[{"data":1,"prerenderedAt":100108},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-imek":1626,"course-stats-imek":1910,"backlinks-imek":1914,"course-topics-imek":1946},{"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 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Bez derivace se neobejdou **mezní veličiny** (mezní náklady, mezní příjem, mezní užitečn …",{"slug":1919,"path":849,"title":1920,"snippet":1921},"elasticita","Elasticita poptávky a nabídky","… [derivace|Derivace]] - **Přednáška:** ImeK — souhrn 2. bloku - **Kurz:** \u003C\u003Cimek>>",{"slug":1923,"path":746,"title":1924,"snippet":1925},"imek-blok-01","KS 1. blok — Kalkul a mikroekonomie","… [lagrangeova-metoda|Lagrange]] a 2D kalkul. ## Související - \u003C\u003Cimek>> - KS 2. blok — Elasticita a produkce - KS 3. blok — Uži …",{"slug":1927,"path":839,"title":1928,"snippet":1929},"imek-blok-02","KS 2. blok — Elasticita a produkce","… 3|KS 3. blok]] — užitečnost (paralela izokvanty ↔ indiferenční křivky) ## Související - \u003C\u003Cimek>>",{"slug":1931,"path":869,"title":1932,"snippet":1933},"imek-blok-03","KS 3. blok — Užitečnost a národní důchod","… nge]], 2D kalkul z Bloku 1 ## Související - \u003C\u003Cimek>>",{"slug":1935,"path":1080,"title":1936,"snippet":1937},"imek-detail-predmetu","Matematická ekonomie — Detail předmětu","# Matematická ekonomie — Detail předmětu Viz \u003C\u003Cimek>>. ## Administrativa | Atribut | Hodnota | | --- | --- | | Zkratka | ImeK | | Fakulta | F …",{"slug":1939,"path":1109,"title":1940,"snippet":1941},"imek-kniha","Kniha — *Úvod do matematické ekonomie pro ekonomy*","# Kniha — *Úvod do matematické ekonomie pro ekonomy* Doporučená literatura k předmětu \u003C\u003Cimek>>, autor **I. 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Studentské naskenované foto …",{"slug":1943,"path":959,"title":1944,"snippet":1945},"imek-vzorce-prehled","ImeK — kompletní přehled vzorců se zdroji a intuicí","… roji a intuicí > [!abstract] TL;DR > Referenční přehled **všech klíčových vzorců** kurzu \u003C\u003Cimek>> v **základním (definičním) tvaru** — od poptávky a nabídky přes optimalizaci firmy a spot …",[1947,3859,9568,11125,11997,16280,17887,27767,36761,50828,55120,74464,86576,95535,95823],{"id":1948,"title":1916,"body":1949,"course":1128,"courses":659,"created":1129,"description":3847,"extension":661,"meta":3848,"navigation":664,"path":3849,"seo":3850,"sources":3851,"stem":3852,"tags":3853,"type":3857,"updated":677,"__hash__":3858},"topics\u002Ftopics\u002Fderivace.md",{"type":9,"value":1950,"toc":3830},[1951,1954,1976,1980,2064,2067,2198,2355,2358,2441,2445,2506,2556,2565,2569,2705,2756,2760,2804,2873,2944,2952,2956,2995,3067,3071,3152,3201,3245,3249,3253,3323,3327,3377,3456,3463,3466,3519,3789,3793],[12,1952,1916],{"id":1953},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,1955,1956,1957,1963,1964,1967,1968,1971,1972,1975],{},"Matematický aparát kurzu ",[207,1958,1962],{"className":1959,"dataFsResolvedFilePath":1960,"href":1961},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","ImeK",". Bez derivace se neobejdou ",[38,1965,1966],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,1969,1970],{},"maximalizace zisku"," ani ",[38,1973,1974],{},"minimalizace nákladů",".",[115,1977,1979],{"id":1978},"funkce-a-polynomy","Funkce a polynomy",[724,1981,1982,1983,2015,2016,2029,2030,2043,2044,1975],{},"Funkce jedné proměnné ",[883,1984,1986],{"className":1985},[886],[888,1987,1988],{"xmlns":890},[892,1989,1990,2012],{},[895,1991,1992,1995,1999,2002,2006,2009],{},[898,1993,1994],{},"y",[1996,1997,1998],"mo",{},"=",[898,2000,2001],{},"f",[1996,2003,2005],{"stretchy":2004},"false","(",[898,2007,2008],{},"x",[1996,2010,2011],{"stretchy":2004},")",[902,2013,2014],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,2017,2019],{"className":2018},[886],[888,2020,2021],{"xmlns":890},[892,2022,2023,2027],{},[895,2024,2025],{},[898,2026,2008],{},[902,2028,2008],{"encoding":904}," (nezávislá) → ",[883,2031,2033],{"className":2032},[886],[888,2034,2035],{"xmlns":890},[892,2036,2037,2041],{},[895,2038,2039],{},[898,2040,1994],{},[902,2042,1994],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,2045,2047],{"className":2046},[886],[888,2048,2049],{"xmlns":890},[892,2050,2051,2061],{},[895,2052,2053,2055,2057,2059],{},[898,2054,2001],{},[1996,2056,2005],{"stretchy":2004},[898,2058,207],{},[1996,2060,2011],{"stretchy":2004},[902,2062,2063],{"encoding":904},"f(a)",[724,2065,2066],{},"Polynomy:",[120,2068,2069,2102,2146],{},[123,2070,2071],{},[152,2072,2073],{},[123,2074,2075,2076],{},"stupně: ",[883,2077,2079],{"className":2078},[886],[888,2080,2081],{"xmlns":890},[892,2082,2083,2099],{},[895,2084,2085,2087,2089,2091,2093,2096],{},[898,2086,1994],{},[1996,2088,1998],{},[898,2090,207],{},[898,2092,2008],{},[1996,2094,2095],{},"+",[898,2097,2098],{},"b",[902,2100,2101],{"encoding":904},"y = ax + b",[123,2103,2104],{},[152,2105,2106],{"start":642},[123,2107,2075,2108],{},[883,2109,2111],{"className":2110},[886],[888,2112,2113],{"xmlns":890},[892,2114,2115,2143],{},[895,2116,2117,2119,2121,2123,2132,2134,2136,2138,2140],{},[898,2118,1994],{},[1996,2120,1998],{},[898,2122,207],{},[2124,2125,2126,2128],"msup",{},[898,2127,2008],{},[2129,2130,2131],"mn",{},"2",[1996,2133,2095],{},[898,2135,2098],{},[898,2137,2008],{},[1996,2139,2095],{},[898,2141,2142],{},"c",[902,2144,2145],{"encoding":904},"y = ax^2 + bx + c",[123,2147,2148],{},[152,2149,2150],{"start":649},[123,2151,2075,2152],{},[883,2153,2155],{"className":2154},[886],[888,2156,2157],{"xmlns":890},[892,2158,2159,2195],{},[895,2160,2161,2163,2165,2167,2174,2176,2178,2184,2186,2188,2190,2192],{},[898,2162,1994],{},[1996,2164,1998],{},[898,2166,207],{},[2124,2168,2169,2171],{},[898,2170,2008],{},[2129,2172,2173],{},"3",[1996,2175,2095],{},[898,2177,2098],{},[2124,2179,2180,2182],{},[898,2181,2008],{},[2129,2183,2131],{},[1996,2185,2095],{},[898,2187,2142],{},[898,2189,2008],{},[1996,2191,2095],{},[898,2193,2194],{},"d",[902,2196,2197],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,2199,2200,2203,2204,2261,2262,2304,2305,1975],{},[38,2201,2202],{},"Příklad rozkladu:"," ",[883,2205,2207],{"className":2206},[886],[888,2208,2209],{"xmlns":890},[892,2210,2211,2258],{},[895,2212,2213,2215,2217,2223,2226,2229,2231,2233,2236,2238,2240,2242,2244,2246,2248,2250,2252,2254,2256],{},[898,2214,1994],{},[1996,2216,1998],{},[2124,2218,2219,2221],{},[898,2220,2008],{},[2129,2222,2131],{},[1996,2224,2225],{},"−",[2129,2227,2228],{},"5",[898,2230,2008],{},[1996,2232,2095],{},[2129,2234,2235],{},"6",[1996,2237,1998],{},[1996,2239,2005],{"stretchy":2004},[898,2241,2008],{},[1996,2243,2225],{},[2129,2245,2131],{},[1996,2247,2011],{"stretchy":2004},[1996,2249,2005],{"stretchy":2004},[898,2251,2008],{},[1996,2253,2225],{},[2129,2255,2173],{},[1996,2257,2011],{"stretchy":2004},[902,2259,2260],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,2263,2265],{"className":2264},[886],[888,2266,2267],{"xmlns":890},[892,2268,2269,2301],{},[895,2270,2271,2279,2281,2283,2287,2291,2297,2299],{},[2272,2273,2274,2276],"msub",{},[898,2275,2008],{},[2129,2277,2278],{},"1",[1996,2280,1998],{},[2129,2282,2131],{},[1996,2284,2286],{"separator":2285},"true",",",[2288,2289,2290],"mtext",{}," ",[2272,2292,2293,2295],{},[898,2294,2008],{},[2129,2296,2131],{},[1996,2298,1998],{},[2129,2300,2173],{},[902,2302,2303],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,2306,2308],{"className":2307},[886],[888,2309,2310],{"xmlns":890},[892,2311,2312,2352],{},[895,2313,2314,2316,2318,2320,2322,2324,2335,2341,2343],{},[898,2315,1994],{},[1996,2317,1998],{},[1996,2319,2005],{"stretchy":2004},[898,2321,2008],{},[1996,2323,2225],{},[2325,2326,2328],"mstyle",{"scriptlevel":2327,"displaystyle":2004},"0",[2329,2330,2331,2333],"mfrac",{},[2129,2332,2228],{},[2129,2334,2131],{},[2124,2336,2337,2339],{},[1996,2338,2011],{"stretchy":2004},[2129,2340,2131],{},[1996,2342,2225],{},[2325,2344,2345],{"scriptlevel":2327,"displaystyle":2004},[2329,2346,2347,2349],{},[2129,2348,2278],{},[2129,2350,2351],{},"4",[902,2353,2354],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,2356,2357],{"id":1145},"Derivace",[724,2359,2360,2361,1348,2388,2416,2417,1975],{},"Označení ",[883,2362,2364],{"className":2363},[886],[888,2365,2366],{"xmlns":890},[892,2367,2368,2385],{},[895,2369,2370,2379,2381,2383],{},[2124,2371,2372,2374],{},[898,2373,2001],{},[1996,2375,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},"normal","0em","′",[1996,2380,2005],{"stretchy":2004},[898,2382,2008],{},[1996,2384,2011],{"stretchy":2004},[902,2386,2387],{"encoding":904},"f'(x)",[883,2389,2391],{"className":2390},[886],[888,2392,2393],{"xmlns":890},[892,2394,2395,2413],{},[895,2396,2397],{},[2325,2398,2399],{"scriptlevel":2327,"displaystyle":2285},[2329,2400,2401,2407],{},[895,2402,2403,2405],{},[898,2404,2194],{},[898,2406,1994],{},[895,2408,2409,2411],{},[898,2410,2194],{},[898,2412,2008],{},[902,2414,2415],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,2418,2420],{"className":2419},[886],[888,2421,2422],{"xmlns":890},[892,2423,2424,2438],{},[895,2425,2426,2432,2434,2436],{},[2124,2427,2428,2430],{},[898,2429,2001],{},[1996,2431,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,2433,2005],{"stretchy":2004},[898,2435,207],{},[1996,2437,2011],{"stretchy":2004},[902,2439,2440],{"encoding":904},"f'(a)",[198,2442,2444],{"id":2443},"geometrická-interpretace","Geometrická interpretace",[724,2446,2447,2470,2471,2474,2475,2505],{},[883,2448,2450],{"className":2449},[886],[888,2451,2452],{"xmlns":890},[892,2453,2454,2468],{},[895,2455,2456,2462,2464,2466],{},[2124,2457,2458,2460],{},[898,2459,2001],{},[1996,2461,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,2463,2005],{"stretchy":2004},[898,2465,207],{},[1996,2467,2011],{"stretchy":2004},[902,2469,2440],{"encoding":904}," = ",[38,2472,2473],{},"sklon tečny"," ke grafu funkce v bodě ",[883,2476,2478],{"className":2477},[886],[888,2479,2480],{"xmlns":890},[892,2481,2482,2502],{},[895,2483,2484,2487,2489,2491,2493,2495,2497,2499],{},[1996,2485,2486],{"stretchy":2004},"[",[898,2488,207],{},[1996,2490,2286],{"separator":2285},[898,2492,2001],{},[1996,2494,2005],{"stretchy":2004},[898,2496,207],{},[1996,2498,2011],{"stretchy":2004},[1996,2500,2501],{"stretchy":2004},"]",[902,2503,2504],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,2507,2508],{},[883,2509,2511],{"className":2510},[886],[888,2512,2513],{"xmlns":890},[892,2514,2515,2553],{},[895,2516,2517,2519,2521,2523,2525,2527,2529,2531,2537,2539,2541,2543,2545,2547,2549,2551],{},[898,2518,1994],{},[1996,2520,2225],{},[898,2522,2001],{},[1996,2524,2005],{"stretchy":2004},[898,2526,207],{},[1996,2528,2011],{"stretchy":2004},[1996,2530,1998],{},[2124,2532,2533,2535],{},[898,2534,2001],{},[1996,2536,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,2538,2005],{"stretchy":2004},[898,2540,207],{},[1996,2542,2011],{"stretchy":2004},[1996,2544,2005],{"stretchy":2004},[898,2546,2008],{},[1996,2548,2225],{},[898,2550,207],{},[1996,2552,2011],{"stretchy":2004},[902,2554,2555],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,2557,2558],{},[2559,2560],"img",{"alt":2561,"className":2562,"src":2564},"imek-derivace-tecna",[210,2563],"wikilink-broken","\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,2566,2568],{"id":2567},"inženýrská-interpretace","Inženýrská interpretace",[724,2570,2571,2470,2594,2203,2597,2610,2611,2624,2625,2643,2644,2657,2658,2671,2672,2685,2686,2704],{},[883,2572,2574],{"className":2573},[886],[888,2575,2576],{"xmlns":890},[892,2577,2578,2592],{},[895,2579,2580,2586,2588,2590],{},[2124,2581,2582,2584],{},[898,2583,2001],{},[1996,2585,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,2587,2005],{"stretchy":2004},[898,2589,207],{},[1996,2591,2011],{"stretchy":2004},[902,2593,2440],{"encoding":904},[38,2595,2596],{},"rychlost změny",[883,2598,2600],{"className":2599},[886],[888,2601,2602],{"xmlns":890},[892,2603,2604,2608],{},[895,2605,2606],{},[898,2607,1994],{},[902,2609,1994],{"encoding":904}," vzhledem k ",[883,2612,2614],{"className":2613},[886],[888,2615,2616],{"xmlns":890},[892,2617,2618,2622],{},[895,2619,2620],{},[898,2621,2008],{},[902,2623,2008],{"encoding":904}," v bodě ",[883,2626,2628],{"className":2627},[886],[888,2629,2630],{"xmlns":890},[892,2631,2632,2640],{},[895,2633,2634,2636,2638],{},[898,2635,2008],{},[1996,2637,1998],{},[898,2639,207],{},[902,2641,2642],{"encoding":904},"x = a","; přibližná změna ",[883,2645,2647],{"className":2646},[886],[888,2648,2649],{"xmlns":890},[892,2650,2651,2655],{},[895,2652,2653],{},[898,2654,1994],{},[902,2656,1994],{"encoding":904}," při změně ",[883,2659,2661],{"className":2660},[886],[888,2662,2663],{"xmlns":890},[892,2664,2665,2669],{},[895,2666,2667],{},[898,2668,2008],{},[902,2670,2008],{"encoding":904}," z ",[883,2673,2675],{"className":2674},[886],[888,2676,2677],{"xmlns":890},[892,2678,2679,2683],{},[895,2680,2681],{},[898,2682,207],{},[902,2684,207],{"encoding":904}," na ",[883,2687,2689],{"className":2688},[886],[888,2690,2691],{"xmlns":890},[892,2692,2693,2701],{},[895,2694,2695,2697,2699],{},[898,2696,207],{},[1996,2698,2095],{},[2129,2700,2278],{},[902,2702,2703],{"encoding":904},"a+1",":",[724,2706,2707],{},[883,2708,2710],{"className":2709},[886],[888,2711,2712],{"xmlns":890},[892,2713,2714,2753],{},[895,2715,2716,2718,2720,2722,2724,2726,2728,2731,2733,2735,2737,2739,2741,2747,2749,2751],{},[898,2717,2001],{},[1996,2719,2005],{"stretchy":2004},[898,2721,207],{},[1996,2723,2095],{},[2129,2725,2278],{},[1996,2727,2011],{"stretchy":2004},[1996,2729,2730],{},"≈",[898,2732,2001],{},[1996,2734,2005],{"stretchy":2004},[898,2736,207],{},[1996,2738,2011],{"stretchy":2004},[1996,2740,2095],{},[2124,2742,2743,2745],{},[898,2744,2001],{},[1996,2746,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,2748,2005],{"stretchy":2004},[898,2750,207],{},[1996,2752,2011],{"stretchy":2004},[902,2754,2755],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,2757,2759],{"id":2758},"příklad-mezní-náklady","Příklad — mezní náklady",[724,2761,2762,2763,1975],{},"Celkové náklady ",[883,2764,2766],{"className":2765},[886],[888,2767,2768],{"xmlns":890},[892,2769,2770,2801],{},[895,2771,2772,2775,2778,2780,2783,2785,2787,2790,2792,2795],{},[898,2773,2774],{},"T",[898,2776,2777],{},"C",[1996,2779,1998],{},[2129,2781,2782],{},"1000",[1996,2784,2095],{},[2129,2786,2131],{},[898,2788,2789],{},"Q",[1996,2791,2095],{},[2129,2793,2794],{},"0,1",[2124,2796,2797,2799],{},[898,2798,2789],{},[2129,2800,2131],{},[902,2802,2803],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,2805,2806,2807,2845,2846,1975],{},"Mezní náklady: ",[883,2808,2810],{"className":2809},[886],[888,2811,2812],{"xmlns":890},[892,2813,2814,2842],{},[895,2815,2816,2819,2821,2823,2825,2831,2833,2835,2837,2840],{},[898,2817,2818],{},"M",[898,2820,2777],{},[1996,2822,1998],{},[898,2824,2774],{},[2124,2826,2827,2829],{},[898,2828,2777],{},[1996,2830,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,2832,1998],{},[2129,2834,2131],{},[1996,2836,2095],{},[2129,2838,2839],{},"0,2",[898,2841,2789],{},[902,2843,2844],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,2847,2849],{"className":2848},[886],[888,2850,2851],{"xmlns":890},[892,2852,2853,2870],{},[895,2854,2855,2857,2859,2861,2864,2866,2868],{},[898,2856,2818],{},[898,2858,2777],{},[1996,2860,2005],{"stretchy":2004},[2129,2862,2863],{},"10",[1996,2865,2011],{"stretchy":2004},[1996,2867,1998],{},[2129,2869,2351],{},[902,2871,2872],{"encoding":904},"MC(10) = 4",[724,2874,2875,2203,2878,2927,2928,2203,2931,1975],{},[38,2876,2877],{},"Skutečný přírůstek:",[883,2879,2881],{"className":2880},[886],[888,2882,2883],{"xmlns":890},[892,2884,2885,2924],{},[895,2886,2887,2890,2892,2894,2896,2898,2900,2902,2905,2907,2909,2911,2913,2915,2917,2919,2921],{},[898,2888,2889],{"mathvariant":2376},"Δ",[898,2891,2774],{},[898,2893,2777],{},[1996,2895,1998],{},[898,2897,2774],{},[898,2899,2777],{},[1996,2901,2005],{"stretchy":2004},[2129,2903,2904],{},"11",[1996,2906,2011],{"stretchy":2004},[1996,2908,2225],{},[898,2910,2774],{},[898,2912,2777],{},[1996,2914,2005],{"stretchy":2004},[2129,2916,2863],{},[1996,2918,2011],{"stretchy":2004},[1996,2920,1998],{},[2129,2922,2923],{},"4,2",[902,2925,2926],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",". ",[38,2929,2930],{},"Přibližný (lineární):",[883,2932,2934],{"className":2933},[886],[888,2935,2936],{"xmlns":890},[892,2937,2938,2942],{},[895,2939,2940],{},[2129,2941,2351],{},[902,2943,2351],{"encoding":904},[724,2945,2946,2947,2951],{},"(Viz aplikace v ",[207,2948,2950],{"className":2949,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk",".)",[115,2953,2955],{"id":2954},"diferenciál","Diferenciál",[724,2957,2958],{},[883,2959,2961],{"className":2960},[886],[888,2962,2963],{"xmlns":890},[892,2964,2965,2992],{},[895,2966,2967,2969,2971,2973,2979,2981,2983,2985,2988,2990],{},[898,2968,2194],{},[898,2970,2001],{},[1996,2972,1998],{},[2124,2974,2975,2977],{},[898,2976,2001],{},[1996,2978,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,2980,2005],{"stretchy":2004},[898,2982,2008],{},[1996,2984,2011],{"stretchy":2004},[2288,2986,2987],{}," ",[898,2989,2194],{},[898,2991,2008],{},[902,2993,2994],{"encoding":904},"df = f'(x)\\, dx",[724,2996,2997,2998,3014,3015,3063,3064,1975],{},"Pro malá ",[883,2999,3001],{"className":3000},[886],[888,3002,3003],{"xmlns":890},[892,3004,3005,3011],{},[895,3006,3007,3009],{},[898,3008,2194],{},[898,3010,2008],{},[902,3012,3013],{"encoding":904},"dx"," platí: ",[883,3016,3018],{"className":3017},[886],[888,3019,3020],{"xmlns":890},[892,3021,3022,3060],{},[895,3023,3024,3026,3028,3030,3032,3034,3036,3038,3040,3042,3044,3046,3048,3050,3052,3054,3056,3058],{},[898,3025,2889],{"mathvariant":2376},[898,3027,2001],{},[1996,3029,1998],{},[898,3031,2001],{},[1996,3033,2005],{"stretchy":2004},[898,3035,2008],{},[1996,3037,2095],{},[898,3039,2194],{},[898,3041,2008],{},[1996,3043,2011],{"stretchy":2004},[1996,3045,2225],{},[898,3047,2001],{},[1996,3049,2005],{"stretchy":2004},[898,3051,2008],{},[1996,3053,2011],{"stretchy":2004},[1996,3055,2730],{},[898,3057,2194],{},[898,3059,2001],{},[902,3061,3062],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,3065,3066],{},"lineární odhad přírůstku",[198,3068,3070],{"id":3069},"příklad","Příklad",[724,3072,3073,3104,3105,3130,3131,3151],{},[883,3074,3076],{"className":3075},[886],[888,3077,3078],{"xmlns":890},[892,3079,3080,3101],{},[895,3081,3082,3084,3086,3088,3091,3093,3095],{},[898,3083,2774],{},[898,3085,2777],{},[1996,3087,1998],{},[2129,3089,3090],{},"100",[1996,3092,2095],{},[2129,3094,2794],{},[2124,3096,3097,3099],{},[898,3098,2789],{},[2129,3100,2131],{},[902,3102,3103],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,3106,3108],{"className":3107},[886],[888,3109,3110],{"xmlns":890},[892,3111,3112,3127],{},[895,3113,3114,3116,3118,3121,3124],{},[898,3115,2789],{},[1996,3117,2704],{},[2129,3119,3120],{},"50",[1996,3122,3123],{},"→",[2129,3125,3126],{},"60",[902,3128,3129],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,3132,3134],{"className":3133},[886],[888,3135,3136],{"xmlns":890},[892,3137,3138,3148],{},[895,3139,3140,3142,3144,3146],{},[898,3141,2194],{},[898,3143,2789],{},[1996,3145,1998],{},[2129,3147,2863],{},[902,3149,3150],{"encoding":904},"dQ = 10","):",[724,3153,3154],{},[883,3155,3157],{"className":3156},[886],[888,3158,3159],{"xmlns":890},[892,3160,3161,3198],{},[895,3162,3163,3165,3167,3169,3171,3173,3175,3178,3180,3182,3184,3186,3188,3190,3192,3194,3196],{},[898,3164,2194],{},[898,3166,2774],{},[898,3168,2777],{},[1996,3170,1998],{},[2129,3172,2839],{},[898,3174,2789],{},[1996,3176,3177],{},"⋅",[898,3179,2194],{},[898,3181,2789],{},[1996,3183,1998],{},[2129,3185,2839],{},[1996,3187,3177],{},[2129,3189,3120],{},[1996,3191,3177],{},[2129,3193,2863],{},[1996,3195,1998],{},[2129,3197,3090],{},[902,3199,3200],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,3202,3203,3204,3227,3228,3244],{},"Přesná změna: ",[883,3205,3207],{"className":3206},[886],[888,3208,3209],{"xmlns":890},[892,3210,3211,3224],{},[895,3212,3213,3215,3217,3219,3221],{},[898,3214,2889],{"mathvariant":2376},[898,3216,2774],{},[898,3218,2777],{},[1996,3220,1998],{},[2129,3222,3223],{},"110",[902,3225,3226],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,3229,3231],{"className":3230},[886],[888,3232,3233],{"xmlns":890},[892,3234,3235,3241],{},[895,3236,3237,3239],{},[898,3238,2774],{},[898,3240,2777],{},[902,3242,3243],{"encoding":904},"TC"," je konvexní.",[115,3246,3248],{"id":3247},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,3250,3252],{"id":3251},"nutná-podmínka","Nutná podmínka",[724,3254,3255,3256,2624,3276,3289,3290,3318,3319,3322],{},"Má-li ",[883,3257,3259],{"className":3258},[886],[888,3260,3261],{"xmlns":890},[892,3262,3263,3273],{},[895,3264,3265,3267,3269,3271],{},[898,3266,2001],{},[1996,3268,2005],{"stretchy":2004},[898,3270,2008],{},[1996,3272,2011],{"stretchy":2004},[902,3274,3275],{"encoding":904},"f(x)",[883,3277,3279],{"className":3278},[886],[888,3280,3281],{"xmlns":890},[892,3282,3283,3287],{},[895,3284,3285],{},[898,3286,207],{},[902,3288,207],{"encoding":904}," extrém, pak ",[883,3291,3293],{"className":3292},[886],[888,3294,3295],{"xmlns":890},[892,3296,3297,3315],{},[895,3298,3299,3305,3307,3309,3311,3313],{},[2124,3300,3301,3303],{},[898,3302,2001],{},[1996,3304,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,3306,2005],{"stretchy":2004},[898,3308,207],{},[1996,3310,2011],{"stretchy":2004},[1996,3312,1998],{},[2129,3314,2327],{},[902,3316,3317],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,3320,3321],{},"stacionární"," (podezřelé) body.",[198,3324,3326],{"id":3325},"postačující-podmínka","Postačující podmínka",[724,3328,3329,3330,3343,3344,2704],{},"Pro stacionární bod ",[883,3331,3333],{"className":3332},[886],[888,3334,3335],{"xmlns":890},[892,3336,3337,3341],{},[895,3338,3339],{},[898,3340,207],{},[902,3342,207],{"encoding":904},", je-li ",[883,3345,3347],{"className":3346},[886],[888,3348,3349],{"xmlns":890},[892,3350,3351,3374],{},[895,3352,3353,3363,3365,3367,3369,3372],{},[2124,3354,3355,3357],{},[898,3356,2001],{},[895,3358,3359,3361],{},[1996,3360,2378],{"mathvariant":2376},[1996,3362,2378],{"mathvariant":2376},[1996,3364,2005],{"stretchy":2004},[898,3366,207],{},[1996,3368,2011],{"stretchy":2004},[1996,3370,3371],{"mathvariant":2376},"≠",[2129,3373,2327],{},[902,3375,3376],{"encoding":904},"f''(a) \\neq 0",[120,3378,3379,3418],{},[123,3380,3381,3414,3415],{},[883,3382,3384],{"className":3383},[886],[888,3385,3386],{"xmlns":890},[892,3387,3388,3411],{},[895,3389,3390,3400,3402,3404,3406,3409],{},[2124,3391,3392,3394],{},[898,3393,2001],{},[895,3395,3396,3398],{},[1996,3397,2378],{"mathvariant":2376},[1996,3399,2378],{"mathvariant":2376},[1996,3401,2005],{"stretchy":2004},[898,3403,207],{},[1996,3405,2011],{"stretchy":2004},[1996,3407,3408],{},">",[2129,3410,2327],{},[902,3412,3413],{"encoding":904},"f''(a) > 0"," ⇒ ",[38,3416,3417],{},"lokální minimum",[123,3419,3420,3414,3453],{},[883,3421,3423],{"className":3422},[886],[888,3424,3425],{"xmlns":890},[892,3426,3427,3450],{},[895,3428,3429,3439,3441,3443,3445,3448],{},[2124,3430,3431,3433],{},[898,3432,2001],{},[895,3434,3435,3437],{},[1996,3436,2378],{"mathvariant":2376},[1996,3438,2378],{"mathvariant":2376},[1996,3440,2005],{"stretchy":2004},[898,3442,207],{},[1996,3444,2011],{"stretchy":2004},[1996,3446,3447],{},"\u003C",[2129,3449,2327],{},[902,3451,3452],{"encoding":904},"f''(a) \u003C 0",[38,3454,3455],{},"lokální maximum",[724,3457,3458],{},[2559,3459],{"alt":3460,"className":3461,"src":3462},"imek-extremy-1d",[210,2563],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,3464,3070],{"id":3465},"příklad-1",[724,3467,3468],{},[883,3469,3471],{"className":3470},[886],[888,3472,3473],{"xmlns":890},[892,3474,3475,3516],{},[895,3476,3477,3479,3481,3483,3485,3487,3489,3495,3497,3499,3505,3507,3510,3512,3514],{},[898,3478,2001],{},[1996,3480,2005],{"stretchy":2004},[898,3482,2008],{},[1996,3484,2011],{"stretchy":2004},[1996,3486,1998],{},[2129,3488,2131],{},[2124,3490,3491,3493],{},[898,3492,2008],{},[2129,3494,2173],{},[1996,3496,2225],{},[2129,3498,2173],{},[2124,3500,3501,3503],{},[898,3502,2008],{},[2129,3504,2131],{},[1996,3506,2225],{},[2129,3508,3509],{},"12",[898,3511,2008],{},[1996,3513,2095],{},[2129,3515,2173],{},[902,3517,3518],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,3520,3521,3632,3672,3735],{},[123,3522,3523,3595,3596],{},[883,3524,3526],{"className":3525},[886],[888,3527,3528],{"xmlns":890},[892,3529,3530,3592],{},[895,3531,3532,3538,3540,3542,3544,3546,3548,3554,3556,3558,3560,3562,3564,3566,3568,3570,3572,3574,3576,3578,3580,3582,3584,3586,3588,3590],{},[2124,3533,3534,3536],{},[898,3535,2001],{},[1996,3537,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,3539,2005],{"stretchy":2004},[898,3541,2008],{},[1996,3543,2011],{"stretchy":2004},[1996,3545,1998],{},[2129,3547,2235],{},[2124,3549,3550,3552],{},[898,3551,2008],{},[2129,3553,2131],{},[1996,3555,2225],{},[2129,3557,2235],{},[898,3559,2008],{},[1996,3561,2225],{},[2129,3563,3509],{},[1996,3565,1998],{},[2129,3567,2235],{},[1996,3569,2005],{"stretchy":2004},[898,3571,2008],{},[1996,3573,2095],{},[2129,3575,2278],{},[1996,3577,2011],{"stretchy":2004},[1996,3579,2005],{"stretchy":2004},[898,3581,2008],{},[1996,3583,2225],{},[2129,3585,2131],{},[1996,3587,2011],{"stretchy":2004},[1996,3589,1998],{},[2129,3591,2327],{},[902,3593,3594],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,3597,3599],{"className":3598},[886],[888,3600,3601],{"xmlns":890},[892,3602,3603,3629],{},[895,3604,3605,3611,3613,3615,3617,3619,3625,3627],{},[2272,3606,3607,3609],{},[898,3608,2008],{},[2129,3610,2278],{},[1996,3612,1998],{},[1996,3614,2225],{},[2129,3616,2278],{},[1996,3618,2286],{"separator":2285},[2272,3620,3621,3623],{},[898,3622,2008],{},[2129,3624,2131],{},[1996,3626,1998],{},[2129,3628,2131],{},[902,3630,3631],{"encoding":904},"x_1 = -1, x_2 = 2",[123,3633,3634],{},[883,3635,3637],{"className":3636},[886],[888,3638,3639],{"xmlns":890},[892,3640,3641,3669],{},[895,3642,3643,3653,3655,3657,3659,3661,3663,3665,3667],{},[2124,3644,3645,3647],{},[898,3646,2001],{},[895,3648,3649,3651],{},[1996,3650,2378],{"mathvariant":2376},[1996,3652,2378],{"mathvariant":2376},[1996,3654,2005],{"stretchy":2004},[898,3656,2008],{},[1996,3658,2011],{"stretchy":2004},[1996,3660,1998],{},[2129,3662,3509],{},[898,3664,2008],{},[1996,3666,2225],{},[2129,3668,2235],{},[902,3670,3671],{"encoding":904},"f''(x) = 12x - 6",[123,3673,3674,3414,3715,3718,3719],{},[883,3675,3677],{"className":3676},[886],[888,3678,3679],{"xmlns":890},[892,3680,3681,3712],{},[895,3682,3683,3693,3695,3697,3699,3701,3703,3705,3708,3710],{},[2124,3684,3685,3687],{},[898,3686,2001],{},[895,3688,3689,3691],{},[1996,3690,2378],{"mathvariant":2376},[1996,3692,2378],{"mathvariant":2376},[1996,3694,2005],{"stretchy":2004},[1996,3696,2225],{},[2129,3698,2278],{},[1996,3700,2011],{"stretchy":2004},[1996,3702,1998],{},[1996,3704,2225],{},[2129,3706,3707],{},"18",[1996,3709,3447],{},[2129,3711,2327],{},[902,3713,3714],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,3716,3717],{},"maximum"," v ",[883,3720,3722],{"className":3721},[886],[888,3723,3724],{"xmlns":890},[892,3725,3726,3732],{},[895,3727,3728,3730],{},[1996,3729,2225],{},[2129,3731,2278],{},[902,3733,3734],{"encoding":904},"-1",[123,3736,3737,3414,3773,3718,3776],{},[883,3738,3740],{"className":3739},[886],[888,3741,3742],{"xmlns":890},[892,3743,3744,3770],{},[895,3745,3746,3756,3758,3760,3762,3764,3766,3768],{},[2124,3747,3748,3750],{},[898,3749,2001],{},[895,3751,3752,3754],{},[1996,3753,2378],{"mathvariant":2376},[1996,3755,2378],{"mathvariant":2376},[1996,3757,2005],{"stretchy":2004},[2129,3759,2131],{},[1996,3761,2011],{"stretchy":2004},[1996,3763,1998],{},[2129,3765,3707],{},[1996,3767,3408],{},[2129,3769,2327],{},[902,3771,3772],{"encoding":904},"f''(2) = 18 > 0",[38,3774,3775],{},"minimum",[883,3777,3779],{"className":3778},[886],[888,3780,3781],{"xmlns":890},[892,3782,3783,3787],{},[895,3784,3785],{},[2129,3786,2131],{},[902,3788,2131],{"encoding":904},[115,3790,3792],{"id":3791},"navigace","Navigace",[120,3794,3795,3803,3811],{},[123,3796,3797,2203,3800],{},[38,3798,3799],{},"Předchozí:",[207,3801,757],{"className":3802,"dataFsResolvedFilePath":755,"href":756},[210],[123,3804,3805,2203,3808],{},[38,3806,3807],{},"Navazující:",[207,3809,775],{"className":3810,"dataFsResolvedFilePath":773,"href":774},[210],[123,3812,3813,2203,3816,3819,3820,3824,3825,3829],{},[38,3814,3815],{},"Souvislosti:",[207,3817,784],{"className":3818,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,3821,3823],{"className":3822,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk"," (aplikace mezních veličin), ",[207,3826,3828],{"className":3827,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita"," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":3831},[3832,3833,3838,3841,3846],{"id":1978,"depth":642,"text":1979},{"id":1145,"depth":642,"text":2357,"children":3834},[3835,3836,3837],{"id":2443,"depth":649,"text":2444},{"id":2567,"depth":649,"text":2568},{"id":2758,"depth":649,"text":2759},{"id":2954,"depth":642,"text":2955,"children":3839},[3840],{"id":3069,"depth":649,"text":3070},{"id":3247,"depth":642,"text":3248,"children":3842},[3843,3844,3845],{"id":3251,"depth":649,"text":3252},{"id":3325,"depth":649,"text":3326},{"id":3465,"depth":649,"text":3070},{"id":3791,"depth":642,"text":3792},"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":1916,"description":3847},[1135],"topics\u002Fderivace",[1128,1145,3854,3855,3856],"diferencial","extremy","mezni-naklady","topic","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":3860,"title":1920,"body":3861,"course":1128,"courses":659,"created":9556,"description":641,"extension":661,"meta":9557,"navigation":664,"path":9558,"seo":9559,"sources":9560,"stem":9561,"tags":9562,"type":3857,"updated":677,"__hash__":9567},"topics\u002Ftopics\u002Felasticita.md",{"type":9,"value":3862,"toc":9529},[3863,3866,3889,3893,3919,3923,3965,4056,4100,4104,4128,4135,4139,4149,4161,4165,4194,4203,4260,4266,4269,4275,4302,4308,4406,4566,4857,4861,4941,4947,4951,5049,5115,5283,5287,5365,5396,5423,5429,5461,5539,5626,5630,5693,5699,5702,5708,5822,5907,5951,5955,6001,6008,6325,6330,6354,6383,6450,6547,6551,6558,6565,6636,6756,6840,6843,6849,7176,7180,7343,7351,7487,7495,7733,7741,7744,7749,8005,8009,8183,8317,8354,8398,8401,8531,8621,8639,8643,8650,8656,8717,8720,8744,8747,8753,8756,8762,8765,8769,8807,8865,9054,9058,9131,9137,9144,9148,9154,9296,9300,9306,9342,9347,9524],[12,3864,1920],{"id":3865},"elasticita-poptávky-a-nabídky",[3867,3868,3869],"blockquote",{},[724,3870,3871,3874,3875,3877,3878,3881,3882,3885,3886,1975],{},[883,3872,3873],{},"!abstract"," TL;DR\n",[38,3876,3828],{}," 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: ",[38,3879,3880],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,3883,3884],{},"křížově-cenovou elasticitu"," a ",[38,3887,3888],{},"důchodovou elasticitu",[115,3890,3892],{"id":3891},"úvod-motivace","Úvod — motivace",[724,3894,3895,3896,3898,3899,3902,3903,3906,3907,3910,3911,3914,3915,3918],{},"Termín ",[614,3897,1919],{}," (alternativně ",[614,3900,3901],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,3904,3905],{},"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 ",[614,3908,3909],{},"cenové elasticity poptávky"," (resp. ",[614,3912,3913],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,3916,2357],{"className":3917,"dataFsResolvedFilePath":764,"href":765},[210],").",[198,3920,3922],{"id":3921},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,3924,3925,3926,3945,3946,3964],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,3927,3929],{"className":3928},[886],[888,3930,3931],{"xmlns":890},[892,3932,3933,3942],{},[895,3934,3935,3938,3940],{},[898,3936,3937],{},"P",[1996,3939,1998],{},[2129,3941,2863],{},[902,3943,3944],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,3947,3949],{"className":3948},[886],[888,3950,3951],{"xmlns":890},[892,3952,3953,3961],{},[895,3954,3955,3957,3959],{},[898,3956,2789],{},[1996,3958,1998],{},[2129,3960,3090],{},[902,3962,3963],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,3966,3967,4013],{},[123,3968,3969,3972,3973,4012],{},[38,3970,3971],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,3974,3976],{"className":3975},[886],[888,3977,3978],{"xmlns":890},[892,3979,3980,4009],{},[895,3981,3982,3985,3988,3990,3992,3995,3997,4000,4002,4004,4006],{},[2288,3983,3984],{},"  ",[1996,3986,3987],{},"⇒",[2288,3989,3984],{},[898,3991,2774],{},[898,3993,3994],{},"R",[1996,3996,1998],{},[2129,3998,3999],{},"9",[1996,4001,3177],{},[2129,4003,3223],{},[1996,4005,1998],{},[2129,4007,4008],{},"990",[902,4010,4011],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,4014,4015,4018,4019,4055],{},[38,4016,4017],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,4020,4022],{"className":4021},[886],[888,4023,4024],{"xmlns":890},[892,4025,4026,4052],{},[895,4027,4028,4030,4032,4034,4036,4038,4040,4042,4044,4047,4049],{},[2288,4029,3984],{},[1996,4031,3987],{},[2288,4033,3984],{},[898,4035,2774],{},[898,4037,3994],{},[1996,4039,1998],{},[2129,4041,3999],{},[1996,4043,3177],{},[2129,4045,4046],{},"120",[1996,4048,1998],{},[2129,4050,4051],{},"1080",[902,4053,4054],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,4057,4058,4059,4062,4063,4066,4067,4070,4071,4074,4075,4078,4079,4095,4096,4099],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,4060,4061],{},"nerozumné",", na Trhu 2 ",[38,4064,4065],{},"rozumné",". Trh 2 je ",[38,4068,4069],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,4072,4073],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,4076,4077],{},"neelastická"," a vyššího ",[883,4080,4082],{"className":4081},[886],[888,4083,4084],{"xmlns":890},[892,4085,4086,4092],{},[895,4087,4088,4090],{},[898,4089,2774],{},[898,4091,3994],{},[902,4093,4094],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,4097,4098],{},"zvýšením"," ceny.",[198,4101,4103],{"id":4102},"hypotéza-41","Hypotéza 4.1",[3867,4105,4106],{},[724,4107,4108,4109],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,4110,4112],{"className":4111},[886],[888,4113,4114],{"xmlns":890},[892,4115,4116,4125],{},[895,4117,4118,4120,4123],{},[1996,4119,2005],{"stretchy":2004},[2129,4121,4122],{},"4.1",[1996,4124,2011],{"stretchy":2004},[902,4126,4127],{"encoding":904},"(4.1)",[724,4129,4130,4131,4134],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,4132,4133],{},"procentní změny"," obou faktorů.",[115,4136,4138],{"id":4137},"pojem-elasticity","Pojem elasticity",[724,4140,4141,4142,4144,4145,4148],{},"Obecně ",[38,4143,1919],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,4146,4147],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[3867,4150,4151],{},[724,4152,4153,4156,4157,4160],{},[883,4154,4155],{},"!info"," Intuice\nElasticitu lze číst jako ",[38,4158,4159],{},"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.",[115,4162,4164],{"id":4163},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,4166,4167,4168,4193],{},"Nechť ",[883,4169,4171],{"className":4170},[886],[888,4172,4173],{"xmlns":890},[892,4174,4175,4190],{},[895,4176,4177,4179,4181,4184,4186,4188],{},[898,4178,2789],{},[1996,4180,1998],{},[898,4182,4183],{},"D",[1996,4185,2005],{"stretchy":2004},[898,4187,3937],{},[1996,4189,2011],{"stretchy":2004},[902,4191,4192],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,4195,4196],{},[883,4197,4202],{"className":4198,"title":4200,"style":4201},[4199],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,4204,4205,4206,3885,4222,4238,4239,4259],{},"Znaménko minus je korekce: změny ",[883,4207,4209],{"className":4208},[886],[888,4210,4211],{"xmlns":890},[892,4212,4213,4219],{},[895,4214,4215,4217],{},[898,4216,2889],{"mathvariant":2376},[898,4218,2789],{},[902,4220,4221],{"encoding":904},"\\Delta Q",[883,4223,4225],{"className":4224},[886],[888,4226,4227],{"xmlns":890},[892,4228,4229,4235],{},[895,4230,4231,4233],{},[898,4232,2889],{"mathvariant":2376},[898,4234,3937],{},[902,4236,4237],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,4240,4242],{"className":4241},[886],[888,4243,4244],{"xmlns":890},[892,4245,4246,4256],{},[895,4247,4248],{},[2124,4249,4250,4253],{},[898,4251,4252],{},"E",[898,4254,4255],{},"A",[902,4257,4258],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,4261,4262],{},[883,4263,4265],{"className":4264,"title":4200,"style":4201},[4199],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,4267,4268],{},"Po dosazení:",[724,4270,4271],{},[883,4272,4274],{"className":4273,"title":4200,"style":4201},[4199],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,4276,4277,4278,4298,4299,4301],{},"Limitním přechodem ",[883,4279,4281],{"className":4280},[886],[888,4282,4283],{"xmlns":890},[892,4284,4285,4295],{},[895,4286,4287,4289,4291,4293],{},[898,4288,2889],{"mathvariant":2376},[898,4290,3937],{},[1996,4292,3123],{},[2129,4294,2327],{},[902,4296,4297],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,4300,3909],{}," (price elasticity of demand):",[724,4303,4304],{},[883,4305,4307],{"className":4306,"title":4200,"style":4201},[4199],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,4309,4310,4311,4334,4335,4358,4359,4383,4384,4405],{},"kde ",[883,4312,4314],{"className":4313},[886],[888,4315,4316],{"xmlns":890},[892,4317,4318,4332],{},[895,4319,4320,4322,4324,4326,4328,4330],{},[898,4321,2789],{},[1996,4323,1998],{},[898,4325,4183],{},[1996,4327,2005],{"stretchy":2004},[898,4329,3937],{},[1996,4331,2011],{"stretchy":2004},[902,4333,4192],{"encoding":904},". Pro pevnou cenu ",[883,4336,4338],{"className":4337},[886],[888,4339,4340],{"xmlns":890},[892,4341,4342,4355],{},[895,4343,4344,4346,4348],{},[898,4345,3937],{},[1996,4347,1998],{},[2124,4349,4350,4352],{},[898,4351,3937],{},[1996,4353,4354],{},"∗",[902,4356,4357],{"encoding":904},"P = P^*"," se ",[883,4360,4362],{"className":4361},[886],[888,4363,4364],{"xmlns":890},[892,4365,4366,4380],{},[895,4367,4368,4370,4372,4378],{},[898,4369,4252],{},[1996,4371,2005],{"stretchy":2004},[2124,4373,4374,4376],{},[898,4375,3937],{},[1996,4377,4354],{},[1996,4379,2011],{"stretchy":2004},[902,4381,4382],{"encoding":904},"E(P^*)"," nazývá ",[614,4385,4386,4387],{},"elasticita poptávky při ceně ",[883,4388,4390],{"className":4389},[886],[888,4391,4392],{"xmlns":890},[892,4393,4394,4402],{},[895,4395,4396],{},[2124,4397,4398,4400],{},[898,4399,3937],{},[1996,4401,4354],{},[902,4403,4404],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[3867,4407,4408],{},[724,4409,4410,4413,4414,4432,4433,4461,4462,4491,4492,1343,4510,1343,4528,4546,4547,4562,4563,1975],{},[883,4411,4412],{},"!warning"," Pozor na znaménko\nV (4.5) je ",[38,4415,4416,4417],{},"explicitní ",[883,4418,4420],{"className":4419},[886],[888,4421,4422],{"xmlns":890},[892,4423,4424,4430],{},[895,4425,4426,4428],{},[1996,4427,2225],{},[2129,4429,2278],{},[902,4431,3734],{"encoding":904}," právě proto, že ",[883,4434,4436],{"className":4435},[886],[888,4437,4438],{"xmlns":890},[892,4439,4440,4458],{},[895,4441,4442,4448,4450,4452,4454,4456],{},[2124,4443,4444,4446],{},[898,4445,2789],{},[1996,4447,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,4449,2005],{"stretchy":2004},[898,4451,3937],{},[1996,4453,2011],{"stretchy":2004},[1996,4455,3447],{},[2129,4457,2327],{},[902,4459,4460],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,4463,4465],{"className":4464},[886],[888,4466,4467],{"xmlns":890},[892,4468,4469,4488],{},[895,4470,4471,4473,4475,4481,4483,4486],{},[898,4472,4252],{},[1996,4474,2005],{"stretchy":2004},[2124,4476,4477,4479],{},[898,4478,3937],{},[1996,4480,4354],{},[1996,4482,2011],{"stretchy":2004},[1996,4484,4485],{},"≥",[2129,4487,2327],{},[902,4489,4490],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,4493,4495],{"className":4494},[886],[888,4496,4497],{"xmlns":890},[892,4498,4499,4507],{},[895,4500,4501,4503,4505],{},[898,4502,4252],{},[1996,4504,3408],{},[2129,4506,2278],{},[902,4508,4509],{"encoding":904},"E > 1",[883,4511,4513],{"className":4512},[886],[888,4514,4515],{"xmlns":890},[892,4516,4517,4525],{},[895,4518,4519,4521,4523],{},[898,4520,4252],{},[1996,4522,3447],{},[2129,4524,2278],{},[902,4526,4527],{"encoding":904},"E \u003C 1",[883,4529,4531],{"className":4530},[886],[888,4532,4533],{"xmlns":890},[892,4534,4535,4543],{},[895,4536,4537,4539,4541],{},[898,4538,4252],{},[1996,4540,1998],{},[2129,4542,2278],{},[902,4544,4545],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,4548,4550],{"className":4549},[886],[888,4551,4552],{"xmlns":890},[892,4553,4554,4560],{},[895,4555,4556,4558],{},[1996,4557,2225],{},[2129,4559,2278],{},[902,4561,3734],{"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 ",[38,4564,4565],{},"absolutní hodnotou",[3867,4567,4568,4588],{},[724,4569,4570,4573,4574,4587],{},[883,4571,4572],{},"!tip"," Postup: jak spočítat ",[883,4575,4577],{"className":4576},[886],[888,4578,4579],{"xmlns":890},[892,4580,4581,4585],{},[895,4582,4583],{},[898,4584,4252],{},[902,4586,4252],{"encoding":904}," v bodě",[152,4589,4590,4642,4682,4735,4800],{},[123,4591,4592,4593,4616,4617,4641],{},"Zapište ",[883,4594,4596],{"className":4595},[886],[888,4597,4598],{"xmlns":890},[892,4599,4600,4614],{},[895,4601,4602,4604,4606,4608,4610,4612],{},[898,4603,2789],{},[1996,4605,1998],{},[898,4607,4183],{},[1996,4609,2005],{"stretchy":2004},[898,4611,3937],{},[1996,4613,2011],{"stretchy":2004},[902,4615,4192],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,4618,4620],{"className":4619},[886],[888,4621,4622],{"xmlns":890},[892,4623,4624,4638],{},[895,4625,4626,4628,4630,4632,4634,4636],{},[898,4627,3937],{},[1996,4629,1998],{},[898,4631,4183],{},[1996,4633,2005],{"stretchy":2004},[898,4635,2789],{},[1996,4637,2011],{"stretchy":2004},[902,4639,4640],{"encoding":904},"P = D(Q)",", použijte vztah (4.9).",[123,4643,4644,4645,1975],{},"Spočítejte derivaci ",[883,4646,4648],{"className":4647},[886],[888,4649,4650],{"xmlns":890},[892,4651,4652,4679],{},[895,4653,4654,4660,4662,4664,4666,4668,4670,4672,4675,4677],{},[2124,4655,4656,4658],{},[898,4657,2789],{},[1996,4659,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,4661,2005],{"stretchy":2004},[898,4663,3937],{},[1996,4665,2011],{"stretchy":2004},[1996,4667,1998],{},[898,4669,2194],{"mathvariant":2376},[898,4671,2789],{},[898,4673,4674],{"mathvariant":2376},"\u002F",[898,4676,2194],{"mathvariant":2376},[898,4678,3937],{},[902,4680,4681],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,4683,4684,4685,4702,4703,1975],{},"Dosaďte zadanou cenu ",[883,4686,4688],{"className":4687},[886],[888,4689,4690],{"xmlns":890},[892,4691,4692,4700],{},[895,4693,4694],{},[2124,4695,4696,4698],{},[898,4697,3937],{},[1996,4699,4354],{},[902,4701,4404],{"encoding":904}," a dopočítejte odpovídající ",[883,4704,4706],{"className":4705},[886],[888,4707,4708],{"xmlns":890},[892,4709,4710,4732],{},[895,4711,4712,4718,4720,4722,4724,4730],{},[2124,4713,4714,4716],{},[898,4715,2789],{},[1996,4717,4354],{},[1996,4719,1998],{},[898,4721,4183],{},[1996,4723,2005],{"stretchy":2004},[2124,4725,4726,4728],{},[898,4727,3937],{},[1996,4729,4354],{},[1996,4731,2011],{"stretchy":2004},[902,4733,4734],{"encoding":904},"Q^* = D(P^*)",[123,4736,4737,4738,1975],{},"Dosaďte do (4.5): ",[883,4739,4741],{"className":4740},[886],[888,4742,4743],{"xmlns":890},[892,4744,4745,4797],{},[895,4746,4747,4749,4751,4757,4759,4761,4763,4779,4781,4787,4789,4795],{},[898,4748,4252],{},[1996,4750,2005],{"stretchy":2004},[2124,4752,4753,4755],{},[898,4754,3937],{},[1996,4756,4354],{},[1996,4758,2011],{"stretchy":2004},[1996,4760,1998],{},[1996,4762,2225],{},[2325,4764,4765],{"scriptlevel":2327,"displaystyle":2285},[2329,4766,4767,4773],{},[2124,4768,4769,4771],{},[898,4770,3937],{},[1996,4772,4354],{},[2124,4774,4775,4777],{},[898,4776,2789],{},[1996,4778,4354],{},[2288,4780,2987],{},[2124,4782,4783,4785],{},[898,4784,2789],{},[1996,4786,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,4788,2005],{"stretchy":2004},[2124,4790,4791,4793],{},[898,4792,3937],{},[1996,4794,4354],{},[1996,4796,2011],{"stretchy":2004},[902,4798,4799],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,4801,4802,4803,4820,4821,4838,4839,4856],{},"Klasifikujte: ",[883,4804,4806],{"className":4805},[886],[888,4807,4808],{"xmlns":890},[892,4809,4810,4818],{},[895,4811,4812,4814,4816],{},[898,4813,4252],{},[1996,4815,3408],{},[2129,4817,2278],{},[902,4819,4509],{"encoding":904}," elastická, ",[883,4822,4824],{"className":4823},[886],[888,4825,4826],{"xmlns":890},[892,4827,4828,4836],{},[895,4829,4830,4832,4834],{},[898,4831,4252],{},[1996,4833,1998],{},[2129,4835,2278],{},[902,4837,4545],{"encoding":904}," jednotková, ",[883,4840,4842],{"className":4841},[886],[888,4843,4844],{"xmlns":890},[892,4845,4846,4854],{},[895,4847,4848,4850,4852],{},[898,4849,4252],{},[1996,4851,3447],{},[2129,4853,2278],{},[902,4855,4527],{"encoding":904}," neelastická.",[198,4858,4860],{"id":4859},"interpretace-46","Interpretace (4.6)",[3867,4862,4863],{},[724,4864,4865,4866,4889,4890,4903,4904,4921,4922],{},"Číslo ",[883,4867,4869],{"className":4868},[886],[888,4870,4871],{"xmlns":890},[892,4872,4873,4887],{},[895,4874,4875,4877,4879,4885],{},[898,4876,4252],{},[1996,4878,2005],{"stretchy":2004},[2124,4880,4881,4883],{},[898,4882,3937],{},[1996,4884,4354],{},[1996,4886,2011],{"stretchy":2004},[902,4888,4382],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,4891,4893],{"className":4892},[886],[888,4894,4895],{"xmlns":890},[892,4896,4897,4901],{},[895,4898,4899],{},[898,4900,2789],{},[902,4902,2789],{"encoding":904},", jestliže se cena ",[883,4905,4907],{"className":4906},[886],[888,4908,4909],{"xmlns":890},[892,4910,4911,4919],{},[895,4912,4913],{},[2124,4914,4915,4917],{},[898,4916,3937],{},[1996,4918,4354],{},[902,4920,4404],{"encoding":904}," změní o 1 %. ",[883,4923,4925],{"className":4924},[886],[888,4926,4927],{"xmlns":890},[892,4928,4929,4938],{},[895,4930,4931,4933,4936],{},[1996,4932,2005],{"stretchy":2004},[2129,4934,4935],{},"4.6",[1996,4937,2011],{"stretchy":2004},[902,4939,4940],{"encoding":904},"(4.6)",[724,4942,4943,4946],{},[38,4944,4945],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,4948,4950],{"id":4949},"příklad-41","Příklad 4.1",[724,4952,4953,4954,4988,4989,1343,5015,2704],{},"Poptávka ",[883,4955,4957],{"className":4956},[886],[888,4958,4959],{"xmlns":890},[892,4960,4961,4985],{},[895,4962,4963,4965,4967,4969,4971,4973,4975,4977,4979,4981,4983],{},[898,4964,3937],{},[1996,4966,1998],{},[898,4968,4183],{},[1996,4970,2005],{"stretchy":2004},[898,4972,2789],{},[1996,4974,2011],{"stretchy":2004},[1996,4976,1998],{},[2129,4978,3120],{},[1996,4980,2225],{},[2129,4982,2131],{},[898,4984,2789],{},[902,4986,4987],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,4990,4992],{"className":4991},[886],[888,4993,4994],{"xmlns":890},[892,4995,4996,5012],{},[895,4997,4998,5000,5002,5005,5007,5010],{},[898,4999,2789],{},[1996,5001,1998],{},[2129,5003,5004],{},"25",[1996,5006,2225],{},[2129,5008,5009],{},"0,5",[898,5011,3937],{},[902,5013,5014],{"encoding":904},"Q = 25 - 0{,}5P",[883,5016,5018],{"className":5017},[886],[888,5019,5020],{"xmlns":890},[892,5021,5022,5046],{},[895,5023,5024,5040,5042,5044],{},[2325,5025,5026],{"scriptlevel":2327,"displaystyle":2285},[2329,5027,5028,5034],{},[895,5029,5030,5032],{},[898,5031,2194],{"mathvariant":2376},[898,5033,2789],{},[895,5035,5036,5038],{},[898,5037,2194],{"mathvariant":2376},[898,5039,3937],{},[1996,5041,1998],{},[1996,5043,2225],{},[2129,5045,5009],{},[902,5047,5048],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,5050,5051],{},[883,5052,5054],{"className":5053},[886],[888,5055,5056],{"xmlns":890},[892,5057,5058,5112],{},[895,5059,5060,5062,5064,5066,5080,5082,5084,5086,5088,5090,5092,5110],{},[898,5061,4252],{},[1996,5063,1998],{},[1996,5065,2225],{},[2329,5067,5068,5070],{},[898,5069,3937],{},[895,5071,5072,5074,5076,5078],{},[2129,5073,5004],{},[1996,5075,2225],{},[2129,5077,5009],{},[898,5079,3937],{},[1996,5081,3177],{},[1996,5083,2005],{"stretchy":2004},[1996,5085,2225],{},[2129,5087,5009],{},[1996,5089,2011],{"stretchy":2004},[1996,5091,1998],{},[2329,5093,5094,5100],{},[895,5095,5096,5098],{},[2129,5097,5009],{},[898,5099,3937],{},[895,5101,5102,5104,5106,5108],{},[2129,5103,5004],{},[1996,5105,2225],{},[2129,5107,5009],{},[898,5109,3937],{},[898,5111,1975],{"mathvariant":2376},[902,5113,5114],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,5116,5117,5118,1343,5142,1343,5172,1343,5196,5221,5222,5245,5246,2685,5264,3918],{},"Potom ",[883,5119,5121],{"className":5120},[886],[888,5122,5123],{"xmlns":890},[892,5124,5125,5139],{},[895,5126,5127,5129,5131,5133,5135,5137],{},[898,5128,4252],{},[1996,5130,2005],{"stretchy":2004},[2129,5132,2327],{},[1996,5134,2011],{"stretchy":2004},[1996,5136,1998],{},[2129,5138,2327],{},[902,5140,5141],{"encoding":904},"E(0)=0",[883,5143,5145],{"className":5144},[886],[888,5146,5147],{"xmlns":890},[892,5148,5149,5169],{},[895,5150,5151,5153,5155,5157,5159,5161],{},[898,5152,4252],{},[1996,5154,2005],{"stretchy":2004},[2129,5156,2863],{},[1996,5158,2011],{"stretchy":2004},[1996,5160,1998],{},[2325,5162,5163],{"scriptlevel":2327,"displaystyle":2004},[2329,5164,5165,5167],{},[2129,5166,2278],{},[2129,5168,2351],{},[902,5170,5171],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,5173,5175],{"className":5174},[886],[888,5176,5177],{"xmlns":890},[892,5178,5179,5193],{},[895,5180,5181,5183,5185,5187,5189,5191],{},[898,5182,4252],{},[1996,5184,2005],{"stretchy":2004},[2129,5186,5004],{},[1996,5188,2011],{"stretchy":2004},[1996,5190,1998],{},[2129,5192,2278],{},[902,5194,5195],{"encoding":904},"E(25)=1",[883,5197,5199],{"className":5198},[886],[888,5200,5201],{"xmlns":890},[892,5202,5203,5218],{},[895,5204,5205,5207,5209,5212,5214,5216],{},[898,5206,4252],{},[1996,5208,2005],{"stretchy":2004},[2129,5210,5211],{},"40",[1996,5213,2011],{"stretchy":2004},[1996,5215,1998],{},[2129,5217,2351],{},[902,5219,5220],{"encoding":904},"E(40)=4",". Např. ",[883,5223,5225],{"className":5224},[886],[888,5226,5227],{"xmlns":890},[892,5228,5229,5243],{},[895,5230,5231,5233,5235,5237,5239,5241],{},[898,5232,4252],{},[1996,5234,2005],{"stretchy":2004},[2129,5236,5211],{},[1996,5238,2011],{"stretchy":2004},[1996,5240,1998],{},[2129,5242,2351],{},[902,5244,5220],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,5247,5249],{"className":5248},[886],[888,5250,5251],{"xmlns":890},[892,5252,5253,5261],{},[895,5254,5255,5257,5259],{},[898,5256,2789],{},[1996,5258,1998],{},[2129,5260,2228],{},[902,5262,5263],{"encoding":904},"Q=5",[883,5265,5267],{"className":5266},[886],[888,5268,5269],{"xmlns":890},[892,5270,5271,5280],{},[895,5272,5273,5275,5277],{},[898,5274,2789],{},[1996,5276,1998],{},[2129,5278,5279],{},"4,8",[902,5281,5282],{"encoding":904},"Q=4{,}8",[198,5284,5286],{"id":5285},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,5288,5289,5345],{},[123,5290,5291,5294,5295,5312,5313,1975],{},[38,5292,5293],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,5296,5298],{"className":5297},[886],[888,5299,5300],{"xmlns":890},[892,5301,5302,5310],{},[895,5303,5304],{},[2124,5305,5306,5308],{},[898,5307,4252],{},[898,5309,4255],{},[902,5311,4258],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,5314,5316],{"className":5315},[886],[888,5317,5318],{"xmlns":890},[892,5319,5320,5342],{},[895,5321,5322,5325,5327,5329,5331,5333,5335,5337,5339],{},[1996,5323,5324],{"stretchy":2004},"⟨",[898,5326,3937],{},[1996,5328,2286],{"separator":2285},[2288,5330,2987],{},[898,5332,3937],{},[1996,5334,2095],{},[898,5336,2889],{"mathvariant":2376},[898,5338,3937],{},[1996,5340,5341],{"stretchy":2004},"⟩",[902,5343,5344],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,5346,5347,5350,5351,5364],{},[38,5348,5349],{},"Bodová"," (okamžitá) elasticita: ",[883,5352,5354],{"className":5353},[886],[888,5355,5356],{"xmlns":890},[892,5357,5358,5362],{},[895,5359,5360],{},[898,5361,4252],{},[902,5363,4252],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,5366,5368,5369,5382,5383],{"id":5367},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,5370,5372],{"className":5371},[886],[888,5373,5374],{"xmlns":890},[892,5375,5376,5380],{},[895,5377,5378],{},[898,5379,3937],{},[902,5381,3937],{"encoding":904}," jako funkce ",[883,5384,5386],{"className":5385},[886],[888,5387,5388],{"xmlns":890},[892,5389,5390,5394],{},[895,5391,5392],{},[898,5393,2789],{},[902,5395,2789],{"encoding":904},[724,5397,5398,5399,5422],{},"Pokud je poptávka zadaná ve tvaru ",[883,5400,5402],{"className":5401},[886],[888,5403,5404],{"xmlns":890},[892,5405,5406,5420],{},[895,5407,5408,5410,5412,5414,5416,5418],{},[898,5409,3937],{},[1996,5411,1998],{},[898,5413,4183],{},[1996,5415,2005],{"stretchy":2004},[898,5417,2789],{},[1996,5419,2011],{"stretchy":2004},[902,5421,4640],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,5424,5425],{},[883,5426,5428],{"className":5427,"title":4200,"style":4201},[4199],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,5430,5431,2203,5434,5460],{},[38,5432,5433],{},"Příklad 4.3.",[883,5435,5437],{"className":5436},[886],[888,5438,5439],{"xmlns":890},[892,5440,5441,5457],{},[895,5442,5443,5445,5447,5449,5451],{},[898,5444,3937],{},[1996,5446,1998],{},[2129,5448,3090],{},[1996,5450,2225],{},[2124,5452,5453,5455],{},[898,5454,2789],{},[2129,5456,2131],{},[902,5458,5459],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,5462,5463],{},[883,5464,5466],{"className":5465},[886],[888,5467,5468],{"xmlns":890},[892,5469,5470,5536],{},[895,5471,5472,5474,5476,5478,5494,5496,5508,5510,5534],{},[898,5473,4252],{},[1996,5475,1998],{},[1996,5477,2225],{},[2329,5479,5480,5492],{},[895,5481,5482,5484,5486],{},[2129,5483,3090],{},[1996,5485,2225],{},[2124,5487,5488,5490],{},[898,5489,2789],{},[2129,5491,2131],{},[898,5493,2789],{},[1996,5495,3177],{},[2329,5497,5498,5500],{},[2129,5499,2278],{},[895,5501,5502,5504,5506],{},[1996,5503,2225],{},[2129,5505,2131],{},[898,5507,2789],{},[1996,5509,1998],{},[2329,5511,5512,5524],{},[895,5513,5514,5516,5518],{},[2129,5515,3090],{},[1996,5517,2225],{},[2124,5519,5520,5522],{},[898,5521,2789],{},[2129,5523,2131],{},[895,5525,5526,5528],{},[2129,5527,2131],{},[2124,5529,5530,5532],{},[898,5531,2789],{},[2129,5533,2131],{},[898,5535,1975],{"mathvariant":2376},[902,5537,5538],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,5540,5541,5542,5569,5570,5589,5590,1975],{},"Z rovnice ",[883,5543,5545],{"className":5544},[886],[888,5546,5547],{"xmlns":890},[892,5548,5549,5566],{},[895,5550,5551,5553,5555,5561,5563],{},[2129,5552,3090],{},[1996,5554,2225],{},[2124,5556,5557,5559],{},[898,5558,2789],{},[2129,5560,2131],{},[1996,5562,1998],{},[2129,5564,5565],{},"36",[902,5567,5568],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,5571,5573],{"className":5572},[886],[888,5574,5575],{"xmlns":890},[892,5576,5577,5586],{},[895,5578,5579,5581,5583],{},[898,5580,2789],{},[1996,5582,1998],{},[2129,5584,5585],{},"8",[902,5587,5588],{"encoding":904},"Q = 8",", tedy ",[883,5591,5593],{"className":5592},[886],[888,5594,5595],{"xmlns":890},[892,5596,5597,5623],{},[895,5598,5599,5601,5603,5605,5607,5609,5618,5620],{},[898,5600,4252],{},[1996,5602,2005],{"stretchy":2004},[2129,5604,5585],{},[1996,5606,2011],{"stretchy":2004},[1996,5608,1998],{},[2325,5610,5611],{"scriptlevel":2327,"displaystyle":2004},[2329,5612,5613,5615],{},[2129,5614,5565],{},[2129,5616,5617],{},"128",[1996,5619,1998],{},[2129,5621,5622],{},"0,281",[902,5624,5625],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,5627,5629],{"id":5628},"přibližné-změny","Přibližné změny",[724,5631,5632,5633,5669,5670,5692],{},"Diferenciál ",[883,5634,5636],{"className":5635},[886],[888,5637,5638],{"xmlns":890},[892,5639,5640,5666],{},[895,5641,5642,5644,5646,5648,5654,5656,5658,5660,5662,5664],{},[898,5643,2194],{"mathvariant":2376},[898,5645,2789],{},[1996,5647,1998],{},[2124,5649,5650,5652],{},[898,5651,2789],{},[1996,5653,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,5655,2005],{"stretchy":2004},[898,5657,3937],{},[1996,5659,2011],{"stretchy":2004},[2288,5661,2987],{},[898,5663,2194],{"mathvariant":2376},[898,5665,3937],{},[902,5667,5668],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[883,5671,5673],{"className":5672},[886],[888,5674,5675],{"xmlns":890},[892,5676,5677,5689],{},[895,5678,5679,5681,5683,5685,5687],{},[898,5680,2194],{"mathvariant":2376},[898,5682,3937],{},[1996,5684,1998],{},[898,5686,2889],{"mathvariant":2376},[898,5688,3937],{},[902,5690,5691],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,5694,5695],{},[883,5696,5698],{"className":5697,"title":4200,"style":4201},[4199],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,5700,5701],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,5703,5704],{},[883,5705,5707],{"className":5706,"title":4200,"style":4201},[4199],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,5709,5710,2203,5713,5748,5749,5768,5769,5803,5804,5821],{},[38,5711,5712],{},"Příklad 4.5.",[883,5714,5716],{"className":5715},[886],[888,5717,5718],{"xmlns":890},[892,5719,5720,5745],{},[895,5721,5722,5724,5726,5728,5734,5736,5738,5740,5742],{},[898,5723,3937],{},[1996,5725,1998],{},[1996,5727,2225],{},[2124,5729,5730,5732],{},[898,5731,2789],{},[2129,5733,2131],{},[1996,5735,2225],{},[2129,5737,2351],{},[898,5739,2789],{},[1996,5741,2095],{},[2129,5743,5744],{},"96",[902,5746,5747],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,5750,5752],{"className":5751},[886],[888,5753,5754],{"xmlns":890},[892,5755,5756,5765],{},[895,5757,5758,5760,5762],{},[898,5759,3937],{},[1996,5761,1998],{},[2129,5763,5764],{},"51",[902,5766,5767],{"encoding":904},"P=51",". Z rovnice ",[883,5770,5772],{"className":5771},[886],[888,5773,5774],{"xmlns":890},[892,5775,5776,5800],{},[895,5777,5778,5780,5782,5784,5790,5792,5794,5796,5798],{},[2129,5779,5764],{},[1996,5781,1998],{},[1996,5783,2225],{},[2124,5785,5786,5788],{},[898,5787,2789],{},[2129,5789,2131],{},[1996,5791,2225],{},[2129,5793,2351],{},[898,5795,2789],{},[1996,5797,2095],{},[2129,5799,5744],{},[902,5801,5802],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,5805,5807],{"className":5806},[886],[888,5808,5809],{"xmlns":890},[892,5810,5811,5819],{},[895,5812,5813,5815,5817],{},[898,5814,2789],{},[1996,5816,1998],{},[2129,5818,2228],{},[902,5820,5263],{"encoding":904},". Elasticita:",[724,5823,5824],{},[883,5825,5827],{"className":5826},[886],[888,5828,5829],{"xmlns":890},[892,5830,5831,5904],{},[895,5832,5833,5835,5837,5875,5877,5881,5883,5885,5887,5889,5891,5898,5901],{},[898,5834,4252],{},[1996,5836,1998],{},[2329,5838,5839,5859],{},[895,5840,5841,5843,5849,5851,5853,5855,5857],{},[1996,5842,2225],{},[2124,5844,5845,5847],{},[898,5846,2789],{},[2129,5848,2131],{},[1996,5850,2225],{},[2129,5852,2351],{},[898,5854,2789],{},[1996,5856,2095],{},[2129,5858,5744],{},[895,5860,5861,5863,5865,5867,5869,5871,5873],{},[898,5862,2789],{},[1996,5864,2005],{"stretchy":2004},[2129,5866,2131],{},[898,5868,2789],{},[1996,5870,2095],{},[2129,5872,2351],{},[1996,5874,2011],{"stretchy":2004},[1996,5876,2286],{"separator":2285},[5878,5879],"mspace",{"width":5880},"2em",[898,5882,4252],{},[1996,5884,2005],{"stretchy":2004},[2129,5886,2228],{},[1996,5888,2011],{"stretchy":2004},[1996,5890,1998],{},[2329,5892,5893,5895],{},[2129,5894,5764],{},[2129,5896,5897],{},"70",[1996,5899,5900],{},"≐",[2129,5902,5903],{},"0,728.",[902,5905,5906],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,5908,5909,5910,1975],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,5911,5913],{"className":5912},[886],[888,5914,5915],{"xmlns":890},[892,5916,5917,5948],{},[895,5918,5919,5921,5923,5926,5928,5930,5933,5935,5937,5939,5941,5944,5946],{},[898,5920,2889],{"mathvariant":2376},[898,5922,2789],{},[898,5924,5925],{"mathvariant":2376},"%",[1996,5927,2730],{},[1996,5929,2225],{},[2129,5931,5932],{},"0,728",[1996,5934,3177],{},[2129,5936,2131],{},[1996,5938,1998],{},[1996,5940,2225],{},[2129,5942,5943],{},"1,456",[2288,5945,2987],{},[898,5947,5925],{"mathvariant":2376},[902,5949,5950],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,5952,5954],{"id":5953},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,5956,5957,5958,5981,5982,2704],{},"V závislosti na hodnotě ",[883,5959,5961],{"className":5960},[886],[888,5962,5963],{"xmlns":890},[892,5964,5965,5979],{},[895,5966,5967,5969,5971,5977],{},[898,5968,4252],{},[1996,5970,2005],{"stretchy":2004},[2124,5972,5973,5975],{},[898,5974,3937],{},[1996,5976,4354],{},[1996,5978,2011],{"stretchy":2004},[902,5980,4382],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,5983,5985],{"className":5984},[886],[888,5986,5987],{"xmlns":890},[892,5988,5989,5998],{},[895,5990,5991,5993,5996],{},[1996,5992,2005],{"stretchy":2004},[2129,5994,5995],{},"4.7",[1996,5997,2011],{"stretchy":2004},[902,5999,6000],{"encoding":904},"(4.7)",[724,6002,6003],{},[2559,6004],{"alt":6005,"className":6006,"src":6007},"imek-typy-elasticity-5panelu",[210,2563],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,6009,6010,6049],{},[19,6011,6012],{},[22,6013,6014,6040,6043,6046],{},[25,6015,6016,6017],{},"Hodnota ",[883,6018,6020],{"className":6019},[886],[888,6021,6022],{"xmlns":890},[892,6023,6024,6038],{},[895,6025,6026,6028,6030,6036],{},[898,6027,4252],{},[1996,6029,2005],{"stretchy":2004},[2124,6031,6032,6034],{},[898,6033,3937],{},[1996,6035,4354],{},[1996,6037,2011],{"stretchy":2004},[902,6039,4382],{"encoding":904},[25,6041,6042],{},"Typ poptávky",[25,6044,6045],{},"Termín",[25,6047,6048],{},"Význam",[30,6050,6051,6084,6146,6221,6278],{},[22,6052,6053,6073,6078,6081],{},[35,6054,6055],{},[883,6056,6058],{"className":6057},[886],[888,6059,6060],{"xmlns":890},[892,6061,6062,6070],{},[895,6063,6064,6066,6068],{},[898,6065,4252],{},[1996,6067,1998],{},[2129,6069,2327],{},[902,6071,6072],{"encoding":904},"E = 0",[35,6074,6075],{},[38,6076,6077],{},"dokonale neelastická",[35,6079,6080],{},"perfectly inelastic",[35,6082,6083],{},"množství se nemění bez ohledu na cenu",[22,6085,6086,6110,6114,6117],{},[35,6087,6088],{},[883,6089,6091],{"className":6090},[886],[888,6092,6093],{"xmlns":890},[892,6094,6095,6107],{},[895,6096,6097,6099,6101,6103,6105],{},[2129,6098,2327],{},[1996,6100,3447],{},[898,6102,4252],{},[1996,6104,3447],{},[2129,6106,2278],{},[902,6108,6109],{"encoding":904},"0 \u003C E \u003C 1",[35,6111,6112],{},[38,6113,4077],{},[35,6115,6116],{},"inelastic",[35,6118,6119,6132,6133],{},[883,6120,6122],{"className":6121},[886],[888,6123,6124],{"xmlns":890},[892,6125,6126,6130],{},[895,6127,6128],{},[898,6129,2789],{},[902,6131,2789],{"encoding":904}," se mění pomaleji než ",[883,6134,6136],{"className":6135},[886],[888,6137,6138],{"xmlns":890},[892,6139,6140,6144],{},[895,6141,6142],{},[898,6143,3937],{},[902,6145,3937],{"encoding":904},[22,6147,6148,6167,6172,6175],{},[35,6149,6150],{},[883,6151,6153],{"className":6152},[886],[888,6154,6155],{"xmlns":890},[892,6156,6157,6165],{},[895,6158,6159,6161,6163],{},[898,6160,4252],{},[1996,6162,1998],{},[2129,6164,2278],{},[902,6166,4545],{"encoding":904},[35,6168,6169],{},[38,6170,6171],{},"jednotkově elastická",[35,6173,6174],{},"unit elastic",[35,6176,6177,6190,6191,6204,6205,6220],{},[883,6178,6180],{"className":6179},[886],[888,6181,6182],{"xmlns":890},[892,6183,6184,6188],{},[895,6185,6186],{},[898,6187,2789],{},[902,6189,2789],{"encoding":904}," i ",[883,6192,6194],{"className":6193},[886],[888,6195,6196],{"xmlns":890},[892,6197,6198,6202],{},[895,6199,6200],{},[898,6201,3937],{},[902,6203,3937],{"encoding":904}," se mění stejně rychle; ",[883,6206,6208],{"className":6207},[886],[888,6209,6210],{"xmlns":890},[892,6211,6212,6218],{},[895,6213,6214,6216],{},[898,6215,2774],{},[898,6217,3994],{},[902,6219,4094],{"encoding":904}," má maximum",[22,6222,6223,6242,6246,6249],{},[35,6224,6225],{},[883,6226,6228],{"className":6227},[886],[888,6229,6230],{"xmlns":890},[892,6231,6232,6240],{},[895,6233,6234,6236,6238],{},[898,6235,4252],{},[1996,6237,3408],{},[2129,6239,2278],{},[902,6241,4509],{"encoding":904},[35,6243,6244],{},[38,6245,4073],{},[35,6247,6248],{},"elastic",[35,6250,6251,6264,6265],{},[883,6252,6254],{"className":6253},[886],[888,6255,6256],{"xmlns":890},[892,6257,6258,6262],{},[895,6259,6260],{},[898,6261,2789],{},[902,6263,2789],{"encoding":904}," se mění rychleji než ",[883,6266,6268],{"className":6267},[886],[888,6269,6270],{"xmlns":890},[892,6271,6272,6276],{},[895,6273,6274],{},[898,6275,3937],{},[902,6277,3937],{"encoding":904},[22,6279,6280,6301,6306,6309],{},[35,6281,6282],{},[883,6283,6285],{"className":6284},[886],[888,6286,6287],{"xmlns":890},[892,6288,6289,6298],{},[895,6290,6291,6293,6295],{},[898,6292,4252],{},[1996,6294,3123],{},[898,6296,6297],{"mathvariant":2376},"∞",[902,6299,6300],{"encoding":904},"E \\to \\infty",[35,6302,6303],{},[38,6304,6305],{},"dokonale elastická",[35,6307,6308],{},"perfectly elastic",[35,6310,6311,6312],{},"sebemenší změna ceny úplně mění ",[883,6313,6315],{"className":6314},[886],[888,6316,6317],{"xmlns":890},[892,6318,6319,6323],{},[895,6320,6321],{},[898,6322,2789],{},[902,6324,2789],{"encoding":904},[724,6326,6327],{},[38,6328,6329],{},"Pravidlo růstu elasticity s cenou:",[3867,6331,6332],{},[724,6333,6334,6335],{},"S rostoucí cenou elasticita poptávky roste. ",[883,6336,6338],{"className":6337},[886],[888,6339,6340],{"xmlns":890},[892,6341,6342,6351],{},[895,6343,6344,6346,6349],{},[1996,6345,2005],{"stretchy":2004},[2129,6347,6348],{},"4.8",[1996,6350,2011],{"stretchy":2004},[902,6352,6353],{"encoding":904},"(4.8)",[724,6355,6356,6357,6360,6361,6364,6365,6382],{},"Z toho plyne, že při ",[614,6358,6359],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,6362,6363],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,6366,6368],{"className":6367},[886],[888,6369,6370],{"xmlns":890},[892,6371,6372,6380],{},[895,6373,6374],{},[2124,6375,6376,6378],{},[898,6377,3937],{},[1996,6379,4354],{},[902,6381,4404],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[3867,6384,6385,6390],{},[724,6386,6387,6389],{},[883,6388,4572],{}," Postup: jak klasifikovat poptávku",[152,6391,6392,6419,6422],{},[123,6393,6394,6395,6418],{},"Spočítejte ",[883,6396,6398],{"className":6397},[886],[888,6399,6400],{"xmlns":890},[892,6401,6402,6416],{},[895,6403,6404,6406,6408,6414],{},[898,6405,4252],{},[1996,6407,2005],{"stretchy":2004},[2124,6409,6410,6412],{},[898,6411,3937],{},[1996,6413,4354],{},[1996,6415,2011],{"stretchy":2004},[902,6417,4382],{"encoding":904}," dle (4.5).",[123,6420,6421],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,6423,6424,6425,6449],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,6426,6428],{"className":6427},[886],[888,6429,6430],{"xmlns":890},[892,6431,6432,6446],{},[895,6433,6434,6436,6438,6440,6442,6444],{},[898,6435,4252],{},[1996,6437,2005],{"stretchy":2004},[898,6439,3937],{},[1996,6441,2011],{"stretchy":2004},[1996,6443,1998],{},[2129,6445,2278],{},[902,6447,6448],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,6451,6452,6455,6456,6473,6474,6492,6493,6520,6521,1975],{},[38,6453,6454],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,6457,6459],{"className":6458},[886],[888,6460,6461],{"xmlns":890},[892,6462,6463,6471],{},[895,6464,6465,6467,6469],{},[898,6466,4252],{},[1996,6468,1998],{},[2129,6470,2278],{},[902,6472,4545],{"encoding":904}," pro ",[883,6475,6477],{"className":6476},[886],[888,6478,6479],{"xmlns":890},[892,6480,6481,6489],{},[895,6482,6483,6485,6487],{},[898,6484,3937],{},[1996,6486,1998],{},[2129,6488,5004],{},[902,6490,6491],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,6494,6496],{"className":6495},[886],[888,6497,6498],{"xmlns":890},[892,6499,6500,6517],{},[895,6501,6502,6504,6507,6509,6511,6513,6515],{},[898,6503,3937],{},[1996,6505,6506],{},"∈",[1996,6508,5324],{"stretchy":2004},[2129,6510,2327],{},[1996,6512,2286],{"separator":2285},[2129,6514,5004],{},[1996,6516,2011],{"stretchy":2004},[902,6518,6519],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,6522,6524],{"className":6523},[886],[888,6525,6526],{"xmlns":890},[892,6527,6528,6544],{},[895,6529,6530,6532,6534,6536,6538,6540,6542],{},[898,6531,3937],{},[1996,6533,6506],{},[1996,6535,2005],{"stretchy":2004},[2129,6537,5004],{},[1996,6539,2286],{"separator":2285},[2129,6541,3120],{},[1996,6543,5341],{"stretchy":2004},[902,6545,6546],{"encoding":904},"P \\in (25, 50\\rangle",[115,6548,6550],{"id":6549},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,6552,6553],{},[2559,6554],{"alt":6555,"className":6556,"src":6557},"imek-elasticita-tr",[210,2563],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,6559,6560],{},[2559,6561],{"alt":6562,"className":6563,"src":6564},"imek-elasticita-podel-linearni-poptavky",[210,2563],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,6566,6567,6568,6618,6619,6635],{},"Pro celkový příjem platí ",[883,6569,6571],{"className":6570},[886],[888,6572,6573],{"xmlns":890},[892,6574,6575,6615],{},[895,6576,6577,6579,6581,6583,6585,6587,6589,6591,6593,6595,6597,6599,6601,6603,6605,6607,6609,6611,6613],{},[898,6578,2774],{},[898,6580,3994],{},[1996,6582,1998],{},[898,6584,2774],{},[898,6586,3994],{},[1996,6588,2005],{"stretchy":2004},[898,6590,2789],{},[1996,6592,2011],{"stretchy":2004},[1996,6594,1998],{},[898,6596,3937],{},[1996,6598,3177],{},[898,6600,2789],{},[1996,6602,1998],{},[898,6604,2789],{},[1996,6606,3177],{},[898,6608,4183],{},[1996,6610,2005],{"stretchy":2004},[898,6612,2789],{},[1996,6614,2011],{"stretchy":2004},[902,6616,6617],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,6620,6622],{"className":6621},[886],[888,6623,6624],{"xmlns":890},[892,6625,6626,6632],{},[895,6627,6628,6630],{},[898,6629,2818],{},[898,6631,3994],{},[902,6633,6634],{"encoding":904},"MR"," odvodíme:",[724,6637,6638],{},[883,6639,6641],{"className":6640},[886],[888,6642,6643],{"xmlns":890},[892,6644,6645,6753],{},[895,6646,6647,6649,6651,6653,6655,6661,6663,6665,6667,6669,6671,6673,6675,6677,6679,6681,6683,6689,6691,6693,6695,6697,6699,6701,6703,6717,6719,6721],{},[898,6648,2818],{},[898,6650,3994],{},[1996,6652,1998],{},[898,6654,2774],{},[2124,6656,6657,6659],{},[898,6658,3994],{},[1996,6660,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,6662,2005],{"stretchy":2004},[898,6664,2789],{},[1996,6666,2011],{"stretchy":2004},[1996,6668,1998],{},[898,6670,4183],{},[1996,6672,2005],{"stretchy":2004},[898,6674,2789],{},[1996,6676,2011],{"stretchy":2004},[1996,6678,2095],{},[898,6680,2789],{},[2288,6682,2987],{},[2124,6684,6685,6687],{},[898,6686,4183],{},[1996,6688,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,6690,2005],{"stretchy":2004},[898,6692,2789],{},[1996,6694,2011],{"stretchy":2004},[1996,6696,1998],{},[898,6698,3937],{},[1996,6700,2095],{},[898,6702,2789],{},[2329,6704,6705,6711],{},[895,6706,6707,6709],{},[898,6708,2194],{"mathvariant":2376},[898,6710,3937],{},[895,6712,6713,6715],{},[898,6714,2194],{"mathvariant":2376},[898,6716,2789],{},[1996,6718,1998],{},[898,6720,3937],{},[895,6722,6723,6725,6727,6729,6735,6737,6751],{},[1996,6724,2005],{"fence":2285},[2129,6726,2278],{},[1996,6728,2095],{},[2329,6730,6731,6733],{},[898,6732,2789],{},[898,6734,3937],{},[1996,6736,3177],{},[2329,6738,6739,6745],{},[895,6740,6741,6743],{},[898,6742,2194],{"mathvariant":2376},[898,6744,3937],{},[895,6746,6747,6749],{},[898,6748,2194],{"mathvariant":2376},[898,6750,2789],{},[1996,6752,2011],{"fence":2285},[902,6754,6755],{"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)",[724,6757,6758],{},[883,6759,6761],{"className":6760},[886],[888,6762,6763],{"xmlns":890},[892,6764,6765,6837],{},[895,6766,6767,6769,6771,6813,6815,6817],{},[1996,6768,1998],{},[898,6770,3937],{},[895,6772,6773,6775,6777,6779,6811],{},[1996,6774,2005],{"fence":2285},[2129,6776,2278],{},[1996,6778,2095],{},[2329,6780,6781,6783],{},[2129,6782,2278],{},[895,6784,6785,6793,6795],{},[2325,6786,6787],{"scriptlevel":2327,"displaystyle":2004},[2329,6788,6789,6791],{},[898,6790,3937],{},[898,6792,2789],{},[1996,6794,3177],{},[2325,6796,6797],{"scriptlevel":2327,"displaystyle":2004},[2329,6798,6799,6805],{},[895,6800,6801,6803],{},[898,6802,2194],{"mathvariant":2376},[898,6804,2789],{},[895,6806,6807,6809],{},[898,6808,2194],{"mathvariant":2376},[898,6810,3937],{},[1996,6812,2011],{"fence":2285},[1996,6814,1998],{},[898,6816,3937],{},[895,6818,6819,6821,6823,6825,6835],{},[1996,6820,2005],{"fence":2285},[2129,6822,2278],{},[1996,6824,2095],{},[2329,6826,6827,6829],{},[2129,6828,2278],{},[895,6830,6831,6833],{},[1996,6832,2225],{},[898,6834,4252],{},[1996,6836,2011],{"fence":2285},[902,6838,6839],{"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)",[724,6841,6842],{},"a tedy",[724,6844,6845],{},[883,6846,6848],{"className":6847,"title":4200,"style":4201},[4199],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[3867,6850,6851,6920,7170],{},[724,6852,6853,6855,6856,6890,6891,6906,6907,2704],{},[883,6854,4155],{}," Intuice: vztah ",[883,6857,6859],{"className":6858},[886],[888,6860,6861],{"xmlns":890},[892,6862,6863,6887],{},[895,6864,6865,6867,6869,6871,6873,6875,6877,6879,6881,6883,6885],{},[898,6866,2818],{},[898,6868,3994],{},[1996,6870,1998],{},[898,6872,3937],{},[1996,6874,2005],{"stretchy":2004},[2129,6876,2278],{},[1996,6878,2225],{},[2129,6880,2278],{},[898,6882,4674],{"mathvariant":2376},[898,6884,4252],{},[1996,6886,2011],{"stretchy":2004},[902,6888,6889],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,6892,6894],{"className":6893},[886],[888,6895,6896],{"xmlns":890},[892,6897,6898,6904],{},[895,6899,6900,6902],{},[898,6901,2818],{},[898,6903,3994],{},[902,6905,6634],{"encoding":904}," jednoznačně určuje hodnota ",[883,6908,6910],{"className":6909},[886],[888,6911,6912],{"xmlns":890},[892,6913,6914,6918],{},[895,6915,6916],{},[898,6917,4252],{},[902,6919,4252],{"encoding":904},[120,6921,6922,7032,7101],{},[123,6923,6924,6941,6942,2203,6956,2203,6982,2203,6995,7015,7016,7031],{},[883,6925,6927],{"className":6926},[886],[888,6928,6929],{"xmlns":890},[892,6930,6931,6939],{},[895,6932,6933,6935,6937],{},[898,6934,4252],{},[1996,6936,3408],{},[2129,6938,2278],{},[902,6940,4509],{"encoding":904}," (elastická) ",[883,6943,6945],{"className":6944},[886],[888,6946,6947],{"xmlns":890},[892,6948,6949,6953],{},[895,6950,6951],{},[1996,6952,3987],{},[902,6954,6955],{"encoding":904},"\\Rightarrow",[883,6957,6959],{"className":6958},[886],[888,6960,6961],{"xmlns":890},[892,6962,6963,6979],{},[895,6964,6965,6967,6969,6971,6973,6975,6977],{},[2129,6966,2278],{},[1996,6968,2225],{},[2129,6970,2278],{},[898,6972,4674],{"mathvariant":2376},[898,6974,4252],{},[1996,6976,3408],{},[2129,6978,2327],{},[902,6980,6981],{"encoding":904},"1 - 1\u002FE > 0",[883,6983,6985],{"className":6984},[886],[888,6986,6987],{"xmlns":890},[892,6988,6989,6993],{},[895,6990,6991],{},[1996,6992,3987],{},[902,6994,6955],{"encoding":904},[883,6996,6998],{"className":6997},[886],[888,6999,7000],{"xmlns":890},[892,7001,7002,7012],{},[895,7003,7004,7006,7008,7010],{},[898,7005,2818],{},[898,7007,3994],{},[1996,7009,3408],{},[2129,7011,2327],{},[902,7013,7014],{"encoding":904},"MR > 0"," — ",[883,7017,7019],{"className":7018},[886],[888,7020,7021],{"xmlns":890},[892,7022,7023,7029],{},[895,7024,7025,7027],{},[898,7026,2774],{},[898,7028,3994],{},[902,7030,4094],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,7033,7034,7051,7052,2203,7065,7015,7085,7100],{},[883,7035,7037],{"className":7036},[886],[888,7038,7039],{"xmlns":890},[892,7040,7041,7049],{},[895,7042,7043,7045,7047],{},[898,7044,4252],{},[1996,7046,1998],{},[2129,7048,2278],{},[902,7050,4545],{"encoding":904}," (jednotková) ",[883,7053,7055],{"className":7054},[886],[888,7056,7057],{"xmlns":890},[892,7058,7059,7063],{},[895,7060,7061],{},[1996,7062,3987],{},[902,7064,6955],{"encoding":904},[883,7066,7068],{"className":7067},[886],[888,7069,7070],{"xmlns":890},[892,7071,7072,7082],{},[895,7073,7074,7076,7078,7080],{},[898,7075,2818],{},[898,7077,3994],{},[1996,7079,1998],{},[2129,7081,2327],{},[902,7083,7084],{"encoding":904},"MR = 0",[883,7086,7088],{"className":7087},[886],[888,7089,7090],{"xmlns":890},[892,7091,7092,7098],{},[895,7093,7094,7096],{},[898,7095,2774],{},[898,7097,3994],{},[902,7099,4094],{"encoding":904}," je extrém (maximum).",[123,7102,7103,7120,7121,2203,7134,7015,7154,7169],{},[883,7104,7106],{"className":7105},[886],[888,7107,7108],{"xmlns":890},[892,7109,7110,7118],{},[895,7111,7112,7114,7116],{},[898,7113,4252],{},[1996,7115,3447],{},[2129,7117,2278],{},[902,7119,4527],{"encoding":904}," (neelastická) ",[883,7122,7124],{"className":7123},[886],[888,7125,7126],{"xmlns":890},[892,7127,7128,7132],{},[895,7129,7130],{},[1996,7131,3987],{},[902,7133,6955],{"encoding":904},[883,7135,7137],{"className":7136},[886],[888,7138,7139],{"xmlns":890},[892,7140,7141,7151],{},[895,7142,7143,7145,7147,7149],{},[898,7144,2818],{},[898,7146,3994],{},[1996,7148,3447],{},[2129,7150,2327],{},[902,7152,7153],{"encoding":904},"MR \u003C 0",[883,7155,7157],{"className":7156},[886],[888,7158,7159],{"xmlns":890},[892,7160,7161,7167],{},[895,7162,7163,7165],{},[898,7164,2774],{},[898,7166,3994],{},[902,7168,4094],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,7171,7172,7173,1975],{},"Viz také ",[207,7174,3823],{"className":7175,"dataFsResolvedFilePath":827,"href":828},[210],[198,7177,7179],{"id":7178},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,7181,7182,7202,7203,7229,7230,7245,7246,7259,7260,7273,7274,7287,7288,7304,7305,2203,7320,7323,7324,7304,7340,1975],{},[38,7183,7184,7185,3918],{},"(a) Poptávka elastická (",[883,7186,7188],{"className":7187},[886],[888,7189,7190],{"xmlns":890},[892,7191,7192,7200],{},[895,7193,7194,7196,7198],{},[898,7195,4252],{},[1996,7197,3408],{},[2129,7199,2278],{},[902,7201,4509],{"encoding":904}," Z (4.12) plyne ",[883,7204,7206],{"className":7205},[886],[888,7207,7208],{"xmlns":890},[892,7209,7210,7226],{},[895,7211,7212,7214,7216,7218,7220,7222,7224],{},[898,7213,2818],{},[898,7215,3994],{},[1996,7217,2005],{"stretchy":2004},[898,7219,2789],{},[1996,7221,2011],{"stretchy":2004},[1996,7223,3408],{},[2129,7225,2327],{},[902,7227,7228],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,7231,7233],{"className":7232},[886],[888,7234,7235],{"xmlns":890},[892,7236,7237,7243],{},[895,7238,7239,7241],{},[898,7240,2774],{},[898,7242,3994],{},[902,7244,4094],{"encoding":904}," je rostoucí funkcí ",[883,7247,7249],{"className":7248},[886],[888,7250,7251],{"xmlns":890},[892,7252,7253,7257],{},[895,7254,7255],{},[898,7256,2789],{},[902,7258,2789],{"encoding":904},". Avšak růst ",[883,7261,7263],{"className":7262},[886],[888,7264,7265],{"xmlns":890},[892,7266,7267,7271],{},[895,7268,7269],{},[898,7270,2789],{},[902,7272,2789],{"encoding":904}," je odezvou na pokles ceny ",[883,7275,7277],{"className":7276},[886],[888,7278,7279],{"xmlns":890},[892,7280,7281,7285],{},[895,7282,7283],{},[898,7284,3937],{},[902,7286,3937],{"encoding":904},". Tudíž s ",[614,7289,7290,7291],{},"poklesem ceny ",[883,7292,7294],{"className":7293},[886],[888,7295,7296],{"xmlns":890},[892,7297,7298,7302],{},[895,7299,7300],{},[898,7301,3937],{},[902,7303,3937],{"encoding":904}," celkový příjem ",[883,7306,7308],{"className":7307},[886],[888,7309,7310],{"xmlns":890},[892,7311,7312,7318],{},[895,7313,7314,7316],{},[898,7315,2774],{},[898,7317,3994],{},[902,7319,4094],{"encoding":904},[614,7321,7322],{},"roste"," a s ",[614,7325,7326,7327],{},"růstem ceny ",[883,7328,7330],{"className":7329},[886],[888,7331,7332],{"xmlns":890},[892,7333,7334,7338],{},[895,7335,7336],{},[898,7337,3937],{},[902,7339,3937],{"encoding":904},[614,7341,7342],{},"klesá",[3867,7344,7345],{},[724,7346,7347,7350],{},[38,7348,7349],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,7352,7353,7202,7373,1343,7399,7414,7415,7428,7429,7442,7443,7456,7457,7304,7470,2203,7485,1975],{},[38,7354,7355,7356,3918],{},"(b) Poptávka neelastická (",[883,7357,7359],{"className":7358},[886],[888,7360,7361],{"xmlns":890},[892,7362,7363,7371],{},[895,7364,7365,7367,7369],{},[898,7366,4252],{},[1996,7368,3447],{},[2129,7370,2278],{},[902,7372,4527],{"encoding":904},[883,7374,7376],{"className":7375},[886],[888,7377,7378],{"xmlns":890},[892,7379,7380,7396],{},[895,7381,7382,7384,7386,7388,7390,7392,7394],{},[898,7383,2818],{},[898,7385,3994],{},[1996,7387,2005],{"stretchy":2004},[898,7389,2789],{},[1996,7391,2011],{"stretchy":2004},[1996,7393,3447],{},[2129,7395,2327],{},[902,7397,7398],{"encoding":904},"MR(Q) \u003C 0",[883,7400,7402],{"className":7401},[886],[888,7403,7404],{"xmlns":890},[892,7405,7406,7412],{},[895,7407,7408,7410],{},[898,7409,2774],{},[898,7411,3994],{},[902,7413,4094],{"encoding":904}," je klesající funkce ",[883,7416,7418],{"className":7417},[886],[888,7419,7420],{"xmlns":890},[892,7421,7422,7426],{},[895,7423,7424],{},[898,7425,2789],{},[902,7427,2789],{"encoding":904},", tj. s růstem ",[883,7430,7432],{"className":7431},[886],[888,7433,7434],{"xmlns":890},[892,7435,7436,7440],{},[895,7437,7438],{},[898,7439,2789],{},[902,7441,2789],{"encoding":904}," (s poklesem ceny ",[883,7444,7446],{"className":7445},[886],[888,7447,7448],{"xmlns":890},[892,7449,7450,7454],{},[895,7451,7452],{},[898,7453,3937],{},[902,7455,3937],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,7458,7460],{"className":7459},[886],[888,7461,7462],{"xmlns":890},[892,7463,7464,7468],{},[895,7465,7466],{},[898,7467,3937],{},[902,7469,3937],{"encoding":904},[883,7471,7473],{"className":7472},[886],[888,7474,7475],{"xmlns":890},[892,7476,7477,7483],{},[895,7478,7479,7481],{},[898,7480,2774],{},[898,7482,3994],{},[902,7484,4094],{"encoding":904},[614,7486,7322],{},[3867,7488,7489],{},[724,7490,7491,7494],{},[38,7492,7493],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,7496,7497,7202,7517,7536,7537,7552,7553,7623,7624,3885,7652,7685,7686,5589,7714,7729,7730,1975],{},[38,7498,7499,7500,3918],{},"(c) Jednotková elasticita (",[883,7501,7503],{"className":7502},[886],[888,7504,7505],{"xmlns":890},[892,7506,7507,7515],{},[895,7508,7509,7511,7513],{},[898,7510,4252],{},[1996,7512,1998],{},[2129,7514,2278],{},[902,7516,4545],{"encoding":904},[883,7518,7520],{"className":7519},[886],[888,7521,7522],{"xmlns":890},[892,7523,7524,7534],{},[895,7525,7526,7528,7530,7532],{},[898,7527,2818],{},[898,7529,3994],{},[1996,7531,1998],{},[2129,7533,2327],{},[902,7535,7084],{"encoding":904}," — nutná podmínka extrému ",[883,7538,7540],{"className":7539},[886],[888,7541,7542],{"xmlns":890},[892,7543,7544,7550],{},[895,7545,7546,7548],{},[898,7547,2774],{},[898,7549,3994],{},[902,7551,4094],{"encoding":904},". Dále ",[883,7554,7556],{"className":7555},[886],[888,7557,7558],{"xmlns":890},[892,7559,7560,7620],{},[895,7561,7562,7564,7574,7576,7578,7584,7586,7592,7594,7596,7598,7600,7602,7604,7614,7616,7618],{},[898,7563,2774],{},[2124,7565,7566,7568],{},[898,7567,3994],{},[895,7569,7570,7572],{},[1996,7571,2378],{"mathvariant":2376},[1996,7573,2378],{"mathvariant":2376},[1996,7575,1998],{},[898,7577,2818],{},[2124,7579,7580,7582],{},[898,7581,3994],{},[1996,7583,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,7585,1998],{},[2124,7587,7588,7590],{},[898,7589,4183],{},[1996,7591,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,7593,2005],{"stretchy":2004},[898,7595,2789],{},[1996,7597,2011],{"stretchy":2004},[1996,7599,2095],{},[898,7601,2789],{},[2288,7603,2987],{},[2124,7605,7606,7608],{},[898,7607,4183],{},[895,7609,7610,7612],{},[1996,7611,2378],{"mathvariant":2376},[1996,7613,2378],{"mathvariant":2376},[1996,7615,2005],{"stretchy":2004},[898,7617,2789],{},[1996,7619,2011],{"stretchy":2004},[902,7621,7622],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,7625,7627],{"className":7626},[886],[888,7628,7629],{"xmlns":890},[892,7630,7631,7649],{},[895,7632,7633,7639,7641,7643,7645,7647],{},[2124,7634,7635,7637],{},[898,7636,4183],{},[1996,7638,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,7640,2005],{"stretchy":2004},[898,7642,2789],{},[1996,7644,2011],{"stretchy":2004},[1996,7646,3447],{},[2129,7648,2327],{},[902,7650,7651],{"encoding":904},"D'(Q) \u003C 0",[883,7653,7655],{"className":7654},[886],[888,7656,7657],{"xmlns":890},[892,7658,7659,7682],{},[895,7660,7661,7671,7673,7675,7677,7680],{},[2124,7662,7663,7665],{},[898,7664,4183],{},[895,7666,7667,7669],{},[1996,7668,2378],{"mathvariant":2376},[1996,7670,2378],{"mathvariant":2376},[1996,7672,2005],{"stretchy":2004},[898,7674,2789],{},[1996,7676,2011],{"stretchy":2004},[1996,7678,7679],{},"≤",[2129,7681,2327],{},[902,7683,7684],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,7687,7689],{"className":7688},[886],[888,7690,7691],{"xmlns":890},[892,7692,7693,7711],{},[895,7694,7695,7697,7707,7709],{},[898,7696,2774],{},[2124,7698,7699,7701],{},[898,7700,3994],{},[895,7702,7703,7705],{},[1996,7704,2378],{"mathvariant":2376},[1996,7706,2378],{"mathvariant":2376},[1996,7708,3447],{},[2129,7710,2327],{},[902,7712,7713],{"encoding":904},"TR'' \u003C 0",[883,7715,7717],{"className":7716},[886],[888,7718,7719],{"xmlns":890},[892,7720,7721,7727],{},[895,7722,7723,7725],{},[898,7724,2774],{},[898,7726,3994],{},[902,7728,4094],{"encoding":904}," nabývá ",[38,7731,7732],{},"maxima",[3867,7734,7735],{},[724,7736,7737,7740],{},[38,7738,7739],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,7742,7743],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,7745,7746],{},[38,7747,7748],{},"Souhrnná tabulka Pravidel 1–3:",[16,7750,7751,7855],{},[19,7752,7753],{},[22,7754,7755,7758,7773,7790,7821,7852],{},[25,7756,7757],{},"Charakter poptávky",[25,7759,7760],{},[883,7761,7763],{"className":7762},[886],[888,7764,7765],{"xmlns":890},[892,7766,7767,7771],{},[895,7768,7769],{},[898,7770,4252],{},[902,7772,4252],{"encoding":904},[25,7774,7775],{},[883,7776,7778],{"className":7777},[886],[888,7779,7780],{"xmlns":890},[892,7781,7782,7788],{},[895,7783,7784,7786],{},[898,7785,2818],{},[898,7787,3994],{},[902,7789,6634],{"encoding":904},[25,7791,7792,7793,2203,7806],{},"Pokles ceny ",[883,7794,7796],{"className":7795},[886],[888,7797,7798],{"xmlns":890},[892,7799,7800,7804],{},[895,7801,7802],{},[1996,7803,3987],{},[902,7805,6955],{"encoding":904},[883,7807,7809],{"className":7808},[886],[888,7810,7811],{"xmlns":890},[892,7812,7813,7819],{},[895,7814,7815,7817],{},[898,7816,2774],{},[898,7818,3994],{},[902,7820,4094],{"encoding":904},[25,7822,7823,7824,2203,7837],{},"Růst ceny ",[883,7825,7827],{"className":7826},[886],[888,7828,7829],{"xmlns":890},[892,7830,7831,7835],{},[895,7832,7833],{},[1996,7834,3987],{},[902,7836,6955],{"encoding":904},[883,7838,7840],{"className":7839},[886],[888,7841,7842],{"xmlns":890},[892,7843,7844,7850],{},[895,7845,7846,7848],{},[898,7847,2774],{},[898,7849,3994],{},[902,7851,4094],{"encoding":904},[25,7853,7854],{},"Doporučení",[30,7856,7857,7906,7956],{},[22,7858,7859,7861,7879,7897,7899,7901],{},[35,7860,4073],{},[35,7862,7863],{},[883,7864,7866],{"className":7865},[886],[888,7867,7868],{"xmlns":890},[892,7869,7870,7876],{},[895,7871,7872,7874],{},[1996,7873,3408],{},[2129,7875,2278],{},[902,7877,7878],{"encoding":904},"> 1",[35,7880,7881],{},[883,7882,7884],{"className":7883},[886],[888,7885,7886],{"xmlns":890},[892,7887,7888,7894],{},[895,7889,7890,7892],{},[1996,7891,3408],{},[2129,7893,2327],{},[902,7895,7896],{"encoding":904},"> 0",[35,7898,7322],{},[35,7900,7342],{},[35,7902,7903],{},[38,7904,7905],{},"snížit cenu",[22,7907,7908,7911,7929,7947,7949,7951],{},[35,7909,7910],{},"jednotková",[35,7912,7913],{},[883,7914,7916],{"className":7915},[886],[888,7917,7918],{"xmlns":890},[892,7919,7920,7926],{},[895,7921,7922,7924],{},[1996,7923,1998],{},[2129,7925,2278],{},[902,7927,7928],{"encoding":904},"= 1",[35,7930,7931],{},[883,7932,7934],{"className":7933},[886],[888,7935,7936],{"xmlns":890},[892,7937,7938,7944],{},[895,7939,7940,7942],{},[1996,7941,1998],{},[2129,7943,2327],{},[902,7945,7946],{"encoding":904},"= 0",[35,7948,3717],{},[35,7950,3717],{},[35,7952,7953],{},[38,7954,7955],{},"držet cenu",[22,7957,7958,7960,7978,7996,7998,8000],{},[35,7959,4077],{},[35,7961,7962],{},[883,7963,7965],{"className":7964},[886],[888,7966,7967],{"xmlns":890},[892,7968,7969,7975],{},[895,7970,7971,7973],{},[1996,7972,3447],{},[2129,7974,2278],{},[902,7976,7977],{"encoding":904},"\u003C 1",[35,7979,7980],{},[883,7981,7983],{"className":7982},[886],[888,7984,7985],{"xmlns":890},[892,7986,7987,7993],{},[895,7988,7989,7991],{},[1996,7990,3447],{},[2129,7992,2327],{},[902,7994,7995],{"encoding":904},"\u003C 0",[35,7997,7342],{},[35,7999,7322],{},[35,8001,8002],{},[38,8003,8004],{},"zvýšit cenu",[198,8006,8008],{"id":8007},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,8010,8011,8012,8037,8038,8060,8061,8074,8075,8088,8089,8102,8103,5589,8130,8182],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,8013,8015],{"className":8014},[886],[888,8016,8017],{"xmlns":890},[892,8018,8019,8035],{},[895,8020,8021,8023,8025,8027,8029],{},[898,8022,3937],{},[1996,8024,1998],{},[2129,8026,3090],{},[1996,8028,2225],{},[2124,8030,8031,8033],{},[898,8032,2789],{},[2129,8034,2131],{},[902,8036,5459],{"encoding":904},". Reálné cenové rozpětí je ",[883,8039,8041],{"className":8040},[886],[888,8042,8043],{"xmlns":890},[892,8044,8045,8057],{},[895,8046,8047,8049,8051,8053,8055],{},[1996,8048,5324],{"stretchy":2004},[2129,8050,2278],{},[1996,8052,2286],{"separator":2285},[2129,8054,3090],{},[1996,8056,5341],{"stretchy":2004},[902,8058,8059],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,8062,8064],{"className":8063},[886],[888,8065,8066],{"xmlns":890},[892,8067,8068,8072],{},[895,8069,8070],{},[898,8071,2789],{},[902,8073,2789],{"encoding":904}," jako funkci ",[883,8076,8078],{"className":8077},[886],[888,8079,8080],{"xmlns":890},[892,8081,8082,8086],{},[895,8083,8084],{},[898,8085,3937],{},[902,8087,3937],{"encoding":904},"; pro nezáporné ",[883,8090,8092],{"className":8091},[886],[888,8093,8094],{"xmlns":890},[892,8095,8096,8100],{},[895,8097,8098],{},[898,8099,2789],{},[902,8101,2789],{"encoding":904}," je ",[883,8104,8106],{"className":8105},[886],[888,8107,8108],{"xmlns":890},[892,8109,8110,8127],{},[895,8111,8112,8114,8116],{},[898,8113,2789],{},[1996,8115,1998],{},[8117,8118,8119],"msqrt",{},[895,8120,8121,8123,8125],{},[2129,8122,3090],{},[1996,8124,2225],{},[898,8126,3937],{},[902,8128,8129],{"encoding":904},"Q = \\sqrt{100 - P}",[883,8131,8133],{"className":8132},[886],[888,8134,8135],{"xmlns":890},[892,8136,8137,8179],{},[895,8138,8139,8155,8157,8159],{},[2325,8140,8141],{"scriptlevel":2327,"displaystyle":2285},[2329,8142,8143,8149],{},[895,8144,8145,8147],{},[898,8146,2194],{"mathvariant":2376},[898,8148,2789],{},[895,8150,8151,8153],{},[898,8152,2194],{"mathvariant":2376},[898,8154,3937],{},[1996,8156,1998],{},[1996,8158,2225],{},[2325,8160,8161],{"scriptlevel":2327,"displaystyle":2285},[2329,8162,8163,8165],{},[2129,8164,2278],{},[895,8166,8167,8169],{},[2129,8168,2131],{},[8117,8170,8171],{},[895,8172,8173,8175,8177],{},[2129,8174,3090],{},[1996,8176,2225],{},[898,8178,3937],{},[902,8180,8181],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,8184,8185],{},[883,8186,8188],{"className":8187},[886],[888,8189,8190],{"xmlns":890},[892,8191,8192,8314],{},[895,8193,8194,8196,8198,8200,8202,8204,8206,8212,8214,8228,8230,8232,8246,8248,8274,8276,8294,8296,8312],{},[898,8195,4252],{},[1996,8197,2005],{"stretchy":2004},[898,8199,3937],{},[1996,8201,2011],{"stretchy":2004},[1996,8203,1998],{},[1996,8205,2225],{},[2329,8207,8208,8210],{},[898,8209,3937],{},[898,8211,2789],{},[1996,8213,3177],{},[2329,8215,8216,8222],{},[895,8217,8218,8220],{},[898,8219,2194],{"mathvariant":2376},[898,8221,2789],{},[895,8223,8224,8226],{},[898,8225,2194],{"mathvariant":2376},[898,8227,3937],{},[1996,8229,1998],{},[1996,8231,2225],{},[2329,8233,8234,8236],{},[898,8235,3937],{},[8117,8237,8238],{},[895,8239,8240,8242,8244],{},[2129,8241,3090],{},[1996,8243,2225],{},[898,8245,3937],{},[1996,8247,3177],{},[895,8249,8250,8252,8254,8272],{},[1996,8251,2005],{"fence":2285},[1996,8253,2225],{},[2329,8255,8256,8258],{},[2129,8257,2278],{},[895,8259,8260,8262],{},[2129,8261,2131],{},[8117,8263,8264],{},[895,8265,8266,8268,8270],{},[2129,8267,3090],{},[1996,8269,2225],{},[898,8271,3937],{},[1996,8273,2011],{"fence":2285},[1996,8275,1998],{},[2329,8277,8278,8280],{},[898,8279,3937],{},[895,8281,8282,8284,8286,8288,8290,8292],{},[2129,8283,2131],{},[1996,8285,2005],{"stretchy":2004},[2129,8287,3090],{},[1996,8289,2225],{},[898,8291,3937],{},[1996,8293,2011],{"stretchy":2004},[1996,8295,1998],{},[2329,8297,8298,8304],{},[895,8299,8300,8302],{},[2129,8301,5009],{},[898,8303,3937],{},[895,8305,8306,8308,8310],{},[2129,8307,3090],{},[1996,8309,2225],{},[898,8311,3937],{},[898,8313,1975],{"mathvariant":2376},[902,8315,8316],{"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}.",[724,8318,8319,8320,2704],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,8321,8323],{"className":8322},[886],[888,8324,8325],{"xmlns":890},[892,8326,8327,8351],{},[895,8328,8329,8347,8349],{},[2325,8330,8331],{"scriptlevel":2327,"displaystyle":2285},[2329,8332,8333,8339],{},[895,8334,8335,8337],{},[2129,8336,5009],{},[898,8338,3937],{},[895,8340,8341,8343,8345],{},[2129,8342,3090],{},[1996,8344,2225],{},[898,8346,3937],{},[1996,8348,1998],{},[2129,8350,2278],{},[902,8352,8353],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,8355,8356],{},[883,8357,8359],{"className":8358},[886],[888,8360,8361],{"xmlns":890},[892,8362,8363,8395],{},[895,8364,8365,8371,8373,8380,8382,8385,8393],{},[2124,8366,8367,8369],{},[898,8368,3937],{},[1996,8370,4354],{},[1996,8372,1998],{},[2329,8374,8375,8378],{},[2129,8376,8377],{},"200",[2129,8379,2173],{},[1996,8381,5900],{},[2129,8383,8384],{},"66,",[8386,8387,8388,8390],"mover",{"accent":2285},[2129,8389,2235],{},[1996,8391,8392],{"stretchy":2285},"‾",[898,8394,1975],{"mathvariant":2376},[902,8396,8397],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,8399,8400],{},"S využitím vlastnosti (4.8):",[120,8402,8403,8449,8491],{},[123,8404,8405,8406,8441,8442,8444,8445,8448],{},"Při cenách ",[883,8407,8409],{"className":8408},[886],[888,8410,8411],{"xmlns":890},[892,8412,8413,8438],{},[895,8414,8415,8417,8419,8421,8423,8426,8428,8430,8436],{},[898,8416,3937],{},[1996,8418,6506],{},[1996,8420,5324],{"stretchy":2004},[2129,8422,2278],{},[1996,8424,8425],{"separator":2285},";",[2288,8427,2987],{},[2129,8429,8384],{},[8386,8431,8432,8434],{"accent":2285},[2129,8433,2235],{},[1996,8435,8392],{"stretchy":2285},[1996,8437,2011],{"stretchy":2004},[902,8439,8440],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,8443,4077],{}," — dle ",[614,8446,8447],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,8450,8405,8451,8441,8485,8444,8487,8490],{},[883,8452,8454],{"className":8453},[886],[888,8455,8456],{"xmlns":890},[892,8457,8458,8482],{},[895,8459,8460,8462,8464,8466,8468,8474,8476,8478,8480],{},[898,8461,3937],{},[1996,8463,6506],{},[1996,8465,2005],{"stretchy":2004},[2129,8467,8384],{},[8386,8469,8470,8472],{"accent":2285},[2129,8471,2235],{},[1996,8473,8392],{"stretchy":2285},[1996,8475,8425],{"separator":2285},[2288,8477,2987],{},[2129,8479,3090],{},[1996,8481,5341],{"stretchy":2004},[902,8483,8484],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,8486,4073],{},[614,8488,8489],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,8492,8493,8494,8497,8498,8526,8527,8530],{},"Dle ",[614,8495,8496],{},"Pravidla 3"," je při ceně ",[883,8499,8501],{"className":8500},[886],[888,8502,8503],{"xmlns":890},[892,8504,8505,8523],{},[895,8506,8507,8513,8515,8517],{},[2124,8508,8509,8511],{},[898,8510,3937],{},[1996,8512,4354],{},[1996,8514,1998],{},[2129,8516,8384],{},[8386,8518,8519,8521],{"accent":2285},[2129,8520,2235],{},[1996,8522,8392],{"stretchy":2285},[902,8524,8525],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,8528,8529],{},"maxima celkového příjmu"," ve výši",[724,8532,8533],{},[883,8534,8536],{"className":8535},[886],[888,8537,8538],{"xmlns":890},[892,8539,8540,8618],{},[895,8541,8542,8544,8546,8548,8554,8556,8558,8564,8566,8580,8582,8588,8590,8598,8600,8613,8615],{},[898,8543,2774],{},[898,8545,3994],{},[1996,8547,2005],{"stretchy":2004},[2124,8549,8550,8552],{},[898,8551,3937],{},[1996,8553,4354],{},[1996,8555,2011],{"stretchy":2004},[1996,8557,1998],{},[2124,8559,8560,8562],{},[898,8561,3937],{},[1996,8563,4354],{},[1996,8565,3177],{},[8117,8567,8568],{},[895,8569,8570,8572,8574],{},[2129,8571,3090],{},[1996,8573,2225],{},[2124,8575,8576,8578],{},[898,8577,3937],{},[1996,8579,4354],{},[1996,8581,1998],{},[2329,8583,8584,8586],{},[2129,8585,8377],{},[2129,8587,2173],{},[1996,8589,3177],{},[8117,8591,8592],{},[2329,8593,8594,8596],{},[2129,8595,3090],{},[2129,8597,2173],{},[1996,8599,1998],{},[2329,8601,8602,8605],{},[2129,8603,8604],{},"2000",[895,8606,8607,8609],{},[2129,8608,2173],{},[8117,8610,8611],{},[2129,8612,2173],{},[1996,8614,5900],{},[2129,8616,8617],{},"384,9.",[902,8619,8620],{"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.",[724,8622,8623,8624,1975],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,8625,8627],{"className":8626},[886],[888,8628,8629],{"xmlns":890},[892,8630,8631,8637],{},[895,8632,8633,8635],{},[898,8634,2774],{},[898,8636,3994],{},[902,8638,4094],{"encoding":904},[115,8640,8642],{"id":8641},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,8644,8645,8646,8649],{},"Analogicky se definuje ",[38,8647,8648],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,8651,8652],{},[883,8653,8655],{"className":8654,"title":4200,"style":4201},[4199],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,8657,4310,8658,8683,8684,8716],{},[883,8659,8661],{"className":8660},[886],[888,8662,8663],{"xmlns":890},[892,8664,8665,8680],{},[895,8666,8667,8669,8671,8674,8676,8678],{},[898,8668,2789],{},[1996,8670,1998],{},[898,8672,8673],{},"S",[1996,8675,2005],{"stretchy":2004},[898,8677,3937],{},[1996,8679,2011],{"stretchy":2004},[902,8681,8682],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,8685,8687],{"className":8686},[886],[888,8688,8689],{"xmlns":890},[892,8690,8691,8713],{},[895,8692,8693,8709,8711],{},[2325,8694,8695],{"scriptlevel":2327,"displaystyle":2285},[2329,8696,8697,8703],{},[895,8698,8699,8701],{},[898,8700,2194],{"mathvariant":2376},[898,8702,2789],{},[895,8704,8705,8707],{},[898,8706,2194],{"mathvariant":2376},[898,8708,3937],{},[1996,8710,3408],{},[2129,8712,2327],{},[902,8714,8715],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,8718,8719],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[3867,8721,8722],{},[724,8723,8724,8725],{},"S rostoucí cenou elasticita nabídky roste. ",[883,8726,8728],{"className":8727},[886],[888,8729,8730],{"xmlns":890},[892,8731,8732,8741],{},[895,8733,8734,8736,8739],{},[1996,8735,2005],{"stretchy":2004},[2129,8737,8738],{},"4.14",[1996,8740,2011],{"stretchy":2004},[902,8742,8743],{"encoding":904},"(4.14)",[724,8745,8746],{},"Pro nominální změny platí",[724,8748,8749],{},[883,8750,8752],{"className":8751,"title":4200,"style":4201},[4199],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,8754,8755],{},"a pro procentní změny",[724,8757,8758],{},[883,8759,8761],{"className":8760,"title":4200,"style":4201},[4199],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,8763,8764],{},"(bez znaménka minus).",[198,8766,8768],{"id":8767},"příklad-47","Příklad 4.7",[724,8770,8771,8772,2704],{},"Nabídka ",[883,8773,8775],{"className":8774},[886],[888,8776,8777],{"xmlns":890},[892,8778,8779,8804],{},[895,8780,8781,8783,8785,8787,8793,8795,8797,8799,8801],{},[898,8782,2789],{},[1996,8784,1998],{},[2129,8786,2794],{},[2124,8788,8789,8791],{},[898,8790,3937],{},[2129,8792,2131],{},[1996,8794,2095],{},[2129,8796,2228],{},[898,8798,3937],{},[1996,8800,2095],{},[2129,8802,8803],{},"150",[902,8805,8806],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,8808,8809],{},[883,8810,8812],{"className":8811},[886],[888,8813,8814],{"xmlns":890},[892,8815,8816,8862],{},[895,8817,8818,8820,8822,8846,8848,8850,8852,8854,8856,8858,8860],{},[898,8819,4252],{},[1996,8821,1998],{},[2329,8823,8824,8826],{},[898,8825,3937],{},[895,8827,8828,8830,8836,8838,8840,8842,8844],{},[2129,8829,2794],{},[2124,8831,8832,8834],{},[898,8833,3937],{},[2129,8835,2131],{},[1996,8837,2095],{},[2129,8839,2228],{},[898,8841,3937],{},[1996,8843,2095],{},[2129,8845,8803],{},[2288,8847,2987],{},[1996,8849,2005],{"stretchy":2004},[2129,8851,2839],{},[898,8853,3937],{},[1996,8855,2095],{},[2129,8857,2228],{},[1996,8859,2011],{"stretchy":2004},[898,8861,1975],{"mathvariant":2376},[902,8863,8864],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,8866,5117,8867,1343,8897,1343,8924,8960,8961,8986,8987,9005,9006,1975],{},[883,8868,8870],{"className":8869},[886],[888,8871,8872],{"xmlns":890},[892,8873,8874,8894],{},[895,8875,8876,8878,8880,8882,8884,8886],{},[898,8877,4252],{},[1996,8879,2005],{"stretchy":2004},[2129,8881,2863],{},[1996,8883,2011],{"stretchy":2004},[1996,8885,1998],{},[2325,8887,8888],{"scriptlevel":2327,"displaystyle":2004},[2329,8889,8890,8892],{},[2129,8891,2278],{},[2129,8893,2173],{},[902,8895,8896],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,8898,8900],{"className":8899},[886],[888,8901,8902],{"xmlns":890},[892,8903,8904,8921],{},[895,8905,8906,8908,8910,8915,8917,8919],{},[898,8907,4252],{},[1996,8909,2005],{"stretchy":2004},[8117,8911,8912],{},[2129,8913,8914],{},"1500",[1996,8916,2011],{"stretchy":2004},[1996,8918,1998],{},[2129,8920,2278],{},[902,8922,8923],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,8925,8927],{"className":8926},[886],[888,8928,8929],{"xmlns":890},[892,8930,8931,8957],{},[895,8932,8933,8935,8937,8939,8941,8943,8952,8954],{},[898,8934,4252],{},[1996,8936,2005],{"stretchy":2004},[2129,8938,3090],{},[1996,8940,2011],{"stretchy":2004},[1996,8942,1998],{},[2325,8944,8945],{"scriptlevel":2327,"displaystyle":2004},[2329,8946,8947,8949],{},[2129,8948,3120],{},[2129,8950,8951],{},"33",[1996,8953,5900],{},[2129,8955,8956],{},"1,515",[902,8958,8959],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,8962,8964],{"className":8963},[886],[888,8965,8966],{"xmlns":890},[892,8967,8968,8983],{},[895,8969,8970,8972,8974,8978,8980],{},[898,8971,3937],{},[1996,8973,3408],{},[8117,8975,8976],{},[2129,8977,8914],{},[1996,8979,2730],{},[2129,8981,8982],{},"38,7",[902,8984,8985],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,8988,8990],{"className":8989},[886],[888,8991,8992],{"xmlns":890},[892,8993,8994,9002],{},[895,8995,8996,8998,9000],{},[898,8997,3937],{},[1996,8999,3447],{},[2129,9001,8982],{},[902,9003,9004],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,9007,9009],{"className":9008},[886],[888,9010,9011],{"xmlns":890},[892,9012,9013,9051],{},[895,9014,9015,9017,9019,9021,9023,9031,9033,9036,9038,9041,9047,9049],{},[898,9016,2889],{"mathvariant":2376},[898,9018,2789],{},[898,9020,5925],{"mathvariant":2376},[1996,9022,2730],{},[2325,9024,9025],{"scriptlevel":2327,"displaystyle":2004},[2329,9026,9027,9029],{},[2129,9028,2278],{},[2129,9030,2173],{},[1996,9032,3177],{},[2129,9034,9035],{},"20",[1996,9037,1998],{},[2129,9039,9040],{},"6,",[8386,9042,9043,9045],{"accent":2285},[2129,9044,2235],{},[1996,9046,8392],{"stretchy":2285},[2288,9048,2987],{},[898,9050,5925],{"mathvariant":2376},[902,9052,9053],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,9055,9057],{"id":9056},"vícefaktorový-model","Vícefaktorový model",[724,9059,9060,9061,9074,9075,2203,9078,9091,9092,2203,9095,9113,9114,2203,9117,2704],{},"Předpokládejme, že poptávané množství ",[883,9062,9064],{"className":9063},[886],[888,9065,9066],{"xmlns":890},[892,9067,9068,9072],{},[895,9069,9070],{},[898,9071,2789],{},[902,9073,2789],{"encoding":904}," závisí na ",[38,9076,9077],{},"ceně základního zboží",[883,9079,9081],{"className":9080},[886],[888,9082,9083],{"xmlns":890},[892,9084,9085,9089],{},[895,9086,9087],{},[898,9088,3937],{},[902,9090,3937],{"encoding":904},", na ",[38,9093,9094],{},"ceně alternativního zboží",[883,9096,9098],{"className":9097},[886],[888,9099,9100],{"xmlns":890},[892,9101,9102,9110],{},[895,9103,9104],{},[2272,9105,9106,9108],{},[898,9107,3937],{},[898,9109,4255],{},[902,9111,9112],{"encoding":904},"P_A"," a na ",[38,9115,9116],{},"důchodu",[883,9118,9120],{"className":9119},[886],[888,9121,9122],{"xmlns":890},[892,9123,9124,9129],{},[895,9125,9126],{},[898,9127,9128],{},"Y",[902,9130,9128],{"encoding":904},[724,9132,9133],{},[883,9134,9136],{"className":9135,"title":4200,"style":4201},[4199],"Q = D(P, P_A, Y). \\tag{4.17}",[724,9138,9139,9140,9143],{},"V analogii jednofaktorového modelu pracujeme s ",[38,9141,9142],{},"parciálními derivacemi"," funkce poptávky.",[198,9145,9147],{"id":9146},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,9149,9150],{},[883,9151,9153],{"className":9152,"title":4200,"style":4201},[4199],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,9155,4310,9156,9177,9178,9191,9192,2927,9214,2203,9217,9263,9264,9277,9278,9295],{},[883,9157,9159],{"className":9158},[886],[888,9160,9161],{"xmlns":890},[892,9162,9163,9174],{},[895,9164,9165],{},[9166,9167,9168,9170,9172],"msubsup",{},[898,9169,2789],{},[898,9171,3937],{},[1996,9173,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,9175,9176],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,9179,9181],{"className":9180},[886],[888,9182,9183],{"xmlns":890},[892,9184,9185,9189],{},[895,9186,9187],{},[898,9188,3937],{},[902,9190,3937],{"encoding":904},". Vždy ",[883,9193,9195],{"className":9194},[886],[888,9196,9197],{"xmlns":890},[892,9198,9199,9211],{},[895,9200,9201,9207,9209],{},[2272,9202,9203,9205],{},[898,9204,4252],{},[898,9206,3937],{},[1996,9208,4485],{},[2129,9210,2327],{},[902,9212,9213],{"encoding":904},"E_P \\ge 0",[614,9215,9216],{},"Interpretace:",[883,9218,9220],{"className":9219},[886],[888,9221,9222],{"xmlns":890},[892,9223,9224,9260],{},[895,9225,9226,9232,9234,9240,9242,9250,9252,9258],{},[2272,9227,9228,9230],{},[898,9229,4252],{},[898,9231,3937],{},[1996,9233,2005],{"stretchy":2004},[2124,9235,9236,9238],{},[898,9237,3937],{},[1996,9239,4354],{},[1996,9241,2286],{"separator":2285},[9166,9243,9244,9246,9248],{},[898,9245,3937],{},[898,9247,4255],{},[1996,9249,4354],{},[1996,9251,2286],{"separator":2285},[2124,9253,9254,9256],{},[898,9255,9128],{},[1996,9257,4354],{},[1996,9259,2011],{"stretchy":2004},[902,9261,9262],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,9265,9267],{"className":9266},[886],[888,9268,9269],{"xmlns":890},[892,9270,9271,9275],{},[895,9272,9273],{},[898,9274,2789],{},[902,9276,2789],{"encoding":904}," při 1% změně ",[883,9279,9281],{"className":9280},[886],[888,9282,9283],{"xmlns":890},[892,9284,9285,9293],{},[895,9286,9287],{},[2124,9288,9289,9291],{},[898,9290,3937],{},[1996,9292,4354],{},[902,9294,4404],{"encoding":904},", ceteris paribus.",[198,9297,9299],{"id":9298},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,9301,9302],{},[883,9303,9305],{"className":9304,"title":4200,"style":4201},[4199],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,9307,9308,9263,9310,9323,9324,9341],{},[614,9309,9216],{},[883,9311,9313],{"className":9312},[886],[888,9314,9315],{"xmlns":890},[892,9316,9317,9321],{},[895,9318,9319],{},[898,9320,2789],{},[902,9322,2789],{"encoding":904}," základního zboží při 1% změně ceny ",[883,9325,9327],{"className":9326},[886],[888,9328,9329],{"xmlns":890},[892,9330,9331,9339],{},[895,9332,9333],{},[2272,9334,9335,9337],{},[898,9336,3937],{},[898,9338,4255],{},[902,9340,9112],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,9343,9344],{},[38,9345,9346],{},"Znaménko závisí na povaze alternativního zboží:",[120,9348,9349,9437],{},[123,9350,9351,9352,9355,9356,9373,9374,2203,9387,1975],{},"Je-li alternativní zboží ",[38,9353,9354],{},"komplement",", růst ",[883,9357,9359],{"className":9358},[886],[888,9360,9361],{"xmlns":890},[892,9362,9363,9371],{},[895,9364,9365],{},[2272,9366,9367,9369],{},[898,9368,3937],{},[898,9370,4255],{},[902,9372,9112],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,9375,9377],{"className":9376},[886],[888,9378,9379],{"xmlns":890},[892,9380,9381,9385],{},[895,9382,9383],{},[898,9384,2789],{},[902,9386,2789],{"encoding":904},[883,9388,9390],{"className":9389},[886],[888,9391,9392],{"xmlns":890},[892,9393,9394,9434],{},[895,9395,9396,9398,9400,9412,9414,9416,9418,9420,9430,9432],{},[1996,9397,3987],{},[2288,9399,3984],{},[9166,9401,9402,9404,9410],{},[898,9403,2789],{},[2272,9405,9406,9408],{},[898,9407,3937],{},[898,9409,4255],{},[1996,9411,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,9413,3447],{},[2129,9415,2327],{},[1996,9417,2286],{"separator":2285},[2288,9419,3984],{},[2272,9421,9422,9424],{},[898,9423,4252],{},[2272,9425,9426,9428],{},[898,9427,3937],{},[898,9429,4255],{},[1996,9431,3447],{},[2129,9433,2327],{},[902,9435,9436],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,9438,9351,9439,9355,9442,9459,9460,9473,9474,1975],{},[38,9440,9441],{},"substitut",[883,9443,9445],{"className":9444},[886],[888,9446,9447],{"xmlns":890},[892,9448,9449,9457],{},[895,9450,9451],{},[2272,9452,9453,9455],{},[898,9454,3937],{},[898,9456,4255],{},[902,9458,9112],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,9461,9463],{"className":9462},[886],[888,9464,9465],{"xmlns":890},[892,9466,9467,9471],{},[895,9468,9469],{},[898,9470,2789],{},[902,9472,2789],{"encoding":904}," roste ",[883,9475,9477],{"className":9476},[886],[888,9478,9479],{"xmlns":890},[892,9480,9481,9521],{},[895,9482,9483,9485,9487,9499,9501,9503,9505,9507,9517,9519],{},[1996,9484,3987],{},[2288,9486,3984],{},[9166,9488,9489,9491,9497],{},[898,9490,2789],{},[2272,9492,9493,9495],{},[898,9494,3937],{},[898,9496,4255],{},[1996,9498,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,9500,3408],{},[2129,9502,2327],{},[1996,9504,2286],{"separator":2285},[2288,9506,3984],{},[2272,9508,9509,9511],{},[898,9510,4252],{},[2272,9512,9513,9515],{},[898,9514,3937],{},[898,9516,4255],{},[1996,9518,3408],{},[2129,9520,2327],{},[902,9522,9523],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,9525,9528],{"className":9526,"title":9527,"style":4201},[4199],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":9530},[9531,9535,9536,9544,9545,9549,9552],{"id":3891,"depth":642,"text":3892,"children":9532},[9533,9534],{"id":3921,"depth":649,"text":3922},{"id":4102,"depth":649,"text":4103},{"id":4137,"depth":642,"text":4138},{"id":4163,"depth":642,"text":4164,"children":9537},[9538,9539,9540,9541,9543],{"id":4859,"depth":649,"text":4860},{"id":4949,"depth":649,"text":4950},{"id":5285,"depth":649,"text":5286},{"id":5367,"depth":649,"text":9542},"Výpočet, je-li dáno PP jako funkce QQ",{"id":5628,"depth":649,"text":5629},{"id":5953,"depth":642,"text":5954},{"id":6549,"depth":642,"text":6550,"children":9546},[9547,9548],{"id":7178,"depth":649,"text":7179},{"id":8007,"depth":649,"text":8008},{"id":8641,"depth":642,"text":8642,"children":9550},[9551],{"id":8767,"depth":649,"text":8768},{"id":9056,"depth":642,"text":9057,"children":9553},[9554,9555],{"id":9146,"depth":649,"text":9147},{"id":9298,"depth":649,"text":9299},"2026-04-22",{},"\u002Ftopics\u002Felasticita",{"title":1920,"description":641},[1138,1136],"topics\u002Felasticita",[1128,1919,9563,9564,9565,9566],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":9569,"title":9570,"body":9571,"course":1128,"courses":659,"created":1129,"description":11113,"extension":661,"meta":11114,"navigation":664,"path":11115,"seo":11116,"sources":11117,"stem":11118,"tags":11119,"type":3857,"updated":677,"__hash__":11124},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":9572,"toc":11098},[9573,9576,9650,9657,9661,9725,9814,9818,9845,9912,9967,9971,9998,10091,10093,10125,10296,10300,10370,10418,10422,10483,10589,10604,10608,10610,10638,10703,10705,10712,10800,10825,11023,11027,11063,11065],[12,9574,9570],{"id":9575},"kalkul-funkcí-více-proměnných",[724,9577,9578,9579,9582,9583,1343,9612,1975],{},"Většina ekonomických veličin závisí na ",[38,9580,9581],{},"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 ",[883,9584,9586],{"className":9585},[886],[888,9587,9588],{"xmlns":890},[892,9589,9590,9609],{},[895,9591,9592,9595,9597,9599,9601,9603,9605,9607],{},[898,9593,9594],{},"z",[1996,9596,1998],{},[898,9598,2001],{},[1996,9600,2005],{"stretchy":2004},[898,9602,2008],{},[1996,9604,2286],{"separator":2285},[898,9606,1994],{},[1996,9608,2011],{"stretchy":2004},[902,9610,9611],{"encoding":904},"z = f(x, y)",[883,9613,9615],{"className":9614},[886],[888,9616,9617],{"xmlns":890},[892,9618,9619,9647],{},[895,9620,9621,9624,9626,9628,9630,9632,9634,9636,9638,9640,9642,9644],{},[898,9622,9623],{},"w",[1996,9625,1998],{},[898,9627,2001],{},[1996,9629,2005],{"stretchy":2004},[898,9631,2008],{},[1996,9633,2286],{"separator":2285},[898,9635,1994],{},[1996,9637,2286],{"separator":2285},[898,9639,9594],{},[1996,9641,2011],{"stretchy":2004},[1996,9643,2286],{"separator":2285},[1996,9645,9646],{},"…",[902,9648,9649],{"encoding":904},"w = f(x, y, z), \\ldots",[724,9651,9652],{},[2559,9653],{"alt":9654,"className":9655,"src":9656},"imek-funkce-2d-vrstevnice",[210,2563],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,9658,9660],{"id":9659},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,9662,9663,9664,9691,9692,9720,9721,9724],{},"Pro ",[883,9665,9667],{"className":9666},[886],[888,9668,9669],{"xmlns":890},[892,9670,9671,9689],{},[895,9672,9673,9675,9677,9679,9681,9683,9685,9687],{},[898,9674,9594],{},[1996,9676,1998],{},[898,9678,2001],{},[1996,9680,2005],{"stretchy":2004},[898,9682,2008],{},[1996,9684,2286],{"separator":2285},[898,9686,1994],{},[1996,9688,2011],{"stretchy":2004},[902,9690,9611],{"encoding":904}," se křivkou s předpisem ",[883,9693,9695],{"className":9694},[886],[888,9696,9697],{"xmlns":890},[892,9698,9699,9717],{},[895,9700,9701,9703,9705,9707,9709,9711,9713,9715],{},[898,9702,2001],{},[1996,9704,2005],{"stretchy":2004},[898,9706,2008],{},[1996,9708,2286],{"separator":2285},[898,9710,1994],{},[1996,9712,2011],{"stretchy":2004},[1996,9714,1998],{},[898,9716,2142],{},[902,9718,9719],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,9722,9723],{},"vrstevnice"," funkce. V ekonomii:",[120,9726,9727,9774],{},[123,9728,9729,9732,9733,9769,9770,1975],{},[38,9730,9731],{},"Indiferenční křivky"," užitečnosti ",[883,9734,9736],{"className":9735},[886],[888,9737,9738],{"xmlns":890},[892,9739,9740,9766],{},[895,9741,9742,9744,9746,9752,9754,9760,9762,9764],{},[898,9743,900],{},[1996,9745,2005],{"stretchy":2004},[2272,9747,9748,9750],{},[898,9749,2789],{},[2129,9751,2278],{},[1996,9753,2286],{"separator":2285},[2272,9755,9756,9758],{},[898,9757,2789],{},[2129,9759,2131],{},[1996,9761,2011],{"stretchy":2004},[1996,9763,1998],{},[898,9765,2142],{},[902,9767,9768],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,9771,9773],{"className":9772,"dataFsResolvedFilePath":878,"href":879},[210],"uzitecnost",[123,9775,9776,9779,9780,9769,9810,1975],{},[38,9777,9778],{},"Izokvanty"," produkce ",[883,9781,9783],{"className":9782},[886],[888,9784,9785],{"xmlns":890},[892,9786,9787,9807],{},[895,9788,9789,9791,9793,9796,9798,9801,9803,9805],{},[898,9790,2789],{},[1996,9792,2005],{"stretchy":2004},[898,9794,9795],{},"L",[1996,9797,2286],{"separator":2285},[898,9799,9800],{},"K",[1996,9802,2011],{"stretchy":2004},[1996,9804,1998],{},[898,9806,2142],{},[902,9808,9809],{"encoding":904},"Q(L, K) = c",[207,9811,9813],{"className":9812,"dataFsResolvedFilePath":857,"href":858},[210],"produkce",[115,9815,9817],{"id":9816},"parciální-derivace","Parciální derivace",[724,9819,9663,9820,9844],{},[883,9821,9823],{"className":9822},[886],[888,9824,9825],{"xmlns":890},[892,9826,9827,9841],{},[895,9828,9829,9831,9833,9835,9837,9839],{},[898,9830,2001],{},[1996,9832,2005],{"stretchy":2004},[898,9834,2008],{},[1996,9836,2286],{"separator":2285},[898,9838,1994],{},[1996,9840,2011],{"stretchy":2004},[902,9842,9843],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,9846,9847],{},[883,9848,9850],{"className":9849},[886],[888,9851,9852],{"xmlns":890},[892,9853,9854,9909],{},[895,9855,9856,9864,9866,9881,9883,9885,9893,9895],{},[9166,9857,9858,9860,9862],{},[898,9859,2001],{},[898,9861,2008],{},[1996,9863,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,9865,1998],{},[2329,9867,9868,9875],{},[895,9869,9870,9873],{},[898,9871,9872],{"mathvariant":2376},"∂",[898,9874,2001],{},[895,9876,9877,9879],{},[898,9878,9872],{"mathvariant":2376},[898,9880,2008],{},[1996,9882,2286],{"separator":2285},[5878,9884],{"width":5880},[9166,9886,9887,9889,9891],{},[898,9888,2001],{},[898,9890,1994],{},[1996,9892,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,9894,1998],{},[2329,9896,9897,9903],{},[895,9898,9899,9901],{},[898,9900,9872],{"mathvariant":2376},[898,9902,2001],{},[895,9904,9905,9907],{},[898,9906,9872],{"mathvariant":2376},[898,9908,1994],{},[902,9910,9911],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,9913,9914,9915,1975],{},"Hodnoty v bodě: ",[883,9916,9918],{"className":9917},[886],[888,9919,9920],{"xmlns":890},[892,9921,9922,9964],{},[895,9923,9924,9932,9934,9936,9938,9940,9942,9944,9946,9954,9956,9958,9960,9962],{},[9166,9925,9926,9928,9930],{},[898,9927,2001],{},[898,9929,2008],{},[1996,9931,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,9933,2005],{"stretchy":2004},[898,9935,207],{},[1996,9937,2286],{"separator":2285},[898,9939,2098],{},[1996,9941,2011],{"stretchy":2004},[1996,9943,2286],{"separator":2285},[2288,9945,2290],{},[9166,9947,9948,9950,9952],{},[898,9949,2001],{},[898,9951,1994],{},[1996,9953,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,9955,2005],{"stretchy":2004},[898,9957,207],{},[1996,9959,2286],{"separator":2285},[898,9961,2098],{},[1996,9963,2011],{"stretchy":2004},[902,9965,9966],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,9968,9970],{"id":9969},"ekonomické-značení","Ekonomické značení",[724,9972,9973,9974,2704],{},"Pro produkční funkci ",[883,9975,9977],{"className":9976},[886],[888,9978,9979],{"xmlns":890},[892,9980,9981,9995],{},[895,9982,9983,9985,9987,9989,9991,9993],{},[898,9984,2789],{},[1996,9986,2005],{"stretchy":2004},[898,9988,9795],{},[1996,9990,2286],{"separator":2285},[898,9992,9800],{},[1996,9994,2011],{"stretchy":2004},[902,9996,9997],{"encoding":904},"Q(L, K)",[120,9999,10000,10046],{},[123,10001,10002,2470,10022,10025,10026,2011],{},[883,10003,10005],{"className":10004},[886],[888,10006,10007],{"xmlns":890},[892,10008,10009,10019],{},[895,10010,10011],{},[9166,10012,10013,10015,10017],{},[898,10014,2789],{},[898,10016,9795],{},[1996,10018,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,10020,10021],{"encoding":904},"Q'_L",[38,10023,10024],{},"mezní produkt práce"," (",[883,10027,10029],{"className":10028},[886],[888,10030,10031],{"xmlns":890},[892,10032,10033,10043],{},[895,10034,10035,10037],{},[898,10036,2818],{},[2272,10038,10039,10041],{},[898,10040,3937],{},[898,10042,9795],{},[902,10044,10045],{"encoding":904},"MP_L",[123,10047,10048,2470,10068,10025,10071,2011],{},[883,10049,10051],{"className":10050},[886],[888,10052,10053],{"xmlns":890},[892,10054,10055,10065],{},[895,10056,10057],{},[9166,10058,10059,10061,10063],{},[898,10060,2789],{},[898,10062,9800],{},[1996,10064,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,10066,10067],{"encoding":904},"Q'_K",[38,10069,10070],{},"mezní produkt kapitálu",[883,10072,10074],{"className":10073},[886],[888,10075,10076],{"xmlns":890},[892,10077,10078,10088],{},[895,10079,10080,10082],{},[898,10081,2818],{},[2272,10083,10084,10086],{},[898,10085,3937],{},[898,10087,9800],{},[902,10089,10090],{"encoding":904},"MP_K",[198,10092,2568],{"id":2567},[724,10094,10095,2704],{},[883,10096,10098],{"className":10097},[886],[888,10099,10100],{"xmlns":890},[892,10101,10102,10122],{},[895,10103,10104,10112,10114,10116,10118,10120],{},[9166,10105,10106,10108,10110],{},[898,10107,2001],{},[898,10109,2008],{},[1996,10111,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,10113,2005],{"stretchy":2004},[898,10115,207],{},[1996,10117,2286],{"separator":2285},[898,10119,2098],{},[1996,10121,2011],{"stretchy":2004},[902,10123,10124],{"encoding":904},"f'_x(a, b)",[120,10126,10127,10185],{},[123,10128,10129,10130,10143,10144,10157,10158,10184],{},"rychlost změny ",[883,10131,10133],{"className":10132},[886],[888,10134,10135],{"xmlns":890},[892,10136,10137,10141],{},[895,10138,10139],{},[898,10140,2001],{},[902,10142,2001],{"encoding":904}," vůči ",[883,10145,10147],{"className":10146},[886],[888,10148,10149],{"xmlns":890},[892,10150,10151,10155],{},[895,10152,10153],{},[898,10154,2008],{},[902,10156,2008],{"encoding":904}," při ",[883,10159,10161],{"className":10160},[886],[888,10162,10163],{"xmlns":890},[892,10164,10165,10181],{},[895,10166,10167,10169,10171,10173,10175,10177,10179],{},[898,10168,2008],{},[1996,10170,1998],{},[898,10172,207],{},[1996,10174,2286],{"separator":2285},[898,10176,1994],{},[1996,10178,1998],{},[898,10180,2098],{},[902,10182,10183],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,10186,10187,10188,2657,10201,10214,10215,10233,10234,1975],{},"přibližná změna ",[883,10189,10191],{"className":10190},[886],[888,10192,10193],{"xmlns":890},[892,10194,10195,10199],{},[895,10196,10197],{},[898,10198,2001],{},[902,10200,2001],{"encoding":904},[883,10202,10204],{"className":10203},[886],[888,10205,10206],{"xmlns":890},[892,10207,10208,10212],{},[895,10209,10210],{},[898,10211,2008],{},[902,10213,2008],{"encoding":904}," o 1 (a pevném ",[883,10216,10218],{"className":10217},[886],[888,10219,10220],{"xmlns":890},[892,10221,10222,10230],{},[895,10223,10224,10226,10228],{},[898,10225,1994],{},[1996,10227,1998],{},[898,10229,2098],{},[902,10231,10232],{"encoding":904},"y = b","): ",[883,10235,10237],{"className":10236},[886],[888,10238,10239],{"xmlns":890},[892,10240,10241,10293],{},[895,10242,10243,10245,10247,10249,10251,10253,10255,10257,10259,10261,10263,10265,10267,10269,10271,10273,10275,10283,10285,10287,10289,10291],{},[898,10244,2001],{},[1996,10246,2005],{"stretchy":2004},[898,10248,207],{},[1996,10250,2095],{},[2129,10252,2278],{},[1996,10254,2286],{"separator":2285},[898,10256,2098],{},[1996,10258,2011],{"stretchy":2004},[1996,10260,2730],{},[898,10262,2001],{},[1996,10264,2005],{"stretchy":2004},[898,10266,207],{},[1996,10268,2286],{"separator":2285},[898,10270,2098],{},[1996,10272,2011],{"stretchy":2004},[1996,10274,2095],{},[9166,10276,10277,10279,10281],{},[898,10278,2001],{},[898,10280,2008],{},[1996,10282,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,10284,2005],{"stretchy":2004},[898,10286,207],{},[1996,10288,2286],{"separator":2285},[898,10290,2098],{},[1996,10292,2011],{"stretchy":2004},[902,10294,10295],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,10297,10299],{"id":10298},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,10301,10302],{},[883,10303,10305],{"className":10304},[886],[888,10306,10307],{"xmlns":890},[892,10308,10309,10367],{},[895,10310,10311,10313,10315,10317,10325,10327,10329,10331,10333,10335,10337,10339,10341,10343,10351,10353,10355,10357,10359,10361,10363,10365],{},[898,10312,2194],{},[898,10314,2001],{},[1996,10316,1998],{},[9166,10318,10319,10321,10323],{},[898,10320,2001],{},[898,10322,2008],{},[1996,10324,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,10326,2005],{"stretchy":2004},[898,10328,2008],{},[1996,10330,2286],{"separator":2285},[898,10332,1994],{},[1996,10334,2011],{"stretchy":2004},[2288,10336,2987],{},[898,10338,2194],{},[898,10340,2008],{},[1996,10342,2095],{},[9166,10344,10345,10347,10349],{},[898,10346,2001],{},[898,10348,1994],{},[1996,10350,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,10352,2005],{"stretchy":2004},[898,10354,2008],{},[1996,10356,2286],{"separator":2285},[898,10358,1994],{},[1996,10360,2011],{"stretchy":2004},[2288,10362,2987],{},[898,10364,2194],{},[898,10366,1994],{},[902,10368,10369],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,10371,2997,10372,10394,10395,10417],{},[883,10373,10375],{"className":10374},[886],[888,10376,10377],{"xmlns":890},[892,10378,10379,10391],{},[895,10380,10381,10383,10385,10387,10389],{},[898,10382,2194],{},[898,10384,2008],{},[1996,10386,2286],{"separator":2285},[898,10388,2194],{},[898,10390,1994],{},[902,10392,10393],{"encoding":904},"dx, dy"," platí ",[883,10396,10398],{"className":10397},[886],[888,10399,10400],{"xmlns":890},[892,10401,10402,10414],{},[895,10403,10404,10406,10408,10410,10412],{},[898,10405,2889],{"mathvariant":2376},[898,10407,2001],{},[1996,10409,2730],{},[898,10411,2194],{},[898,10413,2001],{},[902,10415,10416],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,10419,10421],{"id":10420},"implicitní-funkce","Implicitní funkce",[724,10423,10424,10425,10454,10455,10468,10469,10482],{},"Je-li vztah dán rovnicí ",[883,10426,10428],{"className":10427},[886],[888,10429,10430],{"xmlns":890},[892,10431,10432,10451],{},[895,10433,10434,10437,10439,10441,10443,10445,10447,10449],{},[898,10435,10436],{},"F",[1996,10438,2005],{"stretchy":2004},[898,10440,2008],{},[1996,10442,2286],{"separator":2285},[898,10444,1994],{},[1996,10446,2011],{"stretchy":2004},[1996,10448,1998],{},[2129,10450,2327],{},[902,10452,10453],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,10456,10458],{"className":10457},[886],[888,10459,10460],{"xmlns":890},[892,10461,10462,10466],{},[895,10463,10464],{},[898,10465,1994],{},[902,10467,1994],{"encoding":904}," podle ",[883,10470,10472],{"className":10471},[886],[888,10473,10474],{"xmlns":890},[892,10475,10476,10480],{},[895,10477,10478],{},[898,10479,2008],{},[902,10481,2008],{"encoding":904}," (nebo naopak):",[724,10484,10485],{},[883,10486,10488],{"className":10487},[886],[888,10489,10490],{"xmlns":890},[892,10491,10492,10586],{},[895,10493,10494,10500,10502,10516,10518,10520,10538,10540,10542,10548,10550,10564,10566,10568],{},[2124,10495,10496,10498],{},[898,10497,1994],{},[1996,10499,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,10501,1998],{},[2329,10503,10504,10510],{},[895,10505,10506,10508],{},[898,10507,2194],{},[898,10509,1994],{},[895,10511,10512,10514],{},[898,10513,2194],{},[898,10515,2008],{},[1996,10517,1998],{},[1996,10519,2225],{},[2329,10521,10522,10530],{},[9166,10523,10524,10526,10528],{},[898,10525,10436],{},[898,10527,2008],{},[1996,10529,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[9166,10531,10532,10534,10536],{},[898,10533,10436],{},[898,10535,1994],{},[1996,10537,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,10539,2286],{"separator":2285},[5878,10541],{"width":5880},[2124,10543,10544,10546],{},[898,10545,2008],{},[1996,10547,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,10549,1998],{},[2329,10551,10552,10558],{},[895,10553,10554,10556],{},[898,10555,2194],{},[898,10557,2008],{},[895,10559,10560,10562],{},[898,10561,2194],{},[898,10563,1994],{},[1996,10565,1998],{},[1996,10567,2225],{},[2329,10569,10570,10578],{},[9166,10571,10572,10574,10576],{},[898,10573,10436],{},[898,10575,1994],{},[1996,10577,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[9166,10579,10580,10582,10584],{},[898,10581,10436],{},[898,10583,2008],{},[1996,10585,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,10587,10588],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,10590,10591,10592,10595,10596,3885,10600,1975],{},"Tato vzorec dává ",[38,10593,10594],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,10597,10599],{"className":10598,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS",[207,10601,10603],{"className":10602,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS",[115,10605,10607],{"id":10606},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,10609,3252],{"id":3251},[724,10611,10612,10613,10637],{},"V bodě extrému ",[883,10614,10616],{"className":10615},[886],[888,10617,10618],{"xmlns":890},[892,10619,10620,10634],{},[895,10621,10622,10624,10626,10628,10630,10632],{},[898,10623,4255],{},[1996,10625,2486],{"stretchy":2004},[898,10627,207],{},[1996,10629,2286],{"separator":2285},[898,10631,2098],{},[1996,10633,2501],{"stretchy":2004},[902,10635,10636],{"encoding":904},"A[a, b]"," musí platit současně:",[724,10639,10640],{},[883,10641,10643],{"className":10642},[886],[888,10644,10645],{"xmlns":890},[892,10646,10647,10700],{},[895,10648,10649,10657,10659,10661,10663,10665,10667,10669,10671,10673,10676,10678,10686,10688,10690,10692,10694,10696,10698],{},[9166,10650,10651,10653,10655],{},[898,10652,2001],{},[898,10654,2008],{},[1996,10656,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,10658,2005],{"stretchy":2004},[898,10660,207],{},[1996,10662,2286],{"separator":2285},[898,10664,2098],{},[1996,10666,2011],{"stretchy":2004},[1996,10668,1998],{},[2129,10670,2327],{},[2288,10672,3984],{},[1996,10674,10675],{},"∧",[2288,10677,3984],{},[9166,10679,10680,10682,10684],{},[898,10681,2001],{},[898,10683,1994],{},[1996,10685,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,10687,2005],{"stretchy":2004},[898,10689,207],{},[1996,10691,2286],{"separator":2285},[898,10693,2098],{},[1996,10695,2011],{"stretchy":2004},[1996,10697,1998],{},[2129,10699,2327],{},[902,10701,10702],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,10704,3326],{"id":3325},[724,10706,10707,10708,10711],{},"Definujeme ",[38,10709,10710],{},"diskriminant"," (Hessián zjednodušeně):",[724,10713,10714],{},[883,10715,10717],{"className":10716},[886],[888,10718,10719],{"xmlns":890},[892,10720,10721,10797],{},[895,10722,10723,10725,10727,10729,10731,10733,10735,10737,10753,10755,10771,10773,10775,10791],{},[898,10724,4183],{},[1996,10726,2005],{"stretchy":2004},[898,10728,2008],{},[1996,10730,2286],{"separator":2285},[898,10732,1994],{},[1996,10734,2011],{"stretchy":2004},[1996,10736,1998],{},[9166,10738,10739,10741,10747],{},[898,10740,2001],{},[895,10742,10743,10745],{},[898,10744,2008],{},[898,10746,2008],{},[895,10748,10749,10751],{},[1996,10750,2378],{"mathvariant":2376},[1996,10752,2378],{"mathvariant":2376},[1996,10754,3177],{},[9166,10756,10757,10759,10765],{},[898,10758,2001],{},[895,10760,10761,10763],{},[898,10762,1994],{},[898,10764,1994],{},[895,10766,10767,10769],{},[1996,10768,2378],{"mathvariant":2376},[1996,10770,2378],{"mathvariant":2376},[1996,10772,2225],{},[1996,10774,2005],{"stretchy":2004},[9166,10776,10777,10779,10785],{},[898,10778,2001],{},[895,10780,10781,10783],{},[898,10782,2008],{},[898,10784,1994],{},[895,10786,10787,10789],{},[1996,10788,2378],{"mathvariant":2376},[1996,10790,2378],{"mathvariant":2376},[2124,10792,10793,10795],{},[1996,10794,2011],{"stretchy":2004},[2129,10796,2131],{},[902,10798,10799],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,10801,10802,10803,2704],{},"V podezřelém bodě ",[883,10804,10806],{"className":10805},[886],[888,10807,10808],{"xmlns":890},[892,10809,10810,10822],{},[895,10811,10812,10814,10816,10818,10820],{},[1996,10813,2486],{"stretchy":2004},[898,10815,207],{},[1996,10817,2286],{"separator":2285},[898,10819,2098],{},[1996,10821,2501],{"stretchy":2004},[902,10823,10824],{"encoding":904},"[a, b]",[152,10826,10827,10954,10990],{},[123,10828,10829,10859,10860],{},[38,10830,10831,2704],{},[883,10832,10834],{"className":10833},[886],[888,10835,10836],{"xmlns":890},[892,10837,10838,10856],{},[895,10839,10840,10842,10844,10846,10848,10850,10852,10854],{},[898,10841,4183],{},[1996,10843,2005],{"stretchy":2004},[898,10845,207],{},[1996,10847,2286],{"separator":2285},[898,10849,2098],{},[1996,10851,2011],{"stretchy":2004},[1996,10853,3408],{},[2129,10855,2327],{},[902,10857,10858],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,10861,10862,10908],{},[123,10863,10864,3414,10906],{},[883,10865,10867],{"className":10866},[886],[888,10868,10869],{"xmlns":890},[892,10870,10871,10903],{},[895,10872,10873,10889,10891,10893,10895,10897,10899,10901],{},[9166,10874,10875,10877,10883],{},[898,10876,2001],{},[895,10878,10879,10881],{},[898,10880,2008],{},[898,10882,2008],{},[895,10884,10885,10887],{},[1996,10886,2378],{"mathvariant":2376},[1996,10888,2378],{"mathvariant":2376},[1996,10890,2005],{"stretchy":2004},[898,10892,207],{},[1996,10894,2286],{"separator":2285},[898,10896,2098],{},[1996,10898,2011],{"stretchy":2004},[1996,10900,3408],{},[2129,10902,2327],{},[902,10904,10905],{"encoding":904},"f''_{xx}(a, b) > 0",[38,10907,3775],{},[123,10909,10910,3414,10952],{},[883,10911,10913],{"className":10912},[886],[888,10914,10915],{"xmlns":890},[892,10916,10917,10949],{},[895,10918,10919,10935,10937,10939,10941,10943,10945,10947],{},[9166,10920,10921,10923,10929],{},[898,10922,2001],{},[895,10924,10925,10927],{},[898,10926,2008],{},[898,10928,2008],{},[895,10930,10931,10933],{},[1996,10932,2378],{"mathvariant":2376},[1996,10934,2378],{"mathvariant":2376},[1996,10936,2005],{"stretchy":2004},[898,10938,207],{},[1996,10940,2286],{"separator":2285},[898,10942,2098],{},[1996,10944,2011],{"stretchy":2004},[1996,10946,3447],{},[2129,10948,2327],{},[902,10950,10951],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,10953,3717],{},[123,10955,10956,2203,10986,10989],{},[38,10957,10958,2704],{},[883,10959,10961],{"className":10960},[886],[888,10962,10963],{"xmlns":890},[892,10964,10965,10983],{},[895,10966,10967,10969,10971,10973,10975,10977,10979,10981],{},[898,10968,4183],{},[1996,10970,2005],{"stretchy":2004},[898,10972,207],{},[1996,10974,2286],{"separator":2285},[898,10976,2098],{},[1996,10978,2011],{"stretchy":2004},[1996,10980,3447],{},[2129,10982,2327],{},[902,10984,10985],{"encoding":904},"D(a, b) \u003C 0",[38,10987,10988],{},"sedlo"," (v daném bodě extrém není).",[123,10991,10992,11022],{},[38,10993,10994,2704],{},[883,10995,10997],{"className":10996},[886],[888,10998,10999],{"xmlns":890},[892,11000,11001,11019],{},[895,11002,11003,11005,11007,11009,11011,11013,11015,11017],{},[898,11004,4183],{},[1996,11006,2005],{"stretchy":2004},[898,11008,207],{},[1996,11010,2286],{"separator":2285},[898,11012,2098],{},[1996,11014,2011],{"stretchy":2004},[1996,11016,1998],{},[2129,11018,2327],{},[902,11020,11021],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,11024,11026],{"id":11025},"vázané-extrémy","Vázané extrémy",[724,11028,11029,11030,11059,11060,1975],{},"Pro extrémy s omezující podmínkou ",[883,11031,11033],{"className":11032},[886],[888,11034,11035],{"xmlns":890},[892,11036,11037,11056],{},[895,11038,11039,11042,11044,11046,11048,11050,11052,11054],{},[898,11040,11041],{},"g",[1996,11043,2005],{"stretchy":2004},[898,11045,2008],{},[1996,11047,2286],{"separator":2285},[898,11049,1994],{},[1996,11051,2011],{"stretchy":2004},[1996,11053,1998],{},[2129,11055,2327],{},[902,11057,11058],{"encoding":904},"g(x, y) = 0"," se používá ",[207,11061,793],{"className":11062,"dataFsResolvedFilePath":791,"href":792},[210],[115,11064,3792],{"id":3791},[120,11066,11067,11074,11081],{},[123,11068,11069,2203,11071],{},[38,11070,3799],{},[207,11072,775],{"className":11073,"dataFsResolvedFilePath":773,"href":774},[210],[123,11075,11076,2203,11078],{},[38,11077,3807],{},[207,11079,793],{"className":11080,"dataFsResolvedFilePath":791,"href":792},[210],[123,11082,11083,2203,11085,11089,11090,11093,11094,11097],{},[38,11084,3815],{},[207,11086,11088],{"className":11087,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (parciální derivace = mezní produkty), ",[207,11091,880],{"className":11092,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,11095,3828],{"className":11096,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":11099},[11100,11101,11105,11106,11107,11111,11112],{"id":9659,"depth":642,"text":9660},{"id":9816,"depth":642,"text":9817,"children":11102},[11103,11104],{"id":9969,"depth":649,"text":9970},{"id":2567,"depth":649,"text":2568},{"id":10298,"depth":642,"text":10299},{"id":10420,"depth":642,"text":10421},{"id":10606,"depth":642,"text":10607,"children":11108},[11109,11110],{"id":3251,"depth":649,"text":3252},{"id":3325,"depth":649,"text":3326},{"id":11025,"depth":642,"text":11026},{"id":3791,"depth":642,"text":3792},"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":9570,"description":11113},[1135],"topics\u002Ffunkce-vice-promennych",[1128,11120,3854,11121,11122,11123],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":11126,"title":775,"body":11127,"course":1128,"courses":659,"created":1129,"description":11983,"extension":661,"meta":11984,"navigation":664,"path":11985,"seo":11986,"sources":11987,"stem":11988,"tags":11989,"type":3857,"updated":677,"__hash__":11996},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":11128,"toc":11973},[11129,11132,11143,11147,11192,11272,11276,11352,11394,11401,11405,11409,11438,11496,11543,11581,11585,11635,11687,11739,11783,11786,11789,11861,11864,11936,11943,11945],[12,11130,775],{"id":11131},"integrál",[724,11133,11134,11135,11138,11139,11142],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,11136,11137],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,11140,11141],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,11144,11146],{"id":11145},"neurčitý-integrál","Neurčitý integrál",[724,11148,11149],{},[883,11150,11152],{"className":11151},[886],[888,11153,11154],{"xmlns":890},[892,11155,11156,11189],{},[895,11157,11158,11160,11162,11164,11166,11168,11171,11173,11175,11177,11179,11181,11183,11185,11187],{},[898,11159,10436],{},[1996,11161,2005],{"stretchy":2004},[898,11163,2008],{},[1996,11165,2011],{"stretchy":2004},[1996,11167,1998],{},[1996,11169,11170],{},"∫",[898,11172,2001],{},[1996,11174,2005],{"stretchy":2004},[898,11176,2008],{},[1996,11178,2011],{"stretchy":2004},[2288,11180,2987],{},[898,11182,2194],{},[898,11184,2008],{},[1996,11186,2095],{},[898,11188,2777],{},[902,11190,11191],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,11193,4310,11194,2927,11228,8102,11241,11244,11245,1343,11258,11271],{},[883,11195,11197],{"className":11196},[886],[888,11198,11199],{"xmlns":890},[892,11200,11201,11225],{},[895,11202,11203,11209,11211,11213,11215,11217,11219,11221,11223],{},[2124,11204,11205,11207],{},[898,11206,10436],{},[1996,11208,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,11210,2005],{"stretchy":2004},[898,11212,2008],{},[1996,11214,2011],{"stretchy":2004},[1996,11216,1998],{},[898,11218,2001],{},[1996,11220,2005],{"stretchy":2004},[898,11222,2008],{},[1996,11224,2011],{"stretchy":2004},[902,11226,11227],{"encoding":904},"F'(x) = f(x)",[883,11229,11231],{"className":11230},[886],[888,11232,11233],{"xmlns":890},[892,11234,11235,11239],{},[895,11236,11237],{},[898,11238,10436],{},[902,11240,10436],{"encoding":904},[38,11242,11243],{},"primitivní funkce"," k ",[883,11246,11248],{"className":11247},[886],[888,11249,11250],{"xmlns":890},[892,11251,11252,11256],{},[895,11253,11254],{},[898,11255,2001],{},[902,11257,2001],{"encoding":904},[883,11259,11261],{"className":11260},[886],[888,11262,11263],{"xmlns":890},[892,11264,11265,11269],{},[895,11266,11267],{},[898,11268,2777],{},[902,11270,2777],{"encoding":904}," konstanta.",[115,11273,11275],{"id":11274},"určitý-integrál","Určitý integrál",[724,11277,11278],{},[883,11279,11281],{"className":11280},[886],[888,11282,11283],{"xmlns":890},[892,11284,11285,11349],{},[895,11286,11287,11295,11297,11299,11301,11303,11305,11307,11309,11311,11313,11315,11317,11319,11321,11329,11331,11333,11335,11337,11339,11341,11343,11345,11347],{},[9166,11288,11289,11291,11293],{},[1996,11290,11170],{},[898,11292,207],{},[898,11294,2098],{},[898,11296,2001],{},[1996,11298,2005],{"stretchy":2004},[898,11300,2008],{},[1996,11302,2011],{"stretchy":2004},[2288,11304,2987],{},[898,11306,2194],{},[898,11308,2008],{},[1996,11310,1998],{},[1996,11312,2486],{"stretchy":2004},[898,11314,10436],{},[1996,11316,2005],{"stretchy":2004},[898,11318,2008],{},[1996,11320,2011],{"stretchy":2004},[9166,11322,11323,11325,11327],{},[1996,11324,2501],{"stretchy":2004},[898,11326,207],{},[898,11328,2098],{},[1996,11330,1998],{},[898,11332,10436],{},[1996,11334,2005],{"stretchy":2004},[898,11336,2098],{},[1996,11338,2011],{"stretchy":2004},[1996,11340,2225],{},[898,11342,10436],{},[1996,11344,2005],{"stretchy":2004},[898,11346,207],{},[1996,11348,2011],{"stretchy":2004},[902,11350,11351],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,11353,11354,11355,2203,11358,11371,11372,11393],{},"Geometricky ",[38,11356,11357],{},"plocha pod grafem",[883,11359,11361],{"className":11360},[886],[888,11362,11363],{"xmlns":890},[892,11364,11365,11369],{},[895,11366,11367],{},[898,11368,2001],{},[902,11370,2001],{"encoding":904}," na intervalu ",[883,11373,11375],{"className":11374},[886],[888,11376,11377],{"xmlns":890},[892,11378,11379,11391],{},[895,11380,11381,11383,11385,11387,11389],{},[1996,11382,2486],{"stretchy":2004},[898,11384,207],{},[1996,11386,2286],{"separator":2285},[898,11388,2098],{},[1996,11390,2501],{"stretchy":2004},[902,11392,10824],{"encoding":904}," (orientovaná).",[724,11395,11396],{},[2559,11397],{"alt":11398,"className":11399,"src":11400},"imek-integral-plocha",[210,2563],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,11402,11404],{"id":11403},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,11406,11408],{"id":11407},"příklad-tr-z-mr","Příklad — TR z MR",[724,11410,11411,11412,1975],{},"Mezní příjem ",[883,11413,11415],{"className":11414},[886],[888,11416,11417],{"xmlns":890},[892,11418,11419,11435],{},[895,11420,11421,11423,11425,11427,11429,11431,11433],{},[898,11422,2818],{},[898,11424,3994],{},[1996,11426,1998],{},[2129,11428,3090],{},[1996,11430,2225],{},[2129,11432,2131],{},[898,11434,2789],{},[902,11436,11437],{"encoding":904},"MR = 100 - 2Q",[724,11439,11440],{},[883,11441,11443],{"className":11442},[886],[888,11444,11445],{"xmlns":890},[892,11446,11447,11493],{},[895,11448,11449,11451,11453,11455,11457,11459,11461,11463,11465,11467,11469,11471,11473,11475,11477,11479,11481,11483,11489,11491],{},[898,11450,2774],{},[898,11452,3994],{},[1996,11454,1998],{},[1996,11456,11170],{},[1996,11458,2005],{"stretchy":2004},[2129,11460,3090],{},[1996,11462,2225],{},[2129,11464,2131],{},[898,11466,2789],{},[1996,11468,2011],{"stretchy":2004},[2288,11470,2987],{},[898,11472,2194],{},[898,11474,2789],{},[1996,11476,1998],{},[2129,11478,3090],{},[898,11480,2789],{},[1996,11482,2225],{},[2124,11484,11485,11487],{},[898,11486,2789],{},[2129,11488,2131],{},[1996,11490,2095],{},[898,11492,2142],{},[902,11494,11495],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,11497,11498,11499,3414,11525,2704],{},"Okrajová podmínka ",[883,11500,11502],{"className":11501},[886],[888,11503,11504],{"xmlns":890},[892,11505,11506,11522],{},[895,11507,11508,11510,11512,11514,11516,11518,11520],{},[898,11509,2774],{},[898,11511,3994],{},[1996,11513,2005],{"stretchy":2004},[2129,11515,2327],{},[1996,11517,2011],{"stretchy":2004},[1996,11519,1998],{},[2129,11521,2327],{},[902,11523,11524],{"encoding":904},"TR(0) = 0",[883,11526,11528],{"className":11527},[886],[888,11529,11530],{"xmlns":890},[892,11531,11532,11540],{},[895,11533,11534,11536,11538],{},[898,11535,2142],{},[1996,11537,1998],{},[2129,11539,2327],{},[902,11541,11542],{"encoding":904},"c = 0",[724,11544,11545],{},[883,11546,11548],{"className":11547},[886],[888,11549,11550],{"xmlns":890},[892,11551,11552,11578],{},[895,11553,11554,11556,11558,11560,11562,11564,11566,11568,11570,11572],{},[898,11555,2774],{},[898,11557,3994],{},[1996,11559,2005],{"stretchy":2004},[898,11561,2789],{},[1996,11563,2011],{"stretchy":2004},[1996,11565,1998],{},[2129,11567,3090],{},[898,11569,2789],{},[1996,11571,2225],{},[2124,11573,11574,11576],{},[898,11575,2789],{},[2129,11577,2131],{},[902,11579,11580],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,11582,11584],{"id":11583},"příklad-tc-z-mc","Příklad — TC z MC",[724,11586,11587,11588,11614,11615,1975],{},"Mezní náklady ",[883,11589,11591],{"className":11590},[886],[888,11592,11593],{"xmlns":890},[892,11594,11595,11611],{},[895,11596,11597,11599,11601,11603,11605,11607,11609],{},[898,11598,2818],{},[898,11600,2777],{},[1996,11602,1998],{},[2129,11604,2131],{},[1996,11606,2095],{},[2129,11608,2839],{},[898,11610,2789],{},[902,11612,11613],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,11616,11618],{"className":11617},[886],[888,11619,11620],{"xmlns":890},[892,11621,11622,11632],{},[895,11623,11624,11626,11628,11630],{},[898,11625,10436],{},[898,11627,2777],{},[1996,11629,1998],{},[2129,11631,3090],{},[902,11633,11634],{"encoding":904},"FC = 100",[724,11636,11637],{},[883,11638,11640],{"className":11639},[886],[888,11641,11642],{"xmlns":890},[892,11643,11644,11684],{},[895,11645,11646,11648,11650,11652,11654,11656,11658,11660,11662,11664,11666,11668,11670,11672,11674,11680,11682],{},[898,11647,2774],{},[898,11649,2777],{},[1996,11651,1998],{},[1996,11653,11170],{},[898,11655,2818],{},[898,11657,2777],{},[2288,11659,2987],{},[898,11661,2194],{},[898,11663,2789],{},[1996,11665,1998],{},[2129,11667,2131],{},[898,11669,2789],{},[1996,11671,2095],{},[2129,11673,2794],{},[2124,11675,11676,11678],{},[898,11677,2789],{},[2129,11679,2131],{},[1996,11681,2095],{},[898,11683,2142],{},[902,11685,11686],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,11688,11498,11689,3414,11721,2704],{},[883,11690,11692],{"className":11691},[886],[888,11693,11694],{"xmlns":890},[892,11695,11696,11718],{},[895,11697,11698,11700,11702,11704,11706,11708,11710,11712,11714,11716],{},[898,11699,2774],{},[898,11701,2777],{},[1996,11703,2005],{"stretchy":2004},[2129,11705,2327],{},[1996,11707,2011],{"stretchy":2004},[1996,11709,1998],{},[898,11711,10436],{},[898,11713,2777],{},[1996,11715,1998],{},[2129,11717,3090],{},[902,11719,11720],{"encoding":904},"TC(0) = FC = 100",[883,11722,11724],{"className":11723},[886],[888,11725,11726],{"xmlns":890},[892,11727,11728,11736],{},[895,11729,11730,11732,11734],{},[898,11731,2142],{},[1996,11733,1998],{},[2129,11735,3090],{},[902,11737,11738],{"encoding":904},"c = 100",[724,11740,11741],{},[883,11742,11744],{"className":11743},[886],[888,11745,11746],{"xmlns":890},[892,11747,11748,11780],{},[895,11749,11750,11752,11754,11756,11758,11760,11762,11764,11766,11768,11770,11772,11774],{},[898,11751,2774],{},[898,11753,2777],{},[1996,11755,2005],{"stretchy":2004},[898,11757,2789],{},[1996,11759,2011],{"stretchy":2004},[1996,11761,1998],{},[2129,11763,3090],{},[1996,11765,2095],{},[2129,11767,2131],{},[898,11769,2789],{},[1996,11771,2095],{},[2129,11773,2794],{},[2124,11775,11776,11778],{},[898,11777,2789],{},[2129,11779,2131],{},[902,11781,11782],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,11784,820],{"id":11785},"přebytek-spotřebitele-a-výrobce",[724,11787,11788],{},"Přebytek spotřebitele:",[724,11790,11791],{},[883,11792,11794],{"className":11793},[886],[888,11795,11796],{"xmlns":890},[892,11797,11798,11858],{},[895,11799,11800,11802,11804,11806,11812,11814,11816,11828,11830,11832,11834,11836,11838,11840,11842,11844,11850,11852],{},[898,11801,2777],{},[898,11803,8673],{},[1996,11805,2005],{"stretchy":2004},[2272,11807,11808,11810],{},[898,11809,2789],{},[2129,11811,2327],{},[1996,11813,2011],{"stretchy":2004},[1996,11815,1998],{},[9166,11817,11818,11820,11822],{},[1996,11819,11170],{},[2129,11821,2327],{},[2272,11823,11824,11826],{},[898,11825,2789],{},[2129,11827,2327],{},[898,11829,4183],{},[1996,11831,2005],{"stretchy":2004},[898,11833,2789],{},[1996,11835,2011],{"stretchy":2004},[2288,11837,2987],{},[898,11839,2194],{},[898,11841,2789],{},[1996,11843,2225],{},[2272,11845,11846,11848],{},[898,11847,3937],{},[2129,11849,2327],{},[2288,11851,2987],{},[2272,11853,11854,11856],{},[898,11855,2789],{},[2129,11857,2327],{},[902,11859,11860],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,11862,11863],{},"Přebytek výrobce:",[724,11865,11866],{},[883,11867,11869],{"className":11868},[886],[888,11870,11871],{"xmlns":890},[892,11872,11873,11933],{},[895,11874,11875,11877,11879,11881,11887,11889,11891,11897,11899,11905,11907,11919,11921,11923,11925,11927,11929,11931],{},[898,11876,3937],{},[898,11878,8673],{},[1996,11880,2005],{"stretchy":2004},[2272,11882,11883,11885],{},[898,11884,2789],{},[2129,11886,2327],{},[1996,11888,2011],{"stretchy":2004},[1996,11890,1998],{},[2272,11892,11893,11895],{},[898,11894,3937],{},[2129,11896,2327],{},[2288,11898,2987],{},[2272,11900,11901,11903],{},[898,11902,2789],{},[2129,11904,2327],{},[1996,11906,2225],{},[9166,11908,11909,11911,11913],{},[1996,11910,11170],{},[2129,11912,2327],{},[2272,11914,11915,11917],{},[898,11916,2789],{},[2129,11918,2327],{},[898,11920,8673],{},[1996,11922,2005],{"stretchy":2004},[898,11924,2789],{},[1996,11926,2011],{"stretchy":2004},[2288,11928,2987],{},[898,11930,2194],{},[898,11932,2789],{},[902,11934,11935],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,11937,11938,11939,1975],{},"Detailně viz ",[207,11940,11942],{"className":11941,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka",[115,11944,3792],{"id":3791},[120,11946,11947,11954,11961],{},[123,11948,11949,2203,11951],{},[38,11950,3799],{},[207,11952,766],{"className":11953,"dataFsResolvedFilePath":764,"href":765},[210],[123,11955,11956,2203,11958],{},[38,11957,3807],{},[207,11959,784],{"className":11960,"dataFsResolvedFilePath":782,"href":783},[210],[123,11962,11963,2203,11965,11968,11969,11972],{},[38,11964,3815],{},[207,11966,3823],{"className":11967,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,11970,11942],{"className":11971,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":11974},[11975,11976,11977,11982],{"id":11145,"depth":642,"text":11146},{"id":11274,"depth":642,"text":11275},{"id":11403,"depth":642,"text":11404,"children":11978},[11979,11980,11981],{"id":11407,"depth":649,"text":11408},{"id":11583,"depth":649,"text":11584},{"id":11785,"depth":649,"text":820},{"id":3791,"depth":642,"text":3792},"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":11983},[1135],"topics\u002Fintegral",[1128,11990,11991,11992,11993,11994,11995],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":11998,"title":11999,"body":12000,"course":1128,"courses":659,"created":9556,"description":641,"extension":661,"meta":16268,"navigation":664,"path":16269,"seo":16270,"sources":16271,"stem":16272,"tags":16273,"type":3857,"updated":677,"__hash__":16279},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":12001,"toc":16256},[12002,12005,12009,12153,12160,12164,12234,12272,12375,12379,12409,12475,12522,12525,12594,12597,12632,12668,12672,12720,12727,12773,12819,12822,12901,12998,13081,13085,13129,13159,13165,13194,13216,13266,13319,13385,13388,13454,13483,13542,13558,13645,13743,13874,13878,14035,14184,14564,14568,14571,14630,14633,14719,14747,14785,14788,14825,14865,14899,14901,14938,14970,15068,15073,15197,15249,15331,15470,15474,15594,15601,15712,15719,15723,16198,16200],[12,12003,11999],{"id":12004},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,12006,12008],{"id":12007},"tldr","TL;DR",[724,12010,12011,12014,12015,10025,12018,12031,12032,12046,12047,12050,12051,1343,12054,12057,12058,1343,12061,12064,12065,2203,12068,12098,12099,12102,12103,1343,12117,12130,12131,12134,12135,3918],{},[38,12012,12013],{},"IS-LM"," je makroekonomický model se ",[38,12016,12017],{},"dvěma neznámými",[883,12019,12021],{"className":12020},[886],[888,12022,12023],{"xmlns":890},[892,12024,12025,12029],{},[895,12026,12027],{},[898,12028,9128],{},[902,12030,9128],{"encoding":904}," — národní důchod a ",[883,12033,12035],{"className":12034},[886],[888,12036,12037],{"xmlns":890},[892,12038,12039,12044],{},[895,12040,12041],{},[898,12042,12043],{},"r",[902,12045,12043],{"encoding":904}," — úroková míra) a ",[38,12048,12049],{},"dvěma trhy",": trhem zboží (křivka ",[38,12052,12053],{},"IS",[614,12055,12056],{},"Investment = Savings",") a trhem peněz (křivka ",[38,12059,12060],{},"LM",[614,12062,12063],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,12066,12067],{},"simultánní rovnováhu",[883,12069,12071],{"className":12070},[886],[888,12072,12073],{"xmlns":890},[892,12074,12075,12095],{},[895,12076,12077,12079,12085,12087,12093],{},[1996,12078,2005],{"stretchy":2004},[2124,12080,12081,12083],{},[898,12082,9128],{},[898,12084,4252],{},[1996,12086,2286],{"separator":2285},[2124,12088,12089,12091],{},[898,12090,12043],{},[898,12092,4252],{},[1996,12094,2011],{"stretchy":2004},[902,12096,12097],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,12100,12101],{},"fiskální politiky"," (posun IS změnou ",[883,12104,12106],{"className":12105},[886],[888,12107,12108],{"xmlns":890},[892,12109,12110,12115],{},[895,12111,12112],{},[898,12113,12114],{},"G",[902,12116,12114],{"encoding":904},[883,12118,12120],{"className":12119},[886],[888,12121,12122],{"xmlns":890},[892,12123,12124,12128],{},[895,12125,12126],{},[898,12127,2774],{},[902,12129,2774],{"encoding":904},") a ",[38,12132,12133],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,12136,12138],{"className":12137},[886],[888,12139,12140],{"xmlns":890},[892,12141,12142,12150],{},[895,12143,12144],{},[2124,12145,12146,12148],{},[898,12147,2818],{},[1996,12149,4354],{},[902,12151,12152],{"encoding":904},"M^*",[724,12154,12155],{},[2559,12156],{"alt":12157,"className":12158,"src":12159},"imek-is-lm-model",[210,2563],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,12161,12163],{"id":12162},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,12165,12166,12167,12171,12172,10025,12175,12198,12199,12202,12203,12219,12220,12233],{},"V modelech ",[207,12168,12170],{"className":12169,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,12173,12174],{},"investice pokládány za konstantní",[883,12176,12178],{"className":12177},[886],[888,12179,12180],{"xmlns":890},[892,12181,12182,12195],{},[895,12183,12184,12187,12189],{},[898,12185,12186],{},"I",[1996,12188,1998],{},[2124,12190,12191,12193],{},[898,12192,12186],{},[1996,12194,4354],{},[902,12196,12197],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,12200,12201],{},"ceně peněz",", tedy na ",[38,12204,12205,12206],{},"úrokové míře ",[883,12207,12209],{"className":12208},[886],[888,12210,12211],{"xmlns":890},[892,12212,12213,12217],{},[895,12214,12215],{},[898,12216,12043],{},[902,12218,12043],{"encoding":904},": čím vyšší ",[883,12221,12223],{"className":12222},[886],[888,12224,12225],{"xmlns":890},[892,12226,12227,12231],{},[895,12228,12229],{},[898,12230,12043],{},[902,12232,12043],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,12235,12236,12266],{},[123,12237,12238,2203,12241,12265],{},[38,12239,12240],{},"funkci investic",[883,12242,12244],{"className":12243},[886],[888,12245,12246],{"xmlns":890},[892,12247,12248,12262],{},[895,12249,12250,12252,12254,12256,12258,12260],{},[898,12251,12186],{},[1996,12253,1998],{},[898,12255,12186],{},[1996,12257,2005],{"stretchy":2004},[898,12259,12043],{},[1996,12261,2011],{"stretchy":2004},[902,12263,12264],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,12267,12268,12271],{},[38,12269,12270],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[3867,12273,12274],{},[724,12275,12276,12278,12279,12298,12299,12326,12327,12340,12341,12370,12371,12374],{},[883,12277,4412],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,12280,12282],{"className":12281},[886],[888,12283,12284],{"xmlns":890},[892,12285,12286,12295],{},[895,12287,12288,12290,12293],{},[898,12289,2777],{},[2288,12291,12292],{},"-",[898,12294,12186],{},[902,12296,12297],{"encoding":904},"C\\text{-}I"," až ",[883,12300,12302],{"className":12301},[886],[888,12303,12304],{"xmlns":890},[892,12305,12306,12323],{},[895,12307,12308,12310,12312,12314,12316,12318,12320],{},[898,12309,2777],{},[2288,12311,12292],{},[898,12313,12186],{},[2288,12315,12292],{},[898,12317,12114],{},[2288,12319,12292],{},[898,12321,12322],{},"X",[902,12324,12325],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,12328,12330],{"className":12329},[886],[888,12331,12332],{"xmlns":890},[892,12333,12334,12338],{},[895,12335,12336],{},[898,12337,9128],{},[902,12339,9128],{"encoding":904},". V IS-LM jsou ",[38,12342,12343,12344,3885,12357],{},"dvě neznámé ",[883,12345,12347],{"className":12346},[886],[888,12348,12349],{"xmlns":890},[892,12350,12351,12355],{},[895,12352,12353],{},[898,12354,9128],{},[902,12356,9128],{"encoding":904},[883,12358,12360],{"className":12359},[886],[888,12361,12362],{"xmlns":890},[892,12363,12364,12368],{},[895,12365,12366],{},[898,12367,12043],{},[902,12369,12043],{"encoding":904},", a proto potřebujeme ",[38,12372,12373],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,12376,12378],{"id":12377},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,12380,12381,12382,12395,12396,2704],{},"Lineární závislost investic ",[883,12383,12385],{"className":12384},[886],[888,12386,12387],{"xmlns":890},[892,12388,12389,12393],{},[895,12390,12391],{},[898,12392,12186],{},[902,12394,12186],{"encoding":904}," na úrokové míře ",[883,12397,12399],{"className":12398},[886],[888,12400,12401],{"xmlns":890},[892,12402,12403,12407],{},[895,12404,12405],{},[898,12406,12043],{},[902,12408,12043],{"encoding":904},[724,12410,12411],{},[883,12412,12414],{"className":12413},[886],[888,12415,12416],{"xmlns":890},[892,12417,12418,12472],{},[895,12419,12420,12422,12424,12426,12428,12430,12432,12434,12436,12438,12440,12442,12444,12446,12448,12450,12452,12454,12456,12458,12460,12463,12465,12467,12470],{},[898,12421,12186],{},[1996,12423,1998],{},[898,12425,12186],{},[1996,12427,2005],{"stretchy":2004},[898,12429,12043],{},[1996,12431,2011],{"stretchy":2004},[1996,12433,1998],{},[898,12435,2142],{},[898,12437,12043],{},[1996,12439,2095],{},[898,12441,2194],{},[1996,12443,2286],{"separator":2285},[5878,12445],{"width":5880},[898,12447,2142],{},[1996,12449,3447],{},[2129,12451,2327],{},[1996,12453,2286],{"separator":2285},[2288,12455,2290],{},[898,12457,2194],{},[1996,12459,3408],{},[2129,12461,12462],{},"0.",[5878,12464],{"width":5880},[1996,12466,2005],{"stretchy":2004},[2129,12468,12469],{},"7.11",[1996,12471,2011],{"stretchy":2004},[902,12473,12474],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,12476,12477,12498],{},[123,12478,12479,12497],{},[883,12480,12482],{"className":12481},[886],[888,12483,12484],{"xmlns":890},[892,12485,12486,12494],{},[895,12487,12488,12490,12492],{},[898,12489,2194],{},[1996,12491,3408],{},[2129,12493,2327],{},[902,12495,12496],{"encoding":904},"d > 0"," zřejmé,",[123,12499,12500,12518,12519,1975],{},[883,12501,12503],{"className":12502},[886],[888,12504,12505],{"xmlns":890},[892,12506,12507,12515],{},[895,12508,12509,12511,12513],{},[898,12510,2142],{},[1996,12512,3447],{},[2129,12514,2327],{},[902,12516,12517],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,12520,12521],{},"klesající",[724,12523,12524],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,12526,12527],{},[883,12528,12530],{"className":12529},[886],[888,12531,12532],{"xmlns":890},[892,12533,12534,12591],{},[895,12535,12536,12538,12540,12542,12544,12546,12548,12550,12552,12554,12556,12558,12560,12562,12564,12566,12568,12570,12572,12574,12576,12578,12580,12582,12584,12586,12589],{},[898,12537,2777],{},[1996,12539,1998],{},[898,12541,2777],{},[1996,12543,2005],{"stretchy":2004},[898,12545,9128],{},[1996,12547,2011],{"stretchy":2004},[1996,12549,1998],{},[898,12551,207],{},[898,12553,9128],{},[1996,12555,2095],{},[898,12557,2098],{},[1996,12559,2286],{"separator":2285},[5878,12561],{"width":5880},[2129,12563,2327],{},[1996,12565,3447],{},[898,12567,207],{},[1996,12569,3447],{},[2129,12571,2278],{},[1996,12573,2286],{"separator":2285},[2288,12575,2290],{},[898,12577,2098],{},[1996,12579,3408],{},[2129,12581,12462],{},[5878,12583],{"width":5880},[1996,12585,2005],{"stretchy":2004},[2129,12587,12588],{},"7.12",[1996,12590,2011],{"stretchy":2004},[902,12592,12593],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,12595,12596],{},"Podmínka rovnováhy na trhu zboží:",[724,12598,12599],{},[883,12600,12602],{"className":12601},[886],[888,12603,12604],{"xmlns":890},[892,12605,12606,12629],{},[895,12607,12608,12610,12612,12614,12616,12618,12620,12622,12624,12627],{},[898,12609,9128],{},[1996,12611,1998],{},[898,12613,2777],{},[1996,12615,2095],{},[898,12617,12186],{},[898,12619,1975],{"mathvariant":2376},[5878,12621],{"width":5880},[1996,12623,2005],{"stretchy":2004},[2129,12625,12626],{},"7.13",[1996,12628,2011],{"stretchy":2004},[902,12630,12631],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,12633,12634,12635,2203,12638,12664,12665,1975],{},"To dává ",[38,12636,12637],{},"tři rovnice o čtyřech neznámých",[883,12639,12641],{"className":12640},[886],[888,12642,12643],{"xmlns":890},[892,12644,12645,12661],{},[895,12646,12647,12649,12651,12653,12655,12657,12659],{},[898,12648,9128],{},[1996,12650,2286],{"separator":2285},[898,12652,2777],{},[1996,12654,2286],{"separator":2285},[898,12656,12186],{},[1996,12658,2286],{"separator":2285},[898,12660,12043],{},[902,12662,12663],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,12666,12667],{},"rovnováhy na trhu peněz",[115,12669,12671],{"id":12670},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,12673,12674,12675,5569,12697,12715,12716,12719],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,12676,12678],{"className":12677},[886],[888,12679,12680],{"xmlns":890},[892,12681,12682,12694],{},[895,12683,12684,12686,12688,12690,12692],{},[898,12685,9128],{},[1996,12687,1998],{},[898,12689,2777],{},[1996,12691,2095],{},[898,12693,8673],{},[902,12695,12696],{"encoding":904},"Y = C + S",[883,12698,12700],{"className":12699},[886],[888,12701,12702],{"xmlns":890},[892,12703,12704,12712],{},[895,12705,12706,12708,12710],{},[898,12707,12186],{},[1996,12709,1998],{},[898,12711,8673],{},[902,12713,12714],{"encoding":904},"I = S"," (plánované ",[38,12717,12718],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,12721,12722],{},[2559,12723],{"alt":12724,"className":12725,"src":12726},"imek-odvozeni-is-4panelu",[210,2563],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,12728,12729],{},[883,12730,12732],{"className":12731},[886],[888,12733,12734],{"xmlns":890},[892,12735,12736,12770],{},[895,12737,12738,12740,12742,12744,12746,12748,12750,12752,12754,12756,12758,12760,12762,12764,12766,12768],{},[898,12739,9128],{},[1996,12741,1998],{},[1996,12743,2005],{"stretchy":2004},[898,12745,207],{},[898,12747,9128],{},[1996,12749,2095],{},[898,12751,2098],{},[1996,12753,2011],{"stretchy":2004},[1996,12755,2095],{},[1996,12757,2005],{"stretchy":2004},[898,12759,2142],{},[898,12761,12043],{},[1996,12763,2095],{},[898,12765,2194],{},[1996,12767,2011],{"stretchy":2004},[1996,12769,2286],{"separator":2285},[902,12771,12772],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,12774,12775],{},[883,12776,12778],{"className":12777},[886],[888,12779,12780],{"xmlns":890},[892,12781,12782,12816],{},[895,12783,12784,12786,12788,12790,12792,12794,12796,12798,12800,12802,12804,12806,12808,12810,12812,12814],{},[1996,12785,2005],{"stretchy":2004},[2129,12787,2278],{},[1996,12789,2225],{},[898,12791,207],{},[1996,12793,2011],{"stretchy":2004},[898,12795,9128],{},[1996,12797,2225],{},[898,12799,2142],{},[898,12801,12043],{},[1996,12803,2225],{},[898,12805,2098],{},[1996,12807,2225],{},[898,12809,2194],{},[1996,12811,1998],{},[2129,12813,2327],{},[1996,12815,2286],{"separator":2285},[902,12817,12818],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,12820,12821],{},"odkud",[724,12823,12824],{},[883,12825,12827],{"className":12826},[886],[888,12828,12829],{"xmlns":890},[892,12830,12831,12898],{},[895,12832,12833,12889,12891,12893,12896],{},[12834,12835,12837],"menclose",{"notation":12836},"box",[2325,12838,12839],{"scriptlevel":2327,"displaystyle":2004},[2325,12840,12841],{"scriptlevel":2327,"displaystyle":2004},[2325,12842,12843],{"scriptlevel":2327,"displaystyle":2285},[895,12844,12845,12847,12849,12851,12863,12865,12867,12869,12887],{},[2288,12846,2987],{},[898,12848,9128],{},[1996,12850,1998],{},[2329,12852,12853,12855],{},[898,12854,2142],{},[895,12856,12857,12859,12861],{},[2129,12858,2278],{},[1996,12860,2225],{},[898,12862,207],{},[2288,12864,2987],{},[898,12866,12043],{},[1996,12868,2095],{},[2329,12870,12871,12879],{},[895,12872,12873,12875,12877],{},[898,12874,2098],{},[1996,12876,2095],{},[898,12878,2194],{},[895,12880,12881,12883,12885],{},[2129,12882,2278],{},[1996,12884,2225],{},[898,12886,207],{},[2288,12888,2987],{},[5878,12890],{"width":5880},[1996,12892,2005],{"stretchy":2004},[2129,12894,12895],{},"7.14",[1996,12897,2011],{"stretchy":2004},[902,12899,12900],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,12902,12903,12904,10025,12907,12910,12911,12914,12915,12917,12918,12940,12941,12969,12970,12991,12992,12994,12995,12997],{},"Tento vztah se nazývá ",[38,12905,12906],{},"funkce IS",[614,12908,12909],{},"IS schedule",") a její graf ",[38,12912,12913],{},"křivka IS",". Křivka je ",[38,12916,12521],{}," přímka v rovině ",[883,12919,12921],{"className":12920},[886],[888,12922,12923],{"xmlns":890},[892,12924,12925,12937],{},[895,12926,12927,12929,12931,12933,12935],{},[1996,12928,2005],{"stretchy":2004},[898,12930,12043],{},[1996,12932,2286],{"separator":2285},[898,12934,9128],{},[1996,12936,2011],{"stretchy":2004},[902,12938,12939],{"encoding":904},"(r, Y)",", neboť ",[883,12942,12944],{"className":12943},[886],[888,12945,12946],{"xmlns":890},[892,12947,12948,12966],{},[895,12949,12950,12962,12964],{},[2329,12951,12952,12954],{},[898,12953,2142],{},[895,12955,12956,12958,12960],{},[2129,12957,2278],{},[1996,12959,2225],{},[898,12961,207],{},[1996,12963,3447],{},[2129,12965,2327],{},[902,12967,12968],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,12971,12973],{"className":12972},[886],[888,12974,12975],{"xmlns":890},[892,12976,12977,12989],{},[895,12978,12979,12981,12983,12985,12987],{},[1996,12980,2005],{"stretchy":2004},[898,12982,12043],{},[1996,12984,2286],{"separator":2285},[898,12986,9128],{},[1996,12988,2011],{"stretchy":2004},[902,12990,12939],{"encoding":904},", pro které plánované ",[38,12993,12186],{},"nvestment = ",[38,12996,8673],{},"avings.",[3867,12999,13000],{},[724,13001,13002,13004,13005,13018,13019,2203,13022,13035,13036,13049,13050,3885,13063,13076,13077,13080],{},[883,13003,4155],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,13006,13008],{"className":13007},[886],[888,13009,13010],{"xmlns":890},[892,13011,13012,13016],{},[895,13013,13014],{},[898,13015,12043],{},[902,13017,12043],{"encoding":904}," → levnější úvěr → ",[38,13020,13021],{},"více investic",[883,13023,13025],{"className":13024},[886],[888,13026,13027],{"xmlns":890},[892,13028,13029,13033],{},[895,13030,13031],{},[898,13032,12186],{},[902,13034,12186],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,13037,13039],{"className":13038},[886],[888,13040,13041],{"xmlns":890},[892,13042,13043,13047],{},[895,13044,13045],{},[898,13046,9128],{},[902,13048,9128],{"encoding":904},". Vztah mezi ",[883,13051,13053],{"className":13052},[886],[888,13054,13055],{"xmlns":890},[892,13056,13057,13061],{},[895,13058,13059],{},[898,13060,12043],{},[902,13062,12043],{"encoding":904},[883,13064,13066],{"className":13065},[886],[888,13067,13068],{"xmlns":890},[892,13069,13070,13074],{},[895,13071,13072],{},[898,13073,9128],{},[902,13075,9128],{"encoding":904}," na trhu zboží je proto ",[38,13078,13079],{},"nepřímý"," (klesající křivka).",[115,13082,13084],{"id":13083},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,13086,13087,13088,13106,13107,2927,13125,13128],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,13089,13091],{"className":13090},[886],[888,13092,13093],{"xmlns":890},[892,13094,13095,13103],{},[895,13096,13097],{},[2124,13098,13099,13101],{},[898,13100,2818],{},[898,13102,4183],{},[902,13104,13105],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,13108,13110],{"className":13109},[886],[888,13111,13112],{"xmlns":890},[892,13113,13114,13122],{},[895,13115,13116],{},[2124,13117,13118,13120],{},[898,13119,2818],{},[898,13121,8673],{},[902,13123,13124],{"encoding":904},"M^S",[38,13126,13127],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,13130,13131],{},[883,13132,13134],{"className":13133},[886],[888,13135,13136],{"xmlns":890},[892,13137,13138,13156],{},[895,13139,13140,13146,13148,13154],{},[2124,13141,13142,13144],{},[898,13143,2818],{},[898,13145,8673],{},[1996,13147,1998],{},[2124,13149,13150,13152],{},[898,13151,2818],{},[1996,13153,4354],{},[898,13155,1975],{"mathvariant":2376},[902,13157,13158],{"encoding":904},"M^S = M^*.",[724,13160,13161,13164],{},[38,13162,13163],{},"Poptávka"," po penězích má tři zdroje:",[120,13166,13167,13176,13185],{},[123,13168,13169,10025,13172,13175],{},[38,13170,13171],{},"transakční poptávka",[614,13173,13174],{},"transactions demand",") — peníze pro nákup zboží,",[123,13177,13178,10025,13181,13184],{},[38,13179,13180],{},"opatrnostní poptávka",[614,13182,13183],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,13186,13187,10025,13190,13193],{},[38,13188,13189],{},"spekulační poptávka",[614,13191,13192],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,13195,13196,13197,13215],{},"Součet transakční a opatrnostní poptávky ",[883,13198,13200],{"className":13199},[886],[888,13201,13202],{"xmlns":890},[892,13203,13204,13212],{},[895,13205,13206],{},[2272,13207,13208,13210],{},[898,13209,9795],{},[2129,13211,2278],{},[902,13213,13214],{"encoding":904},"L_1"," je úměrný důchodu:",[724,13217,13218],{},[883,13219,13221],{"className":13220},[886],[888,13222,13223],{"xmlns":890},[892,13224,13225,13263],{},[895,13226,13227,13233,13235,13242,13244,13246,13248,13250,13252,13258,13260],{},[2272,13228,13229,13231],{},[898,13230,9795],{},[2129,13232,2278],{},[1996,13234,1998],{},[2272,13236,13237,13240],{},[898,13238,13239],{},"k",[2129,13241,2278],{},[898,13243,9128],{},[1996,13245,2286],{"separator":2285},[5878,13247],{"width":5880},[2129,13249,2327],{},[1996,13251,3447],{},[2272,13253,13254,13256],{},[898,13255,13239],{},[2129,13257,2278],{},[1996,13259,3447],{},[2129,13261,13262],{},"1.",[902,13264,13265],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,13267,13268,13269,13287,13288,1343,13301,13318],{},"Spekulační poptávka ",[883,13270,13272],{"className":13271},[886],[888,13273,13274],{"xmlns":890},[892,13275,13276,13284],{},[895,13277,13278],{},[2272,13279,13280,13282],{},[898,13281,9795],{},[2129,13283,2131],{},[902,13285,13286],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,13289,13291],{"className":13290},[886],[888,13292,13293],{"xmlns":890},[892,13294,13295,13299],{},[895,13296,13297],{},[898,13298,12043],{},[902,13300,12043],{"encoding":904},[883,13302,13304],{"className":13303},[886],[888,13305,13306],{"xmlns":890},[892,13307,13308,13316],{},[895,13309,13310],{},[2272,13311,13312,13314],{},[898,13313,9795],{},[2129,13315,2131],{},[902,13317,13286],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,13320,13321],{},[883,13322,13324],{"className":13323},[886],[888,13325,13326],{"xmlns":890},[892,13327,13328,13382],{},[895,13329,13330,13336,13338,13344,13346,13348,13354,13356,13358,13364,13366,13368,13370,13372,13378,13380],{},[2272,13331,13332,13334],{},[898,13333,9795],{},[2129,13335,2131],{},[1996,13337,1998],{},[2272,13339,13340,13342],{},[898,13341,13239],{},[2129,13343,2131],{},[898,13345,12043],{},[1996,13347,2095],{},[2272,13349,13350,13352],{},[898,13351,13239],{},[2129,13353,2173],{},[1996,13355,2286],{"separator":2285},[5878,13357],{"width":5880},[2272,13359,13360,13362],{},[898,13361,13239],{},[2129,13363,2131],{},[1996,13365,3447],{},[2129,13367,2327],{},[1996,13369,2286],{"separator":2285},[2288,13371,2290],{},[2272,13373,13374,13376],{},[898,13375,13239],{},[2129,13377,2173],{},[1996,13379,3408],{},[2129,13381,12462],{},[902,13383,13384],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,13386,13387],{},"Celková poptávka po penězích:",[724,13389,13390],{},[883,13391,13393],{"className":13392},[886],[888,13394,13395],{"xmlns":890},[892,13396,13397,13451],{},[895,13398,13399,13405,13407,13413,13415,13421,13423,13429,13431,13433,13439,13441,13443,13449],{},[2124,13400,13401,13403],{},[898,13402,2818],{},[898,13404,4183],{},[1996,13406,1998],{},[2272,13408,13409,13411],{},[898,13410,9795],{},[2129,13412,2278],{},[1996,13414,2095],{},[2272,13416,13417,13419],{},[898,13418,9795],{},[2129,13420,2131],{},[1996,13422,1998],{},[2272,13424,13425,13427],{},[898,13426,13239],{},[2129,13428,2278],{},[898,13430,9128],{},[1996,13432,2095],{},[2272,13434,13435,13437],{},[898,13436,13239],{},[2129,13438,2131],{},[898,13440,12043],{},[1996,13442,2095],{},[2272,13444,13445,13447],{},[898,13446,13239],{},[2129,13448,2173],{},[898,13450,1975],{"mathvariant":2376},[902,13452,13453],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,13455,13456,13457,2704],{},"Podmínka rovnováhy na trhu peněz ",[883,13458,13460],{"className":13459},[886],[888,13461,13462],{"xmlns":890},[892,13463,13464,13480],{},[895,13465,13466,13472,13474],{},[2124,13467,13468,13470],{},[898,13469,2818],{},[898,13471,4183],{},[1996,13473,1998],{},[2124,13475,13476,13478],{},[898,13477,2818],{},[1996,13479,4354],{},[902,13481,13482],{"encoding":904},"M^D = M^*",[724,13484,13485],{},[883,13486,13488],{"className":13487},[886],[888,13489,13490],{"xmlns":890},[892,13491,13492,13539],{},[895,13493,13494,13500,13502,13508,13510,13512,13518,13520,13522,13528,13530,13532,13534,13537],{},[2124,13495,13496,13498],{},[898,13497,2818],{},[1996,13499,4354],{},[1996,13501,1998],{},[2272,13503,13504,13506],{},[898,13505,13239],{},[2129,13507,2278],{},[898,13509,9128],{},[1996,13511,2095],{},[2272,13513,13514,13516],{},[898,13515,13239],{},[2129,13517,2131],{},[898,13519,12043],{},[1996,13521,2095],{},[2272,13523,13524,13526],{},[898,13525,13239],{},[2129,13527,2173],{},[1996,13529,2286],{"separator":2285},[5878,13531],{"width":5880},[1996,13533,2005],{"stretchy":2004},[2129,13535,13536],{},"7.15",[1996,13538,2011],{"stretchy":2004},[902,13540,13541],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,13543,13544,13545,3151],{},"po úpravě (vyjádření ",[883,13546,13548],{"className":13547},[886],[888,13549,13550],{"xmlns":890},[892,13551,13552,13556],{},[895,13553,13554],{},[898,13555,9128],{},[902,13557,9128],{"encoding":904},[724,13559,13560],{},[883,13561,13563],{"className":13562},[886],[888,13564,13565],{"xmlns":890},[892,13566,13567,13642],{},[895,13568,13569,13633,13635,13637,13640],{},[12834,13570,13571],{"notation":12836},[2325,13572,13573],{"scriptlevel":2327,"displaystyle":2004},[2325,13574,13575],{"scriptlevel":2327,"displaystyle":2004},[2325,13576,13577],{"scriptlevel":2327,"displaystyle":2285},[895,13578,13579,13581,13583,13585,13587,13601,13603,13605,13607,13631],{},[2288,13580,2987],{},[898,13582,9128],{},[1996,13584,1998],{},[1996,13586,2225],{},[2329,13588,13589,13595],{},[2272,13590,13591,13593],{},[898,13592,13239],{},[2129,13594,2131],{},[2272,13596,13597,13599],{},[898,13598,13239],{},[2129,13600,2278],{},[2288,13602,2987],{},[898,13604,12043],{},[1996,13606,2095],{},[2329,13608,13609,13625],{},[895,13610,13611,13617,13619],{},[2124,13612,13613,13615],{},[898,13614,2818],{},[1996,13616,4354],{},[1996,13618,2225],{},[2272,13620,13621,13623],{},[898,13622,13239],{},[2129,13624,2173],{},[2272,13626,13627,13629],{},[898,13628,13239],{},[2129,13630,2278],{},[2288,13632,2987],{},[5878,13634],{"width":5880},[1996,13636,2005],{"stretchy":2004},[2129,13638,13639],{},"7.16",[1996,13641,2011],{"stretchy":2004},[902,13643,13644],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,13646,12903,13647,10025,13650,13653,13654,12914,13657,12917,13660,12940,13681,13713,13714,13736,13737,13739,13740,13742],{},[38,13648,13649],{},"funkce LM",[614,13651,13652],{},"LM schedule","), její graf ",[38,13655,13656],{},"křivka LM",[38,13658,13659],{},"rostoucí",[883,13661,13663],{"className":13662},[886],[888,13664,13665],{"xmlns":890},[892,13666,13667,13679],{},[895,13668,13669,13671,13673,13675,13677],{},[1996,13670,2005],{"stretchy":2004},[898,13672,12043],{},[1996,13674,2286],{"separator":2285},[898,13676,9128],{},[1996,13678,2011],{"stretchy":2004},[902,13680,12939],{"encoding":904},[883,13682,13684],{"className":13683},[886],[888,13685,13686],{"xmlns":890},[892,13687,13688,13710],{},[895,13689,13690,13692,13706,13708],{},[1996,13691,2225],{},[2329,13693,13694,13700],{},[2272,13695,13696,13698],{},[898,13697,13239],{},[2129,13699,2131],{},[2272,13701,13702,13704],{},[898,13703,13239],{},[2129,13705,2278],{},[1996,13707,3408],{},[2129,13709,2327],{},[902,13711,13712],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,13715,13717],{"className":13716},[886],[888,13718,13719],{"xmlns":890},[892,13720,13721,13733],{},[895,13722,13723,13729,13731],{},[2272,13724,13725,13727],{},[898,13726,13239],{},[2129,13728,2131],{},[1996,13730,3447],{},[2129,13732,2327],{},[902,13734,13735],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,13738,9795],{},"iquidity of ",[38,13741,2818],{},"oney.",[3867,13744,13745],{},[724,13746,13747,13749,13750,13763,13764,13792,13793,13810,13811,13824,13825,13842,13843,3885,13856,13869,13870,13873],{},[883,13748,4155],{}," Intuice — proč LM roste\nVyšší důchod ",[883,13751,13753],{"className":13752},[886],[888,13754,13755],{"xmlns":890},[892,13756,13757,13761],{},[895,13758,13759],{},[898,13760,9128],{},[902,13762,9128],{"encoding":904}," → větší transakční poptávka po penězích ",[883,13765,13767],{"className":13766},[886],[888,13768,13769],{"xmlns":890},[892,13770,13771,13789],{},[895,13772,13773,13779,13781,13787],{},[2272,13774,13775,13777],{},[898,13776,9795],{},[2129,13778,2278],{},[1996,13780,1998],{},[2272,13782,13783,13785],{},[898,13784,13239],{},[2129,13786,2278],{},[898,13788,9128],{},[902,13790,13791],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,13794,13796],{"className":13795},[886],[888,13797,13798],{"xmlns":890},[892,13799,13800,13808],{},[895,13801,13802],{},[2124,13803,13804,13806],{},[898,13805,2818],{},[1996,13807,4354],{},[902,13809,12152],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,13812,13814],{"className":13813},[886],[888,13815,13816],{"xmlns":890},[892,13817,13818,13822],{},[895,13819,13820],{},[898,13821,12043],{},[902,13823,12043],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,13826,13828],{"className":13827},[886],[888,13829,13830],{"xmlns":890},[892,13831,13832,13840],{},[895,13833,13834],{},[2272,13835,13836,13838],{},[898,13837,9795],{},[2129,13839,2131],{},[902,13841,13286],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,13844,13846],{"className":13845},[886],[888,13847,13848],{"xmlns":890},[892,13849,13850,13854],{},[895,13851,13852],{},[898,13853,9128],{},[902,13855,9128],{"encoding":904},[883,13857,13859],{"className":13858},[886],[888,13860,13861],{"xmlns":890},[892,13862,13863,13867],{},[895,13864,13865],{},[898,13866,12043],{},[902,13868,12043],{"encoding":904}," na trhu peněz je proto ",[38,13871,13872],{},"přímý"," (rostoucí křivka).",[115,13875,13877],{"id":13876},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,13879,13880,13881,13884,13885,2203,13888,3885,13906,2203,13909,13927,13928,13946,13947,13965,13966,13982,13983,3885,13998,14013,14014,1975],{},"Řešením ",[38,13882,13883],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,13886,13887],{},"rovnovážný důchod",[883,13889,13891],{"className":13890},[886],[888,13892,13893],{"xmlns":890},[892,13894,13895,13903],{},[895,13896,13897],{},[2124,13898,13899,13901],{},[898,13900,9128],{},[898,13902,4252],{},[902,13904,13905],{"encoding":904},"Y^E",[38,13907,13908],{},"rovnovážnou úrokovou míru",[883,13910,13912],{"className":13911},[886],[888,13913,13914],{"xmlns":890},[892,13915,13916,13924],{},[895,13917,13918],{},[2124,13919,13920,13922],{},[898,13921,12043],{},[898,13923,4252],{},[902,13925,13926],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,13929,13931],{"className":13930},[886],[888,13932,13933],{"xmlns":890},[892,13934,13935,13943],{},[895,13936,13937],{},[2124,13938,13939,13941],{},[898,13940,12186],{},[898,13942,4252],{},[902,13944,13945],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,13948,13950],{"className":13949},[886],[888,13951,13952],{"xmlns":890},[892,13953,13954,13962],{},[895,13955,13956],{},[2124,13957,13958,13960],{},[898,13959,2777],{},[898,13961,4252],{},[902,13963,13964],{"encoding":904},"C^E",". Graficky jde o ",[38,13967,13968,13969],{},"průsečík ",[883,13970,13972],{"className":13971},[886],[888,13973,13974],{"xmlns":890},[892,13975,13976,13980],{},[895,13977,13978],{},[898,13979,4252],{},[902,13981,4252],{"encoding":904}," křivek ",[883,13984,13986],{"className":13985},[886],[888,13987,13988],{"xmlns":890},[892,13989,13990,13996],{},[895,13991,13992,13994],{},[898,13993,12186],{},[898,13995,8673],{},[902,13997,12053],{"encoding":904},[883,13999,14001],{"className":14000},[886],[888,14002,14003],{"xmlns":890},[892,14004,14005,14011],{},[895,14006,14007,14009],{},[898,14008,9795],{},[898,14010,2818],{},[902,14012,12060],{"encoding":904}," v rovině ",[883,14015,14017],{"className":14016},[886],[888,14018,14019],{"xmlns":890},[892,14020,14021,14033],{},[895,14022,14023,14025,14027,14029,14031],{},[1996,14024,2005],{"stretchy":2004},[898,14026,12043],{},[1996,14028,2286],{"separator":2285},[898,14030,9128],{},[1996,14032,2011],{"stretchy":2004},[902,14034,12939],{"encoding":904},[724,14036,14037],{},[614,14038,14039,14040,14061,14062,14077,14078,14093,14094,14107,14108,14125,14126,12130,14139,14125,14156,14169,14170,14183],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,14041,14043],{"className":14042},[886],[888,14044,14045],{"xmlns":890},[892,14046,14047,14059],{},[895,14048,14049,14051,14053,14055,14057],{},[1996,14050,2005],{"stretchy":2004},[898,14052,12043],{},[1996,14054,2286],{"separator":2285},[898,14056,9128],{},[1996,14058,2011],{"stretchy":2004},[902,14060,12939],{"encoding":904},". Rostoucí přímka ",[883,14063,14065],{"className":14064},[886],[888,14066,14067],{"xmlns":890},[892,14068,14069,14075],{},[895,14070,14071,14073],{},[898,14072,9795],{},[898,14074,2818],{},[902,14076,12060],{"encoding":904}," a klesající přímka ",[883,14079,14081],{"className":14080},[886],[888,14082,14083],{"xmlns":890},[892,14084,14085,14091],{},[895,14086,14087,14089],{},[898,14088,12186],{},[898,14090,8673],{},[902,14092,12053],{"encoding":904}," se protínají v bodě ",[883,14095,14097],{"className":14096},[886],[888,14098,14099],{"xmlns":890},[892,14100,14101,14105],{},[895,14102,14103],{},[898,14104,4252],{},[902,14106,4252],{"encoding":904}," se souřadnicemi ",[883,14109,14111],{"className":14110},[886],[888,14112,14113],{"xmlns":890},[892,14114,14115,14123],{},[895,14116,14117],{},[2124,14118,14119,14121],{},[898,14120,12043],{},[898,14122,4252],{},[902,14124,13926],{"encoding":904}," (na ose ",[883,14127,14129],{"className":14128},[886],[888,14130,14131],{"xmlns":890},[892,14132,14133,14137],{},[895,14134,14135],{},[898,14136,12043],{},[902,14138,12043],{"encoding":904},[883,14140,14142],{"className":14141},[886],[888,14143,14144],{"xmlns":890},[892,14145,14146,14154],{},[895,14147,14148],{},[2124,14149,14150,14152],{},[898,14151,9128],{},[898,14153,4252],{},[902,14155,13905],{"encoding":904},[883,14157,14159],{"className":14158},[886],[888,14160,14161],{"xmlns":890},[892,14162,14163,14167],{},[895,14164,14165],{},[898,14166,9128],{},[902,14168,9128],{"encoding":904},"); tečkované čáry z ",[883,14171,14173],{"className":14172},[886],[888,14174,14175],{"xmlns":890},[892,14176,14177,14181],{},[895,14178,14179],{},[898,14180,4252],{},[902,14182,4252],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[3867,14185,14186,14191],{},[724,14187,14188,14190],{},[883,14189,4572],{}," Postup — jak najít IS-LM rovnováhu",[152,14192,14193,14269,14337,14395,14468],{},[123,14194,14195,14198,14199,3885,14219,14239,14240,3885,14253,14266,14267,1975],{},[38,14196,14197],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,14200,14202],{"className":14201},[886],[888,14203,14204],{"xmlns":890},[892,14205,14206,14216],{},[895,14207,14208,14210,14212,14214],{},[898,14209,2777],{},[1996,14211,2005],{"stretchy":2004},[898,14213,9128],{},[1996,14215,2011],{"stretchy":2004},[902,14217,14218],{"encoding":904},"C(Y)",[883,14220,14222],{"className":14221},[886],[888,14223,14224],{"xmlns":890},[892,14225,14226,14236],{},[895,14227,14228,14230,14232,14234],{},[898,14229,12186],{},[1996,14231,2005],{"stretchy":2004},[898,14233,12043],{},[1996,14235,2011],{"stretchy":2004},[902,14237,14238],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,14241,14243],{"className":14242},[886],[888,14244,14245],{"xmlns":890},[892,14246,14247,14251],{},[895,14248,14249],{},[898,14250,9128],{},[902,14252,9128],{"encoding":904},[883,14254,14256],{"className":14255},[886],[888,14257,14258],{"xmlns":890},[892,14259,14260,14264],{},[895,14261,14262],{},[898,14263,12043],{},[902,14265,12043],{"encoding":904}," — dostaneš rovnici ",[38,14268,12053],{},[123,14270,14271,14274,14275,3885,14292,14309,14310,14266,14335,1975],{},[38,14272,14273],{},"Z trhu peněz (7.15)"," dosaď ",[883,14276,14278],{"className":14277},[886],[888,14279,14280],{"xmlns":890},[892,14281,14282,14290],{},[895,14283,14284],{},[2272,14285,14286,14288],{},[898,14287,9795],{},[2129,14289,2278],{},[902,14291,13214],{"encoding":904},[883,14293,14295],{"className":14294},[886],[888,14296,14297],{"xmlns":890},[892,14298,14299,14307],{},[895,14300,14301],{},[2272,14302,14303,14305],{},[898,14304,9795],{},[2129,14306,2131],{},[902,14308,13286],{"encoding":904}," a vztah ",[883,14311,14313],{"className":14312},[886],[888,14314,14315],{"xmlns":890},[892,14316,14317,14333],{},[895,14318,14319,14325,14327],{},[2124,14320,14321,14323],{},[898,14322,2818],{},[898,14324,4183],{},[1996,14326,1998],{},[2124,14328,14329,14331],{},[898,14330,2818],{},[1996,14332,4354],{},[902,14334,13482],{"encoding":904},[38,14336,12060],{},[123,14338,14339,14342,14343,3885,14356,14369,14370,14394],{},[38,14340,14341],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,14344,14346],{"className":14345},[886],[888,14347,14348],{"xmlns":890},[892,14349,14350,14354],{},[895,14351,14352],{},[898,14353,9128],{},[902,14355,9128],{"encoding":904},[883,14357,14359],{"className":14358},[886],[888,14360,14361],{"xmlns":890},[892,14362,14363,14367],{},[895,14364,14365],{},[898,14366,12043],{},[902,14368,12043],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,14371,14373],{"className":14372},[886],[888,14374,14375],{"xmlns":890},[892,14376,14377,14391],{},[895,14378,14379,14381,14383,14385,14387,14389],{},[898,14380,9128],{},[1996,14382,1998],{},[898,14384,2001],{},[1996,14386,2005],{"stretchy":2004},[898,14388,12043],{},[1996,14390,2011],{"stretchy":2004},[902,14392,14393],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,14396,14397,2203,14400,3885,14434,1975],{},[38,14398,14399],{},"Zpětně dopočítej",[883,14401,14403],{"className":14402},[886],[888,14404,14405],{"xmlns":890},[892,14406,14407,14431],{},[895,14408,14409,14415,14417,14419,14421,14427,14429],{},[2124,14410,14411,14413],{},[898,14412,2777],{},[898,14414,4252],{},[1996,14416,1998],{},[898,14418,207],{},[2288,14420,2987],{},[2124,14422,14423,14425],{},[898,14424,9128],{},[898,14426,4252],{},[1996,14428,2095],{},[898,14430,2098],{},[902,14432,14433],{"encoding":904},"C^E = a\\,Y^E + b",[883,14435,14437],{"className":14436},[886],[888,14438,14439],{"xmlns":890},[892,14440,14441,14465],{},[895,14442,14443,14449,14451,14453,14455,14461,14463],{},[2124,14444,14445,14447],{},[898,14446,12186],{},[898,14448,4252],{},[1996,14450,1998],{},[898,14452,2142],{},[2288,14454,2987],{},[2124,14456,14457,14459],{},[898,14458,12043],{},[898,14460,4252],{},[1996,14462,2095],{},[898,14464,2194],{},[902,14466,14467],{"encoding":904},"I^E = c\\,r^E + d",[123,14469,14470,14473,14474,14508,14509,14563],{},[38,14471,14472],{},"Ověř:"," musí platit ",[883,14475,14477],{"className":14476},[886],[888,14478,14479],{"xmlns":890},[892,14480,14481,14505],{},[895,14482,14483,14489,14491,14497,14499],{},[2124,14484,14485,14487],{},[898,14486,9128],{},[898,14488,4252],{},[1996,14490,1998],{},[2124,14492,14493,14495],{},[898,14494,2777],{},[898,14496,4252],{},[1996,14498,2095],{},[2124,14500,14501,14503],{},[898,14502,12186],{},[898,14504,4252],{},[902,14506,14507],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,14510,14512],{"className":14511},[886],[888,14513,14514],{"xmlns":890},[892,14515,14516,14560],{},[895,14517,14518,14524,14526,14532,14538,14540,14546,14552,14554],{},[2124,14519,14520,14522],{},[898,14521,2818],{},[1996,14523,4354],{},[1996,14525,1998],{},[2272,14527,14528,14530],{},[898,14529,13239],{},[2129,14531,2278],{},[2124,14533,14534,14536],{},[898,14535,9128],{},[898,14537,4252],{},[1996,14539,2095],{},[2272,14541,14542,14544],{},[898,14543,13239],{},[2129,14545,2131],{},[2124,14547,14548,14550],{},[898,14549,12043],{},[898,14551,4252],{},[1996,14553,2095],{},[2272,14555,14556,14558],{},[898,14557,13239],{},[2129,14559,2173],{},[902,14561,14562],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,14565,14567],{"id":14566},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,14569,14570],{},"Pro trh zboží jsou dány:",[120,14572,14573,14601],{},[123,14574,14575,14576,2286],{},"spotřeba ",[883,14577,14579],{"className":14578},[886],[888,14580,14581],{"xmlns":890},[892,14582,14583,14598],{},[895,14584,14585,14587,14589,14592,14594,14596],{},[898,14586,2777],{},[1996,14588,1998],{},[2129,14590,14591],{},"0,8",[898,14593,9128],{},[1996,14595,2095],{},[2129,14597,3090],{},[902,14599,14600],{"encoding":904},"C = 0{,}8Y + 100",[123,14602,14603,14604,1975],{},"investice ",[883,14605,14607],{"className":14606},[886],[888,14608,14609],{"xmlns":890},[892,14610,14611,14627],{},[895,14612,14613,14615,14617,14619,14621,14623,14625],{},[898,14614,12186],{},[1996,14616,1998],{},[1996,14618,2225],{},[2129,14620,9035],{},[898,14622,12043],{},[1996,14624,2095],{},[2129,14626,2782],{},[902,14628,14629],{"encoding":904},"I = -20r + 1000",[724,14631,14632],{},"Pro trh peněz:",[120,14634,14635,14661,14693],{},[123,14636,14637,2286],{},[883,14638,14640],{"className":14639},[886],[888,14641,14642],{"xmlns":890},[892,14643,14644,14658],{},[895,14645,14646,14652,14654,14656],{},[2272,14647,14648,14650],{},[898,14649,9795],{},[2129,14651,2278],{},[1996,14653,1998],{},[2129,14655,2794],{},[898,14657,9128],{},[902,14659,14660],{"encoding":904},"L_1 = 0{,}1Y",[123,14662,14663,2286],{},[883,14664,14666],{"className":14665},[886],[888,14667,14668],{"xmlns":890},[892,14669,14670,14690],{},[895,14671,14672,14678,14680,14682,14684,14686,14688],{},[2272,14673,14674,14676],{},[898,14675,9795],{},[2129,14677,2131],{},[1996,14679,1998],{},[1996,14681,2225],{},[2129,14683,5004],{},[898,14685,12043],{},[1996,14687,2095],{},[2129,14689,8604],{},[902,14691,14692],{"encoding":904},"L_2 = -25r + 2000",[123,14694,14695,14696,1975],{},"nabídka peněz ",[883,14697,14699],{"className":14698},[886],[888,14700,14701],{"xmlns":890},[892,14702,14703,14716],{},[895,14704,14705,14711,14713],{},[2124,14706,14707,14709],{},[898,14708,2818],{},[1996,14710,4354],{},[1996,14712,1998],{},[2129,14714,14715],{},"2375",[902,14717,14718],{"encoding":904},"M^* = 2375",[724,14720,14721,14724,14725,2704],{},[38,14722,14723],{},"Funkce IS"," — dosazením do (7.13) ",[883,14726,14728],{"className":14727},[886],[888,14729,14730],{"xmlns":890},[892,14731,14732,14744],{},[895,14733,14734,14736,14738,14740,14742],{},[898,14735,9128],{},[1996,14737,1998],{},[898,14739,2777],{},[1996,14741,2095],{},[898,14743,12186],{},[902,14745,14746],{"encoding":904},"Y = C + I",[724,14748,14749],{},[883,14750,14752],{"className":14751},[886],[888,14753,14754],{"xmlns":890},[892,14755,14756,14782],{},[895,14757,14758,14760,14762,14764,14766,14768,14770,14772,14774,14776,14778,14780],{},[898,14759,9128],{},[1996,14761,1998],{},[2129,14763,14591],{},[898,14765,9128],{},[1996,14767,2095],{},[2129,14769,3090],{},[1996,14771,2225],{},[2129,14773,9035],{},[898,14775,12043],{},[1996,14777,2095],{},[2129,14779,2782],{},[1996,14781,2286],{"separator":2285},[902,14783,14784],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,14786,14787],{},"tj.",[724,14789,14790],{},[883,14791,14793],{"className":14792},[886],[888,14794,14795],{"xmlns":890},[892,14796,14797,14822],{},[895,14798,14799,14801,14803,14805,14807,14809,14811,14814,14816,14818,14820],{},[2129,14800,2839],{},[898,14802,9128],{},[1996,14804,2095],{},[2129,14806,9035],{},[898,14808,12043],{},[1996,14810,1998],{},[2129,14812,14813],{},"1100.",[5878,14815],{"width":5880},[1996,14817,2005],{"stretchy":2004},[2288,14819,12053],{},[1996,14821,2011],{"stretchy":2004},[902,14823,14824],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,14826,14827,14830,14831,2704],{},[38,14828,14829],{},"Funkce LM"," — dosazením do (7.15) ",[883,14832,14834],{"className":14833},[886],[888,14835,14836],{"xmlns":890},[892,14837,14838,14862],{},[895,14839,14840,14846,14848,14854,14856],{},[2124,14841,14842,14844],{},[898,14843,2818],{},[1996,14845,4354],{},[1996,14847,1998],{},[2272,14849,14850,14852],{},[898,14851,9795],{},[2129,14853,2278],{},[1996,14855,2095],{},[2272,14857,14858,14860],{},[898,14859,9795],{},[2129,14861,2131],{},[902,14863,14864],{"encoding":904},"M^* = L_1 + L_2",[724,14866,14867],{},[883,14868,14870],{"className":14869},[886],[888,14871,14872],{"xmlns":890},[892,14873,14874,14896],{},[895,14875,14876,14878,14880,14882,14884,14886,14888,14890,14892,14894],{},[2129,14877,14715],{},[1996,14879,1998],{},[2129,14881,2794],{},[898,14883,9128],{},[1996,14885,2225],{},[2129,14887,5004],{},[898,14889,12043],{},[1996,14891,2095],{},[2129,14893,8604],{},[1996,14895,2286],{"separator":2285},[902,14897,14898],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,14900,14787],{},[724,14902,14903],{},[883,14904,14906],{"className":14905},[886],[888,14907,14908],{"xmlns":890},[892,14909,14910,14935],{},[895,14911,14912,14914,14916,14918,14920,14922,14924,14927,14929,14931,14933],{},[2129,14913,2794],{},[898,14915,9128],{},[1996,14917,2225],{},[2129,14919,5004],{},[898,14921,12043],{},[1996,14923,1998],{},[2129,14925,14926],{},"375.",[5878,14928],{"width":5880},[1996,14930,2005],{"stretchy":2004},[2288,14932,12060],{},[1996,14934,2011],{"stretchy":2004},[902,14936,14937],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,14939,14940,14943,14944,14969],{},[38,14941,14942],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,14945,14947],{"className":14946},[886],[888,14948,14949],{"xmlns":890},[892,14950,14951,14966],{},[895,14952,14953,14955,14957,14960,14962,14964],{},[898,14954,9128],{},[1996,14956,1998],{},[2129,14958,14959],{},"5500",[1996,14961,2225],{},[2129,14963,3090],{},[898,14965,12043],{},[902,14967,14968],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,14971,14972],{},[883,14973,14975],{"className":14974},[886],[888,14976,14977],{"xmlns":890},[892,14978,14979,15065],{},[895,14980,14981,14983,14985,14987,14989,14991,14993,14995,14997,14999,15001,15003,15006,15008,15011,15013,15016,15018,15020,15022,15024,15026,15028,15030,15032,15034,15036,15038,15041,15043,15045,15048,15050,15052,15054,15060,15062],{},[2129,14982,2794],{},[1996,14984,2005],{"stretchy":2004},[2129,14986,14959],{},[1996,14988,2225],{},[2129,14990,3090],{},[898,14992,12043],{},[1996,14994,2011],{"stretchy":2004},[1996,14996,2225],{},[2129,14998,5004],{},[898,15000,12043],{},[1996,15002,1998],{},[2129,15004,15005],{},"375",[2288,15007,3984],{},[1996,15009,15010],{},"⟹",[2288,15012,3984],{},[2129,15014,15015],{},"550",[1996,15017,2225],{},[2129,15019,2863],{},[898,15021,12043],{},[1996,15023,2225],{},[2129,15025,5004],{},[898,15027,12043],{},[1996,15029,1998],{},[2129,15031,15005],{},[2288,15033,3984],{},[1996,15035,15010],{},[2288,15037,3984],{},[2129,15039,15040],{},"35",[898,15042,12043],{},[1996,15044,1998],{},[2129,15046,15047],{},"175",[2288,15049,3984],{},[1996,15051,15010],{},[2288,15053,3984],{},[2124,15055,15056,15058],{},[898,15057,12043],{},[898,15059,4252],{},[1996,15061,1998],{},[2129,15063,15064],{},"5.",[902,15066,15067],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,15069,15070],{},[38,15071,15072],{},"Zpětné dosazení:",[120,15074,15075,15121,15158],{},[123,15076,15077,2286],{},[883,15078,15080],{"className":15079},[886],[888,15081,15082],{"xmlns":890},[892,15083,15084,15118],{},[895,15085,15086,15092,15094,15096,15098,15100,15102,15104,15106,15108,15110,15113,15115],{},[2124,15087,15088,15090],{},[898,15089,9128],{},[898,15091,4252],{},[1996,15093,1998],{},[2129,15095,14959],{},[1996,15097,2225],{},[2129,15099,3090],{},[1996,15101,3177],{},[2129,15103,2228],{},[1996,15105,1998],{},[2129,15107,14959],{},[1996,15109,2225],{},[2129,15111,15112],{},"500",[1996,15114,1998],{},[2129,15116,15117],{},"5000",[902,15119,15120],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,15122,15123,2286],{},[883,15124,15126],{"className":15125},[886],[888,15127,15128],{"xmlns":890},[892,15129,15130,15155],{},[895,15131,15132,15138,15140,15142,15144,15146,15148,15150,15152],{},[2124,15133,15134,15136],{},[898,15135,2777],{},[898,15137,4252],{},[1996,15139,1998],{},[2129,15141,14591],{},[1996,15143,3177],{},[2129,15145,15117],{},[1996,15147,2095],{},[2129,15149,3090],{},[1996,15151,1998],{},[2129,15153,15154],{},"4100",[902,15156,15157],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,15159,15160,1975],{},[883,15161,15163],{"className":15162},[886],[888,15164,15165],{"xmlns":890},[892,15166,15167,15194],{},[895,15168,15169,15175,15177,15179,15181,15183,15185,15187,15189,15191],{},[2124,15170,15171,15173],{},[898,15172,12186],{},[898,15174,4252],{},[1996,15176,1998],{},[1996,15178,2225],{},[2129,15180,9035],{},[1996,15182,3177],{},[2129,15184,2228],{},[1996,15186,2095],{},[2129,15188,2782],{},[1996,15190,1998],{},[2129,15192,15193],{},"900",[902,15195,15196],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,15198,15199,2203,15202,15248],{},[38,15200,15201],{},"Ověření:",[883,15203,15205],{"className":15204},[886],[888,15206,15207],{"xmlns":890},[892,15208,15209,15245],{},[895,15210,15211,15217,15219,15225,15227,15229,15231,15233,15235,15237,15239],{},[2124,15212,15213,15215],{},[898,15214,2777],{},[898,15216,4252],{},[1996,15218,2095],{},[2124,15220,15221,15223],{},[898,15222,12186],{},[898,15224,4252],{},[1996,15226,1998],{},[2129,15228,15154],{},[1996,15230,2095],{},[2129,15232,15193],{},[1996,15234,1998],{},[2129,15236,15117],{},[1996,15238,1998],{},[2124,15240,15241,15243],{},[898,15242,9128],{},[898,15244,4252],{},[902,15246,15247],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,15250,15251],{},[883,15252,15254],{"className":15253},[886],[888,15255,15256],{"xmlns":890},[892,15257,15258,15328],{},[895,15259,15260],{},[12834,15261,15262],{"notation":12836},[2325,15263,15264],{"scriptlevel":2327,"displaystyle":2004},[2325,15265,15266],{"scriptlevel":2327,"displaystyle":2004},[2325,15267,15268],{"scriptlevel":2327,"displaystyle":2285},[895,15269,15270,15272,15278,15280,15282,15284,15287,15293,15295,15297,15299,15301,15307,15309,15311,15313,15315,15321,15323,15326],{},[2288,15271,2987],{},[2124,15273,15274,15276],{},[898,15275,9128],{},[898,15277,4252],{},[1996,15279,1998],{},[2129,15281,15117],{},[1996,15283,2286],{"separator":2285},[5878,15285],{"width":15286},"1em",[2124,15288,15289,15291],{},[898,15290,12043],{},[898,15292,4252],{},[1996,15294,1998],{},[2129,15296,2228],{},[1996,15298,2286],{"separator":2285},[5878,15300],{"width":15286},[2124,15302,15303,15305],{},[898,15304,2777],{},[898,15306,4252],{},[1996,15308,1998],{},[2129,15310,15154],{},[1996,15312,2286],{"separator":2285},[5878,15314],{"width":15286},[2124,15316,15317,15319],{},[898,15318,12186],{},[898,15320,4252],{},[1996,15322,1998],{},[2129,15324,15325],{},"900.",[2288,15327,2987],{},[902,15329,15330],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,15332,15333],{},[614,15334,15335,15336,15349,15350,15363,15364,15379,15380,15393,15394,15409,15410,15423,15424,15437,15438,1975],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,15337,15339],{"className":15338},[886],[888,15340,15341],{"xmlns":890},[892,15342,15343,15347],{},[895,15344,15345],{},[898,15346,9128],{},[902,15348,9128],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,15351,15353],{"className":15352},[886],[888,15354,15355],{"xmlns":890},[892,15356,15357,15361],{},[895,15358,15359],{},[898,15360,12043],{},[902,15362,12043],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,15365,15367],{"className":15366},[886],[888,15368,15369],{"xmlns":890},[892,15370,15371,15377],{},[895,15372,15373,15375],{},[898,15374,9795],{},[898,15376,2818],{},[902,15378,12060],{"encoding":904}," stoupá z oblasti nízkých ",[883,15381,15383],{"className":15382},[886],[888,15384,15385],{"xmlns":890},[892,15386,15387,15391],{},[895,15388,15389],{},[898,15390,12043],{},[902,15392,12043],{"encoding":904},", přímka ",[883,15395,15397],{"className":15396},[886],[888,15398,15399],{"xmlns":890},[892,15400,15401,15407],{},[895,15402,15403,15405],{},[898,15404,12186],{},[898,15406,8673],{},[902,15408,12053],{"encoding":904}," klesá a protíná osu ",[883,15411,15413],{"className":15412},[886],[888,15414,15415],{"xmlns":890},[892,15416,15417,15421],{},[895,15418,15419],{},[898,15420,12043],{},[902,15422,12043],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,15425,15427],{"className":15426},[886],[888,15428,15429],{"xmlns":890},[892,15430,15431,15435],{},[895,15432,15433],{},[898,15434,4252],{},[902,15436,4252],{"encoding":904}," leží v bodě ",[883,15439,15441],{"className":15440},[886],[888,15442,15443],{"xmlns":890},[892,15444,15445,15467],{},[895,15446,15447,15449,15451,15453,15455,15457,15459,15461,15463,15465],{},[1996,15448,2486],{"stretchy":2004},[898,15450,12043],{},[1996,15452,1998],{},[2129,15454,2228],{},[1996,15456,2286],{"separator":2285},[2288,15458,2290],{},[898,15460,9128],{},[1996,15462,1998],{},[2129,15464,15117],{},[1996,15466,2501],{"stretchy":2004},[902,15468,15469],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,15471,15473],{"id":15472},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,15475,15476,15479,15480,15493,15494,7015,15507,15510,15511,15529,15530,15547,15548,15565,15566,15579,15580,15593],{},[38,15477,15478],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,15481,15483],{"className":15482},[886],[888,15484,15485],{"xmlns":890},[892,15486,15487,15491],{},[895,15488,15489],{},[898,15490,12114],{},[902,15492,12114],{"encoding":904}," nebo snížení daní ",[883,15495,15497],{"className":15496},[886],[888,15498,15499],{"xmlns":890},[892,15500,15501,15505],{},[895,15502,15503],{},[898,15504,2774],{},[902,15506,2774],{"encoding":904},[38,15508,15509],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,15512,15514],{"className":15513},[886],[888,15515,15516],{"xmlns":890},[892,15517,15518,15526],{},[895,15519,15520],{},[2124,15521,15522,15524],{},[898,15523,4252],{},[1996,15525,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,15527,15528],{"encoding":904},"E'"," má vyšší ",[883,15531,15533],{"className":15532},[886],[888,15534,15535],{"xmlns":890},[892,15536,15537,15545],{},[895,15538,15539],{},[2124,15540,15541,15543],{},[898,15542,9128],{},[898,15544,4252],{},[902,15546,13905],{"encoding":904}," i vyšší ",[883,15549,15551],{"className":15550},[886],[888,15552,15553],{"xmlns":890},[892,15554,15555,15563],{},[895,15556,15557],{},[2124,15558,15559,15561],{},[898,15560,12043],{},[898,15562,4252],{},[902,15564,13926],{"encoding":904}," (vyšší ",[883,15567,15569],{"className":15568},[886],[888,15570,15571],{"xmlns":890},[892,15572,15573,15577],{},[895,15574,15575],{},[898,15576,9128],{},[902,15578,9128],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,15581,15583],{"className":15582},[886],[888,15584,15585],{"xmlns":890},[892,15586,15587,15591],{},[895,15588,15589],{},[898,15590,12043],{},[902,15592,12043],{"encoding":904}," nahoru).",[724,15595,15596],{},[2559,15597],{"alt":15598,"className":15599,"src":15600},"imek-posun-is-lm-politiky",[210,2563],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,15602,15603,15606,15607,15624,15625,15628,15629,15646,15647,15664,15665,15678,15679,15698,15699,3918],{},[38,15604,15605],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,15608,15610],{"className":15609},[886],[888,15611,15612],{"xmlns":890},[892,15613,15614,15622],{},[895,15615,15616],{},[2124,15617,15618,15620],{},[898,15619,2818],{},[1996,15621,4354],{},[902,15623,12152],{"encoding":904}," národní bankou — ",[38,15626,15627],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,15630,15632],{"className":15631},[886],[888,15633,15634],{"xmlns":890},[892,15635,15636,15644],{},[895,15637,15638],{},[2124,15639,15640,15642],{},[898,15641,12043],{},[898,15643,4252],{},[902,15645,13926],{"encoding":904}," a vyšší ",[883,15648,15650],{"className":15649},[886],[888,15651,15652],{"xmlns":890},[892,15653,15654,15662],{},[895,15655,15656],{},[2124,15657,15658,15660],{},[898,15659,9128],{},[898,15661,4252],{},[902,15663,13905],{"encoding":904}," (nižší ",[883,15666,15668],{"className":15667},[886],[888,15669,15670],{"xmlns":890},[892,15671,15672,15676],{},[895,15673,15674],{},[898,15675,12043],{},[902,15677,12043],{"encoding":904}," povzbuzuje investice ",[883,15680,15682],{"className":15681},[886],[888,15683,15684],{"xmlns":890},[892,15685,15686,15696],{},[895,15687,15688,15690,15692,15694],{},[898,15689,12186],{},[1996,15691,2005],{"stretchy":2004},[898,15693,12043],{},[1996,15695,2011],{"stretchy":2004},[902,15697,14238],{"encoding":904},", ty zvedají ",[883,15700,15702],{"className":15701},[886],[888,15703,15704],{"xmlns":890},[892,15705,15706,15710],{},[895,15707,15708],{},[898,15709,9128],{},[902,15711,9128],{"encoding":904},[724,15713,15714,15715,15718],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,15716,15717],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,15720,15722],{"id":15721},"klíčové-pojmy","Klíčové pojmy",[120,15724,15725,15798,15844,15926,15976,16043,16100,16141,16174],{},[123,15726,15727,7015,15760,1343,15777,15794,15795,15797],{},[38,15728,15729,15730],{},"Funkce investic ",[883,15731,15733],{"className":15732},[886],[888,15734,15735],{"xmlns":890},[892,15736,15737,15757],{},[895,15738,15739,15741,15743,15745,15747,15749,15751,15753,15755],{},[898,15740,12186],{},[1996,15742,2005],{"stretchy":2004},[898,15744,12043],{},[1996,15746,2011],{"stretchy":2004},[1996,15748,1998],{},[898,15750,2142],{},[898,15752,12043],{},[1996,15754,2095],{},[898,15756,2194],{},[902,15758,15759],{"encoding":904},"I(r) = cr + d",[883,15761,15763],{"className":15762},[886],[888,15764,15765],{"xmlns":890},[892,15766,15767,15775],{},[895,15768,15769,15771,15773],{},[898,15770,2142],{},[1996,15772,3447],{},[2129,15774,2327],{},[902,15776,12517],{"encoding":904},[883,15778,15780],{"className":15779},[886],[888,15781,15782],{"xmlns":890},[892,15783,15784,15792],{},[895,15785,15786,15788,15790],{},[898,15787,2194],{},[1996,15789,3408],{},[2129,15791,2327],{},[902,15793,12496],{"encoding":904},"; ",[38,15796,12521],{}," funkce úrokové míry.",[123,15799,15800,15803,15804,15825,15826,15843],{},[38,15801,15802],{},"Trh zboží"," — rovnováha ",[883,15805,15807],{"className":15806},[886],[888,15808,15809],{"xmlns":890},[892,15810,15811,15823],{},[895,15812,15813,15815,15817,15819,15821],{},[898,15814,9128],{},[1996,15816,1998],{},[898,15818,2777],{},[1996,15820,2095],{},[898,15822,12186],{},[902,15824,14746],{"encoding":904},", ekvivalentně ",[883,15827,15829],{"className":15828},[886],[888,15830,15831],{"xmlns":890},[892,15832,15833,15841],{},[895,15834,15835,15837,15839],{},[898,15836,12186],{},[1996,15838,1998],{},[898,15840,8673],{},[902,15842,12714],{"encoding":904}," (investice = úspory).",[123,15845,15846,10025,15849,15851,15852,15902,15903,12917,15905,1975],{},[38,15847,15848],{},"Křivka IS",[614,15850,12056],{},") — ",[883,15853,15855],{"className":15854},[886],[888,15856,15857],{"xmlns":890},[892,15858,15859,15899],{},[895,15860,15861,15863,15865,15877,15879,15881],{},[898,15862,9128],{},[1996,15864,1998],{},[2329,15866,15867,15869],{},[898,15868,2142],{},[895,15870,15871,15873,15875],{},[2129,15872,2278],{},[1996,15874,2225],{},[898,15876,207],{},[898,15878,12043],{},[1996,15880,2095],{},[2329,15882,15883,15891],{},[895,15884,15885,15887,15889],{},[898,15886,2098],{},[1996,15888,2095],{},[898,15890,2194],{},[895,15892,15893,15895,15897],{},[2129,15894,2278],{},[1996,15896,2225],{},[898,15898,207],{},[902,15900,15901],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,15904,12521],{},[883,15906,15908],{"className":15907},[886],[888,15909,15910],{"xmlns":890},[892,15911,15912,15924],{},[895,15913,15914,15916,15918,15920,15922],{},[1996,15915,2005],{"stretchy":2004},[898,15917,12043],{},[1996,15919,2286],{"separator":2285},[898,15921,9128],{},[1996,15923,2011],{"stretchy":2004},[902,15925,12939],{"encoding":904},[123,15927,15928,15803,15931,15957,15958,1975],{},[38,15929,15930],{},"Trh peněz",[883,15932,15934],{"className":15933},[886],[888,15935,15936],{"xmlns":890},[892,15937,15938,15954],{},[895,15939,15940,15946,15948],{},[2124,15941,15942,15944],{},[898,15943,2818],{},[898,15945,4183],{},[1996,15947,1998],{},[2124,15949,15950,15952],{},[898,15951,2818],{},[898,15953,8673],{},[902,15955,15956],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,15959,15961],{"className":15960},[886],[888,15962,15963],{"xmlns":890},[892,15964,15965,15973],{},[895,15966,15967],{},[2124,15968,15969,15971],{},[898,15970,2818],{},[1996,15972,4354],{},[902,15974,15975],{"encoding":904},"M^* ",[123,15977,15978,7015,15981,1975],{},[38,15979,15980],{},"Transakční, opatrnostní, spekulační poptávka",[883,15982,15984],{"className":15983},[886],[888,15985,15986],{"xmlns":890},[892,15987,15988,16040],{},[895,15989,15990,15996,15998,16004,16006,16012,16014,16020,16022,16024,16030,16032,16034],{},[2124,15991,15992,15994],{},[898,15993,2818],{},[898,15995,4183],{},[1996,15997,1998],{},[2272,15999,16000,16002],{},[898,16001,9795],{},[2129,16003,2278],{},[1996,16005,2095],{},[2272,16007,16008,16010],{},[898,16009,9795],{},[2129,16011,2131],{},[1996,16013,1998],{},[2272,16015,16016,16018],{},[898,16017,13239],{},[2129,16019,2278],{},[898,16021,9128],{},[1996,16023,2095],{},[2272,16025,16026,16028],{},[898,16027,13239],{},[2129,16029,2131],{},[898,16031,12043],{},[1996,16033,2095],{},[2272,16035,16036,16038],{},[898,16037,13239],{},[2129,16039,2173],{},[902,16041,16042],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,16044,16045,10025,16048,15851,16050,16096,16097,16099],{},[38,16046,16047],{},"Křivka LM",[614,16049,12063],{},[883,16051,16053],{"className":16052},[886],[888,16054,16055],{"xmlns":890},[892,16056,16057,16093],{},[895,16058,16059,16065,16067,16073,16075,16077,16083,16085,16087],{},[2124,16060,16061,16063],{},[898,16062,2818],{},[1996,16064,4354],{},[1996,16066,1998],{},[2272,16068,16069,16071],{},[898,16070,13239],{},[2129,16072,2278],{},[898,16074,9128],{},[1996,16076,2095],{},[2272,16078,16079,16081],{},[898,16080,13239],{},[2129,16082,2131],{},[898,16084,12043],{},[1996,16086,2095],{},[2272,16088,16089,16091],{},[898,16090,13239],{},[2129,16092,2173],{},[902,16094,16095],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,16098,13659],{}," přímka.",[123,16101,16102,16105,16106,16140],{},[38,16103,16104],{},"Simultánní rovnováha"," — průsečík ",[883,16107,16109],{"className":16108},[886],[888,16110,16111],{"xmlns":890},[892,16112,16113,16137],{},[895,16114,16115,16117,16119,16121,16127,16129,16135],{},[898,16116,4252],{},[1996,16118,1998],{},[1996,16120,2005],{"stretchy":2004},[2124,16122,16123,16125],{},[898,16124,12043],{},[898,16126,4252],{},[1996,16128,2286],{"separator":2285},[2124,16130,16131,16133],{},[898,16132,9128],{},[898,16134,4252],{},[1996,16136,2011],{"stretchy":2004},[902,16138,16139],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,16142,16143,16146,16147,1343,16160,16173],{},[38,16144,16145],{},"Fiskální politika"," — nástroje ",[883,16148,16150],{"className":16149},[886],[888,16151,16152],{"xmlns":890},[892,16153,16154,16158],{},[895,16155,16156],{},[898,16157,12114],{},[902,16159,12114],{"encoding":904},[883,16161,16163],{"className":16162},[886],[888,16164,16165],{"xmlns":890},[892,16166,16167,16171],{},[895,16168,16169],{},[898,16170,2774],{},[902,16172,2774],{"encoding":904}," posouvající křivku IS.",[123,16175,16176,16179,16180,16197],{},[38,16177,16178],{},"Monetární politika"," — nástroj ",[883,16181,16183],{"className":16182},[886],[888,16184,16185],{"xmlns":890},[892,16186,16187,16195],{},[895,16188,16189],{},[2124,16190,16191,16193],{},[898,16192,2818],{},[1996,16194,4354],{},[902,16196,12152],{"encoding":904}," posouvající křivku LM.",[115,16199,3792],{"id":3791},[120,16201,16202,16211,16219,16229],{},[123,16203,16204,2203,16207],{},[38,16205,16206],{},"Kurz:",[207,16208,16210],{"className":16209,"dataFsResolvedFilePath":1960,"href":1961},[210],"Matematická ekonomie",[123,16212,16213,2203,16216],{},[38,16214,16215],{},"Přednáška:",[207,16217,1931],{"className":16218,"dataFsResolvedFilePath":868,"href":869},[210],[123,16220,16221,2203,16224,16228],{},[38,16222,16223],{},"Nadřazené téma:",[207,16225,16227],{"className":16226,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,16230,16231,16234],{},[38,16232,16233],{},"Související:",[120,16235,16236,16243,16249],{},[123,16237,16238,16242],{},[207,16239,16241],{"className":16240,"dataFsResolvedFilePath":800,"href":801},[210],"poptavka-nabidka"," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,16244,16245,16248],{},[207,16246,1145],{"className":16247,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,16250,16251,16255],{},[207,16252,16254],{"className":16253,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":16257},[16258,16259,16260,16261,16262,16263,16264,16265,16266,16267],{"id":12007,"depth":642,"text":12008},{"id":12162,"depth":642,"text":12163},{"id":12377,"depth":642,"text":12378},{"id":12670,"depth":642,"text":12671},{"id":13083,"depth":642,"text":13084},{"id":13876,"depth":642,"text":13877},{"id":14566,"depth":642,"text":14567},{"id":15472,"depth":642,"text":15473},{"id":15721,"depth":642,"text":15722},{"id":3791,"depth":642,"text":3792},{},"\u002Ftopics\u002Fis-lm",{"title":11999,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,16274,1143,16275,16276,16277,16278,16227],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":16281,"title":16282,"body":16283,"course":659,"courses":17876,"created":1129,"description":17877,"extension":661,"meta":17878,"navigation":664,"path":17879,"seo":17880,"sources":17881,"stem":17882,"tags":17883,"type":3857,"updated":677,"__hash__":17886},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":16284,"toc":17864},[16285,16288,16384,16391,16411,16415,16420,16483,16502,16504,16507,16643,16645,16855,16889,17026,17030,17094,17110,17138,17142,17240,17244,17248,17301,17407,17621,17625,17668,17774,17826,17828],[12,16286,16282],{"id":16287},"lagrangeova-metoda-vázané-extrémy",[724,16289,16290,16291,3910,16314,16346,16347,16350,16351,16378,16379,16383],{},"Hledáme extrém funkce ",[883,16292,16294],{"className":16293},[886],[888,16295,16296],{"xmlns":890},[892,16297,16298,16312],{},[895,16299,16300,16302,16304,16306,16308,16310],{},[898,16301,2001],{},[1996,16303,2005],{"stretchy":2004},[898,16305,2008],{},[1996,16307,2286],{"separator":2285},[898,16309,1994],{},[1996,16311,2011],{"stretchy":2004},[902,16313,9843],{"encoding":904},[883,16315,16317],{"className":16316},[886],[888,16318,16319],{"xmlns":890},[892,16320,16321,16343],{},[895,16322,16323,16325,16327,16333,16335,16341],{},[898,16324,900],{},[1996,16326,2005],{"stretchy":2004},[2272,16328,16329,16331],{},[898,16330,2789],{},[2129,16332,2278],{},[1996,16334,2286],{"separator":2285},[2272,16336,16337,16339],{},[898,16338,2789],{},[2129,16340,2131],{},[1996,16342,2011],{"stretchy":2004},[902,16344,16345],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,16348,16349],{},"podmíněný"," rovnicí ",[883,16352,16354],{"className":16353},[886],[888,16355,16356],{"xmlns":890},[892,16357,16358,16376],{},[895,16359,16360,16362,16364,16366,16368,16370,16372,16374],{},[898,16361,11041],{},[1996,16363,2005],{"stretchy":2004},[898,16365,2008],{},[1996,16367,2286],{"separator":2285},[898,16369,1994],{},[1996,16371,2011],{"stretchy":2004},[1996,16373,1998],{},[2129,16375,2327],{},[902,16377,11058],{"encoding":904},". V ",[207,16380,16382],{"className":16381,"dataFsResolvedFilePath":1960,"href":1961},[210],"matematické ekonomii"," se používá pro:",[724,16385,16386],{},[2559,16387],{"alt":16388,"className":16389,"src":16390},"imek-lagrange-tecnost",[210,2563],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,16392,16393,16402,16408],{},[123,16394,16395,16398,16399,2011],{},[38,16396,16397],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,16400,9773],{"className":16401,"dataFsResolvedFilePath":878,"href":879},[210],[123,16403,16404,16407],{},[38,16405,16406],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,16409,16410],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,16412,16414],{"id":16413},"princip","Princip",[724,16416,10707,16417,2704],{},[38,16418,16419],{},"Lagrangeovu funkci",[724,16421,16422],{},[883,16423,16425],{"className":16424},[886],[888,16426,16427],{"xmlns":890},[892,16428,16429,16480],{},[895,16430,16431,16433,16435,16437,16439,16441,16443,16446,16448,16450,16452,16454,16456,16458,16460,16462,16464,16466,16468,16470,16472,16474,16476,16478],{},[898,16432,9795],{},[1996,16434,2005],{"stretchy":2004},[898,16436,2008],{},[1996,16438,2286],{"separator":2285},[898,16440,1994],{},[1996,16442,2286],{"separator":2285},[898,16444,16445],{},"λ",[1996,16447,2011],{"stretchy":2004},[1996,16449,1998],{},[898,16451,2001],{},[1996,16453,2005],{"stretchy":2004},[898,16455,2008],{},[1996,16457,2286],{"separator":2285},[898,16459,1994],{},[1996,16461,2011],{"stretchy":2004},[1996,16463,2095],{},[898,16465,16445],{},[2288,16467,2987],{},[898,16469,11041],{},[1996,16471,2005],{"stretchy":2004},[898,16473,2008],{},[1996,16475,2286],{"separator":2285},[898,16477,1994],{},[1996,16479,2011],{"stretchy":2004},[902,16481,16482],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,16484,4310,16485,8102,16499,1975],{},[883,16486,16488],{"className":16487},[886],[888,16489,16490],{"xmlns":890},[892,16491,16492,16496],{},[895,16493,16494],{},[898,16495,16445],{},[902,16497,16498],{"encoding":904},"\\lambda",[38,16500,16501],{},"Lagrangeův multiplikátor",[115,16503,3252],{"id":3251},[724,16505,16506],{},"Řešíme soustavu:",[724,16508,16509,16557,16605],{},[883,16510,16512],{"className":16511},[886],[888,16513,16514],{"xmlns":890},[892,16515,16516,16554],{},[895,16517,16518,16526,16528,16536,16538,16540,16542,16550,16552],{},[9166,16519,16520,16522,16524],{},[898,16521,9795],{},[898,16523,2008],{},[1996,16525,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,16527,1998],{},[9166,16529,16530,16532,16534],{},[898,16531,2001],{},[898,16533,2008],{},[1996,16535,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,16537,2095],{},[898,16539,16445],{},[2288,16541,2987],{},[9166,16543,16544,16546,16548],{},[898,16545,11041],{},[898,16547,2008],{},[1996,16549,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,16551,1998],{},[2129,16553,2327],{},[902,16555,16556],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,16558,16560],{"className":16559},[886],[888,16561,16562],{"xmlns":890},[892,16563,16564,16602],{},[895,16565,16566,16574,16576,16584,16586,16588,16590,16598,16600],{},[9166,16567,16568,16570,16572],{},[898,16569,9795],{},[898,16571,1994],{},[1996,16573,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,16575,1998],{},[9166,16577,16578,16580,16582],{},[898,16579,2001],{},[898,16581,1994],{},[1996,16583,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,16585,2095],{},[898,16587,16445],{},[2288,16589,2987],{},[9166,16591,16592,16594,16596],{},[898,16593,11041],{},[898,16595,1994],{},[1996,16597,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,16599,1998],{},[2129,16601,2327],{},[902,16603,16604],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,16606,16608],{"className":16607},[886],[888,16609,16610],{"xmlns":890},[892,16611,16612,16640],{},[895,16613,16614,16622,16624,16626,16628,16630,16632,16634,16636,16638],{},[9166,16615,16616,16618,16620],{},[898,16617,9795],{},[898,16619,16445],{},[1996,16621,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,16623,1998],{},[898,16625,11041],{},[1996,16627,2005],{"stretchy":2004},[898,16629,2008],{},[1996,16631,2286],{"separator":2285},[898,16633,1994],{},[1996,16635,2011],{"stretchy":2004},[1996,16637,1998],{},[2129,16639,2327],{},[902,16641,16642],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,16644,3326],{"id":3325},[724,16646,16647],{},[883,16648,16650],{"className":16649},[886],[888,16651,16652],{"xmlns":890},[892,16653,16654,16852],{},[895,16655,16656,16658,16660,16662,16664,16666,16668,16670,16672,16674,16676,16692,16694,16696,16712,16714,16716,16724,16730,16732,16734,16750,16752,16754,16770,16772,16774,16782,16788,16790,16792,16794,16810,16812,16814,16830,16832,16834,16842,16844],{},[898,16657,4183],{},[1996,16659,2005],{"stretchy":2004},[898,16661,2008],{},[1996,16663,2286],{"separator":2285},[898,16665,1994],{},[1996,16667,2286],{"separator":2285},[898,16669,16445],{},[1996,16671,2011],{"stretchy":2004},[1996,16673,1998],{},[1996,16675,2005],{"stretchy":2004},[9166,16677,16678,16680,16686],{},[898,16679,2001],{},[895,16681,16682,16684],{},[898,16683,2008],{},[898,16685,2008],{},[895,16687,16688,16690],{},[1996,16689,2378],{"mathvariant":2376},[1996,16691,2378],{"mathvariant":2376},[1996,16693,2095],{},[898,16695,16445],{},[9166,16697,16698,16700,16706],{},[898,16699,11041],{},[895,16701,16702,16704],{},[898,16703,2008],{},[898,16705,2008],{},[895,16707,16708,16710],{},[1996,16709,2378],{"mathvariant":2376},[1996,16711,2378],{"mathvariant":2376},[1996,16713,2011],{"stretchy":2004},[1996,16715,2005],{"stretchy":2004},[9166,16717,16718,16720,16722],{},[898,16719,11041],{},[898,16721,1994],{},[1996,16723,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[2124,16725,16726,16728],{},[1996,16727,2011],{"stretchy":2004},[2129,16729,2131],{},[1996,16731,2095],{},[1996,16733,2005],{"stretchy":2004},[9166,16735,16736,16738,16744],{},[898,16737,2001],{},[895,16739,16740,16742],{},[898,16741,1994],{},[898,16743,1994],{},[895,16745,16746,16748],{},[1996,16747,2378],{"mathvariant":2376},[1996,16749,2378],{"mathvariant":2376},[1996,16751,2095],{},[898,16753,16445],{},[9166,16755,16756,16758,16764],{},[898,16757,11041],{},[895,16759,16760,16762],{},[898,16761,1994],{},[898,16763,1994],{},[895,16765,16766,16768],{},[1996,16767,2378],{"mathvariant":2376},[1996,16769,2378],{"mathvariant":2376},[1996,16771,2011],{"stretchy":2004},[1996,16773,2005],{"stretchy":2004},[9166,16775,16776,16778,16780],{},[898,16777,11041],{},[898,16779,2008],{},[1996,16781,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[2124,16783,16784,16786],{},[1996,16785,2011],{"stretchy":2004},[2129,16787,2131],{},[1996,16789,2225],{},[2129,16791,2131],{},[1996,16793,2005],{"stretchy":2004},[9166,16795,16796,16798,16804],{},[898,16797,2001],{},[895,16799,16800,16802],{},[898,16801,2008],{},[898,16803,1994],{},[895,16805,16806,16808],{},[1996,16807,2378],{"mathvariant":2376},[1996,16809,2378],{"mathvariant":2376},[1996,16811,2095],{},[898,16813,16445],{},[9166,16815,16816,16818,16824],{},[898,16817,11041],{},[895,16819,16820,16822],{},[898,16821,2008],{},[898,16823,1994],{},[895,16825,16826,16828],{},[1996,16827,2378],{"mathvariant":2376},[1996,16829,2378],{"mathvariant":2376},[1996,16831,2011],{"stretchy":2004},[2288,16833,2987],{},[9166,16835,16836,16838,16840],{},[898,16837,11041],{},[898,16839,2008],{},[1996,16841,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[2288,16843,2987],{},[9166,16845,16846,16848,16850],{},[898,16847,11041],{},[898,16849,1994],{},[1996,16851,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,16853,16854],{"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",[724,16856,16857,16858,16888],{},"Je-li ",[883,16859,16861],{"className":16860},[886],[888,16862,16863],{"xmlns":890},[892,16864,16865,16885],{},[895,16866,16867,16869,16871,16873,16875,16877,16883],{},[1996,16868,2486],{"stretchy":2004},[898,16870,207],{},[1996,16872,2286],{"separator":2285},[898,16874,2098],{},[1996,16876,2286],{"separator":2285},[2272,16878,16879,16881],{},[898,16880,16445],{},[2129,16882,2327],{},[1996,16884,2501],{"stretchy":2004},[902,16886,16887],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,16890,16891,16959],{},[123,16892,16893,3414,16929,16931,16932],{},[883,16894,16896],{"className":16895},[886],[888,16897,16898],{"xmlns":890},[892,16899,16900,16926],{},[895,16901,16902,16904,16906,16908,16910,16912,16914,16920,16922,16924],{},[898,16903,4183],{},[1996,16905,2005],{"stretchy":2004},[898,16907,207],{},[1996,16909,2286],{"separator":2285},[898,16911,2098],{},[1996,16913,2286],{"separator":2285},[2272,16915,16916,16918],{},[898,16917,16445],{},[2129,16919,2327],{},[1996,16921,2011],{"stretchy":2004},[1996,16923,3447],{},[2129,16925,2327],{},[902,16927,16928],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,16930,3717],{}," vázané podmínkou ",[883,16933,16935],{"className":16934},[886],[888,16936,16937],{"xmlns":890},[892,16938,16939,16957],{},[895,16940,16941,16943,16945,16947,16949,16951,16953,16955],{},[898,16942,11041],{},[1996,16944,2005],{"stretchy":2004},[898,16946,2008],{},[1996,16948,2286],{"separator":2285},[898,16950,1994],{},[1996,16952,2011],{"stretchy":2004},[1996,16954,1998],{},[2129,16956,2327],{},[902,16958,11058],{"encoding":904},[123,16960,16961,3414,16997,16931,16999],{},[883,16962,16964],{"className":16963},[886],[888,16965,16966],{"xmlns":890},[892,16967,16968,16994],{},[895,16969,16970,16972,16974,16976,16978,16980,16982,16988,16990,16992],{},[898,16971,4183],{},[1996,16973,2005],{"stretchy":2004},[898,16975,207],{},[1996,16977,2286],{"separator":2285},[898,16979,2098],{},[1996,16981,2286],{"separator":2285},[2272,16983,16984,16986],{},[898,16985,16445],{},[2129,16987,2327],{},[1996,16989,2011],{"stretchy":2004},[1996,16991,3408],{},[2129,16993,2327],{},[902,16995,16996],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,16998,3775],{},[883,17000,17002],{"className":17001},[886],[888,17003,17004],{"xmlns":890},[892,17005,17006,17024],{},[895,17007,17008,17010,17012,17014,17016,17018,17020,17022],{},[898,17009,11041],{},[1996,17011,2005],{"stretchy":2004},[898,17013,2008],{},[1996,17015,2286],{"separator":2285},[898,17017,1994],{},[1996,17019,2011],{"stretchy":2004},[1996,17021,1998],{},[2129,17023,2327],{},[902,17025,11058],{"encoding":904},[115,17027,17029],{"id":17028},"význam-multiplikátoru","Význam multiplikátoru",[724,17031,17032],{},[883,17033,17035],{"className":17034},[886],[888,17036,17037],{"xmlns":890},[892,17038,17039,17091],{},[895,17040,17041,17043,17045,17067,17069],{},[898,17042,16445],{},[1996,17044,1998],{},[2329,17046,17047,17055],{},[9166,17048,17049,17051,17053],{},[898,17050,2001],{},[898,17052,2008],{},[1996,17054,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[895,17056,17057,17059],{},[1996,17058,2225],{},[9166,17060,17061,17063,17065],{},[898,17062,11041],{},[898,17064,2008],{},[1996,17066,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,17068,1998],{},[2329,17070,17071,17079],{},[9166,17072,17073,17075,17077],{},[898,17074,2001],{},[898,17076,1994],{},[1996,17078,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[895,17080,17081,17083],{},[1996,17082,2225],{},[9166,17084,17085,17087,17089],{},[898,17086,11041],{},[898,17088,1994],{},[1996,17090,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,17092,17093],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,17095,17096,17109],{},[883,17097,17099],{"className":17098},[886],[888,17100,17101],{"xmlns":890},[892,17102,17103,17107],{},[895,17104,17105],{},[898,17106,16445],{},[902,17108,16498],{"encoding":904}," udává:",[120,17111,17112,17118],{},[123,17113,17114,17115],{},"konstantní ",[38,17116,17117],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,17119,17120,17123,17124,17137],{},[38,17121,17122],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,17125,17127],{"className":17126},[886],[888,17128,17129],{"xmlns":890},[892,17130,17131,17135],{},[895,17132,17133],{},[898,17134,2001],{},[902,17136,2001],{"encoding":904},", uvolní-li se omezení o jednotku",[115,17139,17141],{"id":17140},"alternativní-postup","Alternativní postup",[724,17143,17144,17145,17172,17173,17197,17198,17222,17223,17236,17237,1975],{},"Lze-li z ",[883,17146,17148],{"className":17147},[886],[888,17149,17150],{"xmlns":890},[892,17151,17152,17170],{},[895,17153,17154,17156,17158,17160,17162,17164,17166,17168],{},[898,17155,11041],{},[1996,17157,2005],{"stretchy":2004},[898,17159,2008],{},[1996,17161,2286],{"separator":2285},[898,17163,1994],{},[1996,17165,2011],{"stretchy":2004},[1996,17167,1998],{},[2129,17169,2327],{},[902,17171,11058],{"encoding":904}," vyjádřit ",[883,17174,17176],{"className":17175},[886],[888,17177,17178],{"xmlns":890},[892,17179,17180,17194],{},[895,17181,17182,17184,17186,17188,17190,17192],{},[898,17183,1994],{},[1996,17185,1998],{},[898,17187,1994],{},[1996,17189,2005],{"stretchy":2004},[898,17191,2008],{},[1996,17193,2011],{"stretchy":2004},[902,17195,17196],{"encoding":904},"y = y(x)"," (nebo ",[883,17199,17201],{"className":17200},[886],[888,17202,17203],{"xmlns":890},[892,17204,17205,17219],{},[895,17206,17207,17209,17211,17213,17215,17217],{},[898,17208,2008],{},[1996,17210,1998],{},[898,17212,2008],{},[1996,17214,2005],{"stretchy":2004},[898,17216,1994],{},[1996,17218,2011],{"stretchy":2004},[902,17220,17221],{"encoding":904},"x = x(y)","), dosadíme do ",[883,17224,17226],{"className":17225},[886],[888,17227,17228],{"xmlns":890},[892,17229,17230,17234],{},[895,17231,17232],{},[898,17233,2001],{},[902,17235,2001],{"encoding":904}," a převedeme na ",[38,17238,17239],{},"extrém funkce jedné proměnné",[115,17241,17243],{"id":17242},"použití-v-imek","Použití v ImeK",[198,17245,17247],{"id":17246},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,17249,17250,17251,1975],{},"Rozpočtové omezení: ",[883,17252,17254],{"className":17253},[886],[888,17255,17256],{"xmlns":890},[892,17257,17258,17298],{},[895,17259,17260,17266,17268,17276,17282,17284,17292],{},[2124,17261,17262,17264],{},[898,17263,9128],{},[1996,17265,4354],{},[1996,17267,1998],{},[9166,17269,17270,17272,17274],{},[898,17271,3937],{},[2129,17273,2278],{},[1996,17275,4354],{},[2272,17277,17278,17280],{},[898,17279,2789],{},[2129,17281,2278],{},[1996,17283,2095],{},[9166,17285,17286,17288,17290],{},[898,17287,3937],{},[2129,17289,2131],{},[1996,17291,4354],{},[2272,17293,17294,17296],{},[898,17295,2789],{},[2129,17297,2131],{},[902,17299,17300],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,17302,17303],{},[883,17304,17306],{"className":17305},[886],[888,17307,17308],{"xmlns":890},[892,17309,17310,17404],{},[895,17311,17312,17314,17316,17322,17324,17330,17332,17334,17336,17338,17340,17342,17348,17350,17356,17358,17360,17362,17364,17370,17372,17380,17386,17388,17396,17402],{},[898,17313,9795],{},[1996,17315,2005],{"stretchy":2004},[2272,17317,17318,17320],{},[898,17319,2789],{},[2129,17321,2278],{},[1996,17323,2286],{"separator":2285},[2272,17325,17326,17328],{},[898,17327,2789],{},[2129,17329,2131],{},[1996,17331,2286],{"separator":2285},[898,17333,16445],{},[1996,17335,2011],{"stretchy":2004},[1996,17337,1998],{},[898,17339,900],{},[1996,17341,2005],{"stretchy":2004},[2272,17343,17344,17346],{},[898,17345,2789],{},[2129,17347,2278],{},[1996,17349,2286],{"separator":2285},[2272,17351,17352,17354],{},[898,17353,2789],{},[2129,17355,2131],{},[1996,17357,2011],{"stretchy":2004},[1996,17359,2095],{},[898,17361,16445],{},[1996,17363,2005],{"stretchy":2004},[2124,17365,17366,17368],{},[898,17367,9128],{},[1996,17369,4354],{},[1996,17371,2225],{},[9166,17373,17374,17376,17378],{},[898,17375,3937],{},[2129,17377,2278],{},[1996,17379,4354],{},[2272,17381,17382,17384],{},[898,17383,2789],{},[2129,17385,2278],{},[1996,17387,2225],{},[9166,17389,17390,17392,17394],{},[898,17391,3937],{},[2129,17393,2131],{},[1996,17395,4354],{},[2272,17397,17398,17400],{},[898,17399,2789],{},[2129,17401,2131],{},[1996,17403,2011],{"stretchy":2004},[902,17405,17406],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,17408,17409,17410,1343,17442,1343,17474,17523,17524,17578,17579,1975],{},"Soustava: ",[883,17411,17413],{"className":17412},[886],[888,17414,17415],{"xmlns":890},[892,17416,17417,17439],{},[895,17418,17419,17427,17429,17431],{},[9166,17420,17421,17423,17425],{},[898,17422,900],{},[2129,17424,2278],{},[1996,17426,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,17428,1998],{},[898,17430,16445],{},[9166,17432,17433,17435,17437],{},[898,17434,3937],{},[2129,17436,2278],{},[1996,17438,4354],{},[902,17440,17441],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,17443,17445],{"className":17444},[886],[888,17446,17447],{"xmlns":890},[892,17448,17449,17471],{},[895,17450,17451,17459,17461,17463],{},[9166,17452,17453,17455,17457],{},[898,17454,900],{},[2129,17456,2131],{},[1996,17458,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,17460,1998],{},[898,17462,16445],{},[9166,17464,17465,17467,17469],{},[898,17466,3937],{},[2129,17468,2131],{},[1996,17470,4354],{},[902,17472,17473],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,17475,17477],{"className":17476},[886],[888,17478,17479],{"xmlns":890},[892,17480,17481,17521],{},[895,17482,17483,17489,17491,17499,17505,17507,17515],{},[2124,17484,17485,17487],{},[898,17486,9128],{},[1996,17488,4354],{},[1996,17490,1998],{},[9166,17492,17493,17495,17497],{},[898,17494,3937],{},[2129,17496,2278],{},[1996,17498,4354],{},[2272,17500,17501,17503],{},[898,17502,2789],{},[2129,17504,2278],{},[1996,17506,2095],{},[9166,17508,17509,17511,17513],{},[898,17510,3937],{},[2129,17512,2131],{},[1996,17514,4354],{},[2272,17516,17517,17519],{},[898,17518,2789],{},[2129,17520,2131],{},[902,17522,17300],{"encoding":904},". Z prvních dvou: ",[883,17525,17527],{"className":17526},[886],[888,17528,17529],{"xmlns":890},[892,17530,17531,17575],{},[895,17532,17533,17553,17555],{},[2325,17534,17535],{"scriptlevel":2327,"displaystyle":2004},[2329,17536,17537,17545],{},[9166,17538,17539,17541,17543],{},[898,17540,900],{},[2129,17542,2278],{},[1996,17544,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[9166,17546,17547,17549,17551],{},[898,17548,900],{},[2129,17550,2131],{},[1996,17552,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,17554,1998],{},[2325,17556,17557],{"scriptlevel":2327,"displaystyle":2004},[2329,17558,17559,17567],{},[9166,17560,17561,17563,17565],{},[898,17562,3937],{},[2129,17564,2278],{},[1996,17566,4354],{},[9166,17568,17569,17571,17573],{},[898,17570,3937],{},[2129,17572,2131],{},[1996,17574,4354],{},[902,17576,17577],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,17580,17582],{"className":17581},[886],[888,17583,17584],{"xmlns":890},[892,17585,17586,17618],{},[895,17587,17588,17590,17592,17594,17596,17598],{},[898,17589,2818],{},[898,17591,3994],{},[898,17593,2777],{},[898,17595,8673],{},[1996,17597,1998],{},[2325,17599,17600],{"scriptlevel":2327,"displaystyle":2004},[2329,17601,17602,17610],{},[9166,17603,17604,17606,17608],{},[898,17605,3937],{},[2129,17607,2278],{},[1996,17609,4354],{},[9166,17611,17612,17614,17616],{},[898,17613,3937],{},[2129,17615,2131],{},[1996,17617,4354],{},[902,17619,17620],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,17622,17624],{"id":17623},"minimalizace-výdajů","Minimalizace výdajů",[724,17626,17627,17628,1975],{},"Podmínka dané užitečnosti ",[883,17629,17631],{"className":17630},[886],[888,17632,17633],{"xmlns":890},[892,17634,17635,17665],{},[895,17636,17637,17643,17645,17647,17649,17655,17657,17663],{},[2124,17638,17639,17641],{},[898,17640,900],{},[1996,17642,4354],{},[1996,17644,1998],{},[898,17646,900],{},[1996,17648,2005],{"stretchy":2004},[2272,17650,17651,17653],{},[898,17652,2789],{},[2129,17654,2278],{},[1996,17656,2286],{"separator":2285},[2272,17658,17659,17661],{},[898,17660,2789],{},[2129,17662,2131],{},[1996,17664,2011],{"stretchy":2004},[902,17666,17667],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,17669,17670],{},[883,17671,17673],{"className":17672},[886],[888,17674,17675],{"xmlns":890},[892,17676,17677,17771],{},[895,17678,17679,17681,17683,17689,17691,17697,17699,17701,17703,17705,17713,17719,17721,17729,17735,17737,17739,17741,17747,17749,17751,17753,17759,17761,17767,17769],{},[898,17680,9795],{},[1996,17682,2005],{"stretchy":2004},[2272,17684,17685,17687],{},[898,17686,2789],{},[2129,17688,2278],{},[1996,17690,2286],{"separator":2285},[2272,17692,17693,17695],{},[898,17694,2789],{},[2129,17696,2131],{},[1996,17698,2286],{"separator":2285},[898,17700,16445],{},[1996,17702,2011],{"stretchy":2004},[1996,17704,1998],{},[9166,17706,17707,17709,17711],{},[898,17708,3937],{},[2129,17710,2278],{},[1996,17712,4354],{},[2272,17714,17715,17717],{},[898,17716,2789],{},[2129,17718,2278],{},[1996,17720,2095],{},[9166,17722,17723,17725,17727],{},[898,17724,3937],{},[2129,17726,2131],{},[1996,17728,4354],{},[2272,17730,17731,17733],{},[898,17732,2789],{},[2129,17734,2131],{},[1996,17736,2095],{},[898,17738,16445],{},[1996,17740,2005],{"stretchy":2004},[2124,17742,17743,17745],{},[898,17744,900],{},[1996,17746,4354],{},[1996,17748,2225],{},[898,17750,900],{},[1996,17752,2005],{"stretchy":2004},[2272,17754,17755,17757],{},[898,17756,2789],{},[2129,17758,2278],{},[1996,17760,2286],{"separator":2285},[2272,17762,17763,17765],{},[898,17764,2789],{},[2129,17766,2131],{},[1996,17768,2011],{"stretchy":2004},[1996,17770,2011],{"stretchy":2004},[902,17772,17773],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,17775,17776,17777,1975],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,17778,17780],{"className":17779},[886],[888,17781,17782],{"xmlns":890},[892,17783,17784,17823],{},[895,17785,17786,17793,17795,17801,17803,17809,17811,17817,17819,17821],{},[2272,17787,17788,17790],{},[898,17789,2789],{},[898,17791,17792],{},"i",[1996,17794,1998],{},[2272,17796,17797,17799],{},[898,17798,4183],{},[898,17800,17792],{},[1996,17802,2005],{"stretchy":2004},[2272,17804,17805,17807],{},[898,17806,3937],{},[2129,17808,2278],{},[1996,17810,2286],{"separator":2285},[2272,17812,17813,17815],{},[898,17814,3937],{},[2129,17816,2131],{},[1996,17818,2286],{"separator":2285},[898,17820,900],{},[1996,17822,2011],{"stretchy":2004},[902,17824,17825],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,17827,3792],{"id":3791},[120,17829,17830,17837,17844,17853],{},[123,17831,17832,2203,17834],{},[38,17833,3799],{},[207,17835,784],{"className":17836,"dataFsResolvedFilePath":782,"href":783},[210],[123,17838,17839,2203,17841],{},[38,17840,3807],{},[207,17842,11942],{"className":17843,"dataFsResolvedFilePath":800,"href":801},[210],[123,17845,17846,2203,17849,17852],{},[38,17847,17848],{},"Aplikace v kurzu:",[207,17850,880],{"className":17851,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,17854,17855,2203,17857,1343,17860,17863],{},[38,17856,3815],{},[207,17858,936],{"className":17859,"dataFsResolvedFilePath":934,"href":935},[210],[207,17861,1400],{"className":17862,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":17865},[17866,17867,17868,17869,17870,17871,17875],{"id":16413,"depth":642,"text":16414},{"id":3251,"depth":642,"text":3252},{"id":3325,"depth":642,"text":3326},{"id":17028,"depth":642,"text":17029},{"id":17140,"depth":642,"text":17141},{"id":17242,"depth":642,"text":17243,"children":17872},[17873,17874],{"id":17246,"depth":649,"text":17247},{"id":17623,"depth":649,"text":17624},{"id":3791,"depth":642,"text":3792},[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":16282,"description":17877},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,17884,17885],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":17888,"title":936,"body":17889,"course":1128,"courses":659,"created":9556,"description":641,"extension":661,"meta":27757,"navigation":664,"path":27758,"seo":27759,"sources":27760,"stem":27761,"tags":27762,"type":3857,"updated":677,"__hash__":27766},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":17890,"toc":27719},[17891,17894,17896,18019,18154,18158,18161,18274,18278,18306,18353,18356,18422,18467,18470,18496,18527,18531,18535,18579,18623,18685,18740,18743,18747,18750,18797,18894,19000,19006,19083,19112,19251,19255,19284,19334,19481,19571,19575,19601,19639,19666,19704,19766,19841,19919,19977,20043,20087,20091,20149,20198,20243,20456,20576,20582,20586,20609,20613,20620,20624,20655,20690,20694,20744,20832,20874,20895,20957,21017,21021,21092,21160,21232,21347,21395,21399,21402,21443,21482,21505,21619,21783,21791,21818,21848,21851,21928,22081,22165,22504,22508,22632,22768,22904,22957,22960,23210,23291,23295,23298,23356,23388,23391,23440,23443,23514,23710,23714,23865,24095,24133,24186,24232,24235,24291,24340,24544,24634,24638,24654,24661,24830,24834,24905,24986,25067,25146,25292,25380,25384,25567,25698,25743,25840,25844,26583,26585,27636,27638],[12,17892,936],{"id":17893},"národní-důchod",[115,17895,12008],{"id":12007},[724,17897,17898,17899,2203,17903,17906,17907,2203,17910,17923,17924,17927,17928,17931,17932,17935,17936,17938,17939,2203,17941,17958,17959,17976,17977,17980,17981,3918],{},"Kapitola 7 ",[207,17900,17902],{"className":17901,"dataFsResolvedFilePath":1960,"href":1961},[210],"Matematické ekonomie",[38,17904,17905],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,17908,17909],{},"národním důchodem",[883,17911,17913],{"className":17912},[886],[888,17914,17915],{"xmlns":890},[892,17916,17917,17921],{},[895,17918,17919],{},[898,17920,9128],{},[902,17922,9128],{"encoding":904},". Budují se postupně bohatší modely — ",[38,17925,17926],{},"C-I"," (jen spotřeba a investice) → ",[38,17929,17930],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,17933,17934],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,17937,12013],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,17940,13887],{},[883,17942,17944],{"className":17943},[886],[888,17945,17946],{"xmlns":890},[892,17947,17948,17956],{},[895,17949,17950],{},[2124,17951,17952,17954],{},[898,17953,9128],{},[898,17955,4252],{},[902,17957,13905],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,17960,17962],{"className":17961},[886],[888,17963,17964],{"xmlns":890},[892,17965,17966,17974],{},[895,17967,17968],{},[2124,17969,17970,17972],{},[898,17971,9128],{},[898,17973,4252],{},[902,17975,13905],{"encoding":904}," na exogenní veličiny popisují ",[38,17978,17979],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,17982,17984],{"className":17983},[886],[888,17985,17986],{"xmlns":890},[892,17987,17988,18016],{},[895,17989,17990,17992,17994,17996,17998,18000,18002,18004,18006,18008,18010,18012,18014],{},[2129,17991,2278],{},[898,17993,4674],{"mathvariant":2376},[1996,17995,2005],{"stretchy":2004},[2129,17997,2278],{},[1996,17999,2225],{},[898,18001,207],{},[1996,18003,2011],{"stretchy":2004},[1996,18005,1998],{},[2129,18007,2278],{},[898,18009,4674],{"mathvariant":2376},[898,18011,2818],{},[898,18013,3937],{},[898,18015,8673],{},[902,18017,18018],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[3867,18020,18021],{},[724,18022,18023,18025,18026,18029,18030,18048,18049,18079,18080,18127,18128,18130,18131,18153],{},[883,18024,4155],{}," Intuice\n",[38,18027,18028],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,18031,18033],{"className":18032},[886],[888,18034,18035],{"xmlns":890},[892,18036,18037,18045],{},[895,18038,18039,18041,18043],{},[898,18040,2818],{},[898,18042,3937],{},[898,18044,2777],{},[902,18046,18047],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,18050,18052],{"className":18051},[886],[888,18053,18054],{"xmlns":890},[892,18055,18056,18076],{},[895,18057,18058,18060,18062,18064,18066,18068,18070,18072,18074],{},[898,18059,2818],{},[898,18061,3937],{},[898,18063,8673],{},[1996,18065,1998],{},[2129,18067,2278],{},[1996,18069,2225],{},[898,18071,2818],{},[898,18073,3937],{},[898,18075,2777],{},[902,18077,18078],{"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 ",[883,18081,18083],{"className":18082},[886],[888,18084,18085],{"xmlns":890},[892,18086,18087,18124],{},[895,18088,18089,18091,18093,18095,18097,18103,18105,18108,18110,18112,18114,18116,18118,18120,18122],{},[2129,18090,2278],{},[1996,18092,2095],{},[898,18094,207],{},[1996,18096,2095],{},[2124,18098,18099,18101],{},[898,18100,207],{},[2129,18102,2131],{},[1996,18104,2095],{},[1996,18106,18107],{},"⋯",[1996,18109,1998],{},[2129,18111,2278],{},[898,18113,4674],{"mathvariant":2376},[1996,18115,2005],{"stretchy":2004},[2129,18117,2278],{},[1996,18119,2225],{},[898,18121,207],{},[1996,18123,2011],{"stretchy":2004},[902,18125,18126],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,18129,12013],{}," 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 ",[883,18132,18134],{"className":18133},[886],[888,18135,18136],{"xmlns":890},[892,18137,18138,18150],{},[895,18139,18140,18142,18144,18146,18148],{},[1996,18141,2005],{"stretchy":2004},[898,18143,9128],{},[1996,18145,2286],{"separator":2285},[898,18147,12043],{},[1996,18149,2011],{"stretchy":2004},[902,18151,18152],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,18155,18157],{"id":18156},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,18159,18160],{},"Po prostudování kapitoly by čtenář měl umět:",[120,18162,18163,18166,18169,18172,18175,18178,18181,18271],{},[123,18164,18165],{},"popsat zjednodušený model národní ekonomiky,",[123,18167,18168],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,18170,18171],{},"popsat lineární model spotřeby a úspor,",[123,18173,18174],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,18176,18177],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,18179,18180],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,18182,18183,18184,1343,18201,1343,18223,3885,18248,18270],{},"popsat modely ",[883,18185,18187],{"className":18186},[886],[888,18188,18189],{"xmlns":890},[892,18190,18191,18199],{},[895,18192,18193,18195,18197],{},[898,18194,2777],{},[2288,18196,12292],{},[898,18198,12186],{},[902,18200,12297],{"encoding":904},[883,18202,18204],{"className":18203},[886],[888,18205,18206],{"xmlns":890},[892,18207,18208,18220],{},[895,18209,18210,18212,18214,18216,18218],{},[898,18211,2777],{},[2288,18213,12292],{},[898,18215,12186],{},[2288,18217,12292],{},[898,18219,12114],{},[902,18221,18222],{"encoding":904},"C\\text{-}I\\text{-}G",[883,18224,18226],{"className":18225},[886],[888,18227,18228],{"xmlns":890},[892,18229,18230,18246],{},[895,18231,18232,18234,18236,18238,18240,18242,18244],{},[898,18233,2777],{},[2288,18235,12292],{},[898,18237,12186],{},[2288,18239,12292],{},[898,18241,12114],{},[2288,18243,12292],{},[898,18245,12322],{},[902,18247,12325],{"encoding":904},[883,18249,18251],{"className":18250},[886],[888,18252,18253],{"xmlns":890},[892,18254,18255,18267],{},[895,18256,18257,18259,18261,18263,18265],{},[898,18258,12186],{},[898,18260,8673],{},[2288,18262,12292],{},[898,18264,9795],{},[898,18266,2818],{},[902,18268,18269],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,18272,18273],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,18275,18277],{"id":18276},"gnp-a-národní-důchod","GNP a národní důchod",[724,18279,18280,2203,18283,10025,18302,18305],{},[38,18281,18282],{},"Hrubý národní produkt",[883,18284,18286],{"className":18285},[886],[888,18287,18288],{"xmlns":890},[892,18289,18290,18299],{},[895,18291,18292,18294,18297],{},[898,18293,12114],{},[898,18295,18296],{},"N",[898,18298,3937],{},[902,18300,18301],{"encoding":904},"GNP",[614,18303,18304],{},"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:",[724,18307,18308],{},[883,18309,18311],{"className":18310},[886],[888,18312,18313],{"xmlns":890},[892,18314,18315,18350],{},[895,18316,18317,18319,18321,18323,18325,18327,18329,18331,18333,18335,18337,18339,18341,18343,18345,18348],{},[898,18318,12114],{},[898,18320,18296],{},[898,18322,3937],{},[1996,18324,1998],{},[898,18326,2777],{},[1996,18328,2095],{},[898,18330,12186],{},[1996,18332,2095],{},[898,18334,12114],{},[1996,18336,2095],{},[898,18338,12322],{},[1996,18340,2286],{"separator":2285},[5878,18342],{"width":5880},[1996,18344,2005],{"stretchy":2004},[2129,18346,18347],{},"7.1",[1996,18349,2011],{"stretchy":2004},[902,18351,18352],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,18354,18355],{},"kde",[120,18357,18358,18374,18390,18406],{},[123,18359,18360,18373],{},[883,18361,18363],{"className":18362},[886],[888,18364,18365],{"xmlns":890},[892,18366,18367,18371],{},[895,18368,18369],{},[898,18370,2777],{},[902,18372,2777],{"encoding":904}," — výdaje domácností na spotřebu,",[123,18375,18376,18389],{},[883,18377,18379],{"className":18378},[886],[888,18380,18381],{"xmlns":890},[892,18382,18383,18387],{},[895,18384,18385],{},[898,18386,12186],{},[902,18388,12186],{"encoding":904}," — hrubé domácí investice,",[123,18391,18392,18405],{},[883,18393,18395],{"className":18394},[886],[888,18396,18397],{"xmlns":890},[892,18398,18399,18403],{},[895,18400,18401],{},[898,18402,12114],{},[902,18404,12114],{"encoding":904}," — vládní výdaje,",[123,18407,18408,18421],{},[883,18409,18411],{"className":18410},[886],[888,18412,18413],{"xmlns":890},[892,18414,18415,18419],{},[895,18416,18417],{},[898,18418,12322],{},[902,18420,12322],{"encoding":904}," — čistý export.",[724,18423,18424,18425,18442,18443,18446,18447,2203,18450,10025,18463,18466],{},"K měření ",[883,18426,18428],{"className":18427},[886],[888,18429,18430],{"xmlns":890},[892,18431,18432,18440],{},[895,18433,18434,18436,18438],{},[898,18435,12114],{},[898,18437,18296],{},[898,18439,3937],{},[902,18441,18301],{"encoding":904}," se užívá ",[38,18444,18445],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,18448,18449],{},"národní důchod",[883,18451,18453],{"className":18452},[886],[888,18454,18455],{"xmlns":890},[892,18456,18457,18461],{},[895,18458,18459],{},[898,18460,9128],{},[902,18462,9128],{"encoding":904},[614,18464,18465],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,18468,18469],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,18471,18472],{},[883,18473,18475],{"className":18474},[886],[888,18476,18477],{"xmlns":890},[892,18478,18479,18493],{},[895,18480,18481,18483,18485,18487,18489,18491],{},[898,18482,12114],{},[898,18484,18296],{},[898,18486,3937],{},[1996,18488,2730],{},[898,18490,9128],{},[1996,18492,2286],{"separator":2285},[902,18494,18495],{"encoding":904},"GNP \\approx Y,",[724,18497,18498,18499,10025,18502,18505,18506,18519,18520,18523,18524,1975],{},"a užívá se společného názvu ",[38,18500,18501],{},"důchod",[614,18503,18504],{},"income",") s označením ",[883,18507,18509],{"className":18508},[886],[888,18510,18511],{"xmlns":890},[892,18512,18513,18517],{},[895,18514,18515],{},[898,18516,9128],{},[902,18518,9128],{"encoding":904},". Domácnosti důchod použijí ke ",[38,18521,18522],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,18525,18526],{},"úspor",[115,18528,18530],{"id":18529},"spotřeba-a-úspory","Spotřeba a úspory",[198,18532,18534],{"id":18533},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,18536,18537,18538,18551,18552,18565,18566,2704],{},"Jak spotřeba ",[883,18539,18541],{"className":18540},[886],[888,18542,18543],{"xmlns":890},[892,18544,18545,18549],{},[895,18546,18547],{},[898,18548,2777],{},[902,18550,2777],{"encoding":904},", tak úspory ",[883,18553,18555],{"className":18554},[886],[888,18556,18557],{"xmlns":890},[892,18558,18559,18563],{},[895,18560,18561],{},[898,18562,8673],{},[902,18564,8673],{"encoding":904}," závisejí na důchodu ",[883,18567,18569],{"className":18568},[886],[888,18570,18571],{"xmlns":890},[892,18572,18573,18577],{},[895,18574,18575],{},[898,18576,9128],{},[902,18578,9128],{"encoding":904},[724,18580,18581],{},[883,18582,18584],{"className":18583},[886],[888,18585,18586],{"xmlns":890},[892,18587,18588,18620],{},[895,18589,18590,18592,18594,18596,18598,18600,18602,18604,18606,18608,18610,18612,18614,18616,18618],{},[898,18591,2777],{},[1996,18593,1998],{},[898,18595,2777],{},[1996,18597,2005],{"stretchy":2004},[898,18599,9128],{},[1996,18601,2011],{"stretchy":2004},[1996,18603,2286],{"separator":2285},[5878,18605],{"width":5880},[898,18607,8673],{},[1996,18609,1998],{},[898,18611,8673],{},[1996,18613,2005],{"stretchy":2004},[898,18615,9128],{},[1996,18617,2011],{"stretchy":2004},[898,18619,1975],{"mathvariant":2376},[902,18621,18622],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,18624,18625,8102,18644,10025,18647,18650,18651,8102,18671,10025,18674,18677,18678,3885,18681,18684],{},[883,18626,18628],{"className":18627},[886],[888,18629,18630],{"xmlns":890},[892,18631,18632,18642],{},[895,18633,18634,18636,18638,18640],{},[898,18635,2777],{},[1996,18637,2005],{"stretchy":2004},[898,18639,9128],{},[1996,18641,2011],{"stretchy":2004},[902,18643,14218],{"encoding":904},[38,18645,18646],{},"funkce spotřeby",[614,18648,18649],{},"consumption function","), ",[883,18652,18654],{"className":18653},[886],[888,18655,18656],{"xmlns":890},[892,18657,18658,18668],{},[895,18659,18660,18662,18664,18666],{},[898,18661,8673],{},[1996,18663,2005],{"stretchy":2004},[898,18665,9128],{},[1996,18667,2011],{"stretchy":2004},[902,18669,18670],{"encoding":904},"S(Y)",[38,18672,18673],{},"funkce úspor",[614,18675,18676],{},"savings function","); jejich grafy se nazývají ",[38,18679,18680],{},"křivka spotřeby",[38,18682,18683],{},"křivka úspor",". Platí základní identita",[724,18686,18687],{},[883,18688,18690],{"className":18689},[886],[888,18691,18692],{"xmlns":890},[892,18693,18694,18737],{},[895,18695,18696,18698,18700,18702,18704,18706,18708,18710,18712,18714,18716,18718,18720,18722,18724,18726,18728,18730,18732,18735],{},[898,18697,9128],{},[1996,18699,1998],{},[898,18701,2777],{},[1996,18703,2095],{},[898,18705,8673],{},[1996,18707,1998],{},[898,18709,2777],{},[1996,18711,2005],{"stretchy":2004},[898,18713,9128],{},[1996,18715,2011],{"stretchy":2004},[1996,18717,2095],{},[898,18719,8673],{},[1996,18721,2005],{"stretchy":2004},[898,18723,9128],{},[1996,18725,2011],{"stretchy":2004},[898,18727,1975],{"mathvariant":2376},[5878,18729],{"width":5880},[1996,18731,2005],{"stretchy":2004},[2129,18733,18734],{},"7.2",[1996,18736,2011],{"stretchy":2004},[902,18738,18739],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,18741,18742],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,18744,18746],{"id":18745},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,18748,18749],{},"Nejjednodušší model předpokládá lineární tvar",[724,18751,18752],{},[883,18753,18755],{"className":18754},[886],[888,18756,18757],{"xmlns":890},[892,18758,18759,18794],{},[895,18760,18761,18763,18765,18767,18769,18771,18773,18775,18777,18779,18781,18783,18785,18787,18789,18792],{},[898,18762,2777],{},[1996,18764,1998],{},[898,18766,2777],{},[1996,18768,2005],{"stretchy":2004},[898,18770,9128],{},[1996,18772,2011],{"stretchy":2004},[1996,18774,1998],{},[898,18776,207],{},[898,18778,9128],{},[1996,18780,2095],{},[898,18782,2098],{},[1996,18784,2286],{"separator":2285},[5878,18786],{"width":5880},[1996,18788,2005],{"stretchy":2004},[2129,18790,18791],{},"7.3",[1996,18793,2011],{"stretchy":2004},[902,18795,18796],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,18798,4310,18799,3885,18817,18839,18840,18880,18881,1975],{},[883,18800,18802],{"className":18801},[886],[888,18803,18804],{"xmlns":890},[892,18805,18806,18814],{},[895,18807,18808,18810,18812],{},[898,18809,2098],{},[1996,18811,3408],{},[2129,18813,2327],{},[902,18815,18816],{"encoding":904},"b > 0",[883,18818,18820],{"className":18819},[886],[888,18821,18822],{"xmlns":890},[892,18823,18824,18836],{},[895,18825,18826,18828,18830,18832,18834],{},[2129,18827,2327],{},[1996,18829,3447],{},[898,18831,207],{},[1996,18833,3447],{},[2129,18835,2278],{},[902,18837,18838],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,18841,18843],{"className":18842},[886],[888,18844,18845],{"xmlns":890},[892,18846,18847,18877],{},[895,18848,18849,18851,18853,18860,18862,18865,18867,18869,18871,18873,18875],{},[898,18850,207],{},[1996,18852,1998],{},[895,18854,18855,18858],{},[898,18856,18857],{"mathvariant":2376},"t",[898,18859,11041],{"mathvariant":2376},[2288,18861,2987],{},[898,18863,18864],{},"α",[1996,18866,1998],{},[898,18868,2889],{"mathvariant":2376},[898,18870,2777],{},[898,18872,4674],{"mathvariant":2376},[898,18874,2889],{"mathvariant":2376},[898,18876,9128],{},[902,18878,18879],{"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 ",[883,18882,18884],{"className":18883},[886],[888,18885,18886],{"xmlns":890},[892,18887,18888,18892],{},[895,18889,18890],{},[898,18891,9128],{},[902,18893,9128],{"encoding":904},[724,18895,18896],{},[614,18897,18898,18899,18923,18924,18962,18963,18979,18980,1975],{},"Obrázek 7.1 — Přímka spotřeby ",[883,18900,18902],{"className":18901},[886],[888,18903,18904],{"xmlns":890},[892,18905,18906,18920],{},[895,18907,18908,18910,18912,18914,18916,18918],{},[898,18909,2777],{},[1996,18911,1998],{},[898,18913,207],{},[898,18915,9128],{},[1996,18917,2095],{},[898,18919,2098],{},[902,18921,18922],{"encoding":904},"C = aY + b"," se směrnicí ",[883,18925,18927],{"className":18926},[886],[888,18928,18929],{"xmlns":890},[892,18930,18931,18959],{},[895,18932,18933,18935,18937,18943,18945,18947,18949,18951,18953,18955,18957],{},[898,18934,207],{},[1996,18936,1998],{},[895,18938,18939,18941],{},[898,18940,18857],{"mathvariant":2376},[898,18942,11041],{"mathvariant":2376},[2288,18944,2987],{},[898,18946,18864],{},[1996,18948,1998],{},[898,18950,2889],{"mathvariant":2376},[898,18952,2777],{},[898,18954,4674],{"mathvariant":2376},[898,18956,2889],{"mathvariant":2376},[898,18958,9128],{},[902,18960,18961],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,18964,18966],{"className":18965},[886],[888,18967,18968],{"xmlns":890},[892,18969,18970,18976],{},[895,18971,18972,18974],{},[898,18973,2889],{"mathvariant":2376},[898,18975,2777],{},[902,18977,18978],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,18981,18983],{"className":18982},[886],[888,18984,18985],{"xmlns":890},[892,18986,18987,18997],{},[895,18988,18989,18991,18993,18995],{},[898,18990,2889],{"mathvariant":2376},[898,18992,9128],{},[1996,18994,1998],{},[2129,18996,2278],{},[902,18998,18999],{"encoding":904},"\\Delta Y = 1",[724,19001,19002,19003,2704],{},"Dosazením do (7.2) plyne ",[38,19004,19005],{},"lineární model úspor",[724,19007,19008],{},[883,19009,19011],{"className":19010},[886],[888,19012,19013],{"xmlns":890},[892,19014,19015,19080],{},[895,19016,19017,19019,19021,19023,19025,19027,19029,19031,19033,19035,19037,19039,19041,19043,19045,19047,19049,19051,19053,19055,19057,19059,19061,19063,19065,19067,19069,19071,19073,19075,19078],{},[898,19018,8673],{},[1996,19020,1998],{},[898,19022,9128],{},[1996,19024,2225],{},[898,19026,2777],{},[1996,19028,2005],{"stretchy":2004},[898,19030,9128],{},[1996,19032,2011],{"stretchy":2004},[1996,19034,1998],{},[898,19036,9128],{},[1996,19038,2225],{},[1996,19040,2005],{"stretchy":2004},[898,19042,207],{},[898,19044,9128],{},[1996,19046,2095],{},[898,19048,2098],{},[1996,19050,2011],{"stretchy":2004},[1996,19052,1998],{},[1996,19054,2005],{"stretchy":2004},[2129,19056,2278],{},[1996,19058,2225],{},[898,19060,207],{},[1996,19062,2011],{"stretchy":2004},[898,19064,9128],{},[1996,19066,2225],{},[898,19068,2098],{},[898,19070,1975],{"mathvariant":2376},[5878,19072],{"width":5880},[1996,19074,2005],{"stretchy":2004},[2129,19076,19077],{},"7.4",[1996,19079,2011],{"stretchy":2004},[902,19081,19082],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,19084,19085,19086,3918],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,19087,19089],{"className":19088},[886],[888,19090,19091],{"xmlns":890},[892,19092,19093,19109],{},[895,19094,19095,19097,19099,19101,19103,19105,19107],{},[2129,19096,2327],{},[1996,19098,3447],{},[2129,19100,2278],{},[1996,19102,2225],{},[898,19104,207],{},[1996,19106,3447],{},[2129,19108,2278],{},[902,19110,19111],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,19113,19114],{},[614,19115,19116,19117,3885,19140,19172,19173,2624,19186,19216,19217,2624,19235,1975],{},"Obrázek 7.2 — Přímky ",[883,19118,19120],{"className":19119},[886],[888,19121,19122],{"xmlns":890},[892,19123,19124,19138],{},[895,19125,19126,19128,19130,19132,19134,19136],{},[898,19127,2777],{},[1996,19129,1998],{},[898,19131,207],{},[898,19133,9128],{},[1996,19135,2095],{},[898,19137,2098],{},[902,19139,18922],{"encoding":904},[883,19141,19143],{"className":19142},[886],[888,19144,19145],{"xmlns":890},[892,19146,19147,19169],{},[895,19148,19149,19151,19153,19155,19157,19159,19161,19163,19165,19167],{},[898,19150,8673],{},[1996,19152,1998],{},[1996,19154,2005],{"stretchy":2004},[2129,19156,2278],{},[1996,19158,2225],{},[898,19160,207],{},[1996,19162,2011],{"stretchy":2004},[898,19164,9128],{},[1996,19166,2225],{},[898,19168,2098],{},[902,19170,19171],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,19174,19176],{"className":19175},[886],[888,19177,19178],{"xmlns":890},[892,19179,19180,19184],{},[895,19181,19182],{},[898,19183,9128],{},[902,19185,9128],{"encoding":904},[883,19187,19189],{"className":19188},[886],[888,19190,19191],{"xmlns":890},[892,19192,19193,19213],{},[895,19194,19195,19197,19199,19201,19203,19205,19207,19209,19211],{},[898,19196,9128],{},[1996,19198,1998],{},[898,19200,2098],{},[898,19202,4674],{"mathvariant":2376},[1996,19204,2005],{"stretchy":2004},[2129,19206,2278],{},[1996,19208,2225],{},[898,19210,207],{},[1996,19212,2011],{"stretchy":2004},[902,19214,19215],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,19218,19220],{"className":19219},[886],[888,19221,19222],{"xmlns":890},[892,19223,19224,19232],{},[895,19225,19226,19228,19230],{},[898,19227,2777],{},[1996,19229,2286],{"separator":2285},[898,19231,8673],{},[902,19233,19234],{"encoding":904},"C, S",[883,19236,19238],{"className":19237},[886],[888,19239,19240],{"xmlns":890},[892,19241,19242,19248],{},[895,19243,19244,19246],{},[1996,19245,2225],{},[898,19247,2098],{},[902,19249,19250],{"encoding":904},"-b",[198,19252,19254],{"id":19253},"příklad-71","Příklad 7.1",[724,19256,19257,19258,19283],{},"Pro spotřebu ",[883,19259,19261],{"className":19260},[886],[888,19262,19263],{"xmlns":890},[892,19264,19265,19280],{},[895,19266,19267,19269,19271,19274,19276,19278],{},[898,19268,2777],{},[1996,19270,1998],{},[2129,19272,19273],{},"0,4",[898,19275,9128],{},[1996,19277,2095],{},[2129,19279,2863],{},[902,19281,19282],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,19285,19286],{},[883,19287,19289],{"className":19288},[886],[888,19290,19291],{"xmlns":890},[892,19292,19293,19331],{},[895,19294,19295,19297,19299,19301,19303,19305,19307,19309,19311,19313,19315,19317,19319,19321,19324,19326,19328],{},[898,19296,8673],{},[1996,19298,1998],{},[898,19300,9128],{},[1996,19302,2225],{},[898,19304,2777],{},[1996,19306,1998],{},[898,19308,9128],{},[1996,19310,2225],{},[2129,19312,19273],{},[898,19314,9128],{},[1996,19316,2225],{},[2129,19318,2863],{},[1996,19320,1998],{},[2129,19322,19323],{},"0,6",[898,19325,9128],{},[1996,19327,2225],{},[2129,19329,19330],{},"10.",[902,19332,19333],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,19335,19336],{},[614,19337,19338,19339,3885,19362,19386,19387,8102,19400,19424,19425,8102,19442,19458,19459,1975],{},"Obrázek 7.3 — Přímky ",[883,19340,19342],{"className":19341},[886],[888,19343,19344],{"xmlns":890},[892,19345,19346,19360],{},[895,19347,19348,19350,19352,19354,19356,19358],{},[898,19349,2777],{},[1996,19351,1998],{},[2129,19353,19273],{},[898,19355,9128],{},[1996,19357,2095],{},[2129,19359,2863],{},[902,19361,19282],{"encoding":904},[883,19363,19365],{"className":19364},[886],[888,19366,19367],{"xmlns":890},[892,19368,19369,19383],{},[895,19370,19371,19373,19375,19377,19379,19381],{},[898,19372,8673],{},[1996,19374,1998],{},[2129,19376,19323],{},[898,19378,9128],{},[1996,19380,2225],{},[2129,19382,2863],{},[902,19384,19385],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,19388,19390],{"className":19389},[886],[888,19391,19392],{"xmlns":890},[892,19393,19394,19398],{},[895,19395,19396],{},[898,19397,9128],{},[902,19399,9128],{"encoding":904},[883,19401,19403],{"className":19402},[886],[888,19404,19405],{"xmlns":890},[892,19406,19407,19421],{},[895,19408,19409,19411,19414],{},[1996,19410,2730],{},[2129,19412,19413],{},"16,",[8386,19415,19416,19418],{"accent":2285},[2129,19417,2235],{},[1996,19419,19420],{},"ˉ",[902,19422,19423],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,19426,19428],{"className":19427},[886],[888,19429,19430],{"xmlns":890},[892,19431,19432,19440],{},[895,19433,19434,19436,19438],{},[898,19435,2777],{},[1996,19437,2286],{"separator":2285},[898,19439,8673],{},[902,19441,19234],{"encoding":904},[883,19443,19445],{"className":19444},[886],[888,19446,19447],{"xmlns":890},[892,19448,19449,19455],{},[895,19450,19451,19453],{},[1996,19452,2225],{},[2129,19454,2863],{},[902,19456,19457],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,19460,19462],{"className":19461},[886],[888,19463,19464],{"xmlns":890},[892,19465,19466,19478],{},[895,19467,19468,19470,19472,19474,19476],{},[1996,19469,2005],{"stretchy":2004},[2129,19471,2327],{},[1996,19473,2286],{"separator":2285},[2129,19475,2863],{},[1996,19477,2011],{"stretchy":2004},[902,19479,19480],{"encoding":904},"(0, 10)",[724,19482,19483,19484,8102,19502,19532,19533,10025,19536,19539,19540,8102,19564,10025,19567,19570],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,19485,19487],{"className":19486},[886],[888,19488,19489],{"xmlns":890},[892,19490,19491,19499],{},[895,19492,19493,19495,19497],{},[898,19494,9128],{},[1996,19496,1998],{},[2129,19498,2327],{},[902,19500,19501],{"encoding":904},"Y = 0",[883,19503,19505],{"className":19504},[886],[888,19506,19507],{"xmlns":890},[892,19508,19509,19529],{},[895,19510,19511,19513,19515,19517,19519,19521,19523,19525,19527],{},[898,19512,8673],{},[1996,19514,2005],{"stretchy":2004},[2129,19516,2327],{},[1996,19518,2011],{"stretchy":2004},[1996,19520,1998],{},[1996,19522,2225],{},[898,19524,2098],{},[1996,19526,3447],{},[2129,19528,2327],{},[902,19530,19531],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,19534,19535],{},"autonomních úsporách",[614,19537,19538],{},"autonomous savings","). Analogicky ",[883,19541,19543],{"className":19542},[886],[888,19544,19545],{"xmlns":890},[892,19546,19547,19561],{},[895,19548,19549,19551,19553,19555,19557,19559],{},[898,19550,2777],{},[1996,19552,2005],{"stretchy":2004},[2129,19554,2327],{},[1996,19556,2011],{"stretchy":2004},[1996,19558,1998],{},[898,19560,2098],{},[902,19562,19563],{"encoding":904},"C(0) = b",[38,19565,19566],{},"autonomní spotřeba",[614,19568,19569],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,19572,19574],{"id":19573},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,19576,19577,2203,19580,10025,19597,19600],{},[38,19578,19579],{},"Mezní sklon ke spotřebě",[883,19581,19583],{"className":19582},[886],[888,19584,19585],{"xmlns":890},[892,19586,19587,19595],{},[895,19588,19589,19591,19593],{},[898,19590,2818],{},[898,19592,3937],{},[898,19594,2777],{},[902,19596,18047],{"encoding":904},[614,19598,19599],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,19602,19603],{},[883,19604,19606],{"className":19605},[886],[888,19607,19608],{"xmlns":890},[892,19609,19610,19636],{},[895,19611,19612,19614,19616,19618,19620,19634],{},[898,19613,2818],{},[898,19615,3937],{},[898,19617,2777],{},[1996,19619,1998],{},[2329,19621,19622,19628],{},[895,19623,19624,19626],{},[898,19625,2194],{"mathvariant":2376},[898,19627,2777],{},[895,19629,19630,19632],{},[898,19631,2194],{"mathvariant":2376},[898,19633,9128],{},[898,19635,1975],{"mathvariant":2376},[902,19637,19638],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,19640,19641,2203,19644,10025,19662,19665],{},[38,19642,19643],{},"Mezní sklon k úsporám",[883,19645,19647],{"className":19646},[886],[888,19648,19649],{"xmlns":890},[892,19650,19651,19659],{},[895,19652,19653,19655,19657],{},[898,19654,2818],{},[898,19656,3937],{},[898,19658,8673],{},[902,19660,19661],{"encoding":904},"MPS",[614,19663,19664],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,19667,19668],{},[883,19669,19671],{"className":19670},[886],[888,19672,19673],{"xmlns":890},[892,19674,19675,19701],{},[895,19676,19677,19679,19681,19683,19685,19699],{},[898,19678,2818],{},[898,19680,3937],{},[898,19682,8673],{},[1996,19684,1998],{},[2329,19686,19687,19693],{},[895,19688,19689,19691],{},[898,19690,2194],{"mathvariant":2376},[898,19692,8673],{},[895,19694,19695,19697],{},[898,19696,2194],{"mathvariant":2376},[898,19698,9128],{},[898,19700,1975],{"mathvariant":2376},[902,19702,19703],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,19705,19706,19707,19765],{},"Z (7.2) plyne ",[883,19708,19710],{"className":19709},[886],[888,19711,19712],{"xmlns":890},[892,19713,19714,19762],{},[895,19715,19716,19730,19732,19746,19748],{},[2329,19717,19718,19724],{},[895,19719,19720,19722],{},[898,19721,2194],{"mathvariant":2376},[898,19723,9128],{},[895,19725,19726,19728],{},[898,19727,2194],{"mathvariant":2376},[898,19729,9128],{},[1996,19731,1998],{},[2329,19733,19734,19740],{},[895,19735,19736,19738],{},[898,19737,2194],{"mathvariant":2376},[898,19739,2777],{},[895,19741,19742,19744],{},[898,19743,2194],{"mathvariant":2376},[898,19745,9128],{},[1996,19747,2095],{},[2329,19749,19750,19756],{},[895,19751,19752,19754],{},[898,19753,2194],{"mathvariant":2376},[898,19755,8673],{},[895,19757,19758,19760],{},[898,19759,2194],{"mathvariant":2376},[898,19761,9128],{},[902,19763,19764],{"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",[724,19767,19768],{},[883,19769,19771],{"className":19770},[886],[888,19772,19773],{"xmlns":890},[892,19774,19775,19838],{},[895,19776,19777,19829,19831,19833,19836],{},[12834,19778,19779],{"notation":12836},[2325,19780,19781],{"scriptlevel":2327,"displaystyle":2004},[2325,19782,19783],{"scriptlevel":2327,"displaystyle":2004},[2325,19784,19785],{"scriptlevel":2327,"displaystyle":2285},[895,19786,19787,19789,19791,19793,19795,19797,19799,19801,19803,19805,19807,19809,19811,19813,19815,19817,19819,19821,19823,19825,19827],{},[898,19788,2818],{},[898,19790,3937],{},[898,19792,2777],{},[1996,19794,2095],{},[898,19796,2818],{},[898,19798,3937],{},[898,19800,8673],{},[1996,19802,1998],{},[2129,19804,2278],{},[1996,19806,2286],{"separator":2285},[5878,19808],{"width":5880},[898,19810,2818],{},[898,19812,3937],{},[898,19814,8673],{},[1996,19816,1998],{},[2129,19818,2278],{},[1996,19820,2225],{},[898,19822,2818],{},[898,19824,3937],{},[898,19826,2777],{},[898,19828,1975],{"mathvariant":2376},[5878,19830],{"width":5880},[1996,19832,2005],{"stretchy":2004},[2129,19834,19835],{},"7.5",[1996,19837,2011],{"stretchy":2004},[902,19839,19840],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,19842,19843,2203,19846,19869,19870,3885,19892,19918],{},[38,19844,19845],{},"Pro lineární model",[883,19847,19849],{"className":19848},[886],[888,19850,19851],{"xmlns":890},[892,19852,19853,19867],{},[895,19854,19855,19857,19859,19861,19863,19865],{},[898,19856,2777],{},[1996,19858,1998],{},[898,19860,207],{},[898,19862,9128],{},[1996,19864,2095],{},[898,19866,2098],{},[902,19868,18922],{"encoding":904}," vychází ",[883,19871,19873],{"className":19872},[886],[888,19874,19875],{"xmlns":890},[892,19876,19877,19889],{},[895,19878,19879,19881,19883,19885,19887],{},[898,19880,2818],{},[898,19882,3937],{},[898,19884,2777],{},[1996,19886,1998],{},[898,19888,207],{},[902,19890,19891],{"encoding":904},"MPC = a",[883,19893,19895],{"className":19894},[886],[888,19896,19897],{"xmlns":890},[892,19898,19899,19915],{},[895,19900,19901,19903,19905,19907,19909,19911,19913],{},[898,19902,2818],{},[898,19904,3937],{},[898,19906,8673],{},[1996,19908,1998],{},[2129,19910,2278],{},[1996,19912,2225],{},[898,19914,207],{},[902,19916,19917],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,19920,19921,19924,19925,19947,19948,19976],{},[38,19922,19923],{},"Interpretace diferenciálem."," Pro pevné ",[883,19926,19928],{"className":19927},[886],[888,19929,19930],{"xmlns":890},[892,19931,19932,19944],{},[895,19933,19934,19936,19938],{},[898,19935,9128],{},[1996,19937,1998],{},[2124,19939,19940,19942],{},[898,19941,9128],{},[1996,19943,4354],{},[902,19945,19946],{"encoding":904},"Y = Y^*"," udává ",[883,19949,19951],{"className":19950},[886],[888,19952,19953],{"xmlns":890},[892,19954,19955,19973],{},[895,19956,19957,19959,19961,19963,19965,19971],{},[898,19958,2818],{},[898,19960,3937],{},[898,19962,2777],{},[1996,19964,2005],{"stretchy":2004},[2124,19966,19967,19969],{},[898,19968,9128],{},[1996,19970,4354],{},[1996,19972,2011],{"stretchy":2004},[902,19974,19975],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,19978,19979],{},[883,19980,19982],{"className":19981},[886],[888,19983,19984],{"xmlns":890},[892,19985,19986,20040],{},[895,19987,19988,19990,19992,19994,19996,19998,20000,20006,20008,20010,20012,20014,20016,20018,20020,20022,20024,20026,20028,20030,20032,20034,20036,20038],{},[898,19989,2889],{"mathvariant":2376},[898,19991,2777],{},[1996,19993,2730],{},[898,19995,2194],{"mathvariant":2376},[898,19997,2777],{},[1996,19999,1998],{},[2124,20001,20002,20004],{},[898,20003,2777],{},[1996,20005,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,20007,2005],{"stretchy":2004},[898,20009,9128],{},[1996,20011,2011],{"stretchy":2004},[2288,20013,2987],{},[898,20015,2194],{"mathvariant":2376},[898,20017,9128],{},[1996,20019,1998],{},[898,20021,2818],{},[898,20023,3937],{},[898,20025,2777],{},[1996,20027,2005],{"stretchy":2004},[898,20029,9128],{},[1996,20031,2011],{"stretchy":2004},[2288,20033,2987],{},[898,20035,2194],{"mathvariant":2376},[898,20037,9128],{},[898,20039,1975],{"mathvariant":2376},[902,20041,20042],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,20044,20045,20046,20082,20083,20086],{},"Analogicky ",[883,20047,20049],{"className":20048},[886],[888,20050,20051],{"xmlns":890},[892,20052,20053,20079],{},[895,20054,20055,20057,20059,20061,20063,20065,20067,20069,20071,20073,20075,20077],{},[898,20056,2889],{"mathvariant":2376},[898,20058,8673],{},[1996,20060,2730],{},[898,20062,2818],{},[898,20064,3937],{},[898,20066,8673],{},[1996,20068,2005],{"stretchy":2004},[898,20070,9128],{},[1996,20072,2011],{"stretchy":2004},[2288,20074,2987],{},[898,20076,2194],{"mathvariant":2376},[898,20078,9128],{},[902,20080,20081],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,20084,1145],{"className":20085,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,20088,20090],{"id":20089},"příklad-72","Příklad 7.2",[724,20092,19257,20093,20128,20129,20148],{},[883,20094,20096],{"className":20095},[886],[888,20097,20098],{"xmlns":890},[892,20099,20100,20125],{},[895,20101,20102,20104,20106,20109,20115,20117,20119,20121,20123],{},[898,20103,2777],{},[1996,20105,1998],{},[2129,20107,20108],{},"0,001",[2124,20110,20111,20113],{},[898,20112,9128],{},[2129,20114,2131],{},[1996,20116,2095],{},[2129,20118,2839],{},[898,20120,9128],{},[1996,20122,2095],{},[2129,20124,3120],{},[902,20126,20127],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,20130,20132],{"className":20131},[886],[888,20133,20134],{"xmlns":890},[892,20135,20136,20145],{},[895,20137,20138,20140,20142],{},[898,20139,9128],{},[1996,20141,3447],{},[2129,20143,20144],{},"400",[902,20146,20147],{"encoding":904},"Y \u003C 400",") platí",[724,20150,20151],{},[883,20152,20154],{"className":20153},[886],[888,20155,20156],{"xmlns":890},[892,20157,20158,20195],{},[895,20159,20160,20162,20164,20166,20168,20182,20184,20187,20189,20191,20193],{},[898,20161,2818],{},[898,20163,3937],{},[898,20165,2777],{},[1996,20167,1998],{},[2329,20169,20170,20176],{},[895,20171,20172,20174],{},[898,20173,2194],{"mathvariant":2376},[898,20175,2777],{},[895,20177,20178,20180],{},[898,20179,2194],{"mathvariant":2376},[898,20181,9128],{},[1996,20183,1998],{},[2129,20185,20186],{},"0,002",[898,20188,9128],{},[1996,20190,2095],{},[2129,20192,2839],{},[1996,20194,2286],{"separator":2285},[902,20196,20197],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,20199,20200],{},[883,20201,20203],{"className":20202},[886],[888,20204,20205],{"xmlns":890},[892,20206,20207,20240],{},[895,20208,20209,20211,20213,20215,20217,20219,20221,20223,20225,20227,20229,20231,20233,20235,20237],{},[898,20210,2818],{},[898,20212,3937],{},[898,20214,8673],{},[1996,20216,1998],{},[2129,20218,2278],{},[1996,20220,2225],{},[898,20222,2818],{},[898,20224,3937],{},[898,20226,2777],{},[1996,20228,1998],{},[1996,20230,2225],{},[2129,20232,20186],{},[898,20234,9128],{},[1996,20236,2095],{},[2129,20238,20239],{},"0,8.",[902,20241,20242],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,20244,20245,20325,20404],{},[123,20246,20247,1343,20275,20303,20304,8102,20322,1975],{},[883,20248,20250],{"className":20249},[886],[888,20251,20252],{"xmlns":890},[892,20253,20254,20272],{},[895,20255,20256,20258,20260,20262,20264,20266,20268,20270],{},[898,20257,2818],{},[898,20259,3937],{},[898,20261,2777],{},[1996,20263,2005],{"stretchy":2004},[2129,20265,3090],{},[1996,20267,2011],{"stretchy":2004},[1996,20269,1998],{},[2129,20271,19273],{},[902,20273,20274],{"encoding":904},"MPC(100) = 0{,}4",[883,20276,20278],{"className":20277},[886],[888,20279,20280],{"xmlns":890},[892,20281,20282,20300],{},[895,20283,20284,20286,20288,20290,20292,20294,20296,20298],{},[898,20285,2818],{},[898,20287,3937],{},[898,20289,8673],{},[1996,20291,2005],{"stretchy":2004},[2129,20293,3090],{},[1996,20295,2011],{"stretchy":2004},[1996,20297,1998],{},[2129,20299,19323],{},[902,20301,20302],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,20305,20307],{"className":20306},[886],[888,20308,20309],{"xmlns":890},[892,20310,20311,20319],{},[895,20312,20313,20315,20317],{},[898,20314,9128],{},[1996,20316,1998],{},[2129,20318,3090],{},[902,20320,20321],{"encoding":904},"Y = 100",[38,20323,20324],{},"větší sklon k úsporám",[123,20326,20327,1343,20355,20303,20383,8102,20401,1975],{},[883,20328,20330],{"className":20329},[886],[888,20331,20332],{"xmlns":890},[892,20333,20334,20352],{},[895,20335,20336,20338,20340,20342,20344,20346,20348,20350],{},[898,20337,2818],{},[898,20339,3937],{},[898,20341,2777],{},[1996,20343,2005],{"stretchy":2004},[2129,20345,8377],{},[1996,20347,2011],{"stretchy":2004},[1996,20349,1998],{},[2129,20351,19323],{},[902,20353,20354],{"encoding":904},"MPC(200) = 0{,}6",[883,20356,20358],{"className":20357},[886],[888,20359,20360],{"xmlns":890},[892,20361,20362,20380],{},[895,20363,20364,20366,20368,20370,20372,20374,20376,20378],{},[898,20365,2818],{},[898,20367,3937],{},[898,20369,8673],{},[1996,20371,2005],{"stretchy":2004},[2129,20373,8377],{},[1996,20375,2011],{"stretchy":2004},[1996,20377,1998],{},[2129,20379,19273],{},[902,20381,20382],{"encoding":904},"MPS(200) = 0{,}4",[883,20384,20386],{"className":20385},[886],[888,20387,20388],{"xmlns":890},[892,20389,20390,20398],{},[895,20391,20392,20394,20396],{},[898,20393,9128],{},[1996,20395,1998],{},[2129,20397,8377],{},[902,20399,20400],{"encoding":904},"Y = 200",[38,20402,20403],{},"větší sklon ke spotřebě",[123,20405,20406,20407,20425,20426,3918],{},"Přesně při ",[883,20408,20410],{"className":20409},[886],[888,20411,20412],{"xmlns":890},[892,20413,20414,20422],{},[895,20415,20416,20418,20420],{},[898,20417,9128],{},[1996,20419,1998],{},[2129,20421,8803],{},[902,20423,20424],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,20427,20429],{"className":20428},[886],[888,20430,20431],{"xmlns":890},[892,20432,20433,20453],{},[895,20434,20435,20437,20439,20441,20443,20445,20447,20449,20451],{},[898,20436,2818],{},[898,20438,3937],{},[898,20440,2777],{},[1996,20442,1998],{},[898,20444,2818],{},[898,20446,3937],{},[898,20448,8673],{},[1996,20450,1998],{},[2129,20452,5009],{},[902,20454,20455],{"encoding":904},"MPC = MPS = 0{,}5",[724,20457,20458,20459,20476,20477,20491,20492,2685,20505,20519,20520,20533,20534,20575],{},"Interpretace: při ",[883,20460,20462],{"className":20461},[886],[888,20463,20464],{"xmlns":890},[892,20465,20466,20474],{},[895,20467,20468,20470,20472],{},[898,20469,9128],{},[1996,20471,1998],{},[2129,20473,3090],{},[902,20475,20321],{"encoding":904}," se spotřeba mění ",[883,20478,20480],{"className":20479},[886],[888,20481,20482],{"xmlns":890},[892,20483,20484,20488],{},[895,20485,20486],{},[2129,20487,19273],{},[902,20489,20490],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,20493,20495],{"className":20494},[886],[888,20496,20497],{"xmlns":890},[892,20498,20499,20503],{},[895,20500,20501],{},[2129,20502,3090],{},[902,20504,3090],{"encoding":904},[883,20506,20508],{"className":20507},[886],[888,20509,20510],{"xmlns":890},[892,20511,20512,20517],{},[895,20513,20514],{},[2129,20515,20516],{},"101",[902,20518,20516],{"encoding":904},", změní se spotřeba přibližně o ",[883,20521,20523],{"className":20522},[886],[888,20524,20525],{"xmlns":890},[892,20526,20527,20531],{},[895,20528,20529],{},[2129,20530,19273],{},[902,20532,20490],{"encoding":904},". Skutečná změna ",[883,20535,20537],{"className":20536},[886],[888,20538,20539],{"xmlns":890},[892,20540,20541,20572],{},[895,20542,20543,20545,20547,20549,20551,20553,20555,20557,20559,20561,20563,20565,20567,20569],{},[898,20544,2889],{"mathvariant":2376},[898,20546,2777],{},[1996,20548,1998],{},[898,20550,2777],{},[1996,20552,2005],{"stretchy":2004},[2129,20554,20516],{},[1996,20556,2011],{"stretchy":2004},[1996,20558,2225],{},[898,20560,2777],{},[1996,20562,2005],{"stretchy":2004},[2129,20564,3090],{},[1996,20566,2011],{"stretchy":2004},[1996,20568,1998],{},[2129,20570,20571],{},"0,401",[902,20573,20574],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,20577,20578,20579],{},"Obecný trend: ",[38,20580,20581],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,20583,20585],{"id":20584},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,20587,20588,20589,10025,20592,20595,20596,10025,20599,12130,20602,10025,20605,20608],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,20590,20591],{},"makroekonomická rovnováha",[614,20593,20594],{},"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 ",[38,20597,20598],{},"agregátní poptávky",[614,20600,20601],{},"aggregate demand",[38,20603,20604],{},"agregátní nabídky",[614,20606,20607],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,20610,20612],{"id":20611},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,20614,20615],{},[2559,20616],{"alt":20617,"className":20618,"src":20619},"imek-keynesian-kriz",[210,2563],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,20621,20623],{"id":20622},"zadání-modelu","Zadání modelu",[724,20625,20626,20627,20640,20641,20654],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,20628,20630],{"className":20629},[886],[888,20631,20632],{"xmlns":890},[892,20633,20634,20638],{},[895,20635,20636],{},[898,20637,2777],{},[902,20639,2777],{"encoding":904}," a investice ",[883,20642,20644],{"className":20643},[886],[888,20645,20646],{"xmlns":890},[892,20647,20648,20652],{},[895,20649,20650],{},[898,20651,12186],{},[902,20653,12186],{"encoding":904},". Podmínka rovnováhy:",[724,20656,20657],{},[883,20658,20660],{"className":20659},[886],[888,20661,20662],{"xmlns":890},[892,20663,20664,20687],{},[895,20665,20666,20668,20670,20672,20674,20676,20678,20680,20682,20685],{},[898,20667,9128],{},[1996,20669,1998],{},[898,20671,2777],{},[1996,20673,2095],{},[898,20675,12186],{},[898,20677,1975],{"mathvariant":2376},[5878,20679],{"width":5880},[1996,20681,2005],{"stretchy":2004},[2129,20683,20684],{},"7.6",[1996,20686,2011],{"stretchy":2004},[902,20688,20689],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,20691,20693],{"id":20692},"soustava-rovnic","Soustava rovnic",[724,20695,20696,20697,20718,20719,20743],{},"Pro pevně zadané (plánované) investice ",[883,20698,20700],{"className":20699},[886],[888,20701,20702],{"xmlns":890},[892,20703,20704,20716],{},[895,20705,20706,20708,20710],{},[898,20707,12186],{},[1996,20709,1998],{},[2124,20711,20712,20714],{},[898,20713,12186],{},[1996,20715,4354],{},[902,20717,12197],{"encoding":904}," a funkci spotřeby ",[883,20720,20722],{"className":20721},[886],[888,20723,20724],{"xmlns":890},[892,20725,20726,20740],{},[895,20727,20728,20730,20732,20734,20736,20738],{},[898,20729,2777],{},[1996,20731,1998],{},[898,20733,2777],{},[1996,20735,2005],{"stretchy":2004},[898,20737,9128],{},[1996,20739,2011],{"stretchy":2004},[902,20741,20742],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,20745,20746],{},[883,20747,20749],{"className":20748},[886],[888,20750,20751],{"xmlns":890},[892,20752,20753,20829],{},[895,20754,20755,20820,20822,20824,20827],{},[20756,20757,20760,20792],"mtable",{"rowspacing":20758,"columnalign":20759,"columnspacing":2377},"0.25em","right left",[20761,20762,20763,20770],"mtr",{},[20764,20765,20766],"mtd",{},[2325,20767,20768],{"scriptlevel":2327,"displaystyle":2285},[898,20769,9128],{},[20764,20771,20772],{},[2325,20773,20774],{"scriptlevel":2327,"displaystyle":2285},[895,20775,20776,20778,20780,20782,20784,20790],{},[895,20777],{},[1996,20779,1998],{},[898,20781,2777],{},[1996,20783,2095],{},[2124,20785,20786,20788],{},[898,20787,12186],{},[1996,20789,4354],{},[1996,20791,2286],{"separator":2285},[20761,20793,20794,20800],{},[20764,20795,20796],{},[2325,20797,20798],{"scriptlevel":2327,"displaystyle":2285},[898,20799,2777],{},[20764,20801,20802],{},[2325,20803,20804],{"scriptlevel":2327,"displaystyle":2285},[895,20805,20806,20808,20810,20812,20814,20816,20818],{},[895,20807],{},[1996,20809,1998],{},[898,20811,2777],{},[1996,20813,2005],{"stretchy":2004},[898,20815,9128],{},[1996,20817,2011],{"stretchy":2004},[1996,20819,2286],{"separator":2285},[5878,20821],{"width":5880},[1996,20823,2005],{"stretchy":2004},[2129,20825,20826],{},"7.7",[1996,20828,2011],{"stretchy":2004},[902,20830,20831],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,20833,20834,20835,2203,20837,3885,20854,2203,20857,1975],{},"jejímž řešením jsou ",[38,20836,13887],{},[883,20838,20840],{"className":20839},[886],[888,20841,20842],{"xmlns":890},[892,20843,20844,20852],{},[895,20845,20846],{},[2124,20847,20848,20850],{},[898,20849,9128],{},[898,20851,4252],{},[902,20853,13905],{"encoding":904},[38,20855,20856],{},"rovnovážná spotřeba",[883,20858,20860],{"className":20859},[886],[888,20861,20862],{"xmlns":890},[892,20863,20864,20872],{},[895,20865,20866],{},[2124,20867,20868,20870],{},[898,20869,2777],{},[898,20871,4252],{},[902,20873,13964],{"encoding":904},[198,20875,20877,20878],{"id":20876},"výpočet-yeye","Výpočet ",[883,20879,20881],{"className":20880},[886],[888,20882,20883],{"xmlns":890},[892,20884,20885,20893],{},[895,20886,20887],{},[2124,20888,20889,20891],{},[898,20890,9128],{},[898,20892,4252],{},[902,20894,13905],{"encoding":904},[724,20896,20897,20898,20921,20922,7685,20954],{},"Pro lineární spotřebu ",[883,20899,20901],{"className":20900},[886],[888,20902,20903],{"xmlns":890},[892,20904,20905,20919],{},[895,20906,20907,20909,20911,20913,20915,20917],{},[898,20908,2777],{},[1996,20910,1998],{},[898,20912,207],{},[898,20914,9128],{},[1996,20916,2095],{},[898,20918,2098],{},[902,20920,18922],{"encoding":904}," plyne z (7.7) rovnice ",[883,20923,20925],{"className":20924},[886],[888,20926,20927],{"xmlns":890},[892,20928,20929,20951],{},[895,20930,20931,20933,20935,20937,20939,20941,20943,20945],{},[898,20932,9128],{},[1996,20934,1998],{},[898,20936,207],{},[898,20938,9128],{},[1996,20940,2095],{},[898,20942,2098],{},[1996,20944,2095],{},[2124,20946,20947,20949],{},[898,20948,12186],{},[1996,20950,4354],{},[902,20952,20953],{"encoding":904},"Y = aY + b + I^*",[38,20955,20956],{},"redukovaný tvar",[724,20958,20959],{},[883,20960,20962],{"className":20961},[886],[888,20963,20964],{"xmlns":890},[892,20965,20966,21014],{},[895,20967,20968],{},[12834,20969,20970],{"notation":12836},[2325,20971,20972],{"scriptlevel":2327,"displaystyle":2004},[2325,20973,20974],{"scriptlevel":2327,"displaystyle":2004},[2325,20975,20976],{"scriptlevel":2327,"displaystyle":2285},[895,20977,20978,20980,20986,20988,21010,21012],{},[2288,20979,2987],{},[2124,20981,20982,20984],{},[898,20983,9128],{},[898,20985,4252],{},[1996,20987,1998],{},[2329,20989,20990,21002],{},[895,20991,20992,20994,20996],{},[898,20993,2098],{},[1996,20995,2095],{},[2124,20997,20998,21000],{},[898,20999,12186],{},[1996,21001,4354],{},[895,21003,21004,21006,21008],{},[2129,21005,2278],{},[1996,21007,2225],{},[898,21009,207],{},[898,21011,1975],{"mathvariant":2376},[2288,21013,2987],{},[902,21015,21016],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,21018,21020],{"id":21019},"příklad-73","Příklad 7.3",[724,21022,21023,21024,8102,21041,3885,21065,21091],{},"V modelu ",[883,21025,21027],{"className":21026},[886],[888,21028,21029],{"xmlns":890},[892,21030,21031,21039],{},[895,21032,21033,21035,21037],{},[898,21034,2777],{},[2288,21036,12292],{},[898,21038,12186],{},[902,21040,12297],{"encoding":904},[883,21042,21044],{"className":21043},[886],[888,21045,21046],{"xmlns":890},[892,21047,21048,21062],{},[895,21049,21050,21052,21054,21056,21058,21060],{},[898,21051,2777],{},[1996,21053,1998],{},[2129,21055,19323],{},[898,21057,9128],{},[1996,21059,2095],{},[2129,21061,2863],{},[902,21063,21064],{"encoding":904},"C = 0{,}6Y + 10",[883,21066,21068],{"className":21067},[886],[888,21069,21070],{"xmlns":890},[892,21071,21072,21088],{},[895,21073,21074,21076,21078,21080,21082],{},[898,21075,12186],{},[1996,21077,1998],{},[2129,21079,3509],{},[1996,21081,1998],{},[2124,21083,21084,21086],{},[898,21085,12186],{},[1996,21087,4354],{},[902,21089,21090],{"encoding":904},"I = 12 = I^*",". Soustava",[724,21093,21094],{},[883,21095,21097],{"className":21096},[886],[888,21098,21099],{"xmlns":890},[892,21100,21101,21157],{},[20756,21102,21103,21129],{"rowspacing":20758,"columnalign":20759,"columnspacing":2377},[20761,21104,21105,21111],{},[20764,21106,21107],{},[2325,21108,21109],{"scriptlevel":2327,"displaystyle":2285},[898,21110,9128],{},[20764,21112,21113],{},[2325,21114,21115],{"scriptlevel":2327,"displaystyle":2285},[895,21116,21117,21119,21121,21123,21125,21127],{},[895,21118],{},[1996,21120,1998],{},[898,21122,2777],{},[1996,21124,2095],{},[2129,21126,3509],{},[1996,21128,2286],{"separator":2285},[20761,21130,21131,21137],{},[20764,21132,21133],{},[2325,21134,21135],{"scriptlevel":2327,"displaystyle":2285},[898,21136,2777],{},[20764,21138,21139],{},[2325,21140,21141],{"scriptlevel":2327,"displaystyle":2285},[895,21142,21143,21145,21147,21149,21151,21153,21155],{},[895,21144],{},[1996,21146,1998],{},[2129,21148,19323],{},[898,21150,9128],{},[1996,21152,2095],{},[2129,21154,2863],{},[1996,21156,2286],{"separator":2285},[902,21158,21159],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,21161,21162,21163,1343,21186,21209,21210,3918],{},"má řešení ",[883,21164,21166],{"className":21165},[886],[888,21167,21168],{"xmlns":890},[892,21169,21170,21183],{},[895,21171,21172,21178,21180],{},[2124,21173,21174,21176],{},[898,21175,9128],{},[898,21177,4252],{},[1996,21179,1998],{},[2129,21181,21182],{},"55",[902,21184,21185],{"encoding":904},"Y^E = 55",[883,21187,21189],{"className":21188},[886],[888,21190,21191],{"xmlns":890},[892,21192,21193,21206],{},[895,21194,21195,21201,21203],{},[2124,21196,21197,21199],{},[898,21198,2777],{},[898,21200,4252],{},[1996,21202,1998],{},[2129,21204,21205],{},"43",[902,21207,21208],{"encoding":904},"C^E = 43"," (a ",[883,21211,21213],{"className":21212},[886],[888,21214,21215],{"xmlns":890},[892,21216,21217,21229],{},[895,21218,21219,21225,21227],{},[2124,21220,21221,21223],{},[898,21222,8673],{},[898,21224,4252],{},[1996,21226,1998],{},[2129,21228,3509],{},[902,21230,21231],{"encoding":904},"S^E = 12",[724,21233,21234],{},[614,21235,21236,21237,21259,21260,12130,21281,21304,21305,1975],{},"Obrázek 7.5 — Přímky ",[883,21238,21240],{"className":21239},[886],[888,21241,21242],{"xmlns":890},[892,21243,21244,21256],{},[895,21245,21246,21248,21250,21252,21254],{},[898,21247,2777],{},[1996,21249,1998],{},[898,21251,9128],{},[1996,21253,2225],{},[2129,21255,3509],{},[902,21257,21258],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,21261,21263],{"className":21262},[886],[888,21264,21265],{"xmlns":890},[892,21266,21267,21279],{},[895,21268,21269,21271,21273,21275,21277],{},[898,21270,9128],{},[1996,21272,1998],{},[898,21274,2777],{},[1996,21276,2095],{},[898,21278,12186],{},[902,21280,14746],{"encoding":904},[883,21282,21284],{"className":21283},[886],[888,21285,21286],{"xmlns":890},[892,21287,21288,21302],{},[895,21289,21290,21292,21294,21296,21298,21300],{},[898,21291,2777],{},[1996,21293,1998],{},[2129,21295,19323],{},[898,21297,9128],{},[1996,21299,2095],{},[2129,21301,2863],{},[902,21303,21064],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,21306,21308],{"className":21307},[886],[888,21309,21310],{"xmlns":890},[892,21311,21312,21344],{},[895,21313,21314,21316,21322,21324,21330,21332,21334,21336,21338,21340,21342],{},[1996,21315,2486],{"stretchy":2004},[2124,21317,21318,21320],{},[898,21319,9128],{},[898,21321,4252],{},[1996,21323,2286],{"separator":2285},[2124,21325,21326,21328],{},[898,21327,2777],{},[898,21329,4252],{},[1996,21331,2501],{"stretchy":2004},[1996,21333,1998],{},[1996,21335,2486],{"stretchy":2004},[2129,21337,21182],{},[1996,21339,2286],{"separator":2285},[2129,21341,21205],{},[1996,21343,2501],{"stretchy":2004},[902,21345,21346],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,21348,21349,21352,21353,21370,21371,1975],{},[38,21350,21351],{},"Komentář k přechodu."," Model ",[883,21354,21356],{"className":21355},[886],[888,21357,21358],{"xmlns":890},[892,21359,21360,21368],{},[895,21361,21362,21364,21366],{},[898,21363,2777],{},[2288,21365,12292],{},[898,21367,12186],{},[902,21369,12297],{"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 ",[38,21372,21373,21374],{},"model ",[883,21375,21377],{"className":21376},[886],[888,21378,21379],{"xmlns":890},[892,21380,21381,21393],{},[895,21382,21383,21385,21387,21389,21391],{},[898,21384,2777],{},[2288,21386,12292],{},[898,21388,12186],{},[2288,21390,12292],{},[898,21392,12114],{},[902,21394,18222],{"encoding":904},[115,21396,21398],{"id":21397},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,21400,20623],{"id":21401},"zadání-modelu-1",[724,21403,21404,21405,21422,21423,2203,21426,10025,21439,21442],{},"Rozšíření modelu ",[883,21406,21408],{"className":21407},[886],[888,21409,21410],{"xmlns":890},[892,21411,21412,21420],{},[895,21413,21414,21416,21418],{},[898,21415,2777],{},[2288,21417,12292],{},[898,21419,12186],{},[902,21421,12297],{"encoding":904}," o ",[38,21424,21425],{},"vládní výdaje",[883,21427,21429],{"className":21428},[886],[888,21430,21431],{"xmlns":890},[892,21432,21433,21437],{},[895,21434,21435],{},[898,21436,12114],{},[902,21438,12114],{"encoding":904},[614,21440,21441],{},"government expenditure","). Podmínka rovnováhy:",[724,21444,21445],{},[883,21446,21448],{"className":21447},[886],[888,21449,21450],{"xmlns":890},[892,21451,21452,21479],{},[895,21453,21454,21456,21458,21460,21462,21464,21466,21468,21470,21472,21474,21477],{},[898,21455,9128],{},[1996,21457,1998],{},[898,21459,2777],{},[1996,21461,2095],{},[898,21463,12186],{},[1996,21465,2095],{},[898,21467,12114],{},[898,21469,1975],{"mathvariant":2376},[5878,21471],{"width":5880},[1996,21473,2005],{"stretchy":2004},[2129,21475,21476],{},"7.8",[1996,21478,2011],{"stretchy":2004},[902,21480,21481],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,21483,21484,21485,2203,21488,10025,21501,21504],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,21486,21487],{},"zdaněním domácností",[883,21489,21491],{"className":21490},[886],[888,21492,21493],{"xmlns":890},[892,21494,21495,21499],{},[895,21496,21497],{},[898,21498,2774],{},[902,21500,2774],{"encoding":904},[614,21502,21503],{},"taxation","). Zdanění bývá:",[120,21506,21507,21540,21565],{},[123,21508,21509,21510,2286],{},"úměrné důchodu: ",[883,21511,21513],{"className":21512},[886],[888,21514,21515],{"xmlns":890},[892,21516,21517,21537],{},[895,21518,21519,21521,21523,21525,21527,21529,21531,21533,21535],{},[898,21520,2774],{},[1996,21522,1998],{},[898,21524,2774],{},[1996,21526,2005],{"stretchy":2004},[898,21528,9128],{},[1996,21530,2011],{"stretchy":2004},[1996,21532,1998],{},[898,21534,18857],{},[898,21536,9128],{},[902,21538,21539],{"encoding":904},"T = T(Y) = tY",[123,21541,21542,21543,2286],{},"fixní: ",[883,21544,21546],{"className":21545},[886],[888,21547,21548],{"xmlns":890},[892,21549,21550,21562],{},[895,21551,21552,21554,21556],{},[898,21553,2774],{},[1996,21555,1998],{},[2124,21557,21558,21560],{},[898,21559,2774],{},[1996,21561,4354],{},[902,21563,21564],{"encoding":904},"T = T^*",[123,21566,21567,21568,21596,21597,1975],{},"kombinované: ",[883,21569,21571],{"className":21570},[886],[888,21572,21573],{"xmlns":890},[892,21574,21575,21593],{},[895,21576,21577,21579,21581,21587,21589,21591],{},[898,21578,2774],{},[1996,21580,1998],{},[2124,21582,21583,21585],{},[898,21584,2774],{},[1996,21586,4354],{},[1996,21588,2095],{},[898,21590,18857],{},[898,21592,9128],{},[902,21594,21595],{"encoding":904},"T = T^* + tY",", kde ",[883,21598,21600],{"className":21599},[886],[888,21601,21602],{"xmlns":890},[892,21603,21604,21616],{},[895,21605,21606,21608,21610,21612,21614],{},[2129,21607,2327],{},[1996,21609,7679],{},[898,21611,18857],{},[1996,21613,3447],{},[2129,21615,2278],{},[902,21617,21618],{"encoding":904},"0 \\le t \u003C 1",[3867,21620,21621],{},[724,21622,21623,21625,21626,21647,21648,21651,21652,21665,21666,12130,21692,2203,21695,21721,21722,21750,21751,3885,21764,21782],{},[883,21624,4412],{}," Pozor na disponibilní důchod\nV modelu ",[883,21627,21629],{"className":21628},[886],[888,21630,21631],{"xmlns":890},[892,21632,21633,21645],{},[895,21634,21635,21637,21639,21641,21643],{},[898,21636,2777],{},[2288,21638,12292],{},[898,21640,12186],{},[2288,21642,12292],{},[898,21644,12114],{},[902,21646,18222],{"encoding":904}," je nutné ",[38,21649,21650],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,21653,21655],{"className":21654},[886],[888,21656,21657],{"xmlns":890},[892,21658,21659,21663],{},[895,21660,21661],{},[898,21662,9128],{},[902,21664,9128],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,21667,21669],{"className":21668},[886],[888,21670,21671],{"xmlns":890},[892,21672,21673,21689],{},[895,21674,21675,21677,21679,21681,21683,21685,21687],{},[898,21676,9128],{},[1996,21678,1998],{},[898,21680,2777],{},[1996,21682,2095],{},[898,21684,12186],{},[1996,21686,2095],{},[898,21688,12114],{},[902,21690,21691],{"encoding":904},"Y = C + I + G",[38,21693,21694],{},"disponibilní důchod",[883,21696,21698],{"className":21697},[886],[888,21699,21700],{"xmlns":890},[892,21701,21702,21718],{},[895,21703,21704,21710,21712,21714,21716],{},[2272,21705,21706,21708],{},[898,21707,9128],{},[898,21709,4183],{},[1996,21711,1998],{},[898,21713,9128],{},[1996,21715,2225],{},[898,21717,2774],{},[902,21719,21720],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,21723,21725],{"className":21724},[886],[888,21726,21727],{"xmlns":890},[892,21728,21729,21747],{},[895,21730,21731,21733,21735,21737,21739,21745],{},[898,21732,2777],{},[1996,21734,1998],{},[898,21736,2777],{},[1996,21738,2005],{"stretchy":2004},[2272,21740,21741,21743],{},[898,21742,9128],{},[898,21744,4183],{},[1996,21746,2011],{"stretchy":2004},[902,21748,21749],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,21752,21754],{"className":21753},[886],[888,21755,21756],{"xmlns":890},[892,21757,21758,21762],{},[895,21759,21760],{},[898,21761,9128],{},[902,21763,9128],{"encoding":904},[883,21765,21767],{"className":21766},[886],[888,21768,21769],{"xmlns":890},[892,21770,21771,21779],{},[895,21772,21773],{},[2272,21774,21775,21777],{},[898,21776,9128],{},[898,21778,4183],{},[902,21780,21781],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,21784,21785,10025,21788,2011],{},[38,21786,21787],{},"Disponibilní důchod",[614,21789,21790],{},"disposable income",[724,21792,21793],{},[883,21794,21796],{"className":21795},[886],[888,21797,21798],{"xmlns":890},[892,21799,21800,21816],{},[895,21801,21802,21808,21810,21812,21814],{},[2272,21803,21804,21806],{},[898,21805,9128],{},[898,21807,4183],{},[1996,21809,1998],{},[898,21811,9128],{},[1996,21813,2225],{},[898,21815,2774],{},[902,21817,21720],{"encoding":904},[724,21819,21820,21821,1975],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,21822,21824],{"className":21823},[886],[888,21825,21826],{"xmlns":890},[892,21827,21828,21846],{},[895,21829,21830,21832,21834,21836,21838,21844],{},[898,21831,2777],{},[1996,21833,1998],{},[898,21835,2777],{},[1996,21837,2005],{"stretchy":2004},[2272,21839,21840,21842],{},[898,21841,9128],{},[898,21843,4183],{},[1996,21845,2011],{"stretchy":2004},[902,21847,21749],{"encoding":904},[198,21849,20693],{"id":21850},"soustava-rovnic-1",[724,21852,21853,21854,1343,21875,21897,21898,2704],{},"Pro pevně zadané ",[883,21855,21857],{"className":21856},[886],[888,21858,21859],{"xmlns":890},[892,21860,21861,21873],{},[895,21862,21863,21865,21867],{},[898,21864,12186],{},[1996,21866,1998],{},[2124,21868,21869,21871],{},[898,21870,12186],{},[1996,21872,4354],{},[902,21874,12197],{"encoding":904},[883,21876,21878],{"className":21877},[886],[888,21879,21880],{"xmlns":890},[892,21881,21882,21894],{},[895,21883,21884,21886,21888],{},[898,21885,12114],{},[1996,21887,1998],{},[2124,21889,21890,21892],{},[898,21891,12114],{},[1996,21893,4354],{},[902,21895,21896],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,21899,21901],{"className":21900},[886],[888,21902,21903],{"xmlns":890},[892,21904,21905,21925],{},[895,21906,21907,21909,21911,21913,21915,21921,21923],{},[898,21908,9128],{},[1996,21910,2286],{"separator":2285},[898,21912,2777],{},[1996,21914,2286],{"separator":2285},[2272,21916,21917,21919],{},[898,21918,9128],{},[898,21920,4183],{},[1996,21922,2286],{"separator":2285},[898,21924,2774],{},[902,21926,21927],{"encoding":904},"Y, C, Y_D, T",[724,21929,21930],{},[883,21931,21933],{"className":21932},[886],[888,21934,21935],{"xmlns":890},[892,21936,21937,22078],{},[895,21938,21939,22069,22071,22073,22076],{},[20756,21940,21941,21979,22007,22039],{"rowspacing":20758,"columnalign":20759,"columnspacing":2377},[20761,21942,21943,21949],{},[20764,21944,21945],{},[2325,21946,21947],{"scriptlevel":2327,"displaystyle":2285},[898,21948,9128],{},[20764,21950,21951],{},[2325,21952,21953],{"scriptlevel":2327,"displaystyle":2285},[895,21954,21955,21957,21959,21961,21963,21969,21971,21977],{},[895,21956],{},[1996,21958,1998],{},[898,21960,2777],{},[1996,21962,2095],{},[2124,21964,21965,21967],{},[898,21966,12186],{},[1996,21968,4354],{},[1996,21970,2095],{},[2124,21972,21973,21975],{},[898,21974,12114],{},[1996,21976,4354],{},[1996,21978,2286],{"separator":2285},[20761,21980,21981,21987],{},[20764,21982,21983],{},[2325,21984,21985],{"scriptlevel":2327,"displaystyle":2285},[898,21986,2774],{},[20764,21988,21989],{},[2325,21990,21991],{"scriptlevel":2327,"displaystyle":2285},[895,21992,21993,21995,21997,21999,22001,22003,22005],{},[895,21994],{},[1996,21996,1998],{},[898,21998,2774],{},[1996,22000,2005],{"stretchy":2004},[898,22002,9128],{},[1996,22004,2011],{"stretchy":2004},[1996,22006,2286],{"separator":2285},[20761,22008,22009,22015],{},[20764,22010,22011],{},[2325,22012,22013],{"scriptlevel":2327,"displaystyle":2285},[898,22014,2777],{},[20764,22016,22017],{},[2325,22018,22019],{"scriptlevel":2327,"displaystyle":2285},[895,22020,22021,22023,22025,22027,22029,22035,22037],{},[895,22022],{},[1996,22024,1998],{},[898,22026,2777],{},[1996,22028,2005],{"stretchy":2004},[2272,22030,22031,22033],{},[898,22032,9128],{},[898,22034,4183],{},[1996,22036,2011],{"stretchy":2004},[1996,22038,2286],{"separator":2285},[20761,22040,22041,22051],{},[20764,22042,22043],{},[2325,22044,22045],{"scriptlevel":2327,"displaystyle":2285},[2272,22046,22047,22049],{},[898,22048,9128],{},[898,22050,4183],{},[20764,22052,22053],{},[2325,22054,22055],{"scriptlevel":2327,"displaystyle":2285},[895,22056,22057,22059,22061,22063,22065,22067],{},[895,22058],{},[1996,22060,1998],{},[898,22062,9128],{},[1996,22064,2225],{},[898,22066,2774],{},[1996,22068,2286],{"separator":2285},[5878,22070],{"width":5880},[1996,22072,2005],{"stretchy":2004},[2129,22074,22075],{},"7.9",[1996,22077,2011],{"stretchy":2004},[902,22079,22080],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,22082,22083,22084,22128,22129,1975],{},"s řešeními ",[883,22085,22087],{"className":22086},[886],[888,22088,22089],{"xmlns":890},[892,22090,22091,22125],{},[895,22092,22093,22099,22101,22107,22109,22115,22117],{},[2124,22094,22095,22097],{},[898,22096,9128],{},[898,22098,4252],{},[1996,22100,2286],{"separator":2285},[2124,22102,22103,22105],{},[898,22104,2777],{},[898,22106,4252],{},[1996,22108,2286],{"separator":2285},[2124,22110,22111,22113],{},[898,22112,2774],{},[898,22114,4252],{},[1996,22116,2286],{"separator":2285},[9166,22118,22119,22121,22123],{},[898,22120,9128],{},[898,22122,4183],{},[898,22124,4252],{},[902,22126,22127],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,22130,22132],{"className":22131},[886],[888,22133,22134],{"xmlns":890},[892,22135,22136,22162],{},[895,22137,22138,22144,22146,22154,22156],{},[2124,22139,22140,22142],{},[898,22141,8673],{},[898,22143,4252],{},[1996,22145,1998],{},[9166,22147,22148,22150,22152],{},[898,22149,9128],{},[898,22151,4183],{},[898,22153,4252],{},[1996,22155,2225],{},[2124,22157,22158,22160],{},[898,22159,2777],{},[898,22161,4252],{},[902,22163,22164],{"encoding":904},"S^E = Y_D^E - C^E",[3867,22166,22167,22172],{},[724,22168,22169,22171],{},[883,22170,4572],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,22173,22174,22197,22280,22335,22425],{},[123,22175,22176,22179,22180,1975],{},[38,22177,22178],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,22181,22183],{"className":22182},[886],[888,22184,22185],{"xmlns":890},[892,22186,22187,22195],{},[895,22188,22189],{},[2272,22190,22191,22193],{},[898,22192,9128],{},[898,22194,4183],{},[902,22196,21781],{"encoding":904},[123,22198,22199,22248,22249,22266,22267,1975],{},[38,22200,22201,22202,22222,22223],{},"Dosaď ",[883,22203,22205],{"className":22204},[886],[888,22206,22207],{"xmlns":890},[892,22208,22209,22219],{},[895,22210,22211,22213,22215,22217],{},[898,22212,2774],{},[1996,22214,2005],{"stretchy":2004},[898,22216,9128],{},[1996,22218,2011],{"stretchy":2004},[902,22220,22221],{"encoding":904},"T(Y)"," do ",[883,22224,22226],{"className":22225},[886],[888,22227,22228],{"xmlns":890},[892,22229,22230,22246],{},[895,22231,22232,22238,22240,22242,22244],{},[2272,22233,22234,22236],{},[898,22235,9128],{},[898,22237,4183],{},[1996,22239,1998],{},[898,22241,9128],{},[1996,22243,2225],{},[898,22245,2774],{},[902,22247,21720],{"encoding":904}," — dostaneš ",[883,22250,22252],{"className":22251},[886],[888,22253,22254],{"xmlns":890},[892,22255,22256,22264],{},[895,22257,22258],{},[2272,22259,22260,22262],{},[898,22261,9128],{},[898,22263,4183],{},[902,22265,21781],{"encoding":904}," jako lineární funkci ",[883,22268,22270],{"className":22269},[886],[888,22271,22272],{"xmlns":890},[892,22273,22274,22278],{},[895,22275,22276],{},[898,22277,9128],{},[902,22279,9128],{"encoding":904},[123,22281,22282,22248,22309,22266,22322,1975],{},[38,22283,22201,22284,22308],{},[883,22285,22287],{"className":22286},[886],[888,22288,22289],{"xmlns":890},[892,22290,22291,22305],{},[895,22292,22293,22299,22301,22303],{},[2272,22294,22295,22297],{},[898,22296,9128],{},[898,22298,4183],{},[1996,22300,2005],{"stretchy":2004},[898,22302,9128],{},[1996,22304,2011],{"stretchy":2004},[902,22306,22307],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,22310,22312],{"className":22311},[886],[888,22313,22314],{"xmlns":890},[892,22315,22316,22320],{},[895,22317,22318],{},[898,22319,2777],{},[902,22321,2777],{"encoding":904},[883,22323,22325],{"className":22324},[886],[888,22326,22327],{"xmlns":890},[892,22328,22329,22333],{},[895,22330,22331],{},[898,22332,9128],{},[902,22334,9128],{"encoding":904},[123,22336,22337,2203,22359,22393,22394,22407,22408,1975],{},[38,22338,22201,22339,22358],{},[883,22340,22342],{"className":22341},[886],[888,22343,22344],{"xmlns":890},[892,22345,22346,22356],{},[895,22347,22348,22350,22352,22354],{},[898,22349,2777],{},[1996,22351,2005],{"stretchy":2004},[898,22353,9128],{},[1996,22355,2011],{"stretchy":2004},[902,22357,14218],{"encoding":904}," do podmínky rovnováhy",[883,22360,22362],{"className":22361},[886],[888,22363,22364],{"xmlns":890},[892,22365,22366,22390],{},[895,22367,22368,22370,22372,22374,22376,22382,22384],{},[898,22369,9128],{},[1996,22371,1998],{},[898,22373,2777],{},[1996,22375,2095],{},[2124,22377,22378,22380],{},[898,22379,12186],{},[1996,22381,4354],{},[1996,22383,2095],{},[2124,22385,22386,22388],{},[898,22387,12114],{},[1996,22389,4354],{},[902,22391,22392],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,22395,22397],{"className":22396},[886],[888,22398,22399],{"xmlns":890},[892,22400,22401,22405],{},[895,22402,22403],{},[898,22404,9128],{},[902,22406,9128],{"encoding":904},", odtud ",[883,22409,22411],{"className":22410},[886],[888,22412,22413],{"xmlns":890},[892,22414,22415,22423],{},[895,22416,22417],{},[2124,22418,22419,22421],{},[898,22420,9128],{},[898,22422,4252],{},[902,22424,13905],{"encoding":904},[123,22426,22427,22430,22431,1343,22449,1343,22469,1343,22486,1975],{},[38,22428,22429],{},"Zpětným dosazením"," dopočítej ",[883,22432,22434],{"className":22433},[886],[888,22435,22436],{"xmlns":890},[892,22437,22438,22446],{},[895,22439,22440],{},[2124,22441,22442,22444],{},[898,22443,2774],{},[898,22445,4252],{},[902,22447,22448],{"encoding":904},"T^E",[883,22450,22452],{"className":22451},[886],[888,22453,22454],{"xmlns":890},[892,22455,22456,22466],{},[895,22457,22458],{},[9166,22459,22460,22462,22464],{},[898,22461,9128],{},[898,22463,4183],{},[898,22465,4252],{},[902,22467,22468],{"encoding":904},"Y_D^E",[883,22470,22472],{"className":22471},[886],[888,22473,22474],{"xmlns":890},[892,22475,22476,22484],{},[895,22477,22478],{},[2124,22479,22480,22482],{},[898,22481,2777],{},[898,22483,4252],{},[902,22485,13964],{"encoding":904},[883,22487,22489],{"className":22488},[886],[888,22490,22491],{"xmlns":890},[892,22492,22493,22501],{},[895,22494,22495],{},[2124,22496,22497,22499],{},[898,22498,8673],{},[898,22500,4252],{},[902,22502,22503],{"encoding":904},"S^E",[198,22505,22507],{"id":22506},"příklad-74","Příklad 7.4",[724,22509,21023,22510,22531,22532,1343,22563,1343,22587,1343,22609,22631],{},[883,22511,22513],{"className":22512},[886],[888,22514,22515],{"xmlns":890},[892,22516,22517,22529],{},[895,22518,22519,22521,22523,22525,22527],{},[898,22520,2777],{},[2288,22522,12292],{},[898,22524,12186],{},[2288,22526,12292],{},[898,22528,12114],{},[902,22530,18222],{"encoding":904}," jsou dány ",[883,22533,22535],{"className":22534},[886],[888,22536,22537],{"xmlns":890},[892,22538,22539,22560],{},[895,22540,22541,22543,22545,22548,22550,22556,22558],{},[898,22542,2777],{},[1996,22544,1998],{},[2129,22546,22547],{},"0,9",[2288,22549,2987],{},[2272,22551,22552,22554],{},[898,22553,9128],{},[898,22555,4183],{},[1996,22557,2095],{},[2129,22559,5897],{},[902,22561,22562],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,22564,22566],{"className":22565},[886],[888,22567,22568],{"xmlns":890},[892,22569,22570,22584],{},[895,22571,22572,22574,22576,22578,22580,22582],{},[898,22573,2774],{},[1996,22575,1998],{},[2129,22577,2839],{},[898,22579,9128],{},[1996,22581,2095],{},[2129,22583,5004],{},[902,22585,22586],{"encoding":904},"T = 0{,}2Y + 25",[883,22588,22590],{"className":22589},[886],[888,22591,22592],{"xmlns":890},[892,22593,22594,22606],{},[895,22595,22596,22602,22604],{},[2124,22597,22598,22600],{},[898,22599,12186],{},[1996,22601,4354],{},[1996,22603,1998],{},[2129,22605,15040],{},[902,22607,22608],{"encoding":904},"I^* = 35",[883,22610,22612],{"className":22611},[886],[888,22613,22614],{"xmlns":890},[892,22615,22616,22628],{},[895,22617,22618,22624,22626],{},[2124,22619,22620,22622],{},[898,22621,12114],{},[1996,22623,4354],{},[1996,22625,1998],{},[2129,22627,9035],{},[902,22629,22630],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,22633,22634],{},[883,22635,22637],{"className":22636},[886],[888,22638,22639],{"xmlns":890},[892,22640,22641,22765],{},[20756,22642,22643,22673,22701,22735],{"rowspacing":20758,"columnalign":20759,"columnspacing":2377},[20761,22644,22645,22651],{},[20764,22646,22647],{},[2325,22648,22649],{"scriptlevel":2327,"displaystyle":2285},[898,22650,9128],{},[20764,22652,22653],{},[2325,22654,22655],{"scriptlevel":2327,"displaystyle":2285},[895,22656,22657,22659,22661,22663,22665,22667,22669,22671],{},[895,22658],{},[1996,22660,1998],{},[898,22662,2777],{},[1996,22664,2095],{},[2129,22666,15040],{},[1996,22668,2095],{},[2129,22670,9035],{},[1996,22672,2286],{"separator":2285},[20761,22674,22675,22681],{},[20764,22676,22677],{},[2325,22678,22679],{"scriptlevel":2327,"displaystyle":2285},[898,22680,2774],{},[20764,22682,22683],{},[2325,22684,22685],{"scriptlevel":2327,"displaystyle":2285},[895,22686,22687,22689,22691,22693,22695,22697,22699],{},[895,22688],{},[1996,22690,1998],{},[2129,22692,2839],{},[898,22694,9128],{},[1996,22696,2095],{},[2129,22698,5004],{},[1996,22700,2286],{"separator":2285},[20761,22702,22703,22709],{},[20764,22704,22705],{},[2325,22706,22707],{"scriptlevel":2327,"displaystyle":2285},[898,22708,2777],{},[20764,22710,22711],{},[2325,22712,22713],{"scriptlevel":2327,"displaystyle":2285},[895,22714,22715,22717,22719,22721,22723,22729,22731,22733],{},[895,22716],{},[1996,22718,1998],{},[2129,22720,22547],{},[2288,22722,2987],{},[2272,22724,22725,22727],{},[898,22726,9128],{},[898,22728,4183],{},[1996,22730,2095],{},[2129,22732,5897],{},[1996,22734,2286],{"separator":2285},[20761,22736,22737,22747],{},[20764,22738,22739],{},[2325,22740,22741],{"scriptlevel":2327,"displaystyle":2285},[2272,22742,22743,22745],{},[898,22744,9128],{},[898,22746,4183],{},[20764,22748,22749],{},[2325,22750,22751],{"scriptlevel":2327,"displaystyle":2285},[895,22752,22753,22755,22757,22759,22761,22763],{},[895,22754],{},[1996,22756,1998],{},[898,22758,9128],{},[1996,22760,2225],{},[898,22762,2774],{},[898,22764,1975],{"mathvariant":2376},[902,22766,22767],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,22769,22770,22773,22774,22828,22829,22875,22876,2704],{},[38,22771,22772],{},"Řešení."," Z definice ",[883,22775,22777],{"className":22776},[886],[888,22778,22779],{"xmlns":890},[892,22780,22781,22825],{},[895,22782,22783,22789,22791,22793,22795,22797,22799,22801,22803,22805,22807,22809,22811,22813,22815,22817,22819,22821,22823],{},[2272,22784,22785,22787],{},[898,22786,9128],{},[898,22788,4183],{},[1996,22790,1998],{},[898,22792,9128],{},[1996,22794,2225],{},[898,22796,2774],{},[1996,22798,1998],{},[898,22800,9128],{},[1996,22802,2225],{},[1996,22804,2005],{"stretchy":2004},[2129,22806,2839],{},[898,22808,9128],{},[1996,22810,2095],{},[2129,22812,5004],{},[1996,22814,2011],{"stretchy":2004},[1996,22816,1998],{},[2129,22818,14591],{},[898,22820,9128],{},[1996,22822,2225],{},[2129,22824,5004],{},[902,22826,22827],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,22830,22832],{"className":22831},[886],[888,22833,22834],{"xmlns":890},[892,22835,22836,22872],{},[895,22837,22838,22840,22842,22844,22846,22848,22850,22852,22854,22856,22858,22860,22862,22865,22867,22869],{},[898,22839,2777],{},[1996,22841,1998],{},[2129,22843,22547],{},[1996,22845,2005],{"stretchy":2004},[2129,22847,14591],{},[898,22849,9128],{},[1996,22851,2225],{},[2129,22853,5004],{},[1996,22855,2011],{"stretchy":2004},[1996,22857,2095],{},[2129,22859,5897],{},[1996,22861,1998],{},[2129,22863,22864],{},"0,72",[898,22866,9128],{},[1996,22868,2095],{},[2129,22870,22871],{},"47,5",[902,22873,22874],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,22877,22879],{"className":22878},[886],[888,22880,22881],{"xmlns":890},[892,22882,22883,22901],{},[895,22884,22885,22887,22889,22891,22893,22895,22897,22899],{},[898,22886,9128],{},[1996,22888,1998],{},[2129,22890,22864],{},[898,22892,9128],{},[1996,22894,2095],{},[2129,22896,22871],{},[1996,22898,2095],{},[2129,22900,21182],{},[902,22902,22903],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,22905,22906],{},[883,22907,22909],{"className":22908},[886],[888,22910,22911],{"xmlns":890},[892,22912,22913,22954],{},[895,22914,22915,22918,22920,22922,22925,22927,22929,22931,22937,22939,22949,22951],{},[2129,22916,22917],{},"0,28",[898,22919,9128],{},[1996,22921,1998],{},[2129,22923,22924],{},"102,5",[2288,22926,3984],{},[1996,22928,15010],{},[2288,22930,3984],{},[2124,22932,22933,22935],{},[898,22934,9128],{},[898,22936,4252],{},[1996,22938,1998],{},[2325,22940,22941],{"scriptlevel":2327,"displaystyle":2004},[2329,22942,22943,22946],{},[2129,22944,22945],{},"5125",[2129,22947,22948],{},"14",[1996,22950,5900],{},[2129,22952,22953],{},"366,071.",[902,22955,22956],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,22958,22959],{},"Rovnovážné veličiny:",[120,22961,22962,22997,23049,23103,23151],{},[123,22963,22964,2286],{},[883,22965,22967],{"className":22966},[886],[888,22968,22969],{"xmlns":890},[892,22970,22971,22994],{},[895,22972,22973,22979,22981,22989,22991],{},[2124,22974,22975,22977],{},[898,22976,9128],{},[898,22978,4252],{},[1996,22980,1998],{},[2325,22982,22983],{"scriptlevel":2327,"displaystyle":2004},[2329,22984,22985,22987],{},[2129,22986,22945],{},[2129,22988,22948],{},[1996,22990,5900],{},[2129,22992,22993],{},"366,071",[902,22995,22996],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,22998,22999,2286],{},[883,23000,23002],{"className":23001},[886],[888,23003,23004],{"xmlns":890},[892,23005,23006,23046],{},[895,23007,23008,23014,23016,23018,23020,23026,23028,23030,23032,23041,23043],{},[2124,23009,23010,23012],{},[898,23011,2774],{},[898,23013,4252],{},[1996,23015,1998],{},[2129,23017,2839],{},[2288,23019,2987],{},[2124,23021,23022,23024],{},[898,23023,9128],{},[898,23025,4252],{},[1996,23027,2095],{},[2129,23029,5004],{},[1996,23031,1998],{},[2325,23033,23034],{"scriptlevel":2327,"displaystyle":2004},[2329,23035,23036,23039],{},[2129,23037,23038],{},"1375",[2129,23040,22948],{},[1996,23042,5900],{},[2129,23044,23045],{},"98,214",[902,23047,23048],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,23050,23051,2286],{},[883,23052,23054],{"className":23053},[886],[888,23055,23056],{"xmlns":890},[892,23057,23058,23100],{},[895,23059,23060,23068,23070,23076,23078,23084,23086,23095,23097],{},[9166,23061,23062,23064,23066],{},[898,23063,9128],{},[898,23065,4183],{},[898,23067,4252],{},[1996,23069,1998],{},[2124,23071,23072,23074],{},[898,23073,9128],{},[898,23075,4252],{},[1996,23077,2225],{},[2124,23079,23080,23082],{},[898,23081,2774],{},[898,23083,4252],{},[1996,23085,1998],{},[2325,23087,23088],{"scriptlevel":2327,"displaystyle":2004},[2329,23089,23090,23093],{},[2129,23091,23092],{},"3750",[2129,23094,22948],{},[1996,23096,5900],{},[2129,23098,23099],{},"267,857",[902,23101,23102],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,23104,23105,2286],{},[883,23106,23108],{"className":23107},[886],[888,23109,23110],{"xmlns":890},[892,23111,23112,23148],{},[895,23113,23114,23120,23122,23128,23130,23132,23134,23143,23145],{},[2124,23115,23116,23118],{},[898,23117,2777],{},[898,23119,4252],{},[1996,23121,1998],{},[2124,23123,23124,23126],{},[898,23125,9128],{},[898,23127,4252],{},[1996,23129,2225],{},[2129,23131,21182],{},[1996,23133,1998],{},[2325,23135,23136],{"scriptlevel":2327,"displaystyle":2004},[2329,23137,23138,23141],{},[2129,23139,23140],{},"4355",[2129,23142,22948],{},[1996,23144,5900],{},[2129,23146,23147],{},"311,071",[902,23149,23150],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,23152,23153,23209],{},[883,23154,23156],{"className":23155},[886],[888,23157,23158],{"xmlns":890},[892,23159,23160,23206],{},[895,23161,23162,23168,23170,23178,23180,23186,23188,23190,23199,23201,23203],{},[2124,23163,23164,23166],{},[898,23165,8673],{},[898,23167,4252],{},[1996,23169,1998],{},[9166,23171,23172,23174,23176],{},[898,23173,9128],{},[898,23175,4183],{},[898,23177,4252],{},[1996,23179,2225],{},[2124,23181,23182,23184],{},[898,23183,2777],{},[898,23185,4252],{},[1996,23187,1998],{},[1996,23189,2225],{},[2325,23191,23192],{"scriptlevel":2327,"displaystyle":2004},[2329,23193,23194,23197],{},[2129,23195,23196],{},"605",[2129,23198,22948],{},[1996,23200,5900],{},[1996,23202,2225],{},[2129,23204,23205],{},"43,214",[902,23207,23208],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,23211,23212,21352,23214,23235,23236,23239,23240,23263,23264,1975],{},[38,23213,21351],{},[883,23215,23217],{"className":23216},[886],[888,23218,23219],{"xmlns":890},[892,23220,23221,23233],{},[895,23222,23223,23225,23227,23229,23231],{},[898,23224,2777],{},[2288,23226,12292],{},[898,23228,12186],{},[2288,23230,12292],{},[898,23232,12114],{},[902,23234,18222],{"encoding":904}," stále uvažuje ",[38,23237,23238],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,23241,23243],{"className":23242},[886],[888,23244,23245],{"xmlns":890},[892,23246,23247,23260],{},[895,23248,23249,23251,23253,23256,23258],{},[898,23250,12322],{},[1996,23252,1998],{},[898,23254,23255],{},"B",[1996,23257,2225],{},[898,23259,2818],{},[902,23261,23262],{"encoding":904},"X = B - M"," dává ",[38,23265,21373,23266],{},[883,23267,23269],{"className":23268},[886],[888,23270,23271],{"xmlns":890},[892,23272,23273,23289],{},[895,23274,23275,23277,23279,23281,23283,23285,23287],{},[898,23276,2777],{},[2288,23278,12292],{},[898,23280,12186],{},[2288,23282,12292],{},[898,23284,12114],{},[2288,23286,12292],{},[898,23288,12322],{},[902,23290,12325],{"encoding":904},[115,23292,23294],{"id":23293},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,23296,20623],{"id":23297},"zadání-modelu-2",[724,23299,23300,23301,2203,23304,21596,23325,23338,23339,12130,23342,23355],{},"Rozšíření o ",[38,23302,23303],{},"čistý export",[883,23305,23307],{"className":23306},[886],[888,23308,23309],{"xmlns":890},[892,23310,23311,23323],{},[895,23312,23313,23315,23317,23319,23321],{},[898,23314,12322],{},[1996,23316,1998],{},[898,23318,23255],{},[1996,23320,2225],{},[898,23322,2818],{},[902,23324,23262],{"encoding":904},[883,23326,23328],{"className":23327},[886],[888,23329,23330],{"xmlns":890},[892,23331,23332,23336],{},[895,23333,23334],{},[898,23335,23255],{},[902,23337,23255],{"encoding":904}," je hrubý export (",[614,23340,23341],{},"brutto export",[883,23343,23345],{"className":23344},[886],[888,23346,23347],{"xmlns":890},[892,23348,23349,23353],{},[895,23350,23351],{},[898,23352,2818],{},[902,23354,2818],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,23357,23358],{},[883,23359,23361],{"className":23360},[886],[888,23362,23363],{"xmlns":890},[892,23364,23365,23385],{},[895,23366,23367,23369,23371,23373,23375,23381,23383],{},[898,23368,2818],{},[1996,23370,1998],{},[898,23372,2818],{},[1996,23374,2005],{"stretchy":2004},[2272,23376,23377,23379],{},[898,23378,9128],{},[898,23380,4183],{},[1996,23382,2011],{"stretchy":2004},[898,23384,1975],{"mathvariant":2376},[902,23386,23387],{"encoding":904},"M = M(Y_D).",[724,23389,23390],{},"Podmínka rovnováhy:",[724,23392,23393],{},[883,23394,23396],{"className":23395},[886],[888,23397,23398],{"xmlns":890},[892,23399,23400,23437],{},[895,23401,23402,23404,23406,23408,23410,23412,23414,23416,23418,23420,23422,23424,23426,23428,23430,23433,23435],{},[898,23403,9128],{},[1996,23405,1998],{},[898,23407,2777],{},[1996,23409,2095],{},[898,23411,12186],{},[1996,23413,2095],{},[898,23415,12114],{},[1996,23417,2095],{},[898,23419,23255],{},[1996,23421,2225],{},[898,23423,2818],{},[898,23425,1975],{"mathvariant":2376},[5878,23427],{"width":5880},[1996,23429,2005],{"stretchy":2004},[2129,23431,23432],{},"7.10",[2288,23434,207],{},[1996,23436,2011],{"stretchy":2004},[902,23438,23439],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,23441,20693],{"id":23442},"soustava-rovnic-2",[724,23444,21853,23445,23479,23480,2704],{},[883,23446,23448],{"className":23447},[886],[888,23449,23450],{"xmlns":890},[892,23451,23452,23476],{},[895,23453,23454,23460,23462,23468,23470],{},[2124,23455,23456,23458],{},[898,23457,12186],{},[1996,23459,4354],{},[1996,23461,2286],{"separator":2285},[2124,23463,23464,23466],{},[898,23465,12114],{},[1996,23467,4354],{},[1996,23469,2286],{"separator":2285},[2124,23471,23472,23474],{},[898,23473,23255],{},[1996,23475,4354],{},[902,23477,23478],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,23481,23483],{"className":23482},[886],[888,23484,23485],{"xmlns":890},[892,23486,23487,23511],{},[895,23488,23489,23491,23493,23495,23497,23499,23501,23507,23509],{},[898,23490,9128],{},[1996,23492,2286],{"separator":2285},[898,23494,2777],{},[1996,23496,2286],{"separator":2285},[898,23498,2774],{},[1996,23500,2286],{"separator":2285},[2272,23502,23503,23505],{},[898,23504,9128],{},[898,23506,4183],{},[1996,23508,2286],{"separator":2285},[898,23510,2818],{},[902,23512,23513],{"encoding":904},"Y, C, T, Y_D, M",[724,23515,23516],{},[883,23517,23519],{"className":23518},[886],[888,23520,23521],{"xmlns":890},[892,23522,23523,23707],{},[895,23524,23525,23699,23701,23703,23705],{},[20756,23526,23527,23559,23589,23617,23649],{"rowspacing":20758,"columnalign":20759,"columnspacing":2377},[20761,23528,23529,23535],{},[20764,23530,23531],{},[2325,23532,23533],{"scriptlevel":2327,"displaystyle":2285},[898,23534,2777],{},[20764,23536,23537],{},[2325,23538,23539],{"scriptlevel":2327,"displaystyle":2285},[895,23540,23541,23543,23545,23547,23549,23555,23557],{},[895,23542],{},[1996,23544,1998],{},[898,23546,2777],{},[1996,23548,2005],{"stretchy":2004},[2272,23550,23551,23553],{},[898,23552,9128],{},[898,23554,4183],{},[1996,23556,2011],{"stretchy":2004},[1996,23558,2286],{"separator":2285},[20761,23560,23561,23571],{},[20764,23562,23563],{},[2325,23564,23565],{"scriptlevel":2327,"displaystyle":2285},[2272,23566,23567,23569],{},[898,23568,9128],{},[898,23570,4183],{},[20764,23572,23573],{},[2325,23574,23575],{"scriptlevel":2327,"displaystyle":2285},[895,23576,23577,23579,23581,23583,23585,23587],{},[895,23578],{},[1996,23580,1998],{},[898,23582,9128],{},[1996,23584,2225],{},[898,23586,2774],{},[1996,23588,2286],{"separator":2285},[20761,23590,23591,23597],{},[20764,23592,23593],{},[2325,23594,23595],{"scriptlevel":2327,"displaystyle":2285},[898,23596,2774],{},[20764,23598,23599],{},[2325,23600,23601],{"scriptlevel":2327,"displaystyle":2285},[895,23602,23603,23605,23607,23609,23611,23613,23615],{},[895,23604],{},[1996,23606,1998],{},[898,23608,2774],{},[1996,23610,2005],{"stretchy":2004},[898,23612,9128],{},[1996,23614,2011],{"stretchy":2004},[1996,23616,2286],{"separator":2285},[20761,23618,23619,23625],{},[20764,23620,23621],{},[2325,23622,23623],{"scriptlevel":2327,"displaystyle":2285},[898,23624,2818],{},[20764,23626,23627],{},[2325,23628,23629],{"scriptlevel":2327,"displaystyle":2285},[895,23630,23631,23633,23635,23637,23639,23645,23647],{},[895,23632],{},[1996,23634,1998],{},[898,23636,2818],{},[1996,23638,2005],{"stretchy":2004},[2272,23640,23641,23643],{},[898,23642,9128],{},[898,23644,4183],{},[1996,23646,2011],{"stretchy":2004},[1996,23648,2286],{"separator":2285},[20761,23650,23651,23657],{},[20764,23652,23653],{},[2325,23654,23655],{"scriptlevel":2327,"displaystyle":2285},[898,23656,9128],{},[20764,23658,23659],{},[2325,23660,23661],{"scriptlevel":2327,"displaystyle":2285},[895,23662,23663,23665,23667,23669,23671,23677,23679,23685,23687,23693,23695,23697],{},[895,23664],{},[1996,23666,1998],{},[898,23668,2777],{},[1996,23670,2095],{},[2124,23672,23673,23675],{},[898,23674,12186],{},[1996,23676,4354],{},[1996,23678,2095],{},[2124,23680,23681,23683],{},[898,23682,12114],{},[1996,23684,4354],{},[1996,23686,2095],{},[2124,23688,23689,23691],{},[898,23690,23255],{},[1996,23692,4354],{},[1996,23694,2225],{},[898,23696,2818],{},[898,23698,1975],{"mathvariant":2376},[5878,23700],{"width":5880},[1996,23702,2005],{"stretchy":2004},[2129,23704,23432],{},[1996,23706,2011],{"stretchy":2004},[902,23708,23709],{"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)",[198,23711,23713],{"id":23712},"příklad-75","Příklad 7.5",[724,23715,23716,23717,1343,23749,1343,23776,1343,23797,1343,23819,1343,23841,23864],{},"Dáno: ",[883,23718,23720],{"className":23719},[886],[888,23721,23722],{"xmlns":890},[892,23723,23724,23746],{},[895,23725,23726,23728,23730,23733,23735,23741,23743],{},[898,23727,2777],{},[1996,23729,1998],{},[2129,23731,23732],{},"0,75",[2288,23734,2987],{},[2272,23736,23737,23739],{},[898,23738,9128],{},[898,23740,4183],{},[1996,23742,2095],{},[2129,23744,23745],{},"750",[902,23747,23748],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,23750,23752],{"className":23751},[886],[888,23753,23754],{"xmlns":890},[892,23755,23756,23773],{},[895,23757,23758,23760,23762,23765,23767],{},[898,23759,2818],{},[1996,23761,1998],{},[2129,23763,23764],{},"0,15",[2288,23766,2987],{},[2272,23768,23769,23771],{},[898,23770,9128],{},[898,23772,4183],{},[902,23774,23775],{"encoding":904},"M = 0{,}15\\,Y_D",[883,23777,23779],{"className":23778},[886],[888,23780,23781],{"xmlns":890},[892,23782,23783,23794],{},[895,23784,23785,23787,23789,23792],{},[898,23786,2774],{},[1996,23788,1998],{},[2129,23790,23791],{},"0,25",[898,23793,9128],{},[902,23795,23796],{"encoding":904},"T = 0{,}25Y",[883,23798,23800],{"className":23799},[886],[888,23801,23802],{"xmlns":890},[892,23803,23804,23816],{},[895,23805,23806,23812,23814],{},[2124,23807,23808,23810],{},[898,23809,12186],{},[1996,23811,4354],{},[1996,23813,1998],{},[2129,23815,15112],{},[902,23817,23818],{"encoding":904},"I^* = 500",[883,23820,23822],{"className":23821},[886],[888,23823,23824],{"xmlns":890},[892,23825,23826,23838],{},[895,23827,23828,23834,23836],{},[2124,23829,23830,23832],{},[898,23831,12114],{},[1996,23833,4354],{},[1996,23835,1998],{},[2129,23837,8803],{},[902,23839,23840],{"encoding":904},"G^* = 150",[883,23842,23844],{"className":23843},[886],[888,23845,23846],{"xmlns":890},[892,23847,23848,23861],{},[895,23849,23850,23856,23858],{},[2124,23851,23852,23854],{},[898,23853,23255],{},[1996,23855,4354],{},[1996,23857,1998],{},[2129,23859,23860],{},"800",[902,23862,23863],{"encoding":904},"B^* = 800",". Soustava:",[724,23866,23867],{},[883,23868,23870],{"className":23869},[886],[888,23871,23872],{"xmlns":890},[892,23873,23874,24092],{},[20756,23875,23876,23922,23964,24000,24042],{"rowspacing":20758,"columnalign":20759,"columnspacing":2377},[20761,23877,23878,23894],{},[20764,23879,23880],{},[2325,23881,23882],{"scriptlevel":2327,"displaystyle":2285},[895,23883,23884,23886,23888,23890,23892],{},[1996,23885,2005],{"stretchy":2004},[898,23887,12043],{},[2129,23889,2278],{},[1996,23891,2011],{"stretchy":2004},[2288,23893,2290],{},[20764,23895,23896],{},[2325,23897,23898],{"scriptlevel":2327,"displaystyle":2285},[895,23899,23900,23902,23904,23906,23908,23910,23916,23918,23920],{},[895,23901],{},[898,23903,2777],{},[1996,23905,1998],{},[2129,23907,23732],{},[2288,23909,2987],{},[2272,23911,23912,23914],{},[898,23913,9128],{},[898,23915,4183],{},[1996,23917,2095],{},[2129,23919,23745],{},[1996,23921,2286],{"separator":2285},[20761,23923,23924,23940],{},[20764,23925,23926],{},[2325,23927,23928],{"scriptlevel":2327,"displaystyle":2285},[895,23929,23930,23932,23934,23936,23938],{},[1996,23931,2005],{"stretchy":2004},[898,23933,12043],{},[2129,23935,2131],{},[1996,23937,2011],{"stretchy":2004},[2288,23939,2290],{},[20764,23941,23942],{},[2325,23943,23944],{"scriptlevel":2327,"displaystyle":2285},[895,23945,23946,23948,23954,23956,23958,23960,23962],{},[895,23947],{},[2272,23949,23950,23952],{},[898,23951,9128],{},[898,23953,4183],{},[1996,23955,1998],{},[898,23957,9128],{},[1996,23959,2225],{},[898,23961,2774],{},[1996,23963,2286],{"separator":2285},[20761,23965,23966,23982],{},[20764,23967,23968],{},[2325,23969,23970],{"scriptlevel":2327,"displaystyle":2285},[895,23971,23972,23974,23976,23978,23980],{},[1996,23973,2005],{"stretchy":2004},[898,23975,12043],{},[2129,23977,2173],{},[1996,23979,2011],{"stretchy":2004},[2288,23981,2290],{},[20764,23983,23984],{},[2325,23985,23986],{"scriptlevel":2327,"displaystyle":2285},[895,23987,23988,23990,23992,23994,23996,23998],{},[895,23989],{},[898,23991,2774],{},[1996,23993,1998],{},[2129,23995,23791],{},[898,23997,9128],{},[1996,23999,2286],{"separator":2285},[20761,24001,24002,24018],{},[20764,24003,24004],{},[2325,24005,24006],{"scriptlevel":2327,"displaystyle":2285},[895,24007,24008,24010,24012,24014,24016],{},[1996,24009,2005],{"stretchy":2004},[898,24011,12043],{},[2129,24013,2351],{},[1996,24015,2011],{"stretchy":2004},[2288,24017,2290],{},[20764,24019,24020],{},[2325,24021,24022],{"scriptlevel":2327,"displaystyle":2285},[895,24023,24024,24026,24028,24030,24032,24034,24040],{},[895,24025],{},[898,24027,2818],{},[1996,24029,1998],{},[2129,24031,23764],{},[2288,24033,2987],{},[2272,24035,24036,24038],{},[898,24037,9128],{},[898,24039,4183],{},[1996,24041,2286],{"separator":2285},[20761,24043,24044,24060],{},[20764,24045,24046],{},[2325,24047,24048],{"scriptlevel":2327,"displaystyle":2285},[895,24049,24050,24052,24054,24056,24058],{},[1996,24051,2005],{"stretchy":2004},[898,24053,12043],{},[2129,24055,2228],{},[1996,24057,2011],{"stretchy":2004},[2288,24059,2290],{},[20764,24061,24062],{},[2325,24063,24064],{"scriptlevel":2327,"displaystyle":2285},[895,24065,24066,24068,24070,24072,24074,24076,24078,24080,24082,24084,24086,24088,24090],{},[895,24067],{},[898,24069,9128],{},[1996,24071,1998],{},[898,24073,2777],{},[1996,24075,2095],{},[2129,24077,15112],{},[1996,24079,2095],{},[2129,24081,8803],{},[1996,24083,2095],{},[2129,24085,23860],{},[1996,24087,2225],{},[898,24089,2818],{},[898,24091,1975],{"mathvariant":2376},[902,24093,24094],{"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}",[724,24096,24097,24098,24132],{},"Postupná substituce — z (r3) do (r2): ",[883,24099,24101],{"className":24100},[886],[888,24102,24103],{"xmlns":890},[892,24104,24105,24129],{},[895,24106,24107,24113,24115,24117,24119,24121,24123,24125,24127],{},[2272,24108,24109,24111],{},[898,24110,9128],{},[898,24112,4183],{},[1996,24114,1998],{},[898,24116,9128],{},[1996,24118,2225],{},[2129,24120,23791],{},[898,24122,9128],{},[1996,24124,1998],{},[2129,24126,23732],{},[898,24128,9128],{},[902,24130,24131],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,24134,24135],{},[883,24136,24138],{"className":24137},[886],[888,24139,24140],{"xmlns":890},[892,24141,24142,24183],{},[895,24143,24144,24146,24148,24150,24152,24154,24156,24158,24160,24162,24164,24166,24168,24170,24172,24175,24177,24179,24181],{},[1996,24145,2005],{"stretchy":2004},[898,24147,12043],{},[2129,24149,2235],{},[1996,24151,2011],{"stretchy":2004},[2288,24153,2290],{},[898,24155,2777],{},[1996,24157,1998],{},[2129,24159,23732],{},[1996,24161,3177],{},[2129,24163,23732],{},[898,24165,9128],{},[1996,24167,2095],{},[2129,24169,23745],{},[1996,24171,1998],{},[2129,24173,24174],{},"0,5625",[898,24176,9128],{},[1996,24178,2095],{},[2129,24180,23745],{},[1996,24182,2286],{"separator":2285},[902,24184,24185],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,24187,24188],{},[883,24189,24191],{"className":24190},[886],[888,24192,24193],{"xmlns":890},[892,24194,24195,24229],{},[895,24196,24197,24199,24201,24204,24206,24208,24210,24212,24214,24216,24218,24220,24222,24225,24227],{},[1996,24198,2005],{"stretchy":2004},[898,24200,12043],{},[2129,24202,24203],{},"7",[1996,24205,2011],{"stretchy":2004},[2288,24207,2290],{},[898,24209,2818],{},[1996,24211,1998],{},[2129,24213,23764],{},[1996,24215,3177],{},[2129,24217,23732],{},[898,24219,9128],{},[1996,24221,1998],{},[2129,24223,24224],{},"0,1125",[898,24226,9128],{},[898,24228,1975],{"mathvariant":2376},[902,24230,24231],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,24233,24234],{},"Dosazením do (r5):",[724,24236,24237],{},[883,24238,24240],{"className":24239},[886],[888,24241,24242],{"xmlns":890},[892,24243,24244,24288],{},[895,24245,24246,24248,24250,24252,24254,24256,24258,24260,24262,24264,24266,24268,24270,24272,24274,24276,24278,24281,24283,24285],{},[898,24247,9128],{},[1996,24249,1998],{},[2129,24251,24174],{},[898,24253,9128],{},[1996,24255,2095],{},[2129,24257,23745],{},[1996,24259,2095],{},[2129,24261,15112],{},[1996,24263,2095],{},[2129,24265,8803],{},[1996,24267,2095],{},[2129,24269,23860],{},[1996,24271,2225],{},[2129,24273,24224],{},[898,24275,9128],{},[1996,24277,1998],{},[2129,24279,24280],{},"0,45",[898,24282,9128],{},[1996,24284,2095],{},[2129,24286,24287],{},"2200.",[902,24289,24290],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,24292,24293,24294,5589,24316,24339],{},"Odtud ",[883,24295,24297],{"className":24296},[886],[888,24298,24299],{"xmlns":890},[892,24300,24301,24313],{},[895,24302,24303,24306,24308,24310],{},[2129,24304,24305],{},"0,55",[898,24307,9128],{},[1996,24309,1998],{},[2129,24311,24312],{},"2200",[902,24314,24315],{"encoding":904},"0{,}55Y = 2200",[883,24317,24319],{"className":24318},[886],[888,24320,24321],{"xmlns":890},[892,24322,24323,24336],{},[895,24324,24325,24331,24333],{},[2124,24326,24327,24329],{},[898,24328,9128],{},[898,24330,4252],{},[1996,24332,1998],{},[2129,24334,24335],{},"4000",[902,24337,24338],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,24341,24342,24365,24397,24432,24465,24501],{},[123,24343,24344,2286],{},[883,24345,24347],{"className":24346},[886],[888,24348,24349],{"xmlns":890},[892,24350,24351,24363],{},[895,24352,24353,24359,24361],{},[2124,24354,24355,24357],{},[898,24356,9128],{},[898,24358,4252],{},[1996,24360,1998],{},[2129,24362,24335],{},[902,24364,24338],{"encoding":904},[123,24366,24367,2286],{},[883,24368,24370],{"className":24369},[886],[888,24371,24372],{"xmlns":890},[892,24373,24374,24394],{},[895,24375,24376,24382,24384,24386,24388,24390,24392],{},[2124,24377,24378,24380],{},[898,24379,2774],{},[898,24381,4252],{},[1996,24383,1998],{},[2129,24385,23791],{},[1996,24387,3177],{},[2129,24389,24335],{},[1996,24391,1998],{},[2129,24393,2782],{},[902,24395,24396],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,24398,24399,2286],{},[883,24400,24402],{"className":24401},[886],[888,24403,24404],{"xmlns":890},[892,24405,24406,24429],{},[895,24407,24408,24416,24418,24420,24422,24424,24426],{},[9166,24409,24410,24412,24414],{},[898,24411,9128],{},[898,24413,4183],{},[898,24415,4252],{},[1996,24417,1998],{},[2129,24419,23732],{},[1996,24421,3177],{},[2129,24423,24335],{},[1996,24425,1998],{},[2129,24427,24428],{},"3000",[902,24430,24431],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,24433,24434,2286],{},[883,24435,24437],{"className":24436},[886],[888,24438,24439],{"xmlns":890},[892,24440,24441,24462],{},[895,24442,24443,24449,24451,24453,24455,24457,24459],{},[2124,24444,24445,24447],{},[898,24446,2818],{},[898,24448,4252],{},[1996,24450,1998],{},[2129,24452,23764],{},[1996,24454,3177],{},[2129,24456,24428],{},[1996,24458,1998],{},[2129,24460,24461],{},"450",[902,24463,24464],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,24466,24467,2286],{},[883,24468,24470],{"className":24469},[886],[888,24471,24472],{"xmlns":890},[892,24473,24474,24498],{},[895,24475,24476,24482,24484,24486,24488,24490,24492,24494,24496],{},[2124,24477,24478,24480],{},[898,24479,2777],{},[898,24481,4252],{},[1996,24483,1998],{},[2129,24485,23732],{},[1996,24487,3177],{},[2129,24489,24428],{},[1996,24491,2095],{},[2129,24493,23745],{},[1996,24495,1998],{},[2129,24497,24428],{},[902,24499,24500],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,24502,24503,24543],{},[883,24504,24506],{"className":24505},[886],[888,24507,24508],{"xmlns":890},[892,24509,24510,24540],{},[895,24511,24512,24518,24520,24528,24530,24536,24538],{},[2124,24513,24514,24516],{},[898,24515,8673],{},[898,24517,4252],{},[1996,24519,1998],{},[9166,24521,24522,24524,24526],{},[898,24523,9128],{},[898,24525,4183],{},[898,24527,4252],{},[1996,24529,2225],{},[2124,24531,24532,24534],{},[898,24533,2777],{},[898,24535,4252],{},[1996,24537,1998],{},[2129,24539,2327],{},[902,24541,24542],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,24545,24546,24548,24549,1343,24566,3885,24587,24612,24613,24616,24617,24630,24631,1975],{},[38,24547,21351],{}," Modely ",[883,24550,24552],{"className":24551},[886],[888,24553,24554],{"xmlns":890},[892,24555,24556,24564],{},[895,24557,24558,24560,24562],{},[898,24559,2777],{},[2288,24561,12292],{},[898,24563,12186],{},[902,24565,12297],{"encoding":904},[883,24567,24569],{"className":24568},[886],[888,24570,24571],{"xmlns":890},[892,24572,24573,24585],{},[895,24574,24575,24577,24579,24581,24583],{},[898,24576,2777],{},[2288,24578,12292],{},[898,24580,12186],{},[2288,24582,12292],{},[898,24584,12114],{},[902,24586,18222],{"encoding":904},[883,24588,24590],{"className":24589},[886],[888,24591,24592],{"xmlns":890},[892,24593,24594,24610],{},[895,24595,24596,24598,24600,24602,24604,24606,24608],{},[898,24597,2777],{},[2288,24599,12292],{},[898,24601,12186],{},[2288,24603,12292],{},[898,24605,12114],{},[2288,24607,12292],{},[898,24609,12322],{},[902,24611,12325],{"encoding":904}," pokládají investice za ",[38,24614,24615],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,24618,24620],{"className":24619},[886],[888,24621,24622],{"xmlns":890},[892,24623,24624,24628],{},[895,24625,24626],{},[898,24627,12043],{},[902,24629,12043],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,24632,24633],{},"model IS-LM",[115,24635,24637],{"id":24636},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,24639,24640,24641,24645,24646,24649,24650,24653],{},"V článku ",[207,24642,24644],{"className":24643,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,24647,24648],{},"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 ",[38,24651,24652],{},"výraznější"," než v mikroekonomických modelech.",[724,24655,24656],{},[2559,24657],{"alt":24658,"className":24659,"src":24660},"imek-multiplikatorovy-efekt-chain",[210,2563],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,24662,12166,24663,1343,24680,1343,24701,24726,24727,24730,24731,24749,24750,24768,24769,24787,24788,24791,24792,1343,24809,24826,24827,24829],{},[883,24664,24666],{"className":24665},[886],[888,24667,24668],{"xmlns":890},[892,24669,24670,24678],{},[895,24671,24672,24674,24676],{},[898,24673,2777],{},[2288,24675,12292],{},[898,24677,12186],{},[902,24679,12297],{"encoding":904},[883,24681,24683],{"className":24682},[886],[888,24684,24685],{"xmlns":890},[892,24686,24687,24699],{},[895,24688,24689,24691,24693,24695,24697],{},[898,24690,2777],{},[2288,24692,12292],{},[898,24694,12186],{},[2288,24696,12292],{},[898,24698,12114],{},[902,24700,18222],{"encoding":904},[883,24702,24704],{"className":24703},[886],[888,24705,24706],{"xmlns":890},[892,24707,24708,24724],{},[895,24709,24710,24712,24714,24716,24718,24720,24722],{},[898,24711,2777],{},[2288,24713,12292],{},[898,24715,12186],{},[2288,24717,12292],{},[898,24719,12114],{},[2288,24721,12292],{},[898,24723,12322],{},[902,24725,12325],{"encoding":904}," se vyšetřuje vliv změn ",[38,24728,24729],{},"exogenních"," veličin (plánovaných investic ",[883,24732,24734],{"className":24733},[886],[888,24735,24736],{"xmlns":890},[892,24737,24738,24746],{},[895,24739,24740],{},[2124,24741,24742,24744],{},[898,24743,12186],{},[1996,24745,4354],{},[902,24747,24748],{"encoding":904},"I^*",", vládních výdajů ",[883,24751,24753],{"className":24752},[886],[888,24754,24755],{"xmlns":890},[892,24756,24757,24765],{},[895,24758,24759],{},[2124,24760,24761,24763],{},[898,24762,12114],{},[1996,24764,4354],{},[902,24766,24767],{"encoding":904},"G^*",", exportu ",[883,24770,24772],{"className":24771},[886],[888,24773,24774],{"xmlns":890},[892,24775,24776,24784],{},[895,24777,24778],{},[2124,24779,24780,24782],{},[898,24781,23255],{},[1996,24783,4354],{},[902,24785,24786],{"encoding":904},"B^*",") na změny ",[38,24789,24790],{},"endogenních"," rovnovážných veličin (",[883,24793,24795],{"className":24794},[886],[888,24796,24797],{"xmlns":890},[892,24798,24799,24807],{},[895,24800,24801],{},[2124,24802,24803,24805],{},[898,24804,9128],{},[898,24806,4252],{},[902,24808,13905],{"encoding":904},[883,24810,24812],{"className":24811},[886],[888,24813,24814],{"xmlns":890},[892,24815,24816,24824],{},[895,24817,24818],{},[2124,24819,24820,24822],{},[898,24821,2777],{},[898,24823,4252],{},[902,24825,13964],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,24828,17979],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,24831,24833],{"id":24832},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,24835,20897,24836,24859,24860,24904],{},[883,24837,24839],{"className":24838},[886],[888,24840,24841],{"xmlns":890},[892,24842,24843,24857],{},[895,24844,24845,24847,24849,24851,24853,24855],{},[898,24846,2777],{},[1996,24848,1998],{},[898,24850,207],{},[898,24852,9128],{},[1996,24854,2095],{},[898,24856,2098],{},[902,24858,18922],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,24861,24863],{"className":24862},[886],[888,24864,24865],{"xmlns":890},[892,24866,24867,24901],{},[895,24868,24869,24875,24877],{},[2124,24870,24871,24873],{},[898,24872,9128],{},[898,24874,4252],{},[1996,24876,1998],{},[2325,24878,24879],{"scriptlevel":2327,"displaystyle":2285},[2329,24880,24881,24893],{},[895,24882,24883,24885,24887],{},[898,24884,2098],{},[1996,24886,2095],{},[2124,24888,24889,24891],{},[898,24890,12186],{},[1996,24892,4354],{},[895,24894,24895,24897,24899],{},[2129,24896,2278],{},[1996,24898,2225],{},[898,24900,207],{},[902,24902,24903],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,24906,24907],{},[883,24908,24910],{"className":24909},[886],[888,24911,24912],{"xmlns":890},[892,24913,24914,24983],{},[895,24915,24916,24934,24936,24966,24968],{},[2329,24917,24918,24928],{},[895,24919,24920,24922],{},[898,24921,9872],{"mathvariant":2376},[2124,24923,24924,24926],{},[898,24925,9128],{},[898,24927,4252],{},[895,24929,24930,24932],{},[898,24931,9872],{"mathvariant":2376},[898,24933,207],{},[1996,24935,1998],{},[2329,24937,24938,24950],{},[895,24939,24940,24942,24944],{},[898,24941,2098],{},[1996,24943,2095],{},[2124,24945,24946,24948],{},[898,24947,12186],{},[1996,24949,4354],{},[895,24951,24952,24954,24956,24958,24960],{},[1996,24953,2005],{"stretchy":2004},[2129,24955,2278],{},[1996,24957,2225],{},[898,24959,207],{},[2124,24961,24962,24964],{},[1996,24963,2011],{"stretchy":2004},[2129,24965,2131],{},[5878,24967],{"width":5880},[895,24969,24970,24973,24980],{},[2288,24971,24972],{},"(multiplik",[8386,24974,24975,24977],{"accent":2285},[2288,24976,207],{},[1996,24978,24979],{},"ˊ",[2288,24981,24982],{},"tor MPC)",[902,24984,24985],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,24987,24988],{},[883,24989,24991],{"className":24990},[886],[888,24992,24993],{"xmlns":890},[892,24994,24995,25064],{},[895,24996,24997,25015,25017,25029,25031],{},[2329,24998,24999,25009],{},[895,25000,25001,25003],{},[898,25002,9872],{"mathvariant":2376},[2124,25004,25005,25007],{},[898,25006,9128],{},[898,25008,4252],{},[895,25010,25011,25013],{},[898,25012,9872],{"mathvariant":2376},[898,25014,2098],{},[1996,25016,1998],{},[2329,25018,25019,25021],{},[2129,25020,2278],{},[895,25022,25023,25025,25027],{},[2129,25024,2278],{},[1996,25026,2225],{},[898,25028,207],{},[5878,25030],{"width":5880},[895,25032,25033,25035,25041,25044,25051,25054,25061],{},[2288,25034,24972],{},[8386,25036,25037,25039],{"accent":2285},[2288,25038,207],{},[1996,25040,24979],{},[2288,25042,25043],{},"tor autonomn",[8386,25045,25046,25049],{"accent":2285},[2288,25047,25048],{},"ı",[1996,25050,24979],{},[2288,25052,25053],{}," spot",[8386,25055,25056,25058],{"accent":2285},[2288,25057,12043],{},[1996,25059,25060],{},"ˇ",[2288,25062,25063],{},"eby)",[902,25065,25066],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,25068,25069],{},[883,25070,25072],{"className":25071},[886],[888,25073,25074],{"xmlns":890},[892,25075,25076,25143],{},[895,25077,25078,25100,25102,25114,25116,25128,25130],{},[2329,25079,25080,25090],{},[895,25081,25082,25084],{},[898,25083,9872],{"mathvariant":2376},[2124,25085,25086,25088],{},[898,25087,9128],{},[898,25089,4252],{},[895,25091,25092,25094],{},[898,25093,9872],{"mathvariant":2376},[2124,25095,25096,25098],{},[898,25097,12186],{},[1996,25099,4354],{},[1996,25101,1998],{},[2329,25103,25104,25106],{},[2129,25105,2278],{},[895,25107,25108,25110,25112],{},[2129,25109,2278],{},[1996,25111,2225],{},[898,25113,207],{},[1996,25115,1998],{},[2329,25117,25118,25120],{},[2129,25119,2278],{},[895,25121,25122,25124,25126],{},[898,25123,2818],{},[898,25125,3937],{},[898,25127,8673],{},[5878,25129],{"width":5880},[895,25131,25132,25134,25140],{},[2288,25133,24972],{},[8386,25135,25136,25138],{"accent":2285},[2288,25137,207],{},[1996,25139,24979],{},[2288,25141,25142],{},"tor investic)",[902,25144,25145],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[3867,25147,25148],{},[724,25149,25150,25152,25153,25156,25157,25170,25171,25188,25189,25207,25208,25252,25253,21422,25270,25273,25274,25291],{},[883,25151,4155],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,25154,25155],{},"důchodem","; z něj se utratí ",[883,25158,25160],{"className":25159},[886],[888,25161,25162],{"xmlns":890},[892,25163,25164,25168],{},[895,25165,25166],{},[898,25167,207],{},[902,25169,207],{"encoding":904}," Kč (= ",[883,25172,25174],{"className":25173},[886],[888,25175,25176],{"xmlns":890},[892,25177,25178,25186],{},[895,25179,25180,25182,25184],{},[898,25181,2818],{},[898,25183,3937],{},[898,25185,2777],{},[902,25187,18047],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,25190,25192],{"className":25191},[886],[888,25193,25194],{"xmlns":890},[892,25195,25196,25204],{},[895,25197,25198],{},[2124,25199,25200,25202],{},[898,25201,207],{},[2129,25203,2131],{},[902,25205,25206],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,25209,25211],{"className":25210},[886],[888,25212,25213],{"xmlns":890},[892,25214,25215,25249],{},[895,25216,25217,25219,25221,25223,25225,25231,25233,25235,25237],{},[2129,25218,2278],{},[1996,25220,2095],{},[898,25222,207],{},[1996,25224,2095],{},[2124,25226,25227,25229],{},[898,25228,207],{},[2129,25230,2131],{},[1996,25232,2095],{},[1996,25234,18107],{},[1996,25236,1998],{},[2329,25238,25239,25241],{},[2129,25240,2278],{},[895,25242,25243,25245,25247],{},[2129,25244,2278],{},[1996,25246,2225],{},[898,25248,207],{},[902,25250,25251],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,25254,25256],{"className":25255},[886],[888,25257,25258],{"xmlns":890},[892,25259,25260,25268],{},[895,25261,25262],{},[2124,25263,25264,25266],{},[898,25265,9128],{},[898,25267,4252],{},[902,25269,13905],{"encoding":904},[38,25271,25272],{},"více"," než korunu — čím vyšší ",[883,25275,25277],{"className":25276},[886],[888,25278,25279],{"xmlns":890},[892,25280,25281,25289],{},[895,25282,25283,25285,25287],{},[898,25284,2818],{},[898,25286,3937],{},[898,25288,2777],{},[902,25290,18047],{"encoding":904},", tím silnější multiplikační efekt.",[724,25293,25294,25297,25298,25324,25325,25328,25329,3885,25350,25375,25376,1975],{},[38,25295,25296],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,25299,25301],{"className":25300},[886],[888,25302,25303],{"xmlns":890},[892,25304,25305,25321],{},[895,25306,25307],{},[2325,25308,25309],{"scriptlevel":2327,"displaystyle":2004},[2329,25310,25311,25313],{},[2129,25312,2278],{},[895,25314,25315,25317,25319],{},[2129,25316,2278],{},[1996,25318,2225],{},[898,25320,207],{},[902,25322,25323],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,25326,25327],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,25330,25332],{"className":25331},[886],[888,25333,25334],{"xmlns":890},[892,25335,25336,25348],{},[895,25337,25338,25340,25342,25344,25346],{},[898,25339,2777],{},[2288,25341,12292],{},[898,25343,12186],{},[2288,25345,12292],{},[898,25347,12114],{},[902,25349,18222],{"encoding":904},[883,25351,25353],{"className":25352},[886],[888,25354,25355],{"xmlns":890},[892,25356,25357,25373],{},[895,25358,25359,25361,25363,25365,25367,25369,25371],{},[898,25360,2777],{},[2288,25362,12292],{},[898,25364,12186],{},[2288,25366,12292],{},[898,25368,12114],{},[2288,25370,12292],{},[898,25372,12322],{},[902,25374,12325],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,25377,25379],{"className":25378,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,25381,25383],{"id":25382},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,25385,12166,25386,1343,25403,3885,25424,12171,25449,10025,25452,25473,25474,2203,25477,25490,25491,5669,25520,25537,25538,25541,25542,25544,25545,25566],{},[883,25387,25389],{"className":25388},[886],[888,25390,25391],{"xmlns":890},[892,25392,25393,25401],{},[895,25394,25395,25397,25399],{},[898,25396,2777],{},[2288,25398,12292],{},[898,25400,12186],{},[902,25402,12297],{"encoding":904},[883,25404,25406],{"className":25405},[886],[888,25407,25408],{"xmlns":890},[892,25409,25410,25422],{},[895,25411,25412,25414,25416,25418,25420],{},[898,25413,2777],{},[2288,25415,12292],{},[898,25417,12186],{},[2288,25419,12292],{},[898,25421,12114],{},[902,25423,18222],{"encoding":904},[883,25425,25427],{"className":25426},[886],[888,25428,25429],{"xmlns":890},[892,25430,25431,25447],{},[895,25432,25433,25435,25437,25439,25441,25443,25445],{},[898,25434,2777],{},[2288,25436,12292],{},[898,25438,12186],{},[2288,25440,12292],{},[898,25442,12114],{},[2288,25444,12292],{},[898,25446,12322],{},[902,25448,12325],{"encoding":904},[38,25450,25451],{},"investice konstantní",[883,25453,25455],{"className":25454},[886],[888,25456,25457],{"xmlns":890},[892,25458,25459,25471],{},[895,25460,25461,25463,25465],{},[898,25462,12186],{},[1996,25464,1998],{},[2124,25466,25467,25469],{},[898,25468,12186],{},[1996,25470,4354],{},[902,25472,12197],{"encoding":904},"). Reálnější je předpoklad, že ",[38,25475,25476],{},"investice závisejí na úrokové míře",[883,25478,25480],{"className":25479},[886],[888,25481,25482],{"xmlns":890},[892,25483,25484,25488],{},[895,25485,25486],{},[898,25487,12043],{},[902,25489,12043],{"encoding":904}," — klesající funkce ",[883,25492,25494],{"className":25493},[886],[888,25495,25496],{"xmlns":890},[892,25497,25498,25518],{},[895,25499,25500,25502,25504,25506,25508,25510,25512,25514,25516],{},[898,25501,12186],{},[1996,25503,2005],{"stretchy":2004},[898,25505,12043],{},[1996,25507,2011],{"stretchy":2004},[1996,25509,1998],{},[898,25511,2142],{},[898,25513,12043],{},[1996,25515,2095],{},[898,25517,2194],{},[902,25519,15759],{"encoding":904},[883,25521,25523],{"className":25522},[886],[888,25524,25525],{"xmlns":890},[892,25526,25527,25535],{},[895,25528,25529,25531,25533],{},[898,25530,2142],{},[1996,25532,3447],{},[2129,25534,2327],{},[902,25536,12517],{"encoding":904},". Přidáním ",[38,25539,25540],{},"trhu peněz"," k trhu zboží vzniká model ",[38,25543,12013],{}," se dvěma neznámými ",[883,25546,25548],{"className":25547},[886],[888,25549,25550],{"xmlns":890},[892,25551,25552,25564],{},[895,25553,25554,25556,25558,25560,25562],{},[1996,25555,2005],{"stretchy":2004},[898,25557,9128],{},[1996,25559,2286],{"separator":2285},[898,25561,12043],{},[1996,25563,2011],{"stretchy":2004},[902,25565,18152],{"encoding":904}," a dvěma rovnicemi:",[120,25568,25569,25619],{},[123,25570,25571,10025,25573,25575,25576,25597,25598,1975],{},[38,25572,15848],{},[614,25574,12056],{},") — klesající přímka v rovině ",[883,25577,25579],{"className":25578},[886],[888,25580,25581],{"xmlns":890},[892,25582,25583,25595],{},[895,25584,25585,25587,25589,25591,25593],{},[1996,25586,2005],{"stretchy":2004},[898,25588,12043],{},[1996,25590,2286],{"separator":2285},[898,25592,9128],{},[1996,25594,2011],{"stretchy":2004},[902,25596,12939],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,25599,25601],{"className":25600},[886],[888,25602,25603],{"xmlns":890},[892,25604,25605,25617],{},[895,25606,25607,25609,25611,25613,25615],{},[898,25608,9128],{},[1996,25610,1998],{},[898,25612,2777],{},[1996,25614,2095],{},[898,25616,12186],{},[902,25618,14746],{"encoding":904},[123,25620,25621,10025,25623,25625,25626,21596,25651,25697],{},[38,25622,16047],{},[614,25624,12063],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,25627,25629],{"className":25628},[886],[888,25630,25631],{"xmlns":890},[892,25632,25633,25649],{},[895,25634,25635,25641,25643],{},[2124,25636,25637,25639],{},[898,25638,2818],{},[898,25640,4183],{},[1996,25642,1998],{},[2124,25644,25645,25647],{},[898,25646,2818],{},[1996,25648,4354],{},[902,25650,13482],{"encoding":904},[883,25652,25654],{"className":25653},[886],[888,25655,25656],{"xmlns":890},[892,25657,25658,25694],{},[895,25659,25660,25666,25668,25674,25676,25678,25684,25686,25688],{},[2124,25661,25662,25664],{},[898,25663,2818],{},[898,25665,4183],{},[1996,25667,1998],{},[2272,25669,25670,25672],{},[898,25671,13239],{},[2129,25673,2278],{},[898,25675,9128],{},[1996,25677,2095],{},[2272,25679,25680,25682],{},[898,25681,13239],{},[2129,25683,2131],{},[898,25685,12043],{},[1996,25687,2095],{},[2272,25689,25690,25692],{},[898,25691,13239],{},[2129,25693,2173],{},[902,25695,25696],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,25699,25700,2203,25703,25736,25737,25739,25740,25742],{},[38,25701,25702],{},"Simultánní rovnovážný bod",[883,25704,25706],{"className":25705},[886],[888,25707,25708],{"xmlns":890},[892,25709,25710,25734],{},[895,25711,25712,25714,25716,25718,25724,25726,25732],{},[898,25713,4252],{},[1996,25715,1998],{},[1996,25717,2005],{"stretchy":2004},[2124,25719,25720,25722],{},[898,25721,12043],{},[898,25723,4252],{},[1996,25725,2286],{"separator":2285},[2124,25727,25728,25730],{},[898,25729,9128],{},[898,25731,4252],{},[1996,25733,2011],{"stretchy":2004},[902,25735,16139],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,25738,12101],{}," (posun IS) a ",[38,25741,12133],{}," (posun LM).",[724,25744,25745],{},[38,25746,25747,25748,1343,25770,1343,25792,1343,25814,25836,25837,1975],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,25749,25751],{"className":25750},[886],[888,25752,25753],{"xmlns":890},[892,25754,25755,25767],{},[895,25756,25757,25763,25765],{},[2124,25758,25759,25761],{},[898,25760,9128],{},[898,25762,4252],{},[1996,25764,1998],{},[2129,25766,15117],{},[902,25768,25769],{"encoding":904},"Y^E = 5000",[883,25771,25773],{"className":25772},[886],[888,25774,25775],{"xmlns":890},[892,25776,25777,25789],{},[895,25778,25779,25785,25787],{},[2124,25780,25781,25783],{},[898,25782,12043],{},[898,25784,4252],{},[1996,25786,1998],{},[2129,25788,2228],{},[902,25790,25791],{"encoding":904},"r^E = 5",[883,25793,25795],{"className":25794},[886],[888,25796,25797],{"xmlns":890},[892,25798,25799,25811],{},[895,25800,25801,25807,25809],{},[2124,25802,25803,25805],{},[898,25804,2777],{},[898,25806,4252],{},[1996,25808,1998],{},[2129,25810,15154],{},[902,25812,25813],{"encoding":904},"C^E = 4100",[883,25815,25817],{"className":25816},[886],[888,25818,25819],{"xmlns":890},[892,25820,25821,25833],{},[895,25822,25823,25829,25831],{},[2124,25824,25825,25827],{},[898,25826,12186],{},[898,25828,4252],{},[1996,25830,1998],{},[2129,25832,15193],{},[902,25834,25835],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,25838,945],{"className":25839,"dataFsResolvedFilePath":943,"href":944},[210],[115,25841,25843],{"id":25842},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,25845,25846,25910,26021,26164,26406,26474],{},[123,25847,25848,25851,25852,25874,25875,25909],{},[38,25849,25850],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,25853,25855],{"className":25854},[886],[888,25856,25857],{"xmlns":890},[892,25858,25859,25871],{},[895,25860,25861,25863,25865,25867,25869],{},[898,25862,12114],{},[898,25864,18296],{},[898,25866,3937],{},[1996,25868,2730],{},[898,25870,9128],{},[902,25872,25873],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,25876,25878],{"className":25877},[886],[888,25879,25880],{"xmlns":890},[892,25881,25882,25906],{},[895,25883,25884,25886,25888,25890,25892,25894,25896,25898,25900,25902,25904],{},[898,25885,12114],{},[898,25887,18296],{},[898,25889,3937],{},[1996,25891,1998],{},[898,25893,2777],{},[1996,25895,2095],{},[898,25897,12186],{},[1996,25899,2095],{},[898,25901,12114],{},[1996,25903,2095],{},[898,25905,12322],{},[902,25907,25908],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,25911,25912,25914,25915,25936,25937,1343,25960,25991,25992,26005,26006,1975],{},[38,25913,18530],{}," splňují ",[883,25916,25918],{"className":25917},[886],[888,25919,25920],{"xmlns":890},[892,25921,25922,25934],{},[895,25923,25924,25926,25928,25930,25932],{},[898,25925,9128],{},[1996,25927,1998],{},[898,25929,2777],{},[1996,25931,2095],{},[898,25933,8673],{},[902,25935,12696],{"encoding":904}," (7.2); lineární model ",[883,25938,25940],{"className":25939},[886],[888,25941,25942],{"xmlns":890},[892,25943,25944,25958],{},[895,25945,25946,25948,25950,25952,25954,25956],{},[898,25947,2777],{},[1996,25949,1998],{},[898,25951,207],{},[898,25953,9128],{},[1996,25955,2095],{},[898,25957,2098],{},[902,25959,18922],{"encoding":904},[883,25961,25963],{"className":25962},[886],[888,25964,25965],{"xmlns":890},[892,25966,25967,25989],{},[895,25968,25969,25971,25973,25975,25977,25979,25981,25983,25985,25987],{},[898,25970,8673],{},[1996,25972,1998],{},[1996,25974,2005],{"stretchy":2004},[2129,25976,2278],{},[1996,25978,2225],{},[898,25980,207],{},[1996,25982,2011],{"stretchy":2004},[898,25984,9128],{},[1996,25986,2225],{},[898,25988,2098],{},[902,25990,19171],{"encoding":904}," s autonomní spotřebou ",[883,25993,25995],{"className":25994},[886],[888,25996,25997],{"xmlns":890},[892,25998,25999,26003],{},[895,26000,26001],{},[898,26002,2098],{},[902,26004,2098],{"encoding":904}," a autonomními úsporami ",[883,26007,26009],{"className":26008},[886],[888,26010,26011],{"xmlns":890},[892,26012,26013,26019],{},[895,26014,26015,26017],{},[1996,26016,2225],{},[898,26018,2098],{},[902,26020,19250],{"encoding":904},[123,26022,26023,2203,26026,1343,26056,26086,26087,26117,26118,1343,26139,1975],{},[38,26024,26025],{},"Mezní sklony",[883,26027,26029],{"className":26028},[886],[888,26030,26031],{"xmlns":890},[892,26032,26033,26053],{},[895,26034,26035,26037,26039,26041,26043,26045,26047,26049,26051],{},[898,26036,2818],{},[898,26038,3937],{},[898,26040,2777],{},[1996,26042,1998],{},[898,26044,2194],{"mathvariant":2376},[898,26046,2777],{},[898,26048,4674],{"mathvariant":2376},[898,26050,2194],{"mathvariant":2376},[898,26052,9128],{},[902,26054,26055],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,26057,26059],{"className":26058},[886],[888,26060,26061],{"xmlns":890},[892,26062,26063,26083],{},[895,26064,26065,26067,26069,26071,26073,26075,26077,26079,26081],{},[898,26066,2818],{},[898,26068,3937],{},[898,26070,8673],{},[1996,26072,1998],{},[898,26074,2194],{"mathvariant":2376},[898,26076,8673],{},[898,26078,4674],{"mathvariant":2376},[898,26080,2194],{"mathvariant":2376},[898,26082,9128],{},[902,26084,26085],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,26088,26090],{"className":26089},[886],[888,26091,26092],{"xmlns":890},[892,26093,26094,26114],{},[895,26095,26096,26098,26100,26102,26104,26106,26108,26110,26112],{},[898,26097,2818],{},[898,26099,3937],{},[898,26101,2777],{},[1996,26103,2095],{},[898,26105,2818],{},[898,26107,3937],{},[898,26109,8673],{},[1996,26111,1998],{},[2129,26113,2278],{},[902,26115,26116],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,26119,26121],{"className":26120},[886],[888,26122,26123],{"xmlns":890},[892,26124,26125,26137],{},[895,26126,26127,26129,26131,26133,26135],{},[898,26128,2818],{},[898,26130,3937],{},[898,26132,2777],{},[1996,26134,1998],{},[898,26136,207],{},[902,26138,19891],{"encoding":904},[883,26140,26142],{"className":26141},[886],[888,26143,26144],{"xmlns":890},[892,26145,26146,26162],{},[895,26147,26148,26150,26152,26154,26156,26158,26160],{},[898,26149,2818],{},[898,26151,3937],{},[898,26153,8673],{},[1996,26155,1998],{},[2129,26157,2278],{},[1996,26159,2225],{},[898,26161,207],{},[902,26163,19917],{"encoding":904},[123,26165,26166,26169,26170],{},[38,26167,26168],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,26171,26172,26260,26329],{},[123,26173,26174,26191,26192,26213,26214,2286],{},[883,26175,26177],{"className":26176},[886],[888,26178,26179],{"xmlns":890},[892,26180,26181,26189],{},[895,26182,26183,26185,26187],{},[898,26184,2777],{},[2288,26186,12292],{},[898,26188,12186],{},[902,26190,12297],{"encoding":904},": ",[883,26193,26195],{"className":26194},[886],[888,26196,26197],{"xmlns":890},[892,26198,26199,26211],{},[895,26200,26201,26203,26205,26207,26209],{},[898,26202,9128],{},[1996,26204,1998],{},[898,26206,2777],{},[1996,26208,2095],{},[898,26210,12186],{},[902,26212,14746],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,26215,26217],{"className":26216},[886],[888,26218,26219],{"xmlns":890},[892,26220,26221,26257],{},[895,26222,26223,26229,26231,26233,26235,26237,26243,26245,26247,26249,26251,26253,26255],{},[2124,26224,26225,26227],{},[898,26226,9128],{},[898,26228,4252],{},[1996,26230,1998],{},[1996,26232,2005],{"stretchy":2004},[898,26234,2098],{},[1996,26236,2095],{},[2124,26238,26239,26241],{},[898,26240,12186],{},[1996,26242,4354],{},[1996,26244,2011],{"stretchy":2004},[898,26246,4674],{"mathvariant":2376},[1996,26248,2005],{"stretchy":2004},[2129,26250,2278],{},[1996,26252,2225],{},[898,26254,207],{},[1996,26256,2011],{"stretchy":2004},[902,26258,26259],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,26261,26262,26283,26284,26303,26304,2286],{},[883,26263,26265],{"className":26264},[886],[888,26266,26267],{"xmlns":890},[892,26268,26269,26281],{},[895,26270,26271,26273,26275,26277,26279],{},[898,26272,2777],{},[2288,26274,12292],{},[898,26276,12186],{},[2288,26278,12292],{},[898,26280,12114],{},[902,26282,18222],{"encoding":904},": přidává vládu, zdanění ",[883,26285,26287],{"className":26286},[886],[888,26288,26289],{"xmlns":890},[892,26290,26291,26301],{},[895,26292,26293,26295,26297,26299],{},[898,26294,2774],{},[1996,26296,2005],{"stretchy":2004},[898,26298,9128],{},[1996,26300,2011],{"stretchy":2004},[902,26302,22221],{"encoding":904}," a disponibilní důchod ",[883,26305,26307],{"className":26306},[886],[888,26308,26309],{"xmlns":890},[892,26310,26311,26327],{},[895,26312,26313,26319,26321,26323,26325],{},[2272,26314,26315,26317],{},[898,26316,9128],{},[898,26318,4183],{},[1996,26320,1998],{},[898,26322,9128],{},[1996,26324,2225],{},[898,26326,2774],{},[902,26328,21720],{"encoding":904},[123,26330,26331,26356,26357,21596,26378,1975],{},[883,26332,26334],{"className":26333},[886],[888,26335,26336],{"xmlns":890},[892,26337,26338,26354],{},[895,26339,26340,26342,26344,26346,26348,26350,26352],{},[898,26341,2777],{},[2288,26343,12292],{},[898,26345,12186],{},[2288,26347,12292],{},[898,26349,12114],{},[2288,26351,12292],{},[898,26353,12322],{},[902,26355,12325],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,26358,26360],{"className":26359},[886],[888,26361,26362],{"xmlns":890},[892,26363,26364,26376],{},[895,26365,26366,26368,26370,26372,26374],{},[898,26367,12322],{},[1996,26369,1998],{},[898,26371,23255],{},[1996,26373,2225],{},[898,26375,2818],{},[902,26377,23262],{"encoding":904},[883,26379,26381],{"className":26380},[886],[888,26382,26383],{"xmlns":890},[892,26384,26385,26403],{},[895,26386,26387,26389,26391,26393,26395,26401],{},[898,26388,2818],{},[1996,26390,1998],{},[898,26392,2818],{},[1996,26394,2005],{"stretchy":2004},[2272,26396,26397,26399],{},[898,26398,9128],{},[898,26400,4183],{},[1996,26402,2011],{"stretchy":2004},[902,26404,26405],{"encoding":904},"M = M(Y_D)",[123,26407,26408,26411,26412,2203,26415,26473],{},[38,26409,26410],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,26413,26414],{},"multiplikátor investic",[883,26416,26418],{"className":26417},[886],[888,26419,26420],{"xmlns":890},[892,26421,26422,26470],{},[895,26423,26424,26426,26432,26434,26436,26442,26444,26446,26448,26450,26452,26454,26456,26458,26460,26462,26464,26466,26468],{},[898,26425,9872],{"mathvariant":2376},[2124,26427,26428,26430],{},[898,26429,9128],{},[898,26431,4252],{},[898,26433,4674],{"mathvariant":2376},[898,26435,9872],{"mathvariant":2376},[2124,26437,26438,26440],{},[898,26439,12186],{},[1996,26441,4354],{},[1996,26443,1998],{},[2129,26445,2278],{},[898,26447,4674],{"mathvariant":2376},[1996,26449,2005],{"stretchy":2004},[2129,26451,2278],{},[1996,26453,2225],{},[898,26455,207],{},[1996,26457,2011],{"stretchy":2004},[1996,26459,1998],{},[2129,26461,2278],{},[898,26463,4674],{"mathvariant":2376},[898,26465,2818],{},[898,26467,3937],{},[898,26469,8673],{},[902,26471,26472],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,26475,26476,26478,26479,26494,26495,18650,26512,26527,26528,26553,26554,1975],{},[38,26477,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,26480,26482],{"className":26481},[886],[888,26483,26484],{"xmlns":890},[892,26485,26486,26492],{},[895,26487,26488,26490],{},[898,26489,12186],{},[898,26491,8673],{},[902,26493,12053],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,26496,26498],{"className":26497},[886],[888,26499,26500],{"xmlns":890},[892,26501,26502,26510],{},[895,26503,26504,26506,26508],{},[898,26505,12186],{},[1996,26507,1998],{},[898,26509,8673],{},[902,26511,12714],{"encoding":904},[883,26513,26515],{"className":26514},[886],[888,26516,26517],{"xmlns":890},[892,26518,26519,26525],{},[895,26520,26521,26523],{},[898,26522,9795],{},[898,26524,2818],{},[902,26526,12060],{"encoding":904}," rovnováhu trhu peněz (",[883,26529,26531],{"className":26530},[886],[888,26532,26533],{"xmlns":890},[892,26534,26535,26551],{},[895,26536,26537,26543,26545],{},[2124,26538,26539,26541],{},[898,26540,2818],{},[898,26542,4183],{},[1996,26544,1998],{},[2124,26546,26547,26549],{},[898,26548,2818],{},[1996,26550,4354],{},[902,26552,13482],{"encoding":904},"); průsečík dává ",[883,26555,26557],{"className":26556},[886],[888,26558,26559],{"xmlns":890},[892,26560,26561,26581],{},[895,26562,26563,26565,26571,26573,26579],{},[1996,26564,2005],{"stretchy":2004},[2124,26566,26567,26569],{},[898,26568,9128],{},[898,26570,4252],{},[1996,26572,2286],{"separator":2285},[2124,26574,26575,26577],{},[898,26576,12043],{},[898,26578,4252],{},[1996,26580,2011],{"stretchy":2004},[902,26582,12097],{"encoding":904},[115,26584,15722],{"id":15721},[120,26586,26587,26625,26665,26755,26837,26891,26947,27006,27041,27046,27118,27193,27279,27341,27409,27467,27520,27559],{},[123,26588,26589,7015,26592,25909],{},[38,26590,26591],{},"Hrubý národní produkt (GNP)",[883,26593,26595],{"className":26594},[886],[888,26596,26597],{"xmlns":890},[892,26598,26599,26623],{},[895,26600,26601,26603,26605,26607,26609,26611,26613,26615,26617,26619,26621],{},[898,26602,12114],{},[898,26604,18296],{},[898,26606,3937],{},[1996,26608,1998],{},[898,26610,2777],{},[1996,26612,2095],{},[898,26614,12186],{},[1996,26616,2095],{},[898,26618,12114],{},[1996,26620,2095],{},[898,26622,12322],{},[902,26624,25908],{"encoding":904},[123,26626,26627,26643,26644,1975],{},[38,26628,26629,26630],{},"Národní důchod ",[883,26631,26633],{"className":26632},[886],[888,26634,26635],{"xmlns":890},[892,26636,26637,26641],{},[895,26638,26639],{},[898,26640,9128],{},[902,26642,9128],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,26645,26647],{"className":26646},[886],[888,26648,26649],{"xmlns":890},[892,26650,26651,26663],{},[895,26652,26653,26655,26657,26659,26661],{},[898,26654,12114],{},[898,26656,18296],{},[898,26658,3937],{},[1996,26660,2730],{},[898,26662,9128],{},[902,26664,25873],{"encoding":904},[123,26666,26667,26693,26694,1343,26717,1343,26738,1975],{},[38,26668,26669,26670],{},"Funkce spotřeby ",[883,26671,26673],{"className":26672},[886],[888,26674,26675],{"xmlns":890},[892,26676,26677,26691],{},[895,26678,26679,26681,26683,26685,26687,26689],{},[898,26680,2777],{},[1996,26682,1998],{},[898,26684,2777],{},[1996,26686,2005],{"stretchy":2004},[898,26688,9128],{},[1996,26690,2011],{"stretchy":2004},[902,26692,20742],{"encoding":904}," — lineární model ",[883,26695,26697],{"className":26696},[886],[888,26698,26699],{"xmlns":890},[892,26700,26701,26715],{},[895,26702,26703,26705,26707,26709,26711,26713],{},[898,26704,2777],{},[1996,26706,1998],{},[898,26708,207],{},[898,26710,9128],{},[1996,26712,2095],{},[898,26714,2098],{},[902,26716,18922],{"encoding":904},[883,26718,26720],{"className":26719},[886],[888,26721,26722],{"xmlns":890},[892,26723,26724,26736],{},[895,26725,26726,26728,26730,26732,26734],{},[2129,26727,2327],{},[1996,26729,3447],{},[898,26731,207],{},[1996,26733,3447],{},[2129,26735,2278],{},[902,26737,18838],{"encoding":904},[883,26739,26741],{"className":26740},[886],[888,26742,26743],{"xmlns":890},[892,26744,26745,26753],{},[895,26746,26747,26749,26751],{},[898,26748,2098],{},[1996,26750,3408],{},[2129,26752,2327],{},[902,26754,18816],{"encoding":904},[123,26756,26757,7015,26784,26805,26806,1975],{},[38,26758,26759,26760],{},"Funkce úspor ",[883,26761,26763],{"className":26762},[886],[888,26764,26765],{"xmlns":890},[892,26766,26767,26781],{},[895,26768,26769,26771,26773,26775,26777,26779],{},[898,26770,8673],{},[1996,26772,1998],{},[898,26774,8673],{},[1996,26776,2005],{"stretchy":2004},[898,26778,9128],{},[1996,26780,2011],{"stretchy":2004},[902,26782,26783],{"encoding":904},"S = S(Y)",[883,26785,26787],{"className":26786},[886],[888,26788,26789],{"xmlns":890},[892,26790,26791,26803],{},[895,26792,26793,26795,26797,26799,26801],{},[898,26794,9128],{},[1996,26796,1998],{},[898,26798,2777],{},[1996,26800,2095],{},[898,26802,8673],{},[902,26804,12696],{"encoding":904},"; lineární ",[883,26807,26809],{"className":26808},[886],[888,26810,26811],{"xmlns":890},[892,26812,26813,26835],{},[895,26814,26815,26817,26819,26821,26823,26825,26827,26829,26831,26833],{},[898,26816,8673],{},[1996,26818,1998],{},[1996,26820,2005],{"stretchy":2004},[2129,26822,2278],{},[1996,26824,2225],{},[898,26826,207],{},[1996,26828,2011],{"stretchy":2004},[898,26830,9128],{},[1996,26832,2225],{},[898,26834,2098],{},[902,26836,19171],{"encoding":904},[123,26838,26839,7015,26842,1343,26865,1975],{},[38,26840,26841],{},"Autonomní spotřeba\u002Fúspory",[883,26843,26845],{"className":26844},[886],[888,26846,26847],{"xmlns":890},[892,26848,26849,26863],{},[895,26850,26851,26853,26855,26857,26859,26861],{},[898,26852,2777],{},[1996,26854,2005],{"stretchy":2004},[2129,26856,2327],{},[1996,26858,2011],{"stretchy":2004},[1996,26860,1998],{},[898,26862,2098],{},[902,26864,19563],{"encoding":904},[883,26866,26868],{"className":26867},[886],[888,26869,26870],{"xmlns":890},[892,26871,26872,26888],{},[895,26873,26874,26876,26878,26880,26882,26884,26886],{},[898,26875,8673],{},[1996,26877,2005],{"stretchy":2004},[2129,26879,2327],{},[1996,26881,2011],{"stretchy":2004},[1996,26883,1998],{},[1996,26885,2225],{},[898,26887,2098],{},[902,26889,26890],{"encoding":904},"S(0) = -b",[123,26892,26893,26925,26926,3918],{},[38,26894,26895,26896],{},"Mezní sklon ke spotřebě ",[883,26897,26899],{"className":26898},[886],[888,26900,26901],{"xmlns":890},[892,26902,26903,26923],{},[895,26904,26905,26907,26909,26911,26913,26915,26917,26919,26921],{},[898,26906,2818],{},[898,26908,3937],{},[898,26910,2777],{},[1996,26912,1998],{},[898,26914,2194],{"mathvariant":2376},[898,26916,2777],{},[898,26918,4674],{"mathvariant":2376},[898,26920,2194],{"mathvariant":2376},[898,26922,9128],{},[902,26924,26055],{"encoding":904}," (v lineárním modelu ",[883,26927,26929],{"className":26928},[886],[888,26930,26931],{"xmlns":890},[892,26932,26933,26945],{},[895,26934,26935,26937,26939,26941,26943],{},[898,26936,2818],{},[898,26938,3937],{},[898,26940,2777],{},[1996,26942,1998],{},[898,26944,207],{},[902,26946,19891],{"encoding":904},[123,26948,26949,26925,26981,3918],{},[38,26950,26951,26952],{},"Mezní sklon k úsporám ",[883,26953,26955],{"className":26954},[886],[888,26956,26957],{"xmlns":890},[892,26958,26959,26979],{},[895,26960,26961,26963,26965,26967,26969,26971,26973,26975,26977],{},[898,26962,2818],{},[898,26964,3937],{},[898,26966,8673],{},[1996,26968,1998],{},[898,26970,2194],{"mathvariant":2376},[898,26972,8673],{},[898,26974,4674],{"mathvariant":2376},[898,26976,2194],{"mathvariant":2376},[898,26978,9128],{},[902,26980,26085],{"encoding":904},[883,26982,26984],{"className":26983},[886],[888,26985,26986],{"xmlns":890},[892,26987,26988,27004],{},[895,26989,26990,26992,26994,26996,26998,27000,27002],{},[898,26991,2818],{},[898,26993,3937],{},[898,26995,8673],{},[1996,26997,1998],{},[2129,26999,2278],{},[1996,27001,2225],{},[898,27003,207],{},[902,27005,19917],{"encoding":904},[123,27007,27008,2203,27011,27040],{},[38,27009,27010],{},"Vztah",[883,27012,27014],{"className":27013},[886],[888,27015,27016],{"xmlns":890},[892,27017,27018,27038],{},[895,27019,27020,27022,27024,27026,27028,27030,27032,27034,27036],{},[898,27021,2818],{},[898,27023,3937],{},[898,27025,2777],{},[1996,27027,2095],{},[898,27029,2818],{},[898,27031,3937],{},[898,27033,8673],{},[1996,27035,1998],{},[2129,27037,2278],{},[902,27039,26116],{"encoding":904}," (7.5).",[123,27042,27043,27045],{},[38,27044,20585],{}," — rovnováha agregátní poptávky a nabídky.",[123,27047,27048,27051,27052,15794,27073,1975],{},[38,27049,27050],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,27053,27055],{"className":27054},[886],[888,27056,27057],{"xmlns":890},[892,27058,27059,27071],{},[895,27060,27061,27063,27065,27067,27069],{},[898,27062,9128],{},[1996,27064,1998],{},[898,27066,2777],{},[1996,27068,2095],{},[898,27070,12186],{},[902,27072,14746],{"encoding":904},[883,27074,27076],{"className":27075},[886],[888,27077,27078],{"xmlns":890},[892,27079,27080,27116],{},[895,27081,27082,27088,27090,27092,27094,27096,27102,27104,27106,27108,27110,27112,27114],{},[2124,27083,27084,27086],{},[898,27085,9128],{},[898,27087,4252],{},[1996,27089,1998],{},[1996,27091,2005],{"stretchy":2004},[898,27093,2098],{},[1996,27095,2095],{},[2124,27097,27098,27100],{},[898,27099,12186],{},[1996,27101,4354],{},[1996,27103,2011],{"stretchy":2004},[898,27105,4674],{"mathvariant":2376},[1996,27107,2005],{"stretchy":2004},[2129,27109,2278],{},[1996,27111,2225],{},[898,27113,207],{},[1996,27115,2011],{"stretchy":2004},[902,27117,26259],{"encoding":904},[123,27119,27120,27123,27124,1343,27143,15794,27168,1975],{},[38,27121,27122],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,27125,27127],{"className":27126},[886],[888,27128,27129],{"xmlns":890},[892,27130,27131,27141],{},[895,27132,27133,27135,27137,27139],{},[898,27134,2774],{},[1996,27136,2005],{"stretchy":2004},[898,27138,9128],{},[1996,27140,2011],{"stretchy":2004},[902,27142,22221],{"encoding":904},[883,27144,27146],{"className":27145},[886],[888,27147,27148],{"xmlns":890},[892,27149,27150,27166],{},[895,27151,27152,27158,27160,27162,27164],{},[2272,27153,27154,27156],{},[898,27155,9128],{},[898,27157,4183],{},[1996,27159,1998],{},[898,27161,9128],{},[1996,27163,2225],{},[898,27165,2774],{},[902,27167,21720],{"encoding":904},[883,27169,27171],{"className":27170},[886],[888,27172,27173],{"xmlns":890},[892,27174,27175,27191],{},[895,27176,27177,27179,27181,27183,27185,27187,27189],{},[898,27178,9128],{},[1996,27180,1998],{},[898,27182,2777],{},[1996,27184,2095],{},[898,27186,12186],{},[1996,27188,2095],{},[898,27190,12114],{},[902,27192,21691],{"encoding":904},[123,27194,27195,27198,27199,27220,27221,15794,27245,1975],{},[38,27196,27197],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,27200,27202],{"className":27201},[886],[888,27203,27204],{"xmlns":890},[892,27205,27206,27218],{},[895,27207,27208,27210,27212,27214,27216],{},[898,27209,12322],{},[1996,27211,1998],{},[898,27213,23255],{},[1996,27215,2225],{},[898,27217,2818],{},[902,27219,23262],{"encoding":904},", importem ",[883,27222,27224],{"className":27223},[886],[888,27225,27226],{"xmlns":890},[892,27227,27228,27242],{},[895,27229,27230,27232,27234,27240],{},[898,27231,2818],{},[1996,27233,2005],{"stretchy":2004},[2272,27235,27236,27238],{},[898,27237,9128],{},[898,27239,4183],{},[1996,27241,2011],{"stretchy":2004},[902,27243,27244],{"encoding":904},"M(Y_D)",[883,27246,27248],{"className":27247},[886],[888,27249,27250],{"xmlns":890},[892,27251,27252,27276],{},[895,27253,27254,27256,27258,27260,27262,27264,27266,27268,27270,27272,27274],{},[898,27255,9128],{},[1996,27257,1998],{},[898,27259,2777],{},[1996,27261,2095],{},[898,27263,12186],{},[1996,27265,2095],{},[898,27267,12114],{},[1996,27269,2095],{},[898,27271,23255],{},[1996,27273,2225],{},[898,27275,2818],{},[902,27277,27278],{"encoding":904},"Y = C + I + G + B - M",[123,27280,27281,7015,27284,26473],{},[38,27282,27283],{},"Multiplikátor investic",[883,27285,27287],{"className":27286},[886],[888,27288,27289],{"xmlns":890},[892,27290,27291,27339],{},[895,27292,27293,27295,27301,27303,27305,27311,27313,27315,27317,27319,27321,27323,27325,27327,27329,27331,27333,27335,27337],{},[898,27294,9872],{"mathvariant":2376},[2124,27296,27297,27299],{},[898,27298,9128],{},[898,27300,4252],{},[898,27302,4674],{"mathvariant":2376},[898,27304,9872],{"mathvariant":2376},[2124,27306,27307,27309],{},[898,27308,12186],{},[1996,27310,4354],{},[1996,27312,1998],{},[2129,27314,2278],{},[898,27316,4674],{"mathvariant":2376},[1996,27318,2005],{"stretchy":2004},[2129,27320,2278],{},[1996,27322,2225],{},[898,27324,207],{},[1996,27326,2011],{"stretchy":2004},[1996,27328,1998],{},[2129,27330,2278],{},[898,27332,4674],{"mathvariant":2376},[898,27334,2818],{},[898,27336,3937],{},[898,27338,8673],{},[902,27340,26472],{"encoding":904},[123,27342,27343,7015,27374,1343,27391,27408],{},[38,27344,15729,27345],{},[883,27346,27348],{"className":27347},[886],[888,27349,27350],{"xmlns":890},[892,27351,27352,27372],{},[895,27353,27354,27356,27358,27360,27362,27364,27366,27368,27370],{},[898,27355,12186],{},[1996,27357,2005],{"stretchy":2004},[898,27359,12043],{},[1996,27361,2011],{"stretchy":2004},[1996,27363,1998],{},[898,27365,2142],{},[898,27367,12043],{},[1996,27369,2095],{},[898,27371,2194],{},[902,27373,15759],{"encoding":904},[883,27375,27377],{"className":27376},[886],[888,27378,27379],{"xmlns":890},[892,27380,27381,27389],{},[895,27382,27383,27385,27387],{},[898,27384,2142],{},[1996,27386,3447],{},[2129,27388,2327],{},[902,27390,12517],{"encoding":904},[883,27392,27394],{"className":27393},[886],[888,27395,27396],{"xmlns":890},[892,27397,27398,27406],{},[895,27399,27400,27402,27404],{},[898,27401,2194],{},[1996,27403,3408],{},[2129,27405,2327],{},[902,27407,12496],{"encoding":904},"; klesající.",[123,27410,27411,27413,27414,27416,27417,27466],{},[38,27412,15848],{}," — rovnováha na trhu zboží (",[614,27415,12056],{},"); ",[883,27418,27420],{"className":27419},[886],[888,27421,27422],{"xmlns":890},[892,27423,27424,27464],{},[895,27425,27426,27428,27430,27442,27444,27446],{},[898,27427,9128],{},[1996,27429,1998],{},[2329,27431,27432,27434],{},[898,27433,2142],{},[895,27435,27436,27438,27440],{},[2129,27437,2278],{},[1996,27439,2225],{},[898,27441,207],{},[898,27443,12043],{},[1996,27445,2095],{},[2329,27447,27448,27456],{},[895,27449,27450,27452,27454],{},[898,27451,2098],{},[1996,27453,2095],{},[898,27455,2194],{},[895,27457,27458,27460,27462],{},[2129,27459,2278],{},[1996,27461,2225],{},[898,27463,207],{},[902,27465,15901],{"encoding":904}," (7.14); klesající.",[123,27468,27469,27471,27472,27416,27474,27519],{},[38,27470,16047],{}," — rovnováha na trhu peněz (",[614,27473,12063],{},[883,27475,27477],{"className":27476},[886],[888,27478,27479],{"xmlns":890},[892,27480,27481,27517],{},[895,27482,27483,27489,27491,27497,27499,27501,27507,27509,27511],{},[2124,27484,27485,27487],{},[898,27486,2818],{},[1996,27488,4354],{},[1996,27490,1998],{},[2272,27492,27493,27495],{},[898,27494,13239],{},[2129,27496,2278],{},[898,27498,9128],{},[1996,27500,2095],{},[2272,27502,27503,27505],{},[898,27504,13239],{},[2129,27506,2131],{},[898,27508,12043],{},[1996,27510,2095],{},[2272,27512,27513,27515],{},[898,27514,13239],{},[2129,27516,2173],{},[902,27518,16095],{"encoding":904}," (7.15); rostoucí.",[123,27521,27522,7015,27525,1975],{},[38,27523,27524],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,27526,27528],{"className":27527},[886],[888,27529,27530],{"xmlns":890},[892,27531,27532,27556],{},[895,27533,27534,27540,27542,27548,27550],{},[2124,27535,27536,27538],{},[898,27537,2818],{},[898,27539,4183],{},[1996,27541,1998],{},[2272,27543,27544,27546],{},[898,27545,9795],{},[2129,27547,2278],{},[1996,27549,2095],{},[2272,27551,27552,27554],{},[898,27553,9795],{},[2129,27555,2131],{},[902,27557,27558],{"encoding":904},"M^D = L_1 + L_2",[123,27560,27561,16105,27563,13982,27576,3885,27591,27606,27607,1975],{},[38,27562,945],{},[883,27564,27566],{"className":27565},[886],[888,27567,27568],{"xmlns":890},[892,27569,27570,27574],{},[895,27571,27572],{},[898,27573,4252],{},[902,27575,4252],{"encoding":904},[883,27577,27579],{"className":27578},[886],[888,27580,27581],{"xmlns":890},[892,27582,27583,27589],{},[895,27584,27585,27587],{},[898,27586,12186],{},[898,27588,8673],{},[902,27590,12053],{"encoding":904},[883,27592,27594],{"className":27593},[886],[888,27595,27596],{"xmlns":890},[892,27597,27598,27604],{},[895,27599,27600,27602],{},[898,27601,9795],{},[898,27603,2818],{},[902,27605,12060],{"encoding":904}," určuje ",[883,27608,27610],{"className":27609},[886],[888,27611,27612],{"xmlns":890},[892,27613,27614,27634],{},[895,27615,27616,27618,27624,27626,27632],{},[1996,27617,2005],{"stretchy":2004},[2124,27619,27620,27622],{},[898,27621,9128],{},[898,27623,4252],{},[1996,27625,2286],{"separator":2285},[2124,27627,27628,27630],{},[898,27629,12043],{},[898,27631,4252],{},[1996,27633,2011],{"stretchy":2004},[902,27635,12097],{"encoding":904},[115,27637,3792],{"id":3791},[120,27639,27640,27647,27654],{},[123,27641,27642,2203,27644],{},[38,27643,16206],{},[207,27645,16210],{"className":27646,"dataFsResolvedFilePath":1960,"href":1961},[210],[123,27648,27649,2203,27651],{},[38,27650,16215],{},[207,27652,1931],{"className":27653,"dataFsResolvedFilePath":868,"href":869},[210],[123,27655,27656,27658],{},[38,27657,16233],{},[120,27659,27660,27666,27672,27678],{},[123,27661,27662,27665],{},[207,27663,16274],{"className":27664,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,27667,27668,27671],{},[207,27669,16241],{"className":27670,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,27673,27674,27677],{},[207,27675,2950],{"className":27676,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,27679,27680,27683,27684,1343,27701,27718],{},[207,27681,1145],{"className":27682,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,27685,27687],{"className":27686},[886],[888,27688,27689],{"xmlns":890},[892,27690,27691,27699],{},[895,27692,27693,27695,27697],{},[898,27694,2818],{},[898,27696,3937],{},[898,27698,2777],{},[902,27700,18047],{"encoding":904},[883,27702,27704],{"className":27703},[886],[888,27705,27706],{"xmlns":890},[892,27707,27708,27716],{},[895,27709,27710,27712,27714],{},[898,27711,2818],{},[898,27713,3937],{},[898,27715,8673],{},[902,27717,19661],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":27720},[27721,27722,27723,27724,27729,27732,27733,27740,27745,27750,27753,27754,27755,27756],{"id":12007,"depth":642,"text":12008},{"id":18156,"depth":642,"text":18157},{"id":18276,"depth":642,"text":18277},{"id":18529,"depth":642,"text":18530,"children":27725},[27726,27727,27728],{"id":18533,"depth":649,"text":18534},{"id":18745,"depth":649,"text":18746},{"id":19253,"depth":649,"text":19254},{"id":19573,"depth":642,"text":19574,"children":27730},[27731],{"id":20089,"depth":649,"text":20090},{"id":20584,"depth":642,"text":20585},{"id":20611,"depth":642,"text":20612,"children":27734},[27735,27736,27737,27739],{"id":20622,"depth":649,"text":20623},{"id":20692,"depth":649,"text":20693},{"id":20876,"depth":649,"text":27738},"Výpočet YEY^E",{"id":21019,"depth":649,"text":21020},{"id":21397,"depth":642,"text":21398,"children":27741},[27742,27743,27744],{"id":21401,"depth":649,"text":20623},{"id":21850,"depth":649,"text":20693},{"id":22506,"depth":649,"text":22507},{"id":23293,"depth":642,"text":23294,"children":27746},[27747,27748,27749],{"id":23297,"depth":649,"text":20623},{"id":23442,"depth":649,"text":20693},{"id":23712,"depth":649,"text":23713},{"id":24636,"depth":642,"text":24637,"children":27751},[27752],{"id":24832,"depth":649,"text":24833},{"id":25382,"depth":642,"text":25383},{"id":25842,"depth":642,"text":25843},{"id":15721,"depth":642,"text":15722},{"id":3791,"depth":642,"text":3792},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,16227,1143,27763,27764,27765,16274,17885],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":27768,"title":27769,"body":27770,"course":1128,"courses":659,"created":9556,"description":641,"extension":661,"meta":36750,"navigation":664,"path":36751,"seo":36752,"sources":36753,"stem":36754,"tags":36755,"type":3857,"updated":677,"__hash__":36760},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":27771,"toc":36719},[27772,27775,27777,28006,28010,28063,28133,28245,28404,28408,28524,28528,28531,28653,28656,28849,28873,28941,29105,29123,29189,29567,29571,29578,29822,29878,29882,29947,30065,30197,30229,30349,30431,30434,30556,30749,30970,30974,31014,31119,31176,31276,31453,31583,31636,31639,31726,31730,31906,31910,31913,31998,32001,32058,32163,32167,32288,32291,32474,32477,32585,32794,33114,33162,33235,33309,33311,33535,33770,34038,34042,34045,34150,34207,34241,34288,34321,34405,34407,34639,34772,34849,34971,35126,35130,35271,35278,35502,35513,35517,35521,35626,35768,35878,35977,35981,36140,36250,36252,36645,36647],[12,27773,27769],{"id":27774},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,27776,12008],{"id":12007},[724,27778,27779,27781,27782,27816,27817,27820,27821,27852,27853,27899,27900,27903,27904,27946,27947,27965,27966,27970,27971,28001,28002,28005],{},[38,27780,913],{}," řeší, jaký svazek zboží ",[883,27783,27785],{"className":27784},[886],[888,27786,27787],{"xmlns":890},[892,27788,27789,27813],{},[895,27790,27791,27793,27801,27803,27811],{},[1996,27792,2486],{"stretchy":2004},[9166,27794,27795,27797,27799],{},[898,27796,2789],{},[2129,27798,2278],{},[1996,27800,4354],{},[1996,27802,2286],{"separator":2285},[9166,27804,27805,27807,27809],{},[898,27806,2789],{},[2129,27808,2131],{},[1996,27810,4354],{},[1996,27812,2501],{"stretchy":2004},[902,27814,27815],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,27818,27819],{},"primární úloha"," — maximalizace užitečnosti ",[883,27822,27824],{"className":27823},[886],[888,27825,27826],{"xmlns":890},[892,27827,27828,27850],{},[895,27829,27830,27832,27834,27840,27842,27848],{},[898,27831,900],{},[1996,27833,2005],{"stretchy":2004},[2272,27835,27836,27838],{},[898,27837,2789],{},[2129,27839,2278],{},[1996,27841,2286],{"separator":2285},[2272,27843,27844,27846],{},[898,27845,2789],{},[2129,27847,2131],{},[1996,27849,2011],{"stretchy":2004},[902,27851,16345],{"encoding":904}," při rozpočtovém omezení ",[883,27854,27856],{"className":27855},[886],[888,27857,27858],{"xmlns":890},[892,27859,27860,27896],{},[895,27861,27862,27868,27870,27876,27882,27884,27890],{},[2124,27863,27864,27866],{},[898,27865,9128],{},[1996,27867,4354],{},[1996,27869,1998],{},[2272,27871,27872,27874],{},[898,27873,3937],{},[2129,27875,2278],{},[2272,27877,27878,27880],{},[898,27879,2789],{},[2129,27881,2278],{},[1996,27883,2095],{},[2272,27885,27886,27888],{},[898,27887,3937],{},[2129,27889,2131],{},[2272,27891,27892,27894],{},[898,27893,2789],{},[2129,27895,2131],{},[902,27897,27898],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,27901,27902],{},"duální úloha"," — minimalizace výdajů ",[883,27905,27907],{"className":27906},[886],[888,27908,27909],{"xmlns":890},[892,27910,27911,27943],{},[895,27912,27913,27915,27917,27923,27929,27931,27937],{},[898,27914,4252],{},[1996,27916,1998],{},[2272,27918,27919,27921],{},[898,27920,3937],{},[2129,27922,2278],{},[2272,27924,27925,27927],{},[898,27926,2789],{},[2129,27928,2278],{},[1996,27930,2095],{},[2272,27932,27933,27935],{},[898,27934,3937],{},[2129,27936,2131],{},[2272,27938,27939,27941],{},[898,27940,2789],{},[2129,27942,2131],{},[902,27944,27945],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,27948,27950],{"className":27949},[886],[888,27951,27952],{"xmlns":890},[892,27953,27954,27962],{},[895,27955,27956],{},[2124,27957,27958,27960],{},[898,27959,900],{},[1996,27961,4354],{},[902,27963,27964],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,27967,27969],{"className":27968,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,27972,27974],{"className":27973},[886],[888,27975,27976],{"xmlns":890},[892,27977,27978,27998],{},[895,27979,27980,27982,27984,27990,27992],{},[2288,27981,10603],{},[1996,27983,1998],{},[2272,27985,27986,27988],{},[898,27987,3937],{},[2129,27989,2278],{},[898,27991,4674],{"mathvariant":2376},[2272,27993,27994,27996],{},[898,27995,3937],{},[2129,27997,2131],{},[902,27999,28000],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,28003,28004],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,28007,28009],{"id":28008},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,28011,28012,28013,28031,28032,28062],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,28014,28016],{"className":28015},[886],[888,28017,28018],{"xmlns":890},[892,28019,28020,28028],{},[895,28021,28022],{},[2124,28023,28024,28026],{},[898,28025,9128],{},[1996,28027,4354],{},[902,28029,28030],{"encoding":904},"Y^*"," a ceny ",[883,28033,28035],{"className":28034},[886],[888,28036,28037],{"xmlns":890},[892,28038,28039,28059],{},[895,28040,28041,28049,28051],{},[9166,28042,28043,28045,28047],{},[898,28044,3937],{},[2129,28046,2278],{},[1996,28048,4354],{},[1996,28050,2286],{"separator":2285},[9166,28052,28053,28055,28057],{},[898,28054,3937],{},[2129,28056,2131],{},[1996,28058,4354],{},[902,28060,28061],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,28064,28066],{"className":28065},[886],[888,28067,28069],{"xmlns":890,"display":28068},"block",[892,28070,28071,28130],{},[20756,28072,28074],{"width":28073},"100%",[20761,28075,28076,28079,28123,28125],{},[20764,28077],{"width":28078},"50%",[20764,28080,28081],{},[895,28082,28083,28089,28091,28099,28105,28107,28115,28121],{},[2124,28084,28085,28087],{},[898,28086,9128],{},[1996,28088,4354],{},[1996,28090,1998],{},[9166,28092,28093,28095,28097],{},[898,28094,3937],{},[2129,28096,2278],{},[1996,28098,4354],{},[2272,28100,28101,28103],{},[898,28102,2789],{},[2129,28104,2278],{},[1996,28106,2095],{},[9166,28108,28109,28111,28113],{},[898,28110,3937],{},[2129,28112,2131],{},[1996,28114,4354],{},[2272,28116,28117,28119],{},[898,28118,2789],{},[2129,28120,2131],{},[1996,28122,2286],{"separator":2285},[20764,28124],{"width":28078},[20764,28126,28127],{},[2288,28128,28129],{},"(6.12)",[902,28131,28132],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,28134,28135,28136,28139,28140,3885,28176,28212,28213,28226,28227,28241,28242,1975],{},"geometricky ",[38,28137,28138],{},"rozpočtová přímka (budget line)"," procházející body ",[883,28141,28143],{"className":28142},[886],[888,28144,28145],{"xmlns":890},[892,28146,28147,28173],{},[895,28148,28149,28151,28157,28159,28167,28169,28171],{},[1996,28150,2486],{"stretchy":2004},[2124,28152,28153,28155],{},[898,28154,9128],{},[1996,28156,4354],{},[898,28158,4674],{"mathvariant":2376},[9166,28160,28161,28163,28165],{},[898,28162,3937],{},[2129,28164,2278],{},[1996,28166,4354],{},[1996,28168,2286],{"separator":2285},[2129,28170,2327],{},[1996,28172,2501],{"stretchy":2004},[902,28174,28175],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,28177,28179],{"className":28178},[886],[888,28180,28181],{"xmlns":890},[892,28182,28183,28209],{},[895,28184,28185,28187,28189,28191,28197,28199,28207],{},[1996,28186,2486],{"stretchy":2004},[2129,28188,2327],{},[1996,28190,2286],{"separator":2285},[2124,28192,28193,28195],{},[898,28194,9128],{},[1996,28196,4354],{},[898,28198,4674],{"mathvariant":2376},[9166,28200,28201,28203,28205],{},[898,28202,3937],{},[2129,28204,2131],{},[1996,28206,4354],{},[1996,28208,2501],{"stretchy":2004},[902,28210,28211],{"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 ",[883,28214,28216],{"className":28215},[886],[888,28217,28218],{"xmlns":890},[892,28219,28220,28224],{},[895,28221,28222],{},[898,28223,900],{},[902,28225,900],{"encoding":904},", indiferenční křivky a ",[883,28228,28230],{"className":28229},[886],[888,28231,28232],{"xmlns":890},[892,28233,28234,28238],{},[895,28235,28236],{},[2288,28237,10603],{},[902,28239,28240],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,28243,880],{"className":28244,"dataFsResolvedFilePath":878,"href":879},[210],[3867,28246,28247],{},[724,28248,28249,28251,28252,28255,28256,28269,28270,28272,28273,28286,28287,2203,28290,28330,28331,28348,28349,28366,28367,28384,28385,28403],{},[883,28250,4412],{}," Pozor — dvě úlohy, totéž řešení\n",[38,28253,28254],{},"Primární úloha"," (max ",[883,28257,28259],{"className":28258},[886],[888,28260,28261],{"xmlns":890},[892,28262,28263,28267],{},[895,28264,28265],{},[898,28266,900],{},[902,28268,900],{"encoding":904}," při pevném rozpočtu) a ",[38,28271,27902],{}," (min ",[883,28274,28276],{"className":28275},[886],[888,28277,28278],{"xmlns":890},[892,28279,28280,28284],{},[895,28281,28282],{},[898,28283,4252],{},[902,28285,4252],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,28288,28289],{},"tentýž bod",[883,28291,28293],{"className":28292},[886],[888,28294,28295],{"xmlns":890},[892,28296,28297,28327],{},[895,28298,28299,28305,28307,28315,28317,28325],{},[2124,28300,28301,28303],{},[898,28302,2789],{},[1996,28304,4354],{},[1996,28306,2486],{"stretchy":2004},[9166,28308,28309,28311,28313],{},[898,28310,2789],{},[2129,28312,2278],{},[1996,28314,4354],{},[1996,28316,2286],{"separator":2285},[9166,28318,28319,28321,28323],{},[898,28320,2789],{},[2129,28322,2131],{},[1996,28324,4354],{},[1996,28326,2501],{"stretchy":2004},[902,28328,28329],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,28332,28334],{"className":28333},[886],[888,28335,28336],{"xmlns":890},[892,28337,28338,28346],{},[895,28339,28340],{},[2124,28341,28342,28344],{},[898,28343,9128],{},[1996,28345,4354],{},[902,28347,28030],{"encoding":904}," a hledáme maximální ",[883,28350,28352],{"className":28351},[886],[888,28353,28354],{"xmlns":890},[892,28355,28356,28364],{},[895,28357,28358],{},[2124,28359,28360,28362],{},[898,28361,900],{},[1996,28363,4354],{},[902,28365,27964],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,28368,28370],{"className":28369},[886],[888,28371,28372],{"xmlns":890},[892,28373,28374,28382],{},[895,28375,28376],{},[2124,28377,28378,28380],{},[898,28379,900],{},[1996,28381,4354],{},[902,28383,27964],{"encoding":904}," a hledáme minimální ",[883,28386,28388],{"className":28387},[886],[888,28389,28390],{"xmlns":890},[892,28391,28392,28400],{},[895,28393,28394],{},[2124,28395,28396,28398],{},[898,28397,4252],{},[1996,28399,4354],{},[902,28401,28402],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,28405,28407],{"id":28406},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,28409,28410,28411,28442,28443,28519,28520,1975],{},"Úlohou je najít maximum ",[883,28412,28414],{"className":28413},[886],[888,28415,28416],{"xmlns":890},[892,28417,28418,28440],{},[895,28419,28420,28422,28424,28430,28432,28438],{},[898,28421,900],{},[1996,28423,2005],{"stretchy":2004},[2272,28425,28426,28428],{},[898,28427,2789],{},[2129,28429,2278],{},[1996,28431,2286],{"separator":2285},[2272,28433,28434,28436],{},[898,28435,2789],{},[2129,28437,2131],{},[1996,28439,2011],{"stretchy":2004},[902,28441,16345],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,28444,28446],{"className":28445},[886],[888,28447,28448],{"xmlns":890},[892,28449,28450,28516],{},[895,28451,28452,28454,28456,28462,28464,28470,28472,28474,28480,28482,28490,28496,28498,28506,28512,28514],{},[898,28453,11041],{},[1996,28455,2005],{"stretchy":2004},[2272,28457,28458,28460],{},[898,28459,2789],{},[2129,28461,2278],{},[1996,28463,2286],{"separator":2285},[2272,28465,28466,28468],{},[898,28467,2789],{},[2129,28469,2131],{},[1996,28471,2011],{"stretchy":2004},[1996,28473,1998],{},[2124,28475,28476,28478],{},[898,28477,9128],{},[1996,28479,4354],{},[1996,28481,2225],{},[9166,28483,28484,28486,28488],{},[898,28485,3937],{},[2129,28487,2278],{},[1996,28489,4354],{},[2272,28491,28492,28494],{},[898,28493,2789],{},[2129,28495,2278],{},[1996,28497,2225],{},[9166,28499,28500,28502,28504],{},[898,28501,3937],{},[2129,28503,2131],{},[1996,28505,4354],{},[2272,28507,28508,28510],{},[898,28509,2789],{},[2129,28511,2131],{},[1996,28513,1998],{},[2129,28515,2327],{},[902,28517,28518],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,28521,28523],{"className":28522,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,28525,28527],{"id":28526},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,28529,28530],{},"Sestavíme",[883,28532,28534],{"className":28533},[886],[888,28535,28536],{"xmlns":890,"display":28068},[892,28537,28538,28650],{},[20756,28539,28540],{"width":28073},[20761,28541,28542,28544,28643,28645],{},[20764,28543],{"width":28078},[20764,28545,28546],{},[895,28547,28548,28551,28553,28559,28561,28567,28569,28571,28573,28575,28577,28579,28585,28587,28593,28595,28597,28599,28601,28607,28609,28617,28623,28625,28633,28639,28641],{},[898,28549,9795],{"mathvariant":28550},"script",[1996,28552,2005],{"stretchy":2004},[2272,28554,28555,28557],{},[898,28556,2789],{},[2129,28558,2278],{},[1996,28560,2286],{"separator":2285},[2272,28562,28563,28565],{},[898,28564,2789],{},[2129,28566,2131],{},[1996,28568,2286],{"separator":2285},[898,28570,16445],{},[1996,28572,2011],{"stretchy":2004},[1996,28574,1998],{},[898,28576,900],{},[1996,28578,2005],{"stretchy":2004},[2272,28580,28581,28583],{},[898,28582,2789],{},[2129,28584,2278],{},[1996,28586,2286],{"separator":2285},[2272,28588,28589,28591],{},[898,28590,2789],{},[2129,28592,2131],{},[1996,28594,2011],{"stretchy":2004},[1996,28596,2095],{},[898,28598,16445],{},[1996,28600,2005],{"stretchy":2004},[2124,28602,28603,28605],{},[898,28604,9128],{},[1996,28606,4354],{},[1996,28608,2225],{},[9166,28610,28611,28613,28615],{},[898,28612,3937],{},[2129,28614,2278],{},[1996,28616,4354],{},[2272,28618,28619,28621],{},[898,28620,2789],{},[2129,28622,2278],{},[1996,28624,2225],{},[9166,28626,28627,28629,28631],{},[898,28628,3937],{},[2129,28630,2131],{},[1996,28632,4354],{},[2272,28634,28635,28637],{},[898,28636,2789],{},[2129,28638,2131],{},[1996,28640,2011],{"stretchy":2004},[898,28642,1975],{"mathvariant":2376},[20764,28644],{"width":28078},[20764,28646,28647],{},[2288,28648,28649],{},"(6.13)",[902,28651,28652],{"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}",[724,28654,28655],{},"Soustava prvního řádu:",[883,28657,28659],{"className":28658},[886],[888,28660,28661],{"xmlns":890,"display":28068},[892,28662,28663,28846],{},[20756,28664,28665],{"width":28073},[20761,28666,28667,28669,28839,28841],{},[20764,28668],{"width":28078},[20764,28670,28671],{},[20756,28672,28673,28723,28773],{"rowspacing":20758,"columnalign":20759,"columnspacing":2377},[20761,28674,28675,28687],{},[20764,28676,28677],{},[2325,28678,28679],{"scriptlevel":2327,"displaystyle":2285},[9166,28680,28681,28683,28685],{},[898,28682,9795],{"mathvariant":28550},[2129,28684,2278],{},[1996,28686,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[20764,28688,28689],{},[2325,28690,28691],{"scriptlevel":2327,"displaystyle":2285},[895,28692,28693,28695,28697,28705,28707,28709,28717,28719,28721],{},[895,28694],{},[1996,28696,1998],{},[9166,28698,28699,28701,28703],{},[898,28700,900],{},[2129,28702,2278],{},[1996,28704,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,28706,2225],{},[898,28708,16445],{},[9166,28710,28711,28713,28715],{},[898,28712,3937],{},[2129,28714,2278],{},[1996,28716,4354],{},[1996,28718,1998],{},[2129,28720,2327],{},[1996,28722,2286],{"separator":2285},[20761,28724,28725,28737],{},[20764,28726,28727],{},[2325,28728,28729],{"scriptlevel":2327,"displaystyle":2285},[9166,28730,28731,28733,28735],{},[898,28732,9795],{"mathvariant":28550},[2129,28734,2131],{},[1996,28736,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[20764,28738,28739],{},[2325,28740,28741],{"scriptlevel":2327,"displaystyle":2285},[895,28742,28743,28745,28747,28755,28757,28759,28767,28769,28771],{},[895,28744],{},[1996,28746,1998],{},[9166,28748,28749,28751,28753],{},[898,28750,900],{},[2129,28752,2131],{},[1996,28754,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,28756,2225],{},[898,28758,16445],{},[9166,28760,28761,28763,28765],{},[898,28762,3937],{},[2129,28764,2131],{},[1996,28766,4354],{},[1996,28768,1998],{},[2129,28770,2327],{},[1996,28772,2286],{"separator":2285},[20761,28774,28775,28787],{},[20764,28776,28777],{},[2325,28778,28779],{"scriptlevel":2327,"displaystyle":2285},[9166,28780,28781,28783,28785],{},[898,28782,9795],{"mathvariant":28550},[898,28784,16445],{},[1996,28786,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[20764,28788,28789],{},[2325,28790,28791],{"scriptlevel":2327,"displaystyle":2285},[895,28792,28793,28795,28797,28803,28805,28813,28819,28821,28829,28835,28837],{},[895,28794],{},[1996,28796,1998],{},[2124,28798,28799,28801],{},[898,28800,9128],{},[1996,28802,4354],{},[1996,28804,2225],{},[9166,28806,28807,28809,28811],{},[898,28808,3937],{},[2129,28810,2278],{},[1996,28812,4354],{},[2272,28814,28815,28817],{},[898,28816,2789],{},[2129,28818,2278],{},[1996,28820,2225],{},[9166,28822,28823,28825,28827],{},[898,28824,3937],{},[2129,28826,2131],{},[1996,28828,4354],{},[2272,28830,28831,28833],{},[898,28832,2789],{},[2129,28834,2131],{},[1996,28836,1998],{},[2129,28838,12462],{},[20764,28840],{"width":28078},[20764,28842,28843],{},[2288,28844,28845],{},"(6.14)",[902,28847,28848],{"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}",[724,28850,28851,28852,28855,28856,28869,28870,2704],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,28853,28854],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,28857,28859],{"className":28858},[886],[888,28860,28861],{"xmlns":890},[892,28862,28863,28867],{},[895,28864,28865],{},[898,28866,16445],{},[902,28868,16498],{"encoding":904}," dostáváme ",[38,28871,28872],{},"podmínku optimality",[883,28874,28876],{"className":28875},[886],[888,28877,28878],{"xmlns":890,"display":28068},[892,28879,28880,28938],{},[895,28881,28882],{},[12834,28883,28884],{"notation":12836},[2325,28885,28886],{"scriptlevel":2327,"displaystyle":2004},[2325,28887,28888],{"scriptlevel":2327,"displaystyle":2004},[2325,28889,28890],{"scriptlevel":2327,"displaystyle":2285},[895,28891,28892,28894,28896,28898,28916,28918,28936],{},[2288,28893,3984],{},[2288,28895,10603],{},[1996,28897,1998],{},[2329,28899,28900,28908],{},[9166,28901,28902,28904,28906],{},[898,28903,900],{},[2129,28905,2278],{},[1996,28907,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[9166,28909,28910,28912,28914],{},[898,28911,900],{},[2129,28913,2131],{},[1996,28915,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,28917,1998],{},[2329,28919,28920,28928],{},[9166,28921,28922,28924,28926],{},[898,28923,3937],{},[2129,28925,2278],{},[1996,28927,4354],{},[9166,28929,28930,28932,28934],{},[898,28931,3937],{},[2129,28933,2131],{},[1996,28935,4354],{},[2288,28937,3984],{},[902,28939,28940],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[3867,28942,28943],{},[724,28944,28945,28947,28948,28982,28983,28986,28987,29005,29006,29024,29025,29055,29056,29073,29074,29104],{},[883,28946,4155],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,28949,28951],{"className":28950},[886],[888,28952,28953],{"xmlns":890},[892,28954,28955,28979],{},[895,28956,28957,28959,28961,28969,28971],{},[2288,28958,10603],{},[1996,28960,1998],{},[9166,28962,28963,28965,28967],{},[898,28964,3937],{},[2129,28966,2278],{},[1996,28968,4354],{},[898,28970,4674],{"mathvariant":2376},[9166,28972,28973,28975,28977],{},[898,28974,3937],{},[2129,28976,2131],{},[1996,28978,4354],{},[902,28980,28981],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,28984,28985],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,28988,28990],{"className":28989},[886],[888,28991,28992],{"xmlns":890},[892,28993,28994,29002],{},[895,28995,28996],{},[2272,28997,28998,29000],{},[898,28999,2789],{},[2129,29001,2278],{},[902,29003,29004],{"encoding":904},"Q_1"," za ",[883,29007,29009],{"className":29008},[886],[888,29010,29011],{"xmlns":890},[892,29012,29013,29021],{},[895,29014,29015],{},[2272,29016,29017,29019],{},[898,29018,2789],{},[2129,29020,2131],{},[902,29022,29023],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,29026,29028],{"className":29027},[886],[888,29029,29030],{"xmlns":890},[892,29031,29032,29052],{},[895,29033,29034,29036,29038,29044,29046],{},[2288,29035,10603],{},[1996,29037,3408],{},[2272,29039,29040,29042],{},[898,29041,3937],{},[2129,29043,2278],{},[898,29045,4674],{"mathvariant":2376},[2272,29047,29048,29050],{},[898,29049,3937],{},[2129,29051,2131],{},[902,29053,29054],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,29057,29059],{"className":29058},[886],[888,29060,29061],{"xmlns":890},[892,29062,29063,29071],{},[895,29064,29065],{},[2272,29066,29067,29069],{},[898,29068,2789],{},[2129,29070,2278],{},[902,29072,29004],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,29075,29077],{"className":29076},[886],[888,29078,29079],{"xmlns":890},[892,29080,29081,29101],{},[895,29082,29083,29085,29087,29093,29095],{},[2288,29084,10603],{},[1996,29086,3447],{},[2272,29088,29089,29091],{},[898,29090,3937],{},[2129,29092,2278],{},[898,29094,4674],{"mathvariant":2376},[2272,29096,29097,29099],{},[898,29098,3937],{},[2129,29100,2131],{},[902,29102,29103],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,29106,29108,29109,29122],{"id":29107},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,29110,29112],{"className":29111},[886],[888,29113,29114],{"xmlns":890},[892,29115,29116,29120],{},[895,29117,29118],{},[898,29119,16445],{},[902,29121,16498],{"encoding":904}," — mezní užitečnost důchodu",[724,29124,29125,29126,29144,29145,29148,29149,29166,29167,29184,29185,29188],{},"Lagrangeův multiplikátor ",[883,29127,29129],{"className":29128},[886],[888,29130,29131],{"xmlns":890},[892,29132,29133,29141],{},[895,29134,29135],{},[2124,29136,29137,29139],{},[898,29138,16445],{},[1996,29140,4354],{},[902,29142,29143],{"encoding":904},"\\lambda^*"," představuje ",[38,29146,29147],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,29150,29152],{"className":29151},[886],[888,29153,29154],{"xmlns":890},[892,29155,29156,29164],{},[895,29157,29158],{},[2124,29159,29160,29162],{},[898,29161,900],{},[1996,29163,4354],{},[902,29165,27964],{"encoding":904}," při jednotkové změně důchodu ",[883,29168,29170],{"className":29169},[886],[888,29171,29172],{"xmlns":890},[892,29173,29174,29182],{},[895,29175,29176],{},[2124,29177,29178,29180],{},[898,29179,9128],{},[1996,29181,4354],{},[902,29183,28030],{"encoding":904},". Je to ",[38,29186,29187],{},"stínová cena"," rozpočtového omezení.",[3867,29190,29191,29196],{},[724,29192,29193,29195],{},[883,29194,4572],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,29197,29198,29258,29345,29381,29468],{},[123,29199,29200,29203,29204,1975],{},[38,29201,29202],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,29205,29207],{"className":29206},[886],[888,29208,29209],{"xmlns":890},[892,29210,29211,29255],{},[895,29212,29213,29219,29221,29229,29235,29237,29245,29251,29253],{},[2124,29214,29215,29217],{},[898,29216,9128],{},[1996,29218,4354],{},[1996,29220,2225],{},[9166,29222,29223,29225,29227],{},[898,29224,3937],{},[2129,29226,2278],{},[1996,29228,4354],{},[2272,29230,29231,29233],{},[898,29232,2789],{},[2129,29234,2278],{},[1996,29236,2225],{},[9166,29238,29239,29241,29243],{},[898,29240,3937],{},[2129,29242,2131],{},[1996,29244,4354],{},[2272,29246,29247,29249],{},[898,29248,2789],{},[2129,29250,2131],{},[1996,29252,1998],{},[2129,29254,2327],{},[902,29256,29257],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,29259,29260,2203,29263,1975],{},[38,29261,29262],{},"Sestav Lagrangeovu funkci",[883,29264,29266],{"className":29265},[886],[888,29267,29268],{"xmlns":890},[892,29269,29270,29342],{},[895,29271,29272,29274,29276,29278,29280,29286,29288,29294,29296,29298,29300,29302,29308,29310,29318,29324,29326,29334,29340],{},[898,29273,9795],{"mathvariant":28550},[1996,29275,1998],{},[898,29277,900],{},[1996,29279,2005],{"stretchy":2004},[2272,29281,29282,29284],{},[898,29283,2789],{},[2129,29285,2278],{},[1996,29287,2286],{"separator":2285},[2272,29289,29290,29292],{},[898,29291,2789],{},[2129,29293,2131],{},[1996,29295,2011],{"stretchy":2004},[1996,29297,2095],{},[898,29299,16445],{},[1996,29301,2005],{"stretchy":2004},[2124,29303,29304,29306],{},[898,29305,9128],{},[1996,29307,4354],{},[1996,29309,2225],{},[9166,29311,29312,29314,29316],{},[898,29313,3937],{},[2129,29315,2278],{},[1996,29317,4354],{},[2272,29319,29320,29322],{},[898,29321,2789],{},[2129,29323,2278],{},[1996,29325,2225],{},[9166,29327,29328,29330,29332],{},[898,29329,3937],{},[2129,29331,2131],{},[1996,29333,4354],{},[2272,29335,29336,29338],{},[898,29337,2789],{},[2129,29339,2131],{},[1996,29341,2011],{"stretchy":2004},[902,29343,29344],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,29346,29347,10468,29350,29380],{},[38,29348,29349],{},"Spočítej parciální derivace",[883,29351,29353],{"className":29352},[886],[888,29354,29355],{"xmlns":890},[892,29356,29357,29377],{},[895,29358,29359,29365,29367,29373,29375],{},[2272,29360,29361,29363],{},[898,29362,2789],{},[2129,29364,2278],{},[1996,29366,2286],{"separator":2285},[2272,29368,29369,29371],{},[898,29370,2789],{},[2129,29372,2131],{},[1996,29374,2286],{"separator":2285},[898,29376,16445],{},[902,29378,29379],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,29382,29383,29399,29400,29433,29434,3885,29451,1975],{},[38,29384,29385,29386],{},"Vyluč ",[883,29387,29389],{"className":29388},[886],[888,29390,29391],{"xmlns":890},[892,29392,29393,29397],{},[895,29394,29395],{},[898,29396,16445],{},[902,29398,16498],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,29401,29403],{"className":29402},[886],[888,29404,29405],{"xmlns":890},[892,29406,29407,29431],{},[895,29408,29409,29411,29413,29421,29423],{},[2288,29410,10603],{},[1996,29412,1998],{},[9166,29414,29415,29417,29419],{},[898,29416,3937],{},[2129,29418,2278],{},[1996,29420,4354],{},[898,29422,4674],{"mathvariant":2376},[9166,29424,29425,29427,29429],{},[898,29426,3937],{},[2129,29428,2131],{},[1996,29430,4354],{},[902,29432,28981],{"encoding":904},", která dá vztah mezi ",[883,29435,29437],{"className":29436},[886],[888,29438,29439],{"xmlns":890},[892,29440,29441,29449],{},[895,29442,29443],{},[2272,29444,29445,29447],{},[898,29446,2789],{},[2129,29448,2278],{},[902,29450,29004],{"encoding":904},[883,29452,29454],{"className":29453},[886],[888,29455,29456],{"xmlns":890},[892,29457,29458,29466],{},[895,29459,29460],{},[2272,29461,29462,29464],{},[898,29463,2789],{},[2129,29465,2131],{},[902,29467,29023],{"encoding":904},[123,29469,29470,29473,29474,29504,29505,29522,29523,1975],{},[38,29471,29472],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,29475,29477],{"className":29476},[886],[888,29478,29479],{"xmlns":890},[892,29480,29481,29501],{},[895,29482,29483,29491,29493],{},[9166,29484,29485,29487,29489],{},[898,29486,2789],{},[2129,29488,2278],{},[1996,29490,4354],{},[1996,29492,2286],{"separator":2285},[9166,29494,29495,29497,29499],{},[898,29496,2789],{},[2129,29498,2131],{},[1996,29500,4354],{},[902,29502,29503],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,29506,29508],{"className":29507},[886],[888,29509,29510],{"xmlns":890},[892,29511,29512,29520],{},[895,29513,29514],{},[2124,29515,29516,29518],{},[898,29517,16445],{},[1996,29519,4354],{},[902,29521,29143],{"encoding":904}," a maximální užitečnost ",[883,29524,29526],{"className":29525},[886],[888,29527,29528],{"xmlns":890},[892,29529,29530,29564],{},[895,29531,29532,29538,29540,29542,29544,29552,29554,29562],{},[2124,29533,29534,29536],{},[898,29535,900],{},[1996,29537,4354],{},[1996,29539,1998],{},[898,29541,900],{},[1996,29543,2005],{"stretchy":2004},[9166,29545,29546,29548,29550],{},[898,29547,2789],{},[2129,29549,2278],{},[1996,29551,4354],{},[1996,29553,2286],{"separator":2285},[9166,29555,29556,29558,29560],{},[898,29557,2789],{},[2129,29559,2131],{},[1996,29561,4354],{},[1996,29563,2011],{"stretchy":2004},[902,29565,29566],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,29568,29570],{"id":29569},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,29572,29573],{},[2559,29574],{"alt":29575,"className":29576,"src":29577},"imek-uzitecnost-optimum",[210,2563],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,29579,29580],{},[614,29581,29582,29583,29632,29633,3885,29661,29689,29690,29724,29725,29764,29765,29783,29784,29802,29803,29821],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,29584,29586],{"className":29585},[886],[888,29587,29588],{"xmlns":890},[892,29589,29590,29630],{},[895,29591,29592,29598,29600,29608,29614,29616,29624],{},[2124,29593,29594,29596],{},[898,29595,9128],{},[1996,29597,4354],{},[1996,29599,1998],{},[9166,29601,29602,29604,29606],{},[898,29603,3937],{},[2129,29605,2278],{},[1996,29607,4354],{},[2272,29609,29610,29612],{},[898,29611,2789],{},[2129,29613,2278],{},[1996,29615,2095],{},[9166,29617,29618,29620,29622],{},[898,29619,3937],{},[2129,29621,2131],{},[1996,29623,4354],{},[2272,29625,29626,29628],{},[898,29627,2789],{},[2129,29629,2131],{},[902,29631,17300],{"encoding":904}," protíná osy v ",[883,29634,29636],{"className":29635},[886],[888,29637,29638],{"xmlns":890},[892,29639,29640,29658],{},[895,29641,29642,29648,29650],{},[2124,29643,29644,29646],{},[898,29645,9128],{},[1996,29647,4354],{},[898,29649,4674],{"mathvariant":2376},[9166,29651,29652,29654,29656],{},[898,29653,3937],{},[2129,29655,2278],{},[1996,29657,4354],{},[902,29659,29660],{"encoding":904},"Y^*\u002FP_1^*",[883,29662,29664],{"className":29663},[886],[888,29665,29666],{"xmlns":890},[892,29667,29668,29686],{},[895,29669,29670,29676,29678],{},[2124,29671,29672,29674],{},[898,29673,9128],{},[1996,29675,4354],{},[898,29677,4674],{"mathvariant":2376},[9166,29679,29680,29682,29684],{},[898,29681,3937],{},[2129,29683,2131],{},[1996,29685,4354],{},[902,29687,29688],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,29691,29693],{"className":29692},[886],[888,29694,29695],{"xmlns":890},[892,29696,29697,29721],{},[895,29698,29699,29705,29707,29713,29715],{},[2272,29700,29701,29703],{},[898,29702,2142],{},[2129,29704,2278],{},[1996,29706,3447],{},[2124,29708,29709,29711],{},[898,29710,2142],{},[1996,29712,4354],{},[1996,29714,3447],{},[2272,29716,29717,29719],{},[898,29718,2142],{},[2129,29720,2131],{},[902,29722,29723],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,29726,29728],{"className":29727},[886],[888,29729,29730],{"xmlns":890},[892,29731,29732,29762],{},[895,29733,29734,29740,29742,29750,29752,29760],{},[2124,29735,29736,29738],{},[898,29737,2789],{},[1996,29739,4354],{},[1996,29741,2486],{"stretchy":2004},[9166,29743,29744,29746,29748],{},[898,29745,2789],{},[2129,29747,2278],{},[1996,29749,4354],{},[1996,29751,2286],{"separator":2285},[9166,29753,29754,29756,29758],{},[898,29755,2789],{},[2129,29757,2131],{},[1996,29759,4354],{},[1996,29761,2501],{"stretchy":2004},[902,29763,28329],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,29766,29768],{"className":29767},[886],[888,29769,29770],{"xmlns":890},[892,29771,29772,29780],{},[895,29773,29774],{},[2124,29775,29776,29778],{},[898,29777,2142],{},[1996,29779,4354],{},[902,29781,29782],{"encoding":904},"c^*",". Křivka ",[883,29785,29787],{"className":29786},[886],[888,29788,29789],{"xmlns":890},[892,29790,29791,29799],{},[895,29792,29793],{},[2272,29794,29795,29797],{},[898,29796,2142],{},[2129,29798,2278],{},[902,29800,29801],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,29804,29806],{"className":29805},[886],[888,29807,29808],{"xmlns":890},[892,29809,29810,29818],{},[895,29811,29812],{},[2272,29813,29814,29816],{},[898,29815,2142],{},[2129,29817,2131],{},[902,29819,29820],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,29823,29824,29825,29828,29829,29847,29848,29877],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,29826,29827],{},"dotýkají",", tj. mají v bodě ",[883,29830,29832],{"className":29831},[886],[888,29833,29834],{"xmlns":890},[892,29835,29836,29844],{},[895,29837,29838],{},[2124,29839,29840,29842],{},[898,29841,2789],{},[1996,29843,4354],{},[902,29845,29846],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,29849,29851],{"className":29850},[886],[888,29852,29853],{"xmlns":890},[892,29854,29855,29875],{},[895,29856,29857,29859,29861,29867,29869],{},[2288,29858,10603],{},[1996,29860,1998],{},[2272,29862,29863,29865],{},[898,29864,3937],{},[2129,29866,2278],{},[898,29868,4674],{"mathvariant":2376},[2272,29870,29871,29873],{},[898,29872,3937],{},[2129,29874,2131],{},[902,29876,28000],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,29879,29881],{"id":29880},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,29883,9663,29884,29946],{},[883,29885,29887],{"className":29886},[886],[888,29888,29889],{"xmlns":890},[892,29890,29891,29943],{},[895,29892,29893,29895,29897,29903,29905,29911,29913,29915,29929],{},[898,29894,900],{},[1996,29896,2005],{"stretchy":2004},[2272,29898,29899,29901],{},[898,29900,2789],{},[2129,29902,2278],{},[1996,29904,2286],{"separator":2285},[2272,29906,29907,29909],{},[898,29908,2789],{},[2129,29910,2131],{},[1996,29912,2011],{"stretchy":2004},[1996,29914,1998],{},[9166,29916,29917,29919,29921],{},[898,29918,2789],{},[2129,29920,2278],{},[895,29922,29923,29925,29927],{},[2129,29924,2278],{},[898,29926,4674],{"mathvariant":2376},[2129,29928,2131],{},[9166,29930,29931,29933,29935],{},[898,29932,2789],{},[2129,29934,2131],{},[895,29936,29937,29939,29941],{},[2129,29938,2278],{},[898,29940,4674],{"mathvariant":2376},[2129,29942,2131],{},[902,29944,29945],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[724,29948,29949],{},[883,29950,29952],{"className":29951},[886],[888,29953,29954],{"xmlns":890},[892,29955,29956,30062],{},[895,29957,29958,29960,29962,30044,30046,30060],{},[2288,29959,10603],{},[1996,29961,1998],{},[2329,29963,29964,30004],{},[895,29965,29966,29974,29990],{},[2325,29967,29968],{"scriptlevel":2327,"displaystyle":2004},[2329,29969,29970,29972],{},[2129,29971,2278],{},[2129,29973,2131],{},[9166,29975,29976,29978,29980],{},[898,29977,2789],{},[2129,29979,2278],{},[895,29981,29982,29984,29986,29988],{},[1996,29983,2225],{},[2129,29985,2278],{},[898,29987,4674],{"mathvariant":2376},[2129,29989,2131],{},[9166,29991,29992,29994,29996],{},[898,29993,2789],{},[2129,29995,2131],{},[895,29997,29998,30000,30002],{},[2129,29999,2278],{},[898,30001,4674],{"mathvariant":2376},[2129,30003,2131],{},[895,30005,30006,30014,30028],{},[2325,30007,30008],{"scriptlevel":2327,"displaystyle":2004},[2329,30009,30010,30012],{},[2129,30011,2278],{},[2129,30013,2131],{},[9166,30015,30016,30018,30020],{},[898,30017,2789],{},[2129,30019,2278],{},[895,30021,30022,30024,30026],{},[2129,30023,2278],{},[898,30025,4674],{"mathvariant":2376},[2129,30027,2131],{},[9166,30029,30030,30032,30034],{},[898,30031,2789],{},[2129,30033,2131],{},[895,30035,30036,30038,30040,30042],{},[1996,30037,2225],{},[2129,30039,2278],{},[898,30041,4674],{"mathvariant":2376},[2129,30043,2131],{},[1996,30045,1998],{},[2329,30047,30048,30054],{},[2272,30049,30050,30052],{},[898,30051,2789],{},[2129,30053,2131],{},[2272,30055,30056,30058],{},[898,30057,2789],{},[2129,30059,2278],{},[898,30061,1975],{"mathvariant":2376},[902,30063,30064],{"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}.",[724,30066,30067,30068,2927,30113,30115,30116,30136,30137,30167,30168,1975],{},"Tedy ",[883,30069,30071],{"className":30070},[886],[888,30072,30073],{"xmlns":890},[892,30074,30075,30110],{},[895,30076,30077,30079,30081,30084,30086,30088,30090,30092,30100,30102],{},[2288,30078,10603],{},[1996,30080,2005],{"stretchy":2004},[2129,30082,30083],{},"300",[1996,30085,2286],{"separator":2285},[2129,30087,15112],{},[1996,30089,2011],{"stretchy":2004},[1996,30091,1998],{},[2325,30093,30094],{"scriptlevel":2327,"displaystyle":2004},[2329,30095,30096,30098],{},[2129,30097,15112],{},[2129,30099,30083],{},[1996,30101,1998],{},[2325,30103,30104],{"scriptlevel":2327,"displaystyle":2004},[2329,30105,30106,30108],{},[2129,30107,2228],{},[2129,30109,2173],{},[902,30111,30112],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,30114,9216],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,30117,30119],{"className":30118},[886],[888,30120,30121],{"xmlns":890},[892,30122,30123,30133],{},[895,30124,30125],{},[2325,30126,30127],{"scriptlevel":2327,"displaystyle":2004},[2329,30128,30129,30131],{},[2129,30130,2228],{},[2129,30132,2173],{},[902,30134,30135],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,30138,30140],{"className":30139},[886],[888,30141,30142],{"xmlns":890},[892,30143,30144,30164],{},[895,30145,30146,30148,30150,30156,30158],{},[2288,30147,10603],{},[1996,30149,1998],{},[2272,30151,30152,30154],{},[898,30153,2789],{},[2129,30155,2131],{},[898,30157,4674],{"mathvariant":2376},[2272,30159,30160,30162],{},[898,30161,2789],{},[2129,30163,2278],{},[902,30165,30166],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,30169,30171],{"className":30170},[886],[888,30172,30173],{"xmlns":890},[892,30174,30175,30195],{},[895,30176,30177,30179,30181,30187,30189],{},[2288,30178,10603],{},[1996,30180,1998],{},[2272,30182,30183,30185],{},[898,30184,3937],{},[2129,30186,2278],{},[898,30188,4674],{"mathvariant":2376},[2272,30190,30191,30193],{},[898,30192,3937],{},[2129,30194,2131],{},[902,30196,28000],{"encoding":904},[115,30198,30200,30201],{"id":30199},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,30202,30204],{"className":30203},[886],[888,30205,30206],{"xmlns":890},[892,30207,30208,30226],{},[895,30209,30210,30212,30214,30220],{},[898,30211,900],{},[1996,30213,1998],{},[2272,30215,30216,30218],{},[898,30217,2789],{},[2129,30219,2278],{},[2272,30221,30222,30224],{},[898,30223,2789],{},[2129,30225,2131],{},[902,30227,30228],{"encoding":904},"U = Q_1 Q_2",[724,30230,30231,30232,1343,30278,1343,30302,1343,30326,30348],{},"Je dána ",[883,30233,30235],{"className":30234},[886],[888,30236,30237],{"xmlns":890},[892,30238,30239,30275],{},[895,30240,30241,30243,30245,30251,30253,30259,30261,30263,30269],{},[898,30242,900],{},[1996,30244,2005],{"stretchy":2004},[2272,30246,30247,30249],{},[898,30248,2789],{},[2129,30250,2278],{},[1996,30252,2286],{"separator":2285},[2272,30254,30255,30257],{},[898,30256,2789],{},[2129,30258,2131],{},[1996,30260,2011],{"stretchy":2004},[1996,30262,1998],{},[2272,30264,30265,30267],{},[898,30266,2789],{},[2129,30268,2278],{},[2272,30270,30271,30273],{},[898,30272,2789],{},[2129,30274,2131],{},[902,30276,30277],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,30279,30281],{"className":30280},[886],[888,30282,30283],{"xmlns":890},[892,30284,30285,30299],{},[895,30286,30287,30295,30297],{},[9166,30288,30289,30291,30293],{},[898,30290,3937],{},[2129,30292,2278],{},[1996,30294,4354],{},[1996,30296,1998],{},[2129,30298,2131],{},[902,30300,30301],{"encoding":904},"P_1^* = 2",[883,30303,30305],{"className":30304},[886],[888,30306,30307],{"xmlns":890},[892,30308,30309,30323],{},[895,30310,30311,30319,30321],{},[9166,30312,30313,30315,30317],{},[898,30314,3937],{},[2129,30316,2131],{},[1996,30318,4354],{},[1996,30320,1998],{},[2129,30322,2228],{},[902,30324,30325],{"encoding":904},"P_2^* = 5",[883,30327,30329],{"className":30328},[886],[888,30330,30331],{"xmlns":890},[892,30332,30333,30345],{},[895,30334,30335,30341,30343],{},[2124,30336,30337,30339],{},[898,30338,9128],{},[1996,30340,4354],{},[1996,30342,1998],{},[2129,30344,3090],{},[902,30346,30347],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,30350,30352],{"className":30351},[886],[888,30353,30354],{"xmlns":890,"display":28068},[892,30355,30356,30428],{},[895,30357,30358,30360,30362,30368,30370,30376,30378,30380,30382,30384,30390,30396,30398,30400,30402,30404,30406,30408,30414,30416,30418,30424,30426],{},[898,30359,9795],{"mathvariant":28550},[1996,30361,2005],{"stretchy":2004},[2272,30363,30364,30366],{},[898,30365,2789],{},[2129,30367,2278],{},[1996,30369,2286],{"separator":2285},[2272,30371,30372,30374],{},[898,30373,2789],{},[2129,30375,2131],{},[1996,30377,2286],{"separator":2285},[898,30379,16445],{},[1996,30381,2011],{"stretchy":2004},[1996,30383,1998],{},[2272,30385,30386,30388],{},[898,30387,2789],{},[2129,30389,2278],{},[2272,30391,30392,30394],{},[898,30393,2789],{},[2129,30395,2131],{},[1996,30397,2095],{},[898,30399,16445],{},[1996,30401,2005],{"stretchy":2004},[2129,30403,3090],{},[1996,30405,2225],{},[2129,30407,2131],{},[2272,30409,30410,30412],{},[898,30411,2789],{},[2129,30413,2278],{},[1996,30415,2225],{},[2129,30417,2228],{},[2272,30419,30420,30422],{},[898,30421,2789],{},[2129,30423,2131],{},[1996,30425,2011],{"stretchy":2004},[898,30427,1975],{"mathvariant":2376},[902,30429,30430],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,30432,30433],{},"Soustava:",[883,30435,30437],{"className":30436},[886],[888,30438,30439],{"xmlns":890,"display":28068},[892,30440,30441,30553],{},[20756,30442,30443,30477,30511],{"rowspacing":20758,"columnalign":20759,"columnspacing":2377},[20761,30444,30445,30463],{},[20764,30446,30447],{},[2325,30448,30449],{"scriptlevel":2327,"displaystyle":2285},[895,30450,30451,30457,30459,30461],{},[2272,30452,30453,30455],{},[898,30454,2789],{},[2129,30456,2131],{},[1996,30458,2225],{},[2129,30460,2131],{},[898,30462,16445],{},[20764,30464,30465],{},[2325,30466,30467],{"scriptlevel":2327,"displaystyle":2285},[895,30468,30469,30471,30473,30475],{},[895,30470],{},[1996,30472,1998],{},[2129,30474,2327],{},[1996,30476,2286],{"separator":2285},[20761,30478,30479,30497],{},[20764,30480,30481],{},[2325,30482,30483],{"scriptlevel":2327,"displaystyle":2285},[895,30484,30485,30491,30493,30495],{},[2272,30486,30487,30489],{},[898,30488,2789],{},[2129,30490,2278],{},[1996,30492,2225],{},[2129,30494,2228],{},[898,30496,16445],{},[20764,30498,30499],{},[2325,30500,30501],{"scriptlevel":2327,"displaystyle":2285},[895,30502,30503,30505,30507,30509],{},[895,30504],{},[1996,30506,1998],{},[2129,30508,2327],{},[1996,30510,2286],{"separator":2285},[20761,30512,30513,30541],{},[20764,30514,30515],{},[2325,30516,30517],{"scriptlevel":2327,"displaystyle":2285},[895,30518,30519,30521,30523,30525,30531,30533,30535],{},[2129,30520,3090],{},[1996,30522,2225],{},[2129,30524,2131],{},[2272,30526,30527,30529],{},[898,30528,2789],{},[2129,30530,2278],{},[1996,30532,2225],{},[2129,30534,2228],{},[2272,30536,30537,30539],{},[898,30538,2789],{},[2129,30540,2131],{},[20764,30542,30543],{},[2325,30544,30545],{"scriptlevel":2327,"displaystyle":2285},[895,30546,30547,30549,30551],{},[895,30548],{},[1996,30550,1998],{},[2129,30552,12462],{},[902,30554,30555],{"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}",[724,30557,30558,30559,1343,30583,30607,30608,5589,30648,30666,30667,30717,30718,1975],{},"Z prvních dvou rovnic ",[883,30560,30562],{"className":30561},[886],[888,30563,30564],{"xmlns":890},[892,30565,30566,30580],{},[895,30567,30568,30574,30576,30578],{},[2272,30569,30570,30572],{},[898,30571,2789],{},[2129,30573,2131],{},[1996,30575,1998],{},[2129,30577,2131],{},[898,30579,16445],{},[902,30581,30582],{"encoding":904},"Q_2 = 2\\lambda",[883,30584,30586],{"className":30585},[886],[888,30587,30588],{"xmlns":890},[892,30589,30590,30604],{},[895,30591,30592,30598,30600,30602],{},[2272,30593,30594,30596],{},[898,30595,2789],{},[2129,30597,2278],{},[1996,30599,1998],{},[2129,30601,2228],{},[898,30603,16445],{},[902,30605,30606],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,30609,30611],{"className":30610},[886],[888,30612,30613],{"xmlns":890},[892,30614,30615,30645],{},[895,30616,30617,30619,30621,30623,30625,30627,30629,30631,30633,30635,30637,30639,30641,30643],{},[2129,30618,3090],{},[1996,30620,1998],{},[2129,30622,2131],{},[1996,30624,3177],{},[2129,30626,2228],{},[898,30628,16445],{},[1996,30630,2095],{},[2129,30632,2228],{},[1996,30634,3177],{},[2129,30636,2131],{},[898,30638,16445],{},[1996,30640,1998],{},[2129,30642,9035],{},[898,30644,16445],{},[902,30646,30647],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,30649,30651],{"className":30650},[886],[888,30652,30653],{"xmlns":890},[892,30654,30655,30663],{},[895,30656,30657,30659,30661],{},[898,30658,16445],{},[1996,30660,1998],{},[2129,30662,2228],{},[902,30664,30665],{"encoding":904},"\\lambda = 5",". Odtud ",[38,30668,30669,1343,30693],{},[883,30670,30672],{"className":30671},[886],[888,30673,30674],{"xmlns":890},[892,30675,30676,30690],{},[895,30677,30678,30686,30688],{},[9166,30679,30680,30682,30684],{},[898,30681,2789],{},[2129,30683,2278],{},[1996,30685,4354],{},[1996,30687,1998],{},[2129,30689,5004],{},[902,30691,30692],{"encoding":904},"Q_1^* = 25",[883,30694,30696],{"className":30695},[886],[888,30697,30698],{"xmlns":890},[892,30699,30700,30714],{},[895,30701,30702,30710,30712],{},[9166,30703,30704,30706,30708],{},[898,30705,2789],{},[2129,30707,2131],{},[1996,30709,4354],{},[1996,30711,1998],{},[2129,30713,2863],{},[902,30715,30716],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,30719,30721],{"className":30720},[886],[888,30722,30723],{"xmlns":890},[892,30724,30725,30746],{},[895,30726,30727,30733,30735,30737,30739,30741,30743],{},[2124,30728,30729,30731],{},[898,30730,900],{},[1996,30732,4354],{},[1996,30734,1998],{},[2129,30736,5004],{},[1996,30738,3177],{},[2129,30740,2863],{},[1996,30742,1998],{},[2129,30744,30745],{},"250",[902,30747,30748],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,30750,30751],{},[614,30752,30753,30754,28139,30792,3885,30816,30840,30841,30871,30872,30896,30897,30919,30920,1975],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,30755,30757],{"className":30756},[886],[888,30758,30759],{"xmlns":890},[892,30760,30761,30789],{},[895,30762,30763,30765,30767,30769,30775,30777,30779,30785,30787],{},[2129,30764,3090],{},[1996,30766,2225],{},[2129,30768,2131],{},[2272,30770,30771,30773],{},[898,30772,2789],{},[2129,30774,2278],{},[1996,30776,2225],{},[2129,30778,2228],{},[2272,30780,30781,30783],{},[898,30782,2789],{},[2129,30784,2131],{},[1996,30786,1998],{},[2129,30788,2327],{},[902,30790,30791],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,30793,30795],{"className":30794},[886],[888,30796,30797],{"xmlns":890},[892,30798,30799,30813],{},[895,30800,30801,30803,30805,30807,30809,30811],{},[898,30802,4255],{},[1996,30804,2486],{"stretchy":2004},[2129,30806,2327],{},[1996,30808,2286],{"separator":2285},[2129,30810,9035],{},[1996,30812,2501],{"stretchy":2004},[902,30814,30815],{"encoding":904},"A[0, 20]",[883,30817,30819],{"className":30818},[886],[888,30820,30821],{"xmlns":890},[892,30822,30823,30837],{},[895,30824,30825,30827,30829,30831,30833,30835],{},[898,30826,23255],{},[1996,30828,2486],{"stretchy":2004},[2129,30830,3120],{},[1996,30832,2286],{"separator":2285},[2129,30834,2327],{},[1996,30836,2501],{"stretchy":2004},[902,30838,30839],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,30842,30844],{"className":30843},[886],[888,30845,30846],{"xmlns":890},[892,30847,30848,30868],{},[895,30849,30850,30856,30858,30860,30862],{},[2272,30851,30852,30854],{},[898,30853,2789],{},[2129,30855,2131],{},[1996,30857,1998],{},[2129,30859,30745],{},[898,30861,4674],{"mathvariant":2376},[2272,30863,30864,30866],{},[898,30865,2789],{},[2129,30867,2278],{},[902,30869,30870],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,30873,30875],{"className":30874},[886],[888,30876,30877],{"xmlns":890},[892,30878,30879,30893],{},[895,30880,30881,30883,30885,30887,30889,30891],{},[898,30882,4252],{},[1996,30884,2486],{"stretchy":2004},[2129,30886,5004],{},[1996,30888,2286],{"separator":2285},[2129,30890,2863],{},[1996,30892,2501],{"stretchy":2004},[902,30894,30895],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,30898,30900],{"className":30899},[886],[888,30901,30902],{"xmlns":890},[892,30903,30904,30916],{},[895,30905,30906,30908],{},[1996,30907,2225],{},[2325,30909,30910],{"scriptlevel":2327,"displaystyle":2004},[2329,30911,30912,30914],{},[2129,30913,2131],{},[2129,30915,2228],{},[902,30917,30918],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,30921,30923],{"className":30922},[886],[888,30924,30925],{"xmlns":890},[892,30926,30927,30967],{},[895,30928,30929,30931,30933,30935,30937,30939,30941,30943,30945,30947,30955,30957,30959],{},[1996,30930,2225],{},[2288,30932,10603],{},[1996,30934,2005],{"stretchy":2004},[2129,30936,5004],{},[1996,30938,2286],{"separator":2285},[2129,30940,2863],{},[1996,30942,2011],{"stretchy":2004},[1996,30944,1998],{},[1996,30946,2225],{},[2325,30948,30949],{"scriptlevel":2327,"displaystyle":2004},[2329,30950,30951,30953],{},[2129,30952,2863],{},[2129,30954,5004],{},[1996,30956,1998],{},[1996,30958,2225],{},[2325,30960,30961],{"scriptlevel":2327,"displaystyle":2004},[2329,30962,30963,30965],{},[2129,30964,2131],{},[2129,30966,2228],{},[902,30968,30969],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,30971,30973],{"id":30972},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,30975,30976,30977,29005,31007,31010,31011,2704],{},"Považujeme-li v úloze ",[883,30978,30980],{"className":30979},[886],[888,30981,30982],{"xmlns":890},[892,30983,30984,31004],{},[895,30985,30986,30992,30994,31000,31002],{},[2272,30987,30988,30990],{},[898,30989,3937],{},[2129,30991,2278],{},[1996,30993,2286],{"separator":2285},[2272,30995,30996,30998],{},[898,30997,3937],{},[2129,30999,2131],{},[1996,31001,2286],{"separator":2285},[898,31003,9128],{},[902,31005,31006],{"encoding":904},"P_1, P_2, Y",[38,31008,31009],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,31012,31013],{},"Marshallovy poptávkové funkce",[883,31015,31017],{"className":31016},[886],[888,31018,31019],{"xmlns":890,"display":28068},[892,31020,31021,31116],{},[20756,31022,31023],{"width":28073},[20761,31024,31025,31027,31109,31111],{},[20764,31026],{"width":28078},[20764,31028,31029],{},[895,31030,31031,31037,31039,31045,31047,31053,31055,31061,31063,31065,31067,31069,31071,31077,31079,31085,31087,31093,31095,31101,31103,31105,31107],{},[2272,31032,31033,31035],{},[898,31034,2789],{},[2129,31036,2278],{},[1996,31038,1998],{},[2272,31040,31041,31043],{},[898,31042,4183],{},[2129,31044,2278],{},[1996,31046,2005],{"stretchy":2004},[2272,31048,31049,31051],{},[898,31050,3937],{},[2129,31052,2278],{},[1996,31054,2286],{"separator":2285},[2272,31056,31057,31059],{},[898,31058,3937],{},[2129,31060,2131],{},[1996,31062,2286],{"separator":2285},[898,31064,9128],{},[1996,31066,2011],{"stretchy":2004},[1996,31068,2286],{"separator":2285},[5878,31070],{"width":15286},[2272,31072,31073,31075],{},[898,31074,2789],{},[2129,31076,2131],{},[1996,31078,1998],{},[2272,31080,31081,31083],{},[898,31082,4183],{},[2129,31084,2131],{},[1996,31086,2005],{"stretchy":2004},[2272,31088,31089,31091],{},[898,31090,3937],{},[2129,31092,2278],{},[1996,31094,2286],{"separator":2285},[2272,31096,31097,31099],{},[898,31098,3937],{},[2129,31100,2131],{},[1996,31102,2286],{"separator":2285},[898,31104,9128],{},[1996,31106,2011],{"stretchy":2004},[1996,31108,2286],{"separator":2285},[20764,31110],{"width":28078},[20764,31112,31113],{},[2288,31114,31115],{},"(6.15)",[902,31117,31118],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,31120,31122],{"className":31121},[886],[888,31123,31124],{"xmlns":890,"display":28068},[892,31125,31126,31173],{},[20756,31127,31128],{"width":28073},[20761,31129,31130,31132,31166,31168],{},[20764,31131],{"width":28078},[20764,31133,31134],{},[895,31135,31136,31138,31140,31142,31144,31150,31152,31158,31160,31162,31164],{},[898,31137,16445],{},[1996,31139,1998],{},[898,31141,16445],{},[1996,31143,2005],{"stretchy":2004},[2272,31145,31146,31148],{},[898,31147,3937],{},[2129,31149,2278],{},[1996,31151,2286],{"separator":2285},[2272,31153,31154,31156],{},[898,31155,3937],{},[2129,31157,2131],{},[1996,31159,2286],{"separator":2285},[898,31161,9128],{},[1996,31163,2011],{"stretchy":2004},[898,31165,1975],{"mathvariant":2376},[20764,31167],{"width":28078},[20764,31169,31170],{},[2288,31171,31172],{},"(6.16)",[902,31174,31175],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,31177,31178,31208,31209,31275],{},[38,31179,31180,31181,1975],{},"Odvození pro ",[883,31182,31184],{"className":31183},[886],[888,31185,31186],{"xmlns":890},[892,31187,31188,31206],{},[895,31189,31190,31192,31194,31200],{},[898,31191,900],{},[1996,31193,1998],{},[2272,31195,31196,31198],{},[898,31197,2789],{},[2129,31199,2278],{},[2272,31201,31202,31204],{},[898,31203,2789],{},[2129,31205,2131],{},[902,31207,30228],{"encoding":904}," Lagrangeova funkce ",[883,31210,31212],{"className":31211},[886],[888,31213,31214],{"xmlns":890},[892,31215,31216,31272],{},[895,31217,31218,31220,31222,31228,31234,31236,31238,31240,31242,31244,31250,31256,31258,31264,31270],{},[898,31219,9795],{"mathvariant":28550},[1996,31221,1998],{},[2272,31223,31224,31226],{},[898,31225,2789],{},[2129,31227,2278],{},[2272,31229,31230,31232],{},[898,31231,2789],{},[2129,31233,2131],{},[1996,31235,2095],{},[898,31237,16445],{},[1996,31239,2005],{"stretchy":2004},[898,31241,9128],{},[1996,31243,2225],{},[2272,31245,31246,31248],{},[898,31247,3937],{},[2129,31249,2278],{},[2272,31251,31252,31254],{},[898,31253,2789],{},[2129,31255,2278],{},[1996,31257,2225],{},[2272,31259,31260,31262],{},[898,31261,3937],{},[2129,31263,2131],{},[2272,31265,31266,31268],{},[898,31267,2789],{},[2129,31269,2131],{},[1996,31271,2011],{"stretchy":2004},[902,31273,31274],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,31277,31279],{"className":31278},[886],[888,31280,31281],{"xmlns":890,"display":28068},[892,31282,31283,31450],{},[20756,31284,31285],{"width":28073},[20761,31286,31287,31289,31443,31445],{},[20764,31288],{"width":28078},[20764,31290,31291],{},[20756,31292,31293,31339,31385],{"rowspacing":20758,"columnalign":20759,"columnspacing":2377},[20761,31294,31295,31307],{},[20764,31296,31297],{},[2325,31298,31299],{"scriptlevel":2327,"displaystyle":2285},[9166,31300,31301,31303,31305],{},[898,31302,9795],{"mathvariant":28550},[2129,31304,2278],{},[1996,31306,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[20764,31308,31309],{},[2325,31310,31311],{"scriptlevel":2327,"displaystyle":2285},[895,31312,31313,31315,31317,31323,31325,31327,31333,31335,31337],{},[895,31314],{},[1996,31316,1998],{},[2272,31318,31319,31321],{},[898,31320,2789],{},[2129,31322,2131],{},[1996,31324,2225],{},[898,31326,16445],{},[2272,31328,31329,31331],{},[898,31330,3937],{},[2129,31332,2278],{},[1996,31334,1998],{},[2129,31336,2327],{},[1996,31338,2286],{"separator":2285},[20761,31340,31341,31353],{},[20764,31342,31343],{},[2325,31344,31345],{"scriptlevel":2327,"displaystyle":2285},[9166,31346,31347,31349,31351],{},[898,31348,9795],{"mathvariant":28550},[2129,31350,2131],{},[1996,31352,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[20764,31354,31355],{},[2325,31356,31357],{"scriptlevel":2327,"displaystyle":2285},[895,31358,31359,31361,31363,31369,31371,31373,31379,31381,31383],{},[895,31360],{},[1996,31362,1998],{},[2272,31364,31365,31367],{},[898,31366,2789],{},[2129,31368,2278],{},[1996,31370,2225],{},[898,31372,16445],{},[2272,31374,31375,31377],{},[898,31376,3937],{},[2129,31378,2131],{},[1996,31380,1998],{},[2129,31382,2327],{},[1996,31384,2286],{"separator":2285},[20761,31386,31387,31399],{},[20764,31388,31389],{},[2325,31390,31391],{"scriptlevel":2327,"displaystyle":2285},[9166,31392,31393,31395,31397],{},[898,31394,9795],{"mathvariant":28550},[898,31396,16445],{},[1996,31398,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[20764,31400,31401],{},[2325,31402,31403],{"scriptlevel":2327,"displaystyle":2285},[895,31404,31405,31407,31409,31411,31413,31419,31425,31427,31433,31439,31441],{},[895,31406],{},[1996,31408,1998],{},[898,31410,9128],{},[1996,31412,2225],{},[2272,31414,31415,31417],{},[898,31416,3937],{},[2129,31418,2278],{},[2272,31420,31421,31423],{},[898,31422,2789],{},[2129,31424,2278],{},[1996,31426,2225],{},[2272,31428,31429,31431],{},[898,31430,3937],{},[2129,31432,2131],{},[2272,31434,31435,31437],{},[898,31436,2789],{},[2129,31438,2131],{},[1996,31440,1998],{},[2129,31442,12462],{},[20764,31444],{"width":28078},[20764,31446,31447],{},[2288,31448,31449],{},"(6.17)",[902,31451,31452],{"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}",[724,31454,31455,31456,31484,31485,31513,31514,31582],{},"Z prvních dvou: ",[883,31457,31459],{"className":31458},[886],[888,31460,31461],{"xmlns":890},[892,31462,31463,31481],{},[895,31464,31465,31471,31473,31479],{},[2272,31466,31467,31469],{},[898,31468,2789],{},[2129,31470,2131],{},[1996,31472,1998],{},[2272,31474,31475,31477],{},[898,31476,3937],{},[2129,31478,2278],{},[898,31480,16445],{},[902,31482,31483],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,31486,31488],{"className":31487},[886],[888,31489,31490],{"xmlns":890},[892,31491,31492,31510],{},[895,31493,31494,31500,31502,31508],{},[2272,31495,31496,31498],{},[898,31497,2789],{},[2129,31499,2278],{},[1996,31501,1998],{},[2272,31503,31504,31506],{},[898,31505,3937],{},[2129,31507,2131],{},[898,31509,16445],{},[902,31511,31512],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,31515,31517],{"className":31516},[886],[888,31518,31519],{"xmlns":890},[892,31520,31521,31579],{},[895,31522,31523,31525,31527,31533,31535,31541,31543,31545,31551,31553,31559,31561,31563,31565,31571,31577],{},[898,31524,9128],{},[1996,31526,1998],{},[2272,31528,31529,31531],{},[898,31530,3937],{},[2129,31532,2278],{},[1996,31534,3177],{},[2272,31536,31537,31539],{},[898,31538,3937],{},[2129,31540,2131],{},[898,31542,16445],{},[1996,31544,2095],{},[2272,31546,31547,31549],{},[898,31548,3937],{},[2129,31550,2131],{},[1996,31552,3177],{},[2272,31554,31555,31557],{},[898,31556,3937],{},[2129,31558,2278],{},[898,31560,16445],{},[1996,31562,1998],{},[2129,31564,2131],{},[2272,31566,31567,31569],{},[898,31568,3937],{},[2129,31570,2278],{},[2272,31572,31573,31575],{},[898,31574,3937],{},[2129,31576,2131],{},[898,31578,16445],{},[902,31580,31581],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,31584,31586],{"className":31585},[886],[888,31587,31588],{"xmlns":890,"display":28068},[892,31589,31590,31633],{},[20756,31591,31592],{"width":28073},[20761,31593,31594,31596,31626,31628],{},[20764,31595],{"width":28078},[20764,31597,31598],{},[895,31599,31600,31602,31604,31624],{},[898,31601,16445],{},[1996,31603,1998],{},[2329,31605,31606,31608],{},[898,31607,9128],{},[895,31609,31610,31612,31618],{},[2129,31611,2131],{},[2272,31613,31614,31616],{},[898,31615,3937],{},[2129,31617,2278],{},[2272,31619,31620,31622],{},[898,31621,3937],{},[2129,31623,2131],{},[898,31625,1975],{"mathvariant":2376},[20764,31627],{"width":28078},[20764,31629,31630],{},[2288,31631,31632],{},"(6.20)",[902,31634,31635],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,31637,31638],{},"Zpětně:",[883,31640,31642],{"className":31641},[886],[888,31643,31644],{"xmlns":890,"display":28068},[892,31645,31646,31723],{},[20756,31647,31648],{"width":28073},[20761,31649,31650,31652,31716,31718],{},[20764,31651],{"width":28078},[20764,31653,31654],{},[12834,31655,31656],{"notation":12836},[2325,31657,31658],{"scriptlevel":2327,"displaystyle":2004},[2325,31659,31660],{"scriptlevel":2327,"displaystyle":2004},[2325,31661,31662],{"scriptlevel":2327,"displaystyle":2285},[895,31663,31664,31666,31672,31674,31688,31690,31692,31698,31700,31714],{},[2288,31665,3984],{},[2272,31667,31668,31670],{},[898,31669,2789],{},[2129,31671,2278],{},[1996,31673,1998],{},[2329,31675,31676,31678],{},[898,31677,9128],{},[895,31679,31680,31682],{},[2129,31681,2131],{},[2272,31683,31684,31686],{},[898,31685,3937],{},[2129,31687,2278],{},[1996,31689,2286],{"separator":2285},[5878,31691],{"width":15286},[2272,31693,31694,31696],{},[898,31695,2789],{},[2129,31697,2131],{},[1996,31699,1998],{},[2329,31701,31702,31704],{},[898,31703,9128],{},[895,31705,31706,31708],{},[2129,31707,2131],{},[2272,31709,31710,31712],{},[898,31711,3937],{},[2129,31713,2131],{},[2288,31715,3984],{},[20764,31717],{"width":28078},[20764,31719,31720],{},[2288,31721,31722],{},"(6.21)",[902,31724,31725],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,31727,31729],{"id":31728},"engelova-funkce","Engelova funkce",[724,31731,9663,31732,31735,31736,31739,31740,19869,31757,1343,31787,31817,31818,31852,31853,1343,31879,31905],{},[38,31733,31734],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,31737,31738],{},"Engelovou funkcí",": pro ",[883,31741,31743],{"className":31742},[886],[888,31744,31745],{"xmlns":890},[892,31746,31747,31755],{},[895,31748,31749,31751,31753],{},[898,31750,9128],{},[1996,31752,1998],{},[2129,31754,3090],{},[902,31756,20321],{"encoding":904},[883,31758,31760],{"className":31759},[886],[888,31761,31762],{"xmlns":890},[892,31763,31764,31784],{},[895,31765,31766,31772,31774,31776,31778],{},[2272,31767,31768,31770],{},[898,31769,2789],{},[2129,31771,2278],{},[1996,31773,1998],{},[2129,31775,3120],{},[898,31777,4674],{"mathvariant":2376},[2272,31779,31780,31782],{},[898,31781,3937],{},[2129,31783,2278],{},[902,31785,31786],{"encoding":904},"Q_1 = 50\u002FP_1",[883,31788,31790],{"className":31789},[886],[888,31791,31792],{"xmlns":890},[892,31793,31794,31814],{},[895,31795,31796,31802,31804,31806,31808],{},[2272,31797,31798,31800],{},[898,31799,2789],{},[2129,31801,2131],{},[1996,31803,1998],{},[2129,31805,3120],{},[898,31807,4674],{"mathvariant":2376},[2272,31809,31810,31812],{},[898,31811,3937],{},[2129,31813,2131],{},[902,31815,31816],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,31819,31821],{"className":31820},[886],[888,31822,31823],{"xmlns":890},[892,31824,31825,31849],{},[895,31826,31827,31833,31835,31837,31839,31845,31847],{},[2272,31828,31829,31831],{},[898,31830,3937],{},[2129,31832,2278],{},[1996,31834,1998],{},[2129,31836,2863],{},[1996,31838,2286],{"separator":2285},[2272,31840,31841,31843],{},[898,31842,3937],{},[2129,31844,2131],{},[1996,31846,1998],{},[2129,31848,9035],{},[902,31850,31851],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,31854,31856],{"className":31855},[886],[888,31857,31858],{"xmlns":890},[892,31859,31860,31876],{},[895,31861,31862,31868,31870,31872,31874],{},[2272,31863,31864,31866],{},[898,31865,2789],{},[2129,31867,2278],{},[1996,31869,1998],{},[898,31871,9128],{},[898,31873,4674],{"mathvariant":2376},[2129,31875,9035],{},[902,31877,31878],{"encoding":904},"Q_1 = Y\u002F20",[883,31880,31882],{"className":31881},[886],[888,31883,31884],{"xmlns":890},[892,31885,31886,31902],{},[895,31887,31888,31894,31896,31898,31900],{},[2272,31889,31890,31892],{},[898,31891,2789],{},[2129,31893,2131],{},[1996,31895,1998],{},[898,31897,9128],{},[898,31899,4674],{"mathvariant":2376},[2129,31901,5211],{},[902,31903,31904],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,31907,31909],{"id":31908},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,31911,31912],{},"Výdaje spotřebitele jsou",[883,31914,31916],{"className":31915},[886],[888,31917,31918],{"xmlns":890,"display":28068},[892,31919,31920,31995],{},[20756,31921,31922],{"width":28073},[20761,31923,31924,31926,31988,31990],{},[20764,31925],{"width":28078},[20764,31927,31928],{},[895,31929,31930,31932,31934,31936,31938,31944,31946,31952,31954,31956,31964,31970,31972,31980,31986],{},[898,31931,4252],{},[1996,31933,1998],{},[898,31935,4252],{},[1996,31937,2005],{"stretchy":2004},[2272,31939,31940,31942],{},[898,31941,2789],{},[2129,31943,2278],{},[1996,31945,2286],{"separator":2285},[2272,31947,31948,31950],{},[898,31949,2789],{},[2129,31951,2131],{},[1996,31953,2011],{"stretchy":2004},[1996,31955,1998],{},[9166,31957,31958,31960,31962],{},[898,31959,3937],{},[2129,31961,2278],{},[1996,31963,4354],{},[2272,31965,31966,31968],{},[898,31967,2789],{},[2129,31969,2278],{},[1996,31971,2095],{},[9166,31973,31974,31976,31978],{},[898,31975,3937],{},[2129,31977,2131],{},[1996,31979,4354],{},[2272,31981,31982,31984],{},[898,31983,2789],{},[2129,31985,2131],{},[1996,31987,2286],{"separator":2285},[20764,31989],{"width":28078},[20764,31991,31992],{},[2288,31993,31994],{},"(6.22)",[902,31996,31997],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,31999,32000],{},"a je pevně zadána hladina užitečnosti",[883,32002,32004],{"className":32003},[886],[888,32005,32006],{"xmlns":890,"display":28068},[892,32007,32008,32055],{},[20756,32009,32010],{"width":28073},[20761,32011,32012,32014,32048,32050],{},[20764,32013],{"width":28078},[20764,32015,32016],{},[895,32017,32018,32024,32026,32028,32030,32036,32038,32044,32046],{},[2124,32019,32020,32022],{},[898,32021,900],{},[1996,32023,4354],{},[1996,32025,1998],{},[898,32027,900],{},[1996,32029,2005],{"stretchy":2004},[2272,32031,32032,32034],{},[898,32033,2789],{},[2129,32035,2278],{},[1996,32037,2286],{"separator":2285},[2272,32039,32040,32042],{},[898,32041,2789],{},[2129,32043,2131],{},[1996,32045,2011],{"stretchy":2004},[898,32047,1975],{"mathvariant":2376},[20764,32049],{"width":28078},[20764,32051,32052],{},[2288,32053,32054],{},"(6.23)",[902,32056,32057],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,32059,32060,32063,32064,32096,32097,1975],{},[38,32061,32062],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,32065,32067],{"className":32066},[886],[888,32068,32069],{"xmlns":890},[892,32070,32071,32093],{},[895,32072,32073,32075,32077,32083,32085,32091],{},[898,32074,4252],{},[1996,32076,2005],{"stretchy":2004},[2272,32078,32079,32081],{},[898,32080,2789],{},[2129,32082,2278],{},[1996,32084,2286],{"separator":2285},[2272,32086,32087,32089],{},[898,32088,2789],{},[2129,32090,2131],{},[1996,32092,2011],{"stretchy":2004},[902,32094,32095],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,32098,32100],{"className":32099},[886],[888,32101,32102],{"xmlns":890},[892,32103,32104,32160],{},[895,32105,32106,32108,32110,32116,32118,32124,32126,32128,32134,32136,32138,32140,32146,32148,32154,32156,32158],{},[898,32107,11041],{},[1996,32109,2005],{"stretchy":2004},[2272,32111,32112,32114],{},[898,32113,2789],{},[2129,32115,2278],{},[1996,32117,2286],{"separator":2285},[2272,32119,32120,32122],{},[898,32121,2789],{},[2129,32123,2131],{},[1996,32125,2011],{"stretchy":2004},[1996,32127,1998],{},[2124,32129,32130,32132],{},[898,32131,900],{},[1996,32133,4354],{},[1996,32135,2225],{},[898,32137,900],{},[1996,32139,2005],{"stretchy":2004},[2272,32141,32142,32144],{},[898,32143,2789],{},[2129,32145,2278],{},[1996,32147,2286],{"separator":2285},[2272,32149,32150,32152],{},[898,32151,2789],{},[2129,32153,2131],{},[1996,32155,2011],{"stretchy":2004},[1996,32157,1998],{},[2129,32159,2327],{},[902,32161,32162],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,32164,32166],{"id":32165},"lagrangeova-funkce","Lagrangeova funkce",[883,32168,32170],{"className":32169},[886],[888,32171,32172],{"xmlns":890,"display":28068},[892,32173,32174,32285],{},[20756,32175,32176],{"width":28073},[20761,32177,32178,32180,32278,32280],{},[20764,32179],{"width":28078},[20764,32181,32182],{},[895,32183,32184,32186,32188,32194,32196,32202,32204,32206,32208,32210,32218,32224,32226,32234,32240,32242,32244,32246,32252,32254,32256,32258,32264,32266,32272,32274,32276],{},[898,32185,9795],{"mathvariant":28550},[1996,32187,2005],{"stretchy":2004},[2272,32189,32190,32192],{},[898,32191,2789],{},[2129,32193,2278],{},[1996,32195,2286],{"separator":2285},[2272,32197,32198,32200],{},[898,32199,2789],{},[2129,32201,2131],{},[1996,32203,2286],{"separator":2285},[898,32205,16445],{},[1996,32207,2011],{"stretchy":2004},[1996,32209,1998],{},[9166,32211,32212,32214,32216],{},[898,32213,3937],{},[2129,32215,2278],{},[1996,32217,4354],{},[2272,32219,32220,32222],{},[898,32221,2789],{},[2129,32223,2278],{},[1996,32225,2095],{},[9166,32227,32228,32230,32232],{},[898,32229,3937],{},[2129,32231,2131],{},[1996,32233,4354],{},[2272,32235,32236,32238],{},[898,32237,2789],{},[2129,32239,2131],{},[1996,32241,2095],{},[898,32243,16445],{},[1996,32245,2005],{"stretchy":2004},[2124,32247,32248,32250],{},[898,32249,900],{},[1996,32251,4354],{},[1996,32253,2225],{},[898,32255,900],{},[1996,32257,2005],{"stretchy":2004},[2272,32259,32260,32262],{},[898,32261,2789],{},[2129,32263,2278],{},[1996,32265,2286],{"separator":2285},[2272,32267,32268,32270],{},[898,32269,2789],{},[2129,32271,2131],{},[1996,32273,2011],{"stretchy":2004},[1996,32275,2011],{"stretchy":2004},[898,32277,1975],{"mathvariant":2376},[20764,32279],{"width":28078},[20764,32281,32282],{},[2288,32283,32284],{},"(6.24)",[902,32286,32287],{"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}",[724,32289,32290],{},"Soustava podmínek prvního řádu:",[883,32292,32294],{"className":32293},[886],[888,32295,32296],{"xmlns":890,"display":28068},[892,32297,32298,32471],{},[20756,32299,32300],{"width":28073},[20761,32301,32302,32304,32464,32466],{},[20764,32303],{"width":28078},[20764,32305,32306],{},[20756,32307,32308,32358,32408],{"rowspacing":20758,"columnalign":20759,"columnspacing":2377},[20761,32309,32310,32322],{},[20764,32311,32312],{},[2325,32313,32314],{"scriptlevel":2327,"displaystyle":2285},[9166,32315,32316,32318,32320],{},[898,32317,9795],{"mathvariant":28550},[2129,32319,2278],{},[1996,32321,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[20764,32323,32324],{},[2325,32325,32326],{"scriptlevel":2327,"displaystyle":2285},[895,32327,32328,32330,32332,32340,32342,32344,32352,32354,32356],{},[895,32329],{},[1996,32331,1998],{},[9166,32333,32334,32336,32338],{},[898,32335,3937],{},[2129,32337,2278],{},[1996,32339,4354],{},[1996,32341,2225],{},[898,32343,16445],{},[9166,32345,32346,32348,32350],{},[898,32347,900],{},[2129,32349,2278],{},[1996,32351,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,32353,1998],{},[2129,32355,2327],{},[1996,32357,2286],{"separator":2285},[20761,32359,32360,32372],{},[20764,32361,32362],{},[2325,32363,32364],{"scriptlevel":2327,"displaystyle":2285},[9166,32365,32366,32368,32370],{},[898,32367,9795],{"mathvariant":28550},[2129,32369,2131],{},[1996,32371,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[20764,32373,32374],{},[2325,32375,32376],{"scriptlevel":2327,"displaystyle":2285},[895,32377,32378,32380,32382,32390,32392,32394,32402,32404,32406],{},[895,32379],{},[1996,32381,1998],{},[9166,32383,32384,32386,32388],{},[898,32385,3937],{},[2129,32387,2131],{},[1996,32389,4354],{},[1996,32391,2225],{},[898,32393,16445],{},[9166,32395,32396,32398,32400],{},[898,32397,900],{},[2129,32399,2131],{},[1996,32401,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,32403,1998],{},[2129,32405,2327],{},[1996,32407,2286],{"separator":2285},[20761,32409,32410,32422],{},[20764,32411,32412],{},[2325,32413,32414],{"scriptlevel":2327,"displaystyle":2285},[9166,32415,32416,32418,32420],{},[898,32417,9795],{"mathvariant":28550},[898,32419,16445],{},[1996,32421,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[20764,32423,32424],{},[2325,32425,32426],{"scriptlevel":2327,"displaystyle":2285},[895,32427,32428,32430,32432,32438,32440,32442,32444,32450,32452,32458,32460,32462],{},[895,32429],{},[1996,32431,1998],{},[2124,32433,32434,32436],{},[898,32435,900],{},[1996,32437,4354],{},[1996,32439,2225],{},[898,32441,900],{},[1996,32443,2005],{"stretchy":2004},[2272,32445,32446,32448],{},[898,32447,2789],{},[2129,32449,2278],{},[1996,32451,2286],{"separator":2285},[2272,32453,32454,32456],{},[898,32455,2789],{},[2129,32457,2131],{},[1996,32459,2011],{"stretchy":2004},[1996,32461,1998],{},[2129,32463,12462],{},[20764,32465],{"width":28078},[20764,32467,32468],{},[2288,32469,32470],{},"(6.25)",[902,32472,32473],{"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}",[724,32475,32476],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,32478,32480],{"className":32479},[886],[888,32481,32482],{"xmlns":890,"display":28068},[892,32483,32484,32582],{},[20756,32485,32486],{"width":28073},[20761,32487,32488,32490,32575,32577],{},[20764,32489],{"width":28078},[20764,32491,32492],{},[895,32493,32494,32496,32498,32504,32506,32512,32514,32516,32518,32520,32522,32524,32573],{},[898,32495,4183],{},[1996,32497,2005],{"stretchy":2004},[2272,32499,32500,32502],{},[898,32501,2789],{},[2129,32503,2278],{},[1996,32505,2286],{"separator":2285},[2272,32507,32508,32510],{},[898,32509,2789],{},[2129,32511,2131],{},[1996,32513,2286],{"separator":2285},[898,32515,16445],{},[1996,32517,2011],{"stretchy":2004},[1996,32519,1998],{},[1996,32521,2225],{},[898,32523,16445],{},[895,32525,32526,32528,32540,32542,32555,32557,32559,32571],{},[1996,32527,2005],{"fence":2285},[9166,32529,32530,32532,32534],{},[898,32531,900],{},[2129,32533,2904],{},[895,32535,32536,32538],{},[1996,32537,2378],{"mathvariant":2376},[1996,32539,2378],{"mathvariant":2376},[1996,32541,2095],{},[9166,32543,32544,32546,32549],{},[898,32545,900],{},[2129,32547,32548],{},"22",[895,32550,32551,32553],{},[1996,32552,2378],{"mathvariant":2376},[1996,32554,2378],{"mathvariant":2376},[1996,32556,2095],{},[2129,32558,2131],{},[9166,32560,32561,32563,32565],{},[898,32562,900],{},[2129,32564,3509],{},[895,32566,32567,32569],{},[1996,32568,2378],{"mathvariant":2376},[1996,32570,2378],{"mathvariant":2376},[1996,32572,2011],{"fence":2285},[898,32574,1975],{"mathvariant":2376},[20764,32576],{"width":28078},[20764,32578,32579],{},[2288,32580,32581],{},"(6.26)",[902,32583,32584],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,32586,32587,32590,32591,32630,32631,32670,32671,32721,32722,32748,32749,32766,32767,32793],{},[38,32588,32589],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,32592,32594],{"className":32593},[886],[888,32595,32596],{"xmlns":890},[892,32597,32598,32628],{},[895,32599,32600,32606,32608,32616,32618,32626],{},[2124,32601,32602,32604],{},[898,32603,2789],{},[1996,32605,4354],{},[1996,32607,2486],{"stretchy":2004},[9166,32609,32610,32612,32614],{},[898,32611,2789],{},[2129,32613,2278],{},[1996,32615,4354],{},[1996,32617,2286],{"separator":2285},[9166,32619,32620,32622,32624],{},[898,32621,2789],{},[2129,32623,2131],{},[1996,32625,4354],{},[1996,32627,2501],{"stretchy":2004},[902,32629,28329],{"encoding":904}," dotyku křivky užitečnosti ",[883,32632,32634],{"className":32633},[886],[888,32635,32636],{"xmlns":890},[892,32637,32638,32668],{},[895,32639,32640,32646,32648,32650,32652,32658,32660,32666],{},[2124,32641,32642,32644],{},[898,32643,900],{},[1996,32645,4354],{},[1996,32647,1998],{},[898,32649,900],{},[1996,32651,2005],{"stretchy":2004},[2272,32653,32654,32656],{},[898,32655,2789],{},[2129,32657,2278],{},[1996,32659,2286],{"separator":2285},[2272,32661,32662,32664],{},[898,32663,2789],{},[2129,32665,2131],{},[1996,32667,2011],{"stretchy":2004},[902,32669,17667],{"encoding":904}," s přímkou výdajů ",[883,32672,32674],{"className":32673},[886],[888,32675,32676],{"xmlns":890},[892,32677,32678,32718],{},[895,32679,32680,32686,32688,32696,32702,32704,32712],{},[2124,32681,32682,32684],{},[898,32683,4252],{},[1996,32685,4354],{},[1996,32687,1998],{},[9166,32689,32690,32692,32694],{},[898,32691,3937],{},[2129,32693,2278],{},[1996,32695,4354],{},[2272,32697,32698,32700],{},[898,32699,2789],{},[2129,32701,2278],{},[1996,32703,2095],{},[9166,32705,32706,32708,32710],{},[898,32707,3937],{},[2129,32709,2131],{},[1996,32711,4354],{},[2272,32713,32714,32716],{},[898,32715,2789],{},[2129,32717,2131],{},[902,32719,32720],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,32723,32725],{"className":32724},[886],[888,32726,32727],{"xmlns":890},[892,32728,32729,32745],{},[895,32730,32731,32737,32739],{},[2272,32732,32733,32735],{},[898,32734,4252],{},[2129,32736,2327],{},[1996,32738,3447],{},[2124,32740,32741,32743],{},[898,32742,4252],{},[1996,32744,4354],{},[902,32746,32747],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,32750,32752],{"className":32751},[886],[888,32753,32754],{"xmlns":890},[892,32755,32756,32764],{},[895,32757,32758],{},[2124,32759,32760,32762],{},[898,32761,900],{},[1996,32763,4354],{},[902,32765,27964],{"encoding":904},", hladina ",[883,32768,32770],{"className":32769},[886],[888,32771,32772],{"xmlns":890},[892,32773,32774,32790],{},[895,32775,32776,32782,32784],{},[2272,32777,32778,32780],{},[898,32779,4252],{},[2129,32781,2278],{},[1996,32783,3408],{},[2124,32785,32786,32788],{},[898,32787,4252],{},[1996,32789,4354],{},[902,32791,32792],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[3867,32795,32796,32801],{},[724,32797,32798,32800],{},[883,32799,4572],{}," Postup — duální úloha (minimalizace výdajů)",[152,32802,32803,32853,32939,32979,33054],{},[123,32804,32805,2203,32808,32852],{},[38,32806,32807],{},"Zapiš vazbu",[883,32809,32811],{"className":32810},[886],[888,32812,32813],{"xmlns":890},[892,32814,32815,32849],{},[895,32816,32817,32823,32825,32827,32829,32835,32837,32843,32845,32847],{},[2124,32818,32819,32821],{},[898,32820,900],{},[1996,32822,4354],{},[1996,32824,2225],{},[898,32826,900],{},[1996,32828,2005],{"stretchy":2004},[2272,32830,32831,32833],{},[898,32832,2789],{},[2129,32834,2278],{},[1996,32836,2286],{"separator":2285},[2272,32838,32839,32841],{},[898,32840,2789],{},[2129,32842,2131],{},[1996,32844,2011],{"stretchy":2004},[1996,32846,1998],{},[2129,32848,2327],{},[902,32850,32851],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,32854,32855,2203,32857,1975],{},[38,32856,29262],{},[883,32858,32860],{"className":32859},[886],[888,32861,32862],{"xmlns":890},[892,32863,32864,32936],{},[895,32865,32866,32868,32870,32878,32884,32886,32894,32900,32902,32904,32906,32912,32914,32916,32918,32924,32926,32932,32934],{},[898,32867,9795],{"mathvariant":28550},[1996,32869,1998],{},[9166,32871,32872,32874,32876],{},[898,32873,3937],{},[2129,32875,2278],{},[1996,32877,4354],{},[2272,32879,32880,32882],{},[898,32881,2789],{},[2129,32883,2278],{},[1996,32885,2095],{},[9166,32887,32888,32890,32892],{},[898,32889,3937],{},[2129,32891,2131],{},[1996,32893,4354],{},[2272,32895,32896,32898],{},[898,32897,2789],{},[2129,32899,2131],{},[1996,32901,2095],{},[898,32903,16445],{},[1996,32905,2005],{"stretchy":2004},[2124,32907,32908,32910],{},[898,32909,900],{},[1996,32911,4354],{},[1996,32913,2225],{},[898,32915,900],{},[1996,32917,2005],{"stretchy":2004},[2272,32919,32920,32922],{},[898,32921,2789],{},[2129,32923,2278],{},[1996,32925,2286],{"separator":2285},[2272,32927,32928,32930],{},[898,32929,2789],{},[2129,32931,2131],{},[1996,32933,2011],{"stretchy":2004},[1996,32935,2011],{"stretchy":2004},[902,32937,32938],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,32940,32941,32944,32945,32978],{},[38,32942,32943],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,32946,32948],{"className":32947},[886],[888,32949,32950],{"xmlns":890},[892,32951,32952,32976],{},[895,32953,32954,32956,32958,32966,32968],{},[2288,32955,10603],{},[1996,32957,1998],{},[9166,32959,32960,32962,32964],{},[898,32961,3937],{},[2129,32963,2278],{},[1996,32965,4354],{},[898,32967,4674],{"mathvariant":2376},[9166,32969,32970,32972,32974],{},[898,32971,3937],{},[2129,32973,2131],{},[1996,32975,4354],{},[902,32977,28981],{"encoding":904}," (stejná jako u maximalizace!).",[123,32980,32981,2203,32984,33024,33025,1975],{},[38,32982,32983],{},"Dosaď do vazby",[883,32985,32987],{"className":32986},[886],[888,32988,32989],{"xmlns":890},[892,32990,32991,33021],{},[895,32992,32993,32995,32997,33003,33005,33011,33013,33015],{},[898,32994,900],{},[1996,32996,2005],{"stretchy":2004},[2272,32998,32999,33001],{},[898,33000,2789],{},[2129,33002,2278],{},[1996,33004,2286],{"separator":2285},[2272,33006,33007,33009],{},[898,33008,2789],{},[2129,33010,2131],{},[1996,33012,2011],{"stretchy":2004},[1996,33014,1998],{},[2124,33016,33017,33019],{},[898,33018,900],{},[1996,33020,4354],{},[902,33022,33023],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,33026,33028],{"className":33027},[886],[888,33029,33030],{"xmlns":890},[892,33031,33032,33052],{},[895,33033,33034,33042,33044],{},[9166,33035,33036,33038,33040],{},[898,33037,2789],{},[2129,33039,2278],{},[1996,33041,4354],{},[1996,33043,2286],{"separator":2285},[9166,33045,33046,33048,33050],{},[898,33047,2789],{},[2129,33049,2131],{},[1996,33051,4354],{},[902,33053,29503],{"encoding":904},[123,33055,33056,2203,33059,33113],{},[38,33057,33058],{},"Vypočítej minimální výdaje",[883,33060,33062],{"className":33061},[886],[888,33063,33064],{"xmlns":890},[892,33065,33066,33110],{},[895,33067,33068,33074,33076,33084,33092,33094,33102],{},[2124,33069,33070,33072],{},[898,33071,4252],{},[1996,33073,4354],{},[1996,33075,1998],{},[9166,33077,33078,33080,33082],{},[898,33079,3937],{},[2129,33081,2278],{},[1996,33083,4354],{},[9166,33085,33086,33088,33090],{},[898,33087,2789],{},[2129,33089,2278],{},[1996,33091,4354],{},[1996,33093,2095],{},[9166,33095,33096,33098,33100],{},[898,33097,3937],{},[2129,33099,2131],{},[1996,33101,4354],{},[9166,33103,33104,33106,33108],{},[898,33105,2789],{},[2129,33107,2131],{},[1996,33109,4354],{},[902,33111,33112],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,33115,33117,33118],{"id":33116},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,33119,33121],{"className":33120},[886],[888,33122,33123],{"xmlns":890},[892,33124,33125,33159],{},[895,33126,33127,33129,33131,33145],{},[898,33128,900],{},[1996,33130,1998],{},[9166,33132,33133,33135,33137],{},[898,33134,2789],{},[2129,33136,2278],{},[895,33138,33139,33141,33143],{},[2129,33140,2278],{},[898,33142,4674],{"mathvariant":2376},[2129,33144,2131],{},[9166,33146,33147,33149,33151],{},[898,33148,2789],{},[2129,33150,2131],{},[895,33152,33153,33155,33157],{},[2129,33154,2278],{},[898,33156,4674],{"mathvariant":2376},[2129,33158,2131],{},[902,33160,33161],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,33163,33164,33165,1343,33187,1343,33211,30348],{},"Dáno ",[883,33166,33168],{"className":33167},[886],[888,33169,33170],{"xmlns":890},[892,33171,33172,33184],{},[895,33173,33174,33180,33182],{},[2124,33175,33176,33178],{},[898,33177,900],{},[1996,33179,4354],{},[1996,33181,1998],{},[2129,33183,2131],{},[902,33185,33186],{"encoding":904},"U^* = 2",[883,33188,33190],{"className":33189},[886],[888,33191,33192],{"xmlns":890},[892,33193,33194,33208],{},[895,33195,33196,33204,33206],{},[9166,33197,33198,33200,33202],{},[898,33199,3937],{},[2129,33201,2278],{},[1996,33203,4354],{},[1996,33205,1998],{},[2129,33207,23791],{},[902,33209,33210],{"encoding":904},"P_1^* = 0{,}25",[883,33212,33214],{"className":33213},[886],[888,33215,33216],{"xmlns":890},[892,33217,33218,33232],{},[895,33219,33220,33228,33230],{},[9166,33221,33222,33224,33226],{},[898,33223,3937],{},[2129,33225,2131],{},[1996,33227,4354],{},[1996,33229,1998],{},[2129,33231,2278],{},[902,33233,33234],{"encoding":904},"P_2^* = 1",[883,33236,33238],{"className":33237},[886],[888,33239,33240],{"xmlns":890,"display":28068},[892,33241,33242,33306],{},[895,33243,33244,33246,33248,33250,33256,33258,33264,33266,33268,33270,33272,33274,33288,33302,33304],{},[898,33245,9795],{"mathvariant":28550},[1996,33247,1998],{},[2129,33249,23791],{},[2272,33251,33252,33254],{},[898,33253,2789],{},[2129,33255,2278],{},[1996,33257,2095],{},[2272,33259,33260,33262],{},[898,33261,2789],{},[2129,33263,2131],{},[1996,33265,2095],{},[898,33267,16445],{},[1996,33269,2005],{"stretchy":2004},[2129,33271,2131],{},[1996,33273,2225],{},[9166,33275,33276,33278,33280],{},[898,33277,2789],{},[2129,33279,2278],{},[895,33281,33282,33284,33286],{},[2129,33283,2278],{},[898,33285,4674],{"mathvariant":2376},[2129,33287,2131],{},[9166,33289,33290,33292,33294],{},[898,33291,2789],{},[2129,33293,2131],{},[895,33295,33296,33298,33300],{},[2129,33297,2278],{},[898,33299,4674],{"mathvariant":2376},[2129,33301,2131],{},[1996,33303,2011],{"stretchy":2004},[898,33305,1975],{"mathvariant":2376},[902,33307,33308],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,33310,30433],{},[883,33312,33314],{"className":33313},[886],[888,33315,33316],{"xmlns":890,"display":28068},[892,33317,33318,33532],{},[20756,33319,33320,33396,33472],{"rowspacing":20758,"columnalign":20759,"columnspacing":2377},[20761,33321,33322,33334],{},[20764,33323,33324],{},[2325,33325,33326],{"scriptlevel":2327,"displaystyle":2285},[9166,33327,33328,33330,33332],{},[898,33329,9795],{"mathvariant":28550},[2129,33331,2278],{},[1996,33333,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[20764,33335,33336],{},[2325,33337,33338],{"scriptlevel":2327,"displaystyle":2285},[895,33339,33340,33342,33344,33346,33348,33350,33352,33360,33376,33390,33392,33394],{},[895,33341],{},[1996,33343,1998],{},[2129,33345,23791],{},[1996,33347,2225],{},[898,33349,16445],{},[1996,33351,3177],{},[2325,33353,33354],{"scriptlevel":2327,"displaystyle":2004},[2329,33355,33356,33358],{},[2129,33357,2278],{},[2129,33359,2131],{},[9166,33361,33362,33364,33366],{},[898,33363,2789],{},[2129,33365,2278],{},[895,33367,33368,33370,33372,33374],{},[1996,33369,2225],{},[2129,33371,2278],{},[898,33373,4674],{"mathvariant":2376},[2129,33375,2131],{},[9166,33377,33378,33380,33382],{},[898,33379,2789],{},[2129,33381,2131],{},[895,33383,33384,33386,33388],{},[2129,33385,2278],{},[898,33387,4674],{"mathvariant":2376},[2129,33389,2131],{},[1996,33391,1998],{},[2129,33393,2327],{},[1996,33395,2286],{"separator":2285},[20761,33397,33398,33410],{},[20764,33399,33400],{},[2325,33401,33402],{"scriptlevel":2327,"displaystyle":2285},[9166,33403,33404,33406,33408],{},[898,33405,9795],{"mathvariant":28550},[2129,33407,2131],{},[1996,33409,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[20764,33411,33412],{},[2325,33413,33414],{"scriptlevel":2327,"displaystyle":2285},[895,33415,33416,33418,33420,33422,33424,33426,33428,33436,33450,33466,33468,33470],{},[895,33417],{},[1996,33419,1998],{},[2129,33421,2278],{},[1996,33423,2225],{},[898,33425,16445],{},[1996,33427,3177],{},[2325,33429,33430],{"scriptlevel":2327,"displaystyle":2004},[2329,33431,33432,33434],{},[2129,33433,2278],{},[2129,33435,2131],{},[9166,33437,33438,33440,33442],{},[898,33439,2789],{},[2129,33441,2278],{},[895,33443,33444,33446,33448],{},[2129,33445,2278],{},[898,33447,4674],{"mathvariant":2376},[2129,33449,2131],{},[9166,33451,33452,33454,33456],{},[898,33453,2789],{},[2129,33455,2131],{},[895,33457,33458,33460,33462,33464],{},[1996,33459,2225],{},[2129,33461,2278],{},[898,33463,4674],{"mathvariant":2376},[2129,33465,2131],{},[1996,33467,1998],{},[2129,33469,2327],{},[1996,33471,2286],{"separator":2285},[20761,33473,33474,33486],{},[20764,33475,33476],{},[2325,33477,33478],{"scriptlevel":2327,"displaystyle":2285},[9166,33479,33480,33482,33484],{},[898,33481,9795],{"mathvariant":28550},[898,33483,16445],{},[1996,33485,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[20764,33487,33488],{},[2325,33489,33490],{"scriptlevel":2327,"displaystyle":2285},[895,33491,33492,33494,33496,33498,33500,33514,33528,33530],{},[895,33493],{},[1996,33495,1998],{},[2129,33497,2131],{},[1996,33499,2225],{},[9166,33501,33502,33504,33506],{},[898,33503,2789],{},[2129,33505,2278],{},[895,33507,33508,33510,33512],{},[2129,33509,2278],{},[898,33511,4674],{"mathvariant":2376},[2129,33513,2131],{},[9166,33515,33516,33518,33520],{},[898,33517,2789],{},[2129,33519,2131],{},[895,33521,33522,33524,33526],{},[2129,33523,2278],{},[898,33525,4674],{"mathvariant":2376},[2129,33527,2131],{},[1996,33529,1998],{},[2129,33531,12462],{},[902,33533,33534],{"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}",[724,33536,33537,33538,17578,33568,33596,33597,5589,33659,1343,33709,33731,33732,1975],{},"Podílem prvních dvou rovnic: ",[883,33539,33541],{"className":33540},[886],[888,33542,33543],{"xmlns":890},[892,33544,33545,33565],{},[895,33546,33547,33549,33551,33557,33559],{},[2129,33548,23791],{},[1996,33550,1998],{},[2272,33552,33553,33555],{},[898,33554,2789],{},[2129,33556,2131],{},[898,33558,4674],{"mathvariant":2376},[2272,33560,33561,33563],{},[898,33562,2789],{},[2129,33564,2278],{},[902,33566,33567],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,33569,33571],{"className":33570},[886],[888,33572,33573],{"xmlns":890},[892,33574,33575,33593],{},[895,33576,33577,33583,33585,33587],{},[2272,33578,33579,33581],{},[898,33580,2789],{},[2129,33582,2131],{},[1996,33584,1998],{},[2129,33586,23791],{},[2272,33588,33589,33591],{},[898,33590,2789],{},[2129,33592,2278],{},[902,33594,33595],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,33598,33600],{"className":33599},[886],[888,33601,33602],{"xmlns":890},[892,33603,33604,33656],{},[895,33605,33606,33620,33622,33624,33630,33642,33644,33646,33652,33654],{},[9166,33607,33608,33610,33612],{},[898,33609,2789],{},[2129,33611,2278],{},[895,33613,33614,33616,33618],{},[2129,33615,2278],{},[898,33617,4674],{"mathvariant":2376},[2129,33619,2131],{},[1996,33621,2005],{"stretchy":2004},[2129,33623,23791],{},[2272,33625,33626,33628],{},[898,33627,2789],{},[2129,33629,2278],{},[2124,33631,33632,33634],{},[1996,33633,2011],{"stretchy":2004},[895,33635,33636,33638,33640],{},[2129,33637,2278],{},[898,33639,4674],{"mathvariant":2376},[2129,33641,2131],{},[1996,33643,1998],{},[2129,33645,5009],{},[2272,33647,33648,33650],{},[898,33649,2789],{},[2129,33651,2278],{},[1996,33653,1998],{},[2129,33655,2131],{},[902,33657,33658],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,33660,33661,1343,33685],{},[883,33662,33664],{"className":33663},[886],[888,33665,33666],{"xmlns":890},[892,33667,33668,33682],{},[895,33669,33670,33678,33680],{},[9166,33671,33672,33674,33676],{},[898,33673,2789],{},[2129,33675,2278],{},[1996,33677,4354],{},[1996,33679,1998],{},[2129,33681,2351],{},[902,33683,33684],{"encoding":904},"Q_1^* = 4",[883,33686,33688],{"className":33687},[886],[888,33689,33690],{"xmlns":890},[892,33691,33692,33706],{},[895,33693,33694,33702,33704],{},[9166,33695,33696,33698,33700],{},[898,33697,2789],{},[2129,33699,2131],{},[1996,33701,4354],{},[1996,33703,1998],{},[2129,33705,2278],{},[902,33707,33708],{"encoding":904},"Q_2^* = 1",[883,33710,33712],{"className":33711},[886],[888,33713,33714],{"xmlns":890},[892,33715,33716,33728],{},[895,33717,33718,33724,33726],{},[2124,33719,33720,33722],{},[898,33721,16445],{},[1996,33723,4354],{},[1996,33725,1998],{},[2129,33727,2278],{},[902,33729,33730],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,33733,33735],{"className":33734},[886],[888,33736,33737],{"xmlns":890},[892,33738,33739,33767],{},[895,33740,33741,33747,33749,33751,33753,33755,33757,33759,33761,33763,33765],{},[2124,33742,33743,33745],{},[898,33744,4252],{},[1996,33746,4354],{},[1996,33748,1998],{},[2129,33750,23791],{},[1996,33752,3177],{},[2129,33754,2351],{},[1996,33756,2095],{},[2129,33758,2278],{},[1996,33760,3177],{},[2129,33762,2278],{},[1996,33764,1998],{},[2129,33766,2131],{},[902,33768,33769],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,33771,33772,33775,33776,1343,33842,1343,33908,33974,33975,34012,34013,34035,34036,1975],{},[614,33773,33774],{},"Ověření postačující podmínky"," (6.26): ",[883,33777,33779],{"className":33778},[886],[888,33780,33781],{"xmlns":890},[892,33782,33783,33839],{},[895,33784,33785,33797,33799,33801,33809,33825],{},[9166,33786,33787,33789,33791],{},[898,33788,900],{},[2129,33790,2904],{},[895,33792,33793,33795],{},[1996,33794,2378],{"mathvariant":2376},[1996,33796,2378],{"mathvariant":2376},[1996,33798,1998],{},[1996,33800,2225],{},[2325,33802,33803],{"scriptlevel":2327,"displaystyle":2004},[2329,33804,33805,33807],{},[2129,33806,2278],{},[2129,33808,2351],{},[9166,33810,33811,33813,33815],{},[898,33812,2789],{},[2129,33814,2278],{},[895,33816,33817,33819,33821,33823],{},[1996,33818,2225],{},[2129,33820,2173],{},[898,33822,4674],{"mathvariant":2376},[2129,33824,2131],{},[9166,33826,33827,33829,33831],{},[898,33828,2789],{},[2129,33830,2131],{},[895,33832,33833,33835,33837],{},[2129,33834,2278],{},[898,33836,4674],{"mathvariant":2376},[2129,33838,2131],{},[902,33840,33841],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,33843,33845],{"className":33844},[886],[888,33846,33847],{"xmlns":890},[892,33848,33849,33905],{},[895,33850,33851,33863,33865,33867,33875,33889],{},[9166,33852,33853,33855,33857],{},[898,33854,900],{},[2129,33856,32548],{},[895,33858,33859,33861],{},[1996,33860,2378],{"mathvariant":2376},[1996,33862,2378],{"mathvariant":2376},[1996,33864,1998],{},[1996,33866,2225],{},[2325,33868,33869],{"scriptlevel":2327,"displaystyle":2004},[2329,33870,33871,33873],{},[2129,33872,2278],{},[2129,33874,2351],{},[9166,33876,33877,33879,33881],{},[898,33878,2789],{},[2129,33880,2278],{},[895,33882,33883,33885,33887],{},[2129,33884,2278],{},[898,33886,4674],{"mathvariant":2376},[2129,33888,2131],{},[9166,33890,33891,33893,33895],{},[898,33892,2789],{},[2129,33894,2131],{},[895,33896,33897,33899,33901,33903],{},[1996,33898,2225],{},[2129,33900,2173],{},[898,33902,4674],{"mathvariant":2376},[2129,33904,2131],{},[902,33906,33907],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,33909,33911],{"className":33910},[886],[888,33912,33913],{"xmlns":890},[892,33914,33915,33971],{},[895,33916,33917,33929,33931,33939,33955],{},[9166,33918,33919,33921,33923],{},[898,33920,900],{},[2129,33922,3509],{},[895,33924,33925,33927],{},[1996,33926,2378],{"mathvariant":2376},[1996,33928,2378],{"mathvariant":2376},[1996,33930,1998],{},[2325,33932,33933],{"scriptlevel":2327,"displaystyle":2004},[2329,33934,33935,33937],{},[2129,33936,2278],{},[2129,33938,2351],{},[9166,33940,33941,33943,33945],{},[898,33942,2789],{},[2129,33944,2278],{},[895,33946,33947,33949,33951,33953],{},[1996,33948,2225],{},[2129,33950,2278],{},[898,33952,4674],{"mathvariant":2376},[2129,33954,2131],{},[9166,33956,33957,33959,33961],{},[898,33958,2789],{},[2129,33960,2131],{},[895,33962,33963,33965,33967,33969],{},[1996,33964,2225],{},[2129,33966,2278],{},[898,33968,4674],{"mathvariant":2376},[2129,33970,2131],{},[902,33972,33973],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,33976,33978],{"className":33977},[886],[888,33979,33980],{"xmlns":890},[892,33981,33982,34009],{},[895,33983,33984,33986,33988,33990,33992,33994,33996,33998,34000,34002,34005,34007],{},[898,33985,4183],{},[1996,33987,2005],{"stretchy":2004},[2129,33989,2351],{},[1996,33991,2286],{"separator":2285},[2129,33993,2278],{},[1996,33995,2286],{"separator":2285},[2129,33997,2278],{},[1996,33999,2011],{"stretchy":2004},[1996,34001,1998],{},[2129,34003,34004],{},"0,28125",[1996,34006,3408],{},[2129,34008,2327],{},[902,34010,34011],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,34014,34016],{"className":34015},[886],[888,34017,34018],{"xmlns":890},[892,34019,34020,34032],{},[895,34021,34022,34024,34026,34028,34030],{},[1996,34023,2486],{"stretchy":2004},[2129,34025,2351],{},[1996,34027,2286],{"separator":2285},[2129,34029,2278],{},[1996,34031,2501],{"stretchy":2004},[902,34033,34034],{"encoding":904},"[4, 1]"," je vázané ",[38,34037,3775],{},[115,34039,34041],{"id":34040},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,34043,34044],{},"Obecně:",[883,34046,34048],{"className":34047},[886],[888,34049,34050],{"xmlns":890,"display":28068},[892,34051,34052,34147],{},[20756,34053,34054],{"width":28073},[20761,34055,34056,34058,34140,34142],{},[20764,34057],{"width":28078},[20764,34059,34060],{},[895,34061,34062,34068,34070,34076,34078,34084,34086,34092,34094,34096,34098,34100,34102,34108,34110,34116,34118,34124,34126,34132,34134,34136,34138],{},[2272,34063,34064,34066],{},[898,34065,2789],{},[2129,34067,2278],{},[1996,34069,1998],{},[2272,34071,34072,34074],{},[898,34073,4183],{},[2129,34075,2278],{},[1996,34077,2005],{"stretchy":2004},[2272,34079,34080,34082],{},[898,34081,3937],{},[2129,34083,2278],{},[1996,34085,2286],{"separator":2285},[2272,34087,34088,34090],{},[898,34089,3937],{},[2129,34091,2131],{},[1996,34093,2286],{"separator":2285},[898,34095,900],{},[1996,34097,2011],{"stretchy":2004},[1996,34099,2286],{"separator":2285},[5878,34101],{"width":15286},[2272,34103,34104,34106],{},[898,34105,2789],{},[2129,34107,2131],{},[1996,34109,1998],{},[2272,34111,34112,34114],{},[898,34113,4183],{},[2129,34115,2131],{},[1996,34117,2005],{"stretchy":2004},[2272,34119,34120,34122],{},[898,34121,3937],{},[2129,34123,2278],{},[1996,34125,2286],{"separator":2285},[2272,34127,34128,34130],{},[898,34129,3937],{},[2129,34131,2131],{},[1996,34133,2286],{"separator":2285},[898,34135,900],{},[1996,34137,2011],{"stretchy":2004},[1996,34139,2286],{"separator":2285},[20764,34141],{"width":28078},[20764,34143,34144],{},[2288,34145,34146],{},"(6.27)",[902,34148,34149],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,34151,34153],{"className":34152},[886],[888,34154,34155],{"xmlns":890,"display":28068},[892,34156,34157,34204],{},[20756,34158,34159],{"width":28073},[20761,34160,34161,34163,34197,34199],{},[20764,34162],{"width":28078},[20764,34164,34165],{},[895,34166,34167,34169,34171,34173,34175,34181,34183,34189,34191,34193,34195],{},[898,34168,16445],{},[1996,34170,1998],{},[898,34172,16445],{},[1996,34174,2005],{"stretchy":2004},[2272,34176,34177,34179],{},[898,34178,3937],{},[2129,34180,2278],{},[1996,34182,2286],{"separator":2285},[2272,34184,34185,34187],{},[898,34186,3937],{},[2129,34188,2131],{},[1996,34190,2286],{"separator":2285},[898,34192,900],{},[1996,34194,2011],{"stretchy":2004},[898,34196,1975],{"mathvariant":2376},[20764,34198],{"width":28078},[20764,34200,34201],{},[2288,34202,34203],{},"(6.28)",[902,34205,34206],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,34208,34209,34210,2203,34213,34226,34227,34240],{},"Hicksova poptávka závisí na ",[38,34211,34212],{},"hladině užitečnosti",[883,34214,34216],{"className":34215},[886],[888,34217,34218],{"xmlns":890},[892,34219,34220,34224],{},[895,34221,34222],{},[898,34223,900],{},[902,34225,900],{"encoding":904}," (nikoli na důchodu ",[883,34228,34230],{"className":34229},[886],[888,34231,34232],{"xmlns":890},[892,34233,34234,34238],{},[895,34235,34236],{},[898,34237,9128],{},[902,34239,9128],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,34242,34244,34245],{"id":34243},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,34246,34248],{"className":34247},[886],[888,34249,34250],{"xmlns":890},[892,34251,34252,34286],{},[895,34253,34254,34256,34258,34272],{},[898,34255,900],{},[1996,34257,1998],{},[9166,34259,34260,34262,34264],{},[898,34261,2789],{},[2129,34263,2278],{},[895,34265,34266,34268,34270],{},[2129,34267,2278],{},[898,34269,4674],{"mathvariant":2376},[2129,34271,2131],{},[9166,34273,34274,34276,34278],{},[898,34275,2789],{},[2129,34277,2131],{},[895,34279,34280,34282,34284],{},[2129,34281,2278],{},[898,34283,4674],{"mathvariant":2376},[2129,34285,2131],{},[902,34287,33161],{"encoding":904},[724,34289,34290,34320],{},[883,34291,34293],{"className":34292},[886],[888,34294,34295],{"xmlns":890},[892,34296,34297,34317],{},[895,34298,34299,34305,34307,34313,34315],{},[2272,34300,34301,34303],{},[898,34302,3937],{},[2129,34304,2278],{},[1996,34306,2286],{"separator":2285},[2272,34308,34309,34311],{},[898,34310,3937],{},[2129,34312,2131],{},[1996,34314,2286],{"separator":2285},[898,34316,900],{},[902,34318,34319],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,34322,34324],{"className":34323},[886],[888,34325,34326],{"xmlns":890,"display":28068},[892,34327,34328,34402],{},[895,34329,34330,34332,34334,34340,34346,34348,34354,34360,34362,34364,34366,34368,34370,34384,34398,34400],{},[898,34331,9795],{"mathvariant":28550},[1996,34333,1998],{},[2272,34335,34336,34338],{},[898,34337,3937],{},[2129,34339,2278],{},[2272,34341,34342,34344],{},[898,34343,2789],{},[2129,34345,2278],{},[1996,34347,2095],{},[2272,34349,34350,34352],{},[898,34351,3937],{},[2129,34353,2131],{},[2272,34355,34356,34358],{},[898,34357,2789],{},[2129,34359,2131],{},[1996,34361,2095],{},[898,34363,16445],{},[1996,34365,2005],{"stretchy":2004},[898,34367,900],{},[1996,34369,2225],{},[9166,34371,34372,34374,34376],{},[898,34373,2789],{},[2129,34375,2278],{},[895,34377,34378,34380,34382],{},[2129,34379,2278],{},[898,34381,4674],{"mathvariant":2376},[2129,34383,2131],{},[9166,34385,34386,34388,34390],{},[898,34387,2789],{},[2129,34389,2131],{},[895,34391,34392,34394,34396],{},[2129,34393,2278],{},[898,34395,4674],{"mathvariant":2376},[2129,34397,2131],{},[1996,34399,2011],{"stretchy":2004},[898,34401,1975],{"mathvariant":2376},[902,34403,34404],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,34406,30433],{},[883,34408,34410],{"className":34409},[886],[888,34411,34412],{"xmlns":890,"display":28068},[892,34413,34414,34636],{},[20756,34415,34416,34496,34576],{"rowspacing":20758,"columnalign":20759,"columnspacing":2377},[20761,34417,34418,34430],{},[20764,34419,34420],{},[2325,34421,34422],{"scriptlevel":2327,"displaystyle":2285},[9166,34423,34424,34426,34428],{},[898,34425,9795],{"mathvariant":28550},[2129,34427,2278],{},[1996,34429,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[20764,34431,34432],{},[2325,34433,34434],{"scriptlevel":2327,"displaystyle":2285},[895,34435,34436,34438,34440,34446,34448,34450,34452,34460,34476,34490,34492,34494],{},[895,34437],{},[1996,34439,1998],{},[2272,34441,34442,34444],{},[898,34443,3937],{},[2129,34445,2278],{},[1996,34447,2225],{},[898,34449,16445],{},[1996,34451,3177],{},[2325,34453,34454],{"scriptlevel":2327,"displaystyle":2004},[2329,34455,34456,34458],{},[2129,34457,2278],{},[2129,34459,2131],{},[9166,34461,34462,34464,34466],{},[898,34463,2789],{},[2129,34465,2278],{},[895,34467,34468,34470,34472,34474],{},[1996,34469,2225],{},[2129,34471,2278],{},[898,34473,4674],{"mathvariant":2376},[2129,34475,2131],{},[9166,34477,34478,34480,34482],{},[898,34479,2789],{},[2129,34481,2131],{},[895,34483,34484,34486,34488],{},[2129,34485,2278],{},[898,34487,4674],{"mathvariant":2376},[2129,34489,2131],{},[1996,34491,1998],{},[2129,34493,2327],{},[1996,34495,2286],{"separator":2285},[20761,34497,34498,34510],{},[20764,34499,34500],{},[2325,34501,34502],{"scriptlevel":2327,"displaystyle":2285},[9166,34503,34504,34506,34508],{},[898,34505,9795],{"mathvariant":28550},[2129,34507,2131],{},[1996,34509,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[20764,34511,34512],{},[2325,34513,34514],{"scriptlevel":2327,"displaystyle":2285},[895,34515,34516,34518,34520,34526,34528,34530,34532,34540,34554,34570,34572,34574],{},[895,34517],{},[1996,34519,1998],{},[2272,34521,34522,34524],{},[898,34523,3937],{},[2129,34525,2131],{},[1996,34527,2225],{},[898,34529,16445],{},[1996,34531,3177],{},[2325,34533,34534],{"scriptlevel":2327,"displaystyle":2004},[2329,34535,34536,34538],{},[2129,34537,2278],{},[2129,34539,2131],{},[9166,34541,34542,34544,34546],{},[898,34543,2789],{},[2129,34545,2278],{},[895,34547,34548,34550,34552],{},[2129,34549,2278],{},[898,34551,4674],{"mathvariant":2376},[2129,34553,2131],{},[9166,34555,34556,34558,34560],{},[898,34557,2789],{},[2129,34559,2131],{},[895,34561,34562,34564,34566,34568],{},[1996,34563,2225],{},[2129,34565,2278],{},[898,34567,4674],{"mathvariant":2376},[2129,34569,2131],{},[1996,34571,1998],{},[2129,34573,2327],{},[1996,34575,2286],{"separator":2285},[20761,34577,34578,34590],{},[20764,34579,34580],{},[2325,34581,34582],{"scriptlevel":2327,"displaystyle":2285},[9166,34583,34584,34586,34588],{},[898,34585,9795],{"mathvariant":28550},[898,34587,16445],{},[1996,34589,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[20764,34591,34592],{},[2325,34593,34594],{"scriptlevel":2327,"displaystyle":2285},[895,34595,34596,34598,34600,34602,34604,34618,34632,34634],{},[895,34597],{},[1996,34599,1998],{},[898,34601,900],{},[1996,34603,2225],{},[9166,34605,34606,34608,34610],{},[898,34607,2789],{},[2129,34609,2278],{},[895,34611,34612,34614,34616],{},[2129,34613,2278],{},[898,34615,4674],{"mathvariant":2376},[2129,34617,2131],{},[9166,34619,34620,34622,34624],{},[898,34621,2789],{},[2129,34623,2131],{},[895,34625,34626,34628,34630],{},[2129,34627,2278],{},[898,34629,4674],{"mathvariant":2376},[2129,34631,2131],{},[1996,34633,1998],{},[2129,34635,12462],{},[902,34637,34638],{"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}",[724,34640,34641,34642,34712,34713,34771],{},"Podílem rovnic: ",[883,34643,34645],{"className":34644},[886],[888,34646,34647],{"xmlns":890},[892,34648,34649,34709],{},[895,34650,34651,34657,34659,34665,34667,34673,34675,34681,34683,34689,34695,34697,34703],{},[2272,34652,34653,34655],{},[898,34654,3937],{},[2129,34656,2278],{},[898,34658,4674],{"mathvariant":2376},[2272,34660,34661,34663],{},[898,34662,3937],{},[2129,34664,2131],{},[1996,34666,1998],{},[2272,34668,34669,34671],{},[898,34670,2789],{},[2129,34672,2131],{},[898,34674,4674],{"mathvariant":2376},[2272,34676,34677,34679],{},[898,34678,2789],{},[2129,34680,2278],{},[1996,34682,3987],{},[2272,34684,34685,34687],{},[898,34686,3937],{},[2129,34688,2278],{},[2272,34690,34691,34693],{},[898,34692,2789],{},[2129,34694,2278],{},[1996,34696,1998],{},[2272,34698,34699,34701],{},[898,34700,3937],{},[2129,34702,2131],{},[2272,34704,34705,34707],{},[898,34706,2789],{},[2129,34708,2131],{},[902,34710,34711],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,34714,34716],{"className":34715},[886],[888,34717,34718],{"xmlns":890},[892,34719,34720,34768],{},[895,34721,34722,34724,34726,34732,34738,34740,34746,34752,34754,34756,34762],{},[898,34723,4252],{},[1996,34725,1998],{},[2272,34727,34728,34730],{},[898,34729,3937],{},[2129,34731,2278],{},[2272,34733,34734,34736],{},[898,34735,2789],{},[2129,34737,2278],{},[1996,34739,2095],{},[2272,34741,34742,34744],{},[898,34743,3937],{},[2129,34745,2131],{},[2272,34747,34748,34750],{},[898,34749,2789],{},[2129,34751,2131],{},[1996,34753,1998],{},[2129,34755,2131],{},[2272,34757,34758,34760],{},[898,34759,3937],{},[2129,34761,2278],{},[2272,34763,34764,34766],{},[898,34765,2789],{},[2129,34767,2278],{},[902,34769,34770],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,34773,34775],{"className":34774},[886],[888,34776,34777],{"xmlns":890,"display":28068},[892,34778,34779,34846],{},[20756,34780,34781],{"width":28073},[20761,34782,34783,34785,34839,34841],{},[20764,34784],{"width":28078},[20764,34786,34787],{},[895,34788,34789,34795,34797,34811,34813,34815,34821,34823,34837],{},[2272,34790,34791,34793],{},[898,34792,2789],{},[2129,34794,2278],{},[1996,34796,1998],{},[2329,34798,34799,34801],{},[898,34800,4252],{},[895,34802,34803,34805],{},[2129,34804,2131],{},[2272,34806,34807,34809],{},[898,34808,3937],{},[2129,34810,2278],{},[1996,34812,2286],{"separator":2285},[5878,34814],{"width":15286},[2272,34816,34817,34819],{},[898,34818,2789],{},[2129,34820,2131],{},[1996,34822,1998],{},[2329,34824,34825,34827],{},[898,34826,4252],{},[895,34828,34829,34831],{},[2129,34830,2131],{},[2272,34832,34833,34835],{},[898,34834,3937],{},[2129,34836,2131],{},[898,34838,1975],{"mathvariant":2376},[20764,34840],{"width":28078},[20764,34842,34843],{},[2288,34844,34845],{},"(6.29)",[902,34847,34848],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,34850,34851,34852,17578,34934,34970],{},"Ze třetí rovnice ",[883,34853,34855],{"className":34854},[886],[888,34856,34857],{"xmlns":890},[892,34858,34859,34931],{},[895,34860,34861,34863,34865,34903,34905],{},[898,34862,900],{},[1996,34864,1998],{},[8117,34866,34867],{},[895,34868,34869,34885,34887],{},[2325,34870,34871],{"scriptlevel":2327,"displaystyle":2004},[2329,34872,34873,34875],{},[898,34874,4252],{},[895,34876,34877,34879],{},[2129,34878,2131],{},[2272,34880,34881,34883],{},[898,34882,3937],{},[2129,34884,2278],{},[1996,34886,3177],{},[2325,34888,34889],{"scriptlevel":2327,"displaystyle":2004},[2329,34890,34891,34893],{},[898,34892,4252],{},[895,34894,34895,34897],{},[2129,34896,2131],{},[2272,34898,34899,34901],{},[898,34900,3937],{},[2129,34902,2131],{},[1996,34904,1998],{},[2325,34906,34907],{"scriptlevel":2327,"displaystyle":2004},[2329,34908,34909,34911],{},[898,34910,4252],{},[895,34912,34913,34915],{},[2129,34914,2131],{},[8117,34916,34917],{},[895,34918,34919,34925],{},[2272,34920,34921,34923],{},[898,34922,3937],{},[2129,34924,2278],{},[2272,34926,34927,34929],{},[898,34928,3937],{},[2129,34930,2131],{},[902,34932,34933],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,34935,34937],{"className":34936},[886],[888,34938,34939],{"xmlns":890},[892,34940,34941,34967],{},[895,34942,34943,34945,34947,34949,34951],{},[898,34944,4252],{},[1996,34946,1998],{},[2129,34948,2131],{},[898,34950,900],{},[8117,34952,34953],{},[895,34954,34955,34961],{},[2272,34956,34957,34959],{},[898,34958,3937],{},[2129,34960,2278],{},[2272,34962,34963,34965],{},[898,34964,3937],{},[2129,34966,2131],{},[902,34968,34969],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,34972,34974],{"className":34973},[886],[888,34975,34976],{"xmlns":890,"display":28068},[892,34977,34978,35123],{},[20756,34979,34980],{"width":28073},[20761,34981,34982,34984,35116,35118],{},[20764,34983],{"width":28078},[20764,34985,34986],{},[12834,34987,34988],{"notation":12836},[2325,34989,34990],{"scriptlevel":2327,"displaystyle":2004},[2325,34991,34992],{"scriptlevel":2327,"displaystyle":2004},[2325,34993,34994],{"scriptlevel":2327,"displaystyle":2285},[895,34995,34996,34998,35004,35006,35008,35024,35026,35032,35034,35040,35042,35048,35050,35052,35054,35056,35058,35064,35066,35068,35084,35086,35092,35094,35100,35102,35108,35110,35112,35114],{},[2288,34997,3984],{},[2272,34999,35000,35002],{},[898,35001,2789],{},[2129,35003,2278],{},[1996,35005,1998],{},[898,35007,900],{},[8117,35009,35010],{},[2329,35011,35012,35018],{},[2272,35013,35014,35016],{},[898,35015,3937],{},[2129,35017,2131],{},[2272,35019,35020,35022],{},[898,35021,3937],{},[2129,35023,2278],{},[1996,35025,1998],{},[2272,35027,35028,35030],{},[898,35029,4183],{},[2129,35031,2278],{},[1996,35033,2005],{"stretchy":2004},[2272,35035,35036,35038],{},[898,35037,3937],{},[2129,35039,2278],{},[1996,35041,2286],{"separator":2285},[2272,35043,35044,35046],{},[898,35045,3937],{},[2129,35047,2131],{},[1996,35049,2286],{"separator":2285},[898,35051,900],{},[1996,35053,2011],{"stretchy":2004},[1996,35055,2286],{"separator":2285},[5878,35057],{"width":15286},[2272,35059,35060,35062],{},[898,35061,2789],{},[2129,35063,2131],{},[1996,35065,1998],{},[898,35067,900],{},[8117,35069,35070],{},[2329,35071,35072,35078],{},[2272,35073,35074,35076],{},[898,35075,3937],{},[2129,35077,2278],{},[2272,35079,35080,35082],{},[898,35081,3937],{},[2129,35083,2131],{},[1996,35085,1998],{},[2272,35087,35088,35090],{},[898,35089,4183],{},[2129,35091,2131],{},[1996,35093,2005],{"stretchy":2004},[2272,35095,35096,35098],{},[898,35097,3937],{},[2129,35099,2278],{},[1996,35101,2286],{"separator":2285},[2272,35103,35104,35106],{},[898,35105,3937],{},[2129,35107,2131],{},[1996,35109,2286],{"separator":2285},[898,35111,900],{},[1996,35113,2011],{"stretchy":2004},[2288,35115,3984],{},[20764,35117],{"width":28078},[20764,35119,35120],{},[2288,35121,35122],{},"(6.30)",[902,35124,35125],{"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}",[115,35127,35129],{"id":35128},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,35131,35132,35133,35146,35147,35164,35165,35178,35179,35196,35197,35200,35201,35240,35241,35270],{},"Primární (max ",[883,35134,35136],{"className":35135},[886],[888,35137,35138],{"xmlns":890},[892,35139,35140,35144],{},[895,35141,35142],{},[898,35143,900],{},[902,35145,900],{"encoding":904}," při rozpočtu ",[883,35148,35150],{"className":35149},[886],[888,35151,35152],{"xmlns":890},[892,35153,35154,35162],{},[895,35155,35156],{},[2124,35157,35158,35160],{},[898,35159,9128],{},[1996,35161,4354],{},[902,35163,28030],{"encoding":904},") a duální (min ",[883,35166,35168],{"className":35167},[886],[888,35169,35170],{"xmlns":890},[892,35171,35172,35176],{},[895,35173,35174],{},[898,35175,4252],{},[902,35177,4252],{"encoding":904}," při užitečnosti ",[883,35180,35182],{"className":35181},[886],[888,35183,35184],{"xmlns":890},[892,35185,35186,35194],{},[895,35187,35188],{},[2124,35189,35190,35192],{},[898,35191,900],{},[1996,35193,4354],{},[902,35195,27964],{"encoding":904},") úloha jsou ",[38,35198,35199],{},"ekvivalentní",": mají tentýž bod optima ",[883,35202,35204],{"className":35203},[886],[888,35205,35206],{"xmlns":890},[892,35207,35208,35238],{},[895,35209,35210,35216,35218,35226,35228,35236],{},[2124,35211,35212,35214],{},[898,35213,2789],{},[1996,35215,4354],{},[1996,35217,2486],{"stretchy":2004},[9166,35219,35220,35222,35224],{},[898,35221,2789],{},[2129,35223,2278],{},[1996,35225,4354],{},[1996,35227,2286],{"separator":2285},[9166,35229,35230,35232,35234],{},[898,35231,2789],{},[2129,35233,2131],{},[1996,35235,4354],{},[1996,35237,2501],{"stretchy":2004},[902,35239,28329],{"encoding":904}," a v obou platí ",[883,35242,35244],{"className":35243},[886],[888,35245,35246],{"xmlns":890},[892,35247,35248,35268],{},[895,35249,35250,35252,35254,35260,35262],{},[2288,35251,10603],{},[1996,35253,1998],{},[2272,35255,35256,35258],{},[898,35257,3937],{},[2129,35259,2278],{},[898,35261,4674],{"mathvariant":2376},[2272,35263,35264,35266],{},[898,35265,3937],{},[2129,35267,2131],{},[902,35269,28000],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,35272,35273],{},[2559,35274],{"alt":35275,"className":35276,"src":35277},"imek-primarni-vs-dualni",[210,2563],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,35279,35280,35391],{},[123,35281,35282,35285,35286,35299,35300,35340,35341,1975],{},[38,35283,35284],{},"Primární"," (Marshall): zadáno ",[883,35287,35289],{"className":35288},[886],[888,35290,35291],{"xmlns":890},[892,35292,35293,35297],{},[895,35294,35295],{},[898,35296,9128],{},[902,35298,9128],{"encoding":904},", hledáme maximální ",[883,35301,35303],{"className":35302},[886],[888,35304,35305],{"xmlns":890},[892,35306,35307,35337],{},[895,35308,35309,35315,35317,35323,35325,35331,35333,35335],{},[2124,35310,35311,35313],{},[898,35312,900],{},[1996,35314,4354],{},[1996,35316,2005],{"stretchy":2004},[2272,35318,35319,35321],{},[898,35320,3937],{},[2129,35322,2278],{},[1996,35324,2286],{"separator":2285},[2272,35326,35327,35329],{},[898,35328,3937],{},[2129,35330,2131],{},[1996,35332,2286],{"separator":2285},[898,35334,9128],{},[1996,35336,2011],{"stretchy":2004},[902,35338,35339],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,35342,35344],{"className":35343},[886],[888,35345,35346],{"xmlns":890},[892,35347,35348,35388],{},[895,35349,35350,35356,35358,35366,35368,35374,35376,35382,35384,35386],{},[2272,35351,35352,35354],{},[898,35353,2789],{},[898,35355,17792],{},[1996,35357,1998],{},[9166,35359,35360,35362,35364],{},[898,35361,4183],{},[898,35363,17792],{},[898,35365,2818],{},[1996,35367,2005],{"stretchy":2004},[2272,35369,35370,35372],{},[898,35371,3937],{},[2129,35373,2278],{},[1996,35375,2286],{"separator":2285},[2272,35377,35378,35380],{},[898,35379,3937],{},[2129,35381,2131],{},[1996,35383,2286],{"separator":2285},[898,35385,9128],{},[1996,35387,2011],{"stretchy":2004},[902,35389,35390],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,35392,35393,35396,35397,35410,35411,35340,35451,1975],{},[38,35394,35395],{},"Duální"," (Hicks): zadáno ",[883,35398,35400],{"className":35399},[886],[888,35401,35402],{"xmlns":890},[892,35403,35404,35408],{},[895,35405,35406],{},[898,35407,900],{},[902,35409,900],{"encoding":904},", hledáme minimální ",[883,35412,35414],{"className":35413},[886],[888,35415,35416],{"xmlns":890},[892,35417,35418,35448],{},[895,35419,35420,35426,35428,35434,35436,35442,35444,35446],{},[2124,35421,35422,35424],{},[898,35423,4252],{},[1996,35425,4354],{},[1996,35427,2005],{"stretchy":2004},[2272,35429,35430,35432],{},[898,35431,3937],{},[2129,35433,2278],{},[1996,35435,2286],{"separator":2285},[2272,35437,35438,35440],{},[898,35439,3937],{},[2129,35441,2131],{},[1996,35443,2286],{"separator":2285},[898,35445,900],{},[1996,35447,2011],{"stretchy":2004},[902,35449,35450],{"encoding":904},"E^*(P_1, P_2, U)",[883,35452,35454],{"className":35453},[886],[888,35455,35456],{"xmlns":890},[892,35457,35458,35499],{},[895,35459,35460,35466,35468,35477,35479,35485,35487,35493,35495,35497],{},[2272,35461,35462,35464],{},[898,35463,2789],{},[898,35465,17792],{},[1996,35467,1998],{},[9166,35469,35470,35472,35474],{},[898,35471,4183],{},[898,35473,17792],{},[898,35475,35476],{},"H",[1996,35478,2005],{"stretchy":2004},[2272,35480,35481,35483],{},[898,35482,3937],{},[2129,35484,2278],{},[1996,35486,2286],{"separator":2285},[2272,35488,35489,35491],{},[898,35490,3937],{},[2129,35492,2131],{},[1996,35494,2286],{"separator":2285},[898,35496,900],{},[1996,35498,2011],{"stretchy":2004},[902,35500,35501],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,35503,35504,35505,35508,35509,35512],{},"Proč se studují obě? Marshallova poptávka je ",[38,35506,35507],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,35510,35511],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,35514,35516],{"id":35515},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,35518,35520],{"id":35519},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,35522,35523,35526,35527,35559,35560,35598,35599,35625],{},[38,35524,35525],{},"6.8"," Jsou dány užitečnost ",[883,35528,35530],{"className":35529},[886],[888,35531,35532],{"xmlns":890},[892,35533,35534,35556],{},[895,35535,35536,35538,35540,35548],{},[898,35537,900],{},[1996,35539,1998],{},[9166,35541,35542,35544,35546],{},[898,35543,2789],{},[2129,35545,2278],{},[2129,35547,5009],{},[9166,35549,35550,35552,35554],{},[898,35551,2789],{},[2129,35553,2131],{},[2129,35555,5009],{},[902,35557,35558],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,35561,35563],{"className":35562},[886],[888,35564,35565],{"xmlns":890},[892,35566,35567,35595],{},[895,35568,35569,35577,35579,35581,35583,35591,35593],{},[9166,35570,35571,35573,35575],{},[898,35572,3937],{},[2129,35574,2278],{},[1996,35576,4354],{},[1996,35578,1998],{},[2129,35580,2351],{},[1996,35582,2286],{"separator":2285},[9166,35584,35585,35587,35589],{},[898,35586,3937],{},[2129,35588,2131],{},[1996,35590,4354],{},[1996,35592,1998],{},[2129,35594,2863],{},[902,35596,35597],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,35600,35602],{"className":35601},[886],[888,35603,35604],{"xmlns":890},[892,35605,35606,35622],{},[895,35607,35608,35614,35616],{},[2272,35609,35610,35612],{},[898,35611,2789],{},[2129,35613,2278],{},[1996,35615,2286],{"separator":2285},[2272,35617,35618,35620],{},[898,35619,2789],{},[2129,35621,2131],{},[902,35623,35624],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,35627,35628,35631,35632,35674,35675,35706,35707,35729,35730,1975],{},[38,35629,35630],{},"6.9"," Jsou dány rozpočtové omezení ",[883,35633,35635],{"className":35634},[886],[888,35636,35637],{"xmlns":890},[892,35638,35639,35671],{},[895,35640,35641,35643,35645,35651,35657,35659,35665],{},[898,35642,9128],{},[1996,35644,1998],{},[2272,35646,35647,35649],{},[898,35648,3937],{},[2129,35650,2278],{},[2272,35652,35653,35655],{},[898,35654,2789],{},[2129,35656,2278],{},[1996,35658,2095],{},[2272,35660,35661,35663],{},[898,35662,3937],{},[2129,35664,2131],{},[2272,35666,35667,35669],{},[898,35668,2789],{},[2129,35670,2131],{},[902,35672,35673],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,35676,35678],{"className":35677},[886],[888,35679,35680],{"xmlns":890},[892,35681,35682,35704],{},[895,35683,35684,35686,35688,35696],{},[898,35685,900],{},[1996,35687,1998],{},[9166,35689,35690,35692,35694],{},[898,35691,2789],{},[2129,35693,2278],{},[2129,35695,5009],{},[9166,35697,35698,35700,35702],{},[898,35699,2789],{},[2129,35701,2131],{},[2129,35703,5009],{},[902,35705,35558],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,35708,35710],{"className":35709},[886],[888,35711,35712],{"xmlns":890},[892,35713,35714,35726],{},[895,35715,35716,35722,35724],{},[2124,35717,35718,35720],{},[898,35719,9128],{},[1996,35721,4354],{},[1996,35723,1998],{},[2129,35725,15112],{},[902,35727,35728],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,35731,35733],{"className":35732},[886],[888,35734,35735],{"xmlns":890},[892,35736,35737,35765],{},[895,35738,35739,35747,35749,35751,35753,35761,35763],{},[9166,35740,35741,35743,35745],{},[898,35742,3937],{},[2129,35744,2278],{},[1996,35746,4354],{},[1996,35748,1998],{},[2129,35750,2228],{},[1996,35752,2286],{"separator":2285},[9166,35754,35755,35757,35759],{},[898,35756,3937],{},[2129,35758,2131],{},[1996,35760,4354],{},[1996,35762,1998],{},[2129,35764,2863],{},[902,35766,35767],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,35769,35770,35773,35774,21596,35806,35836,35837,1975],{},[38,35771,35772],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,35775,35777],{"className":35776},[886],[888,35778,35779],{"xmlns":890},[892,35780,35781,35803],{},[895,35782,35783,35785,35787,35795],{},[898,35784,900],{},[1996,35786,1998],{},[9166,35788,35789,35791,35793],{},[898,35790,2789],{},[2129,35792,2278],{},[898,35794,207],{},[9166,35796,35797,35799,35801],{},[898,35798,2789],{},[2129,35800,2131],{},[898,35802,2098],{},[902,35804,35805],{"encoding":904},"U = Q_1^a Q_2^b",[883,35807,35809],{"className":35808},[886],[888,35810,35811],{"xmlns":890},[892,35812,35813,35833],{},[895,35814,35815,35817,35819,35821,35823,35825,35827,35829,35831],{},[898,35816,207],{},[1996,35818,2286],{"separator":2285},[898,35820,2098],{},[1996,35822,6506],{},[1996,35824,5324],{"stretchy":2004},[2129,35826,2327],{},[1996,35828,2286],{"separator":2285},[2129,35830,2278],{},[1996,35832,5341],{"stretchy":2004},[902,35834,35835],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,35838,35840],{"className":35839},[886],[888,35841,35842],{"xmlns":890},[892,35843,35844,35876],{},[895,35845,35846,35848,35850,35856,35862,35864,35870],{},[898,35847,9128],{},[1996,35849,1998],{},[2272,35851,35852,35854],{},[898,35853,3937],{},[2129,35855,2278],{},[2272,35857,35858,35860],{},[898,35859,2789],{},[2129,35861,2278],{},[1996,35863,2095],{},[2272,35865,35866,35868],{},[898,35867,3937],{},[2129,35869,2131],{},[2272,35871,35872,35874],{},[898,35873,2789],{},[2129,35875,2131],{},[902,35877,35673],{"encoding":904},[724,35879,35880,35883,35884,21596,35918,35836,35936,1975],{},[38,35881,35882],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,35885,35887],{"className":35886},[886],[888,35888,35889],{"xmlns":890},[892,35890,35891,35915],{},[895,35892,35893,35895,35897,35905,35907],{},[898,35894,900],{},[1996,35896,1998],{},[9166,35898,35899,35901,35903],{},[898,35900,2789],{},[2129,35902,2278],{},[898,35904,207],{},[1996,35906,2095],{},[9166,35908,35909,35911,35913],{},[898,35910,2789],{},[2129,35912,2131],{},[898,35914,207],{},[902,35916,35917],{"encoding":904},"U = Q_1^a + Q_2^a",[883,35919,35921],{"className":35920},[886],[888,35922,35923],{"xmlns":890},[892,35924,35925,35933],{},[895,35926,35927,35929,35931],{},[898,35928,207],{},[1996,35930,3371],{"mathvariant":2376},[2129,35932,2327],{},[902,35934,35935],{"encoding":904},"a \\neq 0",[883,35937,35939],{"className":35938},[886],[888,35940,35941],{"xmlns":890},[892,35942,35943,35975],{},[895,35944,35945,35947,35949,35955,35961,35963,35969],{},[898,35946,9128],{},[1996,35948,1998],{},[2272,35950,35951,35953],{},[898,35952,3937],{},[2129,35954,2278],{},[2272,35956,35957,35959],{},[898,35958,2789],{},[2129,35960,2278],{},[1996,35962,2095],{},[2272,35964,35965,35967],{},[898,35966,3937],{},[2129,35968,2131],{},[2272,35970,35971,35973],{},[898,35972,2789],{},[2129,35974,2131],{},[902,35976,35673],{"encoding":904},[198,35978,35980],{"id":35979},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,35982,35983,35526,35986,1343,36013,36035,36036,1343,36059,36083,36084,36109,36110,1975],{},[38,35984,35985],{},"6.12",[883,35987,35989],{"className":35988},[886],[888,35990,35991],{"xmlns":890},[892,35992,35993,36011],{},[895,35994,35995,35997,35999,36005],{},[898,35996,900],{},[1996,35998,1998],{},[2272,36000,36001,36003],{},[898,36002,2789],{},[2129,36004,2278],{},[2272,36006,36007,36009],{},[898,36008,2789],{},[2129,36010,2131],{},[902,36012,30228],{"encoding":904},[883,36014,36016],{"className":36015},[886],[888,36017,36018],{"xmlns":890},[892,36019,36020,36032],{},[895,36021,36022,36028,36030],{},[2124,36023,36024,36026],{},[898,36025,900],{},[1996,36027,4354],{},[1996,36029,1998],{},[2129,36031,2863],{},[902,36033,36034],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,36037,36039],{"className":36038},[886],[888,36040,36041],{"xmlns":890},[892,36042,36043,36057],{},[895,36044,36045,36053,36055],{},[9166,36046,36047,36049,36051],{},[898,36048,3937],{},[2129,36050,2278],{},[1996,36052,4354],{},[1996,36054,1998],{},[2129,36056,2131],{},[902,36058,30301],{"encoding":904},[883,36060,36062],{"className":36061},[886],[888,36063,36064],{"xmlns":890},[892,36065,36066,36080],{},[895,36067,36068,36076,36078],{},[9166,36069,36070,36072,36074],{},[898,36071,3937],{},[2129,36073,2131],{},[1996,36075,4354],{},[1996,36077,1998],{},[2129,36079,2351],{},[902,36081,36082],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,36085,36087],{"className":36086},[886],[888,36088,36089],{"xmlns":890},[892,36090,36091,36107],{},[895,36092,36093,36099,36101],{},[2272,36094,36095,36097],{},[898,36096,2789],{},[2129,36098,2278],{},[1996,36100,2286],{"separator":2285},[2272,36102,36103,36105],{},[898,36104,2789],{},[2129,36106,2131],{},[902,36108,35624],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,36111,36113],{"className":36112},[886],[888,36114,36115],{"xmlns":890},[892,36116,36117,36137],{},[895,36118,36119,36121,36123,36129,36131],{},[898,36120,900],{},[1996,36122,1998],{},[2272,36124,36125,36127],{},[898,36126,2789],{},[2129,36128,2278],{},[1996,36130,3177],{},[2272,36132,36133,36135],{},[898,36134,2789],{},[2129,36136,2131],{},[902,36138,36139],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,36141,36142,36145,36146,36187,36188,36210,36211,1975],{},[38,36143,36144],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,36147,36149],{"className":36148},[886],[888,36150,36151],{"xmlns":890},[892,36152,36153,36185],{},[895,36154,36155,36157,36159,36165,36171,36173,36179],{},[898,36156,4252],{},[1996,36158,1998],{},[2272,36160,36161,36163],{},[898,36162,3937],{},[2129,36164,2278],{},[2272,36166,36167,36169],{},[898,36168,2789],{},[2129,36170,2278],{},[1996,36172,2095],{},[2272,36174,36175,36177],{},[898,36176,3937],{},[2129,36178,2131],{},[2272,36180,36181,36183],{},[898,36182,2789],{},[2129,36184,2131],{},[902,36186,27945],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,36189,36191],{"className":36190},[886],[888,36192,36193],{"xmlns":890},[892,36194,36195,36207],{},[895,36196,36197,36203,36205],{},[2124,36198,36199,36201],{},[898,36200,900],{},[1996,36202,4354],{},[1996,36204,1998],{},[2129,36206,5004],{},[902,36208,36209],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,36212,36214],{"className":36213},[886],[888,36215,36216],{"xmlns":890},[892,36217,36218,36247],{},[895,36219,36220,36228,36230,36232,36234,36242,36244],{},[9166,36221,36222,36224,36226],{},[898,36223,3937],{},[2129,36225,2278],{},[1996,36227,4354],{},[1996,36229,1998],{},[2129,36231,9035],{},[1996,36233,2286],{"separator":2285},[9166,36235,36236,36238,36240],{},[898,36237,3937],{},[2129,36239,2131],{},[1996,36241,4354],{},[1996,36243,1998],{},[2129,36245,36246],{},"15",[902,36248,36249],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,36251,15722],{"id":15721},[120,36253,36254,36311,36350,36370,36405,36459,36464,36470,36566,36611],{},[123,36255,36256,2203,36259,36308,36309,1975],{},[38,36257,36258],{},"Rozpočtové omezení (budget constraint)",[883,36260,36262],{"className":36261},[886],[888,36263,36264],{"xmlns":890},[892,36265,36266,36306],{},[895,36267,36268,36274,36276,36284,36290,36292,36300],{},[2124,36269,36270,36272],{},[898,36271,9128],{},[1996,36273,4354],{},[1996,36275,1998],{},[9166,36277,36278,36280,36282],{},[898,36279,3937],{},[2129,36281,2278],{},[1996,36283,4354],{},[2272,36285,36286,36288],{},[898,36287,2789],{},[2129,36289,2278],{},[1996,36291,2095],{},[9166,36293,36294,36296,36298],{},[898,36295,3937],{},[2129,36297,2131],{},[1996,36299,4354],{},[2272,36301,36302,36304],{},[898,36303,2789],{},[2129,36305,2131],{},[902,36307,17300],{"encoding":904}," — (6.12); ",[38,36310,28138],{},[123,36312,36313,36316,36317,1975],{},[38,36314,36315],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,36318,36320],{"className":36319},[886],[888,36321,36322],{"xmlns":890},[892,36323,36324,36348],{},[895,36325,36326,36328,36330,36338,36340],{},[2288,36327,10603],{},[1996,36329,1998],{},[9166,36331,36332,36334,36336],{},[898,36333,3937],{},[2129,36335,2278],{},[1996,36337,4354],{},[898,36339,4674],{"mathvariant":2376},[9166,36341,36342,36344,36346],{},[898,36343,3937],{},[2129,36345,2131],{},[1996,36347,4354],{},[902,36349,28981],{"encoding":904},[123,36351,36352,36367,36368,1975],{},[38,36353,29125,36354],{},[883,36355,36357],{"className":36356},[886],[888,36358,36359],{"xmlns":890},[892,36360,36361,36365],{},[895,36362,36363],{},[898,36364,16445],{},[902,36366,16498],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,36369,29147],{},[123,36371,36372,36375,36376,1975],{},[38,36373,36374],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,36377,36379],{"className":36378},[886],[888,36380,36381],{"xmlns":890},[892,36382,36383,36403],{},[895,36384,36385,36387,36389,36395,36397],{},[2288,36386,10603],{},[1996,36388,1998],{},[2272,36390,36391,36393],{},[898,36392,3937],{},[2129,36394,2278],{},[898,36396,4674],{"mathvariant":2376},[2272,36398,36399,36401],{},[898,36400,3937],{},[2129,36402,2131],{},[902,36404,28000],{"encoding":904},[123,36406,36407,7015,36410,36458],{},[38,36408,36409],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,36411,36413],{"className":36412},[886],[888,36414,36415],{"xmlns":890},[892,36416,36417,36455],{},[895,36418,36419,36425,36427,36433,36435,36441,36443,36449,36451,36453],{},[2272,36420,36421,36423],{},[898,36422,2789],{},[898,36424,17792],{},[1996,36426,1998],{},[2272,36428,36429,36431],{},[898,36430,4183],{},[898,36432,17792],{},[1996,36434,2005],{"stretchy":2004},[2272,36436,36437,36439],{},[898,36438,3937],{},[2129,36440,2278],{},[1996,36442,2286],{"separator":2285},[2272,36444,36445,36447],{},[898,36446,3937],{},[2129,36448,2131],{},[1996,36450,2286],{"separator":2285},[898,36452,9128],{},[1996,36454,2011],{"stretchy":2004},[902,36456,36457],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,36460,36461,36463],{},[38,36462,31729],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,36465,36466,36469],{},[38,36467,36468],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,36471,36472,7015,36474,36521,36522,36565],{},[38,36473,34041],{},[883,36475,36477],{"className":36476},[886],[888,36478,36479],{"xmlns":890},[892,36480,36481,36519],{},[895,36482,36483,36489,36491,36497,36499,36505,36507,36513,36515,36517],{},[2272,36484,36485,36487],{},[898,36486,2789],{},[898,36488,17792],{},[1996,36490,1998],{},[2272,36492,36493,36495],{},[898,36494,4183],{},[898,36496,17792],{},[1996,36498,2005],{"stretchy":2004},[2272,36500,36501,36503],{},[898,36502,3937],{},[2129,36504,2278],{},[1996,36506,2286],{"separator":2285},[2272,36508,36509,36511],{},[898,36510,3937],{},[2129,36512,2131],{},[1996,36514,2286],{"separator":2285},[898,36516,900],{},[1996,36518,2011],{"stretchy":2004},[902,36520,17825],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,36523,36525],{"className":36524},[886],[888,36526,36527],{"xmlns":890},[892,36528,36529,36563],{},[895,36530,36531,36533,36535,36549],{},[898,36532,900],{},[1996,36534,1998],{},[9166,36536,36537,36539,36541],{},[898,36538,2789],{},[2129,36540,2278],{},[895,36542,36543,36545,36547],{},[2129,36544,2278],{},[898,36546,4674],{"mathvariant":2376},[2129,36548,2131],{},[9166,36550,36551,36553,36555],{},[898,36552,2789],{},[2129,36554,2131],{},[895,36556,36557,36559,36561],{},[2129,36558,2278],{},[898,36560,4674],{"mathvariant":2376},[2129,36562,2131],{},[902,36564,33161],{"encoding":904},": (6.30).",[123,36567,36568,36610],{},[38,36569,36570,36571],{},"Bod dotyku ",[883,36572,36574],{"className":36573},[886],[888,36575,36576],{"xmlns":890},[892,36577,36578,36608],{},[895,36579,36580,36586,36588,36596,36598,36606],{},[2124,36581,36582,36584],{},[898,36583,2789],{},[1996,36585,4354],{},[1996,36587,2486],{"stretchy":2004},[9166,36589,36590,36592,36594],{},[898,36591,2789],{},[2129,36593,2278],{},[1996,36595,4354],{},[1996,36597,2286],{"separator":2285},[9166,36599,36600,36602,36604],{},[898,36601,2789],{},[2129,36603,2131],{},[1996,36605,4354],{},[1996,36607,2501],{"stretchy":2004},[902,36609,28329],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,36612,36613,36616,36617,36630,36631,36644],{},[38,36614,36615],{},"Dualita"," — ekvivalence max ",[883,36618,36620],{"className":36619},[886],[888,36621,36622],{"xmlns":890},[892,36623,36624,36628],{},[895,36625,36626],{},[898,36627,900],{},[902,36629,900],{"encoding":904}," a min ",[883,36632,36634],{"className":36633},[886],[888,36635,36636],{"xmlns":890},[892,36637,36638,36642],{},[895,36639,36640],{},[898,36641,4252],{},[902,36643,4252],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,36646,3792],{"id":3791},[120,36648,36649,36672,36688,36701,36712],{},[123,36650,36651,2203,36654,36657,36658,36671],{},[38,36652,36653],{},"Teorie před optimalizací:",[207,36655,880],{"className":36656,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,36659,36661],{"className":36660},[886],[888,36662,36663],{"xmlns":890},[892,36664,36665,36669],{},[895,36666,36667],{},[898,36668,900],{},[902,36670,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,36673,36674,2203,36677,36680,36681,36684,36685,1975],{},[38,36675,36676],{},"Matematický aparát:",[207,36678,793],{"className":36679,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,36682,784],{"className":36683,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,36686,2357],{"className":36687,"dataFsResolvedFilePath":764,"href":765},[210],[123,36689,36690,2203,36693,36696,36697,36700],{},[38,36691,36692],{},"Paralely:",[207,36694,11088],{"className":36695,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,36698,11942],{"className":36699,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,36702,36703,2203,36706,1343,36709],{},[38,36704,36705],{},"Přednášky:",[207,36707,1094],{"className":36708,"dataFsResolvedFilePath":838,"href":839},[210],[207,36710,1101],{"className":36711,"dataFsResolvedFilePath":868,"href":869},[210],[123,36713,36714,2203,36716],{},[38,36715,16206],{},[207,36717,16210],{"className":36718,"dataFsResolvedFilePath":1960,"href":1961},[210],{"title":641,"searchDepth":642,"depth":642,"links":36720},[36721,36722,36723,36728,36729,36730,36732,36735,36738,36740,36741,36743,36744,36748,36749],{"id":12007,"depth":642,"text":12008},{"id":28008,"depth":642,"text":28009},{"id":28406,"depth":642,"text":28407,"children":36724},[36725,36726],{"id":28526,"depth":649,"text":28527},{"id":29107,"depth":649,"text":36727},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":29569,"depth":642,"text":29570},{"id":29880,"depth":642,"text":29881},{"id":30199,"depth":642,"text":36731},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":30972,"depth":642,"text":30973,"children":36733},[36734],{"id":31728,"depth":649,"text":31729},{"id":31908,"depth":642,"text":31909,"children":36736},[36737],{"id":32165,"depth":649,"text":32166},{"id":33116,"depth":642,"text":36739},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":34040,"depth":642,"text":34041},{"id":34243,"depth":642,"text":36742},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":35128,"depth":642,"text":35129},{"id":35515,"depth":642,"text":35516,"children":36745},[36746,36747],{"id":35519,"depth":649,"text":35520},{"id":35979,"depth":649,"text":35980},{"id":15721,"depth":642,"text":15722},{"id":3791,"depth":642,"text":3792},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":27769,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,36756,1144,9773,36757,36758,36759],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":36762,"title":802,"body":36763,"course":1128,"courses":659,"created":9556,"description":641,"extension":661,"meta":50816,"navigation":664,"path":50817,"seo":50818,"sources":50819,"stem":50820,"tags":50821,"type":3857,"updated":677,"__hash__":50827},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":36764,"toc":50772},[36765,36768,36794,36798,36805,36957,36971,36974,36976,37063,37067,37103,37176,37197,37322,37332,37345,37349,37354,37384,37446,37455,37459,37521,37528,37549,37667,37745,37749,37752,37811,37926,37931,37963,38025,38073,38128,38132,38153,38177,38225,38229,38241,38245,38355,38359,38375,38416,38427,38586,38596,38601,38605,38727,38737,38744,38748,38826,38837,38917,38923,38930,39069,39076,39079,39136,39140,39218,39264,39308,39314,39427,39431,39434,39629,39633,39870,39873,40027,40180,40182,40184,40264,40267,40372,40441,40450,40454,40457,40518,40527,40531,40564,40642,40681,40685,40734,40788,40792,40821,40850,40902,40909,40963,41041,41045,41088,41155,41199,41303,41322,41324,41328,41436,41440,41508,41557,41564,41649,41653,41725,41730,41778,41967,41971,41976,42152,42157,42216,42321,42325,42352,42356,42363,42527,42614,42619,42621,42624,42724,42874,42946,43020,43022,43026,43040,43044,43177,43232,43344,43421,43425,43482,43585,43644,43805,43809,43884,43956,44054,44112,44206,44259,44280,44334,44339,44417,44465,44552,44590,44678,44831,44867,44921,44924,44926,44928,44977,44984,44992,45079,45088,45175,45182,45184,45188,45413,45415,45419,45423,45492,45543,45746,45752,45763,45831,45837,46259,46263,46327,46351,46547,46553,46567,46635,46638,46678,46902,46970,47272,47681,47758,47924,47930,47933,48008,48461,48512,48918,49023,49686,49689,49766,49774,49848,49879,49881,49885,49929,49931,49933,49937,50167,50171,50262,50267,50361,50366,50539,50543,50661,50666,50715,50717,50719],[12,36766,802],{"id":36767},"poptávka-nabídka-a-tržní-rovnováha",[3867,36769,36770],{},[724,36771,36772,36774,36775,36778,36779,36782,36783,36786,36787,36789,36790,36793],{},[883,36773,4155],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,36776,36777],{},"poptávka",") a výrobce (",[38,36780,36781],{},"nabídka","), jejich interakci v ",[38,36784,36785],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,36788,17979],{},"). Uzavírá ji pojem ",[38,36791,36792],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,36795,36797],{"id":36796},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,36799,36800,36801,36804],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,36802,36803],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,36806,36807,36824,36866,36882],{},[123,36808,36809,36810,36823],{},"cena ",[883,36811,36813],{"className":36812},[886],[888,36814,36815],{"xmlns":890},[892,36816,36817,36821],{},[895,36818,36819],{},[898,36820,3937],{},[902,36822,3937],{"encoding":904}," zkoumaného zboží,",[123,36825,36826,36827,2286],{},"ceny alternativních zboží ",[883,36828,36830],{"className":36829},[886],[888,36831,36832],{"xmlns":890},[892,36833,36834,36863],{},[895,36835,36836,36842,36844,36850,36852,36854,36856],{},[2272,36837,36838,36840],{},[898,36839,3937],{},[2129,36841,2278],{},[1996,36843,2286],{"separator":2285},[2272,36845,36846,36848],{},[898,36847,3937],{},[2129,36849,2131],{},[1996,36851,2286],{"separator":2285},[1996,36853,9646],{},[1996,36855,2286],{"separator":2285},[2272,36857,36858,36860],{},[898,36859,3937],{},[898,36861,36862],{},"n",[902,36864,36865],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,36867,36868,36869,2286],{},"důchod ",[883,36870,36872],{"className":36871},[886],[888,36873,36874],{"xmlns":890},[892,36875,36876,36880],{},[895,36877,36878],{},[898,36879,9128],{},[902,36881,9128],{"encoding":904},[123,36883,36884,36885,36898,36899,36912,36913,36926,36927,36941,36942,36956],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,36886,36888],{"className":36887},[886],[888,36889,36890],{"xmlns":890},[892,36891,36892,36896],{},[895,36893,36894],{},[898,36895,9795],{},[902,36897,9795],{"encoding":904},", kapitál ",[883,36900,36902],{"className":36901},[886],[888,36903,36904],{"xmlns":890},[892,36905,36906,36910],{},[895,36907,36908],{},[898,36909,9800],{},[902,36911,9800],{"encoding":904},", půda ",[883,36914,36916],{"className":36915},[886],[888,36917,36918],{"xmlns":890},[892,36919,36920,36924],{},[895,36921,36922],{},[898,36923,4252],{},[902,36925,4252],{"encoding":904},"), technologie, počet výrobců ",[883,36928,36930],{"className":36929},[886],[888,36931,36932],{"xmlns":890},[892,36933,36934,36939],{},[895,36935,36936],{},[898,36937,36938],{},"O",[902,36940,36938],{"encoding":904},", počasí ",[883,36943,36945],{"className":36944},[886],[888,36946,36947],{"xmlns":890},[892,36948,36949,36954],{},[895,36950,36951],{},[898,36952,36953],{},"W",[902,36955,36953],{"encoding":904}," atd.",[724,36958,36959,36960,36963,36964,36967,36968,1975],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,36961,36962],{},"ceteris paribus","), hovoříme o ",[38,36965,36966],{},"jednofaktorovém modelu","; jinak jde o model ",[38,36969,36970],{},"vícefaktorový",[36972,36973],"hr",{},[115,36975,13163],{"id":36777},[3867,36977,36978],{},[724,36979,36980,36982,36983,36996,36997,37010,37011,37014,37015,37038,37039,1975],{},[883,36981,4155],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,36984,36986],{"className":36985},[886],[888,36987,36988],{"xmlns":890},[892,36989,36990,36994],{},[895,36991,36992],{},[898,36993,2789],{},[902,36995,2789],{"encoding":904}," na ceně ",[883,36998,37000],{"className":36999},[886],[888,37001,37002],{"xmlns":890},[892,37003,37004,37008],{},[895,37005,37006],{},[898,37007,3937],{},[902,37009,3937],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,37012,37013],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,37016,37018],{"className":37017},[886],[888,37019,37020],{"xmlns":890},[892,37021,37022,37036],{},[895,37023,37024,37026,37028,37030,37032,37034],{},[898,37025,2789],{},[1996,37027,1998],{},[898,37029,4183],{},[1996,37031,2005],{"stretchy":2004},[898,37033,3937],{},[1996,37035,2011],{"stretchy":2004},[902,37037,4192],{"encoding":904}," a jeho lineární verzí ",[883,37040,37042],{"className":37041},[886],[888,37043,37044],{"xmlns":890},[892,37045,37046,37060],{},[895,37047,37048,37050,37052,37054,37056,37058],{},[898,37049,3937],{},[1996,37051,1998],{},[898,37053,207],{},[898,37055,2789],{},[1996,37057,2095],{},[898,37059,2098],{},[902,37061,37062],{"encoding":904},"P = aQ + b",[198,37064,37066],{"id":37065},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,37068,37069,37070,37083,37084,37097,37098,10025,37100,3151],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,37071,37073],{"className":37072},[886],[888,37074,37075],{"xmlns":890},[892,37076,37077,37081],{},[895,37078,37079],{},[898,37080,2789],{},[902,37082,2789],{"encoding":904}," závisí na ceně ",[883,37085,37087],{"className":37086},[886],[888,37088,37089],{"xmlns":890},[892,37090,37091,37095],{},[895,37092,37093],{},[898,37094,3937],{},[902,37096,3937],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,37099,28004],{},[614,37101,37102],{},"demand function",[883,37104,37106],{"className":37105},[886],[888,37107,37108],{"xmlns":890,"display":28068},[892,37109,37110,37173],{},[20756,37111,37112],{"width":28073},[20761,37113,37114,37116,37166,37168],{},[20764,37115],{"width":28078},[20764,37117,37118],{},[895,37119,37120,37122,37124,37126,37128,37130,37132,37138,37140,37146,37148,37150,37152,37158,37160,37162,37164],{},[898,37121,2789],{},[1996,37123,1998],{},[898,37125,4183],{},[1996,37127,2005],{"stretchy":2004},[898,37129,3937],{},[1996,37131,2286],{"separator":2285},[2272,37133,37134,37136],{},[898,37135,3937],{},[2129,37137,2278],{},[1996,37139,2286],{"separator":2285},[2272,37141,37142,37144],{},[898,37143,3937],{},[2129,37145,2131],{},[1996,37147,2286],{"separator":2285},[1996,37149,9646],{},[1996,37151,2286],{"separator":2285},[2272,37153,37154,37156],{},[898,37155,3937],{},[898,37157,36862],{},[1996,37159,2286],{"separator":2285},[898,37161,9128],{},[1996,37163,2011],{"stretchy":2004},[898,37165,1975],{"mathvariant":2376},[20764,37167],{"width":28078},[20764,37169,37170],{},[2288,37171,37172],{},"(2.1)",[902,37174,37175],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,37177,37178,37179,37182,37183,37196],{},"Důležitou vlastností je ",[38,37180,37181],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,37184,37186],{"className":37185},[886],[888,37187,37188],{"xmlns":890},[892,37189,37190,37194],{},[895,37191,37192],{},[898,37193,12043],{},[902,37195,12043],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,37198,37200],{"className":37199},[886],[888,37201,37202],{"xmlns":890,"display":28068},[892,37203,37204,37319],{},[20756,37205,37206],{"width":28073},[20761,37207,37208,37210,37312,37314],{},[20764,37209],{"width":28078},[20764,37211,37212],{},[895,37213,37214,37216,37218,37220,37222,37224,37226,37228,37230,37236,37238,37240,37246,37248,37250,37252,37254,37260,37262,37264,37266,37268,37270,37272,37274,37276,37278,37284,37286,37292,37294,37296,37298,37304,37306,37308,37310],{},[898,37215,2789],{},[1996,37217,1998],{},[898,37219,4183],{},[1996,37221,2005],{"stretchy":2004},[898,37223,12043],{},[898,37225,3937],{},[1996,37227,2286],{"separator":2285},[898,37229,12043],{},[2272,37231,37232,37234],{},[898,37233,3937],{},[2129,37235,2278],{},[1996,37237,2286],{"separator":2285},[898,37239,12043],{},[2272,37241,37242,37244],{},[898,37243,3937],{},[2129,37245,2131],{},[1996,37247,2286],{"separator":2285},[1996,37249,9646],{},[1996,37251,2286],{"separator":2285},[898,37253,12043],{},[2272,37255,37256,37258],{},[898,37257,3937],{},[898,37259,36862],{},[1996,37261,2286],{"separator":2285},[898,37263,12043],{},[898,37265,9128],{},[1996,37267,2011],{"stretchy":2004},[1996,37269,1998],{},[898,37271,4183],{},[1996,37273,2005],{"stretchy":2004},[898,37275,3937],{},[1996,37277,2286],{"separator":2285},[2272,37279,37280,37282],{},[898,37281,3937],{},[2129,37283,2278],{},[1996,37285,2286],{"separator":2285},[2272,37287,37288,37290],{},[898,37289,3937],{},[2129,37291,2131],{},[1996,37293,2286],{"separator":2285},[1996,37295,9646],{},[1996,37297,2286],{"separator":2285},[2272,37299,37300,37302],{},[898,37301,3937],{},[898,37303,36862],{},[1996,37305,2286],{"separator":2285},[898,37307,9128],{},[1996,37309,2011],{"stretchy":2004},[898,37311,1975],{"mathvariant":2376},[20764,37313],{"width":28078},[20764,37315,37316],{},[2288,37317,37318],{},"(2.2)",[902,37320,37321],{"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}",[3867,37323,37324],{},[724,37325,37326,37328,37329,1975],{},[883,37327,4412],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,37330,37331],{},"v jednofaktorových modelech neplatí",[724,37333,37334,37335,1343,37338,3885,37341,37344],{},"Rozlišuje se poptávka ",[38,37336,37337],{},"individuální",[38,37339,37340],{},"tržní",[38,37342,37343],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,37346,37348],{"id":37347},"jednofaktorové-modely","Jednofaktorové modely",[37350,37351,37353],"h4",{"id":37352},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,37355,37356,37357,37370,37371,2704],{},"Poptávané množství ",[883,37358,37360],{"className":37359},[886],[888,37361,37362],{"xmlns":890},[892,37363,37364,37368],{},[895,37365,37366],{},[898,37367,2789],{},[902,37369,2789],{"encoding":904}," závisí pouze na ceně ",[883,37372,37374],{"className":37373},[886],[888,37375,37376],{"xmlns":890},[892,37377,37378,37382],{},[895,37379,37380],{},[898,37381,3937],{},[902,37383,3937],{"encoding":904},[883,37385,37387],{"className":37386},[886],[888,37388,37389],{"xmlns":890,"display":28068},[892,37390,37391,37443],{},[20756,37392,37393],{"width":28073},[20761,37394,37395,37397,37436,37438],{},[20764,37396],{"width":28078},[20764,37398,37399],{},[895,37400,37401,37403,37405,37407,37409,37411,37413,37415,37417,37420,37422,37424,37426,37428,37430,37432,37434],{},[898,37402,2789],{},[1996,37404,1998],{},[898,37406,4183],{},[1996,37408,2005],{"stretchy":2004},[898,37410,3937],{},[1996,37412,2011],{"stretchy":2004},[1996,37414,2286],{"separator":2285},[5878,37416],{"width":5880},[2288,37418,37419],{},"resp.",[5878,37421],{"width":5880},[898,37423,3937],{},[1996,37425,1998],{},[898,37427,4183],{},[1996,37429,2005],{"stretchy":2004},[898,37431,2789],{},[1996,37433,2011],{"stretchy":2004},[898,37435,1975],{"mathvariant":2376},[20764,37437],{"width":28078},[20764,37439,37440],{},[2288,37441,37442],{},"(2.3)",[902,37444,37445],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,37447,37448,37449,10025,37452,3918],{},"Graf této funkce se nazývá ",[38,37450,37451],{},"křivka poptávky",[614,37453,37454],{},"demand curve",[37350,37456,37458],{"id":37457},"zákon-klesající-poptávky","Zákon klesající poptávky",[3867,37460,37461],{},[724,37462,37463],{},[38,37464,37465,37466,37479,37480,37493,37494,37479,37507,37520],{},"Roste-li cena ",[883,37467,37469],{"className":37468},[886],[888,37470,37471],{"xmlns":890},[892,37472,37473,37477],{},[895,37474,37475],{},[898,37476,3937],{},[902,37478,3937],{"encoding":904},", pak množství ",[883,37481,37483],{"className":37482},[886],[888,37484,37485],{"xmlns":890},[892,37486,37487,37491],{},[895,37488,37489],{},[898,37490,2789],{},[902,37492,2789],{"encoding":904}," klesá; klesá-li cena ",[883,37495,37497],{"className":37496},[886],[888,37498,37499],{"xmlns":890},[892,37500,37501,37505],{},[895,37502,37503],{},[898,37504,3937],{},[902,37506,3937],{"encoding":904},[883,37508,37510],{"className":37509},[886],[888,37511,37512],{"xmlns":890},[892,37513,37514,37518],{},[895,37515,37516],{},[898,37517,2789],{},[902,37519,2789],{"encoding":904}," roste.",[724,37522,37523,37524,37527],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,37525,37526],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[3867,37529,37530,37535],{},[724,37531,37532,37534],{},[883,37533,4155],{}," Intuice — proč zákon platí",[120,37536,37537,37543],{},[123,37538,37539,37542],{},[38,37540,37541],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,37544,37545,37548],{},[38,37546,37547],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,37550,37551,37552,37565,37566,37579,37580,37606,37607,37633,37634,8102,37660,37663,37664,1975],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,37553,37555],{"className":37554},[886],[888,37556,37557],{"xmlns":890},[892,37558,37559,37563],{},[895,37560,37561],{},[898,37562,3937],{},[902,37564,3937],{"encoding":904}," se vynáší na svislou osu, množství ",[883,37567,37569],{"className":37568},[886],[888,37570,37571],{"xmlns":890},[892,37572,37573,37577],{},[895,37574,37575],{},[898,37576,2789],{},[902,37578,2789],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,37581,37583],{"className":37582},[886],[888,37584,37585],{"xmlns":890},[892,37586,37587,37603],{},[895,37588,37589,37591,37593,37595,37601],{},[1996,37590,2486],{"stretchy":2004},[2129,37592,2327],{},[1996,37594,2286],{"separator":2285},[2272,37596,37597,37599],{},[898,37598,3937],{},[2129,37600,2327],{},[1996,37602,2501],{"stretchy":2004},[902,37604,37605],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,37608,37610],{"className":37609},[886],[888,37611,37612],{"xmlns":890},[892,37613,37614,37630],{},[895,37615,37616,37618,37624,37626,37628],{},[1996,37617,2486],{"stretchy":2004},[2272,37619,37620,37622],{},[898,37621,2789],{},[2129,37623,2327],{},[1996,37625,2286],{"separator":2285},[2129,37627,2327],{},[1996,37629,2501],{"stretchy":2004},[902,37631,37632],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,37635,37637],{"className":37636},[886],[888,37638,37639],{"xmlns":890},[892,37640,37641,37657],{},[895,37642,37643,37645,37647,37649,37655],{},[1996,37644,2005],{"stretchy":2004},[2129,37646,2327],{},[1996,37648,2286],{"separator":2285},[2272,37650,37651,37653],{},[898,37652,3937],{},[2129,37654,2327],{},[1996,37656,2011],{"stretchy":2004},[902,37658,37659],{"encoding":904},"(0, P_0)",[38,37661,37662],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,37665,37666],{},"konvexní",[724,37668,37669],{},[614,37670,37671,37672,37694,37695,3885,37720,1975],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,37673,37675],{"className":37674},[886],[888,37676,37677],{"xmlns":890},[892,37678,37679,37691],{},[895,37680,37681,37683,37685,37687,37689],{},[1996,37682,2005],{"stretchy":2004},[898,37684,2789],{},[1996,37686,2286],{"separator":2285},[898,37688,3937],{},[1996,37690,2011],{"stretchy":2004},[902,37692,37693],{"encoding":904},"(Q, P)"," — klesající, konvexní, procházející body ",[883,37696,37698],{"className":37697},[886],[888,37699,37700],{"xmlns":890},[892,37701,37702,37718],{},[895,37703,37704,37706,37708,37710,37716],{},[1996,37705,2486],{"stretchy":2004},[2129,37707,2327],{},[1996,37709,2286],{"separator":2285},[2272,37711,37712,37714],{},[898,37713,3937],{},[2129,37715,2327],{},[1996,37717,2501],{"stretchy":2004},[902,37719,37605],{"encoding":904},[883,37721,37723],{"className":37722},[886],[888,37724,37725],{"xmlns":890},[892,37726,37727,37743],{},[895,37728,37729,37731,37737,37739,37741],{},[1996,37730,2486],{"stretchy":2004},[2272,37732,37733,37735],{},[898,37734,2789],{},[2129,37736,2327],{},[1996,37738,2286],{"separator":2285},[2129,37740,2327],{},[1996,37742,2501],{"stretchy":2004},[902,37744,37632],{"encoding":904},[37350,37746,37748],{"id":37747},"lineární-model-poptávky","Lineární model poptávky",[724,37750,37751],{},"Nejjednodušší závislostí je",[883,37753,37755],{"className":37754},[886],[888,37756,37757],{"xmlns":890,"display":28068},[892,37758,37759,37808],{},[20756,37760,37761],{"width":28073},[20761,37762,37763,37765,37801,37803],{},[20764,37764],{"width":28078},[20764,37766,37767],{},[895,37768,37769,37771,37773,37775,37777,37779,37781,37783,37785,37787,37789,37791,37793,37795,37797,37799],{},[898,37770,3937],{},[1996,37772,1998],{},[898,37774,207],{},[898,37776,2789],{},[1996,37778,2095],{},[898,37780,2098],{},[1996,37782,2286],{"separator":2285},[5878,37784],{"width":5880},[898,37786,207],{},[1996,37788,3447],{},[2129,37790,2327],{},[1996,37792,2286],{"separator":2285},[2288,37794,2290],{},[898,37796,2098],{},[1996,37798,3408],{},[2129,37800,12462],{},[20764,37802],{"width":28078},[20764,37804,37805],{},[2288,37806,37807],{},"(2.4)",[902,37809,37810],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,37812,37813,37814,21596,37850,3885,37874,8037,37900,37922,37923,1975],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,37815,37817],{"className":37816},[886],[888,37818,37819],{"xmlns":890},[892,37820,37821,37847],{},[895,37822,37823,37825,37827,37835,37837,37839],{},[898,37824,2789],{},[1996,37826,1998],{},[2325,37828,37829],{"scriptlevel":2327,"displaystyle":2004},[2329,37830,37831,37833],{},[2129,37832,2278],{},[898,37834,207],{},[898,37836,3937],{},[1996,37838,2225],{},[2325,37840,37841],{"scriptlevel":2327,"displaystyle":2004},[2329,37842,37843,37845],{},[898,37844,2098],{},[898,37846,207],{},[902,37848,37849],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,37851,37853],{"className":37852},[886],[888,37854,37855],{"xmlns":890},[892,37856,37857,37871],{},[895,37858,37859,37867,37869],{},[2325,37860,37861],{"scriptlevel":2327,"displaystyle":2004},[2329,37862,37863,37865],{},[2129,37864,2278],{},[898,37866,207],{},[1996,37868,3447],{},[2129,37870,2327],{},[902,37872,37873],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,37875,37877],{"className":37876},[886],[888,37878,37879],{"xmlns":890},[892,37880,37881,37897],{},[895,37882,37883,37885,37893,37895],{},[1996,37884,2225],{},[2325,37886,37887],{"scriptlevel":2327,"displaystyle":2004},[2329,37888,37889,37891],{},[898,37890,2098],{},[898,37892,207],{},[1996,37894,3408],{},[2129,37896,2327],{},[902,37898,37899],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,37901,37903],{"className":37902},[886],[888,37904,37905],{"xmlns":890},[892,37906,37907,37919],{},[895,37908,37909,37911,37913,37915,37917],{},[1996,37910,2005],{"stretchy":2004},[2129,37912,2327],{},[1996,37914,2286],{"separator":2285},[898,37916,2098],{},[1996,37918,2011],{"stretchy":2004},[902,37920,37921],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,37924,37925],{},"nedokonalé konkurenci",[37927,37928,37930],"h5",{"id":37929},"příklad-21","Příklad 2.1",[724,37932,37933,37936,37937,1975],{},[38,37934,37935],{},"Zadání:"," Lineární poptávka ",[883,37938,37940],{"className":37939},[886],[888,37941,37942],{"xmlns":890},[892,37943,37944,37960],{},[895,37945,37946,37948,37950,37952,37954,37956,37958],{},[898,37947,3937],{},[1996,37949,1998],{},[1996,37951,2225],{},[2129,37953,2131],{},[898,37955,2789],{},[1996,37957,2095],{},[2129,37959,3126],{},[902,37961,37962],{"encoding":904},"P = -2Q + 60",[724,37964,37965,37968,37969,37991,37992,1975],{},[38,37966,37967],{},"Řešení:"," Reálné cenové rozpětí je ",[883,37970,37972],{"className":37971},[886],[888,37973,37974],{"xmlns":890},[892,37975,37976,37988],{},[895,37977,37978,37980,37982,37984,37986],{},[1996,37979,2005],{"stretchy":2004},[2129,37981,2327],{},[1996,37983,2286],{"separator":2285},[2129,37985,3126],{},[1996,37987,2011],{"stretchy":2004},[902,37989,37990],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,37993,37995],{"className":37994},[886],[888,37996,37997],{"xmlns":890},[892,37998,37999,38022],{},[895,38000,38001,38003,38005,38007,38015,38017,38019],{},[898,38002,2789],{},[1996,38004,1998],{},[1996,38006,2225],{},[2325,38008,38009],{"scriptlevel":2327,"displaystyle":2004},[2329,38010,38011,38013],{},[2129,38012,2278],{},[2129,38014,2131],{},[898,38016,3937],{},[1996,38018,2095],{},[2129,38020,38021],{},"30",[902,38023,38024],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,38026,38027,38050],{},[19,38028,38029],{},[22,38030,38031,38046,38048],{},[25,38032,38033],{},[883,38034,38036],{"className":38035},[886],[888,38037,38038],{"xmlns":890},[892,38039,38040,38044],{},[895,38041,38042],{},[898,38043,3937],{},[902,38045,3937],{"encoding":904},[25,38047,5211],{},[25,38049,9035],{},[30,38051,38052],{},[22,38053,38054,38069,38071],{},[35,38055,38056],{},[883,38057,38059],{"className":38058},[886],[888,38060,38061],{"xmlns":890},[892,38062,38063,38067],{},[895,38064,38065],{},[898,38066,2789],{},[902,38068,2789],{"encoding":904},[35,38070,2863],{},[35,38072,9035],{},[724,38074,38075],{},[614,38076,38077,38078,3885,38100,1975],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,38079,38081],{"className":38080},[886],[888,38082,38083],{"xmlns":890},[892,38084,38085,38097],{},[895,38086,38087,38089,38091,38093,38095],{},[1996,38088,2486],{"stretchy":2004},[2129,38090,2327],{},[1996,38092,2286],{"separator":2285},[898,38094,2098],{},[1996,38096,2501],{"stretchy":2004},[902,38098,38099],{"encoding":904},"[0, b]",[883,38101,38103],{"className":38102},[886],[888,38104,38105],{"xmlns":890},[892,38106,38107,38125],{},[895,38108,38109,38111,38113,38115,38117,38119,38121,38123],{},[1996,38110,2486],{"stretchy":2004},[1996,38112,2225],{},[898,38114,2098],{},[898,38116,4674],{"mathvariant":2376},[898,38118,207],{},[1996,38120,2286],{"separator":2285},[2129,38122,2327],{},[1996,38124,2501],{"stretchy":2004},[902,38126,38127],{"encoding":904},"[-b\u002Fa, 0]",[37350,38129,38131],{"id":38130},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,38133,38134,38135,38152],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,38136,38138],{"className":38137},[886],[888,38139,38140],{"xmlns":890},[892,38141,38142,38150],{},[895,38143,38144],{},[2124,38145,38146,38148],{},[898,38147,3937],{},[1996,38149,4354],{},[902,38151,4404],{"encoding":904},", je funkce poptávky konstantní:",[883,38154,38156],{"className":38155},[886],[888,38157,38158],{"xmlns":890,"display":28068},[892,38159,38160,38174],{},[895,38161,38162,38164,38166,38172],{},[898,38163,3937],{},[1996,38165,1998],{},[2124,38167,38168,38170],{},[898,38169,3937],{},[1996,38171,4354],{},[898,38173,1975],{"mathvariant":2376},[902,38175,38176],{"encoding":904},"P = P^*.",[724,38178,38179],{},[614,38180,38181,38182,38203,38204,1975],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,38183,38185],{"className":38184},[886],[888,38186,38187],{"xmlns":890},[892,38188,38189,38201],{},[895,38190,38191,38193,38195,38197,38199],{},[1996,38192,2005],{"stretchy":2004},[898,38194,2789],{},[1996,38196,2286],{"separator":2285},[898,38198,3937],{},[1996,38200,2011],{"stretchy":2004},[902,38202,37693],{"encoding":904}," na úrovni ",[883,38205,38207],{"className":38206},[886],[888,38208,38209],{"xmlns":890},[892,38210,38211,38223],{},[895,38212,38213,38215,38217],{},[898,38214,3937],{},[1996,38216,1998],{},[2124,38218,38219,38221],{},[898,38220,3937],{},[1996,38222,4354],{},[902,38224,4357],{"encoding":904},[37350,38226,38228],{"id":38227},"giffenův-statek","Giffenův statek",[724,38230,38231,38232,38234,38235,38237,38238,1975],{},"Existují zboží, u nichž je křivka poptávky ",[38,38233,13659],{}," — tzv. ",[38,38236,38228],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,38239,38240],{},"podřadnému zboží",[37927,38242,38244],{"id":38243},"příklad-22","Příklad 2.2",[724,38246,38247,38250,38251,38269,38270,38292,38293,38311,38312,38330,38331,38354],{},[38,38248,38249],{},"Zadání a popis:"," Křivka ",[883,38252,38254],{"className":38253},[886],[888,38255,38256],{"xmlns":890},[892,38257,38258,38266],{},[895,38259,38260],{},[2272,38261,38262,38264],{},[898,38263,4183],{},[2129,38265,2278],{},[902,38267,38268],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,38271,38273],{"className":38272},[886],[888,38274,38275],{"xmlns":890},[892,38276,38277,38289],{},[895,38278,38279,38281,38283,38285,38287],{},[1996,38280,2005],{"stretchy":2004},[2129,38282,2327],{},[1996,38284,2286],{"separator":2285},[2129,38286,36246],{},[1996,38288,2011],{"stretchy":2004},[902,38290,38291],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,38294,38296],{"className":38295},[886],[888,38297,38298],{"xmlns":890},[892,38299,38300,38308],{},[895,38301,38302],{},[2272,38303,38304,38306],{},[898,38305,2789],{},[2129,38307,2327],{},[902,38309,38310],{"encoding":904},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[883,38313,38315],{"className":38314},[886],[888,38316,38317],{"xmlns":890},[892,38318,38319,38327],{},[895,38320,38321],{},[2272,38322,38323,38325],{},[898,38324,4183],{},[2129,38326,2131],{},[902,38328,38329],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,38332,38334],{"className":38333},[886],[888,38335,38336],{"xmlns":890},[892,38337,38338,38351],{},[895,38339,38340,38342,38344,38346,38349],{},[1996,38341,2486],{"stretchy":2004},[2129,38343,2327],{},[1996,38345,2286],{"separator":2285},[2129,38347,38348],{},"21",[1996,38350,2501],{"stretchy":2004},[902,38352,38353],{"encoding":904},"[0, 21]"," centů.",[198,38356,38358],{"id":38357},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,38360,38361,38362,2704],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,38363,38365],{"className":38364},[886],[888,38366,38367],{"xmlns":890},[892,38368,38369,38373],{},[895,38370,38371],{},[898,38372,9128],{},[902,38374,9128],{"encoding":904},[883,38376,38378],{"className":38377},[886],[888,38379,38380],{"xmlns":890,"display":28068},[892,38381,38382,38413],{},[20756,38383,38384],{"width":28073},[20761,38385,38386,38388,38406,38408],{},[20764,38387],{"width":28078},[20764,38389,38390],{},[895,38391,38392,38394,38396,38398,38400,38402,38404],{},[898,38393,2789],{},[1996,38395,1998],{},[898,38397,4252],{},[1996,38399,2005],{"stretchy":2004},[898,38401,9128],{},[1996,38403,2011],{"stretchy":2004},[898,38405,1975],{"mathvariant":2376},[20764,38407],{"width":28078},[20764,38409,38410],{},[2288,38411,38412],{},"(2.5)",[902,38414,38415],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,38417,38418,38419,38422,38423,38426],{},"Funkce se nazývá ",[38,38420,38421],{},"Engelova",", její graf ",[38,38424,38425],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,38428,38429,38561],{},[123,38430,38431,7015,38434,38447,38448,38461,38462,38479,38480],{},[38,38432,38433],{},"Normální (superior) zboží",[883,38435,38437],{"className":38436},[886],[888,38438,38439],{"xmlns":890},[892,38440,38441,38445],{},[895,38442,38443],{},[898,38444,2789],{},[902,38446,2789],{"encoding":904}," roste s ",[883,38449,38451],{"className":38450},[886],[888,38452,38453],{"xmlns":890},[892,38454,38455,38459],{},[895,38456,38457],{},[898,38458,9128],{},[902,38460,9128],{"encoding":904},", nepřesáhne hodnotu ",[883,38463,38465],{"className":38464},[886],[888,38466,38467],{"xmlns":890},[892,38468,38469,38477],{},[895,38470,38471],{},[2272,38472,38473,38475],{},[898,38474,2789],{},[2129,38476,2327],{},[902,38478,38310],{"encoding":904},":\n",[120,38481,38482,38514],{},[123,38483,38484,38487,38488,38491,38492,1975],{},[38,38485,38486],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,38489,38490],{},"konkávní"," křivka, autonomní spotřeba ",[883,38493,38495],{"className":38494},[886],[888,38496,38497],{"xmlns":890},[892,38498,38499,38511],{},[895,38500,38501,38507,38509],{},[2272,38502,38503,38505],{},[898,38504,2789],{},[2129,38506,2278],{},[1996,38508,3408],{},[2129,38510,2327],{},[902,38512,38513],{"encoding":904},"Q_1 > 0",[123,38515,38516,38519,38520,38538,38539,38541,38542,2203,38559,1975],{},[38,38517,38518],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,38521,38523],{"className":38522},[886],[888,38524,38525],{"xmlns":890},[892,38526,38527,38535],{},[895,38528,38529],{},[2272,38530,38531,38533],{},[898,38532,9128],{},[2129,38534,2278],{},[902,38536,38537],{"encoding":904},"Y_1",", křivka je nejprve ",[38,38540,37666],{}," a od ",[883,38543,38545],{"className":38544},[886],[888,38546,38547],{"xmlns":890},[892,38548,38549,38557],{},[895,38550,38551],{},[2272,38552,38553,38555],{},[898,38554,9128],{},[2129,38556,2278],{},[902,38558,38537],{"encoding":904},[38,38560,38490],{},[123,38562,38563,38566,38567,38585],{},[38,38564,38565],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,38568,38570],{"className":38569},[886],[888,38571,38572],{"xmlns":890},[892,38573,38574,38582],{},[895,38575,38576],{},[2272,38577,38578,38580],{},[898,38579,9128],{},[2129,38581,2327],{},[902,38583,38584],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,38587,38588,38589,38592,38593,3918],{},"Mírou citlivosti je ",[614,38590,38591],{},"důchodová elasticita"," (viz ",[207,38594,1919],{"className":38595,"dataFsResolvedFilePath":848,"href":849},[210],[724,38597,38598],{},[614,38599,38600],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[37350,38602,38604],{"id":38603},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[3867,38606,38607,38678,38721],{},[724,38608,38609,38611,38612,2203,38615,2203,38628,5669,38630,38643,38644,38647,38648,1975],{},[883,38610,4412],{}," Pozor — nezbytné ≠ podřadné\n",[38,38613,38614],{},"Nezbytné zboží:",[883,38616,38618],{"className":38617},[886],[888,38619,38620],{"xmlns":890},[892,38621,38622,38626],{},[895,38623,38624],{},[898,38625,2789],{},[902,38627,2789],{"encoding":904},[38,38629,7322],{},[883,38631,38633],{"className":38632},[886],[888,38634,38635],{"xmlns":890},[892,38636,38637,38641],{},[895,38638,38639],{},[898,38640,9128],{},[902,38642,9128],{"encoding":904},", ale ",[38,38645,38646],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,38649,38651],{"className":38650},[886],[888,38652,38653],{"xmlns":890},[892,38654,38655,38675],{},[895,38656,38657,38663,38665,38667,38669,38671,38673],{},[2272,38658,38659,38661],{},[898,38660,4252],{},[898,38662,9128],{},[1996,38664,6506],{},[1996,38666,2005],{"stretchy":2004},[2129,38668,2327],{},[1996,38670,2286],{"separator":2285},[2129,38672,2278],{},[1996,38674,2011],{"stretchy":2004},[902,38676,38677],{"encoding":904},"E_Y \\in (0, 1)",[724,38679,38680,2203,38683,2203,38696,38698,38699,1975],{},[38,38681,38682],{},"Podřadné zboží:",[883,38684,38686],{"className":38685},[886],[888,38687,38688],{"xmlns":890},[892,38689,38690,38694],{},[895,38691,38692],{},[898,38693,2789],{},[902,38695,2789],{"encoding":904},[38,38697,7342],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,38700,38702],{"className":38701},[886],[888,38703,38704],{"xmlns":890},[892,38705,38706,38718],{},[895,38707,38708,38714,38716],{},[2272,38709,38710,38712],{},[898,38711,4252],{},[898,38713,9128],{},[1996,38715,3447],{},[2129,38717,2327],{},[902,38719,38720],{"encoding":904},"E_Y \u003C 0",[724,38722,38723,38724,1975],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,38725,38726],{},"méně kusů, ne jen proporčně méně",[724,38728,38729,38732,38733,38736],{},[38,38730,38731],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,38734,38735],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,38738,38739],{},[2559,38740],{"alt":38741,"className":38742,"src":38743},"imek-engelovy-krivky-3typy",[210,2563],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[37927,38745,38747],{"id":38746},"české-příklady","České příklady",[16,38749,38750,38760],{},[19,38751,38752],{},[22,38753,38754,38757],{},[25,38755,38756],{},"Podřadné",[25,38758,38759],{},"Nahradí se za",[30,38761,38762,38770,38778,38786,38794,38802,38810,38818],{},[22,38763,38764,38767],{},[35,38765,38766],{},"Instantní polévky, ramen",[35,38768,38769],{},"Čerstvé jídlo, restaurace",[22,38771,38772,38775],{},[35,38773,38774],{},"MHD (autobus, tramvaj)",[35,38776,38777],{},"Vlastní auto, Uber, taxi",[22,38779,38780,38783],{},[35,38781,38782],{},"Mražené polotovary, pizza z mrazáku",[35,38784,38785],{},"Čerstvé suroviny, hotovky",[22,38787,38788,38791],{},[35,38789,38790],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,38792,38793],{},"Značkové produkty",[22,38795,38796,38799],{},[35,38797,38798],{},"Paštika Májka, obyčejný měkký salám",[35,38800,38801],{},"Kvalitní uzeniny, šunka od kosti",[22,38803,38804,38807],{},[35,38805,38806],{},"Second hand oblečení",[35,38808,38809],{},"Nové oblečení, značky",[22,38811,38812,38815],{},[35,38813,38814],{},"Krabicové víno, nejlevnější pivo",[35,38816,38817],{},"Lahvové víno, řemeslná piva",[22,38819,38820,38823],{},[35,38821,38822],{},"Ojetá auta nižších tříd",[35,38824,38825],{},"Nová auta, prémiové značky",[3867,38827,38828],{},[724,38829,38830,38832,38833,38836],{},[883,38831,4572],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,38834,38835],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,38838,38839,38842,38843,10025,38846,38868,38869,10025,38872,38893,38894,38912,38913,38916],{},[38,38840,38841],{},"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 ",[38,38844,38845],{},"luxus",[883,38847,38849],{"className":38848},[886],[888,38850,38851],{"xmlns":890},[892,38852,38853,38865],{},[895,38854,38855,38861,38863],{},[2272,38856,38857,38859],{},[898,38858,4252],{},[898,38860,9128],{},[1996,38862,3408],{},[2129,38864,2278],{},[902,38866,38867],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,38870,38871],{},"podřadné",[883,38873,38875],{"className":38874},[886],[888,38876,38877],{"xmlns":890},[892,38878,38879,38891],{},[895,38880,38881,38887,38889],{},[2272,38882,38883,38885],{},[898,38884,4252],{},[898,38886,9128],{},[1996,38888,3447],{},[2129,38890,2327],{},[902,38892,38720],{"encoding":904},"). Proto je ",[883,38895,38897],{"className":38896},[886],[888,38898,38899],{"xmlns":890},[892,38900,38901,38909],{},[895,38902,38903],{},[2272,38904,38905,38907],{},[898,38906,4252],{},[898,38908,9128],{},[902,38910,38911],{"encoding":904},"E_Y"," vždy ",[38,38914,38915],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,38918,38919,38920,38922],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,38921,38228],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,38924,38926,38927,2011],{"id":38925},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,38928,38929],{},"shift of demand",[724,38931,38932,38933,38951,38952,38969,38970,38983,38984,2685,38997,39019,39020,39037,39038,39064,39065,39068],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,38934,38936],{"className":38935},[886],[888,38937,38938],{"xmlns":890},[892,38939,38940,38948],{},[895,38941,38942],{},[2272,38943,38944,38946],{},[898,38945,3937],{},[2129,38947,2327],{},[902,38949,38950],{"encoding":904},"P_0"," odpovídá množství ",[883,38953,38955],{"className":38954},[886],[888,38956,38957],{"xmlns":890},[892,38958,38959,38967],{},[895,38960,38961],{},[2272,38962,38963,38965],{},[898,38964,2789],{},[2129,38966,2327],{},[902,38968,38310],{"encoding":904}," na křivce ",[883,38971,38973],{"className":38972},[886],[888,38974,38975],{"xmlns":890},[892,38976,38977,38981],{},[895,38978,38979],{},[898,38980,4183],{},[902,38982,4183],{"encoding":904},"; vzroste-li důchod z ",[883,38985,38987],{"className":38986},[886],[888,38988,38989],{"xmlns":890},[892,38990,38991,38995],{},[895,38992,38993],{},[898,38994,9128],{},[902,38996,9128],{"encoding":904},[883,38998,39000],{"className":38999},[886],[888,39001,39002],{"xmlns":890},[892,39003,39004,39016],{},[895,39005,39006,39012,39014],{},[2272,39007,39008,39010],{},[898,39009,9128],{},[2129,39011,2278],{},[1996,39013,3408],{},[898,39015,9128],{},[902,39017,39018],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,39021,39023],{"className":39022},[886],[888,39024,39025],{"xmlns":890},[892,39026,39027,39035],{},[895,39028,39029],{},[2272,39030,39031,39033],{},[898,39032,3937],{},[2129,39034,2327],{},[902,39036,38950],{"encoding":904}," odpovídá vyšší ",[883,39039,39041],{"className":39040},[886],[888,39042,39043],{"xmlns":890},[892,39044,39045,39061],{},[895,39046,39047,39053,39055],{},[2272,39048,39049,39051],{},[898,39050,2789],{},[2129,39052,2278],{},[1996,39054,3408],{},[2272,39056,39057,39059],{},[898,39058,2789],{},[2129,39060,2327],{},[902,39062,39063],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,39066,39067],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,39070,39071],{},[2559,39072],{"alt":39073,"className":39074,"src":39075},"imek-posun-vs-pohyb-po-krivce",[210,2563],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,39077,39078],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,39080,39081],{},[614,39082,39083,39084,14013,39114,39135],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,39085,39087],{"className":39086},[886],[888,39088,39089],{"xmlns":890},[892,39090,39091,39111],{},[895,39092,39093,39099,39101,39103,39105],{},[2272,39094,39095,39097],{},[898,39096,4183],{},[2129,39098,2131],{},[1996,39100,2286],{"separator":2285},[898,39102,4183],{},[1996,39104,2286],{"separator":2285},[2272,39106,39107,39109],{},[898,39108,4183],{},[2129,39110,2278],{},[902,39112,39113],{"encoding":904},"D_2, D, D_1",[883,39115,39117],{"className":39116},[886],[888,39118,39119],{"xmlns":890},[892,39120,39121,39133],{},[895,39122,39123,39125,39127,39129,39131],{},[1996,39124,2005],{"stretchy":2004},[898,39126,2789],{},[1996,39128,2286],{"separator":2285},[898,39130,3937],{},[1996,39132,2011],{"stretchy":2004},[902,39134,37693],{"encoding":904},", šipky naznačují posuny.",[37927,39137,39139],{"id":39138},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,39141,39142,39144,39145,39168,39169,39186,39187,39204,39205,1975],{},[38,39143,37935],{}," Poptávce ",[883,39146,39148],{"className":39147},[886],[888,39149,39150],{"xmlns":890},[892,39151,39152,39166],{},[895,39153,39154,39156,39158,39160,39162,39164],{},[898,39155,3937],{},[1996,39157,1998],{},[898,39159,4183],{},[1996,39161,2005],{"stretchy":2004},[898,39163,2789],{},[1996,39165,2011],{"stretchy":2004},[902,39167,4640],{"encoding":904}," odpovídá ceně ",[883,39170,39172],{"className":39171},[886],[888,39173,39174],{"xmlns":890},[892,39175,39176,39184],{},[895,39177,39178],{},[2272,39179,39180,39182],{},[898,39181,3937],{},[2129,39183,2327],{},[902,39185,38950],{"encoding":904}," množství ",[883,39188,39190],{"className":39189},[886],[888,39191,39192],{"xmlns":890},[892,39193,39194,39202],{},[895,39195,39196],{},[2272,39197,39198,39200],{},[898,39199,2789],{},[2129,39201,2327],{},[902,39203,38310],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,39206,39208],{"className":39207},[886],[888,39209,39210],{"xmlns":890},[892,39211,39212,39216],{},[895,39213,39214],{},[898,39215,2774],{},[902,39217,2774],{"encoding":904},[724,39219,39220,39222,39223,39240,39241,39263],{},[38,39221,37967],{}," Kupující nakupuje množství ",[883,39224,39226],{"className":39225},[886],[888,39227,39228],{"xmlns":890},[892,39229,39230,39238],{},[895,39231,39232],{},[2272,39233,39234,39236],{},[898,39235,2789],{},[2129,39237,2278],{},[902,39239,29004],{"encoding":904},", které odpovídá ceně ",[883,39242,39244],{"className":39243},[886],[888,39245,39246],{"xmlns":890},[892,39247,39248,39260],{},[895,39249,39250,39256,39258],{},[2272,39251,39252,39254],{},[898,39253,3937],{},[2129,39255,2327],{},[1996,39257,2095],{},[898,39259,2774],{},[902,39261,39262],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,39265,39267],{"className":39266},[886],[888,39268,39269],{"xmlns":890,"display":28068},[892,39270,39271,39305],{},[895,39272,39273,39275,39277,39283,39285,39287,39289,39291,39293,39295,39297,39299,39301,39303],{},[898,39274,3937],{},[1996,39276,1998],{},[2272,39278,39279,39281],{},[898,39280,4183],{},[2129,39282,2278],{},[1996,39284,2005],{"stretchy":2004},[898,39286,2789],{},[1996,39288,2011],{"stretchy":2004},[1996,39290,1998],{},[898,39292,4183],{},[1996,39294,2005],{"stretchy":2004},[898,39296,2789],{},[1996,39298,2011],{"stretchy":2004},[1996,39300,2225],{},[898,39302,2774],{},[1996,39304,2286],{"separator":2285},[902,39306,39307],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,39309,39310,39311,1975],{},"tj. dojde k ",[38,39312,39313],{},"posunu poptávky doleva",[724,39315,39316],{},[614,39317,39318,39319,39340,39341,1343,39358,1343,39371,39392,39393,3885,39410,1975],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,39320,39322],{"className":39321},[886],[888,39323,39324],{"xmlns":890},[892,39325,39326,39338],{},[895,39327,39328,39330,39332,39334,39336],{},[1996,39329,2005],{"stretchy":2004},[898,39331,2789],{},[1996,39333,2286],{"separator":2285},[898,39335,3937],{},[1996,39337,2011],{"stretchy":2004},[902,39339,37693],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,39342,39344],{"className":39343},[886],[888,39345,39346],{"xmlns":890},[892,39347,39348,39356],{},[895,39349,39350],{},[2272,39351,39352,39354],{},[898,39353,3937],{},[2129,39355,2327],{},[902,39357,38950],{"encoding":904},[883,39359,39361],{"className":39360},[886],[888,39362,39363],{"xmlns":890},[892,39364,39365,39369],{},[895,39366,39367],{},[898,39368,2774],{},[902,39370,2774],{"encoding":904},[883,39372,39374],{"className":39373},[886],[888,39375,39376],{"xmlns":890},[892,39377,39378,39390],{},[895,39379,39380,39386,39388],{},[2272,39381,39382,39384],{},[898,39383,3937],{},[2129,39385,2327],{},[1996,39387,2095],{},[898,39389,2774],{},[902,39391,39262],{"encoding":904},"; na vodorovné ",[883,39394,39396],{"className":39395},[886],[888,39397,39398],{"xmlns":890},[892,39399,39400,39408],{},[895,39401,39402],{},[2272,39403,39404,39406],{},[898,39405,2789],{},[2129,39407,2278],{},[902,39409,29004],{"encoding":904},[883,39411,39413],{"className":39412},[886],[888,39414,39415],{"xmlns":890},[892,39416,39417,39425],{},[895,39418,39419],{},[2272,39420,39421,39423],{},[898,39422,2789],{},[2129,39424,2327],{},[902,39426,38310],{"encoding":904},[198,39428,39430],{"id":39429},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,39432,39433],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,39435,39437],{"className":39436},[886],[888,39438,39439],{"xmlns":890,"display":28068},[892,39440,39441,39626],{},[20756,39442,39443],{"width":28073},[20761,39444,39445,39447,39619,39621],{},[20764,39446],{"width":28078},[20764,39448,39449],{},[20756,39450,39451,39535],{"rowspacing":20758,"columnalign":20759,"columnspacing":2377},[20761,39452,39453,39463],{},[20764,39454,39455],{},[2325,39456,39457],{"scriptlevel":2327,"displaystyle":2285},[2272,39458,39459,39461],{},[898,39460,2789],{},[2129,39462,2278],{},[20764,39464,39465],{},[2325,39466,39467],{"scriptlevel":2327,"displaystyle":2285},[895,39468,39469,39471,39473,39479,39481,39487,39489,39495,39497,39499,39505,39507,39513,39519,39521,39527,39533],{},[895,39470],{},[1996,39472,1998],{},[2272,39474,39475,39477],{},[898,39476,4183],{},[2129,39478,2278],{},[1996,39480,2005],{"stretchy":2004},[2272,39482,39483,39485],{},[898,39484,3937],{},[2129,39486,2278],{},[1996,39488,2286],{"separator":2285},[2272,39490,39491,39493],{},[898,39492,3937],{},[2129,39494,2131],{},[1996,39496,2011],{"stretchy":2004},[1996,39498,1998],{},[2272,39500,39501,39503],{},[898,39502,207],{},[2129,39504,2278],{},[1996,39506,2095],{},[2272,39508,39509,39511],{},[898,39510,2098],{},[2129,39512,2278],{},[2272,39514,39515,39517],{},[898,39516,3937],{},[2129,39518,2278],{},[1996,39520,2095],{},[2272,39522,39523,39525],{},[898,39524,2142],{},[2129,39526,2278],{},[2272,39528,39529,39531],{},[898,39530,3937],{},[2129,39532,2131],{},[1996,39534,2286],{"separator":2285},[20761,39536,39537,39547],{},[20764,39538,39539],{},[2325,39540,39541],{"scriptlevel":2327,"displaystyle":2285},[2272,39542,39543,39545],{},[898,39544,2789],{},[2129,39546,2131],{},[20764,39548,39549],{},[2325,39550,39551],{"scriptlevel":2327,"displaystyle":2285},[895,39552,39553,39555,39557,39563,39565,39571,39573,39579,39581,39583,39589,39591,39597,39603,39605,39611,39617],{},[895,39554],{},[1996,39556,1998],{},[2272,39558,39559,39561],{},[898,39560,4183],{},[2129,39562,2131],{},[1996,39564,2005],{"stretchy":2004},[2272,39566,39567,39569],{},[898,39568,3937],{},[2129,39570,2278],{},[1996,39572,2286],{"separator":2285},[2272,39574,39575,39577],{},[898,39576,3937],{},[2129,39578,2131],{},[1996,39580,2011],{"stretchy":2004},[1996,39582,1998],{},[2272,39584,39585,39587],{},[898,39586,207],{},[2129,39588,2131],{},[1996,39590,2095],{},[2272,39592,39593,39595],{},[898,39594,2098],{},[2129,39596,2131],{},[2272,39598,39599,39601],{},[898,39600,3937],{},[2129,39602,2278],{},[1996,39604,2095],{},[2272,39606,39607,39609],{},[898,39608,2142],{},[2129,39610,2131],{},[2272,39612,39613,39615],{},[898,39614,3937],{},[2129,39616,2131],{},[898,39618,1975],{"mathvariant":2376},[20764,39620],{"width":28078},[20764,39622,39623],{},[2288,39624,39625],{},"(2.6)",[902,39627,39628],{"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}",[37350,39630,39632],{"id":39631},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,39634,39635,39682,39729],{},[123,39636,39637,1343,39659,39681],{},[883,39638,39640],{"className":39639},[886],[888,39641,39642],{"xmlns":890},[892,39643,39644,39656],{},[895,39645,39646,39652,39654],{},[2272,39647,39648,39650],{},[898,39649,207],{},[2129,39651,2278],{},[1996,39653,3408],{},[2129,39655,2327],{},[902,39657,39658],{"encoding":904},"a_1 > 0",[883,39660,39662],{"className":39661},[886],[888,39663,39664],{"xmlns":890},[892,39665,39666,39678],{},[895,39667,39668,39674,39676],{},[2272,39669,39670,39672],{},[898,39671,207],{},[2129,39673,2131],{},[1996,39675,3408],{},[2129,39677,2327],{},[902,39679,39680],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,39683,39684,1343,39706,39728],{},[883,39685,39687],{"className":39686},[886],[888,39688,39689],{"xmlns":890},[892,39690,39691,39703],{},[895,39692,39693,39699,39701],{},[2272,39694,39695,39697],{},[898,39696,2098],{},[2129,39698,2278],{},[1996,39700,3447],{},[2129,39702,2327],{},[902,39704,39705],{"encoding":904},"b_1 \u003C 0",[883,39707,39709],{"className":39708},[886],[888,39710,39711],{"xmlns":890},[892,39712,39713,39725],{},[895,39714,39715,39721,39723],{},[2272,39716,39717,39719],{},[898,39718,2142],{},[2129,39720,2131],{},[1996,39722,3447],{},[2129,39724,2327],{},[902,39726,39727],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,39730,39731,39732,1343,39749,39767,39768],{},"zkřížené koeficienty ",[883,39733,39735],{"className":39734},[886],[888,39736,39737],{"xmlns":890},[892,39738,39739,39747],{},[895,39740,39741],{},[2272,39742,39743,39745],{},[898,39744,2142],{},[2129,39746,2278],{},[902,39748,29801],{"encoding":904},[883,39750,39752],{"className":39751},[886],[888,39753,39754],{"xmlns":890},[892,39755,39756,39764],{},[895,39757,39758],{},[2272,39759,39760,39762],{},[898,39761,2098],{},[2129,39763,2131],{},[902,39765,39766],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,39769,39770,39820],{},[123,39771,39772,39775,39776,1343,39798,2286],{},[38,39773,39774],{},"substituty"," (máslo vs. margarín): ",[883,39777,39779],{"className":39778},[886],[888,39780,39781],{"xmlns":890},[892,39782,39783,39795],{},[895,39784,39785,39791,39793],{},[2272,39786,39787,39789],{},[898,39788,2142],{},[2129,39790,2278],{},[1996,39792,3408],{},[2129,39794,2327],{},[902,39796,39797],{"encoding":904},"c_1 > 0",[883,39799,39801],{"className":39800},[886],[888,39802,39803],{"xmlns":890},[892,39804,39805,39817],{},[895,39806,39807,39813,39815],{},[2272,39808,39809,39811],{},[898,39810,2098],{},[2129,39812,2131],{},[1996,39814,3408],{},[2129,39816,2327],{},[902,39818,39819],{"encoding":904},"b_2 > 0",[123,39821,39822,39825,39826,1343,39848,1975],{},[38,39823,39824],{},"komplementy"," (auto vs. benzín): ",[883,39827,39829],{"className":39828},[886],[888,39830,39831],{"xmlns":890},[892,39832,39833,39845],{},[895,39834,39835,39841,39843],{},[2272,39836,39837,39839],{},[898,39838,2142],{},[2129,39840,2278],{},[1996,39842,3447],{},[2129,39844,2327],{},[902,39846,39847],{"encoding":904},"c_1 \u003C 0",[883,39849,39851],{"className":39850},[886],[888,39852,39853],{"xmlns":890},[892,39854,39855,39867],{},[895,39856,39857,39863,39865],{},[2272,39858,39859,39861],{},[898,39860,2098],{},[2129,39862,2131],{},[1996,39864,3447],{},[2129,39866,2327],{},[902,39868,39869],{"encoding":904},"b_2 \u003C 0",[724,39871,39872],{},"Schematicky:",[724,39874,39875,39878],{},[38,39876,39877],{},"Substituty",[883,39879,39881],{"className":39880},[886],[888,39882,39883],{"xmlns":890},[892,39884,39885,40024],{},[895,39886,39887,39893,39895,39910,39912,39932,39934,39954,39956,39958,39964,39966,39980,39982,40002,40004],{},[2272,39888,39889,39891],{},[898,39890,2789],{},[2129,39892,2278],{},[1996,39894,1998],{},[898,39896,39897],{},[39898,39899,39900,39908],"munder",{},[1996,39901,39902],{},[2272,39903,39904,39906],{},[898,39905,207],{},[2129,39907,2278],{},[1996,39909,2095],{"lspace":2377,"rspace":2377},[1996,39911,2095],{},[898,39913,39914],{},[39898,39915,39916,39930],{},[1996,39917,39918,39924],{},[2272,39919,39920,39922],{},[898,39921,2098],{},[2129,39923,2278],{},[2272,39925,39926,39928],{},[898,39927,3937],{},[2129,39929,2278],{},[1996,39931,2225],{"lspace":2377,"rspace":2377},[1996,39933,2095],{},[898,39935,39936],{},[39898,39937,39938,39952],{},[1996,39939,39940,39946],{},[2272,39941,39942,39944],{},[898,39943,2142],{},[2129,39945,2278],{},[2272,39947,39948,39950],{},[898,39949,3937],{},[2129,39951,2131],{},[1996,39953,2095],{"lspace":2377,"rspace":2377},[1996,39955,2286],{"separator":2285},[5878,39957],{"width":5880},[2272,39959,39960,39962],{},[898,39961,2789],{},[2129,39963,2131],{},[1996,39965,1998],{},[898,39967,39968],{},[39898,39969,39970,39978],{},[1996,39971,39972],{},[2272,39973,39974,39976],{},[898,39975,207],{},[2129,39977,2131],{},[1996,39979,2095],{"lspace":2377,"rspace":2377},[1996,39981,2095],{},[898,39983,39984],{},[39898,39985,39986,40000],{},[1996,39987,39988,39994],{},[2272,39989,39990,39992],{},[898,39991,2098],{},[2129,39993,2131],{},[2272,39995,39996,39998],{},[898,39997,3937],{},[2129,39999,2278],{},[1996,40001,2095],{"lspace":2377,"rspace":2377},[1996,40003,2095],{},[898,40005,40006],{},[39898,40007,40008,40022],{},[1996,40009,40010,40016],{},[2272,40011,40012,40014],{},[898,40013,2142],{},[2129,40015,2131],{},[2272,40017,40018,40020],{},[898,40019,3937],{},[2129,40021,2131],{},[1996,40023,2225],{"lspace":2377,"rspace":2377},[902,40025,40026],{"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}",[724,40028,40029,40032],{},[38,40030,40031],{},"Komplementy",[883,40033,40035],{"className":40034},[886],[888,40036,40037],{"xmlns":890},[892,40038,40039,40177],{},[895,40040,40041,40047,40049,40063,40065,40085,40087,40107,40109,40111,40117,40119,40133,40135,40155,40157],{},[2272,40042,40043,40045],{},[898,40044,2789],{},[2129,40046,2278],{},[1996,40048,1998],{},[898,40050,40051],{},[39898,40052,40053,40061],{},[1996,40054,40055],{},[2272,40056,40057,40059],{},[898,40058,207],{},[2129,40060,2278],{},[1996,40062,2095],{"lspace":2377,"rspace":2377},[1996,40064,2095],{},[898,40066,40067],{},[39898,40068,40069,40083],{},[1996,40070,40071,40077],{},[2272,40072,40073,40075],{},[898,40074,2098],{},[2129,40076,2278],{},[2272,40078,40079,40081],{},[898,40080,3937],{},[2129,40082,2278],{},[1996,40084,2225],{"lspace":2377,"rspace":2377},[1996,40086,2095],{},[898,40088,40089],{},[39898,40090,40091,40105],{},[1996,40092,40093,40099],{},[2272,40094,40095,40097],{},[898,40096,2142],{},[2129,40098,2278],{},[2272,40100,40101,40103],{},[898,40102,3937],{},[2129,40104,2131],{},[1996,40106,2225],{"lspace":2377,"rspace":2377},[1996,40108,2286],{"separator":2285},[5878,40110],{"width":5880},[2272,40112,40113,40115],{},[898,40114,2789],{},[2129,40116,2131],{},[1996,40118,1998],{},[898,40120,40121],{},[39898,40122,40123,40131],{},[1996,40124,40125],{},[2272,40126,40127,40129],{},[898,40128,207],{},[2129,40130,2131],{},[1996,40132,2095],{"lspace":2377,"rspace":2377},[1996,40134,2095],{},[898,40136,40137],{},[39898,40138,40139,40153],{},[1996,40140,40141,40147],{},[2272,40142,40143,40145],{},[898,40144,2098],{},[2129,40146,2131],{},[2272,40148,40149,40151],{},[898,40150,3937],{},[2129,40152,2278],{},[1996,40154,2225],{"lspace":2377,"rspace":2377},[1996,40156,2095],{},[898,40158,40159],{},[39898,40160,40161,40175],{},[1996,40162,40163,40169],{},[2272,40164,40165,40167],{},[898,40166,2142],{},[2129,40168,2131],{},[2272,40170,40171,40173],{},[898,40172,3937],{},[2129,40174,2131],{},[1996,40176,2225],{"lspace":2377,"rspace":2377},[902,40178,40179],{"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}",[36972,40181],{},[115,40183,13127],{"id":36781},[3867,40185,40186],{},[724,40187,40188,40190,40191,36996,40204,37010,40217,40220,40221,5669,40245,40263],{},[883,40189,4155],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,40192,40194],{"className":40193},[886],[888,40195,40196],{"xmlns":890},[892,40197,40198,40202],{},[895,40199,40200],{},[898,40201,2789],{},[902,40203,2789],{"encoding":904},[883,40205,40207],{"className":40206},[886],[888,40208,40209],{"xmlns":890},[892,40210,40211,40215],{},[895,40212,40213],{},[898,40214,3937],{},[902,40216,3937],{"encoding":904},[38,40218,40219],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,40222,40224],{"className":40223},[886],[888,40225,40226],{"xmlns":890},[892,40227,40228,40242],{},[895,40229,40230,40232,40234,40236,40238,40240],{},[898,40231,3937],{},[1996,40233,1998],{},[898,40235,2142],{},[898,40237,2789],{},[1996,40239,2095],{},[898,40241,2194],{},[902,40243,40244],{"encoding":904},"P = cQ + d",[883,40246,40248],{"className":40247},[886],[888,40249,40250],{"xmlns":890},[892,40251,40252,40260],{},[895,40253,40254,40256,40258],{},[898,40255,2142],{},[1996,40257,3408],{},[2129,40259,2327],{},[902,40261,40262],{"encoding":904},"c > 0"," je standardní aproximací.",[198,40265,37066],{"id":40266},"obecný-vícefaktorový-model-1",[724,40268,40269,10025,40272,40275,40276,40289,40290,36898,40303,36912,40316,40329,40330,40344,40345,36941,40358,40371],{},[38,40270,40271],{},"Nabízené množství",[614,40273,40274],{},"quantity supplied",") závisí na ceně ",[883,40277,40279],{"className":40278},[886],[888,40280,40281],{"xmlns":890},[892,40282,40283,40287],{},[895,40284,40285],{},[898,40286,3937],{},[902,40288,3937],{"encoding":904},", cenách výrobních faktorů (práce ",[883,40291,40293],{"className":40292},[886],[888,40294,40295],{"xmlns":890},[892,40296,40297,40301],{},[895,40298,40299],{},[898,40300,9795],{},[902,40302,9795],{"encoding":904},[883,40304,40306],{"className":40305},[886],[888,40307,40308],{"xmlns":890},[892,40309,40310,40314],{},[895,40311,40312],{},[898,40313,9800],{},[902,40315,9800],{"encoding":904},[883,40317,40319],{"className":40318},[886],[888,40320,40321],{"xmlns":890},[892,40322,40323,40327],{},[895,40324,40325],{},[898,40326,4252],{},[902,40328,4252],{"encoding":904},"), očekávání ",[883,40331,40333],{"className":40332},[886],[888,40334,40335],{"xmlns":890},[892,40336,40337,40342],{},[895,40338,40339],{},[898,40340,40341],{},"V",[902,40343,40341],{"encoding":904},", počtu výrobců ",[883,40346,40348],{"className":40347},[886],[888,40349,40350],{"xmlns":890},[892,40351,40352,40356],{},[895,40353,40354],{},[898,40355,36938],{},[902,40357,36938],{"encoding":904},[883,40359,40361],{"className":40360},[886],[888,40362,40363],{"xmlns":890},[892,40364,40365,40369],{},[895,40366,40367],{},[898,40368,36953],{},[902,40370,36953],{"encoding":904}," a dalších:",[883,40373,40375],{"className":40374},[886],[888,40376,40377],{"xmlns":890,"display":28068},[892,40378,40379,40438],{},[20756,40380,40381],{"width":28073},[20761,40382,40383,40385,40431,40433],{},[20764,40384],{"width":28078},[20764,40386,40387],{},[895,40388,40389,40391,40393,40395,40397,40399,40401,40403,40405,40407,40409,40411,40413,40415,40417,40419,40421,40423,40425,40427,40429],{},[898,40390,2789],{},[1996,40392,1998],{},[898,40394,8673],{},[1996,40396,2005],{"stretchy":2004},[898,40398,3937],{},[1996,40400,2286],{"separator":2285},[898,40402,9795],{},[1996,40404,2286],{"separator":2285},[898,40406,9800],{},[1996,40408,2286],{"separator":2285},[898,40410,4252],{},[1996,40412,2286],{"separator":2285},[898,40414,40341],{},[1996,40416,2286],{"separator":2285},[898,40418,36938],{},[1996,40420,2286],{"separator":2285},[898,40422,36953],{},[1996,40424,2286],{"separator":2285},[1996,40426,9646],{},[1996,40428,2011],{"stretchy":2004},[898,40430,1975],{"mathvariant":2376},[20764,40432],{"width":28078},[20764,40434,40435],{},[2288,40436,40437],{},"(2.7)",[902,40439,40440],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,40442,38418,40443,10025,40446,40449],{},[38,40444,40445],{},"funkce nabídky",[614,40447,40448],{},"supply function",") v širším slova smyslu.",[198,40451,40453],{"id":40452},"jednofaktorový-model","Jednofaktorový model",[724,40455,40456],{},"V nejpřirozenějším jednofaktorovém modelu",[883,40458,40460],{"className":40459},[886],[888,40461,40462],{"xmlns":890,"display":28068},[892,40463,40464,40515],{},[20756,40465,40466],{"width":28073},[20761,40467,40468,40470,40508,40510],{},[20764,40469],{"width":28078},[20764,40471,40472],{},[895,40473,40474,40476,40478,40480,40482,40484,40486,40488,40490,40492,40494,40496,40498,40500,40502,40504,40506],{},[898,40475,2789],{},[1996,40477,1998],{},[898,40479,8673],{},[1996,40481,2005],{"stretchy":2004},[898,40483,3937],{},[1996,40485,2011],{"stretchy":2004},[1996,40487,2286],{"separator":2285},[5878,40489],{"width":5880},[2288,40491,37419],{},[5878,40493],{"width":5880},[898,40495,3937],{},[1996,40497,1998],{},[898,40499,8673],{},[1996,40501,2005],{"stretchy":2004},[898,40503,2789],{},[1996,40505,2011],{"stretchy":2004},[898,40507,1975],{"mathvariant":2376},[20764,40509],{"width":28078},[20764,40511,40512],{},[2288,40513,40514],{},"(2.8)",[902,40516,40517],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,40519,40520,40521,10025,40524,3918],{},"Graf je ",[38,40522,40523],{},"křivka nabídky",[614,40525,40526],{},"supply curve",[37350,40528,40530],{"id":40529},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[3867,40532,40533],{},[724,40534,40535],{},[38,40536,37465,40537,40550,40551,37520],{},[883,40538,40540],{"className":40539},[886],[888,40541,40542],{"xmlns":890},[892,40543,40544,40548],{},[895,40545,40546],{},[898,40547,3937],{},[902,40549,3937],{"encoding":904},", pak nabízené množství ",[883,40552,40554],{"className":40553},[886],[888,40555,40556],{"xmlns":890},[892,40557,40558,40562],{},[895,40559,40560],{},[898,40561,2789],{},[902,40563,2789],{"encoding":904},[724,40565,40566,40567,40592,40593,40623,40624,40641],{},"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 ",[883,40568,40570],{"className":40569},[886],[888,40571,40572],{"xmlns":890},[892,40573,40574,40590],{},[895,40575,40576,40578,40580,40582,40588],{},[1996,40577,2486],{"stretchy":2004},[2129,40579,2327],{},[1996,40581,2286],{"separator":2285},[2272,40583,40584,40586],{},[898,40585,3937],{},[2129,40587,2327],{},[1996,40589,2501],{"stretchy":2004},[902,40591,37605],{"encoding":904}," na svislé ose (případně z ",[883,40594,40596],{"className":40595},[886],[888,40597,40598],{"xmlns":890},[892,40599,40600,40620],{},[895,40601,40602,40604,40610,40612,40618],{},[1996,40603,2486],{"stretchy":2004},[2272,40605,40606,40608],{},[898,40607,2789],{},[2129,40609,2278],{},[1996,40611,2286],{"separator":2285},[2272,40613,40614,40616],{},[898,40615,3937],{},[2129,40617,2278],{},[1996,40619,2501],{"stretchy":2004},[902,40621,40622],{"encoding":904},"[Q_1, P_1]","), kde ",[883,40625,40627],{"className":40626},[886],[888,40628,40629],{"xmlns":890},[892,40630,40631,40639],{},[895,40632,40633],{},[2272,40634,40635,40637],{},[898,40636,3937],{},[2129,40638,2327],{},[902,40640,38950],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,40643,40644],{},[614,40645,40646,40647,3718,40660,1975],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,40648,40650],{"className":40649},[886],[888,40651,40652],{"xmlns":890},[892,40653,40654,40658],{},[895,40655,40656],{},[898,40657,8673],{},[902,40659,8673],{"encoding":904},[883,40661,40663],{"className":40662},[886],[888,40664,40665],{"xmlns":890},[892,40666,40667,40679],{},[895,40668,40669,40671,40673,40675,40677],{},[1996,40670,2005],{"stretchy":2004},[898,40672,2789],{},[1996,40674,2286],{"separator":2285},[898,40676,3937],{},[1996,40678,2011],{"stretchy":2004},[902,40680,37693],{"encoding":904},[37350,40682,40684],{"id":40683},"lineární-model-nabídky","Lineární model nabídky",[883,40686,40688],{"className":40687},[886],[888,40689,40690],{"xmlns":890,"display":28068},[892,40691,40692,40731],{},[20756,40693,40694],{"width":28073},[20761,40695,40696,40698,40724,40726],{},[20764,40697],{"width":28078},[20764,40699,40700],{},[895,40701,40702,40704,40706,40708,40710,40712,40714,40716,40718,40720,40722],{},[898,40703,3937],{},[1996,40705,1998],{},[898,40707,2142],{},[898,40709,2789],{},[1996,40711,2095],{},[898,40713,2194],{},[1996,40715,2286],{"separator":2285},[5878,40717],{"width":5880},[898,40719,2142],{},[1996,40721,3408],{},[2129,40723,12462],{},[20764,40725],{"width":28078},[20764,40727,40728],{},[2288,40729,40730],{},"(2.9)",[902,40732,40733],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,40735,40736,40737,40773,40774,40787],{},"Alternativně ",[883,40738,40740],{"className":40739},[886],[888,40741,40742],{"xmlns":890},[892,40743,40744,40770],{},[895,40745,40746,40748,40750,40758,40760,40762],{},[898,40747,2789],{},[1996,40749,1998],{},[2325,40751,40752],{"scriptlevel":2327,"displaystyle":2004},[2329,40753,40754,40756],{},[2129,40755,2278],{},[898,40757,2142],{},[898,40759,3937],{},[1996,40761,2225],{},[2325,40763,40764],{"scriptlevel":2327,"displaystyle":2004},[2329,40765,40766,40768],{},[898,40767,2194],{},[898,40769,2142],{},[902,40771,40772],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,40775,40777],{"className":40776},[886],[888,40778,40779],{"xmlns":890},[892,40780,40781,40785],{},[895,40782,40783],{},[898,40784,3937],{},[902,40786,3937],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[37927,40789,40791],{"id":40790},"příklad-25","Příklad 2.5",[724,40793,40794,40796,40797,1975],{},[38,40795,37935],{}," Lineární nabídka ",[883,40798,40800],{"className":40799},[886],[888,40801,40802],{"xmlns":890},[892,40803,40804,40818],{},[895,40805,40806,40808,40810,40812,40814,40816],{},[898,40807,3937],{},[1996,40809,1998],{},[2129,40811,5009],{},[898,40813,2789],{},[1996,40815,2095],{},[2129,40817,5004],{},[902,40819,40820],{"encoding":904},"P = 0{,}5Q + 25",[724,40822,40823,40825,40826,1975],{},[38,40824,37967],{}," Alternativní tvar ",[883,40827,40829],{"className":40828},[886],[888,40830,40831],{"xmlns":890},[892,40832,40833,40847],{},[895,40834,40835,40837,40839,40841,40843,40845],{},[898,40836,2789],{},[1996,40838,1998],{},[2129,40840,2131],{},[898,40842,3937],{},[1996,40844,2225],{},[2129,40846,3120],{},[902,40848,40849],{"encoding":904},"Q = 2P - 50",[16,40851,40852,40877],{},[19,40853,40854],{},[22,40855,40856,40871,40873,40875],{},[25,40857,40858],{},[883,40859,40861],{"className":40860},[886],[888,40862,40863],{"xmlns":890},[892,40864,40865,40869],{},[895,40866,40867],{},[898,40868,3937],{},[902,40870,3937],{"encoding":904},[25,40872,38021],{},[25,40874,15040],{},[25,40876,5211],{},[30,40878,40879],{},[22,40880,40881,40896,40898,40900],{},[35,40882,40883],{},[883,40884,40886],{"className":40885},[886],[888,40887,40888],{"xmlns":890},[892,40889,40890,40894],{},[895,40891,40892],{},[898,40893,2789],{},[902,40895,2789],{"encoding":904},[35,40897,2863],{},[35,40899,9035],{},[35,40901,38021],{},[198,40903,40905,40906,2011],{"id":40904},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,40907,40908],{},"shift of supply",[724,40910,40911,40912,40915,40916,40933,40934,40959,40960,1975],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,40913,40914],{},"doprava",": při stejné ceně ",[883,40917,40919],{"className":40918},[886],[888,40920,40921],{"xmlns":890},[892,40922,40923,40931],{},[895,40924,40925],{},[2272,40926,40927,40929],{},[898,40928,3937],{},[2129,40930,2327],{},[902,40932,38950],{"encoding":904}," vyrobí výrobce větší ",[883,40935,40937],{"className":40936},[886],[888,40938,40939],{"xmlns":890},[892,40940,40941,40957],{},[895,40942,40943,40949,40951],{},[2272,40944,40945,40947],{},[898,40946,2789],{},[2129,40948,2278],{},[1996,40950,3408],{},[2272,40952,40953,40955],{},[898,40954,2789],{},[2129,40956,2327],{},[902,40958,39063],{"encoding":904},"); zdražení vstupů posune křivku ",[38,40961,40962],{},"doleva",[724,40964,40965],{},[614,40966,40967,40968,40981,40982,41000,41001,41019,41020,1975],{},"Obrázek 2.11: Původní ",[883,40969,40971],{"className":40970},[886],[888,40972,40973],{"xmlns":890},[892,40974,40975,40979],{},[895,40976,40977],{},[898,40978,8673],{},[902,40980,8673],{"encoding":904},", posunuté ",[883,40983,40985],{"className":40984},[886],[888,40986,40987],{"xmlns":890},[892,40988,40989,40997],{},[895,40990,40991],{},[2272,40992,40993,40995],{},[898,40994,8673],{},[2129,40996,2278],{},[902,40998,40999],{"encoding":904},"S_1"," (doprava) a ",[883,41002,41004],{"className":41003},[886],[888,41005,41006],{"xmlns":890},[892,41007,41008,41016],{},[895,41009,41010],{},[2272,41011,41012,41014],{},[898,41013,8673],{},[2129,41015,2131],{},[902,41017,41018],{"encoding":904},"S_2"," (doleva) v ",[883,41021,41023],{"className":41022},[886],[888,41024,41025],{"xmlns":890},[892,41026,41027,41039],{},[895,41028,41029,41031,41033,41035,41037],{},[1996,41030,2005],{"stretchy":2004},[898,41032,2789],{},[1996,41034,2286],{"separator":2285},[898,41036,3937],{},[1996,41038,2011],{"stretchy":2004},[902,41040,37693],{"encoding":904},[37927,41042,41044],{"id":41043},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,41046,41047,41049,41050,41074,41075,1975],{},[38,41048,37935],{}," Nabídka ",[883,41051,41053],{"className":41052},[886],[888,41054,41055],{"xmlns":890},[892,41056,41057,41071],{},[895,41058,41059,41061,41063,41065,41067,41069],{},[898,41060,3937],{},[1996,41062,1998],{},[898,41064,8673],{},[1996,41066,2005],{"stretchy":2004},[898,41068,2789],{},[1996,41070,2011],{"stretchy":2004},[902,41072,41073],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,41076,41078],{"className":41077},[886],[888,41079,41080],{"xmlns":890},[892,41081,41082,41086],{},[895,41083,41084],{},[898,41085,2774],{},[902,41087,2774],{"encoding":904},[724,41089,41090,41092,41093,41106,41107,41125,41126,41154],{},[38,41091,37967],{}," Spotřebitel zaplatí ",[883,41094,41096],{"className":41095},[886],[888,41097,41098],{"xmlns":890},[892,41099,41100,41104],{},[895,41101,41102],{},[898,41103,3937],{},[902,41105,3937],{"encoding":904},", výrobce obdrží ",[883,41108,41110],{"className":41109},[886],[888,41111,41112],{"xmlns":890},[892,41113,41114,41122],{},[895,41115,41116,41118,41120],{},[898,41117,3937],{},[1996,41119,2225],{},[898,41121,2774],{},[902,41123,41124],{"encoding":904},"P - T",". Z podmínky ",[883,41127,41129],{"className":41128},[886],[888,41130,41131],{"xmlns":890},[892,41132,41133,41151],{},[895,41134,41135,41137,41139,41141,41143,41145,41147,41149],{},[898,41136,3937],{},[1996,41138,2225],{},[898,41140,2774],{},[1996,41142,1998],{},[898,41144,8673],{},[1996,41146,2005],{"stretchy":2004},[898,41148,2789],{},[1996,41150,2011],{"stretchy":2004},[902,41152,41153],{"encoding":904},"P - T = S(Q)"," plyne",[883,41156,41158],{"className":41157},[886],[888,41159,41160],{"xmlns":890,"display":28068},[892,41161,41162,41196],{},[895,41163,41164,41166,41168,41174,41176,41178,41180,41182,41184,41186,41188,41190,41192,41194],{},[898,41165,3937],{},[1996,41167,1998],{},[2272,41169,41170,41172],{},[898,41171,8673],{},[2129,41173,2278],{},[1996,41175,2005],{"stretchy":2004},[898,41177,2789],{},[1996,41179,2011],{"stretchy":2004},[1996,41181,1998],{},[898,41183,8673],{},[1996,41185,2005],{"stretchy":2004},[898,41187,2789],{},[1996,41189,2011],{"stretchy":2004},[1996,41191,2095],{},[898,41193,2774],{},[898,41195,1975],{"mathvariant":2376},[902,41197,41198],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,41200,41201,41202,41215,41216,2203,41229,41232,41233,3885,41253,8102,41271,1975],{},"Křivka ",[883,41203,41205],{"className":41204},[886],[888,41206,41207],{"xmlns":890},[892,41208,41209,41213],{},[895,41210,41211],{},[898,41212,8673],{},[902,41214,8673],{"encoding":904}," se tedy posune o ",[883,41217,41219],{"className":41218},[886],[888,41220,41221],{"xmlns":890},[892,41222,41223,41227],{},[895,41224,41225],{},[898,41226,2774],{},[902,41228,2774],{"encoding":904},[38,41230,41231],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,41234,41236],{"className":41235},[886],[888,41237,41238],{"xmlns":890},[892,41239,41240,41250],{},[895,41241,41242,41244,41246,41248],{},[898,41243,3937],{},[1996,41245,1998],{},[2129,41247,2131],{},[898,41249,2789],{},[902,41251,41252],{"encoding":904},"P = 2Q",[883,41254,41256],{"className":41255},[886],[888,41257,41258],{"xmlns":890},[892,41259,41260,41268],{},[895,41261,41262,41264,41266],{},[898,41263,2774],{},[1996,41265,1998],{},[2129,41267,2235],{},[902,41269,41270],{"encoding":904},"T = 6",[883,41272,41274],{"className":41273},[886],[888,41275,41276],{"xmlns":890},[892,41277,41278,41300],{},[895,41279,41280,41286,41288,41290,41292,41294,41296,41298],{},[2272,41281,41282,41284],{},[898,41283,8673],{},[2129,41285,2278],{},[1996,41287,2704],{},[898,41289,3937],{},[1996,41291,1998],{},[2129,41293,2131],{},[898,41295,2789],{},[1996,41297,2095],{},[2129,41299,2235],{},[902,41301,41302],{"encoding":904},"S_1: P = 2Q + 6",[724,41304,41305],{},[614,41306,41307,41308,41321],{},"Obrázek 2.12: Posun nabídky o ",[883,41309,41311],{"className":41310},[886],[888,41312,41313],{"xmlns":890},[892,41314,41315,41319],{},[895,41316,41317],{},[898,41318,2774],{},[902,41320,2774],{"encoding":904}," svisle nahoru.",[36972,41323],{},[115,41325,41327],{"id":41326},"tržní-rovnováha","Tržní rovnováha",[3867,41329,41330],{},[724,41331,41332,41334,41335,2203,41338,41370,41371,1343,41394,41417,41418,41421,41422,41435],{},[883,41333,4155],{}," TL;DR\nV ",[38,41336,41337],{},"rovnovážném bodě",[883,41339,41341],{"className":41340},[886],[888,41342,41343],{"xmlns":890},[892,41344,41345,41367],{},[895,41346,41347,41349,41351,41357,41359,41365],{},[898,41348,4252],{},[1996,41350,2486],{"stretchy":2004},[2124,41352,41353,41355],{},[898,41354,2789],{},[898,41356,4252],{},[1996,41358,2286],{"separator":2285},[2124,41360,41361,41363],{},[898,41362,3937],{},[898,41364,4252],{},[1996,41366,2501],{"stretchy":2004},[902,41368,41369],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,41372,41374],{"className":41373},[886],[888,41375,41376],{"xmlns":890},[892,41377,41378,41392],{},[895,41379,41380,41382,41384,41386,41388,41390],{},[898,41381,3937],{},[1996,41383,1998],{},[898,41385,4183],{},[1996,41387,2005],{"stretchy":2004},[898,41389,2789],{},[1996,41391,2011],{"stretchy":2004},[902,41393,4640],{"encoding":904},[883,41395,41397],{"className":41396},[886],[888,41398,41399],{"xmlns":890},[892,41400,41401,41415],{},[895,41402,41403,41405,41407,41409,41411,41413],{},[898,41404,3937],{},[1996,41406,1998],{},[898,41408,8673],{},[1996,41410,2005],{"stretchy":2004},[898,41412,2789],{},[1996,41414,2011],{"stretchy":2004},[902,41416,41073],{"encoding":904},". Čtyři ",[38,41419,41420],{},"pravidla komparativní statiky"," popisují, jak se ",[883,41423,41425],{"className":41424},[886],[888,41426,41427],{"xmlns":890},[892,41428,41429,41433],{},[895,41430,41431],{},[898,41432,4252],{},[902,41434,4252],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,41437,41439],{"id":41438},"definice","Definice",[724,41441,41442,10025,41444,41447,41448,2203,41451,41469,41470,41501,41502,10025,41505,3918],{},[38,41443,41327],{},[614,41445,41446],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,41449,41450],{},"rovnovážné ceně",[883,41452,41454],{"className":41453},[886],[888,41455,41456],{"xmlns":890},[892,41457,41458,41466],{},[895,41459,41460],{},[2124,41461,41462,41464],{},[898,41463,3937],{},[898,41465,4252],{},[902,41467,41468],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,41471,41473],{"className":41472},[886],[888,41474,41475],{"xmlns":890},[892,41476,41477,41499],{},[895,41478,41479,41481,41483,41489,41491,41497],{},[898,41480,4252],{},[1996,41482,2486],{"stretchy":2004},[2124,41484,41485,41487],{},[898,41486,2789],{},[898,41488,4252],{},[1996,41490,2286],{"separator":2285},[2124,41492,41493,41495],{},[898,41494,3937],{},[898,41496,4252],{},[1996,41498,2501],{"stretchy":2004},[902,41500,41369],{"encoding":904}," se nazývá ",[38,41503,41504],{},"rovnovážný bod",[614,41506,41507],{},"equilibrium point",[724,41509,41510,41511,1343,41534,1975],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,41512,41514],{"className":41513},[886],[888,41515,41516],{"xmlns":890},[892,41517,41518,41532],{},[895,41519,41520,41522,41524,41526,41528,41530],{},[898,41521,3937],{},[1996,41523,1998],{},[898,41525,4183],{},[1996,41527,2005],{"stretchy":2004},[898,41529,2789],{},[1996,41531,2011],{"stretchy":2004},[902,41533,4640],{"encoding":904},[883,41535,41537],{"className":41536},[886],[888,41538,41539],{"xmlns":890},[892,41540,41541,41555],{},[895,41542,41543,41545,41547,41549,41551,41553],{},[898,41544,3937],{},[1996,41546,1998],{},[898,41548,8673],{},[1996,41550,2005],{"stretchy":2004},[898,41552,2789],{},[1996,41554,2011],{"stretchy":2004},[902,41556,41073],{"encoding":904},[724,41558,41559],{},[2559,41560],{"alt":41561,"className":41562,"src":41563},"imek-poptavka-nabidka-rovnovaha",[210,2563],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,41565,41566],{},[614,41567,41568,41569,41582,41583,14013,41596,41617,41618,1975],{},"Obrázek 2.13: Klesající ",[883,41570,41572],{"className":41571},[886],[888,41573,41574],{"xmlns":890},[892,41575,41576,41580],{},[895,41577,41578],{},[898,41579,4183],{},[902,41581,4183],{"encoding":904}," a rostoucí ",[883,41584,41586],{"className":41585},[886],[888,41587,41588],{"xmlns":890},[892,41589,41590,41594],{},[895,41591,41592],{},[898,41593,8673],{},[902,41595,8673],{"encoding":904},[883,41597,41599],{"className":41598},[886],[888,41600,41601],{"xmlns":890},[892,41602,41603,41615],{},[895,41604,41605,41607,41609,41611,41613],{},[1996,41606,2005],{"stretchy":2004},[898,41608,2789],{},[1996,41610,2286],{"separator":2285},[898,41612,3937],{},[1996,41614,2011],{"stretchy":2004},[902,41616,37693],{"encoding":904}," protínající se v ",[883,41619,41621],{"className":41620},[886],[888,41622,41623],{"xmlns":890},[892,41624,41625,41647],{},[895,41626,41627,41629,41631,41637,41639,41645],{},[898,41628,4252],{},[1996,41630,2486],{"stretchy":2004},[2124,41632,41633,41635],{},[898,41634,2789],{},[898,41636,4252],{},[1996,41638,2286],{"separator":2285},[2124,41640,41641,41643],{},[898,41642,3937],{},[898,41644,4252],{},[1996,41646,2501],{"stretchy":2004},[902,41648,41369],{"encoding":904},[198,41650,41652],{"id":41651},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,41654,41655,41657,41658,41692,41693,1975],{},[38,41656,37935],{}," Poptávka ",[883,41659,41661],{"className":41660},[886],[888,41662,41663],{"xmlns":890},[892,41664,41665,41689],{},[895,41666,41667,41669,41671,41673,41679,41681,41683,41685,41687],{},[898,41668,3937],{},[1996,41670,1998],{},[1996,41672,2225],{},[2124,41674,41675,41677],{},[898,41676,2789],{},[2129,41678,2131],{},[1996,41680,2225],{},[2129,41682,2863],{},[898,41684,2789],{},[1996,41686,2095],{},[2129,41688,8803],{},[902,41690,41691],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,41694,41696],{"className":41695},[886],[888,41697,41698],{"xmlns":890},[892,41699,41700,41722],{},[895,41701,41702,41704,41706,41712,41714,41716,41718,41720],{},[898,41703,3937],{},[1996,41705,1998],{},[2124,41707,41708,41710],{},[898,41709,2789],{},[2129,41711,2131],{},[1996,41713,2095],{},[2129,41715,22948],{},[898,41717,2789],{},[1996,41719,2095],{},[2129,41721,32548],{},[902,41723,41724],{"encoding":904},"P = Q^2 + 14Q + 22",[724,41726,41727,41729],{},[38,41728,37967],{}," Z rovnosti",[883,41731,41733],{"className":41732},[886],[888,41734,41735],{"xmlns":890,"display":28068},[892,41736,41737,41775],{},[895,41738,41739,41741,41747,41749,41751,41753,41755,41757,41759,41765,41767,41769,41771,41773],{},[1996,41740,2225],{},[2124,41742,41743,41745],{},[898,41744,2789],{},[2129,41746,2131],{},[1996,41748,2225],{},[2129,41750,2863],{},[898,41752,2789],{},[1996,41754,2095],{},[2129,41756,8803],{},[1996,41758,1998],{},[2124,41760,41761,41763],{},[898,41762,2789],{},[2129,41764,2131],{},[1996,41766,2095],{},[2129,41768,22948],{},[898,41770,2789],{},[1996,41772,2095],{},[2129,41774,32548],{},[902,41776,41777],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,41779,41780,41781,41816,41817,41850,41851,41868,41869,41882,41883,1343,41905,41942,41943,1975],{},"dostaneme ",[883,41782,41784],{"className":41783},[886],[888,41785,41786],{"xmlns":890},[892,41787,41788,41813],{},[895,41789,41790,41792,41798,41800,41803,41805,41807,41809,41811],{},[2129,41791,2131],{},[2124,41793,41794,41796],{},[898,41795,2789],{},[2129,41797,2131],{},[1996,41799,2095],{},[2129,41801,41802],{},"24",[898,41804,2789],{},[1996,41806,2225],{},[2129,41808,5617],{},[1996,41810,1998],{},[2129,41812,2327],{},[902,41814,41815],{"encoding":904},"2Q^2 + 24Q - 128 = 0",", resp. ",[883,41818,41820],{"className":41819},[886],[888,41821,41822],{"xmlns":890},[892,41823,41824,41847],{},[895,41825,41826,41832,41834,41836,41838,41840,41843,41845],{},[2124,41827,41828,41830],{},[898,41829,2789],{},[2129,41831,2131],{},[1996,41833,2095],{},[2129,41835,3509],{},[898,41837,2789],{},[1996,41839,2225],{},[2129,41841,41842],{},"64",[1996,41844,1998],{},[2129,41846,2327],{},[902,41848,41849],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,41852,41854],{"className":41853},[886],[888,41855,41856],{"xmlns":890},[892,41857,41858,41865],{},[895,41859,41860,41862],{},[1996,41861,2225],{},[2129,41863,41864],{},"16",[902,41866,41867],{"encoding":904},"-16"," (nevyhovuje) a ",[883,41870,41872],{"className":41871},[886],[888,41873,41874],{"xmlns":890},[892,41875,41876,41880],{},[895,41877,41878],{},[2129,41879,2351],{},[902,41881,2351],{"encoding":904},". Tedy ",[883,41884,41886],{"className":41885},[886],[888,41887,41888],{"xmlns":890},[892,41889,41890,41902],{},[895,41891,41892,41898,41900],{},[2124,41893,41894,41896],{},[898,41895,2789],{},[898,41897,4252],{},[1996,41899,1998],{},[2129,41901,2351],{},[902,41903,41904],{"encoding":904},"Q^E = 4",[883,41906,41908],{"className":41907},[886],[888,41909,41910],{"xmlns":890},[892,41911,41912,41939],{},[895,41913,41914,41920,41922,41924,41926,41928,41930,41932,41934,41936],{},[2124,41915,41916,41918],{},[898,41917,3937],{},[898,41919,4252],{},[1996,41921,1998],{},[1996,41923,2225],{},[2129,41925,41864],{},[1996,41927,2225],{},[2129,41929,5211],{},[1996,41931,2095],{},[2129,41933,8803],{},[1996,41935,1998],{},[2129,41937,41938],{},"94",[902,41940,41941],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,41944,41946],{"className":41945},[886],[888,41947,41948],{"xmlns":890},[892,41949,41950,41964],{},[895,41951,41952,41954,41956,41958,41960,41962],{},[898,41953,4252],{},[1996,41955,2486],{"stretchy":2004},[2129,41957,2351],{},[1996,41959,2286],{"separator":2285},[2129,41961,41938],{},[1996,41963,2501],{"stretchy":2004},[902,41965,41966],{"encoding":904},"E[4, 94]",[198,41968,41970],{"id":41969},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,41972,41973,41975],{},[38,41974,37935],{}," Poptávky a nabídky dvou zboží",[883,41977,41979],{"className":41978},[886],[888,41980,41981],{"xmlns":890,"display":28068},[892,41982,41983,42149],{},[20756,41984,41987,42075],{"rowspacing":20758,"columnalign":41985,"columnspacing":41986},"right left right left","0em 1em 0em",[20761,41988,41989,41999,42031,42041],{},[20764,41990,41991],{},[2325,41992,41993],{"scriptlevel":2327,"displaystyle":2285},[2272,41994,41995,41997],{},[898,41996,2789],{},[2129,41998,2278],{},[20764,42000,42001],{},[2325,42002,42003],{"scriptlevel":2327,"displaystyle":2285},[895,42004,42005,42007,42009,42011,42013,42015,42021,42023,42029],{},[895,42006],{},[1996,42008,1998],{},[2129,42010,5211],{},[1996,42012,2225],{},[2129,42014,2228],{},[2272,42016,42017,42019],{},[898,42018,3937],{},[2129,42020,2278],{},[1996,42022,2225],{},[2272,42024,42025,42027],{},[898,42026,3937],{},[2129,42028,2131],{},[1996,42030,2286],{"separator":2285},[20764,42032,42033],{},[2325,42034,42035],{"scriptlevel":2327,"displaystyle":2285},[2272,42036,42037,42039],{},[898,42038,2789],{},[2129,42040,2131],{},[20764,42042,42043],{},[2325,42044,42045],{"scriptlevel":2327,"displaystyle":2285},[895,42046,42047,42049,42051,42053,42055,42057,42063,42065,42067,42073],{},[895,42048],{},[1996,42050,1998],{},[2129,42052,3120],{},[1996,42054,2225],{},[2129,42056,2131],{},[2272,42058,42059,42061],{},[898,42060,3937],{},[2129,42062,2278],{},[1996,42064,2225],{},[2129,42066,2351],{},[2272,42068,42069,42071],{},[898,42070,3937],{},[2129,42072,2131],{},[1996,42074,2286],{"separator":2285},[20761,42076,42077,42087,42113,42123],{},[20764,42078,42079],{},[2325,42080,42081],{"scriptlevel":2327,"displaystyle":2285},[2272,42082,42083,42085],{},[898,42084,2789],{},[2129,42086,2278],{},[20764,42088,42089],{},[2325,42090,42091],{"scriptlevel":2327,"displaystyle":2285},[895,42092,42093,42095,42097,42099,42101,42103,42105,42111],{},[895,42094],{},[1996,42096,1998],{},[1996,42098,2225],{},[2129,42100,2173],{},[1996,42102,2095],{},[2129,42104,2351],{},[2272,42106,42107,42109],{},[898,42108,3937],{},[2129,42110,2278],{},[1996,42112,2286],{"separator":2285},[20764,42114,42115],{},[2325,42116,42117],{"scriptlevel":2327,"displaystyle":2285},[2272,42118,42119,42121],{},[898,42120,2789],{},[2129,42122,2131],{},[20764,42124,42125],{},[2325,42126,42127],{"scriptlevel":2327,"displaystyle":2285},[895,42128,42129,42131,42133,42135,42137,42139,42141,42147],{},[895,42130],{},[1996,42132,1998],{},[1996,42134,2225],{},[2129,42136,24203],{},[1996,42138,2095],{},[2129,42140,2173],{},[2272,42142,42143,42145],{},[898,42144,3937],{},[2129,42146,2131],{},[898,42148,1975],{"mathvariant":2376},[902,42150,42151],{"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}",[724,42153,42154,42156],{},[38,42155,37967],{}," Z rovností poptávek a nabídek dostaneme",[883,42158,42160],{"className":42159},[886],[888,42161,42162],{"xmlns":890,"display":28068},[892,42163,42164,42213],{},[895,42165,42166,42168,42174,42176,42182,42184,42186,42188,42190,42192,42198,42200,42202,42208,42210],{},[2129,42167,3999],{},[2272,42169,42170,42172],{},[898,42171,3937],{},[2129,42173,2278],{},[1996,42175,2095],{},[2272,42177,42178,42180],{},[898,42179,3937],{},[2129,42181,2131],{},[1996,42183,1998],{},[2129,42185,21205],{},[1996,42187,2286],{"separator":2285},[5878,42189],{"width":5880},[2129,42191,2131],{},[2272,42193,42194,42196],{},[898,42195,3937],{},[2129,42197,2278],{},[1996,42199,2095],{},[2129,42201,24203],{},[2272,42203,42204,42206],{},[898,42205,3937],{},[2129,42207,2131],{},[1996,42209,1998],{},[2129,42211,42212],{},"57.",[902,42214,42215],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,42217,42218,42219,1343,42243,42267,42268,1343,42293,42317,42318,42320],{},"Řešením je ",[883,42220,42222],{"className":42221},[886],[888,42223,42224],{"xmlns":890},[892,42225,42226,42240],{},[895,42227,42228,42236,42238],{},[9166,42229,42230,42232,42234],{},[898,42231,3937],{},[2129,42233,2278],{},[898,42235,4252],{},[1996,42237,1998],{},[2129,42239,2351],{},[902,42241,42242],{"encoding":904},"P_1^E = 4",[883,42244,42246],{"className":42245},[886],[888,42247,42248],{"xmlns":890},[892,42249,42250,42264],{},[895,42251,42252,42260,42262],{},[9166,42253,42254,42256,42258],{},[898,42255,3937],{},[2129,42257,2131],{},[898,42259,4252],{},[1996,42261,1998],{},[2129,42263,24203],{},[902,42265,42266],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,42269,42271],{"className":42270},[886],[888,42272,42273],{"xmlns":890},[892,42274,42275,42290],{},[895,42276,42277,42285,42287],{},[9166,42278,42279,42281,42283],{},[898,42280,2789],{},[2129,42282,2278],{},[898,42284,4252],{},[1996,42286,1998],{},[2129,42288,42289],{},"13",[902,42291,42292],{"encoding":904},"Q_1^E = 13",[883,42294,42296],{"className":42295},[886],[888,42297,42298],{"xmlns":890},[892,42299,42300,42314],{},[895,42301,42302,42310,42312],{},[9166,42303,42304,42306,42308],{},[898,42305,2789],{},[2129,42307,2131],{},[898,42309,4252],{},[1996,42311,1998],{},[2129,42313,22948],{},[902,42315,42316],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,42319,39824],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,42322,42324],{"id":42323},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,42326,42327,42328,42345,42346,10025,42349,3918],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,42329,42331],{"className":42330},[886],[888,42332,42333],{"xmlns":890},[892,42334,42335,42343],{},[895,42336,42337],{},[2124,42338,42339,42341],{},[898,42340,3937],{},[898,42342,4252],{},[902,42344,41468],{"encoding":904},"; mechanismus popisuje ",[38,42347,42348],{},"teorém pavučiny",[614,42350,42351],{},"cobweb model",[198,42353,42355],{"id":42354},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,42357,42358],{},[2559,42359],{"alt":42360,"className":42361,"src":42362},"imek-komparativni-statika-4pripady",[210,2563],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[3867,42364,42365,42406,42446,42486],{},[724,42366,42367,42370,42371,6190,42388,1975],{},[38,42368,42369],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,42372,42374],{"className":42373},[886],[888,42375,42376],{"xmlns":890},[892,42377,42378,42386],{},[895,42379,42380],{},[2124,42381,42382,42384],{},[898,42383,3937],{},[898,42385,4252],{},[902,42387,41468],{"encoding":904},[883,42389,42391],{"className":42390},[886],[888,42392,42393],{"xmlns":890},[892,42394,42395,42403],{},[895,42396,42397],{},[2124,42398,42399,42401],{},[898,42400,2789],{},[898,42402,4252],{},[902,42404,42405],{"encoding":904},"Q^E",[724,42407,42408,42411,42412,6190,42429,1975],{},[38,42409,42410],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,42413,42415],{"className":42414},[886],[888,42416,42417],{"xmlns":890},[892,42418,42419,42427],{},[895,42420,42421],{},[2124,42422,42423,42425],{},[898,42424,3937],{},[898,42426,4252],{},[902,42428,41468],{"encoding":904},[883,42430,42432],{"className":42431},[886],[888,42433,42434],{"xmlns":890},[892,42435,42436,42444],{},[895,42437,42438],{},[2124,42439,42440,42442],{},[898,42441,2789],{},[898,42443,4252],{},[902,42445,42405],{"encoding":904},[724,42447,42448,42451,42452,9355,42469,1975],{},[38,42449,42450],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,42453,42455],{"className":42454},[886],[888,42456,42457],{"xmlns":890},[892,42458,42459,42467],{},[895,42460,42461],{},[2124,42462,42463,42465],{},[898,42464,3937],{},[898,42466,4252],{},[902,42468,41468],{"encoding":904},[883,42470,42472],{"className":42471},[886],[888,42473,42474],{"xmlns":890},[892,42475,42476,42484],{},[895,42477,42478],{},[2124,42479,42480,42482],{},[898,42481,2789],{},[898,42483,4252],{},[902,42485,42405],{"encoding":904},[724,42487,42488,42491,42492,42509,42510,1975],{},[38,42489,42490],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,42493,42495],{"className":42494},[886],[888,42496,42497],{"xmlns":890},[892,42498,42499,42507],{},[895,42500,42501],{},[2124,42502,42503,42505],{},[898,42504,3937],{},[898,42506,4252],{},[902,42508,41468],{"encoding":904},", pokles ",[883,42511,42513],{"className":42512},[886],[888,42514,42515],{"xmlns":890},[892,42516,42517,42525],{},[895,42518,42519],{},[2124,42520,42521,42523],{},[898,42522,2789],{},[898,42524,4252],{},[902,42526,42405],{"encoding":904},[16,42528,42529,42574],{},[19,42530,42531],{},[22,42532,42533,42536,42555],{},[25,42534,42535],{},"Změna",[25,42537,42538],{},[883,42539,42541],{"className":42540},[886],[888,42542,42543],{"xmlns":890},[892,42544,42545,42553],{},[895,42546,42547],{},[2124,42548,42549,42551],{},[898,42550,3937],{},[898,42552,4252],{},[902,42554,41468],{"encoding":904},[25,42556,42557],{},[883,42558,42560],{"className":42559},[886],[888,42561,42562],{"xmlns":890},[892,42563,42564,42572],{},[895,42565,42566],{},[2124,42567,42568,42570],{},[898,42569,2789],{},[898,42571,4252],{},[902,42573,42405],{"encoding":904},[30,42575,42576,42586,42596,42605],{},[22,42577,42578,42581,42584],{},[35,42579,42580],{},"Růst poptávky",[35,42582,42583],{},"↑",[35,42585,42583],{},[22,42587,42588,42591,42594],{},[35,42589,42590],{},"Pokles poptávky",[35,42592,42593],{},"↓",[35,42595,42593],{},[22,42597,42598,42601,42603],{},[35,42599,42600],{},"Růst nabídky",[35,42602,42593],{},[35,42604,42583],{},[22,42606,42607,42610,42612],{},[35,42608,42609],{},"Pokles nabídky",[35,42611,42583],{},[35,42613,42593],{},[724,42615,42616],{},[614,42617,42618],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[36972,42620],{},[115,42622,811],{"id":42623},"zdanění-trhu",[3867,42625,42626,42715],{},[724,42627,42628,42630,42631,42644,42645,2927,42658,42661,42662,36778,42685,42710,42711,42714],{},[883,42629,4155],{}," TL;DR\nJednotková daň ",[883,42632,42634],{"className":42633},[886],[888,42635,42636],{"xmlns":890},[892,42637,42638,42642],{},[895,42639,42640],{},[898,42641,2774],{},[902,42643,2774],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,42646,42648],{"className":42647},[886],[888,42649,42650],{"xmlns":890},[892,42651,42652,42656],{},[895,42653,42654],{},[898,42655,2774],{},[902,42657,2774],{"encoding":904},[38,42659,42660],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,42663,42665],{"className":42664},[886],[888,42666,42667],{"xmlns":890},[892,42668,42669,42682],{},[895,42670,42671],{},[2272,42672,42673,42675],{},[898,42674,2774],{},[895,42676,42677,42680],{},[898,42678,42679],{},"s",[898,42681,724],{},[902,42683,42684],{"encoding":904},"T_{sp}",[883,42686,42688],{"className":42687},[886],[888,42689,42690],{"xmlns":890},[892,42691,42692,42707],{},[895,42693,42694],{},[2272,42695,42696,42698],{},[898,42697,2774],{},[895,42699,42700,42703,42705],{},[898,42701,42702],{},"v",[898,42704,1994],{},[898,42706,12043],{},[902,42708,42709],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,42712,42713],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,42716,42717],{},[614,42718,42719,42720,1975],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,42721,42723],{"className":42722,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,42725,42726,42727,42730,42731,42757,42758,42761,42762,42788,42789,42806,42807,42847,42848,3885,42861,1975],{},"Existují dvě formy zdanění — daň uložená ",[38,42728,42729],{},"výrobci"," (posun nabídky ",[883,42732,42734],{"className":42733},[886],[888,42735,42736],{"xmlns":890},[892,42737,42738,42754],{},[895,42739,42740,42746,42748,42750,42752],{},[2272,42741,42742,42744],{},[898,42743,8673],{},[2129,42745,2278],{},[1996,42747,1998],{},[898,42749,8673],{},[1996,42751,2095],{},[898,42753,2774],{},[902,42755,42756],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,42759,42760],{},"spotřebiteli"," (posun poptávky ",[883,42763,42765],{"className":42764},[886],[888,42766,42767],{"xmlns":890},[892,42768,42769,42785],{},[895,42770,42771,42777,42779,42781,42783],{},[2272,42772,42773,42775],{},[898,42774,4183],{},[2129,42776,2131],{},[1996,42778,1998],{},[898,42780,4183],{},[1996,42782,2225],{},[898,42784,2774],{},[902,42786,42787],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,42790,42792],{"className":42791},[886],[888,42793,42794],{"xmlns":890},[892,42795,42796,42804],{},[895,42797,42798],{},[2124,42799,42800,42802],{},[898,42801,2789],{},[898,42803,4252],{},[902,42805,42405],{"encoding":904}," klesá a vzniká rozklad daně ",[883,42808,42810],{"className":42809},[886],[888,42811,42812],{"xmlns":890},[892,42813,42814,42844],{},[895,42815,42816,42818,42820,42830,42832],{},[898,42817,2774],{},[1996,42819,1998],{},[2272,42821,42822,42824],{},[898,42823,2774],{},[895,42825,42826,42828],{},[898,42827,42679],{},[898,42829,724],{},[1996,42831,2095],{},[2272,42833,42834,42836],{},[898,42835,2774],{},[895,42837,42838,42840,42842],{},[898,42839,42702],{},[898,42841,1994],{},[898,42843,12043],{},[902,42845,42846],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,42849,42851],{"className":42850},[886],[888,42852,42853],{"xmlns":890},[892,42854,42855,42859],{},[895,42856,42857],{},[898,42858,4183],{},[902,42860,4183],{"encoding":904},[883,42862,42864],{"className":42863},[886],[888,42865,42866],{"xmlns":890},[892,42867,42868,42872],{},[895,42869,42870],{},[898,42871,8673],{},[902,42873,8673],{"encoding":904},[724,42875,42876,42877,42880,42881,3885,42911,42945],{},"Zásadním výsledkem kapitoly je ",[38,42878,42879],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,42882,42884],{"className":42883},[886],[888,42885,42886],{"xmlns":890},[892,42887,42888,42908],{},[895,42889,42890,42898,42900],{},[9166,42891,42892,42894,42896],{},[898,42893,2789],{},[2129,42895,2278],{},[898,42897,4252],{},[1996,42899,1998],{},[9166,42901,42902,42904,42906],{},[898,42903,2789],{},[2129,42905,2131],{},[898,42907,4252],{},[902,42909,42910],{"encoding":904},"Q_1^E = Q_2^E",[883,42912,42914],{"className":42913},[886],[888,42915,42916],{"xmlns":890},[892,42917,42918,42942],{},[895,42919,42920,42928,42930,42932,42934],{},[9166,42921,42922,42924,42926],{},[898,42923,3937],{},[2129,42925,2278],{},[898,42927,4252],{},[1996,42929,2225],{},[898,42931,2774],{},[1996,42933,1998],{},[9166,42935,42936,42938,42940],{},[898,42937,3937],{},[2129,42939,2131],{},[898,42941,4252],{},[902,42943,42944],{"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.",[724,42947,42948,42949,42952,42953,42979,42980,43008,43009,43012,43013,43016,43017,1975],{},"Podrobný výklad, Příklady ",[38,42950,42951],{},"2.9"," (daň výrobci, ",[883,42954,42956],{"className":42955},[886],[888,42957,42958],{"xmlns":890},[892,42959,42960,42976],{},[895,42961,42962,42972,42974],{},[2272,42963,42964,42966],{},[898,42965,2774],{},[895,42967,42968,42970],{},[898,42969,42679],{},[898,42971,724],{},[1996,42973,1998],{},[2129,42975,2131],{},[902,42977,42978],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,42981,42983],{"className":42982},[886],[888,42984,42985],{"xmlns":890},[892,42986,42987,43005],{},[895,42988,42989,43001,43003],{},[2272,42990,42991,42993],{},[898,42992,2774],{},[895,42994,42995,42997,42999],{},[898,42996,42702],{},[898,42998,1994],{},[898,43000,12043],{},[1996,43002,1998],{},[2129,43004,2351],{},[902,43006,43007],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,43010,43011],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,43014,43015],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,43018,42723],{"className":43019,"dataFsResolvedFilePath":809,"href":810},[210],[36972,43021],{},[115,43023,43025],{"id":43024},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[3867,43027,43028],{},[724,43029,43030,43032,43033,43036,43037,43039],{},[883,43031,4155],{}," TL;DR\nMultiplikátory jsou ",[38,43034,43035],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,43038,36962],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,43041,43043],{"id":43042},"redukovaný-tvar","Redukovaný tvar",[724,43045,43046,43047,10025,43070,1343,43088,12130,43105,10025,43128,43145,43146,43176],{},"Pro lineární model ",[883,43048,43050],{"className":43049},[886],[888,43051,43052],{"xmlns":890},[892,43053,43054,43068],{},[895,43055,43056,43058,43060,43062,43064,43066],{},[898,43057,3937],{},[1996,43059,1998],{},[898,43061,207],{},[898,43063,2789],{},[1996,43065,2095],{},[898,43067,2098],{},[902,43069,37062],{"encoding":904},[883,43071,43073],{"className":43072},[886],[888,43074,43075],{"xmlns":890},[892,43076,43077,43085],{},[895,43078,43079,43081,43083],{},[898,43080,207],{},[1996,43082,3447],{},[2129,43084,2327],{},[902,43086,43087],{"encoding":904},"a \u003C 0",[883,43089,43091],{"className":43090},[886],[888,43092,43093],{"xmlns":890},[892,43094,43095,43103],{},[895,43096,43097,43099,43101],{},[898,43098,2098],{},[1996,43100,3408],{},[2129,43102,2327],{},[902,43104,18816],{"encoding":904},[883,43106,43108],{"className":43107},[886],[888,43109,43110],{"xmlns":890},[892,43111,43112,43126],{},[895,43113,43114,43116,43118,43120,43122,43124],{},[898,43115,3937],{},[1996,43117,1998],{},[898,43119,2142],{},[898,43121,2789],{},[1996,43123,2095],{},[898,43125,2194],{},[902,43127,40244],{"encoding":904},[883,43129,43131],{"className":43130},[886],[888,43132,43133],{"xmlns":890},[892,43134,43135,43143],{},[895,43136,43137,43139,43141],{},[898,43138,2142],{},[1996,43140,3408],{},[2129,43142,2327],{},[902,43144,40262],{"encoding":904},") dává podmínka rovnováhy ",[883,43147,43149],{"className":43148},[886],[888,43150,43151],{"xmlns":890},[892,43152,43153,43173],{},[895,43154,43155,43157,43159,43161,43163,43165,43167,43169,43171],{},[898,43156,207],{},[898,43158,2789],{},[1996,43160,2095],{},[898,43162,2098],{},[1996,43164,1998],{},[898,43166,2142],{},[898,43168,2789],{},[1996,43170,2095],{},[898,43172,2194],{},[902,43174,43175],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,43178,43180],{"className":43179},[886],[888,43181,43182],{"xmlns":890,"display":28068},[892,43183,43184,43229],{},[20756,43185,43186],{"width":28073},[20761,43187,43188,43190,43222,43224],{},[20764,43189],{"width":28078},[20764,43191,43192],{},[895,43193,43194,43200,43202,43220],{},[2124,43195,43196,43198],{},[898,43197,2789],{},[898,43199,4252],{},[1996,43201,1998],{},[2329,43203,43204,43212],{},[895,43205,43206,43208,43210],{},[898,43207,2098],{},[1996,43209,2225],{},[898,43211,2194],{},[895,43213,43214,43216,43218],{},[898,43215,2142],{},[1996,43217,2225],{},[898,43219,207],{},[898,43221,1975],{"mathvariant":2376},[20764,43223],{"width":28078},[20764,43225,43226],{},[2288,43227,43228],{},"(2.10)",[902,43230,43231],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,43233,43234,43235,10025,43237,43240,43241,43258,43259,2203,43262,43288,43289,43302,43303,43321,43322,3918],{},"Vztah (2.10) je ",[38,43236,20956],{},[614,43238,43239],{},"reduced form",") pro ",[883,43242,43244],{"className":43243},[886],[888,43245,43246],{"xmlns":890},[892,43247,43248,43256],{},[895,43249,43250],{},[2124,43251,43252,43254],{},[898,43253,2789],{},[898,43255,4252],{},[902,43257,42405],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,43260,43261],{},"parametrů",[883,43263,43265],{"className":43264},[886],[888,43266,43267],{"xmlns":890},[892,43268,43269,43285],{},[895,43270,43271,43273,43275,43277,43279,43281,43283],{},[898,43272,207],{},[1996,43274,2286],{"separator":2285},[898,43276,2098],{},[1996,43278,2286],{"separator":2285},[898,43280,2142],{},[1996,43282,2286],{"separator":2285},[898,43284,2194],{},[902,43286,43287],{"encoding":904},"a, b, c, d",". Aby ",[883,43290,43292],{"className":43291},[886],[888,43293,43294],{"xmlns":890},[892,43295,43296,43300],{},[895,43297,43298],{},[898,43299,4252],{},[902,43301,4252],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,43304,43306],{"className":43305},[886],[888,43307,43308],{"xmlns":890},[892,43309,43310,43318],{},[895,43311,43312,43314,43316],{},[898,43313,2098],{},[1996,43315,3408],{},[898,43317,2194],{},[902,43319,43320],{"encoding":904},"b > d"," (neboť ",[883,43323,43325],{"className":43324},[886],[888,43326,43327],{"xmlns":890},[892,43328,43329,43341],{},[895,43330,43331,43333,43335,43337,43339],{},[898,43332,2142],{},[1996,43334,2225],{},[898,43336,207],{},[1996,43338,3408],{},[2129,43340,2327],{},[902,43342,43343],{"encoding":904},"c - a > 0",[724,43345,43346],{},[614,43347,43348,43349,43362,43363,43376,43377,18650,43390,41942,43407,43420],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,43350,43352],{"className":43351},[886],[888,43353,43354],{"xmlns":890},[892,43355,43356,43360],{},[895,43357,43358],{},[898,43359,2098],{},[902,43361,2098],{"encoding":904}," na ose ",[883,43364,43366],{"className":43365},[886],[888,43367,43368],{"xmlns":890},[892,43369,43370,43374],{},[895,43371,43372],{},[898,43373,3937],{},[902,43375,3937],{"encoding":904},") a nabídka (úsek ",[883,43378,43380],{"className":43379},[886],[888,43381,43382],{"xmlns":890},[892,43383,43384,43388],{},[895,43385,43386],{},[898,43387,2194],{},[902,43389,2194],{"encoding":904},[883,43391,43393],{"className":43392},[886],[888,43394,43395],{"xmlns":890},[892,43396,43397,43405],{},[895,43398,43399,43401,43403],{},[898,43400,2098],{},[1996,43402,3408],{},[898,43404,2194],{},[902,43406,43320],{"encoding":904},[883,43408,43410],{"className":43409},[886],[888,43411,43412],{"xmlns":890},[892,43413,43414,43418],{},[895,43415,43416],{},[898,43417,4252],{},[902,43419,4252],{"encoding":904}," v 1. kvadrantu.",[198,43422,43424],{"id":43423},"definice-multiplikátorů","Definice multiplikátorů",[724,43426,43427,43428,43453,43454,43467,43468,43481],{},"V komparativní statice jsou ",[883,43429,43431],{"className":43430},[886],[888,43432,43433],{"xmlns":890},[892,43434,43435,43451],{},[895,43436,43437,43439,43441,43443,43445,43447,43449],{},[898,43438,207],{},[1996,43440,2286],{"separator":2285},[898,43442,2098],{},[1996,43444,2286],{"separator":2285},[898,43446,2142],{},[1996,43448,2286],{"separator":2285},[898,43450,2194],{},[902,43452,43287],{"encoding":904}," exogenní proměnné a ",[883,43455,43457],{"className":43456},[886],[888,43458,43459],{"xmlns":890},[892,43460,43461,43465],{},[895,43462,43463],{},[898,43464,2789],{},[902,43466,2789],{"encoding":904}," endogenní. Přibližná změna ",[883,43469,43471],{"className":43470},[886],[888,43472,43473],{"xmlns":890},[892,43474,43475,43479],{},[895,43476,43477],{},[898,43478,2789],{},[902,43480,2789],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,43483,43485],{"className":43484},[886],[888,43486,43487],{"xmlns":890,"display":28068},[892,43488,43489,43582],{},[20756,43490,43491],{"width":28073},[20761,43492,43493,43495,43575,43577],{},[20764,43494],{"width":28078},[20764,43496,43497],{},[895,43498,43499,43501,43503,43505,43507,43509,43511,43519,43521,43523,43525,43527,43535,43537,43539,43541,43543,43551,43553,43555,43557,43559,43567,43569,43571,43573],{},[898,43500,2889],{"mathvariant":2376},[898,43502,2789],{},[1996,43504,2730],{},[898,43506,2194],{},[898,43508,2789],{},[1996,43510,1998],{},[9166,43512,43513,43515,43517],{},[898,43514,2789],{},[898,43516,207],{},[1996,43518,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[2288,43520,2987],{},[898,43522,2194],{},[898,43524,207],{},[1996,43526,2095],{},[9166,43528,43529,43531,43533],{},[898,43530,2789],{},[898,43532,2098],{},[1996,43534,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[2288,43536,2987],{},[898,43538,2194],{},[898,43540,2098],{},[1996,43542,2095],{},[9166,43544,43545,43547,43549],{},[898,43546,2789],{},[898,43548,2142],{},[1996,43550,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[2288,43552,2987],{},[898,43554,2194],{},[898,43556,2142],{},[1996,43558,2095],{},[9166,43560,43561,43563,43565],{},[898,43562,2789],{},[898,43564,2194],{},[1996,43566,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[2288,43568,2987],{},[898,43570,2194],{},[898,43572,2194],{},[898,43574,1975],{"mathvariant":2376},[20764,43576],{"width":28078},[20764,43578,43579],{},[2288,43580,43581],{},"(2.11)",[902,43583,43584],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,43586,43587,43588,43638,43639,10025,43641,3151],{},"Parciální derivace ",[883,43589,43591],{"className":43590},[886],[888,43592,43593],{"xmlns":890},[892,43594,43595,43635],{},[895,43596,43597,43605,43607,43615,43617,43625,43627],{},[9166,43598,43599,43601,43603],{},[898,43600,2789],{},[898,43602,207],{},[1996,43604,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,43606,2286],{"separator":2285},[9166,43608,43609,43611,43613],{},[898,43610,2789],{},[898,43612,2098],{},[1996,43614,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,43616,2286],{"separator":2285},[9166,43618,43619,43621,43623],{},[898,43620,2789],{},[898,43622,2142],{},[1996,43624,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,43626,2286],{"separator":2285},[9166,43628,43629,43631,43633],{},[898,43630,2789],{},[898,43632,2194],{},[1996,43634,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,43636,43637],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,43640,17979],{},[614,43642,43643],{},"multipliers",[883,43645,43647],{"className":43646},[886],[888,43648,43649],{"xmlns":890,"display":28068},[892,43650,43651,43802],{},[20756,43652,43653],{"width":28073},[20761,43654,43655,43657,43795,43797],{},[20764,43656],{"width":28078},[20764,43658,43659],{},[895,43660,43661,43669,43671,43697,43699,43701,43709,43711,43723,43725,43727,43735,43737,43739,43765,43767,43769,43777,43779,43781,43793],{},[9166,43662,43663,43665,43667],{},[898,43664,2789],{},[898,43666,207],{},[1996,43668,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,43670,1998],{},[2329,43672,43673,43681],{},[895,43674,43675,43677,43679],{},[898,43676,2098],{},[1996,43678,2225],{},[898,43680,2194],{},[895,43682,43683,43685,43687,43689,43691],{},[1996,43684,2005],{"stretchy":2004},[898,43686,2142],{},[1996,43688,2225],{},[898,43690,207],{},[2124,43692,43693,43695],{},[1996,43694,2011],{"stretchy":2004},[2129,43696,2131],{},[1996,43698,2286],{"separator":2285},[5878,43700],{"width":15286},[9166,43702,43703,43705,43707],{},[898,43704,2789],{},[898,43706,2098],{},[1996,43708,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,43710,1998],{},[2329,43712,43713,43715],{},[2129,43714,2278],{},[895,43716,43717,43719,43721],{},[898,43718,2142],{},[1996,43720,2225],{},[898,43722,207],{},[1996,43724,2286],{"separator":2285},[5878,43726],{"width":15286},[9166,43728,43729,43731,43733],{},[898,43730,2789],{},[898,43732,2142],{},[1996,43734,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,43736,1998],{},[1996,43738,2225],{},[2329,43740,43741,43749],{},[895,43742,43743,43745,43747],{},[898,43744,2098],{},[1996,43746,2225],{},[898,43748,2194],{},[895,43750,43751,43753,43755,43757,43759],{},[1996,43752,2005],{"stretchy":2004},[898,43754,2142],{},[1996,43756,2225],{},[898,43758,207],{},[2124,43760,43761,43763],{},[1996,43762,2011],{"stretchy":2004},[2129,43764,2131],{},[1996,43766,2286],{"separator":2285},[5878,43768],{"width":15286},[9166,43770,43771,43773,43775],{},[898,43772,2789],{},[898,43774,2194],{},[1996,43776,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,43778,1998],{},[1996,43780,2225],{},[2329,43782,43783,43785],{},[2129,43784,2278],{},[895,43786,43787,43789,43791],{},[898,43788,2142],{},[1996,43790,2225],{},[898,43792,207],{},[898,43794,1975],{"mathvariant":2376},[20764,43796],{"width":28078},[20764,43798,43799],{},[2288,43800,43801],{},"(2.12)",[902,43803,43804],{"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}",[198,43806,43808],{"id":43807},"znaménka-a-interpretace","Znaménka a interpretace",[724,43810,43811,43812,1343,43829,1343,43846,1343,43863,43880,43881,3151],{},"Za podmínek ",[883,43813,43815],{"className":43814},[886],[888,43816,43817],{"xmlns":890},[892,43818,43819,43827],{},[895,43820,43821,43823,43825],{},[898,43822,207],{},[1996,43824,3447],{},[2129,43826,2327],{},[902,43828,43087],{"encoding":904},[883,43830,43832],{"className":43831},[886],[888,43833,43834],{"xmlns":890},[892,43835,43836,43844],{},[895,43837,43838,43840,43842],{},[898,43839,2098],{},[1996,43841,3408],{},[2129,43843,2327],{},[902,43845,18816],{"encoding":904},[883,43847,43849],{"className":43848},[886],[888,43850,43851],{"xmlns":890},[892,43852,43853,43861],{},[895,43854,43855,43857,43859],{},[898,43856,2142],{},[1996,43858,3408],{},[2129,43860,2327],{},[902,43862,40262],{"encoding":904},[883,43864,43866],{"className":43865},[886],[888,43867,43868],{"xmlns":890},[892,43869,43870,43878],{},[895,43871,43872,43874,43876],{},[898,43873,2098],{},[1996,43875,3408],{},[898,43877,2194],{},[902,43879,43320],{"encoding":904}," platí (znaménka se ",[38,43882,43883],{},"nemění",[883,43885,43887],{"className":43886},[886],[888,43888,43889],{"xmlns":890,"display":28068},[892,43890,43891,43953],{},[895,43892,43893,43901,43903,43905,43907,43909,43917,43919,43921,43923,43925,43933,43935,43937,43939,43941,43949,43951],{},[9166,43894,43895,43897,43899],{},[898,43896,2789],{},[898,43898,207],{},[1996,43900,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,43902,3408],{},[2129,43904,2327],{},[1996,43906,2286],{"separator":2285},[5878,43908],{"width":5880},[9166,43910,43911,43913,43915],{},[898,43912,2789],{},[898,43914,2098],{},[1996,43916,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,43918,3408],{},[2129,43920,2327],{},[1996,43922,2286],{"separator":2285},[5878,43924],{"width":5880},[9166,43926,43927,43929,43931],{},[898,43928,2789],{},[898,43930,2142],{},[1996,43932,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,43934,3447],{},[2129,43936,2327],{},[1996,43938,2286],{"separator":2285},[5878,43940],{"width":5880},[9166,43942,43943,43945,43947],{},[898,43944,2789],{},[898,43946,2194],{},[1996,43948,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,43950,3447],{},[2129,43952,12462],{},[902,43954,43955],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,43957,43958,44017],{},[123,43959,43960,2203,43963,43983,43984,44001,44002,1343,44015,1975],{},[38,43961,43962],{},"Kvantitativní smysl:",[883,43964,43966],{"className":43965},[886],[888,43967,43968],{"xmlns":890},[892,43969,43970,43980],{},[895,43971,43972],{},[9166,43973,43974,43976,43978],{},[898,43975,2789],{},[898,43977,2008],{},[1996,43979,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,43981,43982],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,43985,43987],{"className":43986},[886],[888,43988,43989],{"xmlns":890},[892,43990,43991,43999],{},[895,43992,43993],{},[2124,43994,43995,43997],{},[898,43996,2789],{},[898,43998,4252],{},[902,44000,42405],{"encoding":904}," při jednotkové změně parametru ",[883,44003,44005],{"className":44004},[886],[888,44006,44007],{"xmlns":890},[892,44008,44009,44013],{},[895,44010,44011],{},[898,44012,2008],{},[902,44014,2008],{"encoding":904},[614,44016,36962],{},[123,44018,44019,44022,44023,44040,44041,1975],{},[38,44020,44021],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,44024,44026],{"className":44025},[886],[888,44027,44028],{"xmlns":890},[892,44029,44030,44038],{},[895,44031,44032],{},[2124,44033,44034,44036],{},[898,44035,2789],{},[898,44037,4252],{},[902,44039,42405],{"encoding":904}," na růst ",[883,44042,44044],{"className":44043},[886],[888,44045,44046],{"xmlns":890},[892,44047,44048,44052],{},[895,44049,44050],{},[898,44051,2008],{},[902,44053,2008],{"encoding":904},[724,44055,44056,44057,44070,44071,43321,44088,3918],{},"Např. růst ",[883,44058,44060],{"className":44059},[886],[888,44061,44062],{"xmlns":890},[892,44063,44064,44068],{},[895,44065,44066],{},[898,44067,2142],{},[902,44069,2142],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,44072,44074],{"className":44073},[886],[888,44075,44076],{"xmlns":890},[892,44077,44078,44086],{},[895,44079,44080],{},[2124,44081,44082,44084],{},[898,44083,2789],{},[898,44085,4252],{},[902,44087,42405],{"encoding":904},[883,44089,44091],{"className":44090},[886],[888,44092,44093],{"xmlns":890},[892,44094,44095,44109],{},[895,44096,44097,44105,44107],{},[9166,44098,44099,44101,44103],{},[898,44100,2789],{},[898,44102,2142],{},[1996,44104,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,44106,3447],{},[2129,44108,2327],{},[902,44110,44111],{"encoding":904},"Q'_c \u003C 0",[724,44113,44114],{},[614,44115,44116,44117,44137,44138,44162,44163,44185,44186,1975],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,44118,44120],{"className":44119},[886],[888,44121,44122],{"xmlns":890},[892,44123,44124,44134],{},[895,44125,44126,44128,44130,44132],{},[898,44127,2142],{},[898,44129,2789],{},[1996,44131,2095],{},[898,44133,2194],{},[902,44135,44136],{"encoding":904},"cQ + d"," na strmější ",[883,44139,44141],{"className":44140},[886],[888,44142,44143],{"xmlns":890},[892,44144,44145,44159],{},[895,44146,44147,44153,44155,44157],{},[2272,44148,44149,44151],{},[898,44150,2142],{},[2129,44152,2278],{},[898,44154,2789],{},[1996,44156,2095],{},[898,44158,2194],{},[902,44160,44161],{"encoding":904},"c_1 Q + d"," (při ",[883,44164,44166],{"className":44165},[886],[888,44167,44168],{"xmlns":890},[892,44169,44170,44182],{},[895,44171,44172,44178,44180],{},[2272,44173,44174,44176],{},[898,44175,2142],{},[2129,44177,2278],{},[1996,44179,3408],{},[898,44181,2142],{},[902,44183,44184],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,44187,44189],{"className":44188},[886],[888,44190,44191],{"xmlns":890},[892,44192,44193,44203],{},[895,44194,44195,44201],{},[2124,44196,44197,44199],{},[898,44198,2789],{},[898,44200,4252],{},[1996,44202,42593],{},[902,44204,44205],{"encoding":904},"Q^E \\downarrow",[724,44207,44208,44209,44241,44242,1975],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,44210,44212],{"className":44211},[886],[888,44213,44214],{"xmlns":890},[892,44215,44216,44238],{},[895,44217,44218,44220,44222,44224,44232,44234,44236],{},[898,44219,2889],{"mathvariant":2376},[898,44221,2789],{},[1996,44223,2730],{},[9166,44225,44226,44228,44230],{},[898,44227,2789],{},[898,44229,2098],{},[1996,44231,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[2288,44233,2987],{},[898,44235,2194],{},[898,44237,2098],{},[902,44239,44240],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,44243,44245],{"className":44244},[886],[888,44246,44247],{"xmlns":890},[892,44248,44249,44257],{},[895,44250,44251],{},[2124,44252,44253,44255],{},[898,44254,3937],{},[898,44256,4252],{},[902,44258,41468],{"encoding":904},[198,44260,44262,44263],{"id":44261},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,44264,44266],{"className":44265},[886],[888,44267,44268],{"xmlns":890},[892,44269,44270,44278],{},[895,44271,44272],{},[2124,44273,44274,44276],{},[898,44275,2789],{},[898,44277,4252],{},[902,44279,42405],{"encoding":904},[724,44281,44282,41657,44284,41692,44310,1975],{},[38,44283,37935],{},[883,44285,44287],{"className":44286},[886],[888,44288,44289],{"xmlns":890},[892,44290,44291,44307],{},[895,44292,44293,44295,44297,44299,44301,44303,44305],{},[898,44294,3937],{},[1996,44296,1998],{},[1996,44298,2225],{},[2129,44300,2173],{},[898,44302,2789],{},[1996,44304,2095],{},[2129,44306,5211],{},[902,44308,44309],{"encoding":904},"P = -3Q + 40",[883,44311,44313],{"className":44312},[886],[888,44314,44315],{"xmlns":890},[892,44316,44317,44331],{},[895,44318,44319,44321,44323,44325,44327,44329],{},[898,44320,3937],{},[1996,44322,1998],{},[2129,44324,5009],{},[898,44326,2789],{},[1996,44328,2095],{},[2129,44330,2863],{},[902,44332,44333],{"encoding":904},"P = 0{,}5Q + 10",[724,44335,44336,44338],{},[38,44337,37967],{}," Rovnovážné množství",[883,44340,44342],{"className":44341},[886],[888,44343,44344],{"xmlns":890,"display":28068},[892,44345,44346,44414],{},[895,44347,44348,44354,44356,44374,44376,44400,44402,44409,44411],{},[2124,44349,44350,44352],{},[898,44351,2789],{},[898,44353,4252],{},[1996,44355,1998],{},[2329,44357,44358,44366],{},[895,44359,44360,44362,44364],{},[898,44361,2098],{},[1996,44363,2225],{},[898,44365,2194],{},[895,44367,44368,44370,44372],{},[898,44369,2142],{},[1996,44371,2225],{},[898,44373,207],{},[1996,44375,1998],{},[2329,44377,44378,44386],{},[895,44379,44380,44382,44384],{},[2129,44381,5211],{},[1996,44383,2225],{},[2129,44385,2863],{},[895,44387,44388,44390,44392,44394,44396,44398],{},[2129,44389,5009],{},[1996,44391,2225],{},[1996,44393,2005],{"stretchy":2004},[1996,44395,2225],{},[2129,44397,2173],{},[1996,44399,2011],{"stretchy":2004},[1996,44401,1998],{},[2329,44403,44404,44406],{},[2129,44405,38021],{},[2129,44407,44408],{},"3,5",[1996,44410,2730],{},[2129,44412,44413],{},"8,571.",[902,44415,44416],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,44418,44419,44464],{},[38,44420,44421,44422,2671,44435,2685,44449,44463],{},"(a) Změna ",[883,44423,44425],{"className":44424},[886],[888,44426,44427],{"xmlns":890},[892,44428,44429,44433],{},[895,44430,44431],{},[898,44432,2142],{},[902,44434,2142],{"encoding":904},[883,44436,44438],{"className":44437},[886],[888,44439,44440],{"xmlns":890},[892,44441,44442,44446],{},[895,44443,44444],{},[2129,44445,5009],{},[902,44447,44448],{"encoding":904},"0{,}5",[883,44450,44452],{"className":44451},[886],[888,44453,44454],{"xmlns":890},[892,44455,44456,44460],{},[895,44457,44458],{},[2129,44459,19323],{},[902,44461,44462],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,44466,44468],{"className":44467},[886],[888,44469,44470],{"xmlns":890,"display":28068},[892,44471,44472,44549],{},[895,44473,44474,44482,44484,44486,44488,44490,44492,44518,44520,44522,44524,44526,44528,44538,44540,44542,44544,44546],{},[9166,44475,44476,44478,44480],{},[898,44477,2789],{},[898,44479,2142],{},[1996,44481,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[2288,44483,2987],{},[898,44485,2194],{},[898,44487,2142],{},[1996,44489,1998],{},[1996,44491,2225],{},[2329,44493,44494,44502],{},[895,44495,44496,44498,44500],{},[898,44497,2098],{},[1996,44499,2225],{},[898,44501,2194],{},[895,44503,44504,44506,44508,44510,44512],{},[1996,44505,2005],{"stretchy":2004},[898,44507,2142],{},[1996,44509,2225],{},[898,44511,207],{},[2124,44513,44514,44516],{},[1996,44515,2011],{"stretchy":2004},[2129,44517,2131],{},[2288,44519,2987],{},[898,44521,2194],{},[898,44523,2142],{},[1996,44525,1998],{},[1996,44527,2225],{},[2329,44529,44530,44532],{},[2129,44531,38021],{},[2124,44533,44534,44536],{},[2129,44535,44408],{},[2129,44537,2131],{},[1996,44539,3177],{},[2129,44541,2794],{},[1996,44543,2730],{},[1996,44545,2225],{},[2129,44547,44548],{},"0,245.",[902,44550,44551],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,44553,44554,44555,1975],{},"Nové rovnovážné množství ",[883,44556,44558],{"className":44557},[886],[888,44559,44560],{"xmlns":890},[892,44561,44562,44587],{},[895,44563,44564,44572,44574,44577,44579,44582,44584],{},[9166,44565,44566,44568,44570],{},[898,44567,2789],{},[2129,44569,2278],{},[898,44571,4252],{},[1996,44573,2730],{},[2129,44575,44576],{},"8,571",[1996,44578,2225],{},[2129,44580,44581],{},"0,245",[1996,44583,1998],{},[2129,44585,44586],{},"8,326",[902,44588,44589],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,44591,44592,44677],{},[38,44593,44594,44595,1343,44615,1343,44637,1343,44657,1975],{},"(b) Současné změny ",[883,44596,44598],{"className":44597},[886],[888,44599,44600],{"xmlns":890},[892,44601,44602,44612],{},[895,44603,44604,44606,44608,44610],{},[898,44605,2194],{},[898,44607,207],{},[1996,44609,1998],{},[2129,44611,5009],{},[902,44613,44614],{"encoding":904},"da = 0{,}5",[883,44616,44618],{"className":44617},[886],[888,44619,44620],{"xmlns":890},[892,44621,44622,44634],{},[895,44623,44624,44626,44628,44630,44632],{},[898,44625,2194],{},[898,44627,2098],{},[1996,44629,1998],{},[1996,44631,2225],{},[2129,44633,2228],{},[902,44635,44636],{"encoding":904},"db = -5",[883,44638,44640],{"className":44639},[886],[888,44641,44642],{"xmlns":890},[892,44643,44644,44654],{},[895,44645,44646,44648,44650,44652],{},[898,44647,2194],{},[898,44649,2142],{},[1996,44651,1998],{},[2129,44653,2794],{},[902,44655,44656],{"encoding":904},"dc = 0{,}1",[883,44658,44660],{"className":44659},[886],[888,44661,44662],{"xmlns":890},[892,44663,44664,44674],{},[895,44665,44666,44668,44670,44672],{},[898,44667,2194],{},[898,44669,2194],{},[1996,44671,1998],{},[2129,44673,2278],{},[902,44675,44676],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,44679,44681],{"className":44680},[886],[888,44682,44683],{"xmlns":890,"display":28068},[892,44684,44685,44828],{},[20756,44686,44687,44769,44805],{"rowspacing":20758,"columnalign":20759,"columnspacing":2377},[20761,44688,44689,44699],{},[20764,44690,44691],{},[2325,44692,44693],{"scriptlevel":2327,"displaystyle":2285},[895,44694,44695,44697],{},[898,44696,2889],{"mathvariant":2376},[898,44698,2789],{},[20764,44700,44701],{},[2325,44702,44703],{"scriptlevel":2327,"displaystyle":2285},[895,44704,44705,44707,44709,44719,44721,44723,44725,44731,44733,44735,44737,44739,44741,44743,44753,44755,44757,44759,44765,44767],{},[895,44706],{},[1996,44708,2730],{},[2329,44710,44711,44713],{},[2129,44712,38021],{},[2124,44714,44715,44717],{},[2129,44716,44408],{},[2129,44718,2131],{},[1996,44720,3177],{},[2129,44722,5009],{},[1996,44724,2095],{},[2329,44726,44727,44729],{},[2129,44728,2278],{},[2129,44730,44408],{},[1996,44732,3177],{},[1996,44734,2005],{"stretchy":2004},[1996,44736,2225],{},[2129,44738,2228],{},[1996,44740,2011],{"stretchy":2004},[1996,44742,2225],{},[2329,44744,44745,44747],{},[2129,44746,38021],{},[2124,44748,44749,44751],{},[2129,44750,44408],{},[2129,44752,2131],{},[1996,44754,3177],{},[2129,44756,2794],{},[1996,44758,2225],{},[2329,44760,44761,44763],{},[2129,44762,2278],{},[2129,44764,44408],{},[1996,44766,3177],{},[2129,44768,2278],{},[20761,44770,44771,44777],{},[20764,44772,44773],{},[2325,44774,44775],{"scriptlevel":2327,"displaystyle":2285},[895,44776],{},[20764,44778,44779],{},[2325,44780,44781],{"scriptlevel":2327,"displaystyle":2285},[895,44782,44783,44785,44787,44790,44792,44795,44797,44800,44802],{},[895,44784],{},[1996,44786,1998],{},[2129,44788,44789],{},"1,2245",[1996,44791,2225],{},[2129,44793,44794],{},"1,4286",[1996,44796,2225],{},[2129,44798,44799],{},"0,2449",[1996,44801,2225],{},[2129,44803,44804],{},"0,2857",[20761,44806,44807,44813],{},[20764,44808,44809],{},[2325,44810,44811],{"scriptlevel":2327,"displaystyle":2285},[895,44812],{},[20764,44814,44815],{},[2325,44816,44817],{"scriptlevel":2327,"displaystyle":2285},[895,44818,44819,44821,44823,44825],{},[895,44820],{},[1996,44822,2730],{},[1996,44824,2225],{},[2129,44826,44827],{},"0,735.",[902,44829,44830],{"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}",[724,44832,30067,44833,1975],{},[883,44834,44836],{"className":44835},[886],[888,44837,44838],{"xmlns":890},[892,44839,44840,44864],{},[895,44841,44842,44850,44852,44854,44856,44859,44861],{},[9166,44843,44844,44846,44848],{},[898,44845,2789],{},[2129,44847,2278],{},[898,44849,4252],{},[1996,44851,2730],{},[2129,44853,44576],{},[1996,44855,2225],{},[2129,44857,44858],{},"0,735",[1996,44860,1998],{},[2129,44862,44863],{},"7,836",[902,44865,44866],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[3867,44868,44869],{},[724,44870,44871,44873,44874,44897,44898,44920],{},[883,44872,4412],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,44875,44877],{"className":44876},[886],[888,44878,44879],{"xmlns":890},[892,44880,44881,44894],{},[895,44882,44883,44885,44887,44889,44891],{},[898,44884,2889],{"mathvariant":2376},[898,44886,2789],{},[1996,44888,2730],{},[1996,44890,2225],{},[2129,44892,44893],{},"2,69",[902,44895,44896],{"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 ",[883,44899,44901],{"className":44900},[886],[888,44902,44903],{"xmlns":890},[892,44904,44905,44917],{},[895,44906,44907,44909,44911,44913,44915],{},[898,44908,2889],{"mathvariant":2376},[898,44910,2789],{},[1996,44912,2730],{},[1996,44914,2225],{},[2129,44916,44858],{},[902,44918,44919],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,44922,44923],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[36972,44925],{},[115,44927,820],{"id":11785},[3867,44929,44930],{},[724,44931,44932,3874,44934,10025,44937,12130,44953,10025,44956,44972,44973,1975],{},[883,44933,4155],{},[38,44935,44936],{},"Přebytek spotřebitele",[883,44938,44940],{"className":44939},[886],[888,44941,44942],{"xmlns":890},[892,44943,44944,44950],{},[895,44945,44946,44948],{},[898,44947,2777],{},[898,44949,8673],{},[902,44951,44952],{"encoding":904},"CS",[38,44954,44955],{},"přebytek výrobce",[883,44957,44959],{"className":44958},[886],[888,44960,44961],{"xmlns":890},[892,44962,44963,44969],{},[895,44964,44965,44967],{},[898,44966,3937],{},[898,44968,8673],{},[902,44970,44971],{"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 ",[207,44974,44976],{"className":44975,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,44978,44979],{},[2559,44980],{"alt":44981,"className":44982,"src":44983},"imek-prebytky-cs-ps",[210,2563],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,44985,44986,10025,44988,44991],{},[38,44987,44936],{},[614,44989,44990],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,44993,44995],{"className":44994},[886],[888,44996,44997],{"xmlns":890,"display":28068},[892,44998,44999,45076],{},[20756,45000,45001],{"width":28073},[20761,45002,45003,45005,45069,45071],{},[20764,45004],{"width":28078},[20764,45006,45007],{},[895,45008,45009,45011,45013,45015,45021,45023,45025,45037,45039,45041,45043,45045,45047,45049,45051,45053,45059,45061,45067],{},[898,45010,2777],{},[898,45012,8673],{},[1996,45014,2005],{"stretchy":2004},[2272,45016,45017,45019],{},[898,45018,2789],{},[2129,45020,2327],{},[1996,45022,2011],{"stretchy":2004},[1996,45024,1998],{},[9166,45026,45027,45029,45031],{},[1996,45028,11170],{},[2129,45030,2327],{},[2272,45032,45033,45035],{},[898,45034,2789],{},[2129,45036,2327],{},[898,45038,4183],{},[1996,45040,2005],{"stretchy":2004},[898,45042,2789],{},[1996,45044,2011],{"stretchy":2004},[2288,45046,2987],{},[898,45048,2194],{},[898,45050,2789],{},[1996,45052,2225],{},[2272,45054,45055,45057],{},[898,45056,3937],{},[2129,45058,2327],{},[2288,45060,2987],{},[2272,45062,45063,45065],{},[898,45064,2789],{},[2129,45066,2327],{},[898,45068,1975],{"mathvariant":2376},[20764,45070],{"width":28078},[20764,45072,45073],{},[2288,45074,45075],{},"(2.14)",[902,45077,45078],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,45080,45081,10025,45084,45087],{},[38,45082,45083],{},"Přebytek výrobce",[614,45085,45086],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,45089,45091],{"className":45090},[886],[888,45092,45093],{"xmlns":890,"display":28068},[892,45094,45095,45172],{},[20756,45096,45097],{"width":28073},[20761,45098,45099,45101,45165,45167],{},[20764,45100],{"width":28078},[20764,45102,45103],{},[895,45104,45105,45107,45109,45111,45117,45119,45121,45127,45129,45135,45137,45149,45151,45153,45155,45157,45159,45161,45163],{},[898,45106,3937],{},[898,45108,8673],{},[1996,45110,2005],{"stretchy":2004},[2272,45112,45113,45115],{},[898,45114,2789],{},[2129,45116,2327],{},[1996,45118,2011],{"stretchy":2004},[1996,45120,1998],{},[2272,45122,45123,45125],{},[898,45124,3937],{},[2129,45126,2327],{},[2288,45128,2987],{},[2272,45130,45131,45133],{},[898,45132,2789],{},[2129,45134,2327],{},[1996,45136,2225],{},[9166,45138,45139,45141,45143],{},[1996,45140,11170],{},[2129,45142,2327],{},[2272,45144,45145,45147],{},[898,45146,2789],{},[2129,45148,2327],{},[898,45150,8673],{},[1996,45152,2005],{"stretchy":2004},[898,45154,2789],{},[1996,45156,2011],{"stretchy":2004},[2288,45158,2987],{},[898,45160,2194],{},[898,45162,2789],{},[898,45164,1975],{"mathvariant":2376},[20764,45166],{"width":28078},[20764,45168,45169],{},[2288,45170,45171],{},"(2.15)",[902,45173,45174],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,45176,45177,45178,1975],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,45179,45181],{"className":45180,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[36972,45183],{},[115,45185,45187],{"id":45186},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,45189,45190,45221,45226,45232,45260,45266,45295,45301,45381,45407],{},[123,45191,45192,45194,45195,45220],{},[38,45193,37930],{}," — lineární poptávka ",[883,45196,45198],{"className":45197},[886],[888,45199,45200],{"xmlns":890},[892,45201,45202,45218],{},[895,45203,45204,45206,45208,45210,45212,45214,45216],{},[898,45205,3937],{},[1996,45207,1998],{},[1996,45209,2225],{},[2129,45211,2131],{},[898,45213,2789],{},[1996,45215,2095],{},[2129,45217,3126],{},[902,45219,37962],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,45222,45223,45225],{},[38,45224,38244],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,45227,45228,45231],{},[38,45229,45230],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,45233,45234,45236,45237,1975],{},[38,45235,40791],{}," — lineární nabídka ",[883,45238,45240],{"className":45239},[886],[888,45241,45242],{"xmlns":890},[892,45243,45244,45258],{},[895,45245,45246,45248,45250,45252,45254,45256],{},[898,45247,3937],{},[1996,45249,1998],{},[2129,45251,5009],{},[898,45253,2789],{},[1996,45255,2095],{},[2129,45257,5004],{},[902,45259,40820],{"encoding":904},[123,45261,45262,45265],{},[38,45263,45264],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,45267,45268,45271,45272,1975],{},[38,45269,45270],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,45273,45275],{"className":45274},[886],[888,45276,45277],{"xmlns":890},[892,45278,45279,45293],{},[895,45280,45281,45283,45285,45287,45289,45291],{},[898,45282,4252],{},[1996,45284,2486],{"stretchy":2004},[2129,45286,2351],{},[1996,45288,2286],{"separator":2285},[2129,45290,41938],{},[1996,45292,2501],{"stretchy":2004},[902,45294,41966],{"encoding":904},[123,45296,45297,45300],{},[38,45298,45299],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,45302,45303,45306,45307,45324,45325,1343,45350,45377,45378,2951],{},[38,45304,45305],{},"Příklad 2.9"," — daň ",[883,45308,45310],{"className":45309},[886],[888,45311,45312],{"xmlns":890},[892,45313,45314,45322],{},[895,45315,45316,45318,45320],{},[898,45317,2774],{},[1996,45319,1998],{},[2129,45321,2235],{},[902,45323,41270],{"encoding":904}," na výrobce; rozklad ",[883,45326,45328],{"className":45327},[886],[888,45329,45330],{"xmlns":890},[892,45331,45332,45348],{},[895,45333,45334,45344,45346],{},[2272,45335,45336,45338],{},[898,45337,2774],{},[895,45339,45340,45342],{},[898,45341,42679],{},[898,45343,724],{},[1996,45345,1998],{},[2129,45347,2131],{},[902,45349,42978],{"encoding":904},[883,45351,45353],{"className":45352},[886],[888,45354,45355],{"xmlns":890},[892,45356,45357,45375],{},[895,45358,45359,45371,45373],{},[2272,45360,45361,45363],{},[898,45362,2774],{},[895,45364,45365,45367,45369],{},[898,45366,42702],{},[898,45368,1994],{},[898,45370,12043],{},[1996,45372,1998],{},[2129,45374,2351],{},[902,45376,43007],{"encoding":904},". (Viz ",[207,45379,42723],{"className":45380,"dataFsResolvedFilePath":809,"href":810},[210],[123,45382,45383,45306,45386,45403,45404,2951],{},[38,45384,45385],{},"Příklad 2.10",[883,45387,45389],{"className":45388},[886],[888,45390,45391],{"xmlns":890},[892,45392,45393,45401],{},[895,45394,45395,45397,45399],{},[898,45396,2774],{},[1996,45398,1998],{},[2129,45400,2235],{},[902,45402,41270],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,45405,42723],{"className":45406,"dataFsResolvedFilePath":809,"href":810},[210],[123,45408,45409,45412],{},[38,45410,45411],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[36972,45414],{},[115,45416,45418],{"id":45417},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,45420,45422],{"id":45421},"základní-analýza-poptávky","Základní analýza poptávky",[724,45424,45425,45428,45429,45464,45465,45491],{},[38,45426,45427],{},"2.1"," Je dána poptávka ",[883,45430,45432],{"className":45431},[886],[888,45433,45434],{"xmlns":890},[892,45435,45436,45461],{},[895,45437,45438,45440,45442,45444,45446,45448,45450,45452,45455,45457,45459],{},[898,45439,2789],{},[1996,45441,1998],{},[898,45443,4183],{},[1996,45445,2005],{"stretchy":2004},[898,45447,3937],{},[1996,45449,2011],{"stretchy":2004},[1996,45451,1998],{},[2129,45453,45454],{},"75",[1996,45456,2225],{},[2129,45458,2228],{},[898,45460,3937],{},[902,45462,45463],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,45466,45468],{"className":45467},[886],[888,45469,45470],{"xmlns":890},[892,45471,45472,45488],{},[895,45473,45474,45476,45478,45480,45482,45484,45486],{},[2129,45475,2327],{},[1996,45477,2286],{"separator":2285},[2129,45479,2228],{},[1996,45481,2286],{"separator":2285},[2129,45483,2863],{},[1996,45485,2286],{"separator":2285},[2129,45487,36246],{},[902,45489,45490],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,45493,45494,45497,45498,45516,45517,3151],{},[38,45495,45496],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,45499,45501],{"className":45500},[886],[888,45502,45503],{"xmlns":890},[892,45504,45505,45513],{},[895,45506,45507,45509,45511],{},[898,45508,3937],{},[1996,45510,2286],{"separator":2285},[898,45512,2789],{},[902,45514,45515],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,45518,45520],{"className":45519},[886],[888,45521,45522],{"xmlns":890},[892,45523,45524,45540],{},[895,45525,45526,45528,45530,45532,45534,45536,45538],{},[898,45527,207],{},[1996,45529,2286],{"separator":2285},[898,45531,2098],{},[1996,45533,2286],{"separator":2285},[898,45535,2142],{},[1996,45537,3408],{},[2129,45539,2327],{},[902,45541,45542],{"encoding":904},"a, b, c > 0",[120,45544,45545,45578,45609,45644,45675,45710],{},[123,45546,45547,45548],{},"(a) ",[883,45549,45551],{"className":45550},[886],[888,45552,45553],{"xmlns":890},[892,45554,45555,45575],{},[895,45556,45557,45559,45561],{},[898,45558,2789],{},[1996,45560,1998],{},[2325,45562,45563],{"scriptlevel":2327,"displaystyle":2285},[2329,45564,45565,45567],{},[898,45566,207],{},[895,45568,45569,45571,45573],{},[898,45570,3937],{},[1996,45572,2095],{},[898,45574,2142],{},[902,45576,45577],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,45579,45580,45581],{},"(b) ",[883,45582,45584],{"className":45583},[886],[888,45585,45586],{"xmlns":890},[892,45587,45588,45606],{},[895,45589,45590,45592,45594],{},[898,45591,2789],{},[1996,45593,1998],{},[8117,45595,45596],{},[895,45597,45598,45600,45602,45604],{},[898,45599,207],{},[1996,45601,2225],{},[898,45603,2098],{},[898,45605,2789],{},[902,45607,45608],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,45610,45611,45612],{},"(c) ",[883,45613,45615],{"className":45614},[886],[888,45616,45617],{"xmlns":890},[892,45618,45619,45641],{},[895,45620,45621,45623,45625],{},[898,45622,2789],{},[1996,45624,1998],{},[2325,45626,45627],{"scriptlevel":2327,"displaystyle":2285},[2329,45628,45629,45639],{},[895,45630,45631,45633,45635],{},[898,45632,207],{},[1996,45634,2225],{},[8117,45636,45637],{},[898,45638,3937],{},[898,45640,2098],{},[902,45642,45643],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,45645,45646,45647],{},"(d) ",[883,45648,45650],{"className":45649},[886],[888,45651,45652],{"xmlns":890},[892,45653,45654,45672],{},[895,45655,45656,45658,45660,45662,45664,45666],{},[898,45657,3937],{},[1996,45659,1998],{},[898,45661,207],{},[1996,45663,2225],{},[898,45665,2098],{},[2124,45667,45668,45670],{},[898,45669,2789],{},[2129,45671,2131],{},[902,45673,45674],{"encoding":904},"P = a - bQ^2",[123,45676,45677,45678],{},"(e) ",[883,45679,45681],{"className":45680},[886],[888,45682,45683],{"xmlns":890},[892,45684,45685,45707],{},[895,45686,45687,45689,45691,45693,45703,45705],{},[898,45688,2789],{},[1996,45690,1998],{},[898,45692,2098],{},[2124,45694,45695,45697],{},[898,45696,3937],{},[895,45698,45699,45701],{},[1996,45700,2225],{},[898,45702,207],{},[1996,45704,2095],{},[898,45706,2142],{},[902,45708,45709],{"encoding":904},"Q = bP^{-a} + c",[123,45711,45712,45713],{},"(f) ",[883,45714,45716],{"className":45715},[886],[888,45717,45718],{"xmlns":890},[892,45719,45720,45743],{},[895,45721,45722,45724,45726,45728,45730],{},[898,45723,2789],{},[1996,45725,1998],{},[898,45727,207],{},[1996,45729,3177],{},[2124,45731,45732,45735],{},[898,45733,45734],{},"e",[895,45736,45737,45739,45741],{},[1996,45738,2225],{},[898,45740,2098],{},[898,45742,3937],{},[902,45744,45745],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,45747,45748,45751],{},[38,45749,45750],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,45753,45754,45757,45760],{},[123,45755,45756],{},"(a) Cena substitutu.",[123,45758,45759],{},"(b) Cena komplementu.",[123,45761,45762],{},"(c) Výdaje na reklamu.",[724,45764,45765,45428,45767,45801,45802,45830],{},[38,45766,24644],{},[883,45768,45770],{"className":45769},[886],[888,45771,45772],{"xmlns":890},[892,45773,45774,45798],{},[895,45775,45776,45778,45780,45782,45784,45786,45788,45790,45792,45794,45796],{},[898,45777,3937],{},[1996,45779,1998],{},[898,45781,4183],{},[1996,45783,2005],{"stretchy":2004},[898,45785,2789],{},[1996,45787,2011],{"stretchy":2004},[1996,45789,1998],{},[2129,45791,3509],{},[1996,45793,2225],{},[2129,45795,2131],{},[898,45797,2789],{},[902,45799,45800],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,45803,45805],{"className":45804},[886],[888,45806,45807],{"xmlns":890},[892,45808,45809,45827],{},[895,45810,45811,45813,45815,45821,45823,45825],{},[898,45812,3937],{},[1996,45814,1998],{},[2124,45816,45817,45819],{},[898,45818,4183],{},[1996,45820,4354],{},[1996,45822,2005],{"stretchy":2004},[898,45824,2789],{},[1996,45826,2011],{"stretchy":2004},[902,45828,45829],{"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.",[724,45832,45833,45836],{},[38,45834,45835],{},"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:",[120,45838,45839,45923,45999,46085,46173],{},[123,45840,45547,45841,1343,45881,1975],{},[883,45842,45844],{"className":45843},[886],[888,45845,45846],{"xmlns":890},[892,45847,45848,45878],{},[895,45849,45850,45856,45858,45860,45862,45864,45870,45872],{},[2272,45851,45852,45854],{},[898,45853,23255],{},[2129,45855,2278],{},[1996,45857,1998],{},[2129,45859,9035],{},[1996,45861,2225],{},[2129,45863,2351],{},[2272,45865,45866,45868],{},[898,45867,4255],{},[2129,45869,2278],{},[1996,45871,2095],{},[2272,45873,45874,45876],{},[898,45875,4255],{},[2129,45877,2131],{},[902,45879,45880],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,45882,45884],{"className":45883},[886],[888,45885,45886],{"xmlns":890},[892,45887,45888,45920],{},[895,45889,45890,45896,45898,45900,45902,45904,45910,45912,45914],{},[2272,45891,45892,45894],{},[898,45893,23255],{},[2129,45895,2131],{},[1996,45897,1998],{},[2129,45899,2863],{},[1996,45901,2095],{},[2129,45903,2131],{},[2272,45905,45906,45908],{},[898,45907,4255],{},[2129,45909,2278],{},[1996,45911,2225],{},[2129,45913,2351],{},[2272,45915,45916,45918],{},[898,45917,4255],{},[2129,45919,2131],{},[902,45921,45922],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,45924,45580,45925,1343,45967,1975],{},[883,45926,45928],{"className":45927},[886],[888,45929,45930],{"xmlns":890},[892,45931,45932,45964],{},[895,45933,45934,45940,45942,45944,45946,45948,45954,45956,45958],{},[2272,45935,45936,45938],{},[898,45937,23255],{},[2129,45939,2278],{},[1996,45941,1998],{},[2129,45943,3120],{},[1996,45945,2225],{},[2129,45947,2863],{},[2272,45949,45950,45952],{},[898,45951,4255],{},[2129,45953,2278],{},[1996,45955,2225],{},[2129,45957,2235],{},[2272,45959,45960,45962],{},[898,45961,4255],{},[2129,45963,2131],{},[902,45965,45966],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,45968,45970],{"className":45969},[886],[888,45971,45972],{"xmlns":890},[892,45973,45974,45996],{},[895,45975,45976,45982,45984,45986,45988,45990],{},[2272,45977,45978,45980],{},[898,45979,23255],{},[2129,45981,2131],{},[1996,45983,1998],{},[2129,45985,36246],{},[1996,45987,2225],{},[2129,45989,2863],{},[2272,45991,45992,45994],{},[898,45993,4255],{},[2129,45995,2131],{},[902,45997,45998],{"encoding":904},"B_2 = 15 - 10A_2",[123,46000,45611,46001,1343,46043,1975],{},[883,46002,46004],{"className":46003},[886],[888,46005,46006],{"xmlns":890},[892,46007,46008,46040],{},[895,46009,46010,46016,46018,46020,46022,46024,46030,46032,46034],{},[2272,46011,46012,46014],{},[898,46013,23255],{},[2129,46015,2278],{},[1996,46017,1998],{},[2129,46019,38021],{},[1996,46021,2225],{},[2129,46023,2131],{},[2272,46025,46026,46028],{},[898,46027,4255],{},[2129,46029,2278],{},[1996,46031,2225],{},[2129,46033,2351],{},[2272,46035,46036,46038],{},[898,46037,4255],{},[2129,46039,2131],{},[902,46041,46042],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,46044,46046],{"className":46045},[886],[888,46047,46048],{"xmlns":890},[892,46049,46050,46082],{},[895,46051,46052,46058,46060,46062,46064,46066,46072,46074,46076],{},[2272,46053,46054,46056],{},[898,46055,23255],{},[2129,46057,2131],{},[1996,46059,1998],{},[2129,46061,36246],{},[1996,46063,2095],{},[2129,46065,2131],{},[2272,46067,46068,46070],{},[898,46069,4255],{},[2129,46071,2278],{},[1996,46073,2225],{},[2129,46075,2131],{},[2272,46077,46078,46080],{},[898,46079,4255],{},[2129,46081,2131],{},[902,46083,46084],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,46086,45646,46087,1343,46131,1975],{},[883,46088,46090],{"className":46089},[886],[888,46091,46092],{"xmlns":890},[892,46093,46094,46128],{},[895,46095,46096,46102,46104,46106,46108,46110,46112,46118,46120,46122],{},[2272,46097,46098,46100],{},[898,46099,23255],{},[2129,46101,2278],{},[1996,46103,1998],{},[1996,46105,2225],{},[2129,46107,9035],{},[1996,46109,2225],{},[2129,46111,2131],{},[2272,46113,46114,46116],{},[898,46115,4255],{},[2129,46117,2278],{},[1996,46119,2095],{},[2129,46121,2173],{},[2272,46123,46124,46126],{},[898,46125,4255],{},[2129,46127,2131],{},[902,46129,46130],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,46132,46134],{"className":46133},[886],[888,46135,46136],{"xmlns":890},[892,46137,46138,46170],{},[895,46139,46140,46146,46148,46150,46152,46154,46160,46162,46164],{},[2272,46141,46142,46144],{},[898,46143,23255],{},[2129,46145,2131],{},[1996,46147,1998],{},[2129,46149,2863],{},[1996,46151,2095],{},[2129,46153,2131],{},[2272,46155,46156,46158],{},[898,46157,4255],{},[2129,46159,2278],{},[1996,46161,2225],{},[2129,46163,2131],{},[2272,46165,46166,46168],{},[898,46167,4255],{},[2129,46169,2131],{},[902,46171,46172],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,46174,45677,46175,1343,46217,1975],{},[883,46176,46178],{"className":46177},[886],[888,46179,46180],{"xmlns":890},[892,46181,46182,46214],{},[895,46183,46184,46190,46192,46194,46196,46198,46204,46206,46208],{},[2272,46185,46186,46188],{},[898,46187,23255],{},[2129,46189,2278],{},[1996,46191,1998],{},[2129,46193,9035],{},[1996,46195,2095],{},[2129,46197,2131],{},[2272,46199,46200,46202],{},[898,46201,4255],{},[2129,46203,2278],{},[1996,46205,2095],{},[2129,46207,2351],{},[2272,46209,46210,46212],{},[898,46211,4255],{},[2129,46213,2131],{},[902,46215,46216],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,46218,46220],{"className":46219},[886],[888,46221,46222],{"xmlns":890},[892,46223,46224,46256],{},[895,46225,46226,46232,46234,46236,46238,46240,46246,46248,46250],{},[2272,46227,46228,46230],{},[898,46229,23255],{},[2129,46231,2131],{},[1996,46233,1998],{},[2129,46235,5211],{},[1996,46237,2225],{},[2129,46239,2173],{},[2272,46241,46242,46244],{},[898,46243,4255],{},[2129,46245,2278],{},[1996,46247,2095],{},[2129,46249,2228],{},[2272,46251,46252,46254],{},[898,46253,4255],{},[2129,46255,2131],{},[902,46257,46258],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,46260,46262],{"id":46261},"základní-analýza-nabídky","Základní analýza nabídky",[724,46264,46265,46268,46269,46303,46304,46326],{},[38,46266,46267],{},"2.6"," Je dána nabídka ",[883,46270,46272],{"className":46271},[886],[888,46273,46274],{"xmlns":890},[892,46275,46276,46300],{},[895,46277,46278,46280,46282,46284,46286,46288,46290,46292,46294,46296,46298],{},[898,46279,3937],{},[1996,46281,1998],{},[898,46283,8673],{},[1996,46285,2005],{"stretchy":2004},[898,46287,2789],{},[1996,46289,2011],{"stretchy":2004},[1996,46291,1998],{},[2129,46293,9035],{},[1996,46295,2095],{},[2129,46297,2839],{},[898,46299,2789],{},[902,46301,46302],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,46305,46307],{"className":46306},[886],[888,46308,46309],{"xmlns":890},[892,46310,46311,46323],{},[895,46312,46313,46315,46317,46319,46321],{},[2129,46314,5004],{},[1996,46316,2286],{"separator":2285},[2129,46318,38021],{},[1996,46320,2286],{"separator":2285},[2129,46322,15040],{},[902,46324,46325],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,46328,46329,46332,46333,46350],{},[38,46330,46331],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,46334,46336],{"className":46335},[886],[888,46337,46338],{"xmlns":890},[892,46339,46340,46348],{},[895,46341,46342,46344,46346],{},[898,46343,3937],{},[1996,46345,2286],{"separator":2285},[898,46347,2789],{},[902,46349,45515],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,46352,46353,46379,46407,46440,46474,46510],{},[123,46354,45547,46355],{},[883,46356,46358],{"className":46357},[886],[888,46359,46360],{"xmlns":890},[892,46361,46362,46376],{},[895,46363,46364,46366,46368,46370,46372,46374],{},[898,46365,3937],{},[1996,46367,1998],{},[2129,46369,38021],{},[1996,46371,2095],{},[2129,46373,2131],{},[898,46375,2789],{},[902,46377,46378],{"encoding":904},"P = 30 + 2Q",[123,46380,45580,46381],{},[883,46382,46384],{"className":46383},[886],[888,46385,46386],{"xmlns":890},[892,46387,46388,46404],{},[895,46389,46390,46392,46394,46396,46398,46400,46402],{},[898,46391,2789],{},[1996,46393,1998],{},[1996,46395,2225],{},[2129,46397,2173],{},[1996,46399,2095],{},[2129,46401,3509],{},[898,46403,3937],{},[902,46405,46406],{"encoding":904},"Q = -3 + 12P",[123,46408,45611,46409],{},[883,46410,46412],{"className":46411},[886],[888,46413,46414],{"xmlns":890},[892,46415,46416,46438],{},[895,46417,46418,46420,46422,46428,46430,46432,46434,46436],{},[898,46419,3937],{},[1996,46421,1998],{},[2124,46423,46424,46426],{},[898,46425,2789],{},[2129,46427,2131],{},[1996,46429,2095],{},[2129,46431,22948],{},[898,46433,2789],{},[1996,46435,2095],{},[2129,46437,32548],{},[902,46439,41724],{"encoding":904},[123,46441,45646,46442],{},[883,46443,46445],{"className":46444},[886],[888,46446,46447],{"xmlns":890},[892,46448,46449,46471],{},[895,46450,46451,46453,46455,46461,46463,46465,46467,46469],{},[898,46452,3937],{},[1996,46454,1998],{},[2124,46456,46457,46459],{},[898,46458,2789],{},[2129,46460,2131],{},[1996,46462,2095],{},[2129,46464,2131],{},[898,46466,2789],{},[1996,46468,2095],{},[2129,46470,3509],{},[902,46472,46473],{"encoding":904},"P = Q^2 + 2Q + 12",[123,46475,45677,46476],{},[883,46477,46479],{"className":46478},[886],[888,46480,46481],{"xmlns":890},[892,46482,46483,46507],{},[895,46484,46485,46487,46489,46491,46493,46495,46497,46499,46501],{},[898,46486,2789],{},[1996,46488,1998],{},[2129,46490,8803],{},[1996,46492,2095],{},[2129,46494,2228],{},[898,46496,3937],{},[1996,46498,2095],{},[2129,46500,2794],{},[2124,46502,46503,46505],{},[898,46504,3937],{},[2129,46506,2131],{},[902,46508,46509],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,46511,45712,46512],{},[883,46513,46515],{"className":46514},[886],[888,46516,46517],{"xmlns":890},[892,46518,46519,46544],{},[895,46520,46521,46523,46525,46527,46529,46531,46533,46535,46538],{},[898,46522,2789],{},[1996,46524,1998],{},[2129,46526,24203],{},[1996,46528,2095],{},[2129,46530,2794],{},[898,46532,3937],{},[1996,46534,2095],{},[2129,46536,46537],{},"0,004",[2124,46539,46540,46542],{},[898,46541,3937],{},[2129,46543,2131],{},[902,46545,46546],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,46548,46549,46552],{},[38,46550,46551],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,46554,46555,46558,46561,46564],{},[123,46556,46557],{},"(a) Sníží ceny surovin — vstupů.",[123,46559,46560],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,46562,46563],{},"(c) Zvýší ceny všech energií.",[123,46565,46566],{},"(d) Sníží daňové odvody státu.",[724,46568,46569,46268,46571,46605,46606,46634],{},[38,46570,42951],{},[883,46572,46574],{"className":46573},[886],[888,46575,46576],{"xmlns":890},[892,46577,46578,46602],{},[895,46579,46580,46582,46584,46586,46588,46590,46592,46594,46596,46598,46600],{},[898,46581,3937],{},[1996,46583,1998],{},[898,46585,8673],{},[1996,46587,2005],{"stretchy":2004},[898,46589,2789],{},[1996,46591,2011],{"stretchy":2004},[1996,46593,1998],{},[2129,46595,5009],{},[898,46597,2789],{},[1996,46599,2095],{},[2129,46601,36246],{},[902,46603,46604],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,46607,46609],{"className":46608},[886],[888,46610,46611],{"xmlns":890},[892,46612,46613,46631],{},[895,46614,46615,46617,46619,46625,46627,46629],{},[898,46616,3937],{},[1996,46618,1998],{},[2124,46620,46621,46623],{},[898,46622,8673],{},[1996,46624,4354],{},[1996,46626,2005],{"stretchy":2004},[898,46628,2789],{},[1996,46630,2011],{"stretchy":2004},[902,46632,46633],{"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.",[198,46636,41327],{"id":46637},"tržní-rovnováha-1",[724,46639,46640,46642,46643,46660,46661,2704],{},[38,46641,43011],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,46644,46646],{"className":46645},[886],[888,46647,46648],{"xmlns":890},[892,46649,46650,46658],{},[895,46651,46652],{},[2124,46653,46654,46656],{},[898,46655,2789],{},[898,46657,4252],{},[902,46659,42405],{"encoding":904}," a rovnovážnou cenu ",[883,46662,46664],{"className":46663},[886],[888,46665,46666],{"xmlns":890},[892,46667,46668,46676],{},[895,46669,46670],{},[2124,46671,46672,46674],{},[898,46673,3937],{},[898,46675,4252],{},[902,46677,41468],{"encoding":904},[120,46679,46680,46733,46784,46843],{},[123,46681,45547,46682,1343,46709,1975],{},[883,46683,46685],{"className":46684},[886],[888,46686,46687],{"xmlns":890},[892,46688,46689,46706],{},[895,46690,46691,46693,46695,46697,46699,46701,46703],{},[898,46692,3937],{},[1996,46694,1998],{},[1996,46696,2225],{},[2129,46698,2228],{},[898,46700,2789],{},[1996,46702,2095],{},[2129,46704,46705],{},"80",[902,46707,46708],{"encoding":904},"P = -5Q + 80",[883,46710,46712],{"className":46711},[886],[888,46713,46714],{"xmlns":890},[892,46715,46716,46730],{},[895,46717,46718,46720,46722,46724,46726,46728],{},[898,46719,3937],{},[1996,46721,1998],{},[2129,46723,2131],{},[898,46725,2789],{},[1996,46727,2095],{},[2129,46729,2863],{},[902,46731,46732],{"encoding":904},"P = 2Q + 10",[123,46734,45580,46735,1343,46761,1975],{},[883,46736,46738],{"className":46737},[886],[888,46739,46740],{"xmlns":890},[892,46741,46742,46758],{},[895,46743,46744,46746,46748,46750,46752,46754,46756],{},[898,46745,2789],{},[1996,46747,1998],{},[1996,46749,2225],{},[2129,46751,5009],{},[898,46753,3937],{},[1996,46755,2095],{},[2129,46757,5004],{},[902,46759,46760],{"encoding":904},"Q = -0{,}5P + 25",[883,46762,46764],{"className":46763},[886],[888,46765,46766],{"xmlns":890},[892,46767,46768,46782],{},[895,46769,46770,46772,46774,46776,46778,46780],{},[898,46771,2789],{},[1996,46773,1998],{},[2129,46775,2131],{},[898,46777,3937],{},[1996,46779,2225],{},[2129,46781,3120],{},[902,46783,40849],{"encoding":904},[123,46785,45611,46786,1343,46812,1975],{},[883,46787,46789],{"className":46788},[886],[888,46790,46791],{"xmlns":890},[892,46792,46793,46809],{},[895,46794,46795,46797,46799,46801,46803,46805,46807],{},[898,46796,3937],{},[1996,46798,1998],{},[1996,46800,2225],{},[2129,46802,2351],{},[898,46804,2789],{},[1996,46806,2095],{},[2129,46808,4046],{},[902,46810,46811],{"encoding":904},"P = -4Q + 120",[883,46813,46815],{"className":46814},[886],[888,46816,46817],{"xmlns":890},[892,46818,46819,46840],{},[895,46820,46821,46823,46825,46833,46835,46837],{},[898,46822,3937],{},[1996,46824,1998],{},[2325,46826,46827],{"scriptlevel":2327,"displaystyle":2004},[2329,46828,46829,46831],{},[2129,46830,2278],{},[2129,46832,2173],{},[898,46834,2789],{},[1996,46836,2095],{},[2129,46838,46839],{},"29",[902,46841,46842],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,46844,45646,46845,1343,46874,1975],{},[883,46846,46848],{"className":46847},[886],[888,46849,46850],{"xmlns":890},[892,46851,46852,46871],{},[895,46853,46854,46856,46858,46860,46866,46868],{},[898,46855,3937],{},[1996,46857,1998],{},[1996,46859,2225],{},[2124,46861,46862,46864],{},[898,46863,2789],{},[2129,46865,2131],{},[1996,46867,2095],{},[2129,46869,46870],{},"52",[902,46872,46873],{"encoding":904},"P = -Q^2 + 52",[883,46875,46877],{"className":46876},[886],[888,46878,46879],{"xmlns":890},[892,46880,46881,46899],{},[895,46882,46883,46885,46887,46889,46895,46897],{},[898,46884,3937],{},[1996,46886,1998],{},[2129,46888,2131],{},[2124,46890,46891,46893],{},[898,46892,2789],{},[2129,46894,2131],{},[1996,46896,2095],{},[2129,46898,2863],{},[902,46900,46901],{"encoding":904},"P = 2Q^2 + 10",[724,46903,46904,46907,46908,46938,46939,46969],{},[38,46905,46906],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,46909,46911],{"className":46910},[886],[888,46912,46913],{"xmlns":890},[892,46914,46915,46935],{},[895,46916,46917,46925,46927],{},[9166,46918,46919,46921,46923],{},[898,46920,2789],{},[2129,46922,2278],{},[898,46924,4252],{},[1996,46926,2286],{"separator":2285},[9166,46928,46929,46931,46933],{},[898,46930,2789],{},[2129,46932,2131],{},[898,46934,4252],{},[902,46936,46937],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,46940,46942],{"className":46941},[886],[888,46943,46944],{"xmlns":890},[892,46945,46946,46966],{},[895,46947,46948,46956,46958],{},[9166,46949,46950,46952,46954],{},[898,46951,3937],{},[2129,46953,2278],{},[898,46955,4252],{},[1996,46957,2286],{"separator":2285},[9166,46959,46960,46962,46964],{},[898,46961,3937],{},[2129,46963,2131],{},[898,46965,4252],{},[902,46967,46968],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,46971,46972,47124],{},[123,46973,45547,46974,1343,47014,1343,47056,1343,47090,1975],{},[883,46975,46977],{"className":46976},[886],[888,46978,46979],{"xmlns":890},[892,46980,46981,47011],{},[895,46982,46983,46989,46991,46993,46995,46997,47003,47005],{},[2272,46984,46985,46987],{},[898,46986,2789],{},[2129,46988,2278],{},[1996,46990,1998],{},[2129,46992,2863],{},[1996,46994,2225],{},[2129,46996,2131],{},[2272,46998,46999,47001],{},[898,47000,3937],{},[2129,47002,2278],{},[1996,47004,2095],{},[2272,47006,47007,47009],{},[898,47008,3937],{},[2129,47010,2131],{},[902,47012,47013],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,47015,47017],{"className":47016},[886],[888,47018,47019],{"xmlns":890},[892,47020,47021,47053],{},[895,47022,47023,47029,47031,47033,47035,47037,47043,47045,47047],{},[2272,47024,47025,47027],{},[898,47026,2789],{},[2129,47028,2131],{},[1996,47030,1998],{},[2129,47032,2228],{},[1996,47034,2095],{},[2129,47036,2131],{},[2272,47038,47039,47041],{},[898,47040,3937],{},[2129,47042,2278],{},[1996,47044,2225],{},[2129,47046,2131],{},[2272,47048,47049,47051],{},[898,47050,3937],{},[2129,47052,2131],{},[902,47054,47055],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,47057,47059],{"className":47058},[886],[888,47060,47061],{"xmlns":890},[892,47062,47063,47087],{},[895,47064,47065,47071,47073,47075,47077,47079,47081],{},[2272,47066,47067,47069],{},[898,47068,2789],{},[2129,47070,2278],{},[1996,47072,1998],{},[1996,47074,2225],{},[2129,47076,2173],{},[1996,47078,2095],{},[2129,47080,2131],{},[2272,47082,47083,47085],{},[898,47084,3937],{},[2129,47086,2278],{},[902,47088,47089],{"encoding":904},"Q_1 = -3 + 2P_1",[883,47091,47093],{"className":47092},[886],[888,47094,47095],{"xmlns":890},[892,47096,47097,47121],{},[895,47098,47099,47105,47107,47109,47111,47113,47115],{},[2272,47100,47101,47103],{},[898,47102,2789],{},[2129,47104,2131],{},[1996,47106,1998],{},[1996,47108,2225],{},[2129,47110,2131],{},[1996,47112,2095],{},[2129,47114,2173],{},[2272,47116,47117,47119],{},[898,47118,3937],{},[2129,47120,2131],{},[902,47122,47123],{"encoding":904},"Q_2 = -2 + 3P_2",[123,47125,45580,47126,1343,47166,1343,47208,1343,47240,1975],{},[883,47127,47129],{"className":47128},[886],[888,47130,47131],{"xmlns":890},[892,47132,47133,47163],{},[895,47134,47135,47141,47143,47145,47147,47149,47155,47157],{},[2272,47136,47137,47139],{},[898,47138,2789],{},[2129,47140,2278],{},[1996,47142,1998],{},[2129,47144,3090],{},[1996,47146,2225],{},[2129,47148,2131],{},[2272,47150,47151,47153],{},[898,47152,3937],{},[2129,47154,2278],{},[1996,47156,2095],{},[2272,47158,47159,47161],{},[898,47160,3937],{},[2129,47162,2131],{},[902,47164,47165],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,47167,47169],{"className":47168},[886],[888,47170,47171],{"xmlns":890},[892,47172,47173,47205],{},[895,47174,47175,47181,47183,47185,47187,47189,47195,47197,47199],{},[2272,47176,47177,47179],{},[898,47178,2789],{},[2129,47180,2131],{},[1996,47182,1998],{},[2129,47184,2228],{},[1996,47186,2095],{},[2129,47188,2131],{},[2272,47190,47191,47193],{},[898,47192,3937],{},[2129,47194,2278],{},[1996,47196,2225],{},[2129,47198,2173],{},[2272,47200,47201,47203],{},[898,47202,3937],{},[2129,47204,2131],{},[902,47206,47207],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,47209,47211],{"className":47210},[886],[888,47212,47213],{"xmlns":890},[892,47214,47215,47237],{},[895,47216,47217,47223,47225,47227,47229,47231],{},[2272,47218,47219,47221],{},[898,47220,2789],{},[2129,47222,2278],{},[1996,47224,1998],{},[1996,47226,2225],{},[2129,47228,2863],{},[1996,47230,2095],{},[2272,47232,47233,47235],{},[898,47234,3937],{},[2129,47236,2278],{},[902,47238,47239],{"encoding":904},"Q_1 = -10 + P_1",[883,47241,47243],{"className":47242},[886],[888,47244,47245],{"xmlns":890},[892,47246,47247,47269],{},[895,47248,47249,47255,47257,47259,47261,47263],{},[2272,47250,47251,47253],{},[898,47252,2789],{},[2129,47254,2131],{},[1996,47256,1998],{},[2129,47258,2228],{},[1996,47260,2095],{},[2129,47262,2235],{},[2272,47264,47265,47267],{},[898,47266,3937],{},[2129,47268,2131],{},[902,47270,47271],{"encoding":904},"Q_2 = 5 + 6P_2",[724,47273,47274,47277,47278,1343,47326,1343,47372,47422,47423,1343,47455,1343,47489,21596,47523,3885,47541,47559,47560,47573,47574,47600,47601,46938,47641,1975],{},[38,47275,47276],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,47279,47281],{"className":47280},[886],[888,47282,47283],{"xmlns":890},[892,47284,47285,47323],{},[895,47286,47287,47293,47295,47297,47299,47305,47307,47309,47315,47317],{},[2272,47288,47289,47291],{},[898,47290,2789],{},[2129,47292,2278],{},[1996,47294,1998],{},[2129,47296,36246],{},[1996,47298,2225],{},[2272,47300,47301,47303],{},[898,47302,3937],{},[2129,47304,2278],{},[1996,47306,2095],{},[2129,47308,2131],{},[2272,47310,47311,47313],{},[898,47312,3937],{},[2129,47314,2131],{},[1996,47316,2095],{},[2272,47318,47319,47321],{},[898,47320,3937],{},[2129,47322,2173],{},[902,47324,47325],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,47327,47329],{"className":47328},[886],[888,47330,47331],{"xmlns":890},[892,47332,47333,47369],{},[895,47334,47335,47341,47343,47345,47347,47353,47355,47361,47363],{},[2272,47336,47337,47339],{},[898,47338,2789],{},[2129,47340,2131],{},[1996,47342,1998],{},[2129,47344,3999],{},[1996,47346,2095],{},[2272,47348,47349,47351],{},[898,47350,3937],{},[2129,47352,2278],{},[1996,47354,2225],{},[2272,47356,47357,47359],{},[898,47358,3937],{},[2129,47360,2131],{},[1996,47362,2225],{},[2272,47364,47365,47367],{},[898,47366,3937],{},[2129,47368,2173],{},[902,47370,47371],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,47373,47375],{"className":47374},[886],[888,47376,47377],{"xmlns":890},[892,47378,47379,47419],{},[895,47380,47381,47387,47389,47391,47393,47395,47401,47403,47409,47411,47413],{},[2272,47382,47383,47385],{},[898,47384,2789],{},[2129,47386,2173],{},[1996,47388,1998],{},[2129,47390,5585],{},[1996,47392,2095],{},[2129,47394,2131],{},[2272,47396,47397,47399],{},[898,47398,3937],{},[2129,47400,2278],{},[1996,47402,2225],{},[2272,47404,47405,47407],{},[898,47406,3937],{},[2129,47408,2131],{},[1996,47410,2225],{},[2129,47412,2351],{},[2272,47414,47415,47417],{},[898,47416,3937],{},[2129,47418,2173],{},[902,47420,47421],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,47424,47426],{"className":47425},[886],[888,47427,47428],{"xmlns":890},[892,47429,47430,47452],{},[895,47431,47432,47438,47440,47442,47444,47446],{},[2272,47433,47434,47436],{},[898,47435,2789],{},[2129,47437,2278],{},[1996,47439,1998],{},[1996,47441,2225],{},[2129,47443,24203],{},[1996,47445,2095],{},[2272,47447,47448,47450],{},[898,47449,3937],{},[2129,47451,2278],{},[902,47453,47454],{"encoding":904},"Q_1 = -7 + P_1",[883,47456,47458],{"className":47457},[886],[888,47459,47460],{"xmlns":890},[892,47461,47462,47486],{},[895,47463,47464,47470,47472,47474,47476,47478,47480],{},[2272,47465,47466,47468],{},[898,47467,2789],{},[2129,47469,2131],{},[1996,47471,1998],{},[1996,47473,2225],{},[2129,47475,2351],{},[1996,47477,2095],{},[2129,47479,2351],{},[2272,47481,47482,47484],{},[898,47483,3937],{},[2129,47485,2131],{},[902,47487,47488],{"encoding":904},"Q_2 = -4 + 4P_2",[883,47490,47492],{"className":47491},[886],[888,47493,47494],{"xmlns":890},[892,47495,47496,47520],{},[895,47497,47498,47504,47506,47508,47510,47512,47514],{},[2272,47499,47500,47502],{},[898,47501,2789],{},[2129,47503,2173],{},[1996,47505,1998],{},[1996,47507,2225],{},[2129,47509,2228],{},[1996,47511,2095],{},[2129,47513,2131],{},[2272,47515,47516,47518],{},[898,47517,3937],{},[2129,47519,2173],{},[902,47521,47522],{"encoding":904},"Q_3 = -5 + 2P_3",[883,47524,47526],{"className":47525},[886],[888,47527,47528],{"xmlns":890},[892,47529,47530,47538],{},[895,47531,47532],{},[2272,47533,47534,47536],{},[898,47535,2789],{},[898,47537,17792],{},[902,47539,47540],{"encoding":904},"Q_i",[883,47542,47544],{"className":47543},[886],[888,47545,47546],{"xmlns":890},[892,47547,47548,47556],{},[895,47549,47550],{},[2272,47551,47552,47554],{},[898,47553,3937],{},[898,47555,17792],{},[902,47557,47558],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,47561,47563],{"className":47562},[886],[888,47564,47565],{"xmlns":890},[892,47566,47567,47571],{},[895,47568,47569],{},[898,47570,17792],{},[902,47572,17792],{"encoding":904},"-tého zboží, ",[883,47575,47577],{"className":47576},[886],[888,47578,47579],{"xmlns":890},[892,47580,47581,47597],{},[895,47582,47583,47585,47587,47589,47591,47593,47595],{},[898,47584,17792],{},[1996,47586,1998],{},[2129,47588,2278],{},[1996,47590,2286],{"separator":2285},[2129,47592,2131],{},[1996,47594,2286],{"separator":2285},[2129,47596,2173],{},[902,47598,47599],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,47602,47604],{"className":47603},[886],[888,47605,47606],{"xmlns":890},[892,47607,47608,47638],{},[895,47609,47610,47618,47620,47628,47630],{},[9166,47611,47612,47614,47616],{},[898,47613,2789],{},[2129,47615,2278],{},[898,47617,4252],{},[1996,47619,2286],{"separator":2285},[9166,47621,47622,47624,47626],{},[898,47623,2789],{},[2129,47625,2131],{},[898,47627,4252],{},[1996,47629,2286],{"separator":2285},[9166,47631,47632,47634,47636],{},[898,47633,2789],{},[2129,47635,2173],{},[898,47637,4252],{},[902,47639,47640],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,47642,47644],{"className":47643},[886],[888,47645,47646],{"xmlns":890},[892,47647,47648,47678],{},[895,47649,47650,47658,47660,47668,47670],{},[9166,47651,47652,47654,47656],{},[898,47653,3937],{},[2129,47655,2278],{},[898,47657,4252],{},[1996,47659,2286],{"separator":2285},[9166,47661,47662,47664,47666],{},[898,47663,3937],{},[2129,47665,2131],{},[898,47667,4252],{},[1996,47669,2286],{"separator":2285},[9166,47671,47672,47674,47676],{},[898,47673,3937],{},[2129,47675,2173],{},[898,47677,4252],{},[902,47679,47680],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,47682,47683,47686,47687,47723,47724,1975],{},[38,47684,47685],{},"2.13"," Jsou dány poptávka ",[883,47688,47690],{"className":47689},[886],[888,47691,47692],{"xmlns":890},[892,47693,47694,47720],{},[895,47695,47696,47698,47700,47702,47704,47706,47708,47710,47712,47714,47716,47718],{},[898,47697,3937],{},[1996,47699,1998],{},[898,47701,4183],{},[1996,47703,2005],{"stretchy":2004},[898,47705,2789],{},[1996,47707,2011],{"stretchy":2004},[1996,47709,1998],{},[1996,47711,2225],{},[2129,47713,2351],{},[898,47715,2789],{},[1996,47717,2095],{},[2129,47719,46705],{},[902,47721,47722],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,47725,47727],{"className":47726},[886],[888,47728,47729],{"xmlns":890},[892,47730,47731,47755],{},[895,47732,47733,47735,47737,47739,47741,47743,47745,47747,47749,47751,47753],{},[898,47734,3937],{},[1996,47736,1998],{},[898,47738,8673],{},[1996,47740,2005],{"stretchy":2004},[898,47742,2789],{},[1996,47744,2011],{"stretchy":2004},[1996,47746,1998],{},[2129,47748,2173],{},[898,47750,2789],{},[1996,47752,2095],{},[2129,47754,2863],{},[902,47756,47757],{"encoding":904},"P = S(Q) = 3Q + 10",[120,47759,47760,47797,47861,47921],{},[123,47761,47762,47763,46660,47780,1975],{},"(a) Určete rovnovážné množství ",[883,47764,47766],{"className":47765},[886],[888,47767,47768],{"xmlns":890},[892,47769,47770,47778],{},[895,47771,47772],{},[2124,47773,47774,47776],{},[898,47775,2789],{},[898,47777,4252],{},[902,47779,42405],{"encoding":904},[883,47781,47783],{"className":47782},[886],[888,47784,47785],{"xmlns":890},[892,47786,47787,47795],{},[895,47788,47789],{},[2124,47790,47791,47793],{},[898,47792,3937],{},[898,47794,4252],{},[902,47796,41468],{"encoding":904},[123,47798,47799,47800,47818,47819,47839,47840,47860],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,47801,47803],{"className":47802},[886],[888,47804,47805],{"xmlns":890},[892,47806,47807,47815],{},[895,47808,47809,47811,47813],{},[898,47810,2774],{},[1996,47812,1998],{},[2129,47814,24203],{},[902,47816,47817],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,47820,47822],{"className":47821},[886],[888,47823,47824],{"xmlns":890},[892,47825,47826,47836],{},[895,47827,47828],{},[9166,47829,47830,47832,47834],{},[898,47831,2789],{},[2129,47833,2278],{},[898,47835,4252],{},[902,47837,47838],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,47841,47843],{"className":47842},[886],[888,47844,47845],{"xmlns":890},[892,47846,47847,47857],{},[895,47848,47849],{},[9166,47850,47851,47853,47855],{},[898,47852,3937],{},[2129,47854,2278],{},[898,47856,4252],{},[902,47858,47859],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,47862,47863,47864,47818,47881,47839,47901,47860],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,47865,47867],{"className":47866},[886],[888,47868,47869],{"xmlns":890},[892,47870,47871,47879],{},[895,47872,47873,47875,47877],{},[898,47874,2774],{},[1996,47876,1998],{},[2129,47878,24203],{},[902,47880,47817],{"encoding":904},[883,47882,47884],{"className":47883},[886],[888,47885,47886],{"xmlns":890},[892,47887,47888,47898],{},[895,47889,47890],{},[9166,47891,47892,47894,47896],{},[898,47893,2789],{},[2129,47895,2131],{},[898,47897,4252],{},[902,47899,47900],{"encoding":904},"Q_2^E",[883,47902,47904],{"className":47903},[886],[888,47905,47906],{"xmlns":890},[892,47907,47908,47918],{},[895,47909,47910],{},[9166,47911,47912,47914,47916],{},[898,47913,3937],{},[2129,47915,2131],{},[898,47917,4252],{},[902,47919,47920],{"encoding":904},"P_2^E",[123,47922,47923],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,47925,47926,47927,1975],{},"Viz též ",[207,47928,42723],{"className":47929,"dataFsResolvedFilePath":809,"href":810},[210],[198,47931,43025],{"id":47932},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,47934,47935,47686,47938,47723,47974,1975],{},[38,47936,47937],{},"2.14",[883,47939,47941],{"className":47940},[886],[888,47942,47943],{"xmlns":890},[892,47944,47945,47971],{},[895,47946,47947,47949,47951,47953,47955,47957,47959,47961,47963,47965,47967,47969],{},[898,47948,3937],{},[1996,47950,1998],{},[898,47952,207],{},[898,47954,2789],{},[1996,47956,2095],{},[898,47958,2098],{},[1996,47960,1998],{},[1996,47962,2225],{},[2129,47964,2131],{},[898,47966,2789],{},[1996,47968,2095],{},[2129,47970,3120],{},[902,47972,47973],{"encoding":904},"P = aQ + b = -2Q + 50",[883,47975,47977],{"className":47976},[886],[888,47978,47979],{"xmlns":890},[892,47980,47981,48005],{},[895,47982,47983,47985,47987,47989,47991,47993,47995,47997,47999,48001,48003],{},[898,47984,3937],{},[1996,47986,1998],{},[898,47988,2142],{},[898,47990,2789],{},[1996,47992,2095],{},[898,47994,2194],{},[1996,47996,1998],{},[2129,47998,19323],{},[898,48000,2789],{},[1996,48002,2095],{},[2129,48004,9035],{},[902,48006,48007],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,48009,48010,48046,48049,48135,48188,48268,48322],{},[123,48011,47762,48012,46660,48029,1975],{},[883,48013,48015],{"className":48014},[886],[888,48016,48017],{"xmlns":890},[892,48018,48019,48027],{},[895,48020,48021],{},[2124,48022,48023,48025],{},[898,48024,2789],{},[898,48026,4252],{},[902,48028,42405],{"encoding":904},[883,48030,48032],{"className":48031},[886],[888,48033,48034],{"xmlns":890},[892,48035,48036,48044],{},[895,48037,48038],{},[2124,48039,48040,48042],{},[898,48041,3937],{},[898,48043,4252],{},[902,48045,41468],{"encoding":904},[123,48047,48048],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,48050,48051,48052,48069,48070,2671,48083,2685,48099,48115,48116,1975],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,48053,48055],{"className":48054},[886],[888,48056,48057],{"xmlns":890},[892,48058,48059,48067],{},[895,48060,48061],{},[2124,48062,48063,48065],{},[898,48064,2789],{},[898,48066,4252],{},[902,48068,42405],{"encoding":904}," odpovídající změně ",[883,48071,48073],{"className":48072},[886],[888,48074,48075],{"xmlns":890},[892,48076,48077,48081],{},[895,48078,48079],{},[898,48080,207],{},[902,48082,207],{"encoding":904},[883,48084,48086],{"className":48085},[886],[888,48087,48088],{"xmlns":890},[892,48089,48090,48096],{},[895,48091,48092,48094],{},[1996,48093,2225],{},[2129,48095,2131],{},[902,48097,48098],{"encoding":904},"-2",[883,48100,48102],{"className":48101},[886],[888,48103,48104],{"xmlns":890},[892,48105,48106,48112],{},[895,48107,48108,48110],{},[1996,48109,2225],{},[2129,48111,2173],{},[902,48113,48114],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48117,48119],{"className":48118},[886],[888,48120,48121],{"xmlns":890},[892,48122,48123,48133],{},[895,48124,48125],{},[9166,48126,48127,48129,48131],{},[898,48128,2789],{},[2129,48130,2278],{},[898,48132,4252],{},[902,48134,47838],{"encoding":904},[123,48136,48137,48138,48069,48155,48168,48169,1975],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,48139,48141],{"className":48140},[886],[888,48142,48143],{"xmlns":890},[892,48144,48145,48153],{},[895,48146,48147],{},[2124,48148,48149,48151],{},[898,48150,2789],{},[898,48152,4252],{},[902,48154,42405],{"encoding":904},[883,48156,48158],{"className":48157},[886],[888,48159,48160],{"xmlns":890},[892,48161,48162,48166],{},[895,48163,48164],{},[898,48165,2098],{},[902,48167,2098],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48170,48172],{"className":48171},[886],[888,48173,48174],{"xmlns":890},[892,48175,48176,48186],{},[895,48177,48178],{},[9166,48179,48180,48182,48184],{},[898,48181,2789],{},[2129,48183,2131],{},[898,48185,4252],{},[902,48187,47900],{"encoding":904},[123,48189,48190,48191,48069,48208,2671,48221,2685,48234,48115,48248,1975],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,48192,48194],{"className":48193},[886],[888,48195,48196],{"xmlns":890},[892,48197,48198,48206],{},[895,48199,48200],{},[2124,48201,48202,48204],{},[898,48203,2789],{},[898,48205,4252],{},[902,48207,42405],{"encoding":904},[883,48209,48211],{"className":48210},[886],[888,48212,48213],{"xmlns":890},[892,48214,48215,48219],{},[895,48216,48217],{},[898,48218,2142],{},[902,48220,2142],{"encoding":904},[883,48222,48224],{"className":48223},[886],[888,48225,48226],{"xmlns":890},[892,48227,48228,48232],{},[895,48229,48230],{},[2129,48231,19323],{},[902,48233,44462],{"encoding":904},[883,48235,48237],{"className":48236},[886],[888,48238,48239],{"xmlns":890},[892,48240,48241,48245],{},[895,48242,48243],{},[2129,48244,14591],{},[902,48246,48247],{"encoding":904},"0{,}8",[883,48249,48251],{"className":48250},[886],[888,48252,48253],{"xmlns":890},[892,48254,48255,48265],{},[895,48256,48257],{},[9166,48258,48259,48261,48263],{},[898,48260,2789],{},[2129,48262,2173],{},[898,48264,4252],{},[902,48266,48267],{"encoding":904},"Q_3^E",[123,48269,48270,48271,48069,48288,48301,48302,1975],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,48272,48274],{"className":48273},[886],[888,48275,48276],{"xmlns":890},[892,48277,48278,48286],{},[895,48279,48280],{},[2124,48281,48282,48284],{},[898,48283,2789],{},[898,48285,4252],{},[902,48287,42405],{"encoding":904},[883,48289,48291],{"className":48290},[886],[888,48292,48293],{"xmlns":890},[892,48294,48295,48299],{},[895,48296,48297],{},[898,48298,2194],{},[902,48300,2194],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48303,48305],{"className":48304},[886],[888,48306,48307],{"xmlns":890},[892,48308,48309,48319],{},[895,48310,48311],{},[9166,48312,48313,48315,48317],{},[898,48314,2789],{},[2129,48316,2351],{},[898,48318,4252],{},[902,48320,48321],{"encoding":904},"Q_4^E",[123,48323,48324,48325,48342,48343,48356,48357,21422,48370,1343,48385,21422,48398,3885,48412,21422,48425,48440,48441,1975],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,48326,48328],{"className":48327},[886],[888,48329,48330],{"xmlns":890},[892,48331,48332,48340],{},[895,48333,48334],{},[2124,48335,48336,48338],{},[898,48337,2789],{},[898,48339,4252],{},[902,48341,42405],{"encoding":904}," odpovídající změnám ",[883,48344,48346],{"className":48345},[886],[888,48347,48348],{"xmlns":890},[892,48349,48350,48354],{},[895,48351,48352],{},[898,48353,207],{},[902,48355,207],{"encoding":904}," o 1, ",[883,48358,48360],{"className":48359},[886],[888,48361,48362],{"xmlns":890},[892,48363,48364,48368],{},[895,48365,48366],{},[898,48367,2098],{},[902,48369,2098],{"encoding":904},[883,48371,48373],{"className":48372},[886],[888,48374,48375],{"xmlns":890},[892,48376,48377,48383],{},[895,48378,48379,48381],{},[1996,48380,2225],{},[2129,48382,2863],{},[902,48384,19457],{"encoding":904},[883,48386,48388],{"className":48387},[886],[888,48389,48390],{"xmlns":890},[892,48391,48392,48396],{},[895,48393,48394],{},[898,48395,2142],{},[902,48397,2142],{"encoding":904},[883,48399,48401],{"className":48400},[886],[888,48402,48403],{"xmlns":890},[892,48404,48405,48409],{},[895,48406,48407],{},[2129,48408,2794],{},[902,48410,48411],{"encoding":904},"0{,}1",[883,48413,48415],{"className":48414},[886],[888,48416,48417],{"xmlns":890},[892,48418,48419,48423],{},[895,48420,48421],{},[898,48422,2194],{},[902,48424,2194],{"encoding":904},[883,48426,48428],{"className":48427},[886],[888,48429,48430],{"xmlns":890},[892,48431,48432,48438],{},[895,48433,48434,48436],{},[1996,48435,2225],{},[2129,48437,2863],{},[902,48439,19457],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,48442,48444],{"className":48443},[886],[888,48445,48446],{"xmlns":890},[892,48447,48448,48458],{},[895,48449,48450],{},[9166,48451,48452,48454,48456],{},[898,48453,2789],{},[2129,48455,2228],{},[898,48457,4252],{},[902,48459,48460],{"encoding":904},"Q_5^E",[724,48462,48463,47686,48466,47723,48489,1975],{},[38,48464,48465],{},"2.15",[883,48467,48469],{"className":48468},[886],[888,48470,48471],{"xmlns":890},[892,48472,48473,48487],{},[895,48474,48475,48477,48479,48481,48483,48485],{},[898,48476,3937],{},[1996,48478,1998],{},[898,48480,207],{},[898,48482,2789],{},[1996,48484,2095],{},[898,48486,2098],{},[902,48488,37062],{"encoding":904},[883,48490,48492],{"className":48491},[886],[888,48493,48494],{"xmlns":890},[892,48495,48496,48510],{},[895,48497,48498,48500,48502,48504,48506,48508],{},[898,48499,3937],{},[1996,48501,1998],{},[898,48503,2142],{},[898,48505,2789],{},[1996,48507,2095],{},[898,48509,2194],{},[902,48511,40244],{"encoding":904},[120,48513,48514,48589,48606,48715,48768,48822],{},[123,48515,48516,48517,48530,48531,48556,48557,48588],{},"(a) Odvoďte redukovaný tvar pro ",[883,48518,48520],{"className":48519},[886],[888,48521,48522],{"xmlns":890},[892,48523,48524,48528],{},[895,48525,48526],{},[898,48527,3937],{},[902,48529,3937],{"encoding":904},". Stanovte podmínky pro ",[883,48532,48534],{"className":48533},[886],[888,48535,48536],{"xmlns":890},[892,48537,48538,48554],{},[895,48539,48540,48542,48544,48546,48548,48550,48552],{},[898,48541,207],{},[1996,48543,2286],{"separator":2285},[898,48545,2098],{},[1996,48547,2286],{"separator":2285},[898,48549,2142],{},[1996,48551,2286],{"separator":2285},[898,48553,2194],{},[902,48555,43287],{"encoding":904}," tak, aby rovnovážný bod ",[883,48558,48560],{"className":48559},[886],[888,48561,48562],{"xmlns":890},[892,48563,48564,48586],{},[895,48565,48566,48568,48570,48576,48578,48584],{},[898,48567,4252],{},[1996,48569,2486],{"stretchy":2004},[2124,48571,48572,48574],{},[898,48573,2789],{},[898,48575,4252],{},[1996,48577,2286],{"separator":2285},[2124,48579,48580,48582],{},[898,48581,3937],{},[898,48583,4252],{},[1996,48585,2501],{"stretchy":2004},[902,48587,41369],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,48590,48591,48592,48605],{},"(b) Vypočtěte multiplikátory pro ",[883,48593,48595],{"className":48594},[886],[888,48596,48597],{"xmlns":890},[892,48598,48599,48603],{},[895,48600,48601],{},[898,48602,3937],{},[902,48604,3937],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,48607,48608,48609,1343,48629,1343,48647,1343,48665,48683,48684,48701,48702,1975],{},"(c) Pro hodnoty parametrů ",[883,48610,48612],{"className":48611},[886],[888,48613,48614],{"xmlns":890},[892,48615,48616,48626],{},[895,48617,48618,48620,48622,48624],{},[898,48619,207],{},[1996,48621,1998],{},[1996,48623,2225],{},[2129,48625,2131],{},[902,48627,48628],{"encoding":904},"a = -2",[883,48630,48632],{"className":48631},[886],[888,48633,48634],{"xmlns":890},[892,48635,48636,48644],{},[895,48637,48638,48640,48642],{},[898,48639,2098],{},[1996,48641,1998],{},[2129,48643,5211],{},[902,48645,48646],{"encoding":904},"b = 40",[883,48648,48650],{"className":48649},[886],[888,48651,48652],{"xmlns":890},[892,48653,48654,48662],{},[895,48655,48656,48658,48660],{},[898,48657,2142],{},[1996,48659,1998],{},[2129,48661,5009],{},[902,48663,48664],{"encoding":904},"c = 0{,}5",[883,48666,48668],{"className":48667},[886],[888,48669,48670],{"xmlns":890},[892,48671,48672,48680],{},[895,48673,48674,48676,48678],{},[898,48675,2194],{},[1996,48677,1998],{},[2129,48679,2863],{},[902,48681,48682],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,48685,48687],{"className":48686},[886],[888,48688,48689],{"xmlns":890},[892,48690,48691,48699],{},[895,48692,48693],{},[2124,48694,48695,48697],{},[898,48696,3937],{},[898,48698,4252],{},[902,48700,41468],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,48703,48705],{"className":48704},[886],[888,48706,48707],{"xmlns":890},[892,48708,48709,48713],{},[895,48710,48711],{},[898,48712,3937],{},[902,48714,3937],{"encoding":904},[123,48716,48717,48718,48069,48735,48748,48749,1975],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,48719,48721],{"className":48720},[886],[888,48722,48723],{"xmlns":890},[892,48724,48725,48733],{},[895,48726,48727],{},[2124,48728,48729,48731],{},[898,48730,3937],{},[898,48732,4252],{},[902,48734,41468],{"encoding":904},[883,48736,48738],{"className":48737},[886],[888,48739,48740],{"xmlns":890},[892,48741,48742,48746],{},[895,48743,48744],{},[898,48745,207],{},[902,48747,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,48750,48752],{"className":48751},[886],[888,48753,48754],{"xmlns":890},[892,48755,48756,48766],{},[895,48757,48758],{},[9166,48759,48760,48762,48764],{},[898,48761,3937],{},[2129,48763,2278],{},[898,48765,4252],{},[902,48767,47859],{"encoding":904},[123,48769,48770,48771,48788,48789,48802,48803,1975],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,48772,48774],{"className":48773},[886],[888,48775,48776],{"xmlns":890},[892,48777,48778,48786],{},[895,48779,48780],{},[2124,48781,48782,48784],{},[898,48783,3937],{},[898,48785,4252],{},[902,48787,41468],{"encoding":904}," odpovídající poklesu ",[883,48790,48792],{"className":48791},[886],[888,48793,48794],{"xmlns":890},[892,48795,48796,48800],{},[895,48797,48798],{},[898,48799,207],{},[902,48801,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,48804,48806],{"className":48805},[886],[888,48807,48808],{"xmlns":890},[892,48809,48810,48820],{},[895,48811,48812],{},[9166,48813,48814,48816,48818],{},[898,48815,3937],{},[2129,48817,2131],{},[898,48819,4252],{},[902,48821,47920],{"encoding":904},[123,48823,48824,48825,48342,48842,48855,48856,2685,48869,3885,48884,48897,48898,1975],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,48826,48828],{"className":48827},[886],[888,48829,48830],{"xmlns":890},[892,48831,48832,48840],{},[895,48833,48834],{},[2124,48835,48836,48838],{},[898,48837,3937],{},[898,48839,4252],{},[902,48841,41468],{"encoding":904},[883,48843,48845],{"className":48844},[886],[888,48846,48847],{"xmlns":890},[892,48848,48849,48853],{},[895,48850,48851],{},[898,48852,207],{},[902,48854,207],{"encoding":904}," na 35, ",[883,48857,48859],{"className":48858},[886],[888,48860,48861],{"xmlns":890},[892,48862,48863,48867],{},[895,48864,48865],{},[898,48866,2142],{},[902,48868,2142],{"encoding":904},[883,48870,48872],{"className":48871},[886],[888,48873,48874],{"xmlns":890},[892,48875,48876,48881],{},[895,48877,48878],{},[2129,48879,48880],{},"0,7",[902,48882,48883],{"encoding":904},"0{,}7",[883,48885,48887],{"className":48886},[886],[888,48888,48889],{"xmlns":890},[892,48890,48891,48895],{},[895,48892,48893],{},[898,48894,2194],{},[902,48896,2194],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,48899,48901],{"className":48900},[886],[888,48902,48903],{"xmlns":890},[892,48904,48905,48915],{},[895,48906,48907],{},[9166,48908,48909,48911,48913],{},[898,48910,3937],{},[2129,48912,2173],{},[898,48914,4252],{},[902,48916,48917],{"encoding":904},"P_3^E",[724,48919,48920,47686,48923,47723,48951,21596,48979,3885,49005,1975],{},[38,48921,48922],{},"2.16",[883,48924,48926],{"className":48925},[886],[888,48927,48928],{"xmlns":890},[892,48929,48930,48948],{},[895,48931,48932,48934,48936,48938,48940,48942],{},[898,48933,3937],{},[1996,48935,1998],{},[898,48937,207],{},[1996,48939,2095],{},[898,48941,2098],{},[2124,48943,48944,48946],{},[898,48945,2789],{},[2129,48947,2131],{},[902,48949,48950],{"encoding":904},"P = a + bQ^2",[883,48952,48954],{"className":48953},[886],[888,48955,48956],{"xmlns":890},[892,48957,48958,48976],{},[895,48959,48960,48962,48964,48966,48968,48970],{},[898,48961,3937],{},[1996,48963,1998],{},[898,48965,2142],{},[1996,48967,2095],{},[898,48969,2194],{},[2124,48971,48972,48974],{},[898,48973,2789],{},[2129,48975,2131],{},[902,48977,48978],{"encoding":904},"P = c + dQ^2",[883,48980,48982],{"className":48981},[886],[888,48983,48984],{"xmlns":890},[892,48985,48986,49002],{},[895,48987,48988,48990,48992,48994,48996,48998,49000],{},[898,48989,207],{},[1996,48991,2286],{"separator":2285},[898,48993,2142],{},[1996,48995,2286],{"separator":2285},[898,48997,2194],{},[1996,48999,3408],{},[2129,49001,2327],{},[902,49003,49004],{"encoding":904},"a, c, d > 0",[883,49006,49008],{"className":49007},[886],[888,49009,49010],{"xmlns":890},[892,49011,49012,49020],{},[895,49013,49014,49016,49018],{},[898,49015,2098],{},[1996,49017,3447],{},[2129,49019,2327],{},[902,49021,49022],{"encoding":904},"b \u003C 0",[120,49024,49025,49073,49089,49196,49248,49300,49409,49425,49524,49577],{},[123,49026,48516,49027,49040,49041,49072],{},[883,49028,49030],{"className":49029},[886],[888,49031,49032],{"xmlns":890},[892,49033,49034,49038],{},[895,49035,49036],{},[898,49037,2789],{},[902,49039,2789],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,49042,49044],{"className":49043},[886],[888,49045,49046],{"xmlns":890},[892,49047,49048,49070],{},[895,49049,49050,49052,49054,49060,49062,49068],{},[898,49051,4252],{},[1996,49053,2486],{"stretchy":2004},[2124,49055,49056,49058],{},[898,49057,2789],{},[898,49059,4252],{},[1996,49061,2286],{"separator":2285},[2124,49063,49064,49066],{},[898,49065,3937],{},[898,49067,4252],{},[1996,49069,2501],{"stretchy":2004},[902,49071,41369],{"encoding":904}," patřil do 1. kvadrantu.",[123,49074,48591,49075,49088],{},[883,49076,49078],{"className":49077},[886],[888,49079,49080],{"xmlns":890},[892,49081,49082,49086],{},[895,49083,49084],{},[898,49085,2789],{},[902,49087,2789],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,49090,48608,49091,1343,49109,1343,49129,1343,49147,49165,49166,48701,49183,1975],{},[883,49092,49094],{"className":49093},[886],[888,49095,49096],{"xmlns":890},[892,49097,49098,49106],{},[895,49099,49100,49102,49104],{},[898,49101,207],{},[1996,49103,1998],{},[2129,49105,3090],{},[902,49107,49108],{"encoding":904},"a = 100",[883,49110,49112],{"className":49111},[886],[888,49113,49114],{"xmlns":890},[892,49115,49116,49126],{},[895,49117,49118,49120,49122,49124],{},[898,49119,2098],{},[1996,49121,1998],{},[1996,49123,2225],{},[2129,49125,2278],{},[902,49127,49128],{"encoding":904},"b = -1",[883,49130,49132],{"className":49131},[886],[888,49133,49134],{"xmlns":890},[892,49135,49136,49144],{},[895,49137,49138,49140,49142],{},[898,49139,2142],{},[1996,49141,1998],{},[2129,49143,9035],{},[902,49145,49146],{"encoding":904},"c = 20",[883,49148,49150],{"className":49149},[886],[888,49151,49152],{"xmlns":890},[892,49153,49154,49162],{},[895,49155,49156,49158,49160],{},[898,49157,2194],{},[1996,49159,1998],{},[2129,49161,2278],{},[902,49163,49164],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,49167,49169],{"className":49168},[886],[888,49170,49171],{"xmlns":890},[892,49172,49173,49181],{},[895,49174,49175],{},[2124,49176,49177,49179],{},[898,49178,2789],{},[898,49180,4252],{},[902,49182,42405],{"encoding":904},[883,49184,49186],{"className":49185},[886],[888,49187,49188],{"xmlns":890},[892,49189,49190,49194],{},[895,49191,49192],{},[898,49193,2789],{},[902,49195,2789],{"encoding":904},[123,49197,48137,49198,48069,49215,49228,49229,1975],{},[883,49199,49201],{"className":49200},[886],[888,49202,49203],{"xmlns":890},[892,49204,49205,49213],{},[895,49206,49207],{},[2124,49208,49209,49211],{},[898,49210,2789],{},[898,49212,4252],{},[902,49214,42405],{"encoding":904},[883,49216,49218],{"className":49217},[886],[888,49219,49220],{"xmlns":890},[892,49221,49222,49226],{},[895,49223,49224],{},[898,49225,207],{},[902,49227,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49230,49232],{"className":49231},[886],[888,49233,49234],{"xmlns":890},[892,49235,49236,49246],{},[895,49237,49238],{},[9166,49239,49240,49242,49244],{},[898,49241,2789],{},[2129,49243,2278],{},[898,49245,4252],{},[902,49247,47838],{"encoding":904},[123,49249,48190,49250,48069,49267,49280,49281,1975],{},[883,49251,49253],{"className":49252},[886],[888,49254,49255],{"xmlns":890},[892,49256,49257,49265],{},[895,49258,49259],{},[2124,49260,49261,49263],{},[898,49262,2789],{},[898,49264,4252],{},[902,49266,42405],{"encoding":904},[883,49268,49270],{"className":49269},[886],[888,49271,49272],{"xmlns":890},[892,49273,49274,49278],{},[895,49275,49276],{},[898,49277,2142],{},[902,49279,2142],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49282,49284],{"className":49283},[886],[888,49285,49286],{"xmlns":890},[892,49287,49288,49298],{},[895,49289,49290],{},[9166,49291,49292,49294,49296],{},[898,49293,2789],{},[2129,49295,2131],{},[898,49297,4252],{},[902,49299,47900],{"encoding":904},[123,49301,48270,49302,48342,49319,49332,49333,2685,49346,49361,49362,49375,49376,49389,49390,1975],{},[883,49303,49305],{"className":49304},[886],[888,49306,49307],{"xmlns":890},[892,49308,49309,49317],{},[895,49310,49311],{},[2124,49312,49313,49315],{},[898,49314,2789],{},[898,49316,4252],{},[902,49318,42405],{"encoding":904},[883,49320,49322],{"className":49321},[886],[888,49323,49324],{"xmlns":890},[892,49325,49326,49330],{},[895,49327,49328],{},[898,49329,207],{},[902,49331,207],{"encoding":904}," na 110, poklesu ",[883,49334,49336],{"className":49335},[886],[888,49337,49338],{"xmlns":890},[892,49339,49340,49344],{},[895,49341,49342],{},[898,49343,2098],{},[902,49345,2098],{"encoding":904},[883,49347,49349],{"className":49348},[886],[888,49350,49351],{"xmlns":890},[892,49352,49353,49359],{},[895,49354,49355,49357],{},[1996,49356,2225],{},[2129,49358,2131],{},[902,49360,48098],{"encoding":904},", růstu ",[883,49363,49365],{"className":49364},[886],[888,49366,49367],{"xmlns":890},[892,49368,49369,49373],{},[895,49370,49371],{},[898,49372,2142],{},[902,49374,2142],{"encoding":904}," na 25 a růstu ",[883,49377,49379],{"className":49378},[886],[888,49380,49381],{"xmlns":890},[892,49382,49383,49387],{},[895,49384,49385],{},[898,49386,2194],{},[902,49388,2194],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,49391,49393],{"className":49392},[886],[888,49394,49395],{"xmlns":890},[892,49396,49397,49407],{},[895,49398,49399],{},[9166,49400,49401,49403,49405],{},[898,49402,2789],{},[2129,49404,2173],{},[898,49406,4252],{},[902,49408,48267],{"encoding":904},[123,49410,49411,49412,49088],{},"(i) Vypočtěte multiplikátory pro ",[883,49413,49415],{"className":49414},[886],[888,49416,49417],{"xmlns":890},[892,49418,49419,49423],{},[895,49420,49421],{},[898,49422,3937],{},[902,49424,3937],{"encoding":904},[123,49426,49427,49428,48701,49445,49458,49459,48069,49476,2685,49489,49504,49505,1975],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,49429,49431],{"className":49430},[886],[888,49432,49433],{"xmlns":890},[892,49434,49435,49443],{},[895,49436,49437],{},[2124,49438,49439,49441],{},[898,49440,3937],{},[898,49442,4252],{},[902,49444,41468],{"encoding":904},[883,49446,49448],{"className":49447},[886],[888,49449,49450],{"xmlns":890},[892,49451,49452,49456],{},[895,49453,49454],{},[898,49455,3937],{},[902,49457,3937],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,49460,49462],{"className":49461},[886],[888,49463,49464],{"xmlns":890},[892,49465,49466,49474],{},[895,49467,49468],{},[2124,49469,49470,49472],{},[898,49471,3937],{},[898,49473,4252],{},[902,49475,41468],{"encoding":904},[883,49477,49479],{"className":49478},[886],[888,49480,49481],{"xmlns":890},[892,49482,49483,49487],{},[895,49484,49485],{},[898,49486,207],{},[902,49488,207],{"encoding":904},[883,49490,49492],{"className":49491},[886],[888,49493,49494],{"xmlns":890},[892,49495,49496,49502],{},[895,49497,49498,49500],{},[1996,49499,2225],{},[2129,49501,2173],{},[902,49503,48114],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,49506,49508],{"className":49507},[886],[888,49509,49510],{"xmlns":890},[892,49511,49512,49522],{},[895,49513,49514],{},[9166,49515,49516,49518,49520],{},[898,49517,3937],{},[2129,49519,2278],{},[898,49521,4252],{},[902,49523,47859],{"encoding":904},[123,49525,49526,49527,48069,49544,49557,49558,1975],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,49528,49530],{"className":49529},[886],[888,49531,49532],{"xmlns":890},[892,49533,49534,49542],{},[895,49535,49536],{},[2124,49537,49538,49540],{},[898,49539,3937],{},[898,49541,4252],{},[902,49543,41468],{"encoding":904},[883,49545,49547],{"className":49546},[886],[888,49548,49549],{"xmlns":890},[892,49550,49551,49555],{},[895,49552,49553],{},[898,49554,207],{},[902,49556,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,49559,49561],{"className":49560},[886],[888,49562,49563],{"xmlns":890},[892,49564,49565,49575],{},[895,49566,49567],{},[9166,49568,49569,49571,49573],{},[898,49570,3937],{},[2129,49572,2131],{},[898,49574,4252],{},[902,49576,47920],{"encoding":904},[123,49578,49579,49580,48788,49597,49610,49611,2685,49624,49361,49639,49652,49653,49666,49667,1975],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,49581,49583],{"className":49582},[886],[888,49584,49585],{"xmlns":890},[892,49586,49587,49595],{},[895,49588,49589],{},[2124,49590,49591,49593],{},[898,49592,3937],{},[898,49594,4252],{},[902,49596,41468],{"encoding":904},[883,49598,49600],{"className":49599},[886],[888,49601,49602],{"xmlns":890},[892,49603,49604,49608],{},[895,49605,49606],{},[898,49607,207],{},[902,49609,207],{"encoding":904}," na 90, poklesu ",[883,49612,49614],{"className":49613},[886],[888,49615,49616],{"xmlns":890},[892,49617,49618,49622],{},[895,49619,49620],{},[898,49621,2098],{},[902,49623,2098],{"encoding":904},[883,49625,49627],{"className":49626},[886],[888,49628,49629],{"xmlns":890},[892,49630,49631,49637],{},[895,49632,49633,49635],{},[1996,49634,2225],{},[2129,49636,2173],{},[902,49638,48114],{"encoding":904},[883,49640,49642],{"className":49641},[886],[888,49643,49644],{"xmlns":890},[892,49645,49646,49650],{},[895,49647,49648],{},[898,49649,2142],{},[902,49651,2142],{"encoding":904}," na 30 a růstu ",[883,49654,49656],{"className":49655},[886],[888,49657,49658],{"xmlns":890},[892,49659,49660,49664],{},[895,49661,49662],{},[898,49663,2194],{},[902,49665,2194],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,49668,49670],{"className":49669},[886],[888,49671,49672],{"xmlns":890},[892,49673,49674,49684],{},[895,49675,49676],{},[9166,49677,49678,49680,49682],{},[898,49679,3937],{},[2129,49681,2173],{},[898,49683,4252],{},[902,49685,48917],{"encoding":904},[198,49687,820],{"id":49688},"přebytek-spotřebitele-a-výrobce-1",[724,49690,49691,47686,49694,47723,49730,1975],{},[38,49692,49693],{},"2.17",[883,49695,49697],{"className":49696},[886],[888,49698,49699],{"xmlns":890},[892,49700,49701,49727],{},[895,49702,49703,49705,49707,49709,49711,49713,49715,49717,49719,49721],{},[898,49704,3937],{},[1996,49706,1998],{},[898,49708,4183],{},[1996,49710,2005],{"stretchy":2004},[898,49712,2789],{},[1996,49714,2011],{"stretchy":2004},[1996,49716,1998],{},[2129,49718,15040],{},[1996,49720,2225],{},[2124,49722,49723,49725],{},[898,49724,2789],{},[2129,49726,2131],{},[902,49728,49729],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,49731,49733],{"className":49732},[886],[888,49734,49735],{"xmlns":890},[892,49736,49737,49763],{},[895,49738,49739,49741,49743,49745,49747,49749,49751,49753,49755,49757],{},[898,49740,3937],{},[1996,49742,1998],{},[898,49744,8673],{},[1996,49746,2005],{"stretchy":2004},[898,49748,2789],{},[1996,49750,2011],{"stretchy":2004},[1996,49752,1998],{},[2129,49754,2173],{},[1996,49756,2095],{},[2124,49758,49759,49761],{},[898,49760,2789],{},[2129,49762,2131],{},[902,49764,49765],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,49767,49768,49771],{},[123,49769,49770],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,49772,49773],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,49775,49776,47686,49779,47723,49813,1975],{},[38,49777,49778],{},"2.18",[883,49780,49782],{"className":49781},[886],[888,49783,49784],{"xmlns":890},[892,49785,49786,49810],{},[895,49787,49788,49790,49792,49794,49796,49798,49800,49802,49804,49806,49808],{},[898,49789,3937],{},[1996,49791,1998],{},[898,49793,4183],{},[1996,49795,2005],{"stretchy":2004},[898,49797,2789],{},[1996,49799,2011],{"stretchy":2004},[1996,49801,1998],{},[2129,49803,3707],{},[1996,49805,2225],{},[2129,49807,2131],{},[898,49809,2789],{},[902,49811,49812],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,49814,49816],{"className":49815},[886],[888,49817,49818],{"xmlns":890},[892,49819,49820,49846],{},[895,49821,49822,49824,49826,49828,49830,49832,49834,49836,49838,49840],{},[898,49823,3937],{},[1996,49825,1998],{},[898,49827,8673],{},[1996,49829,2005],{"stretchy":2004},[898,49831,2789],{},[1996,49833,2011],{"stretchy":2004},[1996,49835,1998],{},[2129,49837,2173],{},[1996,49839,2095],{},[2124,49841,49842,49844],{},[898,49843,2789],{},[2129,49845,2131],{},[902,49847,49765],{"encoding":904},[120,49849,49850,49870,49873,49876],{},[123,49851,49852,49853,1975],{},"(a) Vypočtěte rovnovážné množství ",[883,49854,49856],{"className":49855},[886],[888,49857,49858],{"xmlns":890},[892,49859,49860,49868],{},[895,49861,49862],{},[2124,49863,49864,49866],{},[898,49865,2789],{},[898,49867,4252],{},[902,49869,42405],{"encoding":904},[123,49871,49872],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,49874,49875],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,49877,49878],{},"(c) Graficky interpretujte.",[36972,49880],{},[115,49882,49884],{"id":49883},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,49886,49887,49890,49893,49896,49899,49902,49905,49908,49911,49914,49917,49920,49923,49926],{},[123,49888,49889],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,49891,49892],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,49894,49895],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,49897,49898],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,49900,49901],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,49903,49904],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,49906,49907],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,49909,49910],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,49912,49913],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,49915,49916],{},"K čemu slouží multiplikátory?",[123,49918,49919],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,49921,49922],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,49924,49925],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,49927,49928],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[36972,49930],{},[115,49932,15722],{"id":15721},[724,49934,49935],{},[38,49936,13163],{},[120,49938,49939,49974,49979,50009,50014,50077,50103,50108,50138,50147,50154,50160],{},[123,49940,49941,10025,49944,18650,49947,2203,49949,1343,49972],{},[38,49942,49943],{},"Poptávané množství",[614,49945,49946],{},"quantity demanded",[38,49948,28004],{},[883,49950,49952],{"className":49951},[886],[888,49953,49954],{"xmlns":890},[892,49955,49956,49970],{},[895,49957,49958,49960,49962,49964,49966,49968],{},[898,49959,2789],{},[1996,49961,1998],{},[898,49963,4183],{},[1996,49965,2005],{"stretchy":2004},[898,49967,3937],{},[1996,49969,2011],{"stretchy":2004},[902,49971,4192],{"encoding":904},[38,49973,37451],{},[123,49975,49976,49978],{},[38,49977,37458],{}," — substituční + důchodový efekt",[123,49980,49981,2203,49984],{},[38,49982,49983],{},"Reálné cenové rozpětí",[883,49985,49987],{"className":49986},[886],[888,49988,49989],{"xmlns":890},[892,49990,49991,50007],{},[895,49992,49993,49995,49997,49999,50005],{},[1996,49994,2005],{"stretchy":2004},[2129,49996,2327],{},[1996,49998,2286],{"separator":2285},[2272,50000,50001,50003],{},[898,50002,3937],{},[2129,50004,2327],{},[1996,50006,2011],{"stretchy":2004},[902,50008,37659],{"encoding":904},[123,50010,50011,11097],{},[38,50012,50013],{},"Homogenita poptávky",[123,50015,50016,2203,50019,1343,50042,1343,50059,50076],{},[38,50017,50018],{},"Lineární poptávka",[883,50020,50022],{"className":50021},[886],[888,50023,50024],{"xmlns":890},[892,50025,50026,50040],{},[895,50027,50028,50030,50032,50034,50036,50038],{},[898,50029,3937],{},[1996,50031,1998],{},[898,50033,207],{},[898,50035,2789],{},[1996,50037,2095],{},[898,50039,2098],{},[902,50041,37062],{"encoding":904},[883,50043,50045],{"className":50044},[886],[888,50046,50047],{"xmlns":890},[892,50048,50049,50057],{},[895,50050,50051,50053,50055],{},[898,50052,207],{},[1996,50054,3447],{},[2129,50056,2327],{},[902,50058,43087],{"encoding":904},[883,50060,50062],{"className":50061},[886],[888,50063,50064],{"xmlns":890},[892,50065,50066,50074],{},[895,50067,50068,50070,50072],{},[898,50069,2098],{},[1996,50071,3408],{},[2129,50073,2327],{},[902,50075,18816],{"encoding":904}," — nedokonalá konkurence",[123,50078,50079,7015,50082],{},[38,50080,50081],{},"Dokonalá konkurence",[883,50083,50085],{"className":50084},[886],[888,50086,50087],{"xmlns":890},[892,50088,50089,50101],{},[895,50090,50091,50093,50095],{},[898,50092,3937],{},[1996,50094,1998],{},[2124,50096,50097,50099],{},[898,50098,3937],{},[1996,50100,4354],{},[902,50102,4357],{"encoding":904},[123,50104,50105,50107],{},[38,50106,38228],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,50109,50110,2203,50112,1343,50136],{},[38,50111,31729],{},[883,50113,50115],{"className":50114},[886],[888,50116,50117],{"xmlns":890},[892,50118,50119,50133],{},[895,50120,50121,50123,50125,50127,50129,50131],{},[898,50122,2789],{},[1996,50124,1998],{},[898,50126,4252],{},[1996,50128,2005],{"stretchy":2004},[898,50130,9128],{},[1996,50132,2011],{"stretchy":2004},[902,50134,50135],{"encoding":904},"Q = E(Y)",[38,50137,38425],{},[123,50139,50140,50143,50144,50146],{},[38,50141,50142],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,50145,38871],{}," zboží",[123,50148,50149,3885,50151,50153],{},[38,50150,39877],{},[38,50152,39824],{}," — znaménka zkřížených koeficientů",[123,50155,50156,50159],{},[38,50157,50158],{},"Dvoukomoditní trh"," (2.6)",[123,50161,50162,10025,50165,2011],{},[38,50163,50164],{},"Posun poptávky",[614,50166,38929],{},[724,50168,50169],{},[38,50170,13127],{},[120,50172,50173,50206,50210,50255],{},[123,50174,50175,10025,50177,18650,50179,2203,50181,1343,50204],{},[38,50176,40271],{},[614,50178,40274],{},[38,50180,40445],{},[883,50182,50184],{"className":50183},[886],[888,50185,50186],{"xmlns":890},[892,50187,50188,50202],{},[895,50189,50190,50192,50194,50196,50198,50200],{},[898,50191,2789],{},[1996,50193,1998],{},[898,50195,8673],{},[1996,50197,2005],{"stretchy":2004},[898,50199,3937],{},[1996,50201,2011],{"stretchy":2004},[902,50203,8682],{"encoding":904},[38,50205,40523],{},[123,50207,50208],{},[38,50209,40530],{},[123,50211,50212,2203,50215,1343,50238],{},[38,50213,50214],{},"Lineární nabídka",[883,50216,50218],{"className":50217},[886],[888,50219,50220],{"xmlns":890},[892,50221,50222,50236],{},[895,50223,50224,50226,50228,50230,50232,50234],{},[898,50225,3937],{},[1996,50227,1998],{},[898,50229,2142],{},[898,50231,2789],{},[1996,50233,2095],{},[898,50235,2194],{},[902,50237,40244],{"encoding":904},[883,50239,50241],{"className":50240},[886],[888,50242,50243],{"xmlns":890},[892,50244,50245,50253],{},[895,50246,50247,50249,50251],{},[898,50248,2142],{},[1996,50250,3408],{},[2129,50252,2327],{},[902,50254,40262],{"encoding":904},[123,50256,50257,10025,50260,2011],{},[38,50258,50259],{},"Posun nabídky",[614,50261,40908],{},[724,50263,50264],{},[38,50265,50266],{},"Rovnováha a komparativní statika",[120,50268,50269,50348,50354],{},[123,50270,50271,10025,50273,18650,50275,2203,50278,1343,50295,2203,50298,1343,50315,2203,50317],{},[38,50272,41327],{},[614,50274,41446],{},[38,50276,50277],{},"rovnovážná cena",[883,50279,50281],{"className":50280},[886],[888,50282,50283],{"xmlns":890},[892,50284,50285,50293],{},[895,50286,50287],{},[2124,50288,50289,50291],{},[898,50290,3937],{},[898,50292,4252],{},[902,50294,41468],{"encoding":904},[38,50296,50297],{},"rovnovážné množství",[883,50299,50301],{"className":50300},[886],[888,50302,50303],{"xmlns":890},[892,50304,50305,50313],{},[895,50306,50307],{},[2124,50308,50309,50311],{},[898,50310,2789],{},[898,50312,4252],{},[902,50314,42405],{"encoding":904},[38,50316,41504],{},[883,50318,50320],{"className":50319},[886],[888,50321,50322],{"xmlns":890},[892,50323,50324,50346],{},[895,50325,50326,50328,50330,50336,50338,50344],{},[898,50327,4252],{},[1996,50329,2486],{"stretchy":2004},[2124,50331,50332,50334],{},[898,50333,2789],{},[898,50335,4252],{},[1996,50337,2286],{"separator":2285},[2124,50339,50340,50342],{},[898,50341,3937],{},[898,50343,4252],{},[1996,50345,2501],{"stretchy":2004},[902,50347,41369],{"encoding":904},[123,50349,50350,50353],{},[38,50351,50352],{},"Pravidla 1–4"," komparativní statiky",[123,50355,50356,10025,50359,2011],{},[38,50357,50358],{},"Teorém pavučiny",[614,50360,42351],{},[724,50362,50363],{},[38,50364,50365],{},"Zdanění",[120,50367,50368,50424,50472],{},[123,50369,50370,50372,50373,50398,50399,2011],{},[38,50371,50365],{}," — daň výrobci (",[883,50374,50376],{"className":50375},[886],[888,50377,50378],{"xmlns":890},[892,50379,50380,50396],{},[895,50381,50382,50388,50390,50392,50394],{},[2272,50383,50384,50386],{},[898,50385,8673],{},[2129,50387,2278],{},[1996,50389,1998],{},[898,50391,8673],{},[1996,50393,2095],{},[898,50395,2774],{},[902,50397,42756],{"encoding":904},") vs. daň spotřebiteli (",[883,50400,50402],{"className":50401},[886],[888,50403,50404],{"xmlns":890},[892,50405,50406,50422],{},[895,50407,50408,50414,50416,50418,50420],{},[2272,50409,50410,50412],{},[898,50411,4183],{},[2129,50413,2131],{},[1996,50415,1998],{},[898,50417,4183],{},[1996,50419,2225],{},[898,50421,2774],{},[902,50423,42787],{"encoding":904},[123,50425,50426,2203,50428,1343,50449],{},[38,50427,42660],{},[883,50429,50431],{"className":50430},[886],[888,50432,50433],{"xmlns":890},[892,50434,50435,50447],{},[895,50436,50437],{},[2272,50438,50439,50441],{},[898,50440,2774],{},[895,50442,50443,50445],{},[898,50444,42679],{},[898,50446,724],{},[902,50448,42684],{"encoding":904},[883,50450,50452],{"className":50451},[886],[888,50453,50454],{"xmlns":890},[892,50455,50456,50470],{},[895,50457,50458],{},[2272,50459,50460,50462],{},[898,50461,2774],{},[895,50463,50464,50466,50468],{},[898,50465,42702],{},[898,50467,1994],{},[898,50469,12043],{},[902,50471,42709],{"encoding":904},[123,50473,50474,2203,50477,1343,50506],{},[38,50475,50476],{},"Ekvivalence zdanění",[883,50478,50480],{"className":50479},[886],[888,50481,50482],{"xmlns":890},[892,50483,50484,50504],{},[895,50485,50486,50494,50496],{},[9166,50487,50488,50490,50492],{},[898,50489,2789],{},[2129,50491,2278],{},[898,50493,4252],{},[1996,50495,1998],{},[9166,50497,50498,50500,50502],{},[898,50499,2789],{},[2129,50501,2131],{},[898,50503,4252],{},[902,50505,42910],{"encoding":904},[883,50507,50509],{"className":50508},[886],[888,50510,50511],{"xmlns":890},[892,50512,50513,50537],{},[895,50514,50515,50523,50525,50527,50529],{},[9166,50516,50517,50519,50521],{},[898,50518,3937],{},[2129,50520,2278],{},[898,50522,4252],{},[1996,50524,2225],{},[898,50526,2774],{},[1996,50528,1998],{},[9166,50530,50531,50533,50535],{},[898,50532,3937],{},[2129,50534,2131],{},[898,50536,4252],{},[902,50538,42944],{"encoding":904},[724,50540,50541],{},[38,50542,26410],{},[120,50544,50545,50591,50622,50627,50633,50640],{},[123,50546,50547,2203,50549],{},[38,50548,43043],{},[883,50550,50552],{"className":50551},[886],[888,50553,50554],{"xmlns":890},[892,50555,50556,50588],{},[895,50557,50558,50564,50566,50568,50570,50572,50574,50576,50578,50580,50582,50584,50586],{},[2124,50559,50560,50562],{},[898,50561,2789],{},[898,50563,4252],{},[1996,50565,1998],{},[1996,50567,2005],{"stretchy":2004},[898,50569,2098],{},[1996,50571,2225],{},[898,50573,2194],{},[1996,50575,2011],{"stretchy":2004},[898,50577,4674],{"mathvariant":2376},[1996,50579,2005],{"stretchy":2004},[898,50581,2142],{},[1996,50583,2225],{},[898,50585,207],{},[1996,50587,2011],{"stretchy":2004},[902,50589,50590],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,50592,50593,2203,50596,50621],{},[38,50594,50595],{},"Parametry",[883,50597,50599],{"className":50598},[886],[888,50600,50601],{"xmlns":890},[892,50602,50603,50619],{},[895,50604,50605,50607,50609,50611,50613,50615,50617],{},[898,50606,207],{},[1996,50608,2286],{"separator":2285},[898,50610,2098],{},[1996,50612,2286],{"separator":2285},[898,50614,2142],{},[1996,50616,2286],{"separator":2285},[898,50618,2194],{},[902,50620,43287],{"encoding":904}," — exogenní proměnné",[123,50623,50624],{},[38,50625,50626],{},"Endogenní \u002F exogenní proměnná",[123,50628,50629,50632],{},[38,50630,50631],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,50634,50635,1343,50638],{},[38,50636,50637],{},"Komparativní statika",[38,50639,36962],{},[123,50641,50642,2203,50644,50660],{},[38,50643,2955],{},[883,50645,50647],{"className":50646},[886],[888,50648,50649],{"xmlns":890},[892,50650,50651,50657],{},[895,50652,50653,50655],{},[898,50654,2194],{},[898,50656,2789],{},[902,50658,50659],{"encoding":904},"dQ"," (2.11)",[724,50662,50663],{},[38,50664,50665],{},"Přebytky a ostatní",[120,50667,50668,50706],{},[123,50669,50670,2203,50672,50687,50688,2203,50690,50705],{},[38,50671,44936],{},[883,50673,50675],{"className":50674},[886],[888,50676,50677],{"xmlns":890},[892,50678,50679,50685],{},[895,50680,50681,50683],{},[898,50682,2777],{},[898,50684,8673],{},[902,50686,44952],{"encoding":904}," (2.14), ",[38,50689,44955],{},[883,50691,50693],{"className":50692},[886],[888,50694,50695],{"xmlns":890},[892,50696,50697,50703],{},[895,50698,50699,50701],{},[898,50700,3937],{},[898,50702,8673],{},[902,50704,44971],{"encoding":904}," (2.15)",[123,50707,50708,1343,50711,50714],{},[38,50709,50710],{},"Homo economicus",[38,50712,50713],{},"Marshallova formulace"," (1890)",[36972,50716],{},[115,50718,3792],{"id":3791},[120,50720,50721,50756,50765],{},[123,50722,50723,2203,50726,50729,50730,1343,50733,50736,50737,50740,50741,50744,50745,50748,50749,50752,50753],{},[38,50724,50725],{},"Související témata:",[207,50727,811],{"className":50728,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,50731,820],{"className":50732,"dataFsResolvedFilePath":818,"href":819},[210],[207,50734,2357],{"className":50735,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,50738,775],{"className":50739,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,50742,784],{"className":50743,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,50746,793],{"className":50747,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,50750,3828],{"className":50751,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,50754,3823],{"className":50755,"dataFsResolvedFilePath":827,"href":828},[210],[123,50757,50758,2203,50761],{},[38,50759,50760],{},"Shrnutí přednášek:",[207,50762,50764],{"className":50763,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,50766,50767,2203,50769],{},[38,50768,16206],{},[207,50770,16210],{"className":50771,"dataFsResolvedFilePath":1960,"href":1961},[210],{"title":641,"searchDepth":642,"depth":642,"links":50773},[50774,50775,50783,50789,50796,50797,50804,50805,50806,50813,50814,50815],{"id":36796,"depth":642,"text":36797},{"id":36777,"depth":642,"text":13163,"children":50776},[50777,50778,50779,50780,50782],{"id":37065,"depth":649,"text":37066},{"id":37347,"depth":649,"text":37348},{"id":38357,"depth":649,"text":38358},{"id":38925,"depth":649,"text":50781},"Posun poptávky (shift of demand)",{"id":39429,"depth":649,"text":39430},{"id":36781,"depth":642,"text":13127,"children":50784},[50785,50786,50787],{"id":40266,"depth":649,"text":37066},{"id":40452,"depth":649,"text":40453},{"id":40904,"depth":649,"text":50788},"Posun nabídky (shift of supply)",{"id":41326,"depth":642,"text":41327,"children":50790},[50791,50792,50793,50794,50795],{"id":41438,"depth":649,"text":41439},{"id":41651,"depth":649,"text":41652},{"id":41969,"depth":649,"text":41970},{"id":42323,"depth":649,"text":42324},{"id":42354,"depth":649,"text":42355},{"id":42623,"depth":642,"text":811},{"id":43024,"depth":642,"text":43025,"children":50798},[50799,50800,50801,50802],{"id":43042,"depth":649,"text":43043},{"id":43423,"depth":649,"text":43424},{"id":43807,"depth":649,"text":43808},{"id":44261,"depth":649,"text":50803},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":11785,"depth":642,"text":820},{"id":45186,"depth":642,"text":45187},{"id":45417,"depth":642,"text":45418,"children":50807},[50808,50809,50810,50811,50812],{"id":45421,"depth":649,"text":45422},{"id":46261,"depth":649,"text":46262},{"id":46637,"depth":649,"text":41327},{"id":47932,"depth":649,"text":43025},{"id":49688,"depth":649,"text":820},{"id":49883,"depth":642,"text":49884},{"id":15721,"depth":642,"text":15722},{"id":3791,"depth":642,"text":3792},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,50822,50823,50824,17885,50825,50826],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":50829,"title":820,"body":50830,"course":1128,"courses":659,"created":9556,"description":641,"extension":661,"meta":55109,"navigation":664,"path":55110,"seo":55111,"sources":55112,"stem":55113,"tags":55114,"type":3857,"updated":677,"__hash__":55119},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":50831,"toc":55087},[50832,50834,50902,50952,50954,50957,51215,51291,51296,51298,51317,51321,51397,51482,51484,51798,51891,51893,51912,51916,51990,52075,52078,52254,52259,52261,52681,52683,52687,52691,52927,52971,53071,53137,53140,53173,53349,53411,53541,53619,53730,53764,53962,53981,54000,54065,54069,54072,54117,54120,54238,54284,54286,54290,54638,54640,54642,54920,54922,54926,54961,54968,55041,55043,55045],[12,50833,820],{"id":11785},[3867,50835,50836],{},[724,50837,50838,3874,50840,10025,50842,50857,50858,10025,50860,50875,50876,50898,50899,1975],{},[883,50839,3873],{},[38,50841,44936],{},[883,50843,50845],{"className":50844},[886],[888,50846,50847],{"xmlns":890},[892,50848,50849,50855],{},[895,50850,50851,50853],{},[898,50852,2777],{},[898,50854,8673],{},[902,50856,44952],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,50859,45083],{},[883,50861,50863],{"className":50862},[886],[888,50864,50865],{"xmlns":890},[892,50866,50867,50873],{},[895,50868,50869,50871],{},[898,50870,3937],{},[898,50872,8673],{},[902,50874,44971],{"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 ",[883,50877,50879],{"className":50878},[886],[888,50880,50881],{"xmlns":890},[892,50882,50883,50895],{},[895,50884,50885,50887,50889,50891,50893],{},[898,50886,2777],{},[898,50888,8673],{},[1996,50890,2095],{},[898,50892,3937],{},[898,50894,8673],{},[902,50896,50897],{"encoding":904},"CS + PS"," měří ",[38,50900,50901],{},"celkový blahobyt trhu",[724,50903,50904,10025,50906,1343,50908,12130,50923,10025,50925,1343,50927,50942,50943,50947,50948,1975],{},[38,50905,44936],{},[614,50907,44990],{},[883,50909,50911],{"className":50910},[886],[888,50912,50913],{"xmlns":890},[892,50914,50915,50921],{},[895,50916,50917,50919],{},[898,50918,2777],{},[898,50920,8673],{},[902,50922,44952],{"encoding":904},[38,50924,44955],{},[614,50926,45086],{},[883,50928,50930],{"className":50929},[886],[888,50931,50932],{"xmlns":890},[892,50933,50934,50940],{},[895,50935,50936,50938],{},[898,50937,3937],{},[898,50939,8673],{},[902,50941,44971],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,50944,50946],{"className":50945,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,50949,50951],{"className":50950,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[36972,50953],{},[115,50955,1241],{"id":50956},"úvod",[724,50958,50959,50960,50983,50984,51007,51008,51025,51026,3910,51058,51090,51091,51117,51118,51121,51122,51125,51126,14013,51160,21596,51181,1975],{},"Je dána funkce poptávky ",[883,50961,50963],{"className":50962},[886],[888,50964,50965],{"xmlns":890},[892,50966,50967,50981],{},[895,50968,50969,50971,50973,50975,50977,50979],{},[898,50970,3937],{},[1996,50972,1998],{},[898,50974,4183],{},[1996,50976,2005],{"stretchy":2004},[898,50978,2789],{},[1996,50980,2011],{"stretchy":2004},[902,50982,4640],{"encoding":904},", resp. funkce nabídky ",[883,50985,50987],{"className":50986},[886],[888,50988,50989],{"xmlns":890},[892,50990,50991,51005],{},[895,50992,50993,50995,50997,50999,51001,51003],{},[898,50994,3937],{},[1996,50996,1998],{},[898,50998,8673],{},[1996,51000,2005],{"stretchy":2004},[898,51002,2789],{},[1996,51004,2011],{"stretchy":2004},[902,51006,41073],{"encoding":904},". Pro pevně zadané množství ",[883,51009,51011],{"className":51010},[886],[888,51012,51013],{"xmlns":890},[892,51014,51015,51023],{},[895,51016,51017],{},[2272,51018,51019,51021],{},[898,51020,2789],{},[2129,51022,2327],{},[902,51024,38310],{"encoding":904}," je odpovídající cena ",[883,51027,51029],{"className":51028},[886],[888,51030,51031],{"xmlns":890},[892,51032,51033,51055],{},[895,51034,51035,51041,51043,51045,51047,51053],{},[2272,51036,51037,51039],{},[898,51038,3937],{},[2129,51040,2327],{},[1996,51042,1998],{},[898,51044,4183],{},[1996,51046,2005],{"stretchy":2004},[2272,51048,51049,51051],{},[898,51050,2789],{},[2129,51052,2327],{},[1996,51054,2011],{"stretchy":2004},[902,51056,51057],{"encoding":904},"P_0 = D(Q_0)",[883,51059,51061],{"className":51060},[886],[888,51062,51063],{"xmlns":890},[892,51064,51065,51087],{},[895,51066,51067,51073,51075,51077,51079,51085],{},[2272,51068,51069,51071],{},[898,51070,3937],{},[2129,51072,2327],{},[1996,51074,1998],{},[898,51076,8673],{},[1996,51078,2005],{"stretchy":2004},[2272,51080,51081,51083],{},[898,51082,2789],{},[2129,51084,2327],{},[1996,51086,2011],{"stretchy":2004},[902,51088,51089],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,51092,51094],{"className":51093},[886],[888,51095,51096],{"xmlns":890},[892,51097,51098,51114],{},[895,51099,51100,51106,51108],{},[2272,51101,51102,51104],{},[898,51103,3937],{},[2129,51105,2327],{},[2288,51107,2987],{},[2272,51109,51110,51112],{},[898,51111,2789],{},[2129,51113,2327],{},[902,51115,51116],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,51119,51120],{},"výdaje spotřebitele",", nebo ",[38,51123,51124],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,51127,51129],{"className":51128},[886],[888,51130,51131],{"xmlns":890},[892,51132,51133,51157],{},[895,51134,51135,51137,51139,51145,51147,51149,51151],{},[2129,51136,2327],{},[2288,51138,2987],{},[2272,51140,51141,51143],{},[898,51142,2789],{},[2129,51144,2327],{},[2288,51146,2987],{},[898,51148,4255],{},[2288,51150,2987],{},[2272,51152,51153,51155],{},[898,51154,3937],{},[2129,51156,2327],{},[902,51158,51159],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,51161,51163],{"className":51162},[886],[888,51164,51165],{"xmlns":890},[892,51166,51167,51179],{},[895,51168,51169,51171,51173,51175,51177],{},[1996,51170,2005],{"stretchy":2004},[898,51172,2789],{},[1996,51174,2286],{"separator":2285},[898,51176,3937],{},[1996,51178,2011],{"stretchy":2004},[902,51180,37693],{"encoding":904},[883,51182,51184],{"className":51183},[886],[888,51185,51186],{"xmlns":890},[892,51187,51188,51212],{},[895,51189,51190,51192,51194,51196,51202,51204,51210],{},[898,51191,4255],{},[1996,51193,1998],{},[1996,51195,2486],{"stretchy":2004},[2272,51197,51198,51200],{},[898,51199,2789],{},[2129,51201,2327],{},[1996,51203,2286],{"separator":2285},[2272,51205,51206,51208],{},[898,51207,3937],{},[2129,51209,2327],{},[1996,51211,2501],{"stretchy":2004},[902,51213,51214],{"encoding":904},"A = [Q_0, P_0]",[3867,51216,51217,51222,51280],{},[724,51218,51219,51221],{},[883,51220,4155],{}," Intuice",[120,51223,51224,51252],{},[123,51225,51226,51227,51230,51231,51233,51234,51251],{},"Za jednotky zboží nakoupené ",[38,51228,51229],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,51232,25272],{}," než ",[883,51235,51237],{"className":51236},[886],[888,51238,51239],{"xmlns":890},[892,51240,51241,51249],{},[895,51242,51243],{},[2272,51244,51245,51247],{},[898,51246,3937],{},[2129,51248,2327],{},[902,51250,38950],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,51253,51254,51255,51257,51258,51261,51262,51279],{},"Za jednotky zboží prodané ",[38,51256,51229],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,51259,51260],{},"nižší"," cenu než ",[883,51263,51265],{"className":51264},[886],[888,51266,51267],{"xmlns":890},[892,51268,51269,51277],{},[895,51270,51271],{},[2272,51272,51273,51275],{},[898,51274,3937],{},[2129,51276,2327],{},[902,51278,38950],{"encoding":904}," — rozdíl je jeho přebytek.",[724,51281,51282,51283,51286,51287,51290],{},"Přebytek je tedy rozdíl mezi ",[614,51284,51285],{},"ochotou"," (platit \u002F prodávat) a ",[614,51288,51289],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,51292,51293],{},[2559,51294],{"alt":44981,"className":51295,"src":44983},[210,2563],[36972,51297],{},[115,51299,51301,51302,2011],{"id":51300},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,51303,51305],{"className":51304},[886],[888,51306,51307],{"xmlns":890},[892,51308,51309,51315],{},[895,51310,51311,51313],{},[898,51312,2777],{},[898,51314,8673],{},[902,51316,44952],{"encoding":904},[198,51318,51320],{"id":51319},"definice-vzorec-214","Definice (vzorec 2.14)",[724,51322,51323,51324,51347,51348,51365,51366,2704],{},"Pro poptávku ",[883,51325,51327],{"className":51326},[886],[888,51328,51329],{"xmlns":890},[892,51330,51331,51345],{},[895,51332,51333,51335,51337,51339,51341,51343],{},[898,51334,3937],{},[1996,51336,1998],{},[898,51338,4183],{},[1996,51340,2005],{"stretchy":2004},[898,51342,2789],{},[1996,51344,2011],{"stretchy":2004},[902,51346,4640],{"encoding":904}," a pevně zadané ",[883,51349,51351],{"className":51350},[886],[888,51352,51353],{"xmlns":890},[892,51354,51355,51363],{},[895,51356,51357],{},[2272,51358,51359,51361],{},[898,51360,2789],{},[2129,51362,2327],{},[902,51364,38310],{"encoding":904}," s cenou ",[883,51367,51369],{"className":51368},[886],[888,51370,51371],{"xmlns":890},[892,51372,51373,51395],{},[895,51374,51375,51381,51383,51385,51387,51393],{},[2272,51376,51377,51379],{},[898,51378,3937],{},[2129,51380,2327],{},[1996,51382,1998],{},[898,51384,4183],{},[1996,51386,2005],{"stretchy":2004},[2272,51388,51389,51391],{},[898,51390,2789],{},[2129,51392,2327],{},[1996,51394,2011],{"stretchy":2004},[902,51396,51057],{"encoding":904},[883,51398,51400],{"className":51399},[886],[888,51401,51402],{"xmlns":890,"display":28068},[892,51403,51404,51480],{},[20756,51405,51406],{"width":28073},[20761,51407,51408,51410,51474,51476],{},[20764,51409],{"width":28078},[20764,51411,51412],{},[895,51413,51414,51416,51418,51420,51426,51428,51430,51442,51444,51446,51448,51450,51452,51454,51456,51458,51464,51466,51472],{},[898,51415,2777],{},[898,51417,8673],{},[1996,51419,2005],{"stretchy":2004},[2272,51421,51422,51424],{},[898,51423,2789],{},[2129,51425,2327],{},[1996,51427,2011],{"stretchy":2004},[1996,51429,1998],{},[9166,51431,51432,51434,51436],{},[1996,51433,11170],{},[2129,51435,2327],{},[2272,51437,51438,51440],{},[898,51439,2789],{},[2129,51441,2327],{},[898,51443,4183],{},[1996,51445,2005],{"stretchy":2004},[898,51447,2789],{},[1996,51449,2011],{"stretchy":2004},[2288,51451,2987],{},[898,51453,2194],{},[898,51455,2789],{},[1996,51457,2225],{},[2272,51459,51460,51462],{},[898,51461,3937],{},[2129,51463,2327],{},[2288,51465,2987],{},[2272,51467,51468,51470],{},[898,51469,2789],{},[2129,51471,2327],{},[898,51473,1975],{"mathvariant":2376},[20764,51475],{"width":28078},[20764,51477,51478],{},[2288,51479,45075],{},[902,51481,45078],{"encoding":904},[198,51483,2444],{"id":2443},[120,51485,51486,51578,51640],{},[123,51487,51488,51528,51529,51555,51556,51559,51560,51577],{},[883,51489,51491],{"className":51490},[886],[888,51492,51493],{"xmlns":890},[892,51494,51495,51525],{},[895,51496,51497],{},[2325,51498,51499,51511,51513,51515,51517,51519,51521,51523],{"scriptlevel":2327,"displaystyle":2285},[9166,51500,51501,51503,51505],{},[1996,51502,11170],{},[2129,51504,2327],{},[2272,51506,51507,51509],{},[898,51508,2789],{},[2129,51510,2327],{},[898,51512,4183],{},[1996,51514,2005],{"stretchy":2004},[898,51516,2789],{},[1996,51518,2011],{"stretchy":2004},[2288,51520,2987],{},[898,51522,2194],{},[898,51524,2789],{},[902,51526,51527],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,51530,51532],{"className":51531},[886],[888,51533,51534],{"xmlns":890},[892,51535,51536,51552],{},[895,51537,51538,51540,51542,51544,51550],{},[1996,51539,2486],{"stretchy":2004},[2129,51541,2327],{},[1996,51543,2286],{"separator":2285},[2272,51545,51546,51548],{},[898,51547,2789],{},[2129,51549,2327],{},[1996,51551,2501],{"stretchy":2004},[902,51553,51554],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,51557,51558],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,51561,51563],{"className":51562},[886],[888,51564,51565],{"xmlns":890},[892,51566,51567,51575],{},[895,51568,51569],{},[2272,51570,51571,51573],{},[898,51572,2789],{},[2129,51574,2327],{},[902,51576,38310],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,51579,51580,51606,51607,3918],{},[883,51581,51583],{"className":51582},[886],[888,51584,51585],{"xmlns":890},[892,51586,51587,51603],{},[895,51588,51589,51595,51597],{},[2272,51590,51591,51593],{},[898,51592,3937],{},[2129,51594,2327],{},[2288,51596,2987],{},[2272,51598,51599,51601],{},[898,51600,2789],{},[2129,51602,2327],{},[902,51604,51605],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,51608,51610],{"className":51609},[886],[888,51611,51612],{"xmlns":890},[892,51613,51614,51638],{},[895,51615,51616,51618,51620,51626,51628,51630,51632],{},[2129,51617,2327],{},[2288,51619,2987],{},[2272,51621,51622,51624],{},[898,51623,2789],{},[2129,51625,2327],{},[2288,51627,2987],{},[898,51629,4255],{},[2288,51631,2987],{},[2272,51633,51634,51636],{},[898,51635,3937],{},[2129,51637,2327],{},[902,51639,51159],{"encoding":904},[123,51641,51642,51657,51658,51680,51681,51706,51707,21596,51733,3885,51765,1975],{},[883,51643,51645],{"className":51644},[886],[888,51646,51647],{"xmlns":890},[892,51648,51649,51655],{},[895,51650,51651,51653],{},[898,51652,2777],{},[898,51654,8673],{},[902,51656,44952],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,51659,51661],{"className":51660},[886],[888,51662,51663],{"xmlns":890},[892,51664,51665,51677],{},[895,51666,51667,51669,51671],{},[898,51668,3937],{},[1996,51670,1998],{},[2272,51672,51673,51675],{},[898,51674,3937],{},[2129,51676,2327],{},[902,51678,51679],{"encoding":904},"P = P_0"," v pásu ",[883,51682,51684],{"className":51683},[886],[888,51685,51686],{"xmlns":890},[892,51687,51688,51704],{},[895,51689,51690,51692,51694,51696,51702],{},[1996,51691,2486],{"stretchy":2004},[2129,51693,2327],{},[1996,51695,2286],{"separator":2285},[2272,51697,51698,51700],{},[898,51699,2789],{},[2129,51701,2327],{},[1996,51703,2501],{"stretchy":2004},[902,51705,51554],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,51708,51710],{"className":51709},[886],[888,51711,51712],{"xmlns":890},[892,51713,51714,51730],{},[895,51715,51716,51722,51724,51726,51728],{},[2272,51717,51718,51720],{},[898,51719,3937],{},[2129,51721,2327],{},[2288,51723,2987],{},[898,51725,23255],{},[2288,51727,2987],{},[898,51729,4255],{},[902,51731,51732],{"encoding":904},"P_0\\,B\\,A",[883,51734,51736],{"className":51735},[886],[888,51737,51738],{"xmlns":890},[892,51739,51740,51762],{},[895,51741,51742,51744,51746,51748,51750,51752,51754,51756,51758,51760],{},[898,51743,23255],{},[1996,51745,1998],{},[1996,51747,2486],{"stretchy":2004},[2129,51749,2327],{},[1996,51751,2286],{"separator":2285},[898,51753,4183],{},[1996,51755,2005],{"stretchy":2004},[2129,51757,2327],{},[1996,51759,2011],{"stretchy":2004},[1996,51761,2501],{"stretchy":2004},[902,51763,51764],{"encoding":904},"B = [0, D(0)]",[883,51766,51768],{"className":51767},[886],[888,51769,51770],{"xmlns":890},[892,51771,51772,51796],{},[895,51773,51774,51776,51778,51780,51786,51788,51794],{},[898,51775,4255],{},[1996,51777,1998],{},[1996,51779,2486],{"stretchy":2004},[2272,51781,51782,51784],{},[898,51783,2789],{},[2129,51785,2327],{},[1996,51787,2286],{"separator":2285},[2272,51789,51790,51792],{},[898,51791,3937],{},[2129,51793,2327],{},[1996,51795,2501],{"stretchy":2004},[902,51797,51214],{"encoding":904},[724,51799,51800],{},[614,51801,51802,51803,51816,51817,51850,51851,29144,51876,1975],{},"Obrázek 2.24: Křivka poptávky ",[883,51804,51806],{"className":51805},[886],[888,51807,51808],{"xmlns":890},[892,51809,51810,51814],{},[895,51811,51812],{},[898,51813,4183],{},[902,51815,4183],{"encoding":904},", bod ",[883,51818,51820],{"className":51819},[886],[888,51821,51822],{"xmlns":890},[892,51823,51824,51848],{},[895,51825,51826,51828,51830,51832,51838,51840,51846],{},[898,51827,4255],{},[1996,51829,1998],{},[1996,51831,2486],{"stretchy":2004},[2272,51833,51834,51836],{},[898,51835,2789],{},[2129,51837,2327],{},[1996,51839,2286],{"separator":2285},[2272,51841,51842,51844],{},[898,51843,3937],{},[2129,51845,2327],{},[1996,51847,2501],{"stretchy":2004},[902,51849,51214],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,51852,51854],{"className":51853},[886],[888,51855,51856],{"xmlns":890},[892,51857,51858,51874],{},[895,51859,51860,51866,51868,51870,51872],{},[2272,51861,51862,51864],{},[898,51863,3937],{},[2129,51865,2327],{},[2288,51867,2987],{},[898,51869,23255],{},[2288,51871,2987],{},[898,51873,4255],{},[902,51875,51732],{"encoding":904},[883,51877,51879],{"className":51878},[886],[888,51880,51881],{"xmlns":890},[892,51882,51883,51889],{},[895,51884,51885,51887],{},[898,51886,2777],{},[898,51888,8673],{},[902,51890,44952],{"encoding":904},[36972,51892],{},[115,51894,51896,51897,2011],{"id":51895},"přebytek-výrobce-psps","Přebytek výrobce (",[883,51898,51900],{"className":51899},[886],[888,51901,51902],{"xmlns":890},[892,51903,51904,51910],{},[895,51905,51906,51908],{},[898,51907,3937],{},[898,51909,8673],{},[902,51911,44971],{"encoding":904},[198,51913,51915],{"id":51914},"definice-vzorec-215","Definice (vzorec 2.15)",[724,51917,51918,51919,51347,51942,51365,51959,2704],{},"Analogicky — pro nabídku ",[883,51920,51922],{"className":51921},[886],[888,51923,51924],{"xmlns":890},[892,51925,51926,51940],{},[895,51927,51928,51930,51932,51934,51936,51938],{},[898,51929,3937],{},[1996,51931,1998],{},[898,51933,8673],{},[1996,51935,2005],{"stretchy":2004},[898,51937,2789],{},[1996,51939,2011],{"stretchy":2004},[902,51941,41073],{"encoding":904},[883,51943,51945],{"className":51944},[886],[888,51946,51947],{"xmlns":890},[892,51948,51949,51957],{},[895,51950,51951],{},[2272,51952,51953,51955],{},[898,51954,2789],{},[2129,51956,2327],{},[902,51958,38310],{"encoding":904},[883,51960,51962],{"className":51961},[886],[888,51963,51964],{"xmlns":890},[892,51965,51966,51988],{},[895,51967,51968,51974,51976,51978,51980,51986],{},[2272,51969,51970,51972],{},[898,51971,3937],{},[2129,51973,2327],{},[1996,51975,1998],{},[898,51977,8673],{},[1996,51979,2005],{"stretchy":2004},[2272,51981,51982,51984],{},[898,51983,2789],{},[2129,51985,2327],{},[1996,51987,2011],{"stretchy":2004},[902,51989,51089],{"encoding":904},[883,51991,51993],{"className":51992},[886],[888,51994,51995],{"xmlns":890,"display":28068},[892,51996,51997,52073],{},[20756,51998,51999],{"width":28073},[20761,52000,52001,52003,52067,52069],{},[20764,52002],{"width":28078},[20764,52004,52005],{},[895,52006,52007,52009,52011,52013,52019,52021,52023,52029,52031,52037,52039,52051,52053,52055,52057,52059,52061,52063,52065],{},[898,52008,3937],{},[898,52010,8673],{},[1996,52012,2005],{"stretchy":2004},[2272,52014,52015,52017],{},[898,52016,2789],{},[2129,52018,2327],{},[1996,52020,2011],{"stretchy":2004},[1996,52022,1998],{},[2272,52024,52025,52027],{},[898,52026,3937],{},[2129,52028,2327],{},[2288,52030,2987],{},[2272,52032,52033,52035],{},[898,52034,2789],{},[2129,52036,2327],{},[1996,52038,2225],{},[9166,52040,52041,52043,52045],{},[1996,52042,11170],{},[2129,52044,2327],{},[2272,52046,52047,52049],{},[898,52048,2789],{},[2129,52050,2327],{},[898,52052,8673],{},[1996,52054,2005],{"stretchy":2004},[898,52056,2789],{},[1996,52058,2011],{"stretchy":2004},[2288,52060,2987],{},[898,52062,2194],{},[898,52064,2789],{},[898,52066,1975],{"mathvariant":2376},[20764,52068],{"width":28078},[20764,52070,52071],{},[2288,52072,45171],{},[902,52074,45174],{"encoding":904},[198,52076,2444],{"id":52077},"geometrická-interpretace-1",[120,52079,52080,52128,52189],{},[123,52081,52082,7015,52107,52110,52111,1975],{},[883,52083,52085],{"className":52084},[886],[888,52086,52087],{"xmlns":890},[892,52088,52089,52105],{},[895,52090,52091,52097,52099],{},[2272,52092,52093,52095],{},[898,52094,3937],{},[2129,52096,2327],{},[2288,52098,2987],{},[2272,52100,52101,52103],{},[898,52102,2789],{},[2129,52104,2327],{},[902,52106,51605],{"encoding":904},[38,52108,52109],{},"tržba"," výrobce za prodané množství ",[883,52112,52114],{"className":52113},[886],[888,52115,52116],{"xmlns":890},[892,52117,52118,52126],{},[895,52119,52120],{},[2272,52121,52122,52124],{},[898,52123,2789],{},[2129,52125,2327],{},[902,52127,38310],{"encoding":904},[123,52129,52130,52170,52171,52188],{},[883,52131,52133],{"className":52132},[886],[888,52134,52135],{"xmlns":890},[892,52136,52137,52167],{},[895,52138,52139],{},[2325,52140,52141,52153,52155,52157,52159,52161,52163,52165],{"scriptlevel":2327,"displaystyle":2285},[9166,52142,52143,52145,52147],{},[1996,52144,11170],{},[2129,52146,2327],{},[2272,52148,52149,52151],{},[898,52150,2789],{},[2129,52152,2327],{},[898,52154,8673],{},[1996,52156,2005],{"stretchy":2004},[898,52158,2789],{},[1996,52160,2011],{"stretchy":2004},[2288,52162,2987],{},[898,52164,2194],{},[898,52166,2789],{},[902,52168,52169],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,52172,52174],{"className":52173},[886],[888,52175,52176],{"xmlns":890},[892,52177,52178,52186],{},[895,52179,52180],{},[2272,52181,52182,52184],{},[898,52183,2789],{},[2129,52185,2327],{},[902,52187,38310],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,52190,52191,52206,52207,52228,52229,1975],{},[883,52192,52194],{"className":52193},[886],[888,52195,52196],{"xmlns":890},[892,52197,52198,52204],{},[895,52199,52200,52202],{},[898,52201,3937],{},[898,52203,8673],{},[902,52205,44971],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,52208,52210],{"className":52209},[886],[888,52211,52212],{"xmlns":890},[892,52213,52214,52226],{},[895,52215,52216,52218,52220],{},[898,52217,3937],{},[1996,52219,1998],{},[2272,52221,52222,52224],{},[898,52223,3937],{},[2129,52225,2327],{},[902,52227,51679],{"encoding":904}," a křivkou nabídky v pásu ",[883,52230,52232],{"className":52231},[886],[888,52233,52234],{"xmlns":890},[892,52235,52236,52252],{},[895,52237,52238,52240,52242,52244,52250],{},[1996,52239,2486],{"stretchy":2004},[2129,52241,2327],{},[1996,52243,2286],{"separator":2285},[2272,52245,52246,52248],{},[898,52247,2789],{},[2129,52249,2327],{},[1996,52251,2501],{"stretchy":2004},[902,52253,51554],{"encoding":904},[724,52255,52256],{},[614,52257,52258],{},"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.",[36972,52260],{},[3867,52262,52263,52268],{},[724,52264,52265,52267],{},[883,52266,4572],{}," Postup výpočtu CS a PS",[152,52269,52270,52401,52511,52540,52674],{},[123,52271,52272,52273,52290,52291,52322,52323,52354,52355,1975],{},"Zjisti (nebo si zvol) množství ",[883,52274,52276],{"className":52275},[886],[888,52277,52278],{"xmlns":890},[892,52279,52280,52288],{},[895,52281,52282],{},[2272,52283,52284,52286],{},[898,52285,2789],{},[2129,52287,2327],{},[902,52289,38310],{"encoding":904}," a odpovídající cenu ",[883,52292,52294],{"className":52293},[886],[888,52295,52296],{"xmlns":890},[892,52297,52298,52320],{},[895,52299,52300,52306,52308,52310,52312,52318],{},[2272,52301,52302,52304],{},[898,52303,3937],{},[2129,52305,2327],{},[1996,52307,1998],{},[898,52309,4183],{},[1996,52311,2005],{"stretchy":2004},[2272,52313,52314,52316],{},[898,52315,2789],{},[2129,52317,2327],{},[1996,52319,2011],{"stretchy":2004},[902,52321,51057],{"encoding":904}," resp. ",[883,52324,52326],{"className":52325},[886],[888,52327,52328],{"xmlns":890},[892,52329,52330,52352],{},[895,52331,52332,52338,52340,52342,52344,52350],{},[2272,52333,52334,52336],{},[898,52335,3937],{},[2129,52337,2327],{},[1996,52339,1998],{},[898,52341,8673],{},[1996,52343,2005],{"stretchy":2004},[2272,52345,52346,52348],{},[898,52347,2789],{},[2129,52349,2327],{},[1996,52351,2011],{"stretchy":2004},[902,52353,51089],{"encoding":904},". V rovnováze platí ",[883,52356,52358],{"className":52357},[886],[888,52359,52360],{"xmlns":890},[892,52361,52362,52398],{},[895,52363,52364,52366,52368,52374,52376,52378,52380,52382,52388,52390,52392],{},[898,52365,4183],{},[1996,52367,2005],{"stretchy":2004},[2124,52369,52370,52372],{},[898,52371,2789],{},[898,52373,4252],{},[1996,52375,2011],{"stretchy":2004},[1996,52377,1998],{},[898,52379,8673],{},[1996,52381,2005],{"stretchy":2004},[2124,52383,52384,52386],{},[898,52385,2789],{},[898,52387,4252],{},[1996,52389,2011],{"stretchy":2004},[1996,52391,1998],{},[2124,52393,52394,52396],{},[898,52395,3937],{},[898,52397,4252],{},[902,52399,52400],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,52402,52403,52404,20128,52442,52457,52458,20128,52496,3918],{},"Spočti určitý integrál ",[883,52405,52407],{"className":52406},[886],[888,52408,52409],{"xmlns":890},[892,52410,52411,52439],{},[895,52412,52413,52425,52427,52429,52431,52433,52435,52437],{},[9166,52414,52415,52417,52419],{},[1996,52416,11170],{},[2129,52418,2327],{},[2272,52420,52421,52423],{},[898,52422,2789],{},[2129,52424,2327],{},[898,52426,4183],{},[1996,52428,2005],{"stretchy":2004},[898,52430,2789],{},[1996,52432,2011],{"stretchy":2004},[2288,52434,2987],{},[898,52436,2194],{},[898,52438,2789],{},[902,52440,52441],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,52443,52445],{"className":52444},[886],[888,52446,52447],{"xmlns":890},[892,52448,52449,52455],{},[895,52450,52451,52453],{},[898,52452,2777],{},[898,52454,8673],{},[902,52456,44952],{"encoding":904},") nebo ",[883,52459,52461],{"className":52460},[886],[888,52462,52463],{"xmlns":890},[892,52464,52465,52493],{},[895,52466,52467,52479,52481,52483,52485,52487,52489,52491],{},[9166,52468,52469,52471,52473],{},[1996,52470,11170],{},[2129,52472,2327],{},[2272,52474,52475,52477],{},[898,52476,2789],{},[2129,52478,2327],{},[898,52480,8673],{},[1996,52482,2005],{"stretchy":2004},[898,52484,2789],{},[1996,52486,2011],{"stretchy":2004},[2288,52488,2987],{},[898,52490,2194],{},[898,52492,2789],{},[902,52494,52495],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,52497,52499],{"className":52498},[886],[888,52500,52501],{"xmlns":890},[892,52502,52503,52509],{},[895,52504,52505,52507],{},[898,52506,3937],{},[898,52508,8673],{},[902,52510,44971],{"encoding":904},[123,52512,52513,52514,1975],{},"Sestav obdélník ",[883,52515,52517],{"className":52516},[886],[888,52518,52519],{"xmlns":890},[892,52520,52521,52537],{},[895,52522,52523,52529,52531],{},[2272,52524,52525,52527],{},[898,52526,3937],{},[2129,52528,2327],{},[1996,52530,3177],{},[2272,52532,52533,52535],{},[898,52534,2789],{},[2129,52536,2327],{},[902,52538,52539],{"encoding":904},"P_0 \\cdot Q_0",[123,52541,52542,52543],{},"Dosaď:\n",[120,52544,52545,52610],{},[123,52546,52547,52605,52606,52609],{},[883,52548,52550],{"className":52549},[886],[888,52551,52552],{"xmlns":890},[892,52553,52554,52602],{},[895,52555,52556,52558,52560,52562,52574,52576,52578,52580,52582,52584,52586,52588,52590,52596],{},[898,52557,2777],{},[898,52559,8673],{},[1996,52561,1998],{},[9166,52563,52564,52566,52568],{},[1996,52565,11170],{},[2129,52567,2327],{},[2272,52569,52570,52572],{},[898,52571,2789],{},[2129,52573,2327],{},[898,52575,4183],{},[1996,52577,2005],{"stretchy":2004},[898,52579,2789],{},[1996,52581,2011],{"stretchy":2004},[2288,52583,2987],{},[898,52585,2194],{},[898,52587,2789],{},[1996,52589,2225],{},[2272,52591,52592,52594],{},[898,52593,3937],{},[2129,52595,2327],{},[2272,52597,52598,52600],{},[898,52599,2789],{},[2129,52601,2327],{},[902,52603,52604],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,52607,52608],{},"mínus"," obdélník)",[123,52611,52612,52670,52671,52673],{},[883,52613,52615],{"className":52614},[886],[888,52616,52617],{"xmlns":890},[892,52618,52619,52667],{},[895,52620,52621,52623,52625,52627,52633,52639,52641,52653,52655,52657,52659,52661,52663,52665],{},[898,52622,3937],{},[898,52624,8673],{},[1996,52626,1998],{},[2272,52628,52629,52631],{},[898,52630,3937],{},[2129,52632,2327],{},[2272,52634,52635,52637],{},[898,52636,2789],{},[2129,52638,2327],{},[1996,52640,2225],{},[9166,52642,52643,52645,52647],{},[1996,52644,11170],{},[2129,52646,2327],{},[2272,52648,52649,52651],{},[898,52650,2789],{},[2129,52652,2327],{},[898,52654,8673],{},[1996,52656,2005],{"stretchy":2004},[898,52658,2789],{},[1996,52660,2011],{"stretchy":2004},[2288,52662,2987],{},[898,52664,2194],{},[898,52666,2789],{},[902,52668,52669],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,52672,52608],{}," integrál)",[123,52675,52676,52677,52680],{},"Kontrola znaménka: obě hodnoty musí být ",[38,52678,52679],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[36972,52682],{},[115,52684,52686],{"id":52685},"příklady","Příklady",[198,52688,52690],{"id":52689},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[3867,52692,52693],{},[724,52694,52695,52698,52699,47723,52722,52745,52746,1343,52766,1343,52783,1343,52800,52817,52818,52894,52895,52912,52913,52926],{},[883,52696,52697],{},"!example"," Zadání\nJsou dány poptávka ",[883,52700,52702],{"className":52701},[886],[888,52703,52704],{"xmlns":890},[892,52705,52706,52720],{},[895,52707,52708,52710,52712,52714,52716,52718],{},[898,52709,3937],{},[1996,52711,1998],{},[898,52713,207],{},[898,52715,2789],{},[1996,52717,2095],{},[898,52719,2098],{},[902,52721,37062],{"encoding":904},[883,52723,52725],{"className":52724},[886],[888,52726,52727],{"xmlns":890},[892,52728,52729,52743],{},[895,52730,52731,52733,52735,52737,52739,52741],{},[898,52732,3937],{},[1996,52734,1998],{},[898,52736,2142],{},[898,52738,2789],{},[1996,52740,2095],{},[898,52742,2194],{},[902,52744,40244],{"encoding":904}," s hodnotami ",[883,52747,52749],{"className":52748},[886],[888,52750,52751],{"xmlns":890},[892,52752,52753,52763],{},[895,52754,52755,52757,52759,52761],{},[898,52756,207],{},[1996,52758,1998],{},[1996,52760,2225],{},[2129,52762,2173],{},[902,52764,52765],{"encoding":904},"a = -3",[883,52767,52769],{"className":52768},[886],[888,52770,52771],{"xmlns":890},[892,52772,52773,52781],{},[895,52774,52775,52777,52779],{},[898,52776,2098],{},[1996,52778,1998],{},[2129,52780,5211],{},[902,52782,48646],{"encoding":904},[883,52784,52786],{"className":52785},[886],[888,52787,52788],{"xmlns":890},[892,52789,52790,52798],{},[895,52791,52792,52794,52796],{},[898,52793,2142],{},[1996,52795,1998],{},[2129,52797,5009],{},[902,52799,48664],{"encoding":904},[883,52801,52803],{"className":52802},[886],[888,52804,52805],{"xmlns":890},[892,52806,52807,52815],{},[895,52808,52809,52811,52813],{},[898,52810,2194],{},[1996,52812,1998],{},[2129,52814,2863],{},[902,52816,48682],{"encoding":904},".\nRovnovážné množství:\n",[883,52819,52821],{"className":52820},[886],[888,52822,52823],{"xmlns":890},[892,52824,52825,52891],{},[895,52826,52827,52833,52835,52853,52855,52879,52881,52887,52889],{},[2124,52828,52829,52831],{},[898,52830,2789],{},[898,52832,4252],{},[1996,52834,1998],{},[2329,52836,52837,52845],{},[895,52838,52839,52841,52843],{},[898,52840,2098],{},[1996,52842,2225],{},[898,52844,2194],{},[895,52846,52847,52849,52851],{},[898,52848,2142],{},[1996,52850,2225],{},[898,52852,207],{},[1996,52854,1998],{},[2329,52856,52857,52865],{},[895,52858,52859,52861,52863],{},[2129,52860,5211],{},[1996,52862,2225],{},[2129,52864,2863],{},[895,52866,52867,52869,52871,52873,52875,52877],{},[2129,52868,5009],{},[1996,52870,2225],{},[1996,52872,2005],{"stretchy":2004},[1996,52874,2225],{},[2129,52876,2173],{},[1996,52878,2011],{"stretchy":2004},[1996,52880,1998],{},[2329,52882,52883,52885],{},[2129,52884,38021],{},[2129,52886,44408],{},[1996,52888,5900],{},[2129,52890,44413],{},[902,52892,52893],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,52896,52898],{"className":52897},[886],[888,52899,52900],{"xmlns":890},[892,52901,52902,52910],{},[895,52903,52904],{},[2124,52905,52906,52908],{},[898,52907,2789],{},[898,52909,4252],{},[902,52911,42405],{"encoding":904}," (a) při změně samotného parametru ",[883,52914,52916],{"className":52915},[886],[888,52917,52918],{"xmlns":890},[892,52919,52920,52924],{},[895,52921,52922],{},[898,52923,2142],{},[902,52925,2142],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,52928,52929],{},[38,52930,52931,52932,2671,52945,2685,52958,9295],{},"Řešení (a) — změna ",[883,52933,52935],{"className":52934},[886],[888,52936,52937],{"xmlns":890},[892,52938,52939,52943],{},[895,52940,52941],{},[898,52942,2142],{},[902,52944,2142],{"encoding":904},[883,52946,52948],{"className":52947},[886],[888,52949,52950],{"xmlns":890},[892,52951,52952,52956],{},[895,52953,52954],{},[2129,52955,5009],{},[902,52957,44448],{"encoding":904},[883,52959,52961],{"className":52960},[886],[888,52962,52963],{"xmlns":890},[892,52964,52965,52969],{},[895,52966,52967],{},[2129,52968,19323],{},[902,52970,44462],{"encoding":904},[724,52972,52973,52974,53038,53039,2704],{},"Pomocí vzorce (2.13) pro ",[883,52975,52977],{"className":52976},[886],[888,52978,52979],{"xmlns":890},[892,52980,52981,53035],{},[895,52982,52983,53003,53005,53007],{},[2325,52984,52985],{"scriptlevel":2327,"displaystyle":2285},[2329,52986,52987,52997],{},[895,52988,52989,52991],{},[898,52990,9872],{"mathvariant":2376},[2124,52992,52993,52995],{},[898,52994,2789],{},[898,52996,4252],{},[895,52998,52999,53001],{},[898,53000,9872],{"mathvariant":2376},[898,53002,2142],{},[1996,53004,1998],{},[1996,53006,2225],{},[2325,53008,53009],{"scriptlevel":2327,"displaystyle":2285},[2329,53010,53011,53019],{},[895,53012,53013,53015,53017],{},[898,53014,2098],{},[1996,53016,2225],{},[898,53018,2194],{},[895,53020,53021,53023,53025,53027,53029],{},[1996,53022,2005],{"stretchy":2004},[898,53024,2142],{},[1996,53026,2225],{},[898,53028,207],{},[2124,53030,53031,53033],{},[1996,53032,2011],{"stretchy":2004},[2129,53034,2131],{},[902,53036,53037],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,53040,53042],{"className":53041},[886],[888,53043,53044],{"xmlns":890},[892,53045,53046,53068],{},[895,53047,53048,53050],{},[1996,53049,2225],{},[2325,53051,53052],{"scriptlevel":2327,"displaystyle":2285},[2329,53053,53054,53060],{},[2124,53055,53056,53058],{},[898,53057,2789],{},[898,53059,4252],{},[895,53061,53062,53064,53066],{},[898,53063,2142],{},[1996,53065,2225],{},[898,53067,207],{},[902,53069,53070],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,53072,53074],{"className":53073},[886],[888,53075,53076],{"xmlns":890,"display":28068},[892,53077,53078,53134],{},[895,53079,53080,53082,53088,53090,53092,53108,53110,53112,53114,53116,53118,53124,53126,53128,53130,53132],{},[898,53081,2194],{},[2124,53083,53084,53086],{},[898,53085,2789],{},[898,53087,4252],{},[1996,53089,1998],{},[1996,53091,2225],{},[2329,53093,53094,53100],{},[2124,53095,53096,53098],{},[898,53097,2789],{},[898,53099,4252],{},[895,53101,53102,53104,53106],{},[898,53103,2142],{},[1996,53105,2225],{},[898,53107,207],{},[2288,53109,2987],{},[898,53111,2194],{},[898,53113,2142],{},[1996,53115,1998],{},[1996,53117,2225],{},[2329,53119,53120,53122],{},[2129,53121,44576],{},[2129,53123,44408],{},[1996,53125,3177],{},[2129,53127,2794],{},[1996,53129,5900],{},[1996,53131,2225],{},[2129,53133,44548],{},[902,53135,53136],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,53138,53139],{},"Nové rovnovážné množství:",[883,53141,53143],{"className":53142},[886],[888,53144,53145],{"xmlns":890,"display":28068},[892,53146,53147,53170],{},[895,53148,53149,53157,53159,53161,53163,53165,53167],{},[9166,53150,53151,53153,53155],{},[898,53152,2789],{},[2129,53154,2278],{},[898,53156,4252],{},[1996,53158,2730],{},[2129,53160,44576],{},[1996,53162,2225],{},[2129,53164,44581],{},[1996,53166,1998],{},[2129,53168,53169],{},"8,326.",[902,53171,53172],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,53174,53175,2203,53178,1343,53205,1343,53227,1343,53249,5589,53271,1343,53290,1343,53311,1343,53330,1975],{},[38,53176,53177],{},"Řešení (b) — současná změna všech parametrů:",[883,53179,53181],{"className":53180},[886],[888,53182,53183],{"xmlns":890},[892,53184,53185,53202],{},[895,53186,53187,53189,53191,53193,53195,53197,53199],{},[898,53188,207],{},[1996,53190,2704],{},[1996,53192,2225],{},[2129,53194,2173],{},[1996,53196,3123],{},[1996,53198,2225],{},[2129,53200,53201],{},"2,5",[902,53203,53204],{"encoding":904},"a: -3 \\to -2{,}5",[883,53206,53208],{"className":53207},[886],[888,53209,53210],{"xmlns":890},[892,53211,53212,53224],{},[895,53213,53214,53216,53218,53220,53222],{},[898,53215,2098],{},[1996,53217,2704],{},[2129,53219,5211],{},[1996,53221,3123],{},[2129,53223,15040],{},[902,53225,53226],{"encoding":904},"b: 40 \\to 35",[883,53228,53230],{"className":53229},[886],[888,53231,53232],{"xmlns":890},[892,53233,53234,53246],{},[895,53235,53236,53238,53240,53242,53244],{},[898,53237,2142],{},[1996,53239,2704],{},[2129,53241,5009],{},[1996,53243,3123],{},[2129,53245,19323],{},[902,53247,53248],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,53250,53252],{"className":53251},[886],[888,53253,53254],{"xmlns":890},[892,53255,53256,53268],{},[895,53257,53258,53260,53262,53264,53266],{},[898,53259,2194],{},[1996,53261,2704],{},[2129,53263,2863],{},[1996,53265,3123],{},[2129,53267,2904],{},[902,53269,53270],{"encoding":904},"d: 10 \\to 11",[883,53272,53274],{"className":53273},[886],[888,53275,53276],{"xmlns":890},[892,53277,53278,53288],{},[895,53279,53280,53282,53284,53286],{},[898,53281,2194],{},[898,53283,207],{},[1996,53285,1998],{},[2129,53287,5009],{},[902,53289,44614],{"encoding":904},[883,53291,53293],{"className":53292},[886],[888,53294,53295],{"xmlns":890},[892,53296,53297,53309],{},[895,53298,53299,53301,53303,53305,53307],{},[898,53300,2194],{},[898,53302,2098],{},[1996,53304,1998],{},[1996,53306,2225],{},[2129,53308,2228],{},[902,53310,44636],{"encoding":904},[883,53312,53314],{"className":53313},[886],[888,53315,53316],{"xmlns":890},[892,53317,53318,53328],{},[895,53319,53320,53322,53324,53326],{},[898,53321,2194],{},[898,53323,2142],{},[1996,53325,1998],{},[2129,53327,2794],{},[902,53329,44656],{"encoding":904},[883,53331,53333],{"className":53332},[886],[888,53334,53335],{"xmlns":890},[892,53336,53337,53347],{},[895,53338,53339,53341,53343,53345],{},[898,53340,2194],{},[898,53342,2194],{},[1996,53344,1998],{},[2129,53346,2278],{},[902,53348,44676],{"encoding":904},[724,53350,53351,53352,53410],{},"Totální diferenciál ",[883,53353,53355],{"className":53354},[886],[888,53356,53357],{"xmlns":890},[892,53358,53359,53407],{},[895,53360,53361,53367,53369,53371,53373,53375,53377,53379,53381,53383,53385,53387],{},[2124,53362,53363,53365],{},[898,53364,2789],{},[898,53366,4252],{},[1996,53368,2005],{"stretchy":2004},[898,53370,207],{},[1996,53372,2286],{"separator":2285},[898,53374,2098],{},[1996,53376,2286],{"separator":2285},[898,53378,2142],{},[1996,53380,2286],{"separator":2285},[898,53382,2194],{},[1996,53384,2011],{"stretchy":2004},[1996,53386,1998],{},[2325,53388,53389],{"scriptlevel":2327,"displaystyle":2285},[2329,53390,53391,53399],{},[895,53392,53393,53395,53397],{},[898,53394,2098],{},[1996,53396,2225],{},[898,53398,2194],{},[895,53400,53401,53403,53405],{},[898,53402,2142],{},[1996,53404,2225],{},[898,53406,207],{},[902,53408,53409],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,53412,53414],{"className":53413},[886],[888,53415,53416],{"xmlns":890,"display":28068},[892,53417,53418,53538],{},[895,53419,53420,53422,53428,53430,53456,53458,53460,53462,53464,53476,53478,53480,53482,53484,53510,53512,53514,53516,53518,53530,53532,53534,53536],{},[898,53421,2194],{},[2124,53423,53424,53426],{},[898,53425,2789],{},[898,53427,4252],{},[1996,53429,1998],{},[2329,53431,53432,53440],{},[895,53433,53434,53436,53438],{},[898,53435,2098],{},[1996,53437,2225],{},[898,53439,2194],{},[895,53441,53442,53444,53446,53448,53450],{},[1996,53443,2005],{"stretchy":2004},[898,53445,2142],{},[1996,53447,2225],{},[898,53449,207],{},[2124,53451,53452,53454],{},[1996,53453,2011],{"stretchy":2004},[2129,53455,2131],{},[2288,53457,2987],{},[898,53459,2194],{},[898,53461,207],{},[1996,53463,2095],{},[2329,53465,53466,53468],{},[2129,53467,2278],{},[895,53469,53470,53472,53474],{},[898,53471,2142],{},[1996,53473,2225],{},[898,53475,207],{},[2288,53477,2987],{},[898,53479,2194],{},[898,53481,2098],{},[1996,53483,2225],{},[2329,53485,53486,53494],{},[895,53487,53488,53490,53492],{},[898,53489,2098],{},[1996,53491,2225],{},[898,53493,2194],{},[895,53495,53496,53498,53500,53502,53504],{},[1996,53497,2005],{"stretchy":2004},[898,53499,2142],{},[1996,53501,2225],{},[898,53503,207],{},[2124,53505,53506,53508],{},[1996,53507,2011],{"stretchy":2004},[2129,53509,2131],{},[2288,53511,2987],{},[898,53513,2194],{},[898,53515,2142],{},[1996,53517,2225],{},[2329,53519,53520,53522],{},[2129,53521,2278],{},[895,53523,53524,53526,53528],{},[898,53525,2142],{},[1996,53527,2225],{},[898,53529,207],{},[2288,53531,2987],{},[898,53533,2194],{},[898,53535,2194],{},[898,53537,1975],{"mathvariant":2376},[902,53539,53540],{"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.",[724,53542,53543,53544,1343,53566,1343,53597,3151],{},"Dosazením číselných hodnot (",[883,53545,53547],{"className":53546},[886],[888,53548,53549],{"xmlns":890},[892,53550,53551,53563],{},[895,53552,53553,53555,53557,53559,53561],{},[898,53554,2142],{},[1996,53556,2225],{},[898,53558,207],{},[1996,53560,1998],{},[2129,53562,44408],{},[902,53564,53565],{"encoding":904},"c - a = 3{,}5",[883,53567,53569],{"className":53568},[886],[888,53570,53571],{"xmlns":890},[892,53572,53573,53594],{},[895,53574,53575,53577,53579,53581,53583,53589,53591],{},[1996,53576,2005],{"stretchy":2004},[898,53578,2142],{},[1996,53580,2225],{},[898,53582,207],{},[2124,53584,53585,53587],{},[1996,53586,2011],{"stretchy":2004},[2129,53588,2131],{},[1996,53590,1998],{},[2129,53592,53593],{},"12,25",[902,53595,53596],{"encoding":904},"(c-a)^2 = 12{,}25",[883,53598,53600],{"className":53599},[886],[888,53601,53602],{"xmlns":890},[892,53603,53604,53616],{},[895,53605,53606,53608,53610,53612,53614],{},[898,53607,2098],{},[1996,53609,2225],{},[898,53611,2194],{},[1996,53613,1998],{},[2129,53615,38021],{},[902,53617,53618],{"encoding":904},"b - d = 30",[883,53620,53622],{"className":53621},[886],[888,53623,53624],{"xmlns":890,"display":28068},[892,53625,53626,53727],{},[895,53627,53628,53630,53636,53638,53646,53648,53650,53652,53654,53662,53664,53666,53668,53670,53672,53680,53682,53684,53686,53688,53696,53698,53700,53702,53704,53707,53709,53712,53714,53716,53718,53721,53723,53725],{},[898,53629,2194],{},[2124,53631,53632,53634],{},[898,53633,2789],{},[898,53635,4252],{},[1996,53637,2730],{},[2325,53639,53640],{"scriptlevel":2327,"displaystyle":2004},[2329,53641,53642,53644],{},[2129,53643,38021],{},[2129,53645,53593],{},[1996,53647,2005],{"stretchy":2004},[2129,53649,5009],{},[1996,53651,2011],{"stretchy":2004},[1996,53653,2095],{},[2325,53655,53656],{"scriptlevel":2327,"displaystyle":2004},[2329,53657,53658,53660],{},[2129,53659,2278],{},[2129,53661,44408],{},[1996,53663,2005],{"stretchy":2004},[1996,53665,2225],{},[2129,53667,2228],{},[1996,53669,2011],{"stretchy":2004},[1996,53671,2225],{},[2325,53673,53674],{"scriptlevel":2327,"displaystyle":2004},[2329,53675,53676,53678],{},[2129,53677,38021],{},[2129,53679,53593],{},[1996,53681,2005],{"stretchy":2004},[2129,53683,2794],{},[1996,53685,2011],{"stretchy":2004},[1996,53687,2225],{},[2325,53689,53690],{"scriptlevel":2327,"displaystyle":2004},[2329,53691,53692,53694],{},[2129,53693,2278],{},[2129,53695,44408],{},[1996,53697,2005],{"stretchy":2004},[2129,53699,2278],{},[1996,53701,2011],{"stretchy":2004},[1996,53703,5900],{},[2129,53705,53706],{},"1,224",[1996,53708,2225],{},[2129,53710,53711],{},"1,429",[1996,53713,2225],{},[2129,53715,44581],{},[1996,53717,2225],{},[2129,53719,53720],{},"0,286",[1996,53722,5900],{},[1996,53724,2225],{},[2129,53726,44827],{},[902,53728,53729],{"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.",[724,53731,30067,53732,1975],{},[883,53733,53735],{"className":53734},[886],[888,53736,53737],{"xmlns":890},[892,53738,53739,53761],{},[895,53740,53741,53749,53751,53753,53755,53757,53759],{},[9166,53742,53743,53745,53747],{},[898,53744,2789],{},[2129,53746,2278],{},[898,53748,4252],{},[1996,53750,2730],{},[2129,53752,44576],{},[1996,53754,2225],{},[2129,53756,44858],{},[1996,53758,5900],{},[2129,53760,44863],{},[902,53762,53763],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[3867,53765,53766],{},[724,53767,53768,53770,53771,53792,53793,53819,53820,53823,53824,53920,53921,53944,53945,53961],{},[883,53769,4412],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,53772,53774],{"className":53773},[886],[888,53775,53776],{"xmlns":890},[892,53777,53778,53790],{},[895,53779,53780,53782,53784,53786,53788],{},[898,53781,2889],{"mathvariant":2376},[898,53783,2789],{},[1996,53785,2730],{},[1996,53787,2225],{},[2129,53789,44893],{},[902,53791,44896],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,53794,53796],{"className":53795},[886],[888,53797,53798],{"xmlns":890},[892,53799,53800,53816],{},[895,53801,53802,53804,53810,53812,53814],{},[898,53803,2194],{},[2124,53805,53806,53808],{},[898,53807,2789],{},[898,53809,4252],{},[1996,53811,5900],{},[1996,53813,2225],{},[2129,53815,44858],{},[902,53817,53818],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,53821,53822],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,53825,53827],{"className":53826},[886],[888,53828,53829],{"xmlns":890},[892,53830,53831,53917],{},[895,53832,53833,53841,53843,53877,53879,53903,53905,53912,53914],{},[9166,53834,53835,53837,53839],{},[898,53836,2789],{},[2129,53838,2278],{},[898,53840,4252],{},[1996,53842,1998],{},[2329,53844,53845,53861],{},[895,53846,53847,53853,53855],{},[2124,53848,53849,53851],{},[898,53850,2098],{},[1996,53852,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,53854,2225],{},[2124,53856,53857,53859],{},[898,53858,2194],{},[1996,53860,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[895,53862,53863,53869,53871],{},[2124,53864,53865,53867],{},[898,53866,2142],{},[1996,53868,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,53870,2225],{},[2124,53872,53873,53875],{},[898,53874,207],{},[1996,53876,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,53878,1998],{},[2329,53880,53881,53889],{},[895,53882,53883,53885,53887],{},[2129,53884,15040],{},[1996,53886,2225],{},[2129,53888,2904],{},[895,53890,53891,53893,53895,53897,53899,53901],{},[2129,53892,19323],{},[1996,53894,2225],{},[1996,53896,2005],{"stretchy":2004},[1996,53898,2225],{},[2129,53900,53201],{},[1996,53902,2011],{"stretchy":2004},[1996,53904,1998],{},[2329,53906,53907,53909],{},[2129,53908,41802],{},[2129,53910,53911],{},"3,1",[1996,53913,5900],{},[2129,53915,53916],{},"7,742",[902,53918,53919],{"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 ",[883,53922,53924],{"className":53923},[886],[888,53925,53926],{"xmlns":890},[892,53927,53928,53941],{},[895,53929,53930,53932,53934,53936,53938],{},[898,53931,2889],{"mathvariant":2376},[898,53933,2789],{},[1996,53935,5900],{},[1996,53937,2225],{},[2129,53939,53940],{},"0,829",[902,53942,53943],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,53946,53948],{"className":53947},[886],[888,53949,53950],{"xmlns":890},[892,53951,53952,53958],{},[895,53953,53954,53956],{},[1996,53955,2225],{},[2129,53957,44893],{},[902,53959,53960],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,53963,53964],{},[614,53965,53966,53967,53980],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,53968,53970],{"className":53969},[886],[888,53971,53972],{"xmlns":890},[892,53973,53974,53978],{},[895,53975,53976],{},[898,53977,2789],{},[902,53979,2789],{"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.",[198,53982,53984,53985],{"id":53983},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,53986,53988],{"className":53987},[886],[888,53989,53990],{"xmlns":890},[892,53991,53992,53998],{},[895,53993,53994,53996],{},[898,53995,3937],{},[898,53997,8673],{},[902,53999,44971],{"encoding":904},[3867,54001,54002],{},[724,54003,54004,54006,54007,54041,54042,54064],{},[883,54005,52697],{}," Zadání\nPro nabídku ",[883,54008,54010],{"className":54009},[886],[888,54011,54012],{"xmlns":890},[892,54013,54014,54038],{},[895,54015,54016,54018,54020,54022,54024,54026,54028,54030,54032,54034,54036],{},[898,54017,3937],{},[1996,54019,1998],{},[898,54021,8673],{},[1996,54023,2005],{"stretchy":2004},[898,54025,2789],{},[1996,54027,2011],{"stretchy":2004},[1996,54029,1998],{},[2129,54031,2863],{},[1996,54033,2095],{},[2129,54035,2131],{},[898,54037,2789],{},[902,54039,54040],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,54043,54045],{"className":54044},[886],[888,54046,54047],{"xmlns":890},[892,54048,54049,54061],{},[895,54050,54051,54057,54059],{},[2272,54052,54053,54055],{},[898,54054,2789],{},[2129,54056,2327],{},[1996,54058,1998],{},[2129,54060,2863],{},[902,54062,54063],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,54066,54067],{},[38,54068,22772],{},[724,54070,54071],{},"Odpovídající cena:",[883,54073,54075],{"className":54074},[886],[888,54076,54077],{"xmlns":890,"display":28068},[892,54078,54079,54114],{},[895,54080,54081,54087,54089,54091,54093,54095,54097,54099,54101,54103,54105,54107,54109,54111],{},[2272,54082,54083,54085],{},[898,54084,3937],{},[2129,54086,2327],{},[1996,54088,1998],{},[898,54090,8673],{},[1996,54092,2005],{"stretchy":2004},[2129,54094,2863],{},[1996,54096,2011],{"stretchy":2004},[1996,54098,1998],{},[2129,54100,2863],{},[1996,54102,2095],{},[2129,54104,2131],{},[1996,54106,3177],{},[2129,54108,2863],{},[1996,54110,1998],{},[2129,54112,54113],{},"30.",[902,54115,54116],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,54118,54119],{},"Dle vzorce (2.15):",[883,54121,54123],{"className":54122},[886],[888,54124,54125],{"xmlns":890,"display":28068},[892,54126,54127,54235],{},[895,54128,54129,54131,54133,54135,54137,54139,54141,54147,54153,54155,54163,54165,54167,54169,54171,54173,54175,54177,54179,54181,54183,54185,54187,54189,54191,54194,54196,54198,54200,54206,54214,54216,54218,54220,54222,54224,54226,54228,54230,54232],{},[898,54130,3937],{},[898,54132,8673],{},[1996,54134,2005],{"stretchy":2004},[2129,54136,2863],{},[1996,54138,2011],{"stretchy":2004},[1996,54140,1998],{},[2272,54142,54143,54145],{},[898,54144,3937],{},[2129,54146,2327],{},[2272,54148,54149,54151],{},[898,54150,2789],{},[2129,54152,2327],{},[1996,54154,2225],{},[9166,54156,54157,54159,54161],{},[1996,54158,11170],{},[2129,54160,2327],{},[2129,54162,2863],{},[1996,54164,2005],{"stretchy":2004},[2129,54166,2863],{},[1996,54168,2095],{},[2129,54170,2131],{},[898,54172,2789],{},[1996,54174,2011],{"stretchy":2004},[2288,54176,2987],{},[898,54178,2194],{},[898,54180,2789],{},[1996,54182,1998],{},[2129,54184,2863],{},[1996,54186,3177],{},[2129,54188,38021],{},[1996,54190,2225],{},[1996,54192,2486],{"fence":2004,"stretchy":2285,"minsize":54193,"maxsize":54193},"1.8em",[2129,54195,2863],{},[898,54197,2789],{},[1996,54199,2095],{},[2124,54201,54202,54204],{},[898,54203,2789],{},[2129,54205,2131],{},[9166,54207,54208,54210,54212],{},[1996,54209,2501],{"fence":2004,"stretchy":2285,"minsize":54193,"maxsize":54193},[2129,54211,2327],{},[2129,54213,2863],{},[1996,54215,1998],{},[2129,54217,30083],{},[1996,54219,2225],{},[1996,54221,2005],{"stretchy":2004},[2129,54223,3090],{},[1996,54225,2095],{},[2129,54227,3090],{},[1996,54229,2011],{"stretchy":2004},[1996,54231,1998],{},[2129,54233,54234],{},"100.",[902,54236,54237],{"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.",[724,54239,54240,54241,54262,54263,54283],{},"Přebytek výrobce při množství ",[883,54242,54244],{"className":54243},[886],[888,54245,54246],{"xmlns":890},[892,54247,54248,54260],{},[895,54249,54250,54256,54258],{},[2272,54251,54252,54254],{},[898,54253,2789],{},[2129,54255,2327],{},[1996,54257,1998],{},[2129,54259,2863],{},[902,54261,54063],{"encoding":904}," je tedy ",[883,54264,54266],{"className":54265},[886],[888,54267,54268],{"xmlns":890},[892,54269,54270,54280],{},[895,54271,54272,54274,54276,54278],{},[898,54273,3937],{},[898,54275,8673],{},[1996,54277,1998],{},[2129,54279,3090],{},[902,54281,54282],{"encoding":904},"PS = 100"," (peněžních jednotek).",[36972,54285],{},[115,54287,54289],{"id":54288},"cheat-sheet","Cheat sheet",[16,54291,54292,54305],{},[19,54293,54294],{},[22,54295,54296,54299,54302],{},[25,54297,54298],{},"Veličina",[25,54300,54301],{},"Vzorec",[25,54303,54304],{},"Geometrie",[30,54306,54307,54425,54539,54607],{},[22,54308,54309,54337,54393],{},[35,54310,54311],{},[883,54312,54314],{"className":54313},[886],[888,54315,54316],{"xmlns":890},[892,54317,54318,54334],{},[895,54319,54320,54322,54324,54326,54332],{},[898,54321,2777],{},[898,54323,8673],{},[1996,54325,2005],{"stretchy":2004},[2272,54327,54328,54330],{},[898,54329,2789],{},[2129,54331,2327],{},[1996,54333,2011],{"stretchy":2004},[902,54335,54336],{"encoding":904},"CS(Q_0)",[35,54338,54339],{},[883,54340,54342],{"className":54341},[886],[888,54343,54344],{"xmlns":890},[892,54345,54346,54390],{},[895,54347,54348],{},[2325,54349,54350,54362,54364,54366,54368,54370,54372,54374,54376,54378,54384],{"scriptlevel":2327,"displaystyle":2285},[9166,54351,54352,54354,54356],{},[1996,54353,11170],{},[2129,54355,2327],{},[2272,54357,54358,54360],{},[898,54359,2789],{},[2129,54361,2327],{},[898,54363,4183],{},[1996,54365,2005],{"stretchy":2004},[898,54367,2789],{},[1996,54369,2011],{"stretchy":2004},[2288,54371,2987],{},[898,54373,2194],{},[898,54375,2789],{},[1996,54377,2225],{},[2272,54379,54380,54382],{},[898,54381,3937],{},[2129,54383,2327],{},[2272,54385,54386,54388],{},[898,54387,2789],{},[2129,54389,2327],{},[902,54391,54392],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,54394,54395,54396,54399,54400,54403,54404],{},"plocha ",[38,54397,54398],{},"pod"," křivkou poptávky, ",[38,54401,54402],{},"nad"," čárou ",[883,54405,54407],{"className":54406},[886],[888,54408,54409],{"xmlns":890},[892,54410,54411,54423],{},[895,54412,54413,54415,54417],{},[898,54414,3937],{},[1996,54416,1998],{},[2272,54418,54419,54421],{},[898,54420,3937],{},[2129,54422,2327],{},[902,54424,51679],{"encoding":904},[22,54426,54427,54455,54511],{},[35,54428,54429],{},[883,54430,54432],{"className":54431},[886],[888,54433,54434],{"xmlns":890},[892,54435,54436,54452],{},[895,54437,54438,54440,54442,54444,54450],{},[898,54439,3937],{},[898,54441,8673],{},[1996,54443,2005],{"stretchy":2004},[2272,54445,54446,54448],{},[898,54447,2789],{},[2129,54449,2327],{},[1996,54451,2011],{"stretchy":2004},[902,54453,54454],{"encoding":904},"PS(Q_0)",[35,54456,54457],{},[883,54458,54460],{"className":54459},[886],[888,54461,54462],{"xmlns":890},[892,54463,54464,54508],{},[895,54465,54466],{},[2325,54467,54468,54474,54480,54482,54494,54496,54498,54500,54502,54504,54506],{"scriptlevel":2327,"displaystyle":2285},[2272,54469,54470,54472],{},[898,54471,3937],{},[2129,54473,2327],{},[2272,54475,54476,54478],{},[898,54477,2789],{},[2129,54479,2327],{},[1996,54481,2225],{},[9166,54483,54484,54486,54488],{},[1996,54485,11170],{},[2129,54487,2327],{},[2272,54489,54490,54492],{},[898,54491,2789],{},[2129,54493,2327],{},[898,54495,8673],{},[1996,54497,2005],{"stretchy":2004},[898,54499,2789],{},[1996,54501,2011],{"stretchy":2004},[2288,54503,2987],{},[898,54505,2194],{},[898,54507,2789],{},[902,54509,54510],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,54512,54395,54513,54515,54516,54403,54518],{},[38,54514,54402],{}," křivkou nabídky, ",[38,54517,54398],{},[883,54519,54521],{"className":54520},[886],[888,54522,54523],{"xmlns":890},[892,54524,54525,54537],{},[895,54526,54527,54529,54531],{},[898,54528,3937],{},[1996,54530,1998],{},[2272,54532,54533,54535],{},[898,54534,3937],{},[2129,54536,2327],{},[902,54538,51679],{"encoding":904},[22,54540,54541,54544,54571],{},[35,54542,54543],{},"Výdaje \u002F tržby",[35,54545,54546],{},[883,54547,54549],{"className":54548},[886],[888,54550,54551],{"xmlns":890},[892,54552,54553,54569],{},[895,54554,54555,54561,54563],{},[2272,54556,54557,54559],{},[898,54558,3937],{},[2129,54560,2327],{},[1996,54562,3177],{},[2272,54564,54565,54567],{},[898,54566,2789],{},[2129,54568,2327],{},[902,54570,52539],{"encoding":904},[35,54572,54573,54574],{},"obdélník ",[883,54575,54577],{"className":54576},[886],[888,54578,54579],{"xmlns":890},[892,54580,54581,54605],{},[895,54582,54583,54585,54587,54593,54595,54597,54599],{},[2129,54584,2327],{},[2288,54586,2987],{},[2272,54588,54589,54591],{},[898,54590,2789],{},[2129,54592,2327],{},[2288,54594,2987],{},[898,54596,4255],{},[2288,54598,2987],{},[2272,54600,54601,54603],{},[898,54602,3937],{},[2129,54604,2327],{},[902,54606,51159],{"encoding":904},[22,54608,54609,54612,54635],{},[35,54610,54611],{},"Celkový přebytek",[35,54613,54614],{},[883,54615,54617],{"className":54616},[886],[888,54618,54619],{"xmlns":890},[892,54620,54621,54633],{},[895,54622,54623,54625,54627,54629,54631],{},[898,54624,2777],{},[898,54626,8673],{},[1996,54628,2095],{},[898,54630,3937],{},[898,54632,8673],{},[902,54634,50897],{"encoding":904},[35,54636,54637],{},"součet obou ploch v rovnováze",[36972,54639],{},[115,54641,15722],{"id":15721},[120,54643,54644,54666,54688,54732,54776,54839,54867],{},[123,54645,54646,10025,54648,1343,54663,54665],{},[38,54647,44936],{},[883,54649,54651],{"className":54650},[886],[888,54652,54653],{"xmlns":890},[892,54654,54655,54661],{},[895,54656,54657,54659],{},[898,54658,2777],{},[898,54660,8673],{},[902,54662,44952],{"encoding":904},[614,54664,44990],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,54667,54668,10025,54670,1343,54685,54687],{},[38,54669,45083],{},[883,54671,54673],{"className":54672},[886],[888,54674,54675],{"xmlns":890},[892,54676,54677,54683],{},[895,54678,54679,54681],{},[898,54680,3937],{},[898,54682,8673],{},[902,54684,44971],{"encoding":904},[614,54686,45086],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,54689,54690,7015,54693,1975],{},[38,54691,54692],{},"Ochota platit",[883,54694,54696],{"className":54695},[886],[888,54697,54698],{"xmlns":890},[892,54699,54700,54730],{},[895,54701,54702],{},[2325,54703,54704,54716,54718,54720,54722,54724,54726,54728],{"scriptlevel":2327,"displaystyle":2285},[9166,54705,54706,54708,54710],{},[1996,54707,11170],{},[2129,54709,2327],{},[2272,54711,54712,54714],{},[898,54713,2789],{},[2129,54715,2327],{},[898,54717,4183],{},[1996,54719,2005],{"stretchy":2004},[898,54721,2789],{},[1996,54723,2011],{"stretchy":2004},[2288,54725,2987],{},[898,54727,2194],{},[898,54729,2789],{},[902,54731,51527],{"encoding":904},[123,54733,54734,7015,54737,1975],{},[38,54735,54736],{},"Minimální cena výrobce",[883,54738,54740],{"className":54739},[886],[888,54741,54742],{"xmlns":890},[892,54743,54744,54774],{},[895,54745,54746],{},[2325,54747,54748,54760,54762,54764,54766,54768,54770,54772],{"scriptlevel":2327,"displaystyle":2285},[9166,54749,54750,54752,54754],{},[1996,54751,11170],{},[2129,54753,2327],{},[2272,54755,54756,54758],{},[898,54757,2789],{},[2129,54759,2327],{},[898,54761,8673],{},[1996,54763,2005],{"stretchy":2004},[898,54765,2789],{},[1996,54767,2011],{"stretchy":2004},[2288,54769,2987],{},[898,54771,2194],{},[898,54773,2789],{},[902,54775,52169],{"encoding":904},[123,54777,54778,7015,54781,52670,54806,3918],{},[38,54779,54780],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,54782,54784],{"className":54783},[886],[888,54785,54786],{"xmlns":890},[892,54787,54788,54804],{},[895,54789,54790,54796,54798],{},[2272,54791,54792,54794],{},[898,54793,3937],{},[2129,54795,2327],{},[2288,54797,2987],{},[2272,54799,54800,54802],{},[898,54801,2789],{},[2129,54803,2327],{},[902,54805,51605],{"encoding":904},[883,54807,54809],{"className":54808},[886],[888,54810,54811],{"xmlns":890},[892,54812,54813,54837],{},[895,54814,54815,54817,54819,54825,54827,54829,54831],{},[2129,54816,2327],{},[2288,54818,2987],{},[2272,54820,54821,54823],{},[898,54822,2789],{},[2129,54824,2327],{},[2288,54826,2987],{},[898,54828,4255],{},[2288,54830,2987],{},[2272,54832,54833,54835],{},[898,54834,3937],{},[2129,54836,2327],{},[902,54838,51159],{"encoding":904},[123,54840,54841,54844,54845,54866],{},[38,54842,54843],{},"Celkový přebytek trhu"," — součet ",[883,54846,54848],{"className":54847},[886],[888,54849,54850],{"xmlns":890},[892,54851,54852,54864],{},[895,54853,54854,54856,54858,54860,54862],{},[898,54855,2777],{},[898,54857,8673],{},[1996,54859,2095],{},[898,54861,3937],{},[898,54863,8673],{},[902,54865,50897],{"encoding":904}," v rovnovážném bodě.",[123,54868,54869,54871,54872,1343,54885,54898,54899,1975],{},[38,54870,2444],{}," — plochy ohraničené křivkami ",[883,54873,54875],{"className":54874},[886],[888,54876,54877],{"xmlns":890},[892,54878,54879,54883],{},[895,54880,54881],{},[898,54882,4183],{},[902,54884,4183],{"encoding":904},[883,54886,54888],{"className":54887},[886],[888,54889,54890],{"xmlns":890},[892,54891,54892,54896],{},[895,54893,54894],{},[898,54895,8673],{},[902,54897,8673],{"encoding":904}," a přímkou ",[883,54900,54902],{"className":54901},[886],[888,54903,54904],{"xmlns":890},[892,54905,54906,54918],{},[895,54907,54908,54910,54912],{},[898,54909,3937],{},[1996,54911,1998],{},[2272,54913,54914,54916],{},[898,54915,3937],{},[2129,54917,2327],{},[902,54919,51679],{"encoding":904},[36972,54921],{},[115,54923,54925],{"id":54924},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,54927,54928,54929,54942,54943,54960],{},"Uvalení jednotkové daně ",[883,54930,54932],{"className":54931},[886],[888,54933,54934],{"xmlns":890},[892,54935,54936,54940],{},[895,54937,54938],{},[898,54939,2774],{},[902,54941,2774],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,54944,54946],{"className":54945},[886],[888,54947,54948],{"xmlns":890},[892,54949,54950,54958],{},[895,54951,54952],{},[2124,54953,54954,54956],{},[898,54955,2789],{},[898,54957,4252],{},[902,54959,42405],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,54962,54963],{},[2559,54964],{"alt":54965,"className":54966,"src":54967},"imek-prebytky-s-dani-deadweight",[210,2563],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,54969,54970,54971,54986,54987,55002,55003,52670,55006,55030,55031,10025,55034,55037,55038,1975],{},"Přebytek spotřebitele ",[883,54972,54974],{"className":54973},[886],[888,54975,54976],{"xmlns":890},[892,54977,54978,54984],{},[895,54979,54980,54982],{},[898,54981,2777],{},[898,54983,8673],{},[902,54985,44952],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,54988,54990],{"className":54989},[886],[888,54991,54992],{"xmlns":890},[892,54993,54994,55000],{},[895,54995,54996,54998],{},[898,54997,3937],{},[898,54999,8673],{},[902,55001,44971],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,55004,55005],{},"daňový příjem",[883,55007,55009],{"className":55008},[886],[888,55010,55011],{"xmlns":890},[892,55012,55013,55027],{},[895,55014,55015,55017,55019],{},[898,55016,2774],{},[1996,55018,3177],{},[9166,55020,55021,55023,55025],{},[898,55022,2789],{},[2129,55024,2278],{},[898,55026,4252],{},[902,55028,55029],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,55032,55033],{},"mrtvá ztráta",[614,55035,55036],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,55039,811],{"className":55040,"dataFsResolvedFilePath":809,"href":810},[210],[36972,55042],{},[115,55044,3792],{"id":3791},[120,55046,55047,55054,55066,55073,55080],{},[123,55048,55049,2203,55051],{},[38,55050,16223],{},[207,55052,802],{"className":55053,"dataFsResolvedFilePath":800,"href":801},[210],[123,55055,55056,2203,55058,55061,55062,55065],{},[38,55057,36676],{},[207,55059,775],{"className":55060,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,55063,2357],{"className":55064,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,55067,55068,2203,55070],{},[38,55069,16233],{},[207,55071,3823],{"className":55072,"dataFsResolvedFilePath":827,"href":828},[210],[123,55074,55075,2203,55077],{},[38,55076,50760],{},[207,55078,50764],{"className":55079,"dataFsResolvedFilePath":745,"href":746},[210],[123,55081,55082,2203,55084],{},[38,55083,16206],{},[207,55085,16210],{"className":55086,"dataFsResolvedFilePath":1960,"href":1961},[210],{"title":641,"searchDepth":642,"depth":642,"links":55088},[55089,55090,55095,55100,55105,55106,55107,55108],{"id":50956,"depth":642,"text":1241},{"id":51300,"depth":642,"text":55091,"children":55092},"Přebytek spotřebitele (CSCS)",[55093,55094],{"id":51319,"depth":649,"text":51320},{"id":2443,"depth":649,"text":2444},{"id":51895,"depth":642,"text":55096,"children":55097},"Přebytek výrobce (PSPS)",[55098,55099],{"id":51914,"depth":649,"text":51915},{"id":52077,"depth":649,"text":2444},{"id":52685,"depth":642,"text":52686,"children":55101},[55102,55103],{"id":52689,"depth":649,"text":52690},{"id":53983,"depth":649,"text":55104},"Příklad 2.13 — numerický výpočet PSPS",{"id":54288,"depth":642,"text":54289},{"id":15721,"depth":642,"text":15722},{"id":54924,"depth":642,"text":54925},{"id":3791,"depth":642,"text":3792},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,50826,55115,55116,11990,16241,55117,55118],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":55121,"title":55122,"body":55123,"course":1128,"courses":659,"created":9556,"description":641,"extension":661,"meta":74452,"navigation":664,"path":74453,"seo":74454,"sources":74455,"stem":74456,"tags":74457,"type":3857,"updated":677,"__hash__":74463},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":55124,"toc":74416},[55125,55128,55314,55316,55407,55412,55738,55742,55749,55753,55798,55865,55896,55946,55981,55985,56044,56049,56115,56233,56335,56339,56362,56440,56483,56487,56516,56583,56589,56703,56707,56787,56824,56876,57074,57138,57225,57229,57232,57311,57314,57432,57451,57516,57520,57612,57680,57721,57775,57843,57880,57884,57942,57972,58183,58255,58307,58473,58566,58601,58605,58609,58646,58711,58766,58770,58793,58882,58986,59055,59059,59156,59269,59325,59379,59437,59498,59501,59537,59602,59632,59861,59919,59953,59957,59984,60063,60177,60198,60277,60279,60387,60391,60529,60851,60855,60858,60862,60911,60915,61169,61321,61328,61401,61585,61590,61933,61937,61960,61962,61983,62042,62052,62101,62243,62317,62412,62527,62625,62743,62747,62816,62821,62933,63078,63129,63241,63283,63287,63307,63368,63395,63457,63461,63483,63552,63832,63839,63869,63876,64069,64073,64151,64156,64232,64235,64323,64399,64466,64515,64618,64691,64812,65163,65276,65378,65382,65385,65392,65395,65431,65490,65499,65648,65872,65876,65939,66118,66210,66265,66269,66325,66395,66447,66468,66549,66552,66627,66671,66675,66716,66759,66785,66789,66860,66956,67018,67070,67173,67251,67274,67303,67307,67473,67590,67662,67977,68137,68141,68192,68254,68289,68319,68419,68461,68630,68635,68731,68769,68773,68892,69193,69195,69230,69234,69238,69366,69498,69820,70008,70086,70090,70395,70508,70654,70839,70945,71177,71292,71374,71493,71591,71632,71636,71691,71835,71989,72149,72242,72436,72748,72879,73008,73012,73084,73126,73177,73179,74374,74376],[12,55126,55122],{"id":55127},"příjem-náklady-zisk-a-nabídka-firmy",[3867,55129,55130],{},[724,55131,55132,3874,55134,2203,55137,55152,55153,2203,55156,55171,55172,2203,55175,55203,55204,55226,55227,55251,55252,55274,55275,55278,55279,55295,55296,1975],{},[883,55133,3873],{},[38,55135,55136],{},"Příjem",[883,55138,55140],{"className":55139},[886],[888,55141,55142],{"xmlns":890},[892,55143,55144,55150],{},[895,55145,55146,55148],{},[898,55147,2774],{},[898,55149,3994],{},[902,55151,4094],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,55154,55155],{},"náklady",[883,55157,55159],{"className":55158},[886],[888,55160,55161],{"xmlns":890},[892,55162,55163,55169],{},[895,55164,55165,55167],{},[898,55166,2774],{},[898,55168,2777],{},[902,55170,3243],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,55173,55174],{},"zisk",[883,55176,55178],{"className":55177},[886],[888,55179,55180],{"xmlns":890},[892,55181,55182,55200],{},[895,55183,55184,55186,55188,55190,55192,55194,55196,55198],{},[898,55185,3937],{},[898,55187,3994],{},[1996,55189,1998],{},[898,55191,2774],{},[898,55193,3994],{},[1996,55195,2225],{},[898,55197,2774],{},[898,55199,2777],{},[902,55201,55202],{"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: ",[883,55205,55207],{"className":55206},[886],[888,55208,55209],{"xmlns":890},[892,55210,55211,55223],{},[895,55212,55213,55215,55217,55219,55221],{},[898,55214,4255],{},[898,55216,2777],{},[1996,55218,1998],{},[898,55220,2818],{},[898,55222,2777],{},[902,55224,55225],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,55228,55230],{"className":55229},[886],[888,55231,55232],{"xmlns":890},[892,55233,55234,55248],{},[895,55235,55236,55238,55240,55242,55244,55246],{},[898,55237,4255],{},[898,55239,40341],{},[898,55241,2777],{},[1996,55243,1998],{},[898,55245,2818],{},[898,55247,2777],{},[902,55249,55250],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,55253,55255],{"className":55254},[886],[888,55256,55257],{"xmlns":890},[892,55258,55259,55271],{},[895,55260,55261,55263,55265,55267,55269],{},[898,55262,2818],{},[898,55264,3994],{},[1996,55266,1998],{},[898,55268,2818],{},[898,55270,2777],{},[902,55272,55273],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,55276,55277],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,55280,55282],{"className":55281},[886],[888,55283,55284],{"xmlns":890},[892,55285,55286,55292],{},[895,55287,55288,55290],{},[898,55289,2818],{},[898,55291,2777],{},[902,55293,55294],{"encoding":904},"MC"," nad bodem minima ",[883,55297,55299],{"className":55298},[886],[888,55300,55301],{"xmlns":890},[892,55302,55303,55311],{},[895,55304,55305,55307,55309],{},[898,55306,4255],{},[898,55308,40341],{},[898,55310,2777],{},[902,55312,55313],{"encoding":904},"AVC",[115,55315,1241],{"id":50956},[724,55317,55318,55319,55322,55323,55325,55326,1343,55329,1343,55332,55334,55335,55338,55339,55342,55343,55346,55347,2671,55362,1348,55377,2671,55392,3918],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,55320,55321],{},"příjmem"," (revenue) a ",[38,55324,55155],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,55327,55328],{},"zisku",[38,55330,55331],{},"bodů zvratu",[38,55333,1970],{}," a konstrukcí ",[38,55336,55337],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,55340,1145],{"className":55341,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,55344,11131],{"className":55345,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,55348,55350],{"className":55349},[886],[888,55351,55352],{"xmlns":890},[892,55353,55354,55360],{},[895,55355,55356,55358],{},[898,55357,2774],{},[898,55359,3994],{},[902,55361,4094],{"encoding":904},[883,55363,55365],{"className":55364},[886],[888,55366,55367],{"xmlns":890},[892,55368,55369,55375],{},[895,55370,55371,55373],{},[898,55372,2818],{},[898,55374,3994],{},[902,55376,6634],{"encoding":904},[883,55378,55380],{"className":55379},[886],[888,55381,55382],{"xmlns":890},[892,55383,55384,55390],{},[895,55385,55386,55388],{},[898,55387,2774],{},[898,55389,2777],{},[902,55391,3243],{"encoding":904},[883,55393,55395],{"className":55394},[886],[888,55396,55397],{"xmlns":890},[892,55398,55399,55405],{},[895,55400,55401,55403],{},[898,55402,2818],{},[898,55404,2777],{},[902,55406,55294],{"encoding":904},[724,55408,55409],{},[38,55410,55411],{},"Cílové znalosti:",[120,55413,55414,55578,55581,55584,55677,55724,55731],{},[123,55415,55416,55417,1343,55432,1343,55448,3885,55463,1343,55478,1343,55494,1343,55512,1343,55530,1343,55547,1343,55563,8425],{},"odvodit a interpretovat funkce ",[883,55418,55420],{"className":55419},[886],[888,55421,55422],{"xmlns":890},[892,55423,55424,55430],{},[895,55425,55426,55428],{},[898,55427,2774],{},[898,55429,3994],{},[902,55431,4094],{"encoding":904},[883,55433,55435],{"className":55434},[886],[888,55436,55437],{"xmlns":890},[892,55438,55439,55445],{},[895,55440,55441,55443],{},[898,55442,4255],{},[898,55444,3994],{},[902,55446,55447],{"encoding":904},"AR",[883,55449,55451],{"className":55450},[886],[888,55452,55453],{"xmlns":890},[892,55454,55455,55461],{},[895,55456,55457,55459],{},[898,55458,2818],{},[898,55460,3994],{},[902,55462,6634],{"encoding":904},[883,55464,55466],{"className":55465},[886],[888,55467,55468],{"xmlns":890},[892,55469,55470,55476],{},[895,55471,55472,55474],{},[898,55473,2774],{},[898,55475,2777],{},[902,55477,3243],{"encoding":904},[883,55479,55481],{"className":55480},[886],[888,55482,55483],{"xmlns":890},[892,55484,55485,55491],{},[895,55486,55487,55489],{},[898,55488,10436],{},[898,55490,2777],{},[902,55492,55493],{"encoding":904},"FC",[883,55495,55497],{"className":55496},[886],[888,55498,55499],{"xmlns":890},[892,55500,55501,55509],{},[895,55502,55503,55505,55507],{},[898,55504,2774],{},[898,55506,40341],{},[898,55508,2777],{},[902,55510,55511],{"encoding":904},"TVC",[883,55513,55515],{"className":55514},[886],[888,55516,55517],{"xmlns":890},[892,55518,55519,55527],{},[895,55520,55521,55523,55525],{},[898,55522,4255],{},[898,55524,10436],{},[898,55526,2777],{},[902,55528,55529],{"encoding":904},"AFC",[883,55531,55533],{"className":55532},[886],[888,55534,55535],{"xmlns":890},[892,55536,55537,55545],{},[895,55538,55539,55541,55543],{},[898,55540,4255],{},[898,55542,40341],{},[898,55544,2777],{},[902,55546,55313],{"encoding":904},[883,55548,55550],{"className":55549},[886],[888,55551,55552],{"xmlns":890},[892,55553,55554,55560],{},[895,55555,55556,55558],{},[898,55557,4255],{},[898,55559,2777],{},[902,55561,55562],{"encoding":904},"AC",[883,55564,55566],{"className":55565},[886],[888,55567,55568],{"xmlns":890},[892,55569,55570,55576],{},[895,55571,55572,55574],{},[898,55573,2818],{},[898,55575,2777],{},[902,55577,55294],{"encoding":904},[123,55579,55580],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,55582,55583],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,55585,55586,55587,55590,55591,41816,55633,8425],{},"osvojit si ",[38,55588,55589],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,55592,55594],{"className":55593},[886],[888,55595,55596],{"xmlns":890},[892,55597,55598,55630],{},[895,55599,55600,55602,55604,55606,55612,55614,55616,55618,55620,55622,55628],{},[898,55601,4255],{},[898,55603,2777],{},[1996,55605,2005],{"stretchy":2004},[2272,55607,55608,55610],{},[898,55609,2789],{},[2129,55611,2327],{},[1996,55613,2011],{"stretchy":2004},[1996,55615,1998],{},[898,55617,2818],{},[898,55619,2777],{},[1996,55621,2005],{"stretchy":2004},[2272,55623,55624,55626],{},[898,55625,2789],{},[2129,55627,2327],{},[1996,55629,2011],{"stretchy":2004},[902,55631,55632],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,55634,55636],{"className":55635},[886],[888,55637,55638],{"xmlns":890},[892,55639,55640,55674],{},[895,55641,55642,55644,55646,55648,55650,55656,55658,55660,55662,55664,55666,55672],{},[898,55643,4255],{},[898,55645,40341],{},[898,55647,2777],{},[1996,55649,2005],{"stretchy":2004},[2272,55651,55652,55654],{},[898,55653,2789],{},[2129,55655,2327],{},[1996,55657,2011],{"stretchy":2004},[1996,55659,1998],{},[898,55661,2818],{},[898,55663,2777],{},[1996,55665,2005],{"stretchy":2004},[2272,55667,55668,55670],{},[898,55669,2789],{},[2129,55671,2327],{},[1996,55673,2011],{"stretchy":2004},[902,55675,55676],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,55678,55586,55679,55590,55682,8425],{},[38,55680,55681],{},"princip maximalizace zisku",[883,55683,55685],{"className":55684},[886],[888,55686,55687],{"xmlns":890},[892,55688,55689,55721],{},[895,55690,55691,55693,55695,55697,55703,55705,55707,55709,55711,55713,55719],{},[898,55692,2818],{},[898,55694,3994],{},[1996,55696,2005],{"stretchy":2004},[2272,55698,55699,55701],{},[898,55700,2789],{},[2129,55702,2327],{},[1996,55704,2011],{"stretchy":2004},[1996,55706,1998],{},[898,55708,2818],{},[898,55710,2777],{},[1996,55712,2005],{"stretchy":2004},[2272,55714,55715,55717],{},[898,55716,2789],{},[2129,55718,2327],{},[1996,55720,2011],{"stretchy":2004},[902,55722,55723],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,55725,55726,55727,55730],{},"stanovit ",[38,55728,55729],{},"body zvratu"," a interval zisku;",[123,55732,55733,55734,55737],{},"zkonstruovat ",[38,55735,55736],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,55739,55741],{"id":55740},"příjem-firmy","Příjem firmy",[724,55743,55744],{},[2559,55745],{"alt":55746,"className":55747,"src":55748},"imek-ar-mr-dvojnasobny-sklon",[210,2563],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,55750,55752],{"id":55751},"celkový-příjem","Celkový příjem",[724,55754,55755,55756,10025,55771,55774,55775,29946],{},"Celkový příjem ",[883,55757,55759],{"className":55758},[886],[888,55760,55761],{"xmlns":890},[892,55762,55763,55769],{},[895,55764,55765,55767],{},[898,55766,2774],{},[898,55768,3994],{},[902,55770,4094],{"encoding":904},[38,55772,55773],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,55776,55778],{"className":55777},[886],[888,55779,55780],{"xmlns":890},[892,55781,55782,55796],{},[895,55783,55784,55786,55788,55790,55792,55794],{},[898,55785,3937],{},[1996,55787,1998],{},[898,55789,4183],{},[1996,55791,2005],{"stretchy":2004},[898,55793,2789],{},[1996,55795,2011],{"stretchy":2004},[902,55797,4640],{"encoding":904},[883,55799,55801],{"className":55800},[886],[888,55802,55803],{"xmlns":890,"display":28068},[892,55804,55805,55862],{},[20756,55806,55807],{"width":28073},[20761,55808,55809,55811,55855,55857],{},[20764,55810],{"width":28078},[20764,55812,55813],{},[895,55814,55815,55817,55819,55821,55823,55825,55827,55829,55831,55833,55835,55837,55839,55841,55843,55845,55847,55849,55851,55853],{},[898,55816,2774],{},[898,55818,3994],{},[1996,55820,1998],{},[898,55822,2774],{},[898,55824,3994],{},[1996,55826,2005],{"stretchy":2004},[898,55828,2789],{},[1996,55830,2011],{"stretchy":2004},[1996,55832,1998],{},[898,55834,3937],{},[1996,55836,3177],{},[898,55838,2789],{},[1996,55840,1998],{},[898,55842,4183],{},[1996,55844,2005],{"stretchy":2004},[898,55846,2789],{},[1996,55848,2011],{"stretchy":2004},[1996,55850,3177],{},[898,55852,2789],{},[898,55854,1975],{"mathvariant":2376},[20764,55856],{"width":28078},[20764,55858,55859],{},[2288,55860,55861],{},"(3.1)",[902,55863,55864],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,55866,55867,55868,55871,55872,55895],{},"Graf funkce se nazývá ",[38,55869,55870],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,55873,55875],{"className":55874},[886],[888,55876,55877],{"xmlns":890},[892,55878,55879,55893],{},[895,55880,55881,55883,55885,55887,55889,55891],{},[898,55882,3937],{},[1996,55884,1998],{},[898,55886,207],{},[898,55888,2789],{},[1996,55890,2095],{},[898,55892,2098],{},[902,55894,37062],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,55897,55899],{"className":55898},[886],[888,55900,55901],{"xmlns":890,"display":28068},[892,55902,55903,55943],{},[895,55904,55905,55907,55909,55911,55913,55915,55917,55919,55921,55923,55925,55927,55929,55935,55937,55939,55941],{},[898,55906,2774],{},[898,55908,3994],{},[1996,55910,1998],{},[898,55912,2789],{},[1996,55914,2005],{"stretchy":2004},[898,55916,207],{},[898,55918,2789],{},[1996,55920,2095],{},[898,55922,2098],{},[1996,55924,2011],{"stretchy":2004},[1996,55926,1998],{},[898,55928,207],{},[2124,55930,55931,55933],{},[898,55932,2789],{},[2129,55934,2131],{},[1996,55936,2095],{},[898,55938,2098],{},[898,55940,2789],{},[1996,55942,2286],{"separator":2285},[902,55944,55945],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,55947,55948,55949,55962,55963,55980],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,55950,55952],{"className":55951},[886],[888,55953,55954],{"xmlns":890},[892,55955,55956,55960],{},[895,55957,55958],{},[898,55959,900],{},[902,55961,900],{"encoding":904}," (jelikož ",[883,55964,55966],{"className":55965},[886],[888,55967,55968],{"xmlns":890},[892,55969,55970,55978],{},[895,55971,55972,55974,55976],{},[898,55973,207],{},[1996,55975,3447],{},[2129,55977,2327],{},[902,55979,43087],{"encoding":904},") procházející počátkem.",[37350,55982,55984],{"id":55983},"příklad-31","Příklad 3.1",[724,55986,55987,55990,55991,56027,56028,56043],{},[38,55988,55989],{},"Zadání."," Pro poptávku ",[883,55992,55994],{"className":55993},[886],[888,55995,55996],{"xmlns":890},[892,55997,55998,56024],{},[895,55999,56000,56002,56004,56006,56008,56010,56012,56014,56016,56018,56020,56022],{},[898,56001,3937],{},[1996,56003,1998],{},[898,56005,4183],{},[1996,56007,2005],{"stretchy":2004},[898,56009,2789],{},[1996,56011,2011],{"stretchy":2004},[1996,56013,1998],{},[1996,56015,2225],{},[2129,56017,2131],{},[898,56019,2789],{},[1996,56021,2095],{},[2129,56023,3090],{},[902,56025,56026],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,56029,56031],{"className":56030},[886],[888,56032,56033],{"xmlns":890},[892,56034,56035,56041],{},[895,56036,56037,56039],{},[898,56038,2774],{},[898,56040,3994],{},[902,56042,4094],{"encoding":904}," a charakterizujte jeho křivku.",[724,56045,56046,56048],{},[38,56047,22772],{}," Celkový příjem je",[883,56050,56052],{"className":56051},[886],[888,56053,56054],{"xmlns":890,"display":28068},[892,56055,56056,56112],{},[895,56057,56058,56060,56062,56064,56066,56068,56070,56072,56074,56076,56078,56080,56082,56084,56086,56088,56090,56092,56094,56096,56098,56104,56106,56108,56110],{},[898,56059,2774],{},[898,56061,3994],{},[1996,56063,1998],{},[898,56065,2774],{},[898,56067,3994],{},[1996,56069,2005],{"stretchy":2004},[898,56071,2789],{},[1996,56073,2011],{"stretchy":2004},[1996,56075,1998],{},[898,56077,2789],{},[1996,56079,2005],{"stretchy":2004},[1996,56081,2225],{},[2129,56083,2131],{},[898,56085,2789],{},[1996,56087,2095],{},[2129,56089,3090],{},[1996,56091,2011],{"stretchy":2004},[1996,56093,1998],{},[1996,56095,2225],{},[2129,56097,2131],{},[2124,56099,56100,56102],{},[898,56101,2789],{},[2129,56103,2131],{},[1996,56105,2095],{},[2129,56107,3090],{},[898,56109,2789],{},[898,56111,1975],{"mathvariant":2376},[902,56113,56114],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,56116,56117,56118,3885,56140,56162,56163,56181,56182,1975],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,56119,56121],{"className":56120},[886],[888,56122,56123],{"xmlns":890},[892,56124,56125,56137],{},[895,56126,56127,56133,56135],{},[2272,56128,56129,56131],{},[898,56130,2789],{},[2129,56132,2278],{},[1996,56134,1998],{},[2129,56136,2327],{},[902,56138,56139],{"encoding":904},"Q_1 = 0",[883,56141,56143],{"className":56142},[886],[888,56144,56145],{"xmlns":890},[892,56146,56147,56159],{},[895,56148,56149,56155,56157],{},[2272,56150,56151,56153],{},[898,56152,2789],{},[2129,56154,2131],{},[1996,56156,1998],{},[2129,56158,3120],{},[902,56160,56161],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,56164,56166],{"className":56165},[886],[888,56167,56168],{"xmlns":890},[892,56169,56170,56178],{},[895,56171,56172,56174,56176],{},[898,56173,2789],{},[1996,56175,1998],{},[2129,56177,5004],{},[902,56179,56180],{"encoding":904},"Q = 25"," ve výši ",[883,56183,56185],{"className":56184},[886],[888,56186,56187],{"xmlns":890},[892,56188,56189,56230],{},[895,56190,56191,56193,56203,56205,56207,56209,56211,56214,56216,56218,56220,56222,56224,56226,56228],{},[898,56192,2774],{},[2272,56194,56195,56197,56200],{},[898,56196,3994],{},[898,56198,56199],{},"max",[1996,56201,56202],{},"⁡",[1996,56204,1998],{},[1996,56206,2225],{},[2129,56208,2131],{},[1996,56210,3177],{},[2129,56212,56213],{},"625",[1996,56215,2095],{},[2129,56217,3090],{},[1996,56219,3177],{},[2129,56221,5004],{},[1996,56223,1998],{},[2129,56225,2278],{},[2288,56227,2987],{},[2129,56229,30745],{},[902,56231,56232],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,56234,56235],{},[614,56236,56237,56238,56272,56273,3885,56286,56299,56300,2624,56318,1975],{},"Obrázek 3.1: Parabola ",[883,56239,56241],{"className":56240},[886],[888,56242,56243],{"xmlns":890},[892,56244,56245,56269],{},[895,56246,56247,56249,56251,56253,56255,56257,56263,56265,56267],{},[898,56248,2774],{},[898,56250,3994],{},[1996,56252,1998],{},[1996,56254,2225],{},[2129,56256,2131],{},[2124,56258,56259,56261],{},[898,56260,2789],{},[2129,56262,2131],{},[1996,56264,2095],{},[2129,56266,3090],{},[898,56268,2789],{},[902,56270,56271],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,56274,56276],{"className":56275},[886],[888,56277,56278],{"xmlns":890},[892,56279,56280,56284],{},[895,56281,56282],{},[2129,56283,2327],{},[902,56285,2327],{"encoding":904},[883,56287,56289],{"className":56288},[886],[888,56290,56291],{"xmlns":890},[892,56292,56293,56297],{},[895,56294,56295],{},[2129,56296,3120],{},[902,56298,3120],{"encoding":904}," a maximem ",[883,56301,56303],{"className":56302},[886],[888,56304,56305],{"xmlns":890},[892,56306,56307,56315],{},[895,56308,56309,56311,56313],{},[2129,56310,2278],{},[2288,56312,2987],{},[2129,56314,30745],{},[902,56316,56317],{"encoding":904},"1\\,250",[883,56319,56321],{"className":56320},[886],[888,56322,56323],{"xmlns":890},[892,56324,56325,56333],{},[895,56326,56327,56329,56331],{},[898,56328,2789],{},[1996,56330,1998],{},[2129,56332,5004],{},[902,56334,56180],{"encoding":904},[198,56336,56338],{"id":56337},"průměrný-příjem","Průměrný příjem",[724,56340,56341,2203,56343,10025,56358,56361],{},[38,56342,56338],{},[883,56344,56346],{"className":56345},[886],[888,56347,56348],{"xmlns":890},[892,56349,56350,56356],{},[895,56351,56352,56354],{},[898,56353,4255],{},[898,56355,3994],{},[902,56357,55447],{"encoding":904},[38,56359,56360],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,56363,56365],{"className":56364},[886],[888,56366,56367],{"xmlns":890,"display":28068},[892,56368,56369,56437],{},[895,56370,56371,56373,56375,56377,56379,56381,56383,56385,56387,56389,56405,56407,56425,56427,56429,56431,56433,56435],{},[898,56372,4255],{},[898,56374,3994],{},[1996,56376,1998],{},[898,56378,4255],{},[898,56380,3994],{},[1996,56382,2005],{"stretchy":2004},[898,56384,2789],{},[1996,56386,2011],{"stretchy":2004},[1996,56388,1998],{},[2329,56390,56391,56403],{},[895,56392,56393,56395,56397,56399,56401],{},[898,56394,2774],{},[898,56396,3994],{},[1996,56398,2005],{"stretchy":2004},[898,56400,2789],{},[1996,56402,2011],{"stretchy":2004},[898,56404,2789],{},[1996,56406,1998],{},[2329,56408,56409,56423],{},[895,56410,56411,56413,56415,56417,56419,56421],{},[898,56412,2789],{},[2288,56414,2987],{},[898,56416,4183],{},[1996,56418,2005],{"stretchy":2004},[898,56420,2789],{},[1996,56422,2011],{"stretchy":2004},[898,56424,2789],{},[1996,56426,1998],{},[898,56428,4183],{},[1996,56430,2005],{"stretchy":2004},[898,56432,2789],{},[1996,56434,2011],{"stretchy":2004},[898,56436,1975],{"mathvariant":2376},[902,56438,56439],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[3867,56441,56442],{},[724,56443,56444,56447,56448,1343,56451,1975],{},[883,56445,56446],{},"!note"," Klíčové pozorování\n",[38,56449,56450],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,56452,56454],{"className":56453},[886],[888,56455,56456],{"xmlns":890},[892,56457,56458,56480],{},[895,56459,56460,56462,56464,56466,56468,56470,56472,56474,56476,56478],{},[898,56461,4255],{},[898,56463,3994],{},[1996,56465,2005],{"stretchy":2004},[898,56467,2789],{},[1996,56469,2011],{"stretchy":2004},[1996,56471,1998],{},[898,56473,4183],{},[1996,56475,2005],{"stretchy":2004},[898,56477,2789],{},[1996,56479,2011],{"stretchy":2004},[902,56481,56482],{"encoding":904},"AR(Q) = D(Q)",[198,56484,56486],{"id":56485},"mezní-příjem","Mezní příjem",[724,56488,56489,56490,2203,56493,10025,56508,56511,56512,56515],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,56491,56492],{},"mezní příjem",[883,56494,56496],{"className":56495},[886],[888,56497,56498],{"xmlns":890},[892,56499,56500,56506],{},[895,56501,56502,56504],{},[898,56503,2818],{},[898,56505,3994],{},[902,56507,6634],{"encoding":904},[38,56509,56510],{},"marginal revenue","), definovaný jako ",[207,56513,1145],{"className":56514,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,56517,56519],{"className":56518},[886],[888,56520,56521],{"xmlns":890,"display":28068},[892,56522,56523,56580],{},[20756,56524,56525],{"width":28073},[20761,56526,56527,56529,56573,56575],{},[20764,56528],{"width":28078},[20764,56530,56531],{},[895,56532,56533,56535,56537,56539,56555,56557,56559,56565,56567,56569,56571],{},[898,56534,2818],{},[898,56536,3994],{},[1996,56538,1998],{},[2329,56540,56541,56549],{},[895,56542,56543,56545,56547],{},[898,56544,2194],{"mathvariant":2376},[898,56546,2774],{},[898,56548,3994],{},[895,56550,56551,56553],{},[898,56552,2194],{"mathvariant":2376},[898,56554,2789],{},[1996,56556,1998],{},[898,56558,2774],{},[2124,56560,56561,56563],{},[898,56562,3994],{},[1996,56564,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,56566,2005],{"stretchy":2004},[898,56568,2789],{},[1996,56570,2011],{"stretchy":2004},[898,56572,1975],{"mathvariant":2376},[20764,56574],{"width":28078},[20764,56576,56577],{},[2288,56578,56579],{},"(3.2)",[902,56581,56582],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,56584,56585,56586,56588],{},"Mezní příjem udává ",[38,56587,2596],{}," celkového příjmu vzhledem k množství.",[3867,56590,56591],{},[724,56592,56593,56595,56596,56622,56623,56640,56641,1975],{},[883,56594,4155],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,56597,56599],{"className":56598},[886],[888,56600,56601],{"xmlns":890},[892,56602,56603,56619],{},[895,56604,56605,56607,56609,56611,56617],{},[898,56606,2818],{},[898,56608,3994],{},[1996,56610,2005],{"stretchy":2004},[2124,56612,56613,56615],{},[898,56614,2789],{},[1996,56616,4354],{},[1996,56618,2011],{"stretchy":2004},[902,56620,56621],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,56624,56626],{"className":56625},[886],[888,56627,56628],{"xmlns":890},[892,56629,56630,56638],{},[895,56631,56632],{},[2124,56633,56634,56636],{},[898,56635,2789],{},[1996,56637,4354],{},[902,56639,29846],{"encoding":904},". Jinak řečeno: ",[883,56642,56644],{"className":56643},[886],[888,56645,56646],{"xmlns":890},[892,56647,56648,56700],{},[895,56649,56650,56652,56654,56656,56662,56664,56666,56668,56670,56672,56678,56680,56682,56684,56686,56688,56690,56692,56698],{},[898,56651,2818],{},[898,56653,3994],{},[1996,56655,2005],{"stretchy":2004},[2124,56657,56658,56660],{},[898,56659,2789],{},[1996,56661,4354],{},[1996,56663,2011],{"stretchy":2004},[1996,56665,2730],{},[898,56667,2774],{},[898,56669,3994],{},[1996,56671,2005],{"stretchy":2004},[2124,56673,56674,56676],{},[898,56675,2789],{},[1996,56677,4354],{},[1996,56679,2095],{},[2129,56681,2278],{},[1996,56683,2011],{"stretchy":2004},[1996,56685,2225],{},[898,56687,2774],{},[898,56689,3994],{},[1996,56691,2005],{"stretchy":2004},[2124,56693,56694,56696],{},[898,56695,2789],{},[1996,56697,4354],{},[1996,56699,2011],{"stretchy":2004},[902,56701,56702],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[37350,56704,56706],{"id":56705},"příklad-32","Příklad 3.2",[724,56708,56709,55990,56711,56027,56745,56760,56761,1975],{},[38,56710,55989],{},[883,56712,56714],{"className":56713},[886],[888,56715,56716],{"xmlns":890},[892,56717,56718,56742],{},[895,56719,56720,56722,56724,56726,56728,56730,56732,56734,56736,56738,56740],{},[898,56721,3937],{},[1996,56723,1998],{},[898,56725,4183],{},[1996,56727,2005],{"stretchy":2004},[898,56729,2789],{},[1996,56731,2011],{"stretchy":2004},[1996,56733,1998],{},[2129,56735,3090],{},[1996,56737,2225],{},[2129,56739,2131],{},[898,56741,2789],{},[902,56743,56744],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,56746,56748],{"className":56747},[886],[888,56749,56750],{"xmlns":890},[892,56751,56752,56758],{},[895,56753,56754,56756],{},[898,56755,2818],{},[898,56757,3994],{},[902,56759,6634],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,56762,56764],{"className":56763},[886],[888,56765,56766],{"xmlns":890},[892,56767,56768,56784],{},[895,56769,56770,56772,56774,56776,56778,56780,56782],{},[898,56771,2789],{},[1996,56773,1998],{},[2129,56775,36246],{},[1996,56777,2286],{"separator":2285},[2129,56779,41864],{},[1996,56781,2286],{"separator":2285},[2129,56783,9035],{},[902,56785,56786],{"encoding":904},"Q = 15, 16, 20",[724,56788,56789,2203,56791,56823],{},[38,56790,22772],{},[883,56792,56794],{"className":56793},[886],[888,56795,56796],{"xmlns":890},[892,56797,56798,56820],{},[895,56799,56800,56802,56804,56806,56808,56810,56812,56814],{},[898,56801,2774],{},[898,56803,3994],{},[1996,56805,1998],{},[2129,56807,3090],{},[898,56809,2789],{},[1996,56811,2225],{},[2129,56813,2131],{},[2124,56815,56816,56818],{},[898,56817,2789],{},[2129,56819,2131],{},[902,56821,56822],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,56825,56827],{"className":56826},[886],[888,56828,56829],{"xmlns":890,"display":28068},[892,56830,56831,56873],{},[895,56832,56833,56835,56837,56839,56841,56843,56845,56847,56849,56855,56861,56863,56865,56867,56869,56871],{},[898,56834,2818],{},[898,56836,3994],{},[1996,56838,1998],{},[1996,56840,2005],{"stretchy":2004},[2129,56842,3090],{},[898,56844,2789],{},[1996,56846,2225],{},[2129,56848,2131],{},[2124,56850,56851,56853],{},[898,56852,2789],{},[2129,56854,2131],{},[2124,56856,56857,56859],{},[1996,56858,2011],{"stretchy":2004},[1996,56860,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,56862,1998],{},[2129,56864,3090],{},[1996,56866,2225],{},[2129,56868,2351],{},[898,56870,2789],{},[898,56872,1975],{"mathvariant":2376},[902,56874,56875],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,56877,9663,56878,8102,56896,56922,56923,4358,56936,56951,56952,56965,56966,21422,56979,4358,56992,57007,57008,57021,57022,57053,57054,57073],{},[883,56879,56881],{"className":56880},[886],[888,56882,56883],{"xmlns":890},[892,56884,56885,56893],{},[895,56886,56887,56889,56891],{},[898,56888,2789],{},[1996,56890,1998],{},[2129,56892,36246],{},[902,56894,56895],{"encoding":904},"Q = 15",[883,56897,56899],{"className":56898},[886],[888,56900,56901],{"xmlns":890},[892,56902,56903,56919],{},[895,56904,56905,56907,56909,56911,56913,56915,56917],{},[898,56906,2818],{},[898,56908,3994],{},[1996,56910,2005],{"stretchy":2004},[2129,56912,36246],{},[1996,56914,2011],{"stretchy":2004},[1996,56916,1998],{},[2129,56918,5211],{},[902,56920,56921],{"encoding":904},"MR(15) = 40",": při množství ",[883,56924,56926],{"className":56925},[886],[888,56927,56928],{"xmlns":890},[892,56929,56930,56934],{},[895,56931,56932],{},[2129,56933,36246],{},[902,56935,36246],{"encoding":904},[883,56937,56939],{"className":56938},[886],[888,56940,56941],{"xmlns":890},[892,56942,56943,56949],{},[895,56944,56945,56947],{},[898,56946,2774],{},[898,56948,3994],{},[902,56950,4094],{"encoding":904}," mění asi ",[883,56953,56955],{"className":56954},[886],[888,56956,56957],{"xmlns":890},[892,56958,56959,56963],{},[895,56960,56961],{},[2129,56962,5211],{},[902,56964,5211],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,56967,56969],{"className":56968},[886],[888,56970,56971],{"xmlns":890},[892,56972,56973,56977],{},[895,56974,56975],{},[898,56976,2789],{},[902,56978,2789],{"encoding":904},[883,56980,56982],{"className":56981},[886],[888,56983,56984],{"xmlns":890},[892,56985,56986,56990],{},[895,56987,56988],{},[2129,56989,2278],{},[902,56991,2278],{"encoding":904},[883,56993,56995],{"className":56994},[886],[888,56996,56997],{"xmlns":890},[892,56998,56999,57005],{},[895,57000,57001,57003],{},[898,57002,2774],{},[898,57004,3994],{},[902,57006,4094],{"encoding":904}," zvýší přibližně o ",[883,57009,57011],{"className":57010},[886],[888,57012,57013],{"xmlns":890},[892,57014,57015,57019],{},[895,57016,57017],{},[2129,57018,5211],{},[902,57020,5211],{"encoding":904},", tj. ze skutečné hodnoty ",[883,57023,57025],{"className":57024},[886],[888,57026,57027],{"xmlns":890},[892,57028,57029,57050],{},[895,57030,57031,57033,57035,57037,57039,57041,57043,57045,57047],{},[898,57032,2774],{},[898,57034,3994],{},[1996,57036,2005],{"stretchy":2004},[2129,57038,36246],{},[1996,57040,2011],{"stretchy":2004},[1996,57042,1998],{},[2129,57044,2278],{},[2288,57046,2987],{},[2129,57048,57049],{},"050",[902,57051,57052],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,57055,57057],{"className":57056},[886],[888,57058,57059],{"xmlns":890},[892,57060,57061,57070],{},[895,57062,57063,57065,57067],{},[2129,57064,2278],{},[2288,57066,2987],{},[2129,57068,57069],{},"090",[902,57071,57072],{"encoding":904},"1\\,090",". Skutečná změna je",[883,57075,57077],{"className":57076},[886],[888,57078,57079],{"xmlns":890,"display":28068},[892,57080,57081,57135],{},[895,57082,57083,57085,57087,57089,57091,57093,57095,57097,57099,57101,57103,57105,57107,57109,57111,57113,57115,57117,57119,57122,57124,57126,57128,57130,57132],{},[898,57084,2889],{"mathvariant":2376},[898,57086,2774],{},[898,57088,3994],{},[1996,57090,1998],{},[898,57092,2774],{},[898,57094,3994],{},[1996,57096,2005],{"stretchy":2004},[2129,57098,41864],{},[1996,57100,2011],{"stretchy":2004},[1996,57102,2225],{},[898,57104,2774],{},[898,57106,3994],{},[1996,57108,2005],{"stretchy":2004},[2129,57110,36246],{},[1996,57112,2011],{"stretchy":2004},[1996,57114,1998],{},[2129,57116,2278],{},[2288,57118,2987],{},[2129,57120,57121],{},"088",[1996,57123,2225],{},[2129,57125,2278],{},[2288,57127,2987],{},[2129,57129,57049],{},[1996,57131,1998],{},[2129,57133,57134],{},"38.",[902,57136,57137],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,57139,57140,57141,1343,57167,2927,57193,57208,57209,57224],{},"Podobně ",[883,57142,57144],{"className":57143},[886],[888,57145,57146],{"xmlns":890},[892,57147,57148,57164],{},[895,57149,57150,57152,57154,57156,57158,57160,57162],{},[898,57151,2818],{},[898,57153,3994],{},[1996,57155,2005],{"stretchy":2004},[2129,57157,41864],{},[1996,57159,2011],{"stretchy":2004},[1996,57161,1998],{},[2129,57163,5565],{},[902,57165,57166],{"encoding":904},"MR(16) = 36",[883,57168,57170],{"className":57169},[886],[888,57171,57172],{"xmlns":890},[892,57173,57174,57190],{},[895,57175,57176,57178,57180,57182,57184,57186,57188],{},[898,57177,2818],{},[898,57179,3994],{},[1996,57181,2005],{"stretchy":2004},[2129,57183,9035],{},[1996,57185,2011],{"stretchy":2004},[1996,57187,1998],{},[2129,57189,9035],{},[902,57191,57192],{"encoding":904},"MR(20) = 20",[883,57194,57196],{"className":57195},[886],[888,57197,57198],{"xmlns":890},[892,57199,57200,57206],{},[895,57201,57202,57204],{},[898,57203,2818],{},[898,57205,3994],{},[902,57207,6634],{"encoding":904}," je klesající funkce — rychlost změny ",[883,57210,57212],{"className":57211},[886],[888,57213,57214],{"xmlns":890},[892,57215,57216,57222],{},[895,57217,57218,57220],{},[898,57219,2774],{},[898,57221,3994],{},[902,57223,4094],{"encoding":904}," s růstem množství klesá.",[198,57226,57228],{"id":57227},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,57230,57231],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,57233,57235],{"className":57234},[886],[888,57236,57237],{"xmlns":890,"display":28068},[892,57238,57239,57308],{},[20756,57240,57241],{"width":28073},[20761,57242,57243,57245,57301,57303],{},[20764,57244],{"width":28078},[20764,57246,57247],{},[895,57248,57249,57251,57253,57255,57257,57259,57261,57263,57265,57267,57269,57271,57273,57275,57281,57283,57285,57287,57289,57291,57293,57295,57297,57299],{},[898,57250,2889],{"mathvariant":2376},[898,57252,2774],{},[898,57254,3994],{},[2288,57256,3984],{},[1996,57258,2730],{},[2288,57260,3984],{},[898,57262,2194],{"mathvariant":2376},[898,57264,2774],{},[898,57266,3994],{},[1996,57268,1998],{},[1996,57270,2005],{"stretchy":2004},[898,57272,2774],{},[898,57274,3994],{},[2124,57276,57277,57279],{},[1996,57278,2011],{"stretchy":2004},[1996,57280,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[2288,57282,2987],{},[898,57284,2194],{"mathvariant":2376},[898,57286,2789],{},[1996,57288,1998],{},[898,57290,2818],{},[898,57292,3994],{},[2288,57294,2987],{},[898,57296,2194],{"mathvariant":2376},[898,57298,2789],{},[1996,57300,2286],{"separator":2285},[20764,57302],{"width":28078},[20764,57304,57305],{},[2288,57306,57307],{},"(3.3)",[902,57309,57310],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,57312,57313],{},"schematicky:",[883,57315,57317],{"className":57316},[886],[888,57318,57319],{"xmlns":890,"display":28068},[892,57320,57321,57429],{},[895,57322,57323,57361,57363,57365,57367,57396,57399,57427],{},[895,57324,57325,57328,57334,57337,57343,57346,57352,57358],{},[2288,57326,57327],{},"zm",[8386,57329,57330,57332],{"accent":2285},[2288,57331,45734],{},[1996,57333,25060],{},[2288,57335,57336],{},"na celkov",[8386,57338,57339,57341],{"accent":2285},[2288,57340,45734],{},[1996,57342,24979],{},[2288,57344,57345],{},"ho p",[8386,57347,57348,57350],{"accent":2285},[2288,57349,12043],{},[1996,57351,25060],{},[8386,57353,57354,57356],{"accent":2285},[2288,57355,25048],{},[1996,57357,24979],{},[2288,57359,57360],{},"jmu",[2288,57362,3984],{},[1996,57364,2730],{},[2288,57366,3984],{},[895,57368,57369,57372,57378,57381,57387,57393],{},[2288,57370,57371],{},"mezn",[8386,57373,57374,57376],{"accent":2285},[2288,57375,25048],{},[1996,57377,24979],{},[2288,57379,57380],{}," p",[8386,57382,57383,57385],{"accent":2285},[2288,57384,12043],{},[1996,57386,25060],{},[8386,57388,57389,57391],{"accent":2285},[2288,57390,25048],{},[1996,57392,24979],{},[2288,57394,57395],{},"jem",[1996,57397,57398],{},"×",[895,57400,57401,57403,57409,57412,57418,57421],{},[2288,57402,57327],{},[8386,57404,57405,57407],{"accent":2285},[2288,57406,45734],{},[1996,57408,25060],{},[2288,57410,57411],{},"na mno",[8386,57413,57414,57416],{"accent":2285},[2288,57415,9594],{},[1996,57417,25060],{},[2288,57419,57420],{},"stv",[8386,57422,57423,57425],{"accent":2285},[2288,57424,25048],{},[1996,57426,24979],{},[898,57428,1975],{"mathvariant":2376},[902,57430,57431],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,57433,57434,57435,57450],{},"Pro porovnání skutečná změna ",[883,57436,57438],{"className":57437},[886],[888,57439,57440],{"xmlns":890},[892,57441,57442,57448],{},[895,57443,57444,57446],{},[898,57445,2774],{},[898,57447,3994],{},[902,57449,4094],{"encoding":904}," je",[883,57452,57454],{"className":57453},[886],[888,57455,57456],{"xmlns":890,"display":28068},[892,57457,57458,57513],{},[20756,57459,57460],{"width":28073},[20761,57461,57462,57464,57506,57508],{},[20764,57463],{"width":28078},[20764,57465,57466],{},[895,57467,57468,57470,57472,57474,57476,57478,57480,57482,57484,57486,57488,57490,57492,57494,57496,57498,57500,57502,57504],{},[898,57469,2889],{"mathvariant":2376},[898,57471,2774],{},[898,57473,3994],{},[1996,57475,1998],{},[898,57477,2774],{},[898,57479,3994],{},[1996,57481,2005],{"stretchy":2004},[898,57483,2789],{},[1996,57485,2095],{},[898,57487,2194],{"mathvariant":2376},[898,57489,2789],{},[1996,57491,2011],{"stretchy":2004},[1996,57493,2225],{},[898,57495,2774],{},[898,57497,3994],{},[1996,57499,2005],{"stretchy":2004},[898,57501,2789],{},[1996,57503,2011],{"stretchy":2004},[898,57505,1975],{"mathvariant":2376},[20764,57507],{"width":28078},[20764,57509,57510],{},[2288,57511,57512],{},"(3.4)",[902,57514,57515],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[37350,57517,57519],{"id":57518},"příklad-33","Příklad 3.3",[724,57521,57522,57524,57525,57555,57556,2657,57571,2671,57584,2685,57597,57611],{},[38,57523,55989],{}," Pro ",[883,57526,57528],{"className":57527},[886],[888,57529,57530],{"xmlns":890},[892,57531,57532,57552],{},[895,57533,57534,57536,57538,57540,57542,57544,57546],{},[898,57535,2774],{},[898,57537,3994],{},[1996,57539,1998],{},[2129,57541,3090],{},[898,57543,2789],{},[1996,57545,2225],{},[2124,57547,57548,57550],{},[898,57549,2789],{},[2129,57551,2131],{},[902,57553,57554],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,57557,57559],{"className":57558},[886],[888,57560,57561],{"xmlns":890},[892,57562,57563,57569],{},[895,57564,57565,57567],{},[898,57566,2774],{},[898,57568,3994],{},[902,57570,4094],{"encoding":904},[883,57572,57574],{"className":57573},[886],[888,57575,57576],{"xmlns":890},[892,57577,57578,57582],{},[895,57579,57580],{},[898,57581,2789],{},[902,57583,2789],{"encoding":904},[883,57585,57587],{"className":57586},[886],[888,57588,57589],{"xmlns":890},[892,57590,57591,57595],{},[895,57592,57593],{},[2129,57594,3126],{},[902,57596,3126],{"encoding":904},[883,57598,57600],{"className":57599},[886],[888,57601,57602],{"xmlns":890},[892,57603,57604,57609],{},[895,57605,57606],{},[2129,57607,57608],{},"63",[902,57610,57608],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,57613,57614,2203,57616,57641,57642,1343,57660,2704],{},[38,57615,22772],{},[883,57617,57619],{"className":57618},[886],[888,57620,57621],{"xmlns":890},[892,57622,57623,57639],{},[895,57624,57625,57627,57629,57631,57633,57635,57637],{},[898,57626,2818],{},[898,57628,3994],{},[1996,57630,1998],{},[2129,57632,3090],{},[1996,57634,2225],{},[2129,57636,2131],{},[898,57638,2789],{},[902,57640,11437],{"encoding":904},", tedy při ",[883,57643,57645],{"className":57644},[886],[888,57646,57647],{"xmlns":890},[892,57648,57649,57657],{},[895,57650,57651,57653,57655],{},[898,57652,2789],{},[1996,57654,1998],{},[2129,57656,3126],{},[902,57658,57659],{"encoding":904},"Q = 60",[883,57661,57663],{"className":57662},[886],[888,57664,57665],{"xmlns":890},[892,57666,57667,57677],{},[895,57668,57669,57671,57673,57675],{},[898,57670,2194],{"mathvariant":2376},[898,57672,2789],{},[1996,57674,1998],{},[2129,57676,2173],{},[902,57678,57679],{"encoding":904},"\\mathrm{d}Q = 3",[883,57681,57683],{"className":57682},[886],[888,57684,57685],{"xmlns":890,"display":28068},[892,57686,57687,57718],{},[895,57688,57689,57691,57693,57695,57697,57699,57701,57703,57705,57707,57709,57711,57713,57715],{},[898,57690,2194],{"mathvariant":2376},[898,57692,2774],{},[898,57694,3994],{},[1996,57696,1998],{},[1996,57698,2005],{"stretchy":2004},[2129,57700,3090],{},[1996,57702,2225],{},[2129,57704,4046],{},[1996,57706,2011],{"stretchy":2004},[1996,57708,3177],{},[2129,57710,2173],{},[1996,57712,1998],{},[1996,57714,2225],{},[2129,57716,57717],{},"60.",[902,57719,57720],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,57722,57723,57724,57754,57755,57774],{},"Celkový příjem klesne z ",[883,57725,57727],{"className":57726},[886],[888,57728,57729],{"xmlns":890},[892,57730,57731,57751],{},[895,57732,57733,57735,57737,57739,57741,57743,57745,57747,57749],{},[898,57734,2774],{},[898,57736,3994],{},[1996,57738,2005],{"stretchy":2004},[2129,57740,3126],{},[1996,57742,2011],{"stretchy":2004},[1996,57744,1998],{},[2129,57746,2131],{},[2288,57748,2987],{},[2129,57750,20144],{},[902,57752,57753],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,57756,57758],{"className":57757},[886],[888,57759,57760],{"xmlns":890},[892,57761,57762,57771],{},[895,57763,57764,57766,57768],{},[2129,57765,2131],{},[2288,57767,2987],{},[2129,57769,57770],{},"340",[902,57772,57773],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,57776,57778],{"className":57777},[886],[888,57779,57780],{"xmlns":890,"display":28068},[892,57781,57782,57840],{},[895,57783,57784,57786,57788,57790,57792,57794,57796,57798,57800,57802,57804,57806,57808,57810,57812,57814,57816,57818,57820,57823,57825,57827,57829,57831,57833,57835,57838],{},[898,57785,2889],{"mathvariant":2376},[898,57787,2774],{},[898,57789,3994],{},[1996,57791,1998],{},[898,57793,2774],{},[898,57795,3994],{},[1996,57797,2005],{"stretchy":2004},[2129,57799,57608],{},[1996,57801,2011],{"stretchy":2004},[1996,57803,2225],{},[898,57805,2774],{},[898,57807,3994],{},[1996,57809,2005],{"stretchy":2004},[2129,57811,3126],{},[1996,57813,2011],{"stretchy":2004},[1996,57815,1998],{},[2129,57817,2131],{},[2288,57819,2987],{},[2129,57821,57822],{},"331",[1996,57824,2225],{},[2129,57826,2131],{},[2288,57828,2987],{},[2129,57830,20144],{},[1996,57832,1998],{},[1996,57834,2225],{},[2129,57836,57837],{},"69",[1996,57839,2286],{"separator":2285},[902,57841,57842],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,57844,57845,57846,57861,57862,1975],{},"tj. ",[883,57847,57849],{"className":57848},[886],[888,57850,57851],{"xmlns":890},[892,57852,57853,57859],{},[895,57854,57855,57857],{},[898,57856,2774],{},[898,57858,3994],{},[902,57860,4094],{"encoding":904}," klesne na ",[883,57863,57865],{"className":57864},[886],[888,57866,57867],{"xmlns":890},[892,57868,57869,57877],{},[895,57870,57871,57873,57875],{},[2129,57872,2131],{},[2288,57874,2987],{},[2129,57876,57822],{},[902,57878,57879],{"encoding":904},"2\\,331",[198,57881,57883],{"id":57882},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,57885,57886,57887,10394,57910,31582],{},"Obecně pro lineární poptávku ",[883,57888,57890],{"className":57889},[886],[888,57891,57892],{"xmlns":890},[892,57893,57894,57908],{},[895,57895,57896,57898,57900,57902,57904,57906],{},[898,57897,3937],{},[1996,57899,1998],{},[898,57901,207],{},[898,57903,2789],{},[1996,57905,2095],{},[898,57907,2098],{},[902,57909,37062],{"encoding":904},[883,57911,57913],{"className":57912},[886],[888,57914,57915],{"xmlns":890},[892,57916,57917,57939],{},[895,57918,57919,57921,57923,57925,57927,57933,57935,57937],{},[898,57920,2774],{},[898,57922,3994],{},[1996,57924,1998],{},[898,57926,207],{},[2124,57928,57929,57931],{},[898,57930,2789],{},[2129,57932,2131],{},[1996,57934,2095],{},[898,57936,2098],{},[898,57938,2789],{},[902,57940,57941],{"encoding":904},"TR = aQ^2 + bQ",[883,57943,57945],{"className":57944},[886],[888,57946,57947],{"xmlns":890,"display":28068},[892,57948,57949,57969],{},[895,57950,57951,57953,57955,57957,57959,57961,57963,57965,57967],{},[898,57952,2818],{},[898,57954,3994],{},[1996,57956,1998],{},[2129,57958,2131],{},[898,57960,207],{},[898,57962,2789],{},[1996,57964,2095],{},[898,57966,2098],{},[898,57968,1975],{"mathvariant":2376},[902,57970,57971],{"encoding":904},"MR = 2aQ + b.",[724,57973,57974,57975,57990,57991,58006,58007,58020,58021,10025,58024,58040,58041,58054,58055,58070,58071,58086,58087,58102,58103,2624,58116,58146,58147,58166,58167,58182],{},"Křivky ",[883,57976,57978],{"className":57977},[886],[888,57979,57980],{"xmlns":890},[892,57981,57982,57988],{},[895,57983,57984,57986],{},[898,57985,2818],{},[898,57987,3994],{},[902,57989,6634],{"encoding":904}," a poptávky (resp. ",[883,57992,57994],{"className":57993},[886],[888,57995,57996],{"xmlns":890},[892,57997,57998,58004],{},[895,57999,58000,58002],{},[898,58001,4255],{},[898,58003,3994],{},[902,58005,55447],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,58008,58010],{"className":58009},[886],[888,58011,58012],{"xmlns":890},[892,58013,58014,58018],{},[895,58015,58016],{},[898,58017,2098],{},[902,58019,2098],{"encoding":904},", přičemž ",[38,58022,58023],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,58025,58027],{"className":58026},[886],[888,58028,58029],{"xmlns":890},[892,58030,58031,58037],{},[895,58032,58033,58035],{},[2129,58034,2131],{},[898,58036,207],{},[902,58038,58039],{"encoding":904},"2a"," vs. ",[883,58042,58044],{"className":58043},[886],[888,58045,58046],{"xmlns":890},[892,58047,58048,58052],{},[895,58049,58050],{},[898,58051,207],{},[902,58053,207],{"encoding":904},", obrázek 3.2). ",[883,58056,58058],{"className":58057},[886],[888,58059,58060],{"xmlns":890},[892,58061,58062,58068],{},[895,58063,58064,58066],{},[898,58065,2818],{},[898,58067,3994],{},[902,58069,6634],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,58072,58074],{"className":58073},[886],[888,58075,58076],{"xmlns":890},[892,58077,58078,58084],{},[895,58079,58080,58082],{},[898,58081,2774],{},[898,58083,3994],{},[902,58085,4094],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,58088,58090],{"className":58089},[886],[888,58091,58092],{"xmlns":890},[892,58093,58094,58100],{},[895,58095,58096,58098],{},[898,58097,2818],{},[898,58099,3994],{},[902,58101,6634],{"encoding":904}," osu ",[883,58104,58106],{"className":58105},[886],[888,58107,58108],{"xmlns":890},[892,58109,58110,58114],{},[895,58111,58112],{},[898,58113,2789],{},[902,58115,2789],{"encoding":904},[883,58117,58119],{"className":58118},[886],[888,58120,58121],{"xmlns":890},[892,58122,58123,58143],{},[895,58124,58125,58127,58129,58131],{},[898,58126,2789],{},[1996,58128,1998],{},[1996,58130,2225],{},[2325,58132,58133],{"scriptlevel":2327,"displaystyle":2004},[2329,58134,58135,58137],{},[898,58136,2098],{},[895,58138,58139,58141],{},[2129,58140,2131],{},[898,58142,207],{},[902,58144,58145],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,58148,58150],{"className":58149},[886],[888,58151,58152],{"xmlns":890},[892,58153,58154,58164],{},[895,58155,58156,58158,58160,58162],{},[898,58157,2818],{},[898,58159,3994],{},[1996,58161,1998],{},[2129,58163,2327],{},[902,58165,7084],{"encoding":904},", a dále ",[883,58168,58170],{"className":58169},[886],[888,58171,58172],{"xmlns":890},[892,58173,58174,58180],{},[895,58175,58176,58178],{},[898,58177,2774],{},[898,58179,3994],{},[902,58181,4094],{"encoding":904}," klesá.",[724,58184,58185,58186,58192,58193,58225,58226,58254],{},"V případě ",[38,58187,58188],{},[207,58189,58191],{"className":58190,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,58194,58196],{"className":58195},[886],[888,58197,58198],{"xmlns":890},[892,58199,58200,58222],{},[895,58201,58202,58204,58206,58208,58210,58212,58214,58216],{},[898,58203,3937],{},[1996,58205,1998],{},[898,58207,4183],{},[1996,58209,2005],{"stretchy":2004},[898,58211,2789],{},[1996,58213,2011],{"stretchy":2004},[1996,58215,1998],{},[2124,58217,58218,58220],{},[898,58219,3937],{},[1996,58221,4354],{},[902,58223,58224],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,58227,58229],{"className":58228},[886],[888,58230,58231],{"xmlns":890},[892,58232,58233,58251],{},[895,58234,58235,58237,58239,58241,58243,58245],{},[898,58236,2774],{},[898,58238,3994],{},[1996,58240,1998],{},[898,58242,2789],{},[1996,58244,3177],{},[2124,58246,58247,58249],{},[898,58248,3937],{},[1996,58250,4354],{},[902,58252,58253],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,58256,58258],{"className":58257},[886],[888,58259,58260],{"xmlns":890,"display":28068},[892,58261,58262,58304],{},[895,58263,58264,58266,58268,58270,58272,58274,58276,58282,58284,58286,58300,58302],{},[898,58265,2818],{},[898,58267,3994],{},[1996,58269,1998],{},[898,58271,4255],{},[898,58273,3994],{},[1996,58275,1998],{},[2124,58277,58278,58280],{},[898,58279,3937],{},[1996,58281,4354],{},[5878,58283],{"width":15286},[1996,58285,2005],{"stretchy":2004},[895,58287,58288,58291,58297],{},[2288,58289,58290],{},"obr",[8386,58292,58293,58295],{"accent":2285},[2288,58294,207],{},[1996,58296,24979],{},[2288,58298,58299],{},"zek 3.4",[1996,58301,2011],{"stretchy":2004},[898,58303,1975],{"mathvariant":2376},[902,58305,58306],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,58308,58309],{},[614,58310,58311,58312,3885,58338,58366,58367,58380,58381,58396,58397,3718,58410,1343,58436,3718,58451,1975],{},"Obrázek 3.2: Přímky ",[883,58313,58315],{"className":58314},[886],[888,58316,58317],{"xmlns":890},[892,58318,58319,58335],{},[895,58320,58321,58323,58325,58327,58329,58331,58333],{},[898,58322,4255],{},[898,58324,3994],{},[1996,58326,1998],{},[898,58328,207],{},[898,58330,2789],{},[1996,58332,2095],{},[898,58334,2098],{},[902,58336,58337],{"encoding":904},"AR = aQ + b",[883,58339,58341],{"className":58340},[886],[888,58342,58343],{"xmlns":890},[892,58344,58345,58363],{},[895,58346,58347,58349,58351,58353,58355,58357,58359,58361],{},[898,58348,2818],{},[898,58350,3994],{},[1996,58352,1998],{},[2129,58354,2131],{},[898,58356,207],{},[898,58358,2789],{},[1996,58360,2095],{},[898,58362,2098],{},[902,58364,58365],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,58368,58370],{"className":58369},[886],[888,58371,58372],{"xmlns":890},[892,58373,58374,58378],{},[895,58375,58376],{},[898,58377,2098],{},[902,58379,2098],{"encoding":904}," se svislou osou, ",[883,58382,58384],{"className":58383},[886],[888,58385,58386],{"xmlns":890},[892,58387,58388,58394],{},[895,58389,58390,58392],{},[898,58391,2818],{},[898,58393,3994],{},[902,58395,6634],{"encoding":904}," protíná osu ",[883,58398,58400],{"className":58399},[886],[888,58401,58402],{"xmlns":890},[892,58403,58404,58408],{},[895,58405,58406],{},[898,58407,2789],{},[902,58409,2789],{"encoding":904},[883,58411,58413],{"className":58412},[886],[888,58414,58415],{"xmlns":890},[892,58416,58417,58433],{},[895,58418,58419,58421],{},[1996,58420,2225],{},[2325,58422,58423],{"scriptlevel":2327,"displaystyle":2004},[2329,58424,58425,58427],{},[898,58426,2098],{},[895,58428,58429,58431],{},[2129,58430,2131],{},[898,58432,207],{},[902,58434,58435],{"encoding":904},"-\\tfrac{b}{2a}",[883,58437,58439],{"className":58438},[886],[888,58440,58441],{"xmlns":890},[892,58442,58443,58449],{},[895,58444,58445,58447],{},[898,58446,4255],{},[898,58448,3994],{},[902,58450,55447],{"encoding":904},[883,58452,58454],{"className":58453},[886],[888,58455,58456],{"xmlns":890},[892,58457,58458,58470],{},[895,58459,58460,58462],{},[1996,58461,2225],{},[2325,58463,58464],{"scriptlevel":2327,"displaystyle":2004},[2329,58465,58466,58468],{},[898,58467,2098],{},[898,58469,207],{},[902,58471,58472],{"encoding":904},"-\\tfrac{b}{a}",[724,58474,58475],{},[614,58476,58477,58478,58509,58510,58539,58540,1975],{},"Obrázek 3.3: Parabola ",[883,58479,58481],{"className":58480},[886],[888,58482,58483],{"xmlns":890},[892,58484,58485,58507],{},[895,58486,58487,58489,58491,58493,58495,58501,58503,58505],{},[898,58488,2774],{},[898,58490,3994],{},[1996,58492,1998],{},[898,58494,207],{},[2124,58496,58497,58499],{},[898,58498,2789],{},[2129,58500,2131],{},[1996,58502,2095],{},[898,58504,2098],{},[898,58506,2789],{},[902,58508,57941],{"encoding":904}," s maximem v ",[883,58511,58513],{"className":58512},[886],[888,58514,58515],{"xmlns":890},[892,58516,58517,58537],{},[895,58518,58519,58521,58523,58525],{},[898,58520,2789],{},[1996,58522,1998],{},[1996,58524,2225],{},[2325,58526,58527],{"scriptlevel":2327,"displaystyle":2004},[2329,58528,58529,58531],{},[898,58530,2098],{},[895,58532,58533,58535],{},[2129,58534,2131],{},[898,58536,207],{},[902,58538,58145],{"encoding":904}," a nulou v ",[883,58541,58543],{"className":58542},[886],[888,58544,58545],{"xmlns":890},[892,58546,58547,58563],{},[895,58548,58549,58551,58553,58555],{},[898,58550,2789],{},[1996,58552,1998],{},[1996,58554,2225],{},[2325,58556,58557],{"scriptlevel":2327,"displaystyle":2004},[2329,58558,58559,58561],{},[898,58560,2098],{},[898,58562,207],{},[902,58564,58565],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,58567,58568],{},[614,58569,58570,58571,1975],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,58572,58574],{"className":58573},[886],[888,58575,58576],{"xmlns":890},[892,58577,58578,58598],{},[895,58579,58580,58582,58584,58586,58588,58590,58592],{},[898,58581,4255],{},[898,58583,3994],{},[1996,58585,1998],{},[898,58587,2818],{},[898,58589,3994],{},[1996,58591,1998],{},[2124,58593,58594,58596],{},[898,58595,3937],{},[1996,58597,4354],{},[902,58599,58600],{"encoding":904},"AR = MR = P^*",[115,58602,58604],{"id":58603},"náklady-firmy","Náklady firmy",[198,58606,58608],{"id":58607},"celkové-náklady","Celkové náklady",[724,58610,58611,2203,58613,10025,58628,58631,58632,58645],{},[38,58612,58608],{},[883,58614,58616],{"className":58615},[886],[888,58617,58618],{"xmlns":890},[892,58619,58620,58626],{},[895,58621,58622,58624],{},[898,58623,2774],{},[898,58625,2777],{},[902,58627,3243],{"encoding":904},[38,58629,58630],{},"total cost",") jsou veškeré náklady na realizaci ",[883,58633,58635],{"className":58634},[886],[888,58636,58637],{"xmlns":890},[892,58638,58639,58643],{},[895,58640,58641],{},[898,58642,2789],{},[902,58644,2789],{"encoding":904}," jednotek produkce:",[883,58647,58649],{"className":58648},[886],[888,58650,58651],{"xmlns":890,"display":28068},[892,58652,58653,58708],{},[20756,58654,58655],{"width":28073},[20761,58656,58657,58659,58701,58703],{},[20764,58658],{"width":28078},[20764,58660,58661],{},[895,58662,58663,58665,58667,58669,58671,58673,58675,58677,58679,58681,58683,58685,58687,58689,58691,58693,58695,58697,58699],{},[898,58664,2774],{},[898,58666,2777],{},[1996,58668,1998],{},[898,58670,2774],{},[898,58672,2777],{},[1996,58674,2005],{"stretchy":2004},[898,58676,2789],{},[1996,58678,2011],{"stretchy":2004},[1996,58680,1998],{},[898,58682,10436],{},[898,58684,2777],{},[1996,58686,2095],{},[898,58688,2774],{},[898,58690,40341],{},[898,58692,2777],{},[1996,58694,2005],{"stretchy":2004},[898,58696,2789],{},[1996,58698,2011],{"stretchy":2004},[1996,58700,2286],{"separator":2285},[20764,58702],{"width":28078},[20764,58704,58705],{},[2288,58706,58707],{},"(3.5)",[902,58709,58710],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,58712,4310,58713,58728,58729,10025,58732,12130,58735,58728,58759,10025,58762,58765],{},[883,58714,58716],{"className":58715},[886],[888,58717,58718],{"xmlns":890},[892,58719,58720,58726],{},[895,58721,58722,58724],{},[898,58723,10436],{},[898,58725,2777],{},[902,58727,55493],{"encoding":904}," jsou ",[38,58730,58731],{},"fixní náklady",[38,58733,58734],{},"fixed cost",[883,58736,58738],{"className":58737},[886],[888,58739,58740],{"xmlns":890},[892,58741,58742,58756],{},[895,58743,58744,58746,58748,58750,58752,58754],{},[898,58745,2774],{},[898,58747,40341],{},[898,58749,2777],{},[1996,58751,2005],{"stretchy":2004},[898,58753,2789],{},[1996,58755,2011],{"stretchy":2004},[902,58757,58758],{"encoding":904},"TVC(Q)",[38,58760,58761],{},"celkové variabilní náklady",[38,58763,58764],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,58767,58769],{"id":58768},"průměrné-náklady","Průměrné náklady",[724,58771,58772,2203,58774,10025,58789,58792],{},[38,58773,58769],{},[883,58775,58777],{"className":58776},[886],[888,58778,58779],{"xmlns":890},[892,58780,58781,58787],{},[895,58782,58783,58785],{},[898,58784,4255],{},[898,58786,2777],{},[902,58788,55562],{"encoding":904},[38,58790,58791],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,58794,58796],{"className":58795},[886],[888,58797,58798],{"xmlns":890,"display":28068},[892,58799,58800,58879],{},[20756,58801,58802],{"width":28073},[20761,58803,58804,58806,58872,58874],{},[20764,58805],{"width":28078},[20764,58807,58808],{},[895,58809,58810,58812,58814,58816,58818,58820,58822,58824,58826,58828,58838,58840,58850,58852,58870],{},[898,58811,4255],{},[898,58813,2777],{},[1996,58815,1998],{},[898,58817,4255],{},[898,58819,2777],{},[1996,58821,2005],{"stretchy":2004},[898,58823,2789],{},[1996,58825,2011],{"stretchy":2004},[1996,58827,1998],{},[2329,58829,58830,58836],{},[895,58831,58832,58834],{},[898,58833,2774],{},[898,58835,2777],{},[898,58837,2789],{},[1996,58839,1998],{},[2329,58841,58842,58848],{},[895,58843,58844,58846],{},[898,58845,10436],{},[898,58847,2777],{},[898,58849,2789],{},[1996,58851,2095],{},[2329,58853,58854,58868],{},[895,58855,58856,58858,58860,58862,58864,58866],{},[898,58857,2774],{},[898,58859,40341],{},[898,58861,2777],{},[1996,58863,2005],{"stretchy":2004},[898,58865,2789],{},[1996,58867,2011],{"stretchy":2004},[898,58869,2789],{},[1996,58871,2286],{"separator":2285},[20764,58873],{"width":28078},[20764,58875,58876],{},[2288,58877,58878],{},"(3.6)",[902,58880,58881],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,58883,4310,58884,58728,58908,2203,58911,10025,58928,12130,58931,58728,58963,2203,58966,10025,58983,3151],{},[883,58885,58887],{"className":58886},[886],[888,58888,58889],{"xmlns":890},[892,58890,58891,58905],{},[895,58892,58893],{},[2325,58894,58895],{"scriptlevel":2327,"displaystyle":2004},[2329,58896,58897,58903],{},[895,58898,58899,58901],{},[898,58900,10436],{},[898,58902,2777],{},[898,58904,2789],{},[902,58906,58907],{"encoding":904},"\\tfrac{FC}{Q}",[38,58909,58910],{},"průměrné fixní náklady",[883,58912,58914],{"className":58913},[886],[888,58915,58916],{"xmlns":890},[892,58917,58918,58926],{},[895,58919,58920,58922,58924],{},[898,58921,4255],{},[898,58923,10436],{},[898,58925,2777],{},[902,58927,55529],{"encoding":904},[38,58929,58930],{},"average fixed cost",[883,58932,58934],{"className":58933},[886],[888,58935,58936],{"xmlns":890},[892,58937,58938,58960],{},[895,58939,58940],{},[2325,58941,58942],{"scriptlevel":2327,"displaystyle":2004},[2329,58943,58944,58958],{},[895,58945,58946,58948,58950,58952,58954,58956],{},[898,58947,2774],{},[898,58949,40341],{},[898,58951,2777],{},[1996,58953,2005],{"stretchy":2004},[898,58955,2789],{},[1996,58957,2011],{"stretchy":2004},[898,58959,2789],{},[902,58961,58962],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,58964,58965],{},"průměrné variabilní náklady",[883,58967,58969],{"className":58968},[886],[888,58970,58971],{"xmlns":890},[892,58972,58973,58981],{},[895,58974,58975,58977,58979],{},[898,58976,4255],{},[898,58978,40341],{},[898,58980,2777],{},[902,58982,55313],{"encoding":904},[38,58984,58985],{},"average variable cost",[883,58987,58989],{"className":58988},[886],[888,58990,58991],{"xmlns":890,"display":28068},[892,58992,58993,59052],{},[20756,58994,58995],{"width":28073},[20761,58996,58997,58999,59045,59047],{},[20764,58998],{"width":28078},[20764,59000,59001],{},[895,59002,59003,59005,59007,59009,59011,59013,59015,59017,59019,59021,59023,59025,59043],{},[898,59004,4255],{},[898,59006,40341],{},[898,59008,2777],{},[1996,59010,1998],{},[898,59012,4255],{},[898,59014,40341],{},[898,59016,2777],{},[1996,59018,2005],{"stretchy":2004},[898,59020,2789],{},[1996,59022,2011],{"stretchy":2004},[1996,59024,1998],{},[2329,59026,59027,59041],{},[895,59028,59029,59031,59033,59035,59037,59039],{},[898,59030,2774],{},[898,59032,40341],{},[898,59034,2777],{},[1996,59036,2005],{"stretchy":2004},[898,59038,2789],{},[1996,59040,2011],{"stretchy":2004},[898,59042,2789],{},[898,59044,1975],{"mathvariant":2376},[20764,59046],{"width":28078},[20764,59048,59049],{},[2288,59050,59051],{},"(3.7)",[902,59053,59054],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[37350,59056,59058],{"id":59057},"příklad-34","Příklad 3.4",[724,59060,59061,57524,59063,3885,59088,56027,59112,3885,59127,59142,59143,1975],{},[38,59062,55989],{},[883,59064,59066],{"className":59065},[886],[888,59067,59068],{"xmlns":890},[892,59069,59070,59085],{},[895,59071,59072,59074,59076,59078,59080,59082],{},[898,59073,10436],{},[898,59075,2777],{},[1996,59077,1998],{},[2129,59079,2278],{},[2288,59081,2987],{},[2129,59083,59084],{},"000",[902,59086,59087],{"encoding":904},"FC = 1\\,000",[883,59089,59091],{"className":59090},[886],[888,59092,59093],{"xmlns":890},[892,59094,59095,59109],{},[895,59096,59097,59099,59101,59103,59105,59107],{},[898,59098,2774],{},[898,59100,40341],{},[898,59102,2777],{},[1996,59104,1998],{},[2129,59106,2351],{},[898,59108,2789],{},[902,59110,59111],{"encoding":904},"TVC = 4Q",[883,59113,59115],{"className":59114},[886],[888,59116,59117],{"xmlns":890},[892,59118,59119,59125],{},[895,59120,59121,59123],{},[898,59122,2774],{},[898,59124,2777],{},[902,59126,3243],{"encoding":904},[883,59128,59130],{"className":59129},[886],[888,59131,59132],{"xmlns":890},[892,59133,59134,59140],{},[895,59135,59136,59138],{},[898,59137,4255],{},[898,59139,2777],{},[902,59141,55562],{"encoding":904}," a jejich chování s rostoucím ",[883,59144,59146],{"className":59145},[886],[888,59147,59148],{"xmlns":890},[892,59149,59150,59154],{},[895,59151,59152],{},[898,59153,2789],{},[902,59155,2789],{"encoding":904},[724,59157,59158,2203,59160,3885,59190,59226,59227,4358,59240,59255,59256,2704],{},[38,59159,22772],{},[883,59161,59163],{"className":59162},[886],[888,59164,59165],{"xmlns":890},[892,59166,59167,59187],{},[895,59168,59169,59171,59173,59175,59177,59179,59181,59183,59185],{},[898,59170,2774],{},[898,59172,2777],{},[1996,59174,1998],{},[2129,59176,2278],{},[2288,59178,2987],{},[2129,59180,59084],{},[1996,59182,2095],{},[2129,59184,2351],{},[898,59186,2789],{},[902,59188,59189],{"encoding":904},"TC = 1\\,000 + 4Q",[883,59191,59193],{"className":59192},[886],[888,59194,59195],{"xmlns":890},[892,59196,59197,59223],{},[895,59198,59199,59201,59203,59205,59219,59221],{},[898,59200,4255],{},[898,59202,2777],{},[1996,59204,1998],{},[2325,59206,59207],{"scriptlevel":2327,"displaystyle":2004},[2329,59208,59209,59217],{},[895,59210,59211,59213,59215],{},[2129,59212,2278],{},[2288,59214,2987],{},[2129,59216,59084],{},[898,59218,2789],{},[1996,59220,2095],{},[2129,59222,2351],{},[902,59224,59225],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,59228,59230],{"className":59229},[886],[888,59231,59232],{"xmlns":890},[892,59233,59234,59238],{},[895,59235,59236],{},[898,59237,2789],{},[902,59239,2789],{"encoding":904},[883,59241,59243],{"className":59242},[886],[888,59244,59245],{"xmlns":890},[892,59246,59247,59253],{},[895,59248,59249,59251],{},[898,59250,4255],{},[898,59252,2777],{},[902,59254,55562],{"encoding":904}," blíží ",[883,59257,59259],{"className":59258},[886],[888,59260,59261],{"xmlns":890},[892,59262,59263,59267],{},[895,59264,59265],{},[2129,59266,2351],{},[902,59268,2351],{"encoding":904},[883,59270,59272],{"className":59271},[886],[888,59273,59274],{"xmlns":890,"display":28068},[892,59275,59276,59322],{},[895,59277,59278,59295,59317,59319],{},[39898,59279,59280,59287],{},[895,59281,59282,59285],{},[898,59283,59284],{},"lim",[1996,59286,56202],{},[895,59288,59289,59291,59293],{},[898,59290,2789],{},[1996,59292,3123],{},[898,59294,6297],{"mathvariant":2376},[895,59296,59297,59299,59311,59313,59315],{},[1996,59298,2005],{"fence":2285},[2329,59300,59301,59309],{},[895,59302,59303,59305,59307],{},[2129,59304,2278],{},[2288,59306,2987],{},[2129,59308,59084],{},[898,59310,2789],{},[1996,59312,2095],{},[2129,59314,2351],{},[1996,59316,2011],{"fence":2285},[1996,59318,1998],{},[2129,59320,59321],{},"4.",[902,59323,59324],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,59326,59327,59365,59366,1975],{},[883,59328,59330],{"className":59329},[886],[888,59331,59332],{"xmlns":890},[892,59333,59334,59362],{},[895,59335,59336,59338,59340,59342,59344,59358,59360],{},[898,59337,4255],{},[898,59339,10436],{},[898,59341,2777],{},[1996,59343,1998],{},[2325,59345,59346],{"scriptlevel":2327,"displaystyle":2004},[2329,59347,59348,59356],{},[895,59349,59350,59352,59354],{},[2129,59351,2278],{},[2288,59353,2987],{},[2129,59355,59084],{},[898,59357,2789],{},[1996,59359,3123],{},[2129,59361,2327],{},[902,59363,59364],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,59367,59369],{"className":59368},[886],[888,59370,59371],{"xmlns":890},[892,59372,59373,59377],{},[895,59374,59375],{},[898,59376,2789],{},[902,59378,2789],{"encoding":904},[724,59380,59381],{},[614,59382,59383,59384,59413,59414,1975],{},"Obrázek 3.5: Přímka ",[883,59385,59387],{"className":59386},[886],[888,59388,59389],{"xmlns":890},[892,59390,59391,59411],{},[895,59392,59393,59395,59397,59399,59401,59403,59405,59407,59409],{},[898,59394,2774],{},[898,59396,2777],{},[1996,59398,1998],{},[2129,59400,2278],{},[2288,59402,2987],{},[2129,59404,59084],{},[1996,59406,2095],{},[2129,59408,2351],{},[898,59410,2789],{},[902,59412,59189],{"encoding":904}," protínající svislou osu ve výši ",[883,59415,59417],{"className":59416},[886],[888,59418,59419],{"xmlns":890},[892,59420,59421,59435],{},[895,59422,59423,59425,59427,59429,59431,59433],{},[898,59424,10436],{},[898,59426,2777],{},[1996,59428,1998],{},[2129,59430,2278],{},[2288,59432,2987],{},[2129,59434,59084],{},[902,59436,59087],{"encoding":904},[724,59438,59439],{},[614,59440,59441,59442,59477,59478,1975],{},"Obrázek 3.6: Hyperbola ",[883,59443,59445],{"className":59444},[886],[888,59446,59447],{"xmlns":890},[892,59448,59449,59475],{},[895,59450,59451,59453,59455,59457,59471,59473],{},[898,59452,4255],{},[898,59454,2777],{},[1996,59456,1998],{},[2325,59458,59459],{"scriptlevel":2327,"displaystyle":2004},[2329,59460,59461,59469],{},[895,59462,59463,59465,59467],{},[2129,59464,2278],{},[2288,59466,2987],{},[2129,59468,59084],{},[898,59470,2789],{},[1996,59472,2095],{},[2129,59474,2351],{},[902,59476,59225],{"encoding":904}," s vodorovnou asymptotou ",[883,59479,59481],{"className":59480},[886],[888,59482,59483],{"xmlns":890},[892,59484,59485,59495],{},[895,59486,59487,59489,59491,59493],{},[898,59488,4255],{},[898,59490,2777],{},[1996,59492,1998],{},[2129,59494,2351],{},[902,59496,59497],{"encoding":904},"AC = 4",[724,59499,59500],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,59502,59504],{"className":59503},[886],[888,59505,59506],{"xmlns":890,"display":28068},[892,59507,59508,59534],{},[895,59509,59510,59512,59514,59516,59518,59520,59522,59524,59526,59528,59530,59532],{},[898,59511,2774],{},[898,59513,40341],{},[898,59515,2777],{},[1996,59517,1998],{},[898,59519,2789],{},[1996,59521,3177],{},[898,59523,40341],{},[898,59525,2777],{},[1996,59527,2005],{"stretchy":2004},[898,59529,2789],{},[1996,59531,2011],{"stretchy":2004},[1996,59533,2286],{"separator":2285},[902,59535,59536],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,59538,4310,59539,58728,59567,59570,59571,59601],{},[883,59540,59542],{"className":59541},[886],[888,59543,59544],{"xmlns":890},[892,59545,59546,59564],{},[895,59547,59548,59550,59552,59554,59556,59558,59560,59562],{},[898,59549,40341],{},[898,59551,2777],{},[1996,59553,1998],{},[898,59555,40341],{},[898,59557,2777],{},[1996,59559,2005],{"stretchy":2004},[898,59561,2789],{},[1996,59563,2011],{"stretchy":2004},[902,59565,59566],{"encoding":904},"VC = VC(Q)",[38,59568,59569],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,59572,59574],{"className":59573},[886],[888,59575,59576],{"xmlns":890},[892,59577,59578,59598],{},[895,59579,59580,59582,59584,59586,59588,59590,59592,59594,59596],{},[898,59581,2774],{},[898,59583,40341],{},[898,59585,2777],{},[1996,59587,2005],{"stretchy":2004},[898,59589,2789],{},[1996,59591,2011],{"stretchy":2004},[1996,59593,1998],{},[898,59595,207],{},[898,59597,2789],{},[902,59599,59600],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,59603,59605],{"className":59604},[886],[888,59606,59607],{"xmlns":890,"display":28068},[892,59608,59609,59629],{},[895,59610,59611,59613,59615,59617,59619,59621,59623,59625,59627],{},[898,59612,2774],{},[898,59614,2777],{},[1996,59616,1998],{},[898,59618,10436],{},[898,59620,2777],{},[1996,59622,2095],{},[898,59624,207],{},[898,59626,2789],{},[898,59628,1975],{"mathvariant":2376},[902,59630,59631],{"encoding":904},"TC = FC + aQ.",[724,59633,59634,59635,59650,59651,59666,59667,59690,59691,59725,59726,59477,59739,59752,59753,3885,59801,59845,59846,1975],{},"Křivkou ",[883,59636,59638],{"className":59637},[886],[888,59639,59640],{"xmlns":890},[892,59641,59642,59648],{},[895,59643,59644,59646],{},[898,59645,2774],{},[898,59647,2777],{},[902,59649,3243],{"encoding":904}," je přímka se svislým průsečíkem ",[883,59652,59654],{"className":59653},[886],[888,59655,59656],{"xmlns":890},[892,59657,59658,59664],{},[895,59659,59660,59662],{},[898,59661,10436],{},[898,59663,2777],{},[902,59665,55493],{"encoding":904}," a sklonem ",[883,59668,59670],{"className":59669},[886],[888,59671,59672],{"xmlns":890},[892,59673,59674,59687],{},[895,59675,59676,59679,59681,59683,59685],{},[898,59677,59678],{},"tan",[1996,59680,56202],{},[898,59682,18864],{},[1996,59684,1998],{},[898,59686,207],{},[902,59688,59689],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,59692,59694],{"className":59693},[886],[888,59695,59696],{"xmlns":890},[892,59697,59698,59722],{},[895,59699,59700,59702,59704,59706,59718,59720],{},[898,59701,4255],{},[898,59703,2777],{},[1996,59705,1998],{},[2325,59707,59708],{"scriptlevel":2327,"displaystyle":2004},[2329,59709,59710,59716],{},[895,59711,59712,59714],{},[898,59713,10436],{},[898,59715,2777],{},[898,59717,2789],{},[1996,59719,2095],{},[898,59721,207],{},[902,59723,59724],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,59727,59729],{"className":59728},[886],[888,59730,59731],{"xmlns":890},[892,59732,59733,59737],{},[895,59734,59735],{},[898,59736,9795],{},[902,59738,9795],{"encoding":904},[883,59740,59742],{"className":59741},[886],[888,59743,59744],{"xmlns":890},[892,59745,59746,59750],{},[895,59747,59748],{},[898,59749,207],{},[902,59751,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,59754,59756],{"className":59755},[886],[888,59757,59758],{"xmlns":890},[892,59759,59760,59798],{},[895,59761,59762,59782,59794,59796],{},[2272,59763,59764,59770],{},[895,59765,59766,59768],{},[898,59767,59284],{},[1996,59769,56202],{},[895,59771,59772,59774,59776],{},[898,59773,2789],{},[1996,59775,3123],{},[2124,59777,59778,59780],{},[2129,59779,2327],{},[1996,59781,2095],{},[2325,59783,59784],{"scriptlevel":2327,"displaystyle":2004},[2329,59785,59786,59792],{},[895,59787,59788,59790],{},[898,59789,10436],{},[898,59791,2777],{},[898,59793,2789],{},[1996,59795,1998],{},[898,59797,6297],{"mathvariant":2376},[902,59799,59800],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,59802,59804],{"className":59803},[886],[888,59805,59806],{"xmlns":890},[892,59807,59808,59842],{},[895,59809,59810,59826,59838,59840],{},[2272,59811,59812,59818],{},[895,59813,59814,59816],{},[898,59815,59284],{},[1996,59817,56202],{},[895,59819,59820,59822,59824],{},[898,59821,2789],{},[1996,59823,3123],{},[898,59825,6297],{"mathvariant":2376},[2325,59827,59828],{"scriptlevel":2327,"displaystyle":2004},[2329,59829,59830,59836],{},[895,59831,59832,59834],{},[898,59833,10436],{},[898,59835,2777],{},[898,59837,2789],{},[1996,59839,1998],{},[2129,59841,2327],{},[902,59843,59844],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,59847,59849],{"className":59848},[886],[888,59850,59851],{"xmlns":890},[892,59852,59853,59859],{},[895,59854,59855,59857],{},[898,59856,4255],{},[898,59858,2777],{},[902,59860,55562],{"encoding":904},[724,59862,59863],{},[614,59864,59865,59866,59881,59882,59897,59898,1975],{},"Obrázek 3.7: Přímka ",[883,59867,59869],{"className":59868},[886],[888,59870,59871],{"xmlns":890},[892,59872,59873,59879],{},[895,59874,59875,59877],{},[898,59876,2774],{},[898,59878,2777],{},[902,59880,3243],{"encoding":904}," s osovým průsečíkem ve výši ",[883,59883,59885],{"className":59884},[886],[888,59886,59887],{"xmlns":890},[892,59888,59889,59895],{},[895,59890,59891,59893],{},[898,59892,10436],{},[898,59894,2777],{},[902,59896,55493],{"encoding":904}," a se sklonem ",[883,59899,59901],{"className":59900},[886],[888,59902,59903],{"xmlns":890},[892,59904,59905,59917],{},[895,59906,59907,59909,59911,59913,59915],{},[898,59908,59678],{},[1996,59910,56202],{},[898,59912,18864],{},[1996,59914,1998],{},[898,59916,207],{},[902,59918,59689],{"encoding":904},[724,59920,59921],{},[614,59922,59923,59924,59939,59940,1975],{},"Obrázek 3.8: Klesající hyperbola ",[883,59925,59927],{"className":59926},[886],[888,59928,59929],{"xmlns":890},[892,59930,59931,59937],{},[895,59932,59933,59935],{},[898,59934,4255],{},[898,59936,2777],{},[902,59938,55562],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,59941,59943],{"className":59942},[886],[888,59944,59945],{"xmlns":890},[892,59946,59947,59951],{},[895,59948,59949],{},[898,59950,207],{},[902,59952,207],{"encoding":904},[198,59954,59956],{"id":59955},"mezní-náklady","Mezní náklady",[724,59958,59959,2203,59961,10025,59976,59979,59980,59983],{},[38,59960,59956],{},[883,59962,59964],{"className":59963},[886],[888,59965,59966],{"xmlns":890},[892,59967,59968,59974],{},[895,59969,59970,59972],{},[898,59971,2818],{},[898,59973,2777],{},[902,59975,55294],{"encoding":904},[38,59977,59978],{},"marginal cost",") jsou ",[207,59981,1145],{"className":59982,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,59985,59987],{"className":59986},[886],[888,59988,59989],{"xmlns":890,"display":28068},[892,59990,59991,60060],{},[20756,59992,59993],{"width":28073},[20761,59994,59995,59997,60053,60055],{},[20764,59996],{"width":28078},[20764,59998,59999],{},[895,60000,60001,60003,60005,60007,60009,60011,60013,60015,60017,60019,60035,60037,60039,60045,60047,60049,60051],{},[898,60002,2818],{},[898,60004,2777],{},[1996,60006,1998],{},[898,60008,2818],{},[898,60010,2777],{},[1996,60012,2005],{"stretchy":2004},[898,60014,2789],{},[1996,60016,2011],{"stretchy":2004},[1996,60018,1998],{},[2329,60020,60021,60029],{},[895,60022,60023,60025,60027],{},[898,60024,2194],{"mathvariant":2376},[898,60026,2774],{},[898,60028,2777],{},[895,60030,60031,60033],{},[898,60032,2194],{"mathvariant":2376},[898,60034,2789],{},[1996,60036,1998],{},[898,60038,2774],{},[2124,60040,60041,60043],{},[898,60042,2777],{},[1996,60044,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,60046,2005],{"stretchy":2004},[898,60048,2789],{},[1996,60050,2011],{"stretchy":2004},[898,60052,1975],{"mathvariant":2376},[20764,60054],{"width":28078},[20764,60056,60057],{},[2288,60058,60059],{},"(3.8)",[902,60061,60062],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[3867,60064,60065],{},[724,60066,60067,60069,60070,60096,60097,60114,60115,1975],{},[883,60068,4155],{}," Intuice — „kolik stojí další kus\"\n",[883,60071,60073],{"className":60072},[886],[888,60074,60075],{"xmlns":890},[892,60076,60077,60093],{},[895,60078,60079,60081,60083,60085,60091],{},[898,60080,2818],{},[898,60082,2777],{},[1996,60084,2005],{"stretchy":2004},[2124,60086,60087,60089],{},[898,60088,2789],{},[1996,60090,4354],{},[1996,60092,2011],{"stretchy":2004},[902,60094,60095],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,60098,60100],{"className":60099},[886],[888,60101,60102],{"xmlns":890},[892,60103,60104,60112],{},[895,60105,60106],{},[2124,60107,60108,60110],{},[898,60109,2789],{},[1996,60111,4354],{},[902,60113,29846],{"encoding":904},". Formálně ",[883,60116,60118],{"className":60117},[886],[888,60119,60120],{"xmlns":890},[892,60121,60122,60174],{},[895,60123,60124,60126,60128,60130,60136,60138,60140,60142,60144,60146,60152,60154,60156,60158,60160,60162,60164,60166,60172],{},[898,60125,2818],{},[898,60127,2777],{},[1996,60129,2005],{"stretchy":2004},[2124,60131,60132,60134],{},[898,60133,2789],{},[1996,60135,4354],{},[1996,60137,2011],{"stretchy":2004},[1996,60139,2730],{},[898,60141,2774],{},[898,60143,2777],{},[1996,60145,2005],{"stretchy":2004},[2124,60147,60148,60150],{},[898,60149,2789],{},[1996,60151,4354],{},[1996,60153,2095],{},[2129,60155,2278],{},[1996,60157,2011],{"stretchy":2004},[1996,60159,2225],{},[898,60161,2774],{},[898,60163,2777],{},[1996,60165,2005],{"stretchy":2004},[2124,60167,60168,60170],{},[898,60169,2789],{},[1996,60171,4354],{},[1996,60173,2011],{"stretchy":2004},[902,60175,60176],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,60178,60179,60180,2704],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,60181,60183],{"className":60182},[886],[888,60184,60185],{"xmlns":890},[892,60186,60187,60195],{},[895,60188,60189,60191,60193],{},[898,60190,2889],{"mathvariant":2376},[898,60192,2774],{},[898,60194,2777],{},[902,60196,60197],{"encoding":904},"\\Delta TC",[883,60199,60201],{"className":60200},[886],[888,60202,60203],{"xmlns":890,"display":28068},[892,60204,60205,60274],{},[20756,60206,60207],{"width":28073},[20761,60208,60209,60211,60267,60269],{},[20764,60210],{"width":28078},[20764,60212,60213],{},[895,60214,60215,60217,60219,60221,60223,60225,60227,60229,60231,60233,60235,60237,60239,60241,60247,60249,60251,60253,60255,60257,60259,60261,60263,60265],{},[898,60216,2889],{"mathvariant":2376},[898,60218,2774],{},[898,60220,2777],{},[2288,60222,3984],{},[1996,60224,2730],{},[2288,60226,3984],{},[898,60228,2194],{"mathvariant":2376},[898,60230,2774],{},[898,60232,2777],{},[1996,60234,1998],{},[1996,60236,2005],{"stretchy":2004},[898,60238,2774],{},[898,60240,2777],{},[2124,60242,60243,60245],{},[1996,60244,2011],{"stretchy":2004},[1996,60246,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[2288,60248,2987],{},[898,60250,2194],{"mathvariant":2376},[898,60252,2789],{},[1996,60254,1998],{},[898,60256,2818],{},[898,60258,2777],{},[2288,60260,2987],{},[898,60262,2194],{"mathvariant":2376},[898,60264,2789],{},[1996,60266,2286],{"separator":2285},[20764,60268],{"width":28078},[20764,60270,60271],{},[2288,60272,60273],{},"(3.9)",[902,60275,60276],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,60278,57313],{},[883,60280,60282],{"className":60281},[886],[888,60283,60284],{"xmlns":890,"display":28068},[892,60285,60286,60384],{},[895,60287,60288,60326,60328,60330,60332,60354,60356,60382],{},[895,60289,60290,60292,60298,60300,60306,60309,60315,60318],{},[2288,60291,57327],{},[8386,60293,60294,60296],{"accent":2285},[2288,60295,45734],{},[1996,60297,25060],{},[2288,60299,57336],{},[8386,60301,60302,60304],{"accent":2285},[2288,60303,1994],{},[1996,60305,24979],{},[2288,60307,60308],{},"ch n",[8386,60310,60311,60313],{"accent":2285},[2288,60312,207],{},[1996,60314,24979],{},[2288,60316,60317],{},"klad",[8386,60319,60320,60323],{"accent":2285},[2288,60321,60322],{},"u",[1996,60324,60325],{},"˚",[2288,60327,3984],{},[1996,60329,2730],{},[2288,60331,3984],{},[895,60333,60334,60336,60342,60345,60351],{},[2288,60335,57371],{},[8386,60337,60338,60340],{"accent":2285},[2288,60339,25048],{},[1996,60341,24979],{},[2288,60343,60344],{}," n",[8386,60346,60347,60349],{"accent":2285},[2288,60348,207],{},[1996,60350,24979],{},[2288,60352,60353],{},"klady",[1996,60355,57398],{},[895,60357,60358,60360,60366,60368,60374,60376],{},[2288,60359,57327],{},[8386,60361,60362,60364],{"accent":2285},[2288,60363,45734],{},[1996,60365,25060],{},[2288,60367,57411],{},[8386,60369,60370,60372],{"accent":2285},[2288,60371,9594],{},[1996,60373,25060],{},[2288,60375,57420],{},[8386,60377,60378,60380],{"accent":2285},[2288,60379,25048],{},[1996,60381,24979],{},[898,60383,1975],{"mathvariant":2376},[902,60385,60386],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[37350,60388,60390],{"id":60389},"příklad-35","Příklad 3.5",[724,60392,60393,57524,60395,56027,60431,60446,60447,60462,60463,2671,60476,2685,60489,60502,60503,2685,60516,1975],{},[38,60394,55989],{},[883,60396,60398],{"className":60397},[886],[888,60399,60400],{"xmlns":890},[892,60401,60402,60428],{},[895,60403,60404,60406,60408,60410,60412,60414,60416,60418,60420,60422],{},[898,60405,2774],{},[898,60407,2777],{},[1996,60409,1998],{},[2129,60411,8377],{},[1996,60413,2095],{},[2129,60415,2235],{},[898,60417,2789],{},[1996,60419,2095],{},[2129,60421,2131],{},[2124,60423,60424,60426],{},[898,60425,2789],{},[2129,60427,2131],{},[902,60429,60430],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,60432,60434],{"className":60433},[886],[888,60435,60436],{"xmlns":890},[892,60437,60438,60444],{},[895,60439,60440,60442],{},[898,60441,2818],{},[898,60443,2777],{},[902,60445,55294],{"encoding":904}," a odhadněte změny ",[883,60448,60450],{"className":60449},[886],[888,60451,60452],{"xmlns":890},[892,60453,60454,60460],{},[895,60455,60456,60458],{},[898,60457,2774],{},[898,60459,2777],{},[902,60461,3243],{"encoding":904}," při změnách ",[883,60464,60466],{"className":60465},[886],[888,60467,60468],{"xmlns":890},[892,60469,60470,60474],{},[895,60471,60472],{},[898,60473,2789],{},[902,60475,2789],{"encoding":904},[883,60477,60479],{"className":60478},[886],[888,60480,60481],{"xmlns":890},[892,60482,60483,60487],{},[895,60484,60485],{},[2129,60486,36246],{},[902,60488,36246],{"encoding":904},[883,60490,60492],{"className":60491},[886],[888,60493,60494],{"xmlns":890},[892,60495,60496,60500],{},[895,60497,60498],{},[2129,60499,41864],{},[902,60501,41864],{"encoding":904}," a z ",[883,60504,60506],{"className":60505},[886],[888,60507,60508],{"xmlns":890},[892,60509,60510,60514],{},[895,60511,60512],{},[2129,60513,36246],{},[902,60515,36246],{"encoding":904},[883,60517,60519],{"className":60518},[886],[888,60520,60521],{"xmlns":890},[892,60522,60523,60527],{},[895,60524,60525],{},[2129,60526,3509],{},[902,60528,3509],{"encoding":904},[724,60530,60531,2203,60533,2927,60559,1343,60586,60613,60614,60629,60630,60645,60646,60673,60674,60694,60695,20533,60716,60772,60773,2671,60786,2685,60799,8102,60812,1975],{},[38,60532,22772],{},[883,60534,60536],{"className":60535},[886],[888,60537,60538],{"xmlns":890},[892,60539,60540,60556],{},[895,60541,60542,60544,60546,60548,60550,60552,60554],{},[898,60543,2818],{},[898,60545,2777],{},[1996,60547,1998],{},[2129,60549,2235],{},[1996,60551,2095],{},[2129,60553,2351],{},[898,60555,2789],{},[902,60557,60558],{"encoding":904},"MC = 6 + 4Q",[883,60560,60562],{"className":60561},[886],[888,60563,60564],{"xmlns":890},[892,60565,60566,60583],{},[895,60567,60568,60570,60572,60574,60576,60578,60580],{},[898,60569,2818],{},[898,60571,2777],{},[1996,60573,2005],{"stretchy":2004},[2129,60575,36246],{},[1996,60577,2011],{"stretchy":2004},[1996,60579,1998],{},[2129,60581,60582],{},"66",[902,60584,60585],{"encoding":904},"MC(15) = 66",[883,60587,60589],{"className":60588},[886],[888,60590,60591],{"xmlns":890},[892,60592,60593,60610],{},[895,60594,60595,60597,60599,60601,60603,60605,60607],{},[898,60596,2818],{},[898,60598,2777],{},[1996,60600,2005],{"stretchy":2004},[2129,60602,9035],{},[1996,60604,2011],{"stretchy":2004},[1996,60606,1998],{},[2129,60608,60609],{},"86",[902,60611,60612],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,60615,60617],{"className":60616},[886],[888,60618,60619],{"xmlns":890},[892,60620,60621,60627],{},[895,60622,60623,60625],{},[898,60624,2774],{},[898,60626,2777],{},[902,60628,3243],{"encoding":904}," zvyšuje (",[883,60631,60633],{"className":60632},[886],[888,60634,60635],{"xmlns":890},[892,60636,60637,60643],{},[895,60638,60639,60641],{},[898,60640,2818],{},[898,60642,2777],{},[902,60644,55294],{"encoding":904}," je rostoucí). Z ",[883,60647,60649],{"className":60648},[886],[888,60650,60651],{"xmlns":890},[892,60652,60653,60670],{},[895,60654,60655,60657,60659,60661,60663,60665,60667],{},[898,60656,2774],{},[898,60658,2777],{},[1996,60660,2005],{"stretchy":2004},[2129,60662,36246],{},[1996,60664,2011],{"stretchy":2004},[1996,60666,1998],{},[2129,60668,60669],{},"740",[902,60671,60672],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,60675,60677],{"className":60676},[886],[888,60678,60679],{"xmlns":890},[892,60680,60681,60691],{},[895,60682,60683,60685,60687,60689],{},[898,60684,2194],{"mathvariant":2376},[898,60686,2789],{},[1996,60688,1998],{},[2129,60690,2278],{},[902,60692,60693],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,60696,60698],{"className":60697},[886],[888,60699,60700],{"xmlns":890},[892,60701,60702,60713],{},[895,60703,60704,60706,60708,60710],{},[898,60705,2774],{},[898,60707,2777],{},[1996,60709,2730],{},[2129,60711,60712],{},"806",[902,60714,60715],{"encoding":904},"TC \\approx 806",[883,60717,60719],{"className":60718},[886],[888,60720,60721],{"xmlns":890},[892,60722,60723,60769],{},[895,60724,60725,60727,60729,60731,60733,60735,60737,60739,60741,60743,60745,60747,60749,60751,60753,60755,60757,60760,60762,60764,60766],{},[898,60726,2889],{"mathvariant":2376},[898,60728,2774],{},[898,60730,2777],{},[1996,60732,1998],{},[898,60734,2774],{},[898,60736,2777],{},[1996,60738,2005],{"stretchy":2004},[2129,60740,41864],{},[1996,60742,2011],{"stretchy":2004},[1996,60744,2225],{},[898,60746,2774],{},[898,60748,2777],{},[1996,60750,2005],{"stretchy":2004},[2129,60752,36246],{},[1996,60754,2011],{"stretchy":2004},[1996,60756,1998],{},[2129,60758,60759],{},"808",[1996,60761,2225],{},[2129,60763,60669],{},[1996,60765,1998],{},[2129,60767,60768],{},"68",[902,60770,60771],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,60774,60776],{"className":60775},[886],[888,60777,60778],{"xmlns":890},[892,60779,60780,60784],{},[895,60781,60782],{},[898,60783,2789],{},[902,60785,2789],{"encoding":904},[883,60787,60789],{"className":60788},[886],[888,60790,60791],{"xmlns":890},[892,60792,60793,60797],{},[895,60794,60795],{},[2129,60796,36246],{},[902,60798,36246],{"encoding":904},[883,60800,60802],{"className":60801},[886],[888,60803,60804],{"xmlns":890},[892,60805,60806,60810],{},[895,60807,60808],{},[2129,60809,3509],{},[902,60811,3509],{"encoding":904},[883,60813,60815],{"className":60814},[886],[888,60816,60817],{"xmlns":890},[892,60818,60819,60848],{},[895,60820,60821,60823,60825,60827,60829,60831,60833,60835,60837,60839,60841,60843,60845],{},[898,60822,2889],{"mathvariant":2376},[898,60824,2774],{},[898,60826,2777],{},[1996,60828,2730],{},[2129,60830,60582],{},[1996,60832,3177],{},[1996,60834,2005],{"stretchy":2004},[1996,60836,2225],{},[2129,60838,2173],{},[1996,60840,2011],{"stretchy":2004},[1996,60842,1998],{},[1996,60844,2225],{},[2129,60846,60847],{},"198",[902,60849,60850],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,60852,60854],{"id":60853},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,60856,60857],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[37350,60859,60861],{"id":60860},"příklad-36","Příklad 3.6",[724,60863,60864,57524,60866,60910],{},[38,60865,55989],{},[883,60867,60869],{"className":60868},[886],[888,60870,60871],{"xmlns":890},[892,60872,60873,60907],{},[895,60874,60875,60877,60879,60881,60883,60885,60887,60889,60891,60893,60899,60901],{},[898,60876,2774],{},[898,60878,2777],{},[1996,60880,1998],{},[2129,60882,3090],{},[1996,60884,2095],{},[2129,60886,5004],{},[898,60888,2789],{},[1996,60890,2225],{},[2129,60892,2228],{},[2124,60894,60895,60897],{},[898,60896,2789],{},[2129,60898,2131],{},[1996,60900,2095],{},[2124,60902,60903,60905],{},[898,60904,2789],{},[2129,60906,2173],{},[902,60908,60909],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,60912,60913],{},[38,60914,22772],{},[883,60916,60918],{"className":60917},[886],[888,60919,60920],{"xmlns":890,"display":28068},[892,60921,60922,61166],{},[20756,60923,60924,60950,60998,61032,61074,61124],{"rowspacing":20758,"columnalign":20759,"columnspacing":2377},[20761,60925,60926,60936],{},[20764,60927,60928],{},[2325,60929,60930],{"scriptlevel":2327,"displaystyle":2285},[895,60931,60932,60934],{},[898,60933,10436],{},[898,60935,2777],{},[20764,60937,60938],{},[2325,60939,60940],{"scriptlevel":2327,"displaystyle":2285},[895,60941,60942,60944,60946,60948],{},[895,60943],{},[1996,60945,1998],{},[2129,60947,3090],{},[1996,60949,2286],{"separator":2285},[20761,60951,60952,60964],{},[20764,60953,60954],{},[2325,60955,60956],{"scriptlevel":2327,"displaystyle":2285},[895,60957,60958,60960,60962],{},[898,60959,2774],{},[898,60961,40341],{},[898,60963,2777],{},[20764,60965,60966],{},[2325,60967,60968],{"scriptlevel":2327,"displaystyle":2285},[895,60969,60970,60972,60974,60976,60978,60980,60982,60988,60990,60996],{},[895,60971],{},[1996,60973,1998],{},[2129,60975,5004],{},[898,60977,2789],{},[1996,60979,2225],{},[2129,60981,2228],{},[2124,60983,60984,60986],{},[898,60985,2789],{},[2129,60987,2131],{},[1996,60989,2095],{},[2124,60991,60992,60994],{},[898,60993,2789],{},[2129,60995,2173],{},[1996,60997,2286],{"separator":2285},[20761,60999,61000,61012],{},[20764,61001,61002],{},[2325,61003,61004],{"scriptlevel":2327,"displaystyle":2285},[895,61005,61006,61008,61010],{},[898,61007,4255],{},[898,61009,10436],{},[898,61011,2777],{},[20764,61013,61014],{},[2325,61015,61016],{"scriptlevel":2327,"displaystyle":2285},[895,61017,61018,61020,61022,61030],{},[895,61019],{},[1996,61021,1998],{},[2325,61023,61024],{"scriptlevel":2327,"displaystyle":2004},[2329,61025,61026,61028],{},[2129,61027,3090],{},[898,61029,2789],{},[1996,61031,2286],{"separator":2285},[20761,61033,61034,61046],{},[20764,61035,61036],{},[2325,61037,61038],{"scriptlevel":2327,"displaystyle":2285},[895,61039,61040,61042,61044],{},[898,61041,4255],{},[898,61043,40341],{},[898,61045,2777],{},[20764,61047,61048],{},[2325,61049,61050],{"scriptlevel":2327,"displaystyle":2285},[895,61051,61052,61054,61056,61058,61060,61062,61064,61066,61072],{},[895,61053],{},[1996,61055,1998],{},[2129,61057,5004],{},[1996,61059,2225],{},[2129,61061,2228],{},[898,61063,2789],{},[1996,61065,2095],{},[2124,61067,61068,61070],{},[898,61069,2789],{},[2129,61071,2131],{},[1996,61073,2286],{"separator":2285},[20761,61075,61076,61086],{},[20764,61077,61078],{},[2325,61079,61080],{"scriptlevel":2327,"displaystyle":2285},[895,61081,61082,61084],{},[898,61083,4255],{},[898,61085,2777],{},[20764,61087,61088],{},[2325,61089,61090],{"scriptlevel":2327,"displaystyle":2285},[895,61091,61092,61094,61096,61104,61106,61108,61110,61112,61114,61116,61122],{},[895,61093],{},[1996,61095,1998],{},[2325,61097,61098],{"scriptlevel":2327,"displaystyle":2004},[2329,61099,61100,61102],{},[2129,61101,3090],{},[898,61103,2789],{},[1996,61105,2095],{},[2129,61107,5004],{},[1996,61109,2225],{},[2129,61111,2228],{},[898,61113,2789],{},[1996,61115,2095],{},[2124,61117,61118,61120],{},[898,61119,2789],{},[2129,61121,2131],{},[1996,61123,2286],{"separator":2285},[20761,61125,61126,61136],{},[20764,61127,61128],{},[2325,61129,61130],{"scriptlevel":2327,"displaystyle":2285},[895,61131,61132,61134],{},[898,61133,2818],{},[898,61135,2777],{},[20764,61137,61138],{},[2325,61139,61140],{"scriptlevel":2327,"displaystyle":2285},[895,61141,61142,61144,61146,61148,61150,61152,61154,61156,61158,61164],{},[895,61143],{},[1996,61145,1998],{},[2129,61147,5004],{},[1996,61149,2225],{},[2129,61151,2863],{},[898,61153,2789],{},[1996,61155,2095],{},[2129,61157,2173],{},[2124,61159,61160,61162],{},[898,61161,2789],{},[2129,61163,2131],{},[898,61165,1975],{"mathvariant":2376},[902,61167,61168],{"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}",[724,61170,61171,61172,15794,61187,15794,61202,61217,61218,61233,61234,1343,61252,61233,61269,1343,61287,61233,61302,61320],{},"Význačné body ",[883,61173,61175],{"className":61174},[886],[888,61176,61177],{"xmlns":890},[892,61178,61179,61184],{},[895,61180,61181],{},[2129,61182,61183],{},"1,67",[902,61185,61186],{"encoding":904},"1{,}67",[883,61188,61190],{"className":61189},[886],[888,61191,61192],{"xmlns":890},[892,61193,61194,61199],{},[895,61195,61196],{},[2129,61197,61198],{},"2,50",[902,61200,61201],{"encoding":904},"2{,}50",[883,61203,61205],{"className":61204},[886],[888,61206,61207],{"xmlns":890},[892,61208,61209,61214],{},[895,61210,61211],{},[2129,61212,61213],{},"4,73",[902,61215,61216],{"encoding":904},"4{,}73"," odpovídají: ",[883,61219,61221],{"className":61220},[886],[888,61222,61223],{"xmlns":890},[892,61224,61225,61231],{},[895,61226,61227,61229],{},[898,61228,2818],{},[898,61230,2777],{},[902,61232,55294],{"encoding":904}," minimum v ",[883,61235,61237],{"className":61236},[886],[888,61238,61239],{"xmlns":890},[892,61240,61241,61249],{},[895,61242,61243,61245,61247],{},[898,61244,2789],{},[1996,61246,5900],{},[2129,61248,61183],{},[902,61250,61251],{"encoding":904},"Q \\doteq 1{,}67",[883,61253,61255],{"className":61254},[886],[888,61256,61257],{"xmlns":890},[892,61258,61259,61267],{},[895,61260,61261,61263,61265],{},[898,61262,4255],{},[898,61264,40341],{},[898,61266,2777],{},[902,61268,55313],{"encoding":904},[883,61270,61272],{"className":61271},[886],[888,61273,61274],{"xmlns":890},[892,61275,61276,61284],{},[895,61277,61278,61280,61282],{},[898,61279,2789],{},[1996,61281,1998],{},[2129,61283,61198],{},[902,61285,61286],{"encoding":904},"Q = 2{,}50",[883,61288,61290],{"className":61289},[886],[888,61291,61292],{"xmlns":890},[892,61293,61294,61300],{},[895,61295,61296,61298],{},[898,61297,4255],{},[898,61299,2777],{},[902,61301,55562],{"encoding":904},[883,61303,61305],{"className":61304},[886],[888,61306,61307],{"xmlns":890},[892,61308,61309,61317],{},[895,61310,61311,61313,61315],{},[898,61312,2789],{},[1996,61314,5900],{},[2129,61316,61213],{},[902,61318,61319],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,61322,61323],{},[2559,61324],{"alt":61325,"className":61326,"src":61327},"imek-ac-avc-mc",[210,2563],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,61329,61330],{},[614,61331,61332,61333,3885,61348,61365,61366,15794,61385,61400],{},"Obrázek 3.9: Kubické křivky ",[883,61334,61336],{"className":61335},[886],[888,61337,61338],{"xmlns":890},[892,61339,61340,61346],{},[895,61341,61342,61344],{},[898,61343,2774],{},[898,61345,2777],{},[902,61347,3243],{"encoding":904},[883,61349,61351],{"className":61350},[886],[888,61352,61353],{"xmlns":890},[892,61354,61355,61363],{},[895,61356,61357,61359,61361],{},[898,61358,2774],{},[898,61360,40341],{},[898,61362,2777],{},[902,61364,55511],{"encoding":904}," rostoucí od bodu ",[883,61367,61369],{"className":61368},[886],[888,61370,61371],{"xmlns":890},[892,61372,61373,61383],{},[895,61374,61375,61377,61379,61381],{},[898,61376,10436],{},[898,61378,2777],{},[1996,61380,1998],{},[2129,61382,3090],{},[902,61384,11634],{"encoding":904},[883,61386,61388],{"className":61387},[886],[888,61389,61390],{"xmlns":890},[892,61391,61392,61398],{},[895,61393,61394,61396],{},[898,61395,10436],{},[898,61397,2777],{},[902,61399,55493],{"encoding":904}," je vodorovná přímka.",[724,61402,61403],{},[614,61404,61405,61406,1343,61421,1343,61438,29203,61453,61466,61467,2927,61484,61499,61500,6190,61517,61532,61533,26191,61546,1343,61559,1343,61572,1975],{},"Obrázek 3.10: Křivky ",[883,61407,61409],{"className":61408},[886],[888,61410,61411],{"xmlns":890},[892,61412,61413,61419],{},[895,61414,61415,61417],{},[898,61416,4255],{},[898,61418,2777],{},[902,61420,55562],{"encoding":904},[883,61422,61424],{"className":61423},[886],[888,61425,61426],{"xmlns":890},[892,61427,61428,61436],{},[895,61429,61430,61432,61434],{},[898,61431,4255],{},[898,61433,40341],{},[898,61435,2777],{},[902,61437,55313],{"encoding":904},[883,61439,61441],{"className":61440},[886],[888,61442,61443],{"xmlns":890},[892,61444,61445,61451],{},[895,61446,61447,61449],{},[898,61448,2818],{},[898,61450,2777],{},[902,61452,55294],{"encoding":904},[883,61454,61456],{"className":61455},[886],[888,61457,61458],{"xmlns":890},[892,61459,61460,61464],{},[895,61461,61462],{},[898,61463,900],{},[902,61465,900],{"encoding":904}," a klesající hyperbola ",[883,61468,61470],{"className":61469},[886],[888,61471,61472],{"xmlns":890},[892,61473,61474,61482],{},[895,61475,61476,61478,61480],{},[898,61477,4255],{},[898,61479,10436],{},[898,61481,2777],{},[902,61483,55529],{"encoding":904},[883,61485,61487],{"className":61486},[886],[888,61488,61489],{"xmlns":890},[892,61490,61491,61497],{},[895,61492,61493,61495],{},[898,61494,2818],{},[898,61496,2777],{},[902,61498,55294],{"encoding":904}," protíná ",[883,61501,61503],{"className":61502},[886],[888,61504,61505],{"xmlns":890},[892,61506,61507,61515],{},[895,61508,61509,61511,61513],{},[898,61510,4255],{},[898,61512,40341],{},[898,61514,2777],{},[902,61516,55313],{"encoding":904},[883,61518,61520],{"className":61519},[886],[888,61521,61522],{"xmlns":890},[892,61523,61524,61530],{},[895,61525,61526,61528],{},[898,61527,4255],{},[898,61529,2777],{},[902,61531,55562],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,61534,61536],{"className":61535},[886],[888,61537,61538],{"xmlns":890},[892,61539,61540,61544],{},[895,61541,61542],{},[898,61543,2789],{},[902,61545,2789],{"encoding":904},[883,61547,61549],{"className":61548},[886],[888,61550,61551],{"xmlns":890},[892,61552,61553,61557],{},[895,61554,61555],{},[2129,61556,61183],{},[902,61558,61186],{"encoding":904},[883,61560,61562],{"className":61561},[886],[888,61563,61564],{"xmlns":890},[892,61565,61566,61570],{},[895,61567,61568],{},[2129,61569,61198],{},[902,61571,61201],{"encoding":904},[883,61573,61575],{"className":61574},[886],[888,61576,61577],{"xmlns":890},[892,61578,61579,61583],{},[895,61580,61581],{},[2129,61582,61213],{},[902,61584,61216],{"encoding":904},[724,61586,61587],{},[38,61588,61589],{},"Standardní vlastnosti:",[120,61591,61592,61627,61691,61759,61809,61829],{},[123,61593,61594,3885,61609,61626],{},[883,61595,61597],{"className":61596},[886],[888,61598,61599],{"xmlns":890},[892,61600,61601,61607],{},[895,61602,61603,61605],{},[898,61604,2774],{},[898,61606,2777],{},[902,61608,3243],{"encoding":904},[883,61610,61612],{"className":61611},[886],[888,61613,61614],{"xmlns":890},[892,61615,61616,61624],{},[895,61617,61618,61620,61622],{},[898,61619,2774],{},[898,61621,40341],{},[898,61623,2777],{},[902,61625,55511],{"encoding":904}," jsou kubické funkce;",[123,61628,61629,1343,61644,1343,61661,61676,61677,61690],{},[883,61630,61632],{"className":61631},[886],[888,61633,61634],{"xmlns":890},[892,61635,61636,61642],{},[895,61637,61638,61640],{},[898,61639,4255],{},[898,61641,2777],{},[902,61643,55562],{"encoding":904},[883,61645,61647],{"className":61646},[886],[888,61648,61649],{"xmlns":890},[892,61650,61651,61659],{},[895,61652,61653,61655,61657],{},[898,61654,4255],{},[898,61656,40341],{},[898,61658,2777],{},[902,61660,55313],{"encoding":904},[883,61662,61664],{"className":61663},[886],[888,61665,61666],{"xmlns":890},[892,61667,61668,61674],{},[895,61669,61670,61672],{},[898,61671,2818],{},[898,61673,2777],{},[902,61675,55294],{"encoding":904}," jsou křivky tvaru ",[883,61678,61680],{"className":61679},[886],[888,61681,61682],{"xmlns":890},[892,61683,61684,61688],{},[895,61685,61686],{},[898,61687,900],{},[902,61689,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,61692,61693,61708,61709,1343,61726,61743,61744,8425],{},[883,61694,61696],{"className":61695},[886],[888,61697,61698],{"xmlns":890},[892,61699,61700,61706],{},[895,61701,61702,61704],{},[898,61703,2818],{},[898,61705,2777],{},[902,61707,55294],{"encoding":904}," nabývá minima před ",[883,61710,61712],{"className":61711},[886],[888,61713,61714],{"xmlns":890},[892,61715,61716,61724],{},[895,61717,61718,61720,61722],{},[898,61719,4255],{},[898,61721,40341],{},[898,61723,2777],{},[902,61725,55313],{"encoding":904},[883,61727,61729],{"className":61728},[886],[888,61730,61731],{"xmlns":890},[892,61732,61733,61741],{},[895,61734,61735,61737,61739],{},[898,61736,4255],{},[898,61738,40341],{},[898,61740,2777],{},[902,61742,55313],{"encoding":904}," před ",[883,61745,61747],{"className":61746},[886],[888,61748,61749],{"xmlns":890},[892,61750,61751,61757],{},[895,61752,61753,61755],{},[898,61754,4255],{},[898,61756,2777],{},[902,61758,55562],{"encoding":904},[123,61760,61761,61499,61776,3885,61791,61808],{},[883,61762,61764],{"className":61763},[886],[888,61765,61766],{"xmlns":890},[892,61767,61768,61774],{},[895,61769,61770,61772],{},[898,61771,2818],{},[898,61773,2777],{},[902,61775,55294],{"encoding":904},[883,61777,61779],{"className":61778},[886],[888,61780,61781],{"xmlns":890},[892,61782,61783,61789],{},[895,61784,61785,61787],{},[898,61786,4255],{},[898,61788,2777],{},[902,61790,55562],{"encoding":904},[883,61792,61794],{"className":61793},[886],[888,61795,61796],{"xmlns":890},[892,61797,61798,61806],{},[895,61799,61800,61802,61804],{},[898,61801,4255],{},[898,61803,40341],{},[898,61805,2777],{},[902,61807,55313],{"encoding":904}," zdola právě v jejich minimech;",[123,61810,61811,61828],{},[883,61812,61814],{"className":61813},[886],[888,61815,61816],{"xmlns":890},[892,61817,61818,61826],{},[895,61819,61820,61822,61824],{},[898,61821,4255],{},[898,61823,10436],{},[898,61825,2777],{},[902,61827,55529],{"encoding":904}," je hyperbola, stále klesající;",[123,61830,61831,61863,61864,3885,61879,61896,61897,61910,61911,3918],{},[883,61832,61834],{"className":61833},[886],[888,61835,61836],{"xmlns":890},[892,61837,61838,61860],{},[895,61839,61840,61842,61844,61846,61848,61850,61852,61854,61856,61858],{},[898,61841,4255],{},[898,61843,2777],{},[1996,61845,1998],{},[898,61847,4255],{},[898,61849,10436],{},[898,61851,2777],{},[1996,61853,2095],{},[898,61855,4255],{},[898,61857,40341],{},[898,61859,2777],{},[902,61861,61862],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,61865,61867],{"className":61866},[886],[888,61868,61869],{"xmlns":890},[892,61870,61871,61877],{},[895,61872,61873,61875],{},[898,61874,4255],{},[898,61876,2777],{},[902,61878,55562],{"encoding":904},[883,61880,61882],{"className":61881},[886],[888,61883,61884],{"xmlns":890},[892,61885,61886,61894],{},[895,61887,61888,61890,61892],{},[898,61889,4255],{},[898,61891,40341],{},[898,61893,2777],{},[902,61895,55313],{"encoding":904}," klesá s rostoucím ",[883,61898,61900],{"className":61899},[886],[888,61901,61902],{"xmlns":890},[892,61903,61904,61908],{},[895,61905,61906],{},[898,61907,2789],{},[902,61909,2789],{"encoding":904}," (protože ",[883,61912,61914],{"className":61913},[886],[888,61915,61916],{"xmlns":890},[892,61917,61918,61930],{},[895,61919,61920,61922,61924,61926,61928],{},[898,61921,4255],{},[898,61923,10436],{},[898,61925,2777],{},[1996,61927,3123],{},[2129,61929,2327],{},[902,61931,61932],{"encoding":904},"AFC \\to 0",[115,61934,61936],{"id":61935},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,61938,61939,61940,61943,61944,61959],{},"Častou optimalizační úlohou je ",[38,61941,61942],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,61945,61947],{"className":61946},[886],[888,61948,61949],{"xmlns":890},[892,61950,61951,61957],{},[895,61952,61953,61955],{},[898,61954,4255],{},[898,61956,2777],{},[902,61958,55562],{"encoding":904}," minimální.",[198,61961,16414],{"id":16413},[724,61963,61964,61965,61982],{},"Mají-li průměrné náklady minimum v bodě ",[883,61966,61968],{"className":61967},[886],[888,61969,61970],{"xmlns":890},[892,61971,61972,61980],{},[895,61973,61974],{},[2272,61975,61976,61978],{},[898,61977,2789],{},[2129,61979,2327],{},[902,61981,38310],{"encoding":904},", pak platí",[883,61984,61986],{"className":61985},[886],[888,61987,61988],{"xmlns":890,"display":28068},[892,61989,61990,62039],{},[20756,61991,61992],{"width":28073},[20761,61993,61994,61996,62032,62034],{},[20764,61995],{"width":28078},[20764,61997,61998],{},[895,61999,62000,62002,62004,62006,62012,62014,62016,62018,62020,62022,62028,62030],{},[898,62001,4255],{},[898,62003,2777],{},[1996,62005,2005],{"stretchy":2004},[2272,62007,62008,62010],{},[898,62009,2789],{},[2129,62011,2327],{},[1996,62013,2011],{"stretchy":2004},[1996,62015,1998],{},[898,62017,2818],{},[898,62019,2777],{},[1996,62021,2005],{"stretchy":2004},[2272,62023,62024,62026],{},[898,62025,2789],{},[2129,62027,2327],{},[1996,62029,2011],{"stretchy":2004},[898,62031,1975],{"mathvariant":2376},[20764,62033],{"width":28078},[20764,62035,62036],{},[2288,62037,62038],{},"(3.10)",[902,62040,62041],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[3867,62043,62044],{},[724,62045,62046,62048,62049],{},[883,62047,56446],{}," Princip\n",[38,62050,62051],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,62053,62054,62057,62058,62100],{},[38,62055,62056],{},"Odvození."," Z ",[883,62059,62061],{"className":62060},[886],[888,62062,62063],{"xmlns":890},[892,62064,62065,62097],{},[895,62066,62067,62069,62071,62073,62075,62077,62079],{},[898,62068,4255],{},[898,62070,2777],{},[1996,62072,2005],{"stretchy":2004},[898,62074,2789],{},[1996,62076,2011],{"stretchy":2004},[1996,62078,1998],{},[2325,62080,62081],{"scriptlevel":2327,"displaystyle":2004},[2329,62082,62083,62095],{},[895,62084,62085,62087,62089,62091,62093],{},[898,62086,2774],{},[898,62088,2777],{},[1996,62090,2005],{"stretchy":2004},[898,62092,2789],{},[1996,62094,2011],{"stretchy":2004},[898,62096,2789],{},[902,62098,62099],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,62102,62104],{"className":62103},[886],[888,62105,62106],{"xmlns":890,"display":28068},[892,62107,62108,62240],{},[895,62109,62110,62112,62118,62120,62122,62124,62126,62166,62168,62208,62210,62238],{},[898,62111,4255],{},[2124,62113,62114,62116],{},[898,62115,2777],{},[1996,62117,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,62119,2005],{"stretchy":2004},[898,62121,2789],{},[1996,62123,2011],{"stretchy":2004},[1996,62125,1998],{},[2329,62127,62128,62160],{},[895,62129,62130,62132,62138,62140,62142,62144,62146,62148,62150,62152,62154,62156,62158],{},[898,62131,2774],{},[2124,62133,62134,62136],{},[898,62135,2777],{},[1996,62137,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,62139,2005],{"stretchy":2004},[898,62141,2789],{},[1996,62143,2011],{"stretchy":2004},[1996,62145,3177],{},[898,62147,2789],{},[1996,62149,2225],{},[898,62151,2774],{},[898,62153,2777],{},[1996,62155,2005],{"stretchy":2004},[898,62157,2789],{},[1996,62159,2011],{"stretchy":2004},[2124,62161,62162,62164],{},[898,62163,2789],{},[2129,62165,2131],{},[1996,62167,1998],{},[2329,62169,62170,62202],{},[895,62171,62172,62174,62176,62178,62180,62182,62184,62186,62188,62190,62192,62194,62196,62198,62200],{},[898,62173,2818],{},[898,62175,2777],{},[1996,62177,2005],{"stretchy":2004},[898,62179,2789],{},[1996,62181,2011],{"stretchy":2004},[1996,62183,3177],{},[898,62185,2789],{},[1996,62187,2225],{},[898,62189,4255],{},[898,62191,2777],{},[1996,62193,2005],{"stretchy":2004},[898,62195,2789],{},[1996,62197,2011],{"stretchy":2004},[1996,62199,3177],{},[898,62201,2789],{},[2124,62203,62204,62206],{},[898,62205,2789],{},[2129,62207,2131],{},[1996,62209,1998],{},[2329,62211,62212,62236],{},[895,62213,62214,62216,62218,62220,62222,62224,62226,62228,62230,62232,62234],{},[898,62215,2818],{},[898,62217,2777],{},[1996,62219,2005],{"stretchy":2004},[898,62221,2789],{},[1996,62223,2011],{"stretchy":2004},[1996,62225,2225],{},[898,62227,4255],{},[898,62229,2777],{},[1996,62231,2005],{"stretchy":2004},[898,62233,2789],{},[1996,62235,2011],{"stretchy":2004},[898,62237,2789],{},[898,62239,1975],{"mathvariant":2376},[902,62241,62242],{"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}.",[724,62244,62245,62246,2624,62261,8102,62283,56823],{},"Nutnou podmínkou minima ",[883,62247,62249],{"className":62248},[886],[888,62250,62251],{"xmlns":890},[892,62252,62253,62259],{},[895,62254,62255,62257],{},[898,62256,4255],{},[898,62258,2777],{},[902,62260,55562],{"encoding":904},[883,62262,62264],{"className":62263},[886],[888,62265,62266],{"xmlns":890},[892,62267,62268,62280],{},[895,62269,62270,62276,62278],{},[2272,62271,62272,62274],{},[898,62273,2789],{},[2129,62275,2327],{},[1996,62277,3408],{},[2129,62279,2327],{},[902,62281,62282],{"encoding":904},"Q_0 > 0",[883,62284,62286],{"className":62285},[886],[888,62287,62288],{"xmlns":890},[892,62289,62290,62314],{},[895,62291,62292,62294,62300,62302,62308,62310,62312],{},[898,62293,4255],{},[2124,62295,62296,62298],{},[898,62297,2777],{},[1996,62299,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,62301,2005],{"stretchy":2004},[2272,62303,62304,62306],{},[898,62305,2789],{},[2129,62307,2327],{},[1996,62309,2011],{"stretchy":2004},[1996,62311,1998],{},[2129,62313,2327],{},[902,62315,62316],{"encoding":904},"AC'(Q_0) = 0",[883,62318,62320],{"className":62319},[886],[888,62321,62322],{"xmlns":890,"display":28068},[892,62323,62324,62409],{},[895,62325,62326,62366,62368,62370,62372,62375,62377,62379,62381,62383,62389,62391,62393,62395,62397,62399,62405,62407],{},[2329,62327,62328,62360],{},[895,62329,62330,62332,62334,62336,62342,62344,62346,62348,62350,62352,62358],{},[898,62331,2818],{},[898,62333,2777],{},[1996,62335,2005],{"stretchy":2004},[2272,62337,62338,62340],{},[898,62339,2789],{},[2129,62341,2327],{},[1996,62343,2011],{"stretchy":2004},[1996,62345,2225],{},[898,62347,4255],{},[898,62349,2777],{},[1996,62351,2005],{"stretchy":2004},[2272,62353,62354,62356],{},[898,62355,2789],{},[2129,62357,2327],{},[1996,62359,2011],{"stretchy":2004},[2272,62361,62362,62364],{},[898,62363,2789],{},[2129,62365,2327],{},[1996,62367,1998],{},[2129,62369,2327],{},[5878,62371],{"width":15286},[1996,62373,62374],{},"⟺",[5878,62376],{"width":15286},[898,62378,2818],{},[898,62380,2777],{},[1996,62382,2005],{"stretchy":2004},[2272,62384,62385,62387],{},[898,62386,2789],{},[2129,62388,2327],{},[1996,62390,2011],{"stretchy":2004},[1996,62392,1998],{},[898,62394,4255],{},[898,62396,2777],{},[1996,62398,2005],{"stretchy":2004},[2272,62400,62401,62403],{},[898,62402,2789],{},[2129,62404,2327],{},[1996,62406,2011],{"stretchy":2004},[898,62408,1975],{"mathvariant":2376},[902,62410,62411],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,62413,62414,2203,62417,61499,62432,62447,62448,62463,62464,8102,62481,62503,62504,62526],{},[38,62415,62416],{},"Geometrická interpretace.",[883,62418,62420],{"className":62419},[886],[888,62421,62422],{"xmlns":890},[892,62423,62424,62430],{},[895,62425,62426,62428],{},[898,62427,2818],{},[898,62429,2777],{},[902,62431,55294],{"encoding":904},[883,62433,62435],{"className":62434},[886],[888,62436,62437],{"xmlns":890},[892,62438,62439,62445],{},[895,62440,62441,62443],{},[898,62442,4255],{},[898,62444,2777],{},[902,62446,55562],{"encoding":904}," právě v bodě minima ",[883,62449,62451],{"className":62450},[886],[888,62452,62453],{"xmlns":890},[892,62454,62455,62461],{},[895,62456,62457,62459],{},[898,62458,4255],{},[898,62460,2777],{},[902,62462,55562],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,62465,62467],{"className":62466},[886],[888,62468,62469],{"xmlns":890},[892,62470,62471,62479],{},[895,62472,62473],{},[2272,62474,62475,62477],{},[898,62476,2789],{},[2129,62478,2327],{},[902,62480,38310],{"encoding":904},[883,62482,62484],{"className":62483},[886],[888,62485,62486],{"xmlns":890},[892,62487,62488,62500],{},[895,62489,62490,62492,62494,62496,62498],{},[898,62491,2818],{},[898,62493,2777],{},[1996,62495,3447],{},[898,62497,4255],{},[898,62499,2777],{},[902,62501,62502],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,62505,62507],{"className":62506},[886],[888,62508,62509],{"xmlns":890},[892,62510,62511,62523],{},[895,62512,62513,62515,62517,62519,62521],{},[898,62514,2818],{},[898,62516,2777],{},[1996,62518,3408],{},[898,62520,4255],{},[898,62522,2777],{},[902,62524,62525],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,62528,62529,62530,62572,62573,62590,62591,1975],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,62531,62533],{"className":62532},[886],[888,62534,62535],{"xmlns":890},[892,62536,62537,62569],{},[895,62538,62539,62541,62543,62545,62551,62553,62555,62557,62559,62561,62567],{},[898,62540,4255],{},[898,62542,2777],{},[1996,62544,2005],{"stretchy":2004},[2272,62546,62547,62549],{},[898,62548,2789],{},[2129,62550,2327],{},[1996,62552,2011],{"stretchy":2004},[1996,62554,1998],{},[898,62556,2818],{},[898,62558,2777],{},[1996,62560,2005],{"stretchy":2004},[2272,62562,62563,62565],{},[898,62564,2789],{},[2129,62566,2327],{},[1996,62568,2011],{"stretchy":2004},[902,62570,62571],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,62574,62576],{"className":62575},[886],[888,62577,62578],{"xmlns":890},[892,62579,62580,62588],{},[895,62581,62582],{},[2272,62583,62584,62586],{},[898,62585,2789],{},[2129,62587,2327],{},[902,62589,38310],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,62592,62594],{"className":62593},[886],[888,62595,62596],{"xmlns":890},[892,62597,62598,62622],{},[895,62599,62600,62602,62604,62606,62608,62610,62612,62614,62616,62618,62620],{},[898,62601,4255],{},[898,62603,2777],{},[1996,62605,2005],{"stretchy":2004},[898,62607,2789],{},[1996,62609,2011],{"stretchy":2004},[1996,62611,1998],{},[898,62613,2818],{},[898,62615,2777],{},[1996,62617,2005],{"stretchy":2004},[898,62619,2789],{},[1996,62621,2011],{"stretchy":2004},[902,62623,62624],{"encoding":904},"AC(Q) = MC(Q)",[3867,62626,62627],{},[724,62628,62629,62631,62632,10394,62650,62671,62672,10394,62675,62696,62697,62712,62713,58040,62728,3918],{},[883,62630,4412],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,62633,62634,62635],{},"minimum ",[883,62636,62638],{"className":62637},[886],[888,62639,62640],{"xmlns":890},[892,62641,62642,62648],{},[895,62643,62644,62646],{},[898,62645,4255],{},[898,62647,2777],{},[902,62649,55562],{"encoding":904},[883,62651,62653],{"className":62652},[886],[888,62654,62655],{"xmlns":890},[892,62656,62657,62669],{},[895,62658,62659,62661,62663,62665,62667],{},[898,62660,4255],{},[898,62662,2777],{},[1996,62664,1998],{},[898,62666,2818],{},[898,62668,2777],{},[902,62670,55225],{"encoding":904},", pro ",[38,62673,62674],{},"maximum zisku",[883,62676,62678],{"className":62677},[886],[888,62679,62680],{"xmlns":890},[892,62681,62682,62694],{},[895,62683,62684,62686,62688,62690,62692],{},[898,62685,2818],{},[898,62687,3994],{},[1996,62689,1998],{},[898,62691,2818],{},[898,62693,2777],{},[902,62695,55273],{"encoding":904},". Obě podmínky využívají ",[883,62698,62700],{"className":62699},[886],[888,62701,62702],{"xmlns":890},[892,62703,62704,62710],{},[895,62705,62706,62708],{},[898,62707,2818],{},[898,62709,2777],{},[902,62711,55294],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,62714,62716],{"className":62715},[886],[888,62717,62718],{"xmlns":890},[892,62719,62720,62726],{},[895,62721,62722,62724],{},[898,62723,4255],{},[898,62725,2777],{},[902,62727,55562],{"encoding":904},[883,62729,62731],{"className":62730},[886],[888,62732,62733],{"xmlns":890},[892,62734,62735,62741],{},[895,62736,62737,62739],{},[898,62738,2818],{},[898,62740,3994],{},[902,62742,6634],{"encoding":904},[37350,62744,62746],{"id":62745},"příklad-37","Příklad 3.7",[724,62748,62749,57524,62751,62785,62786,62799,62800,62815],{},[38,62750,55989],{},[883,62752,62754],{"className":62753},[886],[888,62755,62756],{"xmlns":890},[892,62757,62758,62782],{},[895,62759,62760,62762,62764,62766,62772,62774,62776,62778,62780],{},[898,62761,2774],{},[898,62763,2777],{},[1996,62765,1998],{},[2124,62767,62768,62770],{},[898,62769,2789],{},[2129,62771,2131],{},[1996,62773,2095],{},[2129,62775,2173],{},[898,62777,2789],{},[1996,62779,2095],{},[2129,62781,5565],{},[902,62783,62784],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,62787,62789],{"className":62788},[886],[888,62790,62791],{"xmlns":890},[892,62792,62793,62797],{},[895,62794,62795],{},[898,62796,2789],{},[902,62798,2789],{"encoding":904}," minimalizující ",[883,62801,62803],{"className":62802},[886],[888,62804,62805],{"xmlns":890},[892,62806,62807,62813],{},[895,62808,62809,62811],{},[898,62810,4255],{},[898,62812,2777],{},[902,62814,55562],{"encoding":904}," a ověřte princip (3.10).",[724,62817,62818,62820],{},[38,62819,22772],{}," Přímý výpočet:",[883,62822,62824],{"className":62823},[886],[888,62825,62826],{"xmlns":890,"display":28068},[892,62827,62828,62930],{},[895,62829,62830,62832,62834,62836,62858,62860,62862,62864,62866,62868,62874,62876,62878,62880,62882,62884,62890,62892,62894,62896,62906,62908,62928],{},[898,62831,4255],{},[898,62833,2777],{},[1996,62835,1998],{},[2329,62837,62838,62856],{},[895,62839,62840,62846,62848,62850,62852,62854],{},[2124,62841,62842,62844],{},[898,62843,2789],{},[2129,62845,2131],{},[1996,62847,2095],{},[2129,62849,2173],{},[898,62851,2789],{},[1996,62853,2095],{},[2129,62855,5565],{},[898,62857,2789],{},[1996,62859,1998],{},[898,62861,2789],{},[1996,62863,2095],{},[2129,62865,2173],{},[1996,62867,2095],{},[2329,62869,62870,62872],{},[2129,62871,5565],{},[898,62873,2789],{},[1996,62875,2286],{"separator":2285},[5878,62877],{"width":5880},[1996,62879,2005],{"stretchy":2004},[898,62881,4255],{},[898,62883,2777],{},[2124,62885,62886,62888],{},[1996,62887,2011],{"stretchy":2004},[1996,62889,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,62891,1998],{},[2129,62893,2278],{},[1996,62895,2225],{},[2329,62897,62898,62900],{},[2129,62899,5565],{},[2124,62901,62902,62904],{},[898,62903,2789],{},[2129,62905,2131],{},[1996,62907,1998],{},[2329,62909,62910,62922],{},[895,62911,62912,62918,62920],{},[2124,62913,62914,62916],{},[898,62915,2789],{},[2129,62917,2131],{},[1996,62919,2225],{},[2129,62921,5565],{},[2124,62923,62924,62926],{},[898,62925,2789],{},[2129,62927,2131],{},[898,62929,1975],{"mathvariant":2376},[902,62931,62932],{"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}.",[724,62934,62935,62975,62976,63000,63001,63051,63052,1975],{},[883,62936,62938],{"className":62937},[886],[888,62939,62940],{"xmlns":890},[892,62941,62942,62972],{},[895,62943,62944,62946,62948,62950,62956,62958,62960,62962,62968,62970],{},[1996,62945,2005],{"stretchy":2004},[898,62947,4255],{},[898,62949,2777],{},[2124,62951,62952,62954],{},[1996,62953,2011],{"stretchy":2004},[1996,62955,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,62957,1998],{},[2129,62959,2327],{},[1996,62961,3987],{},[2272,62963,62964,62966],{},[898,62965,2789],{},[2129,62967,2278],{},[1996,62969,1998],{},[2129,62971,2235],{},[902,62973,62974],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,62977,62979],{"className":62978},[886],[888,62980,62981],{"xmlns":890},[892,62982,62983,62997],{},[895,62984,62985,62991,62993,62995],{},[2272,62986,62987,62989],{},[898,62988,2789],{},[2129,62990,2131],{},[1996,62992,1998],{},[1996,62994,2225],{},[2129,62996,2235],{},[902,62998,62999],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,63002,63004],{"className":63003},[886],[888,63005,63006],{"xmlns":890},[892,63007,63008,63048],{},[895,63009,63010,63012,63014,63016,63026,63028,63030,63032,63034,63042,63044,63046],{},[1996,63011,2005],{"stretchy":2004},[898,63013,4255],{},[898,63015,2777],{},[2124,63017,63018,63020],{},[1996,63019,2011],{"stretchy":2004},[895,63021,63022,63024],{},[1996,63023,2378],{"mathvariant":2376},[1996,63025,2378],{"mathvariant":2376},[1996,63027,2005],{"stretchy":2004},[2129,63029,2235],{},[1996,63031,2011],{"stretchy":2004},[1996,63033,1998],{},[2325,63035,63036],{"scriptlevel":2327,"displaystyle":2004},[2329,63037,63038,63040],{},[2129,63039,2278],{},[2129,63041,2173],{},[1996,63043,3408],{},[2129,63045,2327],{},[1996,63047,3987],{},[902,63049,63050],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,63053,63055],{"className":63054},[886],[888,63056,63057],{"xmlns":890},[892,63058,63059,63075],{},[895,63060,63061,63063,63065,63067,63069,63071,63073],{},[898,63062,4255],{},[898,63064,2777],{},[1996,63066,2005],{"stretchy":2004},[2129,63068,2235],{},[1996,63070,2011],{"stretchy":2004},[1996,63072,1998],{},[2129,63074,36246],{},[902,63076,63077],{"encoding":904},"AC(6) = 15",[724,63079,63080,63081,63107,63108,2704],{},"Pomocí principu: ",[883,63082,63084],{"className":63083},[886],[888,63085,63086],{"xmlns":890},[892,63087,63088,63104],{},[895,63089,63090,63092,63094,63096,63098,63100,63102],{},[898,63091,2818],{},[898,63093,2777],{},[1996,63095,1998],{},[2129,63097,2131],{},[898,63099,2789],{},[1996,63101,2095],{},[2129,63103,2173],{},[902,63105,63106],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,63109,63111],{"className":63110},[886],[888,63112,63113],{"xmlns":890},[892,63114,63115,63127],{},[895,63116,63117,63119,63121,63123,63125],{},[898,63118,4255],{},[898,63120,2777],{},[1996,63122,1998],{},[898,63124,2818],{},[898,63126,2777],{},[902,63128,55225],{"encoding":904},[883,63130,63132],{"className":63131},[886],[888,63133,63134],{"xmlns":890,"display":28068},[892,63135,63136,63238],{},[895,63137,63138,63160,63162,63164,63166,63168,63170,63172,63174,63176,63182,63184,63186,63188,63190,63192,63194,63196,63202,63204,63206,63208,63210,63212,63214,63220,63222,63224,63226,63228,63230,63232,63234,63236],{},[2329,63139,63140,63158],{},[895,63141,63142,63148,63150,63152,63154,63156],{},[2124,63143,63144,63146],{},[898,63145,2789],{},[2129,63147,2131],{},[1996,63149,2095],{},[2129,63151,2173],{},[898,63153,2789],{},[1996,63155,2095],{},[2129,63157,5565],{},[898,63159,2789],{},[1996,63161,1998],{},[2129,63163,2131],{},[898,63165,2789],{},[1996,63167,2095],{},[2129,63169,2173],{},[2288,63171,3984],{},[1996,63173,3987],{},[2288,63175,3984],{},[2124,63177,63178,63180],{},[898,63179,2789],{},[2129,63181,2131],{},[1996,63183,2095],{},[2129,63185,2173],{},[898,63187,2789],{},[1996,63189,2095],{},[2129,63191,5565],{},[1996,63193,1998],{},[2129,63195,2131],{},[2124,63197,63198,63200],{},[898,63199,2789],{},[2129,63201,2131],{},[1996,63203,2095],{},[2129,63205,2173],{},[898,63207,2789],{},[2288,63209,3984],{},[1996,63211,3987],{},[2288,63213,3984],{},[2124,63215,63216,63218],{},[898,63217,2789],{},[2129,63219,2131],{},[1996,63221,1998],{},[2129,63223,5565],{},[2288,63225,3984],{},[1996,63227,3987],{},[2288,63229,3984],{},[898,63231,2789],{},[1996,63233,1998],{},[2129,63235,2235],{},[1996,63237,2286],{"separator":2285},[902,63239,63240],{"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,",[724,63242,63243,63244,63282],{},"a ",[883,63245,63247],{"className":63246},[886],[888,63248,63249],{"xmlns":890},[892,63250,63251,63279],{},[895,63252,63253,63255,63257,63259,63261,63263,63265,63267,63269,63271,63273,63275,63277],{},[898,63254,4255],{},[898,63256,2777],{},[1996,63258,2005],{"stretchy":2004},[2129,63260,2235],{},[1996,63262,2011],{"stretchy":2004},[1996,63264,1998],{},[898,63266,2818],{},[898,63268,2777],{},[1996,63270,2005],{"stretchy":2004},[2129,63272,2235],{},[1996,63274,2011],{"stretchy":2004},[1996,63276,1998],{},[2129,63278,36246],{},[902,63280,63281],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,63284,63286],{"id":63285},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,63288,63289,63290,2704],{},"Analogicky pro ",[883,63291,63293],{"className":63292},[886],[888,63294,63295],{"xmlns":890},[892,63296,63297,63305],{},[895,63298,63299,63301,63303],{},[898,63300,4255],{},[898,63302,40341],{},[898,63304,2777],{},[902,63306,55313],{"encoding":904},[883,63308,63310],{"className":63309},[886],[888,63311,63312],{"xmlns":890,"display":28068},[892,63313,63314,63365],{},[20756,63315,63316],{"width":28073},[20761,63317,63318,63320,63358,63360],{},[20764,63319],{"width":28078},[20764,63321,63322],{},[895,63323,63324,63326,63328,63330,63332,63338,63340,63342,63344,63346,63348,63354,63356],{},[898,63325,4255],{},[898,63327,40341],{},[898,63329,2777],{},[1996,63331,2005],{"stretchy":2004},[2272,63333,63334,63336],{},[898,63335,2789],{},[2129,63337,2327],{},[1996,63339,2011],{"stretchy":2004},[1996,63341,1998],{},[898,63343,2818],{},[898,63345,2777],{},[1996,63347,2005],{"stretchy":2004},[2272,63349,63350,63352],{},[898,63351,2789],{},[2129,63353,2327],{},[1996,63355,2011],{"stretchy":2004},[898,63357,1975],{"mathvariant":2376},[20764,63359],{"width":28078},[20764,63361,63362],{},[2288,63363,63364],{},"(3.11)",[902,63366,63367],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[3867,63369,63370],{},[724,63371,63372,62048,63374],{},[883,63373,56446],{},[38,63375,63376,63377,63394],{},"V bodě minima průměrných variabilních nákladů se ",[883,63378,63380],{"className":63379},[886],[888,63381,63382],{"xmlns":890},[892,63383,63384,63392],{},[895,63385,63386,63388,63390],{},[898,63387,4255],{},[898,63389,40341],{},[898,63391,2777],{},[902,63393,55313],{"encoding":904}," rovnají mezním nákladům.",[724,63396,63397,63398,63420,63421,1975],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,63399,63401],{"className":63400},[886],[888,63402,63403],{"xmlns":890},[892,63404,63405,63417],{},[895,63406,63407,63413,63415],{},[2272,63408,63409,63411],{},[898,63410,2789],{},[2129,63412,2327],{},[1996,63414,1998],{},[2129,63416,53201],{},[902,63418,63419],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,63422,63424],{"className":63423},[886],[888,63425,63426],{"xmlns":890},[892,63427,63428,63454],{},[895,63429,63430,63432,63434,63436,63438,63440,63442,63444,63446,63448,63450,63452],{},[898,63431,4255],{},[898,63433,40341],{},[898,63435,2777],{},[1996,63437,2005],{"stretchy":2004},[898,63439,2789],{},[1996,63441,2011],{"stretchy":2004},[1996,63443,1998],{},[898,63445,2818],{},[898,63447,2777],{},[1996,63449,2005],{"stretchy":2004},[898,63451,2789],{},[1996,63453,2011],{"stretchy":2004},[902,63455,63456],{"encoding":904},"AVC(Q) = MC(Q)",[115,63458,63460],{"id":63459},"zisk-a-body-zvratu","Zisk a body zvratu",[724,63462,63463,2203,63466,63482],{},[38,63464,63465],{},"Zisk",[883,63467,63469],{"className":63468},[886],[888,63470,63471],{"xmlns":890},[892,63472,63473,63479],{},[895,63474,63475,63477],{},[898,63476,3937],{},[898,63478,3994],{},[902,63480,63481],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,63484,63486],{"className":63485},[886],[888,63487,63488],{"xmlns":890,"display":28068},[892,63489,63490,63549],{},[20756,63491,63492],{"width":28073},[20761,63493,63494,63496,63542,63544],{},[20764,63495],{"width":28078},[20764,63497,63498],{},[895,63499,63500,63502,63504,63506,63508,63510,63512,63514,63516,63518,63520,63522,63524,63526,63528,63530,63532,63534,63536,63538,63540],{},[898,63501,3937],{},[898,63503,3994],{},[1996,63505,1998],{},[898,63507,3937],{},[898,63509,3994],{},[1996,63511,2005],{"stretchy":2004},[898,63513,2789],{},[1996,63515,2011],{"stretchy":2004},[1996,63517,1998],{},[898,63519,2774],{},[898,63521,3994],{},[1996,63523,2005],{"stretchy":2004},[898,63525,2789],{},[1996,63527,2011],{"stretchy":2004},[1996,63529,2225],{},[898,63531,2774],{},[898,63533,2777],{},[1996,63535,2005],{"stretchy":2004},[898,63537,2789],{},[1996,63539,2011],{"stretchy":2004},[898,63541,1975],{"mathvariant":2376},[20764,63543],{"width":28078},[20764,63545,63546],{},[2288,63547,63548],{},"(3.12)",[902,63550,63551],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,63553,63554,63555,3885,63570,43638,63585,63587,63588,63591,63592,63608,63609,63624,63625,63640,63641,1343,63654,63667,63668,1343,63686,63704,63705,10025,63708,63711,63712,1348,63734,8102,63756,63778,63779,8102,63809,63831],{},"Body rovnosti ",[883,63556,63558],{"className":63557},[886],[888,63559,63560],{"xmlns":890},[892,63561,63562,63568],{},[895,63563,63564,63566],{},[898,63565,2774],{},[898,63567,3994],{},[902,63569,4094],{"encoding":904},[883,63571,63573],{"className":63572},[886],[888,63574,63575],{"xmlns":890},[892,63576,63577,63583],{},[895,63578,63579,63581],{},[898,63580,2774],{},[898,63582,2777],{},[902,63584,3243],{"encoding":904},[38,63586,55729],{}," (též vyrovnání, ",[614,63589,63590],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,63593,63595],{"className":63594},[886],[888,63596,63597],{"xmlns":890},[892,63598,63599,63605],{},[895,63600,63601,63603],{},[898,63602,40341],{},[898,63604,2777],{},[902,63606,63607],{"encoding":904},"VC",") je ",[883,63610,63612],{"className":63611},[886],[888,63613,63614],{"xmlns":890},[892,63615,63616,63622],{},[895,63617,63618,63620],{},[898,63619,2774],{},[898,63621,3994],{},[902,63623,4094],{"encoding":904}," kvadratická a ",[883,63626,63628],{"className":63627},[886],[888,63629,63630],{"xmlns":890},[892,63631,63632,63638],{},[895,63633,63634,63636],{},[898,63635,2774],{},[898,63637,2777],{},[902,63639,3243],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,63642,63644],{"className":63643},[886],[888,63645,63646],{"xmlns":890},[892,63647,63648,63652],{},[895,63649,63650],{},[898,63651,4255],{},[902,63653,4255],{"encoding":904},[883,63655,63657],{"className":63656},[886],[888,63658,63659],{"xmlns":890},[892,63660,63661,63665],{},[895,63662,63663],{},[898,63664,23255],{},[902,63666,23255],{"encoding":904}," odpovídajících množstvím ",[883,63669,63671],{"className":63670},[886],[888,63672,63673],{"xmlns":890},[892,63674,63675,63683],{},[895,63676,63677],{},[2272,63678,63679,63681],{},[898,63680,2789],{},[898,63682,4255],{},[902,63684,63685],{"encoding":904},"Q_A",[883,63687,63689],{"className":63688},[886],[888,63690,63691],{"xmlns":890},[892,63692,63693,63701],{},[895,63694,63695],{},[2272,63696,63697,63699],{},[898,63698,2789],{},[898,63700,23255],{},[902,63702,63703],{"encoding":904},"Q_B"," — firma je na ",[38,63706,63707],{},"prahu rentability",[614,63709,63710],{},"break even","). Pro ",[883,63713,63715],{"className":63714},[886],[888,63716,63717],{"xmlns":890},[892,63718,63719,63731],{},[895,63720,63721,63723,63725],{},[898,63722,2789],{},[1996,63724,3447],{},[2272,63726,63727,63729],{},[898,63728,2789],{},[898,63730,4255],{},[902,63732,63733],{"encoding":904},"Q \u003C Q_A",[883,63735,63737],{"className":63736},[886],[888,63738,63739],{"xmlns":890},[892,63740,63741,63753],{},[895,63742,63743,63745,63747],{},[898,63744,2789],{},[1996,63746,3408],{},[2272,63748,63749,63751],{},[898,63750,2789],{},[898,63752,23255],{},[902,63754,63755],{"encoding":904},"Q > Q_B",[883,63757,63759],{"className":63758},[886],[888,63760,63761],{"xmlns":890},[892,63762,63763,63775],{},[895,63764,63765,63767,63769,63771,63773],{},[898,63766,2774],{},[898,63768,2777],{},[1996,63770,3408],{},[898,63772,2774],{},[898,63774,3994],{},[902,63776,63777],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,63780,63782],{"className":63781},[886],[888,63783,63784],{"xmlns":890},[892,63785,63786,63806],{},[895,63787,63788,63794,63796,63798,63800],{},[2272,63789,63790,63792],{},[898,63791,2789],{},[898,63793,4255],{},[1996,63795,3447],{},[898,63797,2789],{},[1996,63799,3447],{},[2272,63801,63802,63804],{},[898,63803,2789],{},[898,63805,23255],{},[902,63807,63808],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,63810,63812],{"className":63811},[886],[888,63813,63814],{"xmlns":890},[892,63815,63816,63828],{},[895,63817,63818,63820,63822,63824,63826],{},[898,63819,2774],{},[898,63821,3994],{},[1996,63823,3408],{},[898,63825,2774],{},[898,63827,2777],{},[902,63829,63830],{"encoding":904},"TR > TC"," (zisk).",[3867,63833,63834],{},[724,63835,63836,63838],{},[883,63837,4155],{}," 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.",[724,63840,63841,63842,63868],{},"Body zvratu jsou řešení rovnice ",[883,63843,63845],{"className":63844},[886],[888,63846,63847],{"xmlns":890},[892,63848,63849,63865],{},[895,63850,63851,63853,63855,63857,63859,63861,63863],{},[898,63852,3937],{},[898,63854,3994],{},[1996,63856,2005],{"stretchy":2004},[898,63858,2789],{},[1996,63860,2011],{"stretchy":2004},[1996,63862,1998],{},[2129,63864,2327],{},[902,63866,63867],{"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.",[724,63870,63871],{},[2559,63872],{"alt":63873,"className":63874,"src":63875},"imek-tr-tc-body-zvratu",[210,2563],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,63877,63878],{},[614,63879,63880,63881,63896,63897,63912,63913,3885,63926,43362,63939,63952,63953,3885,63970,63987,63988,64008,64009,3885,64024,6473,64039,64068],{},"Obrázek 3.11: Body zvratu — křivky ",[883,63882,63884],{"className":63883},[886],[888,63885,63886],{"xmlns":890},[892,63887,63888,63894],{},[895,63889,63890,63892],{},[898,63891,2774],{},[898,63893,3994],{},[902,63895,4094],{"encoding":904}," (obrácená parabola) a ",[883,63898,63900],{"className":63899},[886],[888,63901,63902],{"xmlns":890},[892,63903,63904,63910],{},[895,63905,63906,63908],{},[898,63907,2774],{},[898,63909,2777],{},[902,63911,3243],{"encoding":904}," (přímka) se protínají v bodech ",[883,63914,63916],{"className":63915},[886],[888,63917,63918],{"xmlns":890},[892,63919,63920,63924],{},[895,63921,63922],{},[898,63923,4255],{},[902,63925,4255],{"encoding":904},[883,63927,63929],{"className":63928},[886],[888,63930,63931],{"xmlns":890},[892,63932,63933,63937],{},[895,63934,63935],{},[898,63936,23255],{},[902,63938,23255],{"encoding":904},[883,63940,63942],{"className":63941},[886],[888,63943,63944],{"xmlns":890},[892,63945,63946,63950],{},[895,63947,63948],{},[898,63949,2789],{},[902,63951,2789],{"encoding":904}," v hodnotách ",[883,63954,63956],{"className":63955},[886],[888,63957,63958],{"xmlns":890},[892,63959,63960,63968],{},[895,63961,63962],{},[2272,63963,63964,63966],{},[898,63965,2789],{},[898,63967,4255],{},[902,63969,63685],{"encoding":904},[883,63971,63973],{"className":63972},[886],[888,63974,63975],{"xmlns":890},[892,63976,63977,63985],{},[895,63978,63979],{},[2272,63980,63981,63983],{},[898,63982,2789],{},[898,63984,23255],{},[902,63986,63703],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,63989,63991],{"className":63990},[886],[888,63992,63993],{"xmlns":890},[892,63994,63995,64005],{},[895,63996,63997],{},[2272,63998,63999,64001,64003],{},[898,64000,2789],{},[898,64002,56199],{},[1996,64004,56202],{},[902,64006,64007],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,64010,64012],{"className":64011},[886],[888,64013,64014],{"xmlns":890},[892,64015,64016,64022],{},[895,64017,64018,64020],{},[898,64019,2774],{},[898,64021,3994],{},[902,64023,4094],{"encoding":904},[883,64025,64027],{"className":64026},[886],[888,64028,64029],{"xmlns":890},[892,64030,64031,64037],{},[895,64032,64033,64035],{},[898,64034,2774],{},[898,64036,2777],{},[902,64038,3243],{"encoding":904},[883,64040,64042],{"className":64041},[886],[888,64043,64044],{"xmlns":890},[892,64045,64046,64066],{},[895,64047,64048,64054,64056,64058,64060],{},[2272,64049,64050,64052],{},[898,64051,2789],{},[898,64053,4255],{},[1996,64055,3447],{},[898,64057,2789],{},[1996,64059,3447],{},[2272,64061,64062,64064],{},[898,64063,2789],{},[898,64065,23255],{},[902,64067,63808],{"encoding":904}," vyznačuje zisk.",[37350,64070,64072],{"id":64071},"příklad-38","Příklad 3.8",[724,64074,64075,64077,64078,1343,64098,1343,64124,64150],{},[38,64076,55989],{}," Dáno ",[883,64079,64081],{"className":64080},[886],[888,64082,64083],{"xmlns":890},[892,64084,64085,64095],{},[895,64086,64087,64089,64091,64093],{},[898,64088,10436],{},[898,64090,2777],{},[1996,64092,1998],{},[2129,64094,2351],{},[902,64096,64097],{"encoding":904},"FC = 4",[883,64099,64101],{"className":64100},[886],[888,64102,64103],{"xmlns":890},[892,64104,64105,64121],{},[895,64106,64107,64109,64111,64113,64115],{},[898,64108,2774],{},[898,64110,40341],{},[898,64112,2777],{},[1996,64114,1998],{},[2124,64116,64117,64119],{},[898,64118,2789],{},[2129,64120,2131],{},[902,64122,64123],{"encoding":904},"TVC = Q^2",[883,64125,64127],{"className":64126},[886],[888,64128,64129],{"xmlns":890},[892,64130,64131,64147],{},[895,64132,64133,64135,64137,64139,64141,64143,64145],{},[898,64134,3937],{},[1996,64136,1998],{},[1996,64138,2225],{},[2129,64140,2131],{},[898,64142,2789],{},[1996,64144,2095],{},[2129,64146,3999],{},[902,64148,64149],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,64152,64153,64155],{},[38,64154,22772],{}," Celkové náklady a příjem:",[883,64157,64159],{"className":64158},[886],[888,64160,64161],{"xmlns":890,"display":28068},[892,64162,64163,64229],{},[895,64164,64165,64167,64169,64171,64173,64175,64181,64183,64185,64187,64189,64191,64193,64195,64197,64199,64201,64203,64205,64207,64209,64211,64213,64215,64221,64223,64225,64227],{},[898,64166,2774],{},[898,64168,2777],{},[1996,64170,1998],{},[2129,64172,2351],{},[1996,64174,2095],{},[2124,64176,64177,64179],{},[898,64178,2789],{},[2129,64180,2131],{},[1996,64182,2286],{"separator":2285},[5878,64184],{"width":5880},[898,64186,2774],{},[898,64188,3994],{},[1996,64190,1998],{},[898,64192,2789],{},[1996,64194,3177],{},[1996,64196,2005],{"stretchy":2004},[1996,64198,2225],{},[2129,64200,2131],{},[898,64202,2789],{},[1996,64204,2095],{},[2129,64206,3999],{},[1996,64208,2011],{"stretchy":2004},[1996,64210,1998],{},[1996,64212,2225],{},[2129,64214,2131],{},[2124,64216,64217,64219],{},[898,64218,2789],{},[2129,64220,2131],{},[1996,64222,2095],{},[2129,64224,3999],{},[898,64226,2789],{},[898,64228,1975],{"mathvariant":2376},[902,64230,64231],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,64233,64234],{},"Zisk dle (3.12):",[883,64236,64238],{"className":64237},[886],[888,64239,64240],{"xmlns":890,"display":28068},[892,64241,64242,64320],{},[895,64243,64244,64246,64248,64250,64252,64254,64256,64258,64260,64262,64264,64266,64268,64274,64276,64278,64280,64282,64284,64286,64288,64290,64296,64298,64300,64302,64304,64310,64312,64314,64316,64318],{},[898,64245,3937],{},[898,64247,3994],{},[1996,64249,1998],{},[898,64251,2774],{},[898,64253,3994],{},[1996,64255,2225],{},[898,64257,2774],{},[898,64259,2777],{},[1996,64261,1998],{},[1996,64263,2005],{"stretchy":2004},[1996,64265,2225],{},[2129,64267,2131],{},[2124,64269,64270,64272],{},[898,64271,2789],{},[2129,64273,2131],{},[1996,64275,2095],{},[2129,64277,3999],{},[898,64279,2789],{},[1996,64281,2011],{"stretchy":2004},[1996,64283,2225],{},[1996,64285,2005],{"stretchy":2004},[2129,64287,2351],{},[1996,64289,2095],{},[2124,64291,64292,64294],{},[898,64293,2789],{},[2129,64295,2131],{},[1996,64297,2011],{"stretchy":2004},[1996,64299,1998],{},[1996,64301,2225],{},[2129,64303,2173],{},[2124,64305,64306,64308],{},[898,64307,2789],{},[2129,64309,2131],{},[1996,64311,2095],{},[2129,64313,3999],{},[898,64315,2789],{},[1996,64317,2225],{},[2129,64319,59321],{},[902,64321,64322],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,64324,64325,64328,64329,17578,64365,2704],{},[38,64326,64327],{},"Body zvratu"," jsou kořeny rovnice ",[883,64330,64332],{"className":64331},[886],[888,64333,64334],{"xmlns":890},[892,64335,64336,64362],{},[895,64337,64338,64340,64342,64348,64350,64352,64354,64356,64358,64360],{},[1996,64339,2225],{},[2129,64341,2173],{},[2124,64343,64344,64346],{},[898,64345,2789],{},[2129,64347,2131],{},[1996,64349,2095],{},[2129,64351,3999],{},[898,64353,2789],{},[1996,64355,2225],{},[2129,64357,2351],{},[1996,64359,1998],{},[2129,64361,2327],{},[902,64363,64364],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,64366,64368],{"className":64367},[886],[888,64369,64370],{"xmlns":890},[892,64371,64372,64396],{},[895,64373,64374,64376,64382,64384,64386,64388,64390,64392,64394],{},[2129,64375,2173],{},[2124,64377,64378,64380],{},[898,64379,2789],{},[2129,64381,2131],{},[1996,64383,2225],{},[2129,64385,3999],{},[898,64387,2789],{},[1996,64389,2095],{},[2129,64391,2351],{},[1996,64393,1998],{},[2129,64395,2327],{},[902,64397,64398],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,64400,64402],{"className":64401},[886],[888,64403,64404],{"xmlns":890,"display":28068},[892,64405,64406,64463],{},[895,64407,64408,64420,64422,64445,64447,64461],{},[2272,64409,64410,64412],{},[898,64411,2789],{},[895,64413,64414,64416,64418],{},[2129,64415,2278],{},[1996,64417,2286],{"separator":2285},[2129,64419,2131],{},[1996,64421,1998],{},[2329,64423,64424,64443],{},[895,64425,64426,64428,64431],{},[2129,64427,3999],{},[1996,64429,64430],{},"±",[8117,64432,64433],{},[895,64434,64435,64438,64440],{},[2129,64436,64437],{},"81",[1996,64439,2225],{},[2129,64441,64442],{},"48",[2129,64444,2235],{},[1996,64446,1998],{},[2329,64448,64449,64459],{},[895,64450,64451,64453,64455],{},[2129,64452,3999],{},[1996,64454,64430],{},[8117,64456,64457],{},[2129,64458,8951],{},[2129,64460,2235],{},[1996,64462,2286],{"separator":2285},[902,64464,64465],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,64467,64468,64469,3885,64492,1975],{},"numericky ",[883,64470,64472],{"className":64471},[886],[888,64473,64474],{"xmlns":890},[892,64475,64476,64489],{},[895,64477,64478,64484,64486],{},[2272,64479,64480,64482],{},[898,64481,2789],{},[2129,64483,2278],{},[1996,64485,5900],{},[2129,64487,64488],{},"0,543",[902,64490,64491],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,64493,64495],{"className":64494},[886],[888,64496,64497],{"xmlns":890},[892,64498,64499,64512],{},[895,64500,64501,64507,64509],{},[2272,64502,64503,64505],{},[898,64504,2789],{},[2129,64506,2131],{},[1996,64508,5900],{},[2129,64510,64511],{},"2,457",[902,64513,64514],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,64516,64517,2203,64520,7552,64565,17578,64599,64617],{},[38,64518,64519],{},"Maximum zisku.",[883,64521,64523],{"className":64522},[886],[888,64524,64525],{"xmlns":890},[892,64526,64527,64562],{},[895,64528,64529,64531,64537,64539,64541,64543,64545,64547,64549,64551,64553,64555,64557,64559],{},[898,64530,3937],{},[2124,64532,64533,64535],{},[898,64534,3994],{},[1996,64536,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,64538,1998],{},[1996,64540,2225],{},[2129,64542,2235],{},[898,64544,2789],{},[1996,64546,2095],{},[2129,64548,3999],{},[1996,64550,1998],{},[2129,64552,2327],{},[1996,64554,3987],{},[898,64556,2789],{},[1996,64558,1998],{},[2129,64560,64561],{},"1,5",[902,64563,64564],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,64566,64568],{"className":64567},[886],[888,64569,64570],{"xmlns":890},[892,64571,64572,64596],{},[895,64573,64574,64576,64586,64588,64590,64592,64594],{},[898,64575,3937],{},[2124,64577,64578,64580],{},[898,64579,3994],{},[895,64581,64582,64584],{},[1996,64583,2378],{"mathvariant":2376},[1996,64585,2378],{"mathvariant":2376},[1996,64587,1998],{},[1996,64589,2225],{},[2129,64591,2235],{},[1996,64593,3447],{},[2129,64595,2327],{},[902,64597,64598],{"encoding":904},"PR'' = -6 \u003C 0",[883,64600,64602],{"className":64601},[886],[888,64603,64604],{"xmlns":890},[892,64605,64606,64614],{},[895,64607,64608,64610,64612],{},[898,64609,2789],{},[1996,64611,1998],{},[2129,64613,64561],{},[902,64615,64616],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,64619,64621],{"className":64620},[886],[888,64622,64623],{"xmlns":890,"display":28068},[892,64624,64625,64688],{},[895,64626,64627,64629,64631,64633,64635,64637,64639,64641,64643,64645,64647,64649,64655,64657,64659,64661,64663,64665,64667,64669,64671,64674,64676,64679,64681,64683,64685],{},[898,64628,3937],{},[898,64630,3994],{},[1996,64632,2005],{"stretchy":2004},[2129,64634,64561],{},[1996,64636,2011],{"stretchy":2004},[1996,64638,1998],{},[1996,64640,2225],{},[2129,64642,2173],{},[1996,64644,3177],{},[1996,64646,2005],{"stretchy":2004},[2129,64648,64561],{},[2124,64650,64651,64653],{},[1996,64652,2011],{"stretchy":2004},[2129,64654,2131],{},[1996,64656,2095],{},[2129,64658,3999],{},[1996,64660,3177],{},[2129,64662,64561],{},[1996,64664,2225],{},[2129,64666,2351],{},[1996,64668,1998],{},[1996,64670,2225],{},[2129,64672,64673],{},"6,75",[1996,64675,2095],{},[2129,64677,64678],{},"13,5",[1996,64680,2225],{},[2129,64682,2351],{},[1996,64684,1998],{},[2129,64686,64687],{},"2,75.",[902,64689,64690],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,64692,64693,64694,1343,64739,64792,64793,64811],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,64695,64697],{"className":64696},[886],[888,64698,64699],{"xmlns":890},[892,64700,64701,64736],{},[895,64702,64703,64705,64711,64713,64715,64717,64719,64721,64723,64725,64727,64729,64731,64733],{},[898,64704,2774],{},[2124,64706,64707,64709],{},[898,64708,3994],{},[1996,64710,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,64712,1998],{},[1996,64714,2225],{},[2129,64716,2351],{},[898,64718,2789],{},[1996,64720,2095],{},[2129,64722,3999],{},[1996,64724,1998],{},[2129,64726,2327],{},[1996,64728,3987],{},[898,64730,2789],{},[1996,64732,1998],{},[2129,64734,64735],{},"2,25",[902,64737,64738],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,64740,64742],{"className":64741},[886],[888,64743,64744],{"xmlns":890},[892,64745,64746,64789],{},[895,64747,64748,64750,64758,64760,64762,64764,64766,64768,64770,64776,64778,64780,64782,64784,64786],{},[898,64749,2774],{},[2272,64751,64752,64754,64756],{},[898,64753,3994],{},[898,64755,56199],{},[1996,64757,56202],{},[1996,64759,1998],{},[1996,64761,2225],{},[2129,64763,2131],{},[1996,64765,3177],{},[1996,64767,2005],{"stretchy":2004},[2129,64769,64735],{},[2124,64771,64772,64774],{},[1996,64773,2011],{"stretchy":2004},[2129,64775,2131],{},[1996,64777,2095],{},[2129,64779,3999],{},[1996,64781,3177],{},[2129,64783,64735],{},[1996,64785,1998],{},[2129,64787,64788],{},"10,125",[902,64790,64791],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,64794,64796],{"className":64795},[886],[888,64797,64798],{"xmlns":890},[892,64799,64800,64808],{},[895,64801,64802,64804,64806],{},[898,64803,2789],{},[1996,64805,1998],{},[2129,64807,64735],{},[902,64809,64810],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[3867,64813,64814],{},[724,64815,64816,64818,64819,1343,64841,64863,64864,1343,64881,64902,64903,64935,64936,64974,64975,2671,64993,65010,65011,3885,65039,65073,65074,7685,65112,3885,65136,1975],{},[883,64817,4412],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,64820,64822],{"className":64821},[886],[888,64823,64824],{"xmlns":890},[892,64825,64826,64838],{},[895,64827,64828,64834,64836],{},[2272,64829,64830,64832],{},[898,64831,2789],{},[2129,64833,2278],{},[1996,64835,1998],{},[2129,64837,5009],{},[902,64839,64840],{"encoding":904},"Q_1 = 0{,}5",[883,64842,64844],{"className":64843},[886],[888,64845,64846],{"xmlns":890},[892,64847,64848,64860],{},[895,64849,64850,64856,64858],{},[2272,64851,64852,64854],{},[898,64853,2789],{},[2129,64855,2131],{},[1996,64857,1998],{},[2129,64859,2351],{},[902,64861,64862],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,64865,64867],{"className":64866},[886],[888,64868,64869],{"xmlns":890},[892,64870,64871,64879],{},[895,64872,64873,64875,64877],{},[898,64874,2789],{},[1996,64876,1998],{},[2129,64878,64735],{},[902,64880,64810],{"encoding":904},[883,64882,64884],{"className":64883},[886],[888,64885,64886],{"xmlns":890},[892,64887,64888,64899],{},[895,64889,64890,64892,64894,64896],{},[898,64891,3937],{},[898,64893,3994],{},[1996,64895,1998],{},[2129,64897,64898],{},"6,125",[902,64900,64901],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,64904,64906],{"className":64905},[886],[888,64907,64908],{"xmlns":890},[892,64909,64910,64932],{},[895,64911,64912,64914,64920,64922,64924,64926,64928,64930],{},[898,64913,3937],{},[2124,64915,64916,64918],{},[898,64917,3994],{},[1996,64919,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,64921,1998],{},[1996,64923,2225],{},[2129,64925,2351],{},[898,64927,2789],{},[1996,64929,2095],{},[2129,64931,3999],{},[902,64933,64934],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,64937,64939],{"className":64938},[886],[888,64940,64941],{"xmlns":890},[892,64942,64943,64971],{},[895,64944,64945,64947,64949,64951,64953,64955,64961,64963,64965,64967,64969],{},[898,64946,3937],{},[898,64948,3994],{},[1996,64950,1998],{},[1996,64952,2225],{},[2129,64954,2131],{},[2124,64956,64957,64959],{},[898,64958,2789],{},[2129,64960,2131],{},[1996,64962,2095],{},[2129,64964,3999],{},[898,64966,2789],{},[1996,64968,2225],{},[2129,64970,2351],{},[902,64972,64973],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,64976,64978],{"className":64977},[886],[888,64979,64980],{"xmlns":890},[892,64981,64982,64990],{},[895,64983,64984],{},[2124,64985,64986,64988],{},[898,64987,2789],{},[2129,64989,2131],{},[902,64991,64992],{"encoding":904},"Q^2",[883,64994,64996],{"className":64995},[886],[888,64997,64998],{"xmlns":890},[892,64999,65000,65008],{},[895,65001,65002,65004,65006],{},[898,65003,2774],{},[898,65005,40341],{},[898,65007,2777],{},[902,65009,55511],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,65012,65014],{"className":65013},[886],[888,65015,65016],{"xmlns":890},[892,65017,65018,65036],{},[895,65019,65020,65022,65024,65026,65028,65030],{},[898,65021,2774],{},[898,65023,2777],{},[1996,65025,1998],{},[2129,65027,2351],{},[1996,65029,2095],{},[2124,65031,65032,65034],{},[898,65033,2789],{},[2129,65035,2131],{},[902,65037,65038],{"encoding":904},"TC = 4 + Q^2",[883,65040,65042],{"className":65041},[886],[888,65043,65044],{"xmlns":890},[892,65045,65046,65070],{},[895,65047,65048,65050,65052,65054,65056,65058,65064,65066,65068],{},[898,65049,2774],{},[898,65051,3994],{},[1996,65053,1998],{},[1996,65055,2225],{},[2129,65057,2131],{},[2124,65059,65060,65062],{},[898,65061,2789],{},[2129,65063,2131],{},[1996,65065,2095],{},[2129,65067,3999],{},[898,65069,2789],{},[902,65071,65072],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,65075,65077],{"className":65076},[886],[888,65078,65079],{"xmlns":890},[892,65080,65081,65109],{},[895,65082,65083,65085,65087,65089,65091,65093,65099,65101,65103,65105,65107],{},[898,65084,3937],{},[898,65086,3994],{},[1996,65088,1998],{},[1996,65090,2225],{},[2129,65092,2173],{},[2124,65094,65095,65097],{},[898,65096,2789],{},[2129,65098,2131],{},[1996,65100,2095],{},[2129,65102,3999],{},[898,65104,2789],{},[1996,65106,2225],{},[2129,65108,2351],{},[902,65110,65111],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,65113,65115],{"className":65114},[886],[888,65116,65117],{"xmlns":890},[892,65118,65119,65133],{},[895,65120,65121,65129,65131],{},[2272,65122,65123,65125,65127],{},[898,65124,2789],{},[898,65126,56199],{},[1996,65128,56202],{},[1996,65130,1998],{},[2129,65132,64561],{},[902,65134,65135],{"encoding":904},"Q_{\\max} = 1{,}5",[883,65137,65139],{"className":65138},[886],[888,65140,65141],{"xmlns":890},[892,65142,65143,65160],{},[895,65144,65145,65147,65155,65157],{},[898,65146,3937],{},[2272,65148,65149,65151,65153],{},[898,65150,3994],{},[898,65152,56199],{},[1996,65154,56202],{},[1996,65156,1998],{},[2129,65158,65159],{},"2,75",[902,65161,65162],{"encoding":904},"PR_{\\max} = 2{,}75",[724,65164,65165],{},[614,65166,65167,65168,65195,65196,65229,65230,1343,65253,1975],{},"Obrázek 3.12: Graf ",[883,65169,65171],{"className":65170},[886],[888,65172,65173],{"xmlns":890},[892,65174,65175,65193],{},[895,65176,65177,65179,65181,65183,65185,65187],{},[898,65178,2774],{},[898,65180,2777],{},[1996,65182,1998],{},[2129,65184,2351],{},[1996,65186,2095],{},[2124,65188,65189,65191],{},[898,65190,2789],{},[2129,65192,2131],{},[902,65194,65038],{"encoding":904}," (parabola) a ",[883,65197,65199],{"className":65198},[886],[888,65200,65201],{"xmlns":890},[892,65202,65203,65227],{},[895,65204,65205,65207,65209,65211,65213,65215,65221,65223,65225],{},[898,65206,2774],{},[898,65208,3994],{},[1996,65210,1998],{},[1996,65212,2225],{},[2129,65214,2131],{},[2124,65216,65217,65219],{},[898,65218,2789],{},[2129,65220,2131],{},[1996,65222,2095],{},[2129,65224,3999],{},[898,65226,2789],{},[902,65228,65072],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,65231,65233],{"className":65232},[886],[888,65234,65235],{"xmlns":890},[892,65236,65237,65250],{},[895,65238,65239,65245,65247],{},[2272,65240,65241,65243],{},[898,65242,2789],{},[2129,65244,2278],{},[1996,65246,5900],{},[2129,65248,65249],{},"0,54",[902,65251,65252],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,65254,65256],{"className":65255},[886],[888,65257,65258],{"xmlns":890},[892,65259,65260,65273],{},[895,65261,65262,65268,65270],{},[2272,65263,65264,65266],{},[898,65265,2789],{},[2129,65267,2131],{},[1996,65269,5900],{},[2129,65271,65272],{},"2,46",[902,65274,65275],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,65277,65278],{},[614,65279,65280,65281,58509,65318,65335,65336,1343,65357,1975],{},"Obrázek 3.13: Graf zisku ",[883,65282,65284],{"className":65283},[886],[888,65285,65286],{"xmlns":890},[892,65287,65288,65316],{},[895,65289,65290,65292,65294,65296,65298,65300,65306,65308,65310,65312,65314],{},[898,65291,3937],{},[898,65293,3994],{},[1996,65295,1998],{},[1996,65297,2225],{},[2129,65299,2173],{},[2124,65301,65302,65304],{},[898,65303,2789],{},[2129,65305,2131],{},[1996,65307,2095],{},[2129,65309,3999],{},[898,65311,2789],{},[1996,65313,2225],{},[2129,65315,2351],{},[902,65317,65111],{"encoding":904},[883,65319,65321],{"className":65320},[886],[888,65322,65323],{"xmlns":890},[892,65324,65325,65333],{},[895,65326,65327,65329,65331],{},[898,65328,2789],{},[1996,65330,1998],{},[2129,65332,64561],{},[902,65334,64616],{"encoding":904}," a nulami ",[883,65337,65339],{"className":65338},[886],[888,65340,65341],{"xmlns":890},[892,65342,65343,65355],{},[895,65344,65345,65351,65353],{},[2272,65346,65347,65349],{},[898,65348,2789],{},[2129,65350,2278],{},[1996,65352,5900],{},[2129,65354,65249],{},[902,65356,65252],{"encoding":904},[883,65358,65360],{"className":65359},[886],[888,65361,65362],{"xmlns":890},[892,65363,65364,65376],{},[895,65365,65366,65372,65374],{},[2272,65367,65368,65370],{},[898,65369,2789],{},[2129,65371,2131],{},[1996,65373,5900],{},[2129,65375,65272],{},[902,65377,65275],{"encoding":904},[115,65379,65381],{"id":65380},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,65383,65384],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,65386,65387],{},[2559,65388],{"alt":65389,"className":65390,"src":65391},"imek-max-zisku-dva-pohledy",[210,2563],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,65393,16414],{"id":65394},"princip-1",[724,65396,65397,65398,2624,65413,65430],{},"Má-li zisk ",[883,65399,65401],{"className":65400},[886],[888,65402,65403],{"xmlns":890},[892,65404,65405,65411],{},[895,65406,65407,65409],{},[898,65408,3937],{},[898,65410,3994],{},[902,65412,63481],{"encoding":904},[883,65414,65416],{"className":65415},[886],[888,65417,65418],{"xmlns":890},[892,65419,65420,65428],{},[895,65421,65422],{},[2272,65423,65424,65426],{},[898,65425,2789],{},[2129,65427,2327],{},[902,65429,38310],{"encoding":904}," maximum, pak platí",[883,65432,65434],{"className":65433},[886],[888,65435,65436],{"xmlns":890,"display":28068},[892,65437,65438,65487],{},[20756,65439,65440],{"width":28073},[20761,65441,65442,65444,65480,65482],{},[20764,65443],{"width":28078},[20764,65445,65446],{},[895,65447,65448,65450,65452,65454,65460,65462,65464,65466,65468,65470,65476,65478],{},[898,65449,2818],{},[898,65451,3994],{},[1996,65453,2005],{"stretchy":2004},[2272,65455,65456,65458],{},[898,65457,2789],{},[2129,65459,2327],{},[1996,65461,2011],{"stretchy":2004},[1996,65463,1998],{},[898,65465,2818],{},[898,65467,2777],{},[1996,65469,2005],{"stretchy":2004},[2272,65471,65472,65474],{},[898,65473,2789],{},[2129,65475,2327],{},[1996,65477,2011],{"stretchy":2004},[898,65479,1975],{"mathvariant":2376},[20764,65481],{"width":28078},[20764,65483,65484],{},[2288,65485,65486],{},"(3.13)",[902,65488,65489],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[3867,65491,65492],{},[724,65493,65494,62048,65496],{},[883,65495,56446],{},[38,65497,65498],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,65500,65501,65504,65505,8102,65532,17578,65606,1975],{},[38,65502,65503],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,65506,65508],{"className":65507},[886],[888,65509,65510],{"xmlns":890},[892,65511,65512,65530],{},[895,65513,65514,65516,65518,65520,65522,65524,65526,65528],{},[898,65515,3937],{},[898,65517,3994],{},[1996,65519,1998],{},[898,65521,2774],{},[898,65523,3994],{},[1996,65525,2225],{},[898,65527,2774],{},[898,65529,2777],{},[902,65531,55202],{"encoding":904},[883,65533,65535],{"className":65534},[886],[888,65536,65537],{"xmlns":890},[892,65538,65539,65603],{},[895,65540,65541,65543,65549,65551,65557,65559,65561,65563,65569,65571,65577,65579,65581,65583,65589,65591,65597,65599,65601],{},[898,65542,3937],{},[2124,65544,65545,65547],{},[898,65546,3994],{},[1996,65548,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,65550,2005],{"stretchy":2004},[2272,65552,65553,65555],{},[898,65554,2789],{},[2129,65556,2327],{},[1996,65558,2011],{"stretchy":2004},[1996,65560,1998],{},[898,65562,2774],{},[2124,65564,65565,65567],{},[898,65566,3994],{},[1996,65568,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,65570,2005],{"stretchy":2004},[2272,65572,65573,65575],{},[898,65574,2789],{},[2129,65576,2327],{},[1996,65578,2011],{"stretchy":2004},[1996,65580,2225],{},[898,65582,2774],{},[2124,65584,65585,65587],{},[898,65586,2777],{},[1996,65588,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,65590,2005],{"stretchy":2004},[2272,65592,65593,65595],{},[898,65594,2789],{},[2129,65596,2327],{},[1996,65598,2011],{"stretchy":2004},[1996,65600,1998],{},[2129,65602,2327],{},[902,65604,65605],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,65607,65609],{"className":65608},[886],[888,65610,65611],{"xmlns":890},[892,65612,65613,65645],{},[895,65614,65615,65617,65619,65621,65627,65629,65631,65633,65635,65637,65643],{},[898,65616,2818],{},[898,65618,3994],{},[1996,65620,2005],{"stretchy":2004},[2272,65622,65623,65625],{},[898,65624,2789],{},[2129,65626,2327],{},[1996,65628,2011],{"stretchy":2004},[1996,65630,1998],{},[898,65632,2818],{},[898,65634,2777],{},[1996,65636,2005],{"stretchy":2004},[2272,65638,65639,65641],{},[898,65640,2789],{},[2129,65642,2327],{},[1996,65644,2011],{"stretchy":2004},[902,65646,65647],{"encoding":904},"MR(Q_0) = MC(Q_0)",[3867,65649,65650,65655],{},[724,65651,65652,65654],{},[883,65653,4572],{}," Postup — jak najít maximum zisku",[152,65656,65657,65721,65776,65813,65841],{},[123,65658,65659,65660,3885,65675,65690,65691,3918],{},"Sestavte ",[883,65661,65663],{"className":65662},[886],[888,65664,65665],{"xmlns":890},[892,65666,65667,65673],{},[895,65668,65669,65671],{},[898,65670,2774],{},[898,65672,3994],{},[902,65674,4094],{"encoding":904},[883,65676,65678],{"className":65677},[886],[888,65679,65680],{"xmlns":890},[892,65681,65682,65688],{},[895,65683,65684,65686],{},[898,65685,2774],{},[898,65687,2777],{},[902,65689,3243],{"encoding":904}," ze zadání (typicky ",[883,65692,65694],{"className":65693},[886],[888,65695,65696],{"xmlns":890},[892,65697,65698,65718],{},[895,65699,65700,65702,65704,65706,65708,65710,65712,65714,65716],{},[898,65701,2774],{},[898,65703,3994],{},[1996,65705,1998],{},[898,65707,3937],{},[1996,65709,2005],{"stretchy":2004},[898,65711,2789],{},[1996,65713,2011],{"stretchy":2004},[1996,65715,3177],{},[898,65717,2789],{},[902,65719,65720],{"encoding":904},"TR = P(Q) \\cdot Q",[123,65722,65723,65724,3885,65750,1975],{},"Vypočtěte ",[883,65725,65727],{"className":65726},[886],[888,65728,65729],{"xmlns":890},[892,65730,65731,65747],{},[895,65732,65733,65735,65737,65739,65741],{},[898,65734,2818],{},[898,65736,3994],{},[1996,65738,1998],{},[898,65740,2774],{},[2124,65742,65743,65745],{},[898,65744,3994],{},[1996,65746,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,65748,65749],{"encoding":904},"MR = TR'",[883,65751,65753],{"className":65752},[886],[888,65754,65755],{"xmlns":890},[892,65756,65757,65773],{},[895,65758,65759,65761,65763,65765,65767],{},[898,65760,2818],{},[898,65762,2777],{},[1996,65764,1998],{},[898,65766,2774],{},[2124,65768,65769,65771],{},[898,65770,2777],{},[1996,65772,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,65774,65775],{"encoding":904},"MC = TC'",[123,65777,65778,65779,1975],{},"Řešte rovnici ",[883,65780,65782],{"className":65781},[886],[888,65783,65784],{"xmlns":890},[892,65785,65786,65810],{},[895,65787,65788,65790,65792,65794,65796,65798,65800,65802,65804,65806,65808],{},[898,65789,2818],{},[898,65791,3994],{},[1996,65793,2005],{"stretchy":2004},[898,65795,2789],{},[1996,65797,2011],{"stretchy":2004},[1996,65799,1998],{},[898,65801,2818],{},[898,65803,2777],{},[1996,65805,2005],{"stretchy":2004},[898,65807,2789],{},[1996,65809,2011],{"stretchy":2004},[902,65811,65812],{"encoding":904},"MR(Q) = MC(Q)",[123,65814,65815,65816,65840],{},"Ověřte druhou derivaci ",[883,65817,65819],{"className":65818},[886],[888,65820,65821],{"xmlns":890},[892,65822,65823,65837],{},[895,65824,65825,65827],{},[898,65826,3937],{},[2124,65828,65829,65831],{},[898,65830,3994],{},[895,65832,65833,65835],{},[1996,65834,2378],{"mathvariant":2376},[1996,65836,2378],{"mathvariant":2376},[902,65838,65839],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,65842,65843,65844,65871],{},"Dosaďte do ",[883,65845,65847],{"className":65846},[886],[888,65848,65849],{"xmlns":890},[892,65850,65851,65869],{},[895,65852,65853,65855,65857,65859,65861,65863,65865,65867],{},[898,65854,3937],{},[898,65856,3994],{},[1996,65858,1998],{},[898,65860,2774],{},[898,65862,3994],{},[1996,65864,2225],{},[898,65866,2774],{},[898,65868,2777],{},[902,65870,55202],{"encoding":904}," pro hodnotu maxima.",[37350,65873,65875],{"id":65874},"příklad-39","Příklad 3.9",[724,65877,65878,55990,65880,3885,65902,65938],{},[38,65879,55989],{},[883,65881,65883],{"className":65882},[886],[888,65884,65885],{"xmlns":890},[892,65886,65887,65899],{},[895,65888,65889,65891,65893,65895,65897],{},[898,65890,3937],{},[1996,65892,1998],{},[2129,65894,38021],{},[1996,65896,2225],{},[898,65898,2789],{},[902,65900,65901],{"encoding":904},"P = 30 - Q",[883,65903,65905],{"className":65904},[886],[888,65906,65907],{"xmlns":890},[892,65908,65909,65935],{},[895,65910,65911,65913,65915,65917,65919,65925,65927,65929,65931,65933],{},[898,65912,2774],{},[898,65914,2777],{},[1996,65916,1998],{},[2129,65918,5009],{},[2124,65920,65921,65923],{},[898,65922,2789],{},[2129,65924,2131],{},[1996,65926,2095],{},[2129,65928,2235],{},[898,65930,2789],{},[1996,65932,2095],{},[2129,65934,24203],{},[902,65936,65937],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,65940,65941,2203,65943,1343,65973,66011,66012,15794,66056,66090,66091,1975],{},[38,65942,22772],{},[883,65944,65946],{"className":65945},[886],[888,65947,65948],{"xmlns":890},[892,65949,65950,65970],{},[895,65951,65952,65954,65956,65958,65960,65962,65964],{},[898,65953,2774],{},[898,65955,3994],{},[1996,65957,1998],{},[2129,65959,38021],{},[898,65961,2789],{},[1996,65963,2225],{},[2124,65965,65966,65968],{},[898,65967,2789],{},[2129,65969,2131],{},[902,65971,65972],{"encoding":904},"TR = 30Q - Q^2",[883,65974,65976],{"className":65975},[886],[888,65977,65978],{"xmlns":890},[892,65979,65980,66008],{},[895,65981,65982,65984,65986,65988,65990,65992,65998,66000,66002,66004,66006],{},[898,65983,3937],{},[898,65985,3994],{},[1996,65987,1998],{},[1996,65989,2225],{},[2129,65991,64561],{},[2124,65993,65994,65996],{},[898,65995,2789],{},[2129,65997,2131],{},[1996,65999,2095],{},[2129,66001,41802],{},[898,66003,2789],{},[1996,66005,2225],{},[2129,66007,24203],{},[902,66009,66010],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,66013,66015],{"className":66014},[886],[888,66016,66017],{"xmlns":890},[892,66018,66019,66053],{},[895,66020,66021,66023,66029,66031,66033,66035,66037,66039,66041,66043,66045,66047,66049,66051],{},[898,66022,3937],{},[2124,66024,66025,66027],{},[898,66026,3994],{},[1996,66028,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,66030,1998],{},[1996,66032,2225],{},[2129,66034,2173],{},[898,66036,2789],{},[1996,66038,2095],{},[2129,66040,41802],{},[1996,66042,1998],{},[2129,66044,2327],{},[1996,66046,3987],{},[898,66048,2789],{},[1996,66050,1998],{},[2129,66052,5585],{},[902,66054,66055],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,66057,66059],{"className":66058},[886],[888,66060,66061],{"xmlns":890},[892,66062,66063,66087],{},[895,66064,66065,66067,66077,66079,66081,66083,66085],{},[898,66066,3937],{},[2124,66068,66069,66071],{},[898,66070,3994],{},[895,66072,66073,66075],{},[1996,66074,2378],{"mathvariant":2376},[1996,66076,2378],{"mathvariant":2376},[1996,66078,1998],{},[1996,66080,2225],{},[2129,66082,2173],{},[1996,66084,3447],{},[2129,66086,2327],{},[902,66088,66089],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,66092,66094],{"className":66093},[886],[888,66095,66096],{"xmlns":890},[892,66097,66098,66115],{},[895,66099,66100,66102,66104,66106,66108,66110,66112],{},[898,66101,3937],{},[898,66103,3994],{},[1996,66105,2005],{"stretchy":2004},[2129,66107,5585],{},[1996,66109,2011],{"stretchy":2004},[1996,66111,1998],{},[2129,66113,66114],{},"89",[902,66116,66117],{"encoding":904},"PR(8) = 89",[724,66119,66120,66121,1343,66147,15794,66171,66209],{},"Ověření principu: ",[883,66122,66124],{"className":66123},[886],[888,66125,66126],{"xmlns":890},[892,66127,66128,66144],{},[895,66129,66130,66132,66134,66136,66138,66140,66142],{},[898,66131,2818],{},[898,66133,3994],{},[1996,66135,1998],{},[2129,66137,38021],{},[1996,66139,2225],{},[2129,66141,2131],{},[898,66143,2789],{},[902,66145,66146],{"encoding":904},"MR = 30 - 2Q",[883,66148,66150],{"className":66149},[886],[888,66151,66152],{"xmlns":890},[892,66153,66154,66168],{},[895,66155,66156,66158,66160,66162,66164,66166],{},[898,66157,2818],{},[898,66159,2777],{},[1996,66161,1998],{},[898,66163,2789],{},[1996,66165,2095],{},[2129,66167,2235],{},[902,66169,66170],{"encoding":904},"MC = Q + 6",[883,66172,66174],{"className":66173},[886],[888,66175,66176],{"xmlns":890},[892,66177,66178,66206],{},[895,66179,66180,66182,66184,66186,66188,66190,66192,66194,66196,66198,66200,66202,66204],{},[898,66181,2818],{},[898,66183,3994],{},[1996,66185,2005],{"stretchy":2004},[2129,66187,5585],{},[1996,66189,2011],{"stretchy":2004},[1996,66191,1998],{},[2129,66193,22948],{},[1996,66195,1998],{},[898,66197,2818],{},[898,66199,2777],{},[1996,66201,2005],{"stretchy":2004},[2129,66203,5585],{},[1996,66205,2011],{"stretchy":2004},[902,66207,66208],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,66211,66212,66213,66246,66247,66264],{},"V řadě případů — má-li rovnice ",[883,66214,66216],{"className":66215},[886],[888,66217,66218],{"xmlns":890},[892,66219,66220,66244],{},[895,66221,66222,66224,66226,66228,66230,66232,66234,66236,66238,66240,66242],{},[898,66223,2818],{},[898,66225,3994],{},[1996,66227,2005],{"stretchy":2004},[898,66229,2789],{},[1996,66231,2011],{"stretchy":2004},[1996,66233,1998],{},[898,66235,2818],{},[898,66237,2777],{},[1996,66239,2005],{"stretchy":2004},[898,66241,2789],{},[1996,66243,2011],{"stretchy":2004},[902,66245,65812],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,66248,66250],{"className":66249},[886],[888,66251,66252],{"xmlns":890},[892,66253,66254,66262],{},[895,66255,66256],{},[2272,66257,66258,66260],{},[898,66259,2789],{},[2129,66261,2327],{},[902,66263,38310],{"encoding":904}," — není třeba provádět test druhé derivace.",[37350,66266,66268],{"id":66267},"příklad-310","Příklad 3.10",[724,66270,66271,66273,66274,66278,66279,66292,66293,66324],{},[38,66272,55989],{}," Firma vyrábí minipočítače v ",[207,66275,66277],{"className":66276,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,66280,66282],{"className":66281},[886],[888,66283,66284],{"xmlns":890},[892,66285,66286,66290],{},[895,66287,66288],{},[2129,66289,15193],{},[902,66291,15193],{"encoding":904}," EUR\u002Fks. ",[883,66294,66296],{"className":66295},[886],[888,66297,66298],{"xmlns":890},[892,66299,66300,66321],{},[895,66301,66302,66304,66306,66308,66310,66312,66315],{},[898,66303,2774],{},[898,66305,2777],{},[1996,66307,1998],{},[2129,66309,3120],{},[1996,66311,2095],{},[2129,66313,66314],{},"28",[2124,66316,66317,66319],{},[898,66318,2789],{},[2129,66320,2131],{},[902,66322,66323],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,66326,66327,2203,66329,1343,66351,1343,66371,66394],{},[38,66328,22772],{},[883,66330,66332],{"className":66331},[886],[888,66333,66334],{"xmlns":890},[892,66335,66336,66348],{},[895,66337,66338,66340,66342,66344,66346],{},[898,66339,2774],{},[898,66341,3994],{},[1996,66343,1998],{},[2129,66345,15193],{},[898,66347,2789],{},[902,66349,66350],{"encoding":904},"TR = 900Q",[883,66352,66354],{"className":66353},[886],[888,66355,66356],{"xmlns":890},[892,66357,66358,66368],{},[895,66359,66360,66362,66364,66366],{},[898,66361,2818],{},[898,66363,3994],{},[1996,66365,1998],{},[2129,66367,15193],{},[902,66369,66370],{"encoding":904},"MR = 900",[883,66372,66374],{"className":66373},[886],[888,66375,66376],{"xmlns":890},[892,66377,66378,66391],{},[895,66379,66380,66382,66384,66386,66389],{},[898,66381,2818],{},[898,66383,2777],{},[1996,66385,1998],{},[2129,66387,66388],{},"56",[898,66390,2789],{},[902,66392,66393],{"encoding":904},"MC = 56Q",". Z principu:",[883,66396,66398],{"className":66397},[886],[888,66399,66400],{"xmlns":890,"display":28068},[892,66401,66402,66444],{},[895,66403,66404,66406,66408,66410,66412,66414,66416,66418,66420,66422,66430,66432,66435,66437,66439,66441],{},[2129,66405,15193],{},[1996,66407,1998],{},[2129,66409,66388],{},[898,66411,2789],{},[2288,66413,3984],{},[1996,66415,3987],{},[2288,66417,3984],{},[898,66419,2789],{},[1996,66421,1998],{},[2325,66423,66424],{"scriptlevel":2327,"displaystyle":2004},[2329,66425,66426,66428],{},[2129,66427,15193],{},[2129,66429,66388],{},[1996,66431,5900],{},[2129,66433,66434],{},"16,07",[2288,66436,3984],{},[1996,66438,2730],{},[2288,66440,3984],{},[2129,66442,66443],{},"16.",[902,66445,66446],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,66448,66449,66450,2704],{},"Zisk při ",[883,66451,66453],{"className":66452},[886],[888,66454,66455],{"xmlns":890},[892,66456,66457,66465],{},[895,66458,66459,66461,66463],{},[898,66460,2789],{},[1996,66462,1998],{},[2129,66464,41864],{},[902,66466,66467],{"encoding":904},"Q = 16",[883,66469,66471],{"className":66470},[886],[888,66472,66473],{"xmlns":890,"display":28068},[892,66474,66475,66546],{},[895,66476,66477,66479,66481,66483,66485,66487,66489,66491,66493,66495,66497,66499,66501,66503,66505,66507,66513,66515,66517,66519,66521,66523,66525,66527,66529,66532,66534,66536,66538,66541,66544],{},[898,66478,3937],{},[898,66480,3994],{},[1996,66482,2005],{"stretchy":2004},[2129,66484,41864],{},[1996,66486,2011],{"stretchy":2004},[1996,66488,1998],{},[2129,66490,15193],{},[1996,66492,3177],{},[2129,66494,41864],{},[1996,66496,2225],{},[1996,66498,2005],{"stretchy":2004},[2129,66500,3120],{},[1996,66502,2095],{},[2129,66504,66314],{},[1996,66506,3177],{},[2124,66508,66509,66511],{},[2129,66510,41864],{},[2129,66512,2131],{},[1996,66514,2011],{"stretchy":2004},[1996,66516,1998],{},[2129,66518,22948],{},[2288,66520,2987],{},[2129,66522,20144],{},[1996,66524,2225],{},[2129,66526,24203],{},[2288,66528,2987],{},[2129,66530,66531],{},"218",[1996,66533,1998],{},[2129,66535,24203],{},[2288,66537,2987],{},[2129,66539,66540],{},"182",[2288,66542,66543],{}," EUR",[898,66545,1975],{"mathvariant":2376},[902,66547,66548],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,66550,66551],{},"Pro srovnání při původních 30 ks:",[883,66553,66555],{"className":66554},[886],[888,66556,66557],{"xmlns":890,"display":28068},[892,66558,66559,66624],{},[895,66560,66561,66563,66565,66567,66569,66571,66573,66575,66577,66579,66581,66583,66585,66587,66589,66591,66593,66595,66597,66600,66602,66604,66606,66608,66610,66612,66614,66616,66618,66620,66622],{},[898,66562,3937],{},[898,66564,3994],{},[1996,66566,2005],{"stretchy":2004},[2129,66568,38021],{},[1996,66570,2011],{"stretchy":2004},[1996,66572,1998],{},[2129,66574,15193],{},[1996,66576,3177],{},[2129,66578,38021],{},[1996,66580,2225],{},[1996,66582,2005],{"stretchy":2004},[2129,66584,3120],{},[1996,66586,2095],{},[2129,66588,66314],{},[1996,66590,3177],{},[2129,66592,15193],{},[1996,66594,2011],{"stretchy":2004},[1996,66596,1998],{},[2129,66598,66599],{},"27",[2288,66601,2987],{},[2129,66603,59084],{},[1996,66605,2225],{},[2129,66607,5004],{},[2288,66609,2987],{},[2129,66611,30745],{},[1996,66613,1998],{},[2129,66615,2278],{},[2288,66617,2987],{},[2129,66619,23745],{},[2288,66621,66543],{},[898,66623,1975],{"mathvariant":2376},[902,66625,66626],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,66628,66629,66632,66633,66651,66652,66670],{},[38,66630,66631],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,66634,66636],{"className":66635},[886],[888,66637,66638],{"xmlns":890},[892,66639,66640,66648],{},[895,66641,66642,66644,66646],{},[2129,66643,24203],{},[2288,66645,2987],{},[2129,66647,66540],{},[902,66649,66650],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,66653,66655],{"className":66654},[886],[888,66656,66657],{"xmlns":890},[892,66658,66659,66667],{},[895,66660,66661,66663,66665],{},[2129,66662,2278],{},[2288,66664,2987],{},[2129,66666,23745],{},[902,66668,66669],{"encoding":904},"1\\,750"," EUR.",[198,66672,66674],{"id":66673},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,66676,66677,66678,62572,66691,66715],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,66679,66681],{"className":66680},[886],[888,66682,66683],{"xmlns":890},[892,66684,66685,66689],{},[895,66686,66687],{},[898,66688,3937],{},[902,66690,3937],{"encoding":904},[883,66692,66694],{"className":66693},[886],[888,66695,66696],{"xmlns":890},[892,66697,66698,66712],{},[895,66699,66700,66702,66704,66706,66708,66710],{},[898,66701,2774],{},[898,66703,3994],{},[1996,66705,1998],{},[898,66707,3937],{},[1996,66709,3177],{},[898,66711,2789],{},[902,66713,66714],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,66717,66719],{"className":66718},[886],[888,66720,66721],{"xmlns":890,"display":28068},[892,66722,66723,66756],{},[20756,66724,66725],{"width":28073},[20761,66726,66727,66729,66749,66751],{},[20764,66728],{"width":28078},[20764,66730,66731],{},[895,66732,66733,66735,66737,66739,66741,66743,66745,66747],{},[898,66734,3937],{},[1996,66736,1998],{},[898,66738,2818],{},[898,66740,2777],{},[1996,66742,2005],{"stretchy":2004},[898,66744,2789],{},[1996,66746,2011],{"stretchy":2004},[898,66748,1975],{"mathvariant":2376},[20764,66750],{"width":28078},[20764,66752,66753],{},[2288,66754,66755],{},"(3.14)",[902,66757,66758],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,66760,66761,66762,1975],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,66763,66765],{"className":66764},[886],[888,66766,66767],{"xmlns":890},[892,66768,66769,66783],{},[895,66770,66771,66773],{},[898,66772,3937],{},[2124,66774,66775,66777],{},[898,66776,3994],{},[895,66778,66779,66781],{},[1996,66780,2378],{"mathvariant":2376},[1996,66782,2378],{"mathvariant":2376},[902,66784,65839],{"encoding":904},[37350,66786,66788],{"id":66787},"příklad-311","Příklad 3.11",[724,66790,66791,57524,66793,66840,66841,66859],{},[38,66792,55989],{},[883,66794,66796],{"className":66795},[886],[888,66797,66798],{"xmlns":890},[892,66799,66800,66837],{},[895,66801,66802,66804,66806,66808,66811,66817,66819,66821,66827,66829,66831,66833,66835],{},[898,66803,2774],{},[898,66805,2777],{},[1996,66807,1998],{},[2129,66809,66810],{},"0,04",[2124,66812,66813,66815],{},[898,66814,2789],{},[2129,66816,2173],{},[1996,66818,2225],{},[2129,66820,22547],{},[2124,66822,66823,66825],{},[898,66824,2789],{},[2129,66826,2131],{},[1996,66828,2095],{},[2129,66830,2863],{},[898,66832,2789],{},[1996,66834,2095],{},[2129,66836,2228],{},[902,66838,66839],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,66842,66844],{"className":66843},[886],[888,66845,66846],{"xmlns":890},[892,66847,66848,66856],{},[895,66849,66850,66852,66854],{},[898,66851,3937],{},[1996,66853,1998],{},[2129,66855,2351],{},[902,66857,66858],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,66861,66862,66864,66865,17578,66907,66941,66942,2704],{},[38,66863,22772],{}," Z (3.14): ",[883,66866,66868],{"className":66867},[886],[888,66869,66870],{"xmlns":890},[892,66871,66872,66904],{},[895,66873,66874,66876,66878,66880,66883,66889,66891,66894,66896,66898,66900,66902],{},[898,66875,2818],{},[898,66877,2777],{},[1996,66879,1998],{},[2129,66881,66882],{},"0,12",[2124,66884,66885,66887],{},[898,66886,2789],{},[2129,66888,2131],{},[1996,66890,2225],{},[2129,66892,66893],{},"1,8",[898,66895,2789],{},[1996,66897,2095],{},[2129,66899,2863],{},[1996,66901,1998],{},[2129,66903,2351],{},[902,66905,66906],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,66908,66910],{"className":66909},[886],[888,66911,66912],{"xmlns":890},[892,66913,66914,66938],{},[895,66915,66916,66918,66924,66926,66928,66930,66932,66934,66936],{},[2129,66917,66882],{},[2124,66919,66920,66922],{},[898,66921,2789],{},[2129,66923,2131],{},[1996,66925,2225],{},[2129,66927,66893],{},[898,66929,2789],{},[1996,66931,2095],{},[2129,66933,2235],{},[1996,66935,1998],{},[2129,66937,2327],{},[902,66939,66940],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,66943,66945],{"className":66944},[886],[888,66946,66947],{"xmlns":890},[892,66948,66949,66953],{},[895,66950,66951],{},[2129,66952,66882],{},[902,66954,66955],{"encoding":904},"0{,}12",[883,66957,66959],{"className":66958},[886],[888,66960,66961],{"xmlns":890,"display":28068},[892,66962,66963,67015],{},[895,66964,66965,66971,66973,66975,66977,66979,66981,66983,66985,66987,66989,66991,66997,66999,67001,67003,67005,67011,67013],{},[2124,66966,66967,66969],{},[898,66968,2789],{},[2129,66970,2131],{},[1996,66972,2225],{},[2129,66974,36246],{},[898,66976,2789],{},[1996,66978,2095],{},[2129,66980,3120],{},[1996,66982,1998],{},[2129,66984,2327],{},[2288,66986,3984],{},[1996,66988,3987],{},[2288,66990,3984],{},[2272,66992,66993,66995],{},[898,66994,2789],{},[2129,66996,2278],{},[1996,66998,1998],{},[2129,67000,2228],{},[1996,67002,2286],{"separator":2285},[2288,67004,3984],{},[2272,67006,67007,67009],{},[898,67008,2789],{},[2129,67010,2131],{},[1996,67012,1998],{},[2129,67014,19330],{},[902,67016,67017],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,67019,67020,67021,2704],{},"Dále ",[883,67022,67024],{"className":67023},[886],[888,67025,67026],{"xmlns":890},[892,67027,67028,67067],{},[895,67029,67030,67032,67042,67044,67046,67048,67054,67056,67058,67061,67063,67065],{},[898,67031,3937],{},[2124,67033,67034,67036],{},[898,67035,3994],{},[895,67037,67038,67040],{},[1996,67039,2378],{"mathvariant":2376},[1996,67041,2378],{"mathvariant":2376},[1996,67043,1998],{},[1996,67045,2225],{},[898,67047,2818],{},[2124,67049,67050,67052],{},[898,67051,2777],{},[1996,67053,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,67055,1998],{},[1996,67057,2225],{},[2129,67059,67060],{},"0,24",[898,67062,2789],{},[1996,67064,2095],{},[2129,67066,66893],{},[902,67068,67069],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,67071,67072,67122],{},[123,67073,67074,67118,67119,67121],{},[883,67075,67077],{"className":67076},[886],[888,67078,67079],{"xmlns":890},[892,67080,67081,67115],{},[895,67082,67083,67085,67095,67097,67099,67101,67103,67105,67107,67109,67111,67113],{},[898,67084,3937],{},[2124,67086,67087,67089],{},[898,67088,3994],{},[895,67090,67091,67093],{},[1996,67092,2378],{"mathvariant":2376},[1996,67094,2378],{"mathvariant":2376},[1996,67096,2005],{"stretchy":2004},[2129,67098,2228],{},[1996,67100,2011],{"stretchy":2004},[1996,67102,1998],{},[2129,67104,19323],{},[1996,67106,3408],{},[2129,67108,2327],{},[2288,67110,3984],{},[1996,67112,3987],{},[2288,67114,3984],{},[902,67116,67117],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,67120,3775],{}," zisku (minimalizace ztráty);",[123,67123,67124,67118,67170,67172],{},[883,67125,67127],{"className":67126},[886],[888,67128,67129],{"xmlns":890},[892,67130,67131,67167],{},[895,67132,67133,67135,67145,67147,67149,67151,67153,67155,67157,67159,67161,67163,67165],{},[898,67134,3937],{},[2124,67136,67137,67139],{},[898,67138,3994],{},[895,67140,67141,67143],{},[1996,67142,2378],{"mathvariant":2376},[1996,67144,2378],{"mathvariant":2376},[1996,67146,2005],{"stretchy":2004},[2129,67148,2863],{},[1996,67150,2011],{"stretchy":2004},[1996,67152,1998],{},[1996,67154,2225],{},[2129,67156,19323],{},[1996,67158,3447],{},[2129,67160,2327],{},[2288,67162,3984],{},[1996,67164,3987],{},[2288,67166,3984],{},[902,67168,67169],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,67171,3717],{}," zisku, avšak",[883,67174,67176],{"className":67175},[886],[888,67177,67178],{"xmlns":890,"display":28068},[892,67179,67180,67248],{},[895,67181,67182,67184,67186,67188,67190,67192,67194,67196,67198,67200,67202,67204,67206,67208,67210,67212,67214,67216,67218,67220,67222,67224,67226,67228,67230,67232,67234,67236,67238,67240,67242,67244,67246],{},[898,67183,3937],{},[898,67185,3994],{},[1996,67187,2005],{"stretchy":2004},[2129,67189,2863],{},[1996,67191,2011],{"stretchy":2004},[1996,67193,1998],{},[2129,67195,2351],{},[1996,67197,3177],{},[2129,67199,2863],{},[1996,67201,2225],{},[1996,67203,2005],{"stretchy":2004},[2129,67205,66810],{},[1996,67207,3177],{},[2129,67209,2278],{},[2288,67211,2987],{},[2129,67213,59084],{},[1996,67215,2225],{},[2129,67217,22547],{},[1996,67219,3177],{},[2129,67221,3090],{},[1996,67223,2095],{},[2129,67225,3090],{},[1996,67227,2095],{},[2129,67229,2228],{},[1996,67231,2011],{"stretchy":2004},[1996,67233,1998],{},[2129,67235,5211],{},[1996,67237,2225],{},[2129,67239,21182],{},[1996,67241,1998],{},[1996,67243,2225],{},[2129,67245,36246],{},[1996,67247,2286],{"separator":2285},[902,67249,67250],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,67252,67253,67254,1975],{},"tj. ztráta větší než ",[883,67255,67257],{"className":67256},[886],[888,67258,67259],{"xmlns":890},[892,67260,67261,67271],{},[895,67262,67263,67265,67267,67269],{},[898,67264,10436],{},[898,67266,2777],{},[1996,67268,1998],{},[2129,67270,2228],{},[902,67272,67273],{"encoding":904},"FC = 5",[724,67275,67276,67279,67280,67283,67284,1975],{},[38,67277,67278],{},"Závěr:"," firma by měla ",[38,67281,67282],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,67285,67287],{"className":67286},[886],[888,67288,67289],{"xmlns":890},[892,67290,67291,67301],{},[895,67292,67293,67295,67297,67299],{},[898,67294,10436],{},[898,67296,2777],{},[1996,67298,1998],{},[2129,67300,2228],{},[902,67302,67273],{"encoding":904},[115,67304,67306],{"id":67305},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,67308,67309,67310,67312,67313,67328,67329,67342,67343,67369,67370,67383,67384,67401,67402,2624,67419,67422,67423,67443,67444,67459,67460,2704],{},"Důležitým završením analýzy je konstrukce ",[38,67311,55277],{},". S nabízeným množstvím rostou mezní náklady ",[883,67314,67316],{"className":67315},[886],[888,67317,67318],{"xmlns":890},[892,67319,67320,67326],{},[895,67321,67322,67324],{},[898,67323,2818],{},[898,67325,2777],{},[902,67327,55294],{"encoding":904}," a tyto určují cenu ",[883,67330,67332],{"className":67331},[886],[888,67333,67334],{"xmlns":890},[892,67335,67336,67340],{},[895,67337,67338],{},[898,67339,3937],{},[902,67341,3937],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,67344,67346],{"className":67345},[886],[888,67347,67348],{"xmlns":890},[892,67349,67350,67366],{},[895,67351,67352,67354,67356,67358,67360,67362,67364],{},[898,67353,3937],{},[1996,67355,1998],{},[898,67357,2818],{},[898,67359,2777],{},[1996,67361,2005],{"stretchy":2004},[898,67363,2789],{},[1996,67365,2011],{"stretchy":2004},[902,67367,67368],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,67371,67373],{"className":67372},[886],[888,67374,67375],{"xmlns":890},[892,67376,67377,67381],{},[895,67378,67379],{},[898,67380,3937],{},[902,67382,3937],{"encoding":904}," však nemůže být nižší než ",[883,67385,67387],{"className":67386},[886],[888,67388,67389],{"xmlns":890},[892,67390,67391,67399],{},[895,67392,67393],{},[2124,67394,67395,67397],{},[898,67396,3937],{},[1996,67398,4354],{},[902,67400,4404],{"encoding":904}," odpovídající množství ",[883,67403,67405],{"className":67404},[886],[888,67406,67407],{"xmlns":890},[892,67408,67409,67417],{},[895,67410,67411],{},[2124,67412,67413,67415],{},[898,67414,2789],{},[1996,67416,4354],{},[902,67418,29846],{"encoding":904},[38,67420,67421],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,67424,67426],{"className":67425},[886],[888,67427,67428],{"xmlns":890},[892,67429,67430,67440],{},[895,67431,67432,67434],{},[2129,67433,2327],{},[2124,67435,67436,67438],{},[898,67437,2789],{},[1996,67439,4354],{},[902,67441,67442],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,67445,67447],{"className":67446},[886],[888,67448,67449],{"xmlns":890},[892,67450,67451,67457],{},[895,67452,67453,67455],{},[898,67454,2818],{},[898,67456,2777],{},[902,67458,55294],{"encoding":904}," nad bodem ",[883,67461,67463],{"className":67462},[886],[888,67464,67465],{"xmlns":890},[892,67466,67467,67471],{},[895,67468,67469],{},[898,67470,4255],{},[902,67472,4255],{"encoding":904},[883,67474,67476],{"className":67475},[886],[888,67477,67478],{"xmlns":890,"display":28068},[892,67479,67480,67587],{},[20756,67481,67482],{"width":28073},[20761,67483,67484,67486,67580,67582],{},[20764,67485],{"width":28078},[20764,67487,67488],{},[895,67489,67490,67492,67494,67496,67498,67500,67502,67504],{},[898,67491,3937],{},[1996,67493,1998],{},[898,67495,8673],{},[1996,67497,2005],{"stretchy":2004},[898,67499,2789],{},[1996,67501,2011],{"stretchy":2004},[1996,67503,1998],{},[895,67505,67506,67509],{},[1996,67507,67508],{"fence":2285},"{",[20756,67510,67513,67552],{"rowspacing":67511,"columnalign":67512,"columnspacing":15286},"0.36em","left left",[20761,67514,67515,67531],{},[20764,67516,67517],{},[2325,67518,67519],{"scriptlevel":2327,"displaystyle":2004},[895,67520,67521,67523,67525,67527,67529],{},[898,67522,2818],{},[898,67524,2777],{},[1996,67526,2005],{"stretchy":2004},[898,67528,2789],{},[1996,67530,2011],{"stretchy":2004},[20764,67532,67533],{},[2325,67534,67535],{"scriptlevel":2327,"displaystyle":2004},[895,67536,67537,67540,67542,67544,67550],{},[2288,67538,67539],{},"pro ",[898,67541,2789],{},[1996,67543,4485],{},[2124,67545,67546,67548],{},[898,67547,2789],{},[1996,67549,4354],{},[1996,67551,2286],{"separator":2285},[20761,67553,67554,67560],{},[20764,67555,67556],{},[2325,67557,67558],{"scriptlevel":2327,"displaystyle":2004},[2129,67559,2327],{},[20764,67561,67562],{},[2325,67563,67564],{"scriptlevel":2327,"displaystyle":2004},[895,67565,67566,67568,67570,67572,67578],{},[2288,67567,67539],{},[898,67569,2789],{},[1996,67571,3447],{},[2124,67573,67574,67576],{},[898,67575,2789],{},[1996,67577,4354],{},[1996,67579,2286],{"separator":2285},[20764,67581],{"width":28078},[20764,67583,67584],{},[2288,67585,67586],{},"(3.15)",[902,67588,67589],{"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}",[724,67591,4310,67592,67609,67610,67627,67628,41501,67658,67661],{},[883,67593,67595],{"className":67594},[886],[888,67596,67597],{"xmlns":890},[892,67598,67599,67607],{},[895,67600,67601],{},[2124,67602,67603,67605],{},[898,67604,2789],{},[1996,67606,4354],{},[902,67608,29846],{"encoding":904}," je bod minima ",[883,67611,67613],{"className":67612},[886],[888,67614,67615],{"xmlns":890},[892,67616,67617,67625],{},[895,67618,67619,67621,67623],{},[898,67620,4255],{},[898,67622,40341],{},[898,67624,2777],{},[902,67626,55313],{"encoding":904},". Bod ",[883,67629,67631],{"className":67630},[886],[888,67632,67633],{"xmlns":890},[892,67634,67635,67655],{},[895,67636,67637,67639,67645,67647,67653],{},[1996,67638,2005],{"stretchy":2004},[2124,67640,67641,67643],{},[898,67642,2789],{},[1996,67644,4354],{},[1996,67646,2286],{"separator":2285},[2124,67648,67649,67651],{},[898,67650,3937],{},[1996,67652,4354],{},[1996,67654,2011],{"stretchy":2004},[902,67656,67657],{"encoding":904},"(Q^*, P^*)",[38,67659,67660],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[3867,67663,67664,67669],{},[724,67665,67666,67668],{},[883,67667,4572],{}," Postup — jak odvodit nabídku firmy",[152,67670,67671,67720,67815,67870,67941],{},[123,67672,67673,67674,3885,67696,1975],{},"Ze zadaných nákladů určete ",[883,67675,67677],{"className":67676},[886],[888,67678,67679],{"xmlns":890},[892,67680,67681,67693],{},[895,67682,67683,67685,67687,67689,67691],{},[898,67684,2818],{},[898,67686,2777],{},[1996,67688,2005],{"stretchy":2004},[898,67690,2789],{},[1996,67692,2011],{"stretchy":2004},[902,67694,67695],{"encoding":904},"MC(Q)",[883,67697,67699],{"className":67698},[886],[888,67700,67701],{"xmlns":890},[892,67702,67703,67717],{},[895,67704,67705,67707,67709,67711,67713,67715],{},[898,67706,4255],{},[898,67708,40341],{},[898,67710,2777],{},[1996,67712,2005],{"stretchy":2004},[898,67714,2789],{},[1996,67716,2011],{"stretchy":2004},[902,67718,67719],{"encoding":904},"AVC(Q)",[123,67721,67722,67723,67740,67741,67758,67759,67791,67792,3918],{},"Najděte ",[883,67724,67726],{"className":67725},[886],[888,67727,67728],{"xmlns":890},[892,67729,67730,67738],{},[895,67731,67732],{},[2124,67733,67734,67736],{},[898,67735,2789],{},[1996,67737,4354],{},[902,67739,29846],{"encoding":904}," jako bod minima ",[883,67742,67744],{"className":67743},[886],[888,67745,67746],{"xmlns":890},[892,67747,67748,67756],{},[895,67749,67750,67752,67754],{},[898,67751,4255],{},[898,67753,40341],{},[898,67755,2777],{},[902,67757,55313],{"encoding":904}," (řešením ",[883,67760,67762],{"className":67761},[886],[888,67763,67764],{"xmlns":890},[892,67765,67766,67788],{},[895,67767,67768,67770,67772,67778,67780,67782,67784,67786],{},[898,67769,4255],{},[898,67771,40341],{},[2124,67773,67774,67776],{},[898,67775,2777],{},[1996,67777,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,67779,2005],{"stretchy":2004},[898,67781,2789],{},[1996,67783,2011],{"stretchy":2004},[1996,67785,1998],{},[2129,67787,2327],{},[902,67789,67790],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,67793,67795],{"className":67794},[886],[888,67796,67797],{"xmlns":890},[892,67798,67799,67813],{},[895,67800,67801,67803,67805,67807,67809,67811],{},[898,67802,4255],{},[898,67804,40341],{},[898,67806,2777],{},[1996,67808,1998],{},[898,67810,2818],{},[898,67812,2777],{},[902,67814,55250],{"encoding":904},[123,67816,65723,67817,67869],{},[883,67818,67820],{"className":67819},[886],[888,67821,67822],{"xmlns":890},[892,67823,67824,67866],{},[895,67825,67826,67832,67834,67836,67838,67840,67846,67848,67850,67852,67854,67856,67858,67864],{},[2124,67827,67828,67830],{},[898,67829,3937],{},[1996,67831,4354],{},[1996,67833,1998],{},[898,67835,2818],{},[898,67837,2777],{},[1996,67839,2005],{"stretchy":2004},[2124,67841,67842,67844],{},[898,67843,2789],{},[1996,67845,4354],{},[1996,67847,2011],{"stretchy":2004},[1996,67849,1998],{},[898,67851,4255],{},[898,67853,40341],{},[898,67855,2777],{},[1996,67857,2005],{"stretchy":2004},[2124,67859,67860,67862],{},[898,67861,2789],{},[1996,67863,4354],{},[1996,67865,2011],{"stretchy":2004},[902,67867,67868],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,67871,67872,67873,6473,67905,67927,67928,1975],{},"Zapište nabídku: ",[883,67874,67876],{"className":67875},[886],[888,67877,67878],{"xmlns":890},[892,67879,67880,67902],{},[895,67881,67882,67884,67886,67888,67890,67892,67894,67896,67898,67900],{},[898,67883,8673],{},[1996,67885,2005],{"stretchy":2004},[898,67887,2789],{},[1996,67889,2011],{"stretchy":2004},[1996,67891,1998],{},[898,67893,2818],{},[898,67895,2777],{},[1996,67897,2005],{"stretchy":2004},[898,67899,2789],{},[1996,67901,2011],{"stretchy":2004},[902,67903,67904],{"encoding":904},"S(Q) = MC(Q)",[883,67906,67908],{"className":67907},[886],[888,67909,67910],{"xmlns":890},[892,67911,67912,67924],{},[895,67913,67914,67916,67918],{},[898,67915,2789],{},[1996,67917,4485],{},[2124,67919,67920,67922],{},[898,67921,2789],{},[1996,67923,4354],{},[902,67925,67926],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,67929,67931],{"className":67930},[886],[888,67932,67933],{"xmlns":890},[892,67934,67935,67939],{},[895,67936,67937],{},[2129,67938,2327],{},[902,67940,2327],{"encoding":904},[123,67942,67943,67944,67976],{},"V případě potřeby vyjádřete inverzi ",[883,67945,67947],{"className":67946},[886],[888,67948,67949],{"xmlns":890},[892,67950,67951,67973],{},[895,67952,67953,67955,67957,67967,67969,67971],{},[898,67954,2789],{},[1996,67956,1998],{},[2124,67958,67959,67961],{},[898,67960,8673],{},[895,67962,67963,67965],{},[1996,67964,2225],{},[2129,67966,2278],{},[1996,67968,2005],{"stretchy":2004},[898,67970,3937],{},[1996,67972,2011],{"stretchy":2004},[902,67974,67975],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,67978,67979],{},[614,67980,67981,67982,1343,67997,3885,68014,29203,68029,68042,68043,68068,68069,68082,68083,68100,68101,68118,68119,68136],{},"Obrázek 3.14: Křivky ",[883,67983,67985],{"className":67984},[886],[888,67986,67987],{"xmlns":890},[892,67988,67989,67995],{},[895,67990,67991,67993],{},[898,67992,4255],{},[898,67994,2777],{},[902,67996,55562],{"encoding":904},[883,67998,68000],{"className":67999},[886],[888,68001,68002],{"xmlns":890},[892,68003,68004,68012],{},[895,68005,68006,68008,68010],{},[898,68007,4255],{},[898,68009,40341],{},[898,68011,2777],{},[902,68013,55313],{"encoding":904},[883,68015,68017],{"className":68016},[886],[888,68018,68019],{"xmlns":890},[892,68020,68021,68027],{},[895,68022,68023,68025],{},[898,68024,2818],{},[898,68026,2777],{},[902,68028,55294],{"encoding":904},[883,68030,68032],{"className":68031},[886],[888,68033,68034],{"xmlns":890},[892,68035,68036,68040],{},[895,68037,68038],{},[898,68039,900],{},[902,68041,900],{"encoding":904},"; křivka nabídky ",[883,68044,68046],{"className":68045},[886],[888,68047,68048],{"xmlns":890},[892,68049,68050,68066],{},[895,68051,68052,68054,68056,68058,68060,68062,68064],{},[898,68053,3937],{},[1996,68055,1998],{},[898,68057,2818],{},[898,68059,2777],{},[1996,68061,2005],{"stretchy":2004},[898,68063,2789],{},[1996,68065,2011],{"stretchy":2004},[902,68067,67368],{"encoding":904}," začíná v bodě ",[883,68070,68072],{"className":68071},[886],[888,68073,68074],{"xmlns":890},[892,68075,68076,68080],{},[895,68077,68078],{},[898,68079,4255],{},[902,68081,4255],{"encoding":904}," odpovídajícím minimu ",[883,68084,68086],{"className":68085},[886],[888,68087,68088],{"xmlns":890},[892,68089,68090,68098],{},[895,68091,68092,68094,68096],{},[898,68093,4255],{},[898,68095,40341],{},[898,68097,2777],{},[902,68099,55313],{"encoding":904}," při ceně ",[883,68102,68104],{"className":68103},[886],[888,68105,68106],{"xmlns":890},[892,68107,68108,68116],{},[895,68109,68110],{},[2124,68111,68112,68114],{},[898,68113,3937],{},[1996,68115,4354],{},[902,68117,4404],{"encoding":904}," (minimální cena nabídky); pod ",[883,68120,68122],{"className":68121},[886],[888,68123,68124],{"xmlns":890},[892,68125,68126,68134],{},[895,68127,68128],{},[2124,68129,68130,68132],{},[898,68131,2789],{},[1996,68133,4354],{},[902,68135,29846],{"encoding":904}," je nabídka nulová.",[37350,68138,68140],{"id":68139},"příklad-312","Příklad 3.12",[724,68142,68143,57524,68145,68191],{},[38,68144,55989],{},[883,68146,68148],{"className":68147},[886],[888,68149,68150],{"xmlns":890},[892,68151,68152,68188],{},[895,68153,68154,68156,68158,68160,68162,68168,68170,68172,68178,68180,68182,68184,68186],{},[898,68155,2774],{},[898,68157,2777],{},[1996,68159,1998],{},[2129,68161,2794],{},[2124,68163,68164,68166],{},[898,68165,2789],{},[2129,68167,2173],{},[1996,68169,2225],{},[2129,68171,2131],{},[2124,68173,68174,68176],{},[898,68175,2789],{},[2129,68177,2131],{},[1996,68179,2095],{},[2129,68181,36246],{},[898,68183,2789],{},[1996,68185,2095],{},[2129,68187,2863],{},[902,68189,68190],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,68193,68194,2203,68196,68233,68234,2704],{},[38,68195,22772],{},[883,68197,68199],{"className":68198},[886],[888,68200,68201],{"xmlns":890},[892,68202,68203,68230],{},[895,68204,68205,68207,68209,68211,68214,68220,68222,68224,68226,68228],{},[898,68206,2818],{},[898,68208,2777],{},[1996,68210,1998],{},[2129,68212,68213],{},"0,3",[2124,68215,68216,68218],{},[898,68217,2789],{},[2129,68219,2131],{},[1996,68221,2225],{},[2129,68223,2351],{},[898,68225,2789],{},[1996,68227,2095],{},[2129,68229,36246],{},[902,68231,68232],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,68235,68237],{"className":68236},[886],[888,68238,68239],{"xmlns":890},[892,68240,68241,68251],{},[895,68242,68243,68245,68247,68249],{},[898,68244,3937],{},[1996,68246,1998],{},[898,68248,2818],{},[898,68250,2777],{},[902,68252,68253],{"encoding":904},"P = MC",[883,68255,68257],{"className":68256},[886],[888,68258,68259],{"xmlns":890,"display":28068},[892,68260,68261,68286],{},[895,68262,68263,68265,68267,68269,68275,68277,68279,68281,68283],{},[898,68264,3937],{},[1996,68266,1998],{},[2129,68268,68213],{},[2124,68270,68271,68273],{},[898,68272,2789],{},[2129,68274,2131],{},[1996,68276,2225],{},[2129,68278,2351],{},[898,68280,2789],{},[1996,68282,2095],{},[2129,68284,68285],{},"15.",[902,68287,68288],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,68290,68291,68292,5382,68305,68318],{},"Vyjádření ",[883,68293,68295],{"className":68294},[886],[888,68296,68297],{"xmlns":890},[892,68298,68299,68303],{},[895,68300,68301],{},[898,68302,2789],{},[902,68304,2789],{"encoding":904},[883,68306,68308],{"className":68307},[886],[888,68309,68310],{"xmlns":890},[892,68311,68312,68316],{},[895,68313,68314],{},[898,68315,3937],{},[902,68317,3937],{"encoding":904}," doplněním na čtverec:",[883,68320,68322],{"className":68321},[886],[888,68323,68324],{"xmlns":890,"display":28068},[892,68325,68326,68416],{},[895,68327,68328,68330,68332,68334,68372,68374,68376,68398,68400,68414],{},[898,68329,3937],{},[1996,68331,1998],{},[2129,68333,68213],{},[895,68335,68336,68338,68360,68362,68370],{},[1996,68337,2005],{"fence":2285},[2124,68339,68340,68358],{},[895,68341,68342,68344,68346,68348,68356],{},[1996,68343,2005],{"fence":2285},[898,68345,2789],{},[1996,68347,2225],{},[2325,68349,68350],{"scriptlevel":2327,"displaystyle":2004},[2329,68351,68352,68354],{},[2129,68353,9035],{},[2129,68355,2173],{},[1996,68357,2011],{"fence":2285},[2129,68359,2131],{},[1996,68361,2095],{},[2325,68363,68364],{"scriptlevel":2327,"displaystyle":2004},[2329,68365,68366,68368],{},[2129,68367,3120],{},[2129,68369,3999],{},[1996,68371,2011],{"fence":2285},[1996,68373,2286],{"separator":2285},[5878,68375],{"width":5880},[2124,68377,68378,68396],{},[895,68379,68380,68382,68384,68386,68394],{},[1996,68381,2005],{"fence":2285},[898,68383,2789],{},[1996,68385,2225],{},[2325,68387,68388],{"scriptlevel":2327,"displaystyle":2004},[2329,68389,68390,68392],{},[2129,68391,9035],{},[2129,68393,2173],{},[1996,68395,2011],{"fence":2285},[2129,68397,2131],{},[1996,68399,1998],{},[2329,68401,68402,68412],{},[895,68403,68404,68406,68408,68410],{},[2129,68405,38021],{},[898,68407,3937],{},[1996,68409,2225],{},[2129,68411,3120],{},[2129,68413,3999],{},[1996,68415,2286],{"separator":2285},[902,68417,68418],{"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},",[883,68420,68422],{"className":68421},[886],[888,68423,68424],{"xmlns":890,"display":28068},[892,68425,68426,68458],{},[895,68427,68428,68430,68432,68438,68440,68456],{},[898,68429,2789],{},[1996,68431,1998],{},[2329,68433,68434,68436],{},[2129,68435,9035],{},[2129,68437,2173],{},[1996,68439,2095],{},[2329,68441,68442,68454],{},[8117,68443,68444],{},[895,68445,68446,68448,68450,68452],{},[2129,68447,38021],{},[898,68449,3937],{},[1996,68451,2225],{},[2129,68453,3120],{},[2129,68455,2173],{},[898,68457,1975],{"mathvariant":2376},[902,68459,68460],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,68462,67020,68463,1343,68501,1343,68549,68583,68584,1975],{},[883,68464,68466],{"className":68465},[886],[888,68467,68468],{"xmlns":890},[892,68469,68470,68498],{},[895,68471,68472,68474,68476,68478,68480,68482,68488,68490,68492,68494,68496],{},[898,68473,4255],{},[898,68475,40341],{},[898,68477,2777],{},[1996,68479,1998],{},[2129,68481,2794],{},[2124,68483,68484,68486],{},[898,68485,2789],{},[2129,68487,2131],{},[1996,68489,2225],{},[2129,68491,2131],{},[898,68493,2789],{},[1996,68495,2095],{},[2129,68497,36246],{},[902,68499,68500],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,68502,68504],{"className":68503},[886],[888,68505,68506],{"xmlns":890},[892,68507,68508,68546],{},[895,68509,68510,68512,68514,68520,68522,68524,68526,68528,68530,68532,68534,68536,68542,68544],{},[898,68511,4255],{},[898,68513,40341],{},[2124,68515,68516,68518],{},[898,68517,2777],{},[1996,68519,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,68521,1998],{},[2129,68523,2839],{},[898,68525,2789],{},[1996,68527,2225],{},[2129,68529,2131],{},[1996,68531,1998],{},[2129,68533,2327],{},[1996,68535,3987],{},[2124,68537,68538,68540],{},[898,68539,2789],{},[1996,68541,4354],{},[1996,68543,1998],{},[2129,68545,2863],{},[902,68547,68548],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,68550,68552],{"className":68551},[886],[888,68553,68554],{"xmlns":890},[892,68555,68556,68580],{},[895,68557,68558,68560,68562,68572,68574,68576,68578],{},[898,68559,4255],{},[898,68561,40341],{},[2124,68563,68564,68566],{},[898,68565,2777],{},[895,68567,68568,68570],{},[1996,68569,2378],{"mathvariant":2376},[1996,68571,2378],{"mathvariant":2376},[1996,68573,1998],{},[2129,68575,2839],{},[1996,68577,3408],{},[2129,68579,2327],{},[902,68581,68582],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,68585,68587],{"className":68586},[886],[888,68588,68589],{"xmlns":890},[892,68590,68591,68627],{},[895,68592,68593,68599,68601,68603,68605,68607,68609,68611,68613,68615,68617,68619,68621,68623,68625],{},[2124,68594,68595,68597],{},[898,68596,3937],{},[1996,68598,4354],{},[1996,68600,1998],{},[898,68602,2818],{},[898,68604,2777],{},[1996,68606,2005],{"stretchy":2004},[2129,68608,2863],{},[1996,68610,2011],{"stretchy":2004},[1996,68612,1998],{},[2129,68614,38021],{},[1996,68616,2225],{},[2129,68618,5211],{},[1996,68620,2095],{},[2129,68622,36246],{},[1996,68624,1998],{},[2129,68626,2228],{},[902,68628,68629],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,68631,68632],{},[38,68633,68634],{},"Závěr.",[883,68636,68638],{"className":68637},[886],[888,68639,68640],{"xmlns":890,"display":28068},[892,68641,68642,68728],{},[895,68643,68644,68646,68648,68650,68652,68654,68656,68658],{},[898,68645,3937],{},[1996,68647,1998],{},[898,68649,8673],{},[1996,68651,2005],{"stretchy":2004},[898,68653,2789],{},[1996,68655,2011],{"stretchy":2004},[1996,68657,1998],{},[895,68659,68660,68662],{},[1996,68661,67508],{"fence":2285},[20756,68663,68664,68706],{"rowspacing":67511,"columnalign":67512,"columnspacing":15286},[20761,68665,68666,68690],{},[20764,68667,68668],{},[2325,68669,68670],{"scriptlevel":2327,"displaystyle":2004},[895,68671,68672,68674,68680,68682,68684,68686,68688],{},[2129,68673,68213],{},[2124,68675,68676,68678],{},[898,68677,2789],{},[2129,68679,2131],{},[1996,68681,2225],{},[2129,68683,2351],{},[898,68685,2789],{},[1996,68687,2095],{},[2129,68689,36246],{},[20764,68691,68692],{},[2325,68693,68694],{"scriptlevel":2327,"displaystyle":2004},[895,68695,68696,68698,68700,68702,68704],{},[2288,68697,67539],{},[898,68699,2789],{},[1996,68701,4485],{},[2129,68703,2863],{},[1996,68705,2286],{"separator":2285},[20761,68707,68708,68714],{},[20764,68709,68710],{},[2325,68711,68712],{"scriptlevel":2327,"displaystyle":2004},[2129,68713,2327],{},[20764,68715,68716],{},[2325,68717,68718],{"scriptlevel":2327,"displaystyle":2004},[895,68719,68720,68722,68724,68726],{},[2288,68721,67539],{},[898,68723,2789],{},[1996,68725,3447],{},[2129,68727,19330],{},[902,68729,68730],{"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}",[724,68732,68733],{},[614,68734,68735,68736,68751,68752,1975],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,68737,68739],{"className":68738},[886],[888,68740,68741],{"xmlns":890},[892,68742,68743,68749],{},[895,68744,68745,68747],{},[898,68746,2818],{},[898,68748,2777],{},[902,68750,55294],{"encoding":904}," ležící nad minimem ",[883,68753,68755],{"className":68754},[886],[888,68756,68757],{"xmlns":890},[892,68758,68759,68767],{},[895,68760,68761,68763,68765],{},[898,68762,4255],{},[898,68764,40341],{},[898,68766,2777],{},[902,68768,55313],{"encoding":904},[115,68770,68772],{"id":68771},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,68774,68775,68776,68780,68781,68796,68797,68817,68818,3885,68821,68824,68825,68827,68828,19947,68850,68852,68853,3885,68855,58728,68858,2203,68861,41816,68876,68891],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,68777,68779],{"className":68778,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,68782,68784],{"className":68783},[886],[888,68785,68786],{"xmlns":890},[892,68787,68788,68794],{},[895,68789,68790,68792],{},[898,68791,2774],{},[898,68793,3994],{},[902,68795,4094],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,68798,68800],{"className":68799},[886],[888,68801,68802],{"xmlns":890},[892,68803,68804,68814],{},[895,68805,68806,68808,68810,68812],{},[898,68807,2774],{},[898,68809,3994],{},[898,68811,4674],{"mathvariant":2376},[898,68813,2789],{},[902,68815,68816],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,68819,68820],{},"fixních",[38,68822,68823],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,68826,64327],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,68829,68831],{"className":68830},[886],[888,68832,68833],{"xmlns":890},[892,68834,68835,68847],{},[895,68836,68837,68839,68841,68843,68845],{},[898,68838,2774],{},[898,68840,3994],{},[1996,68842,2225],{},[898,68844,2774],{},[898,68846,2777],{},[902,68848,68849],{"encoding":904},"TR - TC",[38,68851,55174],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,68854,56486],{},[38,68856,68857],{},"mezní náklady",[207,68859,1145],{"className":68860,"dataFsResolvedFilePath":764,"href":765},[210],[883,68862,68864],{"className":68863},[886],[888,68865,68866],{"xmlns":890},[892,68867,68868,68874],{},[895,68869,68870,68872],{},[898,68871,2774],{},[898,68873,3994],{},[902,68875,4094],{"encoding":904},[883,68877,68879],{"className":68878},[886],[888,68880,68881],{"xmlns":890},[892,68882,68883,68889],{},[895,68884,68885,68887],{},[898,68886,2774],{},[898,68888,2777],{},[902,68890,3243],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,68893,68894,68956,69022,69084],{},[123,68895,68896,68899,68900,10394,68915,1975],{},[38,68897,68898],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,68901,68903],{"className":68902},[886],[888,68904,68905],{"xmlns":890},[892,68906,68907,68913],{},[895,68908,68909,68911],{},[898,68910,4255],{},[898,68912,2777],{},[902,68914,55562],{"encoding":904},[883,68916,68918],{"className":68917},[886],[888,68919,68920],{"xmlns":890},[892,68921,68922,68954],{},[895,68923,68924,68926,68928,68930,68936,68938,68940,68942,68944,68946,68952],{},[898,68925,4255],{},[898,68927,2777],{},[1996,68929,2005],{"stretchy":2004},[2272,68931,68932,68934],{},[898,68933,2789],{},[2129,68935,2327],{},[1996,68937,2011],{"stretchy":2004},[1996,68939,1998],{},[898,68941,2818],{},[898,68943,2777],{},[1996,68945,2005],{"stretchy":2004},[2272,68947,68948,68950],{},[898,68949,2789],{},[2129,68951,2327],{},[1996,68953,2011],{"stretchy":2004},[902,68955,62571],{"encoding":904},[123,68957,68958,68899,68961,10394,68978,1975],{},[38,68959,68960],{},"Princip minimalizace průměrných variabilních nákladů:",[883,68962,68964],{"className":68963},[886],[888,68965,68966],{"xmlns":890},[892,68967,68968,68976],{},[895,68969,68970,68972,68974],{},[898,68971,4255],{},[898,68973,40341],{},[898,68975,2777],{},[902,68977,55313],{"encoding":904},[883,68979,68981],{"className":68980},[886],[888,68982,68983],{"xmlns":890},[892,68984,68985,69019],{},[895,68986,68987,68989,68991,68993,68995,69001,69003,69005,69007,69009,69011,69017],{},[898,68988,4255],{},[898,68990,40341],{},[898,68992,2777],{},[1996,68994,2005],{"stretchy":2004},[2272,68996,68997,68999],{},[898,68998,2789],{},[2129,69000,2327],{},[1996,69002,2011],{"stretchy":2004},[1996,69004,1998],{},[898,69006,2818],{},[898,69008,2777],{},[1996,69010,2005],{"stretchy":2004},[2272,69012,69013,69015],{},[898,69014,2789],{},[2129,69016,2327],{},[1996,69018,2011],{"stretchy":2004},[902,69020,69021],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,69023,69024,69027,69028,10394,69043,1975],{},[38,69025,69026],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,69029,69031],{"className":69030},[886],[888,69032,69033],{"xmlns":890},[892,69034,69035,69041],{},[895,69036,69037,69039],{},[898,69038,3937],{},[898,69040,3994],{},[902,69042,63481],{"encoding":904},[883,69044,69046],{"className":69045},[886],[888,69047,69048],{"xmlns":890},[892,69049,69050,69082],{},[895,69051,69052,69054,69056,69058,69064,69066,69068,69070,69072,69074,69080],{},[898,69053,2818],{},[898,69055,3994],{},[1996,69057,2005],{"stretchy":2004},[2272,69059,69060,69062],{},[898,69061,2789],{},[2129,69063,2327],{},[1996,69065,2011],{"stretchy":2004},[1996,69067,1998],{},[898,69069,2818],{},[898,69071,2777],{},[1996,69073,2005],{"stretchy":2004},[2272,69075,69076,69078],{},[898,69077,2789],{},[2129,69079,2327],{},[1996,69081,2011],{"stretchy":2004},[902,69083,65647],{"encoding":904},[123,69085,69086,2203,69089,6473,69125,67927,69146,21596,69159,67609,69176,1975],{},[38,69087,69088],{},"Funkce nabídky firmy:",[883,69090,69092],{"className":69091},[886],[888,69093,69094],{"xmlns":890},[892,69095,69096,69122],{},[895,69097,69098,69100,69102,69104,69106,69108,69110,69112,69114,69116,69118,69120],{},[898,69099,3937],{},[1996,69101,1998],{},[898,69103,8673],{},[1996,69105,2005],{"stretchy":2004},[898,69107,2789],{},[1996,69109,2011],{"stretchy":2004},[1996,69111,1998],{},[898,69113,2818],{},[898,69115,2777],{},[1996,69117,2005],{"stretchy":2004},[898,69119,2789],{},[1996,69121,2011],{"stretchy":2004},[902,69123,69124],{"encoding":904},"P = S(Q) = MC(Q)",[883,69126,69128],{"className":69127},[886],[888,69129,69130],{"xmlns":890},[892,69131,69132,69144],{},[895,69133,69134,69136,69138],{},[898,69135,2789],{},[1996,69137,4485],{},[2124,69139,69140,69142],{},[898,69141,2789],{},[1996,69143,4354],{},[902,69145,67926],{"encoding":904},[883,69147,69149],{"className":69148},[886],[888,69150,69151],{"xmlns":890},[892,69152,69153,69157],{},[895,69154,69155],{},[2129,69156,2327],{},[902,69158,2327],{"encoding":904},[883,69160,69162],{"className":69161},[886],[888,69163,69164],{"xmlns":890},[892,69165,69166,69174],{},[895,69167,69168],{},[2124,69169,69170,69172],{},[898,69171,2789],{},[1996,69173,4354],{},[902,69175,29846],{"encoding":904},[883,69177,69179],{"className":69178},[886],[888,69180,69181],{"xmlns":890},[892,69182,69183,69191],{},[895,69184,69185,69187,69189],{},[898,69186,4255],{},[898,69188,40341],{},[898,69190,2777],{},[902,69192,55313],{"encoding":904},[115,69194,49884],{"id":49883},[152,69196,69197,69200,69203,69206,69209,69212,69215,69218,69221,69224,69227],{},[123,69198,69199],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,69201,69202],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,69204,69205],{},"Jak se vypočte mezní příjem a co udává?",[123,69207,69208],{},"Z jakých složek se skládají celkové náklady?",[123,69210,69211],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,69213,69214],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,69216,69217],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,69219,69220],{},"Jak se vypočte zisk?",[123,69222,69223],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,69225,69226],{},"Co jsou body zvratu? Jak se najdou?",[123,69228,69229],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,69231,69233],{"id":69232},"úlohy-31328","Úlohy 3.1–3.28",[198,69235,69237],{"id":69236},"příjem-3135","Příjem (3.1–3.5)",[724,69239,69240,45428,69243,69271,69272,69287,69288,69303,69304,69319,69320,1343,69335,1343,69350,69365],{},[38,69241,69242],{},"3.1",[883,69244,69246],{"className":69245},[886],[888,69247,69248],{"xmlns":890},[892,69249,69250,69268],{},[895,69251,69252,69254,69256,69258,69260,69262,69264,69266],{},[898,69253,3937],{},[1996,69255,1998],{},[898,69257,4183],{},[1996,69259,2005],{"stretchy":2004},[898,69261,2789],{},[1996,69263,2011],{"stretchy":2004},[1996,69265,1998],{},[2129,69267,3090],{},[902,69269,69270],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,69273,69275],{"className":69274},[886],[888,69276,69277],{"xmlns":890},[892,69278,69279,69285],{},[895,69280,69281,69283],{},[898,69282,2774],{},[898,69284,3994],{},[902,69286,4094],{"encoding":904},", průměrný příjem ",[883,69289,69291],{"className":69290},[886],[888,69292,69293],{"xmlns":890},[892,69294,69295,69301],{},[895,69296,69297,69299],{},[898,69298,4255],{},[898,69300,3994],{},[902,69302,55447],{"encoding":904}," a mezní příjem ",[883,69305,69307],{"className":69306},[886],[888,69308,69309],{"xmlns":890},[892,69310,69311,69317],{},[895,69312,69313,69315],{},[898,69314,2818],{},[898,69316,3994],{},[902,69318,6634],{"encoding":904},". (c) Vypočtěte ",[883,69321,69323],{"className":69322},[886],[888,69324,69325],{"xmlns":890},[892,69326,69327,69333],{},[895,69328,69329,69331],{},[898,69330,2774],{},[898,69332,3994],{},[902,69334,4094],{"encoding":904},[883,69336,69338],{"className":69337},[886],[888,69339,69340],{"xmlns":890},[892,69341,69342,69348],{},[895,69343,69344,69346],{},[898,69345,4255],{},[898,69347,3994],{},[902,69349,55447],{"encoding":904},[883,69351,69353],{"className":69352},[886],[888,69354,69355],{"xmlns":890},[892,69356,69357,69363],{},[895,69358,69359,69361],{},[898,69360,2818],{},[898,69362,3994],{},[902,69364,6634],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,69367,69368,45428,69371,69271,69407,69287,69422,69303,69437,69319,69452,1343,69467,1343,69482,69497],{},[38,69369,69370],{},"3.2",[883,69372,69374],{"className":69373},[886],[888,69375,69376],{"xmlns":890},[892,69377,69378,69404],{},[895,69379,69380,69382,69384,69386,69388,69390,69392,69394,69396,69398,69400,69402],{},[898,69381,3937],{},[1996,69383,1998],{},[898,69385,4183],{},[1996,69387,2005],{"stretchy":2004},[898,69389,2789],{},[1996,69391,2011],{"stretchy":2004},[1996,69393,1998],{},[1996,69395,2225],{},[2129,69397,5009],{},[898,69399,2789],{},[1996,69401,2095],{},[2129,69403,9035],{},[902,69405,69406],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,69408,69410],{"className":69409},[886],[888,69411,69412],{"xmlns":890},[892,69413,69414,69420],{},[895,69415,69416,69418],{},[898,69417,2774],{},[898,69419,3994],{},[902,69421,4094],{"encoding":904},[883,69423,69425],{"className":69424},[886],[888,69426,69427],{"xmlns":890},[892,69428,69429,69435],{},[895,69430,69431,69433],{},[898,69432,4255],{},[898,69434,3994],{},[902,69436,55447],{"encoding":904},[883,69438,69440],{"className":69439},[886],[888,69441,69442],{"xmlns":890},[892,69443,69444,69450],{},[895,69445,69446,69448],{},[898,69447,2818],{},[898,69449,3994],{},[902,69451,6634],{"encoding":904},[883,69453,69455],{"className":69454},[886],[888,69456,69457],{"xmlns":890},[892,69458,69459,69465],{},[895,69460,69461,69463],{},[898,69462,2774],{},[898,69464,3994],{},[902,69466,4094],{"encoding":904},[883,69468,69470],{"className":69469},[886],[888,69471,69472],{"xmlns":890},[892,69473,69474,69480],{},[895,69475,69476,69478],{},[898,69477,4255],{},[898,69479,3994],{},[902,69481,55447],{"encoding":904},[883,69483,69485],{"className":69484},[886],[888,69486,69487],{"xmlns":890},[892,69488,69489,69495],{},[895,69490,69491,69493],{},[898,69492,2818],{},[898,69494,3994],{},[902,69496,6634],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,69499,69500,45428,69503,69540,69541,69287,69556,69303,69571,69586,69587,6473,69602,69628,69629,69644,69645,1343,69660,6473,69675,69628,69700,69715,69716,69729,69730,69745,69746,69761,69762,1343,69775,1343,69790,1343,69805,1975],{},[38,69501,69502],{},"3.3",[883,69504,69506],{"className":69505},[886],[888,69507,69508],{"xmlns":890},[892,69509,69510,69537],{},[895,69511,69512,69514,69516,69518,69520,69522,69524,69526,69529,69531],{},[898,69513,3937],{},[1996,69515,1998],{},[898,69517,4183],{},[1996,69519,2005],{"stretchy":2004},[898,69521,2789],{},[1996,69523,2011],{"stretchy":2004},[1996,69525,1998],{},[2129,69527,69528],{},"1200",[1996,69530,2225],{},[2124,69532,69533,69535],{},[898,69534,2789],{},[2129,69536,2131],{},[902,69538,69539],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,69542,69544],{"className":69543},[886],[888,69545,69546],{"xmlns":890},[892,69547,69548,69554],{},[895,69549,69550,69552],{},[898,69551,2774],{},[898,69553,3994],{},[902,69555,4094],{"encoding":904},[883,69557,69559],{"className":69558},[886],[888,69560,69561],{"xmlns":890},[892,69562,69563,69569],{},[895,69564,69565,69567],{},[898,69566,4255],{},[898,69568,3994],{},[902,69570,55447],{"encoding":904},[883,69572,69574],{"className":69573},[886],[888,69575,69576],{"xmlns":890},[892,69577,69578,69584],{},[895,69579,69580,69582],{},[898,69581,2818],{},[898,69583,3994],{},[902,69585,6634],{"encoding":904},". (b) Vypočtěte ",[883,69588,69590],{"className":69589},[886],[888,69591,69592],{"xmlns":890},[892,69593,69594,69600],{},[895,69595,69596,69598],{},[898,69597,2774],{},[898,69599,3994],{},[902,69601,4094],{"encoding":904},[883,69603,69605],{"className":69604},[886],[888,69606,69607],{"xmlns":890},[892,69608,69609,69625],{},[895,69610,69611,69613,69615,69617,69619,69621,69623],{},[898,69612,2789],{},[1996,69614,1998],{},[2129,69616,2863],{},[1996,69618,2286],{"separator":2285},[2129,69620,9035],{},[1996,69622,2286],{"separator":2285},[2129,69624,38021],{},[902,69626,69627],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,69630,69632],{"className":69631},[886],[888,69633,69634],{"xmlns":890},[892,69635,69636,69642],{},[895,69637,69638,69640],{},[898,69639,2774],{},[898,69641,3994],{},[902,69643,4094],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,69646,69648],{"className":69647},[886],[888,69649,69650],{"xmlns":890},[892,69651,69652,69658],{},[895,69653,69654,69656],{},[898,69655,4255],{},[898,69657,3994],{},[902,69659,55447],{"encoding":904},[883,69661,69663],{"className":69662},[886],[888,69664,69665],{"xmlns":890},[892,69666,69667,69673],{},[895,69668,69669,69671],{},[898,69670,2818],{},[898,69672,3994],{},[902,69674,6634],{"encoding":904},[883,69676,69678],{"className":69677},[886],[888,69679,69680],{"xmlns":890},[892,69681,69682,69698],{},[895,69683,69684,69686,69688,69690,69692,69694,69696],{},[898,69685,2789],{},[1996,69687,1998],{},[2129,69689,2863],{},[1996,69691,2286],{"separator":2285},[2129,69693,9035],{},[1996,69695,2286],{"separator":2285},[2129,69697,38021],{},[902,69699,69627],{"encoding":904},[883,69701,69703],{"className":69702},[886],[888,69704,69705],{"xmlns":890},[892,69706,69707,69713],{},[895,69708,69709,69711],{},[898,69710,2818],{},[898,69712,3994],{},[902,69714,6634],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,69717,69719],{"className":69718},[886],[888,69720,69721],{"xmlns":890},[892,69722,69723,69727],{},[895,69724,69725],{},[898,69726,2789],{},[902,69728,2789],{"encoding":904},", které maximalizuje ",[883,69731,69733],{"className":69732},[886],[888,69734,69735],{"xmlns":890},[892,69736,69737,69743],{},[895,69738,69739,69741],{},[898,69740,2774],{},[898,69742,3994],{},[902,69744,4094],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,69747,69749],{"className":69748},[886],[888,69750,69751],{"xmlns":890},[892,69752,69753,69759],{},[895,69754,69755,69757],{},[898,69756,2774],{},[898,69758,3994],{},[902,69760,4094],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,69763,69765],{"className":69764},[886],[888,69766,69767],{"xmlns":890},[892,69768,69769,69773],{},[895,69770,69771],{},[898,69772,4183],{},[902,69774,4183],{"encoding":904},[883,69776,69778],{"className":69777},[886],[888,69779,69780],{"xmlns":890},[892,69781,69782,69788],{},[895,69783,69784,69786],{},[898,69785,2774],{},[898,69787,3994],{},[902,69789,4094],{"encoding":904},[883,69791,69793],{"className":69792},[886],[888,69794,69795],{"xmlns":890},[892,69796,69797,69803],{},[895,69798,69799,69801],{},[898,69800,4255],{},[898,69802,3994],{},[902,69804,55447],{"encoding":904},[883,69806,69808],{"className":69807},[886],[888,69809,69810],{"xmlns":890},[892,69811,69812,69818],{},[895,69813,69814,69816],{},[898,69815,2818],{},[898,69817,3994],{},[902,69819,6634],{"encoding":904},[724,69821,69822,69825,69826,69856,69857,69872,69873,10157,69886,1343,69904,1343,69921,69939,69940,69962,69963,69978,69979,69992,69993,1975],{},[38,69823,69824],{},"3.4"," Je dán celkový příjem ",[883,69827,69829],{"className":69828},[886],[888,69830,69831],{"xmlns":890},[892,69832,69833,69853],{},[895,69834,69835,69837,69839,69841,69843,69845,69847],{},[898,69836,2774],{},[898,69838,3994],{},[1996,69840,1998],{},[2129,69842,69528],{},[898,69844,2789],{},[1996,69846,2225],{},[2124,69848,69849,69851],{},[898,69850,2789],{},[2129,69852,2173],{},[902,69854,69855],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,69858,69860],{"className":69859},[886],[888,69861,69862],{"xmlns":890},[892,69863,69864,69870],{},[895,69865,69866,69868],{},[898,69867,2774],{},[898,69869,3994],{},[902,69871,4094],{"encoding":904}," vzhledem ke ",[883,69874,69876],{"className":69875},[886],[888,69877,69878],{"xmlns":890},[892,69879,69880,69884],{},[895,69881,69882],{},[898,69883,2789],{},[902,69885,2789],{"encoding":904},[883,69887,69889],{"className":69888},[886],[888,69890,69891],{"xmlns":890},[892,69892,69893,69901],{},[895,69894,69895,69897,69899],{},[898,69896,2789],{},[1996,69898,1998],{},[2129,69900,2228],{},[902,69902,69903],{"encoding":904},"Q = 5",[883,69905,69907],{"className":69906},[886],[888,69908,69909],{"xmlns":890},[892,69910,69911,69919],{},[895,69912,69913,69915,69917],{},[898,69914,2789],{},[1996,69916,1998],{},[2129,69918,5585],{},[902,69920,5588],{"encoding":904},[883,69922,69924],{"className":69923},[886],[888,69925,69926],{"xmlns":890},[892,69927,69928,69936],{},[895,69929,69930,69932,69934],{},[898,69931,2789],{},[1996,69933,1998],{},[2129,69935,3509],{},[902,69937,69938],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,69941,69943],{"className":69942},[886],[888,69944,69945],{"xmlns":890},[892,69946,69947,69959],{},[895,69948,69949,69951,69953,69955,69957],{},[898,69950,2818],{},[898,69952,3994],{},[1996,69954,2005],{"stretchy":2004},[2129,69956,2863],{},[1996,69958,2011],{"stretchy":2004},[902,69960,69961],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,69964,69966],{"className":69965},[886],[888,69967,69968],{"xmlns":890},[892,69969,69970,69976],{},[895,69971,69972,69974],{},[898,69973,2774],{},[898,69975,3994],{},[902,69977,4094],{"encoding":904},", jestliže se ",[883,69980,69982],{"className":69981},[886],[888,69983,69984],{"xmlns":890},[892,69985,69986,69990],{},[895,69987,69988],{},[898,69989,2789],{},[902,69991,2789],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,69994,69996],{"className":69995},[886],[888,69997,69998],{"xmlns":890},[892,69999,70000,70006],{},[895,70001,70002,70004],{},[898,70003,2774],{},[898,70005,3994],{},[902,70007,4094],{"encoding":904},[724,70009,70010,70013,70014,70040,70041,70056,70057,69978,70072,70085],{},[38,70011,70012],{},"3.5"," Je dán mezní příjem ",[883,70015,70017],{"className":70016},[886],[888,70018,70019],{"xmlns":890},[892,70020,70021,70037],{},[895,70022,70023,70025,70027,70029,70031,70033,70035],{},[898,70024,2818],{},[898,70026,3994],{},[1996,70028,1998],{},[1996,70030,2225],{},[898,70032,2789],{},[1996,70034,2095],{},[2129,70036,9035],{},[902,70038,70039],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,70042,70044],{"className":70043},[886],[888,70045,70046],{"xmlns":890},[892,70047,70048,70054],{},[895,70049,70050,70052],{},[898,70051,2774],{},[898,70053,3994],{},[902,70055,4094],{"encoding":904},". (b) Vypočtěte změnu ",[883,70058,70060],{"className":70059},[886],[888,70061,70062],{"xmlns":890},[892,70063,70064,70070],{},[895,70065,70066,70068],{},[898,70067,2774],{},[898,70069,3994],{},[902,70071,4094],{"encoding":904},[883,70073,70075],{"className":70074},[886],[888,70076,70077],{"xmlns":890},[892,70078,70079,70083],{},[895,70080,70081],{},[898,70082,2789],{},[902,70084,2789],{"encoding":904}," změní z 8 na 12.",[198,70087,70089],{"id":70088},"náklady-36316","Náklady (3.6–3.16)",[724,70091,70092,70095,70096,70136,70137,70152,70153,70170,70171,70188,70189,70204,70205,70220,70221,69586,70236,1343,70251,1343,70268,1343,70285,1343,70300,1343,70315,6473,70330,70348,70349,1343,70364,1343,70379,70394],{},[38,70093,70094],{},"3.6"," Jsou dány celkové náklady ",[883,70097,70099],{"className":70098},[886],[888,70100,70101],{"xmlns":890},[892,70102,70103,70133],{},[895,70104,70105,70107,70109,70111,70113,70115,70117,70119,70121],{},[898,70106,2774],{},[898,70108,2777],{},[1996,70110,1998],{},[2129,70112,3090],{},[1996,70114,2095],{},[2129,70116,2131],{},[898,70118,2789],{},[1996,70120,2095],{},[2325,70122,70123],{"scriptlevel":2327,"displaystyle":2004},[2329,70124,70125,70131],{},[2124,70126,70127,70129],{},[898,70128,2789],{},[2129,70130,2131],{},[2129,70132,2863],{},[902,70134,70135],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,70138,70140],{"className":70139},[886],[888,70141,70142],{"xmlns":890},[892,70143,70144,70150],{},[895,70145,70146,70148],{},[898,70147,10436],{},[898,70149,2777],{},[902,70151,55493],{"encoding":904},", celkové variabilní náklady ",[883,70154,70156],{"className":70155},[886],[888,70157,70158],{"xmlns":890},[892,70159,70160,70168],{},[895,70161,70162,70164,70166],{},[898,70163,2774],{},[898,70165,40341],{},[898,70167,2777],{},[902,70169,55511],{"encoding":904},", průměrné variabilní náklady ",[883,70172,70174],{"className":70173},[886],[888,70175,70176],{"xmlns":890},[892,70177,70178,70186],{},[895,70179,70180,70182,70184],{},[898,70181,4255],{},[898,70183,40341],{},[898,70185,2777],{},[902,70187,55313],{"encoding":904},", variabilní náklady na jednotku ",[883,70190,70192],{"className":70191},[886],[888,70193,70194],{"xmlns":890},[892,70195,70196,70202],{},[895,70197,70198,70200],{},[898,70199,40341],{},[898,70201,2777],{},[902,70203,63607],{"encoding":904},", průměrné náklady ",[883,70206,70208],{"className":70207},[886],[888,70209,70210],{"xmlns":890},[892,70211,70212,70218],{},[895,70213,70214,70216],{},[898,70215,4255],{},[898,70217,2777],{},[902,70219,55562],{"encoding":904}," a mezní náklady ",[883,70222,70224],{"className":70223},[886],[888,70225,70226],{"xmlns":890},[892,70227,70228,70234],{},[895,70229,70230,70232],{},[898,70231,2818],{},[898,70233,2777],{},[902,70235,55294],{"encoding":904},[883,70237,70239],{"className":70238},[886],[888,70240,70241],{"xmlns":890},[892,70242,70243,70249],{},[895,70244,70245,70247],{},[898,70246,2774],{},[898,70248,2777],{},[902,70250,3243],{"encoding":904},[883,70252,70254],{"className":70253},[886],[888,70255,70256],{"xmlns":890},[892,70257,70258,70266],{},[895,70259,70260,70262,70264],{},[898,70261,2774],{},[898,70263,40341],{},[898,70265,2777],{},[902,70267,55511],{"encoding":904},[883,70269,70271],{"className":70270},[886],[888,70272,70273],{"xmlns":890},[892,70274,70275,70283],{},[895,70276,70277,70279,70281],{},[898,70278,4255],{},[898,70280,40341],{},[898,70282,2777],{},[902,70284,55313],{"encoding":904},[883,70286,70288],{"className":70287},[886],[888,70289,70290],{"xmlns":890},[892,70291,70292,70298],{},[895,70293,70294,70296],{},[898,70295,40341],{},[898,70297,2777],{},[902,70299,63607],{"encoding":904},[883,70301,70303],{"className":70302},[886],[888,70304,70305],{"xmlns":890},[892,70306,70307,70313],{},[895,70308,70309,70311],{},[898,70310,4255],{},[898,70312,2777],{},[902,70314,55562],{"encoding":904},[883,70316,70318],{"className":70317},[886],[888,70319,70320],{"xmlns":890},[892,70321,70322,70328],{},[895,70323,70324,70326],{},[898,70325,2818],{},[898,70327,2777],{},[902,70329,55294],{"encoding":904},[883,70331,70333],{"className":70332},[886],[888,70334,70335],{"xmlns":890},[892,70336,70337,70345],{},[895,70338,70339,70341,70343],{},[898,70340,2789],{},[1996,70342,1998],{},[2129,70344,3120],{},[902,70346,70347],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,70350,70352],{"className":70351},[886],[888,70353,70354],{"xmlns":890},[892,70355,70356,70362],{},[895,70357,70358,70360],{},[898,70359,2774],{},[898,70361,2777],{},[902,70363,3243],{"encoding":904},[883,70365,70367],{"className":70366},[886],[888,70368,70369],{"xmlns":890},[892,70370,70371,70377],{},[895,70372,70373,70375],{},[898,70374,4255],{},[898,70376,2777],{},[902,70378,55562],{"encoding":904},[883,70380,70382],{"className":70381},[886],[888,70383,70384],{"xmlns":890},[892,70385,70386,70392],{},[895,70387,70388,70390],{},[898,70389,2818],{},[898,70391,2777],{},[902,70393,55294],{"encoding":904}," rostou, resp. klesají.",[724,70396,70397,70400,70401,70220,70431,70446,70447,70462,70463,1343,70478,1343,70493,1975],{},[38,70398,70399],{},"3.7"," Jsou dány průměrné náklady ",[883,70402,70404],{"className":70403},[886],[888,70405,70406],{"xmlns":890},[892,70407,70408,70428],{},[895,70409,70410,70412,70414,70416,70424,70426],{},[898,70411,4255],{},[898,70413,2777],{},[1996,70415,1998],{},[2325,70417,70418],{"scriptlevel":2327,"displaystyle":2004},[2329,70419,70420,70422],{},[2129,70421,3090],{},[898,70423,2789],{},[1996,70425,2095],{},[2129,70427,9035],{},[902,70429,70430],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,70432,70434],{"className":70433},[886],[888,70435,70436],{"xmlns":890},[892,70437,70438,70444],{},[895,70439,70440,70442],{},[898,70441,2818],{},[898,70443,2777],{},[902,70445,55294],{"encoding":904},". (a) Určete celkové náklady ",[883,70448,70450],{"className":70449},[886],[888,70451,70452],{"xmlns":890},[892,70453,70454,70460],{},[895,70455,70456,70458],{},[898,70457,2774],{},[898,70459,2777],{},[902,70461,3243],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,70464,70466],{"className":70465},[886],[888,70467,70468],{"xmlns":890},[892,70469,70470,70476],{},[895,70471,70472,70474],{},[898,70473,4255],{},[898,70475,2777],{},[902,70477,55562],{"encoding":904},[883,70479,70481],{"className":70480},[886],[888,70482,70483],{"xmlns":890},[892,70484,70485,70491],{},[895,70486,70487,70489],{},[898,70488,2774],{},[898,70490,2777],{},[902,70492,3243],{"encoding":904},[883,70494,70496],{"className":70495},[886],[888,70497,70498],{"xmlns":890},[892,70499,70500,70506],{},[895,70501,70502,70504],{},[898,70503,2818],{},[898,70505,2777],{},[902,70507,55294],{"encoding":904},[724,70509,70510,70095,70513,70557,70558,1343,70575,1343,70590,1343,70607,1343,70622,1343,70639,1975],{},[38,70511,70512],{},"3.8",[883,70514,70516],{"className":70515},[886],[888,70517,70518],{"xmlns":890},[892,70519,70520,70554],{},[895,70521,70522,70524,70526,70528,70530,70532,70534,70536,70538,70540,70546,70548],{},[898,70523,2774],{},[898,70525,2777],{},[1996,70527,1998],{},[2129,70529,46705],{},[1996,70531,2095],{},[2129,70533,38021],{},[898,70535,2789],{},[1996,70537,2225],{},[2129,70539,2235],{},[2124,70541,70542,70544],{},[898,70543,2789],{},[2129,70545,2131],{},[1996,70547,2095],{},[2124,70549,70550,70552],{},[898,70551,2789],{},[2129,70553,2173],{},[902,70555,70556],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,70559,70561],{"className":70560},[886],[888,70562,70563],{"xmlns":890},[892,70564,70565,70573],{},[895,70566,70567,70569,70571],{},[898,70568,2774],{},[898,70570,40341],{},[898,70572,2777],{},[902,70574,55511],{"encoding":904},[883,70576,70578],{"className":70577},[886],[888,70579,70580],{"xmlns":890},[892,70581,70582,70588],{},[895,70583,70584,70586],{},[898,70585,10436],{},[898,70587,2777],{},[902,70589,55493],{"encoding":904},[883,70591,70593],{"className":70592},[886],[888,70594,70595],{"xmlns":890},[892,70596,70597,70605],{},[895,70598,70599,70601,70603],{},[898,70600,4255],{},[898,70602,40341],{},[898,70604,2777],{},[902,70606,55313],{"encoding":904},[883,70608,70610],{"className":70609},[886],[888,70611,70612],{"xmlns":890},[892,70613,70614,70620],{},[895,70615,70616,70618],{},[898,70617,4255],{},[898,70619,2777],{},[902,70621,55562],{"encoding":904},[883,70623,70625],{"className":70624},[886],[888,70626,70627],{"xmlns":890},[892,70628,70629,70637],{},[895,70630,70631,70633,70635],{},[898,70632,4255],{},[898,70634,10436],{},[898,70636,2777],{},[902,70638,55529],{"encoding":904},[883,70640,70642],{"className":70641},[886],[888,70643,70644],{"xmlns":890},[892,70645,70646,70652],{},[895,70647,70648,70650],{},[898,70649,2818],{},[898,70651,2777],{},[902,70653,55294],{"encoding":904},[724,70655,70656,70095,70659,70689,70690,69872,70705,6473,70718,1343,70736,1343,70754,69939,70772,69962,70794,70809,70810,70823,70824,1975],{},[38,70657,70658],{},"3.9",[883,70660,70662],{"className":70661},[886],[888,70663,70664],{"xmlns":890},[892,70665,70666,70686],{},[895,70667,70668,70670,70672,70674,70676,70678,70680],{},[898,70669,2774],{},[898,70671,2777],{},[1996,70673,1998],{},[2129,70675,15112],{},[1996,70677,2095],{},[2129,70679,19323],{},[2124,70681,70682,70684],{},[898,70683,2789],{},[2129,70685,2131],{},[902,70687,70688],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,70691,70693],{"className":70692},[886],[888,70694,70695],{"xmlns":890},[892,70696,70697,70703],{},[895,70698,70699,70701],{},[898,70700,2774],{},[898,70702,2777],{},[902,70704,3243],{"encoding":904},[883,70706,70708],{"className":70707},[886],[888,70709,70710],{"xmlns":890},[892,70711,70712,70716],{},[895,70713,70714],{},[898,70715,2789],{},[902,70717,2789],{"encoding":904},[883,70719,70721],{"className":70720},[886],[888,70722,70723],{"xmlns":890},[892,70724,70725,70733],{},[895,70726,70727,70729,70731],{},[898,70728,2789],{},[1996,70730,1998],{},[2129,70732,2863],{},[902,70734,70735],{"encoding":904},"Q = 10",[883,70737,70739],{"className":70738},[886],[888,70740,70741],{"xmlns":890},[892,70742,70743,70751],{},[895,70744,70745,70747,70749],{},[898,70746,2789],{},[1996,70748,1998],{},[2129,70750,9035],{},[902,70752,70753],{"encoding":904},"Q = 20",[883,70755,70757],{"className":70756},[886],[888,70758,70759],{"xmlns":890},[892,70760,70761,70769],{},[895,70762,70763,70765,70767],{},[898,70764,2789],{},[1996,70766,1998],{},[2129,70768,38021],{},[902,70770,70771],{"encoding":904},"Q = 30",[883,70773,70775],{"className":70774},[886],[888,70776,70777],{"xmlns":890},[892,70778,70779,70791],{},[895,70780,70781,70783,70785,70787,70789],{},[898,70782,2818],{},[898,70784,2777],{},[1996,70786,2005],{"stretchy":2004},[2129,70788,36246],{},[1996,70790,2011],{"stretchy":2004},[902,70792,70793],{"encoding":904},"MC(15)",[883,70795,70797],{"className":70796},[886],[888,70798,70799],{"xmlns":890},[892,70800,70801,70807],{},[895,70802,70803,70805],{},[898,70804,2774],{},[898,70806,2777],{},[902,70808,3243],{"encoding":904}," v důsledku změny ",[883,70811,70813],{"className":70812},[886],[888,70814,70815],{"xmlns":890},[892,70816,70817,70821],{},[895,70818,70819],{},[898,70820,2789],{},[902,70822,2789],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,70825,70827],{"className":70826},[886],[888,70828,70829],{"xmlns":890},[892,70830,70831,70837],{},[895,70832,70833,70835],{},[898,70834,2774],{},[898,70836,2777],{},[902,70838,3243],{"encoding":904},[724,70840,70841,70844,70845,70446,70881,70896,70897,70056,70916,70809,70931,70944],{},[38,70842,70843],{},"3.10"," Jsou dány mezní náklady ",[883,70846,70848],{"className":70847},[886],[888,70849,70850],{"xmlns":890},[892,70851,70852,70878],{},[895,70853,70854,70856,70858,70860,70862,70864,70866,70868,70870,70872],{},[898,70855,2818],{},[898,70857,2777],{},[1996,70859,1998],{},[2129,70861,3126],{},[1996,70863,2225],{},[2129,70865,41864],{},[898,70867,2789],{},[1996,70869,2095],{},[2129,70871,64561],{},[2124,70873,70874,70876],{},[898,70875,2789],{},[2129,70877,2131],{},[902,70879,70880],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,70882,70884],{"className":70883},[886],[888,70885,70886],{"xmlns":890},[892,70887,70888,70894],{},[895,70889,70890,70892],{},[898,70891,2774],{},[898,70893,2777],{},[902,70895,3243],{"encoding":904},", jestliže fixní náklady ",[883,70898,70900],{"className":70899},[886],[888,70901,70902],{"xmlns":890},[892,70903,70904,70914],{},[895,70905,70906,70908,70910,70912],{},[898,70907,10436],{},[898,70909,2777],{},[1996,70911,1998],{},[2129,70913,3090],{},[902,70915,11634],{"encoding":904},[883,70917,70919],{"className":70918},[886],[888,70920,70921],{"xmlns":890},[892,70922,70923,70929],{},[895,70924,70925,70927],{},[898,70926,2774],{},[898,70928,2777],{},[902,70930,3243],{"encoding":904},[883,70932,70934],{"className":70933},[886],[888,70935,70936],{"xmlns":890},[892,70937,70938,70942],{},[895,70939,70940],{},[898,70941,2789],{},[902,70943,2789],{"encoding":904}," z 15 na 20.",[724,70946,70947,70095,70950,70993,70994,71007,71008,71023,71024,71039,71040,71007,71053,71023,71070,71087,71088,71007,71101,71023,71116,71131,71132,71152,71153,71176],{},[38,70948,70949],{},"3.11",[883,70951,70953],{"className":70952},[886],[888,70954,70955],{"xmlns":890},[892,70956,70957,70991],{},[895,70958,70959,70961,70963,70965,70967,70969,70971,70973,70975,70977,70983,70985],{},[898,70960,2774],{},[898,70962,2777],{},[1996,70964,1998],{},[2129,70966,3090],{},[1996,70968,2095],{},[2129,70970,5004],{},[898,70972,2789],{},[1996,70974,2225],{},[2129,70976,2228],{},[2124,70978,70979,70981],{},[898,70980,2789],{},[2129,70982,2131],{},[1996,70984,2095],{},[2124,70986,70987,70989],{},[898,70988,2789],{},[2129,70990,2173],{},[902,70992,60909],{"encoding":904},". (a) Určete ",[883,70995,70997],{"className":70996},[886],[888,70998,70999],{"xmlns":890},[892,71000,71001,71005],{},[895,71002,71003],{},[898,71004,2789],{},[902,71006,2789],{"encoding":904},", které minimalizuje ",[883,71009,71011],{"className":71010},[886],[888,71012,71013],{"xmlns":890},[892,71014,71015,71021],{},[895,71016,71017,71019],{},[898,71018,2818],{},[898,71020,2777],{},[902,71022,55294],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,71025,71027],{"className":71026},[886],[888,71028,71029],{"xmlns":890},[892,71030,71031,71037],{},[895,71032,71033,71035],{},[898,71034,2818],{},[898,71036,2777],{},[902,71038,55294],{"encoding":904},". (b) Určete ",[883,71041,71043],{"className":71042},[886],[888,71044,71045],{"xmlns":890},[892,71046,71047,71051],{},[895,71048,71049],{},[898,71050,2789],{},[902,71052,2789],{"encoding":904},[883,71054,71056],{"className":71055},[886],[888,71057,71058],{"xmlns":890},[892,71059,71060,71068],{},[895,71061,71062,71064,71066],{},[898,71063,4255],{},[898,71065,40341],{},[898,71067,2777],{},[902,71069,55313],{"encoding":904},[883,71071,71073],{"className":71072},[886],[888,71074,71075],{"xmlns":890},[892,71076,71077,71085],{},[895,71078,71079,71081,71083],{},[898,71080,4255],{},[898,71082,40341],{},[898,71084,2777],{},[902,71086,55313],{"encoding":904},". (c) Určete ",[883,71089,71091],{"className":71090},[886],[888,71092,71093],{"xmlns":890},[892,71094,71095,71099],{},[895,71096,71097],{},[898,71098,2789],{},[902,71100,2789],{"encoding":904},[883,71102,71104],{"className":71103},[886],[888,71105,71106],{"xmlns":890},[892,71107,71108,71114],{},[895,71109,71110,71112],{},[898,71111,4255],{},[898,71113,2777],{},[902,71115,55562],{"encoding":904},[883,71117,71119],{"className":71118},[886],[888,71120,71121],{"xmlns":890},[892,71122,71123,71129],{},[895,71124,71125,71127],{},[898,71126,4255],{},[898,71128,2777],{},[902,71130,55562],{"encoding":904}," (rada: hledaný kořen ",[883,71133,71135],{"className":71134},[886],[888,71136,71137],{"xmlns":890},[892,71138,71139,71149],{},[895,71140,71141,71143],{},[898,71142,4255],{},[2124,71144,71145,71147],{},[898,71146,2777],{},[1996,71148,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,71150,71151],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,71154,71156],{"className":71155},[886],[888,71157,71158],{"xmlns":890},[892,71159,71160,71173],{},[895,71161,71162,71164,71167,71169,71171],{},[1996,71163,2005],{"stretchy":2004},[2129,71165,71166],{},"4,7",[1996,71168,8425],{"separator":2285},[2129,71170,5279],{},[1996,71172,2011],{"stretchy":2004},[902,71174,71175],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,71178,71179,71182,71183,2624,71211,71228,71229,21596,71270,71291],{},[38,71180,71181],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,71184,71186],{"className":71185},[886],[888,71187,71188],{"xmlns":890},[892,71189,71190,71208],{},[895,71191,71192,71194,71196,71198,71200,71202,71204,71206],{},[898,71193,4255],{},[898,71195,2777],{},[1996,71197,1998],{},[898,71199,4255],{},[898,71201,2777],{},[1996,71203,2005],{"stretchy":2004},[898,71205,2789],{},[1996,71207,2011],{"stretchy":2004},[902,71209,71210],{"encoding":904},"AC = AC(Q)",[883,71212,71214],{"className":71213},[886],[888,71215,71216],{"xmlns":890},[892,71217,71218,71226],{},[895,71219,71220],{},[2272,71221,71222,71224],{},[898,71223,2789],{},[2129,71225,2327],{},[902,71227,38310],{"encoding":904}," minimum, pak platí ",[883,71230,71232],{"className":71231},[886],[888,71233,71234],{"xmlns":890},[892,71235,71236,71268],{},[895,71237,71238,71240,71242,71244,71250,71252,71254,71256,71258,71260,71266],{},[898,71239,4255],{},[898,71241,2777],{},[1996,71243,2005],{"stretchy":2004},[2272,71245,71246,71248],{},[898,71247,2789],{},[2129,71249,2327],{},[1996,71251,2011],{"stretchy":2004},[1996,71253,1998],{},[898,71255,2818],{},[898,71257,2777],{},[1996,71259,2005],{"stretchy":2004},[2272,71261,71262,71264],{},[898,71263,2789],{},[2129,71265,2327],{},[1996,71267,2011],{"stretchy":2004},[902,71269,62571],{"encoding":904},[883,71271,71273],{"className":71272},[886],[888,71274,71275],{"xmlns":890},[892,71276,71277,71289],{},[895,71278,71279,71281,71283,71285,71287],{},[898,71280,2818],{},[898,71282,2777],{},[1996,71284,2005],{"stretchy":2004},[898,71286,2789],{},[1996,71288,2011],{"stretchy":2004},[902,71290,67695],{"encoding":904}," jsou mezní náklady.",[724,71293,71294,70095,71297,70557,71331,71007,71344,71023,71359,1975],{},[38,71295,71296],{},"3.13",[883,71298,71300],{"className":71299},[886],[888,71301,71302],{"xmlns":890},[892,71303,71304,71328],{},[895,71305,71306,71308,71310,71312,71318,71320,71322,71324,71326],{},[898,71307,2774],{},[898,71309,2777],{},[1996,71311,1998],{},[2124,71313,71314,71316],{},[898,71315,2789],{},[2129,71317,2131],{},[1996,71319,2095],{},[2129,71321,2131],{},[898,71323,2789],{},[1996,71325,2095],{},[2129,71327,5004],{},[902,71329,71330],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,71332,71334],{"className":71333},[886],[888,71335,71336],{"xmlns":890},[892,71337,71338,71342],{},[895,71339,71340],{},[898,71341,2789],{},[902,71343,2789],{"encoding":904},[883,71345,71347],{"className":71346},[886],[888,71348,71349],{"xmlns":890},[892,71350,71351,71357],{},[895,71352,71353,71355],{},[898,71354,4255],{},[898,71356,2777],{},[902,71358,55562],{"encoding":904},[883,71360,71362],{"className":71361},[886],[888,71363,71364],{"xmlns":890},[892,71365,71366,71372],{},[895,71367,71368,71370],{},[898,71369,4255],{},[898,71371,2777],{},[902,71373,55562],{"encoding":904},[724,71375,71376,71379,71380,2624,71412,71228,71429,21596,71472,71291],{},[38,71377,71378],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,71381,71383],{"className":71382},[886],[888,71384,71385],{"xmlns":890},[892,71386,71387,71409],{},[895,71388,71389,71391,71393,71395,71397,71399,71401,71403,71405,71407],{},[898,71390,4255],{},[898,71392,40341],{},[898,71394,2777],{},[1996,71396,1998],{},[898,71398,4255],{},[898,71400,40341],{},[898,71402,2777],{},[1996,71404,2005],{"stretchy":2004},[898,71406,2789],{},[1996,71408,2011],{"stretchy":2004},[902,71410,71411],{"encoding":904},"AVC = AVC(Q)",[883,71413,71415],{"className":71414},[886],[888,71416,71417],{"xmlns":890},[892,71418,71419,71427],{},[895,71420,71421],{},[2272,71422,71423,71425],{},[898,71424,2789],{},[2129,71426,2327],{},[902,71428,38310],{"encoding":904},[883,71430,71432],{"className":71431},[886],[888,71433,71434],{"xmlns":890},[892,71435,71436,71470],{},[895,71437,71438,71440,71442,71444,71446,71452,71454,71456,71458,71460,71462,71468],{},[898,71439,4255],{},[898,71441,40341],{},[898,71443,2777],{},[1996,71445,2005],{"stretchy":2004},[2272,71447,71448,71450],{},[898,71449,2789],{},[2129,71451,2327],{},[1996,71453,2011],{"stretchy":2004},[1996,71455,1998],{},[898,71457,2818],{},[898,71459,2777],{},[1996,71461,2005],{"stretchy":2004},[2272,71463,71464,71466],{},[898,71465,2789],{},[2129,71467,2327],{},[1996,71469,2011],{"stretchy":2004},[902,71471,69021],{"encoding":904},[883,71473,71475],{"className":71474},[886],[888,71476,71477],{"xmlns":890},[892,71478,71479,71491],{},[895,71480,71481,71483,71485,71487,71489],{},[898,71482,2818],{},[898,71484,2777],{},[1996,71486,2005],{"stretchy":2004},[898,71488,2789],{},[1996,71490,2011],{"stretchy":2004},[902,71492,67695],{"encoding":904},[724,71494,71495,70095,71498,70557,71544,71007,71557,71023,71574,1975],{},[38,71496,71497],{},"3.15",[883,71499,71501],{"className":71500},[886],[888,71502,71503],{"xmlns":890},[892,71504,71505,71541],{},[895,71506,71507,71509,71511,71513,71515,71517,71519,71521,71523,71525,71531,71533,71535],{},[898,71508,2774],{},[898,71510,2777],{},[1996,71512,1998],{},[2129,71514,3120],{},[1996,71516,2095],{},[2129,71518,36246],{},[898,71520,2789],{},[1996,71522,2225],{},[2129,71524,2131],{},[2124,71526,71527,71529],{},[898,71528,2789],{},[2129,71530,2131],{},[1996,71532,2095],{},[2129,71534,2839],{},[2124,71536,71537,71539],{},[898,71538,2789],{},[2129,71540,2173],{},[902,71542,71543],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,71545,71547],{"className":71546},[886],[888,71548,71549],{"xmlns":890},[892,71550,71551,71555],{},[895,71552,71553],{},[898,71554,2789],{},[902,71556,2789],{"encoding":904},[883,71558,71560],{"className":71559},[886],[888,71561,71562],{"xmlns":890},[892,71563,71564,71572],{},[895,71565,71566,71568,71570],{},[898,71567,4255],{},[898,71569,40341],{},[898,71571,2777],{},[902,71573,55313],{"encoding":904},[883,71575,71577],{"className":71576},[886],[888,71578,71579],{"xmlns":890},[892,71580,71581,71589],{},[895,71582,71583,71585,71587],{},[898,71584,4255],{},[898,71586,40341],{},[898,71588,2777],{},[902,71590,55313],{"encoding":904},[724,71592,71593,71596,71597,71610,71611,71631],{},[38,71594,71595],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,71598,71600],{"className":71599},[886],[888,71601,71602],{"xmlns":890},[892,71603,71604,71608],{},[895,71605,71606],{},[898,71607,2008],{},[902,71609,2008],{"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 ",[883,71612,71614],{"className":71613},[886],[888,71615,71616],{"xmlns":890},[892,71617,71618,71628],{},[895,71619,71620,71622,71624,71626],{},[2129,71621,2863],{},[2288,71623,2987],{},[2129,71625,59084],{},[898,71627,2008],{},[902,71629,71630],{"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.",[198,71633,71635],{"id":71634},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,71637,71638,71641,71642,3885,71664,71690],{},[38,71639,71640],{},"3.17"," Jsou dány ",[883,71643,71645],{"className":71644},[886],[888,71646,71647],{"xmlns":890},[892,71648,71649,71661],{},[895,71650,71651,71653,71655,71657,71659],{},[898,71652,2774],{},[898,71654,3994],{},[1996,71656,1998],{},[2129,71658,2863],{},[898,71660,2789],{},[902,71662,71663],{"encoding":904},"TR = 10Q",[883,71665,71667],{"className":71666},[886],[888,71668,71669],{"xmlns":890},[892,71670,71671,71687],{},[895,71672,71673,71675,71677,71679,71681,71683,71685],{},[898,71674,2774],{},[898,71676,2777],{},[1996,71678,1998],{},[2129,71680,3090],{},[1996,71682,2095],{},[2129,71684,2228],{},[898,71686,2789],{},[902,71688,71689],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,71692,71693,71696,71697,6190,71712,71727,71728,1343,71750,21596,71777,71799,71800,71834],{},[38,71694,71695],{},"3.18"," Odvoďte, že jestliže ",[883,71698,71700],{"className":71699},[886],[888,71701,71702],{"xmlns":890},[892,71703,71704,71710],{},[895,71705,71706,71708],{},[898,71707,2774],{},[898,71709,3994],{},[902,71711,4094],{"encoding":904},[883,71713,71715],{"className":71714},[886],[888,71716,71717],{"xmlns":890},[892,71718,71719,71725],{},[895,71720,71721,71723],{},[898,71722,2774],{},[898,71724,2777],{},[902,71726,3243],{"encoding":904}," jsou lineární tvaru ",[883,71729,71731],{"className":71730},[886],[888,71732,71733],{"xmlns":890},[892,71734,71735,71747],{},[895,71736,71737,71739,71741,71743,71745],{},[898,71738,2774],{},[898,71740,3994],{},[1996,71742,1998],{},[898,71744,724],{},[898,71746,2789],{},[902,71748,71749],{"encoding":904},"TR = pQ",[883,71751,71753],{"className":71752},[886],[888,71754,71755],{"xmlns":890},[892,71756,71757,71774],{},[895,71758,71759,71761,71763,71765,71768,71770,71772],{},[898,71760,2774],{},[898,71762,2777],{},[1996,71764,1998],{},[898,71766,71767],{},"m",[1996,71769,2095],{},[898,71771,36862],{},[898,71773,2789],{},[902,71775,71776],{"encoding":904},"TC = m + nQ",[883,71778,71780],{"className":71779},[886],[888,71781,71782],{"xmlns":890},[892,71783,71784,71796],{},[895,71785,71786,71788,71790,71792,71794],{},[898,71787,71767],{},[1996,71789,2286],{"separator":2285},[898,71791,36862],{},[1996,71793,2286],{"separator":2285},[898,71795,724],{},[902,71797,71798],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,71801,71803],{"className":71802},[886],[888,71804,71805],{"xmlns":890},[892,71806,71807,71831],{},[895,71808,71809,71815,71817],{},[2124,71810,71811,71813],{},[898,71812,2789],{},[1996,71814,4354],{},[1996,71816,1998],{},[2325,71818,71819],{"scriptlevel":2327,"displaystyle":2004},[2329,71820,71821,71823],{},[898,71822,71767],{},[895,71824,71825,71827,71829],{},[898,71826,724],{},[1996,71828,2225],{},[898,71830,36862],{},[902,71832,71833],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,71836,71837,71641,71840,3885,71874,70993,71900,71913,71914,69745,71929,71944,71945,69729,71958,69745,71973,71988],{},[38,71838,71839],{},"3.19",[883,71841,71843],{"className":71842},[886],[888,71844,71845],{"xmlns":890},[892,71846,71847,71871],{},[895,71848,71849,71851,71853,71855,71857,71859,71865,71867,71869],{},[898,71850,2774],{},[898,71852,3994],{},[1996,71854,1998],{},[1996,71856,2225],{},[2129,71858,2131],{},[2124,71860,71861,71863],{},[898,71862,2789],{},[2129,71864,2131],{},[1996,71866,2095],{},[2129,71868,22948],{},[898,71870,2789],{},[902,71872,71873],{"encoding":904},"TR = -2Q^2 + 14Q",[883,71875,71877],{"className":71876},[886],[888,71878,71879],{"xmlns":890},[892,71880,71881,71897],{},[895,71882,71883,71885,71887,71889,71891,71893,71895],{},[898,71884,2774],{},[898,71886,2777],{},[1996,71888,1998],{},[2129,71890,2131],{},[898,71892,2789],{},[1996,71894,2095],{},[2129,71896,2863],{},[902,71898,71899],{"encoding":904},"TC = 2Q + 10",[883,71901,71903],{"className":71902},[886],[888,71904,71905],{"xmlns":890},[892,71906,71907,71911],{},[895,71908,71909],{},[898,71910,2789],{},[902,71912,2789],{"encoding":904},", které maximalizuje zisk ",[883,71915,71917],{"className":71916},[886],[888,71918,71919],{"xmlns":890},[892,71920,71921,71927],{},[895,71922,71923,71925],{},[898,71924,3937],{},[898,71926,3994],{},[902,71928,63481],{"encoding":904},[883,71930,71932],{"className":71931},[886],[888,71933,71934],{"xmlns":890},[892,71935,71936,71942],{},[895,71937,71938,71940],{},[898,71939,3937],{},[898,71941,3994],{},[902,71943,63481],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,71946,71948],{"className":71947},[886],[888,71949,71950],{"xmlns":890},[892,71951,71952,71956],{},[895,71953,71954],{},[898,71955,2789],{},[902,71957,2789],{"encoding":904},[883,71959,71961],{"className":71960},[886],[888,71962,71963],{"xmlns":890},[892,71964,71965,71971],{},[895,71966,71967,71969],{},[898,71968,2774],{},[898,71970,3994],{},[902,71972,4094],{"encoding":904},[883,71974,71976],{"className":71975},[886],[888,71977,71978],{"xmlns":890},[892,71979,71980,71986],{},[895,71981,71982,71984],{},[898,71983,2774],{},[898,71985,3994],{},[902,71987,4094],{"encoding":904},". (d) Graficky interpretujte.",[724,71990,71991,47686,71994,1343,72020,1343,72039,70993,72059,71913,72072,69745,72087,72102,72103,72125,72126,71176],{},[38,71992,71993],{},"3.20",[883,71995,71997],{"className":71996},[886],[888,71998,71999],{"xmlns":890},[892,72000,72001,72017],{},[895,72002,72003,72005,72007,72009,72011],{},[898,72004,3937],{},[1996,72006,1998],{},[2129,72008,20144],{},[1996,72010,2225],{},[2124,72012,72013,72015],{},[898,72014,2789],{},[2129,72016,2131],{},[902,72018,72019],{"encoding":904},"P = 400 - Q^2",[883,72021,72023],{"className":72022},[886],[888,72024,72025],{"xmlns":890},[892,72026,72027,72037],{},[895,72028,72029,72031,72033,72035],{},[898,72030,10436],{},[898,72032,2777],{},[1996,72034,1998],{},[2129,72036,3090],{},[902,72038,11634],{"encoding":904},[883,72040,72042],{"className":72041},[886],[888,72043,72044],{"xmlns":890},[892,72045,72046,72056],{},[895,72047,72048,72050,72052,72054],{},[898,72049,2818],{},[898,72051,2777],{},[1996,72053,1998],{},[2129,72055,9035],{},[902,72057,72058],{"encoding":904},"MC = 20",[883,72060,72062],{"className":72061},[886],[888,72063,72064],{"xmlns":890},[892,72065,72066,72070],{},[895,72067,72068],{},[898,72069,2789],{},[902,72071,2789],{"encoding":904},[883,72073,72075],{"className":72074},[886],[888,72076,72077],{"xmlns":890},[892,72078,72079,72085],{},[895,72080,72081,72083],{},[898,72082,3937],{},[898,72084,3994],{},[902,72086,63481],{"encoding":904},[883,72088,72090],{"className":72089},[886],[888,72091,72092],{"xmlns":890},[892,72093,72094,72100],{},[895,72095,72096,72098],{},[898,72097,3937],{},[898,72099,3994],{},[902,72101,63481],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,72104,72106],{"className":72105},[886],[888,72107,72108],{"xmlns":890},[892,72109,72110,72122],{},[895,72111,72112,72114,72116,72118,72120],{},[1996,72113,2005],{"stretchy":2004},[2129,72115,2327],{},[1996,72117,2286],{"separator":2285},[2129,72119,2278],{},[1996,72121,2011],{"stretchy":2004},[902,72123,72124],{"encoding":904},"(0, 1)",", druhý do ",[883,72127,72129],{"className":72128},[886],[888,72130,72131],{"xmlns":890},[892,72132,72133,72146],{},[895,72134,72135,72137,72140,72142,72144],{},[1996,72136,2005],{"stretchy":2004},[2129,72138,72139],{},"19",[1996,72141,2286],{"separator":2285},[2129,72143,9035],{},[1996,72145,2011],{"stretchy":2004},[902,72147,72148],{"encoding":904},"(19, 20)",[724,72150,72151,72154,72155,2624,72183,72200,72201,1975],{},[38,72152,72153],{},"3.21"," Dokažte, že má-li zisk ",[883,72156,72158],{"className":72157},[886],[888,72159,72160],{"xmlns":890},[892,72161,72162,72180],{},[895,72163,72164,72166,72168,72170,72172,72174,72176,72178],{},[898,72165,3937],{},[898,72167,3994],{},[1996,72169,1998],{},[898,72171,3937],{},[898,72173,3994],{},[1996,72175,2005],{"stretchy":2004},[898,72177,2789],{},[1996,72179,2011],{"stretchy":2004},[902,72181,72182],{"encoding":904},"PR = PR(Q)",[883,72184,72186],{"className":72185},[886],[888,72187,72188],{"xmlns":890},[892,72189,72190,72198],{},[895,72191,72192],{},[2272,72193,72194,72196],{},[898,72195,2789],{},[2129,72197,2327],{},[902,72199,38310],{"encoding":904}," maximum, pak platí ",[883,72202,72204],{"className":72203},[886],[888,72205,72206],{"xmlns":890},[892,72207,72208,72240],{},[895,72209,72210,72212,72214,72216,72222,72224,72226,72228,72230,72232,72238],{},[898,72211,2818],{},[898,72213,3994],{},[1996,72215,2005],{"stretchy":2004},[2272,72217,72218,72220],{},[898,72219,2789],{},[2129,72221,2327],{},[1996,72223,2011],{"stretchy":2004},[1996,72225,1998],{},[898,72227,2818],{},[898,72229,2777],{},[1996,72231,2005],{"stretchy":2004},[2272,72233,72234,72236],{},[898,72235,2789],{},[2129,72237,2327],{},[1996,72239,2011],{"stretchy":2004},[902,72241,65647],{"encoding":904},[724,72243,72244,72247,72248,3885,72263,56027,72278,71913,72291,72306,72307,1343,72334,72371,72372,1343,72399,1975],{},[38,72245,72246],{},"3.22"," Pro zadané ",[883,72249,72251],{"className":72250},[886],[888,72252,72253],{"xmlns":890},[892,72254,72255,72261],{},[895,72256,72257,72259],{},[898,72258,2818],{},[898,72260,3994],{},[902,72262,6634],{"encoding":904},[883,72264,72266],{"className":72265},[886],[888,72267,72268],{"xmlns":890},[892,72269,72270,72276],{},[895,72271,72272,72274],{},[898,72273,2818],{},[898,72275,2777],{},[902,72277,55294],{"encoding":904},[883,72279,72281],{"className":72280},[886],[888,72282,72283],{"xmlns":890},[892,72284,72285,72289],{},[895,72286,72287],{},[898,72288,2789],{},[902,72290,2789],{"encoding":904},[883,72292,72294],{"className":72293},[886],[888,72295,72296],{"xmlns":890},[892,72297,72298,72304],{},[895,72299,72300,72302],{},[898,72301,3937],{},[898,72303,3994],{},[902,72305,63481],{"encoding":904},". (a) ",[883,72308,72310],{"className":72309},[886],[888,72311,72312],{"xmlns":890},[892,72313,72314,72331],{},[895,72315,72316,72318,72320,72322,72325,72327,72329],{},[898,72317,2818],{},[898,72319,3994],{},[1996,72321,1998],{},[2129,72323,72324],{},"236",[1996,72326,2225],{},[2129,72328,41864],{},[898,72330,2789],{},[902,72332,72333],{"encoding":904},"MR = 236 - 16Q",[883,72335,72337],{"className":72336},[886],[888,72338,72339],{"xmlns":890},[892,72340,72341,72368],{},[895,72342,72343,72345,72347,72349,72351,72357,72359,72362,72364,72366],{},[898,72344,2818],{},[898,72346,2777],{},[1996,72348,1998],{},[2129,72350,2173],{},[2124,72352,72353,72355],{},[898,72354,2789],{},[2129,72356,2131],{},[1996,72358,2225],{},[2129,72360,72361],{},"32",[898,72363,2789],{},[1996,72365,2095],{},[2129,72367,5744],{},[902,72369,72370],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,72373,72375],{"className":72374},[886],[888,72376,72377],{"xmlns":890},[892,72378,72379,72396],{},[895,72380,72381,72383,72385,72387,72390,72392,72394],{},[898,72382,2818],{},[898,72384,3994],{},[1996,72386,1998],{},[2129,72388,72389],{},"280",[1996,72391,2225],{},[2129,72393,9035],{},[898,72395,2789],{},[902,72397,72398],{"encoding":904},"MR = 280 - 20Q",[883,72400,72402],{"className":72401},[886],[888,72403,72404],{"xmlns":890},[892,72405,72406,72433],{},[895,72407,72408,72410,72412,72414,72417,72423,72425,72427,72429,72431],{},[898,72409,2818],{},[898,72411,2777],{},[1996,72413,1998],{},[2129,72415,72416],{},"1,6",[2124,72418,72419,72421],{},[898,72420,2789],{},[2129,72422,2131],{},[1996,72424,2225],{},[2129,72426,36246],{},[898,72428,2789],{},[1996,72430,2095],{},[2129,72432,3126],{},[902,72434,72435],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,72437,72438,72247,72441,3885,72456,56027,72471,69729,72484,69745,72499,72306,72514,1343,72545,72371,72581,1343,72613,72657,72658,1343,72690,1975],{},[38,72439,72440],{},"3.23",[883,72442,72444],{"className":72443},[886],[888,72445,72446],{"xmlns":890},[892,72447,72448,72454],{},[895,72449,72450,72452],{},[898,72451,2774],{},[898,72453,3994],{},[902,72455,4094],{"encoding":904},[883,72457,72459],{"className":72458},[886],[888,72460,72461],{"xmlns":890},[892,72462,72463,72469],{},[895,72464,72465,72467],{},[898,72466,2774],{},[898,72468,2777],{},[902,72470,3243],{"encoding":904},[883,72472,72474],{"className":72473},[886],[888,72475,72476],{"xmlns":890},[892,72477,72478,72482],{},[895,72479,72480],{},[898,72481,2789],{},[902,72483,2789],{"encoding":904},[883,72485,72487],{"className":72486},[886],[888,72488,72489],{"xmlns":890},[892,72490,72491,72497],{},[895,72492,72493,72495],{},[898,72494,3937],{},[898,72496,3994],{},[902,72498,63481],{"encoding":904},[883,72500,72502],{"className":72501},[886],[888,72503,72504],{"xmlns":890},[892,72505,72506,72512],{},[895,72507,72508,72510],{},[898,72509,3937],{},[898,72511,3994],{},[902,72513,63481],{"encoding":904},[883,72515,72517],{"className":72516},[886],[888,72518,72519],{"xmlns":890},[892,72520,72521,72542],{},[895,72522,72523,72525,72527,72529,72532,72534,72536],{},[898,72524,2774],{},[898,72526,3994],{},[1996,72528,1998],{},[2129,72530,72531],{},"125",[898,72533,2789],{},[1996,72535,2225],{},[2124,72537,72538,72540],{},[898,72539,2789],{},[2129,72541,2131],{},[902,72543,72544],{"encoding":904},"TR = 125Q - Q^2",[883,72546,72548],{"className":72547},[886],[888,72549,72550],{"xmlns":890},[892,72551,72552,72578],{},[895,72553,72554,72556,72558,72560,72562,72564,72566,72568,72570,72572],{},[898,72555,2774],{},[898,72557,2777],{},[1996,72559,1998],{},[2129,72561,15112],{},[1996,72563,2095],{},[2129,72565,2228],{},[898,72567,2789],{},[1996,72569,2095],{},[2129,72571,5009],{},[2124,72573,72574,72576],{},[898,72575,2789],{},[2129,72577,2131],{},[902,72579,72580],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,72582,72584],{"className":72583},[886],[888,72585,72586],{"xmlns":890},[892,72587,72588,72610],{},[895,72589,72590,72592,72594,72596,72598,72600,72602,72604],{},[898,72591,2774],{},[898,72593,3994],{},[1996,72595,1998],{},[2129,72597,9035],{},[898,72599,2789],{},[1996,72601,2225],{},[2129,72603,2131],{},[2124,72605,72606,72608],{},[898,72607,2789],{},[2129,72609,2131],{},[902,72611,72612],{"encoding":904},"TR = 20Q - 2Q^2",[883,72614,72616],{"className":72615},[886],[888,72617,72618],{"xmlns":890},[892,72619,72620,72654],{},[895,72621,72622,72624,72626,72628,72630,72632,72634,72636,72638,72640,72646,72648],{},[898,72623,2774],{},[898,72625,2777],{},[1996,72627,1998],{},[2129,72629,2131],{},[1996,72631,2095],{},[2129,72633,9035],{},[898,72635,2789],{},[1996,72637,2225],{},[2129,72639,5585],{},[2124,72641,72642,72644],{},[898,72643,2789],{},[2129,72645,2131],{},[1996,72647,2095],{},[2124,72649,72650,72652],{},[898,72651,2789],{},[2129,72653,2173],{},[902,72655,72656],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,72659,72661],{"className":72660},[886],[888,72662,72663],{"xmlns":890},[892,72664,72665,72687],{},[895,72666,72667,72669,72671,72673,72675,72677,72679,72681],{},[898,72668,2774],{},[898,72670,3994],{},[1996,72672,1998],{},[2129,72674,2351],{},[898,72676,2789],{},[1996,72678,2225],{},[2129,72680,23791],{},[2124,72682,72683,72685],{},[898,72684,2789],{},[2129,72686,2131],{},[902,72688,72689],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,72691,72693],{"className":72692},[886],[888,72694,72695],{"xmlns":890},[892,72696,72697,72745],{},[895,72698,72699,72701,72703,72705,72707,72709,72711,72713,72715,72731,72733],{},[898,72700,2774],{},[898,72702,2777],{},[1996,72704,1998],{},[2129,72706,2351],{},[1996,72708,2095],{},[2129,72710,2131],{},[898,72712,2789],{},[1996,72714,2225],{},[2325,72716,72717],{"scriptlevel":2327,"displaystyle":2004},[2329,72718,72719,72729],{},[895,72720,72721,72723],{},[2129,72722,2173],{},[2124,72724,72725,72727],{},[898,72726,2789],{},[2129,72728,2131],{},[2129,72730,2863],{},[1996,72732,2095],{},[2325,72734,72735],{"scriptlevel":2327,"displaystyle":2004},[2329,72736,72737,72743],{},[2124,72738,72739,72741],{},[898,72740,2789],{},[2129,72742,2173],{},[2129,72744,9035],{},[902,72746,72747],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,72749,72750,72753,72754,72784,72785,72817,72818,21596,72848,72878],{},[38,72751,72752],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,72755,72757],{"className":72756},[886],[888,72758,72759],{"xmlns":890},[892,72760,72761,72781],{},[895,72762,72763,72769,72771,72773,72775],{},[2272,72764,72765,72767],{},[898,72766,3937],{},[2129,72768,2278],{},[1996,72770,1998],{},[2129,72772,15112],{},[1996,72774,2225],{},[2272,72776,72777,72779],{},[898,72778,2789],{},[2129,72780,2278],{},[902,72782,72783],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,72786,72788],{"className":72787},[886],[888,72789,72790],{"xmlns":890},[892,72791,72792,72814],{},[895,72793,72794,72800,72802,72804,72806,72808],{},[2272,72795,72796,72798],{},[898,72797,3937],{},[2129,72799,2131],{},[1996,72801,1998],{},[2129,72803,30083],{},[1996,72805,2225],{},[2129,72807,64561],{},[2272,72809,72810,72812],{},[898,72811,2789],{},[2129,72813,2131],{},[902,72815,72816],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,72819,72821],{"className":72820},[886],[888,72822,72823],{"xmlns":890},[892,72824,72825,72845],{},[895,72826,72827,72829,72831,72833,72835,72837,72839,72841,72843],{},[898,72828,2774],{},[898,72830,2777],{},[1996,72832,1998],{},[2129,72834,3120],{},[2288,72836,2987],{},[2129,72838,59084],{},[1996,72840,2095],{},[2129,72842,9035],{},[898,72844,2789],{},[902,72846,72847],{"encoding":904},"TC = 50\\,000 + 20Q",[883,72849,72851],{"className":72850},[886],[888,72852,72853],{"xmlns":890},[892,72854,72855,72875],{},[895,72856,72857,72859,72861,72867,72869],{},[898,72858,2789],{},[1996,72860,1998],{},[2272,72862,72863,72865],{},[898,72864,2789],{},[2129,72866,2278],{},[1996,72868,2095],{},[2272,72870,72871,72873],{},[898,72872,2789],{},[2129,72874,2131],{},[902,72876,72877],{"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.",[724,72880,72881,72884,72885,72915,72916,72817,72948,21596,72978,73007],{},[38,72882,72883],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,72886,72888],{"className":72887},[886],[888,72889,72890],{"xmlns":890},[892,72891,72892,72912],{},[895,72893,72894,72900,72902,72904,72906],{},[2272,72895,72896,72898],{},[898,72897,3937],{},[2129,72899,2278],{},[1996,72901,1998],{},[2129,72903,30083],{},[1996,72905,2225],{},[2272,72907,72908,72910],{},[898,72909,2789],{},[2129,72911,2278],{},[902,72913,72914],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,72917,72919],{"className":72918},[886],[888,72920,72921],{"xmlns":890},[892,72922,72923,72945],{},[895,72924,72925,72931,72933,72935,72937,72939],{},[2272,72926,72927,72929],{},[898,72928,3937],{},[2129,72930,2131],{},[1996,72932,1998],{},[2129,72934,8377],{},[1996,72936,2225],{},[2129,72938,5009],{},[2272,72940,72941,72943],{},[898,72942,2789],{},[2129,72944,2131],{},[902,72946,72947],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,72949,72951],{"className":72950},[886],[888,72952,72953],{"xmlns":890},[892,72954,72955,72975],{},[895,72956,72957,72959,72961,72963,72965,72967,72969,72971,72973],{},[898,72958,2774],{},[898,72960,2777],{},[1996,72962,1998],{},[2129,72964,2228],{},[2288,72966,2987],{},[2129,72968,59084],{},[1996,72970,2095],{},[2129,72972,3090],{},[898,72974,2789],{},[902,72976,72977],{"encoding":904},"TC = 5\\,000 + 100Q",[883,72979,72981],{"className":72980},[886],[888,72982,72983],{"xmlns":890},[892,72984,72985,73005],{},[895,72986,72987,72989,72991,72997,72999],{},[898,72988,2789],{},[1996,72990,1998],{},[2272,72992,72993,72995],{},[898,72994,2789],{},[2129,72996,2278],{},[1996,72998,2095],{},[2272,73000,73001,73003],{},[898,73002,2789],{},[2129,73004,2131],{},[902,73006,72877],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,73009,73011],{"id":73010},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,73013,73014,73017,73018,73065,73066,73083],{},[38,73015,73016],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,73019,73021],{"className":73020},[886],[888,73022,73023],{"xmlns":890},[892,73024,73025,73062],{},[895,73026,73027,73029,73031,73033,73035,73038,73044,73046,73049,73055,73057,73060],{},[898,73028,2774],{},[898,73030,40341],{},[898,73032,2777],{},[1996,73034,1998],{},[2129,73036,73037],{},"0,85",[2124,73039,73040,73042],{},[898,73041,2789],{},[2129,73043,2173],{},[1996,73045,2225],{},[2129,73047,73048],{},"11,9",[2124,73050,73051,73053],{},[898,73052,2789],{},[2129,73054,2131],{},[1996,73056,2095],{},[2129,73058,73059],{},"102",[898,73061,2789],{},[902,73063,73064],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,73067,73069],{"className":73068},[886],[888,73070,73071],{"xmlns":890},[892,73072,73073,73081],{},[895,73074,73075],{},[2124,73076,73077,73079],{},[898,73078,3937],{},[1996,73080,4354],{},[902,73082,4404],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,73085,73086,70844,73089,73125],{},[38,73087,73088],{},"3.27",[883,73090,73092],{"className":73091},[886],[888,73093,73094],{"xmlns":890},[892,73095,73096,73122],{},[895,73097,73098,73100,73102,73104,73106,73112,73114,73116,73118,73120],{},[898,73099,2818],{},[898,73101,2777],{},[1996,73103,1998],{},[2129,73105,2923],{},[2124,73107,73108,73110],{},[898,73109,2789],{},[2129,73111,2131],{},[1996,73113,2225],{},[2129,73115,64442],{},[898,73117,2789],{},[1996,73119,2095],{},[2129,73121,30745],{},[902,73123,73124],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,73127,73128,70095,73131,73125],{},[38,73129,73130],{},"3.28",[883,73132,73134],{"className":73133},[886],[888,73135,73136],{"xmlns":890},[892,73137,73138,73174],{},[895,73139,73140,73142,73144,73146,73148,73154,73156,73158,73164,73166,73168,73170,73172],{},[898,73141,2774],{},[898,73143,2777],{},[1996,73145,1998],{},[2129,73147,5009],{},[2124,73149,73150,73152],{},[898,73151,2789],{},[2129,73153,2173],{},[1996,73155,2225],{},[2129,73157,24203],{},[2124,73159,73160,73162],{},[898,73161,2789],{},[2129,73163,2131],{},[1996,73165,2095],{},[2129,73167,3126],{},[898,73169,2789],{},[1996,73171,2095],{},[2129,73173,15112],{},[902,73175,73176],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,73178,15722],{"id":15721},[120,73180,73181,73209,73254,73326,73391,73431,73523,73629,73669,73783,73876,73940,73972,74032,74038,74102,74151,74205,74313,74368],{},[123,73182,73183,2203,73185,73208],{},[38,73184,55752],{},[883,73186,73188],{"className":73187},[886],[888,73189,73190],{"xmlns":890},[892,73191,73192,73206],{},[895,73193,73194,73196,73198,73200,73202,73204],{},[898,73195,2774],{},[898,73197,3994],{},[1996,73199,1998],{},[898,73201,3937],{},[1996,73203,3177],{},[898,73205,2789],{},[902,73207,66714],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,73210,73211,2203,73213,73253],{},[38,73212,56338],{},[883,73214,73216],{"className":73215},[886],[888,73217,73218],{"xmlns":890},[892,73219,73220,73250],{},[895,73221,73222,73224,73226,73228,73240,73242,73244,73246,73248],{},[898,73223,4255],{},[898,73225,3994],{},[1996,73227,1998],{},[2325,73229,73230],{"scriptlevel":2327,"displaystyle":2004},[2329,73231,73232,73238],{},[895,73233,73234,73236],{},[898,73235,2774],{},[898,73237,3994],{},[898,73239,2789],{},[1996,73241,1998],{},[898,73243,4183],{},[1996,73245,2005],{"stretchy":2004},[898,73247,2789],{},[1996,73249,2011],{"stretchy":2004},[902,73251,73252],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,73255,73256,2203,73258,73294,73295,73310,73311,1975],{},[38,73257,56486],{},[883,73259,73261],{"className":73260},[886],[888,73262,73263],{"xmlns":890},[892,73264,73265,73291],{},[895,73266,73267,73269,73271,73273],{},[898,73268,2818],{},[898,73270,3994],{},[1996,73272,1998],{},[2325,73274,73275],{"scriptlevel":2327,"displaystyle":2004},[2329,73276,73277,73285],{},[895,73278,73279,73281,73283],{},[898,73280,2194],{"mathvariant":2376},[898,73282,2774],{},[898,73284,3994],{},[895,73286,73287,73289],{},[898,73288,2194],{"mathvariant":2376},[898,73290,2789],{},[902,73292,73293],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,73296,73298],{"className":73297},[886],[888,73299,73300],{"xmlns":890},[892,73301,73302,73308],{},[895,73303,73304,73306],{},[898,73305,2774],{},[898,73307,3994],{},[902,73309,4094],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,73312,73314],{"className":73313},[886],[888,73315,73316],{"xmlns":890},[892,73317,73318,73324],{},[895,73319,73320,73322],{},[898,73321,4255],{},[898,73323,3994],{},[902,73325,55447],{"encoding":904},[123,73327,73328,2203,73331,1343,73361,1975],{},[38,73329,73330],{},"Diferenciál příjmu\u002Fnákladů",[883,73332,73334],{"className":73333},[886],[888,73335,73336],{"xmlns":890},[892,73337,73338,73358],{},[895,73339,73340,73342,73344,73346,73348,73350,73352,73354,73356],{},[898,73341,2889],{"mathvariant":2376},[898,73343,2774],{},[898,73345,3994],{},[1996,73347,2730],{},[898,73349,2818],{},[898,73351,3994],{},[2288,73353,2987],{},[898,73355,2194],{"mathvariant":2376},[898,73357,2789],{},[902,73359,73360],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,73362,73364],{"className":73363},[886],[888,73365,73366],{"xmlns":890},[892,73367,73368,73388],{},[895,73369,73370,73372,73374,73376,73378,73380,73382,73384,73386],{},[898,73371,2889],{"mathvariant":2376},[898,73373,2774],{},[898,73375,2777],{},[1996,73377,2730],{},[898,73379,2818],{},[898,73381,2777],{},[2288,73383,2987],{},[898,73385,2194],{"mathvariant":2376},[898,73387,2789],{},[902,73389,73390],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,73392,73393,2203,73395,1975],{},[38,73394,58608],{},[883,73396,73398],{"className":73397},[886],[888,73399,73400],{"xmlns":890},[892,73401,73402,73428],{},[895,73403,73404,73406,73408,73410,73412,73414,73416,73418,73420,73422,73424,73426],{},[898,73405,2774],{},[898,73407,2777],{},[1996,73409,1998],{},[898,73411,10436],{},[898,73413,2777],{},[1996,73415,2095],{},[898,73417,2774],{},[898,73419,40341],{},[898,73421,2777],{},[1996,73423,2005],{"stretchy":2004},[898,73425,2789],{},[1996,73427,2011],{"stretchy":2004},[902,73429,73430],{"encoding":904},"TC = FC + TVC(Q)",[123,73432,73433,2203,73436,1343,73451,2203,73453,1343,73476,2203,73479,1975],{},[38,73434,73435],{},"Fixní náklady",[883,73437,73439],{"className":73438},[886],[888,73440,73441],{"xmlns":890},[892,73442,73443,73449],{},[895,73444,73445,73447],{},[898,73446,10436],{},[898,73448,2777],{},[902,73450,55493],{"encoding":904},[38,73452,58761],{},[883,73454,73456],{"className":73455},[886],[888,73457,73458],{"xmlns":890},[892,73459,73460,73474],{},[895,73461,73462,73464,73466,73468,73470,73472],{},[898,73463,2774],{},[898,73465,40341],{},[898,73467,2777],{},[1996,73469,2005],{"stretchy":2004},[898,73471,2789],{},[1996,73473,2011],{"stretchy":2004},[902,73475,58758],{"encoding":904},[38,73477,73478],{},"variabilní náklady na jednotku",[883,73480,73482],{"className":73481},[886],[888,73483,73484],{"xmlns":890},[892,73485,73486,73520],{},[895,73487,73488,73490,73492,73494,73496,73498,73500],{},[898,73489,40341],{},[898,73491,2777],{},[1996,73493,2005],{"stretchy":2004},[898,73495,2789],{},[1996,73497,2011],{"stretchy":2004},[1996,73499,1998],{},[2325,73501,73502],{"scriptlevel":2327,"displaystyle":2004},[2329,73503,73504,73518],{},[895,73505,73506,73508,73510,73512,73514,73516],{},[898,73507,2774],{},[898,73509,40341],{},[898,73511,2777],{},[1996,73513,2005],{"stretchy":2004},[898,73515,2789],{},[1996,73517,2011],{"stretchy":2004},[898,73519,2789],{},[902,73521,73522],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,73524,73525,2203,73527,1343,73557,2203,73560,1343,73592,2203,73595,1975],{},[38,73526,58769],{},[883,73528,73530],{"className":73529},[886],[888,73531,73532],{"xmlns":890},[892,73533,73534,73554],{},[895,73535,73536,73538,73540,73542],{},[898,73537,4255],{},[898,73539,2777],{},[1996,73541,1998],{},[2325,73543,73544],{"scriptlevel":2327,"displaystyle":2004},[2329,73545,73546,73552],{},[895,73547,73548,73550],{},[898,73549,2774],{},[898,73551,2777],{},[898,73553,2789],{},[902,73555,73556],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,73558,73559],{},"průměrné fixní",[883,73561,73563],{"className":73562},[886],[888,73564,73565],{"xmlns":890},[892,73566,73567,73589],{},[895,73568,73569,73571,73573,73575,73577],{},[898,73570,4255],{},[898,73572,10436],{},[898,73574,2777],{},[1996,73576,1998],{},[2325,73578,73579],{"scriptlevel":2327,"displaystyle":2004},[2329,73580,73581,73587],{},[895,73582,73583,73585],{},[898,73584,10436],{},[898,73586,2777],{},[898,73588,2789],{},[902,73590,73591],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,73593,73594],{},"průměrné variabilní",[883,73596,73598],{"className":73597},[886],[888,73599,73600],{"xmlns":890},[892,73601,73602,73626],{},[895,73603,73604,73606,73608,73610,73612],{},[898,73605,4255],{},[898,73607,40341],{},[898,73609,2777],{},[1996,73611,1998],{},[2325,73613,73614],{"scriptlevel":2327,"displaystyle":2004},[2329,73615,73616,73624],{},[895,73617,73618,73620,73622],{},[898,73619,2774],{},[898,73621,40341],{},[898,73623,2777],{},[898,73625,2789],{},[902,73627,73628],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,73630,73631,2203,73633,1975],{},[38,73632,59956],{},[883,73634,73636],{"className":73635},[886],[888,73637,73638],{"xmlns":890},[892,73639,73640,73666],{},[895,73641,73642,73644,73646,73648],{},[898,73643,2818],{},[898,73645,2777],{},[1996,73647,1998],{},[2325,73649,73650],{"scriptlevel":2327,"displaystyle":2004},[2329,73651,73652,73660],{},[895,73653,73654,73656,73658],{},[898,73655,2194],{"mathvariant":2376},[898,73657,2774],{},[898,73659,2777],{},[895,73661,73662,73664],{},[898,73663,2194],{"mathvariant":2376},[898,73665,2789],{},[902,73667,73668],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,73670,73671,2203,73673,73721,73722,73735,73736,1343,73751,1343,73768,1975],{},[38,73672,60854],{},[883,73674,73676],{"className":73675},[886],[888,73677,73678],{"xmlns":890},[892,73679,73680,73718],{},[895,73681,73682,73684,73686,73688,73690,73692,73694,73696,73698,73700,73702,73708,73710,73712],{},[898,73683,2774],{},[898,73685,2777],{},[1996,73687,1998],{},[898,73689,10436],{},[898,73691,2777],{},[1996,73693,2095],{},[898,73695,207],{},[898,73697,2789],{},[1996,73699,2095],{},[898,73701,2098],{},[2124,73703,73704,73706],{},[898,73705,2789],{},[2129,73707,2131],{},[1996,73709,2095],{},[898,73711,2142],{},[2124,73713,73714,73716],{},[898,73715,2789],{},[2129,73717,2173],{},[902,73719,73720],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,73723,73725],{"className":73724},[886],[888,73726,73727],{"xmlns":890},[892,73728,73729,73733],{},[895,73730,73731],{},[898,73732,900],{},[902,73734,900],{"encoding":904},"-průběhem ",[883,73737,73739],{"className":73738},[886],[888,73740,73741],{"xmlns":890},[892,73742,73743,73749],{},[895,73744,73745,73747],{},[898,73746,4255],{},[898,73748,2777],{},[902,73750,55562],{"encoding":904},[883,73752,73754],{"className":73753},[886],[888,73755,73756],{"xmlns":890},[892,73757,73758,73766],{},[895,73759,73760,73762,73764],{},[898,73761,4255],{},[898,73763,40341],{},[898,73765,2777],{},[902,73767,55313],{"encoding":904},[883,73769,73771],{"className":73770},[886],[888,73772,73773],{"xmlns":890},[892,73774,73775,73781],{},[895,73776,73777,73779],{},[898,73778,2818],{},[898,73780,2777],{},[902,73782,55294],{"encoding":904},[123,73784,73785,73787,73788,10394,73803,73844,73845,61499,73860,73875],{},[38,73786,61936],{},": v bodě minima ",[883,73789,73791],{"className":73790},[886],[888,73792,73793],{"xmlns":890},[892,73794,73795,73801],{},[895,73796,73797,73799],{},[898,73798,4255],{},[898,73800,2777],{},[902,73802,55562],{"encoding":904},[883,73804,73806],{"className":73805},[886],[888,73807,73808],{"xmlns":890},[892,73809,73810,73842],{},[895,73811,73812,73814,73816,73818,73824,73826,73828,73830,73832,73834,73840],{},[898,73813,4255],{},[898,73815,2777],{},[1996,73817,2005],{"stretchy":2004},[2272,73819,73820,73822],{},[898,73821,2789],{},[2129,73823,2327],{},[1996,73825,2011],{"stretchy":2004},[1996,73827,1998],{},[898,73829,2818],{},[898,73831,2777],{},[1996,73833,2005],{"stretchy":2004},[2272,73835,73836,73838],{},[898,73837,2789],{},[2129,73839,2327],{},[1996,73841,2011],{"stretchy":2004},[902,73843,62571],{"encoding":904},"; geometricky ",[883,73846,73848],{"className":73847},[886],[888,73849,73850],{"xmlns":890},[892,73851,73852,73858],{},[895,73853,73854,73856],{},[898,73855,2818],{},[898,73857,2777],{},[902,73859,55294],{"encoding":904},[883,73861,73863],{"className":73862},[886],[888,73864,73865],{"xmlns":890},[892,73866,73867,73873],{},[895,73868,73869,73871],{},[898,73870,4255],{},[898,73872,2777],{},[902,73874,55562],{"encoding":904}," v jejím minimu.",[123,73877,73878,73787,73880,10394,73897,1975],{},[38,73879,63286],{},[883,73881,73883],{"className":73882},[886],[888,73884,73885],{"xmlns":890},[892,73886,73887,73895],{},[895,73888,73889,73891,73893],{},[898,73890,4255],{},[898,73892,40341],{},[898,73894,2777],{},[902,73896,55313],{"encoding":904},[883,73898,73900],{"className":73899},[886],[888,73901,73902],{"xmlns":890},[892,73903,73904,73938],{},[895,73905,73906,73908,73910,73912,73914,73920,73922,73924,73926,73928,73930,73936],{},[898,73907,4255],{},[898,73909,40341],{},[898,73911,2777],{},[1996,73913,2005],{"stretchy":2004},[2272,73915,73916,73918],{},[898,73917,2789],{},[2129,73919,2327],{},[1996,73921,2011],{"stretchy":2004},[1996,73923,1998],{},[898,73925,2818],{},[898,73927,2777],{},[1996,73929,2005],{"stretchy":2004},[2272,73931,73932,73934],{},[898,73933,2789],{},[2129,73935,2327],{},[1996,73937,2011],{"stretchy":2004},[902,73939,69021],{"encoding":904},[123,73941,73942,2203,73944,73971],{},[38,73943,63465],{},[883,73945,73947],{"className":73946},[886],[888,73948,73949],{"xmlns":890},[892,73950,73951,73969],{},[895,73952,73953,73955,73957,73959,73961,73963,73965,73967],{},[898,73954,3937],{},[898,73956,3994],{},[1996,73958,1998],{},[898,73960,2774],{},[898,73962,3994],{},[1996,73964,2225],{},[898,73966,2774],{},[898,73968,2777],{},[902,73970,55202],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,73973,73974,10025,73976,73978,73979,74005,74006,74031],{},[38,73975,64327],{},[614,73977,63590],{},") — hodnoty ",[883,73980,73982],{"className":73981},[886],[888,73983,73984],{"xmlns":890},[892,73985,73986,74002],{},[895,73987,73988,73994,73996],{},[2272,73989,73990,73992],{},[898,73991,2789],{},[898,73993,4255],{},[1996,73995,2286],{"separator":2285},[2272,73997,73998,74000],{},[898,73999,2789],{},[898,74001,23255],{},[902,74003,74004],{"encoding":904},"Q_A, Q_B"," splňující ",[883,74007,74009],{"className":74008},[886],[888,74010,74011],{"xmlns":890},[892,74012,74013,74029],{},[895,74014,74015,74017,74019,74021,74023,74025,74027],{},[898,74016,3937],{},[898,74018,3994],{},[1996,74020,2005],{"stretchy":2004},[898,74022,2789],{},[1996,74024,2011],{"stretchy":2004},[1996,74026,1998],{},[2129,74028,2327],{},[902,74030,63867],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,74033,74034,74037],{},[38,74035,74036],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,74039,74040,74042,74043,10394,74060,74101],{},[38,74041,65381],{}," — v bodě maxima zisku ",[883,74044,74046],{"className":74045},[886],[888,74047,74048],{"xmlns":890},[892,74049,74050,74058],{},[895,74051,74052],{},[2272,74053,74054,74056],{},[898,74055,2789],{},[2129,74057,2327],{},[902,74059,38310],{"encoding":904},[883,74061,74063],{"className":74062},[886],[888,74064,74065],{"xmlns":890},[892,74066,74067,74099],{},[895,74068,74069,74071,74073,74075,74081,74083,74085,74087,74089,74091,74097],{},[898,74070,2818],{},[898,74072,3994],{},[1996,74074,2005],{"stretchy":2004},[2272,74076,74077,74079],{},[898,74078,2789],{},[2129,74080,2327],{},[1996,74082,2011],{"stretchy":2004},[1996,74084,1998],{},[898,74086,2818],{},[898,74088,2777],{},[1996,74090,2005],{"stretchy":2004},[2272,74092,74093,74095],{},[898,74094,2789],{},[2129,74096,2327],{},[1996,74098,2011],{"stretchy":2004},[902,74100,65647],{"encoding":904}," (3.13).",[123,74103,74104,20303,74106,10394,74125,74150],{},[38,74105,66674],{},[883,74107,74109],{"className":74108},[886],[888,74110,74111],{"xmlns":890},[892,74112,74113,74122],{},[895,74114,74115,74117,74119],{},[898,74116,3937],{},[1996,74118,1998],{},[2288,74120,74121],{},"konst",[902,74123,74124],{"encoding":904},"P = \\text{konst}",[883,74126,74128],{"className":74127},[886],[888,74129,74130],{"xmlns":890},[892,74131,74132,74148],{},[895,74133,74134,74136,74138,74140,74142,74144,74146],{},[898,74135,3937],{},[1996,74137,1998],{},[898,74139,2818],{},[898,74141,2777],{},[1996,74143,2005],{"stretchy":2004},[898,74145,2789],{},[1996,74147,2011],{"stretchy":2004},[902,74149,67368],{"encoding":904}," (3.14).",[123,74152,74153,74156,74157,74186,74187,74204],{},[38,74154,74155],{},"Shutdown point"," — bod ",[883,74158,74160],{"className":74159},[886],[888,74161,74162],{"xmlns":890},[892,74163,74164,74184],{},[895,74165,74166,74168,74174,74176,74182],{},[1996,74167,2005],{"stretchy":2004},[2124,74169,74170,74172],{},[898,74171,2789],{},[1996,74173,4354],{},[1996,74175,2286],{"separator":2285},[2124,74177,74178,74180],{},[898,74179,3937],{},[1996,74181,4354],{},[1996,74183,2011],{"stretchy":2004},[902,74185,67657],{"encoding":904}," v minimu ",[883,74188,74190],{"className":74189},[886],[888,74191,74192],{"xmlns":890},[892,74193,74194,74202],{},[895,74195,74196,74198,74200],{},[898,74197,4255],{},[898,74199,40341],{},[898,74201,2777],{},[902,74203,55313],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,74206,74207,2203,74210,6473,74245,67927,74266,74279,74280,74295,74296,1975],{},[38,74208,74209],{},"Funkce nabídky firmy",[883,74211,74213],{"className":74212},[886],[888,74214,74215],{"xmlns":890},[892,74216,74217,74243],{},[895,74218,74219,74221,74223,74225,74227,74229,74231,74233,74235,74237,74239,74241],{},[898,74220,3937],{},[1996,74222,1998],{},[898,74224,8673],{},[1996,74226,2005],{"stretchy":2004},[898,74228,2789],{},[1996,74230,2011],{"stretchy":2004},[1996,74232,1998],{},[898,74234,2818],{},[898,74236,2777],{},[1996,74238,2005],{"stretchy":2004},[898,74240,2789],{},[1996,74242,2011],{"stretchy":2004},[902,74244,69124],{"encoding":904},[883,74246,74248],{"className":74247},[886],[888,74249,74250],{"xmlns":890},[892,74251,74252,74264],{},[895,74253,74254,74256,74258],{},[898,74255,2789],{},[1996,74257,4485],{},[2124,74259,74260,74262],{},[898,74261,2789],{},[1996,74263,4354],{},[902,74265,67926],{"encoding":904},[883,74267,74269],{"className":74268},[886],[888,74270,74271],{"xmlns":890},[892,74272,74273,74277],{},[895,74274,74275],{},[2129,74276,2327],{},[902,74278,2327],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,74281,74283],{"className":74282},[886],[888,74284,74285],{"xmlns":890},[892,74286,74287,74293],{},[895,74288,74289,74291],{},[898,74290,2818],{},[898,74292,2777],{},[902,74294,55294],{"encoding":904}," nad minimem ",[883,74297,74299],{"className":74298},[886],[888,74300,74301],{"xmlns":890},[892,74302,74303,74311],{},[895,74304,74305,74307,74309],{},[898,74306,4255],{},[898,74308,40341],{},[898,74310,2777],{},[902,74312,55313],{"encoding":904},[123,74314,74315,7015,74317,74338,74339,1975],{},[38,74316,50081],{},[883,74318,74320],{"className":74319},[886],[888,74321,74322],{"xmlns":890},[892,74323,74324,74336],{},[895,74325,74326,74328,74330],{},[898,74327,3937],{},[1996,74329,1998],{},[2124,74331,74332,74334],{},[898,74333,3937],{},[1996,74335,4354],{},[902,74337,4357],{"encoding":904}," konstantní ⇒ ",[883,74340,74342],{"className":74341},[886],[888,74343,74344],{"xmlns":890},[892,74345,74346,74366],{},[895,74347,74348,74350,74352,74354,74356,74358,74360],{},[898,74349,4255],{},[898,74351,3994],{},[1996,74353,1998],{},[898,74355,2818],{},[898,74357,3994],{},[1996,74359,1998],{},[2124,74361,74362,74364],{},[898,74363,3937],{},[1996,74365,4354],{},[902,74367,58600],{"encoding":904},[123,74369,74370,74373],{},[38,74371,74372],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,74375,3792],{"id":3791},[120,74377,74378,74397,74409],{},[123,74379,74380,2203,74382,1343,74385,1343,74388,1343,74391,1343,74394],{},[38,74381,50725],{},[207,74383,11942],{"className":74384,"dataFsResolvedFilePath":800,"href":801},[210],[207,74386,3828],{"className":74387,"dataFsResolvedFilePath":848,"href":849},[210],[207,74389,2357],{"className":74390,"dataFsResolvedFilePath":764,"href":765},[210],[207,74392,775],{"className":74393,"dataFsResolvedFilePath":773,"href":774},[210],[207,74395,859],{"className":74396,"dataFsResolvedFilePath":857,"href":858},[210],[123,74398,74399,2203,74401,1343,74405],{},[38,74400,36705],{},[207,74402,74404],{"className":74403,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,74406,74408],{"className":74407,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,74410,74411,2203,74413],{},[38,74412,16206],{},[207,74414,16210],{"className":74415,"dataFsResolvedFilePath":1960,"href":1961},[210],{"title":641,"searchDepth":642,"depth":642,"links":74417},[74418,74419,74426,74432,74436,74437,74441,74442,74443,74444,74450,74451],{"id":50956,"depth":642,"text":1241},{"id":55740,"depth":642,"text":55741,"children":74420},[74421,74422,74423,74424,74425],{"id":55751,"depth":649,"text":55752},{"id":56337,"depth":649,"text":56338},{"id":56485,"depth":649,"text":56486},{"id":57227,"depth":649,"text":57228},{"id":57882,"depth":649,"text":57883},{"id":58603,"depth":642,"text":58604,"children":74427},[74428,74429,74430,74431],{"id":58607,"depth":649,"text":58608},{"id":58768,"depth":649,"text":58769},{"id":59955,"depth":649,"text":59956},{"id":60853,"depth":649,"text":60854},{"id":61935,"depth":642,"text":61936,"children":74433},[74434,74435],{"id":16413,"depth":649,"text":16414},{"id":63285,"depth":649,"text":63286},{"id":63459,"depth":642,"text":63460},{"id":65380,"depth":642,"text":65381,"children":74438},[74439,74440],{"id":65394,"depth":649,"text":16414},{"id":66673,"depth":649,"text":66674},{"id":67305,"depth":642,"text":67306},{"id":68771,"depth":642,"text":68772},{"id":49883,"depth":642,"text":49884},{"id":69232,"depth":642,"text":69233,"children":74445},[74446,74447,74448,74449],{"id":69236,"depth":649,"text":69237},{"id":70088,"depth":649,"text":70089},{"id":71634,"depth":649,"text":71635},{"id":73010,"depth":649,"text":73011},{"id":15721,"depth":642,"text":15722},{"id":3791,"depth":642,"text":3792},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":55122,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,74458,74459,55174,74460,74461,74462],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":74465,"title":74466,"body":74467,"course":1128,"courses":659,"created":9556,"description":641,"extension":661,"meta":86564,"navigation":664,"path":86565,"seo":86566,"sources":86567,"stem":86568,"tags":86569,"type":3857,"updated":677,"__hash__":86575},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":74468,"toc":86521},[74469,74472,74828,74832,74835,74903,74955,74965,74969,75003,75044,75068,75091,75120,75187,75294,75337,75394,75469,75514,75518,75526,75534,75537,75802,75853,75933,76003,76026,76054,76099,76121,76125,76132,76181,76207,76358,76361,76398,76561,76669,76673,76710,76785,76854,76973,77095,77176,77182,77223,77296,77389,77393,77429,77517,77631,77736,77821,77961,77965,78013,78058,78064,78068,78071,78122,78172,78179,78245,78378,78423,78427,78448,78827,78922,78939,78993,78997,79079,79163,79333,79336,79379,79446,79520,79524,79529,79598,79606,79615,79693,79759,79764,79859,79902,79907,79955,79960,80008,80126,80209,80247,80350,80409,80550,80554,80597,80670,80694,80748,80755,80757,80802,80847,80858,80863,80899,80961,80984,80993,81094,81161,81234,81241,81332,81394,81430,81487,81546,81731,81827,81831,81835,81914,81919,82043,82129,82135,82245,82282,82373,82471,82474,82478,82544,82581,82703,82755,82759,82787,82839,82913,83018,83042,83101,83105,83123,83266,83414,83416,83451,83455,83457,83547,83677,83803,83895,83970,83974,84090,84194,84384,84420,84514,84520,84633,84936,84942,85060,85159,85235,85237,86399,86401],[12,74470,74466],{"id":74471},"produkce-produkční-funkce-cobb-douglas-mrts",[3867,74473,74474],{},[724,74475,74476,3874,74478,74480,74481,36898,74494,74507,74508,16378,74521,10025,74523,74547,74548,2203,74550,3885,74584,2203,74587,74615,74616,10394,74636,74666,74667,10025,74670,74698,74699,74702,74703,74733,74734,74764,74765,2203,74768,74808,74809,74827],{},[883,74477,3873],{},[38,74479,859],{}," popisuje vztah mezi vstupy (práce ",[883,74482,74484],{"className":74483},[886],[888,74485,74486],{"xmlns":890},[892,74487,74488,74492],{},[895,74489,74490],{},[898,74491,9795],{},[902,74493,9795],{"encoding":904},[883,74495,74497],{"className":74496},[886],[888,74498,74499],{"xmlns":890},[892,74500,74501,74505],{},[895,74502,74503],{},[898,74504,9800],{},[902,74506,9800],{"encoding":904},") a výstupem ",[883,74509,74511],{"className":74510},[886],[888,74512,74513],{"xmlns":890},[892,74514,74515,74519],{},[895,74516,74517],{},[898,74518,2789],{},[902,74520,2789],{"encoding":904},[38,74522,36966],{},[883,74524,74526],{"className":74525},[886],[888,74527,74528],{"xmlns":890},[892,74529,74530,74544],{},[895,74531,74532,74534,74536,74538,74540,74542],{},[898,74533,2789],{},[1996,74535,1998],{},[898,74537,2789],{},[1996,74539,2005],{"stretchy":2004},[898,74541,9795],{},[1996,74543,2011],{"stretchy":2004},[902,74545,74546],{"encoding":904},"Q = Q(L)",") studujeme ",[614,74549,10024],{},[883,74551,74553],{"className":74552},[886],[888,74554,74555],{"xmlns":890},[892,74556,74557,74581],{},[895,74558,74559,74561,74567,74569,74575,74577,74579],{},[898,74560,2818],{},[2272,74562,74563,74565],{},[898,74564,3937],{},[898,74566,9795],{},[1996,74568,1998],{},[2124,74570,74571,74573],{},[898,74572,2789],{},[1996,74574,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,74576,2005],{"stretchy":2004},[898,74578,9795],{},[1996,74580,2011],{"stretchy":2004},[902,74582,74583],{"encoding":904},"MP_L = Q'(L)",[614,74585,74586],{},"průměrný produkt",[883,74588,74590],{"className":74589},[886],[888,74591,74592],{"xmlns":890},[892,74593,74594,74612],{},[895,74595,74596,74598,74604,74606,74608,74610],{},[898,74597,4255],{},[2272,74599,74600,74602],{},[898,74601,3937],{},[898,74603,9795],{},[1996,74605,1998],{},[898,74607,2789],{},[898,74609,4674],{"mathvariant":2376},[898,74611,9795],{},[902,74613,74614],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,74617,74619],{"className":74618},[886],[888,74620,74621],{"xmlns":890},[892,74622,74623,74633],{},[895,74624,74625,74627],{},[898,74626,4255],{},[2272,74628,74629,74631],{},[898,74630,3937],{},[898,74632,9795],{},[902,74634,74635],{"encoding":904},"AP_L",[883,74637,74639],{"className":74638},[886],[888,74640,74641],{"xmlns":890},[892,74642,74643,74663],{},[895,74644,74645,74647,74653,74655,74657],{},[898,74646,2818],{},[2272,74648,74649,74651],{},[898,74650,3937],{},[898,74652,9795],{},[1996,74654,1998],{},[898,74656,4255],{},[2272,74658,74659,74661],{},[898,74660,3937],{},[898,74662,9795],{},[902,74664,74665],{"encoding":904},"MP_L = AP_L",". Ve ",[38,74668,74669],{},"dvoufaktorovém modelu",[883,74671,74673],{"className":74672},[886],[888,74674,74675],{"xmlns":890},[892,74676,74677,74695],{},[895,74678,74679,74681,74683,74685,74687,74689,74691,74693],{},[898,74680,2789],{},[1996,74682,1998],{},[898,74684,2789],{},[1996,74686,2005],{"stretchy":2004},[898,74688,9795],{},[1996,74690,2286],{"separator":2285},[898,74692,9800],{},[1996,74694,2011],{"stretchy":2004},[902,74696,74697],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,74700,74701],{},"Cobb-Douglasovy"," funkce ",[883,74704,74706],{"className":74705},[886],[888,74707,74708],{"xmlns":890},[892,74709,74710,74730],{},[895,74711,74712,74714,74716,74718,74724],{},[898,74713,2789],{},[1996,74715,1998],{},[898,74717,4255],{},[2124,74719,74720,74722],{},[898,74721,9795],{},[898,74723,207],{},[2124,74725,74726,74728],{},[898,74727,9800],{},[898,74729,2098],{},[902,74731,74732],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,74735,74737],{"className":74736},[886],[888,74738,74739],{"xmlns":890},[892,74740,74741,74761],{},[895,74742,74743,74745,74751,74753,74755],{},[898,74744,2818],{},[2272,74746,74747,74749],{},[898,74748,3937],{},[898,74750,9795],{},[1996,74752,2286],{"separator":2285},[898,74754,2818],{},[2272,74756,74757,74759],{},[898,74758,3937],{},[898,74760,9800],{},[902,74762,74763],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,74766,74767],{},"mezní míru technické substituce",[883,74769,74771],{"className":74770},[886],[888,74772,74773],{"xmlns":890},[892,74774,74775,74805],{},[895,74776,74777,74779,74781,74783,74785,74787,74789,74795,74797,74799],{},[898,74778,2818],{},[898,74780,3994],{},[898,74782,2774],{},[898,74784,8673],{},[1996,74786,1998],{},[898,74788,2818],{},[2272,74790,74791,74793],{},[898,74792,3937],{},[898,74794,9795],{},[898,74796,4674],{"mathvariant":2376},[898,74798,2818],{},[2272,74800,74801,74803],{},[898,74802,3937],{},[898,74804,9800],{},[902,74806,74807],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,74810,74812],{"className":74811},[886],[888,74813,74814],{"xmlns":890},[892,74815,74816,74824],{},[895,74817,74818,74820,74822],{},[898,74819,207],{},[1996,74821,2095],{},[898,74823,2098],{},[902,74825,74826],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,74829,74831],{"id":74830},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,74833,74834],{},"Po prostudování kapitoly 5 student umí:",[120,74836,74837,74843,74853,74859,74865,74870,74876,74886,74891,74897],{},[123,74838,74839,74840,2286],{},"popsat ",[38,74841,74842],{},"jednofaktorový model produkce",[123,74844,74845,74846,3885,74849,74852],{},"vypočítat ",[38,74847,74848],{},"mezní",[38,74850,74851],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,74854,74855,74856,2286],{},"charakterizovat průběh ",[38,74857,74858],{},"křivky produkce",[123,74860,74861,74862,2286],{},"formulovat ",[38,74863,74864],{},"princip maximalizace průměrného produktu práce",[123,74866,74839,74867,2286],{},[38,74868,74869],{},"dvoufaktorový model produkce",[123,74871,74872,74873,2286],{},"uvést tvar ",[38,74874,74875],{},"Cobb–Douglasových produkčních funkcí",[123,74877,74878,74879,1343,74881,1343,74883,2286],{},"vyložit, co jsou ",[38,74880,24615],{},[38,74882,13659],{},[38,74884,74885],{},"klesající výnosy z rozsahu",[123,74887,74845,74888,74852],{},[38,74889,74890],{},"mezní produkty práce a kapitálu",[123,74892,74893,74894,2286],{},"najít ",[38,74895,74896],{},"izokvanty",[123,74898,74845,74899,74902],{},[38,74900,74901],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,74904,74905,74906,74909,74910,74913,74914,2203,74917,1343,74930,2203,74933,3885,74946,74949,74950,74952,74953,1975],{},"Každý proces produkce je určován ",[38,74907,74908],{},"faktory"," (též ",[38,74911,74912],{},"vstupy",") produkce. K hlavním patří ",[38,74915,74916],{},"práce",[883,74918,74920],{"className":74919},[886],[888,74921,74922],{"xmlns":890},[892,74923,74924,74928],{},[895,74925,74926],{},[898,74927,9795],{},[902,74929,9795],{"encoding":904},[38,74931,74932],{},"kapitál",[883,74934,74936],{"className":74935},[886],[888,74937,74938],{"xmlns":890},[892,74939,74940,74944],{},[895,74941,74942],{},[898,74943,9800],{},[902,74945,9800],{"encoding":904},[38,74947,74948],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,74951,36966],{}," (produkce závisí jen na práci); v opačném případě o ",[38,74954,74669],{},[724,74956,74957,74958,1343,74961,74964],{},"Související matematický aparát: ",[207,74959,2357],{"className":74960,"dataFsResolvedFilePath":764,"href":765},[210],[207,74962,784],{"className":74963,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,74966,74968],{"id":74967},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,74970,74971,74972,74985,74986,74999,75000],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,74973,74975],{"className":74974},[886],[888,74976,74977],{"xmlns":890},[892,74978,74979,74983],{},[895,74980,74981],{},[898,74982,2789],{},[902,74984,2789],{"encoding":904}," na práci ",[883,74987,74989],{"className":74988},[886],[888,74990,74991],{"xmlns":890},[892,74992,74993,74997],{},[895,74994,74995],{},[898,74996,9795],{},[902,74998,9795],{"encoding":904}," vyjadřuje ",[38,75001,75002],{},"produkční funkce",[883,75004,75006],{"className":75005},[886],[888,75007,75008],{"xmlns":890,"display":28068},[892,75009,75010,75041],{},[20756,75011,75012],{"width":28073},[20761,75013,75014,75016,75034,75036],{},[20764,75015],{"width":28078},[20764,75017,75018],{},[895,75019,75020,75022,75024,75026,75028,75030,75032],{},[898,75021,2789],{},[1996,75023,1998],{},[898,75025,2789],{},[1996,75027,2005],{"stretchy":2004},[898,75029,9795],{},[1996,75031,2011],{"stretchy":2004},[1996,75033,2286],{"separator":2285},[20764,75035],{"width":28078},[20764,75037,75038],{},[2288,75039,75040],{},"(5.1)",[902,75042,75043],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,75045,75046,75047,10025,75050,75053,75054,75067],{},"jejíž graf se nazývá ",[38,75048,75049],{},"křivka produkce",[614,75051,75052],{},"production curve","). Práce ",[883,75055,75057],{"className":75056},[886],[888,75058,75059],{"xmlns":890},[892,75060,75061,75065],{},[895,75062,75063],{},[898,75064,9795],{},[902,75066,9795],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,75069,75071,75072,2011],{"id":75070},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,75073,75075],{"className":75074},[886],[888,75076,75077],{"xmlns":890},[892,75078,75079,75089],{},[895,75080,75081,75083],{},[898,75082,2818],{},[2272,75084,75085,75087],{},[898,75086,3937],{},[898,75088,9795],{},[902,75090,10045],{"encoding":904},[724,75092,75093,10025,75096,75099,75100,75119],{},[38,75094,75095],{},"Mezní produkt práce",[614,75097,75098],{},"marginal product of labour",") ",[883,75101,75103],{"className":75102},[886],[888,75104,75105],{"xmlns":890},[892,75106,75107,75117],{},[895,75108,75109,75111],{},[898,75110,2818],{},[2272,75112,75113,75115],{},[898,75114,3937],{},[898,75116,9795],{},[902,75118,10045],{"encoding":904}," je derivace produkce podle práce:",[883,75121,75123],{"className":75122},[886],[888,75124,75125],{"xmlns":890,"display":28068},[892,75126,75127,75184],{},[20756,75128,75129],{"width":28073},[20761,75130,75131,75133,75177,75179],{},[20764,75132],{"width":28078},[20764,75134,75135],{},[895,75136,75137,75139,75145,75147,75161,75163,75169,75171,75173,75175],{},[898,75138,2818],{},[2272,75140,75141,75143],{},[898,75142,3937],{},[898,75144,9795],{},[1996,75146,1998],{},[2329,75148,75149,75155],{},[895,75150,75151,75153],{},[898,75152,2194],{},[898,75154,2789],{},[895,75156,75157,75159],{},[898,75158,2194],{},[898,75160,9795],{},[1996,75162,1998],{},[2124,75164,75165,75167],{},[898,75166,2789],{},[1996,75168,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,75170,2005],{"stretchy":2004},[898,75172,9795],{},[1996,75174,2011],{"stretchy":2004},[898,75176,1975],{"mathvariant":2376},[20764,75178],{"width":28078},[20764,75180,75181],{},[2288,75182,75183],{},"(5.2)",[902,75185,75186],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,75188,75189,75190,19947,75208,75236,75237,75254,75255,2685,75272,3918],{},"Pro pevnou hodnotu ",[883,75191,75193],{"className":75192},[886],[888,75194,75195],{"xmlns":890},[892,75196,75197,75205],{},[895,75198,75199],{},[2124,75200,75201,75203],{},[898,75202,9795],{},[1996,75204,4354],{},[902,75206,75207],{"encoding":904},"L^*",[883,75209,75211],{"className":75210},[886],[888,75212,75213],{"xmlns":890},[892,75214,75215,75233],{},[895,75216,75217,75223,75225,75231],{},[2124,75218,75219,75221],{},[898,75220,2789],{},[1996,75222,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,75224,2005],{"stretchy":2004},[2124,75226,75227,75229],{},[898,75228,9795],{},[1996,75230,4354],{},[1996,75232,2011],{"stretchy":2004},[902,75234,75235],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,75238,75240],{"className":75239},[886],[888,75241,75242],{"xmlns":890},[892,75243,75244,75252],{},[895,75245,75246],{},[2124,75247,75248,75250],{},[898,75249,9795],{},[1996,75251,4354],{},[902,75253,75207],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,75256,75258],{"className":75257},[886],[888,75259,75260],{"xmlns":890},[892,75261,75262,75270],{},[895,75263,75264],{},[2124,75265,75266,75268],{},[898,75267,9795],{},[1996,75269,4354],{},[902,75271,75207],{"encoding":904},[883,75273,75275],{"className":75274},[886],[888,75276,75277],{"xmlns":890},[892,75278,75279,75291],{},[895,75280,75281,75287,75289],{},[2124,75282,75283,75285],{},[898,75284,9795],{},[1996,75286,4354],{},[1996,75288,2095],{},[2129,75290,2278],{},[902,75292,75293],{"encoding":904},"L^*+1",[3867,75295,75296],{},[724,75297,75298,18025,75300,75319,75320,75323,75324,1975],{},[883,75299,4155],{},[883,75301,75303],{"className":75302},[886],[888,75304,75305],{"xmlns":890},[892,75306,75307,75317],{},[895,75308,75309,75311],{},[898,75310,2818],{},[2272,75312,75313,75315],{},[898,75314,3937],{},[898,75316,9795],{},[902,75318,10045],{"encoding":904}," odpovídá na otázku „",[38,75321,75322],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,75325,75327],{"className":75326},[886],[888,75328,75329],{"xmlns":890},[892,75330,75331,75335],{},[895,75332,75333],{},[898,75334,9795],{},[902,75336,9795],{"encoding":904},[724,75338,75339,75342,75343,75359,75360,2685,75373,75393],{},[38,75340,75341],{},"Přibližná změna produkce"," pro změnu práce o ",[883,75344,75346],{"className":75345},[886],[888,75347,75348],{"xmlns":890},[892,75349,75350,75356],{},[895,75351,75352,75354],{},[898,75353,2194],{},[898,75355,9795],{},[902,75357,75358],{"encoding":904},"dL"," (z ",[883,75361,75363],{"className":75362},[886],[888,75364,75365],{"xmlns":890},[892,75366,75367,75371],{},[895,75368,75369],{},[898,75370,9795],{},[902,75372,9795],{"encoding":904},[883,75374,75376],{"className":75375},[886],[888,75377,75378],{"xmlns":890},[892,75379,75380,75390],{},[895,75381,75382,75384,75386,75388],{},[898,75383,9795],{},[1996,75385,2095],{},[898,75387,2194],{},[898,75389,9795],{},[902,75391,75392],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,75395,75397],{"className":75396},[886],[888,75398,75399],{"xmlns":890,"display":28068},[892,75400,75401,75466],{},[20756,75402,75403],{"width":28073},[20761,75404,75405,75407,75459,75461],{},[20764,75406],{"width":28078},[20764,75408,75409],{},[895,75410,75411,75413,75415,75417,75419,75421,75423,75429,75431,75433,75435,75437,75439,75441,75443,75445,75451,75453,75455,75457],{},[898,75412,2889],{"mathvariant":2376},[898,75414,2789],{},[1996,75416,2730],{},[898,75418,2194],{},[898,75420,2789],{},[1996,75422,1998],{},[2124,75424,75425,75427],{},[898,75426,2789],{},[1996,75428,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,75430,2005],{"stretchy":2004},[898,75432,9795],{},[1996,75434,2011],{"stretchy":2004},[2288,75436,2987],{},[898,75438,2194],{},[898,75440,9795],{},[1996,75442,1998],{},[898,75444,2818],{},[2272,75446,75447,75449],{},[898,75448,3937],{},[898,75450,9795],{},[2288,75452,2987],{},[898,75454,2194],{},[898,75456,9795],{},[898,75458,1975],{"mathvariant":2376},[20764,75460],{"width":28078},[20764,75462,75463],{},[2288,75464,75465],{},"(5.3)",[902,75467,75468],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,75470,75471,75472,1975],{},"Skutečná změna je ",[883,75473,75475],{"className":75474},[886],[888,75476,75477],{"xmlns":890},[892,75478,75479,75511],{},[895,75480,75481,75483,75485,75487,75489,75491,75493,75495,75497,75499,75501,75503,75505,75507,75509],{},[898,75482,2889],{"mathvariant":2376},[898,75484,2789],{},[1996,75486,1998],{},[898,75488,2789],{},[1996,75490,2005],{"stretchy":2004},[898,75492,9795],{},[1996,75494,2095],{},[898,75496,2194],{},[898,75498,9795],{},[1996,75500,2011],{"stretchy":2004},[1996,75502,2225],{},[898,75504,2789],{},[1996,75506,2005],{"stretchy":2004},[898,75508,9795],{},[1996,75510,2011],{"stretchy":2004},[902,75512,75513],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,75515,75517],{"id":75516},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,75519,75520,10025,75523,3151],{},[38,75521,75522],{},"Zákon klesajících výnosů",[614,75524,75525],{},"law of diminishing marginal productivity",[3867,75527,75528],{},[724,75529,75530,75531,75533],{},"Roste-li postupně některý ze vstupů (",[614,75532,36962],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,75535,75536],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,75538,75539,75540,2203,75561,75580,75581,75631,75632,75634,75635,2203,75655,75674,75675,75631,75707,2927,75709,75728,75729,21596,75746,75780,75781,8102,75798,75801],{},"1° ",[38,75541,75542,75543,2704],{},"Do bodu ",[883,75544,75546],{"className":75545},[886],[888,75547,75548],{"xmlns":890},[892,75549,75550,75558],{},[895,75551,75552],{},[2272,75553,75554,75556],{},[898,75555,9795],{},[2129,75557,2327],{},[902,75559,75560],{"encoding":904},"L_0",[883,75562,75564],{"className":75563},[886],[888,75565,75566],{"xmlns":890},[892,75567,75568,75578],{},[895,75569,75570,75572],{},[898,75571,2818],{},[2272,75573,75574,75576],{},[898,75575,3937],{},[898,75577,9795],{},[902,75579,10045],{"encoding":904}," roste, tj. ",[883,75582,75584],{"className":75583},[886],[888,75585,75586],{"xmlns":890},[892,75587,75588,75628],{},[895,75589,75590,75592,75594,75600,75606,75608,75618,75620,75622,75624,75626],{},[1996,75591,2005],{"stretchy":2004},[898,75593,2818],{},[2272,75595,75596,75598],{},[898,75597,3937],{},[898,75599,9795],{},[2124,75601,75602,75604],{},[1996,75603,2011],{"stretchy":2004},[1996,75605,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,75607,1998],{},[2124,75609,75610,75612],{},[898,75611,2789],{},[895,75613,75614,75616],{},[1996,75615,2378],{"mathvariant":2376},[1996,75617,2378],{"mathvariant":2376},[1996,75619,2005],{"stretchy":2004},[898,75621,9795],{},[1996,75623,2011],{"stretchy":2004},[1996,75625,3408],{},[2129,75627,2327],{},[902,75629,75630],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,75633,37666],{},".\n2° ",[38,75636,75637,75638,2704],{},"Od bodu ",[883,75639,75641],{"className":75640},[886],[888,75642,75643],{"xmlns":890},[892,75644,75645,75653],{},[895,75646,75647],{},[2272,75648,75649,75651],{},[898,75650,9795],{},[2129,75652,2327],{},[902,75654,75560],{"encoding":904},[883,75656,75658],{"className":75657},[886],[888,75659,75660],{"xmlns":890},[892,75661,75662,75672],{},[895,75663,75664,75666],{},[898,75665,2818],{},[2272,75667,75668,75670],{},[898,75669,3937],{},[898,75671,9795],{},[902,75673,10045],{"encoding":904}," klesá, ",[883,75676,75678],{"className":75677},[886],[888,75679,75680],{"xmlns":890},[892,75681,75682,75704],{},[895,75683,75684,75694,75696,75698,75700,75702],{},[2124,75685,75686,75688],{},[898,75687,2789],{},[895,75689,75690,75692],{},[1996,75691,2378],{"mathvariant":2376},[1996,75693,2378],{"mathvariant":2376},[1996,75695,2005],{"stretchy":2004},[898,75697,9795],{},[1996,75699,2011],{"stretchy":2004},[1996,75701,3447],{},[2129,75703,2327],{},[902,75705,75706],{"encoding":904},"Q''(L) \u003C 0",[38,75708,38490],{},[883,75710,75712],{"className":75711},[886],[888,75713,75714],{"xmlns":890},[892,75715,75716,75726],{},[895,75717,75718,75720],{},[898,75719,2818],{},[2272,75721,75722,75724],{},[898,75723,3937],{},[898,75725,9795],{},[902,75727,10045],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,75730,75732],{"className":75731},[886],[888,75733,75734],{"xmlns":890},[892,75735,75736,75744],{},[895,75737,75738],{},[2272,75739,75740,75742],{},[898,75741,9795],{},[2129,75743,2278],{},[902,75745,13214],{"encoding":904},[883,75747,75749],{"className":75748},[886],[888,75750,75751],{"xmlns":890},[892,75752,75753,75777],{},[895,75754,75755,75757,75763,75765,75771,75773,75775],{},[898,75756,2818],{},[2272,75758,75759,75761],{},[898,75760,3937],{},[898,75762,9795],{},[1996,75764,2005],{"stretchy":2004},[2272,75766,75767,75769],{},[898,75768,9795],{},[2129,75770,2278],{},[1996,75772,2011],{"stretchy":2004},[1996,75774,1998],{},[2129,75776,2327],{},[902,75778,75779],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,75782,75784],{"className":75783},[886],[888,75785,75786],{"xmlns":890},[892,75787,75788,75796],{},[895,75789,75790],{},[2272,75791,75792,75794],{},[898,75793,9795],{},[2129,75795,2327],{},[902,75797,75560],{"encoding":904},[38,75799,75800],{},"inflexním bodem"," produkční funkce.",[724,75803,75804,75805,10394,75822,1975],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,75806,75808],{"className":75807},[886],[888,75809,75810],{"xmlns":890},[892,75811,75812,75820],{},[895,75813,75814],{},[2272,75815,75816,75818],{},[898,75817,9795],{},[2129,75819,2327],{},[902,75821,75560],{"encoding":904},[883,75823,75825],{"className":75824},[886],[888,75826,75827],{"xmlns":890},[892,75828,75829,75851],{},[895,75830,75831,75841,75843,75845,75847,75849],{},[2124,75832,75833,75835],{},[898,75834,2789],{},[895,75836,75837,75839],{},[1996,75838,2378],{"mathvariant":2376},[1996,75840,2378],{"mathvariant":2376},[1996,75842,2005],{"stretchy":2004},[898,75844,9795],{},[1996,75846,2011],{"stretchy":2004},[1996,75848,3447],{},[2129,75850,2327],{},[902,75852,75706],{"encoding":904},[724,75854,75855,2203,75858,5669,75898,1343,75915,75932],{},[38,75856,75857],{},"Typický polynom třetího stupně:",[883,75859,75861],{"className":75860},[886],[888,75862,75863],{"xmlns":890},[892,75864,75865,75895],{},[895,75866,75867,75869,75871,75873,75875,75877,75879,75885,75887,75889],{},[898,75868,2789],{},[1996,75870,2005],{"stretchy":2004},[898,75872,9795],{},[1996,75874,2011],{"stretchy":2004},[1996,75876,1998],{},[898,75878,207],{},[2124,75880,75881,75883],{},[898,75882,9795],{},[2129,75884,2173],{},[1996,75886,2095],{},[898,75888,2098],{},[2124,75890,75891,75893],{},[898,75892,9795],{},[2129,75894,2131],{},[902,75896,75897],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,75899,75901],{"className":75900},[886],[888,75902,75903],{"xmlns":890},[892,75904,75905,75913],{},[895,75906,75907,75909,75911],{},[898,75908,207],{},[1996,75910,3447],{},[2129,75912,2327],{},[902,75914,43087],{"encoding":904},[883,75916,75918],{"className":75917},[886],[888,75919,75920],{"xmlns":890},[892,75921,75922,75930],{},[895,75923,75924,75926,75928],{},[898,75925,2098],{},[1996,75927,3408],{},[2129,75929,2327],{},[902,75931,18816],{"encoding":904},". Pak",[883,75934,75936],{"className":75935},[886],[888,75937,75938],{"xmlns":890,"display":28068},[892,75939,75940,76000],{},[895,75941,75942,75948,75950,75952,75960,75968,75970,75972,75978,75980,75982,75990,75998],{},[2272,75943,75944,75946],{},[898,75945,9795],{},[2129,75947,2327],{},[1996,75949,1998],{},[1996,75951,2225],{},[2325,75953,75954],{"scriptlevel":2327,"displaystyle":2004},[2329,75955,75956,75958],{},[2129,75957,2278],{},[2129,75959,2173],{},[2325,75961,75962],{"scriptlevel":2327,"displaystyle":2004},[2329,75963,75964,75966],{},[898,75965,2098],{},[898,75967,207],{},[1996,75969,2286],{"separator":2285},[5878,75971],{"width":5880},[2272,75973,75974,75976],{},[898,75975,9795],{},[2129,75977,2278],{},[1996,75979,1998],{},[1996,75981,2225],{},[2325,75983,75984],{"scriptlevel":2327,"displaystyle":2004},[2329,75985,75986,75988],{},[2129,75987,2131],{},[2129,75989,2173],{},[2325,75991,75992],{"scriptlevel":2327,"displaystyle":2004},[2329,75993,75994,75996],{},[898,75995,2098],{},[898,75997,207],{},[898,75999,1975],{"mathvariant":2376},[902,76001,76002],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,76004,76006,76007,2011],{"id":76005},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,76008,76010],{"className":76009},[886],[888,76011,76012],{"xmlns":890},[892,76013,76014,76024],{},[895,76015,76016,76018],{},[898,76017,4255],{},[2272,76019,76020,76022],{},[898,76021,3937],{},[898,76023,9795],{},[902,76025,74635],{"encoding":904},[724,76027,76028,10025,76031,75099,76034,76053],{},[38,76029,76030],{},"Průměrný produkt práce",[614,76032,76033],{},"average product of labour",[883,76035,76037],{"className":76036},[886],[888,76038,76039],{"xmlns":890},[892,76040,76041,76051],{},[895,76042,76043,76045],{},[898,76044,4255],{},[2272,76046,76047,76049],{},[898,76048,3937],{},[898,76050,9795],{},[902,76052,74635],{"encoding":904}," je podíl produkce a práce:",[883,76055,76057],{"className":76056},[886],[888,76058,76059],{"xmlns":890,"display":28068},[892,76060,76061,76096],{},[20756,76062,76063],{"width":28073},[20761,76064,76065,76067,76089,76091],{},[20764,76066],{"width":28078},[20764,76068,76069],{},[895,76070,76071,76073,76079,76081,76087],{},[898,76072,4255],{},[2272,76074,76075,76077],{},[898,76076,3937],{},[898,76078,9795],{},[1996,76080,1998],{},[2329,76082,76083,76085],{},[898,76084,2789],{},[898,76086,9795],{},[898,76088,1975],{"mathvariant":2376},[20764,76090],{"width":28078},[20764,76092,76093],{},[2288,76094,76095],{},"(5.4)",[902,76097,76098],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,76100,76101,76102,1975],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,76103,76105],{"className":76104},[886],[888,76106,76107],{"xmlns":890},[892,76108,76109,76119],{},[895,76110,76111,76113],{},[898,76112,4255],{},[2272,76114,76115,76117],{},[898,76116,3937],{},[898,76118,9795],{},[902,76120,74635],{"encoding":904},[115,76122,76124],{"id":76123},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,76126,76127],{},[2559,76128],{"alt":76129,"className":76130,"src":76131},"imek-q-mpl-apl-tripanel",[210,2563],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[3867,76133,76134],{},[724,76135,76136,76139,76140,2624,76159,76176,76177],{},[38,76137,76138],{},"Princip:"," Má-li ",[883,76141,76143],{"className":76142},[886],[888,76144,76145],{"xmlns":890},[892,76146,76147,76157],{},[895,76148,76149,76151],{},[898,76150,4255],{},[2272,76152,76153,76155],{},[898,76154,3937],{},[898,76156,9795],{},[902,76158,74635],{"encoding":904},[883,76160,76162],{"className":76161},[886],[888,76163,76164],{"xmlns":890},[892,76165,76166,76174],{},[895,76167,76168],{},[2272,76169,76170,76172],{},[898,76171,9795],{},[2129,76173,2327],{},[902,76175,75560],{"encoding":904}," maximum, pak platí\n",[883,76178,76180],{"className":76179,"title":4200,"style":4201},[4199],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,76182,76183,76184,76187,76188,2203,76192,1975],{},"Slovně: ",[38,76185,76186],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,76189,76191],{"className":76190,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,76193,76195],{"className":76194},[886],[888,76196,76197],{"xmlns":890},[892,76198,76199,76205],{},[895,76200,76201,76203],{},[898,76202,4255],{},[898,76204,2777],{},[902,76206,55562],{"encoding":904},[3867,76208,76209,76233],{},[724,76210,76211,76213,76214],{},[883,76212,4572],{}," Postup — jak najít max ",[883,76215,76217],{"className":76216},[886],[888,76218,76219],{"xmlns":890},[892,76220,76221,76231],{},[895,76222,76223,76225],{},[898,76224,4255],{},[2272,76226,76227,76229],{},[898,76228,3937],{},[898,76230,9795],{},[902,76232,74635],{"encoding":904},[152,76234,76235,76273,76355],{},[123,76236,76237,76238,76272],{},"Napište ",[883,76239,76241],{"className":76240},[886],[888,76242,76243],{"xmlns":890},[892,76244,76245,76269],{},[895,76246,76247,76249,76255,76257,76259,76261,76263,76265,76267],{},[898,76248,4255],{},[2272,76250,76251,76253],{},[898,76252,3937],{},[898,76254,9795],{},[1996,76256,1998],{},[898,76258,2789],{},[1996,76260,2005],{"stretchy":2004},[898,76262,9795],{},[1996,76264,2011],{"stretchy":2004},[898,76266,4674],{"mathvariant":2376},[898,76268,9795],{},[902,76270,76271],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,76274,76275,76276,76308,76309,76312,76313,1975],{},"Položte ",[883,76277,76279],{"className":76278},[886],[888,76280,76281],{"xmlns":890},[892,76282,76283,76305],{},[895,76284,76285,76287,76289,76295,76301,76303],{},[1996,76286,2005],{"stretchy":2004},[898,76288,4255],{},[2272,76290,76291,76293],{},[898,76292,3937],{},[898,76294,9795],{},[2124,76296,76297,76299],{},[1996,76298,2011],{"stretchy":2004},[1996,76300,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,76302,1998],{},[2129,76304,2327],{},[902,76306,76307],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,76310,76311],{},"Zkratka:"," můžete rovnou řešit ",[883,76314,76316],{"className":76315},[886],[888,76317,76318],{"xmlns":890},[892,76319,76320,76352],{},[895,76321,76322,76324,76330,76332,76334,76336,76338,76340,76346,76348,76350],{},[898,76323,2818],{},[2272,76325,76326,76328],{},[898,76327,3937],{},[898,76329,9795],{},[1996,76331,2005],{"stretchy":2004},[898,76333,9795],{},[1996,76335,2011],{"stretchy":2004},[1996,76337,1998],{},[898,76339,4255],{},[2272,76341,76342,76344],{},[898,76343,3937],{},[898,76345,9795],{},[1996,76347,2005],{"stretchy":2004},[898,76349,9795],{},[1996,76351,2011],{"stretchy":2004},[902,76353,76354],{"encoding":904},"MP_L(L) = AP_L(L)",[123,76356,76357],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,76359,65503],{"id":76360},"odvození",[724,76362,76363,76364,76397],{},"Z ",[883,76365,76367],{"className":76366},[886],[888,76368,76369],{"xmlns":890},[892,76370,76371,76395],{},[895,76372,76373,76375,76381,76383,76385,76387,76389,76391,76393],{},[898,76374,4255],{},[2272,76376,76377,76379],{},[898,76378,3937],{},[898,76380,9795],{},[1996,76382,1998],{},[898,76384,2789],{},[1996,76386,2005],{"stretchy":2004},[898,76388,9795],{},[1996,76390,2011],{"stretchy":2004},[898,76392,4674],{"mathvariant":2376},[898,76394,9795],{},[902,76396,76271],{"encoding":904}," a derivace podílu:",[883,76399,76401],{"className":76400},[886],[888,76402,76403],{"xmlns":890,"display":28068},[892,76404,76405,76558],{},[895,76406,76407,76409,76411,76417,76423,76425,76427,76429,76431,76471,76473,76479,76513,76515,76521,76524,76526,76532,76534,76536,76538,76540,76542,76548,76550,76552,76554,76556],{},[1996,76408,2005],{"stretchy":2004},[898,76410,4255],{},[2272,76412,76413,76415],{},[898,76414,3937],{},[898,76416,9795],{},[2124,76418,76419,76421],{},[1996,76420,2011],{"stretchy":2004},[1996,76422,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,76424,2005],{"stretchy":2004},[898,76426,9795],{},[1996,76428,2011],{"stretchy":2004},[1996,76430,1998],{},[2329,76432,76433,76465],{},[895,76434,76435,76441,76443,76445,76447,76449,76451,76453,76455,76457,76459,76461,76463],{},[2124,76436,76437,76439],{},[898,76438,2789],{},[1996,76440,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,76442,2005],{"stretchy":2004},[898,76444,9795],{},[1996,76446,2011],{"stretchy":2004},[1996,76448,3177],{},[898,76450,9795],{},[1996,76452,2225],{},[898,76454,2789],{},[1996,76456,2005],{"stretchy":2004},[898,76458,9795],{},[1996,76460,2011],{"stretchy":2004},[1996,76462,3177],{},[2129,76464,2278],{},[2124,76466,76467,76469],{},[898,76468,9795],{},[2129,76470,2131],{},[1996,76472,1998],{},[2329,76474,76475,76477],{},[2129,76476,2278],{},[898,76478,9795],{},[895,76480,76481,76483,76489,76491,76493,76495,76497,76511],{},[1996,76482,2005],{"fence":2285},[2124,76484,76485,76487],{},[898,76486,2789],{},[1996,76488,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,76490,2005],{"stretchy":2004},[898,76492,9795],{},[1996,76494,2011],{"stretchy":2004},[1996,76496,2225],{},[2329,76498,76499,76509],{},[895,76500,76501,76503,76505,76507],{},[898,76502,2789],{},[1996,76504,2005],{"stretchy":2004},[898,76506,9795],{},[1996,76508,2011],{"stretchy":2004},[898,76510,9795],{},[1996,76512,2011],{"fence":2285},[1996,76514,1998],{},[2329,76516,76517,76519],{},[2129,76518,2278],{},[898,76520,9795],{},[1996,76522,2005],{"fence":2285,"stretchy":2285,"minsize":76523,"maxsize":76523},"1.2em",[898,76525,2818],{},[2272,76527,76528,76530],{},[898,76529,3937],{},[898,76531,9795],{},[1996,76533,2005],{"stretchy":2004},[898,76535,9795],{},[1996,76537,2011],{"stretchy":2004},[1996,76539,2225],{},[898,76541,4255],{},[2272,76543,76544,76546],{},[898,76545,3937],{},[898,76547,9795],{},[1996,76549,2005],{"stretchy":2004},[898,76551,9795],{},[1996,76553,2011],{"stretchy":2004},[1996,76555,2011],{"fence":2285,"stretchy":2285,"minsize":76523,"maxsize":76523},[898,76557,1975],{"mathvariant":2376},[902,76559,76560],{"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).",[724,76562,9663,76563,8102,76585,76668],{},[883,76564,76566],{"className":76565},[886],[888,76567,76568],{"xmlns":890},[892,76569,76570,76582],{},[895,76571,76572,76578,76580],{},[2272,76573,76574,76576],{},[898,76575,9795],{},[2129,76577,2327],{},[1996,76579,3408],{},[2129,76581,2327],{},[902,76583,76584],{"encoding":904},"L_0 > 0",[883,76586,76588],{"className":76587},[886],[888,76589,76590],{"xmlns":890},[892,76591,76592,76665],{},[895,76593,76594,76596,76598,76604,76610,76612,76618,76620,76622,76624,76627,76629,76635,76637,76643,76645,76647,76649,76655,76657,76663],{},[1996,76595,2005],{"stretchy":2004},[898,76597,4255],{},[2272,76599,76600,76602],{},[898,76601,3937],{},[898,76603,9795],{},[2124,76605,76606,76608],{},[1996,76607,2011],{"stretchy":2004},[1996,76609,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,76611,2005],{"stretchy":2004},[2272,76613,76614,76616],{},[898,76615,9795],{},[2129,76617,2327],{},[1996,76619,2011],{"stretchy":2004},[1996,76621,1998],{},[2129,76623,2327],{},[1996,76625,76626],{},"⇔",[898,76628,2818],{},[2272,76630,76631,76633],{},[898,76632,3937],{},[898,76634,9795],{},[1996,76636,2005],{"stretchy":2004},[2272,76638,76639,76641],{},[898,76640,9795],{},[2129,76642,2327],{},[1996,76644,2011],{"stretchy":2004},[1996,76646,1998],{},[898,76648,4255],{},[2272,76650,76651,76653],{},[898,76652,3937],{},[898,76654,9795],{},[1996,76656,2005],{"stretchy":2004},[2272,76658,76659,76661],{},[898,76660,9795],{},[2129,76662,2327],{},[1996,76664,2011],{"stretchy":2004},[902,76666,76667],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,76670,76672],{"id":76671},"příklad-51","Příklad 5.1",[724,76674,76675,76676,1975],{},"Je dána produkce ",[883,76677,76679],{"className":76678},[886],[888,76680,76681],{"xmlns":890},[892,76682,76683,76707],{},[895,76684,76685,76687,76689,76691,76697,76699,76701],{},[898,76686,2789],{},[1996,76688,1998],{},[2129,76690,2235],{},[2124,76692,76693,76695],{},[898,76694,9795],{},[2129,76696,2131],{},[1996,76698,2225],{},[2129,76700,2839],{},[2124,76702,76703,76705],{},[898,76704,9795],{},[2129,76706,2173],{},[902,76708,76709],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,76711,76712,57524,76715,76765,76766,1975],{},[38,76713,76714],{},"(a)",[883,76716,76718],{"className":76717},[886],[888,76719,76720],{"xmlns":890},[892,76721,76722,76762],{},[895,76723,76724,76726,76728,76730,76732,76734,76736,76738,76740,76742,76744,76746,76748,76750,76752,76754,76756,76758,76760],{},[898,76725,9795],{},[1996,76727,1998],{},[2129,76729,2131],{},[1996,76731,2286],{"separator":2285},[2129,76733,2228],{},[1996,76735,2286],{"separator":2285},[2129,76737,5585],{},[1996,76739,2286],{"separator":2285},[2129,76741,2863],{},[1996,76743,2286],{"separator":2285},[2129,76745,22948],{},[1996,76747,2286],{"separator":2285},[2129,76749,3707],{},[1996,76751,2286],{"separator":2285},[2129,76753,9035],{},[1996,76755,2286],{"separator":2285},[2129,76757,38348],{},[1996,76759,2286],{"separator":2285},[2129,76761,5004],{},[902,76763,76764],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,76767,76769],{"className":76768},[886],[888,76770,76771],{"xmlns":890},[892,76772,76773,76783],{},[895,76774,76775,76777],{},[898,76776,2818],{},[2272,76778,76779,76781],{},[898,76780,3937],{},[898,76782,9795],{},[902,76784,10045],{"encoding":904},[724,76786,76787,76788,34970],{},"Podle (5.2): ",[883,76789,76791],{"className":76790},[886],[888,76792,76793],{"xmlns":890},[892,76794,76795,76851],{},[895,76796,76797,76799,76805,76807,76813,76815,76817,76819,76821,76823,76825,76827,76829,76835,76837,76839,76841,76843,76845,76847,76849],{},[898,76798,2818],{},[2272,76800,76801,76803],{},[898,76802,3937],{},[898,76804,9795],{},[1996,76806,1998],{},[2124,76808,76809,76811],{},[898,76810,2789],{},[1996,76812,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,76814,2005],{"stretchy":2004},[898,76816,9795],{},[1996,76818,2011],{"stretchy":2004},[1996,76820,1998],{},[2129,76822,3509],{},[898,76824,9795],{},[1996,76826,2225],{},[2129,76828,19323],{},[2124,76830,76831,76833],{},[898,76832,9795],{},[2129,76834,2131],{},[1996,76836,1998],{},[898,76838,9795],{},[1996,76840,2005],{"stretchy":2004},[2129,76842,3509],{},[1996,76844,2225],{},[2129,76846,19323],{},[898,76848,9795],{},[1996,76850,2011],{"stretchy":2004},[902,76852,76853],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,76855,76856,76893],{},[19,76857,76858],{},[22,76859,76860,76875,76877,76879,76881,76883,76885,76887,76889,76891],{},[25,76861,76862],{},[883,76863,76865],{"className":76864},[886],[888,76866,76867],{"xmlns":890},[892,76868,76869,76873],{},[895,76870,76871],{},[898,76872,9795],{},[902,76874,9795],{"encoding":904},[25,76876,2131],{},[25,76878,2228],{},[25,76880,5585],{},[25,76882,2863],{},[25,76884,22948],{},[25,76886,3707],{},[25,76888,9035],{},[25,76890,38348],{},[25,76892,5004],{},[30,76894,76895],{},[22,76896,76897,76918,76921,76924,76927,76929,76932,76934,76936,76955],{},[35,76898,76899],{},[883,76900,76902],{"className":76901},[886],[888,76903,76904],{"xmlns":890},[892,76905,76906,76916],{},[895,76907,76908,76910],{},[898,76909,2818],{},[2272,76911,76912,76914],{},[898,76913,3937],{},[898,76915,9795],{},[902,76917,10045],{"encoding":904},[35,76919,76920],{},"21,6",[35,76922,76923],{},"45",[35,76925,76926],{},"57,6",[35,76928,3126],{},[35,76930,76931],{},"50,4",[35,76933,76920],{},[35,76935,2327],{},[35,76937,76938],{},[883,76939,76941],{"className":76940},[886],[888,76942,76943],{"xmlns":890},[892,76944,76945,76952],{},[895,76946,76947,76949],{},[1996,76948,2225],{},[2129,76950,76951],{},"12,6",[902,76953,76954],{"encoding":904},"-12{,}6",[35,76956,76957],{},[883,76958,76960],{"className":76959},[886],[888,76961,76962],{"xmlns":890},[892,76963,76964,76970],{},[895,76965,76966,76968],{},[1996,76967,2225],{},[2129,76969,45454],{},[902,76971,76972],{"encoding":904},"-75",[724,76974,76975,76994,76995,77013,77014,77031,77032,77050,77051,77075,77076,77094],{},[883,76976,76978],{"className":76977},[886],[888,76979,76980],{"xmlns":890},[892,76981,76982,76992],{},[895,76983,76984,76986],{},[898,76985,2818],{},[2272,76987,76988,76990],{},[898,76989,3937],{},[898,76991,9795],{},[902,76993,10045],{"encoding":904}," nabývá maxima pro ",[883,76996,76998],{"className":76997},[886],[888,76999,77000],{"xmlns":890},[892,77001,77002,77010],{},[895,77003,77004,77006,77008],{},[898,77005,9795],{},[1996,77007,1998],{},[2129,77009,2863],{},[902,77011,77012],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,77015,77017],{"className":77016},[886],[888,77018,77019],{"xmlns":890},[892,77020,77021,77029],{},[895,77022,77023,77025,77027],{},[898,77024,9795],{},[1996,77026,1998],{},[2129,77028,2863],{},[902,77030,77012],{"encoding":904}," přírůstky klesají, v ",[883,77033,77035],{"className":77034},[886],[888,77036,77037],{"xmlns":890},[892,77038,77039,77047],{},[895,77040,77041,77043,77045],{},[898,77042,9795],{},[1996,77044,1998],{},[2129,77046,9035],{},[902,77048,77049],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,77052,77054],{"className":77053},[886],[888,77055,77056],{"xmlns":890},[892,77057,77058,77072],{},[895,77059,77060,77062,77064,77066,77068,77070],{},[898,77061,2789],{},[1996,77063,2005],{"stretchy":2004},[2129,77065,9035],{},[1996,77067,2011],{"stretchy":2004},[1996,77069,1998],{},[2129,77071,23860],{},[902,77073,77074],{"encoding":904},"Q(20) = 800","), od ",[883,77077,77079],{"className":77078},[886],[888,77080,77081],{"xmlns":890},[892,77082,77083,77091],{},[895,77084,77085,77087,77089],{},[898,77086,9795],{},[1996,77088,3408],{},[2129,77090,9035],{},[902,77092,77093],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,77096,77097],{},[614,77098,77099,77100,77140,77141,2624,77159,1975],{},"Obrázek 5.1 — graf produkce ",[883,77101,77103],{"className":77102},[886],[888,77104,77105],{"xmlns":890},[892,77106,77107,77137],{},[895,77108,77109,77111,77113,77115,77117,77119,77121,77127,77129,77131],{},[898,77110,2789],{},[1996,77112,2005],{"stretchy":2004},[898,77114,9795],{},[1996,77116,2011],{"stretchy":2004},[1996,77118,1998],{},[2129,77120,2235],{},[2124,77122,77123,77125],{},[898,77124,9795],{},[2129,77126,2131],{},[1996,77128,2225],{},[2129,77130,2839],{},[2124,77132,77133,77135],{},[898,77134,9795],{},[2129,77136,2173],{},[902,77138,77139],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,77142,77144],{"className":77143},[886],[888,77145,77146],{"xmlns":890},[892,77147,77148,77156],{},[895,77149,77150,77152,77154],{},[898,77151,2789],{},[1996,77153,1998],{},[2129,77155,23860],{},[902,77157,77158],{"encoding":904},"Q = 800",[883,77160,77162],{"className":77161},[886],[888,77163,77164],{"xmlns":890},[892,77165,77166,77174],{},[895,77167,77168,77170,77172],{},[898,77169,9795],{},[1996,77171,1998],{},[2129,77173,9035],{},[902,77175,77049],{"encoding":904},[724,77177,77178,77181],{},[38,77179,77180],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,77183,77184,77185,1343,77203,2704],{},"Podle (5.3) s ",[883,77186,77188],{"className":77187},[886],[888,77189,77190],{"xmlns":890},[892,77191,77192,77200],{},[895,77193,77194,77196,77198],{},[898,77195,9795],{},[1996,77197,1998],{},[2129,77199,2235],{},[902,77201,77202],{"encoding":904},"L = 6",[883,77204,77206],{"className":77205},[886],[888,77207,77208],{"xmlns":890},[892,77209,77210,77220],{},[895,77211,77212,77214,77216,77218],{},[898,77213,2194],{},[898,77215,9795],{},[1996,77217,1998],{},[2129,77219,2173],{},[902,77221,77222],{"encoding":904},"dL = 3",[883,77224,77226],{"className":77225},[886],[888,77227,77228],{"xmlns":890,"display":28068},[892,77229,77230,77293],{},[895,77231,77232,77234,77236,77238,77240,77246,77248,77250,77252,77254,77256,77258,77260,77262,77264,77266,77268,77270,77272,77274,77276,77278,77280,77282,77284,77286,77288,77290],{},[898,77233,2194],{},[898,77235,2789],{},[1996,77237,1998],{},[898,77239,2818],{},[2272,77241,77242,77244],{},[898,77243,3937],{},[898,77245,9795],{},[1996,77247,2005],{"stretchy":2004},[2129,77249,2235],{},[1996,77251,2011],{"stretchy":2004},[1996,77253,3177],{},[2129,77255,2173],{},[1996,77257,1998],{},[1996,77259,2005],{"stretchy":2004},[2129,77261,3509],{},[1996,77263,3177],{},[2129,77265,2235],{},[1996,77267,2225],{},[2129,77269,19323],{},[1996,77271,3177],{},[2129,77273,5565],{},[1996,77275,2011],{"stretchy":2004},[1996,77277,3177],{},[2129,77279,2173],{},[1996,77281,1998],{},[2129,77283,76931],{},[1996,77285,3177],{},[2129,77287,2173],{},[1996,77289,1998],{},[2129,77291,77292],{},"151,2.",[902,77294,77295],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,77297,77298,77299,57754,77324,77338,77339,1975],{},"Produkce vzroste z ",[883,77300,77302],{"className":77301},[886],[888,77303,77304],{"xmlns":890},[892,77305,77306,77321],{},[895,77307,77308,77310,77312,77314,77316,77318],{},[898,77309,2789],{},[1996,77311,2005],{"stretchy":2004},[2129,77313,2235],{},[1996,77315,2011],{"stretchy":2004},[1996,77317,1998],{},[2129,77319,77320],{},"172,8",[902,77322,77323],{"encoding":904},"Q(6) = 172{,}8",[883,77325,77327],{"className":77326},[886],[888,77328,77329],{"xmlns":890},[892,77330,77331,77336],{},[895,77332,77333],{},[2129,77334,77335],{},"324",[902,77337,77335],{"encoding":904},". Skutečná hodnota: ",[883,77340,77342],{"className":77341},[886],[888,77343,77344],{"xmlns":890},[892,77345,77346,77386],{},[895,77347,77348,77350,77352,77354,77356,77358,77360,77362,77364,77366,77368,77370,77372,77374,77377,77379,77381,77383],{},[898,77349,2889],{"mathvariant":2376},[898,77351,2789],{},[1996,77353,1998],{},[898,77355,2789],{},[1996,77357,2005],{"stretchy":2004},[2129,77359,3999],{},[1996,77361,2011],{"stretchy":2004},[1996,77363,2225],{},[898,77365,2789],{},[1996,77367,2005],{"stretchy":2004},[2129,77369,2235],{},[1996,77371,2011],{"stretchy":2004},[1996,77373,1998],{},[2129,77375,77376],{},"340,2",[1996,77378,2225],{},[2129,77380,77320],{},[1996,77382,1998],{},[2129,77384,77385],{},"167,4",[902,77387,77388],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,77390,77392],{"id":77391},"příklad-52","Příklad 5.2",[724,77394,77395,77396,1975],{},"Ověříme princip (5.5) pro ",[883,77397,77399],{"className":77398},[886],[888,77400,77401],{"xmlns":890},[892,77402,77403,77427],{},[895,77404,77405,77407,77409,77411,77417,77419,77421],{},[898,77406,2789],{},[1996,77408,1998],{},[2129,77410,2235],{},[2124,77412,77413,77415],{},[898,77414,9795],{},[2129,77416,2131],{},[1996,77418,2225],{},[2129,77420,2839],{},[2124,77422,77423,77425],{},[898,77424,9795],{},[2129,77426,2173],{},[902,77428,76709],{"encoding":904},[883,77430,77432],{"className":77431},[886],[888,77433,77434],{"xmlns":890,"display":28068},[892,77435,77436,77514],{},[895,77437,77438,77440,77446,77448,77454,77456,77458,77460,77462,77464,77470,77472,77474,77476,77484,77486,77488,77490,77492,77494,77496,77498,77500,77502,77504,77510,77512],{},[898,77439,4255],{},[2272,77441,77442,77444],{},[898,77443,3937],{},[898,77445,9795],{},[1996,77447,1998],{},[2329,77449,77450,77452],{},[898,77451,2789],{},[898,77453,9795],{},[1996,77455,1998],{},[2129,77457,2235],{},[898,77459,9795],{},[1996,77461,2225],{},[2129,77463,2839],{},[2124,77465,77466,77468],{},[898,77467,9795],{},[2129,77469,2131],{},[1996,77471,2286],{"separator":2285},[5878,77473],{"width":15286},[898,77475,4255],{},[9166,77477,77478,77480,77482],{},[898,77479,3937],{},[898,77481,9795],{},[1996,77483,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,77485,1998],{},[2129,77487,2235],{},[1996,77489,2225],{},[2129,77491,19273],{},[898,77493,9795],{},[1996,77495,1998],{},[2129,77497,2327],{},[2288,77499,3984],{},[1996,77501,3987],{},[2288,77503,3984],{},[2272,77505,77506,77508],{},[898,77507,9795],{},[2129,77509,2327],{},[1996,77511,1998],{},[2129,77513,68285],{},[902,77515,77516],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,77518,77519,77555,77556,77574,77575,1975],{},[883,77520,77522],{"className":77521},[886],[888,77523,77524],{"xmlns":890},[892,77525,77526,77552],{},[895,77527,77528,77530,77542,77544,77546,77548,77550],{},[898,77529,4255],{},[9166,77531,77532,77534,77536],{},[898,77533,3937],{},[898,77535,9795],{},[895,77537,77538,77540],{},[1996,77539,2378],{"mathvariant":2376},[1996,77541,2378],{"mathvariant":2376},[1996,77543,1998],{},[1996,77545,2225],{},[2129,77547,19273],{},[1996,77549,3447],{},[2129,77551,2327],{},[902,77553,77554],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,77557,77559],{"className":77558},[886],[888,77560,77561],{"xmlns":890},[892,77562,77563,77571],{},[895,77564,77565,77567,77569],{},[898,77566,9795],{},[1996,77568,1998],{},[2129,77570,36246],{},[902,77572,77573],{"encoding":904},"L = 15"," je maximum, ",[883,77576,77578],{"className":77577},[886],[888,77579,77580],{"xmlns":890},[892,77581,77582,77628],{},[895,77583,77584,77586,77592,77594,77596,77598,77600,77602,77604,77606,77608,77610,77612,77615,77617,77620,77622,77624,77626],{},[898,77585,4255],{},[2272,77587,77588,77590],{},[898,77589,3937],{},[898,77591,9795],{},[1996,77593,2005],{"stretchy":2004},[2129,77595,36246],{},[1996,77597,2011],{"stretchy":2004},[1996,77599,1998],{},[2129,77601,2235],{},[1996,77603,3177],{},[2129,77605,36246],{},[1996,77607,2225],{},[2129,77609,2839],{},[1996,77611,3177],{},[2129,77613,77614],{},"225",[1996,77616,1998],{},[2129,77618,77619],{},"90",[1996,77621,2225],{},[2129,77623,76923],{},[1996,77625,1998],{},[2129,77627,76923],{},[902,77629,77630],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,77632,77633,41882,77689,77735],{},[883,77634,77636],{"className":77635},[886],[888,77637,77638],{"xmlns":890},[892,77639,77640,77686],{},[895,77641,77642,77644,77650,77652,77654,77656,77658,77660,77662,77664,77666,77668,77670,77672,77674,77677,77679,77682,77684],{},[898,77643,2818],{},[2272,77645,77646,77648],{},[898,77647,3937],{},[898,77649,9795],{},[1996,77651,2005],{"stretchy":2004},[2129,77653,36246],{},[1996,77655,2011],{"stretchy":2004},[1996,77657,1998],{},[2129,77659,3509],{},[1996,77661,3177],{},[2129,77663,36246],{},[1996,77665,2225],{},[2129,77667,19323],{},[1996,77669,3177],{},[2129,77671,77614],{},[1996,77673,1998],{},[2129,77675,77676],{},"180",[1996,77678,2225],{},[2129,77680,77681],{},"135",[1996,77683,1998],{},[2129,77685,76923],{},[902,77687,77688],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,77690,77692],{"className":77691},[886],[888,77693,77694],{"xmlns":890},[892,77695,77696,77732],{},[895,77697,77698,77700,77706,77708,77710,77712,77714,77716,77722,77724,77726,77728,77730],{},[898,77699,2818],{},[2272,77701,77702,77704],{},[898,77703,3937],{},[898,77705,9795],{},[1996,77707,2005],{"stretchy":2004},[2129,77709,36246],{},[1996,77711,2011],{"stretchy":2004},[1996,77713,1998],{},[898,77715,4255],{},[2272,77717,77718,77720],{},[898,77719,3937],{},[898,77721,9795],{},[1996,77723,2005],{"stretchy":2004},[2129,77725,36246],{},[1996,77727,2011],{"stretchy":2004},[1996,77729,1998],{},[2129,77731,76923],{},[902,77733,77734],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,77737,77738,77741,77742,17578,77771,1975],{},[38,77739,77740],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,77743,77745],{"className":77744},[886],[888,77746,77747],{"xmlns":890},[892,77748,77749,77769],{},[895,77750,77751,77753,77759,77761,77763],{},[898,77752,2818],{},[2272,77754,77755,77757],{},[898,77756,3937],{},[898,77758,9795],{},[1996,77760,1998],{},[898,77762,4255],{},[2272,77764,77765,77767],{},[898,77766,3937],{},[898,77768,9795],{},[902,77770,74665],{"encoding":904},[883,77772,77774],{"className":77773},[886],[888,77775,77776],{"xmlns":890},[892,77777,77778,77818],{},[895,77779,77780,77782,77784,77786,77788,77794,77796,77798,77800,77802,77804,77810,77812,77814,77816],{},[2129,77781,3509],{},[898,77783,9795],{},[1996,77785,2225],{},[2129,77787,19323],{},[2124,77789,77790,77792],{},[898,77791,9795],{},[2129,77793,2131],{},[1996,77795,1998],{},[2129,77797,2235],{},[898,77799,9795],{},[1996,77801,2225],{},[2129,77803,2839],{},[2124,77805,77806,77808],{},[898,77807,9795],{},[2129,77809,2131],{},[1996,77811,3987],{},[898,77813,9795],{},[1996,77815,1998],{},[2129,77817,36246],{},[902,77819,77820],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,77822,77823],{},[614,77824,77825,77826,77845,77846,12130,77864,77883,77884,77902,77903,77920,77921,77940,77941,77960],{},"Obrázek 5.3 — křivky ",[883,77827,77829],{"className":77828},[886],[888,77830,77831],{"xmlns":890},[892,77832,77833,77843],{},[895,77834,77835,77837],{},[898,77836,2818],{},[2272,77838,77839,77841],{},[898,77840,3937],{},[898,77842,9795],{},[902,77844,10045],{"encoding":904}," (max 60 při ",[883,77847,77849],{"className":77848},[886],[888,77850,77851],{"xmlns":890},[892,77852,77853,77861],{},[895,77854,77855,77857,77859],{},[898,77856,9795],{},[1996,77858,1998],{},[2129,77860,2863],{},[902,77862,77863],{"encoding":904},"L=10",[883,77865,77867],{"className":77866},[886],[888,77868,77869],{"xmlns":890},[892,77870,77871,77881],{},[895,77872,77873,77875],{},[898,77874,4255],{},[2272,77876,77877,77879],{},[898,77878,3937],{},[898,77880,9795],{},[902,77882,74635],{"encoding":904}," (max 45 při ",[883,77885,77887],{"className":77886},[886],[888,77888,77889],{"xmlns":890},[892,77890,77891,77899],{},[895,77892,77893,77895,77897],{},[898,77894,9795],{},[1996,77896,1998],{},[2129,77898,36246],{},[902,77900,77901],{"encoding":904},"L=15","), průsečík v ",[883,77904,77906],{"className":77905},[886],[888,77907,77908],{"xmlns":890},[892,77909,77910,77918],{},[895,77911,77912,77914,77916],{},[898,77913,9795],{},[1996,77915,1998],{},[2129,77917,36246],{},[902,77919,77573],{"encoding":904},". Nalevo od 15 leží ",[883,77922,77924],{"className":77923},[886],[888,77925,77926],{"xmlns":890},[892,77927,77928,77938],{},[895,77929,77930,77932],{},[898,77931,2818],{},[2272,77933,77934,77936],{},[898,77935,3937],{},[898,77937,9795],{},[902,77939,10045],{"encoding":904}," nad ",[883,77942,77944],{"className":77943},[886],[888,77945,77946],{"xmlns":890},[892,77947,77948,77958],{},[895,77949,77950,77952],{},[898,77951,4255],{},[2272,77953,77954,77956],{},[898,77955,3937],{},[898,77957,9795],{},[902,77959,74635],{"encoding":904},", napravo pod ní.",[115,77962,77964],{"id":77963},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,77966,77967,77968,2685,77981,2203,77984,6190,77997,2203,78000,2704],{},"V dvoufaktorovém modelu závisí produkce ",[883,77969,77971],{"className":77970},[886],[888,77972,77973],{"xmlns":890},[892,77974,77975,77979],{},[895,77976,77977],{},[898,77978,2789],{},[902,77980,2789],{"encoding":904},[38,77982,77983],{},"práci",[883,77985,77987],{"className":77986},[886],[888,77988,77989],{"xmlns":890},[892,77990,77991,77995],{},[895,77992,77993],{},[898,77994,9795],{},[902,77996,9795],{"encoding":904},[38,77998,77999],{},"kapitálu",[883,78001,78003],{"className":78002},[886],[888,78004,78005],{"xmlns":890},[892,78006,78007,78011],{},[895,78008,78009],{},[898,78010,9800],{},[902,78012,9800],{"encoding":904},[883,78014,78016],{"className":78015},[886],[888,78017,78018],{"xmlns":890,"display":28068},[892,78019,78020,78055],{},[20756,78021,78022],{"width":28073},[20761,78023,78024,78026,78048,78050],{},[20764,78025],{"width":28078},[20764,78027,78028],{},[895,78029,78030,78032,78034,78036,78038,78040,78042,78044,78046],{},[898,78031,2789],{},[1996,78033,1998],{},[898,78035,2789],{},[1996,78037,2005],{"stretchy":2004},[898,78039,9795],{},[1996,78041,2286],{"separator":2285},[898,78043,9800],{},[1996,78045,2011],{"stretchy":2004},[898,78047,1975],{"mathvariant":2376},[20764,78049],{"width":28078},[20764,78051,78052],{},[2288,78053,78054],{},"(5.6)",[902,78056,78057],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,78059,78060,78061,78063],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,78062,75002],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,78065,78067],{"id":78066},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,78069,78070],{},"Široce používané produkční funkce mají tvar",[883,78072,78074],{"className":78073},[886],[888,78075,78076],{"xmlns":890,"display":28068},[892,78077,78078,78119],{},[20756,78079,78080],{"width":28073},[20761,78081,78082,78084,78112,78114],{},[20764,78083],{"width":28078},[20764,78085,78086],{},[895,78087,78088,78090,78092,78094,78096,78102,78104,78110],{},[898,78089,2789],{},[1996,78091,1998],{},[898,78093,4255],{},[2288,78095,2987],{},[2124,78097,78098,78100],{},[898,78099,9795],{},[898,78101,207],{},[2288,78103,2987],{},[2124,78105,78106,78108],{},[898,78107,9800],{},[898,78109,2098],{},[1996,78111,2286],{"separator":2285},[20764,78113],{"width":28078},[20764,78115,78116],{},[2288,78117,78118],{},"(5.7)",[902,78120,78121],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,78123,4310,78124,78146,78147,78149,78150,1975],{},[883,78125,78127],{"className":78126},[886],[888,78128,78129],{"xmlns":890},[892,78130,78131,78143],{},[895,78132,78133,78135,78137,78139,78141],{},[898,78134,4255],{},[1996,78136,2286],{"separator":2285},[898,78138,207],{},[1996,78140,2286],{"separator":2285},[898,78142,2098],{},[902,78144,78145],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,78148,74701],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,78151,78153],{"className":78152},[886],[888,78154,78155],{"xmlns":890},[892,78156,78157,78169],{},[895,78158,78159,78161,78163,78165,78167],{},[898,78160,207],{},[1996,78162,2286],{"separator":2285},[898,78164,2098],{},[1996,78166,3447],{},[2129,78168,2278],{},[902,78170,78171],{"encoding":904},"a, b \u003C 1",[724,78173,78174],{},[2559,78175],{"alt":78176,"className":78177,"src":78178},"imek-vynosy-z-rozsahu-3typy",[210,2563],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,78180,78181,78182,78185,78186,2685,78199,78215,78216,2685,78229,2704],{},"Reflektují ekonomickou zákonitost, že ",[38,78183,78184],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,78187,78189],{"className":78188},[886],[888,78190,78191],{"xmlns":890},[892,78192,78193,78197],{},[895,78194,78195],{},[898,78196,9795],{},[902,78198,9795],{"encoding":904},[883,78200,78202],{"className":78201},[886],[888,78203,78204],{"xmlns":890},[892,78205,78206,78212],{},[895,78207,78208,78210],{},[898,78209,12043],{},[898,78211,9795],{},[902,78213,78214],{"encoding":904},"rL"," a kapitál z ",[883,78217,78219],{"className":78218},[886],[888,78220,78221],{"xmlns":890},[892,78222,78223,78227],{},[895,78224,78225],{},[898,78226,9800],{},[902,78228,9800],{"encoding":904},[883,78230,78232],{"className":78231},[886],[888,78233,78234],{"xmlns":890},[892,78235,78236,78242],{},[895,78237,78238,78240],{},[898,78239,12043],{},[898,78241,9800],{},[902,78243,78244],{"encoding":904},"rK",[883,78246,78248],{"className":78247},[886],[888,78249,78250],{"xmlns":890,"display":28068},[892,78251,78252,78375],{},[20756,78253,78254],{"width":28073},[20761,78255,78256,78258,78368,78370],{},[20764,78257],{"width":28078},[20764,78259,78260],{},[895,78261,78262,78264,78266,78268,78270,78272,78274,78276,78278,78280,78282,78284,78286,78288,78294,78296,78298,78300,78306,78308,78310,78312,78324,78326,78332,78338,78340,78352,78354,78356,78358,78360,78362,78364,78366],{},[898,78263,2789],{},[1996,78265,2005],{"stretchy":2004},[898,78267,12043],{},[898,78269,9795],{},[1996,78271,2286],{"separator":2285},[898,78273,12043],{},[898,78275,9800],{},[1996,78277,2011],{"stretchy":2004},[1996,78279,1998],{},[898,78281,4255],{},[1996,78283,2005],{"stretchy":2004},[898,78285,12043],{},[898,78287,9795],{},[2124,78289,78290,78292],{},[1996,78291,2011],{"stretchy":2004},[898,78293,207],{},[1996,78295,2005],{"stretchy":2004},[898,78297,12043],{},[898,78299,9800],{},[2124,78301,78302,78304],{},[1996,78303,2011],{"stretchy":2004},[898,78305,2098],{},[1996,78307,1998],{},[898,78309,4255],{},[2288,78311,2987],{},[2124,78313,78314,78316],{},[898,78315,12043],{},[895,78317,78318,78320,78322],{},[898,78319,207],{},[1996,78321,2095],{},[898,78323,2098],{},[2288,78325,2987],{},[2124,78327,78328,78330],{},[898,78329,9795],{},[898,78331,207],{},[2124,78333,78334,78336],{},[898,78335,9800],{},[898,78337,2098],{},[1996,78339,1998],{},[2124,78341,78342,78344],{},[898,78343,12043],{},[895,78345,78346,78348,78350],{},[898,78347,207],{},[1996,78349,2095],{},[898,78351,2098],{},[2288,78353,2987],{},[898,78355,2789],{},[1996,78357,2005],{"stretchy":2004},[898,78359,9795],{},[1996,78361,2286],{"separator":2285},[898,78363,9800],{},[1996,78365,2011],{"stretchy":2004},[898,78367,1975],{"mathvariant":2376},[20764,78369],{"width":28078},[20764,78371,78372],{},[2288,78373,78374],{},"(5.8)",[902,78376,78377],{"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}",[724,78379,78380,78381],{},"Volně: ",[38,78382,78383,78384,78397,78398,78422],{},"změní-li se vstupy ",[883,78385,78387],{"className":78386},[886],[888,78388,78389],{"xmlns":890},[892,78390,78391,78395],{},[895,78392,78393],{},[898,78394,12043],{},[902,78396,12043],{"encoding":904},"-krát, změní se výstup ",[883,78399,78401],{"className":78400},[886],[888,78402,78403],{"xmlns":890},[892,78404,78405,78419],{},[895,78406,78407],{},[2124,78408,78409,78411],{},[898,78410,12043],{},[895,78412,78413,78415,78417],{},[898,78414,207],{},[1996,78416,2095],{},[898,78418,2098],{},[902,78420,78421],{"encoding":904},"r^{a+b}","-krát.",[198,78424,78426],{"id":78425},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,78428,78429,78430,78447],{},"Součet exponentů ",[883,78431,78433],{"className":78432},[886],[888,78434,78435],{"xmlns":890},[892,78436,78437,78445],{},[895,78438,78439,78441,78443],{},[898,78440,207],{},[1996,78442,2095],{},[898,78444,2098],{},[902,78446,74826],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,78449,78450,78479],{},[19,78451,78452],{},[22,78453,78454,78457,78460,78477],{},[25,78455,78456],{},"Typ",[25,78458,78459],{},"Podmínka",[25,78461,78462,78463,78476],{},"Chování produkce při ",[883,78464,78466],{"className":78465},[886],[888,78467,78468],{"xmlns":890},[892,78469,78470,78474],{},[895,78471,78472],{},[898,78473,12043],{},[902,78475,12043],{"encoding":904},"-násobném zvýšení vstupů",[25,78478,3070],{},[30,78480,78481,78592,78707],{},[22,78482,78483,78491,78515,78548],{},[35,78484,75539,78485,10025,78488,2011],{},[38,78486,78487],{},"Konstantní",[614,78489,78490],{},"constant returns",[35,78492,78493],{},[883,78494,78496],{"className":78495},[886],[888,78497,78498],{"xmlns":890},[892,78499,78500,78512],{},[895,78501,78502,78504,78506,78508,78510],{},[898,78503,207],{},[1996,78505,2095],{},[898,78507,2098],{},[1996,78509,1998],{},[2129,78511,2278],{},[902,78513,78514],{"encoding":904},"a+b = 1",[35,78516,78517,78530,78531,2203,78534,78547],{},[883,78518,78520],{"className":78519},[886],[888,78521,78522],{"xmlns":890},[892,78523,78524,78528],{},[895,78525,78526],{},[898,78527,2789],{},[902,78529,2789],{"encoding":904}," vzroste ",[38,78532,78533],{},"přesně",[883,78535,78537],{"className":78536},[886],[888,78538,78539],{"xmlns":890},[892,78540,78541,78545],{},[895,78542,78543],{},[898,78544,12043],{},[902,78546,12043],{"encoding":904},"-krát",[35,78549,78550],{},[883,78551,78553],{"className":78552},[886],[888,78554,78555],{"xmlns":890},[892,78556,78557,78589],{},[895,78558,78559,78561,78563,78565,78577],{},[898,78560,2789],{},[1996,78562,1998],{},[2129,78564,2131],{},[2124,78566,78567,78569],{},[898,78568,9795],{},[895,78570,78571,78573,78575],{},[2129,78572,2278],{},[898,78574,4674],{"mathvariant":2376},[2129,78576,2351],{},[2124,78578,78579,78581],{},[898,78580,9800],{},[895,78582,78583,78585,78587],{},[2129,78584,2173],{},[898,78586,4674],{"mathvariant":2376},[2129,78588,2351],{},[902,78590,78591],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,78593,78594,78603,78627,78657],{},[35,78595,78596,78597,10025,78600,2011],{},"2° ",[38,78598,78599],{},"Rostoucí",[614,78601,78602],{},"increasing returns",[35,78604,78605],{},[883,78606,78608],{"className":78607},[886],[888,78609,78610],{"xmlns":890},[892,78611,78612,78624],{},[895,78613,78614,78616,78618,78620,78622],{},[898,78615,207],{},[1996,78617,2095],{},[898,78619,2098],{},[1996,78621,3408],{},[2129,78623,2278],{},[902,78625,78626],{"encoding":904},"a+b > 1",[35,78628,78629,78530,78642,51233,78644,78547],{},[883,78630,78632],{"className":78631},[886],[888,78633,78634],{"xmlns":890},[892,78635,78636,78640],{},[895,78637,78638],{},[898,78639,2789],{},[902,78641,2789],{"encoding":904},[38,78643,25272],{},[883,78645,78647],{"className":78646},[886],[888,78648,78649],{"xmlns":890},[892,78650,78651,78655],{},[895,78652,78653],{},[898,78654,12043],{},[902,78656,12043],{"encoding":904},[35,78658,78659,10025,78685,2011],{},[883,78660,78662],{"className":78661},[886],[888,78663,78664],{"xmlns":890},[892,78665,78666,78682],{},[895,78667,78668,78670,78672,78674,78676],{},[898,78669,2789],{},[1996,78671,1998],{},[2129,78673,24203],{},[898,78675,9795],{},[2124,78677,78678,78680],{},[898,78679,9800],{},[2129,78681,2131],{},[902,78683,78684],{"encoding":904},"Q = 7LK^2",[883,78686,78688],{"className":78687},[886],[888,78689,78690],{"xmlns":890},[892,78691,78692,78704],{},[895,78693,78694,78696,78698,78700,78702],{},[898,78695,207],{},[1996,78697,2095],{},[898,78699,2098],{},[1996,78701,1998],{},[2129,78703,2173],{},[902,78705,78706],{"encoding":904},"a+b = 3",[22,78708,78709,78718,78742,78773],{},[35,78710,78711,78712,10025,78715,2011],{},"3° ",[38,78713,78714],{},"Klesající",[614,78716,78717],{},"decreasing returns",[35,78719,78720],{},[883,78721,78723],{"className":78722},[886],[888,78724,78725],{"xmlns":890},[892,78726,78727,78739],{},[895,78728,78729,78731,78733,78735,78737],{},[898,78730,207],{},[1996,78732,2095],{},[898,78734,2098],{},[1996,78736,3447],{},[2129,78738,2278],{},[902,78740,78741],{"encoding":904},"a+b \u003C 1",[35,78743,78744,78530,78757,51233,78760,78547],{},[883,78745,78747],{"className":78746},[886],[888,78748,78749],{"xmlns":890},[892,78750,78751,78755],{},[895,78752,78753],{},[898,78754,2789],{},[902,78756,2789],{"encoding":904},[38,78758,78759],{},"méně",[883,78761,78763],{"className":78762},[886],[888,78764,78765],{"xmlns":890},[892,78766,78767,78771],{},[895,78768,78769],{},[898,78770,12043],{},[902,78772,12043],{"encoding":904},[35,78774,78775,10025,78805,2011],{},[883,78776,78778],{"className":78777},[886],[888,78779,78780],{"xmlns":890},[892,78781,78782,78802],{},[895,78783,78784,78786,78788,78790,78796],{},[898,78785,2789],{},[1996,78787,1998],{},[2129,78789,2863],{},[2124,78791,78792,78794],{},[898,78793,9795],{},[2129,78795,68213],{},[2124,78797,78798,78800],{},[898,78799,9800],{},[2129,78801,5009],{},[902,78803,78804],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,78806,78808],{"className":78807},[886],[888,78809,78810],{"xmlns":890},[892,78811,78812,78824],{},[895,78813,78814,78816,78818,78820,78822],{},[898,78815,207],{},[1996,78817,2095],{},[898,78819,2098],{},[1996,78821,1998],{},[2129,78823,14591],{},[902,78825,78826],{"encoding":904},"a+b = 0{,}8",[3867,78828,78829],{},[724,78830,78831,78833,78834,78851,78852,78855,78856,2203,78859,78895,78896,78918,78919,1975],{},[883,78832,4412],{}," Pozor\nSoučet ",[883,78835,78837],{"className":78836},[886],[888,78838,78839],{"xmlns":890},[892,78840,78841,78849],{},[895,78842,78843,78845,78847],{},[898,78844,207],{},[1996,78846,2095],{},[898,78848,2098],{},[902,78850,74826],{"encoding":904}," neudává velikost produkce, ale ",[38,78853,78854],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,78857,78858],{},"ryzí Cobb-Douglas",[883,78860,78862],{"className":78861},[886],[888,78863,78864],{"xmlns":890},[892,78865,78866,78892],{},[895,78867,78868,78870,78872,78874,78880],{},[898,78869,2789],{},[1996,78871,1998],{},[898,78873,4255],{},[2124,78875,78876,78878],{},[898,78877,9795],{},[898,78879,207],{},[2124,78881,78882,78884],{},[898,78883,9800],{},[895,78885,78886,78888,78890],{},[2129,78887,2278],{},[1996,78889,2225],{},[898,78891,207],{},[902,78893,78894],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,78897,78899],{"className":78898},[886],[888,78900,78901],{"xmlns":890},[892,78902,78903,78915],{},[895,78904,78905,78907,78909,78911,78913],{},[898,78906,2098],{},[1996,78908,1998],{},[2129,78910,2278],{},[1996,78912,2225],{},[898,78914,207],{},[902,78916,78917],{"encoding":904},"b = 1-a",", tedy vždy ",[38,78920,78921],{},"konstantní výnosy z rozsahu",[198,78923,78925,78926],{"id":78924},"parametr-efektivity-aa","Parametr efektivity ",[883,78927,78929],{"className":78928},[886],[888,78930,78931],{"xmlns":890},[892,78932,78933,78937],{},[895,78934,78935],{},[898,78936,4255],{},[902,78938,4255],{"encoding":904},[724,78940,78941,78942,78955,78956,78969,78970,78988,78989,78992],{},"Konstanta ",[883,78943,78945],{"className":78944},[886],[888,78946,78947],{"xmlns":890},[892,78948,78949,78953],{},[895,78950,78951],{},[898,78952,4255],{},[902,78954,4255],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,78957,78959],{"className":78958},[886],[888,78960,78961],{"xmlns":890},[892,78962,78963,78967],{},[895,78964,78965],{},[898,78966,2789],{},[902,78968,2789],{"encoding":904}," při pevně zadaných ",[883,78971,78973],{"className":78972},[886],[888,78974,78975],{"xmlns":890},[892,78976,78977,78985],{},[895,78978,78979,78981,78983],{},[898,78980,9795],{},[1996,78982,2286],{"separator":2285},[898,78984,9800],{},[902,78986,78987],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,78990,78991],{},"parametr efektivity"," — indikátor stavu technologie.",[198,78994,78996],{"id":78995},"příklad-53","Příklad 5.3",[724,78998,78999,79000,78895,79042,79044,79045,1975],{},"Produkční funkce ",[883,79001,79003],{"className":79002},[886],[888,79004,79005],{"xmlns":890},[892,79006,79007,79039],{},[895,79008,79009,79011,79013,79015,79027],{},[898,79010,2789],{},[1996,79012,1998],{},[2129,79014,2131],{},[2124,79016,79017,79019],{},[898,79018,9795],{},[895,79020,79021,79023,79025],{},[2129,79022,2278],{},[898,79024,4674],{"mathvariant":2376},[2129,79026,2351],{},[2124,79028,79029,79031],{},[898,79030,9800],{},[895,79032,79033,79035,79037],{},[2129,79034,2173],{},[898,79036,4674],{"mathvariant":2376},[2129,79038,2351],{},[902,79040,79041],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,79043,24615],{}," výnosy z rozsahu, neboť ",[883,79046,79048],{"className":79047},[886],[888,79049,79050],{"xmlns":890},[892,79051,79052,79076],{},[895,79053,79054,79062,79064,79072,79074],{},[2325,79055,79056],{"scriptlevel":2327,"displaystyle":2004},[2329,79057,79058,79060],{},[2129,79059,2278],{},[2129,79061,2351],{},[1996,79063,2095],{},[2325,79065,79066],{"scriptlevel":2327,"displaystyle":2004},[2329,79067,79068,79070],{},[2129,79069,2173],{},[2129,79071,2351],{},[1996,79073,1998],{},[2129,79075,2278],{},[902,79077,79078],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,79080,79081,79082,6190,79095,79108,79109,2203,79122,79162],{},"Změní-li se ",[883,79083,79085],{"className":79084},[886],[888,79086,79087],{"xmlns":890},[892,79088,79089,79093],{},[895,79090,79091],{},[898,79092,9795],{},[902,79094,9795],{"encoding":904},[883,79096,79098],{"className":79097},[886],[888,79099,79100],{"xmlns":890},[892,79101,79102,79106],{},[895,79103,79104],{},[898,79105,9800],{},[902,79107,9800],{"encoding":904}," čtyřnásobně, změní se ",[883,79110,79112],{"className":79111},[886],[888,79113,79114],{"xmlns":890},[892,79115,79116,79120],{},[895,79117,79118],{},[898,79119,2789],{},[902,79121,2789],{"encoding":904},[883,79123,79125],{"className":79124},[886],[888,79126,79127],{"xmlns":890},[892,79128,79129,79159],{},[895,79130,79131,79151,79153],{},[2124,79132,79133,79135],{},[2129,79134,2351],{},[895,79136,79137,79139,79141,79143,79145,79147,79149],{},[2129,79138,2278],{},[898,79140,4674],{"mathvariant":2376},[2129,79142,2351],{},[1996,79144,2095],{},[2129,79146,2173],{},[898,79148,4674],{"mathvariant":2376},[2129,79150,2351],{},[1996,79152,1998],{},[2124,79154,79155,79157],{},[2129,79156,2351],{},[2129,79158,2278],{},[902,79160,79161],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,79164,79166],{"className":79165},[886],[888,79167,79168],{"xmlns":890,"display":28068},[892,79169,79170,79330],{},[895,79171,79172,79174,79176,79178,79180,79182,79184,79186,79188,79190,79192,79194,79196,79198,79210,79212,79214,79216,79228,79230,79232,79234,79254,79266,79278,79280,79282,79284,79286,79298,79310,79312,79314,79316,79318,79320,79322,79324,79326,79328],{},[898,79173,2789],{},[1996,79175,2005],{"stretchy":2004},[2129,79177,2351],{},[898,79179,9795],{},[1996,79181,2286],{"separator":2285},[2129,79183,2351],{},[898,79185,9800],{},[1996,79187,2011],{"stretchy":2004},[1996,79189,1998],{},[2129,79191,2131],{},[1996,79193,2005],{"stretchy":2004},[2129,79195,2351],{},[898,79197,9795],{},[2124,79199,79200,79202],{},[1996,79201,2011],{"stretchy":2004},[895,79203,79204,79206,79208],{},[2129,79205,2278],{},[898,79207,4674],{"mathvariant":2376},[2129,79209,2351],{},[1996,79211,2005],{"stretchy":2004},[2129,79213,2351],{},[898,79215,9800],{},[2124,79217,79218,79220],{},[1996,79219,2011],{"stretchy":2004},[895,79221,79222,79224,79226],{},[2129,79223,2173],{},[898,79225,4674],{"mathvariant":2376},[2129,79227,2351],{},[1996,79229,1998],{},[2129,79231,2131],{},[1996,79233,3177],{},[2124,79235,79236,79238],{},[2129,79237,2351],{},[895,79239,79240,79242,79244,79246,79248,79250,79252],{},[2129,79241,2278],{},[898,79243,4674],{"mathvariant":2376},[2129,79245,2351],{},[1996,79247,2095],{},[2129,79249,2173],{},[898,79251,4674],{"mathvariant":2376},[2129,79253,2351],{},[2124,79255,79256,79258],{},[898,79257,9795],{},[895,79259,79260,79262,79264],{},[2129,79261,2278],{},[898,79263,4674],{"mathvariant":2376},[2129,79265,2351],{},[2124,79267,79268,79270],{},[898,79269,9800],{},[895,79271,79272,79274,79276],{},[2129,79273,2173],{},[898,79275,4674],{"mathvariant":2376},[2129,79277,2351],{},[1996,79279,1998],{},[2129,79281,2351],{},[1996,79283,3177],{},[2129,79285,2131],{},[2124,79287,79288,79290],{},[898,79289,9795],{},[895,79291,79292,79294,79296],{},[2129,79293,2278],{},[898,79295,4674],{"mathvariant":2376},[2129,79297,2351],{},[2124,79299,79300,79302],{},[898,79301,9800],{},[895,79303,79304,79306,79308],{},[2129,79305,2173],{},[898,79307,4674],{"mathvariant":2376},[2129,79309,2351],{},[1996,79311,1998],{},[2129,79313,2351],{},[2288,79315,2987],{},[898,79317,2789],{},[1996,79319,2005],{"stretchy":2004},[898,79321,9795],{},[1996,79323,2286],{"separator":2285},[898,79325,9800],{},[1996,79327,2011],{"stretchy":2004},[898,79329,1975],{"mathvariant":2376},[902,79331,79332],{"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).",[198,79334,79335],{"id":37181},"Homogenita",[724,79337,79338,79339,8102,79362,79378],{},"Funkce ",[883,79340,79342],{"className":79341},[886],[888,79343,79344],{"xmlns":890},[892,79345,79346,79360],{},[895,79347,79348,79350,79352,79354,79356,79358],{},[898,79349,2789],{},[1996,79351,2005],{"stretchy":2004},[898,79353,9795],{},[1996,79355,2286],{"separator":2285},[898,79357,9800],{},[1996,79359,2011],{"stretchy":2004},[902,79361,9997],{"encoding":904},[38,79363,79364,79365],{},"homogenní stupně ",[883,79366,79368],{"className":79367},[886],[888,79369,79370],{"xmlns":890},[892,79371,79372,79376],{},[895,79373,79374],{},[898,79375,36862],{},[902,79377,36862],{"encoding":904},", jestliže",[883,79380,79382],{"className":79381},[886],[888,79383,79384],{"xmlns":890,"display":28068},[892,79385,79386,79443],{},[20756,79387,79388],{"width":28073},[20761,79389,79390,79392,79436,79438],{},[20764,79391],{"width":28078},[20764,79393,79394],{},[895,79395,79396,79398,79400,79402,79404,79406,79408,79410,79412,79414,79420,79422,79424,79426,79428,79430,79432,79434],{},[898,79397,2789],{},[1996,79399,2005],{"stretchy":2004},[898,79401,12043],{},[898,79403,9795],{},[1996,79405,2286],{"separator":2285},[898,79407,12043],{},[898,79409,9800],{},[1996,79411,2011],{"stretchy":2004},[1996,79413,1998],{},[2124,79415,79416,79418],{},[898,79417,12043],{},[898,79419,36862],{},[2288,79421,2987],{},[898,79423,2789],{},[1996,79425,2005],{"stretchy":2004},[898,79427,9795],{},[1996,79429,2286],{"separator":2285},[898,79431,9800],{},[1996,79433,2011],{"stretchy":2004},[1996,79435,2286],{"separator":2285},[20764,79437],{"width":28078},[20764,79439,79440],{},[2288,79441,79442],{},"(5.10)",[902,79444,79445],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,79447,4310,79448,79466,79467,79485,79486,43638,79499,79502,79503,1975],{},[883,79449,79451],{"className":79450},[886],[888,79452,79453],{"xmlns":890},[892,79454,79455,79463],{},[895,79456,79457,79459,79461],{},[898,79458,36862],{},[1996,79460,4485],{},[2129,79462,2327],{},[902,79464,79465],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,79468,79470],{"className":79469},[886],[888,79471,79472],{"xmlns":890},[892,79473,79474,79482],{},[895,79475,79476,79478,79480],{},[898,79477,12043],{},[1996,79479,3408],{},[2129,79481,2327],{},[902,79483,79484],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,79487,79489],{"className":79488},[886],[888,79490,79491],{"xmlns":890},[892,79492,79493,79497],{},[895,79494,79495],{},[2129,79496,2278],{},[902,79498,2278],{"encoding":904},[38,79500,79501],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,79504,79506],{"className":79505},[886],[888,79507,79508],{"xmlns":890},[892,79509,79510,79518],{},[895,79511,79512,79514,79516],{},[898,79513,207],{},[1996,79515,2095],{},[898,79517,2098],{},[902,79519,74826],{"encoding":904},[115,79521,79523],{"id":79522},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,79525,79526],{},[38,79527,79528],{},"Ryzí Cobb-Douglasovy funkce:",[883,79530,79532],{"className":79531},[886],[888,79533,79534],{"xmlns":890,"display":28068},[892,79535,79536,79595],{},[20756,79537,79538],{"width":28073},[20761,79539,79540,79542,79588,79590],{},[20764,79541],{"width":28078},[20764,79543,79544],{},[895,79545,79546,79548,79550,79552,79554,79560,79562,79574,79576,79578,79580,79582,79584,79586],{},[898,79547,2789],{},[1996,79549,1998],{},[898,79551,4255],{},[2288,79553,2987],{},[2124,79555,79556,79558],{},[898,79557,9795],{},[898,79559,207],{},[2288,79561,2987],{},[2124,79563,79564,79566],{},[898,79565,9800],{},[895,79567,79568,79570,79572],{},[2129,79569,2278],{},[1996,79571,2225],{},[898,79573,207],{},[1996,79575,2286],{"separator":2285},[5878,79577],{"width":15286},[2129,79579,2327],{},[1996,79581,3447],{},[898,79583,207],{},[1996,79585,3447],{},[2129,79587,13262],{},[20764,79589],{"width":28078},[20764,79591,79592],{},[2288,79593,79594],{},"(5.9)",[902,79596,79597],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,79599,79600,79601,79603,79604,1975],{},"Mají vždy ",[38,79602,78921],{}," a jsou ",[38,79605,79501],{},[724,79607,79608,10025,79611,79614],{},[38,79609,79610],{},"CES produkční funkce",[614,79612,79613],{},"Constant Elasticity of Substitution",", 1961):",[883,79616,79618],{"className":79617},[886],[888,79619,79620],{"xmlns":890,"display":28068},[892,79621,79622,79690],{},[895,79623,79624,79626,79628,79630,79688],{},[898,79625,2789],{},[1996,79627,1998],{},[898,79629,4255],{},[2124,79631,79632,79676],{},[895,79633,79634,79636,79638,79640,79642,79644,79646,79648,79658,79660,79662,79664,79674],{},[1996,79635,2486],{"fence":2285},[1996,79637,2005],{"stretchy":2004},[2129,79639,2278],{},[1996,79641,2225],{},[898,79643,207],{},[1996,79645,2011],{"stretchy":2004},[2288,79647,2987],{},[2124,79649,79650,79652],{},[898,79651,9795],{},[895,79653,79654,79656],{},[1996,79655,2225],{},[898,79657,2098],{},[1996,79659,2095],{},[898,79661,207],{},[2288,79663,2987],{},[2124,79665,79666,79668],{},[898,79667,9800],{},[895,79669,79670,79672],{},[1996,79671,2225],{},[898,79673,2098],{},[1996,79675,2501],{"fence":2285},[895,79677,79678,79680],{},[1996,79679,2225],{},[2325,79681,79682],{"scriptlevel":2327,"displaystyle":2004},[2329,79683,79684,79686],{},[2129,79685,2278],{},[898,79687,2098],{},[1996,79689,2286],{"separator":2285},[902,79691,79692],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,79694,4310,79695,1343,79713,1343,79734,79758],{},[883,79696,79698],{"className":79697},[886],[888,79699,79700],{"xmlns":890},[892,79701,79702,79710],{},[895,79703,79704,79706,79708],{},[898,79705,4255],{},[1996,79707,3408],{},[2129,79709,2327],{},[902,79711,79712],{"encoding":904},"A > 0",[883,79714,79716],{"className":79715},[886],[888,79717,79718],{"xmlns":890},[892,79719,79720,79732],{},[895,79721,79722,79724,79726,79728,79730],{},[2129,79723,2327],{},[1996,79725,3447],{},[898,79727,207],{},[1996,79729,3447],{},[2129,79731,2278],{},[902,79733,18838],{"encoding":904},[883,79735,79737],{"className":79736},[886],[888,79738,79739],{"xmlns":890},[892,79740,79741,79755],{},[895,79742,79743,79745,79747,79749,79751,79753],{},[1996,79744,2225],{},[2129,79746,2278],{},[1996,79748,3447],{},[898,79750,2098],{},[1996,79752,3371],{"mathvariant":2376},[2129,79754,2327],{},[902,79756,79757],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,79760,79761],{},[38,79762,79763],{},"Další typy:",[120,79765,79766,79808],{},[123,79767,79768,2203,79771,79807],{},[38,79769,79770],{},"Lineární:",[883,79772,79774],{"className":79773},[886],[888,79775,79776],{"xmlns":890},[892,79777,79778,79804],{},[895,79779,79780,79782,79784,79786,79788,79790,79792,79794,79796,79798,79800,79802],{},[898,79781,2789],{},[1996,79783,2005],{"stretchy":2004},[898,79785,9795],{},[1996,79787,2286],{"separator":2285},[898,79789,9800],{},[1996,79791,2011],{"stretchy":2004},[1996,79793,1998],{},[898,79795,207],{},[898,79797,9795],{},[1996,79799,2095],{},[898,79801,2098],{},[898,79803,9800],{},[902,79805,79806],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,79809,79810,2203,79813,79858],{},[38,79811,79812],{},"Leontiefova:",[883,79814,79816],{"className":79815},[886],[888,79817,79818],{"xmlns":890},[892,79819,79820,79855],{},[895,79821,79822,79824,79826,79828,79830,79832,79834,79836,79839,79841,79843,79845,79847,79849,79851,79853],{},[898,79823,2789],{},[1996,79825,2005],{"stretchy":2004},[898,79827,9795],{},[1996,79829,2286],{"separator":2285},[898,79831,9800],{},[1996,79833,2011],{"stretchy":2004},[1996,79835,1998],{},[898,79837,79838],{},"min",[1996,79840,56202],{},[1996,79842,2005],{"stretchy":2004},[898,79844,207],{},[898,79846,9795],{},[1996,79848,2286],{"separator":2285},[898,79850,2098],{},[898,79852,9800],{},[1996,79854,2011],{"stretchy":2004},[902,79856,79857],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,79860,79862,79863,1343,79882,79901],{"id":79861},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,79864,79866],{"className":79865},[886],[888,79867,79868],{"xmlns":890},[892,79869,79870,79880],{},[895,79871,79872,79874],{},[898,79873,2818],{},[2272,79875,79876,79878],{},[898,79877,3937],{},[898,79879,9795],{},[902,79881,10045],{"encoding":904},[883,79883,79885],{"className":79884},[886],[888,79886,79887],{"xmlns":890},[892,79888,79889,79899],{},[895,79890,79891,79893],{},[898,79892,2818],{},[2272,79894,79895,79897],{},[898,79896,3937],{},[898,79898,9800],{},[902,79900,10090],{"encoding":904}," a totální diferenciál",[724,79903,79904],{},[38,79905,79906],{},"Mezní produkt práce:",[883,79908,79910],{"className":79909},[886],[888,79911,79912],{"xmlns":890,"display":28068},[892,79913,79914,79952],{},[895,79915,79916,79918,79924,79926,79934,79936,79950],{},[898,79917,2818],{},[2272,79919,79920,79922],{},[898,79921,3937],{},[898,79923,9795],{},[1996,79925,1998],{},[9166,79927,79928,79930,79932],{},[898,79929,2789],{},[898,79931,9795],{},[1996,79933,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,79935,1998],{},[2329,79937,79938,79944],{},[895,79939,79940,79942],{},[898,79941,9872],{"mathvariant":2376},[898,79943,2789],{},[895,79945,79946,79948],{},[898,79947,9872],{"mathvariant":2376},[898,79949,9795],{},[898,79951,1975],{"mathvariant":2376},[902,79953,79954],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,79956,79957],{},[38,79958,79959],{},"Mezní produkt kapitálu:",[883,79961,79963],{"className":79962},[886],[888,79964,79965],{"xmlns":890,"display":28068},[892,79966,79967,80005],{},[895,79968,79969,79971,79977,79979,79987,79989,80003],{},[898,79970,2818],{},[2272,79972,79973,79975],{},[898,79974,3937],{},[898,79976,9800],{},[1996,79978,1998],{},[9166,79980,79981,79983,79985],{},[898,79982,2789],{},[898,79984,9800],{},[1996,79986,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,79988,1998],{},[2329,79990,79991,79997],{},[895,79992,79993,79995],{},[898,79994,9872],{"mathvariant":2376},[898,79996,2789],{},[895,79998,79999,80001],{},[898,80000,9872],{"mathvariant":2376},[898,80002,9800],{},[898,80004,1975],{"mathvariant":2376},[902,80006,80007],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,80009,80010,80040,80041,80062,80063,80081,80082,80095,80096,1975],{},[883,80011,80013],{"className":80012},[886],[888,80014,80015],{"xmlns":890},[892,80016,80017,80037],{},[895,80018,80019,80021,80027,80029,80031,80033,80035],{},[898,80020,2818],{},[2272,80022,80023,80025],{},[898,80024,3937],{},[898,80026,9795],{},[1996,80028,2005],{"stretchy":2004},[898,80030,207],{},[1996,80032,2286],{"separator":2285},[898,80034,2098],{},[1996,80036,2011],{"stretchy":2004},[902,80038,80039],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,80042,80044],{"className":80043},[886],[888,80045,80046],{"xmlns":890},[892,80047,80048,80060],{},[895,80049,80050,80052,80054,80056,80058],{},[1996,80051,2486],{"stretchy":2004},[898,80053,207],{},[1996,80055,2286],{"separator":2285},[898,80057,2098],{},[1996,80059,2501],{"stretchy":2004},[902,80061,10824],{"encoding":904}," (na hladině ",[883,80064,80066],{"className":80065},[886],[888,80067,80068],{"xmlns":890},[892,80069,80070,80078],{},[895,80071,80072,80074,80076],{},[898,80073,9800],{},[1996,80075,1998],{},[898,80077,2098],{},[902,80079,80080],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,80083,80085],{"className":80084},[886],[888,80086,80087],{"xmlns":890},[892,80088,80089,80093],{},[895,80090,80091],{},[898,80092,9795],{},[902,80094,9795],{"encoding":904},". Analogicky ",[883,80097,80099],{"className":80098},[886],[888,80100,80101],{"xmlns":890},[892,80102,80103,80123],{},[895,80104,80105,80107,80113,80115,80117,80119,80121],{},[898,80106,2818],{},[2272,80108,80109,80111],{},[898,80110,3937],{},[898,80112,9800],{},[1996,80114,2005],{"stretchy":2004},[898,80116,207],{},[1996,80118,2286],{"separator":2285},[898,80120,2098],{},[1996,80122,2011],{"stretchy":2004},[902,80124,80125],{"encoding":904},"MP_K(a, b)",[3867,80127,80128,80132],{},[724,80129,80130,51221],{},[883,80131,4155],{},[120,80133,80134,80172],{},[123,80135,80136,26191,80155],{},[883,80137,80139],{"className":80138},[886],[888,80140,80141],{"xmlns":890},[892,80142,80143,80153],{},[895,80144,80145,80147],{},[898,80146,2818],{},[2272,80148,80149,80151],{},[898,80150,3937],{},[898,80152,9795],{},[902,80154,10045],{"encoding":904},[614,80156,80157,80158,80171],{},"„o kolik vzroste ",[883,80159,80161],{"className":80160},[886],[888,80162,80163],{"xmlns":890},[892,80164,80165,80169],{},[895,80166,80167],{},[898,80168,2789],{},[902,80170,2789],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,80173,80174,26191,80193],{},[883,80175,80177],{"className":80176},[886],[888,80178,80179],{"xmlns":890},[892,80180,80181,80191],{},[895,80182,80183,80185],{},[898,80184,2818],{},[2272,80186,80187,80189],{},[898,80188,3937],{},[898,80190,9800],{},[902,80192,10090],{"encoding":904},[614,80194,80157,80195,80208],{},[883,80196,80198],{"className":80197},[886],[888,80199,80200],{"xmlns":890},[892,80201,80202,80206],{},[895,80203,80204],{},[898,80205,2789],{},[902,80207,2789],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,80210,80211,80214,80215,80230,80231,2704],{},[38,80212,80213],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,80216,80218],{"className":80217},[886],[888,80219,80220],{"xmlns":890},[892,80221,80222,80228],{},[895,80223,80224,80226],{},[898,80225,2194],{},[898,80227,9795],{},[902,80229,75358],{"encoding":904}," a kapitálu o ",[883,80232,80234],{"className":80233},[886],[888,80235,80236],{"xmlns":890},[892,80237,80238,80244],{},[895,80239,80240,80242],{},[898,80241,2194],{},[898,80243,9800],{},[902,80245,80246],{"encoding":904},"dK",[883,80248,80250],{"className":80249},[886],[888,80251,80252],{"xmlns":890,"display":28068},[892,80253,80254,80347],{},[20756,80255,80256],{"width":28073},[20761,80257,80258,80260,80340,80342],{},[20764,80259],{"width":28078},[20764,80261,80262],{},[895,80263,80264,80266,80268,80270,80272,80274,80276,80284,80286,80288,80290,80292,80300,80302,80304,80306,80308,80310,80316,80318,80320,80322,80324,80326,80332,80334,80336,80338],{},[898,80265,2889],{"mathvariant":2376},[898,80267,2789],{},[1996,80269,2730],{},[898,80271,2194],{},[898,80273,2789],{},[1996,80275,1998],{},[9166,80277,80278,80280,80282],{},[898,80279,2789],{},[898,80281,9795],{},[1996,80283,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[2288,80285,2987],{},[898,80287,2194],{},[898,80289,9795],{},[1996,80291,2095],{},[9166,80293,80294,80296,80298],{},[898,80295,2789],{},[898,80297,9800],{},[1996,80299,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[2288,80301,2987],{},[898,80303,2194],{},[898,80305,9800],{},[1996,80307,1998],{},[898,80309,2818],{},[2272,80311,80312,80314],{},[898,80313,3937],{},[898,80315,9795],{},[2288,80317,2987],{},[898,80319,2194],{},[898,80321,9795],{},[1996,80323,2095],{},[898,80325,2818],{},[2272,80327,80328,80330],{},[898,80329,3937],{},[898,80331,9800],{},[2288,80333,2987],{},[898,80335,2194],{},[898,80337,9800],{},[898,80339,1975],{"mathvariant":2376},[20764,80341],{"width":28078},[20764,80343,80344],{},[2288,80345,80346],{},"(5.11)",[902,80348,80349],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,80351,80352,80353,1975],{},"Skutečná změna: ",[883,80354,80356],{"className":80355},[886],[888,80357,80358],{"xmlns":890},[892,80359,80360,80406],{},[895,80361,80362,80364,80366,80368,80370,80372,80374,80376,80378,80380,80382,80384,80386,80388,80390,80392,80394,80396,80398,80400,80402,80404],{},[898,80363,2889],{"mathvariant":2376},[898,80365,2789],{},[1996,80367,1998],{},[898,80369,2789],{},[1996,80371,2005],{"stretchy":2004},[898,80373,9795],{},[1996,80375,2095],{},[898,80377,2194],{},[898,80379,9795],{},[1996,80381,2286],{"separator":2285},[898,80383,9800],{},[1996,80385,2095],{},[898,80387,2194],{},[898,80389,9800],{},[1996,80391,2011],{"stretchy":2004},[1996,80393,2225],{},[898,80395,2789],{},[1996,80397,2005],{"stretchy":2004},[898,80399,9795],{},[1996,80401,2286],{"separator":2285},[898,80403,9800],{},[1996,80405,2011],{"stretchy":2004},[902,80407,80408],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,80410,80411,80413,80414,80432,80433,80446,80447,80466,80467,80499,80500,80532,80533,1975],{},[38,80412,75522],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,80415,80417],{"className":80416},[886],[888,80418,80419],{"xmlns":890},[892,80420,80421,80429],{},[895,80422,80423],{},[2272,80424,80425,80427],{},[898,80426,9800],{},[2129,80428,2327],{},[902,80430,80431],{"encoding":904},"K_0"," se od jistého ",[883,80434,80436],{"className":80435},[886],[888,80437,80438],{"xmlns":890},[892,80439,80440,80444],{},[895,80441,80442],{},[898,80443,9795],{},[902,80445,9795],{"encoding":904}," stane ",[883,80448,80450],{"className":80449},[886],[888,80451,80452],{"xmlns":890},[892,80453,80454,80464],{},[895,80455,80456,80458],{},[898,80457,2818],{},[2272,80459,80460,80462],{},[898,80461,3937],{},[898,80463,9795],{},[902,80465,10045],{"encoding":904}," klesající (",[883,80468,80470],{"className":80469},[886],[888,80471,80472],{"xmlns":890},[892,80473,80474,80496],{},[895,80475,80476,80492,80494],{},[9166,80477,80478,80480,80486],{},[898,80479,2789],{},[895,80481,80482,80484],{},[898,80483,9795],{},[898,80485,9795],{},[895,80487,80488,80490],{},[1996,80489,2378],{"mathvariant":2376},[1996,80491,2378],{"mathvariant":2376},[1996,80493,3447],{},[2129,80495,2327],{},[902,80497,80498],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,80501,80503],{"className":80502},[886],[888,80504,80505],{"xmlns":890},[892,80506,80507,80529],{},[895,80508,80509,80525,80527],{},[9166,80510,80511,80513,80519],{},[898,80512,2789],{},[895,80514,80515,80517],{},[898,80516,9800],{},[898,80518,9800],{},[895,80520,80521,80523],{},[1996,80522,2378],{"mathvariant":2376},[1996,80524,2378],{"mathvariant":2376},[1996,80526,3447],{},[2129,80528,2327],{},[902,80530,80531],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,80534,80536],{"className":80535},[886],[888,80537,80538],{"xmlns":890},[892,80539,80540,80548],{},[895,80541,80542],{},[2272,80543,80544,80546],{},[898,80545,9795],{},[2129,80547,2327],{},[902,80549,75560],{"encoding":904},[115,80551,80553],{"id":80552},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,80555,80556,80559,80560,80583,80584,29946],{},[38,80557,80558],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,80561,80563],{"className":80562},[886],[888,80564,80565],{"xmlns":890},[892,80566,80567,80581],{},[895,80568,80569,80571,80573,80575,80577,80579],{},[898,80570,2789],{},[1996,80572,2005],{"stretchy":2004},[898,80574,9795],{},[1996,80576,2286],{"separator":2285},[898,80578,9800],{},[1996,80580,2011],{"stretchy":2004},[902,80582,9997],{"encoding":904}," stupně ",[883,80585,80587],{"className":80586},[886],[888,80588,80589],{"xmlns":890},[892,80590,80591,80595],{},[895,80592,80593],{},[898,80594,36862],{},[902,80596,36862],{"encoding":904},[883,80598,80600],{"className":80599},[886],[888,80601,80602],{"xmlns":890,"display":28068},[892,80603,80604,80667],{},[20756,80605,80606],{"width":28073},[20761,80607,80608,80610,80660,80662],{},[20764,80609],{"width":28078},[20764,80611,80612],{},[895,80613,80614,80616,80618,80626,80628,80630,80632,80640,80642,80644,80646,80648,80650,80652,80654,80656,80658],{},[898,80615,9795],{},[2288,80617,2987],{},[9166,80619,80620,80622,80624],{},[898,80621,2789],{},[898,80623,9795],{},[1996,80625,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,80627,2095],{},[898,80629,9800],{},[2288,80631,2987],{},[9166,80633,80634,80636,80638],{},[898,80635,2789],{},[898,80637,9800],{},[1996,80639,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,80641,1998],{},[898,80643,36862],{},[2288,80645,2987],{},[898,80647,2789],{},[1996,80649,2005],{"stretchy":2004},[898,80651,9795],{},[1996,80653,2286],{"separator":2285},[898,80655,9800],{},[1996,80657,2011],{"stretchy":2004},[898,80659,1975],{"mathvariant":2376},[20764,80661],{"width":28078},[20764,80663,80664],{},[2288,80665,80666],{},"(5.12)",[902,80668,80669],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,80671,80672,80693],{},[38,80673,80674,80675],{},"Speciální případ ",[883,80676,80678],{"className":80677},[886],[888,80679,80680],{"xmlns":890},[892,80681,80682,80690],{},[895,80683,80684,80686,80688],{},[898,80685,36862],{},[1996,80687,1998],{},[2129,80689,2278],{},[902,80691,80692],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,80695,80697],{"className":80696},[886],[888,80698,80699],{"xmlns":890,"display":28068},[892,80700,80701,80745],{},[895,80702,80703,80705,80707,80709,80715,80717,80719,80721,80723,80729,80731,80733,80735,80737,80739,80741,80743],{},[898,80704,9795],{},[1996,80706,3177],{},[898,80708,2818],{},[2272,80710,80711,80713],{},[898,80712,3937],{},[898,80714,9795],{},[1996,80716,2095],{},[898,80718,9800],{},[1996,80720,3177],{},[898,80722,2818],{},[2272,80724,80725,80727],{},[898,80726,3937],{},[898,80728,9800],{},[1996,80730,1998],{},[898,80732,2789],{},[1996,80734,2005],{"stretchy":2004},[898,80736,9795],{},[1996,80738,2286],{"separator":2285},[898,80740,9800],{},[1996,80742,2011],{"stretchy":2004},[898,80744,1975],{"mathvariant":2376},[902,80746,80747],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,80749,80750,80751,80754],{},"Slovně — ",[38,80752,80753],{},"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).",[115,80756,9778],{"id":74896},[724,80758,80759,10025,80761,80764,80765,80787,80788,2704],{},[38,80760,9778],{},[614,80762,80763],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,80766,80768],{"className":80767},[886],[888,80769,80770],{"xmlns":890},[892,80771,80772,80784],{},[895,80773,80774,80776,80778,80780,80782],{},[1996,80775,2486],{"stretchy":2004},[898,80777,9795],{},[1996,80779,2286],{"separator":2285},[898,80781,9800],{},[1996,80783,2501],{"stretchy":2004},[902,80785,80786],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,80789,80791],{"className":80790},[886],[888,80792,80793],{"xmlns":890},[892,80794,80795,80800],{},[895,80796,80797],{},[898,80798,80799],{},"q",[902,80801,80799],{"encoding":904},[883,80803,80805],{"className":80804},[886],[888,80806,80807],{"xmlns":890,"display":28068},[892,80808,80809,80844],{},[20756,80810,80811],{"width":28073},[20761,80812,80813,80815,80837,80839],{},[20764,80814],{"width":28078},[20764,80816,80817],{},[895,80818,80819,80821,80823,80825,80827,80829,80831,80833,80835],{},[898,80820,2789],{},[1996,80822,2005],{"stretchy":2004},[898,80824,9795],{},[1996,80826,2286],{"separator":2285},[898,80828,9800],{},[1996,80830,2011],{"stretchy":2004},[1996,80832,1998],{},[898,80834,80799],{},[898,80836,1975],{"mathvariant":2376},[20764,80838],{"width":28078},[20764,80840,80841],{},[2288,80842,80843],{},"(5.13)",[902,80845,80846],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,80848,80849,80850,80853,80854,3918],{},"Jsou to ",[38,80851,80852],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,80855,80857],{"className":80856,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,80859,80860],{},[38,80861,80862],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,80864,80865,80870,80875,80880],{},[123,80866,80867,80869],{},[38,80868,12521],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,80871,80872,80874],{},[38,80873,37666],{}," (úloha 5.14);",[123,80876,80877,8425],{},[38,80878,80879],{},"neprotínají se",[123,80881,80882,80883,4358,80896,1975],{},"s rostoucím ",[883,80884,80886],{"className":80885},[886],[888,80887,80888],{"xmlns":890},[892,80889,80890,80894],{},[895,80891,80892],{},[898,80893,80799],{},[902,80895,80799],{"encoding":904},[38,80897,80898],{},"vzdalují od počátku",[724,80900,80901],{},[614,80902,80903,80904,80926,80927,1975],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,80905,80907],{"className":80906},[886],[888,80908,80909],{"xmlns":890},[892,80910,80911,80923],{},[895,80912,80913,80915,80917,80919,80921],{},[1996,80914,2005],{"stretchy":2004},[898,80916,9795],{},[1996,80918,2286],{"separator":2285},[898,80920,9800],{},[1996,80922,2011],{"stretchy":2004},[902,80924,80925],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,80928,80930],{"className":80929},[886],[888,80931,80932],{"xmlns":890},[892,80933,80934,80958],{},[895,80935,80936,80942,80944,80950,80952],{},[2272,80937,80938,80940],{},[898,80939,80799],{},[2129,80941,2278],{},[1996,80943,3447],{},[2272,80945,80946,80948],{},[898,80947,80799],{},[2129,80949,2327],{},[1996,80951,3447],{},[2272,80953,80954,80956],{},[898,80955,80799],{},[2129,80957,2131],{},[902,80959,80960],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,80962,80964,80965,2011],{"id":80963},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,80966,80968],{"className":80967},[886],[888,80969,80970],{"xmlns":890},[892,80971,80972,80982],{},[895,80973,80974,80976,80978,80980],{},[898,80975,2818],{},[898,80977,3994],{},[898,80979,2774],{},[898,80981,8673],{},[902,80983,10599],{"encoding":904},[724,80985,80986,10025,80989,80992],{},[38,80987,80988],{},"Mezní míra technické substituce",[614,80990,80991],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,80994,80996],{"className":80995},[886],[888,80997,80998],{"xmlns":890,"display":28068},[892,80999,81000,81091],{},[20756,81001,81002],{"width":28073},[20761,81003,81004,81006,81084,81086],{},[20764,81005],{"width":28078},[20764,81007,81008],{},[895,81009,81010,81012,81014,81016,81018,81020,81022,81024,81026,81028,81030,81032,81034,81036,81038,81040,81062,81064,81082],{},[898,81011,2818],{},[898,81013,3994],{},[898,81015,2774],{},[898,81017,8673],{},[1996,81019,1998],{},[898,81021,2818],{},[898,81023,3994],{},[898,81025,2774],{},[898,81027,8673],{},[1996,81029,2005],{"stretchy":2004},[898,81031,9795],{},[1996,81033,2286],{"separator":2285},[898,81035,9800],{},[1996,81037,2011],{"stretchy":2004},[1996,81039,1998],{},[2329,81041,81042,81052],{},[895,81043,81044,81046],{},[898,81045,2818],{},[2272,81047,81048,81050],{},[898,81049,3937],{},[898,81051,9795],{},[895,81053,81054,81056],{},[898,81055,2818],{},[2272,81057,81058,81060],{},[898,81059,3937],{},[898,81061,9800],{},[1996,81063,1998],{},[2329,81065,81066,81074],{},[9166,81067,81068,81070,81072],{},[898,81069,2789],{},[898,81071,9795],{},[1996,81073,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[9166,81075,81076,81078,81080],{},[898,81077,2789],{},[898,81079,9800],{},[1996,81081,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[898,81083,1975],{"mathvariant":2376},[20764,81085],{"width":28078},[20764,81087,81088],{},[2288,81089,81090],{},"(5.14)",[902,81092,81093],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,81095,81096,2203,81098,81128,81129,81160],{},[38,81097,9216],{},[883,81099,81101],{"className":81100},[886],[888,81102,81103],{"xmlns":890},[892,81104,81105,81125],{},[895,81106,81107,81109,81111,81113,81115,81117,81119,81121,81123],{},[898,81108,2818],{},[898,81110,3994],{},[898,81112,2774],{},[898,81114,8673],{},[1996,81116,2005],{"stretchy":2004},[898,81118,9795],{},[1996,81120,2286],{"separator":2285},[898,81122,9800],{},[1996,81124,2011],{"stretchy":2004},[902,81126,81127],{"encoding":904},"MRTS(L, K)"," udává, ",[38,81130,81131,81132,81145,81146,81159],{},"o kolik se musí přibližně změnit kapitál ",[883,81133,81135],{"className":81134},[886],[888,81136,81137],{"xmlns":890},[892,81138,81139,81143],{},[895,81140,81141],{},[898,81142,9800],{},[902,81144,9800],{"encoding":904},", jestliže se práce ",[883,81147,81149],{"className":81148},[886],[888,81150,81151],{"xmlns":890},[892,81152,81153,81157],{},[895,81154,81155],{},[898,81156,9795],{},[902,81158,9795],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[3867,81162,81163],{},[724,81164,81165,18025,81167,81186,81187,81224,81225,81228,81229,81233],{},[883,81166,4155],{},[883,81168,81170],{"className":81169},[886],[888,81171,81172],{"xmlns":890},[892,81173,81174,81184],{},[895,81175,81176,81178,81180,81182],{},[898,81177,2818],{},[898,81179,3994],{},[898,81181,2774],{},[898,81183,8673],{},[902,81185,10599],{"encoding":904}," říká: ",[614,81188,81189,81190,81209,81210,81223],{},"„jednu jednotku práce musím nahradit přibližně ",[883,81191,81193],{"className":81192},[886],[888,81194,81195],{"xmlns":890},[892,81196,81197,81207],{},[895,81198,81199,81201,81203,81205],{},[898,81200,2818],{},[898,81202,3994],{},[898,81204,2774],{},[898,81206,8673],{},[902,81208,10599],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,81211,81213],{"className":81212},[886],[888,81214,81215],{"xmlns":890},[892,81216,81217,81221],{},[895,81218,81219],{},[898,81220,2789],{},[902,81222,2789],{"encoding":904}," zůstala stejná.\""," Je to ",[38,81226,81227],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,81230,81232],{"className":81231,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,81235,81236],{},[2559,81237],{"alt":81238,"className":81239,"src":81240},"imek-izokvanty-mrts",[210,2563],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,81242,81243,81246,81247,8102,81277,81299,81300,3151],{},[38,81244,81245],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,81248,81250],{"className":81249},[886],[888,81251,81252],{"xmlns":890},[892,81253,81254,81274],{},[895,81255,81256,81258,81264,81266,81272],{},[1996,81257,2486],{"stretchy":2004},[2272,81259,81260,81262],{},[898,81261,9795],{},[2129,81263,2327],{},[1996,81265,2286],{"separator":2285},[2272,81267,81268,81270],{},[898,81269,9800],{},[2129,81271,2327],{},[1996,81273,2501],{"stretchy":2004},[902,81275,81276],{"encoding":904},"[L_0, K_0]",[883,81278,81280],{"className":81279},[886],[888,81281,81282],{"xmlns":890},[892,81283,81284,81296],{},[895,81285,81286,81288,81290,81292,81294],{},[1996,81287,2225],{},[898,81289,2818],{},[898,81291,3994],{},[898,81293,2774],{},[898,81295,8673],{},[902,81297,81298],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,81301,81303],{"className":81302},[886],[888,81304,81305],{"xmlns":890},[892,81306,81307,81329],{},[895,81308,81309,81311,81313,81315,81317,81319,81321,81323],{},[898,81310,2789],{},[1996,81312,2005],{"stretchy":2004},[898,81314,9795],{},[1996,81316,2286],{"separator":2285},[898,81318,9800],{},[1996,81320,2011],{"stretchy":2004},[1996,81322,1998],{},[2272,81324,81325,81327],{},[898,81326,80799],{},[2129,81328,2327],{},[902,81330,81331],{"encoding":904},"Q(L,K) = q_0",[883,81333,81335],{"className":81334},[886],[888,81336,81337],{"xmlns":890,"display":28068},[892,81338,81339,81391],{},[895,81340,81341,81355,81357,81359,81377,81379,81381,81383,81385,81387,81389],{},[2329,81342,81343,81349],{},[895,81344,81345,81347],{},[898,81346,2194],{},[898,81348,9800],{},[895,81350,81351,81353],{},[898,81352,2194],{},[898,81354,9795],{},[1996,81356,1998],{},[1996,81358,2225],{},[2329,81360,81361,81369],{},[9166,81362,81363,81365,81367],{},[898,81364,2789],{},[898,81366,9795],{},[1996,81368,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[9166,81370,81371,81373,81375],{},[898,81372,2789],{},[898,81374,9800],{},[1996,81376,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,81378,1998],{},[1996,81380,2225],{},[898,81382,2818],{},[898,81384,3994],{},[898,81386,2774],{},[898,81388,8673],{},[898,81390,1975],{"mathvariant":2376},[902,81392,81393],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,81395,81396,81397,81412,81413,81429],{},"Změní-li se práce o ",[883,81398,81400],{"className":81399},[886],[888,81401,81402],{"xmlns":890},[892,81403,81404,81410],{},[895,81405,81406,81408],{},[898,81407,2194],{},[898,81409,9795],{},[902,81411,75358],{"encoding":904},", lze pro odhad změny kapitálu ",[883,81414,81416],{"className":81415},[886],[888,81417,81418],{"xmlns":890},[892,81419,81420,81426],{},[895,81421,81422,81424],{},[898,81423,2889],{"mathvariant":2376},[898,81425,9800],{},[902,81427,81428],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,81431,81433],{"className":81432},[886],[888,81434,81435],{"xmlns":890,"display":28068},[892,81436,81437,81484],{},[20756,81438,81439],{"width":28073},[20761,81440,81441,81443,81477,81479],{},[20764,81442],{"width":28078},[20764,81444,81445],{},[895,81446,81447,81449,81451,81453,81455,81457,81459,81461,81463,81465,81467,81469,81471,81473,81475],{},[898,81448,2889],{"mathvariant":2376},[898,81450,9800],{},[1996,81452,2730],{},[898,81454,2194],{},[898,81456,9800],{},[1996,81458,1998],{},[1996,81460,2225],{},[898,81462,2818],{},[898,81464,3994],{},[898,81466,2774],{},[898,81468,8673],{},[2288,81470,2987],{},[898,81472,2194],{},[898,81474,9795],{},[1996,81476,2286],{"separator":2285},[20764,81478],{"width":28078},[20764,81480,81481],{},[2288,81482,81483],{},"(5.15)",[902,81485,81486],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,81488,81490],{"className":81489},[886],[888,81491,81492],{"xmlns":890,"display":28068},[892,81493,81494,81543],{},[20756,81495,81496],{"width":28073},[20761,81497,81498,81500,81536,81538],{},[20764,81499],{"width":28078},[20764,81501,81502],{},[895,81503,81504,81506,81508,81510,81528,81530,81532,81534],{},[898,81505,2194],{},[898,81507,9795],{},[1996,81509,1998],{},[2329,81511,81512,81518],{},[895,81513,81514,81516],{},[1996,81515,2225],{},[2129,81517,2278],{},[895,81519,81520,81522,81524,81526],{},[898,81521,2818],{},[898,81523,3994],{},[898,81525,2774],{},[898,81527,8673],{},[2288,81529,2987],{},[898,81531,2194],{},[898,81533,9800],{},[898,81535,1975],{"mathvariant":2376},[20764,81537],{"width":28078},[20764,81539,81540],{},[2288,81541,81542],{},"(5.16)",[902,81544,81545],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[3867,81547,81548,81572],{},[724,81549,81550,81552,81553],{},[883,81551,4572],{}," Postup — jak spočítat ",[883,81554,81556],{"className":81555},[886],[888,81557,81558],{"xmlns":890},[892,81559,81560,81570],{},[895,81561,81562,81564,81566,81568],{},[898,81563,2818],{},[898,81565,3994],{},[898,81567,2774],{},[898,81569,8673],{},[902,81571,10599],{"encoding":904},[152,81573,81574,81615,81658,81690],{},[123,81575,81576,81577,3885,81596,1975],{},"Vypočtěte parciální derivace ",[883,81578,81580],{"className":81579},[886],[888,81581,81582],{"xmlns":890},[892,81583,81584,81594],{},[895,81585,81586],{},[9166,81587,81588,81590,81592],{},[898,81589,2789],{},[898,81591,9795],{},[1996,81593,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,81595,10021],{"encoding":904},[883,81597,81599],{"className":81598},[886],[888,81600,81601],{"xmlns":890},[892,81602,81603,81613],{},[895,81604,81605],{},[9166,81606,81607,81609,81611],{},[898,81608,2789],{},[898,81610,9800],{},[1996,81612,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,81614,10067],{"encoding":904},[123,81616,65843,81617,81657],{},[883,81618,81620],{"className":81619},[886],[888,81621,81622],{"xmlns":890},[892,81623,81624,81654],{},[895,81625,81626,81628,81630,81632,81634,81636,81644,81646],{},[898,81627,2818],{},[898,81629,3994],{},[898,81631,2774],{},[898,81633,8673],{},[1996,81635,1998],{},[9166,81637,81638,81640,81642],{},[898,81639,2789],{},[898,81641,9795],{},[1996,81643,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[898,81645,4674],{"mathvariant":2376},[9166,81647,81648,81650,81652],{},[898,81649,2789],{},[898,81651,9800],{},[1996,81653,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,81655,81656],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,81659,81660,81661,1975],{},"Případně dosaďte konkrétní ",[883,81662,81664],{"className":81663},[886],[888,81665,81666],{"xmlns":890},[892,81667,81668,81688],{},[895,81669,81670,81672,81678,81680,81686],{},[1996,81671,2486],{"stretchy":2004},[2272,81673,81674,81676],{},[898,81675,9795],{},[2129,81677,2327],{},[1996,81679,2286],{"separator":2285},[2272,81681,81682,81684],{},[898,81683,9800],{},[2129,81685,2327],{},[1996,81687,2501],{"stretchy":2004},[902,81689,81276],{"encoding":904},[123,81691,81692,81693,81727,81728,81730],{},"Pro odhad substituce použijte ",[883,81694,81696],{"className":81695},[886],[888,81697,81698],{"xmlns":890},[892,81699,81700,81724],{},[895,81701,81702,81704,81706,81708,81710,81712,81714,81716,81718,81720,81722],{},[898,81703,2889],{"mathvariant":2376},[898,81705,9800],{},[1996,81707,2730],{},[1996,81709,2225],{},[898,81711,2818],{},[898,81713,3994],{},[898,81715,2774],{},[898,81717,8673],{},[1996,81719,3177],{},[898,81721,2889],{"mathvariant":2376},[898,81723,9795],{},[902,81725,81726],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,81729,52608],{}," — substituce, ne doplnění).",[724,81732,81733],{},[614,81734,81735,81736,81768,81769,2624,81782,15794,81811,81826],{},"Obrázek 5.7 — izokvanta ",[883,81737,81739],{"className":81738},[886],[888,81740,81741],{"xmlns":890},[892,81742,81743,81765],{},[895,81744,81745,81751,81753,81755,81757,81759,81761,81763],{},[2272,81746,81747,81749],{},[898,81748,80799],{},[2129,81750,2327],{},[1996,81752,1998],{},[898,81754,2789],{},[1996,81756,2005],{"stretchy":2004},[898,81758,9795],{},[1996,81760,2286],{"separator":2285},[898,81762,9800],{},[1996,81764,2011],{"stretchy":2004},[902,81766,81767],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,81770,81772],{"className":81771},[886],[888,81773,81774],{"xmlns":890},[892,81775,81776,81780],{},[895,81777,81778],{},[898,81779,18857],{},[902,81781,18857],{"encoding":904},[883,81783,81785],{"className":81784},[886],[888,81786,81787],{"xmlns":890},[892,81788,81789,81809],{},[895,81790,81791,81793,81799,81801,81807],{},[1996,81792,2486],{"stretchy":2004},[2272,81794,81795,81797],{},[898,81796,9795],{},[2129,81798,2327],{},[1996,81800,2286],{"separator":2285},[2272,81802,81803,81805],{},[898,81804,9800],{},[2129,81806,2327],{},[1996,81808,2501],{"stretchy":2004},[902,81810,81276],{"encoding":904},[883,81812,81814],{"className":81813},[886],[888,81815,81816],{"xmlns":890},[892,81817,81818,81824],{},[895,81819,81820,81822],{},[898,81821,2889],{"mathvariant":2376},[898,81823,9800],{},[902,81825,81428],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,81828,81830],{"id":81829},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,81832,81834],{"id":81833},"příklad-54","Příklad 5.4",[724,81836,76675,81837,1343,81879,1343,81896,1975],{},[883,81838,81840],{"className":81839},[886],[888,81841,81842],{"xmlns":890},[892,81843,81844,81876],{},[895,81845,81846,81848,81850,81852,81864],{},[898,81847,2789],{},[1996,81849,1998],{},[2129,81851,36246],{},[2124,81853,81854,81856],{},[898,81855,9795],{},[895,81857,81858,81860,81862],{},[2129,81859,2278],{},[898,81861,4674],{"mathvariant":2376},[2129,81863,2131],{},[2124,81865,81866,81868],{},[898,81867,9800],{},[895,81869,81870,81872,81874],{},[2129,81871,2278],{},[898,81873,4674],{"mathvariant":2376},[2129,81875,2173],{},[902,81877,81878],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,81880,81882],{"className":81881},[886],[888,81883,81884],{"xmlns":890},[892,81885,81886,81894],{},[895,81887,81888,81890,81892],{},[898,81889,9795],{},[1996,81891,1998],{},[2129,81893,9035],{},[902,81895,77049],{"encoding":904},[883,81897,81899],{"className":81898},[886],[888,81900,81901],{"xmlns":890},[892,81902,81903,81911],{},[895,81904,81905,81907,81909],{},[898,81906,9800],{},[1996,81908,1998],{},[2129,81910,3090],{},[902,81912,81913],{"encoding":904},"K = 100",[724,81915,81916],{},[38,81917,81918],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,81920,81922],{"className":81921},[886],[888,81923,81924],{"xmlns":890,"display":28068},[892,81925,81926,82040],{},[895,81927,81928,81930,81936,81938,81946,81948,81956,81970,81982,81984,81986,81988,81994,81996,81998,82000,82002,82004,82006,82014,82016,82026,82028,82035,82037],{},[898,81929,2818],{},[2272,81931,81932,81934],{},[898,81933,3937],{},[898,81935,9795],{},[1996,81937,1998],{},[9166,81939,81940,81942,81944],{},[898,81941,2789],{},[898,81943,9795],{},[1996,81945,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,81947,1998],{},[2325,81949,81950],{"scriptlevel":2327,"displaystyle":2004},[2329,81951,81952,81954],{},[2129,81953,36246],{},[2129,81955,2131],{},[2124,81957,81958,81960],{},[898,81959,9795],{},[895,81961,81962,81964,81966,81968],{},[1996,81963,2225],{},[2129,81965,2278],{},[898,81967,4674],{"mathvariant":2376},[2129,81969,2131],{},[2124,81971,81972,81974],{},[898,81973,9800],{},[895,81975,81976,81978,81980],{},[2129,81977,2278],{},[898,81979,4674],{"mathvariant":2376},[2129,81981,2173],{},[1996,81983,2286],{"separator":2285},[5878,81985],{"width":15286},[898,81987,2818],{},[2272,81989,81990,81992],{},[898,81991,3937],{},[898,81993,9795],{},[1996,81995,2005],{"stretchy":2004},[2129,81997,9035],{},[1996,81999,2286],{"separator":2285},[2129,82001,3090],{},[1996,82003,2011],{"stretchy":2004},[1996,82005,1998],{},[2325,82007,82008],{"scriptlevel":2327,"displaystyle":2004},[2329,82009,82010,82012],{},[2129,82011,36246],{},[2129,82013,2131],{},[1996,82015,3177],{},[2325,82017,82018],{"scriptlevel":2327,"displaystyle":2004},[2329,82019,82020,82022],{},[2129,82021,2278],{},[8117,82023,82024],{},[2129,82025,9035],{},[1996,82027,3177],{},[82029,82030,82031,82033],"mroot",{},[2129,82032,3090],{},[2129,82034,2173],{},[1996,82036,2730],{},[2129,82038,82039],{},"7,153.",[902,82041,82042],{"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.",[724,82044,82045,82046,44162,82068,10233,82085,82106,82107,82128],{},"Přibližná změna při ",[883,82047,82049],{"className":82048},[886],[888,82050,82051],{"xmlns":890},[892,82052,82053,82065],{},[895,82054,82055,82057,82059,82061,82063],{},[898,82056,9795],{},[1996,82058,2704],{},[2129,82060,9035],{},[1996,82062,3123],{},[2129,82064,38348],{},[902,82066,82067],{"encoding":904},"L: 20 \\to 21",[883,82069,82071],{"className":82070},[886],[888,82072,82073],{"xmlns":890},[892,82074,82075,82083],{},[895,82076,82077,82079,82081],{},[898,82078,9800],{},[1996,82080,1998],{},[2129,82082,3090],{},[902,82084,81913],{"encoding":904},[883,82086,82088],{"className":82087},[886],[888,82089,82090],{"xmlns":890},[892,82091,82092,82103],{},[895,82093,82094,82096,82098,82100],{},[898,82095,2889],{"mathvariant":2376},[898,82097,2789],{},[1996,82099,2730],{},[2129,82101,82102],{},"7,153",[902,82104,82105],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,82108,82110],{"className":82109},[886],[888,82111,82112],{"xmlns":890},[892,82113,82114,82125],{},[895,82115,82116,82118,82120,82122],{},[898,82117,2889],{"mathvariant":2376},[898,82119,2789],{},[1996,82121,2730],{},[2129,82123,82124],{},"26,888",[902,82126,82127],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,82130,82131,82134],{},[38,82132,82133],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,82136,82138],{"className":82137},[886],[888,82139,82140],{"xmlns":890,"display":28068},[892,82141,82142,82242],{},[895,82143,82144,82146,82152,82154,82162,82164,82166,82178,82192,82194,82196,82198,82204,82206,82208,82210,82212,82214,82216,82218,82222,82224,82237,82239],{},[898,82145,2818],{},[2272,82147,82148,82150],{},[898,82149,3937],{},[898,82151,9800],{},[1996,82153,1998],{},[9166,82155,82156,82158,82160],{},[898,82157,2789],{},[898,82159,9800],{},[1996,82161,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,82163,1998],{},[2129,82165,2228],{},[2124,82167,82168,82170],{},[898,82169,9795],{},[895,82171,82172,82174,82176],{},[2129,82173,2278],{},[898,82175,4674],{"mathvariant":2376},[2129,82177,2131],{},[2124,82179,82180,82182],{},[898,82181,9800],{},[895,82183,82184,82186,82188,82190],{},[1996,82185,2225],{},[2129,82187,2131],{},[898,82189,4674],{"mathvariant":2376},[2129,82191,2173],{},[1996,82193,2286],{"separator":2285},[5878,82195],{"width":15286},[898,82197,2818],{},[2272,82199,82200,82202],{},[898,82201,3937],{},[898,82203,9800],{},[1996,82205,2005],{"stretchy":2004},[2129,82207,9035],{},[1996,82209,2286],{"separator":2285},[2129,82211,3090],{},[1996,82213,2011],{"stretchy":2004},[1996,82215,1998],{},[2129,82217,2228],{},[8117,82219,82220],{},[2129,82221,9035],{},[1996,82223,3177],{},[2325,82225,82226],{"scriptlevel":2327,"displaystyle":2004},[2329,82227,82228,82230],{},[2129,82229,2278],{},[82029,82231,82232,82235],{},[2129,82233,82234],{},"10000",[2129,82236,2173],{},[1996,82238,2730],{},[2129,82240,82241],{},"4,525.",[902,82243,82244],{"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.",[724,82246,82247,82248,2685,82265,3918],{},"Produkce poklesne přibližně o 4,525 (z ",[883,82249,82251],{"className":82250},[886],[888,82252,82253],{"xmlns":890},[892,82254,82255,82262],{},[895,82256,82257,82259],{},[1996,82258,2730],{},[2129,82260,82261],{},"905,126",[902,82263,82264],{"encoding":904},"\\approx 905{,}126",[883,82266,82268],{"className":82267},[886],[888,82269,82270],{"xmlns":890},[892,82271,82272,82279],{},[895,82273,82274,82276],{},[1996,82275,2730],{},[2129,82277,82278],{},"900,601",[902,82280,82281],{"encoding":904},"\\approx 900{,}601",[724,82283,82284,3130,82331,1343,82353,3918],{},[38,82285,82286,82287,3885,82309],{},"(c) Změna ",[883,82288,82290],{"className":82289},[886],[888,82291,82292],{"xmlns":890},[892,82293,82294,82306],{},[895,82295,82296,82298,82300,82302,82304],{},[898,82297,9795],{},[1996,82299,2704],{},[2129,82301,9035],{},[1996,82303,3123],{},[2129,82305,36246],{},[902,82307,82308],{"encoding":904},"L: 20 \\to 15",[883,82310,82312],{"className":82311},[886],[888,82313,82314],{"xmlns":890},[892,82315,82316,82328],{},[895,82317,82318,82320,82322,82324,82326],{},[898,82319,9800],{},[1996,82321,2704],{},[2129,82323,3090],{},[1996,82325,3123],{},[2129,82327,8803],{},[902,82329,82330],{"encoding":904},"K: 100 \\to 150",[883,82332,82334],{"className":82333},[886],[888,82335,82336],{"xmlns":890},[892,82337,82338,82350],{},[895,82339,82340,82342,82344,82346,82348],{},[898,82341,2194],{},[898,82343,9795],{},[1996,82345,1998],{},[1996,82347,2225],{},[2129,82349,2228],{},[902,82351,82352],{"encoding":904},"dL = -5",[883,82354,82356],{"className":82355},[886],[888,82357,82358],{"xmlns":890},[892,82359,82360,82370],{},[895,82361,82362,82364,82366,82368],{},[898,82363,2194],{},[898,82365,9800],{},[1996,82367,1998],{},[2129,82369,3120],{},[902,82371,82372],{"encoding":904},"dK = 50",[883,82374,82376],{"className":82375},[886],[888,82377,82378],{"xmlns":890,"display":28068},[892,82379,82380,82468],{},[895,82381,82382,82384,82386,82388,82390,82396,82398,82400,82402,82404,82406,82408,82410,82412,82414,82416,82418,82420,82426,82428,82430,82432,82434,82436,82438,82440,82442,82444,82446,82448,82450,82452,82454,82456,82459,82461,82463,82465],{},[898,82383,2194],{},[898,82385,2789],{},[1996,82387,1998],{},[898,82389,2818],{},[2272,82391,82392,82394],{},[898,82393,3937],{},[898,82395,9795],{},[1996,82397,2005],{"stretchy":2004},[2129,82399,9035],{},[1996,82401,2286],{"separator":2285},[2129,82403,3090],{},[1996,82405,2011],{"stretchy":2004},[1996,82407,3177],{},[1996,82409,2005],{"stretchy":2004},[1996,82411,2225],{},[2129,82413,2228],{},[1996,82415,2011],{"stretchy":2004},[1996,82417,2095],{},[898,82419,2818],{},[2272,82421,82422,82424],{},[898,82423,3937],{},[898,82425,9800],{},[1996,82427,2005],{"stretchy":2004},[2129,82429,9035],{},[1996,82431,2286],{"separator":2285},[2129,82433,3090],{},[1996,82435,2011],{"stretchy":2004},[1996,82437,3177],{},[2129,82439,3120],{},[1996,82441,1998],{},[2129,82443,82102],{},[1996,82445,3177],{},[1996,82447,2005],{"stretchy":2004},[1996,82449,2225],{},[2129,82451,2228],{},[1996,82453,2011],{"stretchy":2004},[1996,82455,2095],{},[2129,82457,82458],{},"4,525",[1996,82460,3177],{},[2129,82462,3120],{},[1996,82464,2730],{},[2129,82466,82467],{},"190,485.",[902,82469,82470],{"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.",[724,82472,82473],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,82475,82477],{"id":82476},"příklad-55","Příklad 5.5",[724,82479,82480,82481,82517,82518,1975],{},"Pro produkci ",[883,82482,82484],{"className":82483},[886],[888,82485,82486],{"xmlns":890},[892,82487,82488,82514],{},[895,82489,82490,82492,82494,82496,82498,82500,82502,82504,82510],{},[898,82491,2789],{},[1996,82493,2005],{"stretchy":2004},[898,82495,9795],{},[1996,82497,2286],{"separator":2285},[898,82499,9800],{},[1996,82501,2011],{"stretchy":2004},[1996,82503,1998],{},[82029,82505,82506,82508],{},[898,82507,9795],{},[2129,82509,2173],{},[8117,82511,82512],{},[898,82513,9800],{},[902,82515,82516],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,82519,82521],{"className":82520},[886],[888,82522,82523],{"xmlns":890},[892,82524,82525,82541],{},[895,82526,82527,82533,82537,82539],{},[82029,82528,82529,82531],{},[898,82530,9795],{},[2129,82532,2173],{},[8117,82534,82535],{},[898,82536,9800],{},[1996,82538,1998],{},[898,82540,80799],{},[902,82542,82543],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,82545,82546,82547,1975],{},"Umocněním na druhou: ",[883,82548,82550],{"className":82549},[886],[888,82551,82552],{"xmlns":890},[892,82553,82554,82578],{},[895,82555,82556,82558,82560,82566,82568],{},[898,82557,9800],{},[1996,82559,1998],{},[2124,82561,82562,82564],{},[898,82563,80799],{},[2129,82565,2131],{},[898,82567,4674],{"mathvariant":2376},[82029,82569,82570,82576],{},[2124,82571,82572,82574],{},[898,82573,9795],{},[2129,82575,2131],{},[2129,82577,2173],{},[902,82579,82580],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,82582,82583,82623,82663],{},[123,82584,82585],{},[883,82586,82588],{"className":82587},[886],[888,82589,82590],{"xmlns":890},[892,82591,82592,82620],{},[895,82593,82594,82596,82598,82600,82602,82604,82606,82608,82610],{},[898,82595,80799],{},[1996,82597,1998],{},[2129,82599,2278],{},[1996,82601,3987],{},[898,82603,9800],{},[1996,82605,1998],{},[2129,82607,2278],{},[898,82609,4674],{"mathvariant":2376},[82029,82611,82612,82618],{},[2124,82613,82614,82616],{},[898,82615,9795],{},[2129,82617,2131],{},[2129,82619,2173],{},[902,82621,82622],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,82624,82625],{},[883,82626,82628],{"className":82627},[886],[888,82629,82630],{"xmlns":890},[892,82631,82632,82660],{},[895,82633,82634,82636,82638,82640,82642,82644,82646,82648,82650],{},[898,82635,80799],{},[1996,82637,1998],{},[2129,82639,2131],{},[1996,82641,3987],{},[898,82643,9800],{},[1996,82645,1998],{},[2129,82647,2351],{},[898,82649,4674],{"mathvariant":2376},[82029,82651,82652,82658],{},[2124,82653,82654,82656],{},[898,82655,9795],{},[2129,82657,2131],{},[2129,82659,2173],{},[902,82661,82662],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,82664,82665],{},[883,82666,82668],{"className":82667},[886],[888,82669,82670],{"xmlns":890},[892,82671,82672,82700],{},[895,82673,82674,82676,82678,82680,82682,82684,82686,82688,82690],{},[898,82675,80799],{},[1996,82677,1998],{},[2129,82679,2173],{},[1996,82681,3987],{},[898,82683,9800],{},[1996,82685,1998],{},[2129,82687,3999],{},[898,82689,4674],{"mathvariant":2376},[82029,82691,82692,82698],{},[2124,82693,82694,82696],{},[898,82695,9795],{},[2129,82697,2131],{},[2129,82699,2173],{},[902,82701,82702],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,82704,82705],{},[614,82706,82707,82708,6473,82729,1975],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,82709,82711],{"className":82710},[886],[888,82712,82713],{"xmlns":890},[892,82714,82715,82727],{},[895,82716,82717,82719,82721,82723,82725],{},[1996,82718,2005],{"stretchy":2004},[898,82720,9795],{},[1996,82722,2286],{"separator":2285},[898,82724,9800],{},[1996,82726,2011],{"stretchy":2004},[902,82728,80925],{"encoding":904},[883,82730,82732],{"className":82731},[886],[888,82733,82734],{"xmlns":890},[892,82735,82736,82752],{},[895,82737,82738,82740,82742,82744,82746,82748,82750],{},[898,82739,80799],{},[1996,82741,1998],{},[2129,82743,2278],{},[1996,82745,2286],{"separator":2285},[2129,82747,2131],{},[1996,82749,2286],{"separator":2285},[2129,82751,2173],{},[902,82753,82754],{"encoding":904},"q = 1, 2, 3",[198,82756,82758],{"id":82757},"příklad-56","Příklad 5.6",[724,82760,76675,82761,1975],{},[883,82762,82764],{"className":82763},[886],[888,82765,82766],{"xmlns":890},[892,82767,82768,82784],{},[895,82769,82770,82772,82774,82776,82778,82780],{},[898,82771,2789],{},[1996,82773,1998],{},[2129,82775,2131],{},[898,82777,9795],{},[1996,82779,2095],{},[8117,82781,82782],{},[898,82783,9800],{},[902,82785,82786],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,82788,82790],{"className":82789},[886],[888,82791,82792],{"xmlns":890,"display":28068},[892,82793,82794,82836],{},[895,82795,82796,82798,82804,82806,82808,82810,82812,82814,82820,82822,82834],{},[898,82797,2818],{},[2272,82799,82800,82802],{},[898,82801,3937],{},[898,82803,9795],{},[1996,82805,1998],{},[2129,82807,2131],{},[1996,82809,2286],{"separator":2285},[5878,82811],{"width":5880},[898,82813,2818],{},[2272,82815,82816,82818],{},[898,82817,3937],{},[898,82819,9800],{},[1996,82821,1998],{},[2329,82823,82824,82826],{},[2129,82825,2278],{},[895,82827,82828,82830],{},[2129,82829,2131],{},[8117,82831,82832],{},[898,82833,9800],{},[898,82835,1975],{"mathvariant":2376},[902,82837,82838],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,82840,82842],{"className":82841},[886],[888,82843,82844],{"xmlns":890,"display":28068},[892,82845,82846,82910],{},[895,82847,82848,82850,82852,82854,82856,82858,82880,82882,82900,82902,82904,82908],{},[898,82849,2818],{},[898,82851,3994],{},[898,82853,2774],{},[898,82855,8673],{},[1996,82857,1998],{},[2329,82859,82860,82870],{},[895,82861,82862,82864],{},[898,82863,2818],{},[2272,82865,82866,82868],{},[898,82867,3937],{},[898,82869,9795],{},[895,82871,82872,82874],{},[898,82873,2818],{},[2272,82875,82876,82878],{},[898,82877,3937],{},[898,82879,9800],{},[1996,82881,1998],{},[2329,82883,82884,82886],{},[2129,82885,2131],{},[2325,82887,82888],{"scriptlevel":2327,"displaystyle":2004},[2329,82889,82890,82892],{},[2129,82891,2278],{},[895,82893,82894,82896],{},[2129,82895,2131],{},[8117,82897,82898],{},[898,82899,9800],{},[1996,82901,1998],{},[2129,82903,2351],{},[8117,82905,82906],{},[898,82907,9800],{},[898,82909,1975],{"mathvariant":2376},[902,82911,82912],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,82914,82915,82916,82959,82960,82999,83000,1975],{},"Například ",[883,82917,82919],{"className":82918},[886],[888,82920,82921],{"xmlns":890},[892,82922,82923,82956],{},[895,82924,82925,82927,82929,82931,82933,82935,82937,82939,82941,82943,82945,82947,82951,82953],{},[898,82926,2818],{},[898,82928,3994],{},[898,82930,2774],{},[898,82932,8673],{},[1996,82934,2005],{"stretchy":2004},[2129,82936,2351],{},[1996,82938,2286],{"separator":2285},[2129,82940,24203],{},[1996,82942,2011],{"stretchy":2004},[1996,82944,1998],{},[2129,82946,2351],{},[8117,82948,82949],{},[2129,82950,24203],{},[1996,82952,2730],{},[2129,82954,82955],{},"10,58",[902,82957,82958],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,82961,82963],{"className":82962},[886],[888,82964,82965],{"xmlns":890},[892,82966,82967,82996],{},[895,82968,82969,82971,82973,82975,82977,82979,82981,82983,82985,82987,82991,82993],{},[898,82970,2789],{},[1996,82972,2005],{"stretchy":2004},[2129,82974,2351],{},[1996,82976,2286],{"separator":2285},[2129,82978,24203],{},[1996,82980,2011],{"stretchy":2004},[1996,82982,1998],{},[2129,82984,5585],{},[1996,82986,2095],{},[8117,82988,82989],{},[2129,82990,24203],{},[1996,82992,2730],{},[2129,82994,82995],{},"10,646",[902,82997,82998],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,83001,83003],{"className":83002},[886],[888,83004,83005],{"xmlns":890},[892,83006,83007,83015],{},[895,83008,83009,83011],{},[2129,83010,2351],{},[8117,83012,83013],{},[2129,83014,24203],{},[902,83016,83017],{"encoding":904},"4\\sqrt{7}",[724,83019,83020,83021,83041],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,83022,83024],{"className":83023},[886],[888,83025,83026],{"xmlns":890},[892,83027,83028,83038],{},[895,83029,83030,83032,83034,83036],{},[898,83031,2194],{},[898,83033,9795],{},[1996,83035,1998],{},[2129,83037,2131],{},[902,83039,83040],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,83043,83045],{"className":83044},[886],[888,83046,83047],{"xmlns":890,"display":28068},[892,83048,83049,83098],{},[895,83050,83051,83053,83055,83057,83059,83061,83063,83065,83067,83069,83071,83073,83075,83077,83079,83081,83083,83085,83087,83091,83093,83095],{},[898,83052,2194],{},[898,83054,9800],{},[1996,83056,1998],{},[1996,83058,2225],{},[898,83060,2818],{},[898,83062,3994],{},[898,83064,2774],{},[898,83066,8673],{},[1996,83068,2005],{"stretchy":2004},[2129,83070,2351],{},[1996,83072,2286],{"separator":2285},[2129,83074,24203],{},[1996,83076,2011],{"stretchy":2004},[1996,83078,3177],{},[2129,83080,2131],{},[1996,83082,1998],{},[1996,83084,2225],{},[2129,83086,5585],{},[8117,83088,83089],{},[2129,83090,24203],{},[1996,83092,2730],{},[1996,83094,2225],{},[2129,83096,83097],{},"21,17.",[902,83099,83100],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,83102,83104],{"id":83103},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,83106,83107,83108,1343,83110,3885,83112,83114,83115,83118,83119,83122],{},"Hlavními faktory produkce jsou ",[38,83109,74916],{},[38,83111,74932],{},[38,83113,74948],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,83116,83117],{},"jednofaktorový"," (pouze práce) a ",[38,83120,83121],{},"dvoufaktorový"," (práce + kapitál) model.",[724,83124,83125,83126,83129,83130,83132,83133,83135,83136,26191,83139,83158,83159,83176,83177,83194,83195,83217,83218,4358,83237,1975],{},"V ",[38,83127,83128],{},"1F modelu"," se definuje ",[38,83131,10024],{}," (derivace produkce podle práce) a ",[38,83134,74851],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,83137,83138],{},"zákonu klesajících výnosů",[883,83140,83142],{"className":83141},[886],[888,83143,83144],{"xmlns":890},[892,83145,83146,83156],{},[895,83147,83148,83150],{},[898,83149,2818],{},[2272,83151,83152,83154],{},[898,83153,3937],{},[898,83155,9795],{},[902,83157,10045],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,83160,83162],{"className":83161},[886],[888,83163,83164],{"xmlns":890},[892,83165,83166,83174],{},[895,83167,83168],{},[2272,83169,83170,83172],{},[898,83171,9795],{},[2129,83173,2327],{},[902,83175,75560],{"encoding":904}," klesá a v bodě ",[883,83178,83180],{"className":83179},[886],[888,83181,83182],{"xmlns":890},[892,83183,83184,83192],{},[895,83185,83186],{},[2272,83187,83188,83190],{},[898,83189,9795],{},[2129,83191,2278],{},[902,83193,13214],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,83196,83197,83198],{},"princip maximalizace ",[883,83199,83201],{"className":83200},[886],[888,83202,83203],{"xmlns":890},[892,83204,83205,83215],{},[895,83206,83207,83209],{},[898,83208,4255],{},[2272,83210,83211,83213],{},[898,83212,3937],{},[898,83214,9795],{},[902,83216,74635],{"encoding":904},": v bodě maxima ",[883,83219,83221],{"className":83220},[886],[888,83222,83223],{"xmlns":890},[892,83224,83225,83235],{},[895,83226,83227,83229],{},[898,83228,4255],{},[2272,83230,83231,83233],{},[898,83232,3937],{},[898,83234,9795],{},[902,83236,74635],{"encoding":904},[883,83238,83240],{"className":83239},[886],[888,83241,83242],{"xmlns":890},[892,83243,83244,83264],{},[895,83245,83246,83248,83254,83256,83258],{},[898,83247,2818],{},[2272,83249,83250,83252],{},[898,83251,3937],{},[898,83253,9795],{},[1996,83255,1998],{},[898,83257,4255],{},[2272,83259,83260,83262],{},[898,83261,3937],{},[898,83263,9795],{},[902,83265,74665],{"encoding":904},[724,83267,83268,83269,83272,83273,2203,83276,83305,83306,83323,83324,83327,83328,83357,83358,83360,83361,8102,83391,83413],{},"Ve ",[38,83270,83271],{},"2F modelu"," se obvykle používají ",[38,83274,83275],{},"Cobb-Douglasovy funkce",[883,83277,83279],{"className":83278},[886],[888,83280,83281],{"xmlns":890},[892,83282,83283,83303],{},[895,83284,83285,83287,83289,83291,83297],{},[898,83286,2789],{},[1996,83288,1998],{},[898,83290,4255],{},[2124,83292,83293,83295],{},[898,83294,9795],{},[898,83296,207],{},[2124,83298,83299,83301],{},[898,83300,9800],{},[898,83302,2098],{},[902,83304,74732],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,83307,83309],{"className":83308},[886],[888,83310,83311],{"xmlns":890},[892,83312,83313,83321],{},[895,83314,83315,83317,83319],{},[898,83316,207],{},[1996,83318,2095],{},[898,83320,2098],{},[902,83322,74826],{"encoding":904}," rozlišujeme ",[38,83325,83326],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,83329,83331],{"className":83330},[886],[888,83332,83333],{"xmlns":890},[892,83334,83335,83355],{},[895,83336,83337,83339,83345,83347,83349],{},[898,83338,2818],{},[2272,83340,83341,83343],{},[898,83342,3937],{},[898,83344,9795],{},[1996,83346,2286],{"separator":2285},[898,83348,2818],{},[2272,83350,83351,83353],{},[898,83352,3937],{},[898,83354,9800],{},[902,83356,74763],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,83359,9778],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,83362,83364],{"className":83363},[886],[888,83365,83366],{"xmlns":890},[892,83367,83368,83388],{},[895,83369,83370,83372,83378,83380,83382],{},[898,83371,2818],{},[2272,83373,83374,83376],{},[898,83375,3937],{},[898,83377,9795],{},[898,83379,4674],{"mathvariant":2376},[898,83381,2818],{},[2272,83383,83384,83386],{},[898,83385,3937],{},[898,83387,9800],{},[902,83389,83390],{"encoding":904},"MP_L\u002FMP_K",[38,83392,83393,83394,2011],{},"mezní míra technické substituce (",[883,83395,83397],{"className":83396},[886],[888,83398,83399],{"xmlns":890},[892,83400,83401,83411],{},[895,83402,83403,83405,83407,83409],{},[898,83404,2818],{},[898,83406,3994],{},[898,83408,2774],{},[898,83410,8673],{},[902,83412,10599],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,83415,49884],{"id":49883},[152,83417,83418,83421,83424,83427,83430,83433,83436,83439,83442,83445,83448],{},[123,83419,83420],{},"Jaké jsou faktory produkce?",[123,83422,83423],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,83425,83426],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,83428,83429],{},"Co udává mezní produkt práce?",[123,83431,83432],{},"Co musí respektovat průběh křivky produkce?",[123,83434,83435],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,83437,83438],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,83440,83441],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,83443,83444],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,83446,83447],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,83449,83450],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,83452,83454],{"id":83453},"úlohy-51517","Úlohy 5.1–5.17",[198,83456,40453],{"id":40452},[724,83458,83459,83462,83463,83485,83486,1343,83506,1343,83526,83546],{},[38,83460,83461],{},"5.1"," Je dána produkce ",[883,83464,83466],{"className":83465},[886],[888,83467,83468],{"xmlns":890},[892,83469,83470,83482],{},[895,83471,83472,83474,83476,83478],{},[898,83473,2789],{},[1996,83475,1998],{},[2129,83477,2863],{},[8117,83479,83480],{},[898,83481,9795],{},[902,83483,83484],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,83487,83489],{"className":83488},[886],[888,83490,83491],{"xmlns":890},[892,83492,83493,83503],{},[895,83494,83495,83497,83499,83501],{},[898,83496,2789],{},[1996,83498,2005],{"stretchy":2004},[2129,83500,2278],{},[1996,83502,2011],{"stretchy":2004},[902,83504,83505],{"encoding":904},"Q(1)",[883,83507,83509],{"className":83508},[886],[888,83510,83511],{"xmlns":890},[892,83512,83513,83523],{},[895,83514,83515,83517,83519,83521],{},[898,83516,2789],{},[1996,83518,2005],{"stretchy":2004},[2129,83520,2351],{},[1996,83522,2011],{"stretchy":2004},[902,83524,83525],{"encoding":904},"Q(4)",[883,83527,83529],{"className":83528},[886],[888,83530,83531],{"xmlns":890},[892,83532,83533,83543],{},[895,83534,83535,83537,83539,83541],{},[898,83536,2789],{},[1996,83538,2005],{"stretchy":2004},[2129,83540,3999],{},[1996,83542,2011],{"stretchy":2004},[902,83544,83545],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,83548,83549,83462,83552,83588,83589,83602,83603,83622,83623,83649,83650,2685,83663,83676],{},[38,83550,83551],{},"5.2",[883,83553,83555],{"className":83554},[886],[888,83556,83557],{"xmlns":890},[892,83558,83559,83585],{},[895,83560,83561,83563,83565,83567,83569,83575,83577,83579],{},[898,83562,2789],{},[1996,83564,1998],{},[1996,83566,2225],{},[2129,83568,2794],{},[2124,83570,83571,83573],{},[898,83572,9795],{},[2129,83574,2173],{},[1996,83576,2095],{},[2129,83578,3999],{},[2124,83580,83581,83583],{},[898,83582,9795],{},[2129,83584,2131],{},[902,83586,83587],{"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 ",[883,83590,83592],{"className":83591},[886],[888,83593,83594],{"xmlns":890},[892,83595,83596,83600],{},[895,83597,83598],{},[898,83599,9795],{},[902,83601,9795],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,83604,83606],{"className":83605},[886],[888,83607,83608],{"xmlns":890},[892,83609,83610,83620],{},[895,83611,83612,83614],{},[898,83613,2818],{},[2272,83615,83616,83618],{},[898,83617,3937],{},[898,83619,9795],{},[902,83621,10045],{"encoding":904},". (f) Vypočtěte ",[883,83624,83626],{"className":83625},[886],[888,83627,83628],{"xmlns":890},[892,83629,83630,83646],{},[895,83631,83632,83634,83640,83642,83644],{},[898,83633,2818],{},[2272,83635,83636,83638],{},[898,83637,3937],{},[898,83639,9795],{},[1996,83641,2005],{"stretchy":2004},[2129,83643,2863],{},[1996,83645,2011],{"stretchy":2004},[902,83647,83648],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,83651,83653],{"className":83652},[886],[888,83654,83655],{"xmlns":890},[892,83656,83657,83661],{},[895,83658,83659],{},[2129,83660,2863],{},[902,83662,2863],{"encoding":904},[883,83664,83666],{"className":83665},[886],[888,83667,83668],{"xmlns":890},[892,83669,83670,83674],{},[895,83671,83672],{},[2129,83673,42289],{},[902,83675,42289],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,83678,83679,83682,83683,83705,83706,83734,83735,83766,83767,1975],{},[38,83680,83681],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,83684,83686],{"className":83685},[886],[888,83687,83688],{"xmlns":890},[892,83689,83690,83702],{},[895,83691,83692,83694,83696,83698],{},[898,83693,2789],{},[1996,83695,1998],{},[2129,83697,15112],{},[8117,83699,83700],{},[898,83701,9795],{},[902,83703,83704],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,83707,83709],{"className":83708},[886],[888,83710,83711],{"xmlns":890},[892,83712,83713,83731],{},[895,83714,83715,83717,83719,83721,83725,83727,83729],{},[898,83716,2789],{},[1996,83718,1998],{},[2129,83720,30083],{},[8117,83722,83723],{},[898,83724,9795],{},[1996,83726,2225],{},[2129,83728,2351],{},[898,83730,9795],{},[902,83732,83733],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,83736,83738],{"className":83737},[886],[888,83739,83740],{"xmlns":890},[892,83741,83742,83763],{},[895,83743,83744,83746,83748,83750,83752,83754,83757],{},[898,83745,2789],{},[1996,83747,1998],{},[2129,83749,3120],{},[898,83751,9795],{},[1996,83753,2225],{},[2129,83755,83756],{},"0,01",[2124,83758,83759,83761],{},[898,83760,9795],{},[2129,83762,2131],{},[902,83764,83765],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,83768,83770],{"className":83769},[886],[888,83771,83772],{"xmlns":890},[892,83773,83774,83800],{},[895,83775,83776,83778,83780,83782,83784,83790,83792,83794],{},[898,83777,2789],{},[1996,83779,1998],{},[1996,83781,2225],{},[2129,83783,68213],{},[2124,83785,83786,83788],{},[898,83787,9795],{},[2129,83789,2173],{},[1996,83791,2095],{},[2129,83793,3999],{},[2124,83795,83796,83798],{},[898,83797,9795],{},[2129,83799,2131],{},[902,83801,83802],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,83804,83805,83808,83809,2624,83828,72200,83845,1975],{},[38,83806,83807],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,83810,83812],{"className":83811},[886],[888,83813,83814],{"xmlns":890},[892,83815,83816,83826],{},[895,83817,83818,83820],{},[898,83819,4255],{},[2272,83821,83822,83824],{},[898,83823,3937],{},[898,83825,9795],{},[902,83827,74635],{"encoding":904},[883,83829,83831],{"className":83830},[886],[888,83832,83833],{"xmlns":890},[892,83834,83835,83843],{},[895,83836,83837],{},[2272,83838,83839,83841],{},[898,83840,9795],{},[2129,83842,2327],{},[902,83844,75560],{"encoding":904},[883,83846,83848],{"className":83847},[886],[888,83849,83850],{"xmlns":890},[892,83851,83852,83892],{},[895,83853,83854,83856,83862,83864,83870,83872,83874,83876,83882,83884,83890],{},[898,83855,4255],{},[2272,83857,83858,83860],{},[898,83859,3937],{},[898,83861,9795],{},[1996,83863,2005],{"stretchy":2004},[2272,83865,83866,83868],{},[898,83867,9795],{},[2129,83869,2327],{},[1996,83871,2011],{"stretchy":2004},[1996,83873,1998],{},[898,83875,2818],{},[2272,83877,83878,83880],{},[898,83879,3937],{},[898,83881,9795],{},[1996,83883,2005],{"stretchy":2004},[2272,83885,83886,83888],{},[898,83887,9795],{},[2129,83889,2327],{},[1996,83891,2011],{"stretchy":2004},[902,83893,83894],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,83896,83897,83462,83900,21596,83936,83949,83950,83969],{},[38,83898,83899],{},"5.5",[883,83901,83903],{"className":83902},[886],[888,83904,83905],{"xmlns":890},[892,83906,83907,83933],{},[895,83908,83909,83911,83913,83915,83917,83923,83925,83927],{},[898,83910,2789],{},[1996,83912,1998],{},[1996,83914,2225],{},[2129,83916,2839],{},[2124,83918,83919,83921],{},[898,83920,9795],{},[2129,83922,2173],{},[1996,83924,2095],{},[2129,83926,3509],{},[2124,83928,83929,83931],{},[898,83930,9795],{},[2129,83932,2131],{},[902,83934,83935],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,83937,83939],{"className":83938},[886],[888,83940,83941],{"xmlns":890},[892,83942,83943,83947],{},[895,83944,83945],{},[898,83946,9795],{},[902,83948,9795],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,83951,83953],{"className":83952},[886],[888,83954,83955],{"xmlns":890},[892,83956,83957,83967],{},[895,83958,83959,83961],{},[898,83960,4255],{},[2272,83962,83963,83965],{},[898,83964,3937],{},[898,83966,9795],{},[902,83968,74635],{"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.",[198,83971,83973],{"id":83972},"dvoufaktorový-model","Dvoufaktorový model",[724,83975,83976,83979,83980,83705,84006,83734,84048,1975],{},[38,83977,83978],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,83981,83983],{"className":83982},[886],[888,83984,83985],{"xmlns":890},[892,83986,83987,84003],{},[895,83988,83989,83991,83993,83995,83997],{},[898,83990,2789],{},[1996,83992,1998],{},[2129,83994,24203],{},[898,83996,9795],{},[2124,83998,83999,84001],{},[898,84000,9800],{},[2129,84002,2131],{},[902,84004,84005],{"encoding":904},"Q = 7 L K^{2}",[883,84007,84009],{"className":84008},[886],[888,84010,84011],{"xmlns":890},[892,84012,84013,84045],{},[895,84014,84015,84017,84019,84021,84033],{},[898,84016,2789],{},[1996,84018,1998],{},[2129,84020,3120],{},[2124,84022,84023,84025],{},[898,84024,9795],{},[895,84026,84027,84029,84031],{},[2129,84028,2131],{},[898,84030,4674],{"mathvariant":2376},[2129,84032,2173],{},[2124,84034,84035,84037],{},[898,84036,9800],{},[895,84038,84039,84041,84043],{},[2129,84040,2278],{},[898,84042,4674],{"mathvariant":2376},[2129,84044,2173],{},[902,84046,84047],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,84049,84051],{"className":84050},[886],[888,84052,84053],{"xmlns":890},[892,84054,84055,84087],{},[895,84056,84057,84059,84061,84063,84075],{},[898,84058,2789],{},[1996,84060,1998],{},[2129,84062,3707],{},[2124,84064,84065,84067],{},[898,84066,9795],{},[895,84068,84069,84071,84073],{},[2129,84070,2173],{},[898,84072,4674],{"mathvariant":2376},[2129,84074,2228],{},[2124,84076,84077,84079],{},[898,84078,9800],{},[895,84080,84081,84083,84085],{},[2129,84082,2131],{},[898,84084,4674],{"mathvariant":2376},[2129,84086,2228],{},[902,84088,84089],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,84091,84092,83462,84095,84137,84138,1343,84156,84175,84176,84193],{},[38,84093,84094],{},"5.7",[883,84096,84098],{"className":84097},[886],[888,84099,84100],{"xmlns":890},[892,84101,84102,84134],{},[895,84103,84104,84106,84108,84110,84122],{},[898,84105,2789],{},[1996,84107,1998],{},[2129,84109,2863],{},[2124,84111,84112,84114],{},[898,84113,9795],{},[895,84115,84116,84118,84120],{},[2129,84117,2278],{},[898,84119,4674],{"mathvariant":2376},[2129,84121,2131],{},[2124,84123,84124,84126],{},[898,84125,9800],{},[895,84127,84128,84130,84132],{},[2129,84129,2278],{},[898,84131,4674],{"mathvariant":2376},[2129,84133,2131],{},[902,84135,84136],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,84139,84141],{"className":84140},[886],[888,84142,84143],{"xmlns":890},[892,84144,84145,84153],{},[895,84146,84147,84149,84151],{},[898,84148,9795],{},[1996,84150,1998],{},[2129,84152,20144],{},[902,84154,84155],{"encoding":904},"L = 400",[883,84157,84159],{"className":84158},[886],[888,84160,84161],{"xmlns":890},[892,84162,84163,84172],{},[895,84164,84165,84167,84169],{},[898,84166,9800],{},[1996,84168,1998],{},[2129,84170,84171],{},"17576",[902,84173,84174],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,84177,84179],{"className":84178},[886],[888,84180,84181],{"xmlns":890},[892,84182,84183,84191],{},[895,84184,84185,84187,84189],{},[898,84186,9795],{},[1996,84188,2286],{"separator":2285},[898,84190,9800],{},[902,84192,78987],{"encoding":904}," zdvojnásobí.",[724,84195,84196,84199,84200,84137,84231,1343,84249,69586,84267,84297,84298,84328,84329,2685,84342,84356,84357,2685,84370,84383],{},[38,84197,84198],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,84201,84203],{"className":84202},[886],[888,84204,84205],{"xmlns":890},[892,84206,84207,84228],{},[895,84208,84209,84211,84213,84216,84222],{},[898,84210,2789],{},[1996,84212,1998],{},[2129,84214,84215],{},"1,01",[2124,84217,84218,84220],{},[898,84219,9795],{},[2129,84221,23732],{},[2124,84223,84224,84226],{},[898,84225,9800],{},[2129,84227,23791],{},[902,84229,84230],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,84232,84234],{"className":84233},[886],[888,84235,84236],{"xmlns":890},[892,84237,84238,84246],{},[895,84239,84240,84242,84244],{},[898,84241,9795],{},[1996,84243,1998],{},[2129,84245,30745],{},[902,84247,84248],{"encoding":904},"L = 250",[883,84250,84252],{"className":84251},[886],[888,84253,84254],{"xmlns":890},[892,84255,84256,84264],{},[895,84257,84258,84260,84262],{},[898,84259,9800],{},[1996,84261,1998],{},[2129,84263,2782],{},[902,84265,84266],{"encoding":904},"K = 1000",[883,84268,84270],{"className":84269},[886],[888,84271,84272],{"xmlns":890},[892,84273,84274,84294],{},[895,84275,84276,84278,84284,84286,84288,84290,84292],{},[898,84277,2818],{},[2272,84279,84280,84282],{},[898,84281,3937],{},[898,84283,9795],{},[1996,84285,2005],{"stretchy":2004},[2129,84287,30745],{},[1996,84289,2286],{"separator":2285},[2129,84291,2782],{},[1996,84293,2011],{"stretchy":2004},[902,84295,84296],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,84299,84301],{"className":84300},[886],[888,84302,84303],{"xmlns":890},[892,84304,84305,84325],{},[895,84306,84307,84309,84315,84317,84319,84321,84323],{},[898,84308,2818],{},[2272,84310,84311,84313],{},[898,84312,3937],{},[898,84314,9800],{},[1996,84316,2005],{"stretchy":2004},[2129,84318,30745],{},[1996,84320,2286],{"separator":2285},[2129,84322,2782],{},[1996,84324,2011],{"stretchy":2004},[902,84326,84327],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,84330,84332],{"className":84331},[886],[888,84333,84334],{"xmlns":890},[892,84335,84336,84340],{},[895,84337,84338],{},[898,84339,9795],{},[902,84341,9795],{"encoding":904},[883,84343,84345],{"className":84344},[886],[888,84346,84347],{"xmlns":890},[892,84348,84349,84354],{},[895,84350,84351],{},[2129,84352,84353],{},"260",[902,84355,84353],{"encoding":904}," a současném poklesu ",[883,84358,84360],{"className":84359},[886],[888,84361,84362],{"xmlns":890},[892,84363,84364,84368],{},[895,84365,84366],{},[898,84367,9800],{},[902,84369,9800],{"encoding":904},[883,84371,84373],{"className":84372},[886],[888,84374,84375],{"xmlns":890},[892,84376,84377,84381],{},[895,84378,84379],{},[2129,84380,15193],{},[902,84382,15193],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,84385,84386,84389,84390,1975],{},[38,84387,84388],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,84391,84393],{"className":84392},[886],[888,84394,84395],{"xmlns":890},[892,84396,84397,84417],{},[895,84398,84399,84401,84403,84405,84411],{},[898,84400,2789],{},[1996,84402,1998],{},[2129,84404,2863],{},[2124,84406,84407,84409],{},[898,84408,9795],{},[2129,84410,68213],{},[2124,84412,84413,84415],{},[898,84414,9800],{},[2129,84416,5009],{},[902,84418,84419],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,84421,84422,84425,84426,80583,84449,10394,84462,10025,84512,3918],{},[38,84423,84424],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,84427,84429],{"className":84428},[886],[888,84430,84431],{"xmlns":890},[892,84432,84433,84447],{},[895,84434,84435,84437,84439,84441,84443,84445],{},[898,84436,2789],{},[1996,84438,2005],{"stretchy":2004},[898,84440,9795],{},[1996,84442,2286],{"separator":2285},[898,84444,9800],{},[1996,84446,2011],{"stretchy":2004},[902,84448,9997],{"encoding":904},[883,84450,84452],{"className":84451},[886],[888,84453,84454],{"xmlns":890},[892,84455,84456,84460],{},[895,84457,84458],{},[898,84459,36862],{},[902,84461,36862],{"encoding":904},[883,84463,84465],{"className":84464},[886],[888,84466,84467],{"xmlns":890},[892,84468,84469,84509],{},[895,84470,84471,84473,84481,84483,84485,84493,84495,84497,84499,84501,84503,84505,84507],{},[898,84472,9795],{},[9166,84474,84475,84477,84479],{},[898,84476,2789],{},[898,84478,9795],{},[1996,84480,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,84482,2095],{},[898,84484,9800],{},[9166,84486,84487,84489,84491],{},[898,84488,2789],{},[898,84490,9800],{},[1996,84492,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,84494,1998],{},[898,84496,36862],{},[898,84498,2789],{},[1996,84500,2005],{"stretchy":2004},[898,84502,9795],{},[1996,84504,2286],{"separator":2285},[898,84506,9800],{},[1996,84508,2011],{"stretchy":2004},[902,84510,84511],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,84513,80558],{},[724,84515,84516,84519],{},[38,84517,84518],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,84521,84522,83462,84525,84565,84566,1343,84588,1343,84610,84632],{},[38,84523,84524],{},"5.12",[883,84526,84528],{"className":84527},[886],[888,84529,84530],{"xmlns":890},[892,84531,84532,84562],{},[895,84533,84534,84536,84538,84550],{},[898,84535,2789],{},[1996,84537,1998],{},[2124,84539,84540,84542],{},[898,84541,9795],{},[895,84543,84544,84546,84548],{},[2129,84545,2278],{},[898,84547,4674],{"mathvariant":2376},[2129,84549,2173],{},[2124,84551,84552,84554],{},[898,84553,9800],{},[895,84555,84556,84558,84560],{},[2129,84557,2278],{},[898,84559,4674],{"mathvariant":2376},[2129,84561,2351],{},[902,84563,84564],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,84567,84569],{"className":84568},[886],[888,84570,84571],{"xmlns":890},[892,84572,84573,84585],{},[895,84574,84575,84581,84583],{},[2272,84576,84577,84579],{},[898,84578,80799],{},[2129,84580,2327],{},[1996,84582,1998],{},[2129,84584,2278],{},[902,84586,84587],{"encoding":904},"q_0 = 1",[883,84589,84591],{"className":84590},[886],[888,84592,84593],{"xmlns":890},[892,84594,84595,84607],{},[895,84596,84597,84603,84605],{},[2272,84598,84599,84601],{},[898,84600,80799],{},[2129,84602,2278],{},[1996,84604,1998],{},[2129,84606,2131],{},[902,84608,84609],{"encoding":904},"q_1 = 2",[883,84611,84613],{"className":84612},[886],[888,84614,84615],{"xmlns":890},[892,84616,84617,84629],{},[895,84618,84619,84625,84627],{},[2272,84620,84621,84623],{},[898,84622,80799],{},[2129,84624,2131],{},[1996,84626,1998],{},[2129,84628,2173],{},[902,84630,84631],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,84634,84635,83462,84638,84678,84679,1343,84707,1343,84735,1343,84763,1343,84792,1343,84821,1343,84850,1343,84879,1343,84908,1975],{},[38,84636,84637],{},"5.13",[883,84639,84641],{"className":84640},[886],[888,84642,84643],{"xmlns":890},[892,84644,84645,84675],{},[895,84646,84647,84649,84651,84663],{},[898,84648,2789],{},[1996,84650,1998],{},[2124,84652,84653,84655],{},[898,84654,9795],{},[895,84656,84657,84659,84661],{},[2129,84658,2278],{},[898,84660,4674],{"mathvariant":2376},[2129,84662,2173],{},[2124,84664,84665,84667],{},[898,84666,9800],{},[895,84668,84669,84671,84673],{},[2129,84670,2278],{},[898,84672,4674],{"mathvariant":2376},[2129,84674,2131],{},[902,84676,84677],{"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): ",[883,84680,84682],{"className":84681},[886],[888,84683,84684],{"xmlns":890},[892,84685,84686,84704],{},[895,84687,84688,84694,84696,84698,84700,84702],{},[2272,84689,84690,84692],{},[898,84691,4255],{},[2129,84693,2278],{},[1996,84695,2486],{"stretchy":2004},[2129,84697,2278],{},[1996,84699,8425],{"separator":2285},[2129,84701,2278],{},[1996,84703,2501],{"stretchy":2004},[902,84705,84706],{"encoding":904},"A_1[1; 1]",[883,84708,84710],{"className":84709},[886],[888,84711,84712],{"xmlns":890},[892,84713,84714,84732],{},[895,84715,84716,84722,84724,84726,84728,84730],{},[2272,84717,84718,84720],{},[898,84719,4255],{},[2129,84721,2131],{},[1996,84723,2486],{"stretchy":2004},[2129,84725,2278],{},[1996,84727,8425],{"separator":2285},[2129,84729,5585],{},[1996,84731,2501],{"stretchy":2004},[902,84733,84734],{"encoding":904},"A_2[1; 8]",[883,84736,84738],{"className":84737},[886],[888,84739,84740],{"xmlns":890},[892,84741,84742,84760],{},[895,84743,84744,84750,84752,84754,84756,84758],{},[2272,84745,84746,84748],{},[898,84747,4255],{},[2129,84749,2173],{},[1996,84751,2486],{"stretchy":2004},[2129,84753,2278],{},[1996,84755,8425],{"separator":2285},[2129,84757,66599],{},[1996,84759,2501],{"stretchy":2004},[902,84761,84762],{"encoding":904},"A_3[1; 27]",[883,84764,84766],{"className":84765},[886],[888,84767,84768],{"xmlns":890},[892,84769,84770,84789],{},[895,84771,84772,84778,84780,84782,84784,84787],{},[2272,84773,84774,84776],{},[898,84775,4255],{},[2129,84777,2351],{},[1996,84779,2486],{"stretchy":2004},[2129,84781,2131],{},[1996,84783,8425],{"separator":2285},[2129,84785,84786],{},"0,353",[1996,84788,2501],{"stretchy":2004},[902,84790,84791],{"encoding":904},"A_4[2; 0{,}353]",[883,84793,84795],{"className":84794},[886],[888,84796,84797],{"xmlns":890},[892,84798,84799,84818],{},[895,84800,84801,84807,84809,84811,84813,84816],{},[2272,84802,84803,84805],{},[898,84804,4255],{},[2129,84806,2228],{},[1996,84808,2486],{"stretchy":2004},[2129,84810,2131],{},[1996,84812,8425],{"separator":2285},[2129,84814,84815],{},"2,828",[1996,84817,2501],{"stretchy":2004},[902,84819,84820],{"encoding":904},"A_5[2; 2{,}828]",[883,84822,84824],{"className":84823},[886],[888,84825,84826],{"xmlns":890},[892,84827,84828,84847],{},[895,84829,84830,84836,84838,84840,84842,84845],{},[2272,84831,84832,84834],{},[898,84833,4255],{},[2129,84835,2235],{},[1996,84837,2486],{"stretchy":2004},[2129,84839,2131],{},[1996,84841,8425],{"separator":2285},[2129,84843,84844],{},"9,545",[1996,84846,2501],{"stretchy":2004},[902,84848,84849],{"encoding":904},"A_6[2; 9{,}545]",[883,84851,84853],{"className":84852},[886],[888,84854,84855],{"xmlns":890},[892,84856,84857,84876],{},[895,84858,84859,84865,84867,84869,84871,84874],{},[2272,84860,84861,84863],{},[898,84862,4255],{},[2129,84864,24203],{},[1996,84866,2486],{"stretchy":2004},[2129,84868,64561],{},[1996,84870,8425],{"separator":2285},[2129,84872,84873],{},"0,544",[1996,84875,2501],{"stretchy":2004},[902,84877,84878],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,84880,84882],{"className":84881},[886],[888,84883,84884],{"xmlns":890},[892,84885,84886,84905],{},[895,84887,84888,84894,84896,84898,84900,84903],{},[2272,84889,84890,84892],{},[898,84891,4255],{},[2129,84893,5585],{},[1996,84895,2486],{"stretchy":2004},[2129,84897,64561],{},[1996,84899,8425],{"separator":2285},[2129,84901,84902],{},"14,696",[1996,84904,2501],{"stretchy":2004},[902,84906,84907],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,84909,84911],{"className":84910},[886],[888,84912,84913],{"xmlns":890},[892,84914,84915,84933],{},[895,84916,84917,84923,84925,84927,84929,84931],{},[2272,84918,84919,84921],{},[898,84920,4255],{},[2129,84922,3999],{},[1996,84924,2486],{"stretchy":2004},[2129,84926,2131],{},[1996,84928,8425],{"separator":2285},[2129,84930,2228],{},[1996,84932,2501],{"stretchy":2004},[902,84934,84935],{"encoding":904},"A_9[2; 5]",[724,84937,84938,84941],{},[38,84939,84940],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,84943,84944,84947,84948,84978,84979,84992,84993,85006,85007,69319,85026,85045,85046,1975],{},[38,84945,84946],{},"5.15"," Produkce firmy je dána vztahem ",[883,84949,84951],{"className":84950},[886],[888,84952,84953],{"xmlns":890},[892,84954,84955,84975],{},[895,84956,84957,84959,84961,84963,84969],{},[898,84958,2789],{},[1996,84960,1998],{},[2129,84962,2131],{},[2124,84964,84965,84967],{},[898,84966,9795],{},[2129,84968,5009],{},[2124,84970,84971,84973],{},[898,84972,9800],{},[2129,84974,23791],{},[902,84976,84977],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,84980,84982],{"className":84981},[886],[888,84983,84984],{"xmlns":890},[892,84985,84986,84990],{},[895,84987,84988],{},[2129,84989,3090],{},[902,84991,3090],{"encoding":904}," pracovníků a disponuje-li ",[883,84994,84996],{"className":84995},[886],[888,84997,84998],{"xmlns":890},[892,84999,85000,85004],{},[895,85001,85002],{},[2129,85003,64437],{},[902,85005,64437],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,85008,85010],{"className":85009},[886],[888,85011,85012],{"xmlns":890},[892,85013,85014,85024],{},[895,85015,85016,85018,85020,85022],{},[898,85017,2818],{},[898,85019,3994],{},[898,85021,2774],{},[898,85023,8673],{},[902,85025,10599],{"encoding":904},[883,85027,85029],{"className":85028},[886],[888,85030,85031],{"xmlns":890},[892,85032,85033,85043],{},[895,85034,85035,85037,85039,85041],{},[898,85036,2818],{},[898,85038,3994],{},[898,85040,2774],{},[898,85042,8673],{},[902,85044,10599],{"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 ",[883,85047,85049],{"className":85048},[886],[888,85050,85051],{"xmlns":890},[892,85052,85053,85058],{},[895,85054,85055],{},[2129,85056,85057],{},"95",[902,85059,85057],{"encoding":904},[724,85061,85062,83462,85065,70993,85097,85116,85117,85130,85131,85144,85145,85158],{},[38,85063,85064],{},"5.16",[883,85066,85068],{"className":85067},[886],[888,85069,85070],{"xmlns":890},[892,85071,85072,85094],{},[895,85073,85074,85076,85078,85084,85086,85088],{},[898,85075,2789],{},[1996,85077,1998],{},[2124,85079,85080,85082],{},[898,85081,9800],{},[2129,85083,2131],{},[1996,85085,2095],{},[2129,85087,2131],{},[2124,85089,85090,85092],{},[898,85091,9795],{},[2129,85093,2131],{},[902,85095,85096],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,85098,85100],{"className":85099},[886],[888,85101,85102],{"xmlns":890},[892,85103,85104,85114],{},[895,85105,85106,85108,85110,85112],{},[898,85107,2818],{},[898,85109,3994],{},[898,85111,2774],{},[898,85113,8673],{},[902,85115,10599],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,85118,85120],{"className":85119},[886],[888,85121,85122],{"xmlns":890},[892,85123,85124,85128],{},[895,85125,85126],{},[2129,85127,3120],{},[902,85129,3120],{"encoding":904}," pracovníky a ",[883,85132,85134],{"className":85133},[886],[888,85135,85136],{"xmlns":890},[892,85137,85138,85142],{},[895,85139,85140],{},[2129,85141,77619],{},[902,85143,77619],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,85146,85148],{"className":85147},[886],[888,85149,85150],{"xmlns":890},[892,85151,85152,85156],{},[895,85153,85154],{},[2129,85155,46705],{},[902,85157,46705],{"encoding":904}," jednotek.",[724,85160,85161,85164,85165,10394,85195,1975],{},[38,85162,85163],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,85166,85168],{"className":85167},[886],[888,85169,85170],{"xmlns":890},[892,85171,85172,85192],{},[895,85173,85174,85176,85178,85180,85186],{},[898,85175,2789],{},[1996,85177,1998],{},[898,85179,4255],{},[2124,85181,85182,85184],{},[898,85183,9795],{},[898,85185,207],{},[2124,85187,85188,85190],{},[898,85189,9800],{},[898,85191,2098],{},[902,85193,85194],{"encoding":904},"Q = A L^{a} K^{b}",[883,85196,85198],{"className":85197},[886],[888,85199,85200],{"xmlns":890},[892,85201,85202,85232],{},[895,85203,85204,85206,85208,85210,85212,85214,85222,85224],{},[898,85205,2818],{},[898,85207,3994],{},[898,85209,2774],{},[898,85211,8673],{},[1996,85213,1998],{},[2325,85215,85216],{"scriptlevel":2327,"displaystyle":2004},[2329,85217,85218,85220],{},[898,85219,207],{},[898,85221,2098],{},[1996,85223,3177],{},[2325,85225,85226],{"scriptlevel":2327,"displaystyle":2004},[2329,85227,85228,85230],{},[898,85229,9800],{},[898,85231,9795],{},[902,85233,85234],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,85236,15722],{"id":15721},[120,85238,85239,85272,85299,85308,85358,85389,85442,85465,85520,85593,85671,85714,85746,85779,85820,85892,85953,86019,86036,86109,86175,86227,86283,86317,86360],{},[123,85240,85241,85244,85245,36898,85258,85271],{},[38,85242,85243],{},"Faktory (vstupy) produkce:"," práce ",[883,85246,85248],{"className":85247},[886],[888,85249,85250],{"xmlns":890},[892,85251,85252,85256],{},[895,85253,85254],{},[898,85255,9795],{},[902,85257,9795],{"encoding":904},[883,85259,85261],{"className":85260},[886],[888,85262,85263],{"xmlns":890},[892,85264,85265,85269],{},[895,85266,85267],{},[898,85268,9800],{},[902,85270,9800],{"encoding":904},", půda.",[123,85273,85274,7015,85276,1975],{},[38,85275,40453],{},[883,85277,85279],{"className":85278},[886],[888,85280,85281],{"xmlns":890},[892,85282,85283,85297],{},[895,85284,85285,85287,85289,85291,85293,85295],{},[898,85286,2789],{},[1996,85288,1998],{},[898,85290,2789],{},[1996,85292,2005],{"stretchy":2004},[898,85294,9795],{},[1996,85296,2011],{"stretchy":2004},[902,85298,74546],{"encoding":904},[123,85300,85301,10025,85303,12130,85306,1975],{},[38,85302,859],{},[614,85304,85305],{},"production function",[38,85307,75049],{},[123,85309,85310,2203,85312,1975],{},[38,85311,75095],{},[883,85313,85315],{"className":85314},[886],[888,85316,85317],{"xmlns":890},[892,85318,85319,85355],{},[895,85320,85321,85323,85329,85331,85333,85335,85337,85339,85341,85343,85349,85351,85353],{},[898,85322,2818],{},[2272,85324,85325,85327],{},[898,85326,3937],{},[898,85328,9795],{},[1996,85330,1998],{},[898,85332,2194],{},[898,85334,2789],{},[898,85336,4674],{"mathvariant":2376},[898,85338,2194],{},[898,85340,9795],{},[1996,85342,1998],{},[2124,85344,85345,85347],{},[898,85346,2789],{},[1996,85348,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,85350,2005],{"stretchy":2004},[898,85352,9795],{},[1996,85354,2011],{"stretchy":2004},[902,85356,85357],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,85359,85360,2203,85362,1975],{},[38,85361,76030],{},[883,85363,85365],{"className":85364},[886],[888,85366,85367],{"xmlns":890},[892,85368,85369,85387],{},[895,85370,85371,85373,85379,85381,85383,85385],{},[898,85372,4255],{},[2272,85374,85375,85377],{},[898,85376,3937],{},[898,85378,9795],{},[1996,85380,1998],{},[898,85382,2789],{},[898,85384,4674],{"mathvariant":2376},[898,85386,9795],{},[902,85388,74614],{"encoding":904},[123,85390,85391,85393,85394,10394,85411,1975],{},[38,85392,75517],{}," — od určitého ",[883,85395,85397],{"className":85396},[886],[888,85398,85399],{"xmlns":890},[892,85400,85401,85409],{},[895,85402,85403],{},[2272,85404,85405,85407],{},[898,85406,9795],{},[2129,85408,2327],{},[902,85410,75560],{"encoding":904},[883,85412,85414],{"className":85413},[886],[888,85415,85416],{"xmlns":890},[892,85417,85418,85440],{},[895,85419,85420,85430,85432,85434,85436,85438],{},[2124,85421,85422,85424],{},[898,85423,2789],{},[895,85425,85426,85428],{},[1996,85427,2378],{"mathvariant":2376},[1996,85429,2378],{"mathvariant":2376},[1996,85431,2005],{"stretchy":2004},[898,85433,9795],{},[1996,85435,2011],{"stretchy":2004},[1996,85437,3447],{},[2129,85439,2327],{},[902,85441,75706],{"encoding":904},[123,85443,85444,2203,85447,85464],{},[38,85445,85446],{},"Inflexní bod",[883,85448,85450],{"className":85449},[886],[888,85451,85452],{"xmlns":890},[892,85453,85454,85462],{},[895,85455,85456],{},[2272,85457,85458,85460],{},[898,85459,9795],{},[2129,85461,2327],{},[902,85463,75560],{"encoding":904}," — přechod z konvexity do konkavity.",[123,85466,85467,2203,85470,7015,85487,1975],{},[38,85468,85469],{},"Bod maxima produkce",[883,85471,85473],{"className":85472},[886],[888,85474,85475],{"xmlns":890},[892,85476,85477,85485],{},[895,85478,85479],{},[2272,85480,85481,85483],{},[898,85482,9795],{},[2129,85484,2278],{},[902,85486,13214],{"encoding":904},[883,85488,85490],{"className":85489},[886],[888,85491,85492],{"xmlns":890},[892,85493,85494,85518],{},[895,85495,85496,85498,85504,85506,85512,85514,85516],{},[898,85497,2818],{},[2272,85499,85500,85502],{},[898,85501,3937],{},[898,85503,9795],{},[1996,85505,2005],{"stretchy":2004},[2272,85507,85508,85510],{},[898,85509,9795],{},[2129,85511,2278],{},[1996,85513,2011],{"stretchy":2004},[1996,85515,1998],{},[2129,85517,2327],{},[902,85519,75779],{"encoding":904},[123,85521,85522,85544,85545,10394,85564,1975],{},[38,85523,85524,85525],{},"Princip maximalizace ",[883,85526,85528],{"className":85527},[886],[888,85529,85530],{"xmlns":890},[892,85531,85532,85542],{},[895,85533,85534,85536],{},[898,85535,4255],{},[2272,85537,85538,85540],{},[898,85539,3937],{},[898,85541,9795],{},[902,85543,74635],{"encoding":904}," — v bodě maxima ",[883,85546,85548],{"className":85547},[886],[888,85549,85550],{"xmlns":890},[892,85551,85552,85562],{},[895,85553,85554,85556],{},[898,85555,4255],{},[2272,85557,85558,85560],{},[898,85559,3937],{},[898,85561,9795],{},[902,85563,74635],{"encoding":904},[883,85565,85567],{"className":85566},[886],[888,85568,85569],{"xmlns":890},[892,85570,85571,85591],{},[895,85572,85573,85575,85581,85583,85585],{},[898,85574,2818],{},[2272,85576,85577,85579],{},[898,85578,3937],{},[898,85580,9795],{},[1996,85582,1998],{},[898,85584,4255],{},[2272,85586,85587,85589],{},[898,85588,3937],{},[898,85590,9795],{},[902,85592,74665],{"encoding":904},[123,85594,85595,2203,85598,1343,85637,1343,85654,1975],{},[38,85596,85597],{},"Polynomiální produkční funkce",[883,85599,85601],{"className":85600},[886],[888,85602,85603],{"xmlns":890},[892,85604,85605,85635],{},[895,85606,85607,85609,85611,85613,85615,85617,85619,85625,85627,85629],{},[898,85608,2789],{},[1996,85610,2005],{"stretchy":2004},[898,85612,9795],{},[1996,85614,2011],{"stretchy":2004},[1996,85616,1998],{},[898,85618,207],{},[2124,85620,85621,85623],{},[898,85622,9795],{},[2129,85624,2173],{},[1996,85626,2095],{},[898,85628,2098],{},[2124,85630,85631,85633],{},[898,85632,9795],{},[2129,85634,2131],{},[902,85636,75897],{"encoding":904},[883,85638,85640],{"className":85639},[886],[888,85641,85642],{"xmlns":890},[892,85643,85644,85652],{},[895,85645,85646,85648,85650],{},[898,85647,207],{},[1996,85649,3447],{},[2129,85651,2327],{},[902,85653,43087],{"encoding":904},[883,85655,85657],{"className":85656},[886],[888,85658,85659],{"xmlns":890},[892,85660,85661,85669],{},[895,85662,85663,85665,85667],{},[898,85664,2098],{},[1996,85666,3408],{},[2129,85668,2327],{},[902,85670,18816],{"encoding":904},[123,85672,85673,2203,85676,1975],{},[38,85674,85675],{},"Diferenciál produkce",[883,85677,85679],{"className":85678},[886],[888,85680,85681],{"xmlns":890},[892,85682,85683,85711],{},[895,85684,85685,85687,85689,85691,85693,85695,85697,85699,85705,85707,85709],{},[898,85686,2889],{"mathvariant":2376},[898,85688,2789],{},[1996,85690,2730],{},[898,85692,2194],{},[898,85694,2789],{},[1996,85696,1998],{},[898,85698,2818],{},[2272,85700,85701,85703],{},[898,85702,3937],{},[898,85704,9795],{},[2288,85706,2987],{},[898,85708,2194],{},[898,85710,9795],{},[902,85712,85713],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,85715,85716,7015,85718,1975],{},[38,85717,83973],{},[883,85719,85721],{"className":85720},[886],[888,85722,85723],{"xmlns":890},[892,85724,85725,85743],{},[895,85726,85727,85729,85731,85733,85735,85737,85739,85741],{},[898,85728,2789],{},[1996,85730,1998],{},[898,85732,2789],{},[1996,85734,2005],{"stretchy":2004},[898,85736,9795],{},[1996,85738,2286],{"separator":2285},[898,85740,9800],{},[1996,85742,2011],{"stretchy":2004},[902,85744,85745],{"encoding":904},"Q = Q(L, K)",[123,85747,85748,7015,85750,1975],{},[38,85749,78067],{},[883,85751,85753],{"className":85752},[886],[888,85754,85755],{"xmlns":890},[892,85756,85757,85777],{},[895,85758,85759,85761,85763,85765,85771],{},[898,85760,2789],{},[1996,85762,1998],{},[898,85764,4255],{},[2124,85766,85767,85769],{},[898,85768,9795],{},[898,85770,207],{},[2124,85772,85773,85775],{},[898,85774,9800],{},[898,85776,2098],{},[902,85778,74732],{"encoding":904},[123,85780,85781,7015,85784,85819],{},[38,85782,85783],{},"Ryzí Cobb-Douglas",[883,85785,85787],{"className":85786},[886],[888,85788,85789],{"xmlns":890},[892,85790,85791,85817],{},[895,85792,85793,85795,85797,85799,85805],{},[898,85794,2789],{},[1996,85796,1998],{},[898,85798,4255],{},[2124,85800,85801,85803],{},[898,85802,9795],{},[898,85804,207],{},[2124,85806,85807,85809],{},[898,85808,9800],{},[895,85810,85811,85813,85815],{},[2129,85812,2278],{},[1996,85814,2225],{},[898,85816,207],{},[902,85818,78894],{"encoding":904}," (konstantní výnosy).",[123,85821,85822,7015,85824,1975],{},[38,85823,79610],{},[883,85825,85827],{"className":85826},[886],[888,85828,85829],{"xmlns":890},[892,85830,85831,85889],{},[895,85832,85833,85835,85837,85839,85841,85843,85845,85847,85849,85851,85861,85863,85865,85875],{},[898,85834,2789],{},[1996,85836,1998],{},[898,85838,4255],{},[1996,85840,2486],{"stretchy":2004},[1996,85842,2005],{"stretchy":2004},[2129,85844,2278],{},[1996,85846,2225],{},[898,85848,207],{},[1996,85850,2011],{"stretchy":2004},[2124,85852,85853,85855],{},[898,85854,9795],{},[895,85856,85857,85859],{},[1996,85858,2225],{},[898,85860,2098],{},[1996,85862,2095],{},[898,85864,207],{},[2124,85866,85867,85869],{},[898,85868,9800],{},[895,85870,85871,85873],{},[1996,85872,2225],{},[898,85874,2098],{},[2124,85876,85877,85879],{},[1996,85878,2501],{"stretchy":2004},[895,85880,85881,85883,85885,85887],{},[1996,85882,2225],{},[2129,85884,2278],{},[898,85886,4674],{"mathvariant":2376},[898,85888,2098],{},[902,85890,85891],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,85893,85894,10025,85897,12130,85919,10025,85922,85952],{},[38,85895,85896],{},"Lineární",[883,85898,85900],{"className":85899},[886],[888,85901,85902],{"xmlns":890},[892,85903,85904,85916],{},[895,85905,85906,85908,85910,85912,85914],{},[898,85907,207],{},[898,85909,9795],{},[1996,85911,2095],{},[898,85913,2098],{},[898,85915,9800],{},[902,85917,85918],{"encoding":904},"aL + bK",[38,85920,85921],{},"Leontiefova",[883,85923,85925],{"className":85924},[886],[888,85926,85927],{"xmlns":890},[892,85928,85929,85949],{},[895,85930,85931,85933,85935,85937,85939,85941,85943,85945,85947],{},[898,85932,79838],{},[1996,85934,56202],{},[1996,85936,2005],{"stretchy":2004},[898,85938,207],{},[898,85940,9795],{},[1996,85942,2286],{"separator":2285},[898,85944,2098],{},[898,85946,9800],{},[1996,85948,2011],{"stretchy":2004},[902,85950,85951],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,85954,85955,7015,85971,1975],{},[38,85956,85957,85958],{},"Homogenita stupně ",[883,85959,85961],{"className":85960},[886],[888,85962,85963],{"xmlns":890},[892,85964,85965,85969],{},[895,85966,85967],{},[898,85968,36862],{},[902,85970,36862],{"encoding":904},[883,85972,85974],{"className":85973},[886],[888,85975,85976],{"xmlns":890},[892,85977,85978,86016],{},[895,85979,85980,85982,85984,85986,85988,85990,85992,85994,85996,85998,86004,86006,86008,86010,86012,86014],{},[898,85981,2789],{},[1996,85983,2005],{"stretchy":2004},[898,85985,12043],{},[898,85987,9795],{},[1996,85989,2286],{"separator":2285},[898,85991,12043],{},[898,85993,9800],{},[1996,85995,2011],{"stretchy":2004},[1996,85997,1998],{},[2124,85999,86000,86002],{},[898,86001,12043],{},[898,86003,36862],{},[898,86005,2789],{},[1996,86007,2005],{"stretchy":2004},[898,86009,9795],{},[1996,86011,2286],{"separator":2285},[898,86013,9800],{},[1996,86015,2011],{"stretchy":2004},[902,86017,86018],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,86020,86021,78992],{},[38,86022,78925,86023],{},[883,86024,86026],{"className":86025},[886],[888,86027,86028],{"xmlns":890},[892,86029,86030,86034],{},[895,86031,86032],{},[898,86033,4255],{},[902,86035,4255],{"encoding":904},[123,86037,86038,86040,86041,86063,86064,86086,86087,3918],{},[38,86039,78426],{}," — konstantní (",[883,86042,86044],{"className":86043},[886],[888,86045,86046],{"xmlns":890},[892,86047,86048,86060],{},[895,86049,86050,86052,86054,86056,86058],{},[898,86051,207],{},[1996,86053,2095],{},[898,86055,2098],{},[1996,86057,1998],{},[2129,86059,2278],{},[902,86061,86062],{"encoding":904},"a+b=1","), rostoucí (",[883,86065,86067],{"className":86066},[886],[888,86068,86069],{"xmlns":890},[892,86070,86071,86083],{},[895,86072,86073,86075,86077,86079,86081],{},[898,86074,207],{},[1996,86076,2095],{},[898,86078,2098],{},[1996,86080,3408],{},[2129,86082,2278],{},[902,86084,86085],{"encoding":904},"a+b>1","), klesající (",[883,86088,86090],{"className":86089},[886],[888,86091,86092],{"xmlns":890},[892,86093,86094,86106],{},[895,86095,86096,86098,86100,86102,86104],{},[898,86097,207],{},[1996,86099,2095],{},[898,86101,2098],{},[1996,86103,3447],{},[2129,86105,2278],{},[902,86107,86108],{"encoding":904},"a+b\u003C1",[123,86110,86111,2203,86113,1343,86143,2203,86145,1975],{},[38,86112,75095],{},[883,86114,86116],{"className":86115},[886],[888,86117,86118],{"xmlns":890},[892,86119,86120,86140],{},[895,86121,86122,86124,86130,86132],{},[898,86123,2818],{},[2272,86125,86126,86128],{},[898,86127,3937],{},[898,86129,9795],{},[1996,86131,1998],{},[9166,86133,86134,86136,86138],{},[898,86135,2789],{},[898,86137,9795],{},[1996,86139,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,86141,86142],{"encoding":904},"MP_L = Q'_L",[38,86144,77999],{},[883,86146,86148],{"className":86147},[886],[888,86149,86150],{"xmlns":890},[892,86151,86152,86172],{},[895,86153,86154,86156,86162,86164],{},[898,86155,2818],{},[2272,86157,86158,86160],{},[898,86159,3937],{},[898,86161,9800],{},[1996,86163,1998],{},[9166,86165,86166,86168,86170],{},[898,86167,2789],{},[898,86169,9800],{},[1996,86171,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,86173,86174],{"encoding":904},"MP_K = Q'_K",[123,86176,86177,2203,86179,1975],{},[38,86178,80213],{},[883,86180,86182],{"className":86181},[886],[888,86183,86184],{"xmlns":890},[892,86185,86186,86224],{},[895,86187,86188,86190,86192,86194,86196,86202,86204,86206,86208,86210,86212,86218,86220,86222],{},[898,86189,2194],{},[898,86191,2789],{},[1996,86193,1998],{},[898,86195,2818],{},[2272,86197,86198,86200],{},[898,86199,3937],{},[898,86201,9795],{},[2288,86203,2987],{},[898,86205,2194],{},[898,86207,9795],{},[1996,86209,2095],{},[898,86211,2818],{},[2272,86213,86214,86216],{},[898,86215,3937],{},[898,86217,9800],{},[2288,86219,2987],{},[898,86221,2194],{},[898,86223,9800],{},[902,86225,86226],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,86228,86229,7015,86231,1975],{},[38,86230,80558],{},[883,86232,86234],{"className":86233},[886],[888,86235,86236],{"xmlns":890},[892,86237,86238,86280],{},[895,86239,86240,86242,86250,86252,86254,86262,86264,86266,86268,86270,86272,86274,86276,86278],{},[898,86241,9795],{},[9166,86243,86244,86246,86248],{},[898,86245,2789],{},[898,86247,9795],{},[1996,86249,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,86251,2095],{},[898,86253,9800],{},[9166,86255,86256,86258,86260],{},[898,86257,2789],{},[898,86259,9800],{},[1996,86261,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,86263,1998],{},[898,86265,36862],{},[2288,86267,2987],{},[898,86269,2789],{},[1996,86271,2005],{"stretchy":2004},[898,86273,9795],{},[1996,86275,2286],{"separator":2285},[898,86277,9800],{},[1996,86279,2011],{"stretchy":2004},[902,86281,86282],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,86284,86285,86288,86289,1975],{},[38,86286,86287],{},"Izokvanta"," — křivka ",[883,86290,86292],{"className":86291},[886],[888,86293,86294],{"xmlns":890},[892,86295,86296,86314],{},[895,86297,86298,86300,86302,86304,86306,86308,86310,86312],{},[898,86299,2789],{},[1996,86301,2005],{"stretchy":2004},[898,86303,9795],{},[1996,86305,2286],{"separator":2285},[898,86307,9800],{},[1996,86309,2011],{"stretchy":2004},[1996,86311,1998],{},[898,86313,80799],{},[902,86315,86316],{"encoding":904},"Q(L, K) = q",[123,86318,86319,2203,86321,1975],{},[38,86320,80988],{},[883,86322,86324],{"className":86323},[886],[888,86325,86326],{"xmlns":890},[892,86327,86328,86358],{},[895,86329,86330,86332,86334,86336,86338,86340,86342,86348,86350,86352],{},[898,86331,2818],{},[898,86333,3994],{},[898,86335,2774],{},[898,86337,8673],{},[1996,86339,1998],{},[898,86341,2818],{},[2272,86343,86344,86346],{},[898,86345,3937],{},[898,86347,9795],{},[898,86349,4674],{"mathvariant":2376},[898,86351,2818],{},[2272,86353,86354,86356],{},[898,86355,3937],{},[898,86357,9800],{},[902,86359,74807],{"encoding":904},[123,86361,86362,2203,86365,1975],{},[38,86363,86364],{},"Substituční vztah",[883,86366,86368],{"className":86367},[886],[888,86369,86370],{"xmlns":890},[892,86371,86372,86396],{},[895,86373,86374,86376,86378,86380,86382,86384,86386,86388,86390,86392,86394],{},[898,86375,2889],{"mathvariant":2376},[898,86377,9800],{},[1996,86379,2730],{},[1996,86381,2225],{},[898,86383,2818],{},[898,86385,3994],{},[898,86387,2774],{},[898,86389,8673],{},[2288,86391,2987],{},[898,86393,2194],{},[898,86395,9795],{},[902,86397,86398],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,86400,3792],{"id":3791},[120,86402,86403,86500,86507,86514],{},[123,86404,86405,2203,86407,86410,86411,1343,86414,86417,86418,86421,86422,86441,86442,18650,86461,86464,86465,86484,86485,3918],{},[38,86406,50725],{},[207,86408,784],{"className":86409,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,86412,2357],{"className":86413,"dataFsResolvedFilePath":764,"href":765},[210],[207,86415,793],{"className":86416,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,86419,880],{"className":86420,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,86423,86425],{"className":86424},[886],[888,86426,86427],{"xmlns":890},[892,86428,86429,86439],{},[895,86430,86431,86433,86435,86437],{},[898,86432,2818],{},[898,86434,3994],{},[898,86436,2774],{},[898,86438,8673],{},[902,86440,10599],{"encoding":904}," ↔ ",[883,86443,86445],{"className":86444},[886],[888,86446,86447],{"xmlns":890},[892,86448,86449,86459],{},[895,86450,86451,86453,86455,86457],{},[898,86452,2818],{},[898,86454,3994],{},[898,86456,2777],{},[898,86458,8673],{},[902,86460,10603],{"encoding":904},[207,86462,3823],{"className":86463,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,86466,86468],{"className":86467},[886],[888,86469,86470],{"xmlns":890},[892,86471,86472,86482],{},[895,86473,86474,86476],{},[898,86475,4255],{},[2272,86477,86478,86480],{},[898,86479,3937],{},[898,86481,9795],{},[902,86483,74635],{"encoding":904}," ↔ min ",[883,86486,86488],{"className":86487},[886],[888,86489,86490],{"xmlns":890},[892,86491,86492,86498],{},[895,86493,86494,86496],{},[898,86495,4255],{},[898,86497,2777],{},[902,86499,55562],{"encoding":904},[123,86501,86502,2203,86504,1975],{},[38,86503,3799],{},[207,86505,3828],{"className":86506,"dataFsResolvedFilePath":848,"href":849},[210],[123,86508,86509,2203,86511,1975],{},[38,86510,16215],{},[207,86512,1094],{"className":86513,"dataFsResolvedFilePath":838,"href":839},[210],[123,86515,86516,2203,86518,1975],{},[38,86517,16206],{},[207,86519,16210],{"className":86520,"dataFsResolvedFilePath":1960,"href":1961},[210],{"title":641,"searchDepth":642,"depth":642,"links":86522},[86523,86524,86525,86529,86531,86536,86537,86544,86545,86547,86548,86549,86551,86556,86557,86558,86562,86563],{"id":74830,"depth":642,"text":74831},{"id":74967,"depth":642,"text":74968},{"id":75070,"depth":642,"text":86526,"children":86527},"Mezní produkt práce (MPLMP_L)",[86528],{"id":75516,"depth":649,"text":75517},{"id":76005,"depth":642,"text":86530},"Průměrný produkt práce (APLAP_L)",{"id":76123,"depth":642,"text":76124,"children":86532},[86533,86534,86535],{"id":76360,"depth":649,"text":65503},{"id":76671,"depth":649,"text":76672},{"id":77391,"depth":649,"text":77392},{"id":77963,"depth":642,"text":77964},{"id":78066,"depth":642,"text":78067,"children":86538},[86539,86540,86542,86543],{"id":78425,"depth":649,"text":78426},{"id":78924,"depth":649,"text":86541},"Parametr efektivity AA",{"id":78995,"depth":649,"text":78996},{"id":37181,"depth":649,"text":79335},{"id":79522,"depth":642,"text":79523},{"id":79861,"depth":642,"text":86546},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":80552,"depth":642,"text":80553},{"id":74896,"depth":642,"text":9778},{"id":80963,"depth":642,"text":86550},"Mezní míra technické substituce (MRTSMRTS)",{"id":81829,"depth":642,"text":81830,"children":86552},[86553,86554,86555],{"id":81833,"depth":649,"text":81834},{"id":82476,"depth":649,"text":82477},{"id":82757,"depth":649,"text":82758},{"id":83103,"depth":642,"text":83104},{"id":49883,"depth":642,"text":49884},{"id":83453,"depth":642,"text":83454,"children":86559},[86560,86561],{"id":40452,"depth":649,"text":40453},{"id":83972,"depth":649,"text":83973},{"id":15721,"depth":642,"text":15722},{"id":3791,"depth":642,"text":3792},{},"\u002Ftopics\u002Fprodukce",{"title":74466,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,9813,86570,86571,86572,74896,86573,86574],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":86577,"title":86578,"body":86579,"course":1128,"courses":659,"created":9556,"description":641,"extension":661,"meta":95526,"navigation":664,"path":95527,"seo":95528,"sources":95529,"stem":95530,"tags":95531,"type":3857,"updated":677,"__hash__":95534},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":86580,"toc":95500},[86581,86584,86586,86783,86792,86796,86799,86852,86856,86868,86872,86875,86892,87015,87021,87165,87175,87179,87214,87252,87300,87357,87417,87459,88035,88039,88122,88231,88324,88582,88585,88638,88749,88831,88835,88846,89079,89134,89140,89180,89243,89254,89445,89551,89704,89752,89757,89871,89909,90035,90081,90108,90185,90260,90340,90470,90531,90619,90623,90626,90695,90778,90785,90845,91155,91159,91165,91218,91234,91285,91423,91499,91612,91929,91933,91940,92100,92159,92163,92185,92282,92403,92517,92540,92603,92660,92912,92920,92924,92931,93185,93235,93291,93294,93458,93462,93560,93562,93594,93598,93731,93973,94157,94325,94632,94765,94952,94964,94966,95401,95403],[12,86582,86578],{"id":86583},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,86585,12008],{"id":12007},[724,86587,86588,2203,86590,86621,86622,86625,86626,86656,86657,86675,86676,86716,86717,86720,86721,86734,86735,28255,86738,86751,86752,86765,86766,86779,86780,1975],{},[38,86589,880],{},[883,86591,86593],{"className":86592},[886],[888,86594,86595],{"xmlns":890},[892,86596,86597,86619],{},[895,86598,86599,86601,86603,86609,86611,86617],{},[898,86600,900],{},[1996,86602,2005],{"stretchy":2004},[2272,86604,86605,86607],{},[898,86606,2789],{},[2129,86608,2278],{},[1996,86610,2286],{"separator":2285},[2272,86612,86613,86615],{},[898,86614,2789],{},[2129,86616,2131],{},[1996,86618,2011],{"stretchy":2004},[902,86620,16345],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,86623,86624],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,86627,86629],{"className":86628},[886],[888,86630,86631],{"xmlns":890},[892,86632,86633,86653],{},[895,86634,86635,86637,86643,86645],{},[898,86636,2818],{},[2272,86638,86639,86641],{},[898,86640,900],{},[898,86642,17792],{},[1996,86644,1998],{},[9166,86646,86647,86649,86651],{},[898,86648,900],{},[898,86650,17792],{},[1996,86652,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,86654,86655],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,86658,86660],{"className":86659},[886],[888,86661,86662],{"xmlns":890},[892,86663,86664,86672],{},[895,86665,86666,86668,86670],{},[898,86667,900],{},[1996,86669,1998],{},[898,86671,2142],{},[902,86673,86674],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,86677,86679],{"className":86678},[886],[888,86680,86681],{"xmlns":890},[892,86682,86683,86713],{},[895,86684,86685,86687,86689,86691,86693,86695,86697,86703,86705,86707],{},[898,86686,2818],{},[898,86688,3994],{},[898,86690,2777],{},[898,86692,8673],{},[1996,86694,1998],{},[898,86696,2818],{},[2272,86698,86699,86701],{},[898,86700,900],{},[2129,86702,2278],{},[898,86704,4674],{"mathvariant":2376},[898,86706,2818],{},[2272,86708,86709,86711],{},[898,86710,900],{},[2129,86712,2131],{},[902,86714,86715],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,86718,86719],{},"teorii užitečnosti"," — funkce ",[883,86722,86724],{"className":86723},[886],[888,86725,86726],{"xmlns":890},[892,86727,86728,86732],{},[895,86729,86730],{},[898,86731,900],{},[902,86733,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,86736,86737],{},"Optimalizaci spotřebitele",[883,86739,86741],{"className":86740},[886],[888,86742,86743],{"xmlns":890},[892,86744,86745,86749],{},[895,86746,86747],{},[898,86748,900],{},[902,86750,900],{"encoding":904}," při rozpočtu, min ",[883,86753,86755],{"className":86754},[886],[888,86756,86757],{"xmlns":890},[892,86758,86759,86763],{},[895,86760,86761],{},[898,86762,4252],{},[902,86764,4252],{"encoding":904}," při dané ",[883,86767,86769],{"className":86768},[886],[888,86770,86771],{"xmlns":890},[892,86772,86773,86777],{},[895,86774,86775],{},[898,86776,900],{},[902,86778,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,86781,913],{"className":86782,"dataFsResolvedFilePath":911,"href":912},[210],[724,86784,86785,86786,86788,86789,1975],{},"Kapitola 6 knihy ",[614,86787,16210],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,86790,36756],{"className":86791,"dataFsResolvedFilePath":911,"href":912},[210],[115,86793,86795],{"id":86794},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,86797,86798],{},"Po prostudování této kapitoly byste měli umět:",[120,86800,86801,86807,86816,86821,86824,86830,86836,86839,86845],{},[123,86802,86803,86804,2286],{},"vyložit, co se rozumí termínem ",[38,86805,86806],{},"užitečnost",[123,86808,86809,86810,3885,86813,2286],{},"definovat pojmy ",[38,86811,86812],{},"svazek zboží",[38,86814,86815],{},"funkce užitečnosti",[123,86817,74845,86818,74852],{},[38,86819,86820],{},"mezní užitečnosti",[123,86822,86823],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,86825,74872,86826,86829],{},[38,86827,86828],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,86831,74893,86832,86835],{},[38,86833,86834],{},"křivky užitečnosti"," (indiferenční křivky),",[123,86837,86838],{},"vyjmenovat jejich základní vlastnosti,",[123,86840,74845,86841,86844],{},[38,86842,86843],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,86846,86847,86848,86851],{},"řešit ",[38,86849,86850],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,86853,86855],{"id":86854},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,86857,86858,86859,86863,86864,86867],{},"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 ",[207,86860,86862],{"className":86861,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,86865,86866],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,86869,86871],{"id":86870},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,86873,86874],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,86876,86877,86883],{},[123,86878,86879,86882],{},[38,86880,86881],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,86884,86885,86888,86889,86891],{},[38,86886,86887],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,86890,86624],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[3867,86893,86894],{},[724,86895,86896,86898,86899,86902,86903,2203,86916,86919,86920,3885,86933,86952,86953,1343,86979,87006,87007,87010,87011,87014],{},[883,86897,4412],{}," Pozor — ordinalisté užitečnost ",[38,86900,86901],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,86904,86906],{"className":86905},[886],[888,86907,86908],{"xmlns":890},[892,86909,86910,86914],{},[895,86911,86912],{},[898,86913,900],{},[902,86915,900],{"encoding":904},[38,86917,86918],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,86921,86923],{"className":86922},[886],[888,86924,86925],{"xmlns":890},[892,86926,86927,86931],{},[895,86928,86929],{},[898,86930,900],{},[902,86932,900],{"encoding":904},[883,86934,86936],{"className":86935},[886],[888,86937,86938],{"xmlns":890},[892,86939,86940,86949],{},[895,86941,86942],{},[8386,86943,86944,86946],{"accent":2285},[898,86945,900],{},[1996,86947,86948],{},"~",[902,86950,86951],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,86954,86956],{"className":86955},[886],[888,86957,86958],{"xmlns":890},[892,86959,86960,86976],{},[895,86961,86962,86968,86970],{},[8386,86963,86964,86966],{"accent":2285},[898,86965,900],{},[1996,86967,86948],{},[1996,86969,1998],{},[2124,86971,86972,86974],{},[898,86973,900],{},[2129,86975,2131],{},[902,86977,86978],{"encoding":904},"\\tilde U = U^2",[883,86980,86982],{"className":86981},[886],[888,86983,86984],{"xmlns":890},[892,86985,86986,87003],{},[895,86987,86988,86994,86996,86999,87001],{},[8386,86989,86990,86992],{"accent":2285},[898,86991,900],{},[1996,86993,86948],{},[1996,86995,1998],{},[898,86997,86998],{},"ln",[1996,87000,56202],{},[898,87002,900],{},[902,87004,87005],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,87008,87009],{},"porovnání"," mezi svazky a ",[38,87012,87013],{},"poměry"," mezních veličin.",[724,87016,87017,87018,2704],{},"Ordinalistický přístup vychází z ",[38,87019,87020],{},"pěti hlavních předpokladů",[152,87022,87023,87029,87035,87153,87159],{},[123,87024,87025,87028],{},[38,87026,87027],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,87030,87031,87034],{},[38,87032,87033],{},"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.",[123,87036,87037,87040,87041,61743,87054,87067,87068,61743,87081,2927,87094,87097,87098,3885,87117,62572,87135,1975],{},[38,87038,87039],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,87042,87044],{"className":87043},[886],[888,87045,87046],{"xmlns":890},[892,87047,87048,87052],{},[895,87049,87050],{},[898,87051,4255],{},[902,87053,4255],{"encoding":904},[883,87055,87057],{"className":87056},[886],[888,87058,87059],{"xmlns":890},[892,87060,87061,87065],{},[895,87062,87063],{},[898,87064,23255],{},[902,87066,23255],{"encoding":904},", nebude jindy preferovat ",[883,87069,87071],{"className":87070},[886],[888,87072,87073],{"xmlns":890},[892,87074,87075,87079],{},[895,87076,87077],{},[898,87078,23255],{},[902,87080,23255],{"encoding":904},[883,87082,87084],{"className":87083},[886],[888,87085,87086],{"xmlns":890},[892,87087,87088,87092],{},[895,87089,87090],{},[898,87091,4255],{},[902,87093,4255],{"encoding":904},[38,87095,87096],{},"Tranzitivita",": pokud ",[883,87099,87101],{"className":87100},[886],[888,87102,87103],{"xmlns":890},[892,87104,87105,87114],{},[895,87106,87107,87109,87112],{},[898,87108,4255],{},[1996,87110,87111],{},"≻",[898,87113,23255],{},[902,87115,87116],{"encoding":904},"A \\succ B",[883,87118,87120],{"className":87119},[886],[888,87121,87122],{"xmlns":890},[892,87123,87124,87132],{},[895,87125,87126,87128,87130],{},[898,87127,23255],{},[1996,87129,87111],{},[898,87131,2777],{},[902,87133,87134],{"encoding":904},"B \\succ C",[883,87136,87138],{"className":87137},[886],[888,87139,87140],{"xmlns":890},[892,87141,87142,87150],{},[895,87143,87144,87146,87148],{},[898,87145,4255],{},[1996,87147,87111],{},[898,87149,2777],{},[902,87151,87152],{"encoding":904},"A \\succ C",[123,87154,87155,87158],{},[38,87156,87157],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,87160,87161,87164],{},[38,87162,87163],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,87166,87167,87168,87171,87172,1975],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,87169,87170],{},"preference"," a na příbuzné ",[614,87173,87174],{},"funkci užitečnosti",[115,87176,87178],{"id":87177},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,87180,87181,87182,87195,87196,87199,87200,87213],{},"Uvažujme ",[883,87183,87185],{"className":87184},[886],[888,87186,87187],{"xmlns":890},[892,87188,87189,87193],{},[895,87190,87191],{},[898,87192,36862],{},[902,87194,36862],{"encoding":904}," různých zboží. ",[38,87197,87198],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,87201,87203],{"className":87202},[886],[888,87204,87205],{"xmlns":890},[892,87206,87207,87211],{},[895,87208,87209],{},[898,87210,36862],{},[902,87212,36862],{"encoding":904},"-tice",[724,87215,87216],{},[883,87217,87219],{"className":87218},[886],[888,87220,87221],{"xmlns":890},[892,87222,87223,87249],{},[895,87224,87225,87227,87233,87235,87237,87239,87245,87247],{},[1996,87226,2005],{"stretchy":2004},[2272,87228,87229,87231],{},[898,87230,2789],{},[2129,87232,2278],{},[1996,87234,2286],{"separator":2285},[1996,87236,9646],{},[1996,87238,2286],{"separator":2285},[2272,87240,87241,87243],{},[898,87242,2789],{},[898,87244,36862],{},[1996,87246,2011],{"stretchy":2004},[1996,87248,2286],{"separator":2285},[902,87250,87251],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,87253,4310,87254,87271,87272,87285,87286,87289,87290,87293,87294,87297,87298,2704],{},[883,87255,87257],{"className":87256},[886],[888,87258,87259],{"xmlns":890},[892,87260,87261,87269],{},[895,87262,87263],{},[2272,87264,87265,87267],{},[898,87266,2789],{},[898,87268,17792],{},[902,87270,47540],{"encoding":904}," značí množství ",[883,87273,87275],{"className":87274},[886],[888,87276,87277],{"xmlns":890},[892,87278,87279,87283],{},[895,87280,87281],{},[898,87282,17792],{},[902,87284,17792],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,87287,87288],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,87291,87292],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,87295,87296],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,87299,87174],{},[883,87301,87303],{"className":87302},[886],[888,87304,87305],{"xmlns":890,"display":28068},[892,87306,87307,87354],{},[20756,87308,87309],{"width":28073},[20761,87310,87311,87313,87347,87349],{},[20764,87312],{"width":28078},[20764,87314,87315],{},[895,87316,87317,87319,87321,87323,87325,87331,87333,87335,87337,87343,87345],{},[898,87318,900],{},[1996,87320,1998],{},[898,87322,900],{},[1996,87324,2005],{"stretchy":2004},[2272,87326,87327,87329],{},[898,87328,2789],{},[2129,87330,2278],{},[1996,87332,2286],{"separator":2285},[1996,87334,9646],{},[1996,87336,2286],{"separator":2285},[2272,87338,87339,87341],{},[898,87340,2789],{},[898,87342,36862],{},[1996,87344,2011],{"stretchy":2004},[1996,87346,2286],{"separator":2285},[20764,87348],{"width":28078},[20764,87350,87351],{},[2288,87352,87353],{},"(6.1)",[902,87355,87356],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,87358,4310,87359,87389,87390,87412,87413,87416],{},[883,87360,87362],{"className":87361},[886],[888,87363,87364],{"xmlns":890},[892,87365,87366,87386],{},[895,87367,87368,87374,87376,87378,87380],{},[2272,87369,87370,87372],{},[898,87371,2789],{},[2129,87373,2278],{},[1996,87375,2286],{"separator":2285},[1996,87377,9646],{},[1996,87379,2286],{"separator":2285},[2272,87381,87382,87384],{},[898,87383,2789],{},[898,87385,36862],{},[902,87387,87388],{"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 ",[883,87391,87393],{"className":87392},[886],[888,87394,87395],{"xmlns":890},[892,87396,87397,87409],{},[895,87398,87399,87401,87403],{},[898,87400,900],{},[1996,87402,2286],{"separator":2285},[8386,87404,87405,87407],{"accent":2285},[898,87406,900],{},[1996,87408,86948],{},[902,87410,87411],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,87414,87415],{},"monotónní transformace"," zachovávající pořadí.",[724,87418,87419,87420,7015,87423,1975],{},"Dále se omezíme na funkce pro ",[38,87421,87422],{},"dvě zboží",[883,87424,87426],{"className":87425},[886],[888,87427,87428],{"xmlns":890},[892,87429,87430,87456],{},[895,87431,87432,87434,87436,87438,87440,87446,87448,87454],{},[898,87433,900],{},[1996,87435,1998],{},[898,87437,900],{},[1996,87439,2005],{"stretchy":2004},[2272,87441,87442,87444],{},[898,87443,2789],{},[2129,87445,2278],{},[1996,87447,2286],{"separator":2285},[2272,87449,87450,87452],{},[898,87451,2789],{},[2129,87453,2131],{},[1996,87455,2011],{"stretchy":2004},[902,87457,87458],{"encoding":904},"U = U(Q_1, Q_2)",[3867,87460,87461,87536],{},[724,87462,87463,87465,87466,2704],{},[883,87464,52697],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,87467,87469],{"className":87468},[886],[888,87470,87471],{"xmlns":890},[892,87472,87473,87533],{},[895,87474,87475,87477,87479,87481,87483,87489,87491,87497,87499,87505,87507,87509,87511],{},[898,87476,900],{},[1996,87478,1998],{},[898,87480,900],{},[1996,87482,2005],{"stretchy":2004},[2272,87484,87485,87487],{},[898,87486,2789],{},[2129,87488,2278],{},[1996,87490,2286],{"separator":2285},[2272,87492,87493,87495],{},[898,87494,2789],{},[2129,87496,2131],{},[1996,87498,2286],{"separator":2285},[2272,87500,87501,87503],{},[898,87502,2789],{},[2129,87504,2173],{},[1996,87506,2011],{"stretchy":2004},[1996,87508,1998],{},[2129,87510,2131],{},[8117,87512,87513],{},[895,87514,87515,87521,87527],{},[2272,87516,87517,87519],{},[898,87518,2789],{},[2129,87520,2278],{},[2272,87522,87523,87525],{},[898,87524,2789],{},[2129,87526,2131],{},[2272,87528,87529,87531],{},[898,87530,2789],{},[2129,87532,2173],{},[902,87534,87535],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,87537,87538,87731],{},[123,87539,87540,87541,87567,87568,12940,87594,3885,87653,5589,87713,8425],{},"svazek ",[883,87542,87544],{"className":87543},[886],[888,87545,87546],{"xmlns":890},[892,87547,87548,87564],{},[895,87549,87550,87552,87554,87556,87558,87560,87562],{},[1996,87551,2005],{"stretchy":2004},[2129,87553,41864],{},[1996,87555,2286],{"separator":2285},[2129,87557,2351],{},[1996,87559,2286],{"separator":2285},[2129,87561,41842],{},[1996,87563,2011],{"stretchy":2004},[902,87565,87566],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,87569,87571],{"className":87570},[886],[888,87572,87573],{"xmlns":890},[892,87574,87575,87591],{},[895,87576,87577,87579,87581,87583,87585,87587,87589],{},[1996,87578,2005],{"stretchy":2004},[2129,87580,3999],{},[1996,87582,2286],{"separator":2285},[2129,87584,3999],{},[1996,87586,2286],{"separator":2285},[2129,87588,66599],{},[1996,87590,2011],{"stretchy":2004},[902,87592,87593],{"encoding":904},"(9, 9, 27)",[883,87595,87597],{"className":87596},[886],[888,87598,87599],{"xmlns":890},[892,87600,87601,87650],{},[895,87602,87603,87605,87607,87609,87611,87613,87615,87617,87619,87621,87623,87637,87639,87641,87646,87648],{},[898,87604,900],{},[1996,87606,2005],{"stretchy":2004},[2129,87608,41864],{},[1996,87610,2286],{"separator":2285},[2129,87612,2351],{},[1996,87614,2286],{"separator":2285},[2129,87616,41842],{},[1996,87618,2011],{"stretchy":2004},[1996,87620,1998],{},[2129,87622,2131],{},[8117,87624,87625],{},[895,87626,87627,87629,87631,87633,87635],{},[2129,87628,41864],{},[1996,87630,3177],{},[2129,87632,2351],{},[1996,87634,3177],{},[2129,87636,41842],{},[1996,87638,1998],{},[2129,87640,2131],{},[8117,87642,87643],{},[2129,87644,87645],{},"4096",[1996,87647,1998],{},[2129,87649,5617],{},[902,87651,87652],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,87654,87656],{"className":87655},[886],[888,87657,87658],{"xmlns":890},[892,87659,87660,87710],{},[895,87661,87662,87664,87666,87668,87670,87672,87674,87676,87678,87680,87682,87696,87698,87700,87705,87707],{},[898,87663,900],{},[1996,87665,2005],{"stretchy":2004},[2129,87667,3999],{},[1996,87669,2286],{"separator":2285},[2129,87671,3999],{},[1996,87673,2286],{"separator":2285},[2129,87675,66599],{},[1996,87677,2011],{"stretchy":2004},[1996,87679,1998],{},[2129,87681,2131],{},[8117,87683,87684],{},[895,87685,87686,87688,87690,87692,87694],{},[2129,87687,3999],{},[1996,87689,3177],{},[2129,87691,3999],{},[1996,87693,3177],{},[2129,87695,66599],{},[1996,87697,1998],{},[2129,87699,2131],{},[8117,87701,87702],{},[2129,87703,87704],{},"2187",[1996,87706,5900],{},[2129,87708,87709],{},"93,53",[902,87711,87712],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,87714,87716],{"className":87715},[886],[888,87717,87718],{"xmlns":890},[892,87719,87720,87728],{},[895,87721,87722,87724,87726],{},[2129,87723,5617],{},[1996,87725,3408],{},[2129,87727,87709],{},[902,87729,87730],{"encoding":904},"128 > 93{,}53",[123,87732,87733,87734,3885,87760,87786,87787,3885,87827,87868,87869,87915,87916,3885,87942,2845,87968,3885,87986,88004,88005,1975],{},"svazky ",[883,87735,87737],{"className":87736},[886],[888,87738,87739],{"xmlns":890},[892,87740,87741,87757],{},[895,87742,87743,87745,87747,87749,87751,87753,87755],{},[1996,87744,2005],{"stretchy":2004},[2129,87746,2351],{},[1996,87748,2286],{"separator":2285},[2129,87750,5585],{},[1996,87752,2286],{"separator":2285},[2129,87754,2131],{},[1996,87756,2011],{"stretchy":2004},[902,87758,87759],{"encoding":904},"(4, 8, 2)",[883,87761,87763],{"className":87762},[886],[888,87764,87765],{"xmlns":890},[892,87766,87767,87783],{},[895,87768,87769,87771,87773,87775,87777,87779,87781],{},[1996,87770,2005],{"stretchy":2004},[2129,87772,41842],{},[1996,87774,2286],{"separator":2285},[2129,87776,2278],{},[1996,87778,2286],{"separator":2285},[2129,87780,2351],{},[1996,87782,2011],{"stretchy":2004},[902,87784,87785],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,87788,87790],{"className":87789},[886],[888,87791,87792],{"xmlns":890},[892,87793,87794,87824],{},[895,87795,87796,87798,87800,87802,87804,87806,87808,87810,87812,87814,87816,87820,87822],{},[898,87797,900],{},[1996,87799,2005],{"stretchy":2004},[2129,87801,2351],{},[1996,87803,2286],{"separator":2285},[2129,87805,5585],{},[1996,87807,2286],{"separator":2285},[2129,87809,2131],{},[1996,87811,2011],{"stretchy":2004},[1996,87813,1998],{},[2129,87815,2131],{},[8117,87817,87818],{},[2129,87819,41842],{},[1996,87821,1998],{},[2129,87823,41864],{},[902,87825,87826],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,87828,87830],{"className":87829},[886],[888,87831,87832],{"xmlns":890},[892,87833,87834,87865],{},[895,87835,87836,87838,87840,87842,87844,87846,87848,87850,87852,87854,87856,87861,87863],{},[898,87837,900],{},[1996,87839,2005],{"stretchy":2004},[2129,87841,41842],{},[1996,87843,2286],{"separator":2285},[2129,87845,2278],{},[1996,87847,2286],{"separator":2285},[2129,87849,2351],{},[1996,87851,2011],{"stretchy":2004},[1996,87853,1998],{},[2129,87855,2131],{},[8117,87857,87858],{},[2129,87859,87860],{},"256",[1996,87862,1998],{},[2129,87864,72361],{},[902,87866,87867],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,87870,87872],{"className":87871},[886],[888,87873,87874],{"xmlns":890},[892,87875,87876,87912],{},[895,87877,87878,87880,87882,87884,87886,87888,87890,87892,87894,87896,87898,87900,87902,87904,87906,87908,87910],{},[898,87879,900],{},[1996,87881,2005],{"stretchy":2004},[2129,87883,2351],{},[1996,87885,2286],{"separator":2285},[2129,87887,5585],{},[1996,87889,2286],{"separator":2285},[2129,87891,2131],{},[1996,87893,2011],{"stretchy":2004},[1996,87895,1998],{},[898,87897,900],{},[1996,87899,2005],{"stretchy":2004},[2129,87901,41842],{},[1996,87903,2286],{"separator":2285},[2129,87905,2278],{},[1996,87907,2286],{"separator":2285},[2129,87909,2351],{},[1996,87911,2011],{"stretchy":2004},[902,87913,87914],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,87917,87919],{"className":87918},[886],[888,87920,87921],{"xmlns":890},[892,87922,87923,87939],{},[895,87924,87925,87927,87929,87931,87933,87935,87937],{},[2129,87926,2351],{},[1996,87928,3177],{},[2129,87930,5585],{},[1996,87932,3177],{},[2129,87934,2131],{},[1996,87936,1998],{},[2129,87938,41842],{},[902,87940,87941],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,87943,87945],{"className":87944},[886],[888,87946,87947],{"xmlns":890},[892,87948,87949,87965],{},[895,87950,87951,87953,87955,87957,87959,87961,87963],{},[2129,87952,41842],{},[1996,87954,3177],{},[2129,87956,2278],{},[1996,87958,3177],{},[2129,87960,2351],{},[1996,87962,1998],{},[2129,87964,87860],{},[902,87966,87967],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,87969,87971],{"className":87970},[886],[888,87972,87973],{"xmlns":890},[892,87974,87975,87983],{},[895,87976,87977,87979,87981],{},[898,87978,900],{},[1996,87980,1998],{},[2129,87982,41864],{},[902,87984,87985],{"encoding":904},"U = 16",[883,87987,87989],{"className":87988},[886],[888,87990,87991],{"xmlns":890},[892,87992,87993,88001],{},[895,87994,87995,87997,87999],{},[898,87996,900],{},[1996,87998,1998],{},[2129,88000,72361],{},[902,88002,88003],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,88006,88008],{"className":88007},[886],[888,88009,88010],{"xmlns":890},[892,88011,88012,88032],{},[895,88013,88014,88020,88026],{},[2272,88015,88016,88018],{},[898,88017,2789],{},[2129,88019,2278],{},[2272,88021,88022,88024],{},[898,88023,2789],{},[2129,88025,2131],{},[2272,88027,88028,88030],{},[898,88029,2789],{},[2129,88031,2173],{},[902,88033,88034],{"encoding":904},"Q_1 Q_2 Q_3",[115,88036,88038],{"id":88037},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,88040,88041,88042,8102,88077,2203,88080,41816,88097,10025,88114,88117,88118,88121],{},"Pro funkci užitečnosti ",[883,88043,88045],{"className":88044},[886],[888,88046,88047],{"xmlns":890},[892,88048,88049,88075],{},[895,88050,88051,88053,88055,88057,88059,88065,88067,88073],{},[898,88052,900],{},[1996,88054,1998],{},[898,88056,900],{},[1996,88058,2005],{"stretchy":2004},[2272,88060,88061,88063],{},[898,88062,2789],{},[2129,88064,2278],{},[1996,88066,2286],{"separator":2285},[2272,88068,88069,88071],{},[898,88070,2789],{},[2129,88072,2131],{},[1996,88074,2011],{"stretchy":2004},[902,88076,87458],{"encoding":904},[38,88078,88079],{},"mezní užitečnost",[883,88081,88083],{"className":88082},[886],[888,88084,88085],{"xmlns":890},[892,88086,88087,88095],{},[895,88088,88089],{},[2272,88090,88091,88093],{},[898,88092,2789],{},[2129,88094,2278],{},[902,88096,29004],{"encoding":904},[883,88098,88100],{"className":88099},[886],[888,88101,88102],{"xmlns":890},[892,88103,88104,88112],{},[895,88105,88106],{},[2272,88107,88108,88110],{},[898,88109,2789],{},[2129,88111,2131],{},[902,88113,29023],{"encoding":904},[38,88115,88116],{},"marginal utility",") parciální ",[207,88119,1145],{"className":88120,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,88123,88125],{"className":88124},[886],[888,88126,88127],{"xmlns":890,"display":28068},[892,88128,88129,88228],{},[20756,88130,88131],{"width":28073},[20761,88132,88133,88135,88221,88223],{},[20764,88134],{"width":28078},[20764,88136,88137],{},[895,88138,88139,88141,88147,88149,88157,88159,88177,88179,88181,88183,88189,88191,88199,88201,88219],{},[898,88140,2818],{},[2272,88142,88143,88145],{},[898,88144,900],{},[2129,88146,2278],{},[1996,88148,1998],{},[9166,88150,88151,88153,88155],{},[898,88152,900],{},[2129,88154,2278],{},[1996,88156,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,88158,1998],{},[2329,88160,88161,88167],{},[895,88162,88163,88165],{},[898,88164,9872],{"mathvariant":2376},[898,88166,900],{},[895,88168,88169,88171],{},[898,88170,9872],{"mathvariant":2376},[2272,88172,88173,88175],{},[898,88174,2789],{},[2129,88176,2278],{},[1996,88178,2286],{"separator":2285},[5878,88180],{"width":15286},[898,88182,2818],{},[2272,88184,88185,88187],{},[898,88186,900],{},[2129,88188,2131],{},[1996,88190,1998],{},[9166,88192,88193,88195,88197],{},[898,88194,900],{},[2129,88196,2131],{},[1996,88198,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,88200,1998],{},[2329,88202,88203,88209],{},[895,88204,88205,88207],{},[898,88206,9872],{"mathvariant":2376},[898,88208,900],{},[895,88210,88211,88213],{},[898,88212,9872],{"mathvariant":2376},[2272,88214,88215,88217],{},[898,88216,2789],{},[2129,88218,2131],{},[898,88220,1975],{"mathvariant":2376},[20764,88222],{"width":28078},[20764,88224,88225],{},[2288,88226,88227],{},"(6.2)",[902,88229,88230],{"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}",[724,88232,88233,88234,88268,88269,88299,88300,2203,88303,1975],{},"Pro pevné ",[883,88235,88237],{"className":88236},[886],[888,88238,88239],{"xmlns":890},[892,88240,88241,88265],{},[895,88242,88243,88249,88251,88253,88255,88261,88263],{},[2272,88244,88245,88247],{},[898,88246,2789],{},[2129,88248,2278],{},[1996,88250,1998],{},[898,88252,207],{},[1996,88254,2286],{"separator":2285},[2272,88256,88257,88259],{},[898,88258,2789],{},[2129,88260,2131],{},[1996,88262,1998],{},[898,88264,2098],{},[902,88266,88267],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,88270,88272],{"className":88271},[886],[888,88273,88274],{"xmlns":890},[892,88275,88276,88296],{},[895,88277,88278,88280,88286,88288,88290,88292,88294],{},[898,88279,2818],{},[2272,88281,88282,88284],{},[898,88283,900],{},[2129,88285,2278],{},[1996,88287,2005],{"stretchy":2004},[898,88289,207],{},[1996,88291,2286],{"separator":2285},[898,88293,2098],{},[1996,88295,2011],{"stretchy":2004},[902,88297,88298],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,88301,88302],{},"v bodě (na hladině)",[883,88304,88306],{"className":88305},[886],[888,88307,88308],{"xmlns":890},[892,88309,88310,88322],{},[895,88311,88312,88314,88316,88318,88320],{},[1996,88313,2486],{"stretchy":2004},[898,88315,207],{},[1996,88317,2286],{"separator":2285},[898,88319,2098],{},[1996,88321,2501],{"stretchy":2004},[902,88323,10824],{"encoding":904},[3867,88325,88326],{},[724,88327,88328,88330,88331,88361,88390,88391,2610,88404,2624,88421,88442,88443,2671,88460,2685,88473,88490,88491,88513,88514,88543,88544,6473,88564,88581],{},[883,88329,4155],{}," Intuice — co říká ",[883,88332,88334],{"className":88333},[886],[888,88335,88336],{"xmlns":890},[892,88337,88338,88358],{},[895,88339,88340,88342,88348,88350,88352,88354,88356],{},[898,88341,2818],{},[2272,88343,88344,88346],{},[898,88345,900],{},[2129,88347,2278],{},[1996,88349,2005],{"stretchy":2004},[898,88351,207],{},[1996,88353,2286],{"separator":2285},[898,88355,2098],{},[1996,88357,2011],{"stretchy":2004},[902,88359,88360],{"encoding":904},"MU_1(a,b)",[883,88362,88364],{"className":88363},[886],[888,88365,88366],{"xmlns":890},[892,88367,88368,88388],{},[895,88369,88370,88372,88378,88380,88382,88384,88386],{},[898,88371,2818],{},[2272,88373,88374,88376],{},[898,88375,900],{},[2129,88377,2278],{},[1996,88379,2005],{"stretchy":2004},[898,88381,207],{},[1996,88383,2286],{"separator":2285},[898,88385,2098],{},[1996,88387,2011],{"stretchy":2004},[902,88389,88298],{"encoding":904}," je rychlost změny ",[883,88392,88394],{"className":88393},[886],[888,88395,88396],{"xmlns":890},[892,88397,88398,88402],{},[895,88399,88400],{},[898,88401,900],{},[902,88403,900],{"encoding":904},[883,88405,88407],{"className":88406},[886],[888,88408,88409],{"xmlns":890},[892,88410,88411,88419],{},[895,88412,88413],{},[2272,88414,88415,88417],{},[898,88416,2789],{},[2129,88418,2278],{},[902,88420,29004],{"encoding":904},[883,88422,88424],{"className":88423},[886],[888,88425,88426],{"xmlns":890},[892,88427,88428,88440],{},[895,88429,88430,88432,88434,88436,88438],{},[1996,88431,2486],{"stretchy":2004},[898,88433,207],{},[1996,88435,2286],{"separator":2285},[898,88437,2098],{},[1996,88439,2501],{"stretchy":2004},[902,88441,10824],{"encoding":904},". Přibližně: změní-li se ",[883,88444,88446],{"className":88445},[886],[888,88447,88448],{"xmlns":890},[892,88449,88450,88458],{},[895,88451,88452],{},[2272,88453,88454,88456],{},[898,88455,2789],{},[2129,88457,2278],{},[902,88459,29004],{"encoding":904},[883,88461,88463],{"className":88462},[886],[888,88464,88465],{"xmlns":890},[892,88466,88467,88471],{},[895,88468,88469],{},[898,88470,207],{},[902,88472,207],{"encoding":904},[883,88474,88476],{"className":88475},[886],[888,88477,88478],{"xmlns":890},[892,88479,88480,88488],{},[895,88481,88482,88484,88486],{},[898,88483,207],{},[1996,88485,2095],{},[2129,88487,2278],{},[902,88489,2703],{"encoding":904}," při pevném ",[883,88492,88494],{"className":88493},[886],[888,88495,88496],{"xmlns":890},[892,88497,88498,88510],{},[895,88499,88500,88506,88508],{},[2272,88501,88502,88504],{},[898,88503,2789],{},[2129,88505,2131],{},[1996,88507,1998],{},[898,88509,2098],{},[902,88511,88512],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,88515,88517],{"className":88516},[886],[888,88518,88519],{"xmlns":890},[892,88520,88521,88541],{},[895,88522,88523,88525,88531,88533,88535,88537,88539],{},[898,88524,2818],{},[2272,88526,88527,88529],{},[898,88528,900],{},[2129,88530,2278],{},[1996,88532,2005],{"stretchy":2004},[898,88534,207],{},[1996,88536,2286],{"separator":2285},[898,88538,2098],{},[1996,88540,2011],{"stretchy":2004},[902,88542,88298],{"encoding":904},". Stejně tak ",[883,88545,88547],{"className":88546},[886],[888,88548,88549],{"xmlns":890},[892,88550,88551,88561],{},[895,88552,88553,88555],{},[898,88554,2818],{},[2272,88556,88557,88559],{},[898,88558,900],{},[2129,88560,2131],{},[902,88562,88563],{"encoding":904},"MU_2",[883,88565,88567],{"className":88566},[886],[888,88568,88569],{"xmlns":890},[892,88570,88571,88579],{},[895,88572,88573],{},[2272,88574,88575,88577],{},[898,88576,2789],{},[2129,88578,2131],{},[902,88580,29023],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,88583,80213],{"id":88584},"totální-diferenciál",[724,88586,88587,88588,48342,88604,88634,88635,2704],{},"Přibližnou změnu užitečnosti ",[883,88589,88591],{"className":88590},[886],[888,88592,88593],{"xmlns":890},[892,88594,88595,88601],{},[895,88596,88597,88599],{},[898,88598,2889],{"mathvariant":2376},[898,88600,900],{},[902,88602,88603],{"encoding":904},"\\Delta U",[883,88605,88607],{"className":88606},[886],[888,88608,88609],{"xmlns":890},[892,88610,88611,88631],{},[895,88612,88613,88615,88621,88623,88625],{},[898,88614,2194],{"mathvariant":2376},[2272,88616,88617,88619],{},[898,88618,2789],{},[2129,88620,2278],{},[1996,88622,2286],{"separator":2285},[898,88624,2194],{"mathvariant":2376},[2272,88626,88627,88629],{},[898,88628,2789],{},[2129,88630,2131],{},[902,88632,88633],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,88636,88637],{},"totálního diferenciálu",[883,88639,88641],{"className":88640},[886],[888,88642,88643],{"xmlns":890,"display":28068},[892,88644,88645,88746],{},[20756,88646,88647],{"width":28073},[20761,88648,88649,88651,88739,88741],{},[20764,88650],{"width":28078},[20764,88652,88653],{},[895,88654,88655,88657,88659,88661,88663,88665,88667,88675,88677,88683,88685,88693,88695,88701,88703,88705,88711,88713,88719,88721,88723,88729,88731,88737],{},[898,88656,2889],{"mathvariant":2376},[898,88658,900],{},[1996,88660,2730],{},[898,88662,2194],{"mathvariant":2376},[898,88664,900],{},[1996,88666,1998],{},[9166,88668,88669,88671,88673],{},[898,88670,900],{},[2129,88672,2278],{},[1996,88674,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[898,88676,2194],{"mathvariant":2376},[2272,88678,88679,88681],{},[898,88680,2789],{},[2129,88682,2278],{},[1996,88684,2095],{},[9166,88686,88687,88689,88691],{},[898,88688,900],{},[2129,88690,2131],{},[1996,88692,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[898,88694,2194],{"mathvariant":2376},[2272,88696,88697,88699],{},[898,88698,2789],{},[2129,88700,2131],{},[1996,88702,1998],{},[898,88704,2818],{},[2272,88706,88707,88709],{},[898,88708,900],{},[2129,88710,2278],{},[898,88712,2194],{"mathvariant":2376},[2272,88714,88715,88717],{},[898,88716,2789],{},[2129,88718,2278],{},[1996,88720,2095],{},[898,88722,2818],{},[2272,88724,88725,88727],{},[898,88726,900],{},[2129,88728,2131],{},[898,88730,2194],{"mathvariant":2376},[2272,88732,88733,88735],{},[898,88734,2789],{},[2129,88736,2131],{},[898,88738,1975],{"mathvariant":2376},[20764,88740],{"width":28078},[20764,88742,88743],{},[2288,88744,88745],{},"(6.3)",[902,88747,88748],{"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}",[724,88750,75471,88751,1975],{},[883,88752,88754],{"className":88753},[886],[888,88755,88756],{"xmlns":890},[892,88757,88758,88828],{},[895,88759,88760,88762,88764,88766,88768,88770,88776,88778,88780,88786,88788,88794,88796,88798,88804,88806,88808,88810,88812,88818,88820,88826],{},[898,88761,2889],{"mathvariant":2376},[898,88763,900],{},[1996,88765,1998],{},[898,88767,900],{},[1996,88769,2005],{"stretchy":2004},[2272,88771,88772,88774],{},[898,88773,2789],{},[2129,88775,2278],{},[1996,88777,2095],{},[898,88779,2194],{"mathvariant":2376},[2272,88781,88782,88784],{},[898,88783,2789],{},[2129,88785,2278],{},[1996,88787,2286],{"separator":2285},[2272,88789,88790,88792],{},[898,88791,2789],{},[2129,88793,2131],{},[1996,88795,2095],{},[898,88797,2194],{"mathvariant":2376},[2272,88799,88800,88802],{},[898,88801,2789],{},[2129,88803,2131],{},[1996,88805,2011],{"stretchy":2004},[1996,88807,2225],{},[898,88809,900],{},[1996,88811,2005],{"stretchy":2004},[2272,88813,88814,88816],{},[898,88815,2789],{},[2129,88817,2278],{},[1996,88819,2286],{"separator":2285},[2272,88821,88822,88824],{},[898,88823,2789],{},[2129,88825,2131],{},[1996,88827,2011],{"stretchy":2004},[902,88829,88830],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,88832,88834],{"id":88833},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,88836,88837,88838,88841,88842,88845],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,88839,88840],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,88843,88844],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,88847,88848,88851,88852,41816,88878,88904,88905,1343,88937,88969,88970,3885,89024,89078],{},[38,88849,88850],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,88853,88855],{"className":88854},[886],[888,88856,88857],{"xmlns":890},[892,88858,88859,88875],{},[895,88860,88861,88867,88869],{},[2272,88862,88863,88865],{},[898,88864,2789],{},[2129,88866,2131],{},[1996,88868,1998],{},[2272,88870,88871,88873],{},[898,88872,207],{},[2129,88874,2327],{},[902,88876,88877],{"encoding":904},"Q_2 = a_0",[883,88879,88881],{"className":88880},[886],[888,88882,88883],{"xmlns":890},[892,88884,88885,88901],{},[895,88886,88887,88893,88895],{},[2272,88888,88889,88891],{},[898,88890,2789],{},[2129,88892,2278],{},[1996,88894,1998],{},[2272,88896,88897,88899],{},[898,88898,2098],{},[2129,88900,2327],{},[902,88902,88903],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,88906,88908],{"className":88907},[886],[888,88909,88910],{"xmlns":890},[892,88911,88912,88934],{},[895,88913,88914,88916,88918,88924,88926,88932],{},[898,88915,900],{},[1996,88917,2005],{"stretchy":2004},[2272,88919,88920,88922],{},[898,88921,2789],{},[2129,88923,2278],{},[1996,88925,2286],{"separator":2285},[2272,88927,88928,88930],{},[898,88929,207],{},[2129,88931,2327],{},[1996,88933,2011],{"stretchy":2004},[902,88935,88936],{"encoding":904},"U(Q_1, a_0)",[883,88938,88940],{"className":88939},[886],[888,88941,88942],{"xmlns":890},[892,88943,88944,88966],{},[895,88945,88946,88948,88950,88956,88958,88964],{},[898,88947,900],{},[1996,88949,2005],{"stretchy":2004},[2272,88951,88952,88954],{},[898,88953,2098],{},[2129,88955,2327],{},[1996,88957,2286],{"separator":2285},[2272,88959,88960,88962],{},[898,88961,2789],{},[2129,88963,2131],{},[1996,88965,2011],{"stretchy":2004},[902,88967,88968],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,88971,88973],{"className":88972},[886],[888,88974,88975],{"xmlns":890},[892,88976,88977,89021],{},[895,88978,88979,89017,89019],{},[2325,88980,88981],{"scriptlevel":2327,"displaystyle":2285},[2329,88982,88983,89007],{},[895,88984,88985,88987,88989,88991,88997,88999,89005],{},[898,88986,2194],{"mathvariant":2376},[898,88988,900],{},[1996,88990,2005],{"stretchy":2004},[2272,88992,88993,88995],{},[898,88994,2789],{},[2129,88996,2278],{},[1996,88998,2286],{"separator":2285},[2272,89000,89001,89003],{},[898,89002,207],{},[2129,89004,2327],{},[1996,89006,2011],{"stretchy":2004},[895,89008,89009,89011],{},[898,89010,2194],{"mathvariant":2376},[2272,89012,89013,89015],{},[898,89014,2789],{},[2129,89016,2278],{},[1996,89018,3408],{},[2129,89020,2327],{},[902,89022,89023],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,89025,89027],{"className":89026},[886],[888,89028,89029],{"xmlns":890},[892,89030,89031,89075],{},[895,89032,89033,89071,89073],{},[2325,89034,89035],{"scriptlevel":2327,"displaystyle":2285},[2329,89036,89037,89061],{},[895,89038,89039,89041,89043,89045,89051,89053,89059],{},[898,89040,2194],{"mathvariant":2376},[898,89042,900],{},[1996,89044,2005],{"stretchy":2004},[2272,89046,89047,89049],{},[898,89048,2098],{},[2129,89050,2327],{},[1996,89052,2286],{"separator":2285},[2272,89054,89055,89057],{},[898,89056,2789],{},[2129,89058,2131],{},[1996,89060,2011],{"stretchy":2004},[895,89062,89063,89065],{},[898,89064,2194],{"mathvariant":2376},[2272,89066,89067,89069],{},[898,89068,2789],{},[2129,89070,2131],{},[1996,89072,3408],{},[2129,89074,2327],{},[902,89076,89077],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,89080,89082],{"className":89081},[886],[888,89083,89084],{"xmlns":890,"display":28068},[892,89085,89086,89131],{},[20756,89087,89088],{"width":28073},[20761,89089,89090,89092,89124,89126],{},[20764,89091],{"width":28078},[20764,89093,89094],{},[895,89095,89096,89104,89106,89108,89110,89112,89120,89122],{},[9166,89097,89098,89100,89102],{},[898,89099,900],{},[2129,89101,2278],{},[1996,89103,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,89105,3408],{},[2129,89107,2327],{},[1996,89109,2286],{"separator":2285},[5878,89111],{"width":15286},[9166,89113,89114,89116,89118],{},[898,89115,900],{},[2129,89117,2131],{},[1996,89119,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,89121,3408],{},[2129,89123,12462],{},[20764,89125],{"width":28078},[20764,89127,89128],{},[2288,89129,89130],{},"(6.4)",[902,89132,89133],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,89135,89136,89137,89139],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,89138,52679],{}," — užitečnost roste s množstvím každého zboží.",[724,89141,89142,89145,89146,89176,89177,2704],{},[38,89143,89144],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,89147,89149],{"className":89148},[886],[888,89150,89151],{"xmlns":890},[892,89152,89153,89173],{},[895,89154,89155,89163,89165],{},[9166,89156,89157,89159,89161],{},[898,89158,900],{},[2129,89160,2278],{},[1996,89162,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,89164,2286],{"separator":2285},[9166,89166,89167,89169,89171],{},[898,89168,900],{},[2129,89170,2131],{},[1996,89172,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,89174,89175],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,89178,89179],{},"záporné",[883,89181,89183],{"className":89182},[886],[888,89184,89185],{"xmlns":890,"display":28068},[892,89186,89187,89240],{},[20756,89188,89189],{"width":28073},[20761,89190,89191,89193,89233,89235],{},[20764,89192],{"width":28078},[20764,89194,89195],{},[895,89196,89197,89209,89211,89213,89215,89217,89229,89231],{},[9166,89198,89199,89201,89203],{},[898,89200,900],{},[2129,89202,2904],{},[895,89204,89205,89207],{},[1996,89206,2378],{"mathvariant":2376},[1996,89208,2378],{"mathvariant":2376},[1996,89210,3447],{},[2129,89212,2327],{},[1996,89214,2286],{"separator":2285},[5878,89216],{"width":15286},[9166,89218,89219,89221,89223],{},[898,89220,900],{},[2129,89222,32548],{},[895,89224,89225,89227],{},[1996,89226,2378],{"mathvariant":2376},[1996,89228,2378],{"mathvariant":2376},[1996,89230,3447],{},[2129,89232,12462],{},[20764,89234],{"width":28078},[20764,89236,89237],{},[2288,89238,89239],{},"(6.5)",[902,89241,89242],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,89244,89245,89246,89249,89250,1975],{},"Podmínka (6.5) je známa jako ",[38,89247,89248],{},"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 ",[207,89251,89253],{"className":89252,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,89255,89256,89257,3885,89289,89321,89322,3885,89348,89374,89375,89403,89404,3885,89406,89408,89409,89444],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,89258,89260],{"className":89259},[886],[888,89261,89262],{"xmlns":890},[892,89263,89264,89286],{},[895,89265,89266,89268,89270,89276,89278,89284],{},[898,89267,900],{},[1996,89269,2005],{"stretchy":2004},[2272,89271,89272,89274],{},[898,89273,2789],{},[2129,89275,2278],{},[1996,89277,2286],{"separator":2285},[2272,89279,89280,89282],{},[898,89281,2098],{},[2129,89283,2327],{},[1996,89285,2011],{"stretchy":2004},[902,89287,89288],{"encoding":904},"U(Q_1, b_0)",[883,89290,89292],{"className":89291},[886],[888,89293,89294],{"xmlns":890},[892,89295,89296,89318],{},[895,89297,89298,89300,89302,89308,89310,89316],{},[898,89299,900],{},[1996,89301,2005],{"stretchy":2004},[2272,89303,89304,89306],{},[898,89305,207],{},[2129,89307,2327],{},[1996,89309,2286],{"separator":2285},[2272,89311,89312,89314],{},[898,89313,2789],{},[2129,89315,2131],{},[1996,89317,2011],{"stretchy":2004},[902,89319,89320],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,89323,89325],{"className":89324},[886],[888,89326,89327],{"xmlns":890},[892,89328,89329,89345],{},[895,89330,89331,89333,89335,89337,89343],{},[1996,89332,2005],{"stretchy":2004},[898,89334,900],{},[1996,89336,2286],{"separator":2285},[2272,89338,89339,89341],{},[898,89340,2789],{},[2129,89342,2278],{},[1996,89344,2011],{"stretchy":2004},[902,89346,89347],{"encoding":904},"(U, Q_1)",[883,89349,89351],{"className":89350},[886],[888,89352,89353],{"xmlns":890},[892,89354,89355,89371],{},[895,89356,89357,89359,89361,89363,89369],{},[1996,89358,2005],{"stretchy":2004},[898,89360,900],{},[1996,89362,2286],{"separator":2285},[2272,89364,89365,89367],{},[898,89366,2789],{},[2129,89368,2131],{},[1996,89370,2011],{"stretchy":2004},[902,89372,89373],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,89376,89378],{"className":89377},[886],[888,89379,89380],{"xmlns":890},[892,89381,89382,89400],{},[895,89383,89384,89386,89388,89390,89392,89394,89396,89398],{},[898,89385,900],{},[1996,89387,2005],{"stretchy":2004},[2129,89389,2327],{},[1996,89391,2286],{"separator":2285},[2129,89393,2327],{},[1996,89395,2011],{"stretchy":2004},[1996,89397,1998],{},[2129,89399,2327],{},[902,89401,89402],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,89405,13659],{},[38,89407,38490],{},". Typický tvar grafu ",[883,89410,89412],{"className":89411},[886],[888,89413,89414],{"xmlns":890},[892,89415,89416,89442],{},[895,89417,89418,89420,89422,89424,89426,89432,89434,89440],{},[898,89419,900],{},[1996,89421,1998],{},[898,89423,900],{},[1996,89425,2005],{"stretchy":2004},[2272,89427,89428,89430],{},[898,89429,2789],{},[2129,89431,2278],{},[1996,89433,2286],{"separator":2285},[2272,89435,89436,89438],{},[898,89437,2789],{},[2129,89439,2131],{},[1996,89441,2011],{"stretchy":2004},[902,89443,87458],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,89446,89447],{},[614,89448,89449,89450,88490,89478,89499,89500,88490,89528,89550],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,89451,89453],{"className":89452},[886],[888,89454,89455],{"xmlns":890},[892,89456,89457,89475],{},[895,89458,89459,89461,89463,89469,89471,89473],{},[898,89460,900],{},[1996,89462,2005],{"stretchy":2004},[2272,89464,89465,89467],{},[898,89466,2789],{},[2129,89468,2278],{},[1996,89470,2286],{"separator":2285},[898,89472,2098],{},[1996,89474,2011],{"stretchy":2004},[902,89476,89477],{"encoding":904},"U(Q_1, b)",[883,89479,89481],{"className":89480},[886],[888,89482,89483],{"xmlns":890},[892,89484,89485,89497],{},[895,89486,89487,89493,89495],{},[2272,89488,89489,89491],{},[898,89490,2789],{},[2129,89492,2131],{},[1996,89494,1998],{},[898,89496,2098],{},[902,89498,88512],{"encoding":904}," (vlevo) a ",[883,89501,89503],{"className":89502},[886],[888,89504,89505],{"xmlns":890},[892,89506,89507,89525],{},[895,89508,89509,89511,89513,89515,89517,89523],{},[898,89510,900],{},[1996,89512,2005],{"stretchy":2004},[898,89514,207],{},[1996,89516,2286],{"separator":2285},[2272,89518,89519,89521],{},[898,89520,2789],{},[2129,89522,2131],{},[1996,89524,2011],{"stretchy":2004},[902,89526,89527],{"encoding":904},"U(a, Q_2)",[883,89529,89531],{"className":89530},[886],[888,89532,89533],{"xmlns":890},[892,89534,89535,89547],{},[895,89536,89537,89543,89545],{},[2272,89538,89539,89541],{},[898,89540,2789],{},[2129,89542,2278],{},[1996,89544,1998],{},[898,89546,207],{},[902,89548,89549],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,89552,89553],{},[614,89554,89555,89556,89591,89592,89622,89623,3885,89646,89668,89669,1975],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,89557,89559],{"className":89558},[886],[888,89560,89561],{"xmlns":890},[892,89562,89563,89589],{},[895,89564,89565,89567,89569,89571,89573,89579,89581,89587],{},[898,89566,900],{},[1996,89568,1998],{},[898,89570,900],{},[1996,89572,2005],{"stretchy":2004},[2272,89574,89575,89577],{},[898,89576,2789],{},[2129,89578,2278],{},[1996,89580,2286],{"separator":2285},[2272,89582,89583,89585],{},[898,89584,2789],{},[2129,89586,2131],{},[1996,89588,2011],{"stretchy":2004},[902,89590,87458],{"encoding":904}," nad rovinou ",[883,89593,89595],{"className":89594},[886],[888,89596,89597],{"xmlns":890},[892,89598,89599,89619],{},[895,89600,89601,89603,89609,89611,89617],{},[1996,89602,2005],{"stretchy":2004},[2272,89604,89605,89607],{},[898,89606,2789],{},[2129,89608,2278],{},[1996,89610,2286],{"separator":2285},[2272,89612,89613,89615],{},[898,89614,2789],{},[2129,89616,2131],{},[1996,89618,2011],{"stretchy":2004},[902,89620,89621],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,89624,89626],{"className":89625},[886],[888,89627,89628],{"xmlns":890},[892,89629,89630,89643],{},[895,89631,89632,89638,89640],{},[2272,89633,89634,89636],{},[898,89635,2789],{},[2129,89637,2278],{},[1996,89639,1998],{},[2288,89641,89642],{},"const",[902,89644,89645],{"encoding":904},"Q_1 = \\text{const}",[883,89647,89649],{"className":89648},[886],[888,89650,89651],{"xmlns":890},[892,89652,89653,89665],{},[895,89654,89655,89661,89663],{},[2272,89656,89657,89659],{},[898,89658,2789],{},[2129,89660,2131],{},[1996,89662,1998],{},[2288,89664,89642],{},[902,89666,89667],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,89670,89672],{"className":89671},[886],[888,89673,89674],{"xmlns":890},[892,89675,89676,89702],{},[895,89677,89678,89680,89682,89688,89690,89696,89698,89700],{},[898,89679,900],{},[1996,89681,2005],{"stretchy":2004},[2272,89683,89684,89686],{},[898,89685,2789],{},[2129,89687,2278],{},[1996,89689,2286],{"separator":2285},[2272,89691,89692,89694],{},[898,89693,2789],{},[2129,89695,2131],{},[1996,89697,2011],{"stretchy":2004},[1996,89699,1998],{},[898,89701,2142],{},[902,89703,9768],{"encoding":904},[198,89705,89707,89708],{"id":89706},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,89709,89711],{"className":89710},[886],[888,89712,89713],{"xmlns":890},[892,89714,89715,89749],{},[895,89716,89717,89719,89721,89735],{},[898,89718,900],{},[1996,89720,1998],{},[9166,89722,89723,89725,89727],{},[898,89724,2789],{},[2129,89726,2278],{},[895,89728,89729,89731,89733],{},[2129,89730,2278],{},[898,89732,4674],{"mathvariant":2376},[2129,89734,2131],{},[9166,89736,89737,89739,89741],{},[898,89738,2789],{},[2129,89740,2131],{},[895,89742,89743,89745,89747],{},[2129,89744,2278],{},[898,89746,4674],{"mathvariant":2376},[2129,89748,2173],{},[902,89750,89751],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,89753,89754],{},[38,89755,89756],{},"Ověření (6.4) a (6.5).",[883,89758,89760],{"className":89759},[886],[888,89761,89762],{"xmlns":890,"display":28068},[892,89763,89764,89868],{},[895,89765,89766,89774,89776,89784,89800,89814,89816,89818,89826,89828,89836,89850,89866],{},[9166,89767,89768,89770,89772],{},[898,89769,900],{},[2129,89771,2278],{},[1996,89773,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,89775,1998],{},[2325,89777,89778],{"scriptlevel":2327,"displaystyle":2004},[2329,89779,89780,89782],{},[2129,89781,2278],{},[2129,89783,2131],{},[9166,89785,89786,89788,89790],{},[898,89787,2789],{},[2129,89789,2278],{},[895,89791,89792,89794,89796,89798],{},[1996,89793,2225],{},[2129,89795,2278],{},[898,89797,4674],{"mathvariant":2376},[2129,89799,2131],{},[9166,89801,89802,89804,89806],{},[898,89803,2789],{},[2129,89805,2131],{},[895,89807,89808,89810,89812],{},[2129,89809,2278],{},[898,89811,4674],{"mathvariant":2376},[2129,89813,2173],{},[1996,89815,2286],{"separator":2285},[5878,89817],{"width":15286},[9166,89819,89820,89822,89824],{},[898,89821,900],{},[2129,89823,2131],{},[1996,89825,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,89827,1998],{},[2325,89829,89830],{"scriptlevel":2327,"displaystyle":2004},[2329,89831,89832,89834],{},[2129,89833,2278],{},[2129,89835,2173],{},[9166,89837,89838,89840,89842],{},[898,89839,2789],{},[2129,89841,2278],{},[895,89843,89844,89846,89848],{},[2129,89845,2278],{},[898,89847,4674],{"mathvariant":2376},[2129,89849,2131],{},[9166,89851,89852,89854,89856],{},[898,89853,2789],{},[2129,89855,2131],{},[895,89857,89858,89860,89862,89864],{},[1996,89859,2225],{},[2129,89861,2131],{},[898,89863,4674],{"mathvariant":2376},[2129,89865,2173],{},[1996,89867,2286],{"separator":2285},[902,89869,89870],{"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},",[724,89872,89873,89874,89908],{},"zřejmě ",[883,89875,89877],{"className":89876},[886],[888,89878,89879],{"xmlns":890},[892,89880,89881,89905],{},[895,89882,89883,89891,89893,89901,89903],{},[9166,89884,89885,89887,89889],{},[898,89886,900],{},[2129,89888,2278],{},[1996,89890,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,89892,2286],{"separator":2285},[9166,89894,89895,89897,89899],{},[898,89896,900],{},[2129,89898,2131],{},[1996,89900,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,89902,3408],{},[2129,89904,2327],{},[902,89906,89907],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,89910,89912],{"className":89911},[886],[888,89913,89914],{"xmlns":890,"display":28068},[892,89915,89916,90032],{},[895,89917,89918,89930,89932,89934,89942,89958,89972,89974,89976,89988,89990,89992,90000,90014,90030],{},[9166,89919,89920,89922,89924],{},[898,89921,900],{},[2129,89923,2904],{},[895,89925,89926,89928],{},[1996,89927,2378],{"mathvariant":2376},[1996,89929,2378],{"mathvariant":2376},[1996,89931,1998],{},[1996,89933,2225],{},[2325,89935,89936],{"scriptlevel":2327,"displaystyle":2004},[2329,89937,89938,89940],{},[2129,89939,2278],{},[2129,89941,2351],{},[9166,89943,89944,89946,89948],{},[898,89945,2789],{},[2129,89947,2278],{},[895,89949,89950,89952,89954,89956],{},[1996,89951,2225],{},[2129,89953,2173],{},[898,89955,4674],{"mathvariant":2376},[2129,89957,2131],{},[9166,89959,89960,89962,89964],{},[898,89961,2789],{},[2129,89963,2131],{},[895,89965,89966,89968,89970],{},[2129,89967,2278],{},[898,89969,4674],{"mathvariant":2376},[2129,89971,2173],{},[1996,89973,2286],{"separator":2285},[5878,89975],{"width":15286},[9166,89977,89978,89980,89982],{},[898,89979,900],{},[2129,89981,32548],{},[895,89983,89984,89986],{},[1996,89985,2378],{"mathvariant":2376},[1996,89987,2378],{"mathvariant":2376},[1996,89989,1998],{},[1996,89991,2225],{},[2325,89993,89994],{"scriptlevel":2327,"displaystyle":2004},[2329,89995,89996,89998],{},[2129,89997,2131],{},[2129,89999,3999],{},[9166,90001,90002,90004,90006],{},[898,90003,2789],{},[2129,90005,2278],{},[895,90007,90008,90010,90012],{},[2129,90009,2278],{},[898,90011,4674],{"mathvariant":2376},[2129,90013,2131],{},[9166,90015,90016,90018,90020],{},[898,90017,2789],{},[2129,90019,2131],{},[895,90021,90022,90024,90026,90028],{},[1996,90023,2225],{},[2129,90025,2228],{},[898,90027,4674],{"mathvariant":2376},[2129,90029,2173],{},[1996,90031,2286],{"separator":2285},[902,90033,90034],{"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},",[724,90036,90037,90038,90080],{},"opět ",[883,90039,90041],{"className":90040},[886],[888,90042,90043],{"xmlns":890},[892,90044,90045,90077],{},[895,90046,90047,90059,90061,90073,90075],{},[9166,90048,90049,90051,90053],{},[898,90050,900],{},[2129,90052,2904],{},[895,90054,90055,90057],{},[1996,90056,2378],{"mathvariant":2376},[1996,90058,2378],{"mathvariant":2376},[1996,90060,2286],{"separator":2285},[9166,90062,90063,90065,90067],{},[898,90064,900],{},[2129,90066,32548],{},[895,90068,90069,90071],{},[1996,90070,2378],{"mathvariant":2376},[1996,90072,2378],{"mathvariant":2376},[1996,90074,3447],{},[2129,90076,2327],{},[902,90078,90079],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,90082,90083],{},[38,90084,90085,90086,1975],{},"(a) Mezní užitečnosti v bodě ",[883,90087,90089],{"className":90088},[886],[888,90090,90091],{"xmlns":890},[892,90092,90093,90105],{},[895,90094,90095,90097,90099,90101,90103],{},[1996,90096,2486],{"stretchy":2004},[2129,90098,3090],{},[1996,90100,2286],{"separator":2285},[2129,90102,8377],{},[1996,90104,2501],{"stretchy":2004},[902,90106,90107],{"encoding":904},"[100, 200]",[883,90109,90111],{"className":90110},[886],[888,90112,90113],{"xmlns":890,"display":28068},[892,90114,90115,90182],{},[895,90116,90117,90119,90125,90127,90129,90131,90133,90135,90137,90145,90147,90161,90163,90175,90177,90180],{},[898,90118,2818],{},[2272,90120,90121,90123],{},[898,90122,900],{},[2129,90124,2278],{},[1996,90126,2005],{"stretchy":2004},[2129,90128,3090],{},[1996,90130,2286],{"separator":2285},[2129,90132,8377],{},[1996,90134,2011],{"stretchy":2004},[1996,90136,1998],{},[2325,90138,90139],{"scriptlevel":2327,"displaystyle":2004},[2329,90140,90141,90143],{},[2129,90142,2278],{},[2129,90144,2131],{},[1996,90146,3177],{},[2124,90148,90149,90151],{},[2129,90150,3090],{},[895,90152,90153,90155,90157,90159],{},[1996,90154,2225],{},[2129,90156,2278],{},[898,90158,4674],{"mathvariant":2376},[2129,90160,2131],{},[1996,90162,3177],{},[2124,90164,90165,90167],{},[2129,90166,8377],{},[895,90168,90169,90171,90173],{},[2129,90170,2278],{},[898,90172,4674],{"mathvariant":2376},[2129,90174,2173],{},[1996,90176,5900],{},[2129,90178,90179],{},"0,4204",[1996,90181,2286],{"separator":2285},[902,90183,90184],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,90186,90188],{"className":90187},[886],[888,90189,90190],{"xmlns":890,"display":28068},[892,90191,90192,90257],{},[895,90193,90194,90196,90202,90204,90206,90208,90210,90212,90214,90222,90224,90236,90238,90252,90254],{},[898,90195,2818],{},[2272,90197,90198,90200],{},[898,90199,900],{},[2129,90201,2131],{},[1996,90203,2005],{"stretchy":2004},[2129,90205,3090],{},[1996,90207,2286],{"separator":2285},[2129,90209,8377],{},[1996,90211,2011],{"stretchy":2004},[1996,90213,1998],{},[2325,90215,90216],{"scriptlevel":2327,"displaystyle":2004},[2329,90217,90218,90220],{},[2129,90219,2278],{},[2129,90221,2173],{},[1996,90223,3177],{},[2124,90225,90226,90228],{},[2129,90227,3090],{},[895,90229,90230,90232,90234],{},[2129,90231,2278],{},[898,90233,4674],{"mathvariant":2376},[2129,90235,2131],{},[1996,90237,3177],{},[2124,90239,90240,90242],{},[2129,90241,8377],{},[895,90243,90244,90246,90248,90250],{},[1996,90245,2225],{},[2129,90247,2131],{},[898,90249,4674],{"mathvariant":2376},[2129,90251,2173],{},[1996,90253,5900],{},[2129,90255,90256],{},"0,63067.",[902,90258,90259],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,90261,90262,2203,90264,90299,90300,90321,90322,90339],{},[614,90263,9216],{},[883,90265,90267],{"className":90266},[886],[888,90268,90269],{"xmlns":890},[892,90270,90271,90296],{},[895,90272,90273,90275,90281,90283,90285,90287,90289,90291,90293],{},[898,90274,2818],{},[2272,90276,90277,90279],{},[898,90278,900],{},[2129,90280,2131],{},[1996,90282,2005],{"stretchy":2004},[2129,90284,3090],{},[1996,90286,2286],{"separator":2285},[2129,90288,8377],{},[1996,90290,2011],{"stretchy":2004},[1996,90292,5900],{},[2129,90294,90295],{},"0,63067",[902,90297,90298],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,90301,90303],{"className":90302},[886],[888,90304,90305],{"xmlns":890},[892,90306,90307,90319],{},[895,90308,90309,90311,90313,90315,90317],{},[1996,90310,2486],{"stretchy":2004},[2129,90312,3090],{},[1996,90314,2286],{"separator":2285},[2129,90316,8377],{},[1996,90318,2501],{"stretchy":2004},[902,90320,90107],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,90323,90325],{"className":90324},[886],[888,90326,90327],{"xmlns":890},[892,90328,90329,90337],{},[895,90330,90331],{},[2272,90332,90333,90335],{},[898,90334,2789],{},[2129,90336,2131],{},[902,90338,29023],{"encoding":904}," přibližně o 0,63067.",[724,90341,90342,90361,90362,39186,90383,90400,90401,90427,90428,90445,90446,3151],{},[38,90343,90344,90345,90360],{},"(b) Odhad změny ",[883,90346,90348],{"className":90347},[886],[888,90349,90350],{"xmlns":890},[892,90351,90352,90358],{},[895,90353,90354,90356],{},[898,90355,2889],{"mathvariant":2376},[898,90357,900],{},[902,90359,88603],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,90363,90365],{"className":90364},[886],[888,90366,90367],{"xmlns":890},[892,90368,90369,90381],{},[895,90370,90371,90373,90375,90377,90379],{},[1996,90372,2486],{"stretchy":2004},[2129,90374,3090],{},[1996,90376,2286],{"separator":2285},[2129,90378,8377],{},[1996,90380,2501],{"stretchy":2004},[902,90382,90107],{"encoding":904},[883,90384,90386],{"className":90385},[886],[888,90387,90388],{"xmlns":890},[892,90389,90390,90398],{},[895,90391,90392],{},[2272,90393,90394,90396],{},[898,90395,2789],{},[2129,90397,2278],{},[902,90399,29004],{"encoding":904}," na 98 (tj. ",[883,90402,90404],{"className":90403},[886],[888,90405,90406],{"xmlns":890},[892,90407,90408,90424],{},[895,90409,90410,90412,90418,90420,90422],{},[898,90411,2194],{"mathvariant":2376},[2272,90413,90414,90416],{},[898,90415,2789],{},[2129,90417,2278],{},[1996,90419,1998],{},[1996,90421,2225],{},[2129,90423,2131],{},[902,90425,90426],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,90429,90431],{"className":90430},[886],[888,90432,90433],{"xmlns":890},[892,90434,90435,90443],{},[895,90436,90437],{},[2272,90438,90439,90441],{},[898,90440,2789],{},[2129,90442,2131],{},[902,90444,29023],{"encoding":904}," o 3 (tj. ",[883,90447,90449],{"className":90448},[886],[888,90450,90451],{"xmlns":890},[892,90452,90453,90467],{},[895,90454,90455,90457,90463,90465],{},[898,90456,2194],{"mathvariant":2376},[2272,90458,90459,90461],{},[898,90460,2789],{},[2129,90462,2131],{},[1996,90464,1998],{},[2129,90466,2173],{},[902,90468,90469],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,90471,90473],{"className":90472},[886],[888,90474,90475],{"xmlns":890,"display":28068},[892,90476,90477,90528],{},[895,90478,90479,90481,90483,90485,90487,90489,90491,90493,90495,90497,90499,90501,90503,90505,90507,90509,90511,90513,90515,90518,90520,90523,90525],{},[898,90480,2889],{"mathvariant":2376},[898,90482,900],{},[1996,90484,2730],{},[898,90486,2194],{"mathvariant":2376},[898,90488,900],{},[1996,90490,1998],{},[2129,90492,90179],{},[1996,90494,3177],{},[1996,90496,2005],{"stretchy":2004},[1996,90498,2225],{},[2129,90500,2131],{},[1996,90502,2011],{"stretchy":2004},[1996,90504,2095],{},[2129,90506,90295],{},[1996,90508,3177],{},[2129,90510,2173],{},[1996,90512,1998],{},[1996,90514,2225],{},[2129,90516,90517],{},"0,8408",[1996,90519,2095],{},[2129,90521,90522],{},"1,89201",[1996,90524,5900],{},[2129,90526,90527],{},"1,05.",[902,90529,90530],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,90532,90533,90534,90537,90538,90589,90590,1975],{},"Užitečnost se tedy zvýší přibližně o ",[38,90535,90536],{},"1,05",". Skutečná změna je ",[883,90539,90541],{"className":90540},[886],[888,90542,90543],{"xmlns":890},[892,90544,90545,90586],{},[895,90546,90547,90549,90551,90553,90555,90557,90560,90562,90565,90567,90569,90571,90573,90575,90577,90579,90581,90583],{},[898,90548,2889],{"mathvariant":2376},[898,90550,900],{},[1996,90552,1998],{},[898,90554,900],{},[1996,90556,2005],{"stretchy":2004},[2129,90558,90559],{},"98",[1996,90561,2286],{"separator":2285},[2129,90563,90564],{},"203",[1996,90566,2011],{"stretchy":2004},[1996,90568,2225],{},[898,90570,900],{},[1996,90572,2005],{"stretchy":2004},[2129,90574,3090],{},[1996,90576,2286],{"separator":2285},[2129,90578,8377],{},[1996,90580,2011],{"stretchy":2004},[1996,90582,5900],{},[2129,90584,90585],{},"1,031",[902,90587,90588],{"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 ",[883,90591,90593],{"className":90592},[886],[888,90594,90595],{"xmlns":890},[892,90596,90597,90617],{},[895,90598,90599,90601,90607,90609,90611],{},[898,90600,2194],{"mathvariant":2376},[2272,90602,90603,90605],{},[898,90604,2789],{},[2129,90606,2278],{},[1996,90608,2286],{"separator":2285},[898,90610,2194],{"mathvariant":2376},[2272,90612,90613,90615],{},[898,90614,2789],{},[2129,90616,2131],{},[902,90618,88633],{"encoding":904},[115,90620,90622],{"id":90621},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,90624,90625],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,90627,90629],{"className":90628},[886],[888,90630,90631],{"xmlns":890,"display":28068},[892,90632,90633,90692],{},[20756,90634,90635],{"width":28073},[20761,90636,90637,90639,90685,90687],{},[20764,90638],{"width":28078},[20764,90640,90641],{},[895,90642,90643,90645,90647,90653,90655,90661,90663,90665,90673,90675,90683],{},[898,90644,900],{},[1996,90646,2005],{"stretchy":2004},[2272,90648,90649,90651],{},[898,90650,2789],{},[2129,90652,2278],{},[1996,90654,2286],{"separator":2285},[2272,90656,90657,90659],{},[898,90658,2789],{},[2129,90660,2131],{},[1996,90662,2011],{"stretchy":2004},[1996,90664,1998],{},[9166,90666,90667,90669,90671],{},[898,90668,2789],{},[2129,90670,2278],{},[898,90672,207],{},[1996,90674,3177],{},[9166,90676,90677,90679,90681],{},[898,90678,2789],{},[2129,90680,2131],{},[898,90682,2098],{},[1996,90684,2286],{"separator":2285},[20764,90686],{"width":28078},[20764,90688,90689],{},[2288,90690,90691],{},"(6.6)",[902,90693,90694],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,90696,4310,90697,90715,90716,90718,90719,90723,90724,90754,90755,90777],{},[883,90698,90700],{"className":90699},[886],[888,90701,90702],{"xmlns":890},[892,90703,90704,90712],{},[895,90705,90706,90708,90710],{},[898,90707,207],{},[1996,90709,2286],{"separator":2285},[898,90711,2098],{},[902,90713,90714],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,90717,74701],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,90720,90722],{"className":90721,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,90725,90727],{"className":90726},[886],[888,90728,90729],{"xmlns":890},[892,90730,90731,90751],{},[895,90732,90733,90735,90737,90739,90741,90743,90745,90747,90749],{},[898,90734,207],{},[1996,90736,2286],{"separator":2285},[898,90738,2098],{},[1996,90740,6506],{},[1996,90742,2005],{"stretchy":2004},[2129,90744,2327],{},[1996,90746,2286],{"separator":2285},[2129,90748,2278],{},[1996,90750,2011],{"stretchy":2004},[902,90752,90753],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,90756,90758],{"className":90757},[886],[888,90759,90760],{"xmlns":890},[892,90761,90762,90774],{},[895,90763,90764,90766,90768,90770,90772],{},[898,90765,2098],{},[1996,90767,1998],{},[2129,90769,2278],{},[1996,90771,2225],{},[898,90773,207],{},[902,90775,90776],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,90779,90780],{},[2559,90781],{"alt":90782,"className":90783,"src":90784},"imek-cobb-douglas-3d-plus-ic",[210,2563],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,90786,90788],{"className":90787},[886],[888,90789,90790],{"xmlns":890,"display":28068},[892,90791,90792,90842],{},[895,90793,90794,90796,90798,90804,90806,90812,90814,90816,90824,90826,90840],{},[898,90795,900],{},[1996,90797,2005],{"stretchy":2004},[2272,90799,90800,90802],{},[898,90801,2789],{},[2129,90803,2278],{},[1996,90805,2286],{"separator":2285},[2272,90807,90808,90810],{},[898,90809,2789],{},[2129,90811,2131],{},[1996,90813,2011],{"stretchy":2004},[1996,90815,1998],{},[9166,90817,90818,90820,90822],{},[898,90819,2789],{},[2129,90821,2278],{},[898,90823,207],{},[1996,90825,3177],{},[9166,90827,90828,90830,90832],{},[898,90829,2789],{},[2129,90831,2131],{},[895,90833,90834,90836,90838],{},[2129,90835,2278],{},[1996,90837,2225],{},[898,90839,207],{},[898,90841,1975],{"mathvariant":2376},[902,90843,90844],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[3867,90846,90847,90896,91018,91152],{},[724,90848,90849,90851,90852],{},[883,90850,52697],{}," Příklad 6.3 — ověření vlastností pro ",[883,90853,90855],{"className":90854},[886],[888,90856,90857],{"xmlns":890},[892,90858,90859,90893],{},[895,90860,90861,90863,90865,90879],{},[898,90862,900],{},[1996,90864,1998],{},[9166,90866,90867,90869,90871],{},[898,90868,2789],{},[2129,90870,2278],{},[895,90872,90873,90875,90877],{},[2129,90874,2278],{},[898,90876,4674],{"mathvariant":2376},[2129,90878,2351],{},[9166,90880,90881,90883,90885],{},[898,90882,2789],{},[2129,90884,2131],{},[895,90886,90887,90889,90891],{},[2129,90888,2173],{},[898,90890,4674],{"mathvariant":2376},[2129,90892,2351],{},[902,90894,90895],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,90897,90899],{"className":90898},[886],[888,90900,90901],{"xmlns":890,"display":28068},[892,90902,90903,91015],{},[895,90904,90905,90913,90915,90923,90939,90953,90955,90957,90959,90961,90969,90971,90979,90993,91009,91011,91013],{},[9166,90906,90907,90909,90911],{},[898,90908,900],{},[2129,90910,2278],{},[1996,90912,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,90914,1998],{},[2325,90916,90917],{"scriptlevel":2327,"displaystyle":2004},[2329,90918,90919,90921],{},[2129,90920,2278],{},[2129,90922,2351],{},[9166,90924,90925,90927,90929],{},[898,90926,2789],{},[2129,90928,2278],{},[895,90930,90931,90933,90935,90937],{},[1996,90932,2225],{},[2129,90934,2173],{},[898,90936,4674],{"mathvariant":2376},[2129,90938,2351],{},[9166,90940,90941,90943,90945],{},[898,90942,2789],{},[2129,90944,2131],{},[895,90946,90947,90949,90951],{},[2129,90948,2173],{},[898,90950,4674],{"mathvariant":2376},[2129,90952,2351],{},[1996,90954,3408],{},[2129,90956,2327],{},[1996,90958,2286],{"separator":2285},[5878,90960],{"width":15286},[9166,90962,90963,90965,90967],{},[898,90964,900],{},[2129,90966,2131],{},[1996,90968,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,90970,1998],{},[2325,90972,90973],{"scriptlevel":2327,"displaystyle":2004},[2329,90974,90975,90977],{},[2129,90976,2173],{},[2129,90978,2351],{},[9166,90980,90981,90983,90985],{},[898,90982,2789],{},[2129,90984,2278],{},[895,90986,90987,90989,90991],{},[2129,90988,2278],{},[898,90990,4674],{"mathvariant":2376},[2129,90992,2351],{},[9166,90994,90995,90997,90999],{},[898,90996,2789],{},[2129,90998,2131],{},[895,91000,91001,91003,91005,91007],{},[1996,91002,2225],{},[2129,91004,2278],{},[898,91006,4674],{"mathvariant":2376},[2129,91008,2351],{},[1996,91010,3408],{},[2129,91012,2327],{},[1996,91014,2286],{"separator":2285},[902,91016,91017],{"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,",[883,91019,91021],{"className":91020},[886],[888,91022,91023],{"xmlns":890,"display":28068},[892,91024,91025,91149],{},[895,91026,91027,91039,91041,91043,91051,91067,91081,91083,91085,91087,91089,91101,91103,91105,91113,91127,91143,91145,91147],{},[9166,91028,91029,91031,91033],{},[898,91030,900],{},[2129,91032,2904],{},[895,91034,91035,91037],{},[1996,91036,2378],{"mathvariant":2376},[1996,91038,2378],{"mathvariant":2376},[1996,91040,1998],{},[1996,91042,2225],{},[2325,91044,91045],{"scriptlevel":2327,"displaystyle":2004},[2329,91046,91047,91049],{},[2129,91048,2173],{},[2129,91050,41864],{},[9166,91052,91053,91055,91057],{},[898,91054,2789],{},[2129,91056,2278],{},[895,91058,91059,91061,91063,91065],{},[1996,91060,2225],{},[2129,91062,24203],{},[898,91064,4674],{"mathvariant":2376},[2129,91066,2351],{},[9166,91068,91069,91071,91073],{},[898,91070,2789],{},[2129,91072,2131],{},[895,91074,91075,91077,91079],{},[2129,91076,2173],{},[898,91078,4674],{"mathvariant":2376},[2129,91080,2351],{},[1996,91082,3447],{},[2129,91084,2327],{},[1996,91086,2286],{"separator":2285},[5878,91088],{"width":15286},[9166,91090,91091,91093,91095],{},[898,91092,900],{},[2129,91094,32548],{},[895,91096,91097,91099],{},[1996,91098,2378],{"mathvariant":2376},[1996,91100,2378],{"mathvariant":2376},[1996,91102,1998],{},[1996,91104,2225],{},[2325,91106,91107],{"scriptlevel":2327,"displaystyle":2004},[2329,91108,91109,91111],{},[2129,91110,2173],{},[2129,91112,41864],{},[9166,91114,91115,91117,91119],{},[898,91116,2789],{},[2129,91118,2278],{},[895,91120,91121,91123,91125],{},[2129,91122,2278],{},[898,91124,4674],{"mathvariant":2376},[2129,91126,2351],{},[9166,91128,91129,91131,91133],{},[898,91130,2789],{},[2129,91132,2131],{},[895,91134,91135,91137,91139,91141],{},[1996,91136,2225],{},[2129,91138,2228],{},[898,91140,4674],{"mathvariant":2376},[2129,91142,2351],{},[1996,91144,3447],{},[2129,91146,2327],{},[1996,91148,2286],{"separator":2285},[902,91150,91151],{"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,",[724,91153,91154],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,91156,91158],{"id":91157},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,91160,91161,91164],{},[38,91162,91163],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,91166,91168],{"className":91167},[886],[888,91169,91170],{"xmlns":890,"display":28068},[892,91171,91172,91215],{},[20756,91173,91174],{"width":28073},[20761,91175,91176,91178,91208,91210],{},[20764,91177],{"width":28078},[20764,91179,91180],{},[895,91181,91182,91184,91186,91192,91194,91200,91202,91204,91206],{},[898,91183,900],{},[1996,91185,2005],{"stretchy":2004},[2272,91187,91188,91190],{},[898,91189,2789],{},[2129,91191,2278],{},[1996,91193,2286],{"separator":2285},[2272,91195,91196,91198],{},[898,91197,2789],{},[2129,91199,2131],{},[1996,91201,2011],{"stretchy":2004},[1996,91203,1998],{},[898,91205,2142],{},[1996,91207,2286],{"separator":2285},[20764,91209],{"width":28078},[20764,91211,91212],{},[2288,91213,91214],{},"(6.7)",[902,91216,91217],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,91219,4310,91220,91233],{},[883,91221,91223],{"className":91222},[886],[888,91224,91225],{"xmlns":890},[892,91226,91227,91231],{},[895,91228,91229],{},[898,91230,2142],{},[902,91232,2142],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,91235,91237],{"className":91236},[886],[888,91238,91239],{"xmlns":890,"display":28068},[892,91240,91241,91282],{},[20756,91242,91243],{"width":28073},[20761,91244,91245,91247,91275,91277],{},[20764,91246],{"width":28078},[20764,91248,91249],{},[895,91250,91251,91259,91261,91269,91271,91273],{},[9166,91252,91253,91255,91257],{},[898,91254,2789],{},[2129,91256,2278],{},[898,91258,207],{},[1996,91260,3177],{},[9166,91262,91263,91265,91267],{},[898,91264,2789],{},[2129,91266,2131],{},[898,91268,2098],{},[1996,91270,1998],{},[898,91272,2142],{},[898,91274,1975],{"mathvariant":2376},[20764,91276],{"width":28078},[20764,91278,91279],{},[2288,91280,91281],{},"(6.8)",[902,91283,91284],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,91286,91287,91288,4358,91318,2203,91321,91334,91335,91370,91371,91388,91389,91418,91419,91422],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,91289,91291],{"className":91290},[886],[888,91292,91293],{"xmlns":890},[892,91294,91295,91315],{},[895,91296,91297,91299,91305,91307,91313],{},[1996,91298,2486],{"stretchy":2004},[2272,91300,91301,91303],{},[898,91302,2789],{},[2129,91304,2278],{},[1996,91306,2286],{"separator":2285},[2272,91308,91309,91311],{},[898,91310,2789],{},[2129,91312,2131],{},[1996,91314,2501],{"stretchy":2004},[902,91316,91317],{"encoding":904},"[Q_1, Q_2]",[38,91319,91320],{},"stejnou úrovní uspokojení",[883,91322,91324],{"className":91323},[886],[888,91325,91326],{"xmlns":890},[892,91327,91328,91332],{},[895,91329,91330],{},[898,91331,2142],{},[902,91333,2142],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,91336,91338],{"className":91337},[886],[888,91339,91340],{"xmlns":890},[892,91341,91342,91368],{},[895,91343,91344,91346,91348,91350,91352,91358,91360,91366],{},[898,91345,900],{},[1996,91347,1998],{},[898,91349,900],{},[1996,91351,2005],{"stretchy":2004},[2272,91353,91354,91356],{},[898,91355,2789],{},[2129,91357,2278],{},[1996,91359,2286],{"separator":2285},[2272,91361,91362,91364],{},[898,91363,2789],{},[2129,91365,2131],{},[1996,91367,2011],{"stretchy":2004},[902,91369,87458],{"encoding":904}," s rovinami ",[883,91372,91374],{"className":91373},[886],[888,91375,91376],{"xmlns":890},[892,91377,91378,91386],{},[895,91379,91380,91382,91384],{},[898,91381,900],{},[1996,91383,1998],{},[898,91385,2142],{},[902,91387,86674],{"encoding":904}," rovnoběžnými s rovinou ",[883,91390,91392],{"className":91391},[886],[888,91393,91394],{"xmlns":890},[892,91395,91396,91416],{},[895,91397,91398,91400,91406,91408,91414],{},[1996,91399,2005],{"stretchy":2004},[2272,91401,91402,91404],{},[898,91403,2789],{},[2129,91405,2278],{},[1996,91407,2286],{"separator":2285},[2272,91409,91410,91412],{},[898,91411,2789],{},[2129,91413,2131],{},[1996,91415,2011],{"stretchy":2004},[902,91417,89621],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,91420,91421],{},"izokvantami"," produkčních funkcí.",[724,91424,91425],{},[614,91426,91427,91428,89499,91446,91464,91465,1975],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,91429,91431],{"className":91430},[886],[888,91432,91433],{"xmlns":890},[892,91434,91435,91443],{},[895,91436,91437,91439,91441],{},[898,91438,207],{},[1996,91440,3447],{},[898,91442,2098],{},[902,91444,91445],{"encoding":904},"a \u003C b",[883,91447,91449],{"className":91448},[886],[888,91450,91451],{"xmlns":890},[892,91452,91453,91461],{},[895,91454,91455,91457,91459],{},[898,91456,207],{},[1996,91458,3408],{},[898,91460,2098],{},[902,91462,91463],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,91466,91468],{"className":91467},[886],[888,91469,91470],{"xmlns":890},[892,91471,91472,91496],{},[895,91473,91474,91480,91482,91488,91490],{},[2272,91475,91476,91478],{},[898,91477,2142],{},[2129,91479,2327],{},[1996,91481,3447],{},[2272,91483,91484,91486],{},[898,91485,2142],{},[2129,91487,2278],{},[1996,91489,3447],{},[2272,91491,91492,91494],{},[898,91493,2142],{},[2129,91495,2131],{},[902,91497,91498],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,91500,91501],{},[614,91502,91503,91504,91533,91534,91592,91593,91611],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,91505,91507],{"className":91506},[886],[888,91508,91509],{"xmlns":890},[892,91510,91511,91531],{},[895,91512,91513,91515,91521,91523,91529],{},[1996,91514,2005],{"stretchy":2004},[2272,91516,91517,91519],{},[898,91518,2789],{},[2129,91520,2278],{},[1996,91522,2286],{"separator":2285},[2272,91524,91525,91527],{},[898,91526,2789],{},[2129,91528,2131],{},[1996,91530,2011],{"stretchy":2004},[902,91532,89621],{"encoding":904},"; body ",[883,91535,91537],{"className":91536},[886],[888,91538,91539],{"xmlns":890},[892,91540,91541,91589],{},[895,91542,91543,91545,91547,91549,91555,91557,91563,91565,91567,91569,91571,91573,91579,91581,91587],{},[898,91544,4255],{},[1996,91546,1998],{},[1996,91548,2486],{"stretchy":2004},[2272,91550,91551,91553],{},[898,91552,207],{},[2129,91554,2278],{},[1996,91556,2286],{"separator":2285},[2272,91558,91559,91561],{},[898,91560,207],{},[2129,91562,2131],{},[1996,91564,2501],{"stretchy":2004},[1996,91566,2286],{"separator":2285},[898,91568,23255],{},[1996,91570,1998],{},[1996,91572,2486],{"stretchy":2004},[2272,91574,91575,91577],{},[898,91576,2098],{},[2129,91578,2278],{},[1996,91580,2286],{"separator":2285},[2272,91582,91583,91585],{},[898,91584,2098],{},[2129,91586,2131],{},[1996,91588,2501],{"stretchy":2004},[902,91590,91591],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,91594,91596],{"className":91595},[886],[888,91597,91598],{"xmlns":890},[892,91599,91600,91608],{},[895,91601,91602,91604,91606],{},[898,91603,2777],{},[1996,91605,2286],{"separator":2285},[898,91607,4183],{},[902,91609,91610],{"encoding":904},"C, D"," na vyšší hladině.",[3867,91613,91614],{},[724,91615,91616,91618,91619,91681,91682,91726,91727,91761,91762,26191,91780,91761,91834,26191,91852,91928],{},[883,91617,52697],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,91620,91622],{"className":91621},[886],[888,91623,91624],{"xmlns":890},[892,91625,91626,91678],{},[895,91627,91628,91630,91632,91638,91640,91646,91648,91650,91664],{},[898,91629,900],{},[1996,91631,2005],{"stretchy":2004},[2272,91633,91634,91636],{},[898,91635,2789],{},[2129,91637,2278],{},[1996,91639,2286],{"separator":2285},[2272,91641,91642,91644],{},[898,91643,2789],{},[2129,91645,2131],{},[1996,91647,2011],{"stretchy":2004},[1996,91649,1998],{},[9166,91651,91652,91654,91656],{},[898,91653,2789],{},[2129,91655,2278],{},[895,91657,91658,91660,91662],{},[2129,91659,2278],{},[898,91661,4674],{"mathvariant":2376},[2129,91663,2351],{},[9166,91665,91666,91668,91670],{},[898,91667,2789],{},[2129,91669,2131],{},[895,91671,91672,91674,91676],{},[2129,91673,2173],{},[898,91675,4674],{"mathvariant":2376},[2129,91677,2351],{},[902,91679,91680],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,91683,91685],{"className":91684},[886],[888,91686,91687],{"xmlns":890},[892,91688,91689,91723],{},[895,91690,91691,91705,91719,91721],{},[9166,91692,91693,91695,91697],{},[898,91694,2789],{},[2129,91696,2278],{},[895,91698,91699,91701,91703],{},[2129,91700,2278],{},[898,91702,4674],{"mathvariant":2376},[2129,91704,2351],{},[9166,91706,91707,91709,91711],{},[898,91708,2789],{},[2129,91710,2131],{},[895,91712,91713,91715,91717],{},[2129,91714,2173],{},[898,91716,4674],{"mathvariant":2376},[2129,91718,2351],{},[1996,91720,1998],{},[898,91722,2142],{},[902,91724,91725],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,91728,91730],{"className":91729},[886],[888,91731,91732],{"xmlns":890},[892,91733,91734,91758],{},[895,91735,91736,91742,91750,91752],{},[2272,91737,91738,91740],{},[898,91739,2789],{},[2129,91741,2278],{},[9166,91743,91744,91746,91748],{},[898,91745,2789],{},[2129,91747,2131],{},[2129,91749,2173],{},[1996,91751,1998],{},[2124,91753,91754,91756],{},[898,91755,2142],{},[2129,91757,2351],{},[902,91759,91760],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,91763,91765],{"className":91764},[886],[888,91766,91767],{"xmlns":890},[892,91768,91769,91777],{},[895,91770,91771,91773,91775],{},[898,91772,2142],{},[1996,91774,1998],{},[2129,91776,2278],{},[902,91778,91779],{"encoding":904},"c = 1",[883,91781,91783],{"className":91782},[886],[888,91784,91785],{"xmlns":890},[892,91786,91787,91831],{},[895,91788,91789,91795,91797,91813,91815],{},[2272,91790,91791,91793],{},[898,91792,2789],{},[2129,91794,2131],{},[1996,91796,1998],{},[9166,91798,91799,91801,91803],{},[898,91800,2789],{},[2129,91802,2278],{},[895,91804,91805,91807,91809,91811],{},[1996,91806,2225],{},[2129,91808,2278],{},[898,91810,4674],{"mathvariant":2376},[2129,91812,2173],{},[1996,91814,1998],{},[2325,91816,91817],{"scriptlevel":2327,"displaystyle":2285},[2329,91818,91819,91821],{},[2129,91820,2278],{},[82029,91822,91823,91829],{},[2272,91824,91825,91827],{},[898,91826,2789],{},[2129,91828,2278],{},[2129,91830,2173],{},[902,91832,91833],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,91835,91837],{"className":91836},[886],[888,91838,91839],{"xmlns":890},[892,91840,91841,91849],{},[895,91842,91843,91845,91847],{},[898,91844,2142],{},[1996,91846,1998],{},[2129,91848,2131],{},[902,91850,91851],{"encoding":904},"c = 2",[883,91853,91855],{"className":91854},[886],[888,91856,91857],{"xmlns":890},[892,91858,91859,91925],{},[895,91860,91861,91867,91869,91881,91883,91899,91901],{},[2272,91862,91863,91865],{},[898,91864,2789],{},[2129,91866,2131],{},[1996,91868,1998],{},[2124,91870,91871,91873],{},[2129,91872,2131],{},[895,91874,91875,91877,91879],{},[2129,91876,2351],{},[898,91878,4674],{"mathvariant":2376},[2129,91880,2173],{},[1996,91882,3177],{},[9166,91884,91885,91887,91889],{},[898,91886,2789],{},[2129,91888,2278],{},[895,91890,91891,91893,91895,91897],{},[1996,91892,2225],{},[2129,91894,2278],{},[898,91896,4674],{"mathvariant":2376},[2129,91898,2173],{},[1996,91900,1998],{},[2325,91902,91903],{"scriptlevel":2327,"displaystyle":2285},[2329,91904,91905,91915],{},[895,91906,91907,91909],{},[2129,91908,2131],{},[82029,91910,91911,91913],{},[2129,91912,2131],{},[2129,91914,2173],{},[82029,91916,91917,91923],{},[2272,91918,91919,91921],{},[898,91920,2789],{},[2129,91922,2278],{},[2129,91924,2173],{},[902,91926,91927],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,91930,91932],{"id":91931},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,91934,91935],{},[2559,91936],{"alt":91937,"className":91938,"src":91939},"imek-ic-4vlastnosti-anotovane",[210,2563],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[3867,91941,91942,91951,91998,92042,92048,92054],{},[724,91943,91944,91946,91947,91950],{},[883,91945,4412],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,91948,91949],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,91952,91953],{},[883,91954,91956],{"className":91955},[886],[888,91957,91958],{"xmlns":890},[892,91959,91960,91995],{},[895,91961,91962,91965,91967,91969,91971,91973,91991,91993],{},[898,91963,91964],{"mathvariant":2376},"tg",[1996,91966,56202],{},[898,91968,18864],{},[1996,91970,1998],{},[1996,91972,2225],{},[2329,91974,91975,91983],{},[9166,91976,91977,91979,91981],{},[898,91978,900],{},[2129,91980,2278],{},[1996,91982,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[9166,91984,91985,91987,91989],{},[898,91986,900],{},[2129,91988,2131],{},[1996,91990,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,91992,3447],{},[2129,91994,2327],{},[902,91996,91997],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,91999,92000,92001,92041],{},"(derivace implicitně zadané funkce ",[883,92002,92004],{"className":92003},[886],[888,92005,92006],{"xmlns":890},[892,92007,92008,92038],{},[895,92009,92010,92012,92014,92020,92022,92028,92030,92032,92034,92036],{},[898,92011,900],{},[1996,92013,2005],{"stretchy":2004},[2272,92015,92016,92018],{},[898,92017,2789],{},[2129,92019,2278],{},[1996,92021,2286],{"separator":2285},[2272,92023,92024,92026],{},[898,92025,2789],{},[2129,92027,2131],{},[1996,92029,2011],{"stretchy":2004},[1996,92031,2225],{},[898,92033,2142],{},[1996,92035,1998],{},[2129,92037,2327],{},[902,92039,92040],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,92043,92044,92047],{},[38,92045,92046],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,92049,92050,92053],{},[38,92051,92052],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,92055,92056,92059,92060,92078,92079,92095,92096,92099],{},[38,92057,92058],{},"4° Konvexní."," Pro každé dva body ",[883,92061,92063],{"className":92062},[886],[888,92064,92065],{"xmlns":890},[892,92066,92067,92075],{},[895,92068,92069,92071,92073],{},[898,92070,4255],{},[1996,92072,2286],{"separator":2285},[898,92074,23255],{},[902,92076,92077],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,92080,92082],{"className":92081},[886],[888,92083,92084],{"xmlns":890},[892,92085,92086,92092],{},[895,92087,92088,92090],{},[898,92089,4255],{},[898,92091,23255],{},[902,92093,92094],{"encoding":904},"AB"," ve ",[38,92097,92098],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,92101,92102],{},[614,92103,92104,92105,92140,92141,1975],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,92106,92108],{"className":92107},[886],[888,92109,92110],{"xmlns":890},[892,92111,92112,92138],{},[895,92113,92114,92116,92118,92124,92126,92132,92134,92136],{},[898,92115,900],{},[1996,92117,2005],{"stretchy":2004},[2272,92119,92120,92122],{},[898,92121,2789],{},[2129,92123,2278],{},[1996,92125,2286],{"separator":2285},[2272,92127,92128,92130],{},[898,92129,2789],{},[2129,92131,2131],{},[1996,92133,2011],{"stretchy":2004},[1996,92135,1998],{},[898,92137,2142],{},[902,92139,9768],{"encoding":904}," s tečnou se sklonem ",[883,92142,92144],{"className":92143},[886],[888,92145,92146],{"xmlns":890},[892,92147,92148,92156],{},[895,92149,92150,92152,92154],{},[898,92151,91964],{"mathvariant":2376},[1996,92153,56202],{},[898,92155,18864],{},[902,92157,92158],{"encoding":904},"\\operatorname{tg}\\alpha",[115,92160,92162],{"id":92161},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,92164,92165,2203,92168,10025,92181,92184],{},[38,92166,92167],{},"Mezní míra komoditní substituce",[883,92169,92171],{"className":92170},[886],[888,92172,92173],{"xmlns":890},[892,92174,92175,92179],{},[895,92176,92177],{},[2288,92178,10603],{},[902,92180,28240],{"encoding":904},[38,92182,92183],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,92186,92188],{"className":92187},[886],[888,92189,92190],{"xmlns":890,"display":28068},[892,92191,92192,92279],{},[20756,92193,92194],{"width":28073},[20761,92195,92196,92198,92272,92274],{},[20764,92197],{"width":28078},[20764,92199,92200],{},[895,92201,92202,92204,92206,92208,92210,92216,92218,92224,92226,92228,92250,92252,92270],{},[2288,92203,10603],{},[1996,92205,1998],{},[2288,92207,10603],{},[1996,92209,2005],{"stretchy":2004},[2272,92211,92212,92214],{},[898,92213,2789],{},[2129,92215,2278],{},[1996,92217,2286],{"separator":2285},[2272,92219,92220,92222],{},[898,92221,2789],{},[2129,92223,2131],{},[1996,92225,2011],{"stretchy":2004},[1996,92227,1998],{},[2329,92229,92230,92240],{},[895,92231,92232,92234],{},[898,92233,2818],{},[2272,92235,92236,92238],{},[898,92237,900],{},[2129,92239,2278],{},[895,92241,92242,92244],{},[898,92243,2818],{},[2272,92245,92246,92248],{},[898,92247,900],{},[2129,92249,2131],{},[1996,92251,1998],{},[2329,92253,92254,92262],{},[9166,92255,92256,92258,92260],{},[898,92257,900],{},[2129,92259,2278],{},[1996,92261,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[9166,92263,92264,92266,92268],{},[898,92265,900],{},[2129,92267,2131],{},[1996,92269,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[898,92271,1975],{"mathvariant":2376},[20764,92273],{"width":28078},[20764,92275,92276],{},[2288,92277,92278],{},"(6.9)",[902,92280,92281],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,92283,92284,92285,92319,92320,92352,92353,92388,92389,92402],{},"Geometricky: ",[883,92286,92288],{"className":92287},[886],[888,92289,92290],{"xmlns":890},[892,92291,92292,92316],{},[895,92293,92294,92296],{},[1996,92295,2225],{},[2325,92297,92298],{"scriptlevel":2327,"displaystyle":2004},[2329,92299,92300,92308],{},[9166,92301,92302,92304,92306],{},[898,92303,900],{},[2129,92305,2278],{},[1996,92307,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[9166,92309,92310,92312,92314],{},[898,92311,900],{},[2129,92313,2131],{},[1996,92315,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,92317,92318],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,92321,92323],{"className":92322},[886],[888,92324,92325],{"xmlns":890},[892,92326,92327,92349],{},[895,92328,92329,92335,92337,92339,92341,92347],{},[2272,92330,92331,92333],{},[898,92332,2789],{},[2129,92334,2131],{},[1996,92336,1998],{},[898,92338,2001],{},[1996,92340,2005],{"stretchy":2004},[2272,92342,92343,92345],{},[898,92344,2789],{},[2129,92346,2278],{},[1996,92348,2011],{"stretchy":2004},[902,92350,92351],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,92354,92356],{"className":92355},[886],[888,92357,92358],{"xmlns":890},[892,92359,92360,92386],{},[895,92361,92362,92364,92366,92372,92374,92380,92382,92384],{},[898,92363,900],{},[1996,92365,2005],{"stretchy":2004},[2272,92367,92368,92370],{},[898,92369,2789],{},[2129,92371,2278],{},[1996,92373,2286],{"separator":2285},[2272,92375,92376,92378],{},[898,92377,2789],{},[2129,92379,2131],{},[1996,92381,2011],{"stretchy":2004},[1996,92383,1998],{},[898,92385,2142],{},[902,92387,9768],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,92390,92392],{"className":92391},[886],[888,92393,92394],{"xmlns":890},[892,92395,92396,92400],{},[895,92397,92398],{},[2288,92399,10603],{},[902,92401,28240],{"encoding":904}," chápeme jako velikost kompenzace.",[3867,92404,92405],{},[724,92406,92407,92409,92410,8102,92442,92480,92481,92498,92499,92516],{},[883,92408,4155],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,92411,92413],{"className":92412},[886],[888,92414,92415],{"xmlns":890},[892,92416,92417,92439],{},[895,92418,92419,92421,92423,92429,92431,92437],{},[2288,92420,10603],{},[1996,92422,2005],{"stretchy":2004},[2272,92424,92425,92427],{},[898,92426,2789],{},[2129,92428,2278],{},[1996,92430,2286],{"separator":2285},[2272,92432,92433,92435],{},[898,92434,2789],{},[2129,92436,2131],{},[1996,92438,2011],{"stretchy":2004},[902,92440,92441],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,92443,92444,92445,29005,92462,92479],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,92446,92448],{"className":92447},[886],[888,92449,92450],{"xmlns":890},[892,92451,92452,92460],{},[895,92453,92454],{},[2272,92455,92456,92458],{},[898,92457,2789],{},[2129,92459,2278],{},[902,92461,29004],{"encoding":904},[883,92463,92465],{"className":92464},[886],[888,92466,92467],{"xmlns":890},[892,92468,92469,92477],{},[895,92470,92471],{},[2272,92472,92473,92475],{},[898,92474,2789],{},[2129,92476,2131],{},[902,92478,29023],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,92482,92484],{"className":92483},[886],[888,92485,92486],{"xmlns":890},[892,92487,92488,92496],{},[895,92489,92490],{},[2272,92491,92492,92494],{},[898,92493,2789],{},[2129,92495,2131],{},[902,92497,29023],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,92500,92502],{"className":92501},[886],[888,92503,92504],{"xmlns":890},[892,92505,92506,92514],{},[895,92507,92508],{},[2272,92509,92510,92512],{},[898,92511,2789],{},[2129,92513,2278],{},[902,92515,29004],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,92518,92519,92520,29946],{},"Pro obecnou změnu ",[883,92521,92523],{"className":92522},[886],[888,92524,92525],{"xmlns":890},[892,92526,92527,92537],{},[895,92528,92529,92531],{},[898,92530,2194],{"mathvariant":2376},[2272,92532,92533,92535],{},[898,92534,2789],{},[2129,92536,2278],{},[902,92538,92539],{"encoding":904},"\\mathrm{d} Q_1",[883,92541,92543],{"className":92542},[886],[888,92544,92545],{"xmlns":890,"display":28068},[892,92546,92547,92600],{},[20756,92548,92549],{"width":28073},[20761,92550,92551,92553,92593,92595],{},[20764,92552],{"width":28078},[20764,92554,92555],{},[895,92556,92557,92559,92565,92567,92569,92575,92577,92579,92581,92583,92585,92591],{},[898,92558,2889],{"mathvariant":2376},[2272,92560,92561,92563],{},[898,92562,2789],{},[2129,92564,2131],{},[1996,92566,2730],{},[898,92568,2194],{"mathvariant":2376},[2272,92570,92571,92573],{},[898,92572,2789],{},[2129,92574,2131],{},[1996,92576,1998],{},[1996,92578,2225],{},[2288,92580,10603],{},[1996,92582,3177],{},[898,92584,2194],{"mathvariant":2376},[2272,92586,92587,92589],{},[898,92588,2789],{},[2129,92590,2278],{},[1996,92592,2286],{"separator":2285},[20764,92594],{"width":28078},[20764,92596,92597],{},[2288,92598,92599],{},"(6.10)",[902,92601,92602],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,92604,92606],{"className":92605},[886],[888,92607,92608],{"xmlns":890,"display":28068},[892,92609,92610,92657],{},[20756,92611,92612],{"width":28073},[20761,92613,92614,92616,92650,92652],{},[20764,92615],{"width":28078},[20764,92617,92618],{},[895,92619,92620,92622,92628,92630,92632,92638,92640,92642,92648],{},[898,92621,2194],{"mathvariant":2376},[2272,92623,92624,92626],{},[898,92625,2789],{},[2129,92627,2278],{},[1996,92629,1998],{},[1996,92631,2225],{},[2329,92633,92634,92636],{},[2129,92635,2278],{},[2288,92637,10603],{},[2288,92639,2987],{},[898,92641,2194],{"mathvariant":2376},[2272,92643,92644,92646],{},[898,92645,2789],{},[2129,92647,2131],{},[898,92649,1975],{"mathvariant":2376},[20764,92651],{"width":28078},[20764,92653,92654],{},[2288,92655,92656],{},"(6.11)",[902,92658,92659],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[3867,92661,92662,92728,92845],{},[724,92663,92664,92666,92667,29946],{},[883,92665,52697],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,92668,92670],{"className":92669},[886],[888,92671,92672],{"xmlns":890},[892,92673,92674,92726],{},[895,92675,92676,92678,92680,92686,92688,92694,92696,92698,92712],{},[898,92677,900],{},[1996,92679,2005],{"stretchy":2004},[2272,92681,92682,92684],{},[898,92683,2789],{},[2129,92685,2278],{},[1996,92687,2286],{"separator":2285},[2272,92689,92690,92692],{},[898,92691,2789],{},[2129,92693,2131],{},[1996,92695,2011],{"stretchy":2004},[1996,92697,1998],{},[9166,92699,92700,92702,92704],{},[898,92701,2789],{},[2129,92703,2278],{},[895,92705,92706,92708,92710],{},[2129,92707,2278],{},[898,92709,4674],{"mathvariant":2376},[2129,92711,2131],{},[9166,92713,92714,92716,92718],{},[898,92715,2789],{},[2129,92717,2131],{},[895,92719,92720,92722,92724],{},[2129,92721,2278],{},[898,92723,4674],{"mathvariant":2376},[2129,92725,2131],{},[902,92727,29945],{"encoding":904},[724,92729,92730],{},[883,92731,92733],{"className":92732},[886],[888,92734,92735],{"xmlns":890},[892,92736,92737,92843],{},[895,92738,92739,92741,92743,92825,92827,92841],{},[2288,92740,10603],{},[1996,92742,1998],{},[2329,92744,92745,92785],{},[895,92746,92747,92755,92771],{},[2325,92748,92749],{"scriptlevel":2327,"displaystyle":2004},[2329,92750,92751,92753],{},[2129,92752,2278],{},[2129,92754,2131],{},[9166,92756,92757,92759,92761],{},[898,92758,2789],{},[2129,92760,2278],{},[895,92762,92763,92765,92767,92769],{},[1996,92764,2225],{},[2129,92766,2278],{},[898,92768,4674],{"mathvariant":2376},[2129,92770,2131],{},[9166,92772,92773,92775,92777],{},[898,92774,2789],{},[2129,92776,2131],{},[895,92778,92779,92781,92783],{},[2129,92780,2278],{},[898,92782,4674],{"mathvariant":2376},[2129,92784,2131],{},[895,92786,92787,92795,92809],{},[2325,92788,92789],{"scriptlevel":2327,"displaystyle":2004},[2329,92790,92791,92793],{},[2129,92792,2278],{},[2129,92794,2131],{},[9166,92796,92797,92799,92801],{},[898,92798,2789],{},[2129,92800,2278],{},[895,92802,92803,92805,92807],{},[2129,92804,2278],{},[898,92806,4674],{"mathvariant":2376},[2129,92808,2131],{},[9166,92810,92811,92813,92815],{},[898,92812,2789],{},[2129,92814,2131],{},[895,92816,92817,92819,92821,92823],{},[1996,92818,2225],{},[2129,92820,2278],{},[898,92822,4674],{"mathvariant":2376},[2129,92824,2131],{},[1996,92826,1998],{},[2329,92828,92829,92835],{},[2272,92830,92831,92833],{},[898,92832,2789],{},[2129,92834,2131],{},[2272,92836,92837,92839],{},[898,92838,2789],{},[2129,92840,2278],{},[898,92842,1975],{"mathvariant":2376},[902,92844,30064],{"encoding":904},[724,92846,30067,92847,2927,92890,30115,92892,92911],{},[883,92848,92850],{"className":92849},[886],[888,92851,92852],{"xmlns":890},[892,92853,92854,92888],{},[895,92855,92856,92858,92860,92862,92864,92866,92868,92870,92878,92880],{},[2288,92857,10603],{},[1996,92859,2005],{"stretchy":2004},[2129,92861,30083],{},[1996,92863,2286],{"separator":2285},[2129,92865,15112],{},[1996,92867,2011],{"stretchy":2004},[1996,92869,1998],{},[2325,92871,92872],{"scriptlevel":2327,"displaystyle":2004},[2329,92873,92874,92876],{},[2129,92875,15112],{},[2129,92877,30083],{},[1996,92879,1998],{},[2325,92881,92882],{"scriptlevel":2327,"displaystyle":2004},[2329,92883,92884,92886],{},[2129,92885,2228],{},[2129,92887,2173],{},[902,92889,30112],{"encoding":904},[614,92891,9216],{},[883,92893,92895],{"className":92894},[886],[888,92896,92897],{"xmlns":890},[892,92898,92899,92909],{},[895,92900,92901],{},[2325,92902,92903],{"scriptlevel":2327,"displaystyle":2004},[2329,92904,92905,92907],{},[2129,92906,2228],{},[2129,92908,2173],{},[902,92910,30135],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,92913,92914,92915,92919],{},"(Paralelou je ",[207,92916,92918],{"className":92917,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,92921,92923],{"id":92922},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,92925,92926,92927,92930],{},"Rámcově se v kapitole 6 studují ",[38,92928,92929],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,92932,92933,93069],{},[123,92934,92935,92937,92938,10157,92969,2203,92972,93021,93022,1975],{},[38,92936,28254],{}," — maximalizace ",[883,92939,92941],{"className":92940},[886],[888,92942,92943],{"xmlns":890},[892,92944,92945,92967],{},[895,92946,92947,92949,92951,92957,92959,92965],{},[898,92948,900],{},[1996,92950,2005],{"stretchy":2004},[2272,92952,92953,92955],{},[898,92954,2789],{},[2129,92956,2278],{},[1996,92958,2286],{"separator":2285},[2272,92960,92961,92963],{},[898,92962,2789],{},[2129,92964,2131],{},[1996,92966,2011],{"stretchy":2004},[902,92968,16345],{"encoding":904},[38,92970,92971],{},"rozpočtovém omezení",[883,92973,92975],{"className":92974},[886],[888,92976,92977],{"xmlns":890},[892,92978,92979,93019],{},[895,92980,92981,92987,92989,92997,93003,93005,93013],{},[2124,92982,92983,92985],{},[898,92984,9128],{},[1996,92986,4354],{},[1996,92988,1998],{},[9166,92990,92991,92993,92995],{},[898,92992,3937],{},[2129,92994,2278],{},[1996,92996,4354],{},[2272,92998,92999,93001],{},[898,93000,2789],{},[2129,93002,2278],{},[1996,93004,2095],{},[9166,93006,93007,93009,93011],{},[898,93008,3937],{},[2129,93010,2131],{},[1996,93012,4354],{},[2272,93014,93015,93017],{},[898,93016,2789],{},[2129,93018,2131],{},[902,93020,17300],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,93023,93025],{"className":93024},[886],[888,93026,93027],{"xmlns":890},[892,93028,93029,93067],{},[895,93030,93031,93037,93039,93045,93047,93053,93055,93061,93063,93065],{},[2272,93032,93033,93035],{},[898,93034,2789],{},[898,93036,17792],{},[1996,93038,1998],{},[2272,93040,93041,93043],{},[898,93042,4183],{},[898,93044,17792],{},[1996,93046,2005],{"stretchy":2004},[2272,93048,93049,93051],{},[898,93050,3937],{},[2129,93052,2278],{},[1996,93054,2286],{"separator":2285},[2272,93056,93057,93059],{},[898,93058,3937],{},[2129,93060,2131],{},[1996,93062,2286],{"separator":2285},[898,93064,9128],{},[1996,93066,2011],{"stretchy":2004},[902,93068,36457],{"encoding":904},[123,93070,93071,27903,93074,27946,93120,93137,93138,1975],{},[38,93072,93073],{},"Duální úloha",[883,93075,93077],{"className":93076},[886],[888,93078,93079],{"xmlns":890},[892,93080,93081,93117],{},[895,93082,93083,93085,93087,93095,93101,93103,93111],{},[898,93084,4252],{},[1996,93086,1998],{},[9166,93088,93089,93091,93093],{},[898,93090,3937],{},[2129,93092,2278],{},[1996,93094,4354],{},[2272,93096,93097,93099],{},[898,93098,2789],{},[2129,93100,2278],{},[1996,93102,2095],{},[9166,93104,93105,93107,93109],{},[898,93106,3937],{},[2129,93108,2131],{},[1996,93110,4354],{},[2272,93112,93113,93115],{},[898,93114,2789],{},[2129,93116,2131],{},[902,93118,93119],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,93121,93123],{"className":93122},[886],[888,93124,93125],{"xmlns":890},[892,93126,93127,93135],{},[895,93128,93129],{},[2124,93130,93131,93133],{},[898,93132,900],{},[1996,93134,4354],{},[902,93136,27964],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,93139,93141],{"className":93140},[886],[888,93142,93143],{"xmlns":890},[892,93144,93145,93183],{},[895,93146,93147,93153,93155,93161,93163,93169,93171,93177,93179,93181],{},[2272,93148,93149,93151],{},[898,93150,2789],{},[898,93152,17792],{},[1996,93154,1998],{},[2272,93156,93157,93159],{},[898,93158,4183],{},[898,93160,17792],{},[1996,93162,2005],{"stretchy":2004},[2272,93164,93165,93167],{},[898,93166,3937],{},[2129,93168,2278],{},[1996,93170,2286],{"separator":2285},[2272,93172,93173,93175],{},[898,93174,3937],{},[2129,93176,2131],{},[1996,93178,2286],{"separator":2285},[898,93180,900],{},[1996,93182,2011],{"stretchy":2004},[902,93184,17825],{"encoding":904},[724,93186,93187,93188,93191,93192,2203,93195,93234],{},"Obě úlohy se řeší ",[207,93189,27969],{"className":93190,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,93193,93194],{},"tentýž bod dotyku",[883,93196,93198],{"className":93197},[886],[888,93199,93200],{"xmlns":890},[892,93201,93202,93232],{},[895,93203,93204,93210,93212,93220,93222,93230],{},[2124,93205,93206,93208],{},[898,93207,2789],{},[1996,93209,4354],{},[1996,93211,2486],{"stretchy":2004},[9166,93213,93214,93216,93218],{},[898,93215,2789],{},[2129,93217,2278],{},[1996,93219,4354],{},[1996,93221,2286],{"separator":2285},[9166,93223,93224,93226,93228],{},[898,93225,2789],{},[2129,93227,2131],{},[1996,93229,4354],{},[1996,93231,2501],{"stretchy":2004},[902,93233,28329],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,93236,93238],{"className":93237},[886],[888,93239,93240],{"xmlns":890,"display":28068},[892,93241,93242,93288],{},[895,93243,93244,93246,93248,93266,93268,93286],{},[2288,93245,10603],{},[1996,93247,1998],{},[2329,93249,93250,93258],{},[9166,93251,93252,93254,93256],{},[898,93253,900],{},[2129,93255,2278],{},[1996,93257,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[9166,93259,93260,93262,93264],{},[898,93261,900],{},[2129,93263,2131],{},[1996,93265,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,93267,1998],{},[2329,93269,93270,93278],{},[9166,93271,93272,93274,93276],{},[898,93273,3937],{},[2129,93275,2278],{},[1996,93277,4354],{},[9166,93279,93280,93282,93284],{},[898,93281,3937],{},[2129,93283,2131],{},[1996,93285,4354],{},[898,93287,1975],{"mathvariant":2376},[902,93289,93290],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,93292,93293],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[3867,93295,93296],{},[724,93297,93298,93300,93301,93304,93305,93308,93309,93336,93337,93371,93372,93406,93407,93450,93451,93454,93455,1975],{},[883,93299,4155],{}," Pro detailní postup viz ",[207,93302,36756],{"className":93303,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,93306,93307],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,93310,93312],{"className":93311},[886],[888,93313,93314],{"xmlns":890},[892,93315,93316,93334],{},[895,93317,93318,93320,93322,93328],{},[898,93319,900],{},[1996,93321,1998],{},[2272,93323,93324,93326],{},[898,93325,2789],{},[2129,93327,2278],{},[2272,93329,93330,93332],{},[898,93331,2789],{},[2129,93333,2131],{},[902,93335,30228],{"encoding":904}," s výsledkem ",[883,93338,93340],{"className":93339},[886],[888,93341,93342],{"xmlns":890},[892,93343,93344,93368],{},[895,93345,93346,93352,93354,93356,93358,93364,93366],{},[2272,93347,93348,93350],{},[898,93349,2789],{},[2129,93351,2278],{},[1996,93353,1998],{},[2129,93355,5004],{},[1996,93357,2286],{"separator":2285},[2272,93359,93360,93362],{},[898,93361,2789],{},[2129,93363,2131],{},[1996,93365,1998],{},[2129,93367,2863],{},[902,93369,93370],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,93373,93375],{"className":93374},[886],[888,93376,93377],{"xmlns":890},[892,93378,93379,93403],{},[895,93380,93381,93387,93389,93391,93393,93399,93401],{},[2272,93382,93383,93385],{},[898,93384,2789],{},[2129,93386,2278],{},[1996,93388,1998],{},[2129,93390,2351],{},[1996,93392,2286],{"separator":2285},[2272,93394,93395,93397],{},[898,93396,2789],{},[2129,93398,2131],{},[1996,93400,1998],{},[2129,93402,2278],{},[902,93404,93405],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,93408,93410],{"className":93409},[886],[888,93411,93412],{"xmlns":890},[892,93413,93414,93448],{},[895,93415,93416,93418,93420,93434],{},[898,93417,900],{},[1996,93419,1998],{},[9166,93421,93422,93424,93426],{},[898,93423,2789],{},[2129,93425,2278],{},[895,93427,93428,93430,93432],{},[2129,93429,2278],{},[898,93431,4674],{"mathvariant":2376},[2129,93433,2131],{},[9166,93435,93436,93438,93440],{},[898,93437,2789],{},[2129,93439,2131],{},[895,93441,93442,93444,93446],{},[2129,93443,2278],{},[898,93445,4674],{"mathvariant":2376},[2129,93447,2131],{},[902,93449,33161],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,93452,93453],{},"6.8–6.13"," jsou na stránce ",[207,93456,27769],{"className":93457,"dataFsResolvedFilePath":911,"href":912},[210],[115,93459,93461],{"id":93460},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,93463,93464,93465,93478,93479,93481,93482,93484,93485,93487,93488,93490,93491,93493,93494,93496,93497,2203,93499,93534,93535,93548,93549,93552,93553,93556,93557,1975],{},"Každá ",[883,93466,93468],{"className":93467},[886],[888,93469,93470],{"xmlns":890},[892,93471,93472,93476],{},[895,93473,93474],{},[898,93475,36862],{},[902,93477,36862],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,93480,86812],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,93483,87296],{}," a současně ",[38,93486,86815],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,93489,86820],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,93492,52679],{}," (6.4) a druhé parciální derivace ",[38,93495,89179],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,93498,9731],{},[883,93500,93502],{"className":93501},[886],[888,93503,93504],{"xmlns":890},[892,93505,93506,93532],{},[895,93507,93508,93510,93512,93518,93520,93526,93528,93530],{},[898,93509,900],{},[1996,93511,2005],{"stretchy":2004},[2272,93513,93514,93516],{},[898,93515,2789],{},[2129,93517,2278],{},[1996,93519,2286],{"separator":2285},[2272,93521,93522,93524],{},[898,93523,2789],{},[2129,93525,2131],{},[1996,93527,2011],{"stretchy":2004},[1996,93529,1998],{},[898,93531,2142],{},[902,93533,9768],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,93536,93538],{"className":93537},[886],[888,93539,93540],{"xmlns":890},[892,93541,93542,93546],{},[895,93543,93544],{},[2288,93545,10603],{},[902,93547,28240],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,93550,93551],{},"maximalizace užitečnosti"," a duální ",[38,93554,93555],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,93558,36756],{"className":93559,"dataFsResolvedFilePath":911,"href":912},[210],[115,93561,49884],{"id":49883},[152,93563,93564,93567,93570,93573,93576,93579,93582,93585,93588,93591],{},[123,93565,93566],{},"Co se zahrnuje pod termín užitečnost?",[123,93568,93569],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,93571,93572],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,93574,93575],{},"Jak se vypočítá mezní užitečnost?",[123,93577,93578],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,93580,93581],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,93583,93584],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,93586,93587],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,93589,93590],{},"Proč mají křivky užitečnosti záporný sklon?",[123,93592,93593],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,93595,93597],{"id":93596},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,93599,93600,93603,93604,83485,93646,1343,93674,1343,93702,93730],{},[38,93601,93602],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,93605,93607],{"className":93606},[886],[888,93608,93609],{"xmlns":890},[892,93610,93611,93643],{},[895,93612,93613,93615,93617,93623,93625,93627,93633,93635,93637],{},[898,93614,900],{},[1996,93616,1998],{},[2272,93618,93619,93621],{},[898,93620,2789],{},[2129,93622,2278],{},[1996,93624,2095],{},[2129,93626,64561],{},[2272,93628,93629,93631],{},[898,93630,2789],{},[2129,93632,2131],{},[1996,93634,2095],{},[2129,93636,2131],{},[2272,93638,93639,93641],{},[898,93640,2789],{},[2129,93642,2173],{},[902,93644,93645],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,93647,93649],{"className":93648},[886],[888,93650,93651],{"xmlns":890},[892,93652,93653,93671],{},[895,93654,93655,93657,93659,93661,93663,93665,93667,93669],{},[898,93656,900],{},[1996,93658,2005],{"stretchy":2004},[2129,93660,2351],{},[1996,93662,2286],{"separator":2285},[2129,93664,2131],{},[1996,93666,2286],{"separator":2285},[2129,93668,2131],{},[1996,93670,2011],{"stretchy":2004},[902,93672,93673],{"encoding":904},"U(4, 2, 2)",[883,93675,93677],{"className":93676},[886],[888,93678,93679],{"xmlns":890},[892,93680,93681,93699],{},[895,93682,93683,93685,93687,93689,93691,93693,93695,93697],{},[898,93684,900],{},[1996,93686,2005],{"stretchy":2004},[2129,93688,2278],{},[1996,93690,2286],{"separator":2285},[2129,93692,2351],{},[1996,93694,2286],{"separator":2285},[2129,93696,2131],{},[1996,93698,2011],{"stretchy":2004},[902,93700,93701],{"encoding":904},"U(1, 4, 2)",[883,93703,93705],{"className":93704},[886],[888,93706,93707],{"xmlns":890},[892,93708,93709,93727],{},[895,93710,93711,93713,93715,93717,93719,93721,93723,93725],{},[898,93712,900],{},[1996,93714,2005],{"stretchy":2004},[2129,93716,2131],{},[1996,93718,2286],{"separator":2285},[2129,93720,2173],{},[1996,93722,2286],{"separator":2285},[2129,93724,2278],{},[1996,93726,2011],{"stretchy":2004},[902,93728,93729],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,93732,93733,93736,93737,93789,93790,1343,93816,1343,93842,1343,93868,1343,93894,1343,93920,1343,93946,93972],{},[38,93734,93735],{},"6.2"," Je dána užitečnost ",[883,93738,93740],{"className":93739},[886],[888,93741,93742],{"xmlns":890},[892,93743,93744,93786],{},[895,93745,93746,93748,93750,93752,93766,93780],{},[898,93747,900],{},[1996,93749,1998],{},[2129,93751,2131],{},[9166,93753,93754,93756,93758],{},[898,93755,2789],{},[2129,93757,2278],{},[895,93759,93760,93762,93764],{},[2129,93761,2278],{},[898,93763,4674],{"mathvariant":2376},[2129,93765,2173],{},[9166,93767,93768,93770,93772],{},[898,93769,2789],{},[2129,93771,2131],{},[895,93773,93774,93776,93778],{},[2129,93775,2278],{},[898,93777,4674],{"mathvariant":2376},[2129,93779,2131],{},[2272,93781,93782,93784],{},[898,93783,2789],{},[2129,93785,2173],{},[902,93787,93788],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,93791,93793],{"className":93792},[886],[888,93794,93795],{"xmlns":890},[892,93796,93797,93813],{},[895,93798,93799,93801,93803,93805,93807,93809,93811],{},[1996,93800,2005],{"stretchy":2004},[2129,93802,5565],{},[1996,93804,2286],{"separator":2285},[2129,93806,66599],{},[1996,93808,2286],{"separator":2285},[2129,93810,2863],{},[1996,93812,2011],{"stretchy":2004},[902,93814,93815],{"encoding":904},"(36, 27, 10)",[883,93817,93819],{"className":93818},[886],[888,93820,93821],{"xmlns":890},[892,93822,93823,93839],{},[895,93824,93825,93827,93829,93831,93833,93835,93837],{},[1996,93826,2005],{"stretchy":2004},[2129,93828,41842],{},[1996,93830,2286],{"separator":2285},[2129,93832,5585],{},[1996,93834,2286],{"separator":2285},[2129,93836,9035],{},[1996,93838,2011],{"stretchy":2004},[902,93840,93841],{"encoding":904},"(64, 8, 20)",[883,93843,93845],{"className":93844},[886],[888,93846,93847],{"xmlns":890},[892,93848,93849,93865],{},[895,93850,93851,93853,93855,93857,93859,93861,93863],{},[1996,93852,2005],{"stretchy":2004},[2129,93854,5004],{},[1996,93856,2286],{"separator":2285},[2129,93858,41842],{},[1996,93860,2286],{"separator":2285},[2129,93862,5585],{},[1996,93864,2011],{"stretchy":2004},[902,93866,93867],{"encoding":904},"(25, 64, 8)",[883,93869,93871],{"className":93870},[886],[888,93872,93873],{"xmlns":890},[892,93874,93875,93891],{},[895,93876,93877,93879,93881,93883,93885,93887,93889],{},[1996,93878,2005],{"stretchy":2004},[2129,93880,2351],{},[1996,93882,2286],{"separator":2285},[2129,93884,72531],{},[1996,93886,2286],{"separator":2285},[2129,93888,2235],{},[1996,93890,2011],{"stretchy":2004},[902,93892,93893],{"encoding":904},"(4, 125, 6)",[883,93895,93897],{"className":93896},[886],[888,93898,93899],{"xmlns":890},[892,93900,93901,93917],{},[895,93902,93903,93905,93907,93909,93911,93913,93915],{},[1996,93904,2005],{"stretchy":2004},[2129,93906,3999],{},[1996,93908,2286],{"separator":2285},[2129,93910,5211],{},[1996,93912,2286],{"separator":2285},[2129,93914,3509],{},[1996,93916,2011],{"stretchy":2004},[902,93918,93919],{"encoding":904},"(9, 40, 12)",[883,93921,93923],{"className":93922},[886],[888,93924,93925],{"xmlns":890},[892,93926,93927,93943],{},[895,93928,93929,93931,93933,93935,93937,93939,93941],{},[1996,93930,2005],{"stretchy":2004},[2129,93932,3999],{},[1996,93934,2286],{"separator":2285},[2129,93936,41842],{},[1996,93938,2286],{"separator":2285},[2129,93940,2228],{},[1996,93942,2011],{"stretchy":2004},[902,93944,93945],{"encoding":904},"(9, 64, 5)",[883,93947,93949],{"className":93948},[886],[888,93950,93951],{"xmlns":890},[892,93952,93953,93969],{},[895,93954,93955,93957,93959,93961,93963,93965,93967],{},[1996,93956,2005],{"stretchy":2004},[2129,93958,41842],{},[1996,93960,2286],{"separator":2285},[2129,93962,5585],{},[1996,93964,2286],{"separator":2285},[2129,93966,2863],{},[1996,93968,2011],{"stretchy":2004},[902,93970,93971],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,93974,93975,93736,93978,94021,94022,94056,94057,6473,94087,94120,94121,94138,94139,94156],{},[38,93976,93977],{},"6.3",[883,93979,93981],{"className":93980},[886],[888,93982,93983],{"xmlns":890},[892,93984,93985,94019],{},[895,93986,93987,93989,93991,94005],{},[898,93988,900],{},[1996,93990,1998],{},[9166,93992,93993,93995,93997],{},[898,93994,2789],{},[2129,93996,2278],{},[895,93998,93999,94001,94003],{},[2129,94000,2278],{},[898,94002,4674],{"mathvariant":2376},[2129,94004,2131],{},[9166,94006,94007,94009,94011],{},[898,94008,2789],{},[2129,94010,2131],{},[895,94012,94013,94015,94017],{},[2129,94014,2278],{},[898,94016,4674],{"mathvariant":2376},[2129,94018,2131],{},[902,94020,33161],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,94023,94025],{"className":94024},[886],[888,94026,94027],{"xmlns":890},[892,94028,94029,94053],{},[895,94030,94031,94037,94039,94041,94043,94049,94051],{},[2272,94032,94033,94035],{},[898,94034,2789],{},[2129,94036,2278],{},[1996,94038,1998],{},[2129,94040,3120],{},[1996,94042,2286],{"separator":2285},[2272,94044,94045,94047],{},[898,94046,2789],{},[2129,94048,2131],{},[1996,94050,1998],{},[2129,94052,46705],{},[902,94054,94055],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,94058,94060],{"className":94059},[886],[888,94061,94062],{"xmlns":890},[892,94063,94064,94084],{},[895,94065,94066,94068,94074,94076,94078],{},[898,94067,2818],{},[2272,94069,94070,94072],{},[898,94071,900],{},[2129,94073,2278],{},[1996,94075,2286],{"separator":2285},[898,94077,2818],{},[2272,94079,94080,94082],{},[898,94081,900],{},[2129,94083,2131],{},[902,94085,94086],{"encoding":904},"MU_1, MU_2",[883,94088,94090],{"className":94089},[886],[888,94091,94092],{"xmlns":890},[892,94093,94094,94118],{},[895,94095,94096,94102,94104,94106,94108,94114,94116],{},[2272,94097,94098,94100],{},[898,94099,2789],{},[2129,94101,2278],{},[1996,94103,1998],{},[2129,94105,3120],{},[1996,94107,2286],{"separator":2285},[2272,94109,94110,94112],{},[898,94111,2789],{},[2129,94113,2131],{},[1996,94115,1998],{},[2129,94117,46705],{},[902,94119,94055],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,94122,94124],{"className":94123},[886],[888,94125,94126],{"xmlns":890},[892,94127,94128,94136],{},[895,94129,94130],{},[2272,94131,94132,94134],{},[898,94133,2789],{},[2129,94135,2278],{},[902,94137,29004],{"encoding":904}," na 60 a poklesu ",[883,94140,94142],{"className":94141},[886],[888,94143,94144],{"xmlns":890},[892,94145,94146,94154],{},[895,94147,94148],{},[2272,94149,94150,94152],{},[898,94151,2789],{},[2129,94153,2131],{},[902,94155,29023],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,94158,94159,94162,94163,94224,94225,1975],{},[38,94160,94161],{},"6.4"," Je dána funkce ",[883,94164,94166],{"className":94165},[886],[888,94167,94168],{"xmlns":890},[892,94169,94170,94222],{},[895,94171,94172,94174,94176,94182,94184,94190,94192,94194,94208],{},[898,94173,900],{},[1996,94175,2005],{"stretchy":2004},[2272,94177,94178,94180],{},[898,94179,2789],{},[2129,94181,2278],{},[1996,94183,2286],{"separator":2285},[2272,94185,94186,94188],{},[898,94187,2789],{},[2129,94189,2131],{},[1996,94191,2011],{"stretchy":2004},[1996,94193,1998],{},[9166,94195,94196,94198,94200],{},[898,94197,2789],{},[2129,94199,2278],{},[895,94201,94202,94204,94206],{},[2129,94203,2278],{},[898,94205,4674],{"mathvariant":2376},[2129,94207,2131],{},[9166,94209,94210,94212,94214],{},[898,94211,2789],{},[2129,94213,2131],{},[895,94215,94216,94218,94220],{},[2129,94217,2278],{},[898,94219,4674],{"mathvariant":2376},[2129,94221,2131],{},[902,94223,29945],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,94226,94228],{"className":94227},[886],[888,94229,94230],{"xmlns":890},[892,94231,94232,94322],{},[895,94233,94234,94236,94238,94244,94246,94248,94250,94252,94254,94256,94262,94264,94266,94268,94270,94272,94274,94276,94278,94284,94286,94288,94290,94292,94294,94296,94302,94304,94306,94308,94310,94312,94314,94320],{},[898,94235,900],{},[1996,94237,2005],{"stretchy":2004},[2272,94239,94240,94242],{},[898,94241,2789],{},[2129,94243,2278],{},[1996,94245,2286],{"separator":2285},[2129,94247,2278],{},[1996,94249,2011],{"stretchy":2004},[1996,94251,2286],{"separator":2285},[898,94253,900],{},[1996,94255,2005],{"stretchy":2004},[2272,94257,94258,94260],{},[898,94259,2789],{},[2129,94261,2278],{},[1996,94263,2286],{"separator":2285},[2129,94265,2131],{},[1996,94267,2011],{"stretchy":2004},[1996,94269,2286],{"separator":2285},[898,94271,900],{},[1996,94273,2005],{"stretchy":2004},[2129,94275,2278],{},[1996,94277,2286],{"separator":2285},[2272,94279,94280,94282],{},[898,94281,2789],{},[2129,94283,2131],{},[1996,94285,2011],{"stretchy":2004},[1996,94287,2286],{"separator":2285},[898,94289,900],{},[1996,94291,2005],{"stretchy":2004},[2129,94293,2131],{},[1996,94295,2286],{"separator":2285},[2272,94297,94298,94300],{},[898,94299,2789],{},[2129,94301,2131],{},[1996,94303,2011],{"stretchy":2004},[1996,94305,2286],{"separator":2285},[898,94307,900],{},[1996,94309,2005],{"stretchy":2004},[2129,94311,2173],{},[1996,94313,2286],{"separator":2285},[2272,94315,94316,94318],{},[898,94317,2789],{},[2129,94319,2131],{},[1996,94321,2011],{"stretchy":2004},[902,94323,94324],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,94326,94327,93736,94330,94374,94375,94483,94484,1343,94509,1343,94534,94576,94577,1343,94606,94631],{},[38,94328,94329],{},"6.5",[883,94331,94333],{"className":94332},[886],[888,94334,94335],{"xmlns":890},[892,94336,94337,94371],{},[895,94338,94339,94341,94343,94357],{},[898,94340,900],{},[1996,94342,1998],{},[9166,94344,94345,94347,94349],{},[898,94346,2789],{},[2129,94348,2278],{},[895,94350,94351,94353,94355],{},[2129,94352,2131],{},[898,94354,4674],{"mathvariant":2376},[2129,94356,2173],{},[9166,94358,94359,94361,94363],{},[898,94360,2789],{},[2129,94362,2131],{},[895,94364,94365,94367,94369],{},[2129,94366,2278],{},[898,94368,4674],{"mathvariant":2376},[2129,94370,2173],{},[902,94372,94373],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,94376,94378],{"className":94377},[886],[888,94379,94380],{"xmlns":890},[892,94381,94382,94480],{},[895,94383,94384,94386,94388,94394,94396,94402,94404,94406,94408,94410,94412,94414,94420,94422,94424,94426,94428,94430,94432,94438,94440,94442,94444,94446,94448,94450,94452,94454,94460,94462,94464,94466,94468,94470,94472,94478],{},[898,94385,900],{},[1996,94387,2005],{"stretchy":2004},[2272,94389,94390,94392],{},[898,94391,2789],{},[2129,94393,2278],{},[1996,94395,2286],{"separator":2285},[2272,94397,94398,94400],{},[898,94399,2789],{},[2129,94401,2131],{},[1996,94403,2011],{"stretchy":2004},[1996,94405,1998],{},[2129,94407,2131],{},[1996,94409,2286],{"separator":2285},[898,94411,900],{},[1996,94413,2005],{"stretchy":2004},[2272,94415,94416,94418],{},[898,94417,2789],{},[2129,94419,2278],{},[1996,94421,2286],{"separator":2285},[2129,94423,2173],{},[1996,94425,2011],{"stretchy":2004},[1996,94427,2286],{"separator":2285},[898,94429,900],{},[1996,94431,2005],{"stretchy":2004},[2272,94433,94434,94436],{},[898,94435,2789],{},[2129,94437,2278],{},[1996,94439,2286],{"separator":2285},[2129,94441,2131],{},[1996,94443,2011],{"stretchy":2004},[1996,94445,2286],{"separator":2285},[898,94447,900],{},[1996,94449,2005],{"stretchy":2004},[2129,94451,2131],{},[1996,94453,2286],{"separator":2285},[2272,94455,94456,94458],{},[898,94457,2789],{},[2129,94459,2131],{},[1996,94461,2011],{"stretchy":2004},[1996,94463,2286],{"separator":2285},[898,94465,900],{},[1996,94467,2005],{"stretchy":2004},[2129,94469,2173],{},[1996,94471,2286],{"separator":2285},[2272,94473,94474,94476],{},[898,94475,2789],{},[2129,94477,2131],{},[1996,94479,2011],{"stretchy":2004},[902,94481,94482],{"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 ",[883,94485,94487],{"className":94486},[886],[888,94488,94489],{"xmlns":890},[892,94490,94491,94506],{},[895,94492,94493,94495,94497,94499,94501,94504],{},[898,94494,4255],{},[1996,94496,2486],{"stretchy":2004},[2129,94498,64561],{},[1996,94500,8425],{"separator":2285},[2129,94502,94503],{},"3,555",[1996,94505,2501],{"stretchy":2004},[902,94507,94508],{"encoding":904},"A[1{,}5; 3{,}555]",[883,94510,94512],{"className":94511},[886],[888,94513,94514],{"xmlns":890},[892,94515,94516,94531],{},[895,94517,94518,94520,94522,94524,94526,94529],{},[898,94519,23255],{},[1996,94521,2486],{"stretchy":2004},[2129,94523,53201],{},[1996,94525,8425],{"separator":2285},[2129,94527,94528],{},"1,28",[1996,94530,2501],{"stretchy":2004},[902,94532,94533],{"encoding":904},"B[2{,}5; 1{,}28]",[883,94535,94537],{"className":94536},[886],[888,94538,94539],{"xmlns":890},[892,94540,94541,94573],{},[895,94542,94543,94545,94547,94549,94551,94553,94555,94561,94563,94565,94567,94569,94571],{},[898,94544,2777],{},[1996,94546,2486],{"stretchy":2004},[2129,94548,2131],{},[1996,94550,8425],{"separator":2285},[898,94552,900],{},[1996,94554,2005],{"stretchy":2004},[2272,94556,94557,94559],{},[898,94558,2789],{},[2129,94560,2278],{},[1996,94562,2286],{"separator":2285},[2129,94564,2173],{},[1996,94566,2011],{"stretchy":2004},[1996,94568,1998],{},[2129,94570,2173],{},[1996,94572,2501],{"stretchy":2004},[902,94574,94575],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,94578,94580],{"className":94579},[886],[888,94581,94582],{"xmlns":890},[892,94583,94584,94603],{},[895,94585,94586,94588,94590,94592,94594,94596,94598,94601],{},[898,94587,4183],{},[1996,94589,2486],{"stretchy":2004},[2129,94591,2173],{},[1996,94593,8425],{"separator":2285},[2129,94595,2278],{},[1996,94597,8425],{"separator":2285},[2129,94599,94600],{},"0,832",[1996,94602,2501],{"stretchy":2004},[902,94604,94605],{"encoding":904},"D[3; 1; 0{,}832]",[883,94607,94609],{"className":94608},[886],[888,94610,94611],{"xmlns":890},[892,94612,94613,94628],{},[895,94614,94615,94617,94619,94621,94623,94626],{},[898,94616,4252],{},[1996,94618,2486],{"stretchy":2004},[2129,94620,53201],{},[1996,94622,8425],{"separator":2285},[2129,94624,94625],{},"4,32",[1996,94627,2501],{"stretchy":2004},[902,94629,94630],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,94633,94634,93736,94637,94680,94681,6473,94694,94728,94729,94746,94747,94764],{},[38,94635,94636],{},"6.6",[883,94638,94640],{"className":94639},[886],[888,94641,94642],{"xmlns":890},[892,94643,94644,94678],{},[895,94645,94646,94648,94650,94664],{},[898,94647,900],{},[1996,94649,1998],{},[9166,94651,94652,94654,94656],{},[898,94653,2789],{},[2129,94655,2278],{},[895,94657,94658,94660,94662],{},[2129,94659,2131],{},[898,94661,4674],{"mathvariant":2376},[2129,94663,2173],{},[9166,94665,94666,94668,94670],{},[898,94667,2789],{},[2129,94669,2131],{},[895,94671,94672,94674,94676],{},[2129,94673,2278],{},[898,94675,4674],{"mathvariant":2376},[2129,94677,2173],{},[902,94679,94373],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,94682,94684],{"className":94683},[886],[888,94685,94686],{"xmlns":890},[892,94687,94688,94692],{},[895,94689,94690],{},[2288,94691,10603],{},[902,94693,28240],{"encoding":904},[883,94695,94697],{"className":94696},[886],[888,94698,94699],{"xmlns":890},[892,94700,94701,94725],{},[895,94702,94703,94709,94711,94713,94715,94721,94723],{},[2272,94704,94705,94707],{},[898,94706,2789],{},[2129,94708,2278],{},[1996,94710,1998],{},[2129,94712,3090],{},[1996,94714,2286],{"separator":2285},[2272,94716,94717,94719],{},[898,94718,2789],{},[2129,94720,2131],{},[1996,94722,1998],{},[2129,94724,8377],{},[902,94726,94727],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,94730,94732],{"className":94731},[886],[888,94733,94734],{"xmlns":890},[892,94735,94736,94744],{},[895,94737,94738],{},[2272,94739,94740,94742],{},[898,94741,2789],{},[2129,94743,2278],{},[902,94745,29004],{"encoding":904},", poklesne-li ",[883,94748,94750],{"className":94749},[886],[888,94751,94752],{"xmlns":890},[892,94753,94754,94762],{},[895,94755,94756],{},[2272,94757,94758,94760],{},[898,94759,2789],{},[2129,94761,2131],{},[902,94763,29023],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,94766,94767,94770,94771,94788,94789,94806,94807,94839,94840,94865,94866,94879,94880,1343,94904,1343,94928,1975],{},[38,94768,94769],{},"6.7"," Míra uspokojení z nákupu množství ",[883,94772,94774],{"className":94773},[886],[888,94775,94776],{"xmlns":890},[892,94777,94778,94786],{},[895,94779,94780],{},[2272,94781,94782,94784],{},[898,94783,2789],{},[2129,94785,2278],{},[902,94787,29004],{"encoding":904}," nealko nápojů a množství ",[883,94790,94792],{"className":94791},[886],[888,94793,94794],{"xmlns":890},[892,94795,94796,94804],{},[895,94797,94798],{},[2272,94799,94800,94802],{},[898,94801,2789],{},[2129,94803,2131],{},[902,94805,29023],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,94808,94810],{"className":94809},[886],[888,94811,94812],{"xmlns":890},[892,94813,94814,94836],{},[895,94815,94816,94818,94820],{},[898,94817,900],{},[1996,94819,1998],{},[8117,94821,94822],{},[895,94823,94824,94830],{},[2272,94825,94826,94828],{},[898,94827,2789],{},[2129,94829,2278],{},[2272,94831,94832,94834],{},[898,94833,2789],{},[2129,94835,2131],{},[902,94837,94838],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,94841,94843],{"className":94842},[886],[888,94844,94845],{"xmlns":890},[892,94846,94847,94863],{},[895,94848,94849,94855,94857],{},[2272,94850,94851,94853],{},[898,94852,2789],{},[2129,94854,2278],{},[1996,94856,2286],{"separator":2285},[2272,94858,94859,94861],{},[898,94860,2789],{},[2129,94862,2131],{},[902,94864,35624],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,94867,94869],{"className":94868},[886],[888,94870,94871],{"xmlns":890},[892,94872,94873,94877],{},[895,94874,94875],{},[2288,94876,10603],{},[902,94878,28240],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,94881,94883],{"className":94882},[886],[888,94884,94885],{"xmlns":890},[892,94886,94887,94901],{},[895,94888,94889,94891,94893,94895,94897,94899],{},[2288,94890,10603],{},[1996,94892,2005],{"stretchy":2004},[2129,94894,2228],{},[1996,94896,2286],{"separator":2285},[2129,94898,9035],{},[1996,94900,2011],{"stretchy":2004},[902,94902,94903],{"encoding":904},"\\text{MRCS}(5, 20)",[883,94905,94907],{"className":94906},[886],[888,94908,94909],{"xmlns":890},[892,94910,94911,94925],{},[895,94912,94913,94915,94917,94919,94921,94923],{},[2288,94914,10603],{},[1996,94916,2005],{"stretchy":2004},[2129,94918,9035],{},[1996,94920,2286],{"separator":2285},[2129,94922,2228],{},[1996,94924,2011],{"stretchy":2004},[902,94926,94927],{"encoding":904},"\\text{MRCS}(20, 5)",[883,94929,94931],{"className":94930},[886],[888,94932,94933],{"xmlns":890},[892,94934,94935,94949],{},[895,94936,94937,94939,94941,94943,94945,94947],{},[2288,94938,10603],{},[1996,94940,2005],{"stretchy":2004},[2129,94942,2131],{},[1996,94944,2286],{"separator":2285},[2129,94946,3120],{},[1996,94948,2011],{"stretchy":2004},[902,94950,94951],{"encoding":904},"\\text{MRCS}(2, 50)",[3867,94953,94954],{},[724,94955,94956,94958,94959,1975],{},[883,94957,4572],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,94960,94963],{"className":94961,"dataFsResolvedFilePath":911,"href":94962},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,94965,15722],{"id":15721},[120,94967,94968,94974,94979,94985,95038,95048,95094,95149,95212,95269,95324,95363],{},[123,94969,94970,94973],{},[38,94971,94972],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,94975,94976,94978],{},[38,94977,86871],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,94980,94981,94984],{},[38,94982,94983],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,94986,94987,94989,94990,95003,95004,1975],{},[38,94988,87198],{}," — uspořádaná ",[883,94991,94993],{"className":94992},[886],[888,94994,94995],{"xmlns":890},[892,94996,94997,95001],{},[895,94998,94999],{},[898,95000,36862],{},[902,95002,36862],{"encoding":904},"-tice ",[883,95005,95007],{"className":95006},[886],[888,95008,95009],{"xmlns":890},[892,95010,95011,95035],{},[895,95012,95013,95015,95021,95023,95025,95027,95033],{},[1996,95014,2005],{"stretchy":2004},[2272,95016,95017,95019],{},[898,95018,2789],{},[2129,95020,2278],{},[1996,95022,2286],{"separator":2285},[1996,95024,9646],{},[1996,95026,2286],{"separator":2285},[2272,95028,95029,95031],{},[898,95030,2789],{},[898,95032,36862],{},[1996,95034,2011],{"stretchy":2004},[902,95036,95037],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,95039,95040,95043,95044,95047],{},[38,95041,95042],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,95045,95046],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,95049,95050,2203,95053,95093],{},[38,95051,95052],{},"Funkce užitečnosti",[883,95054,95056],{"className":95055},[886],[888,95057,95058],{"xmlns":890},[892,95059,95060,95090],{},[895,95061,95062,95064,95066,95068,95070,95076,95078,95080,95082,95088],{},[898,95063,900],{},[1996,95065,1998],{},[898,95067,900],{},[1996,95069,2005],{"stretchy":2004},[2272,95071,95072,95074],{},[898,95073,2789],{},[2129,95075,2278],{},[1996,95077,2286],{"separator":2285},[1996,95079,9646],{},[1996,95081,2286],{"separator":2285},[2272,95083,95084,95086],{},[898,95085,2789],{},[898,95087,36862],{},[1996,95089,2011],{"stretchy":2004},[902,95091,95092],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,95095,95096,2203,95099,95128,95129,2203,95132,95148],{},[38,95097,95098],{},"Mezní užitečnost",[883,95100,95102],{"className":95101},[886],[888,95103,95104],{"xmlns":890},[892,95105,95106,95126],{},[895,95107,95108,95110,95116,95118],{},[898,95109,2818],{},[2272,95111,95112,95114],{},[898,95113,900],{},[898,95115,17792],{},[1996,95117,1998],{},[9166,95119,95120,95122,95124],{},[898,95121,900],{},[898,95123,17792],{},[1996,95125,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[902,95127,86655],{"encoding":904}," — vzorec (6.2); ",[38,95130,95131],{},"totální diferenciál",[883,95133,95135],{"className":95134},[886],[888,95136,95137],{"xmlns":890},[892,95138,95139,95145],{},[895,95140,95141,95143],{},[898,95142,2194],{"mathvariant":2376},[898,95144,900],{},[902,95146,95147],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,95150,95151,95153,95154,95178,95179,95211],{},[38,95152,88834],{}," — (6.4) ",[883,95155,95157],{"className":95156},[886],[888,95158,95159],{"xmlns":890},[892,95160,95161,95175],{},[895,95162,95163,95171,95173],{},[9166,95164,95165,95167,95169],{},[898,95166,900],{},[898,95168,17792],{},[1996,95170,2378],{"mathvariant":2376,"lspace":2377,"rspace":2377},[1996,95172,3408],{},[2129,95174,2327],{},[902,95176,95177],{"encoding":904},"U'_i > 0",", (6.5) ",[883,95180,95182],{"className":95181},[886],[888,95183,95184],{"xmlns":890},[892,95185,95186,95208],{},[895,95187,95188,95204,95206],{},[9166,95189,95190,95192,95198],{},[898,95191,900],{},[895,95193,95194,95196],{},[898,95195,17792],{},[898,95197,17792],{},[895,95199,95200,95202],{},[1996,95201,2378],{"mathvariant":2376},[1996,95203,2378],{"mathvariant":2376},[1996,95205,3447],{},[2129,95207,2327],{},[902,95209,95210],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,95213,95214,2203,95216,95247,95248,1975],{},[38,95215,90622],{},[883,95217,95219],{"className":95218},[886],[888,95220,95221],{"xmlns":890},[892,95222,95223,95245],{},[895,95224,95225,95227,95229,95237],{},[898,95226,900],{},[1996,95228,1998],{},[9166,95230,95231,95233,95235],{},[898,95232,2789],{},[2129,95234,2278],{},[898,95236,207],{},[9166,95238,95239,95241,95243],{},[898,95240,2789],{},[2129,95242,2131],{},[898,95244,2098],{},[902,95246,35805],{"encoding":904}," — (6.6), speciálně ",[883,95249,95251],{"className":95250},[886],[888,95252,95253],{"xmlns":890},[892,95254,95255,95267],{},[895,95256,95257,95259,95261,95263,95265],{},[898,95258,2098],{},[1996,95260,1998],{},[2129,95262,2278],{},[1996,95264,2225],{},[898,95266,207],{},[902,95268,90776],{"encoding":904},[123,95270,95271,2203,95274,95309,95310,95323],{},[38,95272,95273],{},"Křivky užitečnosti (indiferenční)",[883,95275,95277],{"className":95276},[886],[888,95278,95279],{"xmlns":890},[892,95280,95281,95307],{},[895,95282,95283,95285,95287,95293,95295,95301,95303,95305],{},[898,95284,900],{},[1996,95286,2005],{"stretchy":2004},[2272,95288,95289,95291],{},[898,95290,2789],{},[2129,95292,2278],{},[1996,95294,2286],{"separator":2285},[2272,95296,95297,95299],{},[898,95298,2789],{},[2129,95300,2131],{},[1996,95302,2011],{"stretchy":2004},[1996,95304,1998],{},[898,95306,2142],{},[902,95308,9768],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,95311,95313],{"className":95312},[886],[888,95314,95315],{"xmlns":890},[892,95316,95317,95321],{},[895,95318,95319],{},[898,95320,900],{},[902,95322,900],{"encoding":904},", konvexní.",[123,95325,95326,2203,95328,95362],{},[38,95327,92167],{},[883,95329,95331],{"className":95330},[886],[888,95332,95333],{"xmlns":890},[892,95334,95335,95359],{},[895,95336,95337,95339,95341,95343,95349,95351,95353],{},[2288,95338,10603],{},[1996,95340,1998],{},[898,95342,2818],{},[2272,95344,95345,95347],{},[898,95346,900],{},[2129,95348,2278],{},[898,95350,4674],{"mathvariant":2376},[898,95352,2818],{},[2272,95354,95355,95357],{},[898,95356,900],{},[2129,95358,2131],{},[902,95360,95361],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,95364,95365,2203,95368,9769,95397,95400],{},[38,95366,95367],{},"Podmínka optimality",[883,95369,95371],{"className":95370},[886],[888,95372,95373],{"xmlns":890},[892,95374,95375,95395],{},[895,95376,95377,95379,95381,95387,95389],{},[2288,95378,10603],{},[1996,95380,1998],{},[2272,95382,95383,95385],{},[898,95384,3937],{},[2129,95386,2278],{},[898,95388,4674],{"mathvariant":2376},[2272,95390,95391,95393],{},[898,95392,3937],{},[2129,95394,2131],{},[902,95396,28000],{"encoding":904},[207,95398,36756],{"className":95399,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,95402,3792],{"id":3791},[120,95404,95405,95442,95483,95493],{},[123,95406,95407,2203,95410,95413,95414,95427,95428,95441],{},[38,95408,95409],{},"Navazující téma:",[207,95411,913],{"className":95412,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,95415,95417],{"className":95416},[886],[888,95418,95419],{"xmlns":890},[892,95420,95421,95425],{},[895,95422,95423],{},[898,95424,900],{},[902,95426,900],{"encoding":904},", min ",[883,95429,95431],{"className":95430},[886],[888,95432,95433],{"xmlns":890},[892,95434,95435,95439],{},[895,95436,95437],{},[898,95438,4252],{},[902,95440,4252],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,95443,95444,2203,95447,11093,95450,86410,95453,95456,95457,95460,95461,18650,95479,95482],{},[38,95445,95446],{},"Související pojmy:",[207,95448,784],{"className":95449,"dataFsResolvedFilePath":782,"href":783},[210],[207,95451,2357],{"className":95452,"dataFsResolvedFilePath":764,"href":765},[210],[207,95454,11088],{"className":95455,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,95458,11942],{"className":95459,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,95462,95464],{"className":95463},[886],[888,95465,95466],{"xmlns":890},[892,95467,95468,95476],{},[895,95469,95470],{},[2272,95471,95472,95474],{},[898,95473,4183],{},[898,95475,17792],{},[902,95477,95478],{"encoding":904},"D_i",[207,95480,793],{"className":95481,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,95484,95485,2203,95487,1343,95490],{},[38,95486,36705],{},[207,95488,1094],{"className":95489,"dataFsResolvedFilePath":838,"href":839},[210],[207,95491,1101],{"className":95492,"dataFsResolvedFilePath":868,"href":869},[210],[123,95494,95495,2203,95497],{},[38,95496,16206],{},[207,95498,16210],{"className":95499,"dataFsResolvedFilePath":1960,"href":1961},[210],{"title":641,"searchDepth":642,"depth":642,"links":95501},[95502,95503,95504,95507,95508,95511,95515,95516,95519,95520,95521,95522,95523,95524,95525],{"id":12007,"depth":642,"text":12008},{"id":86794,"depth":642,"text":86795},{"id":86854,"depth":642,"text":86855,"children":95505},[95506],{"id":86870,"depth":649,"text":86871},{"id":87177,"depth":642,"text":87178},{"id":88037,"depth":642,"text":88038,"children":95509},[95510],{"id":88584,"depth":649,"text":80213},{"id":88833,"depth":642,"text":88834,"children":95512},[95513],{"id":89706,"depth":649,"text":95514},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":90621,"depth":642,"text":90622},{"id":91157,"depth":642,"text":91158,"children":95517},[95518],{"id":91931,"depth":649,"text":91932},{"id":92161,"depth":642,"text":92162},{"id":92922,"depth":642,"text":92923},{"id":93460,"depth":642,"text":93461},{"id":49883,"depth":642,"text":49884},{"id":93596,"depth":642,"text":93597},{"id":15721,"depth":642,"text":15722},{"id":3791,"depth":642,"text":3792},{},"\u002Ftopics\u002Fuzitecnost",{"title":86578,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,9773,95532,86572,11123,95533],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":95536,"title":757,"body":95537,"course":1128,"courses":659,"created":1129,"description":95810,"extension":661,"meta":95811,"navigation":664,"path":95812,"seo":95813,"sources":95814,"stem":95815,"tags":95816,"type":3857,"updated":677,"__hash__":95822},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":95538,"toc":95802},[95539,95542,95549,95556,95560,95570,95572,95606,95610,95653,95656,95714,95718,95748,95752,95773,95775],[12,95540,757],{"id":95541},"základy-matematické-ekonomie",[724,95543,95544,95545,95548],{},"Úvodní pojmy a princip modelování v ",[207,95546,16382],{"className":95547,"dataFsResolvedFilePath":1960,"href":1961},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,95550,95551],{},[2559,95552],{"alt":95553,"className":95554,"src":95555},"imek-model-promenne",[210,2563],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,95557,95559],{"id":95558},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,95561,95562,95565,95566,95569],{},[38,95563,95564],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,95567,95568],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,95571,15722],{"id":15721},[120,95573,95574,95580,95586,95592,95601],{},[123,95575,95576,95579],{},[38,95577,95578],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,95581,95582,95585],{},[38,95583,95584],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,95587,95588,95591],{},[38,95589,95590],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,95593,95594,7015,95597,95600],{},[38,95595,95596],{},"Ceteris paribus",[614,95598,95599],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,95602,95603,95605],{},[38,95604,50637],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,95607,95609],{"id":95608},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,95611,95612,95652],{},[883,95613,95615],{"className":95614},[886],[888,95616,95617],{"xmlns":890},[892,95618,95619,95649],{},[895,95620,95621,95623,95625,95627,95629,95631,95633,95635,95637,95639,95641,95643,95645,95647],{},[898,95622,2789],{},[1996,95624,1998],{},[898,95626,4183],{},[1996,95628,2005],{"stretchy":2004},[898,95630,3937],{},[1996,95632,2286],{"separator":2285},[898,95634,9128],{},[1996,95636,2286],{"separator":2285},[898,95638,18296],{},[1996,95640,2286],{"separator":2285},[898,95642,900],{},[1996,95644,2286],{"separator":2285},[1996,95646,9646],{},[1996,95648,2011],{"stretchy":2004},[902,95650,95651],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,95654,95655],{},"Zjednodušení:",[120,95657,95658,95686],{},[123,95659,95660,2203,95663],{},[38,95661,95662],{},"Jednofaktorový model:",[883,95664,95666],{"className":95665},[886],[888,95667,95668],{"xmlns":890},[892,95669,95670,95684],{},[895,95671,95672,95674,95676,95678,95680,95682],{},[898,95673,2789],{},[1996,95675,1998],{},[898,95677,4183],{},[1996,95679,2005],{"stretchy":2004},[898,95681,3937],{},[1996,95683,2011],{"stretchy":2004},[902,95685,4192],{"encoding":904},[123,95687,95688,2203,95691],{},[38,95689,95690],{},"Inverzní zápis:",[883,95692,95694],{"className":95693},[886],[888,95695,95696],{"xmlns":890},[892,95697,95698,95712],{},[895,95699,95700,95702,95704,95706,95708,95710],{},[898,95701,3937],{},[1996,95703,1998],{},[898,95705,4183],{},[1996,95707,2005],{"stretchy":2004},[898,95709,2789],{},[1996,95711,2011],{"stretchy":2004},[902,95713,4640],{"encoding":904},[115,95715,95717],{"id":95716},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,95719,95720,95729],{},[123,95721,95722,95725,95726,3918],{},[38,95723,95724],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,95727,16241],{"className":95728,"dataFsResolvedFilePath":800,"href":801},[210],[123,95730,95731,95734,95735,95738,95739,95742,95743,95747],{},[38,95732,95733],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,95736,1145],{"className":95737,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,95740,16254],{"className":95741,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,95744,95746],{"className":95745,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,95749,95751],{"id":95750},"konvence-z-přednášek","Konvence z přednášek",[120,95753,95754,95761,95767],{},[123,95755,95756,95757,95760],{},"Symbol ",[95758,95759,2730],"code",{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,95762,95763,95764,1975],{},"Numerické výsledky ",[38,95765,95766],{},"na 3 desetinná místa",[123,95768,3895,95769,95772],{},[614,95770,95771],{},"jednotková změna"," má standardní význam (změna o 1).",[115,95774,3792],{"id":3791},[120,95776,95777,95782,95790],{},[123,95778,95779,95781],{},[38,95780,3799],{}," —",[123,95783,95784,2203,95786],{},[38,95785,3807],{},[207,95787,95789],{"className":95788,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,95791,95792,2203,95794,1343,95798],{},[38,95793,3815],{},[207,95795,95797],{"className":95796,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,95799,95801],{"className":95800,"dataFsResolvedFilePath":1960,"href":1961},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":95803},[95804,95805,95806,95807,95808,95809],{"id":95558,"depth":642,"text":95559},{"id":15721,"depth":642,"text":15722},{"id":95608,"depth":642,"text":95609},{"id":95716,"depth":642,"text":95717},{"id":95750,"depth":642,"text":95751},{"id":3791,"depth":642,"text":3792},"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":95810},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,95817,95818,95819,95820,95821],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":95824,"title":95825,"body":95826,"course":1128,"courses":659,"created":9556,"description":641,"extension":661,"meta":100098,"navigation":664,"path":100099,"seo":100100,"sources":100101,"stem":100102,"tags":100103,"type":3857,"updated":677,"__hash__":100107},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":95827,"toc":100081},[95828,95831,95925,95929,95951,95965,96017,96019,96023,96086,96129,96148,96311,96410,96413,96480,96484,96613,96652,96682,96794,96839,96905,96958,97034,97090,97092,97096,97160,97204,97224,97385,97388,97472,97569,97572,97638,97642,97691,97717,97822,97886,97891,97987,98034,98036,98039,98061,98103,98110,98143,98145,98216,98270,98379,98383,98472,98548,98812,98850,98852,98856,98859,98866,99177,99180,99238,99418,99447,99449,99453,99459,99597,99606,99608,99610,100035,100037,100039],[12,95829,95825],{"id":95830},"zdanění-trhu-dopady-daně-na-rovnováhu",[3867,95832,95833],{},[724,95834,95835,42630,95837,95850,95851,95854,95855,95857,95858,95861,95862,95883,95884,95907,95908,95911,95912,1975],{},[883,95836,4155],{},[883,95838,95840],{"className":95839},[886],[888,95841,95842],{"xmlns":890},[892,95843,95844,95848],{},[895,95845,95846],{},[898,95847,2774],{},[902,95849,2774],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,95852,95853],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,95856,86862],{}," (je-li uložena spotřebiteli). Výsledné ",[38,95859,95860],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,95863,95865],{"className":95864},[886],[888,95866,95867],{"xmlns":890},[892,95868,95869,95881],{},[895,95870,95871],{},[2272,95872,95873,95875],{},[898,95874,2774],{},[895,95876,95877,95879],{},[898,95878,42679],{},[898,95880,724],{},[902,95882,42684],{"encoding":904}," (spotřebitel) a ",[883,95885,95887],{"className":95886},[886],[888,95888,95889],{"xmlns":890},[892,95890,95891,95905],{},[895,95892,95893],{},[2272,95894,95895,95897],{},[898,95896,2774],{},[895,95898,95899,95901,95903],{},[898,95900,42702],{},[898,95902,1994],{},[898,95904,12043],{},[902,95906,42709],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,95909,95910],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,95913,95915],{"className":95914},[886],[888,95916,95917],{"xmlns":890},[892,95918,95919,95923],{},[895,95920,95921],{},[898,95922,2774],{},[902,95924,2774],{"encoding":904},[115,95926,95928],{"id":95927},"dvě-formy-zdanění","Dvě formy zdanění",[724,95930,95931,95932,95950],{},"Uvažujme jednotkovou daň ",[883,95933,95935],{"className":95934},[886],[888,95936,95937],{"xmlns":890},[892,95938,95939,95947],{},[895,95940,95941,95943,95945],{},[898,95942,2774],{},[1996,95944,3408],{},[2129,95946,2327],{},[902,95948,95949],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,95952,95953,95959],{},[123,95954,95955,95958],{},[38,95956,95957],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,95960,95961,95964],{},[38,95962,95963],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,95966,95967,95968,95981,95982,95985,95986,1975],{},"V obou případech dochází k posunu jedné z křivek o ",[883,95969,95971],{"className":95970},[886],[888,95972,95973],{"xmlns":890},[892,95974,95975,95979],{},[895,95976,95977],{},[898,95978,2774],{},[902,95980,2774],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,95983,95984],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,95987,95989],{"className":95988},[886],[888,95990,95991],{"xmlns":890},[892,95992,95993,96015],{},[895,95994,95995,95997,95999,96005,96007,96013],{},[898,95996,4252],{},[1996,95998,2486],{"stretchy":2004},[2124,96000,96001,96003],{},[898,96002,2789],{},[898,96004,4252],{},[1996,96006,2286],{"separator":2285},[2124,96008,96009,96011],{},[898,96010,3937],{},[898,96012,4252],{},[1996,96014,2501],{"stretchy":2004},[902,96016,41369],{"encoding":904},[36972,96018],{},[115,96020,96022],{"id":96021},"daň-uložená-výrobci","Daň uložená výrobci",[724,96024,96025,96026,96039,96040,96057,96058,96085],{},"Je-li daň ",[883,96027,96029],{"className":96028},[886],[888,96030,96031],{"xmlns":890},[892,96032,96033,96037],{},[895,96034,96035],{},[898,96036,2774],{},[902,96038,2774],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,96041,96043],{"className":96042},[886],[888,96044,96045],{"xmlns":890},[892,96046,96047,96055],{},[895,96048,96049,96051,96053],{},[898,96050,3937],{},[1996,96052,2225],{},[898,96054,2774],{},[902,96056,41124],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,96059,96061],{"className":96060},[886],[888,96062,96063],{"xmlns":890},[892,96064,96065,96083],{},[895,96066,96067,96069,96071,96073,96075,96077,96079,96081],{},[898,96068,3937],{},[1996,96070,2225],{},[898,96072,2774],{},[1996,96074,1998],{},[898,96076,8673],{},[1996,96078,2005],{"stretchy":2004},[898,96080,2789],{},[1996,96082,2011],{"stretchy":2004},[902,96084,41153],{"encoding":904}," nová funkce nabídky:",[883,96087,96089],{"className":96088},[886],[888,96090,96091],{"xmlns":890,"display":28068},[892,96092,96093,96127],{},[895,96094,96095,96097,96099,96105,96107,96109,96111,96113,96115,96117,96119,96121,96123,96125],{},[898,96096,3937],{},[1996,96098,1998],{},[2272,96100,96101,96103],{},[898,96102,8673],{},[2129,96104,2278],{},[1996,96106,2005],{"stretchy":2004},[898,96108,2789],{},[1996,96110,2011],{"stretchy":2004},[1996,96112,1998],{},[898,96114,8673],{},[1996,96116,2005],{"stretchy":2004},[898,96118,2789],{},[1996,96120,2011],{"stretchy":2004},[1996,96122,2095],{},[898,96124,2774],{},[898,96126,1975],{"mathvariant":2376},[902,96128,41198],{"encoding":904},[724,96130,96131,96132,2203,96145,96147],{},"Nabídka se tedy posouvá o ",[883,96133,96135],{"className":96134},[886],[888,96136,96137],{"xmlns":890},[892,96138,96139,96143],{},[895,96140,96141],{},[898,96142,2774],{},[902,96144,2774],{"encoding":904},[38,96146,41231],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,96149,96150,96151,96191,96192,3885,96220,96248,96249,96268,96269,96293,96294,3918],{},"Nový rovnovážný bod ",[883,96152,96154],{"className":96153},[886],[888,96155,96156],{"xmlns":890},[892,96157,96158,96188],{},[895,96159,96160,96166,96168,96176,96178,96186],{},[2272,96161,96162,96164],{},[898,96163,4252],{},[2129,96165,2278],{},[1996,96167,2486],{"stretchy":2004},[9166,96169,96170,96172,96174],{},[898,96171,2789],{},[2129,96173,2278],{},[898,96175,4252],{},[1996,96177,2286],{"separator":2285},[9166,96179,96180,96182,96184],{},[898,96181,3937],{},[2129,96183,2278],{},[898,96185,4252],{},[1996,96187,2501],{"stretchy":2004},[902,96189,96190],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,96193,96195],{"className":96194},[886],[888,96196,96197],{"xmlns":890},[892,96198,96199,96217],{},[895,96200,96201,96209,96211],{},[9166,96202,96203,96205,96207],{},[898,96204,2789],{},[2129,96206,2278],{},[898,96208,4252],{},[1996,96210,3447],{},[2124,96212,96213,96215],{},[898,96214,2789],{},[898,96216,4252],{},[902,96218,96219],{"encoding":904},"Q_1^E \u003C Q^E",[883,96221,96223],{"className":96222},[886],[888,96224,96225],{"xmlns":890},[892,96226,96227,96245],{},[895,96228,96229,96237,96239],{},[9166,96230,96231,96233,96235],{},[898,96232,3937],{},[2129,96234,2278],{},[898,96236,4252],{},[1996,96238,3408],{},[2124,96240,96241,96243],{},[898,96242,3937],{},[898,96244,4252],{},[902,96246,96247],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,96250,96252],{"className":96251},[886],[888,96253,96254],{"xmlns":890},[892,96255,96256,96266],{},[895,96257,96258],{},[9166,96259,96260,96262,96264],{},[898,96261,3937],{},[2129,96263,2278],{},[898,96265,4252],{},[902,96267,47859],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,96270,96272],{"className":96271},[886],[888,96273,96274],{"xmlns":890},[892,96275,96276,96290],{},[895,96277,96278,96286,96288],{},[9166,96279,96280,96282,96284],{},[898,96281,3937],{},[2129,96283,2278],{},[898,96285,4252],{},[1996,96287,2225],{},[898,96289,2774],{},[902,96291,96292],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,96295,96297],{"className":96296},[886],[888,96298,96299],{"xmlns":890},[892,96300,96301,96309],{},[895,96302,96303],{},[2124,96304,96305,96307],{},[898,96306,3937],{},[898,96308,4252],{},[902,96310,41468],{"encoding":904},[724,96312,96313],{},[614,96314,96315,96316,96346,96347,96360,96361,5669,96378,96391,96392,1975],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,96317,96319],{"className":96318},[886],[888,96320,96321],{"xmlns":890},[892,96322,96323,96343],{},[895,96324,96325,96327,96329,96335,96337,96339,96341],{},[898,96326,8673],{},[1996,96328,3123],{},[2272,96330,96331,96333],{},[898,96332,8673],{},[2129,96334,2278],{},[1996,96336,1998],{},[898,96338,8673],{},[1996,96340,2095],{},[898,96342,2774],{},[902,96344,96345],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,96348,96350],{"className":96349},[886],[888,96351,96352],{"xmlns":890},[892,96353,96354,96358],{},[895,96355,96356],{},[898,96357,2774],{},[902,96359,2774],{"encoding":904},". Průsečík ",[883,96362,96364],{"className":96363},[886],[888,96365,96366],{"xmlns":890},[892,96367,96368,96376],{},[895,96369,96370],{},[2272,96371,96372,96374],{},[898,96373,8673],{},[2129,96375,2278],{},[902,96377,40999],{"encoding":904},[883,96379,96381],{"className":96380},[886],[888,96382,96383],{"xmlns":890},[892,96384,96385,96389],{},[895,96386,96387],{},[898,96388,4183],{},[902,96390,4183],{"encoding":904}," je nový rovnovážný bod ",[883,96393,96395],{"className":96394},[886],[888,96396,96397],{"xmlns":890},[892,96398,96399,96407],{},[895,96400,96401],{},[2272,96402,96403,96405],{},[898,96404,4252],{},[2129,96406,2278],{},[902,96408,96409],{"encoding":904},"E_1",[198,96411,45305],{"id":96412},"příklad-29",[724,96414,96415,41657,96417,41692,96441,96461,96462,96479],{},[38,96416,37935],{},[883,96418,96420],{"className":96419},[886],[888,96421,96422],{"xmlns":890},[892,96423,96424,96438],{},[895,96425,96426,96428,96430,96432,96434,96436],{},[898,96427,3937],{},[1996,96429,1998],{},[2129,96431,3509],{},[1996,96433,2225],{},[2129,96435,2131],{},[898,96437,2789],{},[902,96439,96440],{"encoding":904},"P = 12 - 2Q",[883,96442,96444],{"className":96443},[886],[888,96445,96446],{"xmlns":890},[892,96447,96448,96458],{},[895,96449,96450,96452,96454,96456],{},[898,96451,3937],{},[1996,96453,1998],{},[2129,96455,2351],{},[898,96457,2789],{},[902,96459,96460],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,96463,96465],{"className":96464},[886],[888,96466,96467],{"xmlns":890},[892,96468,96469,96477],{},[895,96470,96471,96473,96475],{},[898,96472,2774],{},[1996,96474,1998],{},[2129,96476,2235],{},[902,96478,41270],{"encoding":904}," Kč.",[724,96481,96482],{},[38,96483,37967],{},[724,96485,96486,96489,96490,5569,96516,5589,96536,1343,96558,96588,96589,1975],{},[614,96487,96488],{},"Bez daně."," Z rovnosti ",[883,96491,96493],{"className":96492},[886],[888,96494,96495],{"xmlns":890},[892,96496,96497,96513],{},[895,96498,96499,96501,96503,96505,96507,96509,96511],{},[2129,96500,3509],{},[1996,96502,2225],{},[2129,96504,2131],{},[898,96506,2789],{},[1996,96508,1998],{},[2129,96510,2351],{},[898,96512,2789],{},[902,96514,96515],{"encoding":904},"12 - 2Q = 4Q",[883,96517,96519],{"className":96518},[886],[888,96520,96521],{"xmlns":890},[892,96522,96523,96533],{},[895,96524,96525,96527,96529,96531],{},[2129,96526,2235],{},[898,96528,2789],{},[1996,96530,1998],{},[2129,96532,3509],{},[902,96534,96535],{"encoding":904},"6Q = 12",[883,96537,96539],{"className":96538},[886],[888,96540,96541],{"xmlns":890},[892,96542,96543,96555],{},[895,96544,96545,96551,96553],{},[2124,96546,96547,96549],{},[898,96548,2789],{},[898,96550,4252],{},[1996,96552,1998],{},[2129,96554,2131],{},[902,96556,96557],{"encoding":904},"Q^E = 2",[883,96559,96561],{"className":96560},[886],[888,96562,96563],{"xmlns":890},[892,96564,96565,96585],{},[895,96566,96567,96573,96575,96577,96579,96581,96583],{},[2124,96568,96569,96571],{},[898,96570,3937],{},[898,96572,4252],{},[1996,96574,1998],{},[2129,96576,2351],{},[1996,96578,3177],{},[2129,96580,2131],{},[1996,96582,1998],{},[2129,96584,5585],{},[902,96586,96587],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,96590,96592],{"className":96591},[886],[888,96593,96594],{"xmlns":890},[892,96595,96596,96610],{},[895,96597,96598,96600,96602,96604,96606,96608],{},[898,96599,4252],{},[1996,96601,2486],{"stretchy":2004},[2129,96603,2131],{},[1996,96605,2286],{"separator":2285},[2129,96607,5585],{},[1996,96609,2501],{"stretchy":2004},[902,96611,96612],{"encoding":904},"E[2, 8]",[724,96614,96615,96618,96619,96651],{},[614,96616,96617],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,96620,96622],{"className":96621},[886],[888,96623,96624],{"xmlns":890},[892,96625,96626,96648],{},[895,96627,96628,96634,96636,96638,96640,96642,96644,96646],{},[2272,96629,96630,96632],{},[898,96631,8673],{},[2129,96633,2278],{},[1996,96635,2704],{},[898,96637,3937],{},[1996,96639,1998],{},[2129,96641,2351],{},[898,96643,2789],{},[1996,96645,2095],{},[2129,96647,2235],{},[902,96649,96650],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,96653,96655],{"className":96654},[886],[888,96656,96657],{"xmlns":890,"display":28068},[892,96658,96659,96679],{},[895,96660,96661,96663,96665,96667,96669,96671,96673,96675,96677],{},[2129,96662,3509],{},[1996,96664,2225],{},[2129,96666,2131],{},[898,96668,2789],{},[1996,96670,1998],{},[2129,96672,2351],{},[898,96674,2789],{},[1996,96676,2095],{},[2129,96678,2235],{},[902,96680,96681],{"encoding":904},"12 - 2Q = 4Q + 6",[724,96683,96684,96685,5589,96705,1343,96729,96765,96766,1975],{},"plyne ",[883,96686,96688],{"className":96687},[886],[888,96689,96690],{"xmlns":890},[892,96691,96692,96702],{},[895,96693,96694,96696,96698,96700],{},[2129,96695,2235],{},[898,96697,2789],{},[1996,96699,1998],{},[2129,96701,2235],{},[902,96703,96704],{"encoding":904},"6Q = 6",[883,96706,96708],{"className":96707},[886],[888,96709,96710],{"xmlns":890},[892,96711,96712,96726],{},[895,96713,96714,96722,96724],{},[9166,96715,96716,96718,96720],{},[898,96717,2789],{},[2129,96719,2278],{},[898,96721,4252],{},[1996,96723,1998],{},[2129,96725,2278],{},[902,96727,96728],{"encoding":904},"Q_1^E = 1",[883,96730,96732],{"className":96731},[886],[888,96733,96734],{"xmlns":890},[892,96735,96736,96762],{},[895,96737,96738,96746,96748,96750,96752,96754,96756,96758,96760],{},[9166,96739,96740,96742,96744],{},[898,96741,3937],{},[2129,96743,2278],{},[898,96745,4252],{},[1996,96747,1998],{},[2129,96749,2351],{},[1996,96751,3177],{},[2129,96753,2278],{},[1996,96755,2095],{},[2129,96757,2235],{},[1996,96759,1998],{},[2129,96761,2863],{},[902,96763,96764],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,96767,96769],{"className":96768},[886],[888,96770,96771],{"xmlns":890},[892,96772,96773,96791],{},[895,96774,96775,96781,96783,96785,96787,96789],{},[2272,96776,96777,96779],{},[898,96778,4252],{},[2129,96780,2278],{},[1996,96782,2486],{"stretchy":2004},[2129,96784,2278],{},[1996,96786,2286],{"separator":2285},[2129,96788,2863],{},[1996,96790,2501],{"stretchy":2004},[902,96792,96793],{"encoding":904},"E_1[1, 10]",[724,96795,96796,96799,96800,96824,96825,96838],{},[614,96797,96798],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,96801,96803],{"className":96802},[886],[888,96804,96805],{"xmlns":890},[892,96806,96807,96821],{},[895,96808,96809,96817,96819],{},[9166,96810,96811,96813,96815],{},[898,96812,3937],{},[2129,96814,2278],{},[898,96816,4252],{},[1996,96818,1998],{},[2129,96820,2863],{},[902,96822,96823],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,96826,96828],{"className":96827},[886],[888,96829,96830],{"xmlns":890},[892,96831,96832,96836],{},[895,96833,96834],{},[2129,96835,5585],{},[902,96837,5585],{"encoding":904},", navýšení je",[883,96840,96842],{"className":96841},[886],[888,96843,96844],{"xmlns":890,"display":28068},[892,96845,96846,96902],{},[895,96847,96848,96858,96860,96868,96870,96876,96878,96880,96882,96884,96886,96888,96890,96900],{},[2272,96849,96850,96852],{},[898,96851,2774],{},[895,96853,96854,96856],{},[898,96855,42679],{},[898,96857,724],{},[1996,96859,1998],{},[9166,96861,96862,96864,96866],{},[898,96863,3937],{},[2129,96865,2278],{},[898,96867,4252],{},[1996,96869,2225],{},[2124,96871,96872,96874],{},[898,96873,3937],{},[898,96875,4252],{},[1996,96877,1998],{},[2129,96879,2863],{},[1996,96881,2225],{},[2129,96883,5585],{},[1996,96885,1998],{},[2129,96887,2131],{},[2288,96889,2290],{},[895,96891,96892,96894],{},[2288,96893,9800],{},[8386,96895,96896,96898],{"accent":2285},[2288,96897,2142],{},[1996,96899,25060],{},[898,96901,1975],{"mathvariant":2376},[902,96903,96904],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,96906,96907,96908,96824,96944,96957],{},"Výrobci zůstává čistá cena ",[883,96909,96911],{"className":96910},[886],[888,96912,96913],{"xmlns":890},[892,96914,96915,96941],{},[895,96916,96917,96925,96927,96929,96931,96933,96935,96937,96939],{},[9166,96918,96919,96921,96923],{},[898,96920,3937],{},[2129,96922,2278],{},[898,96924,4252],{},[1996,96926,2225],{},[898,96928,2774],{},[1996,96930,1998],{},[2129,96932,2863],{},[1996,96934,2225],{},[2129,96936,2235],{},[1996,96938,1998],{},[2129,96940,2351],{},[902,96942,96943],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,96945,96947],{"className":96946},[886],[888,96948,96949],{"xmlns":890},[892,96950,96951,96955],{},[895,96952,96953],{},[2129,96954,5585],{},[902,96956,5585],{"encoding":904},", pokles je",[883,96959,96961],{"className":96960},[886],[888,96962,96963],{"xmlns":890,"display":28068},[892,96964,96965,97031],{},[895,96966,96967,96979,96981,96987,96989,96991,96999,97001,97003,97005,97007,97009,97011,97013,97015,97017,97019,97029],{},[2272,96968,96969,96971],{},[898,96970,2774],{},[895,96972,96973,96975,96977],{},[898,96974,42702],{},[898,96976,1994],{},[898,96978,12043],{},[1996,96980,1998],{},[2124,96982,96983,96985],{},[898,96984,3937],{},[898,96986,4252],{},[1996,96988,2225],{},[1996,96990,2005],{"stretchy":2004},[9166,96992,96993,96995,96997],{},[898,96994,3937],{},[2129,96996,2278],{},[898,96998,4252],{},[1996,97000,2225],{},[898,97002,2774],{},[1996,97004,2011],{"stretchy":2004},[1996,97006,1998],{},[2129,97008,5585],{},[1996,97010,2225],{},[2129,97012,2351],{},[1996,97014,1998],{},[2129,97016,2351],{},[2288,97018,2290],{},[895,97020,97021,97023],{},[2288,97022,9800],{},[8386,97024,97025,97027],{"accent":2285},[2288,97026,2142],{},[1996,97028,25060],{},[898,97030,1975],{"mathvariant":2376},[902,97032,97033],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,97035,97036,97037,97089],{},"Kontrola: ",[883,97038,97040],{"className":97039},[886],[888,97041,97042],{"xmlns":890},[892,97043,97044,97086],{},[895,97045,97046,97056,97058,97070,97072,97074,97076,97078,97080,97082,97084],{},[2272,97047,97048,97050],{},[898,97049,2774],{},[895,97051,97052,97054],{},[898,97053,42679],{},[898,97055,724],{},[1996,97057,2095],{},[2272,97059,97060,97062],{},[898,97061,2774],{},[895,97063,97064,97066,97068],{},[898,97065,42702],{},[898,97067,1994],{},[898,97069,12043],{},[1996,97071,1998],{},[2129,97073,2131],{},[1996,97075,2095],{},[2129,97077,2351],{},[1996,97079,1998],{},[2129,97081,2235],{},[1996,97083,1998],{},[898,97085,2774],{},[902,97087,97088],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[36972,97091],{},[115,97093,97095],{"id":97094},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,97097,96025,97098,97111,97112,97130,97131,97159],{},[883,97099,97101],{"className":97100},[886],[888,97102,97103],{"xmlns":890},[892,97104,97105,97109],{},[895,97106,97107],{},[898,97108,2774],{},[902,97110,2774],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,97113,97115],{"className":97114},[886],[888,97116,97117],{"xmlns":890},[892,97118,97119,97127],{},[895,97120,97121,97123,97125],{},[898,97122,3937],{},[1996,97124,2095],{},[898,97126,2774],{},[902,97128,97129],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,97132,97134],{"className":97133},[886],[888,97135,97136],{"xmlns":890},[892,97137,97138,97156],{},[895,97139,97140,97142,97144,97146,97148,97150,97152,97154],{},[898,97141,3937],{},[1996,97143,2095],{},[898,97145,2774],{},[1996,97147,1998],{},[898,97149,4183],{},[1996,97151,2005],{"stretchy":2004},[898,97153,2789],{},[1996,97155,2011],{"stretchy":2004},[902,97157,97158],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,97161,97163],{"className":97162},[886],[888,97164,97165],{"xmlns":890,"display":28068},[892,97166,97167,97201],{},[895,97168,97169,97171,97173,97179,97181,97183,97185,97187,97189,97191,97193,97195,97197,97199],{},[898,97170,3937],{},[1996,97172,1998],{},[2272,97174,97175,97177],{},[898,97176,4183],{},[2129,97178,2131],{},[1996,97180,2005],{"stretchy":2004},[898,97182,2789],{},[1996,97184,2011],{"stretchy":2004},[1996,97186,1998],{},[898,97188,4183],{},[1996,97190,2005],{"stretchy":2004},[898,97192,2789],{},[1996,97194,2011],{"stretchy":2004},[1996,97196,2225],{},[898,97198,2774],{},[898,97200,1975],{"mathvariant":2376},[902,97202,97203],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,97205,97206,97207,2203,97220,97223],{},"Poptávka se tedy posouvá o ",[883,97208,97210],{"className":97209},[886],[888,97211,97212],{"xmlns":890},[892,97213,97214,97218],{},[895,97215,97216],{},[898,97217,2774],{},[902,97219,2774],{"encoding":904},[38,97221,97222],{},"svisle dolů",". Nabídka se nemění.",[724,97225,96150,97226,96191,97266,3885,97294,97322,97323,97342,97343,97367,97368,3918],{},[883,97227,97229],{"className":97228},[886],[888,97230,97231],{"xmlns":890},[892,97232,97233,97263],{},[895,97234,97235,97241,97243,97251,97253,97261],{},[2272,97236,97237,97239],{},[898,97238,4252],{},[2129,97240,2131],{},[1996,97242,2486],{"stretchy":2004},[9166,97244,97245,97247,97249],{},[898,97246,2789],{},[2129,97248,2131],{},[898,97250,4252],{},[1996,97252,2286],{"separator":2285},[9166,97254,97255,97257,97259],{},[898,97256,3937],{},[2129,97258,2131],{},[898,97260,4252],{},[1996,97262,2501],{"stretchy":2004},[902,97264,97265],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,97267,97269],{"className":97268},[886],[888,97270,97271],{"xmlns":890},[892,97272,97273,97291],{},[895,97274,97275,97283,97285],{},[9166,97276,97277,97279,97281],{},[898,97278,2789],{},[2129,97280,2131],{},[898,97282,4252],{},[1996,97284,3447],{},[2124,97286,97287,97289],{},[898,97288,2789],{},[898,97290,4252],{},[902,97292,97293],{"encoding":904},"Q_2^E \u003C Q^E",[883,97295,97297],{"className":97296},[886],[888,97298,97299],{"xmlns":890},[892,97300,97301,97319],{},[895,97302,97303,97311,97313],{},[9166,97304,97305,97307,97309],{},[898,97306,3937],{},[2129,97308,2131],{},[898,97310,4252],{},[1996,97312,3447],{},[2124,97314,97315,97317],{},[898,97316,3937],{},[898,97318,4252],{},[902,97320,97321],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,97324,97326],{"className":97325},[886],[888,97327,97328],{"xmlns":890},[892,97329,97330,97340],{},[895,97331,97332],{},[9166,97333,97334,97336,97338],{},[898,97335,3937],{},[2129,97337,2131],{},[898,97339,4252],{},[902,97341,47920],{"encoding":904},", spotřebitel platí celkem ",[883,97344,97346],{"className":97345},[886],[888,97347,97348],{"xmlns":890},[892,97349,97350,97364],{},[895,97351,97352,97360,97362],{},[9166,97353,97354,97356,97358],{},[898,97355,3937],{},[2129,97357,2131],{},[898,97359,4252],{},[1996,97361,2095],{},[898,97363,2774],{},[902,97365,97366],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,97369,97371],{"className":97370},[886],[888,97372,97373],{"xmlns":890},[892,97374,97375,97383],{},[895,97376,97377],{},[2124,97378,97379,97381],{},[898,97380,3937],{},[898,97382,4252],{},[902,97384,41468],{"encoding":904},[724,97386,97387],{},"Daňové břemeno:",[883,97389,97391],{"className":97390},[886],[888,97392,97393],{"xmlns":890,"display":28068},[892,97394,97395,97469],{},[895,97396,97397,97407,97409,97411,97419,97421,97423,97425,97427,97433,97435,97437,97449,97451,97457,97459,97467],{},[2272,97398,97399,97401],{},[898,97400,2774],{},[895,97402,97403,97405],{},[898,97404,42679],{},[898,97406,724],{},[1996,97408,1998],{},[1996,97410,2005],{"stretchy":2004},[9166,97412,97413,97415,97417],{},[898,97414,3937],{},[2129,97416,2131],{},[898,97418,4252],{},[1996,97420,2095],{},[898,97422,2774],{},[1996,97424,2011],{"stretchy":2004},[1996,97426,2225],{},[2124,97428,97429,97431],{},[898,97430,3937],{},[898,97432,4252],{},[1996,97434,2286],{"separator":2285},[5878,97436],{"width":5880},[2272,97438,97439,97441],{},[898,97440,2774],{},[895,97442,97443,97445,97447],{},[898,97444,42702],{},[898,97446,1994],{},[898,97448,12043],{},[1996,97450,1998],{},[2124,97452,97453,97455],{},[898,97454,3937],{},[898,97456,4252],{},[1996,97458,2225],{},[9166,97460,97461,97463,97465],{},[898,97462,3937],{},[2129,97464,2131],{},[898,97466,4252],{},[898,97468,1975],{"mathvariant":2376},[902,97470,97471],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,97473,97474],{},[614,97475,97476,97477,97507,97508,96360,97521,5669,97538,96391,97551,1975],{},"Obrázek 2.19: Posun ",[883,97478,97480],{"className":97479},[886],[888,97481,97482],{"xmlns":890},[892,97483,97484,97504],{},[895,97485,97486,97488,97490,97496,97498,97500,97502],{},[898,97487,4183],{},[1996,97489,3123],{},[2272,97491,97492,97494],{},[898,97493,4183],{},[2129,97495,2131],{},[1996,97497,1998],{},[898,97499,4183],{},[1996,97501,2225],{},[898,97503,2774],{},[902,97505,97506],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,97509,97511],{"className":97510},[886],[888,97512,97513],{"xmlns":890},[892,97514,97515,97519],{},[895,97516,97517],{},[898,97518,2774],{},[902,97520,2774],{"encoding":904},[883,97522,97524],{"className":97523},[886],[888,97525,97526],{"xmlns":890},[892,97527,97528,97536],{},[895,97529,97530],{},[2272,97531,97532,97534],{},[898,97533,4183],{},[2129,97535,2131],{},[902,97537,38329],{"encoding":904},[883,97539,97541],{"className":97540},[886],[888,97542,97543],{"xmlns":890},[892,97544,97545,97549],{},[895,97546,97547],{},[898,97548,8673],{},[902,97550,8673],{"encoding":904},[883,97552,97554],{"className":97553},[886],[888,97555,97556],{"xmlns":890},[892,97557,97558,97566],{},[895,97559,97560],{},[2272,97561,97562,97564],{},[898,97563,4252],{},[2129,97565,2131],{},[902,97567,97568],{"encoding":904},"E_2",[198,97570,45385],{"id":97571},"příklad-210",[724,97573,97574,97576,97577,41692,97600,97619,97620,97637],{},[38,97575,37935],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,97578,97580],{"className":97579},[886],[888,97581,97582],{"xmlns":890},[892,97583,97584,97598],{},[895,97585,97586,97588,97590,97592,97594,97596],{},[898,97587,3937],{},[1996,97589,1998],{},[2129,97591,3509],{},[1996,97593,2225],{},[2129,97595,2131],{},[898,97597,2789],{},[902,97599,96440],{"encoding":904},[883,97601,97603],{"className":97602},[886],[888,97604,97605],{"xmlns":890},[892,97606,97607,97617],{},[895,97608,97609,97611,97613,97615],{},[898,97610,3937],{},[1996,97612,1998],{},[2129,97614,2351],{},[898,97616,2789],{},[902,97618,96460],{"encoding":904},". Daň ",[883,97621,97623],{"className":97622},[886],[888,97624,97625],{"xmlns":890},[892,97626,97627,97635],{},[895,97628,97629,97631,97633],{},[898,97630,2774],{},[1996,97632,1998],{},[2129,97634,2235],{},[902,97636,41270],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,97639,97640],{},[38,97641,37967],{},[724,97643,97644,97645,96651],{},"Nová poptávka je ",[883,97646,97648],{"className":97647},[886],[888,97649,97650],{"xmlns":890},[892,97651,97652,97688],{},[895,97653,97654,97660,97662,97664,97666,97668,97670,97672,97674,97676,97678,97680,97682,97684,97686],{},[2272,97655,97656,97658],{},[898,97657,4183],{},[2129,97659,2131],{},[1996,97661,2704],{},[898,97663,3937],{},[1996,97665,1998],{},[2129,97667,3509],{},[1996,97669,2225],{},[2129,97671,2131],{},[898,97673,2789],{},[1996,97675,2225],{},[2129,97677,2235],{},[1996,97679,1998],{},[2129,97681,2235],{},[1996,97683,2225],{},[2129,97685,2131],{},[898,97687,2789],{},[902,97689,97690],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,97692,97694],{"className":97693},[886],[888,97695,97696],{"xmlns":890,"display":28068},[892,97697,97698,97714],{},[895,97699,97700,97702,97704,97706,97708,97710,97712],{},[2129,97701,2235],{},[1996,97703,2225],{},[2129,97705,2131],{},[898,97707,2789],{},[1996,97709,1998],{},[2129,97711,2351],{},[898,97713,2789],{},[902,97715,97716],{"encoding":904},"6 - 2Q = 4Q",[724,97718,96684,97719,5589,97738,1343,97762,96765,97794,1975],{},[883,97720,97722],{"className":97721},[886],[888,97723,97724],{"xmlns":890},[892,97725,97726,97736],{},[895,97727,97728,97730,97732,97734],{},[2129,97729,2235],{},[898,97731,2789],{},[1996,97733,1998],{},[2129,97735,2235],{},[902,97737,96704],{"encoding":904},[883,97739,97741],{"className":97740},[886],[888,97742,97743],{"xmlns":890},[892,97744,97745,97759],{},[895,97746,97747,97755,97757],{},[9166,97748,97749,97751,97753],{},[898,97750,2789],{},[2129,97752,2131],{},[898,97754,4252],{},[1996,97756,1998],{},[2129,97758,2278],{},[902,97760,97761],{"encoding":904},"Q_2^E = 1",[883,97763,97765],{"className":97764},[886],[888,97766,97767],{"xmlns":890},[892,97768,97769,97791],{},[895,97770,97771,97779,97781,97783,97785,97787,97789],{},[9166,97772,97773,97775,97777],{},[898,97774,3937],{},[2129,97776,2131],{},[898,97778,4252],{},[1996,97780,1998],{},[2129,97782,2351],{},[1996,97784,3177],{},[2129,97786,2278],{},[1996,97788,1998],{},[2129,97790,2351],{},[902,97792,97793],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,97795,97797],{"className":97796},[886],[888,97798,97799],{"xmlns":890},[892,97800,97801,97819],{},[895,97802,97803,97809,97811,97813,97815,97817],{},[2272,97804,97805,97807],{},[898,97806,4252],{},[2129,97808,2131],{},[1996,97810,2486],{"stretchy":2004},[2129,97812,2278],{},[1996,97814,2286],{"separator":2285},[2129,97816,2351],{},[1996,97818,2501],{"stretchy":2004},[902,97820,97821],{"encoding":904},"E_2[1, 4]",[724,97823,97824,97825,97861,97862,96479],{},"Spotřebitel platí celkem ",[883,97826,97828],{"className":97827},[886],[888,97829,97830],{"xmlns":890},[892,97831,97832,97858],{},[895,97833,97834,97842,97844,97846,97848,97850,97852,97854,97856],{},[9166,97835,97836,97838,97840],{},[898,97837,3937],{},[2129,97839,2131],{},[898,97841,4252],{},[1996,97843,2095],{},[898,97845,2774],{},[1996,97847,1998],{},[2129,97849,2351],{},[1996,97851,2095],{},[2129,97853,2235],{},[1996,97855,1998],{},[2129,97857,2863],{},[902,97859,97860],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,97863,97865],{"className":97864},[886],[888,97866,97867],{"xmlns":890},[892,97868,97869,97883],{},[895,97870,97871,97879,97881],{},[9166,97872,97873,97875,97877],{},[898,97874,3937],{},[2129,97876,2131],{},[898,97878,4252],{},[1996,97880,1998],{},[2129,97882,2351],{},[902,97884,97885],{"encoding":904},"P_2^E = 4",[724,97887,97888],{},[614,97889,97890],{},"Rozklad daňového břemene:",[883,97892,97894],{"className":97893},[886],[888,97895,97896],{"xmlns":890,"display":28068},[892,97897,97898,97984],{},[895,97899,97900,97910,97912,97914,97916,97918,97920,97922,97924,97926,97928,97930,97932,97942,97944,97946,97958,97960,97962,97964,97966,97968,97970,97972,97982],{},[2272,97901,97902,97904],{},[898,97903,2774],{},[895,97905,97906,97908],{},[898,97907,42679],{},[898,97909,724],{},[1996,97911,1998],{},[1996,97913,2005],{"stretchy":2004},[2129,97915,2351],{},[1996,97917,2095],{},[2129,97919,2235],{},[1996,97921,2011],{"stretchy":2004},[1996,97923,2225],{},[2129,97925,5585],{},[1996,97927,1998],{},[2129,97929,2131],{},[2288,97931,2290],{},[895,97933,97934,97936],{},[2288,97935,9800],{},[8386,97937,97938,97940],{"accent":2285},[2288,97939,2142],{},[1996,97941,25060],{},[1996,97943,2286],{"separator":2285},[5878,97945],{"width":5880},[2272,97947,97948,97950],{},[898,97949,2774],{},[895,97951,97952,97954,97956],{},[898,97953,42702],{},[898,97955,1994],{},[898,97957,12043],{},[1996,97959,1998],{},[2129,97961,5585],{},[1996,97963,2225],{},[2129,97965,2351],{},[1996,97967,1998],{},[2129,97969,2351],{},[2288,97971,2290],{},[895,97973,97974,97976],{},[2288,97975,9800],{},[8386,97977,97978,97980],{"accent":2285},[2288,97979,2142],{},[1996,97981,25060],{},[898,97983,1975],{"mathvariant":2376},[902,97985,97986],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,97988,97989,97990,1975],{},"Opět ",[883,97991,97993],{"className":97992},[886],[888,97994,97995],{"xmlns":890},[892,97996,97997,98031],{},[895,97998,97999,98009,98011,98023,98025,98027,98029],{},[2272,98000,98001,98003],{},[898,98002,2774],{},[895,98004,98005,98007],{},[898,98006,42679],{},[898,98008,724],{},[1996,98010,2095],{},[2272,98012,98013,98015],{},[898,98014,2774],{},[895,98016,98017,98019,98021],{},[898,98018,42702],{},[898,98020,1994],{},[898,98022,12043],{},[1996,98024,1998],{},[2129,98026,2235],{},[1996,98028,1998],{},[898,98030,2774],{},[902,98032,98033],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[36972,98035],{},[115,98037,42660],{"id":98038},"daňové-břemeno",[724,98040,98041,10025,98043,98046,98047,98060],{},[38,98042,42660],{},[614,98044,98045],{},"tax burden",") je rozdělení zaplacené daně ",[883,98048,98050],{"className":98049},[886],[888,98051,98052],{"xmlns":890},[892,98053,98054,98058],{},[895,98055,98056],{},[898,98057,2774],{},[902,98059,2774],{"encoding":904}," mezi spotřebitele a výrobce:",[883,98062,98064],{"className":98063},[886],[888,98065,98066],{"xmlns":890,"display":28068},[892,98067,98068,98100],{},[895,98069,98070,98072,98074,98084,98086,98098],{},[898,98071,2774],{},[1996,98073,1998],{},[2272,98075,98076,98078],{},[898,98077,2774],{},[895,98079,98080,98082],{},[898,98081,42679],{},[898,98083,724],{},[1996,98085,2095],{},[2272,98087,98088,98090],{},[898,98089,2774],{},[895,98091,98092,98094,98096],{},[898,98093,42702],{},[898,98095,1994],{},[898,98097,12043],{},[898,98099,1975],{"mathvariant":2376},[902,98101,98102],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,98104,98105],{},[2559,98106],{"alt":98107,"className":98108,"src":98109},"imek-dan-rozklad-bremene-sklony",[210,2563],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[3867,98111,98112],{},[724,98113,98114,98116,98117,3885,98130,1975],{},[883,98115,4155],{}," 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 ",[883,98118,98120],{"className":98119},[886],[888,98121,98122],{"xmlns":890},[892,98123,98124,98128],{},[895,98125,98126],{},[898,98127,4183],{},[902,98129,4183],{"encoding":904},[883,98131,98133],{"className":98132},[886],[888,98134,98135],{"xmlns":890},[892,98136,98137,98141],{},[895,98138,98139],{},[898,98140,8673],{},[902,98142,8673],{"encoding":904},[198,98144,2444],{"id":2443},[724,98146,98147,98148,98169,98170,98183,98184,98201,98202,98215],{},"V grafu ",[883,98149,98151],{"className":98150},[886],[888,98152,98153],{"xmlns":890},[892,98154,98155,98167],{},[895,98156,98157,98159,98161,98163,98165],{},[1996,98158,2005],{"stretchy":2004},[898,98160,2789],{},[1996,98162,2286],{"separator":2285},[898,98164,3937],{},[1996,98166,2011],{"stretchy":2004},[902,98168,37693],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,98171,98173],{"className":98172},[886],[888,98174,98175],{"xmlns":890},[892,98176,98177,98181],{},[895,98178,98179],{},[898,98180,2774],{},[902,98182,2774],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,98185,98187],{"className":98186},[886],[888,98188,98189],{"xmlns":890},[892,98190,98191,98199],{},[895,98192,98193],{},[2124,98194,98195,98197],{},[898,98196,3937],{},[898,98198,4252],{},[902,98200,41468],{"encoding":904},", rozdělí se úsečka ",[883,98203,98205],{"className":98204},[886],[888,98206,98207],{"xmlns":890},[892,98208,98209,98213],{},[895,98210,98211],{},[898,98212,2774],{},[902,98214,2774],{"encoding":904}," na dvě části:",[120,98217,98218,98243],{},[123,98219,98220,98221,98242],{},"horní část odpovídá ",[883,98222,98224],{"className":98223},[886],[888,98225,98226],{"xmlns":890},[892,98227,98228,98240],{},[895,98229,98230],{},[2272,98231,98232,98234],{},[898,98233,2774],{},[895,98235,98236,98238],{},[898,98237,42679],{},[898,98239,724],{},[902,98241,42684],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,98244,98245,98246,98269],{},"dolní část odpovídá ",[883,98247,98249],{"className":98248},[886],[888,98250,98251],{"xmlns":890},[892,98252,98253,98267],{},[895,98254,98255],{},[2272,98256,98257,98259],{},[898,98258,2774],{},[895,98260,98261,98263,98265],{},[898,98262,42702],{},[898,98264,1994],{},[898,98266,12043],{},[902,98268,42709],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,98271,98272],{},[614,98273,98274,98275,2685,98288,98309,98310,98333,98334,3885,98355,98378],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,98276,98278],{"className":98277},[886],[888,98279,98280],{"xmlns":890},[892,98281,98282,98286],{},[895,98283,98284],{},[898,98285,2774],{},[902,98287,2774],{"encoding":904},[883,98289,98291],{"className":98290},[886],[888,98292,98293],{"xmlns":890},[892,98294,98295,98307],{},[895,98296,98297],{},[2272,98298,98299,98301],{},[898,98300,2774],{},[895,98302,98303,98305],{},[898,98304,42679],{},[898,98306,724],{},[902,98308,42684],{"encoding":904}," (nahoře) a ",[883,98311,98313],{"className":98312},[886],[888,98314,98315],{"xmlns":890},[892,98316,98317,98331],{},[895,98318,98319],{},[2272,98320,98321,98323],{},[898,98322,2774],{},[895,98324,98325,98327,98329],{},[898,98326,42702],{},[898,98328,1994],{},[898,98330,12043],{},[902,98332,42709],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,98335,98337],{"className":98336},[886],[888,98338,98339],{"xmlns":890},[892,98340,98341,98353],{},[895,98342,98343],{},[2272,98344,98345,98347],{},[898,98346,2774],{},[895,98348,98349,98351],{},[898,98350,42679],{},[898,98352,724],{},[902,98354,42684],{"encoding":904},[883,98356,98358],{"className":98357},[886],[888,98359,98360],{"xmlns":890},[892,98361,98362,98376],{},[895,98363,98364],{},[2272,98365,98366,98368],{},[898,98367,2774],{},[895,98369,98370,98372,98374],{},[898,98371,42702],{},[898,98373,1994],{},[898,98375,12043],{},[902,98377,42709],{"encoding":904}," je v obou případech stejná.",[198,98380,98382],{"id":98381},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,98384,98385,98386,98389,98390,10025,98413,98430,98431,10025,98454,98471],{},"Platí obecně: ",[38,98387,98388],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,98391,98393],{"className":98392},[886],[888,98394,98395],{"xmlns":890},[892,98396,98397,98411],{},[895,98398,98399,98401,98403,98405,98407,98409],{},[898,98400,3937],{},[1996,98402,1998],{},[898,98404,207],{},[898,98406,2789],{},[1996,98408,2095],{},[898,98410,2098],{},[902,98412,37062],{"encoding":904},[883,98414,98416],{"className":98415},[886],[888,98417,98418],{"xmlns":890},[892,98419,98420,98428],{},[895,98421,98422,98424,98426],{},[898,98423,207],{},[1996,98425,3447],{},[2129,98427,2327],{},[902,98429,43087],{"encoding":904},") a lineární nabídku ",[883,98432,98434],{"className":98433},[886],[888,98435,98436],{"xmlns":890},[892,98437,98438,98452],{},[895,98439,98440,98442,98444,98446,98448,98450],{},[898,98441,3937],{},[1996,98443,1998],{},[898,98445,2142],{},[898,98447,2789],{},[1996,98449,2095],{},[898,98451,2194],{},[902,98453,40244],{"encoding":904},[883,98455,98457],{"className":98456},[886],[888,98458,98459],{"xmlns":890},[892,98460,98461,98469],{},[895,98462,98463,98465,98467],{},[898,98464,2142],{},[1996,98466,3408],{},[2129,98468,2327],{},[902,98470,40262],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,98473,98475],{"className":98474},[886],[888,98476,98477],{"xmlns":890,"display":28068},[892,98478,98479,98545],{},[895,98480,98481,98505,98507,98517,98519,98543],{},[2329,98482,98483,98493],{},[2272,98484,98485,98487],{},[898,98486,2774],{},[895,98488,98489,98491],{},[898,98490,42679],{},[898,98492,724],{},[2272,98494,98495,98497],{},[898,98496,2774],{},[895,98498,98499,98501,98503],{},[898,98500,42702],{},[898,98502,1994],{},[898,98504,12043],{},[1996,98506,1998],{},[2329,98508,98509,98511],{},[898,98510,2142],{},[895,98512,98513,98515],{},[1996,98514,2225],{},[898,98516,207],{},[1996,98518,1998],{},[2329,98520,98521,98533],{},[895,98522,98523,98526,98529,98531],{},[898,98524,98525],{"mathvariant":2376},"∣",[2288,98527,98528],{},"sklon ",[898,98530,8673],{},[898,98532,98525],{"mathvariant":2376},[895,98534,98535,98537,98539,98541],{},[898,98536,98525],{"mathvariant":2376},[2288,98538,98528],{},[898,98540,4183],{},[898,98542,98525],{"mathvariant":2376},[898,98544,1975],{"mathvariant":2376},[902,98546,98547],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[3867,98549,98550,98555],{},[724,98551,98552,98554],{},[883,98553,4572],{}," Postup výpočtu rozkladu",[152,98556,98557,98592,98645,98724],{},[123,98558,98559,98560,98591],{},"Spočti rovnovážný bod ",[883,98561,98563],{"className":98562},[886],[888,98564,98565],{"xmlns":890},[892,98566,98567,98589],{},[895,98568,98569,98571,98573,98579,98581,98587],{},[898,98570,4252],{},[1996,98572,2486],{"stretchy":2004},[2124,98574,98575,98577],{},[898,98576,2789],{},[898,98578,4252],{},[1996,98580,2286],{"separator":2285},[2124,98582,98583,98585],{},[898,98584,3937],{},[898,98586,4252],{},[1996,98588,2501],{"stretchy":2004},[902,98590,41369],{"encoding":904}," bez daně.",[123,98593,98594,98595,1348,98620,3918],{},"Urči posunutou křivku (",[883,98596,98598],{"className":98597},[886],[888,98599,98600],{"xmlns":890},[892,98601,98602,98618],{},[895,98603,98604,98610,98612,98614,98616],{},[2272,98605,98606,98608],{},[898,98607,8673],{},[2129,98609,2278],{},[1996,98611,1998],{},[898,98613,8673],{},[1996,98615,2095],{},[898,98617,2774],{},[902,98619,42756],{"encoding":904},[883,98621,98623],{"className":98622},[886],[888,98624,98625],{"xmlns":890},[892,98626,98627,98643],{},[895,98628,98629,98635,98637,98639,98641],{},[2272,98630,98631,98633],{},[898,98632,4183],{},[2129,98634,2131],{},[1996,98636,1998],{},[898,98638,4183],{},[1996,98640,2225],{},[898,98642,2774],{},[902,98644,42787],{"encoding":904},[123,98646,98647,98648,3910,98667,12130,98686,3910,98705,3918],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,98649,98651],{"className":98650},[886],[888,98652,98653],{"xmlns":890},[892,98654,98655,98665],{},[895,98656,98657],{},[9166,98658,98659,98661,98663],{},[898,98660,2789],{},[2129,98662,2278],{},[898,98664,4252],{},[902,98666,47838],{"encoding":904},[883,98668,98670],{"className":98669},[886],[888,98671,98672],{"xmlns":890},[892,98673,98674,98684],{},[895,98675,98676],{},[9166,98677,98678,98680,98682],{},[898,98679,2789],{},[2129,98681,2131],{},[898,98683,4252],{},[902,98685,47900],{"encoding":904},[883,98687,98689],{"className":98688},[886],[888,98690,98691],{"xmlns":890},[892,98692,98693,98703],{},[895,98694,98695],{},[9166,98696,98697,98699,98701],{},[898,98698,3937],{},[2129,98700,2278],{},[898,98702,4252],{},[902,98704,47859],{"encoding":904},[883,98706,98708],{"className":98707},[886],[888,98709,98710],{"xmlns":890},[892,98711,98712,98722],{},[895,98713,98714],{},[9166,98715,98716,98718,98720],{},[898,98717,3937],{},[2129,98719,2131],{},[898,98721,4252],{},[902,98723,47920],{"encoding":904},[123,98725,98726,98727,3885,98748,98771,98772,1975],{},"Dopočítej ",[883,98728,98730],{"className":98729},[886],[888,98731,98732],{"xmlns":890},[892,98733,98734,98746],{},[895,98735,98736],{},[2272,98737,98738,98740],{},[898,98739,2774],{},[895,98741,98742,98744],{},[898,98743,42679],{},[898,98745,724],{},[902,98747,42684],{"encoding":904},[883,98749,98751],{"className":98750},[886],[888,98752,98753],{"xmlns":890},[892,98754,98755,98769],{},[895,98756,98757],{},[2272,98758,98759,98761],{},[898,98760,2774],{},[895,98762,98763,98765,98767],{},[898,98764,42702],{},[898,98766,1994],{},[898,98768,12043],{},[902,98770,42709],{"encoding":904}," z definice, vždy ověř ",[883,98773,98775],{"className":98774},[886],[888,98776,98777],{"xmlns":890},[892,98778,98779,98809],{},[895,98780,98781,98791,98793,98805,98807],{},[2272,98782,98783,98785],{},[898,98784,2774],{},[895,98786,98787,98789],{},[898,98788,42679],{},[898,98790,724],{},[1996,98792,2095],{},[2272,98794,98795,98797],{},[898,98796,2774],{},[895,98798,98799,98801,98803],{},[898,98800,42702],{},[898,98802,1994],{},[898,98804,12043],{},[1996,98806,1998],{},[898,98808,2774],{},[902,98810,98811],{"encoding":904},"T_{sp} + T_{vyr} = T",[3867,98813,98814],{},[724,98815,98816,98818,98819,98822,98823,3885,98836,98849],{},[883,98817,4412],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,98820,98821],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,98824,98826],{"className":98825},[886],[888,98827,98828],{"xmlns":890},[892,98829,98830,98834],{},[895,98831,98832],{},[898,98833,4183],{},[902,98835,4183],{"encoding":904},[883,98837,98839],{"className":98838},[886],[888,98840,98841],{"xmlns":890},[892,98842,98843,98847],{},[895,98844,98845],{},[898,98846,8673],{},[902,98848,8673],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[36972,98851],{},[115,98853,98855],{"id":98854},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,98857,98858],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,98860,98861],{},[2559,98862],{"alt":98863,"className":98864,"src":98865},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,2563],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,98867,98868,98880],{},[19,98869,98870],{},[22,98871,98872,98874,98877],{},[25,98873,54298],{},[25,98875,98876],{},"(a) daň výrobci",[25,98878,98879],{},"(b) daň spotřebiteli",[30,98881,98882,98937,99004,99064],{},[22,98883,98884,98887,98912],{},[35,98885,98886],{},"Rovnovážné množství",[35,98888,98889],{},[883,98890,98892],{"className":98891},[886],[888,98893,98894],{"xmlns":890},[892,98895,98896,98910],{},[895,98897,98898,98906,98908],{},[9166,98899,98900,98902,98904],{},[898,98901,2789],{},[2129,98903,2278],{},[898,98905,4252],{},[1996,98907,1998],{},[2129,98909,2278],{},[902,98911,96728],{"encoding":904},[35,98913,98914],{},[883,98915,98917],{"className":98916},[886],[888,98918,98919],{"xmlns":890},[892,98920,98921,98935],{},[895,98922,98923,98931,98933],{},[9166,98924,98925,98927,98929],{},[898,98926,2789],{},[2129,98928,2131],{},[898,98930,4252],{},[1996,98932,1998],{},[2129,98934,2278],{},[902,98936,97761],{"encoding":904},[22,98938,98939,98942,98967],{},[35,98940,98941],{},"Cena placená spotřebitelem",[35,98943,98944],{},[883,98945,98947],{"className":98946},[886],[888,98948,98949],{"xmlns":890},[892,98950,98951,98965],{},[895,98952,98953,98961,98963],{},[9166,98954,98955,98957,98959],{},[898,98956,3937],{},[2129,98958,2278],{},[898,98960,4252],{},[1996,98962,1998],{},[2129,98964,2863],{},[902,98966,96823],{"encoding":904},[35,98968,98969],{},[883,98970,98972],{"className":98971},[886],[888,98973,98974],{"xmlns":890},[892,98975,98976,99002],{},[895,98977,98978,98986,98988,98990,98992,98994,98996,98998,99000],{},[9166,98979,98980,98982,98984],{},[898,98981,3937],{},[2129,98983,2131],{},[898,98985,4252],{},[1996,98987,2095],{},[898,98989,2774],{},[1996,98991,1998],{},[2129,98993,2351],{},[1996,98995,2095],{},[2129,98997,2235],{},[1996,98999,1998],{},[2129,99001,2863],{},[902,99003,97860],{"encoding":904},[22,99005,99006,99009,99039],{},[35,99007,99008],{},"Cena přijímaná výrobcem",[35,99010,99011],{},[883,99012,99014],{"className":99013},[886],[888,99015,99016],{"xmlns":890},[892,99017,99018,99036],{},[895,99019,99020,99028,99030,99032,99034],{},[9166,99021,99022,99024,99026],{},[898,99023,3937],{},[2129,99025,2278],{},[898,99027,4252],{},[1996,99029,2225],{},[898,99031,2774],{},[1996,99033,1998],{},[2129,99035,2351],{},[902,99037,99038],{"encoding":904},"P_1^E - T = 4",[35,99040,99041],{},[883,99042,99044],{"className":99043},[886],[888,99045,99046],{"xmlns":890},[892,99047,99048,99062],{},[895,99049,99050,99058,99060],{},[9166,99051,99052,99054,99056],{},[898,99053,3937],{},[2129,99055,2131],{},[898,99057,4252],{},[1996,99059,1998],{},[2129,99061,2351],{},[902,99063,97885],{"encoding":904},[22,99065,99066,99069,99123],{},[35,99067,99068],{},"Rozklad břemene",[35,99070,99071,1343,99096],{},[883,99072,99074],{"className":99073},[886],[888,99075,99076],{"xmlns":890},[892,99077,99078,99094],{},[895,99079,99080,99090,99092],{},[2272,99081,99082,99084],{},[898,99083,2774],{},[895,99085,99086,99088],{},[898,99087,42679],{},[898,99089,724],{},[1996,99091,1998],{},[2129,99093,2131],{},[902,99095,42978],{"encoding":904},[883,99097,99099],{"className":99098},[886],[888,99100,99101],{"xmlns":890},[892,99102,99103,99121],{},[895,99104,99105,99117,99119],{},[2272,99106,99107,99109],{},[898,99108,2774],{},[895,99110,99111,99113,99115],{},[898,99112,42702],{},[898,99114,1994],{},[898,99116,12043],{},[1996,99118,1998],{},[2129,99120,2351],{},[902,99122,43007],{"encoding":904},[35,99124,99125,1343,99150],{},[883,99126,99128],{"className":99127},[886],[888,99129,99130],{"xmlns":890},[892,99131,99132,99148],{},[895,99133,99134,99144,99146],{},[2272,99135,99136,99138],{},[898,99137,2774],{},[895,99139,99140,99142],{},[898,99141,42679],{},[898,99143,724],{},[1996,99145,1998],{},[2129,99147,2131],{},[902,99149,42978],{"encoding":904},[883,99151,99153],{"className":99152},[886],[888,99154,99155],{"xmlns":890},[892,99156,99157,99175],{},[895,99158,99159,99171,99173],{},[2272,99160,99161,99163],{},[898,99162,2774],{},[895,99164,99165,99167,99169],{},[898,99166,42702],{},[898,99168,1994],{},[898,99170,12043],{},[1996,99172,1998],{},[2129,99174,2351],{},[902,99176,43007],{"encoding":904},[724,99178,99179],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,99181,99183],{"className":99182},[886],[888,99184,99185],{"xmlns":890,"display":28068},[892,99186,99187,99235],{},[895,99188,99189,99197,99199,99207,99209,99211,99219,99221,99223,99225,99233],{},[9166,99190,99191,99193,99195],{},[898,99192,2789],{},[2129,99194,2278],{},[898,99196,4252],{},[1996,99198,1998],{},[9166,99200,99201,99203,99205],{},[898,99202,2789],{},[2129,99204,2131],{},[898,99206,4252],{},[1996,99208,2286],{"separator":2285},[5878,99210],{"width":5880},[9166,99212,99213,99215,99217],{},[898,99214,3937],{},[2129,99216,2278],{},[898,99218,4252],{},[1996,99220,2225],{},[898,99222,2774],{},[1996,99224,1998],{},[9166,99226,99227,99229,99231],{},[898,99228,3937],{},[2129,99230,2131],{},[898,99232,4252],{},[898,99234,1975],{"mathvariant":2376},[902,99236,99237],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[3867,99239,99240,99259,99413],{},[724,99241,99242,99244,99245,99258],{},[883,99243,4572],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,99246,99248],{"className":99247},[886],[888,99249,99250],{"xmlns":890},[892,99251,99252,99256],{},[895,99253,99254],{},[898,99255,2774],{},[902,99257,2774],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,99260,99261,99293,99329,99366],{},[123,99262,99263,99264,2286],{},"rovnovážná množství obou režimů, ",[883,99265,99267],{"className":99266},[886],[888,99268,99269],{"xmlns":890},[892,99270,99271,99291],{},[895,99272,99273,99281,99283],{},[9166,99274,99275,99277,99279],{},[898,99276,2789],{},[2129,99278,2278],{},[898,99280,4252],{},[1996,99282,1998],{},[9166,99284,99285,99287,99289],{},[898,99286,2789],{},[2129,99288,2131],{},[898,99290,4252],{},[902,99292,42910],{"encoding":904},[123,99294,99295,99296,2286],{},"čistá cena přijímaná výrobcem, ",[883,99297,99299],{"className":99298},[886],[888,99300,99301],{"xmlns":890},[892,99302,99303,99327],{},[895,99304,99305,99313,99315,99317,99319],{},[9166,99306,99307,99309,99311],{},[898,99308,3937],{},[2129,99310,2278],{},[898,99312,4252],{},[1996,99314,2225],{},[898,99316,2774],{},[1996,99318,1998],{},[9166,99320,99321,99323,99325],{},[898,99322,3937],{},[2129,99324,2131],{},[898,99326,4252],{},[902,99328,42944],{"encoding":904},[123,99330,99331,99332,2286],{},"celková cena placená spotřebitelem, ",[883,99333,99335],{"className":99334},[886],[888,99336,99337],{"xmlns":890},[892,99338,99339,99363],{},[895,99340,99341,99349,99351,99359,99361],{},[9166,99342,99343,99345,99347],{},[898,99344,3937],{},[2129,99346,2278],{},[898,99348,4252],{},[1996,99350,1998],{},[9166,99352,99353,99355,99357],{},[898,99354,3937],{},[2129,99356,2131],{},[898,99358,4252],{},[1996,99360,2095],{},[898,99362,2774],{},[902,99364,99365],{"encoding":904},"P_1^E = P_2^E + T",[123,99367,99368,99369,3885,99390,1975],{},"rozklad daňového břemene ",[883,99370,99372],{"className":99371},[886],[888,99373,99374],{"xmlns":890},[892,99375,99376,99388],{},[895,99377,99378],{},[2272,99379,99380,99382],{},[898,99381,2774],{},[895,99383,99384,99386],{},[898,99385,42679],{},[898,99387,724],{},[902,99389,42684],{"encoding":904},[883,99391,99393],{"className":99392},[886],[888,99394,99395],{"xmlns":890},[892,99396,99397,99411],{},[895,99398,99399],{},[2272,99400,99401,99403],{},[898,99402,2774],{},[895,99404,99405,99407,99409],{},[898,99406,42702],{},[898,99408,1994],{},[898,99410,12043],{},[902,99412,42709],{"encoding":904},[724,99414,99415,99416,1975],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,99417,35199],{},[724,99419,99420,99421,3885,99434,3918],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,99422,99424],{"className":99423},[886],[888,99425,99426],{"xmlns":890},[892,99427,99428,99432],{},[895,99429,99430],{},[898,99431,4183],{},[902,99433,4183],{"encoding":904},[883,99435,99437],{"className":99436},[886],[888,99438,99439],{"xmlns":890},[892,99440,99441,99445],{},[895,99442,99443],{},[898,99444,8673],{},[902,99446,8673],{"encoding":904},[36972,99448],{},[115,99450,99452],{"id":99451},"úlohy","Úlohy",[724,99454,99455,99456,3151],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,99457,16241],{"className":99458,"dataFsResolvedFilePath":800,"href":801},[210],[120,99460,99461,99491,99522],{},[123,99462,99463,99466,99467,99490],{},[38,99464,99465],{},"Úloha 2.4"," — Poptávka ",[883,99468,99470],{"className":99469},[886],[888,99471,99472],{"xmlns":890},[892,99473,99474,99488],{},[895,99475,99476,99478,99480,99482,99484,99486],{},[898,99477,3937],{},[1996,99479,1998],{},[2129,99481,3509],{},[1996,99483,2225],{},[2129,99485,2131],{},[898,99487,2789],{},[902,99489,96440],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,99492,99493,99496,99497,99521],{},[38,99494,99495],{},"Úloha 2.9"," — Nabídka ",[883,99498,99500],{"className":99499},[886],[888,99501,99502],{"xmlns":890},[892,99503,99504,99518],{},[895,99505,99506,99508,99510,99512,99514,99516],{},[898,99507,3937],{},[1996,99509,1998],{},[2129,99511,5009],{},[898,99513,2789],{},[1996,99515,2095],{},[2129,99517,36246],{},[902,99519,99520],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,99523,99524,99527,99528,3885,99554,99578,99579,99596],{},[38,99525,99526],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,99529,99531],{"className":99530},[886],[888,99532,99533],{"xmlns":890},[892,99534,99535,99551],{},[895,99536,99537,99539,99541,99543,99545,99547,99549],{},[898,99538,3937],{},[1996,99540,1998],{},[1996,99542,2225],{},[2129,99544,2351],{},[898,99546,2789],{},[1996,99548,2095],{},[2129,99550,46705],{},[902,99552,99553],{"encoding":904},"P = -4Q + 80",[883,99555,99557],{"className":99556},[886],[888,99558,99559],{"xmlns":890},[892,99560,99561,99575],{},[895,99562,99563,99565,99567,99569,99571,99573],{},[898,99564,3937],{},[1996,99566,1998],{},[2129,99568,2173],{},[898,99570,2789],{},[1996,99572,2095],{},[2129,99574,2863],{},[902,99576,99577],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,99580,99582],{"className":99581},[886],[888,99583,99584],{"xmlns":890},[892,99585,99586,99594],{},[895,99587,99588,99590,99592],{},[898,99589,2774],{},[1996,99591,1998],{},[2129,99593,24203],{},[902,99595,47817],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,99598,99599,99600,99602,99603,99605],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,99601,45230],{}," (posun poptávky při zdanění kupujícího) a ",[38,99604,45264],{}," (posun nabídky při zdanění výrobce).",[36972,99607],{},[115,99609,15722],{"id":15721},[120,99611,99612,99631,99689,99746,99829,99875,99918,99963,100029],{},[123,99613,99614,2203,99617,99630],{},[38,99615,99616],{},"Jednotková daň",[883,99618,99620],{"className":99619},[886],[888,99621,99622],{"xmlns":890},[892,99623,99624,99628],{},[895,99625,99626],{},[898,99627,2774],{},[902,99629,2774],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,99632,99633,99635,99636,99674,99675,99688],{},[38,99634,96022],{}," — posun nabídky ",[883,99637,99639],{"className":99638},[886],[888,99640,99641],{"xmlns":890},[892,99642,99643,99671],{},[895,99644,99645,99651,99653,99655,99657,99659,99661,99663,99665,99667,99669],{},[2272,99646,99647,99649],{},[898,99648,8673],{},[2129,99650,2278],{},[1996,99652,2005],{"stretchy":2004},[898,99654,2789],{},[1996,99656,2011],{"stretchy":2004},[1996,99658,1998],{},[898,99660,8673],{},[1996,99662,2005],{"stretchy":2004},[898,99664,2789],{},[1996,99666,2011],{"stretchy":2004},[1996,99668,2095],{},[898,99670,2774],{},[902,99672,99673],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,99676,99678],{"className":99677},[886],[888,99679,99680],{"xmlns":890},[892,99681,99682,99686],{},[895,99683,99684],{},[898,99685,2774],{},[902,99687,2774],{"encoding":904}," svisle nahoru)",[123,99690,99691,99693,99694,99674,99732,99745],{},[38,99692,97095],{}," — posun poptávky ",[883,99695,99697],{"className":99696},[886],[888,99698,99699],{"xmlns":890},[892,99700,99701,99729],{},[895,99702,99703,99709,99711,99713,99715,99717,99719,99721,99723,99725,99727],{},[2272,99704,99705,99707],{},[898,99706,4183],{},[2129,99708,2131],{},[1996,99710,2005],{"stretchy":2004},[898,99712,2789],{},[1996,99714,2011],{"stretchy":2004},[1996,99716,1998],{},[898,99718,4183],{},[1996,99720,2005],{"stretchy":2004},[898,99722,2789],{},[1996,99724,2011],{"stretchy":2004},[1996,99726,2225],{},[898,99728,2774],{},[902,99730,99731],{"encoding":904},"D_2(Q) = D(Q) - T",[883,99733,99735],{"className":99734},[886],[888,99736,99737],{"xmlns":890},[892,99738,99739,99743],{},[895,99740,99741],{},[898,99742,2774],{},[902,99744,2774],{"encoding":904}," svisle dolů)",[123,99747,99748,7015,99751,41816,99790],{},[38,99749,99750],{},"Rovnovážný bod s daní",[883,99752,99754],{"className":99753},[886],[888,99755,99756],{"xmlns":890},[892,99757,99758,99788],{},[895,99759,99760,99766,99768,99776,99778,99786],{},[2272,99761,99762,99764],{},[898,99763,4252],{},[2129,99765,2278],{},[1996,99767,2486],{"stretchy":2004},[9166,99769,99770,99772,99774],{},[898,99771,2789],{},[2129,99773,2278],{},[898,99775,4252],{},[1996,99777,2286],{"separator":2285},[9166,99779,99780,99782,99784],{},[898,99781,3937],{},[2129,99783,2278],{},[898,99785,4252],{},[1996,99787,2501],{"stretchy":2004},[902,99789,96190],{"encoding":904},[883,99791,99793],{"className":99792},[886],[888,99794,99795],{"xmlns":890},[892,99796,99797,99827],{},[895,99798,99799,99805,99807,99815,99817,99825],{},[2272,99800,99801,99803],{},[898,99802,4252],{},[2129,99804,2131],{},[1996,99806,2486],{"stretchy":2004},[9166,99808,99809,99811,99813],{},[898,99810,2789],{},[2129,99812,2131],{},[898,99814,4252],{},[1996,99816,2286],{"separator":2285},[9166,99818,99819,99821,99823],{},[898,99820,3937],{},[2129,99822,2131],{},[898,99824,4252],{},[1996,99826,2501],{"stretchy":2004},[902,99828,97265],{"encoding":904},[123,99830,99831,10025,99833,99835,99836],{},[38,99832,42660],{},[614,99834,98045],{},") — rozklad ",[883,99837,99839],{"className":99838},[886],[888,99840,99841],{"xmlns":890},[892,99842,99843,99873],{},[895,99844,99845,99847,99849,99859,99861],{},[898,99846,2774],{},[1996,99848,1998],{},[2272,99850,99851,99853],{},[898,99852,2774],{},[895,99854,99855,99857],{},[898,99856,42679],{},[898,99858,724],{},[1996,99860,2095],{},[2272,99862,99863,99865],{},[898,99864,2774],{},[895,99866,99867,99869,99871],{},[898,99868,42702],{},[898,99870,1994],{},[898,99872,12043],{},[902,99874,42846],{"encoding":904},[123,99876,99877,99900,99901,2011],{},[38,99878,99879],{},[883,99880,99882],{"className":99881},[886],[888,99883,99884],{"xmlns":890},[892,99885,99886,99898],{},[895,99887,99888],{},[2272,99889,99890,99892],{},[898,99891,2774],{},[895,99893,99894,99896],{},[898,99895,42679],{},[898,99897,724],{},[902,99899,42684],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,99902,99904],{"className":99903},[886],[888,99905,99906],{"xmlns":890},[892,99907,99908,99916],{},[895,99909,99910],{},[2124,99911,99912,99914],{},[898,99913,3937],{},[898,99915,4252],{},[902,99917,41468],{"encoding":904},[123,99919,99920,99945,99946,2011],{},[38,99921,99922],{},[883,99923,99925],{"className":99924},[886],[888,99926,99927],{"xmlns":890},[892,99928,99929,99943],{},[895,99930,99931],{},[2272,99932,99933,99935],{},[898,99934,2774],{},[895,99936,99937,99939,99941],{},[898,99938,42702],{},[898,99940,1994],{},[898,99942,12043],{},[902,99944,42709],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,99947,99949],{"className":99948},[886],[888,99950,99951],{"xmlns":890},[892,99952,99953,99961],{},[895,99954,99955],{},[2124,99956,99957,99959],{},[898,99958,3937],{},[898,99960,4252],{},[902,99962,41468],{"encoding":904},[123,99964,99965,7015,99967,1343,99996],{},[38,99966,50476],{},[883,99968,99970],{"className":99969},[886],[888,99971,99972],{"xmlns":890},[892,99973,99974,99994],{},[895,99975,99976,99984,99986],{},[9166,99977,99978,99980,99982],{},[898,99979,2789],{},[2129,99981,2278],{},[898,99983,4252],{},[1996,99985,1998],{},[9166,99987,99988,99990,99992],{},[898,99989,2789],{},[2129,99991,2131],{},[898,99993,4252],{},[902,99995,42910],{"encoding":904},[883,99997,99999],{"className":99998},[886],[888,100000,100001],{"xmlns":890},[892,100002,100003,100027],{},[895,100004,100005,100013,100015,100017,100019],{},[9166,100006,100007,100009,100011],{},[898,100008,3937],{},[2129,100010,2278],{},[898,100012,4252],{},[1996,100014,2225],{},[898,100016,2774],{},[1996,100018,1998],{},[9166,100020,100021,100023,100025],{},[898,100022,3937],{},[2129,100024,2131],{},[898,100026,4252],{},[902,100028,42944],{"encoding":904},[123,100030,100031,100034],{},[38,100032,100033],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[36972,100036],{},[115,100038,3792],{"id":3791},[120,100040,100041,100049,100067,100074],{},[123,100042,100043,2203,100046],{},[38,100044,100045],{},"Kontext (hub):",[207,100047,802],{"className":100048,"dataFsResolvedFilePath":800,"href":801},[210],[123,100050,100051,2203,100053,100056,100057,18650,100059,100062,100063,100066],{},[38,100052,50725],{},[207,100054,820],{"className":100055,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,100058,55036],{},[207,100060,2357],{"className":100061,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,100064,3828],{"className":100065,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[123,100068,100069,2203,100071],{},[38,100070,50760],{},[207,100072,50764],{"className":100073,"dataFsResolvedFilePath":745,"href":746},[210],[123,100075,100076,2203,100078],{},[38,100077,16206],{},[207,100079,16210],{"className":100080,"dataFsResolvedFilePath":1960,"href":1961},[210],{"title":641,"searchDepth":642,"depth":642,"links":100082},[100083,100084,100087,100090,100094,100095,100096,100097],{"id":95927,"depth":642,"text":95928},{"id":96021,"depth":642,"text":96022,"children":100085},[100086],{"id":96412,"depth":649,"text":45305},{"id":97094,"depth":642,"text":97095,"children":100088},[100089],{"id":97571,"depth":649,"text":45385},{"id":98038,"depth":642,"text":42660,"children":100091},[100092,100093],{"id":2443,"depth":649,"text":2444},{"id":98381,"depth":649,"text":98382},{"id":98854,"depth":642,"text":98855},{"id":99451,"depth":642,"text":99452},{"id":15721,"depth":642,"text":15722},{"id":3791,"depth":642,"text":3792},{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":95825,"description":641},[1138,1135],"topics\u002Fzdaneni-trhu",[1128,50825,100104,100105,100106,16241],"dane","danove-bremeno","posun-krivek","cFuKqHgzIrqvY-l4jNdqjFEM7_ixjw33HOL0So8cPn0",1777154859724]