,4104],{},[895,101104,101105,101107],{},[898,101106,43890],{},[898,101108,724],{},[902,101110,43895],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,101113,101115],{"className":101114},[886],[888,101116,101117],{"xmlns":890},[892,101118,101119,101127],{},[895,101120,101121],{},[2115,101122,101123,101125],{},[898,101124,2675],{},[898,101126,5561],{},[902,101128,42679],{"encoding":904},[123,101130,101131,101156,101157,1667],{},[38,101132,101133],{},[883,101134,101136],{"className":101135},[886],[888,101137,101138],{"xmlns":890},[892,101139,101140,101154],{},[895,101141,101142],{},[1686,101143,101144,101146],{},[898,101145,4104],{},[895,101147,101148,101150,101152],{},[898,101149,43913],{},[898,101151,1664],{},[898,101153,13339],{},[902,101155,43920],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,101158,101160],{"className":101159},[886],[888,101161,101162],{"xmlns":890},[892,101163,101164,101172],{},[895,101165,101166],{},[2115,101167,101168,101170],{},[898,101169,2675],{},[898,101171,5561],{},[902,101173,42679],{"encoding":904},[123,101175,101176,8322,101178,1343,101207],{},[38,101177,51687],{},[883,101179,101181],{"className":101180},[886],[888,101182,101183],{"xmlns":890},[892,101184,101185,101205],{},[895,101186,101187,101195,101197],{},[1902,101188,101189,101191,101193],{},[898,101190,1690],{},[1692,101192,1694],{},[898,101194,5561],{},[1651,101196,1738],{},[1902,101198,101199,101201,101203],{},[898,101200,1690],{},[1692,101202,1703],{},[898,101204,5561],{},[902,101206,44121],{"encoding":904},[883,101208,101210],{"className":101209},[886],[888,101211,101212],{"xmlns":890},[892,101213,101214,101238],{},[895,101215,101216,101224,101226,101228,101230],{},[1902,101217,101218,101220,101222],{},[898,101219,2675],{},[1692,101221,1694],{},[898,101223,5561],{},[1651,101225,2181],{},[898,101227,4104],{},[1651,101229,1738],{},[1902,101231,101232,101234,101236],{},[898,101233,2675],{},[1692,101235,1703],{},[898,101237,5561],{},[902,101239,44155],{"encoding":904},[123,101241,101242,101245],{},[38,101243,101244],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[38183,101247],{},[115,101249,3238],{"id":3237},[120,101251,101252,101260,101278,101285],{},[123,101253,101254,3246,101257],{},[38,101255,101256],{},"Kontext (hub):",[207,101258,802],{"className":101259,"dataFsResolvedFilePath":800,"href":801},[210],[123,101261,101262,3246,101264,101267,101268,19861,101270,101273,101274,101277],{},[38,101263,51936],{},[207,101265,820],{"className":101266,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,101269,56247],{},[207,101271,3695],{"className":101272,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,101275,5140],{"className":101276,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[123,101279,101280,3246,101282],{},[38,101281,51971],{},[207,101283,51975],{"className":101284,"dataFsResolvedFilePath":745,"href":746},[210],[123,101286,101287,3246,101289],{},[38,101288,17502],{},[207,101290,17506],{"className":101291,"dataFsResolvedFilePath":1749,"href":1750},[210],{"title":641,"searchDepth":642,"depth":642,"links":101293},[101294,101295,101298,101301,101305,101306,101307,101308],{"id":97138,"depth":642,"text":97139},{"id":97232,"depth":642,"text":97233,"children":101296},[101297],{"id":97623,"depth":649,"text":46516},{"id":98305,"depth":642,"text":98306,"children":101299},[101300],{"id":98782,"depth":649,"text":46596},{"id":99249,"depth":642,"text":43871,"children":101302},[101303,101304],{"id":3778,"depth":649,"text":3779},{"id":99592,"depth":649,"text":99593},{"id":100065,"depth":642,"text":100066},{"id":100662,"depth":642,"text":100663},{"id":17017,"depth":642,"text":17018},{"id":3237,"depth":642,"text":3238},{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":97036,"description":641},[1138,1135],"topics\u002Fzdaneni-trhu",[1128,52036,101315,101316,101317,17538],"dane","danove-bremeno","posun-krivek","cFuKqHgzIrqvY-l4jNdqjFEM7_ixjw33HOL0So8cPn0",[101320,101322,101324,101328,101331,101335,101339,101341],{"slug":17551,"path":783,"title":10873,"snippet":101321},"… 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