[{"data":1,"prerenderedAt":108342},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-optimalizace-spotrebitele":1626,"course-stats-imek":10739,"course-topics-imek":10743,"backlinks-optimalizace-spotrebitele":108326,"related-optimalizace-spotrebitele":108335},{"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":10738},{"id":1628,"title":1629,"body":1630,"course":1128,"courses":659,"created":10724,"description":641,"extension":661,"meta":10725,"navigation":664,"path":10726,"seo":10727,"sources":10728,"stem":10729,"tags":10730,"type":10736,"updated":677,"__hash__":10737},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":1631,"toc":10693},[1632,1635,1639,1894,1898,1951,2024,2139,2301,2305,2423,2427,2430,2554,2557,2756,2782,2854,3021,3039,3105,3485,3489,3498,3744,3800,3804,3870,3988,4125,4157,4278,4360,4363,4485,4683,4907,4911,4951,5059,5116,5216,5393,5523,5576,5579,5666,5670,5849,5853,5856,5941,5944,6001,6106,6110,6231,6234,6417,6420,6530,6740,7060,7108,7182,7256,7258,7482,7720,7989,7993,7996,8101,8158,8192,8239,8272,8356,8358,8590,8724,8801,8924,9079,9083,9224,9231,9457,9468,9472,9476,9581,9723,9838,9938,9942,10101,10211,10215,10610,10614],[12,1633,1629],{"id":1634},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,1636,1638],{"id":1637},"tldr","TL;DR",[724,1640,1641,1643,1644,1690,1691,1694,1695,1730,1731,1782,1783,1786,1787,1830,1831,1849,1850,1854,1855,1889,1890,1893],{},[38,1642,913],{}," řeší, jaký svazek zboží ",[883,1645,1647],{"className":1646},[886],[888,1648,1649],{"xmlns":890},[892,1650,1651,1687],{},[895,1652,1653,1658,1671,1675,1684],{},[1654,1655,1657],"mo",{"stretchy":1656},"false","[",[1659,1660,1661,1664,1668],"msubsup",{},[898,1662,1663],{},"Q",[1665,1666,1667],"mn",{},"1",[1654,1669,1670],{},"∗",[1654,1672,1674],{"separator":1673},"true",",",[1659,1676,1677,1679,1682],{},[898,1678,1663],{},[1665,1680,1681],{},"2",[1654,1683,1670],{},[1654,1685,1686],{"stretchy":1656},"]",[902,1688,1689],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,1692,1693],{},"primární úloha"," — maximalizace užitečnosti ",[883,1696,1698],{"className":1697},[886],[888,1699,1700],{"xmlns":890},[892,1701,1702,1727],{},[895,1703,1704,1706,1709,1716,1718,1724],{},[898,1705,900],{},[1654,1707,1708],{"stretchy":1656},"(",[1710,1711,1712,1714],"msub",{},[898,1713,1663],{},[1665,1715,1667],{},[1654,1717,1674],{"separator":1673},[1710,1719,1720,1722],{},[898,1721,1663],{},[1665,1723,1681],{},[1654,1725,1726],{"stretchy":1656},")",[902,1728,1729],{"encoding":904},"U(Q_1, Q_2)"," při rozpočtovém omezení ",[883,1732,1734],{"className":1733},[886],[888,1735,1736],{"xmlns":890},[892,1737,1738,1779],{},[895,1739,1740,1748,1751,1758,1764,1767,1773],{},[1741,1742,1743,1746],"msup",{},[898,1744,1745],{},"Y",[1654,1747,1670],{},[1654,1749,1750],{},"=",[1710,1752,1753,1756],{},[898,1754,1755],{},"P",[1665,1757,1667],{},[1710,1759,1760,1762],{},[898,1761,1663],{},[1665,1763,1667],{},[1654,1765,1766],{},"+",[1710,1768,1769,1771],{},[898,1770,1755],{},[1665,1772,1681],{},[1710,1774,1775,1777],{},[898,1776,1663],{},[1665,1778,1681],{},[902,1780,1781],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,1784,1785],{},"duální úloha"," — minimalizace výdajů ",[883,1788,1790],{"className":1789},[886],[888,1791,1792],{"xmlns":890},[892,1793,1794,1827],{},[895,1795,1796,1799,1801,1807,1813,1815,1821],{},[898,1797,1798],{},"E",[1654,1800,1750],{},[1710,1802,1803,1805],{},[898,1804,1755],{},[1665,1806,1667],{},[1710,1808,1809,1811],{},[898,1810,1663],{},[1665,1812,1667],{},[1654,1814,1766],{},[1710,1816,1817,1819],{},[898,1818,1755],{},[1665,1820,1681],{},[1710,1822,1823,1825],{},[898,1824,1663],{},[1665,1826,1681],{},[902,1828,1829],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,1832,1834],{"className":1833},[886],[888,1835,1836],{"xmlns":890},[892,1837,1838,1846],{},[895,1839,1840],{},[1741,1841,1842,1844],{},[898,1843,900],{},[1654,1845,1670],{},[902,1847,1848],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,1851,1853],{"className":1852,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,1856,1858],{"className":1857},[886],[888,1859,1860],{"xmlns":890},[892,1861,1862,1886],{},[895,1863,1864,1868,1870,1876,1880],{},[1865,1866,1867],"mtext",{},"MRCS",[1654,1869,1750],{},[1710,1871,1872,1874],{},[898,1873,1755],{},[1665,1875,1667],{},[898,1877,1879],{"mathvariant":1878},"normal","\u002F",[1710,1881,1882,1884],{},[898,1883,1755],{},[1665,1885,1681],{},[902,1887,1888],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,1891,1892],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,1895,1897],{"id":1896},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,1899,1900,1901,1919,1920,1950],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,1902,1904],{"className":1903},[886],[888,1905,1906],{"xmlns":890},[892,1907,1908,1916],{},[895,1909,1910],{},[1741,1911,1912,1914],{},[898,1913,1745],{},[1654,1915,1670],{},[902,1917,1918],{"encoding":904},"Y^*"," a ceny ",[883,1921,1923],{"className":1922},[886],[888,1924,1925],{"xmlns":890},[892,1926,1927,1947],{},[895,1928,1929,1937,1939],{},[1659,1930,1931,1933,1935],{},[898,1932,1755],{},[1665,1934,1667],{},[1654,1936,1670],{},[1654,1938,1674],{"separator":1673},[1659,1940,1941,1943,1945],{},[898,1942,1755],{},[1665,1944,1681],{},[1654,1946,1670],{},[902,1948,1949],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,1952,1954],{"className":1953},[886],[888,1955,1957],{"xmlns":890,"display":1956},"block",[892,1958,1959,2021],{},[1960,1961,1963],"mtable",{"width":1962},"100%",[1964,1965,1966,1970,2014,2016],"mtr",{},[1967,1968],"mtd",{"width":1969},"50%",[1967,1971,1972],{},[895,1973,1974,1980,1982,1990,1996,1998,2006,2012],{},[1741,1975,1976,1978],{},[898,1977,1745],{},[1654,1979,1670],{},[1654,1981,1750],{},[1659,1983,1984,1986,1988],{},[898,1985,1755],{},[1665,1987,1667],{},[1654,1989,1670],{},[1710,1991,1992,1994],{},[898,1993,1663],{},[1665,1995,1667],{},[1654,1997,1766],{},[1659,1999,2000,2002,2004],{},[898,2001,1755],{},[1665,2003,1681],{},[1654,2005,1670],{},[1710,2007,2008,2010],{},[898,2009,1663],{},[1665,2011,1681],{},[1654,2013,1674],{"separator":1673},[1967,2015],{"width":1969},[1967,2017,2018],{},[1865,2019,2020],{},"(6.12)",[902,2022,2023],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,2025,2026,2027,2030,2031,2068,2069,2105,2106,2119,2120,2134,2135,2138],{},"geometricky ",[38,2028,2029],{},"rozpočtová přímka (budget line)"," procházející body ",[883,2032,2034],{"className":2033},[886],[888,2035,2036],{"xmlns":890},[892,2037,2038,2065],{},[895,2039,2040,2042,2048,2050,2058,2060,2063],{},[1654,2041,1657],{"stretchy":1656},[1741,2043,2044,2046],{},[898,2045,1745],{},[1654,2047,1670],{},[898,2049,1879],{"mathvariant":1878},[1659,2051,2052,2054,2056],{},[898,2053,1755],{},[1665,2055,1667],{},[1654,2057,1670],{},[1654,2059,1674],{"separator":1673},[1665,2061,2062],{},"0",[1654,2064,1686],{"stretchy":1656},[902,2066,2067],{"encoding":904},"[Y^*\u002FP_1^*, 0]"," a ",[883,2070,2072],{"className":2071},[886],[888,2073,2074],{"xmlns":890},[892,2075,2076,2102],{},[895,2077,2078,2080,2082,2084,2090,2092,2100],{},[1654,2079,1657],{"stretchy":1656},[1665,2081,2062],{},[1654,2083,1674],{"separator":1673},[1741,2085,2086,2088],{},[898,2087,1745],{},[1654,2089,1670],{},[898,2091,1879],{"mathvariant":1878},[1659,2093,2094,2096,2098],{},[898,2095,1755],{},[1665,2097,1681],{},[1654,2099,1670],{},[1654,2101,1686],{"stretchy":1656},[902,2103,2104],{"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 ",[883,2107,2109],{"className":2108},[886],[888,2110,2111],{"xmlns":890},[892,2112,2113,2117],{},[895,2114,2115],{},[898,2116,900],{},[902,2118,900],{"encoding":904},", indiferenční křivky a ",[883,2121,2123],{"className":2122},[886],[888,2124,2125],{"xmlns":890},[892,2126,2127,2131],{},[895,2128,2129],{},[1865,2130,1867],{},[902,2132,2133],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,2136,880],{"className":2137,"dataFsResolvedFilePath":878,"href":879},[210],".",[2140,2141,2142],"blockquote",{},[724,2143,2144,2147,2148,2151,2152,2165,2166,2168,2169,2182,2183,2186,2187,2227,2228,2245,2246,2263,2264,2281,2282,2300],{},[883,2145,2146],{},"!warning"," Pozor — dvě úlohy, totéž řešení\n",[38,2149,2150],{},"Primární úloha"," (max ",[883,2153,2155],{"className":2154},[886],[888,2156,2157],{"xmlns":890},[892,2158,2159,2163],{},[895,2160,2161],{},[898,2162,900],{},[902,2164,900],{"encoding":904}," při pevném rozpočtu) a ",[38,2167,1785],{}," (min ",[883,2170,2172],{"className":2171},[886],[888,2173,2174],{"xmlns":890},[892,2175,2176,2180],{},[895,2177,2178],{},[898,2179,1798],{},[902,2181,1798],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,2184,2185],{},"tentýž bod"," ",[883,2188,2190],{"className":2189},[886],[888,2191,2192],{"xmlns":890},[892,2193,2194,2224],{},[895,2195,2196,2202,2204,2212,2214,2222],{},[1741,2197,2198,2200],{},[898,2199,1663],{},[1654,2201,1670],{},[1654,2203,1657],{"stretchy":1656},[1659,2205,2206,2208,2210],{},[898,2207,1663],{},[1665,2209,1667],{},[1654,2211,1670],{},[1654,2213,1674],{"separator":1673},[1659,2215,2216,2218,2220],{},[898,2217,1663],{},[1665,2219,1681],{},[1654,2221,1670],{},[1654,2223,1686],{"stretchy":1656},[902,2225,2226],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,2229,2231],{"className":2230},[886],[888,2232,2233],{"xmlns":890},[892,2234,2235,2243],{},[895,2236,2237],{},[1741,2238,2239,2241],{},[898,2240,1745],{},[1654,2242,1670],{},[902,2244,1918],{"encoding":904}," a hledáme maximální ",[883,2247,2249],{"className":2248},[886],[888,2250,2251],{"xmlns":890},[892,2252,2253,2261],{},[895,2254,2255],{},[1741,2256,2257,2259],{},[898,2258,900],{},[1654,2260,1670],{},[902,2262,1848],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,2265,2267],{"className":2266},[886],[888,2268,2269],{"xmlns":890},[892,2270,2271,2279],{},[895,2272,2273],{},[1741,2274,2275,2277],{},[898,2276,900],{},[1654,2278,1670],{},[902,2280,1848],{"encoding":904}," a hledáme minimální ",[883,2283,2285],{"className":2284},[886],[888,2286,2287],{"xmlns":890},[892,2288,2289,2297],{},[895,2290,2291],{},[1741,2292,2293,2295],{},[898,2294,1798],{},[1654,2296,1670],{},[902,2298,2299],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,2302,2304],{"id":2303},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,2306,2307,2308,2339,2340,2418,2419,2138],{},"Úlohou je najít maximum ",[883,2309,2311],{"className":2310},[886],[888,2312,2313],{"xmlns":890},[892,2314,2315,2337],{},[895,2316,2317,2319,2321,2327,2329,2335],{},[898,2318,900],{},[1654,2320,1708],{"stretchy":1656},[1710,2322,2323,2325],{},[898,2324,1663],{},[1665,2326,1667],{},[1654,2328,1674],{"separator":1673},[1710,2330,2331,2333],{},[898,2332,1663],{},[1665,2334,1681],{},[1654,2336,1726],{"stretchy":1656},[902,2338,1729],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,2341,2343],{"className":2342},[886],[888,2344,2345],{"xmlns":890},[892,2346,2347,2415],{},[895,2348,2349,2352,2354,2360,2362,2368,2370,2372,2378,2381,2389,2395,2397,2405,2411,2413],{},[898,2350,2351],{},"g",[1654,2353,1708],{"stretchy":1656},[1710,2355,2356,2358],{},[898,2357,1663],{},[1665,2359,1667],{},[1654,2361,1674],{"separator":1673},[1710,2363,2364,2366],{},[898,2365,1663],{},[1665,2367,1681],{},[1654,2369,1726],{"stretchy":1656},[1654,2371,1750],{},[1741,2373,2374,2376],{},[898,2375,1745],{},[1654,2377,1670],{},[1654,2379,2380],{},"−",[1659,2382,2383,2385,2387],{},[898,2384,1755],{},[1665,2386,1667],{},[1654,2388,1670],{},[1710,2390,2391,2393],{},[898,2392,1663],{},[1665,2394,1667],{},[1654,2396,2380],{},[1659,2398,2399,2401,2403],{},[898,2400,1755],{},[1665,2402,1681],{},[1654,2404,1670],{},[1710,2406,2407,2409],{},[898,2408,1663],{},[1665,2410,1681],{},[1654,2412,1750],{},[1665,2414,2062],{},[902,2416,2417],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,2420,2422],{"className":2421,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,2424,2426],{"id":2425},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,2428,2429],{},"Sestavíme",[883,2431,2433],{"className":2432},[886],[888,2434,2435],{"xmlns":890,"display":1956},[892,2436,2437,2551],{},[1960,2438,2439],{"width":1962},[1964,2440,2441,2443,2544,2546],{},[1967,2442],{"width":1969},[1967,2444,2445],{},[895,2446,2447,2451,2453,2459,2461,2467,2469,2472,2474,2476,2478,2480,2486,2488,2494,2496,2498,2500,2502,2508,2510,2518,2524,2526,2534,2540,2542],{},[898,2448,2450],{"mathvariant":2449},"script","L",[1654,2452,1708],{"stretchy":1656},[1710,2454,2455,2457],{},[898,2456,1663],{},[1665,2458,1667],{},[1654,2460,1674],{"separator":1673},[1710,2462,2463,2465],{},[898,2464,1663],{},[1665,2466,1681],{},[1654,2468,1674],{"separator":1673},[898,2470,2471],{},"λ",[1654,2473,1726],{"stretchy":1656},[1654,2475,1750],{},[898,2477,900],{},[1654,2479,1708],{"stretchy":1656},[1710,2481,2482,2484],{},[898,2483,1663],{},[1665,2485,1667],{},[1654,2487,1674],{"separator":1673},[1710,2489,2490,2492],{},[898,2491,1663],{},[1665,2493,1681],{},[1654,2495,1726],{"stretchy":1656},[1654,2497,1766],{},[898,2499,2471],{},[1654,2501,1708],{"stretchy":1656},[1741,2503,2504,2506],{},[898,2505,1745],{},[1654,2507,1670],{},[1654,2509,2380],{},[1659,2511,2512,2514,2516],{},[898,2513,1755],{},[1665,2515,1667],{},[1654,2517,1670],{},[1710,2519,2520,2522],{},[898,2521,1663],{},[1665,2523,1667],{},[1654,2525,2380],{},[1659,2527,2528,2530,2532],{},[898,2529,1755],{},[1665,2531,1681],{},[1654,2533,1670],{},[1710,2535,2536,2538],{},[898,2537,1663],{},[1665,2539,1681],{},[1654,2541,1726],{"stretchy":1656},[898,2543,2138],{"mathvariant":1878},[1967,2545],{"width":1969},[1967,2547,2548],{},[1865,2549,2550],{},"(6.13)",[902,2552,2553],{"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}",[724,2555,2556],{},"Soustava prvního řádu:",[883,2558,2560],{"className":2559},[886],[888,2561,2562],{"xmlns":890,"display":1956},[892,2563,2564,2753],{},[1960,2565,2566],{"width":1962},[1964,2567,2568,2570,2746,2748],{},[1967,2569],{"width":1969},[1967,2571,2572],{},[1960,2573,2577,2629,2679],{"rowspacing":2574,"columnalign":2575,"columnspacing":2576},"0.25em","right left","0em",[1964,2578,2579,2593],{},[1967,2580,2581],{},[2582,2583,2584],"mstyle",{"scriptlevel":2062,"displaystyle":1673},[1659,2585,2586,2588,2590],{},[898,2587,2450],{"mathvariant":2449},[1665,2589,1667],{},[1654,2591,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},"′",[1967,2594,2595],{},[2582,2596,2597],{"scriptlevel":2062,"displaystyle":1673},[895,2598,2599,2601,2603,2611,2613,2615,2623,2625,2627],{},[895,2600],{},[1654,2602,1750],{},[1659,2604,2605,2607,2609],{},[898,2606,900],{},[1665,2608,1667],{},[1654,2610,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,2612,2380],{},[898,2614,2471],{},[1659,2616,2617,2619,2621],{},[898,2618,1755],{},[1665,2620,1667],{},[1654,2622,1670],{},[1654,2624,1750],{},[1665,2626,2062],{},[1654,2628,1674],{"separator":1673},[1964,2630,2631,2643],{},[1967,2632,2633],{},[2582,2634,2635],{"scriptlevel":2062,"displaystyle":1673},[1659,2636,2637,2639,2641],{},[898,2638,2450],{"mathvariant":2449},[1665,2640,1681],{},[1654,2642,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1967,2644,2645],{},[2582,2646,2647],{"scriptlevel":2062,"displaystyle":1673},[895,2648,2649,2651,2653,2661,2663,2665,2673,2675,2677],{},[895,2650],{},[1654,2652,1750],{},[1659,2654,2655,2657,2659],{},[898,2656,900],{},[1665,2658,1681],{},[1654,2660,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,2662,2380],{},[898,2664,2471],{},[1659,2666,2667,2669,2671],{},[898,2668,1755],{},[1665,2670,1681],{},[1654,2672,1670],{},[1654,2674,1750],{},[1665,2676,2062],{},[1654,2678,1674],{"separator":1673},[1964,2680,2681,2693],{},[1967,2682,2683],{},[2582,2684,2685],{"scriptlevel":2062,"displaystyle":1673},[1659,2686,2687,2689,2691],{},[898,2688,2450],{"mathvariant":2449},[898,2690,2471],{},[1654,2692,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1967,2694,2695],{},[2582,2696,2697],{"scriptlevel":2062,"displaystyle":1673},[895,2698,2699,2701,2703,2709,2711,2719,2725,2727,2735,2741,2743],{},[895,2700],{},[1654,2702,1750],{},[1741,2704,2705,2707],{},[898,2706,1745],{},[1654,2708,1670],{},[1654,2710,2380],{},[1659,2712,2713,2715,2717],{},[898,2714,1755],{},[1665,2716,1667],{},[1654,2718,1670],{},[1710,2720,2721,2723],{},[898,2722,1663],{},[1665,2724,1667],{},[1654,2726,2380],{},[1659,2728,2729,2731,2733],{},[898,2730,1755],{},[1665,2732,1681],{},[1654,2734,1670],{},[1710,2736,2737,2739],{},[898,2738,1663],{},[1665,2740,1681],{},[1654,2742,1750],{},[1665,2744,2745],{},"0.",[1967,2747],{"width":1969},[1967,2749,2750],{},[1865,2751,2752],{},"(6.14)",[902,2754,2755],{"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}",[724,2757,2758,2759,2762,2763,2777,2778,2781],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,2760,2761],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,2764,2766],{"className":2765},[886],[888,2767,2768],{"xmlns":890},[892,2769,2770,2774],{},[895,2771,2772],{},[898,2773,2471],{},[902,2775,2776],{"encoding":904},"\\lambda"," dostáváme ",[38,2779,2780],{},"podmínku optimality",":",[883,2783,2785],{"className":2784},[886],[888,2786,2787],{"xmlns":890,"display":1956},[892,2788,2789,2851],{},[895,2790,2791],{},[2792,2793,2795],"menclose",{"notation":2794},"box",[2582,2796,2797],{"scriptlevel":2062,"displaystyle":1656},[2582,2798,2799],{"scriptlevel":2062,"displaystyle":1656},[2582,2800,2801],{"scriptlevel":2062,"displaystyle":1673},[895,2802,2803,2806,2808,2810,2829,2831,2849],{},[1865,2804,2805],{},"  ",[1865,2807,1867],{},[1654,2809,1750],{},[2811,2812,2813,2821],"mfrac",{},[1659,2814,2815,2817,2819],{},[898,2816,900],{},[1665,2818,1667],{},[1654,2820,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1659,2822,2823,2825,2827],{},[898,2824,900],{},[1665,2826,1681],{},[1654,2828,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,2830,1750],{},[2811,2832,2833,2841],{},[1659,2834,2835,2837,2839],{},[898,2836,1755],{},[1665,2838,1667],{},[1654,2840,1670],{},[1659,2842,2843,2845,2847],{},[898,2844,1755],{},[1665,2846,1681],{},[1654,2848,1670],{},[1865,2850,2805],{},[902,2852,2853],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[2140,2855,2856],{},[724,2857,2858,2861,2862,2896,2897,2900,2901,2919,2920,2938,2939,2970,2971,2988,2989,3020],{},[883,2859,2860],{},"!info"," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,2863,2865],{"className":2864},[886],[888,2866,2867],{"xmlns":890},[892,2868,2869,2893],{},[895,2870,2871,2873,2875,2883,2885],{},[1865,2872,1867],{},[1654,2874,1750],{},[1659,2876,2877,2879,2881],{},[898,2878,1755],{},[1665,2880,1667],{},[1654,2882,1670],{},[898,2884,1879],{"mathvariant":1878},[1659,2886,2887,2889,2891],{},[898,2888,1755],{},[1665,2890,1681],{},[1654,2892,1670],{},[902,2894,2895],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,2898,2899],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,2902,2904],{"className":2903},[886],[888,2905,2906],{"xmlns":890},[892,2907,2908,2916],{},[895,2909,2910],{},[1710,2911,2912,2914],{},[898,2913,1663],{},[1665,2915,1667],{},[902,2917,2918],{"encoding":904},"Q_1"," za ",[883,2921,2923],{"className":2922},[886],[888,2924,2925],{"xmlns":890},[892,2926,2927,2935],{},[895,2928,2929],{},[1710,2930,2931,2933],{},[898,2932,1663],{},[1665,2934,1681],{},[902,2936,2937],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,2940,2942],{"className":2941},[886],[888,2943,2944],{"xmlns":890},[892,2945,2946,2967],{},[895,2947,2948,2950,2953,2959,2961],{},[1865,2949,1867],{},[1654,2951,2952],{},">",[1710,2954,2955,2957],{},[898,2956,1755],{},[1665,2958,1667],{},[898,2960,1879],{"mathvariant":1878},[1710,2962,2963,2965],{},[898,2964,1755],{},[1665,2966,1681],{},[902,2968,2969],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,2972,2974],{"className":2973},[886],[888,2975,2976],{"xmlns":890},[892,2977,2978,2986],{},[895,2979,2980],{},[1710,2981,2982,2984],{},[898,2983,1663],{},[1665,2985,1667],{},[902,2987,2918],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,2990,2992],{"className":2991},[886],[888,2993,2994],{"xmlns":890},[892,2995,2996,3017],{},[895,2997,2998,3000,3003,3009,3011],{},[1865,2999,1867],{},[1654,3001,3002],{},"\u003C",[1710,3004,3005,3007],{},[898,3006,1755],{},[1665,3008,1667],{},[898,3010,1879],{"mathvariant":1878},[1710,3012,3013,3015],{},[898,3014,1755],{},[1665,3016,1681],{},[902,3018,3019],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,3022,3024,3025,3038],{"id":3023},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,3026,3028],{"className":3027},[886],[888,3029,3030],{"xmlns":890},[892,3031,3032,3036],{},[895,3033,3034],{},[898,3035,2471],{},[902,3037,2776],{"encoding":904}," — mezní užitečnost důchodu",[724,3040,3041,3042,3060,3061,3064,3065,3082,3083,3100,3101,3104],{},"Lagrangeův multiplikátor ",[883,3043,3045],{"className":3044},[886],[888,3046,3047],{"xmlns":890},[892,3048,3049,3057],{},[895,3050,3051],{},[1741,3052,3053,3055],{},[898,3054,2471],{},[1654,3056,1670],{},[902,3058,3059],{"encoding":904},"\\lambda^*"," představuje ",[38,3062,3063],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,3066,3068],{"className":3067},[886],[888,3069,3070],{"xmlns":890},[892,3071,3072,3080],{},[895,3073,3074],{},[1741,3075,3076,3078],{},[898,3077,900],{},[1654,3079,1670],{},[902,3081,1848],{"encoding":904}," při jednotkové změně důchodu ",[883,3084,3086],{"className":3085},[886],[888,3087,3088],{"xmlns":890},[892,3089,3090,3098],{},[895,3091,3092],{},[1741,3093,3094,3096],{},[898,3095,1745],{},[1654,3097,1670],{},[902,3099,1918],{"encoding":904},". Je to ",[38,3102,3103],{},"stínová cena"," rozpočtového omezení.",[2140,3106,3107,3113],{},[724,3108,3109,3112],{},[883,3110,3111],{},"!tip"," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,3114,3115,3175,3262,3299,3386],{},[123,3116,3117,3120,3121,2138],{},[38,3118,3119],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,3122,3124],{"className":3123},[886],[888,3125,3126],{"xmlns":890},[892,3127,3128,3172],{},[895,3129,3130,3136,3138,3146,3152,3154,3162,3168,3170],{},[1741,3131,3132,3134],{},[898,3133,1745],{},[1654,3135,1670],{},[1654,3137,2380],{},[1659,3139,3140,3142,3144],{},[898,3141,1755],{},[1665,3143,1667],{},[1654,3145,1670],{},[1710,3147,3148,3150],{},[898,3149,1663],{},[1665,3151,1667],{},[1654,3153,2380],{},[1659,3155,3156,3158,3160],{},[898,3157,1755],{},[1665,3159,1681],{},[1654,3161,1670],{},[1710,3163,3164,3166],{},[898,3165,1663],{},[1665,3167,1681],{},[1654,3169,1750],{},[1665,3171,2062],{},[902,3173,3174],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,3176,3177,2186,3180,2138],{},[38,3178,3179],{},"Sestav Lagrangeovu funkci",[883,3181,3183],{"className":3182},[886],[888,3184,3185],{"xmlns":890},[892,3186,3187,3259],{},[895,3188,3189,3191,3193,3195,3197,3203,3205,3211,3213,3215,3217,3219,3225,3227,3235,3241,3243,3251,3257],{},[898,3190,2450],{"mathvariant":2449},[1654,3192,1750],{},[898,3194,900],{},[1654,3196,1708],{"stretchy":1656},[1710,3198,3199,3201],{},[898,3200,1663],{},[1665,3202,1667],{},[1654,3204,1674],{"separator":1673},[1710,3206,3207,3209],{},[898,3208,1663],{},[1665,3210,1681],{},[1654,3212,1726],{"stretchy":1656},[1654,3214,1766],{},[898,3216,2471],{},[1654,3218,1708],{"stretchy":1656},[1741,3220,3221,3223],{},[898,3222,1745],{},[1654,3224,1670],{},[1654,3226,2380],{},[1659,3228,3229,3231,3233],{},[898,3230,1755],{},[1665,3232,1667],{},[1654,3234,1670],{},[1710,3236,3237,3239],{},[898,3238,1663],{},[1665,3240,1667],{},[1654,3242,2380],{},[1659,3244,3245,3247,3249],{},[898,3246,1755],{},[1665,3248,1681],{},[1654,3250,1670],{},[1710,3252,3253,3255],{},[898,3254,1663],{},[1665,3256,1681],{},[1654,3258,1726],{"stretchy":1656},[902,3260,3261],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,3263,3264,3267,3268,3298],{},[38,3265,3266],{},"Spočítej parciální derivace"," podle ",[883,3269,3271],{"className":3270},[886],[888,3272,3273],{"xmlns":890},[892,3274,3275,3295],{},[895,3276,3277,3283,3285,3291,3293],{},[1710,3278,3279,3281],{},[898,3280,1663],{},[1665,3282,1667],{},[1654,3284,1674],{"separator":1673},[1710,3286,3287,3289],{},[898,3288,1663],{},[1665,3290,1681],{},[1654,3292,1674],{"separator":1673},[898,3294,2471],{},[902,3296,3297],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,3300,3301,3317,3318,3351,3352,2068,3369,2138],{},[38,3302,3303,3304],{},"Vyluč ",[883,3305,3307],{"className":3306},[886],[888,3308,3309],{"xmlns":890},[892,3310,3311,3315],{},[895,3312,3313],{},[898,3314,2471],{},[902,3316,2776],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,3319,3321],{"className":3320},[886],[888,3322,3323],{"xmlns":890},[892,3324,3325,3349],{},[895,3326,3327,3329,3331,3339,3341],{},[1865,3328,1867],{},[1654,3330,1750],{},[1659,3332,3333,3335,3337],{},[898,3334,1755],{},[1665,3336,1667],{},[1654,3338,1670],{},[898,3340,1879],{"mathvariant":1878},[1659,3342,3343,3345,3347],{},[898,3344,1755],{},[1665,3346,1681],{},[1654,3348,1670],{},[902,3350,2895],{"encoding":904},", která dá vztah mezi ",[883,3353,3355],{"className":3354},[886],[888,3356,3357],{"xmlns":890},[892,3358,3359,3367],{},[895,3360,3361],{},[1710,3362,3363,3365],{},[898,3364,1663],{},[1665,3366,1667],{},[902,3368,2918],{"encoding":904},[883,3370,3372],{"className":3371},[886],[888,3373,3374],{"xmlns":890},[892,3375,3376,3384],{},[895,3377,3378],{},[1710,3379,3380,3382],{},[898,3381,1663],{},[1665,3383,1681],{},[902,3385,2937],{"encoding":904},[123,3387,3388,3391,3392,3422,3423,3440,3441,2138],{},[38,3389,3390],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,3393,3395],{"className":3394},[886],[888,3396,3397],{"xmlns":890},[892,3398,3399,3419],{},[895,3400,3401,3409,3411],{},[1659,3402,3403,3405,3407],{},[898,3404,1663],{},[1665,3406,1667],{},[1654,3408,1670],{},[1654,3410,1674],{"separator":1673},[1659,3412,3413,3415,3417],{},[898,3414,1663],{},[1665,3416,1681],{},[1654,3418,1670],{},[902,3420,3421],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,3424,3426],{"className":3425},[886],[888,3427,3428],{"xmlns":890},[892,3429,3430,3438],{},[895,3431,3432],{},[1741,3433,3434,3436],{},[898,3435,2471],{},[1654,3437,1670],{},[902,3439,3059],{"encoding":904}," a maximální užitečnost ",[883,3442,3444],{"className":3443},[886],[888,3445,3446],{"xmlns":890},[892,3447,3448,3482],{},[895,3449,3450,3456,3458,3460,3462,3470,3472,3480],{},[1741,3451,3452,3454],{},[898,3453,900],{},[1654,3455,1670],{},[1654,3457,1750],{},[898,3459,900],{},[1654,3461,1708],{"stretchy":1656},[1659,3463,3464,3466,3468],{},[898,3465,1663],{},[1665,3467,1667],{},[1654,3469,1670],{},[1654,3471,1674],{"separator":1673},[1659,3473,3474,3476,3478],{},[898,3475,1663],{},[1665,3477,1681],{},[1654,3479,1670],{},[1654,3481,1726],{"stretchy":1656},[902,3483,3484],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,3486,3488],{"id":3487},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,3490,3491],{},[3492,3493],"img",{"alt":3494,"className":3495,"src":3497},"imek-uzitecnost-optimum",[210,3496],"wikilink-broken","\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,3499,3500],{},[614,3501,3502,3503,3553,3554,2068,3582,3610,3611,3646,3647,3686,3687,3705,3706,3724,3725,3743],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,3504,3506],{"className":3505},[886],[888,3507,3508],{"xmlns":890},[892,3509,3510,3550],{},[895,3511,3512,3518,3520,3528,3534,3536,3544],{},[1741,3513,3514,3516],{},[898,3515,1745],{},[1654,3517,1670],{},[1654,3519,1750],{},[1659,3521,3522,3524,3526],{},[898,3523,1755],{},[1665,3525,1667],{},[1654,3527,1670],{},[1710,3529,3530,3532],{},[898,3531,1663],{},[1665,3533,1667],{},[1654,3535,1766],{},[1659,3537,3538,3540,3542],{},[898,3539,1755],{},[1665,3541,1681],{},[1654,3543,1670],{},[1710,3545,3546,3548],{},[898,3547,1663],{},[1665,3549,1681],{},[902,3551,3552],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2"," protíná osy v ",[883,3555,3557],{"className":3556},[886],[888,3558,3559],{"xmlns":890},[892,3560,3561,3579],{},[895,3562,3563,3569,3571],{},[1741,3564,3565,3567],{},[898,3566,1745],{},[1654,3568,1670],{},[898,3570,1879],{"mathvariant":1878},[1659,3572,3573,3575,3577],{},[898,3574,1755],{},[1665,3576,1667],{},[1654,3578,1670],{},[902,3580,3581],{"encoding":904},"Y^*\u002FP_1^*",[883,3583,3585],{"className":3584},[886],[888,3586,3587],{"xmlns":890},[892,3588,3589,3607],{},[895,3590,3591,3597,3599],{},[1741,3592,3593,3595],{},[898,3594,1745],{},[1654,3596,1670],{},[898,3598,1879],{"mathvariant":1878},[1659,3600,3601,3603,3605],{},[898,3602,1755],{},[1665,3604,1681],{},[1654,3606,1670],{},[902,3608,3609],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,3612,3614],{"className":3613},[886],[888,3615,3616],{"xmlns":890},[892,3617,3618,3643],{},[895,3619,3620,3627,3629,3635,3637],{},[1710,3621,3622,3625],{},[898,3623,3624],{},"c",[1665,3626,1667],{},[1654,3628,3002],{},[1741,3630,3631,3633],{},[898,3632,3624],{},[1654,3634,1670],{},[1654,3636,3002],{},[1710,3638,3639,3641],{},[898,3640,3624],{},[1665,3642,1681],{},[902,3644,3645],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,3648,3650],{"className":3649},[886],[888,3651,3652],{"xmlns":890},[892,3653,3654,3684],{},[895,3655,3656,3662,3664,3672,3674,3682],{},[1741,3657,3658,3660],{},[898,3659,1663],{},[1654,3661,1670],{},[1654,3663,1657],{"stretchy":1656},[1659,3665,3666,3668,3670],{},[898,3667,1663],{},[1665,3669,1667],{},[1654,3671,1670],{},[1654,3673,1674],{"separator":1673},[1659,3675,3676,3678,3680],{},[898,3677,1663],{},[1665,3679,1681],{},[1654,3681,1670],{},[1654,3683,1686],{"stretchy":1656},[902,3685,2226],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,3688,3690],{"className":3689},[886],[888,3691,3692],{"xmlns":890},[892,3693,3694,3702],{},[895,3695,3696],{},[1741,3697,3698,3700],{},[898,3699,3624],{},[1654,3701,1670],{},[902,3703,3704],{"encoding":904},"c^*",". Křivka ",[883,3707,3709],{"className":3708},[886],[888,3710,3711],{"xmlns":890},[892,3712,3713,3721],{},[895,3714,3715],{},[1710,3716,3717,3719],{},[898,3718,3624],{},[1665,3720,1667],{},[902,3722,3723],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,3726,3728],{"className":3727},[886],[888,3729,3730],{"xmlns":890},[892,3731,3732,3740],{},[895,3733,3734],{},[1710,3735,3736,3738],{},[898,3737,3624],{},[1665,3739,1681],{},[902,3741,3742],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,3745,3746,3747,3750,3751,3769,3770,3799],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,3748,3749],{},"dotýkají",", tj. mají v bodě ",[883,3752,3754],{"className":3753},[886],[888,3755,3756],{"xmlns":890},[892,3757,3758,3766],{},[895,3759,3760],{},[1741,3761,3762,3764],{},[898,3763,1663],{},[1654,3765,1670],{},[902,3767,3768],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,3771,3773],{"className":3772},[886],[888,3774,3775],{"xmlns":890},[892,3776,3777,3797],{},[895,3778,3779,3781,3783,3789,3791],{},[1865,3780,1867],{},[1654,3782,1750],{},[1710,3784,3785,3787],{},[898,3786,1755],{},[1665,3788,1667],{},[898,3790,1879],{"mathvariant":1878},[1710,3792,3793,3795],{},[898,3794,1755],{},[1665,3796,1681],{},[902,3798,1888],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,3801,3803],{"id":3802},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,3805,3806,3807,3869],{},"Pro ",[883,3808,3810],{"className":3809},[886],[888,3811,3812],{"xmlns":890},[892,3813,3814,3866],{},[895,3815,3816,3818,3820,3826,3828,3834,3836,3838,3852],{},[898,3817,900],{},[1654,3819,1708],{"stretchy":1656},[1710,3821,3822,3824],{},[898,3823,1663],{},[1665,3825,1667],{},[1654,3827,1674],{"separator":1673},[1710,3829,3830,3832],{},[898,3831,1663],{},[1665,3833,1681],{},[1654,3835,1726],{"stretchy":1656},[1654,3837,1750],{},[1659,3839,3840,3842,3844],{},[898,3841,1663],{},[1665,3843,1667],{},[895,3845,3846,3848,3850],{},[1665,3847,1667],{},[898,3849,1879],{"mathvariant":1878},[1665,3851,1681],{},[1659,3853,3854,3856,3858],{},[898,3855,1663],{},[1665,3857,1681],{},[895,3859,3860,3862,3864],{},[1665,3861,1667],{},[898,3863,1879],{"mathvariant":1878},[1665,3865,1681],{},[902,3867,3868],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[724,3871,3872],{},[883,3873,3875],{"className":3874},[886],[888,3876,3877],{"xmlns":890},[892,3878,3879,3985],{},[895,3880,3881,3883,3885,3967,3969,3983],{},[1865,3882,1867],{},[1654,3884,1750],{},[2811,3886,3887,3927],{},[895,3888,3889,3897,3913],{},[2582,3890,3891],{"scriptlevel":2062,"displaystyle":1656},[2811,3892,3893,3895],{},[1665,3894,1667],{},[1665,3896,1681],{},[1659,3898,3899,3901,3903],{},[898,3900,1663],{},[1665,3902,1667],{},[895,3904,3905,3907,3909,3911],{},[1654,3906,2380],{},[1665,3908,1667],{},[898,3910,1879],{"mathvariant":1878},[1665,3912,1681],{},[1659,3914,3915,3917,3919],{},[898,3916,1663],{},[1665,3918,1681],{},[895,3920,3921,3923,3925],{},[1665,3922,1667],{},[898,3924,1879],{"mathvariant":1878},[1665,3926,1681],{},[895,3928,3929,3937,3951],{},[2582,3930,3931],{"scriptlevel":2062,"displaystyle":1656},[2811,3932,3933,3935],{},[1665,3934,1667],{},[1665,3936,1681],{},[1659,3938,3939,3941,3943],{},[898,3940,1663],{},[1665,3942,1667],{},[895,3944,3945,3947,3949],{},[1665,3946,1667],{},[898,3948,1879],{"mathvariant":1878},[1665,3950,1681],{},[1659,3952,3953,3955,3957],{},[898,3954,1663],{},[1665,3956,1681],{},[895,3958,3959,3961,3963,3965],{},[1654,3960,2380],{},[1665,3962,1667],{},[898,3964,1879],{"mathvariant":1878},[1665,3966,1681],{},[1654,3968,1750],{},[2811,3970,3971,3977],{},[1710,3972,3973,3975],{},[898,3974,1663],{},[1665,3976,1681],{},[1710,3978,3979,3981],{},[898,3980,1663],{},[1665,3982,1667],{},[898,3984,2138],{"mathvariant":1878},[902,3986,3987],{"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}.",[724,3989,3990,3991,4039,4040,4043,4044,4064,4065,4095,4096,2138],{},"Tedy ",[883,3992,3994],{"className":3993},[886],[888,3995,3996],{"xmlns":890},[892,3997,3998,4036],{},[895,3999,4000,4002,4004,4007,4009,4012,4014,4016,4024,4026],{},[1865,4001,1867],{},[1654,4003,1708],{"stretchy":1656},[1665,4005,4006],{},"300",[1654,4008,1674],{"separator":1673},[1665,4010,4011],{},"500",[1654,4013,1726],{"stretchy":1656},[1654,4015,1750],{},[2582,4017,4018],{"scriptlevel":2062,"displaystyle":1656},[2811,4019,4020,4022],{},[1665,4021,4011],{},[1665,4023,4006],{},[1654,4025,1750],{},[2582,4027,4028],{"scriptlevel":2062,"displaystyle":1656},[2811,4029,4030,4033],{},[1665,4031,4032],{},"5",[1665,4034,4035],{},"3",[902,4037,4038],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",". ",[614,4041,4042],{},"Interpretace:"," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,4045,4047],{"className":4046},[886],[888,4048,4049],{"xmlns":890},[892,4050,4051,4061],{},[895,4052,4053],{},[2582,4054,4055],{"scriptlevel":2062,"displaystyle":1656},[2811,4056,4057,4059],{},[1665,4058,4032],{},[1665,4060,4035],{},[902,4062,4063],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,4066,4068],{"className":4067},[886],[888,4069,4070],{"xmlns":890},[892,4071,4072,4092],{},[895,4073,4074,4076,4078,4084,4086],{},[1865,4075,1867],{},[1654,4077,1750],{},[1710,4079,4080,4082],{},[898,4081,1663],{},[1665,4083,1681],{},[898,4085,1879],{"mathvariant":1878},[1710,4087,4088,4090],{},[898,4089,1663],{},[1665,4091,1667],{},[902,4093,4094],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,4097,4099],{"className":4098},[886],[888,4100,4101],{"xmlns":890},[892,4102,4103,4123],{},[895,4104,4105,4107,4109,4115,4117],{},[1865,4106,1867],{},[1654,4108,1750],{},[1710,4110,4111,4113],{},[898,4112,1755],{},[1665,4114,1667],{},[898,4116,1879],{"mathvariant":1878},[1710,4118,4119,4121],{},[898,4120,1755],{},[1665,4122,1681],{},[902,4124,1888],{"encoding":904},[115,4126,4128,4129],{"id":4127},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,4130,4132],{"className":4131},[886],[888,4133,4134],{"xmlns":890},[892,4135,4136,4154],{},[895,4137,4138,4140,4142,4148],{},[898,4139,900],{},[1654,4141,1750],{},[1710,4143,4144,4146],{},[898,4145,1663],{},[1665,4147,1667],{},[1710,4149,4150,4152],{},[898,4151,1663],{},[1665,4153,1681],{},[902,4155,4156],{"encoding":904},"U = Q_1 Q_2",[724,4158,4159,4160,1343,4206,1343,4230,1343,4254,4277],{},"Je dána ",[883,4161,4163],{"className":4162},[886],[888,4164,4165],{"xmlns":890},[892,4166,4167,4203],{},[895,4168,4169,4171,4173,4179,4181,4187,4189,4191,4197],{},[898,4170,900],{},[1654,4172,1708],{"stretchy":1656},[1710,4174,4175,4177],{},[898,4176,1663],{},[1665,4178,1667],{},[1654,4180,1674],{"separator":1673},[1710,4182,4183,4185],{},[898,4184,1663],{},[1665,4186,1681],{},[1654,4188,1726],{"stretchy":1656},[1654,4190,1750],{},[1710,4192,4193,4195],{},[898,4194,1663],{},[1665,4196,1667],{},[1710,4198,4199,4201],{},[898,4200,1663],{},[1665,4202,1681],{},[902,4204,4205],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,4207,4209],{"className":4208},[886],[888,4210,4211],{"xmlns":890},[892,4212,4213,4227],{},[895,4214,4215,4223,4225],{},[1659,4216,4217,4219,4221],{},[898,4218,1755],{},[1665,4220,1667],{},[1654,4222,1670],{},[1654,4224,1750],{},[1665,4226,1681],{},[902,4228,4229],{"encoding":904},"P_1^* = 2",[883,4231,4233],{"className":4232},[886],[888,4234,4235],{"xmlns":890},[892,4236,4237,4251],{},[895,4238,4239,4247,4249],{},[1659,4240,4241,4243,4245],{},[898,4242,1755],{},[1665,4244,1681],{},[1654,4246,1670],{},[1654,4248,1750],{},[1665,4250,4032],{},[902,4252,4253],{"encoding":904},"P_2^* = 5",[883,4255,4257],{"className":4256},[886],[888,4258,4259],{"xmlns":890},[892,4260,4261,4274],{},[895,4262,4263,4269,4271],{},[1741,4264,4265,4267],{},[898,4266,1745],{},[1654,4268,1670],{},[1654,4270,1750],{},[1665,4272,4273],{},"100",[902,4275,4276],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,4279,4281],{"className":4280},[886],[888,4282,4283],{"xmlns":890,"display":1956},[892,4284,4285,4357],{},[895,4286,4287,4289,4291,4297,4299,4305,4307,4309,4311,4313,4319,4325,4327,4329,4331,4333,4335,4337,4343,4345,4347,4353,4355],{},[898,4288,2450],{"mathvariant":2449},[1654,4290,1708],{"stretchy":1656},[1710,4292,4293,4295],{},[898,4294,1663],{},[1665,4296,1667],{},[1654,4298,1674],{"separator":1673},[1710,4300,4301,4303],{},[898,4302,1663],{},[1665,4304,1681],{},[1654,4306,1674],{"separator":1673},[898,4308,2471],{},[1654,4310,1726],{"stretchy":1656},[1654,4312,1750],{},[1710,4314,4315,4317],{},[898,4316,1663],{},[1665,4318,1667],{},[1710,4320,4321,4323],{},[898,4322,1663],{},[1665,4324,1681],{},[1654,4326,1766],{},[898,4328,2471],{},[1654,4330,1708],{"stretchy":1656},[1665,4332,4273],{},[1654,4334,2380],{},[1665,4336,1681],{},[1710,4338,4339,4341],{},[898,4340,1663],{},[1665,4342,1667],{},[1654,4344,2380],{},[1665,4346,4032],{},[1710,4348,4349,4351],{},[898,4350,1663],{},[1665,4352,1681],{},[1654,4354,1726],{"stretchy":1656},[898,4356,2138],{"mathvariant":1878},[902,4358,4359],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,4361,4362],{},"Soustava:",[883,4364,4366],{"className":4365},[886],[888,4367,4368],{"xmlns":890,"display":1956},[892,4369,4370,4482],{},[1960,4371,4372,4406,4440],{"rowspacing":2574,"columnalign":2575,"columnspacing":2576},[1964,4373,4374,4392],{},[1967,4375,4376],{},[2582,4377,4378],{"scriptlevel":2062,"displaystyle":1673},[895,4379,4380,4386,4388,4390],{},[1710,4381,4382,4384],{},[898,4383,1663],{},[1665,4385,1681],{},[1654,4387,2380],{},[1665,4389,1681],{},[898,4391,2471],{},[1967,4393,4394],{},[2582,4395,4396],{"scriptlevel":2062,"displaystyle":1673},[895,4397,4398,4400,4402,4404],{},[895,4399],{},[1654,4401,1750],{},[1665,4403,2062],{},[1654,4405,1674],{"separator":1673},[1964,4407,4408,4426],{},[1967,4409,4410],{},[2582,4411,4412],{"scriptlevel":2062,"displaystyle":1673},[895,4413,4414,4420,4422,4424],{},[1710,4415,4416,4418],{},[898,4417,1663],{},[1665,4419,1667],{},[1654,4421,2380],{},[1665,4423,4032],{},[898,4425,2471],{},[1967,4427,4428],{},[2582,4429,4430],{"scriptlevel":2062,"displaystyle":1673},[895,4431,4432,4434,4436,4438],{},[895,4433],{},[1654,4435,1750],{},[1665,4437,2062],{},[1654,4439,1674],{"separator":1673},[1964,4441,4442,4470],{},[1967,4443,4444],{},[2582,4445,4446],{"scriptlevel":2062,"displaystyle":1673},[895,4447,4448,4450,4452,4454,4460,4462,4464],{},[1665,4449,4273],{},[1654,4451,2380],{},[1665,4453,1681],{},[1710,4455,4456,4458],{},[898,4457,1663],{},[1665,4459,1667],{},[1654,4461,2380],{},[1665,4463,4032],{},[1710,4465,4466,4468],{},[898,4467,1663],{},[1665,4469,1681],{},[1967,4471,4472],{},[2582,4473,4474],{"scriptlevel":2062,"displaystyle":1673},[895,4475,4476,4478,4480],{},[895,4477],{},[1654,4479,1750],{},[1665,4481,2745],{},[902,4483,4484],{"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}",[724,4486,4487,4488,1343,4512,4536,4537,4579,4580,4598,4599,4651,4652,2138],{},"Z prvních dvou rovnic ",[883,4489,4491],{"className":4490},[886],[888,4492,4493],{"xmlns":890},[892,4494,4495,4509],{},[895,4496,4497,4503,4505,4507],{},[1710,4498,4499,4501],{},[898,4500,1663],{},[1665,4502,1681],{},[1654,4504,1750],{},[1665,4506,1681],{},[898,4508,2471],{},[902,4510,4511],{"encoding":904},"Q_2 = 2\\lambda",[883,4513,4515],{"className":4514},[886],[888,4516,4517],{"xmlns":890},[892,4518,4519,4533],{},[895,4520,4521,4527,4529,4531],{},[1710,4522,4523,4525],{},[898,4524,1663],{},[1665,4526,1667],{},[1654,4528,1750],{},[1665,4530,4032],{},[898,4532,2471],{},[902,4534,4535],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,4538,4540],{"className":4539},[886],[888,4541,4542],{"xmlns":890},[892,4543,4544,4576],{},[895,4545,4546,4548,4550,4552,4555,4557,4559,4561,4563,4565,4567,4569,4571,4574],{},[1665,4547,4273],{},[1654,4549,1750],{},[1665,4551,1681],{},[1654,4553,4554],{},"⋅",[1665,4556,4032],{},[898,4558,2471],{},[1654,4560,1766],{},[1665,4562,4032],{},[1654,4564,4554],{},[1665,4566,1681],{},[898,4568,2471],{},[1654,4570,1750],{},[1665,4572,4573],{},"20",[898,4575,2471],{},[902,4577,4578],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",", tedy ",[883,4581,4583],{"className":4582},[886],[888,4584,4585],{"xmlns":890},[892,4586,4587,4595],{},[895,4588,4589,4591,4593],{},[898,4590,2471],{},[1654,4592,1750],{},[1665,4594,4032],{},[902,4596,4597],{"encoding":904},"\\lambda = 5",". Odtud ",[38,4600,4601,1343,4626],{},[883,4602,4604],{"className":4603},[886],[888,4605,4606],{"xmlns":890},[892,4607,4608,4623],{},[895,4609,4610,4618,4620],{},[1659,4611,4612,4614,4616],{},[898,4613,1663],{},[1665,4615,1667],{},[1654,4617,1670],{},[1654,4619,1750],{},[1665,4621,4622],{},"25",[902,4624,4625],{"encoding":904},"Q_1^* = 25",[883,4627,4629],{"className":4628},[886],[888,4630,4631],{"xmlns":890},[892,4632,4633,4648],{},[895,4634,4635,4643,4645],{},[1659,4636,4637,4639,4641],{},[898,4638,1663],{},[1665,4640,1681],{},[1654,4642,1670],{},[1654,4644,1750],{},[1665,4646,4647],{},"10",[902,4649,4650],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,4653,4655],{"className":4654},[886],[888,4656,4657],{"xmlns":890},[892,4658,4659,4680],{},[895,4660,4661,4667,4669,4671,4673,4675,4677],{},[1741,4662,4663,4665],{},[898,4664,900],{},[1654,4666,1670],{},[1654,4668,1750],{},[1665,4670,4622],{},[1654,4672,4554],{},[1665,4674,4647],{},[1654,4676,1750],{},[1665,4678,4679],{},"250",[902,4681,4682],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,4684,4685],{},[614,4686,4687,4688,2030,4726,2068,4751,4777,4778,4808,4809,4833,4834,4856,4857,2138],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,4689,4691],{"className":4690},[886],[888,4692,4693],{"xmlns":890},[892,4694,4695,4723],{},[895,4696,4697,4699,4701,4703,4709,4711,4713,4719,4721],{},[1665,4698,4273],{},[1654,4700,2380],{},[1665,4702,1681],{},[1710,4704,4705,4707],{},[898,4706,1663],{},[1665,4708,1667],{},[1654,4710,2380],{},[1665,4712,4032],{},[1710,4714,4715,4717],{},[898,4716,1663],{},[1665,4718,1681],{},[1654,4720,1750],{},[1665,4722,2062],{},[902,4724,4725],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,4727,4729],{"className":4728},[886],[888,4730,4731],{"xmlns":890},[892,4732,4733,4748],{},[895,4734,4735,4738,4740,4742,4744,4746],{},[898,4736,4737],{},"A",[1654,4739,1657],{"stretchy":1656},[1665,4741,2062],{},[1654,4743,1674],{"separator":1673},[1665,4745,4573],{},[1654,4747,1686],{"stretchy":1656},[902,4749,4750],{"encoding":904},"A[0, 20]",[883,4752,4754],{"className":4753},[886],[888,4755,4756],{"xmlns":890},[892,4757,4758,4774],{},[895,4759,4760,4763,4765,4768,4770,4772],{},[898,4761,4762],{},"B",[1654,4764,1657],{"stretchy":1656},[1665,4766,4767],{},"50",[1654,4769,1674],{"separator":1673},[1665,4771,2062],{},[1654,4773,1686],{"stretchy":1656},[902,4775,4776],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,4779,4781],{"className":4780},[886],[888,4782,4783],{"xmlns":890},[892,4784,4785,4805],{},[895,4786,4787,4793,4795,4797,4799],{},[1710,4788,4789,4791],{},[898,4790,1663],{},[1665,4792,1681],{},[1654,4794,1750],{},[1665,4796,4679],{},[898,4798,1879],{"mathvariant":1878},[1710,4800,4801,4803],{},[898,4802,1663],{},[1665,4804,1667],{},[902,4806,4807],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,4810,4812],{"className":4811},[886],[888,4813,4814],{"xmlns":890},[892,4815,4816,4830],{},[895,4817,4818,4820,4822,4824,4826,4828],{},[898,4819,1798],{},[1654,4821,1657],{"stretchy":1656},[1665,4823,4622],{},[1654,4825,1674],{"separator":1673},[1665,4827,4647],{},[1654,4829,1686],{"stretchy":1656},[902,4831,4832],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,4835,4837],{"className":4836},[886],[888,4838,4839],{"xmlns":890},[892,4840,4841,4853],{},[895,4842,4843,4845],{},[1654,4844,2380],{},[2582,4846,4847],{"scriptlevel":2062,"displaystyle":1656},[2811,4848,4849,4851],{},[1665,4850,1681],{},[1665,4852,4032],{},[902,4854,4855],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,4858,4860],{"className":4859},[886],[888,4861,4862],{"xmlns":890},[892,4863,4864,4904],{},[895,4865,4866,4868,4870,4872,4874,4876,4878,4880,4882,4884,4892,4894,4896],{},[1654,4867,2380],{},[1865,4869,1867],{},[1654,4871,1708],{"stretchy":1656},[1665,4873,4622],{},[1654,4875,1674],{"separator":1673},[1665,4877,4647],{},[1654,4879,1726],{"stretchy":1656},[1654,4881,1750],{},[1654,4883,2380],{},[2582,4885,4886],{"scriptlevel":2062,"displaystyle":1656},[2811,4887,4888,4890],{},[1665,4889,4647],{},[1665,4891,4622],{},[1654,4893,1750],{},[1654,4895,2380],{},[2582,4897,4898],{"scriptlevel":2062,"displaystyle":1656},[2811,4899,4900,4902],{},[1665,4901,1681],{},[1665,4903,4032],{},[902,4905,4906],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,4908,4910],{"id":4909},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,4912,4913,4914,2919,4944,4947,4948,2781],{},"Považujeme-li v úloze ",[883,4915,4917],{"className":4916},[886],[888,4918,4919],{"xmlns":890},[892,4920,4921,4941],{},[895,4922,4923,4929,4931,4937,4939],{},[1710,4924,4925,4927],{},[898,4926,1755],{},[1665,4928,1667],{},[1654,4930,1674],{"separator":1673},[1710,4932,4933,4935],{},[898,4934,1755],{},[1665,4936,1681],{},[1654,4938,1674],{"separator":1673},[898,4940,1745],{},[902,4942,4943],{"encoding":904},"P_1, P_2, Y",[38,4945,4946],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,4949,4950],{},"Marshallovy poptávkové funkce",[883,4952,4954],{"className":4953},[886],[888,4955,4956],{"xmlns":890,"display":1956},[892,4957,4958,5056],{},[1960,4959,4960],{"width":1962},[1964,4961,4962,4964,5049,5051],{},[1967,4963],{"width":1969},[1967,4965,4966],{},[895,4967,4968,4974,4976,4983,4985,4991,4993,4999,5001,5003,5005,5007,5011,5017,5019,5025,5027,5033,5035,5041,5043,5045,5047],{},[1710,4969,4970,4972],{},[898,4971,1663],{},[1665,4973,1667],{},[1654,4975,1750],{},[1710,4977,4978,4981],{},[898,4979,4980],{},"D",[1665,4982,1667],{},[1654,4984,1708],{"stretchy":1656},[1710,4986,4987,4989],{},[898,4988,1755],{},[1665,4990,1667],{},[1654,4992,1674],{"separator":1673},[1710,4994,4995,4997],{},[898,4996,1755],{},[1665,4998,1681],{},[1654,5000,1674],{"separator":1673},[898,5002,1745],{},[1654,5004,1726],{"stretchy":1656},[1654,5006,1674],{"separator":1673},[5008,5009],"mspace",{"width":5010},"1em",[1710,5012,5013,5015],{},[898,5014,1663],{},[1665,5016,1681],{},[1654,5018,1750],{},[1710,5020,5021,5023],{},[898,5022,4980],{},[1665,5024,1681],{},[1654,5026,1708],{"stretchy":1656},[1710,5028,5029,5031],{},[898,5030,1755],{},[1665,5032,1667],{},[1654,5034,1674],{"separator":1673},[1710,5036,5037,5039],{},[898,5038,1755],{},[1665,5040,1681],{},[1654,5042,1674],{"separator":1673},[898,5044,1745],{},[1654,5046,1726],{"stretchy":1656},[1654,5048,1674],{"separator":1673},[1967,5050],{"width":1969},[1967,5052,5053],{},[1865,5054,5055],{},"(6.15)",[902,5057,5058],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,5060,5062],{"className":5061},[886],[888,5063,5064],{"xmlns":890,"display":1956},[892,5065,5066,5113],{},[1960,5067,5068],{"width":1962},[1964,5069,5070,5072,5106,5108],{},[1967,5071],{"width":1969},[1967,5073,5074],{},[895,5075,5076,5078,5080,5082,5084,5090,5092,5098,5100,5102,5104],{},[898,5077,2471],{},[1654,5079,1750],{},[898,5081,2471],{},[1654,5083,1708],{"stretchy":1656},[1710,5085,5086,5088],{},[898,5087,1755],{},[1665,5089,1667],{},[1654,5091,1674],{"separator":1673},[1710,5093,5094,5096],{},[898,5095,1755],{},[1665,5097,1681],{},[1654,5099,1674],{"separator":1673},[898,5101,1745],{},[1654,5103,1726],{"stretchy":1656},[898,5105,2138],{"mathvariant":1878},[1967,5107],{"width":1969},[1967,5109,5110],{},[1865,5111,5112],{},"(6.16)",[902,5114,5115],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,5117,5118,5148,5149,5215],{},[38,5119,5120,5121,2138],{},"Odvození pro ",[883,5122,5124],{"className":5123},[886],[888,5125,5126],{"xmlns":890},[892,5127,5128,5146],{},[895,5129,5130,5132,5134,5140],{},[898,5131,900],{},[1654,5133,1750],{},[1710,5135,5136,5138],{},[898,5137,1663],{},[1665,5139,1667],{},[1710,5141,5142,5144],{},[898,5143,1663],{},[1665,5145,1681],{},[902,5147,4156],{"encoding":904}," Lagrangeova funkce ",[883,5150,5152],{"className":5151},[886],[888,5153,5154],{"xmlns":890},[892,5155,5156,5212],{},[895,5157,5158,5160,5162,5168,5174,5176,5178,5180,5182,5184,5190,5196,5198,5204,5210],{},[898,5159,2450],{"mathvariant":2449},[1654,5161,1750],{},[1710,5163,5164,5166],{},[898,5165,1663],{},[1665,5167,1667],{},[1710,5169,5170,5172],{},[898,5171,1663],{},[1665,5173,1681],{},[1654,5175,1766],{},[898,5177,2471],{},[1654,5179,1708],{"stretchy":1656},[898,5181,1745],{},[1654,5183,2380],{},[1710,5185,5186,5188],{},[898,5187,1755],{},[1665,5189,1667],{},[1710,5191,5192,5194],{},[898,5193,1663],{},[1665,5195,1667],{},[1654,5197,2380],{},[1710,5199,5200,5202],{},[898,5201,1755],{},[1665,5203,1681],{},[1710,5205,5206,5208],{},[898,5207,1663],{},[1665,5209,1681],{},[1654,5211,1726],{"stretchy":1656},[902,5213,5214],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,5217,5219],{"className":5218},[886],[888,5220,5221],{"xmlns":890,"display":1956},[892,5222,5223,5390],{},[1960,5224,5225],{"width":1962},[1964,5226,5227,5229,5383,5385],{},[1967,5228],{"width":1969},[1967,5230,5231],{},[1960,5232,5233,5279,5325],{"rowspacing":2574,"columnalign":2575,"columnspacing":2576},[1964,5234,5235,5247],{},[1967,5236,5237],{},[2582,5238,5239],{"scriptlevel":2062,"displaystyle":1673},[1659,5240,5241,5243,5245],{},[898,5242,2450],{"mathvariant":2449},[1665,5244,1667],{},[1654,5246,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1967,5248,5249],{},[2582,5250,5251],{"scriptlevel":2062,"displaystyle":1673},[895,5252,5253,5255,5257,5263,5265,5267,5273,5275,5277],{},[895,5254],{},[1654,5256,1750],{},[1710,5258,5259,5261],{},[898,5260,1663],{},[1665,5262,1681],{},[1654,5264,2380],{},[898,5266,2471],{},[1710,5268,5269,5271],{},[898,5270,1755],{},[1665,5272,1667],{},[1654,5274,1750],{},[1665,5276,2062],{},[1654,5278,1674],{"separator":1673},[1964,5280,5281,5293],{},[1967,5282,5283],{},[2582,5284,5285],{"scriptlevel":2062,"displaystyle":1673},[1659,5286,5287,5289,5291],{},[898,5288,2450],{"mathvariant":2449},[1665,5290,1681],{},[1654,5292,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1967,5294,5295],{},[2582,5296,5297],{"scriptlevel":2062,"displaystyle":1673},[895,5298,5299,5301,5303,5309,5311,5313,5319,5321,5323],{},[895,5300],{},[1654,5302,1750],{},[1710,5304,5305,5307],{},[898,5306,1663],{},[1665,5308,1667],{},[1654,5310,2380],{},[898,5312,2471],{},[1710,5314,5315,5317],{},[898,5316,1755],{},[1665,5318,1681],{},[1654,5320,1750],{},[1665,5322,2062],{},[1654,5324,1674],{"separator":1673},[1964,5326,5327,5339],{},[1967,5328,5329],{},[2582,5330,5331],{"scriptlevel":2062,"displaystyle":1673},[1659,5332,5333,5335,5337],{},[898,5334,2450],{"mathvariant":2449},[898,5336,2471],{},[1654,5338,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1967,5340,5341],{},[2582,5342,5343],{"scriptlevel":2062,"displaystyle":1673},[895,5344,5345,5347,5349,5351,5353,5359,5365,5367,5373,5379,5381],{},[895,5346],{},[1654,5348,1750],{},[898,5350,1745],{},[1654,5352,2380],{},[1710,5354,5355,5357],{},[898,5356,1755],{},[1665,5358,1667],{},[1710,5360,5361,5363],{},[898,5362,1663],{},[1665,5364,1667],{},[1654,5366,2380],{},[1710,5368,5369,5371],{},[898,5370,1755],{},[1665,5372,1681],{},[1710,5374,5375,5377],{},[898,5376,1663],{},[1665,5378,1681],{},[1654,5380,1750],{},[1665,5382,2745],{},[1967,5384],{"width":1969},[1967,5386,5387],{},[1865,5388,5389],{},"(6.17)",[902,5391,5392],{"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}",[724,5394,5395,5396,5424,5425,5453,5454,5522],{},"Z prvních dvou: ",[883,5397,5399],{"className":5398},[886],[888,5400,5401],{"xmlns":890},[892,5402,5403,5421],{},[895,5404,5405,5411,5413,5419],{},[1710,5406,5407,5409],{},[898,5408,1663],{},[1665,5410,1681],{},[1654,5412,1750],{},[1710,5414,5415,5417],{},[898,5416,1755],{},[1665,5418,1667],{},[898,5420,2471],{},[902,5422,5423],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,5426,5428],{"className":5427},[886],[888,5429,5430],{"xmlns":890},[892,5431,5432,5450],{},[895,5433,5434,5440,5442,5448],{},[1710,5435,5436,5438],{},[898,5437,1663],{},[1665,5439,1667],{},[1654,5441,1750],{},[1710,5443,5444,5446],{},[898,5445,1755],{},[1665,5447,1681],{},[898,5449,2471],{},[902,5451,5452],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,5455,5457],{"className":5456},[886],[888,5458,5459],{"xmlns":890},[892,5460,5461,5519],{},[895,5462,5463,5465,5467,5473,5475,5481,5483,5485,5491,5493,5499,5501,5503,5505,5511,5517],{},[898,5464,1745],{},[1654,5466,1750],{},[1710,5468,5469,5471],{},[898,5470,1755],{},[1665,5472,1667],{},[1654,5474,4554],{},[1710,5476,5477,5479],{},[898,5478,1755],{},[1665,5480,1681],{},[898,5482,2471],{},[1654,5484,1766],{},[1710,5486,5487,5489],{},[898,5488,1755],{},[1665,5490,1681],{},[1654,5492,4554],{},[1710,5494,5495,5497],{},[898,5496,1755],{},[1665,5498,1667],{},[898,5500,2471],{},[1654,5502,1750],{},[1665,5504,1681],{},[1710,5506,5507,5509],{},[898,5508,1755],{},[1665,5510,1667],{},[1710,5512,5513,5515],{},[898,5514,1755],{},[1665,5516,1681],{},[898,5518,2471],{},[902,5520,5521],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,5524,5526],{"className":5525},[886],[888,5527,5528],{"xmlns":890,"display":1956},[892,5529,5530,5573],{},[1960,5531,5532],{"width":1962},[1964,5533,5534,5536,5566,5568],{},[1967,5535],{"width":1969},[1967,5537,5538],{},[895,5539,5540,5542,5544,5564],{},[898,5541,2471],{},[1654,5543,1750],{},[2811,5545,5546,5548],{},[898,5547,1745],{},[895,5549,5550,5552,5558],{},[1665,5551,1681],{},[1710,5553,5554,5556],{},[898,5555,1755],{},[1665,5557,1667],{},[1710,5559,5560,5562],{},[898,5561,1755],{},[1665,5563,1681],{},[898,5565,2138],{"mathvariant":1878},[1967,5567],{"width":1969},[1967,5569,5570],{},[1865,5571,5572],{},"(6.20)",[902,5574,5575],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,5577,5578],{},"Zpětně:",[883,5580,5582],{"className":5581},[886],[888,5583,5584],{"xmlns":890,"display":1956},[892,5585,5586,5663],{},[1960,5587,5588],{"width":1962},[1964,5589,5590,5592,5656,5658],{},[1967,5591],{"width":1969},[1967,5593,5594],{},[2792,5595,5596],{"notation":2794},[2582,5597,5598],{"scriptlevel":2062,"displaystyle":1656},[2582,5599,5600],{"scriptlevel":2062,"displaystyle":1656},[2582,5601,5602],{"scriptlevel":2062,"displaystyle":1673},[895,5603,5604,5606,5612,5614,5628,5630,5632,5638,5640,5654],{},[1865,5605,2805],{},[1710,5607,5608,5610],{},[898,5609,1663],{},[1665,5611,1667],{},[1654,5613,1750],{},[2811,5615,5616,5618],{},[898,5617,1745],{},[895,5619,5620,5622],{},[1665,5621,1681],{},[1710,5623,5624,5626],{},[898,5625,1755],{},[1665,5627,1667],{},[1654,5629,1674],{"separator":1673},[5008,5631],{"width":5010},[1710,5633,5634,5636],{},[898,5635,1663],{},[1665,5637,1681],{},[1654,5639,1750],{},[2811,5641,5642,5644],{},[898,5643,1745],{},[895,5645,5646,5648],{},[1665,5647,1681],{},[1710,5649,5650,5652],{},[898,5651,1755],{},[1665,5653,1681],{},[1865,5655,2805],{},[1967,5657],{"width":1969},[1967,5659,5660],{},[1865,5661,5662],{},"(6.21)",[902,5664,5665],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,5667,5669],{"id":5668},"engelova-funkce","Engelova funkce",[724,5671,3806,5672,5675,5676,5679,5680,5698,5699,1343,5729,5759,5760,5794,5795,1343,5821,5848],{},[38,5673,5674],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,5677,5678],{},"Engelovou funkcí",": pro ",[883,5681,5683],{"className":5682},[886],[888,5684,5685],{"xmlns":890},[892,5686,5687,5695],{},[895,5688,5689,5691,5693],{},[898,5690,1745],{},[1654,5692,1750],{},[1665,5694,4273],{},[902,5696,5697],{"encoding":904},"Y = 100"," vychází ",[883,5700,5702],{"className":5701},[886],[888,5703,5704],{"xmlns":890},[892,5705,5706,5726],{},[895,5707,5708,5714,5716,5718,5720],{},[1710,5709,5710,5712],{},[898,5711,1663],{},[1665,5713,1667],{},[1654,5715,1750],{},[1665,5717,4767],{},[898,5719,1879],{"mathvariant":1878},[1710,5721,5722,5724],{},[898,5723,1755],{},[1665,5725,1667],{},[902,5727,5728],{"encoding":904},"Q_1 = 50\u002FP_1",[883,5730,5732],{"className":5731},[886],[888,5733,5734],{"xmlns":890},[892,5735,5736,5756],{},[895,5737,5738,5744,5746,5748,5750],{},[1710,5739,5740,5742],{},[898,5741,1663],{},[1665,5743,1681],{},[1654,5745,1750],{},[1665,5747,4767],{},[898,5749,1879],{"mathvariant":1878},[1710,5751,5752,5754],{},[898,5753,1755],{},[1665,5755,1681],{},[902,5757,5758],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,5761,5763],{"className":5762},[886],[888,5764,5765],{"xmlns":890},[892,5766,5767,5791],{},[895,5768,5769,5775,5777,5779,5781,5787,5789],{},[1710,5770,5771,5773],{},[898,5772,1755],{},[1665,5774,1667],{},[1654,5776,1750],{},[1665,5778,4647],{},[1654,5780,1674],{"separator":1673},[1710,5782,5783,5785],{},[898,5784,1755],{},[1665,5786,1681],{},[1654,5788,1750],{},[1665,5790,4573],{},[902,5792,5793],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,5796,5798],{"className":5797},[886],[888,5799,5800],{"xmlns":890},[892,5801,5802,5818],{},[895,5803,5804,5810,5812,5814,5816],{},[1710,5805,5806,5808],{},[898,5807,1663],{},[1665,5809,1667],{},[1654,5811,1750],{},[898,5813,1745],{},[898,5815,1879],{"mathvariant":1878},[1665,5817,4573],{},[902,5819,5820],{"encoding":904},"Q_1 = Y\u002F20",[883,5822,5824],{"className":5823},[886],[888,5825,5826],{"xmlns":890},[892,5827,5828,5845],{},[895,5829,5830,5836,5838,5840,5842],{},[1710,5831,5832,5834],{},[898,5833,1663],{},[1665,5835,1681],{},[1654,5837,1750],{},[898,5839,1745],{},[898,5841,1879],{"mathvariant":1878},[1665,5843,5844],{},"40",[902,5846,5847],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,5850,5852],{"id":5851},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,5854,5855],{},"Výdaje spotřebitele jsou",[883,5857,5859],{"className":5858},[886],[888,5860,5861],{"xmlns":890,"display":1956},[892,5862,5863,5938],{},[1960,5864,5865],{"width":1962},[1964,5866,5867,5869,5931,5933],{},[1967,5868],{"width":1969},[1967,5870,5871],{},[895,5872,5873,5875,5877,5879,5881,5887,5889,5895,5897,5899,5907,5913,5915,5923,5929],{},[898,5874,1798],{},[1654,5876,1750],{},[898,5878,1798],{},[1654,5880,1708],{"stretchy":1656},[1710,5882,5883,5885],{},[898,5884,1663],{},[1665,5886,1667],{},[1654,5888,1674],{"separator":1673},[1710,5890,5891,5893],{},[898,5892,1663],{},[1665,5894,1681],{},[1654,5896,1726],{"stretchy":1656},[1654,5898,1750],{},[1659,5900,5901,5903,5905],{},[898,5902,1755],{},[1665,5904,1667],{},[1654,5906,1670],{},[1710,5908,5909,5911],{},[898,5910,1663],{},[1665,5912,1667],{},[1654,5914,1766],{},[1659,5916,5917,5919,5921],{},[898,5918,1755],{},[1665,5920,1681],{},[1654,5922,1670],{},[1710,5924,5925,5927],{},[898,5926,1663],{},[1665,5928,1681],{},[1654,5930,1674],{"separator":1673},[1967,5932],{"width":1969},[1967,5934,5935],{},[1865,5936,5937],{},"(6.22)",[902,5939,5940],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,5942,5943],{},"a je pevně zadána hladina užitečnosti",[883,5945,5947],{"className":5946},[886],[888,5948,5949],{"xmlns":890,"display":1956},[892,5950,5951,5998],{},[1960,5952,5953],{"width":1962},[1964,5954,5955,5957,5991,5993],{},[1967,5956],{"width":1969},[1967,5958,5959],{},[895,5960,5961,5967,5969,5971,5973,5979,5981,5987,5989],{},[1741,5962,5963,5965],{},[898,5964,900],{},[1654,5966,1670],{},[1654,5968,1750],{},[898,5970,900],{},[1654,5972,1708],{"stretchy":1656},[1710,5974,5975,5977],{},[898,5976,1663],{},[1665,5978,1667],{},[1654,5980,1674],{"separator":1673},[1710,5982,5983,5985],{},[898,5984,1663],{},[1665,5986,1681],{},[1654,5988,1726],{"stretchy":1656},[898,5990,2138],{"mathvariant":1878},[1967,5992],{"width":1969},[1967,5994,5995],{},[1865,5996,5997],{},"(6.23)",[902,5999,6000],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,6002,6003,6006,6007,6039,6040,2138],{},[38,6004,6005],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,6008,6010],{"className":6009},[886],[888,6011,6012],{"xmlns":890},[892,6013,6014,6036],{},[895,6015,6016,6018,6020,6026,6028,6034],{},[898,6017,1798],{},[1654,6019,1708],{"stretchy":1656},[1710,6021,6022,6024],{},[898,6023,1663],{},[1665,6025,1667],{},[1654,6027,1674],{"separator":1673},[1710,6029,6030,6032],{},[898,6031,1663],{},[1665,6033,1681],{},[1654,6035,1726],{"stretchy":1656},[902,6037,6038],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,6041,6043],{"className":6042},[886],[888,6044,6045],{"xmlns":890},[892,6046,6047,6103],{},[895,6048,6049,6051,6053,6059,6061,6067,6069,6071,6077,6079,6081,6083,6089,6091,6097,6099,6101],{},[898,6050,2351],{},[1654,6052,1708],{"stretchy":1656},[1710,6054,6055,6057],{},[898,6056,1663],{},[1665,6058,1667],{},[1654,6060,1674],{"separator":1673},[1710,6062,6063,6065],{},[898,6064,1663],{},[1665,6066,1681],{},[1654,6068,1726],{"stretchy":1656},[1654,6070,1750],{},[1741,6072,6073,6075],{},[898,6074,900],{},[1654,6076,1670],{},[1654,6078,2380],{},[898,6080,900],{},[1654,6082,1708],{"stretchy":1656},[1710,6084,6085,6087],{},[898,6086,1663],{},[1665,6088,1667],{},[1654,6090,1674],{"separator":1673},[1710,6092,6093,6095],{},[898,6094,1663],{},[1665,6096,1681],{},[1654,6098,1726],{"stretchy":1656},[1654,6100,1750],{},[1665,6102,2062],{},[902,6104,6105],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,6107,6109],{"id":6108},"lagrangeova-funkce","Lagrangeova funkce",[883,6111,6113],{"className":6112},[886],[888,6114,6115],{"xmlns":890,"display":1956},[892,6116,6117,6228],{},[1960,6118,6119],{"width":1962},[1964,6120,6121,6123,6221,6223],{},[1967,6122],{"width":1969},[1967,6124,6125],{},[895,6126,6127,6129,6131,6137,6139,6145,6147,6149,6151,6153,6161,6167,6169,6177,6183,6185,6187,6189,6195,6197,6199,6201,6207,6209,6215,6217,6219],{},[898,6128,2450],{"mathvariant":2449},[1654,6130,1708],{"stretchy":1656},[1710,6132,6133,6135],{},[898,6134,1663],{},[1665,6136,1667],{},[1654,6138,1674],{"separator":1673},[1710,6140,6141,6143],{},[898,6142,1663],{},[1665,6144,1681],{},[1654,6146,1674],{"separator":1673},[898,6148,2471],{},[1654,6150,1726],{"stretchy":1656},[1654,6152,1750],{},[1659,6154,6155,6157,6159],{},[898,6156,1755],{},[1665,6158,1667],{},[1654,6160,1670],{},[1710,6162,6163,6165],{},[898,6164,1663],{},[1665,6166,1667],{},[1654,6168,1766],{},[1659,6170,6171,6173,6175],{},[898,6172,1755],{},[1665,6174,1681],{},[1654,6176,1670],{},[1710,6178,6179,6181],{},[898,6180,1663],{},[1665,6182,1681],{},[1654,6184,1766],{},[898,6186,2471],{},[1654,6188,1708],{"stretchy":1656},[1741,6190,6191,6193],{},[898,6192,900],{},[1654,6194,1670],{},[1654,6196,2380],{},[898,6198,900],{},[1654,6200,1708],{"stretchy":1656},[1710,6202,6203,6205],{},[898,6204,1663],{},[1665,6206,1667],{},[1654,6208,1674],{"separator":1673},[1710,6210,6211,6213],{},[898,6212,1663],{},[1665,6214,1681],{},[1654,6216,1726],{"stretchy":1656},[1654,6218,1726],{"stretchy":1656},[898,6220,2138],{"mathvariant":1878},[1967,6222],{"width":1969},[1967,6224,6225],{},[1865,6226,6227],{},"(6.24)",[902,6229,6230],{"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}",[724,6232,6233],{},"Soustava podmínek prvního řádu:",[883,6235,6237],{"className":6236},[886],[888,6238,6239],{"xmlns":890,"display":1956},[892,6240,6241,6414],{},[1960,6242,6243],{"width":1962},[1964,6244,6245,6247,6407,6409],{},[1967,6246],{"width":1969},[1967,6248,6249],{},[1960,6250,6251,6301,6351],{"rowspacing":2574,"columnalign":2575,"columnspacing":2576},[1964,6252,6253,6265],{},[1967,6254,6255],{},[2582,6256,6257],{"scriptlevel":2062,"displaystyle":1673},[1659,6258,6259,6261,6263],{},[898,6260,2450],{"mathvariant":2449},[1665,6262,1667],{},[1654,6264,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1967,6266,6267],{},[2582,6268,6269],{"scriptlevel":2062,"displaystyle":1673},[895,6270,6271,6273,6275,6283,6285,6287,6295,6297,6299],{},[895,6272],{},[1654,6274,1750],{},[1659,6276,6277,6279,6281],{},[898,6278,1755],{},[1665,6280,1667],{},[1654,6282,1670],{},[1654,6284,2380],{},[898,6286,2471],{},[1659,6288,6289,6291,6293],{},[898,6290,900],{},[1665,6292,1667],{},[1654,6294,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,6296,1750],{},[1665,6298,2062],{},[1654,6300,1674],{"separator":1673},[1964,6302,6303,6315],{},[1967,6304,6305],{},[2582,6306,6307],{"scriptlevel":2062,"displaystyle":1673},[1659,6308,6309,6311,6313],{},[898,6310,2450],{"mathvariant":2449},[1665,6312,1681],{},[1654,6314,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1967,6316,6317],{},[2582,6318,6319],{"scriptlevel":2062,"displaystyle":1673},[895,6320,6321,6323,6325,6333,6335,6337,6345,6347,6349],{},[895,6322],{},[1654,6324,1750],{},[1659,6326,6327,6329,6331],{},[898,6328,1755],{},[1665,6330,1681],{},[1654,6332,1670],{},[1654,6334,2380],{},[898,6336,2471],{},[1659,6338,6339,6341,6343],{},[898,6340,900],{},[1665,6342,1681],{},[1654,6344,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,6346,1750],{},[1665,6348,2062],{},[1654,6350,1674],{"separator":1673},[1964,6352,6353,6365],{},[1967,6354,6355],{},[2582,6356,6357],{"scriptlevel":2062,"displaystyle":1673},[1659,6358,6359,6361,6363],{},[898,6360,2450],{"mathvariant":2449},[898,6362,2471],{},[1654,6364,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1967,6366,6367],{},[2582,6368,6369],{"scriptlevel":2062,"displaystyle":1673},[895,6370,6371,6373,6375,6381,6383,6385,6387,6393,6395,6401,6403,6405],{},[895,6372],{},[1654,6374,1750],{},[1741,6376,6377,6379],{},[898,6378,900],{},[1654,6380,1670],{},[1654,6382,2380],{},[898,6384,900],{},[1654,6386,1708],{"stretchy":1656},[1710,6388,6389,6391],{},[898,6390,1663],{},[1665,6392,1667],{},[1654,6394,1674],{"separator":1673},[1710,6396,6397,6399],{},[898,6398,1663],{},[1665,6400,1681],{},[1654,6402,1726],{"stretchy":1656},[1654,6404,1750],{},[1665,6406,2745],{},[1967,6408],{"width":1969},[1967,6410,6411],{},[1865,6412,6413],{},"(6.25)",[902,6415,6416],{"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}",[724,6418,6419],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,6421,6423],{"className":6422},[886],[888,6424,6425],{"xmlns":890,"display":1956},[892,6426,6427,6527],{},[1960,6428,6429],{"width":1962},[1964,6430,6431,6433,6520,6522],{},[1967,6432],{"width":1969},[1967,6434,6435],{},[895,6436,6437,6439,6441,6447,6449,6455,6457,6459,6461,6463,6465,6467,6518],{},[898,6438,4980],{},[1654,6440,1708],{"stretchy":1656},[1710,6442,6443,6445],{},[898,6444,1663],{},[1665,6446,1667],{},[1654,6448,1674],{"separator":1673},[1710,6450,6451,6453],{},[898,6452,1663],{},[1665,6454,1681],{},[1654,6456,1674],{"separator":1673},[898,6458,2471],{},[1654,6460,1726],{"stretchy":1656},[1654,6462,1750],{},[1654,6464,2380],{},[898,6466,2471],{},[895,6468,6469,6471,6484,6486,6499,6501,6503,6516],{},[1654,6470,1708],{"fence":1673},[1659,6472,6473,6475,6478],{},[898,6474,900],{},[1665,6476,6477],{},"11",[895,6479,6480,6482],{},[1654,6481,2592],{"mathvariant":1878},[1654,6483,2592],{"mathvariant":1878},[1654,6485,1766],{},[1659,6487,6488,6490,6493],{},[898,6489,900],{},[1665,6491,6492],{},"22",[895,6494,6495,6497],{},[1654,6496,2592],{"mathvariant":1878},[1654,6498,2592],{"mathvariant":1878},[1654,6500,1766],{},[1665,6502,1681],{},[1659,6504,6505,6507,6510],{},[898,6506,900],{},[1665,6508,6509],{},"12",[895,6511,6512,6514],{},[1654,6513,2592],{"mathvariant":1878},[1654,6515,2592],{"mathvariant":1878},[1654,6517,1726],{"fence":1673},[898,6519,2138],{"mathvariant":1878},[1967,6521],{"width":1969},[1967,6523,6524],{},[1865,6525,6526],{},"(6.26)",[902,6528,6529],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,6531,6532,6535,6536,6575,6576,6616,6617,6667,6668,6694,6695,6712,6713,6739],{},[38,6533,6534],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,6537,6539],{"className":6538},[886],[888,6540,6541],{"xmlns":890},[892,6542,6543,6573],{},[895,6544,6545,6551,6553,6561,6563,6571],{},[1741,6546,6547,6549],{},[898,6548,1663],{},[1654,6550,1670],{},[1654,6552,1657],{"stretchy":1656},[1659,6554,6555,6557,6559],{},[898,6556,1663],{},[1665,6558,1667],{},[1654,6560,1670],{},[1654,6562,1674],{"separator":1673},[1659,6564,6565,6567,6569],{},[898,6566,1663],{},[1665,6568,1681],{},[1654,6570,1670],{},[1654,6572,1686],{"stretchy":1656},[902,6574,2226],{"encoding":904}," dotyku křivky užitečnosti ",[883,6577,6579],{"className":6578},[886],[888,6580,6581],{"xmlns":890},[892,6582,6583,6613],{},[895,6584,6585,6591,6593,6595,6597,6603,6605,6611],{},[1741,6586,6587,6589],{},[898,6588,900],{},[1654,6590,1670],{},[1654,6592,1750],{},[898,6594,900],{},[1654,6596,1708],{"stretchy":1656},[1710,6598,6599,6601],{},[898,6600,1663],{},[1665,6602,1667],{},[1654,6604,1674],{"separator":1673},[1710,6606,6607,6609],{},[898,6608,1663],{},[1665,6610,1681],{},[1654,6612,1726],{"stretchy":1656},[902,6614,6615],{"encoding":904},"U^* = U(Q_1, Q_2)"," s přímkou výdajů ",[883,6618,6620],{"className":6619},[886],[888,6621,6622],{"xmlns":890},[892,6623,6624,6664],{},[895,6625,6626,6632,6634,6642,6648,6650,6658],{},[1741,6627,6628,6630],{},[898,6629,1798],{},[1654,6631,1670],{},[1654,6633,1750],{},[1659,6635,6636,6638,6640],{},[898,6637,1755],{},[1665,6639,1667],{},[1654,6641,1670],{},[1710,6643,6644,6646],{},[898,6645,1663],{},[1665,6647,1667],{},[1654,6649,1766],{},[1659,6651,6652,6654,6656],{},[898,6653,1755],{},[1665,6655,1681],{},[1654,6657,1670],{},[1710,6659,6660,6662],{},[898,6661,1663],{},[1665,6663,1681],{},[902,6665,6666],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,6669,6671],{"className":6670},[886],[888,6672,6673],{"xmlns":890},[892,6674,6675,6691],{},[895,6676,6677,6683,6685],{},[1710,6678,6679,6681],{},[898,6680,1798],{},[1665,6682,2062],{},[1654,6684,3002],{},[1741,6686,6687,6689],{},[898,6688,1798],{},[1654,6690,1670],{},[902,6692,6693],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,6696,6698],{"className":6697},[886],[888,6699,6700],{"xmlns":890},[892,6701,6702,6710],{},[895,6703,6704],{},[1741,6705,6706,6708],{},[898,6707,900],{},[1654,6709,1670],{},[902,6711,1848],{"encoding":904},", hladina ",[883,6714,6716],{"className":6715},[886],[888,6717,6718],{"xmlns":890},[892,6719,6720,6736],{},[895,6721,6722,6728,6730],{},[1710,6723,6724,6726],{},[898,6725,1798],{},[1665,6727,1667],{},[1654,6729,2952],{},[1741,6731,6732,6734],{},[898,6733,1798],{},[1654,6735,1670],{},[902,6737,6738],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[2140,6741,6742,6747],{},[724,6743,6744,6746],{},[883,6745,3111],{}," Postup — duální úloha (minimalizace výdajů)",[152,6748,6749,6799,6885,6925,7000],{},[123,6750,6751,2186,6754,6798],{},[38,6752,6753],{},"Zapiš vazbu",[883,6755,6757],{"className":6756},[886],[888,6758,6759],{"xmlns":890},[892,6760,6761,6795],{},[895,6762,6763,6769,6771,6773,6775,6781,6783,6789,6791,6793],{},[1741,6764,6765,6767],{},[898,6766,900],{},[1654,6768,1670],{},[1654,6770,2380],{},[898,6772,900],{},[1654,6774,1708],{"stretchy":1656},[1710,6776,6777,6779],{},[898,6778,1663],{},[1665,6780,1667],{},[1654,6782,1674],{"separator":1673},[1710,6784,6785,6787],{},[898,6786,1663],{},[1665,6788,1681],{},[1654,6790,1726],{"stretchy":1656},[1654,6792,1750],{},[1665,6794,2062],{},[902,6796,6797],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,6800,6801,2186,6803,2138],{},[38,6802,3179],{},[883,6804,6806],{"className":6805},[886],[888,6807,6808],{"xmlns":890},[892,6809,6810,6882],{},[895,6811,6812,6814,6816,6824,6830,6832,6840,6846,6848,6850,6852,6858,6860,6862,6864,6870,6872,6878,6880],{},[898,6813,2450],{"mathvariant":2449},[1654,6815,1750],{},[1659,6817,6818,6820,6822],{},[898,6819,1755],{},[1665,6821,1667],{},[1654,6823,1670],{},[1710,6825,6826,6828],{},[898,6827,1663],{},[1665,6829,1667],{},[1654,6831,1766],{},[1659,6833,6834,6836,6838],{},[898,6835,1755],{},[1665,6837,1681],{},[1654,6839,1670],{},[1710,6841,6842,6844],{},[898,6843,1663],{},[1665,6845,1681],{},[1654,6847,1766],{},[898,6849,2471],{},[1654,6851,1708],{"stretchy":1656},[1741,6853,6854,6856],{},[898,6855,900],{},[1654,6857,1670],{},[1654,6859,2380],{},[898,6861,900],{},[1654,6863,1708],{"stretchy":1656},[1710,6865,6866,6868],{},[898,6867,1663],{},[1665,6869,1667],{},[1654,6871,1674],{"separator":1673},[1710,6873,6874,6876],{},[898,6875,1663],{},[1665,6877,1681],{},[1654,6879,1726],{"stretchy":1656},[1654,6881,1726],{"stretchy":1656},[902,6883,6884],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,6886,6887,6890,6891,6924],{},[38,6888,6889],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,6892,6894],{"className":6893},[886],[888,6895,6896],{"xmlns":890},[892,6897,6898,6922],{},[895,6899,6900,6902,6904,6912,6914],{},[1865,6901,1867],{},[1654,6903,1750],{},[1659,6905,6906,6908,6910],{},[898,6907,1755],{},[1665,6909,1667],{},[1654,6911,1670],{},[898,6913,1879],{"mathvariant":1878},[1659,6915,6916,6918,6920],{},[898,6917,1755],{},[1665,6919,1681],{},[1654,6921,1670],{},[902,6923,2895],{"encoding":904}," (stejná jako u maximalizace!).",[123,6926,6927,2186,6930,6970,6971,2138],{},[38,6928,6929],{},"Dosaď do vazby",[883,6931,6933],{"className":6932},[886],[888,6934,6935],{"xmlns":890},[892,6936,6937,6967],{},[895,6938,6939,6941,6943,6949,6951,6957,6959,6961],{},[898,6940,900],{},[1654,6942,1708],{"stretchy":1656},[1710,6944,6945,6947],{},[898,6946,1663],{},[1665,6948,1667],{},[1654,6950,1674],{"separator":1673},[1710,6952,6953,6955],{},[898,6954,1663],{},[1665,6956,1681],{},[1654,6958,1726],{"stretchy":1656},[1654,6960,1750],{},[1741,6962,6963,6965],{},[898,6964,900],{},[1654,6966,1670],{},[902,6968,6969],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,6972,6974],{"className":6973},[886],[888,6975,6976],{"xmlns":890},[892,6977,6978,6998],{},[895,6979,6980,6988,6990],{},[1659,6981,6982,6984,6986],{},[898,6983,1663],{},[1665,6985,1667],{},[1654,6987,1670],{},[1654,6989,1674],{"separator":1673},[1659,6991,6992,6994,6996],{},[898,6993,1663],{},[1665,6995,1681],{},[1654,6997,1670],{},[902,6999,3421],{"encoding":904},[123,7001,7002,2186,7005,7059],{},[38,7003,7004],{},"Vypočítej minimální výdaje",[883,7006,7008],{"className":7007},[886],[888,7009,7010],{"xmlns":890},[892,7011,7012,7056],{},[895,7013,7014,7020,7022,7030,7038,7040,7048],{},[1741,7015,7016,7018],{},[898,7017,1798],{},[1654,7019,1670],{},[1654,7021,1750],{},[1659,7023,7024,7026,7028],{},[898,7025,1755],{},[1665,7027,1667],{},[1654,7029,1670],{},[1659,7031,7032,7034,7036],{},[898,7033,1663],{},[1665,7035,1667],{},[1654,7037,1670],{},[1654,7039,1766],{},[1659,7041,7042,7044,7046],{},[898,7043,1755],{},[1665,7045,1681],{},[1654,7047,1670],{},[1659,7049,7050,7052,7054],{},[898,7051,1663],{},[1665,7053,1681],{},[1654,7055,1670],{},[902,7057,7058],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,7061,7063,7064],{"id":7062},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,7065,7067],{"className":7066},[886],[888,7068,7069],{"xmlns":890},[892,7070,7071,7105],{},[895,7072,7073,7075,7077,7091],{},[898,7074,900],{},[1654,7076,1750],{},[1659,7078,7079,7081,7083],{},[898,7080,1663],{},[1665,7082,1667],{},[895,7084,7085,7087,7089],{},[1665,7086,1667],{},[898,7088,1879],{"mathvariant":1878},[1665,7090,1681],{},[1659,7092,7093,7095,7097],{},[898,7094,1663],{},[1665,7096,1681],{},[895,7098,7099,7101,7103],{},[1665,7100,1667],{},[898,7102,1879],{"mathvariant":1878},[1665,7104,1681],{},[902,7106,7107],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,7109,7110,7111,1343,7133,1343,7158,4277],{},"Dáno ",[883,7112,7114],{"className":7113},[886],[888,7115,7116],{"xmlns":890},[892,7117,7118,7130],{},[895,7119,7120,7126,7128],{},[1741,7121,7122,7124],{},[898,7123,900],{},[1654,7125,1670],{},[1654,7127,1750],{},[1665,7129,1681],{},[902,7131,7132],{"encoding":904},"U^* = 2",[883,7134,7136],{"className":7135},[886],[888,7137,7138],{"xmlns":890},[892,7139,7140,7155],{},[895,7141,7142,7150,7152],{},[1659,7143,7144,7146,7148],{},[898,7145,1755],{},[1665,7147,1667],{},[1654,7149,1670],{},[1654,7151,1750],{},[1665,7153,7154],{},"0,25",[902,7156,7157],{"encoding":904},"P_1^* = 0{,}25",[883,7159,7161],{"className":7160},[886],[888,7162,7163],{"xmlns":890},[892,7164,7165,7179],{},[895,7166,7167,7175,7177],{},[1659,7168,7169,7171,7173],{},[898,7170,1755],{},[1665,7172,1681],{},[1654,7174,1670],{},[1654,7176,1750],{},[1665,7178,1667],{},[902,7180,7181],{"encoding":904},"P_2^* = 1",[883,7183,7185],{"className":7184},[886],[888,7186,7187],{"xmlns":890,"display":1956},[892,7188,7189,7253],{},[895,7190,7191,7193,7195,7197,7203,7205,7211,7213,7215,7217,7219,7221,7235,7249,7251],{},[898,7192,2450],{"mathvariant":2449},[1654,7194,1750],{},[1665,7196,7154],{},[1710,7198,7199,7201],{},[898,7200,1663],{},[1665,7202,1667],{},[1654,7204,1766],{},[1710,7206,7207,7209],{},[898,7208,1663],{},[1665,7210,1681],{},[1654,7212,1766],{},[898,7214,2471],{},[1654,7216,1708],{"stretchy":1656},[1665,7218,1681],{},[1654,7220,2380],{},[1659,7222,7223,7225,7227],{},[898,7224,1663],{},[1665,7226,1667],{},[895,7228,7229,7231,7233],{},[1665,7230,1667],{},[898,7232,1879],{"mathvariant":1878},[1665,7234,1681],{},[1659,7236,7237,7239,7241],{},[898,7238,1663],{},[1665,7240,1681],{},[895,7242,7243,7245,7247],{},[1665,7244,1667],{},[898,7246,1879],{"mathvariant":1878},[1665,7248,1681],{},[1654,7250,1726],{"stretchy":1656},[898,7252,2138],{"mathvariant":1878},[902,7254,7255],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,7257,4362],{},[883,7259,7261],{"className":7260},[886],[888,7262,7263],{"xmlns":890,"display":1956},[892,7264,7265,7479],{},[1960,7266,7267,7343,7419],{"rowspacing":2574,"columnalign":2575,"columnspacing":2576},[1964,7268,7269,7281],{},[1967,7270,7271],{},[2582,7272,7273],{"scriptlevel":2062,"displaystyle":1673},[1659,7274,7275,7277,7279],{},[898,7276,2450],{"mathvariant":2449},[1665,7278,1667],{},[1654,7280,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1967,7282,7283],{},[2582,7284,7285],{"scriptlevel":2062,"displaystyle":1673},[895,7286,7287,7289,7291,7293,7295,7297,7299,7307,7323,7337,7339,7341],{},[895,7288],{},[1654,7290,1750],{},[1665,7292,7154],{},[1654,7294,2380],{},[898,7296,2471],{},[1654,7298,4554],{},[2582,7300,7301],{"scriptlevel":2062,"displaystyle":1656},[2811,7302,7303,7305],{},[1665,7304,1667],{},[1665,7306,1681],{},[1659,7308,7309,7311,7313],{},[898,7310,1663],{},[1665,7312,1667],{},[895,7314,7315,7317,7319,7321],{},[1654,7316,2380],{},[1665,7318,1667],{},[898,7320,1879],{"mathvariant":1878},[1665,7322,1681],{},[1659,7324,7325,7327,7329],{},[898,7326,1663],{},[1665,7328,1681],{},[895,7330,7331,7333,7335],{},[1665,7332,1667],{},[898,7334,1879],{"mathvariant":1878},[1665,7336,1681],{},[1654,7338,1750],{},[1665,7340,2062],{},[1654,7342,1674],{"separator":1673},[1964,7344,7345,7357],{},[1967,7346,7347],{},[2582,7348,7349],{"scriptlevel":2062,"displaystyle":1673},[1659,7350,7351,7353,7355],{},[898,7352,2450],{"mathvariant":2449},[1665,7354,1681],{},[1654,7356,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1967,7358,7359],{},[2582,7360,7361],{"scriptlevel":2062,"displaystyle":1673},[895,7362,7363,7365,7367,7369,7371,7373,7375,7383,7397,7413,7415,7417],{},[895,7364],{},[1654,7366,1750],{},[1665,7368,1667],{},[1654,7370,2380],{},[898,7372,2471],{},[1654,7374,4554],{},[2582,7376,7377],{"scriptlevel":2062,"displaystyle":1656},[2811,7378,7379,7381],{},[1665,7380,1667],{},[1665,7382,1681],{},[1659,7384,7385,7387,7389],{},[898,7386,1663],{},[1665,7388,1667],{},[895,7390,7391,7393,7395],{},[1665,7392,1667],{},[898,7394,1879],{"mathvariant":1878},[1665,7396,1681],{},[1659,7398,7399,7401,7403],{},[898,7400,1663],{},[1665,7402,1681],{},[895,7404,7405,7407,7409,7411],{},[1654,7406,2380],{},[1665,7408,1667],{},[898,7410,1879],{"mathvariant":1878},[1665,7412,1681],{},[1654,7414,1750],{},[1665,7416,2062],{},[1654,7418,1674],{"separator":1673},[1964,7420,7421,7433],{},[1967,7422,7423],{},[2582,7424,7425],{"scriptlevel":2062,"displaystyle":1673},[1659,7426,7427,7429,7431],{},[898,7428,2450],{"mathvariant":2449},[898,7430,2471],{},[1654,7432,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1967,7434,7435],{},[2582,7436,7437],{"scriptlevel":2062,"displaystyle":1673},[895,7438,7439,7441,7443,7445,7447,7461,7475,7477],{},[895,7440],{},[1654,7442,1750],{},[1665,7444,1681],{},[1654,7446,2380],{},[1659,7448,7449,7451,7453],{},[898,7450,1663],{},[1665,7452,1667],{},[895,7454,7455,7457,7459],{},[1665,7456,1667],{},[898,7458,1879],{"mathvariant":1878},[1665,7460,1681],{},[1659,7462,7463,7465,7467],{},[898,7464,1663],{},[1665,7466,1681],{},[895,7468,7469,7471,7473],{},[1665,7470,1667],{},[898,7472,1879],{"mathvariant":1878},[1665,7474,1681],{},[1654,7476,1750],{},[1665,7478,2745],{},[902,7480,7481],{"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}",[724,7483,7484,7485,7515,7516,7544,7545,4579,7608,1343,7659,7681,7682,2138],{},"Podílem prvních dvou rovnic: ",[883,7486,7488],{"className":7487},[886],[888,7489,7490],{"xmlns":890},[892,7491,7492,7512],{},[895,7493,7494,7496,7498,7504,7506],{},[1665,7495,7154],{},[1654,7497,1750],{},[1710,7499,7500,7502],{},[898,7501,1663],{},[1665,7503,1681],{},[898,7505,1879],{"mathvariant":1878},[1710,7507,7508,7510],{},[898,7509,1663],{},[1665,7511,1667],{},[902,7513,7514],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",", tj. ",[883,7517,7519],{"className":7518},[886],[888,7520,7521],{"xmlns":890},[892,7522,7523,7541],{},[895,7524,7525,7531,7533,7535],{},[1710,7526,7527,7529],{},[898,7528,1663],{},[1665,7530,1681],{},[1654,7532,1750],{},[1665,7534,7154],{},[1710,7536,7537,7539],{},[898,7538,1663],{},[1665,7540,1667],{},[902,7542,7543],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,7546,7548],{"className":7547},[886],[888,7549,7550],{"xmlns":890},[892,7551,7552,7605],{},[895,7553,7554,7568,7570,7572,7578,7590,7592,7595,7601,7603],{},[1659,7555,7556,7558,7560],{},[898,7557,1663],{},[1665,7559,1667],{},[895,7561,7562,7564,7566],{},[1665,7563,1667],{},[898,7565,1879],{"mathvariant":1878},[1665,7567,1681],{},[1654,7569,1708],{"stretchy":1656},[1665,7571,7154],{},[1710,7573,7574,7576],{},[898,7575,1663],{},[1665,7577,1667],{},[1741,7579,7580,7582],{},[1654,7581,1726],{"stretchy":1656},[895,7583,7584,7586,7588],{},[1665,7585,1667],{},[898,7587,1879],{"mathvariant":1878},[1665,7589,1681],{},[1654,7591,1750],{},[1665,7593,7594],{},"0,5",[1710,7596,7597,7599],{},[898,7598,1663],{},[1665,7600,1667],{},[1654,7602,1750],{},[1665,7604,1681],{},[902,7606,7607],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,7609,7610,1343,7635],{},[883,7611,7613],{"className":7612},[886],[888,7614,7615],{"xmlns":890},[892,7616,7617,7632],{},[895,7618,7619,7627,7629],{},[1659,7620,7621,7623,7625],{},[898,7622,1663],{},[1665,7624,1667],{},[1654,7626,1670],{},[1654,7628,1750],{},[1665,7630,7631],{},"4",[902,7633,7634],{"encoding":904},"Q_1^* = 4",[883,7636,7638],{"className":7637},[886],[888,7639,7640],{"xmlns":890},[892,7641,7642,7656],{},[895,7643,7644,7652,7654],{},[1659,7645,7646,7648,7650],{},[898,7647,1663],{},[1665,7649,1681],{},[1654,7651,1670],{},[1654,7653,1750],{},[1665,7655,1667],{},[902,7657,7658],{"encoding":904},"Q_2^* = 1",[883,7660,7662],{"className":7661},[886],[888,7663,7664],{"xmlns":890},[892,7665,7666,7678],{},[895,7667,7668,7674,7676],{},[1741,7669,7670,7672],{},[898,7671,2471],{},[1654,7673,1670],{},[1654,7675,1750],{},[1665,7677,1667],{},[902,7679,7680],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,7683,7685],{"className":7684},[886],[888,7686,7687],{"xmlns":890},[892,7688,7689,7717],{},[895,7690,7691,7697,7699,7701,7703,7705,7707,7709,7711,7713,7715],{},[1741,7692,7693,7695],{},[898,7694,1798],{},[1654,7696,1670],{},[1654,7698,1750],{},[1665,7700,7154],{},[1654,7702,4554],{},[1665,7704,7631],{},[1654,7706,1766],{},[1665,7708,1667],{},[1654,7710,4554],{},[1665,7712,1667],{},[1654,7714,1750],{},[1665,7716,1681],{},[902,7718,7719],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,7721,7722,7725,7726,1343,7792,1343,7858,7924,7925,7962,7963,7985,7986,2138],{},[614,7723,7724],{},"Ověření postačující podmínky"," (6.26): ",[883,7727,7729],{"className":7728},[886],[888,7730,7731],{"xmlns":890},[892,7732,7733,7789],{},[895,7734,7735,7747,7749,7751,7759,7775],{},[1659,7736,7737,7739,7741],{},[898,7738,900],{},[1665,7740,6477],{},[895,7742,7743,7745],{},[1654,7744,2592],{"mathvariant":1878},[1654,7746,2592],{"mathvariant":1878},[1654,7748,1750],{},[1654,7750,2380],{},[2582,7752,7753],{"scriptlevel":2062,"displaystyle":1656},[2811,7754,7755,7757],{},[1665,7756,1667],{},[1665,7758,7631],{},[1659,7760,7761,7763,7765],{},[898,7762,1663],{},[1665,7764,1667],{},[895,7766,7767,7769,7771,7773],{},[1654,7768,2380],{},[1665,7770,4035],{},[898,7772,1879],{"mathvariant":1878},[1665,7774,1681],{},[1659,7776,7777,7779,7781],{},[898,7778,1663],{},[1665,7780,1681],{},[895,7782,7783,7785,7787],{},[1665,7784,1667],{},[898,7786,1879],{"mathvariant":1878},[1665,7788,1681],{},[902,7790,7791],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,7793,7795],{"className":7794},[886],[888,7796,7797],{"xmlns":890},[892,7798,7799,7855],{},[895,7800,7801,7813,7815,7817,7825,7839],{},[1659,7802,7803,7805,7807],{},[898,7804,900],{},[1665,7806,6492],{},[895,7808,7809,7811],{},[1654,7810,2592],{"mathvariant":1878},[1654,7812,2592],{"mathvariant":1878},[1654,7814,1750],{},[1654,7816,2380],{},[2582,7818,7819],{"scriptlevel":2062,"displaystyle":1656},[2811,7820,7821,7823],{},[1665,7822,1667],{},[1665,7824,7631],{},[1659,7826,7827,7829,7831],{},[898,7828,1663],{},[1665,7830,1667],{},[895,7832,7833,7835,7837],{},[1665,7834,1667],{},[898,7836,1879],{"mathvariant":1878},[1665,7838,1681],{},[1659,7840,7841,7843,7845],{},[898,7842,1663],{},[1665,7844,1681],{},[895,7846,7847,7849,7851,7853],{},[1654,7848,2380],{},[1665,7850,4035],{},[898,7852,1879],{"mathvariant":1878},[1665,7854,1681],{},[902,7856,7857],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,7859,7861],{"className":7860},[886],[888,7862,7863],{"xmlns":890},[892,7864,7865,7921],{},[895,7866,7867,7879,7881,7889,7905],{},[1659,7868,7869,7871,7873],{},[898,7870,900],{},[1665,7872,6509],{},[895,7874,7875,7877],{},[1654,7876,2592],{"mathvariant":1878},[1654,7878,2592],{"mathvariant":1878},[1654,7880,1750],{},[2582,7882,7883],{"scriptlevel":2062,"displaystyle":1656},[2811,7884,7885,7887],{},[1665,7886,1667],{},[1665,7888,7631],{},[1659,7890,7891,7893,7895],{},[898,7892,1663],{},[1665,7894,1667],{},[895,7896,7897,7899,7901,7903],{},[1654,7898,2380],{},[1665,7900,1667],{},[898,7902,1879],{"mathvariant":1878},[1665,7904,1681],{},[1659,7906,7907,7909,7911],{},[898,7908,1663],{},[1665,7910,1681],{},[895,7912,7913,7915,7917,7919],{},[1654,7914,2380],{},[1665,7916,1667],{},[898,7918,1879],{"mathvariant":1878},[1665,7920,1681],{},[902,7922,7923],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,7926,7928],{"className":7927},[886],[888,7929,7930],{"xmlns":890},[892,7931,7932,7959],{},[895,7933,7934,7936,7938,7940,7942,7944,7946,7948,7950,7952,7955,7957],{},[898,7935,4980],{},[1654,7937,1708],{"stretchy":1656},[1665,7939,7631],{},[1654,7941,1674],{"separator":1673},[1665,7943,1667],{},[1654,7945,1674],{"separator":1673},[1665,7947,1667],{},[1654,7949,1726],{"stretchy":1656},[1654,7951,1750],{},[1665,7953,7954],{},"0,28125",[1654,7956,2952],{},[1665,7958,2062],{},[902,7960,7961],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,7964,7966],{"className":7965},[886],[888,7967,7968],{"xmlns":890},[892,7969,7970,7982],{},[895,7971,7972,7974,7976,7978,7980],{},[1654,7973,1657],{"stretchy":1656},[1665,7975,7631],{},[1654,7977,1674],{"separator":1673},[1665,7979,1667],{},[1654,7981,1686],{"stretchy":1656},[902,7983,7984],{"encoding":904},"[4, 1]"," je vázané ",[38,7987,7988],{},"minimum",[115,7990,7992],{"id":7991},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,7994,7995],{},"Obecně:",[883,7997,7999],{"className":7998},[886],[888,8000,8001],{"xmlns":890,"display":1956},[892,8002,8003,8098],{},[1960,8004,8005],{"width":1962},[1964,8006,8007,8009,8091,8093],{},[1967,8008],{"width":1969},[1967,8010,8011],{},[895,8012,8013,8019,8021,8027,8029,8035,8037,8043,8045,8047,8049,8051,8053,8059,8061,8067,8069,8075,8077,8083,8085,8087,8089],{},[1710,8014,8015,8017],{},[898,8016,1663],{},[1665,8018,1667],{},[1654,8020,1750],{},[1710,8022,8023,8025],{},[898,8024,4980],{},[1665,8026,1667],{},[1654,8028,1708],{"stretchy":1656},[1710,8030,8031,8033],{},[898,8032,1755],{},[1665,8034,1667],{},[1654,8036,1674],{"separator":1673},[1710,8038,8039,8041],{},[898,8040,1755],{},[1665,8042,1681],{},[1654,8044,1674],{"separator":1673},[898,8046,900],{},[1654,8048,1726],{"stretchy":1656},[1654,8050,1674],{"separator":1673},[5008,8052],{"width":5010},[1710,8054,8055,8057],{},[898,8056,1663],{},[1665,8058,1681],{},[1654,8060,1750],{},[1710,8062,8063,8065],{},[898,8064,4980],{},[1665,8066,1681],{},[1654,8068,1708],{"stretchy":1656},[1710,8070,8071,8073],{},[898,8072,1755],{},[1665,8074,1667],{},[1654,8076,1674],{"separator":1673},[1710,8078,8079,8081],{},[898,8080,1755],{},[1665,8082,1681],{},[1654,8084,1674],{"separator":1673},[898,8086,900],{},[1654,8088,1726],{"stretchy":1656},[1654,8090,1674],{"separator":1673},[1967,8092],{"width":1969},[1967,8094,8095],{},[1865,8096,8097],{},"(6.27)",[902,8099,8100],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,8102,8104],{"className":8103},[886],[888,8105,8106],{"xmlns":890,"display":1956},[892,8107,8108,8155],{},[1960,8109,8110],{"width":1962},[1964,8111,8112,8114,8148,8150],{},[1967,8113],{"width":1969},[1967,8115,8116],{},[895,8117,8118,8120,8122,8124,8126,8132,8134,8140,8142,8144,8146],{},[898,8119,2471],{},[1654,8121,1750],{},[898,8123,2471],{},[1654,8125,1708],{"stretchy":1656},[1710,8127,8128,8130],{},[898,8129,1755],{},[1665,8131,1667],{},[1654,8133,1674],{"separator":1673},[1710,8135,8136,8138],{},[898,8137,1755],{},[1665,8139,1681],{},[1654,8141,1674],{"separator":1673},[898,8143,900],{},[1654,8145,1726],{"stretchy":1656},[898,8147,2138],{"mathvariant":1878},[1967,8149],{"width":1969},[1967,8151,8152],{},[1865,8153,8154],{},"(6.28)",[902,8156,8157],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,8159,8160,8161,2186,8164,8177,8178,8191],{},"Hicksova poptávka závisí na ",[38,8162,8163],{},"hladině užitečnosti",[883,8165,8167],{"className":8166},[886],[888,8168,8169],{"xmlns":890},[892,8170,8171,8175],{},[895,8172,8173],{},[898,8174,900],{},[902,8176,900],{"encoding":904}," (nikoli na důchodu ",[883,8179,8181],{"className":8180},[886],[888,8182,8183],{"xmlns":890},[892,8184,8185,8189],{},[895,8186,8187],{},[898,8188,1745],{},[902,8190,1745],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,8193,8195,8196],{"id":8194},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,8197,8199],{"className":8198},[886],[888,8200,8201],{"xmlns":890},[892,8202,8203,8237],{},[895,8204,8205,8207,8209,8223],{},[898,8206,900],{},[1654,8208,1750],{},[1659,8210,8211,8213,8215],{},[898,8212,1663],{},[1665,8214,1667],{},[895,8216,8217,8219,8221],{},[1665,8218,1667],{},[898,8220,1879],{"mathvariant":1878},[1665,8222,1681],{},[1659,8224,8225,8227,8229],{},[898,8226,1663],{},[1665,8228,1681],{},[895,8230,8231,8233,8235],{},[1665,8232,1667],{},[898,8234,1879],{"mathvariant":1878},[1665,8236,1681],{},[902,8238,7107],{"encoding":904},[724,8240,8241,8271],{},[883,8242,8244],{"className":8243},[886],[888,8245,8246],{"xmlns":890},[892,8247,8248,8268],{},[895,8249,8250,8256,8258,8264,8266],{},[1710,8251,8252,8254],{},[898,8253,1755],{},[1665,8255,1667],{},[1654,8257,1674],{"separator":1673},[1710,8259,8260,8262],{},[898,8261,1755],{},[1665,8263,1681],{},[1654,8265,1674],{"separator":1673},[898,8267,900],{},[902,8269,8270],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,8273,8275],{"className":8274},[886],[888,8276,8277],{"xmlns":890,"display":1956},[892,8278,8279,8353],{},[895,8280,8281,8283,8285,8291,8297,8299,8305,8311,8313,8315,8317,8319,8321,8335,8349,8351],{},[898,8282,2450],{"mathvariant":2449},[1654,8284,1750],{},[1710,8286,8287,8289],{},[898,8288,1755],{},[1665,8290,1667],{},[1710,8292,8293,8295],{},[898,8294,1663],{},[1665,8296,1667],{},[1654,8298,1766],{},[1710,8300,8301,8303],{},[898,8302,1755],{},[1665,8304,1681],{},[1710,8306,8307,8309],{},[898,8308,1663],{},[1665,8310,1681],{},[1654,8312,1766],{},[898,8314,2471],{},[1654,8316,1708],{"stretchy":1656},[898,8318,900],{},[1654,8320,2380],{},[1659,8322,8323,8325,8327],{},[898,8324,1663],{},[1665,8326,1667],{},[895,8328,8329,8331,8333],{},[1665,8330,1667],{},[898,8332,1879],{"mathvariant":1878},[1665,8334,1681],{},[1659,8336,8337,8339,8341],{},[898,8338,1663],{},[1665,8340,1681],{},[895,8342,8343,8345,8347],{},[1665,8344,1667],{},[898,8346,1879],{"mathvariant":1878},[1665,8348,1681],{},[1654,8350,1726],{"stretchy":1656},[898,8352,2138],{"mathvariant":1878},[902,8354,8355],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,8357,4362],{},[883,8359,8361],{"className":8360},[886],[888,8362,8363],{"xmlns":890,"display":1956},[892,8364,8365,8587],{},[1960,8366,8367,8447,8527],{"rowspacing":2574,"columnalign":2575,"columnspacing":2576},[1964,8368,8369,8381],{},[1967,8370,8371],{},[2582,8372,8373],{"scriptlevel":2062,"displaystyle":1673},[1659,8374,8375,8377,8379],{},[898,8376,2450],{"mathvariant":2449},[1665,8378,1667],{},[1654,8380,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1967,8382,8383],{},[2582,8384,8385],{"scriptlevel":2062,"displaystyle":1673},[895,8386,8387,8389,8391,8397,8399,8401,8403,8411,8427,8441,8443,8445],{},[895,8388],{},[1654,8390,1750],{},[1710,8392,8393,8395],{},[898,8394,1755],{},[1665,8396,1667],{},[1654,8398,2380],{},[898,8400,2471],{},[1654,8402,4554],{},[2582,8404,8405],{"scriptlevel":2062,"displaystyle":1656},[2811,8406,8407,8409],{},[1665,8408,1667],{},[1665,8410,1681],{},[1659,8412,8413,8415,8417],{},[898,8414,1663],{},[1665,8416,1667],{},[895,8418,8419,8421,8423,8425],{},[1654,8420,2380],{},[1665,8422,1667],{},[898,8424,1879],{"mathvariant":1878},[1665,8426,1681],{},[1659,8428,8429,8431,8433],{},[898,8430,1663],{},[1665,8432,1681],{},[895,8434,8435,8437,8439],{},[1665,8436,1667],{},[898,8438,1879],{"mathvariant":1878},[1665,8440,1681],{},[1654,8442,1750],{},[1665,8444,2062],{},[1654,8446,1674],{"separator":1673},[1964,8448,8449,8461],{},[1967,8450,8451],{},[2582,8452,8453],{"scriptlevel":2062,"displaystyle":1673},[1659,8454,8455,8457,8459],{},[898,8456,2450],{"mathvariant":2449},[1665,8458,1681],{},[1654,8460,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1967,8462,8463],{},[2582,8464,8465],{"scriptlevel":2062,"displaystyle":1673},[895,8466,8467,8469,8471,8477,8479,8481,8483,8491,8505,8521,8523,8525],{},[895,8468],{},[1654,8470,1750],{},[1710,8472,8473,8475],{},[898,8474,1755],{},[1665,8476,1681],{},[1654,8478,2380],{},[898,8480,2471],{},[1654,8482,4554],{},[2582,8484,8485],{"scriptlevel":2062,"displaystyle":1656},[2811,8486,8487,8489],{},[1665,8488,1667],{},[1665,8490,1681],{},[1659,8492,8493,8495,8497],{},[898,8494,1663],{},[1665,8496,1667],{},[895,8498,8499,8501,8503],{},[1665,8500,1667],{},[898,8502,1879],{"mathvariant":1878},[1665,8504,1681],{},[1659,8506,8507,8509,8511],{},[898,8508,1663],{},[1665,8510,1681],{},[895,8512,8513,8515,8517,8519],{},[1654,8514,2380],{},[1665,8516,1667],{},[898,8518,1879],{"mathvariant":1878},[1665,8520,1681],{},[1654,8522,1750],{},[1665,8524,2062],{},[1654,8526,1674],{"separator":1673},[1964,8528,8529,8541],{},[1967,8530,8531],{},[2582,8532,8533],{"scriptlevel":2062,"displaystyle":1673},[1659,8534,8535,8537,8539],{},[898,8536,2450],{"mathvariant":2449},[898,8538,2471],{},[1654,8540,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1967,8542,8543],{},[2582,8544,8545],{"scriptlevel":2062,"displaystyle":1673},[895,8546,8547,8549,8551,8553,8555,8569,8583,8585],{},[895,8548],{},[1654,8550,1750],{},[898,8552,900],{},[1654,8554,2380],{},[1659,8556,8557,8559,8561],{},[898,8558,1663],{},[1665,8560,1667],{},[895,8562,8563,8565,8567],{},[1665,8564,1667],{},[898,8566,1879],{"mathvariant":1878},[1665,8568,1681],{},[1659,8570,8571,8573,8575],{},[898,8572,1663],{},[1665,8574,1681],{},[895,8576,8577,8579,8581],{},[1665,8578,1667],{},[898,8580,1879],{"mathvariant":1878},[1665,8582,1681],{},[1654,8584,1750],{},[1665,8586,2745],{},[902,8588,8589],{"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}",[724,8591,8592,8593,8664,8665,8723],{},"Podílem rovnic: ",[883,8594,8596],{"className":8595},[886],[888,8597,8598],{"xmlns":890},[892,8599,8600,8661],{},[895,8601,8602,8608,8610,8616,8618,8624,8626,8632,8635,8641,8647,8649,8655],{},[1710,8603,8604,8606],{},[898,8605,1755],{},[1665,8607,1667],{},[898,8609,1879],{"mathvariant":1878},[1710,8611,8612,8614],{},[898,8613,1755],{},[1665,8615,1681],{},[1654,8617,1750],{},[1710,8619,8620,8622],{},[898,8621,1663],{},[1665,8623,1681],{},[898,8625,1879],{"mathvariant":1878},[1710,8627,8628,8630],{},[898,8629,1663],{},[1665,8631,1667],{},[1654,8633,8634],{},"⇒",[1710,8636,8637,8639],{},[898,8638,1755],{},[1665,8640,1667],{},[1710,8642,8643,8645],{},[898,8644,1663],{},[1665,8646,1667],{},[1654,8648,1750],{},[1710,8650,8651,8653],{},[898,8652,1755],{},[1665,8654,1681],{},[1710,8656,8657,8659],{},[898,8658,1663],{},[1665,8660,1681],{},[902,8662,8663],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,8666,8668],{"className":8667},[886],[888,8669,8670],{"xmlns":890},[892,8671,8672,8720],{},[895,8673,8674,8676,8678,8684,8690,8692,8698,8704,8706,8708,8714],{},[898,8675,1798],{},[1654,8677,1750],{},[1710,8679,8680,8682],{},[898,8681,1755],{},[1665,8683,1667],{},[1710,8685,8686,8688],{},[898,8687,1663],{},[1665,8689,1667],{},[1654,8691,1766],{},[1710,8693,8694,8696],{},[898,8695,1755],{},[1665,8697,1681],{},[1710,8699,8700,8702],{},[898,8701,1663],{},[1665,8703,1681],{},[1654,8705,1750],{},[1665,8707,1681],{},[1710,8709,8710,8712],{},[898,8711,1755],{},[1665,8713,1667],{},[1710,8715,8716,8718],{},[898,8717,1663],{},[1665,8719,1667],{},[902,8721,8722],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,8725,8727],{"className":8726},[886],[888,8728,8729],{"xmlns":890,"display":1956},[892,8730,8731,8798],{},[1960,8732,8733],{"width":1962},[1964,8734,8735,8737,8791,8793],{},[1967,8736],{"width":1969},[1967,8738,8739],{},[895,8740,8741,8747,8749,8763,8765,8767,8773,8775,8789],{},[1710,8742,8743,8745],{},[898,8744,1663],{},[1665,8746,1667],{},[1654,8748,1750],{},[2811,8750,8751,8753],{},[898,8752,1798],{},[895,8754,8755,8757],{},[1665,8756,1681],{},[1710,8758,8759,8761],{},[898,8760,1755],{},[1665,8762,1667],{},[1654,8764,1674],{"separator":1673},[5008,8766],{"width":5010},[1710,8768,8769,8771],{},[898,8770,1663],{},[1665,8772,1681],{},[1654,8774,1750],{},[2811,8776,8777,8779],{},[898,8778,1798],{},[895,8780,8781,8783],{},[1665,8782,1681],{},[1710,8784,8785,8787],{},[898,8786,1755],{},[1665,8788,1681],{},[898,8790,2138],{"mathvariant":1878},[1967,8792],{"width":1969},[1967,8794,8795],{},[1865,8796,8797],{},"(6.29)",[902,8799,8800],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,8802,8803,8804,7515,8887,8923],{},"Ze třetí rovnice ",[883,8805,8807],{"className":8806},[886],[888,8808,8809],{"xmlns":890},[892,8810,8811,8884],{},[895,8812,8813,8815,8817,8856,8858],{},[898,8814,900],{},[1654,8816,1750],{},[8818,8819,8820],"msqrt",{},[895,8821,8822,8838,8840],{},[2582,8823,8824],{"scriptlevel":2062,"displaystyle":1656},[2811,8825,8826,8828],{},[898,8827,1798],{},[895,8829,8830,8832],{},[1665,8831,1681],{},[1710,8833,8834,8836],{},[898,8835,1755],{},[1665,8837,1667],{},[1654,8839,4554],{},[2582,8841,8842],{"scriptlevel":2062,"displaystyle":1656},[2811,8843,8844,8846],{},[898,8845,1798],{},[895,8847,8848,8850],{},[1665,8849,1681],{},[1710,8851,8852,8854],{},[898,8853,1755],{},[1665,8855,1681],{},[1654,8857,1750],{},[2582,8859,8860],{"scriptlevel":2062,"displaystyle":1656},[2811,8861,8862,8864],{},[898,8863,1798],{},[895,8865,8866,8868],{},[1665,8867,1681],{},[8818,8869,8870],{},[895,8871,8872,8878],{},[1710,8873,8874,8876],{},[898,8875,1755],{},[1665,8877,1667],{},[1710,8879,8880,8882],{},[898,8881,1755],{},[1665,8883,1681],{},[902,8885,8886],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,8888,8890],{"className":8889},[886],[888,8891,8892],{"xmlns":890},[892,8893,8894,8920],{},[895,8895,8896,8898,8900,8902,8904],{},[898,8897,1798],{},[1654,8899,1750],{},[1665,8901,1681],{},[898,8903,900],{},[8818,8905,8906],{},[895,8907,8908,8914],{},[1710,8909,8910,8912],{},[898,8911,1755],{},[1665,8913,1667],{},[1710,8915,8916,8918],{},[898,8917,1755],{},[1665,8919,1681],{},[902,8921,8922],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,8925,8927],{"className":8926},[886],[888,8928,8929],{"xmlns":890,"display":1956},[892,8930,8931,9076],{},[1960,8932,8933],{"width":1962},[1964,8934,8935,8937,9069,9071],{},[1967,8936],{"width":1969},[1967,8938,8939],{},[2792,8940,8941],{"notation":2794},[2582,8942,8943],{"scriptlevel":2062,"displaystyle":1656},[2582,8944,8945],{"scriptlevel":2062,"displaystyle":1656},[2582,8946,8947],{"scriptlevel":2062,"displaystyle":1673},[895,8948,8949,8951,8957,8959,8961,8977,8979,8985,8987,8993,8995,9001,9003,9005,9007,9009,9011,9017,9019,9021,9037,9039,9045,9047,9053,9055,9061,9063,9065,9067],{},[1865,8950,2805],{},[1710,8952,8953,8955],{},[898,8954,1663],{},[1665,8956,1667],{},[1654,8958,1750],{},[898,8960,900],{},[8818,8962,8963],{},[2811,8964,8965,8971],{},[1710,8966,8967,8969],{},[898,8968,1755],{},[1665,8970,1681],{},[1710,8972,8973,8975],{},[898,8974,1755],{},[1665,8976,1667],{},[1654,8978,1750],{},[1710,8980,8981,8983],{},[898,8982,4980],{},[1665,8984,1667],{},[1654,8986,1708],{"stretchy":1656},[1710,8988,8989,8991],{},[898,8990,1755],{},[1665,8992,1667],{},[1654,8994,1674],{"separator":1673},[1710,8996,8997,8999],{},[898,8998,1755],{},[1665,9000,1681],{},[1654,9002,1674],{"separator":1673},[898,9004,900],{},[1654,9006,1726],{"stretchy":1656},[1654,9008,1674],{"separator":1673},[5008,9010],{"width":5010},[1710,9012,9013,9015],{},[898,9014,1663],{},[1665,9016,1681],{},[1654,9018,1750],{},[898,9020,900],{},[8818,9022,9023],{},[2811,9024,9025,9031],{},[1710,9026,9027,9029],{},[898,9028,1755],{},[1665,9030,1667],{},[1710,9032,9033,9035],{},[898,9034,1755],{},[1665,9036,1681],{},[1654,9038,1750],{},[1710,9040,9041,9043],{},[898,9042,4980],{},[1665,9044,1681],{},[1654,9046,1708],{"stretchy":1656},[1710,9048,9049,9051],{},[898,9050,1755],{},[1665,9052,1667],{},[1654,9054,1674],{"separator":1673},[1710,9056,9057,9059],{},[898,9058,1755],{},[1665,9060,1681],{},[1654,9062,1674],{"separator":1673},[898,9064,900],{},[1654,9066,1726],{"stretchy":1656},[1865,9068,2805],{},[1967,9070],{"width":1969},[1967,9072,9073],{},[1865,9074,9075],{},"(6.30)",[902,9077,9078],{"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}",[115,9080,9082],{"id":9081},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,9084,9085,9086,9099,9100,9117,9118,9131,9132,9149,9150,9153,9154,9193,9194,9223],{},"Primární (max ",[883,9087,9089],{"className":9088},[886],[888,9090,9091],{"xmlns":890},[892,9092,9093,9097],{},[895,9094,9095],{},[898,9096,900],{},[902,9098,900],{"encoding":904}," při rozpočtu ",[883,9101,9103],{"className":9102},[886],[888,9104,9105],{"xmlns":890},[892,9106,9107,9115],{},[895,9108,9109],{},[1741,9110,9111,9113],{},[898,9112,1745],{},[1654,9114,1670],{},[902,9116,1918],{"encoding":904},") a duální (min ",[883,9119,9121],{"className":9120},[886],[888,9122,9123],{"xmlns":890},[892,9124,9125,9129],{},[895,9126,9127],{},[898,9128,1798],{},[902,9130,1798],{"encoding":904}," při užitečnosti ",[883,9133,9135],{"className":9134},[886],[888,9136,9137],{"xmlns":890},[892,9138,9139,9147],{},[895,9140,9141],{},[1741,9142,9143,9145],{},[898,9144,900],{},[1654,9146,1670],{},[902,9148,1848],{"encoding":904},") úloha jsou ",[38,9151,9152],{},"ekvivalentní",": mají tentýž bod optima ",[883,9155,9157],{"className":9156},[886],[888,9158,9159],{"xmlns":890},[892,9160,9161,9191],{},[895,9162,9163,9169,9171,9179,9181,9189],{},[1741,9164,9165,9167],{},[898,9166,1663],{},[1654,9168,1670],{},[1654,9170,1657],{"stretchy":1656},[1659,9172,9173,9175,9177],{},[898,9174,1663],{},[1665,9176,1667],{},[1654,9178,1670],{},[1654,9180,1674],{"separator":1673},[1659,9182,9183,9185,9187],{},[898,9184,1663],{},[1665,9186,1681],{},[1654,9188,1670],{},[1654,9190,1686],{"stretchy":1656},[902,9192,2226],{"encoding":904}," a v obou platí ",[883,9195,9197],{"className":9196},[886],[888,9198,9199],{"xmlns":890},[892,9200,9201,9221],{},[895,9202,9203,9205,9207,9213,9215],{},[1865,9204,1867],{},[1654,9206,1750],{},[1710,9208,9209,9211],{},[898,9210,1755],{},[1665,9212,1667],{},[898,9214,1879],{"mathvariant":1878},[1710,9216,9217,9219],{},[898,9218,1755],{},[1665,9220,1681],{},[902,9222,1888],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,9225,9226],{},[3492,9227],{"alt":9228,"className":9229,"src":9230},"imek-primarni-vs-dualni",[210,3496],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,9232,9233,9346],{},[123,9234,9235,9238,9239,9252,9253,9293,9294,2138],{},[38,9236,9237],{},"Primární"," (Marshall): zadáno ",[883,9240,9242],{"className":9241},[886],[888,9243,9244],{"xmlns":890},[892,9245,9246,9250],{},[895,9247,9248],{},[898,9249,1745],{},[902,9251,1745],{"encoding":904},", hledáme maximální ",[883,9254,9256],{"className":9255},[886],[888,9257,9258],{"xmlns":890},[892,9259,9260,9290],{},[895,9261,9262,9268,9270,9276,9278,9284,9286,9288],{},[1741,9263,9264,9266],{},[898,9265,900],{},[1654,9267,1670],{},[1654,9269,1708],{"stretchy":1656},[1710,9271,9272,9274],{},[898,9273,1755],{},[1665,9275,1667],{},[1654,9277,1674],{"separator":1673},[1710,9279,9280,9282],{},[898,9281,1755],{},[1665,9283,1681],{},[1654,9285,1674],{"separator":1673},[898,9287,1745],{},[1654,9289,1726],{"stretchy":1656},[902,9291,9292],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,9295,9297],{"className":9296},[886],[888,9298,9299],{"xmlns":890},[892,9300,9301,9343],{},[895,9302,9303,9310,9312,9321,9323,9329,9331,9337,9339,9341],{},[1710,9304,9305,9307],{},[898,9306,1663],{},[898,9308,9309],{},"i",[1654,9311,1750],{},[1659,9313,9314,9316,9318],{},[898,9315,4980],{},[898,9317,9309],{},[898,9319,9320],{},"M",[1654,9322,1708],{"stretchy":1656},[1710,9324,9325,9327],{},[898,9326,1755],{},[1665,9328,1667],{},[1654,9330,1674],{"separator":1673},[1710,9332,9333,9335],{},[898,9334,1755],{},[1665,9336,1681],{},[1654,9338,1674],{"separator":1673},[898,9340,1745],{},[1654,9342,1726],{"stretchy":1656},[902,9344,9345],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,9347,9348,9351,9352,9365,9366,9293,9406,2138],{},[38,9349,9350],{},"Duální"," (Hicks): zadáno ",[883,9353,9355],{"className":9354},[886],[888,9356,9357],{"xmlns":890},[892,9358,9359,9363],{},[895,9360,9361],{},[898,9362,900],{},[902,9364,900],{"encoding":904},", hledáme minimální ",[883,9367,9369],{"className":9368},[886],[888,9370,9371],{"xmlns":890},[892,9372,9373,9403],{},[895,9374,9375,9381,9383,9389,9391,9397,9399,9401],{},[1741,9376,9377,9379],{},[898,9378,1798],{},[1654,9380,1670],{},[1654,9382,1708],{"stretchy":1656},[1710,9384,9385,9387],{},[898,9386,1755],{},[1665,9388,1667],{},[1654,9390,1674],{"separator":1673},[1710,9392,9393,9395],{},[898,9394,1755],{},[1665,9396,1681],{},[1654,9398,1674],{"separator":1673},[898,9400,900],{},[1654,9402,1726],{"stretchy":1656},[902,9404,9405],{"encoding":904},"E^*(P_1, P_2, U)",[883,9407,9409],{"className":9408},[886],[888,9410,9411],{"xmlns":890},[892,9412,9413,9454],{},[895,9414,9415,9421,9423,9432,9434,9440,9442,9448,9450,9452],{},[1710,9416,9417,9419],{},[898,9418,1663],{},[898,9420,9309],{},[1654,9422,1750],{},[1659,9424,9425,9427,9429],{},[898,9426,4980],{},[898,9428,9309],{},[898,9430,9431],{},"H",[1654,9433,1708],{"stretchy":1656},[1710,9435,9436,9438],{},[898,9437,1755],{},[1665,9439,1667],{},[1654,9441,1674],{"separator":1673},[1710,9443,9444,9446],{},[898,9445,1755],{},[1665,9447,1681],{},[1654,9449,1674],{"separator":1673},[898,9451,900],{},[1654,9453,1726],{"stretchy":1656},[902,9455,9456],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,9458,9459,9460,9463,9464,9467],{},"Proč se studují obě? Marshallova poptávka je ",[38,9461,9462],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,9465,9466],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,9469,9471],{"id":9470},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,9473,9475],{"id":9474},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,9477,9478,9481,9482,9514,9515,9553,9554,9580],{},[38,9479,9480],{},"6.8"," Jsou dány užitečnost ",[883,9483,9485],{"className":9484},[886],[888,9486,9487],{"xmlns":890},[892,9488,9489,9511],{},[895,9490,9491,9493,9495,9503],{},[898,9492,900],{},[1654,9494,1750],{},[1659,9496,9497,9499,9501],{},[898,9498,1663],{},[1665,9500,1667],{},[1665,9502,7594],{},[1659,9504,9505,9507,9509],{},[898,9506,1663],{},[1665,9508,1681],{},[1665,9510,7594],{},[902,9512,9513],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,9516,9518],{"className":9517},[886],[888,9519,9520],{"xmlns":890},[892,9521,9522,9550],{},[895,9523,9524,9532,9534,9536,9538,9546,9548],{},[1659,9525,9526,9528,9530],{},[898,9527,1755],{},[1665,9529,1667],{},[1654,9531,1670],{},[1654,9533,1750],{},[1665,9535,7631],{},[1654,9537,1674],{"separator":1673},[1659,9539,9540,9542,9544],{},[898,9541,1755],{},[1665,9543,1681],{},[1654,9545,1670],{},[1654,9547,1750],{},[1665,9549,4647],{},[902,9551,9552],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,9555,9557],{"className":9556},[886],[888,9558,9559],{"xmlns":890},[892,9560,9561,9577],{},[895,9562,9563,9569,9571],{},[1710,9564,9565,9567],{},[898,9566,1663],{},[1665,9568,1667],{},[1654,9570,1674],{"separator":1673},[1710,9572,9573,9575],{},[898,9574,1663],{},[1665,9576,1681],{},[902,9578,9579],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,9582,9583,9586,9587,9629,9630,9661,9662,9684,9685,2138],{},[38,9584,9585],{},"6.9"," Jsou dány rozpočtové omezení ",[883,9588,9590],{"className":9589},[886],[888,9591,9592],{"xmlns":890},[892,9593,9594,9626],{},[895,9595,9596,9598,9600,9606,9612,9614,9620],{},[898,9597,1745],{},[1654,9599,1750],{},[1710,9601,9602,9604],{},[898,9603,1755],{},[1665,9605,1667],{},[1710,9607,9608,9610],{},[898,9609,1663],{},[1665,9611,1667],{},[1654,9613,1766],{},[1710,9615,9616,9618],{},[898,9617,1755],{},[1665,9619,1681],{},[1710,9621,9622,9624],{},[898,9623,1663],{},[1665,9625,1681],{},[902,9627,9628],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,9631,9633],{"className":9632},[886],[888,9634,9635],{"xmlns":890},[892,9636,9637,9659],{},[895,9638,9639,9641,9643,9651],{},[898,9640,900],{},[1654,9642,1750],{},[1659,9644,9645,9647,9649],{},[898,9646,1663],{},[1665,9648,1667],{},[1665,9650,7594],{},[1659,9652,9653,9655,9657],{},[898,9654,1663],{},[1665,9656,1681],{},[1665,9658,7594],{},[902,9660,9513],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,9663,9665],{"className":9664},[886],[888,9666,9667],{"xmlns":890},[892,9668,9669,9681],{},[895,9670,9671,9677,9679],{},[1741,9672,9673,9675],{},[898,9674,1745],{},[1654,9676,1670],{},[1654,9678,1750],{},[1665,9680,4011],{},[902,9682,9683],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,9686,9688],{"className":9687},[886],[888,9689,9690],{"xmlns":890},[892,9691,9692,9720],{},[895,9693,9694,9702,9704,9706,9708,9716,9718],{},[1659,9695,9696,9698,9700],{},[898,9697,1755],{},[1665,9699,1667],{},[1654,9701,1670],{},[1654,9703,1750],{},[1665,9705,4032],{},[1654,9707,1674],{"separator":1673},[1659,9709,9710,9712,9714],{},[898,9711,1755],{},[1665,9713,1681],{},[1654,9715,1670],{},[1654,9717,1750],{},[1665,9719,4647],{},[902,9721,9722],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,9724,9725,9728,9729,9762,9763,9796,9797,2138],{},[38,9726,9727],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,9730,9732],{"className":9731},[886],[888,9733,9734],{"xmlns":890},[892,9735,9736,9759],{},[895,9737,9738,9740,9742,9750],{},[898,9739,900],{},[1654,9741,1750],{},[1659,9743,9744,9746,9748],{},[898,9745,1663],{},[1665,9747,1667],{},[898,9749,207],{},[1659,9751,9752,9754,9756],{},[898,9753,1663],{},[1665,9755,1681],{},[898,9757,9758],{},"b",[902,9760,9761],{"encoding":904},"U = Q_1^a Q_2^b",", kde ",[883,9764,9766],{"className":9765},[886],[888,9767,9768],{"xmlns":890},[892,9769,9770,9793],{},[895,9771,9772,9774,9776,9778,9781,9784,9786,9788,9790],{},[898,9773,207],{},[1654,9775,1674],{"separator":1673},[898,9777,9758],{},[1654,9779,9780],{},"∈",[1654,9782,9783],{"stretchy":1656},"⟨",[1665,9785,2062],{},[1654,9787,1674],{"separator":1673},[1665,9789,1667],{},[1654,9791,9792],{"stretchy":1656},"⟩",[902,9794,9795],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,9798,9800],{"className":9799},[886],[888,9801,9802],{"xmlns":890},[892,9803,9804,9836],{},[895,9805,9806,9808,9810,9816,9822,9824,9830],{},[898,9807,1745],{},[1654,9809,1750],{},[1710,9811,9812,9814],{},[898,9813,1755],{},[1665,9815,1667],{},[1710,9817,9818,9820],{},[898,9819,1663],{},[1665,9821,1667],{},[1654,9823,1766],{},[1710,9825,9826,9828],{},[898,9827,1755],{},[1665,9829,1681],{},[1710,9831,9832,9834],{},[898,9833,1663],{},[1665,9835,1681],{},[902,9837,9628],{"encoding":904},[724,9839,9840,9843,9844,9762,9878,9796,9897,2138],{},[38,9841,9842],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,9845,9847],{"className":9846},[886],[888,9848,9849],{"xmlns":890},[892,9850,9851,9875],{},[895,9852,9853,9855,9857,9865,9867],{},[898,9854,900],{},[1654,9856,1750],{},[1659,9858,9859,9861,9863],{},[898,9860,1663],{},[1665,9862,1667],{},[898,9864,207],{},[1654,9866,1766],{},[1659,9868,9869,9871,9873],{},[898,9870,1663],{},[1665,9872,1681],{},[898,9874,207],{},[902,9876,9877],{"encoding":904},"U = Q_1^a + Q_2^a",[883,9879,9881],{"className":9880},[886],[888,9882,9883],{"xmlns":890},[892,9884,9885,9894],{},[895,9886,9887,9889,9892],{},[898,9888,207],{},[1654,9890,9891],{"mathvariant":1878},"≠",[1665,9893,2062],{},[902,9895,9896],{"encoding":904},"a \\neq 0",[883,9898,9900],{"className":9899},[886],[888,9901,9902],{"xmlns":890},[892,9903,9904,9936],{},[895,9905,9906,9908,9910,9916,9922,9924,9930],{},[898,9907,1745],{},[1654,9909,1750],{},[1710,9911,9912,9914],{},[898,9913,1755],{},[1665,9915,1667],{},[1710,9917,9918,9920],{},[898,9919,1663],{},[1665,9921,1667],{},[1654,9923,1766],{},[1710,9925,9926,9928],{},[898,9927,1755],{},[1665,9929,1681],{},[1710,9931,9932,9934],{},[898,9933,1663],{},[1665,9935,1681],{},[902,9937,9628],{"encoding":904},[198,9939,9941],{"id":9940},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,9943,9944,9481,9947,1343,9974,9996,9997,1343,10020,10044,10045,10070,10071,2138],{},[38,9945,9946],{},"6.12",[883,9948,9950],{"className":9949},[886],[888,9951,9952],{"xmlns":890},[892,9953,9954,9972],{},[895,9955,9956,9958,9960,9966],{},[898,9957,900],{},[1654,9959,1750],{},[1710,9961,9962,9964],{},[898,9963,1663],{},[1665,9965,1667],{},[1710,9967,9968,9970],{},[898,9969,1663],{},[1665,9971,1681],{},[902,9973,4156],{"encoding":904},[883,9975,9977],{"className":9976},[886],[888,9978,9979],{"xmlns":890},[892,9980,9981,9993],{},[895,9982,9983,9989,9991],{},[1741,9984,9985,9987],{},[898,9986,900],{},[1654,9988,1670],{},[1654,9990,1750],{},[1665,9992,4647],{},[902,9994,9995],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,9998,10000],{"className":9999},[886],[888,10001,10002],{"xmlns":890},[892,10003,10004,10018],{},[895,10005,10006,10014,10016],{},[1659,10007,10008,10010,10012],{},[898,10009,1755],{},[1665,10011,1667],{},[1654,10013,1670],{},[1654,10015,1750],{},[1665,10017,1681],{},[902,10019,4229],{"encoding":904},[883,10021,10023],{"className":10022},[886],[888,10024,10025],{"xmlns":890},[892,10026,10027,10041],{},[895,10028,10029,10037,10039],{},[1659,10030,10031,10033,10035],{},[898,10032,1755],{},[1665,10034,1681],{},[1654,10036,1670],{},[1654,10038,1750],{},[1665,10040,7631],{},[902,10042,10043],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,10046,10048],{"className":10047},[886],[888,10049,10050],{"xmlns":890},[892,10051,10052,10068],{},[895,10053,10054,10060,10062],{},[1710,10055,10056,10058],{},[898,10057,1663],{},[1665,10059,1667],{},[1654,10061,1674],{"separator":1673},[1710,10063,10064,10066],{},[898,10065,1663],{},[1665,10067,1681],{},[902,10069,9579],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,10072,10074],{"className":10073},[886],[888,10075,10076],{"xmlns":890},[892,10077,10078,10098],{},[895,10079,10080,10082,10084,10090,10092],{},[898,10081,900],{},[1654,10083,1750],{},[1710,10085,10086,10088],{},[898,10087,1663],{},[1665,10089,1667],{},[1654,10091,4554],{},[1710,10093,10094,10096],{},[898,10095,1663],{},[1665,10097,1681],{},[902,10099,10100],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,10102,10103,10106,10107,10148,10149,10171,10172,2138],{},[38,10104,10105],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,10108,10110],{"className":10109},[886],[888,10111,10112],{"xmlns":890},[892,10113,10114,10146],{},[895,10115,10116,10118,10120,10126,10132,10134,10140],{},[898,10117,1798],{},[1654,10119,1750],{},[1710,10121,10122,10124],{},[898,10123,1755],{},[1665,10125,1667],{},[1710,10127,10128,10130],{},[898,10129,1663],{},[1665,10131,1667],{},[1654,10133,1766],{},[1710,10135,10136,10138],{},[898,10137,1755],{},[1665,10139,1681],{},[1710,10141,10142,10144],{},[898,10143,1663],{},[1665,10145,1681],{},[902,10147,1829],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,10150,10152],{"className":10151},[886],[888,10153,10154],{"xmlns":890},[892,10155,10156,10168],{},[895,10157,10158,10164,10166],{},[1741,10159,10160,10162],{},[898,10161,900],{},[1654,10163,1670],{},[1654,10165,1750],{},[1665,10167,4622],{},[902,10169,10170],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,10173,10175],{"className":10174},[886],[888,10176,10177],{"xmlns":890},[892,10178,10179,10208],{},[895,10180,10181,10189,10191,10193,10195,10203,10205],{},[1659,10182,10183,10185,10187],{},[898,10184,1755],{},[1665,10186,1667],{},[1654,10188,1670],{},[1654,10190,1750],{},[1665,10192,4573],{},[1654,10194,1674],{"separator":1673},[1659,10196,10197,10199,10201],{},[898,10198,1755],{},[1665,10200,1681],{},[1654,10202,1670],{},[1654,10204,1750],{},[1665,10206,10207],{},"15",[902,10209,10210],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,10212,10214],{"id":10213},"klíčové-pojmy","Klíčové pojmy",[120,10216,10217,10274,10313,10333,10368,10423,10428,10434,10531,10576],{},[123,10218,10219,2186,10222,10271,10272,2138],{},[38,10220,10221],{},"Rozpočtové omezení (budget constraint)",[883,10223,10225],{"className":10224},[886],[888,10226,10227],{"xmlns":890},[892,10228,10229,10269],{},[895,10230,10231,10237,10239,10247,10253,10255,10263],{},[1741,10232,10233,10235],{},[898,10234,1745],{},[1654,10236,1670],{},[1654,10238,1750],{},[1659,10240,10241,10243,10245],{},[898,10242,1755],{},[1665,10244,1667],{},[1654,10246,1670],{},[1710,10248,10249,10251],{},[898,10250,1663],{},[1665,10252,1667],{},[1654,10254,1766],{},[1659,10256,10257,10259,10261],{},[898,10258,1755],{},[1665,10260,1681],{},[1654,10262,1670],{},[1710,10264,10265,10267],{},[898,10266,1663],{},[1665,10268,1681],{},[902,10270,3552],{"encoding":904}," — (6.12); ",[38,10273,2029],{},[123,10275,10276,10279,10280,2138],{},[38,10277,10278],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,10281,10283],{"className":10282},[886],[888,10284,10285],{"xmlns":890},[892,10286,10287,10311],{},[895,10288,10289,10291,10293,10301,10303],{},[1865,10290,1867],{},[1654,10292,1750],{},[1659,10294,10295,10297,10299],{},[898,10296,1755],{},[1665,10298,1667],{},[1654,10300,1670],{},[898,10302,1879],{"mathvariant":1878},[1659,10304,10305,10307,10309],{},[898,10306,1755],{},[1665,10308,1681],{},[1654,10310,1670],{},[902,10312,2895],{"encoding":904},[123,10314,10315,10330,10331,2138],{},[38,10316,3041,10317],{},[883,10318,10320],{"className":10319},[886],[888,10321,10322],{"xmlns":890},[892,10323,10324,10328],{},[895,10325,10326],{},[898,10327,2471],{},[902,10329,2776],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,10332,3063],{},[123,10334,10335,10338,10339,2138],{},[38,10336,10337],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,10340,10342],{"className":10341},[886],[888,10343,10344],{"xmlns":890},[892,10345,10346,10366],{},[895,10347,10348,10350,10352,10358,10360],{},[1865,10349,1867],{},[1654,10351,1750],{},[1710,10353,10354,10356],{},[898,10355,1755],{},[1665,10357,1667],{},[898,10359,1879],{"mathvariant":1878},[1710,10361,10362,10364],{},[898,10363,1755],{},[1665,10365,1681],{},[902,10367,1888],{"encoding":904},[123,10369,10370,10373,10374,10422],{},[38,10371,10372],{},"Poptávka maximalizující užitečnost (Marshallova)"," — ",[883,10375,10377],{"className":10376},[886],[888,10378,10379],{"xmlns":890},[892,10380,10381,10419],{},[895,10382,10383,10389,10391,10397,10399,10405,10407,10413,10415,10417],{},[1710,10384,10385,10387],{},[898,10386,1663],{},[898,10388,9309],{},[1654,10390,1750],{},[1710,10392,10393,10395],{},[898,10394,4980],{},[898,10396,9309],{},[1654,10398,1708],{"stretchy":1656},[1710,10400,10401,10403],{},[898,10402,1755],{},[1665,10404,1667],{},[1654,10406,1674],{"separator":1673},[1710,10408,10409,10411],{},[898,10410,1755],{},[1665,10412,1681],{},[1654,10414,1674],{"separator":1673},[898,10416,1745],{},[1654,10418,1726],{"stretchy":1656},[902,10420,10421],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,10424,10425,10427],{},[38,10426,5669],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,10429,10430,10433],{},[38,10431,10432],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,10435,10436,10373,10438,10486,10487,10530],{},[38,10437,7992],{},[883,10439,10441],{"className":10440},[886],[888,10442,10443],{"xmlns":890},[892,10444,10445,10483],{},[895,10446,10447,10453,10455,10461,10463,10469,10471,10477,10479,10481],{},[1710,10448,10449,10451],{},[898,10450,1663],{},[898,10452,9309],{},[1654,10454,1750],{},[1710,10456,10457,10459],{},[898,10458,4980],{},[898,10460,9309],{},[1654,10462,1708],{"stretchy":1656},[1710,10464,10465,10467],{},[898,10466,1755],{},[1665,10468,1667],{},[1654,10470,1674],{"separator":1673},[1710,10472,10473,10475],{},[898,10474,1755],{},[1665,10476,1681],{},[1654,10478,1674],{"separator":1673},[898,10480,900],{},[1654,10482,1726],{"stretchy":1656},[902,10484,10485],{"encoding":904},"Q_i = D_i(P_1, P_2, U)"," — (6.27); obecný výsledek pro ",[883,10488,10490],{"className":10489},[886],[888,10491,10492],{"xmlns":890},[892,10493,10494,10528],{},[895,10495,10496,10498,10500,10514],{},[898,10497,900],{},[1654,10499,1750],{},[1659,10501,10502,10504,10506],{},[898,10503,1663],{},[1665,10505,1667],{},[895,10507,10508,10510,10512],{},[1665,10509,1667],{},[898,10511,1879],{"mathvariant":1878},[1665,10513,1681],{},[1659,10515,10516,10518,10520],{},[898,10517,1663],{},[1665,10519,1681],{},[895,10521,10522,10524,10526],{},[1665,10523,1667],{},[898,10525,1879],{"mathvariant":1878},[1665,10527,1681],{},[902,10529,7107],{"encoding":904},": (6.30).",[123,10532,10533,10575],{},[38,10534,10535,10536],{},"Bod dotyku ",[883,10537,10539],{"className":10538},[886],[888,10540,10541],{"xmlns":890},[892,10542,10543,10573],{},[895,10544,10545,10551,10553,10561,10563,10571],{},[1741,10546,10547,10549],{},[898,10548,1663],{},[1654,10550,1670],{},[1654,10552,1657],{"stretchy":1656},[1659,10554,10555,10557,10559],{},[898,10556,1663],{},[1665,10558,1667],{},[1654,10560,1670],{},[1654,10562,1674],{"separator":1673},[1659,10564,10565,10567,10569],{},[898,10566,1663],{},[1665,10568,1681],{},[1654,10570,1670],{},[1654,10572,1686],{"stretchy":1656},[902,10574,2226],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,10577,10578,10581,10582,10595,10596,10609],{},[38,10579,10580],{},"Dualita"," — ekvivalence max ",[883,10583,10585],{"className":10584},[886],[888,10586,10587],{"xmlns":890},[892,10588,10589,10593],{},[895,10590,10591],{},[898,10592,900],{},[902,10594,900],{"encoding":904}," a min ",[883,10597,10599],{"className":10598},[886],[888,10600,10601],{"xmlns":890},[892,10602,10603,10607],{},[895,10604,10605],{},[898,10606,1798],{},[902,10608,1798],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,10611,10613],{"id":10612},"navigace","Navigace",[120,10615,10616,10639,10656,10671,10682],{},[123,10617,10618,2186,10621,10624,10625,10638],{},[38,10619,10620],{},"Teorie před optimalizací:",[207,10622,880],{"className":10623,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,10626,10628],{"className":10627},[886],[888,10629,10630],{"xmlns":890},[892,10631,10632,10636],{},[895,10633,10634],{},[898,10635,900],{},[902,10637,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,10640,10641,2186,10644,10647,10648,10651,10652,2138],{},[38,10642,10643],{},"Matematický aparát:",[207,10645,793],{"className":10646,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,10649,784],{"className":10650,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,10653,10655],{"className":10654,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace",[123,10657,10658,2186,10661,10665,10666,10670],{},[38,10659,10660],{},"Paralely:",[207,10662,10664],{"className":10663,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,10667,10669],{"className":10668,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka"," (Marshallova poptávka jako vstup tržního modelu).",[123,10672,10673,2186,10676,1343,10679],{},[38,10674,10675],{},"Přednášky:",[207,10677,1094],{"className":10678,"dataFsResolvedFilePath":838,"href":839},[210],[207,10680,1101],{"className":10681,"dataFsResolvedFilePath":868,"href":869},[210],[123,10683,10684,2186,10687],{},[38,10685,10686],{},"Kurz:",[207,10688,10692],{"className":10689,"dataFsResolvedFilePath":10690,"href":10691},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","Matematická ekonomie",{"title":641,"searchDepth":642,"depth":642,"links":10694},[10695,10696,10697,10702,10703,10704,10706,10709,10712,10714,10715,10717,10718,10722,10723],{"id":1637,"depth":642,"text":1638},{"id":1896,"depth":642,"text":1897},{"id":2303,"depth":642,"text":2304,"children":10698},[10699,10700],{"id":2425,"depth":649,"text":2426},{"id":3023,"depth":649,"text":10701},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":3487,"depth":642,"text":3488},{"id":3802,"depth":642,"text":3803},{"id":4127,"depth":642,"text":10705},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":4909,"depth":642,"text":4910,"children":10707},[10708],{"id":5668,"depth":649,"text":5669},{"id":5851,"depth":642,"text":5852,"children":10710},[10711],{"id":6108,"depth":649,"text":6109},{"id":7062,"depth":642,"text":10713},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":7991,"depth":642,"text":7992},{"id":8194,"depth":642,"text":10716},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":9081,"depth":642,"text":9082},{"id":9470,"depth":642,"text":9471,"children":10719},[10720,10721],{"id":9474,"depth":649,"text":9475},{"id":9940,"depth":649,"text":9941},{"id":10213,"depth":642,"text":10214},{"id":10612,"depth":642,"text":10613},"2026-04-22",{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":1629,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,10731,1144,10732,10733,10734,10735],"optimalizace-spotrebitele","uzitecnost","poptavka-spotrebitele","minimalizace-vydaju","dualita","topic","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o","topics",{"zapisku":1625,"topics":10740,"summaries":10741,"outputs":10742},15,5,1,[10744,12605,18288,19838,20709,24982,26581,36451,44979,59046,63338,82682,94794,103753,104041],{"id":10745,"title":10746,"body":10747,"course":1128,"courses":659,"created":1129,"description":12594,"extension":661,"meta":12595,"navigation":664,"path":12596,"seo":12597,"sources":12598,"stem":12599,"tags":12600,"type":10736,"updated":677,"__hash__":12604},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":10748,"toc":12577},[10749,10752,10771,10775,10854,10857,10981,11126,11128,11208,11212,11271,11321,11328,11332,11467,11518,11522,11565,11632,11701,11709,11713,11752,11824,11828,11907,11955,11999,12003,12007,12077,12081,12130,12207,12214,12217,12269,12538,12540],[12,10750,10746],{"id":10751},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,10753,10754,10755,10759,10760,10763,10764,10767,10768,2138],{},"Matematický aparát kurzu ",[207,10756,10758],{"className":10757,"dataFsResolvedFilePath":10690,"href":10691},[210],"ImeK",". Bez derivace se neobejdou ",[38,10761,10762],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,10765,10766],{},"maximalizace zisku"," ani ",[38,10769,10770],{},"minimalizace nákladů",[115,10772,10774],{"id":10773},"funkce-a-polynomy","Funkce a polynomy",[724,10776,10777,10778,10805,10806,10819,10820,10833,10834,2138],{},"Funkce jedné proměnné ",[883,10779,10781],{"className":10780},[886],[888,10782,10783],{"xmlns":890},[892,10784,10785,10802],{},[895,10786,10787,10790,10792,10795,10797,10800],{},[898,10788,10789],{},"y",[1654,10791,1750],{},[898,10793,10794],{},"f",[1654,10796,1708],{"stretchy":1656},[898,10798,10799],{},"x",[1654,10801,1726],{"stretchy":1656},[902,10803,10804],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,10807,10809],{"className":10808},[886],[888,10810,10811],{"xmlns":890},[892,10812,10813,10817],{},[895,10814,10815],{},[898,10816,10799],{},[902,10818,10799],{"encoding":904}," (nezávislá) → ",[883,10821,10823],{"className":10822},[886],[888,10824,10825],{"xmlns":890},[892,10826,10827,10831],{},[895,10828,10829],{},[898,10830,10789],{},[902,10832,10789],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,10835,10837],{"className":10836},[886],[888,10838,10839],{"xmlns":890},[892,10840,10841,10851],{},[895,10842,10843,10845,10847,10849],{},[898,10844,10794],{},[1654,10846,1708],{"stretchy":1656},[898,10848,207],{},[1654,10850,1726],{"stretchy":1656},[902,10852,10853],{"encoding":904},"f(a)",[724,10855,10856],{},"Polynomy:",[120,10858,10859,10890,10930],{},[123,10860,10861],{},[152,10862,10863],{},[123,10864,10865,10866],{},"stupně: ",[883,10867,10869],{"className":10868},[886],[888,10870,10871],{"xmlns":890},[892,10872,10873,10887],{},[895,10874,10875,10877,10879,10881,10883,10885],{},[898,10876,10789],{},[1654,10878,1750],{},[898,10880,207],{},[898,10882,10799],{},[1654,10884,1766],{},[898,10886,9758],{},[902,10888,10889],{"encoding":904},"y = ax + b",[123,10891,10892],{},[152,10893,10894],{"start":642},[123,10895,10865,10896],{},[883,10897,10899],{"className":10898},[886],[888,10900,10901],{"xmlns":890},[892,10902,10903,10927],{},[895,10904,10905,10907,10909,10911,10917,10919,10921,10923,10925],{},[898,10906,10789],{},[1654,10908,1750],{},[898,10910,207],{},[1741,10912,10913,10915],{},[898,10914,10799],{},[1665,10916,1681],{},[1654,10918,1766],{},[898,10920,9758],{},[898,10922,10799],{},[1654,10924,1766],{},[898,10926,3624],{},[902,10928,10929],{"encoding":904},"y = ax^2 + bx + c",[123,10931,10932],{},[152,10933,10934],{"start":649},[123,10935,10865,10936],{},[883,10937,10939],{"className":10938},[886],[888,10940,10941],{"xmlns":890},[892,10942,10943,10978],{},[895,10944,10945,10947,10949,10951,10957,10959,10961,10967,10969,10971,10973,10975],{},[898,10946,10789],{},[1654,10948,1750],{},[898,10950,207],{},[1741,10952,10953,10955],{},[898,10954,10799],{},[1665,10956,4035],{},[1654,10958,1766],{},[898,10960,9758],{},[1741,10962,10963,10965],{},[898,10964,10799],{},[1665,10966,1681],{},[1654,10968,1766],{},[898,10970,3624],{},[898,10972,10799],{},[1654,10974,1766],{},[898,10976,10977],{},"d",[902,10979,10980],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,10982,10983,2186,10986,11041,11042,11079,11080,2138],{},[38,10984,10985],{},"Příklad rozkladu:",[883,10987,10989],{"className":10988},[886],[888,10990,10991],{"xmlns":890},[892,10992,10993,11038],{},[895,10994,10995,10997,10999,11005,11007,11009,11011,11013,11016,11018,11020,11022,11024,11026,11028,11030,11032,11034,11036],{},[898,10996,10789],{},[1654,10998,1750],{},[1741,11000,11001,11003],{},[898,11002,10799],{},[1665,11004,1681],{},[1654,11006,2380],{},[1665,11008,4032],{},[898,11010,10799],{},[1654,11012,1766],{},[1665,11014,11015],{},"6",[1654,11017,1750],{},[1654,11019,1708],{"stretchy":1656},[898,11021,10799],{},[1654,11023,2380],{},[1665,11025,1681],{},[1654,11027,1726],{"stretchy":1656},[1654,11029,1708],{"stretchy":1656},[898,11031,10799],{},[1654,11033,2380],{},[1665,11035,4035],{},[1654,11037,1726],{"stretchy":1656},[902,11039,11040],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,11043,11045],{"className":11044},[886],[888,11046,11047],{"xmlns":890},[892,11048,11049,11076],{},[895,11050,11051,11057,11059,11061,11063,11066,11072,11074],{},[1710,11052,11053,11055],{},[898,11054,10799],{},[1665,11056,1667],{},[1654,11058,1750],{},[1665,11060,1681],{},[1654,11062,1674],{"separator":1673},[1865,11064,11065],{}," ",[1710,11067,11068,11070],{},[898,11069,10799],{},[1665,11071,1681],{},[1654,11073,1750],{},[1665,11075,4035],{},[902,11077,11078],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,11081,11083],{"className":11082},[886],[888,11084,11085],{"xmlns":890},[892,11086,11087,11123],{},[895,11088,11089,11091,11093,11095,11097,11099,11107,11113,11115],{},[898,11090,10789],{},[1654,11092,1750],{},[1654,11094,1708],{"stretchy":1656},[898,11096,10799],{},[1654,11098,2380],{},[2582,11100,11101],{"scriptlevel":2062,"displaystyle":1656},[2811,11102,11103,11105],{},[1665,11104,4032],{},[1665,11106,1681],{},[1741,11108,11109,11111],{},[1654,11110,1726],{"stretchy":1656},[1665,11112,1681],{},[1654,11114,2380],{},[2582,11116,11117],{"scriptlevel":2062,"displaystyle":1656},[2811,11118,11119,11121],{},[1665,11120,1667],{},[1665,11122,7631],{},[902,11124,11125],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,11127,10655],{"id":1145},[724,11129,11130,11131,1348,11155,11183,11184,2138],{},"Označení ",[883,11132,11134],{"className":11133},[886],[888,11135,11136],{"xmlns":890},[892,11137,11138,11152],{},[895,11139,11140,11146,11148,11150],{},[1741,11141,11142,11144],{},[898,11143,10794],{},[1654,11145,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,11147,1708],{"stretchy":1656},[898,11149,10799],{},[1654,11151,1726],{"stretchy":1656},[902,11153,11154],{"encoding":904},"f'(x)",[883,11156,11158],{"className":11157},[886],[888,11159,11160],{"xmlns":890},[892,11161,11162,11180],{},[895,11163,11164],{},[2582,11165,11166],{"scriptlevel":2062,"displaystyle":1673},[2811,11167,11168,11174],{},[895,11169,11170,11172],{},[898,11171,10977],{},[898,11173,10789],{},[895,11175,11176,11178],{},[898,11177,10977],{},[898,11179,10799],{},[902,11181,11182],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,11185,11187],{"className":11186},[886],[888,11188,11189],{"xmlns":890},[892,11190,11191,11205],{},[895,11192,11193,11199,11201,11203],{},[1741,11194,11195,11197],{},[898,11196,10794],{},[1654,11198,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,11200,1708],{"stretchy":1656},[898,11202,207],{},[1654,11204,1726],{"stretchy":1656},[902,11206,11207],{"encoding":904},"f'(a)",[198,11209,11211],{"id":11210},"geometrická-interpretace","Geometrická interpretace",[724,11213,11214,11237,11238,11241,11242,11270],{},[883,11215,11217],{"className":11216},[886],[888,11218,11219],{"xmlns":890},[892,11220,11221,11235],{},[895,11222,11223,11229,11231,11233],{},[1741,11224,11225,11227],{},[898,11226,10794],{},[1654,11228,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,11230,1708],{"stretchy":1656},[898,11232,207],{},[1654,11234,1726],{"stretchy":1656},[902,11236,11207],{"encoding":904}," = ",[38,11239,11240],{},"sklon tečny"," ke grafu funkce v bodě ",[883,11243,11245],{"className":11244},[886],[888,11246,11247],{"xmlns":890},[892,11248,11249,11267],{},[895,11250,11251,11253,11255,11257,11259,11261,11263,11265],{},[1654,11252,1657],{"stretchy":1656},[898,11254,207],{},[1654,11256,1674],{"separator":1673},[898,11258,10794],{},[1654,11260,1708],{"stretchy":1656},[898,11262,207],{},[1654,11264,1726],{"stretchy":1656},[1654,11266,1686],{"stretchy":1656},[902,11268,11269],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,11272,11273],{},[883,11274,11276],{"className":11275},[886],[888,11277,11278],{"xmlns":890},[892,11279,11280,11318],{},[895,11281,11282,11284,11286,11288,11290,11292,11294,11296,11302,11304,11306,11308,11310,11312,11314,11316],{},[898,11283,10789],{},[1654,11285,2380],{},[898,11287,10794],{},[1654,11289,1708],{"stretchy":1656},[898,11291,207],{},[1654,11293,1726],{"stretchy":1656},[1654,11295,1750],{},[1741,11297,11298,11300],{},[898,11299,10794],{},[1654,11301,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,11303,1708],{"stretchy":1656},[898,11305,207],{},[1654,11307,1726],{"stretchy":1656},[1654,11309,1708],{"stretchy":1656},[898,11311,10799],{},[1654,11313,2380],{},[898,11315,207],{},[1654,11317,1726],{"stretchy":1656},[902,11319,11320],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,11322,11323],{},[3492,11324],{"alt":11325,"className":11326,"src":11327},"imek-derivace-tecna",[210,3496],"\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,11329,11331],{"id":11330},"inženýrská-interpretace","Inženýrská interpretace",[724,11333,11334,11237,11357,2186,11360,11373,11374,11387,11388,11406,11407,11420,11421,11434,11435,11448,11449,2781],{},[883,11335,11337],{"className":11336},[886],[888,11338,11339],{"xmlns":890},[892,11340,11341,11355],{},[895,11342,11343,11349,11351,11353],{},[1741,11344,11345,11347],{},[898,11346,10794],{},[1654,11348,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,11350,1708],{"stretchy":1656},[898,11352,207],{},[1654,11354,1726],{"stretchy":1656},[902,11356,11207],{"encoding":904},[38,11358,11359],{},"rychlost změny",[883,11361,11363],{"className":11362},[886],[888,11364,11365],{"xmlns":890},[892,11366,11367,11371],{},[895,11368,11369],{},[898,11370,10789],{},[902,11372,10789],{"encoding":904}," vzhledem k ",[883,11375,11377],{"className":11376},[886],[888,11378,11379],{"xmlns":890},[892,11380,11381,11385],{},[895,11382,11383],{},[898,11384,10799],{},[902,11386,10799],{"encoding":904}," v bodě ",[883,11389,11391],{"className":11390},[886],[888,11392,11393],{"xmlns":890},[892,11394,11395,11403],{},[895,11396,11397,11399,11401],{},[898,11398,10799],{},[1654,11400,1750],{},[898,11402,207],{},[902,11404,11405],{"encoding":904},"x = a","; přibližná změna ",[883,11408,11410],{"className":11409},[886],[888,11411,11412],{"xmlns":890},[892,11413,11414,11418],{},[895,11415,11416],{},[898,11417,10789],{},[902,11419,10789],{"encoding":904}," při změně ",[883,11422,11424],{"className":11423},[886],[888,11425,11426],{"xmlns":890},[892,11427,11428,11432],{},[895,11429,11430],{},[898,11431,10799],{},[902,11433,10799],{"encoding":904}," z ",[883,11436,11438],{"className":11437},[886],[888,11439,11440],{"xmlns":890},[892,11441,11442,11446],{},[895,11443,11444],{},[898,11445,207],{},[902,11447,207],{"encoding":904}," na ",[883,11450,11452],{"className":11451},[886],[888,11453,11454],{"xmlns":890},[892,11455,11456,11464],{},[895,11457,11458,11460,11462],{},[898,11459,207],{},[1654,11461,1766],{},[1665,11463,1667],{},[902,11465,11466],{"encoding":904},"a+1",[724,11468,11469],{},[883,11470,11472],{"className":11471},[886],[888,11473,11474],{"xmlns":890},[892,11475,11476,11515],{},[895,11477,11478,11480,11482,11484,11486,11488,11490,11493,11495,11497,11499,11501,11503,11509,11511,11513],{},[898,11479,10794],{},[1654,11481,1708],{"stretchy":1656},[898,11483,207],{},[1654,11485,1766],{},[1665,11487,1667],{},[1654,11489,1726],{"stretchy":1656},[1654,11491,11492],{},"≈",[898,11494,10794],{},[1654,11496,1708],{"stretchy":1656},[898,11498,207],{},[1654,11500,1726],{"stretchy":1656},[1654,11502,1766],{},[1741,11504,11505,11507],{},[898,11506,10794],{},[1654,11508,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,11510,1708],{"stretchy":1656},[898,11512,207],{},[1654,11514,1726],{"stretchy":1656},[902,11516,11517],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,11519,11521],{"id":11520},"příklad-mezní-náklady","Příklad — mezní náklady",[724,11523,11524,11525,2138],{},"Celkové náklady ",[883,11526,11528],{"className":11527},[886],[888,11529,11530],{"xmlns":890},[892,11531,11532,11562],{},[895,11533,11534,11537,11540,11542,11545,11547,11549,11551,11553,11556],{},[898,11535,11536],{},"T",[898,11538,11539],{},"C",[1654,11541,1750],{},[1665,11543,11544],{},"1000",[1654,11546,1766],{},[1665,11548,1681],{},[898,11550,1663],{},[1654,11552,1766],{},[1665,11554,11555],{},"0,1",[1741,11557,11558,11560],{},[898,11559,1663],{},[1665,11561,1681],{},[902,11563,11564],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,11566,11567,11568,11605,11606,2138],{},"Mezní náklady: ",[883,11569,11571],{"className":11570},[886],[888,11572,11573],{"xmlns":890},[892,11574,11575,11602],{},[895,11576,11577,11579,11581,11583,11585,11591,11593,11595,11597,11600],{},[898,11578,9320],{},[898,11580,11539],{},[1654,11582,1750],{},[898,11584,11536],{},[1741,11586,11587,11589],{},[898,11588,11539],{},[1654,11590,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,11592,1750],{},[1665,11594,1681],{},[1654,11596,1766],{},[1665,11598,11599],{},"0,2",[898,11601,1663],{},[902,11603,11604],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,11607,11609],{"className":11608},[886],[888,11610,11611],{"xmlns":890},[892,11612,11613,11629],{},[895,11614,11615,11617,11619,11621,11623,11625,11627],{},[898,11616,9320],{},[898,11618,11539],{},[1654,11620,1708],{"stretchy":1656},[1665,11622,4647],{},[1654,11624,1726],{"stretchy":1656},[1654,11626,1750],{},[1665,11628,7631],{},[902,11630,11631],{"encoding":904},"MC(10) = 4",[724,11633,11634,2186,11637,4039,11685,2186,11688,2138],{},[38,11635,11636],{},"Skutečný přírůstek:",[883,11638,11640],{"className":11639},[886],[888,11641,11642],{"xmlns":890},[892,11643,11644,11682],{},[895,11645,11646,11649,11651,11653,11655,11657,11659,11661,11663,11665,11667,11669,11671,11673,11675,11677,11679],{},[898,11647,11648],{"mathvariant":1878},"Δ",[898,11650,11536],{},[898,11652,11539],{},[1654,11654,1750],{},[898,11656,11536],{},[898,11658,11539],{},[1654,11660,1708],{"stretchy":1656},[1665,11662,6477],{},[1654,11664,1726],{"stretchy":1656},[1654,11666,2380],{},[898,11668,11536],{},[898,11670,11539],{},[1654,11672,1708],{"stretchy":1656},[1665,11674,4647],{},[1654,11676,1726],{"stretchy":1656},[1654,11678,1750],{},[1665,11680,11681],{},"4,2",[902,11683,11684],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",[38,11686,11687],{},"Přibližný (lineární):",[883,11689,11691],{"className":11690},[886],[888,11692,11693],{"xmlns":890},[892,11694,11695,11699],{},[895,11696,11697],{},[1665,11698,7631],{},[902,11700,7631],{"encoding":904},[724,11702,11703,11704,11708],{},"(Viz aplikace v ",[207,11705,11707],{"className":11706,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk",".)",[115,11710,11712],{"id":11711},"diferenciál","Diferenciál",[724,11714,11715],{},[883,11716,11718],{"className":11717},[886],[888,11719,11720],{"xmlns":890},[892,11721,11722,11749],{},[895,11723,11724,11726,11728,11730,11736,11738,11740,11742,11745,11747],{},[898,11725,10977],{},[898,11727,10794],{},[1654,11729,1750],{},[1741,11731,11732,11734],{},[898,11733,10794],{},[1654,11735,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,11737,1708],{"stretchy":1656},[898,11739,10799],{},[1654,11741,1726],{"stretchy":1656},[1865,11743,11744],{}," ",[898,11746,10977],{},[898,11748,10799],{},[902,11750,11751],{"encoding":904},"df = f'(x)\\, dx",[724,11753,11754,11755,11771,11772,11820,11821,2138],{},"Pro malá ",[883,11756,11758],{"className":11757},[886],[888,11759,11760],{"xmlns":890},[892,11761,11762,11768],{},[895,11763,11764,11766],{},[898,11765,10977],{},[898,11767,10799],{},[902,11769,11770],{"encoding":904},"dx"," platí: ",[883,11773,11775],{"className":11774},[886],[888,11776,11777],{"xmlns":890},[892,11778,11779,11817],{},[895,11780,11781,11783,11785,11787,11789,11791,11793,11795,11797,11799,11801,11803,11805,11807,11809,11811,11813,11815],{},[898,11782,11648],{"mathvariant":1878},[898,11784,10794],{},[1654,11786,1750],{},[898,11788,10794],{},[1654,11790,1708],{"stretchy":1656},[898,11792,10799],{},[1654,11794,1766],{},[898,11796,10977],{},[898,11798,10799],{},[1654,11800,1726],{"stretchy":1656},[1654,11802,2380],{},[898,11804,10794],{},[1654,11806,1708],{"stretchy":1656},[898,11808,10799],{},[1654,11810,1726],{"stretchy":1656},[1654,11812,11492],{},[898,11814,10977],{},[898,11816,10794],{},[902,11818,11819],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,11822,11823],{},"lineární odhad přírůstku",[198,11825,11827],{"id":11826},"příklad","Příklad",[724,11829,11830,11860,11861,11885,11886,11906],{},[883,11831,11833],{"className":11832},[886],[888,11834,11835],{"xmlns":890},[892,11836,11837,11857],{},[895,11838,11839,11841,11843,11845,11847,11849,11851],{},[898,11840,11536],{},[898,11842,11539],{},[1654,11844,1750],{},[1665,11846,4273],{},[1654,11848,1766],{},[1665,11850,11555],{},[1741,11852,11853,11855],{},[898,11854,1663],{},[1665,11856,1681],{},[902,11858,11859],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,11862,11864],{"className":11863},[886],[888,11865,11866],{"xmlns":890},[892,11867,11868,11882],{},[895,11869,11870,11872,11874,11876,11879],{},[898,11871,1663],{},[1654,11873,2781],{},[1665,11875,4767],{},[1654,11877,11878],{},"→",[1665,11880,11881],{},"60",[902,11883,11884],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,11887,11889],{"className":11888},[886],[888,11890,11891],{"xmlns":890},[892,11892,11893,11903],{},[895,11894,11895,11897,11899,11901],{},[898,11896,10977],{},[898,11898,1663],{},[1654,11900,1750],{},[1665,11902,4647],{},[902,11904,11905],{"encoding":904},"dQ = 10","):",[724,11908,11909],{},[883,11910,11912],{"className":11911},[886],[888,11913,11914],{"xmlns":890},[892,11915,11916,11952],{},[895,11917,11918,11920,11922,11924,11926,11928,11930,11932,11934,11936,11938,11940,11942,11944,11946,11948,11950],{},[898,11919,10977],{},[898,11921,11536],{},[898,11923,11539],{},[1654,11925,1750],{},[1665,11927,11599],{},[898,11929,1663],{},[1654,11931,4554],{},[898,11933,10977],{},[898,11935,1663],{},[1654,11937,1750],{},[1665,11939,11599],{},[1654,11941,4554],{},[1665,11943,4767],{},[1654,11945,4554],{},[1665,11947,4647],{},[1654,11949,1750],{},[1665,11951,4273],{},[902,11953,11954],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,11956,11957,11958,11981,11982,11998],{},"Přesná změna: ",[883,11959,11961],{"className":11960},[886],[888,11962,11963],{"xmlns":890},[892,11964,11965,11978],{},[895,11966,11967,11969,11971,11973,11975],{},[898,11968,11648],{"mathvariant":1878},[898,11970,11536],{},[898,11972,11539],{},[1654,11974,1750],{},[1665,11976,11977],{},"110",[902,11979,11980],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,11983,11985],{"className":11984},[886],[888,11986,11987],{"xmlns":890},[892,11988,11989,11995],{},[895,11990,11991,11993],{},[898,11992,11536],{},[898,11994,11539],{},[902,11996,11997],{"encoding":904},"TC"," je konvexní.",[115,12000,12002],{"id":12001},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,12004,12006],{"id":12005},"nutná-podmínka","Nutná podmínka",[724,12008,12009,12010,11387,12030,12043,12044,12072,12073,12076],{},"Má-li ",[883,12011,12013],{"className":12012},[886],[888,12014,12015],{"xmlns":890},[892,12016,12017,12027],{},[895,12018,12019,12021,12023,12025],{},[898,12020,10794],{},[1654,12022,1708],{"stretchy":1656},[898,12024,10799],{},[1654,12026,1726],{"stretchy":1656},[902,12028,12029],{"encoding":904},"f(x)",[883,12031,12033],{"className":12032},[886],[888,12034,12035],{"xmlns":890},[892,12036,12037,12041],{},[895,12038,12039],{},[898,12040,207],{},[902,12042,207],{"encoding":904}," extrém, pak ",[883,12045,12047],{"className":12046},[886],[888,12048,12049],{"xmlns":890},[892,12050,12051,12069],{},[895,12052,12053,12059,12061,12063,12065,12067],{},[1741,12054,12055,12057],{},[898,12056,10794],{},[1654,12058,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,12060,1708],{"stretchy":1656},[898,12062,207],{},[1654,12064,1726],{"stretchy":1656},[1654,12066,1750],{},[1665,12068,2062],{},[902,12070,12071],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,12074,12075],{},"stacionární"," (podezřelé) body.",[198,12078,12080],{"id":12079},"postačující-podmínka","Postačující podmínka",[724,12082,12083,12084,12097,12098,2781],{},"Pro stacionární bod ",[883,12085,12087],{"className":12086},[886],[888,12088,12089],{"xmlns":890},[892,12090,12091,12095],{},[895,12092,12093],{},[898,12094,207],{},[902,12096,207],{"encoding":904},", je-li ",[883,12099,12101],{"className":12100},[886],[888,12102,12103],{"xmlns":890},[892,12104,12105,12127],{},[895,12106,12107,12117,12119,12121,12123,12125],{},[1741,12108,12109,12111],{},[898,12110,10794],{},[895,12112,12113,12115],{},[1654,12114,2592],{"mathvariant":1878},[1654,12116,2592],{"mathvariant":1878},[1654,12118,1708],{"stretchy":1656},[898,12120,207],{},[1654,12122,1726],{"stretchy":1656},[1654,12124,9891],{"mathvariant":1878},[1665,12126,2062],{},[902,12128,12129],{"encoding":904},"f''(a) \\neq 0",[120,12131,12132,12170],{},[123,12133,12134,12166,12167],{},[883,12135,12137],{"className":12136},[886],[888,12138,12139],{"xmlns":890},[892,12140,12141,12163],{},[895,12142,12143,12153,12155,12157,12159,12161],{},[1741,12144,12145,12147],{},[898,12146,10794],{},[895,12148,12149,12151],{},[1654,12150,2592],{"mathvariant":1878},[1654,12152,2592],{"mathvariant":1878},[1654,12154,1708],{"stretchy":1656},[898,12156,207],{},[1654,12158,1726],{"stretchy":1656},[1654,12160,2952],{},[1665,12162,2062],{},[902,12164,12165],{"encoding":904},"f''(a) > 0"," ⇒ ",[38,12168,12169],{},"lokální minimum",[123,12171,12172,12166,12204],{},[883,12173,12175],{"className":12174},[886],[888,12176,12177],{"xmlns":890},[892,12178,12179,12201],{},[895,12180,12181,12191,12193,12195,12197,12199],{},[1741,12182,12183,12185],{},[898,12184,10794],{},[895,12186,12187,12189],{},[1654,12188,2592],{"mathvariant":1878},[1654,12190,2592],{"mathvariant":1878},[1654,12192,1708],{"stretchy":1656},[898,12194,207],{},[1654,12196,1726],{"stretchy":1656},[1654,12198,3002],{},[1665,12200,2062],{},[902,12202,12203],{"encoding":904},"f''(a) \u003C 0",[38,12205,12206],{},"lokální maximum",[724,12208,12209],{},[3492,12210],{"alt":12211,"className":12212,"src":12213},"imek-extremy-1d",[210,3496],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,12215,11827],{"id":12216},"příklad-1",[724,12218,12219],{},[883,12220,12222],{"className":12221},[886],[888,12223,12224],{"xmlns":890},[892,12225,12226,12266],{},[895,12227,12228,12230,12232,12234,12236,12238,12240,12246,12248,12250,12256,12258,12260,12262,12264],{},[898,12229,10794],{},[1654,12231,1708],{"stretchy":1656},[898,12233,10799],{},[1654,12235,1726],{"stretchy":1656},[1654,12237,1750],{},[1665,12239,1681],{},[1741,12241,12242,12244],{},[898,12243,10799],{},[1665,12245,4035],{},[1654,12247,2380],{},[1665,12249,4035],{},[1741,12251,12252,12254],{},[898,12253,10799],{},[1665,12255,1681],{},[1654,12257,2380],{},[1665,12259,6509],{},[898,12261,10799],{},[1654,12263,1766],{},[1665,12265,4035],{},[902,12267,12268],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,12270,12271,12382,12422,12485],{},[123,12272,12273,12345,12346],{},[883,12274,12276],{"className":12275},[886],[888,12277,12278],{"xmlns":890},[892,12279,12280,12342],{},[895,12281,12282,12288,12290,12292,12294,12296,12298,12304,12306,12308,12310,12312,12314,12316,12318,12320,12322,12324,12326,12328,12330,12332,12334,12336,12338,12340],{},[1741,12283,12284,12286],{},[898,12285,10794],{},[1654,12287,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,12289,1708],{"stretchy":1656},[898,12291,10799],{},[1654,12293,1726],{"stretchy":1656},[1654,12295,1750],{},[1665,12297,11015],{},[1741,12299,12300,12302],{},[898,12301,10799],{},[1665,12303,1681],{},[1654,12305,2380],{},[1665,12307,11015],{},[898,12309,10799],{},[1654,12311,2380],{},[1665,12313,6509],{},[1654,12315,1750],{},[1665,12317,11015],{},[1654,12319,1708],{"stretchy":1656},[898,12321,10799],{},[1654,12323,1766],{},[1665,12325,1667],{},[1654,12327,1726],{"stretchy":1656},[1654,12329,1708],{"stretchy":1656},[898,12331,10799],{},[1654,12333,2380],{},[1665,12335,1681],{},[1654,12337,1726],{"stretchy":1656},[1654,12339,1750],{},[1665,12341,2062],{},[902,12343,12344],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,12347,12349],{"className":12348},[886],[888,12350,12351],{"xmlns":890},[892,12352,12353,12379],{},[895,12354,12355,12361,12363,12365,12367,12369,12375,12377],{},[1710,12356,12357,12359],{},[898,12358,10799],{},[1665,12360,1667],{},[1654,12362,1750],{},[1654,12364,2380],{},[1665,12366,1667],{},[1654,12368,1674],{"separator":1673},[1710,12370,12371,12373],{},[898,12372,10799],{},[1665,12374,1681],{},[1654,12376,1750],{},[1665,12378,1681],{},[902,12380,12381],{"encoding":904},"x_1 = -1, x_2 = 2",[123,12383,12384],{},[883,12385,12387],{"className":12386},[886],[888,12388,12389],{"xmlns":890},[892,12390,12391,12419],{},[895,12392,12393,12403,12405,12407,12409,12411,12413,12415,12417],{},[1741,12394,12395,12397],{},[898,12396,10794],{},[895,12398,12399,12401],{},[1654,12400,2592],{"mathvariant":1878},[1654,12402,2592],{"mathvariant":1878},[1654,12404,1708],{"stretchy":1656},[898,12406,10799],{},[1654,12408,1726],{"stretchy":1656},[1654,12410,1750],{},[1665,12412,6509],{},[898,12414,10799],{},[1654,12416,2380],{},[1665,12418,11015],{},[902,12420,12421],{"encoding":904},"f''(x) = 12x - 6",[123,12423,12424,12166,12465,12468,12469],{},[883,12425,12427],{"className":12426},[886],[888,12428,12429],{"xmlns":890},[892,12430,12431,12462],{},[895,12432,12433,12443,12445,12447,12449,12451,12453,12455,12458,12460],{},[1741,12434,12435,12437],{},[898,12436,10794],{},[895,12438,12439,12441],{},[1654,12440,2592],{"mathvariant":1878},[1654,12442,2592],{"mathvariant":1878},[1654,12444,1708],{"stretchy":1656},[1654,12446,2380],{},[1665,12448,1667],{},[1654,12450,1726],{"stretchy":1656},[1654,12452,1750],{},[1654,12454,2380],{},[1665,12456,12457],{},"18",[1654,12459,3002],{},[1665,12461,2062],{},[902,12463,12464],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,12466,12467],{},"maximum"," v ",[883,12470,12472],{"className":12471},[886],[888,12473,12474],{"xmlns":890},[892,12475,12476,12482],{},[895,12477,12478,12480],{},[1654,12479,2380],{},[1665,12481,1667],{},[902,12483,12484],{"encoding":904},"-1",[123,12486,12487,12166,12523,12468,12525],{},[883,12488,12490],{"className":12489},[886],[888,12491,12492],{"xmlns":890},[892,12493,12494,12520],{},[895,12495,12496,12506,12508,12510,12512,12514,12516,12518],{},[1741,12497,12498,12500],{},[898,12499,10794],{},[895,12501,12502,12504],{},[1654,12503,2592],{"mathvariant":1878},[1654,12505,2592],{"mathvariant":1878},[1654,12507,1708],{"stretchy":1656},[1665,12509,1681],{},[1654,12511,1726],{"stretchy":1656},[1654,12513,1750],{},[1665,12515,12457],{},[1654,12517,2952],{},[1665,12519,2062],{},[902,12521,12522],{"encoding":904},"f''(2) = 18 > 0",[38,12524,7988],{},[883,12526,12528],{"className":12527},[886],[888,12529,12530],{"xmlns":890},[892,12531,12532,12536],{},[895,12533,12534],{},[1665,12535,1681],{},[902,12537,1681],{"encoding":904},[115,12539,10613],{"id":10612},[120,12541,12542,12550,12558],{},[123,12543,12544,2186,12547],{},[38,12545,12546],{},"Předchozí:",[207,12548,757],{"className":12549,"dataFsResolvedFilePath":755,"href":756},[210],[123,12551,12552,2186,12555],{},[38,12553,12554],{},"Navazující:",[207,12556,775],{"className":12557,"dataFsResolvedFilePath":773,"href":774},[210],[123,12559,12560,2186,12563,12566,12567,12571,12572,12576],{},[38,12561,12562],{},"Souvislosti:",[207,12564,784],{"className":12565,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,12568,12570],{"className":12569,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk"," (aplikace mezních veličin), ",[207,12573,12575],{"className":12574,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita"," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":12578},[12579,12580,12585,12588,12593],{"id":10773,"depth":642,"text":10774},{"id":1145,"depth":642,"text":10655,"children":12581},[12582,12583,12584],{"id":11210,"depth":649,"text":11211},{"id":11330,"depth":649,"text":11331},{"id":11520,"depth":649,"text":11521},{"id":11711,"depth":642,"text":11712,"children":12586},[12587],{"id":11826,"depth":649,"text":11827},{"id":12001,"depth":642,"text":12002,"children":12589},[12590,12591,12592],{"id":12005,"depth":649,"text":12006},{"id":12079,"depth":649,"text":12080},{"id":12216,"depth":649,"text":11827},{"id":10612,"depth":642,"text":10613},"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":10746,"description":12594},[1135],"topics\u002Fderivace",[1128,1145,12601,12602,12603],"diferencial","extremy","mezni-naklady","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":12606,"title":12607,"body":12608,"course":1128,"courses":659,"created":10724,"description":641,"extension":661,"meta":18277,"navigation":664,"path":18278,"seo":18279,"sources":18280,"stem":18281,"tags":18282,"type":10736,"updated":677,"__hash__":18287},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":9,"value":12609,"toc":18250},[12610,12613,12634,12638,12665,12669,12710,12799,12843,12847,12871,12878,12882,12892,12903,12907,12935,12944,12999,13005,13008,13014,13041,13047,13144,13303,13592,13596,13676,13682,13686,13782,13848,14015,14019,14095,14126,14153,14159,14191,14269,14355,14359,14422,14428,14431,14437,14551,14635,14679,14683,14729,14736,15053,15058,15082,15111,15178,15274,15278,15285,15292,15363,15483,15567,15570,15576,15902,15906,16069,16077,16213,16221,16459,16467,16470,16475,16731,16735,16908,17042,17079,17123,17126,17256,17346,17364,17368,17375,17381,17442,17445,17469,17472,17478,17481,17487,17490,17494,17532,17590,17778,17782,17854,17860,17867,17871,17877,18017,18021,18027,18063,18068,18245],[12,12611,12607],{"id":12612},"elasticita-poptávky-a-nabídky",[2140,12614,12615],{},[724,12616,12617,12620,12621,12623,12624,12627,12628,2068,12631,2138],{},[883,12618,12619],{},"!abstract"," TL;DR\n",[38,12622,12575],{}," 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: ",[38,12625,12626],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,12629,12630],{},"křížově-cenovou elasticitu",[38,12632,12633],{},"důchodovou elasticitu",[115,12635,12637],{"id":12636},"úvod-motivace","Úvod — motivace",[724,12639,12640,12641,12644,12645,12648,12649,12652,12653,12656,12657,12660,12661,12664],{},"Termín ",[614,12642,12643],{},"elasticita"," (alternativně ",[614,12646,12647],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,12650,12651],{},"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 ",[614,12654,12655],{},"cenové elasticity poptávky"," (resp. ",[614,12658,12659],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,12662,10655],{"className":12663,"dataFsResolvedFilePath":764,"href":765},[210],").",[198,12666,12668],{"id":12667},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,12670,12671,12672,12690,12691,12709],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,12673,12675],{"className":12674},[886],[888,12676,12677],{"xmlns":890},[892,12678,12679,12687],{},[895,12680,12681,12683,12685],{},[898,12682,1755],{},[1654,12684,1750],{},[1665,12686,4647],{},[902,12688,12689],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,12692,12694],{"className":12693},[886],[888,12695,12696],{"xmlns":890},[892,12697,12698,12706],{},[895,12699,12700,12702,12704],{},[898,12701,1663],{},[1654,12703,1750],{},[1665,12705,4273],{},[902,12707,12708],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,12711,12712,12756],{},[123,12713,12714,12717,12718,12755],{},[38,12715,12716],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,12719,12721],{"className":12720},[886],[888,12722,12723],{"xmlns":890},[892,12724,12725,12752],{},[895,12726,12727,12729,12731,12733,12735,12738,12740,12743,12745,12747,12749],{},[1865,12728,2805],{},[1654,12730,8634],{},[1865,12732,2805],{},[898,12734,11536],{},[898,12736,12737],{},"R",[1654,12739,1750],{},[1665,12741,12742],{},"9",[1654,12744,4554],{},[1665,12746,11977],{},[1654,12748,1750],{},[1665,12750,12751],{},"990",[902,12753,12754],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,12757,12758,12761,12762,12798],{},[38,12759,12760],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,12763,12765],{"className":12764},[886],[888,12766,12767],{"xmlns":890},[892,12768,12769,12795],{},[895,12770,12771,12773,12775,12777,12779,12781,12783,12785,12787,12790,12792],{},[1865,12772,2805],{},[1654,12774,8634],{},[1865,12776,2805],{},[898,12778,11536],{},[898,12780,12737],{},[1654,12782,1750],{},[1665,12784,12742],{},[1654,12786,4554],{},[1665,12788,12789],{},"120",[1654,12791,1750],{},[1665,12793,12794],{},"1080",[902,12796,12797],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,12800,12801,12802,12805,12806,12809,12810,12813,12814,12817,12818,12821,12822,12838,12839,12842],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,12803,12804],{},"nerozumné",", na Trhu 2 ",[38,12807,12808],{},"rozumné",". Trh 2 je ",[38,12811,12812],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,12815,12816],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,12819,12820],{},"neelastická"," a vyššího ",[883,12823,12825],{"className":12824},[886],[888,12826,12827],{"xmlns":890},[892,12828,12829,12835],{},[895,12830,12831,12833],{},[898,12832,11536],{},[898,12834,12737],{},[902,12836,12837],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,12840,12841],{},"zvýšením"," ceny.",[198,12844,12846],{"id":12845},"hypotéza-41","Hypotéza 4.1",[2140,12848,12849],{},[724,12850,12851,12852],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,12853,12855],{"className":12854},[886],[888,12856,12857],{"xmlns":890},[892,12858,12859,12868],{},[895,12860,12861,12863,12866],{},[1654,12862,1708],{"stretchy":1656},[1665,12864,12865],{},"4.1",[1654,12867,1726],{"stretchy":1656},[902,12869,12870],{"encoding":904},"(4.1)",[724,12872,12873,12874,12877],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,12875,12876],{},"procentní změny"," obou faktorů.",[115,12879,12881],{"id":12880},"pojem-elasticity","Pojem elasticity",[724,12883,12884,12885,12887,12888,12891],{},"Obecně ",[38,12886,12643],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,12889,12890],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[2140,12893,12894],{},[724,12895,12896,12898,12899,12902],{},[883,12897,2860],{}," Intuice\nElasticitu lze číst jako ",[38,12900,12901],{},"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.",[115,12904,12906],{"id":12905},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,12908,12909,12910,12934],{},"Nechť ",[883,12911,12913],{"className":12912},[886],[888,12914,12915],{"xmlns":890},[892,12916,12917,12931],{},[895,12918,12919,12921,12923,12925,12927,12929],{},[898,12920,1663],{},[1654,12922,1750],{},[898,12924,4980],{},[1654,12926,1708],{"stretchy":1656},[898,12928,1755],{},[1654,12930,1726],{"stretchy":1656},[902,12932,12933],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,12936,12937],{},[883,12938,12943],{"className":12939,"title":12941,"style":12942},[12940],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,12945,12946,12947,2068,12963,12979,12980,12998],{},"Znaménko minus je korekce: změny ",[883,12948,12950],{"className":12949},[886],[888,12951,12952],{"xmlns":890},[892,12953,12954,12960],{},[895,12955,12956,12958],{},[898,12957,11648],{"mathvariant":1878},[898,12959,1663],{},[902,12961,12962],{"encoding":904},"\\Delta Q",[883,12964,12966],{"className":12965},[886],[888,12967,12968],{"xmlns":890},[892,12969,12970,12976],{},[895,12971,12972,12974],{},[898,12973,11648],{"mathvariant":1878},[898,12975,1755],{},[902,12977,12978],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,12981,12983],{"className":12982},[886],[888,12984,12985],{"xmlns":890},[892,12986,12987,12995],{},[895,12988,12989],{},[1741,12990,12991,12993],{},[898,12992,1798],{},[898,12994,4737],{},[902,12996,12997],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,13000,13001],{},[883,13002,13004],{"className":13003,"title":12941,"style":12942},[12940],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,13006,13007],{},"Po dosazení:",[724,13009,13010],{},[883,13011,13013],{"className":13012,"title":12941,"style":12942},[12940],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,13015,13016,13017,13037,13038,13040],{},"Limitním přechodem ",[883,13018,13020],{"className":13019},[886],[888,13021,13022],{"xmlns":890},[892,13023,13024,13034],{},[895,13025,13026,13028,13030,13032],{},[898,13027,11648],{"mathvariant":1878},[898,13029,1755],{},[1654,13031,11878],{},[1665,13033,2062],{},[902,13035,13036],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,13039,12655],{}," (price elasticity of demand):",[724,13042,13043],{},[883,13044,13046],{"className":13045,"title":12941,"style":12942},[12940],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,13048,13049,13050,13073,13074,13096,13097,13121,13122,13143],{},"kde ",[883,13051,13053],{"className":13052},[886],[888,13054,13055],{"xmlns":890},[892,13056,13057,13071],{},[895,13058,13059,13061,13063,13065,13067,13069],{},[898,13060,1663],{},[1654,13062,1750],{},[898,13064,4980],{},[1654,13066,1708],{"stretchy":1656},[898,13068,1755],{},[1654,13070,1726],{"stretchy":1656},[902,13072,12933],{"encoding":904},". Pro pevnou cenu ",[883,13075,13077],{"className":13076},[886],[888,13078,13079],{"xmlns":890},[892,13080,13081,13093],{},[895,13082,13083,13085,13087],{},[898,13084,1755],{},[1654,13086,1750],{},[1741,13088,13089,13091],{},[898,13090,1755],{},[1654,13092,1670],{},[902,13094,13095],{"encoding":904},"P = P^*"," se ",[883,13098,13100],{"className":13099},[886],[888,13101,13102],{"xmlns":890},[892,13103,13104,13118],{},[895,13105,13106,13108,13110,13116],{},[898,13107,1798],{},[1654,13109,1708],{"stretchy":1656},[1741,13111,13112,13114],{},[898,13113,1755],{},[1654,13115,1670],{},[1654,13117,1726],{"stretchy":1656},[902,13119,13120],{"encoding":904},"E(P^*)"," nazývá ",[614,13123,13124,13125],{},"elasticita poptávky při ceně ",[883,13126,13128],{"className":13127},[886],[888,13129,13130],{"xmlns":890},[892,13131,13132,13140],{},[895,13133,13134],{},[1741,13135,13136,13138],{},[898,13137,1755],{},[1654,13139,1670],{},[902,13141,13142],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[2140,13145,13146],{},[724,13147,13148,13150,13151,13169,13170,13198,13199,13228,13229,1343,13247,1343,13265,13283,13284,13299,13300,2138],{},[883,13149,2146],{}," Pozor na znaménko\nV (4.5) je ",[38,13152,13153,13154],{},"explicitní ",[883,13155,13157],{"className":13156},[886],[888,13158,13159],{"xmlns":890},[892,13160,13161,13167],{},[895,13162,13163,13165],{},[1654,13164,2380],{},[1665,13166,1667],{},[902,13168,12484],{"encoding":904}," právě proto, že ",[883,13171,13173],{"className":13172},[886],[888,13174,13175],{"xmlns":890},[892,13176,13177,13195],{},[895,13178,13179,13185,13187,13189,13191,13193],{},[1741,13180,13181,13183],{},[898,13182,1663],{},[1654,13184,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,13186,1708],{"stretchy":1656},[898,13188,1755],{},[1654,13190,1726],{"stretchy":1656},[1654,13192,3002],{},[1665,13194,2062],{},[902,13196,13197],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,13200,13202],{"className":13201},[886],[888,13203,13204],{"xmlns":890},[892,13205,13206,13225],{},[895,13207,13208,13210,13212,13218,13220,13223],{},[898,13209,1798],{},[1654,13211,1708],{"stretchy":1656},[1741,13213,13214,13216],{},[898,13215,1755],{},[1654,13217,1670],{},[1654,13219,1726],{"stretchy":1656},[1654,13221,13222],{},"≥",[1665,13224,2062],{},[902,13226,13227],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,13230,13232],{"className":13231},[886],[888,13233,13234],{"xmlns":890},[892,13235,13236,13244],{},[895,13237,13238,13240,13242],{},[898,13239,1798],{},[1654,13241,2952],{},[1665,13243,1667],{},[902,13245,13246],{"encoding":904},"E > 1",[883,13248,13250],{"className":13249},[886],[888,13251,13252],{"xmlns":890},[892,13253,13254,13262],{},[895,13255,13256,13258,13260],{},[898,13257,1798],{},[1654,13259,3002],{},[1665,13261,1667],{},[902,13263,13264],{"encoding":904},"E \u003C 1",[883,13266,13268],{"className":13267},[886],[888,13269,13270],{"xmlns":890},[892,13271,13272,13280],{},[895,13273,13274,13276,13278],{},[898,13275,1798],{},[1654,13277,1750],{},[1665,13279,1667],{},[902,13281,13282],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,13285,13287],{"className":13286},[886],[888,13288,13289],{"xmlns":890},[892,13290,13291,13297],{},[895,13292,13293,13295],{},[1654,13294,2380],{},[1665,13296,1667],{},[902,13298,12484],{"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 ",[38,13301,13302],{},"absolutní hodnotou",[2140,13304,13305,13324],{},[724,13306,13307,13309,13310,13323],{},[883,13308,3111],{}," Postup: jak spočítat ",[883,13311,13313],{"className":13312},[886],[888,13314,13315],{"xmlns":890},[892,13316,13317,13321],{},[895,13318,13319],{},[898,13320,1798],{},[902,13322,1798],{"encoding":904}," v bodě",[152,13325,13326,13378,13417,13470,13535],{},[123,13327,13328,13329,13352,13353,13377],{},"Zapište ",[883,13330,13332],{"className":13331},[886],[888,13333,13334],{"xmlns":890},[892,13335,13336,13350],{},[895,13337,13338,13340,13342,13344,13346,13348],{},[898,13339,1663],{},[1654,13341,1750],{},[898,13343,4980],{},[1654,13345,1708],{"stretchy":1656},[898,13347,1755],{},[1654,13349,1726],{"stretchy":1656},[902,13351,12933],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,13354,13356],{"className":13355},[886],[888,13357,13358],{"xmlns":890},[892,13359,13360,13374],{},[895,13361,13362,13364,13366,13368,13370,13372],{},[898,13363,1755],{},[1654,13365,1750],{},[898,13367,4980],{},[1654,13369,1708],{"stretchy":1656},[898,13371,1663],{},[1654,13373,1726],{"stretchy":1656},[902,13375,13376],{"encoding":904},"P = D(Q)",", použijte vztah (4.9).",[123,13379,13380,13381,2138],{},"Spočítejte derivaci ",[883,13382,13384],{"className":13383},[886],[888,13385,13386],{"xmlns":890},[892,13387,13388,13414],{},[895,13389,13390,13396,13398,13400,13402,13404,13406,13408,13410,13412],{},[1741,13391,13392,13394],{},[898,13393,1663],{},[1654,13395,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,13397,1708],{"stretchy":1656},[898,13399,1755],{},[1654,13401,1726],{"stretchy":1656},[1654,13403,1750],{},[898,13405,10977],{"mathvariant":1878},[898,13407,1663],{},[898,13409,1879],{"mathvariant":1878},[898,13411,10977],{"mathvariant":1878},[898,13413,1755],{},[902,13415,13416],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,13418,13419,13420,13437,13438,2138],{},"Dosaďte zadanou cenu ",[883,13421,13423],{"className":13422},[886],[888,13424,13425],{"xmlns":890},[892,13426,13427,13435],{},[895,13428,13429],{},[1741,13430,13431,13433],{},[898,13432,1755],{},[1654,13434,1670],{},[902,13436,13142],{"encoding":904}," a dopočítejte odpovídající ",[883,13439,13441],{"className":13440},[886],[888,13442,13443],{"xmlns":890},[892,13444,13445,13467],{},[895,13446,13447,13453,13455,13457,13459,13465],{},[1741,13448,13449,13451],{},[898,13450,1663],{},[1654,13452,1670],{},[1654,13454,1750],{},[898,13456,4980],{},[1654,13458,1708],{"stretchy":1656},[1741,13460,13461,13463],{},[898,13462,1755],{},[1654,13464,1670],{},[1654,13466,1726],{"stretchy":1656},[902,13468,13469],{"encoding":904},"Q^* = D(P^*)",[123,13471,13472,13473,2138],{},"Dosaďte do (4.5): ",[883,13474,13476],{"className":13475},[886],[888,13477,13478],{"xmlns":890},[892,13479,13480,13532],{},[895,13481,13482,13484,13486,13492,13494,13496,13498,13514,13516,13522,13524,13530],{},[898,13483,1798],{},[1654,13485,1708],{"stretchy":1656},[1741,13487,13488,13490],{},[898,13489,1755],{},[1654,13491,1670],{},[1654,13493,1726],{"stretchy":1656},[1654,13495,1750],{},[1654,13497,2380],{},[2582,13499,13500],{"scriptlevel":2062,"displaystyle":1673},[2811,13501,13502,13508],{},[1741,13503,13504,13506],{},[898,13505,1755],{},[1654,13507,1670],{},[1741,13509,13510,13512],{},[898,13511,1663],{},[1654,13513,1670],{},[1865,13515,11744],{},[1741,13517,13518,13520],{},[898,13519,1663],{},[1654,13521,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,13523,1708],{"stretchy":1656},[1741,13525,13526,13528],{},[898,13527,1755],{},[1654,13529,1670],{},[1654,13531,1726],{"stretchy":1656},[902,13533,13534],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,13536,13537,13538,13555,13556,13573,13574,13591],{},"Klasifikujte: ",[883,13539,13541],{"className":13540},[886],[888,13542,13543],{"xmlns":890},[892,13544,13545,13553],{},[895,13546,13547,13549,13551],{},[898,13548,1798],{},[1654,13550,2952],{},[1665,13552,1667],{},[902,13554,13246],{"encoding":904}," elastická, ",[883,13557,13559],{"className":13558},[886],[888,13560,13561],{"xmlns":890},[892,13562,13563,13571],{},[895,13564,13565,13567,13569],{},[898,13566,1798],{},[1654,13568,1750],{},[1665,13570,1667],{},[902,13572,13282],{"encoding":904}," jednotková, ",[883,13575,13577],{"className":13576},[886],[888,13578,13579],{"xmlns":890},[892,13580,13581,13589],{},[895,13582,13583,13585,13587],{},[898,13584,1798],{},[1654,13586,3002],{},[1665,13588,1667],{},[902,13590,13264],{"encoding":904}," neelastická.",[198,13593,13595],{"id":13594},"interpretace-46","Interpretace (4.6)",[2140,13597,13598],{},[724,13599,13600,13601,13624,13625,13638,13639,13656,13657],{},"Číslo ",[883,13602,13604],{"className":13603},[886],[888,13605,13606],{"xmlns":890},[892,13607,13608,13622],{},[895,13609,13610,13612,13614,13620],{},[898,13611,1798],{},[1654,13613,1708],{"stretchy":1656},[1741,13615,13616,13618],{},[898,13617,1755],{},[1654,13619,1670],{},[1654,13621,1726],{"stretchy":1656},[902,13623,13120],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,13626,13628],{"className":13627},[886],[888,13629,13630],{"xmlns":890},[892,13631,13632,13636],{},[895,13633,13634],{},[898,13635,1663],{},[902,13637,1663],{"encoding":904},", jestliže se cena ",[883,13640,13642],{"className":13641},[886],[888,13643,13644],{"xmlns":890},[892,13645,13646,13654],{},[895,13647,13648],{},[1741,13649,13650,13652],{},[898,13651,1755],{},[1654,13653,1670],{},[902,13655,13142],{"encoding":904}," změní o 1 %. ",[883,13658,13660],{"className":13659},[886],[888,13661,13662],{"xmlns":890},[892,13663,13664,13673],{},[895,13665,13666,13668,13671],{},[1654,13667,1708],{"stretchy":1656},[1665,13669,13670],{},"4.6",[1654,13672,1726],{"stretchy":1656},[902,13674,13675],{"encoding":904},"(4.6)",[724,13677,13678,13681],{},[38,13679,13680],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,13683,13685],{"id":13684},"příklad-41","Příklad 4.1",[724,13687,13688,13689,13723,13724,1343,13748,2781],{},"Poptávka ",[883,13690,13692],{"className":13691},[886],[888,13693,13694],{"xmlns":890},[892,13695,13696,13720],{},[895,13697,13698,13700,13702,13704,13706,13708,13710,13712,13714,13716,13718],{},[898,13699,1755],{},[1654,13701,1750],{},[898,13703,4980],{},[1654,13705,1708],{"stretchy":1656},[898,13707,1663],{},[1654,13709,1726],{"stretchy":1656},[1654,13711,1750],{},[1665,13713,4767],{},[1654,13715,2380],{},[1665,13717,1681],{},[898,13719,1663],{},[902,13721,13722],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,13725,13727],{"className":13726},[886],[888,13728,13729],{"xmlns":890},[892,13730,13731,13745],{},[895,13732,13733,13735,13737,13739,13741,13743],{},[898,13734,1663],{},[1654,13736,1750],{},[1665,13738,4622],{},[1654,13740,2380],{},[1665,13742,7594],{},[898,13744,1755],{},[902,13746,13747],{"encoding":904},"Q = 25 - 0{,}5P",[883,13749,13751],{"className":13750},[886],[888,13752,13753],{"xmlns":890},[892,13754,13755,13779],{},[895,13756,13757,13773,13775,13777],{},[2582,13758,13759],{"scriptlevel":2062,"displaystyle":1673},[2811,13760,13761,13767],{},[895,13762,13763,13765],{},[898,13764,10977],{"mathvariant":1878},[898,13766,1663],{},[895,13768,13769,13771],{},[898,13770,10977],{"mathvariant":1878},[898,13772,1755],{},[1654,13774,1750],{},[1654,13776,2380],{},[1665,13778,7594],{},[902,13780,13781],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,13783,13784],{},[883,13785,13787],{"className":13786},[886],[888,13788,13789],{"xmlns":890},[892,13790,13791,13845],{},[895,13792,13793,13795,13797,13799,13813,13815,13817,13819,13821,13823,13825,13843],{},[898,13794,1798],{},[1654,13796,1750],{},[1654,13798,2380],{},[2811,13800,13801,13803],{},[898,13802,1755],{},[895,13804,13805,13807,13809,13811],{},[1665,13806,4622],{},[1654,13808,2380],{},[1665,13810,7594],{},[898,13812,1755],{},[1654,13814,4554],{},[1654,13816,1708],{"stretchy":1656},[1654,13818,2380],{},[1665,13820,7594],{},[1654,13822,1726],{"stretchy":1656},[1654,13824,1750],{},[2811,13826,13827,13833],{},[895,13828,13829,13831],{},[1665,13830,7594],{},[898,13832,1755],{},[895,13834,13835,13837,13839,13841],{},[1665,13836,4622],{},[1654,13838,2380],{},[1665,13840,7594],{},[898,13842,1755],{},[898,13844,2138],{"mathvariant":1878},[902,13846,13847],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,13849,13850,13851,1343,13875,1343,13905,1343,13929,13953,13954,13977,13978,11448,13996,12664],{},"Potom ",[883,13852,13854],{"className":13853},[886],[888,13855,13856],{"xmlns":890},[892,13857,13858,13872],{},[895,13859,13860,13862,13864,13866,13868,13870],{},[898,13861,1798],{},[1654,13863,1708],{"stretchy":1656},[1665,13865,2062],{},[1654,13867,1726],{"stretchy":1656},[1654,13869,1750],{},[1665,13871,2062],{},[902,13873,13874],{"encoding":904},"E(0)=0",[883,13876,13878],{"className":13877},[886],[888,13879,13880],{"xmlns":890},[892,13881,13882,13902],{},[895,13883,13884,13886,13888,13890,13892,13894],{},[898,13885,1798],{},[1654,13887,1708],{"stretchy":1656},[1665,13889,4647],{},[1654,13891,1726],{"stretchy":1656},[1654,13893,1750],{},[2582,13895,13896],{"scriptlevel":2062,"displaystyle":1656},[2811,13897,13898,13900],{},[1665,13899,1667],{},[1665,13901,7631],{},[902,13903,13904],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,13906,13908],{"className":13907},[886],[888,13909,13910],{"xmlns":890},[892,13911,13912,13926],{},[895,13913,13914,13916,13918,13920,13922,13924],{},[898,13915,1798],{},[1654,13917,1708],{"stretchy":1656},[1665,13919,4622],{},[1654,13921,1726],{"stretchy":1656},[1654,13923,1750],{},[1665,13925,1667],{},[902,13927,13928],{"encoding":904},"E(25)=1",[883,13930,13932],{"className":13931},[886],[888,13933,13934],{"xmlns":890},[892,13935,13936,13950],{},[895,13937,13938,13940,13942,13944,13946,13948],{},[898,13939,1798],{},[1654,13941,1708],{"stretchy":1656},[1665,13943,5844],{},[1654,13945,1726],{"stretchy":1656},[1654,13947,1750],{},[1665,13949,7631],{},[902,13951,13952],{"encoding":904},"E(40)=4",". Např. ",[883,13955,13957],{"className":13956},[886],[888,13958,13959],{"xmlns":890},[892,13960,13961,13975],{},[895,13962,13963,13965,13967,13969,13971,13973],{},[898,13964,1798],{},[1654,13966,1708],{"stretchy":1656},[1665,13968,5844],{},[1654,13970,1726],{"stretchy":1656},[1654,13972,1750],{},[1665,13974,7631],{},[902,13976,13952],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,13979,13981],{"className":13980},[886],[888,13982,13983],{"xmlns":890},[892,13984,13985,13993],{},[895,13986,13987,13989,13991],{},[898,13988,1663],{},[1654,13990,1750],{},[1665,13992,4032],{},[902,13994,13995],{"encoding":904},"Q=5",[883,13997,13999],{"className":13998},[886],[888,14000,14001],{"xmlns":890},[892,14002,14003,14012],{},[895,14004,14005,14007,14009],{},[898,14006,1663],{},[1654,14008,1750],{},[1665,14010,14011],{},"4,8",[902,14013,14014],{"encoding":904},"Q=4{,}8",[198,14016,14018],{"id":14017},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,14020,14021,14075],{},[123,14022,14023,14026,14027,14044,14045,2138],{},[38,14024,14025],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,14028,14030],{"className":14029},[886],[888,14031,14032],{"xmlns":890},[892,14033,14034,14042],{},[895,14035,14036],{},[1741,14037,14038,14040],{},[898,14039,1798],{},[898,14041,4737],{},[902,14043,12997],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,14046,14048],{"className":14047},[886],[888,14049,14050],{"xmlns":890},[892,14051,14052,14072],{},[895,14053,14054,14056,14058,14060,14062,14064,14066,14068,14070],{},[1654,14055,9783],{"stretchy":1656},[898,14057,1755],{},[1654,14059,1674],{"separator":1673},[1865,14061,11744],{},[898,14063,1755],{},[1654,14065,1766],{},[898,14067,11648],{"mathvariant":1878},[898,14069,1755],{},[1654,14071,9792],{"stretchy":1656},[902,14073,14074],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,14076,14077,14080,14081,14094],{},[38,14078,14079],{},"Bodová"," (okamžitá) elasticita: ",[883,14082,14084],{"className":14083},[886],[888,14085,14086],{"xmlns":890},[892,14087,14088,14092],{},[895,14089,14090],{},[898,14091,1798],{},[902,14093,1798],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,14096,14098,14099,14112,14113],{"id":14097},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,14100,14102],{"className":14101},[886],[888,14103,14104],{"xmlns":890},[892,14105,14106,14110],{},[895,14107,14108],{},[898,14109,1755],{},[902,14111,1755],{"encoding":904}," jako funkce ",[883,14114,14116],{"className":14115},[886],[888,14117,14118],{"xmlns":890},[892,14119,14120,14124],{},[895,14121,14122],{},[898,14123,1663],{},[902,14125,1663],{"encoding":904},[724,14127,14128,14129,14152],{},"Pokud je poptávka zadaná ve tvaru ",[883,14130,14132],{"className":14131},[886],[888,14133,14134],{"xmlns":890},[892,14135,14136,14150],{},[895,14137,14138,14140,14142,14144,14146,14148],{},[898,14139,1755],{},[1654,14141,1750],{},[898,14143,4980],{},[1654,14145,1708],{"stretchy":1656},[898,14147,1663],{},[1654,14149,1726],{"stretchy":1656},[902,14151,13376],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,14154,14155],{},[883,14156,14158],{"className":14157,"title":12941,"style":12942},[12940],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,14160,14161,2186,14164,14190],{},[38,14162,14163],{},"Příklad 4.3.",[883,14165,14167],{"className":14166},[886],[888,14168,14169],{"xmlns":890},[892,14170,14171,14187],{},[895,14172,14173,14175,14177,14179,14181],{},[898,14174,1755],{},[1654,14176,1750],{},[1665,14178,4273],{},[1654,14180,2380],{},[1741,14182,14183,14185],{},[898,14184,1663],{},[1665,14186,1681],{},[902,14188,14189],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,14192,14193],{},[883,14194,14196],{"className":14195},[886],[888,14197,14198],{"xmlns":890},[892,14199,14200,14266],{},[895,14201,14202,14204,14206,14208,14224,14226,14238,14240,14264],{},[898,14203,1798],{},[1654,14205,1750],{},[1654,14207,2380],{},[2811,14209,14210,14222],{},[895,14211,14212,14214,14216],{},[1665,14213,4273],{},[1654,14215,2380],{},[1741,14217,14218,14220],{},[898,14219,1663],{},[1665,14221,1681],{},[898,14223,1663],{},[1654,14225,4554],{},[2811,14227,14228,14230],{},[1665,14229,1667],{},[895,14231,14232,14234,14236],{},[1654,14233,2380],{},[1665,14235,1681],{},[898,14237,1663],{},[1654,14239,1750],{},[2811,14241,14242,14254],{},[895,14243,14244,14246,14248],{},[1665,14245,4273],{},[1654,14247,2380],{},[1741,14249,14250,14252],{},[898,14251,1663],{},[1665,14253,1681],{},[895,14255,14256,14258],{},[1665,14257,1681],{},[1741,14259,14260,14262],{},[898,14261,1663],{},[1665,14263,1681],{},[898,14265,2138],{"mathvariant":1878},[902,14267,14268],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,14270,14271,14272,14299,14300,4579,14319,2138],{},"Z rovnice ",[883,14273,14275],{"className":14274},[886],[888,14276,14277],{"xmlns":890},[892,14278,14279,14296],{},[895,14280,14281,14283,14285,14291,14293],{},[1665,14282,4273],{},[1654,14284,2380],{},[1741,14286,14287,14289],{},[898,14288,1663],{},[1665,14290,1681],{},[1654,14292,1750],{},[1665,14294,14295],{},"36",[902,14297,14298],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,14301,14303],{"className":14302},[886],[888,14304,14305],{"xmlns":890},[892,14306,14307,14316],{},[895,14308,14309,14311,14313],{},[898,14310,1663],{},[1654,14312,1750],{},[1665,14314,14315],{},"8",[902,14317,14318],{"encoding":904},"Q = 8",[883,14320,14322],{"className":14321},[886],[888,14323,14324],{"xmlns":890},[892,14325,14326,14352],{},[895,14327,14328,14330,14332,14334,14336,14338,14347,14349],{},[898,14329,1798],{},[1654,14331,1708],{"stretchy":1656},[1665,14333,14315],{},[1654,14335,1726],{"stretchy":1656},[1654,14337,1750],{},[2582,14339,14340],{"scriptlevel":2062,"displaystyle":1656},[2811,14341,14342,14344],{},[1665,14343,14295],{},[1665,14345,14346],{},"128",[1654,14348,1750],{},[1665,14350,14351],{},"0,281",[902,14353,14354],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,14356,14358],{"id":14357},"přibližné-změny","Přibližné změny",[724,14360,14361,14362,14398,14399,14421],{},"Diferenciál ",[883,14363,14365],{"className":14364},[886],[888,14366,14367],{"xmlns":890},[892,14368,14369,14395],{},[895,14370,14371,14373,14375,14377,14383,14385,14387,14389,14391,14393],{},[898,14372,10977],{"mathvariant":1878},[898,14374,1663],{},[1654,14376,1750],{},[1741,14378,14379,14381],{},[898,14380,1663],{},[1654,14382,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,14384,1708],{"stretchy":1656},[898,14386,1755],{},[1654,14388,1726],{"stretchy":1656},[1865,14390,11744],{},[898,14392,10977],{"mathvariant":1878},[898,14394,1755],{},[902,14396,14397],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[883,14400,14402],{"className":14401},[886],[888,14403,14404],{"xmlns":890},[892,14405,14406,14418],{},[895,14407,14408,14410,14412,14414,14416],{},[898,14409,10977],{"mathvariant":1878},[898,14411,1755],{},[1654,14413,1750],{},[898,14415,11648],{"mathvariant":1878},[898,14417,1755],{},[902,14419,14420],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,14423,14424],{},[883,14425,14427],{"className":14426,"title":12941,"style":12942},[12940],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,14429,14430],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,14432,14433],{},[883,14434,14436],{"className":14435,"title":12941,"style":12942},[12940],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,14438,14439,2186,14442,14477,14478,14497,14498,14532,14533,14550],{},[38,14440,14441],{},"Příklad 4.5.",[883,14443,14445],{"className":14444},[886],[888,14446,14447],{"xmlns":890},[892,14448,14449,14474],{},[895,14450,14451,14453,14455,14457,14463,14465,14467,14469,14471],{},[898,14452,1755],{},[1654,14454,1750],{},[1654,14456,2380],{},[1741,14458,14459,14461],{},[898,14460,1663],{},[1665,14462,1681],{},[1654,14464,2380],{},[1665,14466,7631],{},[898,14468,1663],{},[1654,14470,1766],{},[1665,14472,14473],{},"96",[902,14475,14476],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,14479,14481],{"className":14480},[886],[888,14482,14483],{"xmlns":890},[892,14484,14485,14494],{},[895,14486,14487,14489,14491],{},[898,14488,1755],{},[1654,14490,1750],{},[1665,14492,14493],{},"51",[902,14495,14496],{"encoding":904},"P=51",". Z rovnice ",[883,14499,14501],{"className":14500},[886],[888,14502,14503],{"xmlns":890},[892,14504,14505,14529],{},[895,14506,14507,14509,14511,14513,14519,14521,14523,14525,14527],{},[1665,14508,14493],{},[1654,14510,1750],{},[1654,14512,2380],{},[1741,14514,14515,14517],{},[898,14516,1663],{},[1665,14518,1681],{},[1654,14520,2380],{},[1665,14522,7631],{},[898,14524,1663],{},[1654,14526,1766],{},[1665,14528,14473],{},[902,14530,14531],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,14534,14536],{"className":14535},[886],[888,14537,14538],{"xmlns":890},[892,14539,14540,14548],{},[895,14541,14542,14544,14546],{},[898,14543,1663],{},[1654,14545,1750],{},[1665,14547,4032],{},[902,14549,13995],{"encoding":904},". Elasticita:",[724,14552,14553],{},[883,14554,14556],{"className":14555},[886],[888,14557,14558],{"xmlns":890},[892,14559,14560,14632],{},[895,14561,14562,14564,14566,14604,14606,14609,14611,14613,14615,14617,14619,14626,14629],{},[898,14563,1798],{},[1654,14565,1750],{},[2811,14567,14568,14588],{},[895,14569,14570,14572,14578,14580,14582,14584,14586],{},[1654,14571,2380],{},[1741,14573,14574,14576],{},[898,14575,1663],{},[1665,14577,1681],{},[1654,14579,2380],{},[1665,14581,7631],{},[898,14583,1663],{},[1654,14585,1766],{},[1665,14587,14473],{},[895,14589,14590,14592,14594,14596,14598,14600,14602],{},[898,14591,1663],{},[1654,14593,1708],{"stretchy":1656},[1665,14595,1681],{},[898,14597,1663],{},[1654,14599,1766],{},[1665,14601,7631],{},[1654,14603,1726],{"stretchy":1656},[1654,14605,1674],{"separator":1673},[5008,14607],{"width":14608},"2em",[898,14610,1798],{},[1654,14612,1708],{"stretchy":1656},[1665,14614,4032],{},[1654,14616,1726],{"stretchy":1656},[1654,14618,1750],{},[2811,14620,14621,14623],{},[1665,14622,14493],{},[1665,14624,14625],{},"70",[1654,14627,14628],{},"≐",[1665,14630,14631],{},"0,728.",[902,14633,14634],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,14636,14637,14638,2138],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,14639,14641],{"className":14640},[886],[888,14642,14643],{"xmlns":890},[892,14644,14645,14676],{},[895,14646,14647,14649,14651,14654,14656,14658,14661,14663,14665,14667,14669,14672,14674],{},[898,14648,11648],{"mathvariant":1878},[898,14650,1663],{},[898,14652,14653],{"mathvariant":1878},"%",[1654,14655,11492],{},[1654,14657,2380],{},[1665,14659,14660],{},"0,728",[1654,14662,4554],{},[1665,14664,1681],{},[1654,14666,1750],{},[1654,14668,2380],{},[1665,14670,14671],{},"1,456",[1865,14673,11744],{},[898,14675,14653],{"mathvariant":1878},[902,14677,14678],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,14680,14682],{"id":14681},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,14684,14685,14686,14709,14710,2781],{},"V závislosti na hodnotě ",[883,14687,14689],{"className":14688},[886],[888,14690,14691],{"xmlns":890},[892,14692,14693,14707],{},[895,14694,14695,14697,14699,14705],{},[898,14696,1798],{},[1654,14698,1708],{"stretchy":1656},[1741,14700,14701,14703],{},[898,14702,1755],{},[1654,14704,1670],{},[1654,14706,1726],{"stretchy":1656},[902,14708,13120],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,14711,14713],{"className":14712},[886],[888,14714,14715],{"xmlns":890},[892,14716,14717,14726],{},[895,14718,14719,14721,14724],{},[1654,14720,1708],{"stretchy":1656},[1665,14722,14723],{},"4.7",[1654,14725,1726],{"stretchy":1656},[902,14727,14728],{"encoding":904},"(4.7)",[724,14730,14731],{},[3492,14732],{"alt":14733,"className":14734,"src":14735},"imek-typy-elasticity-5panelu",[210,3496],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,14737,14738,14777],{},[19,14739,14740],{},[22,14741,14742,14768,14771,14774],{},[25,14743,14744,14745],{},"Hodnota ",[883,14746,14748],{"className":14747},[886],[888,14749,14750],{"xmlns":890},[892,14751,14752,14766],{},[895,14753,14754,14756,14758,14764],{},[898,14755,1798],{},[1654,14757,1708],{"stretchy":1656},[1741,14759,14760,14762],{},[898,14761,1755],{},[1654,14763,1670],{},[1654,14765,1726],{"stretchy":1656},[902,14767,13120],{"encoding":904},[25,14769,14770],{},"Typ poptávky",[25,14772,14773],{},"Termín",[25,14775,14776],{},"Význam",[30,14778,14779,14812,14874,14949,15006],{},[22,14780,14781,14801,14806,14809],{},[35,14782,14783],{},[883,14784,14786],{"className":14785},[886],[888,14787,14788],{"xmlns":890},[892,14789,14790,14798],{},[895,14791,14792,14794,14796],{},[898,14793,1798],{},[1654,14795,1750],{},[1665,14797,2062],{},[902,14799,14800],{"encoding":904},"E = 0",[35,14802,14803],{},[38,14804,14805],{},"dokonale neelastická",[35,14807,14808],{},"perfectly inelastic",[35,14810,14811],{},"množství se nemění bez ohledu na cenu",[22,14813,14814,14838,14842,14845],{},[35,14815,14816],{},[883,14817,14819],{"className":14818},[886],[888,14820,14821],{"xmlns":890},[892,14822,14823,14835],{},[895,14824,14825,14827,14829,14831,14833],{},[1665,14826,2062],{},[1654,14828,3002],{},[898,14830,1798],{},[1654,14832,3002],{},[1665,14834,1667],{},[902,14836,14837],{"encoding":904},"0 \u003C E \u003C 1",[35,14839,14840],{},[38,14841,12820],{},[35,14843,14844],{},"inelastic",[35,14846,14847,14860,14861],{},[883,14848,14850],{"className":14849},[886],[888,14851,14852],{"xmlns":890},[892,14853,14854,14858],{},[895,14855,14856],{},[898,14857,1663],{},[902,14859,1663],{"encoding":904}," se mění pomaleji než ",[883,14862,14864],{"className":14863},[886],[888,14865,14866],{"xmlns":890},[892,14867,14868,14872],{},[895,14869,14870],{},[898,14871,1755],{},[902,14873,1755],{"encoding":904},[22,14875,14876,14895,14900,14903],{},[35,14877,14878],{},[883,14879,14881],{"className":14880},[886],[888,14882,14883],{"xmlns":890},[892,14884,14885,14893],{},[895,14886,14887,14889,14891],{},[898,14888,1798],{},[1654,14890,1750],{},[1665,14892,1667],{},[902,14894,13282],{"encoding":904},[35,14896,14897],{},[38,14898,14899],{},"jednotkově elastická",[35,14901,14902],{},"unit elastic",[35,14904,14905,14918,14919,14932,14933,14948],{},[883,14906,14908],{"className":14907},[886],[888,14909,14910],{"xmlns":890},[892,14911,14912,14916],{},[895,14913,14914],{},[898,14915,1663],{},[902,14917,1663],{"encoding":904}," i ",[883,14920,14922],{"className":14921},[886],[888,14923,14924],{"xmlns":890},[892,14925,14926,14930],{},[895,14927,14928],{},[898,14929,1755],{},[902,14931,1755],{"encoding":904}," se mění stejně rychle; ",[883,14934,14936],{"className":14935},[886],[888,14937,14938],{"xmlns":890},[892,14939,14940,14946],{},[895,14941,14942,14944],{},[898,14943,11536],{},[898,14945,12737],{},[902,14947,12837],{"encoding":904}," má maximum",[22,14950,14951,14970,14974,14977],{},[35,14952,14953],{},[883,14954,14956],{"className":14955},[886],[888,14957,14958],{"xmlns":890},[892,14959,14960,14968],{},[895,14961,14962,14964,14966],{},[898,14963,1798],{},[1654,14965,2952],{},[1665,14967,1667],{},[902,14969,13246],{"encoding":904},[35,14971,14972],{},[38,14973,12816],{},[35,14975,14976],{},"elastic",[35,14978,14979,14992,14993],{},[883,14980,14982],{"className":14981},[886],[888,14983,14984],{"xmlns":890},[892,14985,14986,14990],{},[895,14987,14988],{},[898,14989,1663],{},[902,14991,1663],{"encoding":904}," se mění rychleji než ",[883,14994,14996],{"className":14995},[886],[888,14997,14998],{"xmlns":890},[892,14999,15000,15004],{},[895,15001,15002],{},[898,15003,1755],{},[902,15005,1755],{"encoding":904},[22,15007,15008,15029,15034,15037],{},[35,15009,15010],{},[883,15011,15013],{"className":15012},[886],[888,15014,15015],{"xmlns":890},[892,15016,15017,15026],{},[895,15018,15019,15021,15023],{},[898,15020,1798],{},[1654,15022,11878],{},[898,15024,15025],{"mathvariant":1878},"∞",[902,15027,15028],{"encoding":904},"E \\to \\infty",[35,15030,15031],{},[38,15032,15033],{},"dokonale elastická",[35,15035,15036],{},"perfectly elastic",[35,15038,15039,15040],{},"sebemenší změna ceny úplně mění ",[883,15041,15043],{"className":15042},[886],[888,15044,15045],{"xmlns":890},[892,15046,15047,15051],{},[895,15048,15049],{},[898,15050,1663],{},[902,15052,1663],{"encoding":904},[724,15054,15055],{},[38,15056,15057],{},"Pravidlo růstu elasticity s cenou:",[2140,15059,15060],{},[724,15061,15062,15063],{},"S rostoucí cenou elasticita poptávky roste. ",[883,15064,15066],{"className":15065},[886],[888,15067,15068],{"xmlns":890},[892,15069,15070,15079],{},[895,15071,15072,15074,15077],{},[1654,15073,1708],{"stretchy":1656},[1665,15075,15076],{},"4.8",[1654,15078,1726],{"stretchy":1656},[902,15080,15081],{"encoding":904},"(4.8)",[724,15083,15084,15085,15088,15089,15092,15093,15110],{},"Z toho plyne, že při ",[614,15086,15087],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,15090,15091],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,15094,15096],{"className":15095},[886],[888,15097,15098],{"xmlns":890},[892,15099,15100,15108],{},[895,15101,15102],{},[1741,15103,15104,15106],{},[898,15105,1755],{},[1654,15107,1670],{},[902,15109,13142],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[2140,15112,15113,15118],{},[724,15114,15115,15117],{},[883,15116,3111],{}," Postup: jak klasifikovat poptávku",[152,15119,15120,15147,15150],{},[123,15121,15122,15123,15146],{},"Spočítejte ",[883,15124,15126],{"className":15125},[886],[888,15127,15128],{"xmlns":890},[892,15129,15130,15144],{},[895,15131,15132,15134,15136,15142],{},[898,15133,1798],{},[1654,15135,1708],{"stretchy":1656},[1741,15137,15138,15140],{},[898,15139,1755],{},[1654,15141,1670],{},[1654,15143,1726],{"stretchy":1656},[902,15145,13120],{"encoding":904}," dle (4.5).",[123,15148,15149],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,15151,15152,15153,15177],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,15154,15156],{"className":15155},[886],[888,15157,15158],{"xmlns":890},[892,15159,15160,15174],{},[895,15161,15162,15164,15166,15168,15170,15172],{},[898,15163,1798],{},[1654,15165,1708],{"stretchy":1656},[898,15167,1755],{},[1654,15169,1726],{"stretchy":1656},[1654,15171,1750],{},[1665,15173,1667],{},[902,15175,15176],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,15179,15180,15183,15184,15201,15202,15220,15221,15247,15248,2138],{},[38,15181,15182],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,15185,15187],{"className":15186},[886],[888,15188,15189],{"xmlns":890},[892,15190,15191,15199],{},[895,15192,15193,15195,15197],{},[898,15194,1798],{},[1654,15196,1750],{},[1665,15198,1667],{},[902,15200,13282],{"encoding":904}," pro ",[883,15203,15205],{"className":15204},[886],[888,15206,15207],{"xmlns":890},[892,15208,15209,15217],{},[895,15210,15211,15213,15215],{},[898,15212,1755],{},[1654,15214,1750],{},[1665,15216,4622],{},[902,15218,15219],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,15222,15224],{"className":15223},[886],[888,15225,15226],{"xmlns":890},[892,15227,15228,15244],{},[895,15229,15230,15232,15234,15236,15238,15240,15242],{},[898,15231,1755],{},[1654,15233,9780],{},[1654,15235,9783],{"stretchy":1656},[1665,15237,2062],{},[1654,15239,1674],{"separator":1673},[1665,15241,4622],{},[1654,15243,1726],{"stretchy":1656},[902,15245,15246],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,15249,15251],{"className":15250},[886],[888,15252,15253],{"xmlns":890},[892,15254,15255,15271],{},[895,15256,15257,15259,15261,15263,15265,15267,15269],{},[898,15258,1755],{},[1654,15260,9780],{},[1654,15262,1708],{"stretchy":1656},[1665,15264,4622],{},[1654,15266,1674],{"separator":1673},[1665,15268,4767],{},[1654,15270,9792],{"stretchy":1656},[902,15272,15273],{"encoding":904},"P \\in (25, 50\\rangle",[115,15275,15277],{"id":15276},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,15279,15280],{},[3492,15281],{"alt":15282,"className":15283,"src":15284},"imek-elasticita-tr",[210,3496],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,15286,15287],{},[3492,15288],{"alt":15289,"className":15290,"src":15291},"imek-elasticita-podel-linearni-poptavky",[210,3496],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,15293,15294,15295,15345,15346,15362],{},"Pro celkový příjem platí ",[883,15296,15298],{"className":15297},[886],[888,15299,15300],{"xmlns":890},[892,15301,15302,15342],{},[895,15303,15304,15306,15308,15310,15312,15314,15316,15318,15320,15322,15324,15326,15328,15330,15332,15334,15336,15338,15340],{},[898,15305,11536],{},[898,15307,12737],{},[1654,15309,1750],{},[898,15311,11536],{},[898,15313,12737],{},[1654,15315,1708],{"stretchy":1656},[898,15317,1663],{},[1654,15319,1726],{"stretchy":1656},[1654,15321,1750],{},[898,15323,1755],{},[1654,15325,4554],{},[898,15327,1663],{},[1654,15329,1750],{},[898,15331,1663],{},[1654,15333,4554],{},[898,15335,4980],{},[1654,15337,1708],{"stretchy":1656},[898,15339,1663],{},[1654,15341,1726],{"stretchy":1656},[902,15343,15344],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,15347,15349],{"className":15348},[886],[888,15350,15351],{"xmlns":890},[892,15352,15353,15359],{},[895,15354,15355,15357],{},[898,15356,9320],{},[898,15358,12737],{},[902,15360,15361],{"encoding":904},"MR"," odvodíme:",[724,15364,15365],{},[883,15366,15368],{"className":15367},[886],[888,15369,15370],{"xmlns":890},[892,15371,15372,15480],{},[895,15373,15374,15376,15378,15380,15382,15388,15390,15392,15394,15396,15398,15400,15402,15404,15406,15408,15410,15416,15418,15420,15422,15424,15426,15428,15430,15444,15446,15448],{},[898,15375,9320],{},[898,15377,12737],{},[1654,15379,1750],{},[898,15381,11536],{},[1741,15383,15384,15386],{},[898,15385,12737],{},[1654,15387,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,15389,1708],{"stretchy":1656},[898,15391,1663],{},[1654,15393,1726],{"stretchy":1656},[1654,15395,1750],{},[898,15397,4980],{},[1654,15399,1708],{"stretchy":1656},[898,15401,1663],{},[1654,15403,1726],{"stretchy":1656},[1654,15405,1766],{},[898,15407,1663],{},[1865,15409,11744],{},[1741,15411,15412,15414],{},[898,15413,4980],{},[1654,15415,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,15417,1708],{"stretchy":1656},[898,15419,1663],{},[1654,15421,1726],{"stretchy":1656},[1654,15423,1750],{},[898,15425,1755],{},[1654,15427,1766],{},[898,15429,1663],{},[2811,15431,15432,15438],{},[895,15433,15434,15436],{},[898,15435,10977],{"mathvariant":1878},[898,15437,1755],{},[895,15439,15440,15442],{},[898,15441,10977],{"mathvariant":1878},[898,15443,1663],{},[1654,15445,1750],{},[898,15447,1755],{},[895,15449,15450,15452,15454,15456,15462,15464,15478],{},[1654,15451,1708],{"fence":1673},[1665,15453,1667],{},[1654,15455,1766],{},[2811,15457,15458,15460],{},[898,15459,1663],{},[898,15461,1755],{},[1654,15463,4554],{},[2811,15465,15466,15472],{},[895,15467,15468,15470],{},[898,15469,10977],{"mathvariant":1878},[898,15471,1755],{},[895,15473,15474,15476],{},[898,15475,10977],{"mathvariant":1878},[898,15477,1663],{},[1654,15479,1726],{"fence":1673},[902,15481,15482],{"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)",[724,15484,15485],{},[883,15486,15488],{"className":15487},[886],[888,15489,15490],{"xmlns":890},[892,15491,15492,15564],{},[895,15493,15494,15496,15498,15540,15542,15544],{},[1654,15495,1750],{},[898,15497,1755],{},[895,15499,15500,15502,15504,15506,15538],{},[1654,15501,1708],{"fence":1673},[1665,15503,1667],{},[1654,15505,1766],{},[2811,15507,15508,15510],{},[1665,15509,1667],{},[895,15511,15512,15520,15522],{},[2582,15513,15514],{"scriptlevel":2062,"displaystyle":1656},[2811,15515,15516,15518],{},[898,15517,1755],{},[898,15519,1663],{},[1654,15521,4554],{},[2582,15523,15524],{"scriptlevel":2062,"displaystyle":1656},[2811,15525,15526,15532],{},[895,15527,15528,15530],{},[898,15529,10977],{"mathvariant":1878},[898,15531,1663],{},[895,15533,15534,15536],{},[898,15535,10977],{"mathvariant":1878},[898,15537,1755],{},[1654,15539,1726],{"fence":1673},[1654,15541,1750],{},[898,15543,1755],{},[895,15545,15546,15548,15550,15552,15562],{},[1654,15547,1708],{"fence":1673},[1665,15549,1667],{},[1654,15551,1766],{},[2811,15553,15554,15556],{},[1665,15555,1667],{},[895,15557,15558,15560],{},[1654,15559,2380],{},[898,15561,1798],{},[1654,15563,1726],{"fence":1673},[902,15565,15566],{"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)",[724,15568,15569],{},"a tedy",[724,15571,15572],{},[883,15573,15575],{"className":15574,"title":12941,"style":12942},[12940],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[2140,15577,15578,15647,15896],{},[724,15579,15580,15582,15583,15617,15618,15633,15634,2781],{},[883,15581,2860],{}," Intuice: vztah ",[883,15584,15586],{"className":15585},[886],[888,15587,15588],{"xmlns":890},[892,15589,15590,15614],{},[895,15591,15592,15594,15596,15598,15600,15602,15604,15606,15608,15610,15612],{},[898,15593,9320],{},[898,15595,12737],{},[1654,15597,1750],{},[898,15599,1755],{},[1654,15601,1708],{"stretchy":1656},[1665,15603,1667],{},[1654,15605,2380],{},[1665,15607,1667],{},[898,15609,1879],{"mathvariant":1878},[898,15611,1798],{},[1654,15613,1726],{"stretchy":1656},[902,15615,15616],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,15619,15621],{"className":15620},[886],[888,15622,15623],{"xmlns":890},[892,15624,15625,15631],{},[895,15626,15627,15629],{},[898,15628,9320],{},[898,15630,12737],{},[902,15632,15361],{"encoding":904}," jednoznačně určuje hodnota ",[883,15635,15637],{"className":15636},[886],[888,15638,15639],{"xmlns":890},[892,15640,15641,15645],{},[895,15642,15643],{},[898,15644,1798],{},[902,15646,1798],{"encoding":904},[120,15648,15649,15758,15827],{},[123,15650,15651,15668,15669,2186,15683,2186,15709,2186,15722,10373,15742,15757],{},[883,15652,15654],{"className":15653},[886],[888,15655,15656],{"xmlns":890},[892,15657,15658,15666],{},[895,15659,15660,15662,15664],{},[898,15661,1798],{},[1654,15663,2952],{},[1665,15665,1667],{},[902,15667,13246],{"encoding":904}," (elastická) ",[883,15670,15672],{"className":15671},[886],[888,15673,15674],{"xmlns":890},[892,15675,15676,15680],{},[895,15677,15678],{},[1654,15679,8634],{},[902,15681,15682],{"encoding":904},"\\Rightarrow",[883,15684,15686],{"className":15685},[886],[888,15687,15688],{"xmlns":890},[892,15689,15690,15706],{},[895,15691,15692,15694,15696,15698,15700,15702,15704],{},[1665,15693,1667],{},[1654,15695,2380],{},[1665,15697,1667],{},[898,15699,1879],{"mathvariant":1878},[898,15701,1798],{},[1654,15703,2952],{},[1665,15705,2062],{},[902,15707,15708],{"encoding":904},"1 - 1\u002FE > 0",[883,15710,15712],{"className":15711},[886],[888,15713,15714],{"xmlns":890},[892,15715,15716,15720],{},[895,15717,15718],{},[1654,15719,8634],{},[902,15721,15682],{"encoding":904},[883,15723,15725],{"className":15724},[886],[888,15726,15727],{"xmlns":890},[892,15728,15729,15739],{},[895,15730,15731,15733,15735,15737],{},[898,15732,9320],{},[898,15734,12737],{},[1654,15736,2952],{},[1665,15738,2062],{},[902,15740,15741],{"encoding":904},"MR > 0",[883,15743,15745],{"className":15744},[886],[888,15746,15747],{"xmlns":890},[892,15748,15749,15755],{},[895,15750,15751,15753],{},[898,15752,11536],{},[898,15754,12737],{},[902,15756,12837],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,15759,15760,15777,15778,2186,15791,10373,15811,15826],{},[883,15761,15763],{"className":15762},[886],[888,15764,15765],{"xmlns":890},[892,15766,15767,15775],{},[895,15768,15769,15771,15773],{},[898,15770,1798],{},[1654,15772,1750],{},[1665,15774,1667],{},[902,15776,13282],{"encoding":904}," (jednotková) ",[883,15779,15781],{"className":15780},[886],[888,15782,15783],{"xmlns":890},[892,15784,15785,15789],{},[895,15786,15787],{},[1654,15788,8634],{},[902,15790,15682],{"encoding":904},[883,15792,15794],{"className":15793},[886],[888,15795,15796],{"xmlns":890},[892,15797,15798,15808],{},[895,15799,15800,15802,15804,15806],{},[898,15801,9320],{},[898,15803,12737],{},[1654,15805,1750],{},[1665,15807,2062],{},[902,15809,15810],{"encoding":904},"MR = 0",[883,15812,15814],{"className":15813},[886],[888,15815,15816],{"xmlns":890},[892,15817,15818,15824],{},[895,15819,15820,15822],{},[898,15821,11536],{},[898,15823,12737],{},[902,15825,12837],{"encoding":904}," je extrém (maximum).",[123,15828,15829,15846,15847,2186,15860,10373,15880,15895],{},[883,15830,15832],{"className":15831},[886],[888,15833,15834],{"xmlns":890},[892,15835,15836,15844],{},[895,15837,15838,15840,15842],{},[898,15839,1798],{},[1654,15841,3002],{},[1665,15843,1667],{},[902,15845,13264],{"encoding":904}," (neelastická) ",[883,15848,15850],{"className":15849},[886],[888,15851,15852],{"xmlns":890},[892,15853,15854,15858],{},[895,15855,15856],{},[1654,15857,8634],{},[902,15859,15682],{"encoding":904},[883,15861,15863],{"className":15862},[886],[888,15864,15865],{"xmlns":890},[892,15866,15867,15877],{},[895,15868,15869,15871,15873,15875],{},[898,15870,9320],{},[898,15872,12737],{},[1654,15874,3002],{},[1665,15876,2062],{},[902,15878,15879],{"encoding":904},"MR \u003C 0",[883,15881,15883],{"className":15882},[886],[888,15884,15885],{"xmlns":890},[892,15886,15887,15893],{},[895,15888,15889,15891],{},[898,15890,11536],{},[898,15892,12737],{},[902,15894,12837],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,15897,15898,15899,2138],{},"Viz také ",[207,15900,12570],{"className":15901,"dataFsResolvedFilePath":827,"href":828},[210],[198,15903,15905],{"id":15904},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,15907,15908,15928,15929,15955,15956,15971,15972,15985,15986,15999,16000,16013,16014,16030,16031,2186,16046,16049,16050,16030,16066,2138],{},[38,15909,15910,15911,12664],{},"(a) Poptávka elastická (",[883,15912,15914],{"className":15913},[886],[888,15915,15916],{"xmlns":890},[892,15917,15918,15926],{},[895,15919,15920,15922,15924],{},[898,15921,1798],{},[1654,15923,2952],{},[1665,15925,1667],{},[902,15927,13246],{"encoding":904}," Z (4.12) plyne ",[883,15930,15932],{"className":15931},[886],[888,15933,15934],{"xmlns":890},[892,15935,15936,15952],{},[895,15937,15938,15940,15942,15944,15946,15948,15950],{},[898,15939,9320],{},[898,15941,12737],{},[1654,15943,1708],{"stretchy":1656},[898,15945,1663],{},[1654,15947,1726],{"stretchy":1656},[1654,15949,2952],{},[1665,15951,2062],{},[902,15953,15954],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,15957,15959],{"className":15958},[886],[888,15960,15961],{"xmlns":890},[892,15962,15963,15969],{},[895,15964,15965,15967],{},[898,15966,11536],{},[898,15968,12737],{},[902,15970,12837],{"encoding":904}," je rostoucí funkcí ",[883,15973,15975],{"className":15974},[886],[888,15976,15977],{"xmlns":890},[892,15978,15979,15983],{},[895,15980,15981],{},[898,15982,1663],{},[902,15984,1663],{"encoding":904},". Avšak růst ",[883,15987,15989],{"className":15988},[886],[888,15990,15991],{"xmlns":890},[892,15992,15993,15997],{},[895,15994,15995],{},[898,15996,1663],{},[902,15998,1663],{"encoding":904}," je odezvou na pokles ceny ",[883,16001,16003],{"className":16002},[886],[888,16004,16005],{"xmlns":890},[892,16006,16007,16011],{},[895,16008,16009],{},[898,16010,1755],{},[902,16012,1755],{"encoding":904},". Tudíž s ",[614,16015,16016,16017],{},"poklesem ceny ",[883,16018,16020],{"className":16019},[886],[888,16021,16022],{"xmlns":890},[892,16023,16024,16028],{},[895,16025,16026],{},[898,16027,1755],{},[902,16029,1755],{"encoding":904}," celkový příjem ",[883,16032,16034],{"className":16033},[886],[888,16035,16036],{"xmlns":890},[892,16037,16038,16044],{},[895,16039,16040,16042],{},[898,16041,11536],{},[898,16043,12737],{},[902,16045,12837],{"encoding":904},[614,16047,16048],{},"roste"," a s ",[614,16051,16052,16053],{},"růstem ceny ",[883,16054,16056],{"className":16055},[886],[888,16057,16058],{"xmlns":890},[892,16059,16060,16064],{},[895,16061,16062],{},[898,16063,1755],{},[902,16065,1755],{"encoding":904},[614,16067,16068],{},"klesá",[2140,16070,16071],{},[724,16072,16073,16076],{},[38,16074,16075],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,16078,16079,15928,16099,1343,16125,16140,16141,16154,16155,16168,16169,16182,16183,16030,16196,2186,16211,2138],{},[38,16080,16081,16082,12664],{},"(b) Poptávka neelastická (",[883,16083,16085],{"className":16084},[886],[888,16086,16087],{"xmlns":890},[892,16088,16089,16097],{},[895,16090,16091,16093,16095],{},[898,16092,1798],{},[1654,16094,3002],{},[1665,16096,1667],{},[902,16098,13264],{"encoding":904},[883,16100,16102],{"className":16101},[886],[888,16103,16104],{"xmlns":890},[892,16105,16106,16122],{},[895,16107,16108,16110,16112,16114,16116,16118,16120],{},[898,16109,9320],{},[898,16111,12737],{},[1654,16113,1708],{"stretchy":1656},[898,16115,1663],{},[1654,16117,1726],{"stretchy":1656},[1654,16119,3002],{},[1665,16121,2062],{},[902,16123,16124],{"encoding":904},"MR(Q) \u003C 0",[883,16126,16128],{"className":16127},[886],[888,16129,16130],{"xmlns":890},[892,16131,16132,16138],{},[895,16133,16134,16136],{},[898,16135,11536],{},[898,16137,12737],{},[902,16139,12837],{"encoding":904}," je klesající funkce ",[883,16142,16144],{"className":16143},[886],[888,16145,16146],{"xmlns":890},[892,16147,16148,16152],{},[895,16149,16150],{},[898,16151,1663],{},[902,16153,1663],{"encoding":904},", tj. s růstem ",[883,16156,16158],{"className":16157},[886],[888,16159,16160],{"xmlns":890},[892,16161,16162,16166],{},[895,16163,16164],{},[898,16165,1663],{},[902,16167,1663],{"encoding":904}," (s poklesem ceny ",[883,16170,16172],{"className":16171},[886],[888,16173,16174],{"xmlns":890},[892,16175,16176,16180],{},[895,16177,16178],{},[898,16179,1755],{},[902,16181,1755],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,16184,16186],{"className":16185},[886],[888,16187,16188],{"xmlns":890},[892,16189,16190,16194],{},[895,16191,16192],{},[898,16193,1755],{},[902,16195,1755],{"encoding":904},[883,16197,16199],{"className":16198},[886],[888,16200,16201],{"xmlns":890},[892,16202,16203,16209],{},[895,16204,16205,16207],{},[898,16206,11536],{},[898,16208,12737],{},[902,16210,12837],{"encoding":904},[614,16212,16048],{},[2140,16214,16215],{},[724,16216,16217,16220],{},[38,16218,16219],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,16222,16223,15928,16243,16262,16263,16278,16279,16349,16350,2068,16378,16411,16412,4579,16440,16455,16456,2138],{},[38,16224,16225,16226,12664],{},"(c) Jednotková elasticita (",[883,16227,16229],{"className":16228},[886],[888,16230,16231],{"xmlns":890},[892,16232,16233,16241],{},[895,16234,16235,16237,16239],{},[898,16236,1798],{},[1654,16238,1750],{},[1665,16240,1667],{},[902,16242,13282],{"encoding":904},[883,16244,16246],{"className":16245},[886],[888,16247,16248],{"xmlns":890},[892,16249,16250,16260],{},[895,16251,16252,16254,16256,16258],{},[898,16253,9320],{},[898,16255,12737],{},[1654,16257,1750],{},[1665,16259,2062],{},[902,16261,15810],{"encoding":904}," — nutná podmínka extrému ",[883,16264,16266],{"className":16265},[886],[888,16267,16268],{"xmlns":890},[892,16269,16270,16276],{},[895,16271,16272,16274],{},[898,16273,11536],{},[898,16275,12737],{},[902,16277,12837],{"encoding":904},". Dále ",[883,16280,16282],{"className":16281},[886],[888,16283,16284],{"xmlns":890},[892,16285,16286,16346],{},[895,16287,16288,16290,16300,16302,16304,16310,16312,16318,16320,16322,16324,16326,16328,16330,16340,16342,16344],{},[898,16289,11536],{},[1741,16291,16292,16294],{},[898,16293,12737],{},[895,16295,16296,16298],{},[1654,16297,2592],{"mathvariant":1878},[1654,16299,2592],{"mathvariant":1878},[1654,16301,1750],{},[898,16303,9320],{},[1741,16305,16306,16308],{},[898,16307,12737],{},[1654,16309,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,16311,1750],{},[1741,16313,16314,16316],{},[898,16315,4980],{},[1654,16317,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,16319,1708],{"stretchy":1656},[898,16321,1663],{},[1654,16323,1726],{"stretchy":1656},[1654,16325,1766],{},[898,16327,1663],{},[1865,16329,11744],{},[1741,16331,16332,16334],{},[898,16333,4980],{},[895,16335,16336,16338],{},[1654,16337,2592],{"mathvariant":1878},[1654,16339,2592],{"mathvariant":1878},[1654,16341,1708],{"stretchy":1656},[898,16343,1663],{},[1654,16345,1726],{"stretchy":1656},[902,16347,16348],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,16351,16353],{"className":16352},[886],[888,16354,16355],{"xmlns":890},[892,16356,16357,16375],{},[895,16358,16359,16365,16367,16369,16371,16373],{},[1741,16360,16361,16363],{},[898,16362,4980],{},[1654,16364,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,16366,1708],{"stretchy":1656},[898,16368,1663],{},[1654,16370,1726],{"stretchy":1656},[1654,16372,3002],{},[1665,16374,2062],{},[902,16376,16377],{"encoding":904},"D'(Q) \u003C 0",[883,16379,16381],{"className":16380},[886],[888,16382,16383],{"xmlns":890},[892,16384,16385,16408],{},[895,16386,16387,16397,16399,16401,16403,16406],{},[1741,16388,16389,16391],{},[898,16390,4980],{},[895,16392,16393,16395],{},[1654,16394,2592],{"mathvariant":1878},[1654,16396,2592],{"mathvariant":1878},[1654,16398,1708],{"stretchy":1656},[898,16400,1663],{},[1654,16402,1726],{"stretchy":1656},[1654,16404,16405],{},"≤",[1665,16407,2062],{},[902,16409,16410],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,16413,16415],{"className":16414},[886],[888,16416,16417],{"xmlns":890},[892,16418,16419,16437],{},[895,16420,16421,16423,16433,16435],{},[898,16422,11536],{},[1741,16424,16425,16427],{},[898,16426,12737],{},[895,16428,16429,16431],{},[1654,16430,2592],{"mathvariant":1878},[1654,16432,2592],{"mathvariant":1878},[1654,16434,3002],{},[1665,16436,2062],{},[902,16438,16439],{"encoding":904},"TR'' \u003C 0",[883,16441,16443],{"className":16442},[886],[888,16444,16445],{"xmlns":890},[892,16446,16447,16453],{},[895,16448,16449,16451],{},[898,16450,11536],{},[898,16452,12737],{},[902,16454,12837],{"encoding":904}," nabývá ",[38,16457,16458],{},"maxima",[2140,16460,16461],{},[724,16462,16463,16466],{},[38,16464,16465],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,16468,16469],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,16471,16472],{},[38,16473,16474],{},"Souhrnná tabulka Pravidel 1–3:",[16,16476,16477,16581],{},[19,16478,16479],{},[22,16480,16481,16484,16499,16516,16547,16578],{},[25,16482,16483],{},"Charakter poptávky",[25,16485,16486],{},[883,16487,16489],{"className":16488},[886],[888,16490,16491],{"xmlns":890},[892,16492,16493,16497],{},[895,16494,16495],{},[898,16496,1798],{},[902,16498,1798],{"encoding":904},[25,16500,16501],{},[883,16502,16504],{"className":16503},[886],[888,16505,16506],{"xmlns":890},[892,16507,16508,16514],{},[895,16509,16510,16512],{},[898,16511,9320],{},[898,16513,12737],{},[902,16515,15361],{"encoding":904},[25,16517,16518,16519,2186,16532],{},"Pokles ceny ",[883,16520,16522],{"className":16521},[886],[888,16523,16524],{"xmlns":890},[892,16525,16526,16530],{},[895,16527,16528],{},[1654,16529,8634],{},[902,16531,15682],{"encoding":904},[883,16533,16535],{"className":16534},[886],[888,16536,16537],{"xmlns":890},[892,16538,16539,16545],{},[895,16540,16541,16543],{},[898,16542,11536],{},[898,16544,12737],{},[902,16546,12837],{"encoding":904},[25,16548,16549,16550,2186,16563],{},"Růst ceny ",[883,16551,16553],{"className":16552},[886],[888,16554,16555],{"xmlns":890},[892,16556,16557,16561],{},[895,16558,16559],{},[1654,16560,8634],{},[902,16562,15682],{"encoding":904},[883,16564,16566],{"className":16565},[886],[888,16567,16568],{"xmlns":890},[892,16569,16570,16576],{},[895,16571,16572,16574],{},[898,16573,11536],{},[898,16575,12737],{},[902,16577,12837],{"encoding":904},[25,16579,16580],{},"Doporučení",[30,16582,16583,16632,16682],{},[22,16584,16585,16587,16605,16623,16625,16627],{},[35,16586,12816],{},[35,16588,16589],{},[883,16590,16592],{"className":16591},[886],[888,16593,16594],{"xmlns":890},[892,16595,16596,16602],{},[895,16597,16598,16600],{},[1654,16599,2952],{},[1665,16601,1667],{},[902,16603,16604],{"encoding":904},"> 1",[35,16606,16607],{},[883,16608,16610],{"className":16609},[886],[888,16611,16612],{"xmlns":890},[892,16613,16614,16620],{},[895,16615,16616,16618],{},[1654,16617,2952],{},[1665,16619,2062],{},[902,16621,16622],{"encoding":904},"> 0",[35,16624,16048],{},[35,16626,16068],{},[35,16628,16629],{},[38,16630,16631],{},"snížit cenu",[22,16633,16634,16637,16655,16673,16675,16677],{},[35,16635,16636],{},"jednotková",[35,16638,16639],{},[883,16640,16642],{"className":16641},[886],[888,16643,16644],{"xmlns":890},[892,16645,16646,16652],{},[895,16647,16648,16650],{},[1654,16649,1750],{},[1665,16651,1667],{},[902,16653,16654],{"encoding":904},"= 1",[35,16656,16657],{},[883,16658,16660],{"className":16659},[886],[888,16661,16662],{"xmlns":890},[892,16663,16664,16670],{},[895,16665,16666,16668],{},[1654,16667,1750],{},[1665,16669,2062],{},[902,16671,16672],{"encoding":904},"= 0",[35,16674,12467],{},[35,16676,12467],{},[35,16678,16679],{},[38,16680,16681],{},"držet cenu",[22,16683,16684,16686,16704,16722,16724,16726],{},[35,16685,12820],{},[35,16687,16688],{},[883,16689,16691],{"className":16690},[886],[888,16692,16693],{"xmlns":890},[892,16694,16695,16701],{},[895,16696,16697,16699],{},[1654,16698,3002],{},[1665,16700,1667],{},[902,16702,16703],{"encoding":904},"\u003C 1",[35,16705,16706],{},[883,16707,16709],{"className":16708},[886],[888,16710,16711],{"xmlns":890},[892,16712,16713,16719],{},[895,16714,16715,16717],{},[1654,16716,3002],{},[1665,16718,2062],{},[902,16720,16721],{"encoding":904},"\u003C 0",[35,16723,16068],{},[35,16725,16048],{},[35,16727,16728],{},[38,16729,16730],{},"zvýšit cenu",[198,16732,16734],{"id":16733},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,16736,16737,16738,16763,16764,16786,16787,16800,16801,16814,16815,16828,16829,4579,16855,16907],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,16739,16741],{"className":16740},[886],[888,16742,16743],{"xmlns":890},[892,16744,16745,16761],{},[895,16746,16747,16749,16751,16753,16755],{},[898,16748,1755],{},[1654,16750,1750],{},[1665,16752,4273],{},[1654,16754,2380],{},[1741,16756,16757,16759],{},[898,16758,1663],{},[1665,16760,1681],{},[902,16762,14189],{"encoding":904},". Reálné cenové rozpětí je ",[883,16765,16767],{"className":16766},[886],[888,16768,16769],{"xmlns":890},[892,16770,16771,16783],{},[895,16772,16773,16775,16777,16779,16781],{},[1654,16774,9783],{"stretchy":1656},[1665,16776,1667],{},[1654,16778,1674],{"separator":1673},[1665,16780,4273],{},[1654,16782,9792],{"stretchy":1656},[902,16784,16785],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,16788,16790],{"className":16789},[886],[888,16791,16792],{"xmlns":890},[892,16793,16794,16798],{},[895,16795,16796],{},[898,16797,1663],{},[902,16799,1663],{"encoding":904}," jako funkci ",[883,16802,16804],{"className":16803},[886],[888,16805,16806],{"xmlns":890},[892,16807,16808,16812],{},[895,16809,16810],{},[898,16811,1755],{},[902,16813,1755],{"encoding":904},"; pro nezáporné ",[883,16816,16818],{"className":16817},[886],[888,16819,16820],{"xmlns":890},[892,16821,16822,16826],{},[895,16823,16824],{},[898,16825,1663],{},[902,16827,1663],{"encoding":904}," je ",[883,16830,16832],{"className":16831},[886],[888,16833,16834],{"xmlns":890},[892,16835,16836,16852],{},[895,16837,16838,16840,16842],{},[898,16839,1663],{},[1654,16841,1750],{},[8818,16843,16844],{},[895,16845,16846,16848,16850],{},[1665,16847,4273],{},[1654,16849,2380],{},[898,16851,1755],{},[902,16853,16854],{"encoding":904},"Q = \\sqrt{100 - P}",[883,16856,16858],{"className":16857},[886],[888,16859,16860],{"xmlns":890},[892,16861,16862,16904],{},[895,16863,16864,16880,16882,16884],{},[2582,16865,16866],{"scriptlevel":2062,"displaystyle":1673},[2811,16867,16868,16874],{},[895,16869,16870,16872],{},[898,16871,10977],{"mathvariant":1878},[898,16873,1663],{},[895,16875,16876,16878],{},[898,16877,10977],{"mathvariant":1878},[898,16879,1755],{},[1654,16881,1750],{},[1654,16883,2380],{},[2582,16885,16886],{"scriptlevel":2062,"displaystyle":1673},[2811,16887,16888,16890],{},[1665,16889,1667],{},[895,16891,16892,16894],{},[1665,16893,1681],{},[8818,16895,16896],{},[895,16897,16898,16900,16902],{},[1665,16899,4273],{},[1654,16901,2380],{},[898,16903,1755],{},[902,16905,16906],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,16909,16910],{},[883,16911,16913],{"className":16912},[886],[888,16914,16915],{"xmlns":890},[892,16916,16917,17039],{},[895,16918,16919,16921,16923,16925,16927,16929,16931,16937,16939,16953,16955,16957,16971,16973,16999,17001,17019,17021,17037],{},[898,16920,1798],{},[1654,16922,1708],{"stretchy":1656},[898,16924,1755],{},[1654,16926,1726],{"stretchy":1656},[1654,16928,1750],{},[1654,16930,2380],{},[2811,16932,16933,16935],{},[898,16934,1755],{},[898,16936,1663],{},[1654,16938,4554],{},[2811,16940,16941,16947],{},[895,16942,16943,16945],{},[898,16944,10977],{"mathvariant":1878},[898,16946,1663],{},[895,16948,16949,16951],{},[898,16950,10977],{"mathvariant":1878},[898,16952,1755],{},[1654,16954,1750],{},[1654,16956,2380],{},[2811,16958,16959,16961],{},[898,16960,1755],{},[8818,16962,16963],{},[895,16964,16965,16967,16969],{},[1665,16966,4273],{},[1654,16968,2380],{},[898,16970,1755],{},[1654,16972,4554],{},[895,16974,16975,16977,16979,16997],{},[1654,16976,1708],{"fence":1673},[1654,16978,2380],{},[2811,16980,16981,16983],{},[1665,16982,1667],{},[895,16984,16985,16987],{},[1665,16986,1681],{},[8818,16988,16989],{},[895,16990,16991,16993,16995],{},[1665,16992,4273],{},[1654,16994,2380],{},[898,16996,1755],{},[1654,16998,1726],{"fence":1673},[1654,17000,1750],{},[2811,17002,17003,17005],{},[898,17004,1755],{},[895,17006,17007,17009,17011,17013,17015,17017],{},[1665,17008,1681],{},[1654,17010,1708],{"stretchy":1656},[1665,17012,4273],{},[1654,17014,2380],{},[898,17016,1755],{},[1654,17018,1726],{"stretchy":1656},[1654,17020,1750],{},[2811,17022,17023,17029],{},[895,17024,17025,17027],{},[1665,17026,7594],{},[898,17028,1755],{},[895,17030,17031,17033,17035],{},[1665,17032,4273],{},[1654,17034,2380],{},[898,17036,1755],{},[898,17038,2138],{"mathvariant":1878},[902,17040,17041],{"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}.",[724,17043,17044,17045,2781],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,17046,17048],{"className":17047},[886],[888,17049,17050],{"xmlns":890},[892,17051,17052,17076],{},[895,17053,17054,17072,17074],{},[2582,17055,17056],{"scriptlevel":2062,"displaystyle":1673},[2811,17057,17058,17064],{},[895,17059,17060,17062],{},[1665,17061,7594],{},[898,17063,1755],{},[895,17065,17066,17068,17070],{},[1665,17067,4273],{},[1654,17069,2380],{},[898,17071,1755],{},[1654,17073,1750],{},[1665,17075,1667],{},[902,17077,17078],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,17080,17081],{},[883,17082,17084],{"className":17083},[886],[888,17085,17086],{"xmlns":890},[892,17087,17088,17120],{},[895,17089,17090,17096,17098,17105,17107,17110,17118],{},[1741,17091,17092,17094],{},[898,17093,1755],{},[1654,17095,1670],{},[1654,17097,1750],{},[2811,17099,17100,17103],{},[1665,17101,17102],{},"200",[1665,17104,4035],{},[1654,17106,14628],{},[1665,17108,17109],{},"66,",[17111,17112,17113,17115],"mover",{"accent":1673},[1665,17114,11015],{},[1654,17116,17117],{"stretchy":1673},"‾",[898,17119,2138],{"mathvariant":1878},[902,17121,17122],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,17124,17125],{},"S využitím vlastnosti (4.8):",[120,17127,17128,17174,17216],{},[123,17129,17130,17131,17166,17167,17169,17170,17173],{},"Při cenách ",[883,17132,17134],{"className":17133},[886],[888,17135,17136],{"xmlns":890},[892,17137,17138,17163],{},[895,17139,17140,17142,17144,17146,17148,17151,17153,17155,17161],{},[898,17141,1755],{},[1654,17143,9780],{},[1654,17145,9783],{"stretchy":1656},[1665,17147,1667],{},[1654,17149,17150],{"separator":1673},";",[1865,17152,11744],{},[1665,17154,17109],{},[17111,17156,17157,17159],{"accent":1673},[1665,17158,11015],{},[1654,17160,17117],{"stretchy":1673},[1654,17162,1726],{"stretchy":1656},[902,17164,17165],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,17168,12820],{}," — dle ",[614,17171,17172],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,17175,17130,17176,17166,17210,17169,17212,17215],{},[883,17177,17179],{"className":17178},[886],[888,17180,17181],{"xmlns":890},[892,17182,17183,17207],{},[895,17184,17185,17187,17189,17191,17193,17199,17201,17203,17205],{},[898,17186,1755],{},[1654,17188,9780],{},[1654,17190,1708],{"stretchy":1656},[1665,17192,17109],{},[17111,17194,17195,17197],{"accent":1673},[1665,17196,11015],{},[1654,17198,17117],{"stretchy":1673},[1654,17200,17150],{"separator":1673},[1865,17202,11744],{},[1665,17204,4273],{},[1654,17206,9792],{"stretchy":1656},[902,17208,17209],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,17211,12816],{},[614,17213,17214],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,17217,17218,17219,17222,17223,17251,17252,17255],{},"Dle ",[614,17220,17221],{},"Pravidla 3"," je při ceně ",[883,17224,17226],{"className":17225},[886],[888,17227,17228],{"xmlns":890},[892,17229,17230,17248],{},[895,17231,17232,17238,17240,17242],{},[1741,17233,17234,17236],{},[898,17235,1755],{},[1654,17237,1670],{},[1654,17239,1750],{},[1665,17241,17109],{},[17111,17243,17244,17246],{"accent":1673},[1665,17245,11015],{},[1654,17247,17117],{"stretchy":1673},[902,17249,17250],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,17253,17254],{},"maxima celkového příjmu"," ve výši",[724,17257,17258],{},[883,17259,17261],{"className":17260},[886],[888,17262,17263],{"xmlns":890},[892,17264,17265,17343],{},[895,17266,17267,17269,17271,17273,17279,17281,17283,17289,17291,17305,17307,17313,17315,17323,17325,17338,17340],{},[898,17268,11536],{},[898,17270,12737],{},[1654,17272,1708],{"stretchy":1656},[1741,17274,17275,17277],{},[898,17276,1755],{},[1654,17278,1670],{},[1654,17280,1726],{"stretchy":1656},[1654,17282,1750],{},[1741,17284,17285,17287],{},[898,17286,1755],{},[1654,17288,1670],{},[1654,17290,4554],{},[8818,17292,17293],{},[895,17294,17295,17297,17299],{},[1665,17296,4273],{},[1654,17298,2380],{},[1741,17300,17301,17303],{},[898,17302,1755],{},[1654,17304,1670],{},[1654,17306,1750],{},[2811,17308,17309,17311],{},[1665,17310,17102],{},[1665,17312,4035],{},[1654,17314,4554],{},[8818,17316,17317],{},[2811,17318,17319,17321],{},[1665,17320,4273],{},[1665,17322,4035],{},[1654,17324,1750],{},[2811,17326,17327,17330],{},[1665,17328,17329],{},"2000",[895,17331,17332,17334],{},[1665,17333,4035],{},[8818,17335,17336],{},[1665,17337,4035],{},[1654,17339,14628],{},[1665,17341,17342],{},"384,9.",[902,17344,17345],{"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.",[724,17347,17348,17349,2138],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,17350,17352],{"className":17351},[886],[888,17353,17354],{"xmlns":890},[892,17355,17356,17362],{},[895,17357,17358,17360],{},[898,17359,11536],{},[898,17361,12737],{},[902,17363,12837],{"encoding":904},[115,17365,17367],{"id":17366},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,17369,17370,17371,17374],{},"Analogicky se definuje ",[38,17372,17373],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,17376,17377],{},[883,17378,17380],{"className":17379,"title":12941,"style":12942},[12940],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,17382,13049,17383,17408,17409,17441],{},[883,17384,17386],{"className":17385},[886],[888,17387,17388],{"xmlns":890},[892,17389,17390,17405],{},[895,17391,17392,17394,17396,17399,17401,17403],{},[898,17393,1663],{},[1654,17395,1750],{},[898,17397,17398],{},"S",[1654,17400,1708],{"stretchy":1656},[898,17402,1755],{},[1654,17404,1726],{"stretchy":1656},[902,17406,17407],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,17410,17412],{"className":17411},[886],[888,17413,17414],{"xmlns":890},[892,17415,17416,17438],{},[895,17417,17418,17434,17436],{},[2582,17419,17420],{"scriptlevel":2062,"displaystyle":1673},[2811,17421,17422,17428],{},[895,17423,17424,17426],{},[898,17425,10977],{"mathvariant":1878},[898,17427,1663],{},[895,17429,17430,17432],{},[898,17431,10977],{"mathvariant":1878},[898,17433,1755],{},[1654,17435,2952],{},[1665,17437,2062],{},[902,17439,17440],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,17443,17444],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[2140,17446,17447],{},[724,17448,17449,17450],{},"S rostoucí cenou elasticita nabídky roste. ",[883,17451,17453],{"className":17452},[886],[888,17454,17455],{"xmlns":890},[892,17456,17457,17466],{},[895,17458,17459,17461,17464],{},[1654,17460,1708],{"stretchy":1656},[1665,17462,17463],{},"4.14",[1654,17465,1726],{"stretchy":1656},[902,17467,17468],{"encoding":904},"(4.14)",[724,17470,17471],{},"Pro nominální změny platí",[724,17473,17474],{},[883,17475,17477],{"className":17476,"title":12941,"style":12942},[12940],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,17479,17480],{},"a pro procentní změny",[724,17482,17483],{},[883,17484,17486],{"className":17485,"title":12941,"style":12942},[12940],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,17488,17489],{},"(bez znaménka minus).",[198,17491,17493],{"id":17492},"příklad-47","Příklad 4.7",[724,17495,17496,17497,2781],{},"Nabídka ",[883,17498,17500],{"className":17499},[886],[888,17501,17502],{"xmlns":890},[892,17503,17504,17529],{},[895,17505,17506,17508,17510,17512,17518,17520,17522,17524,17526],{},[898,17507,1663],{},[1654,17509,1750],{},[1665,17511,11555],{},[1741,17513,17514,17516],{},[898,17515,1755],{},[1665,17517,1681],{},[1654,17519,1766],{},[1665,17521,4032],{},[898,17523,1755],{},[1654,17525,1766],{},[1665,17527,17528],{},"150",[902,17530,17531],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,17533,17534],{},[883,17535,17537],{"className":17536},[886],[888,17538,17539],{"xmlns":890},[892,17540,17541,17587],{},[895,17542,17543,17545,17547,17571,17573,17575,17577,17579,17581,17583,17585],{},[898,17544,1798],{},[1654,17546,1750],{},[2811,17548,17549,17551],{},[898,17550,1755],{},[895,17552,17553,17555,17561,17563,17565,17567,17569],{},[1665,17554,11555],{},[1741,17556,17557,17559],{},[898,17558,1755],{},[1665,17560,1681],{},[1654,17562,1766],{},[1665,17564,4032],{},[898,17566,1755],{},[1654,17568,1766],{},[1665,17570,17528],{},[1865,17572,11744],{},[1654,17574,1708],{"stretchy":1656},[1665,17576,11599],{},[898,17578,1755],{},[1654,17580,1766],{},[1665,17582,4032],{},[1654,17584,1726],{"stretchy":1656},[898,17586,2138],{"mathvariant":1878},[902,17588,17589],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,17591,13850,17592,1343,17622,1343,17649,17685,17686,17711,17712,17730,17731,2138],{},[883,17593,17595],{"className":17594},[886],[888,17596,17597],{"xmlns":890},[892,17598,17599,17619],{},[895,17600,17601,17603,17605,17607,17609,17611],{},[898,17602,1798],{},[1654,17604,1708],{"stretchy":1656},[1665,17606,4647],{},[1654,17608,1726],{"stretchy":1656},[1654,17610,1750],{},[2582,17612,17613],{"scriptlevel":2062,"displaystyle":1656},[2811,17614,17615,17617],{},[1665,17616,1667],{},[1665,17618,4035],{},[902,17620,17621],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,17623,17625],{"className":17624},[886],[888,17626,17627],{"xmlns":890},[892,17628,17629,17646],{},[895,17630,17631,17633,17635,17640,17642,17644],{},[898,17632,1798],{},[1654,17634,1708],{"stretchy":1656},[8818,17636,17637],{},[1665,17638,17639],{},"1500",[1654,17641,1726],{"stretchy":1656},[1654,17643,1750],{},[1665,17645,1667],{},[902,17647,17648],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,17650,17652],{"className":17651},[886],[888,17653,17654],{"xmlns":890},[892,17655,17656,17682],{},[895,17657,17658,17660,17662,17664,17666,17668,17677,17679],{},[898,17659,1798],{},[1654,17661,1708],{"stretchy":1656},[1665,17663,4273],{},[1654,17665,1726],{"stretchy":1656},[1654,17667,1750],{},[2582,17669,17670],{"scriptlevel":2062,"displaystyle":1656},[2811,17671,17672,17674],{},[1665,17673,4767],{},[1665,17675,17676],{},"33",[1654,17678,14628],{},[1665,17680,17681],{},"1,515",[902,17683,17684],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,17687,17689],{"className":17688},[886],[888,17690,17691],{"xmlns":890},[892,17692,17693,17708],{},[895,17694,17695,17697,17699,17703,17705],{},[898,17696,1755],{},[1654,17698,2952],{},[8818,17700,17701],{},[1665,17702,17639],{},[1654,17704,11492],{},[1665,17706,17707],{},"38,7",[902,17709,17710],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,17713,17715],{"className":17714},[886],[888,17716,17717],{"xmlns":890},[892,17718,17719,17727],{},[895,17720,17721,17723,17725],{},[898,17722,1755],{},[1654,17724,3002],{},[1665,17726,17707],{},[902,17728,17729],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,17732,17734],{"className":17733},[886],[888,17735,17736],{"xmlns":890},[892,17737,17738,17775],{},[895,17739,17740,17742,17744,17746,17748,17756,17758,17760,17762,17765,17771,17773],{},[898,17741,11648],{"mathvariant":1878},[898,17743,1663],{},[898,17745,14653],{"mathvariant":1878},[1654,17747,11492],{},[2582,17749,17750],{"scriptlevel":2062,"displaystyle":1656},[2811,17751,17752,17754],{},[1665,17753,1667],{},[1665,17755,4035],{},[1654,17757,4554],{},[1665,17759,4573],{},[1654,17761,1750],{},[1665,17763,17764],{},"6,",[17111,17766,17767,17769],{"accent":1673},[1665,17768,11015],{},[1654,17770,17117],{"stretchy":1673},[1865,17772,11744],{},[898,17774,14653],{"mathvariant":1878},[902,17776,17777],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,17779,17781],{"id":17780},"vícefaktorový-model","Vícefaktorový model",[724,17783,17784,17785,17798,17799,2186,17802,17815,17816,2186,17819,17837,17838,2186,17841,2781],{},"Předpokládejme, že poptávané množství ",[883,17786,17788],{"className":17787},[886],[888,17789,17790],{"xmlns":890},[892,17791,17792,17796],{},[895,17793,17794],{},[898,17795,1663],{},[902,17797,1663],{"encoding":904}," závisí na ",[38,17800,17801],{},"ceně základního zboží",[883,17803,17805],{"className":17804},[886],[888,17806,17807],{"xmlns":890},[892,17808,17809,17813],{},[895,17810,17811],{},[898,17812,1755],{},[902,17814,1755],{"encoding":904},", na ",[38,17817,17818],{},"ceně alternativního zboží",[883,17820,17822],{"className":17821},[886],[888,17823,17824],{"xmlns":890},[892,17825,17826,17834],{},[895,17827,17828],{},[1710,17829,17830,17832],{},[898,17831,1755],{},[898,17833,4737],{},[902,17835,17836],{"encoding":904},"P_A"," a na ",[38,17839,17840],{},"důchodu",[883,17842,17844],{"className":17843},[886],[888,17845,17846],{"xmlns":890},[892,17847,17848,17852],{},[895,17849,17850],{},[898,17851,1745],{},[902,17853,1745],{"encoding":904},[724,17855,17856],{},[883,17857,17859],{"className":17858,"title":12941,"style":12942},[12940],"Q = D(P, P_A, Y). \\tag{4.17}",[724,17861,17862,17863,17866],{},"V analogii jednofaktorového modelu pracujeme s ",[38,17864,17865],{},"parciálními derivacemi"," funkce poptávky.",[198,17868,17870],{"id":17869},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,17872,17873],{},[883,17874,17876],{"className":17875,"title":12941,"style":12942},[12940],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,17878,13049,17879,17899,17900,17913,17914,4039,17936,2186,17938,17984,17985,17998,17999,18016],{},[883,17880,17882],{"className":17881},[886],[888,17883,17884],{"xmlns":890},[892,17885,17886,17896],{},[895,17887,17888],{},[1659,17889,17890,17892,17894],{},[898,17891,1663],{},[898,17893,1755],{},[1654,17895,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,17897,17898],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,17901,17903],{"className":17902},[886],[888,17904,17905],{"xmlns":890},[892,17906,17907,17911],{},[895,17908,17909],{},[898,17910,1755],{},[902,17912,1755],{"encoding":904},". Vždy ",[883,17915,17917],{"className":17916},[886],[888,17918,17919],{"xmlns":890},[892,17920,17921,17933],{},[895,17922,17923,17929,17931],{},[1710,17924,17925,17927],{},[898,17926,1798],{},[898,17928,1755],{},[1654,17930,13222],{},[1665,17932,2062],{},[902,17934,17935],{"encoding":904},"E_P \\ge 0",[614,17937,4042],{},[883,17939,17941],{"className":17940},[886],[888,17942,17943],{"xmlns":890},[892,17944,17945,17981],{},[895,17946,17947,17953,17955,17961,17963,17971,17973,17979],{},[1710,17948,17949,17951],{},[898,17950,1798],{},[898,17952,1755],{},[1654,17954,1708],{"stretchy":1656},[1741,17956,17957,17959],{},[898,17958,1755],{},[1654,17960,1670],{},[1654,17962,1674],{"separator":1673},[1659,17964,17965,17967,17969],{},[898,17966,1755],{},[898,17968,4737],{},[1654,17970,1670],{},[1654,17972,1674],{"separator":1673},[1741,17974,17975,17977],{},[898,17976,1745],{},[1654,17978,1670],{},[1654,17980,1726],{"stretchy":1656},[902,17982,17983],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,17986,17988],{"className":17987},[886],[888,17989,17990],{"xmlns":890},[892,17991,17992,17996],{},[895,17993,17994],{},[898,17995,1663],{},[902,17997,1663],{"encoding":904}," při 1% změně ",[883,18000,18002],{"className":18001},[886],[888,18003,18004],{"xmlns":890},[892,18005,18006,18014],{},[895,18007,18008],{},[1741,18009,18010,18012],{},[898,18011,1755],{},[1654,18013,1670],{},[902,18015,13142],{"encoding":904},", ceteris paribus.",[198,18018,18020],{"id":18019},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,18022,18023],{},[883,18024,18026],{"className":18025,"title":12941,"style":12942},[12940],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,18028,18029,17984,18031,18044,18045,18062],{},[614,18030,4042],{},[883,18032,18034],{"className":18033},[886],[888,18035,18036],{"xmlns":890},[892,18037,18038,18042],{},[895,18039,18040],{},[898,18041,1663],{},[902,18043,1663],{"encoding":904}," základního zboží při 1% změně ceny ",[883,18046,18048],{"className":18047},[886],[888,18049,18050],{"xmlns":890},[892,18051,18052,18060],{},[895,18053,18054],{},[1710,18055,18056,18058],{},[898,18057,1755],{},[898,18059,4737],{},[902,18061,17836],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,18064,18065],{},[38,18066,18067],{},"Znaménko závisí na povaze alternativního zboží:",[120,18069,18070,18158],{},[123,18071,18072,18073,18076,18077,18094,18095,2186,18108,2138],{},"Je-li alternativní zboží ",[38,18074,18075],{},"komplement",", růst ",[883,18078,18080],{"className":18079},[886],[888,18081,18082],{"xmlns":890},[892,18083,18084,18092],{},[895,18085,18086],{},[1710,18087,18088,18090],{},[898,18089,1755],{},[898,18091,4737],{},[902,18093,17836],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,18096,18098],{"className":18097},[886],[888,18099,18100],{"xmlns":890},[892,18101,18102,18106],{},[895,18103,18104],{},[898,18105,1663],{},[902,18107,1663],{"encoding":904},[883,18109,18111],{"className":18110},[886],[888,18112,18113],{"xmlns":890},[892,18114,18115,18155],{},[895,18116,18117,18119,18121,18133,18135,18137,18139,18141,18151,18153],{},[1654,18118,8634],{},[1865,18120,2805],{},[1659,18122,18123,18125,18131],{},[898,18124,1663],{},[1710,18126,18127,18129],{},[898,18128,1755],{},[898,18130,4737],{},[1654,18132,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,18134,3002],{},[1665,18136,2062],{},[1654,18138,1674],{"separator":1673},[1865,18140,2805],{},[1710,18142,18143,18145],{},[898,18144,1798],{},[1710,18146,18147,18149],{},[898,18148,1755],{},[898,18150,4737],{},[1654,18152,3002],{},[1665,18154,2062],{},[902,18156,18157],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,18159,18072,18160,18076,18163,18180,18181,18194,18195,2138],{},[38,18161,18162],{},"substitut",[883,18164,18166],{"className":18165},[886],[888,18167,18168],{"xmlns":890},[892,18169,18170,18178],{},[895,18171,18172],{},[1710,18173,18174,18176],{},[898,18175,1755],{},[898,18177,4737],{},[902,18179,17836],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,18182,18184],{"className":18183},[886],[888,18185,18186],{"xmlns":890},[892,18187,18188,18192],{},[895,18189,18190],{},[898,18191,1663],{},[902,18193,1663],{"encoding":904}," roste ",[883,18196,18198],{"className":18197},[886],[888,18199,18200],{"xmlns":890},[892,18201,18202,18242],{},[895,18203,18204,18206,18208,18220,18222,18224,18226,18228,18238,18240],{},[1654,18205,8634],{},[1865,18207,2805],{},[1659,18209,18210,18212,18218],{},[898,18211,1663],{},[1710,18213,18214,18216],{},[898,18215,1755],{},[898,18217,4737],{},[1654,18219,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,18221,2952],{},[1665,18223,2062],{},[1654,18225,1674],{"separator":1673},[1865,18227,2805],{},[1710,18229,18230,18232],{},[898,18231,1798],{},[1710,18233,18234,18236],{},[898,18235,1755],{},[898,18237,4737],{},[1654,18239,2952],{},[1665,18241,2062],{},[902,18243,18244],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,18246,18249],{"className":18247,"title":18248,"style":12942},[12940],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":18251},[18252,18256,18257,18265,18266,18270,18273],{"id":12636,"depth":642,"text":12637,"children":18253},[18254,18255],{"id":12667,"depth":649,"text":12668},{"id":12845,"depth":649,"text":12846},{"id":12880,"depth":642,"text":12881},{"id":12905,"depth":642,"text":12906,"children":18258},[18259,18260,18261,18262,18264],{"id":13594,"depth":649,"text":13595},{"id":13684,"depth":649,"text":13685},{"id":14017,"depth":649,"text":14018},{"id":14097,"depth":649,"text":18263},"Výpočet, je-li dáno PP jako funkce QQ",{"id":14357,"depth":649,"text":14358},{"id":14681,"depth":642,"text":14682},{"id":15276,"depth":642,"text":15277,"children":18267},[18268,18269],{"id":15904,"depth":649,"text":15905},{"id":16733,"depth":649,"text":16734},{"id":17366,"depth":642,"text":17367,"children":18271},[18272],{"id":17492,"depth":649,"text":17493},{"id":17780,"depth":642,"text":17781,"children":18274},[18275,18276],{"id":17869,"depth":649,"text":17870},{"id":18019,"depth":649,"text":18020},{},"\u002Ftopics\u002Felasticita",{"title":12607,"description":641},[1138,1136],"topics\u002Felasticita",[1128,12643,18283,18284,18285,18286],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":18289,"title":18290,"body":18291,"course":1128,"courses":659,"created":1129,"description":19826,"extension":661,"meta":19827,"navigation":664,"path":19828,"seo":19829,"sources":19830,"stem":19831,"tags":19832,"type":10736,"updated":677,"__hash__":19837},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":18292,"toc":19811},[18293,18296,18370,18377,18381,18444,18531,18535,18562,18629,18684,18688,18715,18808,18810,18842,19013,19017,19087,19135,19139,19199,19305,19319,19323,19325,19353,19418,19420,19427,19515,19540,19738,19742,19777,19779],[12,18294,18290],{"id":18295},"kalkul-funkcí-více-proměnných",[724,18297,18298,18299,18302,18303,1343,18332,2138],{},"Většina ekonomických veličin závisí na ",[38,18300,18301],{},"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 ",[883,18304,18306],{"className":18305},[886],[888,18307,18308],{"xmlns":890},[892,18309,18310,18329],{},[895,18311,18312,18315,18317,18319,18321,18323,18325,18327],{},[898,18313,18314],{},"z",[1654,18316,1750],{},[898,18318,10794],{},[1654,18320,1708],{"stretchy":1656},[898,18322,10799],{},[1654,18324,1674],{"separator":1673},[898,18326,10789],{},[1654,18328,1726],{"stretchy":1656},[902,18330,18331],{"encoding":904},"z = f(x, y)",[883,18333,18335],{"className":18334},[886],[888,18336,18337],{"xmlns":890},[892,18338,18339,18367],{},[895,18340,18341,18344,18346,18348,18350,18352,18354,18356,18358,18360,18362,18364],{},[898,18342,18343],{},"w",[1654,18345,1750],{},[898,18347,10794],{},[1654,18349,1708],{"stretchy":1656},[898,18351,10799],{},[1654,18353,1674],{"separator":1673},[898,18355,10789],{},[1654,18357,1674],{"separator":1673},[898,18359,18314],{},[1654,18361,1726],{"stretchy":1656},[1654,18363,1674],{"separator":1673},[1654,18365,18366],{},"…",[902,18368,18369],{"encoding":904},"w = f(x, y, z), \\ldots",[724,18371,18372],{},[3492,18373],{"alt":18374,"className":18375,"src":18376},"imek-funkce-2d-vrstevnice",[210,3496],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,18378,18380],{"id":18379},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,18382,3806,18383,18410,18411,18439,18440,18443],{},[883,18384,18386],{"className":18385},[886],[888,18387,18388],{"xmlns":890},[892,18389,18390,18408],{},[895,18391,18392,18394,18396,18398,18400,18402,18404,18406],{},[898,18393,18314],{},[1654,18395,1750],{},[898,18397,10794],{},[1654,18399,1708],{"stretchy":1656},[898,18401,10799],{},[1654,18403,1674],{"separator":1673},[898,18405,10789],{},[1654,18407,1726],{"stretchy":1656},[902,18409,18331],{"encoding":904}," se křivkou s předpisem ",[883,18412,18414],{"className":18413},[886],[888,18415,18416],{"xmlns":890},[892,18417,18418,18436],{},[895,18419,18420,18422,18424,18426,18428,18430,18432,18434],{},[898,18421,10794],{},[1654,18423,1708],{"stretchy":1656},[898,18425,10799],{},[1654,18427,1674],{"separator":1673},[898,18429,10789],{},[1654,18431,1726],{"stretchy":1656},[1654,18433,1750],{},[898,18435,3624],{},[902,18437,18438],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,18441,18442],{},"vrstevnice"," funkce. V ekonomii:",[120,18445,18446,18492],{},[123,18447,18448,18451,18452,18488,18489,2138],{},[38,18449,18450],{},"Indiferenční křivky"," užitečnosti ",[883,18453,18455],{"className":18454},[886],[888,18456,18457],{"xmlns":890},[892,18458,18459,18485],{},[895,18460,18461,18463,18465,18471,18473,18479,18481,18483],{},[898,18462,900],{},[1654,18464,1708],{"stretchy":1656},[1710,18466,18467,18469],{},[898,18468,1663],{},[1665,18470,1667],{},[1654,18472,1674],{"separator":1673},[1710,18474,18475,18477],{},[898,18476,1663],{},[1665,18478,1681],{},[1654,18480,1726],{"stretchy":1656},[1654,18482,1750],{},[898,18484,3624],{},[902,18486,18487],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,18490,10732],{"className":18491,"dataFsResolvedFilePath":878,"href":879},[210],[123,18493,18494,18497,18498,18488,18527,2138],{},[38,18495,18496],{},"Izokvanty"," produkce ",[883,18499,18501],{"className":18500},[886],[888,18502,18503],{"xmlns":890},[892,18504,18505,18524],{},[895,18506,18507,18509,18511,18513,18515,18518,18520,18522],{},[898,18508,1663],{},[1654,18510,1708],{"stretchy":1656},[898,18512,2450],{},[1654,18514,1674],{"separator":1673},[898,18516,18517],{},"K",[1654,18519,1726],{"stretchy":1656},[1654,18521,1750],{},[898,18523,3624],{},[902,18525,18526],{"encoding":904},"Q(L, K) = c",[207,18528,18530],{"className":18529,"dataFsResolvedFilePath":857,"href":858},[210],"produkce",[115,18532,18534],{"id":18533},"parciální-derivace","Parciální derivace",[724,18536,3806,18537,18561],{},[883,18538,18540],{"className":18539},[886],[888,18541,18542],{"xmlns":890},[892,18543,18544,18558],{},[895,18545,18546,18548,18550,18552,18554,18556],{},[898,18547,10794],{},[1654,18549,1708],{"stretchy":1656},[898,18551,10799],{},[1654,18553,1674],{"separator":1673},[898,18555,10789],{},[1654,18557,1726],{"stretchy":1656},[902,18559,18560],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,18563,18564],{},[883,18565,18567],{"className":18566},[886],[888,18568,18569],{"xmlns":890},[892,18570,18571,18626],{},[895,18572,18573,18581,18583,18598,18600,18602,18610,18612],{},[1659,18574,18575,18577,18579],{},[898,18576,10794],{},[898,18578,10799],{},[1654,18580,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,18582,1750],{},[2811,18584,18585,18592],{},[895,18586,18587,18590],{},[898,18588,18589],{"mathvariant":1878},"∂",[898,18591,10794],{},[895,18593,18594,18596],{},[898,18595,18589],{"mathvariant":1878},[898,18597,10799],{},[1654,18599,1674],{"separator":1673},[5008,18601],{"width":14608},[1659,18603,18604,18606,18608],{},[898,18605,10794],{},[898,18607,10789],{},[1654,18609,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,18611,1750],{},[2811,18613,18614,18620],{},[895,18615,18616,18618],{},[898,18617,18589],{"mathvariant":1878},[898,18619,10794],{},[895,18621,18622,18624],{},[898,18623,18589],{"mathvariant":1878},[898,18625,10789],{},[902,18627,18628],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,18630,18631,18632,2138],{},"Hodnoty v bodě: ",[883,18633,18635],{"className":18634},[886],[888,18636,18637],{"xmlns":890},[892,18638,18639,18681],{},[895,18640,18641,18649,18651,18653,18655,18657,18659,18661,18663,18671,18673,18675,18677,18679],{},[1659,18642,18643,18645,18647],{},[898,18644,10794],{},[898,18646,10799],{},[1654,18648,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,18650,1708],{"stretchy":1656},[898,18652,207],{},[1654,18654,1674],{"separator":1673},[898,18656,9758],{},[1654,18658,1726],{"stretchy":1656},[1654,18660,1674],{"separator":1673},[1865,18662,11065],{},[1659,18664,18665,18667,18669],{},[898,18666,10794],{},[898,18668,10789],{},[1654,18670,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,18672,1708],{"stretchy":1656},[898,18674,207],{},[1654,18676,1674],{"separator":1673},[898,18678,9758],{},[1654,18680,1726],{"stretchy":1656},[902,18682,18683],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,18685,18687],{"id":18686},"ekonomické-značení","Ekonomické značení",[724,18689,18690,18691,2781],{},"Pro produkční funkci ",[883,18692,18694],{"className":18693},[886],[888,18695,18696],{"xmlns":890},[892,18697,18698,18712],{},[895,18699,18700,18702,18704,18706,18708,18710],{},[898,18701,1663],{},[1654,18703,1708],{"stretchy":1656},[898,18705,2450],{},[1654,18707,1674],{"separator":1673},[898,18709,18517],{},[1654,18711,1726],{"stretchy":1656},[902,18713,18714],{"encoding":904},"Q(L, K)",[120,18716,18717,18763],{},[123,18718,18719,11237,18739,18742,18743,1726],{},[883,18720,18722],{"className":18721},[886],[888,18723,18724],{"xmlns":890},[892,18725,18726,18736],{},[895,18727,18728],{},[1659,18729,18730,18732,18734],{},[898,18731,1663],{},[898,18733,2450],{},[1654,18735,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,18737,18738],{"encoding":904},"Q'_L",[38,18740,18741],{},"mezní produkt práce"," (",[883,18744,18746],{"className":18745},[886],[888,18747,18748],{"xmlns":890},[892,18749,18750,18760],{},[895,18751,18752,18754],{},[898,18753,9320],{},[1710,18755,18756,18758],{},[898,18757,1755],{},[898,18759,2450],{},[902,18761,18762],{"encoding":904},"MP_L",[123,18764,18765,11237,18785,18742,18788,1726],{},[883,18766,18768],{"className":18767},[886],[888,18769,18770],{"xmlns":890},[892,18771,18772,18782],{},[895,18773,18774],{},[1659,18775,18776,18778,18780],{},[898,18777,1663],{},[898,18779,18517],{},[1654,18781,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,18783,18784],{"encoding":904},"Q'_K",[38,18786,18787],{},"mezní produkt kapitálu",[883,18789,18791],{"className":18790},[886],[888,18792,18793],{"xmlns":890},[892,18794,18795,18805],{},[895,18796,18797,18799],{},[898,18798,9320],{},[1710,18800,18801,18803],{},[898,18802,1755],{},[898,18804,18517],{},[902,18806,18807],{"encoding":904},"MP_K",[198,18809,11331],{"id":11330},[724,18811,18812,2781],{},[883,18813,18815],{"className":18814},[886],[888,18816,18817],{"xmlns":890},[892,18818,18819,18839],{},[895,18820,18821,18829,18831,18833,18835,18837],{},[1659,18822,18823,18825,18827],{},[898,18824,10794],{},[898,18826,10799],{},[1654,18828,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,18830,1708],{"stretchy":1656},[898,18832,207],{},[1654,18834,1674],{"separator":1673},[898,18836,9758],{},[1654,18838,1726],{"stretchy":1656},[902,18840,18841],{"encoding":904},"f'_x(a, b)",[120,18843,18844,18902],{},[123,18845,18846,18847,18860,18861,18874,18875,18901],{},"rychlost změny ",[883,18848,18850],{"className":18849},[886],[888,18851,18852],{"xmlns":890},[892,18853,18854,18858],{},[895,18855,18856],{},[898,18857,10794],{},[902,18859,10794],{"encoding":904}," vůči ",[883,18862,18864],{"className":18863},[886],[888,18865,18866],{"xmlns":890},[892,18867,18868,18872],{},[895,18869,18870],{},[898,18871,10799],{},[902,18873,10799],{"encoding":904}," při ",[883,18876,18878],{"className":18877},[886],[888,18879,18880],{"xmlns":890},[892,18881,18882,18898],{},[895,18883,18884,18886,18888,18890,18892,18894,18896],{},[898,18885,10799],{},[1654,18887,1750],{},[898,18889,207],{},[1654,18891,1674],{"separator":1673},[898,18893,10789],{},[1654,18895,1750],{},[898,18897,9758],{},[902,18899,18900],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,18903,18904,18905,11420,18918,18931,18932,18950,18951,2138],{},"přibližná změna ",[883,18906,18908],{"className":18907},[886],[888,18909,18910],{"xmlns":890},[892,18911,18912,18916],{},[895,18913,18914],{},[898,18915,10794],{},[902,18917,10794],{"encoding":904},[883,18919,18921],{"className":18920},[886],[888,18922,18923],{"xmlns":890},[892,18924,18925,18929],{},[895,18926,18927],{},[898,18928,10799],{},[902,18930,10799],{"encoding":904}," o 1 (a pevném ",[883,18933,18935],{"className":18934},[886],[888,18936,18937],{"xmlns":890},[892,18938,18939,18947],{},[895,18940,18941,18943,18945],{},[898,18942,10789],{},[1654,18944,1750],{},[898,18946,9758],{},[902,18948,18949],{"encoding":904},"y = b","): ",[883,18952,18954],{"className":18953},[886],[888,18955,18956],{"xmlns":890},[892,18957,18958,19010],{},[895,18959,18960,18962,18964,18966,18968,18970,18972,18974,18976,18978,18980,18982,18984,18986,18988,18990,18992,19000,19002,19004,19006,19008],{},[898,18961,10794],{},[1654,18963,1708],{"stretchy":1656},[898,18965,207],{},[1654,18967,1766],{},[1665,18969,1667],{},[1654,18971,1674],{"separator":1673},[898,18973,9758],{},[1654,18975,1726],{"stretchy":1656},[1654,18977,11492],{},[898,18979,10794],{},[1654,18981,1708],{"stretchy":1656},[898,18983,207],{},[1654,18985,1674],{"separator":1673},[898,18987,9758],{},[1654,18989,1726],{"stretchy":1656},[1654,18991,1766],{},[1659,18993,18994,18996,18998],{},[898,18995,10794],{},[898,18997,10799],{},[1654,18999,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,19001,1708],{"stretchy":1656},[898,19003,207],{},[1654,19005,1674],{"separator":1673},[898,19007,9758],{},[1654,19009,1726],{"stretchy":1656},[902,19011,19012],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,19014,19016],{"id":19015},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,19018,19019],{},[883,19020,19022],{"className":19021},[886],[888,19023,19024],{"xmlns":890},[892,19025,19026,19084],{},[895,19027,19028,19030,19032,19034,19042,19044,19046,19048,19050,19052,19054,19056,19058,19060,19068,19070,19072,19074,19076,19078,19080,19082],{},[898,19029,10977],{},[898,19031,10794],{},[1654,19033,1750],{},[1659,19035,19036,19038,19040],{},[898,19037,10794],{},[898,19039,10799],{},[1654,19041,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,19043,1708],{"stretchy":1656},[898,19045,10799],{},[1654,19047,1674],{"separator":1673},[898,19049,10789],{},[1654,19051,1726],{"stretchy":1656},[1865,19053,11744],{},[898,19055,10977],{},[898,19057,10799],{},[1654,19059,1766],{},[1659,19061,19062,19064,19066],{},[898,19063,10794],{},[898,19065,10789],{},[1654,19067,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,19069,1708],{"stretchy":1656},[898,19071,10799],{},[1654,19073,1674],{"separator":1673},[898,19075,10789],{},[1654,19077,1726],{"stretchy":1656},[1865,19079,11744],{},[898,19081,10977],{},[898,19083,10789],{},[902,19085,19086],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,19088,11754,19089,19111,19112,19134],{},[883,19090,19092],{"className":19091},[886],[888,19093,19094],{"xmlns":890},[892,19095,19096,19108],{},[895,19097,19098,19100,19102,19104,19106],{},[898,19099,10977],{},[898,19101,10799],{},[1654,19103,1674],{"separator":1673},[898,19105,10977],{},[898,19107,10789],{},[902,19109,19110],{"encoding":904},"dx, dy"," platí ",[883,19113,19115],{"className":19114},[886],[888,19116,19117],{"xmlns":890},[892,19118,19119,19131],{},[895,19120,19121,19123,19125,19127,19129],{},[898,19122,11648],{"mathvariant":1878},[898,19124,10794],{},[1654,19126,11492],{},[898,19128,10977],{},[898,19130,10794],{},[902,19132,19133],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,19136,19138],{"id":19137},"implicitní-funkce","Implicitní funkce",[724,19140,19141,19142,19171,19172,3267,19185,19198],{},"Je-li vztah dán rovnicí ",[883,19143,19145],{"className":19144},[886],[888,19146,19147],{"xmlns":890},[892,19148,19149,19168],{},[895,19150,19151,19154,19156,19158,19160,19162,19164,19166],{},[898,19152,19153],{},"F",[1654,19155,1708],{"stretchy":1656},[898,19157,10799],{},[1654,19159,1674],{"separator":1673},[898,19161,10789],{},[1654,19163,1726],{"stretchy":1656},[1654,19165,1750],{},[1665,19167,2062],{},[902,19169,19170],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,19173,19175],{"className":19174},[886],[888,19176,19177],{"xmlns":890},[892,19178,19179,19183],{},[895,19180,19181],{},[898,19182,10789],{},[902,19184,10789],{"encoding":904},[883,19186,19188],{"className":19187},[886],[888,19189,19190],{"xmlns":890},[892,19191,19192,19196],{},[895,19193,19194],{},[898,19195,10799],{},[902,19197,10799],{"encoding":904}," (nebo naopak):",[724,19200,19201],{},[883,19202,19204],{"className":19203},[886],[888,19205,19206],{"xmlns":890},[892,19207,19208,19302],{},[895,19209,19210,19216,19218,19232,19234,19236,19254,19256,19258,19264,19266,19280,19282,19284],{},[1741,19211,19212,19214],{},[898,19213,10789],{},[1654,19215,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,19217,1750],{},[2811,19219,19220,19226],{},[895,19221,19222,19224],{},[898,19223,10977],{},[898,19225,10789],{},[895,19227,19228,19230],{},[898,19229,10977],{},[898,19231,10799],{},[1654,19233,1750],{},[1654,19235,2380],{},[2811,19237,19238,19246],{},[1659,19239,19240,19242,19244],{},[898,19241,19153],{},[898,19243,10799],{},[1654,19245,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1659,19247,19248,19250,19252],{},[898,19249,19153],{},[898,19251,10789],{},[1654,19253,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,19255,1674],{"separator":1673},[5008,19257],{"width":14608},[1741,19259,19260,19262],{},[898,19261,10799],{},[1654,19263,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,19265,1750],{},[2811,19267,19268,19274],{},[895,19269,19270,19272],{},[898,19271,10977],{},[898,19273,10799],{},[895,19275,19276,19278],{},[898,19277,10977],{},[898,19279,10789],{},[1654,19281,1750],{},[1654,19283,2380],{},[2811,19285,19286,19294],{},[1659,19287,19288,19290,19292],{},[898,19289,19153],{},[898,19291,10789],{},[1654,19293,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1659,19295,19296,19298,19300],{},[898,19297,19153],{},[898,19299,10799],{},[1654,19301,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,19303,19304],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,19306,19307,19308,19311,19312,2068,19316,2138],{},"Tato vzorec dává ",[38,19309,19310],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,19313,19315],{"className":19314,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS",[207,19317,1867],{"className":19318,"dataFsResolvedFilePath":878,"href":879},[210],[115,19320,19322],{"id":19321},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,19324,12006],{"id":12005},[724,19326,19327,19328,19352],{},"V bodě extrému ",[883,19329,19331],{"className":19330},[886],[888,19332,19333],{"xmlns":890},[892,19334,19335,19349],{},[895,19336,19337,19339,19341,19343,19345,19347],{},[898,19338,4737],{},[1654,19340,1657],{"stretchy":1656},[898,19342,207],{},[1654,19344,1674],{"separator":1673},[898,19346,9758],{},[1654,19348,1686],{"stretchy":1656},[902,19350,19351],{"encoding":904},"A[a, b]"," musí platit současně:",[724,19354,19355],{},[883,19356,19358],{"className":19357},[886],[888,19359,19360],{"xmlns":890},[892,19361,19362,19415],{},[895,19363,19364,19372,19374,19376,19378,19380,19382,19384,19386,19388,19391,19393,19401,19403,19405,19407,19409,19411,19413],{},[1659,19365,19366,19368,19370],{},[898,19367,10794],{},[898,19369,10799],{},[1654,19371,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,19373,1708],{"stretchy":1656},[898,19375,207],{},[1654,19377,1674],{"separator":1673},[898,19379,9758],{},[1654,19381,1726],{"stretchy":1656},[1654,19383,1750],{},[1665,19385,2062],{},[1865,19387,2805],{},[1654,19389,19390],{},"∧",[1865,19392,2805],{},[1659,19394,19395,19397,19399],{},[898,19396,10794],{},[898,19398,10789],{},[1654,19400,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,19402,1708],{"stretchy":1656},[898,19404,207],{},[1654,19406,1674],{"separator":1673},[898,19408,9758],{},[1654,19410,1726],{"stretchy":1656},[1654,19412,1750],{},[1665,19414,2062],{},[902,19416,19417],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,19419,12080],{"id":12079},[724,19421,19422,19423,19426],{},"Definujeme ",[38,19424,19425],{},"diskriminant"," (Hessián zjednodušeně):",[724,19428,19429],{},[883,19430,19432],{"className":19431},[886],[888,19433,19434],{"xmlns":890},[892,19435,19436,19512],{},[895,19437,19438,19440,19442,19444,19446,19448,19450,19452,19468,19470,19486,19488,19490,19506],{},[898,19439,4980],{},[1654,19441,1708],{"stretchy":1656},[898,19443,10799],{},[1654,19445,1674],{"separator":1673},[898,19447,10789],{},[1654,19449,1726],{"stretchy":1656},[1654,19451,1750],{},[1659,19453,19454,19456,19462],{},[898,19455,10794],{},[895,19457,19458,19460],{},[898,19459,10799],{},[898,19461,10799],{},[895,19463,19464,19466],{},[1654,19465,2592],{"mathvariant":1878},[1654,19467,2592],{"mathvariant":1878},[1654,19469,4554],{},[1659,19471,19472,19474,19480],{},[898,19473,10794],{},[895,19475,19476,19478],{},[898,19477,10789],{},[898,19479,10789],{},[895,19481,19482,19484],{},[1654,19483,2592],{"mathvariant":1878},[1654,19485,2592],{"mathvariant":1878},[1654,19487,2380],{},[1654,19489,1708],{"stretchy":1656},[1659,19491,19492,19494,19500],{},[898,19493,10794],{},[895,19495,19496,19498],{},[898,19497,10799],{},[898,19499,10789],{},[895,19501,19502,19504],{},[1654,19503,2592],{"mathvariant":1878},[1654,19505,2592],{"mathvariant":1878},[1741,19507,19508,19510],{},[1654,19509,1726],{"stretchy":1656},[1665,19511,1681],{},[902,19513,19514],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,19516,19517,19518,2781],{},"V podezřelém bodě ",[883,19519,19521],{"className":19520},[886],[888,19522,19523],{"xmlns":890},[892,19524,19525,19537],{},[895,19526,19527,19529,19531,19533,19535],{},[1654,19528,1657],{"stretchy":1656},[898,19530,207],{},[1654,19532,1674],{"separator":1673},[898,19534,9758],{},[1654,19536,1686],{"stretchy":1656},[902,19538,19539],{"encoding":904},"[a, b]",[152,19541,19542,19669,19705],{},[123,19543,19544,19574,19575],{},[38,19545,19546,2781],{},[883,19547,19549],{"className":19548},[886],[888,19550,19551],{"xmlns":890},[892,19552,19553,19571],{},[895,19554,19555,19557,19559,19561,19563,19565,19567,19569],{},[898,19556,4980],{},[1654,19558,1708],{"stretchy":1656},[898,19560,207],{},[1654,19562,1674],{"separator":1673},[898,19564,9758],{},[1654,19566,1726],{"stretchy":1656},[1654,19568,2952],{},[1665,19570,2062],{},[902,19572,19573],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,19576,19577,19623],{},[123,19578,19579,12166,19621],{},[883,19580,19582],{"className":19581},[886],[888,19583,19584],{"xmlns":890},[892,19585,19586,19618],{},[895,19587,19588,19604,19606,19608,19610,19612,19614,19616],{},[1659,19589,19590,19592,19598],{},[898,19591,10794],{},[895,19593,19594,19596],{},[898,19595,10799],{},[898,19597,10799],{},[895,19599,19600,19602],{},[1654,19601,2592],{"mathvariant":1878},[1654,19603,2592],{"mathvariant":1878},[1654,19605,1708],{"stretchy":1656},[898,19607,207],{},[1654,19609,1674],{"separator":1673},[898,19611,9758],{},[1654,19613,1726],{"stretchy":1656},[1654,19615,2952],{},[1665,19617,2062],{},[902,19619,19620],{"encoding":904},"f''_{xx}(a, b) > 0",[38,19622,7988],{},[123,19624,19625,12166,19667],{},[883,19626,19628],{"className":19627},[886],[888,19629,19630],{"xmlns":890},[892,19631,19632,19664],{},[895,19633,19634,19650,19652,19654,19656,19658,19660,19662],{},[1659,19635,19636,19638,19644],{},[898,19637,10794],{},[895,19639,19640,19642],{},[898,19641,10799],{},[898,19643,10799],{},[895,19645,19646,19648],{},[1654,19647,2592],{"mathvariant":1878},[1654,19649,2592],{"mathvariant":1878},[1654,19651,1708],{"stretchy":1656},[898,19653,207],{},[1654,19655,1674],{"separator":1673},[898,19657,9758],{},[1654,19659,1726],{"stretchy":1656},[1654,19661,3002],{},[1665,19663,2062],{},[902,19665,19666],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,19668,12467],{},[123,19670,19671,2186,19701,19704],{},[38,19672,19673,2781],{},[883,19674,19676],{"className":19675},[886],[888,19677,19678],{"xmlns":890},[892,19679,19680,19698],{},[895,19681,19682,19684,19686,19688,19690,19692,19694,19696],{},[898,19683,4980],{},[1654,19685,1708],{"stretchy":1656},[898,19687,207],{},[1654,19689,1674],{"separator":1673},[898,19691,9758],{},[1654,19693,1726],{"stretchy":1656},[1654,19695,3002],{},[1665,19697,2062],{},[902,19699,19700],{"encoding":904},"D(a, b) \u003C 0",[38,19702,19703],{},"sedlo"," (v daném bodě extrém není).",[123,19706,19707,19737],{},[38,19708,19709,2781],{},[883,19710,19712],{"className":19711},[886],[888,19713,19714],{"xmlns":890},[892,19715,19716,19734],{},[895,19717,19718,19720,19722,19724,19726,19728,19730,19732],{},[898,19719,4980],{},[1654,19721,1708],{"stretchy":1656},[898,19723,207],{},[1654,19725,1674],{"separator":1673},[898,19727,9758],{},[1654,19729,1726],{"stretchy":1656},[1654,19731,1750],{},[1665,19733,2062],{},[902,19735,19736],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,19739,19741],{"id":19740},"vázané-extrémy","Vázané extrémy",[724,19743,19744,19745,19773,19774,2138],{},"Pro extrémy s omezující podmínkou ",[883,19746,19748],{"className":19747},[886],[888,19749,19750],{"xmlns":890},[892,19751,19752,19770],{},[895,19753,19754,19756,19758,19760,19762,19764,19766,19768],{},[898,19755,2351],{},[1654,19757,1708],{"stretchy":1656},[898,19759,10799],{},[1654,19761,1674],{"separator":1673},[898,19763,10789],{},[1654,19765,1726],{"stretchy":1656},[1654,19767,1750],{},[1665,19769,2062],{},[902,19771,19772],{"encoding":904},"g(x, y) = 0"," se používá ",[207,19775,793],{"className":19776,"dataFsResolvedFilePath":791,"href":792},[210],[115,19778,10613],{"id":10612},[120,19780,19781,19788,19795],{},[123,19782,19783,2186,19785],{},[38,19784,12546],{},[207,19786,775],{"className":19787,"dataFsResolvedFilePath":773,"href":774},[210],[123,19789,19790,2186,19792],{},[38,19791,12554],{},[207,19793,793],{"className":19794,"dataFsResolvedFilePath":791,"href":792},[210],[123,19796,19797,2186,19799,19802,19803,19806,19807,19810],{},[38,19798,12562],{},[207,19800,10664],{"className":19801,"dataFsResolvedFilePath":857,"href":858},[210]," (parciální derivace = mezní produkty), ",[207,19804,880],{"className":19805,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,19808,12575],{"className":19809,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":19812},[19813,19814,19818,19819,19820,19824,19825],{"id":18379,"depth":642,"text":18380},{"id":18533,"depth":642,"text":18534,"children":19815},[19816,19817],{"id":18686,"depth":649,"text":18687},{"id":11330,"depth":649,"text":11331},{"id":19015,"depth":642,"text":19016},{"id":19137,"depth":642,"text":19138},{"id":19321,"depth":642,"text":19322,"children":19821},[19822,19823],{"id":12005,"depth":649,"text":12006},{"id":12079,"depth":649,"text":12080},{"id":19740,"depth":642,"text":19741},{"id":10612,"depth":642,"text":10613},"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":18290,"description":19826},[1135],"topics\u002Ffunkce-vice-promennych",[1128,19833,12601,19834,19835,19836],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":19839,"title":775,"body":19840,"course":1128,"courses":659,"created":1129,"description":20695,"extension":661,"meta":20696,"navigation":664,"path":20697,"seo":20698,"sources":20699,"stem":20700,"tags":20701,"type":10736,"updated":677,"__hash__":20708},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":19841,"toc":20685},[19842,19845,19856,19860,19905,19985,19989,20065,20107,20114,20118,20122,20151,20209,20256,20294,20298,20348,20400,20452,20496,20499,20502,20574,20577,20649,20655,20657],[12,19843,775],{"id":19844},"integrál",[724,19846,19847,19848,19851,19852,19855],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,19849,19850],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,19853,19854],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,19857,19859],{"id":19858},"neurčitý-integrál","Neurčitý integrál",[724,19861,19862],{},[883,19863,19865],{"className":19864},[886],[888,19866,19867],{"xmlns":890},[892,19868,19869,19902],{},[895,19870,19871,19873,19875,19877,19879,19881,19884,19886,19888,19890,19892,19894,19896,19898,19900],{},[898,19872,19153],{},[1654,19874,1708],{"stretchy":1656},[898,19876,10799],{},[1654,19878,1726],{"stretchy":1656},[1654,19880,1750],{},[1654,19882,19883],{},"∫",[898,19885,10794],{},[1654,19887,1708],{"stretchy":1656},[898,19889,10799],{},[1654,19891,1726],{"stretchy":1656},[1865,19893,11744],{},[898,19895,10977],{},[898,19897,10799],{},[1654,19899,1766],{},[898,19901,11539],{},[902,19903,19904],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,19906,13049,19907,4039,19941,16828,19954,19957,19958,1343,19971,19984],{},[883,19908,19910],{"className":19909},[886],[888,19911,19912],{"xmlns":890},[892,19913,19914,19938],{},[895,19915,19916,19922,19924,19926,19928,19930,19932,19934,19936],{},[1741,19917,19918,19920],{},[898,19919,19153],{},[1654,19921,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,19923,1708],{"stretchy":1656},[898,19925,10799],{},[1654,19927,1726],{"stretchy":1656},[1654,19929,1750],{},[898,19931,10794],{},[1654,19933,1708],{"stretchy":1656},[898,19935,10799],{},[1654,19937,1726],{"stretchy":1656},[902,19939,19940],{"encoding":904},"F'(x) = f(x)",[883,19942,19944],{"className":19943},[886],[888,19945,19946],{"xmlns":890},[892,19947,19948,19952],{},[895,19949,19950],{},[898,19951,19153],{},[902,19953,19153],{"encoding":904},[38,19955,19956],{},"primitivní funkce"," k ",[883,19959,19961],{"className":19960},[886],[888,19962,19963],{"xmlns":890},[892,19964,19965,19969],{},[895,19966,19967],{},[898,19968,10794],{},[902,19970,10794],{"encoding":904},[883,19972,19974],{"className":19973},[886],[888,19975,19976],{"xmlns":890},[892,19977,19978,19982],{},[895,19979,19980],{},[898,19981,11539],{},[902,19983,11539],{"encoding":904}," konstanta.",[115,19986,19988],{"id":19987},"určitý-integrál","Určitý integrál",[724,19990,19991],{},[883,19992,19994],{"className":19993},[886],[888,19995,19996],{"xmlns":890},[892,19997,19998,20062],{},[895,19999,20000,20008,20010,20012,20014,20016,20018,20020,20022,20024,20026,20028,20030,20032,20034,20042,20044,20046,20048,20050,20052,20054,20056,20058,20060],{},[1659,20001,20002,20004,20006],{},[1654,20003,19883],{},[898,20005,207],{},[898,20007,9758],{},[898,20009,10794],{},[1654,20011,1708],{"stretchy":1656},[898,20013,10799],{},[1654,20015,1726],{"stretchy":1656},[1865,20017,11744],{},[898,20019,10977],{},[898,20021,10799],{},[1654,20023,1750],{},[1654,20025,1657],{"stretchy":1656},[898,20027,19153],{},[1654,20029,1708],{"stretchy":1656},[898,20031,10799],{},[1654,20033,1726],{"stretchy":1656},[1659,20035,20036,20038,20040],{},[1654,20037,1686],{"stretchy":1656},[898,20039,207],{},[898,20041,9758],{},[1654,20043,1750],{},[898,20045,19153],{},[1654,20047,1708],{"stretchy":1656},[898,20049,9758],{},[1654,20051,1726],{"stretchy":1656},[1654,20053,2380],{},[898,20055,19153],{},[1654,20057,1708],{"stretchy":1656},[898,20059,207],{},[1654,20061,1726],{"stretchy":1656},[902,20063,20064],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,20066,20067,20068,2186,20071,20084,20085,20106],{},"Geometricky ",[38,20069,20070],{},"plocha pod grafem",[883,20072,20074],{"className":20073},[886],[888,20075,20076],{"xmlns":890},[892,20077,20078,20082],{},[895,20079,20080],{},[898,20081,10794],{},[902,20083,10794],{"encoding":904}," na intervalu ",[883,20086,20088],{"className":20087},[886],[888,20089,20090],{"xmlns":890},[892,20091,20092,20104],{},[895,20093,20094,20096,20098,20100,20102],{},[1654,20095,1657],{"stretchy":1656},[898,20097,207],{},[1654,20099,1674],{"separator":1673},[898,20101,9758],{},[1654,20103,1686],{"stretchy":1656},[902,20105,19539],{"encoding":904}," (orientovaná).",[724,20108,20109],{},[3492,20110],{"alt":20111,"className":20112,"src":20113},"imek-integral-plocha",[210,3496],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,20115,20117],{"id":20116},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,20119,20121],{"id":20120},"příklad-tr-z-mr","Příklad — TR z MR",[724,20123,20124,20125,2138],{},"Mezní příjem ",[883,20126,20128],{"className":20127},[886],[888,20129,20130],{"xmlns":890},[892,20131,20132,20148],{},[895,20133,20134,20136,20138,20140,20142,20144,20146],{},[898,20135,9320],{},[898,20137,12737],{},[1654,20139,1750],{},[1665,20141,4273],{},[1654,20143,2380],{},[1665,20145,1681],{},[898,20147,1663],{},[902,20149,20150],{"encoding":904},"MR = 100 - 2Q",[724,20152,20153],{},[883,20154,20156],{"className":20155},[886],[888,20157,20158],{"xmlns":890},[892,20159,20160,20206],{},[895,20161,20162,20164,20166,20168,20170,20172,20174,20176,20178,20180,20182,20184,20186,20188,20190,20192,20194,20196,20202,20204],{},[898,20163,11536],{},[898,20165,12737],{},[1654,20167,1750],{},[1654,20169,19883],{},[1654,20171,1708],{"stretchy":1656},[1665,20173,4273],{},[1654,20175,2380],{},[1665,20177,1681],{},[898,20179,1663],{},[1654,20181,1726],{"stretchy":1656},[1865,20183,11744],{},[898,20185,10977],{},[898,20187,1663],{},[1654,20189,1750],{},[1665,20191,4273],{},[898,20193,1663],{},[1654,20195,2380],{},[1741,20197,20198,20200],{},[898,20199,1663],{},[1665,20201,1681],{},[1654,20203,1766],{},[898,20205,3624],{},[902,20207,20208],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,20210,20211,20212,12166,20238,2781],{},"Okrajová podmínka ",[883,20213,20215],{"className":20214},[886],[888,20216,20217],{"xmlns":890},[892,20218,20219,20235],{},[895,20220,20221,20223,20225,20227,20229,20231,20233],{},[898,20222,11536],{},[898,20224,12737],{},[1654,20226,1708],{"stretchy":1656},[1665,20228,2062],{},[1654,20230,1726],{"stretchy":1656},[1654,20232,1750],{},[1665,20234,2062],{},[902,20236,20237],{"encoding":904},"TR(0) = 0",[883,20239,20241],{"className":20240},[886],[888,20242,20243],{"xmlns":890},[892,20244,20245,20253],{},[895,20246,20247,20249,20251],{},[898,20248,3624],{},[1654,20250,1750],{},[1665,20252,2062],{},[902,20254,20255],{"encoding":904},"c = 0",[724,20257,20258],{},[883,20259,20261],{"className":20260},[886],[888,20262,20263],{"xmlns":890},[892,20264,20265,20291],{},[895,20266,20267,20269,20271,20273,20275,20277,20279,20281,20283,20285],{},[898,20268,11536],{},[898,20270,12737],{},[1654,20272,1708],{"stretchy":1656},[898,20274,1663],{},[1654,20276,1726],{"stretchy":1656},[1654,20278,1750],{},[1665,20280,4273],{},[898,20282,1663],{},[1654,20284,2380],{},[1741,20286,20287,20289],{},[898,20288,1663],{},[1665,20290,1681],{},[902,20292,20293],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,20295,20297],{"id":20296},"příklad-tc-z-mc","Příklad — TC z MC",[724,20299,20300,20301,20327,20328,2138],{},"Mezní náklady ",[883,20302,20304],{"className":20303},[886],[888,20305,20306],{"xmlns":890},[892,20307,20308,20324],{},[895,20309,20310,20312,20314,20316,20318,20320,20322],{},[898,20311,9320],{},[898,20313,11539],{},[1654,20315,1750],{},[1665,20317,1681],{},[1654,20319,1766],{},[1665,20321,11599],{},[898,20323,1663],{},[902,20325,20326],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,20329,20331],{"className":20330},[886],[888,20332,20333],{"xmlns":890},[892,20334,20335,20345],{},[895,20336,20337,20339,20341,20343],{},[898,20338,19153],{},[898,20340,11539],{},[1654,20342,1750],{},[1665,20344,4273],{},[902,20346,20347],{"encoding":904},"FC = 100",[724,20349,20350],{},[883,20351,20353],{"className":20352},[886],[888,20354,20355],{"xmlns":890},[892,20356,20357,20397],{},[895,20358,20359,20361,20363,20365,20367,20369,20371,20373,20375,20377,20379,20381,20383,20385,20387,20393,20395],{},[898,20360,11536],{},[898,20362,11539],{},[1654,20364,1750],{},[1654,20366,19883],{},[898,20368,9320],{},[898,20370,11539],{},[1865,20372,11744],{},[898,20374,10977],{},[898,20376,1663],{},[1654,20378,1750],{},[1665,20380,1681],{},[898,20382,1663],{},[1654,20384,1766],{},[1665,20386,11555],{},[1741,20388,20389,20391],{},[898,20390,1663],{},[1665,20392,1681],{},[1654,20394,1766],{},[898,20396,3624],{},[902,20398,20399],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,20401,20211,20402,12166,20434,2781],{},[883,20403,20405],{"className":20404},[886],[888,20406,20407],{"xmlns":890},[892,20408,20409,20431],{},[895,20410,20411,20413,20415,20417,20419,20421,20423,20425,20427,20429],{},[898,20412,11536],{},[898,20414,11539],{},[1654,20416,1708],{"stretchy":1656},[1665,20418,2062],{},[1654,20420,1726],{"stretchy":1656},[1654,20422,1750],{},[898,20424,19153],{},[898,20426,11539],{},[1654,20428,1750],{},[1665,20430,4273],{},[902,20432,20433],{"encoding":904},"TC(0) = FC = 100",[883,20435,20437],{"className":20436},[886],[888,20438,20439],{"xmlns":890},[892,20440,20441,20449],{},[895,20442,20443,20445,20447],{},[898,20444,3624],{},[1654,20446,1750],{},[1665,20448,4273],{},[902,20450,20451],{"encoding":904},"c = 100",[724,20453,20454],{},[883,20455,20457],{"className":20456},[886],[888,20458,20459],{"xmlns":890},[892,20460,20461,20493],{},[895,20462,20463,20465,20467,20469,20471,20473,20475,20477,20479,20481,20483,20485,20487],{},[898,20464,11536],{},[898,20466,11539],{},[1654,20468,1708],{"stretchy":1656},[898,20470,1663],{},[1654,20472,1726],{"stretchy":1656},[1654,20474,1750],{},[1665,20476,4273],{},[1654,20478,1766],{},[1665,20480,1681],{},[898,20482,1663],{},[1654,20484,1766],{},[1665,20486,11555],{},[1741,20488,20489,20491],{},[898,20490,1663],{},[1665,20492,1681],{},[902,20494,20495],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,20497,820],{"id":20498},"přebytek-spotřebitele-a-výrobce",[724,20500,20501],{},"Přebytek spotřebitele:",[724,20503,20504],{},[883,20505,20507],{"className":20506},[886],[888,20508,20509],{"xmlns":890},[892,20510,20511,20571],{},[895,20512,20513,20515,20517,20519,20525,20527,20529,20541,20543,20545,20547,20549,20551,20553,20555,20557,20563,20565],{},[898,20514,11539],{},[898,20516,17398],{},[1654,20518,1708],{"stretchy":1656},[1710,20520,20521,20523],{},[898,20522,1663],{},[1665,20524,2062],{},[1654,20526,1726],{"stretchy":1656},[1654,20528,1750],{},[1659,20530,20531,20533,20535],{},[1654,20532,19883],{},[1665,20534,2062],{},[1710,20536,20537,20539],{},[898,20538,1663],{},[1665,20540,2062],{},[898,20542,4980],{},[1654,20544,1708],{"stretchy":1656},[898,20546,1663],{},[1654,20548,1726],{"stretchy":1656},[1865,20550,11744],{},[898,20552,10977],{},[898,20554,1663],{},[1654,20556,2380],{},[1710,20558,20559,20561],{},[898,20560,1755],{},[1665,20562,2062],{},[1865,20564,11744],{},[1710,20566,20567,20569],{},[898,20568,1663],{},[1665,20570,2062],{},[902,20572,20573],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,20575,20576],{},"Přebytek výrobce:",[724,20578,20579],{},[883,20580,20582],{"className":20581},[886],[888,20583,20584],{"xmlns":890},[892,20585,20586,20646],{},[895,20587,20588,20590,20592,20594,20600,20602,20604,20610,20612,20618,20620,20632,20634,20636,20638,20640,20642,20644],{},[898,20589,1755],{},[898,20591,17398],{},[1654,20593,1708],{"stretchy":1656},[1710,20595,20596,20598],{},[898,20597,1663],{},[1665,20599,2062],{},[1654,20601,1726],{"stretchy":1656},[1654,20603,1750],{},[1710,20605,20606,20608],{},[898,20607,1755],{},[1665,20609,2062],{},[1865,20611,11744],{},[1710,20613,20614,20616],{},[898,20615,1663],{},[1665,20617,2062],{},[1654,20619,2380],{},[1659,20621,20622,20624,20626],{},[1654,20623,19883],{},[1665,20625,2062],{},[1710,20627,20628,20630],{},[898,20629,1663],{},[1665,20631,2062],{},[898,20633,17398],{},[1654,20635,1708],{"stretchy":1656},[898,20637,1663],{},[1654,20639,1726],{"stretchy":1656},[1865,20641,11744],{},[898,20643,10977],{},[898,20645,1663],{},[902,20647,20648],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,20650,20651,20652,2138],{},"Detailně viz ",[207,20653,10669],{"className":20654,"dataFsResolvedFilePath":800,"href":801},[210],[115,20656,10613],{"id":10612},[120,20658,20659,20666,20673],{},[123,20660,20661,2186,20663],{},[38,20662,12546],{},[207,20664,766],{"className":20665,"dataFsResolvedFilePath":764,"href":765},[210],[123,20667,20668,2186,20670],{},[38,20669,12554],{},[207,20671,784],{"className":20672,"dataFsResolvedFilePath":782,"href":783},[210],[123,20674,20675,2186,20677,20680,20681,20684],{},[38,20676,12562],{},[207,20678,12570],{"className":20679,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,20682,10669],{"className":20683,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":20686},[20687,20688,20689,20694],{"id":19858,"depth":642,"text":19859},{"id":19987,"depth":642,"text":19988},{"id":20116,"depth":642,"text":20117,"children":20690},[20691,20692,20693],{"id":20120,"depth":649,"text":20121},{"id":20296,"depth":649,"text":20297},{"id":20498,"depth":649,"text":820},{"id":10612,"depth":642,"text":10613},"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":20695},[1135],"topics\u002Fintegral",[1128,20702,20703,20704,20705,20706,20707],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":20710,"title":20711,"body":20712,"course":1128,"courses":659,"created":10724,"description":641,"extension":661,"meta":24970,"navigation":664,"path":24971,"seo":24972,"sources":24973,"stem":24974,"tags":24975,"type":10736,"updated":677,"__hash__":24981},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":20713,"toc":24958},[20714,20717,20719,20863,20870,20874,20944,20982,21085,21089,21119,21184,21231,21234,21303,21306,21341,21377,21381,21429,21436,21482,21528,21531,21608,21705,21788,21792,21836,21866,21872,21901,21923,21973,22026,22092,22095,22161,22190,22249,22265,22352,22450,22581,22585,22742,22891,23271,23275,23278,23337,23340,23426,23454,23492,23495,23532,23572,23606,23608,23645,23677,23775,23780,23903,23955,24036,24175,24179,24299,24306,24417,24424,24426,24901,24903],[12,20715,20711],{"id":20716},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,20718,1638],{"id":1637},[724,20720,20721,20724,20725,18742,20728,20741,20742,20756,20757,20760,20761,1343,20764,20767,20768,1343,20771,20774,20775,2186,20778,20808,20809,20812,20813,1343,20827,20840,20841,20844,20845,12664],{},[38,20722,20723],{},"IS-LM"," je makroekonomický model se ",[38,20726,20727],{},"dvěma neznámými",[883,20729,20731],{"className":20730},[886],[888,20732,20733],{"xmlns":890},[892,20734,20735,20739],{},[895,20736,20737],{},[898,20738,1745],{},[902,20740,1745],{"encoding":904}," — národní důchod a ",[883,20743,20745],{"className":20744},[886],[888,20746,20747],{"xmlns":890},[892,20748,20749,20754],{},[895,20750,20751],{},[898,20752,20753],{},"r",[902,20755,20753],{"encoding":904}," — úroková míra) a ",[38,20758,20759],{},"dvěma trhy",": trhem zboží (křivka ",[38,20762,20763],{},"IS",[614,20765,20766],{},"Investment = Savings",") a trhem peněz (křivka ",[38,20769,20770],{},"LM",[614,20772,20773],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,20776,20777],{},"simultánní rovnováhu",[883,20779,20781],{"className":20780},[886],[888,20782,20783],{"xmlns":890},[892,20784,20785,20805],{},[895,20786,20787,20789,20795,20797,20803],{},[1654,20788,1708],{"stretchy":1656},[1741,20790,20791,20793],{},[898,20792,1745],{},[898,20794,1798],{},[1654,20796,1674],{"separator":1673},[1741,20798,20799,20801],{},[898,20800,20753],{},[898,20802,1798],{},[1654,20804,1726],{"stretchy":1656},[902,20806,20807],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,20810,20811],{},"fiskální politiky"," (posun IS změnou ",[883,20814,20816],{"className":20815},[886],[888,20817,20818],{"xmlns":890},[892,20819,20820,20825],{},[895,20821,20822],{},[898,20823,20824],{},"G",[902,20826,20824],{"encoding":904},[883,20828,20830],{"className":20829},[886],[888,20831,20832],{"xmlns":890},[892,20833,20834,20838],{},[895,20835,20836],{},[898,20837,11536],{},[902,20839,11536],{"encoding":904},") a ",[38,20842,20843],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,20846,20848],{"className":20847},[886],[888,20849,20850],{"xmlns":890},[892,20851,20852,20860],{},[895,20853,20854],{},[1741,20855,20856,20858],{},[898,20857,9320],{},[1654,20859,1670],{},[902,20861,20862],{"encoding":904},"M^*",[724,20864,20865],{},[3492,20866],{"alt":20867,"className":20868,"src":20869},"imek-is-lm-model",[210,3496],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,20871,20873],{"id":20872},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,20875,20876,20877,20881,20882,18742,20885,20908,20909,20912,20913,20929,20930,20943],{},"V modelech ",[207,20878,20880],{"className":20879,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,20883,20884],{},"investice pokládány za konstantní",[883,20886,20888],{"className":20887},[886],[888,20889,20890],{"xmlns":890},[892,20891,20892,20905],{},[895,20893,20894,20897,20899],{},[898,20895,20896],{},"I",[1654,20898,1750],{},[1741,20900,20901,20903],{},[898,20902,20896],{},[1654,20904,1670],{},[902,20906,20907],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,20910,20911],{},"ceně peněz",", tedy na ",[38,20914,20915,20916],{},"úrokové míře ",[883,20917,20919],{"className":20918},[886],[888,20920,20921],{"xmlns":890},[892,20922,20923,20927],{},[895,20924,20925],{},[898,20926,20753],{},[902,20928,20753],{"encoding":904},": čím vyšší ",[883,20931,20933],{"className":20932},[886],[888,20934,20935],{"xmlns":890},[892,20936,20937,20941],{},[895,20938,20939],{},[898,20940,20753],{},[902,20942,20753],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,20945,20946,20976],{},[123,20947,20948,2186,20951,20975],{},[38,20949,20950],{},"funkci investic",[883,20952,20954],{"className":20953},[886],[888,20955,20956],{"xmlns":890},[892,20957,20958,20972],{},[895,20959,20960,20962,20964,20966,20968,20970],{},[898,20961,20896],{},[1654,20963,1750],{},[898,20965,20896],{},[1654,20967,1708],{"stretchy":1656},[898,20969,20753],{},[1654,20971,1726],{"stretchy":1656},[902,20973,20974],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,20977,20978,20981],{},[38,20979,20980],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[2140,20983,20984],{},[724,20985,20986,20988,20989,21008,21009,21036,21037,21050,21051,21080,21081,21084],{},[883,20987,2146],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,20990,20992],{"className":20991},[886],[888,20993,20994],{"xmlns":890},[892,20995,20996,21005],{},[895,20997,20998,21000,21003],{},[898,20999,11539],{},[1865,21001,21002],{},"-",[898,21004,20896],{},[902,21006,21007],{"encoding":904},"C\\text{-}I"," až ",[883,21010,21012],{"className":21011},[886],[888,21013,21014],{"xmlns":890},[892,21015,21016,21033],{},[895,21017,21018,21020,21022,21024,21026,21028,21030],{},[898,21019,11539],{},[1865,21021,21002],{},[898,21023,20896],{},[1865,21025,21002],{},[898,21027,20824],{},[1865,21029,21002],{},[898,21031,21032],{},"X",[902,21034,21035],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,21038,21040],{"className":21039},[886],[888,21041,21042],{"xmlns":890},[892,21043,21044,21048],{},[895,21045,21046],{},[898,21047,1745],{},[902,21049,1745],{"encoding":904},". V IS-LM jsou ",[38,21052,21053,21054,2068,21067],{},"dvě neznámé ",[883,21055,21057],{"className":21056},[886],[888,21058,21059],{"xmlns":890},[892,21060,21061,21065],{},[895,21062,21063],{},[898,21064,1745],{},[902,21066,1745],{"encoding":904},[883,21068,21070],{"className":21069},[886],[888,21071,21072],{"xmlns":890},[892,21073,21074,21078],{},[895,21075,21076],{},[898,21077,20753],{},[902,21079,20753],{"encoding":904},", a proto potřebujeme ",[38,21082,21083],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,21086,21088],{"id":21087},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,21090,21091,21092,21105,21106,2781],{},"Lineární závislost investic ",[883,21093,21095],{"className":21094},[886],[888,21096,21097],{"xmlns":890},[892,21098,21099,21103],{},[895,21100,21101],{},[898,21102,20896],{},[902,21104,20896],{"encoding":904}," na úrokové míře ",[883,21107,21109],{"className":21108},[886],[888,21110,21111],{"xmlns":890},[892,21112,21113,21117],{},[895,21114,21115],{},[898,21116,20753],{},[902,21118,20753],{"encoding":904},[724,21120,21121],{},[883,21122,21124],{"className":21123},[886],[888,21125,21126],{"xmlns":890},[892,21127,21128,21181],{},[895,21129,21130,21132,21134,21136,21138,21140,21142,21144,21146,21148,21150,21152,21154,21156,21158,21160,21162,21164,21166,21168,21170,21172,21174,21176,21179],{},[898,21131,20896],{},[1654,21133,1750],{},[898,21135,20896],{},[1654,21137,1708],{"stretchy":1656},[898,21139,20753],{},[1654,21141,1726],{"stretchy":1656},[1654,21143,1750],{},[898,21145,3624],{},[898,21147,20753],{},[1654,21149,1766],{},[898,21151,10977],{},[1654,21153,1674],{"separator":1673},[5008,21155],{"width":14608},[898,21157,3624],{},[1654,21159,3002],{},[1665,21161,2062],{},[1654,21163,1674],{"separator":1673},[1865,21165,11065],{},[898,21167,10977],{},[1654,21169,2952],{},[1665,21171,2745],{},[5008,21173],{"width":14608},[1654,21175,1708],{"stretchy":1656},[1665,21177,21178],{},"7.11",[1654,21180,1726],{"stretchy":1656},[902,21182,21183],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,21185,21186,21207],{},[123,21187,21188,21206],{},[883,21189,21191],{"className":21190},[886],[888,21192,21193],{"xmlns":890},[892,21194,21195,21203],{},[895,21196,21197,21199,21201],{},[898,21198,10977],{},[1654,21200,2952],{},[1665,21202,2062],{},[902,21204,21205],{"encoding":904},"d > 0"," zřejmé,",[123,21208,21209,21227,21228,2138],{},[883,21210,21212],{"className":21211},[886],[888,21213,21214],{"xmlns":890},[892,21215,21216,21224],{},[895,21217,21218,21220,21222],{},[898,21219,3624],{},[1654,21221,3002],{},[1665,21223,2062],{},[902,21225,21226],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,21229,21230],{},"klesající",[724,21232,21233],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,21235,21236],{},[883,21237,21239],{"className":21238},[886],[888,21240,21241],{"xmlns":890},[892,21242,21243,21300],{},[895,21244,21245,21247,21249,21251,21253,21255,21257,21259,21261,21263,21265,21267,21269,21271,21273,21275,21277,21279,21281,21283,21285,21287,21289,21291,21293,21295,21298],{},[898,21246,11539],{},[1654,21248,1750],{},[898,21250,11539],{},[1654,21252,1708],{"stretchy":1656},[898,21254,1745],{},[1654,21256,1726],{"stretchy":1656},[1654,21258,1750],{},[898,21260,207],{},[898,21262,1745],{},[1654,21264,1766],{},[898,21266,9758],{},[1654,21268,1674],{"separator":1673},[5008,21270],{"width":14608},[1665,21272,2062],{},[1654,21274,3002],{},[898,21276,207],{},[1654,21278,3002],{},[1665,21280,1667],{},[1654,21282,1674],{"separator":1673},[1865,21284,11065],{},[898,21286,9758],{},[1654,21288,2952],{},[1665,21290,2745],{},[5008,21292],{"width":14608},[1654,21294,1708],{"stretchy":1656},[1665,21296,21297],{},"7.12",[1654,21299,1726],{"stretchy":1656},[902,21301,21302],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,21304,21305],{},"Podmínka rovnováhy na trhu zboží:",[724,21307,21308],{},[883,21309,21311],{"className":21310},[886],[888,21312,21313],{"xmlns":890},[892,21314,21315,21338],{},[895,21316,21317,21319,21321,21323,21325,21327,21329,21331,21333,21336],{},[898,21318,1745],{},[1654,21320,1750],{},[898,21322,11539],{},[1654,21324,1766],{},[898,21326,20896],{},[898,21328,2138],{"mathvariant":1878},[5008,21330],{"width":14608},[1654,21332,1708],{"stretchy":1656},[1665,21334,21335],{},"7.13",[1654,21337,1726],{"stretchy":1656},[902,21339,21340],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,21342,21343,21344,2186,21347,21373,21374,2138],{},"To dává ",[38,21345,21346],{},"tři rovnice o čtyřech neznámých",[883,21348,21350],{"className":21349},[886],[888,21351,21352],{"xmlns":890},[892,21353,21354,21370],{},[895,21355,21356,21358,21360,21362,21364,21366,21368],{},[898,21357,1745],{},[1654,21359,1674],{"separator":1673},[898,21361,11539],{},[1654,21363,1674],{"separator":1673},[898,21365,20896],{},[1654,21367,1674],{"separator":1673},[898,21369,20753],{},[902,21371,21372],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,21375,21376],{},"rovnováhy na trhu peněz",[115,21378,21380],{"id":21379},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,21382,21383,21384,14299,21406,21424,21425,21428],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,21385,21387],{"className":21386},[886],[888,21388,21389],{"xmlns":890},[892,21390,21391,21403],{},[895,21392,21393,21395,21397,21399,21401],{},[898,21394,1745],{},[1654,21396,1750],{},[898,21398,11539],{},[1654,21400,1766],{},[898,21402,17398],{},[902,21404,21405],{"encoding":904},"Y = C + S",[883,21407,21409],{"className":21408},[886],[888,21410,21411],{"xmlns":890},[892,21412,21413,21421],{},[895,21414,21415,21417,21419],{},[898,21416,20896],{},[1654,21418,1750],{},[898,21420,17398],{},[902,21422,21423],{"encoding":904},"I = S"," (plánované ",[38,21426,21427],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,21430,21431],{},[3492,21432],{"alt":21433,"className":21434,"src":21435},"imek-odvozeni-is-4panelu",[210,3496],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,21437,21438],{},[883,21439,21441],{"className":21440},[886],[888,21442,21443],{"xmlns":890},[892,21444,21445,21479],{},[895,21446,21447,21449,21451,21453,21455,21457,21459,21461,21463,21465,21467,21469,21471,21473,21475,21477],{},[898,21448,1745],{},[1654,21450,1750],{},[1654,21452,1708],{"stretchy":1656},[898,21454,207],{},[898,21456,1745],{},[1654,21458,1766],{},[898,21460,9758],{},[1654,21462,1726],{"stretchy":1656},[1654,21464,1766],{},[1654,21466,1708],{"stretchy":1656},[898,21468,3624],{},[898,21470,20753],{},[1654,21472,1766],{},[898,21474,10977],{},[1654,21476,1726],{"stretchy":1656},[1654,21478,1674],{"separator":1673},[902,21480,21481],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,21483,21484],{},[883,21485,21487],{"className":21486},[886],[888,21488,21489],{"xmlns":890},[892,21490,21491,21525],{},[895,21492,21493,21495,21497,21499,21501,21503,21505,21507,21509,21511,21513,21515,21517,21519,21521,21523],{},[1654,21494,1708],{"stretchy":1656},[1665,21496,1667],{},[1654,21498,2380],{},[898,21500,207],{},[1654,21502,1726],{"stretchy":1656},[898,21504,1745],{},[1654,21506,2380],{},[898,21508,3624],{},[898,21510,20753],{},[1654,21512,2380],{},[898,21514,9758],{},[1654,21516,2380],{},[898,21518,10977],{},[1654,21520,1750],{},[1665,21522,2062],{},[1654,21524,1674],{"separator":1673},[902,21526,21527],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,21529,21530],{},"odkud",[724,21532,21533],{},[883,21534,21536],{"className":21535},[886],[888,21537,21538],{"xmlns":890},[892,21539,21540,21605],{},[895,21541,21542,21596,21598,21600,21603],{},[2792,21543,21544],{"notation":2794},[2582,21545,21546],{"scriptlevel":2062,"displaystyle":1656},[2582,21547,21548],{"scriptlevel":2062,"displaystyle":1656},[2582,21549,21550],{"scriptlevel":2062,"displaystyle":1673},[895,21551,21552,21554,21556,21558,21570,21572,21574,21576,21594],{},[1865,21553,11744],{},[898,21555,1745],{},[1654,21557,1750],{},[2811,21559,21560,21562],{},[898,21561,3624],{},[895,21563,21564,21566,21568],{},[1665,21565,1667],{},[1654,21567,2380],{},[898,21569,207],{},[1865,21571,11744],{},[898,21573,20753],{},[1654,21575,1766],{},[2811,21577,21578,21586],{},[895,21579,21580,21582,21584],{},[898,21581,9758],{},[1654,21583,1766],{},[898,21585,10977],{},[895,21587,21588,21590,21592],{},[1665,21589,1667],{},[1654,21591,2380],{},[898,21593,207],{},[1865,21595,11744],{},[5008,21597],{"width":14608},[1654,21599,1708],{"stretchy":1656},[1665,21601,21602],{},"7.14",[1654,21604,1726],{"stretchy":1656},[902,21606,21607],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,21609,21610,21611,18742,21614,21617,21618,21621,21622,21624,21625,21647,21648,21676,21677,21698,21699,21701,21702,21704],{},"Tento vztah se nazývá ",[38,21612,21613],{},"funkce IS",[614,21615,21616],{},"IS schedule",") a její graf ",[38,21619,21620],{},"křivka IS",". Křivka je ",[38,21623,21230],{}," přímka v rovině ",[883,21626,21628],{"className":21627},[886],[888,21629,21630],{"xmlns":890},[892,21631,21632,21644],{},[895,21633,21634,21636,21638,21640,21642],{},[1654,21635,1708],{"stretchy":1656},[898,21637,20753],{},[1654,21639,1674],{"separator":1673},[898,21641,1745],{},[1654,21643,1726],{"stretchy":1656},[902,21645,21646],{"encoding":904},"(r, Y)",", neboť ",[883,21649,21651],{"className":21650},[886],[888,21652,21653],{"xmlns":890},[892,21654,21655,21673],{},[895,21656,21657,21669,21671],{},[2811,21658,21659,21661],{},[898,21660,3624],{},[895,21662,21663,21665,21667],{},[1665,21664,1667],{},[1654,21666,2380],{},[898,21668,207],{},[1654,21670,3002],{},[1665,21672,2062],{},[902,21674,21675],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,21678,21680],{"className":21679},[886],[888,21681,21682],{"xmlns":890},[892,21683,21684,21696],{},[895,21685,21686,21688,21690,21692,21694],{},[1654,21687,1708],{"stretchy":1656},[898,21689,20753],{},[1654,21691,1674],{"separator":1673},[898,21693,1745],{},[1654,21695,1726],{"stretchy":1656},[902,21697,21646],{"encoding":904},", pro které plánované ",[38,21700,20896],{},"nvestment = ",[38,21703,17398],{},"avings.",[2140,21706,21707],{},[724,21708,21709,21711,21712,21725,21726,2186,21729,21742,21743,21756,21757,2068,21770,21783,21784,21787],{},[883,21710,2860],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,21713,21715],{"className":21714},[886],[888,21716,21717],{"xmlns":890},[892,21718,21719,21723],{},[895,21720,21721],{},[898,21722,20753],{},[902,21724,20753],{"encoding":904}," → levnější úvěr → ",[38,21727,21728],{},"více investic",[883,21730,21732],{"className":21731},[886],[888,21733,21734],{"xmlns":890},[892,21735,21736,21740],{},[895,21737,21738],{},[898,21739,20896],{},[902,21741,20896],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,21744,21746],{"className":21745},[886],[888,21747,21748],{"xmlns":890},[892,21749,21750,21754],{},[895,21751,21752],{},[898,21753,1745],{},[902,21755,1745],{"encoding":904},". Vztah mezi ",[883,21758,21760],{"className":21759},[886],[888,21761,21762],{"xmlns":890},[892,21763,21764,21768],{},[895,21765,21766],{},[898,21767,20753],{},[902,21769,20753],{"encoding":904},[883,21771,21773],{"className":21772},[886],[888,21774,21775],{"xmlns":890},[892,21776,21777,21781],{},[895,21778,21779],{},[898,21780,1745],{},[902,21782,1745],{"encoding":904}," na trhu zboží je proto ",[38,21785,21786],{},"nepřímý"," (klesající křivka).",[115,21789,21791],{"id":21790},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,21793,21794,21795,21813,21814,4039,21832,21835],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,21796,21798],{"className":21797},[886],[888,21799,21800],{"xmlns":890},[892,21801,21802,21810],{},[895,21803,21804],{},[1741,21805,21806,21808],{},[898,21807,9320],{},[898,21809,4980],{},[902,21811,21812],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,21815,21817],{"className":21816},[886],[888,21818,21819],{"xmlns":890},[892,21820,21821,21829],{},[895,21822,21823],{},[1741,21824,21825,21827],{},[898,21826,9320],{},[898,21828,17398],{},[902,21830,21831],{"encoding":904},"M^S",[38,21833,21834],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,21837,21838],{},[883,21839,21841],{"className":21840},[886],[888,21842,21843],{"xmlns":890},[892,21844,21845,21863],{},[895,21846,21847,21853,21855,21861],{},[1741,21848,21849,21851],{},[898,21850,9320],{},[898,21852,17398],{},[1654,21854,1750],{},[1741,21856,21857,21859],{},[898,21858,9320],{},[1654,21860,1670],{},[898,21862,2138],{"mathvariant":1878},[902,21864,21865],{"encoding":904},"M^S = M^*.",[724,21867,21868,21871],{},[38,21869,21870],{},"Poptávka"," po penězích má tři zdroje:",[120,21873,21874,21883,21892],{},[123,21875,21876,18742,21879,21882],{},[38,21877,21878],{},"transakční poptávka",[614,21880,21881],{},"transactions demand",") — peníze pro nákup zboží,",[123,21884,21885,18742,21888,21891],{},[38,21886,21887],{},"opatrnostní poptávka",[614,21889,21890],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,21893,21894,18742,21897,21900],{},[38,21895,21896],{},"spekulační poptávka",[614,21898,21899],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,21902,21903,21904,21922],{},"Součet transakční a opatrnostní poptávky ",[883,21905,21907],{"className":21906},[886],[888,21908,21909],{"xmlns":890},[892,21910,21911,21919],{},[895,21912,21913],{},[1710,21914,21915,21917],{},[898,21916,2450],{},[1665,21918,1667],{},[902,21920,21921],{"encoding":904},"L_1"," je úměrný důchodu:",[724,21924,21925],{},[883,21926,21928],{"className":21927},[886],[888,21929,21930],{"xmlns":890},[892,21931,21932,21970],{},[895,21933,21934,21940,21942,21949,21951,21953,21955,21957,21959,21965,21967],{},[1710,21935,21936,21938],{},[898,21937,2450],{},[1665,21939,1667],{},[1654,21941,1750],{},[1710,21943,21944,21947],{},[898,21945,21946],{},"k",[1665,21948,1667],{},[898,21950,1745],{},[1654,21952,1674],{"separator":1673},[5008,21954],{"width":14608},[1665,21956,2062],{},[1654,21958,3002],{},[1710,21960,21961,21963],{},[898,21962,21946],{},[1665,21964,1667],{},[1654,21966,3002],{},[1665,21968,21969],{},"1.",[902,21971,21972],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,21974,21975,21976,21994,21995,1343,22008,22025],{},"Spekulační poptávka ",[883,21977,21979],{"className":21978},[886],[888,21980,21981],{"xmlns":890},[892,21982,21983,21991],{},[895,21984,21985],{},[1710,21986,21987,21989],{},[898,21988,2450],{},[1665,21990,1681],{},[902,21992,21993],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,21996,21998],{"className":21997},[886],[888,21999,22000],{"xmlns":890},[892,22001,22002,22006],{},[895,22003,22004],{},[898,22005,20753],{},[902,22007,20753],{"encoding":904},[883,22009,22011],{"className":22010},[886],[888,22012,22013],{"xmlns":890},[892,22014,22015,22023],{},[895,22016,22017],{},[1710,22018,22019,22021],{},[898,22020,2450],{},[1665,22022,1681],{},[902,22024,21993],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,22027,22028],{},[883,22029,22031],{"className":22030},[886],[888,22032,22033],{"xmlns":890},[892,22034,22035,22089],{},[895,22036,22037,22043,22045,22051,22053,22055,22061,22063,22065,22071,22073,22075,22077,22079,22085,22087],{},[1710,22038,22039,22041],{},[898,22040,2450],{},[1665,22042,1681],{},[1654,22044,1750],{},[1710,22046,22047,22049],{},[898,22048,21946],{},[1665,22050,1681],{},[898,22052,20753],{},[1654,22054,1766],{},[1710,22056,22057,22059],{},[898,22058,21946],{},[1665,22060,4035],{},[1654,22062,1674],{"separator":1673},[5008,22064],{"width":14608},[1710,22066,22067,22069],{},[898,22068,21946],{},[1665,22070,1681],{},[1654,22072,3002],{},[1665,22074,2062],{},[1654,22076,1674],{"separator":1673},[1865,22078,11065],{},[1710,22080,22081,22083],{},[898,22082,21946],{},[1665,22084,4035],{},[1654,22086,2952],{},[1665,22088,2745],{},[902,22090,22091],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,22093,22094],{},"Celková poptávka po penězích:",[724,22096,22097],{},[883,22098,22100],{"className":22099},[886],[888,22101,22102],{"xmlns":890},[892,22103,22104,22158],{},[895,22105,22106,22112,22114,22120,22122,22128,22130,22136,22138,22140,22146,22148,22150,22156],{},[1741,22107,22108,22110],{},[898,22109,9320],{},[898,22111,4980],{},[1654,22113,1750],{},[1710,22115,22116,22118],{},[898,22117,2450],{},[1665,22119,1667],{},[1654,22121,1766],{},[1710,22123,22124,22126],{},[898,22125,2450],{},[1665,22127,1681],{},[1654,22129,1750],{},[1710,22131,22132,22134],{},[898,22133,21946],{},[1665,22135,1667],{},[898,22137,1745],{},[1654,22139,1766],{},[1710,22141,22142,22144],{},[898,22143,21946],{},[1665,22145,1681],{},[898,22147,20753],{},[1654,22149,1766],{},[1710,22151,22152,22154],{},[898,22153,21946],{},[1665,22155,4035],{},[898,22157,2138],{"mathvariant":1878},[902,22159,22160],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,22162,22163,22164,2781],{},"Podmínka rovnováhy na trhu peněz ",[883,22165,22167],{"className":22166},[886],[888,22168,22169],{"xmlns":890},[892,22170,22171,22187],{},[895,22172,22173,22179,22181],{},[1741,22174,22175,22177],{},[898,22176,9320],{},[898,22178,4980],{},[1654,22180,1750],{},[1741,22182,22183,22185],{},[898,22184,9320],{},[1654,22186,1670],{},[902,22188,22189],{"encoding":904},"M^D = M^*",[724,22191,22192],{},[883,22193,22195],{"className":22194},[886],[888,22196,22197],{"xmlns":890},[892,22198,22199,22246],{},[895,22200,22201,22207,22209,22215,22217,22219,22225,22227,22229,22235,22237,22239,22241,22244],{},[1741,22202,22203,22205],{},[898,22204,9320],{},[1654,22206,1670],{},[1654,22208,1750],{},[1710,22210,22211,22213],{},[898,22212,21946],{},[1665,22214,1667],{},[898,22216,1745],{},[1654,22218,1766],{},[1710,22220,22221,22223],{},[898,22222,21946],{},[1665,22224,1681],{},[898,22226,20753],{},[1654,22228,1766],{},[1710,22230,22231,22233],{},[898,22232,21946],{},[1665,22234,4035],{},[1654,22236,1674],{"separator":1673},[5008,22238],{"width":14608},[1654,22240,1708],{"stretchy":1656},[1665,22242,22243],{},"7.15",[1654,22245,1726],{"stretchy":1656},[902,22247,22248],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,22250,22251,22252,11906],{},"po úpravě (vyjádření ",[883,22253,22255],{"className":22254},[886],[888,22256,22257],{"xmlns":890},[892,22258,22259,22263],{},[895,22260,22261],{},[898,22262,1745],{},[902,22264,1745],{"encoding":904},[724,22266,22267],{},[883,22268,22270],{"className":22269},[886],[888,22271,22272],{"xmlns":890},[892,22273,22274,22349],{},[895,22275,22276,22340,22342,22344,22347],{},[2792,22277,22278],{"notation":2794},[2582,22279,22280],{"scriptlevel":2062,"displaystyle":1656},[2582,22281,22282],{"scriptlevel":2062,"displaystyle":1656},[2582,22283,22284],{"scriptlevel":2062,"displaystyle":1673},[895,22285,22286,22288,22290,22292,22294,22308,22310,22312,22314,22338],{},[1865,22287,11744],{},[898,22289,1745],{},[1654,22291,1750],{},[1654,22293,2380],{},[2811,22295,22296,22302],{},[1710,22297,22298,22300],{},[898,22299,21946],{},[1665,22301,1681],{},[1710,22303,22304,22306],{},[898,22305,21946],{},[1665,22307,1667],{},[1865,22309,11744],{},[898,22311,20753],{},[1654,22313,1766],{},[2811,22315,22316,22332],{},[895,22317,22318,22324,22326],{},[1741,22319,22320,22322],{},[898,22321,9320],{},[1654,22323,1670],{},[1654,22325,2380],{},[1710,22327,22328,22330],{},[898,22329,21946],{},[1665,22331,4035],{},[1710,22333,22334,22336],{},[898,22335,21946],{},[1665,22337,1667],{},[1865,22339,11744],{},[5008,22341],{"width":14608},[1654,22343,1708],{"stretchy":1656},[1665,22345,22346],{},"7.16",[1654,22348,1726],{"stretchy":1656},[902,22350,22351],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,22353,21610,22354,18742,22357,22360,22361,21621,22364,21624,22367,21647,22388,22420,22421,22443,22444,22446,22447,22449],{},[38,22355,22356],{},"funkce LM",[614,22358,22359],{},"LM schedule","), její graf ",[38,22362,22363],{},"křivka LM",[38,22365,22366],{},"rostoucí",[883,22368,22370],{"className":22369},[886],[888,22371,22372],{"xmlns":890},[892,22373,22374,22386],{},[895,22375,22376,22378,22380,22382,22384],{},[1654,22377,1708],{"stretchy":1656},[898,22379,20753],{},[1654,22381,1674],{"separator":1673},[898,22383,1745],{},[1654,22385,1726],{"stretchy":1656},[902,22387,21646],{"encoding":904},[883,22389,22391],{"className":22390},[886],[888,22392,22393],{"xmlns":890},[892,22394,22395,22417],{},[895,22396,22397,22399,22413,22415],{},[1654,22398,2380],{},[2811,22400,22401,22407],{},[1710,22402,22403,22405],{},[898,22404,21946],{},[1665,22406,1681],{},[1710,22408,22409,22411],{},[898,22410,21946],{},[1665,22412,1667],{},[1654,22414,2952],{},[1665,22416,2062],{},[902,22418,22419],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,22422,22424],{"className":22423},[886],[888,22425,22426],{"xmlns":890},[892,22427,22428,22440],{},[895,22429,22430,22436,22438],{},[1710,22431,22432,22434],{},[898,22433,21946],{},[1665,22435,1681],{},[1654,22437,3002],{},[1665,22439,2062],{},[902,22441,22442],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,22445,2450],{},"iquidity of ",[38,22448,9320],{},"oney.",[2140,22451,22452],{},[724,22453,22454,22456,22457,22470,22471,22499,22500,22517,22518,22531,22532,22549,22550,2068,22563,22576,22577,22580],{},[883,22455,2860],{}," Intuice — proč LM roste\nVyšší důchod ",[883,22458,22460],{"className":22459},[886],[888,22461,22462],{"xmlns":890},[892,22463,22464,22468],{},[895,22465,22466],{},[898,22467,1745],{},[902,22469,1745],{"encoding":904}," → větší transakční poptávka po penězích ",[883,22472,22474],{"className":22473},[886],[888,22475,22476],{"xmlns":890},[892,22477,22478,22496],{},[895,22479,22480,22486,22488,22494],{},[1710,22481,22482,22484],{},[898,22483,2450],{},[1665,22485,1667],{},[1654,22487,1750],{},[1710,22489,22490,22492],{},[898,22491,21946],{},[1665,22493,1667],{},[898,22495,1745],{},[902,22497,22498],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,22501,22503],{"className":22502},[886],[888,22504,22505],{"xmlns":890},[892,22506,22507,22515],{},[895,22508,22509],{},[1741,22510,22511,22513],{},[898,22512,9320],{},[1654,22514,1670],{},[902,22516,20862],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,22519,22521],{"className":22520},[886],[888,22522,22523],{"xmlns":890},[892,22524,22525,22529],{},[895,22526,22527],{},[898,22528,20753],{},[902,22530,20753],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,22533,22535],{"className":22534},[886],[888,22536,22537],{"xmlns":890},[892,22538,22539,22547],{},[895,22540,22541],{},[1710,22542,22543,22545],{},[898,22544,2450],{},[1665,22546,1681],{},[902,22548,21993],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,22551,22553],{"className":22552},[886],[888,22554,22555],{"xmlns":890},[892,22556,22557,22561],{},[895,22558,22559],{},[898,22560,1745],{},[902,22562,1745],{"encoding":904},[883,22564,22566],{"className":22565},[886],[888,22567,22568],{"xmlns":890},[892,22569,22570,22574],{},[895,22571,22572],{},[898,22573,20753],{},[902,22575,20753],{"encoding":904}," na trhu peněz je proto ",[38,22578,22579],{},"přímý"," (rostoucí křivka).",[115,22582,22584],{"id":22583},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,22586,22587,22588,22591,22592,2186,22595,2068,22613,2186,22616,22634,22635,22653,22654,22672,22673,22689,22690,2068,22705,22720,22721,2138],{},"Řešením ",[38,22589,22590],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,22593,22594],{},"rovnovážný důchod",[883,22596,22598],{"className":22597},[886],[888,22599,22600],{"xmlns":890},[892,22601,22602,22610],{},[895,22603,22604],{},[1741,22605,22606,22608],{},[898,22607,1745],{},[898,22609,1798],{},[902,22611,22612],{"encoding":904},"Y^E",[38,22614,22615],{},"rovnovážnou úrokovou míru",[883,22617,22619],{"className":22618},[886],[888,22620,22621],{"xmlns":890},[892,22622,22623,22631],{},[895,22624,22625],{},[1741,22626,22627,22629],{},[898,22628,20753],{},[898,22630,1798],{},[902,22632,22633],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,22636,22638],{"className":22637},[886],[888,22639,22640],{"xmlns":890},[892,22641,22642,22650],{},[895,22643,22644],{},[1741,22645,22646,22648],{},[898,22647,20896],{},[898,22649,1798],{},[902,22651,22652],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,22655,22657],{"className":22656},[886],[888,22658,22659],{"xmlns":890},[892,22660,22661,22669],{},[895,22662,22663],{},[1741,22664,22665,22667],{},[898,22666,11539],{},[898,22668,1798],{},[902,22670,22671],{"encoding":904},"C^E",". Graficky jde o ",[38,22674,22675,22676],{},"průsečík ",[883,22677,22679],{"className":22678},[886],[888,22680,22681],{"xmlns":890},[892,22682,22683,22687],{},[895,22684,22685],{},[898,22686,1798],{},[902,22688,1798],{"encoding":904}," křivek ",[883,22691,22693],{"className":22692},[886],[888,22694,22695],{"xmlns":890},[892,22696,22697,22703],{},[895,22698,22699,22701],{},[898,22700,20896],{},[898,22702,17398],{},[902,22704,20763],{"encoding":904},[883,22706,22708],{"className":22707},[886],[888,22709,22710],{"xmlns":890},[892,22711,22712,22718],{},[895,22713,22714,22716],{},[898,22715,2450],{},[898,22717,9320],{},[902,22719,20770],{"encoding":904}," v rovině ",[883,22722,22724],{"className":22723},[886],[888,22725,22726],{"xmlns":890},[892,22727,22728,22740],{},[895,22729,22730,22732,22734,22736,22738],{},[1654,22731,1708],{"stretchy":1656},[898,22733,20753],{},[1654,22735,1674],{"separator":1673},[898,22737,1745],{},[1654,22739,1726],{"stretchy":1656},[902,22741,21646],{"encoding":904},[724,22743,22744],{},[614,22745,22746,22747,22768,22769,22784,22785,22800,22801,22814,22815,22832,22833,20840,22846,22832,22863,22876,22877,22890],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,22748,22750],{"className":22749},[886],[888,22751,22752],{"xmlns":890},[892,22753,22754,22766],{},[895,22755,22756,22758,22760,22762,22764],{},[1654,22757,1708],{"stretchy":1656},[898,22759,20753],{},[1654,22761,1674],{"separator":1673},[898,22763,1745],{},[1654,22765,1726],{"stretchy":1656},[902,22767,21646],{"encoding":904},". Rostoucí přímka ",[883,22770,22772],{"className":22771},[886],[888,22773,22774],{"xmlns":890},[892,22775,22776,22782],{},[895,22777,22778,22780],{},[898,22779,2450],{},[898,22781,9320],{},[902,22783,20770],{"encoding":904}," a klesající přímka ",[883,22786,22788],{"className":22787},[886],[888,22789,22790],{"xmlns":890},[892,22791,22792,22798],{},[895,22793,22794,22796],{},[898,22795,20896],{},[898,22797,17398],{},[902,22799,20763],{"encoding":904}," se protínají v bodě ",[883,22802,22804],{"className":22803},[886],[888,22805,22806],{"xmlns":890},[892,22807,22808,22812],{},[895,22809,22810],{},[898,22811,1798],{},[902,22813,1798],{"encoding":904}," se souřadnicemi ",[883,22816,22818],{"className":22817},[886],[888,22819,22820],{"xmlns":890},[892,22821,22822,22830],{},[895,22823,22824],{},[1741,22825,22826,22828],{},[898,22827,20753],{},[898,22829,1798],{},[902,22831,22633],{"encoding":904}," (na ose ",[883,22834,22836],{"className":22835},[886],[888,22837,22838],{"xmlns":890},[892,22839,22840,22844],{},[895,22841,22842],{},[898,22843,20753],{},[902,22845,20753],{"encoding":904},[883,22847,22849],{"className":22848},[886],[888,22850,22851],{"xmlns":890},[892,22852,22853,22861],{},[895,22854,22855],{},[1741,22856,22857,22859],{},[898,22858,1745],{},[898,22860,1798],{},[902,22862,22612],{"encoding":904},[883,22864,22866],{"className":22865},[886],[888,22867,22868],{"xmlns":890},[892,22869,22870,22874],{},[895,22871,22872],{},[898,22873,1745],{},[902,22875,1745],{"encoding":904},"); tečkované čáry z ",[883,22878,22880],{"className":22879},[886],[888,22881,22882],{"xmlns":890},[892,22883,22884,22888],{},[895,22885,22886],{},[898,22887,1798],{},[902,22889,1798],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[2140,22892,22893,22898],{},[724,22894,22895,22897],{},[883,22896,3111],{}," Postup — jak najít IS-LM rovnováhu",[152,22899,22900,22976,23044,23102,23175],{},[123,22901,22902,22905,22906,2068,22926,22946,22947,2068,22960,22973,22974,2138],{},[38,22903,22904],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,22907,22909],{"className":22908},[886],[888,22910,22911],{"xmlns":890},[892,22912,22913,22923],{},[895,22914,22915,22917,22919,22921],{},[898,22916,11539],{},[1654,22918,1708],{"stretchy":1656},[898,22920,1745],{},[1654,22922,1726],{"stretchy":1656},[902,22924,22925],{"encoding":904},"C(Y)",[883,22927,22929],{"className":22928},[886],[888,22930,22931],{"xmlns":890},[892,22932,22933,22943],{},[895,22934,22935,22937,22939,22941],{},[898,22936,20896],{},[1654,22938,1708],{"stretchy":1656},[898,22940,20753],{},[1654,22942,1726],{"stretchy":1656},[902,22944,22945],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,22948,22950],{"className":22949},[886],[888,22951,22952],{"xmlns":890},[892,22953,22954,22958],{},[895,22955,22956],{},[898,22957,1745],{},[902,22959,1745],{"encoding":904},[883,22961,22963],{"className":22962},[886],[888,22964,22965],{"xmlns":890},[892,22966,22967,22971],{},[895,22968,22969],{},[898,22970,20753],{},[902,22972,20753],{"encoding":904}," — dostaneš rovnici ",[38,22975,20763],{},[123,22977,22978,22981,22982,2068,22999,23016,23017,22973,23042,2138],{},[38,22979,22980],{},"Z trhu peněz (7.15)"," dosaď ",[883,22983,22985],{"className":22984},[886],[888,22986,22987],{"xmlns":890},[892,22988,22989,22997],{},[895,22990,22991],{},[1710,22992,22993,22995],{},[898,22994,2450],{},[1665,22996,1667],{},[902,22998,21921],{"encoding":904},[883,23000,23002],{"className":23001},[886],[888,23003,23004],{"xmlns":890},[892,23005,23006,23014],{},[895,23007,23008],{},[1710,23009,23010,23012],{},[898,23011,2450],{},[1665,23013,1681],{},[902,23015,21993],{"encoding":904}," a vztah ",[883,23018,23020],{"className":23019},[886],[888,23021,23022],{"xmlns":890},[892,23023,23024,23040],{},[895,23025,23026,23032,23034],{},[1741,23027,23028,23030],{},[898,23029,9320],{},[898,23031,4980],{},[1654,23033,1750],{},[1741,23035,23036,23038],{},[898,23037,9320],{},[1654,23039,1670],{},[902,23041,22189],{"encoding":904},[38,23043,20770],{},[123,23045,23046,23049,23050,2068,23063,23076,23077,23101],{},[38,23047,23048],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,23051,23053],{"className":23052},[886],[888,23054,23055],{"xmlns":890},[892,23056,23057,23061],{},[895,23058,23059],{},[898,23060,1745],{},[902,23062,1745],{"encoding":904},[883,23064,23066],{"className":23065},[886],[888,23067,23068],{"xmlns":890},[892,23069,23070,23074],{},[895,23071,23072],{},[898,23073,20753],{},[902,23075,20753],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,23078,23080],{"className":23079},[886],[888,23081,23082],{"xmlns":890},[892,23083,23084,23098],{},[895,23085,23086,23088,23090,23092,23094,23096],{},[898,23087,1745],{},[1654,23089,1750],{},[898,23091,10794],{},[1654,23093,1708],{"stretchy":1656},[898,23095,20753],{},[1654,23097,1726],{"stretchy":1656},[902,23099,23100],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,23103,23104,2186,23107,2068,23141,2138],{},[38,23105,23106],{},"Zpětně dopočítej",[883,23108,23110],{"className":23109},[886],[888,23111,23112],{"xmlns":890},[892,23113,23114,23138],{},[895,23115,23116,23122,23124,23126,23128,23134,23136],{},[1741,23117,23118,23120],{},[898,23119,11539],{},[898,23121,1798],{},[1654,23123,1750],{},[898,23125,207],{},[1865,23127,11744],{},[1741,23129,23130,23132],{},[898,23131,1745],{},[898,23133,1798],{},[1654,23135,1766],{},[898,23137,9758],{},[902,23139,23140],{"encoding":904},"C^E = a\\,Y^E + b",[883,23142,23144],{"className":23143},[886],[888,23145,23146],{"xmlns":890},[892,23147,23148,23172],{},[895,23149,23150,23156,23158,23160,23162,23168,23170],{},[1741,23151,23152,23154],{},[898,23153,20896],{},[898,23155,1798],{},[1654,23157,1750],{},[898,23159,3624],{},[1865,23161,11744],{},[1741,23163,23164,23166],{},[898,23165,20753],{},[898,23167,1798],{},[1654,23169,1766],{},[898,23171,10977],{},[902,23173,23174],{"encoding":904},"I^E = c\\,r^E + d",[123,23176,23177,23180,23181,23215,23216,23270],{},[38,23178,23179],{},"Ověř:"," musí platit ",[883,23182,23184],{"className":23183},[886],[888,23185,23186],{"xmlns":890},[892,23187,23188,23212],{},[895,23189,23190,23196,23198,23204,23206],{},[1741,23191,23192,23194],{},[898,23193,1745],{},[898,23195,1798],{},[1654,23197,1750],{},[1741,23199,23200,23202],{},[898,23201,11539],{},[898,23203,1798],{},[1654,23205,1766],{},[1741,23207,23208,23210],{},[898,23209,20896],{},[898,23211,1798],{},[902,23213,23214],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,23217,23219],{"className":23218},[886],[888,23220,23221],{"xmlns":890},[892,23222,23223,23267],{},[895,23224,23225,23231,23233,23239,23245,23247,23253,23259,23261],{},[1741,23226,23227,23229],{},[898,23228,9320],{},[1654,23230,1670],{},[1654,23232,1750],{},[1710,23234,23235,23237],{},[898,23236,21946],{},[1665,23238,1667],{},[1741,23240,23241,23243],{},[898,23242,1745],{},[898,23244,1798],{},[1654,23246,1766],{},[1710,23248,23249,23251],{},[898,23250,21946],{},[1665,23252,1681],{},[1741,23254,23255,23257],{},[898,23256,20753],{},[898,23258,1798],{},[1654,23260,1766],{},[1710,23262,23263,23265],{},[898,23264,21946],{},[1665,23266,4035],{},[902,23268,23269],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,23272,23274],{"id":23273},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,23276,23277],{},"Pro trh zboží jsou dány:",[120,23279,23280,23308],{},[123,23281,23282,23283,1674],{},"spotřeba ",[883,23284,23286],{"className":23285},[886],[888,23287,23288],{"xmlns":890},[892,23289,23290,23305],{},[895,23291,23292,23294,23296,23299,23301,23303],{},[898,23293,11539],{},[1654,23295,1750],{},[1665,23297,23298],{},"0,8",[898,23300,1745],{},[1654,23302,1766],{},[1665,23304,4273],{},[902,23306,23307],{"encoding":904},"C = 0{,}8Y + 100",[123,23309,23310,23311,2138],{},"investice ",[883,23312,23314],{"className":23313},[886],[888,23315,23316],{"xmlns":890},[892,23317,23318,23334],{},[895,23319,23320,23322,23324,23326,23328,23330,23332],{},[898,23321,20896],{},[1654,23323,1750],{},[1654,23325,2380],{},[1665,23327,4573],{},[898,23329,20753],{},[1654,23331,1766],{},[1665,23333,11544],{},[902,23335,23336],{"encoding":904},"I = -20r + 1000",[724,23338,23339],{},"Pro trh peněz:",[120,23341,23342,23368,23400],{},[123,23343,23344,1674],{},[883,23345,23347],{"className":23346},[886],[888,23348,23349],{"xmlns":890},[892,23350,23351,23365],{},[895,23352,23353,23359,23361,23363],{},[1710,23354,23355,23357],{},[898,23356,2450],{},[1665,23358,1667],{},[1654,23360,1750],{},[1665,23362,11555],{},[898,23364,1745],{},[902,23366,23367],{"encoding":904},"L_1 = 0{,}1Y",[123,23369,23370,1674],{},[883,23371,23373],{"className":23372},[886],[888,23374,23375],{"xmlns":890},[892,23376,23377,23397],{},[895,23378,23379,23385,23387,23389,23391,23393,23395],{},[1710,23380,23381,23383],{},[898,23382,2450],{},[1665,23384,1681],{},[1654,23386,1750],{},[1654,23388,2380],{},[1665,23390,4622],{},[898,23392,20753],{},[1654,23394,1766],{},[1665,23396,17329],{},[902,23398,23399],{"encoding":904},"L_2 = -25r + 2000",[123,23401,23402,23403,2138],{},"nabídka peněz ",[883,23404,23406],{"className":23405},[886],[888,23407,23408],{"xmlns":890},[892,23409,23410,23423],{},[895,23411,23412,23418,23420],{},[1741,23413,23414,23416],{},[898,23415,9320],{},[1654,23417,1670],{},[1654,23419,1750],{},[1665,23421,23422],{},"2375",[902,23424,23425],{"encoding":904},"M^* = 2375",[724,23427,23428,23431,23432,2781],{},[38,23429,23430],{},"Funkce IS"," — dosazením do (7.13) ",[883,23433,23435],{"className":23434},[886],[888,23436,23437],{"xmlns":890},[892,23438,23439,23451],{},[895,23440,23441,23443,23445,23447,23449],{},[898,23442,1745],{},[1654,23444,1750],{},[898,23446,11539],{},[1654,23448,1766],{},[898,23450,20896],{},[902,23452,23453],{"encoding":904},"Y = C + I",[724,23455,23456],{},[883,23457,23459],{"className":23458},[886],[888,23460,23461],{"xmlns":890},[892,23462,23463,23489],{},[895,23464,23465,23467,23469,23471,23473,23475,23477,23479,23481,23483,23485,23487],{},[898,23466,1745],{},[1654,23468,1750],{},[1665,23470,23298],{},[898,23472,1745],{},[1654,23474,1766],{},[1665,23476,4273],{},[1654,23478,2380],{},[1665,23480,4573],{},[898,23482,20753],{},[1654,23484,1766],{},[1665,23486,11544],{},[1654,23488,1674],{"separator":1673},[902,23490,23491],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,23493,23494],{},"tj.",[724,23496,23497],{},[883,23498,23500],{"className":23499},[886],[888,23501,23502],{"xmlns":890},[892,23503,23504,23529],{},[895,23505,23506,23508,23510,23512,23514,23516,23518,23521,23523,23525,23527],{},[1665,23507,11599],{},[898,23509,1745],{},[1654,23511,1766],{},[1665,23513,4573],{},[898,23515,20753],{},[1654,23517,1750],{},[1665,23519,23520],{},"1100.",[5008,23522],{"width":14608},[1654,23524,1708],{"stretchy":1656},[1865,23526,20763],{},[1654,23528,1726],{"stretchy":1656},[902,23530,23531],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,23533,23534,23537,23538,2781],{},[38,23535,23536],{},"Funkce LM"," — dosazením do (7.15) ",[883,23539,23541],{"className":23540},[886],[888,23542,23543],{"xmlns":890},[892,23544,23545,23569],{},[895,23546,23547,23553,23555,23561,23563],{},[1741,23548,23549,23551],{},[898,23550,9320],{},[1654,23552,1670],{},[1654,23554,1750],{},[1710,23556,23557,23559],{},[898,23558,2450],{},[1665,23560,1667],{},[1654,23562,1766],{},[1710,23564,23565,23567],{},[898,23566,2450],{},[1665,23568,1681],{},[902,23570,23571],{"encoding":904},"M^* = L_1 + L_2",[724,23573,23574],{},[883,23575,23577],{"className":23576},[886],[888,23578,23579],{"xmlns":890},[892,23580,23581,23603],{},[895,23582,23583,23585,23587,23589,23591,23593,23595,23597,23599,23601],{},[1665,23584,23422],{},[1654,23586,1750],{},[1665,23588,11555],{},[898,23590,1745],{},[1654,23592,2380],{},[1665,23594,4622],{},[898,23596,20753],{},[1654,23598,1766],{},[1665,23600,17329],{},[1654,23602,1674],{"separator":1673},[902,23604,23605],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,23607,23494],{},[724,23609,23610],{},[883,23611,23613],{"className":23612},[886],[888,23614,23615],{"xmlns":890},[892,23616,23617,23642],{},[895,23618,23619,23621,23623,23625,23627,23629,23631,23634,23636,23638,23640],{},[1665,23620,11555],{},[898,23622,1745],{},[1654,23624,2380],{},[1665,23626,4622],{},[898,23628,20753],{},[1654,23630,1750],{},[1665,23632,23633],{},"375.",[5008,23635],{"width":14608},[1654,23637,1708],{"stretchy":1656},[1865,23639,20770],{},[1654,23641,1726],{"stretchy":1656},[902,23643,23644],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,23646,23647,23650,23651,23676],{},[38,23648,23649],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,23652,23654],{"className":23653},[886],[888,23655,23656],{"xmlns":890},[892,23657,23658,23673],{},[895,23659,23660,23662,23664,23667,23669,23671],{},[898,23661,1745],{},[1654,23663,1750],{},[1665,23665,23666],{},"5500",[1654,23668,2380],{},[1665,23670,4273],{},[898,23672,20753],{},[902,23674,23675],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,23678,23679],{},[883,23680,23682],{"className":23681},[886],[888,23683,23684],{"xmlns":890},[892,23685,23686,23772],{},[895,23687,23688,23690,23692,23694,23696,23698,23700,23702,23704,23706,23708,23710,23713,23715,23718,23720,23723,23725,23727,23729,23731,23733,23735,23737,23739,23741,23743,23745,23748,23750,23752,23755,23757,23759,23761,23767,23769],{},[1665,23689,11555],{},[1654,23691,1708],{"stretchy":1656},[1665,23693,23666],{},[1654,23695,2380],{},[1665,23697,4273],{},[898,23699,20753],{},[1654,23701,1726],{"stretchy":1656},[1654,23703,2380],{},[1665,23705,4622],{},[898,23707,20753],{},[1654,23709,1750],{},[1665,23711,23712],{},"375",[1865,23714,2805],{},[1654,23716,23717],{},"⟹",[1865,23719,2805],{},[1665,23721,23722],{},"550",[1654,23724,2380],{},[1665,23726,4647],{},[898,23728,20753],{},[1654,23730,2380],{},[1665,23732,4622],{},[898,23734,20753],{},[1654,23736,1750],{},[1665,23738,23712],{},[1865,23740,2805],{},[1654,23742,23717],{},[1865,23744,2805],{},[1665,23746,23747],{},"35",[898,23749,20753],{},[1654,23751,1750],{},[1665,23753,23754],{},"175",[1865,23756,2805],{},[1654,23758,23717],{},[1865,23760,2805],{},[1741,23762,23763,23765],{},[898,23764,20753],{},[898,23766,1798],{},[1654,23768,1750],{},[1665,23770,23771],{},"5.",[902,23773,23774],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,23776,23777],{},[38,23778,23779],{},"Zpětné dosazení:",[120,23781,23782,23827,23864],{},[123,23783,23784,1674],{},[883,23785,23787],{"className":23786},[886],[888,23788,23789],{"xmlns":890},[892,23790,23791,23824],{},[895,23792,23793,23799,23801,23803,23805,23807,23809,23811,23813,23815,23817,23819,23821],{},[1741,23794,23795,23797],{},[898,23796,1745],{},[898,23798,1798],{},[1654,23800,1750],{},[1665,23802,23666],{},[1654,23804,2380],{},[1665,23806,4273],{},[1654,23808,4554],{},[1665,23810,4032],{},[1654,23812,1750],{},[1665,23814,23666],{},[1654,23816,2380],{},[1665,23818,4011],{},[1654,23820,1750],{},[1665,23822,23823],{},"5000",[902,23825,23826],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,23828,23829,1674],{},[883,23830,23832],{"className":23831},[886],[888,23833,23834],{"xmlns":890},[892,23835,23836,23861],{},[895,23837,23838,23844,23846,23848,23850,23852,23854,23856,23858],{},[1741,23839,23840,23842],{},[898,23841,11539],{},[898,23843,1798],{},[1654,23845,1750],{},[1665,23847,23298],{},[1654,23849,4554],{},[1665,23851,23823],{},[1654,23853,1766],{},[1665,23855,4273],{},[1654,23857,1750],{},[1665,23859,23860],{},"4100",[902,23862,23863],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,23865,23866,2138],{},[883,23867,23869],{"className":23868},[886],[888,23870,23871],{"xmlns":890},[892,23872,23873,23900],{},[895,23874,23875,23881,23883,23885,23887,23889,23891,23893,23895,23897],{},[1741,23876,23877,23879],{},[898,23878,20896],{},[898,23880,1798],{},[1654,23882,1750],{},[1654,23884,2380],{},[1665,23886,4573],{},[1654,23888,4554],{},[1665,23890,4032],{},[1654,23892,1766],{},[1665,23894,11544],{},[1654,23896,1750],{},[1665,23898,23899],{},"900",[902,23901,23902],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,23904,23905,2186,23908,23954],{},[38,23906,23907],{},"Ověření:",[883,23909,23911],{"className":23910},[886],[888,23912,23913],{"xmlns":890},[892,23914,23915,23951],{},[895,23916,23917,23923,23925,23931,23933,23935,23937,23939,23941,23943,23945],{},[1741,23918,23919,23921],{},[898,23920,11539],{},[898,23922,1798],{},[1654,23924,1766],{},[1741,23926,23927,23929],{},[898,23928,20896],{},[898,23930,1798],{},[1654,23932,1750],{},[1665,23934,23860],{},[1654,23936,1766],{},[1665,23938,23899],{},[1654,23940,1750],{},[1665,23942,23823],{},[1654,23944,1750],{},[1741,23946,23947,23949],{},[898,23948,1745],{},[898,23950,1798],{},[902,23952,23953],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,23956,23957],{},[883,23958,23960],{"className":23959},[886],[888,23961,23962],{"xmlns":890},[892,23963,23964,24033],{},[895,23965,23966],{},[2792,23967,23968],{"notation":2794},[2582,23969,23970],{"scriptlevel":2062,"displaystyle":1656},[2582,23971,23972],{"scriptlevel":2062,"displaystyle":1656},[2582,23973,23974],{"scriptlevel":2062,"displaystyle":1673},[895,23975,23976,23978,23984,23986,23988,23990,23992,23998,24000,24002,24004,24006,24012,24014,24016,24018,24020,24026,24028,24031],{},[1865,23977,11744],{},[1741,23979,23980,23982],{},[898,23981,1745],{},[898,23983,1798],{},[1654,23985,1750],{},[1665,23987,23823],{},[1654,23989,1674],{"separator":1673},[5008,23991],{"width":5010},[1741,23993,23994,23996],{},[898,23995,20753],{},[898,23997,1798],{},[1654,23999,1750],{},[1665,24001,4032],{},[1654,24003,1674],{"separator":1673},[5008,24005],{"width":5010},[1741,24007,24008,24010],{},[898,24009,11539],{},[898,24011,1798],{},[1654,24013,1750],{},[1665,24015,23860],{},[1654,24017,1674],{"separator":1673},[5008,24019],{"width":5010},[1741,24021,24022,24024],{},[898,24023,20896],{},[898,24025,1798],{},[1654,24027,1750],{},[1665,24029,24030],{},"900.",[1865,24032,11744],{},[902,24034,24035],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,24037,24038],{},[614,24039,24040,24041,24054,24055,24068,24069,24084,24085,24098,24099,24114,24115,24128,24129,24142,24143,2138],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,24042,24044],{"className":24043},[886],[888,24045,24046],{"xmlns":890},[892,24047,24048,24052],{},[895,24049,24050],{},[898,24051,1745],{},[902,24053,1745],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,24056,24058],{"className":24057},[886],[888,24059,24060],{"xmlns":890},[892,24061,24062,24066],{},[895,24063,24064],{},[898,24065,20753],{},[902,24067,20753],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,24070,24072],{"className":24071},[886],[888,24073,24074],{"xmlns":890},[892,24075,24076,24082],{},[895,24077,24078,24080],{},[898,24079,2450],{},[898,24081,9320],{},[902,24083,20770],{"encoding":904}," stoupá z oblasti nízkých ",[883,24086,24088],{"className":24087},[886],[888,24089,24090],{"xmlns":890},[892,24091,24092,24096],{},[895,24093,24094],{},[898,24095,20753],{},[902,24097,20753],{"encoding":904},", přímka ",[883,24100,24102],{"className":24101},[886],[888,24103,24104],{"xmlns":890},[892,24105,24106,24112],{},[895,24107,24108,24110],{},[898,24109,20896],{},[898,24111,17398],{},[902,24113,20763],{"encoding":904}," klesá a protíná osu ",[883,24116,24118],{"className":24117},[886],[888,24119,24120],{"xmlns":890},[892,24121,24122,24126],{},[895,24123,24124],{},[898,24125,20753],{},[902,24127,20753],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,24130,24132],{"className":24131},[886],[888,24133,24134],{"xmlns":890},[892,24135,24136,24140],{},[895,24137,24138],{},[898,24139,1798],{},[902,24141,1798],{"encoding":904}," leží v bodě ",[883,24144,24146],{"className":24145},[886],[888,24147,24148],{"xmlns":890},[892,24149,24150,24172],{},[895,24151,24152,24154,24156,24158,24160,24162,24164,24166,24168,24170],{},[1654,24153,1657],{"stretchy":1656},[898,24155,20753],{},[1654,24157,1750],{},[1665,24159,4032],{},[1654,24161,1674],{"separator":1673},[1865,24163,11065],{},[898,24165,1745],{},[1654,24167,1750],{},[1665,24169,23823],{},[1654,24171,1686],{"stretchy":1656},[902,24173,24174],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,24176,24178],{"id":24177},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,24180,24181,24184,24185,24198,24199,10373,24212,24215,24216,24234,24235,24252,24253,24270,24271,24284,24285,24298],{},[38,24182,24183],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,24186,24188],{"className":24187},[886],[888,24189,24190],{"xmlns":890},[892,24191,24192,24196],{},[895,24193,24194],{},[898,24195,20824],{},[902,24197,20824],{"encoding":904}," nebo snížení daní ",[883,24200,24202],{"className":24201},[886],[888,24203,24204],{"xmlns":890},[892,24205,24206,24210],{},[895,24207,24208],{},[898,24209,11536],{},[902,24211,11536],{"encoding":904},[38,24213,24214],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,24217,24219],{"className":24218},[886],[888,24220,24221],{"xmlns":890},[892,24222,24223,24231],{},[895,24224,24225],{},[1741,24226,24227,24229],{},[898,24228,1798],{},[1654,24230,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,24232,24233],{"encoding":904},"E'"," má vyšší ",[883,24236,24238],{"className":24237},[886],[888,24239,24240],{"xmlns":890},[892,24241,24242,24250],{},[895,24243,24244],{},[1741,24245,24246,24248],{},[898,24247,1745],{},[898,24249,1798],{},[902,24251,22612],{"encoding":904}," i vyšší ",[883,24254,24256],{"className":24255},[886],[888,24257,24258],{"xmlns":890},[892,24259,24260,24268],{},[895,24261,24262],{},[1741,24263,24264,24266],{},[898,24265,20753],{},[898,24267,1798],{},[902,24269,22633],{"encoding":904}," (vyšší ",[883,24272,24274],{"className":24273},[886],[888,24275,24276],{"xmlns":890},[892,24277,24278,24282],{},[895,24279,24280],{},[898,24281,1745],{},[902,24283,1745],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,24286,24288],{"className":24287},[886],[888,24289,24290],{"xmlns":890},[892,24291,24292,24296],{},[895,24293,24294],{},[898,24295,20753],{},[902,24297,20753],{"encoding":904}," nahoru).",[724,24300,24301],{},[3492,24302],{"alt":24303,"className":24304,"src":24305},"imek-posun-is-lm-politiky",[210,3496],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,24307,24308,24311,24312,24329,24330,24333,24334,24351,24352,24369,24370,24383,24384,24403,24404,12664],{},[38,24309,24310],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,24313,24315],{"className":24314},[886],[888,24316,24317],{"xmlns":890},[892,24318,24319,24327],{},[895,24320,24321],{},[1741,24322,24323,24325],{},[898,24324,9320],{},[1654,24326,1670],{},[902,24328,20862],{"encoding":904}," národní bankou — ",[38,24331,24332],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,24335,24337],{"className":24336},[886],[888,24338,24339],{"xmlns":890},[892,24340,24341,24349],{},[895,24342,24343],{},[1741,24344,24345,24347],{},[898,24346,20753],{},[898,24348,1798],{},[902,24350,22633],{"encoding":904}," a vyšší ",[883,24353,24355],{"className":24354},[886],[888,24356,24357],{"xmlns":890},[892,24358,24359,24367],{},[895,24360,24361],{},[1741,24362,24363,24365],{},[898,24364,1745],{},[898,24366,1798],{},[902,24368,22612],{"encoding":904}," (nižší ",[883,24371,24373],{"className":24372},[886],[888,24374,24375],{"xmlns":890},[892,24376,24377,24381],{},[895,24378,24379],{},[898,24380,20753],{},[902,24382,20753],{"encoding":904}," povzbuzuje investice ",[883,24385,24387],{"className":24386},[886],[888,24388,24389],{"xmlns":890},[892,24390,24391,24401],{},[895,24392,24393,24395,24397,24399],{},[898,24394,20896],{},[1654,24396,1708],{"stretchy":1656},[898,24398,20753],{},[1654,24400,1726],{"stretchy":1656},[902,24402,22945],{"encoding":904},", ty zvedají ",[883,24405,24407],{"className":24406},[886],[888,24408,24409],{"xmlns":890},[892,24410,24411,24415],{},[895,24412,24413],{},[898,24414,1745],{},[902,24416,1745],{"encoding":904},[724,24418,24419,24420,24423],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,24421,24422],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,24425,10214],{"id":10213},[120,24427,24428,24501,24547,24629,24679,24746,24803,24844,24877],{},[123,24429,24430,10373,24463,1343,24480,24497,24498,24500],{},[38,24431,24432,24433],{},"Funkce investic ",[883,24434,24436],{"className":24435},[886],[888,24437,24438],{"xmlns":890},[892,24439,24440,24460],{},[895,24441,24442,24444,24446,24448,24450,24452,24454,24456,24458],{},[898,24443,20896],{},[1654,24445,1708],{"stretchy":1656},[898,24447,20753],{},[1654,24449,1726],{"stretchy":1656},[1654,24451,1750],{},[898,24453,3624],{},[898,24455,20753],{},[1654,24457,1766],{},[898,24459,10977],{},[902,24461,24462],{"encoding":904},"I(r) = cr + d",[883,24464,24466],{"className":24465},[886],[888,24467,24468],{"xmlns":890},[892,24469,24470,24478],{},[895,24471,24472,24474,24476],{},[898,24473,3624],{},[1654,24475,3002],{},[1665,24477,2062],{},[902,24479,21226],{"encoding":904},[883,24481,24483],{"className":24482},[886],[888,24484,24485],{"xmlns":890},[892,24486,24487,24495],{},[895,24488,24489,24491,24493],{},[898,24490,10977],{},[1654,24492,2952],{},[1665,24494,2062],{},[902,24496,21205],{"encoding":904},"; ",[38,24499,21230],{}," funkce úrokové míry.",[123,24502,24503,24506,24507,24528,24529,24546],{},[38,24504,24505],{},"Trh zboží"," — rovnováha ",[883,24508,24510],{"className":24509},[886],[888,24511,24512],{"xmlns":890},[892,24513,24514,24526],{},[895,24515,24516,24518,24520,24522,24524],{},[898,24517,1745],{},[1654,24519,1750],{},[898,24521,11539],{},[1654,24523,1766],{},[898,24525,20896],{},[902,24527,23453],{"encoding":904},", ekvivalentně ",[883,24530,24532],{"className":24531},[886],[888,24533,24534],{"xmlns":890},[892,24535,24536,24544],{},[895,24537,24538,24540,24542],{},[898,24539,20896],{},[1654,24541,1750],{},[898,24543,17398],{},[902,24545,21423],{"encoding":904}," (investice = úspory).",[123,24548,24549,18742,24552,24554,24555,24605,24606,21624,24608,2138],{},[38,24550,24551],{},"Křivka IS",[614,24553,20766],{},") — ",[883,24556,24558],{"className":24557},[886],[888,24559,24560],{"xmlns":890},[892,24561,24562,24602],{},[895,24563,24564,24566,24568,24580,24582,24584],{},[898,24565,1745],{},[1654,24567,1750],{},[2811,24569,24570,24572],{},[898,24571,3624],{},[895,24573,24574,24576,24578],{},[1665,24575,1667],{},[1654,24577,2380],{},[898,24579,207],{},[898,24581,20753],{},[1654,24583,1766],{},[2811,24585,24586,24594],{},[895,24587,24588,24590,24592],{},[898,24589,9758],{},[1654,24591,1766],{},[898,24593,10977],{},[895,24595,24596,24598,24600],{},[1665,24597,1667],{},[1654,24599,2380],{},[898,24601,207],{},[902,24603,24604],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,24607,21230],{},[883,24609,24611],{"className":24610},[886],[888,24612,24613],{"xmlns":890},[892,24614,24615,24627],{},[895,24616,24617,24619,24621,24623,24625],{},[1654,24618,1708],{"stretchy":1656},[898,24620,20753],{},[1654,24622,1674],{"separator":1673},[898,24624,1745],{},[1654,24626,1726],{"stretchy":1656},[902,24628,21646],{"encoding":904},[123,24630,24631,24506,24634,24660,24661,2138],{},[38,24632,24633],{},"Trh peněz",[883,24635,24637],{"className":24636},[886],[888,24638,24639],{"xmlns":890},[892,24640,24641,24657],{},[895,24642,24643,24649,24651],{},[1741,24644,24645,24647],{},[898,24646,9320],{},[898,24648,4980],{},[1654,24650,1750],{},[1741,24652,24653,24655],{},[898,24654,9320],{},[898,24656,17398],{},[902,24658,24659],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,24662,24664],{"className":24663},[886],[888,24665,24666],{"xmlns":890},[892,24667,24668,24676],{},[895,24669,24670],{},[1741,24671,24672,24674],{},[898,24673,9320],{},[1654,24675,1670],{},[902,24677,24678],{"encoding":904},"M^* ",[123,24680,24681,10373,24684,2138],{},[38,24682,24683],{},"Transakční, opatrnostní, spekulační poptávka",[883,24685,24687],{"className":24686},[886],[888,24688,24689],{"xmlns":890},[892,24690,24691,24743],{},[895,24692,24693,24699,24701,24707,24709,24715,24717,24723,24725,24727,24733,24735,24737],{},[1741,24694,24695,24697],{},[898,24696,9320],{},[898,24698,4980],{},[1654,24700,1750],{},[1710,24702,24703,24705],{},[898,24704,2450],{},[1665,24706,1667],{},[1654,24708,1766],{},[1710,24710,24711,24713],{},[898,24712,2450],{},[1665,24714,1681],{},[1654,24716,1750],{},[1710,24718,24719,24721],{},[898,24720,21946],{},[1665,24722,1667],{},[898,24724,1745],{},[1654,24726,1766],{},[1710,24728,24729,24731],{},[898,24730,21946],{},[1665,24732,1681],{},[898,24734,20753],{},[1654,24736,1766],{},[1710,24738,24739,24741],{},[898,24740,21946],{},[1665,24742,4035],{},[902,24744,24745],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,24747,24748,18742,24751,24554,24753,24799,24800,24802],{},[38,24749,24750],{},"Křivka LM",[614,24752,20773],{},[883,24754,24756],{"className":24755},[886],[888,24757,24758],{"xmlns":890},[892,24759,24760,24796],{},[895,24761,24762,24768,24770,24776,24778,24780,24786,24788,24790],{},[1741,24763,24764,24766],{},[898,24765,9320],{},[1654,24767,1670],{},[1654,24769,1750],{},[1710,24771,24772,24774],{},[898,24773,21946],{},[1665,24775,1667],{},[898,24777,1745],{},[1654,24779,1766],{},[1710,24781,24782,24784],{},[898,24783,21946],{},[1665,24785,1681],{},[898,24787,20753],{},[1654,24789,1766],{},[1710,24791,24792,24794],{},[898,24793,21946],{},[1665,24795,4035],{},[902,24797,24798],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,24801,22366],{}," přímka.",[123,24804,24805,24808,24809,24843],{},[38,24806,24807],{},"Simultánní rovnováha"," — průsečík ",[883,24810,24812],{"className":24811},[886],[888,24813,24814],{"xmlns":890},[892,24815,24816,24840],{},[895,24817,24818,24820,24822,24824,24830,24832,24838],{},[898,24819,1798],{},[1654,24821,1750],{},[1654,24823,1708],{"stretchy":1656},[1741,24825,24826,24828],{},[898,24827,20753],{},[898,24829,1798],{},[1654,24831,1674],{"separator":1673},[1741,24833,24834,24836],{},[898,24835,1745],{},[898,24837,1798],{},[1654,24839,1726],{"stretchy":1656},[902,24841,24842],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,24845,24846,24849,24850,1343,24863,24876],{},[38,24847,24848],{},"Fiskální politika"," — nástroje ",[883,24851,24853],{"className":24852},[886],[888,24854,24855],{"xmlns":890},[892,24856,24857,24861],{},[895,24858,24859],{},[898,24860,20824],{},[902,24862,20824],{"encoding":904},[883,24864,24866],{"className":24865},[886],[888,24867,24868],{"xmlns":890},[892,24869,24870,24874],{},[895,24871,24872],{},[898,24873,11536],{},[902,24875,11536],{"encoding":904}," posouvající křivku IS.",[123,24878,24879,24882,24883,24900],{},[38,24880,24881],{},"Monetární politika"," — nástroj ",[883,24884,24886],{"className":24885},[886],[888,24887,24888],{"xmlns":890},[892,24889,24890,24898],{},[895,24891,24892],{},[1741,24893,24894,24896],{},[898,24895,9320],{},[1654,24897,1670],{},[902,24899,20862],{"encoding":904}," posouvající křivku LM.",[115,24902,10613],{"id":10612},[120,24904,24905,24912,24921,24931],{},[123,24906,24907,2186,24909],{},[38,24908,10686],{},[207,24910,10692],{"className":24911,"dataFsResolvedFilePath":10690,"href":10691},[210],[123,24913,24914,2186,24917],{},[38,24915,24916],{},"Přednáška:",[207,24918,24920],{"className":24919,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,24922,24923,2186,24926,24930],{},[38,24924,24925],{},"Nadřazené téma:",[207,24927,24929],{"className":24928,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,24932,24933,24936],{},[38,24934,24935],{},"Související:",[120,24937,24938,24945,24951],{},[123,24939,24940,24944],{},[207,24941,24943],{"className":24942,"dataFsResolvedFilePath":800,"href":801},[210],"poptavka-nabidka"," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,24946,24947,24950],{},[207,24948,1145],{"className":24949,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,24952,24953,24957],{},[207,24954,24956],{"className":24955,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":24959},[24960,24961,24962,24963,24964,24965,24966,24967,24968,24969],{"id":1637,"depth":642,"text":1638},{"id":20872,"depth":642,"text":20873},{"id":21087,"depth":642,"text":21088},{"id":21379,"depth":642,"text":21380},{"id":21790,"depth":642,"text":21791},{"id":22583,"depth":642,"text":22584},{"id":23273,"depth":642,"text":23274},{"id":24177,"depth":642,"text":24178},{"id":10213,"depth":642,"text":10214},{"id":10612,"depth":642,"text":10613},{},"\u002Ftopics\u002Fis-lm",{"title":20711,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,24976,1143,24977,24978,24979,24980,24929],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":24983,"title":24984,"body":24985,"course":659,"courses":26570,"created":1129,"description":26571,"extension":661,"meta":26572,"navigation":664,"path":26573,"seo":26574,"sources":26575,"stem":26576,"tags":26577,"type":10736,"updated":677,"__hash__":26580},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":24986,"toc":26558},[24987,24990,25085,25092,25112,25116,25121,25183,25201,25203,25206,25342,25344,25554,25588,25725,25729,25793,25809,25837,25841,25939,25943,25947,25999,26105,26318,26322,26364,26470,26520,26522],[12,24988,24984],{"id":24989},"lagrangeova-metoda-vázané-extrémy",[724,24991,24992,24993,12656,25016,25047,25048,25051,25052,25079,25080,25084],{},"Hledáme extrém funkce ",[883,24994,24996],{"className":24995},[886],[888,24997,24998],{"xmlns":890},[892,24999,25000,25014],{},[895,25001,25002,25004,25006,25008,25010,25012],{},[898,25003,10794],{},[1654,25005,1708],{"stretchy":1656},[898,25007,10799],{},[1654,25009,1674],{"separator":1673},[898,25011,10789],{},[1654,25013,1726],{"stretchy":1656},[902,25015,18560],{"encoding":904},[883,25017,25019],{"className":25018},[886],[888,25020,25021],{"xmlns":890},[892,25022,25023,25045],{},[895,25024,25025,25027,25029,25035,25037,25043],{},[898,25026,900],{},[1654,25028,1708],{"stretchy":1656},[1710,25030,25031,25033],{},[898,25032,1663],{},[1665,25034,1667],{},[1654,25036,1674],{"separator":1673},[1710,25038,25039,25041],{},[898,25040,1663],{},[1665,25042,1681],{},[1654,25044,1726],{"stretchy":1656},[902,25046,1729],{"encoding":904}," apod.) ",[38,25049,25050],{},"podmíněný"," rovnicí ",[883,25053,25055],{"className":25054},[886],[888,25056,25057],{"xmlns":890},[892,25058,25059,25077],{},[895,25060,25061,25063,25065,25067,25069,25071,25073,25075],{},[898,25062,2351],{},[1654,25064,1708],{"stretchy":1656},[898,25066,10799],{},[1654,25068,1674],{"separator":1673},[898,25070,10789],{},[1654,25072,1726],{"stretchy":1656},[1654,25074,1750],{},[1665,25076,2062],{},[902,25078,19772],{"encoding":904},". V ",[207,25081,25083],{"className":25082,"dataFsResolvedFilePath":10690,"href":10691},[210],"matematické ekonomii"," se používá pro:",[724,25086,25087],{},[3492,25088],{"alt":25089,"className":25090,"src":25091},"imek-lagrange-tecnost",[210,3496],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,25093,25094,25103,25109],{},[123,25095,25096,25099,25100,1726],{},[38,25097,25098],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,25101,10732],{"className":25102,"dataFsResolvedFilePath":878,"href":879},[210],[123,25104,25105,25108],{},[38,25106,25107],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,25110,25111],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,25113,25115],{"id":25114},"princip","Princip",[724,25117,19422,25118,2781],{},[38,25119,25120],{},"Lagrangeovu funkci",[724,25122,25123],{},[883,25124,25126],{"className":25125},[886],[888,25127,25128],{"xmlns":890},[892,25129,25130,25180],{},[895,25131,25132,25134,25136,25138,25140,25142,25144,25146,25148,25150,25152,25154,25156,25158,25160,25162,25164,25166,25168,25170,25172,25174,25176,25178],{},[898,25133,2450],{},[1654,25135,1708],{"stretchy":1656},[898,25137,10799],{},[1654,25139,1674],{"separator":1673},[898,25141,10789],{},[1654,25143,1674],{"separator":1673},[898,25145,2471],{},[1654,25147,1726],{"stretchy":1656},[1654,25149,1750],{},[898,25151,10794],{},[1654,25153,1708],{"stretchy":1656},[898,25155,10799],{},[1654,25157,1674],{"separator":1673},[898,25159,10789],{},[1654,25161,1726],{"stretchy":1656},[1654,25163,1766],{},[898,25165,2471],{},[1865,25167,11744],{},[898,25169,2351],{},[1654,25171,1708],{"stretchy":1656},[898,25173,10799],{},[1654,25175,1674],{"separator":1673},[898,25177,10789],{},[1654,25179,1726],{"stretchy":1656},[902,25181,25182],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,25184,13049,25185,16828,25198,2138],{},[883,25186,25188],{"className":25187},[886],[888,25189,25190],{"xmlns":890},[892,25191,25192,25196],{},[895,25193,25194],{},[898,25195,2471],{},[902,25197,2776],{"encoding":904},[38,25199,25200],{},"Lagrangeův multiplikátor",[115,25202,12006],{"id":12005},[724,25204,25205],{},"Řešíme soustavu:",[724,25207,25208,25256,25304],{},[883,25209,25211],{"className":25210},[886],[888,25212,25213],{"xmlns":890},[892,25214,25215,25253],{},[895,25216,25217,25225,25227,25235,25237,25239,25241,25249,25251],{},[1659,25218,25219,25221,25223],{},[898,25220,2450],{},[898,25222,10799],{},[1654,25224,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,25226,1750],{},[1659,25228,25229,25231,25233],{},[898,25230,10794],{},[898,25232,10799],{},[1654,25234,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,25236,1766],{},[898,25238,2471],{},[1865,25240,11744],{},[1659,25242,25243,25245,25247],{},[898,25244,2351],{},[898,25246,10799],{},[1654,25248,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,25250,1750],{},[1665,25252,2062],{},[902,25254,25255],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,25257,25259],{"className":25258},[886],[888,25260,25261],{"xmlns":890},[892,25262,25263,25301],{},[895,25264,25265,25273,25275,25283,25285,25287,25289,25297,25299],{},[1659,25266,25267,25269,25271],{},[898,25268,2450],{},[898,25270,10789],{},[1654,25272,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,25274,1750],{},[1659,25276,25277,25279,25281],{},[898,25278,10794],{},[898,25280,10789],{},[1654,25282,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,25284,1766],{},[898,25286,2471],{},[1865,25288,11744],{},[1659,25290,25291,25293,25295],{},[898,25292,2351],{},[898,25294,10789],{},[1654,25296,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,25298,1750],{},[1665,25300,2062],{},[902,25302,25303],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,25305,25307],{"className":25306},[886],[888,25308,25309],{"xmlns":890},[892,25310,25311,25339],{},[895,25312,25313,25321,25323,25325,25327,25329,25331,25333,25335,25337],{},[1659,25314,25315,25317,25319],{},[898,25316,2450],{},[898,25318,2471],{},[1654,25320,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,25322,1750],{},[898,25324,2351],{},[1654,25326,1708],{"stretchy":1656},[898,25328,10799],{},[1654,25330,1674],{"separator":1673},[898,25332,10789],{},[1654,25334,1726],{"stretchy":1656},[1654,25336,1750],{},[1665,25338,2062],{},[902,25340,25341],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,25343,12080],{"id":12079},[724,25345,25346],{},[883,25347,25349],{"className":25348},[886],[888,25350,25351],{"xmlns":890},[892,25352,25353,25551],{},[895,25354,25355,25357,25359,25361,25363,25365,25367,25369,25371,25373,25375,25391,25393,25395,25411,25413,25415,25423,25429,25431,25433,25449,25451,25453,25469,25471,25473,25481,25487,25489,25491,25493,25509,25511,25513,25529,25531,25533,25541,25543],{},[898,25356,4980],{},[1654,25358,1708],{"stretchy":1656},[898,25360,10799],{},[1654,25362,1674],{"separator":1673},[898,25364,10789],{},[1654,25366,1674],{"separator":1673},[898,25368,2471],{},[1654,25370,1726],{"stretchy":1656},[1654,25372,1750],{},[1654,25374,1708],{"stretchy":1656},[1659,25376,25377,25379,25385],{},[898,25378,10794],{},[895,25380,25381,25383],{},[898,25382,10799],{},[898,25384,10799],{},[895,25386,25387,25389],{},[1654,25388,2592],{"mathvariant":1878},[1654,25390,2592],{"mathvariant":1878},[1654,25392,1766],{},[898,25394,2471],{},[1659,25396,25397,25399,25405],{},[898,25398,2351],{},[895,25400,25401,25403],{},[898,25402,10799],{},[898,25404,10799],{},[895,25406,25407,25409],{},[1654,25408,2592],{"mathvariant":1878},[1654,25410,2592],{"mathvariant":1878},[1654,25412,1726],{"stretchy":1656},[1654,25414,1708],{"stretchy":1656},[1659,25416,25417,25419,25421],{},[898,25418,2351],{},[898,25420,10789],{},[1654,25422,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1741,25424,25425,25427],{},[1654,25426,1726],{"stretchy":1656},[1665,25428,1681],{},[1654,25430,1766],{},[1654,25432,1708],{"stretchy":1656},[1659,25434,25435,25437,25443],{},[898,25436,10794],{},[895,25438,25439,25441],{},[898,25440,10789],{},[898,25442,10789],{},[895,25444,25445,25447],{},[1654,25446,2592],{"mathvariant":1878},[1654,25448,2592],{"mathvariant":1878},[1654,25450,1766],{},[898,25452,2471],{},[1659,25454,25455,25457,25463],{},[898,25456,2351],{},[895,25458,25459,25461],{},[898,25460,10789],{},[898,25462,10789],{},[895,25464,25465,25467],{},[1654,25466,2592],{"mathvariant":1878},[1654,25468,2592],{"mathvariant":1878},[1654,25470,1726],{"stretchy":1656},[1654,25472,1708],{"stretchy":1656},[1659,25474,25475,25477,25479],{},[898,25476,2351],{},[898,25478,10799],{},[1654,25480,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1741,25482,25483,25485],{},[1654,25484,1726],{"stretchy":1656},[1665,25486,1681],{},[1654,25488,2380],{},[1665,25490,1681],{},[1654,25492,1708],{"stretchy":1656},[1659,25494,25495,25497,25503],{},[898,25496,10794],{},[895,25498,25499,25501],{},[898,25500,10799],{},[898,25502,10789],{},[895,25504,25505,25507],{},[1654,25506,2592],{"mathvariant":1878},[1654,25508,2592],{"mathvariant":1878},[1654,25510,1766],{},[898,25512,2471],{},[1659,25514,25515,25517,25523],{},[898,25516,2351],{},[895,25518,25519,25521],{},[898,25520,10799],{},[898,25522,10789],{},[895,25524,25525,25527],{},[1654,25526,2592],{"mathvariant":1878},[1654,25528,2592],{"mathvariant":1878},[1654,25530,1726],{"stretchy":1656},[1865,25532,11744],{},[1659,25534,25535,25537,25539],{},[898,25536,2351],{},[898,25538,10799],{},[1654,25540,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1865,25542,11744],{},[1659,25544,25545,25547,25549],{},[898,25546,2351],{},[898,25548,10789],{},[1654,25550,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,25552,25553],{"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",[724,25555,25556,25557,25587],{},"Je-li ",[883,25558,25560],{"className":25559},[886],[888,25561,25562],{"xmlns":890},[892,25563,25564,25584],{},[895,25565,25566,25568,25570,25572,25574,25576,25582],{},[1654,25567,1657],{"stretchy":1656},[898,25569,207],{},[1654,25571,1674],{"separator":1673},[898,25573,9758],{},[1654,25575,1674],{"separator":1673},[1710,25577,25578,25580],{},[898,25579,2471],{},[1665,25581,2062],{},[1654,25583,1686],{"stretchy":1656},[902,25585,25586],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,25589,25590,25658],{},[123,25591,25592,12166,25628,25630,25631],{},[883,25593,25595],{"className":25594},[886],[888,25596,25597],{"xmlns":890},[892,25598,25599,25625],{},[895,25600,25601,25603,25605,25607,25609,25611,25613,25619,25621,25623],{},[898,25602,4980],{},[1654,25604,1708],{"stretchy":1656},[898,25606,207],{},[1654,25608,1674],{"separator":1673},[898,25610,9758],{},[1654,25612,1674],{"separator":1673},[1710,25614,25615,25617],{},[898,25616,2471],{},[1665,25618,2062],{},[1654,25620,1726],{"stretchy":1656},[1654,25622,3002],{},[1665,25624,2062],{},[902,25626,25627],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,25629,12467],{}," vázané podmínkou ",[883,25632,25634],{"className":25633},[886],[888,25635,25636],{"xmlns":890},[892,25637,25638,25656],{},[895,25639,25640,25642,25644,25646,25648,25650,25652,25654],{},[898,25641,2351],{},[1654,25643,1708],{"stretchy":1656},[898,25645,10799],{},[1654,25647,1674],{"separator":1673},[898,25649,10789],{},[1654,25651,1726],{"stretchy":1656},[1654,25653,1750],{},[1665,25655,2062],{},[902,25657,19772],{"encoding":904},[123,25659,25660,12166,25696,25630,25698],{},[883,25661,25663],{"className":25662},[886],[888,25664,25665],{"xmlns":890},[892,25666,25667,25693],{},[895,25668,25669,25671,25673,25675,25677,25679,25681,25687,25689,25691],{},[898,25670,4980],{},[1654,25672,1708],{"stretchy":1656},[898,25674,207],{},[1654,25676,1674],{"separator":1673},[898,25678,9758],{},[1654,25680,1674],{"separator":1673},[1710,25682,25683,25685],{},[898,25684,2471],{},[1665,25686,2062],{},[1654,25688,1726],{"stretchy":1656},[1654,25690,2952],{},[1665,25692,2062],{},[902,25694,25695],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,25697,7988],{},[883,25699,25701],{"className":25700},[886],[888,25702,25703],{"xmlns":890},[892,25704,25705,25723],{},[895,25706,25707,25709,25711,25713,25715,25717,25719,25721],{},[898,25708,2351],{},[1654,25710,1708],{"stretchy":1656},[898,25712,10799],{},[1654,25714,1674],{"separator":1673},[898,25716,10789],{},[1654,25718,1726],{"stretchy":1656},[1654,25720,1750],{},[1665,25722,2062],{},[902,25724,19772],{"encoding":904},[115,25726,25728],{"id":25727},"význam-multiplikátoru","Význam multiplikátoru",[724,25730,25731],{},[883,25732,25734],{"className":25733},[886],[888,25735,25736],{"xmlns":890},[892,25737,25738,25790],{},[895,25739,25740,25742,25744,25766,25768],{},[898,25741,2471],{},[1654,25743,1750],{},[2811,25745,25746,25754],{},[1659,25747,25748,25750,25752],{},[898,25749,10794],{},[898,25751,10799],{},[1654,25753,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[895,25755,25756,25758],{},[1654,25757,2380],{},[1659,25759,25760,25762,25764],{},[898,25761,2351],{},[898,25763,10799],{},[1654,25765,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,25767,1750],{},[2811,25769,25770,25778],{},[1659,25771,25772,25774,25776],{},[898,25773,10794],{},[898,25775,10789],{},[1654,25777,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[895,25779,25780,25782],{},[1654,25781,2380],{},[1659,25783,25784,25786,25788],{},[898,25785,2351],{},[898,25787,10789],{},[1654,25789,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,25791,25792],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,25794,25795,25808],{},[883,25796,25798],{"className":25797},[886],[888,25799,25800],{"xmlns":890},[892,25801,25802,25806],{},[895,25803,25804],{},[898,25805,2471],{},[902,25807,2776],{"encoding":904}," udává:",[120,25810,25811,25817],{},[123,25812,25813,25814],{},"konstantní ",[38,25815,25816],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,25818,25819,25822,25823,25836],{},[38,25820,25821],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,25824,25826],{"className":25825},[886],[888,25827,25828],{"xmlns":890},[892,25829,25830,25834],{},[895,25831,25832],{},[898,25833,10794],{},[902,25835,10794],{"encoding":904},", uvolní-li se omezení o jednotku",[115,25838,25840],{"id":25839},"alternativní-postup","Alternativní postup",[724,25842,25843,25844,25871,25872,25896,25897,25921,25922,25935,25936,2138],{},"Lze-li z ",[883,25845,25847],{"className":25846},[886],[888,25848,25849],{"xmlns":890},[892,25850,25851,25869],{},[895,25852,25853,25855,25857,25859,25861,25863,25865,25867],{},[898,25854,2351],{},[1654,25856,1708],{"stretchy":1656},[898,25858,10799],{},[1654,25860,1674],{"separator":1673},[898,25862,10789],{},[1654,25864,1726],{"stretchy":1656},[1654,25866,1750],{},[1665,25868,2062],{},[902,25870,19772],{"encoding":904}," vyjádřit ",[883,25873,25875],{"className":25874},[886],[888,25876,25877],{"xmlns":890},[892,25878,25879,25893],{},[895,25880,25881,25883,25885,25887,25889,25891],{},[898,25882,10789],{},[1654,25884,1750],{},[898,25886,10789],{},[1654,25888,1708],{"stretchy":1656},[898,25890,10799],{},[1654,25892,1726],{"stretchy":1656},[902,25894,25895],{"encoding":904},"y = y(x)"," (nebo ",[883,25898,25900],{"className":25899},[886],[888,25901,25902],{"xmlns":890},[892,25903,25904,25918],{},[895,25905,25906,25908,25910,25912,25914,25916],{},[898,25907,10799],{},[1654,25909,1750],{},[898,25911,10799],{},[1654,25913,1708],{"stretchy":1656},[898,25915,10789],{},[1654,25917,1726],{"stretchy":1656},[902,25919,25920],{"encoding":904},"x = x(y)","), dosadíme do ",[883,25923,25925],{"className":25924},[886],[888,25926,25927],{"xmlns":890},[892,25928,25929,25933],{},[895,25930,25931],{},[898,25932,10794],{},[902,25934,10794],{"encoding":904}," a převedeme na ",[38,25937,25938],{},"extrém funkce jedné proměnné",[115,25940,25942],{"id":25941},"použití-v-imek","Použití v ImeK",[198,25944,25946],{"id":25945},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,25948,25949,25950,2138],{},"Rozpočtové omezení: ",[883,25951,25953],{"className":25952},[886],[888,25954,25955],{"xmlns":890},[892,25956,25957,25997],{},[895,25958,25959,25965,25967,25975,25981,25983,25991],{},[1741,25960,25961,25963],{},[898,25962,1745],{},[1654,25964,1670],{},[1654,25966,1750],{},[1659,25968,25969,25971,25973],{},[898,25970,1755],{},[1665,25972,1667],{},[1654,25974,1670],{},[1710,25976,25977,25979],{},[898,25978,1663],{},[1665,25980,1667],{},[1654,25982,1766],{},[1659,25984,25985,25987,25989],{},[898,25986,1755],{},[1665,25988,1681],{},[1654,25990,1670],{},[1710,25992,25993,25995],{},[898,25994,1663],{},[1665,25996,1681],{},[902,25998,3552],{"encoding":904},[724,26000,26001],{},[883,26002,26004],{"className":26003},[886],[888,26005,26006],{"xmlns":890},[892,26007,26008,26102],{},[895,26009,26010,26012,26014,26020,26022,26028,26030,26032,26034,26036,26038,26040,26046,26048,26054,26056,26058,26060,26062,26068,26070,26078,26084,26086,26094,26100],{},[898,26011,2450],{},[1654,26013,1708],{"stretchy":1656},[1710,26015,26016,26018],{},[898,26017,1663],{},[1665,26019,1667],{},[1654,26021,1674],{"separator":1673},[1710,26023,26024,26026],{},[898,26025,1663],{},[1665,26027,1681],{},[1654,26029,1674],{"separator":1673},[898,26031,2471],{},[1654,26033,1726],{"stretchy":1656},[1654,26035,1750],{},[898,26037,900],{},[1654,26039,1708],{"stretchy":1656},[1710,26041,26042,26044],{},[898,26043,1663],{},[1665,26045,1667],{},[1654,26047,1674],{"separator":1673},[1710,26049,26050,26052],{},[898,26051,1663],{},[1665,26053,1681],{},[1654,26055,1726],{"stretchy":1656},[1654,26057,1766],{},[898,26059,2471],{},[1654,26061,1708],{"stretchy":1656},[1741,26063,26064,26066],{},[898,26065,1745],{},[1654,26067,1670],{},[1654,26069,2380],{},[1659,26071,26072,26074,26076],{},[898,26073,1755],{},[1665,26075,1667],{},[1654,26077,1670],{},[1710,26079,26080,26082],{},[898,26081,1663],{},[1665,26083,1667],{},[1654,26085,2380],{},[1659,26087,26088,26090,26092],{},[898,26089,1755],{},[1665,26091,1681],{},[1654,26093,1670],{},[1710,26095,26096,26098],{},[898,26097,1663],{},[1665,26099,1681],{},[1654,26101,1726],{"stretchy":1656},[902,26103,26104],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,26106,26107,26108,1343,26140,1343,26172,26221,26222,7515,26276,2138],{},"Soustava: ",[883,26109,26111],{"className":26110},[886],[888,26112,26113],{"xmlns":890},[892,26114,26115,26137],{},[895,26116,26117,26125,26127,26129],{},[1659,26118,26119,26121,26123],{},[898,26120,900],{},[1665,26122,1667],{},[1654,26124,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,26126,1750],{},[898,26128,2471],{},[1659,26130,26131,26133,26135],{},[898,26132,1755],{},[1665,26134,1667],{},[1654,26136,1670],{},[902,26138,26139],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,26141,26143],{"className":26142},[886],[888,26144,26145],{"xmlns":890},[892,26146,26147,26169],{},[895,26148,26149,26157,26159,26161],{},[1659,26150,26151,26153,26155],{},[898,26152,900],{},[1665,26154,1681],{},[1654,26156,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,26158,1750],{},[898,26160,2471],{},[1659,26162,26163,26165,26167],{},[898,26164,1755],{},[1665,26166,1681],{},[1654,26168,1670],{},[902,26170,26171],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,26173,26175],{"className":26174},[886],[888,26176,26177],{"xmlns":890},[892,26178,26179,26219],{},[895,26180,26181,26187,26189,26197,26203,26205,26213],{},[1741,26182,26183,26185],{},[898,26184,1745],{},[1654,26186,1670],{},[1654,26188,1750],{},[1659,26190,26191,26193,26195],{},[898,26192,1755],{},[1665,26194,1667],{},[1654,26196,1670],{},[1710,26198,26199,26201],{},[898,26200,1663],{},[1665,26202,1667],{},[1654,26204,1766],{},[1659,26206,26207,26209,26211],{},[898,26208,1755],{},[1665,26210,1681],{},[1654,26212,1670],{},[1710,26214,26215,26217],{},[898,26216,1663],{},[1665,26218,1681],{},[902,26220,3552],{"encoding":904},". Z prvních dvou: ",[883,26223,26225],{"className":26224},[886],[888,26226,26227],{"xmlns":890},[892,26228,26229,26273],{},[895,26230,26231,26251,26253],{},[2582,26232,26233],{"scriptlevel":2062,"displaystyle":1656},[2811,26234,26235,26243],{},[1659,26236,26237,26239,26241],{},[898,26238,900],{},[1665,26240,1667],{},[1654,26242,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1659,26244,26245,26247,26249],{},[898,26246,900],{},[1665,26248,1681],{},[1654,26250,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,26252,1750],{},[2582,26254,26255],{"scriptlevel":2062,"displaystyle":1656},[2811,26256,26257,26265],{},[1659,26258,26259,26261,26263],{},[898,26260,1755],{},[1665,26262,1667],{},[1654,26264,1670],{},[1659,26266,26267,26269,26271],{},[898,26268,1755],{},[1665,26270,1681],{},[1654,26272,1670],{},[902,26274,26275],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",[883,26277,26279],{"className":26278},[886],[888,26280,26281],{"xmlns":890},[892,26282,26283,26315],{},[895,26284,26285,26287,26289,26291,26293,26295],{},[898,26286,9320],{},[898,26288,12737],{},[898,26290,11539],{},[898,26292,17398],{},[1654,26294,1750],{},[2582,26296,26297],{"scriptlevel":2062,"displaystyle":1656},[2811,26298,26299,26307],{},[1659,26300,26301,26303,26305],{},[898,26302,1755],{},[1665,26304,1667],{},[1654,26306,1670],{},[1659,26308,26309,26311,26313],{},[898,26310,1755],{},[1665,26312,1681],{},[1654,26314,1670],{},[902,26316,26317],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,26319,26321],{"id":26320},"minimalizace-výdajů","Minimalizace výdajů",[724,26323,26324,26325,2138],{},"Podmínka dané užitečnosti ",[883,26326,26328],{"className":26327},[886],[888,26329,26330],{"xmlns":890},[892,26331,26332,26362],{},[895,26333,26334,26340,26342,26344,26346,26352,26354,26360],{},[1741,26335,26336,26338],{},[898,26337,900],{},[1654,26339,1670],{},[1654,26341,1750],{},[898,26343,900],{},[1654,26345,1708],{"stretchy":1656},[1710,26347,26348,26350],{},[898,26349,1663],{},[1665,26351,1667],{},[1654,26353,1674],{"separator":1673},[1710,26355,26356,26358],{},[898,26357,1663],{},[1665,26359,1681],{},[1654,26361,1726],{"stretchy":1656},[902,26363,6615],{"encoding":904},[724,26365,26366],{},[883,26367,26369],{"className":26368},[886],[888,26370,26371],{"xmlns":890},[892,26372,26373,26467],{},[895,26374,26375,26377,26379,26385,26387,26393,26395,26397,26399,26401,26409,26415,26417,26425,26431,26433,26435,26437,26443,26445,26447,26449,26455,26457,26463,26465],{},[898,26376,2450],{},[1654,26378,1708],{"stretchy":1656},[1710,26380,26381,26383],{},[898,26382,1663],{},[1665,26384,1667],{},[1654,26386,1674],{"separator":1673},[1710,26388,26389,26391],{},[898,26390,1663],{},[1665,26392,1681],{},[1654,26394,1674],{"separator":1673},[898,26396,2471],{},[1654,26398,1726],{"stretchy":1656},[1654,26400,1750],{},[1659,26402,26403,26405,26407],{},[898,26404,1755],{},[1665,26406,1667],{},[1654,26408,1670],{},[1710,26410,26411,26413],{},[898,26412,1663],{},[1665,26414,1667],{},[1654,26416,1766],{},[1659,26418,26419,26421,26423],{},[898,26420,1755],{},[1665,26422,1681],{},[1654,26424,1670],{},[1710,26426,26427,26429],{},[898,26428,1663],{},[1665,26430,1681],{},[1654,26432,1766],{},[898,26434,2471],{},[1654,26436,1708],{"stretchy":1656},[1741,26438,26439,26441],{},[898,26440,900],{},[1654,26442,1670],{},[1654,26444,2380],{},[898,26446,900],{},[1654,26448,1708],{"stretchy":1656},[1710,26450,26451,26453],{},[898,26452,1663],{},[1665,26454,1667],{},[1654,26456,1674],{"separator":1673},[1710,26458,26459,26461],{},[898,26460,1663],{},[1665,26462,1681],{},[1654,26464,1726],{"stretchy":1656},[1654,26466,1726],{"stretchy":1656},[902,26468,26469],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,26471,26472,26473,2138],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,26474,26476],{"className":26475},[886],[888,26477,26478],{"xmlns":890},[892,26479,26480,26518],{},[895,26481,26482,26488,26490,26496,26498,26504,26506,26512,26514,26516],{},[1710,26483,26484,26486],{},[898,26485,1663],{},[898,26487,9309],{},[1654,26489,1750],{},[1710,26491,26492,26494],{},[898,26493,4980],{},[898,26495,9309],{},[1654,26497,1708],{"stretchy":1656},[1710,26499,26500,26502],{},[898,26501,1755],{},[1665,26503,1667],{},[1654,26505,1674],{"separator":1673},[1710,26507,26508,26510],{},[898,26509,1755],{},[1665,26511,1681],{},[1654,26513,1674],{"separator":1673},[898,26515,900],{},[1654,26517,1726],{"stretchy":1656},[902,26519,10485],{"encoding":904},[115,26521,10613],{"id":10612},[120,26523,26524,26531,26538,26547],{},[123,26525,26526,2186,26528],{},[38,26527,12546],{},[207,26529,784],{"className":26530,"dataFsResolvedFilePath":782,"href":783},[210],[123,26532,26533,2186,26535],{},[38,26534,12554],{},[207,26536,10669],{"className":26537,"dataFsResolvedFilePath":800,"href":801},[210],[123,26539,26540,2186,26543,26546],{},[38,26541,26542],{},"Aplikace v kurzu:",[207,26544,880],{"className":26545,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,26548,26549,2186,26551,1343,26554,26557],{},[38,26550,12562],{},[207,26552,936],{"className":26553,"dataFsResolvedFilePath":934,"href":935},[210],[207,26555,1400],{"className":26556,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":26559},[26560,26561,26562,26563,26564,26565,26569],{"id":25114,"depth":642,"text":25115},{"id":12005,"depth":642,"text":12006},{"id":12079,"depth":642,"text":12080},{"id":25727,"depth":642,"text":25728},{"id":25839,"depth":642,"text":25840},{"id":25941,"depth":642,"text":25942,"children":26566},[26567,26568],{"id":25945,"depth":649,"text":25946},{"id":26320,"depth":649,"text":26321},{"id":10612,"depth":642,"text":10613},[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":24984,"description":26571},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,26578,26579],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":26582,"title":936,"body":26583,"course":1128,"courses":659,"created":10724,"description":641,"extension":661,"meta":36441,"navigation":664,"path":36442,"seo":36443,"sources":36444,"stem":36445,"tags":36446,"type":10736,"updated":677,"__hash__":36450},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":26584,"toc":36403},[26585,26588,26590,26713,26848,26852,26855,26968,26972,27000,27047,27050,27116,27161,27164,27190,27221,27225,27229,27273,27317,27379,27434,27437,27441,27444,27491,27588,27694,27700,27777,27806,27945,27949,27978,28028,28175,28265,28269,28295,28333,28360,28398,28460,28535,28612,28670,28736,28780,28784,28842,28891,28936,29148,29268,29274,29278,29301,29305,29312,29316,29347,29382,29386,29436,29519,29561,29582,29644,29704,29708,29779,29847,29919,30034,30082,30086,30089,30130,30169,30192,30305,30469,30477,30504,30534,30537,30614,30767,30851,31190,31194,31318,31454,31590,31643,31646,31896,31976,31980,31983,32041,32073,32076,32125,32128,32199,32395,32399,32549,32779,32817,32870,32916,32919,32975,33024,33228,33318,33322,33338,33345,33514,33518,33589,33670,33751,33830,33976,34064,34068,34251,34382,34427,34524,34528,35267,35269,36320,36322],[12,26586,936],{"id":26587},"národní-důchod",[115,26589,1638],{"id":1637},[724,26591,26592,26593,2186,26597,26600,26601,2186,26604,26617,26618,26621,26622,26625,26626,26629,26630,26632,26633,2186,26635,26652,26653,26670,26671,26674,26675,12664],{},"Kapitola 7 ",[207,26594,26596],{"className":26595,"dataFsResolvedFilePath":10690,"href":10691},[210],"Matematické ekonomie",[38,26598,26599],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,26602,26603],{},"národním důchodem",[883,26605,26607],{"className":26606},[886],[888,26608,26609],{"xmlns":890},[892,26610,26611,26615],{},[895,26612,26613],{},[898,26614,1745],{},[902,26616,1745],{"encoding":904},". Budují se postupně bohatší modely — ",[38,26619,26620],{},"C-I"," (jen spotřeba a investice) → ",[38,26623,26624],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,26627,26628],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,26631,20723],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,26634,22594],{},[883,26636,26638],{"className":26637},[886],[888,26639,26640],{"xmlns":890},[892,26641,26642,26650],{},[895,26643,26644],{},[1741,26645,26646,26648],{},[898,26647,1745],{},[898,26649,1798],{},[902,26651,22612],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,26654,26656],{"className":26655},[886],[888,26657,26658],{"xmlns":890},[892,26659,26660,26668],{},[895,26661,26662],{},[1741,26663,26664,26666],{},[898,26665,1745],{},[898,26667,1798],{},[902,26669,22612],{"encoding":904}," na exogenní veličiny popisují ",[38,26672,26673],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,26676,26678],{"className":26677},[886],[888,26679,26680],{"xmlns":890},[892,26681,26682,26710],{},[895,26683,26684,26686,26688,26690,26692,26694,26696,26698,26700,26702,26704,26706,26708],{},[1665,26685,1667],{},[898,26687,1879],{"mathvariant":1878},[1654,26689,1708],{"stretchy":1656},[1665,26691,1667],{},[1654,26693,2380],{},[898,26695,207],{},[1654,26697,1726],{"stretchy":1656},[1654,26699,1750],{},[1665,26701,1667],{},[898,26703,1879],{"mathvariant":1878},[898,26705,9320],{},[898,26707,1755],{},[898,26709,17398],{},[902,26711,26712],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[2140,26714,26715],{},[724,26716,26717,26719,26720,26723,26724,26742,26743,26773,26774,26821,26822,26824,26825,26847],{},[883,26718,2860],{}," Intuice\n",[38,26721,26722],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,26725,26727],{"className":26726},[886],[888,26728,26729],{"xmlns":890},[892,26730,26731,26739],{},[895,26732,26733,26735,26737],{},[898,26734,9320],{},[898,26736,1755],{},[898,26738,11539],{},[902,26740,26741],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,26744,26746],{"className":26745},[886],[888,26747,26748],{"xmlns":890},[892,26749,26750,26770],{},[895,26751,26752,26754,26756,26758,26760,26762,26764,26766,26768],{},[898,26753,9320],{},[898,26755,1755],{},[898,26757,17398],{},[1654,26759,1750],{},[1665,26761,1667],{},[1654,26763,2380],{},[898,26765,9320],{},[898,26767,1755],{},[898,26769,11539],{},[902,26771,26772],{"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 ",[883,26775,26777],{"className":26776},[886],[888,26778,26779],{"xmlns":890},[892,26780,26781,26818],{},[895,26782,26783,26785,26787,26789,26791,26797,26799,26802,26804,26806,26808,26810,26812,26814,26816],{},[1665,26784,1667],{},[1654,26786,1766],{},[898,26788,207],{},[1654,26790,1766],{},[1741,26792,26793,26795],{},[898,26794,207],{},[1665,26796,1681],{},[1654,26798,1766],{},[1654,26800,26801],{},"⋯",[1654,26803,1750],{},[1665,26805,1667],{},[898,26807,1879],{"mathvariant":1878},[1654,26809,1708],{"stretchy":1656},[1665,26811,1667],{},[1654,26813,2380],{},[898,26815,207],{},[1654,26817,1726],{"stretchy":1656},[902,26819,26820],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,26823,20723],{}," 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 ",[883,26826,26828],{"className":26827},[886],[888,26829,26830],{"xmlns":890},[892,26831,26832,26844],{},[895,26833,26834,26836,26838,26840,26842],{},[1654,26835,1708],{"stretchy":1656},[898,26837,1745],{},[1654,26839,1674],{"separator":1673},[898,26841,20753],{},[1654,26843,1726],{"stretchy":1656},[902,26845,26846],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,26849,26851],{"id":26850},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,26853,26854],{},"Po prostudování kapitoly by čtenář měl umět:",[120,26856,26857,26860,26863,26866,26869,26872,26875,26965],{},[123,26858,26859],{},"popsat zjednodušený model národní ekonomiky,",[123,26861,26862],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,26864,26865],{},"popsat lineární model spotřeby a úspor,",[123,26867,26868],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,26870,26871],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,26873,26874],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,26876,26877,26878,1343,26895,1343,26917,2068,26942,26964],{},"popsat modely ",[883,26879,26881],{"className":26880},[886],[888,26882,26883],{"xmlns":890},[892,26884,26885,26893],{},[895,26886,26887,26889,26891],{},[898,26888,11539],{},[1865,26890,21002],{},[898,26892,20896],{},[902,26894,21007],{"encoding":904},[883,26896,26898],{"className":26897},[886],[888,26899,26900],{"xmlns":890},[892,26901,26902,26914],{},[895,26903,26904,26906,26908,26910,26912],{},[898,26905,11539],{},[1865,26907,21002],{},[898,26909,20896],{},[1865,26911,21002],{},[898,26913,20824],{},[902,26915,26916],{"encoding":904},"C\\text{-}I\\text{-}G",[883,26918,26920],{"className":26919},[886],[888,26921,26922],{"xmlns":890},[892,26923,26924,26940],{},[895,26925,26926,26928,26930,26932,26934,26936,26938],{},[898,26927,11539],{},[1865,26929,21002],{},[898,26931,20896],{},[1865,26933,21002],{},[898,26935,20824],{},[1865,26937,21002],{},[898,26939,21032],{},[902,26941,21035],{"encoding":904},[883,26943,26945],{"className":26944},[886],[888,26946,26947],{"xmlns":890},[892,26948,26949,26961],{},[895,26950,26951,26953,26955,26957,26959],{},[898,26952,20896],{},[898,26954,17398],{},[1865,26956,21002],{},[898,26958,2450],{},[898,26960,9320],{},[902,26962,26963],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,26966,26967],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,26969,26971],{"id":26970},"gnp-a-národní-důchod","GNP a národní důchod",[724,26973,26974,2186,26977,18742,26996,26999],{},[38,26975,26976],{},"Hrubý národní produkt",[883,26978,26980],{"className":26979},[886],[888,26981,26982],{"xmlns":890},[892,26983,26984,26993],{},[895,26985,26986,26988,26991],{},[898,26987,20824],{},[898,26989,26990],{},"N",[898,26992,1755],{},[902,26994,26995],{"encoding":904},"GNP",[614,26997,26998],{},"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:",[724,27001,27002],{},[883,27003,27005],{"className":27004},[886],[888,27006,27007],{"xmlns":890},[892,27008,27009,27044],{},[895,27010,27011,27013,27015,27017,27019,27021,27023,27025,27027,27029,27031,27033,27035,27037,27039,27042],{},[898,27012,20824],{},[898,27014,26990],{},[898,27016,1755],{},[1654,27018,1750],{},[898,27020,11539],{},[1654,27022,1766],{},[898,27024,20896],{},[1654,27026,1766],{},[898,27028,20824],{},[1654,27030,1766],{},[898,27032,21032],{},[1654,27034,1674],{"separator":1673},[5008,27036],{"width":14608},[1654,27038,1708],{"stretchy":1656},[1665,27040,27041],{},"7.1",[1654,27043,1726],{"stretchy":1656},[902,27045,27046],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,27048,27049],{},"kde",[120,27051,27052,27068,27084,27100],{},[123,27053,27054,27067],{},[883,27055,27057],{"className":27056},[886],[888,27058,27059],{"xmlns":890},[892,27060,27061,27065],{},[895,27062,27063],{},[898,27064,11539],{},[902,27066,11539],{"encoding":904}," — výdaje domácností na spotřebu,",[123,27069,27070,27083],{},[883,27071,27073],{"className":27072},[886],[888,27074,27075],{"xmlns":890},[892,27076,27077,27081],{},[895,27078,27079],{},[898,27080,20896],{},[902,27082,20896],{"encoding":904}," — hrubé domácí investice,",[123,27085,27086,27099],{},[883,27087,27089],{"className":27088},[886],[888,27090,27091],{"xmlns":890},[892,27092,27093,27097],{},[895,27094,27095],{},[898,27096,20824],{},[902,27098,20824],{"encoding":904}," — vládní výdaje,",[123,27101,27102,27115],{},[883,27103,27105],{"className":27104},[886],[888,27106,27107],{"xmlns":890},[892,27108,27109,27113],{},[895,27110,27111],{},[898,27112,21032],{},[902,27114,21032],{"encoding":904}," — čistý export.",[724,27117,27118,27119,27136,27137,27140,27141,2186,27144,18742,27157,27160],{},"K měření ",[883,27120,27122],{"className":27121},[886],[888,27123,27124],{"xmlns":890},[892,27125,27126,27134],{},[895,27127,27128,27130,27132],{},[898,27129,20824],{},[898,27131,26990],{},[898,27133,1755],{},[902,27135,26995],{"encoding":904}," se užívá ",[38,27138,27139],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,27142,27143],{},"národní důchod",[883,27145,27147],{"className":27146},[886],[888,27148,27149],{"xmlns":890},[892,27150,27151,27155],{},[895,27152,27153],{},[898,27154,1745],{},[902,27156,1745],{"encoding":904},[614,27158,27159],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,27162,27163],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,27165,27166],{},[883,27167,27169],{"className":27168},[886],[888,27170,27171],{"xmlns":890},[892,27172,27173,27187],{},[895,27174,27175,27177,27179,27181,27183,27185],{},[898,27176,20824],{},[898,27178,26990],{},[898,27180,1755],{},[1654,27182,11492],{},[898,27184,1745],{},[1654,27186,1674],{"separator":1673},[902,27188,27189],{"encoding":904},"GNP \\approx Y,",[724,27191,27192,27193,18742,27196,27199,27200,27213,27214,27217,27218,2138],{},"a užívá se společného názvu ",[38,27194,27195],{},"důchod",[614,27197,27198],{},"income",") s označením ",[883,27201,27203],{"className":27202},[886],[888,27204,27205],{"xmlns":890},[892,27206,27207,27211],{},[895,27208,27209],{},[898,27210,1745],{},[902,27212,1745],{"encoding":904},". Domácnosti důchod použijí ke ",[38,27215,27216],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,27219,27220],{},"úspor",[115,27222,27224],{"id":27223},"spotřeba-a-úspory","Spotřeba a úspory",[198,27226,27228],{"id":27227},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,27230,27231,27232,27245,27246,27259,27260,2781],{},"Jak spotřeba ",[883,27233,27235],{"className":27234},[886],[888,27236,27237],{"xmlns":890},[892,27238,27239,27243],{},[895,27240,27241],{},[898,27242,11539],{},[902,27244,11539],{"encoding":904},", tak úspory ",[883,27247,27249],{"className":27248},[886],[888,27250,27251],{"xmlns":890},[892,27252,27253,27257],{},[895,27254,27255],{},[898,27256,17398],{},[902,27258,17398],{"encoding":904}," závisejí na důchodu ",[883,27261,27263],{"className":27262},[886],[888,27264,27265],{"xmlns":890},[892,27266,27267,27271],{},[895,27268,27269],{},[898,27270,1745],{},[902,27272,1745],{"encoding":904},[724,27274,27275],{},[883,27276,27278],{"className":27277},[886],[888,27279,27280],{"xmlns":890},[892,27281,27282,27314],{},[895,27283,27284,27286,27288,27290,27292,27294,27296,27298,27300,27302,27304,27306,27308,27310,27312],{},[898,27285,11539],{},[1654,27287,1750],{},[898,27289,11539],{},[1654,27291,1708],{"stretchy":1656},[898,27293,1745],{},[1654,27295,1726],{"stretchy":1656},[1654,27297,1674],{"separator":1673},[5008,27299],{"width":14608},[898,27301,17398],{},[1654,27303,1750],{},[898,27305,17398],{},[1654,27307,1708],{"stretchy":1656},[898,27309,1745],{},[1654,27311,1726],{"stretchy":1656},[898,27313,2138],{"mathvariant":1878},[902,27315,27316],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,27318,27319,16828,27338,18742,27341,27344,27345,16828,27365,18742,27368,27371,27372,2068,27375,27378],{},[883,27320,27322],{"className":27321},[886],[888,27323,27324],{"xmlns":890},[892,27325,27326,27336],{},[895,27327,27328,27330,27332,27334],{},[898,27329,11539],{},[1654,27331,1708],{"stretchy":1656},[898,27333,1745],{},[1654,27335,1726],{"stretchy":1656},[902,27337,22925],{"encoding":904},[38,27339,27340],{},"funkce spotřeby",[614,27342,27343],{},"consumption function","), ",[883,27346,27348],{"className":27347},[886],[888,27349,27350],{"xmlns":890},[892,27351,27352,27362],{},[895,27353,27354,27356,27358,27360],{},[898,27355,17398],{},[1654,27357,1708],{"stretchy":1656},[898,27359,1745],{},[1654,27361,1726],{"stretchy":1656},[902,27363,27364],{"encoding":904},"S(Y)",[38,27366,27367],{},"funkce úspor",[614,27369,27370],{},"savings function","); jejich grafy se nazývají ",[38,27373,27374],{},"křivka spotřeby",[38,27376,27377],{},"křivka úspor",". Platí základní identita",[724,27380,27381],{},[883,27382,27384],{"className":27383},[886],[888,27385,27386],{"xmlns":890},[892,27387,27388,27431],{},[895,27389,27390,27392,27394,27396,27398,27400,27402,27404,27406,27408,27410,27412,27414,27416,27418,27420,27422,27424,27426,27429],{},[898,27391,1745],{},[1654,27393,1750],{},[898,27395,11539],{},[1654,27397,1766],{},[898,27399,17398],{},[1654,27401,1750],{},[898,27403,11539],{},[1654,27405,1708],{"stretchy":1656},[898,27407,1745],{},[1654,27409,1726],{"stretchy":1656},[1654,27411,1766],{},[898,27413,17398],{},[1654,27415,1708],{"stretchy":1656},[898,27417,1745],{},[1654,27419,1726],{"stretchy":1656},[898,27421,2138],{"mathvariant":1878},[5008,27423],{"width":14608},[1654,27425,1708],{"stretchy":1656},[1665,27427,27428],{},"7.2",[1654,27430,1726],{"stretchy":1656},[902,27432,27433],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,27435,27436],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,27438,27440],{"id":27439},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,27442,27443],{},"Nejjednodušší model předpokládá lineární tvar",[724,27445,27446],{},[883,27447,27449],{"className":27448},[886],[888,27450,27451],{"xmlns":890},[892,27452,27453,27488],{},[895,27454,27455,27457,27459,27461,27463,27465,27467,27469,27471,27473,27475,27477,27479,27481,27483,27486],{},[898,27456,11539],{},[1654,27458,1750],{},[898,27460,11539],{},[1654,27462,1708],{"stretchy":1656},[898,27464,1745],{},[1654,27466,1726],{"stretchy":1656},[1654,27468,1750],{},[898,27470,207],{},[898,27472,1745],{},[1654,27474,1766],{},[898,27476,9758],{},[1654,27478,1674],{"separator":1673},[5008,27480],{"width":14608},[1654,27482,1708],{"stretchy":1656},[1665,27484,27485],{},"7.3",[1654,27487,1726],{"stretchy":1656},[902,27489,27490],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,27492,13049,27493,2068,27511,27533,27534,27574,27575,2138],{},[883,27494,27496],{"className":27495},[886],[888,27497,27498],{"xmlns":890},[892,27499,27500,27508],{},[895,27501,27502,27504,27506],{},[898,27503,9758],{},[1654,27505,2952],{},[1665,27507,2062],{},[902,27509,27510],{"encoding":904},"b > 0",[883,27512,27514],{"className":27513},[886],[888,27515,27516],{"xmlns":890},[892,27517,27518,27530],{},[895,27519,27520,27522,27524,27526,27528],{},[1665,27521,2062],{},[1654,27523,3002],{},[898,27525,207],{},[1654,27527,3002],{},[1665,27529,1667],{},[902,27531,27532],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,27535,27537],{"className":27536},[886],[888,27538,27539],{"xmlns":890},[892,27540,27541,27571],{},[895,27542,27543,27545,27547,27554,27556,27559,27561,27563,27565,27567,27569],{},[898,27544,207],{},[1654,27546,1750],{},[895,27548,27549,27552],{},[898,27550,27551],{"mathvariant":1878},"t",[898,27553,2351],{"mathvariant":1878},[1865,27555,11744],{},[898,27557,27558],{},"α",[1654,27560,1750],{},[898,27562,11648],{"mathvariant":1878},[898,27564,11539],{},[898,27566,1879],{"mathvariant":1878},[898,27568,11648],{"mathvariant":1878},[898,27570,1745],{},[902,27572,27573],{"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 ",[883,27576,27578],{"className":27577},[886],[888,27579,27580],{"xmlns":890},[892,27581,27582,27586],{},[895,27583,27584],{},[898,27585,1745],{},[902,27587,1745],{"encoding":904},[724,27589,27590],{},[614,27591,27592,27593,27617,27618,27656,27657,27673,27674,2138],{},"Obrázek 7.1 — Přímka spotřeby ",[883,27594,27596],{"className":27595},[886],[888,27597,27598],{"xmlns":890},[892,27599,27600,27614],{},[895,27601,27602,27604,27606,27608,27610,27612],{},[898,27603,11539],{},[1654,27605,1750],{},[898,27607,207],{},[898,27609,1745],{},[1654,27611,1766],{},[898,27613,9758],{},[902,27615,27616],{"encoding":904},"C = aY + b"," se směrnicí ",[883,27619,27621],{"className":27620},[886],[888,27622,27623],{"xmlns":890},[892,27624,27625,27653],{},[895,27626,27627,27629,27631,27637,27639,27641,27643,27645,27647,27649,27651],{},[898,27628,207],{},[1654,27630,1750],{},[895,27632,27633,27635],{},[898,27634,27551],{"mathvariant":1878},[898,27636,2351],{"mathvariant":1878},[1865,27638,11744],{},[898,27640,27558],{},[1654,27642,1750],{},[898,27644,11648],{"mathvariant":1878},[898,27646,11539],{},[898,27648,1879],{"mathvariant":1878},[898,27650,11648],{"mathvariant":1878},[898,27652,1745],{},[902,27654,27655],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,27658,27660],{"className":27659},[886],[888,27661,27662],{"xmlns":890},[892,27663,27664,27670],{},[895,27665,27666,27668],{},[898,27667,11648],{"mathvariant":1878},[898,27669,11539],{},[902,27671,27672],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,27675,27677],{"className":27676},[886],[888,27678,27679],{"xmlns":890},[892,27680,27681,27691],{},[895,27682,27683,27685,27687,27689],{},[898,27684,11648],{"mathvariant":1878},[898,27686,1745],{},[1654,27688,1750],{},[1665,27690,1667],{},[902,27692,27693],{"encoding":904},"\\Delta Y = 1",[724,27695,27696,27697,2781],{},"Dosazením do (7.2) plyne ",[38,27698,27699],{},"lineární model úspor",[724,27701,27702],{},[883,27703,27705],{"className":27704},[886],[888,27706,27707],{"xmlns":890},[892,27708,27709,27774],{},[895,27710,27711,27713,27715,27717,27719,27721,27723,27725,27727,27729,27731,27733,27735,27737,27739,27741,27743,27745,27747,27749,27751,27753,27755,27757,27759,27761,27763,27765,27767,27769,27772],{},[898,27712,17398],{},[1654,27714,1750],{},[898,27716,1745],{},[1654,27718,2380],{},[898,27720,11539],{},[1654,27722,1708],{"stretchy":1656},[898,27724,1745],{},[1654,27726,1726],{"stretchy":1656},[1654,27728,1750],{},[898,27730,1745],{},[1654,27732,2380],{},[1654,27734,1708],{"stretchy":1656},[898,27736,207],{},[898,27738,1745],{},[1654,27740,1766],{},[898,27742,9758],{},[1654,27744,1726],{"stretchy":1656},[1654,27746,1750],{},[1654,27748,1708],{"stretchy":1656},[1665,27750,1667],{},[1654,27752,2380],{},[898,27754,207],{},[1654,27756,1726],{"stretchy":1656},[898,27758,1745],{},[1654,27760,2380],{},[898,27762,9758],{},[898,27764,2138],{"mathvariant":1878},[5008,27766],{"width":14608},[1654,27768,1708],{"stretchy":1656},[1665,27770,27771],{},"7.4",[1654,27773,1726],{"stretchy":1656},[902,27775,27776],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,27778,27779,27780,12664],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,27781,27783],{"className":27782},[886],[888,27784,27785],{"xmlns":890},[892,27786,27787,27803],{},[895,27788,27789,27791,27793,27795,27797,27799,27801],{},[1665,27790,2062],{},[1654,27792,3002],{},[1665,27794,1667],{},[1654,27796,2380],{},[898,27798,207],{},[1654,27800,3002],{},[1665,27802,1667],{},[902,27804,27805],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,27807,27808],{},[614,27809,27810,27811,2068,27834,27866,27867,11387,27880,27910,27911,11387,27929,2138],{},"Obrázek 7.2 — Přímky ",[883,27812,27814],{"className":27813},[886],[888,27815,27816],{"xmlns":890},[892,27817,27818,27832],{},[895,27819,27820,27822,27824,27826,27828,27830],{},[898,27821,11539],{},[1654,27823,1750],{},[898,27825,207],{},[898,27827,1745],{},[1654,27829,1766],{},[898,27831,9758],{},[902,27833,27616],{"encoding":904},[883,27835,27837],{"className":27836},[886],[888,27838,27839],{"xmlns":890},[892,27840,27841,27863],{},[895,27842,27843,27845,27847,27849,27851,27853,27855,27857,27859,27861],{},[898,27844,17398],{},[1654,27846,1750],{},[1654,27848,1708],{"stretchy":1656},[1665,27850,1667],{},[1654,27852,2380],{},[898,27854,207],{},[1654,27856,1726],{"stretchy":1656},[898,27858,1745],{},[1654,27860,2380],{},[898,27862,9758],{},[902,27864,27865],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,27868,27870],{"className":27869},[886],[888,27871,27872],{"xmlns":890},[892,27873,27874,27878],{},[895,27875,27876],{},[898,27877,1745],{},[902,27879,1745],{"encoding":904},[883,27881,27883],{"className":27882},[886],[888,27884,27885],{"xmlns":890},[892,27886,27887,27907],{},[895,27888,27889,27891,27893,27895,27897,27899,27901,27903,27905],{},[898,27890,1745],{},[1654,27892,1750],{},[898,27894,9758],{},[898,27896,1879],{"mathvariant":1878},[1654,27898,1708],{"stretchy":1656},[1665,27900,1667],{},[1654,27902,2380],{},[898,27904,207],{},[1654,27906,1726],{"stretchy":1656},[902,27908,27909],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,27912,27914],{"className":27913},[886],[888,27915,27916],{"xmlns":890},[892,27917,27918,27926],{},[895,27919,27920,27922,27924],{},[898,27921,11539],{},[1654,27923,1674],{"separator":1673},[898,27925,17398],{},[902,27927,27928],{"encoding":904},"C, S",[883,27930,27932],{"className":27931},[886],[888,27933,27934],{"xmlns":890},[892,27935,27936,27942],{},[895,27937,27938,27940],{},[1654,27939,2380],{},[898,27941,9758],{},[902,27943,27944],{"encoding":904},"-b",[198,27946,27948],{"id":27947},"příklad-71","Příklad 7.1",[724,27950,27951,27952,27977],{},"Pro spotřebu ",[883,27953,27955],{"className":27954},[886],[888,27956,27957],{"xmlns":890},[892,27958,27959,27974],{},[895,27960,27961,27963,27965,27968,27970,27972],{},[898,27962,11539],{},[1654,27964,1750],{},[1665,27966,27967],{},"0,4",[898,27969,1745],{},[1654,27971,1766],{},[1665,27973,4647],{},[902,27975,27976],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,27979,27980],{},[883,27981,27983],{"className":27982},[886],[888,27984,27985],{"xmlns":890},[892,27986,27987,28025],{},[895,27988,27989,27991,27993,27995,27997,27999,28001,28003,28005,28007,28009,28011,28013,28015,28018,28020,28022],{},[898,27990,17398],{},[1654,27992,1750],{},[898,27994,1745],{},[1654,27996,2380],{},[898,27998,11539],{},[1654,28000,1750],{},[898,28002,1745],{},[1654,28004,2380],{},[1665,28006,27967],{},[898,28008,1745],{},[1654,28010,2380],{},[1665,28012,4647],{},[1654,28014,1750],{},[1665,28016,28017],{},"0,6",[898,28019,1745],{},[1654,28021,2380],{},[1665,28023,28024],{},"10.",[902,28026,28027],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,28029,28030],{},[614,28031,28032,28033,2068,28056,28080,28081,16828,28094,28118,28119,16828,28136,28152,28153,2138],{},"Obrázek 7.3 — Přímky ",[883,28034,28036],{"className":28035},[886],[888,28037,28038],{"xmlns":890},[892,28039,28040,28054],{},[895,28041,28042,28044,28046,28048,28050,28052],{},[898,28043,11539],{},[1654,28045,1750],{},[1665,28047,27967],{},[898,28049,1745],{},[1654,28051,1766],{},[1665,28053,4647],{},[902,28055,27976],{"encoding":904},[883,28057,28059],{"className":28058},[886],[888,28060,28061],{"xmlns":890},[892,28062,28063,28077],{},[895,28064,28065,28067,28069,28071,28073,28075],{},[898,28066,17398],{},[1654,28068,1750],{},[1665,28070,28017],{},[898,28072,1745],{},[1654,28074,2380],{},[1665,28076,4647],{},[902,28078,28079],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,28082,28084],{"className":28083},[886],[888,28085,28086],{"xmlns":890},[892,28087,28088,28092],{},[895,28089,28090],{},[898,28091,1745],{},[902,28093,1745],{"encoding":904},[883,28095,28097],{"className":28096},[886],[888,28098,28099],{"xmlns":890},[892,28100,28101,28115],{},[895,28102,28103,28105,28108],{},[1654,28104,11492],{},[1665,28106,28107],{},"16,",[17111,28109,28110,28112],{"accent":1673},[1665,28111,11015],{},[1654,28113,28114],{},"ˉ",[902,28116,28117],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,28120,28122],{"className":28121},[886],[888,28123,28124],{"xmlns":890},[892,28125,28126,28134],{},[895,28127,28128,28130,28132],{},[898,28129,11539],{},[1654,28131,1674],{"separator":1673},[898,28133,17398],{},[902,28135,27928],{"encoding":904},[883,28137,28139],{"className":28138},[886],[888,28140,28141],{"xmlns":890},[892,28142,28143,28149],{},[895,28144,28145,28147],{},[1654,28146,2380],{},[1665,28148,4647],{},[902,28150,28151],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,28154,28156],{"className":28155},[886],[888,28157,28158],{"xmlns":890},[892,28159,28160,28172],{},[895,28161,28162,28164,28166,28168,28170],{},[1654,28163,1708],{"stretchy":1656},[1665,28165,2062],{},[1654,28167,1674],{"separator":1673},[1665,28169,4647],{},[1654,28171,1726],{"stretchy":1656},[902,28173,28174],{"encoding":904},"(0, 10)",[724,28176,28177,28178,16828,28196,28226,28227,18742,28230,28233,28234,16828,28258,18742,28261,28264],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,28179,28181],{"className":28180},[886],[888,28182,28183],{"xmlns":890},[892,28184,28185,28193],{},[895,28186,28187,28189,28191],{},[898,28188,1745],{},[1654,28190,1750],{},[1665,28192,2062],{},[902,28194,28195],{"encoding":904},"Y = 0",[883,28197,28199],{"className":28198},[886],[888,28200,28201],{"xmlns":890},[892,28202,28203,28223],{},[895,28204,28205,28207,28209,28211,28213,28215,28217,28219,28221],{},[898,28206,17398],{},[1654,28208,1708],{"stretchy":1656},[1665,28210,2062],{},[1654,28212,1726],{"stretchy":1656},[1654,28214,1750],{},[1654,28216,2380],{},[898,28218,9758],{},[1654,28220,3002],{},[1665,28222,2062],{},[902,28224,28225],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,28228,28229],{},"autonomních úsporách",[614,28231,28232],{},"autonomous savings","). Analogicky ",[883,28235,28237],{"className":28236},[886],[888,28238,28239],{"xmlns":890},[892,28240,28241,28255],{},[895,28242,28243,28245,28247,28249,28251,28253],{},[898,28244,11539],{},[1654,28246,1708],{"stretchy":1656},[1665,28248,2062],{},[1654,28250,1726],{"stretchy":1656},[1654,28252,1750],{},[898,28254,9758],{},[902,28256,28257],{"encoding":904},"C(0) = b",[38,28259,28260],{},"autonomní spotřeba",[614,28262,28263],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,28266,28268],{"id":28267},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,28270,28271,2186,28274,18742,28291,28294],{},[38,28272,28273],{},"Mezní sklon ke spotřebě",[883,28275,28277],{"className":28276},[886],[888,28278,28279],{"xmlns":890},[892,28280,28281,28289],{},[895,28282,28283,28285,28287],{},[898,28284,9320],{},[898,28286,1755],{},[898,28288,11539],{},[902,28290,26741],{"encoding":904},[614,28292,28293],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,28296,28297],{},[883,28298,28300],{"className":28299},[886],[888,28301,28302],{"xmlns":890},[892,28303,28304,28330],{},[895,28305,28306,28308,28310,28312,28314,28328],{},[898,28307,9320],{},[898,28309,1755],{},[898,28311,11539],{},[1654,28313,1750],{},[2811,28315,28316,28322],{},[895,28317,28318,28320],{},[898,28319,10977],{"mathvariant":1878},[898,28321,11539],{},[895,28323,28324,28326],{},[898,28325,10977],{"mathvariant":1878},[898,28327,1745],{},[898,28329,2138],{"mathvariant":1878},[902,28331,28332],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,28334,28335,2186,28338,18742,28356,28359],{},[38,28336,28337],{},"Mezní sklon k úsporám",[883,28339,28341],{"className":28340},[886],[888,28342,28343],{"xmlns":890},[892,28344,28345,28353],{},[895,28346,28347,28349,28351],{},[898,28348,9320],{},[898,28350,1755],{},[898,28352,17398],{},[902,28354,28355],{"encoding":904},"MPS",[614,28357,28358],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,28361,28362],{},[883,28363,28365],{"className":28364},[886],[888,28366,28367],{"xmlns":890},[892,28368,28369,28395],{},[895,28370,28371,28373,28375,28377,28379,28393],{},[898,28372,9320],{},[898,28374,1755],{},[898,28376,17398],{},[1654,28378,1750],{},[2811,28380,28381,28387],{},[895,28382,28383,28385],{},[898,28384,10977],{"mathvariant":1878},[898,28386,17398],{},[895,28388,28389,28391],{},[898,28390,10977],{"mathvariant":1878},[898,28392,1745],{},[898,28394,2138],{"mathvariant":1878},[902,28396,28397],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,28399,28400,28401,28459],{},"Z (7.2) plyne ",[883,28402,28404],{"className":28403},[886],[888,28405,28406],{"xmlns":890},[892,28407,28408,28456],{},[895,28409,28410,28424,28426,28440,28442],{},[2811,28411,28412,28418],{},[895,28413,28414,28416],{},[898,28415,10977],{"mathvariant":1878},[898,28417,1745],{},[895,28419,28420,28422],{},[898,28421,10977],{"mathvariant":1878},[898,28423,1745],{},[1654,28425,1750],{},[2811,28427,28428,28434],{},[895,28429,28430,28432],{},[898,28431,10977],{"mathvariant":1878},[898,28433,11539],{},[895,28435,28436,28438],{},[898,28437,10977],{"mathvariant":1878},[898,28439,1745],{},[1654,28441,1766],{},[2811,28443,28444,28450],{},[895,28445,28446,28448],{},[898,28447,10977],{"mathvariant":1878},[898,28449,17398],{},[895,28451,28452,28454],{},[898,28453,10977],{"mathvariant":1878},[898,28455,1745],{},[902,28457,28458],{"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",[724,28461,28462],{},[883,28463,28465],{"className":28464},[886],[888,28466,28467],{"xmlns":890},[892,28468,28469,28532],{},[895,28470,28471,28523,28525,28527,28530],{},[2792,28472,28473],{"notation":2794},[2582,28474,28475],{"scriptlevel":2062,"displaystyle":1656},[2582,28476,28477],{"scriptlevel":2062,"displaystyle":1656},[2582,28478,28479],{"scriptlevel":2062,"displaystyle":1673},[895,28480,28481,28483,28485,28487,28489,28491,28493,28495,28497,28499,28501,28503,28505,28507,28509,28511,28513,28515,28517,28519,28521],{},[898,28482,9320],{},[898,28484,1755],{},[898,28486,11539],{},[1654,28488,1766],{},[898,28490,9320],{},[898,28492,1755],{},[898,28494,17398],{},[1654,28496,1750],{},[1665,28498,1667],{},[1654,28500,1674],{"separator":1673},[5008,28502],{"width":14608},[898,28504,9320],{},[898,28506,1755],{},[898,28508,17398],{},[1654,28510,1750],{},[1665,28512,1667],{},[1654,28514,2380],{},[898,28516,9320],{},[898,28518,1755],{},[898,28520,11539],{},[898,28522,2138],{"mathvariant":1878},[5008,28524],{"width":14608},[1654,28526,1708],{"stretchy":1656},[1665,28528,28529],{},"7.5",[1654,28531,1726],{"stretchy":1656},[902,28533,28534],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,28536,28537,2186,28540,5698,28563,2068,28585,28611],{},[38,28538,28539],{},"Pro lineární model",[883,28541,28543],{"className":28542},[886],[888,28544,28545],{"xmlns":890},[892,28546,28547,28561],{},[895,28548,28549,28551,28553,28555,28557,28559],{},[898,28550,11539],{},[1654,28552,1750],{},[898,28554,207],{},[898,28556,1745],{},[1654,28558,1766],{},[898,28560,9758],{},[902,28562,27616],{"encoding":904},[883,28564,28566],{"className":28565},[886],[888,28567,28568],{"xmlns":890},[892,28569,28570,28582],{},[895,28571,28572,28574,28576,28578,28580],{},[898,28573,9320],{},[898,28575,1755],{},[898,28577,11539],{},[1654,28579,1750],{},[898,28581,207],{},[902,28583,28584],{"encoding":904},"MPC = a",[883,28586,28588],{"className":28587},[886],[888,28589,28590],{"xmlns":890},[892,28591,28592,28608],{},[895,28593,28594,28596,28598,28600,28602,28604,28606],{},[898,28595,9320],{},[898,28597,1755],{},[898,28599,17398],{},[1654,28601,1750],{},[1665,28603,1667],{},[1654,28605,2380],{},[898,28607,207],{},[902,28609,28610],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,28613,28614,28617,28618,28640,28641,28669],{},[38,28615,28616],{},"Interpretace diferenciálem."," Pro pevné ",[883,28619,28621],{"className":28620},[886],[888,28622,28623],{"xmlns":890},[892,28624,28625,28637],{},[895,28626,28627,28629,28631],{},[898,28628,1745],{},[1654,28630,1750],{},[1741,28632,28633,28635],{},[898,28634,1745],{},[1654,28636,1670],{},[902,28638,28639],{"encoding":904},"Y = Y^*"," udává ",[883,28642,28644],{"className":28643},[886],[888,28645,28646],{"xmlns":890},[892,28647,28648,28666],{},[895,28649,28650,28652,28654,28656,28658,28664],{},[898,28651,9320],{},[898,28653,1755],{},[898,28655,11539],{},[1654,28657,1708],{"stretchy":1656},[1741,28659,28660,28662],{},[898,28661,1745],{},[1654,28663,1670],{},[1654,28665,1726],{"stretchy":1656},[902,28667,28668],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,28671,28672],{},[883,28673,28675],{"className":28674},[886],[888,28676,28677],{"xmlns":890},[892,28678,28679,28733],{},[895,28680,28681,28683,28685,28687,28689,28691,28693,28699,28701,28703,28705,28707,28709,28711,28713,28715,28717,28719,28721,28723,28725,28727,28729,28731],{},[898,28682,11648],{"mathvariant":1878},[898,28684,11539],{},[1654,28686,11492],{},[898,28688,10977],{"mathvariant":1878},[898,28690,11539],{},[1654,28692,1750],{},[1741,28694,28695,28697],{},[898,28696,11539],{},[1654,28698,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,28700,1708],{"stretchy":1656},[898,28702,1745],{},[1654,28704,1726],{"stretchy":1656},[1865,28706,11744],{},[898,28708,10977],{"mathvariant":1878},[898,28710,1745],{},[1654,28712,1750],{},[898,28714,9320],{},[898,28716,1755],{},[898,28718,11539],{},[1654,28720,1708],{"stretchy":1656},[898,28722,1745],{},[1654,28724,1726],{"stretchy":1656},[1865,28726,11744],{},[898,28728,10977],{"mathvariant":1878},[898,28730,1745],{},[898,28732,2138],{"mathvariant":1878},[902,28734,28735],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,28737,28738,28739,28775,28776,28779],{},"Analogicky ",[883,28740,28742],{"className":28741},[886],[888,28743,28744],{"xmlns":890},[892,28745,28746,28772],{},[895,28747,28748,28750,28752,28754,28756,28758,28760,28762,28764,28766,28768,28770],{},[898,28749,11648],{"mathvariant":1878},[898,28751,17398],{},[1654,28753,11492],{},[898,28755,9320],{},[898,28757,1755],{},[898,28759,17398],{},[1654,28761,1708],{"stretchy":1656},[898,28763,1745],{},[1654,28765,1726],{"stretchy":1656},[1865,28767,11744],{},[898,28769,10977],{"mathvariant":1878},[898,28771,1745],{},[902,28773,28774],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,28777,1145],{"className":28778,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,28781,28783],{"id":28782},"příklad-72","Příklad 7.2",[724,28785,27951,28786,28821,28822,28841],{},[883,28787,28789],{"className":28788},[886],[888,28790,28791],{"xmlns":890},[892,28792,28793,28818],{},[895,28794,28795,28797,28799,28802,28808,28810,28812,28814,28816],{},[898,28796,11539],{},[1654,28798,1750],{},[1665,28800,28801],{},"0,001",[1741,28803,28804,28806],{},[898,28805,1745],{},[1665,28807,1681],{},[1654,28809,1766],{},[1665,28811,11599],{},[898,28813,1745],{},[1654,28815,1766],{},[1665,28817,4767],{},[902,28819,28820],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,28823,28825],{"className":28824},[886],[888,28826,28827],{"xmlns":890},[892,28828,28829,28838],{},[895,28830,28831,28833,28835],{},[898,28832,1745],{},[1654,28834,3002],{},[1665,28836,28837],{},"400",[902,28839,28840],{"encoding":904},"Y \u003C 400",") platí",[724,28843,28844],{},[883,28845,28847],{"className":28846},[886],[888,28848,28849],{"xmlns":890},[892,28850,28851,28888],{},[895,28852,28853,28855,28857,28859,28861,28875,28877,28880,28882,28884,28886],{},[898,28854,9320],{},[898,28856,1755],{},[898,28858,11539],{},[1654,28860,1750],{},[2811,28862,28863,28869],{},[895,28864,28865,28867],{},[898,28866,10977],{"mathvariant":1878},[898,28868,11539],{},[895,28870,28871,28873],{},[898,28872,10977],{"mathvariant":1878},[898,28874,1745],{},[1654,28876,1750],{},[1665,28878,28879],{},"0,002",[898,28881,1745],{},[1654,28883,1766],{},[1665,28885,11599],{},[1654,28887,1674],{"separator":1673},[902,28889,28890],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,28892,28893],{},[883,28894,28896],{"className":28895},[886],[888,28897,28898],{"xmlns":890},[892,28899,28900,28933],{},[895,28901,28902,28904,28906,28908,28910,28912,28914,28916,28918,28920,28922,28924,28926,28928,28930],{},[898,28903,9320],{},[898,28905,1755],{},[898,28907,17398],{},[1654,28909,1750],{},[1665,28911,1667],{},[1654,28913,2380],{},[898,28915,9320],{},[898,28917,1755],{},[898,28919,11539],{},[1654,28921,1750],{},[1654,28923,2380],{},[1665,28925,28879],{},[898,28927,1745],{},[1654,28929,1766],{},[1665,28931,28932],{},"0,8.",[902,28934,28935],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,28937,28938,29017,29096],{},[123,28939,28940,1343,28968,28996,28997,16828,29014,2138],{},[883,28941,28943],{"className":28942},[886],[888,28944,28945],{"xmlns":890},[892,28946,28947,28965],{},[895,28948,28949,28951,28953,28955,28957,28959,28961,28963],{},[898,28950,9320],{},[898,28952,1755],{},[898,28954,11539],{},[1654,28956,1708],{"stretchy":1656},[1665,28958,4273],{},[1654,28960,1726],{"stretchy":1656},[1654,28962,1750],{},[1665,28964,27967],{},[902,28966,28967],{"encoding":904},"MPC(100) = 0{,}4",[883,28969,28971],{"className":28970},[886],[888,28972,28973],{"xmlns":890},[892,28974,28975,28993],{},[895,28976,28977,28979,28981,28983,28985,28987,28989,28991],{},[898,28978,9320],{},[898,28980,1755],{},[898,28982,17398],{},[1654,28984,1708],{"stretchy":1656},[1665,28986,4273],{},[1654,28988,1726],{"stretchy":1656},[1654,28990,1750],{},[1665,28992,28017],{},[902,28994,28995],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,28998,29000],{"className":28999},[886],[888,29001,29002],{"xmlns":890},[892,29003,29004,29012],{},[895,29005,29006,29008,29010],{},[898,29007,1745],{},[1654,29009,1750],{},[1665,29011,4273],{},[902,29013,5697],{"encoding":904},[38,29015,29016],{},"větší sklon k úsporám",[123,29018,29019,1343,29047,28996,29075,16828,29093,2138],{},[883,29020,29022],{"className":29021},[886],[888,29023,29024],{"xmlns":890},[892,29025,29026,29044],{},[895,29027,29028,29030,29032,29034,29036,29038,29040,29042],{},[898,29029,9320],{},[898,29031,1755],{},[898,29033,11539],{},[1654,29035,1708],{"stretchy":1656},[1665,29037,17102],{},[1654,29039,1726],{"stretchy":1656},[1654,29041,1750],{},[1665,29043,28017],{},[902,29045,29046],{"encoding":904},"MPC(200) = 0{,}6",[883,29048,29050],{"className":29049},[886],[888,29051,29052],{"xmlns":890},[892,29053,29054,29072],{},[895,29055,29056,29058,29060,29062,29064,29066,29068,29070],{},[898,29057,9320],{},[898,29059,1755],{},[898,29061,17398],{},[1654,29063,1708],{"stretchy":1656},[1665,29065,17102],{},[1654,29067,1726],{"stretchy":1656},[1654,29069,1750],{},[1665,29071,27967],{},[902,29073,29074],{"encoding":904},"MPS(200) = 0{,}4",[883,29076,29078],{"className":29077},[886],[888,29079,29080],{"xmlns":890},[892,29081,29082,29090],{},[895,29083,29084,29086,29088],{},[898,29085,1745],{},[1654,29087,1750],{},[1665,29089,17102],{},[902,29091,29092],{"encoding":904},"Y = 200",[38,29094,29095],{},"větší sklon ke spotřebě",[123,29097,29098,29099,29117,29118,12664],{},"Přesně při ",[883,29100,29102],{"className":29101},[886],[888,29103,29104],{"xmlns":890},[892,29105,29106,29114],{},[895,29107,29108,29110,29112],{},[898,29109,1745],{},[1654,29111,1750],{},[1665,29113,17528],{},[902,29115,29116],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,29119,29121],{"className":29120},[886],[888,29122,29123],{"xmlns":890},[892,29124,29125,29145],{},[895,29126,29127,29129,29131,29133,29135,29137,29139,29141,29143],{},[898,29128,9320],{},[898,29130,1755],{},[898,29132,11539],{},[1654,29134,1750],{},[898,29136,9320],{},[898,29138,1755],{},[898,29140,17398],{},[1654,29142,1750],{},[1665,29144,7594],{},[902,29146,29147],{"encoding":904},"MPC = MPS = 0{,}5",[724,29149,29150,29151,29168,29169,29183,29184,11448,29197,29211,29212,29225,29226,29267],{},"Interpretace: při ",[883,29152,29154],{"className":29153},[886],[888,29155,29156],{"xmlns":890},[892,29157,29158,29166],{},[895,29159,29160,29162,29164],{},[898,29161,1745],{},[1654,29163,1750],{},[1665,29165,4273],{},[902,29167,5697],{"encoding":904}," se spotřeba mění ",[883,29170,29172],{"className":29171},[886],[888,29173,29174],{"xmlns":890},[892,29175,29176,29180],{},[895,29177,29178],{},[1665,29179,27967],{},[902,29181,29182],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,29185,29187],{"className":29186},[886],[888,29188,29189],{"xmlns":890},[892,29190,29191,29195],{},[895,29192,29193],{},[1665,29194,4273],{},[902,29196,4273],{"encoding":904},[883,29198,29200],{"className":29199},[886],[888,29201,29202],{"xmlns":890},[892,29203,29204,29209],{},[895,29205,29206],{},[1665,29207,29208],{},"101",[902,29210,29208],{"encoding":904},", změní se spotřeba přibližně o ",[883,29213,29215],{"className":29214},[886],[888,29216,29217],{"xmlns":890},[892,29218,29219,29223],{},[895,29220,29221],{},[1665,29222,27967],{},[902,29224,29182],{"encoding":904},". Skutečná změna ",[883,29227,29229],{"className":29228},[886],[888,29230,29231],{"xmlns":890},[892,29232,29233,29264],{},[895,29234,29235,29237,29239,29241,29243,29245,29247,29249,29251,29253,29255,29257,29259,29261],{},[898,29236,11648],{"mathvariant":1878},[898,29238,11539],{},[1654,29240,1750],{},[898,29242,11539],{},[1654,29244,1708],{"stretchy":1656},[1665,29246,29208],{},[1654,29248,1726],{"stretchy":1656},[1654,29250,2380],{},[898,29252,11539],{},[1654,29254,1708],{"stretchy":1656},[1665,29256,4273],{},[1654,29258,1726],{"stretchy":1656},[1654,29260,1750],{},[1665,29262,29263],{},"0,401",[902,29265,29266],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,29269,29270,29271],{},"Obecný trend: ",[38,29272,29273],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,29275,29277],{"id":29276},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,29279,29280,29281,18742,29284,29287,29288,18742,29291,20840,29294,18742,29297,29300],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,29282,29283],{},"makroekonomická rovnováha",[614,29285,29286],{},"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 ",[38,29289,29290],{},"agregátní poptávky",[614,29292,29293],{},"aggregate demand",[38,29295,29296],{},"agregátní nabídky",[614,29298,29299],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,29302,29304],{"id":29303},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,29306,29307],{},[3492,29308],{"alt":29309,"className":29310,"src":29311},"imek-keynesian-kriz",[210,3496],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,29313,29315],{"id":29314},"zadání-modelu","Zadání modelu",[724,29317,29318,29319,29332,29333,29346],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,29320,29322],{"className":29321},[886],[888,29323,29324],{"xmlns":890},[892,29325,29326,29330],{},[895,29327,29328],{},[898,29329,11539],{},[902,29331,11539],{"encoding":904}," a investice ",[883,29334,29336],{"className":29335},[886],[888,29337,29338],{"xmlns":890},[892,29339,29340,29344],{},[895,29341,29342],{},[898,29343,20896],{},[902,29345,20896],{"encoding":904},". Podmínka rovnováhy:",[724,29348,29349],{},[883,29350,29352],{"className":29351},[886],[888,29353,29354],{"xmlns":890},[892,29355,29356,29379],{},[895,29357,29358,29360,29362,29364,29366,29368,29370,29372,29374,29377],{},[898,29359,1745],{},[1654,29361,1750],{},[898,29363,11539],{},[1654,29365,1766],{},[898,29367,20896],{},[898,29369,2138],{"mathvariant":1878},[5008,29371],{"width":14608},[1654,29373,1708],{"stretchy":1656},[1665,29375,29376],{},"7.6",[1654,29378,1726],{"stretchy":1656},[902,29380,29381],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,29383,29385],{"id":29384},"soustava-rovnic","Soustava rovnic",[724,29387,29388,29389,29410,29411,29435],{},"Pro pevně zadané (plánované) investice ",[883,29390,29392],{"className":29391},[886],[888,29393,29394],{"xmlns":890},[892,29395,29396,29408],{},[895,29397,29398,29400,29402],{},[898,29399,20896],{},[1654,29401,1750],{},[1741,29403,29404,29406],{},[898,29405,20896],{},[1654,29407,1670],{},[902,29409,20907],{"encoding":904}," a funkci spotřeby ",[883,29412,29414],{"className":29413},[886],[888,29415,29416],{"xmlns":890},[892,29417,29418,29432],{},[895,29419,29420,29422,29424,29426,29428,29430],{},[898,29421,11539],{},[1654,29423,1750],{},[898,29425,11539],{},[1654,29427,1708],{"stretchy":1656},[898,29429,1745],{},[1654,29431,1726],{"stretchy":1656},[902,29433,29434],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,29437,29438],{},[883,29439,29441],{"className":29440},[886],[888,29442,29443],{"xmlns":890},[892,29444,29445,29516],{},[895,29446,29447,29507,29509,29511,29514],{},[1960,29448,29449,29479],{"rowspacing":2574,"columnalign":2575,"columnspacing":2576},[1964,29450,29451,29457],{},[1967,29452,29453],{},[2582,29454,29455],{"scriptlevel":2062,"displaystyle":1673},[898,29456,1745],{},[1967,29458,29459],{},[2582,29460,29461],{"scriptlevel":2062,"displaystyle":1673},[895,29462,29463,29465,29467,29469,29471,29477],{},[895,29464],{},[1654,29466,1750],{},[898,29468,11539],{},[1654,29470,1766],{},[1741,29472,29473,29475],{},[898,29474,20896],{},[1654,29476,1670],{},[1654,29478,1674],{"separator":1673},[1964,29480,29481,29487],{},[1967,29482,29483],{},[2582,29484,29485],{"scriptlevel":2062,"displaystyle":1673},[898,29486,11539],{},[1967,29488,29489],{},[2582,29490,29491],{"scriptlevel":2062,"displaystyle":1673},[895,29492,29493,29495,29497,29499,29501,29503,29505],{},[895,29494],{},[1654,29496,1750],{},[898,29498,11539],{},[1654,29500,1708],{"stretchy":1656},[898,29502,1745],{},[1654,29504,1726],{"stretchy":1656},[1654,29506,1674],{"separator":1673},[5008,29508],{"width":14608},[1654,29510,1708],{"stretchy":1656},[1665,29512,29513],{},"7.7",[1654,29515,1726],{"stretchy":1656},[902,29517,29518],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,29520,29521,29522,2186,29524,2068,29541,2186,29544,2138],{},"jejímž řešením jsou ",[38,29523,22594],{},[883,29525,29527],{"className":29526},[886],[888,29528,29529],{"xmlns":890},[892,29530,29531,29539],{},[895,29532,29533],{},[1741,29534,29535,29537],{},[898,29536,1745],{},[898,29538,1798],{},[902,29540,22612],{"encoding":904},[38,29542,29543],{},"rovnovážná spotřeba",[883,29545,29547],{"className":29546},[886],[888,29548,29549],{"xmlns":890},[892,29550,29551,29559],{},[895,29552,29553],{},[1741,29554,29555,29557],{},[898,29556,11539],{},[898,29558,1798],{},[902,29560,22671],{"encoding":904},[198,29562,29564,29565],{"id":29563},"výpočet-yeye","Výpočet ",[883,29566,29568],{"className":29567},[886],[888,29569,29570],{"xmlns":890},[892,29571,29572,29580],{},[895,29573,29574],{},[1741,29575,29576,29578],{},[898,29577,1745],{},[898,29579,1798],{},[902,29581,22612],{"encoding":904},[724,29583,29584,29585,29608,29609,16411,29641],{},"Pro lineární spotřebu ",[883,29586,29588],{"className":29587},[886],[888,29589,29590],{"xmlns":890},[892,29591,29592,29606],{},[895,29593,29594,29596,29598,29600,29602,29604],{},[898,29595,11539],{},[1654,29597,1750],{},[898,29599,207],{},[898,29601,1745],{},[1654,29603,1766],{},[898,29605,9758],{},[902,29607,27616],{"encoding":904}," plyne z (7.7) rovnice ",[883,29610,29612],{"className":29611},[886],[888,29613,29614],{"xmlns":890},[892,29615,29616,29638],{},[895,29617,29618,29620,29622,29624,29626,29628,29630,29632],{},[898,29619,1745],{},[1654,29621,1750],{},[898,29623,207],{},[898,29625,1745],{},[1654,29627,1766],{},[898,29629,9758],{},[1654,29631,1766],{},[1741,29633,29634,29636],{},[898,29635,20896],{},[1654,29637,1670],{},[902,29639,29640],{"encoding":904},"Y = aY + b + I^*",[38,29642,29643],{},"redukovaný tvar",[724,29645,29646],{},[883,29647,29649],{"className":29648},[886],[888,29650,29651],{"xmlns":890},[892,29652,29653,29701],{},[895,29654,29655],{},[2792,29656,29657],{"notation":2794},[2582,29658,29659],{"scriptlevel":2062,"displaystyle":1656},[2582,29660,29661],{"scriptlevel":2062,"displaystyle":1656},[2582,29662,29663],{"scriptlevel":2062,"displaystyle":1673},[895,29664,29665,29667,29673,29675,29697,29699],{},[1865,29666,11744],{},[1741,29668,29669,29671],{},[898,29670,1745],{},[898,29672,1798],{},[1654,29674,1750],{},[2811,29676,29677,29689],{},[895,29678,29679,29681,29683],{},[898,29680,9758],{},[1654,29682,1766],{},[1741,29684,29685,29687],{},[898,29686,20896],{},[1654,29688,1670],{},[895,29690,29691,29693,29695],{},[1665,29692,1667],{},[1654,29694,2380],{},[898,29696,207],{},[898,29698,2138],{"mathvariant":1878},[1865,29700,11744],{},[902,29702,29703],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,29705,29707],{"id":29706},"příklad-73","Příklad 7.3",[724,29709,29710,29711,16828,29728,2068,29752,29778],{},"V modelu ",[883,29712,29714],{"className":29713},[886],[888,29715,29716],{"xmlns":890},[892,29717,29718,29726],{},[895,29719,29720,29722,29724],{},[898,29721,11539],{},[1865,29723,21002],{},[898,29725,20896],{},[902,29727,21007],{"encoding":904},[883,29729,29731],{"className":29730},[886],[888,29732,29733],{"xmlns":890},[892,29734,29735,29749],{},[895,29736,29737,29739,29741,29743,29745,29747],{},[898,29738,11539],{},[1654,29740,1750],{},[1665,29742,28017],{},[898,29744,1745],{},[1654,29746,1766],{},[1665,29748,4647],{},[902,29750,29751],{"encoding":904},"C = 0{,}6Y + 10",[883,29753,29755],{"className":29754},[886],[888,29756,29757],{"xmlns":890},[892,29758,29759,29775],{},[895,29760,29761,29763,29765,29767,29769],{},[898,29762,20896],{},[1654,29764,1750],{},[1665,29766,6509],{},[1654,29768,1750],{},[1741,29770,29771,29773],{},[898,29772,20896],{},[1654,29774,1670],{},[902,29776,29777],{"encoding":904},"I = 12 = I^*",". Soustava",[724,29780,29781],{},[883,29782,29784],{"className":29783},[886],[888,29785,29786],{"xmlns":890},[892,29787,29788,29844],{},[1960,29789,29790,29816],{"rowspacing":2574,"columnalign":2575,"columnspacing":2576},[1964,29791,29792,29798],{},[1967,29793,29794],{},[2582,29795,29796],{"scriptlevel":2062,"displaystyle":1673},[898,29797,1745],{},[1967,29799,29800],{},[2582,29801,29802],{"scriptlevel":2062,"displaystyle":1673},[895,29803,29804,29806,29808,29810,29812,29814],{},[895,29805],{},[1654,29807,1750],{},[898,29809,11539],{},[1654,29811,1766],{},[1665,29813,6509],{},[1654,29815,1674],{"separator":1673},[1964,29817,29818,29824],{},[1967,29819,29820],{},[2582,29821,29822],{"scriptlevel":2062,"displaystyle":1673},[898,29823,11539],{},[1967,29825,29826],{},[2582,29827,29828],{"scriptlevel":2062,"displaystyle":1673},[895,29829,29830,29832,29834,29836,29838,29840,29842],{},[895,29831],{},[1654,29833,1750],{},[1665,29835,28017],{},[898,29837,1745],{},[1654,29839,1766],{},[1665,29841,4647],{},[1654,29843,1674],{"separator":1673},[902,29845,29846],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,29848,29849,29850,1343,29873,29896,29897,12664],{},"má řešení ",[883,29851,29853],{"className":29852},[886],[888,29854,29855],{"xmlns":890},[892,29856,29857,29870],{},[895,29858,29859,29865,29867],{},[1741,29860,29861,29863],{},[898,29862,1745],{},[898,29864,1798],{},[1654,29866,1750],{},[1665,29868,29869],{},"55",[902,29871,29872],{"encoding":904},"Y^E = 55",[883,29874,29876],{"className":29875},[886],[888,29877,29878],{"xmlns":890},[892,29879,29880,29893],{},[895,29881,29882,29888,29890],{},[1741,29883,29884,29886],{},[898,29885,11539],{},[898,29887,1798],{},[1654,29889,1750],{},[1665,29891,29892],{},"43",[902,29894,29895],{"encoding":904},"C^E = 43"," (a ",[883,29898,29900],{"className":29899},[886],[888,29901,29902],{"xmlns":890},[892,29903,29904,29916],{},[895,29905,29906,29912,29914],{},[1741,29907,29908,29910],{},[898,29909,17398],{},[898,29911,1798],{},[1654,29913,1750],{},[1665,29915,6509],{},[902,29917,29918],{"encoding":904},"S^E = 12",[724,29920,29921],{},[614,29922,29923,29924,29946,29947,20840,29968,29991,29992,2138],{},"Obrázek 7.5 — Přímky ",[883,29925,29927],{"className":29926},[886],[888,29928,29929],{"xmlns":890},[892,29930,29931,29943],{},[895,29932,29933,29935,29937,29939,29941],{},[898,29934,11539],{},[1654,29936,1750],{},[898,29938,1745],{},[1654,29940,2380],{},[1665,29942,6509],{},[902,29944,29945],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,29948,29950],{"className":29949},[886],[888,29951,29952],{"xmlns":890},[892,29953,29954,29966],{},[895,29955,29956,29958,29960,29962,29964],{},[898,29957,1745],{},[1654,29959,1750],{},[898,29961,11539],{},[1654,29963,1766],{},[898,29965,20896],{},[902,29967,23453],{"encoding":904},[883,29969,29971],{"className":29970},[886],[888,29972,29973],{"xmlns":890},[892,29974,29975,29989],{},[895,29976,29977,29979,29981,29983,29985,29987],{},[898,29978,11539],{},[1654,29980,1750],{},[1665,29982,28017],{},[898,29984,1745],{},[1654,29986,1766],{},[1665,29988,4647],{},[902,29990,29751],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,29993,29995],{"className":29994},[886],[888,29996,29997],{"xmlns":890},[892,29998,29999,30031],{},[895,30000,30001,30003,30009,30011,30017,30019,30021,30023,30025,30027,30029],{},[1654,30002,1657],{"stretchy":1656},[1741,30004,30005,30007],{},[898,30006,1745],{},[898,30008,1798],{},[1654,30010,1674],{"separator":1673},[1741,30012,30013,30015],{},[898,30014,11539],{},[898,30016,1798],{},[1654,30018,1686],{"stretchy":1656},[1654,30020,1750],{},[1654,30022,1657],{"stretchy":1656},[1665,30024,29869],{},[1654,30026,1674],{"separator":1673},[1665,30028,29892],{},[1654,30030,1686],{"stretchy":1656},[902,30032,30033],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,30035,30036,30039,30040,30057,30058,2138],{},[38,30037,30038],{},"Komentář k přechodu."," Model ",[883,30041,30043],{"className":30042},[886],[888,30044,30045],{"xmlns":890},[892,30046,30047,30055],{},[895,30048,30049,30051,30053],{},[898,30050,11539],{},[1865,30052,21002],{},[898,30054,20896],{},[902,30056,21007],{"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 ",[38,30059,30060,30061],{},"model ",[883,30062,30064],{"className":30063},[886],[888,30065,30066],{"xmlns":890},[892,30067,30068,30080],{},[895,30069,30070,30072,30074,30076,30078],{},[898,30071,11539],{},[1865,30073,21002],{},[898,30075,20896],{},[1865,30077,21002],{},[898,30079,20824],{},[902,30081,26916],{"encoding":904},[115,30083,30085],{"id":30084},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,30087,29315],{"id":30088},"zadání-modelu-1",[724,30090,30091,30092,30109,30110,2186,30113,18742,30126,30129],{},"Rozšíření modelu ",[883,30093,30095],{"className":30094},[886],[888,30096,30097],{"xmlns":890},[892,30098,30099,30107],{},[895,30100,30101,30103,30105],{},[898,30102,11539],{},[1865,30104,21002],{},[898,30106,20896],{},[902,30108,21007],{"encoding":904}," o ",[38,30111,30112],{},"vládní výdaje",[883,30114,30116],{"className":30115},[886],[888,30117,30118],{"xmlns":890},[892,30119,30120,30124],{},[895,30121,30122],{},[898,30123,20824],{},[902,30125,20824],{"encoding":904},[614,30127,30128],{},"government expenditure","). Podmínka rovnováhy:",[724,30131,30132],{},[883,30133,30135],{"className":30134},[886],[888,30136,30137],{"xmlns":890},[892,30138,30139,30166],{},[895,30140,30141,30143,30145,30147,30149,30151,30153,30155,30157,30159,30161,30164],{},[898,30142,1745],{},[1654,30144,1750],{},[898,30146,11539],{},[1654,30148,1766],{},[898,30150,20896],{},[1654,30152,1766],{},[898,30154,20824],{},[898,30156,2138],{"mathvariant":1878},[5008,30158],{"width":14608},[1654,30160,1708],{"stretchy":1656},[1665,30162,30163],{},"7.8",[1654,30165,1726],{"stretchy":1656},[902,30167,30168],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,30170,30171,30172,2186,30175,18742,30188,30191],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,30173,30174],{},"zdaněním domácností",[883,30176,30178],{"className":30177},[886],[888,30179,30180],{"xmlns":890},[892,30181,30182,30186],{},[895,30183,30184],{},[898,30185,11536],{},[902,30187,11536],{"encoding":904},[614,30189,30190],{},"taxation","). Zdanění bývá:",[120,30193,30194,30227,30252],{},[123,30195,30196,30197,1674],{},"úměrné důchodu: ",[883,30198,30200],{"className":30199},[886],[888,30201,30202],{"xmlns":890},[892,30203,30204,30224],{},[895,30205,30206,30208,30210,30212,30214,30216,30218,30220,30222],{},[898,30207,11536],{},[1654,30209,1750],{},[898,30211,11536],{},[1654,30213,1708],{"stretchy":1656},[898,30215,1745],{},[1654,30217,1726],{"stretchy":1656},[1654,30219,1750],{},[898,30221,27551],{},[898,30223,1745],{},[902,30225,30226],{"encoding":904},"T = T(Y) = tY",[123,30228,30229,30230,1674],{},"fixní: ",[883,30231,30233],{"className":30232},[886],[888,30234,30235],{"xmlns":890},[892,30236,30237,30249],{},[895,30238,30239,30241,30243],{},[898,30240,11536],{},[1654,30242,1750],{},[1741,30244,30245,30247],{},[898,30246,11536],{},[1654,30248,1670],{},[902,30250,30251],{"encoding":904},"T = T^*",[123,30253,30254,30255,9762,30283,2138],{},"kombinované: ",[883,30256,30258],{"className":30257},[886],[888,30259,30260],{"xmlns":890},[892,30261,30262,30280],{},[895,30263,30264,30266,30268,30274,30276,30278],{},[898,30265,11536],{},[1654,30267,1750],{},[1741,30269,30270,30272],{},[898,30271,11536],{},[1654,30273,1670],{},[1654,30275,1766],{},[898,30277,27551],{},[898,30279,1745],{},[902,30281,30282],{"encoding":904},"T = T^* + tY",[883,30284,30286],{"className":30285},[886],[888,30287,30288],{"xmlns":890},[892,30289,30290,30302],{},[895,30291,30292,30294,30296,30298,30300],{},[1665,30293,2062],{},[1654,30295,16405],{},[898,30297,27551],{},[1654,30299,3002],{},[1665,30301,1667],{},[902,30303,30304],{"encoding":904},"0 \\le t \u003C 1",[2140,30306,30307],{},[724,30308,30309,30311,30312,30333,30334,30337,30338,30351,30352,20840,30378,2186,30381,30407,30408,30436,30437,2068,30450,30468],{},[883,30310,2146],{}," Pozor na disponibilní důchod\nV modelu ",[883,30313,30315],{"className":30314},[886],[888,30316,30317],{"xmlns":890},[892,30318,30319,30331],{},[895,30320,30321,30323,30325,30327,30329],{},[898,30322,11539],{},[1865,30324,21002],{},[898,30326,20896],{},[1865,30328,21002],{},[898,30330,20824],{},[902,30332,26916],{"encoding":904}," je nutné ",[38,30335,30336],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,30339,30341],{"className":30340},[886],[888,30342,30343],{"xmlns":890},[892,30344,30345,30349],{},[895,30346,30347],{},[898,30348,1745],{},[902,30350,1745],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,30353,30355],{"className":30354},[886],[888,30356,30357],{"xmlns":890},[892,30358,30359,30375],{},[895,30360,30361,30363,30365,30367,30369,30371,30373],{},[898,30362,1745],{},[1654,30364,1750],{},[898,30366,11539],{},[1654,30368,1766],{},[898,30370,20896],{},[1654,30372,1766],{},[898,30374,20824],{},[902,30376,30377],{"encoding":904},"Y = C + I + G",[38,30379,30380],{},"disponibilní důchod",[883,30382,30384],{"className":30383},[886],[888,30385,30386],{"xmlns":890},[892,30387,30388,30404],{},[895,30389,30390,30396,30398,30400,30402],{},[1710,30391,30392,30394],{},[898,30393,1745],{},[898,30395,4980],{},[1654,30397,1750],{},[898,30399,1745],{},[1654,30401,2380],{},[898,30403,11536],{},[902,30405,30406],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,30409,30411],{"className":30410},[886],[888,30412,30413],{"xmlns":890},[892,30414,30415,30433],{},[895,30416,30417,30419,30421,30423,30425,30431],{},[898,30418,11539],{},[1654,30420,1750],{},[898,30422,11539],{},[1654,30424,1708],{"stretchy":1656},[1710,30426,30427,30429],{},[898,30428,1745],{},[898,30430,4980],{},[1654,30432,1726],{"stretchy":1656},[902,30434,30435],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,30438,30440],{"className":30439},[886],[888,30441,30442],{"xmlns":890},[892,30443,30444,30448],{},[895,30445,30446],{},[898,30447,1745],{},[902,30449,1745],{"encoding":904},[883,30451,30453],{"className":30452},[886],[888,30454,30455],{"xmlns":890},[892,30456,30457,30465],{},[895,30458,30459],{},[1710,30460,30461,30463],{},[898,30462,1745],{},[898,30464,4980],{},[902,30466,30467],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,30470,30471,18742,30474,1726],{},[38,30472,30473],{},"Disponibilní důchod",[614,30475,30476],{},"disposable income",[724,30478,30479],{},[883,30480,30482],{"className":30481},[886],[888,30483,30484],{"xmlns":890},[892,30485,30486,30502],{},[895,30487,30488,30494,30496,30498,30500],{},[1710,30489,30490,30492],{},[898,30491,1745],{},[898,30493,4980],{},[1654,30495,1750],{},[898,30497,1745],{},[1654,30499,2380],{},[898,30501,11536],{},[902,30503,30406],{"encoding":904},[724,30505,30506,30507,2138],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,30508,30510],{"className":30509},[886],[888,30511,30512],{"xmlns":890},[892,30513,30514,30532],{},[895,30515,30516,30518,30520,30522,30524,30530],{},[898,30517,11539],{},[1654,30519,1750],{},[898,30521,11539],{},[1654,30523,1708],{"stretchy":1656},[1710,30525,30526,30528],{},[898,30527,1745],{},[898,30529,4980],{},[1654,30531,1726],{"stretchy":1656},[902,30533,30435],{"encoding":904},[198,30535,29385],{"id":30536},"soustava-rovnic-1",[724,30538,30539,30540,1343,30561,30583,30584,2781],{},"Pro pevně zadané ",[883,30541,30543],{"className":30542},[886],[888,30544,30545],{"xmlns":890},[892,30546,30547,30559],{},[895,30548,30549,30551,30553],{},[898,30550,20896],{},[1654,30552,1750],{},[1741,30554,30555,30557],{},[898,30556,20896],{},[1654,30558,1670],{},[902,30560,20907],{"encoding":904},[883,30562,30564],{"className":30563},[886],[888,30565,30566],{"xmlns":890},[892,30567,30568,30580],{},[895,30569,30570,30572,30574],{},[898,30571,20824],{},[1654,30573,1750],{},[1741,30575,30576,30578],{},[898,30577,20824],{},[1654,30579,1670],{},[902,30581,30582],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,30585,30587],{"className":30586},[886],[888,30588,30589],{"xmlns":890},[892,30590,30591,30611],{},[895,30592,30593,30595,30597,30599,30601,30607,30609],{},[898,30594,1745],{},[1654,30596,1674],{"separator":1673},[898,30598,11539],{},[1654,30600,1674],{"separator":1673},[1710,30602,30603,30605],{},[898,30604,1745],{},[898,30606,4980],{},[1654,30608,1674],{"separator":1673},[898,30610,11536],{},[902,30612,30613],{"encoding":904},"Y, C, Y_D, T",[724,30615,30616],{},[883,30617,30619],{"className":30618},[886],[888,30620,30621],{"xmlns":890},[892,30622,30623,30764],{},[895,30624,30625,30755,30757,30759,30762],{},[1960,30626,30627,30665,30693,30725],{"rowspacing":2574,"columnalign":2575,"columnspacing":2576},[1964,30628,30629,30635],{},[1967,30630,30631],{},[2582,30632,30633],{"scriptlevel":2062,"displaystyle":1673},[898,30634,1745],{},[1967,30636,30637],{},[2582,30638,30639],{"scriptlevel":2062,"displaystyle":1673},[895,30640,30641,30643,30645,30647,30649,30655,30657,30663],{},[895,30642],{},[1654,30644,1750],{},[898,30646,11539],{},[1654,30648,1766],{},[1741,30650,30651,30653],{},[898,30652,20896],{},[1654,30654,1670],{},[1654,30656,1766],{},[1741,30658,30659,30661],{},[898,30660,20824],{},[1654,30662,1670],{},[1654,30664,1674],{"separator":1673},[1964,30666,30667,30673],{},[1967,30668,30669],{},[2582,30670,30671],{"scriptlevel":2062,"displaystyle":1673},[898,30672,11536],{},[1967,30674,30675],{},[2582,30676,30677],{"scriptlevel":2062,"displaystyle":1673},[895,30678,30679,30681,30683,30685,30687,30689,30691],{},[895,30680],{},[1654,30682,1750],{},[898,30684,11536],{},[1654,30686,1708],{"stretchy":1656},[898,30688,1745],{},[1654,30690,1726],{"stretchy":1656},[1654,30692,1674],{"separator":1673},[1964,30694,30695,30701],{},[1967,30696,30697],{},[2582,30698,30699],{"scriptlevel":2062,"displaystyle":1673},[898,30700,11539],{},[1967,30702,30703],{},[2582,30704,30705],{"scriptlevel":2062,"displaystyle":1673},[895,30706,30707,30709,30711,30713,30715,30721,30723],{},[895,30708],{},[1654,30710,1750],{},[898,30712,11539],{},[1654,30714,1708],{"stretchy":1656},[1710,30716,30717,30719],{},[898,30718,1745],{},[898,30720,4980],{},[1654,30722,1726],{"stretchy":1656},[1654,30724,1674],{"separator":1673},[1964,30726,30727,30737],{},[1967,30728,30729],{},[2582,30730,30731],{"scriptlevel":2062,"displaystyle":1673},[1710,30732,30733,30735],{},[898,30734,1745],{},[898,30736,4980],{},[1967,30738,30739],{},[2582,30740,30741],{"scriptlevel":2062,"displaystyle":1673},[895,30742,30743,30745,30747,30749,30751,30753],{},[895,30744],{},[1654,30746,1750],{},[898,30748,1745],{},[1654,30750,2380],{},[898,30752,11536],{},[1654,30754,1674],{"separator":1673},[5008,30756],{"width":14608},[1654,30758,1708],{"stretchy":1656},[1665,30760,30761],{},"7.9",[1654,30763,1726],{"stretchy":1656},[902,30765,30766],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,30768,30769,30770,30814,30815,2138],{},"s řešeními ",[883,30771,30773],{"className":30772},[886],[888,30774,30775],{"xmlns":890},[892,30776,30777,30811],{},[895,30778,30779,30785,30787,30793,30795,30801,30803],{},[1741,30780,30781,30783],{},[898,30782,1745],{},[898,30784,1798],{},[1654,30786,1674],{"separator":1673},[1741,30788,30789,30791],{},[898,30790,11539],{},[898,30792,1798],{},[1654,30794,1674],{"separator":1673},[1741,30796,30797,30799],{},[898,30798,11536],{},[898,30800,1798],{},[1654,30802,1674],{"separator":1673},[1659,30804,30805,30807,30809],{},[898,30806,1745],{},[898,30808,4980],{},[898,30810,1798],{},[902,30812,30813],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,30816,30818],{"className":30817},[886],[888,30819,30820],{"xmlns":890},[892,30821,30822,30848],{},[895,30823,30824,30830,30832,30840,30842],{},[1741,30825,30826,30828],{},[898,30827,17398],{},[898,30829,1798],{},[1654,30831,1750],{},[1659,30833,30834,30836,30838],{},[898,30835,1745],{},[898,30837,4980],{},[898,30839,1798],{},[1654,30841,2380],{},[1741,30843,30844,30846],{},[898,30845,11539],{},[898,30847,1798],{},[902,30849,30850],{"encoding":904},"S^E = Y_D^E - C^E",[2140,30852,30853,30858],{},[724,30854,30855,30857],{},[883,30856,3111],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,30859,30860,30883,30966,31021,31111],{},[123,30861,30862,30865,30866,2138],{},[38,30863,30864],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,30867,30869],{"className":30868},[886],[888,30870,30871],{"xmlns":890},[892,30872,30873,30881],{},[895,30874,30875],{},[1710,30876,30877,30879],{},[898,30878,1745],{},[898,30880,4980],{},[902,30882,30467],{"encoding":904},[123,30884,30885,30934,30935,30952,30953,2138],{},[38,30886,30887,30888,30908,30909],{},"Dosaď ",[883,30889,30891],{"className":30890},[886],[888,30892,30893],{"xmlns":890},[892,30894,30895,30905],{},[895,30896,30897,30899,30901,30903],{},[898,30898,11536],{},[1654,30900,1708],{"stretchy":1656},[898,30902,1745],{},[1654,30904,1726],{"stretchy":1656},[902,30906,30907],{"encoding":904},"T(Y)"," do ",[883,30910,30912],{"className":30911},[886],[888,30913,30914],{"xmlns":890},[892,30915,30916,30932],{},[895,30917,30918,30924,30926,30928,30930],{},[1710,30919,30920,30922],{},[898,30921,1745],{},[898,30923,4980],{},[1654,30925,1750],{},[898,30927,1745],{},[1654,30929,2380],{},[898,30931,11536],{},[902,30933,30406],{"encoding":904}," — dostaneš ",[883,30936,30938],{"className":30937},[886],[888,30939,30940],{"xmlns":890},[892,30941,30942,30950],{},[895,30943,30944],{},[1710,30945,30946,30948],{},[898,30947,1745],{},[898,30949,4980],{},[902,30951,30467],{"encoding":904}," jako lineární funkci ",[883,30954,30956],{"className":30955},[886],[888,30957,30958],{"xmlns":890},[892,30959,30960,30964],{},[895,30961,30962],{},[898,30963,1745],{},[902,30965,1745],{"encoding":904},[123,30967,30968,30934,30995,30952,31008,2138],{},[38,30969,30887,30970,30994],{},[883,30971,30973],{"className":30972},[886],[888,30974,30975],{"xmlns":890},[892,30976,30977,30991],{},[895,30978,30979,30985,30987,30989],{},[1710,30980,30981,30983],{},[898,30982,1745],{},[898,30984,4980],{},[1654,30986,1708],{"stretchy":1656},[898,30988,1745],{},[1654,30990,1726],{"stretchy":1656},[902,30992,30993],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,30996,30998],{"className":30997},[886],[888,30999,31000],{"xmlns":890},[892,31001,31002,31006],{},[895,31003,31004],{},[898,31005,11539],{},[902,31007,11539],{"encoding":904},[883,31009,31011],{"className":31010},[886],[888,31012,31013],{"xmlns":890},[892,31014,31015,31019],{},[895,31016,31017],{},[898,31018,1745],{},[902,31020,1745],{"encoding":904},[123,31022,31023,2186,31045,31079,31080,31093,31094,2138],{},[38,31024,30887,31025,31044],{},[883,31026,31028],{"className":31027},[886],[888,31029,31030],{"xmlns":890},[892,31031,31032,31042],{},[895,31033,31034,31036,31038,31040],{},[898,31035,11539],{},[1654,31037,1708],{"stretchy":1656},[898,31039,1745],{},[1654,31041,1726],{"stretchy":1656},[902,31043,22925],{"encoding":904}," do podmínky rovnováhy",[883,31046,31048],{"className":31047},[886],[888,31049,31050],{"xmlns":890},[892,31051,31052,31076],{},[895,31053,31054,31056,31058,31060,31062,31068,31070],{},[898,31055,1745],{},[1654,31057,1750],{},[898,31059,11539],{},[1654,31061,1766],{},[1741,31063,31064,31066],{},[898,31065,20896],{},[1654,31067,1670],{},[1654,31069,1766],{},[1741,31071,31072,31074],{},[898,31073,20824],{},[1654,31075,1670],{},[902,31077,31078],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,31081,31083],{"className":31082},[886],[888,31084,31085],{"xmlns":890},[892,31086,31087,31091],{},[895,31088,31089],{},[898,31090,1745],{},[902,31092,1745],{"encoding":904},", odtud ",[883,31095,31097],{"className":31096},[886],[888,31098,31099],{"xmlns":890},[892,31100,31101,31109],{},[895,31102,31103],{},[1741,31104,31105,31107],{},[898,31106,1745],{},[898,31108,1798],{},[902,31110,22612],{"encoding":904},[123,31112,31113,31116,31117,1343,31135,1343,31155,1343,31172,2138],{},[38,31114,31115],{},"Zpětným dosazením"," dopočítej ",[883,31118,31120],{"className":31119},[886],[888,31121,31122],{"xmlns":890},[892,31123,31124,31132],{},[895,31125,31126],{},[1741,31127,31128,31130],{},[898,31129,11536],{},[898,31131,1798],{},[902,31133,31134],{"encoding":904},"T^E",[883,31136,31138],{"className":31137},[886],[888,31139,31140],{"xmlns":890},[892,31141,31142,31152],{},[895,31143,31144],{},[1659,31145,31146,31148,31150],{},[898,31147,1745],{},[898,31149,4980],{},[898,31151,1798],{},[902,31153,31154],{"encoding":904},"Y_D^E",[883,31156,31158],{"className":31157},[886],[888,31159,31160],{"xmlns":890},[892,31161,31162,31170],{},[895,31163,31164],{},[1741,31165,31166,31168],{},[898,31167,11539],{},[898,31169,1798],{},[902,31171,22671],{"encoding":904},[883,31173,31175],{"className":31174},[886],[888,31176,31177],{"xmlns":890},[892,31178,31179,31187],{},[895,31180,31181],{},[1741,31182,31183,31185],{},[898,31184,17398],{},[898,31186,1798],{},[902,31188,31189],{"encoding":904},"S^E",[198,31191,31193],{"id":31192},"příklad-74","Příklad 7.4",[724,31195,29710,31196,31217,31218,1343,31249,1343,31273,1343,31295,31317],{},[883,31197,31199],{"className":31198},[886],[888,31200,31201],{"xmlns":890},[892,31202,31203,31215],{},[895,31204,31205,31207,31209,31211,31213],{},[898,31206,11539],{},[1865,31208,21002],{},[898,31210,20896],{},[1865,31212,21002],{},[898,31214,20824],{},[902,31216,26916],{"encoding":904}," jsou dány ",[883,31219,31221],{"className":31220},[886],[888,31222,31223],{"xmlns":890},[892,31224,31225,31246],{},[895,31226,31227,31229,31231,31234,31236,31242,31244],{},[898,31228,11539],{},[1654,31230,1750],{},[1665,31232,31233],{},"0,9",[1865,31235,11744],{},[1710,31237,31238,31240],{},[898,31239,1745],{},[898,31241,4980],{},[1654,31243,1766],{},[1665,31245,14625],{},[902,31247,31248],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,31250,31252],{"className":31251},[886],[888,31253,31254],{"xmlns":890},[892,31255,31256,31270],{},[895,31257,31258,31260,31262,31264,31266,31268],{},[898,31259,11536],{},[1654,31261,1750],{},[1665,31263,11599],{},[898,31265,1745],{},[1654,31267,1766],{},[1665,31269,4622],{},[902,31271,31272],{"encoding":904},"T = 0{,}2Y + 25",[883,31274,31276],{"className":31275},[886],[888,31277,31278],{"xmlns":890},[892,31279,31280,31292],{},[895,31281,31282,31288,31290],{},[1741,31283,31284,31286],{},[898,31285,20896],{},[1654,31287,1670],{},[1654,31289,1750],{},[1665,31291,23747],{},[902,31293,31294],{"encoding":904},"I^* = 35",[883,31296,31298],{"className":31297},[886],[888,31299,31300],{"xmlns":890},[892,31301,31302,31314],{},[895,31303,31304,31310,31312],{},[1741,31305,31306,31308],{},[898,31307,20824],{},[1654,31309,1670],{},[1654,31311,1750],{},[1665,31313,4573],{},[902,31315,31316],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,31319,31320],{},[883,31321,31323],{"className":31322},[886],[888,31324,31325],{"xmlns":890},[892,31326,31327,31451],{},[1960,31328,31329,31359,31387,31421],{"rowspacing":2574,"columnalign":2575,"columnspacing":2576},[1964,31330,31331,31337],{},[1967,31332,31333],{},[2582,31334,31335],{"scriptlevel":2062,"displaystyle":1673},[898,31336,1745],{},[1967,31338,31339],{},[2582,31340,31341],{"scriptlevel":2062,"displaystyle":1673},[895,31342,31343,31345,31347,31349,31351,31353,31355,31357],{},[895,31344],{},[1654,31346,1750],{},[898,31348,11539],{},[1654,31350,1766],{},[1665,31352,23747],{},[1654,31354,1766],{},[1665,31356,4573],{},[1654,31358,1674],{"separator":1673},[1964,31360,31361,31367],{},[1967,31362,31363],{},[2582,31364,31365],{"scriptlevel":2062,"displaystyle":1673},[898,31366,11536],{},[1967,31368,31369],{},[2582,31370,31371],{"scriptlevel":2062,"displaystyle":1673},[895,31372,31373,31375,31377,31379,31381,31383,31385],{},[895,31374],{},[1654,31376,1750],{},[1665,31378,11599],{},[898,31380,1745],{},[1654,31382,1766],{},[1665,31384,4622],{},[1654,31386,1674],{"separator":1673},[1964,31388,31389,31395],{},[1967,31390,31391],{},[2582,31392,31393],{"scriptlevel":2062,"displaystyle":1673},[898,31394,11539],{},[1967,31396,31397],{},[2582,31398,31399],{"scriptlevel":2062,"displaystyle":1673},[895,31400,31401,31403,31405,31407,31409,31415,31417,31419],{},[895,31402],{},[1654,31404,1750],{},[1665,31406,31233],{},[1865,31408,11744],{},[1710,31410,31411,31413],{},[898,31412,1745],{},[898,31414,4980],{},[1654,31416,1766],{},[1665,31418,14625],{},[1654,31420,1674],{"separator":1673},[1964,31422,31423,31433],{},[1967,31424,31425],{},[2582,31426,31427],{"scriptlevel":2062,"displaystyle":1673},[1710,31428,31429,31431],{},[898,31430,1745],{},[898,31432,4980],{},[1967,31434,31435],{},[2582,31436,31437],{"scriptlevel":2062,"displaystyle":1673},[895,31438,31439,31441,31443,31445,31447,31449],{},[895,31440],{},[1654,31442,1750],{},[898,31444,1745],{},[1654,31446,2380],{},[898,31448,11536],{},[898,31450,2138],{"mathvariant":1878},[902,31452,31453],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,31455,31456,31459,31460,31514,31515,31561,31562,2781],{},[38,31457,31458],{},"Řešení."," Z definice ",[883,31461,31463],{"className":31462},[886],[888,31464,31465],{"xmlns":890},[892,31466,31467,31511],{},[895,31468,31469,31475,31477,31479,31481,31483,31485,31487,31489,31491,31493,31495,31497,31499,31501,31503,31505,31507,31509],{},[1710,31470,31471,31473],{},[898,31472,1745],{},[898,31474,4980],{},[1654,31476,1750],{},[898,31478,1745],{},[1654,31480,2380],{},[898,31482,11536],{},[1654,31484,1750],{},[898,31486,1745],{},[1654,31488,2380],{},[1654,31490,1708],{"stretchy":1656},[1665,31492,11599],{},[898,31494,1745],{},[1654,31496,1766],{},[1665,31498,4622],{},[1654,31500,1726],{"stretchy":1656},[1654,31502,1750],{},[1665,31504,23298],{},[898,31506,1745],{},[1654,31508,2380],{},[1665,31510,4622],{},[902,31512,31513],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,31516,31518],{"className":31517},[886],[888,31519,31520],{"xmlns":890},[892,31521,31522,31558],{},[895,31523,31524,31526,31528,31530,31532,31534,31536,31538,31540,31542,31544,31546,31548,31551,31553,31555],{},[898,31525,11539],{},[1654,31527,1750],{},[1665,31529,31233],{},[1654,31531,1708],{"stretchy":1656},[1665,31533,23298],{},[898,31535,1745],{},[1654,31537,2380],{},[1665,31539,4622],{},[1654,31541,1726],{"stretchy":1656},[1654,31543,1766],{},[1665,31545,14625],{},[1654,31547,1750],{},[1665,31549,31550],{},"0,72",[898,31552,1745],{},[1654,31554,1766],{},[1665,31556,31557],{},"47,5",[902,31559,31560],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,31563,31565],{"className":31564},[886],[888,31566,31567],{"xmlns":890},[892,31568,31569,31587],{},[895,31570,31571,31573,31575,31577,31579,31581,31583,31585],{},[898,31572,1745],{},[1654,31574,1750],{},[1665,31576,31550],{},[898,31578,1745],{},[1654,31580,1766],{},[1665,31582,31557],{},[1654,31584,1766],{},[1665,31586,29869],{},[902,31588,31589],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,31591,31592],{},[883,31593,31595],{"className":31594},[886],[888,31596,31597],{"xmlns":890},[892,31598,31599,31640],{},[895,31600,31601,31604,31606,31608,31611,31613,31615,31617,31623,31625,31635,31637],{},[1665,31602,31603],{},"0,28",[898,31605,1745],{},[1654,31607,1750],{},[1665,31609,31610],{},"102,5",[1865,31612,2805],{},[1654,31614,23717],{},[1865,31616,2805],{},[1741,31618,31619,31621],{},[898,31620,1745],{},[898,31622,1798],{},[1654,31624,1750],{},[2582,31626,31627],{"scriptlevel":2062,"displaystyle":1656},[2811,31628,31629,31632],{},[1665,31630,31631],{},"5125",[1665,31633,31634],{},"14",[1654,31636,14628],{},[1665,31638,31639],{},"366,071.",[902,31641,31642],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,31644,31645],{},"Rovnovážné veličiny:",[120,31647,31648,31683,31735,31789,31837],{},[123,31649,31650,1674],{},[883,31651,31653],{"className":31652},[886],[888,31654,31655],{"xmlns":890},[892,31656,31657,31680],{},[895,31658,31659,31665,31667,31675,31677],{},[1741,31660,31661,31663],{},[898,31662,1745],{},[898,31664,1798],{},[1654,31666,1750],{},[2582,31668,31669],{"scriptlevel":2062,"displaystyle":1656},[2811,31670,31671,31673],{},[1665,31672,31631],{},[1665,31674,31634],{},[1654,31676,14628],{},[1665,31678,31679],{},"366,071",[902,31681,31682],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,31684,31685,1674],{},[883,31686,31688],{"className":31687},[886],[888,31689,31690],{"xmlns":890},[892,31691,31692,31732],{},[895,31693,31694,31700,31702,31704,31706,31712,31714,31716,31718,31727,31729],{},[1741,31695,31696,31698],{},[898,31697,11536],{},[898,31699,1798],{},[1654,31701,1750],{},[1665,31703,11599],{},[1865,31705,11744],{},[1741,31707,31708,31710],{},[898,31709,1745],{},[898,31711,1798],{},[1654,31713,1766],{},[1665,31715,4622],{},[1654,31717,1750],{},[2582,31719,31720],{"scriptlevel":2062,"displaystyle":1656},[2811,31721,31722,31725],{},[1665,31723,31724],{},"1375",[1665,31726,31634],{},[1654,31728,14628],{},[1665,31730,31731],{},"98,214",[902,31733,31734],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,31736,31737,1674],{},[883,31738,31740],{"className":31739},[886],[888,31741,31742],{"xmlns":890},[892,31743,31744,31786],{},[895,31745,31746,31754,31756,31762,31764,31770,31772,31781,31783],{},[1659,31747,31748,31750,31752],{},[898,31749,1745],{},[898,31751,4980],{},[898,31753,1798],{},[1654,31755,1750],{},[1741,31757,31758,31760],{},[898,31759,1745],{},[898,31761,1798],{},[1654,31763,2380],{},[1741,31765,31766,31768],{},[898,31767,11536],{},[898,31769,1798],{},[1654,31771,1750],{},[2582,31773,31774],{"scriptlevel":2062,"displaystyle":1656},[2811,31775,31776,31779],{},[1665,31777,31778],{},"3750",[1665,31780,31634],{},[1654,31782,14628],{},[1665,31784,31785],{},"267,857",[902,31787,31788],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,31790,31791,1674],{},[883,31792,31794],{"className":31793},[886],[888,31795,31796],{"xmlns":890},[892,31797,31798,31834],{},[895,31799,31800,31806,31808,31814,31816,31818,31820,31829,31831],{},[1741,31801,31802,31804],{},[898,31803,11539],{},[898,31805,1798],{},[1654,31807,1750],{},[1741,31809,31810,31812],{},[898,31811,1745],{},[898,31813,1798],{},[1654,31815,2380],{},[1665,31817,29869],{},[1654,31819,1750],{},[2582,31821,31822],{"scriptlevel":2062,"displaystyle":1656},[2811,31823,31824,31827],{},[1665,31825,31826],{},"4355",[1665,31828,31634],{},[1654,31830,14628],{},[1665,31832,31833],{},"311,071",[902,31835,31836],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,31838,31839,31895],{},[883,31840,31842],{"className":31841},[886],[888,31843,31844],{"xmlns":890},[892,31845,31846,31892],{},[895,31847,31848,31854,31856,31864,31866,31872,31874,31876,31885,31887,31889],{},[1741,31849,31850,31852],{},[898,31851,17398],{},[898,31853,1798],{},[1654,31855,1750],{},[1659,31857,31858,31860,31862],{},[898,31859,1745],{},[898,31861,4980],{},[898,31863,1798],{},[1654,31865,2380],{},[1741,31867,31868,31870],{},[898,31869,11539],{},[898,31871,1798],{},[1654,31873,1750],{},[1654,31875,2380],{},[2582,31877,31878],{"scriptlevel":2062,"displaystyle":1656},[2811,31879,31880,31883],{},[1665,31881,31882],{},"605",[1665,31884,31634],{},[1654,31886,14628],{},[1654,31888,2380],{},[1665,31890,31891],{},"43,214",[902,31893,31894],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,31897,31898,30039,31900,31921,31922,31925,31926,31948,31949,2138],{},[38,31899,30038],{},[883,31901,31903],{"className":31902},[886],[888,31904,31905],{"xmlns":890},[892,31906,31907,31919],{},[895,31908,31909,31911,31913,31915,31917],{},[898,31910,11539],{},[1865,31912,21002],{},[898,31914,20896],{},[1865,31916,21002],{},[898,31918,20824],{},[902,31920,26916],{"encoding":904}," stále uvažuje ",[38,31923,31924],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,31927,31929],{"className":31928},[886],[888,31930,31931],{"xmlns":890},[892,31932,31933,31945],{},[895,31934,31935,31937,31939,31941,31943],{},[898,31936,21032],{},[1654,31938,1750],{},[898,31940,4762],{},[1654,31942,2380],{},[898,31944,9320],{},[902,31946,31947],{"encoding":904},"X = B - M"," dává ",[38,31950,30060,31951],{},[883,31952,31954],{"className":31953},[886],[888,31955,31956],{"xmlns":890},[892,31957,31958,31974],{},[895,31959,31960,31962,31964,31966,31968,31970,31972],{},[898,31961,11539],{},[1865,31963,21002],{},[898,31965,20896],{},[1865,31967,21002],{},[898,31969,20824],{},[1865,31971,21002],{},[898,31973,21032],{},[902,31975,21035],{"encoding":904},[115,31977,31979],{"id":31978},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,31981,29315],{"id":31982},"zadání-modelu-2",[724,31984,31985,31986,2186,31989,9762,32010,32023,32024,20840,32027,32040],{},"Rozšíření o ",[38,31987,31988],{},"čistý export",[883,31990,31992],{"className":31991},[886],[888,31993,31994],{"xmlns":890},[892,31995,31996,32008],{},[895,31997,31998,32000,32002,32004,32006],{},[898,31999,21032],{},[1654,32001,1750],{},[898,32003,4762],{},[1654,32005,2380],{},[898,32007,9320],{},[902,32009,31947],{"encoding":904},[883,32011,32013],{"className":32012},[886],[888,32014,32015],{"xmlns":890},[892,32016,32017,32021],{},[895,32018,32019],{},[898,32020,4762],{},[902,32022,4762],{"encoding":904}," je hrubý export (",[614,32025,32026],{},"brutto export",[883,32028,32030],{"className":32029},[886],[888,32031,32032],{"xmlns":890},[892,32033,32034,32038],{},[895,32035,32036],{},[898,32037,9320],{},[902,32039,9320],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,32042,32043],{},[883,32044,32046],{"className":32045},[886],[888,32047,32048],{"xmlns":890},[892,32049,32050,32070],{},[895,32051,32052,32054,32056,32058,32060,32066,32068],{},[898,32053,9320],{},[1654,32055,1750],{},[898,32057,9320],{},[1654,32059,1708],{"stretchy":1656},[1710,32061,32062,32064],{},[898,32063,1745],{},[898,32065,4980],{},[1654,32067,1726],{"stretchy":1656},[898,32069,2138],{"mathvariant":1878},[902,32071,32072],{"encoding":904},"M = M(Y_D).",[724,32074,32075],{},"Podmínka rovnováhy:",[724,32077,32078],{},[883,32079,32081],{"className":32080},[886],[888,32082,32083],{"xmlns":890},[892,32084,32085,32122],{},[895,32086,32087,32089,32091,32093,32095,32097,32099,32101,32103,32105,32107,32109,32111,32113,32115,32118,32120],{},[898,32088,1745],{},[1654,32090,1750],{},[898,32092,11539],{},[1654,32094,1766],{},[898,32096,20896],{},[1654,32098,1766],{},[898,32100,20824],{},[1654,32102,1766],{},[898,32104,4762],{},[1654,32106,2380],{},[898,32108,9320],{},[898,32110,2138],{"mathvariant":1878},[5008,32112],{"width":14608},[1654,32114,1708],{"stretchy":1656},[1665,32116,32117],{},"7.10",[1865,32119,207],{},[1654,32121,1726],{"stretchy":1656},[902,32123,32124],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,32126,29385],{"id":32127},"soustava-rovnic-2",[724,32129,30539,32130,32164,32165,2781],{},[883,32131,32133],{"className":32132},[886],[888,32134,32135],{"xmlns":890},[892,32136,32137,32161],{},[895,32138,32139,32145,32147,32153,32155],{},[1741,32140,32141,32143],{},[898,32142,20896],{},[1654,32144,1670],{},[1654,32146,1674],{"separator":1673},[1741,32148,32149,32151],{},[898,32150,20824],{},[1654,32152,1670],{},[1654,32154,1674],{"separator":1673},[1741,32156,32157,32159],{},[898,32158,4762],{},[1654,32160,1670],{},[902,32162,32163],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,32166,32168],{"className":32167},[886],[888,32169,32170],{"xmlns":890},[892,32171,32172,32196],{},[895,32173,32174,32176,32178,32180,32182,32184,32186,32192,32194],{},[898,32175,1745],{},[1654,32177,1674],{"separator":1673},[898,32179,11539],{},[1654,32181,1674],{"separator":1673},[898,32183,11536],{},[1654,32185,1674],{"separator":1673},[1710,32187,32188,32190],{},[898,32189,1745],{},[898,32191,4980],{},[1654,32193,1674],{"separator":1673},[898,32195,9320],{},[902,32197,32198],{"encoding":904},"Y, C, T, Y_D, M",[724,32200,32201],{},[883,32202,32204],{"className":32203},[886],[888,32205,32206],{"xmlns":890},[892,32207,32208,32392],{},[895,32209,32210,32384,32386,32388,32390],{},[1960,32211,32212,32244,32274,32302,32334],{"rowspacing":2574,"columnalign":2575,"columnspacing":2576},[1964,32213,32214,32220],{},[1967,32215,32216],{},[2582,32217,32218],{"scriptlevel":2062,"displaystyle":1673},[898,32219,11539],{},[1967,32221,32222],{},[2582,32223,32224],{"scriptlevel":2062,"displaystyle":1673},[895,32225,32226,32228,32230,32232,32234,32240,32242],{},[895,32227],{},[1654,32229,1750],{},[898,32231,11539],{},[1654,32233,1708],{"stretchy":1656},[1710,32235,32236,32238],{},[898,32237,1745],{},[898,32239,4980],{},[1654,32241,1726],{"stretchy":1656},[1654,32243,1674],{"separator":1673},[1964,32245,32246,32256],{},[1967,32247,32248],{},[2582,32249,32250],{"scriptlevel":2062,"displaystyle":1673},[1710,32251,32252,32254],{},[898,32253,1745],{},[898,32255,4980],{},[1967,32257,32258],{},[2582,32259,32260],{"scriptlevel":2062,"displaystyle":1673},[895,32261,32262,32264,32266,32268,32270,32272],{},[895,32263],{},[1654,32265,1750],{},[898,32267,1745],{},[1654,32269,2380],{},[898,32271,11536],{},[1654,32273,1674],{"separator":1673},[1964,32275,32276,32282],{},[1967,32277,32278],{},[2582,32279,32280],{"scriptlevel":2062,"displaystyle":1673},[898,32281,11536],{},[1967,32283,32284],{},[2582,32285,32286],{"scriptlevel":2062,"displaystyle":1673},[895,32287,32288,32290,32292,32294,32296,32298,32300],{},[895,32289],{},[1654,32291,1750],{},[898,32293,11536],{},[1654,32295,1708],{"stretchy":1656},[898,32297,1745],{},[1654,32299,1726],{"stretchy":1656},[1654,32301,1674],{"separator":1673},[1964,32303,32304,32310],{},[1967,32305,32306],{},[2582,32307,32308],{"scriptlevel":2062,"displaystyle":1673},[898,32309,9320],{},[1967,32311,32312],{},[2582,32313,32314],{"scriptlevel":2062,"displaystyle":1673},[895,32315,32316,32318,32320,32322,32324,32330,32332],{},[895,32317],{},[1654,32319,1750],{},[898,32321,9320],{},[1654,32323,1708],{"stretchy":1656},[1710,32325,32326,32328],{},[898,32327,1745],{},[898,32329,4980],{},[1654,32331,1726],{"stretchy":1656},[1654,32333,1674],{"separator":1673},[1964,32335,32336,32342],{},[1967,32337,32338],{},[2582,32339,32340],{"scriptlevel":2062,"displaystyle":1673},[898,32341,1745],{},[1967,32343,32344],{},[2582,32345,32346],{"scriptlevel":2062,"displaystyle":1673},[895,32347,32348,32350,32352,32354,32356,32362,32364,32370,32372,32378,32380,32382],{},[895,32349],{},[1654,32351,1750],{},[898,32353,11539],{},[1654,32355,1766],{},[1741,32357,32358,32360],{},[898,32359,20896],{},[1654,32361,1670],{},[1654,32363,1766],{},[1741,32365,32366,32368],{},[898,32367,20824],{},[1654,32369,1670],{},[1654,32371,1766],{},[1741,32373,32374,32376],{},[898,32375,4762],{},[1654,32377,1670],{},[1654,32379,2380],{},[898,32381,9320],{},[898,32383,2138],{"mathvariant":1878},[5008,32385],{"width":14608},[1654,32387,1708],{"stretchy":1656},[1665,32389,32117],{},[1654,32391,1726],{"stretchy":1656},[902,32393,32394],{"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)",[198,32396,32398],{"id":32397},"příklad-75","Příklad 7.5",[724,32400,32401,32402,1343,32434,1343,32461,1343,32481,1343,32503,1343,32525,32548],{},"Dáno: ",[883,32403,32405],{"className":32404},[886],[888,32406,32407],{"xmlns":890},[892,32408,32409,32431],{},[895,32410,32411,32413,32415,32418,32420,32426,32428],{},[898,32412,11539],{},[1654,32414,1750],{},[1665,32416,32417],{},"0,75",[1865,32419,11744],{},[1710,32421,32422,32424],{},[898,32423,1745],{},[898,32425,4980],{},[1654,32427,1766],{},[1665,32429,32430],{},"750",[902,32432,32433],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,32435,32437],{"className":32436},[886],[888,32438,32439],{"xmlns":890},[892,32440,32441,32458],{},[895,32442,32443,32445,32447,32450,32452],{},[898,32444,9320],{},[1654,32446,1750],{},[1665,32448,32449],{},"0,15",[1865,32451,11744],{},[1710,32453,32454,32456],{},[898,32455,1745],{},[898,32457,4980],{},[902,32459,32460],{"encoding":904},"M = 0{,}15\\,Y_D",[883,32462,32464],{"className":32463},[886],[888,32465,32466],{"xmlns":890},[892,32467,32468,32478],{},[895,32469,32470,32472,32474,32476],{},[898,32471,11536],{},[1654,32473,1750],{},[1665,32475,7154],{},[898,32477,1745],{},[902,32479,32480],{"encoding":904},"T = 0{,}25Y",[883,32482,32484],{"className":32483},[886],[888,32485,32486],{"xmlns":890},[892,32487,32488,32500],{},[895,32489,32490,32496,32498],{},[1741,32491,32492,32494],{},[898,32493,20896],{},[1654,32495,1670],{},[1654,32497,1750],{},[1665,32499,4011],{},[902,32501,32502],{"encoding":904},"I^* = 500",[883,32504,32506],{"className":32505},[886],[888,32507,32508],{"xmlns":890},[892,32509,32510,32522],{},[895,32511,32512,32518,32520],{},[1741,32513,32514,32516],{},[898,32515,20824],{},[1654,32517,1670],{},[1654,32519,1750],{},[1665,32521,17528],{},[902,32523,32524],{"encoding":904},"G^* = 150",[883,32526,32528],{"className":32527},[886],[888,32529,32530],{"xmlns":890},[892,32531,32532,32545],{},[895,32533,32534,32540,32542],{},[1741,32535,32536,32538],{},[898,32537,4762],{},[1654,32539,1670],{},[1654,32541,1750],{},[1665,32543,32544],{},"800",[902,32546,32547],{"encoding":904},"B^* = 800",". Soustava:",[724,32550,32551],{},[883,32552,32554],{"className":32553},[886],[888,32555,32556],{"xmlns":890},[892,32557,32558,32776],{},[1960,32559,32560,32606,32648,32684,32726],{"rowspacing":2574,"columnalign":2575,"columnspacing":2576},[1964,32561,32562,32578],{},[1967,32563,32564],{},[2582,32565,32566],{"scriptlevel":2062,"displaystyle":1673},[895,32567,32568,32570,32572,32574,32576],{},[1654,32569,1708],{"stretchy":1656},[898,32571,20753],{},[1665,32573,1667],{},[1654,32575,1726],{"stretchy":1656},[1865,32577,11065],{},[1967,32579,32580],{},[2582,32581,32582],{"scriptlevel":2062,"displaystyle":1673},[895,32583,32584,32586,32588,32590,32592,32594,32600,32602,32604],{},[895,32585],{},[898,32587,11539],{},[1654,32589,1750],{},[1665,32591,32417],{},[1865,32593,11744],{},[1710,32595,32596,32598],{},[898,32597,1745],{},[898,32599,4980],{},[1654,32601,1766],{},[1665,32603,32430],{},[1654,32605,1674],{"separator":1673},[1964,32607,32608,32624],{},[1967,32609,32610],{},[2582,32611,32612],{"scriptlevel":2062,"displaystyle":1673},[895,32613,32614,32616,32618,32620,32622],{},[1654,32615,1708],{"stretchy":1656},[898,32617,20753],{},[1665,32619,1681],{},[1654,32621,1726],{"stretchy":1656},[1865,32623,11065],{},[1967,32625,32626],{},[2582,32627,32628],{"scriptlevel":2062,"displaystyle":1673},[895,32629,32630,32632,32638,32640,32642,32644,32646],{},[895,32631],{},[1710,32633,32634,32636],{},[898,32635,1745],{},[898,32637,4980],{},[1654,32639,1750],{},[898,32641,1745],{},[1654,32643,2380],{},[898,32645,11536],{},[1654,32647,1674],{"separator":1673},[1964,32649,32650,32666],{},[1967,32651,32652],{},[2582,32653,32654],{"scriptlevel":2062,"displaystyle":1673},[895,32655,32656,32658,32660,32662,32664],{},[1654,32657,1708],{"stretchy":1656},[898,32659,20753],{},[1665,32661,4035],{},[1654,32663,1726],{"stretchy":1656},[1865,32665,11065],{},[1967,32667,32668],{},[2582,32669,32670],{"scriptlevel":2062,"displaystyle":1673},[895,32671,32672,32674,32676,32678,32680,32682],{},[895,32673],{},[898,32675,11536],{},[1654,32677,1750],{},[1665,32679,7154],{},[898,32681,1745],{},[1654,32683,1674],{"separator":1673},[1964,32685,32686,32702],{},[1967,32687,32688],{},[2582,32689,32690],{"scriptlevel":2062,"displaystyle":1673},[895,32691,32692,32694,32696,32698,32700],{},[1654,32693,1708],{"stretchy":1656},[898,32695,20753],{},[1665,32697,7631],{},[1654,32699,1726],{"stretchy":1656},[1865,32701,11065],{},[1967,32703,32704],{},[2582,32705,32706],{"scriptlevel":2062,"displaystyle":1673},[895,32707,32708,32710,32712,32714,32716,32718,32724],{},[895,32709],{},[898,32711,9320],{},[1654,32713,1750],{},[1665,32715,32449],{},[1865,32717,11744],{},[1710,32719,32720,32722],{},[898,32721,1745],{},[898,32723,4980],{},[1654,32725,1674],{"separator":1673},[1964,32727,32728,32744],{},[1967,32729,32730],{},[2582,32731,32732],{"scriptlevel":2062,"displaystyle":1673},[895,32733,32734,32736,32738,32740,32742],{},[1654,32735,1708],{"stretchy":1656},[898,32737,20753],{},[1665,32739,4032],{},[1654,32741,1726],{"stretchy":1656},[1865,32743,11065],{},[1967,32745,32746],{},[2582,32747,32748],{"scriptlevel":2062,"displaystyle":1673},[895,32749,32750,32752,32754,32756,32758,32760,32762,32764,32766,32768,32770,32772,32774],{},[895,32751],{},[898,32753,1745],{},[1654,32755,1750],{},[898,32757,11539],{},[1654,32759,1766],{},[1665,32761,4011],{},[1654,32763,1766],{},[1665,32765,17528],{},[1654,32767,1766],{},[1665,32769,32544],{},[1654,32771,2380],{},[898,32773,9320],{},[898,32775,2138],{"mathvariant":1878},[902,32777,32778],{"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}",[724,32780,32781,32782,32816],{},"Postupná substituce — z (r3) do (r2): ",[883,32783,32785],{"className":32784},[886],[888,32786,32787],{"xmlns":890},[892,32788,32789,32813],{},[895,32790,32791,32797,32799,32801,32803,32805,32807,32809,32811],{},[1710,32792,32793,32795],{},[898,32794,1745],{},[898,32796,4980],{},[1654,32798,1750],{},[898,32800,1745],{},[1654,32802,2380],{},[1665,32804,7154],{},[898,32806,1745],{},[1654,32808,1750],{},[1665,32810,32417],{},[898,32812,1745],{},[902,32814,32815],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,32818,32819],{},[883,32820,32822],{"className":32821},[886],[888,32823,32824],{"xmlns":890},[892,32825,32826,32867],{},[895,32827,32828,32830,32832,32834,32836,32838,32840,32842,32844,32846,32848,32850,32852,32854,32856,32859,32861,32863,32865],{},[1654,32829,1708],{"stretchy":1656},[898,32831,20753],{},[1665,32833,11015],{},[1654,32835,1726],{"stretchy":1656},[1865,32837,11065],{},[898,32839,11539],{},[1654,32841,1750],{},[1665,32843,32417],{},[1654,32845,4554],{},[1665,32847,32417],{},[898,32849,1745],{},[1654,32851,1766],{},[1665,32853,32430],{},[1654,32855,1750],{},[1665,32857,32858],{},"0,5625",[898,32860,1745],{},[1654,32862,1766],{},[1665,32864,32430],{},[1654,32866,1674],{"separator":1673},[902,32868,32869],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,32871,32872],{},[883,32873,32875],{"className":32874},[886],[888,32876,32877],{"xmlns":890},[892,32878,32879,32913],{},[895,32880,32881,32883,32885,32888,32890,32892,32894,32896,32898,32900,32902,32904,32906,32909,32911],{},[1654,32882,1708],{"stretchy":1656},[898,32884,20753],{},[1665,32886,32887],{},"7",[1654,32889,1726],{"stretchy":1656},[1865,32891,11065],{},[898,32893,9320],{},[1654,32895,1750],{},[1665,32897,32449],{},[1654,32899,4554],{},[1665,32901,32417],{},[898,32903,1745],{},[1654,32905,1750],{},[1665,32907,32908],{},"0,1125",[898,32910,1745],{},[898,32912,2138],{"mathvariant":1878},[902,32914,32915],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,32917,32918],{},"Dosazením do (r5):",[724,32920,32921],{},[883,32922,32924],{"className":32923},[886],[888,32925,32926],{"xmlns":890},[892,32927,32928,32972],{},[895,32929,32930,32932,32934,32936,32938,32940,32942,32944,32946,32948,32950,32952,32954,32956,32958,32960,32962,32965,32967,32969],{},[898,32931,1745],{},[1654,32933,1750],{},[1665,32935,32858],{},[898,32937,1745],{},[1654,32939,1766],{},[1665,32941,32430],{},[1654,32943,1766],{},[1665,32945,4011],{},[1654,32947,1766],{},[1665,32949,17528],{},[1654,32951,1766],{},[1665,32953,32544],{},[1654,32955,2380],{},[1665,32957,32908],{},[898,32959,1745],{},[1654,32961,1750],{},[1665,32963,32964],{},"0,45",[898,32966,1745],{},[1654,32968,1766],{},[1665,32970,32971],{},"2200.",[902,32973,32974],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,32976,32977,32978,4579,33000,33023],{},"Odtud ",[883,32979,32981],{"className":32980},[886],[888,32982,32983],{"xmlns":890},[892,32984,32985,32997],{},[895,32986,32987,32990,32992,32994],{},[1665,32988,32989],{},"0,55",[898,32991,1745],{},[1654,32993,1750],{},[1665,32995,32996],{},"2200",[902,32998,32999],{"encoding":904},"0{,}55Y = 2200",[883,33001,33003],{"className":33002},[886],[888,33004,33005],{"xmlns":890},[892,33006,33007,33020],{},[895,33008,33009,33015,33017],{},[1741,33010,33011,33013],{},[898,33012,1745],{},[898,33014,1798],{},[1654,33016,1750],{},[1665,33018,33019],{},"4000",[902,33021,33022],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,33025,33026,33049,33081,33116,33149,33185],{},[123,33027,33028,1674],{},[883,33029,33031],{"className":33030},[886],[888,33032,33033],{"xmlns":890},[892,33034,33035,33047],{},[895,33036,33037,33043,33045],{},[1741,33038,33039,33041],{},[898,33040,1745],{},[898,33042,1798],{},[1654,33044,1750],{},[1665,33046,33019],{},[902,33048,33022],{"encoding":904},[123,33050,33051,1674],{},[883,33052,33054],{"className":33053},[886],[888,33055,33056],{"xmlns":890},[892,33057,33058,33078],{},[895,33059,33060,33066,33068,33070,33072,33074,33076],{},[1741,33061,33062,33064],{},[898,33063,11536],{},[898,33065,1798],{},[1654,33067,1750],{},[1665,33069,7154],{},[1654,33071,4554],{},[1665,33073,33019],{},[1654,33075,1750],{},[1665,33077,11544],{},[902,33079,33080],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,33082,33083,1674],{},[883,33084,33086],{"className":33085},[886],[888,33087,33088],{"xmlns":890},[892,33089,33090,33113],{},[895,33091,33092,33100,33102,33104,33106,33108,33110],{},[1659,33093,33094,33096,33098],{},[898,33095,1745],{},[898,33097,4980],{},[898,33099,1798],{},[1654,33101,1750],{},[1665,33103,32417],{},[1654,33105,4554],{},[1665,33107,33019],{},[1654,33109,1750],{},[1665,33111,33112],{},"3000",[902,33114,33115],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,33117,33118,1674],{},[883,33119,33121],{"className":33120},[886],[888,33122,33123],{"xmlns":890},[892,33124,33125,33146],{},[895,33126,33127,33133,33135,33137,33139,33141,33143],{},[1741,33128,33129,33131],{},[898,33130,9320],{},[898,33132,1798],{},[1654,33134,1750],{},[1665,33136,32449],{},[1654,33138,4554],{},[1665,33140,33112],{},[1654,33142,1750],{},[1665,33144,33145],{},"450",[902,33147,33148],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,33150,33151,1674],{},[883,33152,33154],{"className":33153},[886],[888,33155,33156],{"xmlns":890},[892,33157,33158,33182],{},[895,33159,33160,33166,33168,33170,33172,33174,33176,33178,33180],{},[1741,33161,33162,33164],{},[898,33163,11539],{},[898,33165,1798],{},[1654,33167,1750],{},[1665,33169,32417],{},[1654,33171,4554],{},[1665,33173,33112],{},[1654,33175,1766],{},[1665,33177,32430],{},[1654,33179,1750],{},[1665,33181,33112],{},[902,33183,33184],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,33186,33187,33227],{},[883,33188,33190],{"className":33189},[886],[888,33191,33192],{"xmlns":890},[892,33193,33194,33224],{},[895,33195,33196,33202,33204,33212,33214,33220,33222],{},[1741,33197,33198,33200],{},[898,33199,17398],{},[898,33201,1798],{},[1654,33203,1750],{},[1659,33205,33206,33208,33210],{},[898,33207,1745],{},[898,33209,4980],{},[898,33211,1798],{},[1654,33213,2380],{},[1741,33215,33216,33218],{},[898,33217,11539],{},[898,33219,1798],{},[1654,33221,1750],{},[1665,33223,2062],{},[902,33225,33226],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,33229,33230,33232,33233,1343,33250,2068,33271,33296,33297,33300,33301,33314,33315,2138],{},[38,33231,30038],{}," Modely ",[883,33234,33236],{"className":33235},[886],[888,33237,33238],{"xmlns":890},[892,33239,33240,33248],{},[895,33241,33242,33244,33246],{},[898,33243,11539],{},[1865,33245,21002],{},[898,33247,20896],{},[902,33249,21007],{"encoding":904},[883,33251,33253],{"className":33252},[886],[888,33254,33255],{"xmlns":890},[892,33256,33257,33269],{},[895,33258,33259,33261,33263,33265,33267],{},[898,33260,11539],{},[1865,33262,21002],{},[898,33264,20896],{},[1865,33266,21002],{},[898,33268,20824],{},[902,33270,26916],{"encoding":904},[883,33272,33274],{"className":33273},[886],[888,33275,33276],{"xmlns":890},[892,33277,33278,33294],{},[895,33279,33280,33282,33284,33286,33288,33290,33292],{},[898,33281,11539],{},[1865,33283,21002],{},[898,33285,20896],{},[1865,33287,21002],{},[898,33289,20824],{},[1865,33291,21002],{},[898,33293,21032],{},[902,33295,21035],{"encoding":904}," pokládají investice za ",[38,33298,33299],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,33302,33304],{"className":33303},[886],[888,33305,33306],{"xmlns":890},[892,33307,33308,33312],{},[895,33309,33310],{},[898,33311,20753],{},[902,33313,20753],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,33316,33317],{},"model IS-LM",[115,33319,33321],{"id":33320},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,33323,33324,33325,33329,33330,33333,33334,33337],{},"V článku ",[207,33326,33328],{"className":33327,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,33331,33332],{},"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 ",[38,33335,33336],{},"výraznější"," než v mikroekonomických modelech.",[724,33339,33340],{},[3492,33341],{"alt":33342,"className":33343,"src":33344},"imek-multiplikatorovy-efekt-chain",[210,3496],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,33346,20876,33347,1343,33364,1343,33385,33410,33411,33414,33415,33433,33434,33452,33453,33471,33472,33475,33476,1343,33493,33510,33511,33513],{},[883,33348,33350],{"className":33349},[886],[888,33351,33352],{"xmlns":890},[892,33353,33354,33362],{},[895,33355,33356,33358,33360],{},[898,33357,11539],{},[1865,33359,21002],{},[898,33361,20896],{},[902,33363,21007],{"encoding":904},[883,33365,33367],{"className":33366},[886],[888,33368,33369],{"xmlns":890},[892,33370,33371,33383],{},[895,33372,33373,33375,33377,33379,33381],{},[898,33374,11539],{},[1865,33376,21002],{},[898,33378,20896],{},[1865,33380,21002],{},[898,33382,20824],{},[902,33384,26916],{"encoding":904},[883,33386,33388],{"className":33387},[886],[888,33389,33390],{"xmlns":890},[892,33391,33392,33408],{},[895,33393,33394,33396,33398,33400,33402,33404,33406],{},[898,33395,11539],{},[1865,33397,21002],{},[898,33399,20896],{},[1865,33401,21002],{},[898,33403,20824],{},[1865,33405,21002],{},[898,33407,21032],{},[902,33409,21035],{"encoding":904}," se vyšetřuje vliv změn ",[38,33412,33413],{},"exogenních"," veličin (plánovaných investic ",[883,33416,33418],{"className":33417},[886],[888,33419,33420],{"xmlns":890},[892,33421,33422,33430],{},[895,33423,33424],{},[1741,33425,33426,33428],{},[898,33427,20896],{},[1654,33429,1670],{},[902,33431,33432],{"encoding":904},"I^*",", vládních výdajů ",[883,33435,33437],{"className":33436},[886],[888,33438,33439],{"xmlns":890},[892,33440,33441,33449],{},[895,33442,33443],{},[1741,33444,33445,33447],{},[898,33446,20824],{},[1654,33448,1670],{},[902,33450,33451],{"encoding":904},"G^*",", exportu ",[883,33454,33456],{"className":33455},[886],[888,33457,33458],{"xmlns":890},[892,33459,33460,33468],{},[895,33461,33462],{},[1741,33463,33464,33466],{},[898,33465,4762],{},[1654,33467,1670],{},[902,33469,33470],{"encoding":904},"B^*",") na změny ",[38,33473,33474],{},"endogenních"," rovnovážných veličin (",[883,33477,33479],{"className":33478},[886],[888,33480,33481],{"xmlns":890},[892,33482,33483,33491],{},[895,33484,33485],{},[1741,33486,33487,33489],{},[898,33488,1745],{},[898,33490,1798],{},[902,33492,22612],{"encoding":904},[883,33494,33496],{"className":33495},[886],[888,33497,33498],{"xmlns":890},[892,33499,33500,33508],{},[895,33501,33502],{},[1741,33503,33504,33506],{},[898,33505,11539],{},[898,33507,1798],{},[902,33509,22671],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,33512,26673],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,33515,33517],{"id":33516},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,33519,29584,33520,33543,33544,33588],{},[883,33521,33523],{"className":33522},[886],[888,33524,33525],{"xmlns":890},[892,33526,33527,33541],{},[895,33528,33529,33531,33533,33535,33537,33539],{},[898,33530,11539],{},[1654,33532,1750],{},[898,33534,207],{},[898,33536,1745],{},[1654,33538,1766],{},[898,33540,9758],{},[902,33542,27616],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,33545,33547],{"className":33546},[886],[888,33548,33549],{"xmlns":890},[892,33550,33551,33585],{},[895,33552,33553,33559,33561],{},[1741,33554,33555,33557],{},[898,33556,1745],{},[898,33558,1798],{},[1654,33560,1750],{},[2582,33562,33563],{"scriptlevel":2062,"displaystyle":1673},[2811,33564,33565,33577],{},[895,33566,33567,33569,33571],{},[898,33568,9758],{},[1654,33570,1766],{},[1741,33572,33573,33575],{},[898,33574,20896],{},[1654,33576,1670],{},[895,33578,33579,33581,33583],{},[1665,33580,1667],{},[1654,33582,2380],{},[898,33584,207],{},[902,33586,33587],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,33590,33591],{},[883,33592,33594],{"className":33593},[886],[888,33595,33596],{"xmlns":890},[892,33597,33598,33667],{},[895,33599,33600,33618,33620,33650,33652],{},[2811,33601,33602,33612],{},[895,33603,33604,33606],{},[898,33605,18589],{"mathvariant":1878},[1741,33607,33608,33610],{},[898,33609,1745],{},[898,33611,1798],{},[895,33613,33614,33616],{},[898,33615,18589],{"mathvariant":1878},[898,33617,207],{},[1654,33619,1750],{},[2811,33621,33622,33634],{},[895,33623,33624,33626,33628],{},[898,33625,9758],{},[1654,33627,1766],{},[1741,33629,33630,33632],{},[898,33631,20896],{},[1654,33633,1670],{},[895,33635,33636,33638,33640,33642,33644],{},[1654,33637,1708],{"stretchy":1656},[1665,33639,1667],{},[1654,33641,2380],{},[898,33643,207],{},[1741,33645,33646,33648],{},[1654,33647,1726],{"stretchy":1656},[1665,33649,1681],{},[5008,33651],{"width":14608},[895,33653,33654,33657,33664],{},[1865,33655,33656],{},"(multiplik",[17111,33658,33659,33661],{"accent":1673},[1865,33660,207],{},[1654,33662,33663],{},"ˊ",[1865,33665,33666],{},"tor MPC)",[902,33668,33669],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,33671,33672],{},[883,33673,33675],{"className":33674},[886],[888,33676,33677],{"xmlns":890},[892,33678,33679,33748],{},[895,33680,33681,33699,33701,33713,33715],{},[2811,33682,33683,33693],{},[895,33684,33685,33687],{},[898,33686,18589],{"mathvariant":1878},[1741,33688,33689,33691],{},[898,33690,1745],{},[898,33692,1798],{},[895,33694,33695,33697],{},[898,33696,18589],{"mathvariant":1878},[898,33698,9758],{},[1654,33700,1750],{},[2811,33702,33703,33705],{},[1665,33704,1667],{},[895,33706,33707,33709,33711],{},[1665,33708,1667],{},[1654,33710,2380],{},[898,33712,207],{},[5008,33714],{"width":14608},[895,33716,33717,33719,33725,33728,33735,33738,33745],{},[1865,33718,33656],{},[17111,33720,33721,33723],{"accent":1673},[1865,33722,207],{},[1654,33724,33663],{},[1865,33726,33727],{},"tor autonomn",[17111,33729,33730,33733],{"accent":1673},[1865,33731,33732],{},"ı",[1654,33734,33663],{},[1865,33736,33737],{}," spot",[17111,33739,33740,33742],{"accent":1673},[1865,33741,20753],{},[1654,33743,33744],{},"ˇ",[1865,33746,33747],{},"eby)",[902,33749,33750],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,33752,33753],{},[883,33754,33756],{"className":33755},[886],[888,33757,33758],{"xmlns":890},[892,33759,33760,33827],{},[895,33761,33762,33784,33786,33798,33800,33812,33814],{},[2811,33763,33764,33774],{},[895,33765,33766,33768],{},[898,33767,18589],{"mathvariant":1878},[1741,33769,33770,33772],{},[898,33771,1745],{},[898,33773,1798],{},[895,33775,33776,33778],{},[898,33777,18589],{"mathvariant":1878},[1741,33779,33780,33782],{},[898,33781,20896],{},[1654,33783,1670],{},[1654,33785,1750],{},[2811,33787,33788,33790],{},[1665,33789,1667],{},[895,33791,33792,33794,33796],{},[1665,33793,1667],{},[1654,33795,2380],{},[898,33797,207],{},[1654,33799,1750],{},[2811,33801,33802,33804],{},[1665,33803,1667],{},[895,33805,33806,33808,33810],{},[898,33807,9320],{},[898,33809,1755],{},[898,33811,17398],{},[5008,33813],{"width":14608},[895,33815,33816,33818,33824],{},[1865,33817,33656],{},[17111,33819,33820,33822],{"accent":1673},[1865,33821,207],{},[1654,33823,33663],{},[1865,33825,33826],{},"tor investic)",[902,33828,33829],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[2140,33831,33832],{},[724,33833,33834,33836,33837,33840,33841,33854,33855,33872,33873,33891,33892,33936,33937,30109,33954,33957,33958,33975],{},[883,33835,2860],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,33838,33839],{},"důchodem","; z něj se utratí ",[883,33842,33844],{"className":33843},[886],[888,33845,33846],{"xmlns":890},[892,33847,33848,33852],{},[895,33849,33850],{},[898,33851,207],{},[902,33853,207],{"encoding":904}," Kč (= ",[883,33856,33858],{"className":33857},[886],[888,33859,33860],{"xmlns":890},[892,33861,33862,33870],{},[895,33863,33864,33866,33868],{},[898,33865,9320],{},[898,33867,1755],{},[898,33869,11539],{},[902,33871,26741],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,33874,33876],{"className":33875},[886],[888,33877,33878],{"xmlns":890},[892,33879,33880,33888],{},[895,33881,33882],{},[1741,33883,33884,33886],{},[898,33885,207],{},[1665,33887,1681],{},[902,33889,33890],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,33893,33895],{"className":33894},[886],[888,33896,33897],{"xmlns":890},[892,33898,33899,33933],{},[895,33900,33901,33903,33905,33907,33909,33915,33917,33919,33921],{},[1665,33902,1667],{},[1654,33904,1766],{},[898,33906,207],{},[1654,33908,1766],{},[1741,33910,33911,33913],{},[898,33912,207],{},[1665,33914,1681],{},[1654,33916,1766],{},[1654,33918,26801],{},[1654,33920,1750],{},[2811,33922,33923,33925],{},[1665,33924,1667],{},[895,33926,33927,33929,33931],{},[1665,33928,1667],{},[1654,33930,2380],{},[898,33932,207],{},[902,33934,33935],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,33938,33940],{"className":33939},[886],[888,33941,33942],{"xmlns":890},[892,33943,33944,33952],{},[895,33945,33946],{},[1741,33947,33948,33950],{},[898,33949,1745],{},[898,33951,1798],{},[902,33953,22612],{"encoding":904},[38,33955,33956],{},"více"," než korunu — čím vyšší ",[883,33959,33961],{"className":33960},[886],[888,33962,33963],{"xmlns":890},[892,33964,33965,33973],{},[895,33966,33967,33969,33971],{},[898,33968,9320],{},[898,33970,1755],{},[898,33972,11539],{},[902,33974,26741],{"encoding":904},", tím silnější multiplikační efekt.",[724,33977,33978,33981,33982,34008,34009,34012,34013,2068,34034,34059,34060,2138],{},[38,33979,33980],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,33983,33985],{"className":33984},[886],[888,33986,33987],{"xmlns":890},[892,33988,33989,34005],{},[895,33990,33991],{},[2582,33992,33993],{"scriptlevel":2062,"displaystyle":1656},[2811,33994,33995,33997],{},[1665,33996,1667],{},[895,33998,33999,34001,34003],{},[1665,34000,1667],{},[1654,34002,2380],{},[898,34004,207],{},[902,34006,34007],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,34010,34011],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,34014,34016],{"className":34015},[886],[888,34017,34018],{"xmlns":890},[892,34019,34020,34032],{},[895,34021,34022,34024,34026,34028,34030],{},[898,34023,11539],{},[1865,34025,21002],{},[898,34027,20896],{},[1865,34029,21002],{},[898,34031,20824],{},[902,34033,26916],{"encoding":904},[883,34035,34037],{"className":34036},[886],[888,34038,34039],{"xmlns":890},[892,34040,34041,34057],{},[895,34042,34043,34045,34047,34049,34051,34053,34055],{},[898,34044,11539],{},[1865,34046,21002],{},[898,34048,20896],{},[1865,34050,21002],{},[898,34052,20824],{},[1865,34054,21002],{},[898,34056,21032],{},[902,34058,21035],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,34061,34063],{"className":34062,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,34065,34067],{"id":34066},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,34069,20876,34070,1343,34087,2068,34108,20881,34133,18742,34136,34157,34158,2186,34161,34174,34175,14398,34204,34221,34222,34225,34226,34228,34229,34250],{},[883,34071,34073],{"className":34072},[886],[888,34074,34075],{"xmlns":890},[892,34076,34077,34085],{},[895,34078,34079,34081,34083],{},[898,34080,11539],{},[1865,34082,21002],{},[898,34084,20896],{},[902,34086,21007],{"encoding":904},[883,34088,34090],{"className":34089},[886],[888,34091,34092],{"xmlns":890},[892,34093,34094,34106],{},[895,34095,34096,34098,34100,34102,34104],{},[898,34097,11539],{},[1865,34099,21002],{},[898,34101,20896],{},[1865,34103,21002],{},[898,34105,20824],{},[902,34107,26916],{"encoding":904},[883,34109,34111],{"className":34110},[886],[888,34112,34113],{"xmlns":890},[892,34114,34115,34131],{},[895,34116,34117,34119,34121,34123,34125,34127,34129],{},[898,34118,11539],{},[1865,34120,21002],{},[898,34122,20896],{},[1865,34124,21002],{},[898,34126,20824],{},[1865,34128,21002],{},[898,34130,21032],{},[902,34132,21035],{"encoding":904},[38,34134,34135],{},"investice konstantní",[883,34137,34139],{"className":34138},[886],[888,34140,34141],{"xmlns":890},[892,34142,34143,34155],{},[895,34144,34145,34147,34149],{},[898,34146,20896],{},[1654,34148,1750],{},[1741,34150,34151,34153],{},[898,34152,20896],{},[1654,34154,1670],{},[902,34156,20907],{"encoding":904},"). Reálnější je předpoklad, že ",[38,34159,34160],{},"investice závisejí na úrokové míře",[883,34162,34164],{"className":34163},[886],[888,34165,34166],{"xmlns":890},[892,34167,34168,34172],{},[895,34169,34170],{},[898,34171,20753],{},[902,34173,20753],{"encoding":904}," — klesající funkce ",[883,34176,34178],{"className":34177},[886],[888,34179,34180],{"xmlns":890},[892,34181,34182,34202],{},[895,34183,34184,34186,34188,34190,34192,34194,34196,34198,34200],{},[898,34185,20896],{},[1654,34187,1708],{"stretchy":1656},[898,34189,20753],{},[1654,34191,1726],{"stretchy":1656},[1654,34193,1750],{},[898,34195,3624],{},[898,34197,20753],{},[1654,34199,1766],{},[898,34201,10977],{},[902,34203,24462],{"encoding":904},[883,34205,34207],{"className":34206},[886],[888,34208,34209],{"xmlns":890},[892,34210,34211,34219],{},[895,34212,34213,34215,34217],{},[898,34214,3624],{},[1654,34216,3002],{},[1665,34218,2062],{},[902,34220,21226],{"encoding":904},". Přidáním ",[38,34223,34224],{},"trhu peněz"," k trhu zboží vzniká model ",[38,34227,20723],{}," se dvěma neznámými ",[883,34230,34232],{"className":34231},[886],[888,34233,34234],{"xmlns":890},[892,34235,34236,34248],{},[895,34237,34238,34240,34242,34244,34246],{},[1654,34239,1708],{"stretchy":1656},[898,34241,1745],{},[1654,34243,1674],{"separator":1673},[898,34245,20753],{},[1654,34247,1726],{"stretchy":1656},[902,34249,26846],{"encoding":904}," a dvěma rovnicemi:",[120,34252,34253,34303],{},[123,34254,34255,18742,34257,34259,34260,34281,34282,2138],{},[38,34256,24551],{},[614,34258,20766],{},") — klesající přímka v rovině ",[883,34261,34263],{"className":34262},[886],[888,34264,34265],{"xmlns":890},[892,34266,34267,34279],{},[895,34268,34269,34271,34273,34275,34277],{},[1654,34270,1708],{"stretchy":1656},[898,34272,20753],{},[1654,34274,1674],{"separator":1673},[898,34276,1745],{},[1654,34278,1726],{"stretchy":1656},[902,34280,21646],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,34283,34285],{"className":34284},[886],[888,34286,34287],{"xmlns":890},[892,34288,34289,34301],{},[895,34290,34291,34293,34295,34297,34299],{},[898,34292,1745],{},[1654,34294,1750],{},[898,34296,11539],{},[1654,34298,1766],{},[898,34300,20896],{},[902,34302,23453],{"encoding":904},[123,34304,34305,18742,34307,34309,34310,9762,34335,34381],{},[38,34306,24750],{},[614,34308,20773],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,34311,34313],{"className":34312},[886],[888,34314,34315],{"xmlns":890},[892,34316,34317,34333],{},[895,34318,34319,34325,34327],{},[1741,34320,34321,34323],{},[898,34322,9320],{},[898,34324,4980],{},[1654,34326,1750],{},[1741,34328,34329,34331],{},[898,34330,9320],{},[1654,34332,1670],{},[902,34334,22189],{"encoding":904},[883,34336,34338],{"className":34337},[886],[888,34339,34340],{"xmlns":890},[892,34341,34342,34378],{},[895,34343,34344,34350,34352,34358,34360,34362,34368,34370,34372],{},[1741,34345,34346,34348],{},[898,34347,9320],{},[898,34349,4980],{},[1654,34351,1750],{},[1710,34353,34354,34356],{},[898,34355,21946],{},[1665,34357,1667],{},[898,34359,1745],{},[1654,34361,1766],{},[1710,34363,34364,34366],{},[898,34365,21946],{},[1665,34367,1681],{},[898,34369,20753],{},[1654,34371,1766],{},[1710,34373,34374,34376],{},[898,34375,21946],{},[1665,34377,4035],{},[902,34379,34380],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,34383,34384,2186,34387,34420,34421,34423,34424,34426],{},[38,34385,34386],{},"Simultánní rovnovážný bod",[883,34388,34390],{"className":34389},[886],[888,34391,34392],{"xmlns":890},[892,34393,34394,34418],{},[895,34395,34396,34398,34400,34402,34408,34410,34416],{},[898,34397,1798],{},[1654,34399,1750],{},[1654,34401,1708],{"stretchy":1656},[1741,34403,34404,34406],{},[898,34405,20753],{},[898,34407,1798],{},[1654,34409,1674],{"separator":1673},[1741,34411,34412,34414],{},[898,34413,1745],{},[898,34415,1798],{},[1654,34417,1726],{"stretchy":1656},[902,34419,24842],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,34422,20811],{}," (posun IS) a ",[38,34425,20843],{}," (posun LM).",[724,34428,34429],{},[38,34430,34431,34432,1343,34454,1343,34476,1343,34498,34520,34521,2138],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,34433,34435],{"className":34434},[886],[888,34436,34437],{"xmlns":890},[892,34438,34439,34451],{},[895,34440,34441,34447,34449],{},[1741,34442,34443,34445],{},[898,34444,1745],{},[898,34446,1798],{},[1654,34448,1750],{},[1665,34450,23823],{},[902,34452,34453],{"encoding":904},"Y^E = 5000",[883,34455,34457],{"className":34456},[886],[888,34458,34459],{"xmlns":890},[892,34460,34461,34473],{},[895,34462,34463,34469,34471],{},[1741,34464,34465,34467],{},[898,34466,20753],{},[898,34468,1798],{},[1654,34470,1750],{},[1665,34472,4032],{},[902,34474,34475],{"encoding":904},"r^E = 5",[883,34477,34479],{"className":34478},[886],[888,34480,34481],{"xmlns":890},[892,34482,34483,34495],{},[895,34484,34485,34491,34493],{},[1741,34486,34487,34489],{},[898,34488,11539],{},[898,34490,1798],{},[1654,34492,1750],{},[1665,34494,23860],{},[902,34496,34497],{"encoding":904},"C^E = 4100",[883,34499,34501],{"className":34500},[886],[888,34502,34503],{"xmlns":890},[892,34504,34505,34517],{},[895,34506,34507,34513,34515],{},[1741,34508,34509,34511],{},[898,34510,20896],{},[898,34512,1798],{},[1654,34514,1750],{},[1665,34516,23899],{},[902,34518,34519],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,34522,945],{"className":34523,"dataFsResolvedFilePath":943,"href":944},[210],[115,34525,34527],{"id":34526},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,34529,34530,34594,34705,34848,35090,35158],{},[123,34531,34532,34535,34536,34558,34559,34593],{},[38,34533,34534],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,34537,34539],{"className":34538},[886],[888,34540,34541],{"xmlns":890},[892,34542,34543,34555],{},[895,34544,34545,34547,34549,34551,34553],{},[898,34546,20824],{},[898,34548,26990],{},[898,34550,1755],{},[1654,34552,11492],{},[898,34554,1745],{},[902,34556,34557],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,34560,34562],{"className":34561},[886],[888,34563,34564],{"xmlns":890},[892,34565,34566,34590],{},[895,34567,34568,34570,34572,34574,34576,34578,34580,34582,34584,34586,34588],{},[898,34569,20824],{},[898,34571,26990],{},[898,34573,1755],{},[1654,34575,1750],{},[898,34577,11539],{},[1654,34579,1766],{},[898,34581,20896],{},[1654,34583,1766],{},[898,34585,20824],{},[1654,34587,1766],{},[898,34589,21032],{},[902,34591,34592],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,34595,34596,34598,34599,34620,34621,1343,34644,34675,34676,34689,34690,2138],{},[38,34597,27224],{}," splňují ",[883,34600,34602],{"className":34601},[886],[888,34603,34604],{"xmlns":890},[892,34605,34606,34618],{},[895,34607,34608,34610,34612,34614,34616],{},[898,34609,1745],{},[1654,34611,1750],{},[898,34613,11539],{},[1654,34615,1766],{},[898,34617,17398],{},[902,34619,21405],{"encoding":904}," (7.2); lineární model ",[883,34622,34624],{"className":34623},[886],[888,34625,34626],{"xmlns":890},[892,34627,34628,34642],{},[895,34629,34630,34632,34634,34636,34638,34640],{},[898,34631,11539],{},[1654,34633,1750],{},[898,34635,207],{},[898,34637,1745],{},[1654,34639,1766],{},[898,34641,9758],{},[902,34643,27616],{"encoding":904},[883,34645,34647],{"className":34646},[886],[888,34648,34649],{"xmlns":890},[892,34650,34651,34673],{},[895,34652,34653,34655,34657,34659,34661,34663,34665,34667,34669,34671],{},[898,34654,17398],{},[1654,34656,1750],{},[1654,34658,1708],{"stretchy":1656},[1665,34660,1667],{},[1654,34662,2380],{},[898,34664,207],{},[1654,34666,1726],{"stretchy":1656},[898,34668,1745],{},[1654,34670,2380],{},[898,34672,9758],{},[902,34674,27865],{"encoding":904}," s autonomní spotřebou ",[883,34677,34679],{"className":34678},[886],[888,34680,34681],{"xmlns":890},[892,34682,34683,34687],{},[895,34684,34685],{},[898,34686,9758],{},[902,34688,9758],{"encoding":904}," a autonomními úsporami ",[883,34691,34693],{"className":34692},[886],[888,34694,34695],{"xmlns":890},[892,34696,34697,34703],{},[895,34698,34699,34701],{},[1654,34700,2380],{},[898,34702,9758],{},[902,34704,27944],{"encoding":904},[123,34706,34707,2186,34710,1343,34740,34770,34771,34801,34802,1343,34823,2138],{},[38,34708,34709],{},"Mezní sklony",[883,34711,34713],{"className":34712},[886],[888,34714,34715],{"xmlns":890},[892,34716,34717,34737],{},[895,34718,34719,34721,34723,34725,34727,34729,34731,34733,34735],{},[898,34720,9320],{},[898,34722,1755],{},[898,34724,11539],{},[1654,34726,1750],{},[898,34728,10977],{"mathvariant":1878},[898,34730,11539],{},[898,34732,1879],{"mathvariant":1878},[898,34734,10977],{"mathvariant":1878},[898,34736,1745],{},[902,34738,34739],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,34741,34743],{"className":34742},[886],[888,34744,34745],{"xmlns":890},[892,34746,34747,34767],{},[895,34748,34749,34751,34753,34755,34757,34759,34761,34763,34765],{},[898,34750,9320],{},[898,34752,1755],{},[898,34754,17398],{},[1654,34756,1750],{},[898,34758,10977],{"mathvariant":1878},[898,34760,17398],{},[898,34762,1879],{"mathvariant":1878},[898,34764,10977],{"mathvariant":1878},[898,34766,1745],{},[902,34768,34769],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,34772,34774],{"className":34773},[886],[888,34775,34776],{"xmlns":890},[892,34777,34778,34798],{},[895,34779,34780,34782,34784,34786,34788,34790,34792,34794,34796],{},[898,34781,9320],{},[898,34783,1755],{},[898,34785,11539],{},[1654,34787,1766],{},[898,34789,9320],{},[898,34791,1755],{},[898,34793,17398],{},[1654,34795,1750],{},[1665,34797,1667],{},[902,34799,34800],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,34803,34805],{"className":34804},[886],[888,34806,34807],{"xmlns":890},[892,34808,34809,34821],{},[895,34810,34811,34813,34815,34817,34819],{},[898,34812,9320],{},[898,34814,1755],{},[898,34816,11539],{},[1654,34818,1750],{},[898,34820,207],{},[902,34822,28584],{"encoding":904},[883,34824,34826],{"className":34825},[886],[888,34827,34828],{"xmlns":890},[892,34829,34830,34846],{},[895,34831,34832,34834,34836,34838,34840,34842,34844],{},[898,34833,9320],{},[898,34835,1755],{},[898,34837,17398],{},[1654,34839,1750],{},[1665,34841,1667],{},[1654,34843,2380],{},[898,34845,207],{},[902,34847,28610],{"encoding":904},[123,34849,34850,34853,34854],{},[38,34851,34852],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,34855,34856,34944,35013],{},[123,34857,34858,34875,34876,34897,34898,1674],{},[883,34859,34861],{"className":34860},[886],[888,34862,34863],{"xmlns":890},[892,34864,34865,34873],{},[895,34866,34867,34869,34871],{},[898,34868,11539],{},[1865,34870,21002],{},[898,34872,20896],{},[902,34874,21007],{"encoding":904},": ",[883,34877,34879],{"className":34878},[886],[888,34880,34881],{"xmlns":890},[892,34882,34883,34895],{},[895,34884,34885,34887,34889,34891,34893],{},[898,34886,1745],{},[1654,34888,1750],{},[898,34890,11539],{},[1654,34892,1766],{},[898,34894,20896],{},[902,34896,23453],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,34899,34901],{"className":34900},[886],[888,34902,34903],{"xmlns":890},[892,34904,34905,34941],{},[895,34906,34907,34913,34915,34917,34919,34921,34927,34929,34931,34933,34935,34937,34939],{},[1741,34908,34909,34911],{},[898,34910,1745],{},[898,34912,1798],{},[1654,34914,1750],{},[1654,34916,1708],{"stretchy":1656},[898,34918,9758],{},[1654,34920,1766],{},[1741,34922,34923,34925],{},[898,34924,20896],{},[1654,34926,1670],{},[1654,34928,1726],{"stretchy":1656},[898,34930,1879],{"mathvariant":1878},[1654,34932,1708],{"stretchy":1656},[1665,34934,1667],{},[1654,34936,2380],{},[898,34938,207],{},[1654,34940,1726],{"stretchy":1656},[902,34942,34943],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,34945,34946,34967,34968,34987,34988,1674],{},[883,34947,34949],{"className":34948},[886],[888,34950,34951],{"xmlns":890},[892,34952,34953,34965],{},[895,34954,34955,34957,34959,34961,34963],{},[898,34956,11539],{},[1865,34958,21002],{},[898,34960,20896],{},[1865,34962,21002],{},[898,34964,20824],{},[902,34966,26916],{"encoding":904},": přidává vládu, zdanění ",[883,34969,34971],{"className":34970},[886],[888,34972,34973],{"xmlns":890},[892,34974,34975,34985],{},[895,34976,34977,34979,34981,34983],{},[898,34978,11536],{},[1654,34980,1708],{"stretchy":1656},[898,34982,1745],{},[1654,34984,1726],{"stretchy":1656},[902,34986,30907],{"encoding":904}," a disponibilní důchod ",[883,34989,34991],{"className":34990},[886],[888,34992,34993],{"xmlns":890},[892,34994,34995,35011],{},[895,34996,34997,35003,35005,35007,35009],{},[1710,34998,34999,35001],{},[898,35000,1745],{},[898,35002,4980],{},[1654,35004,1750],{},[898,35006,1745],{},[1654,35008,2380],{},[898,35010,11536],{},[902,35012,30406],{"encoding":904},[123,35014,35015,35040,35041,9762,35062,2138],{},[883,35016,35018],{"className":35017},[886],[888,35019,35020],{"xmlns":890},[892,35021,35022,35038],{},[895,35023,35024,35026,35028,35030,35032,35034,35036],{},[898,35025,11539],{},[1865,35027,21002],{},[898,35029,20896],{},[1865,35031,21002],{},[898,35033,20824],{},[1865,35035,21002],{},[898,35037,21032],{},[902,35039,21035],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,35042,35044],{"className":35043},[886],[888,35045,35046],{"xmlns":890},[892,35047,35048,35060],{},[895,35049,35050,35052,35054,35056,35058],{},[898,35051,21032],{},[1654,35053,1750],{},[898,35055,4762],{},[1654,35057,2380],{},[898,35059,9320],{},[902,35061,31947],{"encoding":904},[883,35063,35065],{"className":35064},[886],[888,35066,35067],{"xmlns":890},[892,35068,35069,35087],{},[895,35070,35071,35073,35075,35077,35079,35085],{},[898,35072,9320],{},[1654,35074,1750],{},[898,35076,9320],{},[1654,35078,1708],{"stretchy":1656},[1710,35080,35081,35083],{},[898,35082,1745],{},[898,35084,4980],{},[1654,35086,1726],{"stretchy":1656},[902,35088,35089],{"encoding":904},"M = M(Y_D)",[123,35091,35092,35095,35096,2186,35099,35157],{},[38,35093,35094],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,35097,35098],{},"multiplikátor investic",[883,35100,35102],{"className":35101},[886],[888,35103,35104],{"xmlns":890},[892,35105,35106,35154],{},[895,35107,35108,35110,35116,35118,35120,35126,35128,35130,35132,35134,35136,35138,35140,35142,35144,35146,35148,35150,35152],{},[898,35109,18589],{"mathvariant":1878},[1741,35111,35112,35114],{},[898,35113,1745],{},[898,35115,1798],{},[898,35117,1879],{"mathvariant":1878},[898,35119,18589],{"mathvariant":1878},[1741,35121,35122,35124],{},[898,35123,20896],{},[1654,35125,1670],{},[1654,35127,1750],{},[1665,35129,1667],{},[898,35131,1879],{"mathvariant":1878},[1654,35133,1708],{"stretchy":1656},[1665,35135,1667],{},[1654,35137,2380],{},[898,35139,207],{},[1654,35141,1726],{"stretchy":1656},[1654,35143,1750],{},[1665,35145,1667],{},[898,35147,1879],{"mathvariant":1878},[898,35149,9320],{},[898,35151,1755],{},[898,35153,17398],{},[902,35155,35156],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,35159,35160,35162,35163,35178,35179,27344,35196,35211,35212,35237,35238,2138],{},[38,35161,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,35164,35166],{"className":35165},[886],[888,35167,35168],{"xmlns":890},[892,35169,35170,35176],{},[895,35171,35172,35174],{},[898,35173,20896],{},[898,35175,17398],{},[902,35177,20763],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,35180,35182],{"className":35181},[886],[888,35183,35184],{"xmlns":890},[892,35185,35186,35194],{},[895,35187,35188,35190,35192],{},[898,35189,20896],{},[1654,35191,1750],{},[898,35193,17398],{},[902,35195,21423],{"encoding":904},[883,35197,35199],{"className":35198},[886],[888,35200,35201],{"xmlns":890},[892,35202,35203,35209],{},[895,35204,35205,35207],{},[898,35206,2450],{},[898,35208,9320],{},[902,35210,20770],{"encoding":904}," rovnováhu trhu peněz (",[883,35213,35215],{"className":35214},[886],[888,35216,35217],{"xmlns":890},[892,35218,35219,35235],{},[895,35220,35221,35227,35229],{},[1741,35222,35223,35225],{},[898,35224,9320],{},[898,35226,4980],{},[1654,35228,1750],{},[1741,35230,35231,35233],{},[898,35232,9320],{},[1654,35234,1670],{},[902,35236,22189],{"encoding":904},"); průsečík dává ",[883,35239,35241],{"className":35240},[886],[888,35242,35243],{"xmlns":890},[892,35244,35245,35265],{},[895,35246,35247,35249,35255,35257,35263],{},[1654,35248,1708],{"stretchy":1656},[1741,35250,35251,35253],{},[898,35252,1745],{},[898,35254,1798],{},[1654,35256,1674],{"separator":1673},[1741,35258,35259,35261],{},[898,35260,20753],{},[898,35262,1798],{},[1654,35264,1726],{"stretchy":1656},[902,35266,20807],{"encoding":904},[115,35268,10214],{"id":10213},[120,35270,35271,35309,35349,35439,35521,35575,35631,35690,35725,35730,35802,35877,35963,36025,36093,36151,36204,36243],{},[123,35272,35273,10373,35276,34593],{},[38,35274,35275],{},"Hrubý národní produkt (GNP)",[883,35277,35279],{"className":35278},[886],[888,35280,35281],{"xmlns":890},[892,35282,35283,35307],{},[895,35284,35285,35287,35289,35291,35293,35295,35297,35299,35301,35303,35305],{},[898,35286,20824],{},[898,35288,26990],{},[898,35290,1755],{},[1654,35292,1750],{},[898,35294,11539],{},[1654,35296,1766],{},[898,35298,20896],{},[1654,35300,1766],{},[898,35302,20824],{},[1654,35304,1766],{},[898,35306,21032],{},[902,35308,34592],{"encoding":904},[123,35310,35311,35327,35328,2138],{},[38,35312,35313,35314],{},"Národní důchod ",[883,35315,35317],{"className":35316},[886],[888,35318,35319],{"xmlns":890},[892,35320,35321,35325],{},[895,35322,35323],{},[898,35324,1745],{},[902,35326,1745],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,35329,35331],{"className":35330},[886],[888,35332,35333],{"xmlns":890},[892,35334,35335,35347],{},[895,35336,35337,35339,35341,35343,35345],{},[898,35338,20824],{},[898,35340,26990],{},[898,35342,1755],{},[1654,35344,11492],{},[898,35346,1745],{},[902,35348,34557],{"encoding":904},[123,35350,35351,35377,35378,1343,35401,1343,35422,2138],{},[38,35352,35353,35354],{},"Funkce spotřeby ",[883,35355,35357],{"className":35356},[886],[888,35358,35359],{"xmlns":890},[892,35360,35361,35375],{},[895,35362,35363,35365,35367,35369,35371,35373],{},[898,35364,11539],{},[1654,35366,1750],{},[898,35368,11539],{},[1654,35370,1708],{"stretchy":1656},[898,35372,1745],{},[1654,35374,1726],{"stretchy":1656},[902,35376,29434],{"encoding":904}," — lineární model ",[883,35379,35381],{"className":35380},[886],[888,35382,35383],{"xmlns":890},[892,35384,35385,35399],{},[895,35386,35387,35389,35391,35393,35395,35397],{},[898,35388,11539],{},[1654,35390,1750],{},[898,35392,207],{},[898,35394,1745],{},[1654,35396,1766],{},[898,35398,9758],{},[902,35400,27616],{"encoding":904},[883,35402,35404],{"className":35403},[886],[888,35405,35406],{"xmlns":890},[892,35407,35408,35420],{},[895,35409,35410,35412,35414,35416,35418],{},[1665,35411,2062],{},[1654,35413,3002],{},[898,35415,207],{},[1654,35417,3002],{},[1665,35419,1667],{},[902,35421,27532],{"encoding":904},[883,35423,35425],{"className":35424},[886],[888,35426,35427],{"xmlns":890},[892,35428,35429,35437],{},[895,35430,35431,35433,35435],{},[898,35432,9758],{},[1654,35434,2952],{},[1665,35436,2062],{},[902,35438,27510],{"encoding":904},[123,35440,35441,10373,35468,35489,35490,2138],{},[38,35442,35443,35444],{},"Funkce úspor ",[883,35445,35447],{"className":35446},[886],[888,35448,35449],{"xmlns":890},[892,35450,35451,35465],{},[895,35452,35453,35455,35457,35459,35461,35463],{},[898,35454,17398],{},[1654,35456,1750],{},[898,35458,17398],{},[1654,35460,1708],{"stretchy":1656},[898,35462,1745],{},[1654,35464,1726],{"stretchy":1656},[902,35466,35467],{"encoding":904},"S = S(Y)",[883,35469,35471],{"className":35470},[886],[888,35472,35473],{"xmlns":890},[892,35474,35475,35487],{},[895,35476,35477,35479,35481,35483,35485],{},[898,35478,1745],{},[1654,35480,1750],{},[898,35482,11539],{},[1654,35484,1766],{},[898,35486,17398],{},[902,35488,21405],{"encoding":904},"; lineární ",[883,35491,35493],{"className":35492},[886],[888,35494,35495],{"xmlns":890},[892,35496,35497,35519],{},[895,35498,35499,35501,35503,35505,35507,35509,35511,35513,35515,35517],{},[898,35500,17398],{},[1654,35502,1750],{},[1654,35504,1708],{"stretchy":1656},[1665,35506,1667],{},[1654,35508,2380],{},[898,35510,207],{},[1654,35512,1726],{"stretchy":1656},[898,35514,1745],{},[1654,35516,2380],{},[898,35518,9758],{},[902,35520,27865],{"encoding":904},[123,35522,35523,10373,35526,1343,35549,2138],{},[38,35524,35525],{},"Autonomní spotřeba\u002Fúspory",[883,35527,35529],{"className":35528},[886],[888,35530,35531],{"xmlns":890},[892,35532,35533,35547],{},[895,35534,35535,35537,35539,35541,35543,35545],{},[898,35536,11539],{},[1654,35538,1708],{"stretchy":1656},[1665,35540,2062],{},[1654,35542,1726],{"stretchy":1656},[1654,35544,1750],{},[898,35546,9758],{},[902,35548,28257],{"encoding":904},[883,35550,35552],{"className":35551},[886],[888,35553,35554],{"xmlns":890},[892,35555,35556,35572],{},[895,35557,35558,35560,35562,35564,35566,35568,35570],{},[898,35559,17398],{},[1654,35561,1708],{"stretchy":1656},[1665,35563,2062],{},[1654,35565,1726],{"stretchy":1656},[1654,35567,1750],{},[1654,35569,2380],{},[898,35571,9758],{},[902,35573,35574],{"encoding":904},"S(0) = -b",[123,35576,35577,35609,35610,12664],{},[38,35578,35579,35580],{},"Mezní sklon ke spotřebě ",[883,35581,35583],{"className":35582},[886],[888,35584,35585],{"xmlns":890},[892,35586,35587,35607],{},[895,35588,35589,35591,35593,35595,35597,35599,35601,35603,35605],{},[898,35590,9320],{},[898,35592,1755],{},[898,35594,11539],{},[1654,35596,1750],{},[898,35598,10977],{"mathvariant":1878},[898,35600,11539],{},[898,35602,1879],{"mathvariant":1878},[898,35604,10977],{"mathvariant":1878},[898,35606,1745],{},[902,35608,34739],{"encoding":904}," (v lineárním modelu ",[883,35611,35613],{"className":35612},[886],[888,35614,35615],{"xmlns":890},[892,35616,35617,35629],{},[895,35618,35619,35621,35623,35625,35627],{},[898,35620,9320],{},[898,35622,1755],{},[898,35624,11539],{},[1654,35626,1750],{},[898,35628,207],{},[902,35630,28584],{"encoding":904},[123,35632,35633,35609,35665,12664],{},[38,35634,35635,35636],{},"Mezní sklon k úsporám ",[883,35637,35639],{"className":35638},[886],[888,35640,35641],{"xmlns":890},[892,35642,35643,35663],{},[895,35644,35645,35647,35649,35651,35653,35655,35657,35659,35661],{},[898,35646,9320],{},[898,35648,1755],{},[898,35650,17398],{},[1654,35652,1750],{},[898,35654,10977],{"mathvariant":1878},[898,35656,17398],{},[898,35658,1879],{"mathvariant":1878},[898,35660,10977],{"mathvariant":1878},[898,35662,1745],{},[902,35664,34769],{"encoding":904},[883,35666,35668],{"className":35667},[886],[888,35669,35670],{"xmlns":890},[892,35671,35672,35688],{},[895,35673,35674,35676,35678,35680,35682,35684,35686],{},[898,35675,9320],{},[898,35677,1755],{},[898,35679,17398],{},[1654,35681,1750],{},[1665,35683,1667],{},[1654,35685,2380],{},[898,35687,207],{},[902,35689,28610],{"encoding":904},[123,35691,35692,2186,35695,35724],{},[38,35693,35694],{},"Vztah",[883,35696,35698],{"className":35697},[886],[888,35699,35700],{"xmlns":890},[892,35701,35702,35722],{},[895,35703,35704,35706,35708,35710,35712,35714,35716,35718,35720],{},[898,35705,9320],{},[898,35707,1755],{},[898,35709,11539],{},[1654,35711,1766],{},[898,35713,9320],{},[898,35715,1755],{},[898,35717,17398],{},[1654,35719,1750],{},[1665,35721,1667],{},[902,35723,34800],{"encoding":904}," (7.5).",[123,35726,35727,35729],{},[38,35728,29277],{}," — rovnováha agregátní poptávky a nabídky.",[123,35731,35732,35735,35736,24497,35757,2138],{},[38,35733,35734],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,35737,35739],{"className":35738},[886],[888,35740,35741],{"xmlns":890},[892,35742,35743,35755],{},[895,35744,35745,35747,35749,35751,35753],{},[898,35746,1745],{},[1654,35748,1750],{},[898,35750,11539],{},[1654,35752,1766],{},[898,35754,20896],{},[902,35756,23453],{"encoding":904},[883,35758,35760],{"className":35759},[886],[888,35761,35762],{"xmlns":890},[892,35763,35764,35800],{},[895,35765,35766,35772,35774,35776,35778,35780,35786,35788,35790,35792,35794,35796,35798],{},[1741,35767,35768,35770],{},[898,35769,1745],{},[898,35771,1798],{},[1654,35773,1750],{},[1654,35775,1708],{"stretchy":1656},[898,35777,9758],{},[1654,35779,1766],{},[1741,35781,35782,35784],{},[898,35783,20896],{},[1654,35785,1670],{},[1654,35787,1726],{"stretchy":1656},[898,35789,1879],{"mathvariant":1878},[1654,35791,1708],{"stretchy":1656},[1665,35793,1667],{},[1654,35795,2380],{},[898,35797,207],{},[1654,35799,1726],{"stretchy":1656},[902,35801,34943],{"encoding":904},[123,35803,35804,35807,35808,1343,35827,24497,35852,2138],{},[38,35805,35806],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,35809,35811],{"className":35810},[886],[888,35812,35813],{"xmlns":890},[892,35814,35815,35825],{},[895,35816,35817,35819,35821,35823],{},[898,35818,11536],{},[1654,35820,1708],{"stretchy":1656},[898,35822,1745],{},[1654,35824,1726],{"stretchy":1656},[902,35826,30907],{"encoding":904},[883,35828,35830],{"className":35829},[886],[888,35831,35832],{"xmlns":890},[892,35833,35834,35850],{},[895,35835,35836,35842,35844,35846,35848],{},[1710,35837,35838,35840],{},[898,35839,1745],{},[898,35841,4980],{},[1654,35843,1750],{},[898,35845,1745],{},[1654,35847,2380],{},[898,35849,11536],{},[902,35851,30406],{"encoding":904},[883,35853,35855],{"className":35854},[886],[888,35856,35857],{"xmlns":890},[892,35858,35859,35875],{},[895,35860,35861,35863,35865,35867,35869,35871,35873],{},[898,35862,1745],{},[1654,35864,1750],{},[898,35866,11539],{},[1654,35868,1766],{},[898,35870,20896],{},[1654,35872,1766],{},[898,35874,20824],{},[902,35876,30377],{"encoding":904},[123,35878,35879,35882,35883,35904,35905,24497,35929,2138],{},[38,35880,35881],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,35884,35886],{"className":35885},[886],[888,35887,35888],{"xmlns":890},[892,35889,35890,35902],{},[895,35891,35892,35894,35896,35898,35900],{},[898,35893,21032],{},[1654,35895,1750],{},[898,35897,4762],{},[1654,35899,2380],{},[898,35901,9320],{},[902,35903,31947],{"encoding":904},", importem ",[883,35906,35908],{"className":35907},[886],[888,35909,35910],{"xmlns":890},[892,35911,35912,35926],{},[895,35913,35914,35916,35918,35924],{},[898,35915,9320],{},[1654,35917,1708],{"stretchy":1656},[1710,35919,35920,35922],{},[898,35921,1745],{},[898,35923,4980],{},[1654,35925,1726],{"stretchy":1656},[902,35927,35928],{"encoding":904},"M(Y_D)",[883,35930,35932],{"className":35931},[886],[888,35933,35934],{"xmlns":890},[892,35935,35936,35960],{},[895,35937,35938,35940,35942,35944,35946,35948,35950,35952,35954,35956,35958],{},[898,35939,1745],{},[1654,35941,1750],{},[898,35943,11539],{},[1654,35945,1766],{},[898,35947,20896],{},[1654,35949,1766],{},[898,35951,20824],{},[1654,35953,1766],{},[898,35955,4762],{},[1654,35957,2380],{},[898,35959,9320],{},[902,35961,35962],{"encoding":904},"Y = C + I + G + B - M",[123,35964,35965,10373,35968,35157],{},[38,35966,35967],{},"Multiplikátor investic",[883,35969,35971],{"className":35970},[886],[888,35972,35973],{"xmlns":890},[892,35974,35975,36023],{},[895,35976,35977,35979,35985,35987,35989,35995,35997,35999,36001,36003,36005,36007,36009,36011,36013,36015,36017,36019,36021],{},[898,35978,18589],{"mathvariant":1878},[1741,35980,35981,35983],{},[898,35982,1745],{},[898,35984,1798],{},[898,35986,1879],{"mathvariant":1878},[898,35988,18589],{"mathvariant":1878},[1741,35990,35991,35993],{},[898,35992,20896],{},[1654,35994,1670],{},[1654,35996,1750],{},[1665,35998,1667],{},[898,36000,1879],{"mathvariant":1878},[1654,36002,1708],{"stretchy":1656},[1665,36004,1667],{},[1654,36006,2380],{},[898,36008,207],{},[1654,36010,1726],{"stretchy":1656},[1654,36012,1750],{},[1665,36014,1667],{},[898,36016,1879],{"mathvariant":1878},[898,36018,9320],{},[898,36020,1755],{},[898,36022,17398],{},[902,36024,35156],{"encoding":904},[123,36026,36027,10373,36058,1343,36075,36092],{},[38,36028,24432,36029],{},[883,36030,36032],{"className":36031},[886],[888,36033,36034],{"xmlns":890},[892,36035,36036,36056],{},[895,36037,36038,36040,36042,36044,36046,36048,36050,36052,36054],{},[898,36039,20896],{},[1654,36041,1708],{"stretchy":1656},[898,36043,20753],{},[1654,36045,1726],{"stretchy":1656},[1654,36047,1750],{},[898,36049,3624],{},[898,36051,20753],{},[1654,36053,1766],{},[898,36055,10977],{},[902,36057,24462],{"encoding":904},[883,36059,36061],{"className":36060},[886],[888,36062,36063],{"xmlns":890},[892,36064,36065,36073],{},[895,36066,36067,36069,36071],{},[898,36068,3624],{},[1654,36070,3002],{},[1665,36072,2062],{},[902,36074,21226],{"encoding":904},[883,36076,36078],{"className":36077},[886],[888,36079,36080],{"xmlns":890},[892,36081,36082,36090],{},[895,36083,36084,36086,36088],{},[898,36085,10977],{},[1654,36087,2952],{},[1665,36089,2062],{},[902,36091,21205],{"encoding":904},"; klesající.",[123,36094,36095,36097,36098,36100,36101,36150],{},[38,36096,24551],{}," — rovnováha na trhu zboží (",[614,36099,20766],{},"); ",[883,36102,36104],{"className":36103},[886],[888,36105,36106],{"xmlns":890},[892,36107,36108,36148],{},[895,36109,36110,36112,36114,36126,36128,36130],{},[898,36111,1745],{},[1654,36113,1750],{},[2811,36115,36116,36118],{},[898,36117,3624],{},[895,36119,36120,36122,36124],{},[1665,36121,1667],{},[1654,36123,2380],{},[898,36125,207],{},[898,36127,20753],{},[1654,36129,1766],{},[2811,36131,36132,36140],{},[895,36133,36134,36136,36138],{},[898,36135,9758],{},[1654,36137,1766],{},[898,36139,10977],{},[895,36141,36142,36144,36146],{},[1665,36143,1667],{},[1654,36145,2380],{},[898,36147,207],{},[902,36149,24604],{"encoding":904}," (7.14); klesající.",[123,36152,36153,36155,36156,36100,36158,36203],{},[38,36154,24750],{}," — rovnováha na trhu peněz (",[614,36157,20773],{},[883,36159,36161],{"className":36160},[886],[888,36162,36163],{"xmlns":890},[892,36164,36165,36201],{},[895,36166,36167,36173,36175,36181,36183,36185,36191,36193,36195],{},[1741,36168,36169,36171],{},[898,36170,9320],{},[1654,36172,1670],{},[1654,36174,1750],{},[1710,36176,36177,36179],{},[898,36178,21946],{},[1665,36180,1667],{},[898,36182,1745],{},[1654,36184,1766],{},[1710,36186,36187,36189],{},[898,36188,21946],{},[1665,36190,1681],{},[898,36192,20753],{},[1654,36194,1766],{},[1710,36196,36197,36199],{},[898,36198,21946],{},[1665,36200,4035],{},[902,36202,24798],{"encoding":904}," (7.15); rostoucí.",[123,36205,36206,10373,36209,2138],{},[38,36207,36208],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,36210,36212],{"className":36211},[886],[888,36213,36214],{"xmlns":890},[892,36215,36216,36240],{},[895,36217,36218,36224,36226,36232,36234],{},[1741,36219,36220,36222],{},[898,36221,9320],{},[898,36223,4980],{},[1654,36225,1750],{},[1710,36227,36228,36230],{},[898,36229,2450],{},[1665,36231,1667],{},[1654,36233,1766],{},[1710,36235,36236,36238],{},[898,36237,2450],{},[1665,36239,1681],{},[902,36241,36242],{"encoding":904},"M^D = L_1 + L_2",[123,36244,36245,24808,36247,22689,36260,2068,36275,36290,36291,2138],{},[38,36246,945],{},[883,36248,36250],{"className":36249},[886],[888,36251,36252],{"xmlns":890},[892,36253,36254,36258],{},[895,36255,36256],{},[898,36257,1798],{},[902,36259,1798],{"encoding":904},[883,36261,36263],{"className":36262},[886],[888,36264,36265],{"xmlns":890},[892,36266,36267,36273],{},[895,36268,36269,36271],{},[898,36270,20896],{},[898,36272,17398],{},[902,36274,20763],{"encoding":904},[883,36276,36278],{"className":36277},[886],[888,36279,36280],{"xmlns":890},[892,36281,36282,36288],{},[895,36283,36284,36286],{},[898,36285,2450],{},[898,36287,9320],{},[902,36289,20770],{"encoding":904}," určuje ",[883,36292,36294],{"className":36293},[886],[888,36295,36296],{"xmlns":890},[892,36297,36298,36318],{},[895,36299,36300,36302,36308,36310,36316],{},[1654,36301,1708],{"stretchy":1656},[1741,36303,36304,36306],{},[898,36305,1745],{},[898,36307,1798],{},[1654,36309,1674],{"separator":1673},[1741,36311,36312,36314],{},[898,36313,20753],{},[898,36315,1798],{},[1654,36317,1726],{"stretchy":1656},[902,36319,20807],{"encoding":904},[115,36321,10613],{"id":10612},[120,36323,36324,36331,36338],{},[123,36325,36326,2186,36328],{},[38,36327,10686],{},[207,36329,10692],{"className":36330,"dataFsResolvedFilePath":10690,"href":10691},[210],[123,36332,36333,2186,36335],{},[38,36334,24916],{},[207,36336,24920],{"className":36337,"dataFsResolvedFilePath":868,"href":869},[210],[123,36339,36340,36342],{},[38,36341,24935],{},[120,36343,36344,36350,36356,36362],{},[123,36345,36346,36349],{},[207,36347,24976],{"className":36348,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,36351,36352,36355],{},[207,36353,24943],{"className":36354,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,36357,36358,36361],{},[207,36359,11707],{"className":36360,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,36363,36364,36367,36368,1343,36385,36402],{},[207,36365,1145],{"className":36366,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro 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diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":36404},[36405,36406,36407,36408,36413,36416,36417,36424,36429,36434,36437,36438,36439,36440],{"id":1637,"depth":642,"text":1638},{"id":26850,"depth":642,"text":26851},{"id":26970,"depth":642,"text":26971},{"id":27223,"depth":642,"text":27224,"children":36409},[36410,36411,36412],{"id":27227,"depth":649,"text":27228},{"id":27439,"depth":649,"text":27440},{"id":27947,"depth":649,"text":27948},{"id":28267,"depth":642,"text":28268,"children":36414},[36415],{"id":28782,"depth":649,"text":28783},{"id":29276,"depth":642,"text":29277},{"id":29303,"depth":642,"text":29304,"children":36418},[36419,36420,36421,36423],{"id":29314,"depth":649,"text":29315},{"id":29384,"depth":649,"text":29385},{"id":29563,"depth":649,"text":36422},"Výpočet 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TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,44994,44995],{},"poptávka",") a výrobce (",[38,44998,44999],{},"nabídka","), jejich interakci v ",[38,45002,45003],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,45006,26673],{},"). Uzavírá ji pojem ",[38,45009,45010],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,45013,45015],{"id":45014},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,45017,45018,45019,45022],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,45020,45021],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,45024,45025,45042,45084,45100],{},[123,45026,45027,45028,45041],{},"cena ",[883,45029,45031],{"className":45030},[886],[888,45032,45033],{"xmlns":890},[892,45034,45035,45039],{},[895,45036,45037],{},[898,45038,1755],{},[902,45040,1755],{"encoding":904}," zkoumaného zboží,",[123,45043,45044,45045,1674],{},"ceny alternativních zboží ",[883,45046,45048],{"className":45047},[886],[888,45049,45050],{"xmlns":890},[892,45051,45052,45081],{},[895,45053,45054,45060,45062,45068,45070,45072,45074],{},[1710,45055,45056,45058],{},[898,45057,1755],{},[1665,45059,1667],{},[1654,45061,1674],{"separator":1673},[1710,45063,45064,45066],{},[898,45065,1755],{},[1665,45067,1681],{},[1654,45069,1674],{"separator":1673},[1654,45071,18366],{},[1654,45073,1674],{"separator":1673},[1710,45075,45076,45078],{},[898,45077,1755],{},[898,45079,45080],{},"n",[902,45082,45083],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,45085,45086,45087,1674],{},"důchod ",[883,45088,45090],{"className":45089},[886],[888,45091,45092],{"xmlns":890},[892,45093,45094,45098],{},[895,45095,45096],{},[898,45097,1745],{},[902,45099,1745],{"encoding":904},[123,45101,45102,45103,45116,45117,45130,45131,45144,45145,45159,45160,45174],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,45104,45106],{"className":45105},[886],[888,45107,45108],{"xmlns":890},[892,45109,45110,45114],{},[895,45111,45112],{},[898,45113,2450],{},[902,45115,2450],{"encoding":904},", kapitál ",[883,45118,45120],{"className":45119},[886],[888,45121,45122],{"xmlns":890},[892,45123,45124,45128],{},[895,45125,45126],{},[898,45127,18517],{},[902,45129,18517],{"encoding":904},", půda ",[883,45132,45134],{"className":45133},[886],[888,45135,45136],{"xmlns":890},[892,45137,45138,45142],{},[895,45139,45140],{},[898,45141,1798],{},[902,45143,1798],{"encoding":904},"), technologie, počet výrobců ",[883,45146,45148],{"className":45147},[886],[888,45149,45150],{"xmlns":890},[892,45151,45152,45157],{},[895,45153,45154],{},[898,45155,45156],{},"O",[902,45158,45156],{"encoding":904},", počasí ",[883,45161,45163],{"className":45162},[886],[888,45164,45165],{"xmlns":890},[892,45166,45167,45172],{},[895,45168,45169],{},[898,45170,45171],{},"W",[902,45173,45171],{"encoding":904}," atd.",[724,45176,45177,45178,45181,45182,45185,45186,2138],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,45179,45180],{},"ceteris paribus","), hovoříme o ",[38,45183,45184],{},"jednofaktorovém modelu","; jinak jde o model ",[38,45187,45188],{},"vícefaktorový",[45190,45191],"hr",{},[115,45193,21870],{"id":44995},[2140,45195,45196],{},[724,45197,45198,45200,45201,45214,45215,45228,45229,45232,45233,45256,45257,2138],{},[883,45199,2860],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,45202,45204],{"className":45203},[886],[888,45205,45206],{"xmlns":890},[892,45207,45208,45212],{},[895,45209,45210],{},[898,45211,1663],{},[902,45213,1663],{"encoding":904}," na ceně ",[883,45216,45218],{"className":45217},[886],[888,45219,45220],{"xmlns":890},[892,45221,45222,45226],{},[895,45223,45224],{},[898,45225,1755],{},[902,45227,1755],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,45230,45231],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,45234,45236],{"className":45235},[886],[888,45237,45238],{"xmlns":890},[892,45239,45240,45254],{},[895,45241,45242,45244,45246,45248,45250,45252],{},[898,45243,1663],{},[1654,45245,1750],{},[898,45247,4980],{},[1654,45249,1708],{"stretchy":1656},[898,45251,1755],{},[1654,45253,1726],{"stretchy":1656},[902,45255,12933],{"encoding":904}," a jeho lineární verzí ",[883,45258,45260],{"className":45259},[886],[888,45261,45262],{"xmlns":890},[892,45263,45264,45278],{},[895,45265,45266,45268,45270,45272,45274,45276],{},[898,45267,1755],{},[1654,45269,1750],{},[898,45271,207],{},[898,45273,1663],{},[1654,45275,1766],{},[898,45277,9758],{},[902,45279,45280],{"encoding":904},"P = aQ + b",[198,45282,45284],{"id":45283},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,45286,45287,45288,45301,45302,45315,45316,18742,45318,11906],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,45289,45291],{"className":45290},[886],[888,45292,45293],{"xmlns":890},[892,45294,45295,45299],{},[895,45296,45297],{},[898,45298,1663],{},[902,45300,1663],{"encoding":904}," závisí na ceně ",[883,45303,45305],{"className":45304},[886],[888,45306,45307],{"xmlns":890},[892,45308,45309,45313],{},[895,45310,45311],{},[898,45312,1755],{},[902,45314,1755],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,45317,1892],{},[614,45319,45320],{},"demand function",[883,45322,45324],{"className":45323},[886],[888,45325,45326],{"xmlns":890,"display":1956},[892,45327,45328,45391],{},[1960,45329,45330],{"width":1962},[1964,45331,45332,45334,45384,45386],{},[1967,45333],{"width":1969},[1967,45335,45336],{},[895,45337,45338,45340,45342,45344,45346,45348,45350,45356,45358,45364,45366,45368,45370,45376,45378,45380,45382],{},[898,45339,1663],{},[1654,45341,1750],{},[898,45343,4980],{},[1654,45345,1708],{"stretchy":1656},[898,45347,1755],{},[1654,45349,1674],{"separator":1673},[1710,45351,45352,45354],{},[898,45353,1755],{},[1665,45355,1667],{},[1654,45357,1674],{"separator":1673},[1710,45359,45360,45362],{},[898,45361,1755],{},[1665,45363,1681],{},[1654,45365,1674],{"separator":1673},[1654,45367,18366],{},[1654,45369,1674],{"separator":1673},[1710,45371,45372,45374],{},[898,45373,1755],{},[898,45375,45080],{},[1654,45377,1674],{"separator":1673},[898,45379,1745],{},[1654,45381,1726],{"stretchy":1656},[898,45383,2138],{"mathvariant":1878},[1967,45385],{"width":1969},[1967,45387,45388],{},[1865,45389,45390],{},"(2.1)",[902,45392,45393],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,45395,45396,45397,45400,45401,45414],{},"Důležitou vlastností je ",[38,45398,45399],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,45402,45404],{"className":45403},[886],[888,45405,45406],{"xmlns":890},[892,45407,45408,45412],{},[895,45409,45410],{},[898,45411,20753],{},[902,45413,20753],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,45416,45418],{"className":45417},[886],[888,45419,45420],{"xmlns":890,"display":1956},[892,45421,45422,45537],{},[1960,45423,45424],{"width":1962},[1964,45425,45426,45428,45530,45532],{},[1967,45427],{"width":1969},[1967,45429,45430],{},[895,45431,45432,45434,45436,45438,45440,45442,45444,45446,45448,45454,45456,45458,45464,45466,45468,45470,45472,45478,45480,45482,45484,45486,45488,45490,45492,45494,45496,45502,45504,45510,45512,45514,45516,45522,45524,45526,45528],{},[898,45433,1663],{},[1654,45435,1750],{},[898,45437,4980],{},[1654,45439,1708],{"stretchy":1656},[898,45441,20753],{},[898,45443,1755],{},[1654,45445,1674],{"separator":1673},[898,45447,20753],{},[1710,45449,45450,45452],{},[898,45451,1755],{},[1665,45453,1667],{},[1654,45455,1674],{"separator":1673},[898,45457,20753],{},[1710,45459,45460,45462],{},[898,45461,1755],{},[1665,45463,1681],{},[1654,45465,1674],{"separator":1673},[1654,45467,18366],{},[1654,45469,1674],{"separator":1673},[898,45471,20753],{},[1710,45473,45474,45476],{},[898,45475,1755],{},[898,45477,45080],{},[1654,45479,1674],{"separator":1673},[898,45481,20753],{},[898,45483,1745],{},[1654,45485,1726],{"stretchy":1656},[1654,45487,1750],{},[898,45489,4980],{},[1654,45491,1708],{"stretchy":1656},[898,45493,1755],{},[1654,45495,1674],{"separator":1673},[1710,45497,45498,45500],{},[898,45499,1755],{},[1665,45501,1667],{},[1654,45503,1674],{"separator":1673},[1710,45505,45506,45508],{},[898,45507,1755],{},[1665,45509,1681],{},[1654,45511,1674],{"separator":1673},[1654,45513,18366],{},[1654,45515,1674],{"separator":1673},[1710,45517,45518,45520],{},[898,45519,1755],{},[898,45521,45080],{},[1654,45523,1674],{"separator":1673},[898,45525,1745],{},[1654,45527,1726],{"stretchy":1656},[898,45529,2138],{"mathvariant":1878},[1967,45531],{"width":1969},[1967,45533,45534],{},[1865,45535,45536],{},"(2.2)",[902,45538,45539],{"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}",[2140,45541,45542],{},[724,45543,45544,45546,45547,2138],{},[883,45545,2146],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,45548,45549],{},"v jednofaktorových modelech neplatí",[724,45551,45552,45553,1343,45556,2068,45559,45562],{},"Rozlišuje se poptávka ",[38,45554,45555],{},"individuální",[38,45557,45558],{},"tržní",[38,45560,45561],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,45564,45566],{"id":45565},"jednofaktorové-modely","Jednofaktorové modely",[45568,45569,45571],"h4",{"id":45570},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,45573,45574,45575,45588,45589,2781],{},"Poptávané množství ",[883,45576,45578],{"className":45577},[886],[888,45579,45580],{"xmlns":890},[892,45581,45582,45586],{},[895,45583,45584],{},[898,45585,1663],{},[902,45587,1663],{"encoding":904}," závisí pouze na ceně ",[883,45590,45592],{"className":45591},[886],[888,45593,45594],{"xmlns":890},[892,45595,45596,45600],{},[895,45597,45598],{},[898,45599,1755],{},[902,45601,1755],{"encoding":904},[883,45603,45605],{"className":45604},[886],[888,45606,45607],{"xmlns":890,"display":1956},[892,45608,45609,45661],{},[1960,45610,45611],{"width":1962},[1964,45612,45613,45615,45654,45656],{},[1967,45614],{"width":1969},[1967,45616,45617],{},[895,45618,45619,45621,45623,45625,45627,45629,45631,45633,45635,45638,45640,45642,45644,45646,45648,45650,45652],{},[898,45620,1663],{},[1654,45622,1750],{},[898,45624,4980],{},[1654,45626,1708],{"stretchy":1656},[898,45628,1755],{},[1654,45630,1726],{"stretchy":1656},[1654,45632,1674],{"separator":1673},[5008,45634],{"width":14608},[1865,45636,45637],{},"resp.",[5008,45639],{"width":14608},[898,45641,1755],{},[1654,45643,1750],{},[898,45645,4980],{},[1654,45647,1708],{"stretchy":1656},[898,45649,1663],{},[1654,45651,1726],{"stretchy":1656},[898,45653,2138],{"mathvariant":1878},[1967,45655],{"width":1969},[1967,45657,45658],{},[1865,45659,45660],{},"(2.3)",[902,45662,45663],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,45665,45666,45667,18742,45670,12664],{},"Graf této funkce se nazývá ",[38,45668,45669],{},"křivka poptávky",[614,45671,45672],{},"demand curve",[45568,45674,45676],{"id":45675},"zákon-klesající-poptávky","Zákon klesající poptávky",[2140,45678,45679],{},[724,45680,45681],{},[38,45682,45683,45684,45697,45698,45711,45712,45697,45725,45738],{},"Roste-li cena ",[883,45685,45687],{"className":45686},[886],[888,45688,45689],{"xmlns":890},[892,45690,45691,45695],{},[895,45692,45693],{},[898,45694,1755],{},[902,45696,1755],{"encoding":904},", pak množství ",[883,45699,45701],{"className":45700},[886],[888,45702,45703],{"xmlns":890},[892,45704,45705,45709],{},[895,45706,45707],{},[898,45708,1663],{},[902,45710,1663],{"encoding":904}," klesá; klesá-li cena ",[883,45713,45715],{"className":45714},[886],[888,45716,45717],{"xmlns":890},[892,45718,45719,45723],{},[895,45720,45721],{},[898,45722,1755],{},[902,45724,1755],{"encoding":904},[883,45726,45728],{"className":45727},[886],[888,45729,45730],{"xmlns":890},[892,45731,45732,45736],{},[895,45733,45734],{},[898,45735,1663],{},[902,45737,1663],{"encoding":904}," roste.",[724,45740,45741,45742,45745],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,45743,45744],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[2140,45747,45748,45753],{},[724,45749,45750,45752],{},[883,45751,2860],{}," Intuice — proč zákon platí",[120,45754,45755,45761],{},[123,45756,45757,45760],{},[38,45758,45759],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,45762,45763,45766],{},[38,45764,45765],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,45768,45769,45770,45783,45784,45797,45798,45824,45825,45851,45852,16828,45878,45881,45882,2138],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,45771,45773],{"className":45772},[886],[888,45774,45775],{"xmlns":890},[892,45776,45777,45781],{},[895,45778,45779],{},[898,45780,1755],{},[902,45782,1755],{"encoding":904}," se vynáší na svislou osu, množství ",[883,45785,45787],{"className":45786},[886],[888,45788,45789],{"xmlns":890},[892,45790,45791,45795],{},[895,45792,45793],{},[898,45794,1663],{},[902,45796,1663],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,45799,45801],{"className":45800},[886],[888,45802,45803],{"xmlns":890},[892,45804,45805,45821],{},[895,45806,45807,45809,45811,45813,45819],{},[1654,45808,1657],{"stretchy":1656},[1665,45810,2062],{},[1654,45812,1674],{"separator":1673},[1710,45814,45815,45817],{},[898,45816,1755],{},[1665,45818,2062],{},[1654,45820,1686],{"stretchy":1656},[902,45822,45823],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,45826,45828],{"className":45827},[886],[888,45829,45830],{"xmlns":890},[892,45831,45832,45848],{},[895,45833,45834,45836,45842,45844,45846],{},[1654,45835,1657],{"stretchy":1656},[1710,45837,45838,45840],{},[898,45839,1663],{},[1665,45841,2062],{},[1654,45843,1674],{"separator":1673},[1665,45845,2062],{},[1654,45847,1686],{"stretchy":1656},[902,45849,45850],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,45853,45855],{"className":45854},[886],[888,45856,45857],{"xmlns":890},[892,45858,45859,45875],{},[895,45860,45861,45863,45865,45867,45873],{},[1654,45862,1708],{"stretchy":1656},[1665,45864,2062],{},[1654,45866,1674],{"separator":1673},[1710,45868,45869,45871],{},[898,45870,1755],{},[1665,45872,2062],{},[1654,45874,1726],{"stretchy":1656},[902,45876,45877],{"encoding":904},"(0, P_0)",[38,45879,45880],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,45883,45884],{},"konvexní",[724,45886,45887],{},[614,45888,45889,45890,45912,45913,2068,45938,2138],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,45891,45893],{"className":45892},[886],[888,45894,45895],{"xmlns":890},[892,45896,45897,45909],{},[895,45898,45899,45901,45903,45905,45907],{},[1654,45900,1708],{"stretchy":1656},[898,45902,1663],{},[1654,45904,1674],{"separator":1673},[898,45906,1755],{},[1654,45908,1726],{"stretchy":1656},[902,45910,45911],{"encoding":904},"(Q, P)"," — klesající, konvexní, procházející body ",[883,45914,45916],{"className":45915},[886],[888,45917,45918],{"xmlns":890},[892,45919,45920,45936],{},[895,45921,45922,45924,45926,45928,45934],{},[1654,45923,1657],{"stretchy":1656},[1665,45925,2062],{},[1654,45927,1674],{"separator":1673},[1710,45929,45930,45932],{},[898,45931,1755],{},[1665,45933,2062],{},[1654,45935,1686],{"stretchy":1656},[902,45937,45823],{"encoding":904},[883,45939,45941],{"className":45940},[886],[888,45942,45943],{"xmlns":890},[892,45944,45945,45961],{},[895,45946,45947,45949,45955,45957,45959],{},[1654,45948,1657],{"stretchy":1656},[1710,45950,45951,45953],{},[898,45952,1663],{},[1665,45954,2062],{},[1654,45956,1674],{"separator":1673},[1665,45958,2062],{},[1654,45960,1686],{"stretchy":1656},[902,45962,45850],{"encoding":904},[45568,45964,45966],{"id":45965},"lineární-model-poptávky","Lineární model poptávky",[724,45968,45969],{},"Nejjednodušší závislostí je",[883,45971,45973],{"className":45972},[886],[888,45974,45975],{"xmlns":890,"display":1956},[892,45976,45977,46026],{},[1960,45978,45979],{"width":1962},[1964,45980,45981,45983,46019,46021],{},[1967,45982],{"width":1969},[1967,45984,45985],{},[895,45986,45987,45989,45991,45993,45995,45997,45999,46001,46003,46005,46007,46009,46011,46013,46015,46017],{},[898,45988,1755],{},[1654,45990,1750],{},[898,45992,207],{},[898,45994,1663],{},[1654,45996,1766],{},[898,45998,9758],{},[1654,46000,1674],{"separator":1673},[5008,46002],{"width":14608},[898,46004,207],{},[1654,46006,3002],{},[1665,46008,2062],{},[1654,46010,1674],{"separator":1673},[1865,46012,11065],{},[898,46014,9758],{},[1654,46016,2952],{},[1665,46018,2745],{},[1967,46020],{"width":1969},[1967,46022,46023],{},[1865,46024,46025],{},"(2.4)",[902,46027,46028],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,46030,46031,46032,9762,46068,2068,46092,16763,46118,46140,46141,2138],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,46033,46035],{"className":46034},[886],[888,46036,46037],{"xmlns":890},[892,46038,46039,46065],{},[895,46040,46041,46043,46045,46053,46055,46057],{},[898,46042,1663],{},[1654,46044,1750],{},[2582,46046,46047],{"scriptlevel":2062,"displaystyle":1656},[2811,46048,46049,46051],{},[1665,46050,1667],{},[898,46052,207],{},[898,46054,1755],{},[1654,46056,2380],{},[2582,46058,46059],{"scriptlevel":2062,"displaystyle":1656},[2811,46060,46061,46063],{},[898,46062,9758],{},[898,46064,207],{},[902,46066,46067],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,46069,46071],{"className":46070},[886],[888,46072,46073],{"xmlns":890},[892,46074,46075,46089],{},[895,46076,46077,46085,46087],{},[2582,46078,46079],{"scriptlevel":2062,"displaystyle":1656},[2811,46080,46081,46083],{},[1665,46082,1667],{},[898,46084,207],{},[1654,46086,3002],{},[1665,46088,2062],{},[902,46090,46091],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,46093,46095],{"className":46094},[886],[888,46096,46097],{"xmlns":890},[892,46098,46099,46115],{},[895,46100,46101,46103,46111,46113],{},[1654,46102,2380],{},[2582,46104,46105],{"scriptlevel":2062,"displaystyle":1656},[2811,46106,46107,46109],{},[898,46108,9758],{},[898,46110,207],{},[1654,46112,2952],{},[1665,46114,2062],{},[902,46116,46117],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,46119,46121],{"className":46120},[886],[888,46122,46123],{"xmlns":890},[892,46124,46125,46137],{},[895,46126,46127,46129,46131,46133,46135],{},[1654,46128,1708],{"stretchy":1656},[1665,46130,2062],{},[1654,46132,1674],{"separator":1673},[898,46134,9758],{},[1654,46136,1726],{"stretchy":1656},[902,46138,46139],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,46142,46143],{},"nedokonalé konkurenci",[46145,46146,46148],"h5",{"id":46147},"příklad-21","Příklad 2.1",[724,46150,46151,46154,46155,2138],{},[38,46152,46153],{},"Zadání:"," Lineární poptávka ",[883,46156,46158],{"className":46157},[886],[888,46159,46160],{"xmlns":890},[892,46161,46162,46178],{},[895,46163,46164,46166,46168,46170,46172,46174,46176],{},[898,46165,1755],{},[1654,46167,1750],{},[1654,46169,2380],{},[1665,46171,1681],{},[898,46173,1663],{},[1654,46175,1766],{},[1665,46177,11881],{},[902,46179,46180],{"encoding":904},"P = -2Q + 60",[724,46182,46183,46186,46187,46209,46210,2138],{},[38,46184,46185],{},"Řešení:"," Reálné cenové rozpětí je ",[883,46188,46190],{"className":46189},[886],[888,46191,46192],{"xmlns":890},[892,46193,46194,46206],{},[895,46195,46196,46198,46200,46202,46204],{},[1654,46197,1708],{"stretchy":1656},[1665,46199,2062],{},[1654,46201,1674],{"separator":1673},[1665,46203,11881],{},[1654,46205,1726],{"stretchy":1656},[902,46207,46208],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,46211,46213],{"className":46212},[886],[888,46214,46215],{"xmlns":890},[892,46216,46217,46240],{},[895,46218,46219,46221,46223,46225,46233,46235,46237],{},[898,46220,1663],{},[1654,46222,1750],{},[1654,46224,2380],{},[2582,46226,46227],{"scriptlevel":2062,"displaystyle":1656},[2811,46228,46229,46231],{},[1665,46230,1667],{},[1665,46232,1681],{},[898,46234,1755],{},[1654,46236,1766],{},[1665,46238,46239],{},"30",[902,46241,46242],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,46244,46245,46268],{},[19,46246,46247],{},[22,46248,46249,46264,46266],{},[25,46250,46251],{},[883,46252,46254],{"className":46253},[886],[888,46255,46256],{"xmlns":890},[892,46257,46258,46262],{},[895,46259,46260],{},[898,46261,1755],{},[902,46263,1755],{"encoding":904},[25,46265,5844],{},[25,46267,4573],{},[30,46269,46270],{},[22,46271,46272,46287,46289],{},[35,46273,46274],{},[883,46275,46277],{"className":46276},[886],[888,46278,46279],{"xmlns":890},[892,46280,46281,46285],{},[895,46282,46283],{},[898,46284,1663],{},[902,46286,1663],{"encoding":904},[35,46288,4647],{},[35,46290,4573],{},[724,46292,46293],{},[614,46294,46295,46296,2068,46318,2138],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,46297,46299],{"className":46298},[886],[888,46300,46301],{"xmlns":890},[892,46302,46303,46315],{},[895,46304,46305,46307,46309,46311,46313],{},[1654,46306,1657],{"stretchy":1656},[1665,46308,2062],{},[1654,46310,1674],{"separator":1673},[898,46312,9758],{},[1654,46314,1686],{"stretchy":1656},[902,46316,46317],{"encoding":904},"[0, b]",[883,46319,46321],{"className":46320},[886],[888,46322,46323],{"xmlns":890},[892,46324,46325,46343],{},[895,46326,46327,46329,46331,46333,46335,46337,46339,46341],{},[1654,46328,1657],{"stretchy":1656},[1654,46330,2380],{},[898,46332,9758],{},[898,46334,1879],{"mathvariant":1878},[898,46336,207],{},[1654,46338,1674],{"separator":1673},[1665,46340,2062],{},[1654,46342,1686],{"stretchy":1656},[902,46344,46345],{"encoding":904},"[-b\u002Fa, 0]",[45568,46347,46349],{"id":46348},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,46351,46352,46353,46370],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,46354,46356],{"className":46355},[886],[888,46357,46358],{"xmlns":890},[892,46359,46360,46368],{},[895,46361,46362],{},[1741,46363,46364,46366],{},[898,46365,1755],{},[1654,46367,1670],{},[902,46369,13142],{"encoding":904},", je funkce poptávky konstantní:",[883,46372,46374],{"className":46373},[886],[888,46375,46376],{"xmlns":890,"display":1956},[892,46377,46378,46392],{},[895,46379,46380,46382,46384,46390],{},[898,46381,1755],{},[1654,46383,1750],{},[1741,46385,46386,46388],{},[898,46387,1755],{},[1654,46389,1670],{},[898,46391,2138],{"mathvariant":1878},[902,46393,46394],{"encoding":904},"P = P^*.",[724,46396,46397],{},[614,46398,46399,46400,46421,46422,2138],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,46401,46403],{"className":46402},[886],[888,46404,46405],{"xmlns":890},[892,46406,46407,46419],{},[895,46408,46409,46411,46413,46415,46417],{},[1654,46410,1708],{"stretchy":1656},[898,46412,1663],{},[1654,46414,1674],{"separator":1673},[898,46416,1755],{},[1654,46418,1726],{"stretchy":1656},[902,46420,45911],{"encoding":904}," na úrovni ",[883,46423,46425],{"className":46424},[886],[888,46426,46427],{"xmlns":890},[892,46428,46429,46441],{},[895,46430,46431,46433,46435],{},[898,46432,1755],{},[1654,46434,1750],{},[1741,46436,46437,46439],{},[898,46438,1755],{},[1654,46440,1670],{},[902,46442,13095],{"encoding":904},[45568,46444,46446],{"id":46445},"giffenův-statek","Giffenův statek",[724,46448,46449,46450,46452,46453,46455,46456,2138],{},"Existují zboží, u nichž je křivka poptávky ",[38,46451,22366],{}," — tzv. ",[38,46454,46446],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,46457,46458],{},"podřadnému zboží",[46145,46460,46462],{"id":46461},"příklad-22","Příklad 2.2",[724,46464,46465,46468,46469,46487,46488,46510,46511,46529,46530,46548,46549,46572],{},[38,46466,46467],{},"Zadání a popis:"," Křivka ",[883,46470,46472],{"className":46471},[886],[888,46473,46474],{"xmlns":890},[892,46475,46476,46484],{},[895,46477,46478],{},[1710,46479,46480,46482],{},[898,46481,4980],{},[1665,46483,1667],{},[902,46485,46486],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,46489,46491],{"className":46490},[886],[888,46492,46493],{"xmlns":890},[892,46494,46495,46507],{},[895,46496,46497,46499,46501,46503,46505],{},[1654,46498,1708],{"stretchy":1656},[1665,46500,2062],{},[1654,46502,1674],{"separator":1673},[1665,46504,10207],{},[1654,46506,1726],{"stretchy":1656},[902,46508,46509],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,46512,46514],{"className":46513},[886],[888,46515,46516],{"xmlns":890},[892,46517,46518,46526],{},[895,46519,46520],{},[1710,46521,46522,46524],{},[898,46523,1663],{},[1665,46525,2062],{},[902,46527,46528],{"encoding":904},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[883,46531,46533],{"className":46532},[886],[888,46534,46535],{"xmlns":890},[892,46536,46537,46545],{},[895,46538,46539],{},[1710,46540,46541,46543],{},[898,46542,4980],{},[1665,46544,1681],{},[902,46546,46547],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,46550,46552],{"className":46551},[886],[888,46553,46554],{"xmlns":890},[892,46555,46556,46569],{},[895,46557,46558,46560,46562,46564,46567],{},[1654,46559,1657],{"stretchy":1656},[1665,46561,2062],{},[1654,46563,1674],{"separator":1673},[1665,46565,46566],{},"21",[1654,46568,1686],{"stretchy":1656},[902,46570,46571],{"encoding":904},"[0, 21]"," centů.",[198,46574,46576],{"id":46575},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,46578,46579,46580,2781],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,46581,46583],{"className":46582},[886],[888,46584,46585],{"xmlns":890},[892,46586,46587,46591],{},[895,46588,46589],{},[898,46590,1745],{},[902,46592,1745],{"encoding":904},[883,46594,46596],{"className":46595},[886],[888,46597,46598],{"xmlns":890,"display":1956},[892,46599,46600,46631],{},[1960,46601,46602],{"width":1962},[1964,46603,46604,46606,46624,46626],{},[1967,46605],{"width":1969},[1967,46607,46608],{},[895,46609,46610,46612,46614,46616,46618,46620,46622],{},[898,46611,1663],{},[1654,46613,1750],{},[898,46615,1798],{},[1654,46617,1708],{"stretchy":1656},[898,46619,1745],{},[1654,46621,1726],{"stretchy":1656},[898,46623,2138],{"mathvariant":1878},[1967,46625],{"width":1969},[1967,46627,46628],{},[1865,46629,46630],{},"(2.5)",[902,46632,46633],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,46635,46636,46637,46640,46641,46644],{},"Funkce se nazývá ",[38,46638,46639],{},"Engelova",", její graf ",[38,46642,46643],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,46646,46647,46779],{},[123,46648,46649,10373,46652,46665,46666,46679,46680,46697,46698],{},[38,46650,46651],{},"Normální (superior) zboží",[883,46653,46655],{"className":46654},[886],[888,46656,46657],{"xmlns":890},[892,46658,46659,46663],{},[895,46660,46661],{},[898,46662,1663],{},[902,46664,1663],{"encoding":904}," roste s ",[883,46667,46669],{"className":46668},[886],[888,46670,46671],{"xmlns":890},[892,46672,46673,46677],{},[895,46674,46675],{},[898,46676,1745],{},[902,46678,1745],{"encoding":904},", nepřesáhne hodnotu ",[883,46681,46683],{"className":46682},[886],[888,46684,46685],{"xmlns":890},[892,46686,46687,46695],{},[895,46688,46689],{},[1710,46690,46691,46693],{},[898,46692,1663],{},[1665,46694,2062],{},[902,46696,46528],{"encoding":904},":\n",[120,46699,46700,46732],{},[123,46701,46702,46705,46706,46709,46710,2138],{},[38,46703,46704],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,46707,46708],{},"konkávní"," křivka, autonomní spotřeba ",[883,46711,46713],{"className":46712},[886],[888,46714,46715],{"xmlns":890},[892,46716,46717,46729],{},[895,46718,46719,46725,46727],{},[1710,46720,46721,46723],{},[898,46722,1663],{},[1665,46724,1667],{},[1654,46726,2952],{},[1665,46728,2062],{},[902,46730,46731],{"encoding":904},"Q_1 > 0",[123,46733,46734,46737,46738,46756,46757,46759,46760,2186,46777,2138],{},[38,46735,46736],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,46739,46741],{"className":46740},[886],[888,46742,46743],{"xmlns":890},[892,46744,46745,46753],{},[895,46746,46747],{},[1710,46748,46749,46751],{},[898,46750,1745],{},[1665,46752,1667],{},[902,46754,46755],{"encoding":904},"Y_1",", křivka je nejprve ",[38,46758,45884],{}," a od ",[883,46761,46763],{"className":46762},[886],[888,46764,46765],{"xmlns":890},[892,46766,46767,46775],{},[895,46768,46769],{},[1710,46770,46771,46773],{},[898,46772,1745],{},[1665,46774,1667],{},[902,46776,46755],{"encoding":904},[38,46778,46708],{},[123,46780,46781,46784,46785,46803],{},[38,46782,46783],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,46786,46788],{"className":46787},[886],[888,46789,46790],{"xmlns":890},[892,46791,46792,46800],{},[895,46793,46794],{},[1710,46795,46796,46798],{},[898,46797,1745],{},[1665,46799,2062],{},[902,46801,46802],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,46805,46806,46807,46810,46811,12664],{},"Mírou citlivosti je ",[614,46808,46809],{},"důchodová elasticita"," (viz ",[207,46812,12643],{"className":46813,"dataFsResolvedFilePath":848,"href":849},[210],[724,46815,46816],{},[614,46817,46818],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[45568,46820,46822],{"id":46821},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[2140,46824,46825,46896,46939],{},[724,46826,46827,46829,46830,2186,46833,2186,46846,14398,46848,46861,46862,46865,46866,2138],{},[883,46828,2146],{}," Pozor — nezbytné ≠ podřadné\n",[38,46831,46832],{},"Nezbytné zboží:",[883,46834,46836],{"className":46835},[886],[888,46837,46838],{"xmlns":890},[892,46839,46840,46844],{},[895,46841,46842],{},[898,46843,1663],{},[902,46845,1663],{"encoding":904},[38,46847,16048],{},[883,46849,46851],{"className":46850},[886],[888,46852,46853],{"xmlns":890},[892,46854,46855,46859],{},[895,46856,46857],{},[898,46858,1745],{},[902,46860,1745],{"encoding":904},", ale ",[38,46863,46864],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,46867,46869],{"className":46868},[886],[888,46870,46871],{"xmlns":890},[892,46872,46873,46893],{},[895,46874,46875,46881,46883,46885,46887,46889,46891],{},[1710,46876,46877,46879],{},[898,46878,1798],{},[898,46880,1745],{},[1654,46882,9780],{},[1654,46884,1708],{"stretchy":1656},[1665,46886,2062],{},[1654,46888,1674],{"separator":1673},[1665,46890,1667],{},[1654,46892,1726],{"stretchy":1656},[902,46894,46895],{"encoding":904},"E_Y \\in (0, 1)",[724,46897,46898,2186,46901,2186,46914,46916,46917,2138],{},[38,46899,46900],{},"Podřadné zboží:",[883,46902,46904],{"className":46903},[886],[888,46905,46906],{"xmlns":890},[892,46907,46908,46912],{},[895,46909,46910],{},[898,46911,1663],{},[902,46913,1663],{"encoding":904},[38,46915,16068],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,46918,46920],{"className":46919},[886],[888,46921,46922],{"xmlns":890},[892,46923,46924,46936],{},[895,46925,46926,46932,46934],{},[1710,46927,46928,46930],{},[898,46929,1798],{},[898,46931,1745],{},[1654,46933,3002],{},[1665,46935,2062],{},[902,46937,46938],{"encoding":904},"E_Y \u003C 0",[724,46940,46941,46942,2138],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,46943,46944],{},"méně kusů, ne jen proporčně méně",[724,46946,46947,46950,46951,46954],{},[38,46948,46949],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,46952,46953],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,46956,46957],{},[3492,46958],{"alt":46959,"className":46960,"src":46961},"imek-engelovy-krivky-3typy",[210,3496],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[46145,46963,46965],{"id":46964},"české-příklady","České příklady",[16,46967,46968,46978],{},[19,46969,46970],{},[22,46971,46972,46975],{},[25,46973,46974],{},"Podřadné",[25,46976,46977],{},"Nahradí se za",[30,46979,46980,46988,46996,47004,47012,47020,47028,47036],{},[22,46981,46982,46985],{},[35,46983,46984],{},"Instantní polévky, ramen",[35,46986,46987],{},"Čerstvé jídlo, restaurace",[22,46989,46990,46993],{},[35,46991,46992],{},"MHD (autobus, tramvaj)",[35,46994,46995],{},"Vlastní auto, Uber, taxi",[22,46997,46998,47001],{},[35,46999,47000],{},"Mražené polotovary, pizza z mrazáku",[35,47002,47003],{},"Čerstvé suroviny, hotovky",[22,47005,47006,47009],{},[35,47007,47008],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,47010,47011],{},"Značkové produkty",[22,47013,47014,47017],{},[35,47015,47016],{},"Paštika Májka, obyčejný měkký salám",[35,47018,47019],{},"Kvalitní uzeniny, šunka od kosti",[22,47021,47022,47025],{},[35,47023,47024],{},"Second hand oblečení",[35,47026,47027],{},"Nové oblečení, značky",[22,47029,47030,47033],{},[35,47031,47032],{},"Krabicové víno, nejlevnější pivo",[35,47034,47035],{},"Lahvové víno, řemeslná piva",[22,47037,47038,47041],{},[35,47039,47040],{},"Ojetá auta nižších tříd",[35,47042,47043],{},"Nová auta, prémiové značky",[2140,47045,47046],{},[724,47047,47048,47050,47051,47054],{},[883,47049,3111],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,47052,47053],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,47056,47057,47060,47061,18742,47064,47086,47087,18742,47090,47111,47112,47130,47131,47134],{},[38,47058,47059],{},"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 ",[38,47062,47063],{},"luxus",[883,47065,47067],{"className":47066},[886],[888,47068,47069],{"xmlns":890},[892,47070,47071,47083],{},[895,47072,47073,47079,47081],{},[1710,47074,47075,47077],{},[898,47076,1798],{},[898,47078,1745],{},[1654,47080,2952],{},[1665,47082,1667],{},[902,47084,47085],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,47088,47089],{},"podřadné",[883,47091,47093],{"className":47092},[886],[888,47094,47095],{"xmlns":890},[892,47096,47097,47109],{},[895,47098,47099,47105,47107],{},[1710,47100,47101,47103],{},[898,47102,1798],{},[898,47104,1745],{},[1654,47106,3002],{},[1665,47108,2062],{},[902,47110,46938],{"encoding":904},"). Proto je ",[883,47113,47115],{"className":47114},[886],[888,47116,47117],{"xmlns":890},[892,47118,47119,47127],{},[895,47120,47121],{},[1710,47122,47123,47125],{},[898,47124,1798],{},[898,47126,1745],{},[902,47128,47129],{"encoding":904},"E_Y"," vždy ",[38,47132,47133],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,47136,47137,47138,47140],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,47139,46446],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,47142,47144,47145,1726],{"id":47143},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,47146,47147],{},"shift of demand",[724,47149,47150,47151,47169,47170,47187,47188,47201,47202,11448,47215,47237,47238,47255,47256,47282,47283,47286],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,47152,47154],{"className":47153},[886],[888,47155,47156],{"xmlns":890},[892,47157,47158,47166],{},[895,47159,47160],{},[1710,47161,47162,47164],{},[898,47163,1755],{},[1665,47165,2062],{},[902,47167,47168],{"encoding":904},"P_0"," odpovídá množství ",[883,47171,47173],{"className":47172},[886],[888,47174,47175],{"xmlns":890},[892,47176,47177,47185],{},[895,47178,47179],{},[1710,47180,47181,47183],{},[898,47182,1663],{},[1665,47184,2062],{},[902,47186,46528],{"encoding":904}," na křivce ",[883,47189,47191],{"className":47190},[886],[888,47192,47193],{"xmlns":890},[892,47194,47195,47199],{},[895,47196,47197],{},[898,47198,4980],{},[902,47200,4980],{"encoding":904},"; vzroste-li důchod z ",[883,47203,47205],{"className":47204},[886],[888,47206,47207],{"xmlns":890},[892,47208,47209,47213],{},[895,47210,47211],{},[898,47212,1745],{},[902,47214,1745],{"encoding":904},[883,47216,47218],{"className":47217},[886],[888,47219,47220],{"xmlns":890},[892,47221,47222,47234],{},[895,47223,47224,47230,47232],{},[1710,47225,47226,47228],{},[898,47227,1745],{},[1665,47229,1667],{},[1654,47231,2952],{},[898,47233,1745],{},[902,47235,47236],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,47239,47241],{"className":47240},[886],[888,47242,47243],{"xmlns":890},[892,47244,47245,47253],{},[895,47246,47247],{},[1710,47248,47249,47251],{},[898,47250,1755],{},[1665,47252,2062],{},[902,47254,47168],{"encoding":904}," odpovídá vyšší ",[883,47257,47259],{"className":47258},[886],[888,47260,47261],{"xmlns":890},[892,47262,47263,47279],{},[895,47264,47265,47271,47273],{},[1710,47266,47267,47269],{},[898,47268,1663],{},[1665,47270,1667],{},[1654,47272,2952],{},[1710,47274,47275,47277],{},[898,47276,1663],{},[1665,47278,2062],{},[902,47280,47281],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,47284,47285],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,47288,47289],{},[3492,47290],{"alt":47291,"className":47292,"src":47293},"imek-posun-vs-pohyb-po-krivce",[210,3496],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,47295,47296],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,47298,47299],{},[614,47300,47301,47302,22720,47332,47353],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,47303,47305],{"className":47304},[886],[888,47306,47307],{"xmlns":890},[892,47308,47309,47329],{},[895,47310,47311,47317,47319,47321,47323],{},[1710,47312,47313,47315],{},[898,47314,4980],{},[1665,47316,1681],{},[1654,47318,1674],{"separator":1673},[898,47320,4980],{},[1654,47322,1674],{"separator":1673},[1710,47324,47325,47327],{},[898,47326,4980],{},[1665,47328,1667],{},[902,47330,47331],{"encoding":904},"D_2, D, D_1",[883,47333,47335],{"className":47334},[886],[888,47336,47337],{"xmlns":890},[892,47338,47339,47351],{},[895,47340,47341,47343,47345,47347,47349],{},[1654,47342,1708],{"stretchy":1656},[898,47344,1663],{},[1654,47346,1674],{"separator":1673},[898,47348,1755],{},[1654,47350,1726],{"stretchy":1656},[902,47352,45911],{"encoding":904},", šipky naznačují posuny.",[46145,47355,47357],{"id":47356},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,47359,47360,47362,47363,47386,47387,47404,47405,47422,47423,2138],{},[38,47361,46153],{}," Poptávce ",[883,47364,47366],{"className":47365},[886],[888,47367,47368],{"xmlns":890},[892,47369,47370,47384],{},[895,47371,47372,47374,47376,47378,47380,47382],{},[898,47373,1755],{},[1654,47375,1750],{},[898,47377,4980],{},[1654,47379,1708],{"stretchy":1656},[898,47381,1663],{},[1654,47383,1726],{"stretchy":1656},[902,47385,13376],{"encoding":904}," odpovídá ceně ",[883,47388,47390],{"className":47389},[886],[888,47391,47392],{"xmlns":890},[892,47393,47394,47402],{},[895,47395,47396],{},[1710,47397,47398,47400],{},[898,47399,1755],{},[1665,47401,2062],{},[902,47403,47168],{"encoding":904}," množství ",[883,47406,47408],{"className":47407},[886],[888,47409,47410],{"xmlns":890},[892,47411,47412,47420],{},[895,47413,47414],{},[1710,47415,47416,47418],{},[898,47417,1663],{},[1665,47419,2062],{},[902,47421,46528],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,47424,47426],{"className":47425},[886],[888,47427,47428],{"xmlns":890},[892,47429,47430,47434],{},[895,47431,47432],{},[898,47433,11536],{},[902,47435,11536],{"encoding":904},[724,47437,47438,47440,47441,47458,47459,47481],{},[38,47439,46185],{}," Kupující nakupuje množství ",[883,47442,47444],{"className":47443},[886],[888,47445,47446],{"xmlns":890},[892,47447,47448,47456],{},[895,47449,47450],{},[1710,47451,47452,47454],{},[898,47453,1663],{},[1665,47455,1667],{},[902,47457,2918],{"encoding":904},", které odpovídá ceně ",[883,47460,47462],{"className":47461},[886],[888,47463,47464],{"xmlns":890},[892,47465,47466,47478],{},[895,47467,47468,47474,47476],{},[1710,47469,47470,47472],{},[898,47471,1755],{},[1665,47473,2062],{},[1654,47475,1766],{},[898,47477,11536],{},[902,47479,47480],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,47483,47485],{"className":47484},[886],[888,47486,47487],{"xmlns":890,"display":1956},[892,47488,47489,47523],{},[895,47490,47491,47493,47495,47501,47503,47505,47507,47509,47511,47513,47515,47517,47519,47521],{},[898,47492,1755],{},[1654,47494,1750],{},[1710,47496,47497,47499],{},[898,47498,4980],{},[1665,47500,1667],{},[1654,47502,1708],{"stretchy":1656},[898,47504,1663],{},[1654,47506,1726],{"stretchy":1656},[1654,47508,1750],{},[898,47510,4980],{},[1654,47512,1708],{"stretchy":1656},[898,47514,1663],{},[1654,47516,1726],{"stretchy":1656},[1654,47518,2380],{},[898,47520,11536],{},[1654,47522,1674],{"separator":1673},[902,47524,47525],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,47527,47528,47529,2138],{},"tj. dojde k ",[38,47530,47531],{},"posunu poptávky doleva",[724,47533,47534],{},[614,47535,47536,47537,47558,47559,1343,47576,1343,47589,47610,47611,2068,47628,2138],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,47538,47540],{"className":47539},[886],[888,47541,47542],{"xmlns":890},[892,47543,47544,47556],{},[895,47545,47546,47548,47550,47552,47554],{},[1654,47547,1708],{"stretchy":1656},[898,47549,1663],{},[1654,47551,1674],{"separator":1673},[898,47553,1755],{},[1654,47555,1726],{"stretchy":1656},[902,47557,45911],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,47560,47562],{"className":47561},[886],[888,47563,47564],{"xmlns":890},[892,47565,47566,47574],{},[895,47567,47568],{},[1710,47569,47570,47572],{},[898,47571,1755],{},[1665,47573,2062],{},[902,47575,47168],{"encoding":904},[883,47577,47579],{"className":47578},[886],[888,47580,47581],{"xmlns":890},[892,47582,47583,47587],{},[895,47584,47585],{},[898,47586,11536],{},[902,47588,11536],{"encoding":904},[883,47590,47592],{"className":47591},[886],[888,47593,47594],{"xmlns":890},[892,47595,47596,47608],{},[895,47597,47598,47604,47606],{},[1710,47599,47600,47602],{},[898,47601,1755],{},[1665,47603,2062],{},[1654,47605,1766],{},[898,47607,11536],{},[902,47609,47480],{"encoding":904},"; na vodorovné ",[883,47612,47614],{"className":47613},[886],[888,47615,47616],{"xmlns":890},[892,47617,47618,47626],{},[895,47619,47620],{},[1710,47621,47622,47624],{},[898,47623,1663],{},[1665,47625,1667],{},[902,47627,2918],{"encoding":904},[883,47629,47631],{"className":47630},[886],[888,47632,47633],{"xmlns":890},[892,47634,47635,47643],{},[895,47636,47637],{},[1710,47638,47639,47641],{},[898,47640,1663],{},[1665,47642,2062],{},[902,47644,46528],{"encoding":904},[198,47646,47648],{"id":47647},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,47650,47651],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,47653,47655],{"className":47654},[886],[888,47656,47657],{"xmlns":890,"display":1956},[892,47658,47659,47844],{},[1960,47660,47661],{"width":1962},[1964,47662,47663,47665,47837,47839],{},[1967,47664],{"width":1969},[1967,47666,47667],{},[1960,47668,47669,47753],{"rowspacing":2574,"columnalign":2575,"columnspacing":2576},[1964,47670,47671,47681],{},[1967,47672,47673],{},[2582,47674,47675],{"scriptlevel":2062,"displaystyle":1673},[1710,47676,47677,47679],{},[898,47678,1663],{},[1665,47680,1667],{},[1967,47682,47683],{},[2582,47684,47685],{"scriptlevel":2062,"displaystyle":1673},[895,47686,47687,47689,47691,47697,47699,47705,47707,47713,47715,47717,47723,47725,47731,47737,47739,47745,47751],{},[895,47688],{},[1654,47690,1750],{},[1710,47692,47693,47695],{},[898,47694,4980],{},[1665,47696,1667],{},[1654,47698,1708],{"stretchy":1656},[1710,47700,47701,47703],{},[898,47702,1755],{},[1665,47704,1667],{},[1654,47706,1674],{"separator":1673},[1710,47708,47709,47711],{},[898,47710,1755],{},[1665,47712,1681],{},[1654,47714,1726],{"stretchy":1656},[1654,47716,1750],{},[1710,47718,47719,47721],{},[898,47720,207],{},[1665,47722,1667],{},[1654,47724,1766],{},[1710,47726,47727,47729],{},[898,47728,9758],{},[1665,47730,1667],{},[1710,47732,47733,47735],{},[898,47734,1755],{},[1665,47736,1667],{},[1654,47738,1766],{},[1710,47740,47741,47743],{},[898,47742,3624],{},[1665,47744,1667],{},[1710,47746,47747,47749],{},[898,47748,1755],{},[1665,47750,1681],{},[1654,47752,1674],{"separator":1673},[1964,47754,47755,47765],{},[1967,47756,47757],{},[2582,47758,47759],{"scriptlevel":2062,"displaystyle":1673},[1710,47760,47761,47763],{},[898,47762,1663],{},[1665,47764,1681],{},[1967,47766,47767],{},[2582,47768,47769],{"scriptlevel":2062,"displaystyle":1673},[895,47770,47771,47773,47775,47781,47783,47789,47791,47797,47799,47801,47807,47809,47815,47821,47823,47829,47835],{},[895,47772],{},[1654,47774,1750],{},[1710,47776,47777,47779],{},[898,47778,4980],{},[1665,47780,1681],{},[1654,47782,1708],{"stretchy":1656},[1710,47784,47785,47787],{},[898,47786,1755],{},[1665,47788,1667],{},[1654,47790,1674],{"separator":1673},[1710,47792,47793,47795],{},[898,47794,1755],{},[1665,47796,1681],{},[1654,47798,1726],{"stretchy":1656},[1654,47800,1750],{},[1710,47802,47803,47805],{},[898,47804,207],{},[1665,47806,1681],{},[1654,47808,1766],{},[1710,47810,47811,47813],{},[898,47812,9758],{},[1665,47814,1681],{},[1710,47816,47817,47819],{},[898,47818,1755],{},[1665,47820,1667],{},[1654,47822,1766],{},[1710,47824,47825,47827],{},[898,47826,3624],{},[1665,47828,1681],{},[1710,47830,47831,47833],{},[898,47832,1755],{},[1665,47834,1681],{},[898,47836,2138],{"mathvariant":1878},[1967,47838],{"width":1969},[1967,47840,47841],{},[1865,47842,47843],{},"(2.6)",[902,47845,47846],{"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}",[45568,47848,47850],{"id":47849},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,47852,47853,47900,47947],{},[123,47854,47855,1343,47877,47899],{},[883,47856,47858],{"className":47857},[886],[888,47859,47860],{"xmlns":890},[892,47861,47862,47874],{},[895,47863,47864,47870,47872],{},[1710,47865,47866,47868],{},[898,47867,207],{},[1665,47869,1667],{},[1654,47871,2952],{},[1665,47873,2062],{},[902,47875,47876],{"encoding":904},"a_1 > 0",[883,47878,47880],{"className":47879},[886],[888,47881,47882],{"xmlns":890},[892,47883,47884,47896],{},[895,47885,47886,47892,47894],{},[1710,47887,47888,47890],{},[898,47889,207],{},[1665,47891,1681],{},[1654,47893,2952],{},[1665,47895,2062],{},[902,47897,47898],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,47901,47902,1343,47924,47946],{},[883,47903,47905],{"className":47904},[886],[888,47906,47907],{"xmlns":890},[892,47908,47909,47921],{},[895,47910,47911,47917,47919],{},[1710,47912,47913,47915],{},[898,47914,9758],{},[1665,47916,1667],{},[1654,47918,3002],{},[1665,47920,2062],{},[902,47922,47923],{"encoding":904},"b_1 \u003C 0",[883,47925,47927],{"className":47926},[886],[888,47928,47929],{"xmlns":890},[892,47930,47931,47943],{},[895,47932,47933,47939,47941],{},[1710,47934,47935,47937],{},[898,47936,3624],{},[1665,47938,1681],{},[1654,47940,3002],{},[1665,47942,2062],{},[902,47944,47945],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,47948,47949,47950,1343,47967,47985,47986],{},"zkřížené koeficienty ",[883,47951,47953],{"className":47952},[886],[888,47954,47955],{"xmlns":890},[892,47956,47957,47965],{},[895,47958,47959],{},[1710,47960,47961,47963],{},[898,47962,3624],{},[1665,47964,1667],{},[902,47966,3723],{"encoding":904},[883,47968,47970],{"className":47969},[886],[888,47971,47972],{"xmlns":890},[892,47973,47974,47982],{},[895,47975,47976],{},[1710,47977,47978,47980],{},[898,47979,9758],{},[1665,47981,1681],{},[902,47983,47984],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,47987,47988,48038],{},[123,47989,47990,47993,47994,1343,48016,1674],{},[38,47991,47992],{},"substituty"," (máslo vs. margarín): ",[883,47995,47997],{"className":47996},[886],[888,47998,47999],{"xmlns":890},[892,48000,48001,48013],{},[895,48002,48003,48009,48011],{},[1710,48004,48005,48007],{},[898,48006,3624],{},[1665,48008,1667],{},[1654,48010,2952],{},[1665,48012,2062],{},[902,48014,48015],{"encoding":904},"c_1 > 0",[883,48017,48019],{"className":48018},[886],[888,48020,48021],{"xmlns":890},[892,48022,48023,48035],{},[895,48024,48025,48031,48033],{},[1710,48026,48027,48029],{},[898,48028,9758],{},[1665,48030,1681],{},[1654,48032,2952],{},[1665,48034,2062],{},[902,48036,48037],{"encoding":904},"b_2 > 0",[123,48039,48040,48043,48044,1343,48066,2138],{},[38,48041,48042],{},"komplementy"," (auto vs. benzín): ",[883,48045,48047],{"className":48046},[886],[888,48048,48049],{"xmlns":890},[892,48050,48051,48063],{},[895,48052,48053,48059,48061],{},[1710,48054,48055,48057],{},[898,48056,3624],{},[1665,48058,1667],{},[1654,48060,3002],{},[1665,48062,2062],{},[902,48064,48065],{"encoding":904},"c_1 \u003C 0",[883,48067,48069],{"className":48068},[886],[888,48070,48071],{"xmlns":890},[892,48072,48073,48085],{},[895,48074,48075,48081,48083],{},[1710,48076,48077,48079],{},[898,48078,9758],{},[1665,48080,1681],{},[1654,48082,3002],{},[1665,48084,2062],{},[902,48086,48087],{"encoding":904},"b_2 \u003C 0",[724,48089,48090],{},"Schematicky:",[724,48092,48093,48096],{},[38,48094,48095],{},"Substituty",[883,48097,48099],{"className":48098},[886],[888,48100,48101],{"xmlns":890},[892,48102,48103,48242],{},[895,48104,48105,48111,48113,48128,48130,48150,48152,48172,48174,48176,48182,48184,48198,48200,48220,48222],{},[1710,48106,48107,48109],{},[898,48108,1663],{},[1665,48110,1667],{},[1654,48112,1750],{},[898,48114,48115],{},[48116,48117,48118,48126],"munder",{},[1654,48119,48120],{},[1710,48121,48122,48124],{},[898,48123,207],{},[1665,48125,1667],{},[1654,48127,1766],{"lspace":2576,"rspace":2576},[1654,48129,1766],{},[898,48131,48132],{},[48116,48133,48134,48148],{},[1654,48135,48136,48142],{},[1710,48137,48138,48140],{},[898,48139,9758],{},[1665,48141,1667],{},[1710,48143,48144,48146],{},[898,48145,1755],{},[1665,48147,1667],{},[1654,48149,2380],{"lspace":2576,"rspace":2576},[1654,48151,1766],{},[898,48153,48154],{},[48116,48155,48156,48170],{},[1654,48157,48158,48164],{},[1710,48159,48160,48162],{},[898,48161,3624],{},[1665,48163,1667],{},[1710,48165,48166,48168],{},[898,48167,1755],{},[1665,48169,1681],{},[1654,48171,1766],{"lspace":2576,"rspace":2576},[1654,48173,1674],{"separator":1673},[5008,48175],{"width":14608},[1710,48177,48178,48180],{},[898,48179,1663],{},[1665,48181,1681],{},[1654,48183,1750],{},[898,48185,48186],{},[48116,48187,48188,48196],{},[1654,48189,48190],{},[1710,48191,48192,48194],{},[898,48193,207],{},[1665,48195,1681],{},[1654,48197,1766],{"lspace":2576,"rspace":2576},[1654,48199,1766],{},[898,48201,48202],{},[48116,48203,48204,48218],{},[1654,48205,48206,48212],{},[1710,48207,48208,48210],{},[898,48209,9758],{},[1665,48211,1681],{},[1710,48213,48214,48216],{},[898,48215,1755],{},[1665,48217,1667],{},[1654,48219,1766],{"lspace":2576,"rspace":2576},[1654,48221,1766],{},[898,48223,48224],{},[48116,48225,48226,48240],{},[1654,48227,48228,48234],{},[1710,48229,48230,48232],{},[898,48231,3624],{},[1665,48233,1681],{},[1710,48235,48236,48238],{},[898,48237,1755],{},[1665,48239,1681],{},[1654,48241,2380],{"lspace":2576,"rspace":2576},[902,48243,48244],{"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}",[724,48246,48247,48250],{},[38,48248,48249],{},"Komplementy",[883,48251,48253],{"className":48252},[886],[888,48254,48255],{"xmlns":890},[892,48256,48257,48395],{},[895,48258,48259,48265,48267,48281,48283,48303,48305,48325,48327,48329,48335,48337,48351,48353,48373,48375],{},[1710,48260,48261,48263],{},[898,48262,1663],{},[1665,48264,1667],{},[1654,48266,1750],{},[898,48268,48269],{},[48116,48270,48271,48279],{},[1654,48272,48273],{},[1710,48274,48275,48277],{},[898,48276,207],{},[1665,48278,1667],{},[1654,48280,1766],{"lspace":2576,"rspace":2576},[1654,48282,1766],{},[898,48284,48285],{},[48116,48286,48287,48301],{},[1654,48288,48289,48295],{},[1710,48290,48291,48293],{},[898,48292,9758],{},[1665,48294,1667],{},[1710,48296,48297,48299],{},[898,48298,1755],{},[1665,48300,1667],{},[1654,48302,2380],{"lspace":2576,"rspace":2576},[1654,48304,1766],{},[898,48306,48307],{},[48116,48308,48309,48323],{},[1654,48310,48311,48317],{},[1710,48312,48313,48315],{},[898,48314,3624],{},[1665,48316,1667],{},[1710,48318,48319,48321],{},[898,48320,1755],{},[1665,48322,1681],{},[1654,48324,2380],{"lspace":2576,"rspace":2576},[1654,48326,1674],{"separator":1673},[5008,48328],{"width":14608},[1710,48330,48331,48333],{},[898,48332,1663],{},[1665,48334,1681],{},[1654,48336,1750],{},[898,48338,48339],{},[48116,48340,48341,48349],{},[1654,48342,48343],{},[1710,48344,48345,48347],{},[898,48346,207],{},[1665,48348,1681],{},[1654,48350,1766],{"lspace":2576,"rspace":2576},[1654,48352,1766],{},[898,48354,48355],{},[48116,48356,48357,48371],{},[1654,48358,48359,48365],{},[1710,48360,48361,48363],{},[898,48362,9758],{},[1665,48364,1681],{},[1710,48366,48367,48369],{},[898,48368,1755],{},[1665,48370,1667],{},[1654,48372,2380],{"lspace":2576,"rspace":2576},[1654,48374,1766],{},[898,48376,48377],{},[48116,48378,48379,48393],{},[1654,48380,48381,48387],{},[1710,48382,48383,48385],{},[898,48384,3624],{},[1665,48386,1681],{},[1710,48388,48389,48391],{},[898,48390,1755],{},[1665,48392,1681],{},[1654,48394,2380],{"lspace":2576,"rspace":2576},[902,48396,48397],{"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}",[45190,48399],{},[115,48401,21834],{"id":44999},[2140,48403,48404],{},[724,48405,48406,48408,48409,45214,48422,45228,48435,48438,48439,14398,48463,48481],{},[883,48407,2860],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,48410,48412],{"className":48411},[886],[888,48413,48414],{"xmlns":890},[892,48415,48416,48420],{},[895,48417,48418],{},[898,48419,1663],{},[902,48421,1663],{"encoding":904},[883,48423,48425],{"className":48424},[886],[888,48426,48427],{"xmlns":890},[892,48428,48429,48433],{},[895,48430,48431],{},[898,48432,1755],{},[902,48434,1755],{"encoding":904},[38,48436,48437],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,48440,48442],{"className":48441},[886],[888,48443,48444],{"xmlns":890},[892,48445,48446,48460],{},[895,48447,48448,48450,48452,48454,48456,48458],{},[898,48449,1755],{},[1654,48451,1750],{},[898,48453,3624],{},[898,48455,1663],{},[1654,48457,1766],{},[898,48459,10977],{},[902,48461,48462],{"encoding":904},"P = cQ + d",[883,48464,48466],{"className":48465},[886],[888,48467,48468],{"xmlns":890},[892,48469,48470,48478],{},[895,48471,48472,48474,48476],{},[898,48473,3624],{},[1654,48475,2952],{},[1665,48477,2062],{},[902,48479,48480],{"encoding":904},"c > 0"," je standardní aproximací.",[198,48483,45284],{"id":48484},"obecný-vícefaktorový-model-1",[724,48486,48487,18742,48490,48493,48494,48507,48508,45116,48521,45130,48534,48547,48548,48562,48563,45159,48576,48589],{},[38,48488,48489],{},"Nabízené množství",[614,48491,48492],{},"quantity supplied",") závisí na ceně ",[883,48495,48497],{"className":48496},[886],[888,48498,48499],{"xmlns":890},[892,48500,48501,48505],{},[895,48502,48503],{},[898,48504,1755],{},[902,48506,1755],{"encoding":904},", cenách výrobních faktorů (práce ",[883,48509,48511],{"className":48510},[886],[888,48512,48513],{"xmlns":890},[892,48514,48515,48519],{},[895,48516,48517],{},[898,48518,2450],{},[902,48520,2450],{"encoding":904},[883,48522,48524],{"className":48523},[886],[888,48525,48526],{"xmlns":890},[892,48527,48528,48532],{},[895,48529,48530],{},[898,48531,18517],{},[902,48533,18517],{"encoding":904},[883,48535,48537],{"className":48536},[886],[888,48538,48539],{"xmlns":890},[892,48540,48541,48545],{},[895,48542,48543],{},[898,48544,1798],{},[902,48546,1798],{"encoding":904},"), očekávání ",[883,48549,48551],{"className":48550},[886],[888,48552,48553],{"xmlns":890},[892,48554,48555,48560],{},[895,48556,48557],{},[898,48558,48559],{},"V",[902,48561,48559],{"encoding":904},", počtu výrobců ",[883,48564,48566],{"className":48565},[886],[888,48567,48568],{"xmlns":890},[892,48569,48570,48574],{},[895,48571,48572],{},[898,48573,45156],{},[902,48575,45156],{"encoding":904},[883,48577,48579],{"className":48578},[886],[888,48580,48581],{"xmlns":890},[892,48582,48583,48587],{},[895,48584,48585],{},[898,48586,45171],{},[902,48588,45171],{"encoding":904}," a dalších:",[883,48591,48593],{"className":48592},[886],[888,48594,48595],{"xmlns":890,"display":1956},[892,48596,48597,48656],{},[1960,48598,48599],{"width":1962},[1964,48600,48601,48603,48649,48651],{},[1967,48602],{"width":1969},[1967,48604,48605],{},[895,48606,48607,48609,48611,48613,48615,48617,48619,48621,48623,48625,48627,48629,48631,48633,48635,48637,48639,48641,48643,48645,48647],{},[898,48608,1663],{},[1654,48610,1750],{},[898,48612,17398],{},[1654,48614,1708],{"stretchy":1656},[898,48616,1755],{},[1654,48618,1674],{"separator":1673},[898,48620,2450],{},[1654,48622,1674],{"separator":1673},[898,48624,18517],{},[1654,48626,1674],{"separator":1673},[898,48628,1798],{},[1654,48630,1674],{"separator":1673},[898,48632,48559],{},[1654,48634,1674],{"separator":1673},[898,48636,45156],{},[1654,48638,1674],{"separator":1673},[898,48640,45171],{},[1654,48642,1674],{"separator":1673},[1654,48644,18366],{},[1654,48646,1726],{"stretchy":1656},[898,48648,2138],{"mathvariant":1878},[1967,48650],{"width":1969},[1967,48652,48653],{},[1865,48654,48655],{},"(2.7)",[902,48657,48658],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,48660,46636,48661,18742,48664,48667],{},[38,48662,48663],{},"funkce nabídky",[614,48665,48666],{},"supply function",") v širším slova smyslu.",[198,48669,48671],{"id":48670},"jednofaktorový-model","Jednofaktorový model",[724,48673,48674],{},"V nejpřirozenějším jednofaktorovém modelu",[883,48676,48678],{"className":48677},[886],[888,48679,48680],{"xmlns":890,"display":1956},[892,48681,48682,48733],{},[1960,48683,48684],{"width":1962},[1964,48685,48686,48688,48726,48728],{},[1967,48687],{"width":1969},[1967,48689,48690],{},[895,48691,48692,48694,48696,48698,48700,48702,48704,48706,48708,48710,48712,48714,48716,48718,48720,48722,48724],{},[898,48693,1663],{},[1654,48695,1750],{},[898,48697,17398],{},[1654,48699,1708],{"stretchy":1656},[898,48701,1755],{},[1654,48703,1726],{"stretchy":1656},[1654,48705,1674],{"separator":1673},[5008,48707],{"width":14608},[1865,48709,45637],{},[5008,48711],{"width":14608},[898,48713,1755],{},[1654,48715,1750],{},[898,48717,17398],{},[1654,48719,1708],{"stretchy":1656},[898,48721,1663],{},[1654,48723,1726],{"stretchy":1656},[898,48725,2138],{"mathvariant":1878},[1967,48727],{"width":1969},[1967,48729,48730],{},[1865,48731,48732],{},"(2.8)",[902,48734,48735],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,48737,48738,48739,18742,48742,12664],{},"Graf je ",[38,48740,48741],{},"křivka nabídky",[614,48743,48744],{},"supply curve",[45568,48746,48748],{"id":48747},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[2140,48750,48751],{},[724,48752,48753],{},[38,48754,45683,48755,48768,48769,45738],{},[883,48756,48758],{"className":48757},[886],[888,48759,48760],{"xmlns":890},[892,48761,48762,48766],{},[895,48763,48764],{},[898,48765,1755],{},[902,48767,1755],{"encoding":904},", pak nabízené množství ",[883,48770,48772],{"className":48771},[886],[888,48773,48774],{"xmlns":890},[892,48775,48776,48780],{},[895,48777,48778],{},[898,48779,1663],{},[902,48781,1663],{"encoding":904},[724,48783,48784,48785,48810,48811,48841,48842,48859],{},"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 ",[883,48786,48788],{"className":48787},[886],[888,48789,48790],{"xmlns":890},[892,48791,48792,48808],{},[895,48793,48794,48796,48798,48800,48806],{},[1654,48795,1657],{"stretchy":1656},[1665,48797,2062],{},[1654,48799,1674],{"separator":1673},[1710,48801,48802,48804],{},[898,48803,1755],{},[1665,48805,2062],{},[1654,48807,1686],{"stretchy":1656},[902,48809,45823],{"encoding":904}," na svislé ose (případně z ",[883,48812,48814],{"className":48813},[886],[888,48815,48816],{"xmlns":890},[892,48817,48818,48838],{},[895,48819,48820,48822,48828,48830,48836],{},[1654,48821,1657],{"stretchy":1656},[1710,48823,48824,48826],{},[898,48825,1663],{},[1665,48827,1667],{},[1654,48829,1674],{"separator":1673},[1710,48831,48832,48834],{},[898,48833,1755],{},[1665,48835,1667],{},[1654,48837,1686],{"stretchy":1656},[902,48839,48840],{"encoding":904},"[Q_1, P_1]","), kde ",[883,48843,48845],{"className":48844},[886],[888,48846,48847],{"xmlns":890},[892,48848,48849,48857],{},[895,48850,48851],{},[1710,48852,48853,48855],{},[898,48854,1755],{},[1665,48856,2062],{},[902,48858,47168],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,48861,48862],{},[614,48863,48864,48865,12468,48878,2138],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,48866,48868],{"className":48867},[886],[888,48869,48870],{"xmlns":890},[892,48871,48872,48876],{},[895,48873,48874],{},[898,48875,17398],{},[902,48877,17398],{"encoding":904},[883,48879,48881],{"className":48880},[886],[888,48882,48883],{"xmlns":890},[892,48884,48885,48897],{},[895,48886,48887,48889,48891,48893,48895],{},[1654,48888,1708],{"stretchy":1656},[898,48890,1663],{},[1654,48892,1674],{"separator":1673},[898,48894,1755],{},[1654,48896,1726],{"stretchy":1656},[902,48898,45911],{"encoding":904},[45568,48900,48902],{"id":48901},"lineární-model-nabídky","Lineární model nabídky",[883,48904,48906],{"className":48905},[886],[888,48907,48908],{"xmlns":890,"display":1956},[892,48909,48910,48949],{},[1960,48911,48912],{"width":1962},[1964,48913,48914,48916,48942,48944],{},[1967,48915],{"width":1969},[1967,48917,48918],{},[895,48919,48920,48922,48924,48926,48928,48930,48932,48934,48936,48938,48940],{},[898,48921,1755],{},[1654,48923,1750],{},[898,48925,3624],{},[898,48927,1663],{},[1654,48929,1766],{},[898,48931,10977],{},[1654,48933,1674],{"separator":1673},[5008,48935],{"width":14608},[898,48937,3624],{},[1654,48939,2952],{},[1665,48941,2745],{},[1967,48943],{"width":1969},[1967,48945,48946],{},[1865,48947,48948],{},"(2.9)",[902,48950,48951],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,48953,48954,48955,48991,48992,49005],{},"Alternativně ",[883,48956,48958],{"className":48957},[886],[888,48959,48960],{"xmlns":890},[892,48961,48962,48988],{},[895,48963,48964,48966,48968,48976,48978,48980],{},[898,48965,1663],{},[1654,48967,1750],{},[2582,48969,48970],{"scriptlevel":2062,"displaystyle":1656},[2811,48971,48972,48974],{},[1665,48973,1667],{},[898,48975,3624],{},[898,48977,1755],{},[1654,48979,2380],{},[2582,48981,48982],{"scriptlevel":2062,"displaystyle":1656},[2811,48983,48984,48986],{},[898,48985,10977],{},[898,48987,3624],{},[902,48989,48990],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,48993,48995],{"className":48994},[886],[888,48996,48997],{"xmlns":890},[892,48998,48999,49003],{},[895,49000,49001],{},[898,49002,1755],{},[902,49004,1755],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[46145,49007,49009],{"id":49008},"příklad-25","Příklad 2.5",[724,49011,49012,49014,49015,2138],{},[38,49013,46153],{}," Lineární nabídka ",[883,49016,49018],{"className":49017},[886],[888,49019,49020],{"xmlns":890},[892,49021,49022,49036],{},[895,49023,49024,49026,49028,49030,49032,49034],{},[898,49025,1755],{},[1654,49027,1750],{},[1665,49029,7594],{},[898,49031,1663],{},[1654,49033,1766],{},[1665,49035,4622],{},[902,49037,49038],{"encoding":904},"P = 0{,}5Q + 25",[724,49040,49041,49043,49044,2138],{},[38,49042,46185],{}," Alternativní tvar ",[883,49045,49047],{"className":49046},[886],[888,49048,49049],{"xmlns":890},[892,49050,49051,49065],{},[895,49052,49053,49055,49057,49059,49061,49063],{},[898,49054,1663],{},[1654,49056,1750],{},[1665,49058,1681],{},[898,49060,1755],{},[1654,49062,2380],{},[1665,49064,4767],{},[902,49066,49067],{"encoding":904},"Q = 2P - 50",[16,49069,49070,49095],{},[19,49071,49072],{},[22,49073,49074,49089,49091,49093],{},[25,49075,49076],{},[883,49077,49079],{"className":49078},[886],[888,49080,49081],{"xmlns":890},[892,49082,49083,49087],{},[895,49084,49085],{},[898,49086,1755],{},[902,49088,1755],{"encoding":904},[25,49090,46239],{},[25,49092,23747],{},[25,49094,5844],{},[30,49096,49097],{},[22,49098,49099,49114,49116,49118],{},[35,49100,49101],{},[883,49102,49104],{"className":49103},[886],[888,49105,49106],{"xmlns":890},[892,49107,49108,49112],{},[895,49109,49110],{},[898,49111,1663],{},[902,49113,1663],{"encoding":904},[35,49115,4647],{},[35,49117,4573],{},[35,49119,46239],{},[198,49121,49123,49124,1726],{"id":49122},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,49125,49126],{},"shift of supply",[724,49128,49129,49130,49133,49134,49151,49152,49177,49178,2138],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,49131,49132],{},"doprava",": při stejné ceně ",[883,49135,49137],{"className":49136},[886],[888,49138,49139],{"xmlns":890},[892,49140,49141,49149],{},[895,49142,49143],{},[1710,49144,49145,49147],{},[898,49146,1755],{},[1665,49148,2062],{},[902,49150,47168],{"encoding":904}," vyrobí výrobce větší ",[883,49153,49155],{"className":49154},[886],[888,49156,49157],{"xmlns":890},[892,49158,49159,49175],{},[895,49160,49161,49167,49169],{},[1710,49162,49163,49165],{},[898,49164,1663],{},[1665,49166,1667],{},[1654,49168,2952],{},[1710,49170,49171,49173],{},[898,49172,1663],{},[1665,49174,2062],{},[902,49176,47281],{"encoding":904},"); zdražení vstupů posune křivku ",[38,49179,49180],{},"doleva",[724,49182,49183],{},[614,49184,49185,49186,49199,49200,49218,49219,49237,49238,2138],{},"Obrázek 2.11: Původní ",[883,49187,49189],{"className":49188},[886],[888,49190,49191],{"xmlns":890},[892,49192,49193,49197],{},[895,49194,49195],{},[898,49196,17398],{},[902,49198,17398],{"encoding":904},", posunuté ",[883,49201,49203],{"className":49202},[886],[888,49204,49205],{"xmlns":890},[892,49206,49207,49215],{},[895,49208,49209],{},[1710,49210,49211,49213],{},[898,49212,17398],{},[1665,49214,1667],{},[902,49216,49217],{"encoding":904},"S_1"," (doprava) a ",[883,49220,49222],{"className":49221},[886],[888,49223,49224],{"xmlns":890},[892,49225,49226,49234],{},[895,49227,49228],{},[1710,49229,49230,49232],{},[898,49231,17398],{},[1665,49233,1681],{},[902,49235,49236],{"encoding":904},"S_2"," (doleva) v ",[883,49239,49241],{"className":49240},[886],[888,49242,49243],{"xmlns":890},[892,49244,49245,49257],{},[895,49246,49247,49249,49251,49253,49255],{},[1654,49248,1708],{"stretchy":1656},[898,49250,1663],{},[1654,49252,1674],{"separator":1673},[898,49254,1755],{},[1654,49256,1726],{"stretchy":1656},[902,49258,45911],{"encoding":904},[46145,49260,49262],{"id":49261},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,49264,49265,49267,49268,49292,49293,2138],{},[38,49266,46153],{}," Nabídka ",[883,49269,49271],{"className":49270},[886],[888,49272,49273],{"xmlns":890},[892,49274,49275,49289],{},[895,49276,49277,49279,49281,49283,49285,49287],{},[898,49278,1755],{},[1654,49280,1750],{},[898,49282,17398],{},[1654,49284,1708],{"stretchy":1656},[898,49286,1663],{},[1654,49288,1726],{"stretchy":1656},[902,49290,49291],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,49294,49296],{"className":49295},[886],[888,49297,49298],{"xmlns":890},[892,49299,49300,49304],{},[895,49301,49302],{},[898,49303,11536],{},[902,49305,11536],{"encoding":904},[724,49307,49308,49310,49311,49324,49325,49343,49344,49372],{},[38,49309,46185],{}," Spotřebitel zaplatí ",[883,49312,49314],{"className":49313},[886],[888,49315,49316],{"xmlns":890},[892,49317,49318,49322],{},[895,49319,49320],{},[898,49321,1755],{},[902,49323,1755],{"encoding":904},", výrobce obdrží ",[883,49326,49328],{"className":49327},[886],[888,49329,49330],{"xmlns":890},[892,49331,49332,49340],{},[895,49333,49334,49336,49338],{},[898,49335,1755],{},[1654,49337,2380],{},[898,49339,11536],{},[902,49341,49342],{"encoding":904},"P - T",". Z podmínky ",[883,49345,49347],{"className":49346},[886],[888,49348,49349],{"xmlns":890},[892,49350,49351,49369],{},[895,49352,49353,49355,49357,49359,49361,49363,49365,49367],{},[898,49354,1755],{},[1654,49356,2380],{},[898,49358,11536],{},[1654,49360,1750],{},[898,49362,17398],{},[1654,49364,1708],{"stretchy":1656},[898,49366,1663],{},[1654,49368,1726],{"stretchy":1656},[902,49370,49371],{"encoding":904},"P - T = S(Q)"," plyne",[883,49374,49376],{"className":49375},[886],[888,49377,49378],{"xmlns":890,"display":1956},[892,49379,49380,49414],{},[895,49381,49382,49384,49386,49392,49394,49396,49398,49400,49402,49404,49406,49408,49410,49412],{},[898,49383,1755],{},[1654,49385,1750],{},[1710,49387,49388,49390],{},[898,49389,17398],{},[1665,49391,1667],{},[1654,49393,1708],{"stretchy":1656},[898,49395,1663],{},[1654,49397,1726],{"stretchy":1656},[1654,49399,1750],{},[898,49401,17398],{},[1654,49403,1708],{"stretchy":1656},[898,49405,1663],{},[1654,49407,1726],{"stretchy":1656},[1654,49409,1766],{},[898,49411,11536],{},[898,49413,2138],{"mathvariant":1878},[902,49415,49416],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,49418,49419,49420,49433,49434,2186,49447,49450,49451,2068,49471,16828,49489,2138],{},"Křivka ",[883,49421,49423],{"className":49422},[886],[888,49424,49425],{"xmlns":890},[892,49426,49427,49431],{},[895,49428,49429],{},[898,49430,17398],{},[902,49432,17398],{"encoding":904}," se tedy posune o ",[883,49435,49437],{"className":49436},[886],[888,49438,49439],{"xmlns":890},[892,49440,49441,49445],{},[895,49442,49443],{},[898,49444,11536],{},[902,49446,11536],{"encoding":904},[38,49448,49449],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,49452,49454],{"className":49453},[886],[888,49455,49456],{"xmlns":890},[892,49457,49458,49468],{},[895,49459,49460,49462,49464,49466],{},[898,49461,1755],{},[1654,49463,1750],{},[1665,49465,1681],{},[898,49467,1663],{},[902,49469,49470],{"encoding":904},"P = 2Q",[883,49472,49474],{"className":49473},[886],[888,49475,49476],{"xmlns":890},[892,49477,49478,49486],{},[895,49479,49480,49482,49484],{},[898,49481,11536],{},[1654,49483,1750],{},[1665,49485,11015],{},[902,49487,49488],{"encoding":904},"T = 6",[883,49490,49492],{"className":49491},[886],[888,49493,49494],{"xmlns":890},[892,49495,49496,49518],{},[895,49497,49498,49504,49506,49508,49510,49512,49514,49516],{},[1710,49499,49500,49502],{},[898,49501,17398],{},[1665,49503,1667],{},[1654,49505,2781],{},[898,49507,1755],{},[1654,49509,1750],{},[1665,49511,1681],{},[898,49513,1663],{},[1654,49515,1766],{},[1665,49517,11015],{},[902,49519,49520],{"encoding":904},"S_1: P = 2Q + 6",[724,49522,49523],{},[614,49524,49525,49526,49539],{},"Obrázek 2.12: Posun nabídky o ",[883,49527,49529],{"className":49528},[886],[888,49530,49531],{"xmlns":890},[892,49532,49533,49537],{},[895,49534,49535],{},[898,49536,11536],{},[902,49538,11536],{"encoding":904}," svisle nahoru.",[45190,49541],{},[115,49543,49545],{"id":49544},"tržní-rovnováha","Tržní rovnováha",[2140,49547,49548],{},[724,49549,49550,49552,49553,2186,49556,49588,49589,1343,49612,49635,49636,49639,49640,49653],{},[883,49551,2860],{}," TL;DR\nV ",[38,49554,49555],{},"rovnovážném bodě",[883,49557,49559],{"className":49558},[886],[888,49560,49561],{"xmlns":890},[892,49562,49563,49585],{},[895,49564,49565,49567,49569,49575,49577,49583],{},[898,49566,1798],{},[1654,49568,1657],{"stretchy":1656},[1741,49570,49571,49573],{},[898,49572,1663],{},[898,49574,1798],{},[1654,49576,1674],{"separator":1673},[1741,49578,49579,49581],{},[898,49580,1755],{},[898,49582,1798],{},[1654,49584,1686],{"stretchy":1656},[902,49586,49587],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,49590,49592],{"className":49591},[886],[888,49593,49594],{"xmlns":890},[892,49595,49596,49610],{},[895,49597,49598,49600,49602,49604,49606,49608],{},[898,49599,1755],{},[1654,49601,1750],{},[898,49603,4980],{},[1654,49605,1708],{"stretchy":1656},[898,49607,1663],{},[1654,49609,1726],{"stretchy":1656},[902,49611,13376],{"encoding":904},[883,49613,49615],{"className":49614},[886],[888,49616,49617],{"xmlns":890},[892,49618,49619,49633],{},[895,49620,49621,49623,49625,49627,49629,49631],{},[898,49622,1755],{},[1654,49624,1750],{},[898,49626,17398],{},[1654,49628,1708],{"stretchy":1656},[898,49630,1663],{},[1654,49632,1726],{"stretchy":1656},[902,49634,49291],{"encoding":904},". Čtyři ",[38,49637,49638],{},"pravidla komparativní statiky"," popisují, jak se ",[883,49641,49643],{"className":49642},[886],[888,49644,49645],{"xmlns":890},[892,49646,49647,49651],{},[895,49648,49649],{},[898,49650,1798],{},[902,49652,1798],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,49655,49657],{"id":49656},"definice","Definice",[724,49659,49660,18742,49662,49665,49666,2186,49669,49687,49688,49719,49720,18742,49723,12664],{},[38,49661,49545],{},[614,49663,49664],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,49667,49668],{},"rovnovážné ceně",[883,49670,49672],{"className":49671},[886],[888,49673,49674],{"xmlns":890},[892,49675,49676,49684],{},[895,49677,49678],{},[1741,49679,49680,49682],{},[898,49681,1755],{},[898,49683,1798],{},[902,49685,49686],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,49689,49691],{"className":49690},[886],[888,49692,49693],{"xmlns":890},[892,49694,49695,49717],{},[895,49696,49697,49699,49701,49707,49709,49715],{},[898,49698,1798],{},[1654,49700,1657],{"stretchy":1656},[1741,49702,49703,49705],{},[898,49704,1663],{},[898,49706,1798],{},[1654,49708,1674],{"separator":1673},[1741,49710,49711,49713],{},[898,49712,1755],{},[898,49714,1798],{},[1654,49716,1686],{"stretchy":1656},[902,49718,49587],{"encoding":904}," se nazývá ",[38,49721,49722],{},"rovnovážný bod",[614,49724,49725],{},"equilibrium point",[724,49727,49728,49729,1343,49752,2138],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,49730,49732],{"className":49731},[886],[888,49733,49734],{"xmlns":890},[892,49735,49736,49750],{},[895,49737,49738,49740,49742,49744,49746,49748],{},[898,49739,1755],{},[1654,49741,1750],{},[898,49743,4980],{},[1654,49745,1708],{"stretchy":1656},[898,49747,1663],{},[1654,49749,1726],{"stretchy":1656},[902,49751,13376],{"encoding":904},[883,49753,49755],{"className":49754},[886],[888,49756,49757],{"xmlns":890},[892,49758,49759,49773],{},[895,49760,49761,49763,49765,49767,49769,49771],{},[898,49762,1755],{},[1654,49764,1750],{},[898,49766,17398],{},[1654,49768,1708],{"stretchy":1656},[898,49770,1663],{},[1654,49772,1726],{"stretchy":1656},[902,49774,49291],{"encoding":904},[724,49776,49777],{},[3492,49778],{"alt":49779,"className":49780,"src":49781},"imek-poptavka-nabidka-rovnovaha",[210,3496],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,49783,49784],{},[614,49785,49786,49787,49800,49801,22720,49814,49835,49836,2138],{},"Obrázek 2.13: Klesající ",[883,49788,49790],{"className":49789},[886],[888,49791,49792],{"xmlns":890},[892,49793,49794,49798],{},[895,49795,49796],{},[898,49797,4980],{},[902,49799,4980],{"encoding":904}," a rostoucí ",[883,49802,49804],{"className":49803},[886],[888,49805,49806],{"xmlns":890},[892,49807,49808,49812],{},[895,49809,49810],{},[898,49811,17398],{},[902,49813,17398],{"encoding":904},[883,49815,49817],{"className":49816},[886],[888,49818,49819],{"xmlns":890},[892,49820,49821,49833],{},[895,49822,49823,49825,49827,49829,49831],{},[1654,49824,1708],{"stretchy":1656},[898,49826,1663],{},[1654,49828,1674],{"separator":1673},[898,49830,1755],{},[1654,49832,1726],{"stretchy":1656},[902,49834,45911],{"encoding":904}," protínající se v ",[883,49837,49839],{"className":49838},[886],[888,49840,49841],{"xmlns":890},[892,49842,49843,49865],{},[895,49844,49845,49847,49849,49855,49857,49863],{},[898,49846,1798],{},[1654,49848,1657],{"stretchy":1656},[1741,49850,49851,49853],{},[898,49852,1663],{},[898,49854,1798],{},[1654,49856,1674],{"separator":1673},[1741,49858,49859,49861],{},[898,49860,1755],{},[898,49862,1798],{},[1654,49864,1686],{"stretchy":1656},[902,49866,49587],{"encoding":904},[198,49868,49870],{"id":49869},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,49872,49873,49875,49876,49910,49911,2138],{},[38,49874,46153],{}," Poptávka ",[883,49877,49879],{"className":49878},[886],[888,49880,49881],{"xmlns":890},[892,49882,49883,49907],{},[895,49884,49885,49887,49889,49891,49897,49899,49901,49903,49905],{},[898,49886,1755],{},[1654,49888,1750],{},[1654,49890,2380],{},[1741,49892,49893,49895],{},[898,49894,1663],{},[1665,49896,1681],{},[1654,49898,2380],{},[1665,49900,4647],{},[898,49902,1663],{},[1654,49904,1766],{},[1665,49906,17528],{},[902,49908,49909],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,49912,49914],{"className":49913},[886],[888,49915,49916],{"xmlns":890},[892,49917,49918,49940],{},[895,49919,49920,49922,49924,49930,49932,49934,49936,49938],{},[898,49921,1755],{},[1654,49923,1750],{},[1741,49925,49926,49928],{},[898,49927,1663],{},[1665,49929,1681],{},[1654,49931,1766],{},[1665,49933,31634],{},[898,49935,1663],{},[1654,49937,1766],{},[1665,49939,6492],{},[902,49941,49942],{"encoding":904},"P = Q^2 + 14Q + 22",[724,49944,49945,49947],{},[38,49946,46185],{}," Z rovnosti",[883,49949,49951],{"className":49950},[886],[888,49952,49953],{"xmlns":890,"display":1956},[892,49954,49955,49993],{},[895,49956,49957,49959,49965,49967,49969,49971,49973,49975,49977,49983,49985,49987,49989,49991],{},[1654,49958,2380],{},[1741,49960,49961,49963],{},[898,49962,1663],{},[1665,49964,1681],{},[1654,49966,2380],{},[1665,49968,4647],{},[898,49970,1663],{},[1654,49972,1766],{},[1665,49974,17528],{},[1654,49976,1750],{},[1741,49978,49979,49981],{},[898,49980,1663],{},[1665,49982,1681],{},[1654,49984,1766],{},[1665,49986,31634],{},[898,49988,1663],{},[1654,49990,1766],{},[1665,49992,6492],{},[902,49994,49995],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,49997,49998,49999,50034,50035,50068,50069,50086,50087,50100,50101,1343,50123,50160,50161,2138],{},"dostaneme ",[883,50000,50002],{"className":50001},[886],[888,50003,50004],{"xmlns":890},[892,50005,50006,50031],{},[895,50007,50008,50010,50016,50018,50021,50023,50025,50027,50029],{},[1665,50009,1681],{},[1741,50011,50012,50014],{},[898,50013,1663],{},[1665,50015,1681],{},[1654,50017,1766],{},[1665,50019,50020],{},"24",[898,50022,1663],{},[1654,50024,2380],{},[1665,50026,14346],{},[1654,50028,1750],{},[1665,50030,2062],{},[902,50032,50033],{"encoding":904},"2Q^2 + 24Q - 128 = 0",", resp. ",[883,50036,50038],{"className":50037},[886],[888,50039,50040],{"xmlns":890},[892,50041,50042,50065],{},[895,50043,50044,50050,50052,50054,50056,50058,50061,50063],{},[1741,50045,50046,50048],{},[898,50047,1663],{},[1665,50049,1681],{},[1654,50051,1766],{},[1665,50053,6509],{},[898,50055,1663],{},[1654,50057,2380],{},[1665,50059,50060],{},"64",[1654,50062,1750],{},[1665,50064,2062],{},[902,50066,50067],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,50070,50072],{"className":50071},[886],[888,50073,50074],{"xmlns":890},[892,50075,50076,50083],{},[895,50077,50078,50080],{},[1654,50079,2380],{},[1665,50081,50082],{},"16",[902,50084,50085],{"encoding":904},"-16"," (nevyhovuje) a ",[883,50088,50090],{"className":50089},[886],[888,50091,50092],{"xmlns":890},[892,50093,50094,50098],{},[895,50095,50096],{},[1665,50097,7631],{},[902,50099,7631],{"encoding":904},". Tedy ",[883,50102,50104],{"className":50103},[886],[888,50105,50106],{"xmlns":890},[892,50107,50108,50120],{},[895,50109,50110,50116,50118],{},[1741,50111,50112,50114],{},[898,50113,1663],{},[898,50115,1798],{},[1654,50117,1750],{},[1665,50119,7631],{},[902,50121,50122],{"encoding":904},"Q^E = 4",[883,50124,50126],{"className":50125},[886],[888,50127,50128],{"xmlns":890},[892,50129,50130,50157],{},[895,50131,50132,50138,50140,50142,50144,50146,50148,50150,50152,50154],{},[1741,50133,50134,50136],{},[898,50135,1755],{},[898,50137,1798],{},[1654,50139,1750],{},[1654,50141,2380],{},[1665,50143,50082],{},[1654,50145,2380],{},[1665,50147,5844],{},[1654,50149,1766],{},[1665,50151,17528],{},[1654,50153,1750],{},[1665,50155,50156],{},"94",[902,50158,50159],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,50162,50164],{"className":50163},[886],[888,50165,50166],{"xmlns":890},[892,50167,50168,50182],{},[895,50169,50170,50172,50174,50176,50178,50180],{},[898,50171,1798],{},[1654,50173,1657],{"stretchy":1656},[1665,50175,7631],{},[1654,50177,1674],{"separator":1673},[1665,50179,50156],{},[1654,50181,1686],{"stretchy":1656},[902,50183,50184],{"encoding":904},"E[4, 94]",[198,50186,50188],{"id":50187},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,50190,50191,50193],{},[38,50192,46153],{}," Poptávky a nabídky dvou zboží",[883,50195,50197],{"className":50196},[886],[888,50198,50199],{"xmlns":890,"display":1956},[892,50200,50201,50367],{},[1960,50202,50205,50293],{"rowspacing":2574,"columnalign":50203,"columnspacing":50204},"right left right left","0em 1em 0em",[1964,50206,50207,50217,50249,50259],{},[1967,50208,50209],{},[2582,50210,50211],{"scriptlevel":2062,"displaystyle":1673},[1710,50212,50213,50215],{},[898,50214,1663],{},[1665,50216,1667],{},[1967,50218,50219],{},[2582,50220,50221],{"scriptlevel":2062,"displaystyle":1673},[895,50222,50223,50225,50227,50229,50231,50233,50239,50241,50247],{},[895,50224],{},[1654,50226,1750],{},[1665,50228,5844],{},[1654,50230,2380],{},[1665,50232,4032],{},[1710,50234,50235,50237],{},[898,50236,1755],{},[1665,50238,1667],{},[1654,50240,2380],{},[1710,50242,50243,50245],{},[898,50244,1755],{},[1665,50246,1681],{},[1654,50248,1674],{"separator":1673},[1967,50250,50251],{},[2582,50252,50253],{"scriptlevel":2062,"displaystyle":1673},[1710,50254,50255,50257],{},[898,50256,1663],{},[1665,50258,1681],{},[1967,50260,50261],{},[2582,50262,50263],{"scriptlevel":2062,"displaystyle":1673},[895,50264,50265,50267,50269,50271,50273,50275,50281,50283,50285,50291],{},[895,50266],{},[1654,50268,1750],{},[1665,50270,4767],{},[1654,50272,2380],{},[1665,50274,1681],{},[1710,50276,50277,50279],{},[898,50278,1755],{},[1665,50280,1667],{},[1654,50282,2380],{},[1665,50284,7631],{},[1710,50286,50287,50289],{},[898,50288,1755],{},[1665,50290,1681],{},[1654,50292,1674],{"separator":1673},[1964,50294,50295,50305,50331,50341],{},[1967,50296,50297],{},[2582,50298,50299],{"scriptlevel":2062,"displaystyle":1673},[1710,50300,50301,50303],{},[898,50302,1663],{},[1665,50304,1667],{},[1967,50306,50307],{},[2582,50308,50309],{"scriptlevel":2062,"displaystyle":1673},[895,50310,50311,50313,50315,50317,50319,50321,50323,50329],{},[895,50312],{},[1654,50314,1750],{},[1654,50316,2380],{},[1665,50318,4035],{},[1654,50320,1766],{},[1665,50322,7631],{},[1710,50324,50325,50327],{},[898,50326,1755],{},[1665,50328,1667],{},[1654,50330,1674],{"separator":1673},[1967,50332,50333],{},[2582,50334,50335],{"scriptlevel":2062,"displaystyle":1673},[1710,50336,50337,50339],{},[898,50338,1663],{},[1665,50340,1681],{},[1967,50342,50343],{},[2582,50344,50345],{"scriptlevel":2062,"displaystyle":1673},[895,50346,50347,50349,50351,50353,50355,50357,50359,50365],{},[895,50348],{},[1654,50350,1750],{},[1654,50352,2380],{},[1665,50354,32887],{},[1654,50356,1766],{},[1665,50358,4035],{},[1710,50360,50361,50363],{},[898,50362,1755],{},[1665,50364,1681],{},[898,50366,2138],{"mathvariant":1878},[902,50368,50369],{"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}",[724,50371,50372,50374],{},[38,50373,46185],{}," Z rovností poptávek a nabídek dostaneme",[883,50376,50378],{"className":50377},[886],[888,50379,50380],{"xmlns":890,"display":1956},[892,50381,50382,50431],{},[895,50383,50384,50386,50392,50394,50400,50402,50404,50406,50408,50410,50416,50418,50420,50426,50428],{},[1665,50385,12742],{},[1710,50387,50388,50390],{},[898,50389,1755],{},[1665,50391,1667],{},[1654,50393,1766],{},[1710,50395,50396,50398],{},[898,50397,1755],{},[1665,50399,1681],{},[1654,50401,1750],{},[1665,50403,29892],{},[1654,50405,1674],{"separator":1673},[5008,50407],{"width":14608},[1665,50409,1681],{},[1710,50411,50412,50414],{},[898,50413,1755],{},[1665,50415,1667],{},[1654,50417,1766],{},[1665,50419,32887],{},[1710,50421,50422,50424],{},[898,50423,1755],{},[1665,50425,1681],{},[1654,50427,1750],{},[1665,50429,50430],{},"57.",[902,50432,50433],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,50435,50436,50437,1343,50461,50485,50486,1343,50511,50535,50536,50538],{},"Řešením je ",[883,50438,50440],{"className":50439},[886],[888,50441,50442],{"xmlns":890},[892,50443,50444,50458],{},[895,50445,50446,50454,50456],{},[1659,50447,50448,50450,50452],{},[898,50449,1755],{},[1665,50451,1667],{},[898,50453,1798],{},[1654,50455,1750],{},[1665,50457,7631],{},[902,50459,50460],{"encoding":904},"P_1^E = 4",[883,50462,50464],{"className":50463},[886],[888,50465,50466],{"xmlns":890},[892,50467,50468,50482],{},[895,50469,50470,50478,50480],{},[1659,50471,50472,50474,50476],{},[898,50473,1755],{},[1665,50475,1681],{},[898,50477,1798],{},[1654,50479,1750],{},[1665,50481,32887],{},[902,50483,50484],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,50487,50489],{"className":50488},[886],[888,50490,50491],{"xmlns":890},[892,50492,50493,50508],{},[895,50494,50495,50503,50505],{},[1659,50496,50497,50499,50501],{},[898,50498,1663],{},[1665,50500,1667],{},[898,50502,1798],{},[1654,50504,1750],{},[1665,50506,50507],{},"13",[902,50509,50510],{"encoding":904},"Q_1^E = 13",[883,50512,50514],{"className":50513},[886],[888,50515,50516],{"xmlns":890},[892,50517,50518,50532],{},[895,50519,50520,50528,50530],{},[1659,50521,50522,50524,50526],{},[898,50523,1663],{},[1665,50525,1681],{},[898,50527,1798],{},[1654,50529,1750],{},[1665,50531,31634],{},[902,50533,50534],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,50537,48042],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,50540,50542],{"id":50541},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,50544,50545,50546,50563,50564,18742,50567,12664],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,50547,50549],{"className":50548},[886],[888,50550,50551],{"xmlns":890},[892,50552,50553,50561],{},[895,50554,50555],{},[1741,50556,50557,50559],{},[898,50558,1755],{},[898,50560,1798],{},[902,50562,49686],{"encoding":904},"; mechanismus popisuje ",[38,50565,50566],{},"teorém pavučiny",[614,50568,50569],{},"cobweb model",[198,50571,50573],{"id":50572},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,50575,50576],{},[3492,50577],{"alt":50578,"className":50579,"src":50580},"imek-komparativni-statika-4pripady",[210,3496],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[2140,50582,50583,50624,50664,50704],{},[724,50584,50585,50588,50589,14918,50606,2138],{},[38,50586,50587],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,50590,50592],{"className":50591},[886],[888,50593,50594],{"xmlns":890},[892,50595,50596,50604],{},[895,50597,50598],{},[1741,50599,50600,50602],{},[898,50601,1755],{},[898,50603,1798],{},[902,50605,49686],{"encoding":904},[883,50607,50609],{"className":50608},[886],[888,50610,50611],{"xmlns":890},[892,50612,50613,50621],{},[895,50614,50615],{},[1741,50616,50617,50619],{},[898,50618,1663],{},[898,50620,1798],{},[902,50622,50623],{"encoding":904},"Q^E",[724,50625,50626,50629,50630,14918,50647,2138],{},[38,50627,50628],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,50631,50633],{"className":50632},[886],[888,50634,50635],{"xmlns":890},[892,50636,50637,50645],{},[895,50638,50639],{},[1741,50640,50641,50643],{},[898,50642,1755],{},[898,50644,1798],{},[902,50646,49686],{"encoding":904},[883,50648,50650],{"className":50649},[886],[888,50651,50652],{"xmlns":890},[892,50653,50654,50662],{},[895,50655,50656],{},[1741,50657,50658,50660],{},[898,50659,1663],{},[898,50661,1798],{},[902,50663,50623],{"encoding":904},[724,50665,50666,50669,50670,18076,50687,2138],{},[38,50667,50668],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,50671,50673],{"className":50672},[886],[888,50674,50675],{"xmlns":890},[892,50676,50677,50685],{},[895,50678,50679],{},[1741,50680,50681,50683],{},[898,50682,1755],{},[898,50684,1798],{},[902,50686,49686],{"encoding":904},[883,50688,50690],{"className":50689},[886],[888,50691,50692],{"xmlns":890},[892,50693,50694,50702],{},[895,50695,50696],{},[1741,50697,50698,50700],{},[898,50699,1663],{},[898,50701,1798],{},[902,50703,50623],{"encoding":904},[724,50705,50706,50709,50710,50727,50728,2138],{},[38,50707,50708],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,50711,50713],{"className":50712},[886],[888,50714,50715],{"xmlns":890},[892,50716,50717,50725],{},[895,50718,50719],{},[1741,50720,50721,50723],{},[898,50722,1755],{},[898,50724,1798],{},[902,50726,49686],{"encoding":904},", pokles ",[883,50729,50731],{"className":50730},[886],[888,50732,50733],{"xmlns":890},[892,50734,50735,50743],{},[895,50736,50737],{},[1741,50738,50739,50741],{},[898,50740,1663],{},[898,50742,1798],{},[902,50744,50623],{"encoding":904},[16,50746,50747,50792],{},[19,50748,50749],{},[22,50750,50751,50754,50773],{},[25,50752,50753],{},"Změna",[25,50755,50756],{},[883,50757,50759],{"className":50758},[886],[888,50760,50761],{"xmlns":890},[892,50762,50763,50771],{},[895,50764,50765],{},[1741,50766,50767,50769],{},[898,50768,1755],{},[898,50770,1798],{},[902,50772,49686],{"encoding":904},[25,50774,50775],{},[883,50776,50778],{"className":50777},[886],[888,50779,50780],{"xmlns":890},[892,50781,50782,50790],{},[895,50783,50784],{},[1741,50785,50786,50788],{},[898,50787,1663],{},[898,50789,1798],{},[902,50791,50623],{"encoding":904},[30,50793,50794,50804,50814,50823],{},[22,50795,50796,50799,50802],{},[35,50797,50798],{},"Růst poptávky",[35,50800,50801],{},"↑",[35,50803,50801],{},[22,50805,50806,50809,50812],{},[35,50807,50808],{},"Pokles poptávky",[35,50810,50811],{},"↓",[35,50813,50811],{},[22,50815,50816,50819,50821],{},[35,50817,50818],{},"Růst nabídky",[35,50820,50811],{},[35,50822,50801],{},[22,50824,50825,50828,50830],{},[35,50826,50827],{},"Pokles nabídky",[35,50829,50801],{},[35,50831,50811],{},[724,50833,50834],{},[614,50835,50836],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[45190,50838],{},[115,50840,811],{"id":50841},"zdanění-trhu",[2140,50843,50844,50933],{},[724,50845,50846,50848,50849,50862,50863,4039,50876,50879,50880,44996,50903,50928,50929,50932],{},[883,50847,2860],{}," TL;DR\nJednotková daň ",[883,50850,50852],{"className":50851},[886],[888,50853,50854],{"xmlns":890},[892,50855,50856,50860],{},[895,50857,50858],{},[898,50859,11536],{},[902,50861,11536],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,50864,50866],{"className":50865},[886],[888,50867,50868],{"xmlns":890},[892,50869,50870,50874],{},[895,50871,50872],{},[898,50873,11536],{},[902,50875,11536],{"encoding":904},[38,50877,50878],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,50881,50883],{"className":50882},[886],[888,50884,50885],{"xmlns":890},[892,50886,50887,50900],{},[895,50888,50889],{},[1710,50890,50891,50893],{},[898,50892,11536],{},[895,50894,50895,50898],{},[898,50896,50897],{},"s",[898,50899,724],{},[902,50901,50902],{"encoding":904},"T_{sp}",[883,50904,50906],{"className":50905},[886],[888,50907,50908],{"xmlns":890},[892,50909,50910,50925],{},[895,50911,50912],{},[1710,50913,50914,50916],{},[898,50915,11536],{},[895,50917,50918,50921,50923],{},[898,50919,50920],{},"v",[898,50922,10789],{},[898,50924,20753],{},[902,50926,50927],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,50930,50931],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,50934,50935],{},[614,50936,50937,50938,2138],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,50939,50941],{"className":50940,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,50943,50944,50945,50948,50949,50975,50976,50979,50980,51006,51007,51024,51025,51065,51066,2068,51079,2138],{},"Existují dvě formy zdanění — daň uložená ",[38,50946,50947],{},"výrobci"," (posun nabídky ",[883,50950,50952],{"className":50951},[886],[888,50953,50954],{"xmlns":890},[892,50955,50956,50972],{},[895,50957,50958,50964,50966,50968,50970],{},[1710,50959,50960,50962],{},[898,50961,17398],{},[1665,50963,1667],{},[1654,50965,1750],{},[898,50967,17398],{},[1654,50969,1766],{},[898,50971,11536],{},[902,50973,50974],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,50977,50978],{},"spotřebiteli"," (posun poptávky ",[883,50981,50983],{"className":50982},[886],[888,50984,50985],{"xmlns":890},[892,50986,50987,51003],{},[895,50988,50989,50995,50997,50999,51001],{},[1710,50990,50991,50993],{},[898,50992,4980],{},[1665,50994,1681],{},[1654,50996,1750],{},[898,50998,4980],{},[1654,51000,2380],{},[898,51002,11536],{},[902,51004,51005],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,51008,51010],{"className":51009},[886],[888,51011,51012],{"xmlns":890},[892,51013,51014,51022],{},[895,51015,51016],{},[1741,51017,51018,51020],{},[898,51019,1663],{},[898,51021,1798],{},[902,51023,50623],{"encoding":904}," klesá a vzniká rozklad daně ",[883,51026,51028],{"className":51027},[886],[888,51029,51030],{"xmlns":890},[892,51031,51032,51062],{},[895,51033,51034,51036,51038,51048,51050],{},[898,51035,11536],{},[1654,51037,1750],{},[1710,51039,51040,51042],{},[898,51041,11536],{},[895,51043,51044,51046],{},[898,51045,50897],{},[898,51047,724],{},[1654,51049,1766],{},[1710,51051,51052,51054],{},[898,51053,11536],{},[895,51055,51056,51058,51060],{},[898,51057,50920],{},[898,51059,10789],{},[898,51061,20753],{},[902,51063,51064],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,51067,51069],{"className":51068},[886],[888,51070,51071],{"xmlns":890},[892,51072,51073,51077],{},[895,51074,51075],{},[898,51076,4980],{},[902,51078,4980],{"encoding":904},[883,51080,51082],{"className":51081},[886],[888,51083,51084],{"xmlns":890},[892,51085,51086,51090],{},[895,51087,51088],{},[898,51089,17398],{},[902,51091,17398],{"encoding":904},[724,51093,51094,51095,51098,51099,2068,51129,51163],{},"Zásadním výsledkem kapitoly je ",[38,51096,51097],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,51100,51102],{"className":51101},[886],[888,51103,51104],{"xmlns":890},[892,51105,51106,51126],{},[895,51107,51108,51116,51118],{},[1659,51109,51110,51112,51114],{},[898,51111,1663],{},[1665,51113,1667],{},[898,51115,1798],{},[1654,51117,1750],{},[1659,51119,51120,51122,51124],{},[898,51121,1663],{},[1665,51123,1681],{},[898,51125,1798],{},[902,51127,51128],{"encoding":904},"Q_1^E = Q_2^E",[883,51130,51132],{"className":51131},[886],[888,51133,51134],{"xmlns":890},[892,51135,51136,51160],{},[895,51137,51138,51146,51148,51150,51152],{},[1659,51139,51140,51142,51144],{},[898,51141,1755],{},[1665,51143,1667],{},[898,51145,1798],{},[1654,51147,2380],{},[898,51149,11536],{},[1654,51151,1750],{},[1659,51153,51154,51156,51158],{},[898,51155,1755],{},[1665,51157,1681],{},[898,51159,1798],{},[902,51161,51162],{"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.",[724,51165,51166,51167,51170,51171,51197,51198,51226,51227,51230,51231,51234,51235,2138],{},"Podrobný výklad, Příklady ",[38,51168,51169],{},"2.9"," (daň výrobci, ",[883,51172,51174],{"className":51173},[886],[888,51175,51176],{"xmlns":890},[892,51177,51178,51194],{},[895,51179,51180,51190,51192],{},[1710,51181,51182,51184],{},[898,51183,11536],{},[895,51185,51186,51188],{},[898,51187,50897],{},[898,51189,724],{},[1654,51191,1750],{},[1665,51193,1681],{},[902,51195,51196],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,51199,51201],{"className":51200},[886],[888,51202,51203],{"xmlns":890},[892,51204,51205,51223],{},[895,51206,51207,51219,51221],{},[1710,51208,51209,51211],{},[898,51210,11536],{},[895,51212,51213,51215,51217],{},[898,51214,50920],{},[898,51216,10789],{},[898,51218,20753],{},[1654,51220,1750],{},[1665,51222,7631],{},[902,51224,51225],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,51228,51229],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,51232,51233],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,51236,50941],{"className":51237,"dataFsResolvedFilePath":809,"href":810},[210],[45190,51239],{},[115,51241,51243],{"id":51242},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[2140,51245,51246],{},[724,51247,51248,51250,51251,51254,51255,51257],{},[883,51249,2860],{}," TL;DR\nMultiplikátory jsou ",[38,51252,51253],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,51256,45180],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,51259,51261],{"id":51260},"redukovaný-tvar","Redukovaný tvar",[724,51263,51264,51265,18742,51288,1343,51306,20840,51323,18742,51346,51363,51364,51394],{},"Pro lineární model ",[883,51266,51268],{"className":51267},[886],[888,51269,51270],{"xmlns":890},[892,51271,51272,51286],{},[895,51273,51274,51276,51278,51280,51282,51284],{},[898,51275,1755],{},[1654,51277,1750],{},[898,51279,207],{},[898,51281,1663],{},[1654,51283,1766],{},[898,51285,9758],{},[902,51287,45280],{"encoding":904},[883,51289,51291],{"className":51290},[886],[888,51292,51293],{"xmlns":890},[892,51294,51295,51303],{},[895,51296,51297,51299,51301],{},[898,51298,207],{},[1654,51300,3002],{},[1665,51302,2062],{},[902,51304,51305],{"encoding":904},"a \u003C 0",[883,51307,51309],{"className":51308},[886],[888,51310,51311],{"xmlns":890},[892,51312,51313,51321],{},[895,51314,51315,51317,51319],{},[898,51316,9758],{},[1654,51318,2952],{},[1665,51320,2062],{},[902,51322,27510],{"encoding":904},[883,51324,51326],{"className":51325},[886],[888,51327,51328],{"xmlns":890},[892,51329,51330,51344],{},[895,51331,51332,51334,51336,51338,51340,51342],{},[898,51333,1755],{},[1654,51335,1750],{},[898,51337,3624],{},[898,51339,1663],{},[1654,51341,1766],{},[898,51343,10977],{},[902,51345,48462],{"encoding":904},[883,51347,51349],{"className":51348},[886],[888,51350,51351],{"xmlns":890},[892,51352,51353,51361],{},[895,51354,51355,51357,51359],{},[898,51356,3624],{},[1654,51358,2952],{},[1665,51360,2062],{},[902,51362,48480],{"encoding":904},") dává podmínka rovnováhy ",[883,51365,51367],{"className":51366},[886],[888,51368,51369],{"xmlns":890},[892,51370,51371,51391],{},[895,51372,51373,51375,51377,51379,51381,51383,51385,51387,51389],{},[898,51374,207],{},[898,51376,1663],{},[1654,51378,1766],{},[898,51380,9758],{},[1654,51382,1750],{},[898,51384,3624],{},[898,51386,1663],{},[1654,51388,1766],{},[898,51390,10977],{},[902,51392,51393],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,51396,51398],{"className":51397},[886],[888,51399,51400],{"xmlns":890,"display":1956},[892,51401,51402,51447],{},[1960,51403,51404],{"width":1962},[1964,51405,51406,51408,51440,51442],{},[1967,51407],{"width":1969},[1967,51409,51410],{},[895,51411,51412,51418,51420,51438],{},[1741,51413,51414,51416],{},[898,51415,1663],{},[898,51417,1798],{},[1654,51419,1750],{},[2811,51421,51422,51430],{},[895,51423,51424,51426,51428],{},[898,51425,9758],{},[1654,51427,2380],{},[898,51429,10977],{},[895,51431,51432,51434,51436],{},[898,51433,3624],{},[1654,51435,2380],{},[898,51437,207],{},[898,51439,2138],{"mathvariant":1878},[1967,51441],{"width":1969},[1967,51443,51444],{},[1865,51445,51446],{},"(2.10)",[902,51448,51449],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,51451,51452,51453,18742,51455,51458,51459,51476,51477,2186,51480,51506,51507,51520,51521,51539,51540,12664],{},"Vztah (2.10) je ",[38,51454,29643],{},[614,51456,51457],{},"reduced form",") pro ",[883,51460,51462],{"className":51461},[886],[888,51463,51464],{"xmlns":890},[892,51465,51466,51474],{},[895,51467,51468],{},[1741,51469,51470,51472],{},[898,51471,1663],{},[898,51473,1798],{},[902,51475,50623],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,51478,51479],{},"parametrů",[883,51481,51483],{"className":51482},[886],[888,51484,51485],{"xmlns":890},[892,51486,51487,51503],{},[895,51488,51489,51491,51493,51495,51497,51499,51501],{},[898,51490,207],{},[1654,51492,1674],{"separator":1673},[898,51494,9758],{},[1654,51496,1674],{"separator":1673},[898,51498,3624],{},[1654,51500,1674],{"separator":1673},[898,51502,10977],{},[902,51504,51505],{"encoding":904},"a, b, c, d",". Aby ",[883,51508,51510],{"className":51509},[886],[888,51511,51512],{"xmlns":890},[892,51513,51514,51518],{},[895,51515,51516],{},[898,51517,1798],{},[902,51519,1798],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,51522,51524],{"className":51523},[886],[888,51525,51526],{"xmlns":890},[892,51527,51528,51536],{},[895,51529,51530,51532,51534],{},[898,51531,9758],{},[1654,51533,2952],{},[898,51535,10977],{},[902,51537,51538],{"encoding":904},"b > d"," (neboť ",[883,51541,51543],{"className":51542},[886],[888,51544,51545],{"xmlns":890},[892,51546,51547,51559],{},[895,51548,51549,51551,51553,51555,51557],{},[898,51550,3624],{},[1654,51552,2380],{},[898,51554,207],{},[1654,51556,2952],{},[1665,51558,2062],{},[902,51560,51561],{"encoding":904},"c - a > 0",[724,51563,51564],{},[614,51565,51566,51567,51580,51581,51594,51595,27344,51608,50160,51625,51638],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,51568,51570],{"className":51569},[886],[888,51571,51572],{"xmlns":890},[892,51573,51574,51578],{},[895,51575,51576],{},[898,51577,9758],{},[902,51579,9758],{"encoding":904}," na ose ",[883,51582,51584],{"className":51583},[886],[888,51585,51586],{"xmlns":890},[892,51587,51588,51592],{},[895,51589,51590],{},[898,51591,1755],{},[902,51593,1755],{"encoding":904},") a nabídka (úsek ",[883,51596,51598],{"className":51597},[886],[888,51599,51600],{"xmlns":890},[892,51601,51602,51606],{},[895,51603,51604],{},[898,51605,10977],{},[902,51607,10977],{"encoding":904},[883,51609,51611],{"className":51610},[886],[888,51612,51613],{"xmlns":890},[892,51614,51615,51623],{},[895,51616,51617,51619,51621],{},[898,51618,9758],{},[1654,51620,2952],{},[898,51622,10977],{},[902,51624,51538],{"encoding":904},[883,51626,51628],{"className":51627},[886],[888,51629,51630],{"xmlns":890},[892,51631,51632,51636],{},[895,51633,51634],{},[898,51635,1798],{},[902,51637,1798],{"encoding":904}," v 1. kvadrantu.",[198,51640,51642],{"id":51641},"definice-multiplikátorů","Definice multiplikátorů",[724,51644,51645,51646,51671,51672,51685,51686,51699],{},"V komparativní statice jsou ",[883,51647,51649],{"className":51648},[886],[888,51650,51651],{"xmlns":890},[892,51652,51653,51669],{},[895,51654,51655,51657,51659,51661,51663,51665,51667],{},[898,51656,207],{},[1654,51658,1674],{"separator":1673},[898,51660,9758],{},[1654,51662,1674],{"separator":1673},[898,51664,3624],{},[1654,51666,1674],{"separator":1673},[898,51668,10977],{},[902,51670,51505],{"encoding":904}," exogenní proměnné a ",[883,51673,51675],{"className":51674},[886],[888,51676,51677],{"xmlns":890},[892,51678,51679,51683],{},[895,51680,51681],{},[898,51682,1663],{},[902,51684,1663],{"encoding":904}," endogenní. Přibližná změna ",[883,51687,51689],{"className":51688},[886],[888,51690,51691],{"xmlns":890},[892,51692,51693,51697],{},[895,51694,51695],{},[898,51696,1663],{},[902,51698,1663],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,51701,51703],{"className":51702},[886],[888,51704,51705],{"xmlns":890,"display":1956},[892,51706,51707,51800],{},[1960,51708,51709],{"width":1962},[1964,51710,51711,51713,51793,51795],{},[1967,51712],{"width":1969},[1967,51714,51715],{},[895,51716,51717,51719,51721,51723,51725,51727,51729,51737,51739,51741,51743,51745,51753,51755,51757,51759,51761,51769,51771,51773,51775,51777,51785,51787,51789,51791],{},[898,51718,11648],{"mathvariant":1878},[898,51720,1663],{},[1654,51722,11492],{},[898,51724,10977],{},[898,51726,1663],{},[1654,51728,1750],{},[1659,51730,51731,51733,51735],{},[898,51732,1663],{},[898,51734,207],{},[1654,51736,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1865,51738,11744],{},[898,51740,10977],{},[898,51742,207],{},[1654,51744,1766],{},[1659,51746,51747,51749,51751],{},[898,51748,1663],{},[898,51750,9758],{},[1654,51752,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1865,51754,11744],{},[898,51756,10977],{},[898,51758,9758],{},[1654,51760,1766],{},[1659,51762,51763,51765,51767],{},[898,51764,1663],{},[898,51766,3624],{},[1654,51768,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1865,51770,11744],{},[898,51772,10977],{},[898,51774,3624],{},[1654,51776,1766],{},[1659,51778,51779,51781,51783],{},[898,51780,1663],{},[898,51782,10977],{},[1654,51784,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1865,51786,11744],{},[898,51788,10977],{},[898,51790,10977],{},[898,51792,2138],{"mathvariant":1878},[1967,51794],{"width":1969},[1967,51796,51797],{},[1865,51798,51799],{},"(2.11)",[902,51801,51802],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,51804,51805,51806,51856,51857,18742,51859,11906],{},"Parciální derivace ",[883,51807,51809],{"className":51808},[886],[888,51810,51811],{"xmlns":890},[892,51812,51813,51853],{},[895,51814,51815,51823,51825,51833,51835,51843,51845],{},[1659,51816,51817,51819,51821],{},[898,51818,1663],{},[898,51820,207],{},[1654,51822,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,51824,1674],{"separator":1673},[1659,51826,51827,51829,51831],{},[898,51828,1663],{},[898,51830,9758],{},[1654,51832,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,51834,1674],{"separator":1673},[1659,51836,51837,51839,51841],{},[898,51838,1663],{},[898,51840,3624],{},[1654,51842,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,51844,1674],{"separator":1673},[1659,51846,51847,51849,51851],{},[898,51848,1663],{},[898,51850,10977],{},[1654,51852,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,51854,51855],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,51858,26673],{},[614,51860,51861],{},"multipliers",[883,51863,51865],{"className":51864},[886],[888,51866,51867],{"xmlns":890,"display":1956},[892,51868,51869,52020],{},[1960,51870,51871],{"width":1962},[1964,51872,51873,51875,52013,52015],{},[1967,51874],{"width":1969},[1967,51876,51877],{},[895,51878,51879,51887,51889,51915,51917,51919,51927,51929,51941,51943,51945,51953,51955,51957,51983,51985,51987,51995,51997,51999,52011],{},[1659,51880,51881,51883,51885],{},[898,51882,1663],{},[898,51884,207],{},[1654,51886,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,51888,1750],{},[2811,51890,51891,51899],{},[895,51892,51893,51895,51897],{},[898,51894,9758],{},[1654,51896,2380],{},[898,51898,10977],{},[895,51900,51901,51903,51905,51907,51909],{},[1654,51902,1708],{"stretchy":1656},[898,51904,3624],{},[1654,51906,2380],{},[898,51908,207],{},[1741,51910,51911,51913],{},[1654,51912,1726],{"stretchy":1656},[1665,51914,1681],{},[1654,51916,1674],{"separator":1673},[5008,51918],{"width":5010},[1659,51920,51921,51923,51925],{},[898,51922,1663],{},[898,51924,9758],{},[1654,51926,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,51928,1750],{},[2811,51930,51931,51933],{},[1665,51932,1667],{},[895,51934,51935,51937,51939],{},[898,51936,3624],{},[1654,51938,2380],{},[898,51940,207],{},[1654,51942,1674],{"separator":1673},[5008,51944],{"width":5010},[1659,51946,51947,51949,51951],{},[898,51948,1663],{},[898,51950,3624],{},[1654,51952,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,51954,1750],{},[1654,51956,2380],{},[2811,51958,51959,51967],{},[895,51960,51961,51963,51965],{},[898,51962,9758],{},[1654,51964,2380],{},[898,51966,10977],{},[895,51968,51969,51971,51973,51975,51977],{},[1654,51970,1708],{"stretchy":1656},[898,51972,3624],{},[1654,51974,2380],{},[898,51976,207],{},[1741,51978,51979,51981],{},[1654,51980,1726],{"stretchy":1656},[1665,51982,1681],{},[1654,51984,1674],{"separator":1673},[5008,51986],{"width":5010},[1659,51988,51989,51991,51993],{},[898,51990,1663],{},[898,51992,10977],{},[1654,51994,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,51996,1750],{},[1654,51998,2380],{},[2811,52000,52001,52003],{},[1665,52002,1667],{},[895,52004,52005,52007,52009],{},[898,52006,3624],{},[1654,52008,2380],{},[898,52010,207],{},[898,52012,2138],{"mathvariant":1878},[1967,52014],{"width":1969},[1967,52016,52017],{},[1865,52018,52019],{},"(2.12)",[902,52021,52022],{"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}",[198,52024,52026],{"id":52025},"znaménka-a-interpretace","Znaménka a interpretace",[724,52028,52029,52030,1343,52047,1343,52064,1343,52081,52098,52099,11906],{},"Za podmínek ",[883,52031,52033],{"className":52032},[886],[888,52034,52035],{"xmlns":890},[892,52036,52037,52045],{},[895,52038,52039,52041,52043],{},[898,52040,207],{},[1654,52042,3002],{},[1665,52044,2062],{},[902,52046,51305],{"encoding":904},[883,52048,52050],{"className":52049},[886],[888,52051,52052],{"xmlns":890},[892,52053,52054,52062],{},[895,52055,52056,52058,52060],{},[898,52057,9758],{},[1654,52059,2952],{},[1665,52061,2062],{},[902,52063,27510],{"encoding":904},[883,52065,52067],{"className":52066},[886],[888,52068,52069],{"xmlns":890},[892,52070,52071,52079],{},[895,52072,52073,52075,52077],{},[898,52074,3624],{},[1654,52076,2952],{},[1665,52078,2062],{},[902,52080,48480],{"encoding":904},[883,52082,52084],{"className":52083},[886],[888,52085,52086],{"xmlns":890},[892,52087,52088,52096],{},[895,52089,52090,52092,52094],{},[898,52091,9758],{},[1654,52093,2952],{},[898,52095,10977],{},[902,52097,51538],{"encoding":904}," platí (znaménka se ",[38,52100,52101],{},"nemění",[883,52103,52105],{"className":52104},[886],[888,52106,52107],{"xmlns":890,"display":1956},[892,52108,52109,52171],{},[895,52110,52111,52119,52121,52123,52125,52127,52135,52137,52139,52141,52143,52151,52153,52155,52157,52159,52167,52169],{},[1659,52112,52113,52115,52117],{},[898,52114,1663],{},[898,52116,207],{},[1654,52118,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,52120,2952],{},[1665,52122,2062],{},[1654,52124,1674],{"separator":1673},[5008,52126],{"width":14608},[1659,52128,52129,52131,52133],{},[898,52130,1663],{},[898,52132,9758],{},[1654,52134,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,52136,2952],{},[1665,52138,2062],{},[1654,52140,1674],{"separator":1673},[5008,52142],{"width":14608},[1659,52144,52145,52147,52149],{},[898,52146,1663],{},[898,52148,3624],{},[1654,52150,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,52152,3002],{},[1665,52154,2062],{},[1654,52156,1674],{"separator":1673},[5008,52158],{"width":14608},[1659,52160,52161,52163,52165],{},[898,52162,1663],{},[898,52164,10977],{},[1654,52166,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,52168,3002],{},[1665,52170,2745],{},[902,52172,52173],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,52175,52176,52235],{},[123,52177,52178,2186,52181,52201,52202,52219,52220,1343,52233,2138],{},[38,52179,52180],{},"Kvantitativní smysl:",[883,52182,52184],{"className":52183},[886],[888,52185,52186],{"xmlns":890},[892,52187,52188,52198],{},[895,52189,52190],{},[1659,52191,52192,52194,52196],{},[898,52193,1663],{},[898,52195,10799],{},[1654,52197,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,52199,52200],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,52203,52205],{"className":52204},[886],[888,52206,52207],{"xmlns":890},[892,52208,52209,52217],{},[895,52210,52211],{},[1741,52212,52213,52215],{},[898,52214,1663],{},[898,52216,1798],{},[902,52218,50623],{"encoding":904}," při jednotkové změně parametru ",[883,52221,52223],{"className":52222},[886],[888,52224,52225],{"xmlns":890},[892,52226,52227,52231],{},[895,52228,52229],{},[898,52230,10799],{},[902,52232,10799],{"encoding":904},[614,52234,45180],{},[123,52236,52237,52240,52241,52258,52259,2138],{},[38,52238,52239],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,52242,52244],{"className":52243},[886],[888,52245,52246],{"xmlns":890},[892,52247,52248,52256],{},[895,52249,52250],{},[1741,52251,52252,52254],{},[898,52253,1663],{},[898,52255,1798],{},[902,52257,50623],{"encoding":904}," na růst ",[883,52260,52262],{"className":52261},[886],[888,52263,52264],{"xmlns":890},[892,52265,52266,52270],{},[895,52267,52268],{},[898,52269,10799],{},[902,52271,10799],{"encoding":904},[724,52273,52274,52275,52288,52289,51539,52306,12664],{},"Např. růst ",[883,52276,52278],{"className":52277},[886],[888,52279,52280],{"xmlns":890},[892,52281,52282,52286],{},[895,52283,52284],{},[898,52285,3624],{},[902,52287,3624],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,52290,52292],{"className":52291},[886],[888,52293,52294],{"xmlns":890},[892,52295,52296,52304],{},[895,52297,52298],{},[1741,52299,52300,52302],{},[898,52301,1663],{},[898,52303,1798],{},[902,52305,50623],{"encoding":904},[883,52307,52309],{"className":52308},[886],[888,52310,52311],{"xmlns":890},[892,52312,52313,52327],{},[895,52314,52315,52323,52325],{},[1659,52316,52317,52319,52321],{},[898,52318,1663],{},[898,52320,3624],{},[1654,52322,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,52324,3002],{},[1665,52326,2062],{},[902,52328,52329],{"encoding":904},"Q'_c \u003C 0",[724,52331,52332],{},[614,52333,52334,52335,52355,52356,52380,52381,52403,52404,2138],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,52336,52338],{"className":52337},[886],[888,52339,52340],{"xmlns":890},[892,52341,52342,52352],{},[895,52343,52344,52346,52348,52350],{},[898,52345,3624],{},[898,52347,1663],{},[1654,52349,1766],{},[898,52351,10977],{},[902,52353,52354],{"encoding":904},"cQ + d"," na strmější ",[883,52357,52359],{"className":52358},[886],[888,52360,52361],{"xmlns":890},[892,52362,52363,52377],{},[895,52364,52365,52371,52373,52375],{},[1710,52366,52367,52369],{},[898,52368,3624],{},[1665,52370,1667],{},[898,52372,1663],{},[1654,52374,1766],{},[898,52376,10977],{},[902,52378,52379],{"encoding":904},"c_1 Q + d"," (při ",[883,52382,52384],{"className":52383},[886],[888,52385,52386],{"xmlns":890},[892,52387,52388,52400],{},[895,52389,52390,52396,52398],{},[1710,52391,52392,52394],{},[898,52393,3624],{},[1665,52395,1667],{},[1654,52397,2952],{},[898,52399,3624],{},[902,52401,52402],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,52405,52407],{"className":52406},[886],[888,52408,52409],{"xmlns":890},[892,52410,52411,52421],{},[895,52412,52413,52419],{},[1741,52414,52415,52417],{},[898,52416,1663],{},[898,52418,1798],{},[1654,52420,50811],{},[902,52422,52423],{"encoding":904},"Q^E \\downarrow",[724,52425,52426,52427,52459,52460,2138],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,52428,52430],{"className":52429},[886],[888,52431,52432],{"xmlns":890},[892,52433,52434,52456],{},[895,52435,52436,52438,52440,52442,52450,52452,52454],{},[898,52437,11648],{"mathvariant":1878},[898,52439,1663],{},[1654,52441,11492],{},[1659,52443,52444,52446,52448],{},[898,52445,1663],{},[898,52447,9758],{},[1654,52449,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1865,52451,11744],{},[898,52453,10977],{},[898,52455,9758],{},[902,52457,52458],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,52461,52463],{"className":52462},[886],[888,52464,52465],{"xmlns":890},[892,52466,52467,52475],{},[895,52468,52469],{},[1741,52470,52471,52473],{},[898,52472,1755],{},[898,52474,1798],{},[902,52476,49686],{"encoding":904},[198,52478,52480,52481],{"id":52479},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,52482,52484],{"className":52483},[886],[888,52485,52486],{"xmlns":890},[892,52487,52488,52496],{},[895,52489,52490],{},[1741,52491,52492,52494],{},[898,52493,1663],{},[898,52495,1798],{},[902,52497,50623],{"encoding":904},[724,52499,52500,49875,52502,49910,52528,2138],{},[38,52501,46153],{},[883,52503,52505],{"className":52504},[886],[888,52506,52507],{"xmlns":890},[892,52508,52509,52525],{},[895,52510,52511,52513,52515,52517,52519,52521,52523],{},[898,52512,1755],{},[1654,52514,1750],{},[1654,52516,2380],{},[1665,52518,4035],{},[898,52520,1663],{},[1654,52522,1766],{},[1665,52524,5844],{},[902,52526,52527],{"encoding":904},"P = -3Q + 40",[883,52529,52531],{"className":52530},[886],[888,52532,52533],{"xmlns":890},[892,52534,52535,52549],{},[895,52536,52537,52539,52541,52543,52545,52547],{},[898,52538,1755],{},[1654,52540,1750],{},[1665,52542,7594],{},[898,52544,1663],{},[1654,52546,1766],{},[1665,52548,4647],{},[902,52550,52551],{"encoding":904},"P = 0{,}5Q + 10",[724,52553,52554,52556],{},[38,52555,46185],{}," Rovnovážné množství",[883,52558,52560],{"className":52559},[886],[888,52561,52562],{"xmlns":890,"display":1956},[892,52563,52564,52632],{},[895,52565,52566,52572,52574,52592,52594,52618,52620,52627,52629],{},[1741,52567,52568,52570],{},[898,52569,1663],{},[898,52571,1798],{},[1654,52573,1750],{},[2811,52575,52576,52584],{},[895,52577,52578,52580,52582],{},[898,52579,9758],{},[1654,52581,2380],{},[898,52583,10977],{},[895,52585,52586,52588,52590],{},[898,52587,3624],{},[1654,52589,2380],{},[898,52591,207],{},[1654,52593,1750],{},[2811,52595,52596,52604],{},[895,52597,52598,52600,52602],{},[1665,52599,5844],{},[1654,52601,2380],{},[1665,52603,4647],{},[895,52605,52606,52608,52610,52612,52614,52616],{},[1665,52607,7594],{},[1654,52609,2380],{},[1654,52611,1708],{"stretchy":1656},[1654,52613,2380],{},[1665,52615,4035],{},[1654,52617,1726],{"stretchy":1656},[1654,52619,1750],{},[2811,52621,52622,52624],{},[1665,52623,46239],{},[1665,52625,52626],{},"3,5",[1654,52628,11492],{},[1665,52630,52631],{},"8,571.",[902,52633,52634],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,52636,52637,52682],{},[38,52638,52639,52640,11434,52653,11448,52667,52681],{},"(a) Změna ",[883,52641,52643],{"className":52642},[886],[888,52644,52645],{"xmlns":890},[892,52646,52647,52651],{},[895,52648,52649],{},[898,52650,3624],{},[902,52652,3624],{"encoding":904},[883,52654,52656],{"className":52655},[886],[888,52657,52658],{"xmlns":890},[892,52659,52660,52664],{},[895,52661,52662],{},[1665,52663,7594],{},[902,52665,52666],{"encoding":904},"0{,}5",[883,52668,52670],{"className":52669},[886],[888,52671,52672],{"xmlns":890},[892,52673,52674,52678],{},[895,52675,52676],{},[1665,52677,28017],{},[902,52679,52680],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,52684,52686],{"className":52685},[886],[888,52687,52688],{"xmlns":890,"display":1956},[892,52689,52690,52767],{},[895,52691,52692,52700,52702,52704,52706,52708,52710,52736,52738,52740,52742,52744,52746,52756,52758,52760,52762,52764],{},[1659,52693,52694,52696,52698],{},[898,52695,1663],{},[898,52697,3624],{},[1654,52699,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1865,52701,11744],{},[898,52703,10977],{},[898,52705,3624],{},[1654,52707,1750],{},[1654,52709,2380],{},[2811,52711,52712,52720],{},[895,52713,52714,52716,52718],{},[898,52715,9758],{},[1654,52717,2380],{},[898,52719,10977],{},[895,52721,52722,52724,52726,52728,52730],{},[1654,52723,1708],{"stretchy":1656},[898,52725,3624],{},[1654,52727,2380],{},[898,52729,207],{},[1741,52731,52732,52734],{},[1654,52733,1726],{"stretchy":1656},[1665,52735,1681],{},[1865,52737,11744],{},[898,52739,10977],{},[898,52741,3624],{},[1654,52743,1750],{},[1654,52745,2380],{},[2811,52747,52748,52750],{},[1665,52749,46239],{},[1741,52751,52752,52754],{},[1665,52753,52626],{},[1665,52755,1681],{},[1654,52757,4554],{},[1665,52759,11555],{},[1654,52761,11492],{},[1654,52763,2380],{},[1665,52765,52766],{},"0,245.",[902,52768,52769],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,52771,52772,52773,2138],{},"Nové rovnovážné množství ",[883,52774,52776],{"className":52775},[886],[888,52777,52778],{"xmlns":890},[892,52779,52780,52805],{},[895,52781,52782,52790,52792,52795,52797,52800,52802],{},[1659,52783,52784,52786,52788],{},[898,52785,1663],{},[1665,52787,1667],{},[898,52789,1798],{},[1654,52791,11492],{},[1665,52793,52794],{},"8,571",[1654,52796,2380],{},[1665,52798,52799],{},"0,245",[1654,52801,1750],{},[1665,52803,52804],{},"8,326",[902,52806,52807],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,52809,52810,52895],{},[38,52811,52812,52813,1343,52833,1343,52855,1343,52875,2138],{},"(b) Současné změny ",[883,52814,52816],{"className":52815},[886],[888,52817,52818],{"xmlns":890},[892,52819,52820,52830],{},[895,52821,52822,52824,52826,52828],{},[898,52823,10977],{},[898,52825,207],{},[1654,52827,1750],{},[1665,52829,7594],{},[902,52831,52832],{"encoding":904},"da = 0{,}5",[883,52834,52836],{"className":52835},[886],[888,52837,52838],{"xmlns":890},[892,52839,52840,52852],{},[895,52841,52842,52844,52846,52848,52850],{},[898,52843,10977],{},[898,52845,9758],{},[1654,52847,1750],{},[1654,52849,2380],{},[1665,52851,4032],{},[902,52853,52854],{"encoding":904},"db = -5",[883,52856,52858],{"className":52857},[886],[888,52859,52860],{"xmlns":890},[892,52861,52862,52872],{},[895,52863,52864,52866,52868,52870],{},[898,52865,10977],{},[898,52867,3624],{},[1654,52869,1750],{},[1665,52871,11555],{},[902,52873,52874],{"encoding":904},"dc = 0{,}1",[883,52876,52878],{"className":52877},[886],[888,52879,52880],{"xmlns":890},[892,52881,52882,52892],{},[895,52883,52884,52886,52888,52890],{},[898,52885,10977],{},[898,52887,10977],{},[1654,52889,1750],{},[1665,52891,1667],{},[902,52893,52894],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,52897,52899],{"className":52898},[886],[888,52900,52901],{"xmlns":890,"display":1956},[892,52902,52903,53046],{},[1960,52904,52905,52987,53023],{"rowspacing":2574,"columnalign":2575,"columnspacing":2576},[1964,52906,52907,52917],{},[1967,52908,52909],{},[2582,52910,52911],{"scriptlevel":2062,"displaystyle":1673},[895,52912,52913,52915],{},[898,52914,11648],{"mathvariant":1878},[898,52916,1663],{},[1967,52918,52919],{},[2582,52920,52921],{"scriptlevel":2062,"displaystyle":1673},[895,52922,52923,52925,52927,52937,52939,52941,52943,52949,52951,52953,52955,52957,52959,52961,52971,52973,52975,52977,52983,52985],{},[895,52924],{},[1654,52926,11492],{},[2811,52928,52929,52931],{},[1665,52930,46239],{},[1741,52932,52933,52935],{},[1665,52934,52626],{},[1665,52936,1681],{},[1654,52938,4554],{},[1665,52940,7594],{},[1654,52942,1766],{},[2811,52944,52945,52947],{},[1665,52946,1667],{},[1665,52948,52626],{},[1654,52950,4554],{},[1654,52952,1708],{"stretchy":1656},[1654,52954,2380],{},[1665,52956,4032],{},[1654,52958,1726],{"stretchy":1656},[1654,52960,2380],{},[2811,52962,52963,52965],{},[1665,52964,46239],{},[1741,52966,52967,52969],{},[1665,52968,52626],{},[1665,52970,1681],{},[1654,52972,4554],{},[1665,52974,11555],{},[1654,52976,2380],{},[2811,52978,52979,52981],{},[1665,52980,1667],{},[1665,52982,52626],{},[1654,52984,4554],{},[1665,52986,1667],{},[1964,52988,52989,52995],{},[1967,52990,52991],{},[2582,52992,52993],{"scriptlevel":2062,"displaystyle":1673},[895,52994],{},[1967,52996,52997],{},[2582,52998,52999],{"scriptlevel":2062,"displaystyle":1673},[895,53000,53001,53003,53005,53008,53010,53013,53015,53018,53020],{},[895,53002],{},[1654,53004,1750],{},[1665,53006,53007],{},"1,2245",[1654,53009,2380],{},[1665,53011,53012],{},"1,4286",[1654,53014,2380],{},[1665,53016,53017],{},"0,2449",[1654,53019,2380],{},[1665,53021,53022],{},"0,2857",[1964,53024,53025,53031],{},[1967,53026,53027],{},[2582,53028,53029],{"scriptlevel":2062,"displaystyle":1673},[895,53030],{},[1967,53032,53033],{},[2582,53034,53035],{"scriptlevel":2062,"displaystyle":1673},[895,53036,53037,53039,53041,53043],{},[895,53038],{},[1654,53040,11492],{},[1654,53042,2380],{},[1665,53044,53045],{},"0,735.",[902,53047,53048],{"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}",[724,53050,3990,53051,2138],{},[883,53052,53054],{"className":53053},[886],[888,53055,53056],{"xmlns":890},[892,53057,53058,53082],{},[895,53059,53060,53068,53070,53072,53074,53077,53079],{},[1659,53061,53062,53064,53066],{},[898,53063,1663],{},[1665,53065,1667],{},[898,53067,1798],{},[1654,53069,11492],{},[1665,53071,52794],{},[1654,53073,2380],{},[1665,53075,53076],{},"0,735",[1654,53078,1750],{},[1665,53080,53081],{},"7,836",[902,53083,53084],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[2140,53086,53087],{},[724,53088,53089,53091,53092,53115,53116,53138],{},[883,53090,2146],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,53093,53095],{"className":53094},[886],[888,53096,53097],{"xmlns":890},[892,53098,53099,53112],{},[895,53100,53101,53103,53105,53107,53109],{},[898,53102,11648],{"mathvariant":1878},[898,53104,1663],{},[1654,53106,11492],{},[1654,53108,2380],{},[1665,53110,53111],{},"2,69",[902,53113,53114],{"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 ",[883,53117,53119],{"className":53118},[886],[888,53120,53121],{"xmlns":890},[892,53122,53123,53135],{},[895,53124,53125,53127,53129,53131,53133],{},[898,53126,11648],{"mathvariant":1878},[898,53128,1663],{},[1654,53130,11492],{},[1654,53132,2380],{},[1665,53134,53076],{},[902,53136,53137],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,53140,53141],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[45190,53143],{},[115,53145,820],{"id":20498},[2140,53147,53148],{},[724,53149,53150,12620,53152,18742,53155,20840,53171,18742,53174,53190,53191,2138],{},[883,53151,2860],{},[38,53153,53154],{},"Přebytek spotřebitele",[883,53156,53158],{"className":53157},[886],[888,53159,53160],{"xmlns":890},[892,53161,53162,53168],{},[895,53163,53164,53166],{},[898,53165,11539],{},[898,53167,17398],{},[902,53169,53170],{"encoding":904},"CS",[38,53172,53173],{},"přebytek výrobce",[883,53175,53177],{"className":53176},[886],[888,53178,53179],{"xmlns":890},[892,53180,53181,53187],{},[895,53182,53183,53185],{},[898,53184,1755],{},[898,53186,17398],{},[902,53188,53189],{"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 ",[207,53192,53194],{"className":53193,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,53196,53197],{},[3492,53198],{"alt":53199,"className":53200,"src":53201},"imek-prebytky-cs-ps",[210,3496],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,53203,53204,18742,53206,53209],{},[38,53205,53154],{},[614,53207,53208],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,53211,53213],{"className":53212},[886],[888,53214,53215],{"xmlns":890,"display":1956},[892,53216,53217,53294],{},[1960,53218,53219],{"width":1962},[1964,53220,53221,53223,53287,53289],{},[1967,53222],{"width":1969},[1967,53224,53225],{},[895,53226,53227,53229,53231,53233,53239,53241,53243,53255,53257,53259,53261,53263,53265,53267,53269,53271,53277,53279,53285],{},[898,53228,11539],{},[898,53230,17398],{},[1654,53232,1708],{"stretchy":1656},[1710,53234,53235,53237],{},[898,53236,1663],{},[1665,53238,2062],{},[1654,53240,1726],{"stretchy":1656},[1654,53242,1750],{},[1659,53244,53245,53247,53249],{},[1654,53246,19883],{},[1665,53248,2062],{},[1710,53250,53251,53253],{},[898,53252,1663],{},[1665,53254,2062],{},[898,53256,4980],{},[1654,53258,1708],{"stretchy":1656},[898,53260,1663],{},[1654,53262,1726],{"stretchy":1656},[1865,53264,11744],{},[898,53266,10977],{},[898,53268,1663],{},[1654,53270,2380],{},[1710,53272,53273,53275],{},[898,53274,1755],{},[1665,53276,2062],{},[1865,53278,11744],{},[1710,53280,53281,53283],{},[898,53282,1663],{},[1665,53284,2062],{},[898,53286,2138],{"mathvariant":1878},[1967,53288],{"width":1969},[1967,53290,53291],{},[1865,53292,53293],{},"(2.14)",[902,53295,53296],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,53298,53299,18742,53302,53305],{},[38,53300,53301],{},"Přebytek výrobce",[614,53303,53304],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,53307,53309],{"className":53308},[886],[888,53310,53311],{"xmlns":890,"display":1956},[892,53312,53313,53390],{},[1960,53314,53315],{"width":1962},[1964,53316,53317,53319,53383,53385],{},[1967,53318],{"width":1969},[1967,53320,53321],{},[895,53322,53323,53325,53327,53329,53335,53337,53339,53345,53347,53353,53355,53367,53369,53371,53373,53375,53377,53379,53381],{},[898,53324,1755],{},[898,53326,17398],{},[1654,53328,1708],{"stretchy":1656},[1710,53330,53331,53333],{},[898,53332,1663],{},[1665,53334,2062],{},[1654,53336,1726],{"stretchy":1656},[1654,53338,1750],{},[1710,53340,53341,53343],{},[898,53342,1755],{},[1665,53344,2062],{},[1865,53346,11744],{},[1710,53348,53349,53351],{},[898,53350,1663],{},[1665,53352,2062],{},[1654,53354,2380],{},[1659,53356,53357,53359,53361],{},[1654,53358,19883],{},[1665,53360,2062],{},[1710,53362,53363,53365],{},[898,53364,1663],{},[1665,53366,2062],{},[898,53368,17398],{},[1654,53370,1708],{"stretchy":1656},[898,53372,1663],{},[1654,53374,1726],{"stretchy":1656},[1865,53376,11744],{},[898,53378,10977],{},[898,53380,1663],{},[898,53382,2138],{"mathvariant":1878},[1967,53384],{"width":1969},[1967,53386,53387],{},[1865,53388,53389],{},"(2.15)",[902,53391,53392],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,53394,53395,53396,2138],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,53397,53399],{"className":53398,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[45190,53401],{},[115,53403,53405],{"id":53404},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,53407,53408,53439,53444,53450,53478,53484,53513,53519,53599,53625],{},[123,53409,53410,53412,53413,53438],{},[38,53411,46148],{}," — lineární poptávka ",[883,53414,53416],{"className":53415},[886],[888,53417,53418],{"xmlns":890},[892,53419,53420,53436],{},[895,53421,53422,53424,53426,53428,53430,53432,53434],{},[898,53423,1755],{},[1654,53425,1750],{},[1654,53427,2380],{},[1665,53429,1681],{},[898,53431,1663],{},[1654,53433,1766],{},[1665,53435,11881],{},[902,53437,46180],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,53440,53441,53443],{},[38,53442,46462],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,53445,53446,53449],{},[38,53447,53448],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,53451,53452,53454,53455,2138],{},[38,53453,49009],{}," — lineární nabídka ",[883,53456,53458],{"className":53457},[886],[888,53459,53460],{"xmlns":890},[892,53461,53462,53476],{},[895,53463,53464,53466,53468,53470,53472,53474],{},[898,53465,1755],{},[1654,53467,1750],{},[1665,53469,7594],{},[898,53471,1663],{},[1654,53473,1766],{},[1665,53475,4622],{},[902,53477,49038],{"encoding":904},[123,53479,53480,53483],{},[38,53481,53482],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,53485,53486,53489,53490,2138],{},[38,53487,53488],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,53491,53493],{"className":53492},[886],[888,53494,53495],{"xmlns":890},[892,53496,53497,53511],{},[895,53498,53499,53501,53503,53505,53507,53509],{},[898,53500,1798],{},[1654,53502,1657],{"stretchy":1656},[1665,53504,7631],{},[1654,53506,1674],{"separator":1673},[1665,53508,50156],{},[1654,53510,1686],{"stretchy":1656},[902,53512,50184],{"encoding":904},[123,53514,53515,53518],{},[38,53516,53517],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,53520,53521,53524,53525,53542,53543,1343,53568,53595,53596,11708],{},[38,53522,53523],{},"Příklad 2.9"," — daň ",[883,53526,53528],{"className":53527},[886],[888,53529,53530],{"xmlns":890},[892,53531,53532,53540],{},[895,53533,53534,53536,53538],{},[898,53535,11536],{},[1654,53537,1750],{},[1665,53539,11015],{},[902,53541,49488],{"encoding":904}," na výrobce; rozklad ",[883,53544,53546],{"className":53545},[886],[888,53547,53548],{"xmlns":890},[892,53549,53550,53566],{},[895,53551,53552,53562,53564],{},[1710,53553,53554,53556],{},[898,53555,11536],{},[895,53557,53558,53560],{},[898,53559,50897],{},[898,53561,724],{},[1654,53563,1750],{},[1665,53565,1681],{},[902,53567,51196],{"encoding":904},[883,53569,53571],{"className":53570},[886],[888,53572,53573],{"xmlns":890},[892,53574,53575,53593],{},[895,53576,53577,53589,53591],{},[1710,53578,53579,53581],{},[898,53580,11536],{},[895,53582,53583,53585,53587],{},[898,53584,50920],{},[898,53586,10789],{},[898,53588,20753],{},[1654,53590,1750],{},[1665,53592,7631],{},[902,53594,51225],{"encoding":904},". (Viz ",[207,53597,50941],{"className":53598,"dataFsResolvedFilePath":809,"href":810},[210],[123,53600,53601,53524,53604,53621,53622,11708],{},[38,53602,53603],{},"Příklad 2.10",[883,53605,53607],{"className":53606},[886],[888,53608,53609],{"xmlns":890},[892,53610,53611,53619],{},[895,53612,53613,53615,53617],{},[898,53614,11536],{},[1654,53616,1750],{},[1665,53618,11015],{},[902,53620,49488],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,53623,50941],{"className":53624,"dataFsResolvedFilePath":809,"href":810},[210],[123,53626,53627,53630],{},[38,53628,53629],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[45190,53632],{},[115,53634,53636],{"id":53635},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,53638,53640],{"id":53639},"základní-analýza-poptávky","Základní analýza poptávky",[724,53642,53643,53646,53647,53682,53683,53709],{},[38,53644,53645],{},"2.1"," Je dána poptávka ",[883,53648,53650],{"className":53649},[886],[888,53651,53652],{"xmlns":890},[892,53653,53654,53679],{},[895,53655,53656,53658,53660,53662,53664,53666,53668,53670,53673,53675,53677],{},[898,53657,1663],{},[1654,53659,1750],{},[898,53661,4980],{},[1654,53663,1708],{"stretchy":1656},[898,53665,1755],{},[1654,53667,1726],{"stretchy":1656},[1654,53669,1750],{},[1665,53671,53672],{},"75",[1654,53674,2380],{},[1665,53676,4032],{},[898,53678,1755],{},[902,53680,53681],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,53684,53686],{"className":53685},[886],[888,53687,53688],{"xmlns":890},[892,53689,53690,53706],{},[895,53691,53692,53694,53696,53698,53700,53702,53704],{},[1665,53693,2062],{},[1654,53695,1674],{"separator":1673},[1665,53697,4032],{},[1654,53699,1674],{"separator":1673},[1665,53701,4647],{},[1654,53703,1674],{"separator":1673},[1665,53705,10207],{},[902,53707,53708],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,53711,53712,53715,53716,53734,53735,11906],{},[38,53713,53714],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,53717,53719],{"className":53718},[886],[888,53720,53721],{"xmlns":890},[892,53722,53723,53731],{},[895,53724,53725,53727,53729],{},[898,53726,1755],{},[1654,53728,1674],{"separator":1673},[898,53730,1663],{},[902,53732,53733],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,53736,53738],{"className":53737},[886],[888,53739,53740],{"xmlns":890},[892,53741,53742,53758],{},[895,53743,53744,53746,53748,53750,53752,53754,53756],{},[898,53745,207],{},[1654,53747,1674],{"separator":1673},[898,53749,9758],{},[1654,53751,1674],{"separator":1673},[898,53753,3624],{},[1654,53755,2952],{},[1665,53757,2062],{},[902,53759,53760],{"encoding":904},"a, b, c > 0",[120,53762,53763,53796,53827,53862,53893,53928],{},[123,53764,53765,53766],{},"(a) ",[883,53767,53769],{"className":53768},[886],[888,53770,53771],{"xmlns":890},[892,53772,53773,53793],{},[895,53774,53775,53777,53779],{},[898,53776,1663],{},[1654,53778,1750],{},[2582,53780,53781],{"scriptlevel":2062,"displaystyle":1673},[2811,53782,53783,53785],{},[898,53784,207],{},[895,53786,53787,53789,53791],{},[898,53788,1755],{},[1654,53790,1766],{},[898,53792,3624],{},[902,53794,53795],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,53797,53798,53799],{},"(b) ",[883,53800,53802],{"className":53801},[886],[888,53803,53804],{"xmlns":890},[892,53805,53806,53824],{},[895,53807,53808,53810,53812],{},[898,53809,1663],{},[1654,53811,1750],{},[8818,53813,53814],{},[895,53815,53816,53818,53820,53822],{},[898,53817,207],{},[1654,53819,2380],{},[898,53821,9758],{},[898,53823,1663],{},[902,53825,53826],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,53828,53829,53830],{},"(c) ",[883,53831,53833],{"className":53832},[886],[888,53834,53835],{"xmlns":890},[892,53836,53837,53859],{},[895,53838,53839,53841,53843],{},[898,53840,1663],{},[1654,53842,1750],{},[2582,53844,53845],{"scriptlevel":2062,"displaystyle":1673},[2811,53846,53847,53857],{},[895,53848,53849,53851,53853],{},[898,53850,207],{},[1654,53852,2380],{},[8818,53854,53855],{},[898,53856,1755],{},[898,53858,9758],{},[902,53860,53861],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,53863,53864,53865],{},"(d) ",[883,53866,53868],{"className":53867},[886],[888,53869,53870],{"xmlns":890},[892,53871,53872,53890],{},[895,53873,53874,53876,53878,53880,53882,53884],{},[898,53875,1755],{},[1654,53877,1750],{},[898,53879,207],{},[1654,53881,2380],{},[898,53883,9758],{},[1741,53885,53886,53888],{},[898,53887,1663],{},[1665,53889,1681],{},[902,53891,53892],{"encoding":904},"P = a - bQ^2",[123,53894,53895,53896],{},"(e) ",[883,53897,53899],{"className":53898},[886],[888,53900,53901],{"xmlns":890},[892,53902,53903,53925],{},[895,53904,53905,53907,53909,53911,53921,53923],{},[898,53906,1663],{},[1654,53908,1750],{},[898,53910,9758],{},[1741,53912,53913,53915],{},[898,53914,1755],{},[895,53916,53917,53919],{},[1654,53918,2380],{},[898,53920,207],{},[1654,53922,1766],{},[898,53924,3624],{},[902,53926,53927],{"encoding":904},"Q = bP^{-a} + c",[123,53929,53930,53931],{},"(f) ",[883,53932,53934],{"className":53933},[886],[888,53935,53936],{"xmlns":890},[892,53937,53938,53961],{},[895,53939,53940,53942,53944,53946,53948],{},[898,53941,1663],{},[1654,53943,1750],{},[898,53945,207],{},[1654,53947,4554],{},[1741,53949,53950,53953],{},[898,53951,53952],{},"e",[895,53954,53955,53957,53959],{},[1654,53956,2380],{},[898,53958,9758],{},[898,53960,1755],{},[902,53962,53963],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,53965,53966,53969],{},[38,53967,53968],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,53971,53972,53975,53978],{},[123,53973,53974],{},"(a) Cena substitutu.",[123,53976,53977],{},"(b) Cena komplementu.",[123,53979,53980],{},"(c) Výdaje na reklamu.",[724,53982,53983,53646,53985,54019,54020,54048],{},[38,53984,33328],{},[883,53986,53988],{"className":53987},[886],[888,53989,53990],{"xmlns":890},[892,53991,53992,54016],{},[895,53993,53994,53996,53998,54000,54002,54004,54006,54008,54010,54012,54014],{},[898,53995,1755],{},[1654,53997,1750],{},[898,53999,4980],{},[1654,54001,1708],{"stretchy":1656},[898,54003,1663],{},[1654,54005,1726],{"stretchy":1656},[1654,54007,1750],{},[1665,54009,6509],{},[1654,54011,2380],{},[1665,54013,1681],{},[898,54015,1663],{},[902,54017,54018],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,54021,54023],{"className":54022},[886],[888,54024,54025],{"xmlns":890},[892,54026,54027,54045],{},[895,54028,54029,54031,54033,54039,54041,54043],{},[898,54030,1755],{},[1654,54032,1750],{},[1741,54034,54035,54037],{},[898,54036,4980],{},[1654,54038,1670],{},[1654,54040,1708],{"stretchy":1656},[898,54042,1663],{},[1654,54044,1726],{"stretchy":1656},[902,54046,54047],{"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.",[724,54050,54051,54054],{},[38,54052,54053],{},"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:",[120,54056,54057,54141,54217,54303,54391],{},[123,54058,53765,54059,1343,54099,2138],{},[883,54060,54062],{"className":54061},[886],[888,54063,54064],{"xmlns":890},[892,54065,54066,54096],{},[895,54067,54068,54074,54076,54078,54080,54082,54088,54090],{},[1710,54069,54070,54072],{},[898,54071,4762],{},[1665,54073,1667],{},[1654,54075,1750],{},[1665,54077,4573],{},[1654,54079,2380],{},[1665,54081,7631],{},[1710,54083,54084,54086],{},[898,54085,4737],{},[1665,54087,1667],{},[1654,54089,1766],{},[1710,54091,54092,54094],{},[898,54093,4737],{},[1665,54095,1681],{},[902,54097,54098],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,54100,54102],{"className":54101},[886],[888,54103,54104],{"xmlns":890},[892,54105,54106,54138],{},[895,54107,54108,54114,54116,54118,54120,54122,54128,54130,54132],{},[1710,54109,54110,54112],{},[898,54111,4762],{},[1665,54113,1681],{},[1654,54115,1750],{},[1665,54117,4647],{},[1654,54119,1766],{},[1665,54121,1681],{},[1710,54123,54124,54126],{},[898,54125,4737],{},[1665,54127,1667],{},[1654,54129,2380],{},[1665,54131,7631],{},[1710,54133,54134,54136],{},[898,54135,4737],{},[1665,54137,1681],{},[902,54139,54140],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,54142,53798,54143,1343,54185,2138],{},[883,54144,54146],{"className":54145},[886],[888,54147,54148],{"xmlns":890},[892,54149,54150,54182],{},[895,54151,54152,54158,54160,54162,54164,54166,54172,54174,54176],{},[1710,54153,54154,54156],{},[898,54155,4762],{},[1665,54157,1667],{},[1654,54159,1750],{},[1665,54161,4767],{},[1654,54163,2380],{},[1665,54165,4647],{},[1710,54167,54168,54170],{},[898,54169,4737],{},[1665,54171,1667],{},[1654,54173,2380],{},[1665,54175,11015],{},[1710,54177,54178,54180],{},[898,54179,4737],{},[1665,54181,1681],{},[902,54183,54184],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,54186,54188],{"className":54187},[886],[888,54189,54190],{"xmlns":890},[892,54191,54192,54214],{},[895,54193,54194,54200,54202,54204,54206,54208],{},[1710,54195,54196,54198],{},[898,54197,4762],{},[1665,54199,1681],{},[1654,54201,1750],{},[1665,54203,10207],{},[1654,54205,2380],{},[1665,54207,4647],{},[1710,54209,54210,54212],{},[898,54211,4737],{},[1665,54213,1681],{},[902,54215,54216],{"encoding":904},"B_2 = 15 - 10A_2",[123,54218,53829,54219,1343,54261,2138],{},[883,54220,54222],{"className":54221},[886],[888,54223,54224],{"xmlns":890},[892,54225,54226,54258],{},[895,54227,54228,54234,54236,54238,54240,54242,54248,54250,54252],{},[1710,54229,54230,54232],{},[898,54231,4762],{},[1665,54233,1667],{},[1654,54235,1750],{},[1665,54237,46239],{},[1654,54239,2380],{},[1665,54241,1681],{},[1710,54243,54244,54246],{},[898,54245,4737],{},[1665,54247,1667],{},[1654,54249,2380],{},[1665,54251,7631],{},[1710,54253,54254,54256],{},[898,54255,4737],{},[1665,54257,1681],{},[902,54259,54260],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,54262,54264],{"className":54263},[886],[888,54265,54266],{"xmlns":890},[892,54267,54268,54300],{},[895,54269,54270,54276,54278,54280,54282,54284,54290,54292,54294],{},[1710,54271,54272,54274],{},[898,54273,4762],{},[1665,54275,1681],{},[1654,54277,1750],{},[1665,54279,10207],{},[1654,54281,1766],{},[1665,54283,1681],{},[1710,54285,54286,54288],{},[898,54287,4737],{},[1665,54289,1667],{},[1654,54291,2380],{},[1665,54293,1681],{},[1710,54295,54296,54298],{},[898,54297,4737],{},[1665,54299,1681],{},[902,54301,54302],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,54304,53864,54305,1343,54349,2138],{},[883,54306,54308],{"className":54307},[886],[888,54309,54310],{"xmlns":890},[892,54311,54312,54346],{},[895,54313,54314,54320,54322,54324,54326,54328,54330,54336,54338,54340],{},[1710,54315,54316,54318],{},[898,54317,4762],{},[1665,54319,1667],{},[1654,54321,1750],{},[1654,54323,2380],{},[1665,54325,4573],{},[1654,54327,2380],{},[1665,54329,1681],{},[1710,54331,54332,54334],{},[898,54333,4737],{},[1665,54335,1667],{},[1654,54337,1766],{},[1665,54339,4035],{},[1710,54341,54342,54344],{},[898,54343,4737],{},[1665,54345,1681],{},[902,54347,54348],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,54350,54352],{"className":54351},[886],[888,54353,54354],{"xmlns":890},[892,54355,54356,54388],{},[895,54357,54358,54364,54366,54368,54370,54372,54378,54380,54382],{},[1710,54359,54360,54362],{},[898,54361,4762],{},[1665,54363,1681],{},[1654,54365,1750],{},[1665,54367,4647],{},[1654,54369,1766],{},[1665,54371,1681],{},[1710,54373,54374,54376],{},[898,54375,4737],{},[1665,54377,1667],{},[1654,54379,2380],{},[1665,54381,1681],{},[1710,54383,54384,54386],{},[898,54385,4737],{},[1665,54387,1681],{},[902,54389,54390],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,54392,53895,54393,1343,54435,2138],{},[883,54394,54396],{"className":54395},[886],[888,54397,54398],{"xmlns":890},[892,54399,54400,54432],{},[895,54401,54402,54408,54410,54412,54414,54416,54422,54424,54426],{},[1710,54403,54404,54406],{},[898,54405,4762],{},[1665,54407,1667],{},[1654,54409,1750],{},[1665,54411,4573],{},[1654,54413,1766],{},[1665,54415,1681],{},[1710,54417,54418,54420],{},[898,54419,4737],{},[1665,54421,1667],{},[1654,54423,1766],{},[1665,54425,7631],{},[1710,54427,54428,54430],{},[898,54429,4737],{},[1665,54431,1681],{},[902,54433,54434],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,54436,54438],{"className":54437},[886],[888,54439,54440],{"xmlns":890},[892,54441,54442,54474],{},[895,54443,54444,54450,54452,54454,54456,54458,54464,54466,54468],{},[1710,54445,54446,54448],{},[898,54447,4762],{},[1665,54449,1681],{},[1654,54451,1750],{},[1665,54453,5844],{},[1654,54455,2380],{},[1665,54457,4035],{},[1710,54459,54460,54462],{},[898,54461,4737],{},[1665,54463,1667],{},[1654,54465,1766],{},[1665,54467,4032],{},[1710,54469,54470,54472],{},[898,54471,4737],{},[1665,54473,1681],{},[902,54475,54476],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,54478,54480],{"id":54479},"základní-analýza-nabídky","Základní analýza nabídky",[724,54482,54483,54486,54487,54521,54522,54544],{},[38,54484,54485],{},"2.6"," Je dána nabídka ",[883,54488,54490],{"className":54489},[886],[888,54491,54492],{"xmlns":890},[892,54493,54494,54518],{},[895,54495,54496,54498,54500,54502,54504,54506,54508,54510,54512,54514,54516],{},[898,54497,1755],{},[1654,54499,1750],{},[898,54501,17398],{},[1654,54503,1708],{"stretchy":1656},[898,54505,1663],{},[1654,54507,1726],{"stretchy":1656},[1654,54509,1750],{},[1665,54511,4573],{},[1654,54513,1766],{},[1665,54515,11599],{},[898,54517,1663],{},[902,54519,54520],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,54523,54525],{"className":54524},[886],[888,54526,54527],{"xmlns":890},[892,54528,54529,54541],{},[895,54530,54531,54533,54535,54537,54539],{},[1665,54532,4622],{},[1654,54534,1674],{"separator":1673},[1665,54536,46239],{},[1654,54538,1674],{"separator":1673},[1665,54540,23747],{},[902,54542,54543],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,54546,54547,54550,54551,54568],{},[38,54548,54549],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,54552,54554],{"className":54553},[886],[888,54555,54556],{"xmlns":890},[892,54557,54558,54566],{},[895,54559,54560,54562,54564],{},[898,54561,1755],{},[1654,54563,1674],{"separator":1673},[898,54565,1663],{},[902,54567,53733],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,54570,54571,54597,54625,54658,54692,54728],{},[123,54572,53765,54573],{},[883,54574,54576],{"className":54575},[886],[888,54577,54578],{"xmlns":890},[892,54579,54580,54594],{},[895,54581,54582,54584,54586,54588,54590,54592],{},[898,54583,1755],{},[1654,54585,1750],{},[1665,54587,46239],{},[1654,54589,1766],{},[1665,54591,1681],{},[898,54593,1663],{},[902,54595,54596],{"encoding":904},"P = 30 + 2Q",[123,54598,53798,54599],{},[883,54600,54602],{"className":54601},[886],[888,54603,54604],{"xmlns":890},[892,54605,54606,54622],{},[895,54607,54608,54610,54612,54614,54616,54618,54620],{},[898,54609,1663],{},[1654,54611,1750],{},[1654,54613,2380],{},[1665,54615,4035],{},[1654,54617,1766],{},[1665,54619,6509],{},[898,54621,1755],{},[902,54623,54624],{"encoding":904},"Q = -3 + 12P",[123,54626,53829,54627],{},[883,54628,54630],{"className":54629},[886],[888,54631,54632],{"xmlns":890},[892,54633,54634,54656],{},[895,54635,54636,54638,54640,54646,54648,54650,54652,54654],{},[898,54637,1755],{},[1654,54639,1750],{},[1741,54641,54642,54644],{},[898,54643,1663],{},[1665,54645,1681],{},[1654,54647,1766],{},[1665,54649,31634],{},[898,54651,1663],{},[1654,54653,1766],{},[1665,54655,6492],{},[902,54657,49942],{"encoding":904},[123,54659,53864,54660],{},[883,54661,54663],{"className":54662},[886],[888,54664,54665],{"xmlns":890},[892,54666,54667,54689],{},[895,54668,54669,54671,54673,54679,54681,54683,54685,54687],{},[898,54670,1755],{},[1654,54672,1750],{},[1741,54674,54675,54677],{},[898,54676,1663],{},[1665,54678,1681],{},[1654,54680,1766],{},[1665,54682,1681],{},[898,54684,1663],{},[1654,54686,1766],{},[1665,54688,6509],{},[902,54690,54691],{"encoding":904},"P = Q^2 + 2Q + 12",[123,54693,53895,54694],{},[883,54695,54697],{"className":54696},[886],[888,54698,54699],{"xmlns":890},[892,54700,54701,54725],{},[895,54702,54703,54705,54707,54709,54711,54713,54715,54717,54719],{},[898,54704,1663],{},[1654,54706,1750],{},[1665,54708,17528],{},[1654,54710,1766],{},[1665,54712,4032],{},[898,54714,1755],{},[1654,54716,1766],{},[1665,54718,11555],{},[1741,54720,54721,54723],{},[898,54722,1755],{},[1665,54724,1681],{},[902,54726,54727],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,54729,53930,54730],{},[883,54731,54733],{"className":54732},[886],[888,54734,54735],{"xmlns":890},[892,54736,54737,54762],{},[895,54738,54739,54741,54743,54745,54747,54749,54751,54753,54756],{},[898,54740,1663],{},[1654,54742,1750],{},[1665,54744,32887],{},[1654,54746,1766],{},[1665,54748,11555],{},[898,54750,1755],{},[1654,54752,1766],{},[1665,54754,54755],{},"0,004",[1741,54757,54758,54760],{},[898,54759,1755],{},[1665,54761,1681],{},[902,54763,54764],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,54766,54767,54770],{},[38,54768,54769],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,54772,54773,54776,54779,54782],{},[123,54774,54775],{},"(a) Sníží ceny surovin — vstupů.",[123,54777,54778],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,54780,54781],{},"(c) Zvýší ceny všech energií.",[123,54783,54784],{},"(d) Sníží daňové odvody státu.",[724,54786,54787,54486,54789,54823,54824,54852],{},[38,54788,51169],{},[883,54790,54792],{"className":54791},[886],[888,54793,54794],{"xmlns":890},[892,54795,54796,54820],{},[895,54797,54798,54800,54802,54804,54806,54808,54810,54812,54814,54816,54818],{},[898,54799,1755],{},[1654,54801,1750],{},[898,54803,17398],{},[1654,54805,1708],{"stretchy":1656},[898,54807,1663],{},[1654,54809,1726],{"stretchy":1656},[1654,54811,1750],{},[1665,54813,7594],{},[898,54815,1663],{},[1654,54817,1766],{},[1665,54819,10207],{},[902,54821,54822],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,54825,54827],{"className":54826},[886],[888,54828,54829],{"xmlns":890},[892,54830,54831,54849],{},[895,54832,54833,54835,54837,54843,54845,54847],{},[898,54834,1755],{},[1654,54836,1750],{},[1741,54838,54839,54841],{},[898,54840,17398],{},[1654,54842,1670],{},[1654,54844,1708],{"stretchy":1656},[898,54846,1663],{},[1654,54848,1726],{"stretchy":1656},[902,54850,54851],{"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.",[198,54854,49545],{"id":54855},"tržní-rovnováha-1",[724,54857,54858,54860,54861,54878,54879,2781],{},[38,54859,51229],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,54862,54864],{"className":54863},[886],[888,54865,54866],{"xmlns":890},[892,54867,54868,54876],{},[895,54869,54870],{},[1741,54871,54872,54874],{},[898,54873,1663],{},[898,54875,1798],{},[902,54877,50623],{"encoding":904}," a rovnovážnou cenu ",[883,54880,54882],{"className":54881},[886],[888,54883,54884],{"xmlns":890},[892,54885,54886,54894],{},[895,54887,54888],{},[1741,54889,54890,54892],{},[898,54891,1755],{},[898,54893,1798],{},[902,54895,49686],{"encoding":904},[120,54897,54898,54951,55002,55061],{},[123,54899,53765,54900,1343,54927,2138],{},[883,54901,54903],{"className":54902},[886],[888,54904,54905],{"xmlns":890},[892,54906,54907,54924],{},[895,54908,54909,54911,54913,54915,54917,54919,54921],{},[898,54910,1755],{},[1654,54912,1750],{},[1654,54914,2380],{},[1665,54916,4032],{},[898,54918,1663],{},[1654,54920,1766],{},[1665,54922,54923],{},"80",[902,54925,54926],{"encoding":904},"P = -5Q + 80",[883,54928,54930],{"className":54929},[886],[888,54931,54932],{"xmlns":890},[892,54933,54934,54948],{},[895,54935,54936,54938,54940,54942,54944,54946],{},[898,54937,1755],{},[1654,54939,1750],{},[1665,54941,1681],{},[898,54943,1663],{},[1654,54945,1766],{},[1665,54947,4647],{},[902,54949,54950],{"encoding":904},"P = 2Q + 10",[123,54952,53798,54953,1343,54979,2138],{},[883,54954,54956],{"className":54955},[886],[888,54957,54958],{"xmlns":890},[892,54959,54960,54976],{},[895,54961,54962,54964,54966,54968,54970,54972,54974],{},[898,54963,1663],{},[1654,54965,1750],{},[1654,54967,2380],{},[1665,54969,7594],{},[898,54971,1755],{},[1654,54973,1766],{},[1665,54975,4622],{},[902,54977,54978],{"encoding":904},"Q = -0{,}5P + 25",[883,54980,54982],{"className":54981},[886],[888,54983,54984],{"xmlns":890},[892,54985,54986,55000],{},[895,54987,54988,54990,54992,54994,54996,54998],{},[898,54989,1663],{},[1654,54991,1750],{},[1665,54993,1681],{},[898,54995,1755],{},[1654,54997,2380],{},[1665,54999,4767],{},[902,55001,49067],{"encoding":904},[123,55003,53829,55004,1343,55030,2138],{},[883,55005,55007],{"className":55006},[886],[888,55008,55009],{"xmlns":890},[892,55010,55011,55027],{},[895,55012,55013,55015,55017,55019,55021,55023,55025],{},[898,55014,1755],{},[1654,55016,1750],{},[1654,55018,2380],{},[1665,55020,7631],{},[898,55022,1663],{},[1654,55024,1766],{},[1665,55026,12789],{},[902,55028,55029],{"encoding":904},"P = -4Q + 120",[883,55031,55033],{"className":55032},[886],[888,55034,55035],{"xmlns":890},[892,55036,55037,55058],{},[895,55038,55039,55041,55043,55051,55053,55055],{},[898,55040,1755],{},[1654,55042,1750],{},[2582,55044,55045],{"scriptlevel":2062,"displaystyle":1656},[2811,55046,55047,55049],{},[1665,55048,1667],{},[1665,55050,4035],{},[898,55052,1663],{},[1654,55054,1766],{},[1665,55056,55057],{},"29",[902,55059,55060],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,55062,53864,55063,1343,55092,2138],{},[883,55064,55066],{"className":55065},[886],[888,55067,55068],{"xmlns":890},[892,55069,55070,55089],{},[895,55071,55072,55074,55076,55078,55084,55086],{},[898,55073,1755],{},[1654,55075,1750],{},[1654,55077,2380],{},[1741,55079,55080,55082],{},[898,55081,1663],{},[1665,55083,1681],{},[1654,55085,1766],{},[1665,55087,55088],{},"52",[902,55090,55091],{"encoding":904},"P = -Q^2 + 52",[883,55093,55095],{"className":55094},[886],[888,55096,55097],{"xmlns":890},[892,55098,55099,55117],{},[895,55100,55101,55103,55105,55107,55113,55115],{},[898,55102,1755],{},[1654,55104,1750],{},[1665,55106,1681],{},[1741,55108,55109,55111],{},[898,55110,1663],{},[1665,55112,1681],{},[1654,55114,1766],{},[1665,55116,4647],{},[902,55118,55119],{"encoding":904},"P = 2Q^2 + 10",[724,55121,55122,55125,55126,55156,55157,55187],{},[38,55123,55124],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,55127,55129],{"className":55128},[886],[888,55130,55131],{"xmlns":890},[892,55132,55133,55153],{},[895,55134,55135,55143,55145],{},[1659,55136,55137,55139,55141],{},[898,55138,1663],{},[1665,55140,1667],{},[898,55142,1798],{},[1654,55144,1674],{"separator":1673},[1659,55146,55147,55149,55151],{},[898,55148,1663],{},[1665,55150,1681],{},[898,55152,1798],{},[902,55154,55155],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,55158,55160],{"className":55159},[886],[888,55161,55162],{"xmlns":890},[892,55163,55164,55184],{},[895,55165,55166,55174,55176],{},[1659,55167,55168,55170,55172],{},[898,55169,1755],{},[1665,55171,1667],{},[898,55173,1798],{},[1654,55175,1674],{"separator":1673},[1659,55177,55178,55180,55182],{},[898,55179,1755],{},[1665,55181,1681],{},[898,55183,1798],{},[902,55185,55186],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,55189,55190,55342],{},[123,55191,53765,55192,1343,55232,1343,55274,1343,55308,2138],{},[883,55193,55195],{"className":55194},[886],[888,55196,55197],{"xmlns":890},[892,55198,55199,55229],{},[895,55200,55201,55207,55209,55211,55213,55215,55221,55223],{},[1710,55202,55203,55205],{},[898,55204,1663],{},[1665,55206,1667],{},[1654,55208,1750],{},[1665,55210,4647],{},[1654,55212,2380],{},[1665,55214,1681],{},[1710,55216,55217,55219],{},[898,55218,1755],{},[1665,55220,1667],{},[1654,55222,1766],{},[1710,55224,55225,55227],{},[898,55226,1755],{},[1665,55228,1681],{},[902,55230,55231],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,55233,55235],{"className":55234},[886],[888,55236,55237],{"xmlns":890},[892,55238,55239,55271],{},[895,55240,55241,55247,55249,55251,55253,55255,55261,55263,55265],{},[1710,55242,55243,55245],{},[898,55244,1663],{},[1665,55246,1681],{},[1654,55248,1750],{},[1665,55250,4032],{},[1654,55252,1766],{},[1665,55254,1681],{},[1710,55256,55257,55259],{},[898,55258,1755],{},[1665,55260,1667],{},[1654,55262,2380],{},[1665,55264,1681],{},[1710,55266,55267,55269],{},[898,55268,1755],{},[1665,55270,1681],{},[902,55272,55273],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,55275,55277],{"className":55276},[886],[888,55278,55279],{"xmlns":890},[892,55280,55281,55305],{},[895,55282,55283,55289,55291,55293,55295,55297,55299],{},[1710,55284,55285,55287],{},[898,55286,1663],{},[1665,55288,1667],{},[1654,55290,1750],{},[1654,55292,2380],{},[1665,55294,4035],{},[1654,55296,1766],{},[1665,55298,1681],{},[1710,55300,55301,55303],{},[898,55302,1755],{},[1665,55304,1667],{},[902,55306,55307],{"encoding":904},"Q_1 = -3 + 2P_1",[883,55309,55311],{"className":55310},[886],[888,55312,55313],{"xmlns":890},[892,55314,55315,55339],{},[895,55316,55317,55323,55325,55327,55329,55331,55333],{},[1710,55318,55319,55321],{},[898,55320,1663],{},[1665,55322,1681],{},[1654,55324,1750],{},[1654,55326,2380],{},[1665,55328,1681],{},[1654,55330,1766],{},[1665,55332,4035],{},[1710,55334,55335,55337],{},[898,55336,1755],{},[1665,55338,1681],{},[902,55340,55341],{"encoding":904},"Q_2 = -2 + 3P_2",[123,55343,53798,55344,1343,55384,1343,55426,1343,55458,2138],{},[883,55345,55347],{"className":55346},[886],[888,55348,55349],{"xmlns":890},[892,55350,55351,55381],{},[895,55352,55353,55359,55361,55363,55365,55367,55373,55375],{},[1710,55354,55355,55357],{},[898,55356,1663],{},[1665,55358,1667],{},[1654,55360,1750],{},[1665,55362,4273],{},[1654,55364,2380],{},[1665,55366,1681],{},[1710,55368,55369,55371],{},[898,55370,1755],{},[1665,55372,1667],{},[1654,55374,1766],{},[1710,55376,55377,55379],{},[898,55378,1755],{},[1665,55380,1681],{},[902,55382,55383],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,55385,55387],{"className":55386},[886],[888,55388,55389],{"xmlns":890},[892,55390,55391,55423],{},[895,55392,55393,55399,55401,55403,55405,55407,55413,55415,55417],{},[1710,55394,55395,55397],{},[898,55396,1663],{},[1665,55398,1681],{},[1654,55400,1750],{},[1665,55402,4032],{},[1654,55404,1766],{},[1665,55406,1681],{},[1710,55408,55409,55411],{},[898,55410,1755],{},[1665,55412,1667],{},[1654,55414,2380],{},[1665,55416,4035],{},[1710,55418,55419,55421],{},[898,55420,1755],{},[1665,55422,1681],{},[902,55424,55425],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,55427,55429],{"className":55428},[886],[888,55430,55431],{"xmlns":890},[892,55432,55433,55455],{},[895,55434,55435,55441,55443,55445,55447,55449],{},[1710,55436,55437,55439],{},[898,55438,1663],{},[1665,55440,1667],{},[1654,55442,1750],{},[1654,55444,2380],{},[1665,55446,4647],{},[1654,55448,1766],{},[1710,55450,55451,55453],{},[898,55452,1755],{},[1665,55454,1667],{},[902,55456,55457],{"encoding":904},"Q_1 = -10 + P_1",[883,55459,55461],{"className":55460},[886],[888,55462,55463],{"xmlns":890},[892,55464,55465,55487],{},[895,55466,55467,55473,55475,55477,55479,55481],{},[1710,55468,55469,55471],{},[898,55470,1663],{},[1665,55472,1681],{},[1654,55474,1750],{},[1665,55476,4032],{},[1654,55478,1766],{},[1665,55480,11015],{},[1710,55482,55483,55485],{},[898,55484,1755],{},[1665,55486,1681],{},[902,55488,55489],{"encoding":904},"Q_2 = 5 + 6P_2",[724,55491,55492,55495,55496,1343,55544,1343,55590,55640,55641,1343,55673,1343,55707,9762,55741,2068,55759,55777,55778,55791,55792,55818,55819,55156,55859,2138],{},[38,55493,55494],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,55497,55499],{"className":55498},[886],[888,55500,55501],{"xmlns":890},[892,55502,55503,55541],{},[895,55504,55505,55511,55513,55515,55517,55523,55525,55527,55533,55535],{},[1710,55506,55507,55509],{},[898,55508,1663],{},[1665,55510,1667],{},[1654,55512,1750],{},[1665,55514,10207],{},[1654,55516,2380],{},[1710,55518,55519,55521],{},[898,55520,1755],{},[1665,55522,1667],{},[1654,55524,1766],{},[1665,55526,1681],{},[1710,55528,55529,55531],{},[898,55530,1755],{},[1665,55532,1681],{},[1654,55534,1766],{},[1710,55536,55537,55539],{},[898,55538,1755],{},[1665,55540,4035],{},[902,55542,55543],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,55545,55547],{"className":55546},[886],[888,55548,55549],{"xmlns":890},[892,55550,55551,55587],{},[895,55552,55553,55559,55561,55563,55565,55571,55573,55579,55581],{},[1710,55554,55555,55557],{},[898,55556,1663],{},[1665,55558,1681],{},[1654,55560,1750],{},[1665,55562,12742],{},[1654,55564,1766],{},[1710,55566,55567,55569],{},[898,55568,1755],{},[1665,55570,1667],{},[1654,55572,2380],{},[1710,55574,55575,55577],{},[898,55576,1755],{},[1665,55578,1681],{},[1654,55580,2380],{},[1710,55582,55583,55585],{},[898,55584,1755],{},[1665,55586,4035],{},[902,55588,55589],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,55591,55593],{"className":55592},[886],[888,55594,55595],{"xmlns":890},[892,55596,55597,55637],{},[895,55598,55599,55605,55607,55609,55611,55613,55619,55621,55627,55629,55631],{},[1710,55600,55601,55603],{},[898,55602,1663],{},[1665,55604,4035],{},[1654,55606,1750],{},[1665,55608,14315],{},[1654,55610,1766],{},[1665,55612,1681],{},[1710,55614,55615,55617],{},[898,55616,1755],{},[1665,55618,1667],{},[1654,55620,2380],{},[1710,55622,55623,55625],{},[898,55624,1755],{},[1665,55626,1681],{},[1654,55628,2380],{},[1665,55630,7631],{},[1710,55632,55633,55635],{},[898,55634,1755],{},[1665,55636,4035],{},[902,55638,55639],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,55642,55644],{"className":55643},[886],[888,55645,55646],{"xmlns":890},[892,55647,55648,55670],{},[895,55649,55650,55656,55658,55660,55662,55664],{},[1710,55651,55652,55654],{},[898,55653,1663],{},[1665,55655,1667],{},[1654,55657,1750],{},[1654,55659,2380],{},[1665,55661,32887],{},[1654,55663,1766],{},[1710,55665,55666,55668],{},[898,55667,1755],{},[1665,55669,1667],{},[902,55671,55672],{"encoding":904},"Q_1 = -7 + P_1",[883,55674,55676],{"className":55675},[886],[888,55677,55678],{"xmlns":890},[892,55679,55680,55704],{},[895,55681,55682,55688,55690,55692,55694,55696,55698],{},[1710,55683,55684,55686],{},[898,55685,1663],{},[1665,55687,1681],{},[1654,55689,1750],{},[1654,55691,2380],{},[1665,55693,7631],{},[1654,55695,1766],{},[1665,55697,7631],{},[1710,55699,55700,55702],{},[898,55701,1755],{},[1665,55703,1681],{},[902,55705,55706],{"encoding":904},"Q_2 = -4 + 4P_2",[883,55708,55710],{"className":55709},[886],[888,55711,55712],{"xmlns":890},[892,55713,55714,55738],{},[895,55715,55716,55722,55724,55726,55728,55730,55732],{},[1710,55717,55718,55720],{},[898,55719,1663],{},[1665,55721,4035],{},[1654,55723,1750],{},[1654,55725,2380],{},[1665,55727,4032],{},[1654,55729,1766],{},[1665,55731,1681],{},[1710,55733,55734,55736],{},[898,55735,1755],{},[1665,55737,4035],{},[902,55739,55740],{"encoding":904},"Q_3 = -5 + 2P_3",[883,55742,55744],{"className":55743},[886],[888,55745,55746],{"xmlns":890},[892,55747,55748,55756],{},[895,55749,55750],{},[1710,55751,55752,55754],{},[898,55753,1663],{},[898,55755,9309],{},[902,55757,55758],{"encoding":904},"Q_i",[883,55760,55762],{"className":55761},[886],[888,55763,55764],{"xmlns":890},[892,55765,55766,55774],{},[895,55767,55768],{},[1710,55769,55770,55772],{},[898,55771,1755],{},[898,55773,9309],{},[902,55775,55776],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,55779,55781],{"className":55780},[886],[888,55782,55783],{"xmlns":890},[892,55784,55785,55789],{},[895,55786,55787],{},[898,55788,9309],{},[902,55790,9309],{"encoding":904},"-tého zboží, ",[883,55793,55795],{"className":55794},[886],[888,55796,55797],{"xmlns":890},[892,55798,55799,55815],{},[895,55800,55801,55803,55805,55807,55809,55811,55813],{},[898,55802,9309],{},[1654,55804,1750],{},[1665,55806,1667],{},[1654,55808,1674],{"separator":1673},[1665,55810,1681],{},[1654,55812,1674],{"separator":1673},[1665,55814,4035],{},[902,55816,55817],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,55820,55822],{"className":55821},[886],[888,55823,55824],{"xmlns":890},[892,55825,55826,55856],{},[895,55827,55828,55836,55838,55846,55848],{},[1659,55829,55830,55832,55834],{},[898,55831,1663],{},[1665,55833,1667],{},[898,55835,1798],{},[1654,55837,1674],{"separator":1673},[1659,55839,55840,55842,55844],{},[898,55841,1663],{},[1665,55843,1681],{},[898,55845,1798],{},[1654,55847,1674],{"separator":1673},[1659,55849,55850,55852,55854],{},[898,55851,1663],{},[1665,55853,4035],{},[898,55855,1798],{},[902,55857,55858],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,55860,55862],{"className":55861},[886],[888,55863,55864],{"xmlns":890},[892,55865,55866,55896],{},[895,55867,55868,55876,55878,55886,55888],{},[1659,55869,55870,55872,55874],{},[898,55871,1755],{},[1665,55873,1667],{},[898,55875,1798],{},[1654,55877,1674],{"separator":1673},[1659,55879,55880,55882,55884],{},[898,55881,1755],{},[1665,55883,1681],{},[898,55885,1798],{},[1654,55887,1674],{"separator":1673},[1659,55889,55890,55892,55894],{},[898,55891,1755],{},[1665,55893,4035],{},[898,55895,1798],{},[902,55897,55898],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,55900,55901,55904,55905,55941,55942,2138],{},[38,55902,55903],{},"2.13"," Jsou dány poptávka ",[883,55906,55908],{"className":55907},[886],[888,55909,55910],{"xmlns":890},[892,55911,55912,55938],{},[895,55913,55914,55916,55918,55920,55922,55924,55926,55928,55930,55932,55934,55936],{},[898,55915,1755],{},[1654,55917,1750],{},[898,55919,4980],{},[1654,55921,1708],{"stretchy":1656},[898,55923,1663],{},[1654,55925,1726],{"stretchy":1656},[1654,55927,1750],{},[1654,55929,2380],{},[1665,55931,7631],{},[898,55933,1663],{},[1654,55935,1766],{},[1665,55937,54923],{},[902,55939,55940],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,55943,55945],{"className":55944},[886],[888,55946,55947],{"xmlns":890},[892,55948,55949,55973],{},[895,55950,55951,55953,55955,55957,55959,55961,55963,55965,55967,55969,55971],{},[898,55952,1755],{},[1654,55954,1750],{},[898,55956,17398],{},[1654,55958,1708],{"stretchy":1656},[898,55960,1663],{},[1654,55962,1726],{"stretchy":1656},[1654,55964,1750],{},[1665,55966,4035],{},[898,55968,1663],{},[1654,55970,1766],{},[1665,55972,4647],{},[902,55974,55975],{"encoding":904},"P = S(Q) = 3Q + 10",[120,55977,55978,56015,56079,56139],{},[123,55979,55980,55981,54878,55998,2138],{},"(a) Určete rovnovážné množství ",[883,55982,55984],{"className":55983},[886],[888,55985,55986],{"xmlns":890},[892,55987,55988,55996],{},[895,55989,55990],{},[1741,55991,55992,55994],{},[898,55993,1663],{},[898,55995,1798],{},[902,55997,50623],{"encoding":904},[883,55999,56001],{"className":56000},[886],[888,56002,56003],{"xmlns":890},[892,56004,56005,56013],{},[895,56006,56007],{},[1741,56008,56009,56011],{},[898,56010,1755],{},[898,56012,1798],{},[902,56014,49686],{"encoding":904},[123,56016,56017,56018,56036,56037,56057,56058,56078],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,56019,56021],{"className":56020},[886],[888,56022,56023],{"xmlns":890},[892,56024,56025,56033],{},[895,56026,56027,56029,56031],{},[898,56028,11536],{},[1654,56030,1750],{},[1665,56032,32887],{},[902,56034,56035],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,56038,56040],{"className":56039},[886],[888,56041,56042],{"xmlns":890},[892,56043,56044,56054],{},[895,56045,56046],{},[1659,56047,56048,56050,56052],{},[898,56049,1663],{},[1665,56051,1667],{},[898,56053,1798],{},[902,56055,56056],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,56059,56061],{"className":56060},[886],[888,56062,56063],{"xmlns":890},[892,56064,56065,56075],{},[895,56066,56067],{},[1659,56068,56069,56071,56073],{},[898,56070,1755],{},[1665,56072,1667],{},[898,56074,1798],{},[902,56076,56077],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,56080,56081,56082,56036,56099,56057,56119,56078],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,56083,56085],{"className":56084},[886],[888,56086,56087],{"xmlns":890},[892,56088,56089,56097],{},[895,56090,56091,56093,56095],{},[898,56092,11536],{},[1654,56094,1750],{},[1665,56096,32887],{},[902,56098,56035],{"encoding":904},[883,56100,56102],{"className":56101},[886],[888,56103,56104],{"xmlns":890},[892,56105,56106,56116],{},[895,56107,56108],{},[1659,56109,56110,56112,56114],{},[898,56111,1663],{},[1665,56113,1681],{},[898,56115,1798],{},[902,56117,56118],{"encoding":904},"Q_2^E",[883,56120,56122],{"className":56121},[886],[888,56123,56124],{"xmlns":890},[892,56125,56126,56136],{},[895,56127,56128],{},[1659,56129,56130,56132,56134],{},[898,56131,1755],{},[1665,56133,1681],{},[898,56135,1798],{},[902,56137,56138],{"encoding":904},"P_2^E",[123,56140,56141],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,56143,56144,56145,2138],{},"Viz též ",[207,56146,50941],{"className":56147,"dataFsResolvedFilePath":809,"href":810},[210],[198,56149,51243],{"id":56150},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,56152,56153,55904,56156,55941,56192,2138],{},[38,56154,56155],{},"2.14",[883,56157,56159],{"className":56158},[886],[888,56160,56161],{"xmlns":890},[892,56162,56163,56189],{},[895,56164,56165,56167,56169,56171,56173,56175,56177,56179,56181,56183,56185,56187],{},[898,56166,1755],{},[1654,56168,1750],{},[898,56170,207],{},[898,56172,1663],{},[1654,56174,1766],{},[898,56176,9758],{},[1654,56178,1750],{},[1654,56180,2380],{},[1665,56182,1681],{},[898,56184,1663],{},[1654,56186,1766],{},[1665,56188,4767],{},[902,56190,56191],{"encoding":904},"P = aQ + b = -2Q + 50",[883,56193,56195],{"className":56194},[886],[888,56196,56197],{"xmlns":890},[892,56198,56199,56223],{},[895,56200,56201,56203,56205,56207,56209,56211,56213,56215,56217,56219,56221],{},[898,56202,1755],{},[1654,56204,1750],{},[898,56206,3624],{},[898,56208,1663],{},[1654,56210,1766],{},[898,56212,10977],{},[1654,56214,1750],{},[1665,56216,28017],{},[898,56218,1663],{},[1654,56220,1766],{},[1665,56222,4573],{},[902,56224,56225],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,56227,56228,56264,56267,56353,56406,56486,56540],{},[123,56229,55980,56230,54878,56247,2138],{},[883,56231,56233],{"className":56232},[886],[888,56234,56235],{"xmlns":890},[892,56236,56237,56245],{},[895,56238,56239],{},[1741,56240,56241,56243],{},[898,56242,1663],{},[898,56244,1798],{},[902,56246,50623],{"encoding":904},[883,56248,56250],{"className":56249},[886],[888,56251,56252],{"xmlns":890},[892,56253,56254,56262],{},[895,56255,56256],{},[1741,56257,56258,56260],{},[898,56259,1755],{},[898,56261,1798],{},[902,56263,49686],{"encoding":904},[123,56265,56266],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,56268,56269,56270,56287,56288,11434,56301,11448,56317,56333,56334,2138],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,56271,56273],{"className":56272},[886],[888,56274,56275],{"xmlns":890},[892,56276,56277,56285],{},[895,56278,56279],{},[1741,56280,56281,56283],{},[898,56282,1663],{},[898,56284,1798],{},[902,56286,50623],{"encoding":904}," odpovídající změně ",[883,56289,56291],{"className":56290},[886],[888,56292,56293],{"xmlns":890},[892,56294,56295,56299],{},[895,56296,56297],{},[898,56298,207],{},[902,56300,207],{"encoding":904},[883,56302,56304],{"className":56303},[886],[888,56305,56306],{"xmlns":890},[892,56307,56308,56314],{},[895,56309,56310,56312],{},[1654,56311,2380],{},[1665,56313,1681],{},[902,56315,56316],{"encoding":904},"-2",[883,56318,56320],{"className":56319},[886],[888,56321,56322],{"xmlns":890},[892,56323,56324,56330],{},[895,56325,56326,56328],{},[1654,56327,2380],{},[1665,56329,4035],{},[902,56331,56332],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,56335,56337],{"className":56336},[886],[888,56338,56339],{"xmlns":890},[892,56340,56341,56351],{},[895,56342,56343],{},[1659,56344,56345,56347,56349],{},[898,56346,1663],{},[1665,56348,1667],{},[898,56350,1798],{},[902,56352,56056],{"encoding":904},[123,56354,56355,56356,56287,56373,56386,56387,2138],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,56357,56359],{"className":56358},[886],[888,56360,56361],{"xmlns":890},[892,56362,56363,56371],{},[895,56364,56365],{},[1741,56366,56367,56369],{},[898,56368,1663],{},[898,56370,1798],{},[902,56372,50623],{"encoding":904},[883,56374,56376],{"className":56375},[886],[888,56377,56378],{"xmlns":890},[892,56379,56380,56384],{},[895,56381,56382],{},[898,56383,9758],{},[902,56385,9758],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,56388,56390],{"className":56389},[886],[888,56391,56392],{"xmlns":890},[892,56393,56394,56404],{},[895,56395,56396],{},[1659,56397,56398,56400,56402],{},[898,56399,1663],{},[1665,56401,1681],{},[898,56403,1798],{},[902,56405,56118],{"encoding":904},[123,56407,56408,56409,56287,56426,11434,56439,11448,56452,56333,56466,2138],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,56410,56412],{"className":56411},[886],[888,56413,56414],{"xmlns":890},[892,56415,56416,56424],{},[895,56417,56418],{},[1741,56419,56420,56422],{},[898,56421,1663],{},[898,56423,1798],{},[902,56425,50623],{"encoding":904},[883,56427,56429],{"className":56428},[886],[888,56430,56431],{"xmlns":890},[892,56432,56433,56437],{},[895,56434,56435],{},[898,56436,3624],{},[902,56438,3624],{"encoding":904},[883,56440,56442],{"className":56441},[886],[888,56443,56444],{"xmlns":890},[892,56445,56446,56450],{},[895,56447,56448],{},[1665,56449,28017],{},[902,56451,52680],{"encoding":904},[883,56453,56455],{"className":56454},[886],[888,56456,56457],{"xmlns":890},[892,56458,56459,56463],{},[895,56460,56461],{},[1665,56462,23298],{},[902,56464,56465],{"encoding":904},"0{,}8",[883,56467,56469],{"className":56468},[886],[888,56470,56471],{"xmlns":890},[892,56472,56473,56483],{},[895,56474,56475],{},[1659,56476,56477,56479,56481],{},[898,56478,1663],{},[1665,56480,4035],{},[898,56482,1798],{},[902,56484,56485],{"encoding":904},"Q_3^E",[123,56487,56488,56489,56287,56506,56519,56520,2138],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,56490,56492],{"className":56491},[886],[888,56493,56494],{"xmlns":890},[892,56495,56496,56504],{},[895,56497,56498],{},[1741,56499,56500,56502],{},[898,56501,1663],{},[898,56503,1798],{},[902,56505,50623],{"encoding":904},[883,56507,56509],{"className":56508},[886],[888,56510,56511],{"xmlns":890},[892,56512,56513,56517],{},[895,56514,56515],{},[898,56516,10977],{},[902,56518,10977],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,56521,56523],{"className":56522},[886],[888,56524,56525],{"xmlns":890},[892,56526,56527,56537],{},[895,56528,56529],{},[1659,56530,56531,56533,56535],{},[898,56532,1663],{},[1665,56534,7631],{},[898,56536,1798],{},[902,56538,56539],{"encoding":904},"Q_4^E",[123,56541,56542,56543,56560,56561,56574,56575,30109,56588,1343,56603,30109,56616,2068,56630,30109,56643,56658,56659,2138],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,56544,56546],{"className":56545},[886],[888,56547,56548],{"xmlns":890},[892,56549,56550,56558],{},[895,56551,56552],{},[1741,56553,56554,56556],{},[898,56555,1663],{},[898,56557,1798],{},[902,56559,50623],{"encoding":904}," odpovídající změnám ",[883,56562,56564],{"className":56563},[886],[888,56565,56566],{"xmlns":890},[892,56567,56568,56572],{},[895,56569,56570],{},[898,56571,207],{},[902,56573,207],{"encoding":904}," o 1, ",[883,56576,56578],{"className":56577},[886],[888,56579,56580],{"xmlns":890},[892,56581,56582,56586],{},[895,56583,56584],{},[898,56585,9758],{},[902,56587,9758],{"encoding":904},[883,56589,56591],{"className":56590},[886],[888,56592,56593],{"xmlns":890},[892,56594,56595,56601],{},[895,56596,56597,56599],{},[1654,56598,2380],{},[1665,56600,4647],{},[902,56602,28151],{"encoding":904},[883,56604,56606],{"className":56605},[886],[888,56607,56608],{"xmlns":890},[892,56609,56610,56614],{},[895,56611,56612],{},[898,56613,3624],{},[902,56615,3624],{"encoding":904},[883,56617,56619],{"className":56618},[886],[888,56620,56621],{"xmlns":890},[892,56622,56623,56627],{},[895,56624,56625],{},[1665,56626,11555],{},[902,56628,56629],{"encoding":904},"0{,}1",[883,56631,56633],{"className":56632},[886],[888,56634,56635],{"xmlns":890},[892,56636,56637,56641],{},[895,56638,56639],{},[898,56640,10977],{},[902,56642,10977],{"encoding":904},[883,56644,56646],{"className":56645},[886],[888,56647,56648],{"xmlns":890},[892,56649,56650,56656],{},[895,56651,56652,56654],{},[1654,56653,2380],{},[1665,56655,4647],{},[902,56657,28151],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,56660,56662],{"className":56661},[886],[888,56663,56664],{"xmlns":890},[892,56665,56666,56676],{},[895,56667,56668],{},[1659,56669,56670,56672,56674],{},[898,56671,1663],{},[1665,56673,4032],{},[898,56675,1798],{},[902,56677,56678],{"encoding":904},"Q_5^E",[724,56680,56681,55904,56684,55941,56707,2138],{},[38,56682,56683],{},"2.15",[883,56685,56687],{"className":56686},[886],[888,56688,56689],{"xmlns":890},[892,56690,56691,56705],{},[895,56692,56693,56695,56697,56699,56701,56703],{},[898,56694,1755],{},[1654,56696,1750],{},[898,56698,207],{},[898,56700,1663],{},[1654,56702,1766],{},[898,56704,9758],{},[902,56706,45280],{"encoding":904},[883,56708,56710],{"className":56709},[886],[888,56711,56712],{"xmlns":890},[892,56713,56714,56728],{},[895,56715,56716,56718,56720,56722,56724,56726],{},[898,56717,1755],{},[1654,56719,1750],{},[898,56721,3624],{},[898,56723,1663],{},[1654,56725,1766],{},[898,56727,10977],{},[902,56729,48462],{"encoding":904},[120,56731,56732,56807,56824,56933,56986,57040],{},[123,56733,56734,56735,56748,56749,56774,56775,56806],{},"(a) Odvoďte redukovaný tvar pro ",[883,56736,56738],{"className":56737},[886],[888,56739,56740],{"xmlns":890},[892,56741,56742,56746],{},[895,56743,56744],{},[898,56745,1755],{},[902,56747,1755],{"encoding":904},". Stanovte podmínky pro ",[883,56750,56752],{"className":56751},[886],[888,56753,56754],{"xmlns":890},[892,56755,56756,56772],{},[895,56757,56758,56760,56762,56764,56766,56768,56770],{},[898,56759,207],{},[1654,56761,1674],{"separator":1673},[898,56763,9758],{},[1654,56765,1674],{"separator":1673},[898,56767,3624],{},[1654,56769,1674],{"separator":1673},[898,56771,10977],{},[902,56773,51505],{"encoding":904}," tak, aby rovnovážný bod ",[883,56776,56778],{"className":56777},[886],[888,56779,56780],{"xmlns":890},[892,56781,56782,56804],{},[895,56783,56784,56786,56788,56794,56796,56802],{},[898,56785,1798],{},[1654,56787,1657],{"stretchy":1656},[1741,56789,56790,56792],{},[898,56791,1663],{},[898,56793,1798],{},[1654,56795,1674],{"separator":1673},[1741,56797,56798,56800],{},[898,56799,1755],{},[898,56801,1798],{},[1654,56803,1686],{"stretchy":1656},[902,56805,49587],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,56808,56809,56810,56823],{},"(b) Vypočtěte multiplikátory pro ",[883,56811,56813],{"className":56812},[886],[888,56814,56815],{"xmlns":890},[892,56816,56817,56821],{},[895,56818,56819],{},[898,56820,1755],{},[902,56822,1755],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,56825,56826,56827,1343,56847,1343,56865,1343,56883,56901,56902,56919,56920,2138],{},"(c) Pro hodnoty parametrů ",[883,56828,56830],{"className":56829},[886],[888,56831,56832],{"xmlns":890},[892,56833,56834,56844],{},[895,56835,56836,56838,56840,56842],{},[898,56837,207],{},[1654,56839,1750],{},[1654,56841,2380],{},[1665,56843,1681],{},[902,56845,56846],{"encoding":904},"a = -2",[883,56848,56850],{"className":56849},[886],[888,56851,56852],{"xmlns":890},[892,56853,56854,56862],{},[895,56855,56856,56858,56860],{},[898,56857,9758],{},[1654,56859,1750],{},[1665,56861,5844],{},[902,56863,56864],{"encoding":904},"b = 40",[883,56866,56868],{"className":56867},[886],[888,56869,56870],{"xmlns":890},[892,56871,56872,56880],{},[895,56873,56874,56876,56878],{},[898,56875,3624],{},[1654,56877,1750],{},[1665,56879,7594],{},[902,56881,56882],{"encoding":904},"c = 0{,}5",[883,56884,56886],{"className":56885},[886],[888,56887,56888],{"xmlns":890},[892,56889,56890,56898],{},[895,56891,56892,56894,56896],{},[898,56893,10977],{},[1654,56895,1750],{},[1665,56897,4647],{},[902,56899,56900],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,56903,56905],{"className":56904},[886],[888,56906,56907],{"xmlns":890},[892,56908,56909,56917],{},[895,56910,56911],{},[1741,56912,56913,56915],{},[898,56914,1755],{},[898,56916,1798],{},[902,56918,49686],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,56921,56923],{"className":56922},[886],[888,56924,56925],{"xmlns":890},[892,56926,56927,56931],{},[895,56928,56929],{},[898,56930,1755],{},[902,56932,1755],{"encoding":904},[123,56934,56935,56936,56287,56953,56966,56967,2138],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,56937,56939],{"className":56938},[886],[888,56940,56941],{"xmlns":890},[892,56942,56943,56951],{},[895,56944,56945],{},[1741,56946,56947,56949],{},[898,56948,1755],{},[898,56950,1798],{},[902,56952,49686],{"encoding":904},[883,56954,56956],{"className":56955},[886],[888,56957,56958],{"xmlns":890},[892,56959,56960,56964],{},[895,56961,56962],{},[898,56963,207],{},[902,56965,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,56968,56970],{"className":56969},[886],[888,56971,56972],{"xmlns":890},[892,56973,56974,56984],{},[895,56975,56976],{},[1659,56977,56978,56980,56982],{},[898,56979,1755],{},[1665,56981,1667],{},[898,56983,1798],{},[902,56985,56077],{"encoding":904},[123,56987,56988,56989,57006,57007,57020,57021,2138],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,56990,56992],{"className":56991},[886],[888,56993,56994],{"xmlns":890},[892,56995,56996,57004],{},[895,56997,56998],{},[1741,56999,57000,57002],{},[898,57001,1755],{},[898,57003,1798],{},[902,57005,49686],{"encoding":904}," odpovídající poklesu ",[883,57008,57010],{"className":57009},[886],[888,57011,57012],{"xmlns":890},[892,57013,57014,57018],{},[895,57015,57016],{},[898,57017,207],{},[902,57019,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,57022,57024],{"className":57023},[886],[888,57025,57026],{"xmlns":890},[892,57027,57028,57038],{},[895,57029,57030],{},[1659,57031,57032,57034,57036],{},[898,57033,1755],{},[1665,57035,1681],{},[898,57037,1798],{},[902,57039,56138],{"encoding":904},[123,57041,57042,57043,56560,57060,57073,57074,11448,57087,2068,57102,57115,57116,2138],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,57044,57046],{"className":57045},[886],[888,57047,57048],{"xmlns":890},[892,57049,57050,57058],{},[895,57051,57052],{},[1741,57053,57054,57056],{},[898,57055,1755],{},[898,57057,1798],{},[902,57059,49686],{"encoding":904},[883,57061,57063],{"className":57062},[886],[888,57064,57065],{"xmlns":890},[892,57066,57067,57071],{},[895,57068,57069],{},[898,57070,207],{},[902,57072,207],{"encoding":904}," na 35, ",[883,57075,57077],{"className":57076},[886],[888,57078,57079],{"xmlns":890},[892,57080,57081,57085],{},[895,57082,57083],{},[898,57084,3624],{},[902,57086,3624],{"encoding":904},[883,57088,57090],{"className":57089},[886],[888,57091,57092],{"xmlns":890},[892,57093,57094,57099],{},[895,57095,57096],{},[1665,57097,57098],{},"0,7",[902,57100,57101],{"encoding":904},"0{,}7",[883,57103,57105],{"className":57104},[886],[888,57106,57107],{"xmlns":890},[892,57108,57109,57113],{},[895,57110,57111],{},[898,57112,10977],{},[902,57114,10977],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,57117,57119],{"className":57118},[886],[888,57120,57121],{"xmlns":890},[892,57122,57123,57133],{},[895,57124,57125],{},[1659,57126,57127,57129,57131],{},[898,57128,1755],{},[1665,57130,4035],{},[898,57132,1798],{},[902,57134,57135],{"encoding":904},"P_3^E",[724,57137,57138,55904,57141,55941,57169,9762,57197,2068,57223,2138],{},[38,57139,57140],{},"2.16",[883,57142,57144],{"className":57143},[886],[888,57145,57146],{"xmlns":890},[892,57147,57148,57166],{},[895,57149,57150,57152,57154,57156,57158,57160],{},[898,57151,1755],{},[1654,57153,1750],{},[898,57155,207],{},[1654,57157,1766],{},[898,57159,9758],{},[1741,57161,57162,57164],{},[898,57163,1663],{},[1665,57165,1681],{},[902,57167,57168],{"encoding":904},"P = a + bQ^2",[883,57170,57172],{"className":57171},[886],[888,57173,57174],{"xmlns":890},[892,57175,57176,57194],{},[895,57177,57178,57180,57182,57184,57186,57188],{},[898,57179,1755],{},[1654,57181,1750],{},[898,57183,3624],{},[1654,57185,1766],{},[898,57187,10977],{},[1741,57189,57190,57192],{},[898,57191,1663],{},[1665,57193,1681],{},[902,57195,57196],{"encoding":904},"P = c + dQ^2",[883,57198,57200],{"className":57199},[886],[888,57201,57202],{"xmlns":890},[892,57203,57204,57220],{},[895,57205,57206,57208,57210,57212,57214,57216,57218],{},[898,57207,207],{},[1654,57209,1674],{"separator":1673},[898,57211,3624],{},[1654,57213,1674],{"separator":1673},[898,57215,10977],{},[1654,57217,2952],{},[1665,57219,2062],{},[902,57221,57222],{"encoding":904},"a, c, d > 0",[883,57224,57226],{"className":57225},[886],[888,57227,57228],{"xmlns":890},[892,57229,57230,57238],{},[895,57231,57232,57234,57236],{},[898,57233,9758],{},[1654,57235,3002],{},[1665,57237,2062],{},[902,57239,57240],{"encoding":904},"b \u003C 0",[120,57242,57243,57291,57307,57414,57466,57518,57627,57643,57742,57795],{},[123,57244,56734,57245,57258,57259,57290],{},[883,57246,57248],{"className":57247},[886],[888,57249,57250],{"xmlns":890},[892,57251,57252,57256],{},[895,57253,57254],{},[898,57255,1663],{},[902,57257,1663],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,57260,57262],{"className":57261},[886],[888,57263,57264],{"xmlns":890},[892,57265,57266,57288],{},[895,57267,57268,57270,57272,57278,57280,57286],{},[898,57269,1798],{},[1654,57271,1657],{"stretchy":1656},[1741,57273,57274,57276],{},[898,57275,1663],{},[898,57277,1798],{},[1654,57279,1674],{"separator":1673},[1741,57281,57282,57284],{},[898,57283,1755],{},[898,57285,1798],{},[1654,57287,1686],{"stretchy":1656},[902,57289,49587],{"encoding":904}," patřil do 1. kvadrantu.",[123,57292,56809,57293,57306],{},[883,57294,57296],{"className":57295},[886],[888,57297,57298],{"xmlns":890},[892,57299,57300,57304],{},[895,57301,57302],{},[898,57303,1663],{},[902,57305,1663],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,57308,56826,57309,1343,57327,1343,57347,1343,57365,57383,57384,56919,57401,2138],{},[883,57310,57312],{"className":57311},[886],[888,57313,57314],{"xmlns":890},[892,57315,57316,57324],{},[895,57317,57318,57320,57322],{},[898,57319,207],{},[1654,57321,1750],{},[1665,57323,4273],{},[902,57325,57326],{"encoding":904},"a = 100",[883,57328,57330],{"className":57329},[886],[888,57331,57332],{"xmlns":890},[892,57333,57334,57344],{},[895,57335,57336,57338,57340,57342],{},[898,57337,9758],{},[1654,57339,1750],{},[1654,57341,2380],{},[1665,57343,1667],{},[902,57345,57346],{"encoding":904},"b = -1",[883,57348,57350],{"className":57349},[886],[888,57351,57352],{"xmlns":890},[892,57353,57354,57362],{},[895,57355,57356,57358,57360],{},[898,57357,3624],{},[1654,57359,1750],{},[1665,57361,4573],{},[902,57363,57364],{"encoding":904},"c = 20",[883,57366,57368],{"className":57367},[886],[888,57369,57370],{"xmlns":890},[892,57371,57372,57380],{},[895,57373,57374,57376,57378],{},[898,57375,10977],{},[1654,57377,1750],{},[1665,57379,1667],{},[902,57381,57382],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,57385,57387],{"className":57386},[886],[888,57388,57389],{"xmlns":890},[892,57390,57391,57399],{},[895,57392,57393],{},[1741,57394,57395,57397],{},[898,57396,1663],{},[898,57398,1798],{},[902,57400,50623],{"encoding":904},[883,57402,57404],{"className":57403},[886],[888,57405,57406],{"xmlns":890},[892,57407,57408,57412],{},[895,57409,57410],{},[898,57411,1663],{},[902,57413,1663],{"encoding":904},[123,57415,56355,57416,56287,57433,57446,57447,2138],{},[883,57417,57419],{"className":57418},[886],[888,57420,57421],{"xmlns":890},[892,57422,57423,57431],{},[895,57424,57425],{},[1741,57426,57427,57429],{},[898,57428,1663],{},[898,57430,1798],{},[902,57432,50623],{"encoding":904},[883,57434,57436],{"className":57435},[886],[888,57437,57438],{"xmlns":890},[892,57439,57440,57444],{},[895,57441,57442],{},[898,57443,207],{},[902,57445,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,57448,57450],{"className":57449},[886],[888,57451,57452],{"xmlns":890},[892,57453,57454,57464],{},[895,57455,57456],{},[1659,57457,57458,57460,57462],{},[898,57459,1663],{},[1665,57461,1667],{},[898,57463,1798],{},[902,57465,56056],{"encoding":904},[123,57467,56408,57468,56287,57485,57498,57499,2138],{},[883,57469,57471],{"className":57470},[886],[888,57472,57473],{"xmlns":890},[892,57474,57475,57483],{},[895,57476,57477],{},[1741,57478,57479,57481],{},[898,57480,1663],{},[898,57482,1798],{},[902,57484,50623],{"encoding":904},[883,57486,57488],{"className":57487},[886],[888,57489,57490],{"xmlns":890},[892,57491,57492,57496],{},[895,57493,57494],{},[898,57495,3624],{},[902,57497,3624],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,57500,57502],{"className":57501},[886],[888,57503,57504],{"xmlns":890},[892,57505,57506,57516],{},[895,57507,57508],{},[1659,57509,57510,57512,57514],{},[898,57511,1663],{},[1665,57513,1681],{},[898,57515,1798],{},[902,57517,56118],{"encoding":904},[123,57519,56488,57520,56560,57537,57550,57551,11448,57564,57579,57580,57593,57594,57607,57608,2138],{},[883,57521,57523],{"className":57522},[886],[888,57524,57525],{"xmlns":890},[892,57526,57527,57535],{},[895,57528,57529],{},[1741,57530,57531,57533],{},[898,57532,1663],{},[898,57534,1798],{},[902,57536,50623],{"encoding":904},[883,57538,57540],{"className":57539},[886],[888,57541,57542],{"xmlns":890},[892,57543,57544,57548],{},[895,57545,57546],{},[898,57547,207],{},[902,57549,207],{"encoding":904}," na 110, poklesu ",[883,57552,57554],{"className":57553},[886],[888,57555,57556],{"xmlns":890},[892,57557,57558,57562],{},[895,57559,57560],{},[898,57561,9758],{},[902,57563,9758],{"encoding":904},[883,57565,57567],{"className":57566},[886],[888,57568,57569],{"xmlns":890},[892,57570,57571,57577],{},[895,57572,57573,57575],{},[1654,57574,2380],{},[1665,57576,1681],{},[902,57578,56316],{"encoding":904},", růstu ",[883,57581,57583],{"className":57582},[886],[888,57584,57585],{"xmlns":890},[892,57586,57587,57591],{},[895,57588,57589],{},[898,57590,3624],{},[902,57592,3624],{"encoding":904}," na 25 a růstu ",[883,57595,57597],{"className":57596},[886],[888,57598,57599],{"xmlns":890},[892,57600,57601,57605],{},[895,57602,57603],{},[898,57604,10977],{},[902,57606,10977],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,57609,57611],{"className":57610},[886],[888,57612,57613],{"xmlns":890},[892,57614,57615,57625],{},[895,57616,57617],{},[1659,57618,57619,57621,57623],{},[898,57620,1663],{},[1665,57622,4035],{},[898,57624,1798],{},[902,57626,56485],{"encoding":904},[123,57628,57629,57630,57306],{},"(i) Vypočtěte multiplikátory pro ",[883,57631,57633],{"className":57632},[886],[888,57634,57635],{"xmlns":890},[892,57636,57637,57641],{},[895,57638,57639],{},[898,57640,1755],{},[902,57642,1755],{"encoding":904},[123,57644,57645,57646,56919,57663,57676,57677,56287,57694,11448,57707,57722,57723,2138],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,57647,57649],{"className":57648},[886],[888,57650,57651],{"xmlns":890},[892,57652,57653,57661],{},[895,57654,57655],{},[1741,57656,57657,57659],{},[898,57658,1755],{},[898,57660,1798],{},[902,57662,49686],{"encoding":904},[883,57664,57666],{"className":57665},[886],[888,57667,57668],{"xmlns":890},[892,57669,57670,57674],{},[895,57671,57672],{},[898,57673,1755],{},[902,57675,1755],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,57678,57680],{"className":57679},[886],[888,57681,57682],{"xmlns":890},[892,57683,57684,57692],{},[895,57685,57686],{},[1741,57687,57688,57690],{},[898,57689,1755],{},[898,57691,1798],{},[902,57693,49686],{"encoding":904},[883,57695,57697],{"className":57696},[886],[888,57698,57699],{"xmlns":890},[892,57700,57701,57705],{},[895,57702,57703],{},[898,57704,207],{},[902,57706,207],{"encoding":904},[883,57708,57710],{"className":57709},[886],[888,57711,57712],{"xmlns":890},[892,57713,57714,57720],{},[895,57715,57716,57718],{},[1654,57717,2380],{},[1665,57719,4035],{},[902,57721,56332],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,57724,57726],{"className":57725},[886],[888,57727,57728],{"xmlns":890},[892,57729,57730,57740],{},[895,57731,57732],{},[1659,57733,57734,57736,57738],{},[898,57735,1755],{},[1665,57737,1667],{},[898,57739,1798],{},[902,57741,56077],{"encoding":904},[123,57743,57744,57745,56287,57762,57775,57776,2138],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,57746,57748],{"className":57747},[886],[888,57749,57750],{"xmlns":890},[892,57751,57752,57760],{},[895,57753,57754],{},[1741,57755,57756,57758],{},[898,57757,1755],{},[898,57759,1798],{},[902,57761,49686],{"encoding":904},[883,57763,57765],{"className":57764},[886],[888,57766,57767],{"xmlns":890},[892,57768,57769,57773],{},[895,57770,57771],{},[898,57772,207],{},[902,57774,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,57777,57779],{"className":57778},[886],[888,57780,57781],{"xmlns":890},[892,57782,57783,57793],{},[895,57784,57785],{},[1659,57786,57787,57789,57791],{},[898,57788,1755],{},[1665,57790,1681],{},[898,57792,1798],{},[902,57794,56138],{"encoding":904},[123,57796,57797,57798,57006,57815,57828,57829,11448,57842,57579,57857,57870,57871,57884,57885,2138],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,57799,57801],{"className":57800},[886],[888,57802,57803],{"xmlns":890},[892,57804,57805,57813],{},[895,57806,57807],{},[1741,57808,57809,57811],{},[898,57810,1755],{},[898,57812,1798],{},[902,57814,49686],{"encoding":904},[883,57816,57818],{"className":57817},[886],[888,57819,57820],{"xmlns":890},[892,57821,57822,57826],{},[895,57823,57824],{},[898,57825,207],{},[902,57827,207],{"encoding":904}," na 90, poklesu ",[883,57830,57832],{"className":57831},[886],[888,57833,57834],{"xmlns":890},[892,57835,57836,57840],{},[895,57837,57838],{},[898,57839,9758],{},[902,57841,9758],{"encoding":904},[883,57843,57845],{"className":57844},[886],[888,57846,57847],{"xmlns":890},[892,57848,57849,57855],{},[895,57850,57851,57853],{},[1654,57852,2380],{},[1665,57854,4035],{},[902,57856,56332],{"encoding":904},[883,57858,57860],{"className":57859},[886],[888,57861,57862],{"xmlns":890},[892,57863,57864,57868],{},[895,57865,57866],{},[898,57867,3624],{},[902,57869,3624],{"encoding":904}," na 30 a růstu ",[883,57872,57874],{"className":57873},[886],[888,57875,57876],{"xmlns":890},[892,57877,57878,57882],{},[895,57879,57880],{},[898,57881,10977],{},[902,57883,10977],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,57886,57888],{"className":57887},[886],[888,57889,57890],{"xmlns":890},[892,57891,57892,57902],{},[895,57893,57894],{},[1659,57895,57896,57898,57900],{},[898,57897,1755],{},[1665,57899,4035],{},[898,57901,1798],{},[902,57903,57135],{"encoding":904},[198,57905,820],{"id":57906},"přebytek-spotřebitele-a-výrobce-1",[724,57908,57909,55904,57912,55941,57948,2138],{},[38,57910,57911],{},"2.17",[883,57913,57915],{"className":57914},[886],[888,57916,57917],{"xmlns":890},[892,57918,57919,57945],{},[895,57920,57921,57923,57925,57927,57929,57931,57933,57935,57937,57939],{},[898,57922,1755],{},[1654,57924,1750],{},[898,57926,4980],{},[1654,57928,1708],{"stretchy":1656},[898,57930,1663],{},[1654,57932,1726],{"stretchy":1656},[1654,57934,1750],{},[1665,57936,23747],{},[1654,57938,2380],{},[1741,57940,57941,57943],{},[898,57942,1663],{},[1665,57944,1681],{},[902,57946,57947],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,57949,57951],{"className":57950},[886],[888,57952,57953],{"xmlns":890},[892,57954,57955,57981],{},[895,57956,57957,57959,57961,57963,57965,57967,57969,57971,57973,57975],{},[898,57958,1755],{},[1654,57960,1750],{},[898,57962,17398],{},[1654,57964,1708],{"stretchy":1656},[898,57966,1663],{},[1654,57968,1726],{"stretchy":1656},[1654,57970,1750],{},[1665,57972,4035],{},[1654,57974,1766],{},[1741,57976,57977,57979],{},[898,57978,1663],{},[1665,57980,1681],{},[902,57982,57983],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,57985,57986,57989],{},[123,57987,57988],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,57990,57991],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,57993,57994,55904,57997,55941,58031,2138],{},[38,57995,57996],{},"2.18",[883,57998,58000],{"className":57999},[886],[888,58001,58002],{"xmlns":890},[892,58003,58004,58028],{},[895,58005,58006,58008,58010,58012,58014,58016,58018,58020,58022,58024,58026],{},[898,58007,1755],{},[1654,58009,1750],{},[898,58011,4980],{},[1654,58013,1708],{"stretchy":1656},[898,58015,1663],{},[1654,58017,1726],{"stretchy":1656},[1654,58019,1750],{},[1665,58021,12457],{},[1654,58023,2380],{},[1665,58025,1681],{},[898,58027,1663],{},[902,58029,58030],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,58032,58034],{"className":58033},[886],[888,58035,58036],{"xmlns":890},[892,58037,58038,58064],{},[895,58039,58040,58042,58044,58046,58048,58050,58052,58054,58056,58058],{},[898,58041,1755],{},[1654,58043,1750],{},[898,58045,17398],{},[1654,58047,1708],{"stretchy":1656},[898,58049,1663],{},[1654,58051,1726],{"stretchy":1656},[1654,58053,1750],{},[1665,58055,4035],{},[1654,58057,1766],{},[1741,58059,58060,58062],{},[898,58061,1663],{},[1665,58063,1681],{},[902,58065,57983],{"encoding":904},[120,58067,58068,58088,58091,58094],{},[123,58069,58070,58071,2138],{},"(a) Vypočtěte rovnovážné množství ",[883,58072,58074],{"className":58073},[886],[888,58075,58076],{"xmlns":890},[892,58077,58078,58086],{},[895,58079,58080],{},[1741,58081,58082,58084],{},[898,58083,1663],{},[898,58085,1798],{},[902,58087,50623],{"encoding":904},[123,58089,58090],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,58092,58093],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,58095,58096],{},"(c) Graficky interpretujte.",[45190,58098],{},[115,58100,58102],{"id":58101},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,58104,58105,58108,58111,58114,58117,58120,58123,58126,58129,58132,58135,58138,58141,58144],{},[123,58106,58107],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,58109,58110],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,58112,58113],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,58115,58116],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,58118,58119],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,58121,58122],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,58124,58125],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,58127,58128],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,58130,58131],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,58133,58134],{},"K čemu slouží multiplikátory?",[123,58136,58137],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,58139,58140],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,58142,58143],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,58145,58146],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[45190,58148],{},[115,58150,10214],{"id":10213},[724,58152,58153],{},[38,58154,21870],{},[120,58156,58157,58192,58197,58227,58232,58295,58321,58326,58356,58365,58372,58378],{},[123,58158,58159,18742,58162,27344,58165,2186,58167,1343,58190],{},[38,58160,58161],{},"Poptávané množství",[614,58163,58164],{},"quantity demanded",[38,58166,1892],{},[883,58168,58170],{"className":58169},[886],[888,58171,58172],{"xmlns":890},[892,58173,58174,58188],{},[895,58175,58176,58178,58180,58182,58184,58186],{},[898,58177,1663],{},[1654,58179,1750],{},[898,58181,4980],{},[1654,58183,1708],{"stretchy":1656},[898,58185,1755],{},[1654,58187,1726],{"stretchy":1656},[902,58189,12933],{"encoding":904},[38,58191,45669],{},[123,58193,58194,58196],{},[38,58195,45676],{}," — substituční + důchodový efekt",[123,58198,58199,2186,58202],{},[38,58200,58201],{},"Reálné cenové rozpětí",[883,58203,58205],{"className":58204},[886],[888,58206,58207],{"xmlns":890},[892,58208,58209,58225],{},[895,58210,58211,58213,58215,58217,58223],{},[1654,58212,1708],{"stretchy":1656},[1665,58214,2062],{},[1654,58216,1674],{"separator":1673},[1710,58218,58219,58221],{},[898,58220,1755],{},[1665,58222,2062],{},[1654,58224,1726],{"stretchy":1656},[902,58226,45877],{"encoding":904},[123,58228,58229,19810],{},[38,58230,58231],{},"Homogenita poptávky",[123,58233,58234,2186,58237,1343,58260,1343,58277,58294],{},[38,58235,58236],{},"Lineární poptávka",[883,58238,58240],{"className":58239},[886],[888,58241,58242],{"xmlns":890},[892,58243,58244,58258],{},[895,58245,58246,58248,58250,58252,58254,58256],{},[898,58247,1755],{},[1654,58249,1750],{},[898,58251,207],{},[898,58253,1663],{},[1654,58255,1766],{},[898,58257,9758],{},[902,58259,45280],{"encoding":904},[883,58261,58263],{"className":58262},[886],[888,58264,58265],{"xmlns":890},[892,58266,58267,58275],{},[895,58268,58269,58271,58273],{},[898,58270,207],{},[1654,58272,3002],{},[1665,58274,2062],{},[902,58276,51305],{"encoding":904},[883,58278,58280],{"className":58279},[886],[888,58281,58282],{"xmlns":890},[892,58283,58284,58292],{},[895,58285,58286,58288,58290],{},[898,58287,9758],{},[1654,58289,2952],{},[1665,58291,2062],{},[902,58293,27510],{"encoding":904}," — nedokonalá konkurence",[123,58296,58297,10373,58300],{},[38,58298,58299],{},"Dokonalá konkurence",[883,58301,58303],{"className":58302},[886],[888,58304,58305],{"xmlns":890},[892,58306,58307,58319],{},[895,58308,58309,58311,58313],{},[898,58310,1755],{},[1654,58312,1750],{},[1741,58314,58315,58317],{},[898,58316,1755],{},[1654,58318,1670],{},[902,58320,13095],{"encoding":904},[123,58322,58323,58325],{},[38,58324,46446],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,58327,58328,2186,58330,1343,58354],{},[38,58329,5669],{},[883,58331,58333],{"className":58332},[886],[888,58334,58335],{"xmlns":890},[892,58336,58337,58351],{},[895,58338,58339,58341,58343,58345,58347,58349],{},[898,58340,1663],{},[1654,58342,1750],{},[898,58344,1798],{},[1654,58346,1708],{"stretchy":1656},[898,58348,1745],{},[1654,58350,1726],{"stretchy":1656},[902,58352,58353],{"encoding":904},"Q = E(Y)",[38,58355,46643],{},[123,58357,58358,58361,58362,58364],{},[38,58359,58360],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,58363,47089],{}," zboží",[123,58366,58367,2068,58369,58371],{},[38,58368,48095],{},[38,58370,48042],{}," — znaménka zkřížených koeficientů",[123,58373,58374,58377],{},[38,58375,58376],{},"Dvoukomoditní trh"," (2.6)",[123,58379,58380,18742,58383,1726],{},[38,58381,58382],{},"Posun poptávky",[614,58384,47147],{},[724,58386,58387],{},[38,58388,21834],{},[120,58390,58391,58424,58428,58473],{},[123,58392,58393,18742,58395,27344,58397,2186,58399,1343,58422],{},[38,58394,48489],{},[614,58396,48492],{},[38,58398,48663],{},[883,58400,58402],{"className":58401},[886],[888,58403,58404],{"xmlns":890},[892,58405,58406,58420],{},[895,58407,58408,58410,58412,58414,58416,58418],{},[898,58409,1663],{},[1654,58411,1750],{},[898,58413,17398],{},[1654,58415,1708],{"stretchy":1656},[898,58417,1755],{},[1654,58419,1726],{"stretchy":1656},[902,58421,17407],{"encoding":904},[38,58423,48741],{},[123,58425,58426],{},[38,58427,48748],{},[123,58429,58430,2186,58433,1343,58456],{},[38,58431,58432],{},"Lineární nabídka",[883,58434,58436],{"className":58435},[886],[888,58437,58438],{"xmlns":890},[892,58439,58440,58454],{},[895,58441,58442,58444,58446,58448,58450,58452],{},[898,58443,1755],{},[1654,58445,1750],{},[898,58447,3624],{},[898,58449,1663],{},[1654,58451,1766],{},[898,58453,10977],{},[902,58455,48462],{"encoding":904},[883,58457,58459],{"className":58458},[886],[888,58460,58461],{"xmlns":890},[892,58462,58463,58471],{},[895,58464,58465,58467,58469],{},[898,58466,3624],{},[1654,58468,2952],{},[1665,58470,2062],{},[902,58472,48480],{"encoding":904},[123,58474,58475,18742,58478,1726],{},[38,58476,58477],{},"Posun nabídky",[614,58479,49126],{},[724,58481,58482],{},[38,58483,58484],{},"Rovnováha a komparativní statika",[120,58486,58487,58566,58572],{},[123,58488,58489,18742,58491,27344,58493,2186,58496,1343,58513,2186,58516,1343,58533,2186,58535],{},[38,58490,49545],{},[614,58492,49664],{},[38,58494,58495],{},"rovnovážná cena",[883,58497,58499],{"className":58498},[886],[888,58500,58501],{"xmlns":890},[892,58502,58503,58511],{},[895,58504,58505],{},[1741,58506,58507,58509],{},[898,58508,1755],{},[898,58510,1798],{},[902,58512,49686],{"encoding":904},[38,58514,58515],{},"rovnovážné množství",[883,58517,58519],{"className":58518},[886],[888,58520,58521],{"xmlns":890},[892,58522,58523,58531],{},[895,58524,58525],{},[1741,58526,58527,58529],{},[898,58528,1663],{},[898,58530,1798],{},[902,58532,50623],{"encoding":904},[38,58534,49722],{},[883,58536,58538],{"className":58537},[886],[888,58539,58540],{"xmlns":890},[892,58541,58542,58564],{},[895,58543,58544,58546,58548,58554,58556,58562],{},[898,58545,1798],{},[1654,58547,1657],{"stretchy":1656},[1741,58549,58550,58552],{},[898,58551,1663],{},[898,58553,1798],{},[1654,58555,1674],{"separator":1673},[1741,58557,58558,58560],{},[898,58559,1755],{},[898,58561,1798],{},[1654,58563,1686],{"stretchy":1656},[902,58565,49587],{"encoding":904},[123,58567,58568,58571],{},[38,58569,58570],{},"Pravidla 1–4"," komparativní statiky",[123,58573,58574,18742,58577,1726],{},[38,58575,58576],{},"Teorém pavučiny",[614,58578,50569],{},[724,58580,58581],{},[38,58582,58583],{},"Zdanění",[120,58585,58586,58642,58690],{},[123,58587,58588,58590,58591,58616,58617,1726],{},[38,58589,58583],{}," — daň výrobci (",[883,58592,58594],{"className":58593},[886],[888,58595,58596],{"xmlns":890},[892,58597,58598,58614],{},[895,58599,58600,58606,58608,58610,58612],{},[1710,58601,58602,58604],{},[898,58603,17398],{},[1665,58605,1667],{},[1654,58607,1750],{},[898,58609,17398],{},[1654,58611,1766],{},[898,58613,11536],{},[902,58615,50974],{"encoding":904},") vs. daň spotřebiteli (",[883,58618,58620],{"className":58619},[886],[888,58621,58622],{"xmlns":890},[892,58623,58624,58640],{},[895,58625,58626,58632,58634,58636,58638],{},[1710,58627,58628,58630],{},[898,58629,4980],{},[1665,58631,1681],{},[1654,58633,1750],{},[898,58635,4980],{},[1654,58637,2380],{},[898,58639,11536],{},[902,58641,51005],{"encoding":904},[123,58643,58644,2186,58646,1343,58667],{},[38,58645,50878],{},[883,58647,58649],{"className":58648},[886],[888,58650,58651],{"xmlns":890},[892,58652,58653,58665],{},[895,58654,58655],{},[1710,58656,58657,58659],{},[898,58658,11536],{},[895,58660,58661,58663],{},[898,58662,50897],{},[898,58664,724],{},[902,58666,50902],{"encoding":904},[883,58668,58670],{"className":58669},[886],[888,58671,58672],{"xmlns":890},[892,58673,58674,58688],{},[895,58675,58676],{},[1710,58677,58678,58680],{},[898,58679,11536],{},[895,58681,58682,58684,58686],{},[898,58683,50920],{},[898,58685,10789],{},[898,58687,20753],{},[902,58689,50927],{"encoding":904},[123,58691,58692,2186,58695,1343,58724],{},[38,58693,58694],{},"Ekvivalence zdanění",[883,58696,58698],{"className":58697},[886],[888,58699,58700],{"xmlns":890},[892,58701,58702,58722],{},[895,58703,58704,58712,58714],{},[1659,58705,58706,58708,58710],{},[898,58707,1663],{},[1665,58709,1667],{},[898,58711,1798],{},[1654,58713,1750],{},[1659,58715,58716,58718,58720],{},[898,58717,1663],{},[1665,58719,1681],{},[898,58721,1798],{},[902,58723,51128],{"encoding":904},[883,58725,58727],{"className":58726},[886],[888,58728,58729],{"xmlns":890},[892,58730,58731,58755],{},[895,58732,58733,58741,58743,58745,58747],{},[1659,58734,58735,58737,58739],{},[898,58736,1755],{},[1665,58738,1667],{},[898,58740,1798],{},[1654,58742,2380],{},[898,58744,11536],{},[1654,58746,1750],{},[1659,58748,58749,58751,58753],{},[898,58750,1755],{},[1665,58752,1681],{},[898,58754,1798],{},[902,58756,51162],{"encoding":904},[724,58758,58759],{},[38,58760,35094],{},[120,58762,58763,58809,58840,58845,58851,58858],{},[123,58764,58765,2186,58767],{},[38,58766,51261],{},[883,58768,58770],{"className":58769},[886],[888,58771,58772],{"xmlns":890},[892,58773,58774,58806],{},[895,58775,58776,58782,58784,58786,58788,58790,58792,58794,58796,58798,58800,58802,58804],{},[1741,58777,58778,58780],{},[898,58779,1663],{},[898,58781,1798],{},[1654,58783,1750],{},[1654,58785,1708],{"stretchy":1656},[898,58787,9758],{},[1654,58789,2380],{},[898,58791,10977],{},[1654,58793,1726],{"stretchy":1656},[898,58795,1879],{"mathvariant":1878},[1654,58797,1708],{"stretchy":1656},[898,58799,3624],{},[1654,58801,2380],{},[898,58803,207],{},[1654,58805,1726],{"stretchy":1656},[902,58807,58808],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,58810,58811,2186,58814,58839],{},[38,58812,58813],{},"Parametry",[883,58815,58817],{"className":58816},[886],[888,58818,58819],{"xmlns":890},[892,58820,58821,58837],{},[895,58822,58823,58825,58827,58829,58831,58833,58835],{},[898,58824,207],{},[1654,58826,1674],{"separator":1673},[898,58828,9758],{},[1654,58830,1674],{"separator":1673},[898,58832,3624],{},[1654,58834,1674],{"separator":1673},[898,58836,10977],{},[902,58838,51505],{"encoding":904}," — exogenní proměnné",[123,58841,58842],{},[38,58843,58844],{},"Endogenní \u002F exogenní proměnná",[123,58846,58847,58850],{},[38,58848,58849],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,58852,58853,1343,58856],{},[38,58854,58855],{},"Komparativní statika",[38,58857,45180],{},[123,58859,58860,2186,58862,58878],{},[38,58861,11712],{},[883,58863,58865],{"className":58864},[886],[888,58866,58867],{"xmlns":890},[892,58868,58869,58875],{},[895,58870,58871,58873],{},[898,58872,10977],{},[898,58874,1663],{},[902,58876,58877],{"encoding":904},"dQ"," (2.11)",[724,58880,58881],{},[38,58882,58883],{},"Přebytky a ostatní",[120,58885,58886,58924],{},[123,58887,58888,2186,58890,58905,58906,2186,58908,58923],{},[38,58889,53154],{},[883,58891,58893],{"className":58892},[886],[888,58894,58895],{"xmlns":890},[892,58896,58897,58903],{},[895,58898,58899,58901],{},[898,58900,11539],{},[898,58902,17398],{},[902,58904,53170],{"encoding":904}," (2.14), ",[38,58907,53173],{},[883,58909,58911],{"className":58910},[886],[888,58912,58913],{"xmlns":890},[892,58914,58915,58921],{},[895,58916,58917,58919],{},[898,58918,1755],{},[898,58920,17398],{},[902,58922,53189],{"encoding":904}," (2.15)",[123,58925,58926,1343,58929,58932],{},[38,58927,58928],{},"Homo economicus",[38,58930,58931],{},"Marshallova formulace"," (1890)",[45190,58934],{},[115,58936,10613],{"id":10612},[120,58938,58939,58974,58983],{},[123,58940,58941,2186,58944,58947,58948,1343,58951,58954,58955,58958,58959,58962,58963,58966,58967,58970,58971],{},[38,58942,58943],{},"Související témata:",[207,58945,811],{"className":58946,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,58949,820],{"className":58950,"dataFsResolvedFilePath":818,"href":819},[210],[207,58952,10655],{"className":58953,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,58956,775],{"className":58957,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,58960,784],{"className":58961,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,58964,793],{"className":58965,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,58968,12575],{"className":58969,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,58972,12570],{"className":58973,"dataFsResolvedFilePath":827,"href":828},[210],[123,58975,58976,2186,58979],{},[38,58977,58978],{},"Shrnutí přednášek:",[207,58980,58982],{"className":58981,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,58984,58985,2186,58987],{},[38,58986,10686],{},[207,58988,10692],{"className":58989,"dataFsResolvedFilePath":10690,"href":10691},[210],{"title":641,"searchDepth":642,"depth":642,"links":58991},[58992,58993,59001,59007,59014,59015,59022,59023,59024,59031,59032,59033],{"id":45014,"depth":642,"text":45015},{"id":44995,"depth":642,"text":21870,"children":58994},[58995,58996,58997,58998,59000],{"id":45283,"depth":649,"text":45284},{"id":45565,"depth":649,"text":45566},{"id":46575,"depth":649,"text":46576},{"id":47143,"depth":649,"text":58999},"Posun poptávky (shift of demand)",{"id":47647,"depth":649,"text":47648},{"id":44999,"depth":642,"text":21834,"children":59002},[59003,59004,59005],{"id":48484,"depth":649,"text":45284},{"id":48670,"depth":649,"text":48671},{"id":49122,"depth":649,"text":59006},"Posun nabídky (shift of supply)",{"id":49544,"depth":642,"text":49545,"children":59008},[59009,59010,59011,59012,59013],{"id":49656,"depth":649,"text":49657},{"id":49869,"depth":649,"text":49870},{"id":50187,"depth":649,"text":50188},{"id":50541,"depth":649,"text":50542},{"id":50572,"depth":649,"text":50573},{"id":50841,"depth":642,"text":811},{"id":51242,"depth":642,"text":51243,"children":59016},[59017,59018,59019,59020],{"id":51260,"depth":649,"text":51261},{"id":51641,"depth":649,"text":51642},{"id":52025,"depth":649,"text":52026},{"id":52479,"depth":649,"text":59021},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":20498,"depth":642,"text":820},{"id":53404,"depth":642,"text":53405},{"id":53635,"depth":642,"text":53636,"children":59025},[59026,59027,59028,59029,59030],{"id":53639,"depth":649,"text":53640},{"id":54479,"depth":649,"text":54480},{"id":54855,"depth":649,"text":49545},{"id":56150,"depth":649,"text":51243},{"id":57906,"depth":649,"text":820},{"id":58101,"depth":642,"text":58102},{"id":10213,"depth":642,"text":10214},{"id":10612,"depth":642,"text":10613},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,59040,59041,59042,26579,59043,59044],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":59047,"title":820,"body":59048,"course":1128,"courses":659,"created":10724,"description":641,"extension":661,"meta":63327,"navigation":664,"path":63328,"seo":63329,"sources":63330,"stem":63331,"tags":63332,"type":10736,"updated":677,"__hash__":63337},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":59049,"toc":63305},[59050,59052,59120,59170,59172,59175,59433,59509,59514,59516,59535,59539,59615,59700,59702,60016,60109,60111,60130,60134,60208,60293,60296,60472,60477,60479,60899,60901,60905,60909,61145,61189,61289,61355,61358,61391,61567,61629,61759,61837,61948,61982,62180,62199,62218,62283,62287,62290,62335,62338,62456,62502,62504,62508,62856,62858,62860,63138,63140,63144,63179,63186,63259,63261,63263],[12,59051,820],{"id":20498},[2140,59053,59054],{},[724,59055,59056,12620,59058,18742,59060,59075,59076,18742,59078,59093,59094,59116,59117,2138],{},[883,59057,12619],{},[38,59059,53154],{},[883,59061,59063],{"className":59062},[886],[888,59064,59065],{"xmlns":890},[892,59066,59067,59073],{},[895,59068,59069,59071],{},[898,59070,11539],{},[898,59072,17398],{},[902,59074,53170],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,59077,53301],{},[883,59079,59081],{"className":59080},[886],[888,59082,59083],{"xmlns":890},[892,59084,59085,59091],{},[895,59086,59087,59089],{},[898,59088,1755],{},[898,59090,17398],{},[902,59092,53189],{"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 ",[883,59095,59097],{"className":59096},[886],[888,59098,59099],{"xmlns":890},[892,59100,59101,59113],{},[895,59102,59103,59105,59107,59109,59111],{},[898,59104,11539],{},[898,59106,17398],{},[1654,59108,1766],{},[898,59110,1755],{},[898,59112,17398],{},[902,59114,59115],{"encoding":904},"CS + PS"," měří ",[38,59118,59119],{},"celkový blahobyt trhu",[724,59121,59122,18742,59124,1343,59126,20840,59141,18742,59143,1343,59145,59160,59161,59165,59166,2138],{},[38,59123,53154],{},[614,59125,53208],{},[883,59127,59129],{"className":59128},[886],[888,59130,59131],{"xmlns":890},[892,59132,59133,59139],{},[895,59134,59135,59137],{},[898,59136,11539],{},[898,59138,17398],{},[902,59140,53170],{"encoding":904},[38,59142,53173],{},[614,59144,53304],{},[883,59146,59148],{"className":59147},[886],[888,59149,59150],{"xmlns":890},[892,59151,59152,59158],{},[895,59153,59154,59156],{},[898,59155,1755],{},[898,59157,17398],{},[902,59159,53189],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,59162,59164],{"className":59163,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,59167,59169],{"className":59168,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[45190,59171],{},[115,59173,1241],{"id":59174},"úvod",[724,59176,59177,59178,59201,59202,59225,59226,59243,59244,12656,59276,59308,59309,59335,59336,59339,59340,59343,59344,22720,59378,9762,59399,2138],{},"Je dána funkce poptávky ",[883,59179,59181],{"className":59180},[886],[888,59182,59183],{"xmlns":890},[892,59184,59185,59199],{},[895,59186,59187,59189,59191,59193,59195,59197],{},[898,59188,1755],{},[1654,59190,1750],{},[898,59192,4980],{},[1654,59194,1708],{"stretchy":1656},[898,59196,1663],{},[1654,59198,1726],{"stretchy":1656},[902,59200,13376],{"encoding":904},", resp. funkce nabídky ",[883,59203,59205],{"className":59204},[886],[888,59206,59207],{"xmlns":890},[892,59208,59209,59223],{},[895,59210,59211,59213,59215,59217,59219,59221],{},[898,59212,1755],{},[1654,59214,1750],{},[898,59216,17398],{},[1654,59218,1708],{"stretchy":1656},[898,59220,1663],{},[1654,59222,1726],{"stretchy":1656},[902,59224,49291],{"encoding":904},". Pro pevně zadané množství ",[883,59227,59229],{"className":59228},[886],[888,59230,59231],{"xmlns":890},[892,59232,59233,59241],{},[895,59234,59235],{},[1710,59236,59237,59239],{},[898,59238,1663],{},[1665,59240,2062],{},[902,59242,46528],{"encoding":904}," je odpovídající cena ",[883,59245,59247],{"className":59246},[886],[888,59248,59249],{"xmlns":890},[892,59250,59251,59273],{},[895,59252,59253,59259,59261,59263,59265,59271],{},[1710,59254,59255,59257],{},[898,59256,1755],{},[1665,59258,2062],{},[1654,59260,1750],{},[898,59262,4980],{},[1654,59264,1708],{"stretchy":1656},[1710,59266,59267,59269],{},[898,59268,1663],{},[1665,59270,2062],{},[1654,59272,1726],{"stretchy":1656},[902,59274,59275],{"encoding":904},"P_0 = D(Q_0)",[883,59277,59279],{"className":59278},[886],[888,59280,59281],{"xmlns":890},[892,59282,59283,59305],{},[895,59284,59285,59291,59293,59295,59297,59303],{},[1710,59286,59287,59289],{},[898,59288,1755],{},[1665,59290,2062],{},[1654,59292,1750],{},[898,59294,17398],{},[1654,59296,1708],{"stretchy":1656},[1710,59298,59299,59301],{},[898,59300,1663],{},[1665,59302,2062],{},[1654,59304,1726],{"stretchy":1656},[902,59306,59307],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,59310,59312],{"className":59311},[886],[888,59313,59314],{"xmlns":890},[892,59315,59316,59332],{},[895,59317,59318,59324,59326],{},[1710,59319,59320,59322],{},[898,59321,1755],{},[1665,59323,2062],{},[1865,59325,11744],{},[1710,59327,59328,59330],{},[898,59329,1663],{},[1665,59331,2062],{},[902,59333,59334],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,59337,59338],{},"výdaje spotřebitele",", nebo ",[38,59341,59342],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,59345,59347],{"className":59346},[886],[888,59348,59349],{"xmlns":890},[892,59350,59351,59375],{},[895,59352,59353,59355,59357,59363,59365,59367,59369],{},[1665,59354,2062],{},[1865,59356,11744],{},[1710,59358,59359,59361],{},[898,59360,1663],{},[1665,59362,2062],{},[1865,59364,11744],{},[898,59366,4737],{},[1865,59368,11744],{},[1710,59370,59371,59373],{},[898,59372,1755],{},[1665,59374,2062],{},[902,59376,59377],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,59379,59381],{"className":59380},[886],[888,59382,59383],{"xmlns":890},[892,59384,59385,59397],{},[895,59386,59387,59389,59391,59393,59395],{},[1654,59388,1708],{"stretchy":1656},[898,59390,1663],{},[1654,59392,1674],{"separator":1673},[898,59394,1755],{},[1654,59396,1726],{"stretchy":1656},[902,59398,45911],{"encoding":904},[883,59400,59402],{"className":59401},[886],[888,59403,59404],{"xmlns":890},[892,59405,59406,59430],{},[895,59407,59408,59410,59412,59414,59420,59422,59428],{},[898,59409,4737],{},[1654,59411,1750],{},[1654,59413,1657],{"stretchy":1656},[1710,59415,59416,59418],{},[898,59417,1663],{},[1665,59419,2062],{},[1654,59421,1674],{"separator":1673},[1710,59423,59424,59426],{},[898,59425,1755],{},[1665,59427,2062],{},[1654,59429,1686],{"stretchy":1656},[902,59431,59432],{"encoding":904},"A = [Q_0, P_0]",[2140,59434,59435,59440,59498],{},[724,59436,59437,59439],{},[883,59438,2860],{}," Intuice",[120,59441,59442,59470],{},[123,59443,59444,59445,59448,59449,59451,59452,59469],{},"Za jednotky zboží nakoupené ",[38,59446,59447],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,59450,33956],{}," než ",[883,59453,59455],{"className":59454},[886],[888,59456,59457],{"xmlns":890},[892,59458,59459,59467],{},[895,59460,59461],{},[1710,59462,59463,59465],{},[898,59464,1755],{},[1665,59466,2062],{},[902,59468,47168],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,59471,59472,59473,59475,59476,59479,59480,59497],{},"Za jednotky zboží prodané ",[38,59474,59447],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,59477,59478],{},"nižší"," cenu než ",[883,59481,59483],{"className":59482},[886],[888,59484,59485],{"xmlns":890},[892,59486,59487,59495],{},[895,59488,59489],{},[1710,59490,59491,59493],{},[898,59492,1755],{},[1665,59494,2062],{},[902,59496,47168],{"encoding":904}," — rozdíl je jeho přebytek.",[724,59499,59500,59501,59504,59505,59508],{},"Přebytek je tedy rozdíl mezi ",[614,59502,59503],{},"ochotou"," (platit \u002F prodávat) a ",[614,59506,59507],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,59510,59511],{},[3492,59512],{"alt":53199,"className":59513,"src":53201},[210,3496],[45190,59515],{},[115,59517,59519,59520,1726],{"id":59518},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,59521,59523],{"className":59522},[886],[888,59524,59525],{"xmlns":890},[892,59526,59527,59533],{},[895,59528,59529,59531],{},[898,59530,11539],{},[898,59532,17398],{},[902,59534,53170],{"encoding":904},[198,59536,59538],{"id":59537},"definice-vzorec-214","Definice (vzorec 2.14)",[724,59540,59541,59542,59565,59566,59583,59584,2781],{},"Pro poptávku ",[883,59543,59545],{"className":59544},[886],[888,59546,59547],{"xmlns":890},[892,59548,59549,59563],{},[895,59550,59551,59553,59555,59557,59559,59561],{},[898,59552,1755],{},[1654,59554,1750],{},[898,59556,4980],{},[1654,59558,1708],{"stretchy":1656},[898,59560,1663],{},[1654,59562,1726],{"stretchy":1656},[902,59564,13376],{"encoding":904}," a pevně zadané ",[883,59567,59569],{"className":59568},[886],[888,59570,59571],{"xmlns":890},[892,59572,59573,59581],{},[895,59574,59575],{},[1710,59576,59577,59579],{},[898,59578,1663],{},[1665,59580,2062],{},[902,59582,46528],{"encoding":904}," s cenou ",[883,59585,59587],{"className":59586},[886],[888,59588,59589],{"xmlns":890},[892,59590,59591,59613],{},[895,59592,59593,59599,59601,59603,59605,59611],{},[1710,59594,59595,59597],{},[898,59596,1755],{},[1665,59598,2062],{},[1654,59600,1750],{},[898,59602,4980],{},[1654,59604,1708],{"stretchy":1656},[1710,59606,59607,59609],{},[898,59608,1663],{},[1665,59610,2062],{},[1654,59612,1726],{"stretchy":1656},[902,59614,59275],{"encoding":904},[883,59616,59618],{"className":59617},[886],[888,59619,59620],{"xmlns":890,"display":1956},[892,59621,59622,59698],{},[1960,59623,59624],{"width":1962},[1964,59625,59626,59628,59692,59694],{},[1967,59627],{"width":1969},[1967,59629,59630],{},[895,59631,59632,59634,59636,59638,59644,59646,59648,59660,59662,59664,59666,59668,59670,59672,59674,59676,59682,59684,59690],{},[898,59633,11539],{},[898,59635,17398],{},[1654,59637,1708],{"stretchy":1656},[1710,59639,59640,59642],{},[898,59641,1663],{},[1665,59643,2062],{},[1654,59645,1726],{"stretchy":1656},[1654,59647,1750],{},[1659,59649,59650,59652,59654],{},[1654,59651,19883],{},[1665,59653,2062],{},[1710,59655,59656,59658],{},[898,59657,1663],{},[1665,59659,2062],{},[898,59661,4980],{},[1654,59663,1708],{"stretchy":1656},[898,59665,1663],{},[1654,59667,1726],{"stretchy":1656},[1865,59669,11744],{},[898,59671,10977],{},[898,59673,1663],{},[1654,59675,2380],{},[1710,59677,59678,59680],{},[898,59679,1755],{},[1665,59681,2062],{},[1865,59683,11744],{},[1710,59685,59686,59688],{},[898,59687,1663],{},[1665,59689,2062],{},[898,59691,2138],{"mathvariant":1878},[1967,59693],{"width":1969},[1967,59695,59696],{},[1865,59697,53293],{},[902,59699,53296],{"encoding":904},[198,59701,11211],{"id":11210},[120,59703,59704,59796,59858],{},[123,59705,59706,59746,59747,59773,59774,59777,59778,59795],{},[883,59707,59709],{"className":59708},[886],[888,59710,59711],{"xmlns":890},[892,59712,59713,59743],{},[895,59714,59715],{},[2582,59716,59717,59729,59731,59733,59735,59737,59739,59741],{"scriptlevel":2062,"displaystyle":1673},[1659,59718,59719,59721,59723],{},[1654,59720,19883],{},[1665,59722,2062],{},[1710,59724,59725,59727],{},[898,59726,1663],{},[1665,59728,2062],{},[898,59730,4980],{},[1654,59732,1708],{"stretchy":1656},[898,59734,1663],{},[1654,59736,1726],{"stretchy":1656},[1865,59738,11744],{},[898,59740,10977],{},[898,59742,1663],{},[902,59744,59745],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,59748,59750],{"className":59749},[886],[888,59751,59752],{"xmlns":890},[892,59753,59754,59770],{},[895,59755,59756,59758,59760,59762,59768],{},[1654,59757,1657],{"stretchy":1656},[1665,59759,2062],{},[1654,59761,1674],{"separator":1673},[1710,59763,59764,59766],{},[898,59765,1663],{},[1665,59767,2062],{},[1654,59769,1686],{"stretchy":1656},[902,59771,59772],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,59775,59776],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,59779,59781],{"className":59780},[886],[888,59782,59783],{"xmlns":890},[892,59784,59785,59793],{},[895,59786,59787],{},[1710,59788,59789,59791],{},[898,59790,1663],{},[1665,59792,2062],{},[902,59794,46528],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,59797,59798,59824,59825,12664],{},[883,59799,59801],{"className":59800},[886],[888,59802,59803],{"xmlns":890},[892,59804,59805,59821],{},[895,59806,59807,59813,59815],{},[1710,59808,59809,59811],{},[898,59810,1755],{},[1665,59812,2062],{},[1865,59814,11744],{},[1710,59816,59817,59819],{},[898,59818,1663],{},[1665,59820,2062],{},[902,59822,59823],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,59826,59828],{"className":59827},[886],[888,59829,59830],{"xmlns":890},[892,59831,59832,59856],{},[895,59833,59834,59836,59838,59844,59846,59848,59850],{},[1665,59835,2062],{},[1865,59837,11744],{},[1710,59839,59840,59842],{},[898,59841,1663],{},[1665,59843,2062],{},[1865,59845,11744],{},[898,59847,4737],{},[1865,59849,11744],{},[1710,59851,59852,59854],{},[898,59853,1755],{},[1665,59855,2062],{},[902,59857,59377],{"encoding":904},[123,59859,59860,59875,59876,59898,59899,59924,59925,9762,59951,2068,59983,2138],{},[883,59861,59863],{"className":59862},[886],[888,59864,59865],{"xmlns":890},[892,59866,59867,59873],{},[895,59868,59869,59871],{},[898,59870,11539],{},[898,59872,17398],{},[902,59874,53170],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,59877,59879],{"className":59878},[886],[888,59880,59881],{"xmlns":890},[892,59882,59883,59895],{},[895,59884,59885,59887,59889],{},[898,59886,1755],{},[1654,59888,1750],{},[1710,59890,59891,59893],{},[898,59892,1755],{},[1665,59894,2062],{},[902,59896,59897],{"encoding":904},"P = P_0"," v pásu ",[883,59900,59902],{"className":59901},[886],[888,59903,59904],{"xmlns":890},[892,59905,59906,59922],{},[895,59907,59908,59910,59912,59914,59920],{},[1654,59909,1657],{"stretchy":1656},[1665,59911,2062],{},[1654,59913,1674],{"separator":1673},[1710,59915,59916,59918],{},[898,59917,1663],{},[1665,59919,2062],{},[1654,59921,1686],{"stretchy":1656},[902,59923,59772],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,59926,59928],{"className":59927},[886],[888,59929,59930],{"xmlns":890},[892,59931,59932,59948],{},[895,59933,59934,59940,59942,59944,59946],{},[1710,59935,59936,59938],{},[898,59937,1755],{},[1665,59939,2062],{},[1865,59941,11744],{},[898,59943,4762],{},[1865,59945,11744],{},[898,59947,4737],{},[902,59949,59950],{"encoding":904},"P_0\\,B\\,A",[883,59952,59954],{"className":59953},[886],[888,59955,59956],{"xmlns":890},[892,59957,59958,59980],{},[895,59959,59960,59962,59964,59966,59968,59970,59972,59974,59976,59978],{},[898,59961,4762],{},[1654,59963,1750],{},[1654,59965,1657],{"stretchy":1656},[1665,59967,2062],{},[1654,59969,1674],{"separator":1673},[898,59971,4980],{},[1654,59973,1708],{"stretchy":1656},[1665,59975,2062],{},[1654,59977,1726],{"stretchy":1656},[1654,59979,1686],{"stretchy":1656},[902,59981,59982],{"encoding":904},"B = [0, D(0)]",[883,59984,59986],{"className":59985},[886],[888,59987,59988],{"xmlns":890},[892,59989,59990,60014],{},[895,59991,59992,59994,59996,59998,60004,60006,60012],{},[898,59993,4737],{},[1654,59995,1750],{},[1654,59997,1657],{"stretchy":1656},[1710,59999,60000,60002],{},[898,60001,1663],{},[1665,60003,2062],{},[1654,60005,1674],{"separator":1673},[1710,60007,60008,60010],{},[898,60009,1755],{},[1665,60011,2062],{},[1654,60013,1686],{"stretchy":1656},[902,60015,59432],{"encoding":904},[724,60017,60018],{},[614,60019,60020,60021,60034,60035,60068,60069,3060,60094,2138],{},"Obrázek 2.24: Křivka poptávky ",[883,60022,60024],{"className":60023},[886],[888,60025,60026],{"xmlns":890},[892,60027,60028,60032],{},[895,60029,60030],{},[898,60031,4980],{},[902,60033,4980],{"encoding":904},", bod ",[883,60036,60038],{"className":60037},[886],[888,60039,60040],{"xmlns":890},[892,60041,60042,60066],{},[895,60043,60044,60046,60048,60050,60056,60058,60064],{},[898,60045,4737],{},[1654,60047,1750],{},[1654,60049,1657],{"stretchy":1656},[1710,60051,60052,60054],{},[898,60053,1663],{},[1665,60055,2062],{},[1654,60057,1674],{"separator":1673},[1710,60059,60060,60062],{},[898,60061,1755],{},[1665,60063,2062],{},[1654,60065,1686],{"stretchy":1656},[902,60067,59432],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,60070,60072],{"className":60071},[886],[888,60073,60074],{"xmlns":890},[892,60075,60076,60092],{},[895,60077,60078,60084,60086,60088,60090],{},[1710,60079,60080,60082],{},[898,60081,1755],{},[1665,60083,2062],{},[1865,60085,11744],{},[898,60087,4762],{},[1865,60089,11744],{},[898,60091,4737],{},[902,60093,59950],{"encoding":904},[883,60095,60097],{"className":60096},[886],[888,60098,60099],{"xmlns":890},[892,60100,60101,60107],{},[895,60102,60103,60105],{},[898,60104,11539],{},[898,60106,17398],{},[902,60108,53170],{"encoding":904},[45190,60110],{},[115,60112,60114,60115,1726],{"id":60113},"přebytek-výrobce-psps","Přebytek výrobce (",[883,60116,60118],{"className":60117},[886],[888,60119,60120],{"xmlns":890},[892,60121,60122,60128],{},[895,60123,60124,60126],{},[898,60125,1755],{},[898,60127,17398],{},[902,60129,53189],{"encoding":904},[198,60131,60133],{"id":60132},"definice-vzorec-215","Definice (vzorec 2.15)",[724,60135,60136,60137,59565,60160,59583,60177,2781],{},"Analogicky — pro nabídku ",[883,60138,60140],{"className":60139},[886],[888,60141,60142],{"xmlns":890},[892,60143,60144,60158],{},[895,60145,60146,60148,60150,60152,60154,60156],{},[898,60147,1755],{},[1654,60149,1750],{},[898,60151,17398],{},[1654,60153,1708],{"stretchy":1656},[898,60155,1663],{},[1654,60157,1726],{"stretchy":1656},[902,60159,49291],{"encoding":904},[883,60161,60163],{"className":60162},[886],[888,60164,60165],{"xmlns":890},[892,60166,60167,60175],{},[895,60168,60169],{},[1710,60170,60171,60173],{},[898,60172,1663],{},[1665,60174,2062],{},[902,60176,46528],{"encoding":904},[883,60178,60180],{"className":60179},[886],[888,60181,60182],{"xmlns":890},[892,60183,60184,60206],{},[895,60185,60186,60192,60194,60196,60198,60204],{},[1710,60187,60188,60190],{},[898,60189,1755],{},[1665,60191,2062],{},[1654,60193,1750],{},[898,60195,17398],{},[1654,60197,1708],{"stretchy":1656},[1710,60199,60200,60202],{},[898,60201,1663],{},[1665,60203,2062],{},[1654,60205,1726],{"stretchy":1656},[902,60207,59307],{"encoding":904},[883,60209,60211],{"className":60210},[886],[888,60212,60213],{"xmlns":890,"display":1956},[892,60214,60215,60291],{},[1960,60216,60217],{"width":1962},[1964,60218,60219,60221,60285,60287],{},[1967,60220],{"width":1969},[1967,60222,60223],{},[895,60224,60225,60227,60229,60231,60237,60239,60241,60247,60249,60255,60257,60269,60271,60273,60275,60277,60279,60281,60283],{},[898,60226,1755],{},[898,60228,17398],{},[1654,60230,1708],{"stretchy":1656},[1710,60232,60233,60235],{},[898,60234,1663],{},[1665,60236,2062],{},[1654,60238,1726],{"stretchy":1656},[1654,60240,1750],{},[1710,60242,60243,60245],{},[898,60244,1755],{},[1665,60246,2062],{},[1865,60248,11744],{},[1710,60250,60251,60253],{},[898,60252,1663],{},[1665,60254,2062],{},[1654,60256,2380],{},[1659,60258,60259,60261,60263],{},[1654,60260,19883],{},[1665,60262,2062],{},[1710,60264,60265,60267],{},[898,60266,1663],{},[1665,60268,2062],{},[898,60270,17398],{},[1654,60272,1708],{"stretchy":1656},[898,60274,1663],{},[1654,60276,1726],{"stretchy":1656},[1865,60278,11744],{},[898,60280,10977],{},[898,60282,1663],{},[898,60284,2138],{"mathvariant":1878},[1967,60286],{"width":1969},[1967,60288,60289],{},[1865,60290,53389],{},[902,60292,53392],{"encoding":904},[198,60294,11211],{"id":60295},"geometrická-interpretace-1",[120,60297,60298,60346,60407],{},[123,60299,60300,10373,60325,60328,60329,2138],{},[883,60301,60303],{"className":60302},[886],[888,60304,60305],{"xmlns":890},[892,60306,60307,60323],{},[895,60308,60309,60315,60317],{},[1710,60310,60311,60313],{},[898,60312,1755],{},[1665,60314,2062],{},[1865,60316,11744],{},[1710,60318,60319,60321],{},[898,60320,1663],{},[1665,60322,2062],{},[902,60324,59823],{"encoding":904},[38,60326,60327],{},"tržba"," výrobce za prodané množství ",[883,60330,60332],{"className":60331},[886],[888,60333,60334],{"xmlns":890},[892,60335,60336,60344],{},[895,60337,60338],{},[1710,60339,60340,60342],{},[898,60341,1663],{},[1665,60343,2062],{},[902,60345,46528],{"encoding":904},[123,60347,60348,60388,60389,60406],{},[883,60349,60351],{"className":60350},[886],[888,60352,60353],{"xmlns":890},[892,60354,60355,60385],{},[895,60356,60357],{},[2582,60358,60359,60371,60373,60375,60377,60379,60381,60383],{"scriptlevel":2062,"displaystyle":1673},[1659,60360,60361,60363,60365],{},[1654,60362,19883],{},[1665,60364,2062],{},[1710,60366,60367,60369],{},[898,60368,1663],{},[1665,60370,2062],{},[898,60372,17398],{},[1654,60374,1708],{"stretchy":1656},[898,60376,1663],{},[1654,60378,1726],{"stretchy":1656},[1865,60380,11744],{},[898,60382,10977],{},[898,60384,1663],{},[902,60386,60387],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,60390,60392],{"className":60391},[886],[888,60393,60394],{"xmlns":890},[892,60395,60396,60404],{},[895,60397,60398],{},[1710,60399,60400,60402],{},[898,60401,1663],{},[1665,60403,2062],{},[902,60405,46528],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,60408,60409,60424,60425,60446,60447,2138],{},[883,60410,60412],{"className":60411},[886],[888,60413,60414],{"xmlns":890},[892,60415,60416,60422],{},[895,60417,60418,60420],{},[898,60419,1755],{},[898,60421,17398],{},[902,60423,53189],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,60426,60428],{"className":60427},[886],[888,60429,60430],{"xmlns":890},[892,60431,60432,60444],{},[895,60433,60434,60436,60438],{},[898,60435,1755],{},[1654,60437,1750],{},[1710,60439,60440,60442],{},[898,60441,1755],{},[1665,60443,2062],{},[902,60445,59897],{"encoding":904}," a křivkou nabídky v pásu ",[883,60448,60450],{"className":60449},[886],[888,60451,60452],{"xmlns":890},[892,60453,60454,60470],{},[895,60455,60456,60458,60460,60462,60468],{},[1654,60457,1657],{"stretchy":1656},[1665,60459,2062],{},[1654,60461,1674],{"separator":1673},[1710,60463,60464,60466],{},[898,60465,1663],{},[1665,60467,2062],{},[1654,60469,1686],{"stretchy":1656},[902,60471,59772],{"encoding":904},[724,60473,60474],{},[614,60475,60476],{},"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.",[45190,60478],{},[2140,60480,60481,60486],{},[724,60482,60483,60485],{},[883,60484,3111],{}," Postup výpočtu CS a PS",[152,60487,60488,60619,60729,60758,60892],{},[123,60489,60490,60491,60508,60509,60540,60541,60572,60573,2138],{},"Zjisti (nebo si zvol) množství ",[883,60492,60494],{"className":60493},[886],[888,60495,60496],{"xmlns":890},[892,60497,60498,60506],{},[895,60499,60500],{},[1710,60501,60502,60504],{},[898,60503,1663],{},[1665,60505,2062],{},[902,60507,46528],{"encoding":904}," a odpovídající cenu ",[883,60510,60512],{"className":60511},[886],[888,60513,60514],{"xmlns":890},[892,60515,60516,60538],{},[895,60517,60518,60524,60526,60528,60530,60536],{},[1710,60519,60520,60522],{},[898,60521,1755],{},[1665,60523,2062],{},[1654,60525,1750],{},[898,60527,4980],{},[1654,60529,1708],{"stretchy":1656},[1710,60531,60532,60534],{},[898,60533,1663],{},[1665,60535,2062],{},[1654,60537,1726],{"stretchy":1656},[902,60539,59275],{"encoding":904}," resp. ",[883,60542,60544],{"className":60543},[886],[888,60545,60546],{"xmlns":890},[892,60547,60548,60570],{},[895,60549,60550,60556,60558,60560,60562,60568],{},[1710,60551,60552,60554],{},[898,60553,1755],{},[1665,60555,2062],{},[1654,60557,1750],{},[898,60559,17398],{},[1654,60561,1708],{"stretchy":1656},[1710,60563,60564,60566],{},[898,60565,1663],{},[1665,60567,2062],{},[1654,60569,1726],{"stretchy":1656},[902,60571,59307],{"encoding":904},". V rovnováze platí ",[883,60574,60576],{"className":60575},[886],[888,60577,60578],{"xmlns":890},[892,60579,60580,60616],{},[895,60581,60582,60584,60586,60592,60594,60596,60598,60600,60606,60608,60610],{},[898,60583,4980],{},[1654,60585,1708],{"stretchy":1656},[1741,60587,60588,60590],{},[898,60589,1663],{},[898,60591,1798],{},[1654,60593,1726],{"stretchy":1656},[1654,60595,1750],{},[898,60597,17398],{},[1654,60599,1708],{"stretchy":1656},[1741,60601,60602,60604],{},[898,60603,1663],{},[898,60605,1798],{},[1654,60607,1726],{"stretchy":1656},[1654,60609,1750],{},[1741,60611,60612,60614],{},[898,60613,1755],{},[898,60615,1798],{},[902,60617,60618],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,60620,60621,60622,28821,60660,60675,60676,28821,60714,12664],{},"Spočti určitý integrál ",[883,60623,60625],{"className":60624},[886],[888,60626,60627],{"xmlns":890},[892,60628,60629,60657],{},[895,60630,60631,60643,60645,60647,60649,60651,60653,60655],{},[1659,60632,60633,60635,60637],{},[1654,60634,19883],{},[1665,60636,2062],{},[1710,60638,60639,60641],{},[898,60640,1663],{},[1665,60642,2062],{},[898,60644,4980],{},[1654,60646,1708],{"stretchy":1656},[898,60648,1663],{},[1654,60650,1726],{"stretchy":1656},[1865,60652,11744],{},[898,60654,10977],{},[898,60656,1663],{},[902,60658,60659],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,60661,60663],{"className":60662},[886],[888,60664,60665],{"xmlns":890},[892,60666,60667,60673],{},[895,60668,60669,60671],{},[898,60670,11539],{},[898,60672,17398],{},[902,60674,53170],{"encoding":904},") nebo ",[883,60677,60679],{"className":60678},[886],[888,60680,60681],{"xmlns":890},[892,60682,60683,60711],{},[895,60684,60685,60697,60699,60701,60703,60705,60707,60709],{},[1659,60686,60687,60689,60691],{},[1654,60688,19883],{},[1665,60690,2062],{},[1710,60692,60693,60695],{},[898,60694,1663],{},[1665,60696,2062],{},[898,60698,17398],{},[1654,60700,1708],{"stretchy":1656},[898,60702,1663],{},[1654,60704,1726],{"stretchy":1656},[1865,60706,11744],{},[898,60708,10977],{},[898,60710,1663],{},[902,60712,60713],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,60715,60717],{"className":60716},[886],[888,60718,60719],{"xmlns":890},[892,60720,60721,60727],{},[895,60722,60723,60725],{},[898,60724,1755],{},[898,60726,17398],{},[902,60728,53189],{"encoding":904},[123,60730,60731,60732,2138],{},"Sestav obdélník ",[883,60733,60735],{"className":60734},[886],[888,60736,60737],{"xmlns":890},[892,60738,60739,60755],{},[895,60740,60741,60747,60749],{},[1710,60742,60743,60745],{},[898,60744,1755],{},[1665,60746,2062],{},[1654,60748,4554],{},[1710,60750,60751,60753],{},[898,60752,1663],{},[1665,60754,2062],{},[902,60756,60757],{"encoding":904},"P_0 \\cdot Q_0",[123,60759,60760,60761],{},"Dosaď:\n",[120,60762,60763,60828],{},[123,60764,60765,60823,60824,60827],{},[883,60766,60768],{"className":60767},[886],[888,60769,60770],{"xmlns":890},[892,60771,60772,60820],{},[895,60773,60774,60776,60778,60780,60792,60794,60796,60798,60800,60802,60804,60806,60808,60814],{},[898,60775,11539],{},[898,60777,17398],{},[1654,60779,1750],{},[1659,60781,60782,60784,60786],{},[1654,60783,19883],{},[1665,60785,2062],{},[1710,60787,60788,60790],{},[898,60789,1663],{},[1665,60791,2062],{},[898,60793,4980],{},[1654,60795,1708],{"stretchy":1656},[898,60797,1663],{},[1654,60799,1726],{"stretchy":1656},[1865,60801,11744],{},[898,60803,10977],{},[898,60805,1663],{},[1654,60807,2380],{},[1710,60809,60810,60812],{},[898,60811,1755],{},[1665,60813,2062],{},[1710,60815,60816,60818],{},[898,60817,1663],{},[1665,60819,2062],{},[902,60821,60822],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,60825,60826],{},"mínus"," obdélník)",[123,60829,60830,60888,60889,60891],{},[883,60831,60833],{"className":60832},[886],[888,60834,60835],{"xmlns":890},[892,60836,60837,60885],{},[895,60838,60839,60841,60843,60845,60851,60857,60859,60871,60873,60875,60877,60879,60881,60883],{},[898,60840,1755],{},[898,60842,17398],{},[1654,60844,1750],{},[1710,60846,60847,60849],{},[898,60848,1755],{},[1665,60850,2062],{},[1710,60852,60853,60855],{},[898,60854,1663],{},[1665,60856,2062],{},[1654,60858,2380],{},[1659,60860,60861,60863,60865],{},[1654,60862,19883],{},[1665,60864,2062],{},[1710,60866,60867,60869],{},[898,60868,1663],{},[1665,60870,2062],{},[898,60872,17398],{},[1654,60874,1708],{"stretchy":1656},[898,60876,1663],{},[1654,60878,1726],{"stretchy":1656},[1865,60880,11744],{},[898,60882,10977],{},[898,60884,1663],{},[902,60886,60887],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,60890,60826],{}," integrál)",[123,60893,60894,60895,60898],{},"Kontrola znaménka: obě hodnoty musí být ",[38,60896,60897],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[45190,60900],{},[115,60902,60904],{"id":60903},"příklady","Příklady",[198,60906,60908],{"id":60907},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[2140,60910,60911],{},[724,60912,60913,60916,60917,55941,60940,60963,60964,1343,60984,1343,61001,1343,61018,61035,61036,61112,61113,61130,61131,61144],{},[883,60914,60915],{},"!example"," Zadání\nJsou dány poptávka ",[883,60918,60920],{"className":60919},[886],[888,60921,60922],{"xmlns":890},[892,60923,60924,60938],{},[895,60925,60926,60928,60930,60932,60934,60936],{},[898,60927,1755],{},[1654,60929,1750],{},[898,60931,207],{},[898,60933,1663],{},[1654,60935,1766],{},[898,60937,9758],{},[902,60939,45280],{"encoding":904},[883,60941,60943],{"className":60942},[886],[888,60944,60945],{"xmlns":890},[892,60946,60947,60961],{},[895,60948,60949,60951,60953,60955,60957,60959],{},[898,60950,1755],{},[1654,60952,1750],{},[898,60954,3624],{},[898,60956,1663],{},[1654,60958,1766],{},[898,60960,10977],{},[902,60962,48462],{"encoding":904}," s hodnotami ",[883,60965,60967],{"className":60966},[886],[888,60968,60969],{"xmlns":890},[892,60970,60971,60981],{},[895,60972,60973,60975,60977,60979],{},[898,60974,207],{},[1654,60976,1750],{},[1654,60978,2380],{},[1665,60980,4035],{},[902,60982,60983],{"encoding":904},"a = -3",[883,60985,60987],{"className":60986},[886],[888,60988,60989],{"xmlns":890},[892,60990,60991,60999],{},[895,60992,60993,60995,60997],{},[898,60994,9758],{},[1654,60996,1750],{},[1665,60998,5844],{},[902,61000,56864],{"encoding":904},[883,61002,61004],{"className":61003},[886],[888,61005,61006],{"xmlns":890},[892,61007,61008,61016],{},[895,61009,61010,61012,61014],{},[898,61011,3624],{},[1654,61013,1750],{},[1665,61015,7594],{},[902,61017,56882],{"encoding":904},[883,61019,61021],{"className":61020},[886],[888,61022,61023],{"xmlns":890},[892,61024,61025,61033],{},[895,61026,61027,61029,61031],{},[898,61028,10977],{},[1654,61030,1750],{},[1665,61032,4647],{},[902,61034,56900],{"encoding":904},".\nRovnovážné množství:\n",[883,61037,61039],{"className":61038},[886],[888,61040,61041],{"xmlns":890},[892,61042,61043,61109],{},[895,61044,61045,61051,61053,61071,61073,61097,61099,61105,61107],{},[1741,61046,61047,61049],{},[898,61048,1663],{},[898,61050,1798],{},[1654,61052,1750],{},[2811,61054,61055,61063],{},[895,61056,61057,61059,61061],{},[898,61058,9758],{},[1654,61060,2380],{},[898,61062,10977],{},[895,61064,61065,61067,61069],{},[898,61066,3624],{},[1654,61068,2380],{},[898,61070,207],{},[1654,61072,1750],{},[2811,61074,61075,61083],{},[895,61076,61077,61079,61081],{},[1665,61078,5844],{},[1654,61080,2380],{},[1665,61082,4647],{},[895,61084,61085,61087,61089,61091,61093,61095],{},[1665,61086,7594],{},[1654,61088,2380],{},[1654,61090,1708],{"stretchy":1656},[1654,61092,2380],{},[1665,61094,4035],{},[1654,61096,1726],{"stretchy":1656},[1654,61098,1750],{},[2811,61100,61101,61103],{},[1665,61102,46239],{},[1665,61104,52626],{},[1654,61106,14628],{},[1665,61108,52631],{},[902,61110,61111],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,61114,61116],{"className":61115},[886],[888,61117,61118],{"xmlns":890},[892,61119,61120,61128],{},[895,61121,61122],{},[1741,61123,61124,61126],{},[898,61125,1663],{},[898,61127,1798],{},[902,61129,50623],{"encoding":904}," (a) při změně samotného parametru ",[883,61132,61134],{"className":61133},[886],[888,61135,61136],{"xmlns":890},[892,61137,61138,61142],{},[895,61139,61140],{},[898,61141,3624],{},[902,61143,3624],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,61146,61147],{},[38,61148,61149,61150,11434,61163,11448,61176,18016],{},"Řešení (a) — změna ",[883,61151,61153],{"className":61152},[886],[888,61154,61155],{"xmlns":890},[892,61156,61157,61161],{},[895,61158,61159],{},[898,61160,3624],{},[902,61162,3624],{"encoding":904},[883,61164,61166],{"className":61165},[886],[888,61167,61168],{"xmlns":890},[892,61169,61170,61174],{},[895,61171,61172],{},[1665,61173,7594],{},[902,61175,52666],{"encoding":904},[883,61177,61179],{"className":61178},[886],[888,61180,61181],{"xmlns":890},[892,61182,61183,61187],{},[895,61184,61185],{},[1665,61186,28017],{},[902,61188,52680],{"encoding":904},[724,61190,61191,61192,61256,61257,2781],{},"Pomocí vzorce (2.13) pro ",[883,61193,61195],{"className":61194},[886],[888,61196,61197],{"xmlns":890},[892,61198,61199,61253],{},[895,61200,61201,61221,61223,61225],{},[2582,61202,61203],{"scriptlevel":2062,"displaystyle":1673},[2811,61204,61205,61215],{},[895,61206,61207,61209],{},[898,61208,18589],{"mathvariant":1878},[1741,61210,61211,61213],{},[898,61212,1663],{},[898,61214,1798],{},[895,61216,61217,61219],{},[898,61218,18589],{"mathvariant":1878},[898,61220,3624],{},[1654,61222,1750],{},[1654,61224,2380],{},[2582,61226,61227],{"scriptlevel":2062,"displaystyle":1673},[2811,61228,61229,61237],{},[895,61230,61231,61233,61235],{},[898,61232,9758],{},[1654,61234,2380],{},[898,61236,10977],{},[895,61238,61239,61241,61243,61245,61247],{},[1654,61240,1708],{"stretchy":1656},[898,61242,3624],{},[1654,61244,2380],{},[898,61246,207],{},[1741,61248,61249,61251],{},[1654,61250,1726],{"stretchy":1656},[1665,61252,1681],{},[902,61254,61255],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,61258,61260],{"className":61259},[886],[888,61261,61262],{"xmlns":890},[892,61263,61264,61286],{},[895,61265,61266,61268],{},[1654,61267,2380],{},[2582,61269,61270],{"scriptlevel":2062,"displaystyle":1673},[2811,61271,61272,61278],{},[1741,61273,61274,61276],{},[898,61275,1663],{},[898,61277,1798],{},[895,61279,61280,61282,61284],{},[898,61281,3624],{},[1654,61283,2380],{},[898,61285,207],{},[902,61287,61288],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,61290,61292],{"className":61291},[886],[888,61293,61294],{"xmlns":890,"display":1956},[892,61295,61296,61352],{},[895,61297,61298,61300,61306,61308,61310,61326,61328,61330,61332,61334,61336,61342,61344,61346,61348,61350],{},[898,61299,10977],{},[1741,61301,61302,61304],{},[898,61303,1663],{},[898,61305,1798],{},[1654,61307,1750],{},[1654,61309,2380],{},[2811,61311,61312,61318],{},[1741,61313,61314,61316],{},[898,61315,1663],{},[898,61317,1798],{},[895,61319,61320,61322,61324],{},[898,61321,3624],{},[1654,61323,2380],{},[898,61325,207],{},[1865,61327,11744],{},[898,61329,10977],{},[898,61331,3624],{},[1654,61333,1750],{},[1654,61335,2380],{},[2811,61337,61338,61340],{},[1665,61339,52794],{},[1665,61341,52626],{},[1654,61343,4554],{},[1665,61345,11555],{},[1654,61347,14628],{},[1654,61349,2380],{},[1665,61351,52766],{},[902,61353,61354],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,61356,61357],{},"Nové rovnovážné množství:",[883,61359,61361],{"className":61360},[886],[888,61362,61363],{"xmlns":890,"display":1956},[892,61364,61365,61388],{},[895,61366,61367,61375,61377,61379,61381,61383,61385],{},[1659,61368,61369,61371,61373],{},[898,61370,1663],{},[1665,61372,1667],{},[898,61374,1798],{},[1654,61376,11492],{},[1665,61378,52794],{},[1654,61380,2380],{},[1665,61382,52799],{},[1654,61384,1750],{},[1665,61386,61387],{},"8,326.",[902,61389,61390],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,61392,61393,2186,61396,1343,61423,1343,61445,1343,61467,4579,61489,1343,61508,1343,61529,1343,61548,2138],{},[38,61394,61395],{},"Řešení (b) — současná změna všech parametrů:",[883,61397,61399],{"className":61398},[886],[888,61400,61401],{"xmlns":890},[892,61402,61403,61420],{},[895,61404,61405,61407,61409,61411,61413,61415,61417],{},[898,61406,207],{},[1654,61408,2781],{},[1654,61410,2380],{},[1665,61412,4035],{},[1654,61414,11878],{},[1654,61416,2380],{},[1665,61418,61419],{},"2,5",[902,61421,61422],{"encoding":904},"a: -3 \\to -2{,}5",[883,61424,61426],{"className":61425},[886],[888,61427,61428],{"xmlns":890},[892,61429,61430,61442],{},[895,61431,61432,61434,61436,61438,61440],{},[898,61433,9758],{},[1654,61435,2781],{},[1665,61437,5844],{},[1654,61439,11878],{},[1665,61441,23747],{},[902,61443,61444],{"encoding":904},"b: 40 \\to 35",[883,61446,61448],{"className":61447},[886],[888,61449,61450],{"xmlns":890},[892,61451,61452,61464],{},[895,61453,61454,61456,61458,61460,61462],{},[898,61455,3624],{},[1654,61457,2781],{},[1665,61459,7594],{},[1654,61461,11878],{},[1665,61463,28017],{},[902,61465,61466],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,61468,61470],{"className":61469},[886],[888,61471,61472],{"xmlns":890},[892,61473,61474,61486],{},[895,61475,61476,61478,61480,61482,61484],{},[898,61477,10977],{},[1654,61479,2781],{},[1665,61481,4647],{},[1654,61483,11878],{},[1665,61485,6477],{},[902,61487,61488],{"encoding":904},"d: 10 \\to 11",[883,61490,61492],{"className":61491},[886],[888,61493,61494],{"xmlns":890},[892,61495,61496,61506],{},[895,61497,61498,61500,61502,61504],{},[898,61499,10977],{},[898,61501,207],{},[1654,61503,1750],{},[1665,61505,7594],{},[902,61507,52832],{"encoding":904},[883,61509,61511],{"className":61510},[886],[888,61512,61513],{"xmlns":890},[892,61514,61515,61527],{},[895,61516,61517,61519,61521,61523,61525],{},[898,61518,10977],{},[898,61520,9758],{},[1654,61522,1750],{},[1654,61524,2380],{},[1665,61526,4032],{},[902,61528,52854],{"encoding":904},[883,61530,61532],{"className":61531},[886],[888,61533,61534],{"xmlns":890},[892,61535,61536,61546],{},[895,61537,61538,61540,61542,61544],{},[898,61539,10977],{},[898,61541,3624],{},[1654,61543,1750],{},[1665,61545,11555],{},[902,61547,52874],{"encoding":904},[883,61549,61551],{"className":61550},[886],[888,61552,61553],{"xmlns":890},[892,61554,61555,61565],{},[895,61556,61557,61559,61561,61563],{},[898,61558,10977],{},[898,61560,10977],{},[1654,61562,1750],{},[1665,61564,1667],{},[902,61566,52894],{"encoding":904},[724,61568,61569,61570,61628],{},"Totální diferenciál ",[883,61571,61573],{"className":61572},[886],[888,61574,61575],{"xmlns":890},[892,61576,61577,61625],{},[895,61578,61579,61585,61587,61589,61591,61593,61595,61597,61599,61601,61603,61605],{},[1741,61580,61581,61583],{},[898,61582,1663],{},[898,61584,1798],{},[1654,61586,1708],{"stretchy":1656},[898,61588,207],{},[1654,61590,1674],{"separator":1673},[898,61592,9758],{},[1654,61594,1674],{"separator":1673},[898,61596,3624],{},[1654,61598,1674],{"separator":1673},[898,61600,10977],{},[1654,61602,1726],{"stretchy":1656},[1654,61604,1750],{},[2582,61606,61607],{"scriptlevel":2062,"displaystyle":1673},[2811,61608,61609,61617],{},[895,61610,61611,61613,61615],{},[898,61612,9758],{},[1654,61614,2380],{},[898,61616,10977],{},[895,61618,61619,61621,61623],{},[898,61620,3624],{},[1654,61622,2380],{},[898,61624,207],{},[902,61626,61627],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,61630,61632],{"className":61631},[886],[888,61633,61634],{"xmlns":890,"display":1956},[892,61635,61636,61756],{},[895,61637,61638,61640,61646,61648,61674,61676,61678,61680,61682,61694,61696,61698,61700,61702,61728,61730,61732,61734,61736,61748,61750,61752,61754],{},[898,61639,10977],{},[1741,61641,61642,61644],{},[898,61643,1663],{},[898,61645,1798],{},[1654,61647,1750],{},[2811,61649,61650,61658],{},[895,61651,61652,61654,61656],{},[898,61653,9758],{},[1654,61655,2380],{},[898,61657,10977],{},[895,61659,61660,61662,61664,61666,61668],{},[1654,61661,1708],{"stretchy":1656},[898,61663,3624],{},[1654,61665,2380],{},[898,61667,207],{},[1741,61669,61670,61672],{},[1654,61671,1726],{"stretchy":1656},[1665,61673,1681],{},[1865,61675,11744],{},[898,61677,10977],{},[898,61679,207],{},[1654,61681,1766],{},[2811,61683,61684,61686],{},[1665,61685,1667],{},[895,61687,61688,61690,61692],{},[898,61689,3624],{},[1654,61691,2380],{},[898,61693,207],{},[1865,61695,11744],{},[898,61697,10977],{},[898,61699,9758],{},[1654,61701,2380],{},[2811,61703,61704,61712],{},[895,61705,61706,61708,61710],{},[898,61707,9758],{},[1654,61709,2380],{},[898,61711,10977],{},[895,61713,61714,61716,61718,61720,61722],{},[1654,61715,1708],{"stretchy":1656},[898,61717,3624],{},[1654,61719,2380],{},[898,61721,207],{},[1741,61723,61724,61726],{},[1654,61725,1726],{"stretchy":1656},[1665,61727,1681],{},[1865,61729,11744],{},[898,61731,10977],{},[898,61733,3624],{},[1654,61735,2380],{},[2811,61737,61738,61740],{},[1665,61739,1667],{},[895,61741,61742,61744,61746],{},[898,61743,3624],{},[1654,61745,2380],{},[898,61747,207],{},[1865,61749,11744],{},[898,61751,10977],{},[898,61753,10977],{},[898,61755,2138],{"mathvariant":1878},[902,61757,61758],{"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.",[724,61760,61761,61762,1343,61784,1343,61815,11906],{},"Dosazením číselných hodnot (",[883,61763,61765],{"className":61764},[886],[888,61766,61767],{"xmlns":890},[892,61768,61769,61781],{},[895,61770,61771,61773,61775,61777,61779],{},[898,61772,3624],{},[1654,61774,2380],{},[898,61776,207],{},[1654,61778,1750],{},[1665,61780,52626],{},[902,61782,61783],{"encoding":904},"c - a = 3{,}5",[883,61785,61787],{"className":61786},[886],[888,61788,61789],{"xmlns":890},[892,61790,61791,61812],{},[895,61792,61793,61795,61797,61799,61801,61807,61809],{},[1654,61794,1708],{"stretchy":1656},[898,61796,3624],{},[1654,61798,2380],{},[898,61800,207],{},[1741,61802,61803,61805],{},[1654,61804,1726],{"stretchy":1656},[1665,61806,1681],{},[1654,61808,1750],{},[1665,61810,61811],{},"12,25",[902,61813,61814],{"encoding":904},"(c-a)^2 = 12{,}25",[883,61816,61818],{"className":61817},[886],[888,61819,61820],{"xmlns":890},[892,61821,61822,61834],{},[895,61823,61824,61826,61828,61830,61832],{},[898,61825,9758],{},[1654,61827,2380],{},[898,61829,10977],{},[1654,61831,1750],{},[1665,61833,46239],{},[902,61835,61836],{"encoding":904},"b - d = 30",[883,61838,61840],{"className":61839},[886],[888,61841,61842],{"xmlns":890,"display":1956},[892,61843,61844,61945],{},[895,61845,61846,61848,61854,61856,61864,61866,61868,61870,61872,61880,61882,61884,61886,61888,61890,61898,61900,61902,61904,61906,61914,61916,61918,61920,61922,61925,61927,61930,61932,61934,61936,61939,61941,61943],{},[898,61847,10977],{},[1741,61849,61850,61852],{},[898,61851,1663],{},[898,61853,1798],{},[1654,61855,11492],{},[2582,61857,61858],{"scriptlevel":2062,"displaystyle":1656},[2811,61859,61860,61862],{},[1665,61861,46239],{},[1665,61863,61811],{},[1654,61865,1708],{"stretchy":1656},[1665,61867,7594],{},[1654,61869,1726],{"stretchy":1656},[1654,61871,1766],{},[2582,61873,61874],{"scriptlevel":2062,"displaystyle":1656},[2811,61875,61876,61878],{},[1665,61877,1667],{},[1665,61879,52626],{},[1654,61881,1708],{"stretchy":1656},[1654,61883,2380],{},[1665,61885,4032],{},[1654,61887,1726],{"stretchy":1656},[1654,61889,2380],{},[2582,61891,61892],{"scriptlevel":2062,"displaystyle":1656},[2811,61893,61894,61896],{},[1665,61895,46239],{},[1665,61897,61811],{},[1654,61899,1708],{"stretchy":1656},[1665,61901,11555],{},[1654,61903,1726],{"stretchy":1656},[1654,61905,2380],{},[2582,61907,61908],{"scriptlevel":2062,"displaystyle":1656},[2811,61909,61910,61912],{},[1665,61911,1667],{},[1665,61913,52626],{},[1654,61915,1708],{"stretchy":1656},[1665,61917,1667],{},[1654,61919,1726],{"stretchy":1656},[1654,61921,14628],{},[1665,61923,61924],{},"1,224",[1654,61926,2380],{},[1665,61928,61929],{},"1,429",[1654,61931,2380],{},[1665,61933,52799],{},[1654,61935,2380],{},[1665,61937,61938],{},"0,286",[1654,61940,14628],{},[1654,61942,2380],{},[1665,61944,53045],{},[902,61946,61947],{"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.",[724,61949,3990,61950,2138],{},[883,61951,61953],{"className":61952},[886],[888,61954,61955],{"xmlns":890},[892,61956,61957,61979],{},[895,61958,61959,61967,61969,61971,61973,61975,61977],{},[1659,61960,61961,61963,61965],{},[898,61962,1663],{},[1665,61964,1667],{},[898,61966,1798],{},[1654,61968,11492],{},[1665,61970,52794],{},[1654,61972,2380],{},[1665,61974,53076],{},[1654,61976,14628],{},[1665,61978,53081],{},[902,61980,61981],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[2140,61983,61984],{},[724,61985,61986,61988,61989,62010,62011,62037,62038,62041,62042,62138,62139,62162,62163,62179],{},[883,61987,2146],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,61990,61992],{"className":61991},[886],[888,61993,61994],{"xmlns":890},[892,61995,61996,62008],{},[895,61997,61998,62000,62002,62004,62006],{},[898,61999,11648],{"mathvariant":1878},[898,62001,1663],{},[1654,62003,11492],{},[1654,62005,2380],{},[1665,62007,53111],{},[902,62009,53114],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,62012,62014],{"className":62013},[886],[888,62015,62016],{"xmlns":890},[892,62017,62018,62034],{},[895,62019,62020,62022,62028,62030,62032],{},[898,62021,10977],{},[1741,62023,62024,62026],{},[898,62025,1663],{},[898,62027,1798],{},[1654,62029,14628],{},[1654,62031,2380],{},[1665,62033,53076],{},[902,62035,62036],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,62039,62040],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,62043,62045],{"className":62044},[886],[888,62046,62047],{"xmlns":890},[892,62048,62049,62135],{},[895,62050,62051,62059,62061,62095,62097,62121,62123,62130,62132],{},[1659,62052,62053,62055,62057],{},[898,62054,1663],{},[1665,62056,1667],{},[898,62058,1798],{},[1654,62060,1750],{},[2811,62062,62063,62079],{},[895,62064,62065,62071,62073],{},[1741,62066,62067,62069],{},[898,62068,9758],{},[1654,62070,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,62072,2380],{},[1741,62074,62075,62077],{},[898,62076,10977],{},[1654,62078,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[895,62080,62081,62087,62089],{},[1741,62082,62083,62085],{},[898,62084,3624],{},[1654,62086,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,62088,2380],{},[1741,62090,62091,62093],{},[898,62092,207],{},[1654,62094,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,62096,1750],{},[2811,62098,62099,62107],{},[895,62100,62101,62103,62105],{},[1665,62102,23747],{},[1654,62104,2380],{},[1665,62106,6477],{},[895,62108,62109,62111,62113,62115,62117,62119],{},[1665,62110,28017],{},[1654,62112,2380],{},[1654,62114,1708],{"stretchy":1656},[1654,62116,2380],{},[1665,62118,61419],{},[1654,62120,1726],{"stretchy":1656},[1654,62122,1750],{},[2811,62124,62125,62127],{},[1665,62126,50020],{},[1665,62128,62129],{},"3,1",[1654,62131,14628],{},[1665,62133,62134],{},"7,742",[902,62136,62137],{"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 ",[883,62140,62142],{"className":62141},[886],[888,62143,62144],{"xmlns":890},[892,62145,62146,62159],{},[895,62147,62148,62150,62152,62154,62156],{},[898,62149,11648],{"mathvariant":1878},[898,62151,1663],{},[1654,62153,14628],{},[1654,62155,2380],{},[1665,62157,62158],{},"0,829",[902,62160,62161],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,62164,62166],{"className":62165},[886],[888,62167,62168],{"xmlns":890},[892,62169,62170,62176],{},[895,62171,62172,62174],{},[1654,62173,2380],{},[1665,62175,53111],{},[902,62177,62178],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,62181,62182],{},[614,62183,62184,62185,62198],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,62186,62188],{"className":62187},[886],[888,62189,62190],{"xmlns":890},[892,62191,62192,62196],{},[895,62193,62194],{},[898,62195,1663],{},[902,62197,1663],{"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.",[198,62200,62202,62203],{"id":62201},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,62204,62206],{"className":62205},[886],[888,62207,62208],{"xmlns":890},[892,62209,62210,62216],{},[895,62211,62212,62214],{},[898,62213,1755],{},[898,62215,17398],{},[902,62217,53189],{"encoding":904},[2140,62219,62220],{},[724,62221,62222,62224,62225,62259,62260,62282],{},[883,62223,60915],{}," Zadání\nPro nabídku ",[883,62226,62228],{"className":62227},[886],[888,62229,62230],{"xmlns":890},[892,62231,62232,62256],{},[895,62233,62234,62236,62238,62240,62242,62244,62246,62248,62250,62252,62254],{},[898,62235,1755],{},[1654,62237,1750],{},[898,62239,17398],{},[1654,62241,1708],{"stretchy":1656},[898,62243,1663],{},[1654,62245,1726],{"stretchy":1656},[1654,62247,1750],{},[1665,62249,4647],{},[1654,62251,1766],{},[1665,62253,1681],{},[898,62255,1663],{},[902,62257,62258],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,62261,62263],{"className":62262},[886],[888,62264,62265],{"xmlns":890},[892,62266,62267,62279],{},[895,62268,62269,62275,62277],{},[1710,62270,62271,62273],{},[898,62272,1663],{},[1665,62274,2062],{},[1654,62276,1750],{},[1665,62278,4647],{},[902,62280,62281],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,62284,62285],{},[38,62286,31458],{},[724,62288,62289],{},"Odpovídající cena:",[883,62291,62293],{"className":62292},[886],[888,62294,62295],{"xmlns":890,"display":1956},[892,62296,62297,62332],{},[895,62298,62299,62305,62307,62309,62311,62313,62315,62317,62319,62321,62323,62325,62327,62329],{},[1710,62300,62301,62303],{},[898,62302,1755],{},[1665,62304,2062],{},[1654,62306,1750],{},[898,62308,17398],{},[1654,62310,1708],{"stretchy":1656},[1665,62312,4647],{},[1654,62314,1726],{"stretchy":1656},[1654,62316,1750],{},[1665,62318,4647],{},[1654,62320,1766],{},[1665,62322,1681],{},[1654,62324,4554],{},[1665,62326,4647],{},[1654,62328,1750],{},[1665,62330,62331],{},"30.",[902,62333,62334],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,62336,62337],{},"Dle vzorce (2.15):",[883,62339,62341],{"className":62340},[886],[888,62342,62343],{"xmlns":890,"display":1956},[892,62344,62345,62453],{},[895,62346,62347,62349,62351,62353,62355,62357,62359,62365,62371,62373,62381,62383,62385,62387,62389,62391,62393,62395,62397,62399,62401,62403,62405,62407,62409,62412,62414,62416,62418,62424,62432,62434,62436,62438,62440,62442,62444,62446,62448,62450],{},[898,62348,1755],{},[898,62350,17398],{},[1654,62352,1708],{"stretchy":1656},[1665,62354,4647],{},[1654,62356,1726],{"stretchy":1656},[1654,62358,1750],{},[1710,62360,62361,62363],{},[898,62362,1755],{},[1665,62364,2062],{},[1710,62366,62367,62369],{},[898,62368,1663],{},[1665,62370,2062],{},[1654,62372,2380],{},[1659,62374,62375,62377,62379],{},[1654,62376,19883],{},[1665,62378,2062],{},[1665,62380,4647],{},[1654,62382,1708],{"stretchy":1656},[1665,62384,4647],{},[1654,62386,1766],{},[1665,62388,1681],{},[898,62390,1663],{},[1654,62392,1726],{"stretchy":1656},[1865,62394,11744],{},[898,62396,10977],{},[898,62398,1663],{},[1654,62400,1750],{},[1665,62402,4647],{},[1654,62404,4554],{},[1665,62406,46239],{},[1654,62408,2380],{},[1654,62410,1657],{"fence":1656,"stretchy":1673,"minsize":62411,"maxsize":62411},"1.8em",[1665,62413,4647],{},[898,62415,1663],{},[1654,62417,1766],{},[1741,62419,62420,62422],{},[898,62421,1663],{},[1665,62423,1681],{},[1659,62425,62426,62428,62430],{},[1654,62427,1686],{"fence":1656,"stretchy":1673,"minsize":62411,"maxsize":62411},[1665,62429,2062],{},[1665,62431,4647],{},[1654,62433,1750],{},[1665,62435,4006],{},[1654,62437,2380],{},[1654,62439,1708],{"stretchy":1656},[1665,62441,4273],{},[1654,62443,1766],{},[1665,62445,4273],{},[1654,62447,1726],{"stretchy":1656},[1654,62449,1750],{},[1665,62451,62452],{},"100.",[902,62454,62455],{"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.",[724,62457,62458,62459,62480,62481,62501],{},"Přebytek výrobce při množství ",[883,62460,62462],{"className":62461},[886],[888,62463,62464],{"xmlns":890},[892,62465,62466,62478],{},[895,62467,62468,62474,62476],{},[1710,62469,62470,62472],{},[898,62471,1663],{},[1665,62473,2062],{},[1654,62475,1750],{},[1665,62477,4647],{},[902,62479,62281],{"encoding":904}," je tedy ",[883,62482,62484],{"className":62483},[886],[888,62485,62486],{"xmlns":890},[892,62487,62488,62498],{},[895,62489,62490,62492,62494,62496],{},[898,62491,1755],{},[898,62493,17398],{},[1654,62495,1750],{},[1665,62497,4273],{},[902,62499,62500],{"encoding":904},"PS = 100"," (peněžních jednotek).",[45190,62503],{},[115,62505,62507],{"id":62506},"cheat-sheet","Cheat sheet",[16,62509,62510,62523],{},[19,62511,62512],{},[22,62513,62514,62517,62520],{},[25,62515,62516],{},"Veličina",[25,62518,62519],{},"Vzorec",[25,62521,62522],{},"Geometrie",[30,62524,62525,62643,62757,62825],{},[22,62526,62527,62555,62611],{},[35,62528,62529],{},[883,62530,62532],{"className":62531},[886],[888,62533,62534],{"xmlns":890},[892,62535,62536,62552],{},[895,62537,62538,62540,62542,62544,62550],{},[898,62539,11539],{},[898,62541,17398],{},[1654,62543,1708],{"stretchy":1656},[1710,62545,62546,62548],{},[898,62547,1663],{},[1665,62549,2062],{},[1654,62551,1726],{"stretchy":1656},[902,62553,62554],{"encoding":904},"CS(Q_0)",[35,62556,62557],{},[883,62558,62560],{"className":62559},[886],[888,62561,62562],{"xmlns":890},[892,62563,62564,62608],{},[895,62565,62566],{},[2582,62567,62568,62580,62582,62584,62586,62588,62590,62592,62594,62596,62602],{"scriptlevel":2062,"displaystyle":1673},[1659,62569,62570,62572,62574],{},[1654,62571,19883],{},[1665,62573,2062],{},[1710,62575,62576,62578],{},[898,62577,1663],{},[1665,62579,2062],{},[898,62581,4980],{},[1654,62583,1708],{"stretchy":1656},[898,62585,1663],{},[1654,62587,1726],{"stretchy":1656},[1865,62589,11744],{},[898,62591,10977],{},[898,62593,1663],{},[1654,62595,2380],{},[1710,62597,62598,62600],{},[898,62599,1755],{},[1665,62601,2062],{},[1710,62603,62604,62606],{},[898,62605,1663],{},[1665,62607,2062],{},[902,62609,62610],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,62612,62613,62614,62617,62618,62621,62622],{},"plocha ",[38,62615,62616],{},"pod"," křivkou poptávky, ",[38,62619,62620],{},"nad"," čárou ",[883,62623,62625],{"className":62624},[886],[888,62626,62627],{"xmlns":890},[892,62628,62629,62641],{},[895,62630,62631,62633,62635],{},[898,62632,1755],{},[1654,62634,1750],{},[1710,62636,62637,62639],{},[898,62638,1755],{},[1665,62640,2062],{},[902,62642,59897],{"encoding":904},[22,62644,62645,62673,62729],{},[35,62646,62647],{},[883,62648,62650],{"className":62649},[886],[888,62651,62652],{"xmlns":890},[892,62653,62654,62670],{},[895,62655,62656,62658,62660,62662,62668],{},[898,62657,1755],{},[898,62659,17398],{},[1654,62661,1708],{"stretchy":1656},[1710,62663,62664,62666],{},[898,62665,1663],{},[1665,62667,2062],{},[1654,62669,1726],{"stretchy":1656},[902,62671,62672],{"encoding":904},"PS(Q_0)",[35,62674,62675],{},[883,62676,62678],{"className":62677},[886],[888,62679,62680],{"xmlns":890},[892,62681,62682,62726],{},[895,62683,62684],{},[2582,62685,62686,62692,62698,62700,62712,62714,62716,62718,62720,62722,62724],{"scriptlevel":2062,"displaystyle":1673},[1710,62687,62688,62690],{},[898,62689,1755],{},[1665,62691,2062],{},[1710,62693,62694,62696],{},[898,62695,1663],{},[1665,62697,2062],{},[1654,62699,2380],{},[1659,62701,62702,62704,62706],{},[1654,62703,19883],{},[1665,62705,2062],{},[1710,62707,62708,62710],{},[898,62709,1663],{},[1665,62711,2062],{},[898,62713,17398],{},[1654,62715,1708],{"stretchy":1656},[898,62717,1663],{},[1654,62719,1726],{"stretchy":1656},[1865,62721,11744],{},[898,62723,10977],{},[898,62725,1663],{},[902,62727,62728],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,62730,62613,62731,62733,62734,62621,62736],{},[38,62732,62620],{}," křivkou nabídky, ",[38,62735,62616],{},[883,62737,62739],{"className":62738},[886],[888,62740,62741],{"xmlns":890},[892,62742,62743,62755],{},[895,62744,62745,62747,62749],{},[898,62746,1755],{},[1654,62748,1750],{},[1710,62750,62751,62753],{},[898,62752,1755],{},[1665,62754,2062],{},[902,62756,59897],{"encoding":904},[22,62758,62759,62762,62789],{},[35,62760,62761],{},"Výdaje \u002F tržby",[35,62763,62764],{},[883,62765,62767],{"className":62766},[886],[888,62768,62769],{"xmlns":890},[892,62770,62771,62787],{},[895,62772,62773,62779,62781],{},[1710,62774,62775,62777],{},[898,62776,1755],{},[1665,62778,2062],{},[1654,62780,4554],{},[1710,62782,62783,62785],{},[898,62784,1663],{},[1665,62786,2062],{},[902,62788,60757],{"encoding":904},[35,62790,62791,62792],{},"obdélník ",[883,62793,62795],{"className":62794},[886],[888,62796,62797],{"xmlns":890},[892,62798,62799,62823],{},[895,62800,62801,62803,62805,62811,62813,62815,62817],{},[1665,62802,2062],{},[1865,62804,11744],{},[1710,62806,62807,62809],{},[898,62808,1663],{},[1665,62810,2062],{},[1865,62812,11744],{},[898,62814,4737],{},[1865,62816,11744],{},[1710,62818,62819,62821],{},[898,62820,1755],{},[1665,62822,2062],{},[902,62824,59377],{"encoding":904},[22,62826,62827,62830,62853],{},[35,62828,62829],{},"Celkový přebytek",[35,62831,62832],{},[883,62833,62835],{"className":62834},[886],[888,62836,62837],{"xmlns":890},[892,62838,62839,62851],{},[895,62840,62841,62843,62845,62847,62849],{},[898,62842,11539],{},[898,62844,17398],{},[1654,62846,1766],{},[898,62848,1755],{},[898,62850,17398],{},[902,62852,59115],{"encoding":904},[35,62854,62855],{},"součet obou ploch v rovnováze",[45190,62857],{},[115,62859,10214],{"id":10213},[120,62861,62862,62884,62906,62950,62994,63057,63085],{},[123,62863,62864,18742,62866,1343,62881,62883],{},[38,62865,53154],{},[883,62867,62869],{"className":62868},[886],[888,62870,62871],{"xmlns":890},[892,62872,62873,62879],{},[895,62874,62875,62877],{},[898,62876,11539],{},[898,62878,17398],{},[902,62880,53170],{"encoding":904},[614,62882,53208],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,62885,62886,18742,62888,1343,62903,62905],{},[38,62887,53301],{},[883,62889,62891],{"className":62890},[886],[888,62892,62893],{"xmlns":890},[892,62894,62895,62901],{},[895,62896,62897,62899],{},[898,62898,1755],{},[898,62900,17398],{},[902,62902,53189],{"encoding":904},[614,62904,53304],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,62907,62908,10373,62911,2138],{},[38,62909,62910],{},"Ochota platit",[883,62912,62914],{"className":62913},[886],[888,62915,62916],{"xmlns":890},[892,62917,62918,62948],{},[895,62919,62920],{},[2582,62921,62922,62934,62936,62938,62940,62942,62944,62946],{"scriptlevel":2062,"displaystyle":1673},[1659,62923,62924,62926,62928],{},[1654,62925,19883],{},[1665,62927,2062],{},[1710,62929,62930,62932],{},[898,62931,1663],{},[1665,62933,2062],{},[898,62935,4980],{},[1654,62937,1708],{"stretchy":1656},[898,62939,1663],{},[1654,62941,1726],{"stretchy":1656},[1865,62943,11744],{},[898,62945,10977],{},[898,62947,1663],{},[902,62949,59745],{"encoding":904},[123,62951,62952,10373,62955,2138],{},[38,62953,62954],{},"Minimální cena výrobce",[883,62956,62958],{"className":62957},[886],[888,62959,62960],{"xmlns":890},[892,62961,62962,62992],{},[895,62963,62964],{},[2582,62965,62966,62978,62980,62982,62984,62986,62988,62990],{"scriptlevel":2062,"displaystyle":1673},[1659,62967,62968,62970,62972],{},[1654,62969,19883],{},[1665,62971,2062],{},[1710,62973,62974,62976],{},[898,62975,1663],{},[1665,62977,2062],{},[898,62979,17398],{},[1654,62981,1708],{"stretchy":1656},[898,62983,1663],{},[1654,62985,1726],{"stretchy":1656},[1865,62987,11744],{},[898,62989,10977],{},[898,62991,1663],{},[902,62993,60387],{"encoding":904},[123,62995,62996,10373,62999,60888,63024,12664],{},[38,62997,62998],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,63000,63002],{"className":63001},[886],[888,63003,63004],{"xmlns":890},[892,63005,63006,63022],{},[895,63007,63008,63014,63016],{},[1710,63009,63010,63012],{},[898,63011,1755],{},[1665,63013,2062],{},[1865,63015,11744],{},[1710,63017,63018,63020],{},[898,63019,1663],{},[1665,63021,2062],{},[902,63023,59823],{"encoding":904},[883,63025,63027],{"className":63026},[886],[888,63028,63029],{"xmlns":890},[892,63030,63031,63055],{},[895,63032,63033,63035,63037,63043,63045,63047,63049],{},[1665,63034,2062],{},[1865,63036,11744],{},[1710,63038,63039,63041],{},[898,63040,1663],{},[1665,63042,2062],{},[1865,63044,11744],{},[898,63046,4737],{},[1865,63048,11744],{},[1710,63050,63051,63053],{},[898,63052,1755],{},[1665,63054,2062],{},[902,63056,59377],{"encoding":904},[123,63058,63059,63062,63063,63084],{},[38,63060,63061],{},"Celkový přebytek trhu"," — součet ",[883,63064,63066],{"className":63065},[886],[888,63067,63068],{"xmlns":890},[892,63069,63070,63082],{},[895,63071,63072,63074,63076,63078,63080],{},[898,63073,11539],{},[898,63075,17398],{},[1654,63077,1766],{},[898,63079,1755],{},[898,63081,17398],{},[902,63083,59115],{"encoding":904}," v rovnovážném bodě.",[123,63086,63087,63089,63090,1343,63103,63116,63117,2138],{},[38,63088,11211],{}," — plochy ohraničené křivkami ",[883,63091,63093],{"className":63092},[886],[888,63094,63095],{"xmlns":890},[892,63096,63097,63101],{},[895,63098,63099],{},[898,63100,4980],{},[902,63102,4980],{"encoding":904},[883,63104,63106],{"className":63105},[886],[888,63107,63108],{"xmlns":890},[892,63109,63110,63114],{},[895,63111,63112],{},[898,63113,17398],{},[902,63115,17398],{"encoding":904}," a přímkou ",[883,63118,63120],{"className":63119},[886],[888,63121,63122],{"xmlns":890},[892,63123,63124,63136],{},[895,63125,63126,63128,63130],{},[898,63127,1755],{},[1654,63129,1750],{},[1710,63131,63132,63134],{},[898,63133,1755],{},[1665,63135,2062],{},[902,63137,59897],{"encoding":904},[45190,63139],{},[115,63141,63143],{"id":63142},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,63145,63146,63147,63160,63161,63178],{},"Uvalení jednotkové daně ",[883,63148,63150],{"className":63149},[886],[888,63151,63152],{"xmlns":890},[892,63153,63154,63158],{},[895,63155,63156],{},[898,63157,11536],{},[902,63159,11536],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,63162,63164],{"className":63163},[886],[888,63165,63166],{"xmlns":890},[892,63167,63168,63176],{},[895,63169,63170],{},[1741,63171,63172,63174],{},[898,63173,1663],{},[898,63175,1798],{},[902,63177,50623],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,63180,63181],{},[3492,63182],{"alt":63183,"className":63184,"src":63185},"imek-prebytky-s-dani-deadweight",[210,3496],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,63187,63188,63189,63204,63205,63220,63221,60888,63224,63248,63249,18742,63252,63255,63256,2138],{},"Přebytek spotřebitele ",[883,63190,63192],{"className":63191},[886],[888,63193,63194],{"xmlns":890},[892,63195,63196,63202],{},[895,63197,63198,63200],{},[898,63199,11539],{},[898,63201,17398],{},[902,63203,53170],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,63206,63208],{"className":63207},[886],[888,63209,63210],{"xmlns":890},[892,63211,63212,63218],{},[895,63213,63214,63216],{},[898,63215,1755],{},[898,63217,17398],{},[902,63219,53189],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,63222,63223],{},"daňový příjem",[883,63225,63227],{"className":63226},[886],[888,63228,63229],{"xmlns":890},[892,63230,63231,63245],{},[895,63232,63233,63235,63237],{},[898,63234,11536],{},[1654,63236,4554],{},[1659,63238,63239,63241,63243],{},[898,63240,1663],{},[1665,63242,1667],{},[898,63244,1798],{},[902,63246,63247],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,63250,63251],{},"mrtvá ztráta",[614,63253,63254],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,63257,811],{"className":63258,"dataFsResolvedFilePath":809,"href":810},[210],[45190,63260],{},[115,63262,10613],{"id":10612},[120,63264,63265,63272,63284,63291,63298],{},[123,63266,63267,2186,63269],{},[38,63268,24925],{},[207,63270,802],{"className":63271,"dataFsResolvedFilePath":800,"href":801},[210],[123,63273,63274,2186,63276,63279,63280,63283],{},[38,63275,10643],{},[207,63277,775],{"className":63278,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,63281,10655],{"className":63282,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,63285,63286,2186,63288],{},[38,63287,24935],{},[207,63289,12570],{"className":63290,"dataFsResolvedFilePath":827,"href":828},[210],[123,63292,63293,2186,63295],{},[38,63294,58978],{},[207,63296,58982],{"className":63297,"dataFsResolvedFilePath":745,"href":746},[210],[123,63299,63300,2186,63302],{},[38,63301,10686],{},[207,63303,10692],{"className":63304,"dataFsResolvedFilePath":10690,"href":10691},[210],{"title":641,"searchDepth":642,"depth":642,"links":63306},[63307,63308,63313,63318,63323,63324,63325,63326],{"id":59174,"depth":642,"text":1241},{"id":59518,"depth":642,"text":63309,"children":63310},"Přebytek spotřebitele (CSCS)",[63311,63312],{"id":59537,"depth":649,"text":59538},{"id":11210,"depth":649,"text":11211},{"id":60113,"depth":642,"text":63314,"children":63315},"Přebytek výrobce (PSPS)",[63316,63317],{"id":60132,"depth":649,"text":60133},{"id":60295,"depth":649,"text":11211},{"id":60903,"depth":642,"text":60904,"children":63319},[63320,63321],{"id":60907,"depth":649,"text":60908},{"id":62201,"depth":649,"text":63322},"Příklad 2.13 — numerický výpočet PSPS",{"id":62506,"depth":642,"text":62507},{"id":10213,"depth":642,"text":10214},{"id":63142,"depth":642,"text":63143},{"id":10612,"depth":642,"text":10613},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,59044,63333,63334,20702,24943,63335,63336],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":63339,"title":63340,"body":63341,"course":1128,"courses":659,"created":10724,"description":641,"extension":661,"meta":82670,"navigation":664,"path":82671,"seo":82672,"sources":82673,"stem":82674,"tags":82675,"type":10736,"updated":677,"__hash__":82681},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":63342,"toc":82634},[63343,63346,63532,63534,63625,63630,63956,63960,63967,63971,64016,64083,64114,64164,64199,64203,64262,64267,64333,64451,64553,64557,64580,64658,64701,64705,64734,64801,64807,64921,64925,65005,65042,65094,65292,65356,65443,65447,65450,65529,65532,65650,65669,65734,65738,65830,65898,65939,65993,66061,66098,66102,66160,66190,66401,66473,66525,66691,66784,66819,66823,66827,66864,66929,66984,66988,67011,67100,67204,67273,67277,67374,67487,67543,67597,67655,67716,67719,67755,67820,67850,68079,68137,68171,68175,68202,68281,68395,68416,68495,68497,68605,68609,68747,69069,69073,69076,69080,69129,69133,69387,69539,69546,69619,69803,69808,70151,70155,70178,70180,70201,70260,70270,70319,70461,70535,70630,70745,70843,70961,70965,71034,71039,71151,71296,71347,71459,71501,71505,71525,71586,71613,71675,71679,71701,71770,72050,72057,72087,72094,72287,72291,72369,72374,72450,72453,72541,72617,72684,72733,72836,72909,73030,73381,73494,73596,73600,73603,73610,73613,73649,73708,73717,73866,74090,74094,74157,74336,74428,74483,74487,74543,74613,74665,74686,74767,74770,74845,74889,74893,74934,74977,75003,75007,75078,75174,75236,75288,75391,75469,75492,75521,75525,75691,75808,75880,76195,76355,76359,76410,76472,76507,76537,76637,76679,76848,76853,76949,76987,76991,77110,77411,77413,77448,77452,77456,77584,77716,78038,78226,78304,78308,78613,78726,78872,79057,79163,79395,79510,79592,79711,79809,79850,79854,79909,80053,80207,80367,80460,80654,80966,81097,81226,81230,81302,81344,81395,81397,82592,82594],[12,63344,63340],{"id":63345},"příjem-náklady-zisk-a-nabídka-firmy",[2140,63347,63348],{},[724,63349,63350,12620,63352,2186,63355,63370,63371,2186,63374,63389,63390,2186,63393,63421,63422,63444,63445,63469,63470,63492,63493,63496,63497,63513,63514,2138],{},[883,63351,12619],{},[38,63353,63354],{},"Příjem",[883,63356,63358],{"className":63357},[886],[888,63359,63360],{"xmlns":890},[892,63361,63362,63368],{},[895,63363,63364,63366],{},[898,63365,11536],{},[898,63367,12737],{},[902,63369,12837],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,63372,63373],{},"náklady",[883,63375,63377],{"className":63376},[886],[888,63378,63379],{"xmlns":890},[892,63380,63381,63387],{},[895,63382,63383,63385],{},[898,63384,11536],{},[898,63386,11539],{},[902,63388,11997],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,63391,63392],{},"zisk",[883,63394,63396],{"className":63395},[886],[888,63397,63398],{"xmlns":890},[892,63399,63400,63418],{},[895,63401,63402,63404,63406,63408,63410,63412,63414,63416],{},[898,63403,1755],{},[898,63405,12737],{},[1654,63407,1750],{},[898,63409,11536],{},[898,63411,12737],{},[1654,63413,2380],{},[898,63415,11536],{},[898,63417,11539],{},[902,63419,63420],{"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: ",[883,63423,63425],{"className":63424},[886],[888,63426,63427],{"xmlns":890},[892,63428,63429,63441],{},[895,63430,63431,63433,63435,63437,63439],{},[898,63432,4737],{},[898,63434,11539],{},[1654,63436,1750],{},[898,63438,9320],{},[898,63440,11539],{},[902,63442,63443],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,63446,63448],{"className":63447},[886],[888,63449,63450],{"xmlns":890},[892,63451,63452,63466],{},[895,63453,63454,63456,63458,63460,63462,63464],{},[898,63455,4737],{},[898,63457,48559],{},[898,63459,11539],{},[1654,63461,1750],{},[898,63463,9320],{},[898,63465,11539],{},[902,63467,63468],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,63471,63473],{"className":63472},[886],[888,63474,63475],{"xmlns":890},[892,63476,63477,63489],{},[895,63478,63479,63481,63483,63485,63487],{},[898,63480,9320],{},[898,63482,12737],{},[1654,63484,1750],{},[898,63486,9320],{},[898,63488,11539],{},[902,63490,63491],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,63494,63495],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,63498,63500],{"className":63499},[886],[888,63501,63502],{"xmlns":890},[892,63503,63504,63510],{},[895,63505,63506,63508],{},[898,63507,9320],{},[898,63509,11539],{},[902,63511,63512],{"encoding":904},"MC"," nad bodem minima ",[883,63515,63517],{"className":63516},[886],[888,63518,63519],{"xmlns":890},[892,63520,63521,63529],{},[895,63522,63523,63525,63527],{},[898,63524,4737],{},[898,63526,48559],{},[898,63528,11539],{},[902,63530,63531],{"encoding":904},"AVC",[115,63533,1241],{"id":59174},[724,63535,63536,63537,63540,63541,63543,63544,1343,63547,1343,63550,63552,63553,63556,63557,63560,63561,63564,63565,11434,63580,1348,63595,11434,63610,12664],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,63538,63539],{},"příjmem"," (revenue) a ",[38,63542,63373],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,63545,63546],{},"zisku",[38,63548,63549],{},"bodů zvratu",[38,63551,10766],{}," a konstrukcí ",[38,63554,63555],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,63558,1145],{"className":63559,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,63562,19844],{"className":63563,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,63566,63568],{"className":63567},[886],[888,63569,63570],{"xmlns":890},[892,63571,63572,63578],{},[895,63573,63574,63576],{},[898,63575,11536],{},[898,63577,12737],{},[902,63579,12837],{"encoding":904},[883,63581,63583],{"className":63582},[886],[888,63584,63585],{"xmlns":890},[892,63586,63587,63593],{},[895,63588,63589,63591],{},[898,63590,9320],{},[898,63592,12737],{},[902,63594,15361],{"encoding":904},[883,63596,63598],{"className":63597},[886],[888,63599,63600],{"xmlns":890},[892,63601,63602,63608],{},[895,63603,63604,63606],{},[898,63605,11536],{},[898,63607,11539],{},[902,63609,11997],{"encoding":904},[883,63611,63613],{"className":63612},[886],[888,63614,63615],{"xmlns":890},[892,63616,63617,63623],{},[895,63618,63619,63621],{},[898,63620,9320],{},[898,63622,11539],{},[902,63624,63512],{"encoding":904},[724,63626,63627],{},[38,63628,63629],{},"Cílové znalosti:",[120,63631,63632,63796,63799,63802,63895,63942,63949],{},[123,63633,63634,63635,1343,63650,1343,63666,2068,63681,1343,63696,1343,63712,1343,63730,1343,63748,1343,63765,1343,63781,17150],{},"odvodit a interpretovat funkce ",[883,63636,63638],{"className":63637},[886],[888,63639,63640],{"xmlns":890},[892,63641,63642,63648],{},[895,63643,63644,63646],{},[898,63645,11536],{},[898,63647,12737],{},[902,63649,12837],{"encoding":904},[883,63651,63653],{"className":63652},[886],[888,63654,63655],{"xmlns":890},[892,63656,63657,63663],{},[895,63658,63659,63661],{},[898,63660,4737],{},[898,63662,12737],{},[902,63664,63665],{"encoding":904},"AR",[883,63667,63669],{"className":63668},[886],[888,63670,63671],{"xmlns":890},[892,63672,63673,63679],{},[895,63674,63675,63677],{},[898,63676,9320],{},[898,63678,12737],{},[902,63680,15361],{"encoding":904},[883,63682,63684],{"className":63683},[886],[888,63685,63686],{"xmlns":890},[892,63687,63688,63694],{},[895,63689,63690,63692],{},[898,63691,11536],{},[898,63693,11539],{},[902,63695,11997],{"encoding":904},[883,63697,63699],{"className":63698},[886],[888,63700,63701],{"xmlns":890},[892,63702,63703,63709],{},[895,63704,63705,63707],{},[898,63706,19153],{},[898,63708,11539],{},[902,63710,63711],{"encoding":904},"FC",[883,63713,63715],{"className":63714},[886],[888,63716,63717],{"xmlns":890},[892,63718,63719,63727],{},[895,63720,63721,63723,63725],{},[898,63722,11536],{},[898,63724,48559],{},[898,63726,11539],{},[902,63728,63729],{"encoding":904},"TVC",[883,63731,63733],{"className":63732},[886],[888,63734,63735],{"xmlns":890},[892,63736,63737,63745],{},[895,63738,63739,63741,63743],{},[898,63740,4737],{},[898,63742,19153],{},[898,63744,11539],{},[902,63746,63747],{"encoding":904},"AFC",[883,63749,63751],{"className":63750},[886],[888,63752,63753],{"xmlns":890},[892,63754,63755,63763],{},[895,63756,63757,63759,63761],{},[898,63758,4737],{},[898,63760,48559],{},[898,63762,11539],{},[902,63764,63531],{"encoding":904},[883,63766,63768],{"className":63767},[886],[888,63769,63770],{"xmlns":890},[892,63771,63772,63778],{},[895,63773,63774,63776],{},[898,63775,4737],{},[898,63777,11539],{},[902,63779,63780],{"encoding":904},"AC",[883,63782,63784],{"className":63783},[886],[888,63785,63786],{"xmlns":890},[892,63787,63788,63794],{},[895,63789,63790,63792],{},[898,63791,9320],{},[898,63793,11539],{},[902,63795,63512],{"encoding":904},[123,63797,63798],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,63800,63801],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,63803,63804,63805,63808,63809,50034,63851,17150],{},"osvojit si ",[38,63806,63807],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,63810,63812],{"className":63811},[886],[888,63813,63814],{"xmlns":890},[892,63815,63816,63848],{},[895,63817,63818,63820,63822,63824,63830,63832,63834,63836,63838,63840,63846],{},[898,63819,4737],{},[898,63821,11539],{},[1654,63823,1708],{"stretchy":1656},[1710,63825,63826,63828],{},[898,63827,1663],{},[1665,63829,2062],{},[1654,63831,1726],{"stretchy":1656},[1654,63833,1750],{},[898,63835,9320],{},[898,63837,11539],{},[1654,63839,1708],{"stretchy":1656},[1710,63841,63842,63844],{},[898,63843,1663],{},[1665,63845,2062],{},[1654,63847,1726],{"stretchy":1656},[902,63849,63850],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,63852,63854],{"className":63853},[886],[888,63855,63856],{"xmlns":890},[892,63857,63858,63892],{},[895,63859,63860,63862,63864,63866,63868,63874,63876,63878,63880,63882,63884,63890],{},[898,63861,4737],{},[898,63863,48559],{},[898,63865,11539],{},[1654,63867,1708],{"stretchy":1656},[1710,63869,63870,63872],{},[898,63871,1663],{},[1665,63873,2062],{},[1654,63875,1726],{"stretchy":1656},[1654,63877,1750],{},[898,63879,9320],{},[898,63881,11539],{},[1654,63883,1708],{"stretchy":1656},[1710,63885,63886,63888],{},[898,63887,1663],{},[1665,63889,2062],{},[1654,63891,1726],{"stretchy":1656},[902,63893,63894],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,63896,63804,63897,63808,63900,17150],{},[38,63898,63899],{},"princip maximalizace zisku",[883,63901,63903],{"className":63902},[886],[888,63904,63905],{"xmlns":890},[892,63906,63907,63939],{},[895,63908,63909,63911,63913,63915,63921,63923,63925,63927,63929,63931,63937],{},[898,63910,9320],{},[898,63912,12737],{},[1654,63914,1708],{"stretchy":1656},[1710,63916,63917,63919],{},[898,63918,1663],{},[1665,63920,2062],{},[1654,63922,1726],{"stretchy":1656},[1654,63924,1750],{},[898,63926,9320],{},[898,63928,11539],{},[1654,63930,1708],{"stretchy":1656},[1710,63932,63933,63935],{},[898,63934,1663],{},[1665,63936,2062],{},[1654,63938,1726],{"stretchy":1656},[902,63940,63941],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,63943,63944,63945,63948],{},"stanovit ",[38,63946,63947],{},"body zvratu"," a interval zisku;",[123,63950,63951,63952,63955],{},"zkonstruovat ",[38,63953,63954],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,63957,63959],{"id":63958},"příjem-firmy","Příjem firmy",[724,63961,63962],{},[3492,63963],{"alt":63964,"className":63965,"src":63966},"imek-ar-mr-dvojnasobny-sklon",[210,3496],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,63968,63970],{"id":63969},"celkový-příjem","Celkový příjem",[724,63972,63973,63974,18742,63989,63992,63993,3869],{},"Celkový příjem ",[883,63975,63977],{"className":63976},[886],[888,63978,63979],{"xmlns":890},[892,63980,63981,63987],{},[895,63982,63983,63985],{},[898,63984,11536],{},[898,63986,12737],{},[902,63988,12837],{"encoding":904},[38,63990,63991],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,63994,63996],{"className":63995},[886],[888,63997,63998],{"xmlns":890},[892,63999,64000,64014],{},[895,64001,64002,64004,64006,64008,64010,64012],{},[898,64003,1755],{},[1654,64005,1750],{},[898,64007,4980],{},[1654,64009,1708],{"stretchy":1656},[898,64011,1663],{},[1654,64013,1726],{"stretchy":1656},[902,64015,13376],{"encoding":904},[883,64017,64019],{"className":64018},[886],[888,64020,64021],{"xmlns":890,"display":1956},[892,64022,64023,64080],{},[1960,64024,64025],{"width":1962},[1964,64026,64027,64029,64073,64075],{},[1967,64028],{"width":1969},[1967,64030,64031],{},[895,64032,64033,64035,64037,64039,64041,64043,64045,64047,64049,64051,64053,64055,64057,64059,64061,64063,64065,64067,64069,64071],{},[898,64034,11536],{},[898,64036,12737],{},[1654,64038,1750],{},[898,64040,11536],{},[898,64042,12737],{},[1654,64044,1708],{"stretchy":1656},[898,64046,1663],{},[1654,64048,1726],{"stretchy":1656},[1654,64050,1750],{},[898,64052,1755],{},[1654,64054,4554],{},[898,64056,1663],{},[1654,64058,1750],{},[898,64060,4980],{},[1654,64062,1708],{"stretchy":1656},[898,64064,1663],{},[1654,64066,1726],{"stretchy":1656},[1654,64068,4554],{},[898,64070,1663],{},[898,64072,2138],{"mathvariant":1878},[1967,64074],{"width":1969},[1967,64076,64077],{},[1865,64078,64079],{},"(3.1)",[902,64081,64082],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,64084,64085,64086,64089,64090,64113],{},"Graf funkce se nazývá ",[38,64087,64088],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,64091,64093],{"className":64092},[886],[888,64094,64095],{"xmlns":890},[892,64096,64097,64111],{},[895,64098,64099,64101,64103,64105,64107,64109],{},[898,64100,1755],{},[1654,64102,1750],{},[898,64104,207],{},[898,64106,1663],{},[1654,64108,1766],{},[898,64110,9758],{},[902,64112,45280],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,64115,64117],{"className":64116},[886],[888,64118,64119],{"xmlns":890,"display":1956},[892,64120,64121,64161],{},[895,64122,64123,64125,64127,64129,64131,64133,64135,64137,64139,64141,64143,64145,64147,64153,64155,64157,64159],{},[898,64124,11536],{},[898,64126,12737],{},[1654,64128,1750],{},[898,64130,1663],{},[1654,64132,1708],{"stretchy":1656},[898,64134,207],{},[898,64136,1663],{},[1654,64138,1766],{},[898,64140,9758],{},[1654,64142,1726],{"stretchy":1656},[1654,64144,1750],{},[898,64146,207],{},[1741,64148,64149,64151],{},[898,64150,1663],{},[1665,64152,1681],{},[1654,64154,1766],{},[898,64156,9758],{},[898,64158,1663],{},[1654,64160,1674],{"separator":1673},[902,64162,64163],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,64165,64166,64167,64180,64181,64198],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,64168,64170],{"className":64169},[886],[888,64171,64172],{"xmlns":890},[892,64173,64174,64178],{},[895,64175,64176],{},[898,64177,900],{},[902,64179,900],{"encoding":904}," (jelikož ",[883,64182,64184],{"className":64183},[886],[888,64185,64186],{"xmlns":890},[892,64187,64188,64196],{},[895,64189,64190,64192,64194],{},[898,64191,207],{},[1654,64193,3002],{},[1665,64195,2062],{},[902,64197,51305],{"encoding":904},") procházející počátkem.",[45568,64200,64202],{"id":64201},"příklad-31","Příklad 3.1",[724,64204,64205,64208,64209,64245,64246,64261],{},[38,64206,64207],{},"Zadání."," Pro poptávku ",[883,64210,64212],{"className":64211},[886],[888,64213,64214],{"xmlns":890},[892,64215,64216,64242],{},[895,64217,64218,64220,64222,64224,64226,64228,64230,64232,64234,64236,64238,64240],{},[898,64219,1755],{},[1654,64221,1750],{},[898,64223,4980],{},[1654,64225,1708],{"stretchy":1656},[898,64227,1663],{},[1654,64229,1726],{"stretchy":1656},[1654,64231,1750],{},[1654,64233,2380],{},[1665,64235,1681],{},[898,64237,1663],{},[1654,64239,1766],{},[1665,64241,4273],{},[902,64243,64244],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,64247,64249],{"className":64248},[886],[888,64250,64251],{"xmlns":890},[892,64252,64253,64259],{},[895,64254,64255,64257],{},[898,64256,11536],{},[898,64258,12737],{},[902,64260,12837],{"encoding":904}," a charakterizujte jeho křivku.",[724,64263,64264,64266],{},[38,64265,31458],{}," Celkový příjem je",[883,64268,64270],{"className":64269},[886],[888,64271,64272],{"xmlns":890,"display":1956},[892,64273,64274,64330],{},[895,64275,64276,64278,64280,64282,64284,64286,64288,64290,64292,64294,64296,64298,64300,64302,64304,64306,64308,64310,64312,64314,64316,64322,64324,64326,64328],{},[898,64277,11536],{},[898,64279,12737],{},[1654,64281,1750],{},[898,64283,11536],{},[898,64285,12737],{},[1654,64287,1708],{"stretchy":1656},[898,64289,1663],{},[1654,64291,1726],{"stretchy":1656},[1654,64293,1750],{},[898,64295,1663],{},[1654,64297,1708],{"stretchy":1656},[1654,64299,2380],{},[1665,64301,1681],{},[898,64303,1663],{},[1654,64305,1766],{},[1665,64307,4273],{},[1654,64309,1726],{"stretchy":1656},[1654,64311,1750],{},[1654,64313,2380],{},[1665,64315,1681],{},[1741,64317,64318,64320],{},[898,64319,1663],{},[1665,64321,1681],{},[1654,64323,1766],{},[1665,64325,4273],{},[898,64327,1663],{},[898,64329,2138],{"mathvariant":1878},[902,64331,64332],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,64334,64335,64336,2068,64358,64380,64381,64399,64400,2138],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,64337,64339],{"className":64338},[886],[888,64340,64341],{"xmlns":890},[892,64342,64343,64355],{},[895,64344,64345,64351,64353],{},[1710,64346,64347,64349],{},[898,64348,1663],{},[1665,64350,1667],{},[1654,64352,1750],{},[1665,64354,2062],{},[902,64356,64357],{"encoding":904},"Q_1 = 0",[883,64359,64361],{"className":64360},[886],[888,64362,64363],{"xmlns":890},[892,64364,64365,64377],{},[895,64366,64367,64373,64375],{},[1710,64368,64369,64371],{},[898,64370,1663],{},[1665,64372,1681],{},[1654,64374,1750],{},[1665,64376,4767],{},[902,64378,64379],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,64382,64384],{"className":64383},[886],[888,64385,64386],{"xmlns":890},[892,64387,64388,64396],{},[895,64389,64390,64392,64394],{},[898,64391,1663],{},[1654,64393,1750],{},[1665,64395,4622],{},[902,64397,64398],{"encoding":904},"Q = 25"," ve výši ",[883,64401,64403],{"className":64402},[886],[888,64404,64405],{"xmlns":890},[892,64406,64407,64448],{},[895,64408,64409,64411,64421,64423,64425,64427,64429,64432,64434,64436,64438,64440,64442,64444,64446],{},[898,64410,11536],{},[1710,64412,64413,64415,64418],{},[898,64414,12737],{},[898,64416,64417],{},"max",[1654,64419,64420],{},"⁡",[1654,64422,1750],{},[1654,64424,2380],{},[1665,64426,1681],{},[1654,64428,4554],{},[1665,64430,64431],{},"625",[1654,64433,1766],{},[1665,64435,4273],{},[1654,64437,4554],{},[1665,64439,4622],{},[1654,64441,1750],{},[1665,64443,1667],{},[1865,64445,11744],{},[1665,64447,4679],{},[902,64449,64450],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,64452,64453],{},[614,64454,64455,64456,64490,64491,2068,64504,64517,64518,11387,64536,2138],{},"Obrázek 3.1: Parabola ",[883,64457,64459],{"className":64458},[886],[888,64460,64461],{"xmlns":890},[892,64462,64463,64487],{},[895,64464,64465,64467,64469,64471,64473,64475,64481,64483,64485],{},[898,64466,11536],{},[898,64468,12737],{},[1654,64470,1750],{},[1654,64472,2380],{},[1665,64474,1681],{},[1741,64476,64477,64479],{},[898,64478,1663],{},[1665,64480,1681],{},[1654,64482,1766],{},[1665,64484,4273],{},[898,64486,1663],{},[902,64488,64489],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,64492,64494],{"className":64493},[886],[888,64495,64496],{"xmlns":890},[892,64497,64498,64502],{},[895,64499,64500],{},[1665,64501,2062],{},[902,64503,2062],{"encoding":904},[883,64505,64507],{"className":64506},[886],[888,64508,64509],{"xmlns":890},[892,64510,64511,64515],{},[895,64512,64513],{},[1665,64514,4767],{},[902,64516,4767],{"encoding":904}," a maximem ",[883,64519,64521],{"className":64520},[886],[888,64522,64523],{"xmlns":890},[892,64524,64525,64533],{},[895,64526,64527,64529,64531],{},[1665,64528,1667],{},[1865,64530,11744],{},[1665,64532,4679],{},[902,64534,64535],{"encoding":904},"1\\,250",[883,64537,64539],{"className":64538},[886],[888,64540,64541],{"xmlns":890},[892,64542,64543,64551],{},[895,64544,64545,64547,64549],{},[898,64546,1663],{},[1654,64548,1750],{},[1665,64550,4622],{},[902,64552,64398],{"encoding":904},[198,64554,64556],{"id":64555},"průměrný-příjem","Průměrný příjem",[724,64558,64559,2186,64561,18742,64576,64579],{},[38,64560,64556],{},[883,64562,64564],{"className":64563},[886],[888,64565,64566],{"xmlns":890},[892,64567,64568,64574],{},[895,64569,64570,64572],{},[898,64571,4737],{},[898,64573,12737],{},[902,64575,63665],{"encoding":904},[38,64577,64578],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,64581,64583],{"className":64582},[886],[888,64584,64585],{"xmlns":890,"display":1956},[892,64586,64587,64655],{},[895,64588,64589,64591,64593,64595,64597,64599,64601,64603,64605,64607,64623,64625,64643,64645,64647,64649,64651,64653],{},[898,64590,4737],{},[898,64592,12737],{},[1654,64594,1750],{},[898,64596,4737],{},[898,64598,12737],{},[1654,64600,1708],{"stretchy":1656},[898,64602,1663],{},[1654,64604,1726],{"stretchy":1656},[1654,64606,1750],{},[2811,64608,64609,64621],{},[895,64610,64611,64613,64615,64617,64619],{},[898,64612,11536],{},[898,64614,12737],{},[1654,64616,1708],{"stretchy":1656},[898,64618,1663],{},[1654,64620,1726],{"stretchy":1656},[898,64622,1663],{},[1654,64624,1750],{},[2811,64626,64627,64641],{},[895,64628,64629,64631,64633,64635,64637,64639],{},[898,64630,1663],{},[1865,64632,11744],{},[898,64634,4980],{},[1654,64636,1708],{"stretchy":1656},[898,64638,1663],{},[1654,64640,1726],{"stretchy":1656},[898,64642,1663],{},[1654,64644,1750],{},[898,64646,4980],{},[1654,64648,1708],{"stretchy":1656},[898,64650,1663],{},[1654,64652,1726],{"stretchy":1656},[898,64654,2138],{"mathvariant":1878},[902,64656,64657],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[2140,64659,64660],{},[724,64661,64662,64665,64666,1343,64669,2138],{},[883,64663,64664],{},"!note"," Klíčové pozorování\n",[38,64667,64668],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,64670,64672],{"className":64671},[886],[888,64673,64674],{"xmlns":890},[892,64675,64676,64698],{},[895,64677,64678,64680,64682,64684,64686,64688,64690,64692,64694,64696],{},[898,64679,4737],{},[898,64681,12737],{},[1654,64683,1708],{"stretchy":1656},[898,64685,1663],{},[1654,64687,1726],{"stretchy":1656},[1654,64689,1750],{},[898,64691,4980],{},[1654,64693,1708],{"stretchy":1656},[898,64695,1663],{},[1654,64697,1726],{"stretchy":1656},[902,64699,64700],{"encoding":904},"AR(Q) = D(Q)",[198,64702,64704],{"id":64703},"mezní-příjem","Mezní příjem",[724,64706,64707,64708,2186,64711,18742,64726,64729,64730,64733],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,64709,64710],{},"mezní příjem",[883,64712,64714],{"className":64713},[886],[888,64715,64716],{"xmlns":890},[892,64717,64718,64724],{},[895,64719,64720,64722],{},[898,64721,9320],{},[898,64723,12737],{},[902,64725,15361],{"encoding":904},[38,64727,64728],{},"marginal revenue","), definovaný jako ",[207,64731,1145],{"className":64732,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,64735,64737],{"className":64736},[886],[888,64738,64739],{"xmlns":890,"display":1956},[892,64740,64741,64798],{},[1960,64742,64743],{"width":1962},[1964,64744,64745,64747,64791,64793],{},[1967,64746],{"width":1969},[1967,64748,64749],{},[895,64750,64751,64753,64755,64757,64773,64775,64777,64783,64785,64787,64789],{},[898,64752,9320],{},[898,64754,12737],{},[1654,64756,1750],{},[2811,64758,64759,64767],{},[895,64760,64761,64763,64765],{},[898,64762,10977],{"mathvariant":1878},[898,64764,11536],{},[898,64766,12737],{},[895,64768,64769,64771],{},[898,64770,10977],{"mathvariant":1878},[898,64772,1663],{},[1654,64774,1750],{},[898,64776,11536],{},[1741,64778,64779,64781],{},[898,64780,12737],{},[1654,64782,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,64784,1708],{"stretchy":1656},[898,64786,1663],{},[1654,64788,1726],{"stretchy":1656},[898,64790,2138],{"mathvariant":1878},[1967,64792],{"width":1969},[1967,64794,64795],{},[1865,64796,64797],{},"(3.2)",[902,64799,64800],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,64802,64803,64804,64806],{},"Mezní příjem udává ",[38,64805,11359],{}," celkového příjmu vzhledem k množství.",[2140,64808,64809],{},[724,64810,64811,64813,64814,64840,64841,64858,64859,2138],{},[883,64812,2860],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,64815,64817],{"className":64816},[886],[888,64818,64819],{"xmlns":890},[892,64820,64821,64837],{},[895,64822,64823,64825,64827,64829,64835],{},[898,64824,9320],{},[898,64826,12737],{},[1654,64828,1708],{"stretchy":1656},[1741,64830,64831,64833],{},[898,64832,1663],{},[1654,64834,1670],{},[1654,64836,1726],{"stretchy":1656},[902,64838,64839],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,64842,64844],{"className":64843},[886],[888,64845,64846],{"xmlns":890},[892,64847,64848,64856],{},[895,64849,64850],{},[1741,64851,64852,64854],{},[898,64853,1663],{},[1654,64855,1670],{},[902,64857,3768],{"encoding":904},". Jinak řečeno: ",[883,64860,64862],{"className":64861},[886],[888,64863,64864],{"xmlns":890},[892,64865,64866,64918],{},[895,64867,64868,64870,64872,64874,64880,64882,64884,64886,64888,64890,64896,64898,64900,64902,64904,64906,64908,64910,64916],{},[898,64869,9320],{},[898,64871,12737],{},[1654,64873,1708],{"stretchy":1656},[1741,64875,64876,64878],{},[898,64877,1663],{},[1654,64879,1670],{},[1654,64881,1726],{"stretchy":1656},[1654,64883,11492],{},[898,64885,11536],{},[898,64887,12737],{},[1654,64889,1708],{"stretchy":1656},[1741,64891,64892,64894],{},[898,64893,1663],{},[1654,64895,1670],{},[1654,64897,1766],{},[1665,64899,1667],{},[1654,64901,1726],{"stretchy":1656},[1654,64903,2380],{},[898,64905,11536],{},[898,64907,12737],{},[1654,64909,1708],{"stretchy":1656},[1741,64911,64912,64914],{},[898,64913,1663],{},[1654,64915,1670],{},[1654,64917,1726],{"stretchy":1656},[902,64919,64920],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[45568,64922,64924],{"id":64923},"příklad-32","Příklad 3.2",[724,64926,64927,64208,64929,64245,64963,64978,64979,2138],{},[38,64928,64207],{},[883,64930,64932],{"className":64931},[886],[888,64933,64934],{"xmlns":890},[892,64935,64936,64960],{},[895,64937,64938,64940,64942,64944,64946,64948,64950,64952,64954,64956,64958],{},[898,64939,1755],{},[1654,64941,1750],{},[898,64943,4980],{},[1654,64945,1708],{"stretchy":1656},[898,64947,1663],{},[1654,64949,1726],{"stretchy":1656},[1654,64951,1750],{},[1665,64953,4273],{},[1654,64955,2380],{},[1665,64957,1681],{},[898,64959,1663],{},[902,64961,64962],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,64964,64966],{"className":64965},[886],[888,64967,64968],{"xmlns":890},[892,64969,64970,64976],{},[895,64971,64972,64974],{},[898,64973,9320],{},[898,64975,12737],{},[902,64977,15361],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,64980,64982],{"className":64981},[886],[888,64983,64984],{"xmlns":890},[892,64985,64986,65002],{},[895,64987,64988,64990,64992,64994,64996,64998,65000],{},[898,64989,1663],{},[1654,64991,1750],{},[1665,64993,10207],{},[1654,64995,1674],{"separator":1673},[1665,64997,50082],{},[1654,64999,1674],{"separator":1673},[1665,65001,4573],{},[902,65003,65004],{"encoding":904},"Q = 15, 16, 20",[724,65006,65007,2186,65009,65041],{},[38,65008,31458],{},[883,65010,65012],{"className":65011},[886],[888,65013,65014],{"xmlns":890},[892,65015,65016,65038],{},[895,65017,65018,65020,65022,65024,65026,65028,65030,65032],{},[898,65019,11536],{},[898,65021,12737],{},[1654,65023,1750],{},[1665,65025,4273],{},[898,65027,1663],{},[1654,65029,2380],{},[1665,65031,1681],{},[1741,65033,65034,65036],{},[898,65035,1663],{},[1665,65037,1681],{},[902,65039,65040],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,65043,65045],{"className":65044},[886],[888,65046,65047],{"xmlns":890,"display":1956},[892,65048,65049,65091],{},[895,65050,65051,65053,65055,65057,65059,65061,65063,65065,65067,65073,65079,65081,65083,65085,65087,65089],{},[898,65052,9320],{},[898,65054,12737],{},[1654,65056,1750],{},[1654,65058,1708],{"stretchy":1656},[1665,65060,4273],{},[898,65062,1663],{},[1654,65064,2380],{},[1665,65066,1681],{},[1741,65068,65069,65071],{},[898,65070,1663],{},[1665,65072,1681],{},[1741,65074,65075,65077],{},[1654,65076,1726],{"stretchy":1656},[1654,65078,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,65080,1750],{},[1665,65082,4273],{},[1654,65084,2380],{},[1665,65086,7631],{},[898,65088,1663],{},[898,65090,2138],{"mathvariant":1878},[902,65092,65093],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,65095,3806,65096,16828,65114,65140,65141,13096,65154,65169,65170,65183,65184,30109,65197,13096,65210,65225,65226,65239,65240,65271,65272,65291],{},[883,65097,65099],{"className":65098},[886],[888,65100,65101],{"xmlns":890},[892,65102,65103,65111],{},[895,65104,65105,65107,65109],{},[898,65106,1663],{},[1654,65108,1750],{},[1665,65110,10207],{},[902,65112,65113],{"encoding":904},"Q = 15",[883,65115,65117],{"className":65116},[886],[888,65118,65119],{"xmlns":890},[892,65120,65121,65137],{},[895,65122,65123,65125,65127,65129,65131,65133,65135],{},[898,65124,9320],{},[898,65126,12737],{},[1654,65128,1708],{"stretchy":1656},[1665,65130,10207],{},[1654,65132,1726],{"stretchy":1656},[1654,65134,1750],{},[1665,65136,5844],{},[902,65138,65139],{"encoding":904},"MR(15) = 40",": při množství ",[883,65142,65144],{"className":65143},[886],[888,65145,65146],{"xmlns":890},[892,65147,65148,65152],{},[895,65149,65150],{},[1665,65151,10207],{},[902,65153,10207],{"encoding":904},[883,65155,65157],{"className":65156},[886],[888,65158,65159],{"xmlns":890},[892,65160,65161,65167],{},[895,65162,65163,65165],{},[898,65164,11536],{},[898,65166,12737],{},[902,65168,12837],{"encoding":904}," mění asi ",[883,65171,65173],{"className":65172},[886],[888,65174,65175],{"xmlns":890},[892,65176,65177,65181],{},[895,65178,65179],{},[1665,65180,5844],{},[902,65182,5844],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,65185,65187],{"className":65186},[886],[888,65188,65189],{"xmlns":890},[892,65190,65191,65195],{},[895,65192,65193],{},[898,65194,1663],{},[902,65196,1663],{"encoding":904},[883,65198,65200],{"className":65199},[886],[888,65201,65202],{"xmlns":890},[892,65203,65204,65208],{},[895,65205,65206],{},[1665,65207,1667],{},[902,65209,1667],{"encoding":904},[883,65211,65213],{"className":65212},[886],[888,65214,65215],{"xmlns":890},[892,65216,65217,65223],{},[895,65218,65219,65221],{},[898,65220,11536],{},[898,65222,12737],{},[902,65224,12837],{"encoding":904}," zvýší přibližně o ",[883,65227,65229],{"className":65228},[886],[888,65230,65231],{"xmlns":890},[892,65232,65233,65237],{},[895,65234,65235],{},[1665,65236,5844],{},[902,65238,5844],{"encoding":904},", tj. ze skutečné hodnoty ",[883,65241,65243],{"className":65242},[886],[888,65244,65245],{"xmlns":890},[892,65246,65247,65268],{},[895,65248,65249,65251,65253,65255,65257,65259,65261,65263,65265],{},[898,65250,11536],{},[898,65252,12737],{},[1654,65254,1708],{"stretchy":1656},[1665,65256,10207],{},[1654,65258,1726],{"stretchy":1656},[1654,65260,1750],{},[1665,65262,1667],{},[1865,65264,11744],{},[1665,65266,65267],{},"050",[902,65269,65270],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,65273,65275],{"className":65274},[886],[888,65276,65277],{"xmlns":890},[892,65278,65279,65288],{},[895,65280,65281,65283,65285],{},[1665,65282,1667],{},[1865,65284,11744],{},[1665,65286,65287],{},"090",[902,65289,65290],{"encoding":904},"1\\,090",". Skutečná změna je",[883,65293,65295],{"className":65294},[886],[888,65296,65297],{"xmlns":890,"display":1956},[892,65298,65299,65353],{},[895,65300,65301,65303,65305,65307,65309,65311,65313,65315,65317,65319,65321,65323,65325,65327,65329,65331,65333,65335,65337,65340,65342,65344,65346,65348,65350],{},[898,65302,11648],{"mathvariant":1878},[898,65304,11536],{},[898,65306,12737],{},[1654,65308,1750],{},[898,65310,11536],{},[898,65312,12737],{},[1654,65314,1708],{"stretchy":1656},[1665,65316,50082],{},[1654,65318,1726],{"stretchy":1656},[1654,65320,2380],{},[898,65322,11536],{},[898,65324,12737],{},[1654,65326,1708],{"stretchy":1656},[1665,65328,10207],{},[1654,65330,1726],{"stretchy":1656},[1654,65332,1750],{},[1665,65334,1667],{},[1865,65336,11744],{},[1665,65338,65339],{},"088",[1654,65341,2380],{},[1665,65343,1667],{},[1865,65345,11744],{},[1665,65347,65267],{},[1654,65349,1750],{},[1665,65351,65352],{},"38.",[902,65354,65355],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,65357,65358,65359,1343,65385,4039,65411,65426,65427,65442],{},"Podobně ",[883,65360,65362],{"className":65361},[886],[888,65363,65364],{"xmlns":890},[892,65365,65366,65382],{},[895,65367,65368,65370,65372,65374,65376,65378,65380],{},[898,65369,9320],{},[898,65371,12737],{},[1654,65373,1708],{"stretchy":1656},[1665,65375,50082],{},[1654,65377,1726],{"stretchy":1656},[1654,65379,1750],{},[1665,65381,14295],{},[902,65383,65384],{"encoding":904},"MR(16) = 36",[883,65386,65388],{"className":65387},[886],[888,65389,65390],{"xmlns":890},[892,65391,65392,65408],{},[895,65393,65394,65396,65398,65400,65402,65404,65406],{},[898,65395,9320],{},[898,65397,12737],{},[1654,65399,1708],{"stretchy":1656},[1665,65401,4573],{},[1654,65403,1726],{"stretchy":1656},[1654,65405,1750],{},[1665,65407,4573],{},[902,65409,65410],{"encoding":904},"MR(20) = 20",[883,65412,65414],{"className":65413},[886],[888,65415,65416],{"xmlns":890},[892,65417,65418,65424],{},[895,65419,65420,65422],{},[898,65421,9320],{},[898,65423,12737],{},[902,65425,15361],{"encoding":904}," je klesající funkce — rychlost změny ",[883,65428,65430],{"className":65429},[886],[888,65431,65432],{"xmlns":890},[892,65433,65434,65440],{},[895,65435,65436,65438],{},[898,65437,11536],{},[898,65439,12737],{},[902,65441,12837],{"encoding":904}," s růstem množství klesá.",[198,65444,65446],{"id":65445},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,65448,65449],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,65451,65453],{"className":65452},[886],[888,65454,65455],{"xmlns":890,"display":1956},[892,65456,65457,65526],{},[1960,65458,65459],{"width":1962},[1964,65460,65461,65463,65519,65521],{},[1967,65462],{"width":1969},[1967,65464,65465],{},[895,65466,65467,65469,65471,65473,65475,65477,65479,65481,65483,65485,65487,65489,65491,65493,65499,65501,65503,65505,65507,65509,65511,65513,65515,65517],{},[898,65468,11648],{"mathvariant":1878},[898,65470,11536],{},[898,65472,12737],{},[1865,65474,2805],{},[1654,65476,11492],{},[1865,65478,2805],{},[898,65480,10977],{"mathvariant":1878},[898,65482,11536],{},[898,65484,12737],{},[1654,65486,1750],{},[1654,65488,1708],{"stretchy":1656},[898,65490,11536],{},[898,65492,12737],{},[1741,65494,65495,65497],{},[1654,65496,1726],{"stretchy":1656},[1654,65498,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1865,65500,11744],{},[898,65502,10977],{"mathvariant":1878},[898,65504,1663],{},[1654,65506,1750],{},[898,65508,9320],{},[898,65510,12737],{},[1865,65512,11744],{},[898,65514,10977],{"mathvariant":1878},[898,65516,1663],{},[1654,65518,1674],{"separator":1673},[1967,65520],{"width":1969},[1967,65522,65523],{},[1865,65524,65525],{},"(3.3)",[902,65527,65528],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,65530,65531],{},"schematicky:",[883,65533,65535],{"className":65534},[886],[888,65536,65537],{"xmlns":890,"display":1956},[892,65538,65539,65647],{},[895,65540,65541,65579,65581,65583,65585,65614,65617,65645],{},[895,65542,65543,65546,65552,65555,65561,65564,65570,65576],{},[1865,65544,65545],{},"zm",[17111,65547,65548,65550],{"accent":1673},[1865,65549,53952],{},[1654,65551,33744],{},[1865,65553,65554],{},"na celkov",[17111,65556,65557,65559],{"accent":1673},[1865,65558,53952],{},[1654,65560,33663],{},[1865,65562,65563],{},"ho p",[17111,65565,65566,65568],{"accent":1673},[1865,65567,20753],{},[1654,65569,33744],{},[17111,65571,65572,65574],{"accent":1673},[1865,65573,33732],{},[1654,65575,33663],{},[1865,65577,65578],{},"jmu",[1865,65580,2805],{},[1654,65582,11492],{},[1865,65584,2805],{},[895,65586,65587,65590,65596,65599,65605,65611],{},[1865,65588,65589],{},"mezn",[17111,65591,65592,65594],{"accent":1673},[1865,65593,33732],{},[1654,65595,33663],{},[1865,65597,65598],{}," p",[17111,65600,65601,65603],{"accent":1673},[1865,65602,20753],{},[1654,65604,33744],{},[17111,65606,65607,65609],{"accent":1673},[1865,65608,33732],{},[1654,65610,33663],{},[1865,65612,65613],{},"jem",[1654,65615,65616],{},"×",[895,65618,65619,65621,65627,65630,65636,65639],{},[1865,65620,65545],{},[17111,65622,65623,65625],{"accent":1673},[1865,65624,53952],{},[1654,65626,33744],{},[1865,65628,65629],{},"na mno",[17111,65631,65632,65634],{"accent":1673},[1865,65633,18314],{},[1654,65635,33744],{},[1865,65637,65638],{},"stv",[17111,65640,65641,65643],{"accent":1673},[1865,65642,33732],{},[1654,65644,33663],{},[898,65646,2138],{"mathvariant":1878},[902,65648,65649],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,65651,65652,65653,65668],{},"Pro porovnání skutečná změna ",[883,65654,65656],{"className":65655},[886],[888,65657,65658],{"xmlns":890},[892,65659,65660,65666],{},[895,65661,65662,65664],{},[898,65663,11536],{},[898,65665,12737],{},[902,65667,12837],{"encoding":904}," je",[883,65670,65672],{"className":65671},[886],[888,65673,65674],{"xmlns":890,"display":1956},[892,65675,65676,65731],{},[1960,65677,65678],{"width":1962},[1964,65679,65680,65682,65724,65726],{},[1967,65681],{"width":1969},[1967,65683,65684],{},[895,65685,65686,65688,65690,65692,65694,65696,65698,65700,65702,65704,65706,65708,65710,65712,65714,65716,65718,65720,65722],{},[898,65687,11648],{"mathvariant":1878},[898,65689,11536],{},[898,65691,12737],{},[1654,65693,1750],{},[898,65695,11536],{},[898,65697,12737],{},[1654,65699,1708],{"stretchy":1656},[898,65701,1663],{},[1654,65703,1766],{},[898,65705,10977],{"mathvariant":1878},[898,65707,1663],{},[1654,65709,1726],{"stretchy":1656},[1654,65711,2380],{},[898,65713,11536],{},[898,65715,12737],{},[1654,65717,1708],{"stretchy":1656},[898,65719,1663],{},[1654,65721,1726],{"stretchy":1656},[898,65723,2138],{"mathvariant":1878},[1967,65725],{"width":1969},[1967,65727,65728],{},[1865,65729,65730],{},"(3.4)",[902,65732,65733],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[45568,65735,65737],{"id":65736},"příklad-33","Příklad 3.3",[724,65739,65740,65742,65743,65773,65774,11420,65789,11434,65802,11448,65815,65829],{},[38,65741,64207],{}," Pro ",[883,65744,65746],{"className":65745},[886],[888,65747,65748],{"xmlns":890},[892,65749,65750,65770],{},[895,65751,65752,65754,65756,65758,65760,65762,65764],{},[898,65753,11536],{},[898,65755,12737],{},[1654,65757,1750],{},[1665,65759,4273],{},[898,65761,1663],{},[1654,65763,2380],{},[1741,65765,65766,65768],{},[898,65767,1663],{},[1665,65769,1681],{},[902,65771,65772],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,65775,65777],{"className":65776},[886],[888,65778,65779],{"xmlns":890},[892,65780,65781,65787],{},[895,65782,65783,65785],{},[898,65784,11536],{},[898,65786,12737],{},[902,65788,12837],{"encoding":904},[883,65790,65792],{"className":65791},[886],[888,65793,65794],{"xmlns":890},[892,65795,65796,65800],{},[895,65797,65798],{},[898,65799,1663],{},[902,65801,1663],{"encoding":904},[883,65803,65805],{"className":65804},[886],[888,65806,65807],{"xmlns":890},[892,65808,65809,65813],{},[895,65810,65811],{},[1665,65812,11881],{},[902,65814,11881],{"encoding":904},[883,65816,65818],{"className":65817},[886],[888,65819,65820],{"xmlns":890},[892,65821,65822,65827],{},[895,65823,65824],{},[1665,65825,65826],{},"63",[902,65828,65826],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,65831,65832,2186,65834,65859,65860,1343,65878,2781],{},[38,65833,31458],{},[883,65835,65837],{"className":65836},[886],[888,65838,65839],{"xmlns":890},[892,65840,65841,65857],{},[895,65842,65843,65845,65847,65849,65851,65853,65855],{},[898,65844,9320],{},[898,65846,12737],{},[1654,65848,1750],{},[1665,65850,4273],{},[1654,65852,2380],{},[1665,65854,1681],{},[898,65856,1663],{},[902,65858,20150],{"encoding":904},", tedy při ",[883,65861,65863],{"className":65862},[886],[888,65864,65865],{"xmlns":890},[892,65866,65867,65875],{},[895,65868,65869,65871,65873],{},[898,65870,1663],{},[1654,65872,1750],{},[1665,65874,11881],{},[902,65876,65877],{"encoding":904},"Q = 60",[883,65879,65881],{"className":65880},[886],[888,65882,65883],{"xmlns":890},[892,65884,65885,65895],{},[895,65886,65887,65889,65891,65893],{},[898,65888,10977],{"mathvariant":1878},[898,65890,1663],{},[1654,65892,1750],{},[1665,65894,4035],{},[902,65896,65897],{"encoding":904},"\\mathrm{d}Q = 3",[883,65899,65901],{"className":65900},[886],[888,65902,65903],{"xmlns":890,"display":1956},[892,65904,65905,65936],{},[895,65906,65907,65909,65911,65913,65915,65917,65919,65921,65923,65925,65927,65929,65931,65933],{},[898,65908,10977],{"mathvariant":1878},[898,65910,11536],{},[898,65912,12737],{},[1654,65914,1750],{},[1654,65916,1708],{"stretchy":1656},[1665,65918,4273],{},[1654,65920,2380],{},[1665,65922,12789],{},[1654,65924,1726],{"stretchy":1656},[1654,65926,4554],{},[1665,65928,4035],{},[1654,65930,1750],{},[1654,65932,2380],{},[1665,65934,65935],{},"60.",[902,65937,65938],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,65940,65941,65942,65972,65973,65992],{},"Celkový příjem klesne z ",[883,65943,65945],{"className":65944},[886],[888,65946,65947],{"xmlns":890},[892,65948,65949,65969],{},[895,65950,65951,65953,65955,65957,65959,65961,65963,65965,65967],{},[898,65952,11536],{},[898,65954,12737],{},[1654,65956,1708],{"stretchy":1656},[1665,65958,11881],{},[1654,65960,1726],{"stretchy":1656},[1654,65962,1750],{},[1665,65964,1681],{},[1865,65966,11744],{},[1665,65968,28837],{},[902,65970,65971],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,65974,65976],{"className":65975},[886],[888,65977,65978],{"xmlns":890},[892,65979,65980,65989],{},[895,65981,65982,65984,65986],{},[1665,65983,1681],{},[1865,65985,11744],{},[1665,65987,65988],{},"340",[902,65990,65991],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,65994,65996],{"className":65995},[886],[888,65997,65998],{"xmlns":890,"display":1956},[892,65999,66000,66058],{},[895,66001,66002,66004,66006,66008,66010,66012,66014,66016,66018,66020,66022,66024,66026,66028,66030,66032,66034,66036,66038,66041,66043,66045,66047,66049,66051,66053,66056],{},[898,66003,11648],{"mathvariant":1878},[898,66005,11536],{},[898,66007,12737],{},[1654,66009,1750],{},[898,66011,11536],{},[898,66013,12737],{},[1654,66015,1708],{"stretchy":1656},[1665,66017,65826],{},[1654,66019,1726],{"stretchy":1656},[1654,66021,2380],{},[898,66023,11536],{},[898,66025,12737],{},[1654,66027,1708],{"stretchy":1656},[1665,66029,11881],{},[1654,66031,1726],{"stretchy":1656},[1654,66033,1750],{},[1665,66035,1681],{},[1865,66037,11744],{},[1665,66039,66040],{},"331",[1654,66042,2380],{},[1665,66044,1681],{},[1865,66046,11744],{},[1665,66048,28837],{},[1654,66050,1750],{},[1654,66052,2380],{},[1665,66054,66055],{},"69",[1654,66057,1674],{"separator":1673},[902,66059,66060],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,66062,66063,66064,66079,66080,2138],{},"tj. ",[883,66065,66067],{"className":66066},[886],[888,66068,66069],{"xmlns":890},[892,66070,66071,66077],{},[895,66072,66073,66075],{},[898,66074,11536],{},[898,66076,12737],{},[902,66078,12837],{"encoding":904}," klesne na ",[883,66081,66083],{"className":66082},[886],[888,66084,66085],{"xmlns":890},[892,66086,66087,66095],{},[895,66088,66089,66091,66093],{},[1665,66090,1681],{},[1865,66092,11744],{},[1665,66094,66040],{},[902,66096,66097],{"encoding":904},"2\\,331",[198,66099,66101],{"id":66100},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,66103,66104,66105,19111,66128,5522],{},"Obecně pro lineární poptávku ",[883,66106,66108],{"className":66107},[886],[888,66109,66110],{"xmlns":890},[892,66111,66112,66126],{},[895,66113,66114,66116,66118,66120,66122,66124],{},[898,66115,1755],{},[1654,66117,1750],{},[898,66119,207],{},[898,66121,1663],{},[1654,66123,1766],{},[898,66125,9758],{},[902,66127,45280],{"encoding":904},[883,66129,66131],{"className":66130},[886],[888,66132,66133],{"xmlns":890},[892,66134,66135,66157],{},[895,66136,66137,66139,66141,66143,66145,66151,66153,66155],{},[898,66138,11536],{},[898,66140,12737],{},[1654,66142,1750],{},[898,66144,207],{},[1741,66146,66147,66149],{},[898,66148,1663],{},[1665,66150,1681],{},[1654,66152,1766],{},[898,66154,9758],{},[898,66156,1663],{},[902,66158,66159],{"encoding":904},"TR = aQ^2 + bQ",[883,66161,66163],{"className":66162},[886],[888,66164,66165],{"xmlns":890,"display":1956},[892,66166,66167,66187],{},[895,66168,66169,66171,66173,66175,66177,66179,66181,66183,66185],{},[898,66170,9320],{},[898,66172,12737],{},[1654,66174,1750],{},[1665,66176,1681],{},[898,66178,207],{},[898,66180,1663],{},[1654,66182,1766],{},[898,66184,9758],{},[898,66186,2138],{"mathvariant":1878},[902,66188,66189],{"encoding":904},"MR = 2aQ + b.",[724,66191,66192,66193,66208,66209,66224,66225,66238,66239,18742,66242,66258,66259,66272,66273,66288,66289,66304,66305,66320,66321,11387,66334,66364,66365,66384,66385,66400],{},"Křivky ",[883,66194,66196],{"className":66195},[886],[888,66197,66198],{"xmlns":890},[892,66199,66200,66206],{},[895,66201,66202,66204],{},[898,66203,9320],{},[898,66205,12737],{},[902,66207,15361],{"encoding":904}," a poptávky (resp. ",[883,66210,66212],{"className":66211},[886],[888,66213,66214],{"xmlns":890},[892,66215,66216,66222],{},[895,66217,66218,66220],{},[898,66219,4737],{},[898,66221,12737],{},[902,66223,63665],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,66226,66228],{"className":66227},[886],[888,66229,66230],{"xmlns":890},[892,66231,66232,66236],{},[895,66233,66234],{},[898,66235,9758],{},[902,66237,9758],{"encoding":904},", přičemž ",[38,66240,66241],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,66243,66245],{"className":66244},[886],[888,66246,66247],{"xmlns":890},[892,66248,66249,66255],{},[895,66250,66251,66253],{},[1665,66252,1681],{},[898,66254,207],{},[902,66256,66257],{"encoding":904},"2a"," vs. ",[883,66260,66262],{"className":66261},[886],[888,66263,66264],{"xmlns":890},[892,66265,66266,66270],{},[895,66267,66268],{},[898,66269,207],{},[902,66271,207],{"encoding":904},", obrázek 3.2). ",[883,66274,66276],{"className":66275},[886],[888,66277,66278],{"xmlns":890},[892,66279,66280,66286],{},[895,66281,66282,66284],{},[898,66283,9320],{},[898,66285,12737],{},[902,66287,15361],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,66290,66292],{"className":66291},[886],[888,66293,66294],{"xmlns":890},[892,66295,66296,66302],{},[895,66297,66298,66300],{},[898,66299,11536],{},[898,66301,12737],{},[902,66303,12837],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,66306,66308],{"className":66307},[886],[888,66309,66310],{"xmlns":890},[892,66311,66312,66318],{},[895,66313,66314,66316],{},[898,66315,9320],{},[898,66317,12737],{},[902,66319,15361],{"encoding":904}," osu ",[883,66322,66324],{"className":66323},[886],[888,66325,66326],{"xmlns":890},[892,66327,66328,66332],{},[895,66329,66330],{},[898,66331,1663],{},[902,66333,1663],{"encoding":904},[883,66335,66337],{"className":66336},[886],[888,66338,66339],{"xmlns":890},[892,66340,66341,66361],{},[895,66342,66343,66345,66347,66349],{},[898,66344,1663],{},[1654,66346,1750],{},[1654,66348,2380],{},[2582,66350,66351],{"scriptlevel":2062,"displaystyle":1656},[2811,66352,66353,66355],{},[898,66354,9758],{},[895,66356,66357,66359],{},[1665,66358,1681],{},[898,66360,207],{},[902,66362,66363],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,66366,66368],{"className":66367},[886],[888,66369,66370],{"xmlns":890},[892,66371,66372,66382],{},[895,66373,66374,66376,66378,66380],{},[898,66375,9320],{},[898,66377,12737],{},[1654,66379,1750],{},[1665,66381,2062],{},[902,66383,15810],{"encoding":904},", a dále ",[883,66386,66388],{"className":66387},[886],[888,66389,66390],{"xmlns":890},[892,66391,66392,66398],{},[895,66393,66394,66396],{},[898,66395,11536],{},[898,66397,12737],{},[902,66399,12837],{"encoding":904}," klesá.",[724,66402,66403,66404,66410,66411,66443,66444,66472],{},"V případě ",[38,66405,66406],{},[207,66407,66409],{"className":66408,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,66412,66414],{"className":66413},[886],[888,66415,66416],{"xmlns":890},[892,66417,66418,66440],{},[895,66419,66420,66422,66424,66426,66428,66430,66432,66434],{},[898,66421,1755],{},[1654,66423,1750],{},[898,66425,4980],{},[1654,66427,1708],{"stretchy":1656},[898,66429,1663],{},[1654,66431,1726],{"stretchy":1656},[1654,66433,1750],{},[1741,66435,66436,66438],{},[898,66437,1755],{},[1654,66439,1670],{},[902,66441,66442],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,66445,66447],{"className":66446},[886],[888,66448,66449],{"xmlns":890},[892,66450,66451,66469],{},[895,66452,66453,66455,66457,66459,66461,66463],{},[898,66454,11536],{},[898,66456,12737],{},[1654,66458,1750],{},[898,66460,1663],{},[1654,66462,4554],{},[1741,66464,66465,66467],{},[898,66466,1755],{},[1654,66468,1670],{},[902,66470,66471],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,66474,66476],{"className":66475},[886],[888,66477,66478],{"xmlns":890,"display":1956},[892,66479,66480,66522],{},[895,66481,66482,66484,66486,66488,66490,66492,66494,66500,66502,66504,66518,66520],{},[898,66483,9320],{},[898,66485,12737],{},[1654,66487,1750],{},[898,66489,4737],{},[898,66491,12737],{},[1654,66493,1750],{},[1741,66495,66496,66498],{},[898,66497,1755],{},[1654,66499,1670],{},[5008,66501],{"width":5010},[1654,66503,1708],{"stretchy":1656},[895,66505,66506,66509,66515],{},[1865,66507,66508],{},"obr",[17111,66510,66511,66513],{"accent":1673},[1865,66512,207],{},[1654,66514,33663],{},[1865,66516,66517],{},"zek 3.4",[1654,66519,1726],{"stretchy":1656},[898,66521,2138],{"mathvariant":1878},[902,66523,66524],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,66526,66527],{},[614,66528,66529,66530,2068,66556,66584,66585,66598,66599,66614,66615,12468,66628,1343,66654,12468,66669,2138],{},"Obrázek 3.2: Přímky ",[883,66531,66533],{"className":66532},[886],[888,66534,66535],{"xmlns":890},[892,66536,66537,66553],{},[895,66538,66539,66541,66543,66545,66547,66549,66551],{},[898,66540,4737],{},[898,66542,12737],{},[1654,66544,1750],{},[898,66546,207],{},[898,66548,1663],{},[1654,66550,1766],{},[898,66552,9758],{},[902,66554,66555],{"encoding":904},"AR = aQ + b",[883,66557,66559],{"className":66558},[886],[888,66560,66561],{"xmlns":890},[892,66562,66563,66581],{},[895,66564,66565,66567,66569,66571,66573,66575,66577,66579],{},[898,66566,9320],{},[898,66568,12737],{},[1654,66570,1750],{},[1665,66572,1681],{},[898,66574,207],{},[898,66576,1663],{},[1654,66578,1766],{},[898,66580,9758],{},[902,66582,66583],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,66586,66588],{"className":66587},[886],[888,66589,66590],{"xmlns":890},[892,66591,66592,66596],{},[895,66593,66594],{},[898,66595,9758],{},[902,66597,9758],{"encoding":904}," se svislou osou, ",[883,66600,66602],{"className":66601},[886],[888,66603,66604],{"xmlns":890},[892,66605,66606,66612],{},[895,66607,66608,66610],{},[898,66609,9320],{},[898,66611,12737],{},[902,66613,15361],{"encoding":904}," protíná osu ",[883,66616,66618],{"className":66617},[886],[888,66619,66620],{"xmlns":890},[892,66621,66622,66626],{},[895,66623,66624],{},[898,66625,1663],{},[902,66627,1663],{"encoding":904},[883,66629,66631],{"className":66630},[886],[888,66632,66633],{"xmlns":890},[892,66634,66635,66651],{},[895,66636,66637,66639],{},[1654,66638,2380],{},[2582,66640,66641],{"scriptlevel":2062,"displaystyle":1656},[2811,66642,66643,66645],{},[898,66644,9758],{},[895,66646,66647,66649],{},[1665,66648,1681],{},[898,66650,207],{},[902,66652,66653],{"encoding":904},"-\\tfrac{b}{2a}",[883,66655,66657],{"className":66656},[886],[888,66658,66659],{"xmlns":890},[892,66660,66661,66667],{},[895,66662,66663,66665],{},[898,66664,4737],{},[898,66666,12737],{},[902,66668,63665],{"encoding":904},[883,66670,66672],{"className":66671},[886],[888,66673,66674],{"xmlns":890},[892,66675,66676,66688],{},[895,66677,66678,66680],{},[1654,66679,2380],{},[2582,66681,66682],{"scriptlevel":2062,"displaystyle":1656},[2811,66683,66684,66686],{},[898,66685,9758],{},[898,66687,207],{},[902,66689,66690],{"encoding":904},"-\\tfrac{b}{a}",[724,66692,66693],{},[614,66694,66695,66696,66727,66728,66757,66758,2138],{},"Obrázek 3.3: Parabola ",[883,66697,66699],{"className":66698},[886],[888,66700,66701],{"xmlns":890},[892,66702,66703,66725],{},[895,66704,66705,66707,66709,66711,66713,66719,66721,66723],{},[898,66706,11536],{},[898,66708,12737],{},[1654,66710,1750],{},[898,66712,207],{},[1741,66714,66715,66717],{},[898,66716,1663],{},[1665,66718,1681],{},[1654,66720,1766],{},[898,66722,9758],{},[898,66724,1663],{},[902,66726,66159],{"encoding":904}," s maximem v ",[883,66729,66731],{"className":66730},[886],[888,66732,66733],{"xmlns":890},[892,66734,66735,66755],{},[895,66736,66737,66739,66741,66743],{},[898,66738,1663],{},[1654,66740,1750],{},[1654,66742,2380],{},[2582,66744,66745],{"scriptlevel":2062,"displaystyle":1656},[2811,66746,66747,66749],{},[898,66748,9758],{},[895,66750,66751,66753],{},[1665,66752,1681],{},[898,66754,207],{},[902,66756,66363],{"encoding":904}," a nulou v ",[883,66759,66761],{"className":66760},[886],[888,66762,66763],{"xmlns":890},[892,66764,66765,66781],{},[895,66766,66767,66769,66771,66773],{},[898,66768,1663],{},[1654,66770,1750],{},[1654,66772,2380],{},[2582,66774,66775],{"scriptlevel":2062,"displaystyle":1656},[2811,66776,66777,66779],{},[898,66778,9758],{},[898,66780,207],{},[902,66782,66783],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,66785,66786],{},[614,66787,66788,66789,2138],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,66790,66792],{"className":66791},[886],[888,66793,66794],{"xmlns":890},[892,66795,66796,66816],{},[895,66797,66798,66800,66802,66804,66806,66808,66810],{},[898,66799,4737],{},[898,66801,12737],{},[1654,66803,1750],{},[898,66805,9320],{},[898,66807,12737],{},[1654,66809,1750],{},[1741,66811,66812,66814],{},[898,66813,1755],{},[1654,66815,1670],{},[902,66817,66818],{"encoding":904},"AR = MR = P^*",[115,66820,66822],{"id":66821},"náklady-firmy","Náklady firmy",[198,66824,66826],{"id":66825},"celkové-náklady","Celkové náklady",[724,66828,66829,2186,66831,18742,66846,66849,66850,66863],{},[38,66830,66826],{},[883,66832,66834],{"className":66833},[886],[888,66835,66836],{"xmlns":890},[892,66837,66838,66844],{},[895,66839,66840,66842],{},[898,66841,11536],{},[898,66843,11539],{},[902,66845,11997],{"encoding":904},[38,66847,66848],{},"total cost",") jsou veškeré náklady na realizaci ",[883,66851,66853],{"className":66852},[886],[888,66854,66855],{"xmlns":890},[892,66856,66857,66861],{},[895,66858,66859],{},[898,66860,1663],{},[902,66862,1663],{"encoding":904}," jednotek produkce:",[883,66865,66867],{"className":66866},[886],[888,66868,66869],{"xmlns":890,"display":1956},[892,66870,66871,66926],{},[1960,66872,66873],{"width":1962},[1964,66874,66875,66877,66919,66921],{},[1967,66876],{"width":1969},[1967,66878,66879],{},[895,66880,66881,66883,66885,66887,66889,66891,66893,66895,66897,66899,66901,66903,66905,66907,66909,66911,66913,66915,66917],{},[898,66882,11536],{},[898,66884,11539],{},[1654,66886,1750],{},[898,66888,11536],{},[898,66890,11539],{},[1654,66892,1708],{"stretchy":1656},[898,66894,1663],{},[1654,66896,1726],{"stretchy":1656},[1654,66898,1750],{},[898,66900,19153],{},[898,66902,11539],{},[1654,66904,1766],{},[898,66906,11536],{},[898,66908,48559],{},[898,66910,11539],{},[1654,66912,1708],{"stretchy":1656},[898,66914,1663],{},[1654,66916,1726],{"stretchy":1656},[1654,66918,1674],{"separator":1673},[1967,66920],{"width":1969},[1967,66922,66923],{},[1865,66924,66925],{},"(3.5)",[902,66927,66928],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,66930,13049,66931,66946,66947,18742,66950,20840,66953,66946,66977,18742,66980,66983],{},[883,66932,66934],{"className":66933},[886],[888,66935,66936],{"xmlns":890},[892,66937,66938,66944],{},[895,66939,66940,66942],{},[898,66941,19153],{},[898,66943,11539],{},[902,66945,63711],{"encoding":904}," jsou ",[38,66948,66949],{},"fixní náklady",[38,66951,66952],{},"fixed cost",[883,66954,66956],{"className":66955},[886],[888,66957,66958],{"xmlns":890},[892,66959,66960,66974],{},[895,66961,66962,66964,66966,66968,66970,66972],{},[898,66963,11536],{},[898,66965,48559],{},[898,66967,11539],{},[1654,66969,1708],{"stretchy":1656},[898,66971,1663],{},[1654,66973,1726],{"stretchy":1656},[902,66975,66976],{"encoding":904},"TVC(Q)",[38,66978,66979],{},"celkové variabilní náklady",[38,66981,66982],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,66985,66987],{"id":66986},"průměrné-náklady","Průměrné náklady",[724,66989,66990,2186,66992,18742,67007,67010],{},[38,66991,66987],{},[883,66993,66995],{"className":66994},[886],[888,66996,66997],{"xmlns":890},[892,66998,66999,67005],{},[895,67000,67001,67003],{},[898,67002,4737],{},[898,67004,11539],{},[902,67006,63780],{"encoding":904},[38,67008,67009],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,67012,67014],{"className":67013},[886],[888,67015,67016],{"xmlns":890,"display":1956},[892,67017,67018,67097],{},[1960,67019,67020],{"width":1962},[1964,67021,67022,67024,67090,67092],{},[1967,67023],{"width":1969},[1967,67025,67026],{},[895,67027,67028,67030,67032,67034,67036,67038,67040,67042,67044,67046,67056,67058,67068,67070,67088],{},[898,67029,4737],{},[898,67031,11539],{},[1654,67033,1750],{},[898,67035,4737],{},[898,67037,11539],{},[1654,67039,1708],{"stretchy":1656},[898,67041,1663],{},[1654,67043,1726],{"stretchy":1656},[1654,67045,1750],{},[2811,67047,67048,67054],{},[895,67049,67050,67052],{},[898,67051,11536],{},[898,67053,11539],{},[898,67055,1663],{},[1654,67057,1750],{},[2811,67059,67060,67066],{},[895,67061,67062,67064],{},[898,67063,19153],{},[898,67065,11539],{},[898,67067,1663],{},[1654,67069,1766],{},[2811,67071,67072,67086],{},[895,67073,67074,67076,67078,67080,67082,67084],{},[898,67075,11536],{},[898,67077,48559],{},[898,67079,11539],{},[1654,67081,1708],{"stretchy":1656},[898,67083,1663],{},[1654,67085,1726],{"stretchy":1656},[898,67087,1663],{},[1654,67089,1674],{"separator":1673},[1967,67091],{"width":1969},[1967,67093,67094],{},[1865,67095,67096],{},"(3.6)",[902,67098,67099],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,67101,13049,67102,66946,67126,2186,67129,18742,67146,20840,67149,66946,67181,2186,67184,18742,67201,11906],{},[883,67103,67105],{"className":67104},[886],[888,67106,67107],{"xmlns":890},[892,67108,67109,67123],{},[895,67110,67111],{},[2582,67112,67113],{"scriptlevel":2062,"displaystyle":1656},[2811,67114,67115,67121],{},[895,67116,67117,67119],{},[898,67118,19153],{},[898,67120,11539],{},[898,67122,1663],{},[902,67124,67125],{"encoding":904},"\\tfrac{FC}{Q}",[38,67127,67128],{},"průměrné fixní náklady",[883,67130,67132],{"className":67131},[886],[888,67133,67134],{"xmlns":890},[892,67135,67136,67144],{},[895,67137,67138,67140,67142],{},[898,67139,4737],{},[898,67141,19153],{},[898,67143,11539],{},[902,67145,63747],{"encoding":904},[38,67147,67148],{},"average fixed cost",[883,67150,67152],{"className":67151},[886],[888,67153,67154],{"xmlns":890},[892,67155,67156,67178],{},[895,67157,67158],{},[2582,67159,67160],{"scriptlevel":2062,"displaystyle":1656},[2811,67161,67162,67176],{},[895,67163,67164,67166,67168,67170,67172,67174],{},[898,67165,11536],{},[898,67167,48559],{},[898,67169,11539],{},[1654,67171,1708],{"stretchy":1656},[898,67173,1663],{},[1654,67175,1726],{"stretchy":1656},[898,67177,1663],{},[902,67179,67180],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,67182,67183],{},"průměrné variabilní náklady",[883,67185,67187],{"className":67186},[886],[888,67188,67189],{"xmlns":890},[892,67190,67191,67199],{},[895,67192,67193,67195,67197],{},[898,67194,4737],{},[898,67196,48559],{},[898,67198,11539],{},[902,67200,63531],{"encoding":904},[38,67202,67203],{},"average variable cost",[883,67205,67207],{"className":67206},[886],[888,67208,67209],{"xmlns":890,"display":1956},[892,67210,67211,67270],{},[1960,67212,67213],{"width":1962},[1964,67214,67215,67217,67263,67265],{},[1967,67216],{"width":1969},[1967,67218,67219],{},[895,67220,67221,67223,67225,67227,67229,67231,67233,67235,67237,67239,67241,67243,67261],{},[898,67222,4737],{},[898,67224,48559],{},[898,67226,11539],{},[1654,67228,1750],{},[898,67230,4737],{},[898,67232,48559],{},[898,67234,11539],{},[1654,67236,1708],{"stretchy":1656},[898,67238,1663],{},[1654,67240,1726],{"stretchy":1656},[1654,67242,1750],{},[2811,67244,67245,67259],{},[895,67246,67247,67249,67251,67253,67255,67257],{},[898,67248,11536],{},[898,67250,48559],{},[898,67252,11539],{},[1654,67254,1708],{"stretchy":1656},[898,67256,1663],{},[1654,67258,1726],{"stretchy":1656},[898,67260,1663],{},[898,67262,2138],{"mathvariant":1878},[1967,67264],{"width":1969},[1967,67266,67267],{},[1865,67268,67269],{},"(3.7)",[902,67271,67272],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[45568,67274,67276],{"id":67275},"příklad-34","Příklad 3.4",[724,67278,67279,65742,67281,2068,67306,64245,67330,2068,67345,67360,67361,2138],{},[38,67280,64207],{},[883,67282,67284],{"className":67283},[886],[888,67285,67286],{"xmlns":890},[892,67287,67288,67303],{},[895,67289,67290,67292,67294,67296,67298,67300],{},[898,67291,19153],{},[898,67293,11539],{},[1654,67295,1750],{},[1665,67297,1667],{},[1865,67299,11744],{},[1665,67301,67302],{},"000",[902,67304,67305],{"encoding":904},"FC = 1\\,000",[883,67307,67309],{"className":67308},[886],[888,67310,67311],{"xmlns":890},[892,67312,67313,67327],{},[895,67314,67315,67317,67319,67321,67323,67325],{},[898,67316,11536],{},[898,67318,48559],{},[898,67320,11539],{},[1654,67322,1750],{},[1665,67324,7631],{},[898,67326,1663],{},[902,67328,67329],{"encoding":904},"TVC = 4Q",[883,67331,67333],{"className":67332},[886],[888,67334,67335],{"xmlns":890},[892,67336,67337,67343],{},[895,67338,67339,67341],{},[898,67340,11536],{},[898,67342,11539],{},[902,67344,11997],{"encoding":904},[883,67346,67348],{"className":67347},[886],[888,67349,67350],{"xmlns":890},[892,67351,67352,67358],{},[895,67353,67354,67356],{},[898,67355,4737],{},[898,67357,11539],{},[902,67359,63780],{"encoding":904}," a jejich chování s rostoucím ",[883,67362,67364],{"className":67363},[886],[888,67365,67366],{"xmlns":890},[892,67367,67368,67372],{},[895,67369,67370],{},[898,67371,1663],{},[902,67373,1663],{"encoding":904},[724,67375,67376,2186,67378,2068,67408,67444,67445,13096,67458,67473,67474,2781],{},[38,67377,31458],{},[883,67379,67381],{"className":67380},[886],[888,67382,67383],{"xmlns":890},[892,67384,67385,67405],{},[895,67386,67387,67389,67391,67393,67395,67397,67399,67401,67403],{},[898,67388,11536],{},[898,67390,11539],{},[1654,67392,1750],{},[1665,67394,1667],{},[1865,67396,11744],{},[1665,67398,67302],{},[1654,67400,1766],{},[1665,67402,7631],{},[898,67404,1663],{},[902,67406,67407],{"encoding":904},"TC = 1\\,000 + 4Q",[883,67409,67411],{"className":67410},[886],[888,67412,67413],{"xmlns":890},[892,67414,67415,67441],{},[895,67416,67417,67419,67421,67423,67437,67439],{},[898,67418,4737],{},[898,67420,11539],{},[1654,67422,1750],{},[2582,67424,67425],{"scriptlevel":2062,"displaystyle":1656},[2811,67426,67427,67435],{},[895,67428,67429,67431,67433],{},[1665,67430,1667],{},[1865,67432,11744],{},[1665,67434,67302],{},[898,67436,1663],{},[1654,67438,1766],{},[1665,67440,7631],{},[902,67442,67443],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,67446,67448],{"className":67447},[886],[888,67449,67450],{"xmlns":890},[892,67451,67452,67456],{},[895,67453,67454],{},[898,67455,1663],{},[902,67457,1663],{"encoding":904},[883,67459,67461],{"className":67460},[886],[888,67462,67463],{"xmlns":890},[892,67464,67465,67471],{},[895,67466,67467,67469],{},[898,67468,4737],{},[898,67470,11539],{},[902,67472,63780],{"encoding":904}," blíží ",[883,67475,67477],{"className":67476},[886],[888,67478,67479],{"xmlns":890},[892,67480,67481,67485],{},[895,67482,67483],{},[1665,67484,7631],{},[902,67486,7631],{"encoding":904},[883,67488,67490],{"className":67489},[886],[888,67491,67492],{"xmlns":890,"display":1956},[892,67493,67494,67540],{},[895,67495,67496,67513,67535,67537],{},[48116,67497,67498,67505],{},[895,67499,67500,67503],{},[898,67501,67502],{},"lim",[1654,67504,64420],{},[895,67506,67507,67509,67511],{},[898,67508,1663],{},[1654,67510,11878],{},[898,67512,15025],{"mathvariant":1878},[895,67514,67515,67517,67529,67531,67533],{},[1654,67516,1708],{"fence":1673},[2811,67518,67519,67527],{},[895,67520,67521,67523,67525],{},[1665,67522,1667],{},[1865,67524,11744],{},[1665,67526,67302],{},[898,67528,1663],{},[1654,67530,1766],{},[1665,67532,7631],{},[1654,67534,1726],{"fence":1673},[1654,67536,1750],{},[1665,67538,67539],{},"4.",[902,67541,67542],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,67544,67545,67583,67584,2138],{},[883,67546,67548],{"className":67547},[886],[888,67549,67550],{"xmlns":890},[892,67551,67552,67580],{},[895,67553,67554,67556,67558,67560,67562,67576,67578],{},[898,67555,4737],{},[898,67557,19153],{},[898,67559,11539],{},[1654,67561,1750],{},[2582,67563,67564],{"scriptlevel":2062,"displaystyle":1656},[2811,67565,67566,67574],{},[895,67567,67568,67570,67572],{},[1665,67569,1667],{},[1865,67571,11744],{},[1665,67573,67302],{},[898,67575,1663],{},[1654,67577,11878],{},[1665,67579,2062],{},[902,67581,67582],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,67585,67587],{"className":67586},[886],[888,67588,67589],{"xmlns":890},[892,67590,67591,67595],{},[895,67592,67593],{},[898,67594,1663],{},[902,67596,1663],{"encoding":904},[724,67598,67599],{},[614,67600,67601,67602,67631,67632,2138],{},"Obrázek 3.5: Přímka ",[883,67603,67605],{"className":67604},[886],[888,67606,67607],{"xmlns":890},[892,67608,67609,67629],{},[895,67610,67611,67613,67615,67617,67619,67621,67623,67625,67627],{},[898,67612,11536],{},[898,67614,11539],{},[1654,67616,1750],{},[1665,67618,1667],{},[1865,67620,11744],{},[1665,67622,67302],{},[1654,67624,1766],{},[1665,67626,7631],{},[898,67628,1663],{},[902,67630,67407],{"encoding":904}," protínající svislou osu ve výši ",[883,67633,67635],{"className":67634},[886],[888,67636,67637],{"xmlns":890},[892,67638,67639,67653],{},[895,67640,67641,67643,67645,67647,67649,67651],{},[898,67642,19153],{},[898,67644,11539],{},[1654,67646,1750],{},[1665,67648,1667],{},[1865,67650,11744],{},[1665,67652,67302],{},[902,67654,67305],{"encoding":904},[724,67656,67657],{},[614,67658,67659,67660,67695,67696,2138],{},"Obrázek 3.6: Hyperbola ",[883,67661,67663],{"className":67662},[886],[888,67664,67665],{"xmlns":890},[892,67666,67667,67693],{},[895,67668,67669,67671,67673,67675,67689,67691],{},[898,67670,4737],{},[898,67672,11539],{},[1654,67674,1750],{},[2582,67676,67677],{"scriptlevel":2062,"displaystyle":1656},[2811,67678,67679,67687],{},[895,67680,67681,67683,67685],{},[1665,67682,1667],{},[1865,67684,11744],{},[1665,67686,67302],{},[898,67688,1663],{},[1654,67690,1766],{},[1665,67692,7631],{},[902,67694,67443],{"encoding":904}," s vodorovnou asymptotou ",[883,67697,67699],{"className":67698},[886],[888,67700,67701],{"xmlns":890},[892,67702,67703,67713],{},[895,67704,67705,67707,67709,67711],{},[898,67706,4737],{},[898,67708,11539],{},[1654,67710,1750],{},[1665,67712,7631],{},[902,67714,67715],{"encoding":904},"AC = 4",[724,67717,67718],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,67720,67722],{"className":67721},[886],[888,67723,67724],{"xmlns":890,"display":1956},[892,67725,67726,67752],{},[895,67727,67728,67730,67732,67734,67736,67738,67740,67742,67744,67746,67748,67750],{},[898,67729,11536],{},[898,67731,48559],{},[898,67733,11539],{},[1654,67735,1750],{},[898,67737,1663],{},[1654,67739,4554],{},[898,67741,48559],{},[898,67743,11539],{},[1654,67745,1708],{"stretchy":1656},[898,67747,1663],{},[1654,67749,1726],{"stretchy":1656},[1654,67751,1674],{"separator":1673},[902,67753,67754],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,67756,13049,67757,66946,67785,67788,67789,67819],{},[883,67758,67760],{"className":67759},[886],[888,67761,67762],{"xmlns":890},[892,67763,67764,67782],{},[895,67765,67766,67768,67770,67772,67774,67776,67778,67780],{},[898,67767,48559],{},[898,67769,11539],{},[1654,67771,1750],{},[898,67773,48559],{},[898,67775,11539],{},[1654,67777,1708],{"stretchy":1656},[898,67779,1663],{},[1654,67781,1726],{"stretchy":1656},[902,67783,67784],{"encoding":904},"VC = VC(Q)",[38,67786,67787],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,67790,67792],{"className":67791},[886],[888,67793,67794],{"xmlns":890},[892,67795,67796,67816],{},[895,67797,67798,67800,67802,67804,67806,67808,67810,67812,67814],{},[898,67799,11536],{},[898,67801,48559],{},[898,67803,11539],{},[1654,67805,1708],{"stretchy":1656},[898,67807,1663],{},[1654,67809,1726],{"stretchy":1656},[1654,67811,1750],{},[898,67813,207],{},[898,67815,1663],{},[902,67817,67818],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,67821,67823],{"className":67822},[886],[888,67824,67825],{"xmlns":890,"display":1956},[892,67826,67827,67847],{},[895,67828,67829,67831,67833,67835,67837,67839,67841,67843,67845],{},[898,67830,11536],{},[898,67832,11539],{},[1654,67834,1750],{},[898,67836,19153],{},[898,67838,11539],{},[1654,67840,1766],{},[898,67842,207],{},[898,67844,1663],{},[898,67846,2138],{"mathvariant":1878},[902,67848,67849],{"encoding":904},"TC = FC + aQ.",[724,67851,67852,67853,67868,67869,67884,67885,67908,67909,67943,67944,67695,67957,67970,67971,2068,68019,68063,68064,2138],{},"Křivkou ",[883,67854,67856],{"className":67855},[886],[888,67857,67858],{"xmlns":890},[892,67859,67860,67866],{},[895,67861,67862,67864],{},[898,67863,11536],{},[898,67865,11539],{},[902,67867,11997],{"encoding":904}," je přímka se svislým průsečíkem ",[883,67870,67872],{"className":67871},[886],[888,67873,67874],{"xmlns":890},[892,67875,67876,67882],{},[895,67877,67878,67880],{},[898,67879,19153],{},[898,67881,11539],{},[902,67883,63711],{"encoding":904}," a sklonem ",[883,67886,67888],{"className":67887},[886],[888,67889,67890],{"xmlns":890},[892,67891,67892,67905],{},[895,67893,67894,67897,67899,67901,67903],{},[898,67895,67896],{},"tan",[1654,67898,64420],{},[898,67900,27558],{},[1654,67902,1750],{},[898,67904,207],{},[902,67906,67907],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,67910,67912],{"className":67911},[886],[888,67913,67914],{"xmlns":890},[892,67915,67916,67940],{},[895,67917,67918,67920,67922,67924,67936,67938],{},[898,67919,4737],{},[898,67921,11539],{},[1654,67923,1750],{},[2582,67925,67926],{"scriptlevel":2062,"displaystyle":1656},[2811,67927,67928,67934],{},[895,67929,67930,67932],{},[898,67931,19153],{},[898,67933,11539],{},[898,67935,1663],{},[1654,67937,1766],{},[898,67939,207],{},[902,67941,67942],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,67945,67947],{"className":67946},[886],[888,67948,67949],{"xmlns":890},[892,67950,67951,67955],{},[895,67952,67953],{},[898,67954,2450],{},[902,67956,2450],{"encoding":904},[883,67958,67960],{"className":67959},[886],[888,67961,67962],{"xmlns":890},[892,67963,67964,67968],{},[895,67965,67966],{},[898,67967,207],{},[902,67969,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,67972,67974],{"className":67973},[886],[888,67975,67976],{"xmlns":890},[892,67977,67978,68016],{},[895,67979,67980,68000,68012,68014],{},[1710,67981,67982,67988],{},[895,67983,67984,67986],{},[898,67985,67502],{},[1654,67987,64420],{},[895,67989,67990,67992,67994],{},[898,67991,1663],{},[1654,67993,11878],{},[1741,67995,67996,67998],{},[1665,67997,2062],{},[1654,67999,1766],{},[2582,68001,68002],{"scriptlevel":2062,"displaystyle":1656},[2811,68003,68004,68010],{},[895,68005,68006,68008],{},[898,68007,19153],{},[898,68009,11539],{},[898,68011,1663],{},[1654,68013,1750],{},[898,68015,15025],{"mathvariant":1878},[902,68017,68018],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,68020,68022],{"className":68021},[886],[888,68023,68024],{"xmlns":890},[892,68025,68026,68060],{},[895,68027,68028,68044,68056,68058],{},[1710,68029,68030,68036],{},[895,68031,68032,68034],{},[898,68033,67502],{},[1654,68035,64420],{},[895,68037,68038,68040,68042],{},[898,68039,1663],{},[1654,68041,11878],{},[898,68043,15025],{"mathvariant":1878},[2582,68045,68046],{"scriptlevel":2062,"displaystyle":1656},[2811,68047,68048,68054],{},[895,68049,68050,68052],{},[898,68051,19153],{},[898,68053,11539],{},[898,68055,1663],{},[1654,68057,1750],{},[1665,68059,2062],{},[902,68061,68062],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,68065,68067],{"className":68066},[886],[888,68068,68069],{"xmlns":890},[892,68070,68071,68077],{},[895,68072,68073,68075],{},[898,68074,4737],{},[898,68076,11539],{},[902,68078,63780],{"encoding":904},[724,68080,68081],{},[614,68082,68083,68084,68099,68100,68115,68116,2138],{},"Obrázek 3.7: Přímka ",[883,68085,68087],{"className":68086},[886],[888,68088,68089],{"xmlns":890},[892,68090,68091,68097],{},[895,68092,68093,68095],{},[898,68094,11536],{},[898,68096,11539],{},[902,68098,11997],{"encoding":904}," s osovým průsečíkem ve výši ",[883,68101,68103],{"className":68102},[886],[888,68104,68105],{"xmlns":890},[892,68106,68107,68113],{},[895,68108,68109,68111],{},[898,68110,19153],{},[898,68112,11539],{},[902,68114,63711],{"encoding":904}," a se sklonem ",[883,68117,68119],{"className":68118},[886],[888,68120,68121],{"xmlns":890},[892,68122,68123,68135],{},[895,68124,68125,68127,68129,68131,68133],{},[898,68126,67896],{},[1654,68128,64420],{},[898,68130,27558],{},[1654,68132,1750],{},[898,68134,207],{},[902,68136,67907],{"encoding":904},[724,68138,68139],{},[614,68140,68141,68142,68157,68158,2138],{},"Obrázek 3.8: Klesající hyperbola ",[883,68143,68145],{"className":68144},[886],[888,68146,68147],{"xmlns":890},[892,68148,68149,68155],{},[895,68150,68151,68153],{},[898,68152,4737],{},[898,68154,11539],{},[902,68156,63780],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,68159,68161],{"className":68160},[886],[888,68162,68163],{"xmlns":890},[892,68164,68165,68169],{},[895,68166,68167],{},[898,68168,207],{},[902,68170,207],{"encoding":904},[198,68172,68174],{"id":68173},"mezní-náklady","Mezní náklady",[724,68176,68177,2186,68179,18742,68194,68197,68198,68201],{},[38,68178,68174],{},[883,68180,68182],{"className":68181},[886],[888,68183,68184],{"xmlns":890},[892,68185,68186,68192],{},[895,68187,68188,68190],{},[898,68189,9320],{},[898,68191,11539],{},[902,68193,63512],{"encoding":904},[38,68195,68196],{},"marginal cost",") jsou ",[207,68199,1145],{"className":68200,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,68203,68205],{"className":68204},[886],[888,68206,68207],{"xmlns":890,"display":1956},[892,68208,68209,68278],{},[1960,68210,68211],{"width":1962},[1964,68212,68213,68215,68271,68273],{},[1967,68214],{"width":1969},[1967,68216,68217],{},[895,68218,68219,68221,68223,68225,68227,68229,68231,68233,68235,68237,68253,68255,68257,68263,68265,68267,68269],{},[898,68220,9320],{},[898,68222,11539],{},[1654,68224,1750],{},[898,68226,9320],{},[898,68228,11539],{},[1654,68230,1708],{"stretchy":1656},[898,68232,1663],{},[1654,68234,1726],{"stretchy":1656},[1654,68236,1750],{},[2811,68238,68239,68247],{},[895,68240,68241,68243,68245],{},[898,68242,10977],{"mathvariant":1878},[898,68244,11536],{},[898,68246,11539],{},[895,68248,68249,68251],{},[898,68250,10977],{"mathvariant":1878},[898,68252,1663],{},[1654,68254,1750],{},[898,68256,11536],{},[1741,68258,68259,68261],{},[898,68260,11539],{},[1654,68262,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,68264,1708],{"stretchy":1656},[898,68266,1663],{},[1654,68268,1726],{"stretchy":1656},[898,68270,2138],{"mathvariant":1878},[1967,68272],{"width":1969},[1967,68274,68275],{},[1865,68276,68277],{},"(3.8)",[902,68279,68280],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[2140,68282,68283],{},[724,68284,68285,68287,68288,68314,68315,68332,68333,2138],{},[883,68286,2860],{}," Intuice — „kolik stojí další kus\"\n",[883,68289,68291],{"className":68290},[886],[888,68292,68293],{"xmlns":890},[892,68294,68295,68311],{},[895,68296,68297,68299,68301,68303,68309],{},[898,68298,9320],{},[898,68300,11539],{},[1654,68302,1708],{"stretchy":1656},[1741,68304,68305,68307],{},[898,68306,1663],{},[1654,68308,1670],{},[1654,68310,1726],{"stretchy":1656},[902,68312,68313],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,68316,68318],{"className":68317},[886],[888,68319,68320],{"xmlns":890},[892,68321,68322,68330],{},[895,68323,68324],{},[1741,68325,68326,68328],{},[898,68327,1663],{},[1654,68329,1670],{},[902,68331,3768],{"encoding":904},". Formálně ",[883,68334,68336],{"className":68335},[886],[888,68337,68338],{"xmlns":890},[892,68339,68340,68392],{},[895,68341,68342,68344,68346,68348,68354,68356,68358,68360,68362,68364,68370,68372,68374,68376,68378,68380,68382,68384,68390],{},[898,68343,9320],{},[898,68345,11539],{},[1654,68347,1708],{"stretchy":1656},[1741,68349,68350,68352],{},[898,68351,1663],{},[1654,68353,1670],{},[1654,68355,1726],{"stretchy":1656},[1654,68357,11492],{},[898,68359,11536],{},[898,68361,11539],{},[1654,68363,1708],{"stretchy":1656},[1741,68365,68366,68368],{},[898,68367,1663],{},[1654,68369,1670],{},[1654,68371,1766],{},[1665,68373,1667],{},[1654,68375,1726],{"stretchy":1656},[1654,68377,2380],{},[898,68379,11536],{},[898,68381,11539],{},[1654,68383,1708],{"stretchy":1656},[1741,68385,68386,68388],{},[898,68387,1663],{},[1654,68389,1670],{},[1654,68391,1726],{"stretchy":1656},[902,68393,68394],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,68396,68397,68398,2781],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,68399,68401],{"className":68400},[886],[888,68402,68403],{"xmlns":890},[892,68404,68405,68413],{},[895,68406,68407,68409,68411],{},[898,68408,11648],{"mathvariant":1878},[898,68410,11536],{},[898,68412,11539],{},[902,68414,68415],{"encoding":904},"\\Delta TC",[883,68417,68419],{"className":68418},[886],[888,68420,68421],{"xmlns":890,"display":1956},[892,68422,68423,68492],{},[1960,68424,68425],{"width":1962},[1964,68426,68427,68429,68485,68487],{},[1967,68428],{"width":1969},[1967,68430,68431],{},[895,68432,68433,68435,68437,68439,68441,68443,68445,68447,68449,68451,68453,68455,68457,68459,68465,68467,68469,68471,68473,68475,68477,68479,68481,68483],{},[898,68434,11648],{"mathvariant":1878},[898,68436,11536],{},[898,68438,11539],{},[1865,68440,2805],{},[1654,68442,11492],{},[1865,68444,2805],{},[898,68446,10977],{"mathvariant":1878},[898,68448,11536],{},[898,68450,11539],{},[1654,68452,1750],{},[1654,68454,1708],{"stretchy":1656},[898,68456,11536],{},[898,68458,11539],{},[1741,68460,68461,68463],{},[1654,68462,1726],{"stretchy":1656},[1654,68464,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1865,68466,11744],{},[898,68468,10977],{"mathvariant":1878},[898,68470,1663],{},[1654,68472,1750],{},[898,68474,9320],{},[898,68476,11539],{},[1865,68478,11744],{},[898,68480,10977],{"mathvariant":1878},[898,68482,1663],{},[1654,68484,1674],{"separator":1673},[1967,68486],{"width":1969},[1967,68488,68489],{},[1865,68490,68491],{},"(3.9)",[902,68493,68494],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,68496,65531],{},[883,68498,68500],{"className":68499},[886],[888,68501,68502],{"xmlns":890,"display":1956},[892,68503,68504,68602],{},[895,68505,68506,68544,68546,68548,68550,68572,68574,68600],{},[895,68507,68508,68510,68516,68518,68524,68527,68533,68536],{},[1865,68509,65545],{},[17111,68511,68512,68514],{"accent":1673},[1865,68513,53952],{},[1654,68515,33744],{},[1865,68517,65554],{},[17111,68519,68520,68522],{"accent":1673},[1865,68521,10789],{},[1654,68523,33663],{},[1865,68525,68526],{},"ch n",[17111,68528,68529,68531],{"accent":1673},[1865,68530,207],{},[1654,68532,33663],{},[1865,68534,68535],{},"klad",[17111,68537,68538,68541],{"accent":1673},[1865,68539,68540],{},"u",[1654,68542,68543],{},"˚",[1865,68545,2805],{},[1654,68547,11492],{},[1865,68549,2805],{},[895,68551,68552,68554,68560,68563,68569],{},[1865,68553,65589],{},[17111,68555,68556,68558],{"accent":1673},[1865,68557,33732],{},[1654,68559,33663],{},[1865,68561,68562],{}," n",[17111,68564,68565,68567],{"accent":1673},[1865,68566,207],{},[1654,68568,33663],{},[1865,68570,68571],{},"klady",[1654,68573,65616],{},[895,68575,68576,68578,68584,68586,68592,68594],{},[1865,68577,65545],{},[17111,68579,68580,68582],{"accent":1673},[1865,68581,53952],{},[1654,68583,33744],{},[1865,68585,65629],{},[17111,68587,68588,68590],{"accent":1673},[1865,68589,18314],{},[1654,68591,33744],{},[1865,68593,65638],{},[17111,68595,68596,68598],{"accent":1673},[1865,68597,33732],{},[1654,68599,33663],{},[898,68601,2138],{"mathvariant":1878},[902,68603,68604],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[45568,68606,68608],{"id":68607},"příklad-35","Příklad 3.5",[724,68610,68611,65742,68613,64245,68649,68664,68665,68680,68681,11434,68694,11448,68707,68720,68721,11448,68734,2138],{},[38,68612,64207],{},[883,68614,68616],{"className":68615},[886],[888,68617,68618],{"xmlns":890},[892,68619,68620,68646],{},[895,68621,68622,68624,68626,68628,68630,68632,68634,68636,68638,68640],{},[898,68623,11536],{},[898,68625,11539],{},[1654,68627,1750],{},[1665,68629,17102],{},[1654,68631,1766],{},[1665,68633,11015],{},[898,68635,1663],{},[1654,68637,1766],{},[1665,68639,1681],{},[1741,68641,68642,68644],{},[898,68643,1663],{},[1665,68645,1681],{},[902,68647,68648],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,68650,68652],{"className":68651},[886],[888,68653,68654],{"xmlns":890},[892,68655,68656,68662],{},[895,68657,68658,68660],{},[898,68659,9320],{},[898,68661,11539],{},[902,68663,63512],{"encoding":904}," a odhadněte změny ",[883,68666,68668],{"className":68667},[886],[888,68669,68670],{"xmlns":890},[892,68671,68672,68678],{},[895,68673,68674,68676],{},[898,68675,11536],{},[898,68677,11539],{},[902,68679,11997],{"encoding":904}," při změnách ",[883,68682,68684],{"className":68683},[886],[888,68685,68686],{"xmlns":890},[892,68687,68688,68692],{},[895,68689,68690],{},[898,68691,1663],{},[902,68693,1663],{"encoding":904},[883,68695,68697],{"className":68696},[886],[888,68698,68699],{"xmlns":890},[892,68700,68701,68705],{},[895,68702,68703],{},[1665,68704,10207],{},[902,68706,10207],{"encoding":904},[883,68708,68710],{"className":68709},[886],[888,68711,68712],{"xmlns":890},[892,68713,68714,68718],{},[895,68715,68716],{},[1665,68717,50082],{},[902,68719,50082],{"encoding":904}," a z ",[883,68722,68724],{"className":68723},[886],[888,68725,68726],{"xmlns":890},[892,68727,68728,68732],{},[895,68729,68730],{},[1665,68731,10207],{},[902,68733,10207],{"encoding":904},[883,68735,68737],{"className":68736},[886],[888,68738,68739],{"xmlns":890},[892,68740,68741,68745],{},[895,68742,68743],{},[1665,68744,6509],{},[902,68746,6509],{"encoding":904},[724,68748,68749,2186,68751,4039,68777,1343,68804,68831,68832,68847,68848,68863,68864,68891,68892,68912,68913,29225,68934,68990,68991,11434,69004,11448,69017,16828,69030,2138],{},[38,68750,31458],{},[883,68752,68754],{"className":68753},[886],[888,68755,68756],{"xmlns":890},[892,68757,68758,68774],{},[895,68759,68760,68762,68764,68766,68768,68770,68772],{},[898,68761,9320],{},[898,68763,11539],{},[1654,68765,1750],{},[1665,68767,11015],{},[1654,68769,1766],{},[1665,68771,7631],{},[898,68773,1663],{},[902,68775,68776],{"encoding":904},"MC = 6 + 4Q",[883,68778,68780],{"className":68779},[886],[888,68781,68782],{"xmlns":890},[892,68783,68784,68801],{},[895,68785,68786,68788,68790,68792,68794,68796,68798],{},[898,68787,9320],{},[898,68789,11539],{},[1654,68791,1708],{"stretchy":1656},[1665,68793,10207],{},[1654,68795,1726],{"stretchy":1656},[1654,68797,1750],{},[1665,68799,68800],{},"66",[902,68802,68803],{"encoding":904},"MC(15) = 66",[883,68805,68807],{"className":68806},[886],[888,68808,68809],{"xmlns":890},[892,68810,68811,68828],{},[895,68812,68813,68815,68817,68819,68821,68823,68825],{},[898,68814,9320],{},[898,68816,11539],{},[1654,68818,1708],{"stretchy":1656},[1665,68820,4573],{},[1654,68822,1726],{"stretchy":1656},[1654,68824,1750],{},[1665,68826,68827],{},"86",[902,68829,68830],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,68833,68835],{"className":68834},[886],[888,68836,68837],{"xmlns":890},[892,68838,68839,68845],{},[895,68840,68841,68843],{},[898,68842,11536],{},[898,68844,11539],{},[902,68846,11997],{"encoding":904}," zvyšuje (",[883,68849,68851],{"className":68850},[886],[888,68852,68853],{"xmlns":890},[892,68854,68855,68861],{},[895,68856,68857,68859],{},[898,68858,9320],{},[898,68860,11539],{},[902,68862,63512],{"encoding":904}," je rostoucí). Z ",[883,68865,68867],{"className":68866},[886],[888,68868,68869],{"xmlns":890},[892,68870,68871,68888],{},[895,68872,68873,68875,68877,68879,68881,68883,68885],{},[898,68874,11536],{},[898,68876,11539],{},[1654,68878,1708],{"stretchy":1656},[1665,68880,10207],{},[1654,68882,1726],{"stretchy":1656},[1654,68884,1750],{},[1665,68886,68887],{},"740",[902,68889,68890],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,68893,68895],{"className":68894},[886],[888,68896,68897],{"xmlns":890},[892,68898,68899,68909],{},[895,68900,68901,68903,68905,68907],{},[898,68902,10977],{"mathvariant":1878},[898,68904,1663],{},[1654,68906,1750],{},[1665,68908,1667],{},[902,68910,68911],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,68914,68916],{"className":68915},[886],[888,68917,68918],{"xmlns":890},[892,68919,68920,68931],{},[895,68921,68922,68924,68926,68928],{},[898,68923,11536],{},[898,68925,11539],{},[1654,68927,11492],{},[1665,68929,68930],{},"806",[902,68932,68933],{"encoding":904},"TC \\approx 806",[883,68935,68937],{"className":68936},[886],[888,68938,68939],{"xmlns":890},[892,68940,68941,68987],{},[895,68942,68943,68945,68947,68949,68951,68953,68955,68957,68959,68961,68963,68965,68967,68969,68971,68973,68975,68978,68980,68982,68984],{},[898,68944,11648],{"mathvariant":1878},[898,68946,11536],{},[898,68948,11539],{},[1654,68950,1750],{},[898,68952,11536],{},[898,68954,11539],{},[1654,68956,1708],{"stretchy":1656},[1665,68958,50082],{},[1654,68960,1726],{"stretchy":1656},[1654,68962,2380],{},[898,68964,11536],{},[898,68966,11539],{},[1654,68968,1708],{"stretchy":1656},[1665,68970,10207],{},[1654,68972,1726],{"stretchy":1656},[1654,68974,1750],{},[1665,68976,68977],{},"808",[1654,68979,2380],{},[1665,68981,68887],{},[1654,68983,1750],{},[1665,68985,68986],{},"68",[902,68988,68989],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,68992,68994],{"className":68993},[886],[888,68995,68996],{"xmlns":890},[892,68997,68998,69002],{},[895,68999,69000],{},[898,69001,1663],{},[902,69003,1663],{"encoding":904},[883,69005,69007],{"className":69006},[886],[888,69008,69009],{"xmlns":890},[892,69010,69011,69015],{},[895,69012,69013],{},[1665,69014,10207],{},[902,69016,10207],{"encoding":904},[883,69018,69020],{"className":69019},[886],[888,69021,69022],{"xmlns":890},[892,69023,69024,69028],{},[895,69025,69026],{},[1665,69027,6509],{},[902,69029,6509],{"encoding":904},[883,69031,69033],{"className":69032},[886],[888,69034,69035],{"xmlns":890},[892,69036,69037,69066],{},[895,69038,69039,69041,69043,69045,69047,69049,69051,69053,69055,69057,69059,69061,69063],{},[898,69040,11648],{"mathvariant":1878},[898,69042,11536],{},[898,69044,11539],{},[1654,69046,11492],{},[1665,69048,68800],{},[1654,69050,4554],{},[1654,69052,1708],{"stretchy":1656},[1654,69054,2380],{},[1665,69056,4035],{},[1654,69058,1726],{"stretchy":1656},[1654,69060,1750],{},[1654,69062,2380],{},[1665,69064,69065],{},"198",[902,69067,69068],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,69070,69072],{"id":69071},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,69074,69075],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[45568,69077,69079],{"id":69078},"příklad-36","Příklad 3.6",[724,69081,69082,65742,69084,69128],{},[38,69083,64207],{},[883,69085,69087],{"className":69086},[886],[888,69088,69089],{"xmlns":890},[892,69090,69091,69125],{},[895,69092,69093,69095,69097,69099,69101,69103,69105,69107,69109,69111,69117,69119],{},[898,69094,11536],{},[898,69096,11539],{},[1654,69098,1750],{},[1665,69100,4273],{},[1654,69102,1766],{},[1665,69104,4622],{},[898,69106,1663],{},[1654,69108,2380],{},[1665,69110,4032],{},[1741,69112,69113,69115],{},[898,69114,1663],{},[1665,69116,1681],{},[1654,69118,1766],{},[1741,69120,69121,69123],{},[898,69122,1663],{},[1665,69124,4035],{},[902,69126,69127],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,69130,69131],{},[38,69132,31458],{},[883,69134,69136],{"className":69135},[886],[888,69137,69138],{"xmlns":890,"display":1956},[892,69139,69140,69384],{},[1960,69141,69142,69168,69216,69250,69292,69342],{"rowspacing":2574,"columnalign":2575,"columnspacing":2576},[1964,69143,69144,69154],{},[1967,69145,69146],{},[2582,69147,69148],{"scriptlevel":2062,"displaystyle":1673},[895,69149,69150,69152],{},[898,69151,19153],{},[898,69153,11539],{},[1967,69155,69156],{},[2582,69157,69158],{"scriptlevel":2062,"displaystyle":1673},[895,69159,69160,69162,69164,69166],{},[895,69161],{},[1654,69163,1750],{},[1665,69165,4273],{},[1654,69167,1674],{"separator":1673},[1964,69169,69170,69182],{},[1967,69171,69172],{},[2582,69173,69174],{"scriptlevel":2062,"displaystyle":1673},[895,69175,69176,69178,69180],{},[898,69177,11536],{},[898,69179,48559],{},[898,69181,11539],{},[1967,69183,69184],{},[2582,69185,69186],{"scriptlevel":2062,"displaystyle":1673},[895,69187,69188,69190,69192,69194,69196,69198,69200,69206,69208,69214],{},[895,69189],{},[1654,69191,1750],{},[1665,69193,4622],{},[898,69195,1663],{},[1654,69197,2380],{},[1665,69199,4032],{},[1741,69201,69202,69204],{},[898,69203,1663],{},[1665,69205,1681],{},[1654,69207,1766],{},[1741,69209,69210,69212],{},[898,69211,1663],{},[1665,69213,4035],{},[1654,69215,1674],{"separator":1673},[1964,69217,69218,69230],{},[1967,69219,69220],{},[2582,69221,69222],{"scriptlevel":2062,"displaystyle":1673},[895,69223,69224,69226,69228],{},[898,69225,4737],{},[898,69227,19153],{},[898,69229,11539],{},[1967,69231,69232],{},[2582,69233,69234],{"scriptlevel":2062,"displaystyle":1673},[895,69235,69236,69238,69240,69248],{},[895,69237],{},[1654,69239,1750],{},[2582,69241,69242],{"scriptlevel":2062,"displaystyle":1656},[2811,69243,69244,69246],{},[1665,69245,4273],{},[898,69247,1663],{},[1654,69249,1674],{"separator":1673},[1964,69251,69252,69264],{},[1967,69253,69254],{},[2582,69255,69256],{"scriptlevel":2062,"displaystyle":1673},[895,69257,69258,69260,69262],{},[898,69259,4737],{},[898,69261,48559],{},[898,69263,11539],{},[1967,69265,69266],{},[2582,69267,69268],{"scriptlevel":2062,"displaystyle":1673},[895,69269,69270,69272,69274,69276,69278,69280,69282,69284,69290],{},[895,69271],{},[1654,69273,1750],{},[1665,69275,4622],{},[1654,69277,2380],{},[1665,69279,4032],{},[898,69281,1663],{},[1654,69283,1766],{},[1741,69285,69286,69288],{},[898,69287,1663],{},[1665,69289,1681],{},[1654,69291,1674],{"separator":1673},[1964,69293,69294,69304],{},[1967,69295,69296],{},[2582,69297,69298],{"scriptlevel":2062,"displaystyle":1673},[895,69299,69300,69302],{},[898,69301,4737],{},[898,69303,11539],{},[1967,69305,69306],{},[2582,69307,69308],{"scriptlevel":2062,"displaystyle":1673},[895,69309,69310,69312,69314,69322,69324,69326,69328,69330,69332,69334,69340],{},[895,69311],{},[1654,69313,1750],{},[2582,69315,69316],{"scriptlevel":2062,"displaystyle":1656},[2811,69317,69318,69320],{},[1665,69319,4273],{},[898,69321,1663],{},[1654,69323,1766],{},[1665,69325,4622],{},[1654,69327,2380],{},[1665,69329,4032],{},[898,69331,1663],{},[1654,69333,1766],{},[1741,69335,69336,69338],{},[898,69337,1663],{},[1665,69339,1681],{},[1654,69341,1674],{"separator":1673},[1964,69343,69344,69354],{},[1967,69345,69346],{},[2582,69347,69348],{"scriptlevel":2062,"displaystyle":1673},[895,69349,69350,69352],{},[898,69351,9320],{},[898,69353,11539],{},[1967,69355,69356],{},[2582,69357,69358],{"scriptlevel":2062,"displaystyle":1673},[895,69359,69360,69362,69364,69366,69368,69370,69372,69374,69376,69382],{},[895,69361],{},[1654,69363,1750],{},[1665,69365,4622],{},[1654,69367,2380],{},[1665,69369,4647],{},[898,69371,1663],{},[1654,69373,1766],{},[1665,69375,4035],{},[1741,69377,69378,69380],{},[898,69379,1663],{},[1665,69381,1681],{},[898,69383,2138],{"mathvariant":1878},[902,69385,69386],{"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}",[724,69388,69389,69390,24497,69405,24497,69420,69435,69436,69451,69452,1343,69470,69451,69487,1343,69505,69451,69520,69538],{},"Význačné body ",[883,69391,69393],{"className":69392},[886],[888,69394,69395],{"xmlns":890},[892,69396,69397,69402],{},[895,69398,69399],{},[1665,69400,69401],{},"1,67",[902,69403,69404],{"encoding":904},"1{,}67",[883,69406,69408],{"className":69407},[886],[888,69409,69410],{"xmlns":890},[892,69411,69412,69417],{},[895,69413,69414],{},[1665,69415,69416],{},"2,50",[902,69418,69419],{"encoding":904},"2{,}50",[883,69421,69423],{"className":69422},[886],[888,69424,69425],{"xmlns":890},[892,69426,69427,69432],{},[895,69428,69429],{},[1665,69430,69431],{},"4,73",[902,69433,69434],{"encoding":904},"4{,}73"," odpovídají: ",[883,69437,69439],{"className":69438},[886],[888,69440,69441],{"xmlns":890},[892,69442,69443,69449],{},[895,69444,69445,69447],{},[898,69446,9320],{},[898,69448,11539],{},[902,69450,63512],{"encoding":904}," minimum v ",[883,69453,69455],{"className":69454},[886],[888,69456,69457],{"xmlns":890},[892,69458,69459,69467],{},[895,69460,69461,69463,69465],{},[898,69462,1663],{},[1654,69464,14628],{},[1665,69466,69401],{},[902,69468,69469],{"encoding":904},"Q \\doteq 1{,}67",[883,69471,69473],{"className":69472},[886],[888,69474,69475],{"xmlns":890},[892,69476,69477,69485],{},[895,69478,69479,69481,69483],{},[898,69480,4737],{},[898,69482,48559],{},[898,69484,11539],{},[902,69486,63531],{"encoding":904},[883,69488,69490],{"className":69489},[886],[888,69491,69492],{"xmlns":890},[892,69493,69494,69502],{},[895,69495,69496,69498,69500],{},[898,69497,1663],{},[1654,69499,1750],{},[1665,69501,69416],{},[902,69503,69504],{"encoding":904},"Q = 2{,}50",[883,69506,69508],{"className":69507},[886],[888,69509,69510],{"xmlns":890},[892,69511,69512,69518],{},[895,69513,69514,69516],{},[898,69515,4737],{},[898,69517,11539],{},[902,69519,63780],{"encoding":904},[883,69521,69523],{"className":69522},[886],[888,69524,69525],{"xmlns":890},[892,69526,69527,69535],{},[895,69528,69529,69531,69533],{},[898,69530,1663],{},[1654,69532,14628],{},[1665,69534,69431],{},[902,69536,69537],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,69540,69541],{},[3492,69542],{"alt":69543,"className":69544,"src":69545},"imek-ac-avc-mc",[210,3496],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,69547,69548],{},[614,69549,69550,69551,2068,69566,69583,69584,24497,69603,69618],{},"Obrázek 3.9: Kubické křivky ",[883,69552,69554],{"className":69553},[886],[888,69555,69556],{"xmlns":890},[892,69557,69558,69564],{},[895,69559,69560,69562],{},[898,69561,11536],{},[898,69563,11539],{},[902,69565,11997],{"encoding":904},[883,69567,69569],{"className":69568},[886],[888,69570,69571],{"xmlns":890},[892,69572,69573,69581],{},[895,69574,69575,69577,69579],{},[898,69576,11536],{},[898,69578,48559],{},[898,69580,11539],{},[902,69582,63729],{"encoding":904}," rostoucí od bodu ",[883,69585,69587],{"className":69586},[886],[888,69588,69589],{"xmlns":890},[892,69590,69591,69601],{},[895,69592,69593,69595,69597,69599],{},[898,69594,19153],{},[898,69596,11539],{},[1654,69598,1750],{},[1665,69600,4273],{},[902,69602,20347],{"encoding":904},[883,69604,69606],{"className":69605},[886],[888,69607,69608],{"xmlns":890},[892,69609,69610,69616],{},[895,69611,69612,69614],{},[898,69613,19153],{},[898,69615,11539],{},[902,69617,63711],{"encoding":904}," je vodorovná přímka.",[724,69620,69621],{},[614,69622,69623,69624,1343,69639,1343,69656,3120,69671,69684,69685,4039,69702,69717,69718,14918,69735,69750,69751,34875,69764,1343,69777,1343,69790,2138],{},"Obrázek 3.10: Křivky ",[883,69625,69627],{"className":69626},[886],[888,69628,69629],{"xmlns":890},[892,69630,69631,69637],{},[895,69632,69633,69635],{},[898,69634,4737],{},[898,69636,11539],{},[902,69638,63780],{"encoding":904},[883,69640,69642],{"className":69641},[886],[888,69643,69644],{"xmlns":890},[892,69645,69646,69654],{},[895,69647,69648,69650,69652],{},[898,69649,4737],{},[898,69651,48559],{},[898,69653,11539],{},[902,69655,63531],{"encoding":904},[883,69657,69659],{"className":69658},[886],[888,69660,69661],{"xmlns":890},[892,69662,69663,69669],{},[895,69664,69665,69667],{},[898,69666,9320],{},[898,69668,11539],{},[902,69670,63512],{"encoding":904},[883,69672,69674],{"className":69673},[886],[888,69675,69676],{"xmlns":890},[892,69677,69678,69682],{},[895,69679,69680],{},[898,69681,900],{},[902,69683,900],{"encoding":904}," a klesající hyperbola ",[883,69686,69688],{"className":69687},[886],[888,69689,69690],{"xmlns":890},[892,69691,69692,69700],{},[895,69693,69694,69696,69698],{},[898,69695,4737],{},[898,69697,19153],{},[898,69699,11539],{},[902,69701,63747],{"encoding":904},[883,69703,69705],{"className":69704},[886],[888,69706,69707],{"xmlns":890},[892,69708,69709,69715],{},[895,69710,69711,69713],{},[898,69712,9320],{},[898,69714,11539],{},[902,69716,63512],{"encoding":904}," protíná ",[883,69719,69721],{"className":69720},[886],[888,69722,69723],{"xmlns":890},[892,69724,69725,69733],{},[895,69726,69727,69729,69731],{},[898,69728,4737],{},[898,69730,48559],{},[898,69732,11539],{},[902,69734,63531],{"encoding":904},[883,69736,69738],{"className":69737},[886],[888,69739,69740],{"xmlns":890},[892,69741,69742,69748],{},[895,69743,69744,69746],{},[898,69745,4737],{},[898,69747,11539],{},[902,69749,63780],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,69752,69754],{"className":69753},[886],[888,69755,69756],{"xmlns":890},[892,69757,69758,69762],{},[895,69759,69760],{},[898,69761,1663],{},[902,69763,1663],{"encoding":904},[883,69765,69767],{"className":69766},[886],[888,69768,69769],{"xmlns":890},[892,69770,69771,69775],{},[895,69772,69773],{},[1665,69774,69401],{},[902,69776,69404],{"encoding":904},[883,69778,69780],{"className":69779},[886],[888,69781,69782],{"xmlns":890},[892,69783,69784,69788],{},[895,69785,69786],{},[1665,69787,69416],{},[902,69789,69419],{"encoding":904},[883,69791,69793],{"className":69792},[886],[888,69794,69795],{"xmlns":890},[892,69796,69797,69801],{},[895,69798,69799],{},[1665,69800,69431],{},[902,69802,69434],{"encoding":904},[724,69804,69805],{},[38,69806,69807],{},"Standardní vlastnosti:",[120,69809,69810,69845,69909,69977,70027,70047],{},[123,69811,69812,2068,69827,69844],{},[883,69813,69815],{"className":69814},[886],[888,69816,69817],{"xmlns":890},[892,69818,69819,69825],{},[895,69820,69821,69823],{},[898,69822,11536],{},[898,69824,11539],{},[902,69826,11997],{"encoding":904},[883,69828,69830],{"className":69829},[886],[888,69831,69832],{"xmlns":890},[892,69833,69834,69842],{},[895,69835,69836,69838,69840],{},[898,69837,11536],{},[898,69839,48559],{},[898,69841,11539],{},[902,69843,63729],{"encoding":904}," jsou kubické funkce;",[123,69846,69847,1343,69862,1343,69879,69894,69895,69908],{},[883,69848,69850],{"className":69849},[886],[888,69851,69852],{"xmlns":890},[892,69853,69854,69860],{},[895,69855,69856,69858],{},[898,69857,4737],{},[898,69859,11539],{},[902,69861,63780],{"encoding":904},[883,69863,69865],{"className":69864},[886],[888,69866,69867],{"xmlns":890},[892,69868,69869,69877],{},[895,69870,69871,69873,69875],{},[898,69872,4737],{},[898,69874,48559],{},[898,69876,11539],{},[902,69878,63531],{"encoding":904},[883,69880,69882],{"className":69881},[886],[888,69883,69884],{"xmlns":890},[892,69885,69886,69892],{},[895,69887,69888,69890],{},[898,69889,9320],{},[898,69891,11539],{},[902,69893,63512],{"encoding":904}," jsou křivky tvaru ",[883,69896,69898],{"className":69897},[886],[888,69899,69900],{"xmlns":890},[892,69901,69902,69906],{},[895,69903,69904],{},[898,69905,900],{},[902,69907,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,69910,69911,69926,69927,1343,69944,69961,69962,17150],{},[883,69912,69914],{"className":69913},[886],[888,69915,69916],{"xmlns":890},[892,69917,69918,69924],{},[895,69919,69920,69922],{},[898,69921,9320],{},[898,69923,11539],{},[902,69925,63512],{"encoding":904}," nabývá minima před ",[883,69928,69930],{"className":69929},[886],[888,69931,69932],{"xmlns":890},[892,69933,69934,69942],{},[895,69935,69936,69938,69940],{},[898,69937,4737],{},[898,69939,48559],{},[898,69941,11539],{},[902,69943,63531],{"encoding":904},[883,69945,69947],{"className":69946},[886],[888,69948,69949],{"xmlns":890},[892,69950,69951,69959],{},[895,69952,69953,69955,69957],{},[898,69954,4737],{},[898,69956,48559],{},[898,69958,11539],{},[902,69960,63531],{"encoding":904}," před ",[883,69963,69965],{"className":69964},[886],[888,69966,69967],{"xmlns":890},[892,69968,69969,69975],{},[895,69970,69971,69973],{},[898,69972,4737],{},[898,69974,11539],{},[902,69976,63780],{"encoding":904},[123,69978,69979,69717,69994,2068,70009,70026],{},[883,69980,69982],{"className":69981},[886],[888,69983,69984],{"xmlns":890},[892,69985,69986,69992],{},[895,69987,69988,69990],{},[898,69989,9320],{},[898,69991,11539],{},[902,69993,63512],{"encoding":904},[883,69995,69997],{"className":69996},[886],[888,69998,69999],{"xmlns":890},[892,70000,70001,70007],{},[895,70002,70003,70005],{},[898,70004,4737],{},[898,70006,11539],{},[902,70008,63780],{"encoding":904},[883,70010,70012],{"className":70011},[886],[888,70013,70014],{"xmlns":890},[892,70015,70016,70024],{},[895,70017,70018,70020,70022],{},[898,70019,4737],{},[898,70021,48559],{},[898,70023,11539],{},[902,70025,63531],{"encoding":904}," zdola právě v jejich minimech;",[123,70028,70029,70046],{},[883,70030,70032],{"className":70031},[886],[888,70033,70034],{"xmlns":890},[892,70035,70036,70044],{},[895,70037,70038,70040,70042],{},[898,70039,4737],{},[898,70041,19153],{},[898,70043,11539],{},[902,70045,63747],{"encoding":904}," je hyperbola, stále klesající;",[123,70048,70049,70081,70082,2068,70097,70114,70115,70128,70129,12664],{},[883,70050,70052],{"className":70051},[886],[888,70053,70054],{"xmlns":890},[892,70055,70056,70078],{},[895,70057,70058,70060,70062,70064,70066,70068,70070,70072,70074,70076],{},[898,70059,4737],{},[898,70061,11539],{},[1654,70063,1750],{},[898,70065,4737],{},[898,70067,19153],{},[898,70069,11539],{},[1654,70071,1766],{},[898,70073,4737],{},[898,70075,48559],{},[898,70077,11539],{},[902,70079,70080],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,70083,70085],{"className":70084},[886],[888,70086,70087],{"xmlns":890},[892,70088,70089,70095],{},[895,70090,70091,70093],{},[898,70092,4737],{},[898,70094,11539],{},[902,70096,63780],{"encoding":904},[883,70098,70100],{"className":70099},[886],[888,70101,70102],{"xmlns":890},[892,70103,70104,70112],{},[895,70105,70106,70108,70110],{},[898,70107,4737],{},[898,70109,48559],{},[898,70111,11539],{},[902,70113,63531],{"encoding":904}," klesá s rostoucím ",[883,70116,70118],{"className":70117},[886],[888,70119,70120],{"xmlns":890},[892,70121,70122,70126],{},[895,70123,70124],{},[898,70125,1663],{},[902,70127,1663],{"encoding":904}," (protože ",[883,70130,70132],{"className":70131},[886],[888,70133,70134],{"xmlns":890},[892,70135,70136,70148],{},[895,70137,70138,70140,70142,70144,70146],{},[898,70139,4737],{},[898,70141,19153],{},[898,70143,11539],{},[1654,70145,11878],{},[1665,70147,2062],{},[902,70149,70150],{"encoding":904},"AFC \\to 0",[115,70152,70154],{"id":70153},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,70156,70157,70158,70161,70162,70177],{},"Častou optimalizační úlohou je ",[38,70159,70160],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,70163,70165],{"className":70164},[886],[888,70166,70167],{"xmlns":890},[892,70168,70169,70175],{},[895,70170,70171,70173],{},[898,70172,4737],{},[898,70174,11539],{},[902,70176,63780],{"encoding":904}," minimální.",[198,70179,25115],{"id":25114},[724,70181,70182,70183,70200],{},"Mají-li průměrné náklady minimum v bodě ",[883,70184,70186],{"className":70185},[886],[888,70187,70188],{"xmlns":890},[892,70189,70190,70198],{},[895,70191,70192],{},[1710,70193,70194,70196],{},[898,70195,1663],{},[1665,70197,2062],{},[902,70199,46528],{"encoding":904},", pak platí",[883,70202,70204],{"className":70203},[886],[888,70205,70206],{"xmlns":890,"display":1956},[892,70207,70208,70257],{},[1960,70209,70210],{"width":1962},[1964,70211,70212,70214,70250,70252],{},[1967,70213],{"width":1969},[1967,70215,70216],{},[895,70217,70218,70220,70222,70224,70230,70232,70234,70236,70238,70240,70246,70248],{},[898,70219,4737],{},[898,70221,11539],{},[1654,70223,1708],{"stretchy":1656},[1710,70225,70226,70228],{},[898,70227,1663],{},[1665,70229,2062],{},[1654,70231,1726],{"stretchy":1656},[1654,70233,1750],{},[898,70235,9320],{},[898,70237,11539],{},[1654,70239,1708],{"stretchy":1656},[1710,70241,70242,70244],{},[898,70243,1663],{},[1665,70245,2062],{},[1654,70247,1726],{"stretchy":1656},[898,70249,2138],{"mathvariant":1878},[1967,70251],{"width":1969},[1967,70253,70254],{},[1865,70255,70256],{},"(3.10)",[902,70258,70259],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[2140,70261,70262],{},[724,70263,70264,70266,70267],{},[883,70265,64664],{}," Princip\n",[38,70268,70269],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,70271,70272,70275,70276,70318],{},[38,70273,70274],{},"Odvození."," Z ",[883,70277,70279],{"className":70278},[886],[888,70280,70281],{"xmlns":890},[892,70282,70283,70315],{},[895,70284,70285,70287,70289,70291,70293,70295,70297],{},[898,70286,4737],{},[898,70288,11539],{},[1654,70290,1708],{"stretchy":1656},[898,70292,1663],{},[1654,70294,1726],{"stretchy":1656},[1654,70296,1750],{},[2582,70298,70299],{"scriptlevel":2062,"displaystyle":1656},[2811,70300,70301,70313],{},[895,70302,70303,70305,70307,70309,70311],{},[898,70304,11536],{},[898,70306,11539],{},[1654,70308,1708],{"stretchy":1656},[898,70310,1663],{},[1654,70312,1726],{"stretchy":1656},[898,70314,1663],{},[902,70316,70317],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,70320,70322],{"className":70321},[886],[888,70323,70324],{"xmlns":890,"display":1956},[892,70325,70326,70458],{},[895,70327,70328,70330,70336,70338,70340,70342,70344,70384,70386,70426,70428,70456],{},[898,70329,4737],{},[1741,70331,70332,70334],{},[898,70333,11539],{},[1654,70335,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,70337,1708],{"stretchy":1656},[898,70339,1663],{},[1654,70341,1726],{"stretchy":1656},[1654,70343,1750],{},[2811,70345,70346,70378],{},[895,70347,70348,70350,70356,70358,70360,70362,70364,70366,70368,70370,70372,70374,70376],{},[898,70349,11536],{},[1741,70351,70352,70354],{},[898,70353,11539],{},[1654,70355,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,70357,1708],{"stretchy":1656},[898,70359,1663],{},[1654,70361,1726],{"stretchy":1656},[1654,70363,4554],{},[898,70365,1663],{},[1654,70367,2380],{},[898,70369,11536],{},[898,70371,11539],{},[1654,70373,1708],{"stretchy":1656},[898,70375,1663],{},[1654,70377,1726],{"stretchy":1656},[1741,70379,70380,70382],{},[898,70381,1663],{},[1665,70383,1681],{},[1654,70385,1750],{},[2811,70387,70388,70420],{},[895,70389,70390,70392,70394,70396,70398,70400,70402,70404,70406,70408,70410,70412,70414,70416,70418],{},[898,70391,9320],{},[898,70393,11539],{},[1654,70395,1708],{"stretchy":1656},[898,70397,1663],{},[1654,70399,1726],{"stretchy":1656},[1654,70401,4554],{},[898,70403,1663],{},[1654,70405,2380],{},[898,70407,4737],{},[898,70409,11539],{},[1654,70411,1708],{"stretchy":1656},[898,70413,1663],{},[1654,70415,1726],{"stretchy":1656},[1654,70417,4554],{},[898,70419,1663],{},[1741,70421,70422,70424],{},[898,70423,1663],{},[1665,70425,1681],{},[1654,70427,1750],{},[2811,70429,70430,70454],{},[895,70431,70432,70434,70436,70438,70440,70442,70444,70446,70448,70450,70452],{},[898,70433,9320],{},[898,70435,11539],{},[1654,70437,1708],{"stretchy":1656},[898,70439,1663],{},[1654,70441,1726],{"stretchy":1656},[1654,70443,2380],{},[898,70445,4737],{},[898,70447,11539],{},[1654,70449,1708],{"stretchy":1656},[898,70451,1663],{},[1654,70453,1726],{"stretchy":1656},[898,70455,1663],{},[898,70457,2138],{"mathvariant":1878},[902,70459,70460],{"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}.",[724,70462,70463,70464,11387,70479,16828,70501,65041],{},"Nutnou podmínkou minima ",[883,70465,70467],{"className":70466},[886],[888,70468,70469],{"xmlns":890},[892,70470,70471,70477],{},[895,70472,70473,70475],{},[898,70474,4737],{},[898,70476,11539],{},[902,70478,63780],{"encoding":904},[883,70480,70482],{"className":70481},[886],[888,70483,70484],{"xmlns":890},[892,70485,70486,70498],{},[895,70487,70488,70494,70496],{},[1710,70489,70490,70492],{},[898,70491,1663],{},[1665,70493,2062],{},[1654,70495,2952],{},[1665,70497,2062],{},[902,70499,70500],{"encoding":904},"Q_0 > 0",[883,70502,70504],{"className":70503},[886],[888,70505,70506],{"xmlns":890},[892,70507,70508,70532],{},[895,70509,70510,70512,70518,70520,70526,70528,70530],{},[898,70511,4737],{},[1741,70513,70514,70516],{},[898,70515,11539],{},[1654,70517,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,70519,1708],{"stretchy":1656},[1710,70521,70522,70524],{},[898,70523,1663],{},[1665,70525,2062],{},[1654,70527,1726],{"stretchy":1656},[1654,70529,1750],{},[1665,70531,2062],{},[902,70533,70534],{"encoding":904},"AC'(Q_0) = 0",[883,70536,70538],{"className":70537},[886],[888,70539,70540],{"xmlns":890,"display":1956},[892,70541,70542,70627],{},[895,70543,70544,70584,70586,70588,70590,70593,70595,70597,70599,70601,70607,70609,70611,70613,70615,70617,70623,70625],{},[2811,70545,70546,70578],{},[895,70547,70548,70550,70552,70554,70560,70562,70564,70566,70568,70570,70576],{},[898,70549,9320],{},[898,70551,11539],{},[1654,70553,1708],{"stretchy":1656},[1710,70555,70556,70558],{},[898,70557,1663],{},[1665,70559,2062],{},[1654,70561,1726],{"stretchy":1656},[1654,70563,2380],{},[898,70565,4737],{},[898,70567,11539],{},[1654,70569,1708],{"stretchy":1656},[1710,70571,70572,70574],{},[898,70573,1663],{},[1665,70575,2062],{},[1654,70577,1726],{"stretchy":1656},[1710,70579,70580,70582],{},[898,70581,1663],{},[1665,70583,2062],{},[1654,70585,1750],{},[1665,70587,2062],{},[5008,70589],{"width":5010},[1654,70591,70592],{},"⟺",[5008,70594],{"width":5010},[898,70596,9320],{},[898,70598,11539],{},[1654,70600,1708],{"stretchy":1656},[1710,70602,70603,70605],{},[898,70604,1663],{},[1665,70606,2062],{},[1654,70608,1726],{"stretchy":1656},[1654,70610,1750],{},[898,70612,4737],{},[898,70614,11539],{},[1654,70616,1708],{"stretchy":1656},[1710,70618,70619,70621],{},[898,70620,1663],{},[1665,70622,2062],{},[1654,70624,1726],{"stretchy":1656},[898,70626,2138],{"mathvariant":1878},[902,70628,70629],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,70631,70632,2186,70635,69717,70650,70665,70666,70681,70682,16828,70699,70721,70722,70744],{},[38,70633,70634],{},"Geometrická interpretace.",[883,70636,70638],{"className":70637},[886],[888,70639,70640],{"xmlns":890},[892,70641,70642,70648],{},[895,70643,70644,70646],{},[898,70645,9320],{},[898,70647,11539],{},[902,70649,63512],{"encoding":904},[883,70651,70653],{"className":70652},[886],[888,70654,70655],{"xmlns":890},[892,70656,70657,70663],{},[895,70658,70659,70661],{},[898,70660,4737],{},[898,70662,11539],{},[902,70664,63780],{"encoding":904}," právě v bodě minima ",[883,70667,70669],{"className":70668},[886],[888,70670,70671],{"xmlns":890},[892,70672,70673,70679],{},[895,70674,70675,70677],{},[898,70676,4737],{},[898,70678,11539],{},[902,70680,63780],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,70683,70685],{"className":70684},[886],[888,70686,70687],{"xmlns":890},[892,70688,70689,70697],{},[895,70690,70691],{},[1710,70692,70693,70695],{},[898,70694,1663],{},[1665,70696,2062],{},[902,70698,46528],{"encoding":904},[883,70700,70702],{"className":70701},[886],[888,70703,70704],{"xmlns":890},[892,70705,70706,70718],{},[895,70707,70708,70710,70712,70714,70716],{},[898,70709,9320],{},[898,70711,11539],{},[1654,70713,3002],{},[898,70715,4737],{},[898,70717,11539],{},[902,70719,70720],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,70723,70725],{"className":70724},[886],[888,70726,70727],{"xmlns":890},[892,70728,70729,70741],{},[895,70730,70731,70733,70735,70737,70739],{},[898,70732,9320],{},[898,70734,11539],{},[1654,70736,2952],{},[898,70738,4737],{},[898,70740,11539],{},[902,70742,70743],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,70746,70747,70748,70790,70791,70808,70809,2138],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,70749,70751],{"className":70750},[886],[888,70752,70753],{"xmlns":890},[892,70754,70755,70787],{},[895,70756,70757,70759,70761,70763,70769,70771,70773,70775,70777,70779,70785],{},[898,70758,4737],{},[898,70760,11539],{},[1654,70762,1708],{"stretchy":1656},[1710,70764,70765,70767],{},[898,70766,1663],{},[1665,70768,2062],{},[1654,70770,1726],{"stretchy":1656},[1654,70772,1750],{},[898,70774,9320],{},[898,70776,11539],{},[1654,70778,1708],{"stretchy":1656},[1710,70780,70781,70783],{},[898,70782,1663],{},[1665,70784,2062],{},[1654,70786,1726],{"stretchy":1656},[902,70788,70789],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,70792,70794],{"className":70793},[886],[888,70795,70796],{"xmlns":890},[892,70797,70798,70806],{},[895,70799,70800],{},[1710,70801,70802,70804],{},[898,70803,1663],{},[1665,70805,2062],{},[902,70807,46528],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,70810,70812],{"className":70811},[886],[888,70813,70814],{"xmlns":890},[892,70815,70816,70840],{},[895,70817,70818,70820,70822,70824,70826,70828,70830,70832,70834,70836,70838],{},[898,70819,4737],{},[898,70821,11539],{},[1654,70823,1708],{"stretchy":1656},[898,70825,1663],{},[1654,70827,1726],{"stretchy":1656},[1654,70829,1750],{},[898,70831,9320],{},[898,70833,11539],{},[1654,70835,1708],{"stretchy":1656},[898,70837,1663],{},[1654,70839,1726],{"stretchy":1656},[902,70841,70842],{"encoding":904},"AC(Q) = MC(Q)",[2140,70844,70845],{},[724,70846,70847,70849,70850,19111,70868,70889,70890,19111,70893,70914,70915,70930,70931,66258,70946,12664],{},[883,70848,2146],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,70851,70852,70853],{},"minimum ",[883,70854,70856],{"className":70855},[886],[888,70857,70858],{"xmlns":890},[892,70859,70860,70866],{},[895,70861,70862,70864],{},[898,70863,4737],{},[898,70865,11539],{},[902,70867,63780],{"encoding":904},[883,70869,70871],{"className":70870},[886],[888,70872,70873],{"xmlns":890},[892,70874,70875,70887],{},[895,70876,70877,70879,70881,70883,70885],{},[898,70878,4737],{},[898,70880,11539],{},[1654,70882,1750],{},[898,70884,9320],{},[898,70886,11539],{},[902,70888,63443],{"encoding":904},", pro ",[38,70891,70892],{},"maximum zisku",[883,70894,70896],{"className":70895},[886],[888,70897,70898],{"xmlns":890},[892,70899,70900,70912],{},[895,70901,70902,70904,70906,70908,70910],{},[898,70903,9320],{},[898,70905,12737],{},[1654,70907,1750],{},[898,70909,9320],{},[898,70911,11539],{},[902,70913,63491],{"encoding":904},". Obě podmínky využívají ",[883,70916,70918],{"className":70917},[886],[888,70919,70920],{"xmlns":890},[892,70921,70922,70928],{},[895,70923,70924,70926],{},[898,70925,9320],{},[898,70927,11539],{},[902,70929,63512],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,70932,70934],{"className":70933},[886],[888,70935,70936],{"xmlns":890},[892,70937,70938,70944],{},[895,70939,70940,70942],{},[898,70941,4737],{},[898,70943,11539],{},[902,70945,63780],{"encoding":904},[883,70947,70949],{"className":70948},[886],[888,70950,70951],{"xmlns":890},[892,70952,70953,70959],{},[895,70954,70955,70957],{},[898,70956,9320],{},[898,70958,12737],{},[902,70960,15361],{"encoding":904},[45568,70962,70964],{"id":70963},"příklad-37","Příklad 3.7",[724,70966,70967,65742,70969,71003,71004,71017,71018,71033],{},[38,70968,64207],{},[883,70970,70972],{"className":70971},[886],[888,70973,70974],{"xmlns":890},[892,70975,70976,71000],{},[895,70977,70978,70980,70982,70984,70990,70992,70994,70996,70998],{},[898,70979,11536],{},[898,70981,11539],{},[1654,70983,1750],{},[1741,70985,70986,70988],{},[898,70987,1663],{},[1665,70989,1681],{},[1654,70991,1766],{},[1665,70993,4035],{},[898,70995,1663],{},[1654,70997,1766],{},[1665,70999,14295],{},[902,71001,71002],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,71005,71007],{"className":71006},[886],[888,71008,71009],{"xmlns":890},[892,71010,71011,71015],{},[895,71012,71013],{},[898,71014,1663],{},[902,71016,1663],{"encoding":904}," minimalizující ",[883,71019,71021],{"className":71020},[886],[888,71022,71023],{"xmlns":890},[892,71024,71025,71031],{},[895,71026,71027,71029],{},[898,71028,4737],{},[898,71030,11539],{},[902,71032,63780],{"encoding":904}," a ověřte princip (3.10).",[724,71035,71036,71038],{},[38,71037,31458],{}," Přímý výpočet:",[883,71040,71042],{"className":71041},[886],[888,71043,71044],{"xmlns":890,"display":1956},[892,71045,71046,71148],{},[895,71047,71048,71050,71052,71054,71076,71078,71080,71082,71084,71086,71092,71094,71096,71098,71100,71102,71108,71110,71112,71114,71124,71126,71146],{},[898,71049,4737],{},[898,71051,11539],{},[1654,71053,1750],{},[2811,71055,71056,71074],{},[895,71057,71058,71064,71066,71068,71070,71072],{},[1741,71059,71060,71062],{},[898,71061,1663],{},[1665,71063,1681],{},[1654,71065,1766],{},[1665,71067,4035],{},[898,71069,1663],{},[1654,71071,1766],{},[1665,71073,14295],{},[898,71075,1663],{},[1654,71077,1750],{},[898,71079,1663],{},[1654,71081,1766],{},[1665,71083,4035],{},[1654,71085,1766],{},[2811,71087,71088,71090],{},[1665,71089,14295],{},[898,71091,1663],{},[1654,71093,1674],{"separator":1673},[5008,71095],{"width":14608},[1654,71097,1708],{"stretchy":1656},[898,71099,4737],{},[898,71101,11539],{},[1741,71103,71104,71106],{},[1654,71105,1726],{"stretchy":1656},[1654,71107,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,71109,1750],{},[1665,71111,1667],{},[1654,71113,2380],{},[2811,71115,71116,71118],{},[1665,71117,14295],{},[1741,71119,71120,71122],{},[898,71121,1663],{},[1665,71123,1681],{},[1654,71125,1750],{},[2811,71127,71128,71140],{},[895,71129,71130,71136,71138],{},[1741,71131,71132,71134],{},[898,71133,1663],{},[1665,71135,1681],{},[1654,71137,2380],{},[1665,71139,14295],{},[1741,71141,71142,71144],{},[898,71143,1663],{},[1665,71145,1681],{},[898,71147,2138],{"mathvariant":1878},[902,71149,71150],{"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}.",[724,71152,71153,71193,71194,71218,71219,71269,71270,2138],{},[883,71154,71156],{"className":71155},[886],[888,71157,71158],{"xmlns":890},[892,71159,71160,71190],{},[895,71161,71162,71164,71166,71168,71174,71176,71178,71180,71186,71188],{},[1654,71163,1708],{"stretchy":1656},[898,71165,4737],{},[898,71167,11539],{},[1741,71169,71170,71172],{},[1654,71171,1726],{"stretchy":1656},[1654,71173,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,71175,1750],{},[1665,71177,2062],{},[1654,71179,8634],{},[1710,71181,71182,71184],{},[898,71183,1663],{},[1665,71185,1667],{},[1654,71187,1750],{},[1665,71189,11015],{},[902,71191,71192],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,71195,71197],{"className":71196},[886],[888,71198,71199],{"xmlns":890},[892,71200,71201,71215],{},[895,71202,71203,71209,71211,71213],{},[1710,71204,71205,71207],{},[898,71206,1663],{},[1665,71208,1681],{},[1654,71210,1750],{},[1654,71212,2380],{},[1665,71214,11015],{},[902,71216,71217],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,71220,71222],{"className":71221},[886],[888,71223,71224],{"xmlns":890},[892,71225,71226,71266],{},[895,71227,71228,71230,71232,71234,71244,71246,71248,71250,71252,71260,71262,71264],{},[1654,71229,1708],{"stretchy":1656},[898,71231,4737],{},[898,71233,11539],{},[1741,71235,71236,71238],{},[1654,71237,1726],{"stretchy":1656},[895,71239,71240,71242],{},[1654,71241,2592],{"mathvariant":1878},[1654,71243,2592],{"mathvariant":1878},[1654,71245,1708],{"stretchy":1656},[1665,71247,11015],{},[1654,71249,1726],{"stretchy":1656},[1654,71251,1750],{},[2582,71253,71254],{"scriptlevel":2062,"displaystyle":1656},[2811,71255,71256,71258],{},[1665,71257,1667],{},[1665,71259,4035],{},[1654,71261,2952],{},[1665,71263,2062],{},[1654,71265,8634],{},[902,71267,71268],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,71271,71273],{"className":71272},[886],[888,71274,71275],{"xmlns":890},[892,71276,71277,71293],{},[895,71278,71279,71281,71283,71285,71287,71289,71291],{},[898,71280,4737],{},[898,71282,11539],{},[1654,71284,1708],{"stretchy":1656},[1665,71286,11015],{},[1654,71288,1726],{"stretchy":1656},[1654,71290,1750],{},[1665,71292,10207],{},[902,71294,71295],{"encoding":904},"AC(6) = 15",[724,71297,71298,71299,71325,71326,2781],{},"Pomocí principu: ",[883,71300,71302],{"className":71301},[886],[888,71303,71304],{"xmlns":890},[892,71305,71306,71322],{},[895,71307,71308,71310,71312,71314,71316,71318,71320],{},[898,71309,9320],{},[898,71311,11539],{},[1654,71313,1750],{},[1665,71315,1681],{},[898,71317,1663],{},[1654,71319,1766],{},[1665,71321,4035],{},[902,71323,71324],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,71327,71329],{"className":71328},[886],[888,71330,71331],{"xmlns":890},[892,71332,71333,71345],{},[895,71334,71335,71337,71339,71341,71343],{},[898,71336,4737],{},[898,71338,11539],{},[1654,71340,1750],{},[898,71342,9320],{},[898,71344,11539],{},[902,71346,63443],{"encoding":904},[883,71348,71350],{"className":71349},[886],[888,71351,71352],{"xmlns":890,"display":1956},[892,71353,71354,71456],{},[895,71355,71356,71378,71380,71382,71384,71386,71388,71390,71392,71394,71400,71402,71404,71406,71408,71410,71412,71414,71420,71422,71424,71426,71428,71430,71432,71438,71440,71442,71444,71446,71448,71450,71452,71454],{},[2811,71357,71358,71376],{},[895,71359,71360,71366,71368,71370,71372,71374],{},[1741,71361,71362,71364],{},[898,71363,1663],{},[1665,71365,1681],{},[1654,71367,1766],{},[1665,71369,4035],{},[898,71371,1663],{},[1654,71373,1766],{},[1665,71375,14295],{},[898,71377,1663],{},[1654,71379,1750],{},[1665,71381,1681],{},[898,71383,1663],{},[1654,71385,1766],{},[1665,71387,4035],{},[1865,71389,2805],{},[1654,71391,8634],{},[1865,71393,2805],{},[1741,71395,71396,71398],{},[898,71397,1663],{},[1665,71399,1681],{},[1654,71401,1766],{},[1665,71403,4035],{},[898,71405,1663],{},[1654,71407,1766],{},[1665,71409,14295],{},[1654,71411,1750],{},[1665,71413,1681],{},[1741,71415,71416,71418],{},[898,71417,1663],{},[1665,71419,1681],{},[1654,71421,1766],{},[1665,71423,4035],{},[898,71425,1663],{},[1865,71427,2805],{},[1654,71429,8634],{},[1865,71431,2805],{},[1741,71433,71434,71436],{},[898,71435,1663],{},[1665,71437,1681],{},[1654,71439,1750],{},[1665,71441,14295],{},[1865,71443,2805],{},[1654,71445,8634],{},[1865,71447,2805],{},[898,71449,1663],{},[1654,71451,1750],{},[1665,71453,11015],{},[1654,71455,1674],{"separator":1673},[902,71457,71458],{"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,",[724,71460,71461,71462,71500],{},"a ",[883,71463,71465],{"className":71464},[886],[888,71466,71467],{"xmlns":890},[892,71468,71469,71497],{},[895,71470,71471,71473,71475,71477,71479,71481,71483,71485,71487,71489,71491,71493,71495],{},[898,71472,4737],{},[898,71474,11539],{},[1654,71476,1708],{"stretchy":1656},[1665,71478,11015],{},[1654,71480,1726],{"stretchy":1656},[1654,71482,1750],{},[898,71484,9320],{},[898,71486,11539],{},[1654,71488,1708],{"stretchy":1656},[1665,71490,11015],{},[1654,71492,1726],{"stretchy":1656},[1654,71494,1750],{},[1665,71496,10207],{},[902,71498,71499],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,71502,71504],{"id":71503},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,71506,71507,71508,2781],{},"Analogicky pro ",[883,71509,71511],{"className":71510},[886],[888,71512,71513],{"xmlns":890},[892,71514,71515,71523],{},[895,71516,71517,71519,71521],{},[898,71518,4737],{},[898,71520,48559],{},[898,71522,11539],{},[902,71524,63531],{"encoding":904},[883,71526,71528],{"className":71527},[886],[888,71529,71530],{"xmlns":890,"display":1956},[892,71531,71532,71583],{},[1960,71533,71534],{"width":1962},[1964,71535,71536,71538,71576,71578],{},[1967,71537],{"width":1969},[1967,71539,71540],{},[895,71541,71542,71544,71546,71548,71550,71556,71558,71560,71562,71564,71566,71572,71574],{},[898,71543,4737],{},[898,71545,48559],{},[898,71547,11539],{},[1654,71549,1708],{"stretchy":1656},[1710,71551,71552,71554],{},[898,71553,1663],{},[1665,71555,2062],{},[1654,71557,1726],{"stretchy":1656},[1654,71559,1750],{},[898,71561,9320],{},[898,71563,11539],{},[1654,71565,1708],{"stretchy":1656},[1710,71567,71568,71570],{},[898,71569,1663],{},[1665,71571,2062],{},[1654,71573,1726],{"stretchy":1656},[898,71575,2138],{"mathvariant":1878},[1967,71577],{"width":1969},[1967,71579,71580],{},[1865,71581,71582],{},"(3.11)",[902,71584,71585],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[2140,71587,71588],{},[724,71589,71590,70266,71592],{},[883,71591,64664],{},[38,71593,71594,71595,71612],{},"V bodě minima průměrných variabilních nákladů se ",[883,71596,71598],{"className":71597},[886],[888,71599,71600],{"xmlns":890},[892,71601,71602,71610],{},[895,71603,71604,71606,71608],{},[898,71605,4737],{},[898,71607,48559],{},[898,71609,11539],{},[902,71611,63531],{"encoding":904}," rovnají mezním nákladům.",[724,71614,71615,71616,71638,71639,2138],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,71617,71619],{"className":71618},[886],[888,71620,71621],{"xmlns":890},[892,71622,71623,71635],{},[895,71624,71625,71631,71633],{},[1710,71626,71627,71629],{},[898,71628,1663],{},[1665,71630,2062],{},[1654,71632,1750],{},[1665,71634,61419],{},[902,71636,71637],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,71640,71642],{"className":71641},[886],[888,71643,71644],{"xmlns":890},[892,71645,71646,71672],{},[895,71647,71648,71650,71652,71654,71656,71658,71660,71662,71664,71666,71668,71670],{},[898,71649,4737],{},[898,71651,48559],{},[898,71653,11539],{},[1654,71655,1708],{"stretchy":1656},[898,71657,1663],{},[1654,71659,1726],{"stretchy":1656},[1654,71661,1750],{},[898,71663,9320],{},[898,71665,11539],{},[1654,71667,1708],{"stretchy":1656},[898,71669,1663],{},[1654,71671,1726],{"stretchy":1656},[902,71673,71674],{"encoding":904},"AVC(Q) = MC(Q)",[115,71676,71678],{"id":71677},"zisk-a-body-zvratu","Zisk a body zvratu",[724,71680,71681,2186,71684,71700],{},[38,71682,71683],{},"Zisk",[883,71685,71687],{"className":71686},[886],[888,71688,71689],{"xmlns":890},[892,71690,71691,71697],{},[895,71692,71693,71695],{},[898,71694,1755],{},[898,71696,12737],{},[902,71698,71699],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,71702,71704],{"className":71703},[886],[888,71705,71706],{"xmlns":890,"display":1956},[892,71707,71708,71767],{},[1960,71709,71710],{"width":1962},[1964,71711,71712,71714,71760,71762],{},[1967,71713],{"width":1969},[1967,71715,71716],{},[895,71717,71718,71720,71722,71724,71726,71728,71730,71732,71734,71736,71738,71740,71742,71744,71746,71748,71750,71752,71754,71756,71758],{},[898,71719,1755],{},[898,71721,12737],{},[1654,71723,1750],{},[898,71725,1755],{},[898,71727,12737],{},[1654,71729,1708],{"stretchy":1656},[898,71731,1663],{},[1654,71733,1726],{"stretchy":1656},[1654,71735,1750],{},[898,71737,11536],{},[898,71739,12737],{},[1654,71741,1708],{"stretchy":1656},[898,71743,1663],{},[1654,71745,1726],{"stretchy":1656},[1654,71747,2380],{},[898,71749,11536],{},[898,71751,11539],{},[1654,71753,1708],{"stretchy":1656},[898,71755,1663],{},[1654,71757,1726],{"stretchy":1656},[898,71759,2138],{"mathvariant":1878},[1967,71761],{"width":1969},[1967,71763,71764],{},[1865,71765,71766],{},"(3.12)",[902,71768,71769],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,71771,71772,71773,2068,71788,51856,71803,71805,71806,71809,71810,71826,71827,71842,71843,71858,71859,1343,71872,71885,71886,1343,71904,71922,71923,18742,71926,71929,71930,1348,71952,16828,71974,71996,71997,16828,72027,72049],{},"Body rovnosti ",[883,71774,71776],{"className":71775},[886],[888,71777,71778],{"xmlns":890},[892,71779,71780,71786],{},[895,71781,71782,71784],{},[898,71783,11536],{},[898,71785,12737],{},[902,71787,12837],{"encoding":904},[883,71789,71791],{"className":71790},[886],[888,71792,71793],{"xmlns":890},[892,71794,71795,71801],{},[895,71796,71797,71799],{},[898,71798,11536],{},[898,71800,11539],{},[902,71802,11997],{"encoding":904},[38,71804,63947],{}," (též vyrovnání, ",[614,71807,71808],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,71811,71813],{"className":71812},[886],[888,71814,71815],{"xmlns":890},[892,71816,71817,71823],{},[895,71818,71819,71821],{},[898,71820,48559],{},[898,71822,11539],{},[902,71824,71825],{"encoding":904},"VC",") je ",[883,71828,71830],{"className":71829},[886],[888,71831,71832],{"xmlns":890},[892,71833,71834,71840],{},[895,71835,71836,71838],{},[898,71837,11536],{},[898,71839,12737],{},[902,71841,12837],{"encoding":904}," kvadratická a ",[883,71844,71846],{"className":71845},[886],[888,71847,71848],{"xmlns":890},[892,71849,71850,71856],{},[895,71851,71852,71854],{},[898,71853,11536],{},[898,71855,11539],{},[902,71857,11997],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,71860,71862],{"className":71861},[886],[888,71863,71864],{"xmlns":890},[892,71865,71866,71870],{},[895,71867,71868],{},[898,71869,4737],{},[902,71871,4737],{"encoding":904},[883,71873,71875],{"className":71874},[886],[888,71876,71877],{"xmlns":890},[892,71878,71879,71883],{},[895,71880,71881],{},[898,71882,4762],{},[902,71884,4762],{"encoding":904}," odpovídajících množstvím ",[883,71887,71889],{"className":71888},[886],[888,71890,71891],{"xmlns":890},[892,71892,71893,71901],{},[895,71894,71895],{},[1710,71896,71897,71899],{},[898,71898,1663],{},[898,71900,4737],{},[902,71902,71903],{"encoding":904},"Q_A",[883,71905,71907],{"className":71906},[886],[888,71908,71909],{"xmlns":890},[892,71910,71911,71919],{},[895,71912,71913],{},[1710,71914,71915,71917],{},[898,71916,1663],{},[898,71918,4762],{},[902,71920,71921],{"encoding":904},"Q_B"," — firma je na ",[38,71924,71925],{},"prahu rentability",[614,71927,71928],{},"break even","). Pro ",[883,71931,71933],{"className":71932},[886],[888,71934,71935],{"xmlns":890},[892,71936,71937,71949],{},[895,71938,71939,71941,71943],{},[898,71940,1663],{},[1654,71942,3002],{},[1710,71944,71945,71947],{},[898,71946,1663],{},[898,71948,4737],{},[902,71950,71951],{"encoding":904},"Q \u003C Q_A",[883,71953,71955],{"className":71954},[886],[888,71956,71957],{"xmlns":890},[892,71958,71959,71971],{},[895,71960,71961,71963,71965],{},[898,71962,1663],{},[1654,71964,2952],{},[1710,71966,71967,71969],{},[898,71968,1663],{},[898,71970,4762],{},[902,71972,71973],{"encoding":904},"Q > Q_B",[883,71975,71977],{"className":71976},[886],[888,71978,71979],{"xmlns":890},[892,71980,71981,71993],{},[895,71982,71983,71985,71987,71989,71991],{},[898,71984,11536],{},[898,71986,11539],{},[1654,71988,2952],{},[898,71990,11536],{},[898,71992,12737],{},[902,71994,71995],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,71998,72000],{"className":71999},[886],[888,72001,72002],{"xmlns":890},[892,72003,72004,72024],{},[895,72005,72006,72012,72014,72016,72018],{},[1710,72007,72008,72010],{},[898,72009,1663],{},[898,72011,4737],{},[1654,72013,3002],{},[898,72015,1663],{},[1654,72017,3002],{},[1710,72019,72020,72022],{},[898,72021,1663],{},[898,72023,4762],{},[902,72025,72026],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,72028,72030],{"className":72029},[886],[888,72031,72032],{"xmlns":890},[892,72033,72034,72046],{},[895,72035,72036,72038,72040,72042,72044],{},[898,72037,11536],{},[898,72039,12737],{},[1654,72041,2952],{},[898,72043,11536],{},[898,72045,11539],{},[902,72047,72048],{"encoding":904},"TR > TC"," (zisk).",[2140,72051,72052],{},[724,72053,72054,72056],{},[883,72055,2860],{}," 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.",[724,72058,72059,72060,72086],{},"Body zvratu jsou řešení rovnice ",[883,72061,72063],{"className":72062},[886],[888,72064,72065],{"xmlns":890},[892,72066,72067,72083],{},[895,72068,72069,72071,72073,72075,72077,72079,72081],{},[898,72070,1755],{},[898,72072,12737],{},[1654,72074,1708],{"stretchy":1656},[898,72076,1663],{},[1654,72078,1726],{"stretchy":1656},[1654,72080,1750],{},[1665,72082,2062],{},[902,72084,72085],{"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.",[724,72088,72089],{},[3492,72090],{"alt":72091,"className":72092,"src":72093},"imek-tr-tc-body-zvratu",[210,3496],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,72095,72096],{},[614,72097,72098,72099,72114,72115,72130,72131,2068,72144,51580,72157,72170,72171,2068,72188,72205,72206,72226,72227,2068,72242,15201,72257,72286],{},"Obrázek 3.11: Body zvratu — křivky ",[883,72100,72102],{"className":72101},[886],[888,72103,72104],{"xmlns":890},[892,72105,72106,72112],{},[895,72107,72108,72110],{},[898,72109,11536],{},[898,72111,12737],{},[902,72113,12837],{"encoding":904}," (obrácená parabola) a ",[883,72116,72118],{"className":72117},[886],[888,72119,72120],{"xmlns":890},[892,72121,72122,72128],{},[895,72123,72124,72126],{},[898,72125,11536],{},[898,72127,11539],{},[902,72129,11997],{"encoding":904}," (přímka) se protínají v bodech ",[883,72132,72134],{"className":72133},[886],[888,72135,72136],{"xmlns":890},[892,72137,72138,72142],{},[895,72139,72140],{},[898,72141,4737],{},[902,72143,4737],{"encoding":904},[883,72145,72147],{"className":72146},[886],[888,72148,72149],{"xmlns":890},[892,72150,72151,72155],{},[895,72152,72153],{},[898,72154,4762],{},[902,72156,4762],{"encoding":904},[883,72158,72160],{"className":72159},[886],[888,72161,72162],{"xmlns":890},[892,72163,72164,72168],{},[895,72165,72166],{},[898,72167,1663],{},[902,72169,1663],{"encoding":904}," v hodnotách ",[883,72172,72174],{"className":72173},[886],[888,72175,72176],{"xmlns":890},[892,72177,72178,72186],{},[895,72179,72180],{},[1710,72181,72182,72184],{},[898,72183,1663],{},[898,72185,4737],{},[902,72187,71903],{"encoding":904},[883,72189,72191],{"className":72190},[886],[888,72192,72193],{"xmlns":890},[892,72194,72195,72203],{},[895,72196,72197],{},[1710,72198,72199,72201],{},[898,72200,1663],{},[898,72202,4762],{},[902,72204,71921],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,72207,72209],{"className":72208},[886],[888,72210,72211],{"xmlns":890},[892,72212,72213,72223],{},[895,72214,72215],{},[1710,72216,72217,72219,72221],{},[898,72218,1663],{},[898,72220,64417],{},[1654,72222,64420],{},[902,72224,72225],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,72228,72230],{"className":72229},[886],[888,72231,72232],{"xmlns":890},[892,72233,72234,72240],{},[895,72235,72236,72238],{},[898,72237,11536],{},[898,72239,12737],{},[902,72241,12837],{"encoding":904},[883,72243,72245],{"className":72244},[886],[888,72246,72247],{"xmlns":890},[892,72248,72249,72255],{},[895,72250,72251,72253],{},[898,72252,11536],{},[898,72254,11539],{},[902,72256,11997],{"encoding":904},[883,72258,72260],{"className":72259},[886],[888,72261,72262],{"xmlns":890},[892,72263,72264,72284],{},[895,72265,72266,72272,72274,72276,72278],{},[1710,72267,72268,72270],{},[898,72269,1663],{},[898,72271,4737],{},[1654,72273,3002],{},[898,72275,1663],{},[1654,72277,3002],{},[1710,72279,72280,72282],{},[898,72281,1663],{},[898,72283,4762],{},[902,72285,72026],{"encoding":904}," vyznačuje zisk.",[45568,72288,72290],{"id":72289},"příklad-38","Příklad 3.8",[724,72292,72293,72295,72296,1343,72316,1343,72342,72368],{},[38,72294,64207],{}," Dáno ",[883,72297,72299],{"className":72298},[886],[888,72300,72301],{"xmlns":890},[892,72302,72303,72313],{},[895,72304,72305,72307,72309,72311],{},[898,72306,19153],{},[898,72308,11539],{},[1654,72310,1750],{},[1665,72312,7631],{},[902,72314,72315],{"encoding":904},"FC = 4",[883,72317,72319],{"className":72318},[886],[888,72320,72321],{"xmlns":890},[892,72322,72323,72339],{},[895,72324,72325,72327,72329,72331,72333],{},[898,72326,11536],{},[898,72328,48559],{},[898,72330,11539],{},[1654,72332,1750],{},[1741,72334,72335,72337],{},[898,72336,1663],{},[1665,72338,1681],{},[902,72340,72341],{"encoding":904},"TVC = Q^2",[883,72343,72345],{"className":72344},[886],[888,72346,72347],{"xmlns":890},[892,72348,72349,72365],{},[895,72350,72351,72353,72355,72357,72359,72361,72363],{},[898,72352,1755],{},[1654,72354,1750],{},[1654,72356,2380],{},[1665,72358,1681],{},[898,72360,1663],{},[1654,72362,1766],{},[1665,72364,12742],{},[902,72366,72367],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,72370,72371,72373],{},[38,72372,31458],{}," Celkové náklady a příjem:",[883,72375,72377],{"className":72376},[886],[888,72378,72379],{"xmlns":890,"display":1956},[892,72380,72381,72447],{},[895,72382,72383,72385,72387,72389,72391,72393,72399,72401,72403,72405,72407,72409,72411,72413,72415,72417,72419,72421,72423,72425,72427,72429,72431,72433,72439,72441,72443,72445],{},[898,72384,11536],{},[898,72386,11539],{},[1654,72388,1750],{},[1665,72390,7631],{},[1654,72392,1766],{},[1741,72394,72395,72397],{},[898,72396,1663],{},[1665,72398,1681],{},[1654,72400,1674],{"separator":1673},[5008,72402],{"width":14608},[898,72404,11536],{},[898,72406,12737],{},[1654,72408,1750],{},[898,72410,1663],{},[1654,72412,4554],{},[1654,72414,1708],{"stretchy":1656},[1654,72416,2380],{},[1665,72418,1681],{},[898,72420,1663],{},[1654,72422,1766],{},[1665,72424,12742],{},[1654,72426,1726],{"stretchy":1656},[1654,72428,1750],{},[1654,72430,2380],{},[1665,72432,1681],{},[1741,72434,72435,72437],{},[898,72436,1663],{},[1665,72438,1681],{},[1654,72440,1766],{},[1665,72442,12742],{},[898,72444,1663],{},[898,72446,2138],{"mathvariant":1878},[902,72448,72449],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,72451,72452],{},"Zisk dle (3.12):",[883,72454,72456],{"className":72455},[886],[888,72457,72458],{"xmlns":890,"display":1956},[892,72459,72460,72538],{},[895,72461,72462,72464,72466,72468,72470,72472,72474,72476,72478,72480,72482,72484,72486,72492,72494,72496,72498,72500,72502,72504,72506,72508,72514,72516,72518,72520,72522,72528,72530,72532,72534,72536],{},[898,72463,1755],{},[898,72465,12737],{},[1654,72467,1750],{},[898,72469,11536],{},[898,72471,12737],{},[1654,72473,2380],{},[898,72475,11536],{},[898,72477,11539],{},[1654,72479,1750],{},[1654,72481,1708],{"stretchy":1656},[1654,72483,2380],{},[1665,72485,1681],{},[1741,72487,72488,72490],{},[898,72489,1663],{},[1665,72491,1681],{},[1654,72493,1766],{},[1665,72495,12742],{},[898,72497,1663],{},[1654,72499,1726],{"stretchy":1656},[1654,72501,2380],{},[1654,72503,1708],{"stretchy":1656},[1665,72505,7631],{},[1654,72507,1766],{},[1741,72509,72510,72512],{},[898,72511,1663],{},[1665,72513,1681],{},[1654,72515,1726],{"stretchy":1656},[1654,72517,1750],{},[1654,72519,2380],{},[1665,72521,4035],{},[1741,72523,72524,72526],{},[898,72525,1663],{},[1665,72527,1681],{},[1654,72529,1766],{},[1665,72531,12742],{},[898,72533,1663],{},[1654,72535,2380],{},[1665,72537,67539],{},[902,72539,72540],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,72542,72543,72546,72547,7515,72583,2781],{},[38,72544,72545],{},"Body zvratu"," jsou kořeny rovnice ",[883,72548,72550],{"className":72549},[886],[888,72551,72552],{"xmlns":890},[892,72553,72554,72580],{},[895,72555,72556,72558,72560,72566,72568,72570,72572,72574,72576,72578],{},[1654,72557,2380],{},[1665,72559,4035],{},[1741,72561,72562,72564],{},[898,72563,1663],{},[1665,72565,1681],{},[1654,72567,1766],{},[1665,72569,12742],{},[898,72571,1663],{},[1654,72573,2380],{},[1665,72575,7631],{},[1654,72577,1750],{},[1665,72579,2062],{},[902,72581,72582],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,72584,72586],{"className":72585},[886],[888,72587,72588],{"xmlns":890},[892,72589,72590,72614],{},[895,72591,72592,72594,72600,72602,72604,72606,72608,72610,72612],{},[1665,72593,4035],{},[1741,72595,72596,72598],{},[898,72597,1663],{},[1665,72599,1681],{},[1654,72601,2380],{},[1665,72603,12742],{},[898,72605,1663],{},[1654,72607,1766],{},[1665,72609,7631],{},[1654,72611,1750],{},[1665,72613,2062],{},[902,72615,72616],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,72618,72620],{"className":72619},[886],[888,72621,72622],{"xmlns":890,"display":1956},[892,72623,72624,72681],{},[895,72625,72626,72638,72640,72663,72665,72679],{},[1710,72627,72628,72630],{},[898,72629,1663],{},[895,72631,72632,72634,72636],{},[1665,72633,1667],{},[1654,72635,1674],{"separator":1673},[1665,72637,1681],{},[1654,72639,1750],{},[2811,72641,72642,72661],{},[895,72643,72644,72646,72649],{},[1665,72645,12742],{},[1654,72647,72648],{},"±",[8818,72650,72651],{},[895,72652,72653,72656,72658],{},[1665,72654,72655],{},"81",[1654,72657,2380],{},[1665,72659,72660],{},"48",[1665,72662,11015],{},[1654,72664,1750],{},[2811,72666,72667,72677],{},[895,72668,72669,72671,72673],{},[1665,72670,12742],{},[1654,72672,72648],{},[8818,72674,72675],{},[1665,72676,17676],{},[1665,72678,11015],{},[1654,72680,1674],{"separator":1673},[902,72682,72683],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,72685,72686,72687,2068,72710,2138],{},"numericky ",[883,72688,72690],{"className":72689},[886],[888,72691,72692],{"xmlns":890},[892,72693,72694,72707],{},[895,72695,72696,72702,72704],{},[1710,72697,72698,72700],{},[898,72699,1663],{},[1665,72701,1667],{},[1654,72703,14628],{},[1665,72705,72706],{},"0,543",[902,72708,72709],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,72711,72713],{"className":72712},[886],[888,72714,72715],{"xmlns":890},[892,72716,72717,72730],{},[895,72718,72719,72725,72727],{},[1710,72720,72721,72723],{},[898,72722,1663],{},[1665,72724,1681],{},[1654,72726,14628],{},[1665,72728,72729],{},"2,457",[902,72731,72732],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,72734,72735,2186,72738,16278,72783,7515,72817,72835],{},[38,72736,72737],{},"Maximum zisku.",[883,72739,72741],{"className":72740},[886],[888,72742,72743],{"xmlns":890},[892,72744,72745,72780],{},[895,72746,72747,72749,72755,72757,72759,72761,72763,72765,72767,72769,72771,72773,72775,72777],{},[898,72748,1755],{},[1741,72750,72751,72753],{},[898,72752,12737],{},[1654,72754,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,72756,1750],{},[1654,72758,2380],{},[1665,72760,11015],{},[898,72762,1663],{},[1654,72764,1766],{},[1665,72766,12742],{},[1654,72768,1750],{},[1665,72770,2062],{},[1654,72772,8634],{},[898,72774,1663],{},[1654,72776,1750],{},[1665,72778,72779],{},"1,5",[902,72781,72782],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,72784,72786],{"className":72785},[886],[888,72787,72788],{"xmlns":890},[892,72789,72790,72814],{},[895,72791,72792,72794,72804,72806,72808,72810,72812],{},[898,72793,1755],{},[1741,72795,72796,72798],{},[898,72797,12737],{},[895,72799,72800,72802],{},[1654,72801,2592],{"mathvariant":1878},[1654,72803,2592],{"mathvariant":1878},[1654,72805,1750],{},[1654,72807,2380],{},[1665,72809,11015],{},[1654,72811,3002],{},[1665,72813,2062],{},[902,72815,72816],{"encoding":904},"PR'' = -6 \u003C 0",[883,72818,72820],{"className":72819},[886],[888,72821,72822],{"xmlns":890},[892,72823,72824,72832],{},[895,72825,72826,72828,72830],{},[898,72827,1663],{},[1654,72829,1750],{},[1665,72831,72779],{},[902,72833,72834],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,72837,72839],{"className":72838},[886],[888,72840,72841],{"xmlns":890,"display":1956},[892,72842,72843,72906],{},[895,72844,72845,72847,72849,72851,72853,72855,72857,72859,72861,72863,72865,72867,72873,72875,72877,72879,72881,72883,72885,72887,72889,72892,72894,72897,72899,72901,72903],{},[898,72846,1755],{},[898,72848,12737],{},[1654,72850,1708],{"stretchy":1656},[1665,72852,72779],{},[1654,72854,1726],{"stretchy":1656},[1654,72856,1750],{},[1654,72858,2380],{},[1665,72860,4035],{},[1654,72862,4554],{},[1654,72864,1708],{"stretchy":1656},[1665,72866,72779],{},[1741,72868,72869,72871],{},[1654,72870,1726],{"stretchy":1656},[1665,72872,1681],{},[1654,72874,1766],{},[1665,72876,12742],{},[1654,72878,4554],{},[1665,72880,72779],{},[1654,72882,2380],{},[1665,72884,7631],{},[1654,72886,1750],{},[1654,72888,2380],{},[1665,72890,72891],{},"6,75",[1654,72893,1766],{},[1665,72895,72896],{},"13,5",[1654,72898,2380],{},[1665,72900,7631],{},[1654,72902,1750],{},[1665,72904,72905],{},"2,75.",[902,72907,72908],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,72910,72911,72912,1343,72957,73010,73011,73029],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,72913,72915],{"className":72914},[886],[888,72916,72917],{"xmlns":890},[892,72918,72919,72954],{},[895,72920,72921,72923,72929,72931,72933,72935,72937,72939,72941,72943,72945,72947,72949,72951],{},[898,72922,11536],{},[1741,72924,72925,72927],{},[898,72926,12737],{},[1654,72928,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,72930,1750],{},[1654,72932,2380],{},[1665,72934,7631],{},[898,72936,1663],{},[1654,72938,1766],{},[1665,72940,12742],{},[1654,72942,1750],{},[1665,72944,2062],{},[1654,72946,8634],{},[898,72948,1663],{},[1654,72950,1750],{},[1665,72952,72953],{},"2,25",[902,72955,72956],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,72958,72960],{"className":72959},[886],[888,72961,72962],{"xmlns":890},[892,72963,72964,73007],{},[895,72965,72966,72968,72976,72978,72980,72982,72984,72986,72988,72994,72996,72998,73000,73002,73004],{},[898,72967,11536],{},[1710,72969,72970,72972,72974],{},[898,72971,12737],{},[898,72973,64417],{},[1654,72975,64420],{},[1654,72977,1750],{},[1654,72979,2380],{},[1665,72981,1681],{},[1654,72983,4554],{},[1654,72985,1708],{"stretchy":1656},[1665,72987,72953],{},[1741,72989,72990,72992],{},[1654,72991,1726],{"stretchy":1656},[1665,72993,1681],{},[1654,72995,1766],{},[1665,72997,12742],{},[1654,72999,4554],{},[1665,73001,72953],{},[1654,73003,1750],{},[1665,73005,73006],{},"10,125",[902,73008,73009],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,73012,73014],{"className":73013},[886],[888,73015,73016],{"xmlns":890},[892,73017,73018,73026],{},[895,73019,73020,73022,73024],{},[898,73021,1663],{},[1654,73023,1750],{},[1665,73025,72953],{},[902,73027,73028],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[2140,73031,73032],{},[724,73033,73034,73036,73037,1343,73059,73081,73082,1343,73099,73120,73121,73153,73154,73192,73193,11434,73211,73228,73229,2068,73257,73291,73292,16411,73330,2068,73354,2138],{},[883,73035,2146],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,73038,73040],{"className":73039},[886],[888,73041,73042],{"xmlns":890},[892,73043,73044,73056],{},[895,73045,73046,73052,73054],{},[1710,73047,73048,73050],{},[898,73049,1663],{},[1665,73051,1667],{},[1654,73053,1750],{},[1665,73055,7594],{},[902,73057,73058],{"encoding":904},"Q_1 = 0{,}5",[883,73060,73062],{"className":73061},[886],[888,73063,73064],{"xmlns":890},[892,73065,73066,73078],{},[895,73067,73068,73074,73076],{},[1710,73069,73070,73072],{},[898,73071,1663],{},[1665,73073,1681],{},[1654,73075,1750],{},[1665,73077,7631],{},[902,73079,73080],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,73083,73085],{"className":73084},[886],[888,73086,73087],{"xmlns":890},[892,73088,73089,73097],{},[895,73090,73091,73093,73095],{},[898,73092,1663],{},[1654,73094,1750],{},[1665,73096,72953],{},[902,73098,73028],{"encoding":904},[883,73100,73102],{"className":73101},[886],[888,73103,73104],{"xmlns":890},[892,73105,73106,73117],{},[895,73107,73108,73110,73112,73114],{},[898,73109,1755],{},[898,73111,12737],{},[1654,73113,1750],{},[1665,73115,73116],{},"6,125",[902,73118,73119],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,73122,73124],{"className":73123},[886],[888,73125,73126],{"xmlns":890},[892,73127,73128,73150],{},[895,73129,73130,73132,73138,73140,73142,73144,73146,73148],{},[898,73131,1755],{},[1741,73133,73134,73136],{},[898,73135,12737],{},[1654,73137,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,73139,1750],{},[1654,73141,2380],{},[1665,73143,7631],{},[898,73145,1663],{},[1654,73147,1766],{},[1665,73149,12742],{},[902,73151,73152],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,73155,73157],{"className":73156},[886],[888,73158,73159],{"xmlns":890},[892,73160,73161,73189],{},[895,73162,73163,73165,73167,73169,73171,73173,73179,73181,73183,73185,73187],{},[898,73164,1755],{},[898,73166,12737],{},[1654,73168,1750],{},[1654,73170,2380],{},[1665,73172,1681],{},[1741,73174,73175,73177],{},[898,73176,1663],{},[1665,73178,1681],{},[1654,73180,1766],{},[1665,73182,12742],{},[898,73184,1663],{},[1654,73186,2380],{},[1665,73188,7631],{},[902,73190,73191],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,73194,73196],{"className":73195},[886],[888,73197,73198],{"xmlns":890},[892,73199,73200,73208],{},[895,73201,73202],{},[1741,73203,73204,73206],{},[898,73205,1663],{},[1665,73207,1681],{},[902,73209,73210],{"encoding":904},"Q^2",[883,73212,73214],{"className":73213},[886],[888,73215,73216],{"xmlns":890},[892,73217,73218,73226],{},[895,73219,73220,73222,73224],{},[898,73221,11536],{},[898,73223,48559],{},[898,73225,11539],{},[902,73227,63729],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,73230,73232],{"className":73231},[886],[888,73233,73234],{"xmlns":890},[892,73235,73236,73254],{},[895,73237,73238,73240,73242,73244,73246,73248],{},[898,73239,11536],{},[898,73241,11539],{},[1654,73243,1750],{},[1665,73245,7631],{},[1654,73247,1766],{},[1741,73249,73250,73252],{},[898,73251,1663],{},[1665,73253,1681],{},[902,73255,73256],{"encoding":904},"TC = 4 + Q^2",[883,73258,73260],{"className":73259},[886],[888,73261,73262],{"xmlns":890},[892,73263,73264,73288],{},[895,73265,73266,73268,73270,73272,73274,73276,73282,73284,73286],{},[898,73267,11536],{},[898,73269,12737],{},[1654,73271,1750],{},[1654,73273,2380],{},[1665,73275,1681],{},[1741,73277,73278,73280],{},[898,73279,1663],{},[1665,73281,1681],{},[1654,73283,1766],{},[1665,73285,12742],{},[898,73287,1663],{},[902,73289,73290],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,73293,73295],{"className":73294},[886],[888,73296,73297],{"xmlns":890},[892,73298,73299,73327],{},[895,73300,73301,73303,73305,73307,73309,73311,73317,73319,73321,73323,73325],{},[898,73302,1755],{},[898,73304,12737],{},[1654,73306,1750],{},[1654,73308,2380],{},[1665,73310,4035],{},[1741,73312,73313,73315],{},[898,73314,1663],{},[1665,73316,1681],{},[1654,73318,1766],{},[1665,73320,12742],{},[898,73322,1663],{},[1654,73324,2380],{},[1665,73326,7631],{},[902,73328,73329],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,73331,73333],{"className":73332},[886],[888,73334,73335],{"xmlns":890},[892,73336,73337,73351],{},[895,73338,73339,73347,73349],{},[1710,73340,73341,73343,73345],{},[898,73342,1663],{},[898,73344,64417],{},[1654,73346,64420],{},[1654,73348,1750],{},[1665,73350,72779],{},[902,73352,73353],{"encoding":904},"Q_{\\max} = 1{,}5",[883,73355,73357],{"className":73356},[886],[888,73358,73359],{"xmlns":890},[892,73360,73361,73378],{},[895,73362,73363,73365,73373,73375],{},[898,73364,1755],{},[1710,73366,73367,73369,73371],{},[898,73368,12737],{},[898,73370,64417],{},[1654,73372,64420],{},[1654,73374,1750],{},[1665,73376,73377],{},"2,75",[902,73379,73380],{"encoding":904},"PR_{\\max} = 2{,}75",[724,73382,73383],{},[614,73384,73385,73386,73413,73414,73447,73448,1343,73471,2138],{},"Obrázek 3.12: Graf ",[883,73387,73389],{"className":73388},[886],[888,73390,73391],{"xmlns":890},[892,73392,73393,73411],{},[895,73394,73395,73397,73399,73401,73403,73405],{},[898,73396,11536],{},[898,73398,11539],{},[1654,73400,1750],{},[1665,73402,7631],{},[1654,73404,1766],{},[1741,73406,73407,73409],{},[898,73408,1663],{},[1665,73410,1681],{},[902,73412,73256],{"encoding":904}," (parabola) a ",[883,73415,73417],{"className":73416},[886],[888,73418,73419],{"xmlns":890},[892,73420,73421,73445],{},[895,73422,73423,73425,73427,73429,73431,73433,73439,73441,73443],{},[898,73424,11536],{},[898,73426,12737],{},[1654,73428,1750],{},[1654,73430,2380],{},[1665,73432,1681],{},[1741,73434,73435,73437],{},[898,73436,1663],{},[1665,73438,1681],{},[1654,73440,1766],{},[1665,73442,12742],{},[898,73444,1663],{},[902,73446,73290],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,73449,73451],{"className":73450},[886],[888,73452,73453],{"xmlns":890},[892,73454,73455,73468],{},[895,73456,73457,73463,73465],{},[1710,73458,73459,73461],{},[898,73460,1663],{},[1665,73462,1667],{},[1654,73464,14628],{},[1665,73466,73467],{},"0,54",[902,73469,73470],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,73472,73474],{"className":73473},[886],[888,73475,73476],{"xmlns":890},[892,73477,73478,73491],{},[895,73479,73480,73486,73488],{},[1710,73481,73482,73484],{},[898,73483,1663],{},[1665,73485,1681],{},[1654,73487,14628],{},[1665,73489,73490],{},"2,46",[902,73492,73493],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,73495,73496],{},[614,73497,73498,73499,66727,73536,73553,73554,1343,73575,2138],{},"Obrázek 3.13: Graf zisku ",[883,73500,73502],{"className":73501},[886],[888,73503,73504],{"xmlns":890},[892,73505,73506,73534],{},[895,73507,73508,73510,73512,73514,73516,73518,73524,73526,73528,73530,73532],{},[898,73509,1755],{},[898,73511,12737],{},[1654,73513,1750],{},[1654,73515,2380],{},[1665,73517,4035],{},[1741,73519,73520,73522],{},[898,73521,1663],{},[1665,73523,1681],{},[1654,73525,1766],{},[1665,73527,12742],{},[898,73529,1663],{},[1654,73531,2380],{},[1665,73533,7631],{},[902,73535,73329],{"encoding":904},[883,73537,73539],{"className":73538},[886],[888,73540,73541],{"xmlns":890},[892,73542,73543,73551],{},[895,73544,73545,73547,73549],{},[898,73546,1663],{},[1654,73548,1750],{},[1665,73550,72779],{},[902,73552,72834],{"encoding":904}," a nulami ",[883,73555,73557],{"className":73556},[886],[888,73558,73559],{"xmlns":890},[892,73560,73561,73573],{},[895,73562,73563,73569,73571],{},[1710,73564,73565,73567],{},[898,73566,1663],{},[1665,73568,1667],{},[1654,73570,14628],{},[1665,73572,73467],{},[902,73574,73470],{"encoding":904},[883,73576,73578],{"className":73577},[886],[888,73579,73580],{"xmlns":890},[892,73581,73582,73594],{},[895,73583,73584,73590,73592],{},[1710,73585,73586,73588],{},[898,73587,1663],{},[1665,73589,1681],{},[1654,73591,14628],{},[1665,73593,73490],{},[902,73595,73493],{"encoding":904},[115,73597,73599],{"id":73598},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,73601,73602],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,73604,73605],{},[3492,73606],{"alt":73607,"className":73608,"src":73609},"imek-max-zisku-dva-pohledy",[210,3496],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,73611,25115],{"id":73612},"princip-1",[724,73614,73615,73616,11387,73631,73648],{},"Má-li zisk ",[883,73617,73619],{"className":73618},[886],[888,73620,73621],{"xmlns":890},[892,73622,73623,73629],{},[895,73624,73625,73627],{},[898,73626,1755],{},[898,73628,12737],{},[902,73630,71699],{"encoding":904},[883,73632,73634],{"className":73633},[886],[888,73635,73636],{"xmlns":890},[892,73637,73638,73646],{},[895,73639,73640],{},[1710,73641,73642,73644],{},[898,73643,1663],{},[1665,73645,2062],{},[902,73647,46528],{"encoding":904}," maximum, pak platí",[883,73650,73652],{"className":73651},[886],[888,73653,73654],{"xmlns":890,"display":1956},[892,73655,73656,73705],{},[1960,73657,73658],{"width":1962},[1964,73659,73660,73662,73698,73700],{},[1967,73661],{"width":1969},[1967,73663,73664],{},[895,73665,73666,73668,73670,73672,73678,73680,73682,73684,73686,73688,73694,73696],{},[898,73667,9320],{},[898,73669,12737],{},[1654,73671,1708],{"stretchy":1656},[1710,73673,73674,73676],{},[898,73675,1663],{},[1665,73677,2062],{},[1654,73679,1726],{"stretchy":1656},[1654,73681,1750],{},[898,73683,9320],{},[898,73685,11539],{},[1654,73687,1708],{"stretchy":1656},[1710,73689,73690,73692],{},[898,73691,1663],{},[1665,73693,2062],{},[1654,73695,1726],{"stretchy":1656},[898,73697,2138],{"mathvariant":1878},[1967,73699],{"width":1969},[1967,73701,73702],{},[1865,73703,73704],{},"(3.13)",[902,73706,73707],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[2140,73709,73710],{},[724,73711,73712,70266,73714],{},[883,73713,64664],{},[38,73715,73716],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,73718,73719,73722,73723,16828,73750,7515,73824,2138],{},[38,73720,73721],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,73724,73726],{"className":73725},[886],[888,73727,73728],{"xmlns":890},[892,73729,73730,73748],{},[895,73731,73732,73734,73736,73738,73740,73742,73744,73746],{},[898,73733,1755],{},[898,73735,12737],{},[1654,73737,1750],{},[898,73739,11536],{},[898,73741,12737],{},[1654,73743,2380],{},[898,73745,11536],{},[898,73747,11539],{},[902,73749,63420],{"encoding":904},[883,73751,73753],{"className":73752},[886],[888,73754,73755],{"xmlns":890},[892,73756,73757,73821],{},[895,73758,73759,73761,73767,73769,73775,73777,73779,73781,73787,73789,73795,73797,73799,73801,73807,73809,73815,73817,73819],{},[898,73760,1755],{},[1741,73762,73763,73765],{},[898,73764,12737],{},[1654,73766,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,73768,1708],{"stretchy":1656},[1710,73770,73771,73773],{},[898,73772,1663],{},[1665,73774,2062],{},[1654,73776,1726],{"stretchy":1656},[1654,73778,1750],{},[898,73780,11536],{},[1741,73782,73783,73785],{},[898,73784,12737],{},[1654,73786,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,73788,1708],{"stretchy":1656},[1710,73790,73791,73793],{},[898,73792,1663],{},[1665,73794,2062],{},[1654,73796,1726],{"stretchy":1656},[1654,73798,2380],{},[898,73800,11536],{},[1741,73802,73803,73805],{},[898,73804,11539],{},[1654,73806,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,73808,1708],{"stretchy":1656},[1710,73810,73811,73813],{},[898,73812,1663],{},[1665,73814,2062],{},[1654,73816,1726],{"stretchy":1656},[1654,73818,1750],{},[1665,73820,2062],{},[902,73822,73823],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,73825,73827],{"className":73826},[886],[888,73828,73829],{"xmlns":890},[892,73830,73831,73863],{},[895,73832,73833,73835,73837,73839,73845,73847,73849,73851,73853,73855,73861],{},[898,73834,9320],{},[898,73836,12737],{},[1654,73838,1708],{"stretchy":1656},[1710,73840,73841,73843],{},[898,73842,1663],{},[1665,73844,2062],{},[1654,73846,1726],{"stretchy":1656},[1654,73848,1750],{},[898,73850,9320],{},[898,73852,11539],{},[1654,73854,1708],{"stretchy":1656},[1710,73856,73857,73859],{},[898,73858,1663],{},[1665,73860,2062],{},[1654,73862,1726],{"stretchy":1656},[902,73864,73865],{"encoding":904},"MR(Q_0) = MC(Q_0)",[2140,73867,73868,73873],{},[724,73869,73870,73872],{},[883,73871,3111],{}," Postup — jak najít maximum zisku",[152,73874,73875,73939,73994,74031,74059],{},[123,73876,73877,73878,2068,73893,73908,73909,12664],{},"Sestavte ",[883,73879,73881],{"className":73880},[886],[888,73882,73883],{"xmlns":890},[892,73884,73885,73891],{},[895,73886,73887,73889],{},[898,73888,11536],{},[898,73890,12737],{},[902,73892,12837],{"encoding":904},[883,73894,73896],{"className":73895},[886],[888,73897,73898],{"xmlns":890},[892,73899,73900,73906],{},[895,73901,73902,73904],{},[898,73903,11536],{},[898,73905,11539],{},[902,73907,11997],{"encoding":904}," ze zadání (typicky ",[883,73910,73912],{"className":73911},[886],[888,73913,73914],{"xmlns":890},[892,73915,73916,73936],{},[895,73917,73918,73920,73922,73924,73926,73928,73930,73932,73934],{},[898,73919,11536],{},[898,73921,12737],{},[1654,73923,1750],{},[898,73925,1755],{},[1654,73927,1708],{"stretchy":1656},[898,73929,1663],{},[1654,73931,1726],{"stretchy":1656},[1654,73933,4554],{},[898,73935,1663],{},[902,73937,73938],{"encoding":904},"TR = P(Q) \\cdot Q",[123,73940,73941,73942,2068,73968,2138],{},"Vypočtěte ",[883,73943,73945],{"className":73944},[886],[888,73946,73947],{"xmlns":890},[892,73948,73949,73965],{},[895,73950,73951,73953,73955,73957,73959],{},[898,73952,9320],{},[898,73954,12737],{},[1654,73956,1750],{},[898,73958,11536],{},[1741,73960,73961,73963],{},[898,73962,12737],{},[1654,73964,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,73966,73967],{"encoding":904},"MR = TR'",[883,73969,73971],{"className":73970},[886],[888,73972,73973],{"xmlns":890},[892,73974,73975,73991],{},[895,73976,73977,73979,73981,73983,73985],{},[898,73978,9320],{},[898,73980,11539],{},[1654,73982,1750],{},[898,73984,11536],{},[1741,73986,73987,73989],{},[898,73988,11539],{},[1654,73990,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,73992,73993],{"encoding":904},"MC = TC'",[123,73995,73996,73997,2138],{},"Řešte rovnici ",[883,73998,74000],{"className":73999},[886],[888,74001,74002],{"xmlns":890},[892,74003,74004,74028],{},[895,74005,74006,74008,74010,74012,74014,74016,74018,74020,74022,74024,74026],{},[898,74007,9320],{},[898,74009,12737],{},[1654,74011,1708],{"stretchy":1656},[898,74013,1663],{},[1654,74015,1726],{"stretchy":1656},[1654,74017,1750],{},[898,74019,9320],{},[898,74021,11539],{},[1654,74023,1708],{"stretchy":1656},[898,74025,1663],{},[1654,74027,1726],{"stretchy":1656},[902,74029,74030],{"encoding":904},"MR(Q) = MC(Q)",[123,74032,74033,74034,74058],{},"Ověřte druhou derivaci ",[883,74035,74037],{"className":74036},[886],[888,74038,74039],{"xmlns":890},[892,74040,74041,74055],{},[895,74042,74043,74045],{},[898,74044,1755],{},[1741,74046,74047,74049],{},[898,74048,12737],{},[895,74050,74051,74053],{},[1654,74052,2592],{"mathvariant":1878},[1654,74054,2592],{"mathvariant":1878},[902,74056,74057],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,74060,74061,74062,74089],{},"Dosaďte do ",[883,74063,74065],{"className":74064},[886],[888,74066,74067],{"xmlns":890},[892,74068,74069,74087],{},[895,74070,74071,74073,74075,74077,74079,74081,74083,74085],{},[898,74072,1755],{},[898,74074,12737],{},[1654,74076,1750],{},[898,74078,11536],{},[898,74080,12737],{},[1654,74082,2380],{},[898,74084,11536],{},[898,74086,11539],{},[902,74088,63420],{"encoding":904}," pro hodnotu maxima.",[45568,74091,74093],{"id":74092},"příklad-39","Příklad 3.9",[724,74095,74096,64208,74098,2068,74120,74156],{},[38,74097,64207],{},[883,74099,74101],{"className":74100},[886],[888,74102,74103],{"xmlns":890},[892,74104,74105,74117],{},[895,74106,74107,74109,74111,74113,74115],{},[898,74108,1755],{},[1654,74110,1750],{},[1665,74112,46239],{},[1654,74114,2380],{},[898,74116,1663],{},[902,74118,74119],{"encoding":904},"P = 30 - Q",[883,74121,74123],{"className":74122},[886],[888,74124,74125],{"xmlns":890},[892,74126,74127,74153],{},[895,74128,74129,74131,74133,74135,74137,74143,74145,74147,74149,74151],{},[898,74130,11536],{},[898,74132,11539],{},[1654,74134,1750],{},[1665,74136,7594],{},[1741,74138,74139,74141],{},[898,74140,1663],{},[1665,74142,1681],{},[1654,74144,1766],{},[1665,74146,11015],{},[898,74148,1663],{},[1654,74150,1766],{},[1665,74152,32887],{},[902,74154,74155],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,74158,74159,2186,74161,1343,74191,74229,74230,24497,74274,74308,74309,2138],{},[38,74160,31458],{},[883,74162,74164],{"className":74163},[886],[888,74165,74166],{"xmlns":890},[892,74167,74168,74188],{},[895,74169,74170,74172,74174,74176,74178,74180,74182],{},[898,74171,11536],{},[898,74173,12737],{},[1654,74175,1750],{},[1665,74177,46239],{},[898,74179,1663],{},[1654,74181,2380],{},[1741,74183,74184,74186],{},[898,74185,1663],{},[1665,74187,1681],{},[902,74189,74190],{"encoding":904},"TR = 30Q - Q^2",[883,74192,74194],{"className":74193},[886],[888,74195,74196],{"xmlns":890},[892,74197,74198,74226],{},[895,74199,74200,74202,74204,74206,74208,74210,74216,74218,74220,74222,74224],{},[898,74201,1755],{},[898,74203,12737],{},[1654,74205,1750],{},[1654,74207,2380],{},[1665,74209,72779],{},[1741,74211,74212,74214],{},[898,74213,1663],{},[1665,74215,1681],{},[1654,74217,1766],{},[1665,74219,50020],{},[898,74221,1663],{},[1654,74223,2380],{},[1665,74225,32887],{},[902,74227,74228],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,74231,74233],{"className":74232},[886],[888,74234,74235],{"xmlns":890},[892,74236,74237,74271],{},[895,74238,74239,74241,74247,74249,74251,74253,74255,74257,74259,74261,74263,74265,74267,74269],{},[898,74240,1755],{},[1741,74242,74243,74245],{},[898,74244,12737],{},[1654,74246,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,74248,1750],{},[1654,74250,2380],{},[1665,74252,4035],{},[898,74254,1663],{},[1654,74256,1766],{},[1665,74258,50020],{},[1654,74260,1750],{},[1665,74262,2062],{},[1654,74264,8634],{},[898,74266,1663],{},[1654,74268,1750],{},[1665,74270,14315],{},[902,74272,74273],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,74275,74277],{"className":74276},[886],[888,74278,74279],{"xmlns":890},[892,74280,74281,74305],{},[895,74282,74283,74285,74295,74297,74299,74301,74303],{},[898,74284,1755],{},[1741,74286,74287,74289],{},[898,74288,12737],{},[895,74290,74291,74293],{},[1654,74292,2592],{"mathvariant":1878},[1654,74294,2592],{"mathvariant":1878},[1654,74296,1750],{},[1654,74298,2380],{},[1665,74300,4035],{},[1654,74302,3002],{},[1665,74304,2062],{},[902,74306,74307],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,74310,74312],{"className":74311},[886],[888,74313,74314],{"xmlns":890},[892,74315,74316,74333],{},[895,74317,74318,74320,74322,74324,74326,74328,74330],{},[898,74319,1755],{},[898,74321,12737],{},[1654,74323,1708],{"stretchy":1656},[1665,74325,14315],{},[1654,74327,1726],{"stretchy":1656},[1654,74329,1750],{},[1665,74331,74332],{},"89",[902,74334,74335],{"encoding":904},"PR(8) = 89",[724,74337,74338,74339,1343,74365,24497,74389,74427],{},"Ověření principu: ",[883,74340,74342],{"className":74341},[886],[888,74343,74344],{"xmlns":890},[892,74345,74346,74362],{},[895,74347,74348,74350,74352,74354,74356,74358,74360],{},[898,74349,9320],{},[898,74351,12737],{},[1654,74353,1750],{},[1665,74355,46239],{},[1654,74357,2380],{},[1665,74359,1681],{},[898,74361,1663],{},[902,74363,74364],{"encoding":904},"MR = 30 - 2Q",[883,74366,74368],{"className":74367},[886],[888,74369,74370],{"xmlns":890},[892,74371,74372,74386],{},[895,74373,74374,74376,74378,74380,74382,74384],{},[898,74375,9320],{},[898,74377,11539],{},[1654,74379,1750],{},[898,74381,1663],{},[1654,74383,1766],{},[1665,74385,11015],{},[902,74387,74388],{"encoding":904},"MC = Q + 6",[883,74390,74392],{"className":74391},[886],[888,74393,74394],{"xmlns":890},[892,74395,74396,74424],{},[895,74397,74398,74400,74402,74404,74406,74408,74410,74412,74414,74416,74418,74420,74422],{},[898,74399,9320],{},[898,74401,12737],{},[1654,74403,1708],{"stretchy":1656},[1665,74405,14315],{},[1654,74407,1726],{"stretchy":1656},[1654,74409,1750],{},[1665,74411,31634],{},[1654,74413,1750],{},[898,74415,9320],{},[898,74417,11539],{},[1654,74419,1708],{"stretchy":1656},[1665,74421,14315],{},[1654,74423,1726],{"stretchy":1656},[902,74425,74426],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,74429,74430,74431,74464,74465,74482],{},"V řadě případů — má-li rovnice ",[883,74432,74434],{"className":74433},[886],[888,74435,74436],{"xmlns":890},[892,74437,74438,74462],{},[895,74439,74440,74442,74444,74446,74448,74450,74452,74454,74456,74458,74460],{},[898,74441,9320],{},[898,74443,12737],{},[1654,74445,1708],{"stretchy":1656},[898,74447,1663],{},[1654,74449,1726],{"stretchy":1656},[1654,74451,1750],{},[898,74453,9320],{},[898,74455,11539],{},[1654,74457,1708],{"stretchy":1656},[898,74459,1663],{},[1654,74461,1726],{"stretchy":1656},[902,74463,74030],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,74466,74468],{"className":74467},[886],[888,74469,74470],{"xmlns":890},[892,74471,74472,74480],{},[895,74473,74474],{},[1710,74475,74476,74478],{},[898,74477,1663],{},[1665,74479,2062],{},[902,74481,46528],{"encoding":904}," — není třeba provádět test druhé derivace.",[45568,74484,74486],{"id":74485},"příklad-310","Příklad 3.10",[724,74488,74489,74491,74492,74496,74497,74510,74511,74542],{},[38,74490,64207],{}," Firma vyrábí minipočítače v ",[207,74493,74495],{"className":74494,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,74498,74500],{"className":74499},[886],[888,74501,74502],{"xmlns":890},[892,74503,74504,74508],{},[895,74505,74506],{},[1665,74507,23899],{},[902,74509,23899],{"encoding":904}," EUR\u002Fks. ",[883,74512,74514],{"className":74513},[886],[888,74515,74516],{"xmlns":890},[892,74517,74518,74539],{},[895,74519,74520,74522,74524,74526,74528,74530,74533],{},[898,74521,11536],{},[898,74523,11539],{},[1654,74525,1750],{},[1665,74527,4767],{},[1654,74529,1766],{},[1665,74531,74532],{},"28",[1741,74534,74535,74537],{},[898,74536,1663],{},[1665,74538,1681],{},[902,74540,74541],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,74544,74545,2186,74547,1343,74569,1343,74589,74612],{},[38,74546,31458],{},[883,74548,74550],{"className":74549},[886],[888,74551,74552],{"xmlns":890},[892,74553,74554,74566],{},[895,74555,74556,74558,74560,74562,74564],{},[898,74557,11536],{},[898,74559,12737],{},[1654,74561,1750],{},[1665,74563,23899],{},[898,74565,1663],{},[902,74567,74568],{"encoding":904},"TR = 900Q",[883,74570,74572],{"className":74571},[886],[888,74573,74574],{"xmlns":890},[892,74575,74576,74586],{},[895,74577,74578,74580,74582,74584],{},[898,74579,9320],{},[898,74581,12737],{},[1654,74583,1750],{},[1665,74585,23899],{},[902,74587,74588],{"encoding":904},"MR = 900",[883,74590,74592],{"className":74591},[886],[888,74593,74594],{"xmlns":890},[892,74595,74596,74609],{},[895,74597,74598,74600,74602,74604,74607],{},[898,74599,9320],{},[898,74601,11539],{},[1654,74603,1750],{},[1665,74605,74606],{},"56",[898,74608,1663],{},[902,74610,74611],{"encoding":904},"MC = 56Q",". Z principu:",[883,74614,74616],{"className":74615},[886],[888,74617,74618],{"xmlns":890,"display":1956},[892,74619,74620,74662],{},[895,74621,74622,74624,74626,74628,74630,74632,74634,74636,74638,74640,74648,74650,74653,74655,74657,74659],{},[1665,74623,23899],{},[1654,74625,1750],{},[1665,74627,74606],{},[898,74629,1663],{},[1865,74631,2805],{},[1654,74633,8634],{},[1865,74635,2805],{},[898,74637,1663],{},[1654,74639,1750],{},[2582,74641,74642],{"scriptlevel":2062,"displaystyle":1656},[2811,74643,74644,74646],{},[1665,74645,23899],{},[1665,74647,74606],{},[1654,74649,14628],{},[1665,74651,74652],{},"16,07",[1865,74654,2805],{},[1654,74656,11492],{},[1865,74658,2805],{},[1665,74660,74661],{},"16.",[902,74663,74664],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,74666,74667,74668,2781],{},"Zisk při ",[883,74669,74671],{"className":74670},[886],[888,74672,74673],{"xmlns":890},[892,74674,74675,74683],{},[895,74676,74677,74679,74681],{},[898,74678,1663],{},[1654,74680,1750],{},[1665,74682,50082],{},[902,74684,74685],{"encoding":904},"Q = 16",[883,74687,74689],{"className":74688},[886],[888,74690,74691],{"xmlns":890,"display":1956},[892,74692,74693,74764],{},[895,74694,74695,74697,74699,74701,74703,74705,74707,74709,74711,74713,74715,74717,74719,74721,74723,74725,74731,74733,74735,74737,74739,74741,74743,74745,74747,74750,74752,74754,74756,74759,74762],{},[898,74696,1755],{},[898,74698,12737],{},[1654,74700,1708],{"stretchy":1656},[1665,74702,50082],{},[1654,74704,1726],{"stretchy":1656},[1654,74706,1750],{},[1665,74708,23899],{},[1654,74710,4554],{},[1665,74712,50082],{},[1654,74714,2380],{},[1654,74716,1708],{"stretchy":1656},[1665,74718,4767],{},[1654,74720,1766],{},[1665,74722,74532],{},[1654,74724,4554],{},[1741,74726,74727,74729],{},[1665,74728,50082],{},[1665,74730,1681],{},[1654,74732,1726],{"stretchy":1656},[1654,74734,1750],{},[1665,74736,31634],{},[1865,74738,11744],{},[1665,74740,28837],{},[1654,74742,2380],{},[1665,74744,32887],{},[1865,74746,11744],{},[1665,74748,74749],{},"218",[1654,74751,1750],{},[1665,74753,32887],{},[1865,74755,11744],{},[1665,74757,74758],{},"182",[1865,74760,74761],{}," EUR",[898,74763,2138],{"mathvariant":1878},[902,74765,74766],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,74768,74769],{},"Pro srovnání při původních 30 ks:",[883,74771,74773],{"className":74772},[886],[888,74774,74775],{"xmlns":890,"display":1956},[892,74776,74777,74842],{},[895,74778,74779,74781,74783,74785,74787,74789,74791,74793,74795,74797,74799,74801,74803,74805,74807,74809,74811,74813,74815,74818,74820,74822,74824,74826,74828,74830,74832,74834,74836,74838,74840],{},[898,74780,1755],{},[898,74782,12737],{},[1654,74784,1708],{"stretchy":1656},[1665,74786,46239],{},[1654,74788,1726],{"stretchy":1656},[1654,74790,1750],{},[1665,74792,23899],{},[1654,74794,4554],{},[1665,74796,46239],{},[1654,74798,2380],{},[1654,74800,1708],{"stretchy":1656},[1665,74802,4767],{},[1654,74804,1766],{},[1665,74806,74532],{},[1654,74808,4554],{},[1665,74810,23899],{},[1654,74812,1726],{"stretchy":1656},[1654,74814,1750],{},[1665,74816,74817],{},"27",[1865,74819,11744],{},[1665,74821,67302],{},[1654,74823,2380],{},[1665,74825,4622],{},[1865,74827,11744],{},[1665,74829,4679],{},[1654,74831,1750],{},[1665,74833,1667],{},[1865,74835,11744],{},[1665,74837,32430],{},[1865,74839,74761],{},[898,74841,2138],{"mathvariant":1878},[902,74843,74844],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,74846,74847,74850,74851,74869,74870,74888],{},[38,74848,74849],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,74852,74854],{"className":74853},[886],[888,74855,74856],{"xmlns":890},[892,74857,74858,74866],{},[895,74859,74860,74862,74864],{},[1665,74861,32887],{},[1865,74863,11744],{},[1665,74865,74758],{},[902,74867,74868],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,74871,74873],{"className":74872},[886],[888,74874,74875],{"xmlns":890},[892,74876,74877,74885],{},[895,74878,74879,74881,74883],{},[1665,74880,1667],{},[1865,74882,11744],{},[1665,74884,32430],{},[902,74886,74887],{"encoding":904},"1\\,750"," EUR.",[198,74890,74892],{"id":74891},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,74894,74895,74896,70790,74909,74933],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,74897,74899],{"className":74898},[886],[888,74900,74901],{"xmlns":890},[892,74902,74903,74907],{},[895,74904,74905],{},[898,74906,1755],{},[902,74908,1755],{"encoding":904},[883,74910,74912],{"className":74911},[886],[888,74913,74914],{"xmlns":890},[892,74915,74916,74930],{},[895,74917,74918,74920,74922,74924,74926,74928],{},[898,74919,11536],{},[898,74921,12737],{},[1654,74923,1750],{},[898,74925,1755],{},[1654,74927,4554],{},[898,74929,1663],{},[902,74931,74932],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,74935,74937],{"className":74936},[886],[888,74938,74939],{"xmlns":890,"display":1956},[892,74940,74941,74974],{},[1960,74942,74943],{"width":1962},[1964,74944,74945,74947,74967,74969],{},[1967,74946],{"width":1969},[1967,74948,74949],{},[895,74950,74951,74953,74955,74957,74959,74961,74963,74965],{},[898,74952,1755],{},[1654,74954,1750],{},[898,74956,9320],{},[898,74958,11539],{},[1654,74960,1708],{"stretchy":1656},[898,74962,1663],{},[1654,74964,1726],{"stretchy":1656},[898,74966,2138],{"mathvariant":1878},[1967,74968],{"width":1969},[1967,74970,74971],{},[1865,74972,74973],{},"(3.14)",[902,74975,74976],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,74978,74979,74980,2138],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,74981,74983],{"className":74982},[886],[888,74984,74985],{"xmlns":890},[892,74986,74987,75001],{},[895,74988,74989,74991],{},[898,74990,1755],{},[1741,74992,74993,74995],{},[898,74994,12737],{},[895,74996,74997,74999],{},[1654,74998,2592],{"mathvariant":1878},[1654,75000,2592],{"mathvariant":1878},[902,75002,74057],{"encoding":904},[45568,75004,75006],{"id":75005},"příklad-311","Příklad 3.11",[724,75008,75009,65742,75011,75058,75059,75077],{},[38,75010,64207],{},[883,75012,75014],{"className":75013},[886],[888,75015,75016],{"xmlns":890},[892,75017,75018,75055],{},[895,75019,75020,75022,75024,75026,75029,75035,75037,75039,75045,75047,75049,75051,75053],{},[898,75021,11536],{},[898,75023,11539],{},[1654,75025,1750],{},[1665,75027,75028],{},"0,04",[1741,75030,75031,75033],{},[898,75032,1663],{},[1665,75034,4035],{},[1654,75036,2380],{},[1665,75038,31233],{},[1741,75040,75041,75043],{},[898,75042,1663],{},[1665,75044,1681],{},[1654,75046,1766],{},[1665,75048,4647],{},[898,75050,1663],{},[1654,75052,1766],{},[1665,75054,4032],{},[902,75056,75057],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,75060,75062],{"className":75061},[886],[888,75063,75064],{"xmlns":890},[892,75065,75066,75074],{},[895,75067,75068,75070,75072],{},[898,75069,1755],{},[1654,75071,1750],{},[1665,75073,7631],{},[902,75075,75076],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,75079,75080,75082,75083,7515,75125,75159,75160,2781],{},[38,75081,31458],{}," Z (3.14): ",[883,75084,75086],{"className":75085},[886],[888,75087,75088],{"xmlns":890},[892,75089,75090,75122],{},[895,75091,75092,75094,75096,75098,75101,75107,75109,75112,75114,75116,75118,75120],{},[898,75093,9320],{},[898,75095,11539],{},[1654,75097,1750],{},[1665,75099,75100],{},"0,12",[1741,75102,75103,75105],{},[898,75104,1663],{},[1665,75106,1681],{},[1654,75108,2380],{},[1665,75110,75111],{},"1,8",[898,75113,1663],{},[1654,75115,1766],{},[1665,75117,4647],{},[1654,75119,1750],{},[1665,75121,7631],{},[902,75123,75124],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,75126,75128],{"className":75127},[886],[888,75129,75130],{"xmlns":890},[892,75131,75132,75156],{},[895,75133,75134,75136,75142,75144,75146,75148,75150,75152,75154],{},[1665,75135,75100],{},[1741,75137,75138,75140],{},[898,75139,1663],{},[1665,75141,1681],{},[1654,75143,2380],{},[1665,75145,75111],{},[898,75147,1663],{},[1654,75149,1766],{},[1665,75151,11015],{},[1654,75153,1750],{},[1665,75155,2062],{},[902,75157,75158],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,75161,75163],{"className":75162},[886],[888,75164,75165],{"xmlns":890},[892,75166,75167,75171],{},[895,75168,75169],{},[1665,75170,75100],{},[902,75172,75173],{"encoding":904},"0{,}12",[883,75175,75177],{"className":75176},[886],[888,75178,75179],{"xmlns":890,"display":1956},[892,75180,75181,75233],{},[895,75182,75183,75189,75191,75193,75195,75197,75199,75201,75203,75205,75207,75209,75215,75217,75219,75221,75223,75229,75231],{},[1741,75184,75185,75187],{},[898,75186,1663],{},[1665,75188,1681],{},[1654,75190,2380],{},[1665,75192,10207],{},[898,75194,1663],{},[1654,75196,1766],{},[1665,75198,4767],{},[1654,75200,1750],{},[1665,75202,2062],{},[1865,75204,2805],{},[1654,75206,8634],{},[1865,75208,2805],{},[1710,75210,75211,75213],{},[898,75212,1663],{},[1665,75214,1667],{},[1654,75216,1750],{},[1665,75218,4032],{},[1654,75220,1674],{"separator":1673},[1865,75222,2805],{},[1710,75224,75225,75227],{},[898,75226,1663],{},[1665,75228,1681],{},[1654,75230,1750],{},[1665,75232,28024],{},[902,75234,75235],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,75237,75238,75239,2781],{},"Dále ",[883,75240,75242],{"className":75241},[886],[888,75243,75244],{"xmlns":890},[892,75245,75246,75285],{},[895,75247,75248,75250,75260,75262,75264,75266,75272,75274,75276,75279,75281,75283],{},[898,75249,1755],{},[1741,75251,75252,75254],{},[898,75253,12737],{},[895,75255,75256,75258],{},[1654,75257,2592],{"mathvariant":1878},[1654,75259,2592],{"mathvariant":1878},[1654,75261,1750],{},[1654,75263,2380],{},[898,75265,9320],{},[1741,75267,75268,75270],{},[898,75269,11539],{},[1654,75271,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,75273,1750],{},[1654,75275,2380],{},[1665,75277,75278],{},"0,24",[898,75280,1663],{},[1654,75282,1766],{},[1665,75284,75111],{},[902,75286,75287],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,75289,75290,75340],{},[123,75291,75292,75336,75337,75339],{},[883,75293,75295],{"className":75294},[886],[888,75296,75297],{"xmlns":890},[892,75298,75299,75333],{},[895,75300,75301,75303,75313,75315,75317,75319,75321,75323,75325,75327,75329,75331],{},[898,75302,1755],{},[1741,75304,75305,75307],{},[898,75306,12737],{},[895,75308,75309,75311],{},[1654,75310,2592],{"mathvariant":1878},[1654,75312,2592],{"mathvariant":1878},[1654,75314,1708],{"stretchy":1656},[1665,75316,4032],{},[1654,75318,1726],{"stretchy":1656},[1654,75320,1750],{},[1665,75322,28017],{},[1654,75324,2952],{},[1665,75326,2062],{},[1865,75328,2805],{},[1654,75330,8634],{},[1865,75332,2805],{},[902,75334,75335],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,75338,7988],{}," zisku (minimalizace ztráty);",[123,75341,75342,75336,75388,75390],{},[883,75343,75345],{"className":75344},[886],[888,75346,75347],{"xmlns":890},[892,75348,75349,75385],{},[895,75350,75351,75353,75363,75365,75367,75369,75371,75373,75375,75377,75379,75381,75383],{},[898,75352,1755],{},[1741,75354,75355,75357],{},[898,75356,12737],{},[895,75358,75359,75361],{},[1654,75360,2592],{"mathvariant":1878},[1654,75362,2592],{"mathvariant":1878},[1654,75364,1708],{"stretchy":1656},[1665,75366,4647],{},[1654,75368,1726],{"stretchy":1656},[1654,75370,1750],{},[1654,75372,2380],{},[1665,75374,28017],{},[1654,75376,3002],{},[1665,75378,2062],{},[1865,75380,2805],{},[1654,75382,8634],{},[1865,75384,2805],{},[902,75386,75387],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,75389,12467],{}," zisku, avšak",[883,75392,75394],{"className":75393},[886],[888,75395,75396],{"xmlns":890,"display":1956},[892,75397,75398,75466],{},[895,75399,75400,75402,75404,75406,75408,75410,75412,75414,75416,75418,75420,75422,75424,75426,75428,75430,75432,75434,75436,75438,75440,75442,75444,75446,75448,75450,75452,75454,75456,75458,75460,75462,75464],{},[898,75401,1755],{},[898,75403,12737],{},[1654,75405,1708],{"stretchy":1656},[1665,75407,4647],{},[1654,75409,1726],{"stretchy":1656},[1654,75411,1750],{},[1665,75413,7631],{},[1654,75415,4554],{},[1665,75417,4647],{},[1654,75419,2380],{},[1654,75421,1708],{"stretchy":1656},[1665,75423,75028],{},[1654,75425,4554],{},[1665,75427,1667],{},[1865,75429,11744],{},[1665,75431,67302],{},[1654,75433,2380],{},[1665,75435,31233],{},[1654,75437,4554],{},[1665,75439,4273],{},[1654,75441,1766],{},[1665,75443,4273],{},[1654,75445,1766],{},[1665,75447,4032],{},[1654,75449,1726],{"stretchy":1656},[1654,75451,1750],{},[1665,75453,5844],{},[1654,75455,2380],{},[1665,75457,29869],{},[1654,75459,1750],{},[1654,75461,2380],{},[1665,75463,10207],{},[1654,75465,1674],{"separator":1673},[902,75467,75468],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,75470,75471,75472,2138],{},"tj. ztráta větší než ",[883,75473,75475],{"className":75474},[886],[888,75476,75477],{"xmlns":890},[892,75478,75479,75489],{},[895,75480,75481,75483,75485,75487],{},[898,75482,19153],{},[898,75484,11539],{},[1654,75486,1750],{},[1665,75488,4032],{},[902,75490,75491],{"encoding":904},"FC = 5",[724,75493,75494,75497,75498,75501,75502,2138],{},[38,75495,75496],{},"Závěr:"," firma by měla ",[38,75499,75500],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,75503,75505],{"className":75504},[886],[888,75506,75507],{"xmlns":890},[892,75508,75509,75519],{},[895,75510,75511,75513,75515,75517],{},[898,75512,19153],{},[898,75514,11539],{},[1654,75516,1750],{},[1665,75518,4032],{},[902,75520,75491],{"encoding":904},[115,75522,75524],{"id":75523},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,75526,75527,75528,75530,75531,75546,75547,75560,75561,75587,75588,75601,75602,75619,75620,11387,75637,75640,75641,75661,75662,75677,75678,2781],{},"Důležitým završením analýzy je konstrukce ",[38,75529,63495],{},". S nabízeným množstvím rostou mezní náklady ",[883,75532,75534],{"className":75533},[886],[888,75535,75536],{"xmlns":890},[892,75537,75538,75544],{},[895,75539,75540,75542],{},[898,75541,9320],{},[898,75543,11539],{},[902,75545,63512],{"encoding":904}," a tyto určují cenu ",[883,75548,75550],{"className":75549},[886],[888,75551,75552],{"xmlns":890},[892,75553,75554,75558],{},[895,75555,75556],{},[898,75557,1755],{},[902,75559,1755],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,75562,75564],{"className":75563},[886],[888,75565,75566],{"xmlns":890},[892,75567,75568,75584],{},[895,75569,75570,75572,75574,75576,75578,75580,75582],{},[898,75571,1755],{},[1654,75573,1750],{},[898,75575,9320],{},[898,75577,11539],{},[1654,75579,1708],{"stretchy":1656},[898,75581,1663],{},[1654,75583,1726],{"stretchy":1656},[902,75585,75586],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,75589,75591],{"className":75590},[886],[888,75592,75593],{"xmlns":890},[892,75594,75595,75599],{},[895,75596,75597],{},[898,75598,1755],{},[902,75600,1755],{"encoding":904}," však nemůže být nižší než ",[883,75603,75605],{"className":75604},[886],[888,75606,75607],{"xmlns":890},[892,75608,75609,75617],{},[895,75610,75611],{},[1741,75612,75613,75615],{},[898,75614,1755],{},[1654,75616,1670],{},[902,75618,13142],{"encoding":904}," odpovídající množství ",[883,75621,75623],{"className":75622},[886],[888,75624,75625],{"xmlns":890},[892,75626,75627,75635],{},[895,75628,75629],{},[1741,75630,75631,75633],{},[898,75632,1663],{},[1654,75634,1670],{},[902,75636,3768],{"encoding":904},[38,75638,75639],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,75642,75644],{"className":75643},[886],[888,75645,75646],{"xmlns":890},[892,75647,75648,75658],{},[895,75649,75650,75652],{},[1665,75651,2062],{},[1741,75653,75654,75656],{},[898,75655,1663],{},[1654,75657,1670],{},[902,75659,75660],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,75663,75665],{"className":75664},[886],[888,75666,75667],{"xmlns":890},[892,75668,75669,75675],{},[895,75670,75671,75673],{},[898,75672,9320],{},[898,75674,11539],{},[902,75676,63512],{"encoding":904}," nad bodem ",[883,75679,75681],{"className":75680},[886],[888,75682,75683],{"xmlns":890},[892,75684,75685,75689],{},[895,75686,75687],{},[898,75688,4737],{},[902,75690,4737],{"encoding":904},[883,75692,75694],{"className":75693},[886],[888,75695,75696],{"xmlns":890,"display":1956},[892,75697,75698,75805],{},[1960,75699,75700],{"width":1962},[1964,75701,75702,75704,75798,75800],{},[1967,75703],{"width":1969},[1967,75705,75706],{},[895,75707,75708,75710,75712,75714,75716,75718,75720,75722],{},[898,75709,1755],{},[1654,75711,1750],{},[898,75713,17398],{},[1654,75715,1708],{"stretchy":1656},[898,75717,1663],{},[1654,75719,1726],{"stretchy":1656},[1654,75721,1750],{},[895,75723,75724,75727],{},[1654,75725,75726],{"fence":1673},"{",[1960,75728,75731,75770],{"rowspacing":75729,"columnalign":75730,"columnspacing":5010},"0.36em","left left",[1964,75732,75733,75749],{},[1967,75734,75735],{},[2582,75736,75737],{"scriptlevel":2062,"displaystyle":1656},[895,75738,75739,75741,75743,75745,75747],{},[898,75740,9320],{},[898,75742,11539],{},[1654,75744,1708],{"stretchy":1656},[898,75746,1663],{},[1654,75748,1726],{"stretchy":1656},[1967,75750,75751],{},[2582,75752,75753],{"scriptlevel":2062,"displaystyle":1656},[895,75754,75755,75758,75760,75762,75768],{},[1865,75756,75757],{},"pro ",[898,75759,1663],{},[1654,75761,13222],{},[1741,75763,75764,75766],{},[898,75765,1663],{},[1654,75767,1670],{},[1654,75769,1674],{"separator":1673},[1964,75771,75772,75778],{},[1967,75773,75774],{},[2582,75775,75776],{"scriptlevel":2062,"displaystyle":1656},[1665,75777,2062],{},[1967,75779,75780],{},[2582,75781,75782],{"scriptlevel":2062,"displaystyle":1656},[895,75783,75784,75786,75788,75790,75796],{},[1865,75785,75757],{},[898,75787,1663],{},[1654,75789,3002],{},[1741,75791,75792,75794],{},[898,75793,1663],{},[1654,75795,1670],{},[1654,75797,1674],{"separator":1673},[1967,75799],{"width":1969},[1967,75801,75802],{},[1865,75803,75804],{},"(3.15)",[902,75806,75807],{"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}",[724,75809,13049,75810,75827,75828,75845,75846,49719,75876,75879],{},[883,75811,75813],{"className":75812},[886],[888,75814,75815],{"xmlns":890},[892,75816,75817,75825],{},[895,75818,75819],{},[1741,75820,75821,75823],{},[898,75822,1663],{},[1654,75824,1670],{},[902,75826,3768],{"encoding":904}," je bod minima ",[883,75829,75831],{"className":75830},[886],[888,75832,75833],{"xmlns":890},[892,75834,75835,75843],{},[895,75836,75837,75839,75841],{},[898,75838,4737],{},[898,75840,48559],{},[898,75842,11539],{},[902,75844,63531],{"encoding":904},". Bod ",[883,75847,75849],{"className":75848},[886],[888,75850,75851],{"xmlns":890},[892,75852,75853,75873],{},[895,75854,75855,75857,75863,75865,75871],{},[1654,75856,1708],{"stretchy":1656},[1741,75858,75859,75861],{},[898,75860,1663],{},[1654,75862,1670],{},[1654,75864,1674],{"separator":1673},[1741,75866,75867,75869],{},[898,75868,1755],{},[1654,75870,1670],{},[1654,75872,1726],{"stretchy":1656},[902,75874,75875],{"encoding":904},"(Q^*, P^*)",[38,75877,75878],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[2140,75881,75882,75887],{},[724,75883,75884,75886],{},[883,75885,3111],{}," Postup — jak odvodit nabídku firmy",[152,75888,75889,75938,76033,76088,76159],{},[123,75890,75891,75892,2068,75914,2138],{},"Ze zadaných nákladů určete ",[883,75893,75895],{"className":75894},[886],[888,75896,75897],{"xmlns":890},[892,75898,75899,75911],{},[895,75900,75901,75903,75905,75907,75909],{},[898,75902,9320],{},[898,75904,11539],{},[1654,75906,1708],{"stretchy":1656},[898,75908,1663],{},[1654,75910,1726],{"stretchy":1656},[902,75912,75913],{"encoding":904},"MC(Q)",[883,75915,75917],{"className":75916},[886],[888,75918,75919],{"xmlns":890},[892,75920,75921,75935],{},[895,75922,75923,75925,75927,75929,75931,75933],{},[898,75924,4737],{},[898,75926,48559],{},[898,75928,11539],{},[1654,75930,1708],{"stretchy":1656},[898,75932,1663],{},[1654,75934,1726],{"stretchy":1656},[902,75936,75937],{"encoding":904},"AVC(Q)",[123,75939,75940,75941,75958,75959,75976,75977,76009,76010,12664],{},"Najděte ",[883,75942,75944],{"className":75943},[886],[888,75945,75946],{"xmlns":890},[892,75947,75948,75956],{},[895,75949,75950],{},[1741,75951,75952,75954],{},[898,75953,1663],{},[1654,75955,1670],{},[902,75957,3768],{"encoding":904}," jako bod minima ",[883,75960,75962],{"className":75961},[886],[888,75963,75964],{"xmlns":890},[892,75965,75966,75974],{},[895,75967,75968,75970,75972],{},[898,75969,4737],{},[898,75971,48559],{},[898,75973,11539],{},[902,75975,63531],{"encoding":904}," (řešením ",[883,75978,75980],{"className":75979},[886],[888,75981,75982],{"xmlns":890},[892,75983,75984,76006],{},[895,75985,75986,75988,75990,75996,75998,76000,76002,76004],{},[898,75987,4737],{},[898,75989,48559],{},[1741,75991,75992,75994],{},[898,75993,11539],{},[1654,75995,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,75997,1708],{"stretchy":1656},[898,75999,1663],{},[1654,76001,1726],{"stretchy":1656},[1654,76003,1750],{},[1665,76005,2062],{},[902,76007,76008],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,76011,76013],{"className":76012},[886],[888,76014,76015],{"xmlns":890},[892,76016,76017,76031],{},[895,76018,76019,76021,76023,76025,76027,76029],{},[898,76020,4737],{},[898,76022,48559],{},[898,76024,11539],{},[1654,76026,1750],{},[898,76028,9320],{},[898,76030,11539],{},[902,76032,63468],{"encoding":904},[123,76034,73941,76035,76087],{},[883,76036,76038],{"className":76037},[886],[888,76039,76040],{"xmlns":890},[892,76041,76042,76084],{},[895,76043,76044,76050,76052,76054,76056,76058,76064,76066,76068,76070,76072,76074,76076,76082],{},[1741,76045,76046,76048],{},[898,76047,1755],{},[1654,76049,1670],{},[1654,76051,1750],{},[898,76053,9320],{},[898,76055,11539],{},[1654,76057,1708],{"stretchy":1656},[1741,76059,76060,76062],{},[898,76061,1663],{},[1654,76063,1670],{},[1654,76065,1726],{"stretchy":1656},[1654,76067,1750],{},[898,76069,4737],{},[898,76071,48559],{},[898,76073,11539],{},[1654,76075,1708],{"stretchy":1656},[1741,76077,76078,76080],{},[898,76079,1663],{},[1654,76081,1670],{},[1654,76083,1726],{"stretchy":1656},[902,76085,76086],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,76089,76090,76091,15201,76123,76145,76146,2138],{},"Zapište nabídku: ",[883,76092,76094],{"className":76093},[886],[888,76095,76096],{"xmlns":890},[892,76097,76098,76120],{},[895,76099,76100,76102,76104,76106,76108,76110,76112,76114,76116,76118],{},[898,76101,17398],{},[1654,76103,1708],{"stretchy":1656},[898,76105,1663],{},[1654,76107,1726],{"stretchy":1656},[1654,76109,1750],{},[898,76111,9320],{},[898,76113,11539],{},[1654,76115,1708],{"stretchy":1656},[898,76117,1663],{},[1654,76119,1726],{"stretchy":1656},[902,76121,76122],{"encoding":904},"S(Q) = MC(Q)",[883,76124,76126],{"className":76125},[886],[888,76127,76128],{"xmlns":890},[892,76129,76130,76142],{},[895,76131,76132,76134,76136],{},[898,76133,1663],{},[1654,76135,13222],{},[1741,76137,76138,76140],{},[898,76139,1663],{},[1654,76141,1670],{},[902,76143,76144],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,76147,76149],{"className":76148},[886],[888,76150,76151],{"xmlns":890},[892,76152,76153,76157],{},[895,76154,76155],{},[1665,76156,2062],{},[902,76158,2062],{"encoding":904},[123,76160,76161,76162,76194],{},"V případě potřeby vyjádřete inverzi ",[883,76163,76165],{"className":76164},[886],[888,76166,76167],{"xmlns":890},[892,76168,76169,76191],{},[895,76170,76171,76173,76175,76185,76187,76189],{},[898,76172,1663],{},[1654,76174,1750],{},[1741,76176,76177,76179],{},[898,76178,17398],{},[895,76180,76181,76183],{},[1654,76182,2380],{},[1665,76184,1667],{},[1654,76186,1708],{"stretchy":1656},[898,76188,1755],{},[1654,76190,1726],{"stretchy":1656},[902,76192,76193],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,76196,76197],{},[614,76198,76199,76200,1343,76215,2068,76232,3120,76247,76260,76261,76286,76287,76300,76301,76318,76319,76336,76337,76354],{},"Obrázek 3.14: Křivky ",[883,76201,76203],{"className":76202},[886],[888,76204,76205],{"xmlns":890},[892,76206,76207,76213],{},[895,76208,76209,76211],{},[898,76210,4737],{},[898,76212,11539],{},[902,76214,63780],{"encoding":904},[883,76216,76218],{"className":76217},[886],[888,76219,76220],{"xmlns":890},[892,76221,76222,76230],{},[895,76223,76224,76226,76228],{},[898,76225,4737],{},[898,76227,48559],{},[898,76229,11539],{},[902,76231,63531],{"encoding":904},[883,76233,76235],{"className":76234},[886],[888,76236,76237],{"xmlns":890},[892,76238,76239,76245],{},[895,76240,76241,76243],{},[898,76242,9320],{},[898,76244,11539],{},[902,76246,63512],{"encoding":904},[883,76248,76250],{"className":76249},[886],[888,76251,76252],{"xmlns":890},[892,76253,76254,76258],{},[895,76255,76256],{},[898,76257,900],{},[902,76259,900],{"encoding":904},"; křivka nabídky ",[883,76262,76264],{"className":76263},[886],[888,76265,76266],{"xmlns":890},[892,76267,76268,76284],{},[895,76269,76270,76272,76274,76276,76278,76280,76282],{},[898,76271,1755],{},[1654,76273,1750],{},[898,76275,9320],{},[898,76277,11539],{},[1654,76279,1708],{"stretchy":1656},[898,76281,1663],{},[1654,76283,1726],{"stretchy":1656},[902,76285,75586],{"encoding":904}," začíná v bodě ",[883,76288,76290],{"className":76289},[886],[888,76291,76292],{"xmlns":890},[892,76293,76294,76298],{},[895,76295,76296],{},[898,76297,4737],{},[902,76299,4737],{"encoding":904}," odpovídajícím minimu ",[883,76302,76304],{"className":76303},[886],[888,76305,76306],{"xmlns":890},[892,76307,76308,76316],{},[895,76309,76310,76312,76314],{},[898,76311,4737],{},[898,76313,48559],{},[898,76315,11539],{},[902,76317,63531],{"encoding":904}," při ceně ",[883,76320,76322],{"className":76321},[886],[888,76323,76324],{"xmlns":890},[892,76325,76326,76334],{},[895,76327,76328],{},[1741,76329,76330,76332],{},[898,76331,1755],{},[1654,76333,1670],{},[902,76335,13142],{"encoding":904}," (minimální cena nabídky); pod ",[883,76338,76340],{"className":76339},[886],[888,76341,76342],{"xmlns":890},[892,76343,76344,76352],{},[895,76345,76346],{},[1741,76347,76348,76350],{},[898,76349,1663],{},[1654,76351,1670],{},[902,76353,3768],{"encoding":904}," je nabídka nulová.",[45568,76356,76358],{"id":76357},"příklad-312","Příklad 3.12",[724,76360,76361,65742,76363,76409],{},[38,76362,64207],{},[883,76364,76366],{"className":76365},[886],[888,76367,76368],{"xmlns":890},[892,76369,76370,76406],{},[895,76371,76372,76374,76376,76378,76380,76386,76388,76390,76396,76398,76400,76402,76404],{},[898,76373,11536],{},[898,76375,11539],{},[1654,76377,1750],{},[1665,76379,11555],{},[1741,76381,76382,76384],{},[898,76383,1663],{},[1665,76385,4035],{},[1654,76387,2380],{},[1665,76389,1681],{},[1741,76391,76392,76394],{},[898,76393,1663],{},[1665,76395,1681],{},[1654,76397,1766],{},[1665,76399,10207],{},[898,76401,1663],{},[1654,76403,1766],{},[1665,76405,4647],{},[902,76407,76408],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,76411,76412,2186,76414,76451,76452,2781],{},[38,76413,31458],{},[883,76415,76417],{"className":76416},[886],[888,76418,76419],{"xmlns":890},[892,76420,76421,76448],{},[895,76422,76423,76425,76427,76429,76432,76438,76440,76442,76444,76446],{},[898,76424,9320],{},[898,76426,11539],{},[1654,76428,1750],{},[1665,76430,76431],{},"0,3",[1741,76433,76434,76436],{},[898,76435,1663],{},[1665,76437,1681],{},[1654,76439,2380],{},[1665,76441,7631],{},[898,76443,1663],{},[1654,76445,1766],{},[1665,76447,10207],{},[902,76449,76450],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,76453,76455],{"className":76454},[886],[888,76456,76457],{"xmlns":890},[892,76458,76459,76469],{},[895,76460,76461,76463,76465,76467],{},[898,76462,1755],{},[1654,76464,1750],{},[898,76466,9320],{},[898,76468,11539],{},[902,76470,76471],{"encoding":904},"P = MC",[883,76473,76475],{"className":76474},[886],[888,76476,76477],{"xmlns":890,"display":1956},[892,76478,76479,76504],{},[895,76480,76481,76483,76485,76487,76493,76495,76497,76499,76501],{},[898,76482,1755],{},[1654,76484,1750],{},[1665,76486,76431],{},[1741,76488,76489,76491],{},[898,76490,1663],{},[1665,76492,1681],{},[1654,76494,2380],{},[1665,76496,7631],{},[898,76498,1663],{},[1654,76500,1766],{},[1665,76502,76503],{},"15.",[902,76505,76506],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,76508,76509,76510,14112,76523,76536],{},"Vyjádření ",[883,76511,76513],{"className":76512},[886],[888,76514,76515],{"xmlns":890},[892,76516,76517,76521],{},[895,76518,76519],{},[898,76520,1663],{},[902,76522,1663],{"encoding":904},[883,76524,76526],{"className":76525},[886],[888,76527,76528],{"xmlns":890},[892,76529,76530,76534],{},[895,76531,76532],{},[898,76533,1755],{},[902,76535,1755],{"encoding":904}," doplněním na čtverec:",[883,76538,76540],{"className":76539},[886],[888,76541,76542],{"xmlns":890,"display":1956},[892,76543,76544,76634],{},[895,76545,76546,76548,76550,76552,76590,76592,76594,76616,76618,76632],{},[898,76547,1755],{},[1654,76549,1750],{},[1665,76551,76431],{},[895,76553,76554,76556,76578,76580,76588],{},[1654,76555,1708],{"fence":1673},[1741,76557,76558,76576],{},[895,76559,76560,76562,76564,76566,76574],{},[1654,76561,1708],{"fence":1673},[898,76563,1663],{},[1654,76565,2380],{},[2582,76567,76568],{"scriptlevel":2062,"displaystyle":1656},[2811,76569,76570,76572],{},[1665,76571,4573],{},[1665,76573,4035],{},[1654,76575,1726],{"fence":1673},[1665,76577,1681],{},[1654,76579,1766],{},[2582,76581,76582],{"scriptlevel":2062,"displaystyle":1656},[2811,76583,76584,76586],{},[1665,76585,4767],{},[1665,76587,12742],{},[1654,76589,1726],{"fence":1673},[1654,76591,1674],{"separator":1673},[5008,76593],{"width":14608},[1741,76595,76596,76614],{},[895,76597,76598,76600,76602,76604,76612],{},[1654,76599,1708],{"fence":1673},[898,76601,1663],{},[1654,76603,2380],{},[2582,76605,76606],{"scriptlevel":2062,"displaystyle":1656},[2811,76607,76608,76610],{},[1665,76609,4573],{},[1665,76611,4035],{},[1654,76613,1726],{"fence":1673},[1665,76615,1681],{},[1654,76617,1750],{},[2811,76619,76620,76630],{},[895,76621,76622,76624,76626,76628],{},[1665,76623,46239],{},[898,76625,1755],{},[1654,76627,2380],{},[1665,76629,4767],{},[1665,76631,12742],{},[1654,76633,1674],{"separator":1673},[902,76635,76636],{"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},",[883,76638,76640],{"className":76639},[886],[888,76641,76642],{"xmlns":890,"display":1956},[892,76643,76644,76676],{},[895,76645,76646,76648,76650,76656,76658,76674],{},[898,76647,1663],{},[1654,76649,1750],{},[2811,76651,76652,76654],{},[1665,76653,4573],{},[1665,76655,4035],{},[1654,76657,1766],{},[2811,76659,76660,76672],{},[8818,76661,76662],{},[895,76663,76664,76666,76668,76670],{},[1665,76665,46239],{},[898,76667,1755],{},[1654,76669,2380],{},[1665,76671,4767],{},[1665,76673,4035],{},[898,76675,2138],{"mathvariant":1878},[902,76677,76678],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,76680,75238,76681,1343,76719,1343,76767,76801,76802,2138],{},[883,76682,76684],{"className":76683},[886],[888,76685,76686],{"xmlns":890},[892,76687,76688,76716],{},[895,76689,76690,76692,76694,76696,76698,76700,76706,76708,76710,76712,76714],{},[898,76691,4737],{},[898,76693,48559],{},[898,76695,11539],{},[1654,76697,1750],{},[1665,76699,11555],{},[1741,76701,76702,76704],{},[898,76703,1663],{},[1665,76705,1681],{},[1654,76707,2380],{},[1665,76709,1681],{},[898,76711,1663],{},[1654,76713,1766],{},[1665,76715,10207],{},[902,76717,76718],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,76720,76722],{"className":76721},[886],[888,76723,76724],{"xmlns":890},[892,76725,76726,76764],{},[895,76727,76728,76730,76732,76738,76740,76742,76744,76746,76748,76750,76752,76754,76760,76762],{},[898,76729,4737],{},[898,76731,48559],{},[1741,76733,76734,76736],{},[898,76735,11539],{},[1654,76737,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,76739,1750],{},[1665,76741,11599],{},[898,76743,1663],{},[1654,76745,2380],{},[1665,76747,1681],{},[1654,76749,1750],{},[1665,76751,2062],{},[1654,76753,8634],{},[1741,76755,76756,76758],{},[898,76757,1663],{},[1654,76759,1670],{},[1654,76761,1750],{},[1665,76763,4647],{},[902,76765,76766],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,76768,76770],{"className":76769},[886],[888,76771,76772],{"xmlns":890},[892,76773,76774,76798],{},[895,76775,76776,76778,76780,76790,76792,76794,76796],{},[898,76777,4737],{},[898,76779,48559],{},[1741,76781,76782,76784],{},[898,76783,11539],{},[895,76785,76786,76788],{},[1654,76787,2592],{"mathvariant":1878},[1654,76789,2592],{"mathvariant":1878},[1654,76791,1750],{},[1665,76793,11599],{},[1654,76795,2952],{},[1665,76797,2062],{},[902,76799,76800],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,76803,76805],{"className":76804},[886],[888,76806,76807],{"xmlns":890},[892,76808,76809,76845],{},[895,76810,76811,76817,76819,76821,76823,76825,76827,76829,76831,76833,76835,76837,76839,76841,76843],{},[1741,76812,76813,76815],{},[898,76814,1755],{},[1654,76816,1670],{},[1654,76818,1750],{},[898,76820,9320],{},[898,76822,11539],{},[1654,76824,1708],{"stretchy":1656},[1665,76826,4647],{},[1654,76828,1726],{"stretchy":1656},[1654,76830,1750],{},[1665,76832,46239],{},[1654,76834,2380],{},[1665,76836,5844],{},[1654,76838,1766],{},[1665,76840,10207],{},[1654,76842,1750],{},[1665,76844,4032],{},[902,76846,76847],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,76849,76850],{},[38,76851,76852],{},"Závěr.",[883,76854,76856],{"className":76855},[886],[888,76857,76858],{"xmlns":890,"display":1956},[892,76859,76860,76946],{},[895,76861,76862,76864,76866,76868,76870,76872,76874,76876],{},[898,76863,1755],{},[1654,76865,1750],{},[898,76867,17398],{},[1654,76869,1708],{"stretchy":1656},[898,76871,1663],{},[1654,76873,1726],{"stretchy":1656},[1654,76875,1750],{},[895,76877,76878,76880],{},[1654,76879,75726],{"fence":1673},[1960,76881,76882,76924],{"rowspacing":75729,"columnalign":75730,"columnspacing":5010},[1964,76883,76884,76908],{},[1967,76885,76886],{},[2582,76887,76888],{"scriptlevel":2062,"displaystyle":1656},[895,76889,76890,76892,76898,76900,76902,76904,76906],{},[1665,76891,76431],{},[1741,76893,76894,76896],{},[898,76895,1663],{},[1665,76897,1681],{},[1654,76899,2380],{},[1665,76901,7631],{},[898,76903,1663],{},[1654,76905,1766],{},[1665,76907,10207],{},[1967,76909,76910],{},[2582,76911,76912],{"scriptlevel":2062,"displaystyle":1656},[895,76913,76914,76916,76918,76920,76922],{},[1865,76915,75757],{},[898,76917,1663],{},[1654,76919,13222],{},[1665,76921,4647],{},[1654,76923,1674],{"separator":1673},[1964,76925,76926,76932],{},[1967,76927,76928],{},[2582,76929,76930],{"scriptlevel":2062,"displaystyle":1656},[1665,76931,2062],{},[1967,76933,76934],{},[2582,76935,76936],{"scriptlevel":2062,"displaystyle":1656},[895,76937,76938,76940,76942,76944],{},[1865,76939,75757],{},[898,76941,1663],{},[1654,76943,3002],{},[1665,76945,28024],{},[902,76947,76948],{"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}",[724,76950,76951],{},[614,76952,76953,76954,76969,76970,2138],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,76955,76957],{"className":76956},[886],[888,76958,76959],{"xmlns":890},[892,76960,76961,76967],{},[895,76962,76963,76965],{},[898,76964,9320],{},[898,76966,11539],{},[902,76968,63512],{"encoding":904}," ležící nad minimem ",[883,76971,76973],{"className":76972},[886],[888,76974,76975],{"xmlns":890},[892,76976,76977,76985],{},[895,76978,76979,76981,76983],{},[898,76980,4737],{},[898,76982,48559],{},[898,76984,11539],{},[902,76986,63531],{"encoding":904},[115,76988,76990],{"id":76989},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,76992,76993,76994,76998,76999,77014,77015,77035,77036,2068,77039,77042,77043,77045,77046,28640,77068,77070,77071,2068,77073,66946,77076,2186,77079,50034,77094,77109],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,76995,76997],{"className":76996,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,77000,77002],{"className":77001},[886],[888,77003,77004],{"xmlns":890},[892,77005,77006,77012],{},[895,77007,77008,77010],{},[898,77009,11536],{},[898,77011,12737],{},[902,77013,12837],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,77016,77018],{"className":77017},[886],[888,77019,77020],{"xmlns":890},[892,77021,77022,77032],{},[895,77023,77024,77026,77028,77030],{},[898,77025,11536],{},[898,77027,12737],{},[898,77029,1879],{"mathvariant":1878},[898,77031,1663],{},[902,77033,77034],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,77037,77038],{},"fixních",[38,77040,77041],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,77044,72545],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,77047,77049],{"className":77048},[886],[888,77050,77051],{"xmlns":890},[892,77052,77053,77065],{},[895,77054,77055,77057,77059,77061,77063],{},[898,77056,11536],{},[898,77058,12737],{},[1654,77060,2380],{},[898,77062,11536],{},[898,77064,11539],{},[902,77066,77067],{"encoding":904},"TR - TC",[38,77069,63392],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,77072,64704],{},[38,77074,77075],{},"mezní náklady",[207,77077,1145],{"className":77078,"dataFsResolvedFilePath":764,"href":765},[210],[883,77080,77082],{"className":77081},[886],[888,77083,77084],{"xmlns":890},[892,77085,77086,77092],{},[895,77087,77088,77090],{},[898,77089,11536],{},[898,77091,12737],{},[902,77093,12837],{"encoding":904},[883,77095,77097],{"className":77096},[886],[888,77098,77099],{"xmlns":890},[892,77100,77101,77107],{},[895,77102,77103,77105],{},[898,77104,11536],{},[898,77106,11539],{},[902,77108,11997],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,77111,77112,77174,77240,77302],{},[123,77113,77114,77117,77118,19111,77133,2138],{},[38,77115,77116],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,77119,77121],{"className":77120},[886],[888,77122,77123],{"xmlns":890},[892,77124,77125,77131],{},[895,77126,77127,77129],{},[898,77128,4737],{},[898,77130,11539],{},[902,77132,63780],{"encoding":904},[883,77134,77136],{"className":77135},[886],[888,77137,77138],{"xmlns":890},[892,77139,77140,77172],{},[895,77141,77142,77144,77146,77148,77154,77156,77158,77160,77162,77164,77170],{},[898,77143,4737],{},[898,77145,11539],{},[1654,77147,1708],{"stretchy":1656},[1710,77149,77150,77152],{},[898,77151,1663],{},[1665,77153,2062],{},[1654,77155,1726],{"stretchy":1656},[1654,77157,1750],{},[898,77159,9320],{},[898,77161,11539],{},[1654,77163,1708],{"stretchy":1656},[1710,77165,77166,77168],{},[898,77167,1663],{},[1665,77169,2062],{},[1654,77171,1726],{"stretchy":1656},[902,77173,70789],{"encoding":904},[123,77175,77176,77117,77179,19111,77196,2138],{},[38,77177,77178],{},"Princip minimalizace průměrných variabilních nákladů:",[883,77180,77182],{"className":77181},[886],[888,77183,77184],{"xmlns":890},[892,77185,77186,77194],{},[895,77187,77188,77190,77192],{},[898,77189,4737],{},[898,77191,48559],{},[898,77193,11539],{},[902,77195,63531],{"encoding":904},[883,77197,77199],{"className":77198},[886],[888,77200,77201],{"xmlns":890},[892,77202,77203,77237],{},[895,77204,77205,77207,77209,77211,77213,77219,77221,77223,77225,77227,77229,77235],{},[898,77206,4737],{},[898,77208,48559],{},[898,77210,11539],{},[1654,77212,1708],{"stretchy":1656},[1710,77214,77215,77217],{},[898,77216,1663],{},[1665,77218,2062],{},[1654,77220,1726],{"stretchy":1656},[1654,77222,1750],{},[898,77224,9320],{},[898,77226,11539],{},[1654,77228,1708],{"stretchy":1656},[1710,77230,77231,77233],{},[898,77232,1663],{},[1665,77234,2062],{},[1654,77236,1726],{"stretchy":1656},[902,77238,77239],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,77241,77242,77245,77246,19111,77261,2138],{},[38,77243,77244],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,77247,77249],{"className":77248},[886],[888,77250,77251],{"xmlns":890},[892,77252,77253,77259],{},[895,77254,77255,77257],{},[898,77256,1755],{},[898,77258,12737],{},[902,77260,71699],{"encoding":904},[883,77262,77264],{"className":77263},[886],[888,77265,77266],{"xmlns":890},[892,77267,77268,77300],{},[895,77269,77270,77272,77274,77276,77282,77284,77286,77288,77290,77292,77298],{},[898,77271,9320],{},[898,77273,12737],{},[1654,77275,1708],{"stretchy":1656},[1710,77277,77278,77280],{},[898,77279,1663],{},[1665,77281,2062],{},[1654,77283,1726],{"stretchy":1656},[1654,77285,1750],{},[898,77287,9320],{},[898,77289,11539],{},[1654,77291,1708],{"stretchy":1656},[1710,77293,77294,77296],{},[898,77295,1663],{},[1665,77297,2062],{},[1654,77299,1726],{"stretchy":1656},[902,77301,73865],{"encoding":904},[123,77303,77304,2186,77307,15201,77343,76145,77364,9762,77377,75827,77394,2138],{},[38,77305,77306],{},"Funkce nabídky firmy:",[883,77308,77310],{"className":77309},[886],[888,77311,77312],{"xmlns":890},[892,77313,77314,77340],{},[895,77315,77316,77318,77320,77322,77324,77326,77328,77330,77332,77334,77336,77338],{},[898,77317,1755],{},[1654,77319,1750],{},[898,77321,17398],{},[1654,77323,1708],{"stretchy":1656},[898,77325,1663],{},[1654,77327,1726],{"stretchy":1656},[1654,77329,1750],{},[898,77331,9320],{},[898,77333,11539],{},[1654,77335,1708],{"stretchy":1656},[898,77337,1663],{},[1654,77339,1726],{"stretchy":1656},[902,77341,77342],{"encoding":904},"P = S(Q) = MC(Q)",[883,77344,77346],{"className":77345},[886],[888,77347,77348],{"xmlns":890},[892,77349,77350,77362],{},[895,77351,77352,77354,77356],{},[898,77353,1663],{},[1654,77355,13222],{},[1741,77357,77358,77360],{},[898,77359,1663],{},[1654,77361,1670],{},[902,77363,76144],{"encoding":904},[883,77365,77367],{"className":77366},[886],[888,77368,77369],{"xmlns":890},[892,77370,77371,77375],{},[895,77372,77373],{},[1665,77374,2062],{},[902,77376,2062],{"encoding":904},[883,77378,77380],{"className":77379},[886],[888,77381,77382],{"xmlns":890},[892,77383,77384,77392],{},[895,77385,77386],{},[1741,77387,77388,77390],{},[898,77389,1663],{},[1654,77391,1670],{},[902,77393,3768],{"encoding":904},[883,77395,77397],{"className":77396},[886],[888,77398,77399],{"xmlns":890},[892,77400,77401,77409],{},[895,77402,77403,77405,77407],{},[898,77404,4737],{},[898,77406,48559],{},[898,77408,11539],{},[902,77410,63531],{"encoding":904},[115,77412,58102],{"id":58101},[152,77414,77415,77418,77421,77424,77427,77430,77433,77436,77439,77442,77445],{},[123,77416,77417],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,77419,77420],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,77422,77423],{},"Jak se vypočte mezní příjem a co udává?",[123,77425,77426],{},"Z jakých složek se skládají celkové náklady?",[123,77428,77429],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,77431,77432],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,77434,77435],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,77437,77438],{},"Jak se vypočte zisk?",[123,77440,77441],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,77443,77444],{},"Co jsou body zvratu? Jak se najdou?",[123,77446,77447],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,77449,77451],{"id":77450},"úlohy-31328","Úlohy 3.1–3.28",[198,77453,77455],{"id":77454},"příjem-3135","Příjem (3.1–3.5)",[724,77457,77458,53646,77461,77489,77490,77505,77506,77521,77522,77537,77538,1343,77553,1343,77568,77583],{},[38,77459,77460],{},"3.1",[883,77462,77464],{"className":77463},[886],[888,77465,77466],{"xmlns":890},[892,77467,77468,77486],{},[895,77469,77470,77472,77474,77476,77478,77480,77482,77484],{},[898,77471,1755],{},[1654,77473,1750],{},[898,77475,4980],{},[1654,77477,1708],{"stretchy":1656},[898,77479,1663],{},[1654,77481,1726],{"stretchy":1656},[1654,77483,1750],{},[1665,77485,4273],{},[902,77487,77488],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,77491,77493],{"className":77492},[886],[888,77494,77495],{"xmlns":890},[892,77496,77497,77503],{},[895,77498,77499,77501],{},[898,77500,11536],{},[898,77502,12737],{},[902,77504,12837],{"encoding":904},", průměrný příjem ",[883,77507,77509],{"className":77508},[886],[888,77510,77511],{"xmlns":890},[892,77512,77513,77519],{},[895,77514,77515,77517],{},[898,77516,4737],{},[898,77518,12737],{},[902,77520,63665],{"encoding":904}," a mezní příjem ",[883,77523,77525],{"className":77524},[886],[888,77526,77527],{"xmlns":890},[892,77528,77529,77535],{},[895,77530,77531,77533],{},[898,77532,9320],{},[898,77534,12737],{},[902,77536,15361],{"encoding":904},". (c) Vypočtěte ",[883,77539,77541],{"className":77540},[886],[888,77542,77543],{"xmlns":890},[892,77544,77545,77551],{},[895,77546,77547,77549],{},[898,77548,11536],{},[898,77550,12737],{},[902,77552,12837],{"encoding":904},[883,77554,77556],{"className":77555},[886],[888,77557,77558],{"xmlns":890},[892,77559,77560,77566],{},[895,77561,77562,77564],{},[898,77563,4737],{},[898,77565,12737],{},[902,77567,63665],{"encoding":904},[883,77569,77571],{"className":77570},[886],[888,77572,77573],{"xmlns":890},[892,77574,77575,77581],{},[895,77576,77577,77579],{},[898,77578,9320],{},[898,77580,12737],{},[902,77582,15361],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,77585,77586,53646,77589,77489,77625,77505,77640,77521,77655,77537,77670,1343,77685,1343,77700,77715],{},[38,77587,77588],{},"3.2",[883,77590,77592],{"className":77591},[886],[888,77593,77594],{"xmlns":890},[892,77595,77596,77622],{},[895,77597,77598,77600,77602,77604,77606,77608,77610,77612,77614,77616,77618,77620],{},[898,77599,1755],{},[1654,77601,1750],{},[898,77603,4980],{},[1654,77605,1708],{"stretchy":1656},[898,77607,1663],{},[1654,77609,1726],{"stretchy":1656},[1654,77611,1750],{},[1654,77613,2380],{},[1665,77615,7594],{},[898,77617,1663],{},[1654,77619,1766],{},[1665,77621,4573],{},[902,77623,77624],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,77626,77628],{"className":77627},[886],[888,77629,77630],{"xmlns":890},[892,77631,77632,77638],{},[895,77633,77634,77636],{},[898,77635,11536],{},[898,77637,12737],{},[902,77639,12837],{"encoding":904},[883,77641,77643],{"className":77642},[886],[888,77644,77645],{"xmlns":890},[892,77646,77647,77653],{},[895,77648,77649,77651],{},[898,77650,4737],{},[898,77652,12737],{},[902,77654,63665],{"encoding":904},[883,77656,77658],{"className":77657},[886],[888,77659,77660],{"xmlns":890},[892,77661,77662,77668],{},[895,77663,77664,77666],{},[898,77665,9320],{},[898,77667,12737],{},[902,77669,15361],{"encoding":904},[883,77671,77673],{"className":77672},[886],[888,77674,77675],{"xmlns":890},[892,77676,77677,77683],{},[895,77678,77679,77681],{},[898,77680,11536],{},[898,77682,12737],{},[902,77684,12837],{"encoding":904},[883,77686,77688],{"className":77687},[886],[888,77689,77690],{"xmlns":890},[892,77691,77692,77698],{},[895,77693,77694,77696],{},[898,77695,4737],{},[898,77697,12737],{},[902,77699,63665],{"encoding":904},[883,77701,77703],{"className":77702},[886],[888,77704,77705],{"xmlns":890},[892,77706,77707,77713],{},[895,77708,77709,77711],{},[898,77710,9320],{},[898,77712,12737],{},[902,77714,15361],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,77717,77718,53646,77721,77758,77759,77505,77774,77521,77789,77804,77805,15201,77820,77846,77847,77862,77863,1343,77878,15201,77893,77846,77918,77933,77934,77947,77948,77963,77964,77979,77980,1343,77993,1343,78008,1343,78023,2138],{},[38,77719,77720],{},"3.3",[883,77722,77724],{"className":77723},[886],[888,77725,77726],{"xmlns":890},[892,77727,77728,77755],{},[895,77729,77730,77732,77734,77736,77738,77740,77742,77744,77747,77749],{},[898,77731,1755],{},[1654,77733,1750],{},[898,77735,4980],{},[1654,77737,1708],{"stretchy":1656},[898,77739,1663],{},[1654,77741,1726],{"stretchy":1656},[1654,77743,1750],{},[1665,77745,77746],{},"1200",[1654,77748,2380],{},[1741,77750,77751,77753],{},[898,77752,1663],{},[1665,77754,1681],{},[902,77756,77757],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,77760,77762],{"className":77761},[886],[888,77763,77764],{"xmlns":890},[892,77765,77766,77772],{},[895,77767,77768,77770],{},[898,77769,11536],{},[898,77771,12737],{},[902,77773,12837],{"encoding":904},[883,77775,77777],{"className":77776},[886],[888,77778,77779],{"xmlns":890},[892,77780,77781,77787],{},[895,77782,77783,77785],{},[898,77784,4737],{},[898,77786,12737],{},[902,77788,63665],{"encoding":904},[883,77790,77792],{"className":77791},[886],[888,77793,77794],{"xmlns":890},[892,77795,77796,77802],{},[895,77797,77798,77800],{},[898,77799,9320],{},[898,77801,12737],{},[902,77803,15361],{"encoding":904},". (b) Vypočtěte ",[883,77806,77808],{"className":77807},[886],[888,77809,77810],{"xmlns":890},[892,77811,77812,77818],{},[895,77813,77814,77816],{},[898,77815,11536],{},[898,77817,12737],{},[902,77819,12837],{"encoding":904},[883,77821,77823],{"className":77822},[886],[888,77824,77825],{"xmlns":890},[892,77826,77827,77843],{},[895,77828,77829,77831,77833,77835,77837,77839,77841],{},[898,77830,1663],{},[1654,77832,1750],{},[1665,77834,4647],{},[1654,77836,1674],{"separator":1673},[1665,77838,4573],{},[1654,77840,1674],{"separator":1673},[1665,77842,46239],{},[902,77844,77845],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,77848,77850],{"className":77849},[886],[888,77851,77852],{"xmlns":890},[892,77853,77854,77860],{},[895,77855,77856,77858],{},[898,77857,11536],{},[898,77859,12737],{},[902,77861,12837],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,77864,77866],{"className":77865},[886],[888,77867,77868],{"xmlns":890},[892,77869,77870,77876],{},[895,77871,77872,77874],{},[898,77873,4737],{},[898,77875,12737],{},[902,77877,63665],{"encoding":904},[883,77879,77881],{"className":77880},[886],[888,77882,77883],{"xmlns":890},[892,77884,77885,77891],{},[895,77886,77887,77889],{},[898,77888,9320],{},[898,77890,12737],{},[902,77892,15361],{"encoding":904},[883,77894,77896],{"className":77895},[886],[888,77897,77898],{"xmlns":890},[892,77899,77900,77916],{},[895,77901,77902,77904,77906,77908,77910,77912,77914],{},[898,77903,1663],{},[1654,77905,1750],{},[1665,77907,4647],{},[1654,77909,1674],{"separator":1673},[1665,77911,4573],{},[1654,77913,1674],{"separator":1673},[1665,77915,46239],{},[902,77917,77845],{"encoding":904},[883,77919,77921],{"className":77920},[886],[888,77922,77923],{"xmlns":890},[892,77924,77925,77931],{},[895,77926,77927,77929],{},[898,77928,9320],{},[898,77930,12737],{},[902,77932,15361],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,77935,77937],{"className":77936},[886],[888,77938,77939],{"xmlns":890},[892,77940,77941,77945],{},[895,77942,77943],{},[898,77944,1663],{},[902,77946,1663],{"encoding":904},", které maximalizuje ",[883,77949,77951],{"className":77950},[886],[888,77952,77953],{"xmlns":890},[892,77954,77955,77961],{},[895,77956,77957,77959],{},[898,77958,11536],{},[898,77960,12737],{},[902,77962,12837],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,77965,77967],{"className":77966},[886],[888,77968,77969],{"xmlns":890},[892,77970,77971,77977],{},[895,77972,77973,77975],{},[898,77974,11536],{},[898,77976,12737],{},[902,77978,12837],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,77981,77983],{"className":77982},[886],[888,77984,77985],{"xmlns":890},[892,77986,77987,77991],{},[895,77988,77989],{},[898,77990,4980],{},[902,77992,4980],{"encoding":904},[883,77994,77996],{"className":77995},[886],[888,77997,77998],{"xmlns":890},[892,77999,78000,78006],{},[895,78001,78002,78004],{},[898,78003,11536],{},[898,78005,12737],{},[902,78007,12837],{"encoding":904},[883,78009,78011],{"className":78010},[886],[888,78012,78013],{"xmlns":890},[892,78014,78015,78021],{},[895,78016,78017,78019],{},[898,78018,4737],{},[898,78020,12737],{},[902,78022,63665],{"encoding":904},[883,78024,78026],{"className":78025},[886],[888,78027,78028],{"xmlns":890},[892,78029,78030,78036],{},[895,78031,78032,78034],{},[898,78033,9320],{},[898,78035,12737],{},[902,78037,15361],{"encoding":904},[724,78039,78040,78043,78044,78074,78075,78090,78091,18874,78104,1343,78122,1343,78139,78157,78158,78180,78181,78196,78197,78210,78211,2138],{},[38,78041,78042],{},"3.4"," Je dán celkový příjem ",[883,78045,78047],{"className":78046},[886],[888,78048,78049],{"xmlns":890},[892,78050,78051,78071],{},[895,78052,78053,78055,78057,78059,78061,78063,78065],{},[898,78054,11536],{},[898,78056,12737],{},[1654,78058,1750],{},[1665,78060,77746],{},[898,78062,1663],{},[1654,78064,2380],{},[1741,78066,78067,78069],{},[898,78068,1663],{},[1665,78070,4035],{},[902,78072,78073],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,78076,78078],{"className":78077},[886],[888,78079,78080],{"xmlns":890},[892,78081,78082,78088],{},[895,78083,78084,78086],{},[898,78085,11536],{},[898,78087,12737],{},[902,78089,12837],{"encoding":904}," vzhledem ke ",[883,78092,78094],{"className":78093},[886],[888,78095,78096],{"xmlns":890},[892,78097,78098,78102],{},[895,78099,78100],{},[898,78101,1663],{},[902,78103,1663],{"encoding":904},[883,78105,78107],{"className":78106},[886],[888,78108,78109],{"xmlns":890},[892,78110,78111,78119],{},[895,78112,78113,78115,78117],{},[898,78114,1663],{},[1654,78116,1750],{},[1665,78118,4032],{},[902,78120,78121],{"encoding":904},"Q = 5",[883,78123,78125],{"className":78124},[886],[888,78126,78127],{"xmlns":890},[892,78128,78129,78137],{},[895,78130,78131,78133,78135],{},[898,78132,1663],{},[1654,78134,1750],{},[1665,78136,14315],{},[902,78138,14318],{"encoding":904},[883,78140,78142],{"className":78141},[886],[888,78143,78144],{"xmlns":890},[892,78145,78146,78154],{},[895,78147,78148,78150,78152],{},[898,78149,1663],{},[1654,78151,1750],{},[1665,78153,6509],{},[902,78155,78156],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,78159,78161],{"className":78160},[886],[888,78162,78163],{"xmlns":890},[892,78164,78165,78177],{},[895,78166,78167,78169,78171,78173,78175],{},[898,78168,9320],{},[898,78170,12737],{},[1654,78172,1708],{"stretchy":1656},[1665,78174,4647],{},[1654,78176,1726],{"stretchy":1656},[902,78178,78179],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,78182,78184],{"className":78183},[886],[888,78185,78186],{"xmlns":890},[892,78187,78188,78194],{},[895,78189,78190,78192],{},[898,78191,11536],{},[898,78193,12737],{},[902,78195,12837],{"encoding":904},", jestliže se ",[883,78198,78200],{"className":78199},[886],[888,78201,78202],{"xmlns":890},[892,78203,78204,78208],{},[895,78205,78206],{},[898,78207,1663],{},[902,78209,1663],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,78212,78214],{"className":78213},[886],[888,78215,78216],{"xmlns":890},[892,78217,78218,78224],{},[895,78219,78220,78222],{},[898,78221,11536],{},[898,78223,12737],{},[902,78225,12837],{"encoding":904},[724,78227,78228,78231,78232,78258,78259,78274,78275,78196,78290,78303],{},[38,78229,78230],{},"3.5"," Je dán mezní příjem ",[883,78233,78235],{"className":78234},[886],[888,78236,78237],{"xmlns":890},[892,78238,78239,78255],{},[895,78240,78241,78243,78245,78247,78249,78251,78253],{},[898,78242,9320],{},[898,78244,12737],{},[1654,78246,1750],{},[1654,78248,2380],{},[898,78250,1663],{},[1654,78252,1766],{},[1665,78254,4573],{},[902,78256,78257],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,78260,78262],{"className":78261},[886],[888,78263,78264],{"xmlns":890},[892,78265,78266,78272],{},[895,78267,78268,78270],{},[898,78269,11536],{},[898,78271,12737],{},[902,78273,12837],{"encoding":904},". (b) Vypočtěte změnu ",[883,78276,78278],{"className":78277},[886],[888,78279,78280],{"xmlns":890},[892,78281,78282,78288],{},[895,78283,78284,78286],{},[898,78285,11536],{},[898,78287,12737],{},[902,78289,12837],{"encoding":904},[883,78291,78293],{"className":78292},[886],[888,78294,78295],{"xmlns":890},[892,78296,78297,78301],{},[895,78298,78299],{},[898,78300,1663],{},[902,78302,1663],{"encoding":904}," změní z 8 na 12.",[198,78305,78307],{"id":78306},"náklady-36316","Náklady (3.6–3.16)",[724,78309,78310,78313,78314,78354,78355,78370,78371,78388,78389,78406,78407,78422,78423,78438,78439,77804,78454,1343,78469,1343,78486,1343,78503,1343,78518,1343,78533,15201,78548,78566,78567,1343,78582,1343,78597,78612],{},[38,78311,78312],{},"3.6"," Jsou dány celkové náklady ",[883,78315,78317],{"className":78316},[886],[888,78318,78319],{"xmlns":890},[892,78320,78321,78351],{},[895,78322,78323,78325,78327,78329,78331,78333,78335,78337,78339],{},[898,78324,11536],{},[898,78326,11539],{},[1654,78328,1750],{},[1665,78330,4273],{},[1654,78332,1766],{},[1665,78334,1681],{},[898,78336,1663],{},[1654,78338,1766],{},[2582,78340,78341],{"scriptlevel":2062,"displaystyle":1656},[2811,78342,78343,78349],{},[1741,78344,78345,78347],{},[898,78346,1663],{},[1665,78348,1681],{},[1665,78350,4647],{},[902,78352,78353],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,78356,78358],{"className":78357},[886],[888,78359,78360],{"xmlns":890},[892,78361,78362,78368],{},[895,78363,78364,78366],{},[898,78365,19153],{},[898,78367,11539],{},[902,78369,63711],{"encoding":904},", celkové variabilní náklady ",[883,78372,78374],{"className":78373},[886],[888,78375,78376],{"xmlns":890},[892,78377,78378,78386],{},[895,78379,78380,78382,78384],{},[898,78381,11536],{},[898,78383,48559],{},[898,78385,11539],{},[902,78387,63729],{"encoding":904},", průměrné variabilní náklady ",[883,78390,78392],{"className":78391},[886],[888,78393,78394],{"xmlns":890},[892,78395,78396,78404],{},[895,78397,78398,78400,78402],{},[898,78399,4737],{},[898,78401,48559],{},[898,78403,11539],{},[902,78405,63531],{"encoding":904},", variabilní náklady na jednotku ",[883,78408,78410],{"className":78409},[886],[888,78411,78412],{"xmlns":890},[892,78413,78414,78420],{},[895,78415,78416,78418],{},[898,78417,48559],{},[898,78419,11539],{},[902,78421,71825],{"encoding":904},", průměrné náklady ",[883,78424,78426],{"className":78425},[886],[888,78427,78428],{"xmlns":890},[892,78429,78430,78436],{},[895,78431,78432,78434],{},[898,78433,4737],{},[898,78435,11539],{},[902,78437,63780],{"encoding":904}," a mezní náklady ",[883,78440,78442],{"className":78441},[886],[888,78443,78444],{"xmlns":890},[892,78445,78446,78452],{},[895,78447,78448,78450],{},[898,78449,9320],{},[898,78451,11539],{},[902,78453,63512],{"encoding":904},[883,78455,78457],{"className":78456},[886],[888,78458,78459],{"xmlns":890},[892,78460,78461,78467],{},[895,78462,78463,78465],{},[898,78464,11536],{},[898,78466,11539],{},[902,78468,11997],{"encoding":904},[883,78470,78472],{"className":78471},[886],[888,78473,78474],{"xmlns":890},[892,78475,78476,78484],{},[895,78477,78478,78480,78482],{},[898,78479,11536],{},[898,78481,48559],{},[898,78483,11539],{},[902,78485,63729],{"encoding":904},[883,78487,78489],{"className":78488},[886],[888,78490,78491],{"xmlns":890},[892,78492,78493,78501],{},[895,78494,78495,78497,78499],{},[898,78496,4737],{},[898,78498,48559],{},[898,78500,11539],{},[902,78502,63531],{"encoding":904},[883,78504,78506],{"className":78505},[886],[888,78507,78508],{"xmlns":890},[892,78509,78510,78516],{},[895,78511,78512,78514],{},[898,78513,48559],{},[898,78515,11539],{},[902,78517,71825],{"encoding":904},[883,78519,78521],{"className":78520},[886],[888,78522,78523],{"xmlns":890},[892,78524,78525,78531],{},[895,78526,78527,78529],{},[898,78528,4737],{},[898,78530,11539],{},[902,78532,63780],{"encoding":904},[883,78534,78536],{"className":78535},[886],[888,78537,78538],{"xmlns":890},[892,78539,78540,78546],{},[895,78541,78542,78544],{},[898,78543,9320],{},[898,78545,11539],{},[902,78547,63512],{"encoding":904},[883,78549,78551],{"className":78550},[886],[888,78552,78553],{"xmlns":890},[892,78554,78555,78563],{},[895,78556,78557,78559,78561],{},[898,78558,1663],{},[1654,78560,1750],{},[1665,78562,4767],{},[902,78564,78565],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,78568,78570],{"className":78569},[886],[888,78571,78572],{"xmlns":890},[892,78573,78574,78580],{},[895,78575,78576,78578],{},[898,78577,11536],{},[898,78579,11539],{},[902,78581,11997],{"encoding":904},[883,78583,78585],{"className":78584},[886],[888,78586,78587],{"xmlns":890},[892,78588,78589,78595],{},[895,78590,78591,78593],{},[898,78592,4737],{},[898,78594,11539],{},[902,78596,63780],{"encoding":904},[883,78598,78600],{"className":78599},[886],[888,78601,78602],{"xmlns":890},[892,78603,78604,78610],{},[895,78605,78606,78608],{},[898,78607,9320],{},[898,78609,11539],{},[902,78611,63512],{"encoding":904}," rostou, resp. klesají.",[724,78614,78615,78618,78619,78438,78649,78664,78665,78680,78681,1343,78696,1343,78711,2138],{},[38,78616,78617],{},"3.7"," Jsou dány průměrné náklady ",[883,78620,78622],{"className":78621},[886],[888,78623,78624],{"xmlns":890},[892,78625,78626,78646],{},[895,78627,78628,78630,78632,78634,78642,78644],{},[898,78629,4737],{},[898,78631,11539],{},[1654,78633,1750],{},[2582,78635,78636],{"scriptlevel":2062,"displaystyle":1656},[2811,78637,78638,78640],{},[1665,78639,4273],{},[898,78641,1663],{},[1654,78643,1766],{},[1665,78645,4573],{},[902,78647,78648],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,78650,78652],{"className":78651},[886],[888,78653,78654],{"xmlns":890},[892,78655,78656,78662],{},[895,78657,78658,78660],{},[898,78659,9320],{},[898,78661,11539],{},[902,78663,63512],{"encoding":904},". (a) Určete celkové náklady ",[883,78666,78668],{"className":78667},[886],[888,78669,78670],{"xmlns":890},[892,78671,78672,78678],{},[895,78673,78674,78676],{},[898,78675,11536],{},[898,78677,11539],{},[902,78679,11997],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,78682,78684],{"className":78683},[886],[888,78685,78686],{"xmlns":890},[892,78687,78688,78694],{},[895,78689,78690,78692],{},[898,78691,4737],{},[898,78693,11539],{},[902,78695,63780],{"encoding":904},[883,78697,78699],{"className":78698},[886],[888,78700,78701],{"xmlns":890},[892,78702,78703,78709],{},[895,78704,78705,78707],{},[898,78706,11536],{},[898,78708,11539],{},[902,78710,11997],{"encoding":904},[883,78712,78714],{"className":78713},[886],[888,78715,78716],{"xmlns":890},[892,78717,78718,78724],{},[895,78719,78720,78722],{},[898,78721,9320],{},[898,78723,11539],{},[902,78725,63512],{"encoding":904},[724,78727,78728,78313,78731,78775,78776,1343,78793,1343,78808,1343,78825,1343,78840,1343,78857,2138],{},[38,78729,78730],{},"3.8",[883,78732,78734],{"className":78733},[886],[888,78735,78736],{"xmlns":890},[892,78737,78738,78772],{},[895,78739,78740,78742,78744,78746,78748,78750,78752,78754,78756,78758,78764,78766],{},[898,78741,11536],{},[898,78743,11539],{},[1654,78745,1750],{},[1665,78747,54923],{},[1654,78749,1766],{},[1665,78751,46239],{},[898,78753,1663],{},[1654,78755,2380],{},[1665,78757,11015],{},[1741,78759,78760,78762],{},[898,78761,1663],{},[1665,78763,1681],{},[1654,78765,1766],{},[1741,78767,78768,78770],{},[898,78769,1663],{},[1665,78771,4035],{},[902,78773,78774],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,78777,78779],{"className":78778},[886],[888,78780,78781],{"xmlns":890},[892,78782,78783,78791],{},[895,78784,78785,78787,78789],{},[898,78786,11536],{},[898,78788,48559],{},[898,78790,11539],{},[902,78792,63729],{"encoding":904},[883,78794,78796],{"className":78795},[886],[888,78797,78798],{"xmlns":890},[892,78799,78800,78806],{},[895,78801,78802,78804],{},[898,78803,19153],{},[898,78805,11539],{},[902,78807,63711],{"encoding":904},[883,78809,78811],{"className":78810},[886],[888,78812,78813],{"xmlns":890},[892,78814,78815,78823],{},[895,78816,78817,78819,78821],{},[898,78818,4737],{},[898,78820,48559],{},[898,78822,11539],{},[902,78824,63531],{"encoding":904},[883,78826,78828],{"className":78827},[886],[888,78829,78830],{"xmlns":890},[892,78831,78832,78838],{},[895,78833,78834,78836],{},[898,78835,4737],{},[898,78837,11539],{},[902,78839,63780],{"encoding":904},[883,78841,78843],{"className":78842},[886],[888,78844,78845],{"xmlns":890},[892,78846,78847,78855],{},[895,78848,78849,78851,78853],{},[898,78850,4737],{},[898,78852,19153],{},[898,78854,11539],{},[902,78856,63747],{"encoding":904},[883,78858,78860],{"className":78859},[886],[888,78861,78862],{"xmlns":890},[892,78863,78864,78870],{},[895,78865,78866,78868],{},[898,78867,9320],{},[898,78869,11539],{},[902,78871,63512],{"encoding":904},[724,78873,78874,78313,78877,78907,78908,78090,78923,15201,78936,1343,78954,1343,78972,78157,78990,78180,79012,79027,79028,79041,79042,2138],{},[38,78875,78876],{},"3.9",[883,78878,78880],{"className":78879},[886],[888,78881,78882],{"xmlns":890},[892,78883,78884,78904],{},[895,78885,78886,78888,78890,78892,78894,78896,78898],{},[898,78887,11536],{},[898,78889,11539],{},[1654,78891,1750],{},[1665,78893,4011],{},[1654,78895,1766],{},[1665,78897,28017],{},[1741,78899,78900,78902],{},[898,78901,1663],{},[1665,78903,1681],{},[902,78905,78906],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,78909,78911],{"className":78910},[886],[888,78912,78913],{"xmlns":890},[892,78914,78915,78921],{},[895,78916,78917,78919],{},[898,78918,11536],{},[898,78920,11539],{},[902,78922,11997],{"encoding":904},[883,78924,78926],{"className":78925},[886],[888,78927,78928],{"xmlns":890},[892,78929,78930,78934],{},[895,78931,78932],{},[898,78933,1663],{},[902,78935,1663],{"encoding":904},[883,78937,78939],{"className":78938},[886],[888,78940,78941],{"xmlns":890},[892,78942,78943,78951],{},[895,78944,78945,78947,78949],{},[898,78946,1663],{},[1654,78948,1750],{},[1665,78950,4647],{},[902,78952,78953],{"encoding":904},"Q = 10",[883,78955,78957],{"className":78956},[886],[888,78958,78959],{"xmlns":890},[892,78960,78961,78969],{},[895,78962,78963,78965,78967],{},[898,78964,1663],{},[1654,78966,1750],{},[1665,78968,4573],{},[902,78970,78971],{"encoding":904},"Q = 20",[883,78973,78975],{"className":78974},[886],[888,78976,78977],{"xmlns":890},[892,78978,78979,78987],{},[895,78980,78981,78983,78985],{},[898,78982,1663],{},[1654,78984,1750],{},[1665,78986,46239],{},[902,78988,78989],{"encoding":904},"Q = 30",[883,78991,78993],{"className":78992},[886],[888,78994,78995],{"xmlns":890},[892,78996,78997,79009],{},[895,78998,78999,79001,79003,79005,79007],{},[898,79000,9320],{},[898,79002,11539],{},[1654,79004,1708],{"stretchy":1656},[1665,79006,10207],{},[1654,79008,1726],{"stretchy":1656},[902,79010,79011],{"encoding":904},"MC(15)",[883,79013,79015],{"className":79014},[886],[888,79016,79017],{"xmlns":890},[892,79018,79019,79025],{},[895,79020,79021,79023],{},[898,79022,11536],{},[898,79024,11539],{},[902,79026,11997],{"encoding":904}," v důsledku změny ",[883,79029,79031],{"className":79030},[886],[888,79032,79033],{"xmlns":890},[892,79034,79035,79039],{},[895,79036,79037],{},[898,79038,1663],{},[902,79040,1663],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,79043,79045],{"className":79044},[886],[888,79046,79047],{"xmlns":890},[892,79048,79049,79055],{},[895,79050,79051,79053],{},[898,79052,11536],{},[898,79054,11539],{},[902,79056,11997],{"encoding":904},[724,79058,79059,79062,79063,78664,79099,79114,79115,78274,79134,79027,79149,79162],{},[38,79060,79061],{},"3.10"," Jsou dány mezní náklady ",[883,79064,79066],{"className":79065},[886],[888,79067,79068],{"xmlns":890},[892,79069,79070,79096],{},[895,79071,79072,79074,79076,79078,79080,79082,79084,79086,79088,79090],{},[898,79073,9320],{},[898,79075,11539],{},[1654,79077,1750],{},[1665,79079,11881],{},[1654,79081,2380],{},[1665,79083,50082],{},[898,79085,1663],{},[1654,79087,1766],{},[1665,79089,72779],{},[1741,79091,79092,79094],{},[898,79093,1663],{},[1665,79095,1681],{},[902,79097,79098],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,79100,79102],{"className":79101},[886],[888,79103,79104],{"xmlns":890},[892,79105,79106,79112],{},[895,79107,79108,79110],{},[898,79109,11536],{},[898,79111,11539],{},[902,79113,11997],{"encoding":904},", jestliže fixní náklady ",[883,79116,79118],{"className":79117},[886],[888,79119,79120],{"xmlns":890},[892,79121,79122,79132],{},[895,79123,79124,79126,79128,79130],{},[898,79125,19153],{},[898,79127,11539],{},[1654,79129,1750],{},[1665,79131,4273],{},[902,79133,20347],{"encoding":904},[883,79135,79137],{"className":79136},[886],[888,79138,79139],{"xmlns":890},[892,79140,79141,79147],{},[895,79142,79143,79145],{},[898,79144,11536],{},[898,79146,11539],{},[902,79148,11997],{"encoding":904},[883,79150,79152],{"className":79151},[886],[888,79153,79154],{"xmlns":890},[892,79155,79156,79160],{},[895,79157,79158],{},[898,79159,1663],{},[902,79161,1663],{"encoding":904}," z 15 na 20.",[724,79164,79165,78313,79168,79211,79212,79225,79226,79241,79242,79257,79258,79225,79271,79241,79288,79305,79306,79225,79319,79241,79334,79349,79350,79370,79371,79394],{},[38,79166,79167],{},"3.11",[883,79169,79171],{"className":79170},[886],[888,79172,79173],{"xmlns":890},[892,79174,79175,79209],{},[895,79176,79177,79179,79181,79183,79185,79187,79189,79191,79193,79195,79201,79203],{},[898,79178,11536],{},[898,79180,11539],{},[1654,79182,1750],{},[1665,79184,4273],{},[1654,79186,1766],{},[1665,79188,4622],{},[898,79190,1663],{},[1654,79192,2380],{},[1665,79194,4032],{},[1741,79196,79197,79199],{},[898,79198,1663],{},[1665,79200,1681],{},[1654,79202,1766],{},[1741,79204,79205,79207],{},[898,79206,1663],{},[1665,79208,4035],{},[902,79210,69127],{"encoding":904},". (a) Určete ",[883,79213,79215],{"className":79214},[886],[888,79216,79217],{"xmlns":890},[892,79218,79219,79223],{},[895,79220,79221],{},[898,79222,1663],{},[902,79224,1663],{"encoding":904},", které minimalizuje ",[883,79227,79229],{"className":79228},[886],[888,79230,79231],{"xmlns":890},[892,79232,79233,79239],{},[895,79234,79235,79237],{},[898,79236,9320],{},[898,79238,11539],{},[902,79240,63512],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,79243,79245],{"className":79244},[886],[888,79246,79247],{"xmlns":890},[892,79248,79249,79255],{},[895,79250,79251,79253],{},[898,79252,9320],{},[898,79254,11539],{},[902,79256,63512],{"encoding":904},". (b) Určete ",[883,79259,79261],{"className":79260},[886],[888,79262,79263],{"xmlns":890},[892,79264,79265,79269],{},[895,79266,79267],{},[898,79268,1663],{},[902,79270,1663],{"encoding":904},[883,79272,79274],{"className":79273},[886],[888,79275,79276],{"xmlns":890},[892,79277,79278,79286],{},[895,79279,79280,79282,79284],{},[898,79281,4737],{},[898,79283,48559],{},[898,79285,11539],{},[902,79287,63531],{"encoding":904},[883,79289,79291],{"className":79290},[886],[888,79292,79293],{"xmlns":890},[892,79294,79295,79303],{},[895,79296,79297,79299,79301],{},[898,79298,4737],{},[898,79300,48559],{},[898,79302,11539],{},[902,79304,63531],{"encoding":904},". (c) Určete ",[883,79307,79309],{"className":79308},[886],[888,79310,79311],{"xmlns":890},[892,79312,79313,79317],{},[895,79314,79315],{},[898,79316,1663],{},[902,79318,1663],{"encoding":904},[883,79320,79322],{"className":79321},[886],[888,79323,79324],{"xmlns":890},[892,79325,79326,79332],{},[895,79327,79328,79330],{},[898,79329,4737],{},[898,79331,11539],{},[902,79333,63780],{"encoding":904},[883,79335,79337],{"className":79336},[886],[888,79338,79339],{"xmlns":890},[892,79340,79341,79347],{},[895,79342,79343,79345],{},[898,79344,4737],{},[898,79346,11539],{},[902,79348,63780],{"encoding":904}," (rada: hledaný kořen ",[883,79351,79353],{"className":79352},[886],[888,79354,79355],{"xmlns":890},[892,79356,79357,79367],{},[895,79358,79359,79361],{},[898,79360,4737],{},[1741,79362,79363,79365],{},[898,79364,11539],{},[1654,79366,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,79368,79369],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,79372,79374],{"className":79373},[886],[888,79375,79376],{"xmlns":890},[892,79377,79378,79391],{},[895,79379,79380,79382,79385,79387,79389],{},[1654,79381,1708],{"stretchy":1656},[1665,79383,79384],{},"4,7",[1654,79386,17150],{"separator":1673},[1665,79388,14011],{},[1654,79390,1726],{"stretchy":1656},[902,79392,79393],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,79396,79397,79400,79401,11387,79429,79446,79447,9762,79488,79509],{},[38,79398,79399],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,79402,79404],{"className":79403},[886],[888,79405,79406],{"xmlns":890},[892,79407,79408,79426],{},[895,79409,79410,79412,79414,79416,79418,79420,79422,79424],{},[898,79411,4737],{},[898,79413,11539],{},[1654,79415,1750],{},[898,79417,4737],{},[898,79419,11539],{},[1654,79421,1708],{"stretchy":1656},[898,79423,1663],{},[1654,79425,1726],{"stretchy":1656},[902,79427,79428],{"encoding":904},"AC = AC(Q)",[883,79430,79432],{"className":79431},[886],[888,79433,79434],{"xmlns":890},[892,79435,79436,79444],{},[895,79437,79438],{},[1710,79439,79440,79442],{},[898,79441,1663],{},[1665,79443,2062],{},[902,79445,46528],{"encoding":904}," minimum, pak platí ",[883,79448,79450],{"className":79449},[886],[888,79451,79452],{"xmlns":890},[892,79453,79454,79486],{},[895,79455,79456,79458,79460,79462,79468,79470,79472,79474,79476,79478,79484],{},[898,79457,4737],{},[898,79459,11539],{},[1654,79461,1708],{"stretchy":1656},[1710,79463,79464,79466],{},[898,79465,1663],{},[1665,79467,2062],{},[1654,79469,1726],{"stretchy":1656},[1654,79471,1750],{},[898,79473,9320],{},[898,79475,11539],{},[1654,79477,1708],{"stretchy":1656},[1710,79479,79480,79482],{},[898,79481,1663],{},[1665,79483,2062],{},[1654,79485,1726],{"stretchy":1656},[902,79487,70789],{"encoding":904},[883,79489,79491],{"className":79490},[886],[888,79492,79493],{"xmlns":890},[892,79494,79495,79507],{},[895,79496,79497,79499,79501,79503,79505],{},[898,79498,9320],{},[898,79500,11539],{},[1654,79502,1708],{"stretchy":1656},[898,79504,1663],{},[1654,79506,1726],{"stretchy":1656},[902,79508,75913],{"encoding":904}," jsou mezní náklady.",[724,79511,79512,78313,79515,78775,79549,79225,79562,79241,79577,2138],{},[38,79513,79514],{},"3.13",[883,79516,79518],{"className":79517},[886],[888,79519,79520],{"xmlns":890},[892,79521,79522,79546],{},[895,79523,79524,79526,79528,79530,79536,79538,79540,79542,79544],{},[898,79525,11536],{},[898,79527,11539],{},[1654,79529,1750],{},[1741,79531,79532,79534],{},[898,79533,1663],{},[1665,79535,1681],{},[1654,79537,1766],{},[1665,79539,1681],{},[898,79541,1663],{},[1654,79543,1766],{},[1665,79545,4622],{},[902,79547,79548],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,79550,79552],{"className":79551},[886],[888,79553,79554],{"xmlns":890},[892,79555,79556,79560],{},[895,79557,79558],{},[898,79559,1663],{},[902,79561,1663],{"encoding":904},[883,79563,79565],{"className":79564},[886],[888,79566,79567],{"xmlns":890},[892,79568,79569,79575],{},[895,79570,79571,79573],{},[898,79572,4737],{},[898,79574,11539],{},[902,79576,63780],{"encoding":904},[883,79578,79580],{"className":79579},[886],[888,79581,79582],{"xmlns":890},[892,79583,79584,79590],{},[895,79585,79586,79588],{},[898,79587,4737],{},[898,79589,11539],{},[902,79591,63780],{"encoding":904},[724,79593,79594,79597,79598,11387,79630,79446,79647,9762,79690,79509],{},[38,79595,79596],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,79599,79601],{"className":79600},[886],[888,79602,79603],{"xmlns":890},[892,79604,79605,79627],{},[895,79606,79607,79609,79611,79613,79615,79617,79619,79621,79623,79625],{},[898,79608,4737],{},[898,79610,48559],{},[898,79612,11539],{},[1654,79614,1750],{},[898,79616,4737],{},[898,79618,48559],{},[898,79620,11539],{},[1654,79622,1708],{"stretchy":1656},[898,79624,1663],{},[1654,79626,1726],{"stretchy":1656},[902,79628,79629],{"encoding":904},"AVC = AVC(Q)",[883,79631,79633],{"className":79632},[886],[888,79634,79635],{"xmlns":890},[892,79636,79637,79645],{},[895,79638,79639],{},[1710,79640,79641,79643],{},[898,79642,1663],{},[1665,79644,2062],{},[902,79646,46528],{"encoding":904},[883,79648,79650],{"className":79649},[886],[888,79651,79652],{"xmlns":890},[892,79653,79654,79688],{},[895,79655,79656,79658,79660,79662,79664,79670,79672,79674,79676,79678,79680,79686],{},[898,79657,4737],{},[898,79659,48559],{},[898,79661,11539],{},[1654,79663,1708],{"stretchy":1656},[1710,79665,79666,79668],{},[898,79667,1663],{},[1665,79669,2062],{},[1654,79671,1726],{"stretchy":1656},[1654,79673,1750],{},[898,79675,9320],{},[898,79677,11539],{},[1654,79679,1708],{"stretchy":1656},[1710,79681,79682,79684],{},[898,79683,1663],{},[1665,79685,2062],{},[1654,79687,1726],{"stretchy":1656},[902,79689,77239],{"encoding":904},[883,79691,79693],{"className":79692},[886],[888,79694,79695],{"xmlns":890},[892,79696,79697,79709],{},[895,79698,79699,79701,79703,79705,79707],{},[898,79700,9320],{},[898,79702,11539],{},[1654,79704,1708],{"stretchy":1656},[898,79706,1663],{},[1654,79708,1726],{"stretchy":1656},[902,79710,75913],{"encoding":904},[724,79712,79713,78313,79716,78775,79762,79225,79775,79241,79792,2138],{},[38,79714,79715],{},"3.15",[883,79717,79719],{"className":79718},[886],[888,79720,79721],{"xmlns":890},[892,79722,79723,79759],{},[895,79724,79725,79727,79729,79731,79733,79735,79737,79739,79741,79743,79749,79751,79753],{},[898,79726,11536],{},[898,79728,11539],{},[1654,79730,1750],{},[1665,79732,4767],{},[1654,79734,1766],{},[1665,79736,10207],{},[898,79738,1663],{},[1654,79740,2380],{},[1665,79742,1681],{},[1741,79744,79745,79747],{},[898,79746,1663],{},[1665,79748,1681],{},[1654,79750,1766],{},[1665,79752,11599],{},[1741,79754,79755,79757],{},[898,79756,1663],{},[1665,79758,4035],{},[902,79760,79761],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,79763,79765],{"className":79764},[886],[888,79766,79767],{"xmlns":890},[892,79768,79769,79773],{},[895,79770,79771],{},[898,79772,1663],{},[902,79774,1663],{"encoding":904},[883,79776,79778],{"className":79777},[886],[888,79779,79780],{"xmlns":890},[892,79781,79782,79790],{},[895,79783,79784,79786,79788],{},[898,79785,4737],{},[898,79787,48559],{},[898,79789,11539],{},[902,79791,63531],{"encoding":904},[883,79793,79795],{"className":79794},[886],[888,79796,79797],{"xmlns":890},[892,79798,79799,79807],{},[895,79800,79801,79803,79805],{},[898,79802,4737],{},[898,79804,48559],{},[898,79806,11539],{},[902,79808,63531],{"encoding":904},[724,79810,79811,79814,79815,79828,79829,79849],{},[38,79812,79813],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,79816,79818],{"className":79817},[886],[888,79819,79820],{"xmlns":890},[892,79821,79822,79826],{},[895,79823,79824],{},[898,79825,10799],{},[902,79827,10799],{"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 ",[883,79830,79832],{"className":79831},[886],[888,79833,79834],{"xmlns":890},[892,79835,79836,79846],{},[895,79837,79838,79840,79842,79844],{},[1665,79839,4647],{},[1865,79841,11744],{},[1665,79843,67302],{},[898,79845,10799],{},[902,79847,79848],{"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.",[198,79851,79853],{"id":79852},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,79855,79856,79859,79860,2068,79882,79908],{},[38,79857,79858],{},"3.17"," Jsou dány ",[883,79861,79863],{"className":79862},[886],[888,79864,79865],{"xmlns":890},[892,79866,79867,79879],{},[895,79868,79869,79871,79873,79875,79877],{},[898,79870,11536],{},[898,79872,12737],{},[1654,79874,1750],{},[1665,79876,4647],{},[898,79878,1663],{},[902,79880,79881],{"encoding":904},"TR = 10Q",[883,79883,79885],{"className":79884},[886],[888,79886,79887],{"xmlns":890},[892,79888,79889,79905],{},[895,79890,79891,79893,79895,79897,79899,79901,79903],{},[898,79892,11536],{},[898,79894,11539],{},[1654,79896,1750],{},[1665,79898,4273],{},[1654,79900,1766],{},[1665,79902,4032],{},[898,79904,1663],{},[902,79906,79907],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,79910,79911,79914,79915,14918,79930,79945,79946,1343,79968,9762,79995,80017,80018,80052],{},[38,79912,79913],{},"3.18"," Odvoďte, že jestliže ",[883,79916,79918],{"className":79917},[886],[888,79919,79920],{"xmlns":890},[892,79921,79922,79928],{},[895,79923,79924,79926],{},[898,79925,11536],{},[898,79927,12737],{},[902,79929,12837],{"encoding":904},[883,79931,79933],{"className":79932},[886],[888,79934,79935],{"xmlns":890},[892,79936,79937,79943],{},[895,79938,79939,79941],{},[898,79940,11536],{},[898,79942,11539],{},[902,79944,11997],{"encoding":904}," jsou lineární tvaru ",[883,79947,79949],{"className":79948},[886],[888,79950,79951],{"xmlns":890},[892,79952,79953,79965],{},[895,79954,79955,79957,79959,79961,79963],{},[898,79956,11536],{},[898,79958,12737],{},[1654,79960,1750],{},[898,79962,724],{},[898,79964,1663],{},[902,79966,79967],{"encoding":904},"TR = pQ",[883,79969,79971],{"className":79970},[886],[888,79972,79973],{"xmlns":890},[892,79974,79975,79992],{},[895,79976,79977,79979,79981,79983,79986,79988,79990],{},[898,79978,11536],{},[898,79980,11539],{},[1654,79982,1750],{},[898,79984,79985],{},"m",[1654,79987,1766],{},[898,79989,45080],{},[898,79991,1663],{},[902,79993,79994],{"encoding":904},"TC = m + nQ",[883,79996,79998],{"className":79997},[886],[888,79999,80000],{"xmlns":890},[892,80001,80002,80014],{},[895,80003,80004,80006,80008,80010,80012],{},[898,80005,79985],{},[1654,80007,1674],{"separator":1673},[898,80009,45080],{},[1654,80011,1674],{"separator":1673},[898,80013,724],{},[902,80015,80016],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,80019,80021],{"className":80020},[886],[888,80022,80023],{"xmlns":890},[892,80024,80025,80049],{},[895,80026,80027,80033,80035],{},[1741,80028,80029,80031],{},[898,80030,1663],{},[1654,80032,1670],{},[1654,80034,1750],{},[2582,80036,80037],{"scriptlevel":2062,"displaystyle":1656},[2811,80038,80039,80041],{},[898,80040,79985],{},[895,80042,80043,80045,80047],{},[898,80044,724],{},[1654,80046,2380],{},[898,80048,45080],{},[902,80050,80051],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,80054,80055,79859,80058,2068,80092,79211,80118,80131,80132,77963,80147,80162,80163,77947,80176,77963,80191,80206],{},[38,80056,80057],{},"3.19",[883,80059,80061],{"className":80060},[886],[888,80062,80063],{"xmlns":890},[892,80064,80065,80089],{},[895,80066,80067,80069,80071,80073,80075,80077,80083,80085,80087],{},[898,80068,11536],{},[898,80070,12737],{},[1654,80072,1750],{},[1654,80074,2380],{},[1665,80076,1681],{},[1741,80078,80079,80081],{},[898,80080,1663],{},[1665,80082,1681],{},[1654,80084,1766],{},[1665,80086,31634],{},[898,80088,1663],{},[902,80090,80091],{"encoding":904},"TR = -2Q^2 + 14Q",[883,80093,80095],{"className":80094},[886],[888,80096,80097],{"xmlns":890},[892,80098,80099,80115],{},[895,80100,80101,80103,80105,80107,80109,80111,80113],{},[898,80102,11536],{},[898,80104,11539],{},[1654,80106,1750],{},[1665,80108,1681],{},[898,80110,1663],{},[1654,80112,1766],{},[1665,80114,4647],{},[902,80116,80117],{"encoding":904},"TC = 2Q + 10",[883,80119,80121],{"className":80120},[886],[888,80122,80123],{"xmlns":890},[892,80124,80125,80129],{},[895,80126,80127],{},[898,80128,1663],{},[902,80130,1663],{"encoding":904},", které maximalizuje zisk ",[883,80133,80135],{"className":80134},[886],[888,80136,80137],{"xmlns":890},[892,80138,80139,80145],{},[895,80140,80141,80143],{},[898,80142,1755],{},[898,80144,12737],{},[902,80146,71699],{"encoding":904},[883,80148,80150],{"className":80149},[886],[888,80151,80152],{"xmlns":890},[892,80153,80154,80160],{},[895,80155,80156,80158],{},[898,80157,1755],{},[898,80159,12737],{},[902,80161,71699],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,80164,80166],{"className":80165},[886],[888,80167,80168],{"xmlns":890},[892,80169,80170,80174],{},[895,80171,80172],{},[898,80173,1663],{},[902,80175,1663],{"encoding":904},[883,80177,80179],{"className":80178},[886],[888,80180,80181],{"xmlns":890},[892,80182,80183,80189],{},[895,80184,80185,80187],{},[898,80186,11536],{},[898,80188,12737],{},[902,80190,12837],{"encoding":904},[883,80192,80194],{"className":80193},[886],[888,80195,80196],{"xmlns":890},[892,80197,80198,80204],{},[895,80199,80200,80202],{},[898,80201,11536],{},[898,80203,12737],{},[902,80205,12837],{"encoding":904},". (d) Graficky interpretujte.",[724,80208,80209,55904,80212,1343,80238,1343,80257,79211,80277,80131,80290,77963,80305,80320,80321,80343,80344,79394],{},[38,80210,80211],{},"3.20",[883,80213,80215],{"className":80214},[886],[888,80216,80217],{"xmlns":890},[892,80218,80219,80235],{},[895,80220,80221,80223,80225,80227,80229],{},[898,80222,1755],{},[1654,80224,1750],{},[1665,80226,28837],{},[1654,80228,2380],{},[1741,80230,80231,80233],{},[898,80232,1663],{},[1665,80234,1681],{},[902,80236,80237],{"encoding":904},"P = 400 - Q^2",[883,80239,80241],{"className":80240},[886],[888,80242,80243],{"xmlns":890},[892,80244,80245,80255],{},[895,80246,80247,80249,80251,80253],{},[898,80248,19153],{},[898,80250,11539],{},[1654,80252,1750],{},[1665,80254,4273],{},[902,80256,20347],{"encoding":904},[883,80258,80260],{"className":80259},[886],[888,80261,80262],{"xmlns":890},[892,80263,80264,80274],{},[895,80265,80266,80268,80270,80272],{},[898,80267,9320],{},[898,80269,11539],{},[1654,80271,1750],{},[1665,80273,4573],{},[902,80275,80276],{"encoding":904},"MC = 20",[883,80278,80280],{"className":80279},[886],[888,80281,80282],{"xmlns":890},[892,80283,80284,80288],{},[895,80285,80286],{},[898,80287,1663],{},[902,80289,1663],{"encoding":904},[883,80291,80293],{"className":80292},[886],[888,80294,80295],{"xmlns":890},[892,80296,80297,80303],{},[895,80298,80299,80301],{},[898,80300,1755],{},[898,80302,12737],{},[902,80304,71699],{"encoding":904},[883,80306,80308],{"className":80307},[886],[888,80309,80310],{"xmlns":890},[892,80311,80312,80318],{},[895,80313,80314,80316],{},[898,80315,1755],{},[898,80317,12737],{},[902,80319,71699],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,80322,80324],{"className":80323},[886],[888,80325,80326],{"xmlns":890},[892,80327,80328,80340],{},[895,80329,80330,80332,80334,80336,80338],{},[1654,80331,1708],{"stretchy":1656},[1665,80333,2062],{},[1654,80335,1674],{"separator":1673},[1665,80337,1667],{},[1654,80339,1726],{"stretchy":1656},[902,80341,80342],{"encoding":904},"(0, 1)",", druhý do ",[883,80345,80347],{"className":80346},[886],[888,80348,80349],{"xmlns":890},[892,80350,80351,80364],{},[895,80352,80353,80355,80358,80360,80362],{},[1654,80354,1708],{"stretchy":1656},[1665,80356,80357],{},"19",[1654,80359,1674],{"separator":1673},[1665,80361,4573],{},[1654,80363,1726],{"stretchy":1656},[902,80365,80366],{"encoding":904},"(19, 20)",[724,80368,80369,80372,80373,11387,80401,80418,80419,2138],{},[38,80370,80371],{},"3.21"," Dokažte, že má-li zisk ",[883,80374,80376],{"className":80375},[886],[888,80377,80378],{"xmlns":890},[892,80379,80380,80398],{},[895,80381,80382,80384,80386,80388,80390,80392,80394,80396],{},[898,80383,1755],{},[898,80385,12737],{},[1654,80387,1750],{},[898,80389,1755],{},[898,80391,12737],{},[1654,80393,1708],{"stretchy":1656},[898,80395,1663],{},[1654,80397,1726],{"stretchy":1656},[902,80399,80400],{"encoding":904},"PR = PR(Q)",[883,80402,80404],{"className":80403},[886],[888,80405,80406],{"xmlns":890},[892,80407,80408,80416],{},[895,80409,80410],{},[1710,80411,80412,80414],{},[898,80413,1663],{},[1665,80415,2062],{},[902,80417,46528],{"encoding":904}," maximum, pak platí ",[883,80420,80422],{"className":80421},[886],[888,80423,80424],{"xmlns":890},[892,80425,80426,80458],{},[895,80427,80428,80430,80432,80434,80440,80442,80444,80446,80448,80450,80456],{},[898,80429,9320],{},[898,80431,12737],{},[1654,80433,1708],{"stretchy":1656},[1710,80435,80436,80438],{},[898,80437,1663],{},[1665,80439,2062],{},[1654,80441,1726],{"stretchy":1656},[1654,80443,1750],{},[898,80445,9320],{},[898,80447,11539],{},[1654,80449,1708],{"stretchy":1656},[1710,80451,80452,80454],{},[898,80453,1663],{},[1665,80455,2062],{},[1654,80457,1726],{"stretchy":1656},[902,80459,73865],{"encoding":904},[724,80461,80462,80465,80466,2068,80481,64245,80496,80131,80509,80524,80525,1343,80552,80589,80590,1343,80617,2138],{},[38,80463,80464],{},"3.22"," Pro zadané ",[883,80467,80469],{"className":80468},[886],[888,80470,80471],{"xmlns":890},[892,80472,80473,80479],{},[895,80474,80475,80477],{},[898,80476,9320],{},[898,80478,12737],{},[902,80480,15361],{"encoding":904},[883,80482,80484],{"className":80483},[886],[888,80485,80486],{"xmlns":890},[892,80487,80488,80494],{},[895,80489,80490,80492],{},[898,80491,9320],{},[898,80493,11539],{},[902,80495,63512],{"encoding":904},[883,80497,80499],{"className":80498},[886],[888,80500,80501],{"xmlns":890},[892,80502,80503,80507],{},[895,80504,80505],{},[898,80506,1663],{},[902,80508,1663],{"encoding":904},[883,80510,80512],{"className":80511},[886],[888,80513,80514],{"xmlns":890},[892,80515,80516,80522],{},[895,80517,80518,80520],{},[898,80519,1755],{},[898,80521,12737],{},[902,80523,71699],{"encoding":904},". (a) ",[883,80526,80528],{"className":80527},[886],[888,80529,80530],{"xmlns":890},[892,80531,80532,80549],{},[895,80533,80534,80536,80538,80540,80543,80545,80547],{},[898,80535,9320],{},[898,80537,12737],{},[1654,80539,1750],{},[1665,80541,80542],{},"236",[1654,80544,2380],{},[1665,80546,50082],{},[898,80548,1663],{},[902,80550,80551],{"encoding":904},"MR = 236 - 16Q",[883,80553,80555],{"className":80554},[886],[888,80556,80557],{"xmlns":890},[892,80558,80559,80586],{},[895,80560,80561,80563,80565,80567,80569,80575,80577,80580,80582,80584],{},[898,80562,9320],{},[898,80564,11539],{},[1654,80566,1750],{},[1665,80568,4035],{},[1741,80570,80571,80573],{},[898,80572,1663],{},[1665,80574,1681],{},[1654,80576,2380],{},[1665,80578,80579],{},"32",[898,80581,1663],{},[1654,80583,1766],{},[1665,80585,14473],{},[902,80587,80588],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,80591,80593],{"className":80592},[886],[888,80594,80595],{"xmlns":890},[892,80596,80597,80614],{},[895,80598,80599,80601,80603,80605,80608,80610,80612],{},[898,80600,9320],{},[898,80602,12737],{},[1654,80604,1750],{},[1665,80606,80607],{},"280",[1654,80609,2380],{},[1665,80611,4573],{},[898,80613,1663],{},[902,80615,80616],{"encoding":904},"MR = 280 - 20Q",[883,80618,80620],{"className":80619},[886],[888,80621,80622],{"xmlns":890},[892,80623,80624,80651],{},[895,80625,80626,80628,80630,80632,80635,80641,80643,80645,80647,80649],{},[898,80627,9320],{},[898,80629,11539],{},[1654,80631,1750],{},[1665,80633,80634],{},"1,6",[1741,80636,80637,80639],{},[898,80638,1663],{},[1665,80640,1681],{},[1654,80642,2380],{},[1665,80644,10207],{},[898,80646,1663],{},[1654,80648,1766],{},[1665,80650,11881],{},[902,80652,80653],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,80655,80656,80465,80659,2068,80674,64245,80689,77947,80702,77963,80717,80524,80732,1343,80763,80589,80799,1343,80831,80875,80876,1343,80908,2138],{},[38,80657,80658],{},"3.23",[883,80660,80662],{"className":80661},[886],[888,80663,80664],{"xmlns":890},[892,80665,80666,80672],{},[895,80667,80668,80670],{},[898,80669,11536],{},[898,80671,12737],{},[902,80673,12837],{"encoding":904},[883,80675,80677],{"className":80676},[886],[888,80678,80679],{"xmlns":890},[892,80680,80681,80687],{},[895,80682,80683,80685],{},[898,80684,11536],{},[898,80686,11539],{},[902,80688,11997],{"encoding":904},[883,80690,80692],{"className":80691},[886],[888,80693,80694],{"xmlns":890},[892,80695,80696,80700],{},[895,80697,80698],{},[898,80699,1663],{},[902,80701,1663],{"encoding":904},[883,80703,80705],{"className":80704},[886],[888,80706,80707],{"xmlns":890},[892,80708,80709,80715],{},[895,80710,80711,80713],{},[898,80712,1755],{},[898,80714,12737],{},[902,80716,71699],{"encoding":904},[883,80718,80720],{"className":80719},[886],[888,80721,80722],{"xmlns":890},[892,80723,80724,80730],{},[895,80725,80726,80728],{},[898,80727,1755],{},[898,80729,12737],{},[902,80731,71699],{"encoding":904},[883,80733,80735],{"className":80734},[886],[888,80736,80737],{"xmlns":890},[892,80738,80739,80760],{},[895,80740,80741,80743,80745,80747,80750,80752,80754],{},[898,80742,11536],{},[898,80744,12737],{},[1654,80746,1750],{},[1665,80748,80749],{},"125",[898,80751,1663],{},[1654,80753,2380],{},[1741,80755,80756,80758],{},[898,80757,1663],{},[1665,80759,1681],{},[902,80761,80762],{"encoding":904},"TR = 125Q - Q^2",[883,80764,80766],{"className":80765},[886],[888,80767,80768],{"xmlns":890},[892,80769,80770,80796],{},[895,80771,80772,80774,80776,80778,80780,80782,80784,80786,80788,80790],{},[898,80773,11536],{},[898,80775,11539],{},[1654,80777,1750],{},[1665,80779,4011],{},[1654,80781,1766],{},[1665,80783,4032],{},[898,80785,1663],{},[1654,80787,1766],{},[1665,80789,7594],{},[1741,80791,80792,80794],{},[898,80793,1663],{},[1665,80795,1681],{},[902,80797,80798],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,80800,80802],{"className":80801},[886],[888,80803,80804],{"xmlns":890},[892,80805,80806,80828],{},[895,80807,80808,80810,80812,80814,80816,80818,80820,80822],{},[898,80809,11536],{},[898,80811,12737],{},[1654,80813,1750],{},[1665,80815,4573],{},[898,80817,1663],{},[1654,80819,2380],{},[1665,80821,1681],{},[1741,80823,80824,80826],{},[898,80825,1663],{},[1665,80827,1681],{},[902,80829,80830],{"encoding":904},"TR = 20Q - 2Q^2",[883,80832,80834],{"className":80833},[886],[888,80835,80836],{"xmlns":890},[892,80837,80838,80872],{},[895,80839,80840,80842,80844,80846,80848,80850,80852,80854,80856,80858,80864,80866],{},[898,80841,11536],{},[898,80843,11539],{},[1654,80845,1750],{},[1665,80847,1681],{},[1654,80849,1766],{},[1665,80851,4573],{},[898,80853,1663],{},[1654,80855,2380],{},[1665,80857,14315],{},[1741,80859,80860,80862],{},[898,80861,1663],{},[1665,80863,1681],{},[1654,80865,1766],{},[1741,80867,80868,80870],{},[898,80869,1663],{},[1665,80871,4035],{},[902,80873,80874],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,80877,80879],{"className":80878},[886],[888,80880,80881],{"xmlns":890},[892,80882,80883,80905],{},[895,80884,80885,80887,80889,80891,80893,80895,80897,80899],{},[898,80886,11536],{},[898,80888,12737],{},[1654,80890,1750],{},[1665,80892,7631],{},[898,80894,1663],{},[1654,80896,2380],{},[1665,80898,7154],{},[1741,80900,80901,80903],{},[898,80902,1663],{},[1665,80904,1681],{},[902,80906,80907],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,80909,80911],{"className":80910},[886],[888,80912,80913],{"xmlns":890},[892,80914,80915,80963],{},[895,80916,80917,80919,80921,80923,80925,80927,80929,80931,80933,80949,80951],{},[898,80918,11536],{},[898,80920,11539],{},[1654,80922,1750],{},[1665,80924,7631],{},[1654,80926,1766],{},[1665,80928,1681],{},[898,80930,1663],{},[1654,80932,2380],{},[2582,80934,80935],{"scriptlevel":2062,"displaystyle":1656},[2811,80936,80937,80947],{},[895,80938,80939,80941],{},[1665,80940,4035],{},[1741,80942,80943,80945],{},[898,80944,1663],{},[1665,80946,1681],{},[1665,80948,4647],{},[1654,80950,1766],{},[2582,80952,80953],{"scriptlevel":2062,"displaystyle":1656},[2811,80954,80955,80961],{},[1741,80956,80957,80959],{},[898,80958,1663],{},[1665,80960,4035],{},[1665,80962,4573],{},[902,80964,80965],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,80967,80968,80971,80972,81002,81003,81035,81036,9762,81066,81096],{},[38,80969,80970],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,80973,80975],{"className":80974},[886],[888,80976,80977],{"xmlns":890},[892,80978,80979,80999],{},[895,80980,80981,80987,80989,80991,80993],{},[1710,80982,80983,80985],{},[898,80984,1755],{},[1665,80986,1667],{},[1654,80988,1750],{},[1665,80990,4011],{},[1654,80992,2380],{},[1710,80994,80995,80997],{},[898,80996,1663],{},[1665,80998,1667],{},[902,81000,81001],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,81004,81006],{"className":81005},[886],[888,81007,81008],{"xmlns":890},[892,81009,81010,81032],{},[895,81011,81012,81018,81020,81022,81024,81026],{},[1710,81013,81014,81016],{},[898,81015,1755],{},[1665,81017,1681],{},[1654,81019,1750],{},[1665,81021,4006],{},[1654,81023,2380],{},[1665,81025,72779],{},[1710,81027,81028,81030],{},[898,81029,1663],{},[1665,81031,1681],{},[902,81033,81034],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,81037,81039],{"className":81038},[886],[888,81040,81041],{"xmlns":890},[892,81042,81043,81063],{},[895,81044,81045,81047,81049,81051,81053,81055,81057,81059,81061],{},[898,81046,11536],{},[898,81048,11539],{},[1654,81050,1750],{},[1665,81052,4767],{},[1865,81054,11744],{},[1665,81056,67302],{},[1654,81058,1766],{},[1665,81060,4573],{},[898,81062,1663],{},[902,81064,81065],{"encoding":904},"TC = 50\\,000 + 20Q",[883,81067,81069],{"className":81068},[886],[888,81070,81071],{"xmlns":890},[892,81072,81073,81093],{},[895,81074,81075,81077,81079,81085,81087],{},[898,81076,1663],{},[1654,81078,1750],{},[1710,81080,81081,81083],{},[898,81082,1663],{},[1665,81084,1667],{},[1654,81086,1766],{},[1710,81088,81089,81091],{},[898,81090,1663],{},[1665,81092,1681],{},[902,81094,81095],{"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.",[724,81098,81099,81102,81103,81133,81134,81035,81166,9762,81196,81225],{},[38,81100,81101],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,81104,81106],{"className":81105},[886],[888,81107,81108],{"xmlns":890},[892,81109,81110,81130],{},[895,81111,81112,81118,81120,81122,81124],{},[1710,81113,81114,81116],{},[898,81115,1755],{},[1665,81117,1667],{},[1654,81119,1750],{},[1665,81121,4006],{},[1654,81123,2380],{},[1710,81125,81126,81128],{},[898,81127,1663],{},[1665,81129,1667],{},[902,81131,81132],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,81135,81137],{"className":81136},[886],[888,81138,81139],{"xmlns":890},[892,81140,81141,81163],{},[895,81142,81143,81149,81151,81153,81155,81157],{},[1710,81144,81145,81147],{},[898,81146,1755],{},[1665,81148,1681],{},[1654,81150,1750],{},[1665,81152,17102],{},[1654,81154,2380],{},[1665,81156,7594],{},[1710,81158,81159,81161],{},[898,81160,1663],{},[1665,81162,1681],{},[902,81164,81165],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,81167,81169],{"className":81168},[886],[888,81170,81171],{"xmlns":890},[892,81172,81173,81193],{},[895,81174,81175,81177,81179,81181,81183,81185,81187,81189,81191],{},[898,81176,11536],{},[898,81178,11539],{},[1654,81180,1750],{},[1665,81182,4032],{},[1865,81184,11744],{},[1665,81186,67302],{},[1654,81188,1766],{},[1665,81190,4273],{},[898,81192,1663],{},[902,81194,81195],{"encoding":904},"TC = 5\\,000 + 100Q",[883,81197,81199],{"className":81198},[886],[888,81200,81201],{"xmlns":890},[892,81202,81203,81223],{},[895,81204,81205,81207,81209,81215,81217],{},[898,81206,1663],{},[1654,81208,1750],{},[1710,81210,81211,81213],{},[898,81212,1663],{},[1665,81214,1667],{},[1654,81216,1766],{},[1710,81218,81219,81221],{},[898,81220,1663],{},[1665,81222,1681],{},[902,81224,81095],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,81227,81229],{"id":81228},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,81231,81232,81235,81236,81283,81284,81301],{},[38,81233,81234],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,81237,81239],{"className":81238},[886],[888,81240,81241],{"xmlns":890},[892,81242,81243,81280],{},[895,81244,81245,81247,81249,81251,81253,81256,81262,81264,81267,81273,81275,81278],{},[898,81246,11536],{},[898,81248,48559],{},[898,81250,11539],{},[1654,81252,1750],{},[1665,81254,81255],{},"0,85",[1741,81257,81258,81260],{},[898,81259,1663],{},[1665,81261,4035],{},[1654,81263,2380],{},[1665,81265,81266],{},"11,9",[1741,81268,81269,81271],{},[898,81270,1663],{},[1665,81272,1681],{},[1654,81274,1766],{},[1665,81276,81277],{},"102",[898,81279,1663],{},[902,81281,81282],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,81285,81287],{"className":81286},[886],[888,81288,81289],{"xmlns":890},[892,81290,81291,81299],{},[895,81292,81293],{},[1741,81294,81295,81297],{},[898,81296,1755],{},[1654,81298,1670],{},[902,81300,13142],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,81303,81304,79062,81307,81343],{},[38,81305,81306],{},"3.27",[883,81308,81310],{"className":81309},[886],[888,81311,81312],{"xmlns":890},[892,81313,81314,81340],{},[895,81315,81316,81318,81320,81322,81324,81330,81332,81334,81336,81338],{},[898,81317,9320],{},[898,81319,11539],{},[1654,81321,1750],{},[1665,81323,11681],{},[1741,81325,81326,81328],{},[898,81327,1663],{},[1665,81329,1681],{},[1654,81331,2380],{},[1665,81333,72660],{},[898,81335,1663],{},[1654,81337,1766],{},[1665,81339,4679],{},[902,81341,81342],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,81345,81346,78313,81349,81343],{},[38,81347,81348],{},"3.28",[883,81350,81352],{"className":81351},[886],[888,81353,81354],{"xmlns":890},[892,81355,81356,81392],{},[895,81357,81358,81360,81362,81364,81366,81372,81374,81376,81382,81384,81386,81388,81390],{},[898,81359,11536],{},[898,81361,11539],{},[1654,81363,1750],{},[1665,81365,7594],{},[1741,81367,81368,81370],{},[898,81369,1663],{},[1665,81371,4035],{},[1654,81373,2380],{},[1665,81375,32887],{},[1741,81377,81378,81380],{},[898,81379,1663],{},[1665,81381,1681],{},[1654,81383,1766],{},[1665,81385,11881],{},[898,81387,1663],{},[1654,81389,1766],{},[1665,81391,4011],{},[902,81393,81394],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,81396,10214],{"id":10213},[120,81398,81399,81427,81472,81544,81609,81649,81741,81847,81887,82001,82094,82158,82190,82250,82256,82320,82369,82423,82531,82586],{},[123,81400,81401,2186,81403,81426],{},[38,81402,63970],{},[883,81404,81406],{"className":81405},[886],[888,81407,81408],{"xmlns":890},[892,81409,81410,81424],{},[895,81411,81412,81414,81416,81418,81420,81422],{},[898,81413,11536],{},[898,81415,12737],{},[1654,81417,1750],{},[898,81419,1755],{},[1654,81421,4554],{},[898,81423,1663],{},[902,81425,74932],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,81428,81429,2186,81431,81471],{},[38,81430,64556],{},[883,81432,81434],{"className":81433},[886],[888,81435,81436],{"xmlns":890},[892,81437,81438,81468],{},[895,81439,81440,81442,81444,81446,81458,81460,81462,81464,81466],{},[898,81441,4737],{},[898,81443,12737],{},[1654,81445,1750],{},[2582,81447,81448],{"scriptlevel":2062,"displaystyle":1656},[2811,81449,81450,81456],{},[895,81451,81452,81454],{},[898,81453,11536],{},[898,81455,12737],{},[898,81457,1663],{},[1654,81459,1750],{},[898,81461,4980],{},[1654,81463,1708],{"stretchy":1656},[898,81465,1663],{},[1654,81467,1726],{"stretchy":1656},[902,81469,81470],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,81473,81474,2186,81476,81512,81513,81528,81529,2138],{},[38,81475,64704],{},[883,81477,81479],{"className":81478},[886],[888,81480,81481],{"xmlns":890},[892,81482,81483,81509],{},[895,81484,81485,81487,81489,81491],{},[898,81486,9320],{},[898,81488,12737],{},[1654,81490,1750],{},[2582,81492,81493],{"scriptlevel":2062,"displaystyle":1656},[2811,81494,81495,81503],{},[895,81496,81497,81499,81501],{},[898,81498,10977],{"mathvariant":1878},[898,81500,11536],{},[898,81502,12737],{},[895,81504,81505,81507],{},[898,81506,10977],{"mathvariant":1878},[898,81508,1663],{},[902,81510,81511],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,81514,81516],{"className":81515},[886],[888,81517,81518],{"xmlns":890},[892,81519,81520,81526],{},[895,81521,81522,81524],{},[898,81523,11536],{},[898,81525,12737],{},[902,81527,12837],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,81530,81532],{"className":81531},[886],[888,81533,81534],{"xmlns":890},[892,81535,81536,81542],{},[895,81537,81538,81540],{},[898,81539,4737],{},[898,81541,12737],{},[902,81543,63665],{"encoding":904},[123,81545,81546,2186,81549,1343,81579,2138],{},[38,81547,81548],{},"Diferenciál příjmu\u002Fnákladů",[883,81550,81552],{"className":81551},[886],[888,81553,81554],{"xmlns":890},[892,81555,81556,81576],{},[895,81557,81558,81560,81562,81564,81566,81568,81570,81572,81574],{},[898,81559,11648],{"mathvariant":1878},[898,81561,11536],{},[898,81563,12737],{},[1654,81565,11492],{},[898,81567,9320],{},[898,81569,12737],{},[1865,81571,11744],{},[898,81573,10977],{"mathvariant":1878},[898,81575,1663],{},[902,81577,81578],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,81580,81582],{"className":81581},[886],[888,81583,81584],{"xmlns":890},[892,81585,81586,81606],{},[895,81587,81588,81590,81592,81594,81596,81598,81600,81602,81604],{},[898,81589,11648],{"mathvariant":1878},[898,81591,11536],{},[898,81593,11539],{},[1654,81595,11492],{},[898,81597,9320],{},[898,81599,11539],{},[1865,81601,11744],{},[898,81603,10977],{"mathvariant":1878},[898,81605,1663],{},[902,81607,81608],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,81610,81611,2186,81613,2138],{},[38,81612,66826],{},[883,81614,81616],{"className":81615},[886],[888,81617,81618],{"xmlns":890},[892,81619,81620,81646],{},[895,81621,81622,81624,81626,81628,81630,81632,81634,81636,81638,81640,81642,81644],{},[898,81623,11536],{},[898,81625,11539],{},[1654,81627,1750],{},[898,81629,19153],{},[898,81631,11539],{},[1654,81633,1766],{},[898,81635,11536],{},[898,81637,48559],{},[898,81639,11539],{},[1654,81641,1708],{"stretchy":1656},[898,81643,1663],{},[1654,81645,1726],{"stretchy":1656},[902,81647,81648],{"encoding":904},"TC = FC + TVC(Q)",[123,81650,81651,2186,81654,1343,81669,2186,81671,1343,81694,2186,81697,2138],{},[38,81652,81653],{},"Fixní náklady",[883,81655,81657],{"className":81656},[886],[888,81658,81659],{"xmlns":890},[892,81660,81661,81667],{},[895,81662,81663,81665],{},[898,81664,19153],{},[898,81666,11539],{},[902,81668,63711],{"encoding":904},[38,81670,66979],{},[883,81672,81674],{"className":81673},[886],[888,81675,81676],{"xmlns":890},[892,81677,81678,81692],{},[895,81679,81680,81682,81684,81686,81688,81690],{},[898,81681,11536],{},[898,81683,48559],{},[898,81685,11539],{},[1654,81687,1708],{"stretchy":1656},[898,81689,1663],{},[1654,81691,1726],{"stretchy":1656},[902,81693,66976],{"encoding":904},[38,81695,81696],{},"variabilní náklady na jednotku",[883,81698,81700],{"className":81699},[886],[888,81701,81702],{"xmlns":890},[892,81703,81704,81738],{},[895,81705,81706,81708,81710,81712,81714,81716,81718],{},[898,81707,48559],{},[898,81709,11539],{},[1654,81711,1708],{"stretchy":1656},[898,81713,1663],{},[1654,81715,1726],{"stretchy":1656},[1654,81717,1750],{},[2582,81719,81720],{"scriptlevel":2062,"displaystyle":1656},[2811,81721,81722,81736],{},[895,81723,81724,81726,81728,81730,81732,81734],{},[898,81725,11536],{},[898,81727,48559],{},[898,81729,11539],{},[1654,81731,1708],{"stretchy":1656},[898,81733,1663],{},[1654,81735,1726],{"stretchy":1656},[898,81737,1663],{},[902,81739,81740],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,81742,81743,2186,81745,1343,81775,2186,81778,1343,81810,2186,81813,2138],{},[38,81744,66987],{},[883,81746,81748],{"className":81747},[886],[888,81749,81750],{"xmlns":890},[892,81751,81752,81772],{},[895,81753,81754,81756,81758,81760],{},[898,81755,4737],{},[898,81757,11539],{},[1654,81759,1750],{},[2582,81761,81762],{"scriptlevel":2062,"displaystyle":1656},[2811,81763,81764,81770],{},[895,81765,81766,81768],{},[898,81767,11536],{},[898,81769,11539],{},[898,81771,1663],{},[902,81773,81774],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,81776,81777],{},"průměrné fixní",[883,81779,81781],{"className":81780},[886],[888,81782,81783],{"xmlns":890},[892,81784,81785,81807],{},[895,81786,81787,81789,81791,81793,81795],{},[898,81788,4737],{},[898,81790,19153],{},[898,81792,11539],{},[1654,81794,1750],{},[2582,81796,81797],{"scriptlevel":2062,"displaystyle":1656},[2811,81798,81799,81805],{},[895,81800,81801,81803],{},[898,81802,19153],{},[898,81804,11539],{},[898,81806,1663],{},[902,81808,81809],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,81811,81812],{},"průměrné variabilní",[883,81814,81816],{"className":81815},[886],[888,81817,81818],{"xmlns":890},[892,81819,81820,81844],{},[895,81821,81822,81824,81826,81828,81830],{},[898,81823,4737],{},[898,81825,48559],{},[898,81827,11539],{},[1654,81829,1750],{},[2582,81831,81832],{"scriptlevel":2062,"displaystyle":1656},[2811,81833,81834,81842],{},[895,81835,81836,81838,81840],{},[898,81837,11536],{},[898,81839,48559],{},[898,81841,11539],{},[898,81843,1663],{},[902,81845,81846],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,81848,81849,2186,81851,2138],{},[38,81850,68174],{},[883,81852,81854],{"className":81853},[886],[888,81855,81856],{"xmlns":890},[892,81857,81858,81884],{},[895,81859,81860,81862,81864,81866],{},[898,81861,9320],{},[898,81863,11539],{},[1654,81865,1750],{},[2582,81867,81868],{"scriptlevel":2062,"displaystyle":1656},[2811,81869,81870,81878],{},[895,81871,81872,81874,81876],{},[898,81873,10977],{"mathvariant":1878},[898,81875,11536],{},[898,81877,11539],{},[895,81879,81880,81882],{},[898,81881,10977],{"mathvariant":1878},[898,81883,1663],{},[902,81885,81886],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,81888,81889,2186,81891,81939,81940,81953,81954,1343,81969,1343,81986,2138],{},[38,81890,69072],{},[883,81892,81894],{"className":81893},[886],[888,81895,81896],{"xmlns":890},[892,81897,81898,81936],{},[895,81899,81900,81902,81904,81906,81908,81910,81912,81914,81916,81918,81920,81926,81928,81930],{},[898,81901,11536],{},[898,81903,11539],{},[1654,81905,1750],{},[898,81907,19153],{},[898,81909,11539],{},[1654,81911,1766],{},[898,81913,207],{},[898,81915,1663],{},[1654,81917,1766],{},[898,81919,9758],{},[1741,81921,81922,81924],{},[898,81923,1663],{},[1665,81925,1681],{},[1654,81927,1766],{},[898,81929,3624],{},[1741,81931,81932,81934],{},[898,81933,1663],{},[1665,81935,4035],{},[902,81937,81938],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,81941,81943],{"className":81942},[886],[888,81944,81945],{"xmlns":890},[892,81946,81947,81951],{},[895,81948,81949],{},[898,81950,900],{},[902,81952,900],{"encoding":904},"-průběhem ",[883,81955,81957],{"className":81956},[886],[888,81958,81959],{"xmlns":890},[892,81960,81961,81967],{},[895,81962,81963,81965],{},[898,81964,4737],{},[898,81966,11539],{},[902,81968,63780],{"encoding":904},[883,81970,81972],{"className":81971},[886],[888,81973,81974],{"xmlns":890},[892,81975,81976,81984],{},[895,81977,81978,81980,81982],{},[898,81979,4737],{},[898,81981,48559],{},[898,81983,11539],{},[902,81985,63531],{"encoding":904},[883,81987,81989],{"className":81988},[886],[888,81990,81991],{"xmlns":890},[892,81992,81993,81999],{},[895,81994,81995,81997],{},[898,81996,9320],{},[898,81998,11539],{},[902,82000,63512],{"encoding":904},[123,82002,82003,82005,82006,19111,82021,82062,82063,69717,82078,82093],{},[38,82004,70154],{},": v bodě minima ",[883,82007,82009],{"className":82008},[886],[888,82010,82011],{"xmlns":890},[892,82012,82013,82019],{},[895,82014,82015,82017],{},[898,82016,4737],{},[898,82018,11539],{},[902,82020,63780],{"encoding":904},[883,82022,82024],{"className":82023},[886],[888,82025,82026],{"xmlns":890},[892,82027,82028,82060],{},[895,82029,82030,82032,82034,82036,82042,82044,82046,82048,82050,82052,82058],{},[898,82031,4737],{},[898,82033,11539],{},[1654,82035,1708],{"stretchy":1656},[1710,82037,82038,82040],{},[898,82039,1663],{},[1665,82041,2062],{},[1654,82043,1726],{"stretchy":1656},[1654,82045,1750],{},[898,82047,9320],{},[898,82049,11539],{},[1654,82051,1708],{"stretchy":1656},[1710,82053,82054,82056],{},[898,82055,1663],{},[1665,82057,2062],{},[1654,82059,1726],{"stretchy":1656},[902,82061,70789],{"encoding":904},"; geometricky ",[883,82064,82066],{"className":82065},[886],[888,82067,82068],{"xmlns":890},[892,82069,82070,82076],{},[895,82071,82072,82074],{},[898,82073,9320],{},[898,82075,11539],{},[902,82077,63512],{"encoding":904},[883,82079,82081],{"className":82080},[886],[888,82082,82083],{"xmlns":890},[892,82084,82085,82091],{},[895,82086,82087,82089],{},[898,82088,4737],{},[898,82090,11539],{},[902,82092,63780],{"encoding":904}," v jejím minimu.",[123,82095,82096,82005,82098,19111,82115,2138],{},[38,82097,71504],{},[883,82099,82101],{"className":82100},[886],[888,82102,82103],{"xmlns":890},[892,82104,82105,82113],{},[895,82106,82107,82109,82111],{},[898,82108,4737],{},[898,82110,48559],{},[898,82112,11539],{},[902,82114,63531],{"encoding":904},[883,82116,82118],{"className":82117},[886],[888,82119,82120],{"xmlns":890},[892,82121,82122,82156],{},[895,82123,82124,82126,82128,82130,82132,82138,82140,82142,82144,82146,82148,82154],{},[898,82125,4737],{},[898,82127,48559],{},[898,82129,11539],{},[1654,82131,1708],{"stretchy":1656},[1710,82133,82134,82136],{},[898,82135,1663],{},[1665,82137,2062],{},[1654,82139,1726],{"stretchy":1656},[1654,82141,1750],{},[898,82143,9320],{},[898,82145,11539],{},[1654,82147,1708],{"stretchy":1656},[1710,82149,82150,82152],{},[898,82151,1663],{},[1665,82153,2062],{},[1654,82155,1726],{"stretchy":1656},[902,82157,77239],{"encoding":904},[123,82159,82160,2186,82162,82189],{},[38,82161,71683],{},[883,82163,82165],{"className":82164},[886],[888,82166,82167],{"xmlns":890},[892,82168,82169,82187],{},[895,82170,82171,82173,82175,82177,82179,82181,82183,82185],{},[898,82172,1755],{},[898,82174,12737],{},[1654,82176,1750],{},[898,82178,11536],{},[898,82180,12737],{},[1654,82182,2380],{},[898,82184,11536],{},[898,82186,11539],{},[902,82188,63420],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,82191,82192,18742,82194,82196,82197,82223,82224,82249],{},[38,82193,72545],{},[614,82195,71808],{},") — hodnoty ",[883,82198,82200],{"className":82199},[886],[888,82201,82202],{"xmlns":890},[892,82203,82204,82220],{},[895,82205,82206,82212,82214],{},[1710,82207,82208,82210],{},[898,82209,1663],{},[898,82211,4737],{},[1654,82213,1674],{"separator":1673},[1710,82215,82216,82218],{},[898,82217,1663],{},[898,82219,4762],{},[902,82221,82222],{"encoding":904},"Q_A, Q_B"," splňující ",[883,82225,82227],{"className":82226},[886],[888,82228,82229],{"xmlns":890},[892,82230,82231,82247],{},[895,82232,82233,82235,82237,82239,82241,82243,82245],{},[898,82234,1755],{},[898,82236,12737],{},[1654,82238,1708],{"stretchy":1656},[898,82240,1663],{},[1654,82242,1726],{"stretchy":1656},[1654,82244,1750],{},[1665,82246,2062],{},[902,82248,72085],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,82251,82252,82255],{},[38,82253,82254],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,82257,82258,82260,82261,19111,82278,82319],{},[38,82259,73599],{}," — v bodě maxima zisku ",[883,82262,82264],{"className":82263},[886],[888,82265,82266],{"xmlns":890},[892,82267,82268,82276],{},[895,82269,82270],{},[1710,82271,82272,82274],{},[898,82273,1663],{},[1665,82275,2062],{},[902,82277,46528],{"encoding":904},[883,82279,82281],{"className":82280},[886],[888,82282,82283],{"xmlns":890},[892,82284,82285,82317],{},[895,82286,82287,82289,82291,82293,82299,82301,82303,82305,82307,82309,82315],{},[898,82288,9320],{},[898,82290,12737],{},[1654,82292,1708],{"stretchy":1656},[1710,82294,82295,82297],{},[898,82296,1663],{},[1665,82298,2062],{},[1654,82300,1726],{"stretchy":1656},[1654,82302,1750],{},[898,82304,9320],{},[898,82306,11539],{},[1654,82308,1708],{"stretchy":1656},[1710,82310,82311,82313],{},[898,82312,1663],{},[1665,82314,2062],{},[1654,82316,1726],{"stretchy":1656},[902,82318,73865],{"encoding":904}," (3.13).",[123,82321,82322,28996,82324,19111,82343,82368],{},[38,82323,74892],{},[883,82325,82327],{"className":82326},[886],[888,82328,82329],{"xmlns":890},[892,82330,82331,82340],{},[895,82332,82333,82335,82337],{},[898,82334,1755],{},[1654,82336,1750],{},[1865,82338,82339],{},"konst",[902,82341,82342],{"encoding":904},"P = \\text{konst}",[883,82344,82346],{"className":82345},[886],[888,82347,82348],{"xmlns":890},[892,82349,82350,82366],{},[895,82351,82352,82354,82356,82358,82360,82362,82364],{},[898,82353,1755],{},[1654,82355,1750],{},[898,82357,9320],{},[898,82359,11539],{},[1654,82361,1708],{"stretchy":1656},[898,82363,1663],{},[1654,82365,1726],{"stretchy":1656},[902,82367,75586],{"encoding":904}," (3.14).",[123,82370,82371,82374,82375,82404,82405,82422],{},[38,82372,82373],{},"Shutdown point"," — bod ",[883,82376,82378],{"className":82377},[886],[888,82379,82380],{"xmlns":890},[892,82381,82382,82402],{},[895,82383,82384,82386,82392,82394,82400],{},[1654,82385,1708],{"stretchy":1656},[1741,82387,82388,82390],{},[898,82389,1663],{},[1654,82391,1670],{},[1654,82393,1674],{"separator":1673},[1741,82395,82396,82398],{},[898,82397,1755],{},[1654,82399,1670],{},[1654,82401,1726],{"stretchy":1656},[902,82403,75875],{"encoding":904}," v minimu ",[883,82406,82408],{"className":82407},[886],[888,82409,82410],{"xmlns":890},[892,82411,82412,82420],{},[895,82413,82414,82416,82418],{},[898,82415,4737],{},[898,82417,48559],{},[898,82419,11539],{},[902,82421,63531],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,82424,82425,2186,82428,15201,82463,76145,82484,82497,82498,82513,82514,2138],{},[38,82426,82427],{},"Funkce nabídky firmy",[883,82429,82431],{"className":82430},[886],[888,82432,82433],{"xmlns":890},[892,82434,82435,82461],{},[895,82436,82437,82439,82441,82443,82445,82447,82449,82451,82453,82455,82457,82459],{},[898,82438,1755],{},[1654,82440,1750],{},[898,82442,17398],{},[1654,82444,1708],{"stretchy":1656},[898,82446,1663],{},[1654,82448,1726],{"stretchy":1656},[1654,82450,1750],{},[898,82452,9320],{},[898,82454,11539],{},[1654,82456,1708],{"stretchy":1656},[898,82458,1663],{},[1654,82460,1726],{"stretchy":1656},[902,82462,77342],{"encoding":904},[883,82464,82466],{"className":82465},[886],[888,82467,82468],{"xmlns":890},[892,82469,82470,82482],{},[895,82471,82472,82474,82476],{},[898,82473,1663],{},[1654,82475,13222],{},[1741,82477,82478,82480],{},[898,82479,1663],{},[1654,82481,1670],{},[902,82483,76144],{"encoding":904},[883,82485,82487],{"className":82486},[886],[888,82488,82489],{"xmlns":890},[892,82490,82491,82495],{},[895,82492,82493],{},[1665,82494,2062],{},[902,82496,2062],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,82499,82501],{"className":82500},[886],[888,82502,82503],{"xmlns":890},[892,82504,82505,82511],{},[895,82506,82507,82509],{},[898,82508,9320],{},[898,82510,11539],{},[902,82512,63512],{"encoding":904}," nad minimem ",[883,82515,82517],{"className":82516},[886],[888,82518,82519],{"xmlns":890},[892,82520,82521,82529],{},[895,82522,82523,82525,82527],{},[898,82524,4737],{},[898,82526,48559],{},[898,82528,11539],{},[902,82530,63531],{"encoding":904},[123,82532,82533,10373,82535,82556,82557,2138],{},[38,82534,58299],{},[883,82536,82538],{"className":82537},[886],[888,82539,82540],{"xmlns":890},[892,82541,82542,82554],{},[895,82543,82544,82546,82548],{},[898,82545,1755],{},[1654,82547,1750],{},[1741,82549,82550,82552],{},[898,82551,1755],{},[1654,82553,1670],{},[902,82555,13095],{"encoding":904}," konstantní ⇒ ",[883,82558,82560],{"className":82559},[886],[888,82561,82562],{"xmlns":890},[892,82563,82564,82584],{},[895,82565,82566,82568,82570,82572,82574,82576,82578],{},[898,82567,4737],{},[898,82569,12737],{},[1654,82571,1750],{},[898,82573,9320],{},[898,82575,12737],{},[1654,82577,1750],{},[1741,82579,82580,82582],{},[898,82581,1755],{},[1654,82583,1670],{},[902,82585,66818],{"encoding":904},[123,82587,82588,82591],{},[38,82589,82590],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,82593,10613],{"id":10612},[120,82595,82596,82615,82627],{},[123,82597,82598,2186,82600,1343,82603,1343,82606,1343,82609,1343,82612],{},[38,82599,58943],{},[207,82601,10669],{"className":82602,"dataFsResolvedFilePath":800,"href":801},[210],[207,82604,12575],{"className":82605,"dataFsResolvedFilePath":848,"href":849},[210],[207,82607,10655],{"className":82608,"dataFsResolvedFilePath":764,"href":765},[210],[207,82610,775],{"className":82611,"dataFsResolvedFilePath":773,"href":774},[210],[207,82613,859],{"className":82614,"dataFsResolvedFilePath":857,"href":858},[210],[123,82616,82617,2186,82619,1343,82623],{},[38,82618,10675],{},[207,82620,82622],{"className":82621,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,82624,82626],{"className":82625,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,82628,82629,2186,82631],{},[38,82630,10686],{},[207,82632,10692],{"className":82633,"dataFsResolvedFilePath":10690,"href":10691},[210],{"title":641,"searchDepth":642,"depth":642,"links":82635},[82636,82637,82644,82650,82654,82655,82659,82660,82661,82662,82668,82669],{"id":59174,"depth":642,"text":1241},{"id":63958,"depth":642,"text":63959,"children":82638},[82639,82640,82641,82642,82643],{"id":63969,"depth":649,"text":63970},{"id":64555,"depth":649,"text":64556},{"id":64703,"depth":649,"text":64704},{"id":65445,"depth":649,"text":65446},{"id":66100,"depth":649,"text":66101},{"id":66821,"depth":642,"text":66822,"children":82645},[82646,82647,82648,82649],{"id":66825,"depth":649,"text":66826},{"id":66986,"depth":649,"text":66987},{"id":68173,"depth":649,"text":68174},{"id":69071,"depth":649,"text":69072},{"id":70153,"depth":642,"text":70154,"children":82651},[82652,82653],{"id":25114,"depth":649,"text":25115},{"id":71503,"depth":649,"text":71504},{"id":71677,"depth":642,"text":71678},{"id":73598,"depth":642,"text":73599,"children":82656},[82657,82658],{"id":73612,"depth":649,"text":25115},{"id":74891,"depth":649,"text":74892},{"id":75523,"depth":642,"text":75524},{"id":76989,"depth":642,"text":76990},{"id":58101,"depth":642,"text":58102},{"id":77450,"depth":642,"text":77451,"children":82663},[82664,82665,82666,82667],{"id":77454,"depth":649,"text":77455},{"id":78306,"depth":649,"text":78307},{"id":79852,"depth":649,"text":79853},{"id":81228,"depth":649,"text":81229},{"id":10213,"depth":642,"text":10214},{"id":10612,"depth":642,"text":10613},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":63340,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,82676,82677,63392,82678,82679,82680],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":82683,"title":82684,"body":82685,"course":1128,"courses":659,"created":10724,"description":641,"extension":661,"meta":94782,"navigation":664,"path":94783,"seo":94784,"sources":94785,"stem":94786,"tags":94787,"type":10736,"updated":677,"__hash__":94793},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":82686,"toc":94739},[82687,82690,83046,83050,83053,83121,83173,83183,83187,83221,83262,83286,83309,83338,83405,83512,83555,83612,83687,83732,83736,83744,83752,83755,84020,84071,84151,84221,84244,84272,84317,84339,84343,84350,84399,84425,84576,84579,84616,84779,84887,84891,84928,85003,85072,85191,85313,85394,85400,85441,85514,85607,85611,85647,85735,85849,85954,86039,86179,86183,86231,86276,86282,86286,86289,86340,86390,86397,86463,86596,86641,86645,86666,87045,87140,87157,87211,87215,87297,87381,87551,87554,87597,87664,87738,87742,87747,87816,87824,87833,87911,87977,87982,88077,88120,88125,88173,88178,88226,88344,88427,88465,88568,88627,88768,88772,88815,88888,88912,88966,88973,88975,89020,89065,89076,89081,89117,89179,89202,89211,89312,89379,89452,89459,89550,89612,89648,89705,89764,89949,90045,90049,90053,90132,90137,90261,90347,90353,90463,90500,90591,90689,90692,90696,90762,90799,90921,90973,90977,91005,91057,91131,91236,91260,91319,91323,91341,91484,91632,91634,91669,91673,91675,91765,91895,92021,92113,92188,92192,92308,92412,92602,92638,92732,92738,92851,93154,93160,93278,93377,93453,93455,94617,94619],[12,82688,82684],{"id":82689},"produkce-produkční-funkce-cobb-douglas-mrts",[2140,82691,82692],{},[724,82693,82694,12620,82696,82698,82699,45116,82712,82725,82726,25079,82739,18742,82741,82765,82766,2186,82768,2068,82802,2186,82805,82833,82834,19111,82854,82884,82885,18742,82888,82916,82917,82920,82921,82951,82952,82982,82983,2186,82986,83026,83027,83045],{},[883,82695,12619],{},[38,82697,859],{}," popisuje vztah mezi vstupy (práce ",[883,82700,82702],{"className":82701},[886],[888,82703,82704],{"xmlns":890},[892,82705,82706,82710],{},[895,82707,82708],{},[898,82709,2450],{},[902,82711,2450],{"encoding":904},[883,82713,82715],{"className":82714},[886],[888,82716,82717],{"xmlns":890},[892,82718,82719,82723],{},[895,82720,82721],{},[898,82722,18517],{},[902,82724,18517],{"encoding":904},") a výstupem ",[883,82727,82729],{"className":82728},[886],[888,82730,82731],{"xmlns":890},[892,82732,82733,82737],{},[895,82734,82735],{},[898,82736,1663],{},[902,82738,1663],{"encoding":904},[38,82740,45184],{},[883,82742,82744],{"className":82743},[886],[888,82745,82746],{"xmlns":890},[892,82747,82748,82762],{},[895,82749,82750,82752,82754,82756,82758,82760],{},[898,82751,1663],{},[1654,82753,1750],{},[898,82755,1663],{},[1654,82757,1708],{"stretchy":1656},[898,82759,2450],{},[1654,82761,1726],{"stretchy":1656},[902,82763,82764],{"encoding":904},"Q = Q(L)",") studujeme ",[614,82767,18741],{},[883,82769,82771],{"className":82770},[886],[888,82772,82773],{"xmlns":890},[892,82774,82775,82799],{},[895,82776,82777,82779,82785,82787,82793,82795,82797],{},[898,82778,9320],{},[1710,82780,82781,82783],{},[898,82782,1755],{},[898,82784,2450],{},[1654,82786,1750],{},[1741,82788,82789,82791],{},[898,82790,1663],{},[1654,82792,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,82794,1708],{"stretchy":1656},[898,82796,2450],{},[1654,82798,1726],{"stretchy":1656},[902,82800,82801],{"encoding":904},"MP_L = Q'(L)",[614,82803,82804],{},"průměrný produkt",[883,82806,82808],{"className":82807},[886],[888,82809,82810],{"xmlns":890},[892,82811,82812,82830],{},[895,82813,82814,82816,82822,82824,82826,82828],{},[898,82815,4737],{},[1710,82817,82818,82820],{},[898,82819,1755],{},[898,82821,2450],{},[1654,82823,1750],{},[898,82825,1663],{},[898,82827,1879],{"mathvariant":1878},[898,82829,2450],{},[902,82831,82832],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,82835,82837],{"className":82836},[886],[888,82838,82839],{"xmlns":890},[892,82840,82841,82851],{},[895,82842,82843,82845],{},[898,82844,4737],{},[1710,82846,82847,82849],{},[898,82848,1755],{},[898,82850,2450],{},[902,82852,82853],{"encoding":904},"AP_L",[883,82855,82857],{"className":82856},[886],[888,82858,82859],{"xmlns":890},[892,82860,82861,82881],{},[895,82862,82863,82865,82871,82873,82875],{},[898,82864,9320],{},[1710,82866,82867,82869],{},[898,82868,1755],{},[898,82870,2450],{},[1654,82872,1750],{},[898,82874,4737],{},[1710,82876,82877,82879],{},[898,82878,1755],{},[898,82880,2450],{},[902,82882,82883],{"encoding":904},"MP_L = AP_L",". Ve ",[38,82886,82887],{},"dvoufaktorovém modelu",[883,82889,82891],{"className":82890},[886],[888,82892,82893],{"xmlns":890},[892,82894,82895,82913],{},[895,82896,82897,82899,82901,82903,82905,82907,82909,82911],{},[898,82898,1663],{},[1654,82900,1750],{},[898,82902,1663],{},[1654,82904,1708],{"stretchy":1656},[898,82906,2450],{},[1654,82908,1674],{"separator":1673},[898,82910,18517],{},[1654,82912,1726],{"stretchy":1656},[902,82914,82915],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,82918,82919],{},"Cobb-Douglasovy"," funkce ",[883,82922,82924],{"className":82923},[886],[888,82925,82926],{"xmlns":890},[892,82927,82928,82948],{},[895,82929,82930,82932,82934,82936,82942],{},[898,82931,1663],{},[1654,82933,1750],{},[898,82935,4737],{},[1741,82937,82938,82940],{},[898,82939,2450],{},[898,82941,207],{},[1741,82943,82944,82946],{},[898,82945,18517],{},[898,82947,9758],{},[902,82949,82950],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,82953,82955],{"className":82954},[886],[888,82956,82957],{"xmlns":890},[892,82958,82959,82979],{},[895,82960,82961,82963,82969,82971,82973],{},[898,82962,9320],{},[1710,82964,82965,82967],{},[898,82966,1755],{},[898,82968,2450],{},[1654,82970,1674],{"separator":1673},[898,82972,9320],{},[1710,82974,82975,82977],{},[898,82976,1755],{},[898,82978,18517],{},[902,82980,82981],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,82984,82985],{},"mezní míru technické substituce",[883,82987,82989],{"className":82988},[886],[888,82990,82991],{"xmlns":890},[892,82992,82993,83023],{},[895,82994,82995,82997,82999,83001,83003,83005,83007,83013,83015,83017],{},[898,82996,9320],{},[898,82998,12737],{},[898,83000,11536],{},[898,83002,17398],{},[1654,83004,1750],{},[898,83006,9320],{},[1710,83008,83009,83011],{},[898,83010,1755],{},[898,83012,2450],{},[898,83014,1879],{"mathvariant":1878},[898,83016,9320],{},[1710,83018,83019,83021],{},[898,83020,1755],{},[898,83022,18517],{},[902,83024,83025],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,83028,83030],{"className":83029},[886],[888,83031,83032],{"xmlns":890},[892,83033,83034,83042],{},[895,83035,83036,83038,83040],{},[898,83037,207],{},[1654,83039,1766],{},[898,83041,9758],{},[902,83043,83044],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,83047,83049],{"id":83048},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,83051,83052],{},"Po prostudování kapitoly 5 student umí:",[120,83054,83055,83061,83071,83077,83083,83088,83094,83104,83109,83115],{},[123,83056,83057,83058,1674],{},"popsat ",[38,83059,83060],{},"jednofaktorový model produkce",[123,83062,83063,83064,2068,83067,83070],{},"vypočítat ",[38,83065,83066],{},"mezní",[38,83068,83069],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,83072,83073,83074,1674],{},"charakterizovat průběh ",[38,83075,83076],{},"křivky produkce",[123,83078,83079,83080,1674],{},"formulovat ",[38,83081,83082],{},"princip maximalizace průměrného produktu práce",[123,83084,83057,83085,1674],{},[38,83086,83087],{},"dvoufaktorový model produkce",[123,83089,83090,83091,1674],{},"uvést tvar ",[38,83092,83093],{},"Cobb–Douglasových produkčních funkcí",[123,83095,83096,83097,1343,83099,1343,83101,1674],{},"vyložit, co jsou ",[38,83098,33299],{},[38,83100,22366],{},[38,83102,83103],{},"klesající výnosy z rozsahu",[123,83105,83063,83106,83070],{},[38,83107,83108],{},"mezní produkty práce a kapitálu",[123,83110,83111,83112,1674],{},"najít ",[38,83113,83114],{},"izokvanty",[123,83116,83063,83117,83120],{},[38,83118,83119],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,83122,83123,83124,83127,83128,83131,83132,2186,83135,1343,83148,2186,83151,2068,83164,83167,83168,83170,83171,2138],{},"Každý proces produkce je určován ",[38,83125,83126],{},"faktory"," (též ",[38,83129,83130],{},"vstupy",") produkce. K hlavním patří ",[38,83133,83134],{},"práce",[883,83136,83138],{"className":83137},[886],[888,83139,83140],{"xmlns":890},[892,83141,83142,83146],{},[895,83143,83144],{},[898,83145,2450],{},[902,83147,2450],{"encoding":904},[38,83149,83150],{},"kapitál",[883,83152,83154],{"className":83153},[886],[888,83155,83156],{"xmlns":890},[892,83157,83158,83162],{},[895,83159,83160],{},[898,83161,18517],{},[902,83163,18517],{"encoding":904},[38,83165,83166],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,83169,45184],{}," (produkce závisí jen na práci); v opačném případě o ",[38,83172,82887],{},[724,83174,83175,83176,1343,83179,83182],{},"Související matematický aparát: ",[207,83177,10655],{"className":83178,"dataFsResolvedFilePath":764,"href":765},[210],[207,83180,784],{"className":83181,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,83184,83186],{"id":83185},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,83188,83189,83190,83203,83204,83217,83218],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,83191,83193],{"className":83192},[886],[888,83194,83195],{"xmlns":890},[892,83196,83197,83201],{},[895,83198,83199],{},[898,83200,1663],{},[902,83202,1663],{"encoding":904}," na práci ",[883,83205,83207],{"className":83206},[886],[888,83208,83209],{"xmlns":890},[892,83210,83211,83215],{},[895,83212,83213],{},[898,83214,2450],{},[902,83216,2450],{"encoding":904}," vyjadřuje ",[38,83219,83220],{},"produkční funkce",[883,83222,83224],{"className":83223},[886],[888,83225,83226],{"xmlns":890,"display":1956},[892,83227,83228,83259],{},[1960,83229,83230],{"width":1962},[1964,83231,83232,83234,83252,83254],{},[1967,83233],{"width":1969},[1967,83235,83236],{},[895,83237,83238,83240,83242,83244,83246,83248,83250],{},[898,83239,1663],{},[1654,83241,1750],{},[898,83243,1663],{},[1654,83245,1708],{"stretchy":1656},[898,83247,2450],{},[1654,83249,1726],{"stretchy":1656},[1654,83251,1674],{"separator":1673},[1967,83253],{"width":1969},[1967,83255,83256],{},[1865,83257,83258],{},"(5.1)",[902,83260,83261],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,83263,83264,83265,18742,83268,83271,83272,83285],{},"jejíž graf se nazývá ",[38,83266,83267],{},"křivka produkce",[614,83269,83270],{},"production curve","). Práce ",[883,83273,83275],{"className":83274},[886],[888,83276,83277],{"xmlns":890},[892,83278,83279,83283],{},[895,83280,83281],{},[898,83282,2450],{},[902,83284,2450],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,83287,83289,83290,1726],{"id":83288},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,83291,83293],{"className":83292},[886],[888,83294,83295],{"xmlns":890},[892,83296,83297,83307],{},[895,83298,83299,83301],{},[898,83300,9320],{},[1710,83302,83303,83305],{},[898,83304,1755],{},[898,83306,2450],{},[902,83308,18762],{"encoding":904},[724,83310,83311,18742,83314,83317,83318,83337],{},[38,83312,83313],{},"Mezní produkt práce",[614,83315,83316],{},"marginal product of labour",") ",[883,83319,83321],{"className":83320},[886],[888,83322,83323],{"xmlns":890},[892,83324,83325,83335],{},[895,83326,83327,83329],{},[898,83328,9320],{},[1710,83330,83331,83333],{},[898,83332,1755],{},[898,83334,2450],{},[902,83336,18762],{"encoding":904}," je derivace produkce podle práce:",[883,83339,83341],{"className":83340},[886],[888,83342,83343],{"xmlns":890,"display":1956},[892,83344,83345,83402],{},[1960,83346,83347],{"width":1962},[1964,83348,83349,83351,83395,83397],{},[1967,83350],{"width":1969},[1967,83352,83353],{},[895,83354,83355,83357,83363,83365,83379,83381,83387,83389,83391,83393],{},[898,83356,9320],{},[1710,83358,83359,83361],{},[898,83360,1755],{},[898,83362,2450],{},[1654,83364,1750],{},[2811,83366,83367,83373],{},[895,83368,83369,83371],{},[898,83370,10977],{},[898,83372,1663],{},[895,83374,83375,83377],{},[898,83376,10977],{},[898,83378,2450],{},[1654,83380,1750],{},[1741,83382,83383,83385],{},[898,83384,1663],{},[1654,83386,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,83388,1708],{"stretchy":1656},[898,83390,2450],{},[1654,83392,1726],{"stretchy":1656},[898,83394,2138],{"mathvariant":1878},[1967,83396],{"width":1969},[1967,83398,83399],{},[1865,83400,83401],{},"(5.2)",[902,83403,83404],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,83406,83407,83408,28640,83426,83454,83455,83472,83473,11448,83490,12664],{},"Pro pevnou hodnotu ",[883,83409,83411],{"className":83410},[886],[888,83412,83413],{"xmlns":890},[892,83414,83415,83423],{},[895,83416,83417],{},[1741,83418,83419,83421],{},[898,83420,2450],{},[1654,83422,1670],{},[902,83424,83425],{"encoding":904},"L^*",[883,83427,83429],{"className":83428},[886],[888,83430,83431],{"xmlns":890},[892,83432,83433,83451],{},[895,83434,83435,83441,83443,83449],{},[1741,83436,83437,83439],{},[898,83438,1663],{},[1654,83440,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,83442,1708],{"stretchy":1656},[1741,83444,83445,83447],{},[898,83446,2450],{},[1654,83448,1670],{},[1654,83450,1726],{"stretchy":1656},[902,83452,83453],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,83456,83458],{"className":83457},[886],[888,83459,83460],{"xmlns":890},[892,83461,83462,83470],{},[895,83463,83464],{},[1741,83465,83466,83468],{},[898,83467,2450],{},[1654,83469,1670],{},[902,83471,83425],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,83474,83476],{"className":83475},[886],[888,83477,83478],{"xmlns":890},[892,83479,83480,83488],{},[895,83481,83482],{},[1741,83483,83484,83486],{},[898,83485,2450],{},[1654,83487,1670],{},[902,83489,83425],{"encoding":904},[883,83491,83493],{"className":83492},[886],[888,83494,83495],{"xmlns":890},[892,83496,83497,83509],{},[895,83498,83499,83505,83507],{},[1741,83500,83501,83503],{},[898,83502,2450],{},[1654,83504,1670],{},[1654,83506,1766],{},[1665,83508,1667],{},[902,83510,83511],{"encoding":904},"L^*+1",[2140,83513,83514],{},[724,83515,83516,26719,83518,83537,83538,83541,83542,2138],{},[883,83517,2860],{},[883,83519,83521],{"className":83520},[886],[888,83522,83523],{"xmlns":890},[892,83524,83525,83535],{},[895,83526,83527,83529],{},[898,83528,9320],{},[1710,83530,83531,83533],{},[898,83532,1755],{},[898,83534,2450],{},[902,83536,18762],{"encoding":904}," odpovídá na otázku „",[38,83539,83540],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,83543,83545],{"className":83544},[886],[888,83546,83547],{"xmlns":890},[892,83548,83549,83553],{},[895,83550,83551],{},[898,83552,2450],{},[902,83554,2450],{"encoding":904},[724,83556,83557,83560,83561,83577,83578,11448,83591,83611],{},[38,83558,83559],{},"Přibližná změna produkce"," pro změnu práce o ",[883,83562,83564],{"className":83563},[886],[888,83565,83566],{"xmlns":890},[892,83567,83568,83574],{},[895,83569,83570,83572],{},[898,83571,10977],{},[898,83573,2450],{},[902,83575,83576],{"encoding":904},"dL"," (z ",[883,83579,83581],{"className":83580},[886],[888,83582,83583],{"xmlns":890},[892,83584,83585,83589],{},[895,83586,83587],{},[898,83588,2450],{},[902,83590,2450],{"encoding":904},[883,83592,83594],{"className":83593},[886],[888,83595,83596],{"xmlns":890},[892,83597,83598,83608],{},[895,83599,83600,83602,83604,83606],{},[898,83601,2450],{},[1654,83603,1766],{},[898,83605,10977],{},[898,83607,2450],{},[902,83609,83610],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,83613,83615],{"className":83614},[886],[888,83616,83617],{"xmlns":890,"display":1956},[892,83618,83619,83684],{},[1960,83620,83621],{"width":1962},[1964,83622,83623,83625,83677,83679],{},[1967,83624],{"width":1969},[1967,83626,83627],{},[895,83628,83629,83631,83633,83635,83637,83639,83641,83647,83649,83651,83653,83655,83657,83659,83661,83663,83669,83671,83673,83675],{},[898,83630,11648],{"mathvariant":1878},[898,83632,1663],{},[1654,83634,11492],{},[898,83636,10977],{},[898,83638,1663],{},[1654,83640,1750],{},[1741,83642,83643,83645],{},[898,83644,1663],{},[1654,83646,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,83648,1708],{"stretchy":1656},[898,83650,2450],{},[1654,83652,1726],{"stretchy":1656},[1865,83654,11744],{},[898,83656,10977],{},[898,83658,2450],{},[1654,83660,1750],{},[898,83662,9320],{},[1710,83664,83665,83667],{},[898,83666,1755],{},[898,83668,2450],{},[1865,83670,11744],{},[898,83672,10977],{},[898,83674,2450],{},[898,83676,2138],{"mathvariant":1878},[1967,83678],{"width":1969},[1967,83680,83681],{},[1865,83682,83683],{},"(5.3)",[902,83685,83686],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,83688,83689,83690,2138],{},"Skutečná změna je ",[883,83691,83693],{"className":83692},[886],[888,83694,83695],{"xmlns":890},[892,83696,83697,83729],{},[895,83698,83699,83701,83703,83705,83707,83709,83711,83713,83715,83717,83719,83721,83723,83725,83727],{},[898,83700,11648],{"mathvariant":1878},[898,83702,1663],{},[1654,83704,1750],{},[898,83706,1663],{},[1654,83708,1708],{"stretchy":1656},[898,83710,2450],{},[1654,83712,1766],{},[898,83714,10977],{},[898,83716,2450],{},[1654,83718,1726],{"stretchy":1656},[1654,83720,2380],{},[898,83722,1663],{},[1654,83724,1708],{"stretchy":1656},[898,83726,2450],{},[1654,83728,1726],{"stretchy":1656},[902,83730,83731],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,83733,83735],{"id":83734},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,83737,83738,18742,83741,11906],{},[38,83739,83740],{},"Zákon klesajících výnosů",[614,83742,83743],{},"law of diminishing marginal productivity",[2140,83745,83746],{},[724,83747,83748,83749,83751],{},"Roste-li postupně některý ze vstupů (",[614,83750,45180],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,83753,83754],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,83756,83757,83758,2186,83779,83798,83799,83849,83850,83852,83853,2186,83873,83892,83893,83849,83925,4039,83927,83946,83947,9762,83964,83998,83999,16828,84016,84019],{},"1° ",[38,83759,83760,83761,2781],{},"Do bodu ",[883,83762,83764],{"className":83763},[886],[888,83765,83766],{"xmlns":890},[892,83767,83768,83776],{},[895,83769,83770],{},[1710,83771,83772,83774],{},[898,83773,2450],{},[1665,83775,2062],{},[902,83777,83778],{"encoding":904},"L_0",[883,83780,83782],{"className":83781},[886],[888,83783,83784],{"xmlns":890},[892,83785,83786,83796],{},[895,83787,83788,83790],{},[898,83789,9320],{},[1710,83791,83792,83794],{},[898,83793,1755],{},[898,83795,2450],{},[902,83797,18762],{"encoding":904}," roste, tj. ",[883,83800,83802],{"className":83801},[886],[888,83803,83804],{"xmlns":890},[892,83805,83806,83846],{},[895,83807,83808,83810,83812,83818,83824,83826,83836,83838,83840,83842,83844],{},[1654,83809,1708],{"stretchy":1656},[898,83811,9320],{},[1710,83813,83814,83816],{},[898,83815,1755],{},[898,83817,2450],{},[1741,83819,83820,83822],{},[1654,83821,1726],{"stretchy":1656},[1654,83823,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,83825,1750],{},[1741,83827,83828,83830],{},[898,83829,1663],{},[895,83831,83832,83834],{},[1654,83833,2592],{"mathvariant":1878},[1654,83835,2592],{"mathvariant":1878},[1654,83837,1708],{"stretchy":1656},[898,83839,2450],{},[1654,83841,1726],{"stretchy":1656},[1654,83843,2952],{},[1665,83845,2062],{},[902,83847,83848],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,83851,45884],{},".\n2° ",[38,83854,83855,83856,2781],{},"Od bodu ",[883,83857,83859],{"className":83858},[886],[888,83860,83861],{"xmlns":890},[892,83862,83863,83871],{},[895,83864,83865],{},[1710,83866,83867,83869],{},[898,83868,2450],{},[1665,83870,2062],{},[902,83872,83778],{"encoding":904},[883,83874,83876],{"className":83875},[886],[888,83877,83878],{"xmlns":890},[892,83879,83880,83890],{},[895,83881,83882,83884],{},[898,83883,9320],{},[1710,83885,83886,83888],{},[898,83887,1755],{},[898,83889,2450],{},[902,83891,18762],{"encoding":904}," klesá, ",[883,83894,83896],{"className":83895},[886],[888,83897,83898],{"xmlns":890},[892,83899,83900,83922],{},[895,83901,83902,83912,83914,83916,83918,83920],{},[1741,83903,83904,83906],{},[898,83905,1663],{},[895,83907,83908,83910],{},[1654,83909,2592],{"mathvariant":1878},[1654,83911,2592],{"mathvariant":1878},[1654,83913,1708],{"stretchy":1656},[898,83915,2450],{},[1654,83917,1726],{"stretchy":1656},[1654,83919,3002],{},[1665,83921,2062],{},[902,83923,83924],{"encoding":904},"Q''(L) \u003C 0",[38,83926,46708],{},[883,83928,83930],{"className":83929},[886],[888,83931,83932],{"xmlns":890},[892,83933,83934,83944],{},[895,83935,83936,83938],{},[898,83937,9320],{},[1710,83939,83940,83942],{},[898,83941,1755],{},[898,83943,2450],{},[902,83945,18762],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,83948,83950],{"className":83949},[886],[888,83951,83952],{"xmlns":890},[892,83953,83954,83962],{},[895,83955,83956],{},[1710,83957,83958,83960],{},[898,83959,2450],{},[1665,83961,1667],{},[902,83963,21921],{"encoding":904},[883,83965,83967],{"className":83966},[886],[888,83968,83969],{"xmlns":890},[892,83970,83971,83995],{},[895,83972,83973,83975,83981,83983,83989,83991,83993],{},[898,83974,9320],{},[1710,83976,83977,83979],{},[898,83978,1755],{},[898,83980,2450],{},[1654,83982,1708],{"stretchy":1656},[1710,83984,83985,83987],{},[898,83986,2450],{},[1665,83988,1667],{},[1654,83990,1726],{"stretchy":1656},[1654,83992,1750],{},[1665,83994,2062],{},[902,83996,83997],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,84000,84002],{"className":84001},[886],[888,84003,84004],{"xmlns":890},[892,84005,84006,84014],{},[895,84007,84008],{},[1710,84009,84010,84012],{},[898,84011,2450],{},[1665,84013,2062],{},[902,84015,83778],{"encoding":904},[38,84017,84018],{},"inflexním bodem"," produkční funkce.",[724,84021,84022,84023,19111,84040,2138],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,84024,84026],{"className":84025},[886],[888,84027,84028],{"xmlns":890},[892,84029,84030,84038],{},[895,84031,84032],{},[1710,84033,84034,84036],{},[898,84035,2450],{},[1665,84037,2062],{},[902,84039,83778],{"encoding":904},[883,84041,84043],{"className":84042},[886],[888,84044,84045],{"xmlns":890},[892,84046,84047,84069],{},[895,84048,84049,84059,84061,84063,84065,84067],{},[1741,84050,84051,84053],{},[898,84052,1663],{},[895,84054,84055,84057],{},[1654,84056,2592],{"mathvariant":1878},[1654,84058,2592],{"mathvariant":1878},[1654,84060,1708],{"stretchy":1656},[898,84062,2450],{},[1654,84064,1726],{"stretchy":1656},[1654,84066,3002],{},[1665,84068,2062],{},[902,84070,83924],{"encoding":904},[724,84072,84073,2186,84076,14398,84116,1343,84133,84150],{},[38,84074,84075],{},"Typický polynom třetího stupně:",[883,84077,84079],{"className":84078},[886],[888,84080,84081],{"xmlns":890},[892,84082,84083,84113],{},[895,84084,84085,84087,84089,84091,84093,84095,84097,84103,84105,84107],{},[898,84086,1663],{},[1654,84088,1708],{"stretchy":1656},[898,84090,2450],{},[1654,84092,1726],{"stretchy":1656},[1654,84094,1750],{},[898,84096,207],{},[1741,84098,84099,84101],{},[898,84100,2450],{},[1665,84102,4035],{},[1654,84104,1766],{},[898,84106,9758],{},[1741,84108,84109,84111],{},[898,84110,2450],{},[1665,84112,1681],{},[902,84114,84115],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,84117,84119],{"className":84118},[886],[888,84120,84121],{"xmlns":890},[892,84122,84123,84131],{},[895,84124,84125,84127,84129],{},[898,84126,207],{},[1654,84128,3002],{},[1665,84130,2062],{},[902,84132,51305],{"encoding":904},[883,84134,84136],{"className":84135},[886],[888,84137,84138],{"xmlns":890},[892,84139,84140,84148],{},[895,84141,84142,84144,84146],{},[898,84143,9758],{},[1654,84145,2952],{},[1665,84147,2062],{},[902,84149,27510],{"encoding":904},". Pak",[883,84152,84154],{"className":84153},[886],[888,84155,84156],{"xmlns":890,"display":1956},[892,84157,84158,84218],{},[895,84159,84160,84166,84168,84170,84178,84186,84188,84190,84196,84198,84200,84208,84216],{},[1710,84161,84162,84164],{},[898,84163,2450],{},[1665,84165,2062],{},[1654,84167,1750],{},[1654,84169,2380],{},[2582,84171,84172],{"scriptlevel":2062,"displaystyle":1656},[2811,84173,84174,84176],{},[1665,84175,1667],{},[1665,84177,4035],{},[2582,84179,84180],{"scriptlevel":2062,"displaystyle":1656},[2811,84181,84182,84184],{},[898,84183,9758],{},[898,84185,207],{},[1654,84187,1674],{"separator":1673},[5008,84189],{"width":14608},[1710,84191,84192,84194],{},[898,84193,2450],{},[1665,84195,1667],{},[1654,84197,1750],{},[1654,84199,2380],{},[2582,84201,84202],{"scriptlevel":2062,"displaystyle":1656},[2811,84203,84204,84206],{},[1665,84205,1681],{},[1665,84207,4035],{},[2582,84209,84210],{"scriptlevel":2062,"displaystyle":1656},[2811,84211,84212,84214],{},[898,84213,9758],{},[898,84215,207],{},[898,84217,2138],{"mathvariant":1878},[902,84219,84220],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,84222,84224,84225,1726],{"id":84223},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,84226,84228],{"className":84227},[886],[888,84229,84230],{"xmlns":890},[892,84231,84232,84242],{},[895,84233,84234,84236],{},[898,84235,4737],{},[1710,84237,84238,84240],{},[898,84239,1755],{},[898,84241,2450],{},[902,84243,82853],{"encoding":904},[724,84245,84246,18742,84249,83317,84252,84271],{},[38,84247,84248],{},"Průměrný produkt práce",[614,84250,84251],{},"average product of labour",[883,84253,84255],{"className":84254},[886],[888,84256,84257],{"xmlns":890},[892,84258,84259,84269],{},[895,84260,84261,84263],{},[898,84262,4737],{},[1710,84264,84265,84267],{},[898,84266,1755],{},[898,84268,2450],{},[902,84270,82853],{"encoding":904}," je podíl produkce a práce:",[883,84273,84275],{"className":84274},[886],[888,84276,84277],{"xmlns":890,"display":1956},[892,84278,84279,84314],{},[1960,84280,84281],{"width":1962},[1964,84282,84283,84285,84307,84309],{},[1967,84284],{"width":1969},[1967,84286,84287],{},[895,84288,84289,84291,84297,84299,84305],{},[898,84290,4737],{},[1710,84292,84293,84295],{},[898,84294,1755],{},[898,84296,2450],{},[1654,84298,1750],{},[2811,84300,84301,84303],{},[898,84302,1663],{},[898,84304,2450],{},[898,84306,2138],{"mathvariant":1878},[1967,84308],{"width":1969},[1967,84310,84311],{},[1865,84312,84313],{},"(5.4)",[902,84315,84316],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,84318,84319,84320,2138],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,84321,84323],{"className":84322},[886],[888,84324,84325],{"xmlns":890},[892,84326,84327,84337],{},[895,84328,84329,84331],{},[898,84330,4737],{},[1710,84332,84333,84335],{},[898,84334,1755],{},[898,84336,2450],{},[902,84338,82853],{"encoding":904},[115,84340,84342],{"id":84341},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,84344,84345],{},[3492,84346],{"alt":84347,"className":84348,"src":84349},"imek-q-mpl-apl-tripanel",[210,3496],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[2140,84351,84352],{},[724,84353,84354,84357,84358,11387,84377,84394,84395],{},[38,84355,84356],{},"Princip:"," Má-li ",[883,84359,84361],{"className":84360},[886],[888,84362,84363],{"xmlns":890},[892,84364,84365,84375],{},[895,84366,84367,84369],{},[898,84368,4737],{},[1710,84370,84371,84373],{},[898,84372,1755],{},[898,84374,2450],{},[902,84376,82853],{"encoding":904},[883,84378,84380],{"className":84379},[886],[888,84381,84382],{"xmlns":890},[892,84383,84384,84392],{},[895,84385,84386],{},[1710,84387,84388,84390],{},[898,84389,2450],{},[1665,84391,2062],{},[902,84393,83778],{"encoding":904}," maximum, pak platí\n",[883,84396,84398],{"className":84397,"title":12941,"style":12942},[12940],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,84400,84401,84402,84405,84406,2186,84410,2138],{},"Slovně: ",[38,84403,84404],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,84407,84409],{"className":84408,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,84411,84413],{"className":84412},[886],[888,84414,84415],{"xmlns":890},[892,84416,84417,84423],{},[895,84418,84419,84421],{},[898,84420,4737],{},[898,84422,11539],{},[902,84424,63780],{"encoding":904},[2140,84426,84427,84451],{},[724,84428,84429,84431,84432],{},[883,84430,3111],{}," Postup — jak najít max ",[883,84433,84435],{"className":84434},[886],[888,84436,84437],{"xmlns":890},[892,84438,84439,84449],{},[895,84440,84441,84443],{},[898,84442,4737],{},[1710,84444,84445,84447],{},[898,84446,1755],{},[898,84448,2450],{},[902,84450,82853],{"encoding":904},[152,84452,84453,84491,84573],{},[123,84454,84455,84456,84490],{},"Napište ",[883,84457,84459],{"className":84458},[886],[888,84460,84461],{"xmlns":890},[892,84462,84463,84487],{},[895,84464,84465,84467,84473,84475,84477,84479,84481,84483,84485],{},[898,84466,4737],{},[1710,84468,84469,84471],{},[898,84470,1755],{},[898,84472,2450],{},[1654,84474,1750],{},[898,84476,1663],{},[1654,84478,1708],{"stretchy":1656},[898,84480,2450],{},[1654,84482,1726],{"stretchy":1656},[898,84484,1879],{"mathvariant":1878},[898,84486,2450],{},[902,84488,84489],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,84492,84493,84494,84526,84527,84530,84531,2138],{},"Položte ",[883,84495,84497],{"className":84496},[886],[888,84498,84499],{"xmlns":890},[892,84500,84501,84523],{},[895,84502,84503,84505,84507,84513,84519,84521],{},[1654,84504,1708],{"stretchy":1656},[898,84506,4737],{},[1710,84508,84509,84511],{},[898,84510,1755],{},[898,84512,2450],{},[1741,84514,84515,84517],{},[1654,84516,1726],{"stretchy":1656},[1654,84518,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,84520,1750],{},[1665,84522,2062],{},[902,84524,84525],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,84528,84529],{},"Zkratka:"," můžete rovnou řešit ",[883,84532,84534],{"className":84533},[886],[888,84535,84536],{"xmlns":890},[892,84537,84538,84570],{},[895,84539,84540,84542,84548,84550,84552,84554,84556,84558,84564,84566,84568],{},[898,84541,9320],{},[1710,84543,84544,84546],{},[898,84545,1755],{},[898,84547,2450],{},[1654,84549,1708],{"stretchy":1656},[898,84551,2450],{},[1654,84553,1726],{"stretchy":1656},[1654,84555,1750],{},[898,84557,4737],{},[1710,84559,84560,84562],{},[898,84561,1755],{},[898,84563,2450],{},[1654,84565,1708],{"stretchy":1656},[898,84567,2450],{},[1654,84569,1726],{"stretchy":1656},[902,84571,84572],{"encoding":904},"MP_L(L) = AP_L(L)",[123,84574,84575],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,84577,73721],{"id":84578},"odvození",[724,84580,84581,84582,84615],{},"Z ",[883,84583,84585],{"className":84584},[886],[888,84586,84587],{"xmlns":890},[892,84588,84589,84613],{},[895,84590,84591,84593,84599,84601,84603,84605,84607,84609,84611],{},[898,84592,4737],{},[1710,84594,84595,84597],{},[898,84596,1755],{},[898,84598,2450],{},[1654,84600,1750],{},[898,84602,1663],{},[1654,84604,1708],{"stretchy":1656},[898,84606,2450],{},[1654,84608,1726],{"stretchy":1656},[898,84610,1879],{"mathvariant":1878},[898,84612,2450],{},[902,84614,84489],{"encoding":904}," a derivace podílu:",[883,84617,84619],{"className":84618},[886],[888,84620,84621],{"xmlns":890,"display":1956},[892,84622,84623,84776],{},[895,84624,84625,84627,84629,84635,84641,84643,84645,84647,84649,84689,84691,84697,84731,84733,84739,84742,84744,84750,84752,84754,84756,84758,84760,84766,84768,84770,84772,84774],{},[1654,84626,1708],{"stretchy":1656},[898,84628,4737],{},[1710,84630,84631,84633],{},[898,84632,1755],{},[898,84634,2450],{},[1741,84636,84637,84639],{},[1654,84638,1726],{"stretchy":1656},[1654,84640,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,84642,1708],{"stretchy":1656},[898,84644,2450],{},[1654,84646,1726],{"stretchy":1656},[1654,84648,1750],{},[2811,84650,84651,84683],{},[895,84652,84653,84659,84661,84663,84665,84667,84669,84671,84673,84675,84677,84679,84681],{},[1741,84654,84655,84657],{},[898,84656,1663],{},[1654,84658,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,84660,1708],{"stretchy":1656},[898,84662,2450],{},[1654,84664,1726],{"stretchy":1656},[1654,84666,4554],{},[898,84668,2450],{},[1654,84670,2380],{},[898,84672,1663],{},[1654,84674,1708],{"stretchy":1656},[898,84676,2450],{},[1654,84678,1726],{"stretchy":1656},[1654,84680,4554],{},[1665,84682,1667],{},[1741,84684,84685,84687],{},[898,84686,2450],{},[1665,84688,1681],{},[1654,84690,1750],{},[2811,84692,84693,84695],{},[1665,84694,1667],{},[898,84696,2450],{},[895,84698,84699,84701,84707,84709,84711,84713,84715,84729],{},[1654,84700,1708],{"fence":1673},[1741,84702,84703,84705],{},[898,84704,1663],{},[1654,84706,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,84708,1708],{"stretchy":1656},[898,84710,2450],{},[1654,84712,1726],{"stretchy":1656},[1654,84714,2380],{},[2811,84716,84717,84727],{},[895,84718,84719,84721,84723,84725],{},[898,84720,1663],{},[1654,84722,1708],{"stretchy":1656},[898,84724,2450],{},[1654,84726,1726],{"stretchy":1656},[898,84728,2450],{},[1654,84730,1726],{"fence":1673},[1654,84732,1750],{},[2811,84734,84735,84737],{},[1665,84736,1667],{},[898,84738,2450],{},[1654,84740,1708],{"fence":1673,"stretchy":1673,"minsize":84741,"maxsize":84741},"1.2em",[898,84743,9320],{},[1710,84745,84746,84748],{},[898,84747,1755],{},[898,84749,2450],{},[1654,84751,1708],{"stretchy":1656},[898,84753,2450],{},[1654,84755,1726],{"stretchy":1656},[1654,84757,2380],{},[898,84759,4737],{},[1710,84761,84762,84764],{},[898,84763,1755],{},[898,84765,2450],{},[1654,84767,1708],{"stretchy":1656},[898,84769,2450],{},[1654,84771,1726],{"stretchy":1656},[1654,84773,1726],{"fence":1673,"stretchy":1673,"minsize":84741,"maxsize":84741},[898,84775,2138],{"mathvariant":1878},[902,84777,84778],{"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).",[724,84780,3806,84781,16828,84803,84886],{},[883,84782,84784],{"className":84783},[886],[888,84785,84786],{"xmlns":890},[892,84787,84788,84800],{},[895,84789,84790,84796,84798],{},[1710,84791,84792,84794],{},[898,84793,2450],{},[1665,84795,2062],{},[1654,84797,2952],{},[1665,84799,2062],{},[902,84801,84802],{"encoding":904},"L_0 > 0",[883,84804,84806],{"className":84805},[886],[888,84807,84808],{"xmlns":890},[892,84809,84810,84883],{},[895,84811,84812,84814,84816,84822,84828,84830,84836,84838,84840,84842,84845,84847,84853,84855,84861,84863,84865,84867,84873,84875,84881],{},[1654,84813,1708],{"stretchy":1656},[898,84815,4737],{},[1710,84817,84818,84820],{},[898,84819,1755],{},[898,84821,2450],{},[1741,84823,84824,84826],{},[1654,84825,1726],{"stretchy":1656},[1654,84827,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,84829,1708],{"stretchy":1656},[1710,84831,84832,84834],{},[898,84833,2450],{},[1665,84835,2062],{},[1654,84837,1726],{"stretchy":1656},[1654,84839,1750],{},[1665,84841,2062],{},[1654,84843,84844],{},"⇔",[898,84846,9320],{},[1710,84848,84849,84851],{},[898,84850,1755],{},[898,84852,2450],{},[1654,84854,1708],{"stretchy":1656},[1710,84856,84857,84859],{},[898,84858,2450],{},[1665,84860,2062],{},[1654,84862,1726],{"stretchy":1656},[1654,84864,1750],{},[898,84866,4737],{},[1710,84868,84869,84871],{},[898,84870,1755],{},[898,84872,2450],{},[1654,84874,1708],{"stretchy":1656},[1710,84876,84877,84879],{},[898,84878,2450],{},[1665,84880,2062],{},[1654,84882,1726],{"stretchy":1656},[902,84884,84885],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,84888,84890],{"id":84889},"příklad-51","Příklad 5.1",[724,84892,84893,84894,2138],{},"Je dána produkce ",[883,84895,84897],{"className":84896},[886],[888,84898,84899],{"xmlns":890},[892,84900,84901,84925],{},[895,84902,84903,84905,84907,84909,84915,84917,84919],{},[898,84904,1663],{},[1654,84906,1750],{},[1665,84908,11015],{},[1741,84910,84911,84913],{},[898,84912,2450],{},[1665,84914,1681],{},[1654,84916,2380],{},[1665,84918,11599],{},[1741,84920,84921,84923],{},[898,84922,2450],{},[1665,84924,4035],{},[902,84926,84927],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,84929,84930,65742,84933,84983,84984,2138],{},[38,84931,84932],{},"(a)",[883,84934,84936],{"className":84935},[886],[888,84937,84938],{"xmlns":890},[892,84939,84940,84980],{},[895,84941,84942,84944,84946,84948,84950,84952,84954,84956,84958,84960,84962,84964,84966,84968,84970,84972,84974,84976,84978],{},[898,84943,2450],{},[1654,84945,1750],{},[1665,84947,1681],{},[1654,84949,1674],{"separator":1673},[1665,84951,4032],{},[1654,84953,1674],{"separator":1673},[1665,84955,14315],{},[1654,84957,1674],{"separator":1673},[1665,84959,4647],{},[1654,84961,1674],{"separator":1673},[1665,84963,31634],{},[1654,84965,1674],{"separator":1673},[1665,84967,12457],{},[1654,84969,1674],{"separator":1673},[1665,84971,4573],{},[1654,84973,1674],{"separator":1673},[1665,84975,46566],{},[1654,84977,1674],{"separator":1673},[1665,84979,4622],{},[902,84981,84982],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,84985,84987],{"className":84986},[886],[888,84988,84989],{"xmlns":890},[892,84990,84991,85001],{},[895,84992,84993,84995],{},[898,84994,9320],{},[1710,84996,84997,84999],{},[898,84998,1755],{},[898,85000,2450],{},[902,85002,18762],{"encoding":904},[724,85004,85005,85006,8923],{},"Podle (5.2): ",[883,85007,85009],{"className":85008},[886],[888,85010,85011],{"xmlns":890},[892,85012,85013,85069],{},[895,85014,85015,85017,85023,85025,85031,85033,85035,85037,85039,85041,85043,85045,85047,85053,85055,85057,85059,85061,85063,85065,85067],{},[898,85016,9320],{},[1710,85018,85019,85021],{},[898,85020,1755],{},[898,85022,2450],{},[1654,85024,1750],{},[1741,85026,85027,85029],{},[898,85028,1663],{},[1654,85030,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,85032,1708],{"stretchy":1656},[898,85034,2450],{},[1654,85036,1726],{"stretchy":1656},[1654,85038,1750],{},[1665,85040,6509],{},[898,85042,2450],{},[1654,85044,2380],{},[1665,85046,28017],{},[1741,85048,85049,85051],{},[898,85050,2450],{},[1665,85052,1681],{},[1654,85054,1750],{},[898,85056,2450],{},[1654,85058,1708],{"stretchy":1656},[1665,85060,6509],{},[1654,85062,2380],{},[1665,85064,28017],{},[898,85066,2450],{},[1654,85068,1726],{"stretchy":1656},[902,85070,85071],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,85073,85074,85111],{},[19,85075,85076],{},[22,85077,85078,85093,85095,85097,85099,85101,85103,85105,85107,85109],{},[25,85079,85080],{},[883,85081,85083],{"className":85082},[886],[888,85084,85085],{"xmlns":890},[892,85086,85087,85091],{},[895,85088,85089],{},[898,85090,2450],{},[902,85092,2450],{"encoding":904},[25,85094,1681],{},[25,85096,4032],{},[25,85098,14315],{},[25,85100,4647],{},[25,85102,31634],{},[25,85104,12457],{},[25,85106,4573],{},[25,85108,46566],{},[25,85110,4622],{},[30,85112,85113],{},[22,85114,85115,85136,85139,85142,85145,85147,85150,85152,85154,85173],{},[35,85116,85117],{},[883,85118,85120],{"className":85119},[886],[888,85121,85122],{"xmlns":890},[892,85123,85124,85134],{},[895,85125,85126,85128],{},[898,85127,9320],{},[1710,85129,85130,85132],{},[898,85131,1755],{},[898,85133,2450],{},[902,85135,18762],{"encoding":904},[35,85137,85138],{},"21,6",[35,85140,85141],{},"45",[35,85143,85144],{},"57,6",[35,85146,11881],{},[35,85148,85149],{},"50,4",[35,85151,85138],{},[35,85153,2062],{},[35,85155,85156],{},[883,85157,85159],{"className":85158},[886],[888,85160,85161],{"xmlns":890},[892,85162,85163,85170],{},[895,85164,85165,85167],{},[1654,85166,2380],{},[1665,85168,85169],{},"12,6",[902,85171,85172],{"encoding":904},"-12{,}6",[35,85174,85175],{},[883,85176,85178],{"className":85177},[886],[888,85179,85180],{"xmlns":890},[892,85181,85182,85188],{},[895,85183,85184,85186],{},[1654,85185,2380],{},[1665,85187,53672],{},[902,85189,85190],{"encoding":904},"-75",[724,85192,85193,85212,85213,85231,85232,85249,85250,85268,85269,85293,85294,85312],{},[883,85194,85196],{"className":85195},[886],[888,85197,85198],{"xmlns":890},[892,85199,85200,85210],{},[895,85201,85202,85204],{},[898,85203,9320],{},[1710,85205,85206,85208],{},[898,85207,1755],{},[898,85209,2450],{},[902,85211,18762],{"encoding":904}," nabývá maxima pro ",[883,85214,85216],{"className":85215},[886],[888,85217,85218],{"xmlns":890},[892,85219,85220,85228],{},[895,85221,85222,85224,85226],{},[898,85223,2450],{},[1654,85225,1750],{},[1665,85227,4647],{},[902,85229,85230],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,85233,85235],{"className":85234},[886],[888,85236,85237],{"xmlns":890},[892,85238,85239,85247],{},[895,85240,85241,85243,85245],{},[898,85242,2450],{},[1654,85244,1750],{},[1665,85246,4647],{},[902,85248,85230],{"encoding":904}," přírůstky klesají, v ",[883,85251,85253],{"className":85252},[886],[888,85254,85255],{"xmlns":890},[892,85256,85257,85265],{},[895,85258,85259,85261,85263],{},[898,85260,2450],{},[1654,85262,1750],{},[1665,85264,4573],{},[902,85266,85267],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,85270,85272],{"className":85271},[886],[888,85273,85274],{"xmlns":890},[892,85275,85276,85290],{},[895,85277,85278,85280,85282,85284,85286,85288],{},[898,85279,1663],{},[1654,85281,1708],{"stretchy":1656},[1665,85283,4573],{},[1654,85285,1726],{"stretchy":1656},[1654,85287,1750],{},[1665,85289,32544],{},[902,85291,85292],{"encoding":904},"Q(20) = 800","), od ",[883,85295,85297],{"className":85296},[886],[888,85298,85299],{"xmlns":890},[892,85300,85301,85309],{},[895,85302,85303,85305,85307],{},[898,85304,2450],{},[1654,85306,2952],{},[1665,85308,4573],{},[902,85310,85311],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,85314,85315],{},[614,85316,85317,85318,85358,85359,11387,85377,2138],{},"Obrázek 5.1 — graf produkce ",[883,85319,85321],{"className":85320},[886],[888,85322,85323],{"xmlns":890},[892,85324,85325,85355],{},[895,85326,85327,85329,85331,85333,85335,85337,85339,85345,85347,85349],{},[898,85328,1663],{},[1654,85330,1708],{"stretchy":1656},[898,85332,2450],{},[1654,85334,1726],{"stretchy":1656},[1654,85336,1750],{},[1665,85338,11015],{},[1741,85340,85341,85343],{},[898,85342,2450],{},[1665,85344,1681],{},[1654,85346,2380],{},[1665,85348,11599],{},[1741,85350,85351,85353],{},[898,85352,2450],{},[1665,85354,4035],{},[902,85356,85357],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,85360,85362],{"className":85361},[886],[888,85363,85364],{"xmlns":890},[892,85365,85366,85374],{},[895,85367,85368,85370,85372],{},[898,85369,1663],{},[1654,85371,1750],{},[1665,85373,32544],{},[902,85375,85376],{"encoding":904},"Q = 800",[883,85378,85380],{"className":85379},[886],[888,85381,85382],{"xmlns":890},[892,85383,85384,85392],{},[895,85385,85386,85388,85390],{},[898,85387,2450],{},[1654,85389,1750],{},[1665,85391,4573],{},[902,85393,85267],{"encoding":904},[724,85395,85396,85399],{},[38,85397,85398],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,85401,85402,85403,1343,85421,2781],{},"Podle (5.3) s ",[883,85404,85406],{"className":85405},[886],[888,85407,85408],{"xmlns":890},[892,85409,85410,85418],{},[895,85411,85412,85414,85416],{},[898,85413,2450],{},[1654,85415,1750],{},[1665,85417,11015],{},[902,85419,85420],{"encoding":904},"L = 6",[883,85422,85424],{"className":85423},[886],[888,85425,85426],{"xmlns":890},[892,85427,85428,85438],{},[895,85429,85430,85432,85434,85436],{},[898,85431,10977],{},[898,85433,2450],{},[1654,85435,1750],{},[1665,85437,4035],{},[902,85439,85440],{"encoding":904},"dL = 3",[883,85442,85444],{"className":85443},[886],[888,85445,85446],{"xmlns":890,"display":1956},[892,85447,85448,85511],{},[895,85449,85450,85452,85454,85456,85458,85464,85466,85468,85470,85472,85474,85476,85478,85480,85482,85484,85486,85488,85490,85492,85494,85496,85498,85500,85502,85504,85506,85508],{},[898,85451,10977],{},[898,85453,1663],{},[1654,85455,1750],{},[898,85457,9320],{},[1710,85459,85460,85462],{},[898,85461,1755],{},[898,85463,2450],{},[1654,85465,1708],{"stretchy":1656},[1665,85467,11015],{},[1654,85469,1726],{"stretchy":1656},[1654,85471,4554],{},[1665,85473,4035],{},[1654,85475,1750],{},[1654,85477,1708],{"stretchy":1656},[1665,85479,6509],{},[1654,85481,4554],{},[1665,85483,11015],{},[1654,85485,2380],{},[1665,85487,28017],{},[1654,85489,4554],{},[1665,85491,14295],{},[1654,85493,1726],{"stretchy":1656},[1654,85495,4554],{},[1665,85497,4035],{},[1654,85499,1750],{},[1665,85501,85149],{},[1654,85503,4554],{},[1665,85505,4035],{},[1654,85507,1750],{},[1665,85509,85510],{},"151,2.",[902,85512,85513],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,85515,85516,85517,65972,85542,85556,85557,2138],{},"Produkce vzroste z ",[883,85518,85520],{"className":85519},[886],[888,85521,85522],{"xmlns":890},[892,85523,85524,85539],{},[895,85525,85526,85528,85530,85532,85534,85536],{},[898,85527,1663],{},[1654,85529,1708],{"stretchy":1656},[1665,85531,11015],{},[1654,85533,1726],{"stretchy":1656},[1654,85535,1750],{},[1665,85537,85538],{},"172,8",[902,85540,85541],{"encoding":904},"Q(6) = 172{,}8",[883,85543,85545],{"className":85544},[886],[888,85546,85547],{"xmlns":890},[892,85548,85549,85554],{},[895,85550,85551],{},[1665,85552,85553],{},"324",[902,85555,85553],{"encoding":904},". Skutečná hodnota: ",[883,85558,85560],{"className":85559},[886],[888,85561,85562],{"xmlns":890},[892,85563,85564,85604],{},[895,85565,85566,85568,85570,85572,85574,85576,85578,85580,85582,85584,85586,85588,85590,85592,85595,85597,85599,85601],{},[898,85567,11648],{"mathvariant":1878},[898,85569,1663],{},[1654,85571,1750],{},[898,85573,1663],{},[1654,85575,1708],{"stretchy":1656},[1665,85577,12742],{},[1654,85579,1726],{"stretchy":1656},[1654,85581,2380],{},[898,85583,1663],{},[1654,85585,1708],{"stretchy":1656},[1665,85587,11015],{},[1654,85589,1726],{"stretchy":1656},[1654,85591,1750],{},[1665,85593,85594],{},"340,2",[1654,85596,2380],{},[1665,85598,85538],{},[1654,85600,1750],{},[1665,85602,85603],{},"167,4",[902,85605,85606],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,85608,85610],{"id":85609},"příklad-52","Příklad 5.2",[724,85612,85613,85614,2138],{},"Ověříme princip (5.5) pro ",[883,85615,85617],{"className":85616},[886],[888,85618,85619],{"xmlns":890},[892,85620,85621,85645],{},[895,85622,85623,85625,85627,85629,85635,85637,85639],{},[898,85624,1663],{},[1654,85626,1750],{},[1665,85628,11015],{},[1741,85630,85631,85633],{},[898,85632,2450],{},[1665,85634,1681],{},[1654,85636,2380],{},[1665,85638,11599],{},[1741,85640,85641,85643],{},[898,85642,2450],{},[1665,85644,4035],{},[902,85646,84927],{"encoding":904},[883,85648,85650],{"className":85649},[886],[888,85651,85652],{"xmlns":890,"display":1956},[892,85653,85654,85732],{},[895,85655,85656,85658,85664,85666,85672,85674,85676,85678,85680,85682,85688,85690,85692,85694,85702,85704,85706,85708,85710,85712,85714,85716,85718,85720,85722,85728,85730],{},[898,85657,4737],{},[1710,85659,85660,85662],{},[898,85661,1755],{},[898,85663,2450],{},[1654,85665,1750],{},[2811,85667,85668,85670],{},[898,85669,1663],{},[898,85671,2450],{},[1654,85673,1750],{},[1665,85675,11015],{},[898,85677,2450],{},[1654,85679,2380],{},[1665,85681,11599],{},[1741,85683,85684,85686],{},[898,85685,2450],{},[1665,85687,1681],{},[1654,85689,1674],{"separator":1673},[5008,85691],{"width":5010},[898,85693,4737],{},[1659,85695,85696,85698,85700],{},[898,85697,1755],{},[898,85699,2450],{},[1654,85701,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,85703,1750],{},[1665,85705,11015],{},[1654,85707,2380],{},[1665,85709,27967],{},[898,85711,2450],{},[1654,85713,1750],{},[1665,85715,2062],{},[1865,85717,2805],{},[1654,85719,8634],{},[1865,85721,2805],{},[1710,85723,85724,85726],{},[898,85725,2450],{},[1665,85727,2062],{},[1654,85729,1750],{},[1665,85731,76503],{},[902,85733,85734],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,85736,85737,85773,85774,85792,85793,2138],{},[883,85738,85740],{"className":85739},[886],[888,85741,85742],{"xmlns":890},[892,85743,85744,85770],{},[895,85745,85746,85748,85760,85762,85764,85766,85768],{},[898,85747,4737],{},[1659,85749,85750,85752,85754],{},[898,85751,1755],{},[898,85753,2450],{},[895,85755,85756,85758],{},[1654,85757,2592],{"mathvariant":1878},[1654,85759,2592],{"mathvariant":1878},[1654,85761,1750],{},[1654,85763,2380],{},[1665,85765,27967],{},[1654,85767,3002],{},[1665,85769,2062],{},[902,85771,85772],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,85775,85777],{"className":85776},[886],[888,85778,85779],{"xmlns":890},[892,85780,85781,85789],{},[895,85782,85783,85785,85787],{},[898,85784,2450],{},[1654,85786,1750],{},[1665,85788,10207],{},[902,85790,85791],{"encoding":904},"L = 15"," je maximum, ",[883,85794,85796],{"className":85795},[886],[888,85797,85798],{"xmlns":890},[892,85799,85800,85846],{},[895,85801,85802,85804,85810,85812,85814,85816,85818,85820,85822,85824,85826,85828,85830,85833,85835,85838,85840,85842,85844],{},[898,85803,4737],{},[1710,85805,85806,85808],{},[898,85807,1755],{},[898,85809,2450],{},[1654,85811,1708],{"stretchy":1656},[1665,85813,10207],{},[1654,85815,1726],{"stretchy":1656},[1654,85817,1750],{},[1665,85819,11015],{},[1654,85821,4554],{},[1665,85823,10207],{},[1654,85825,2380],{},[1665,85827,11599],{},[1654,85829,4554],{},[1665,85831,85832],{},"225",[1654,85834,1750],{},[1665,85836,85837],{},"90",[1654,85839,2380],{},[1665,85841,85141],{},[1654,85843,1750],{},[1665,85845,85141],{},[902,85847,85848],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,85850,85851,50100,85907,85953],{},[883,85852,85854],{"className":85853},[886],[888,85855,85856],{"xmlns":890},[892,85857,85858,85904],{},[895,85859,85860,85862,85868,85870,85872,85874,85876,85878,85880,85882,85884,85886,85888,85890,85892,85895,85897,85900,85902],{},[898,85861,9320],{},[1710,85863,85864,85866],{},[898,85865,1755],{},[898,85867,2450],{},[1654,85869,1708],{"stretchy":1656},[1665,85871,10207],{},[1654,85873,1726],{"stretchy":1656},[1654,85875,1750],{},[1665,85877,6509],{},[1654,85879,4554],{},[1665,85881,10207],{},[1654,85883,2380],{},[1665,85885,28017],{},[1654,85887,4554],{},[1665,85889,85832],{},[1654,85891,1750],{},[1665,85893,85894],{},"180",[1654,85896,2380],{},[1665,85898,85899],{},"135",[1654,85901,1750],{},[1665,85903,85141],{},[902,85905,85906],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,85908,85910],{"className":85909},[886],[888,85911,85912],{"xmlns":890},[892,85913,85914,85950],{},[895,85915,85916,85918,85924,85926,85928,85930,85932,85934,85940,85942,85944,85946,85948],{},[898,85917,9320],{},[1710,85919,85920,85922],{},[898,85921,1755],{},[898,85923,2450],{},[1654,85925,1708],{"stretchy":1656},[1665,85927,10207],{},[1654,85929,1726],{"stretchy":1656},[1654,85931,1750],{},[898,85933,4737],{},[1710,85935,85936,85938],{},[898,85937,1755],{},[898,85939,2450],{},[1654,85941,1708],{"stretchy":1656},[1665,85943,10207],{},[1654,85945,1726],{"stretchy":1656},[1654,85947,1750],{},[1665,85949,85141],{},[902,85951,85952],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,85955,85956,85959,85960,7515,85989,2138],{},[38,85957,85958],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,85961,85963],{"className":85962},[886],[888,85964,85965],{"xmlns":890},[892,85966,85967,85987],{},[895,85968,85969,85971,85977,85979,85981],{},[898,85970,9320],{},[1710,85972,85973,85975],{},[898,85974,1755],{},[898,85976,2450],{},[1654,85978,1750],{},[898,85980,4737],{},[1710,85982,85983,85985],{},[898,85984,1755],{},[898,85986,2450],{},[902,85988,82883],{"encoding":904},[883,85990,85992],{"className":85991},[886],[888,85993,85994],{"xmlns":890},[892,85995,85996,86036],{},[895,85997,85998,86000,86002,86004,86006,86012,86014,86016,86018,86020,86022,86028,86030,86032,86034],{},[1665,85999,6509],{},[898,86001,2450],{},[1654,86003,2380],{},[1665,86005,28017],{},[1741,86007,86008,86010],{},[898,86009,2450],{},[1665,86011,1681],{},[1654,86013,1750],{},[1665,86015,11015],{},[898,86017,2450],{},[1654,86019,2380],{},[1665,86021,11599],{},[1741,86023,86024,86026],{},[898,86025,2450],{},[1665,86027,1681],{},[1654,86029,8634],{},[898,86031,2450],{},[1654,86033,1750],{},[1665,86035,10207],{},[902,86037,86038],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,86040,86041],{},[614,86042,86043,86044,86063,86064,20840,86082,86101,86102,86120,86121,86138,86139,86158,86159,86178],{},"Obrázek 5.3 — křivky ",[883,86045,86047],{"className":86046},[886],[888,86048,86049],{"xmlns":890},[892,86050,86051,86061],{},[895,86052,86053,86055],{},[898,86054,9320],{},[1710,86056,86057,86059],{},[898,86058,1755],{},[898,86060,2450],{},[902,86062,18762],{"encoding":904}," (max 60 při ",[883,86065,86067],{"className":86066},[886],[888,86068,86069],{"xmlns":890},[892,86070,86071,86079],{},[895,86072,86073,86075,86077],{},[898,86074,2450],{},[1654,86076,1750],{},[1665,86078,4647],{},[902,86080,86081],{"encoding":904},"L=10",[883,86083,86085],{"className":86084},[886],[888,86086,86087],{"xmlns":890},[892,86088,86089,86099],{},[895,86090,86091,86093],{},[898,86092,4737],{},[1710,86094,86095,86097],{},[898,86096,1755],{},[898,86098,2450],{},[902,86100,82853],{"encoding":904}," (max 45 při ",[883,86103,86105],{"className":86104},[886],[888,86106,86107],{"xmlns":890},[892,86108,86109,86117],{},[895,86110,86111,86113,86115],{},[898,86112,2450],{},[1654,86114,1750],{},[1665,86116,10207],{},[902,86118,86119],{"encoding":904},"L=15","), průsečík v ",[883,86122,86124],{"className":86123},[886],[888,86125,86126],{"xmlns":890},[892,86127,86128,86136],{},[895,86129,86130,86132,86134],{},[898,86131,2450],{},[1654,86133,1750],{},[1665,86135,10207],{},[902,86137,85791],{"encoding":904},". Nalevo od 15 leží ",[883,86140,86142],{"className":86141},[886],[888,86143,86144],{"xmlns":890},[892,86145,86146,86156],{},[895,86147,86148,86150],{},[898,86149,9320],{},[1710,86151,86152,86154],{},[898,86153,1755],{},[898,86155,2450],{},[902,86157,18762],{"encoding":904}," nad ",[883,86160,86162],{"className":86161},[886],[888,86163,86164],{"xmlns":890},[892,86165,86166,86176],{},[895,86167,86168,86170],{},[898,86169,4737],{},[1710,86171,86172,86174],{},[898,86173,1755],{},[898,86175,2450],{},[902,86177,82853],{"encoding":904},", napravo pod ní.",[115,86180,86182],{"id":86181},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,86184,86185,86186,11448,86199,2186,86202,14918,86215,2186,86218,2781],{},"V dvoufaktorovém modelu závisí produkce ",[883,86187,86189],{"className":86188},[886],[888,86190,86191],{"xmlns":890},[892,86192,86193,86197],{},[895,86194,86195],{},[898,86196,1663],{},[902,86198,1663],{"encoding":904},[38,86200,86201],{},"práci",[883,86203,86205],{"className":86204},[886],[888,86206,86207],{"xmlns":890},[892,86208,86209,86213],{},[895,86210,86211],{},[898,86212,2450],{},[902,86214,2450],{"encoding":904},[38,86216,86217],{},"kapitálu",[883,86219,86221],{"className":86220},[886],[888,86222,86223],{"xmlns":890},[892,86224,86225,86229],{},[895,86226,86227],{},[898,86228,18517],{},[902,86230,18517],{"encoding":904},[883,86232,86234],{"className":86233},[886],[888,86235,86236],{"xmlns":890,"display":1956},[892,86237,86238,86273],{},[1960,86239,86240],{"width":1962},[1964,86241,86242,86244,86266,86268],{},[1967,86243],{"width":1969},[1967,86245,86246],{},[895,86247,86248,86250,86252,86254,86256,86258,86260,86262,86264],{},[898,86249,1663],{},[1654,86251,1750],{},[898,86253,1663],{},[1654,86255,1708],{"stretchy":1656},[898,86257,2450],{},[1654,86259,1674],{"separator":1673},[898,86261,18517],{},[1654,86263,1726],{"stretchy":1656},[898,86265,2138],{"mathvariant":1878},[1967,86267],{"width":1969},[1967,86269,86270],{},[1865,86271,86272],{},"(5.6)",[902,86274,86275],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,86277,86278,86279,86281],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,86280,83220],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,86283,86285],{"id":86284},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,86287,86288],{},"Široce používané produkční funkce mají tvar",[883,86290,86292],{"className":86291},[886],[888,86293,86294],{"xmlns":890,"display":1956},[892,86295,86296,86337],{},[1960,86297,86298],{"width":1962},[1964,86299,86300,86302,86330,86332],{},[1967,86301],{"width":1969},[1967,86303,86304],{},[895,86305,86306,86308,86310,86312,86314,86320,86322,86328],{},[898,86307,1663],{},[1654,86309,1750],{},[898,86311,4737],{},[1865,86313,11744],{},[1741,86315,86316,86318],{},[898,86317,2450],{},[898,86319,207],{},[1865,86321,11744],{},[1741,86323,86324,86326],{},[898,86325,18517],{},[898,86327,9758],{},[1654,86329,1674],{"separator":1673},[1967,86331],{"width":1969},[1967,86333,86334],{},[1865,86335,86336],{},"(5.7)",[902,86338,86339],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,86341,13049,86342,86364,86365,86367,86368,2138],{},[883,86343,86345],{"className":86344},[886],[888,86346,86347],{"xmlns":890},[892,86348,86349,86361],{},[895,86350,86351,86353,86355,86357,86359],{},[898,86352,4737],{},[1654,86354,1674],{"separator":1673},[898,86356,207],{},[1654,86358,1674],{"separator":1673},[898,86360,9758],{},[902,86362,86363],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,86366,82919],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,86369,86371],{"className":86370},[886],[888,86372,86373],{"xmlns":890},[892,86374,86375,86387],{},[895,86376,86377,86379,86381,86383,86385],{},[898,86378,207],{},[1654,86380,1674],{"separator":1673},[898,86382,9758],{},[1654,86384,3002],{},[1665,86386,1667],{},[902,86388,86389],{"encoding":904},"a, b \u003C 1",[724,86391,86392],{},[3492,86393],{"alt":86394,"className":86395,"src":86396},"imek-vynosy-z-rozsahu-3typy",[210,3496],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,86398,86399,86400,86403,86404,11448,86417,86433,86434,11448,86447,2781],{},"Reflektují ekonomickou zákonitost, že ",[38,86401,86402],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,86405,86407],{"className":86406},[886],[888,86408,86409],{"xmlns":890},[892,86410,86411,86415],{},[895,86412,86413],{},[898,86414,2450],{},[902,86416,2450],{"encoding":904},[883,86418,86420],{"className":86419},[886],[888,86421,86422],{"xmlns":890},[892,86423,86424,86430],{},[895,86425,86426,86428],{},[898,86427,20753],{},[898,86429,2450],{},[902,86431,86432],{"encoding":904},"rL"," a kapitál z ",[883,86435,86437],{"className":86436},[886],[888,86438,86439],{"xmlns":890},[892,86440,86441,86445],{},[895,86442,86443],{},[898,86444,18517],{},[902,86446,18517],{"encoding":904},[883,86448,86450],{"className":86449},[886],[888,86451,86452],{"xmlns":890},[892,86453,86454,86460],{},[895,86455,86456,86458],{},[898,86457,20753],{},[898,86459,18517],{},[902,86461,86462],{"encoding":904},"rK",[883,86464,86466],{"className":86465},[886],[888,86467,86468],{"xmlns":890,"display":1956},[892,86469,86470,86593],{},[1960,86471,86472],{"width":1962},[1964,86473,86474,86476,86586,86588],{},[1967,86475],{"width":1969},[1967,86477,86478],{},[895,86479,86480,86482,86484,86486,86488,86490,86492,86494,86496,86498,86500,86502,86504,86506,86512,86514,86516,86518,86524,86526,86528,86530,86542,86544,86550,86556,86558,86570,86572,86574,86576,86578,86580,86582,86584],{},[898,86481,1663],{},[1654,86483,1708],{"stretchy":1656},[898,86485,20753],{},[898,86487,2450],{},[1654,86489,1674],{"separator":1673},[898,86491,20753],{},[898,86493,18517],{},[1654,86495,1726],{"stretchy":1656},[1654,86497,1750],{},[898,86499,4737],{},[1654,86501,1708],{"stretchy":1656},[898,86503,20753],{},[898,86505,2450],{},[1741,86507,86508,86510],{},[1654,86509,1726],{"stretchy":1656},[898,86511,207],{},[1654,86513,1708],{"stretchy":1656},[898,86515,20753],{},[898,86517,18517],{},[1741,86519,86520,86522],{},[1654,86521,1726],{"stretchy":1656},[898,86523,9758],{},[1654,86525,1750],{},[898,86527,4737],{},[1865,86529,11744],{},[1741,86531,86532,86534],{},[898,86533,20753],{},[895,86535,86536,86538,86540],{},[898,86537,207],{},[1654,86539,1766],{},[898,86541,9758],{},[1865,86543,11744],{},[1741,86545,86546,86548],{},[898,86547,2450],{},[898,86549,207],{},[1741,86551,86552,86554],{},[898,86553,18517],{},[898,86555,9758],{},[1654,86557,1750],{},[1741,86559,86560,86562],{},[898,86561,20753],{},[895,86563,86564,86566,86568],{},[898,86565,207],{},[1654,86567,1766],{},[898,86569,9758],{},[1865,86571,11744],{},[898,86573,1663],{},[1654,86575,1708],{"stretchy":1656},[898,86577,2450],{},[1654,86579,1674],{"separator":1673},[898,86581,18517],{},[1654,86583,1726],{"stretchy":1656},[898,86585,2138],{"mathvariant":1878},[1967,86587],{"width":1969},[1967,86589,86590],{},[1865,86591,86592],{},"(5.8)",[902,86594,86595],{"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}",[724,86597,86598,86599],{},"Volně: ",[38,86600,86601,86602,86615,86616,86640],{},"změní-li se vstupy ",[883,86603,86605],{"className":86604},[886],[888,86606,86607],{"xmlns":890},[892,86608,86609,86613],{},[895,86610,86611],{},[898,86612,20753],{},[902,86614,20753],{"encoding":904},"-krát, změní se výstup ",[883,86617,86619],{"className":86618},[886],[888,86620,86621],{"xmlns":890},[892,86622,86623,86637],{},[895,86624,86625],{},[1741,86626,86627,86629],{},[898,86628,20753],{},[895,86630,86631,86633,86635],{},[898,86632,207],{},[1654,86634,1766],{},[898,86636,9758],{},[902,86638,86639],{"encoding":904},"r^{a+b}","-krát.",[198,86642,86644],{"id":86643},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,86646,86647,86648,86665],{},"Součet exponentů ",[883,86649,86651],{"className":86650},[886],[888,86652,86653],{"xmlns":890},[892,86654,86655,86663],{},[895,86656,86657,86659,86661],{},[898,86658,207],{},[1654,86660,1766],{},[898,86662,9758],{},[902,86664,83044],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,86667,86668,86697],{},[19,86669,86670],{},[22,86671,86672,86675,86678,86695],{},[25,86673,86674],{},"Typ",[25,86676,86677],{},"Podmínka",[25,86679,86680,86681,86694],{},"Chování produkce při ",[883,86682,86684],{"className":86683},[886],[888,86685,86686],{"xmlns":890},[892,86687,86688,86692],{},[895,86689,86690],{},[898,86691,20753],{},[902,86693,20753],{"encoding":904},"-násobném zvýšení vstupů",[25,86696,11827],{},[30,86698,86699,86810,86925],{},[22,86700,86701,86709,86733,86766],{},[35,86702,83757,86703,18742,86706,1726],{},[38,86704,86705],{},"Konstantní",[614,86707,86708],{},"constant returns",[35,86710,86711],{},[883,86712,86714],{"className":86713},[886],[888,86715,86716],{"xmlns":890},[892,86717,86718,86730],{},[895,86719,86720,86722,86724,86726,86728],{},[898,86721,207],{},[1654,86723,1766],{},[898,86725,9758],{},[1654,86727,1750],{},[1665,86729,1667],{},[902,86731,86732],{"encoding":904},"a+b = 1",[35,86734,86735,86748,86749,2186,86752,86765],{},[883,86736,86738],{"className":86737},[886],[888,86739,86740],{"xmlns":890},[892,86741,86742,86746],{},[895,86743,86744],{},[898,86745,1663],{},[902,86747,1663],{"encoding":904}," vzroste ",[38,86750,86751],{},"přesně",[883,86753,86755],{"className":86754},[886],[888,86756,86757],{"xmlns":890},[892,86758,86759,86763],{},[895,86760,86761],{},[898,86762,20753],{},[902,86764,20753],{"encoding":904},"-krát",[35,86767,86768],{},[883,86769,86771],{"className":86770},[886],[888,86772,86773],{"xmlns":890},[892,86774,86775,86807],{},[895,86776,86777,86779,86781,86783,86795],{},[898,86778,1663],{},[1654,86780,1750],{},[1665,86782,1681],{},[1741,86784,86785,86787],{},[898,86786,2450],{},[895,86788,86789,86791,86793],{},[1665,86790,1667],{},[898,86792,1879],{"mathvariant":1878},[1665,86794,7631],{},[1741,86796,86797,86799],{},[898,86798,18517],{},[895,86800,86801,86803,86805],{},[1665,86802,4035],{},[898,86804,1879],{"mathvariant":1878},[1665,86806,7631],{},[902,86808,86809],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,86811,86812,86821,86845,86875],{},[35,86813,86814,86815,18742,86818,1726],{},"2° ",[38,86816,86817],{},"Rostoucí",[614,86819,86820],{},"increasing returns",[35,86822,86823],{},[883,86824,86826],{"className":86825},[886],[888,86827,86828],{"xmlns":890},[892,86829,86830,86842],{},[895,86831,86832,86834,86836,86838,86840],{},[898,86833,207],{},[1654,86835,1766],{},[898,86837,9758],{},[1654,86839,2952],{},[1665,86841,1667],{},[902,86843,86844],{"encoding":904},"a+b > 1",[35,86846,86847,86748,86860,59451,86862,86765],{},[883,86848,86850],{"className":86849},[886],[888,86851,86852],{"xmlns":890},[892,86853,86854,86858],{},[895,86855,86856],{},[898,86857,1663],{},[902,86859,1663],{"encoding":904},[38,86861,33956],{},[883,86863,86865],{"className":86864},[886],[888,86866,86867],{"xmlns":890},[892,86868,86869,86873],{},[895,86870,86871],{},[898,86872,20753],{},[902,86874,20753],{"encoding":904},[35,86876,86877,18742,86903,1726],{},[883,86878,86880],{"className":86879},[886],[888,86881,86882],{"xmlns":890},[892,86883,86884,86900],{},[895,86885,86886,86888,86890,86892,86894],{},[898,86887,1663],{},[1654,86889,1750],{},[1665,86891,32887],{},[898,86893,2450],{},[1741,86895,86896,86898],{},[898,86897,18517],{},[1665,86899,1681],{},[902,86901,86902],{"encoding":904},"Q = 7LK^2",[883,86904,86906],{"className":86905},[886],[888,86907,86908],{"xmlns":890},[892,86909,86910,86922],{},[895,86911,86912,86914,86916,86918,86920],{},[898,86913,207],{},[1654,86915,1766],{},[898,86917,9758],{},[1654,86919,1750],{},[1665,86921,4035],{},[902,86923,86924],{"encoding":904},"a+b = 3",[22,86926,86927,86936,86960,86991],{},[35,86928,86929,86930,18742,86933,1726],{},"3° ",[38,86931,86932],{},"Klesající",[614,86934,86935],{},"decreasing returns",[35,86937,86938],{},[883,86939,86941],{"className":86940},[886],[888,86942,86943],{"xmlns":890},[892,86944,86945,86957],{},[895,86946,86947,86949,86951,86953,86955],{},[898,86948,207],{},[1654,86950,1766],{},[898,86952,9758],{},[1654,86954,3002],{},[1665,86956,1667],{},[902,86958,86959],{"encoding":904},"a+b \u003C 1",[35,86961,86962,86748,86975,59451,86978,86765],{},[883,86963,86965],{"className":86964},[886],[888,86966,86967],{"xmlns":890},[892,86968,86969,86973],{},[895,86970,86971],{},[898,86972,1663],{},[902,86974,1663],{"encoding":904},[38,86976,86977],{},"méně",[883,86979,86981],{"className":86980},[886],[888,86982,86983],{"xmlns":890},[892,86984,86985,86989],{},[895,86986,86987],{},[898,86988,20753],{},[902,86990,20753],{"encoding":904},[35,86992,86993,18742,87023,1726],{},[883,86994,86996],{"className":86995},[886],[888,86997,86998],{"xmlns":890},[892,86999,87000,87020],{},[895,87001,87002,87004,87006,87008,87014],{},[898,87003,1663],{},[1654,87005,1750],{},[1665,87007,4647],{},[1741,87009,87010,87012],{},[898,87011,2450],{},[1665,87013,76431],{},[1741,87015,87016,87018],{},[898,87017,18517],{},[1665,87019,7594],{},[902,87021,87022],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,87024,87026],{"className":87025},[886],[888,87027,87028],{"xmlns":890},[892,87029,87030,87042],{},[895,87031,87032,87034,87036,87038,87040],{},[898,87033,207],{},[1654,87035,1766],{},[898,87037,9758],{},[1654,87039,1750],{},[1665,87041,23298],{},[902,87043,87044],{"encoding":904},"a+b = 0{,}8",[2140,87046,87047],{},[724,87048,87049,87051,87052,87069,87070,87073,87074,2186,87077,87113,87114,87136,87137,2138],{},[883,87050,2146],{}," Pozor\nSoučet ",[883,87053,87055],{"className":87054},[886],[888,87056,87057],{"xmlns":890},[892,87058,87059,87067],{},[895,87060,87061,87063,87065],{},[898,87062,207],{},[1654,87064,1766],{},[898,87066,9758],{},[902,87068,83044],{"encoding":904}," neudává velikost produkce, ale ",[38,87071,87072],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,87075,87076],{},"ryzí Cobb-Douglas",[883,87078,87080],{"className":87079},[886],[888,87081,87082],{"xmlns":890},[892,87083,87084,87110],{},[895,87085,87086,87088,87090,87092,87098],{},[898,87087,1663],{},[1654,87089,1750],{},[898,87091,4737],{},[1741,87093,87094,87096],{},[898,87095,2450],{},[898,87097,207],{},[1741,87099,87100,87102],{},[898,87101,18517],{},[895,87103,87104,87106,87108],{},[1665,87105,1667],{},[1654,87107,2380],{},[898,87109,207],{},[902,87111,87112],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,87115,87117],{"className":87116},[886],[888,87118,87119],{"xmlns":890},[892,87120,87121,87133],{},[895,87122,87123,87125,87127,87129,87131],{},[898,87124,9758],{},[1654,87126,1750],{},[1665,87128,1667],{},[1654,87130,2380],{},[898,87132,207],{},[902,87134,87135],{"encoding":904},"b = 1-a",", tedy vždy ",[38,87138,87139],{},"konstantní výnosy z rozsahu",[198,87141,87143,87144],{"id":87142},"parametr-efektivity-aa","Parametr efektivity ",[883,87145,87147],{"className":87146},[886],[888,87148,87149],{"xmlns":890},[892,87150,87151,87155],{},[895,87152,87153],{},[898,87154,4737],{},[902,87156,4737],{"encoding":904},[724,87158,87159,87160,87173,87174,87187,87188,87206,87207,87210],{},"Konstanta ",[883,87161,87163],{"className":87162},[886],[888,87164,87165],{"xmlns":890},[892,87166,87167,87171],{},[895,87168,87169],{},[898,87170,4737],{},[902,87172,4737],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,87175,87177],{"className":87176},[886],[888,87178,87179],{"xmlns":890},[892,87180,87181,87185],{},[895,87182,87183],{},[898,87184,1663],{},[902,87186,1663],{"encoding":904}," při pevně zadaných ",[883,87189,87191],{"className":87190},[886],[888,87192,87193],{"xmlns":890},[892,87194,87195,87203],{},[895,87196,87197,87199,87201],{},[898,87198,2450],{},[1654,87200,1674],{"separator":1673},[898,87202,18517],{},[902,87204,87205],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,87208,87209],{},"parametr efektivity"," — indikátor stavu technologie.",[198,87212,87214],{"id":87213},"příklad-53","Příklad 5.3",[724,87216,87217,87218,87113,87260,87262,87263,2138],{},"Produkční funkce ",[883,87219,87221],{"className":87220},[886],[888,87222,87223],{"xmlns":890},[892,87224,87225,87257],{},[895,87226,87227,87229,87231,87233,87245],{},[898,87228,1663],{},[1654,87230,1750],{},[1665,87232,1681],{},[1741,87234,87235,87237],{},[898,87236,2450],{},[895,87238,87239,87241,87243],{},[1665,87240,1667],{},[898,87242,1879],{"mathvariant":1878},[1665,87244,7631],{},[1741,87246,87247,87249],{},[898,87248,18517],{},[895,87250,87251,87253,87255],{},[1665,87252,4035],{},[898,87254,1879],{"mathvariant":1878},[1665,87256,7631],{},[902,87258,87259],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,87261,33299],{}," výnosy z rozsahu, neboť ",[883,87264,87266],{"className":87265},[886],[888,87267,87268],{"xmlns":890},[892,87269,87270,87294],{},[895,87271,87272,87280,87282,87290,87292],{},[2582,87273,87274],{"scriptlevel":2062,"displaystyle":1656},[2811,87275,87276,87278],{},[1665,87277,1667],{},[1665,87279,7631],{},[1654,87281,1766],{},[2582,87283,87284],{"scriptlevel":2062,"displaystyle":1656},[2811,87285,87286,87288],{},[1665,87287,4035],{},[1665,87289,7631],{},[1654,87291,1750],{},[1665,87293,1667],{},[902,87295,87296],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,87298,87299,87300,14918,87313,87326,87327,2186,87340,87380],{},"Změní-li se ",[883,87301,87303],{"className":87302},[886],[888,87304,87305],{"xmlns":890},[892,87306,87307,87311],{},[895,87308,87309],{},[898,87310,2450],{},[902,87312,2450],{"encoding":904},[883,87314,87316],{"className":87315},[886],[888,87317,87318],{"xmlns":890},[892,87319,87320,87324],{},[895,87321,87322],{},[898,87323,18517],{},[902,87325,18517],{"encoding":904}," čtyřnásobně, změní se ",[883,87328,87330],{"className":87329},[886],[888,87331,87332],{"xmlns":890},[892,87333,87334,87338],{},[895,87335,87336],{},[898,87337,1663],{},[902,87339,1663],{"encoding":904},[883,87341,87343],{"className":87342},[886],[888,87344,87345],{"xmlns":890},[892,87346,87347,87377],{},[895,87348,87349,87369,87371],{},[1741,87350,87351,87353],{},[1665,87352,7631],{},[895,87354,87355,87357,87359,87361,87363,87365,87367],{},[1665,87356,1667],{},[898,87358,1879],{"mathvariant":1878},[1665,87360,7631],{},[1654,87362,1766],{},[1665,87364,4035],{},[898,87366,1879],{"mathvariant":1878},[1665,87368,7631],{},[1654,87370,1750],{},[1741,87372,87373,87375],{},[1665,87374,7631],{},[1665,87376,1667],{},[902,87378,87379],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,87382,87384],{"className":87383},[886],[888,87385,87386],{"xmlns":890,"display":1956},[892,87387,87388,87548],{},[895,87389,87390,87392,87394,87396,87398,87400,87402,87404,87406,87408,87410,87412,87414,87416,87428,87430,87432,87434,87446,87448,87450,87452,87472,87484,87496,87498,87500,87502,87504,87516,87528,87530,87532,87534,87536,87538,87540,87542,87544,87546],{},[898,87391,1663],{},[1654,87393,1708],{"stretchy":1656},[1665,87395,7631],{},[898,87397,2450],{},[1654,87399,1674],{"separator":1673},[1665,87401,7631],{},[898,87403,18517],{},[1654,87405,1726],{"stretchy":1656},[1654,87407,1750],{},[1665,87409,1681],{},[1654,87411,1708],{"stretchy":1656},[1665,87413,7631],{},[898,87415,2450],{},[1741,87417,87418,87420],{},[1654,87419,1726],{"stretchy":1656},[895,87421,87422,87424,87426],{},[1665,87423,1667],{},[898,87425,1879],{"mathvariant":1878},[1665,87427,7631],{},[1654,87429,1708],{"stretchy":1656},[1665,87431,7631],{},[898,87433,18517],{},[1741,87435,87436,87438],{},[1654,87437,1726],{"stretchy":1656},[895,87439,87440,87442,87444],{},[1665,87441,4035],{},[898,87443,1879],{"mathvariant":1878},[1665,87445,7631],{},[1654,87447,1750],{},[1665,87449,1681],{},[1654,87451,4554],{},[1741,87453,87454,87456],{},[1665,87455,7631],{},[895,87457,87458,87460,87462,87464,87466,87468,87470],{},[1665,87459,1667],{},[898,87461,1879],{"mathvariant":1878},[1665,87463,7631],{},[1654,87465,1766],{},[1665,87467,4035],{},[898,87469,1879],{"mathvariant":1878},[1665,87471,7631],{},[1741,87473,87474,87476],{},[898,87475,2450],{},[895,87477,87478,87480,87482],{},[1665,87479,1667],{},[898,87481,1879],{"mathvariant":1878},[1665,87483,7631],{},[1741,87485,87486,87488],{},[898,87487,18517],{},[895,87489,87490,87492,87494],{},[1665,87491,4035],{},[898,87493,1879],{"mathvariant":1878},[1665,87495,7631],{},[1654,87497,1750],{},[1665,87499,7631],{},[1654,87501,4554],{},[1665,87503,1681],{},[1741,87505,87506,87508],{},[898,87507,2450],{},[895,87509,87510,87512,87514],{},[1665,87511,1667],{},[898,87513,1879],{"mathvariant":1878},[1665,87515,7631],{},[1741,87517,87518,87520],{},[898,87519,18517],{},[895,87521,87522,87524,87526],{},[1665,87523,4035],{},[898,87525,1879],{"mathvariant":1878},[1665,87527,7631],{},[1654,87529,1750],{},[1665,87531,7631],{},[1865,87533,11744],{},[898,87535,1663],{},[1654,87537,1708],{"stretchy":1656},[898,87539,2450],{},[1654,87541,1674],{"separator":1673},[898,87543,18517],{},[1654,87545,1726],{"stretchy":1656},[898,87547,2138],{"mathvariant":1878},[902,87549,87550],{"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).",[198,87552,87553],{"id":45399},"Homogenita",[724,87555,87556,87557,16828,87580,87596],{},"Funkce ",[883,87558,87560],{"className":87559},[886],[888,87561,87562],{"xmlns":890},[892,87563,87564,87578],{},[895,87565,87566,87568,87570,87572,87574,87576],{},[898,87567,1663],{},[1654,87569,1708],{"stretchy":1656},[898,87571,2450],{},[1654,87573,1674],{"separator":1673},[898,87575,18517],{},[1654,87577,1726],{"stretchy":1656},[902,87579,18714],{"encoding":904},[38,87581,87582,87583],{},"homogenní stupně ",[883,87584,87586],{"className":87585},[886],[888,87587,87588],{"xmlns":890},[892,87589,87590,87594],{},[895,87591,87592],{},[898,87593,45080],{},[902,87595,45080],{"encoding":904},", jestliže",[883,87598,87600],{"className":87599},[886],[888,87601,87602],{"xmlns":890,"display":1956},[892,87603,87604,87661],{},[1960,87605,87606],{"width":1962},[1964,87607,87608,87610,87654,87656],{},[1967,87609],{"width":1969},[1967,87611,87612],{},[895,87613,87614,87616,87618,87620,87622,87624,87626,87628,87630,87632,87638,87640,87642,87644,87646,87648,87650,87652],{},[898,87615,1663],{},[1654,87617,1708],{"stretchy":1656},[898,87619,20753],{},[898,87621,2450],{},[1654,87623,1674],{"separator":1673},[898,87625,20753],{},[898,87627,18517],{},[1654,87629,1726],{"stretchy":1656},[1654,87631,1750],{},[1741,87633,87634,87636],{},[898,87635,20753],{},[898,87637,45080],{},[1865,87639,11744],{},[898,87641,1663],{},[1654,87643,1708],{"stretchy":1656},[898,87645,2450],{},[1654,87647,1674],{"separator":1673},[898,87649,18517],{},[1654,87651,1726],{"stretchy":1656},[1654,87653,1674],{"separator":1673},[1967,87655],{"width":1969},[1967,87657,87658],{},[1865,87659,87660],{},"(5.10)",[902,87662,87663],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,87665,13049,87666,87684,87685,87703,87704,51856,87717,87720,87721,2138],{},[883,87667,87669],{"className":87668},[886],[888,87670,87671],{"xmlns":890},[892,87672,87673,87681],{},[895,87674,87675,87677,87679],{},[898,87676,45080],{},[1654,87678,13222],{},[1665,87680,2062],{},[902,87682,87683],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,87686,87688],{"className":87687},[886],[888,87689,87690],{"xmlns":890},[892,87691,87692,87700],{},[895,87693,87694,87696,87698],{},[898,87695,20753],{},[1654,87697,2952],{},[1665,87699,2062],{},[902,87701,87702],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,87705,87707],{"className":87706},[886],[888,87708,87709],{"xmlns":890},[892,87710,87711,87715],{},[895,87712,87713],{},[1665,87714,1667],{},[902,87716,1667],{"encoding":904},[38,87718,87719],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,87722,87724],{"className":87723},[886],[888,87725,87726],{"xmlns":890},[892,87727,87728,87736],{},[895,87729,87730,87732,87734],{},[898,87731,207],{},[1654,87733,1766],{},[898,87735,9758],{},[902,87737,83044],{"encoding":904},[115,87739,87741],{"id":87740},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,87743,87744],{},[38,87745,87746],{},"Ryzí Cobb-Douglasovy funkce:",[883,87748,87750],{"className":87749},[886],[888,87751,87752],{"xmlns":890,"display":1956},[892,87753,87754,87813],{},[1960,87755,87756],{"width":1962},[1964,87757,87758,87760,87806,87808],{},[1967,87759],{"width":1969},[1967,87761,87762],{},[895,87763,87764,87766,87768,87770,87772,87778,87780,87792,87794,87796,87798,87800,87802,87804],{},[898,87765,1663],{},[1654,87767,1750],{},[898,87769,4737],{},[1865,87771,11744],{},[1741,87773,87774,87776],{},[898,87775,2450],{},[898,87777,207],{},[1865,87779,11744],{},[1741,87781,87782,87784],{},[898,87783,18517],{},[895,87785,87786,87788,87790],{},[1665,87787,1667],{},[1654,87789,2380],{},[898,87791,207],{},[1654,87793,1674],{"separator":1673},[5008,87795],{"width":5010},[1665,87797,2062],{},[1654,87799,3002],{},[898,87801,207],{},[1654,87803,3002],{},[1665,87805,21969],{},[1967,87807],{"width":1969},[1967,87809,87810],{},[1865,87811,87812],{},"(5.9)",[902,87814,87815],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,87817,87818,87819,87821,87822,2138],{},"Mají vždy ",[38,87820,87139],{}," a jsou ",[38,87823,87719],{},[724,87825,87826,18742,87829,87832],{},[38,87827,87828],{},"CES produkční funkce",[614,87830,87831],{},"Constant Elasticity of Substitution",", 1961):",[883,87834,87836],{"className":87835},[886],[888,87837,87838],{"xmlns":890,"display":1956},[892,87839,87840,87908],{},[895,87841,87842,87844,87846,87848,87906],{},[898,87843,1663],{},[1654,87845,1750],{},[898,87847,4737],{},[1741,87849,87850,87894],{},[895,87851,87852,87854,87856,87858,87860,87862,87864,87866,87876,87878,87880,87882,87892],{},[1654,87853,1657],{"fence":1673},[1654,87855,1708],{"stretchy":1656},[1665,87857,1667],{},[1654,87859,2380],{},[898,87861,207],{},[1654,87863,1726],{"stretchy":1656},[1865,87865,11744],{},[1741,87867,87868,87870],{},[898,87869,2450],{},[895,87871,87872,87874],{},[1654,87873,2380],{},[898,87875,9758],{},[1654,87877,1766],{},[898,87879,207],{},[1865,87881,11744],{},[1741,87883,87884,87886],{},[898,87885,18517],{},[895,87887,87888,87890],{},[1654,87889,2380],{},[898,87891,9758],{},[1654,87893,1686],{"fence":1673},[895,87895,87896,87898],{},[1654,87897,2380],{},[2582,87899,87900],{"scriptlevel":2062,"displaystyle":1656},[2811,87901,87902,87904],{},[1665,87903,1667],{},[898,87905,9758],{},[1654,87907,1674],{"separator":1673},[902,87909,87910],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,87912,13049,87913,1343,87931,1343,87952,87976],{},[883,87914,87916],{"className":87915},[886],[888,87917,87918],{"xmlns":890},[892,87919,87920,87928],{},[895,87921,87922,87924,87926],{},[898,87923,4737],{},[1654,87925,2952],{},[1665,87927,2062],{},[902,87929,87930],{"encoding":904},"A > 0",[883,87932,87934],{"className":87933},[886],[888,87935,87936],{"xmlns":890},[892,87937,87938,87950],{},[895,87939,87940,87942,87944,87946,87948],{},[1665,87941,2062],{},[1654,87943,3002],{},[898,87945,207],{},[1654,87947,3002],{},[1665,87949,1667],{},[902,87951,27532],{"encoding":904},[883,87953,87955],{"className":87954},[886],[888,87956,87957],{"xmlns":890},[892,87958,87959,87973],{},[895,87960,87961,87963,87965,87967,87969,87971],{},[1654,87962,2380],{},[1665,87964,1667],{},[1654,87966,3002],{},[898,87968,9758],{},[1654,87970,9891],{"mathvariant":1878},[1665,87972,2062],{},[902,87974,87975],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,87978,87979],{},[38,87980,87981],{},"Další typy:",[120,87983,87984,88026],{},[123,87985,87986,2186,87989,88025],{},[38,87987,87988],{},"Lineární:",[883,87990,87992],{"className":87991},[886],[888,87993,87994],{"xmlns":890},[892,87995,87996,88022],{},[895,87997,87998,88000,88002,88004,88006,88008,88010,88012,88014,88016,88018,88020],{},[898,87999,1663],{},[1654,88001,1708],{"stretchy":1656},[898,88003,2450],{},[1654,88005,1674],{"separator":1673},[898,88007,18517],{},[1654,88009,1726],{"stretchy":1656},[1654,88011,1750],{},[898,88013,207],{},[898,88015,2450],{},[1654,88017,1766],{},[898,88019,9758],{},[898,88021,18517],{},[902,88023,88024],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,88027,88028,2186,88031,88076],{},[38,88029,88030],{},"Leontiefova:",[883,88032,88034],{"className":88033},[886],[888,88035,88036],{"xmlns":890},[892,88037,88038,88073],{},[895,88039,88040,88042,88044,88046,88048,88050,88052,88054,88057,88059,88061,88063,88065,88067,88069,88071],{},[898,88041,1663],{},[1654,88043,1708],{"stretchy":1656},[898,88045,2450],{},[1654,88047,1674],{"separator":1673},[898,88049,18517],{},[1654,88051,1726],{"stretchy":1656},[1654,88053,1750],{},[898,88055,88056],{},"min",[1654,88058,64420],{},[1654,88060,1708],{"stretchy":1656},[898,88062,207],{},[898,88064,2450],{},[1654,88066,1674],{"separator":1673},[898,88068,9758],{},[898,88070,18517],{},[1654,88072,1726],{"stretchy":1656},[902,88074,88075],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,88078,88080,88081,1343,88100,88119],{"id":88079},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,88082,88084],{"className":88083},[886],[888,88085,88086],{"xmlns":890},[892,88087,88088,88098],{},[895,88089,88090,88092],{},[898,88091,9320],{},[1710,88093,88094,88096],{},[898,88095,1755],{},[898,88097,2450],{},[902,88099,18762],{"encoding":904},[883,88101,88103],{"className":88102},[886],[888,88104,88105],{"xmlns":890},[892,88106,88107,88117],{},[895,88108,88109,88111],{},[898,88110,9320],{},[1710,88112,88113,88115],{},[898,88114,1755],{},[898,88116,18517],{},[902,88118,18807],{"encoding":904}," a totální diferenciál",[724,88121,88122],{},[38,88123,88124],{},"Mezní produkt práce:",[883,88126,88128],{"className":88127},[886],[888,88129,88130],{"xmlns":890,"display":1956},[892,88131,88132,88170],{},[895,88133,88134,88136,88142,88144,88152,88154,88168],{},[898,88135,9320],{},[1710,88137,88138,88140],{},[898,88139,1755],{},[898,88141,2450],{},[1654,88143,1750],{},[1659,88145,88146,88148,88150],{},[898,88147,1663],{},[898,88149,2450],{},[1654,88151,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,88153,1750],{},[2811,88155,88156,88162],{},[895,88157,88158,88160],{},[898,88159,18589],{"mathvariant":1878},[898,88161,1663],{},[895,88163,88164,88166],{},[898,88165,18589],{"mathvariant":1878},[898,88167,2450],{},[898,88169,2138],{"mathvariant":1878},[902,88171,88172],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,88174,88175],{},[38,88176,88177],{},"Mezní produkt kapitálu:",[883,88179,88181],{"className":88180},[886],[888,88182,88183],{"xmlns":890,"display":1956},[892,88184,88185,88223],{},[895,88186,88187,88189,88195,88197,88205,88207,88221],{},[898,88188,9320],{},[1710,88190,88191,88193],{},[898,88192,1755],{},[898,88194,18517],{},[1654,88196,1750],{},[1659,88198,88199,88201,88203],{},[898,88200,1663],{},[898,88202,18517],{},[1654,88204,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,88206,1750],{},[2811,88208,88209,88215],{},[895,88210,88211,88213],{},[898,88212,18589],{"mathvariant":1878},[898,88214,1663],{},[895,88216,88217,88219],{},[898,88218,18589],{"mathvariant":1878},[898,88220,18517],{},[898,88222,2138],{"mathvariant":1878},[902,88224,88225],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,88227,88228,88258,88259,88280,88281,88299,88300,88313,88314,2138],{},[883,88229,88231],{"className":88230},[886],[888,88232,88233],{"xmlns":890},[892,88234,88235,88255],{},[895,88236,88237,88239,88245,88247,88249,88251,88253],{},[898,88238,9320],{},[1710,88240,88241,88243],{},[898,88242,1755],{},[898,88244,2450],{},[1654,88246,1708],{"stretchy":1656},[898,88248,207],{},[1654,88250,1674],{"separator":1673},[898,88252,9758],{},[1654,88254,1726],{"stretchy":1656},[902,88256,88257],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,88260,88262],{"className":88261},[886],[888,88263,88264],{"xmlns":890},[892,88265,88266,88278],{},[895,88267,88268,88270,88272,88274,88276],{},[1654,88269,1657],{"stretchy":1656},[898,88271,207],{},[1654,88273,1674],{"separator":1673},[898,88275,9758],{},[1654,88277,1686],{"stretchy":1656},[902,88279,19539],{"encoding":904}," (na hladině ",[883,88282,88284],{"className":88283},[886],[888,88285,88286],{"xmlns":890},[892,88287,88288,88296],{},[895,88289,88290,88292,88294],{},[898,88291,18517],{},[1654,88293,1750],{},[898,88295,9758],{},[902,88297,88298],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,88301,88303],{"className":88302},[886],[888,88304,88305],{"xmlns":890},[892,88306,88307,88311],{},[895,88308,88309],{},[898,88310,2450],{},[902,88312,2450],{"encoding":904},". Analogicky ",[883,88315,88317],{"className":88316},[886],[888,88318,88319],{"xmlns":890},[892,88320,88321,88341],{},[895,88322,88323,88325,88331,88333,88335,88337,88339],{},[898,88324,9320],{},[1710,88326,88327,88329],{},[898,88328,1755],{},[898,88330,18517],{},[1654,88332,1708],{"stretchy":1656},[898,88334,207],{},[1654,88336,1674],{"separator":1673},[898,88338,9758],{},[1654,88340,1726],{"stretchy":1656},[902,88342,88343],{"encoding":904},"MP_K(a, b)",[2140,88345,88346,88350],{},[724,88347,88348,59439],{},[883,88349,2860],{},[120,88351,88352,88390],{},[123,88353,88354,34875,88373],{},[883,88355,88357],{"className":88356},[886],[888,88358,88359],{"xmlns":890},[892,88360,88361,88371],{},[895,88362,88363,88365],{},[898,88364,9320],{},[1710,88366,88367,88369],{},[898,88368,1755],{},[898,88370,2450],{},[902,88372,18762],{"encoding":904},[614,88374,88375,88376,88389],{},"„o kolik vzroste ",[883,88377,88379],{"className":88378},[886],[888,88380,88381],{"xmlns":890},[892,88382,88383,88387],{},[895,88384,88385],{},[898,88386,1663],{},[902,88388,1663],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,88391,88392,34875,88411],{},[883,88393,88395],{"className":88394},[886],[888,88396,88397],{"xmlns":890},[892,88398,88399,88409],{},[895,88400,88401,88403],{},[898,88402,9320],{},[1710,88404,88405,88407],{},[898,88406,1755],{},[898,88408,18517],{},[902,88410,18807],{"encoding":904},[614,88412,88375,88413,88426],{},[883,88414,88416],{"className":88415},[886],[888,88417,88418],{"xmlns":890},[892,88419,88420,88424],{},[895,88421,88422],{},[898,88423,1663],{},[902,88425,1663],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,88428,88429,88432,88433,88448,88449,2781],{},[38,88430,88431],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,88434,88436],{"className":88435},[886],[888,88437,88438],{"xmlns":890},[892,88439,88440,88446],{},[895,88441,88442,88444],{},[898,88443,10977],{},[898,88445,2450],{},[902,88447,83576],{"encoding":904}," a kapitálu o ",[883,88450,88452],{"className":88451},[886],[888,88453,88454],{"xmlns":890},[892,88455,88456,88462],{},[895,88457,88458,88460],{},[898,88459,10977],{},[898,88461,18517],{},[902,88463,88464],{"encoding":904},"dK",[883,88466,88468],{"className":88467},[886],[888,88469,88470],{"xmlns":890,"display":1956},[892,88471,88472,88565],{},[1960,88473,88474],{"width":1962},[1964,88475,88476,88478,88558,88560],{},[1967,88477],{"width":1969},[1967,88479,88480],{},[895,88481,88482,88484,88486,88488,88490,88492,88494,88502,88504,88506,88508,88510,88518,88520,88522,88524,88526,88528,88534,88536,88538,88540,88542,88544,88550,88552,88554,88556],{},[898,88483,11648],{"mathvariant":1878},[898,88485,1663],{},[1654,88487,11492],{},[898,88489,10977],{},[898,88491,1663],{},[1654,88493,1750],{},[1659,88495,88496,88498,88500],{},[898,88497,1663],{},[898,88499,2450],{},[1654,88501,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1865,88503,11744],{},[898,88505,10977],{},[898,88507,2450],{},[1654,88509,1766],{},[1659,88511,88512,88514,88516],{},[898,88513,1663],{},[898,88515,18517],{},[1654,88517,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1865,88519,11744],{},[898,88521,10977],{},[898,88523,18517],{},[1654,88525,1750],{},[898,88527,9320],{},[1710,88529,88530,88532],{},[898,88531,1755],{},[898,88533,2450],{},[1865,88535,11744],{},[898,88537,10977],{},[898,88539,2450],{},[1654,88541,1766],{},[898,88543,9320],{},[1710,88545,88546,88548],{},[898,88547,1755],{},[898,88549,18517],{},[1865,88551,11744],{},[898,88553,10977],{},[898,88555,18517],{},[898,88557,2138],{"mathvariant":1878},[1967,88559],{"width":1969},[1967,88561,88562],{},[1865,88563,88564],{},"(5.11)",[902,88566,88567],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,88569,88570,88571,2138],{},"Skutečná změna: ",[883,88572,88574],{"className":88573},[886],[888,88575,88576],{"xmlns":890},[892,88577,88578,88624],{},[895,88579,88580,88582,88584,88586,88588,88590,88592,88594,88596,88598,88600,88602,88604,88606,88608,88610,88612,88614,88616,88618,88620,88622],{},[898,88581,11648],{"mathvariant":1878},[898,88583,1663],{},[1654,88585,1750],{},[898,88587,1663],{},[1654,88589,1708],{"stretchy":1656},[898,88591,2450],{},[1654,88593,1766],{},[898,88595,10977],{},[898,88597,2450],{},[1654,88599,1674],{"separator":1673},[898,88601,18517],{},[1654,88603,1766],{},[898,88605,10977],{},[898,88607,18517],{},[1654,88609,1726],{"stretchy":1656},[1654,88611,2380],{},[898,88613,1663],{},[1654,88615,1708],{"stretchy":1656},[898,88617,2450],{},[1654,88619,1674],{"separator":1673},[898,88621,18517],{},[1654,88623,1726],{"stretchy":1656},[902,88625,88626],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,88628,88629,88631,88632,88650,88651,88664,88665,88684,88685,88717,88718,88750,88751,2138],{},[38,88630,83740],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,88633,88635],{"className":88634},[886],[888,88636,88637],{"xmlns":890},[892,88638,88639,88647],{},[895,88640,88641],{},[1710,88642,88643,88645],{},[898,88644,18517],{},[1665,88646,2062],{},[902,88648,88649],{"encoding":904},"K_0"," se od jistého ",[883,88652,88654],{"className":88653},[886],[888,88655,88656],{"xmlns":890},[892,88657,88658,88662],{},[895,88659,88660],{},[898,88661,2450],{},[902,88663,2450],{"encoding":904}," stane ",[883,88666,88668],{"className":88667},[886],[888,88669,88670],{"xmlns":890},[892,88671,88672,88682],{},[895,88673,88674,88676],{},[898,88675,9320],{},[1710,88677,88678,88680],{},[898,88679,1755],{},[898,88681,2450],{},[902,88683,18762],{"encoding":904}," klesající (",[883,88686,88688],{"className":88687},[886],[888,88689,88690],{"xmlns":890},[892,88691,88692,88714],{},[895,88693,88694,88710,88712],{},[1659,88695,88696,88698,88704],{},[898,88697,1663],{},[895,88699,88700,88702],{},[898,88701,2450],{},[898,88703,2450],{},[895,88705,88706,88708],{},[1654,88707,2592],{"mathvariant":1878},[1654,88709,2592],{"mathvariant":1878},[1654,88711,3002],{},[1665,88713,2062],{},[902,88715,88716],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,88719,88721],{"className":88720},[886],[888,88722,88723],{"xmlns":890},[892,88724,88725,88747],{},[895,88726,88727,88743,88745],{},[1659,88728,88729,88731,88737],{},[898,88730,1663],{},[895,88732,88733,88735],{},[898,88734,18517],{},[898,88736,18517],{},[895,88738,88739,88741],{},[1654,88740,2592],{"mathvariant":1878},[1654,88742,2592],{"mathvariant":1878},[1654,88744,3002],{},[1665,88746,2062],{},[902,88748,88749],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,88752,88754],{"className":88753},[886],[888,88755,88756],{"xmlns":890},[892,88757,88758,88766],{},[895,88759,88760],{},[1710,88761,88762,88764],{},[898,88763,2450],{},[1665,88765,2062],{},[902,88767,83778],{"encoding":904},[115,88769,88771],{"id":88770},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,88773,88774,88777,88778,88801,88802,3869],{},[38,88775,88776],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,88779,88781],{"className":88780},[886],[888,88782,88783],{"xmlns":890},[892,88784,88785,88799],{},[895,88786,88787,88789,88791,88793,88795,88797],{},[898,88788,1663],{},[1654,88790,1708],{"stretchy":1656},[898,88792,2450],{},[1654,88794,1674],{"separator":1673},[898,88796,18517],{},[1654,88798,1726],{"stretchy":1656},[902,88800,18714],{"encoding":904}," stupně ",[883,88803,88805],{"className":88804},[886],[888,88806,88807],{"xmlns":890},[892,88808,88809,88813],{},[895,88810,88811],{},[898,88812,45080],{},[902,88814,45080],{"encoding":904},[883,88816,88818],{"className":88817},[886],[888,88819,88820],{"xmlns":890,"display":1956},[892,88821,88822,88885],{},[1960,88823,88824],{"width":1962},[1964,88825,88826,88828,88878,88880],{},[1967,88827],{"width":1969},[1967,88829,88830],{},[895,88831,88832,88834,88836,88844,88846,88848,88850,88858,88860,88862,88864,88866,88868,88870,88872,88874,88876],{},[898,88833,2450],{},[1865,88835,11744],{},[1659,88837,88838,88840,88842],{},[898,88839,1663],{},[898,88841,2450],{},[1654,88843,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,88845,1766],{},[898,88847,18517],{},[1865,88849,11744],{},[1659,88851,88852,88854,88856],{},[898,88853,1663],{},[898,88855,18517],{},[1654,88857,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,88859,1750],{},[898,88861,45080],{},[1865,88863,11744],{},[898,88865,1663],{},[1654,88867,1708],{"stretchy":1656},[898,88869,2450],{},[1654,88871,1674],{"separator":1673},[898,88873,18517],{},[1654,88875,1726],{"stretchy":1656},[898,88877,2138],{"mathvariant":1878},[1967,88879],{"width":1969},[1967,88881,88882],{},[1865,88883,88884],{},"(5.12)",[902,88886,88887],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,88889,88890,88911],{},[38,88891,88892,88893],{},"Speciální případ ",[883,88894,88896],{"className":88895},[886],[888,88897,88898],{"xmlns":890},[892,88899,88900,88908],{},[895,88901,88902,88904,88906],{},[898,88903,45080],{},[1654,88905,1750],{},[1665,88907,1667],{},[902,88909,88910],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,88913,88915],{"className":88914},[886],[888,88916,88917],{"xmlns":890,"display":1956},[892,88918,88919,88963],{},[895,88920,88921,88923,88925,88927,88933,88935,88937,88939,88941,88947,88949,88951,88953,88955,88957,88959,88961],{},[898,88922,2450],{},[1654,88924,4554],{},[898,88926,9320],{},[1710,88928,88929,88931],{},[898,88930,1755],{},[898,88932,2450],{},[1654,88934,1766],{},[898,88936,18517],{},[1654,88938,4554],{},[898,88940,9320],{},[1710,88942,88943,88945],{},[898,88944,1755],{},[898,88946,18517],{},[1654,88948,1750],{},[898,88950,1663],{},[1654,88952,1708],{"stretchy":1656},[898,88954,2450],{},[1654,88956,1674],{"separator":1673},[898,88958,18517],{},[1654,88960,1726],{"stretchy":1656},[898,88962,2138],{"mathvariant":1878},[902,88964,88965],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,88967,88968,88969,88972],{},"Slovně — ",[38,88970,88971],{},"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).",[115,88974,18496],{"id":83114},[724,88976,88977,18742,88979,88982,88983,89005,89006,2781],{},[38,88978,18496],{},[614,88980,88981],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,88984,88986],{"className":88985},[886],[888,88987,88988],{"xmlns":890},[892,88989,88990,89002],{},[895,88991,88992,88994,88996,88998,89000],{},[1654,88993,1657],{"stretchy":1656},[898,88995,2450],{},[1654,88997,1674],{"separator":1673},[898,88999,18517],{},[1654,89001,1686],{"stretchy":1656},[902,89003,89004],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,89007,89009],{"className":89008},[886],[888,89010,89011],{"xmlns":890},[892,89012,89013,89018],{},[895,89014,89015],{},[898,89016,89017],{},"q",[902,89019,89017],{"encoding":904},[883,89021,89023],{"className":89022},[886],[888,89024,89025],{"xmlns":890,"display":1956},[892,89026,89027,89062],{},[1960,89028,89029],{"width":1962},[1964,89030,89031,89033,89055,89057],{},[1967,89032],{"width":1969},[1967,89034,89035],{},[895,89036,89037,89039,89041,89043,89045,89047,89049,89051,89053],{},[898,89038,1663],{},[1654,89040,1708],{"stretchy":1656},[898,89042,2450],{},[1654,89044,1674],{"separator":1673},[898,89046,18517],{},[1654,89048,1726],{"stretchy":1656},[1654,89050,1750],{},[898,89052,89017],{},[898,89054,2138],{"mathvariant":1878},[1967,89056],{"width":1969},[1967,89058,89059],{},[1865,89060,89061],{},"(5.13)",[902,89063,89064],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,89066,89067,89068,89071,89072,12664],{},"Jsou to ",[38,89069,89070],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,89073,89075],{"className":89074,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,89077,89078],{},[38,89079,89080],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,89082,89083,89088,89093,89098],{},[123,89084,89085,89087],{},[38,89086,21230],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,89089,89090,89092],{},[38,89091,45884],{}," (úloha 5.14);",[123,89094,89095,17150],{},[38,89096,89097],{},"neprotínají se",[123,89099,89100,89101,13096,89114,2138],{},"s rostoucím ",[883,89102,89104],{"className":89103},[886],[888,89105,89106],{"xmlns":890},[892,89107,89108,89112],{},[895,89109,89110],{},[898,89111,89017],{},[902,89113,89017],{"encoding":904},[38,89115,89116],{},"vzdalují od počátku",[724,89118,89119],{},[614,89120,89121,89122,89144,89145,2138],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,89123,89125],{"className":89124},[886],[888,89126,89127],{"xmlns":890},[892,89128,89129,89141],{},[895,89130,89131,89133,89135,89137,89139],{},[1654,89132,1708],{"stretchy":1656},[898,89134,2450],{},[1654,89136,1674],{"separator":1673},[898,89138,18517],{},[1654,89140,1726],{"stretchy":1656},[902,89142,89143],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,89146,89148],{"className":89147},[886],[888,89149,89150],{"xmlns":890},[892,89151,89152,89176],{},[895,89153,89154,89160,89162,89168,89170],{},[1710,89155,89156,89158],{},[898,89157,89017],{},[1665,89159,1667],{},[1654,89161,3002],{},[1710,89163,89164,89166],{},[898,89165,89017],{},[1665,89167,2062],{},[1654,89169,3002],{},[1710,89171,89172,89174],{},[898,89173,89017],{},[1665,89175,1681],{},[902,89177,89178],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,89180,89182,89183,1726],{"id":89181},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,89184,89186],{"className":89185},[886],[888,89187,89188],{"xmlns":890},[892,89189,89190,89200],{},[895,89191,89192,89194,89196,89198],{},[898,89193,9320],{},[898,89195,12737],{},[898,89197,11536],{},[898,89199,17398],{},[902,89201,19315],{"encoding":904},[724,89203,89204,18742,89207,89210],{},[38,89205,89206],{},"Mezní míra technické substituce",[614,89208,89209],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,89212,89214],{"className":89213},[886],[888,89215,89216],{"xmlns":890,"display":1956},[892,89217,89218,89309],{},[1960,89219,89220],{"width":1962},[1964,89221,89222,89224,89302,89304],{},[1967,89223],{"width":1969},[1967,89225,89226],{},[895,89227,89228,89230,89232,89234,89236,89238,89240,89242,89244,89246,89248,89250,89252,89254,89256,89258,89280,89282,89300],{},[898,89229,9320],{},[898,89231,12737],{},[898,89233,11536],{},[898,89235,17398],{},[1654,89237,1750],{},[898,89239,9320],{},[898,89241,12737],{},[898,89243,11536],{},[898,89245,17398],{},[1654,89247,1708],{"stretchy":1656},[898,89249,2450],{},[1654,89251,1674],{"separator":1673},[898,89253,18517],{},[1654,89255,1726],{"stretchy":1656},[1654,89257,1750],{},[2811,89259,89260,89270],{},[895,89261,89262,89264],{},[898,89263,9320],{},[1710,89265,89266,89268],{},[898,89267,1755],{},[898,89269,2450],{},[895,89271,89272,89274],{},[898,89273,9320],{},[1710,89275,89276,89278],{},[898,89277,1755],{},[898,89279,18517],{},[1654,89281,1750],{},[2811,89283,89284,89292],{},[1659,89285,89286,89288,89290],{},[898,89287,1663],{},[898,89289,2450],{},[1654,89291,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1659,89293,89294,89296,89298],{},[898,89295,1663],{},[898,89297,18517],{},[1654,89299,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[898,89301,2138],{"mathvariant":1878},[1967,89303],{"width":1969},[1967,89305,89306],{},[1865,89307,89308],{},"(5.14)",[902,89310,89311],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,89313,89314,2186,89316,89346,89347,89378],{},[38,89315,4042],{},[883,89317,89319],{"className":89318},[886],[888,89320,89321],{"xmlns":890},[892,89322,89323,89343],{},[895,89324,89325,89327,89329,89331,89333,89335,89337,89339,89341],{},[898,89326,9320],{},[898,89328,12737],{},[898,89330,11536],{},[898,89332,17398],{},[1654,89334,1708],{"stretchy":1656},[898,89336,2450],{},[1654,89338,1674],{"separator":1673},[898,89340,18517],{},[1654,89342,1726],{"stretchy":1656},[902,89344,89345],{"encoding":904},"MRTS(L, K)"," udává, ",[38,89348,89349,89350,89363,89364,89377],{},"o kolik se musí přibližně změnit kapitál ",[883,89351,89353],{"className":89352},[886],[888,89354,89355],{"xmlns":890},[892,89356,89357,89361],{},[895,89358,89359],{},[898,89360,18517],{},[902,89362,18517],{"encoding":904},", jestliže se práce ",[883,89365,89367],{"className":89366},[886],[888,89368,89369],{"xmlns":890},[892,89370,89371,89375],{},[895,89372,89373],{},[898,89374,2450],{},[902,89376,2450],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[2140,89380,89381],{},[724,89382,89383,26719,89385,89404,89405,89442,89443,89446,89447,89451],{},[883,89384,2860],{},[883,89386,89388],{"className":89387},[886],[888,89389,89390],{"xmlns":890},[892,89391,89392,89402],{},[895,89393,89394,89396,89398,89400],{},[898,89395,9320],{},[898,89397,12737],{},[898,89399,11536],{},[898,89401,17398],{},[902,89403,19315],{"encoding":904}," říká: ",[614,89406,89407,89408,89427,89428,89441],{},"„jednu jednotku práce musím nahradit přibližně ",[883,89409,89411],{"className":89410},[886],[888,89412,89413],{"xmlns":890},[892,89414,89415,89425],{},[895,89416,89417,89419,89421,89423],{},[898,89418,9320],{},[898,89420,12737],{},[898,89422,11536],{},[898,89424,17398],{},[902,89426,19315],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,89429,89431],{"className":89430},[886],[888,89432,89433],{"xmlns":890},[892,89434,89435,89439],{},[895,89436,89437],{},[898,89438,1663],{},[902,89440,1663],{"encoding":904}," zůstala stejná.\""," Je to ",[38,89444,89445],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,89448,89450],{"className":89449,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,89453,89454],{},[3492,89455],{"alt":89456,"className":89457,"src":89458},"imek-izokvanty-mrts",[210,3496],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,89460,89461,89464,89465,16828,89495,89517,89518,11906],{},[38,89462,89463],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,89466,89468],{"className":89467},[886],[888,89469,89470],{"xmlns":890},[892,89471,89472,89492],{},[895,89473,89474,89476,89482,89484,89490],{},[1654,89475,1657],{"stretchy":1656},[1710,89477,89478,89480],{},[898,89479,2450],{},[1665,89481,2062],{},[1654,89483,1674],{"separator":1673},[1710,89485,89486,89488],{},[898,89487,18517],{},[1665,89489,2062],{},[1654,89491,1686],{"stretchy":1656},[902,89493,89494],{"encoding":904},"[L_0, K_0]",[883,89496,89498],{"className":89497},[886],[888,89499,89500],{"xmlns":890},[892,89501,89502,89514],{},[895,89503,89504,89506,89508,89510,89512],{},[1654,89505,2380],{},[898,89507,9320],{},[898,89509,12737],{},[898,89511,11536],{},[898,89513,17398],{},[902,89515,89516],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,89519,89521],{"className":89520},[886],[888,89522,89523],{"xmlns":890},[892,89524,89525,89547],{},[895,89526,89527,89529,89531,89533,89535,89537,89539,89541],{},[898,89528,1663],{},[1654,89530,1708],{"stretchy":1656},[898,89532,2450],{},[1654,89534,1674],{"separator":1673},[898,89536,18517],{},[1654,89538,1726],{"stretchy":1656},[1654,89540,1750],{},[1710,89542,89543,89545],{},[898,89544,89017],{},[1665,89546,2062],{},[902,89548,89549],{"encoding":904},"Q(L,K) = q_0",[883,89551,89553],{"className":89552},[886],[888,89554,89555],{"xmlns":890,"display":1956},[892,89556,89557,89609],{},[895,89558,89559,89573,89575,89577,89595,89597,89599,89601,89603,89605,89607],{},[2811,89560,89561,89567],{},[895,89562,89563,89565],{},[898,89564,10977],{},[898,89566,18517],{},[895,89568,89569,89571],{},[898,89570,10977],{},[898,89572,2450],{},[1654,89574,1750],{},[1654,89576,2380],{},[2811,89578,89579,89587],{},[1659,89580,89581,89583,89585],{},[898,89582,1663],{},[898,89584,2450],{},[1654,89586,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1659,89588,89589,89591,89593],{},[898,89590,1663],{},[898,89592,18517],{},[1654,89594,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,89596,1750],{},[1654,89598,2380],{},[898,89600,9320],{},[898,89602,12737],{},[898,89604,11536],{},[898,89606,17398],{},[898,89608,2138],{"mathvariant":1878},[902,89610,89611],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,89613,89614,89615,89630,89631,89647],{},"Změní-li se práce o ",[883,89616,89618],{"className":89617},[886],[888,89619,89620],{"xmlns":890},[892,89621,89622,89628],{},[895,89623,89624,89626],{},[898,89625,10977],{},[898,89627,2450],{},[902,89629,83576],{"encoding":904},", lze pro odhad změny kapitálu ",[883,89632,89634],{"className":89633},[886],[888,89635,89636],{"xmlns":890},[892,89637,89638,89644],{},[895,89639,89640,89642],{},[898,89641,11648],{"mathvariant":1878},[898,89643,18517],{},[902,89645,89646],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,89649,89651],{"className":89650},[886],[888,89652,89653],{"xmlns":890,"display":1956},[892,89654,89655,89702],{},[1960,89656,89657],{"width":1962},[1964,89658,89659,89661,89695,89697],{},[1967,89660],{"width":1969},[1967,89662,89663],{},[895,89664,89665,89667,89669,89671,89673,89675,89677,89679,89681,89683,89685,89687,89689,89691,89693],{},[898,89666,11648],{"mathvariant":1878},[898,89668,18517],{},[1654,89670,11492],{},[898,89672,10977],{},[898,89674,18517],{},[1654,89676,1750],{},[1654,89678,2380],{},[898,89680,9320],{},[898,89682,12737],{},[898,89684,11536],{},[898,89686,17398],{},[1865,89688,11744],{},[898,89690,10977],{},[898,89692,2450],{},[1654,89694,1674],{"separator":1673},[1967,89696],{"width":1969},[1967,89698,89699],{},[1865,89700,89701],{},"(5.15)",[902,89703,89704],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,89706,89708],{"className":89707},[886],[888,89709,89710],{"xmlns":890,"display":1956},[892,89711,89712,89761],{},[1960,89713,89714],{"width":1962},[1964,89715,89716,89718,89754,89756],{},[1967,89717],{"width":1969},[1967,89719,89720],{},[895,89721,89722,89724,89726,89728,89746,89748,89750,89752],{},[898,89723,10977],{},[898,89725,2450],{},[1654,89727,1750],{},[2811,89729,89730,89736],{},[895,89731,89732,89734],{},[1654,89733,2380],{},[1665,89735,1667],{},[895,89737,89738,89740,89742,89744],{},[898,89739,9320],{},[898,89741,12737],{},[898,89743,11536],{},[898,89745,17398],{},[1865,89747,11744],{},[898,89749,10977],{},[898,89751,18517],{},[898,89753,2138],{"mathvariant":1878},[1967,89755],{"width":1969},[1967,89757,89758],{},[1865,89759,89760],{},"(5.16)",[902,89762,89763],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[2140,89765,89766,89790],{},[724,89767,89768,89770,89771],{},[883,89769,3111],{}," Postup — jak spočítat ",[883,89772,89774],{"className":89773},[886],[888,89775,89776],{"xmlns":890},[892,89777,89778,89788],{},[895,89779,89780,89782,89784,89786],{},[898,89781,9320],{},[898,89783,12737],{},[898,89785,11536],{},[898,89787,17398],{},[902,89789,19315],{"encoding":904},[152,89791,89792,89833,89876,89908],{},[123,89793,89794,89795,2068,89814,2138],{},"Vypočtěte parciální derivace ",[883,89796,89798],{"className":89797},[886],[888,89799,89800],{"xmlns":890},[892,89801,89802,89812],{},[895,89803,89804],{},[1659,89805,89806,89808,89810],{},[898,89807,1663],{},[898,89809,2450],{},[1654,89811,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,89813,18738],{"encoding":904},[883,89815,89817],{"className":89816},[886],[888,89818,89819],{"xmlns":890},[892,89820,89821,89831],{},[895,89822,89823],{},[1659,89824,89825,89827,89829],{},[898,89826,1663],{},[898,89828,18517],{},[1654,89830,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,89832,18784],{"encoding":904},[123,89834,74061,89835,89875],{},[883,89836,89838],{"className":89837},[886],[888,89839,89840],{"xmlns":890},[892,89841,89842,89872],{},[895,89843,89844,89846,89848,89850,89852,89854,89862,89864],{},[898,89845,9320],{},[898,89847,12737],{},[898,89849,11536],{},[898,89851,17398],{},[1654,89853,1750],{},[1659,89855,89856,89858,89860],{},[898,89857,1663],{},[898,89859,2450],{},[1654,89861,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[898,89863,1879],{"mathvariant":1878},[1659,89865,89866,89868,89870],{},[898,89867,1663],{},[898,89869,18517],{},[1654,89871,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,89873,89874],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,89877,89878,89879,2138],{},"Případně dosaďte konkrétní ",[883,89880,89882],{"className":89881},[886],[888,89883,89884],{"xmlns":890},[892,89885,89886,89906],{},[895,89887,89888,89890,89896,89898,89904],{},[1654,89889,1657],{"stretchy":1656},[1710,89891,89892,89894],{},[898,89893,2450],{},[1665,89895,2062],{},[1654,89897,1674],{"separator":1673},[1710,89899,89900,89902],{},[898,89901,18517],{},[1665,89903,2062],{},[1654,89905,1686],{"stretchy":1656},[902,89907,89494],{"encoding":904},[123,89909,89910,89911,89945,89946,89948],{},"Pro odhad substituce použijte ",[883,89912,89914],{"className":89913},[886],[888,89915,89916],{"xmlns":890},[892,89917,89918,89942],{},[895,89919,89920,89922,89924,89926,89928,89930,89932,89934,89936,89938,89940],{},[898,89921,11648],{"mathvariant":1878},[898,89923,18517],{},[1654,89925,11492],{},[1654,89927,2380],{},[898,89929,9320],{},[898,89931,12737],{},[898,89933,11536],{},[898,89935,17398],{},[1654,89937,4554],{},[898,89939,11648],{"mathvariant":1878},[898,89941,2450],{},[902,89943,89944],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,89947,60826],{}," — substituce, ne doplnění).",[724,89950,89951],{},[614,89952,89953,89954,89986,89987,11387,90000,24497,90029,90044],{},"Obrázek 5.7 — izokvanta ",[883,89955,89957],{"className":89956},[886],[888,89958,89959],{"xmlns":890},[892,89960,89961,89983],{},[895,89962,89963,89969,89971,89973,89975,89977,89979,89981],{},[1710,89964,89965,89967],{},[898,89966,89017],{},[1665,89968,2062],{},[1654,89970,1750],{},[898,89972,1663],{},[1654,89974,1708],{"stretchy":1656},[898,89976,2450],{},[1654,89978,1674],{"separator":1673},[898,89980,18517],{},[1654,89982,1726],{"stretchy":1656},[902,89984,89985],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,89988,89990],{"className":89989},[886],[888,89991,89992],{"xmlns":890},[892,89993,89994,89998],{},[895,89995,89996],{},[898,89997,27551],{},[902,89999,27551],{"encoding":904},[883,90001,90003],{"className":90002},[886],[888,90004,90005],{"xmlns":890},[892,90006,90007,90027],{},[895,90008,90009,90011,90017,90019,90025],{},[1654,90010,1657],{"stretchy":1656},[1710,90012,90013,90015],{},[898,90014,2450],{},[1665,90016,2062],{},[1654,90018,1674],{"separator":1673},[1710,90020,90021,90023],{},[898,90022,18517],{},[1665,90024,2062],{},[1654,90026,1686],{"stretchy":1656},[902,90028,89494],{"encoding":904},[883,90030,90032],{"className":90031},[886],[888,90033,90034],{"xmlns":890},[892,90035,90036,90042],{},[895,90037,90038,90040],{},[898,90039,11648],{"mathvariant":1878},[898,90041,18517],{},[902,90043,89646],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,90046,90048],{"id":90047},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,90050,90052],{"id":90051},"příklad-54","Příklad 5.4",[724,90054,84893,90055,1343,90097,1343,90114,2138],{},[883,90056,90058],{"className":90057},[886],[888,90059,90060],{"xmlns":890},[892,90061,90062,90094],{},[895,90063,90064,90066,90068,90070,90082],{},[898,90065,1663],{},[1654,90067,1750],{},[1665,90069,10207],{},[1741,90071,90072,90074],{},[898,90073,2450],{},[895,90075,90076,90078,90080],{},[1665,90077,1667],{},[898,90079,1879],{"mathvariant":1878},[1665,90081,1681],{},[1741,90083,90084,90086],{},[898,90085,18517],{},[895,90087,90088,90090,90092],{},[1665,90089,1667],{},[898,90091,1879],{"mathvariant":1878},[1665,90093,4035],{},[902,90095,90096],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,90098,90100],{"className":90099},[886],[888,90101,90102],{"xmlns":890},[892,90103,90104,90112],{},[895,90105,90106,90108,90110],{},[898,90107,2450],{},[1654,90109,1750],{},[1665,90111,4573],{},[902,90113,85267],{"encoding":904},[883,90115,90117],{"className":90116},[886],[888,90118,90119],{"xmlns":890},[892,90120,90121,90129],{},[895,90122,90123,90125,90127],{},[898,90124,18517],{},[1654,90126,1750],{},[1665,90128,4273],{},[902,90130,90131],{"encoding":904},"K = 100",[724,90133,90134],{},[38,90135,90136],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,90138,90140],{"className":90139},[886],[888,90141,90142],{"xmlns":890,"display":1956},[892,90143,90144,90258],{},[895,90145,90146,90148,90154,90156,90164,90166,90174,90188,90200,90202,90204,90206,90212,90214,90216,90218,90220,90222,90224,90232,90234,90244,90246,90253,90255],{},[898,90147,9320],{},[1710,90149,90150,90152],{},[898,90151,1755],{},[898,90153,2450],{},[1654,90155,1750],{},[1659,90157,90158,90160,90162],{},[898,90159,1663],{},[898,90161,2450],{},[1654,90163,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,90165,1750],{},[2582,90167,90168],{"scriptlevel":2062,"displaystyle":1656},[2811,90169,90170,90172],{},[1665,90171,10207],{},[1665,90173,1681],{},[1741,90175,90176,90178],{},[898,90177,2450],{},[895,90179,90180,90182,90184,90186],{},[1654,90181,2380],{},[1665,90183,1667],{},[898,90185,1879],{"mathvariant":1878},[1665,90187,1681],{},[1741,90189,90190,90192],{},[898,90191,18517],{},[895,90193,90194,90196,90198],{},[1665,90195,1667],{},[898,90197,1879],{"mathvariant":1878},[1665,90199,4035],{},[1654,90201,1674],{"separator":1673},[5008,90203],{"width":5010},[898,90205,9320],{},[1710,90207,90208,90210],{},[898,90209,1755],{},[898,90211,2450],{},[1654,90213,1708],{"stretchy":1656},[1665,90215,4573],{},[1654,90217,1674],{"separator":1673},[1665,90219,4273],{},[1654,90221,1726],{"stretchy":1656},[1654,90223,1750],{},[2582,90225,90226],{"scriptlevel":2062,"displaystyle":1656},[2811,90227,90228,90230],{},[1665,90229,10207],{},[1665,90231,1681],{},[1654,90233,4554],{},[2582,90235,90236],{"scriptlevel":2062,"displaystyle":1656},[2811,90237,90238,90240],{},[1665,90239,1667],{},[8818,90241,90242],{},[1665,90243,4573],{},[1654,90245,4554],{},[90247,90248,90249,90251],"mroot",{},[1665,90250,4273],{},[1665,90252,4035],{},[1654,90254,11492],{},[1665,90256,90257],{},"7,153.",[902,90259,90260],{"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.",[724,90262,90263,90264,52380,90286,18950,90303,90324,90325,90346],{},"Přibližná změna při ",[883,90265,90267],{"className":90266},[886],[888,90268,90269],{"xmlns":890},[892,90270,90271,90283],{},[895,90272,90273,90275,90277,90279,90281],{},[898,90274,2450],{},[1654,90276,2781],{},[1665,90278,4573],{},[1654,90280,11878],{},[1665,90282,46566],{},[902,90284,90285],{"encoding":904},"L: 20 \\to 21",[883,90287,90289],{"className":90288},[886],[888,90290,90291],{"xmlns":890},[892,90292,90293,90301],{},[895,90294,90295,90297,90299],{},[898,90296,18517],{},[1654,90298,1750],{},[1665,90300,4273],{},[902,90302,90131],{"encoding":904},[883,90304,90306],{"className":90305},[886],[888,90307,90308],{"xmlns":890},[892,90309,90310,90321],{},[895,90311,90312,90314,90316,90318],{},[898,90313,11648],{"mathvariant":1878},[898,90315,1663],{},[1654,90317,11492],{},[1665,90319,90320],{},"7,153",[902,90322,90323],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,90326,90328],{"className":90327},[886],[888,90329,90330],{"xmlns":890},[892,90331,90332,90343],{},[895,90333,90334,90336,90338,90340],{},[898,90335,11648],{"mathvariant":1878},[898,90337,1663],{},[1654,90339,11492],{},[1665,90341,90342],{},"26,888",[902,90344,90345],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,90348,90349,90352],{},[38,90350,90351],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,90354,90356],{"className":90355},[886],[888,90357,90358],{"xmlns":890,"display":1956},[892,90359,90360,90460],{},[895,90361,90362,90364,90370,90372,90380,90382,90384,90396,90410,90412,90414,90416,90422,90424,90426,90428,90430,90432,90434,90436,90440,90442,90455,90457],{},[898,90363,9320],{},[1710,90365,90366,90368],{},[898,90367,1755],{},[898,90369,18517],{},[1654,90371,1750],{},[1659,90373,90374,90376,90378],{},[898,90375,1663],{},[898,90377,18517],{},[1654,90379,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,90381,1750],{},[1665,90383,4032],{},[1741,90385,90386,90388],{},[898,90387,2450],{},[895,90389,90390,90392,90394],{},[1665,90391,1667],{},[898,90393,1879],{"mathvariant":1878},[1665,90395,1681],{},[1741,90397,90398,90400],{},[898,90399,18517],{},[895,90401,90402,90404,90406,90408],{},[1654,90403,2380],{},[1665,90405,1681],{},[898,90407,1879],{"mathvariant":1878},[1665,90409,4035],{},[1654,90411,1674],{"separator":1673},[5008,90413],{"width":5010},[898,90415,9320],{},[1710,90417,90418,90420],{},[898,90419,1755],{},[898,90421,18517],{},[1654,90423,1708],{"stretchy":1656},[1665,90425,4573],{},[1654,90427,1674],{"separator":1673},[1665,90429,4273],{},[1654,90431,1726],{"stretchy":1656},[1654,90433,1750],{},[1665,90435,4032],{},[8818,90437,90438],{},[1665,90439,4573],{},[1654,90441,4554],{},[2582,90443,90444],{"scriptlevel":2062,"displaystyle":1656},[2811,90445,90446,90448],{},[1665,90447,1667],{},[90247,90449,90450,90453],{},[1665,90451,90452],{},"10000",[1665,90454,4035],{},[1654,90456,11492],{},[1665,90458,90459],{},"4,525.",[902,90461,90462],{"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.",[724,90464,90465,90466,11448,90483,12664],{},"Produkce poklesne přibližně o 4,525 (z ",[883,90467,90469],{"className":90468},[886],[888,90470,90471],{"xmlns":890},[892,90472,90473,90480],{},[895,90474,90475,90477],{},[1654,90476,11492],{},[1665,90478,90479],{},"905,126",[902,90481,90482],{"encoding":904},"\\approx 905{,}126",[883,90484,90486],{"className":90485},[886],[888,90487,90488],{"xmlns":890},[892,90489,90490,90497],{},[895,90491,90492,90494],{},[1654,90493,11492],{},[1665,90495,90496],{},"900,601",[902,90498,90499],{"encoding":904},"\\approx 900{,}601",[724,90501,90502,11885,90549,1343,90571,12664],{},[38,90503,90504,90505,2068,90527],{},"(c) Změna ",[883,90506,90508],{"className":90507},[886],[888,90509,90510],{"xmlns":890},[892,90511,90512,90524],{},[895,90513,90514,90516,90518,90520,90522],{},[898,90515,2450],{},[1654,90517,2781],{},[1665,90519,4573],{},[1654,90521,11878],{},[1665,90523,10207],{},[902,90525,90526],{"encoding":904},"L: 20 \\to 15",[883,90528,90530],{"className":90529},[886],[888,90531,90532],{"xmlns":890},[892,90533,90534,90546],{},[895,90535,90536,90538,90540,90542,90544],{},[898,90537,18517],{},[1654,90539,2781],{},[1665,90541,4273],{},[1654,90543,11878],{},[1665,90545,17528],{},[902,90547,90548],{"encoding":904},"K: 100 \\to 150",[883,90550,90552],{"className":90551},[886],[888,90553,90554],{"xmlns":890},[892,90555,90556,90568],{},[895,90557,90558,90560,90562,90564,90566],{},[898,90559,10977],{},[898,90561,2450],{},[1654,90563,1750],{},[1654,90565,2380],{},[1665,90567,4032],{},[902,90569,90570],{"encoding":904},"dL = -5",[883,90572,90574],{"className":90573},[886],[888,90575,90576],{"xmlns":890},[892,90577,90578,90588],{},[895,90579,90580,90582,90584,90586],{},[898,90581,10977],{},[898,90583,18517],{},[1654,90585,1750],{},[1665,90587,4767],{},[902,90589,90590],{"encoding":904},"dK = 50",[883,90592,90594],{"className":90593},[886],[888,90595,90596],{"xmlns":890,"display":1956},[892,90597,90598,90686],{},[895,90599,90600,90602,90604,90606,90608,90614,90616,90618,90620,90622,90624,90626,90628,90630,90632,90634,90636,90638,90644,90646,90648,90650,90652,90654,90656,90658,90660,90662,90664,90666,90668,90670,90672,90674,90677,90679,90681,90683],{},[898,90601,10977],{},[898,90603,1663],{},[1654,90605,1750],{},[898,90607,9320],{},[1710,90609,90610,90612],{},[898,90611,1755],{},[898,90613,2450],{},[1654,90615,1708],{"stretchy":1656},[1665,90617,4573],{},[1654,90619,1674],{"separator":1673},[1665,90621,4273],{},[1654,90623,1726],{"stretchy":1656},[1654,90625,4554],{},[1654,90627,1708],{"stretchy":1656},[1654,90629,2380],{},[1665,90631,4032],{},[1654,90633,1726],{"stretchy":1656},[1654,90635,1766],{},[898,90637,9320],{},[1710,90639,90640,90642],{},[898,90641,1755],{},[898,90643,18517],{},[1654,90645,1708],{"stretchy":1656},[1665,90647,4573],{},[1654,90649,1674],{"separator":1673},[1665,90651,4273],{},[1654,90653,1726],{"stretchy":1656},[1654,90655,4554],{},[1665,90657,4767],{},[1654,90659,1750],{},[1665,90661,90320],{},[1654,90663,4554],{},[1654,90665,1708],{"stretchy":1656},[1654,90667,2380],{},[1665,90669,4032],{},[1654,90671,1726],{"stretchy":1656},[1654,90673,1766],{},[1665,90675,90676],{},"4,525",[1654,90678,4554],{},[1665,90680,4767],{},[1654,90682,11492],{},[1665,90684,90685],{},"190,485.",[902,90687,90688],{"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.",[724,90690,90691],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,90693,90695],{"id":90694},"příklad-55","Příklad 5.5",[724,90697,90698,90699,90735,90736,2138],{},"Pro produkci ",[883,90700,90702],{"className":90701},[886],[888,90703,90704],{"xmlns":890},[892,90705,90706,90732],{},[895,90707,90708,90710,90712,90714,90716,90718,90720,90722,90728],{},[898,90709,1663],{},[1654,90711,1708],{"stretchy":1656},[898,90713,2450],{},[1654,90715,1674],{"separator":1673},[898,90717,18517],{},[1654,90719,1726],{"stretchy":1656},[1654,90721,1750],{},[90247,90723,90724,90726],{},[898,90725,2450],{},[1665,90727,4035],{},[8818,90729,90730],{},[898,90731,18517],{},[902,90733,90734],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,90737,90739],{"className":90738},[886],[888,90740,90741],{"xmlns":890},[892,90742,90743,90759],{},[895,90744,90745,90751,90755,90757],{},[90247,90746,90747,90749],{},[898,90748,2450],{},[1665,90750,4035],{},[8818,90752,90753],{},[898,90754,18517],{},[1654,90756,1750],{},[898,90758,89017],{},[902,90760,90761],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,90763,90764,90765,2138],{},"Umocněním na druhou: ",[883,90766,90768],{"className":90767},[886],[888,90769,90770],{"xmlns":890},[892,90771,90772,90796],{},[895,90773,90774,90776,90778,90784,90786],{},[898,90775,18517],{},[1654,90777,1750],{},[1741,90779,90780,90782],{},[898,90781,89017],{},[1665,90783,1681],{},[898,90785,1879],{"mathvariant":1878},[90247,90787,90788,90794],{},[1741,90789,90790,90792],{},[898,90791,2450],{},[1665,90793,1681],{},[1665,90795,4035],{},[902,90797,90798],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,90800,90801,90841,90881],{},[123,90802,90803],{},[883,90804,90806],{"className":90805},[886],[888,90807,90808],{"xmlns":890},[892,90809,90810,90838],{},[895,90811,90812,90814,90816,90818,90820,90822,90824,90826,90828],{},[898,90813,89017],{},[1654,90815,1750],{},[1665,90817,1667],{},[1654,90819,8634],{},[898,90821,18517],{},[1654,90823,1750],{},[1665,90825,1667],{},[898,90827,1879],{"mathvariant":1878},[90247,90829,90830,90836],{},[1741,90831,90832,90834],{},[898,90833,2450],{},[1665,90835,1681],{},[1665,90837,4035],{},[902,90839,90840],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,90842,90843],{},[883,90844,90846],{"className":90845},[886],[888,90847,90848],{"xmlns":890},[892,90849,90850,90878],{},[895,90851,90852,90854,90856,90858,90860,90862,90864,90866,90868],{},[898,90853,89017],{},[1654,90855,1750],{},[1665,90857,1681],{},[1654,90859,8634],{},[898,90861,18517],{},[1654,90863,1750],{},[1665,90865,7631],{},[898,90867,1879],{"mathvariant":1878},[90247,90869,90870,90876],{},[1741,90871,90872,90874],{},[898,90873,2450],{},[1665,90875,1681],{},[1665,90877,4035],{},[902,90879,90880],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,90882,90883],{},[883,90884,90886],{"className":90885},[886],[888,90887,90888],{"xmlns":890},[892,90889,90890,90918],{},[895,90891,90892,90894,90896,90898,90900,90902,90904,90906,90908],{},[898,90893,89017],{},[1654,90895,1750],{},[1665,90897,4035],{},[1654,90899,8634],{},[898,90901,18517],{},[1654,90903,1750],{},[1665,90905,12742],{},[898,90907,1879],{"mathvariant":1878},[90247,90909,90910,90916],{},[1741,90911,90912,90914],{},[898,90913,2450],{},[1665,90915,1681],{},[1665,90917,4035],{},[902,90919,90920],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,90922,90923],{},[614,90924,90925,90926,15201,90947,2138],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,90927,90929],{"className":90928},[886],[888,90930,90931],{"xmlns":890},[892,90932,90933,90945],{},[895,90934,90935,90937,90939,90941,90943],{},[1654,90936,1708],{"stretchy":1656},[898,90938,2450],{},[1654,90940,1674],{"separator":1673},[898,90942,18517],{},[1654,90944,1726],{"stretchy":1656},[902,90946,89143],{"encoding":904},[883,90948,90950],{"className":90949},[886],[888,90951,90952],{"xmlns":890},[892,90953,90954,90970],{},[895,90955,90956,90958,90960,90962,90964,90966,90968],{},[898,90957,89017],{},[1654,90959,1750],{},[1665,90961,1667],{},[1654,90963,1674],{"separator":1673},[1665,90965,1681],{},[1654,90967,1674],{"separator":1673},[1665,90969,4035],{},[902,90971,90972],{"encoding":904},"q = 1, 2, 3",[198,90974,90976],{"id":90975},"příklad-56","Příklad 5.6",[724,90978,84893,90979,2138],{},[883,90980,90982],{"className":90981},[886],[888,90983,90984],{"xmlns":890},[892,90985,90986,91002],{},[895,90987,90988,90990,90992,90994,90996,90998],{},[898,90989,1663],{},[1654,90991,1750],{},[1665,90993,1681],{},[898,90995,2450],{},[1654,90997,1766],{},[8818,90999,91000],{},[898,91001,18517],{},[902,91003,91004],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,91006,91008],{"className":91007},[886],[888,91009,91010],{"xmlns":890,"display":1956},[892,91011,91012,91054],{},[895,91013,91014,91016,91022,91024,91026,91028,91030,91032,91038,91040,91052],{},[898,91015,9320],{},[1710,91017,91018,91020],{},[898,91019,1755],{},[898,91021,2450],{},[1654,91023,1750],{},[1665,91025,1681],{},[1654,91027,1674],{"separator":1673},[5008,91029],{"width":14608},[898,91031,9320],{},[1710,91033,91034,91036],{},[898,91035,1755],{},[898,91037,18517],{},[1654,91039,1750],{},[2811,91041,91042,91044],{},[1665,91043,1667],{},[895,91045,91046,91048],{},[1665,91047,1681],{},[8818,91049,91050],{},[898,91051,18517],{},[898,91053,2138],{"mathvariant":1878},[902,91055,91056],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,91058,91060],{"className":91059},[886],[888,91061,91062],{"xmlns":890,"display":1956},[892,91063,91064,91128],{},[895,91065,91066,91068,91070,91072,91074,91076,91098,91100,91118,91120,91122,91126],{},[898,91067,9320],{},[898,91069,12737],{},[898,91071,11536],{},[898,91073,17398],{},[1654,91075,1750],{},[2811,91077,91078,91088],{},[895,91079,91080,91082],{},[898,91081,9320],{},[1710,91083,91084,91086],{},[898,91085,1755],{},[898,91087,2450],{},[895,91089,91090,91092],{},[898,91091,9320],{},[1710,91093,91094,91096],{},[898,91095,1755],{},[898,91097,18517],{},[1654,91099,1750],{},[2811,91101,91102,91104],{},[1665,91103,1681],{},[2582,91105,91106],{"scriptlevel":2062,"displaystyle":1656},[2811,91107,91108,91110],{},[1665,91109,1667],{},[895,91111,91112,91114],{},[1665,91113,1681],{},[8818,91115,91116],{},[898,91117,18517],{},[1654,91119,1750],{},[1665,91121,7631],{},[8818,91123,91124],{},[898,91125,18517],{},[898,91127,2138],{"mathvariant":1878},[902,91129,91130],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,91132,91133,91134,91177,91178,91217,91218,2138],{},"Například ",[883,91135,91137],{"className":91136},[886],[888,91138,91139],{"xmlns":890},[892,91140,91141,91174],{},[895,91142,91143,91145,91147,91149,91151,91153,91155,91157,91159,91161,91163,91165,91169,91171],{},[898,91144,9320],{},[898,91146,12737],{},[898,91148,11536],{},[898,91150,17398],{},[1654,91152,1708],{"stretchy":1656},[1665,91154,7631],{},[1654,91156,1674],{"separator":1673},[1665,91158,32887],{},[1654,91160,1726],{"stretchy":1656},[1654,91162,1750],{},[1665,91164,7631],{},[8818,91166,91167],{},[1665,91168,32887],{},[1654,91170,11492],{},[1665,91172,91173],{},"10,58",[902,91175,91176],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,91179,91181],{"className":91180},[886],[888,91182,91183],{"xmlns":890},[892,91184,91185,91214],{},[895,91186,91187,91189,91191,91193,91195,91197,91199,91201,91203,91205,91209,91211],{},[898,91188,1663],{},[1654,91190,1708],{"stretchy":1656},[1665,91192,7631],{},[1654,91194,1674],{"separator":1673},[1665,91196,32887],{},[1654,91198,1726],{"stretchy":1656},[1654,91200,1750],{},[1665,91202,14315],{},[1654,91204,1766],{},[8818,91206,91207],{},[1665,91208,32887],{},[1654,91210,11492],{},[1665,91212,91213],{},"10,646",[902,91215,91216],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,91219,91221],{"className":91220},[886],[888,91222,91223],{"xmlns":890},[892,91224,91225,91233],{},[895,91226,91227,91229],{},[1665,91228,7631],{},[8818,91230,91231],{},[1665,91232,32887],{},[902,91234,91235],{"encoding":904},"4\\sqrt{7}",[724,91237,91238,91239,91259],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,91240,91242],{"className":91241},[886],[888,91243,91244],{"xmlns":890},[892,91245,91246,91256],{},[895,91247,91248,91250,91252,91254],{},[898,91249,10977],{},[898,91251,2450],{},[1654,91253,1750],{},[1665,91255,1681],{},[902,91257,91258],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,91261,91263],{"className":91262},[886],[888,91264,91265],{"xmlns":890,"display":1956},[892,91266,91267,91316],{},[895,91268,91269,91271,91273,91275,91277,91279,91281,91283,91285,91287,91289,91291,91293,91295,91297,91299,91301,91303,91305,91309,91311,91313],{},[898,91270,10977],{},[898,91272,18517],{},[1654,91274,1750],{},[1654,91276,2380],{},[898,91278,9320],{},[898,91280,12737],{},[898,91282,11536],{},[898,91284,17398],{},[1654,91286,1708],{"stretchy":1656},[1665,91288,7631],{},[1654,91290,1674],{"separator":1673},[1665,91292,32887],{},[1654,91294,1726],{"stretchy":1656},[1654,91296,4554],{},[1665,91298,1681],{},[1654,91300,1750],{},[1654,91302,2380],{},[1665,91304,14315],{},[8818,91306,91307],{},[1665,91308,32887],{},[1654,91310,11492],{},[1654,91312,2380],{},[1665,91314,91315],{},"21,17.",[902,91317,91318],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,91320,91322],{"id":91321},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,91324,91325,91326,1343,91328,2068,91330,91332,91333,91336,91337,91340],{},"Hlavními faktory produkce jsou ",[38,91327,83134],{},[38,91329,83150],{},[38,91331,83166],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,91334,91335],{},"jednofaktorový"," (pouze práce) a ",[38,91338,91339],{},"dvoufaktorový"," (práce + kapitál) model.",[724,91342,91343,91344,91347,91348,91350,91351,91353,91354,34875,91357,91376,91377,91394,91395,91412,91413,91435,91436,13096,91455,2138],{},"V ",[38,91345,91346],{},"1F modelu"," se definuje ",[38,91349,18741],{}," (derivace produkce podle práce) a ",[38,91352,83069],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,91355,91356],{},"zákonu klesajících výnosů",[883,91358,91360],{"className":91359},[886],[888,91361,91362],{"xmlns":890},[892,91363,91364,91374],{},[895,91365,91366,91368],{},[898,91367,9320],{},[1710,91369,91370,91372],{},[898,91371,1755],{},[898,91373,2450],{},[902,91375,18762],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,91378,91380],{"className":91379},[886],[888,91381,91382],{"xmlns":890},[892,91383,91384,91392],{},[895,91385,91386],{},[1710,91387,91388,91390],{},[898,91389,2450],{},[1665,91391,2062],{},[902,91393,83778],{"encoding":904}," klesá a v bodě ",[883,91396,91398],{"className":91397},[886],[888,91399,91400],{"xmlns":890},[892,91401,91402,91410],{},[895,91403,91404],{},[1710,91405,91406,91408],{},[898,91407,2450],{},[1665,91409,1667],{},[902,91411,21921],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,91414,91415,91416],{},"princip maximalizace ",[883,91417,91419],{"className":91418},[886],[888,91420,91421],{"xmlns":890},[892,91422,91423,91433],{},[895,91424,91425,91427],{},[898,91426,4737],{},[1710,91428,91429,91431],{},[898,91430,1755],{},[898,91432,2450],{},[902,91434,82853],{"encoding":904},": v bodě maxima ",[883,91437,91439],{"className":91438},[886],[888,91440,91441],{"xmlns":890},[892,91442,91443,91453],{},[895,91444,91445,91447],{},[898,91446,4737],{},[1710,91448,91449,91451],{},[898,91450,1755],{},[898,91452,2450],{},[902,91454,82853],{"encoding":904},[883,91456,91458],{"className":91457},[886],[888,91459,91460],{"xmlns":890},[892,91461,91462,91482],{},[895,91463,91464,91466,91472,91474,91476],{},[898,91465,9320],{},[1710,91467,91468,91470],{},[898,91469,1755],{},[898,91471,2450],{},[1654,91473,1750],{},[898,91475,4737],{},[1710,91477,91478,91480],{},[898,91479,1755],{},[898,91481,2450],{},[902,91483,82883],{"encoding":904},[724,91485,91486,91487,91490,91491,2186,91494,91523,91524,91541,91542,91545,91546,91575,91576,91578,91579,16828,91609,91631],{},"Ve ",[38,91488,91489],{},"2F modelu"," se obvykle používají ",[38,91492,91493],{},"Cobb-Douglasovy funkce",[883,91495,91497],{"className":91496},[886],[888,91498,91499],{"xmlns":890},[892,91500,91501,91521],{},[895,91502,91503,91505,91507,91509,91515],{},[898,91504,1663],{},[1654,91506,1750],{},[898,91508,4737],{},[1741,91510,91511,91513],{},[898,91512,2450],{},[898,91514,207],{},[1741,91516,91517,91519],{},[898,91518,18517],{},[898,91520,9758],{},[902,91522,82950],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,91525,91527],{"className":91526},[886],[888,91528,91529],{"xmlns":890},[892,91530,91531,91539],{},[895,91532,91533,91535,91537],{},[898,91534,207],{},[1654,91536,1766],{},[898,91538,9758],{},[902,91540,83044],{"encoding":904}," rozlišujeme ",[38,91543,91544],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,91547,91549],{"className":91548},[886],[888,91550,91551],{"xmlns":890},[892,91552,91553,91573],{},[895,91554,91555,91557,91563,91565,91567],{},[898,91556,9320],{},[1710,91558,91559,91561],{},[898,91560,1755],{},[898,91562,2450],{},[1654,91564,1674],{"separator":1673},[898,91566,9320],{},[1710,91568,91569,91571],{},[898,91570,1755],{},[898,91572,18517],{},[902,91574,82981],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,91577,18496],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,91580,91582],{"className":91581},[886],[888,91583,91584],{"xmlns":890},[892,91585,91586,91606],{},[895,91587,91588,91590,91596,91598,91600],{},[898,91589,9320],{},[1710,91591,91592,91594],{},[898,91593,1755],{},[898,91595,2450],{},[898,91597,1879],{"mathvariant":1878},[898,91599,9320],{},[1710,91601,91602,91604],{},[898,91603,1755],{},[898,91605,18517],{},[902,91607,91608],{"encoding":904},"MP_L\u002FMP_K",[38,91610,91611,91612,1726],{},"mezní míra technické substituce (",[883,91613,91615],{"className":91614},[886],[888,91616,91617],{"xmlns":890},[892,91618,91619,91629],{},[895,91620,91621,91623,91625,91627],{},[898,91622,9320],{},[898,91624,12737],{},[898,91626,11536],{},[898,91628,17398],{},[902,91630,19315],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,91633,58102],{"id":58101},[152,91635,91636,91639,91642,91645,91648,91651,91654,91657,91660,91663,91666],{},[123,91637,91638],{},"Jaké jsou faktory produkce?",[123,91640,91641],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,91643,91644],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,91646,91647],{},"Co udává mezní produkt práce?",[123,91649,91650],{},"Co musí respektovat průběh křivky produkce?",[123,91652,91653],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,91655,91656],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,91658,91659],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,91661,91662],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,91664,91665],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,91667,91668],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,91670,91672],{"id":91671},"úlohy-51517","Úlohy 5.1–5.17",[198,91674,48671],{"id":48670},[724,91676,91677,91680,91681,91703,91704,1343,91724,1343,91744,91764],{},[38,91678,91679],{},"5.1"," Je dána produkce ",[883,91682,91684],{"className":91683},[886],[888,91685,91686],{"xmlns":890},[892,91687,91688,91700],{},[895,91689,91690,91692,91694,91696],{},[898,91691,1663],{},[1654,91693,1750],{},[1665,91695,4647],{},[8818,91697,91698],{},[898,91699,2450],{},[902,91701,91702],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,91705,91707],{"className":91706},[886],[888,91708,91709],{"xmlns":890},[892,91710,91711,91721],{},[895,91712,91713,91715,91717,91719],{},[898,91714,1663],{},[1654,91716,1708],{"stretchy":1656},[1665,91718,1667],{},[1654,91720,1726],{"stretchy":1656},[902,91722,91723],{"encoding":904},"Q(1)",[883,91725,91727],{"className":91726},[886],[888,91728,91729],{"xmlns":890},[892,91730,91731,91741],{},[895,91732,91733,91735,91737,91739],{},[898,91734,1663],{},[1654,91736,1708],{"stretchy":1656},[1665,91738,7631],{},[1654,91740,1726],{"stretchy":1656},[902,91742,91743],{"encoding":904},"Q(4)",[883,91745,91747],{"className":91746},[886],[888,91748,91749],{"xmlns":890},[892,91750,91751,91761],{},[895,91752,91753,91755,91757,91759],{},[898,91754,1663],{},[1654,91756,1708],{"stretchy":1656},[1665,91758,12742],{},[1654,91760,1726],{"stretchy":1656},[902,91762,91763],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,91766,91767,91680,91770,91806,91807,91820,91821,91840,91841,91867,91868,11448,91881,91894],{},[38,91768,91769],{},"5.2",[883,91771,91773],{"className":91772},[886],[888,91774,91775],{"xmlns":890},[892,91776,91777,91803],{},[895,91778,91779,91781,91783,91785,91787,91793,91795,91797],{},[898,91780,1663],{},[1654,91782,1750],{},[1654,91784,2380],{},[1665,91786,11555],{},[1741,91788,91789,91791],{},[898,91790,2450],{},[1665,91792,4035],{},[1654,91794,1766],{},[1665,91796,12742],{},[1741,91798,91799,91801],{},[898,91800,2450],{},[1665,91802,1681],{},[902,91804,91805],{"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 ",[883,91808,91810],{"className":91809},[886],[888,91811,91812],{"xmlns":890},[892,91813,91814,91818],{},[895,91815,91816],{},[898,91817,2450],{},[902,91819,2450],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,91822,91824],{"className":91823},[886],[888,91825,91826],{"xmlns":890},[892,91827,91828,91838],{},[895,91829,91830,91832],{},[898,91831,9320],{},[1710,91833,91834,91836],{},[898,91835,1755],{},[898,91837,2450],{},[902,91839,18762],{"encoding":904},". (f) Vypočtěte ",[883,91842,91844],{"className":91843},[886],[888,91845,91846],{"xmlns":890},[892,91847,91848,91864],{},[895,91849,91850,91852,91858,91860,91862],{},[898,91851,9320],{},[1710,91853,91854,91856],{},[898,91855,1755],{},[898,91857,2450],{},[1654,91859,1708],{"stretchy":1656},[1665,91861,4647],{},[1654,91863,1726],{"stretchy":1656},[902,91865,91866],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,91869,91871],{"className":91870},[886],[888,91872,91873],{"xmlns":890},[892,91874,91875,91879],{},[895,91876,91877],{},[1665,91878,4647],{},[902,91880,4647],{"encoding":904},[883,91882,91884],{"className":91883},[886],[888,91885,91886],{"xmlns":890},[892,91887,91888,91892],{},[895,91889,91890],{},[1665,91891,50507],{},[902,91893,50507],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,91896,91897,91900,91901,91923,91924,91952,91953,91984,91985,2138],{},[38,91898,91899],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,91902,91904],{"className":91903},[886],[888,91905,91906],{"xmlns":890},[892,91907,91908,91920],{},[895,91909,91910,91912,91914,91916],{},[898,91911,1663],{},[1654,91913,1750],{},[1665,91915,4011],{},[8818,91917,91918],{},[898,91919,2450],{},[902,91921,91922],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,91925,91927],{"className":91926},[886],[888,91928,91929],{"xmlns":890},[892,91930,91931,91949],{},[895,91932,91933,91935,91937,91939,91943,91945,91947],{},[898,91934,1663],{},[1654,91936,1750],{},[1665,91938,4006],{},[8818,91940,91941],{},[898,91942,2450],{},[1654,91944,2380],{},[1665,91946,7631],{},[898,91948,2450],{},[902,91950,91951],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,91954,91956],{"className":91955},[886],[888,91957,91958],{"xmlns":890},[892,91959,91960,91981],{},[895,91961,91962,91964,91966,91968,91970,91972,91975],{},[898,91963,1663],{},[1654,91965,1750],{},[1665,91967,4767],{},[898,91969,2450],{},[1654,91971,2380],{},[1665,91973,91974],{},"0,01",[1741,91976,91977,91979],{},[898,91978,2450],{},[1665,91980,1681],{},[902,91982,91983],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,91986,91988],{"className":91987},[886],[888,91989,91990],{"xmlns":890},[892,91991,91992,92018],{},[895,91993,91994,91996,91998,92000,92002,92008,92010,92012],{},[898,91995,1663],{},[1654,91997,1750],{},[1654,91999,2380],{},[1665,92001,76431],{},[1741,92003,92004,92006],{},[898,92005,2450],{},[1665,92007,4035],{},[1654,92009,1766],{},[1665,92011,12742],{},[1741,92013,92014,92016],{},[898,92015,2450],{},[1665,92017,1681],{},[902,92019,92020],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,92022,92023,92026,92027,11387,92046,80418,92063,2138],{},[38,92024,92025],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,92028,92030],{"className":92029},[886],[888,92031,92032],{"xmlns":890},[892,92033,92034,92044],{},[895,92035,92036,92038],{},[898,92037,4737],{},[1710,92039,92040,92042],{},[898,92041,1755],{},[898,92043,2450],{},[902,92045,82853],{"encoding":904},[883,92047,92049],{"className":92048},[886],[888,92050,92051],{"xmlns":890},[892,92052,92053,92061],{},[895,92054,92055],{},[1710,92056,92057,92059],{},[898,92058,2450],{},[1665,92060,2062],{},[902,92062,83778],{"encoding":904},[883,92064,92066],{"className":92065},[886],[888,92067,92068],{"xmlns":890},[892,92069,92070,92110],{},[895,92071,92072,92074,92080,92082,92088,92090,92092,92094,92100,92102,92108],{},[898,92073,4737],{},[1710,92075,92076,92078],{},[898,92077,1755],{},[898,92079,2450],{},[1654,92081,1708],{"stretchy":1656},[1710,92083,92084,92086],{},[898,92085,2450],{},[1665,92087,2062],{},[1654,92089,1726],{"stretchy":1656},[1654,92091,1750],{},[898,92093,9320],{},[1710,92095,92096,92098],{},[898,92097,1755],{},[898,92099,2450],{},[1654,92101,1708],{"stretchy":1656},[1710,92103,92104,92106],{},[898,92105,2450],{},[1665,92107,2062],{},[1654,92109,1726],{"stretchy":1656},[902,92111,92112],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,92114,92115,91680,92118,9762,92154,92167,92168,92187],{},[38,92116,92117],{},"5.5",[883,92119,92121],{"className":92120},[886],[888,92122,92123],{"xmlns":890},[892,92124,92125,92151],{},[895,92126,92127,92129,92131,92133,92135,92141,92143,92145],{},[898,92128,1663],{},[1654,92130,1750],{},[1654,92132,2380],{},[1665,92134,11599],{},[1741,92136,92137,92139],{},[898,92138,2450],{},[1665,92140,4035],{},[1654,92142,1766],{},[1665,92144,6509],{},[1741,92146,92147,92149],{},[898,92148,2450],{},[1665,92150,1681],{},[902,92152,92153],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,92155,92157],{"className":92156},[886],[888,92158,92159],{"xmlns":890},[892,92160,92161,92165],{},[895,92162,92163],{},[898,92164,2450],{},[902,92166,2450],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,92169,92171],{"className":92170},[886],[888,92172,92173],{"xmlns":890},[892,92174,92175,92185],{},[895,92176,92177,92179],{},[898,92178,4737],{},[1710,92180,92181,92183],{},[898,92182,1755],{},[898,92184,2450],{},[902,92186,82853],{"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.",[198,92189,92191],{"id":92190},"dvoufaktorový-model","Dvoufaktorový model",[724,92193,92194,92197,92198,91923,92224,91952,92266,2138],{},[38,92195,92196],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,92199,92201],{"className":92200},[886],[888,92202,92203],{"xmlns":890},[892,92204,92205,92221],{},[895,92206,92207,92209,92211,92213,92215],{},[898,92208,1663],{},[1654,92210,1750],{},[1665,92212,32887],{},[898,92214,2450],{},[1741,92216,92217,92219],{},[898,92218,18517],{},[1665,92220,1681],{},[902,92222,92223],{"encoding":904},"Q = 7 L K^{2}",[883,92225,92227],{"className":92226},[886],[888,92228,92229],{"xmlns":890},[892,92230,92231,92263],{},[895,92232,92233,92235,92237,92239,92251],{},[898,92234,1663],{},[1654,92236,1750],{},[1665,92238,4767],{},[1741,92240,92241,92243],{},[898,92242,2450],{},[895,92244,92245,92247,92249],{},[1665,92246,1681],{},[898,92248,1879],{"mathvariant":1878},[1665,92250,4035],{},[1741,92252,92253,92255],{},[898,92254,18517],{},[895,92256,92257,92259,92261],{},[1665,92258,1667],{},[898,92260,1879],{"mathvariant":1878},[1665,92262,4035],{},[902,92264,92265],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,92267,92269],{"className":92268},[886],[888,92270,92271],{"xmlns":890},[892,92272,92273,92305],{},[895,92274,92275,92277,92279,92281,92293],{},[898,92276,1663],{},[1654,92278,1750],{},[1665,92280,12457],{},[1741,92282,92283,92285],{},[898,92284,2450],{},[895,92286,92287,92289,92291],{},[1665,92288,4035],{},[898,92290,1879],{"mathvariant":1878},[1665,92292,4032],{},[1741,92294,92295,92297],{},[898,92296,18517],{},[895,92298,92299,92301,92303],{},[1665,92300,1681],{},[898,92302,1879],{"mathvariant":1878},[1665,92304,4032],{},[902,92306,92307],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,92309,92310,91680,92313,92355,92356,1343,92374,92393,92394,92411],{},[38,92311,92312],{},"5.7",[883,92314,92316],{"className":92315},[886],[888,92317,92318],{"xmlns":890},[892,92319,92320,92352],{},[895,92321,92322,92324,92326,92328,92340],{},[898,92323,1663],{},[1654,92325,1750],{},[1665,92327,4647],{},[1741,92329,92330,92332],{},[898,92331,2450],{},[895,92333,92334,92336,92338],{},[1665,92335,1667],{},[898,92337,1879],{"mathvariant":1878},[1665,92339,1681],{},[1741,92341,92342,92344],{},[898,92343,18517],{},[895,92345,92346,92348,92350],{},[1665,92347,1667],{},[898,92349,1879],{"mathvariant":1878},[1665,92351,1681],{},[902,92353,92354],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,92357,92359],{"className":92358},[886],[888,92360,92361],{"xmlns":890},[892,92362,92363,92371],{},[895,92364,92365,92367,92369],{},[898,92366,2450],{},[1654,92368,1750],{},[1665,92370,28837],{},[902,92372,92373],{"encoding":904},"L = 400",[883,92375,92377],{"className":92376},[886],[888,92378,92379],{"xmlns":890},[892,92380,92381,92390],{},[895,92382,92383,92385,92387],{},[898,92384,18517],{},[1654,92386,1750],{},[1665,92388,92389],{},"17576",[902,92391,92392],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,92395,92397],{"className":92396},[886],[888,92398,92399],{"xmlns":890},[892,92400,92401,92409],{},[895,92402,92403,92405,92407],{},[898,92404,2450],{},[1654,92406,1674],{"separator":1673},[898,92408,18517],{},[902,92410,87205],{"encoding":904}," zdvojnásobí.",[724,92413,92414,92417,92418,92355,92449,1343,92467,77804,92485,92515,92516,92546,92547,11448,92560,92574,92575,11448,92588,92601],{},[38,92415,92416],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,92419,92421],{"className":92420},[886],[888,92422,92423],{"xmlns":890},[892,92424,92425,92446],{},[895,92426,92427,92429,92431,92434,92440],{},[898,92428,1663],{},[1654,92430,1750],{},[1665,92432,92433],{},"1,01",[1741,92435,92436,92438],{},[898,92437,2450],{},[1665,92439,32417],{},[1741,92441,92442,92444],{},[898,92443,18517],{},[1665,92445,7154],{},[902,92447,92448],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,92450,92452],{"className":92451},[886],[888,92453,92454],{"xmlns":890},[892,92455,92456,92464],{},[895,92457,92458,92460,92462],{},[898,92459,2450],{},[1654,92461,1750],{},[1665,92463,4679],{},[902,92465,92466],{"encoding":904},"L = 250",[883,92468,92470],{"className":92469},[886],[888,92471,92472],{"xmlns":890},[892,92473,92474,92482],{},[895,92475,92476,92478,92480],{},[898,92477,18517],{},[1654,92479,1750],{},[1665,92481,11544],{},[902,92483,92484],{"encoding":904},"K = 1000",[883,92486,92488],{"className":92487},[886],[888,92489,92490],{"xmlns":890},[892,92491,92492,92512],{},[895,92493,92494,92496,92502,92504,92506,92508,92510],{},[898,92495,9320],{},[1710,92497,92498,92500],{},[898,92499,1755],{},[898,92501,2450],{},[1654,92503,1708],{"stretchy":1656},[1665,92505,4679],{},[1654,92507,1674],{"separator":1673},[1665,92509,11544],{},[1654,92511,1726],{"stretchy":1656},[902,92513,92514],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,92517,92519],{"className":92518},[886],[888,92520,92521],{"xmlns":890},[892,92522,92523,92543],{},[895,92524,92525,92527,92533,92535,92537,92539,92541],{},[898,92526,9320],{},[1710,92528,92529,92531],{},[898,92530,1755],{},[898,92532,18517],{},[1654,92534,1708],{"stretchy":1656},[1665,92536,4679],{},[1654,92538,1674],{"separator":1673},[1665,92540,11544],{},[1654,92542,1726],{"stretchy":1656},[902,92544,92545],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,92548,92550],{"className":92549},[886],[888,92551,92552],{"xmlns":890},[892,92553,92554,92558],{},[895,92555,92556],{},[898,92557,2450],{},[902,92559,2450],{"encoding":904},[883,92561,92563],{"className":92562},[886],[888,92564,92565],{"xmlns":890},[892,92566,92567,92572],{},[895,92568,92569],{},[1665,92570,92571],{},"260",[902,92573,92571],{"encoding":904}," a současném poklesu ",[883,92576,92578],{"className":92577},[886],[888,92579,92580],{"xmlns":890},[892,92581,92582,92586],{},[895,92583,92584],{},[898,92585,18517],{},[902,92587,18517],{"encoding":904},[883,92589,92591],{"className":92590},[886],[888,92592,92593],{"xmlns":890},[892,92594,92595,92599],{},[895,92596,92597],{},[1665,92598,23899],{},[902,92600,23899],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,92603,92604,92607,92608,2138],{},[38,92605,92606],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,92609,92611],{"className":92610},[886],[888,92612,92613],{"xmlns":890},[892,92614,92615,92635],{},[895,92616,92617,92619,92621,92623,92629],{},[898,92618,1663],{},[1654,92620,1750],{},[1665,92622,4647],{},[1741,92624,92625,92627],{},[898,92626,2450],{},[1665,92628,76431],{},[1741,92630,92631,92633],{},[898,92632,18517],{},[1665,92634,7594],{},[902,92636,92637],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,92639,92640,92643,92644,88801,92667,19111,92680,18742,92730,12664],{},[38,92641,92642],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,92645,92647],{"className":92646},[886],[888,92648,92649],{"xmlns":890},[892,92650,92651,92665],{},[895,92652,92653,92655,92657,92659,92661,92663],{},[898,92654,1663],{},[1654,92656,1708],{"stretchy":1656},[898,92658,2450],{},[1654,92660,1674],{"separator":1673},[898,92662,18517],{},[1654,92664,1726],{"stretchy":1656},[902,92666,18714],{"encoding":904},[883,92668,92670],{"className":92669},[886],[888,92671,92672],{"xmlns":890},[892,92673,92674,92678],{},[895,92675,92676],{},[898,92677,45080],{},[902,92679,45080],{"encoding":904},[883,92681,92683],{"className":92682},[886],[888,92684,92685],{"xmlns":890},[892,92686,92687,92727],{},[895,92688,92689,92691,92699,92701,92703,92711,92713,92715,92717,92719,92721,92723,92725],{},[898,92690,2450],{},[1659,92692,92693,92695,92697],{},[898,92694,1663],{},[898,92696,2450],{},[1654,92698,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,92700,1766],{},[898,92702,18517],{},[1659,92704,92705,92707,92709],{},[898,92706,1663],{},[898,92708,18517],{},[1654,92710,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,92712,1750],{},[898,92714,45080],{},[898,92716,1663],{},[1654,92718,1708],{"stretchy":1656},[898,92720,2450],{},[1654,92722,1674],{"separator":1673},[898,92724,18517],{},[1654,92726,1726],{"stretchy":1656},[902,92728,92729],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,92731,88776],{},[724,92733,92734,92737],{},[38,92735,92736],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,92739,92740,91680,92743,92783,92784,1343,92806,1343,92828,92850],{},[38,92741,92742],{},"5.12",[883,92744,92746],{"className":92745},[886],[888,92747,92748],{"xmlns":890},[892,92749,92750,92780],{},[895,92751,92752,92754,92756,92768],{},[898,92753,1663],{},[1654,92755,1750],{},[1741,92757,92758,92760],{},[898,92759,2450],{},[895,92761,92762,92764,92766],{},[1665,92763,1667],{},[898,92765,1879],{"mathvariant":1878},[1665,92767,4035],{},[1741,92769,92770,92772],{},[898,92771,18517],{},[895,92773,92774,92776,92778],{},[1665,92775,1667],{},[898,92777,1879],{"mathvariant":1878},[1665,92779,7631],{},[902,92781,92782],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,92785,92787],{"className":92786},[886],[888,92788,92789],{"xmlns":890},[892,92790,92791,92803],{},[895,92792,92793,92799,92801],{},[1710,92794,92795,92797],{},[898,92796,89017],{},[1665,92798,2062],{},[1654,92800,1750],{},[1665,92802,1667],{},[902,92804,92805],{"encoding":904},"q_0 = 1",[883,92807,92809],{"className":92808},[886],[888,92810,92811],{"xmlns":890},[892,92812,92813,92825],{},[895,92814,92815,92821,92823],{},[1710,92816,92817,92819],{},[898,92818,89017],{},[1665,92820,1667],{},[1654,92822,1750],{},[1665,92824,1681],{},[902,92826,92827],{"encoding":904},"q_1 = 2",[883,92829,92831],{"className":92830},[886],[888,92832,92833],{"xmlns":890},[892,92834,92835,92847],{},[895,92836,92837,92843,92845],{},[1710,92838,92839,92841],{},[898,92840,89017],{},[1665,92842,1681],{},[1654,92844,1750],{},[1665,92846,4035],{},[902,92848,92849],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,92852,92853,91680,92856,92896,92897,1343,92925,1343,92953,1343,92981,1343,93010,1343,93039,1343,93068,1343,93097,1343,93126,2138],{},[38,92854,92855],{},"5.13",[883,92857,92859],{"className":92858},[886],[888,92860,92861],{"xmlns":890},[892,92862,92863,92893],{},[895,92864,92865,92867,92869,92881],{},[898,92866,1663],{},[1654,92868,1750],{},[1741,92870,92871,92873],{},[898,92872,2450],{},[895,92874,92875,92877,92879],{},[1665,92876,1667],{},[898,92878,1879],{"mathvariant":1878},[1665,92880,4035],{},[1741,92882,92883,92885],{},[898,92884,18517],{},[895,92886,92887,92889,92891],{},[1665,92888,1667],{},[898,92890,1879],{"mathvariant":1878},[1665,92892,1681],{},[902,92894,92895],{"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): ",[883,92898,92900],{"className":92899},[886],[888,92901,92902],{"xmlns":890},[892,92903,92904,92922],{},[895,92905,92906,92912,92914,92916,92918,92920],{},[1710,92907,92908,92910],{},[898,92909,4737],{},[1665,92911,1667],{},[1654,92913,1657],{"stretchy":1656},[1665,92915,1667],{},[1654,92917,17150],{"separator":1673},[1665,92919,1667],{},[1654,92921,1686],{"stretchy":1656},[902,92923,92924],{"encoding":904},"A_1[1; 1]",[883,92926,92928],{"className":92927},[886],[888,92929,92930],{"xmlns":890},[892,92931,92932,92950],{},[895,92933,92934,92940,92942,92944,92946,92948],{},[1710,92935,92936,92938],{},[898,92937,4737],{},[1665,92939,1681],{},[1654,92941,1657],{"stretchy":1656},[1665,92943,1667],{},[1654,92945,17150],{"separator":1673},[1665,92947,14315],{},[1654,92949,1686],{"stretchy":1656},[902,92951,92952],{"encoding":904},"A_2[1; 8]",[883,92954,92956],{"className":92955},[886],[888,92957,92958],{"xmlns":890},[892,92959,92960,92978],{},[895,92961,92962,92968,92970,92972,92974,92976],{},[1710,92963,92964,92966],{},[898,92965,4737],{},[1665,92967,4035],{},[1654,92969,1657],{"stretchy":1656},[1665,92971,1667],{},[1654,92973,17150],{"separator":1673},[1665,92975,74817],{},[1654,92977,1686],{"stretchy":1656},[902,92979,92980],{"encoding":904},"A_3[1; 27]",[883,92982,92984],{"className":92983},[886],[888,92985,92986],{"xmlns":890},[892,92987,92988,93007],{},[895,92989,92990,92996,92998,93000,93002,93005],{},[1710,92991,92992,92994],{},[898,92993,4737],{},[1665,92995,7631],{},[1654,92997,1657],{"stretchy":1656},[1665,92999,1681],{},[1654,93001,17150],{"separator":1673},[1665,93003,93004],{},"0,353",[1654,93006,1686],{"stretchy":1656},[902,93008,93009],{"encoding":904},"A_4[2; 0{,}353]",[883,93011,93013],{"className":93012},[886],[888,93014,93015],{"xmlns":890},[892,93016,93017,93036],{},[895,93018,93019,93025,93027,93029,93031,93034],{},[1710,93020,93021,93023],{},[898,93022,4737],{},[1665,93024,4032],{},[1654,93026,1657],{"stretchy":1656},[1665,93028,1681],{},[1654,93030,17150],{"separator":1673},[1665,93032,93033],{},"2,828",[1654,93035,1686],{"stretchy":1656},[902,93037,93038],{"encoding":904},"A_5[2; 2{,}828]",[883,93040,93042],{"className":93041},[886],[888,93043,93044],{"xmlns":890},[892,93045,93046,93065],{},[895,93047,93048,93054,93056,93058,93060,93063],{},[1710,93049,93050,93052],{},[898,93051,4737],{},[1665,93053,11015],{},[1654,93055,1657],{"stretchy":1656},[1665,93057,1681],{},[1654,93059,17150],{"separator":1673},[1665,93061,93062],{},"9,545",[1654,93064,1686],{"stretchy":1656},[902,93066,93067],{"encoding":904},"A_6[2; 9{,}545]",[883,93069,93071],{"className":93070},[886],[888,93072,93073],{"xmlns":890},[892,93074,93075,93094],{},[895,93076,93077,93083,93085,93087,93089,93092],{},[1710,93078,93079,93081],{},[898,93080,4737],{},[1665,93082,32887],{},[1654,93084,1657],{"stretchy":1656},[1665,93086,72779],{},[1654,93088,17150],{"separator":1673},[1665,93090,93091],{},"0,544",[1654,93093,1686],{"stretchy":1656},[902,93095,93096],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,93098,93100],{"className":93099},[886],[888,93101,93102],{"xmlns":890},[892,93103,93104,93123],{},[895,93105,93106,93112,93114,93116,93118,93121],{},[1710,93107,93108,93110],{},[898,93109,4737],{},[1665,93111,14315],{},[1654,93113,1657],{"stretchy":1656},[1665,93115,72779],{},[1654,93117,17150],{"separator":1673},[1665,93119,93120],{},"14,696",[1654,93122,1686],{"stretchy":1656},[902,93124,93125],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,93127,93129],{"className":93128},[886],[888,93130,93131],{"xmlns":890},[892,93132,93133,93151],{},[895,93134,93135,93141,93143,93145,93147,93149],{},[1710,93136,93137,93139],{},[898,93138,4737],{},[1665,93140,12742],{},[1654,93142,1657],{"stretchy":1656},[1665,93144,1681],{},[1654,93146,17150],{"separator":1673},[1665,93148,4032],{},[1654,93150,1686],{"stretchy":1656},[902,93152,93153],{"encoding":904},"A_9[2; 5]",[724,93155,93156,93159],{},[38,93157,93158],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,93161,93162,93165,93166,93196,93197,93210,93211,93224,93225,77537,93244,93263,93264,2138],{},[38,93163,93164],{},"5.15"," Produkce firmy je dána vztahem ",[883,93167,93169],{"className":93168},[886],[888,93170,93171],{"xmlns":890},[892,93172,93173,93193],{},[895,93174,93175,93177,93179,93181,93187],{},[898,93176,1663],{},[1654,93178,1750],{},[1665,93180,1681],{},[1741,93182,93183,93185],{},[898,93184,2450],{},[1665,93186,7594],{},[1741,93188,93189,93191],{},[898,93190,18517],{},[1665,93192,7154],{},[902,93194,93195],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,93198,93200],{"className":93199},[886],[888,93201,93202],{"xmlns":890},[892,93203,93204,93208],{},[895,93205,93206],{},[1665,93207,4273],{},[902,93209,4273],{"encoding":904}," pracovníků a disponuje-li ",[883,93212,93214],{"className":93213},[886],[888,93215,93216],{"xmlns":890},[892,93217,93218,93222],{},[895,93219,93220],{},[1665,93221,72655],{},[902,93223,72655],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,93226,93228],{"className":93227},[886],[888,93229,93230],{"xmlns":890},[892,93231,93232,93242],{},[895,93233,93234,93236,93238,93240],{},[898,93235,9320],{},[898,93237,12737],{},[898,93239,11536],{},[898,93241,17398],{},[902,93243,19315],{"encoding":904},[883,93245,93247],{"className":93246},[886],[888,93248,93249],{"xmlns":890},[892,93250,93251,93261],{},[895,93252,93253,93255,93257,93259],{},[898,93254,9320],{},[898,93256,12737],{},[898,93258,11536],{},[898,93260,17398],{},[902,93262,19315],{"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 ",[883,93265,93267],{"className":93266},[886],[888,93268,93269],{"xmlns":890},[892,93270,93271,93276],{},[895,93272,93273],{},[1665,93274,93275],{},"95",[902,93277,93275],{"encoding":904},[724,93279,93280,91680,93283,79211,93315,93334,93335,93348,93349,93362,93363,93376],{},[38,93281,93282],{},"5.16",[883,93284,93286],{"className":93285},[886],[888,93287,93288],{"xmlns":890},[892,93289,93290,93312],{},[895,93291,93292,93294,93296,93302,93304,93306],{},[898,93293,1663],{},[1654,93295,1750],{},[1741,93297,93298,93300],{},[898,93299,18517],{},[1665,93301,1681],{},[1654,93303,1766],{},[1665,93305,1681],{},[1741,93307,93308,93310],{},[898,93309,2450],{},[1665,93311,1681],{},[902,93313,93314],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,93316,93318],{"className":93317},[886],[888,93319,93320],{"xmlns":890},[892,93321,93322,93332],{},[895,93323,93324,93326,93328,93330],{},[898,93325,9320],{},[898,93327,12737],{},[898,93329,11536],{},[898,93331,17398],{},[902,93333,19315],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,93336,93338],{"className":93337},[886],[888,93339,93340],{"xmlns":890},[892,93341,93342,93346],{},[895,93343,93344],{},[1665,93345,4767],{},[902,93347,4767],{"encoding":904}," pracovníky a ",[883,93350,93352],{"className":93351},[886],[888,93353,93354],{"xmlns":890},[892,93355,93356,93360],{},[895,93357,93358],{},[1665,93359,85837],{},[902,93361,85837],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,93364,93366],{"className":93365},[886],[888,93367,93368],{"xmlns":890},[892,93369,93370,93374],{},[895,93371,93372],{},[1665,93373,54923],{},[902,93375,54923],{"encoding":904}," jednotek.",[724,93378,93379,93382,93383,19111,93413,2138],{},[38,93380,93381],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,93384,93386],{"className":93385},[886],[888,93387,93388],{"xmlns":890},[892,93389,93390,93410],{},[895,93391,93392,93394,93396,93398,93404],{},[898,93393,1663],{},[1654,93395,1750],{},[898,93397,4737],{},[1741,93399,93400,93402],{},[898,93401,2450],{},[898,93403,207],{},[1741,93405,93406,93408],{},[898,93407,18517],{},[898,93409,9758],{},[902,93411,93412],{"encoding":904},"Q = A L^{a} K^{b}",[883,93414,93416],{"className":93415},[886],[888,93417,93418],{"xmlns":890},[892,93419,93420,93450],{},[895,93421,93422,93424,93426,93428,93430,93432,93440,93442],{},[898,93423,9320],{},[898,93425,12737],{},[898,93427,11536],{},[898,93429,17398],{},[1654,93431,1750],{},[2582,93433,93434],{"scriptlevel":2062,"displaystyle":1656},[2811,93435,93436,93438],{},[898,93437,207],{},[898,93439,9758],{},[1654,93441,4554],{},[2582,93443,93444],{"scriptlevel":2062,"displaystyle":1656},[2811,93445,93446,93448],{},[898,93447,18517],{},[898,93449,2450],{},[902,93451,93452],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,93454,10214],{"id":10213},[120,93456,93457,93490,93517,93526,93576,93607,93660,93683,93738,93811,93889,93932,93964,93997,94038,94110,94171,94237,94254,94327,94393,94445,94501,94535,94578],{},[123,93458,93459,93462,93463,45116,93476,93489],{},[38,93460,93461],{},"Faktory (vstupy) produkce:"," práce ",[883,93464,93466],{"className":93465},[886],[888,93467,93468],{"xmlns":890},[892,93469,93470,93474],{},[895,93471,93472],{},[898,93473,2450],{},[902,93475,2450],{"encoding":904},[883,93477,93479],{"className":93478},[886],[888,93480,93481],{"xmlns":890},[892,93482,93483,93487],{},[895,93484,93485],{},[898,93486,18517],{},[902,93488,18517],{"encoding":904},", půda.",[123,93491,93492,10373,93494,2138],{},[38,93493,48671],{},[883,93495,93497],{"className":93496},[886],[888,93498,93499],{"xmlns":890},[892,93500,93501,93515],{},[895,93502,93503,93505,93507,93509,93511,93513],{},[898,93504,1663],{},[1654,93506,1750],{},[898,93508,1663],{},[1654,93510,1708],{"stretchy":1656},[898,93512,2450],{},[1654,93514,1726],{"stretchy":1656},[902,93516,82764],{"encoding":904},[123,93518,93519,18742,93521,20840,93524,2138],{},[38,93520,859],{},[614,93522,93523],{},"production function",[38,93525,83267],{},[123,93527,93528,2186,93530,2138],{},[38,93529,83313],{},[883,93531,93533],{"className":93532},[886],[888,93534,93535],{"xmlns":890},[892,93536,93537,93573],{},[895,93538,93539,93541,93547,93549,93551,93553,93555,93557,93559,93561,93567,93569,93571],{},[898,93540,9320],{},[1710,93542,93543,93545],{},[898,93544,1755],{},[898,93546,2450],{},[1654,93548,1750],{},[898,93550,10977],{},[898,93552,1663],{},[898,93554,1879],{"mathvariant":1878},[898,93556,10977],{},[898,93558,2450],{},[1654,93560,1750],{},[1741,93562,93563,93565],{},[898,93564,1663],{},[1654,93566,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,93568,1708],{"stretchy":1656},[898,93570,2450],{},[1654,93572,1726],{"stretchy":1656},[902,93574,93575],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,93577,93578,2186,93580,2138],{},[38,93579,84248],{},[883,93581,93583],{"className":93582},[886],[888,93584,93585],{"xmlns":890},[892,93586,93587,93605],{},[895,93588,93589,93591,93597,93599,93601,93603],{},[898,93590,4737],{},[1710,93592,93593,93595],{},[898,93594,1755],{},[898,93596,2450],{},[1654,93598,1750],{},[898,93600,1663],{},[898,93602,1879],{"mathvariant":1878},[898,93604,2450],{},[902,93606,82832],{"encoding":904},[123,93608,93609,93611,93612,19111,93629,2138],{},[38,93610,83735],{}," — od určitého ",[883,93613,93615],{"className":93614},[886],[888,93616,93617],{"xmlns":890},[892,93618,93619,93627],{},[895,93620,93621],{},[1710,93622,93623,93625],{},[898,93624,2450],{},[1665,93626,2062],{},[902,93628,83778],{"encoding":904},[883,93630,93632],{"className":93631},[886],[888,93633,93634],{"xmlns":890},[892,93635,93636,93658],{},[895,93637,93638,93648,93650,93652,93654,93656],{},[1741,93639,93640,93642],{},[898,93641,1663],{},[895,93643,93644,93646],{},[1654,93645,2592],{"mathvariant":1878},[1654,93647,2592],{"mathvariant":1878},[1654,93649,1708],{"stretchy":1656},[898,93651,2450],{},[1654,93653,1726],{"stretchy":1656},[1654,93655,3002],{},[1665,93657,2062],{},[902,93659,83924],{"encoding":904},[123,93661,93662,2186,93665,93682],{},[38,93663,93664],{},"Inflexní bod",[883,93666,93668],{"className":93667},[886],[888,93669,93670],{"xmlns":890},[892,93671,93672,93680],{},[895,93673,93674],{},[1710,93675,93676,93678],{},[898,93677,2450],{},[1665,93679,2062],{},[902,93681,83778],{"encoding":904}," — přechod z konvexity do konkavity.",[123,93684,93685,2186,93688,10373,93705,2138],{},[38,93686,93687],{},"Bod maxima produkce",[883,93689,93691],{"className":93690},[886],[888,93692,93693],{"xmlns":890},[892,93694,93695,93703],{},[895,93696,93697],{},[1710,93698,93699,93701],{},[898,93700,2450],{},[1665,93702,1667],{},[902,93704,21921],{"encoding":904},[883,93706,93708],{"className":93707},[886],[888,93709,93710],{"xmlns":890},[892,93711,93712,93736],{},[895,93713,93714,93716,93722,93724,93730,93732,93734],{},[898,93715,9320],{},[1710,93717,93718,93720],{},[898,93719,1755],{},[898,93721,2450],{},[1654,93723,1708],{"stretchy":1656},[1710,93725,93726,93728],{},[898,93727,2450],{},[1665,93729,1667],{},[1654,93731,1726],{"stretchy":1656},[1654,93733,1750],{},[1665,93735,2062],{},[902,93737,83997],{"encoding":904},[123,93739,93740,93762,93763,19111,93782,2138],{},[38,93741,93742,93743],{},"Princip maximalizace ",[883,93744,93746],{"className":93745},[886],[888,93747,93748],{"xmlns":890},[892,93749,93750,93760],{},[895,93751,93752,93754],{},[898,93753,4737],{},[1710,93755,93756,93758],{},[898,93757,1755],{},[898,93759,2450],{},[902,93761,82853],{"encoding":904}," — v bodě maxima ",[883,93764,93766],{"className":93765},[886],[888,93767,93768],{"xmlns":890},[892,93769,93770,93780],{},[895,93771,93772,93774],{},[898,93773,4737],{},[1710,93775,93776,93778],{},[898,93777,1755],{},[898,93779,2450],{},[902,93781,82853],{"encoding":904},[883,93783,93785],{"className":93784},[886],[888,93786,93787],{"xmlns":890},[892,93788,93789,93809],{},[895,93790,93791,93793,93799,93801,93803],{},[898,93792,9320],{},[1710,93794,93795,93797],{},[898,93796,1755],{},[898,93798,2450],{},[1654,93800,1750],{},[898,93802,4737],{},[1710,93804,93805,93807],{},[898,93806,1755],{},[898,93808,2450],{},[902,93810,82883],{"encoding":904},[123,93812,93813,2186,93816,1343,93855,1343,93872,2138],{},[38,93814,93815],{},"Polynomiální produkční funkce",[883,93817,93819],{"className":93818},[886],[888,93820,93821],{"xmlns":890},[892,93822,93823,93853],{},[895,93824,93825,93827,93829,93831,93833,93835,93837,93843,93845,93847],{},[898,93826,1663],{},[1654,93828,1708],{"stretchy":1656},[898,93830,2450],{},[1654,93832,1726],{"stretchy":1656},[1654,93834,1750],{},[898,93836,207],{},[1741,93838,93839,93841],{},[898,93840,2450],{},[1665,93842,4035],{},[1654,93844,1766],{},[898,93846,9758],{},[1741,93848,93849,93851],{},[898,93850,2450],{},[1665,93852,1681],{},[902,93854,84115],{"encoding":904},[883,93856,93858],{"className":93857},[886],[888,93859,93860],{"xmlns":890},[892,93861,93862,93870],{},[895,93863,93864,93866,93868],{},[898,93865,207],{},[1654,93867,3002],{},[1665,93869,2062],{},[902,93871,51305],{"encoding":904},[883,93873,93875],{"className":93874},[886],[888,93876,93877],{"xmlns":890},[892,93878,93879,93887],{},[895,93880,93881,93883,93885],{},[898,93882,9758],{},[1654,93884,2952],{},[1665,93886,2062],{},[902,93888,27510],{"encoding":904},[123,93890,93891,2186,93894,2138],{},[38,93892,93893],{},"Diferenciál produkce",[883,93895,93897],{"className":93896},[886],[888,93898,93899],{"xmlns":890},[892,93900,93901,93929],{},[895,93902,93903,93905,93907,93909,93911,93913,93915,93917,93923,93925,93927],{},[898,93904,11648],{"mathvariant":1878},[898,93906,1663],{},[1654,93908,11492],{},[898,93910,10977],{},[898,93912,1663],{},[1654,93914,1750],{},[898,93916,9320],{},[1710,93918,93919,93921],{},[898,93920,1755],{},[898,93922,2450],{},[1865,93924,11744],{},[898,93926,10977],{},[898,93928,2450],{},[902,93930,93931],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,93933,93934,10373,93936,2138],{},[38,93935,92191],{},[883,93937,93939],{"className":93938},[886],[888,93940,93941],{"xmlns":890},[892,93942,93943,93961],{},[895,93944,93945,93947,93949,93951,93953,93955,93957,93959],{},[898,93946,1663],{},[1654,93948,1750],{},[898,93950,1663],{},[1654,93952,1708],{"stretchy":1656},[898,93954,2450],{},[1654,93956,1674],{"separator":1673},[898,93958,18517],{},[1654,93960,1726],{"stretchy":1656},[902,93962,93963],{"encoding":904},"Q = Q(L, K)",[123,93965,93966,10373,93968,2138],{},[38,93967,86285],{},[883,93969,93971],{"className":93970},[886],[888,93972,93973],{"xmlns":890},[892,93974,93975,93995],{},[895,93976,93977,93979,93981,93983,93989],{},[898,93978,1663],{},[1654,93980,1750],{},[898,93982,4737],{},[1741,93984,93985,93987],{},[898,93986,2450],{},[898,93988,207],{},[1741,93990,93991,93993],{},[898,93992,18517],{},[898,93994,9758],{},[902,93996,82950],{"encoding":904},[123,93998,93999,10373,94002,94037],{},[38,94000,94001],{},"Ryzí Cobb-Douglas",[883,94003,94005],{"className":94004},[886],[888,94006,94007],{"xmlns":890},[892,94008,94009,94035],{},[895,94010,94011,94013,94015,94017,94023],{},[898,94012,1663],{},[1654,94014,1750],{},[898,94016,4737],{},[1741,94018,94019,94021],{},[898,94020,2450],{},[898,94022,207],{},[1741,94024,94025,94027],{},[898,94026,18517],{},[895,94028,94029,94031,94033],{},[1665,94030,1667],{},[1654,94032,2380],{},[898,94034,207],{},[902,94036,87112],{"encoding":904}," (konstantní výnosy).",[123,94039,94040,10373,94042,2138],{},[38,94041,87828],{},[883,94043,94045],{"className":94044},[886],[888,94046,94047],{"xmlns":890},[892,94048,94049,94107],{},[895,94050,94051,94053,94055,94057,94059,94061,94063,94065,94067,94069,94079,94081,94083,94093],{},[898,94052,1663],{},[1654,94054,1750],{},[898,94056,4737],{},[1654,94058,1657],{"stretchy":1656},[1654,94060,1708],{"stretchy":1656},[1665,94062,1667],{},[1654,94064,2380],{},[898,94066,207],{},[1654,94068,1726],{"stretchy":1656},[1741,94070,94071,94073],{},[898,94072,2450],{},[895,94074,94075,94077],{},[1654,94076,2380],{},[898,94078,9758],{},[1654,94080,1766],{},[898,94082,207],{},[1741,94084,94085,94087],{},[898,94086,18517],{},[895,94088,94089,94091],{},[1654,94090,2380],{},[898,94092,9758],{},[1741,94094,94095,94097],{},[1654,94096,1686],{"stretchy":1656},[895,94098,94099,94101,94103,94105],{},[1654,94100,2380],{},[1665,94102,1667],{},[898,94104,1879],{"mathvariant":1878},[898,94106,9758],{},[902,94108,94109],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,94111,94112,18742,94115,20840,94137,18742,94140,94170],{},[38,94113,94114],{},"Lineární",[883,94116,94118],{"className":94117},[886],[888,94119,94120],{"xmlns":890},[892,94121,94122,94134],{},[895,94123,94124,94126,94128,94130,94132],{},[898,94125,207],{},[898,94127,2450],{},[1654,94129,1766],{},[898,94131,9758],{},[898,94133,18517],{},[902,94135,94136],{"encoding":904},"aL + bK",[38,94138,94139],{},"Leontiefova",[883,94141,94143],{"className":94142},[886],[888,94144,94145],{"xmlns":890},[892,94146,94147,94167],{},[895,94148,94149,94151,94153,94155,94157,94159,94161,94163,94165],{},[898,94150,88056],{},[1654,94152,64420],{},[1654,94154,1708],{"stretchy":1656},[898,94156,207],{},[898,94158,2450],{},[1654,94160,1674],{"separator":1673},[898,94162,9758],{},[898,94164,18517],{},[1654,94166,1726],{"stretchy":1656},[902,94168,94169],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,94172,94173,10373,94189,2138],{},[38,94174,94175,94176],{},"Homogenita stupně ",[883,94177,94179],{"className":94178},[886],[888,94180,94181],{"xmlns":890},[892,94182,94183,94187],{},[895,94184,94185],{},[898,94186,45080],{},[902,94188,45080],{"encoding":904},[883,94190,94192],{"className":94191},[886],[888,94193,94194],{"xmlns":890},[892,94195,94196,94234],{},[895,94197,94198,94200,94202,94204,94206,94208,94210,94212,94214,94216,94222,94224,94226,94228,94230,94232],{},[898,94199,1663],{},[1654,94201,1708],{"stretchy":1656},[898,94203,20753],{},[898,94205,2450],{},[1654,94207,1674],{"separator":1673},[898,94209,20753],{},[898,94211,18517],{},[1654,94213,1726],{"stretchy":1656},[1654,94215,1750],{},[1741,94217,94218,94220],{},[898,94219,20753],{},[898,94221,45080],{},[898,94223,1663],{},[1654,94225,1708],{"stretchy":1656},[898,94227,2450],{},[1654,94229,1674],{"separator":1673},[898,94231,18517],{},[1654,94233,1726],{"stretchy":1656},[902,94235,94236],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,94238,94239,87210],{},[38,94240,87143,94241],{},[883,94242,94244],{"className":94243},[886],[888,94245,94246],{"xmlns":890},[892,94247,94248,94252],{},[895,94249,94250],{},[898,94251,4737],{},[902,94253,4737],{"encoding":904},[123,94255,94256,94258,94259,94281,94282,94304,94305,12664],{},[38,94257,86644],{}," — konstantní (",[883,94260,94262],{"className":94261},[886],[888,94263,94264],{"xmlns":890},[892,94265,94266,94278],{},[895,94267,94268,94270,94272,94274,94276],{},[898,94269,207],{},[1654,94271,1766],{},[898,94273,9758],{},[1654,94275,1750],{},[1665,94277,1667],{},[902,94279,94280],{"encoding":904},"a+b=1","), rostoucí (",[883,94283,94285],{"className":94284},[886],[888,94286,94287],{"xmlns":890},[892,94288,94289,94301],{},[895,94290,94291,94293,94295,94297,94299],{},[898,94292,207],{},[1654,94294,1766],{},[898,94296,9758],{},[1654,94298,2952],{},[1665,94300,1667],{},[902,94302,94303],{"encoding":904},"a+b>1","), klesající (",[883,94306,94308],{"className":94307},[886],[888,94309,94310],{"xmlns":890},[892,94311,94312,94324],{},[895,94313,94314,94316,94318,94320,94322],{},[898,94315,207],{},[1654,94317,1766],{},[898,94319,9758],{},[1654,94321,3002],{},[1665,94323,1667],{},[902,94325,94326],{"encoding":904},"a+b\u003C1",[123,94328,94329,2186,94331,1343,94361,2186,94363,2138],{},[38,94330,83313],{},[883,94332,94334],{"className":94333},[886],[888,94335,94336],{"xmlns":890},[892,94337,94338,94358],{},[895,94339,94340,94342,94348,94350],{},[898,94341,9320],{},[1710,94343,94344,94346],{},[898,94345,1755],{},[898,94347,2450],{},[1654,94349,1750],{},[1659,94351,94352,94354,94356],{},[898,94353,1663],{},[898,94355,2450],{},[1654,94357,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,94359,94360],{"encoding":904},"MP_L = Q'_L",[38,94362,86217],{},[883,94364,94366],{"className":94365},[886],[888,94367,94368],{"xmlns":890},[892,94369,94370,94390],{},[895,94371,94372,94374,94380,94382],{},[898,94373,9320],{},[1710,94375,94376,94378],{},[898,94377,1755],{},[898,94379,18517],{},[1654,94381,1750],{},[1659,94383,94384,94386,94388],{},[898,94385,1663],{},[898,94387,18517],{},[1654,94389,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,94391,94392],{"encoding":904},"MP_K = Q'_K",[123,94394,94395,2186,94397,2138],{},[38,94396,88431],{},[883,94398,94400],{"className":94399},[886],[888,94401,94402],{"xmlns":890},[892,94403,94404,94442],{},[895,94405,94406,94408,94410,94412,94414,94420,94422,94424,94426,94428,94430,94436,94438,94440],{},[898,94407,10977],{},[898,94409,1663],{},[1654,94411,1750],{},[898,94413,9320],{},[1710,94415,94416,94418],{},[898,94417,1755],{},[898,94419,2450],{},[1865,94421,11744],{},[898,94423,10977],{},[898,94425,2450],{},[1654,94427,1766],{},[898,94429,9320],{},[1710,94431,94432,94434],{},[898,94433,1755],{},[898,94435,18517],{},[1865,94437,11744],{},[898,94439,10977],{},[898,94441,18517],{},[902,94443,94444],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,94446,94447,10373,94449,2138],{},[38,94448,88776],{},[883,94450,94452],{"className":94451},[886],[888,94453,94454],{"xmlns":890},[892,94455,94456,94498],{},[895,94457,94458,94460,94468,94470,94472,94480,94482,94484,94486,94488,94490,94492,94494,94496],{},[898,94459,2450],{},[1659,94461,94462,94464,94466],{},[898,94463,1663],{},[898,94465,2450],{},[1654,94467,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,94469,1766],{},[898,94471,18517],{},[1659,94473,94474,94476,94478],{},[898,94475,1663],{},[898,94477,18517],{},[1654,94479,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,94481,1750],{},[898,94483,45080],{},[1865,94485,11744],{},[898,94487,1663],{},[1654,94489,1708],{"stretchy":1656},[898,94491,2450],{},[1654,94493,1674],{"separator":1673},[898,94495,18517],{},[1654,94497,1726],{"stretchy":1656},[902,94499,94500],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,94502,94503,94506,94507,2138],{},[38,94504,94505],{},"Izokvanta"," — křivka ",[883,94508,94510],{"className":94509},[886],[888,94511,94512],{"xmlns":890},[892,94513,94514,94532],{},[895,94515,94516,94518,94520,94522,94524,94526,94528,94530],{},[898,94517,1663],{},[1654,94519,1708],{"stretchy":1656},[898,94521,2450],{},[1654,94523,1674],{"separator":1673},[898,94525,18517],{},[1654,94527,1726],{"stretchy":1656},[1654,94529,1750],{},[898,94531,89017],{},[902,94533,94534],{"encoding":904},"Q(L, K) = q",[123,94536,94537,2186,94539,2138],{},[38,94538,89206],{},[883,94540,94542],{"className":94541},[886],[888,94543,94544],{"xmlns":890},[892,94545,94546,94576],{},[895,94547,94548,94550,94552,94554,94556,94558,94560,94566,94568,94570],{},[898,94549,9320],{},[898,94551,12737],{},[898,94553,11536],{},[898,94555,17398],{},[1654,94557,1750],{},[898,94559,9320],{},[1710,94561,94562,94564],{},[898,94563,1755],{},[898,94565,2450],{},[898,94567,1879],{"mathvariant":1878},[898,94569,9320],{},[1710,94571,94572,94574],{},[898,94573,1755],{},[898,94575,18517],{},[902,94577,83025],{"encoding":904},[123,94579,94580,2186,94583,2138],{},[38,94581,94582],{},"Substituční vztah",[883,94584,94586],{"className":94585},[886],[888,94587,94588],{"xmlns":890},[892,94589,94590,94614],{},[895,94591,94592,94594,94596,94598,94600,94602,94604,94606,94608,94610,94612],{},[898,94593,11648],{"mathvariant":1878},[898,94595,18517],{},[1654,94597,11492],{},[1654,94599,2380],{},[898,94601,9320],{},[898,94603,12737],{},[898,94605,11536],{},[898,94607,17398],{},[1865,94609,11744],{},[898,94611,10977],{},[898,94613,2450],{},[902,94615,94616],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,94618,10613],{"id":10612},[120,94620,94621,94718,94725,94732],{},[123,94622,94623,2186,94625,94628,94629,1343,94632,94635,94636,94639,94640,94659,94660,27344,94679,94682,94683,94702,94703,12664],{},[38,94624,58943],{},[207,94626,784],{"className":94627,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,94630,10655],{"className":94631,"dataFsResolvedFilePath":764,"href":765},[210],[207,94633,793],{"className":94634,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,94637,880],{"className":94638,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,94641,94643],{"className":94642},[886],[888,94644,94645],{"xmlns":890},[892,94646,94647,94657],{},[895,94648,94649,94651,94653,94655],{},[898,94650,9320],{},[898,94652,12737],{},[898,94654,11536],{},[898,94656,17398],{},[902,94658,19315],{"encoding":904}," ↔ ",[883,94661,94663],{"className":94662},[886],[888,94664,94665],{"xmlns":890},[892,94666,94667,94677],{},[895,94668,94669,94671,94673,94675],{},[898,94670,9320],{},[898,94672,12737],{},[898,94674,11539],{},[898,94676,17398],{},[902,94678,1867],{"encoding":904},[207,94680,12570],{"className":94681,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,94684,94686],{"className":94685},[886],[888,94687,94688],{"xmlns":890},[892,94689,94690,94700],{},[895,94691,94692,94694],{},[898,94693,4737],{},[1710,94695,94696,94698],{},[898,94697,1755],{},[898,94699,2450],{},[902,94701,82853],{"encoding":904}," ↔ min ",[883,94704,94706],{"className":94705},[886],[888,94707,94708],{"xmlns":890},[892,94709,94710,94716],{},[895,94711,94712,94714],{},[898,94713,4737],{},[898,94715,11539],{},[902,94717,63780],{"encoding":904},[123,94719,94720,2186,94722,2138],{},[38,94721,12546],{},[207,94723,12575],{"className":94724,"dataFsResolvedFilePath":848,"href":849},[210],[123,94726,94727,2186,94729,2138],{},[38,94728,24916],{},[207,94730,1094],{"className":94731,"dataFsResolvedFilePath":838,"href":839},[210],[123,94733,94734,2186,94736,2138],{},[38,94735,10686],{},[207,94737,10692],{"className":94738,"dataFsResolvedFilePath":10690,"href":10691},[210],{"title":641,"searchDepth":642,"depth":642,"links":94740},[94741,94742,94743,94747,94749,94754,94755,94762,94763,94765,94766,94767,94769,94774,94775,94776,94780,94781],{"id":83048,"depth":642,"text":83049},{"id":83185,"depth":642,"text":83186},{"id":83288,"depth":642,"text":94744,"children":94745},"Mezní produkt práce (MPLMP_L)",[94746],{"id":83734,"depth":649,"text":83735},{"id":84223,"depth":642,"text":94748},"Průměrný produkt práce (APLAP_L)",{"id":84341,"depth":642,"text":84342,"children":94750},[94751,94752,94753],{"id":84578,"depth":649,"text":73721},{"id":84889,"depth":649,"text":84890},{"id":85609,"depth":649,"text":85610},{"id":86181,"depth":642,"text":86182},{"id":86284,"depth":642,"text":86285,"children":94756},[94757,94758,94760,94761],{"id":86643,"depth":649,"text":86644},{"id":87142,"depth":649,"text":94759},"Parametr efektivity AA",{"id":87213,"depth":649,"text":87214},{"id":45399,"depth":649,"text":87553},{"id":87740,"depth":642,"text":87741},{"id":88079,"depth":642,"text":94764},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":88770,"depth":642,"text":88771},{"id":83114,"depth":642,"text":18496},{"id":89181,"depth":642,"text":94768},"Mezní míra technické substituce (MRTSMRTS)",{"id":90047,"depth":642,"text":90048,"children":94770},[94771,94772,94773],{"id":90051,"depth":649,"text":90052},{"id":90694,"depth":649,"text":90695},{"id":90975,"depth":649,"text":90976},{"id":91321,"depth":642,"text":91322},{"id":58101,"depth":642,"text":58102},{"id":91671,"depth":642,"text":91672,"children":94777},[94778,94779],{"id":48670,"depth":649,"text":48671},{"id":92190,"depth":649,"text":92191},{"id":10213,"depth":642,"text":10214},{"id":10612,"depth":642,"text":10613},{},"\u002Ftopics\u002Fprodukce",{"title":82684,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,18530,94788,94789,94790,83114,94791,94792],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":94795,"title":94796,"body":94797,"course":1128,"courses":659,"created":10724,"description":641,"extension":661,"meta":103744,"navigation":664,"path":103745,"seo":103746,"sources":103747,"stem":103748,"tags":103749,"type":10736,"updated":677,"__hash__":103752},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":94798,"toc":103718},[94799,94802,94804,95001,95010,95014,95017,95070,95074,95086,95090,95093,95110,95233,95239,95383,95393,95397,95432,95470,95518,95575,95635,95677,96253,96257,96340,96449,96542,96800,96803,96856,96967,97049,97053,97064,97297,97352,97358,97398,97461,97472,97663,97769,97922,97970,97975,98089,98127,98253,98299,98326,98403,98478,98558,98688,98749,98837,98841,98844,98913,98996,99003,99063,99373,99377,99383,99436,99452,99503,99641,99717,99830,100147,100151,100158,100318,100377,100381,100403,100500,100621,100735,100758,100821,100878,101130,101138,101142,101149,101403,101453,101509,101512,101676,101680,101778,101780,101812,101816,101949,102191,102375,102543,102850,102983,103170,103182,103184,103619,103621],[12,94800,94796],{"id":94801},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,94803,1638],{"id":1637},[724,94805,94806,2186,94808,94839,94840,94843,94844,94874,94875,94893,94894,94934,94935,94938,94939,94952,94953,2151,94956,94969,94970,94983,94984,94997,94998,2138],{},[38,94807,880],{},[883,94809,94811],{"className":94810},[886],[888,94812,94813],{"xmlns":890},[892,94814,94815,94837],{},[895,94816,94817,94819,94821,94827,94829,94835],{},[898,94818,900],{},[1654,94820,1708],{"stretchy":1656},[1710,94822,94823,94825],{},[898,94824,1663],{},[1665,94826,1667],{},[1654,94828,1674],{"separator":1673},[1710,94830,94831,94833],{},[898,94832,1663],{},[1665,94834,1681],{},[1654,94836,1726],{"stretchy":1656},[902,94838,1729],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,94841,94842],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,94845,94847],{"className":94846},[886],[888,94848,94849],{"xmlns":890},[892,94850,94851,94871],{},[895,94852,94853,94855,94861,94863],{},[898,94854,9320],{},[1710,94856,94857,94859],{},[898,94858,900],{},[898,94860,9309],{},[1654,94862,1750],{},[1659,94864,94865,94867,94869],{},[898,94866,900],{},[898,94868,9309],{},[1654,94870,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,94872,94873],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,94876,94878],{"className":94877},[886],[888,94879,94880],{"xmlns":890},[892,94881,94882,94890],{},[895,94883,94884,94886,94888],{},[898,94885,900],{},[1654,94887,1750],{},[898,94889,3624],{},[902,94891,94892],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,94895,94897],{"className":94896},[886],[888,94898,94899],{"xmlns":890},[892,94900,94901,94931],{},[895,94902,94903,94905,94907,94909,94911,94913,94915,94921,94923,94925],{},[898,94904,9320],{},[898,94906,12737],{},[898,94908,11539],{},[898,94910,17398],{},[1654,94912,1750],{},[898,94914,9320],{},[1710,94916,94917,94919],{},[898,94918,900],{},[1665,94920,1667],{},[898,94922,1879],{"mathvariant":1878},[898,94924,9320],{},[1710,94926,94927,94929],{},[898,94928,900],{},[1665,94930,1681],{},[902,94932,94933],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,94936,94937],{},"teorii užitečnosti"," — funkce ",[883,94940,94942],{"className":94941},[886],[888,94943,94944],{"xmlns":890},[892,94945,94946,94950],{},[895,94947,94948],{},[898,94949,900],{},[902,94951,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,94954,94955],{},"Optimalizaci spotřebitele",[883,94957,94959],{"className":94958},[886],[888,94960,94961],{"xmlns":890},[892,94962,94963,94967],{},[895,94964,94965],{},[898,94966,900],{},[902,94968,900],{"encoding":904}," při rozpočtu, min ",[883,94971,94973],{"className":94972},[886],[888,94974,94975],{"xmlns":890},[892,94976,94977,94981],{},[895,94978,94979],{},[898,94980,1798],{},[902,94982,1798],{"encoding":904}," při dané ",[883,94985,94987],{"className":94986},[886],[888,94988,94989],{"xmlns":890},[892,94990,94991,94995],{},[895,94992,94993],{},[898,94994,900],{},[902,94996,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,94999,913],{"className":95000,"dataFsResolvedFilePath":911,"href":912},[210],[724,95002,95003,95004,95006,95007,2138],{},"Kapitola 6 knihy ",[614,95005,10692],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,95008,10731],{"className":95009,"dataFsResolvedFilePath":911,"href":912},[210],[115,95011,95013],{"id":95012},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,95015,95016],{},"Po prostudování této kapitoly byste měli umět:",[120,95018,95019,95025,95034,95039,95042,95048,95054,95057,95063],{},[123,95020,95021,95022,1674],{},"vyložit, co se rozumí termínem ",[38,95023,95024],{},"užitečnost",[123,95026,95027,95028,2068,95031,1674],{},"definovat pojmy ",[38,95029,95030],{},"svazek zboží",[38,95032,95033],{},"funkce užitečnosti",[123,95035,83063,95036,83070],{},[38,95037,95038],{},"mezní užitečnosti",[123,95040,95041],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,95043,83090,95044,95047],{},[38,95045,95046],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,95049,83111,95050,95053],{},[38,95051,95052],{},"křivky užitečnosti"," (indiferenční křivky),",[123,95055,95056],{},"vyjmenovat jejich základní vlastnosti,",[123,95058,83063,95059,95062],{},[38,95060,95061],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,95064,95065,95066,95069],{},"řešit ",[38,95067,95068],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,95071,95073],{"id":95072},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,95075,95076,95077,95081,95082,95085],{},"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 ",[207,95078,95080],{"className":95079,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,95083,95084],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,95087,95089],{"id":95088},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,95091,95092],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,95094,95095,95101],{},[123,95096,95097,95100],{},[38,95098,95099],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,95102,95103,95106,95107,95109],{},[38,95104,95105],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,95108,94842],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[2140,95111,95112],{},[724,95113,95114,95116,95117,95120,95121,2186,95134,95137,95138,2068,95151,95170,95171,1343,95197,95224,95225,95228,95229,95232],{},[883,95115,2146],{}," Pozor — ordinalisté užitečnost ",[38,95118,95119],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,95122,95124],{"className":95123},[886],[888,95125,95126],{"xmlns":890},[892,95127,95128,95132],{},[895,95129,95130],{},[898,95131,900],{},[902,95133,900],{"encoding":904},[38,95135,95136],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,95139,95141],{"className":95140},[886],[888,95142,95143],{"xmlns":890},[892,95144,95145,95149],{},[895,95146,95147],{},[898,95148,900],{},[902,95150,900],{"encoding":904},[883,95152,95154],{"className":95153},[886],[888,95155,95156],{"xmlns":890},[892,95157,95158,95167],{},[895,95159,95160],{},[17111,95161,95162,95164],{"accent":1673},[898,95163,900],{},[1654,95165,95166],{},"~",[902,95168,95169],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,95172,95174],{"className":95173},[886],[888,95175,95176],{"xmlns":890},[892,95177,95178,95194],{},[895,95179,95180,95186,95188],{},[17111,95181,95182,95184],{"accent":1673},[898,95183,900],{},[1654,95185,95166],{},[1654,95187,1750],{},[1741,95189,95190,95192],{},[898,95191,900],{},[1665,95193,1681],{},[902,95195,95196],{"encoding":904},"\\tilde U = U^2",[883,95198,95200],{"className":95199},[886],[888,95201,95202],{"xmlns":890},[892,95203,95204,95221],{},[895,95205,95206,95212,95214,95217,95219],{},[17111,95207,95208,95210],{"accent":1673},[898,95209,900],{},[1654,95211,95166],{},[1654,95213,1750],{},[898,95215,95216],{},"ln",[1654,95218,64420],{},[898,95220,900],{},[902,95222,95223],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,95226,95227],{},"porovnání"," mezi svazky a ",[38,95230,95231],{},"poměry"," mezních veličin.",[724,95234,95235,95236,2781],{},"Ordinalistický přístup vychází z ",[38,95237,95238],{},"pěti hlavních předpokladů",[152,95240,95241,95247,95253,95371,95377],{},[123,95242,95243,95246],{},[38,95244,95245],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,95248,95249,95252],{},[38,95250,95251],{},"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.",[123,95254,95255,95258,95259,69961,95272,95285,95286,69961,95299,4039,95312,95315,95316,2068,95335,70790,95353,2138],{},[38,95256,95257],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,95260,95262],{"className":95261},[886],[888,95263,95264],{"xmlns":890},[892,95265,95266,95270],{},[895,95267,95268],{},[898,95269,4737],{},[902,95271,4737],{"encoding":904},[883,95273,95275],{"className":95274},[886],[888,95276,95277],{"xmlns":890},[892,95278,95279,95283],{},[895,95280,95281],{},[898,95282,4762],{},[902,95284,4762],{"encoding":904},", nebude jindy preferovat ",[883,95287,95289],{"className":95288},[886],[888,95290,95291],{"xmlns":890},[892,95292,95293,95297],{},[895,95294,95295],{},[898,95296,4762],{},[902,95298,4762],{"encoding":904},[883,95300,95302],{"className":95301},[886],[888,95303,95304],{"xmlns":890},[892,95305,95306,95310],{},[895,95307,95308],{},[898,95309,4737],{},[902,95311,4737],{"encoding":904},[38,95313,95314],{},"Tranzitivita",": pokud ",[883,95317,95319],{"className":95318},[886],[888,95320,95321],{"xmlns":890},[892,95322,95323,95332],{},[895,95324,95325,95327,95330],{},[898,95326,4737],{},[1654,95328,95329],{},"≻",[898,95331,4762],{},[902,95333,95334],{"encoding":904},"A \\succ B",[883,95336,95338],{"className":95337},[886],[888,95339,95340],{"xmlns":890},[892,95341,95342,95350],{},[895,95343,95344,95346,95348],{},[898,95345,4762],{},[1654,95347,95329],{},[898,95349,11539],{},[902,95351,95352],{"encoding":904},"B \\succ C",[883,95354,95356],{"className":95355},[886],[888,95357,95358],{"xmlns":890},[892,95359,95360,95368],{},[895,95361,95362,95364,95366],{},[898,95363,4737],{},[1654,95365,95329],{},[898,95367,11539],{},[902,95369,95370],{"encoding":904},"A \\succ C",[123,95372,95373,95376],{},[38,95374,95375],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,95378,95379,95382],{},[38,95380,95381],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,95384,95385,95386,95389,95390,2138],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,95387,95388],{},"preference"," a na příbuzné ",[614,95391,95392],{},"funkci užitečnosti",[115,95394,95396],{"id":95395},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,95398,95399,95400,95413,95414,95417,95418,95431],{},"Uvažujme ",[883,95401,95403],{"className":95402},[886],[888,95404,95405],{"xmlns":890},[892,95406,95407,95411],{},[895,95408,95409],{},[898,95410,45080],{},[902,95412,45080],{"encoding":904}," různých zboží. ",[38,95415,95416],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,95419,95421],{"className":95420},[886],[888,95422,95423],{"xmlns":890},[892,95424,95425,95429],{},[895,95426,95427],{},[898,95428,45080],{},[902,95430,45080],{"encoding":904},"-tice",[724,95433,95434],{},[883,95435,95437],{"className":95436},[886],[888,95438,95439],{"xmlns":890},[892,95440,95441,95467],{},[895,95442,95443,95445,95451,95453,95455,95457,95463,95465],{},[1654,95444,1708],{"stretchy":1656},[1710,95446,95447,95449],{},[898,95448,1663],{},[1665,95450,1667],{},[1654,95452,1674],{"separator":1673},[1654,95454,18366],{},[1654,95456,1674],{"separator":1673},[1710,95458,95459,95461],{},[898,95460,1663],{},[898,95462,45080],{},[1654,95464,1726],{"stretchy":1656},[1654,95466,1674],{"separator":1673},[902,95468,95469],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,95471,13049,95472,95489,95490,95503,95504,95507,95508,95511,95512,95515,95516,2781],{},[883,95473,95475],{"className":95474},[886],[888,95476,95477],{"xmlns":890},[892,95478,95479,95487],{},[895,95480,95481],{},[1710,95482,95483,95485],{},[898,95484,1663],{},[898,95486,9309],{},[902,95488,55758],{"encoding":904}," značí množství ",[883,95491,95493],{"className":95492},[886],[888,95494,95495],{"xmlns":890},[892,95496,95497,95501],{},[895,95498,95499],{},[898,95500,9309],{},[902,95502,9309],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,95505,95506],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,95509,95510],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,95513,95514],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,95517,95392],{},[883,95519,95521],{"className":95520},[886],[888,95522,95523],{"xmlns":890,"display":1956},[892,95524,95525,95572],{},[1960,95526,95527],{"width":1962},[1964,95528,95529,95531,95565,95567],{},[1967,95530],{"width":1969},[1967,95532,95533],{},[895,95534,95535,95537,95539,95541,95543,95549,95551,95553,95555,95561,95563],{},[898,95536,900],{},[1654,95538,1750],{},[898,95540,900],{},[1654,95542,1708],{"stretchy":1656},[1710,95544,95545,95547],{},[898,95546,1663],{},[1665,95548,1667],{},[1654,95550,1674],{"separator":1673},[1654,95552,18366],{},[1654,95554,1674],{"separator":1673},[1710,95556,95557,95559],{},[898,95558,1663],{},[898,95560,45080],{},[1654,95562,1726],{"stretchy":1656},[1654,95564,1674],{"separator":1673},[1967,95566],{"width":1969},[1967,95568,95569],{},[1865,95570,95571],{},"(6.1)",[902,95573,95574],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,95576,13049,95577,95607,95608,95630,95631,95634],{},[883,95578,95580],{"className":95579},[886],[888,95581,95582],{"xmlns":890},[892,95583,95584,95604],{},[895,95585,95586,95592,95594,95596,95598],{},[1710,95587,95588,95590],{},[898,95589,1663],{},[1665,95591,1667],{},[1654,95593,1674],{"separator":1673},[1654,95595,18366],{},[1654,95597,1674],{"separator":1673},[1710,95599,95600,95602],{},[898,95601,1663],{},[898,95603,45080],{},[902,95605,95606],{"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 ",[883,95609,95611],{"className":95610},[886],[888,95612,95613],{"xmlns":890},[892,95614,95615,95627],{},[895,95616,95617,95619,95621],{},[898,95618,900],{},[1654,95620,1674],{"separator":1673},[17111,95622,95623,95625],{"accent":1673},[898,95624,900],{},[1654,95626,95166],{},[902,95628,95629],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,95632,95633],{},"monotónní transformace"," zachovávající pořadí.",[724,95636,95637,95638,10373,95641,2138],{},"Dále se omezíme na funkce pro ",[38,95639,95640],{},"dvě zboží",[883,95642,95644],{"className":95643},[886],[888,95645,95646],{"xmlns":890},[892,95647,95648,95674],{},[895,95649,95650,95652,95654,95656,95658,95664,95666,95672],{},[898,95651,900],{},[1654,95653,1750],{},[898,95655,900],{},[1654,95657,1708],{"stretchy":1656},[1710,95659,95660,95662],{},[898,95661,1663],{},[1665,95663,1667],{},[1654,95665,1674],{"separator":1673},[1710,95667,95668,95670],{},[898,95669,1663],{},[1665,95671,1681],{},[1654,95673,1726],{"stretchy":1656},[902,95675,95676],{"encoding":904},"U = U(Q_1, Q_2)",[2140,95678,95679,95754],{},[724,95680,95681,95683,95684,2781],{},[883,95682,60915],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,95685,95687],{"className":95686},[886],[888,95688,95689],{"xmlns":890},[892,95690,95691,95751],{},[895,95692,95693,95695,95697,95699,95701,95707,95709,95715,95717,95723,95725,95727,95729],{},[898,95694,900],{},[1654,95696,1750],{},[898,95698,900],{},[1654,95700,1708],{"stretchy":1656},[1710,95702,95703,95705],{},[898,95704,1663],{},[1665,95706,1667],{},[1654,95708,1674],{"separator":1673},[1710,95710,95711,95713],{},[898,95712,1663],{},[1665,95714,1681],{},[1654,95716,1674],{"separator":1673},[1710,95718,95719,95721],{},[898,95720,1663],{},[1665,95722,4035],{},[1654,95724,1726],{"stretchy":1656},[1654,95726,1750],{},[1665,95728,1681],{},[8818,95730,95731],{},[895,95732,95733,95739,95745],{},[1710,95734,95735,95737],{},[898,95736,1663],{},[1665,95738,1667],{},[1710,95740,95741,95743],{},[898,95742,1663],{},[1665,95744,1681],{},[1710,95746,95747,95749],{},[898,95748,1663],{},[1665,95750,4035],{},[902,95752,95753],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,95755,95756,95949],{},[123,95757,95758,95759,95785,95786,21647,95812,2068,95871,4579,95931,17150],{},"svazek ",[883,95760,95762],{"className":95761},[886],[888,95763,95764],{"xmlns":890},[892,95765,95766,95782],{},[895,95767,95768,95770,95772,95774,95776,95778,95780],{},[1654,95769,1708],{"stretchy":1656},[1665,95771,50082],{},[1654,95773,1674],{"separator":1673},[1665,95775,7631],{},[1654,95777,1674],{"separator":1673},[1665,95779,50060],{},[1654,95781,1726],{"stretchy":1656},[902,95783,95784],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,95787,95789],{"className":95788},[886],[888,95790,95791],{"xmlns":890},[892,95792,95793,95809],{},[895,95794,95795,95797,95799,95801,95803,95805,95807],{},[1654,95796,1708],{"stretchy":1656},[1665,95798,12742],{},[1654,95800,1674],{"separator":1673},[1665,95802,12742],{},[1654,95804,1674],{"separator":1673},[1665,95806,74817],{},[1654,95808,1726],{"stretchy":1656},[902,95810,95811],{"encoding":904},"(9, 9, 27)",[883,95813,95815],{"className":95814},[886],[888,95816,95817],{"xmlns":890},[892,95818,95819,95868],{},[895,95820,95821,95823,95825,95827,95829,95831,95833,95835,95837,95839,95841,95855,95857,95859,95864,95866],{},[898,95822,900],{},[1654,95824,1708],{"stretchy":1656},[1665,95826,50082],{},[1654,95828,1674],{"separator":1673},[1665,95830,7631],{},[1654,95832,1674],{"separator":1673},[1665,95834,50060],{},[1654,95836,1726],{"stretchy":1656},[1654,95838,1750],{},[1665,95840,1681],{},[8818,95842,95843],{},[895,95844,95845,95847,95849,95851,95853],{},[1665,95846,50082],{},[1654,95848,4554],{},[1665,95850,7631],{},[1654,95852,4554],{},[1665,95854,50060],{},[1654,95856,1750],{},[1665,95858,1681],{},[8818,95860,95861],{},[1665,95862,95863],{},"4096",[1654,95865,1750],{},[1665,95867,14346],{},[902,95869,95870],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,95872,95874],{"className":95873},[886],[888,95875,95876],{"xmlns":890},[892,95877,95878,95928],{},[895,95879,95880,95882,95884,95886,95888,95890,95892,95894,95896,95898,95900,95914,95916,95918,95923,95925],{},[898,95881,900],{},[1654,95883,1708],{"stretchy":1656},[1665,95885,12742],{},[1654,95887,1674],{"separator":1673},[1665,95889,12742],{},[1654,95891,1674],{"separator":1673},[1665,95893,74817],{},[1654,95895,1726],{"stretchy":1656},[1654,95897,1750],{},[1665,95899,1681],{},[8818,95901,95902],{},[895,95903,95904,95906,95908,95910,95912],{},[1665,95905,12742],{},[1654,95907,4554],{},[1665,95909,12742],{},[1654,95911,4554],{},[1665,95913,74817],{},[1654,95915,1750],{},[1665,95917,1681],{},[8818,95919,95920],{},[1665,95921,95922],{},"2187",[1654,95924,14628],{},[1665,95926,95927],{},"93,53",[902,95929,95930],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,95932,95934],{"className":95933},[886],[888,95935,95936],{"xmlns":890},[892,95937,95938,95946],{},[895,95939,95940,95942,95944],{},[1665,95941,14346],{},[1654,95943,2952],{},[1665,95945,95927],{},[902,95947,95948],{"encoding":904},"128 > 93{,}53",[123,95950,95951,95952,2068,95978,96004,96005,2068,96045,96086,96087,96133,96134,2068,96160,11605,96186,2068,96204,96222,96223,2138],{},"svazky ",[883,95953,95955],{"className":95954},[886],[888,95956,95957],{"xmlns":890},[892,95958,95959,95975],{},[895,95960,95961,95963,95965,95967,95969,95971,95973],{},[1654,95962,1708],{"stretchy":1656},[1665,95964,7631],{},[1654,95966,1674],{"separator":1673},[1665,95968,14315],{},[1654,95970,1674],{"separator":1673},[1665,95972,1681],{},[1654,95974,1726],{"stretchy":1656},[902,95976,95977],{"encoding":904},"(4, 8, 2)",[883,95979,95981],{"className":95980},[886],[888,95982,95983],{"xmlns":890},[892,95984,95985,96001],{},[895,95986,95987,95989,95991,95993,95995,95997,95999],{},[1654,95988,1708],{"stretchy":1656},[1665,95990,50060],{},[1654,95992,1674],{"separator":1673},[1665,95994,1667],{},[1654,95996,1674],{"separator":1673},[1665,95998,7631],{},[1654,96000,1726],{"stretchy":1656},[902,96002,96003],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,96006,96008],{"className":96007},[886],[888,96009,96010],{"xmlns":890},[892,96011,96012,96042],{},[895,96013,96014,96016,96018,96020,96022,96024,96026,96028,96030,96032,96034,96038,96040],{},[898,96015,900],{},[1654,96017,1708],{"stretchy":1656},[1665,96019,7631],{},[1654,96021,1674],{"separator":1673},[1665,96023,14315],{},[1654,96025,1674],{"separator":1673},[1665,96027,1681],{},[1654,96029,1726],{"stretchy":1656},[1654,96031,1750],{},[1665,96033,1681],{},[8818,96035,96036],{},[1665,96037,50060],{},[1654,96039,1750],{},[1665,96041,50082],{},[902,96043,96044],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,96046,96048],{"className":96047},[886],[888,96049,96050],{"xmlns":890},[892,96051,96052,96083],{},[895,96053,96054,96056,96058,96060,96062,96064,96066,96068,96070,96072,96074,96079,96081],{},[898,96055,900],{},[1654,96057,1708],{"stretchy":1656},[1665,96059,50060],{},[1654,96061,1674],{"separator":1673},[1665,96063,1667],{},[1654,96065,1674],{"separator":1673},[1665,96067,7631],{},[1654,96069,1726],{"stretchy":1656},[1654,96071,1750],{},[1665,96073,1681],{},[8818,96075,96076],{},[1665,96077,96078],{},"256",[1654,96080,1750],{},[1665,96082,80579],{},[902,96084,96085],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,96088,96090],{"className":96089},[886],[888,96091,96092],{"xmlns":890},[892,96093,96094,96130],{},[895,96095,96096,96098,96100,96102,96104,96106,96108,96110,96112,96114,96116,96118,96120,96122,96124,96126,96128],{},[898,96097,900],{},[1654,96099,1708],{"stretchy":1656},[1665,96101,7631],{},[1654,96103,1674],{"separator":1673},[1665,96105,14315],{},[1654,96107,1674],{"separator":1673},[1665,96109,1681],{},[1654,96111,1726],{"stretchy":1656},[1654,96113,1750],{},[898,96115,900],{},[1654,96117,1708],{"stretchy":1656},[1665,96119,50060],{},[1654,96121,1674],{"separator":1673},[1665,96123,1667],{},[1654,96125,1674],{"separator":1673},[1665,96127,7631],{},[1654,96129,1726],{"stretchy":1656},[902,96131,96132],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,96135,96137],{"className":96136},[886],[888,96138,96139],{"xmlns":890},[892,96140,96141,96157],{},[895,96142,96143,96145,96147,96149,96151,96153,96155],{},[1665,96144,7631],{},[1654,96146,4554],{},[1665,96148,14315],{},[1654,96150,4554],{},[1665,96152,1681],{},[1654,96154,1750],{},[1665,96156,50060],{},[902,96158,96159],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,96161,96163],{"className":96162},[886],[888,96164,96165],{"xmlns":890},[892,96166,96167,96183],{},[895,96168,96169,96171,96173,96175,96177,96179,96181],{},[1665,96170,50060],{},[1654,96172,4554],{},[1665,96174,1667],{},[1654,96176,4554],{},[1665,96178,7631],{},[1654,96180,1750],{},[1665,96182,96078],{},[902,96184,96185],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,96187,96189],{"className":96188},[886],[888,96190,96191],{"xmlns":890},[892,96192,96193,96201],{},[895,96194,96195,96197,96199],{},[898,96196,900],{},[1654,96198,1750],{},[1665,96200,50082],{},[902,96202,96203],{"encoding":904},"U = 16",[883,96205,96207],{"className":96206},[886],[888,96208,96209],{"xmlns":890},[892,96210,96211,96219],{},[895,96212,96213,96215,96217],{},[898,96214,900],{},[1654,96216,1750],{},[1665,96218,80579],{},[902,96220,96221],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,96224,96226],{"className":96225},[886],[888,96227,96228],{"xmlns":890},[892,96229,96230,96250],{},[895,96231,96232,96238,96244],{},[1710,96233,96234,96236],{},[898,96235,1663],{},[1665,96237,1667],{},[1710,96239,96240,96242],{},[898,96241,1663],{},[1665,96243,1681],{},[1710,96245,96246,96248],{},[898,96247,1663],{},[1665,96249,4035],{},[902,96251,96252],{"encoding":904},"Q_1 Q_2 Q_3",[115,96254,96256],{"id":96255},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,96258,96259,96260,16828,96295,2186,96298,50034,96315,18742,96332,96335,96336,96339],{},"Pro funkci užitečnosti ",[883,96261,96263],{"className":96262},[886],[888,96264,96265],{"xmlns":890},[892,96266,96267,96293],{},[895,96268,96269,96271,96273,96275,96277,96283,96285,96291],{},[898,96270,900],{},[1654,96272,1750],{},[898,96274,900],{},[1654,96276,1708],{"stretchy":1656},[1710,96278,96279,96281],{},[898,96280,1663],{},[1665,96282,1667],{},[1654,96284,1674],{"separator":1673},[1710,96286,96287,96289],{},[898,96288,1663],{},[1665,96290,1681],{},[1654,96292,1726],{"stretchy":1656},[902,96294,95676],{"encoding":904},[38,96296,96297],{},"mezní užitečnost",[883,96299,96301],{"className":96300},[886],[888,96302,96303],{"xmlns":890},[892,96304,96305,96313],{},[895,96306,96307],{},[1710,96308,96309,96311],{},[898,96310,1663],{},[1665,96312,1667],{},[902,96314,2918],{"encoding":904},[883,96316,96318],{"className":96317},[886],[888,96319,96320],{"xmlns":890},[892,96321,96322,96330],{},[895,96323,96324],{},[1710,96325,96326,96328],{},[898,96327,1663],{},[1665,96329,1681],{},[902,96331,2937],{"encoding":904},[38,96333,96334],{},"marginal utility",") parciální ",[207,96337,1145],{"className":96338,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,96341,96343],{"className":96342},[886],[888,96344,96345],{"xmlns":890,"display":1956},[892,96346,96347,96446],{},[1960,96348,96349],{"width":1962},[1964,96350,96351,96353,96439,96441],{},[1967,96352],{"width":1969},[1967,96354,96355],{},[895,96356,96357,96359,96365,96367,96375,96377,96395,96397,96399,96401,96407,96409,96417,96419,96437],{},[898,96358,9320],{},[1710,96360,96361,96363],{},[898,96362,900],{},[1665,96364,1667],{},[1654,96366,1750],{},[1659,96368,96369,96371,96373],{},[898,96370,900],{},[1665,96372,1667],{},[1654,96374,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,96376,1750],{},[2811,96378,96379,96385],{},[895,96380,96381,96383],{},[898,96382,18589],{"mathvariant":1878},[898,96384,900],{},[895,96386,96387,96389],{},[898,96388,18589],{"mathvariant":1878},[1710,96390,96391,96393],{},[898,96392,1663],{},[1665,96394,1667],{},[1654,96396,1674],{"separator":1673},[5008,96398],{"width":5010},[898,96400,9320],{},[1710,96402,96403,96405],{},[898,96404,900],{},[1665,96406,1681],{},[1654,96408,1750],{},[1659,96410,96411,96413,96415],{},[898,96412,900],{},[1665,96414,1681],{},[1654,96416,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,96418,1750],{},[2811,96420,96421,96427],{},[895,96422,96423,96425],{},[898,96424,18589],{"mathvariant":1878},[898,96426,900],{},[895,96428,96429,96431],{},[898,96430,18589],{"mathvariant":1878},[1710,96432,96433,96435],{},[898,96434,1663],{},[1665,96436,1681],{},[898,96438,2138],{"mathvariant":1878},[1967,96440],{"width":1969},[1967,96442,96443],{},[1865,96444,96445],{},"(6.2)",[902,96447,96448],{"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}",[724,96450,96451,96452,96486,96487,96517,96518,2186,96521,2138],{},"Pro pevné ",[883,96453,96455],{"className":96454},[886],[888,96456,96457],{"xmlns":890},[892,96458,96459,96483],{},[895,96460,96461,96467,96469,96471,96473,96479,96481],{},[1710,96462,96463,96465],{},[898,96464,1663],{},[1665,96466,1667],{},[1654,96468,1750],{},[898,96470,207],{},[1654,96472,1674],{"separator":1673},[1710,96474,96475,96477],{},[898,96476,1663],{},[1665,96478,1681],{},[1654,96480,1750],{},[898,96482,9758],{},[902,96484,96485],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,96488,96490],{"className":96489},[886],[888,96491,96492],{"xmlns":890},[892,96493,96494,96514],{},[895,96495,96496,96498,96504,96506,96508,96510,96512],{},[898,96497,9320],{},[1710,96499,96500,96502],{},[898,96501,900],{},[1665,96503,1667],{},[1654,96505,1708],{"stretchy":1656},[898,96507,207],{},[1654,96509,1674],{"separator":1673},[898,96511,9758],{},[1654,96513,1726],{"stretchy":1656},[902,96515,96516],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,96519,96520],{},"v bodě (na hladině)",[883,96522,96524],{"className":96523},[886],[888,96525,96526],{"xmlns":890},[892,96527,96528,96540],{},[895,96529,96530,96532,96534,96536,96538],{},[1654,96531,1657],{"stretchy":1656},[898,96533,207],{},[1654,96535,1674],{"separator":1673},[898,96537,9758],{},[1654,96539,1686],{"stretchy":1656},[902,96541,19539],{"encoding":904},[2140,96543,96544],{},[724,96545,96546,96548,96549,96579,96608,96609,11373,96622,11387,96639,96660,96661,11434,96678,11448,96691,96708,96709,96731,96732,96761,96762,15201,96782,96799],{},[883,96547,2860],{}," Intuice — co říká ",[883,96550,96552],{"className":96551},[886],[888,96553,96554],{"xmlns":890},[892,96555,96556,96576],{},[895,96557,96558,96560,96566,96568,96570,96572,96574],{},[898,96559,9320],{},[1710,96561,96562,96564],{},[898,96563,900],{},[1665,96565,1667],{},[1654,96567,1708],{"stretchy":1656},[898,96569,207],{},[1654,96571,1674],{"separator":1673},[898,96573,9758],{},[1654,96575,1726],{"stretchy":1656},[902,96577,96578],{"encoding":904},"MU_1(a,b)",[883,96580,96582],{"className":96581},[886],[888,96583,96584],{"xmlns":890},[892,96585,96586,96606],{},[895,96587,96588,96590,96596,96598,96600,96602,96604],{},[898,96589,9320],{},[1710,96591,96592,96594],{},[898,96593,900],{},[1665,96595,1667],{},[1654,96597,1708],{"stretchy":1656},[898,96599,207],{},[1654,96601,1674],{"separator":1673},[898,96603,9758],{},[1654,96605,1726],{"stretchy":1656},[902,96607,96516],{"encoding":904}," je rychlost změny ",[883,96610,96612],{"className":96611},[886],[888,96613,96614],{"xmlns":890},[892,96615,96616,96620],{},[895,96617,96618],{},[898,96619,900],{},[902,96621,900],{"encoding":904},[883,96623,96625],{"className":96624},[886],[888,96626,96627],{"xmlns":890},[892,96628,96629,96637],{},[895,96630,96631],{},[1710,96632,96633,96635],{},[898,96634,1663],{},[1665,96636,1667],{},[902,96638,2918],{"encoding":904},[883,96640,96642],{"className":96641},[886],[888,96643,96644],{"xmlns":890},[892,96645,96646,96658],{},[895,96647,96648,96650,96652,96654,96656],{},[1654,96649,1657],{"stretchy":1656},[898,96651,207],{},[1654,96653,1674],{"separator":1673},[898,96655,9758],{},[1654,96657,1686],{"stretchy":1656},[902,96659,19539],{"encoding":904},". Přibližně: změní-li se ",[883,96662,96664],{"className":96663},[886],[888,96665,96666],{"xmlns":890},[892,96667,96668,96676],{},[895,96669,96670],{},[1710,96671,96672,96674],{},[898,96673,1663],{},[1665,96675,1667],{},[902,96677,2918],{"encoding":904},[883,96679,96681],{"className":96680},[886],[888,96682,96683],{"xmlns":890},[892,96684,96685,96689],{},[895,96686,96687],{},[898,96688,207],{},[902,96690,207],{"encoding":904},[883,96692,96694],{"className":96693},[886],[888,96695,96696],{"xmlns":890},[892,96697,96698,96706],{},[895,96699,96700,96702,96704],{},[898,96701,207],{},[1654,96703,1766],{},[1665,96705,1667],{},[902,96707,11466],{"encoding":904}," při pevném ",[883,96710,96712],{"className":96711},[886],[888,96713,96714],{"xmlns":890},[892,96715,96716,96728],{},[895,96717,96718,96724,96726],{},[1710,96719,96720,96722],{},[898,96721,1663],{},[1665,96723,1681],{},[1654,96725,1750],{},[898,96727,9758],{},[902,96729,96730],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,96733,96735],{"className":96734},[886],[888,96736,96737],{"xmlns":890},[892,96738,96739,96759],{},[895,96740,96741,96743,96749,96751,96753,96755,96757],{},[898,96742,9320],{},[1710,96744,96745,96747],{},[898,96746,900],{},[1665,96748,1667],{},[1654,96750,1708],{"stretchy":1656},[898,96752,207],{},[1654,96754,1674],{"separator":1673},[898,96756,9758],{},[1654,96758,1726],{"stretchy":1656},[902,96760,96516],{"encoding":904},". Stejně tak ",[883,96763,96765],{"className":96764},[886],[888,96766,96767],{"xmlns":890},[892,96768,96769,96779],{},[895,96770,96771,96773],{},[898,96772,9320],{},[1710,96774,96775,96777],{},[898,96776,900],{},[1665,96778,1681],{},[902,96780,96781],{"encoding":904},"MU_2",[883,96783,96785],{"className":96784},[886],[888,96786,96787],{"xmlns":890},[892,96788,96789,96797],{},[895,96790,96791],{},[1710,96792,96793,96795],{},[898,96794,1663],{},[1665,96796,1681],{},[902,96798,2937],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,96801,88431],{"id":96802},"totální-diferenciál",[724,96804,96805,96806,56560,96822,96852,96853,2781],{},"Přibližnou změnu užitečnosti ",[883,96807,96809],{"className":96808},[886],[888,96810,96811],{"xmlns":890},[892,96812,96813,96819],{},[895,96814,96815,96817],{},[898,96816,11648],{"mathvariant":1878},[898,96818,900],{},[902,96820,96821],{"encoding":904},"\\Delta U",[883,96823,96825],{"className":96824},[886],[888,96826,96827],{"xmlns":890},[892,96828,96829,96849],{},[895,96830,96831,96833,96839,96841,96843],{},[898,96832,10977],{"mathvariant":1878},[1710,96834,96835,96837],{},[898,96836,1663],{},[1665,96838,1667],{},[1654,96840,1674],{"separator":1673},[898,96842,10977],{"mathvariant":1878},[1710,96844,96845,96847],{},[898,96846,1663],{},[1665,96848,1681],{},[902,96850,96851],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,96854,96855],{},"totálního diferenciálu",[883,96857,96859],{"className":96858},[886],[888,96860,96861],{"xmlns":890,"display":1956},[892,96862,96863,96964],{},[1960,96864,96865],{"width":1962},[1964,96866,96867,96869,96957,96959],{},[1967,96868],{"width":1969},[1967,96870,96871],{},[895,96872,96873,96875,96877,96879,96881,96883,96885,96893,96895,96901,96903,96911,96913,96919,96921,96923,96929,96931,96937,96939,96941,96947,96949,96955],{},[898,96874,11648],{"mathvariant":1878},[898,96876,900],{},[1654,96878,11492],{},[898,96880,10977],{"mathvariant":1878},[898,96882,900],{},[1654,96884,1750],{},[1659,96886,96887,96889,96891],{},[898,96888,900],{},[1665,96890,1667],{},[1654,96892,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[898,96894,10977],{"mathvariant":1878},[1710,96896,96897,96899],{},[898,96898,1663],{},[1665,96900,1667],{},[1654,96902,1766],{},[1659,96904,96905,96907,96909],{},[898,96906,900],{},[1665,96908,1681],{},[1654,96910,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[898,96912,10977],{"mathvariant":1878},[1710,96914,96915,96917],{},[898,96916,1663],{},[1665,96918,1681],{},[1654,96920,1750],{},[898,96922,9320],{},[1710,96924,96925,96927],{},[898,96926,900],{},[1665,96928,1667],{},[898,96930,10977],{"mathvariant":1878},[1710,96932,96933,96935],{},[898,96934,1663],{},[1665,96936,1667],{},[1654,96938,1766],{},[898,96940,9320],{},[1710,96942,96943,96945],{},[898,96944,900],{},[1665,96946,1681],{},[898,96948,10977],{"mathvariant":1878},[1710,96950,96951,96953],{},[898,96952,1663],{},[1665,96954,1681],{},[898,96956,2138],{"mathvariant":1878},[1967,96958],{"width":1969},[1967,96960,96961],{},[1865,96962,96963],{},"(6.3)",[902,96965,96966],{"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}",[724,96968,83689,96969,2138],{},[883,96970,96972],{"className":96971},[886],[888,96973,96974],{"xmlns":890},[892,96975,96976,97046],{},[895,96977,96978,96980,96982,96984,96986,96988,96994,96996,96998,97004,97006,97012,97014,97016,97022,97024,97026,97028,97030,97036,97038,97044],{},[898,96979,11648],{"mathvariant":1878},[898,96981,900],{},[1654,96983,1750],{},[898,96985,900],{},[1654,96987,1708],{"stretchy":1656},[1710,96989,96990,96992],{},[898,96991,1663],{},[1665,96993,1667],{},[1654,96995,1766],{},[898,96997,10977],{"mathvariant":1878},[1710,96999,97000,97002],{},[898,97001,1663],{},[1665,97003,1667],{},[1654,97005,1674],{"separator":1673},[1710,97007,97008,97010],{},[898,97009,1663],{},[1665,97011,1681],{},[1654,97013,1766],{},[898,97015,10977],{"mathvariant":1878},[1710,97017,97018,97020],{},[898,97019,1663],{},[1665,97021,1681],{},[1654,97023,1726],{"stretchy":1656},[1654,97025,2380],{},[898,97027,900],{},[1654,97029,1708],{"stretchy":1656},[1710,97031,97032,97034],{},[898,97033,1663],{},[1665,97035,1667],{},[1654,97037,1674],{"separator":1673},[1710,97039,97040,97042],{},[898,97041,1663],{},[1665,97043,1681],{},[1654,97045,1726],{"stretchy":1656},[902,97047,97048],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,97050,97052],{"id":97051},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,97054,97055,97056,97059,97060,97063],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,97057,97058],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,97061,97062],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,97065,97066,97069,97070,50034,97096,97122,97123,1343,97155,97187,97188,2068,97242,97296],{},[38,97067,97068],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,97071,97073],{"className":97072},[886],[888,97074,97075],{"xmlns":890},[892,97076,97077,97093],{},[895,97078,97079,97085,97087],{},[1710,97080,97081,97083],{},[898,97082,1663],{},[1665,97084,1681],{},[1654,97086,1750],{},[1710,97088,97089,97091],{},[898,97090,207],{},[1665,97092,2062],{},[902,97094,97095],{"encoding":904},"Q_2 = a_0",[883,97097,97099],{"className":97098},[886],[888,97100,97101],{"xmlns":890},[892,97102,97103,97119],{},[895,97104,97105,97111,97113],{},[1710,97106,97107,97109],{},[898,97108,1663],{},[1665,97110,1667],{},[1654,97112,1750],{},[1710,97114,97115,97117],{},[898,97116,9758],{},[1665,97118,2062],{},[902,97120,97121],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,97124,97126],{"className":97125},[886],[888,97127,97128],{"xmlns":890},[892,97129,97130,97152],{},[895,97131,97132,97134,97136,97142,97144,97150],{},[898,97133,900],{},[1654,97135,1708],{"stretchy":1656},[1710,97137,97138,97140],{},[898,97139,1663],{},[1665,97141,1667],{},[1654,97143,1674],{"separator":1673},[1710,97145,97146,97148],{},[898,97147,207],{},[1665,97149,2062],{},[1654,97151,1726],{"stretchy":1656},[902,97153,97154],{"encoding":904},"U(Q_1, a_0)",[883,97156,97158],{"className":97157},[886],[888,97159,97160],{"xmlns":890},[892,97161,97162,97184],{},[895,97163,97164,97166,97168,97174,97176,97182],{},[898,97165,900],{},[1654,97167,1708],{"stretchy":1656},[1710,97169,97170,97172],{},[898,97171,9758],{},[1665,97173,2062],{},[1654,97175,1674],{"separator":1673},[1710,97177,97178,97180],{},[898,97179,1663],{},[1665,97181,1681],{},[1654,97183,1726],{"stretchy":1656},[902,97185,97186],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,97189,97191],{"className":97190},[886],[888,97192,97193],{"xmlns":890},[892,97194,97195,97239],{},[895,97196,97197,97235,97237],{},[2582,97198,97199],{"scriptlevel":2062,"displaystyle":1673},[2811,97200,97201,97225],{},[895,97202,97203,97205,97207,97209,97215,97217,97223],{},[898,97204,10977],{"mathvariant":1878},[898,97206,900],{},[1654,97208,1708],{"stretchy":1656},[1710,97210,97211,97213],{},[898,97212,1663],{},[1665,97214,1667],{},[1654,97216,1674],{"separator":1673},[1710,97218,97219,97221],{},[898,97220,207],{},[1665,97222,2062],{},[1654,97224,1726],{"stretchy":1656},[895,97226,97227,97229],{},[898,97228,10977],{"mathvariant":1878},[1710,97230,97231,97233],{},[898,97232,1663],{},[1665,97234,1667],{},[1654,97236,2952],{},[1665,97238,2062],{},[902,97240,97241],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,97243,97245],{"className":97244},[886],[888,97246,97247],{"xmlns":890},[892,97248,97249,97293],{},[895,97250,97251,97289,97291],{},[2582,97252,97253],{"scriptlevel":2062,"displaystyle":1673},[2811,97254,97255,97279],{},[895,97256,97257,97259,97261,97263,97269,97271,97277],{},[898,97258,10977],{"mathvariant":1878},[898,97260,900],{},[1654,97262,1708],{"stretchy":1656},[1710,97264,97265,97267],{},[898,97266,9758],{},[1665,97268,2062],{},[1654,97270,1674],{"separator":1673},[1710,97272,97273,97275],{},[898,97274,1663],{},[1665,97276,1681],{},[1654,97278,1726],{"stretchy":1656},[895,97280,97281,97283],{},[898,97282,10977],{"mathvariant":1878},[1710,97284,97285,97287],{},[898,97286,1663],{},[1665,97288,1681],{},[1654,97290,2952],{},[1665,97292,2062],{},[902,97294,97295],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,97298,97300],{"className":97299},[886],[888,97301,97302],{"xmlns":890,"display":1956},[892,97303,97304,97349],{},[1960,97305,97306],{"width":1962},[1964,97307,97308,97310,97342,97344],{},[1967,97309],{"width":1969},[1967,97311,97312],{},[895,97313,97314,97322,97324,97326,97328,97330,97338,97340],{},[1659,97315,97316,97318,97320],{},[898,97317,900],{},[1665,97319,1667],{},[1654,97321,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,97323,2952],{},[1665,97325,2062],{},[1654,97327,1674],{"separator":1673},[5008,97329],{"width":5010},[1659,97331,97332,97334,97336],{},[898,97333,900],{},[1665,97335,1681],{},[1654,97337,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,97339,2952],{},[1665,97341,2745],{},[1967,97343],{"width":1969},[1967,97345,97346],{},[1865,97347,97348],{},"(6.4)",[902,97350,97351],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,97353,97354,97355,97357],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,97356,60897],{}," — užitečnost roste s množstvím každého zboží.",[724,97359,97360,97363,97364,97394,97395,2781],{},[38,97361,97362],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,97365,97367],{"className":97366},[886],[888,97368,97369],{"xmlns":890},[892,97370,97371,97391],{},[895,97372,97373,97381,97383],{},[1659,97374,97375,97377,97379],{},[898,97376,900],{},[1665,97378,1667],{},[1654,97380,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,97382,1674],{"separator":1673},[1659,97384,97385,97387,97389],{},[898,97386,900],{},[1665,97388,1681],{},[1654,97390,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,97392,97393],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,97396,97397],{},"záporné",[883,97399,97401],{"className":97400},[886],[888,97402,97403],{"xmlns":890,"display":1956},[892,97404,97405,97458],{},[1960,97406,97407],{"width":1962},[1964,97408,97409,97411,97451,97453],{},[1967,97410],{"width":1969},[1967,97412,97413],{},[895,97414,97415,97427,97429,97431,97433,97435,97447,97449],{},[1659,97416,97417,97419,97421],{},[898,97418,900],{},[1665,97420,6477],{},[895,97422,97423,97425],{},[1654,97424,2592],{"mathvariant":1878},[1654,97426,2592],{"mathvariant":1878},[1654,97428,3002],{},[1665,97430,2062],{},[1654,97432,1674],{"separator":1673},[5008,97434],{"width":5010},[1659,97436,97437,97439,97441],{},[898,97438,900],{},[1665,97440,6492],{},[895,97442,97443,97445],{},[1654,97444,2592],{"mathvariant":1878},[1654,97446,2592],{"mathvariant":1878},[1654,97448,3002],{},[1665,97450,2745],{},[1967,97452],{"width":1969},[1967,97454,97455],{},[1865,97456,97457],{},"(6.5)",[902,97459,97460],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,97462,97463,97464,97467,97468,2138],{},"Podmínka (6.5) je známa jako ",[38,97465,97466],{},"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 ",[207,97469,97471],{"className":97470,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,97473,97474,97475,2068,97507,97539,97540,2068,97566,97592,97593,97621,97622,2068,97624,97626,97627,97662],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,97476,97478],{"className":97477},[886],[888,97479,97480],{"xmlns":890},[892,97481,97482,97504],{},[895,97483,97484,97486,97488,97494,97496,97502],{},[898,97485,900],{},[1654,97487,1708],{"stretchy":1656},[1710,97489,97490,97492],{},[898,97491,1663],{},[1665,97493,1667],{},[1654,97495,1674],{"separator":1673},[1710,97497,97498,97500],{},[898,97499,9758],{},[1665,97501,2062],{},[1654,97503,1726],{"stretchy":1656},[902,97505,97506],{"encoding":904},"U(Q_1, b_0)",[883,97508,97510],{"className":97509},[886],[888,97511,97512],{"xmlns":890},[892,97513,97514,97536],{},[895,97515,97516,97518,97520,97526,97528,97534],{},[898,97517,900],{},[1654,97519,1708],{"stretchy":1656},[1710,97521,97522,97524],{},[898,97523,207],{},[1665,97525,2062],{},[1654,97527,1674],{"separator":1673},[1710,97529,97530,97532],{},[898,97531,1663],{},[1665,97533,1681],{},[1654,97535,1726],{"stretchy":1656},[902,97537,97538],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,97541,97543],{"className":97542},[886],[888,97544,97545],{"xmlns":890},[892,97546,97547,97563],{},[895,97548,97549,97551,97553,97555,97561],{},[1654,97550,1708],{"stretchy":1656},[898,97552,900],{},[1654,97554,1674],{"separator":1673},[1710,97556,97557,97559],{},[898,97558,1663],{},[1665,97560,1667],{},[1654,97562,1726],{"stretchy":1656},[902,97564,97565],{"encoding":904},"(U, Q_1)",[883,97567,97569],{"className":97568},[886],[888,97570,97571],{"xmlns":890},[892,97572,97573,97589],{},[895,97574,97575,97577,97579,97581,97587],{},[1654,97576,1708],{"stretchy":1656},[898,97578,900],{},[1654,97580,1674],{"separator":1673},[1710,97582,97583,97585],{},[898,97584,1663],{},[1665,97586,1681],{},[1654,97588,1726],{"stretchy":1656},[902,97590,97591],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,97594,97596],{"className":97595},[886],[888,97597,97598],{"xmlns":890},[892,97599,97600,97618],{},[895,97601,97602,97604,97606,97608,97610,97612,97614,97616],{},[898,97603,900],{},[1654,97605,1708],{"stretchy":1656},[1665,97607,2062],{},[1654,97609,1674],{"separator":1673},[1665,97611,2062],{},[1654,97613,1726],{"stretchy":1656},[1654,97615,1750],{},[1665,97617,2062],{},[902,97619,97620],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,97623,22366],{},[38,97625,46708],{},". Typický tvar grafu ",[883,97628,97630],{"className":97629},[886],[888,97631,97632],{"xmlns":890},[892,97633,97634,97660],{},[895,97635,97636,97638,97640,97642,97644,97650,97652,97658],{},[898,97637,900],{},[1654,97639,1750],{},[898,97641,900],{},[1654,97643,1708],{"stretchy":1656},[1710,97645,97646,97648],{},[898,97647,1663],{},[1665,97649,1667],{},[1654,97651,1674],{"separator":1673},[1710,97653,97654,97656],{},[898,97655,1663],{},[1665,97657,1681],{},[1654,97659,1726],{"stretchy":1656},[902,97661,95676],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,97664,97665],{},[614,97666,97667,97668,96708,97696,97717,97718,96708,97746,97768],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,97669,97671],{"className":97670},[886],[888,97672,97673],{"xmlns":890},[892,97674,97675,97693],{},[895,97676,97677,97679,97681,97687,97689,97691],{},[898,97678,900],{},[1654,97680,1708],{"stretchy":1656},[1710,97682,97683,97685],{},[898,97684,1663],{},[1665,97686,1667],{},[1654,97688,1674],{"separator":1673},[898,97690,9758],{},[1654,97692,1726],{"stretchy":1656},[902,97694,97695],{"encoding":904},"U(Q_1, b)",[883,97697,97699],{"className":97698},[886],[888,97700,97701],{"xmlns":890},[892,97702,97703,97715],{},[895,97704,97705,97711,97713],{},[1710,97706,97707,97709],{},[898,97708,1663],{},[1665,97710,1681],{},[1654,97712,1750],{},[898,97714,9758],{},[902,97716,96730],{"encoding":904}," (vlevo) a ",[883,97719,97721],{"className":97720},[886],[888,97722,97723],{"xmlns":890},[892,97724,97725,97743],{},[895,97726,97727,97729,97731,97733,97735,97741],{},[898,97728,900],{},[1654,97730,1708],{"stretchy":1656},[898,97732,207],{},[1654,97734,1674],{"separator":1673},[1710,97736,97737,97739],{},[898,97738,1663],{},[1665,97740,1681],{},[1654,97742,1726],{"stretchy":1656},[902,97744,97745],{"encoding":904},"U(a, Q_2)",[883,97747,97749],{"className":97748},[886],[888,97750,97751],{"xmlns":890},[892,97752,97753,97765],{},[895,97754,97755,97761,97763],{},[1710,97756,97757,97759],{},[898,97758,1663],{},[1665,97760,1667],{},[1654,97762,1750],{},[898,97764,207],{},[902,97766,97767],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,97770,97771],{},[614,97772,97773,97774,97809,97810,97840,97841,2068,97864,97886,97887,2138],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,97775,97777],{"className":97776},[886],[888,97778,97779],{"xmlns":890},[892,97780,97781,97807],{},[895,97782,97783,97785,97787,97789,97791,97797,97799,97805],{},[898,97784,900],{},[1654,97786,1750],{},[898,97788,900],{},[1654,97790,1708],{"stretchy":1656},[1710,97792,97793,97795],{},[898,97794,1663],{},[1665,97796,1667],{},[1654,97798,1674],{"separator":1673},[1710,97800,97801,97803],{},[898,97802,1663],{},[1665,97804,1681],{},[1654,97806,1726],{"stretchy":1656},[902,97808,95676],{"encoding":904}," nad rovinou ",[883,97811,97813],{"className":97812},[886],[888,97814,97815],{"xmlns":890},[892,97816,97817,97837],{},[895,97818,97819,97821,97827,97829,97835],{},[1654,97820,1708],{"stretchy":1656},[1710,97822,97823,97825],{},[898,97824,1663],{},[1665,97826,1667],{},[1654,97828,1674],{"separator":1673},[1710,97830,97831,97833],{},[898,97832,1663],{},[1665,97834,1681],{},[1654,97836,1726],{"stretchy":1656},[902,97838,97839],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,97842,97844],{"className":97843},[886],[888,97845,97846],{"xmlns":890},[892,97847,97848,97861],{},[895,97849,97850,97856,97858],{},[1710,97851,97852,97854],{},[898,97853,1663],{},[1665,97855,1667],{},[1654,97857,1750],{},[1865,97859,97860],{},"const",[902,97862,97863],{"encoding":904},"Q_1 = \\text{const}",[883,97865,97867],{"className":97866},[886],[888,97868,97869],{"xmlns":890},[892,97870,97871,97883],{},[895,97872,97873,97879,97881],{},[1710,97874,97875,97877],{},[898,97876,1663],{},[1665,97878,1681],{},[1654,97880,1750],{},[1865,97882,97860],{},[902,97884,97885],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,97888,97890],{"className":97889},[886],[888,97891,97892],{"xmlns":890},[892,97893,97894,97920],{},[895,97895,97896,97898,97900,97906,97908,97914,97916,97918],{},[898,97897,900],{},[1654,97899,1708],{"stretchy":1656},[1710,97901,97902,97904],{},[898,97903,1663],{},[1665,97905,1667],{},[1654,97907,1674],{"separator":1673},[1710,97909,97910,97912],{},[898,97911,1663],{},[1665,97913,1681],{},[1654,97915,1726],{"stretchy":1656},[1654,97917,1750],{},[898,97919,3624],{},[902,97921,18487],{"encoding":904},[198,97923,97925,97926],{"id":97924},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,97927,97929],{"className":97928},[886],[888,97930,97931],{"xmlns":890},[892,97932,97933,97967],{},[895,97934,97935,97937,97939,97953],{},[898,97936,900],{},[1654,97938,1750],{},[1659,97940,97941,97943,97945],{},[898,97942,1663],{},[1665,97944,1667],{},[895,97946,97947,97949,97951],{},[1665,97948,1667],{},[898,97950,1879],{"mathvariant":1878},[1665,97952,1681],{},[1659,97954,97955,97957,97959],{},[898,97956,1663],{},[1665,97958,1681],{},[895,97960,97961,97963,97965],{},[1665,97962,1667],{},[898,97964,1879],{"mathvariant":1878},[1665,97966,4035],{},[902,97968,97969],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,97971,97972],{},[38,97973,97974],{},"Ověření (6.4) a (6.5).",[883,97976,97978],{"className":97977},[886],[888,97979,97980],{"xmlns":890,"display":1956},[892,97981,97982,98086],{},[895,97983,97984,97992,97994,98002,98018,98032,98034,98036,98044,98046,98054,98068,98084],{},[1659,97985,97986,97988,97990],{},[898,97987,900],{},[1665,97989,1667],{},[1654,97991,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,97993,1750],{},[2582,97995,97996],{"scriptlevel":2062,"displaystyle":1656},[2811,97997,97998,98000],{},[1665,97999,1667],{},[1665,98001,1681],{},[1659,98003,98004,98006,98008],{},[898,98005,1663],{},[1665,98007,1667],{},[895,98009,98010,98012,98014,98016],{},[1654,98011,2380],{},[1665,98013,1667],{},[898,98015,1879],{"mathvariant":1878},[1665,98017,1681],{},[1659,98019,98020,98022,98024],{},[898,98021,1663],{},[1665,98023,1681],{},[895,98025,98026,98028,98030],{},[1665,98027,1667],{},[898,98029,1879],{"mathvariant":1878},[1665,98031,4035],{},[1654,98033,1674],{"separator":1673},[5008,98035],{"width":5010},[1659,98037,98038,98040,98042],{},[898,98039,900],{},[1665,98041,1681],{},[1654,98043,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,98045,1750],{},[2582,98047,98048],{"scriptlevel":2062,"displaystyle":1656},[2811,98049,98050,98052],{},[1665,98051,1667],{},[1665,98053,4035],{},[1659,98055,98056,98058,98060],{},[898,98057,1663],{},[1665,98059,1667],{},[895,98061,98062,98064,98066],{},[1665,98063,1667],{},[898,98065,1879],{"mathvariant":1878},[1665,98067,1681],{},[1659,98069,98070,98072,98074],{},[898,98071,1663],{},[1665,98073,1681],{},[895,98075,98076,98078,98080,98082],{},[1654,98077,2380],{},[1665,98079,1681],{},[898,98081,1879],{"mathvariant":1878},[1665,98083,4035],{},[1654,98085,1674],{"separator":1673},[902,98087,98088],{"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},",[724,98090,98091,98092,98126],{},"zřejmě ",[883,98093,98095],{"className":98094},[886],[888,98096,98097],{"xmlns":890},[892,98098,98099,98123],{},[895,98100,98101,98109,98111,98119,98121],{},[1659,98102,98103,98105,98107],{},[898,98104,900],{},[1665,98106,1667],{},[1654,98108,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,98110,1674],{"separator":1673},[1659,98112,98113,98115,98117],{},[898,98114,900],{},[1665,98116,1681],{},[1654,98118,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,98120,2952],{},[1665,98122,2062],{},[902,98124,98125],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,98128,98130],{"className":98129},[886],[888,98131,98132],{"xmlns":890,"display":1956},[892,98133,98134,98250],{},[895,98135,98136,98148,98150,98152,98160,98176,98190,98192,98194,98206,98208,98210,98218,98232,98248],{},[1659,98137,98138,98140,98142],{},[898,98139,900],{},[1665,98141,6477],{},[895,98143,98144,98146],{},[1654,98145,2592],{"mathvariant":1878},[1654,98147,2592],{"mathvariant":1878},[1654,98149,1750],{},[1654,98151,2380],{},[2582,98153,98154],{"scriptlevel":2062,"displaystyle":1656},[2811,98155,98156,98158],{},[1665,98157,1667],{},[1665,98159,7631],{},[1659,98161,98162,98164,98166],{},[898,98163,1663],{},[1665,98165,1667],{},[895,98167,98168,98170,98172,98174],{},[1654,98169,2380],{},[1665,98171,4035],{},[898,98173,1879],{"mathvariant":1878},[1665,98175,1681],{},[1659,98177,98178,98180,98182],{},[898,98179,1663],{},[1665,98181,1681],{},[895,98183,98184,98186,98188],{},[1665,98185,1667],{},[898,98187,1879],{"mathvariant":1878},[1665,98189,4035],{},[1654,98191,1674],{"separator":1673},[5008,98193],{"width":5010},[1659,98195,98196,98198,98200],{},[898,98197,900],{},[1665,98199,6492],{},[895,98201,98202,98204],{},[1654,98203,2592],{"mathvariant":1878},[1654,98205,2592],{"mathvariant":1878},[1654,98207,1750],{},[1654,98209,2380],{},[2582,98211,98212],{"scriptlevel":2062,"displaystyle":1656},[2811,98213,98214,98216],{},[1665,98215,1681],{},[1665,98217,12742],{},[1659,98219,98220,98222,98224],{},[898,98221,1663],{},[1665,98223,1667],{},[895,98225,98226,98228,98230],{},[1665,98227,1667],{},[898,98229,1879],{"mathvariant":1878},[1665,98231,1681],{},[1659,98233,98234,98236,98238],{},[898,98235,1663],{},[1665,98237,1681],{},[895,98239,98240,98242,98244,98246],{},[1654,98241,2380],{},[1665,98243,4032],{},[898,98245,1879],{"mathvariant":1878},[1665,98247,4035],{},[1654,98249,1674],{"separator":1673},[902,98251,98252],{"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},",[724,98254,98255,98256,98298],{},"opět ",[883,98257,98259],{"className":98258},[886],[888,98260,98261],{"xmlns":890},[892,98262,98263,98295],{},[895,98264,98265,98277,98279,98291,98293],{},[1659,98266,98267,98269,98271],{},[898,98268,900],{},[1665,98270,6477],{},[895,98272,98273,98275],{},[1654,98274,2592],{"mathvariant":1878},[1654,98276,2592],{"mathvariant":1878},[1654,98278,1674],{"separator":1673},[1659,98280,98281,98283,98285],{},[898,98282,900],{},[1665,98284,6492],{},[895,98286,98287,98289],{},[1654,98288,2592],{"mathvariant":1878},[1654,98290,2592],{"mathvariant":1878},[1654,98292,3002],{},[1665,98294,2062],{},[902,98296,98297],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,98300,98301],{},[38,98302,98303,98304,2138],{},"(a) Mezní užitečnosti v bodě ",[883,98305,98307],{"className":98306},[886],[888,98308,98309],{"xmlns":890},[892,98310,98311,98323],{},[895,98312,98313,98315,98317,98319,98321],{},[1654,98314,1657],{"stretchy":1656},[1665,98316,4273],{},[1654,98318,1674],{"separator":1673},[1665,98320,17102],{},[1654,98322,1686],{"stretchy":1656},[902,98324,98325],{"encoding":904},"[100, 200]",[883,98327,98329],{"className":98328},[886],[888,98330,98331],{"xmlns":890,"display":1956},[892,98332,98333,98400],{},[895,98334,98335,98337,98343,98345,98347,98349,98351,98353,98355,98363,98365,98379,98381,98393,98395,98398],{},[898,98336,9320],{},[1710,98338,98339,98341],{},[898,98340,900],{},[1665,98342,1667],{},[1654,98344,1708],{"stretchy":1656},[1665,98346,4273],{},[1654,98348,1674],{"separator":1673},[1665,98350,17102],{},[1654,98352,1726],{"stretchy":1656},[1654,98354,1750],{},[2582,98356,98357],{"scriptlevel":2062,"displaystyle":1656},[2811,98358,98359,98361],{},[1665,98360,1667],{},[1665,98362,1681],{},[1654,98364,4554],{},[1741,98366,98367,98369],{},[1665,98368,4273],{},[895,98370,98371,98373,98375,98377],{},[1654,98372,2380],{},[1665,98374,1667],{},[898,98376,1879],{"mathvariant":1878},[1665,98378,1681],{},[1654,98380,4554],{},[1741,98382,98383,98385],{},[1665,98384,17102],{},[895,98386,98387,98389,98391],{},[1665,98388,1667],{},[898,98390,1879],{"mathvariant":1878},[1665,98392,4035],{},[1654,98394,14628],{},[1665,98396,98397],{},"0,4204",[1654,98399,1674],{"separator":1673},[902,98401,98402],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,98404,98406],{"className":98405},[886],[888,98407,98408],{"xmlns":890,"display":1956},[892,98409,98410,98475],{},[895,98411,98412,98414,98420,98422,98424,98426,98428,98430,98432,98440,98442,98454,98456,98470,98472],{},[898,98413,9320],{},[1710,98415,98416,98418],{},[898,98417,900],{},[1665,98419,1681],{},[1654,98421,1708],{"stretchy":1656},[1665,98423,4273],{},[1654,98425,1674],{"separator":1673},[1665,98427,17102],{},[1654,98429,1726],{"stretchy":1656},[1654,98431,1750],{},[2582,98433,98434],{"scriptlevel":2062,"displaystyle":1656},[2811,98435,98436,98438],{},[1665,98437,1667],{},[1665,98439,4035],{},[1654,98441,4554],{},[1741,98443,98444,98446],{},[1665,98445,4273],{},[895,98447,98448,98450,98452],{},[1665,98449,1667],{},[898,98451,1879],{"mathvariant":1878},[1665,98453,1681],{},[1654,98455,4554],{},[1741,98457,98458,98460],{},[1665,98459,17102],{},[895,98461,98462,98464,98466,98468],{},[1654,98463,2380],{},[1665,98465,1681],{},[898,98467,1879],{"mathvariant":1878},[1665,98469,4035],{},[1654,98471,14628],{},[1665,98473,98474],{},"0,63067.",[902,98476,98477],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,98479,98480,2186,98482,98517,98518,98539,98540,98557],{},[614,98481,4042],{},[883,98483,98485],{"className":98484},[886],[888,98486,98487],{"xmlns":890},[892,98488,98489,98514],{},[895,98490,98491,98493,98499,98501,98503,98505,98507,98509,98511],{},[898,98492,9320],{},[1710,98494,98495,98497],{},[898,98496,900],{},[1665,98498,1681],{},[1654,98500,1708],{"stretchy":1656},[1665,98502,4273],{},[1654,98504,1674],{"separator":1673},[1665,98506,17102],{},[1654,98508,1726],{"stretchy":1656},[1654,98510,14628],{},[1665,98512,98513],{},"0,63067",[902,98515,98516],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,98519,98521],{"className":98520},[886],[888,98522,98523],{"xmlns":890},[892,98524,98525,98537],{},[895,98526,98527,98529,98531,98533,98535],{},[1654,98528,1657],{"stretchy":1656},[1665,98530,4273],{},[1654,98532,1674],{"separator":1673},[1665,98534,17102],{},[1654,98536,1686],{"stretchy":1656},[902,98538,98325],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,98541,98543],{"className":98542},[886],[888,98544,98545],{"xmlns":890},[892,98546,98547,98555],{},[895,98548,98549],{},[1710,98550,98551,98553],{},[898,98552,1663],{},[1665,98554,1681],{},[902,98556,2937],{"encoding":904}," přibližně o 0,63067.",[724,98559,98560,98579,98580,47404,98601,98618,98619,98645,98646,98663,98664,11906],{},[38,98561,98562,98563,98578],{},"(b) Odhad změny ",[883,98564,98566],{"className":98565},[886],[888,98567,98568],{"xmlns":890},[892,98569,98570,98576],{},[895,98571,98572,98574],{},[898,98573,11648],{"mathvariant":1878},[898,98575,900],{},[902,98577,96821],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,98581,98583],{"className":98582},[886],[888,98584,98585],{"xmlns":890},[892,98586,98587,98599],{},[895,98588,98589,98591,98593,98595,98597],{},[1654,98590,1657],{"stretchy":1656},[1665,98592,4273],{},[1654,98594,1674],{"separator":1673},[1665,98596,17102],{},[1654,98598,1686],{"stretchy":1656},[902,98600,98325],{"encoding":904},[883,98602,98604],{"className":98603},[886],[888,98605,98606],{"xmlns":890},[892,98607,98608,98616],{},[895,98609,98610],{},[1710,98611,98612,98614],{},[898,98613,1663],{},[1665,98615,1667],{},[902,98617,2918],{"encoding":904}," na 98 (tj. ",[883,98620,98622],{"className":98621},[886],[888,98623,98624],{"xmlns":890},[892,98625,98626,98642],{},[895,98627,98628,98630,98636,98638,98640],{},[898,98629,10977],{"mathvariant":1878},[1710,98631,98632,98634],{},[898,98633,1663],{},[1665,98635,1667],{},[1654,98637,1750],{},[1654,98639,2380],{},[1665,98641,1681],{},[902,98643,98644],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,98647,98649],{"className":98648},[886],[888,98650,98651],{"xmlns":890},[892,98652,98653,98661],{},[895,98654,98655],{},[1710,98656,98657,98659],{},[898,98658,1663],{},[1665,98660,1681],{},[902,98662,2937],{"encoding":904}," o 3 (tj. ",[883,98665,98667],{"className":98666},[886],[888,98668,98669],{"xmlns":890},[892,98670,98671,98685],{},[895,98672,98673,98675,98681,98683],{},[898,98674,10977],{"mathvariant":1878},[1710,98676,98677,98679],{},[898,98678,1663],{},[1665,98680,1681],{},[1654,98682,1750],{},[1665,98684,4035],{},[902,98686,98687],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,98689,98691],{"className":98690},[886],[888,98692,98693],{"xmlns":890,"display":1956},[892,98694,98695,98746],{},[895,98696,98697,98699,98701,98703,98705,98707,98709,98711,98713,98715,98717,98719,98721,98723,98725,98727,98729,98731,98733,98736,98738,98741,98743],{},[898,98698,11648],{"mathvariant":1878},[898,98700,900],{},[1654,98702,11492],{},[898,98704,10977],{"mathvariant":1878},[898,98706,900],{},[1654,98708,1750],{},[1665,98710,98397],{},[1654,98712,4554],{},[1654,98714,1708],{"stretchy":1656},[1654,98716,2380],{},[1665,98718,1681],{},[1654,98720,1726],{"stretchy":1656},[1654,98722,1766],{},[1665,98724,98513],{},[1654,98726,4554],{},[1665,98728,4035],{},[1654,98730,1750],{},[1654,98732,2380],{},[1665,98734,98735],{},"0,8408",[1654,98737,1766],{},[1665,98739,98740],{},"1,89201",[1654,98742,14628],{},[1665,98744,98745],{},"1,05.",[902,98747,98748],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,98750,98751,98752,98755,98756,98807,98808,2138],{},"Užitečnost se tedy zvýší přibližně o ",[38,98753,98754],{},"1,05",". Skutečná změna je ",[883,98757,98759],{"className":98758},[886],[888,98760,98761],{"xmlns":890},[892,98762,98763,98804],{},[895,98764,98765,98767,98769,98771,98773,98775,98778,98780,98783,98785,98787,98789,98791,98793,98795,98797,98799,98801],{},[898,98766,11648],{"mathvariant":1878},[898,98768,900],{},[1654,98770,1750],{},[898,98772,900],{},[1654,98774,1708],{"stretchy":1656},[1665,98776,98777],{},"98",[1654,98779,1674],{"separator":1673},[1665,98781,98782],{},"203",[1654,98784,1726],{"stretchy":1656},[1654,98786,2380],{},[898,98788,900],{},[1654,98790,1708],{"stretchy":1656},[1665,98792,4273],{},[1654,98794,1674],{"separator":1673},[1665,98796,17102],{},[1654,98798,1726],{"stretchy":1656},[1654,98800,14628],{},[1665,98802,98803],{},"1,031",[902,98805,98806],{"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 ",[883,98809,98811],{"className":98810},[886],[888,98812,98813],{"xmlns":890},[892,98814,98815,98835],{},[895,98816,98817,98819,98825,98827,98829],{},[898,98818,10977],{"mathvariant":1878},[1710,98820,98821,98823],{},[898,98822,1663],{},[1665,98824,1667],{},[1654,98826,1674],{"separator":1673},[898,98828,10977],{"mathvariant":1878},[1710,98830,98831,98833],{},[898,98832,1663],{},[1665,98834,1681],{},[902,98836,96851],{"encoding":904},[115,98838,98840],{"id":98839},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,98842,98843],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,98845,98847],{"className":98846},[886],[888,98848,98849],{"xmlns":890,"display":1956},[892,98850,98851,98910],{},[1960,98852,98853],{"width":1962},[1964,98854,98855,98857,98903,98905],{},[1967,98856],{"width":1969},[1967,98858,98859],{},[895,98860,98861,98863,98865,98871,98873,98879,98881,98883,98891,98893,98901],{},[898,98862,900],{},[1654,98864,1708],{"stretchy":1656},[1710,98866,98867,98869],{},[898,98868,1663],{},[1665,98870,1667],{},[1654,98872,1674],{"separator":1673},[1710,98874,98875,98877],{},[898,98876,1663],{},[1665,98878,1681],{},[1654,98880,1726],{"stretchy":1656},[1654,98882,1750],{},[1659,98884,98885,98887,98889],{},[898,98886,1663],{},[1665,98888,1667],{},[898,98890,207],{},[1654,98892,4554],{},[1659,98894,98895,98897,98899],{},[898,98896,1663],{},[1665,98898,1681],{},[898,98900,9758],{},[1654,98902,1674],{"separator":1673},[1967,98904],{"width":1969},[1967,98906,98907],{},[1865,98908,98909],{},"(6.6)",[902,98911,98912],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,98914,13049,98915,98933,98934,98936,98937,98941,98942,98972,98973,98995],{},[883,98916,98918],{"className":98917},[886],[888,98919,98920],{"xmlns":890},[892,98921,98922,98930],{},[895,98923,98924,98926,98928],{},[898,98925,207],{},[1654,98927,1674],{"separator":1673},[898,98929,9758],{},[902,98931,98932],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,98935,82919],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,98938,98940],{"className":98939,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,98943,98945],{"className":98944},[886],[888,98946,98947],{"xmlns":890},[892,98948,98949,98969],{},[895,98950,98951,98953,98955,98957,98959,98961,98963,98965,98967],{},[898,98952,207],{},[1654,98954,1674],{"separator":1673},[898,98956,9758],{},[1654,98958,9780],{},[1654,98960,1708],{"stretchy":1656},[1665,98962,2062],{},[1654,98964,1674],{"separator":1673},[1665,98966,1667],{},[1654,98968,1726],{"stretchy":1656},[902,98970,98971],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,98974,98976],{"className":98975},[886],[888,98977,98978],{"xmlns":890},[892,98979,98980,98992],{},[895,98981,98982,98984,98986,98988,98990],{},[898,98983,9758],{},[1654,98985,1750],{},[1665,98987,1667],{},[1654,98989,2380],{},[898,98991,207],{},[902,98993,98994],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,98997,98998],{},[3492,98999],{"alt":99000,"className":99001,"src":99002},"imek-cobb-douglas-3d-plus-ic",[210,3496],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,99004,99006],{"className":99005},[886],[888,99007,99008],{"xmlns":890,"display":1956},[892,99009,99010,99060],{},[895,99011,99012,99014,99016,99022,99024,99030,99032,99034,99042,99044,99058],{},[898,99013,900],{},[1654,99015,1708],{"stretchy":1656},[1710,99017,99018,99020],{},[898,99019,1663],{},[1665,99021,1667],{},[1654,99023,1674],{"separator":1673},[1710,99025,99026,99028],{},[898,99027,1663],{},[1665,99029,1681],{},[1654,99031,1726],{"stretchy":1656},[1654,99033,1750],{},[1659,99035,99036,99038,99040],{},[898,99037,1663],{},[1665,99039,1667],{},[898,99041,207],{},[1654,99043,4554],{},[1659,99045,99046,99048,99050],{},[898,99047,1663],{},[1665,99049,1681],{},[895,99051,99052,99054,99056],{},[1665,99053,1667],{},[1654,99055,2380],{},[898,99057,207],{},[898,99059,2138],{"mathvariant":1878},[902,99061,99062],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[2140,99064,99065,99114,99236,99370],{},[724,99066,99067,99069,99070],{},[883,99068,60915],{}," Příklad 6.3 — ověření vlastností pro ",[883,99071,99073],{"className":99072},[886],[888,99074,99075],{"xmlns":890},[892,99076,99077,99111],{},[895,99078,99079,99081,99083,99097],{},[898,99080,900],{},[1654,99082,1750],{},[1659,99084,99085,99087,99089],{},[898,99086,1663],{},[1665,99088,1667],{},[895,99090,99091,99093,99095],{},[1665,99092,1667],{},[898,99094,1879],{"mathvariant":1878},[1665,99096,7631],{},[1659,99098,99099,99101,99103],{},[898,99100,1663],{},[1665,99102,1681],{},[895,99104,99105,99107,99109],{},[1665,99106,4035],{},[898,99108,1879],{"mathvariant":1878},[1665,99110,7631],{},[902,99112,99113],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,99115,99117],{"className":99116},[886],[888,99118,99119],{"xmlns":890,"display":1956},[892,99120,99121,99233],{},[895,99122,99123,99131,99133,99141,99157,99171,99173,99175,99177,99179,99187,99189,99197,99211,99227,99229,99231],{},[1659,99124,99125,99127,99129],{},[898,99126,900],{},[1665,99128,1667],{},[1654,99130,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,99132,1750],{},[2582,99134,99135],{"scriptlevel":2062,"displaystyle":1656},[2811,99136,99137,99139],{},[1665,99138,1667],{},[1665,99140,7631],{},[1659,99142,99143,99145,99147],{},[898,99144,1663],{},[1665,99146,1667],{},[895,99148,99149,99151,99153,99155],{},[1654,99150,2380],{},[1665,99152,4035],{},[898,99154,1879],{"mathvariant":1878},[1665,99156,7631],{},[1659,99158,99159,99161,99163],{},[898,99160,1663],{},[1665,99162,1681],{},[895,99164,99165,99167,99169],{},[1665,99166,4035],{},[898,99168,1879],{"mathvariant":1878},[1665,99170,7631],{},[1654,99172,2952],{},[1665,99174,2062],{},[1654,99176,1674],{"separator":1673},[5008,99178],{"width":5010},[1659,99180,99181,99183,99185],{},[898,99182,900],{},[1665,99184,1681],{},[1654,99186,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,99188,1750],{},[2582,99190,99191],{"scriptlevel":2062,"displaystyle":1656},[2811,99192,99193,99195],{},[1665,99194,4035],{},[1665,99196,7631],{},[1659,99198,99199,99201,99203],{},[898,99200,1663],{},[1665,99202,1667],{},[895,99204,99205,99207,99209],{},[1665,99206,1667],{},[898,99208,1879],{"mathvariant":1878},[1665,99210,7631],{},[1659,99212,99213,99215,99217],{},[898,99214,1663],{},[1665,99216,1681],{},[895,99218,99219,99221,99223,99225],{},[1654,99220,2380],{},[1665,99222,1667],{},[898,99224,1879],{"mathvariant":1878},[1665,99226,7631],{},[1654,99228,2952],{},[1665,99230,2062],{},[1654,99232,1674],{"separator":1673},[902,99234,99235],{"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,",[883,99237,99239],{"className":99238},[886],[888,99240,99241],{"xmlns":890,"display":1956},[892,99242,99243,99367],{},[895,99244,99245,99257,99259,99261,99269,99285,99299,99301,99303,99305,99307,99319,99321,99323,99331,99345,99361,99363,99365],{},[1659,99246,99247,99249,99251],{},[898,99248,900],{},[1665,99250,6477],{},[895,99252,99253,99255],{},[1654,99254,2592],{"mathvariant":1878},[1654,99256,2592],{"mathvariant":1878},[1654,99258,1750],{},[1654,99260,2380],{},[2582,99262,99263],{"scriptlevel":2062,"displaystyle":1656},[2811,99264,99265,99267],{},[1665,99266,4035],{},[1665,99268,50082],{},[1659,99270,99271,99273,99275],{},[898,99272,1663],{},[1665,99274,1667],{},[895,99276,99277,99279,99281,99283],{},[1654,99278,2380],{},[1665,99280,32887],{},[898,99282,1879],{"mathvariant":1878},[1665,99284,7631],{},[1659,99286,99287,99289,99291],{},[898,99288,1663],{},[1665,99290,1681],{},[895,99292,99293,99295,99297],{},[1665,99294,4035],{},[898,99296,1879],{"mathvariant":1878},[1665,99298,7631],{},[1654,99300,3002],{},[1665,99302,2062],{},[1654,99304,1674],{"separator":1673},[5008,99306],{"width":5010},[1659,99308,99309,99311,99313],{},[898,99310,900],{},[1665,99312,6492],{},[895,99314,99315,99317],{},[1654,99316,2592],{"mathvariant":1878},[1654,99318,2592],{"mathvariant":1878},[1654,99320,1750],{},[1654,99322,2380],{},[2582,99324,99325],{"scriptlevel":2062,"displaystyle":1656},[2811,99326,99327,99329],{},[1665,99328,4035],{},[1665,99330,50082],{},[1659,99332,99333,99335,99337],{},[898,99334,1663],{},[1665,99336,1667],{},[895,99338,99339,99341,99343],{},[1665,99340,1667],{},[898,99342,1879],{"mathvariant":1878},[1665,99344,7631],{},[1659,99346,99347,99349,99351],{},[898,99348,1663],{},[1665,99350,1681],{},[895,99352,99353,99355,99357,99359],{},[1654,99354,2380],{},[1665,99356,4032],{},[898,99358,1879],{"mathvariant":1878},[1665,99360,7631],{},[1654,99362,3002],{},[1665,99364,2062],{},[1654,99366,1674],{"separator":1673},[902,99368,99369],{"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,",[724,99371,99372],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,99374,99376],{"id":99375},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,99378,99379,99382],{},[38,99380,99381],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,99384,99386],{"className":99385},[886],[888,99387,99388],{"xmlns":890,"display":1956},[892,99389,99390,99433],{},[1960,99391,99392],{"width":1962},[1964,99393,99394,99396,99426,99428],{},[1967,99395],{"width":1969},[1967,99397,99398],{},[895,99399,99400,99402,99404,99410,99412,99418,99420,99422,99424],{},[898,99401,900],{},[1654,99403,1708],{"stretchy":1656},[1710,99405,99406,99408],{},[898,99407,1663],{},[1665,99409,1667],{},[1654,99411,1674],{"separator":1673},[1710,99413,99414,99416],{},[898,99415,1663],{},[1665,99417,1681],{},[1654,99419,1726],{"stretchy":1656},[1654,99421,1750],{},[898,99423,3624],{},[1654,99425,1674],{"separator":1673},[1967,99427],{"width":1969},[1967,99429,99430],{},[1865,99431,99432],{},"(6.7)",[902,99434,99435],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,99437,13049,99438,99451],{},[883,99439,99441],{"className":99440},[886],[888,99442,99443],{"xmlns":890},[892,99444,99445,99449],{},[895,99446,99447],{},[898,99448,3624],{},[902,99450,3624],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,99453,99455],{"className":99454},[886],[888,99456,99457],{"xmlns":890,"display":1956},[892,99458,99459,99500],{},[1960,99460,99461],{"width":1962},[1964,99462,99463,99465,99493,99495],{},[1967,99464],{"width":1969},[1967,99466,99467],{},[895,99468,99469,99477,99479,99487,99489,99491],{},[1659,99470,99471,99473,99475],{},[898,99472,1663],{},[1665,99474,1667],{},[898,99476,207],{},[1654,99478,4554],{},[1659,99480,99481,99483,99485],{},[898,99482,1663],{},[1665,99484,1681],{},[898,99486,9758],{},[1654,99488,1750],{},[898,99490,3624],{},[898,99492,2138],{"mathvariant":1878},[1967,99494],{"width":1969},[1967,99496,99497],{},[1865,99498,99499],{},"(6.8)",[902,99501,99502],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,99504,99505,99506,13096,99536,2186,99539,99552,99553,99588,99589,99606,99607,99636,99637,99640],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,99507,99509],{"className":99508},[886],[888,99510,99511],{"xmlns":890},[892,99512,99513,99533],{},[895,99514,99515,99517,99523,99525,99531],{},[1654,99516,1657],{"stretchy":1656},[1710,99518,99519,99521],{},[898,99520,1663],{},[1665,99522,1667],{},[1654,99524,1674],{"separator":1673},[1710,99526,99527,99529],{},[898,99528,1663],{},[1665,99530,1681],{},[1654,99532,1686],{"stretchy":1656},[902,99534,99535],{"encoding":904},"[Q_1, Q_2]",[38,99537,99538],{},"stejnou úrovní uspokojení",[883,99540,99542],{"className":99541},[886],[888,99543,99544],{"xmlns":890},[892,99545,99546,99550],{},[895,99547,99548],{},[898,99549,3624],{},[902,99551,3624],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,99554,99556],{"className":99555},[886],[888,99557,99558],{"xmlns":890},[892,99559,99560,99586],{},[895,99561,99562,99564,99566,99568,99570,99576,99578,99584],{},[898,99563,900],{},[1654,99565,1750],{},[898,99567,900],{},[1654,99569,1708],{"stretchy":1656},[1710,99571,99572,99574],{},[898,99573,1663],{},[1665,99575,1667],{},[1654,99577,1674],{"separator":1673},[1710,99579,99580,99582],{},[898,99581,1663],{},[1665,99583,1681],{},[1654,99585,1726],{"stretchy":1656},[902,99587,95676],{"encoding":904}," s rovinami ",[883,99590,99592],{"className":99591},[886],[888,99593,99594],{"xmlns":890},[892,99595,99596,99604],{},[895,99597,99598,99600,99602],{},[898,99599,900],{},[1654,99601,1750],{},[898,99603,3624],{},[902,99605,94892],{"encoding":904}," rovnoběžnými s rovinou ",[883,99608,99610],{"className":99609},[886],[888,99611,99612],{"xmlns":890},[892,99613,99614,99634],{},[895,99615,99616,99618,99624,99626,99632],{},[1654,99617,1708],{"stretchy":1656},[1710,99619,99620,99622],{},[898,99621,1663],{},[1665,99623,1667],{},[1654,99625,1674],{"separator":1673},[1710,99627,99628,99630],{},[898,99629,1663],{},[1665,99631,1681],{},[1654,99633,1726],{"stretchy":1656},[902,99635,97839],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,99638,99639],{},"izokvantami"," produkčních funkcí.",[724,99642,99643],{},[614,99644,99645,99646,97717,99664,99682,99683,2138],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,99647,99649],{"className":99648},[886],[888,99650,99651],{"xmlns":890},[892,99652,99653,99661],{},[895,99654,99655,99657,99659],{},[898,99656,207],{},[1654,99658,3002],{},[898,99660,9758],{},[902,99662,99663],{"encoding":904},"a \u003C b",[883,99665,99667],{"className":99666},[886],[888,99668,99669],{"xmlns":890},[892,99670,99671,99679],{},[895,99672,99673,99675,99677],{},[898,99674,207],{},[1654,99676,2952],{},[898,99678,9758],{},[902,99680,99681],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,99684,99686],{"className":99685},[886],[888,99687,99688],{"xmlns":890},[892,99689,99690,99714],{},[895,99691,99692,99698,99700,99706,99708],{},[1710,99693,99694,99696],{},[898,99695,3624],{},[1665,99697,2062],{},[1654,99699,3002],{},[1710,99701,99702,99704],{},[898,99703,3624],{},[1665,99705,1667],{},[1654,99707,3002],{},[1710,99709,99710,99712],{},[898,99711,3624],{},[1665,99713,1681],{},[902,99715,99716],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,99718,99719],{},[614,99720,99721,99722,99751,99752,99810,99811,99829],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,99723,99725],{"className":99724},[886],[888,99726,99727],{"xmlns":890},[892,99728,99729,99749],{},[895,99730,99731,99733,99739,99741,99747],{},[1654,99732,1708],{"stretchy":1656},[1710,99734,99735,99737],{},[898,99736,1663],{},[1665,99738,1667],{},[1654,99740,1674],{"separator":1673},[1710,99742,99743,99745],{},[898,99744,1663],{},[1665,99746,1681],{},[1654,99748,1726],{"stretchy":1656},[902,99750,97839],{"encoding":904},"; body ",[883,99753,99755],{"className":99754},[886],[888,99756,99757],{"xmlns":890},[892,99758,99759,99807],{},[895,99760,99761,99763,99765,99767,99773,99775,99781,99783,99785,99787,99789,99791,99797,99799,99805],{},[898,99762,4737],{},[1654,99764,1750],{},[1654,99766,1657],{"stretchy":1656},[1710,99768,99769,99771],{},[898,99770,207],{},[1665,99772,1667],{},[1654,99774,1674],{"separator":1673},[1710,99776,99777,99779],{},[898,99778,207],{},[1665,99780,1681],{},[1654,99782,1686],{"stretchy":1656},[1654,99784,1674],{"separator":1673},[898,99786,4762],{},[1654,99788,1750],{},[1654,99790,1657],{"stretchy":1656},[1710,99792,99793,99795],{},[898,99794,9758],{},[1665,99796,1667],{},[1654,99798,1674],{"separator":1673},[1710,99800,99801,99803],{},[898,99802,9758],{},[1665,99804,1681],{},[1654,99806,1686],{"stretchy":1656},[902,99808,99809],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,99812,99814],{"className":99813},[886],[888,99815,99816],{"xmlns":890},[892,99817,99818,99826],{},[895,99819,99820,99822,99824],{},[898,99821,11539],{},[1654,99823,1674],{"separator":1673},[898,99825,4980],{},[902,99827,99828],{"encoding":904},"C, D"," na vyšší hladině.",[2140,99831,99832],{},[724,99833,99834,99836,99837,99899,99900,99944,99945,99979,99980,34875,99998,99979,100052,34875,100070,100146],{},[883,99835,60915],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,99838,99840],{"className":99839},[886],[888,99841,99842],{"xmlns":890},[892,99843,99844,99896],{},[895,99845,99846,99848,99850,99856,99858,99864,99866,99868,99882],{},[898,99847,900],{},[1654,99849,1708],{"stretchy":1656},[1710,99851,99852,99854],{},[898,99853,1663],{},[1665,99855,1667],{},[1654,99857,1674],{"separator":1673},[1710,99859,99860,99862],{},[898,99861,1663],{},[1665,99863,1681],{},[1654,99865,1726],{"stretchy":1656},[1654,99867,1750],{},[1659,99869,99870,99872,99874],{},[898,99871,1663],{},[1665,99873,1667],{},[895,99875,99876,99878,99880],{},[1665,99877,1667],{},[898,99879,1879],{"mathvariant":1878},[1665,99881,7631],{},[1659,99883,99884,99886,99888],{},[898,99885,1663],{},[1665,99887,1681],{},[895,99889,99890,99892,99894],{},[1665,99891,4035],{},[898,99893,1879],{"mathvariant":1878},[1665,99895,7631],{},[902,99897,99898],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,99901,99903],{"className":99902},[886],[888,99904,99905],{"xmlns":890},[892,99906,99907,99941],{},[895,99908,99909,99923,99937,99939],{},[1659,99910,99911,99913,99915],{},[898,99912,1663],{},[1665,99914,1667],{},[895,99916,99917,99919,99921],{},[1665,99918,1667],{},[898,99920,1879],{"mathvariant":1878},[1665,99922,7631],{},[1659,99924,99925,99927,99929],{},[898,99926,1663],{},[1665,99928,1681],{},[895,99930,99931,99933,99935],{},[1665,99932,4035],{},[898,99934,1879],{"mathvariant":1878},[1665,99936,7631],{},[1654,99938,1750],{},[898,99940,3624],{},[902,99942,99943],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,99946,99948],{"className":99947},[886],[888,99949,99950],{"xmlns":890},[892,99951,99952,99976],{},[895,99953,99954,99960,99968,99970],{},[1710,99955,99956,99958],{},[898,99957,1663],{},[1665,99959,1667],{},[1659,99961,99962,99964,99966],{},[898,99963,1663],{},[1665,99965,1681],{},[1665,99967,4035],{},[1654,99969,1750],{},[1741,99971,99972,99974],{},[898,99973,3624],{},[1665,99975,7631],{},[902,99977,99978],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,99981,99983],{"className":99982},[886],[888,99984,99985],{"xmlns":890},[892,99986,99987,99995],{},[895,99988,99989,99991,99993],{},[898,99990,3624],{},[1654,99992,1750],{},[1665,99994,1667],{},[902,99996,99997],{"encoding":904},"c = 1",[883,99999,100001],{"className":100000},[886],[888,100002,100003],{"xmlns":890},[892,100004,100005,100049],{},[895,100006,100007,100013,100015,100031,100033],{},[1710,100008,100009,100011],{},[898,100010,1663],{},[1665,100012,1681],{},[1654,100014,1750],{},[1659,100016,100017,100019,100021],{},[898,100018,1663],{},[1665,100020,1667],{},[895,100022,100023,100025,100027,100029],{},[1654,100024,2380],{},[1665,100026,1667],{},[898,100028,1879],{"mathvariant":1878},[1665,100030,4035],{},[1654,100032,1750],{},[2582,100034,100035],{"scriptlevel":2062,"displaystyle":1673},[2811,100036,100037,100039],{},[1665,100038,1667],{},[90247,100040,100041,100047],{},[1710,100042,100043,100045],{},[898,100044,1663],{},[1665,100046,1667],{},[1665,100048,4035],{},[902,100050,100051],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,100053,100055],{"className":100054},[886],[888,100056,100057],{"xmlns":890},[892,100058,100059,100067],{},[895,100060,100061,100063,100065],{},[898,100062,3624],{},[1654,100064,1750],{},[1665,100066,1681],{},[902,100068,100069],{"encoding":904},"c = 2",[883,100071,100073],{"className":100072},[886],[888,100074,100075],{"xmlns":890},[892,100076,100077,100143],{},[895,100078,100079,100085,100087,100099,100101,100117,100119],{},[1710,100080,100081,100083],{},[898,100082,1663],{},[1665,100084,1681],{},[1654,100086,1750],{},[1741,100088,100089,100091],{},[1665,100090,1681],{},[895,100092,100093,100095,100097],{},[1665,100094,7631],{},[898,100096,1879],{"mathvariant":1878},[1665,100098,4035],{},[1654,100100,4554],{},[1659,100102,100103,100105,100107],{},[898,100104,1663],{},[1665,100106,1667],{},[895,100108,100109,100111,100113,100115],{},[1654,100110,2380],{},[1665,100112,1667],{},[898,100114,1879],{"mathvariant":1878},[1665,100116,4035],{},[1654,100118,1750],{},[2582,100120,100121],{"scriptlevel":2062,"displaystyle":1673},[2811,100122,100123,100133],{},[895,100124,100125,100127],{},[1665,100126,1681],{},[90247,100128,100129,100131],{},[1665,100130,1681],{},[1665,100132,4035],{},[90247,100134,100135,100141],{},[1710,100136,100137,100139],{},[898,100138,1663],{},[1665,100140,1667],{},[1665,100142,4035],{},[902,100144,100145],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,100148,100150],{"id":100149},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,100152,100153],{},[3492,100154],{"alt":100155,"className":100156,"src":100157},"imek-ic-4vlastnosti-anotovane",[210,3496],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[2140,100159,100160,100169,100216,100260,100266,100272],{},[724,100161,100162,100164,100165,100168],{},[883,100163,2146],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,100166,100167],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,100170,100171],{},[883,100172,100174],{"className":100173},[886],[888,100175,100176],{"xmlns":890},[892,100177,100178,100213],{},[895,100179,100180,100183,100185,100187,100189,100191,100209,100211],{},[898,100181,100182],{"mathvariant":1878},"tg",[1654,100184,64420],{},[898,100186,27558],{},[1654,100188,1750],{},[1654,100190,2380],{},[2811,100192,100193,100201],{},[1659,100194,100195,100197,100199],{},[898,100196,900],{},[1665,100198,1667],{},[1654,100200,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1659,100202,100203,100205,100207],{},[898,100204,900],{},[1665,100206,1681],{},[1654,100208,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,100210,3002],{},[1665,100212,2062],{},[902,100214,100215],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,100217,100218,100219,100259],{},"(derivace implicitně zadané funkce ",[883,100220,100222],{"className":100221},[886],[888,100223,100224],{"xmlns":890},[892,100225,100226,100256],{},[895,100227,100228,100230,100232,100238,100240,100246,100248,100250,100252,100254],{},[898,100229,900],{},[1654,100231,1708],{"stretchy":1656},[1710,100233,100234,100236],{},[898,100235,1663],{},[1665,100237,1667],{},[1654,100239,1674],{"separator":1673},[1710,100241,100242,100244],{},[898,100243,1663],{},[1665,100245,1681],{},[1654,100247,1726],{"stretchy":1656},[1654,100249,2380],{},[898,100251,3624],{},[1654,100253,1750],{},[1665,100255,2062],{},[902,100257,100258],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,100261,100262,100265],{},[38,100263,100264],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,100267,100268,100271],{},[38,100269,100270],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,100273,100274,100277,100278,100296,100297,100313,100314,100317],{},[38,100275,100276],{},"4° Konvexní."," Pro každé dva body ",[883,100279,100281],{"className":100280},[886],[888,100282,100283],{"xmlns":890},[892,100284,100285,100293],{},[895,100286,100287,100289,100291],{},[898,100288,4737],{},[1654,100290,1674],{"separator":1673},[898,100292,4762],{},[902,100294,100295],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,100298,100300],{"className":100299},[886],[888,100301,100302],{"xmlns":890},[892,100303,100304,100310],{},[895,100305,100306,100308],{},[898,100307,4737],{},[898,100309,4762],{},[902,100311,100312],{"encoding":904},"AB"," ve ",[38,100315,100316],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,100319,100320],{},[614,100321,100322,100323,100358,100359,2138],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,100324,100326],{"className":100325},[886],[888,100327,100328],{"xmlns":890},[892,100329,100330,100356],{},[895,100331,100332,100334,100336,100342,100344,100350,100352,100354],{},[898,100333,900],{},[1654,100335,1708],{"stretchy":1656},[1710,100337,100338,100340],{},[898,100339,1663],{},[1665,100341,1667],{},[1654,100343,1674],{"separator":1673},[1710,100345,100346,100348],{},[898,100347,1663],{},[1665,100349,1681],{},[1654,100351,1726],{"stretchy":1656},[1654,100353,1750],{},[898,100355,3624],{},[902,100357,18487],{"encoding":904}," s tečnou se sklonem ",[883,100360,100362],{"className":100361},[886],[888,100363,100364],{"xmlns":890},[892,100365,100366,100374],{},[895,100367,100368,100370,100372],{},[898,100369,100182],{"mathvariant":1878},[1654,100371,64420],{},[898,100373,27558],{},[902,100375,100376],{"encoding":904},"\\operatorname{tg}\\alpha",[115,100378,100380],{"id":100379},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,100382,100383,2186,100386,18742,100399,100402],{},[38,100384,100385],{},"Mezní míra komoditní substituce",[883,100387,100389],{"className":100388},[886],[888,100390,100391],{"xmlns":890},[892,100392,100393,100397],{},[895,100394,100395],{},[1865,100396,1867],{},[902,100398,2133],{"encoding":904},[38,100400,100401],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,100404,100406],{"className":100405},[886],[888,100407,100408],{"xmlns":890,"display":1956},[892,100409,100410,100497],{},[1960,100411,100412],{"width":1962},[1964,100413,100414,100416,100490,100492],{},[1967,100415],{"width":1969},[1967,100417,100418],{},[895,100419,100420,100422,100424,100426,100428,100434,100436,100442,100444,100446,100468,100470,100488],{},[1865,100421,1867],{},[1654,100423,1750],{},[1865,100425,1867],{},[1654,100427,1708],{"stretchy":1656},[1710,100429,100430,100432],{},[898,100431,1663],{},[1665,100433,1667],{},[1654,100435,1674],{"separator":1673},[1710,100437,100438,100440],{},[898,100439,1663],{},[1665,100441,1681],{},[1654,100443,1726],{"stretchy":1656},[1654,100445,1750],{},[2811,100447,100448,100458],{},[895,100449,100450,100452],{},[898,100451,9320],{},[1710,100453,100454,100456],{},[898,100455,900],{},[1665,100457,1667],{},[895,100459,100460,100462],{},[898,100461,9320],{},[1710,100463,100464,100466],{},[898,100465,900],{},[1665,100467,1681],{},[1654,100469,1750],{},[2811,100471,100472,100480],{},[1659,100473,100474,100476,100478],{},[898,100475,900],{},[1665,100477,1667],{},[1654,100479,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1659,100481,100482,100484,100486],{},[898,100483,900],{},[1665,100485,1681],{},[1654,100487,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[898,100489,2138],{"mathvariant":1878},[1967,100491],{"width":1969},[1967,100493,100494],{},[1865,100495,100496],{},"(6.9)",[902,100498,100499],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,100501,100502,100503,100537,100538,100570,100571,100606,100607,100620],{},"Geometricky: ",[883,100504,100506],{"className":100505},[886],[888,100507,100508],{"xmlns":890},[892,100509,100510,100534],{},[895,100511,100512,100514],{},[1654,100513,2380],{},[2582,100515,100516],{"scriptlevel":2062,"displaystyle":1656},[2811,100517,100518,100526],{},[1659,100519,100520,100522,100524],{},[898,100521,900],{},[1665,100523,1667],{},[1654,100525,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1659,100527,100528,100530,100532],{},[898,100529,900],{},[1665,100531,1681],{},[1654,100533,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,100535,100536],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,100539,100541],{"className":100540},[886],[888,100542,100543],{"xmlns":890},[892,100544,100545,100567],{},[895,100546,100547,100553,100555,100557,100559,100565],{},[1710,100548,100549,100551],{},[898,100550,1663],{},[1665,100552,1681],{},[1654,100554,1750],{},[898,100556,10794],{},[1654,100558,1708],{"stretchy":1656},[1710,100560,100561,100563],{},[898,100562,1663],{},[1665,100564,1667],{},[1654,100566,1726],{"stretchy":1656},[902,100568,100569],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,100572,100574],{"className":100573},[886],[888,100575,100576],{"xmlns":890},[892,100577,100578,100604],{},[895,100579,100580,100582,100584,100590,100592,100598,100600,100602],{},[898,100581,900],{},[1654,100583,1708],{"stretchy":1656},[1710,100585,100586,100588],{},[898,100587,1663],{},[1665,100589,1667],{},[1654,100591,1674],{"separator":1673},[1710,100593,100594,100596],{},[898,100595,1663],{},[1665,100597,1681],{},[1654,100599,1726],{"stretchy":1656},[1654,100601,1750],{},[898,100603,3624],{},[902,100605,18487],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,100608,100610],{"className":100609},[886],[888,100611,100612],{"xmlns":890},[892,100613,100614,100618],{},[895,100615,100616],{},[1865,100617,1867],{},[902,100619,2133],{"encoding":904}," chápeme jako velikost kompenzace.",[2140,100622,100623],{},[724,100624,100625,100627,100628,16828,100660,100698,100699,100716,100717,100734],{},[883,100626,2860],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,100629,100631],{"className":100630},[886],[888,100632,100633],{"xmlns":890},[892,100634,100635,100657],{},[895,100636,100637,100639,100641,100647,100649,100655],{},[1865,100638,1867],{},[1654,100640,1708],{"stretchy":1656},[1710,100642,100643,100645],{},[898,100644,1663],{},[1665,100646,1667],{},[1654,100648,1674],{"separator":1673},[1710,100650,100651,100653],{},[898,100652,1663],{},[1665,100654,1681],{},[1654,100656,1726],{"stretchy":1656},[902,100658,100659],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,100661,100662,100663,2919,100680,100697],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,100664,100666],{"className":100665},[886],[888,100667,100668],{"xmlns":890},[892,100669,100670,100678],{},[895,100671,100672],{},[1710,100673,100674,100676],{},[898,100675,1663],{},[1665,100677,1667],{},[902,100679,2918],{"encoding":904},[883,100681,100683],{"className":100682},[886],[888,100684,100685],{"xmlns":890},[892,100686,100687,100695],{},[895,100688,100689],{},[1710,100690,100691,100693],{},[898,100692,1663],{},[1665,100694,1681],{},[902,100696,2937],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,100700,100702],{"className":100701},[886],[888,100703,100704],{"xmlns":890},[892,100705,100706,100714],{},[895,100707,100708],{},[1710,100709,100710,100712],{},[898,100711,1663],{},[1665,100713,1681],{},[902,100715,2937],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,100718,100720],{"className":100719},[886],[888,100721,100722],{"xmlns":890},[892,100723,100724,100732],{},[895,100725,100726],{},[1710,100727,100728,100730],{},[898,100729,1663],{},[1665,100731,1667],{},[902,100733,2918],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,100736,100737,100738,3869],{},"Pro obecnou změnu ",[883,100739,100741],{"className":100740},[886],[888,100742,100743],{"xmlns":890},[892,100744,100745,100755],{},[895,100746,100747,100749],{},[898,100748,10977],{"mathvariant":1878},[1710,100750,100751,100753],{},[898,100752,1663],{},[1665,100754,1667],{},[902,100756,100757],{"encoding":904},"\\mathrm{d} Q_1",[883,100759,100761],{"className":100760},[886],[888,100762,100763],{"xmlns":890,"display":1956},[892,100764,100765,100818],{},[1960,100766,100767],{"width":1962},[1964,100768,100769,100771,100811,100813],{},[1967,100770],{"width":1969},[1967,100772,100773],{},[895,100774,100775,100777,100783,100785,100787,100793,100795,100797,100799,100801,100803,100809],{},[898,100776,11648],{"mathvariant":1878},[1710,100778,100779,100781],{},[898,100780,1663],{},[1665,100782,1681],{},[1654,100784,11492],{},[898,100786,10977],{"mathvariant":1878},[1710,100788,100789,100791],{},[898,100790,1663],{},[1665,100792,1681],{},[1654,100794,1750],{},[1654,100796,2380],{},[1865,100798,1867],{},[1654,100800,4554],{},[898,100802,10977],{"mathvariant":1878},[1710,100804,100805,100807],{},[898,100806,1663],{},[1665,100808,1667],{},[1654,100810,1674],{"separator":1673},[1967,100812],{"width":1969},[1967,100814,100815],{},[1865,100816,100817],{},"(6.10)",[902,100819,100820],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,100822,100824],{"className":100823},[886],[888,100825,100826],{"xmlns":890,"display":1956},[892,100827,100828,100875],{},[1960,100829,100830],{"width":1962},[1964,100831,100832,100834,100868,100870],{},[1967,100833],{"width":1969},[1967,100835,100836],{},[895,100837,100838,100840,100846,100848,100850,100856,100858,100860,100866],{},[898,100839,10977],{"mathvariant":1878},[1710,100841,100842,100844],{},[898,100843,1663],{},[1665,100845,1667],{},[1654,100847,1750],{},[1654,100849,2380],{},[2811,100851,100852,100854],{},[1665,100853,1667],{},[1865,100855,1867],{},[1865,100857,11744],{},[898,100859,10977],{"mathvariant":1878},[1710,100861,100862,100864],{},[898,100863,1663],{},[1665,100865,1681],{},[898,100867,2138],{"mathvariant":1878},[1967,100869],{"width":1969},[1967,100871,100872],{},[1865,100873,100874],{},"(6.11)",[902,100876,100877],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[2140,100879,100880,100946,101063],{},[724,100881,100882,100884,100885,3869],{},[883,100883,60915],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,100886,100888],{"className":100887},[886],[888,100889,100890],{"xmlns":890},[892,100891,100892,100944],{},[895,100893,100894,100896,100898,100904,100906,100912,100914,100916,100930],{},[898,100895,900],{},[1654,100897,1708],{"stretchy":1656},[1710,100899,100900,100902],{},[898,100901,1663],{},[1665,100903,1667],{},[1654,100905,1674],{"separator":1673},[1710,100907,100908,100910],{},[898,100909,1663],{},[1665,100911,1681],{},[1654,100913,1726],{"stretchy":1656},[1654,100915,1750],{},[1659,100917,100918,100920,100922],{},[898,100919,1663],{},[1665,100921,1667],{},[895,100923,100924,100926,100928],{},[1665,100925,1667],{},[898,100927,1879],{"mathvariant":1878},[1665,100929,1681],{},[1659,100931,100932,100934,100936],{},[898,100933,1663],{},[1665,100935,1681],{},[895,100937,100938,100940,100942],{},[1665,100939,1667],{},[898,100941,1879],{"mathvariant":1878},[1665,100943,1681],{},[902,100945,3868],{"encoding":904},[724,100947,100948],{},[883,100949,100951],{"className":100950},[886],[888,100952,100953],{"xmlns":890},[892,100954,100955,101061],{},[895,100956,100957,100959,100961,101043,101045,101059],{},[1865,100958,1867],{},[1654,100960,1750],{},[2811,100962,100963,101003],{},[895,100964,100965,100973,100989],{},[2582,100966,100967],{"scriptlevel":2062,"displaystyle":1656},[2811,100968,100969,100971],{},[1665,100970,1667],{},[1665,100972,1681],{},[1659,100974,100975,100977,100979],{},[898,100976,1663],{},[1665,100978,1667],{},[895,100980,100981,100983,100985,100987],{},[1654,100982,2380],{},[1665,100984,1667],{},[898,100986,1879],{"mathvariant":1878},[1665,100988,1681],{},[1659,100990,100991,100993,100995],{},[898,100992,1663],{},[1665,100994,1681],{},[895,100996,100997,100999,101001],{},[1665,100998,1667],{},[898,101000,1879],{"mathvariant":1878},[1665,101002,1681],{},[895,101004,101005,101013,101027],{},[2582,101006,101007],{"scriptlevel":2062,"displaystyle":1656},[2811,101008,101009,101011],{},[1665,101010,1667],{},[1665,101012,1681],{},[1659,101014,101015,101017,101019],{},[898,101016,1663],{},[1665,101018,1667],{},[895,101020,101021,101023,101025],{},[1665,101022,1667],{},[898,101024,1879],{"mathvariant":1878},[1665,101026,1681],{},[1659,101028,101029,101031,101033],{},[898,101030,1663],{},[1665,101032,1681],{},[895,101034,101035,101037,101039,101041],{},[1654,101036,2380],{},[1665,101038,1667],{},[898,101040,1879],{"mathvariant":1878},[1665,101042,1681],{},[1654,101044,1750],{},[2811,101046,101047,101053],{},[1710,101048,101049,101051],{},[898,101050,1663],{},[1665,101052,1681],{},[1710,101054,101055,101057],{},[898,101056,1663],{},[1665,101058,1667],{},[898,101060,2138],{"mathvariant":1878},[902,101062,3987],{"encoding":904},[724,101064,3990,101065,4039,101108,4043,101110,101129],{},[883,101066,101068],{"className":101067},[886],[888,101069,101070],{"xmlns":890},[892,101071,101072,101106],{},[895,101073,101074,101076,101078,101080,101082,101084,101086,101088,101096,101098],{},[1865,101075,1867],{},[1654,101077,1708],{"stretchy":1656},[1665,101079,4006],{},[1654,101081,1674],{"separator":1673},[1665,101083,4011],{},[1654,101085,1726],{"stretchy":1656},[1654,101087,1750],{},[2582,101089,101090],{"scriptlevel":2062,"displaystyle":1656},[2811,101091,101092,101094],{},[1665,101093,4011],{},[1665,101095,4006],{},[1654,101097,1750],{},[2582,101099,101100],{"scriptlevel":2062,"displaystyle":1656},[2811,101101,101102,101104],{},[1665,101103,4032],{},[1665,101105,4035],{},[902,101107,4038],{"encoding":904},[614,101109,4042],{},[883,101111,101113],{"className":101112},[886],[888,101114,101115],{"xmlns":890},[892,101116,101117,101127],{},[895,101118,101119],{},[2582,101120,101121],{"scriptlevel":2062,"displaystyle":1656},[2811,101122,101123,101125],{},[1665,101124,4032],{},[1665,101126,4035],{},[902,101128,4063],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,101131,101132,101133,101137],{},"(Paralelou je ",[207,101134,101136],{"className":101135,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,101139,101141],{"id":101140},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,101143,101144,101145,101148],{},"Rámcově se v kapitole 6 studují ",[38,101146,101147],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,101150,101151,101287],{},[123,101152,101153,101155,101156,18874,101187,2186,101190,101239,101240,2138],{},[38,101154,2150],{}," — maximalizace ",[883,101157,101159],{"className":101158},[886],[888,101160,101161],{"xmlns":890},[892,101162,101163,101185],{},[895,101164,101165,101167,101169,101175,101177,101183],{},[898,101166,900],{},[1654,101168,1708],{"stretchy":1656},[1710,101170,101171,101173],{},[898,101172,1663],{},[1665,101174,1667],{},[1654,101176,1674],{"separator":1673},[1710,101178,101179,101181],{},[898,101180,1663],{},[1665,101182,1681],{},[1654,101184,1726],{"stretchy":1656},[902,101186,1729],{"encoding":904},[38,101188,101189],{},"rozpočtovém omezení",[883,101191,101193],{"className":101192},[886],[888,101194,101195],{"xmlns":890},[892,101196,101197,101237],{},[895,101198,101199,101205,101207,101215,101221,101223,101231],{},[1741,101200,101201,101203],{},[898,101202,1745],{},[1654,101204,1670],{},[1654,101206,1750],{},[1659,101208,101209,101211,101213],{},[898,101210,1755],{},[1665,101212,1667],{},[1654,101214,1670],{},[1710,101216,101217,101219],{},[898,101218,1663],{},[1665,101220,1667],{},[1654,101222,1766],{},[1659,101224,101225,101227,101229],{},[898,101226,1755],{},[1665,101228,1681],{},[1654,101230,1670],{},[1710,101232,101233,101235],{},[898,101234,1663],{},[1665,101236,1681],{},[902,101238,3552],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,101241,101243],{"className":101242},[886],[888,101244,101245],{"xmlns":890},[892,101246,101247,101285],{},[895,101248,101249,101255,101257,101263,101265,101271,101273,101279,101281,101283],{},[1710,101250,101251,101253],{},[898,101252,1663],{},[898,101254,9309],{},[1654,101256,1750],{},[1710,101258,101259,101261],{},[898,101260,4980],{},[898,101262,9309],{},[1654,101264,1708],{"stretchy":1656},[1710,101266,101267,101269],{},[898,101268,1755],{},[1665,101270,1667],{},[1654,101272,1674],{"separator":1673},[1710,101274,101275,101277],{},[898,101276,1755],{},[1665,101278,1681],{},[1654,101280,1674],{"separator":1673},[898,101282,1745],{},[1654,101284,1726],{"stretchy":1656},[902,101286,10421],{"encoding":904},[123,101288,101289,1786,101292,1830,101338,101355,101356,2138],{},[38,101290,101291],{},"Duální úloha",[883,101293,101295],{"className":101294},[886],[888,101296,101297],{"xmlns":890},[892,101298,101299,101335],{},[895,101300,101301,101303,101305,101313,101319,101321,101329],{},[898,101302,1798],{},[1654,101304,1750],{},[1659,101306,101307,101309,101311],{},[898,101308,1755],{},[1665,101310,1667],{},[1654,101312,1670],{},[1710,101314,101315,101317],{},[898,101316,1663],{},[1665,101318,1667],{},[1654,101320,1766],{},[1659,101322,101323,101325,101327],{},[898,101324,1755],{},[1665,101326,1681],{},[1654,101328,1670],{},[1710,101330,101331,101333],{},[898,101332,1663],{},[1665,101334,1681],{},[902,101336,101337],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,101339,101341],{"className":101340},[886],[888,101342,101343],{"xmlns":890},[892,101344,101345,101353],{},[895,101346,101347],{},[1741,101348,101349,101351],{},[898,101350,900],{},[1654,101352,1670],{},[902,101354,1848],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,101357,101359],{"className":101358},[886],[888,101360,101361],{"xmlns":890},[892,101362,101363,101401],{},[895,101364,101365,101371,101373,101379,101381,101387,101389,101395,101397,101399],{},[1710,101366,101367,101369],{},[898,101368,1663],{},[898,101370,9309],{},[1654,101372,1750],{},[1710,101374,101375,101377],{},[898,101376,4980],{},[898,101378,9309],{},[1654,101380,1708],{"stretchy":1656},[1710,101382,101383,101385],{},[898,101384,1755],{},[1665,101386,1667],{},[1654,101388,1674],{"separator":1673},[1710,101390,101391,101393],{},[898,101392,1755],{},[1665,101394,1681],{},[1654,101396,1674],{"separator":1673},[898,101398,900],{},[1654,101400,1726],{"stretchy":1656},[902,101402,10485],{"encoding":904},[724,101404,101405,101406,101409,101410,2186,101413,101452],{},"Obě úlohy se řeší ",[207,101407,1853],{"className":101408,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,101411,101412],{},"tentýž bod dotyku",[883,101414,101416],{"className":101415},[886],[888,101417,101418],{"xmlns":890},[892,101419,101420,101450],{},[895,101421,101422,101428,101430,101438,101440,101448],{},[1741,101423,101424,101426],{},[898,101425,1663],{},[1654,101427,1670],{},[1654,101429,1657],{"stretchy":1656},[1659,101431,101432,101434,101436],{},[898,101433,1663],{},[1665,101435,1667],{},[1654,101437,1670],{},[1654,101439,1674],{"separator":1673},[1659,101441,101442,101444,101446],{},[898,101443,1663],{},[1665,101445,1681],{},[1654,101447,1670],{},[1654,101449,1686],{"stretchy":1656},[902,101451,2226],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,101454,101456],{"className":101455},[886],[888,101457,101458],{"xmlns":890,"display":1956},[892,101459,101460,101506],{},[895,101461,101462,101464,101466,101484,101486,101504],{},[1865,101463,1867],{},[1654,101465,1750],{},[2811,101467,101468,101476],{},[1659,101469,101470,101472,101474],{},[898,101471,900],{},[1665,101473,1667],{},[1654,101475,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1659,101477,101478,101480,101482],{},[898,101479,900],{},[1665,101481,1681],{},[1654,101483,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,101485,1750],{},[2811,101487,101488,101496],{},[1659,101489,101490,101492,101494],{},[898,101491,1755],{},[1665,101493,1667],{},[1654,101495,1670],{},[1659,101497,101498,101500,101502],{},[898,101499,1755],{},[1665,101501,1681],{},[1654,101503,1670],{},[898,101505,2138],{"mathvariant":1878},[902,101507,101508],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,101510,101511],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[2140,101513,101514],{},[724,101515,101516,101518,101519,101522,101523,101526,101527,101554,101555,101589,101590,101624,101625,101668,101669,101672,101673,2138],{},[883,101517,2860],{}," Pro detailní postup viz ",[207,101520,10731],{"className":101521,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,101524,101525],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,101528,101530],{"className":101529},[886],[888,101531,101532],{"xmlns":890},[892,101533,101534,101552],{},[895,101535,101536,101538,101540,101546],{},[898,101537,900],{},[1654,101539,1750],{},[1710,101541,101542,101544],{},[898,101543,1663],{},[1665,101545,1667],{},[1710,101547,101548,101550],{},[898,101549,1663],{},[1665,101551,1681],{},[902,101553,4156],{"encoding":904}," s výsledkem ",[883,101556,101558],{"className":101557},[886],[888,101559,101560],{"xmlns":890},[892,101561,101562,101586],{},[895,101563,101564,101570,101572,101574,101576,101582,101584],{},[1710,101565,101566,101568],{},[898,101567,1663],{},[1665,101569,1667],{},[1654,101571,1750],{},[1665,101573,4622],{},[1654,101575,1674],{"separator":1673},[1710,101577,101578,101580],{},[898,101579,1663],{},[1665,101581,1681],{},[1654,101583,1750],{},[1665,101585,4647],{},[902,101587,101588],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,101591,101593],{"className":101592},[886],[888,101594,101595],{"xmlns":890},[892,101596,101597,101621],{},[895,101598,101599,101605,101607,101609,101611,101617,101619],{},[1710,101600,101601,101603],{},[898,101602,1663],{},[1665,101604,1667],{},[1654,101606,1750],{},[1665,101608,7631],{},[1654,101610,1674],{"separator":1673},[1710,101612,101613,101615],{},[898,101614,1663],{},[1665,101616,1681],{},[1654,101618,1750],{},[1665,101620,1667],{},[902,101622,101623],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,101626,101628],{"className":101627},[886],[888,101629,101630],{"xmlns":890},[892,101631,101632,101666],{},[895,101633,101634,101636,101638,101652],{},[898,101635,900],{},[1654,101637,1750],{},[1659,101639,101640,101642,101644],{},[898,101641,1663],{},[1665,101643,1667],{},[895,101645,101646,101648,101650],{},[1665,101647,1667],{},[898,101649,1879],{"mathvariant":1878},[1665,101651,1681],{},[1659,101653,101654,101656,101658],{},[898,101655,1663],{},[1665,101657,1681],{},[895,101659,101660,101662,101664],{},[1665,101661,1667],{},[898,101663,1879],{"mathvariant":1878},[1665,101665,1681],{},[902,101667,7107],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,101670,101671],{},"6.8–6.13"," jsou na stránce ",[207,101674,1629],{"className":101675,"dataFsResolvedFilePath":911,"href":912},[210],[115,101677,101679],{"id":101678},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,101681,101682,101683,101696,101697,101699,101700,101702,101703,101705,101706,101708,101709,101711,101712,101714,101715,2186,101717,101752,101753,101766,101767,101770,101771,101774,101775,2138],{},"Každá ",[883,101684,101686],{"className":101685},[886],[888,101687,101688],{"xmlns":890},[892,101689,101690,101694],{},[895,101691,101692],{},[898,101693,45080],{},[902,101695,45080],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,101698,95030],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,101701,95514],{}," a současně ",[38,101704,95033],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,101707,95038],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,101710,60897],{}," (6.4) a druhé parciální derivace ",[38,101713,97397],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,101716,18450],{},[883,101718,101720],{"className":101719},[886],[888,101721,101722],{"xmlns":890},[892,101723,101724,101750],{},[895,101725,101726,101728,101730,101736,101738,101744,101746,101748],{},[898,101727,900],{},[1654,101729,1708],{"stretchy":1656},[1710,101731,101732,101734],{},[898,101733,1663],{},[1665,101735,1667],{},[1654,101737,1674],{"separator":1673},[1710,101739,101740,101742],{},[898,101741,1663],{},[1665,101743,1681],{},[1654,101745,1726],{"stretchy":1656},[1654,101747,1750],{},[898,101749,3624],{},[902,101751,18487],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,101754,101756],{"className":101755},[886],[888,101757,101758],{"xmlns":890},[892,101759,101760,101764],{},[895,101761,101762],{},[1865,101763,1867],{},[902,101765,2133],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,101768,101769],{},"maximalizace užitečnosti"," a duální ",[38,101772,101773],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,101776,10731],{"className":101777,"dataFsResolvedFilePath":911,"href":912},[210],[115,101779,58102],{"id":58101},[152,101781,101782,101785,101788,101791,101794,101797,101800,101803,101806,101809],{},[123,101783,101784],{},"Co se zahrnuje pod termín užitečnost?",[123,101786,101787],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,101789,101790],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,101792,101793],{},"Jak se vypočítá mezní užitečnost?",[123,101795,101796],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,101798,101799],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,101801,101802],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,101804,101805],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,101807,101808],{},"Proč mají křivky užitečnosti záporný sklon?",[123,101810,101811],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,101813,101815],{"id":101814},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,101817,101818,101821,101822,91703,101864,1343,101892,1343,101920,101948],{},[38,101819,101820],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,101823,101825],{"className":101824},[886],[888,101826,101827],{"xmlns":890},[892,101828,101829,101861],{},[895,101830,101831,101833,101835,101841,101843,101845,101851,101853,101855],{},[898,101832,900],{},[1654,101834,1750],{},[1710,101836,101837,101839],{},[898,101838,1663],{},[1665,101840,1667],{},[1654,101842,1766],{},[1665,101844,72779],{},[1710,101846,101847,101849],{},[898,101848,1663],{},[1665,101850,1681],{},[1654,101852,1766],{},[1665,101854,1681],{},[1710,101856,101857,101859],{},[898,101858,1663],{},[1665,101860,4035],{},[902,101862,101863],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,101865,101867],{"className":101866},[886],[888,101868,101869],{"xmlns":890},[892,101870,101871,101889],{},[895,101872,101873,101875,101877,101879,101881,101883,101885,101887],{},[898,101874,900],{},[1654,101876,1708],{"stretchy":1656},[1665,101878,7631],{},[1654,101880,1674],{"separator":1673},[1665,101882,1681],{},[1654,101884,1674],{"separator":1673},[1665,101886,1681],{},[1654,101888,1726],{"stretchy":1656},[902,101890,101891],{"encoding":904},"U(4, 2, 2)",[883,101893,101895],{"className":101894},[886],[888,101896,101897],{"xmlns":890},[892,101898,101899,101917],{},[895,101900,101901,101903,101905,101907,101909,101911,101913,101915],{},[898,101902,900],{},[1654,101904,1708],{"stretchy":1656},[1665,101906,1667],{},[1654,101908,1674],{"separator":1673},[1665,101910,7631],{},[1654,101912,1674],{"separator":1673},[1665,101914,1681],{},[1654,101916,1726],{"stretchy":1656},[902,101918,101919],{"encoding":904},"U(1, 4, 2)",[883,101921,101923],{"className":101922},[886],[888,101924,101925],{"xmlns":890},[892,101926,101927,101945],{},[895,101928,101929,101931,101933,101935,101937,101939,101941,101943],{},[898,101930,900],{},[1654,101932,1708],{"stretchy":1656},[1665,101934,1681],{},[1654,101936,1674],{"separator":1673},[1665,101938,4035],{},[1654,101940,1674],{"separator":1673},[1665,101942,1667],{},[1654,101944,1726],{"stretchy":1656},[902,101946,101947],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,101950,101951,101954,101955,102007,102008,1343,102034,1343,102060,1343,102086,1343,102112,1343,102138,1343,102164,102190],{},[38,101952,101953],{},"6.2"," Je dána užitečnost ",[883,101956,101958],{"className":101957},[886],[888,101959,101960],{"xmlns":890},[892,101961,101962,102004],{},[895,101963,101964,101966,101968,101970,101984,101998],{},[898,101965,900],{},[1654,101967,1750],{},[1665,101969,1681],{},[1659,101971,101972,101974,101976],{},[898,101973,1663],{},[1665,101975,1667],{},[895,101977,101978,101980,101982],{},[1665,101979,1667],{},[898,101981,1879],{"mathvariant":1878},[1665,101983,4035],{},[1659,101985,101986,101988,101990],{},[898,101987,1663],{},[1665,101989,1681],{},[895,101991,101992,101994,101996],{},[1665,101993,1667],{},[898,101995,1879],{"mathvariant":1878},[1665,101997,1681],{},[1710,101999,102000,102002],{},[898,102001,1663],{},[1665,102003,4035],{},[902,102005,102006],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,102009,102011],{"className":102010},[886],[888,102012,102013],{"xmlns":890},[892,102014,102015,102031],{},[895,102016,102017,102019,102021,102023,102025,102027,102029],{},[1654,102018,1708],{"stretchy":1656},[1665,102020,14295],{},[1654,102022,1674],{"separator":1673},[1665,102024,74817],{},[1654,102026,1674],{"separator":1673},[1665,102028,4647],{},[1654,102030,1726],{"stretchy":1656},[902,102032,102033],{"encoding":904},"(36, 27, 10)",[883,102035,102037],{"className":102036},[886],[888,102038,102039],{"xmlns":890},[892,102040,102041,102057],{},[895,102042,102043,102045,102047,102049,102051,102053,102055],{},[1654,102044,1708],{"stretchy":1656},[1665,102046,50060],{},[1654,102048,1674],{"separator":1673},[1665,102050,14315],{},[1654,102052,1674],{"separator":1673},[1665,102054,4573],{},[1654,102056,1726],{"stretchy":1656},[902,102058,102059],{"encoding":904},"(64, 8, 20)",[883,102061,102063],{"className":102062},[886],[888,102064,102065],{"xmlns":890},[892,102066,102067,102083],{},[895,102068,102069,102071,102073,102075,102077,102079,102081],{},[1654,102070,1708],{"stretchy":1656},[1665,102072,4622],{},[1654,102074,1674],{"separator":1673},[1665,102076,50060],{},[1654,102078,1674],{"separator":1673},[1665,102080,14315],{},[1654,102082,1726],{"stretchy":1656},[902,102084,102085],{"encoding":904},"(25, 64, 8)",[883,102087,102089],{"className":102088},[886],[888,102090,102091],{"xmlns":890},[892,102092,102093,102109],{},[895,102094,102095,102097,102099,102101,102103,102105,102107],{},[1654,102096,1708],{"stretchy":1656},[1665,102098,7631],{},[1654,102100,1674],{"separator":1673},[1665,102102,80749],{},[1654,102104,1674],{"separator":1673},[1665,102106,11015],{},[1654,102108,1726],{"stretchy":1656},[902,102110,102111],{"encoding":904},"(4, 125, 6)",[883,102113,102115],{"className":102114},[886],[888,102116,102117],{"xmlns":890},[892,102118,102119,102135],{},[895,102120,102121,102123,102125,102127,102129,102131,102133],{},[1654,102122,1708],{"stretchy":1656},[1665,102124,12742],{},[1654,102126,1674],{"separator":1673},[1665,102128,5844],{},[1654,102130,1674],{"separator":1673},[1665,102132,6509],{},[1654,102134,1726],{"stretchy":1656},[902,102136,102137],{"encoding":904},"(9, 40, 12)",[883,102139,102141],{"className":102140},[886],[888,102142,102143],{"xmlns":890},[892,102144,102145,102161],{},[895,102146,102147,102149,102151,102153,102155,102157,102159],{},[1654,102148,1708],{"stretchy":1656},[1665,102150,12742],{},[1654,102152,1674],{"separator":1673},[1665,102154,50060],{},[1654,102156,1674],{"separator":1673},[1665,102158,4032],{},[1654,102160,1726],{"stretchy":1656},[902,102162,102163],{"encoding":904},"(9, 64, 5)",[883,102165,102167],{"className":102166},[886],[888,102168,102169],{"xmlns":890},[892,102170,102171,102187],{},[895,102172,102173,102175,102177,102179,102181,102183,102185],{},[1654,102174,1708],{"stretchy":1656},[1665,102176,50060],{},[1654,102178,1674],{"separator":1673},[1665,102180,14315],{},[1654,102182,1674],{"separator":1673},[1665,102184,4647],{},[1654,102186,1726],{"stretchy":1656},[902,102188,102189],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,102192,102193,101954,102196,102239,102240,102274,102275,15201,102305,102338,102339,102356,102357,102374],{},[38,102194,102195],{},"6.3",[883,102197,102199],{"className":102198},[886],[888,102200,102201],{"xmlns":890},[892,102202,102203,102237],{},[895,102204,102205,102207,102209,102223],{},[898,102206,900],{},[1654,102208,1750],{},[1659,102210,102211,102213,102215],{},[898,102212,1663],{},[1665,102214,1667],{},[895,102216,102217,102219,102221],{},[1665,102218,1667],{},[898,102220,1879],{"mathvariant":1878},[1665,102222,1681],{},[1659,102224,102225,102227,102229],{},[898,102226,1663],{},[1665,102228,1681],{},[895,102230,102231,102233,102235],{},[1665,102232,1667],{},[898,102234,1879],{"mathvariant":1878},[1665,102236,1681],{},[902,102238,7107],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,102241,102243],{"className":102242},[886],[888,102244,102245],{"xmlns":890},[892,102246,102247,102271],{},[895,102248,102249,102255,102257,102259,102261,102267,102269],{},[1710,102250,102251,102253],{},[898,102252,1663],{},[1665,102254,1667],{},[1654,102256,1750],{},[1665,102258,4767],{},[1654,102260,1674],{"separator":1673},[1710,102262,102263,102265],{},[898,102264,1663],{},[1665,102266,1681],{},[1654,102268,1750],{},[1665,102270,54923],{},[902,102272,102273],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,102276,102278],{"className":102277},[886],[888,102279,102280],{"xmlns":890},[892,102281,102282,102302],{},[895,102283,102284,102286,102292,102294,102296],{},[898,102285,9320],{},[1710,102287,102288,102290],{},[898,102289,900],{},[1665,102291,1667],{},[1654,102293,1674],{"separator":1673},[898,102295,9320],{},[1710,102297,102298,102300],{},[898,102299,900],{},[1665,102301,1681],{},[902,102303,102304],{"encoding":904},"MU_1, MU_2",[883,102306,102308],{"className":102307},[886],[888,102309,102310],{"xmlns":890},[892,102311,102312,102336],{},[895,102313,102314,102320,102322,102324,102326,102332,102334],{},[1710,102315,102316,102318],{},[898,102317,1663],{},[1665,102319,1667],{},[1654,102321,1750],{},[1665,102323,4767],{},[1654,102325,1674],{"separator":1673},[1710,102327,102328,102330],{},[898,102329,1663],{},[1665,102331,1681],{},[1654,102333,1750],{},[1665,102335,54923],{},[902,102337,102273],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,102340,102342],{"className":102341},[886],[888,102343,102344],{"xmlns":890},[892,102345,102346,102354],{},[895,102347,102348],{},[1710,102349,102350,102352],{},[898,102351,1663],{},[1665,102353,1667],{},[902,102355,2918],{"encoding":904}," na 60 a poklesu ",[883,102358,102360],{"className":102359},[886],[888,102361,102362],{"xmlns":890},[892,102363,102364,102372],{},[895,102365,102366],{},[1710,102367,102368,102370],{},[898,102369,1663],{},[1665,102371,1681],{},[902,102373,2937],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,102376,102377,102380,102381,102442,102443,2138],{},[38,102378,102379],{},"6.4"," Je dána funkce ",[883,102382,102384],{"className":102383},[886],[888,102385,102386],{"xmlns":890},[892,102387,102388,102440],{},[895,102389,102390,102392,102394,102400,102402,102408,102410,102412,102426],{},[898,102391,900],{},[1654,102393,1708],{"stretchy":1656},[1710,102395,102396,102398],{},[898,102397,1663],{},[1665,102399,1667],{},[1654,102401,1674],{"separator":1673},[1710,102403,102404,102406],{},[898,102405,1663],{},[1665,102407,1681],{},[1654,102409,1726],{"stretchy":1656},[1654,102411,1750],{},[1659,102413,102414,102416,102418],{},[898,102415,1663],{},[1665,102417,1667],{},[895,102419,102420,102422,102424],{},[1665,102421,1667],{},[898,102423,1879],{"mathvariant":1878},[1665,102425,1681],{},[1659,102427,102428,102430,102432],{},[898,102429,1663],{},[1665,102431,1681],{},[895,102433,102434,102436,102438],{},[1665,102435,1667],{},[898,102437,1879],{"mathvariant":1878},[1665,102439,1681],{},[902,102441,3868],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,102444,102446],{"className":102445},[886],[888,102447,102448],{"xmlns":890},[892,102449,102450,102540],{},[895,102451,102452,102454,102456,102462,102464,102466,102468,102470,102472,102474,102480,102482,102484,102486,102488,102490,102492,102494,102496,102502,102504,102506,102508,102510,102512,102514,102520,102522,102524,102526,102528,102530,102532,102538],{},[898,102453,900],{},[1654,102455,1708],{"stretchy":1656},[1710,102457,102458,102460],{},[898,102459,1663],{},[1665,102461,1667],{},[1654,102463,1674],{"separator":1673},[1665,102465,1667],{},[1654,102467,1726],{"stretchy":1656},[1654,102469,1674],{"separator":1673},[898,102471,900],{},[1654,102473,1708],{"stretchy":1656},[1710,102475,102476,102478],{},[898,102477,1663],{},[1665,102479,1667],{},[1654,102481,1674],{"separator":1673},[1665,102483,1681],{},[1654,102485,1726],{"stretchy":1656},[1654,102487,1674],{"separator":1673},[898,102489,900],{},[1654,102491,1708],{"stretchy":1656},[1665,102493,1667],{},[1654,102495,1674],{"separator":1673},[1710,102497,102498,102500],{},[898,102499,1663],{},[1665,102501,1681],{},[1654,102503,1726],{"stretchy":1656},[1654,102505,1674],{"separator":1673},[898,102507,900],{},[1654,102509,1708],{"stretchy":1656},[1665,102511,1681],{},[1654,102513,1674],{"separator":1673},[1710,102515,102516,102518],{},[898,102517,1663],{},[1665,102519,1681],{},[1654,102521,1726],{"stretchy":1656},[1654,102523,1674],{"separator":1673},[898,102525,900],{},[1654,102527,1708],{"stretchy":1656},[1665,102529,4035],{},[1654,102531,1674],{"separator":1673},[1710,102533,102534,102536],{},[898,102535,1663],{},[1665,102537,1681],{},[1654,102539,1726],{"stretchy":1656},[902,102541,102542],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,102544,102545,101954,102548,102592,102593,102701,102702,1343,102727,1343,102752,102794,102795,1343,102824,102849],{},[38,102546,102547],{},"6.5",[883,102549,102551],{"className":102550},[886],[888,102552,102553],{"xmlns":890},[892,102554,102555,102589],{},[895,102556,102557,102559,102561,102575],{},[898,102558,900],{},[1654,102560,1750],{},[1659,102562,102563,102565,102567],{},[898,102564,1663],{},[1665,102566,1667],{},[895,102568,102569,102571,102573],{},[1665,102570,1681],{},[898,102572,1879],{"mathvariant":1878},[1665,102574,4035],{},[1659,102576,102577,102579,102581],{},[898,102578,1663],{},[1665,102580,1681],{},[895,102582,102583,102585,102587],{},[1665,102584,1667],{},[898,102586,1879],{"mathvariant":1878},[1665,102588,4035],{},[902,102590,102591],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,102594,102596],{"className":102595},[886],[888,102597,102598],{"xmlns":890},[892,102599,102600,102698],{},[895,102601,102602,102604,102606,102612,102614,102620,102622,102624,102626,102628,102630,102632,102638,102640,102642,102644,102646,102648,102650,102656,102658,102660,102662,102664,102666,102668,102670,102672,102678,102680,102682,102684,102686,102688,102690,102696],{},[898,102603,900],{},[1654,102605,1708],{"stretchy":1656},[1710,102607,102608,102610],{},[898,102609,1663],{},[1665,102611,1667],{},[1654,102613,1674],{"separator":1673},[1710,102615,102616,102618],{},[898,102617,1663],{},[1665,102619,1681],{},[1654,102621,1726],{"stretchy":1656},[1654,102623,1750],{},[1665,102625,1681],{},[1654,102627,1674],{"separator":1673},[898,102629,900],{},[1654,102631,1708],{"stretchy":1656},[1710,102633,102634,102636],{},[898,102635,1663],{},[1665,102637,1667],{},[1654,102639,1674],{"separator":1673},[1665,102641,4035],{},[1654,102643,1726],{"stretchy":1656},[1654,102645,1674],{"separator":1673},[898,102647,900],{},[1654,102649,1708],{"stretchy":1656},[1710,102651,102652,102654],{},[898,102653,1663],{},[1665,102655,1667],{},[1654,102657,1674],{"separator":1673},[1665,102659,1681],{},[1654,102661,1726],{"stretchy":1656},[1654,102663,1674],{"separator":1673},[898,102665,900],{},[1654,102667,1708],{"stretchy":1656},[1665,102669,1681],{},[1654,102671,1674],{"separator":1673},[1710,102673,102674,102676],{},[898,102675,1663],{},[1665,102677,1681],{},[1654,102679,1726],{"stretchy":1656},[1654,102681,1674],{"separator":1673},[898,102683,900],{},[1654,102685,1708],{"stretchy":1656},[1665,102687,4035],{},[1654,102689,1674],{"separator":1673},[1710,102691,102692,102694],{},[898,102693,1663],{},[1665,102695,1681],{},[1654,102697,1726],{"stretchy":1656},[902,102699,102700],{"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 ",[883,102703,102705],{"className":102704},[886],[888,102706,102707],{"xmlns":890},[892,102708,102709,102724],{},[895,102710,102711,102713,102715,102717,102719,102722],{},[898,102712,4737],{},[1654,102714,1657],{"stretchy":1656},[1665,102716,72779],{},[1654,102718,17150],{"separator":1673},[1665,102720,102721],{},"3,555",[1654,102723,1686],{"stretchy":1656},[902,102725,102726],{"encoding":904},"A[1{,}5; 3{,}555]",[883,102728,102730],{"className":102729},[886],[888,102731,102732],{"xmlns":890},[892,102733,102734,102749],{},[895,102735,102736,102738,102740,102742,102744,102747],{},[898,102737,4762],{},[1654,102739,1657],{"stretchy":1656},[1665,102741,61419],{},[1654,102743,17150],{"separator":1673},[1665,102745,102746],{},"1,28",[1654,102748,1686],{"stretchy":1656},[902,102750,102751],{"encoding":904},"B[2{,}5; 1{,}28]",[883,102753,102755],{"className":102754},[886],[888,102756,102757],{"xmlns":890},[892,102758,102759,102791],{},[895,102760,102761,102763,102765,102767,102769,102771,102773,102779,102781,102783,102785,102787,102789],{},[898,102762,11539],{},[1654,102764,1657],{"stretchy":1656},[1665,102766,1681],{},[1654,102768,17150],{"separator":1673},[898,102770,900],{},[1654,102772,1708],{"stretchy":1656},[1710,102774,102775,102777],{},[898,102776,1663],{},[1665,102778,1667],{},[1654,102780,1674],{"separator":1673},[1665,102782,4035],{},[1654,102784,1726],{"stretchy":1656},[1654,102786,1750],{},[1665,102788,4035],{},[1654,102790,1686],{"stretchy":1656},[902,102792,102793],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,102796,102798],{"className":102797},[886],[888,102799,102800],{"xmlns":890},[892,102801,102802,102821],{},[895,102803,102804,102806,102808,102810,102812,102814,102816,102819],{},[898,102805,4980],{},[1654,102807,1657],{"stretchy":1656},[1665,102809,4035],{},[1654,102811,17150],{"separator":1673},[1665,102813,1667],{},[1654,102815,17150],{"separator":1673},[1665,102817,102818],{},"0,832",[1654,102820,1686],{"stretchy":1656},[902,102822,102823],{"encoding":904},"D[3; 1; 0{,}832]",[883,102825,102827],{"className":102826},[886],[888,102828,102829],{"xmlns":890},[892,102830,102831,102846],{},[895,102832,102833,102835,102837,102839,102841,102844],{},[898,102834,1798],{},[1654,102836,1657],{"stretchy":1656},[1665,102838,61419],{},[1654,102840,17150],{"separator":1673},[1665,102842,102843],{},"4,32",[1654,102845,1686],{"stretchy":1656},[902,102847,102848],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,102851,102852,101954,102855,102898,102899,15201,102912,102946,102947,102964,102965,102982],{},[38,102853,102854],{},"6.6",[883,102856,102858],{"className":102857},[886],[888,102859,102860],{"xmlns":890},[892,102861,102862,102896],{},[895,102863,102864,102866,102868,102882],{},[898,102865,900],{},[1654,102867,1750],{},[1659,102869,102870,102872,102874],{},[898,102871,1663],{},[1665,102873,1667],{},[895,102875,102876,102878,102880],{},[1665,102877,1681],{},[898,102879,1879],{"mathvariant":1878},[1665,102881,4035],{},[1659,102883,102884,102886,102888],{},[898,102885,1663],{},[1665,102887,1681],{},[895,102889,102890,102892,102894],{},[1665,102891,1667],{},[898,102893,1879],{"mathvariant":1878},[1665,102895,4035],{},[902,102897,102591],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,102900,102902],{"className":102901},[886],[888,102903,102904],{"xmlns":890},[892,102905,102906,102910],{},[895,102907,102908],{},[1865,102909,1867],{},[902,102911,2133],{"encoding":904},[883,102913,102915],{"className":102914},[886],[888,102916,102917],{"xmlns":890},[892,102918,102919,102943],{},[895,102920,102921,102927,102929,102931,102933,102939,102941],{},[1710,102922,102923,102925],{},[898,102924,1663],{},[1665,102926,1667],{},[1654,102928,1750],{},[1665,102930,4273],{},[1654,102932,1674],{"separator":1673},[1710,102934,102935,102937],{},[898,102936,1663],{},[1665,102938,1681],{},[1654,102940,1750],{},[1665,102942,17102],{},[902,102944,102945],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,102948,102950],{"className":102949},[886],[888,102951,102952],{"xmlns":890},[892,102953,102954,102962],{},[895,102955,102956],{},[1710,102957,102958,102960],{},[898,102959,1663],{},[1665,102961,1667],{},[902,102963,2918],{"encoding":904},", poklesne-li ",[883,102966,102968],{"className":102967},[886],[888,102969,102970],{"xmlns":890},[892,102971,102972,102980],{},[895,102973,102974],{},[1710,102975,102976,102978],{},[898,102977,1663],{},[1665,102979,1681],{},[902,102981,2937],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,102984,102985,102988,102989,103006,103007,103024,103025,103057,103058,103083,103084,103097,103098,1343,103122,1343,103146,2138],{},[38,102986,102987],{},"6.7"," Míra uspokojení z nákupu množství ",[883,102990,102992],{"className":102991},[886],[888,102993,102994],{"xmlns":890},[892,102995,102996,103004],{},[895,102997,102998],{},[1710,102999,103000,103002],{},[898,103001,1663],{},[1665,103003,1667],{},[902,103005,2918],{"encoding":904}," nealko nápojů a množství ",[883,103008,103010],{"className":103009},[886],[888,103011,103012],{"xmlns":890},[892,103013,103014,103022],{},[895,103015,103016],{},[1710,103017,103018,103020],{},[898,103019,1663],{},[1665,103021,1681],{},[902,103023,2937],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,103026,103028],{"className":103027},[886],[888,103029,103030],{"xmlns":890},[892,103031,103032,103054],{},[895,103033,103034,103036,103038],{},[898,103035,900],{},[1654,103037,1750],{},[8818,103039,103040],{},[895,103041,103042,103048],{},[1710,103043,103044,103046],{},[898,103045,1663],{},[1665,103047,1667],{},[1710,103049,103050,103052],{},[898,103051,1663],{},[1665,103053,1681],{},[902,103055,103056],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,103059,103061],{"className":103060},[886],[888,103062,103063],{"xmlns":890},[892,103064,103065,103081],{},[895,103066,103067,103073,103075],{},[1710,103068,103069,103071],{},[898,103070,1663],{},[1665,103072,1667],{},[1654,103074,1674],{"separator":1673},[1710,103076,103077,103079],{},[898,103078,1663],{},[1665,103080,1681],{},[902,103082,9579],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,103085,103087],{"className":103086},[886],[888,103088,103089],{"xmlns":890},[892,103090,103091,103095],{},[895,103092,103093],{},[1865,103094,1867],{},[902,103096,2133],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,103099,103101],{"className":103100},[886],[888,103102,103103],{"xmlns":890},[892,103104,103105,103119],{},[895,103106,103107,103109,103111,103113,103115,103117],{},[1865,103108,1867],{},[1654,103110,1708],{"stretchy":1656},[1665,103112,4032],{},[1654,103114,1674],{"separator":1673},[1665,103116,4573],{},[1654,103118,1726],{"stretchy":1656},[902,103120,103121],{"encoding":904},"\\text{MRCS}(5, 20)",[883,103123,103125],{"className":103124},[886],[888,103126,103127],{"xmlns":890},[892,103128,103129,103143],{},[895,103130,103131,103133,103135,103137,103139,103141],{},[1865,103132,1867],{},[1654,103134,1708],{"stretchy":1656},[1665,103136,4573],{},[1654,103138,1674],{"separator":1673},[1665,103140,4032],{},[1654,103142,1726],{"stretchy":1656},[902,103144,103145],{"encoding":904},"\\text{MRCS}(20, 5)",[883,103147,103149],{"className":103148},[886],[888,103150,103151],{"xmlns":890},[892,103152,103153,103167],{},[895,103154,103155,103157,103159,103161,103163,103165],{},[1865,103156,1867],{},[1654,103158,1708],{"stretchy":1656},[1665,103160,1681],{},[1654,103162,1674],{"separator":1673},[1665,103164,4767],{},[1654,103166,1726],{"stretchy":1656},[902,103168,103169],{"encoding":904},"\\text{MRCS}(2, 50)",[2140,103171,103172],{},[724,103173,103174,103176,103177,2138],{},[883,103175,3111],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,103178,103181],{"className":103179,"dataFsResolvedFilePath":911,"href":103180},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,103183,10214],{"id":10213},[120,103185,103186,103192,103197,103203,103256,103266,103312,103367,103430,103487,103542,103581],{},[123,103187,103188,103191],{},[38,103189,103190],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,103193,103194,103196],{},[38,103195,95089],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,103198,103199,103202],{},[38,103200,103201],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,103204,103205,103207,103208,103221,103222,2138],{},[38,103206,95416],{}," — uspořádaná ",[883,103209,103211],{"className":103210},[886],[888,103212,103213],{"xmlns":890},[892,103214,103215,103219],{},[895,103216,103217],{},[898,103218,45080],{},[902,103220,45080],{"encoding":904},"-tice ",[883,103223,103225],{"className":103224},[886],[888,103226,103227],{"xmlns":890},[892,103228,103229,103253],{},[895,103230,103231,103233,103239,103241,103243,103245,103251],{},[1654,103232,1708],{"stretchy":1656},[1710,103234,103235,103237],{},[898,103236,1663],{},[1665,103238,1667],{},[1654,103240,1674],{"separator":1673},[1654,103242,18366],{},[1654,103244,1674],{"separator":1673},[1710,103246,103247,103249],{},[898,103248,1663],{},[898,103250,45080],{},[1654,103252,1726],{"stretchy":1656},[902,103254,103255],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,103257,103258,103261,103262,103265],{},[38,103259,103260],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,103263,103264],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,103267,103268,2186,103271,103311],{},[38,103269,103270],{},"Funkce užitečnosti",[883,103272,103274],{"className":103273},[886],[888,103275,103276],{"xmlns":890},[892,103277,103278,103308],{},[895,103279,103280,103282,103284,103286,103288,103294,103296,103298,103300,103306],{},[898,103281,900],{},[1654,103283,1750],{},[898,103285,900],{},[1654,103287,1708],{"stretchy":1656},[1710,103289,103290,103292],{},[898,103291,1663],{},[1665,103293,1667],{},[1654,103295,1674],{"separator":1673},[1654,103297,18366],{},[1654,103299,1674],{"separator":1673},[1710,103301,103302,103304],{},[898,103303,1663],{},[898,103305,45080],{},[1654,103307,1726],{"stretchy":1656},[902,103309,103310],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,103313,103314,2186,103317,103346,103347,2186,103350,103366],{},[38,103315,103316],{},"Mezní užitečnost",[883,103318,103320],{"className":103319},[886],[888,103321,103322],{"xmlns":890},[892,103323,103324,103344],{},[895,103325,103326,103328,103334,103336],{},[898,103327,9320],{},[1710,103329,103330,103332],{},[898,103331,900],{},[898,103333,9309],{},[1654,103335,1750],{},[1659,103337,103338,103340,103342],{},[898,103339,900],{},[898,103341,9309],{},[1654,103343,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[902,103345,94873],{"encoding":904}," — vzorec (6.2); ",[38,103348,103349],{},"totální diferenciál",[883,103351,103353],{"className":103352},[886],[888,103354,103355],{"xmlns":890},[892,103356,103357,103363],{},[895,103358,103359,103361],{},[898,103360,10977],{"mathvariant":1878},[898,103362,900],{},[902,103364,103365],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,103368,103369,103371,103372,103396,103397,103429],{},[38,103370,97052],{}," — (6.4) ",[883,103373,103375],{"className":103374},[886],[888,103376,103377],{"xmlns":890},[892,103378,103379,103393],{},[895,103380,103381,103389,103391],{},[1659,103382,103383,103385,103387],{},[898,103384,900],{},[898,103386,9309],{},[1654,103388,2592],{"mathvariant":1878,"lspace":2576,"rspace":2576},[1654,103390,2952],{},[1665,103392,2062],{},[902,103394,103395],{"encoding":904},"U'_i > 0",", (6.5) ",[883,103398,103400],{"className":103399},[886],[888,103401,103402],{"xmlns":890},[892,103403,103404,103426],{},[895,103405,103406,103422,103424],{},[1659,103407,103408,103410,103416],{},[898,103409,900],{},[895,103411,103412,103414],{},[898,103413,9309],{},[898,103415,9309],{},[895,103417,103418,103420],{},[1654,103419,2592],{"mathvariant":1878},[1654,103421,2592],{"mathvariant":1878},[1654,103423,3002],{},[1665,103425,2062],{},[902,103427,103428],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,103431,103432,2186,103434,103465,103466,2138],{},[38,103433,98840],{},[883,103435,103437],{"className":103436},[886],[888,103438,103439],{"xmlns":890},[892,103440,103441,103463],{},[895,103442,103443,103445,103447,103455],{},[898,103444,900],{},[1654,103446,1750],{},[1659,103448,103449,103451,103453],{},[898,103450,1663],{},[1665,103452,1667],{},[898,103454,207],{},[1659,103456,103457,103459,103461],{},[898,103458,1663],{},[1665,103460,1681],{},[898,103462,9758],{},[902,103464,9761],{"encoding":904}," — (6.6), speciálně ",[883,103467,103469],{"className":103468},[886],[888,103470,103471],{"xmlns":890},[892,103472,103473,103485],{},[895,103474,103475,103477,103479,103481,103483],{},[898,103476,9758],{},[1654,103478,1750],{},[1665,103480,1667],{},[1654,103482,2380],{},[898,103484,207],{},[902,103486,98994],{"encoding":904},[123,103488,103489,2186,103492,103527,103528,103541],{},[38,103490,103491],{},"Křivky užitečnosti (indiferenční)",[883,103493,103495],{"className":103494},[886],[888,103496,103497],{"xmlns":890},[892,103498,103499,103525],{},[895,103500,103501,103503,103505,103511,103513,103519,103521,103523],{},[898,103502,900],{},[1654,103504,1708],{"stretchy":1656},[1710,103506,103507,103509],{},[898,103508,1663],{},[1665,103510,1667],{},[1654,103512,1674],{"separator":1673},[1710,103514,103515,103517],{},[898,103516,1663],{},[1665,103518,1681],{},[1654,103520,1726],{"stretchy":1656},[1654,103522,1750],{},[898,103524,3624],{},[902,103526,18487],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,103529,103531],{"className":103530},[886],[888,103532,103533],{"xmlns":890},[892,103534,103535,103539],{},[895,103536,103537],{},[898,103538,900],{},[902,103540,900],{"encoding":904},", konvexní.",[123,103543,103544,2186,103546,103580],{},[38,103545,100385],{},[883,103547,103549],{"className":103548},[886],[888,103550,103551],{"xmlns":890},[892,103552,103553,103577],{},[895,103554,103555,103557,103559,103561,103567,103569,103571],{},[1865,103556,1867],{},[1654,103558,1750],{},[898,103560,9320],{},[1710,103562,103563,103565],{},[898,103564,900],{},[1665,103566,1667],{},[898,103568,1879],{"mathvariant":1878},[898,103570,9320],{},[1710,103572,103573,103575],{},[898,103574,900],{},[1665,103576,1681],{},[902,103578,103579],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,103582,103583,2186,103586,18488,103615,103618],{},[38,103584,103585],{},"Podmínka optimality",[883,103587,103589],{"className":103588},[886],[888,103590,103591],{"xmlns":890},[892,103592,103593,103613],{},[895,103594,103595,103597,103599,103605,103607],{},[1865,103596,1867],{},[1654,103598,1750],{},[1710,103600,103601,103603],{},[898,103602,1755],{},[1665,103604,1667],{},[898,103606,1879],{"mathvariant":1878},[1710,103608,103609,103611],{},[898,103610,1755],{},[1665,103612,1681],{},[902,103614,1888],{"encoding":904},[207,103616,10731],{"className":103617,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,103620,10613],{"id":10612},[120,103622,103623,103660,103701,103711],{},[123,103624,103625,2186,103628,103631,103632,103645,103646,103659],{},[38,103626,103627],{},"Navazující téma:",[207,103629,913],{"className":103630,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,103633,103635],{"className":103634},[886],[888,103636,103637],{"xmlns":890},[892,103638,103639,103643],{},[895,103640,103641],{},[898,103642,900],{},[902,103644,900],{"encoding":904},", min ",[883,103647,103649],{"className":103648},[886],[888,103650,103651],{"xmlns":890},[892,103652,103653,103657],{},[895,103654,103655],{},[898,103656,1798],{},[902,103658,1798],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,103661,103662,2186,103665,19806,103668,94628,103671,103674,103675,103678,103679,27344,103697,103700],{},[38,103663,103664],{},"Související pojmy:",[207,103666,784],{"className":103667,"dataFsResolvedFilePath":782,"href":783},[210],[207,103669,10655],{"className":103670,"dataFsResolvedFilePath":764,"href":765},[210],[207,103672,10664],{"className":103673,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,103676,10669],{"className":103677,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,103680,103682],{"className":103681},[886],[888,103683,103684],{"xmlns":890},[892,103685,103686,103694],{},[895,103687,103688],{},[1710,103689,103690,103692],{},[898,103691,4980],{},[898,103693,9309],{},[902,103695,103696],{"encoding":904},"D_i",[207,103698,793],{"className":103699,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,103702,103703,2186,103705,1343,103708],{},[38,103704,10675],{},[207,103706,1094],{"className":103707,"dataFsResolvedFilePath":838,"href":839},[210],[207,103709,1101],{"className":103710,"dataFsResolvedFilePath":868,"href":869},[210],[123,103712,103713,2186,103715],{},[38,103714,10686],{},[207,103716,10692],{"className":103717,"dataFsResolvedFilePath":10690,"href":10691},[210],{"title":641,"searchDepth":642,"depth":642,"links":103719},[103720,103721,103722,103725,103726,103729,103733,103734,103737,103738,103739,103740,103741,103742,103743],{"id":1637,"depth":642,"text":1638},{"id":95012,"depth":642,"text":95013},{"id":95072,"depth":642,"text":95073,"children":103723},[103724],{"id":95088,"depth":649,"text":95089},{"id":95395,"depth":642,"text":95396},{"id":96255,"depth":642,"text":96256,"children":103727},[103728],{"id":96802,"depth":649,"text":88431},{"id":97051,"depth":642,"text":97052,"children":103730},[103731],{"id":97924,"depth":649,"text":103732},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":98839,"depth":642,"text":98840},{"id":99375,"depth":642,"text":99376,"children":103735},[103736],{"id":100149,"depth":649,"text":100150},{"id":100379,"depth":642,"text":100380},{"id":101140,"depth":642,"text":101141},{"id":101678,"depth":642,"text":101679},{"id":58101,"depth":642,"text":58102},{"id":101814,"depth":642,"text":101815},{"id":10213,"depth":642,"text":10214},{"id":10612,"depth":642,"text":10613},{},"\u002Ftopics\u002Fuzitecnost",{"title":94796,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,10732,103750,94790,19836,103751],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":103754,"title":757,"body":103755,"course":1128,"courses":659,"created":1129,"description":104028,"extension":661,"meta":104029,"navigation":664,"path":104030,"seo":104031,"sources":104032,"stem":104033,"tags":104034,"type":10736,"updated":677,"__hash__":104040},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":103756,"toc":104020},[103757,103760,103767,103774,103778,103788,103790,103824,103828,103871,103874,103932,103936,103966,103970,103991,103993],[12,103758,757],{"id":103759},"základy-matematické-ekonomie",[724,103761,103762,103763,103766],{},"Úvodní pojmy a princip modelování v ",[207,103764,25083],{"className":103765,"dataFsResolvedFilePath":10690,"href":10691},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,103768,103769],{},[3492,103770],{"alt":103771,"className":103772,"src":103773},"imek-model-promenne",[210,3496],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,103775,103777],{"id":103776},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,103779,103780,103783,103784,103787],{},[38,103781,103782],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,103785,103786],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,103789,10214],{"id":10213},[120,103791,103792,103798,103804,103810,103819],{},[123,103793,103794,103797],{},[38,103795,103796],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,103799,103800,103803],{},[38,103801,103802],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,103805,103806,103809],{},[38,103807,103808],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,103811,103812,10373,103815,103818],{},[38,103813,103814],{},"Ceteris paribus",[614,103816,103817],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,103820,103821,103823],{},[38,103822,58855],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,103825,103827],{"id":103826},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,103829,103830,103870],{},[883,103831,103833],{"className":103832},[886],[888,103834,103835],{"xmlns":890},[892,103836,103837,103867],{},[895,103838,103839,103841,103843,103845,103847,103849,103851,103853,103855,103857,103859,103861,103863,103865],{},[898,103840,1663],{},[1654,103842,1750],{},[898,103844,4980],{},[1654,103846,1708],{"stretchy":1656},[898,103848,1755],{},[1654,103850,1674],{"separator":1673},[898,103852,1745],{},[1654,103854,1674],{"separator":1673},[898,103856,26990],{},[1654,103858,1674],{"separator":1673},[898,103860,900],{},[1654,103862,1674],{"separator":1673},[1654,103864,18366],{},[1654,103866,1726],{"stretchy":1656},[902,103868,103869],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,103872,103873],{},"Zjednodušení:",[120,103875,103876,103904],{},[123,103877,103878,2186,103881],{},[38,103879,103880],{},"Jednofaktorový model:",[883,103882,103884],{"className":103883},[886],[888,103885,103886],{"xmlns":890},[892,103887,103888,103902],{},[895,103889,103890,103892,103894,103896,103898,103900],{},[898,103891,1663],{},[1654,103893,1750],{},[898,103895,4980],{},[1654,103897,1708],{"stretchy":1656},[898,103899,1755],{},[1654,103901,1726],{"stretchy":1656},[902,103903,12933],{"encoding":904},[123,103905,103906,2186,103909],{},[38,103907,103908],{},"Inverzní zápis:",[883,103910,103912],{"className":103911},[886],[888,103913,103914],{"xmlns":890},[892,103915,103916,103930],{},[895,103917,103918,103920,103922,103924,103926,103928],{},[898,103919,1755],{},[1654,103921,1750],{},[898,103923,4980],{},[1654,103925,1708],{"stretchy":1656},[898,103927,1663],{},[1654,103929,1726],{"stretchy":1656},[902,103931,13376],{"encoding":904},[115,103933,103935],{"id":103934},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,103937,103938,103947],{},[123,103939,103940,103943,103944,12664],{},[38,103941,103942],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,103945,24943],{"className":103946,"dataFsResolvedFilePath":800,"href":801},[210],[123,103948,103949,103952,103953,103956,103957,103960,103961,103965],{},[38,103950,103951],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,103954,1145],{"className":103955,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,103958,24956],{"className":103959,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,103962,103964],{"className":103963,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,103967,103969],{"id":103968},"konvence-z-přednášek","Konvence z přednášek",[120,103971,103972,103979,103985],{},[123,103973,103974,103975,103978],{},"Symbol ",[103976,103977,11492],"code",{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,103980,103981,103982,2138],{},"Numerické výsledky ",[38,103983,103984],{},"na 3 desetinná místa",[123,103986,12640,103987,103990],{},[614,103988,103989],{},"jednotková změna"," má standardní význam (změna o 1).",[115,103992,10613],{"id":10612},[120,103994,103995,104000,104008],{},[123,103996,103997,103999],{},[38,103998,12546],{}," —",[123,104001,104002,2186,104004],{},[38,104003,12554],{},[207,104005,104007],{"className":104006,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,104009,104010,2186,104012,1343,104016],{},[38,104011,12562],{},[207,104013,104015],{"className":104014,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,104017,104019],{"className":104018,"dataFsResolvedFilePath":10690,"href":10691},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":104021},[104022,104023,104024,104025,104026,104027],{"id":103776,"depth":642,"text":103777},{"id":10213,"depth":642,"text":10214},{"id":103826,"depth":642,"text":103827},{"id":103934,"depth":642,"text":103935},{"id":103968,"depth":642,"text":103969},{"id":10612,"depth":642,"text":10613},"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":104028},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,104035,104036,104037,104038,104039],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":104042,"title":104043,"body":104044,"course":1128,"courses":659,"created":10724,"description":641,"extension":661,"meta":108316,"navigation":664,"path":108317,"seo":108318,"sources":108319,"stem":108320,"tags":108321,"type":10736,"updated":677,"__hash__":108325},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":104045,"toc":108299},[104046,104049,104143,104147,104169,104183,104235,104237,104241,104304,104347,104366,104529,104628,104631,104698,104702,104831,104870,104900,105012,105057,105123,105176,105252,105308,105310,105314,105378,105422,105442,105603,105606,105690,105787,105790,105856,105860,105909,105935,106040,106104,106109,106205,106252,106254,106257,106279,106321,106328,106361,106363,106434,106488,106597,106601,106690,106766,107030,107068,107070,107074,107077,107084,107395,107398,107456,107636,107665,107667,107671,107677,107815,107824,107826,107828,108253,108255,108257],[12,104047,104043],{"id":104048},"zdanění-trhu-dopady-daně-na-rovnováhu",[2140,104050,104051],{},[724,104052,104053,50848,104055,104068,104069,104072,104073,104075,104076,104079,104080,104101,104102,104125,104126,104129,104130,2138],{},[883,104054,2860],{},[883,104056,104058],{"className":104057},[886],[888,104059,104060],{"xmlns":890},[892,104061,104062,104066],{},[895,104063,104064],{},[898,104065,11536],{},[902,104067,11536],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,104070,104071],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,104074,95080],{}," (je-li uložena spotřebiteli). Výsledné ",[38,104077,104078],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,104081,104083],{"className":104082},[886],[888,104084,104085],{"xmlns":890},[892,104086,104087,104099],{},[895,104088,104089],{},[1710,104090,104091,104093],{},[898,104092,11536],{},[895,104094,104095,104097],{},[898,104096,50897],{},[898,104098,724],{},[902,104100,50902],{"encoding":904}," (spotřebitel) a ",[883,104103,104105],{"className":104104},[886],[888,104106,104107],{"xmlns":890},[892,104108,104109,104123],{},[895,104110,104111],{},[1710,104112,104113,104115],{},[898,104114,11536],{},[895,104116,104117,104119,104121],{},[898,104118,50920],{},[898,104120,10789],{},[898,104122,20753],{},[902,104124,50927],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,104127,104128],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,104131,104133],{"className":104132},[886],[888,104134,104135],{"xmlns":890},[892,104136,104137,104141],{},[895,104138,104139],{},[898,104140,11536],{},[902,104142,11536],{"encoding":904},[115,104144,104146],{"id":104145},"dvě-formy-zdanění","Dvě formy zdanění",[724,104148,104149,104150,104168],{},"Uvažujme jednotkovou daň ",[883,104151,104153],{"className":104152},[886],[888,104154,104155],{"xmlns":890},[892,104156,104157,104165],{},[895,104158,104159,104161,104163],{},[898,104160,11536],{},[1654,104162,2952],{},[1665,104164,2062],{},[902,104166,104167],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,104170,104171,104177],{},[123,104172,104173,104176],{},[38,104174,104175],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,104178,104179,104182],{},[38,104180,104181],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,104184,104185,104186,104199,104200,104203,104204,2138],{},"V obou případech dochází k posunu jedné z křivek o ",[883,104187,104189],{"className":104188},[886],[888,104190,104191],{"xmlns":890},[892,104192,104193,104197],{},[895,104194,104195],{},[898,104196,11536],{},[902,104198,11536],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,104201,104202],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,104205,104207],{"className":104206},[886],[888,104208,104209],{"xmlns":890},[892,104210,104211,104233],{},[895,104212,104213,104215,104217,104223,104225,104231],{},[898,104214,1798],{},[1654,104216,1657],{"stretchy":1656},[1741,104218,104219,104221],{},[898,104220,1663],{},[898,104222,1798],{},[1654,104224,1674],{"separator":1673},[1741,104226,104227,104229],{},[898,104228,1755],{},[898,104230,1798],{},[1654,104232,1686],{"stretchy":1656},[902,104234,49587],{"encoding":904},[45190,104236],{},[115,104238,104240],{"id":104239},"daň-uložená-výrobci","Daň uložená výrobci",[724,104242,104243,104244,104257,104258,104275,104276,104303],{},"Je-li daň ",[883,104245,104247],{"className":104246},[886],[888,104248,104249],{"xmlns":890},[892,104250,104251,104255],{},[895,104252,104253],{},[898,104254,11536],{},[902,104256,11536],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,104259,104261],{"className":104260},[886],[888,104262,104263],{"xmlns":890},[892,104264,104265,104273],{},[895,104266,104267,104269,104271],{},[898,104268,1755],{},[1654,104270,2380],{},[898,104272,11536],{},[902,104274,49342],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,104277,104279],{"className":104278},[886],[888,104280,104281],{"xmlns":890},[892,104282,104283,104301],{},[895,104284,104285,104287,104289,104291,104293,104295,104297,104299],{},[898,104286,1755],{},[1654,104288,2380],{},[898,104290,11536],{},[1654,104292,1750],{},[898,104294,17398],{},[1654,104296,1708],{"stretchy":1656},[898,104298,1663],{},[1654,104300,1726],{"stretchy":1656},[902,104302,49371],{"encoding":904}," nová funkce nabídky:",[883,104305,104307],{"className":104306},[886],[888,104308,104309],{"xmlns":890,"display":1956},[892,104310,104311,104345],{},[895,104312,104313,104315,104317,104323,104325,104327,104329,104331,104333,104335,104337,104339,104341,104343],{},[898,104314,1755],{},[1654,104316,1750],{},[1710,104318,104319,104321],{},[898,104320,17398],{},[1665,104322,1667],{},[1654,104324,1708],{"stretchy":1656},[898,104326,1663],{},[1654,104328,1726],{"stretchy":1656},[1654,104330,1750],{},[898,104332,17398],{},[1654,104334,1708],{"stretchy":1656},[898,104336,1663],{},[1654,104338,1726],{"stretchy":1656},[1654,104340,1766],{},[898,104342,11536],{},[898,104344,2138],{"mathvariant":1878},[902,104346,49416],{"encoding":904},[724,104348,104349,104350,2186,104363,104365],{},"Nabídka se tedy posouvá o ",[883,104351,104353],{"className":104352},[886],[888,104354,104355],{"xmlns":890},[892,104356,104357,104361],{},[895,104358,104359],{},[898,104360,11536],{},[902,104362,11536],{"encoding":904},[38,104364,49449],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,104367,104368,104369,104409,104410,2068,104438,104466,104467,104486,104487,104511,104512,12664],{},"Nový rovnovážný bod ",[883,104370,104372],{"className":104371},[886],[888,104373,104374],{"xmlns":890},[892,104375,104376,104406],{},[895,104377,104378,104384,104386,104394,104396,104404],{},[1710,104379,104380,104382],{},[898,104381,1798],{},[1665,104383,1667],{},[1654,104385,1657],{"stretchy":1656},[1659,104387,104388,104390,104392],{},[898,104389,1663],{},[1665,104391,1667],{},[898,104393,1798],{},[1654,104395,1674],{"separator":1673},[1659,104397,104398,104400,104402],{},[898,104399,1755],{},[1665,104401,1667],{},[898,104403,1798],{},[1654,104405,1686],{"stretchy":1656},[902,104407,104408],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,104411,104413],{"className":104412},[886],[888,104414,104415],{"xmlns":890},[892,104416,104417,104435],{},[895,104418,104419,104427,104429],{},[1659,104420,104421,104423,104425],{},[898,104422,1663],{},[1665,104424,1667],{},[898,104426,1798],{},[1654,104428,3002],{},[1741,104430,104431,104433],{},[898,104432,1663],{},[898,104434,1798],{},[902,104436,104437],{"encoding":904},"Q_1^E \u003C Q^E",[883,104439,104441],{"className":104440},[886],[888,104442,104443],{"xmlns":890},[892,104444,104445,104463],{},[895,104446,104447,104455,104457],{},[1659,104448,104449,104451,104453],{},[898,104450,1755],{},[1665,104452,1667],{},[898,104454,1798],{},[1654,104456,2952],{},[1741,104458,104459,104461],{},[898,104460,1755],{},[898,104462,1798],{},[902,104464,104465],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,104468,104470],{"className":104469},[886],[888,104471,104472],{"xmlns":890},[892,104473,104474,104484],{},[895,104475,104476],{},[1659,104477,104478,104480,104482],{},[898,104479,1755],{},[1665,104481,1667],{},[898,104483,1798],{},[902,104485,56077],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,104488,104490],{"className":104489},[886],[888,104491,104492],{"xmlns":890},[892,104493,104494,104508],{},[895,104495,104496,104504,104506],{},[1659,104497,104498,104500,104502],{},[898,104499,1755],{},[1665,104501,1667],{},[898,104503,1798],{},[1654,104505,2380],{},[898,104507,11536],{},[902,104509,104510],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,104513,104515],{"className":104514},[886],[888,104516,104517],{"xmlns":890},[892,104518,104519,104527],{},[895,104520,104521],{},[1741,104522,104523,104525],{},[898,104524,1755],{},[898,104526,1798],{},[902,104528,49686],{"encoding":904},[724,104530,104531],{},[614,104532,104533,104534,104564,104565,104578,104579,14398,104596,104609,104610,2138],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,104535,104537],{"className":104536},[886],[888,104538,104539],{"xmlns":890},[892,104540,104541,104561],{},[895,104542,104543,104545,104547,104553,104555,104557,104559],{},[898,104544,17398],{},[1654,104546,11878],{},[1710,104548,104549,104551],{},[898,104550,17398],{},[1665,104552,1667],{},[1654,104554,1750],{},[898,104556,17398],{},[1654,104558,1766],{},[898,104560,11536],{},[902,104562,104563],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,104566,104568],{"className":104567},[886],[888,104569,104570],{"xmlns":890},[892,104571,104572,104576],{},[895,104573,104574],{},[898,104575,11536],{},[902,104577,11536],{"encoding":904},". Průsečík ",[883,104580,104582],{"className":104581},[886],[888,104583,104584],{"xmlns":890},[892,104585,104586,104594],{},[895,104587,104588],{},[1710,104589,104590,104592],{},[898,104591,17398],{},[1665,104593,1667],{},[902,104595,49217],{"encoding":904},[883,104597,104599],{"className":104598},[886],[888,104600,104601],{"xmlns":890},[892,104602,104603,104607],{},[895,104604,104605],{},[898,104606,4980],{},[902,104608,4980],{"encoding":904}," je nový rovnovážný bod ",[883,104611,104613],{"className":104612},[886],[888,104614,104615],{"xmlns":890},[892,104616,104617,104625],{},[895,104618,104619],{},[1710,104620,104621,104623],{},[898,104622,1798],{},[1665,104624,1667],{},[902,104626,104627],{"encoding":904},"E_1",[198,104629,53523],{"id":104630},"příklad-29",[724,104632,104633,49875,104635,49910,104659,104679,104680,104697],{},[38,104634,46153],{},[883,104636,104638],{"className":104637},[886],[888,104639,104640],{"xmlns":890},[892,104641,104642,104656],{},[895,104643,104644,104646,104648,104650,104652,104654],{},[898,104645,1755],{},[1654,104647,1750],{},[1665,104649,6509],{},[1654,104651,2380],{},[1665,104653,1681],{},[898,104655,1663],{},[902,104657,104658],{"encoding":904},"P = 12 - 2Q",[883,104660,104662],{"className":104661},[886],[888,104663,104664],{"xmlns":890},[892,104665,104666,104676],{},[895,104667,104668,104670,104672,104674],{},[898,104669,1755],{},[1654,104671,1750],{},[1665,104673,7631],{},[898,104675,1663],{},[902,104677,104678],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,104681,104683],{"className":104682},[886],[888,104684,104685],{"xmlns":890},[892,104686,104687,104695],{},[895,104688,104689,104691,104693],{},[898,104690,11536],{},[1654,104692,1750],{},[1665,104694,11015],{},[902,104696,49488],{"encoding":904}," Kč.",[724,104699,104700],{},[38,104701,46185],{},[724,104703,104704,104707,104708,14299,104734,4579,104754,1343,104776,104806,104807,2138],{},[614,104705,104706],{},"Bez daně."," Z rovnosti ",[883,104709,104711],{"className":104710},[886],[888,104712,104713],{"xmlns":890},[892,104714,104715,104731],{},[895,104716,104717,104719,104721,104723,104725,104727,104729],{},[1665,104718,6509],{},[1654,104720,2380],{},[1665,104722,1681],{},[898,104724,1663],{},[1654,104726,1750],{},[1665,104728,7631],{},[898,104730,1663],{},[902,104732,104733],{"encoding":904},"12 - 2Q = 4Q",[883,104735,104737],{"className":104736},[886],[888,104738,104739],{"xmlns":890},[892,104740,104741,104751],{},[895,104742,104743,104745,104747,104749],{},[1665,104744,11015],{},[898,104746,1663],{},[1654,104748,1750],{},[1665,104750,6509],{},[902,104752,104753],{"encoding":904},"6Q = 12",[883,104755,104757],{"className":104756},[886],[888,104758,104759],{"xmlns":890},[892,104760,104761,104773],{},[895,104762,104763,104769,104771],{},[1741,104764,104765,104767],{},[898,104766,1663],{},[898,104768,1798],{},[1654,104770,1750],{},[1665,104772,1681],{},[902,104774,104775],{"encoding":904},"Q^E = 2",[883,104777,104779],{"className":104778},[886],[888,104780,104781],{"xmlns":890},[892,104782,104783,104803],{},[895,104784,104785,104791,104793,104795,104797,104799,104801],{},[1741,104786,104787,104789],{},[898,104788,1755],{},[898,104790,1798],{},[1654,104792,1750],{},[1665,104794,7631],{},[1654,104796,4554],{},[1665,104798,1681],{},[1654,104800,1750],{},[1665,104802,14315],{},[902,104804,104805],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,104808,104810],{"className":104809},[886],[888,104811,104812],{"xmlns":890},[892,104813,104814,104828],{},[895,104815,104816,104818,104820,104822,104824,104826],{},[898,104817,1798],{},[1654,104819,1657],{"stretchy":1656},[1665,104821,1681],{},[1654,104823,1674],{"separator":1673},[1665,104825,14315],{},[1654,104827,1686],{"stretchy":1656},[902,104829,104830],{"encoding":904},"E[2, 8]",[724,104832,104833,104836,104837,104869],{},[614,104834,104835],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,104838,104840],{"className":104839},[886],[888,104841,104842],{"xmlns":890},[892,104843,104844,104866],{},[895,104845,104846,104852,104854,104856,104858,104860,104862,104864],{},[1710,104847,104848,104850],{},[898,104849,17398],{},[1665,104851,1667],{},[1654,104853,2781],{},[898,104855,1755],{},[1654,104857,1750],{},[1665,104859,7631],{},[898,104861,1663],{},[1654,104863,1766],{},[1665,104865,11015],{},[902,104867,104868],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,104871,104873],{"className":104872},[886],[888,104874,104875],{"xmlns":890,"display":1956},[892,104876,104877,104897],{},[895,104878,104879,104881,104883,104885,104887,104889,104891,104893,104895],{},[1665,104880,6509],{},[1654,104882,2380],{},[1665,104884,1681],{},[898,104886,1663],{},[1654,104888,1750],{},[1665,104890,7631],{},[898,104892,1663],{},[1654,104894,1766],{},[1665,104896,11015],{},[902,104898,104899],{"encoding":904},"12 - 2Q = 4Q + 6",[724,104901,104902,104903,4579,104923,1343,104947,104983,104984,2138],{},"plyne ",[883,104904,104906],{"className":104905},[886],[888,104907,104908],{"xmlns":890},[892,104909,104910,104920],{},[895,104911,104912,104914,104916,104918],{},[1665,104913,11015],{},[898,104915,1663],{},[1654,104917,1750],{},[1665,104919,11015],{},[902,104921,104922],{"encoding":904},"6Q = 6",[883,104924,104926],{"className":104925},[886],[888,104927,104928],{"xmlns":890},[892,104929,104930,104944],{},[895,104931,104932,104940,104942],{},[1659,104933,104934,104936,104938],{},[898,104935,1663],{},[1665,104937,1667],{},[898,104939,1798],{},[1654,104941,1750],{},[1665,104943,1667],{},[902,104945,104946],{"encoding":904},"Q_1^E = 1",[883,104948,104950],{"className":104949},[886],[888,104951,104952],{"xmlns":890},[892,104953,104954,104980],{},[895,104955,104956,104964,104966,104968,104970,104972,104974,104976,104978],{},[1659,104957,104958,104960,104962],{},[898,104959,1755],{},[1665,104961,1667],{},[898,104963,1798],{},[1654,104965,1750],{},[1665,104967,7631],{},[1654,104969,4554],{},[1665,104971,1667],{},[1654,104973,1766],{},[1665,104975,11015],{},[1654,104977,1750],{},[1665,104979,4647],{},[902,104981,104982],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,104985,104987],{"className":104986},[886],[888,104988,104989],{"xmlns":890},[892,104990,104991,105009],{},[895,104992,104993,104999,105001,105003,105005,105007],{},[1710,104994,104995,104997],{},[898,104996,1798],{},[1665,104998,1667],{},[1654,105000,1657],{"stretchy":1656},[1665,105002,1667],{},[1654,105004,1674],{"separator":1673},[1665,105006,4647],{},[1654,105008,1686],{"stretchy":1656},[902,105010,105011],{"encoding":904},"E_1[1, 10]",[724,105013,105014,105017,105018,105042,105043,105056],{},[614,105015,105016],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,105019,105021],{"className":105020},[886],[888,105022,105023],{"xmlns":890},[892,105024,105025,105039],{},[895,105026,105027,105035,105037],{},[1659,105028,105029,105031,105033],{},[898,105030,1755],{},[1665,105032,1667],{},[898,105034,1798],{},[1654,105036,1750],{},[1665,105038,4647],{},[902,105040,105041],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,105044,105046],{"className":105045},[886],[888,105047,105048],{"xmlns":890},[892,105049,105050,105054],{},[895,105051,105052],{},[1665,105053,14315],{},[902,105055,14315],{"encoding":904},", navýšení je",[883,105058,105060],{"className":105059},[886],[888,105061,105062],{"xmlns":890,"display":1956},[892,105063,105064,105120],{},[895,105065,105066,105076,105078,105086,105088,105094,105096,105098,105100,105102,105104,105106,105108,105118],{},[1710,105067,105068,105070],{},[898,105069,11536],{},[895,105071,105072,105074],{},[898,105073,50897],{},[898,105075,724],{},[1654,105077,1750],{},[1659,105079,105080,105082,105084],{},[898,105081,1755],{},[1665,105083,1667],{},[898,105085,1798],{},[1654,105087,2380],{},[1741,105089,105090,105092],{},[898,105091,1755],{},[898,105093,1798],{},[1654,105095,1750],{},[1665,105097,4647],{},[1654,105099,2380],{},[1665,105101,14315],{},[1654,105103,1750],{},[1665,105105,1681],{},[1865,105107,11065],{},[895,105109,105110,105112],{},[1865,105111,18517],{},[17111,105113,105114,105116],{"accent":1673},[1865,105115,3624],{},[1654,105117,33744],{},[898,105119,2138],{"mathvariant":1878},[902,105121,105122],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,105124,105125,105126,105042,105162,105175],{},"Výrobci zůstává čistá cena ",[883,105127,105129],{"className":105128},[886],[888,105130,105131],{"xmlns":890},[892,105132,105133,105159],{},[895,105134,105135,105143,105145,105147,105149,105151,105153,105155,105157],{},[1659,105136,105137,105139,105141],{},[898,105138,1755],{},[1665,105140,1667],{},[898,105142,1798],{},[1654,105144,2380],{},[898,105146,11536],{},[1654,105148,1750],{},[1665,105150,4647],{},[1654,105152,2380],{},[1665,105154,11015],{},[1654,105156,1750],{},[1665,105158,7631],{},[902,105160,105161],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,105163,105165],{"className":105164},[886],[888,105166,105167],{"xmlns":890},[892,105168,105169,105173],{},[895,105170,105171],{},[1665,105172,14315],{},[902,105174,14315],{"encoding":904},", pokles je",[883,105177,105179],{"className":105178},[886],[888,105180,105181],{"xmlns":890,"display":1956},[892,105182,105183,105249],{},[895,105184,105185,105197,105199,105205,105207,105209,105217,105219,105221,105223,105225,105227,105229,105231,105233,105235,105237,105247],{},[1710,105186,105187,105189],{},[898,105188,11536],{},[895,105190,105191,105193,105195],{},[898,105192,50920],{},[898,105194,10789],{},[898,105196,20753],{},[1654,105198,1750],{},[1741,105200,105201,105203],{},[898,105202,1755],{},[898,105204,1798],{},[1654,105206,2380],{},[1654,105208,1708],{"stretchy":1656},[1659,105210,105211,105213,105215],{},[898,105212,1755],{},[1665,105214,1667],{},[898,105216,1798],{},[1654,105218,2380],{},[898,105220,11536],{},[1654,105222,1726],{"stretchy":1656},[1654,105224,1750],{},[1665,105226,14315],{},[1654,105228,2380],{},[1665,105230,7631],{},[1654,105232,1750],{},[1665,105234,7631],{},[1865,105236,11065],{},[895,105238,105239,105241],{},[1865,105240,18517],{},[17111,105242,105243,105245],{"accent":1673},[1865,105244,3624],{},[1654,105246,33744],{},[898,105248,2138],{"mathvariant":1878},[902,105250,105251],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,105253,105254,105255,105307],{},"Kontrola: ",[883,105256,105258],{"className":105257},[886],[888,105259,105260],{"xmlns":890},[892,105261,105262,105304],{},[895,105263,105264,105274,105276,105288,105290,105292,105294,105296,105298,105300,105302],{},[1710,105265,105266,105268],{},[898,105267,11536],{},[895,105269,105270,105272],{},[898,105271,50897],{},[898,105273,724],{},[1654,105275,1766],{},[1710,105277,105278,105280],{},[898,105279,11536],{},[895,105281,105282,105284,105286],{},[898,105283,50920],{},[898,105285,10789],{},[898,105287,20753],{},[1654,105289,1750],{},[1665,105291,1681],{},[1654,105293,1766],{},[1665,105295,7631],{},[1654,105297,1750],{},[1665,105299,11015],{},[1654,105301,1750],{},[898,105303,11536],{},[902,105305,105306],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[45190,105309],{},[115,105311,105313],{"id":105312},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,105315,104243,105316,105329,105330,105348,105349,105377],{},[883,105317,105319],{"className":105318},[886],[888,105320,105321],{"xmlns":890},[892,105322,105323,105327],{},[895,105324,105325],{},[898,105326,11536],{},[902,105328,11536],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,105331,105333],{"className":105332},[886],[888,105334,105335],{"xmlns":890},[892,105336,105337,105345],{},[895,105338,105339,105341,105343],{},[898,105340,1755],{},[1654,105342,1766],{},[898,105344,11536],{},[902,105346,105347],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,105350,105352],{"className":105351},[886],[888,105353,105354],{"xmlns":890},[892,105355,105356,105374],{},[895,105357,105358,105360,105362,105364,105366,105368,105370,105372],{},[898,105359,1755],{},[1654,105361,1766],{},[898,105363,11536],{},[1654,105365,1750],{},[898,105367,4980],{},[1654,105369,1708],{"stretchy":1656},[898,105371,1663],{},[1654,105373,1726],{"stretchy":1656},[902,105375,105376],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,105379,105381],{"className":105380},[886],[888,105382,105383],{"xmlns":890,"display":1956},[892,105384,105385,105419],{},[895,105386,105387,105389,105391,105397,105399,105401,105403,105405,105407,105409,105411,105413,105415,105417],{},[898,105388,1755],{},[1654,105390,1750],{},[1710,105392,105393,105395],{},[898,105394,4980],{},[1665,105396,1681],{},[1654,105398,1708],{"stretchy":1656},[898,105400,1663],{},[1654,105402,1726],{"stretchy":1656},[1654,105404,1750],{},[898,105406,4980],{},[1654,105408,1708],{"stretchy":1656},[898,105410,1663],{},[1654,105412,1726],{"stretchy":1656},[1654,105414,2380],{},[898,105416,11536],{},[898,105418,2138],{"mathvariant":1878},[902,105420,105421],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,105423,105424,105425,2186,105438,105441],{},"Poptávka se tedy posouvá o ",[883,105426,105428],{"className":105427},[886],[888,105429,105430],{"xmlns":890},[892,105431,105432,105436],{},[895,105433,105434],{},[898,105435,11536],{},[902,105437,11536],{"encoding":904},[38,105439,105440],{},"svisle dolů",". Nabídka se nemění.",[724,105443,104368,105444,104409,105484,2068,105512,105540,105541,105560,105561,105585,105586,12664],{},[883,105445,105447],{"className":105446},[886],[888,105448,105449],{"xmlns":890},[892,105450,105451,105481],{},[895,105452,105453,105459,105461,105469,105471,105479],{},[1710,105454,105455,105457],{},[898,105456,1798],{},[1665,105458,1681],{},[1654,105460,1657],{"stretchy":1656},[1659,105462,105463,105465,105467],{},[898,105464,1663],{},[1665,105466,1681],{},[898,105468,1798],{},[1654,105470,1674],{"separator":1673},[1659,105472,105473,105475,105477],{},[898,105474,1755],{},[1665,105476,1681],{},[898,105478,1798],{},[1654,105480,1686],{"stretchy":1656},[902,105482,105483],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,105485,105487],{"className":105486},[886],[888,105488,105489],{"xmlns":890},[892,105490,105491,105509],{},[895,105492,105493,105501,105503],{},[1659,105494,105495,105497,105499],{},[898,105496,1663],{},[1665,105498,1681],{},[898,105500,1798],{},[1654,105502,3002],{},[1741,105504,105505,105507],{},[898,105506,1663],{},[898,105508,1798],{},[902,105510,105511],{"encoding":904},"Q_2^E \u003C Q^E",[883,105513,105515],{"className":105514},[886],[888,105516,105517],{"xmlns":890},[892,105518,105519,105537],{},[895,105520,105521,105529,105531],{},[1659,105522,105523,105525,105527],{},[898,105524,1755],{},[1665,105526,1681],{},[898,105528,1798],{},[1654,105530,3002],{},[1741,105532,105533,105535],{},[898,105534,1755],{},[898,105536,1798],{},[902,105538,105539],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,105542,105544],{"className":105543},[886],[888,105545,105546],{"xmlns":890},[892,105547,105548,105558],{},[895,105549,105550],{},[1659,105551,105552,105554,105556],{},[898,105553,1755],{},[1665,105555,1681],{},[898,105557,1798],{},[902,105559,56138],{"encoding":904},", spotřebitel platí celkem ",[883,105562,105564],{"className":105563},[886],[888,105565,105566],{"xmlns":890},[892,105567,105568,105582],{},[895,105569,105570,105578,105580],{},[1659,105571,105572,105574,105576],{},[898,105573,1755],{},[1665,105575,1681],{},[898,105577,1798],{},[1654,105579,1766],{},[898,105581,11536],{},[902,105583,105584],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,105587,105589],{"className":105588},[886],[888,105590,105591],{"xmlns":890},[892,105592,105593,105601],{},[895,105594,105595],{},[1741,105596,105597,105599],{},[898,105598,1755],{},[898,105600,1798],{},[902,105602,49686],{"encoding":904},[724,105604,105605],{},"Daňové břemeno:",[883,105607,105609],{"className":105608},[886],[888,105610,105611],{"xmlns":890,"display":1956},[892,105612,105613,105687],{},[895,105614,105615,105625,105627,105629,105637,105639,105641,105643,105645,105651,105653,105655,105667,105669,105675,105677,105685],{},[1710,105616,105617,105619],{},[898,105618,11536],{},[895,105620,105621,105623],{},[898,105622,50897],{},[898,105624,724],{},[1654,105626,1750],{},[1654,105628,1708],{"stretchy":1656},[1659,105630,105631,105633,105635],{},[898,105632,1755],{},[1665,105634,1681],{},[898,105636,1798],{},[1654,105638,1766],{},[898,105640,11536],{},[1654,105642,1726],{"stretchy":1656},[1654,105644,2380],{},[1741,105646,105647,105649],{},[898,105648,1755],{},[898,105650,1798],{},[1654,105652,1674],{"separator":1673},[5008,105654],{"width":14608},[1710,105656,105657,105659],{},[898,105658,11536],{},[895,105660,105661,105663,105665],{},[898,105662,50920],{},[898,105664,10789],{},[898,105666,20753],{},[1654,105668,1750],{},[1741,105670,105671,105673],{},[898,105672,1755],{},[898,105674,1798],{},[1654,105676,2380],{},[1659,105678,105679,105681,105683],{},[898,105680,1755],{},[1665,105682,1681],{},[898,105684,1798],{},[898,105686,2138],{"mathvariant":1878},[902,105688,105689],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,105691,105692],{},[614,105693,105694,105695,105725,105726,104578,105739,14398,105756,104609,105769,2138],{},"Obrázek 2.19: Posun ",[883,105696,105698],{"className":105697},[886],[888,105699,105700],{"xmlns":890},[892,105701,105702,105722],{},[895,105703,105704,105706,105708,105714,105716,105718,105720],{},[898,105705,4980],{},[1654,105707,11878],{},[1710,105709,105710,105712],{},[898,105711,4980],{},[1665,105713,1681],{},[1654,105715,1750],{},[898,105717,4980],{},[1654,105719,2380],{},[898,105721,11536],{},[902,105723,105724],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,105727,105729],{"className":105728},[886],[888,105730,105731],{"xmlns":890},[892,105732,105733,105737],{},[895,105734,105735],{},[898,105736,11536],{},[902,105738,11536],{"encoding":904},[883,105740,105742],{"className":105741},[886],[888,105743,105744],{"xmlns":890},[892,105745,105746,105754],{},[895,105747,105748],{},[1710,105749,105750,105752],{},[898,105751,4980],{},[1665,105753,1681],{},[902,105755,46547],{"encoding":904},[883,105757,105759],{"className":105758},[886],[888,105760,105761],{"xmlns":890},[892,105762,105763,105767],{},[895,105764,105765],{},[898,105766,17398],{},[902,105768,17398],{"encoding":904},[883,105770,105772],{"className":105771},[886],[888,105773,105774],{"xmlns":890},[892,105775,105776,105784],{},[895,105777,105778],{},[1710,105779,105780,105782],{},[898,105781,1798],{},[1665,105783,1681],{},[902,105785,105786],{"encoding":904},"E_2",[198,105788,53603],{"id":105789},"příklad-210",[724,105791,105792,105794,105795,49910,105818,105837,105838,105855],{},[38,105793,46153],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,105796,105798],{"className":105797},[886],[888,105799,105800],{"xmlns":890},[892,105801,105802,105816],{},[895,105803,105804,105806,105808,105810,105812,105814],{},[898,105805,1755],{},[1654,105807,1750],{},[1665,105809,6509],{},[1654,105811,2380],{},[1665,105813,1681],{},[898,105815,1663],{},[902,105817,104658],{"encoding":904},[883,105819,105821],{"className":105820},[886],[888,105822,105823],{"xmlns":890},[892,105824,105825,105835],{},[895,105826,105827,105829,105831,105833],{},[898,105828,1755],{},[1654,105830,1750],{},[1665,105832,7631],{},[898,105834,1663],{},[902,105836,104678],{"encoding":904},". Daň ",[883,105839,105841],{"className":105840},[886],[888,105842,105843],{"xmlns":890},[892,105844,105845,105853],{},[895,105846,105847,105849,105851],{},[898,105848,11536],{},[1654,105850,1750],{},[1665,105852,11015],{},[902,105854,49488],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,105857,105858],{},[38,105859,46185],{},[724,105861,105862,105863,104869],{},"Nová poptávka je ",[883,105864,105866],{"className":105865},[886],[888,105867,105868],{"xmlns":890},[892,105869,105870,105906],{},[895,105871,105872,105878,105880,105882,105884,105886,105888,105890,105892,105894,105896,105898,105900,105902,105904],{},[1710,105873,105874,105876],{},[898,105875,4980],{},[1665,105877,1681],{},[1654,105879,2781],{},[898,105881,1755],{},[1654,105883,1750],{},[1665,105885,6509],{},[1654,105887,2380],{},[1665,105889,1681],{},[898,105891,1663],{},[1654,105893,2380],{},[1665,105895,11015],{},[1654,105897,1750],{},[1665,105899,11015],{},[1654,105901,2380],{},[1665,105903,1681],{},[898,105905,1663],{},[902,105907,105908],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,105910,105912],{"className":105911},[886],[888,105913,105914],{"xmlns":890,"display":1956},[892,105915,105916,105932],{},[895,105917,105918,105920,105922,105924,105926,105928,105930],{},[1665,105919,11015],{},[1654,105921,2380],{},[1665,105923,1681],{},[898,105925,1663],{},[1654,105927,1750],{},[1665,105929,7631],{},[898,105931,1663],{},[902,105933,105934],{"encoding":904},"6 - 2Q = 4Q",[724,105936,104902,105937,4579,105956,1343,105980,104983,106012,2138],{},[883,105938,105940],{"className":105939},[886],[888,105941,105942],{"xmlns":890},[892,105943,105944,105954],{},[895,105945,105946,105948,105950,105952],{},[1665,105947,11015],{},[898,105949,1663],{},[1654,105951,1750],{},[1665,105953,11015],{},[902,105955,104922],{"encoding":904},[883,105957,105959],{"className":105958},[886],[888,105960,105961],{"xmlns":890},[892,105962,105963,105977],{},[895,105964,105965,105973,105975],{},[1659,105966,105967,105969,105971],{},[898,105968,1663],{},[1665,105970,1681],{},[898,105972,1798],{},[1654,105974,1750],{},[1665,105976,1667],{},[902,105978,105979],{"encoding":904},"Q_2^E = 1",[883,105981,105983],{"className":105982},[886],[888,105984,105985],{"xmlns":890},[892,105986,105987,106009],{},[895,105988,105989,105997,105999,106001,106003,106005,106007],{},[1659,105990,105991,105993,105995],{},[898,105992,1755],{},[1665,105994,1681],{},[898,105996,1798],{},[1654,105998,1750],{},[1665,106000,7631],{},[1654,106002,4554],{},[1665,106004,1667],{},[1654,106006,1750],{},[1665,106008,7631],{},[902,106010,106011],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,106013,106015],{"className":106014},[886],[888,106016,106017],{"xmlns":890},[892,106018,106019,106037],{},[895,106020,106021,106027,106029,106031,106033,106035],{},[1710,106022,106023,106025],{},[898,106024,1798],{},[1665,106026,1681],{},[1654,106028,1657],{"stretchy":1656},[1665,106030,1667],{},[1654,106032,1674],{"separator":1673},[1665,106034,7631],{},[1654,106036,1686],{"stretchy":1656},[902,106038,106039],{"encoding":904},"E_2[1, 4]",[724,106041,106042,106043,106079,106080,104697],{},"Spotřebitel platí celkem ",[883,106044,106046],{"className":106045},[886],[888,106047,106048],{"xmlns":890},[892,106049,106050,106076],{},[895,106051,106052,106060,106062,106064,106066,106068,106070,106072,106074],{},[1659,106053,106054,106056,106058],{},[898,106055,1755],{},[1665,106057,1681],{},[898,106059,1798],{},[1654,106061,1766],{},[898,106063,11536],{},[1654,106065,1750],{},[1665,106067,7631],{},[1654,106069,1766],{},[1665,106071,11015],{},[1654,106073,1750],{},[1665,106075,4647],{},[902,106077,106078],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,106081,106083],{"className":106082},[886],[888,106084,106085],{"xmlns":890},[892,106086,106087,106101],{},[895,106088,106089,106097,106099],{},[1659,106090,106091,106093,106095],{},[898,106092,1755],{},[1665,106094,1681],{},[898,106096,1798],{},[1654,106098,1750],{},[1665,106100,7631],{},[902,106102,106103],{"encoding":904},"P_2^E = 4",[724,106105,106106],{},[614,106107,106108],{},"Rozklad daňového břemene:",[883,106110,106112],{"className":106111},[886],[888,106113,106114],{"xmlns":890,"display":1956},[892,106115,106116,106202],{},[895,106117,106118,106128,106130,106132,106134,106136,106138,106140,106142,106144,106146,106148,106150,106160,106162,106164,106176,106178,106180,106182,106184,106186,106188,106190,106200],{},[1710,106119,106120,106122],{},[898,106121,11536],{},[895,106123,106124,106126],{},[898,106125,50897],{},[898,106127,724],{},[1654,106129,1750],{},[1654,106131,1708],{"stretchy":1656},[1665,106133,7631],{},[1654,106135,1766],{},[1665,106137,11015],{},[1654,106139,1726],{"stretchy":1656},[1654,106141,2380],{},[1665,106143,14315],{},[1654,106145,1750],{},[1665,106147,1681],{},[1865,106149,11065],{},[895,106151,106152,106154],{},[1865,106153,18517],{},[17111,106155,106156,106158],{"accent":1673},[1865,106157,3624],{},[1654,106159,33744],{},[1654,106161,1674],{"separator":1673},[5008,106163],{"width":14608},[1710,106165,106166,106168],{},[898,106167,11536],{},[895,106169,106170,106172,106174],{},[898,106171,50920],{},[898,106173,10789],{},[898,106175,20753],{},[1654,106177,1750],{},[1665,106179,14315],{},[1654,106181,2380],{},[1665,106183,7631],{},[1654,106185,1750],{},[1665,106187,7631],{},[1865,106189,11065],{},[895,106191,106192,106194],{},[1865,106193,18517],{},[17111,106195,106196,106198],{"accent":1673},[1865,106197,3624],{},[1654,106199,33744],{},[898,106201,2138],{"mathvariant":1878},[902,106203,106204],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,106206,106207,106208,2138],{},"Opět ",[883,106209,106211],{"className":106210},[886],[888,106212,106213],{"xmlns":890},[892,106214,106215,106249],{},[895,106216,106217,106227,106229,106241,106243,106245,106247],{},[1710,106218,106219,106221],{},[898,106220,11536],{},[895,106222,106223,106225],{},[898,106224,50897],{},[898,106226,724],{},[1654,106228,1766],{},[1710,106230,106231,106233],{},[898,106232,11536],{},[895,106234,106235,106237,106239],{},[898,106236,50920],{},[898,106238,10789],{},[898,106240,20753],{},[1654,106242,1750],{},[1665,106244,11015],{},[1654,106246,1750],{},[898,106248,11536],{},[902,106250,106251],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[45190,106253],{},[115,106255,50878],{"id":106256},"daňové-břemeno",[724,106258,106259,18742,106261,106264,106265,106278],{},[38,106260,50878],{},[614,106262,106263],{},"tax burden",") je rozdělení zaplacené daně ",[883,106266,106268],{"className":106267},[886],[888,106269,106270],{"xmlns":890},[892,106271,106272,106276],{},[895,106273,106274],{},[898,106275,11536],{},[902,106277,11536],{"encoding":904}," mezi spotřebitele a výrobce:",[883,106280,106282],{"className":106281},[886],[888,106283,106284],{"xmlns":890,"display":1956},[892,106285,106286,106318],{},[895,106287,106288,106290,106292,106302,106304,106316],{},[898,106289,11536],{},[1654,106291,1750],{},[1710,106293,106294,106296],{},[898,106295,11536],{},[895,106297,106298,106300],{},[898,106299,50897],{},[898,106301,724],{},[1654,106303,1766],{},[1710,106305,106306,106308],{},[898,106307,11536],{},[895,106309,106310,106312,106314],{},[898,106311,50920],{},[898,106313,10789],{},[898,106315,20753],{},[898,106317,2138],{"mathvariant":1878},[902,106319,106320],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,106322,106323],{},[3492,106324],{"alt":106325,"className":106326,"src":106327},"imek-dan-rozklad-bremene-sklony",[210,3496],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[2140,106329,106330],{},[724,106331,106332,106334,106335,2068,106348,2138],{},[883,106333,2860],{}," 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 ",[883,106336,106338],{"className":106337},[886],[888,106339,106340],{"xmlns":890},[892,106341,106342,106346],{},[895,106343,106344],{},[898,106345,4980],{},[902,106347,4980],{"encoding":904},[883,106349,106351],{"className":106350},[886],[888,106352,106353],{"xmlns":890},[892,106354,106355,106359],{},[895,106356,106357],{},[898,106358,17398],{},[902,106360,17398],{"encoding":904},[198,106362,11211],{"id":11210},[724,106364,106365,106366,106387,106388,106401,106402,106419,106420,106433],{},"V grafu ",[883,106367,106369],{"className":106368},[886],[888,106370,106371],{"xmlns":890},[892,106372,106373,106385],{},[895,106374,106375,106377,106379,106381,106383],{},[1654,106376,1708],{"stretchy":1656},[898,106378,1663],{},[1654,106380,1674],{"separator":1673},[898,106382,1755],{},[1654,106384,1726],{"stretchy":1656},[902,106386,45911],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,106389,106391],{"className":106390},[886],[888,106392,106393],{"xmlns":890},[892,106394,106395,106399],{},[895,106396,106397],{},[898,106398,11536],{},[902,106400,11536],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,106403,106405],{"className":106404},[886],[888,106406,106407],{"xmlns":890},[892,106408,106409,106417],{},[895,106410,106411],{},[1741,106412,106413,106415],{},[898,106414,1755],{},[898,106416,1798],{},[902,106418,49686],{"encoding":904},", rozdělí se úsečka ",[883,106421,106423],{"className":106422},[886],[888,106424,106425],{"xmlns":890},[892,106426,106427,106431],{},[895,106428,106429],{},[898,106430,11536],{},[902,106432,11536],{"encoding":904}," na dvě části:",[120,106435,106436,106461],{},[123,106437,106438,106439,106460],{},"horní část odpovídá ",[883,106440,106442],{"className":106441},[886],[888,106443,106444],{"xmlns":890},[892,106445,106446,106458],{},[895,106447,106448],{},[1710,106449,106450,106452],{},[898,106451,11536],{},[895,106453,106454,106456],{},[898,106455,50897],{},[898,106457,724],{},[902,106459,50902],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,106462,106463,106464,106487],{},"dolní část odpovídá ",[883,106465,106467],{"className":106466},[886],[888,106468,106469],{"xmlns":890},[892,106470,106471,106485],{},[895,106472,106473],{},[1710,106474,106475,106477],{},[898,106476,11536],{},[895,106478,106479,106481,106483],{},[898,106480,50920],{},[898,106482,10789],{},[898,106484,20753],{},[902,106486,50927],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,106489,106490],{},[614,106491,106492,106493,11448,106506,106527,106528,106551,106552,2068,106573,106596],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,106494,106496],{"className":106495},[886],[888,106497,106498],{"xmlns":890},[892,106499,106500,106504],{},[895,106501,106502],{},[898,106503,11536],{},[902,106505,11536],{"encoding":904},[883,106507,106509],{"className":106508},[886],[888,106510,106511],{"xmlns":890},[892,106512,106513,106525],{},[895,106514,106515],{},[1710,106516,106517,106519],{},[898,106518,11536],{},[895,106520,106521,106523],{},[898,106522,50897],{},[898,106524,724],{},[902,106526,50902],{"encoding":904}," (nahoře) a ",[883,106529,106531],{"className":106530},[886],[888,106532,106533],{"xmlns":890},[892,106534,106535,106549],{},[895,106536,106537],{},[1710,106538,106539,106541],{},[898,106540,11536],{},[895,106542,106543,106545,106547],{},[898,106544,50920],{},[898,106546,10789],{},[898,106548,20753],{},[902,106550,50927],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,106553,106555],{"className":106554},[886],[888,106556,106557],{"xmlns":890},[892,106558,106559,106571],{},[895,106560,106561],{},[1710,106562,106563,106565],{},[898,106564,11536],{},[895,106566,106567,106569],{},[898,106568,50897],{},[898,106570,724],{},[902,106572,50902],{"encoding":904},[883,106574,106576],{"className":106575},[886],[888,106577,106578],{"xmlns":890},[892,106579,106580,106594],{},[895,106581,106582],{},[1710,106583,106584,106586],{},[898,106585,11536],{},[895,106587,106588,106590,106592],{},[898,106589,50920],{},[898,106591,10789],{},[898,106593,20753],{},[902,106595,50927],{"encoding":904}," je v obou případech stejná.",[198,106598,106600],{"id":106599},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,106602,106603,106604,106607,106608,18742,106631,106648,106649,18742,106672,106689],{},"Platí obecně: ",[38,106605,106606],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,106609,106611],{"className":106610},[886],[888,106612,106613],{"xmlns":890},[892,106614,106615,106629],{},[895,106616,106617,106619,106621,106623,106625,106627],{},[898,106618,1755],{},[1654,106620,1750],{},[898,106622,207],{},[898,106624,1663],{},[1654,106626,1766],{},[898,106628,9758],{},[902,106630,45280],{"encoding":904},[883,106632,106634],{"className":106633},[886],[888,106635,106636],{"xmlns":890},[892,106637,106638,106646],{},[895,106639,106640,106642,106644],{},[898,106641,207],{},[1654,106643,3002],{},[1665,106645,2062],{},[902,106647,51305],{"encoding":904},") a lineární nabídku ",[883,106650,106652],{"className":106651},[886],[888,106653,106654],{"xmlns":890},[892,106655,106656,106670],{},[895,106657,106658,106660,106662,106664,106666,106668],{},[898,106659,1755],{},[1654,106661,1750],{},[898,106663,3624],{},[898,106665,1663],{},[1654,106667,1766],{},[898,106669,10977],{},[902,106671,48462],{"encoding":904},[883,106673,106675],{"className":106674},[886],[888,106676,106677],{"xmlns":890},[892,106678,106679,106687],{},[895,106680,106681,106683,106685],{},[898,106682,3624],{},[1654,106684,2952],{},[1665,106686,2062],{},[902,106688,48480],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,106691,106693],{"className":106692},[886],[888,106694,106695],{"xmlns":890,"display":1956},[892,106696,106697,106763],{},[895,106698,106699,106723,106725,106735,106737,106761],{},[2811,106700,106701,106711],{},[1710,106702,106703,106705],{},[898,106704,11536],{},[895,106706,106707,106709],{},[898,106708,50897],{},[898,106710,724],{},[1710,106712,106713,106715],{},[898,106714,11536],{},[895,106716,106717,106719,106721],{},[898,106718,50920],{},[898,106720,10789],{},[898,106722,20753],{},[1654,106724,1750],{},[2811,106726,106727,106729],{},[898,106728,3624],{},[895,106730,106731,106733],{},[1654,106732,2380],{},[898,106734,207],{},[1654,106736,1750],{},[2811,106738,106739,106751],{},[895,106740,106741,106744,106747,106749],{},[898,106742,106743],{"mathvariant":1878},"∣",[1865,106745,106746],{},"sklon ",[898,106748,17398],{},[898,106750,106743],{"mathvariant":1878},[895,106752,106753,106755,106757,106759],{},[898,106754,106743],{"mathvariant":1878},[1865,106756,106746],{},[898,106758,4980],{},[898,106760,106743],{"mathvariant":1878},[898,106762,2138],{"mathvariant":1878},[902,106764,106765],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[2140,106767,106768,106773],{},[724,106769,106770,106772],{},[883,106771,3111],{}," Postup výpočtu rozkladu",[152,106774,106775,106810,106863,106942],{},[123,106776,106777,106778,106809],{},"Spočti rovnovážný bod ",[883,106779,106781],{"className":106780},[886],[888,106782,106783],{"xmlns":890},[892,106784,106785,106807],{},[895,106786,106787,106789,106791,106797,106799,106805],{},[898,106788,1798],{},[1654,106790,1657],{"stretchy":1656},[1741,106792,106793,106795],{},[898,106794,1663],{},[898,106796,1798],{},[1654,106798,1674],{"separator":1673},[1741,106800,106801,106803],{},[898,106802,1755],{},[898,106804,1798],{},[1654,106806,1686],{"stretchy":1656},[902,106808,49587],{"encoding":904}," bez daně.",[123,106811,106812,106813,1348,106838,12664],{},"Urči posunutou křivku (",[883,106814,106816],{"className":106815},[886],[888,106817,106818],{"xmlns":890},[892,106819,106820,106836],{},[895,106821,106822,106828,106830,106832,106834],{},[1710,106823,106824,106826],{},[898,106825,17398],{},[1665,106827,1667],{},[1654,106829,1750],{},[898,106831,17398],{},[1654,106833,1766],{},[898,106835,11536],{},[902,106837,50974],{"encoding":904},[883,106839,106841],{"className":106840},[886],[888,106842,106843],{"xmlns":890},[892,106844,106845,106861],{},[895,106846,106847,106853,106855,106857,106859],{},[1710,106848,106849,106851],{},[898,106850,4980],{},[1665,106852,1681],{},[1654,106854,1750],{},[898,106856,4980],{},[1654,106858,2380],{},[898,106860,11536],{},[902,106862,51005],{"encoding":904},[123,106864,106865,106866,12656,106885,20840,106904,12656,106923,12664],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,106867,106869],{"className":106868},[886],[888,106870,106871],{"xmlns":890},[892,106872,106873,106883],{},[895,106874,106875],{},[1659,106876,106877,106879,106881],{},[898,106878,1663],{},[1665,106880,1667],{},[898,106882,1798],{},[902,106884,56056],{"encoding":904},[883,106886,106888],{"className":106887},[886],[888,106889,106890],{"xmlns":890},[892,106891,106892,106902],{},[895,106893,106894],{},[1659,106895,106896,106898,106900],{},[898,106897,1663],{},[1665,106899,1681],{},[898,106901,1798],{},[902,106903,56118],{"encoding":904},[883,106905,106907],{"className":106906},[886],[888,106908,106909],{"xmlns":890},[892,106910,106911,106921],{},[895,106912,106913],{},[1659,106914,106915,106917,106919],{},[898,106916,1755],{},[1665,106918,1667],{},[898,106920,1798],{},[902,106922,56077],{"encoding":904},[883,106924,106926],{"className":106925},[886],[888,106927,106928],{"xmlns":890},[892,106929,106930,106940],{},[895,106931,106932],{},[1659,106933,106934,106936,106938],{},[898,106935,1755],{},[1665,106937,1681],{},[898,106939,1798],{},[902,106941,56138],{"encoding":904},[123,106943,106944,106945,2068,106966,106989,106990,2138],{},"Dopočítej ",[883,106946,106948],{"className":106947},[886],[888,106949,106950],{"xmlns":890},[892,106951,106952,106964],{},[895,106953,106954],{},[1710,106955,106956,106958],{},[898,106957,11536],{},[895,106959,106960,106962],{},[898,106961,50897],{},[898,106963,724],{},[902,106965,50902],{"encoding":904},[883,106967,106969],{"className":106968},[886],[888,106970,106971],{"xmlns":890},[892,106972,106973,106987],{},[895,106974,106975],{},[1710,106976,106977,106979],{},[898,106978,11536],{},[895,106980,106981,106983,106985],{},[898,106982,50920],{},[898,106984,10789],{},[898,106986,20753],{},[902,106988,50927],{"encoding":904}," z definice, vždy ověř ",[883,106991,106993],{"className":106992},[886],[888,106994,106995],{"xmlns":890},[892,106996,106997,107027],{},[895,106998,106999,107009,107011,107023,107025],{},[1710,107000,107001,107003],{},[898,107002,11536],{},[895,107004,107005,107007],{},[898,107006,50897],{},[898,107008,724],{},[1654,107010,1766],{},[1710,107012,107013,107015],{},[898,107014,11536],{},[895,107016,107017,107019,107021],{},[898,107018,50920],{},[898,107020,10789],{},[898,107022,20753],{},[1654,107024,1750],{},[898,107026,11536],{},[902,107028,107029],{"encoding":904},"T_{sp} + T_{vyr} = T",[2140,107031,107032],{},[724,107033,107034,107036,107037,107040,107041,2068,107054,107067],{},[883,107035,2146],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,107038,107039],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,107042,107044],{"className":107043},[886],[888,107045,107046],{"xmlns":890},[892,107047,107048,107052],{},[895,107049,107050],{},[898,107051,4980],{},[902,107053,4980],{"encoding":904},[883,107055,107057],{"className":107056},[886],[888,107058,107059],{"xmlns":890},[892,107060,107061,107065],{},[895,107062,107063],{},[898,107064,17398],{},[902,107066,17398],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[45190,107069],{},[115,107071,107073],{"id":107072},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,107075,107076],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,107078,107079],{},[3492,107080],{"alt":107081,"className":107082,"src":107083},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,3496],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,107085,107086,107098],{},[19,107087,107088],{},[22,107089,107090,107092,107095],{},[25,107091,62516],{},[25,107093,107094],{},"(a) daň výrobci",[25,107096,107097],{},"(b) daň spotřebiteli",[30,107099,107100,107155,107222,107282],{},[22,107101,107102,107105,107130],{},[35,107103,107104],{},"Rovnovážné množství",[35,107106,107107],{},[883,107108,107110],{"className":107109},[886],[888,107111,107112],{"xmlns":890},[892,107113,107114,107128],{},[895,107115,107116,107124,107126],{},[1659,107117,107118,107120,107122],{},[898,107119,1663],{},[1665,107121,1667],{},[898,107123,1798],{},[1654,107125,1750],{},[1665,107127,1667],{},[902,107129,104946],{"encoding":904},[35,107131,107132],{},[883,107133,107135],{"className":107134},[886],[888,107136,107137],{"xmlns":890},[892,107138,107139,107153],{},[895,107140,107141,107149,107151],{},[1659,107142,107143,107145,107147],{},[898,107144,1663],{},[1665,107146,1681],{},[898,107148,1798],{},[1654,107150,1750],{},[1665,107152,1667],{},[902,107154,105979],{"encoding":904},[22,107156,107157,107160,107185],{},[35,107158,107159],{},"Cena placená spotřebitelem",[35,107161,107162],{},[883,107163,107165],{"className":107164},[886],[888,107166,107167],{"xmlns":890},[892,107168,107169,107183],{},[895,107170,107171,107179,107181],{},[1659,107172,107173,107175,107177],{},[898,107174,1755],{},[1665,107176,1667],{},[898,107178,1798],{},[1654,107180,1750],{},[1665,107182,4647],{},[902,107184,105041],{"encoding":904},[35,107186,107187],{},[883,107188,107190],{"className":107189},[886],[888,107191,107192],{"xmlns":890},[892,107193,107194,107220],{},[895,107195,107196,107204,107206,107208,107210,107212,107214,107216,107218],{},[1659,107197,107198,107200,107202],{},[898,107199,1755],{},[1665,107201,1681],{},[898,107203,1798],{},[1654,107205,1766],{},[898,107207,11536],{},[1654,107209,1750],{},[1665,107211,7631],{},[1654,107213,1766],{},[1665,107215,11015],{},[1654,107217,1750],{},[1665,107219,4647],{},[902,107221,106078],{"encoding":904},[22,107223,107224,107227,107257],{},[35,107225,107226],{},"Cena přijímaná výrobcem",[35,107228,107229],{},[883,107230,107232],{"className":107231},[886],[888,107233,107234],{"xmlns":890},[892,107235,107236,107254],{},[895,107237,107238,107246,107248,107250,107252],{},[1659,107239,107240,107242,107244],{},[898,107241,1755],{},[1665,107243,1667],{},[898,107245,1798],{},[1654,107247,2380],{},[898,107249,11536],{},[1654,107251,1750],{},[1665,107253,7631],{},[902,107255,107256],{"encoding":904},"P_1^E - T = 4",[35,107258,107259],{},[883,107260,107262],{"className":107261},[886],[888,107263,107264],{"xmlns":890},[892,107265,107266,107280],{},[895,107267,107268,107276,107278],{},[1659,107269,107270,107272,107274],{},[898,107271,1755],{},[1665,107273,1681],{},[898,107275,1798],{},[1654,107277,1750],{},[1665,107279,7631],{},[902,107281,106103],{"encoding":904},[22,107283,107284,107287,107341],{},[35,107285,107286],{},"Rozklad břemene",[35,107288,107289,1343,107314],{},[883,107290,107292],{"className":107291},[886],[888,107293,107294],{"xmlns":890},[892,107295,107296,107312],{},[895,107297,107298,107308,107310],{},[1710,107299,107300,107302],{},[898,107301,11536],{},[895,107303,107304,107306],{},[898,107305,50897],{},[898,107307,724],{},[1654,107309,1750],{},[1665,107311,1681],{},[902,107313,51196],{"encoding":904},[883,107315,107317],{"className":107316},[886],[888,107318,107319],{"xmlns":890},[892,107320,107321,107339],{},[895,107322,107323,107335,107337],{},[1710,107324,107325,107327],{},[898,107326,11536],{},[895,107328,107329,107331,107333],{},[898,107330,50920],{},[898,107332,10789],{},[898,107334,20753],{},[1654,107336,1750],{},[1665,107338,7631],{},[902,107340,51225],{"encoding":904},[35,107342,107343,1343,107368],{},[883,107344,107346],{"className":107345},[886],[888,107347,107348],{"xmlns":890},[892,107349,107350,107366],{},[895,107351,107352,107362,107364],{},[1710,107353,107354,107356],{},[898,107355,11536],{},[895,107357,107358,107360],{},[898,107359,50897],{},[898,107361,724],{},[1654,107363,1750],{},[1665,107365,1681],{},[902,107367,51196],{"encoding":904},[883,107369,107371],{"className":107370},[886],[888,107372,107373],{"xmlns":890},[892,107374,107375,107393],{},[895,107376,107377,107389,107391],{},[1710,107378,107379,107381],{},[898,107380,11536],{},[895,107382,107383,107385,107387],{},[898,107384,50920],{},[898,107386,10789],{},[898,107388,20753],{},[1654,107390,1750],{},[1665,107392,7631],{},[902,107394,51225],{"encoding":904},[724,107396,107397],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,107399,107401],{"className":107400},[886],[888,107402,107403],{"xmlns":890,"display":1956},[892,107404,107405,107453],{},[895,107406,107407,107415,107417,107425,107427,107429,107437,107439,107441,107443,107451],{},[1659,107408,107409,107411,107413],{},[898,107410,1663],{},[1665,107412,1667],{},[898,107414,1798],{},[1654,107416,1750],{},[1659,107418,107419,107421,107423],{},[898,107420,1663],{},[1665,107422,1681],{},[898,107424,1798],{},[1654,107426,1674],{"separator":1673},[5008,107428],{"width":14608},[1659,107430,107431,107433,107435],{},[898,107432,1755],{},[1665,107434,1667],{},[898,107436,1798],{},[1654,107438,2380],{},[898,107440,11536],{},[1654,107442,1750],{},[1659,107444,107445,107447,107449],{},[898,107446,1755],{},[1665,107448,1681],{},[898,107450,1798],{},[898,107452,2138],{"mathvariant":1878},[902,107454,107455],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[2140,107457,107458,107477,107631],{},[724,107459,107460,107462,107463,107476],{},[883,107461,3111],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,107464,107466],{"className":107465},[886],[888,107467,107468],{"xmlns":890},[892,107469,107470,107474],{},[895,107471,107472],{},[898,107473,11536],{},[902,107475,11536],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,107478,107479,107511,107547,107584],{},[123,107480,107481,107482,1674],{},"rovnovážná množství obou režimů, ",[883,107483,107485],{"className":107484},[886],[888,107486,107487],{"xmlns":890},[892,107488,107489,107509],{},[895,107490,107491,107499,107501],{},[1659,107492,107493,107495,107497],{},[898,107494,1663],{},[1665,107496,1667],{},[898,107498,1798],{},[1654,107500,1750],{},[1659,107502,107503,107505,107507],{},[898,107504,1663],{},[1665,107506,1681],{},[898,107508,1798],{},[902,107510,51128],{"encoding":904},[123,107512,107513,107514,1674],{},"čistá cena přijímaná výrobcem, ",[883,107515,107517],{"className":107516},[886],[888,107518,107519],{"xmlns":890},[892,107520,107521,107545],{},[895,107522,107523,107531,107533,107535,107537],{},[1659,107524,107525,107527,107529],{},[898,107526,1755],{},[1665,107528,1667],{},[898,107530,1798],{},[1654,107532,2380],{},[898,107534,11536],{},[1654,107536,1750],{},[1659,107538,107539,107541,107543],{},[898,107540,1755],{},[1665,107542,1681],{},[898,107544,1798],{},[902,107546,51162],{"encoding":904},[123,107548,107549,107550,1674],{},"celková cena placená spotřebitelem, ",[883,107551,107553],{"className":107552},[886],[888,107554,107555],{"xmlns":890},[892,107556,107557,107581],{},[895,107558,107559,107567,107569,107577,107579],{},[1659,107560,107561,107563,107565],{},[898,107562,1755],{},[1665,107564,1667],{},[898,107566,1798],{},[1654,107568,1750],{},[1659,107570,107571,107573,107575],{},[898,107572,1755],{},[1665,107574,1681],{},[898,107576,1798],{},[1654,107578,1766],{},[898,107580,11536],{},[902,107582,107583],{"encoding":904},"P_1^E = P_2^E + T",[123,107585,107586,107587,2068,107608,2138],{},"rozklad daňového břemene ",[883,107588,107590],{"className":107589},[886],[888,107591,107592],{"xmlns":890},[892,107593,107594,107606],{},[895,107595,107596],{},[1710,107597,107598,107600],{},[898,107599,11536],{},[895,107601,107602,107604],{},[898,107603,50897],{},[898,107605,724],{},[902,107607,50902],{"encoding":904},[883,107609,107611],{"className":107610},[886],[888,107612,107613],{"xmlns":890},[892,107614,107615,107629],{},[895,107616,107617],{},[1710,107618,107619,107621],{},[898,107620,11536],{},[895,107622,107623,107625,107627],{},[898,107624,50920],{},[898,107626,10789],{},[898,107628,20753],{},[902,107630,50927],{"encoding":904},[724,107632,107633,107634,2138],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,107635,9152],{},[724,107637,107638,107639,2068,107652,12664],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,107640,107642],{"className":107641},[886],[888,107643,107644],{"xmlns":890},[892,107645,107646,107650],{},[895,107647,107648],{},[898,107649,4980],{},[902,107651,4980],{"encoding":904},[883,107653,107655],{"className":107654},[886],[888,107656,107657],{"xmlns":890},[892,107658,107659,107663],{},[895,107660,107661],{},[898,107662,17398],{},[902,107664,17398],{"encoding":904},[45190,107666],{},[115,107668,107670],{"id":107669},"úlohy","Úlohy",[724,107672,107673,107674,11906],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,107675,24943],{"className":107676,"dataFsResolvedFilePath":800,"href":801},[210],[120,107678,107679,107709,107740],{},[123,107680,107681,107684,107685,107708],{},[38,107682,107683],{},"Úloha 2.4"," — Poptávka ",[883,107686,107688],{"className":107687},[886],[888,107689,107690],{"xmlns":890},[892,107691,107692,107706],{},[895,107693,107694,107696,107698,107700,107702,107704],{},[898,107695,1755],{},[1654,107697,1750],{},[1665,107699,6509],{},[1654,107701,2380],{},[1665,107703,1681],{},[898,107705,1663],{},[902,107707,104658],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,107710,107711,107714,107715,107739],{},[38,107712,107713],{},"Úloha 2.9"," — Nabídka ",[883,107716,107718],{"className":107717},[886],[888,107719,107720],{"xmlns":890},[892,107721,107722,107736],{},[895,107723,107724,107726,107728,107730,107732,107734],{},[898,107725,1755],{},[1654,107727,1750],{},[1665,107729,7594],{},[898,107731,1663],{},[1654,107733,1766],{},[1665,107735,10207],{},[902,107737,107738],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,107741,107742,107745,107746,2068,107772,107796,107797,107814],{},[38,107743,107744],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,107747,107749],{"className":107748},[886],[888,107750,107751],{"xmlns":890},[892,107752,107753,107769],{},[895,107754,107755,107757,107759,107761,107763,107765,107767],{},[898,107756,1755],{},[1654,107758,1750],{},[1654,107760,2380],{},[1665,107762,7631],{},[898,107764,1663],{},[1654,107766,1766],{},[1665,107768,54923],{},[902,107770,107771],{"encoding":904},"P = -4Q + 80",[883,107773,107775],{"className":107774},[886],[888,107776,107777],{"xmlns":890},[892,107778,107779,107793],{},[895,107780,107781,107783,107785,107787,107789,107791],{},[898,107782,1755],{},[1654,107784,1750],{},[1665,107786,4035],{},[898,107788,1663],{},[1654,107790,1766],{},[1665,107792,4647],{},[902,107794,107795],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,107798,107800],{"className":107799},[886],[888,107801,107802],{"xmlns":890},[892,107803,107804,107812],{},[895,107805,107806,107808,107810],{},[898,107807,11536],{},[1654,107809,1750],{},[1665,107811,32887],{},[902,107813,56035],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,107816,107817,107818,107820,107821,107823],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,107819,53448],{}," (posun poptávky při zdanění kupujícího) a ",[38,107822,53482],{}," (posun nabídky při zdanění výrobce).",[45190,107825],{},[115,107827,10214],{"id":10213},[120,107829,107830,107849,107907,107964,108047,108093,108136,108181,108247],{},[123,107831,107832,2186,107835,107848],{},[38,107833,107834],{},"Jednotková daň",[883,107836,107838],{"className":107837},[886],[888,107839,107840],{"xmlns":890},[892,107841,107842,107846],{},[895,107843,107844],{},[898,107845,11536],{},[902,107847,11536],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,107850,107851,107853,107854,107892,107893,107906],{},[38,107852,104240],{}," — posun nabídky ",[883,107855,107857],{"className":107856},[886],[888,107858,107859],{"xmlns":890},[892,107860,107861,107889],{},[895,107862,107863,107869,107871,107873,107875,107877,107879,107881,107883,107885,107887],{},[1710,107864,107865,107867],{},[898,107866,17398],{},[1665,107868,1667],{},[1654,107870,1708],{"stretchy":1656},[898,107872,1663],{},[1654,107874,1726],{"stretchy":1656},[1654,107876,1750],{},[898,107878,17398],{},[1654,107880,1708],{"stretchy":1656},[898,107882,1663],{},[1654,107884,1726],{"stretchy":1656},[1654,107886,1766],{},[898,107888,11536],{},[902,107890,107891],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,107894,107896],{"className":107895},[886],[888,107897,107898],{"xmlns":890},[892,107899,107900,107904],{},[895,107901,107902],{},[898,107903,11536],{},[902,107905,11536],{"encoding":904}," svisle nahoru)",[123,107908,107909,107911,107912,107892,107950,107963],{},[38,107910,105313],{}," — posun poptávky ",[883,107913,107915],{"className":107914},[886],[888,107916,107917],{"xmlns":890},[892,107918,107919,107947],{},[895,107920,107921,107927,107929,107931,107933,107935,107937,107939,107941,107943,107945],{},[1710,107922,107923,107925],{},[898,107924,4980],{},[1665,107926,1681],{},[1654,107928,1708],{"stretchy":1656},[898,107930,1663],{},[1654,107932,1726],{"stretchy":1656},[1654,107934,1750],{},[898,107936,4980],{},[1654,107938,1708],{"stretchy":1656},[898,107940,1663],{},[1654,107942,1726],{"stretchy":1656},[1654,107944,2380],{},[898,107946,11536],{},[902,107948,107949],{"encoding":904},"D_2(Q) = D(Q) - T",[883,107951,107953],{"className":107952},[886],[888,107954,107955],{"xmlns":890},[892,107956,107957,107961],{},[895,107958,107959],{},[898,107960,11536],{},[902,107962,11536],{"encoding":904}," svisle dolů)",[123,107965,107966,10373,107969,50034,108008],{},[38,107967,107968],{},"Rovnovážný bod s daní",[883,107970,107972],{"className":107971},[886],[888,107973,107974],{"xmlns":890},[892,107975,107976,108006],{},[895,107977,107978,107984,107986,107994,107996,108004],{},[1710,107979,107980,107982],{},[898,107981,1798],{},[1665,107983,1667],{},[1654,107985,1657],{"stretchy":1656},[1659,107987,107988,107990,107992],{},[898,107989,1663],{},[1665,107991,1667],{},[898,107993,1798],{},[1654,107995,1674],{"separator":1673},[1659,107997,107998,108000,108002],{},[898,107999,1755],{},[1665,108001,1667],{},[898,108003,1798],{},[1654,108005,1686],{"stretchy":1656},[902,108007,104408],{"encoding":904},[883,108009,108011],{"className":108010},[886],[888,108012,108013],{"xmlns":890},[892,108014,108015,108045],{},[895,108016,108017,108023,108025,108033,108035,108043],{},[1710,108018,108019,108021],{},[898,108020,1798],{},[1665,108022,1681],{},[1654,108024,1657],{"stretchy":1656},[1659,108026,108027,108029,108031],{},[898,108028,1663],{},[1665,108030,1681],{},[898,108032,1798],{},[1654,108034,1674],{"separator":1673},[1659,108036,108037,108039,108041],{},[898,108038,1755],{},[1665,108040,1681],{},[898,108042,1798],{},[1654,108044,1686],{"stretchy":1656},[902,108046,105483],{"encoding":904},[123,108048,108049,18742,108051,108053,108054],{},[38,108050,50878],{},[614,108052,106263],{},") — rozklad ",[883,108055,108057],{"className":108056},[886],[888,108058,108059],{"xmlns":890},[892,108060,108061,108091],{},[895,108062,108063,108065,108067,108077,108079],{},[898,108064,11536],{},[1654,108066,1750],{},[1710,108068,108069,108071],{},[898,108070,11536],{},[895,108072,108073,108075],{},[898,108074,50897],{},[898,108076,724],{},[1654,108078,1766],{},[1710,108080,108081,108083],{},[898,108082,11536],{},[895,108084,108085,108087,108089],{},[898,108086,50920],{},[898,108088,10789],{},[898,108090,20753],{},[902,108092,51064],{"encoding":904},[123,108094,108095,108118,108119,1726],{},[38,108096,108097],{},[883,108098,108100],{"className":108099},[886],[888,108101,108102],{"xmlns":890},[892,108103,108104,108116],{},[895,108105,108106],{},[1710,108107,108108,108110],{},[898,108109,11536],{},[895,108111,108112,108114],{},[898,108113,50897],{},[898,108115,724],{},[902,108117,50902],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,108120,108122],{"className":108121},[886],[888,108123,108124],{"xmlns":890},[892,108125,108126,108134],{},[895,108127,108128],{},[1741,108129,108130,108132],{},[898,108131,1755],{},[898,108133,1798],{},[902,108135,49686],{"encoding":904},[123,108137,108138,108163,108164,1726],{},[38,108139,108140],{},[883,108141,108143],{"className":108142},[886],[888,108144,108145],{"xmlns":890},[892,108146,108147,108161],{},[895,108148,108149],{},[1710,108150,108151,108153],{},[898,108152,11536],{},[895,108154,108155,108157,108159],{},[898,108156,50920],{},[898,108158,10789],{},[898,108160,20753],{},[902,108162,50927],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,108165,108167],{"className":108166},[886],[888,108168,108169],{"xmlns":890},[892,108170,108171,108179],{},[895,108172,108173],{},[1741,108174,108175,108177],{},[898,108176,1755],{},[898,108178,1798],{},[902,108180,49686],{"encoding":904},[123,108182,108183,10373,108185,1343,108214],{},[38,108184,58694],{},[883,108186,108188],{"className":108187},[886],[888,108189,108190],{"xmlns":890},[892,108191,108192,108212],{},[895,108193,108194,108202,108204],{},[1659,108195,108196,108198,108200],{},[898,108197,1663],{},[1665,108199,1667],{},[898,108201,1798],{},[1654,108203,1750],{},[1659,108205,108206,108208,108210],{},[898,108207,1663],{},[1665,108209,1681],{},[898,108211,1798],{},[902,108213,51128],{"encoding":904},[883,108215,108217],{"className":108216},[886],[888,108218,108219],{"xmlns":890},[892,108220,108221,108245],{},[895,108222,108223,108231,108233,108235,108237],{},[1659,108224,108225,108227,108229],{},[898,108226,1755],{},[1665,108228,1667],{},[898,108230,1798],{},[1654,108232,2380],{},[898,108234,11536],{},[1654,108236,1750],{},[1659,108238,108239,108241,108243],{},[898,108240,1755],{},[1665,108242,1681],{},[898,108244,1798],{},[902,108246,51162],{"encoding":904},[123,108248,108249,108252],{},[38,108250,108251],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[45190,108254],{},[115,108256,10613],{"id":10612},[120,108258,108259,108267,108285,108292],{},[123,108260,108261,2186,108264],{},[38,108262,108263],{},"Kontext (hub):",[207,108265,802],{"className":108266,"dataFsResolvedFilePath":800,"href":801},[210],[123,108268,108269,2186,108271,108274,108275,27344,108277,108280,108281,108284],{},[38,108270,58943],{},[207,108272,820],{"className":108273,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,108276,63254],{},[207,108278,10655],{"className":108279,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,108282,12575],{"className":108283,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[123,108286,108287,2186,108289],{},[38,108288,58978],{},[207,108290,58982],{"className":108291,"dataFsResolvedFilePath":745,"href":746},[210],[123,108293,108294,2186,108296],{},[38,108295,10686],{},[207,108297,10692],{"className":108298,"dataFsResolvedFilePath":10690,"href":10691},[210],{"title":641,"searchDepth":642,"depth":642,"links":108300},[108301,108302,108305,108308,108312,108313,108314,108315],{"id":104145,"depth":642,"text":104146},{"id":104239,"depth":642,"text":104240,"children":108303},[108304],{"id":104630,"depth":649,"text":53523},{"id":105312,"depth":642,"text":105313,"children":108306},[108307],{"id":105789,"depth":649,"text":53603},{"id":106256,"depth":642,"text":50878,"children":108309},[108310,108311],{"id":11210,"depth":649,"text":11211},{"id":106599,"depth":649,"text":106600},{"id":107072,"depth":642,"text":107073},{"id":107669,"depth":642,"text":107670},{"id":10213,"depth":642,"text":10214},{"id":10612,"depth":642,"text":10613},{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":104043,"description":641},[1138,1135],"topics\u002Fzdaneni-trhu",[1128,59043,108322,108323,108324,24943],"dane","danove-bremeno","posun-krivek","cFuKqHgzIrqvY-l4jNdqjFEM7_ixjw33HOL0So8cPn0",[108327,108329,108333],{"slug":1128,"path":10691,"title":681,"snippet":108328},"… |Užitečnost]] — pojem, mezní užitečnost, Cobb-Douglasova $U$, indiferenční křivky, MRCS - \u003C\u003Coptimalizace-spotrebitele>> — Lagrangeova maximalizace $U$, duální minimalizace výdajů, Marshallova\u002FHicksova poptávka …",{"slug":108330,"path":959,"title":108331,"snippet":108332},"imek-vzorce-prehled","ImeK — kompletní přehled vzorců se zdroji a intuicí","… ukce|MRTS]] z teorie produkce. --- ## 10. Optimalizace spotřebitele **Základní téma:** \u003C\u003Coptimalizace-spotrebitele>> ### Rozpočtové omezení $$Y = P_1 Q_1 + P_2 Q_2$$ **Původ:** identita (vzorec 6.12) — v …",{"slug":10732,"path":879,"title":94796,"snippet":108334},"… potřebitele** (max $U$ při rozpočtu, min $E$ při dané $U$, Lagrange, funkce poptávky) viz \u003C\u003Coptimalizace-spotrebitele>>. Kapitola 6 knihy *Matematická ekonomie* — model rozhodování spotřebitele. Zde: funkce u …",[108336,108338,108341],{"slug":24920,"title":108337,"path":869,"sharedTags":649},"KS 3. blok — Užitečnost a národní důchod",{"slug":108339,"title":108340,"path":746,"sharedTags":642},"imek-blok-01","KS 1. blok — Kalkul a mikroekonomie",{"slug":10732,"title":94796,"path":879,"sharedTags":642},1777154967961]