[{"data":1,"prerenderedAt":103722},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-is-lm":1626,"course-stats-imek":5988,"course-topics-imek":5992,"backlinks-is-lm":103704,"related-is-lm":103713},{"courses":4,"counts":1622},[5,679,1148],{"id":6,"title":7,"body":8,"course":658,"courseName":659,"courses":659,"created":660,"description":641,"examInfo":659,"extension":661,"featured":662,"garant":659,"meta":663,"navigation":664,"path":665,"seo":666,"sources":667,"stem":669,"tags":670,"type":676,"updated":677,"__hash__":678},"courses\u002Fcourses\u002Fimork.md","Management oborových řešení (ImorK)",{"type":9,"value":10,"toc":640},"minimark",[11,15,114,119,147,151,193,197,202,251,255,338,342,371,375,395,399,455,459,533,537,548,552,604,608],[12,13,7],"h1",{"id":14},"management-oborových-řešení-imork",[16,17,18,29],"table",{},[19,20,21],"thead",{},[22,23,24,27],"tr",{},[25,26],"th",{},[25,28],{},[30,31,32,44,54,64,74,84,94,104],"tbody",{},[22,33,34,41],{},[35,36,37],"td",{},[38,39,40],"strong",{},"Zkratka",[35,42,43],{},"ImorK",[22,45,46,51],{},[35,47,48],{},[38,49,50],{},"Fakulta",[35,52,53],{},"Fakulta podnikatelská, VUT v Brně",[22,55,56,61],{},[35,57,58],{},[38,59,60],{},"Semestr",[35,62,63],{},"letní 2025\u002F2026",[22,65,66,71],{},[35,67,68],{},[38,69,70],{},"Ukončení",[35,72,73],{},"zkouška",[22,75,76,81],{},[35,77,78],{},[38,79,80],{},"Garant",[35,82,83],{},"Ing. Lukáš Novák, Ph.D.",[22,85,86,91],{},[35,87,88],{},[38,89,90],{},"Vyučující",[35,92,93],{},"Ing. Petr Sedlák",[22,95,96,101],{},[35,97,98],{},[38,99,100],{},"Ústav",[35,102,103],{},"Ústav informatiky",[22,105,106,111],{},[35,107,108],{},[38,109,110],{},"Prerekvizita",[35,112,113],{},"Management informační bezpečnosti (ImibePA)",[115,116,118],"h2",{"id":117},"cíle-předmětu","Cíle předmětu",[120,121,122,129,135,141],"ul",{},[123,124,125,126],"li",{},"Znalosti o specifických problémech a odlišnostech při ",[38,127,128],{},"oborovém řešení informační bezpečnosti",[123,130,131,132],{},"Porozumění jednotlivých řešení na úrovni ",[38,133,134],{},"případových studií",[123,136,137,138],{},"Přehled o rozdílných aspektech v závislosti na oborové řešení ",[38,139,140],{},"ISMS",[123,142,143,144],{},"Metodika pro budování bezpečných IS na bázi norem řady ",[38,145,146],{},"ISO\u002FIEC 27000",[115,148,150],{"id":149},"osnova","Osnova",[152,153,154,157,160,163,166,169,172,175,178,181,184,187,190],"ol",{},[123,155,156],{},"Bezpečnost v kyberprostoru",[123,158,159],{},"Budování bezpečnostního povědomí — SAE",[123,161,162],{},"Manažerská informační bezpečnost",[123,164,165],{},"Problematika GDPR",[123,167,168],{},"ISMS v ISVS",[123,170,171],{},"ISMS v univerzitním prostředí",[123,173,174],{},"ISMS ve zdravotnictví",[123,176,177],{},"ISMS v energetice",[123,179,180],{},"ISMS poskytovatelů konektivity (ISP)",[123,182,183],{},"Bezpečnost konvergovaných sítí",[123,185,186],{},"Řízení bezpečnosti www aplikací",[123,188,189],{},"Řízení bezpečnosti mailových aplikací",[123,191,192],{},"Řízení mobilní bezpečnosti",[115,194,196],{"id":195},"shrnutí-zdrojů","Shrnutí zdrojů",[198,199,201],"h3",{"id":200},"přednášky","Přednášky",[120,203,204,215,224,233,242],{},[123,205,206,214],{},[207,208,213],"a",{"className":209,"dataFsResolvedFilePath":211,"href":212},[210],"wikilink","summaries\u002Fimork-detail-predmetu.md","\u002Fwiki\u002Fimork-detail-predmetu","Detail předmětu"," — sylabus kurzu, hodnocení, literatura",[123,216,217,223],{},[207,218,222],{"className":219,"dataFsResolvedFilePath":220,"href":221},[210],"summaries\u002Fimork-manazerska-bezpecnost.md","\u002Fwiki\u002Fimork-manazerska-bezpecnost","Manažerská bezpečnost"," — governance, SIEM, log management, bezpečnostní role",[123,225,226,232],{},[207,227,231],{"className":228,"dataFsResolvedFilePath":229,"href":230},[210],"summaries\u002Fimork-bezpecnostni-strategie.md","\u002Fwiki\u002Fimork-bezpecnostni-strategie","Bezpečnostní strategie"," — tvorba a implementace bezpečnostní strategie",[123,234,235,241],{},[207,236,240],{"className":237,"dataFsResolvedFilePath":238,"href":239},[210],"summaries\u002Fimork-sae.md","\u002Fwiki\u002Fimork-sae","SAE"," — budování bezpečnostního povědomí (NIST SP 800-50\u002F16)",[123,243,244,250],{},[207,245,249],{"className":246,"dataFsResolvedFilePath":247,"href":248},[210],"summaries\u002Fimork-risk-management.md","\u002Fwiki\u002Fimork-risk-management","Risk Management"," — ISO 31000, ISO 27005, RTP, PoA\u002FSoA",[198,252,254],{"id":253},"oborová-isms","Oborová ISMS",[120,256,257,266,275,284,293,302,311,320,329],{},[123,258,259,265],{},[207,260,264],{"className":261,"dataFsResolvedFilePath":262,"href":263},[210],"summaries\u002Fimork-akademicke-prostredi.md","\u002Fwiki\u002Fimork-akademicke-prostredi","Akademické prostředí"," — kampus, WiFi, identita, VIS",[123,267,268,274],{},[207,269,273],{"className":270,"dataFsResolvedFilePath":271,"href":272},[210],"summaries\u002Fimork-financni-sektor.md","\u002Fwiki\u002Fimork-financni-sektor","Finanční sektor"," — DORA, MiCA, DLT\u002Fblockchain",[123,276,277,283],{},[207,278,282],{"className":279,"dataFsResolvedFilePath":280,"href":281},[210],"summaries\u002Fimork-zdravotnictvi.md","\u002Fwiki\u002Fimork-zdravotnictvi","Zdravotnictví"," — HIPAA, ISO 27799, PACS, DICOM, eHealth",[123,285,286,292],{},[207,287,291],{"className":288,"dataFsResolvedFilePath":289,"href":290},[210],"summaries\u002Fimork-energetika.md","\u002Fwiki\u002Fimork-energetika","Energetika"," — ISO 27019, IEC 61850, PLC\u002FSBC\u002FRTU",[123,294,295,301],{},[207,296,300],{"className":297,"dataFsResolvedFilePath":298,"href":299},[210],"summaries\u002Fimork-smart-grid.md","\u002Fwiki\u002Fimork-smart-grid","Smart Grid"," — NISTIR 7628, IEC 62351, prosumers",[123,303,304,310],{},[207,305,309],{"className":306,"dataFsResolvedFilePath":307,"href":308},[210],"summaries\u002Fimork-doprava.md","\u002Fwiki\u002Fimork-doprava","Doprava (železnice)"," — CLC\u002FTS 50701, kritická infrastruktura",[123,312,313,319],{},[207,314,318],{"className":315,"dataFsResolvedFilePath":316,"href":317},[210],"summaries\u002Fimork-automotive.md","\u002Fwiki\u002Fimork-automotive","Automotive"," — CAN bus, TISAX, UN Reg. 155",[123,321,322,328],{},[207,323,327],{"className":324,"dataFsResolvedFilePath":325,"href":326},[210],"summaries\u002Fimork-isp.md","\u002Fwiki\u002Fimork-isp","ISP\u002Ftelekomunikace"," — ISO 27011, NGN, 5G bezpečnost",[123,330,331,337],{},[207,332,336],{"className":333,"dataFsResolvedFilePath":334,"href":335},[210],"summaries\u002Fimork-mcn.md","\u002Fwiki\u002Fimork-mcn","Mission Critical Networks"," — NCPI, model hrozeb, dostupnost",[198,339,341],{"id":340},"bezpečnost-aplikací-a-dat","Bezpečnost aplikací a dat",[120,343,344,353,362],{},[123,345,346,352],{},[207,347,351],{"className":348,"dataFsResolvedFilePath":349,"href":350},[210],"summaries\u002Fimork-www.md","\u002Fwiki\u002Fimork-www","Bezpečnost webu"," — OWASP, SQL injection, XSS, Solid",[123,354,355,361],{},[207,356,360],{"className":357,"dataFsResolvedFilePath":358,"href":359},[210],"summaries\u002Fimork-email.md","\u002Fwiki\u002Fimork-email","Bezpečnost emailu"," — SPF, DKIM, DMARC, S\u002FMIME, šifrování",[123,363,364,370],{},[207,365,369],{"className":366,"dataFsResolvedFilePath":367,"href":368},[210],"summaries\u002Fimork-ochrana-dat.md","\u002Fwiki\u002Fimork-ochrana-dat","Ochrana dat"," — NAC, IDS\u002FIPS, SIEM, DLP, IPv6",[198,372,374],{"id":373},"kontinuita-a-obnova","Kontinuita a obnova",[120,376,377,386],{},[123,378,379,385],{},[207,380,384],{"className":381,"dataFsResolvedFilePath":382,"href":383},[210],"summaries\u002Fimork-bcm.md","\u002Fwiki\u002Fimork-bcm","BCM"," — ISO 22301, BIA, STEEPLE, PDCA",[123,387,388,394],{},[207,389,393],{"className":390,"dataFsResolvedFilePath":391,"href":392},[210],"summaries\u002Fimork-dr.md","\u002Fwiki\u002Fimork-dr","Disaster Recovery"," — RPO\u002FRTO, cloud DR, 7 tiers, DRaaS",[198,396,398],{"id":397},"kybernetické-útoky","Kybernetické útoky",[120,400,401,410,419,428,437,446],{},[123,402,403,409],{},[207,404,408],{"className":405,"dataFsResolvedFilePath":406,"href":407},[210],"summaries\u002Fimork-anatomie-utoku.md","\u002Fwiki\u002Fimork-anatomie-utoku","Anatomie útoku"," — APT, vektory, exploit\u002Fpayload",[123,411,412,418],{},[207,413,417],{"className":414,"dataFsResolvedFilePath":415,"href":416},[210],"summaries\u002Fimork-ai-utoky.md","\u002Fwiki\u002Fimork-ai-utoky","AI útoky"," — WormGPT, BEC, phishing",[123,420,421,427],{},[207,422,426],{"className":423,"dataFsResolvedFilePath":424,"href":425},[210],"summaries\u002Fimork-sitove-utoky.md","\u002Fwiki\u002Fimork-sitove-utoky","Síťové útoky"," — DDoS, spoofing, Emotet→Trickbot→Ryuk",[123,429,430,436],{},[207,431,435],{"className":432,"dataFsResolvedFilePath":433,"href":434},[210],"summaries\u002Fimork-ransomware.md","\u002Fwiki\u002Fimork-ransomware","Ransomware"," — historie 1989–2024, RaaS, NISTIR 8374, IR plán",[123,438,439,445],{},[207,440,444],{"className":441,"dataFsResolvedFilePath":442,"href":443},[210],"summaries\u002Fimork-rizeny-hacking.md","\u002Fwiki\u002Fimork-rizeny-hacking","Řízený hacking \u002F APT"," — APT skupiny, informační válka, OSINT",[123,447,448,454],{},[207,449,453],{"className":450,"dataFsResolvedFilePath":451,"href":452},[210],"summaries\u002Fimork-internetova-bezpecnost.md","\u002Fwiki\u002Fimork-internetova-bezpecnost","Internetová bezpečnost"," — kyberprostor, OSINT, behaviorální biometrika",[198,456,458],{"id":457},"případové-studie","Případové studie",[120,460,461,470,479,488,497,506,515,524],{},[123,462,463,469],{},[207,464,468],{"className":465,"dataFsResolvedFilePath":466,"href":467},[210],"summaries\u002Fimork-nemocnice.md","\u002Fwiki\u002Fimork-nemocnice","Útoky na nemocnice"," — Benešov (70M Kč), FN Brno (350M Kč), Nymburk",[123,471,472,478],{},[207,473,477],{"className":474,"dataFsResolvedFilePath":475,"href":476},[210],"summaries\u002Fimork-kradez-dat.md","\u002Fwiki\u002Fimork-kradez-dat","Krádež dat"," — PII, černý trh, IoT botnety, ISO 27701, GDPR",[123,480,481,487],{},[207,482,486],{"className":483,"dataFsResolvedFilePath":484,"href":485},[210],"summaries\u002Fimork-sprava-login.md","\u002Fwiki\u002Fimork-sprava-login","Správa login"," — privilegované účty, NIST SP 800-63, biometrika",[123,489,490,496],{},[207,491,495],{"className":492,"dataFsResolvedFilePath":493,"href":494},[210],"summaries\u002Fimork-ehealth.md","\u002Fwiki\u002Fimork-ehealth","eHealth"," — elektronizace zdravotnictví, telemedicína, NSeZ",[123,498,499,505],{},[207,500,504],{"className":501,"dataFsResolvedFilePath":502,"href":503},[210],"summaries\u002Fimork-tor.md","\u002Fwiki\u002Fimork-tor","TOR"," — anonymizace, onion routing, NSA X-Keyscore",[123,507,508,514],{},[207,509,513],{"className":510,"dataFsResolvedFilePath":511,"href":512},[210],"summaries\u002Fimork-payment.md","\u002Fwiki\u002Fimork-payment","Bezpečnost plateb"," — PCI DSS v4.0, NFC\u002Ftokenizace, EMV, darknet",[123,516,517,523],{},[207,518,522],{"className":519,"dataFsResolvedFilePath":520,"href":521},[210],"summaries\u002Fimork-mobilni-bezpecnost.md","\u002Fwiki\u002Fimork-mobilni-bezpecnost","Mobilní bezpečnost"," — SIMJaker, SIM swapping, 5G, Common Criteria",[123,525,526,532],{},[207,527,531],{"className":528,"dataFsResolvedFilePath":529,"href":530},[210],"summaries\u002Fimork-audio-hack.md","\u002Fwiki\u002Fimork-audio-hack","Audio Hack"," — fyzická zranitelnost HDD, CVE-2022-38392, rezonanční útok",[198,534,536],{"id":535},"další","Další",[120,538,539],{},[123,540,541,547],{},[207,542,546],{"className":543,"dataFsResolvedFilePath":544,"href":545},[210],"summaries\u002Fimork-digitalni-identita.md","\u002Fwiki\u002Fimork-digitalni-identita","Digitální identita a stopa"," — online identita, footprint",[115,549,551],{"id":550},"témata","Témata",[120,553,554,562,571,580,588,596],{},[123,555,556,561],{},[207,557,140],{"className":558,"dataFsResolvedFilePath":559,"href":560},[210],"topics\u002Fisms.md","\u002Fwiki\u002Fisms"," — systém řízení bezpečnosti informací",[123,563,564,570],{},[207,565,569],{"className":566,"dataFsResolvedFilePath":567,"href":568},[210],"topics\u002Frizeni-rizik.md","\u002Fwiki\u002Frizeni-rizik","Řízení rizik"," — proces identifikace a ošetření rizik",[123,572,573,579],{},[207,574,578],{"className":575,"dataFsResolvedFilePath":576,"href":577},[210],"topics\u002Fkyberneticka-bezpecnost.md","\u002Fwiki\u002Fkyberneticka-bezpecnost","Kybernetická bezpečnost"," — hrozby, útoky, obrana",[123,581,582,587],{},[207,583,240],{"className":584,"dataFsResolvedFilePath":585,"href":586},[210],"topics\u002Fsae.md","\u002Fwiki\u002Fsae"," — budování bezpečnostního povědomí",[123,589,590,595],{},[207,591,384],{"className":592,"dataFsResolvedFilePath":593,"href":594},[210],"topics\u002Fbcm.md","\u002Fwiki\u002Fbcm"," — řízení kontinuity činnosti",[123,597,598,603],{},[207,599,369],{"className":600,"dataFsResolvedFilePath":601,"href":602},[210],"topics\u002Fochrana-dat.md","\u002Fwiki\u002Fochrana-dat"," — technologická řešení ochrany",[115,605,607],{"id":606},"doporučená-literatura","Doporučená literatura",[120,609,610,618,625,631,634,637],{},[123,611,612,613,617],{},"JORDÁN, V. a ONDRÁK, V.: ",[614,615,616],"em",{},"Integrovaná podniková infrastruktura."," Brno: CERM, 2016. ISBN 978-80-214-5241-1",[123,619,620,621,624],{},"SEDLÁK, P. a KONEČNÝ, M.: ",[614,622,623],{},"Přeměna ISMS v manažerské informatice."," Brno: CERM, 2023. ISBN 978-80-7623-110-8",[123,626,620,627,630],{},[614,628,629],{},"Kybernetická (ne)bezpečnost."," Brno: CERM, 2021. ISBN 978-80-7623-068-2",[123,632,633],{},"ČSN EN ISO\u002FIEC 27011 — Bezpečnost pro telekomunikační organizace",[123,635,636],{},"ČSN EN ISO\u002FIEC 27019 — Bezpečnost pro energetický průmysl",[123,638,639],{},"ČSN EN ISO\u002FIEC 27799 — Bezpečnost ve zdravotnictví",{"title":641,"searchDepth":642,"depth":642,"links":643},"",2,[644,645,646,656,657],{"id":117,"depth":642,"text":118},{"id":149,"depth":642,"text":150},{"id":195,"depth":642,"text":196,"children":647},[648,650,651,652,653,654,655],{"id":200,"depth":649,"text":201},3,{"id":253,"depth":649,"text":254},{"id":340,"depth":649,"text":341},{"id":373,"depth":649,"text":374},{"id":397,"depth":649,"text":398},{"id":457,"depth":649,"text":458},{"id":535,"depth":649,"text":536},{"id":550,"depth":642,"text":551},{"id":606,"depth":642,"text":607},"imork",null,"2026-04-12","md",false,{},true,"\u002Fcourses\u002Fimork",{"title":7,"description":641},[668],"raw\u002Fimork\u002FDetail předmětu.md","courses\u002Fimork",[658,671,672,673,674,675],"isms","informacni-bezpecnost","kyberneticka-bezpecnost","oborova-reseni","iso-27000","course","2026-04-25","6MdSdXZJ3FNW9uPHrGzZPucQlKskWh23itOKhDSZfGs",{"id":680,"title":681,"body":682,"course":1128,"courseName":659,"courses":659,"created":1129,"description":641,"examInfo":659,"extension":661,"featured":662,"garant":659,"meta":1130,"navigation":664,"path":1131,"seo":1132,"sources":1133,"stem":1139,"tags":1140,"type":676,"updated":677,"__hash__":1147},"courses\u002Fcourses\u002Fimek.md","Matematická ekonomie (ImeK)",{"type":9,"value":683,"toc":1112},[684,687,719,723,731,735,738,748,831,841,861,871,947,951,962,966,969,994,1000,1011,1017,1020,1024,1061,1065,1068,1072],[12,685,681],{"id":686},"matematická-ekonomie-imek",[120,688,689,695,701,707,713],{},[123,690,691,694],{},[38,692,693],{},"Fakulta:"," FP VUT",[123,696,697,700],{},[38,698,699],{},"Garant:"," doc. RNDr. Bedřich Půža, CSc.",[123,702,703,706],{},[38,704,705],{},"Vyučující (kombinované studium):"," Mgr. Martina Bobalová, Ph.D.",[123,708,709,712],{},[38,710,711],{},"Ukončení:"," zkouška (písemná 60 min + ústní ~10 min)",[123,714,715,718],{},[38,716,717],{},"Semestr:"," letní 2025\u002F2026",[115,720,722],{"id":721},"cíl-předmětu","Cíl předmětu",[724,725,726,727,730],"p",{},"Hlouběji proniknout do kauzální podstaty ekonomických vztahů, rozvoj schopnosti vyjadřovat ekonomické vztahy ",[38,728,729],{},"exaktními prostředky"," a provádět jejich analýzy. Matematické modelování mikroekonomie a makroekonomie pomocí prostředků inženýrské matematiky (derivace, integrály, Lagrangeova metoda).",[115,732,734],{"id":733},"obsah-kurzu","Obsah kurzu",[724,736,737],{},"Kurz je v kombinovaném studiu rozčleněn do tří přednáškových bloků:",[198,739,741,742],{"id":740},"blok-1-kalkul-poptávkanabídka-příjemnákladyzisk","Blok 1 — ",[207,743,747],{"className":744,"dataFsResolvedFilePath":745,"href":746},[210],"summaries\u002Fimek-blok-01.md","\u002Fwiki\u002Fimek-blok-01","Kalkul, poptávka\u002Fnabídka, příjem\u002Fnáklady\u002Fzisk",[120,749,750,759,768,777,786,795,804,813,822],{},[123,751,752,758],{},[207,753,757],{"className":754,"dataFsResolvedFilePath":755,"href":756},[210],"topics\u002Fzaklady-matematicke-ekonomie.md","\u002Fwiki\u002Fzaklady-matematicke-ekonomie","Základy matematické ekonomie"," — model, endogenní\u002Fexogenní proměnné, ceteris paribus, komparativní statika",[123,760,761,767],{},[207,762,766],{"className":763,"dataFsResolvedFilePath":764,"href":765},[210],"topics\u002Fderivace.md","\u002Fwiki\u002Fderivace","Derivace, diferenciál a extrémy 1D"," — geometrická a inženýrská interpretace, mezní veličiny",[123,769,770,776],{},[207,771,775],{"className":772,"dataFsResolvedFilePath":773,"href":774},[210],"topics\u002Fintegral.md","\u002Fwiki\u002Fintegral","Integrál"," — neurčitý a určitý, rekonstrukce TR z MR a TC z MC",[123,778,779,785],{},[207,780,784],{"className":781,"dataFsResolvedFilePath":782,"href":783},[210],"topics\u002Ffunkce-vice-promennych.md","\u002Fwiki\u002Ffunkce-vice-promennych","Funkce více proměnných"," — parciální derivace, diferenciál 2D, implicitní funkce, volné extrémy",[123,787,788,794],{},[207,789,793],{"className":790,"dataFsResolvedFilePath":791,"href":792},[210],"topics\u002Flagrangeova-metoda.md","\u002Fwiki\u002Flagrangeova-metoda","Lagrangeova metoda"," — vázané extrémy, multiplikátor jako náklady příležitosti",[123,796,797,803],{},[207,798,802],{"className":799,"dataFsResolvedFilePath":800,"href":801},[210],"topics\u002Fpoptavka-nabidka.md","\u002Fwiki\u002Fpoptavka-nabidka","Poptávka, nabídka a tržní rovnováha"," — modely D a S, rovnováha, multiplikátory",[123,805,806,812],{},[207,807,811],{"className":808,"dataFsResolvedFilePath":809,"href":810},[210],"topics\u002Fzdaneni-trhu.md","\u002Fwiki\u002Fzdaneni-trhu","Zdanění trhu"," — daň výrobci vs. spotřebiteli, rozklad daňového břemene, ekvivalence",[123,814,815,821],{},[207,816,820],{"className":817,"dataFsResolvedFilePath":818,"href":819},[210],"topics\u002Fprebytek-spotrebitele-vyrobce.md","\u002Fwiki\u002Fprebytek-spotrebitele-vyrobce","Přebytek spotřebitele a výrobce"," — CS, PS, plochy pod\u002Fnad křivkami",[123,823,824,830],{},[207,825,829],{"className":826,"dataFsResolvedFilePath":827,"href":828},[210],"topics\u002Fprijem-naklady-zisk.md","\u002Fwiki\u002Fprijem-naklady-zisk","Příjem, náklady a zisk"," — TR, AR, MR, TC, AC, MC, body zvratu, konstrukce nabídky firmy",[198,832,834,835],{"id":833},"blok-2-elasticita-a-produkce","Blok 2 — ",[207,836,840],{"className":837,"dataFsResolvedFilePath":838,"href":839},[210],"summaries\u002Fimek-blok-02.md","\u002Fwiki\u002Fimek-blok-02","Elasticita a produkce",[120,842,843,852],{},[123,844,845,851],{},[207,846,850],{"className":847,"dataFsResolvedFilePath":848,"href":849},[210],"topics\u002Felasticita.md","\u002Fwiki\u002Felasticita","Cenová, křížová a důchodová elasticita"," (jedno- i vícefaktorový model)",[123,853,854,860],{},[207,855,859],{"className":856,"dataFsResolvedFilePath":857,"href":858},[210],"topics\u002Fprodukce.md","\u002Fwiki\u002Fprodukce","Produkční funkce"," — Cobb-Douglasova, CES, lineární, Leontiefova, izokvanty, MRTS, Eulerova věta",[198,862,864,865],{"id":863},"blok-3-užitečnost-a-národní-důchod","Blok 3 — ",[207,866,870],{"className":867,"dataFsResolvedFilePath":868,"href":869},[210],"summaries\u002Fimek-blok-03.md","\u002Fwiki\u002Fimek-blok-03","Užitečnost a národní důchod",[120,872,873,906,929,938],{},[123,874,875,881,882,905],{},[207,876,880],{"className":877,"dataFsResolvedFilePath":878,"href":879},[210],"topics\u002Fuzitecnost.md","\u002Fwiki\u002Fuzitecnost","Užitečnost"," — pojem, mezní užitečnost, Cobb-Douglasova ",[883,884,887],"span",{"className":885},[886],"katex",[888,889,891],"math",{"xmlns":890},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[892,893,894,901],"semantics",{},[895,896,897],"mrow",{},[898,899,900],"mi",{},"U",[902,903,900],"annotation",{"encoding":904},"application\u002Fx-tex",", indiferenční křivky, MRCS",[123,907,908,914,915,928],{},[207,909,913],{"className":910,"dataFsResolvedFilePath":911,"href":912},[210],"topics\u002Foptimalizace-spotrebitele.md","\u002Fwiki\u002Foptimalizace-spotrebitele","Optimalizace spotřebitele"," — Lagrangeova maximalizace ",[883,916,918],{"className":917},[886],[888,919,920],{"xmlns":890},[892,921,922,926],{},[895,923,924],{},[898,925,900],{},[902,927,900],{"encoding":904},", duální minimalizace výdajů, Marshallova\u002FHicksova poptávka",[123,930,931,937],{},[207,932,936],{"className":933,"dataFsResolvedFilePath":934,"href":935},[210],"topics\u002Fnarodni-duchod.md","\u002Fwiki\u002Fnarodni-duchod","Národní důchod"," — GNP, spotřeba\u002Fúspory, MPC\u002FMPS, modely C-I, C-I-G, C-I-G-X",[123,939,940,946],{},[207,941,945],{"className":942,"dataFsResolvedFilePath":943,"href":944},[210],"topics\u002Fis-lm.md","\u002Fwiki\u002Fis-lm","IS-LM analýza"," — simultánní rovnováha trhu zboží a peněz, fiskální\u002Fmonetární politika",[115,948,950],{"id":949},"reference-a-přehledy","Reference a přehledy",[120,952,953],{},[123,954,955,961],{},[207,956,960],{"className":957,"dataFsResolvedFilePath":958,"href":959},[210],"outputs\u002Fimek-vzorce-prehled.md","\u002Fwiki\u002Fimek-vzorce-prehled","Kompletní přehled vzorců"," — všechny klíčové vzorce kurzu v definičním tvaru, se zdrojem a intuicí. Referenční list pro přípravu na zkoušku.",[115,963,965],{"id":964},"hodnocení-zkoušky","Hodnocení zkoušky",[724,967,968],{},"Písemná část (60 min) — 4 úlohy:",[152,970,971,977,983,989],{},[123,972,973,974],{},"Rozhodovací úloha o ekonomické funkci — ",[38,975,976],{},"10 bodů",[123,978,979,980],{},"Definice, formulace vlastnosti, interpretace ekonomické veličiny — ",[38,981,982],{},"20 bodů",[123,984,985,986],{},"Výpočetní úloha — ",[38,987,988],{},"30 bodů",[123,990,985,991],{},[38,992,993],{},"40 bodů",[724,995,996,999],{},[38,997,998],{},"Dílčí podmínky"," (nutné pro A–E):",[120,1001,1002,1005,1008],{},[123,1003,1004],{},"≥ 11 bodů ze součtu úloh 1 a 2",[123,1006,1007],{},"≥ 10 bodů z úlohy 3",[123,1009,1010],{},"≥ 10 bodů z úlohy 4",[724,1012,1013,1016],{},[38,1014,1015],{},"Stupnice:"," A (90–100), B (80–89), C (70–79), D (60–69), E (50–59), F (0–49 nebo nesplnění podmínek).",[724,1018,1019],{},"Doporučeno mít kalkulátor.",[115,1021,1023],{"id":1022},"literatura","Literatura",[120,1025,1026,1033,1040,1047,1054],{},[123,1027,1028,1029,1032],{},"I. Mezník, ",[614,1030,1031],{},"Úvod do matematické ekonomie pro ekonomy",", FP VUT \u002F CERM, Brno 2017 (CZ)",[123,1034,1035,1036,1039],{},"A.C. Chiang, ",[614,1037,1038],{},"Fundamental Methods of Mathematical Economics",", McGraw-Hill, 1984",[123,1041,1042,1043,1046],{},"J.U. Koch, L.A. Ostrosky, ",[614,1044,1045],{},"Introduction to Mathematical Economics",", McGraw-Hill, 1994",[123,1048,1049,1050,1053],{},"C.J. McKenna, R. Rees, ",[614,1051,1052],{},"Economics: A Mathematical Introduction",", Oxford UP, 1992",[123,1055,1056,1057,1060],{},"J. Jacques, ",[614,1058,1059],{},"Mathematics for Economics and Business",", Addison-Wesley, 1995",[115,1062,1064],{"id":1063},"prerekvizity","Prerekvizity",[724,1066,1067],{},"Standardní kurz inženýrské matematiky, mikroekonomie a makroekonomie na bakalářské úrovni.",[115,1069,1071],{"id":1070},"přehled-zdrojů","Přehled zdrojů",[120,1073,1074,1082,1089,1096,1103],{},[123,1075,1076,1081],{},[207,1077,213],{"className":1078,"dataFsResolvedFilePath":1079,"href":1080},[210],"summaries\u002Fimek-detail-predmetu.md","\u002Fwiki\u002Fimek-detail-predmetu"," — sylabus a administrativní informace",[123,1083,1084,1088],{},[207,1085,1087],{"className":1086,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok"," — 57 stran, matematický aparát + mikroekonomie",[123,1090,1091,1095],{},[207,1092,1094],{"className":1093,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok"," — 19 stran, elasticita a produkce",[123,1097,1098,1102],{},[207,1099,1101],{"className":1100,"dataFsResolvedFilePath":868,"href":869},[210],"KS 3. blok"," — 25 stran, užitečnost a národní důchod",[123,1104,1105,1111],{},[207,1106,1110],{"className":1107,"dataFsResolvedFilePath":1108,"href":1109},[210],"summaries\u002Fimek-kniha.md","\u002Fwiki\u002Fimek-kniha","Kniha Mezník — Úvod do matematické ekonomie"," — naskenované kap. 2–7 (107 stran), kompletní teorie + Příklady + Úlohy k samostatnému řešení",{"title":641,"searchDepth":642,"depth":642,"links":1113},[1114,1115,1123,1124,1125,1126,1127],{"id":721,"depth":642,"text":722},{"id":733,"depth":642,"text":734,"children":1116},[1117,1119,1121],{"id":740,"depth":649,"text":1118},"Blok 1 — Kalkul, poptávka\u002Fnabídka, příjem\u002Fnáklady\u002Fzisk",{"id":833,"depth":649,"text":1120},"Blok 2 — Elasticita a produkce",{"id":863,"depth":649,"text":1122},"Blok 3 — Užitečnost a národní důchod",{"id":949,"depth":642,"text":950},{"id":964,"depth":642,"text":965},{"id":1022,"depth":642,"text":1023},{"id":1063,"depth":642,"text":1064},{"id":1070,"depth":642,"text":1071},"imek","2026-04-20",{},"\u002Fcourses\u002Fimek",{"title":681,"description":641},[1134,1135,1136,1137,1138],"raw\u002Fimek\u002FDetail předmětu.md","raw\u002Fimek\u002FKS_prvni_blok.pdf","raw\u002Fimek\u002FKS_druhy_blok.pdf","raw\u002Fimek\u002FKS_treti_blok.pdf","raw\u002Fimek\u002Fkniha_scanned\u002F","courses\u002Fimek",[1128,1141,1142,1143,1144,1145,1146],"ekonomie","mikroekonomie","makroekonomie","lagrange","derivace","integraly","x73RNX_N_uAS3i63VHeCgVFPJa4tJKL2z8kq4DIN24M",{"id":1149,"title":1150,"body":1151,"course":1601,"courseName":659,"courses":659,"created":1602,"description":641,"examInfo":659,"extension":661,"featured":662,"garant":659,"meta":1603,"navigation":664,"path":1604,"seo":1605,"sources":1606,"stem":1612,"tags":1613,"type":676,"updated":677,"__hash__":1621},"courses\u002Fcourses\u002Fipmrk.md","Pokročilé metody v rozhodování (IpmrK)",{"type":9,"value":1152,"toc":1593},[1153,1156,1230,1232,1235,1237,1321,1325,1354,1358,1423,1425,1474,1476],[12,1154,1150],{"id":1155},"pokročilé-metody-v-rozhodování-ipmrk",[16,1157,1158,1166],{},[19,1159,1160],{},[22,1161,1162,1164],{},[25,1163],{},[25,1165],{},[30,1167,1168,1177,1186,1195,1203,1211,1221],{},[22,1169,1170,1174],{},[35,1171,1172],{},[38,1173,40],{},[35,1175,1176],{},"IpmrK",[22,1178,1179,1183],{},[35,1180,1181],{},[38,1182,50],{},[35,1184,1185],{},"Fakulta podnikatelská VUT v Brně",[22,1187,1188,1192],{},[35,1189,1190],{},[38,1191,80],{},[35,1193,1194],{},"prof. Ing. Petr Dostál, CSc.",[22,1196,1197,1201],{},[35,1198,1199],{},[38,1200,100],{},[35,1202,103],{},[22,1204,1205,1209],{},[35,1206,1207],{},[38,1208,60],{},[35,1210,63],{},[22,1212,1213,1218],{},[35,1214,1215],{},[38,1216,1217],{},"Jazyk",[35,1219,1220],{},"čeština",[22,1222,1223,1227],{},[35,1224,1225],{},[38,1226,70],{},[35,1228,1229],{},"zkouška (písemný test 0–20 bodů, ECTS) + seminární práce (8–12 stran)",[115,1231,722],{"id":721},[724,1233,1234],{},"Seznámit se s pokročilými a nestandardními metodami analytických a simulačních technik v ekonomii a financích. Důraz na teorii i aplikaci do manažerské praxe.",[115,1236,150],{"id":149},[152,1238,1239,1242,1251,1257,1263,1271,1277,1285,1290,1298,1306,1315,1318],{},[123,1240,1241],{},"Úvod",[123,1243,1244,1250],{},[207,1245,1249],{"className":1246,"dataFsResolvedFilePath":1247,"href":1248},[210],"topics\u002Ffuzzy-logika.md","\u002Fwiki\u002Ffuzzy-logika","Fuzzy logika"," — teorie",[123,1252,1253,1256],{},[207,1254,1249],{"className":1255,"dataFsResolvedFilePath":1247,"href":1248},[210]," + aplikace — Excel",[123,1258,1259,1262],{},[207,1260,1249],{"className":1261,"dataFsResolvedFilePath":1247,"href":1248},[210]," — aplikace MATLAB",[123,1264,1265,1250],{},[207,1266,1270],{"className":1267,"dataFsResolvedFilePath":1268,"href":1269},[210],"topics\u002Fumele-neuronove-site.md","\u002Fwiki\u002Fumele-neuronove-site","Umělé neuronové sítě",[123,1272,1273,1276],{},[207,1274,1270],{"className":1275,"dataFsResolvedFilePath":1268,"href":1269},[210]," + aplikace MATLAB",[123,1278,1279,1250],{},[207,1280,1284],{"className":1281,"dataFsResolvedFilePath":1282,"href":1283},[210],"topics\u002Fgeneticke-algoritmy.md","\u002Fwiki\u002Fgeneticke-algoritmy","Genetické algoritmy",[123,1286,1287,1276],{},[207,1288,1284],{"className":1289,"dataFsResolvedFilePath":1282,"href":1283},[210],[123,1291,1292],{},[207,1293,1297],{"className":1294,"dataFsResolvedFilePath":1295,"href":1296},[210],"topics\u002Fteorie-chaosu.md","\u002Fwiki\u002Fteorie-chaosu","Teorie chaosu",[123,1299,1300],{},[207,1301,1305],{"className":1302,"dataFsResolvedFilePath":1303,"href":1304},[210],"topics\u002Fdatamining.md","\u002Fwiki\u002Fdatamining","Datamining",[123,1307,1308,1314],{},[207,1309,1313],{"className":1310,"dataFsResolvedFilePath":1311,"href":1312},[210],"topics\u002Fpredikce.md","\u002Fwiki\u002Fpredikce","Predikce",", kapitálový trh",[123,1316,1317],{},"Řízení výroby a řízení rizik",[123,1319,1320],{},"Rozhodování",[115,1322,1324],{"id":1323},"hodnocení","Hodnocení",[120,1326,1327,1333],{},[123,1328,1329,1332],{},[38,1330,1331],{},"Zkouška",": písemný test, 0–20 bodů. A: 20–18, B: 17–16, C: 15–14, D: 13–12, E: 11–10, F: 9–0.",[123,1334,1335,1338,1339,1343,1344,1348,1349,1353],{},[38,1336,1337],{},"Seminární práce",": 8–12 stran, individuální zaměření na problematiku z praxe, řešení pomocí ",[207,1340,1342],{"className":1341,"dataFsResolvedFilePath":1247,"href":1248},[210],"fuzzy logiky",", ",[207,1345,1347],{"className":1346,"dataFsResolvedFilePath":1268,"href":1269},[210],"umělých neuronových sítí"," nebo ",[207,1350,1352],{"className":1351,"dataFsResolvedFilePath":1282,"href":1283},[210],"genetických algoritmů",". Nutná úspěšná obhajoba.",[115,1355,1357],{"id":1356},"hlavní-témata","Hlavní témata",[120,1359,1360,1366,1372,1378,1387,1393,1402,1408,1417],{},[123,1361,1362,1365],{},[207,1363,1249],{"className":1364,"dataFsResolvedFilePath":1247,"href":1248},[210]," — modelování rozhodování s vágními pojmy",[123,1367,1368,1371],{},[207,1369,1270],{"className":1370,"dataFsResolvedFilePath":1268,"href":1269},[210]," — učení z dat, klasifikace, predikce",[123,1373,1374,1377],{},[207,1375,1284],{"className":1376,"dataFsResolvedFilePath":1282,"href":1283},[210]," — evoluční optimalizace",[123,1379,1380,1386],{},[207,1381,1385],{"className":1382,"dataFsResolvedFilePath":1383,"href":1384},[210],"topics\u002Fevolucni-algoritmy.md","\u002Fwiki\u002Fevolucni-algoritmy","Evoluční algoritmy"," — metaheuristiky, rojové algoritmy, prohledávací metody",[123,1388,1389,1392],{},[207,1390,1297],{"className":1391,"dataFsResolvedFilePath":1295,"href":1296},[210]," — nelineární dynamické systémy",[123,1394,1395,1401],{},[207,1396,1400],{"className":1397,"dataFsResolvedFilePath":1398,"href":1399},[210],"topics\u002Foptimalizace.md","\u002Fwiki\u002Foptimalizace","Optimalizace"," — hledání minima\u002Fmaxima, MATLAB Optimization Toolbox",[123,1403,1404,1407],{},[207,1405,1305],{"className":1406,"dataFsResolvedFilePath":1303,"href":1304},[210]," — dolování z dat, klastrování, rozhodovací stromy, Witness Miner",[123,1409,1410,1416],{},[207,1411,1415],{"className":1412,"dataFsResolvedFilePath":1413,"href":1414},[210],"topics\u002Fanfis.md","\u002Fwiki\u002Fanfis","ANFIS"," — hybridní propojení fuzzy logiky a neuronových sítí",[123,1418,1419,1422],{},[207,1420,1313],{"className":1421,"dataFsResolvedFilePath":1311,"href":1312},[210]," — prognózování časových řad v ekonomii a financích",[115,1424,607],{"id":606},[120,1426,1427,1434,1440,1447,1454,1460,1467],{},[123,1428,1429,1430,1433],{},"DOSTÁL, P. ",[614,1431,1432],{},"Pokročilé metody analýz a modelování v podnikatelství a veřejné správě",", CERM, 2008",[123,1435,1429,1436,1439],{},[614,1437,1438],{},"Advanced Decision making in Business and Public Services",", CERM, 2011",[123,1441,1442,1443,1446],{},"DOSTÁL, P., RAIS, K., SOJKA, Z. ",[614,1444,1445],{},"Pokročilé metody manažerského rozhodování",", Grada, 2005",[123,1448,1449,1450,1453],{},"ALTROCK, C. ",[614,1451,1452],{},"Fuzzy Logic & Neurofuzzy",", 1996",[123,1455,1456,1457,1453],{},"GATELY, E. ",[614,1458,1459],{},"Neural Network for Financial Forecasting",[123,1461,1462,1463,1466],{},"DAVIS, L. ",[614,1464,1465],{},"Handbook of Genetic Algorithms",", 1991",[123,1468,1469,1470,1473],{},"PETERS, E. ",[614,1471,1472],{},"Fractal Market Analysis",", 1994",[115,1475,196],{"id":195},[120,1477,1478,1486,1495,1504,1513,1522,1531,1540,1549,1557,1566,1575,1584],{},[123,1479,1480,1485],{},[207,1481,213],{"className":1482,"dataFsResolvedFilePath":1483,"href":1484},[210],"summaries\u002Fipmrk-detail-predmetu.md","\u002Fwiki\u002Fipmrk-detail-predmetu"," — základní informace o kurzu",[123,1487,1488,1494],{},[207,1489,1493],{"className":1490,"dataFsResolvedFilePath":1491,"href":1492},[210],"summaries\u002Fipmrk-fuzzy-excel.md","\u002Fwiki\u002Fipmrk-fuzzy-excel","Fuzzy logika — Excel"," — princip fuzzy logiky, funkce členství, pravidla, implementace",[123,1496,1497,1503],{},[207,1498,1502],{"className":1499,"dataFsResolvedFilePath":1500,"href":1501},[210],"summaries\u002Fipmrk-fuzzy-matlab.md","\u002Fwiki\u002Fipmrk-fuzzy-matlab","Fuzzy logika — MATLAB"," — architektura fuzzy systému, návrh modelu",[123,1505,1506,1512],{},[207,1507,1511],{"className":1508,"dataFsResolvedFilePath":1509,"href":1510},[210],"summaries\u002Fipmrk-nn-teorie.md","\u002Fwiki\u002Fipmrk-nn-teorie","Neuronové sítě — teorie"," — perceptron, aktivační funkce, backpropagation",[123,1514,1515,1521],{},[207,1516,1520],{"className":1517,"dataFsResolvedFilePath":1518,"href":1519},[210],"summaries\u002Fipmrk-nn-vypocet.md","\u002Fwiki\u002Fipmrk-nn-vypocet","Neuronové sítě — výpočet"," — ruční učení neuronu, vícevrstvé sítě, trénování",[123,1523,1524,1530],{},[207,1525,1529],{"className":1526,"dataFsResolvedFilePath":1527,"href":1528},[210],"summaries\u002Fipmrk-nn-aplikace.md","\u002Fwiki\u002Fipmrk-nn-aplikace","Neuronové sítě — aplikace"," — ANFIS, scoring, predikce, deep learning",[123,1532,1533,1539],{},[207,1534,1538],{"className":1535,"dataFsResolvedFilePath":1536,"href":1537},[210],"summaries\u002Fipmrk-ga-teorie.md","\u002Fwiki\u002Fipmrk-ga-teorie","Genetické algoritmy — teorie"," — chromozomy, selekce, křížení, mutace",[123,1541,1542,1548],{},[207,1543,1547],{"className":1544,"dataFsResolvedFilePath":1545,"href":1546},[210],"summaries\u002Fipmrk-ga-vyuziti.md","\u002Fwiki\u002Fipmrk-ga-vyuziti","Genetické algoritmy — využití"," — optimalizace, TSP, knapsack, klastrování",[123,1550,1551,1556],{},[207,1552,1297],{"className":1553,"dataFsResolvedFilePath":1554,"href":1555},[210],"summaries\u002Fipmrk-chaos.md","\u002Fwiki\u002Fipmrk-chaos"," — atraktory, fraktály, motýlí efekt, Hurstův exponent",[123,1558,1559,1565],{},[207,1560,1564],{"className":1561,"dataFsResolvedFilePath":1562,"href":1563},[210],"summaries\u002Fipmrk-kniha.md","\u002Fwiki\u002Fipmrk-kniha","Kniha — Pokročilé metody"," — celá učebnice, 7 kapitol, kontrolní otázky, nová témata (evoluční alg., optimalizace, datamining)",[123,1567,1568,1574],{},[207,1569,1573],{"className":1570,"dataFsResolvedFilePath":1571,"href":1572},[210],"summaries\u002Fipmrk-evolucni-algoritmy.md","\u002Fwiki\u002Fipmrk-evolucni-algoritmy","Evoluční algoritmy — principy a přehled"," — pseudokódy, vzorce SA\u002FTabu\u002FACO\u002FPSO\u002FDE\u002FSOMA\u002FAIS\u002FABC\u002FGSO",[123,1576,1577,1583],{},[207,1578,1582],{"className":1579,"dataFsResolvedFilePath":1580,"href":1581},[210],"summaries\u002Fipmrk-optimalizace.md","\u002Fwiki\u002Fipmrk-optimalizace","Optimalizace — MATLAB Optimization Toolbox"," — kompletní syntaxe fmincon\u002Ffminsearch\u002Flinprog\u002Fintlinprog\u002Fga",[123,1585,1586,1592],{},[207,1587,1591],{"className":1588,"dataFsResolvedFilePath":1589,"href":1590},[210],"summaries\u002Fipmrk-datamining.md","\u002Fwiki\u002Fipmrk-datamining","Datamining — techniky a nástroje"," — CRISP-DM, Link analýza, k-means, rozhodovací stromy, Apriori, Witness Miner, MATLAB kód",{"title":641,"searchDepth":642,"depth":642,"links":1594},[1595,1596,1597,1598,1599,1600],{"id":721,"depth":642,"text":722},{"id":149,"depth":642,"text":150},{"id":1323,"depth":642,"text":1324},{"id":1356,"depth":642,"text":1357},{"id":606,"depth":642,"text":607},{"id":195,"depth":642,"text":196},"ipmrk","2026-04-10",{},"\u002Fcourses\u002Fipmrk",{"title":1150,"description":641},[1607,1608,1609,1610,1611],"raw\u002Fipmrk\u002FDetail předmětu.md","raw\u002Fipmrk\u002Fkniha.md","raw\u002Fipmrk\u002Fevolucni-algoritmy-online.md","raw\u002Fipmrk\u002Foptimalizace-online.md","raw\u002Fipmrk\u002Fdatamining-online.md","courses\u002Fipmrk",[1601,1614,1615,1616,1617,1618,1619,1620],"fuzzy","neuronove-site","geneticke-algoritmy","evolucni-algoritmy","chaos","optimalizace","datamining","_iX_YpjZn-5NmPhFSn_DHNExx_u1xi12WJEbWAHjXpg",{"ipmrk":1623,"imork":1624,"imek":1625},25,41,21,{"page":1627,"collection":5987},{"id":1628,"title":1629,"body":1630,"course":1128,"courses":659,"created":5973,"description":641,"extension":661,"meta":5974,"navigation":664,"path":5975,"seo":5976,"sources":5977,"stem":5978,"tags":5979,"type":5985,"updated":677,"__hash__":5986},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":1631,"toc":5961},[1632,1635,1639,1798,1807,1811,1882,1920,2028,2032,2063,2139,2187,2190,2261,2264,2300,2336,2340,2390,2397,2443,2490,2493,2575,2672,2756,2760,2806,2836,2842,2871,2895,2945,2999,3066,3069,3135,3164,3223,3240,3327,3425,3556,3560,3717,3866,4248,4252,4255,4317,4320,4409,4437,4475,4478,4516,4556,4590,4592,4629,4661,4761,4766,4892,4944,5026,5167,5171,5294,5301,5412,5419,5423,5898,5902],[12,1633,1629],{"id":1634},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,1636,1638],{"id":1637},"tldr","TL;DR",[724,1640,1641,1644,1645,1648,1649,1663,1664,1678,1679,1682,1683,1343,1686,1689,1690,1343,1693,1696,1697,1700,1701,1739,1740,1743,1744,1343,1758,1772,1773,1776,1777,1797],{},[38,1642,1643],{},"IS-LM"," je makroekonomický model se ",[38,1646,1647],{},"dvěma neznámými"," (",[883,1650,1652],{"className":1651},[886],[888,1653,1654],{"xmlns":890},[892,1655,1656,1661],{},[895,1657,1658],{},[898,1659,1660],{},"Y",[902,1662,1660],{"encoding":904}," — národní důchod a ",[883,1665,1667],{"className":1666},[886],[888,1668,1669],{"xmlns":890},[892,1670,1671,1676],{},[895,1672,1673],{},[898,1674,1675],{},"r",[902,1677,1675],{"encoding":904}," — úroková míra) a ",[38,1680,1681],{},"dvěma trhy",": trhem zboží (křivka ",[38,1684,1685],{},"IS",[614,1687,1688],{},"Investment = Savings",") a trhem peněz (křivka ",[38,1691,1692],{},"LM",[614,1694,1695],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,1698,1699],{},"simultánní rovnováhu"," ",[883,1702,1704],{"className":1703},[886],[888,1705,1706],{"xmlns":890},[892,1707,1708,1736],{},[895,1709,1710,1715,1723,1727,1733],{},[1711,1712,1714],"mo",{"stretchy":1713},"false","(",[1716,1717,1718,1720],"msup",{},[898,1719,1660],{},[898,1721,1722],{},"E",[1711,1724,1726],{"separator":1725},"true",",",[1716,1728,1729,1731],{},[898,1730,1675],{},[898,1732,1722],{},[1711,1734,1735],{"stretchy":1713},")",[902,1737,1738],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,1741,1742],{},"fiskální politiky"," (posun IS změnou ",[883,1745,1747],{"className":1746},[886],[888,1748,1749],{"xmlns":890},[892,1750,1751,1756],{},[895,1752,1753],{},[898,1754,1755],{},"G",[902,1757,1755],{"encoding":904},[883,1759,1761],{"className":1760},[886],[888,1762,1763],{"xmlns":890},[892,1764,1765,1770],{},[895,1766,1767],{},[898,1768,1769],{},"T",[902,1771,1769],{"encoding":904},") a ",[38,1774,1775],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,1778,1780],{"className":1779},[886],[888,1781,1782],{"xmlns":890},[892,1783,1784,1794],{},[895,1785,1786],{},[1716,1787,1788,1791],{},[898,1789,1790],{},"M",[1711,1792,1793],{},"∗",[902,1795,1796],{"encoding":904},"M^*",").",[724,1799,1800],{},[1801,1802],"img",{"alt":1803,"className":1804,"src":1806},"imek-is-lm-model",[210,1805],"wikilink-broken","\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,1808,1810],{"id":1809},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,1812,1813,1814,1818,1819,1648,1822,1846,1847,1850,1851,1867,1868,1881],{},"V modelech ",[207,1815,1817],{"className":1816,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,1820,1821],{},"investice pokládány za konstantní",[883,1823,1825],{"className":1824},[886],[888,1826,1827],{"xmlns":890},[892,1828,1829,1843],{},[895,1830,1831,1834,1837],{},[898,1832,1833],{},"I",[1711,1835,1836],{},"=",[1716,1838,1839,1841],{},[898,1840,1833],{},[1711,1842,1793],{},[902,1844,1845],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,1848,1849],{},"ceně peněz",", tedy na ",[38,1852,1853,1854],{},"úrokové míře ",[883,1855,1857],{"className":1856},[886],[888,1858,1859],{"xmlns":890},[892,1860,1861,1865],{},[895,1862,1863],{},[898,1864,1675],{},[902,1866,1675],{"encoding":904},": čím vyšší ",[883,1869,1871],{"className":1870},[886],[888,1872,1873],{"xmlns":890},[892,1874,1875,1879],{},[895,1876,1877],{},[898,1878,1675],{},[902,1880,1675],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,1883,1884,1914],{},[123,1885,1886,1700,1889,1913],{},[38,1887,1888],{},"funkci investic",[883,1890,1892],{"className":1891},[886],[888,1893,1894],{"xmlns":890},[892,1895,1896,1910],{},[895,1897,1898,1900,1902,1904,1906,1908],{},[898,1899,1833],{},[1711,1901,1836],{},[898,1903,1833],{},[1711,1905,1714],{"stretchy":1713},[898,1907,1675],{},[1711,1909,1735],{"stretchy":1713},[902,1911,1912],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,1915,1916,1919],{},[38,1917,1918],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[1921,1922,1923],"blockquote",{},[724,1924,1925,1928,1929,1950,1951,1978,1979,1992,1993,2023,2024,2027],{},[883,1926,1927],{},"!warning"," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,1930,1932],{"className":1931},[886],[888,1933,1934],{"xmlns":890},[892,1935,1936,1947],{},[895,1937,1938,1941,1945],{},[898,1939,1940],{},"C",[1942,1943,1944],"mtext",{},"-",[898,1946,1833],{},[902,1948,1949],{"encoding":904},"C\\text{-}I"," až ",[883,1952,1954],{"className":1953},[886],[888,1955,1956],{"xmlns":890},[892,1957,1958,1975],{},[895,1959,1960,1962,1964,1966,1968,1970,1972],{},[898,1961,1940],{},[1942,1963,1944],{},[898,1965,1833],{},[1942,1967,1944],{},[898,1969,1755],{},[1942,1971,1944],{},[898,1973,1974],{},"X",[902,1976,1977],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,1980,1982],{"className":1981},[886],[888,1983,1984],{"xmlns":890},[892,1985,1986,1990],{},[895,1987,1988],{},[898,1989,1660],{},[902,1991,1660],{"encoding":904},". V IS-LM jsou ",[38,1994,1995,1996,2009,2010],{},"dvě neznámé ",[883,1997,1999],{"className":1998},[886],[888,2000,2001],{"xmlns":890},[892,2002,2003,2007],{},[895,2004,2005],{},[898,2006,1660],{},[902,2008,1660],{"encoding":904}," a ",[883,2011,2013],{"className":2012},[886],[888,2014,2015],{"xmlns":890},[892,2016,2017,2021],{},[895,2018,2019],{},[898,2020,1675],{},[902,2022,1675],{"encoding":904},", a proto potřebujeme ",[38,2025,2026],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,2029,2031],{"id":2030},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,2033,2034,2035,2048,2049,2062],{},"Lineární závislost investic ",[883,2036,2038],{"className":2037},[886],[888,2039,2040],{"xmlns":890},[892,2041,2042,2046],{},[895,2043,2044],{},[898,2045,1833],{},[902,2047,1833],{"encoding":904}," na úrokové míře ",[883,2050,2052],{"className":2051},[886],[888,2053,2054],{"xmlns":890},[892,2055,2056,2060],{},[895,2057,2058],{},[898,2059,1675],{},[902,2061,1675],{"encoding":904},":",[724,2064,2065],{},[883,2066,2068],{"className":2067},[886],[888,2069,2070],{"xmlns":890},[892,2071,2072,2136],{},[895,2073,2074,2076,2078,2080,2082,2084,2086,2088,2091,2093,2096,2099,2101,2105,2107,2110,2114,2116,2119,2121,2124,2127,2129,2131,2134],{},[898,2075,1833],{},[1711,2077,1836],{},[898,2079,1833],{},[1711,2081,1714],{"stretchy":1713},[898,2083,1675],{},[1711,2085,1735],{"stretchy":1713},[1711,2087,1836],{},[898,2089,2090],{},"c",[898,2092,1675],{},[1711,2094,2095],{},"+",[898,2097,2098],{},"d",[1711,2100,1726],{"separator":1725},[2102,2103],"mspace",{"width":2104},"2em",[898,2106,2090],{},[1711,2108,2109],{},"\u003C",[2111,2112,2113],"mn",{},"0",[1711,2115,1726],{"separator":1725},[1942,2117,2118],{}," ",[898,2120,2098],{},[1711,2122,2123],{},">",[2111,2125,2126],{},"0.",[2102,2128],{"width":2104},[1711,2130,1714],{"stretchy":1713},[2111,2132,2133],{},"7.11",[1711,2135,1735],{"stretchy":1713},[902,2137,2138],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,2140,2141,2162],{},[123,2142,2143,2161],{},[883,2144,2146],{"className":2145},[886],[888,2147,2148],{"xmlns":890},[892,2149,2150,2158],{},[895,2151,2152,2154,2156],{},[898,2153,2098],{},[1711,2155,2123],{},[2111,2157,2113],{},[902,2159,2160],{"encoding":904},"d > 0"," zřejmé,",[123,2163,2164,2182,2183,2186],{},[883,2165,2167],{"className":2166},[886],[888,2168,2169],{"xmlns":890},[892,2170,2171,2179],{},[895,2172,2173,2175,2177],{},[898,2174,2090],{},[1711,2176,2109],{},[2111,2178,2113],{},[902,2180,2181],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,2184,2185],{},"klesající",".",[724,2188,2189],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,2191,2192],{},[883,2193,2195],{"className":2194},[886],[888,2196,2197],{"xmlns":890},[892,2198,2199,2258],{},[895,2200,2201,2203,2205,2207,2209,2211,2213,2215,2217,2219,2221,2224,2226,2228,2230,2232,2234,2236,2239,2241,2243,2245,2247,2249,2251,2253,2256],{},[898,2202,1940],{},[1711,2204,1836],{},[898,2206,1940],{},[1711,2208,1714],{"stretchy":1713},[898,2210,1660],{},[1711,2212,1735],{"stretchy":1713},[1711,2214,1836],{},[898,2216,207],{},[898,2218,1660],{},[1711,2220,2095],{},[898,2222,2223],{},"b",[1711,2225,1726],{"separator":1725},[2102,2227],{"width":2104},[2111,2229,2113],{},[1711,2231,2109],{},[898,2233,207],{},[1711,2235,2109],{},[2111,2237,2238],{},"1",[1711,2240,1726],{"separator":1725},[1942,2242,2118],{},[898,2244,2223],{},[1711,2246,2123],{},[2111,2248,2126],{},[2102,2250],{"width":2104},[1711,2252,1714],{"stretchy":1713},[2111,2254,2255],{},"7.12",[1711,2257,1735],{"stretchy":1713},[902,2259,2260],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,2262,2263],{},"Podmínka rovnováhy na trhu zboží:",[724,2265,2266],{},[883,2267,2269],{"className":2268},[886],[888,2270,2271],{"xmlns":890},[892,2272,2273,2297],{},[895,2274,2275,2277,2279,2281,2283,2285,2288,2290,2292,2295],{},[898,2276,1660],{},[1711,2278,1836],{},[898,2280,1940],{},[1711,2282,2095],{},[898,2284,1833],{},[898,2286,2186],{"mathvariant":2287},"normal",[2102,2289],{"width":2104},[1711,2291,1714],{"stretchy":1713},[2111,2293,2294],{},"7.13",[1711,2296,1735],{"stretchy":1713},[902,2298,2299],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,2301,2302,2303,1700,2306,2332,2333,2186],{},"To dává ",[38,2304,2305],{},"tři rovnice o čtyřech neznámých",[883,2307,2309],{"className":2308},[886],[888,2310,2311],{"xmlns":890},[892,2312,2313,2329],{},[895,2314,2315,2317,2319,2321,2323,2325,2327],{},[898,2316,1660],{},[1711,2318,1726],{"separator":1725},[898,2320,1940],{},[1711,2322,1726],{"separator":1725},[898,2324,1833],{},[1711,2326,1726],{"separator":1725},[898,2328,1675],{},[902,2330,2331],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,2334,2335],{},"rovnováhy na trhu peněz",[115,2337,2339],{"id":2338},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,2341,2342,2343,2366,2367,2385,2386,2389],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,2344,2346],{"className":2345},[886],[888,2347,2348],{"xmlns":890},[892,2349,2350,2363],{},[895,2351,2352,2354,2356,2358,2360],{},[898,2353,1660],{},[1711,2355,1836],{},[898,2357,1940],{},[1711,2359,2095],{},[898,2361,2362],{},"S",[902,2364,2365],{"encoding":904},"Y = C + S"," plyne ",[883,2368,2370],{"className":2369},[886],[888,2371,2372],{"xmlns":890},[892,2373,2374,2382],{},[895,2375,2376,2378,2380],{},[898,2377,1833],{},[1711,2379,1836],{},[898,2381,2362],{},[902,2383,2384],{"encoding":904},"I = S"," (plánované ",[38,2387,2388],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,2391,2392],{},[1801,2393],{"alt":2394,"className":2395,"src":2396},"imek-odvozeni-is-4panelu",[210,1805],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,2398,2399],{},[883,2400,2402],{"className":2401},[886],[888,2403,2404],{"xmlns":890},[892,2405,2406,2440],{},[895,2407,2408,2410,2412,2414,2416,2418,2420,2422,2424,2426,2428,2430,2432,2434,2436,2438],{},[898,2409,1660],{},[1711,2411,1836],{},[1711,2413,1714],{"stretchy":1713},[898,2415,207],{},[898,2417,1660],{},[1711,2419,2095],{},[898,2421,2223],{},[1711,2423,1735],{"stretchy":1713},[1711,2425,2095],{},[1711,2427,1714],{"stretchy":1713},[898,2429,2090],{},[898,2431,1675],{},[1711,2433,2095],{},[898,2435,2098],{},[1711,2437,1735],{"stretchy":1713},[1711,2439,1726],{"separator":1725},[902,2441,2442],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,2444,2445],{},[883,2446,2448],{"className":2447},[886],[888,2449,2450],{"xmlns":890},[892,2451,2452,2487],{},[895,2453,2454,2456,2458,2461,2463,2465,2467,2469,2471,2473,2475,2477,2479,2481,2483,2485],{},[1711,2455,1714],{"stretchy":1713},[2111,2457,2238],{},[1711,2459,2460],{},"−",[898,2462,207],{},[1711,2464,1735],{"stretchy":1713},[898,2466,1660],{},[1711,2468,2460],{},[898,2470,2090],{},[898,2472,1675],{},[1711,2474,2460],{},[898,2476,2223],{},[1711,2478,2460],{},[898,2480,2098],{},[1711,2482,1836],{},[2111,2484,2113],{},[1711,2486,1726],{"separator":1725},[902,2488,2489],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,2491,2492],{},"odkud",[724,2494,2495],{},[883,2496,2498],{"className":2497},[886],[888,2499,2500],{"xmlns":890},[892,2501,2502,2572],{},[895,2503,2504,2563,2565,2567,2570],{},[2505,2506,2508],"menclose",{"notation":2507},"box",[2509,2510,2511],"mstyle",{"scriptlevel":2113,"displaystyle":1713},[2509,2512,2513],{"scriptlevel":2113,"displaystyle":1713},[2509,2514,2515],{"scriptlevel":2113,"displaystyle":1725},[895,2516,2517,2520,2522,2524,2537,2539,2541,2543,2561],{},[1942,2518,2519],{}," ",[898,2521,1660],{},[1711,2523,1836],{},[2525,2526,2527,2529],"mfrac",{},[898,2528,2090],{},[895,2530,2531,2533,2535],{},[2111,2532,2238],{},[1711,2534,2460],{},[898,2536,207],{},[1942,2538,2519],{},[898,2540,1675],{},[1711,2542,2095],{},[2525,2544,2545,2553],{},[895,2546,2547,2549,2551],{},[898,2548,2223],{},[1711,2550,2095],{},[898,2552,2098],{},[895,2554,2555,2557,2559],{},[2111,2556,2238],{},[1711,2558,2460],{},[898,2560,207],{},[1942,2562,2519],{},[2102,2564],{"width":2104},[1711,2566,1714],{"stretchy":1713},[2111,2568,2569],{},"7.14",[1711,2571,1735],{"stretchy":1713},[902,2573,2574],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,2576,2577,2578,1648,2581,2584,2585,2588,2589,2591,2592,2614,2615,2643,2644,2665,2666,2668,2669,2671],{},"Tento vztah se nazývá ",[38,2579,2580],{},"funkce IS",[614,2582,2583],{},"IS schedule",") a její graf ",[38,2586,2587],{},"křivka IS",". Křivka je ",[38,2590,2185],{}," přímka v rovině ",[883,2593,2595],{"className":2594},[886],[888,2596,2597],{"xmlns":890},[892,2598,2599,2611],{},[895,2600,2601,2603,2605,2607,2609],{},[1711,2602,1714],{"stretchy":1713},[898,2604,1675],{},[1711,2606,1726],{"separator":1725},[898,2608,1660],{},[1711,2610,1735],{"stretchy":1713},[902,2612,2613],{"encoding":904},"(r, Y)",", neboť ",[883,2616,2618],{"className":2617},[886],[888,2619,2620],{"xmlns":890},[892,2621,2622,2640],{},[895,2623,2624,2636,2638],{},[2525,2625,2626,2628],{},[898,2627,2090],{},[895,2629,2630,2632,2634],{},[2111,2631,2238],{},[1711,2633,2460],{},[898,2635,207],{},[1711,2637,2109],{},[2111,2639,2113],{},[902,2641,2642],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,2645,2647],{"className":2646},[886],[888,2648,2649],{"xmlns":890},[892,2650,2651,2663],{},[895,2652,2653,2655,2657,2659,2661],{},[1711,2654,1714],{"stretchy":1713},[898,2656,1675],{},[1711,2658,1726],{"separator":1725},[898,2660,1660],{},[1711,2662,1735],{"stretchy":1713},[902,2664,2613],{"encoding":904},", pro které plánované ",[38,2667,1833],{},"nvestment = ",[38,2670,2362],{},"avings.",[1921,2673,2674],{},[724,2675,2676,2679,2680,2693,2694,1700,2697,2710,2711,2724,2725,2009,2738,2751,2752,2755],{},[883,2677,2678],{},"!info"," Intuice — proč IS klesá\nNižší úroková míra ",[883,2681,2683],{"className":2682},[886],[888,2684,2685],{"xmlns":890},[892,2686,2687,2691],{},[895,2688,2689],{},[898,2690,1675],{},[902,2692,1675],{"encoding":904}," → levnější úvěr → ",[38,2695,2696],{},"více investic",[883,2698,2700],{"className":2699},[886],[888,2701,2702],{"xmlns":890},[892,2703,2704,2708],{},[895,2705,2706],{},[898,2707,1833],{},[902,2709,1833],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,2712,2714],{"className":2713},[886],[888,2715,2716],{"xmlns":890},[892,2717,2718,2722],{},[895,2719,2720],{},[898,2721,1660],{},[902,2723,1660],{"encoding":904},". Vztah mezi ",[883,2726,2728],{"className":2727},[886],[888,2729,2730],{"xmlns":890},[892,2731,2732,2736],{},[895,2733,2734],{},[898,2735,1675],{},[902,2737,1675],{"encoding":904},[883,2739,2741],{"className":2740},[886],[888,2742,2743],{"xmlns":890},[892,2744,2745,2749],{},[895,2746,2747],{},[898,2748,1660],{},[902,2750,1660],{"encoding":904}," na trhu zboží je proto ",[38,2753,2754],{},"nepřímý"," (klesající křivka).",[115,2757,2759],{"id":2758},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,2761,2762,2763,2782,2783,2801,2802,2805],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,2764,2766],{"className":2765},[886],[888,2767,2768],{"xmlns":890},[892,2769,2770,2779],{},[895,2771,2772],{},[1716,2773,2774,2776],{},[898,2775,1790],{},[898,2777,2778],{},"D",[902,2780,2781],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,2784,2786],{"className":2785},[886],[888,2787,2788],{"xmlns":890},[892,2789,2790,2798],{},[895,2791,2792],{},[1716,2793,2794,2796],{},[898,2795,1790],{},[898,2797,2362],{},[902,2799,2800],{"encoding":904},"M^S",". ",[38,2803,2804],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,2807,2808],{},[883,2809,2811],{"className":2810},[886],[888,2812,2813],{"xmlns":890},[892,2814,2815,2833],{},[895,2816,2817,2823,2825,2831],{},[1716,2818,2819,2821],{},[898,2820,1790],{},[898,2822,2362],{},[1711,2824,1836],{},[1716,2826,2827,2829],{},[898,2828,1790],{},[1711,2830,1793],{},[898,2832,2186],{"mathvariant":2287},[902,2834,2835],{"encoding":904},"M^S = M^*.",[724,2837,2838,2841],{},[38,2839,2840],{},"Poptávka"," po penězích má tři zdroje:",[120,2843,2844,2853,2862],{},[123,2845,2846,1648,2849,2852],{},[38,2847,2848],{},"transakční poptávka",[614,2850,2851],{},"transactions demand",") — peníze pro nákup zboží,",[123,2854,2855,1648,2858,2861],{},[38,2856,2857],{},"opatrnostní poptávka",[614,2859,2860],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,2863,2864,1648,2867,2870],{},[38,2865,2866],{},"spekulační poptávka",[614,2868,2869],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,2872,2873,2874,2894],{},"Součet transakční a opatrnostní poptávky ",[883,2875,2877],{"className":2876},[886],[888,2878,2879],{"xmlns":890},[892,2880,2881,2891],{},[895,2882,2883],{},[2884,2885,2886,2889],"msub",{},[898,2887,2888],{},"L",[2111,2890,2238],{},[902,2892,2893],{"encoding":904},"L_1"," je úměrný důchodu:",[724,2896,2897],{},[883,2898,2900],{"className":2899},[886],[888,2901,2902],{"xmlns":890},[892,2903,2904,2942],{},[895,2905,2906,2912,2914,2921,2923,2925,2927,2929,2931,2937,2939],{},[2884,2907,2908,2910],{},[898,2909,2888],{},[2111,2911,2238],{},[1711,2913,1836],{},[2884,2915,2916,2919],{},[898,2917,2918],{},"k",[2111,2920,2238],{},[898,2922,1660],{},[1711,2924,1726],{"separator":1725},[2102,2926],{"width":2104},[2111,2928,2113],{},[1711,2930,2109],{},[2884,2932,2933,2935],{},[898,2934,2918],{},[2111,2936,2238],{},[1711,2938,2109],{},[2111,2940,2941],{},"1.",[902,2943,2944],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,2946,2947,2948,2967,2968,1343,2981,2998],{},"Spekulační poptávka ",[883,2949,2951],{"className":2950},[886],[888,2952,2953],{"xmlns":890},[892,2954,2955,2964],{},[895,2956,2957],{},[2884,2958,2959,2961],{},[898,2960,2888],{},[2111,2962,2963],{},"2",[902,2965,2966],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,2969,2971],{"className":2970},[886],[888,2972,2973],{"xmlns":890},[892,2974,2975,2979],{},[895,2976,2977],{},[898,2978,1675],{},[902,2980,1675],{"encoding":904},[883,2982,2984],{"className":2983},[886],[888,2985,2986],{"xmlns":890},[892,2987,2988,2996],{},[895,2989,2990],{},[2884,2991,2992,2994],{},[898,2993,2888],{},[2111,2995,2963],{},[902,2997,2966],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,3000,3001],{},[883,3002,3004],{"className":3003},[886],[888,3005,3006],{"xmlns":890},[892,3007,3008,3063],{},[895,3009,3010,3016,3018,3024,3026,3028,3035,3037,3039,3045,3047,3049,3051,3053,3059,3061],{},[2884,3011,3012,3014],{},[898,3013,2888],{},[2111,3015,2963],{},[1711,3017,1836],{},[2884,3019,3020,3022],{},[898,3021,2918],{},[2111,3023,2963],{},[898,3025,1675],{},[1711,3027,2095],{},[2884,3029,3030,3032],{},[898,3031,2918],{},[2111,3033,3034],{},"3",[1711,3036,1726],{"separator":1725},[2102,3038],{"width":2104},[2884,3040,3041,3043],{},[898,3042,2918],{},[2111,3044,2963],{},[1711,3046,2109],{},[2111,3048,2113],{},[1711,3050,1726],{"separator":1725},[1942,3052,2118],{},[2884,3054,3055,3057],{},[898,3056,2918],{},[2111,3058,3034],{},[1711,3060,2123],{},[2111,3062,2126],{},[902,3064,3065],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,3067,3068],{},"Celková poptávka po penězích:",[724,3070,3071],{},[883,3072,3074],{"className":3073},[886],[888,3075,3076],{"xmlns":890},[892,3077,3078,3132],{},[895,3079,3080,3086,3088,3094,3096,3102,3104,3110,3112,3114,3120,3122,3124,3130],{},[1716,3081,3082,3084],{},[898,3083,1790],{},[898,3085,2778],{},[1711,3087,1836],{},[2884,3089,3090,3092],{},[898,3091,2888],{},[2111,3093,2238],{},[1711,3095,2095],{},[2884,3097,3098,3100],{},[898,3099,2888],{},[2111,3101,2963],{},[1711,3103,1836],{},[2884,3105,3106,3108],{},[898,3107,2918],{},[2111,3109,2238],{},[898,3111,1660],{},[1711,3113,2095],{},[2884,3115,3116,3118],{},[898,3117,2918],{},[2111,3119,2963],{},[898,3121,1675],{},[1711,3123,2095],{},[2884,3125,3126,3128],{},[898,3127,2918],{},[2111,3129,3034],{},[898,3131,2186],{"mathvariant":2287},[902,3133,3134],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,3136,3137,3138,2062],{},"Podmínka rovnováhy na trhu peněz ",[883,3139,3141],{"className":3140},[886],[888,3142,3143],{"xmlns":890},[892,3144,3145,3161],{},[895,3146,3147,3153,3155],{},[1716,3148,3149,3151],{},[898,3150,1790],{},[898,3152,2778],{},[1711,3154,1836],{},[1716,3156,3157,3159],{},[898,3158,1790],{},[1711,3160,1793],{},[902,3162,3163],{"encoding":904},"M^D = M^*",[724,3165,3166],{},[883,3167,3169],{"className":3168},[886],[888,3170,3171],{"xmlns":890},[892,3172,3173,3220],{},[895,3174,3175,3181,3183,3189,3191,3193,3199,3201,3203,3209,3211,3213,3215,3218],{},[1716,3176,3177,3179],{},[898,3178,1790],{},[1711,3180,1793],{},[1711,3182,1836],{},[2884,3184,3185,3187],{},[898,3186,2918],{},[2111,3188,2238],{},[898,3190,1660],{},[1711,3192,2095],{},[2884,3194,3195,3197],{},[898,3196,2918],{},[2111,3198,2963],{},[898,3200,1675],{},[1711,3202,2095],{},[2884,3204,3205,3207],{},[898,3206,2918],{},[2111,3208,3034],{},[1711,3210,1726],{"separator":1725},[2102,3212],{"width":2104},[1711,3214,1714],{"stretchy":1713},[2111,3216,3217],{},"7.15",[1711,3219,1735],{"stretchy":1713},[902,3221,3222],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,3224,3225,3226,3239],{},"po úpravě (vyjádření ",[883,3227,3229],{"className":3228},[886],[888,3230,3231],{"xmlns":890},[892,3232,3233,3237],{},[895,3234,3235],{},[898,3236,1660],{},[902,3238,1660],{"encoding":904},"):",[724,3241,3242],{},[883,3243,3245],{"className":3244},[886],[888,3246,3247],{"xmlns":890},[892,3248,3249,3324],{},[895,3250,3251,3315,3317,3319,3322],{},[2505,3252,3253],{"notation":2507},[2509,3254,3255],{"scriptlevel":2113,"displaystyle":1713},[2509,3256,3257],{"scriptlevel":2113,"displaystyle":1713},[2509,3258,3259],{"scriptlevel":2113,"displaystyle":1725},[895,3260,3261,3263,3265,3267,3269,3283,3285,3287,3289,3313],{},[1942,3262,2519],{},[898,3264,1660],{},[1711,3266,1836],{},[1711,3268,2460],{},[2525,3270,3271,3277],{},[2884,3272,3273,3275],{},[898,3274,2918],{},[2111,3276,2963],{},[2884,3278,3279,3281],{},[898,3280,2918],{},[2111,3282,2238],{},[1942,3284,2519],{},[898,3286,1675],{},[1711,3288,2095],{},[2525,3290,3291,3307],{},[895,3292,3293,3299,3301],{},[1716,3294,3295,3297],{},[898,3296,1790],{},[1711,3298,1793],{},[1711,3300,2460],{},[2884,3302,3303,3305],{},[898,3304,2918],{},[2111,3306,3034],{},[2884,3308,3309,3311],{},[898,3310,2918],{},[2111,3312,2238],{},[1942,3314,2519],{},[2102,3316],{"width":2104},[1711,3318,1714],{"stretchy":1713},[2111,3320,3321],{},"7.16",[1711,3323,1735],{"stretchy":1713},[902,3325,3326],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,3328,2577,3329,1648,3332,3335,3336,2588,3339,2591,3342,2614,3363,3395,3396,3418,3419,3421,3422,3424],{},[38,3330,3331],{},"funkce LM",[614,3333,3334],{},"LM schedule","), její graf ",[38,3337,3338],{},"křivka LM",[38,3340,3341],{},"rostoucí",[883,3343,3345],{"className":3344},[886],[888,3346,3347],{"xmlns":890},[892,3348,3349,3361],{},[895,3350,3351,3353,3355,3357,3359],{},[1711,3352,1714],{"stretchy":1713},[898,3354,1675],{},[1711,3356,1726],{"separator":1725},[898,3358,1660],{},[1711,3360,1735],{"stretchy":1713},[902,3362,2613],{"encoding":904},[883,3364,3366],{"className":3365},[886],[888,3367,3368],{"xmlns":890},[892,3369,3370,3392],{},[895,3371,3372,3374,3388,3390],{},[1711,3373,2460],{},[2525,3375,3376,3382],{},[2884,3377,3378,3380],{},[898,3379,2918],{},[2111,3381,2963],{},[2884,3383,3384,3386],{},[898,3385,2918],{},[2111,3387,2238],{},[1711,3389,2123],{},[2111,3391,2113],{},[902,3393,3394],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,3397,3399],{"className":3398},[886],[888,3400,3401],{"xmlns":890},[892,3402,3403,3415],{},[895,3404,3405,3411,3413],{},[2884,3406,3407,3409],{},[898,3408,2918],{},[2111,3410,2963],{},[1711,3412,2109],{},[2111,3414,2113],{},[902,3416,3417],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,3420,2888],{},"iquidity of ",[38,3423,1790],{},"oney.",[1921,3426,3427],{},[724,3428,3429,3431,3432,3445,3446,3474,3475,3492,3493,3506,3507,3524,3525,2009,3538,3551,3552,3555],{},[883,3430,2678],{}," Intuice — proč LM roste\nVyšší důchod ",[883,3433,3435],{"className":3434},[886],[888,3436,3437],{"xmlns":890},[892,3438,3439,3443],{},[895,3440,3441],{},[898,3442,1660],{},[902,3444,1660],{"encoding":904}," → větší transakční poptávka po penězích ",[883,3447,3449],{"className":3448},[886],[888,3450,3451],{"xmlns":890},[892,3452,3453,3471],{},[895,3454,3455,3461,3463,3469],{},[2884,3456,3457,3459],{},[898,3458,2888],{},[2111,3460,2238],{},[1711,3462,1836],{},[2884,3464,3465,3467],{},[898,3466,2918],{},[2111,3468,2238],{},[898,3470,1660],{},[902,3472,3473],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,3476,3478],{"className":3477},[886],[888,3479,3480],{"xmlns":890},[892,3481,3482,3490],{},[895,3483,3484],{},[1716,3485,3486,3488],{},[898,3487,1790],{},[1711,3489,1793],{},[902,3491,1796],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,3494,3496],{"className":3495},[886],[888,3497,3498],{"xmlns":890},[892,3499,3500,3504],{},[895,3501,3502],{},[898,3503,1675],{},[902,3505,1675],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,3508,3510],{"className":3509},[886],[888,3511,3512],{"xmlns":890},[892,3513,3514,3522],{},[895,3515,3516],{},[2884,3517,3518,3520],{},[898,3519,2888],{},[2111,3521,2963],{},[902,3523,2966],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,3526,3528],{"className":3527},[886],[888,3529,3530],{"xmlns":890},[892,3531,3532,3536],{},[895,3533,3534],{},[898,3535,1660],{},[902,3537,1660],{"encoding":904},[883,3539,3541],{"className":3540},[886],[888,3542,3543],{"xmlns":890},[892,3544,3545,3549],{},[895,3546,3547],{},[898,3548,1675],{},[902,3550,1675],{"encoding":904}," na trhu peněz je proto ",[38,3553,3554],{},"přímý"," (rostoucí křivka).",[115,3557,3559],{"id":3558},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,3561,3562,3563,3566,3567,1700,3570,2009,3588,1700,3591,3609,3610,3628,3629,3647,3648,3664,3665,2009,3680,3695,3696,2186],{},"Řešením ",[38,3564,3565],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,3568,3569],{},"rovnovážný důchod",[883,3571,3573],{"className":3572},[886],[888,3574,3575],{"xmlns":890},[892,3576,3577,3585],{},[895,3578,3579],{},[1716,3580,3581,3583],{},[898,3582,1660],{},[898,3584,1722],{},[902,3586,3587],{"encoding":904},"Y^E",[38,3589,3590],{},"rovnovážnou úrokovou míru",[883,3592,3594],{"className":3593},[886],[888,3595,3596],{"xmlns":890},[892,3597,3598,3606],{},[895,3599,3600],{},[1716,3601,3602,3604],{},[898,3603,1675],{},[898,3605,1722],{},[902,3607,3608],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,3611,3613],{"className":3612},[886],[888,3614,3615],{"xmlns":890},[892,3616,3617,3625],{},[895,3618,3619],{},[1716,3620,3621,3623],{},[898,3622,1833],{},[898,3624,1722],{},[902,3626,3627],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,3630,3632],{"className":3631},[886],[888,3633,3634],{"xmlns":890},[892,3635,3636,3644],{},[895,3637,3638],{},[1716,3639,3640,3642],{},[898,3641,1940],{},[898,3643,1722],{},[902,3645,3646],{"encoding":904},"C^E",". Graficky jde o ",[38,3649,3650,3651],{},"průsečík ",[883,3652,3654],{"className":3653},[886],[888,3655,3656],{"xmlns":890},[892,3657,3658,3662],{},[895,3659,3660],{},[898,3661,1722],{},[902,3663,1722],{"encoding":904}," křivek ",[883,3666,3668],{"className":3667},[886],[888,3669,3670],{"xmlns":890},[892,3671,3672,3678],{},[895,3673,3674,3676],{},[898,3675,1833],{},[898,3677,2362],{},[902,3679,1685],{"encoding":904},[883,3681,3683],{"className":3682},[886],[888,3684,3685],{"xmlns":890},[892,3686,3687,3693],{},[895,3688,3689,3691],{},[898,3690,2888],{},[898,3692,1790],{},[902,3694,1692],{"encoding":904}," v rovině ",[883,3697,3699],{"className":3698},[886],[888,3700,3701],{"xmlns":890},[892,3702,3703,3715],{},[895,3704,3705,3707,3709,3711,3713],{},[1711,3706,1714],{"stretchy":1713},[898,3708,1675],{},[1711,3710,1726],{"separator":1725},[898,3712,1660],{},[1711,3714,1735],{"stretchy":1713},[902,3716,2613],{"encoding":904},[724,3718,3719],{},[614,3720,3721,3722,3743,3744,3759,3760,3775,3776,3789,3790,3807,3808,1772,3821,3807,3838,3851,3852,3865],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,3723,3725],{"className":3724},[886],[888,3726,3727],{"xmlns":890},[892,3728,3729,3741],{},[895,3730,3731,3733,3735,3737,3739],{},[1711,3732,1714],{"stretchy":1713},[898,3734,1675],{},[1711,3736,1726],{"separator":1725},[898,3738,1660],{},[1711,3740,1735],{"stretchy":1713},[902,3742,2613],{"encoding":904},". Rostoucí přímka ",[883,3745,3747],{"className":3746},[886],[888,3748,3749],{"xmlns":890},[892,3750,3751,3757],{},[895,3752,3753,3755],{},[898,3754,2888],{},[898,3756,1790],{},[902,3758,1692],{"encoding":904}," a klesající přímka ",[883,3761,3763],{"className":3762},[886],[888,3764,3765],{"xmlns":890},[892,3766,3767,3773],{},[895,3768,3769,3771],{},[898,3770,1833],{},[898,3772,2362],{},[902,3774,1685],{"encoding":904}," se protínají v bodě ",[883,3777,3779],{"className":3778},[886],[888,3780,3781],{"xmlns":890},[892,3782,3783,3787],{},[895,3784,3785],{},[898,3786,1722],{},[902,3788,1722],{"encoding":904}," se souřadnicemi ",[883,3791,3793],{"className":3792},[886],[888,3794,3795],{"xmlns":890},[892,3796,3797,3805],{},[895,3798,3799],{},[1716,3800,3801,3803],{},[898,3802,1675],{},[898,3804,1722],{},[902,3806,3608],{"encoding":904}," (na ose ",[883,3809,3811],{"className":3810},[886],[888,3812,3813],{"xmlns":890},[892,3814,3815,3819],{},[895,3816,3817],{},[898,3818,1675],{},[902,3820,1675],{"encoding":904},[883,3822,3824],{"className":3823},[886],[888,3825,3826],{"xmlns":890},[892,3827,3828,3836],{},[895,3829,3830],{},[1716,3831,3832,3834],{},[898,3833,1660],{},[898,3835,1722],{},[902,3837,3587],{"encoding":904},[883,3839,3841],{"className":3840},[886],[888,3842,3843],{"xmlns":890},[892,3844,3845,3849],{},[895,3846,3847],{},[898,3848,1660],{},[902,3850,1660],{"encoding":904},"); tečkované čáry z ",[883,3853,3855],{"className":3854},[886],[888,3856,3857],{"xmlns":890},[892,3858,3859,3863],{},[895,3860,3861],{},[898,3862,1722],{},[902,3864,1722],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[1921,3867,3868,3874],{},[724,3869,3870,3873],{},[883,3871,3872],{},"!tip"," Postup — jak najít IS-LM rovnováhu",[152,3875,3876,3952,4020,4079,4152],{},[123,3877,3878,3881,3882,2009,3902,3922,3923,2009,3936,3949,3950,2186],{},[38,3879,3880],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,3883,3885],{"className":3884},[886],[888,3886,3887],{"xmlns":890},[892,3888,3889,3899],{},[895,3890,3891,3893,3895,3897],{},[898,3892,1940],{},[1711,3894,1714],{"stretchy":1713},[898,3896,1660],{},[1711,3898,1735],{"stretchy":1713},[902,3900,3901],{"encoding":904},"C(Y)",[883,3903,3905],{"className":3904},[886],[888,3906,3907],{"xmlns":890},[892,3908,3909,3919],{},[895,3910,3911,3913,3915,3917],{},[898,3912,1833],{},[1711,3914,1714],{"stretchy":1713},[898,3916,1675],{},[1711,3918,1735],{"stretchy":1713},[902,3920,3921],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,3924,3926],{"className":3925},[886],[888,3927,3928],{"xmlns":890},[892,3929,3930,3934],{},[895,3931,3932],{},[898,3933,1660],{},[902,3935,1660],{"encoding":904},[883,3937,3939],{"className":3938},[886],[888,3940,3941],{"xmlns":890},[892,3942,3943,3947],{},[895,3944,3945],{},[898,3946,1675],{},[902,3948,1675],{"encoding":904}," — dostaneš rovnici ",[38,3951,1685],{},[123,3953,3954,3957,3958,2009,3975,3992,3993,3949,4018,2186],{},[38,3955,3956],{},"Z trhu peněz (7.15)"," dosaď ",[883,3959,3961],{"className":3960},[886],[888,3962,3963],{"xmlns":890},[892,3964,3965,3973],{},[895,3966,3967],{},[2884,3968,3969,3971],{},[898,3970,2888],{},[2111,3972,2238],{},[902,3974,2893],{"encoding":904},[883,3976,3978],{"className":3977},[886],[888,3979,3980],{"xmlns":890},[892,3981,3982,3990],{},[895,3983,3984],{},[2884,3985,3986,3988],{},[898,3987,2888],{},[2111,3989,2963],{},[902,3991,2966],{"encoding":904}," a vztah ",[883,3994,3996],{"className":3995},[886],[888,3997,3998],{"xmlns":890},[892,3999,4000,4016],{},[895,4001,4002,4008,4010],{},[1716,4003,4004,4006],{},[898,4005,1790],{},[898,4007,2778],{},[1711,4009,1836],{},[1716,4011,4012,4014],{},[898,4013,1790],{},[1711,4015,1793],{},[902,4017,3163],{"encoding":904},[38,4019,1692],{},[123,4021,4022,4025,4026,2009,4039,4052,4053,4078],{},[38,4023,4024],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,4027,4029],{"className":4028},[886],[888,4030,4031],{"xmlns":890},[892,4032,4033,4037],{},[895,4034,4035],{},[898,4036,1660],{},[902,4038,1660],{"encoding":904},[883,4040,4042],{"className":4041},[886],[888,4043,4044],{"xmlns":890},[892,4045,4046,4050],{},[895,4047,4048],{},[898,4049,1675],{},[902,4051,1675],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,4054,4056],{"className":4055},[886],[888,4057,4058],{"xmlns":890},[892,4059,4060,4075],{},[895,4061,4062,4064,4066,4069,4071,4073],{},[898,4063,1660],{},[1711,4065,1836],{},[898,4067,4068],{},"f",[1711,4070,1714],{"stretchy":1713},[898,4072,1675],{},[1711,4074,1735],{"stretchy":1713},[902,4076,4077],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,4080,4081,1700,4084,2009,4118,2186],{},[38,4082,4083],{},"Zpětně dopočítej",[883,4085,4087],{"className":4086},[886],[888,4088,4089],{"xmlns":890},[892,4090,4091,4115],{},[895,4092,4093,4099,4101,4103,4105,4111,4113],{},[1716,4094,4095,4097],{},[898,4096,1940],{},[898,4098,1722],{},[1711,4100,1836],{},[898,4102,207],{},[1942,4104,2519],{},[1716,4106,4107,4109],{},[898,4108,1660],{},[898,4110,1722],{},[1711,4112,2095],{},[898,4114,2223],{},[902,4116,4117],{"encoding":904},"C^E = a\\,Y^E + b",[883,4119,4121],{"className":4120},[886],[888,4122,4123],{"xmlns":890},[892,4124,4125,4149],{},[895,4126,4127,4133,4135,4137,4139,4145,4147],{},[1716,4128,4129,4131],{},[898,4130,1833],{},[898,4132,1722],{},[1711,4134,1836],{},[898,4136,2090],{},[1942,4138,2519],{},[1716,4140,4141,4143],{},[898,4142,1675],{},[898,4144,1722],{},[1711,4146,2095],{},[898,4148,2098],{},[902,4150,4151],{"encoding":904},"I^E = c\\,r^E + d",[123,4153,4154,4157,4158,4192,4193,4247],{},[38,4155,4156],{},"Ověř:"," musí platit ",[883,4159,4161],{"className":4160},[886],[888,4162,4163],{"xmlns":890},[892,4164,4165,4189],{},[895,4166,4167,4173,4175,4181,4183],{},[1716,4168,4169,4171],{},[898,4170,1660],{},[898,4172,1722],{},[1711,4174,1836],{},[1716,4176,4177,4179],{},[898,4178,1940],{},[898,4180,1722],{},[1711,4182,2095],{},[1716,4184,4185,4187],{},[898,4186,1833],{},[898,4188,1722],{},[902,4190,4191],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,4194,4196],{"className":4195},[886],[888,4197,4198],{"xmlns":890},[892,4199,4200,4244],{},[895,4201,4202,4208,4210,4216,4222,4224,4230,4236,4238],{},[1716,4203,4204,4206],{},[898,4205,1790],{},[1711,4207,1793],{},[1711,4209,1836],{},[2884,4211,4212,4214],{},[898,4213,2918],{},[2111,4215,2238],{},[1716,4217,4218,4220],{},[898,4219,1660],{},[898,4221,1722],{},[1711,4223,2095],{},[2884,4225,4226,4228],{},[898,4227,2918],{},[2111,4229,2963],{},[1716,4231,4232,4234],{},[898,4233,1675],{},[898,4235,1722],{},[1711,4237,2095],{},[2884,4239,4240,4242],{},[898,4241,2918],{},[2111,4243,3034],{},[902,4245,4246],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,4249,4251],{"id":4250},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,4253,4254],{},"Pro trh zboží jsou dány:",[120,4256,4257,4286],{},[123,4258,4259,4260,1726],{},"spotřeba ",[883,4261,4263],{"className":4262},[886],[888,4264,4265],{"xmlns":890},[892,4266,4267,4283],{},[895,4268,4269,4271,4273,4276,4278,4280],{},[898,4270,1940],{},[1711,4272,1836],{},[2111,4274,4275],{},"0,8",[898,4277,1660],{},[1711,4279,2095],{},[2111,4281,4282],{},"100",[902,4284,4285],{"encoding":904},"C = 0{,}8Y + 100",[123,4287,4288,4289,2186],{},"investice ",[883,4290,4292],{"className":4291},[886],[888,4293,4294],{"xmlns":890},[892,4295,4296,4314],{},[895,4297,4298,4300,4302,4304,4307,4309,4311],{},[898,4299,1833],{},[1711,4301,1836],{},[1711,4303,2460],{},[2111,4305,4306],{},"20",[898,4308,1675],{},[1711,4310,2095],{},[2111,4312,4313],{},"1000",[902,4315,4316],{"encoding":904},"I = -20r + 1000",[724,4318,4319],{},"Pro trh peněz:",[120,4321,4322,4349,4383],{},[123,4323,4324,1726],{},[883,4325,4327],{"className":4326},[886],[888,4328,4329],{"xmlns":890},[892,4330,4331,4346],{},[895,4332,4333,4339,4341,4344],{},[2884,4334,4335,4337],{},[898,4336,2888],{},[2111,4338,2238],{},[1711,4340,1836],{},[2111,4342,4343],{},"0,1",[898,4345,1660],{},[902,4347,4348],{"encoding":904},"L_1 = 0{,}1Y",[123,4350,4351,1726],{},[883,4352,4354],{"className":4353},[886],[888,4355,4356],{"xmlns":890},[892,4357,4358,4380],{},[895,4359,4360,4366,4368,4370,4373,4375,4377],{},[2884,4361,4362,4364],{},[898,4363,2888],{},[2111,4365,2963],{},[1711,4367,1836],{},[1711,4369,2460],{},[2111,4371,4372],{},"25",[898,4374,1675],{},[1711,4376,2095],{},[2111,4378,4379],{},"2000",[902,4381,4382],{"encoding":904},"L_2 = -25r + 2000",[123,4384,4385,4386,2186],{},"nabídka peněz ",[883,4387,4389],{"className":4388},[886],[888,4390,4391],{"xmlns":890},[892,4392,4393,4406],{},[895,4394,4395,4401,4403],{},[1716,4396,4397,4399],{},[898,4398,1790],{},[1711,4400,1793],{},[1711,4402,1836],{},[2111,4404,4405],{},"2375",[902,4407,4408],{"encoding":904},"M^* = 2375",[724,4410,4411,4414,4415,2062],{},[38,4412,4413],{},"Funkce IS"," — dosazením do (7.13) ",[883,4416,4418],{"className":4417},[886],[888,4419,4420],{"xmlns":890},[892,4421,4422,4434],{},[895,4423,4424,4426,4428,4430,4432],{},[898,4425,1660],{},[1711,4427,1836],{},[898,4429,1940],{},[1711,4431,2095],{},[898,4433,1833],{},[902,4435,4436],{"encoding":904},"Y = C + I",[724,4438,4439],{},[883,4440,4442],{"className":4441},[886],[888,4443,4444],{"xmlns":890},[892,4445,4446,4472],{},[895,4447,4448,4450,4452,4454,4456,4458,4460,4462,4464,4466,4468,4470],{},[898,4449,1660],{},[1711,4451,1836],{},[2111,4453,4275],{},[898,4455,1660],{},[1711,4457,2095],{},[2111,4459,4282],{},[1711,4461,2460],{},[2111,4463,4306],{},[898,4465,1675],{},[1711,4467,2095],{},[2111,4469,4313],{},[1711,4471,1726],{"separator":1725},[902,4473,4474],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,4476,4477],{},"tj.",[724,4479,4480],{},[883,4481,4483],{"className":4482},[886],[888,4484,4485],{"xmlns":890},[892,4486,4487,4513],{},[895,4488,4489,4492,4494,4496,4498,4500,4502,4505,4507,4509,4511],{},[2111,4490,4491],{},"0,2",[898,4493,1660],{},[1711,4495,2095],{},[2111,4497,4306],{},[898,4499,1675],{},[1711,4501,1836],{},[2111,4503,4504],{},"1100.",[2102,4506],{"width":2104},[1711,4508,1714],{"stretchy":1713},[1942,4510,1685],{},[1711,4512,1735],{"stretchy":1713},[902,4514,4515],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,4517,4518,4521,4522,2062],{},[38,4519,4520],{},"Funkce LM"," — dosazením do (7.15) ",[883,4523,4525],{"className":4524},[886],[888,4526,4527],{"xmlns":890},[892,4528,4529,4553],{},[895,4530,4531,4537,4539,4545,4547],{},[1716,4532,4533,4535],{},[898,4534,1790],{},[1711,4536,1793],{},[1711,4538,1836],{},[2884,4540,4541,4543],{},[898,4542,2888],{},[2111,4544,2238],{},[1711,4546,2095],{},[2884,4548,4549,4551],{},[898,4550,2888],{},[2111,4552,2963],{},[902,4554,4555],{"encoding":904},"M^* = L_1 + L_2",[724,4557,4558],{},[883,4559,4561],{"className":4560},[886],[888,4562,4563],{"xmlns":890},[892,4564,4565,4587],{},[895,4566,4567,4569,4571,4573,4575,4577,4579,4581,4583,4585],{},[2111,4568,4405],{},[1711,4570,1836],{},[2111,4572,4343],{},[898,4574,1660],{},[1711,4576,2460],{},[2111,4578,4372],{},[898,4580,1675],{},[1711,4582,2095],{},[2111,4584,4379],{},[1711,4586,1726],{"separator":1725},[902,4588,4589],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,4591,4477],{},[724,4593,4594],{},[883,4595,4597],{"className":4596},[886],[888,4598,4599],{"xmlns":890},[892,4600,4601,4626],{},[895,4602,4603,4605,4607,4609,4611,4613,4615,4618,4620,4622,4624],{},[2111,4604,4343],{},[898,4606,1660],{},[1711,4608,2460],{},[2111,4610,4372],{},[898,4612,1675],{},[1711,4614,1836],{},[2111,4616,4617],{},"375.",[2102,4619],{"width":2104},[1711,4621,1714],{"stretchy":1713},[1942,4623,1692],{},[1711,4625,1735],{"stretchy":1713},[902,4627,4628],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,4630,4631,4634,4635,4660],{},[38,4632,4633],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,4636,4638],{"className":4637},[886],[888,4639,4640],{"xmlns":890},[892,4641,4642,4657],{},[895,4643,4644,4646,4648,4651,4653,4655],{},[898,4645,1660],{},[1711,4647,1836],{},[2111,4649,4650],{},"5500",[1711,4652,2460],{},[2111,4654,4282],{},[898,4656,1675],{},[902,4658,4659],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,4662,4663],{},[883,4664,4666],{"className":4665},[886],[888,4667,4668],{"xmlns":890},[892,4669,4670,4758],{},[895,4671,4672,4674,4676,4678,4680,4682,4684,4686,4688,4690,4692,4694,4697,4700,4703,4705,4708,4710,4713,4715,4717,4719,4721,4723,4725,4727,4729,4731,4734,4736,4738,4741,4743,4745,4747,4753,4755],{},[2111,4673,4343],{},[1711,4675,1714],{"stretchy":1713},[2111,4677,4650],{},[1711,4679,2460],{},[2111,4681,4282],{},[898,4683,1675],{},[1711,4685,1735],{"stretchy":1713},[1711,4687,2460],{},[2111,4689,4372],{},[898,4691,1675],{},[1711,4693,1836],{},[2111,4695,4696],{},"375",[1942,4698,4699],{},"  ",[1711,4701,4702],{},"⟹",[1942,4704,4699],{},[2111,4706,4707],{},"550",[1711,4709,2460],{},[2111,4711,4712],{},"10",[898,4714,1675],{},[1711,4716,2460],{},[2111,4718,4372],{},[898,4720,1675],{},[1711,4722,1836],{},[2111,4724,4696],{},[1942,4726,4699],{},[1711,4728,4702],{},[1942,4730,4699],{},[2111,4732,4733],{},"35",[898,4735,1675],{},[1711,4737,1836],{},[2111,4739,4740],{},"175",[1942,4742,4699],{},[1711,4744,4702],{},[1942,4746,4699],{},[1716,4748,4749,4751],{},[898,4750,1675],{},[898,4752,1722],{},[1711,4754,1836],{},[2111,4756,4757],{},"5.",[902,4759,4760],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,4762,4763],{},[38,4764,4765],{},"Zpětné dosazení:",[120,4767,4768,4816,4853],{},[123,4769,4770,1726],{},[883,4771,4773],{"className":4772},[886],[888,4774,4775],{"xmlns":890},[892,4776,4777,4813],{},[895,4778,4779,4785,4787,4789,4791,4793,4796,4799,4801,4803,4805,4808,4810],{},[1716,4780,4781,4783],{},[898,4782,1660],{},[898,4784,1722],{},[1711,4786,1836],{},[2111,4788,4650],{},[1711,4790,2460],{},[2111,4792,4282],{},[1711,4794,4795],{},"⋅",[2111,4797,4798],{},"5",[1711,4800,1836],{},[2111,4802,4650],{},[1711,4804,2460],{},[2111,4806,4807],{},"500",[1711,4809,1836],{},[2111,4811,4812],{},"5000",[902,4814,4815],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,4817,4818,1726],{},[883,4819,4821],{"className":4820},[886],[888,4822,4823],{"xmlns":890},[892,4824,4825,4850],{},[895,4826,4827,4833,4835,4837,4839,4841,4843,4845,4847],{},[1716,4828,4829,4831],{},[898,4830,1940],{},[898,4832,1722],{},[1711,4834,1836],{},[2111,4836,4275],{},[1711,4838,4795],{},[2111,4840,4812],{},[1711,4842,2095],{},[2111,4844,4282],{},[1711,4846,1836],{},[2111,4848,4849],{},"4100",[902,4851,4852],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,4854,4855,2186],{},[883,4856,4858],{"className":4857},[886],[888,4859,4860],{"xmlns":890},[892,4861,4862,4889],{},[895,4863,4864,4870,4872,4874,4876,4878,4880,4882,4884,4886],{},[1716,4865,4866,4868],{},[898,4867,1833],{},[898,4869,1722],{},[1711,4871,1836],{},[1711,4873,2460],{},[2111,4875,4306],{},[1711,4877,4795],{},[2111,4879,4798],{},[1711,4881,2095],{},[2111,4883,4313],{},[1711,4885,1836],{},[2111,4887,4888],{},"900",[902,4890,4891],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,4893,4894,1700,4897,4943],{},[38,4895,4896],{},"Ověření:",[883,4898,4900],{"className":4899},[886],[888,4901,4902],{"xmlns":890},[892,4903,4904,4940],{},[895,4905,4906,4912,4914,4920,4922,4924,4926,4928,4930,4932,4934],{},[1716,4907,4908,4910],{},[898,4909,1940],{},[898,4911,1722],{},[1711,4913,2095],{},[1716,4915,4916,4918],{},[898,4917,1833],{},[898,4919,1722],{},[1711,4921,1836],{},[2111,4923,4849],{},[1711,4925,2095],{},[2111,4927,4888],{},[1711,4929,1836],{},[2111,4931,4812],{},[1711,4933,1836],{},[1716,4935,4936,4938],{},[898,4937,1660],{},[898,4939,1722],{},[902,4941,4942],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,4945,4946],{},[883,4947,4949],{"className":4948},[886],[888,4950,4951],{"xmlns":890},[892,4952,4953,5023],{},[895,4954,4955],{},[2505,4956,4957],{"notation":2507},[2509,4958,4959],{"scriptlevel":2113,"displaystyle":1713},[2509,4960,4961],{"scriptlevel":2113,"displaystyle":1713},[2509,4962,4963],{"scriptlevel":2113,"displaystyle":1725},[895,4964,4965,4967,4973,4975,4977,4979,4982,4988,4990,4992,4994,4996,5002,5004,5006,5008,5010,5016,5018,5021],{},[1942,4966,2519],{},[1716,4968,4969,4971],{},[898,4970,1660],{},[898,4972,1722],{},[1711,4974,1836],{},[2111,4976,4812],{},[1711,4978,1726],{"separator":1725},[2102,4980],{"width":4981},"1em",[1716,4983,4984,4986],{},[898,4985,1675],{},[898,4987,1722],{},[1711,4989,1836],{},[2111,4991,4798],{},[1711,4993,1726],{"separator":1725},[2102,4995],{"width":4981},[1716,4997,4998,5000],{},[898,4999,1940],{},[898,5001,1722],{},[1711,5003,1836],{},[2111,5005,4849],{},[1711,5007,1726],{"separator":1725},[2102,5009],{"width":4981},[1716,5011,5012,5014],{},[898,5013,1833],{},[898,5015,1722],{},[1711,5017,1836],{},[2111,5019,5020],{},"900.",[1942,5022,2519],{},[902,5024,5025],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,5027,5028],{},[614,5029,5030,5031,5044,5045,5058,5059,5074,5075,5088,5089,5104,5105,5118,5119,5132,5133,2186],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,5032,5034],{"className":5033},[886],[888,5035,5036],{"xmlns":890},[892,5037,5038,5042],{},[895,5039,5040],{},[898,5041,1660],{},[902,5043,1660],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,5046,5048],{"className":5047},[886],[888,5049,5050],{"xmlns":890},[892,5051,5052,5056],{},[895,5053,5054],{},[898,5055,1675],{},[902,5057,1675],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,5060,5062],{"className":5061},[886],[888,5063,5064],{"xmlns":890},[892,5065,5066,5072],{},[895,5067,5068,5070],{},[898,5069,2888],{},[898,5071,1790],{},[902,5073,1692],{"encoding":904}," stoupá z oblasti nízkých ",[883,5076,5078],{"className":5077},[886],[888,5079,5080],{"xmlns":890},[892,5081,5082,5086],{},[895,5083,5084],{},[898,5085,1675],{},[902,5087,1675],{"encoding":904},", přímka ",[883,5090,5092],{"className":5091},[886],[888,5093,5094],{"xmlns":890},[892,5095,5096,5102],{},[895,5097,5098,5100],{},[898,5099,1833],{},[898,5101,2362],{},[902,5103,1685],{"encoding":904}," klesá a protíná osu ",[883,5106,5108],{"className":5107},[886],[888,5109,5110],{"xmlns":890},[892,5111,5112,5116],{},[895,5113,5114],{},[898,5115,1675],{},[902,5117,1675],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,5120,5122],{"className":5121},[886],[888,5123,5124],{"xmlns":890},[892,5125,5126,5130],{},[895,5127,5128],{},[898,5129,1722],{},[902,5131,1722],{"encoding":904}," leží v bodě ",[883,5134,5136],{"className":5135},[886],[888,5137,5138],{"xmlns":890},[892,5139,5140,5164],{},[895,5141,5142,5145,5147,5149,5151,5153,5155,5157,5159,5161],{},[1711,5143,5144],{"stretchy":1713},"[",[898,5146,1675],{},[1711,5148,1836],{},[2111,5150,4798],{},[1711,5152,1726],{"separator":1725},[1942,5154,2118],{},[898,5156,1660],{},[1711,5158,1836],{},[2111,5160,4812],{},[1711,5162,5163],{"stretchy":1713},"]",[902,5165,5166],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,5168,5170],{"id":5169},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,5172,5173,5176,5177,5190,5191,5204,5205,5208,5209,5229,5230,5247,5248,5265,5266,5279,5280,5293],{},[38,5174,5175],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,5178,5180],{"className":5179},[886],[888,5181,5182],{"xmlns":890},[892,5183,5184,5188],{},[895,5185,5186],{},[898,5187,1755],{},[902,5189,1755],{"encoding":904}," nebo snížení daní ",[883,5192,5194],{"className":5193},[886],[888,5195,5196],{"xmlns":890},[892,5197,5198,5202],{},[895,5199,5200],{},[898,5201,1769],{},[902,5203,1769],{"encoding":904}," — ",[38,5206,5207],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,5210,5212],{"className":5211},[886],[888,5213,5214],{"xmlns":890},[892,5215,5216,5226],{},[895,5217,5218],{},[1716,5219,5220,5222],{},[898,5221,1722],{},[1711,5223,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},"0em","′",[902,5227,5228],{"encoding":904},"E'"," má vyšší ",[883,5231,5233],{"className":5232},[886],[888,5234,5235],{"xmlns":890},[892,5236,5237,5245],{},[895,5238,5239],{},[1716,5240,5241,5243],{},[898,5242,1660],{},[898,5244,1722],{},[902,5246,3587],{"encoding":904}," i vyšší ",[883,5249,5251],{"className":5250},[886],[888,5252,5253],{"xmlns":890},[892,5254,5255,5263],{},[895,5256,5257],{},[1716,5258,5259,5261],{},[898,5260,1675],{},[898,5262,1722],{},[902,5264,3608],{"encoding":904}," (vyšší ",[883,5267,5269],{"className":5268},[886],[888,5270,5271],{"xmlns":890},[892,5272,5273,5277],{},[895,5274,5275],{},[898,5276,1660],{},[902,5278,1660],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,5281,5283],{"className":5282},[886],[888,5284,5285],{"xmlns":890},[892,5286,5287,5291],{},[895,5288,5289],{},[898,5290,1675],{},[902,5292,1675],{"encoding":904}," nahoru).",[724,5295,5296],{},[1801,5297],{"alt":5298,"className":5299,"src":5300},"imek-posun-is-lm-politiky",[210,1805],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,5302,5303,5306,5307,5324,5325,5328,5329,5346,5347,5364,5365,5378,5379,5398,5399,1797],{},[38,5304,5305],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,5308,5310],{"className":5309},[886],[888,5311,5312],{"xmlns":890},[892,5313,5314,5322],{},[895,5315,5316],{},[1716,5317,5318,5320],{},[898,5319,1790],{},[1711,5321,1793],{},[902,5323,1796],{"encoding":904}," národní bankou — ",[38,5326,5327],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,5330,5332],{"className":5331},[886],[888,5333,5334],{"xmlns":890},[892,5335,5336,5344],{},[895,5337,5338],{},[1716,5339,5340,5342],{},[898,5341,1675],{},[898,5343,1722],{},[902,5345,3608],{"encoding":904}," a vyšší ",[883,5348,5350],{"className":5349},[886],[888,5351,5352],{"xmlns":890},[892,5353,5354,5362],{},[895,5355,5356],{},[1716,5357,5358,5360],{},[898,5359,1660],{},[898,5361,1722],{},[902,5363,3587],{"encoding":904}," (nižší ",[883,5366,5368],{"className":5367},[886],[888,5369,5370],{"xmlns":890},[892,5371,5372,5376],{},[895,5373,5374],{},[898,5375,1675],{},[902,5377,1675],{"encoding":904}," povzbuzuje investice ",[883,5380,5382],{"className":5381},[886],[888,5383,5384],{"xmlns":890},[892,5385,5386,5396],{},[895,5387,5388,5390,5392,5394],{},[898,5389,1833],{},[1711,5391,1714],{"stretchy":1713},[898,5393,1675],{},[1711,5395,1735],{"stretchy":1713},[902,5397,3921],{"encoding":904},", ty zvedají ",[883,5400,5402],{"className":5401},[886],[888,5403,5404],{"xmlns":890},[892,5405,5406,5410],{},[895,5407,5408],{},[898,5409,1660],{},[902,5411,1660],{"encoding":904},[724,5413,5414,5415,5418],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,5416,5417],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,5420,5422],{"id":5421},"klíčové-pojmy","Klíčové pojmy",[120,5424,5425,5498,5544,5626,5676,5743,5800,5841,5874],{},[123,5426,5427,5204,5460,1343,5477,5494,5495,5497],{},[38,5428,5429,5430],{},"Funkce investic ",[883,5431,5433],{"className":5432},[886],[888,5434,5435],{"xmlns":890},[892,5436,5437,5457],{},[895,5438,5439,5441,5443,5445,5447,5449,5451,5453,5455],{},[898,5440,1833],{},[1711,5442,1714],{"stretchy":1713},[898,5444,1675],{},[1711,5446,1735],{"stretchy":1713},[1711,5448,1836],{},[898,5450,2090],{},[898,5452,1675],{},[1711,5454,2095],{},[898,5456,2098],{},[902,5458,5459],{"encoding":904},"I(r) = cr + d",[883,5461,5463],{"className":5462},[886],[888,5464,5465],{"xmlns":890},[892,5466,5467,5475],{},[895,5468,5469,5471,5473],{},[898,5470,2090],{},[1711,5472,2109],{},[2111,5474,2113],{},[902,5476,2181],{"encoding":904},[883,5478,5480],{"className":5479},[886],[888,5481,5482],{"xmlns":890},[892,5483,5484,5492],{},[895,5485,5486,5488,5490],{},[898,5487,2098],{},[1711,5489,2123],{},[2111,5491,2113],{},[902,5493,2160],{"encoding":904},"; ",[38,5496,2185],{}," funkce úrokové míry.",[123,5499,5500,5503,5504,5525,5526,5543],{},[38,5501,5502],{},"Trh zboží"," — rovnováha ",[883,5505,5507],{"className":5506},[886],[888,5508,5509],{"xmlns":890},[892,5510,5511,5523],{},[895,5512,5513,5515,5517,5519,5521],{},[898,5514,1660],{},[1711,5516,1836],{},[898,5518,1940],{},[1711,5520,2095],{},[898,5522,1833],{},[902,5524,4436],{"encoding":904},", ekvivalentně ",[883,5527,5529],{"className":5528},[886],[888,5530,5531],{"xmlns":890},[892,5532,5533,5541],{},[895,5534,5535,5537,5539],{},[898,5536,1833],{},[1711,5538,1836],{},[898,5540,2362],{},[902,5542,2384],{"encoding":904}," (investice = úspory).",[123,5545,5546,1648,5549,5551,5552,5602,5603,2591,5605,2186],{},[38,5547,5548],{},"Křivka IS",[614,5550,1688],{},") — ",[883,5553,5555],{"className":5554},[886],[888,5556,5557],{"xmlns":890},[892,5558,5559,5599],{},[895,5560,5561,5563,5565,5577,5579,5581],{},[898,5562,1660],{},[1711,5564,1836],{},[2525,5566,5567,5569],{},[898,5568,2090],{},[895,5570,5571,5573,5575],{},[2111,5572,2238],{},[1711,5574,2460],{},[898,5576,207],{},[898,5578,1675],{},[1711,5580,2095],{},[2525,5582,5583,5591],{},[895,5584,5585,5587,5589],{},[898,5586,2223],{},[1711,5588,2095],{},[898,5590,2098],{},[895,5592,5593,5595,5597],{},[2111,5594,2238],{},[1711,5596,2460],{},[898,5598,207],{},[902,5600,5601],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,5604,2185],{},[883,5606,5608],{"className":5607},[886],[888,5609,5610],{"xmlns":890},[892,5611,5612,5624],{},[895,5613,5614,5616,5618,5620,5622],{},[1711,5615,1714],{"stretchy":1713},[898,5617,1675],{},[1711,5619,1726],{"separator":1725},[898,5621,1660],{},[1711,5623,1735],{"stretchy":1713},[902,5625,2613],{"encoding":904},[123,5627,5628,5503,5631,5657,5658,2186],{},[38,5629,5630],{},"Trh peněz",[883,5632,5634],{"className":5633},[886],[888,5635,5636],{"xmlns":890},[892,5637,5638,5654],{},[895,5639,5640,5646,5648],{},[1716,5641,5642,5644],{},[898,5643,1790],{},[898,5645,2778],{},[1711,5647,1836],{},[1716,5649,5650,5652],{},[898,5651,1790],{},[898,5653,2362],{},[902,5655,5656],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,5659,5661],{"className":5660},[886],[888,5662,5663],{"xmlns":890},[892,5664,5665,5673],{},[895,5666,5667],{},[1716,5668,5669,5671],{},[898,5670,1790],{},[1711,5672,1793],{},[902,5674,5675],{"encoding":904},"M^* ",[123,5677,5678,5204,5681,2186],{},[38,5679,5680],{},"Transakční, opatrnostní, spekulační poptávka",[883,5682,5684],{"className":5683},[886],[888,5685,5686],{"xmlns":890},[892,5687,5688,5740],{},[895,5689,5690,5696,5698,5704,5706,5712,5714,5720,5722,5724,5730,5732,5734],{},[1716,5691,5692,5694],{},[898,5693,1790],{},[898,5695,2778],{},[1711,5697,1836],{},[2884,5699,5700,5702],{},[898,5701,2888],{},[2111,5703,2238],{},[1711,5705,2095],{},[2884,5707,5708,5710],{},[898,5709,2888],{},[2111,5711,2963],{},[1711,5713,1836],{},[2884,5715,5716,5718],{},[898,5717,2918],{},[2111,5719,2238],{},[898,5721,1660],{},[1711,5723,2095],{},[2884,5725,5726,5728],{},[898,5727,2918],{},[2111,5729,2963],{},[898,5731,1675],{},[1711,5733,2095],{},[2884,5735,5736,5738],{},[898,5737,2918],{},[2111,5739,3034],{},[902,5741,5742],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,5744,5745,1648,5748,5551,5750,5796,5797,5799],{},[38,5746,5747],{},"Křivka LM",[614,5749,1695],{},[883,5751,5753],{"className":5752},[886],[888,5754,5755],{"xmlns":890},[892,5756,5757,5793],{},[895,5758,5759,5765,5767,5773,5775,5777,5783,5785,5787],{},[1716,5760,5761,5763],{},[898,5762,1790],{},[1711,5764,1793],{},[1711,5766,1836],{},[2884,5768,5769,5771],{},[898,5770,2918],{},[2111,5772,2238],{},[898,5774,1660],{},[1711,5776,2095],{},[2884,5778,5779,5781],{},[898,5780,2918],{},[2111,5782,2963],{},[898,5784,1675],{},[1711,5786,2095],{},[2884,5788,5789,5791],{},[898,5790,2918],{},[2111,5792,3034],{},[902,5794,5795],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,5798,3341],{}," přímka.",[123,5801,5802,5805,5806,5840],{},[38,5803,5804],{},"Simultánní rovnováha"," — průsečík ",[883,5807,5809],{"className":5808},[886],[888,5810,5811],{"xmlns":890},[892,5812,5813,5837],{},[895,5814,5815,5817,5819,5821,5827,5829,5835],{},[898,5816,1722],{},[1711,5818,1836],{},[1711,5820,1714],{"stretchy":1713},[1716,5822,5823,5825],{},[898,5824,1675],{},[898,5826,1722],{},[1711,5828,1726],{"separator":1725},[1716,5830,5831,5833],{},[898,5832,1660],{},[898,5834,1722],{},[1711,5836,1735],{"stretchy":1713},[902,5838,5839],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,5842,5843,5846,5847,1343,5860,5873],{},[38,5844,5845],{},"Fiskální politika"," — nástroje ",[883,5848,5850],{"className":5849},[886],[888,5851,5852],{"xmlns":890},[892,5853,5854,5858],{},[895,5855,5856],{},[898,5857,1755],{},[902,5859,1755],{"encoding":904},[883,5861,5863],{"className":5862},[886],[888,5864,5865],{"xmlns":890},[892,5866,5867,5871],{},[895,5868,5869],{},[898,5870,1769],{},[902,5872,1769],{"encoding":904}," posouvající křivku IS.",[123,5875,5876,5879,5880,5897],{},[38,5877,5878],{},"Monetární politika"," — nástroj ",[883,5881,5883],{"className":5882},[886],[888,5884,5885],{"xmlns":890},[892,5886,5887,5895],{},[895,5888,5889],{},[1716,5890,5891,5893],{},[898,5892,1790],{},[1711,5894,1793],{},[902,5896,1796],{"encoding":904}," posouvající křivku LM.",[115,5899,5901],{"id":5900},"navigace","Navigace",[120,5903,5904,5915,5924,5934],{},[123,5905,5906,1700,5909],{},[38,5907,5908],{},"Kurz:",[207,5910,5914],{"className":5911,"dataFsResolvedFilePath":5912,"href":5913},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","Matematická ekonomie",[123,5916,5917,1700,5920],{},[38,5918,5919],{},"Přednáška:",[207,5921,5923],{"className":5922,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,5925,5926,1700,5929,5933],{},[38,5927,5928],{},"Nadřazené téma:",[207,5930,5932],{"className":5931,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,5935,5936,5939],{},[38,5937,5938],{},"Související:",[120,5940,5941,5948,5954],{},[123,5942,5943,5947],{},[207,5944,5946],{"className":5945,"dataFsResolvedFilePath":800,"href":801},[210],"poptavka-nabidka"," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,5949,5950,5953],{},[207,5951,1145],{"className":5952,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,5955,5956,5960],{},[207,5957,5959],{"className":5958,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":5962},[5963,5964,5965,5966,5967,5968,5969,5970,5971,5972],{"id":1637,"depth":642,"text":1638},{"id":1809,"depth":642,"text":1810},{"id":2030,"depth":642,"text":2031},{"id":2338,"depth":642,"text":2339},{"id":2758,"depth":642,"text":2759},{"id":3558,"depth":642,"text":3559},{"id":4250,"depth":642,"text":4251},{"id":5169,"depth":642,"text":5170},{"id":5421,"depth":642,"text":5422},{"id":5900,"depth":642,"text":5901},"2026-04-22",{},"\u002Ftopics\u002Fis-lm",{"title":1629,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,5980,1143,5981,5982,5983,5984,5932],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","topic","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk","topics",{"zapisku":1625,"topics":5989,"summaries":5990,"outputs":5991},15,5,1,[5993,7852,13543,15098,15970,19876,21483,31363,40357,54424,58716,78060,90172,99131,99419],{"id":5994,"title":5995,"body":5996,"course":1128,"courses":659,"created":1129,"description":7841,"extension":661,"meta":7842,"navigation":664,"path":7843,"seo":7844,"sources":7845,"stem":7846,"tags":7847,"type":5985,"updated":677,"__hash__":7851},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":5997,"toc":7824},[5998,6001,6020,6024,6102,6105,6228,6373,6376,6456,6460,6519,6569,6576,6580,6715,6766,6770,6810,6876,6946,6954,6958,6996,7068,7072,7151,7199,7243,7247,7251,7321,7325,7375,7452,7459,7462,7515,7785,7787],[12,5999,5995],{"id":6000},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,6002,6003,6004,6008,6009,6012,6013,6016,6017,2186],{},"Matematický aparát kurzu ",[207,6005,6007],{"className":6006,"dataFsResolvedFilePath":5912,"href":5913},[210],"ImeK",". Bez derivace se neobejdou ",[38,6010,6011],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,6014,6015],{},"maximalizace zisku"," ani ",[38,6018,6019],{},"minimalizace nákladů",[115,6021,6023],{"id":6022},"funkce-a-polynomy","Funkce a polynomy",[724,6025,6026,6027,6053,6054,6067,6068,6081,6082,2186],{},"Funkce jedné proměnné ",[883,6028,6030],{"className":6029},[886],[888,6031,6032],{"xmlns":890},[892,6033,6034,6050],{},[895,6035,6036,6039,6041,6043,6045,6048],{},[898,6037,6038],{},"y",[1711,6040,1836],{},[898,6042,4068],{},[1711,6044,1714],{"stretchy":1713},[898,6046,6047],{},"x",[1711,6049,1735],{"stretchy":1713},[902,6051,6052],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,6055,6057],{"className":6056},[886],[888,6058,6059],{"xmlns":890},[892,6060,6061,6065],{},[895,6062,6063],{},[898,6064,6047],{},[902,6066,6047],{"encoding":904}," (nezávislá) → ",[883,6069,6071],{"className":6070},[886],[888,6072,6073],{"xmlns":890},[892,6074,6075,6079],{},[895,6076,6077],{},[898,6078,6038],{},[902,6080,6038],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,6083,6085],{"className":6084},[886],[888,6086,6087],{"xmlns":890},[892,6088,6089,6099],{},[895,6090,6091,6093,6095,6097],{},[898,6092,4068],{},[1711,6094,1714],{"stretchy":1713},[898,6096,207],{},[1711,6098,1735],{"stretchy":1713},[902,6100,6101],{"encoding":904},"f(a)",[724,6103,6104],{},"Polynomy:",[120,6106,6107,6138,6178],{},[123,6108,6109],{},[152,6110,6111],{},[123,6112,6113,6114],{},"stupně: ",[883,6115,6117],{"className":6116},[886],[888,6118,6119],{"xmlns":890},[892,6120,6121,6135],{},[895,6122,6123,6125,6127,6129,6131,6133],{},[898,6124,6038],{},[1711,6126,1836],{},[898,6128,207],{},[898,6130,6047],{},[1711,6132,2095],{},[898,6134,2223],{},[902,6136,6137],{"encoding":904},"y = ax + b",[123,6139,6140],{},[152,6141,6142],{"start":642},[123,6143,6113,6144],{},[883,6145,6147],{"className":6146},[886],[888,6148,6149],{"xmlns":890},[892,6150,6151,6175],{},[895,6152,6153,6155,6157,6159,6165,6167,6169,6171,6173],{},[898,6154,6038],{},[1711,6156,1836],{},[898,6158,207],{},[1716,6160,6161,6163],{},[898,6162,6047],{},[2111,6164,2963],{},[1711,6166,2095],{},[898,6168,2223],{},[898,6170,6047],{},[1711,6172,2095],{},[898,6174,2090],{},[902,6176,6177],{"encoding":904},"y = ax^2 + bx + c",[123,6179,6180],{},[152,6181,6182],{"start":649},[123,6183,6113,6184],{},[883,6185,6187],{"className":6186},[886],[888,6188,6189],{"xmlns":890},[892,6190,6191,6225],{},[895,6192,6193,6195,6197,6199,6205,6207,6209,6215,6217,6219,6221,6223],{},[898,6194,6038],{},[1711,6196,1836],{},[898,6198,207],{},[1716,6200,6201,6203],{},[898,6202,6047],{},[2111,6204,3034],{},[1711,6206,2095],{},[898,6208,2223],{},[1716,6210,6211,6213],{},[898,6212,6047],{},[2111,6214,2963],{},[1711,6216,2095],{},[898,6218,2090],{},[898,6220,6047],{},[1711,6222,2095],{},[898,6224,2098],{},[902,6226,6227],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,6229,6230,1700,6233,6288,6289,6325,6326,2186],{},[38,6231,6232],{},"Příklad rozkladu:",[883,6234,6236],{"className":6235},[886],[888,6237,6238],{"xmlns":890},[892,6239,6240,6285],{},[895,6241,6242,6244,6246,6252,6254,6256,6258,6260,6263,6265,6267,6269,6271,6273,6275,6277,6279,6281,6283],{},[898,6243,6038],{},[1711,6245,1836],{},[1716,6247,6248,6250],{},[898,6249,6047],{},[2111,6251,2963],{},[1711,6253,2460],{},[2111,6255,4798],{},[898,6257,6047],{},[1711,6259,2095],{},[2111,6261,6262],{},"6",[1711,6264,1836],{},[1711,6266,1714],{"stretchy":1713},[898,6268,6047],{},[1711,6270,2460],{},[2111,6272,2963],{},[1711,6274,1735],{"stretchy":1713},[1711,6276,1714],{"stretchy":1713},[898,6278,6047],{},[1711,6280,2460],{},[2111,6282,3034],{},[1711,6284,1735],{"stretchy":1713},[902,6286,6287],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,6290,6292],{"className":6291},[886],[888,6293,6294],{"xmlns":890},[892,6295,6296,6322],{},[895,6297,6298,6304,6306,6308,6310,6312,6318,6320],{},[2884,6299,6300,6302],{},[898,6301,6047],{},[2111,6303,2238],{},[1711,6305,1836],{},[2111,6307,2963],{},[1711,6309,1726],{"separator":1725},[1942,6311,2118],{},[2884,6313,6314,6316],{},[898,6315,6047],{},[2111,6317,2963],{},[1711,6319,1836],{},[2111,6321,3034],{},[902,6323,6324],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,6327,6329],{"className":6328},[886],[888,6330,6331],{"xmlns":890},[892,6332,6333,6370],{},[895,6334,6335,6337,6339,6341,6343,6345,6353,6359,6361],{},[898,6336,6038],{},[1711,6338,1836],{},[1711,6340,1714],{"stretchy":1713},[898,6342,6047],{},[1711,6344,2460],{},[2509,6346,6347],{"scriptlevel":2113,"displaystyle":1713},[2525,6348,6349,6351],{},[2111,6350,4798],{},[2111,6352,2963],{},[1716,6354,6355,6357],{},[1711,6356,1735],{"stretchy":1713},[2111,6358,2963],{},[1711,6360,2460],{},[2509,6362,6363],{"scriptlevel":2113,"displaystyle":1713},[2525,6364,6365,6367],{},[2111,6366,2238],{},[2111,6368,6369],{},"4",[902,6371,6372],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,6374,6375],{"id":1145},"Derivace",[724,6377,6378,6379,1348,6403,6431,6432,2186],{},"Označení ",[883,6380,6382],{"className":6381},[886],[888,6383,6384],{"xmlns":890},[892,6385,6386,6400],{},[895,6387,6388,6394,6396,6398],{},[1716,6389,6390,6392],{},[898,6391,4068],{},[1711,6393,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,6395,1714],{"stretchy":1713},[898,6397,6047],{},[1711,6399,1735],{"stretchy":1713},[902,6401,6402],{"encoding":904},"f'(x)",[883,6404,6406],{"className":6405},[886],[888,6407,6408],{"xmlns":890},[892,6409,6410,6428],{},[895,6411,6412],{},[2509,6413,6414],{"scriptlevel":2113,"displaystyle":1725},[2525,6415,6416,6422],{},[895,6417,6418,6420],{},[898,6419,2098],{},[898,6421,6038],{},[895,6423,6424,6426],{},[898,6425,2098],{},[898,6427,6047],{},[902,6429,6430],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,6433,6435],{"className":6434},[886],[888,6436,6437],{"xmlns":890},[892,6438,6439,6453],{},[895,6440,6441,6447,6449,6451],{},[1716,6442,6443,6445],{},[898,6444,4068],{},[1711,6446,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,6448,1714],{"stretchy":1713},[898,6450,207],{},[1711,6452,1735],{"stretchy":1713},[902,6454,6455],{"encoding":904},"f'(a)",[198,6457,6459],{"id":6458},"geometrická-interpretace","Geometrická interpretace",[724,6461,6462,6485,6486,6489,6490,6518],{},[883,6463,6465],{"className":6464},[886],[888,6466,6467],{"xmlns":890},[892,6468,6469,6483],{},[895,6470,6471,6477,6479,6481],{},[1716,6472,6473,6475],{},[898,6474,4068],{},[1711,6476,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,6478,1714],{"stretchy":1713},[898,6480,207],{},[1711,6482,1735],{"stretchy":1713},[902,6484,6455],{"encoding":904}," = ",[38,6487,6488],{},"sklon tečny"," ke grafu funkce v bodě ",[883,6491,6493],{"className":6492},[886],[888,6494,6495],{"xmlns":890},[892,6496,6497,6515],{},[895,6498,6499,6501,6503,6505,6507,6509,6511,6513],{},[1711,6500,5144],{"stretchy":1713},[898,6502,207],{},[1711,6504,1726],{"separator":1725},[898,6506,4068],{},[1711,6508,1714],{"stretchy":1713},[898,6510,207],{},[1711,6512,1735],{"stretchy":1713},[1711,6514,5163],{"stretchy":1713},[902,6516,6517],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,6520,6521],{},[883,6522,6524],{"className":6523},[886],[888,6525,6526],{"xmlns":890},[892,6527,6528,6566],{},[895,6529,6530,6532,6534,6536,6538,6540,6542,6544,6550,6552,6554,6556,6558,6560,6562,6564],{},[898,6531,6038],{},[1711,6533,2460],{},[898,6535,4068],{},[1711,6537,1714],{"stretchy":1713},[898,6539,207],{},[1711,6541,1735],{"stretchy":1713},[1711,6543,1836],{},[1716,6545,6546,6548],{},[898,6547,4068],{},[1711,6549,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,6551,1714],{"stretchy":1713},[898,6553,207],{},[1711,6555,1735],{"stretchy":1713},[1711,6557,1714],{"stretchy":1713},[898,6559,6047],{},[1711,6561,2460],{},[898,6563,207],{},[1711,6565,1735],{"stretchy":1713},[902,6567,6568],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,6570,6571],{},[1801,6572],{"alt":6573,"className":6574,"src":6575},"imek-derivace-tecna",[210,1805],"\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,6577,6579],{"id":6578},"inženýrská-interpretace","Inženýrská interpretace",[724,6581,6582,6485,6605,1700,6608,6621,6622,6635,6636,6654,6655,6668,6669,6682,6683,6696,6697,2062],{},[883,6583,6585],{"className":6584},[886],[888,6586,6587],{"xmlns":890},[892,6588,6589,6603],{},[895,6590,6591,6597,6599,6601],{},[1716,6592,6593,6595],{},[898,6594,4068],{},[1711,6596,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,6598,1714],{"stretchy":1713},[898,6600,207],{},[1711,6602,1735],{"stretchy":1713},[902,6604,6455],{"encoding":904},[38,6606,6607],{},"rychlost změny",[883,6609,6611],{"className":6610},[886],[888,6612,6613],{"xmlns":890},[892,6614,6615,6619],{},[895,6616,6617],{},[898,6618,6038],{},[902,6620,6038],{"encoding":904}," vzhledem k ",[883,6623,6625],{"className":6624},[886],[888,6626,6627],{"xmlns":890},[892,6628,6629,6633],{},[895,6630,6631],{},[898,6632,6047],{},[902,6634,6047],{"encoding":904}," v bodě ",[883,6637,6639],{"className":6638},[886],[888,6640,6641],{"xmlns":890},[892,6642,6643,6651],{},[895,6644,6645,6647,6649],{},[898,6646,6047],{},[1711,6648,1836],{},[898,6650,207],{},[902,6652,6653],{"encoding":904},"x = a","; přibližná změna ",[883,6656,6658],{"className":6657},[886],[888,6659,6660],{"xmlns":890},[892,6661,6662,6666],{},[895,6663,6664],{},[898,6665,6038],{},[902,6667,6038],{"encoding":904}," při změně ",[883,6670,6672],{"className":6671},[886],[888,6673,6674],{"xmlns":890},[892,6675,6676,6680],{},[895,6677,6678],{},[898,6679,6047],{},[902,6681,6047],{"encoding":904}," z ",[883,6684,6686],{"className":6685},[886],[888,6687,6688],{"xmlns":890},[892,6689,6690,6694],{},[895,6691,6692],{},[898,6693,207],{},[902,6695,207],{"encoding":904}," na ",[883,6698,6700],{"className":6699},[886],[888,6701,6702],{"xmlns":890},[892,6703,6704,6712],{},[895,6705,6706,6708,6710],{},[898,6707,207],{},[1711,6709,2095],{},[2111,6711,2238],{},[902,6713,6714],{"encoding":904},"a+1",[724,6716,6717],{},[883,6718,6720],{"className":6719},[886],[888,6721,6722],{"xmlns":890},[892,6723,6724,6763],{},[895,6725,6726,6728,6730,6732,6734,6736,6738,6741,6743,6745,6747,6749,6751,6757,6759,6761],{},[898,6727,4068],{},[1711,6729,1714],{"stretchy":1713},[898,6731,207],{},[1711,6733,2095],{},[2111,6735,2238],{},[1711,6737,1735],{"stretchy":1713},[1711,6739,6740],{},"≈",[898,6742,4068],{},[1711,6744,1714],{"stretchy":1713},[898,6746,207],{},[1711,6748,1735],{"stretchy":1713},[1711,6750,2095],{},[1716,6752,6753,6755],{},[898,6754,4068],{},[1711,6756,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,6758,1714],{"stretchy":1713},[898,6760,207],{},[1711,6762,1735],{"stretchy":1713},[902,6764,6765],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,6767,6769],{"id":6768},"příklad-mezní-náklady","Příklad — mezní náklady",[724,6771,6772,6773,2186],{},"Celkové náklady ",[883,6774,6776],{"className":6775},[886],[888,6777,6778],{"xmlns":890},[892,6779,6780,6807],{},[895,6781,6782,6784,6786,6788,6790,6792,6794,6797,6799,6801],{},[898,6783,1769],{},[898,6785,1940],{},[1711,6787,1836],{},[2111,6789,4313],{},[1711,6791,2095],{},[2111,6793,2963],{},[898,6795,6796],{},"Q",[1711,6798,2095],{},[2111,6800,4343],{},[1716,6802,6803,6805],{},[898,6804,6796],{},[2111,6806,2963],{},[902,6808,6809],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,6811,6812,6813,6849,6850,2186],{},"Mezní náklady: ",[883,6814,6816],{"className":6815},[886],[888,6817,6818],{"xmlns":890},[892,6819,6820,6846],{},[895,6821,6822,6824,6826,6828,6830,6836,6838,6840,6842,6844],{},[898,6823,1790],{},[898,6825,1940],{},[1711,6827,1836],{},[898,6829,1769],{},[1716,6831,6832,6834],{},[898,6833,1940],{},[1711,6835,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,6837,1836],{},[2111,6839,2963],{},[1711,6841,2095],{},[2111,6843,4491],{},[898,6845,6796],{},[902,6847,6848],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,6851,6853],{"className":6852},[886],[888,6854,6855],{"xmlns":890},[892,6856,6857,6873],{},[895,6858,6859,6861,6863,6865,6867,6869,6871],{},[898,6860,1790],{},[898,6862,1940],{},[1711,6864,1714],{"stretchy":1713},[2111,6866,4712],{},[1711,6868,1735],{"stretchy":1713},[1711,6870,1836],{},[2111,6872,6369],{},[902,6874,6875],{"encoding":904},"MC(10) = 4",[724,6877,6878,1700,6881,2801,6930,1700,6933,2186],{},[38,6879,6880],{},"Skutečný přírůstek:",[883,6882,6884],{"className":6883},[886],[888,6885,6886],{"xmlns":890},[892,6887,6888,6927],{},[895,6889,6890,6893,6895,6897,6899,6901,6903,6905,6908,6910,6912,6914,6916,6918,6920,6922,6924],{},[898,6891,6892],{"mathvariant":2287},"Δ",[898,6894,1769],{},[898,6896,1940],{},[1711,6898,1836],{},[898,6900,1769],{},[898,6902,1940],{},[1711,6904,1714],{"stretchy":1713},[2111,6906,6907],{},"11",[1711,6909,1735],{"stretchy":1713},[1711,6911,2460],{},[898,6913,1769],{},[898,6915,1940],{},[1711,6917,1714],{"stretchy":1713},[2111,6919,4712],{},[1711,6921,1735],{"stretchy":1713},[1711,6923,1836],{},[2111,6925,6926],{},"4,2",[902,6928,6929],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",[38,6931,6932],{},"Přibližný (lineární):",[883,6934,6936],{"className":6935},[886],[888,6937,6938],{"xmlns":890},[892,6939,6940,6944],{},[895,6941,6942],{},[2111,6943,6369],{},[902,6945,6369],{"encoding":904},[724,6947,6948,6949,6953],{},"(Viz aplikace v ",[207,6950,6952],{"className":6951,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk",".)",[115,6955,6957],{"id":6956},"diferenciál","Diferenciál",[724,6959,6960],{},[883,6961,6963],{"className":6962},[886],[888,6964,6965],{"xmlns":890},[892,6966,6967,6993],{},[895,6968,6969,6971,6973,6975,6981,6983,6985,6987,6989,6991],{},[898,6970,2098],{},[898,6972,4068],{},[1711,6974,1836],{},[1716,6976,6977,6979],{},[898,6978,4068],{},[1711,6980,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,6982,1714],{"stretchy":1713},[898,6984,6047],{},[1711,6986,1735],{"stretchy":1713},[1942,6988,2519],{},[898,6990,2098],{},[898,6992,6047],{},[902,6994,6995],{"encoding":904},"df = f'(x)\\, dx",[724,6997,6998,6999,7015,7016,7064,7065,2186],{},"Pro malá ",[883,7000,7002],{"className":7001},[886],[888,7003,7004],{"xmlns":890},[892,7005,7006,7012],{},[895,7007,7008,7010],{},[898,7009,2098],{},[898,7011,6047],{},[902,7013,7014],{"encoding":904},"dx"," platí: ",[883,7017,7019],{"className":7018},[886],[888,7020,7021],{"xmlns":890},[892,7022,7023,7061],{},[895,7024,7025,7027,7029,7031,7033,7035,7037,7039,7041,7043,7045,7047,7049,7051,7053,7055,7057,7059],{},[898,7026,6892],{"mathvariant":2287},[898,7028,4068],{},[1711,7030,1836],{},[898,7032,4068],{},[1711,7034,1714],{"stretchy":1713},[898,7036,6047],{},[1711,7038,2095],{},[898,7040,2098],{},[898,7042,6047],{},[1711,7044,1735],{"stretchy":1713},[1711,7046,2460],{},[898,7048,4068],{},[1711,7050,1714],{"stretchy":1713},[898,7052,6047],{},[1711,7054,1735],{"stretchy":1713},[1711,7056,6740],{},[898,7058,2098],{},[898,7060,4068],{},[902,7062,7063],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,7066,7067],{},"lineární odhad přírůstku",[198,7069,7071],{"id":7070},"příklad","Příklad",[724,7073,7074,7104,7105,7130,7131,3239],{},[883,7075,7077],{"className":7076},[886],[888,7078,7079],{"xmlns":890},[892,7080,7081,7101],{},[895,7082,7083,7085,7087,7089,7091,7093,7095],{},[898,7084,1769],{},[898,7086,1940],{},[1711,7088,1836],{},[2111,7090,4282],{},[1711,7092,2095],{},[2111,7094,4343],{},[1716,7096,7097,7099],{},[898,7098,6796],{},[2111,7100,2963],{},[902,7102,7103],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,7106,7108],{"className":7107},[886],[888,7109,7110],{"xmlns":890},[892,7111,7112,7127],{},[895,7113,7114,7116,7118,7121,7124],{},[898,7115,6796],{},[1711,7117,2062],{},[2111,7119,7120],{},"50",[1711,7122,7123],{},"→",[2111,7125,7126],{},"60",[902,7128,7129],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,7132,7134],{"className":7133},[886],[888,7135,7136],{"xmlns":890},[892,7137,7138,7148],{},[895,7139,7140,7142,7144,7146],{},[898,7141,2098],{},[898,7143,6796],{},[1711,7145,1836],{},[2111,7147,4712],{},[902,7149,7150],{"encoding":904},"dQ = 10",[724,7152,7153],{},[883,7154,7156],{"className":7155},[886],[888,7157,7158],{"xmlns":890},[892,7159,7160,7196],{},[895,7161,7162,7164,7166,7168,7170,7172,7174,7176,7178,7180,7182,7184,7186,7188,7190,7192,7194],{},[898,7163,2098],{},[898,7165,1769],{},[898,7167,1940],{},[1711,7169,1836],{},[2111,7171,4491],{},[898,7173,6796],{},[1711,7175,4795],{},[898,7177,2098],{},[898,7179,6796],{},[1711,7181,1836],{},[2111,7183,4491],{},[1711,7185,4795],{},[2111,7187,7120],{},[1711,7189,4795],{},[2111,7191,4712],{},[1711,7193,1836],{},[2111,7195,4282],{},[902,7197,7198],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,7200,7201,7202,7225,7226,7242],{},"Přesná změna: ",[883,7203,7205],{"className":7204},[886],[888,7206,7207],{"xmlns":890},[892,7208,7209,7222],{},[895,7210,7211,7213,7215,7217,7219],{},[898,7212,6892],{"mathvariant":2287},[898,7214,1769],{},[898,7216,1940],{},[1711,7218,1836],{},[2111,7220,7221],{},"110",[902,7223,7224],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,7227,7229],{"className":7228},[886],[888,7230,7231],{"xmlns":890},[892,7232,7233,7239],{},[895,7234,7235,7237],{},[898,7236,1769],{},[898,7238,1940],{},[902,7240,7241],{"encoding":904},"TC"," je konvexní.",[115,7244,7246],{"id":7245},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,7248,7250],{"id":7249},"nutná-podmínka","Nutná podmínka",[724,7252,7253,7254,6635,7274,7287,7288,7316,7317,7320],{},"Má-li ",[883,7255,7257],{"className":7256},[886],[888,7258,7259],{"xmlns":890},[892,7260,7261,7271],{},[895,7262,7263,7265,7267,7269],{},[898,7264,4068],{},[1711,7266,1714],{"stretchy":1713},[898,7268,6047],{},[1711,7270,1735],{"stretchy":1713},[902,7272,7273],{"encoding":904},"f(x)",[883,7275,7277],{"className":7276},[886],[888,7278,7279],{"xmlns":890},[892,7280,7281,7285],{},[895,7282,7283],{},[898,7284,207],{},[902,7286,207],{"encoding":904}," extrém, pak ",[883,7289,7291],{"className":7290},[886],[888,7292,7293],{"xmlns":890},[892,7294,7295,7313],{},[895,7296,7297,7303,7305,7307,7309,7311],{},[1716,7298,7299,7301],{},[898,7300,4068],{},[1711,7302,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,7304,1714],{"stretchy":1713},[898,7306,207],{},[1711,7308,1735],{"stretchy":1713},[1711,7310,1836],{},[2111,7312,2113],{},[902,7314,7315],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,7318,7319],{},"stacionární"," (podezřelé) body.",[198,7322,7324],{"id":7323},"postačující-podmínka","Postačující podmínka",[724,7326,7327,7328,7341,7342,2062],{},"Pro stacionární bod ",[883,7329,7331],{"className":7330},[886],[888,7332,7333],{"xmlns":890},[892,7334,7335,7339],{},[895,7336,7337],{},[898,7338,207],{},[902,7340,207],{"encoding":904},", je-li ",[883,7343,7345],{"className":7344},[886],[888,7346,7347],{"xmlns":890},[892,7348,7349,7372],{},[895,7350,7351,7361,7363,7365,7367,7370],{},[1716,7352,7353,7355],{},[898,7354,4068],{},[895,7356,7357,7359],{},[1711,7358,5225],{"mathvariant":2287},[1711,7360,5225],{"mathvariant":2287},[1711,7362,1714],{"stretchy":1713},[898,7364,207],{},[1711,7366,1735],{"stretchy":1713},[1711,7368,7369],{"mathvariant":2287},"≠",[2111,7371,2113],{},[902,7373,7374],{"encoding":904},"f''(a) \\neq 0",[120,7376,7377,7415],{},[123,7378,7379,7411,7412],{},[883,7380,7382],{"className":7381},[886],[888,7383,7384],{"xmlns":890},[892,7385,7386,7408],{},[895,7387,7388,7398,7400,7402,7404,7406],{},[1716,7389,7390,7392],{},[898,7391,4068],{},[895,7393,7394,7396],{},[1711,7395,5225],{"mathvariant":2287},[1711,7397,5225],{"mathvariant":2287},[1711,7399,1714],{"stretchy":1713},[898,7401,207],{},[1711,7403,1735],{"stretchy":1713},[1711,7405,2123],{},[2111,7407,2113],{},[902,7409,7410],{"encoding":904},"f''(a) > 0"," ⇒ ",[38,7413,7414],{},"lokální minimum",[123,7416,7417,7411,7449],{},[883,7418,7420],{"className":7419},[886],[888,7421,7422],{"xmlns":890},[892,7423,7424,7446],{},[895,7425,7426,7436,7438,7440,7442,7444],{},[1716,7427,7428,7430],{},[898,7429,4068],{},[895,7431,7432,7434],{},[1711,7433,5225],{"mathvariant":2287},[1711,7435,5225],{"mathvariant":2287},[1711,7437,1714],{"stretchy":1713},[898,7439,207],{},[1711,7441,1735],{"stretchy":1713},[1711,7443,2109],{},[2111,7445,2113],{},[902,7447,7448],{"encoding":904},"f''(a) \u003C 0",[38,7450,7451],{},"lokální maximum",[724,7453,7454],{},[1801,7455],{"alt":7456,"className":7457,"src":7458},"imek-extremy-1d",[210,1805],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,7460,7071],{"id":7461},"příklad-1",[724,7463,7464],{},[883,7465,7467],{"className":7466},[886],[888,7468,7469],{"xmlns":890},[892,7470,7471,7512],{},[895,7472,7473,7475,7477,7479,7481,7483,7485,7491,7493,7495,7501,7503,7506,7508,7510],{},[898,7474,4068],{},[1711,7476,1714],{"stretchy":1713},[898,7478,6047],{},[1711,7480,1735],{"stretchy":1713},[1711,7482,1836],{},[2111,7484,2963],{},[1716,7486,7487,7489],{},[898,7488,6047],{},[2111,7490,3034],{},[1711,7492,2460],{},[2111,7494,3034],{},[1716,7496,7497,7499],{},[898,7498,6047],{},[2111,7500,2963],{},[1711,7502,2460],{},[2111,7504,7505],{},"12",[898,7507,6047],{},[1711,7509,2095],{},[2111,7511,3034],{},[902,7513,7514],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,7516,7517,7628,7668,7731],{},[123,7518,7519,7591,7592],{},[883,7520,7522],{"className":7521},[886],[888,7523,7524],{"xmlns":890},[892,7525,7526,7588],{},[895,7527,7528,7534,7536,7538,7540,7542,7544,7550,7552,7554,7556,7558,7560,7562,7564,7566,7568,7570,7572,7574,7576,7578,7580,7582,7584,7586],{},[1716,7529,7530,7532],{},[898,7531,4068],{},[1711,7533,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,7535,1714],{"stretchy":1713},[898,7537,6047],{},[1711,7539,1735],{"stretchy":1713},[1711,7541,1836],{},[2111,7543,6262],{},[1716,7545,7546,7548],{},[898,7547,6047],{},[2111,7549,2963],{},[1711,7551,2460],{},[2111,7553,6262],{},[898,7555,6047],{},[1711,7557,2460],{},[2111,7559,7505],{},[1711,7561,1836],{},[2111,7563,6262],{},[1711,7565,1714],{"stretchy":1713},[898,7567,6047],{},[1711,7569,2095],{},[2111,7571,2238],{},[1711,7573,1735],{"stretchy":1713},[1711,7575,1714],{"stretchy":1713},[898,7577,6047],{},[1711,7579,2460],{},[2111,7581,2963],{},[1711,7583,1735],{"stretchy":1713},[1711,7585,1836],{},[2111,7587,2113],{},[902,7589,7590],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,7593,7595],{"className":7594},[886],[888,7596,7597],{"xmlns":890},[892,7598,7599,7625],{},[895,7600,7601,7607,7609,7611,7613,7615,7621,7623],{},[2884,7602,7603,7605],{},[898,7604,6047],{},[2111,7606,2238],{},[1711,7608,1836],{},[1711,7610,2460],{},[2111,7612,2238],{},[1711,7614,1726],{"separator":1725},[2884,7616,7617,7619],{},[898,7618,6047],{},[2111,7620,2963],{},[1711,7622,1836],{},[2111,7624,2963],{},[902,7626,7627],{"encoding":904},"x_1 = -1, x_2 = 2",[123,7629,7630],{},[883,7631,7633],{"className":7632},[886],[888,7634,7635],{"xmlns":890},[892,7636,7637,7665],{},[895,7638,7639,7649,7651,7653,7655,7657,7659,7661,7663],{},[1716,7640,7641,7643],{},[898,7642,4068],{},[895,7644,7645,7647],{},[1711,7646,5225],{"mathvariant":2287},[1711,7648,5225],{"mathvariant":2287},[1711,7650,1714],{"stretchy":1713},[898,7652,6047],{},[1711,7654,1735],{"stretchy":1713},[1711,7656,1836],{},[2111,7658,7505],{},[898,7660,6047],{},[1711,7662,2460],{},[2111,7664,6262],{},[902,7666,7667],{"encoding":904},"f''(x) = 12x - 6",[123,7669,7670,7411,7711,7714,7715],{},[883,7671,7673],{"className":7672},[886],[888,7674,7675],{"xmlns":890},[892,7676,7677,7708],{},[895,7678,7679,7689,7691,7693,7695,7697,7699,7701,7704,7706],{},[1716,7680,7681,7683],{},[898,7682,4068],{},[895,7684,7685,7687],{},[1711,7686,5225],{"mathvariant":2287},[1711,7688,5225],{"mathvariant":2287},[1711,7690,1714],{"stretchy":1713},[1711,7692,2460],{},[2111,7694,2238],{},[1711,7696,1735],{"stretchy":1713},[1711,7698,1836],{},[1711,7700,2460],{},[2111,7702,7703],{},"18",[1711,7705,2109],{},[2111,7707,2113],{},[902,7709,7710],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,7712,7713],{},"maximum"," v ",[883,7716,7718],{"className":7717},[886],[888,7719,7720],{"xmlns":890},[892,7721,7722,7728],{},[895,7723,7724,7726],{},[1711,7725,2460],{},[2111,7727,2238],{},[902,7729,7730],{"encoding":904},"-1",[123,7732,7733,7411,7769,7714,7772],{},[883,7734,7736],{"className":7735},[886],[888,7737,7738],{"xmlns":890},[892,7739,7740,7766],{},[895,7741,7742,7752,7754,7756,7758,7760,7762,7764],{},[1716,7743,7744,7746],{},[898,7745,4068],{},[895,7747,7748,7750],{},[1711,7749,5225],{"mathvariant":2287},[1711,7751,5225],{"mathvariant":2287},[1711,7753,1714],{"stretchy":1713},[2111,7755,2963],{},[1711,7757,1735],{"stretchy":1713},[1711,7759,1836],{},[2111,7761,7703],{},[1711,7763,2123],{},[2111,7765,2113],{},[902,7767,7768],{"encoding":904},"f''(2) = 18 > 0",[38,7770,7771],{},"minimum",[883,7773,7775],{"className":7774},[886],[888,7776,7777],{"xmlns":890},[892,7778,7779,7783],{},[895,7780,7781],{},[2111,7782,2963],{},[902,7784,2963],{"encoding":904},[115,7786,5901],{"id":5900},[120,7788,7789,7797,7805],{},[123,7790,7791,1700,7794],{},[38,7792,7793],{},"Předchozí:",[207,7795,757],{"className":7796,"dataFsResolvedFilePath":755,"href":756},[210],[123,7798,7799,1700,7802],{},[38,7800,7801],{},"Navazující:",[207,7803,775],{"className":7804,"dataFsResolvedFilePath":773,"href":774},[210],[123,7806,7807,1700,7810,7813,7814,7818,7819,7823],{},[38,7808,7809],{},"Souvislosti:",[207,7811,784],{"className":7812,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,7815,7817],{"className":7816,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk"," (aplikace mezních veličin), ",[207,7820,7822],{"className":7821,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita"," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":7825},[7826,7827,7832,7835,7840],{"id":6022,"depth":642,"text":6023},{"id":1145,"depth":642,"text":6375,"children":7828},[7829,7830,7831],{"id":6458,"depth":649,"text":6459},{"id":6578,"depth":649,"text":6579},{"id":6768,"depth":649,"text":6769},{"id":6956,"depth":642,"text":6957,"children":7833},[7834],{"id":7070,"depth":649,"text":7071},{"id":7245,"depth":642,"text":7246,"children":7836},[7837,7838,7839],{"id":7249,"depth":649,"text":7250},{"id":7323,"depth":649,"text":7324},{"id":7461,"depth":649,"text":7071},{"id":5900,"depth":642,"text":5901},"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":5995,"description":7841},[1135],"topics\u002Fderivace",[1128,1145,7848,7849,7850],"diferencial","extremy","mezni-naklady","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":7853,"title":7854,"body":7855,"course":1128,"courses":659,"created":5973,"description":641,"extension":661,"meta":13532,"navigation":664,"path":13533,"seo":13534,"sources":13535,"stem":13536,"tags":13537,"type":5985,"updated":677,"__hash__":13542},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":9,"value":7856,"toc":13505},[7857,7860,7881,7885,7911,7915,7957,8047,8091,8095,8119,8126,8130,8140,8151,8155,8183,8192,8248,8254,8257,8263,8290,8296,8393,8552,8842,8846,8926,8932,8936,9033,9099,9267,9271,9349,9380,9407,9413,9445,9523,9609,9613,9676,9682,9685,9691,9805,9888,9932,9936,9982,9989,10306,10311,10335,10364,10431,10528,10532,10539,10546,10617,10737,10821,10824,10830,11156,11160,11323,11331,11467,11475,11713,11721,11724,11729,11985,11989,12163,12297,12334,12378,12381,12511,12600,12618,12622,12629,12635,12695,12698,12722,12725,12731,12734,12740,12743,12747,12785,12843,13031,13035,13107,13113,13120,13124,13130,13272,13276,13282,13318,13323,13500],[12,7858,7854],{"id":7859},"elasticita-poptávky-a-nabídky",[1921,7861,7862],{},[724,7863,7864,7867,7868,7870,7871,7874,7875,2009,7878,2186],{},[883,7865,7866],{},"!abstract"," TL;DR\n",[38,7869,7822],{}," 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: ",[38,7872,7873],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,7876,7877],{},"křížově-cenovou elasticitu",[38,7879,7880],{},"důchodovou elasticitu",[115,7882,7884],{"id":7883},"úvod-motivace","Úvod — motivace",[724,7886,7887,7888,7891,7892,7895,7896,7899,7900,7903,7904,7907,7908,1797],{},"Termín ",[614,7889,7890],{},"elasticita"," (alternativně ",[614,7893,7894],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,7897,7898],{},"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 ",[614,7901,7902],{},"cenové elasticity poptávky"," (resp. ",[614,7905,7906],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,7909,6375],{"className":7910,"dataFsResolvedFilePath":764,"href":765},[210],[198,7912,7914],{"id":7913},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,7916,7917,7918,7937,7938,7956],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,7919,7921],{"className":7920},[886],[888,7922,7923],{"xmlns":890},[892,7924,7925,7934],{},[895,7926,7927,7930,7932],{},[898,7928,7929],{},"P",[1711,7931,1836],{},[2111,7933,4712],{},[902,7935,7936],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,7939,7941],{"className":7940},[886],[888,7942,7943],{"xmlns":890},[892,7944,7945,7953],{},[895,7946,7947,7949,7951],{},[898,7948,6796],{},[1711,7950,1836],{},[2111,7952,4282],{},[902,7954,7955],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,7958,7959,8004],{},[123,7960,7961,7964,7965,8003],{},[38,7962,7963],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,7966,7968],{"className":7967},[886],[888,7969,7970],{"xmlns":890},[892,7971,7972,8000],{},[895,7973,7974,7976,7979,7981,7983,7986,7988,7991,7993,7995,7997],{},[1942,7975,4699],{},[1711,7977,7978],{},"⇒",[1942,7980,4699],{},[898,7982,1769],{},[898,7984,7985],{},"R",[1711,7987,1836],{},[2111,7989,7990],{},"9",[1711,7992,4795],{},[2111,7994,7221],{},[1711,7996,1836],{},[2111,7998,7999],{},"990",[902,8001,8002],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,8005,8006,8009,8010,8046],{},[38,8007,8008],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,8011,8013],{"className":8012},[886],[888,8014,8015],{"xmlns":890},[892,8016,8017,8043],{},[895,8018,8019,8021,8023,8025,8027,8029,8031,8033,8035,8038,8040],{},[1942,8020,4699],{},[1711,8022,7978],{},[1942,8024,4699],{},[898,8026,1769],{},[898,8028,7985],{},[1711,8030,1836],{},[2111,8032,7990],{},[1711,8034,4795],{},[2111,8036,8037],{},"120",[1711,8039,1836],{},[2111,8041,8042],{},"1080",[902,8044,8045],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,8048,8049,8050,8053,8054,8057,8058,8061,8062,8065,8066,8069,8070,8086,8087,8090],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,8051,8052],{},"nerozumné",", na Trhu 2 ",[38,8055,8056],{},"rozumné",". Trh 2 je ",[38,8059,8060],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,8063,8064],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,8067,8068],{},"neelastická"," a vyššího ",[883,8071,8073],{"className":8072},[886],[888,8074,8075],{"xmlns":890},[892,8076,8077,8083],{},[895,8078,8079,8081],{},[898,8080,1769],{},[898,8082,7985],{},[902,8084,8085],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,8088,8089],{},"zvýšením"," ceny.",[198,8092,8094],{"id":8093},"hypotéza-41","Hypotéza 4.1",[1921,8096,8097],{},[724,8098,8099,8100],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,8101,8103],{"className":8102},[886],[888,8104,8105],{"xmlns":890},[892,8106,8107,8116],{},[895,8108,8109,8111,8114],{},[1711,8110,1714],{"stretchy":1713},[2111,8112,8113],{},"4.1",[1711,8115,1735],{"stretchy":1713},[902,8117,8118],{"encoding":904},"(4.1)",[724,8120,8121,8122,8125],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,8123,8124],{},"procentní změny"," obou faktorů.",[115,8127,8129],{"id":8128},"pojem-elasticity","Pojem elasticity",[724,8131,8132,8133,8135,8136,8139],{},"Obecně ",[38,8134,7890],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,8137,8138],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[1921,8141,8142],{},[724,8143,8144,8146,8147,8150],{},[883,8145,2678],{}," Intuice\nElasticitu lze číst jako ",[38,8148,8149],{},"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.",[115,8152,8154],{"id":8153},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,8156,8157,8158,8182],{},"Nechť ",[883,8159,8161],{"className":8160},[886],[888,8162,8163],{"xmlns":890},[892,8164,8165,8179],{},[895,8166,8167,8169,8171,8173,8175,8177],{},[898,8168,6796],{},[1711,8170,1836],{},[898,8172,2778],{},[1711,8174,1714],{"stretchy":1713},[898,8176,7929],{},[1711,8178,1735],{"stretchy":1713},[902,8180,8181],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,8184,8185],{},[883,8186,8191],{"className":8187,"title":8189,"style":8190},[8188],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,8193,8194,8195,2009,8211,8227,8228,8247],{},"Znaménko minus je korekce: změny ",[883,8196,8198],{"className":8197},[886],[888,8199,8200],{"xmlns":890},[892,8201,8202,8208],{},[895,8203,8204,8206],{},[898,8205,6892],{"mathvariant":2287},[898,8207,6796],{},[902,8209,8210],{"encoding":904},"\\Delta Q",[883,8212,8214],{"className":8213},[886],[888,8215,8216],{"xmlns":890},[892,8217,8218,8224],{},[895,8219,8220,8222],{},[898,8221,6892],{"mathvariant":2287},[898,8223,7929],{},[902,8225,8226],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,8229,8231],{"className":8230},[886],[888,8232,8233],{"xmlns":890},[892,8234,8235,8244],{},[895,8236,8237],{},[1716,8238,8239,8241],{},[898,8240,1722],{},[898,8242,8243],{},"A",[902,8245,8246],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,8249,8250],{},[883,8251,8253],{"className":8252,"title":8189,"style":8190},[8188],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,8255,8256],{},"Po dosazení:",[724,8258,8259],{},[883,8260,8262],{"className":8261,"title":8189,"style":8190},[8188],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,8264,8265,8266,8286,8287,8289],{},"Limitním přechodem ",[883,8267,8269],{"className":8268},[886],[888,8270,8271],{"xmlns":890},[892,8272,8273,8283],{},[895,8274,8275,8277,8279,8281],{},[898,8276,6892],{"mathvariant":2287},[898,8278,7929],{},[1711,8280,7123],{},[2111,8282,2113],{},[902,8284,8285],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,8288,7902],{}," (price elasticity of demand):",[724,8291,8292],{},[883,8293,8295],{"className":8294,"title":8189,"style":8190},[8188],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,8297,8298,8299,8322,8323,8345,8346,8370,8371,8392],{},"kde ",[883,8300,8302],{"className":8301},[886],[888,8303,8304],{"xmlns":890},[892,8305,8306,8320],{},[895,8307,8308,8310,8312,8314,8316,8318],{},[898,8309,6796],{},[1711,8311,1836],{},[898,8313,2778],{},[1711,8315,1714],{"stretchy":1713},[898,8317,7929],{},[1711,8319,1735],{"stretchy":1713},[902,8321,8181],{"encoding":904},". Pro pevnou cenu ",[883,8324,8326],{"className":8325},[886],[888,8327,8328],{"xmlns":890},[892,8329,8330,8342],{},[895,8331,8332,8334,8336],{},[898,8333,7929],{},[1711,8335,1836],{},[1716,8337,8338,8340],{},[898,8339,7929],{},[1711,8341,1793],{},[902,8343,8344],{"encoding":904},"P = P^*"," se ",[883,8347,8349],{"className":8348},[886],[888,8350,8351],{"xmlns":890},[892,8352,8353,8367],{},[895,8354,8355,8357,8359,8365],{},[898,8356,1722],{},[1711,8358,1714],{"stretchy":1713},[1716,8360,8361,8363],{},[898,8362,7929],{},[1711,8364,1793],{},[1711,8366,1735],{"stretchy":1713},[902,8368,8369],{"encoding":904},"E(P^*)"," nazývá ",[614,8372,8373,8374],{},"elasticita poptávky při ceně ",[883,8375,8377],{"className":8376},[886],[888,8378,8379],{"xmlns":890},[892,8380,8381,8389],{},[895,8382,8383],{},[1716,8384,8385,8387],{},[898,8386,7929],{},[1711,8388,1793],{},[902,8390,8391],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[1921,8394,8395],{},[724,8396,8397,8399,8400,8418,8419,8447,8448,8477,8478,1343,8496,1343,8514,8532,8533,8548,8549,2186],{},[883,8398,1927],{}," Pozor na znaménko\nV (4.5) je ",[38,8401,8402,8403],{},"explicitní ",[883,8404,8406],{"className":8405},[886],[888,8407,8408],{"xmlns":890},[892,8409,8410,8416],{},[895,8411,8412,8414],{},[1711,8413,2460],{},[2111,8415,2238],{},[902,8417,7730],{"encoding":904}," právě proto, že ",[883,8420,8422],{"className":8421},[886],[888,8423,8424],{"xmlns":890},[892,8425,8426,8444],{},[895,8427,8428,8434,8436,8438,8440,8442],{},[1716,8429,8430,8432],{},[898,8431,6796],{},[1711,8433,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,8435,1714],{"stretchy":1713},[898,8437,7929],{},[1711,8439,1735],{"stretchy":1713},[1711,8441,2109],{},[2111,8443,2113],{},[902,8445,8446],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,8449,8451],{"className":8450},[886],[888,8452,8453],{"xmlns":890},[892,8454,8455,8474],{},[895,8456,8457,8459,8461,8467,8469,8472],{},[898,8458,1722],{},[1711,8460,1714],{"stretchy":1713},[1716,8462,8463,8465],{},[898,8464,7929],{},[1711,8466,1793],{},[1711,8468,1735],{"stretchy":1713},[1711,8470,8471],{},"≥",[2111,8473,2113],{},[902,8475,8476],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,8479,8481],{"className":8480},[886],[888,8482,8483],{"xmlns":890},[892,8484,8485,8493],{},[895,8486,8487,8489,8491],{},[898,8488,1722],{},[1711,8490,2123],{},[2111,8492,2238],{},[902,8494,8495],{"encoding":904},"E > 1",[883,8497,8499],{"className":8498},[886],[888,8500,8501],{"xmlns":890},[892,8502,8503,8511],{},[895,8504,8505,8507,8509],{},[898,8506,1722],{},[1711,8508,2109],{},[2111,8510,2238],{},[902,8512,8513],{"encoding":904},"E \u003C 1",[883,8515,8517],{"className":8516},[886],[888,8518,8519],{"xmlns":890},[892,8520,8521,8529],{},[895,8522,8523,8525,8527],{},[898,8524,1722],{},[1711,8526,1836],{},[2111,8528,2238],{},[902,8530,8531],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,8534,8536],{"className":8535},[886],[888,8537,8538],{"xmlns":890},[892,8539,8540,8546],{},[895,8541,8542,8544],{},[1711,8543,2460],{},[2111,8545,2238],{},[902,8547,7730],{"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 ",[38,8550,8551],{},"absolutní hodnotou",[1921,8553,8554,8573],{},[724,8555,8556,8558,8559,8572],{},[883,8557,3872],{}," Postup: jak spočítat ",[883,8560,8562],{"className":8561},[886],[888,8563,8564],{"xmlns":890},[892,8565,8566,8570],{},[895,8567,8568],{},[898,8569,1722],{},[902,8571,1722],{"encoding":904}," v bodě",[152,8574,8575,8627,8667,8720,8785],{},[123,8576,8577,8578,8601,8602,8626],{},"Zapište ",[883,8579,8581],{"className":8580},[886],[888,8582,8583],{"xmlns":890},[892,8584,8585,8599],{},[895,8586,8587,8589,8591,8593,8595,8597],{},[898,8588,6796],{},[1711,8590,1836],{},[898,8592,2778],{},[1711,8594,1714],{"stretchy":1713},[898,8596,7929],{},[1711,8598,1735],{"stretchy":1713},[902,8600,8181],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,8603,8605],{"className":8604},[886],[888,8606,8607],{"xmlns":890},[892,8608,8609,8623],{},[895,8610,8611,8613,8615,8617,8619,8621],{},[898,8612,7929],{},[1711,8614,1836],{},[898,8616,2778],{},[1711,8618,1714],{"stretchy":1713},[898,8620,6796],{},[1711,8622,1735],{"stretchy":1713},[902,8624,8625],{"encoding":904},"P = D(Q)",", použijte vztah (4.9).",[123,8628,8629,8630,2186],{},"Spočítejte derivaci ",[883,8631,8633],{"className":8632},[886],[888,8634,8635],{"xmlns":890},[892,8636,8637,8664],{},[895,8638,8639,8645,8647,8649,8651,8653,8655,8657,8660,8662],{},[1716,8640,8641,8643],{},[898,8642,6796],{},[1711,8644,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,8646,1714],{"stretchy":1713},[898,8648,7929],{},[1711,8650,1735],{"stretchy":1713},[1711,8652,1836],{},[898,8654,2098],{"mathvariant":2287},[898,8656,6796],{},[898,8658,8659],{"mathvariant":2287},"\u002F",[898,8661,2098],{"mathvariant":2287},[898,8663,7929],{},[902,8665,8666],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,8668,8669,8670,8687,8688,2186],{},"Dosaďte zadanou cenu ",[883,8671,8673],{"className":8672},[886],[888,8674,8675],{"xmlns":890},[892,8676,8677,8685],{},[895,8678,8679],{},[1716,8680,8681,8683],{},[898,8682,7929],{},[1711,8684,1793],{},[902,8686,8391],{"encoding":904}," a dopočítejte odpovídající ",[883,8689,8691],{"className":8690},[886],[888,8692,8693],{"xmlns":890},[892,8694,8695,8717],{},[895,8696,8697,8703,8705,8707,8709,8715],{},[1716,8698,8699,8701],{},[898,8700,6796],{},[1711,8702,1793],{},[1711,8704,1836],{},[898,8706,2778],{},[1711,8708,1714],{"stretchy":1713},[1716,8710,8711,8713],{},[898,8712,7929],{},[1711,8714,1793],{},[1711,8716,1735],{"stretchy":1713},[902,8718,8719],{"encoding":904},"Q^* = D(P^*)",[123,8721,8722,8723,2186],{},"Dosaďte do (4.5): ",[883,8724,8726],{"className":8725},[886],[888,8727,8728],{"xmlns":890},[892,8729,8730,8782],{},[895,8731,8732,8734,8736,8742,8744,8746,8748,8764,8766,8772,8774,8780],{},[898,8733,1722],{},[1711,8735,1714],{"stretchy":1713},[1716,8737,8738,8740],{},[898,8739,7929],{},[1711,8741,1793],{},[1711,8743,1735],{"stretchy":1713},[1711,8745,1836],{},[1711,8747,2460],{},[2509,8749,8750],{"scriptlevel":2113,"displaystyle":1725},[2525,8751,8752,8758],{},[1716,8753,8754,8756],{},[898,8755,7929],{},[1711,8757,1793],{},[1716,8759,8760,8762],{},[898,8761,6796],{},[1711,8763,1793],{},[1942,8765,2519],{},[1716,8767,8768,8770],{},[898,8769,6796],{},[1711,8771,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,8773,1714],{"stretchy":1713},[1716,8775,8776,8778],{},[898,8777,7929],{},[1711,8779,1793],{},[1711,8781,1735],{"stretchy":1713},[902,8783,8784],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,8786,8787,8788,8805,8806,8823,8824,8841],{},"Klasifikujte: ",[883,8789,8791],{"className":8790},[886],[888,8792,8793],{"xmlns":890},[892,8794,8795,8803],{},[895,8796,8797,8799,8801],{},[898,8798,1722],{},[1711,8800,2123],{},[2111,8802,2238],{},[902,8804,8495],{"encoding":904}," elastická, ",[883,8807,8809],{"className":8808},[886],[888,8810,8811],{"xmlns":890},[892,8812,8813,8821],{},[895,8814,8815,8817,8819],{},[898,8816,1722],{},[1711,8818,1836],{},[2111,8820,2238],{},[902,8822,8531],{"encoding":904}," jednotková, ",[883,8825,8827],{"className":8826},[886],[888,8828,8829],{"xmlns":890},[892,8830,8831,8839],{},[895,8832,8833,8835,8837],{},[898,8834,1722],{},[1711,8836,2109],{},[2111,8838,2238],{},[902,8840,8513],{"encoding":904}," neelastická.",[198,8843,8845],{"id":8844},"interpretace-46","Interpretace (4.6)",[1921,8847,8848],{},[724,8849,8850,8851,8874,8875,8888,8889,8906,8907],{},"Číslo ",[883,8852,8854],{"className":8853},[886],[888,8855,8856],{"xmlns":890},[892,8857,8858,8872],{},[895,8859,8860,8862,8864,8870],{},[898,8861,1722],{},[1711,8863,1714],{"stretchy":1713},[1716,8865,8866,8868],{},[898,8867,7929],{},[1711,8869,1793],{},[1711,8871,1735],{"stretchy":1713},[902,8873,8369],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,8876,8878],{"className":8877},[886],[888,8879,8880],{"xmlns":890},[892,8881,8882,8886],{},[895,8883,8884],{},[898,8885,6796],{},[902,8887,6796],{"encoding":904},", jestliže se cena ",[883,8890,8892],{"className":8891},[886],[888,8893,8894],{"xmlns":890},[892,8895,8896,8904],{},[895,8897,8898],{},[1716,8899,8900,8902],{},[898,8901,7929],{},[1711,8903,1793],{},[902,8905,8391],{"encoding":904}," změní o 1 %. ",[883,8908,8910],{"className":8909},[886],[888,8911,8912],{"xmlns":890},[892,8913,8914,8923],{},[895,8915,8916,8918,8921],{},[1711,8917,1714],{"stretchy":1713},[2111,8919,8920],{},"4.6",[1711,8922,1735],{"stretchy":1713},[902,8924,8925],{"encoding":904},"(4.6)",[724,8927,8928,8931],{},[38,8929,8930],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,8933,8935],{"id":8934},"příklad-41","Příklad 4.1",[724,8937,8938,8939,8973,8974,1343,8999,2062],{},"Poptávka ",[883,8940,8942],{"className":8941},[886],[888,8943,8944],{"xmlns":890},[892,8945,8946,8970],{},[895,8947,8948,8950,8952,8954,8956,8958,8960,8962,8964,8966,8968],{},[898,8949,7929],{},[1711,8951,1836],{},[898,8953,2778],{},[1711,8955,1714],{"stretchy":1713},[898,8957,6796],{},[1711,8959,1735],{"stretchy":1713},[1711,8961,1836],{},[2111,8963,7120],{},[1711,8965,2460],{},[2111,8967,2963],{},[898,8969,6796],{},[902,8971,8972],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,8975,8977],{"className":8976},[886],[888,8978,8979],{"xmlns":890},[892,8980,8981,8996],{},[895,8982,8983,8985,8987,8989,8991,8994],{},[898,8984,6796],{},[1711,8986,1836],{},[2111,8988,4372],{},[1711,8990,2460],{},[2111,8992,8993],{},"0,5",[898,8995,7929],{},[902,8997,8998],{"encoding":904},"Q = 25 - 0{,}5P",[883,9000,9002],{"className":9001},[886],[888,9003,9004],{"xmlns":890},[892,9005,9006,9030],{},[895,9007,9008,9024,9026,9028],{},[2509,9009,9010],{"scriptlevel":2113,"displaystyle":1725},[2525,9011,9012,9018],{},[895,9013,9014,9016],{},[898,9015,2098],{"mathvariant":2287},[898,9017,6796],{},[895,9019,9020,9022],{},[898,9021,2098],{"mathvariant":2287},[898,9023,7929],{},[1711,9025,1836],{},[1711,9027,2460],{},[2111,9029,8993],{},[902,9031,9032],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,9034,9035],{},[883,9036,9038],{"className":9037},[886],[888,9039,9040],{"xmlns":890},[892,9041,9042,9096],{},[895,9043,9044,9046,9048,9050,9064,9066,9068,9070,9072,9074,9076,9094],{},[898,9045,1722],{},[1711,9047,1836],{},[1711,9049,2460],{},[2525,9051,9052,9054],{},[898,9053,7929],{},[895,9055,9056,9058,9060,9062],{},[2111,9057,4372],{},[1711,9059,2460],{},[2111,9061,8993],{},[898,9063,7929],{},[1711,9065,4795],{},[1711,9067,1714],{"stretchy":1713},[1711,9069,2460],{},[2111,9071,8993],{},[1711,9073,1735],{"stretchy":1713},[1711,9075,1836],{},[2525,9077,9078,9084],{},[895,9079,9080,9082],{},[2111,9081,8993],{},[898,9083,7929],{},[895,9085,9086,9088,9090,9092],{},[2111,9087,4372],{},[1711,9089,2460],{},[2111,9091,8993],{},[898,9093,7929],{},[898,9095,2186],{"mathvariant":2287},[902,9097,9098],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,9100,9101,9102,1343,9126,1343,9156,1343,9180,9205,9206,9229,9230,6696,9248,1797],{},"Potom ",[883,9103,9105],{"className":9104},[886],[888,9106,9107],{"xmlns":890},[892,9108,9109,9123],{},[895,9110,9111,9113,9115,9117,9119,9121],{},[898,9112,1722],{},[1711,9114,1714],{"stretchy":1713},[2111,9116,2113],{},[1711,9118,1735],{"stretchy":1713},[1711,9120,1836],{},[2111,9122,2113],{},[902,9124,9125],{"encoding":904},"E(0)=0",[883,9127,9129],{"className":9128},[886],[888,9130,9131],{"xmlns":890},[892,9132,9133,9153],{},[895,9134,9135,9137,9139,9141,9143,9145],{},[898,9136,1722],{},[1711,9138,1714],{"stretchy":1713},[2111,9140,4712],{},[1711,9142,1735],{"stretchy":1713},[1711,9144,1836],{},[2509,9146,9147],{"scriptlevel":2113,"displaystyle":1713},[2525,9148,9149,9151],{},[2111,9150,2238],{},[2111,9152,6369],{},[902,9154,9155],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,9157,9159],{"className":9158},[886],[888,9160,9161],{"xmlns":890},[892,9162,9163,9177],{},[895,9164,9165,9167,9169,9171,9173,9175],{},[898,9166,1722],{},[1711,9168,1714],{"stretchy":1713},[2111,9170,4372],{},[1711,9172,1735],{"stretchy":1713},[1711,9174,1836],{},[2111,9176,2238],{},[902,9178,9179],{"encoding":904},"E(25)=1",[883,9181,9183],{"className":9182},[886],[888,9184,9185],{"xmlns":890},[892,9186,9187,9202],{},[895,9188,9189,9191,9193,9196,9198,9200],{},[898,9190,1722],{},[1711,9192,1714],{"stretchy":1713},[2111,9194,9195],{},"40",[1711,9197,1735],{"stretchy":1713},[1711,9199,1836],{},[2111,9201,6369],{},[902,9203,9204],{"encoding":904},"E(40)=4",". Např. ",[883,9207,9209],{"className":9208},[886],[888,9210,9211],{"xmlns":890},[892,9212,9213,9227],{},[895,9214,9215,9217,9219,9221,9223,9225],{},[898,9216,1722],{},[1711,9218,1714],{"stretchy":1713},[2111,9220,9195],{},[1711,9222,1735],{"stretchy":1713},[1711,9224,1836],{},[2111,9226,6369],{},[902,9228,9204],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,9231,9233],{"className":9232},[886],[888,9234,9235],{"xmlns":890},[892,9236,9237,9245],{},[895,9238,9239,9241,9243],{},[898,9240,6796],{},[1711,9242,1836],{},[2111,9244,4798],{},[902,9246,9247],{"encoding":904},"Q=5",[883,9249,9251],{"className":9250},[886],[888,9252,9253],{"xmlns":890},[892,9254,9255,9264],{},[895,9256,9257,9259,9261],{},[898,9258,6796],{},[1711,9260,1836],{},[2111,9262,9263],{},"4,8",[902,9265,9266],{"encoding":904},"Q=4{,}8",[198,9268,9270],{"id":9269},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,9272,9273,9329],{},[123,9274,9275,9278,9279,9296,9297,2186],{},[38,9276,9277],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,9280,9282],{"className":9281},[886],[888,9283,9284],{"xmlns":890},[892,9285,9286,9294],{},[895,9287,9288],{},[1716,9289,9290,9292],{},[898,9291,1722],{},[898,9293,8243],{},[902,9295,8246],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,9298,9300],{"className":9299},[886],[888,9301,9302],{"xmlns":890},[892,9303,9304,9326],{},[895,9305,9306,9309,9311,9313,9315,9317,9319,9321,9323],{},[1711,9307,9308],{"stretchy":1713},"⟨",[898,9310,7929],{},[1711,9312,1726],{"separator":1725},[1942,9314,2519],{},[898,9316,7929],{},[1711,9318,2095],{},[898,9320,6892],{"mathvariant":2287},[898,9322,7929],{},[1711,9324,9325],{"stretchy":1713},"⟩",[902,9327,9328],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,9330,9331,9334,9335,9348],{},[38,9332,9333],{},"Bodová"," (okamžitá) elasticita: ",[883,9336,9338],{"className":9337},[886],[888,9339,9340],{"xmlns":890},[892,9341,9342,9346],{},[895,9343,9344],{},[898,9345,1722],{},[902,9347,1722],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,9350,9352,9353,9366,9367],{"id":9351},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,9354,9356],{"className":9355},[886],[888,9357,9358],{"xmlns":890},[892,9359,9360,9364],{},[895,9361,9362],{},[898,9363,7929],{},[902,9365,7929],{"encoding":904}," jako funkce ",[883,9368,9370],{"className":9369},[886],[888,9371,9372],{"xmlns":890},[892,9373,9374,9378],{},[895,9375,9376],{},[898,9377,6796],{},[902,9379,6796],{"encoding":904},[724,9381,9382,9383,9406],{},"Pokud je poptávka zadaná ve tvaru ",[883,9384,9386],{"className":9385},[886],[888,9387,9388],{"xmlns":890},[892,9389,9390,9404],{},[895,9391,9392,9394,9396,9398,9400,9402],{},[898,9393,7929],{},[1711,9395,1836],{},[898,9397,2778],{},[1711,9399,1714],{"stretchy":1713},[898,9401,6796],{},[1711,9403,1735],{"stretchy":1713},[902,9405,8625],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,9408,9409],{},[883,9410,9412],{"className":9411,"title":8189,"style":8190},[8188],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,9414,9415,1700,9418,9444],{},[38,9416,9417],{},"Příklad 4.3.",[883,9419,9421],{"className":9420},[886],[888,9422,9423],{"xmlns":890},[892,9424,9425,9441],{},[895,9426,9427,9429,9431,9433,9435],{},[898,9428,7929],{},[1711,9430,1836],{},[2111,9432,4282],{},[1711,9434,2460],{},[1716,9436,9437,9439],{},[898,9438,6796],{},[2111,9440,2963],{},[902,9442,9443],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,9446,9447],{},[883,9448,9450],{"className":9449},[886],[888,9451,9452],{"xmlns":890},[892,9453,9454,9520],{},[895,9455,9456,9458,9460,9462,9478,9480,9492,9494,9518],{},[898,9457,1722],{},[1711,9459,1836],{},[1711,9461,2460],{},[2525,9463,9464,9476],{},[895,9465,9466,9468,9470],{},[2111,9467,4282],{},[1711,9469,2460],{},[1716,9471,9472,9474],{},[898,9473,6796],{},[2111,9475,2963],{},[898,9477,6796],{},[1711,9479,4795],{},[2525,9481,9482,9484],{},[2111,9483,2238],{},[895,9485,9486,9488,9490],{},[1711,9487,2460],{},[2111,9489,2963],{},[898,9491,6796],{},[1711,9493,1836],{},[2525,9495,9496,9508],{},[895,9497,9498,9500,9502],{},[2111,9499,4282],{},[1711,9501,2460],{},[1716,9503,9504,9506],{},[898,9505,6796],{},[2111,9507,2963],{},[895,9509,9510,9512],{},[2111,9511,2963],{},[1716,9513,9514,9516],{},[898,9515,6796],{},[2111,9517,2963],{},[898,9519,2186],{"mathvariant":2287},[902,9521,9522],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,9524,9525,9526,2366,9553,9572,9573,2186],{},"Z rovnice ",[883,9527,9529],{"className":9528},[886],[888,9530,9531],{"xmlns":890},[892,9532,9533,9550],{},[895,9534,9535,9537,9539,9545,9547],{},[2111,9536,4282],{},[1711,9538,2460],{},[1716,9540,9541,9543],{},[898,9542,6796],{},[2111,9544,2963],{},[1711,9546,1836],{},[2111,9548,9549],{},"36",[902,9551,9552],{"encoding":904},"100 - Q^2 = 36",[883,9554,9556],{"className":9555},[886],[888,9557,9558],{"xmlns":890},[892,9559,9560,9569],{},[895,9561,9562,9564,9566],{},[898,9563,6796],{},[1711,9565,1836],{},[2111,9567,9568],{},"8",[902,9570,9571],{"encoding":904},"Q = 8",", tedy ",[883,9574,9576],{"className":9575},[886],[888,9577,9578],{"xmlns":890},[892,9579,9580,9606],{},[895,9581,9582,9584,9586,9588,9590,9592,9601,9603],{},[898,9583,1722],{},[1711,9585,1714],{"stretchy":1713},[2111,9587,9568],{},[1711,9589,1735],{"stretchy":1713},[1711,9591,1836],{},[2509,9593,9594],{"scriptlevel":2113,"displaystyle":1713},[2525,9595,9596,9598],{},[2111,9597,9549],{},[2111,9599,9600],{},"128",[1711,9602,1836],{},[2111,9604,9605],{},"0,281",[902,9607,9608],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,9610,9612],{"id":9611},"přibližné-změny","Přibližné změny",[724,9614,9615,9616,9652,9653,9675],{},"Diferenciál ",[883,9617,9619],{"className":9618},[886],[888,9620,9621],{"xmlns":890},[892,9622,9623,9649],{},[895,9624,9625,9627,9629,9631,9637,9639,9641,9643,9645,9647],{},[898,9626,2098],{"mathvariant":2287},[898,9628,6796],{},[1711,9630,1836],{},[1716,9632,9633,9635],{},[898,9634,6796],{},[1711,9636,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,9638,1714],{"stretchy":1713},[898,9640,7929],{},[1711,9642,1735],{"stretchy":1713},[1942,9644,2519],{},[898,9646,2098],{"mathvariant":2287},[898,9648,7929],{},[902,9650,9651],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[883,9654,9656],{"className":9655},[886],[888,9657,9658],{"xmlns":890},[892,9659,9660,9672],{},[895,9661,9662,9664,9666,9668,9670],{},[898,9663,2098],{"mathvariant":2287},[898,9665,7929],{},[1711,9667,1836],{},[898,9669,6892],{"mathvariant":2287},[898,9671,7929],{},[902,9673,9674],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,9677,9678],{},[883,9679,9681],{"className":9680,"title":8189,"style":8190},[8188],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,9683,9684],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,9686,9687],{},[883,9688,9690],{"className":9689,"title":8189,"style":8190},[8188],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,9692,9693,1700,9696,9731,9732,9751,9752,9786,9787,9804],{},[38,9694,9695],{},"Příklad 4.5.",[883,9697,9699],{"className":9698},[886],[888,9700,9701],{"xmlns":890},[892,9702,9703,9728],{},[895,9704,9705,9707,9709,9711,9717,9719,9721,9723,9725],{},[898,9706,7929],{},[1711,9708,1836],{},[1711,9710,2460],{},[1716,9712,9713,9715],{},[898,9714,6796],{},[2111,9716,2963],{},[1711,9718,2460],{},[2111,9720,6369],{},[898,9722,6796],{},[1711,9724,2095],{},[2111,9726,9727],{},"96",[902,9729,9730],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,9733,9735],{"className":9734},[886],[888,9736,9737],{"xmlns":890},[892,9738,9739,9748],{},[895,9740,9741,9743,9745],{},[898,9742,7929],{},[1711,9744,1836],{},[2111,9746,9747],{},"51",[902,9749,9750],{"encoding":904},"P=51",". Z rovnice ",[883,9753,9755],{"className":9754},[886],[888,9756,9757],{"xmlns":890},[892,9758,9759,9783],{},[895,9760,9761,9763,9765,9767,9773,9775,9777,9779,9781],{},[2111,9762,9747],{},[1711,9764,1836],{},[1711,9766,2460],{},[1716,9768,9769,9771],{},[898,9770,6796],{},[2111,9772,2963],{},[1711,9774,2460],{},[2111,9776,6369],{},[898,9778,6796],{},[1711,9780,2095],{},[2111,9782,9727],{},[902,9784,9785],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,9788,9790],{"className":9789},[886],[888,9791,9792],{"xmlns":890},[892,9793,9794,9802],{},[895,9795,9796,9798,9800],{},[898,9797,6796],{},[1711,9799,1836],{},[2111,9801,4798],{},[902,9803,9247],{"encoding":904},". Elasticita:",[724,9806,9807],{},[883,9808,9810],{"className":9809},[886],[888,9811,9812],{"xmlns":890},[892,9813,9814,9885],{},[895,9815,9816,9818,9820,9858,9860,9862,9864,9866,9868,9870,9872,9879,9882],{},[898,9817,1722],{},[1711,9819,1836],{},[2525,9821,9822,9842],{},[895,9823,9824,9826,9832,9834,9836,9838,9840],{},[1711,9825,2460],{},[1716,9827,9828,9830],{},[898,9829,6796],{},[2111,9831,2963],{},[1711,9833,2460],{},[2111,9835,6369],{},[898,9837,6796],{},[1711,9839,2095],{},[2111,9841,9727],{},[895,9843,9844,9846,9848,9850,9852,9854,9856],{},[898,9845,6796],{},[1711,9847,1714],{"stretchy":1713},[2111,9849,2963],{},[898,9851,6796],{},[1711,9853,2095],{},[2111,9855,6369],{},[1711,9857,1735],{"stretchy":1713},[1711,9859,1726],{"separator":1725},[2102,9861],{"width":2104},[898,9863,1722],{},[1711,9865,1714],{"stretchy":1713},[2111,9867,4798],{},[1711,9869,1735],{"stretchy":1713},[1711,9871,1836],{},[2525,9873,9874,9876],{},[2111,9875,9747],{},[2111,9877,9878],{},"70",[1711,9880,9881],{},"≐",[2111,9883,9884],{},"0,728.",[902,9886,9887],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,9889,9890,9891,2186],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,9892,9894],{"className":9893},[886],[888,9895,9896],{"xmlns":890},[892,9897,9898,9929],{},[895,9899,9900,9902,9904,9907,9909,9911,9914,9916,9918,9920,9922,9925,9927],{},[898,9901,6892],{"mathvariant":2287},[898,9903,6796],{},[898,9905,9906],{"mathvariant":2287},"%",[1711,9908,6740],{},[1711,9910,2460],{},[2111,9912,9913],{},"0,728",[1711,9915,4795],{},[2111,9917,2963],{},[1711,9919,1836],{},[1711,9921,2460],{},[2111,9923,9924],{},"1,456",[1942,9926,2519],{},[898,9928,9906],{"mathvariant":2287},[902,9930,9931],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,9933,9935],{"id":9934},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,9937,9938,9939,9962,9963,2062],{},"V závislosti na hodnotě ",[883,9940,9942],{"className":9941},[886],[888,9943,9944],{"xmlns":890},[892,9945,9946,9960],{},[895,9947,9948,9950,9952,9958],{},[898,9949,1722],{},[1711,9951,1714],{"stretchy":1713},[1716,9953,9954,9956],{},[898,9955,7929],{},[1711,9957,1793],{},[1711,9959,1735],{"stretchy":1713},[902,9961,8369],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,9964,9966],{"className":9965},[886],[888,9967,9968],{"xmlns":890},[892,9969,9970,9979],{},[895,9971,9972,9974,9977],{},[1711,9973,1714],{"stretchy":1713},[2111,9975,9976],{},"4.7",[1711,9978,1735],{"stretchy":1713},[902,9980,9981],{"encoding":904},"(4.7)",[724,9983,9984],{},[1801,9985],{"alt":9986,"className":9987,"src":9988},"imek-typy-elasticity-5panelu",[210,1805],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,9990,9991,10030],{},[19,9992,9993],{},[22,9994,9995,10021,10024,10027],{},[25,9996,9997,9998],{},"Hodnota ",[883,9999,10001],{"className":10000},[886],[888,10002,10003],{"xmlns":890},[892,10004,10005,10019],{},[895,10006,10007,10009,10011,10017],{},[898,10008,1722],{},[1711,10010,1714],{"stretchy":1713},[1716,10012,10013,10015],{},[898,10014,7929],{},[1711,10016,1793],{},[1711,10018,1735],{"stretchy":1713},[902,10020,8369],{"encoding":904},[25,10022,10023],{},"Typ poptávky",[25,10025,10026],{},"Termín",[25,10028,10029],{},"Význam",[30,10031,10032,10065,10127,10202,10259],{},[22,10033,10034,10054,10059,10062],{},[35,10035,10036],{},[883,10037,10039],{"className":10038},[886],[888,10040,10041],{"xmlns":890},[892,10042,10043,10051],{},[895,10044,10045,10047,10049],{},[898,10046,1722],{},[1711,10048,1836],{},[2111,10050,2113],{},[902,10052,10053],{"encoding":904},"E = 0",[35,10055,10056],{},[38,10057,10058],{},"dokonale neelastická",[35,10060,10061],{},"perfectly inelastic",[35,10063,10064],{},"množství se nemění bez ohledu na cenu",[22,10066,10067,10091,10095,10098],{},[35,10068,10069],{},[883,10070,10072],{"className":10071},[886],[888,10073,10074],{"xmlns":890},[892,10075,10076,10088],{},[895,10077,10078,10080,10082,10084,10086],{},[2111,10079,2113],{},[1711,10081,2109],{},[898,10083,1722],{},[1711,10085,2109],{},[2111,10087,2238],{},[902,10089,10090],{"encoding":904},"0 \u003C E \u003C 1",[35,10092,10093],{},[38,10094,8068],{},[35,10096,10097],{},"inelastic",[35,10099,10100,10113,10114],{},[883,10101,10103],{"className":10102},[886],[888,10104,10105],{"xmlns":890},[892,10106,10107,10111],{},[895,10108,10109],{},[898,10110,6796],{},[902,10112,6796],{"encoding":904}," se mění pomaleji než ",[883,10115,10117],{"className":10116},[886],[888,10118,10119],{"xmlns":890},[892,10120,10121,10125],{},[895,10122,10123],{},[898,10124,7929],{},[902,10126,7929],{"encoding":904},[22,10128,10129,10148,10153,10156],{},[35,10130,10131],{},[883,10132,10134],{"className":10133},[886],[888,10135,10136],{"xmlns":890},[892,10137,10138,10146],{},[895,10139,10140,10142,10144],{},[898,10141,1722],{},[1711,10143,1836],{},[2111,10145,2238],{},[902,10147,8531],{"encoding":904},[35,10149,10150],{},[38,10151,10152],{},"jednotkově elastická",[35,10154,10155],{},"unit elastic",[35,10157,10158,10171,10172,10185,10186,10201],{},[883,10159,10161],{"className":10160},[886],[888,10162,10163],{"xmlns":890},[892,10164,10165,10169],{},[895,10166,10167],{},[898,10168,6796],{},[902,10170,6796],{"encoding":904}," i ",[883,10173,10175],{"className":10174},[886],[888,10176,10177],{"xmlns":890},[892,10178,10179,10183],{},[895,10180,10181],{},[898,10182,7929],{},[902,10184,7929],{"encoding":904}," se mění stejně rychle; ",[883,10187,10189],{"className":10188},[886],[888,10190,10191],{"xmlns":890},[892,10192,10193,10199],{},[895,10194,10195,10197],{},[898,10196,1769],{},[898,10198,7985],{},[902,10200,8085],{"encoding":904}," má maximum",[22,10203,10204,10223,10227,10230],{},[35,10205,10206],{},[883,10207,10209],{"className":10208},[886],[888,10210,10211],{"xmlns":890},[892,10212,10213,10221],{},[895,10214,10215,10217,10219],{},[898,10216,1722],{},[1711,10218,2123],{},[2111,10220,2238],{},[902,10222,8495],{"encoding":904},[35,10224,10225],{},[38,10226,8064],{},[35,10228,10229],{},"elastic",[35,10231,10232,10245,10246],{},[883,10233,10235],{"className":10234},[886],[888,10236,10237],{"xmlns":890},[892,10238,10239,10243],{},[895,10240,10241],{},[898,10242,6796],{},[902,10244,6796],{"encoding":904}," se mění rychleji než ",[883,10247,10249],{"className":10248},[886],[888,10250,10251],{"xmlns":890},[892,10252,10253,10257],{},[895,10254,10255],{},[898,10256,7929],{},[902,10258,7929],{"encoding":904},[22,10260,10261,10282,10287,10290],{},[35,10262,10263],{},[883,10264,10266],{"className":10265},[886],[888,10267,10268],{"xmlns":890},[892,10269,10270,10279],{},[895,10271,10272,10274,10276],{},[898,10273,1722],{},[1711,10275,7123],{},[898,10277,10278],{"mathvariant":2287},"∞",[902,10280,10281],{"encoding":904},"E \\to \\infty",[35,10283,10284],{},[38,10285,10286],{},"dokonale elastická",[35,10288,10289],{},"perfectly elastic",[35,10291,10292,10293],{},"sebemenší změna ceny úplně mění ",[883,10294,10296],{"className":10295},[886],[888,10297,10298],{"xmlns":890},[892,10299,10300,10304],{},[895,10301,10302],{},[898,10303,6796],{},[902,10305,6796],{"encoding":904},[724,10307,10308],{},[38,10309,10310],{},"Pravidlo růstu elasticity s cenou:",[1921,10312,10313],{},[724,10314,10315,10316],{},"S rostoucí cenou elasticita poptávky roste. ",[883,10317,10319],{"className":10318},[886],[888,10320,10321],{"xmlns":890},[892,10322,10323,10332],{},[895,10324,10325,10327,10330],{},[1711,10326,1714],{"stretchy":1713},[2111,10328,10329],{},"4.8",[1711,10331,1735],{"stretchy":1713},[902,10333,10334],{"encoding":904},"(4.8)",[724,10336,10337,10338,10341,10342,10345,10346,10363],{},"Z toho plyne, že při ",[614,10339,10340],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,10343,10344],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,10347,10349],{"className":10348},[886],[888,10350,10351],{"xmlns":890},[892,10352,10353,10361],{},[895,10354,10355],{},[1716,10356,10357,10359],{},[898,10358,7929],{},[1711,10360,1793],{},[902,10362,8391],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[1921,10365,10366,10371],{},[724,10367,10368,10370],{},[883,10369,3872],{}," Postup: jak klasifikovat poptávku",[152,10372,10373,10400,10403],{},[123,10374,10375,10376,10399],{},"Spočítejte ",[883,10377,10379],{"className":10378},[886],[888,10380,10381],{"xmlns":890},[892,10382,10383,10397],{},[895,10384,10385,10387,10389,10395],{},[898,10386,1722],{},[1711,10388,1714],{"stretchy":1713},[1716,10390,10391,10393],{},[898,10392,7929],{},[1711,10394,1793],{},[1711,10396,1735],{"stretchy":1713},[902,10398,8369],{"encoding":904}," dle (4.5).",[123,10401,10402],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,10404,10405,10406,10430],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,10407,10409],{"className":10408},[886],[888,10410,10411],{"xmlns":890},[892,10412,10413,10427],{},[895,10414,10415,10417,10419,10421,10423,10425],{},[898,10416,1722],{},[1711,10418,1714],{"stretchy":1713},[898,10420,7929],{},[1711,10422,1735],{"stretchy":1713},[1711,10424,1836],{},[2111,10426,2238],{},[902,10428,10429],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,10432,10433,10436,10437,10454,10455,10473,10474,10501,10502,2186],{},[38,10434,10435],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,10438,10440],{"className":10439},[886],[888,10441,10442],{"xmlns":890},[892,10443,10444,10452],{},[895,10445,10446,10448,10450],{},[898,10447,1722],{},[1711,10449,1836],{},[2111,10451,2238],{},[902,10453,8531],{"encoding":904}," pro ",[883,10456,10458],{"className":10457},[886],[888,10459,10460],{"xmlns":890},[892,10461,10462,10470],{},[895,10463,10464,10466,10468],{},[898,10465,7929],{},[1711,10467,1836],{},[2111,10469,4372],{},[902,10471,10472],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,10475,10477],{"className":10476},[886],[888,10478,10479],{"xmlns":890},[892,10480,10481,10498],{},[895,10482,10483,10485,10488,10490,10492,10494,10496],{},[898,10484,7929],{},[1711,10486,10487],{},"∈",[1711,10489,9308],{"stretchy":1713},[2111,10491,2113],{},[1711,10493,1726],{"separator":1725},[2111,10495,4372],{},[1711,10497,1735],{"stretchy":1713},[902,10499,10500],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,10503,10505],{"className":10504},[886],[888,10506,10507],{"xmlns":890},[892,10508,10509,10525],{},[895,10510,10511,10513,10515,10517,10519,10521,10523],{},[898,10512,7929],{},[1711,10514,10487],{},[1711,10516,1714],{"stretchy":1713},[2111,10518,4372],{},[1711,10520,1726],{"separator":1725},[2111,10522,7120],{},[1711,10524,9325],{"stretchy":1713},[902,10526,10527],{"encoding":904},"P \\in (25, 50\\rangle",[115,10529,10531],{"id":10530},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,10533,10534],{},[1801,10535],{"alt":10536,"className":10537,"src":10538},"imek-elasticita-tr",[210,1805],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,10540,10541],{},[1801,10542],{"alt":10543,"className":10544,"src":10545},"imek-elasticita-podel-linearni-poptavky",[210,1805],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,10547,10548,10549,10599,10600,10616],{},"Pro celkový příjem platí ",[883,10550,10552],{"className":10551},[886],[888,10553,10554],{"xmlns":890},[892,10555,10556,10596],{},[895,10557,10558,10560,10562,10564,10566,10568,10570,10572,10574,10576,10578,10580,10582,10584,10586,10588,10590,10592,10594],{},[898,10559,1769],{},[898,10561,7985],{},[1711,10563,1836],{},[898,10565,1769],{},[898,10567,7985],{},[1711,10569,1714],{"stretchy":1713},[898,10571,6796],{},[1711,10573,1735],{"stretchy":1713},[1711,10575,1836],{},[898,10577,7929],{},[1711,10579,4795],{},[898,10581,6796],{},[1711,10583,1836],{},[898,10585,6796],{},[1711,10587,4795],{},[898,10589,2778],{},[1711,10591,1714],{"stretchy":1713},[898,10593,6796],{},[1711,10595,1735],{"stretchy":1713},[902,10597,10598],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,10601,10603],{"className":10602},[886],[888,10604,10605],{"xmlns":890},[892,10606,10607,10613],{},[895,10608,10609,10611],{},[898,10610,1790],{},[898,10612,7985],{},[902,10614,10615],{"encoding":904},"MR"," odvodíme:",[724,10618,10619],{},[883,10620,10622],{"className":10621},[886],[888,10623,10624],{"xmlns":890},[892,10625,10626,10734],{},[895,10627,10628,10630,10632,10634,10636,10642,10644,10646,10648,10650,10652,10654,10656,10658,10660,10662,10664,10670,10672,10674,10676,10678,10680,10682,10684,10698,10700,10702],{},[898,10629,1790],{},[898,10631,7985],{},[1711,10633,1836],{},[898,10635,1769],{},[1716,10637,10638,10640],{},[898,10639,7985],{},[1711,10641,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,10643,1714],{"stretchy":1713},[898,10645,6796],{},[1711,10647,1735],{"stretchy":1713},[1711,10649,1836],{},[898,10651,2778],{},[1711,10653,1714],{"stretchy":1713},[898,10655,6796],{},[1711,10657,1735],{"stretchy":1713},[1711,10659,2095],{},[898,10661,6796],{},[1942,10663,2519],{},[1716,10665,10666,10668],{},[898,10667,2778],{},[1711,10669,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,10671,1714],{"stretchy":1713},[898,10673,6796],{},[1711,10675,1735],{"stretchy":1713},[1711,10677,1836],{},[898,10679,7929],{},[1711,10681,2095],{},[898,10683,6796],{},[2525,10685,10686,10692],{},[895,10687,10688,10690],{},[898,10689,2098],{"mathvariant":2287},[898,10691,7929],{},[895,10693,10694,10696],{},[898,10695,2098],{"mathvariant":2287},[898,10697,6796],{},[1711,10699,1836],{},[898,10701,7929],{},[895,10703,10704,10706,10708,10710,10716,10718,10732],{},[1711,10705,1714],{"fence":1725},[2111,10707,2238],{},[1711,10709,2095],{},[2525,10711,10712,10714],{},[898,10713,6796],{},[898,10715,7929],{},[1711,10717,4795],{},[2525,10719,10720,10726],{},[895,10721,10722,10724],{},[898,10723,2098],{"mathvariant":2287},[898,10725,7929],{},[895,10727,10728,10730],{},[898,10729,2098],{"mathvariant":2287},[898,10731,6796],{},[1711,10733,1735],{"fence":1725},[902,10735,10736],{"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)",[724,10738,10739],{},[883,10740,10742],{"className":10741},[886],[888,10743,10744],{"xmlns":890},[892,10745,10746,10818],{},[895,10747,10748,10750,10752,10794,10796,10798],{},[1711,10749,1836],{},[898,10751,7929],{},[895,10753,10754,10756,10758,10760,10792],{},[1711,10755,1714],{"fence":1725},[2111,10757,2238],{},[1711,10759,2095],{},[2525,10761,10762,10764],{},[2111,10763,2238],{},[895,10765,10766,10774,10776],{},[2509,10767,10768],{"scriptlevel":2113,"displaystyle":1713},[2525,10769,10770,10772],{},[898,10771,7929],{},[898,10773,6796],{},[1711,10775,4795],{},[2509,10777,10778],{"scriptlevel":2113,"displaystyle":1713},[2525,10779,10780,10786],{},[895,10781,10782,10784],{},[898,10783,2098],{"mathvariant":2287},[898,10785,6796],{},[895,10787,10788,10790],{},[898,10789,2098],{"mathvariant":2287},[898,10791,7929],{},[1711,10793,1735],{"fence":1725},[1711,10795,1836],{},[898,10797,7929],{},[895,10799,10800,10802,10804,10806,10816],{},[1711,10801,1714],{"fence":1725},[2111,10803,2238],{},[1711,10805,2095],{},[2525,10807,10808,10810],{},[2111,10809,2238],{},[895,10811,10812,10814],{},[1711,10813,2460],{},[898,10815,1722],{},[1711,10817,1735],{"fence":1725},[902,10819,10820],{"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)",[724,10822,10823],{},"a tedy",[724,10825,10826],{},[883,10827,10829],{"className":10828,"title":8189,"style":8190},[8188],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[1921,10831,10832,10901,11150],{},[724,10833,10834,10836,10837,10871,10872,10887,10888,2062],{},[883,10835,2678],{}," Intuice: vztah ",[883,10838,10840],{"className":10839},[886],[888,10841,10842],{"xmlns":890},[892,10843,10844,10868],{},[895,10845,10846,10848,10850,10852,10854,10856,10858,10860,10862,10864,10866],{},[898,10847,1790],{},[898,10849,7985],{},[1711,10851,1836],{},[898,10853,7929],{},[1711,10855,1714],{"stretchy":1713},[2111,10857,2238],{},[1711,10859,2460],{},[2111,10861,2238],{},[898,10863,8659],{"mathvariant":2287},[898,10865,1722],{},[1711,10867,1735],{"stretchy":1713},[902,10869,10870],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,10873,10875],{"className":10874},[886],[888,10876,10877],{"xmlns":890},[892,10878,10879,10885],{},[895,10880,10881,10883],{},[898,10882,1790],{},[898,10884,7985],{},[902,10886,10615],{"encoding":904}," jednoznačně určuje hodnota ",[883,10889,10891],{"className":10890},[886],[888,10892,10893],{"xmlns":890},[892,10894,10895,10899],{},[895,10896,10897],{},[898,10898,1722],{},[902,10900,1722],{"encoding":904},[120,10902,10903,11012,11081],{},[123,10904,10905,10922,10923,1700,10937,1700,10963,1700,10976,5204,10996,11011],{},[883,10906,10908],{"className":10907},[886],[888,10909,10910],{"xmlns":890},[892,10911,10912,10920],{},[895,10913,10914,10916,10918],{},[898,10915,1722],{},[1711,10917,2123],{},[2111,10919,2238],{},[902,10921,8495],{"encoding":904}," (elastická) ",[883,10924,10926],{"className":10925},[886],[888,10927,10928],{"xmlns":890},[892,10929,10930,10934],{},[895,10931,10932],{},[1711,10933,7978],{},[902,10935,10936],{"encoding":904},"\\Rightarrow",[883,10938,10940],{"className":10939},[886],[888,10941,10942],{"xmlns":890},[892,10943,10944,10960],{},[895,10945,10946,10948,10950,10952,10954,10956,10958],{},[2111,10947,2238],{},[1711,10949,2460],{},[2111,10951,2238],{},[898,10953,8659],{"mathvariant":2287},[898,10955,1722],{},[1711,10957,2123],{},[2111,10959,2113],{},[902,10961,10962],{"encoding":904},"1 - 1\u002FE > 0",[883,10964,10966],{"className":10965},[886],[888,10967,10968],{"xmlns":890},[892,10969,10970,10974],{},[895,10971,10972],{},[1711,10973,7978],{},[902,10975,10936],{"encoding":904},[883,10977,10979],{"className":10978},[886],[888,10980,10981],{"xmlns":890},[892,10982,10983,10993],{},[895,10984,10985,10987,10989,10991],{},[898,10986,1790],{},[898,10988,7985],{},[1711,10990,2123],{},[2111,10992,2113],{},[902,10994,10995],{"encoding":904},"MR > 0",[883,10997,10999],{"className":10998},[886],[888,11000,11001],{"xmlns":890},[892,11002,11003,11009],{},[895,11004,11005,11007],{},[898,11006,1769],{},[898,11008,7985],{},[902,11010,8085],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,11013,11014,11031,11032,1700,11045,5204,11065,11080],{},[883,11015,11017],{"className":11016},[886],[888,11018,11019],{"xmlns":890},[892,11020,11021,11029],{},[895,11022,11023,11025,11027],{},[898,11024,1722],{},[1711,11026,1836],{},[2111,11028,2238],{},[902,11030,8531],{"encoding":904}," (jednotková) ",[883,11033,11035],{"className":11034},[886],[888,11036,11037],{"xmlns":890},[892,11038,11039,11043],{},[895,11040,11041],{},[1711,11042,7978],{},[902,11044,10936],{"encoding":904},[883,11046,11048],{"className":11047},[886],[888,11049,11050],{"xmlns":890},[892,11051,11052,11062],{},[895,11053,11054,11056,11058,11060],{},[898,11055,1790],{},[898,11057,7985],{},[1711,11059,1836],{},[2111,11061,2113],{},[902,11063,11064],{"encoding":904},"MR = 0",[883,11066,11068],{"className":11067},[886],[888,11069,11070],{"xmlns":890},[892,11071,11072,11078],{},[895,11073,11074,11076],{},[898,11075,1769],{},[898,11077,7985],{},[902,11079,8085],{"encoding":904}," je extrém (maximum).",[123,11082,11083,11100,11101,1700,11114,5204,11134,11149],{},[883,11084,11086],{"className":11085},[886],[888,11087,11088],{"xmlns":890},[892,11089,11090,11098],{},[895,11091,11092,11094,11096],{},[898,11093,1722],{},[1711,11095,2109],{},[2111,11097,2238],{},[902,11099,8513],{"encoding":904}," (neelastická) ",[883,11102,11104],{"className":11103},[886],[888,11105,11106],{"xmlns":890},[892,11107,11108,11112],{},[895,11109,11110],{},[1711,11111,7978],{},[902,11113,10936],{"encoding":904},[883,11115,11117],{"className":11116},[886],[888,11118,11119],{"xmlns":890},[892,11120,11121,11131],{},[895,11122,11123,11125,11127,11129],{},[898,11124,1790],{},[898,11126,7985],{},[1711,11128,2109],{},[2111,11130,2113],{},[902,11132,11133],{"encoding":904},"MR \u003C 0",[883,11135,11137],{"className":11136},[886],[888,11138,11139],{"xmlns":890},[892,11140,11141,11147],{},[895,11142,11143,11145],{},[898,11144,1769],{},[898,11146,7985],{},[902,11148,8085],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,11151,11152,11153,2186],{},"Viz také ",[207,11154,7817],{"className":11155,"dataFsResolvedFilePath":827,"href":828},[210],[198,11157,11159],{"id":11158},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,11161,11162,11182,11183,11209,11210,11225,11226,11239,11240,11253,11254,11267,11268,11284,11285,1700,11300,11303,11304,11284,11320,2186],{},[38,11163,11164,11165,1797],{},"(a) Poptávka elastická (",[883,11166,11168],{"className":11167},[886],[888,11169,11170],{"xmlns":890},[892,11171,11172,11180],{},[895,11173,11174,11176,11178],{},[898,11175,1722],{},[1711,11177,2123],{},[2111,11179,2238],{},[902,11181,8495],{"encoding":904}," Z (4.12) plyne ",[883,11184,11186],{"className":11185},[886],[888,11187,11188],{"xmlns":890},[892,11189,11190,11206],{},[895,11191,11192,11194,11196,11198,11200,11202,11204],{},[898,11193,1790],{},[898,11195,7985],{},[1711,11197,1714],{"stretchy":1713},[898,11199,6796],{},[1711,11201,1735],{"stretchy":1713},[1711,11203,2123],{},[2111,11205,2113],{},[902,11207,11208],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,11211,11213],{"className":11212},[886],[888,11214,11215],{"xmlns":890},[892,11216,11217,11223],{},[895,11218,11219,11221],{},[898,11220,1769],{},[898,11222,7985],{},[902,11224,8085],{"encoding":904}," je rostoucí funkcí ",[883,11227,11229],{"className":11228},[886],[888,11230,11231],{"xmlns":890},[892,11232,11233,11237],{},[895,11234,11235],{},[898,11236,6796],{},[902,11238,6796],{"encoding":904},". Avšak růst ",[883,11241,11243],{"className":11242},[886],[888,11244,11245],{"xmlns":890},[892,11246,11247,11251],{},[895,11248,11249],{},[898,11250,6796],{},[902,11252,6796],{"encoding":904}," je odezvou na pokles ceny ",[883,11255,11257],{"className":11256},[886],[888,11258,11259],{"xmlns":890},[892,11260,11261,11265],{},[895,11262,11263],{},[898,11264,7929],{},[902,11266,7929],{"encoding":904},". Tudíž s ",[614,11269,11270,11271],{},"poklesem ceny ",[883,11272,11274],{"className":11273},[886],[888,11275,11276],{"xmlns":890},[892,11277,11278,11282],{},[895,11279,11280],{},[898,11281,7929],{},[902,11283,7929],{"encoding":904}," celkový příjem ",[883,11286,11288],{"className":11287},[886],[888,11289,11290],{"xmlns":890},[892,11291,11292,11298],{},[895,11293,11294,11296],{},[898,11295,1769],{},[898,11297,7985],{},[902,11299,8085],{"encoding":904},[614,11301,11302],{},"roste"," a s ",[614,11305,11306,11307],{},"růstem ceny ",[883,11308,11310],{"className":11309},[886],[888,11311,11312],{"xmlns":890},[892,11313,11314,11318],{},[895,11315,11316],{},[898,11317,7929],{},[902,11319,7929],{"encoding":904},[614,11321,11322],{},"klesá",[1921,11324,11325],{},[724,11326,11327,11330],{},[38,11328,11329],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,11332,11333,11182,11353,1343,11379,11394,11395,11408,11409,11422,11423,11436,11437,11284,11450,1700,11465,2186],{},[38,11334,11335,11336,1797],{},"(b) Poptávka neelastická (",[883,11337,11339],{"className":11338},[886],[888,11340,11341],{"xmlns":890},[892,11342,11343,11351],{},[895,11344,11345,11347,11349],{},[898,11346,1722],{},[1711,11348,2109],{},[2111,11350,2238],{},[902,11352,8513],{"encoding":904},[883,11354,11356],{"className":11355},[886],[888,11357,11358],{"xmlns":890},[892,11359,11360,11376],{},[895,11361,11362,11364,11366,11368,11370,11372,11374],{},[898,11363,1790],{},[898,11365,7985],{},[1711,11367,1714],{"stretchy":1713},[898,11369,6796],{},[1711,11371,1735],{"stretchy":1713},[1711,11373,2109],{},[2111,11375,2113],{},[902,11377,11378],{"encoding":904},"MR(Q) \u003C 0",[883,11380,11382],{"className":11381},[886],[888,11383,11384],{"xmlns":890},[892,11385,11386,11392],{},[895,11387,11388,11390],{},[898,11389,1769],{},[898,11391,7985],{},[902,11393,8085],{"encoding":904}," je klesající funkce ",[883,11396,11398],{"className":11397},[886],[888,11399,11400],{"xmlns":890},[892,11401,11402,11406],{},[895,11403,11404],{},[898,11405,6796],{},[902,11407,6796],{"encoding":904},", tj. s růstem ",[883,11410,11412],{"className":11411},[886],[888,11413,11414],{"xmlns":890},[892,11415,11416,11420],{},[895,11417,11418],{},[898,11419,6796],{},[902,11421,6796],{"encoding":904}," (s poklesem ceny ",[883,11424,11426],{"className":11425},[886],[888,11427,11428],{"xmlns":890},[892,11429,11430,11434],{},[895,11431,11432],{},[898,11433,7929],{},[902,11435,7929],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,11438,11440],{"className":11439},[886],[888,11441,11442],{"xmlns":890},[892,11443,11444,11448],{},[895,11445,11446],{},[898,11447,7929],{},[902,11449,7929],{"encoding":904},[883,11451,11453],{"className":11452},[886],[888,11454,11455],{"xmlns":890},[892,11456,11457,11463],{},[895,11458,11459,11461],{},[898,11460,1769],{},[898,11462,7985],{},[902,11464,8085],{"encoding":904},[614,11466,11302],{},[1921,11468,11469],{},[724,11470,11471,11474],{},[38,11472,11473],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,11476,11477,11182,11497,11516,11517,11532,11533,11603,11604,2009,11632,11665,11666,9572,11694,11709,11710,2186],{},[38,11478,11479,11480,1797],{},"(c) Jednotková elasticita (",[883,11481,11483],{"className":11482},[886],[888,11484,11485],{"xmlns":890},[892,11486,11487,11495],{},[895,11488,11489,11491,11493],{},[898,11490,1722],{},[1711,11492,1836],{},[2111,11494,2238],{},[902,11496,8531],{"encoding":904},[883,11498,11500],{"className":11499},[886],[888,11501,11502],{"xmlns":890},[892,11503,11504,11514],{},[895,11505,11506,11508,11510,11512],{},[898,11507,1790],{},[898,11509,7985],{},[1711,11511,1836],{},[2111,11513,2113],{},[902,11515,11064],{"encoding":904}," — nutná podmínka extrému ",[883,11518,11520],{"className":11519},[886],[888,11521,11522],{"xmlns":890},[892,11523,11524,11530],{},[895,11525,11526,11528],{},[898,11527,1769],{},[898,11529,7985],{},[902,11531,8085],{"encoding":904},". Dále ",[883,11534,11536],{"className":11535},[886],[888,11537,11538],{"xmlns":890},[892,11539,11540,11600],{},[895,11541,11542,11544,11554,11556,11558,11564,11566,11572,11574,11576,11578,11580,11582,11584,11594,11596,11598],{},[898,11543,1769],{},[1716,11545,11546,11548],{},[898,11547,7985],{},[895,11549,11550,11552],{},[1711,11551,5225],{"mathvariant":2287},[1711,11553,5225],{"mathvariant":2287},[1711,11555,1836],{},[898,11557,1790],{},[1716,11559,11560,11562],{},[898,11561,7985],{},[1711,11563,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,11565,1836],{},[1716,11567,11568,11570],{},[898,11569,2778],{},[1711,11571,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,11573,1714],{"stretchy":1713},[898,11575,6796],{},[1711,11577,1735],{"stretchy":1713},[1711,11579,2095],{},[898,11581,6796],{},[1942,11583,2519],{},[1716,11585,11586,11588],{},[898,11587,2778],{},[895,11589,11590,11592],{},[1711,11591,5225],{"mathvariant":2287},[1711,11593,5225],{"mathvariant":2287},[1711,11595,1714],{"stretchy":1713},[898,11597,6796],{},[1711,11599,1735],{"stretchy":1713},[902,11601,11602],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,11605,11607],{"className":11606},[886],[888,11608,11609],{"xmlns":890},[892,11610,11611,11629],{},[895,11612,11613,11619,11621,11623,11625,11627],{},[1716,11614,11615,11617],{},[898,11616,2778],{},[1711,11618,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,11620,1714],{"stretchy":1713},[898,11622,6796],{},[1711,11624,1735],{"stretchy":1713},[1711,11626,2109],{},[2111,11628,2113],{},[902,11630,11631],{"encoding":904},"D'(Q) \u003C 0",[883,11633,11635],{"className":11634},[886],[888,11636,11637],{"xmlns":890},[892,11638,11639,11662],{},[895,11640,11641,11651,11653,11655,11657,11660],{},[1716,11642,11643,11645],{},[898,11644,2778],{},[895,11646,11647,11649],{},[1711,11648,5225],{"mathvariant":2287},[1711,11650,5225],{"mathvariant":2287},[1711,11652,1714],{"stretchy":1713},[898,11654,6796],{},[1711,11656,1735],{"stretchy":1713},[1711,11658,11659],{},"≤",[2111,11661,2113],{},[902,11663,11664],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,11667,11669],{"className":11668},[886],[888,11670,11671],{"xmlns":890},[892,11672,11673,11691],{},[895,11674,11675,11677,11687,11689],{},[898,11676,1769],{},[1716,11678,11679,11681],{},[898,11680,7985],{},[895,11682,11683,11685],{},[1711,11684,5225],{"mathvariant":2287},[1711,11686,5225],{"mathvariant":2287},[1711,11688,2109],{},[2111,11690,2113],{},[902,11692,11693],{"encoding":904},"TR'' \u003C 0",[883,11695,11697],{"className":11696},[886],[888,11698,11699],{"xmlns":890},[892,11700,11701,11707],{},[895,11702,11703,11705],{},[898,11704,1769],{},[898,11706,7985],{},[902,11708,8085],{"encoding":904}," nabývá ",[38,11711,11712],{},"maxima",[1921,11714,11715],{},[724,11716,11717,11720],{},[38,11718,11719],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,11722,11723],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,11725,11726],{},[38,11727,11728],{},"Souhrnná tabulka Pravidel 1–3:",[16,11730,11731,11835],{},[19,11732,11733],{},[22,11734,11735,11738,11753,11770,11801,11832],{},[25,11736,11737],{},"Charakter poptávky",[25,11739,11740],{},[883,11741,11743],{"className":11742},[886],[888,11744,11745],{"xmlns":890},[892,11746,11747,11751],{},[895,11748,11749],{},[898,11750,1722],{},[902,11752,1722],{"encoding":904},[25,11754,11755],{},[883,11756,11758],{"className":11757},[886],[888,11759,11760],{"xmlns":890},[892,11761,11762,11768],{},[895,11763,11764,11766],{},[898,11765,1790],{},[898,11767,7985],{},[902,11769,10615],{"encoding":904},[25,11771,11772,11773,1700,11786],{},"Pokles ceny ",[883,11774,11776],{"className":11775},[886],[888,11777,11778],{"xmlns":890},[892,11779,11780,11784],{},[895,11781,11782],{},[1711,11783,7978],{},[902,11785,10936],{"encoding":904},[883,11787,11789],{"className":11788},[886],[888,11790,11791],{"xmlns":890},[892,11792,11793,11799],{},[895,11794,11795,11797],{},[898,11796,1769],{},[898,11798,7985],{},[902,11800,8085],{"encoding":904},[25,11802,11803,11804,1700,11817],{},"Růst ceny ",[883,11805,11807],{"className":11806},[886],[888,11808,11809],{"xmlns":890},[892,11810,11811,11815],{},[895,11812,11813],{},[1711,11814,7978],{},[902,11816,10936],{"encoding":904},[883,11818,11820],{"className":11819},[886],[888,11821,11822],{"xmlns":890},[892,11823,11824,11830],{},[895,11825,11826,11828],{},[898,11827,1769],{},[898,11829,7985],{},[902,11831,8085],{"encoding":904},[25,11833,11834],{},"Doporučení",[30,11836,11837,11886,11936],{},[22,11838,11839,11841,11859,11877,11879,11881],{},[35,11840,8064],{},[35,11842,11843],{},[883,11844,11846],{"className":11845},[886],[888,11847,11848],{"xmlns":890},[892,11849,11850,11856],{},[895,11851,11852,11854],{},[1711,11853,2123],{},[2111,11855,2238],{},[902,11857,11858],{"encoding":904},"> 1",[35,11860,11861],{},[883,11862,11864],{"className":11863},[886],[888,11865,11866],{"xmlns":890},[892,11867,11868,11874],{},[895,11869,11870,11872],{},[1711,11871,2123],{},[2111,11873,2113],{},[902,11875,11876],{"encoding":904},"> 0",[35,11878,11302],{},[35,11880,11322],{},[35,11882,11883],{},[38,11884,11885],{},"snížit cenu",[22,11887,11888,11891,11909,11927,11929,11931],{},[35,11889,11890],{},"jednotková",[35,11892,11893],{},[883,11894,11896],{"className":11895},[886],[888,11897,11898],{"xmlns":890},[892,11899,11900,11906],{},[895,11901,11902,11904],{},[1711,11903,1836],{},[2111,11905,2238],{},[902,11907,11908],{"encoding":904},"= 1",[35,11910,11911],{},[883,11912,11914],{"className":11913},[886],[888,11915,11916],{"xmlns":890},[892,11917,11918,11924],{},[895,11919,11920,11922],{},[1711,11921,1836],{},[2111,11923,2113],{},[902,11925,11926],{"encoding":904},"= 0",[35,11928,7713],{},[35,11930,7713],{},[35,11932,11933],{},[38,11934,11935],{},"držet cenu",[22,11937,11938,11940,11958,11976,11978,11980],{},[35,11939,8068],{},[35,11941,11942],{},[883,11943,11945],{"className":11944},[886],[888,11946,11947],{"xmlns":890},[892,11948,11949,11955],{},[895,11950,11951,11953],{},[1711,11952,2109],{},[2111,11954,2238],{},[902,11956,11957],{"encoding":904},"\u003C 1",[35,11959,11960],{},[883,11961,11963],{"className":11962},[886],[888,11964,11965],{"xmlns":890},[892,11966,11967,11973],{},[895,11968,11969,11971],{},[1711,11970,2109],{},[2111,11972,2113],{},[902,11974,11975],{"encoding":904},"\u003C 0",[35,11977,11322],{},[35,11979,11302],{},[35,11981,11982],{},[38,11983,11984],{},"zvýšit cenu",[198,11986,11988],{"id":11987},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,11990,11991,11992,12017,12018,12040,12041,12054,12055,12068,12069,12082,12083,9572,12110,12162],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,11993,11995],{"className":11994},[886],[888,11996,11997],{"xmlns":890},[892,11998,11999,12015],{},[895,12000,12001,12003,12005,12007,12009],{},[898,12002,7929],{},[1711,12004,1836],{},[2111,12006,4282],{},[1711,12008,2460],{},[1716,12010,12011,12013],{},[898,12012,6796],{},[2111,12014,2963],{},[902,12016,9443],{"encoding":904},". Reálné cenové rozpětí je ",[883,12019,12021],{"className":12020},[886],[888,12022,12023],{"xmlns":890},[892,12024,12025,12037],{},[895,12026,12027,12029,12031,12033,12035],{},[1711,12028,9308],{"stretchy":1713},[2111,12030,2238],{},[1711,12032,1726],{"separator":1725},[2111,12034,4282],{},[1711,12036,9325],{"stretchy":1713},[902,12038,12039],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,12042,12044],{"className":12043},[886],[888,12045,12046],{"xmlns":890},[892,12047,12048,12052],{},[895,12049,12050],{},[898,12051,6796],{},[902,12053,6796],{"encoding":904}," jako funkci ",[883,12056,12058],{"className":12057},[886],[888,12059,12060],{"xmlns":890},[892,12061,12062,12066],{},[895,12063,12064],{},[898,12065,7929],{},[902,12067,7929],{"encoding":904},"; pro nezáporné ",[883,12070,12072],{"className":12071},[886],[888,12073,12074],{"xmlns":890},[892,12075,12076,12080],{},[895,12077,12078],{},[898,12079,6796],{},[902,12081,6796],{"encoding":904}," je ",[883,12084,12086],{"className":12085},[886],[888,12087,12088],{"xmlns":890},[892,12089,12090,12107],{},[895,12091,12092,12094,12096],{},[898,12093,6796],{},[1711,12095,1836],{},[12097,12098,12099],"msqrt",{},[895,12100,12101,12103,12105],{},[2111,12102,4282],{},[1711,12104,2460],{},[898,12106,7929],{},[902,12108,12109],{"encoding":904},"Q = \\sqrt{100 - P}",[883,12111,12113],{"className":12112},[886],[888,12114,12115],{"xmlns":890},[892,12116,12117,12159],{},[895,12118,12119,12135,12137,12139],{},[2509,12120,12121],{"scriptlevel":2113,"displaystyle":1725},[2525,12122,12123,12129],{},[895,12124,12125,12127],{},[898,12126,2098],{"mathvariant":2287},[898,12128,6796],{},[895,12130,12131,12133],{},[898,12132,2098],{"mathvariant":2287},[898,12134,7929],{},[1711,12136,1836],{},[1711,12138,2460],{},[2509,12140,12141],{"scriptlevel":2113,"displaystyle":1725},[2525,12142,12143,12145],{},[2111,12144,2238],{},[895,12146,12147,12149],{},[2111,12148,2963],{},[12097,12150,12151],{},[895,12152,12153,12155,12157],{},[2111,12154,4282],{},[1711,12156,2460],{},[898,12158,7929],{},[902,12160,12161],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,12164,12165],{},[883,12166,12168],{"className":12167},[886],[888,12169,12170],{"xmlns":890},[892,12171,12172,12294],{},[895,12173,12174,12176,12178,12180,12182,12184,12186,12192,12194,12208,12210,12212,12226,12228,12254,12256,12274,12276,12292],{},[898,12175,1722],{},[1711,12177,1714],{"stretchy":1713},[898,12179,7929],{},[1711,12181,1735],{"stretchy":1713},[1711,12183,1836],{},[1711,12185,2460],{},[2525,12187,12188,12190],{},[898,12189,7929],{},[898,12191,6796],{},[1711,12193,4795],{},[2525,12195,12196,12202],{},[895,12197,12198,12200],{},[898,12199,2098],{"mathvariant":2287},[898,12201,6796],{},[895,12203,12204,12206],{},[898,12205,2098],{"mathvariant":2287},[898,12207,7929],{},[1711,12209,1836],{},[1711,12211,2460],{},[2525,12213,12214,12216],{},[898,12215,7929],{},[12097,12217,12218],{},[895,12219,12220,12222,12224],{},[2111,12221,4282],{},[1711,12223,2460],{},[898,12225,7929],{},[1711,12227,4795],{},[895,12229,12230,12232,12234,12252],{},[1711,12231,1714],{"fence":1725},[1711,12233,2460],{},[2525,12235,12236,12238],{},[2111,12237,2238],{},[895,12239,12240,12242],{},[2111,12241,2963],{},[12097,12243,12244],{},[895,12245,12246,12248,12250],{},[2111,12247,4282],{},[1711,12249,2460],{},[898,12251,7929],{},[1711,12253,1735],{"fence":1725},[1711,12255,1836],{},[2525,12257,12258,12260],{},[898,12259,7929],{},[895,12261,12262,12264,12266,12268,12270,12272],{},[2111,12263,2963],{},[1711,12265,1714],{"stretchy":1713},[2111,12267,4282],{},[1711,12269,2460],{},[898,12271,7929],{},[1711,12273,1735],{"stretchy":1713},[1711,12275,1836],{},[2525,12277,12278,12284],{},[895,12279,12280,12282],{},[2111,12281,8993],{},[898,12283,7929],{},[895,12285,12286,12288,12290],{},[2111,12287,4282],{},[1711,12289,2460],{},[898,12291,7929],{},[898,12293,2186],{"mathvariant":2287},[902,12295,12296],{"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}.",[724,12298,12299,12300,2062],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,12301,12303],{"className":12302},[886],[888,12304,12305],{"xmlns":890},[892,12306,12307,12331],{},[895,12308,12309,12327,12329],{},[2509,12310,12311],{"scriptlevel":2113,"displaystyle":1725},[2525,12312,12313,12319],{},[895,12314,12315,12317],{},[2111,12316,8993],{},[898,12318,7929],{},[895,12320,12321,12323,12325],{},[2111,12322,4282],{},[1711,12324,2460],{},[898,12326,7929],{},[1711,12328,1836],{},[2111,12330,2238],{},[902,12332,12333],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,12335,12336],{},[883,12337,12339],{"className":12338},[886],[888,12340,12341],{"xmlns":890},[892,12342,12343,12375],{},[895,12344,12345,12351,12353,12360,12362,12365,12373],{},[1716,12346,12347,12349],{},[898,12348,7929],{},[1711,12350,1793],{},[1711,12352,1836],{},[2525,12354,12355,12358],{},[2111,12356,12357],{},"200",[2111,12359,3034],{},[1711,12361,9881],{},[2111,12363,12364],{},"66,",[12366,12367,12368,12370],"mover",{"accent":1725},[2111,12369,6262],{},[1711,12371,12372],{"stretchy":1725},"‾",[898,12374,2186],{"mathvariant":2287},[902,12376,12377],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,12379,12380],{},"S využitím vlastnosti (4.8):",[120,12382,12383,12429,12471],{},[123,12384,12385,12386,12421,12422,12424,12425,12428],{},"Při cenách ",[883,12387,12389],{"className":12388},[886],[888,12390,12391],{"xmlns":890},[892,12392,12393,12418],{},[895,12394,12395,12397,12399,12401,12403,12406,12408,12410,12416],{},[898,12396,7929],{},[1711,12398,10487],{},[1711,12400,9308],{"stretchy":1713},[2111,12402,2238],{},[1711,12404,12405],{"separator":1725},";",[1942,12407,2519],{},[2111,12409,12364],{},[12366,12411,12412,12414],{"accent":1725},[2111,12413,6262],{},[1711,12415,12372],{"stretchy":1725},[1711,12417,1735],{"stretchy":1713},[902,12419,12420],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,12423,8068],{}," — dle ",[614,12426,12427],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,12430,12385,12431,12421,12465,12424,12467,12470],{},[883,12432,12434],{"className":12433},[886],[888,12435,12436],{"xmlns":890},[892,12437,12438,12462],{},[895,12439,12440,12442,12444,12446,12448,12454,12456,12458,12460],{},[898,12441,7929],{},[1711,12443,10487],{},[1711,12445,1714],{"stretchy":1713},[2111,12447,12364],{},[12366,12449,12450,12452],{"accent":1725},[2111,12451,6262],{},[1711,12453,12372],{"stretchy":1725},[1711,12455,12405],{"separator":1725},[1942,12457,2519],{},[2111,12459,4282],{},[1711,12461,9325],{"stretchy":1713},[902,12463,12464],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,12466,8064],{},[614,12468,12469],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,12472,12473,12474,12477,12478,12506,12507,12510],{},"Dle ",[614,12475,12476],{},"Pravidla 3"," je při ceně ",[883,12479,12481],{"className":12480},[886],[888,12482,12483],{"xmlns":890},[892,12484,12485,12503],{},[895,12486,12487,12493,12495,12497],{},[1716,12488,12489,12491],{},[898,12490,7929],{},[1711,12492,1793],{},[1711,12494,1836],{},[2111,12496,12364],{},[12366,12498,12499,12501],{"accent":1725},[2111,12500,6262],{},[1711,12502,12372],{"stretchy":1725},[902,12504,12505],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,12508,12509],{},"maxima celkového příjmu"," ve výši",[724,12512,12513],{},[883,12514,12516],{"className":12515},[886],[888,12517,12518],{"xmlns":890},[892,12519,12520,12597],{},[895,12521,12522,12524,12526,12528,12534,12536,12538,12544,12546,12560,12562,12568,12570,12578,12580,12592,12594],{},[898,12523,1769],{},[898,12525,7985],{},[1711,12527,1714],{"stretchy":1713},[1716,12529,12530,12532],{},[898,12531,7929],{},[1711,12533,1793],{},[1711,12535,1735],{"stretchy":1713},[1711,12537,1836],{},[1716,12539,12540,12542],{},[898,12541,7929],{},[1711,12543,1793],{},[1711,12545,4795],{},[12097,12547,12548],{},[895,12549,12550,12552,12554],{},[2111,12551,4282],{},[1711,12553,2460],{},[1716,12555,12556,12558],{},[898,12557,7929],{},[1711,12559,1793],{},[1711,12561,1836],{},[2525,12563,12564,12566],{},[2111,12565,12357],{},[2111,12567,3034],{},[1711,12569,4795],{},[12097,12571,12572],{},[2525,12573,12574,12576],{},[2111,12575,4282],{},[2111,12577,3034],{},[1711,12579,1836],{},[2525,12581,12582,12584],{},[2111,12583,4379],{},[895,12585,12586,12588],{},[2111,12587,3034],{},[12097,12589,12590],{},[2111,12591,3034],{},[1711,12593,9881],{},[2111,12595,12596],{},"384,9.",[902,12598,12599],{"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.",[724,12601,12602,12603,2186],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,12604,12606],{"className":12605},[886],[888,12607,12608],{"xmlns":890},[892,12609,12610,12616],{},[895,12611,12612,12614],{},[898,12613,1769],{},[898,12615,7985],{},[902,12617,8085],{"encoding":904},[115,12619,12621],{"id":12620},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,12623,12624,12625,12628],{},"Analogicky se definuje ",[38,12626,12627],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,12630,12631],{},[883,12632,12634],{"className":12633,"title":8189,"style":8190},[8188],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,12636,8298,12637,12661,12662,12694],{},[883,12638,12640],{"className":12639},[886],[888,12641,12642],{"xmlns":890},[892,12643,12644,12658],{},[895,12645,12646,12648,12650,12652,12654,12656],{},[898,12647,6796],{},[1711,12649,1836],{},[898,12651,2362],{},[1711,12653,1714],{"stretchy":1713},[898,12655,7929],{},[1711,12657,1735],{"stretchy":1713},[902,12659,12660],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,12663,12665],{"className":12664},[886],[888,12666,12667],{"xmlns":890},[892,12668,12669,12691],{},[895,12670,12671,12687,12689],{},[2509,12672,12673],{"scriptlevel":2113,"displaystyle":1725},[2525,12674,12675,12681],{},[895,12676,12677,12679],{},[898,12678,2098],{"mathvariant":2287},[898,12680,6796],{},[895,12682,12683,12685],{},[898,12684,2098],{"mathvariant":2287},[898,12686,7929],{},[1711,12688,2123],{},[2111,12690,2113],{},[902,12692,12693],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,12696,12697],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[1921,12699,12700],{},[724,12701,12702,12703],{},"S rostoucí cenou elasticita nabídky roste. ",[883,12704,12706],{"className":12705},[886],[888,12707,12708],{"xmlns":890},[892,12709,12710,12719],{},[895,12711,12712,12714,12717],{},[1711,12713,1714],{"stretchy":1713},[2111,12715,12716],{},"4.14",[1711,12718,1735],{"stretchy":1713},[902,12720,12721],{"encoding":904},"(4.14)",[724,12723,12724],{},"Pro nominální změny platí",[724,12726,12727],{},[883,12728,12730],{"className":12729,"title":8189,"style":8190},[8188],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,12732,12733],{},"a pro procentní změny",[724,12735,12736],{},[883,12737,12739],{"className":12738,"title":8189,"style":8190},[8188],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,12741,12742],{},"(bez znaménka minus).",[198,12744,12746],{"id":12745},"příklad-47","Příklad 4.7",[724,12748,12749,12750,2062],{},"Nabídka ",[883,12751,12753],{"className":12752},[886],[888,12754,12755],{"xmlns":890},[892,12756,12757,12782],{},[895,12758,12759,12761,12763,12765,12771,12773,12775,12777,12779],{},[898,12760,6796],{},[1711,12762,1836],{},[2111,12764,4343],{},[1716,12766,12767,12769],{},[898,12768,7929],{},[2111,12770,2963],{},[1711,12772,2095],{},[2111,12774,4798],{},[898,12776,7929],{},[1711,12778,2095],{},[2111,12780,12781],{},"150",[902,12783,12784],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,12786,12787],{},[883,12788,12790],{"className":12789},[886],[888,12791,12792],{"xmlns":890},[892,12793,12794,12840],{},[895,12795,12796,12798,12800,12824,12826,12828,12830,12832,12834,12836,12838],{},[898,12797,1722],{},[1711,12799,1836],{},[2525,12801,12802,12804],{},[898,12803,7929],{},[895,12805,12806,12808,12814,12816,12818,12820,12822],{},[2111,12807,4343],{},[1716,12809,12810,12812],{},[898,12811,7929],{},[2111,12813,2963],{},[1711,12815,2095],{},[2111,12817,4798],{},[898,12819,7929],{},[1711,12821,2095],{},[2111,12823,12781],{},[1942,12825,2519],{},[1711,12827,1714],{"stretchy":1713},[2111,12829,4491],{},[898,12831,7929],{},[1711,12833,2095],{},[2111,12835,4798],{},[1711,12837,1735],{"stretchy":1713},[898,12839,2186],{"mathvariant":2287},[902,12841,12842],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,12844,9101,12845,1343,12875,1343,12902,12938,12939,12964,12965,12983,12984,2186],{},[883,12846,12848],{"className":12847},[886],[888,12849,12850],{"xmlns":890},[892,12851,12852,12872],{},[895,12853,12854,12856,12858,12860,12862,12864],{},[898,12855,1722],{},[1711,12857,1714],{"stretchy":1713},[2111,12859,4712],{},[1711,12861,1735],{"stretchy":1713},[1711,12863,1836],{},[2509,12865,12866],{"scriptlevel":2113,"displaystyle":1713},[2525,12867,12868,12870],{},[2111,12869,2238],{},[2111,12871,3034],{},[902,12873,12874],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,12876,12878],{"className":12877},[886],[888,12879,12880],{"xmlns":890},[892,12881,12882,12899],{},[895,12883,12884,12886,12888,12893,12895,12897],{},[898,12885,1722],{},[1711,12887,1714],{"stretchy":1713},[12097,12889,12890],{},[2111,12891,12892],{},"1500",[1711,12894,1735],{"stretchy":1713},[1711,12896,1836],{},[2111,12898,2238],{},[902,12900,12901],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,12903,12905],{"className":12904},[886],[888,12906,12907],{"xmlns":890},[892,12908,12909,12935],{},[895,12910,12911,12913,12915,12917,12919,12921,12930,12932],{},[898,12912,1722],{},[1711,12914,1714],{"stretchy":1713},[2111,12916,4282],{},[1711,12918,1735],{"stretchy":1713},[1711,12920,1836],{},[2509,12922,12923],{"scriptlevel":2113,"displaystyle":1713},[2525,12924,12925,12927],{},[2111,12926,7120],{},[2111,12928,12929],{},"33",[1711,12931,9881],{},[2111,12933,12934],{},"1,515",[902,12936,12937],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,12940,12942],{"className":12941},[886],[888,12943,12944],{"xmlns":890},[892,12945,12946,12961],{},[895,12947,12948,12950,12952,12956,12958],{},[898,12949,7929],{},[1711,12951,2123],{},[12097,12953,12954],{},[2111,12955,12892],{},[1711,12957,6740],{},[2111,12959,12960],{},"38,7",[902,12962,12963],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,12966,12968],{"className":12967},[886],[888,12969,12970],{"xmlns":890},[892,12971,12972,12980],{},[895,12973,12974,12976,12978],{},[898,12975,7929],{},[1711,12977,2109],{},[2111,12979,12960],{},[902,12981,12982],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,12985,12987],{"className":12986},[886],[888,12988,12989],{"xmlns":890},[892,12990,12991,13028],{},[895,12992,12993,12995,12997,12999,13001,13009,13011,13013,13015,13018,13024,13026],{},[898,12994,6892],{"mathvariant":2287},[898,12996,6796],{},[898,12998,9906],{"mathvariant":2287},[1711,13000,6740],{},[2509,13002,13003],{"scriptlevel":2113,"displaystyle":1713},[2525,13004,13005,13007],{},[2111,13006,2238],{},[2111,13008,3034],{},[1711,13010,4795],{},[2111,13012,4306],{},[1711,13014,1836],{},[2111,13016,13017],{},"6,",[12366,13019,13020,13022],{"accent":1725},[2111,13021,6262],{},[1711,13023,12372],{"stretchy":1725},[1942,13025,2519],{},[898,13027,9906],{"mathvariant":2287},[902,13029,13030],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,13032,13034],{"id":13033},"vícefaktorový-model","Vícefaktorový model",[724,13036,13037,13038,13051,13052,1700,13055,13068,13069,1700,13072,13090,13091,1700,13094,2062],{},"Předpokládejme, že poptávané množství ",[883,13039,13041],{"className":13040},[886],[888,13042,13043],{"xmlns":890},[892,13044,13045,13049],{},[895,13046,13047],{},[898,13048,6796],{},[902,13050,6796],{"encoding":904}," závisí na ",[38,13053,13054],{},"ceně základního zboží",[883,13056,13058],{"className":13057},[886],[888,13059,13060],{"xmlns":890},[892,13061,13062,13066],{},[895,13063,13064],{},[898,13065,7929],{},[902,13067,7929],{"encoding":904},", na ",[38,13070,13071],{},"ceně alternativního zboží",[883,13073,13075],{"className":13074},[886],[888,13076,13077],{"xmlns":890},[892,13078,13079,13087],{},[895,13080,13081],{},[2884,13082,13083,13085],{},[898,13084,7929],{},[898,13086,8243],{},[902,13088,13089],{"encoding":904},"P_A"," a na ",[38,13092,13093],{},"důchodu",[883,13095,13097],{"className":13096},[886],[888,13098,13099],{"xmlns":890},[892,13100,13101,13105],{},[895,13102,13103],{},[898,13104,1660],{},[902,13106,1660],{"encoding":904},[724,13108,13109],{},[883,13110,13112],{"className":13111,"title":8189,"style":8190},[8188],"Q = D(P, P_A, Y). \\tag{4.17}",[724,13114,13115,13116,13119],{},"V analogii jednofaktorového modelu pracujeme s ",[38,13117,13118],{},"parciálními derivacemi"," funkce poptávky.",[198,13121,13123],{"id":13122},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,13125,13126],{},[883,13127,13129],{"className":13128,"title":8189,"style":8190},[8188],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,13131,8298,13132,13153,13154,13167,13168,2801,13190,1700,13193,13239,13240,13253,13254,13271],{},[883,13133,13135],{"className":13134},[886],[888,13136,13137],{"xmlns":890},[892,13138,13139,13150],{},[895,13140,13141],{},[13142,13143,13144,13146,13148],"msubsup",{},[898,13145,6796],{},[898,13147,7929],{},[1711,13149,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,13151,13152],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,13155,13157],{"className":13156},[886],[888,13158,13159],{"xmlns":890},[892,13160,13161,13165],{},[895,13162,13163],{},[898,13164,7929],{},[902,13166,7929],{"encoding":904},". Vždy ",[883,13169,13171],{"className":13170},[886],[888,13172,13173],{"xmlns":890},[892,13174,13175,13187],{},[895,13176,13177,13183,13185],{},[2884,13178,13179,13181],{},[898,13180,1722],{},[898,13182,7929],{},[1711,13184,8471],{},[2111,13186,2113],{},[902,13188,13189],{"encoding":904},"E_P \\ge 0",[614,13191,13192],{},"Interpretace:",[883,13194,13196],{"className":13195},[886],[888,13197,13198],{"xmlns":890},[892,13199,13200,13236],{},[895,13201,13202,13208,13210,13216,13218,13226,13228,13234],{},[2884,13203,13204,13206],{},[898,13205,1722],{},[898,13207,7929],{},[1711,13209,1714],{"stretchy":1713},[1716,13211,13212,13214],{},[898,13213,7929],{},[1711,13215,1793],{},[1711,13217,1726],{"separator":1725},[13142,13219,13220,13222,13224],{},[898,13221,7929],{},[898,13223,8243],{},[1711,13225,1793],{},[1711,13227,1726],{"separator":1725},[1716,13229,13230,13232],{},[898,13231,1660],{},[1711,13233,1793],{},[1711,13235,1735],{"stretchy":1713},[902,13237,13238],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,13241,13243],{"className":13242},[886],[888,13244,13245],{"xmlns":890},[892,13246,13247,13251],{},[895,13248,13249],{},[898,13250,6796],{},[902,13252,6796],{"encoding":904}," při 1% změně ",[883,13255,13257],{"className":13256},[886],[888,13258,13259],{"xmlns":890},[892,13260,13261,13269],{},[895,13262,13263],{},[1716,13264,13265,13267],{},[898,13266,7929],{},[1711,13268,1793],{},[902,13270,8391],{"encoding":904},", ceteris paribus.",[198,13273,13275],{"id":13274},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,13277,13278],{},[883,13279,13281],{"className":13280,"title":8189,"style":8190},[8188],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,13283,13284,13239,13286,13299,13300,13317],{},[614,13285,13192],{},[883,13287,13289],{"className":13288},[886],[888,13290,13291],{"xmlns":890},[892,13292,13293,13297],{},[895,13294,13295],{},[898,13296,6796],{},[902,13298,6796],{"encoding":904}," základního zboží při 1% změně ceny ",[883,13301,13303],{"className":13302},[886],[888,13304,13305],{"xmlns":890},[892,13306,13307,13315],{},[895,13308,13309],{},[2884,13310,13311,13313],{},[898,13312,7929],{},[898,13314,8243],{},[902,13316,13089],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,13319,13320],{},[38,13321,13322],{},"Znaménko závisí na povaze alternativního zboží:",[120,13324,13325,13413],{},[123,13326,13327,13328,13331,13332,13349,13350,1700,13363,2186],{},"Je-li alternativní zboží ",[38,13329,13330],{},"komplement",", růst ",[883,13333,13335],{"className":13334},[886],[888,13336,13337],{"xmlns":890},[892,13338,13339,13347],{},[895,13340,13341],{},[2884,13342,13343,13345],{},[898,13344,7929],{},[898,13346,8243],{},[902,13348,13089],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,13351,13353],{"className":13352},[886],[888,13354,13355],{"xmlns":890},[892,13356,13357,13361],{},[895,13358,13359],{},[898,13360,6796],{},[902,13362,6796],{"encoding":904},[883,13364,13366],{"className":13365},[886],[888,13367,13368],{"xmlns":890},[892,13369,13370,13410],{},[895,13371,13372,13374,13376,13388,13390,13392,13394,13396,13406,13408],{},[1711,13373,7978],{},[1942,13375,4699],{},[13142,13377,13378,13380,13386],{},[898,13379,6796],{},[2884,13381,13382,13384],{},[898,13383,7929],{},[898,13385,8243],{},[1711,13387,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,13389,2109],{},[2111,13391,2113],{},[1711,13393,1726],{"separator":1725},[1942,13395,4699],{},[2884,13397,13398,13400],{},[898,13399,1722],{},[2884,13401,13402,13404],{},[898,13403,7929],{},[898,13405,8243],{},[1711,13407,2109],{},[2111,13409,2113],{},[902,13411,13412],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,13414,13327,13415,13331,13418,13435,13436,13449,13450,2186],{},[38,13416,13417],{},"substitut",[883,13419,13421],{"className":13420},[886],[888,13422,13423],{"xmlns":890},[892,13424,13425,13433],{},[895,13426,13427],{},[2884,13428,13429,13431],{},[898,13430,7929],{},[898,13432,8243],{},[902,13434,13089],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,13437,13439],{"className":13438},[886],[888,13440,13441],{"xmlns":890},[892,13442,13443,13447],{},[895,13444,13445],{},[898,13446,6796],{},[902,13448,6796],{"encoding":904}," roste ",[883,13451,13453],{"className":13452},[886],[888,13454,13455],{"xmlns":890},[892,13456,13457,13497],{},[895,13458,13459,13461,13463,13475,13477,13479,13481,13483,13493,13495],{},[1711,13460,7978],{},[1942,13462,4699],{},[13142,13464,13465,13467,13473],{},[898,13466,6796],{},[2884,13468,13469,13471],{},[898,13470,7929],{},[898,13472,8243],{},[1711,13474,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,13476,2123],{},[2111,13478,2113],{},[1711,13480,1726],{"separator":1725},[1942,13482,4699],{},[2884,13484,13485,13487],{},[898,13486,1722],{},[2884,13488,13489,13491],{},[898,13490,7929],{},[898,13492,8243],{},[1711,13494,2123],{},[2111,13496,2113],{},[902,13498,13499],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,13501,13504],{"className":13502,"title":13503,"style":8190},[8188],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":13506},[13507,13511,13512,13520,13521,13525,13528],{"id":7883,"depth":642,"text":7884,"children":13508},[13509,13510],{"id":7913,"depth":649,"text":7914},{"id":8093,"depth":649,"text":8094},{"id":8128,"depth":642,"text":8129},{"id":8153,"depth":642,"text":8154,"children":13513},[13514,13515,13516,13517,13519],{"id":8844,"depth":649,"text":8845},{"id":8934,"depth":649,"text":8935},{"id":9269,"depth":649,"text":9270},{"id":9351,"depth":649,"text":13518},"Výpočet, je-li dáno PP jako funkce QQ",{"id":9611,"depth":649,"text":9612},{"id":9934,"depth":642,"text":9935},{"id":10530,"depth":642,"text":10531,"children":13522},[13523,13524],{"id":11158,"depth":649,"text":11159},{"id":11987,"depth":649,"text":11988},{"id":12620,"depth":642,"text":12621,"children":13526},[13527],{"id":12745,"depth":649,"text":12746},{"id":13033,"depth":642,"text":13034,"children":13529},[13530,13531],{"id":13122,"depth":649,"text":13123},{"id":13274,"depth":649,"text":13275},{},"\u002Ftopics\u002Felasticita",{"title":7854,"description":641},[1138,1136],"topics\u002Felasticita",[1128,7890,13538,13539,13540,13541],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":13544,"title":13545,"body":13546,"course":1128,"courses":659,"created":1129,"description":15086,"extension":661,"meta":15087,"navigation":664,"path":15088,"seo":15089,"sources":15090,"stem":15091,"tags":15092,"type":5985,"updated":677,"__hash__":15097},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":13547,"toc":15071},[13548,13551,13625,13632,13636,13700,13788,13792,13819,13886,13941,13945,13972,14064,14066,14098,14269,14273,14343,14391,14395,14456,14562,14577,14581,14583,14611,14676,14678,14685,14773,14798,14996,15000,15036,15038],[12,13549,13545],{"id":13550},"kalkul-funkcí-více-proměnných",[724,13552,13553,13554,13557,13558,1343,13587,2186],{},"Většina ekonomických veličin závisí na ",[38,13555,13556],{},"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 ",[883,13559,13561],{"className":13560},[886],[888,13562,13563],{"xmlns":890},[892,13564,13565,13584],{},[895,13566,13567,13570,13572,13574,13576,13578,13580,13582],{},[898,13568,13569],{},"z",[1711,13571,1836],{},[898,13573,4068],{},[1711,13575,1714],{"stretchy":1713},[898,13577,6047],{},[1711,13579,1726],{"separator":1725},[898,13581,6038],{},[1711,13583,1735],{"stretchy":1713},[902,13585,13586],{"encoding":904},"z = f(x, y)",[883,13588,13590],{"className":13589},[886],[888,13591,13592],{"xmlns":890},[892,13593,13594,13622],{},[895,13595,13596,13599,13601,13603,13605,13607,13609,13611,13613,13615,13617,13619],{},[898,13597,13598],{},"w",[1711,13600,1836],{},[898,13602,4068],{},[1711,13604,1714],{"stretchy":1713},[898,13606,6047],{},[1711,13608,1726],{"separator":1725},[898,13610,6038],{},[1711,13612,1726],{"separator":1725},[898,13614,13569],{},[1711,13616,1735],{"stretchy":1713},[1711,13618,1726],{"separator":1725},[1711,13620,13621],{},"…",[902,13623,13624],{"encoding":904},"w = f(x, y, z), \\ldots",[724,13626,13627],{},[1801,13628],{"alt":13629,"className":13630,"src":13631},"imek-funkce-2d-vrstevnice",[210,1805],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,13633,13635],{"id":13634},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,13637,13638,13639,13666,13667,13695,13696,13699],{},"Pro ",[883,13640,13642],{"className":13641},[886],[888,13643,13644],{"xmlns":890},[892,13645,13646,13664],{},[895,13647,13648,13650,13652,13654,13656,13658,13660,13662],{},[898,13649,13569],{},[1711,13651,1836],{},[898,13653,4068],{},[1711,13655,1714],{"stretchy":1713},[898,13657,6047],{},[1711,13659,1726],{"separator":1725},[898,13661,6038],{},[1711,13663,1735],{"stretchy":1713},[902,13665,13586],{"encoding":904}," se křivkou s předpisem ",[883,13668,13670],{"className":13669},[886],[888,13671,13672],{"xmlns":890},[892,13673,13674,13692],{},[895,13675,13676,13678,13680,13682,13684,13686,13688,13690],{},[898,13677,4068],{},[1711,13679,1714],{"stretchy":1713},[898,13681,6047],{},[1711,13683,1726],{"separator":1725},[898,13685,6038],{},[1711,13687,1735],{"stretchy":1713},[1711,13689,1836],{},[898,13691,2090],{},[902,13693,13694],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,13697,13698],{},"vrstevnice"," funkce. V ekonomii:",[120,13701,13702,13749],{},[123,13703,13704,13707,13708,13744,13745,2186],{},[38,13705,13706],{},"Indiferenční křivky"," užitečnosti ",[883,13709,13711],{"className":13710},[886],[888,13712,13713],{"xmlns":890},[892,13714,13715,13741],{},[895,13716,13717,13719,13721,13727,13729,13735,13737,13739],{},[898,13718,900],{},[1711,13720,1714],{"stretchy":1713},[2884,13722,13723,13725],{},[898,13724,6796],{},[2111,13726,2238],{},[1711,13728,1726],{"separator":1725},[2884,13730,13731,13733],{},[898,13732,6796],{},[2111,13734,2963],{},[1711,13736,1735],{"stretchy":1713},[1711,13738,1836],{},[898,13740,2090],{},[902,13742,13743],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,13746,13748],{"className":13747,"dataFsResolvedFilePath":878,"href":879},[210],"uzitecnost",[123,13750,13751,13754,13755,13744,13784,2186],{},[38,13752,13753],{},"Izokvanty"," produkce ",[883,13756,13758],{"className":13757},[886],[888,13759,13760],{"xmlns":890},[892,13761,13762,13781],{},[895,13763,13764,13766,13768,13770,13772,13775,13777,13779],{},[898,13765,6796],{},[1711,13767,1714],{"stretchy":1713},[898,13769,2888],{},[1711,13771,1726],{"separator":1725},[898,13773,13774],{},"K",[1711,13776,1735],{"stretchy":1713},[1711,13778,1836],{},[898,13780,2090],{},[902,13782,13783],{"encoding":904},"Q(L, K) = c",[207,13785,13787],{"className":13786,"dataFsResolvedFilePath":857,"href":858},[210],"produkce",[115,13789,13791],{"id":13790},"parciální-derivace","Parciální derivace",[724,13793,13638,13794,13818],{},[883,13795,13797],{"className":13796},[886],[888,13798,13799],{"xmlns":890},[892,13800,13801,13815],{},[895,13802,13803,13805,13807,13809,13811,13813],{},[898,13804,4068],{},[1711,13806,1714],{"stretchy":1713},[898,13808,6047],{},[1711,13810,1726],{"separator":1725},[898,13812,6038],{},[1711,13814,1735],{"stretchy":1713},[902,13816,13817],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,13820,13821],{},[883,13822,13824],{"className":13823},[886],[888,13825,13826],{"xmlns":890},[892,13827,13828,13883],{},[895,13829,13830,13838,13840,13855,13857,13859,13867,13869],{},[13142,13831,13832,13834,13836],{},[898,13833,4068],{},[898,13835,6047],{},[1711,13837,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,13839,1836],{},[2525,13841,13842,13849],{},[895,13843,13844,13847],{},[898,13845,13846],{"mathvariant":2287},"∂",[898,13848,4068],{},[895,13850,13851,13853],{},[898,13852,13846],{"mathvariant":2287},[898,13854,6047],{},[1711,13856,1726],{"separator":1725},[2102,13858],{"width":2104},[13142,13860,13861,13863,13865],{},[898,13862,4068],{},[898,13864,6038],{},[1711,13866,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,13868,1836],{},[2525,13870,13871,13877],{},[895,13872,13873,13875],{},[898,13874,13846],{"mathvariant":2287},[898,13876,4068],{},[895,13878,13879,13881],{},[898,13880,13846],{"mathvariant":2287},[898,13882,6038],{},[902,13884,13885],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,13887,13888,13889,2186],{},"Hodnoty v bodě: ",[883,13890,13892],{"className":13891},[886],[888,13893,13894],{"xmlns":890},[892,13895,13896,13938],{},[895,13897,13898,13906,13908,13910,13912,13914,13916,13918,13920,13928,13930,13932,13934,13936],{},[13142,13899,13900,13902,13904],{},[898,13901,4068],{},[898,13903,6047],{},[1711,13905,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,13907,1714],{"stretchy":1713},[898,13909,207],{},[1711,13911,1726],{"separator":1725},[898,13913,2223],{},[1711,13915,1735],{"stretchy":1713},[1711,13917,1726],{"separator":1725},[1942,13919,2118],{},[13142,13921,13922,13924,13926],{},[898,13923,4068],{},[898,13925,6038],{},[1711,13927,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,13929,1714],{"stretchy":1713},[898,13931,207],{},[1711,13933,1726],{"separator":1725},[898,13935,2223],{},[1711,13937,1735],{"stretchy":1713},[902,13939,13940],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,13942,13944],{"id":13943},"ekonomické-značení","Ekonomické značení",[724,13946,13947,13948,2062],{},"Pro produkční funkci ",[883,13949,13951],{"className":13950},[886],[888,13952,13953],{"xmlns":890},[892,13954,13955,13969],{},[895,13956,13957,13959,13961,13963,13965,13967],{},[898,13958,6796],{},[1711,13960,1714],{"stretchy":1713},[898,13962,2888],{},[1711,13964,1726],{"separator":1725},[898,13966,13774],{},[1711,13968,1735],{"stretchy":1713},[902,13970,13971],{"encoding":904},"Q(L, K)",[120,13973,13974,14019],{},[123,13975,13976,6485,13996,1648,13999,1735],{},[883,13977,13979],{"className":13978},[886],[888,13980,13981],{"xmlns":890},[892,13982,13983,13993],{},[895,13984,13985],{},[13142,13986,13987,13989,13991],{},[898,13988,6796],{},[898,13990,2888],{},[1711,13992,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,13994,13995],{"encoding":904},"Q'_L",[38,13997,13998],{},"mezní produkt práce",[883,14000,14002],{"className":14001},[886],[888,14003,14004],{"xmlns":890},[892,14005,14006,14016],{},[895,14007,14008,14010],{},[898,14009,1790],{},[2884,14011,14012,14014],{},[898,14013,7929],{},[898,14015,2888],{},[902,14017,14018],{"encoding":904},"MP_L",[123,14020,14021,6485,14041,1648,14044,1735],{},[883,14022,14024],{"className":14023},[886],[888,14025,14026],{"xmlns":890},[892,14027,14028,14038],{},[895,14029,14030],{},[13142,14031,14032,14034,14036],{},[898,14033,6796],{},[898,14035,13774],{},[1711,14037,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,14039,14040],{"encoding":904},"Q'_K",[38,14042,14043],{},"mezní produkt kapitálu",[883,14045,14047],{"className":14046},[886],[888,14048,14049],{"xmlns":890},[892,14050,14051,14061],{},[895,14052,14053,14055],{},[898,14054,1790],{},[2884,14056,14057,14059],{},[898,14058,7929],{},[898,14060,13774],{},[902,14062,14063],{"encoding":904},"MP_K",[198,14065,6579],{"id":6578},[724,14067,14068,2062],{},[883,14069,14071],{"className":14070},[886],[888,14072,14073],{"xmlns":890},[892,14074,14075,14095],{},[895,14076,14077,14085,14087,14089,14091,14093],{},[13142,14078,14079,14081,14083],{},[898,14080,4068],{},[898,14082,6047],{},[1711,14084,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,14086,1714],{"stretchy":1713},[898,14088,207],{},[1711,14090,1726],{"separator":1725},[898,14092,2223],{},[1711,14094,1735],{"stretchy":1713},[902,14096,14097],{"encoding":904},"f'_x(a, b)",[120,14099,14100,14158],{},[123,14101,14102,14103,14116,14117,14130,14131,14157],{},"rychlost změny ",[883,14104,14106],{"className":14105},[886],[888,14107,14108],{"xmlns":890},[892,14109,14110,14114],{},[895,14111,14112],{},[898,14113,4068],{},[902,14115,4068],{"encoding":904}," vůči ",[883,14118,14120],{"className":14119},[886],[888,14121,14122],{"xmlns":890},[892,14123,14124,14128],{},[895,14125,14126],{},[898,14127,6047],{},[902,14129,6047],{"encoding":904}," při ",[883,14132,14134],{"className":14133},[886],[888,14135,14136],{"xmlns":890},[892,14137,14138,14154],{},[895,14139,14140,14142,14144,14146,14148,14150,14152],{},[898,14141,6047],{},[1711,14143,1836],{},[898,14145,207],{},[1711,14147,1726],{"separator":1725},[898,14149,6038],{},[1711,14151,1836],{},[898,14153,2223],{},[902,14155,14156],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,14159,14160,14161,6668,14174,14187,14188,14206,14207,2186],{},"přibližná změna ",[883,14162,14164],{"className":14163},[886],[888,14165,14166],{"xmlns":890},[892,14167,14168,14172],{},[895,14169,14170],{},[898,14171,4068],{},[902,14173,4068],{"encoding":904},[883,14175,14177],{"className":14176},[886],[888,14178,14179],{"xmlns":890},[892,14180,14181,14185],{},[895,14182,14183],{},[898,14184,6047],{},[902,14186,6047],{"encoding":904}," o 1 (a pevném ",[883,14189,14191],{"className":14190},[886],[888,14192,14193],{"xmlns":890},[892,14194,14195,14203],{},[895,14196,14197,14199,14201],{},[898,14198,6038],{},[1711,14200,1836],{},[898,14202,2223],{},[902,14204,14205],{"encoding":904},"y = b","): ",[883,14208,14210],{"className":14209},[886],[888,14211,14212],{"xmlns":890},[892,14213,14214,14266],{},[895,14215,14216,14218,14220,14222,14224,14226,14228,14230,14232,14234,14236,14238,14240,14242,14244,14246,14248,14256,14258,14260,14262,14264],{},[898,14217,4068],{},[1711,14219,1714],{"stretchy":1713},[898,14221,207],{},[1711,14223,2095],{},[2111,14225,2238],{},[1711,14227,1726],{"separator":1725},[898,14229,2223],{},[1711,14231,1735],{"stretchy":1713},[1711,14233,6740],{},[898,14235,4068],{},[1711,14237,1714],{"stretchy":1713},[898,14239,207],{},[1711,14241,1726],{"separator":1725},[898,14243,2223],{},[1711,14245,1735],{"stretchy":1713},[1711,14247,2095],{},[13142,14249,14250,14252,14254],{},[898,14251,4068],{},[898,14253,6047],{},[1711,14255,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,14257,1714],{"stretchy":1713},[898,14259,207],{},[1711,14261,1726],{"separator":1725},[898,14263,2223],{},[1711,14265,1735],{"stretchy":1713},[902,14267,14268],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,14270,14272],{"id":14271},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,14274,14275],{},[883,14276,14278],{"className":14277},[886],[888,14279,14280],{"xmlns":890},[892,14281,14282,14340],{},[895,14283,14284,14286,14288,14290,14298,14300,14302,14304,14306,14308,14310,14312,14314,14316,14324,14326,14328,14330,14332,14334,14336,14338],{},[898,14285,2098],{},[898,14287,4068],{},[1711,14289,1836],{},[13142,14291,14292,14294,14296],{},[898,14293,4068],{},[898,14295,6047],{},[1711,14297,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,14299,1714],{"stretchy":1713},[898,14301,6047],{},[1711,14303,1726],{"separator":1725},[898,14305,6038],{},[1711,14307,1735],{"stretchy":1713},[1942,14309,2519],{},[898,14311,2098],{},[898,14313,6047],{},[1711,14315,2095],{},[13142,14317,14318,14320,14322],{},[898,14319,4068],{},[898,14321,6038],{},[1711,14323,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,14325,1714],{"stretchy":1713},[898,14327,6047],{},[1711,14329,1726],{"separator":1725},[898,14331,6038],{},[1711,14333,1735],{"stretchy":1713},[1942,14335,2519],{},[898,14337,2098],{},[898,14339,6038],{},[902,14341,14342],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,14344,6998,14345,14367,14368,14390],{},[883,14346,14348],{"className":14347},[886],[888,14349,14350],{"xmlns":890},[892,14351,14352,14364],{},[895,14353,14354,14356,14358,14360,14362],{},[898,14355,2098],{},[898,14357,6047],{},[1711,14359,1726],{"separator":1725},[898,14361,2098],{},[898,14363,6038],{},[902,14365,14366],{"encoding":904},"dx, dy"," platí ",[883,14369,14371],{"className":14370},[886],[888,14372,14373],{"xmlns":890},[892,14374,14375,14387],{},[895,14376,14377,14379,14381,14383,14385],{},[898,14378,6892],{"mathvariant":2287},[898,14380,4068],{},[1711,14382,6740],{},[898,14384,2098],{},[898,14386,4068],{},[902,14388,14389],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,14392,14394],{"id":14393},"implicitní-funkce","Implicitní funkce",[724,14396,14397,14398,14427,14428,14441,14442,14455],{},"Je-li vztah dán rovnicí ",[883,14399,14401],{"className":14400},[886],[888,14402,14403],{"xmlns":890},[892,14404,14405,14424],{},[895,14406,14407,14410,14412,14414,14416,14418,14420,14422],{},[898,14408,14409],{},"F",[1711,14411,1714],{"stretchy":1713},[898,14413,6047],{},[1711,14415,1726],{"separator":1725},[898,14417,6038],{},[1711,14419,1735],{"stretchy":1713},[1711,14421,1836],{},[2111,14423,2113],{},[902,14425,14426],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,14429,14431],{"className":14430},[886],[888,14432,14433],{"xmlns":890},[892,14434,14435,14439],{},[895,14436,14437],{},[898,14438,6038],{},[902,14440,6038],{"encoding":904}," podle ",[883,14443,14445],{"className":14444},[886],[888,14446,14447],{"xmlns":890},[892,14448,14449,14453],{},[895,14450,14451],{},[898,14452,6047],{},[902,14454,6047],{"encoding":904}," (nebo naopak):",[724,14457,14458],{},[883,14459,14461],{"className":14460},[886],[888,14462,14463],{"xmlns":890},[892,14464,14465,14559],{},[895,14466,14467,14473,14475,14489,14491,14493,14511,14513,14515,14521,14523,14537,14539,14541],{},[1716,14468,14469,14471],{},[898,14470,6038],{},[1711,14472,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,14474,1836],{},[2525,14476,14477,14483],{},[895,14478,14479,14481],{},[898,14480,2098],{},[898,14482,6038],{},[895,14484,14485,14487],{},[898,14486,2098],{},[898,14488,6047],{},[1711,14490,1836],{},[1711,14492,2460],{},[2525,14494,14495,14503],{},[13142,14496,14497,14499,14501],{},[898,14498,14409],{},[898,14500,6047],{},[1711,14502,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[13142,14504,14505,14507,14509],{},[898,14506,14409],{},[898,14508,6038],{},[1711,14510,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,14512,1726],{"separator":1725},[2102,14514],{"width":2104},[1716,14516,14517,14519],{},[898,14518,6047],{},[1711,14520,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,14522,1836],{},[2525,14524,14525,14531],{},[895,14526,14527,14529],{},[898,14528,2098],{},[898,14530,6047],{},[895,14532,14533,14535],{},[898,14534,2098],{},[898,14536,6038],{},[1711,14538,1836],{},[1711,14540,2460],{},[2525,14542,14543,14551],{},[13142,14544,14545,14547,14549],{},[898,14546,14409],{},[898,14548,6038],{},[1711,14550,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[13142,14552,14553,14555,14557],{},[898,14554,14409],{},[898,14556,6047],{},[1711,14558,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,14560,14561],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,14563,14564,14565,14568,14569,2009,14573,2186],{},"Tato vzorec dává ",[38,14566,14567],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,14570,14572],{"className":14571,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS",[207,14574,14576],{"className":14575,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS",[115,14578,14580],{"id":14579},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,14582,7250],{"id":7249},[724,14584,14585,14586,14610],{},"V bodě extrému ",[883,14587,14589],{"className":14588},[886],[888,14590,14591],{"xmlns":890},[892,14592,14593,14607],{},[895,14594,14595,14597,14599,14601,14603,14605],{},[898,14596,8243],{},[1711,14598,5144],{"stretchy":1713},[898,14600,207],{},[1711,14602,1726],{"separator":1725},[898,14604,2223],{},[1711,14606,5163],{"stretchy":1713},[902,14608,14609],{"encoding":904},"A[a, b]"," musí platit současně:",[724,14612,14613],{},[883,14614,14616],{"className":14615},[886],[888,14617,14618],{"xmlns":890},[892,14619,14620,14673],{},[895,14621,14622,14630,14632,14634,14636,14638,14640,14642,14644,14646,14649,14651,14659,14661,14663,14665,14667,14669,14671],{},[13142,14623,14624,14626,14628],{},[898,14625,4068],{},[898,14627,6047],{},[1711,14629,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,14631,1714],{"stretchy":1713},[898,14633,207],{},[1711,14635,1726],{"separator":1725},[898,14637,2223],{},[1711,14639,1735],{"stretchy":1713},[1711,14641,1836],{},[2111,14643,2113],{},[1942,14645,4699],{},[1711,14647,14648],{},"∧",[1942,14650,4699],{},[13142,14652,14653,14655,14657],{},[898,14654,4068],{},[898,14656,6038],{},[1711,14658,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,14660,1714],{"stretchy":1713},[898,14662,207],{},[1711,14664,1726],{"separator":1725},[898,14666,2223],{},[1711,14668,1735],{"stretchy":1713},[1711,14670,1836],{},[2111,14672,2113],{},[902,14674,14675],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,14677,7324],{"id":7323},[724,14679,14680,14681,14684],{},"Definujeme ",[38,14682,14683],{},"diskriminant"," (Hessián zjednodušeně):",[724,14686,14687],{},[883,14688,14690],{"className":14689},[886],[888,14691,14692],{"xmlns":890},[892,14693,14694,14770],{},[895,14695,14696,14698,14700,14702,14704,14706,14708,14710,14726,14728,14744,14746,14748,14764],{},[898,14697,2778],{},[1711,14699,1714],{"stretchy":1713},[898,14701,6047],{},[1711,14703,1726],{"separator":1725},[898,14705,6038],{},[1711,14707,1735],{"stretchy":1713},[1711,14709,1836],{},[13142,14711,14712,14714,14720],{},[898,14713,4068],{},[895,14715,14716,14718],{},[898,14717,6047],{},[898,14719,6047],{},[895,14721,14722,14724],{},[1711,14723,5225],{"mathvariant":2287},[1711,14725,5225],{"mathvariant":2287},[1711,14727,4795],{},[13142,14729,14730,14732,14738],{},[898,14731,4068],{},[895,14733,14734,14736],{},[898,14735,6038],{},[898,14737,6038],{},[895,14739,14740,14742],{},[1711,14741,5225],{"mathvariant":2287},[1711,14743,5225],{"mathvariant":2287},[1711,14745,2460],{},[1711,14747,1714],{"stretchy":1713},[13142,14749,14750,14752,14758],{},[898,14751,4068],{},[895,14753,14754,14756],{},[898,14755,6047],{},[898,14757,6038],{},[895,14759,14760,14762],{},[1711,14761,5225],{"mathvariant":2287},[1711,14763,5225],{"mathvariant":2287},[1716,14765,14766,14768],{},[1711,14767,1735],{"stretchy":1713},[2111,14769,2963],{},[902,14771,14772],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,14774,14775,14776,2062],{},"V podezřelém bodě ",[883,14777,14779],{"className":14778},[886],[888,14780,14781],{"xmlns":890},[892,14782,14783,14795],{},[895,14784,14785,14787,14789,14791,14793],{},[1711,14786,5144],{"stretchy":1713},[898,14788,207],{},[1711,14790,1726],{"separator":1725},[898,14792,2223],{},[1711,14794,5163],{"stretchy":1713},[902,14796,14797],{"encoding":904},"[a, b]",[152,14799,14800,14927,14963],{},[123,14801,14802,14832,14833],{},[38,14803,14804,2062],{},[883,14805,14807],{"className":14806},[886],[888,14808,14809],{"xmlns":890},[892,14810,14811,14829],{},[895,14812,14813,14815,14817,14819,14821,14823,14825,14827],{},[898,14814,2778],{},[1711,14816,1714],{"stretchy":1713},[898,14818,207],{},[1711,14820,1726],{"separator":1725},[898,14822,2223],{},[1711,14824,1735],{"stretchy":1713},[1711,14826,2123],{},[2111,14828,2113],{},[902,14830,14831],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,14834,14835,14881],{},[123,14836,14837,7411,14879],{},[883,14838,14840],{"className":14839},[886],[888,14841,14842],{"xmlns":890},[892,14843,14844,14876],{},[895,14845,14846,14862,14864,14866,14868,14870,14872,14874],{},[13142,14847,14848,14850,14856],{},[898,14849,4068],{},[895,14851,14852,14854],{},[898,14853,6047],{},[898,14855,6047],{},[895,14857,14858,14860],{},[1711,14859,5225],{"mathvariant":2287},[1711,14861,5225],{"mathvariant":2287},[1711,14863,1714],{"stretchy":1713},[898,14865,207],{},[1711,14867,1726],{"separator":1725},[898,14869,2223],{},[1711,14871,1735],{"stretchy":1713},[1711,14873,2123],{},[2111,14875,2113],{},[902,14877,14878],{"encoding":904},"f''_{xx}(a, b) > 0",[38,14880,7771],{},[123,14882,14883,7411,14925],{},[883,14884,14886],{"className":14885},[886],[888,14887,14888],{"xmlns":890},[892,14889,14890,14922],{},[895,14891,14892,14908,14910,14912,14914,14916,14918,14920],{},[13142,14893,14894,14896,14902],{},[898,14895,4068],{},[895,14897,14898,14900],{},[898,14899,6047],{},[898,14901,6047],{},[895,14903,14904,14906],{},[1711,14905,5225],{"mathvariant":2287},[1711,14907,5225],{"mathvariant":2287},[1711,14909,1714],{"stretchy":1713},[898,14911,207],{},[1711,14913,1726],{"separator":1725},[898,14915,2223],{},[1711,14917,1735],{"stretchy":1713},[1711,14919,2109],{},[2111,14921,2113],{},[902,14923,14924],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,14926,7713],{},[123,14928,14929,1700,14959,14962],{},[38,14930,14931,2062],{},[883,14932,14934],{"className":14933},[886],[888,14935,14936],{"xmlns":890},[892,14937,14938,14956],{},[895,14939,14940,14942,14944,14946,14948,14950,14952,14954],{},[898,14941,2778],{},[1711,14943,1714],{"stretchy":1713},[898,14945,207],{},[1711,14947,1726],{"separator":1725},[898,14949,2223],{},[1711,14951,1735],{"stretchy":1713},[1711,14953,2109],{},[2111,14955,2113],{},[902,14957,14958],{"encoding":904},"D(a, b) \u003C 0",[38,14960,14961],{},"sedlo"," (v daném bodě extrém není).",[123,14964,14965,14995],{},[38,14966,14967,2062],{},[883,14968,14970],{"className":14969},[886],[888,14971,14972],{"xmlns":890},[892,14973,14974,14992],{},[895,14975,14976,14978,14980,14982,14984,14986,14988,14990],{},[898,14977,2778],{},[1711,14979,1714],{"stretchy":1713},[898,14981,207],{},[1711,14983,1726],{"separator":1725},[898,14985,2223],{},[1711,14987,1735],{"stretchy":1713},[1711,14989,1836],{},[2111,14991,2113],{},[902,14993,14994],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,14997,14999],{"id":14998},"vázané-extrémy","Vázané extrémy",[724,15001,15002,15003,15032,15033,2186],{},"Pro extrémy s omezující podmínkou ",[883,15004,15006],{"className":15005},[886],[888,15007,15008],{"xmlns":890},[892,15009,15010,15029],{},[895,15011,15012,15015,15017,15019,15021,15023,15025,15027],{},[898,15013,15014],{},"g",[1711,15016,1714],{"stretchy":1713},[898,15018,6047],{},[1711,15020,1726],{"separator":1725},[898,15022,6038],{},[1711,15024,1735],{"stretchy":1713},[1711,15026,1836],{},[2111,15028,2113],{},[902,15030,15031],{"encoding":904},"g(x, y) = 0"," se používá ",[207,15034,793],{"className":15035,"dataFsResolvedFilePath":791,"href":792},[210],[115,15037,5901],{"id":5900},[120,15039,15040,15047,15054],{},[123,15041,15042,1700,15044],{},[38,15043,7793],{},[207,15045,775],{"className":15046,"dataFsResolvedFilePath":773,"href":774},[210],[123,15048,15049,1700,15051],{},[38,15050,7801],{},[207,15052,793],{"className":15053,"dataFsResolvedFilePath":791,"href":792},[210],[123,15055,15056,1700,15058,15062,15063,15066,15067,15070],{},[38,15057,7809],{},[207,15059,15061],{"className":15060,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (parciální derivace = mezní produkty), ",[207,15064,880],{"className":15065,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,15068,7822],{"className":15069,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":15072},[15073,15074,15078,15079,15080,15084,15085],{"id":13634,"depth":642,"text":13635},{"id":13790,"depth":642,"text":13791,"children":15075},[15076,15077],{"id":13943,"depth":649,"text":13944},{"id":6578,"depth":649,"text":6579},{"id":14271,"depth":642,"text":14272},{"id":14393,"depth":642,"text":14394},{"id":14579,"depth":642,"text":14580,"children":15081},[15082,15083],{"id":7249,"depth":649,"text":7250},{"id":7323,"depth":649,"text":7324},{"id":14998,"depth":642,"text":14999},{"id":5900,"depth":642,"text":5901},"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":13545,"description":15086},[1135],"topics\u002Ffunkce-vice-promennych",[1128,15093,7848,15094,15095,15096],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":15099,"title":775,"body":15100,"course":1128,"courses":659,"created":1129,"description":15956,"extension":661,"meta":15957,"navigation":664,"path":15958,"seo":15959,"sources":15960,"stem":15961,"tags":15962,"type":5985,"updated":677,"__hash__":15969},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":15101,"toc":15946},[15102,15105,15116,15120,15165,15245,15249,15325,15367,15374,15378,15382,15411,15469,15516,15554,15558,15608,15660,15712,15756,15759,15762,15834,15837,15909,15916,15918],[12,15103,775],{"id":15104},"integrál",[724,15106,15107,15108,15111,15112,15115],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,15109,15110],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,15113,15114],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,15117,15119],{"id":15118},"neurčitý-integrál","Neurčitý integrál",[724,15121,15122],{},[883,15123,15125],{"className":15124},[886],[888,15126,15127],{"xmlns":890},[892,15128,15129,15162],{},[895,15130,15131,15133,15135,15137,15139,15141,15144,15146,15148,15150,15152,15154,15156,15158,15160],{},[898,15132,14409],{},[1711,15134,1714],{"stretchy":1713},[898,15136,6047],{},[1711,15138,1735],{"stretchy":1713},[1711,15140,1836],{},[1711,15142,15143],{},"∫",[898,15145,4068],{},[1711,15147,1714],{"stretchy":1713},[898,15149,6047],{},[1711,15151,1735],{"stretchy":1713},[1942,15153,2519],{},[898,15155,2098],{},[898,15157,6047],{},[1711,15159,2095],{},[898,15161,1940],{},[902,15163,15164],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,15166,8298,15167,2801,15201,12082,15214,15217,15218,1343,15231,15244],{},[883,15168,15170],{"className":15169},[886],[888,15171,15172],{"xmlns":890},[892,15173,15174,15198],{},[895,15175,15176,15182,15184,15186,15188,15190,15192,15194,15196],{},[1716,15177,15178,15180],{},[898,15179,14409],{},[1711,15181,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,15183,1714],{"stretchy":1713},[898,15185,6047],{},[1711,15187,1735],{"stretchy":1713},[1711,15189,1836],{},[898,15191,4068],{},[1711,15193,1714],{"stretchy":1713},[898,15195,6047],{},[1711,15197,1735],{"stretchy":1713},[902,15199,15200],{"encoding":904},"F'(x) = f(x)",[883,15202,15204],{"className":15203},[886],[888,15205,15206],{"xmlns":890},[892,15207,15208,15212],{},[895,15209,15210],{},[898,15211,14409],{},[902,15213,14409],{"encoding":904},[38,15215,15216],{},"primitivní funkce"," k ",[883,15219,15221],{"className":15220},[886],[888,15222,15223],{"xmlns":890},[892,15224,15225,15229],{},[895,15226,15227],{},[898,15228,4068],{},[902,15230,4068],{"encoding":904},[883,15232,15234],{"className":15233},[886],[888,15235,15236],{"xmlns":890},[892,15237,15238,15242],{},[895,15239,15240],{},[898,15241,1940],{},[902,15243,1940],{"encoding":904}," konstanta.",[115,15246,15248],{"id":15247},"určitý-integrál","Určitý integrál",[724,15250,15251],{},[883,15252,15254],{"className":15253},[886],[888,15255,15256],{"xmlns":890},[892,15257,15258,15322],{},[895,15259,15260,15268,15270,15272,15274,15276,15278,15280,15282,15284,15286,15288,15290,15292,15294,15302,15304,15306,15308,15310,15312,15314,15316,15318,15320],{},[13142,15261,15262,15264,15266],{},[1711,15263,15143],{},[898,15265,207],{},[898,15267,2223],{},[898,15269,4068],{},[1711,15271,1714],{"stretchy":1713},[898,15273,6047],{},[1711,15275,1735],{"stretchy":1713},[1942,15277,2519],{},[898,15279,2098],{},[898,15281,6047],{},[1711,15283,1836],{},[1711,15285,5144],{"stretchy":1713},[898,15287,14409],{},[1711,15289,1714],{"stretchy":1713},[898,15291,6047],{},[1711,15293,1735],{"stretchy":1713},[13142,15295,15296,15298,15300],{},[1711,15297,5163],{"stretchy":1713},[898,15299,207],{},[898,15301,2223],{},[1711,15303,1836],{},[898,15305,14409],{},[1711,15307,1714],{"stretchy":1713},[898,15309,2223],{},[1711,15311,1735],{"stretchy":1713},[1711,15313,2460],{},[898,15315,14409],{},[1711,15317,1714],{"stretchy":1713},[898,15319,207],{},[1711,15321,1735],{"stretchy":1713},[902,15323,15324],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,15326,15327,15328,1700,15331,15344,15345,15366],{},"Geometricky ",[38,15329,15330],{},"plocha pod grafem",[883,15332,15334],{"className":15333},[886],[888,15335,15336],{"xmlns":890},[892,15337,15338,15342],{},[895,15339,15340],{},[898,15341,4068],{},[902,15343,4068],{"encoding":904}," na intervalu ",[883,15346,15348],{"className":15347},[886],[888,15349,15350],{"xmlns":890},[892,15351,15352,15364],{},[895,15353,15354,15356,15358,15360,15362],{},[1711,15355,5144],{"stretchy":1713},[898,15357,207],{},[1711,15359,1726],{"separator":1725},[898,15361,2223],{},[1711,15363,5163],{"stretchy":1713},[902,15365,14797],{"encoding":904}," (orientovaná).",[724,15368,15369],{},[1801,15370],{"alt":15371,"className":15372,"src":15373},"imek-integral-plocha",[210,1805],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,15375,15377],{"id":15376},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,15379,15381],{"id":15380},"příklad-tr-z-mr","Příklad — TR z MR",[724,15383,15384,15385,2186],{},"Mezní příjem ",[883,15386,15388],{"className":15387},[886],[888,15389,15390],{"xmlns":890},[892,15391,15392,15408],{},[895,15393,15394,15396,15398,15400,15402,15404,15406],{},[898,15395,1790],{},[898,15397,7985],{},[1711,15399,1836],{},[2111,15401,4282],{},[1711,15403,2460],{},[2111,15405,2963],{},[898,15407,6796],{},[902,15409,15410],{"encoding":904},"MR = 100 - 2Q",[724,15412,15413],{},[883,15414,15416],{"className":15415},[886],[888,15417,15418],{"xmlns":890},[892,15419,15420,15466],{},[895,15421,15422,15424,15426,15428,15430,15432,15434,15436,15438,15440,15442,15444,15446,15448,15450,15452,15454,15456,15462,15464],{},[898,15423,1769],{},[898,15425,7985],{},[1711,15427,1836],{},[1711,15429,15143],{},[1711,15431,1714],{"stretchy":1713},[2111,15433,4282],{},[1711,15435,2460],{},[2111,15437,2963],{},[898,15439,6796],{},[1711,15441,1735],{"stretchy":1713},[1942,15443,2519],{},[898,15445,2098],{},[898,15447,6796],{},[1711,15449,1836],{},[2111,15451,4282],{},[898,15453,6796],{},[1711,15455,2460],{},[1716,15457,15458,15460],{},[898,15459,6796],{},[2111,15461,2963],{},[1711,15463,2095],{},[898,15465,2090],{},[902,15467,15468],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,15470,15471,15472,7411,15498,2062],{},"Okrajová podmínka ",[883,15473,15475],{"className":15474},[886],[888,15476,15477],{"xmlns":890},[892,15478,15479,15495],{},[895,15480,15481,15483,15485,15487,15489,15491,15493],{},[898,15482,1769],{},[898,15484,7985],{},[1711,15486,1714],{"stretchy":1713},[2111,15488,2113],{},[1711,15490,1735],{"stretchy":1713},[1711,15492,1836],{},[2111,15494,2113],{},[902,15496,15497],{"encoding":904},"TR(0) = 0",[883,15499,15501],{"className":15500},[886],[888,15502,15503],{"xmlns":890},[892,15504,15505,15513],{},[895,15506,15507,15509,15511],{},[898,15508,2090],{},[1711,15510,1836],{},[2111,15512,2113],{},[902,15514,15515],{"encoding":904},"c = 0",[724,15517,15518],{},[883,15519,15521],{"className":15520},[886],[888,15522,15523],{"xmlns":890},[892,15524,15525,15551],{},[895,15526,15527,15529,15531,15533,15535,15537,15539,15541,15543,15545],{},[898,15528,1769],{},[898,15530,7985],{},[1711,15532,1714],{"stretchy":1713},[898,15534,6796],{},[1711,15536,1735],{"stretchy":1713},[1711,15538,1836],{},[2111,15540,4282],{},[898,15542,6796],{},[1711,15544,2460],{},[1716,15546,15547,15549],{},[898,15548,6796],{},[2111,15550,2963],{},[902,15552,15553],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,15555,15557],{"id":15556},"příklad-tc-z-mc","Příklad — TC z MC",[724,15559,15560,15561,15587,15588,2186],{},"Mezní náklady ",[883,15562,15564],{"className":15563},[886],[888,15565,15566],{"xmlns":890},[892,15567,15568,15584],{},[895,15569,15570,15572,15574,15576,15578,15580,15582],{},[898,15571,1790],{},[898,15573,1940],{},[1711,15575,1836],{},[2111,15577,2963],{},[1711,15579,2095],{},[2111,15581,4491],{},[898,15583,6796],{},[902,15585,15586],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,15589,15591],{"className":15590},[886],[888,15592,15593],{"xmlns":890},[892,15594,15595,15605],{},[895,15596,15597,15599,15601,15603],{},[898,15598,14409],{},[898,15600,1940],{},[1711,15602,1836],{},[2111,15604,4282],{},[902,15606,15607],{"encoding":904},"FC = 100",[724,15609,15610],{},[883,15611,15613],{"className":15612},[886],[888,15614,15615],{"xmlns":890},[892,15616,15617,15657],{},[895,15618,15619,15621,15623,15625,15627,15629,15631,15633,15635,15637,15639,15641,15643,15645,15647,15653,15655],{},[898,15620,1769],{},[898,15622,1940],{},[1711,15624,1836],{},[1711,15626,15143],{},[898,15628,1790],{},[898,15630,1940],{},[1942,15632,2519],{},[898,15634,2098],{},[898,15636,6796],{},[1711,15638,1836],{},[2111,15640,2963],{},[898,15642,6796],{},[1711,15644,2095],{},[2111,15646,4343],{},[1716,15648,15649,15651],{},[898,15650,6796],{},[2111,15652,2963],{},[1711,15654,2095],{},[898,15656,2090],{},[902,15658,15659],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,15661,15471,15662,7411,15694,2062],{},[883,15663,15665],{"className":15664},[886],[888,15666,15667],{"xmlns":890},[892,15668,15669,15691],{},[895,15670,15671,15673,15675,15677,15679,15681,15683,15685,15687,15689],{},[898,15672,1769],{},[898,15674,1940],{},[1711,15676,1714],{"stretchy":1713},[2111,15678,2113],{},[1711,15680,1735],{"stretchy":1713},[1711,15682,1836],{},[898,15684,14409],{},[898,15686,1940],{},[1711,15688,1836],{},[2111,15690,4282],{},[902,15692,15693],{"encoding":904},"TC(0) = FC = 100",[883,15695,15697],{"className":15696},[886],[888,15698,15699],{"xmlns":890},[892,15700,15701,15709],{},[895,15702,15703,15705,15707],{},[898,15704,2090],{},[1711,15706,1836],{},[2111,15708,4282],{},[902,15710,15711],{"encoding":904},"c = 100",[724,15713,15714],{},[883,15715,15717],{"className":15716},[886],[888,15718,15719],{"xmlns":890},[892,15720,15721,15753],{},[895,15722,15723,15725,15727,15729,15731,15733,15735,15737,15739,15741,15743,15745,15747],{},[898,15724,1769],{},[898,15726,1940],{},[1711,15728,1714],{"stretchy":1713},[898,15730,6796],{},[1711,15732,1735],{"stretchy":1713},[1711,15734,1836],{},[2111,15736,4282],{},[1711,15738,2095],{},[2111,15740,2963],{},[898,15742,6796],{},[1711,15744,2095],{},[2111,15746,4343],{},[1716,15748,15749,15751],{},[898,15750,6796],{},[2111,15752,2963],{},[902,15754,15755],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,15757,820],{"id":15758},"přebytek-spotřebitele-a-výrobce",[724,15760,15761],{},"Přebytek spotřebitele:",[724,15763,15764],{},[883,15765,15767],{"className":15766},[886],[888,15768,15769],{"xmlns":890},[892,15770,15771,15831],{},[895,15772,15773,15775,15777,15779,15785,15787,15789,15801,15803,15805,15807,15809,15811,15813,15815,15817,15823,15825],{},[898,15774,1940],{},[898,15776,2362],{},[1711,15778,1714],{"stretchy":1713},[2884,15780,15781,15783],{},[898,15782,6796],{},[2111,15784,2113],{},[1711,15786,1735],{"stretchy":1713},[1711,15788,1836],{},[13142,15790,15791,15793,15795],{},[1711,15792,15143],{},[2111,15794,2113],{},[2884,15796,15797,15799],{},[898,15798,6796],{},[2111,15800,2113],{},[898,15802,2778],{},[1711,15804,1714],{"stretchy":1713},[898,15806,6796],{},[1711,15808,1735],{"stretchy":1713},[1942,15810,2519],{},[898,15812,2098],{},[898,15814,6796],{},[1711,15816,2460],{},[2884,15818,15819,15821],{},[898,15820,7929],{},[2111,15822,2113],{},[1942,15824,2519],{},[2884,15826,15827,15829],{},[898,15828,6796],{},[2111,15830,2113],{},[902,15832,15833],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,15835,15836],{},"Přebytek výrobce:",[724,15838,15839],{},[883,15840,15842],{"className":15841},[886],[888,15843,15844],{"xmlns":890},[892,15845,15846,15906],{},[895,15847,15848,15850,15852,15854,15860,15862,15864,15870,15872,15878,15880,15892,15894,15896,15898,15900,15902,15904],{},[898,15849,7929],{},[898,15851,2362],{},[1711,15853,1714],{"stretchy":1713},[2884,15855,15856,15858],{},[898,15857,6796],{},[2111,15859,2113],{},[1711,15861,1735],{"stretchy":1713},[1711,15863,1836],{},[2884,15865,15866,15868],{},[898,15867,7929],{},[2111,15869,2113],{},[1942,15871,2519],{},[2884,15873,15874,15876],{},[898,15875,6796],{},[2111,15877,2113],{},[1711,15879,2460],{},[13142,15881,15882,15884,15886],{},[1711,15883,15143],{},[2111,15885,2113],{},[2884,15887,15888,15890],{},[898,15889,6796],{},[2111,15891,2113],{},[898,15893,2362],{},[1711,15895,1714],{"stretchy":1713},[898,15897,6796],{},[1711,15899,1735],{"stretchy":1713},[1942,15901,2519],{},[898,15903,2098],{},[898,15905,6796],{},[902,15907,15908],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,15910,15911,15912,2186],{},"Detailně viz ",[207,15913,15915],{"className":15914,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka",[115,15917,5901],{"id":5900},[120,15919,15920,15927,15934],{},[123,15921,15922,1700,15924],{},[38,15923,7793],{},[207,15925,766],{"className":15926,"dataFsResolvedFilePath":764,"href":765},[210],[123,15928,15929,1700,15931],{},[38,15930,7801],{},[207,15932,784],{"className":15933,"dataFsResolvedFilePath":782,"href":783},[210],[123,15935,15936,1700,15938,15941,15942,15945],{},[38,15937,7809],{},[207,15939,7817],{"className":15940,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,15943,15915],{"className":15944,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":15947},[15948,15949,15950,15955],{"id":15118,"depth":642,"text":15119},{"id":15247,"depth":642,"text":15248},{"id":15376,"depth":642,"text":15377,"children":15951},[15952,15953,15954],{"id":15380,"depth":649,"text":15381},{"id":15556,"depth":649,"text":15557},{"id":15758,"depth":649,"text":820},{"id":5900,"depth":642,"text":5901},"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":15956},[1135],"topics\u002Fintegral",[1128,15963,15964,15965,15966,15967,15968],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":1628,"title":1629,"body":15971,"course":1128,"courses":659,"created":5973,"description":641,"extension":661,"meta":19872,"navigation":664,"path":5975,"seo":19873,"sources":19874,"stem":5978,"tags":19875,"type":5985,"updated":677,"__hash__":5986},{"type":9,"value":15972,"toc":19860},[15973,15975,15977,16097,16102,16104,16162,16195,16286,16288,16316,16379,16421,16423,16490,16492,16525,16556,16558,16600,16605,16650,16695,16697,16772,16855,16930,16932,16970,16999,17003,17023,17042,17089,17138,17203,17205,17270,17297,17354,17369,17454,17541,17662,17664,17806,17947,18303,18305,18307,18361,18363,18444,18469,18506,18508,18543,18580,18613,18615,18650,18677,18768,18772,18889,18938,19017,19147,19149,19258,19263,19365,19369,19371,19814,19816],[12,15974,1629],{"id":1634},[115,15976,1638],{"id":1637},[724,15978,15979,1644,15981,1648,15983,1663,15996,1678,16009,1682,16011,1343,16013,1689,16015,1343,16017,1696,16019,1700,16021,1739,16050,1743,16052,1343,16065,1772,16078,1776,16080,1797],{},[38,15980,1643],{},[38,15982,1647],{},[883,15984,15986],{"className":15985},[886],[888,15987,15988],{"xmlns":890},[892,15989,15990,15994],{},[895,15991,15992],{},[898,15993,1660],{},[902,15995,1660],{"encoding":904},[883,15997,15999],{"className":15998},[886],[888,16000,16001],{"xmlns":890},[892,16002,16003,16007],{},[895,16004,16005],{},[898,16006,1675],{},[902,16008,1675],{"encoding":904},[38,16010,1681],{},[38,16012,1685],{},[614,16014,1688],{},[38,16016,1692],{},[614,16018,1695],{},[38,16020,1699],{},[883,16022,16024],{"className":16023},[886],[888,16025,16026],{"xmlns":890},[892,16027,16028,16048],{},[895,16029,16030,16032,16038,16040,16046],{},[1711,16031,1714],{"stretchy":1713},[1716,16033,16034,16036],{},[898,16035,1660],{},[898,16037,1722],{},[1711,16039,1726],{"separator":1725},[1716,16041,16042,16044],{},[898,16043,1675],{},[898,16045,1722],{},[1711,16047,1735],{"stretchy":1713},[902,16049,1738],{"encoding":904},[38,16051,1742],{},[883,16053,16055],{"className":16054},[886],[888,16056,16057],{"xmlns":890},[892,16058,16059,16063],{},[895,16060,16061],{},[898,16062,1755],{},[902,16064,1755],{"encoding":904},[883,16066,16068],{"className":16067},[886],[888,16069,16070],{"xmlns":890},[892,16071,16072,16076],{},[895,16073,16074],{},[898,16075,1769],{},[902,16077,1769],{"encoding":904},[38,16079,1775],{},[883,16081,16083],{"className":16082},[886],[888,16084,16085],{"xmlns":890},[892,16086,16087,16095],{},[895,16088,16089],{},[1716,16090,16091,16093],{},[898,16092,1790],{},[1711,16094,1793],{},[902,16096,1796],{"encoding":904},[724,16098,16099],{},[1801,16100],{"alt":1803,"className":16101,"src":1806},[210,1805],[115,16103,1810],{"id":1809},[724,16105,1813,16106,1818,16109,1648,16111,1846,16132,1850,16134,1867,16149,1881],{},[207,16107,1817],{"className":16108,"dataFsResolvedFilePath":934,"href":935},[210],[38,16110,1821],{},[883,16112,16114],{"className":16113},[886],[888,16115,16116],{"xmlns":890},[892,16117,16118,16130],{},[895,16119,16120,16122,16124],{},[898,16121,1833],{},[1711,16123,1836],{},[1716,16125,16126,16128],{},[898,16127,1833],{},[1711,16129,1793],{},[902,16131,1845],{"encoding":904},[38,16133,1849],{},[38,16135,1853,16136],{},[883,16137,16139],{"className":16138},[886],[888,16140,16141],{"xmlns":890},[892,16142,16143,16147],{},[895,16144,16145],{},[898,16146,1675],{},[902,16148,1675],{"encoding":904},[883,16150,16152],{"className":16151},[886],[888,16153,16154],{"xmlns":890},[892,16155,16156,16160],{},[895,16157,16158],{},[898,16159,1675],{},[902,16161,1675],{"encoding":904},[120,16163,16164,16191],{},[123,16165,16166,1700,16168,1913],{},[38,16167,1888],{},[883,16169,16171],{"className":16170},[886],[888,16172,16173],{"xmlns":890},[892,16174,16175,16189],{},[895,16176,16177,16179,16181,16183,16185,16187],{},[898,16178,1833],{},[1711,16180,1836],{},[898,16182,1833],{},[1711,16184,1714],{"stretchy":1713},[898,16186,1675],{},[1711,16188,1735],{"stretchy":1713},[902,16190,1912],{"encoding":904},[123,16192,16193,1919],{},[38,16194,1918],{},[1921,16196,16197],{},[724,16198,16199,1928,16201,1950,16218,1978,16243,1992,16256,2023,16284,2027],{},[883,16200,1927],{},[883,16202,16204],{"className":16203},[886],[888,16205,16206],{"xmlns":890},[892,16207,16208,16216],{},[895,16209,16210,16212,16214],{},[898,16211,1940],{},[1942,16213,1944],{},[898,16215,1833],{},[902,16217,1949],{"encoding":904},[883,16219,16221],{"className":16220},[886],[888,16222,16223],{"xmlns":890},[892,16224,16225,16241],{},[895,16226,16227,16229,16231,16233,16235,16237,16239],{},[898,16228,1940],{},[1942,16230,1944],{},[898,16232,1833],{},[1942,16234,1944],{},[898,16236,1755],{},[1942,16238,1944],{},[898,16240,1974],{},[902,16242,1977],{"encoding":904},[883,16244,16246],{"className":16245},[886],[888,16247,16248],{"xmlns":890},[892,16249,16250,16254],{},[895,16251,16252],{},[898,16253,1660],{},[902,16255,1660],{"encoding":904},[38,16257,1995,16258,2009,16271],{},[883,16259,16261],{"className":16260},[886],[888,16262,16263],{"xmlns":890},[892,16264,16265,16269],{},[895,16266,16267],{},[898,16268,1660],{},[902,16270,1660],{"encoding":904},[883,16272,16274],{"className":16273},[886],[888,16275,16276],{"xmlns":890},[892,16277,16278,16282],{},[895,16279,16280],{},[898,16281,1675],{},[902,16283,1675],{"encoding":904},[38,16285,2026],{},[115,16287,2031],{"id":2030},[724,16289,2034,16290,2048,16303,2062],{},[883,16291,16293],{"className":16292},[886],[888,16294,16295],{"xmlns":890},[892,16296,16297,16301],{},[895,16298,16299],{},[898,16300,1833],{},[902,16302,1833],{"encoding":904},[883,16304,16306],{"className":16305},[886],[888,16307,16308],{"xmlns":890},[892,16309,16310,16314],{},[895,16311,16312],{},[898,16313,1675],{},[902,16315,1675],{"encoding":904},[724,16317,16318],{},[883,16319,16321],{"className":16320},[886],[888,16322,16323],{"xmlns":890},[892,16324,16325,16377],{},[895,16326,16327,16329,16331,16333,16335,16337,16339,16341,16343,16345,16347,16349,16351,16353,16355,16357,16359,16361,16363,16365,16367,16369,16371,16373,16375],{},[898,16328,1833],{},[1711,16330,1836],{},[898,16332,1833],{},[1711,16334,1714],{"stretchy":1713},[898,16336,1675],{},[1711,16338,1735],{"stretchy":1713},[1711,16340,1836],{},[898,16342,2090],{},[898,16344,1675],{},[1711,16346,2095],{},[898,16348,2098],{},[1711,16350,1726],{"separator":1725},[2102,16352],{"width":2104},[898,16354,2090],{},[1711,16356,2109],{},[2111,16358,2113],{},[1711,16360,1726],{"separator":1725},[1942,16362,2118],{},[898,16364,2098],{},[1711,16366,2123],{},[2111,16368,2126],{},[2102,16370],{"width":2104},[1711,16372,1714],{"stretchy":1713},[2111,16374,2133],{},[1711,16376,1735],{"stretchy":1713},[902,16378,2138],{"encoding":904},[120,16380,16381,16400],{},[123,16382,16383,2161],{},[883,16384,16386],{"className":16385},[886],[888,16387,16388],{"xmlns":890},[892,16389,16390,16398],{},[895,16391,16392,16394,16396],{},[898,16393,2098],{},[1711,16395,2123],{},[2111,16397,2113],{},[902,16399,2160],{"encoding":904},[123,16401,16402,2182,16419,2186],{},[883,16403,16405],{"className":16404},[886],[888,16406,16407],{"xmlns":890},[892,16408,16409,16417],{},[895,16410,16411,16413,16415],{},[898,16412,2090],{},[1711,16414,2109],{},[2111,16416,2113],{},[902,16418,2181],{"encoding":904},[38,16420,2185],{},[724,16422,2189],{},[724,16424,16425],{},[883,16426,16428],{"className":16427},[886],[888,16429,16430],{"xmlns":890},[892,16431,16432,16488],{},[895,16433,16434,16436,16438,16440,16442,16444,16446,16448,16450,16452,16454,16456,16458,16460,16462,16464,16466,16468,16470,16472,16474,16476,16478,16480,16482,16484,16486],{},[898,16435,1940],{},[1711,16437,1836],{},[898,16439,1940],{},[1711,16441,1714],{"stretchy":1713},[898,16443,1660],{},[1711,16445,1735],{"stretchy":1713},[1711,16447,1836],{},[898,16449,207],{},[898,16451,1660],{},[1711,16453,2095],{},[898,16455,2223],{},[1711,16457,1726],{"separator":1725},[2102,16459],{"width":2104},[2111,16461,2113],{},[1711,16463,2109],{},[898,16465,207],{},[1711,16467,2109],{},[2111,16469,2238],{},[1711,16471,1726],{"separator":1725},[1942,16473,2118],{},[898,16475,2223],{},[1711,16477,2123],{},[2111,16479,2126],{},[2102,16481],{"width":2104},[1711,16483,1714],{"stretchy":1713},[2111,16485,2255],{},[1711,16487,1735],{"stretchy":1713},[902,16489,2260],{"encoding":904},[724,16491,2263],{},[724,16493,16494],{},[883,16495,16497],{"className":16496},[886],[888,16498,16499],{"xmlns":890},[892,16500,16501,16523],{},[895,16502,16503,16505,16507,16509,16511,16513,16515,16517,16519,16521],{},[898,16504,1660],{},[1711,16506,1836],{},[898,16508,1940],{},[1711,16510,2095],{},[898,16512,1833],{},[898,16514,2186],{"mathvariant":2287},[2102,16516],{"width":2104},[1711,16518,1714],{"stretchy":1713},[2111,16520,2294],{},[1711,16522,1735],{"stretchy":1713},[902,16524,2299],{"encoding":904},[724,16526,2302,16527,1700,16529,2332,16554,2186],{},[38,16528,2305],{},[883,16530,16532],{"className":16531},[886],[888,16533,16534],{"xmlns":890},[892,16535,16536,16552],{},[895,16537,16538,16540,16542,16544,16546,16548,16550],{},[898,16539,1660],{},[1711,16541,1726],{"separator":1725},[898,16543,1940],{},[1711,16545,1726],{"separator":1725},[898,16547,1833],{},[1711,16549,1726],{"separator":1725},[898,16551,1675],{},[902,16553,2331],{"encoding":904},[38,16555,2335],{},[115,16557,2339],{"id":2338},[724,16559,2342,16560,2366,16581,2385,16598,2389],{},[883,16561,16563],{"className":16562},[886],[888,16564,16565],{"xmlns":890},[892,16566,16567,16579],{},[895,16568,16569,16571,16573,16575,16577],{},[898,16570,1660],{},[1711,16572,1836],{},[898,16574,1940],{},[1711,16576,2095],{},[898,16578,2362],{},[902,16580,2365],{"encoding":904},[883,16582,16584],{"className":16583},[886],[888,16585,16586],{"xmlns":890},[892,16587,16588,16596],{},[895,16589,16590,16592,16594],{},[898,16591,1833],{},[1711,16593,1836],{},[898,16595,2362],{},[902,16597,2384],{"encoding":904},[38,16599,2388],{},[724,16601,16602],{},[1801,16603],{"alt":2394,"className":16604,"src":2396},[210,1805],[724,16606,16607],{},[883,16608,16610],{"className":16609},[886],[888,16611,16612],{"xmlns":890},[892,16613,16614,16648],{},[895,16615,16616,16618,16620,16622,16624,16626,16628,16630,16632,16634,16636,16638,16640,16642,16644,16646],{},[898,16617,1660],{},[1711,16619,1836],{},[1711,16621,1714],{"stretchy":1713},[898,16623,207],{},[898,16625,1660],{},[1711,16627,2095],{},[898,16629,2223],{},[1711,16631,1735],{"stretchy":1713},[1711,16633,2095],{},[1711,16635,1714],{"stretchy":1713},[898,16637,2090],{},[898,16639,1675],{},[1711,16641,2095],{},[898,16643,2098],{},[1711,16645,1735],{"stretchy":1713},[1711,16647,1726],{"separator":1725},[902,16649,2442],{"encoding":904},[724,16651,16652],{},[883,16653,16655],{"className":16654},[886],[888,16656,16657],{"xmlns":890},[892,16658,16659,16693],{},[895,16660,16661,16663,16665,16667,16669,16671,16673,16675,16677,16679,16681,16683,16685,16687,16689,16691],{},[1711,16662,1714],{"stretchy":1713},[2111,16664,2238],{},[1711,16666,2460],{},[898,16668,207],{},[1711,16670,1735],{"stretchy":1713},[898,16672,1660],{},[1711,16674,2460],{},[898,16676,2090],{},[898,16678,1675],{},[1711,16680,2460],{},[898,16682,2223],{},[1711,16684,2460],{},[898,16686,2098],{},[1711,16688,1836],{},[2111,16690,2113],{},[1711,16692,1726],{"separator":1725},[902,16694,2489],{"encoding":904},[724,16696,2492],{},[724,16698,16699],{},[883,16700,16702],{"className":16701},[886],[888,16703,16704],{"xmlns":890},[892,16705,16706,16770],{},[895,16707,16708,16762,16764,16766,16768],{},[2505,16709,16710],{"notation":2507},[2509,16711,16712],{"scriptlevel":2113,"displaystyle":1713},[2509,16713,16714],{"scriptlevel":2113,"displaystyle":1713},[2509,16715,16716],{"scriptlevel":2113,"displaystyle":1725},[895,16717,16718,16720,16722,16724,16736,16738,16740,16742,16760],{},[1942,16719,2519],{},[898,16721,1660],{},[1711,16723,1836],{},[2525,16725,16726,16728],{},[898,16727,2090],{},[895,16729,16730,16732,16734],{},[2111,16731,2238],{},[1711,16733,2460],{},[898,16735,207],{},[1942,16737,2519],{},[898,16739,1675],{},[1711,16741,2095],{},[2525,16743,16744,16752],{},[895,16745,16746,16748,16750],{},[898,16747,2223],{},[1711,16749,2095],{},[898,16751,2098],{},[895,16753,16754,16756,16758],{},[2111,16755,2238],{},[1711,16757,2460],{},[898,16759,207],{},[1942,16761,2519],{},[2102,16763],{"width":2104},[1711,16765,1714],{"stretchy":1713},[2111,16767,2569],{},[1711,16769,1735],{"stretchy":1713},[902,16771,2574],{"encoding":904},[724,16773,2577,16774,1648,16776,2584,16778,2588,16780,2591,16782,2614,16803,2643,16830,2665,16851,2668,16853,2671],{},[38,16775,2580],{},[614,16777,2583],{},[38,16779,2587],{},[38,16781,2185],{},[883,16783,16785],{"className":16784},[886],[888,16786,16787],{"xmlns":890},[892,16788,16789,16801],{},[895,16790,16791,16793,16795,16797,16799],{},[1711,16792,1714],{"stretchy":1713},[898,16794,1675],{},[1711,16796,1726],{"separator":1725},[898,16798,1660],{},[1711,16800,1735],{"stretchy":1713},[902,16802,2613],{"encoding":904},[883,16804,16806],{"className":16805},[886],[888,16807,16808],{"xmlns":890},[892,16809,16810,16828],{},[895,16811,16812,16824,16826],{},[2525,16813,16814,16816],{},[898,16815,2090],{},[895,16817,16818,16820,16822],{},[2111,16819,2238],{},[1711,16821,2460],{},[898,16823,207],{},[1711,16825,2109],{},[2111,16827,2113],{},[902,16829,2642],{"encoding":904},[883,16831,16833],{"className":16832},[886],[888,16834,16835],{"xmlns":890},[892,16836,16837,16849],{},[895,16838,16839,16841,16843,16845,16847],{},[1711,16840,1714],{"stretchy":1713},[898,16842,1675],{},[1711,16844,1726],{"separator":1725},[898,16846,1660],{},[1711,16848,1735],{"stretchy":1713},[902,16850,2613],{"encoding":904},[38,16852,1833],{},[38,16854,2362],{},[1921,16856,16857],{},[724,16858,16859,2679,16861,2693,16874,1700,16876,2710,16889,2724,16902,2009,16915,2751,16928,2755],{},[883,16860,2678],{},[883,16862,16864],{"className":16863},[886],[888,16865,16866],{"xmlns":890},[892,16867,16868,16872],{},[895,16869,16870],{},[898,16871,1675],{},[902,16873,1675],{"encoding":904},[38,16875,2696],{},[883,16877,16879],{"className":16878},[886],[888,16880,16881],{"xmlns":890},[892,16882,16883,16887],{},[895,16884,16885],{},[898,16886,1833],{},[902,16888,1833],{"encoding":904},[883,16890,16892],{"className":16891},[886],[888,16893,16894],{"xmlns":890},[892,16895,16896,16900],{},[895,16897,16898],{},[898,16899,1660],{},[902,16901,1660],{"encoding":904},[883,16903,16905],{"className":16904},[886],[888,16906,16907],{"xmlns":890},[892,16908,16909,16913],{},[895,16910,16911],{},[898,16912,1675],{},[902,16914,1675],{"encoding":904},[883,16916,16918],{"className":16917},[886],[888,16919,16920],{"xmlns":890},[892,16921,16922,16926],{},[895,16923,16924],{},[898,16925,1660],{},[902,16927,1660],{"encoding":904},[38,16929,2754],{},[115,16931,2759],{"id":2758},[724,16933,2762,16934,2782,16951,2801,16968,2805],{},[883,16935,16937],{"className":16936},[886],[888,16938,16939],{"xmlns":890},[892,16940,16941,16949],{},[895,16942,16943],{},[1716,16944,16945,16947],{},[898,16946,1790],{},[898,16948,2778],{},[902,16950,2781],{"encoding":904},[883,16952,16954],{"className":16953},[886],[888,16955,16956],{"xmlns":890},[892,16957,16958,16966],{},[895,16959,16960],{},[1716,16961,16962,16964],{},[898,16963,1790],{},[898,16965,2362],{},[902,16967,2800],{"encoding":904},[38,16969,2804],{},[724,16971,16972],{},[883,16973,16975],{"className":16974},[886],[888,16976,16977],{"xmlns":890},[892,16978,16979,16997],{},[895,16980,16981,16987,16989,16995],{},[1716,16982,16983,16985],{},[898,16984,1790],{},[898,16986,2362],{},[1711,16988,1836],{},[1716,16990,16991,16993],{},[898,16992,1790],{},[1711,16994,1793],{},[898,16996,2186],{"mathvariant":2287},[902,16998,2835],{"encoding":904},[724,17000,17001,2841],{},[38,17002,2840],{},[120,17004,17005,17011,17017],{},[123,17006,17007,1648,17009,2852],{},[38,17008,2848],{},[614,17010,2851],{},[123,17012,17013,1648,17015,2861],{},[38,17014,2857],{},[614,17016,2860],{},[123,17018,17019,1648,17021,2870],{},[38,17020,2866],{},[614,17022,2869],{},[724,17024,2873,17025,2894],{},[883,17026,17028],{"className":17027},[886],[888,17029,17030],{"xmlns":890},[892,17031,17032,17040],{},[895,17033,17034],{},[2884,17035,17036,17038],{},[898,17037,2888],{},[2111,17039,2238],{},[902,17041,2893],{"encoding":904},[724,17043,17044],{},[883,17045,17047],{"className":17046},[886],[888,17048,17049],{"xmlns":890},[892,17050,17051,17087],{},[895,17052,17053,17059,17061,17067,17069,17071,17073,17075,17077,17083,17085],{},[2884,17054,17055,17057],{},[898,17056,2888],{},[2111,17058,2238],{},[1711,17060,1836],{},[2884,17062,17063,17065],{},[898,17064,2918],{},[2111,17066,2238],{},[898,17068,1660],{},[1711,17070,1726],{"separator":1725},[2102,17072],{"width":2104},[2111,17074,2113],{},[1711,17076,2109],{},[2884,17078,17079,17081],{},[898,17080,2918],{},[2111,17082,2238],{},[1711,17084,2109],{},[2111,17086,2941],{},[902,17088,2944],{"encoding":904},[724,17090,2947,17091,2967,17108,1343,17121,2998],{},[883,17092,17094],{"className":17093},[886],[888,17095,17096],{"xmlns":890},[892,17097,17098,17106],{},[895,17099,17100],{},[2884,17101,17102,17104],{},[898,17103,2888],{},[2111,17105,2963],{},[902,17107,2966],{"encoding":904},[883,17109,17111],{"className":17110},[886],[888,17112,17113],{"xmlns":890},[892,17114,17115,17119],{},[895,17116,17117],{},[898,17118,1675],{},[902,17120,1675],{"encoding":904},[883,17122,17124],{"className":17123},[886],[888,17125,17126],{"xmlns":890},[892,17127,17128,17136],{},[895,17129,17130],{},[2884,17131,17132,17134],{},[898,17133,2888],{},[2111,17135,2963],{},[902,17137,2966],{"encoding":904},[724,17139,17140],{},[883,17141,17143],{"className":17142},[886],[888,17144,17145],{"xmlns":890},[892,17146,17147,17201],{},[895,17148,17149,17155,17157,17163,17165,17167,17173,17175,17177,17183,17185,17187,17189,17191,17197,17199],{},[2884,17150,17151,17153],{},[898,17152,2888],{},[2111,17154,2963],{},[1711,17156,1836],{},[2884,17158,17159,17161],{},[898,17160,2918],{},[2111,17162,2963],{},[898,17164,1675],{},[1711,17166,2095],{},[2884,17168,17169,17171],{},[898,17170,2918],{},[2111,17172,3034],{},[1711,17174,1726],{"separator":1725},[2102,17176],{"width":2104},[2884,17178,17179,17181],{},[898,17180,2918],{},[2111,17182,2963],{},[1711,17184,2109],{},[2111,17186,2113],{},[1711,17188,1726],{"separator":1725},[1942,17190,2118],{},[2884,17192,17193,17195],{},[898,17194,2918],{},[2111,17196,3034],{},[1711,17198,2123],{},[2111,17200,2126],{},[902,17202,3065],{"encoding":904},[724,17204,3068],{},[724,17206,17207],{},[883,17208,17210],{"className":17209},[886],[888,17211,17212],{"xmlns":890},[892,17213,17214,17268],{},[895,17215,17216,17222,17224,17230,17232,17238,17240,17246,17248,17250,17256,17258,17260,17266],{},[1716,17217,17218,17220],{},[898,17219,1790],{},[898,17221,2778],{},[1711,17223,1836],{},[2884,17225,17226,17228],{},[898,17227,2888],{},[2111,17229,2238],{},[1711,17231,2095],{},[2884,17233,17234,17236],{},[898,17235,2888],{},[2111,17237,2963],{},[1711,17239,1836],{},[2884,17241,17242,17244],{},[898,17243,2918],{},[2111,17245,2238],{},[898,17247,1660],{},[1711,17249,2095],{},[2884,17251,17252,17254],{},[898,17253,2918],{},[2111,17255,2963],{},[898,17257,1675],{},[1711,17259,2095],{},[2884,17261,17262,17264],{},[898,17263,2918],{},[2111,17265,3034],{},[898,17267,2186],{"mathvariant":2287},[902,17269,3134],{"encoding":904},[724,17271,3137,17272,2062],{},[883,17273,17275],{"className":17274},[886],[888,17276,17277],{"xmlns":890},[892,17278,17279,17295],{},[895,17280,17281,17287,17289],{},[1716,17282,17283,17285],{},[898,17284,1790],{},[898,17286,2778],{},[1711,17288,1836],{},[1716,17290,17291,17293],{},[898,17292,1790],{},[1711,17294,1793],{},[902,17296,3163],{"encoding":904},[724,17298,17299],{},[883,17300,17302],{"className":17301},[886],[888,17303,17304],{"xmlns":890},[892,17305,17306,17352],{},[895,17307,17308,17314,17316,17322,17324,17326,17332,17334,17336,17342,17344,17346,17348,17350],{},[1716,17309,17310,17312],{},[898,17311,1790],{},[1711,17313,1793],{},[1711,17315,1836],{},[2884,17317,17318,17320],{},[898,17319,2918],{},[2111,17321,2238],{},[898,17323,1660],{},[1711,17325,2095],{},[2884,17327,17328,17330],{},[898,17329,2918],{},[2111,17331,2963],{},[898,17333,1675],{},[1711,17335,2095],{},[2884,17337,17338,17340],{},[898,17339,2918],{},[2111,17341,3034],{},[1711,17343,1726],{"separator":1725},[2102,17345],{"width":2104},[1711,17347,1714],{"stretchy":1713},[2111,17349,3217],{},[1711,17351,1735],{"stretchy":1713},[902,17353,3222],{"encoding":904},[724,17355,3225,17356,3239],{},[883,17357,17359],{"className":17358},[886],[888,17360,17361],{"xmlns":890},[892,17362,17363,17367],{},[895,17364,17365],{},[898,17366,1660],{},[902,17368,1660],{"encoding":904},[724,17370,17371],{},[883,17372,17374],{"className":17373},[886],[888,17375,17376],{"xmlns":890},[892,17377,17378,17452],{},[895,17379,17380,17444,17446,17448,17450],{},[2505,17381,17382],{"notation":2507},[2509,17383,17384],{"scriptlevel":2113,"displaystyle":1713},[2509,17385,17386],{"scriptlevel":2113,"displaystyle":1713},[2509,17387,17388],{"scriptlevel":2113,"displaystyle":1725},[895,17389,17390,17392,17394,17396,17398,17412,17414,17416,17418,17442],{},[1942,17391,2519],{},[898,17393,1660],{},[1711,17395,1836],{},[1711,17397,2460],{},[2525,17399,17400,17406],{},[2884,17401,17402,17404],{},[898,17403,2918],{},[2111,17405,2963],{},[2884,17407,17408,17410],{},[898,17409,2918],{},[2111,17411,2238],{},[1942,17413,2519],{},[898,17415,1675],{},[1711,17417,2095],{},[2525,17419,17420,17436],{},[895,17421,17422,17428,17430],{},[1716,17423,17424,17426],{},[898,17425,1790],{},[1711,17427,1793],{},[1711,17429,2460],{},[2884,17431,17432,17434],{},[898,17433,2918],{},[2111,17435,3034],{},[2884,17437,17438,17440],{},[898,17439,2918],{},[2111,17441,2238],{},[1942,17443,2519],{},[2102,17445],{"width":2104},[1711,17447,1714],{"stretchy":1713},[2111,17449,3321],{},[1711,17451,1735],{"stretchy":1713},[902,17453,3326],{"encoding":904},[724,17455,2577,17456,1648,17458,3335,17460,2588,17462,2591,17464,2614,17485,3395,17516,3418,17537,3421,17539,3424],{},[38,17457,3331],{},[614,17459,3334],{},[38,17461,3338],{},[38,17463,3341],{},[883,17465,17467],{"className":17466},[886],[888,17468,17469],{"xmlns":890},[892,17470,17471,17483],{},[895,17472,17473,17475,17477,17479,17481],{},[1711,17474,1714],{"stretchy":1713},[898,17476,1675],{},[1711,17478,1726],{"separator":1725},[898,17480,1660],{},[1711,17482,1735],{"stretchy":1713},[902,17484,2613],{"encoding":904},[883,17486,17488],{"className":17487},[886],[888,17489,17490],{"xmlns":890},[892,17491,17492,17514],{},[895,17493,17494,17496,17510,17512],{},[1711,17495,2460],{},[2525,17497,17498,17504],{},[2884,17499,17500,17502],{},[898,17501,2918],{},[2111,17503,2963],{},[2884,17505,17506,17508],{},[898,17507,2918],{},[2111,17509,2238],{},[1711,17511,2123],{},[2111,17513,2113],{},[902,17515,3394],{"encoding":904},[883,17517,17519],{"className":17518},[886],[888,17520,17521],{"xmlns":890},[892,17522,17523,17535],{},[895,17524,17525,17531,17533],{},[2884,17526,17527,17529],{},[898,17528,2918],{},[2111,17530,2963],{},[1711,17532,2109],{},[2111,17534,2113],{},[902,17536,3417],{"encoding":904},[38,17538,2888],{},[38,17540,1790],{},[1921,17542,17543],{},[724,17544,17545,3431,17547,3445,17560,3474,17587,3492,17604,3506,17617,3524,17634,2009,17647,3551,17660,3555],{},[883,17546,2678],{},[883,17548,17550],{"className":17549},[886],[888,17551,17552],{"xmlns":890},[892,17553,17554,17558],{},[895,17555,17556],{},[898,17557,1660],{},[902,17559,1660],{"encoding":904},[883,17561,17563],{"className":17562},[886],[888,17564,17565],{"xmlns":890},[892,17566,17567,17585],{},[895,17568,17569,17575,17577,17583],{},[2884,17570,17571,17573],{},[898,17572,2888],{},[2111,17574,2238],{},[1711,17576,1836],{},[2884,17578,17579,17581],{},[898,17580,2918],{},[2111,17582,2238],{},[898,17584,1660],{},[902,17586,3473],{"encoding":904},[883,17588,17590],{"className":17589},[886],[888,17591,17592],{"xmlns":890},[892,17593,17594,17602],{},[895,17595,17596],{},[1716,17597,17598,17600],{},[898,17599,1790],{},[1711,17601,1793],{},[902,17603,1796],{"encoding":904},[883,17605,17607],{"className":17606},[886],[888,17608,17609],{"xmlns":890},[892,17610,17611,17615],{},[895,17612,17613],{},[898,17614,1675],{},[902,17616,1675],{"encoding":904},[883,17618,17620],{"className":17619},[886],[888,17621,17622],{"xmlns":890},[892,17623,17624,17632],{},[895,17625,17626],{},[2884,17627,17628,17630],{},[898,17629,2888],{},[2111,17631,2963],{},[902,17633,2966],{"encoding":904},[883,17635,17637],{"className":17636},[886],[888,17638,17639],{"xmlns":890},[892,17640,17641,17645],{},[895,17642,17643],{},[898,17644,1660],{},[902,17646,1660],{"encoding":904},[883,17648,17650],{"className":17649},[886],[888,17651,17652],{"xmlns":890},[892,17653,17654,17658],{},[895,17655,17656],{},[898,17657,1675],{},[902,17659,1675],{"encoding":904},[38,17661,3554],{},[115,17663,3559],{"id":3558},[724,17665,3562,17666,3566,17668,1700,17670,2009,17687,1700,17689,3609,17706,3628,17723,3647,17740,3664,17755,2009,17770,3695,17785,2186],{},[38,17667,3565],{},[38,17669,3569],{},[883,17671,17673],{"className":17672},[886],[888,17674,17675],{"xmlns":890},[892,17676,17677,17685],{},[895,17678,17679],{},[1716,17680,17681,17683],{},[898,17682,1660],{},[898,17684,1722],{},[902,17686,3587],{"encoding":904},[38,17688,3590],{},[883,17690,17692],{"className":17691},[886],[888,17693,17694],{"xmlns":890},[892,17695,17696,17704],{},[895,17697,17698],{},[1716,17699,17700,17702],{},[898,17701,1675],{},[898,17703,1722],{},[902,17705,3608],{"encoding":904},[883,17707,17709],{"className":17708},[886],[888,17710,17711],{"xmlns":890},[892,17712,17713,17721],{},[895,17714,17715],{},[1716,17716,17717,17719],{},[898,17718,1833],{},[898,17720,1722],{},[902,17722,3627],{"encoding":904},[883,17724,17726],{"className":17725},[886],[888,17727,17728],{"xmlns":890},[892,17729,17730,17738],{},[895,17731,17732],{},[1716,17733,17734,17736],{},[898,17735,1940],{},[898,17737,1722],{},[902,17739,3646],{"encoding":904},[38,17741,3650,17742],{},[883,17743,17745],{"className":17744},[886],[888,17746,17747],{"xmlns":890},[892,17748,17749,17753],{},[895,17750,17751],{},[898,17752,1722],{},[902,17754,1722],{"encoding":904},[883,17756,17758],{"className":17757},[886],[888,17759,17760],{"xmlns":890},[892,17761,17762,17768],{},[895,17763,17764,17766],{},[898,17765,1833],{},[898,17767,2362],{},[902,17769,1685],{"encoding":904},[883,17771,17773],{"className":17772},[886],[888,17774,17775],{"xmlns":890},[892,17776,17777,17783],{},[895,17778,17779,17781],{},[898,17780,2888],{},[898,17782,1790],{},[902,17784,1692],{"encoding":904},[883,17786,17788],{"className":17787},[886],[888,17789,17790],{"xmlns":890},[892,17791,17792,17804],{},[895,17793,17794,17796,17798,17800,17802],{},[1711,17795,1714],{"stretchy":1713},[898,17797,1675],{},[1711,17799,1726],{"separator":1725},[898,17801,1660],{},[1711,17803,1735],{"stretchy":1713},[902,17805,2613],{"encoding":904},[724,17807,17808],{},[614,17809,3721,17810,3743,17831,3759,17846,3775,17861,3789,17874,3807,17891,1772,17904,3807,17921,3851,17934,3865],{},[883,17811,17813],{"className":17812},[886],[888,17814,17815],{"xmlns":890},[892,17816,17817,17829],{},[895,17818,17819,17821,17823,17825,17827],{},[1711,17820,1714],{"stretchy":1713},[898,17822,1675],{},[1711,17824,1726],{"separator":1725},[898,17826,1660],{},[1711,17828,1735],{"stretchy":1713},[902,17830,2613],{"encoding":904},[883,17832,17834],{"className":17833},[886],[888,17835,17836],{"xmlns":890},[892,17837,17838,17844],{},[895,17839,17840,17842],{},[898,17841,2888],{},[898,17843,1790],{},[902,17845,1692],{"encoding":904},[883,17847,17849],{"className":17848},[886],[888,17850,17851],{"xmlns":890},[892,17852,17853,17859],{},[895,17854,17855,17857],{},[898,17856,1833],{},[898,17858,2362],{},[902,17860,1685],{"encoding":904},[883,17862,17864],{"className":17863},[886],[888,17865,17866],{"xmlns":890},[892,17867,17868,17872],{},[895,17869,17870],{},[898,17871,1722],{},[902,17873,1722],{"encoding":904},[883,17875,17877],{"className":17876},[886],[888,17878,17879],{"xmlns":890},[892,17880,17881,17889],{},[895,17882,17883],{},[1716,17884,17885,17887],{},[898,17886,1675],{},[898,17888,1722],{},[902,17890,3608],{"encoding":904},[883,17892,17894],{"className":17893},[886],[888,17895,17896],{"xmlns":890},[892,17897,17898,17902],{},[895,17899,17900],{},[898,17901,1675],{},[902,17903,1675],{"encoding":904},[883,17905,17907],{"className":17906},[886],[888,17908,17909],{"xmlns":890},[892,17910,17911,17919],{},[895,17912,17913],{},[1716,17914,17915,17917],{},[898,17916,1660],{},[898,17918,1722],{},[902,17920,3587],{"encoding":904},[883,17922,17924],{"className":17923},[886],[888,17925,17926],{"xmlns":890},[892,17927,17928,17932],{},[895,17929,17930],{},[898,17931,1660],{},[902,17933,1660],{"encoding":904},[883,17935,17937],{"className":17936},[886],[888,17938,17939],{"xmlns":890},[892,17940,17941,17945],{},[895,17942,17943],{},[898,17944,1722],{},[902,17946,1722],{"encoding":904},[1921,17948,17949,17953],{},[724,17950,17951,3873],{},[883,17952,3872],{},[152,17954,17955,18025,18090,18143,18213],{},[123,17956,17957,3881,17959,2009,17978,3922,17997,2009,18010,3949,18023,2186],{},[38,17958,3880],{},[883,17960,17962],{"className":17961},[886],[888,17963,17964],{"xmlns":890},[892,17965,17966,17976],{},[895,17967,17968,17970,17972,17974],{},[898,17969,1940],{},[1711,17971,1714],{"stretchy":1713},[898,17973,1660],{},[1711,17975,1735],{"stretchy":1713},[902,17977,3901],{"encoding":904},[883,17979,17981],{"className":17980},[886],[888,17982,17983],{"xmlns":890},[892,17984,17985,17995],{},[895,17986,17987,17989,17991,17993],{},[898,17988,1833],{},[1711,17990,1714],{"stretchy":1713},[898,17992,1675],{},[1711,17994,1735],{"stretchy":1713},[902,17996,3921],{"encoding":904},[883,17998,18000],{"className":17999},[886],[888,18001,18002],{"xmlns":890},[892,18003,18004,18008],{},[895,18005,18006],{},[898,18007,1660],{},[902,18009,1660],{"encoding":904},[883,18011,18013],{"className":18012},[886],[888,18014,18015],{"xmlns":890},[892,18016,18017,18021],{},[895,18018,18019],{},[898,18020,1675],{},[902,18022,1675],{"encoding":904},[38,18024,1685],{},[123,18026,18027,3957,18029,2009,18046,3992,18063,3949,18088,2186],{},[38,18028,3956],{},[883,18030,18032],{"className":18031},[886],[888,18033,18034],{"xmlns":890},[892,18035,18036,18044],{},[895,18037,18038],{},[2884,18039,18040,18042],{},[898,18041,2888],{},[2111,18043,2238],{},[902,18045,2893],{"encoding":904},[883,18047,18049],{"className":18048},[886],[888,18050,18051],{"xmlns":890},[892,18052,18053,18061],{},[895,18054,18055],{},[2884,18056,18057,18059],{},[898,18058,2888],{},[2111,18060,2963],{},[902,18062,2966],{"encoding":904},[883,18064,18066],{"className":18065},[886],[888,18067,18068],{"xmlns":890},[892,18069,18070,18086],{},[895,18071,18072,18078,18080],{},[1716,18073,18074,18076],{},[898,18075,1790],{},[898,18077,2778],{},[1711,18079,1836],{},[1716,18081,18082,18084],{},[898,18083,1790],{},[1711,18085,1793],{},[902,18087,3163],{"encoding":904},[38,18089,1692],{},[123,18091,18092,4025,18094,2009,18107,4052,18120,4078],{},[38,18093,4024],{},[883,18095,18097],{"className":18096},[886],[888,18098,18099],{"xmlns":890},[892,18100,18101,18105],{},[895,18102,18103],{},[898,18104,1660],{},[902,18106,1660],{"encoding":904},[883,18108,18110],{"className":18109},[886],[888,18111,18112],{"xmlns":890},[892,18113,18114,18118],{},[895,18115,18116],{},[898,18117,1675],{},[902,18119,1675],{"encoding":904},[883,18121,18123],{"className":18122},[886],[888,18124,18125],{"xmlns":890},[892,18126,18127,18141],{},[895,18128,18129,18131,18133,18135,18137,18139],{},[898,18130,1660],{},[1711,18132,1836],{},[898,18134,4068],{},[1711,18136,1714],{"stretchy":1713},[898,18138,1675],{},[1711,18140,1735],{"stretchy":1713},[902,18142,4077],{"encoding":904},[123,18144,18145,1700,18147,2009,18180,2186],{},[38,18146,4083],{},[883,18148,18150],{"className":18149},[886],[888,18151,18152],{"xmlns":890},[892,18153,18154,18178],{},[895,18155,18156,18162,18164,18166,18168,18174,18176],{},[1716,18157,18158,18160],{},[898,18159,1940],{},[898,18161,1722],{},[1711,18163,1836],{},[898,18165,207],{},[1942,18167,2519],{},[1716,18169,18170,18172],{},[898,18171,1660],{},[898,18173,1722],{},[1711,18175,2095],{},[898,18177,2223],{},[902,18179,4117],{"encoding":904},[883,18181,18183],{"className":18182},[886],[888,18184,18185],{"xmlns":890},[892,18186,18187,18211],{},[895,18188,18189,18195,18197,18199,18201,18207,18209],{},[1716,18190,18191,18193],{},[898,18192,1833],{},[898,18194,1722],{},[1711,18196,1836],{},[898,18198,2090],{},[1942,18200,2519],{},[1716,18202,18203,18205],{},[898,18204,1675],{},[898,18206,1722],{},[1711,18208,2095],{},[898,18210,2098],{},[902,18212,4151],{"encoding":904},[123,18214,18215,4157,18217,4192,18250,4247],{},[38,18216,4156],{},[883,18218,18220],{"className":18219},[886],[888,18221,18222],{"xmlns":890},[892,18223,18224,18248],{},[895,18225,18226,18232,18234,18240,18242],{},[1716,18227,18228,18230],{},[898,18229,1660],{},[898,18231,1722],{},[1711,18233,1836],{},[1716,18235,18236,18238],{},[898,18237,1940],{},[898,18239,1722],{},[1711,18241,2095],{},[1716,18243,18244,18246],{},[898,18245,1833],{},[898,18247,1722],{},[902,18249,4191],{"encoding":904},[883,18251,18253],{"className":18252},[886],[888,18254,18255],{"xmlns":890},[892,18256,18257,18301],{},[895,18258,18259,18265,18267,18273,18279,18281,18287,18293,18295],{},[1716,18260,18261,18263],{},[898,18262,1790],{},[1711,18264,1793],{},[1711,18266,1836],{},[2884,18268,18269,18271],{},[898,18270,2918],{},[2111,18272,2238],{},[1716,18274,18275,18277],{},[898,18276,1660],{},[898,18278,1722],{},[1711,18280,2095],{},[2884,18282,18283,18285],{},[898,18284,2918],{},[2111,18286,2963],{},[1716,18288,18289,18291],{},[898,18290,1675],{},[898,18292,1722],{},[1711,18294,2095],{},[2884,18296,18297,18299],{},[898,18298,2918],{},[2111,18300,3034],{},[902,18302,4246],{"encoding":904},[115,18304,4251],{"id":4250},[724,18306,4254],{},[120,18308,18309,18334],{},[123,18310,4259,18311,1726],{},[883,18312,18314],{"className":18313},[886],[888,18315,18316],{"xmlns":890},[892,18317,18318,18332],{},[895,18319,18320,18322,18324,18326,18328,18330],{},[898,18321,1940],{},[1711,18323,1836],{},[2111,18325,4275],{},[898,18327,1660],{},[1711,18329,2095],{},[2111,18331,4282],{},[902,18333,4285],{"encoding":904},[123,18335,4288,18336,2186],{},[883,18337,18339],{"className":18338},[886],[888,18340,18341],{"xmlns":890},[892,18342,18343,18359],{},[895,18344,18345,18347,18349,18351,18353,18355,18357],{},[898,18346,1833],{},[1711,18348,1836],{},[1711,18350,2460],{},[2111,18352,4306],{},[898,18354,1675],{},[1711,18356,2095],{},[2111,18358,4313],{},[902,18360,4316],{"encoding":904},[724,18362,4319],{},[120,18364,18365,18390,18421],{},[123,18366,18367,1726],{},[883,18368,18370],{"className":18369},[886],[888,18371,18372],{"xmlns":890},[892,18373,18374,18388],{},[895,18375,18376,18382,18384,18386],{},[2884,18377,18378,18380],{},[898,18379,2888],{},[2111,18381,2238],{},[1711,18383,1836],{},[2111,18385,4343],{},[898,18387,1660],{},[902,18389,4348],{"encoding":904},[123,18391,18392,1726],{},[883,18393,18395],{"className":18394},[886],[888,18396,18397],{"xmlns":890},[892,18398,18399,18419],{},[895,18400,18401,18407,18409,18411,18413,18415,18417],{},[2884,18402,18403,18405],{},[898,18404,2888],{},[2111,18406,2963],{},[1711,18408,1836],{},[1711,18410,2460],{},[2111,18412,4372],{},[898,18414,1675],{},[1711,18416,2095],{},[2111,18418,4379],{},[902,18420,4382],{"encoding":904},[123,18422,4385,18423,2186],{},[883,18424,18426],{"className":18425},[886],[888,18427,18428],{"xmlns":890},[892,18429,18430,18442],{},[895,18431,18432,18438,18440],{},[1716,18433,18434,18436],{},[898,18435,1790],{},[1711,18437,1793],{},[1711,18439,1836],{},[2111,18441,4405],{},[902,18443,4408],{"encoding":904},[724,18445,18446,4414,18448,2062],{},[38,18447,4413],{},[883,18449,18451],{"className":18450},[886],[888,18452,18453],{"xmlns":890},[892,18454,18455,18467],{},[895,18456,18457,18459,18461,18463,18465],{},[898,18458,1660],{},[1711,18460,1836],{},[898,18462,1940],{},[1711,18464,2095],{},[898,18466,1833],{},[902,18468,4436],{"encoding":904},[724,18470,18471],{},[883,18472,18474],{"className":18473},[886],[888,18475,18476],{"xmlns":890},[892,18477,18478,18504],{},[895,18479,18480,18482,18484,18486,18488,18490,18492,18494,18496,18498,18500,18502],{},[898,18481,1660],{},[1711,18483,1836],{},[2111,18485,4275],{},[898,18487,1660],{},[1711,18489,2095],{},[2111,18491,4282],{},[1711,18493,2460],{},[2111,18495,4306],{},[898,18497,1675],{},[1711,18499,2095],{},[2111,18501,4313],{},[1711,18503,1726],{"separator":1725},[902,18505,4474],{"encoding":904},[724,18507,4477],{},[724,18509,18510],{},[883,18511,18513],{"className":18512},[886],[888,18514,18515],{"xmlns":890},[892,18516,18517,18541],{},[895,18518,18519,18521,18523,18525,18527,18529,18531,18533,18535,18537,18539],{},[2111,18520,4491],{},[898,18522,1660],{},[1711,18524,2095],{},[2111,18526,4306],{},[898,18528,1675],{},[1711,18530,1836],{},[2111,18532,4504],{},[2102,18534],{"width":2104},[1711,18536,1714],{"stretchy":1713},[1942,18538,1685],{},[1711,18540,1735],{"stretchy":1713},[902,18542,4515],{"encoding":904},[724,18544,18545,4521,18547,2062],{},[38,18546,4520],{},[883,18548,18550],{"className":18549},[886],[888,18551,18552],{"xmlns":890},[892,18553,18554,18578],{},[895,18555,18556,18562,18564,18570,18572],{},[1716,18557,18558,18560],{},[898,18559,1790],{},[1711,18561,1793],{},[1711,18563,1836],{},[2884,18565,18566,18568],{},[898,18567,2888],{},[2111,18569,2238],{},[1711,18571,2095],{},[2884,18573,18574,18576],{},[898,18575,2888],{},[2111,18577,2963],{},[902,18579,4555],{"encoding":904},[724,18581,18582],{},[883,18583,18585],{"className":18584},[886],[888,18586,18587],{"xmlns":890},[892,18588,18589,18611],{},[895,18590,18591,18593,18595,18597,18599,18601,18603,18605,18607,18609],{},[2111,18592,4405],{},[1711,18594,1836],{},[2111,18596,4343],{},[898,18598,1660],{},[1711,18600,2460],{},[2111,18602,4372],{},[898,18604,1675],{},[1711,18606,2095],{},[2111,18608,4379],{},[1711,18610,1726],{"separator":1725},[902,18612,4589],{"encoding":904},[724,18614,4477],{},[724,18616,18617],{},[883,18618,18620],{"className":18619},[886],[888,18621,18622],{"xmlns":890},[892,18623,18624,18648],{},[895,18625,18626,18628,18630,18632,18634,18636,18638,18640,18642,18644,18646],{},[2111,18627,4343],{},[898,18629,1660],{},[1711,18631,2460],{},[2111,18633,4372],{},[898,18635,1675],{},[1711,18637,1836],{},[2111,18639,4617],{},[2102,18641],{"width":2104},[1711,18643,1714],{"stretchy":1713},[1942,18645,1692],{},[1711,18647,1735],{"stretchy":1713},[902,18649,4628],{"encoding":904},[724,18651,18652,4634,18654,4660],{},[38,18653,4633],{},[883,18655,18657],{"className":18656},[886],[888,18658,18659],{"xmlns":890},[892,18660,18661,18675],{},[895,18662,18663,18665,18667,18669,18671,18673],{},[898,18664,1660],{},[1711,18666,1836],{},[2111,18668,4650],{},[1711,18670,2460],{},[2111,18672,4282],{},[898,18674,1675],{},[902,18676,4659],{"encoding":904},[724,18678,18679],{},[883,18680,18682],{"className":18681},[886],[888,18683,18684],{"xmlns":890},[892,18685,18686,18766],{},[895,18687,18688,18690,18692,18694,18696,18698,18700,18702,18704,18706,18708,18710,18712,18714,18716,18718,18720,18722,18724,18726,18728,18730,18732,18734,18736,18738,18740,18742,18744,18746,18748,18750,18752,18754,18756,18762,18764],{},[2111,18689,4343],{},[1711,18691,1714],{"stretchy":1713},[2111,18693,4650],{},[1711,18695,2460],{},[2111,18697,4282],{},[898,18699,1675],{},[1711,18701,1735],{"stretchy":1713},[1711,18703,2460],{},[2111,18705,4372],{},[898,18707,1675],{},[1711,18709,1836],{},[2111,18711,4696],{},[1942,18713,4699],{},[1711,18715,4702],{},[1942,18717,4699],{},[2111,18719,4707],{},[1711,18721,2460],{},[2111,18723,4712],{},[898,18725,1675],{},[1711,18727,2460],{},[2111,18729,4372],{},[898,18731,1675],{},[1711,18733,1836],{},[2111,18735,4696],{},[1942,18737,4699],{},[1711,18739,4702],{},[1942,18741,4699],{},[2111,18743,4733],{},[898,18745,1675],{},[1711,18747,1836],{},[2111,18749,4740],{},[1942,18751,4699],{},[1711,18753,4702],{},[1942,18755,4699],{},[1716,18757,18758,18760],{},[898,18759,1675],{},[898,18761,1722],{},[1711,18763,1836],{},[2111,18765,4757],{},[902,18767,4760],{"encoding":904},[724,18769,18770],{},[38,18771,4765],{},[120,18773,18774,18817,18852],{},[123,18775,18776,1726],{},[883,18777,18779],{"className":18778},[886],[888,18780,18781],{"xmlns":890},[892,18782,18783,18815],{},[895,18784,18785,18791,18793,18795,18797,18799,18801,18803,18805,18807,18809,18811,18813],{},[1716,18786,18787,18789],{},[898,18788,1660],{},[898,18790,1722],{},[1711,18792,1836],{},[2111,18794,4650],{},[1711,18796,2460],{},[2111,18798,4282],{},[1711,18800,4795],{},[2111,18802,4798],{},[1711,18804,1836],{},[2111,18806,4650],{},[1711,18808,2460],{},[2111,18810,4807],{},[1711,18812,1836],{},[2111,18814,4812],{},[902,18816,4815],{"encoding":904},[123,18818,18819,1726],{},[883,18820,18822],{"className":18821},[886],[888,18823,18824],{"xmlns":890},[892,18825,18826,18850],{},[895,18827,18828,18834,18836,18838,18840,18842,18844,18846,18848],{},[1716,18829,18830,18832],{},[898,18831,1940],{},[898,18833,1722],{},[1711,18835,1836],{},[2111,18837,4275],{},[1711,18839,4795],{},[2111,18841,4812],{},[1711,18843,2095],{},[2111,18845,4282],{},[1711,18847,1836],{},[2111,18849,4849],{},[902,18851,4852],{"encoding":904},[123,18853,18854,2186],{},[883,18855,18857],{"className":18856},[886],[888,18858,18859],{"xmlns":890},[892,18860,18861,18887],{},[895,18862,18863,18869,18871,18873,18875,18877,18879,18881,18883,18885],{},[1716,18864,18865,18867],{},[898,18866,1833],{},[898,18868,1722],{},[1711,18870,1836],{},[1711,18872,2460],{},[2111,18874,4306],{},[1711,18876,4795],{},[2111,18878,4798],{},[1711,18880,2095],{},[2111,18882,4313],{},[1711,18884,1836],{},[2111,18886,4888],{},[902,18888,4891],{"encoding":904},[724,18890,18891,1700,18893,4943],{},[38,18892,4896],{},[883,18894,18896],{"className":18895},[886],[888,18897,18898],{"xmlns":890},[892,18899,18900,18936],{},[895,18901,18902,18908,18910,18916,18918,18920,18922,18924,18926,18928,18930],{},[1716,18903,18904,18906],{},[898,18905,1940],{},[898,18907,1722],{},[1711,18909,2095],{},[1716,18911,18912,18914],{},[898,18913,1833],{},[898,18915,1722],{},[1711,18917,1836],{},[2111,18919,4849],{},[1711,18921,2095],{},[2111,18923,4888],{},[1711,18925,1836],{},[2111,18927,4812],{},[1711,18929,1836],{},[1716,18931,18932,18934],{},[898,18933,1660],{},[898,18935,1722],{},[902,18937,4942],{"encoding":904},[724,18939,18940],{},[883,18941,18943],{"className":18942},[886],[888,18944,18945],{"xmlns":890},[892,18946,18947,19015],{},[895,18948,18949],{},[2505,18950,18951],{"notation":2507},[2509,18952,18953],{"scriptlevel":2113,"displaystyle":1713},[2509,18954,18955],{"scriptlevel":2113,"displaystyle":1713},[2509,18956,18957],{"scriptlevel":2113,"displaystyle":1725},[895,18958,18959,18961,18967,18969,18971,18973,18975,18981,18983,18985,18987,18989,18995,18997,18999,19001,19003,19009,19011,19013],{},[1942,18960,2519],{},[1716,18962,18963,18965],{},[898,18964,1660],{},[898,18966,1722],{},[1711,18968,1836],{},[2111,18970,4812],{},[1711,18972,1726],{"separator":1725},[2102,18974],{"width":4981},[1716,18976,18977,18979],{},[898,18978,1675],{},[898,18980,1722],{},[1711,18982,1836],{},[2111,18984,4798],{},[1711,18986,1726],{"separator":1725},[2102,18988],{"width":4981},[1716,18990,18991,18993],{},[898,18992,1940],{},[898,18994,1722],{},[1711,18996,1836],{},[2111,18998,4849],{},[1711,19000,1726],{"separator":1725},[2102,19002],{"width":4981},[1716,19004,19005,19007],{},[898,19006,1833],{},[898,19008,1722],{},[1711,19010,1836],{},[2111,19012,5020],{},[1942,19014,2519],{},[902,19016,5025],{"encoding":904},[724,19018,19019],{},[614,19020,5030,19021,5044,19034,5058,19047,5074,19062,5088,19075,5104,19090,5118,19103,5132,19116,2186],{},[883,19022,19024],{"className":19023},[886],[888,19025,19026],{"xmlns":890},[892,19027,19028,19032],{},[895,19029,19030],{},[898,19031,1660],{},[902,19033,1660],{"encoding":904},[883,19035,19037],{"className":19036},[886],[888,19038,19039],{"xmlns":890},[892,19040,19041,19045],{},[895,19042,19043],{},[898,19044,1675],{},[902,19046,1675],{"encoding":904},[883,19048,19050],{"className":19049},[886],[888,19051,19052],{"xmlns":890},[892,19053,19054,19060],{},[895,19055,19056,19058],{},[898,19057,2888],{},[898,19059,1790],{},[902,19061,1692],{"encoding":904},[883,19063,19065],{"className":19064},[886],[888,19066,19067],{"xmlns":890},[892,19068,19069,19073],{},[895,19070,19071],{},[898,19072,1675],{},[902,19074,1675],{"encoding":904},[883,19076,19078],{"className":19077},[886],[888,19079,19080],{"xmlns":890},[892,19081,19082,19088],{},[895,19083,19084,19086],{},[898,19085,1833],{},[898,19087,2362],{},[902,19089,1685],{"encoding":904},[883,19091,19093],{"className":19092},[886],[888,19094,19095],{"xmlns":890},[892,19096,19097,19101],{},[895,19098,19099],{},[898,19100,1675],{},[902,19102,1675],{"encoding":904},[883,19104,19106],{"className":19105},[886],[888,19107,19108],{"xmlns":890},[892,19109,19110,19114],{},[895,19111,19112],{},[898,19113,1722],{},[902,19115,1722],{"encoding":904},[883,19117,19119],{"className":19118},[886],[888,19120,19121],{"xmlns":890},[892,19122,19123,19145],{},[895,19124,19125,19127,19129,19131,19133,19135,19137,19139,19141,19143],{},[1711,19126,5144],{"stretchy":1713},[898,19128,1675],{},[1711,19130,1836],{},[2111,19132,4798],{},[1711,19134,1726],{"separator":1725},[1942,19136,2118],{},[898,19138,1660],{},[1711,19140,1836],{},[2111,19142,4812],{},[1711,19144,5163],{"stretchy":1713},[902,19146,5166],{"encoding":904},[115,19148,5170],{"id":5169},[724,19150,19151,5176,19153,5190,19166,5204,19179,5208,19181,5229,19198,5247,19215,5265,19232,5279,19245,5293],{},[38,19152,5175],{},[883,19154,19156],{"className":19155},[886],[888,19157,19158],{"xmlns":890},[892,19159,19160,19164],{},[895,19161,19162],{},[898,19163,1755],{},[902,19165,1755],{"encoding":904},[883,19167,19169],{"className":19168},[886],[888,19170,19171],{"xmlns":890},[892,19172,19173,19177],{},[895,19174,19175],{},[898,19176,1769],{},[902,19178,1769],{"encoding":904},[38,19180,5207],{},[883,19182,19184],{"className":19183},[886],[888,19185,19186],{"xmlns":890},[892,19187,19188,19196],{},[895,19189,19190],{},[1716,19191,19192,19194],{},[898,19193,1722],{},[1711,19195,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,19197,5228],{"encoding":904},[883,19199,19201],{"className":19200},[886],[888,19202,19203],{"xmlns":890},[892,19204,19205,19213],{},[895,19206,19207],{},[1716,19208,19209,19211],{},[898,19210,1660],{},[898,19212,1722],{},[902,19214,3587],{"encoding":904},[883,19216,19218],{"className":19217},[886],[888,19219,19220],{"xmlns":890},[892,19221,19222,19230],{},[895,19223,19224],{},[1716,19225,19226,19228],{},[898,19227,1675],{},[898,19229,1722],{},[902,19231,3608],{"encoding":904},[883,19233,19235],{"className":19234},[886],[888,19236,19237],{"xmlns":890},[892,19238,19239,19243],{},[895,19240,19241],{},[898,19242,1660],{},[902,19244,1660],{"encoding":904},[883,19246,19248],{"className":19247},[886],[888,19249,19250],{"xmlns":890},[892,19251,19252,19256],{},[895,19253,19254],{},[898,19255,1675],{},[902,19257,1675],{"encoding":904},[724,19259,19260],{},[1801,19261],{"alt":5298,"className":19262,"src":5300},[210,1805],[724,19264,19265,5306,19267,5324,19284,5328,19286,5346,19303,5364,19320,5378,19333,5398,19352,1797],{},[38,19266,5305],{},[883,19268,19270],{"className":19269},[886],[888,19271,19272],{"xmlns":890},[892,19273,19274,19282],{},[895,19275,19276],{},[1716,19277,19278,19280],{},[898,19279,1790],{},[1711,19281,1793],{},[902,19283,1796],{"encoding":904},[38,19285,5327],{},[883,19287,19289],{"className":19288},[886],[888,19290,19291],{"xmlns":890},[892,19292,19293,19301],{},[895,19294,19295],{},[1716,19296,19297,19299],{},[898,19298,1675],{},[898,19300,1722],{},[902,19302,3608],{"encoding":904},[883,19304,19306],{"className":19305},[886],[888,19307,19308],{"xmlns":890},[892,19309,19310,19318],{},[895,19311,19312],{},[1716,19313,19314,19316],{},[898,19315,1660],{},[898,19317,1722],{},[902,19319,3587],{"encoding":904},[883,19321,19323],{"className":19322},[886],[888,19324,19325],{"xmlns":890},[892,19326,19327,19331],{},[895,19328,19329],{},[898,19330,1675],{},[902,19332,1675],{"encoding":904},[883,19334,19336],{"className":19335},[886],[888,19337,19338],{"xmlns":890},[892,19339,19340,19350],{},[895,19341,19342,19344,19346,19348],{},[898,19343,1833],{},[1711,19345,1714],{"stretchy":1713},[898,19347,1675],{},[1711,19349,1735],{"stretchy":1713},[902,19351,3921],{"encoding":904},[883,19353,19355],{"className":19354},[886],[888,19356,19357],{"xmlns":890},[892,19358,19359,19363],{},[895,19360,19361],{},[898,19362,1660],{},[902,19364,1660],{"encoding":904},[724,19366,5414,19367,5418],{},[38,19368,5417],{},[115,19370,5422],{"id":5421},[120,19372,19373,19442,19484,19562,19608,19673,19726,19763,19793],{},[123,19374,19375,5204,19406,1343,19423,5494,19440,5497],{},[38,19376,5429,19377],{},[883,19378,19380],{"className":19379},[886],[888,19381,19382],{"xmlns":890},[892,19383,19384,19404],{},[895,19385,19386,19388,19390,19392,19394,19396,19398,19400,19402],{},[898,19387,1833],{},[1711,19389,1714],{"stretchy":1713},[898,19391,1675],{},[1711,19393,1735],{"stretchy":1713},[1711,19395,1836],{},[898,19397,2090],{},[898,19399,1675],{},[1711,19401,2095],{},[898,19403,2098],{},[902,19405,5459],{"encoding":904},[883,19407,19409],{"className":19408},[886],[888,19410,19411],{"xmlns":890},[892,19412,19413,19421],{},[895,19414,19415,19417,19419],{},[898,19416,2090],{},[1711,19418,2109],{},[2111,19420,2113],{},[902,19422,2181],{"encoding":904},[883,19424,19426],{"className":19425},[886],[888,19427,19428],{"xmlns":890},[892,19429,19430,19438],{},[895,19431,19432,19434,19436],{},[898,19433,2098],{},[1711,19435,2123],{},[2111,19437,2113],{},[902,19439,2160],{"encoding":904},[38,19441,2185],{},[123,19443,19444,5503,19446,5525,19467,5543],{},[38,19445,5502],{},[883,19447,19449],{"className":19448},[886],[888,19450,19451],{"xmlns":890},[892,19452,19453,19465],{},[895,19454,19455,19457,19459,19461,19463],{},[898,19456,1660],{},[1711,19458,1836],{},[898,19460,1940],{},[1711,19462,2095],{},[898,19464,1833],{},[902,19466,4436],{"encoding":904},[883,19468,19470],{"className":19469},[886],[888,19471,19472],{"xmlns":890},[892,19473,19474,19482],{},[895,19475,19476,19478,19480],{},[898,19477,1833],{},[1711,19479,1836],{},[898,19481,2362],{},[902,19483,2384],{"encoding":904},[123,19485,19486,1648,19488,5551,19490,5602,19539,2591,19541,2186],{},[38,19487,5548],{},[614,19489,1688],{},[883,19491,19493],{"className":19492},[886],[888,19494,19495],{"xmlns":890},[892,19496,19497,19537],{},[895,19498,19499,19501,19503,19515,19517,19519],{},[898,19500,1660],{},[1711,19502,1836],{},[2525,19504,19505,19507],{},[898,19506,2090],{},[895,19508,19509,19511,19513],{},[2111,19510,2238],{},[1711,19512,2460],{},[898,19514,207],{},[898,19516,1675],{},[1711,19518,2095],{},[2525,19520,19521,19529],{},[895,19522,19523,19525,19527],{},[898,19524,2223],{},[1711,19526,2095],{},[898,19528,2098],{},[895,19530,19531,19533,19535],{},[2111,19532,2238],{},[1711,19534,2460],{},[898,19536,207],{},[902,19538,5601],{"encoding":904},[38,19540,2185],{},[883,19542,19544],{"className":19543},[886],[888,19545,19546],{"xmlns":890},[892,19547,19548,19560],{},[895,19549,19550,19552,19554,19556,19558],{},[1711,19551,1714],{"stretchy":1713},[898,19553,1675],{},[1711,19555,1726],{"separator":1725},[898,19557,1660],{},[1711,19559,1735],{"stretchy":1713},[902,19561,2613],{"encoding":904},[123,19563,19564,5503,19566,5657,19591,2186],{},[38,19565,5630],{},[883,19567,19569],{"className":19568},[886],[888,19570,19571],{"xmlns":890},[892,19572,19573,19589],{},[895,19574,19575,19581,19583],{},[1716,19576,19577,19579],{},[898,19578,1790],{},[898,19580,2778],{},[1711,19582,1836],{},[1716,19584,19585,19587],{},[898,19586,1790],{},[898,19588,2362],{},[902,19590,5656],{"encoding":904},[883,19592,19594],{"className":19593},[886],[888,19595,19596],{"xmlns":890},[892,19597,19598,19606],{},[895,19599,19600],{},[1716,19601,19602,19604],{},[898,19603,1790],{},[1711,19605,1793],{},[902,19607,5675],{"encoding":904},[123,19609,19610,5204,19612,2186],{},[38,19611,5680],{},[883,19613,19615],{"className":19614},[886],[888,19616,19617],{"xmlns":890},[892,19618,19619,19671],{},[895,19620,19621,19627,19629,19635,19637,19643,19645,19651,19653,19655,19661,19663,19665],{},[1716,19622,19623,19625],{},[898,19624,1790],{},[898,19626,2778],{},[1711,19628,1836],{},[2884,19630,19631,19633],{},[898,19632,2888],{},[2111,19634,2238],{},[1711,19636,2095],{},[2884,19638,19639,19641],{},[898,19640,2888],{},[2111,19642,2963],{},[1711,19644,1836],{},[2884,19646,19647,19649],{},[898,19648,2918],{},[2111,19650,2238],{},[898,19652,1660],{},[1711,19654,2095],{},[2884,19656,19657,19659],{},[898,19658,2918],{},[2111,19660,2963],{},[898,19662,1675],{},[1711,19664,2095],{},[2884,19666,19667,19669],{},[898,19668,2918],{},[2111,19670,3034],{},[902,19672,5742],{"encoding":904},[123,19674,19675,1648,19677,5551,19679,5796,19724,5799],{},[38,19676,5747],{},[614,19678,1695],{},[883,19680,19682],{"className":19681},[886],[888,19683,19684],{"xmlns":890},[892,19685,19686,19722],{},[895,19687,19688,19694,19696,19702,19704,19706,19712,19714,19716],{},[1716,19689,19690,19692],{},[898,19691,1790],{},[1711,19693,1793],{},[1711,19695,1836],{},[2884,19697,19698,19700],{},[898,19699,2918],{},[2111,19701,2238],{},[898,19703,1660],{},[1711,19705,2095],{},[2884,19707,19708,19710],{},[898,19709,2918],{},[2111,19711,2963],{},[898,19713,1675],{},[1711,19715,2095],{},[2884,19717,19718,19720],{},[898,19719,2918],{},[2111,19721,3034],{},[902,19723,5795],{"encoding":904},[38,19725,3341],{},[123,19727,19728,5805,19730,5840],{},[38,19729,5804],{},[883,19731,19733],{"className":19732},[886],[888,19734,19735],{"xmlns":890},[892,19736,19737,19761],{},[895,19738,19739,19741,19743,19745,19751,19753,19759],{},[898,19740,1722],{},[1711,19742,1836],{},[1711,19744,1714],{"stretchy":1713},[1716,19746,19747,19749],{},[898,19748,1675],{},[898,19750,1722],{},[1711,19752,1726],{"separator":1725},[1716,19754,19755,19757],{},[898,19756,1660],{},[898,19758,1722],{},[1711,19760,1735],{"stretchy":1713},[902,19762,5839],{"encoding":904},[123,19764,19765,5846,19767,1343,19780,5873],{},[38,19766,5845],{},[883,19768,19770],{"className":19769},[886],[888,19771,19772],{"xmlns":890},[892,19773,19774,19778],{},[895,19775,19776],{},[898,19777,1755],{},[902,19779,1755],{"encoding":904},[883,19781,19783],{"className":19782},[886],[888,19784,19785],{"xmlns":890},[892,19786,19787,19791],{},[895,19788,19789],{},[898,19790,1769],{},[902,19792,1769],{"encoding":904},[123,19794,19795,5879,19797,5897],{},[38,19796,5878],{},[883,19798,19800],{"className":19799},[886],[888,19801,19802],{"xmlns":890},[892,19803,19804,19812],{},[895,19805,19806],{},[1716,19807,19808,19810],{},[898,19809,1790],{},[1711,19811,1793],{},[902,19813,1796],{"encoding":904},[115,19815,5901],{"id":5900},[120,19817,19818,19825,19832,19839],{},[123,19819,19820,1700,19822],{},[38,19821,5908],{},[207,19823,5914],{"className":19824,"dataFsResolvedFilePath":5912,"href":5913},[210],[123,19826,19827,1700,19829],{},[38,19828,5919],{},[207,19830,5923],{"className":19831,"dataFsResolvedFilePath":868,"href":869},[210],[123,19833,19834,1700,19836,5933],{},[38,19835,5928],{},[207,19837,5932],{"className":19838,"dataFsResolvedFilePath":934,"href":935},[210],[123,19840,19841,19843],{},[38,19842,5938],{},[120,19844,19845,19850,19855],{},[123,19846,19847,5947],{},[207,19848,5946],{"className":19849,"dataFsResolvedFilePath":800,"href":801},[210],[123,19851,19852,5953],{},[207,19853,1145],{"className":19854,"dataFsResolvedFilePath":764,"href":765},[210],[123,19856,19857,5960],{},[207,19858,5959],{"className":19859,"dataFsResolvedFilePath":782,"href":783},[210],{"title":641,"searchDepth":642,"depth":642,"links":19861},[19862,19863,19864,19865,19866,19867,19868,19869,19870,19871],{"id":1637,"depth":642,"text":1638},{"id":1809,"depth":642,"text":1810},{"id":2030,"depth":642,"text":2031},{"id":2338,"depth":642,"text":2339},{"id":2758,"depth":642,"text":2759},{"id":3558,"depth":642,"text":3559},{"id":4250,"depth":642,"text":4251},{"id":5169,"depth":642,"text":5170},{"id":5421,"depth":642,"text":5422},{"id":5900,"depth":642,"text":5901},{},{"title":1629,"description":641},[1138,1137],[1128,5980,1143,5981,5982,5983,5984,5932],{"id":19877,"title":19878,"body":19879,"course":659,"courses":21472,"created":1129,"description":21473,"extension":661,"meta":21474,"navigation":664,"path":21475,"seo":21476,"sources":21477,"stem":21478,"tags":21479,"type":5985,"updated":677,"__hash__":21482},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":19880,"toc":21460},[19881,19884,19980,19987,20007,20011,20016,20079,20098,20100,20103,20239,20241,20451,20485,20622,20626,20690,20706,20734,20738,20836,20840,20844,20897,21003,21217,21221,21264,21370,21422,21424],[12,19882,19878],{"id":19883},"lagrangeova-metoda-vázané-extrémy",[724,19885,19886,19887,7903,19910,19942,19943,19946,19947,19974,19975,19979],{},"Hledáme extrém funkce ",[883,19888,19890],{"className":19889},[886],[888,19891,19892],{"xmlns":890},[892,19893,19894,19908],{},[895,19895,19896,19898,19900,19902,19904,19906],{},[898,19897,4068],{},[1711,19899,1714],{"stretchy":1713},[898,19901,6047],{},[1711,19903,1726],{"separator":1725},[898,19905,6038],{},[1711,19907,1735],{"stretchy":1713},[902,19909,13817],{"encoding":904},[883,19911,19913],{"className":19912},[886],[888,19914,19915],{"xmlns":890},[892,19916,19917,19939],{},[895,19918,19919,19921,19923,19929,19931,19937],{},[898,19920,900],{},[1711,19922,1714],{"stretchy":1713},[2884,19924,19925,19927],{},[898,19926,6796],{},[2111,19928,2238],{},[1711,19930,1726],{"separator":1725},[2884,19932,19933,19935],{},[898,19934,6796],{},[2111,19936,2963],{},[1711,19938,1735],{"stretchy":1713},[902,19940,19941],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,19944,19945],{},"podmíněný"," rovnicí ",[883,19948,19950],{"className":19949},[886],[888,19951,19952],{"xmlns":890},[892,19953,19954,19972],{},[895,19955,19956,19958,19960,19962,19964,19966,19968,19970],{},[898,19957,15014],{},[1711,19959,1714],{"stretchy":1713},[898,19961,6047],{},[1711,19963,1726],{"separator":1725},[898,19965,6038],{},[1711,19967,1735],{"stretchy":1713},[1711,19969,1836],{},[2111,19971,2113],{},[902,19973,15031],{"encoding":904},". V ",[207,19976,19978],{"className":19977,"dataFsResolvedFilePath":5912,"href":5913},[210],"matematické ekonomii"," se používá pro:",[724,19981,19982],{},[1801,19983],{"alt":19984,"className":19985,"src":19986},"imek-lagrange-tecnost",[210,1805],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,19988,19989,19998,20004],{},[123,19990,19991,19994,19995,1735],{},[38,19992,19993],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,19996,13748],{"className":19997,"dataFsResolvedFilePath":878,"href":879},[210],[123,19999,20000,20003],{},[38,20001,20002],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,20005,20006],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,20008,20010],{"id":20009},"princip","Princip",[724,20012,14680,20013,2062],{},[38,20014,20015],{},"Lagrangeovu funkci",[724,20017,20018],{},[883,20019,20021],{"className":20020},[886],[888,20022,20023],{"xmlns":890},[892,20024,20025,20076],{},[895,20026,20027,20029,20031,20033,20035,20037,20039,20042,20044,20046,20048,20050,20052,20054,20056,20058,20060,20062,20064,20066,20068,20070,20072,20074],{},[898,20028,2888],{},[1711,20030,1714],{"stretchy":1713},[898,20032,6047],{},[1711,20034,1726],{"separator":1725},[898,20036,6038],{},[1711,20038,1726],{"separator":1725},[898,20040,20041],{},"λ",[1711,20043,1735],{"stretchy":1713},[1711,20045,1836],{},[898,20047,4068],{},[1711,20049,1714],{"stretchy":1713},[898,20051,6047],{},[1711,20053,1726],{"separator":1725},[898,20055,6038],{},[1711,20057,1735],{"stretchy":1713},[1711,20059,2095],{},[898,20061,20041],{},[1942,20063,2519],{},[898,20065,15014],{},[1711,20067,1714],{"stretchy":1713},[898,20069,6047],{},[1711,20071,1726],{"separator":1725},[898,20073,6038],{},[1711,20075,1735],{"stretchy":1713},[902,20077,20078],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,20080,8298,20081,12082,20095,2186],{},[883,20082,20084],{"className":20083},[886],[888,20085,20086],{"xmlns":890},[892,20087,20088,20092],{},[895,20089,20090],{},[898,20091,20041],{},[902,20093,20094],{"encoding":904},"\\lambda",[38,20096,20097],{},"Lagrangeův multiplikátor",[115,20099,7250],{"id":7249},[724,20101,20102],{},"Řešíme soustavu:",[724,20104,20105,20153,20201],{},[883,20106,20108],{"className":20107},[886],[888,20109,20110],{"xmlns":890},[892,20111,20112,20150],{},[895,20113,20114,20122,20124,20132,20134,20136,20138,20146,20148],{},[13142,20115,20116,20118,20120],{},[898,20117,2888],{},[898,20119,6047],{},[1711,20121,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,20123,1836],{},[13142,20125,20126,20128,20130],{},[898,20127,4068],{},[898,20129,6047],{},[1711,20131,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,20133,2095],{},[898,20135,20041],{},[1942,20137,2519],{},[13142,20139,20140,20142,20144],{},[898,20141,15014],{},[898,20143,6047],{},[1711,20145,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,20147,1836],{},[2111,20149,2113],{},[902,20151,20152],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,20154,20156],{"className":20155},[886],[888,20157,20158],{"xmlns":890},[892,20159,20160,20198],{},[895,20161,20162,20170,20172,20180,20182,20184,20186,20194,20196],{},[13142,20163,20164,20166,20168],{},[898,20165,2888],{},[898,20167,6038],{},[1711,20169,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,20171,1836],{},[13142,20173,20174,20176,20178],{},[898,20175,4068],{},[898,20177,6038],{},[1711,20179,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,20181,2095],{},[898,20183,20041],{},[1942,20185,2519],{},[13142,20187,20188,20190,20192],{},[898,20189,15014],{},[898,20191,6038],{},[1711,20193,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,20195,1836],{},[2111,20197,2113],{},[902,20199,20200],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,20202,20204],{"className":20203},[886],[888,20205,20206],{"xmlns":890},[892,20207,20208,20236],{},[895,20209,20210,20218,20220,20222,20224,20226,20228,20230,20232,20234],{},[13142,20211,20212,20214,20216],{},[898,20213,2888],{},[898,20215,20041],{},[1711,20217,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,20219,1836],{},[898,20221,15014],{},[1711,20223,1714],{"stretchy":1713},[898,20225,6047],{},[1711,20227,1726],{"separator":1725},[898,20229,6038],{},[1711,20231,1735],{"stretchy":1713},[1711,20233,1836],{},[2111,20235,2113],{},[902,20237,20238],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,20240,7324],{"id":7323},[724,20242,20243],{},[883,20244,20246],{"className":20245},[886],[888,20247,20248],{"xmlns":890},[892,20249,20250,20448],{},[895,20251,20252,20254,20256,20258,20260,20262,20264,20266,20268,20270,20272,20288,20290,20292,20308,20310,20312,20320,20326,20328,20330,20346,20348,20350,20366,20368,20370,20378,20384,20386,20388,20390,20406,20408,20410,20426,20428,20430,20438,20440],{},[898,20253,2778],{},[1711,20255,1714],{"stretchy":1713},[898,20257,6047],{},[1711,20259,1726],{"separator":1725},[898,20261,6038],{},[1711,20263,1726],{"separator":1725},[898,20265,20041],{},[1711,20267,1735],{"stretchy":1713},[1711,20269,1836],{},[1711,20271,1714],{"stretchy":1713},[13142,20273,20274,20276,20282],{},[898,20275,4068],{},[895,20277,20278,20280],{},[898,20279,6047],{},[898,20281,6047],{},[895,20283,20284,20286],{},[1711,20285,5225],{"mathvariant":2287},[1711,20287,5225],{"mathvariant":2287},[1711,20289,2095],{},[898,20291,20041],{},[13142,20293,20294,20296,20302],{},[898,20295,15014],{},[895,20297,20298,20300],{},[898,20299,6047],{},[898,20301,6047],{},[895,20303,20304,20306],{},[1711,20305,5225],{"mathvariant":2287},[1711,20307,5225],{"mathvariant":2287},[1711,20309,1735],{"stretchy":1713},[1711,20311,1714],{"stretchy":1713},[13142,20313,20314,20316,20318],{},[898,20315,15014],{},[898,20317,6038],{},[1711,20319,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1716,20321,20322,20324],{},[1711,20323,1735],{"stretchy":1713},[2111,20325,2963],{},[1711,20327,2095],{},[1711,20329,1714],{"stretchy":1713},[13142,20331,20332,20334,20340],{},[898,20333,4068],{},[895,20335,20336,20338],{},[898,20337,6038],{},[898,20339,6038],{},[895,20341,20342,20344],{},[1711,20343,5225],{"mathvariant":2287},[1711,20345,5225],{"mathvariant":2287},[1711,20347,2095],{},[898,20349,20041],{},[13142,20351,20352,20354,20360],{},[898,20353,15014],{},[895,20355,20356,20358],{},[898,20357,6038],{},[898,20359,6038],{},[895,20361,20362,20364],{},[1711,20363,5225],{"mathvariant":2287},[1711,20365,5225],{"mathvariant":2287},[1711,20367,1735],{"stretchy":1713},[1711,20369,1714],{"stretchy":1713},[13142,20371,20372,20374,20376],{},[898,20373,15014],{},[898,20375,6047],{},[1711,20377,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1716,20379,20380,20382],{},[1711,20381,1735],{"stretchy":1713},[2111,20383,2963],{},[1711,20385,2460],{},[2111,20387,2963],{},[1711,20389,1714],{"stretchy":1713},[13142,20391,20392,20394,20400],{},[898,20393,4068],{},[895,20395,20396,20398],{},[898,20397,6047],{},[898,20399,6038],{},[895,20401,20402,20404],{},[1711,20403,5225],{"mathvariant":2287},[1711,20405,5225],{"mathvariant":2287},[1711,20407,2095],{},[898,20409,20041],{},[13142,20411,20412,20414,20420],{},[898,20413,15014],{},[895,20415,20416,20418],{},[898,20417,6047],{},[898,20419,6038],{},[895,20421,20422,20424],{},[1711,20423,5225],{"mathvariant":2287},[1711,20425,5225],{"mathvariant":2287},[1711,20427,1735],{"stretchy":1713},[1942,20429,2519],{},[13142,20431,20432,20434,20436],{},[898,20433,15014],{},[898,20435,6047],{},[1711,20437,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1942,20439,2519],{},[13142,20441,20442,20444,20446],{},[898,20443,15014],{},[898,20445,6038],{},[1711,20447,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,20449,20450],{"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",[724,20452,20453,20454,20484],{},"Je-li ",[883,20455,20457],{"className":20456},[886],[888,20458,20459],{"xmlns":890},[892,20460,20461,20481],{},[895,20462,20463,20465,20467,20469,20471,20473,20479],{},[1711,20464,5144],{"stretchy":1713},[898,20466,207],{},[1711,20468,1726],{"separator":1725},[898,20470,2223],{},[1711,20472,1726],{"separator":1725},[2884,20474,20475,20477],{},[898,20476,20041],{},[2111,20478,2113],{},[1711,20480,5163],{"stretchy":1713},[902,20482,20483],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,20486,20487,20555],{},[123,20488,20489,7411,20525,20527,20528],{},[883,20490,20492],{"className":20491},[886],[888,20493,20494],{"xmlns":890},[892,20495,20496,20522],{},[895,20497,20498,20500,20502,20504,20506,20508,20510,20516,20518,20520],{},[898,20499,2778],{},[1711,20501,1714],{"stretchy":1713},[898,20503,207],{},[1711,20505,1726],{"separator":1725},[898,20507,2223],{},[1711,20509,1726],{"separator":1725},[2884,20511,20512,20514],{},[898,20513,20041],{},[2111,20515,2113],{},[1711,20517,1735],{"stretchy":1713},[1711,20519,2109],{},[2111,20521,2113],{},[902,20523,20524],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,20526,7713],{}," vázané podmínkou ",[883,20529,20531],{"className":20530},[886],[888,20532,20533],{"xmlns":890},[892,20534,20535,20553],{},[895,20536,20537,20539,20541,20543,20545,20547,20549,20551],{},[898,20538,15014],{},[1711,20540,1714],{"stretchy":1713},[898,20542,6047],{},[1711,20544,1726],{"separator":1725},[898,20546,6038],{},[1711,20548,1735],{"stretchy":1713},[1711,20550,1836],{},[2111,20552,2113],{},[902,20554,15031],{"encoding":904},[123,20556,20557,7411,20593,20527,20595],{},[883,20558,20560],{"className":20559},[886],[888,20561,20562],{"xmlns":890},[892,20563,20564,20590],{},[895,20565,20566,20568,20570,20572,20574,20576,20578,20584,20586,20588],{},[898,20567,2778],{},[1711,20569,1714],{"stretchy":1713},[898,20571,207],{},[1711,20573,1726],{"separator":1725},[898,20575,2223],{},[1711,20577,1726],{"separator":1725},[2884,20579,20580,20582],{},[898,20581,20041],{},[2111,20583,2113],{},[1711,20585,1735],{"stretchy":1713},[1711,20587,2123],{},[2111,20589,2113],{},[902,20591,20592],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,20594,7771],{},[883,20596,20598],{"className":20597},[886],[888,20599,20600],{"xmlns":890},[892,20601,20602,20620],{},[895,20603,20604,20606,20608,20610,20612,20614,20616,20618],{},[898,20605,15014],{},[1711,20607,1714],{"stretchy":1713},[898,20609,6047],{},[1711,20611,1726],{"separator":1725},[898,20613,6038],{},[1711,20615,1735],{"stretchy":1713},[1711,20617,1836],{},[2111,20619,2113],{},[902,20621,15031],{"encoding":904},[115,20623,20625],{"id":20624},"význam-multiplikátoru","Význam multiplikátoru",[724,20627,20628],{},[883,20629,20631],{"className":20630},[886],[888,20632,20633],{"xmlns":890},[892,20634,20635,20687],{},[895,20636,20637,20639,20641,20663,20665],{},[898,20638,20041],{},[1711,20640,1836],{},[2525,20642,20643,20651],{},[13142,20644,20645,20647,20649],{},[898,20646,4068],{},[898,20648,6047],{},[1711,20650,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[895,20652,20653,20655],{},[1711,20654,2460],{},[13142,20656,20657,20659,20661],{},[898,20658,15014],{},[898,20660,6047],{},[1711,20662,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,20664,1836],{},[2525,20666,20667,20675],{},[13142,20668,20669,20671,20673],{},[898,20670,4068],{},[898,20672,6038],{},[1711,20674,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[895,20676,20677,20679],{},[1711,20678,2460],{},[13142,20680,20681,20683,20685],{},[898,20682,15014],{},[898,20684,6038],{},[1711,20686,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,20688,20689],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,20691,20692,20705],{},[883,20693,20695],{"className":20694},[886],[888,20696,20697],{"xmlns":890},[892,20698,20699,20703],{},[895,20700,20701],{},[898,20702,20041],{},[902,20704,20094],{"encoding":904}," udává:",[120,20707,20708,20714],{},[123,20709,20710,20711],{},"konstantní ",[38,20712,20713],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,20715,20716,20719,20720,20733],{},[38,20717,20718],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,20721,20723],{"className":20722},[886],[888,20724,20725],{"xmlns":890},[892,20726,20727,20731],{},[895,20728,20729],{},[898,20730,4068],{},[902,20732,4068],{"encoding":904},", uvolní-li se omezení o jednotku",[115,20735,20737],{"id":20736},"alternativní-postup","Alternativní postup",[724,20739,20740,20741,20768,20769,20793,20794,20818,20819,20832,20833,2186],{},"Lze-li z ",[883,20742,20744],{"className":20743},[886],[888,20745,20746],{"xmlns":890},[892,20747,20748,20766],{},[895,20749,20750,20752,20754,20756,20758,20760,20762,20764],{},[898,20751,15014],{},[1711,20753,1714],{"stretchy":1713},[898,20755,6047],{},[1711,20757,1726],{"separator":1725},[898,20759,6038],{},[1711,20761,1735],{"stretchy":1713},[1711,20763,1836],{},[2111,20765,2113],{},[902,20767,15031],{"encoding":904}," vyjádřit ",[883,20770,20772],{"className":20771},[886],[888,20773,20774],{"xmlns":890},[892,20775,20776,20790],{},[895,20777,20778,20780,20782,20784,20786,20788],{},[898,20779,6038],{},[1711,20781,1836],{},[898,20783,6038],{},[1711,20785,1714],{"stretchy":1713},[898,20787,6047],{},[1711,20789,1735],{"stretchy":1713},[902,20791,20792],{"encoding":904},"y = y(x)"," (nebo ",[883,20795,20797],{"className":20796},[886],[888,20798,20799],{"xmlns":890},[892,20800,20801,20815],{},[895,20802,20803,20805,20807,20809,20811,20813],{},[898,20804,6047],{},[1711,20806,1836],{},[898,20808,6047],{},[1711,20810,1714],{"stretchy":1713},[898,20812,6038],{},[1711,20814,1735],{"stretchy":1713},[902,20816,20817],{"encoding":904},"x = x(y)","), dosadíme do ",[883,20820,20822],{"className":20821},[886],[888,20823,20824],{"xmlns":890},[892,20825,20826,20830],{},[895,20827,20828],{},[898,20829,4068],{},[902,20831,4068],{"encoding":904}," a převedeme na ",[38,20834,20835],{},"extrém funkce jedné proměnné",[115,20837,20839],{"id":20838},"použití-v-imek","Použití v ImeK",[198,20841,20843],{"id":20842},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,20845,20846,20847,2186],{},"Rozpočtové omezení: ",[883,20848,20850],{"className":20849},[886],[888,20851,20852],{"xmlns":890},[892,20853,20854,20894],{},[895,20855,20856,20862,20864,20872,20878,20880,20888],{},[1716,20857,20858,20860],{},[898,20859,1660],{},[1711,20861,1793],{},[1711,20863,1836],{},[13142,20865,20866,20868,20870],{},[898,20867,7929],{},[2111,20869,2238],{},[1711,20871,1793],{},[2884,20873,20874,20876],{},[898,20875,6796],{},[2111,20877,2238],{},[1711,20879,2095],{},[13142,20881,20882,20884,20886],{},[898,20883,7929],{},[2111,20885,2963],{},[1711,20887,1793],{},[2884,20889,20890,20892],{},[898,20891,6796],{},[2111,20893,2963],{},[902,20895,20896],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,20898,20899],{},[883,20900,20902],{"className":20901},[886],[888,20903,20904],{"xmlns":890},[892,20905,20906,21000],{},[895,20907,20908,20910,20912,20918,20920,20926,20928,20930,20932,20934,20936,20938,20944,20946,20952,20954,20956,20958,20960,20966,20968,20976,20982,20984,20992,20998],{},[898,20909,2888],{},[1711,20911,1714],{"stretchy":1713},[2884,20913,20914,20916],{},[898,20915,6796],{},[2111,20917,2238],{},[1711,20919,1726],{"separator":1725},[2884,20921,20922,20924],{},[898,20923,6796],{},[2111,20925,2963],{},[1711,20927,1726],{"separator":1725},[898,20929,20041],{},[1711,20931,1735],{"stretchy":1713},[1711,20933,1836],{},[898,20935,900],{},[1711,20937,1714],{"stretchy":1713},[2884,20939,20940,20942],{},[898,20941,6796],{},[2111,20943,2238],{},[1711,20945,1726],{"separator":1725},[2884,20947,20948,20950],{},[898,20949,6796],{},[2111,20951,2963],{},[1711,20953,1735],{"stretchy":1713},[1711,20955,2095],{},[898,20957,20041],{},[1711,20959,1714],{"stretchy":1713},[1716,20961,20962,20964],{},[898,20963,1660],{},[1711,20965,1793],{},[1711,20967,2460],{},[13142,20969,20970,20972,20974],{},[898,20971,7929],{},[2111,20973,2238],{},[1711,20975,1793],{},[2884,20977,20978,20980],{},[898,20979,6796],{},[2111,20981,2238],{},[1711,20983,2460],{},[13142,20985,20986,20988,20990],{},[898,20987,7929],{},[2111,20989,2963],{},[1711,20991,1793],{},[2884,20993,20994,20996],{},[898,20995,6796],{},[2111,20997,2963],{},[1711,20999,1735],{"stretchy":1713},[902,21001,21002],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,21004,21005,21006,1343,21038,1343,21070,21119,21120,21174,21175,2186],{},"Soustava: ",[883,21007,21009],{"className":21008},[886],[888,21010,21011],{"xmlns":890},[892,21012,21013,21035],{},[895,21014,21015,21023,21025,21027],{},[13142,21016,21017,21019,21021],{},[898,21018,900],{},[2111,21020,2238],{},[1711,21022,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,21024,1836],{},[898,21026,20041],{},[13142,21028,21029,21031,21033],{},[898,21030,7929],{},[2111,21032,2238],{},[1711,21034,1793],{},[902,21036,21037],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,21039,21041],{"className":21040},[886],[888,21042,21043],{"xmlns":890},[892,21044,21045,21067],{},[895,21046,21047,21055,21057,21059],{},[13142,21048,21049,21051,21053],{},[898,21050,900],{},[2111,21052,2963],{},[1711,21054,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,21056,1836],{},[898,21058,20041],{},[13142,21060,21061,21063,21065],{},[898,21062,7929],{},[2111,21064,2963],{},[1711,21066,1793],{},[902,21068,21069],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,21071,21073],{"className":21072},[886],[888,21074,21075],{"xmlns":890},[892,21076,21077,21117],{},[895,21078,21079,21085,21087,21095,21101,21103,21111],{},[1716,21080,21081,21083],{},[898,21082,1660],{},[1711,21084,1793],{},[1711,21086,1836],{},[13142,21088,21089,21091,21093],{},[898,21090,7929],{},[2111,21092,2238],{},[1711,21094,1793],{},[2884,21096,21097,21099],{},[898,21098,6796],{},[2111,21100,2238],{},[1711,21102,2095],{},[13142,21104,21105,21107,21109],{},[898,21106,7929],{},[2111,21108,2963],{},[1711,21110,1793],{},[2884,21112,21113,21115],{},[898,21114,6796],{},[2111,21116,2963],{},[902,21118,20896],{"encoding":904},". Z prvních dvou: ",[883,21121,21123],{"className":21122},[886],[888,21124,21125],{"xmlns":890},[892,21126,21127,21171],{},[895,21128,21129,21149,21151],{},[2509,21130,21131],{"scriptlevel":2113,"displaystyle":1713},[2525,21132,21133,21141],{},[13142,21134,21135,21137,21139],{},[898,21136,900],{},[2111,21138,2238],{},[1711,21140,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[13142,21142,21143,21145,21147],{},[898,21144,900],{},[2111,21146,2963],{},[1711,21148,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,21150,1836],{},[2509,21152,21153],{"scriptlevel":2113,"displaystyle":1713},[2525,21154,21155,21163],{},[13142,21156,21157,21159,21161],{},[898,21158,7929],{},[2111,21160,2238],{},[1711,21162,1793],{},[13142,21164,21165,21167,21169],{},[898,21166,7929],{},[2111,21168,2963],{},[1711,21170,1793],{},[902,21172,21173],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,21176,21178],{"className":21177},[886],[888,21179,21180],{"xmlns":890},[892,21181,21182,21214],{},[895,21183,21184,21186,21188,21190,21192,21194],{},[898,21185,1790],{},[898,21187,7985],{},[898,21189,1940],{},[898,21191,2362],{},[1711,21193,1836],{},[2509,21195,21196],{"scriptlevel":2113,"displaystyle":1713},[2525,21197,21198,21206],{},[13142,21199,21200,21202,21204],{},[898,21201,7929],{},[2111,21203,2238],{},[1711,21205,1793],{},[13142,21207,21208,21210,21212],{},[898,21209,7929],{},[2111,21211,2963],{},[1711,21213,1793],{},[902,21215,21216],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,21218,21220],{"id":21219},"minimalizace-výdajů","Minimalizace výdajů",[724,21222,21223,21224,2186],{},"Podmínka dané užitečnosti ",[883,21225,21227],{"className":21226},[886],[888,21228,21229],{"xmlns":890},[892,21230,21231,21261],{},[895,21232,21233,21239,21241,21243,21245,21251,21253,21259],{},[1716,21234,21235,21237],{},[898,21236,900],{},[1711,21238,1793],{},[1711,21240,1836],{},[898,21242,900],{},[1711,21244,1714],{"stretchy":1713},[2884,21246,21247,21249],{},[898,21248,6796],{},[2111,21250,2238],{},[1711,21252,1726],{"separator":1725},[2884,21254,21255,21257],{},[898,21256,6796],{},[2111,21258,2963],{},[1711,21260,1735],{"stretchy":1713},[902,21262,21263],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,21265,21266],{},[883,21267,21269],{"className":21268},[886],[888,21270,21271],{"xmlns":890},[892,21272,21273,21367],{},[895,21274,21275,21277,21279,21285,21287,21293,21295,21297,21299,21301,21309,21315,21317,21325,21331,21333,21335,21337,21343,21345,21347,21349,21355,21357,21363,21365],{},[898,21276,2888],{},[1711,21278,1714],{"stretchy":1713},[2884,21280,21281,21283],{},[898,21282,6796],{},[2111,21284,2238],{},[1711,21286,1726],{"separator":1725},[2884,21288,21289,21291],{},[898,21290,6796],{},[2111,21292,2963],{},[1711,21294,1726],{"separator":1725},[898,21296,20041],{},[1711,21298,1735],{"stretchy":1713},[1711,21300,1836],{},[13142,21302,21303,21305,21307],{},[898,21304,7929],{},[2111,21306,2238],{},[1711,21308,1793],{},[2884,21310,21311,21313],{},[898,21312,6796],{},[2111,21314,2238],{},[1711,21316,2095],{},[13142,21318,21319,21321,21323],{},[898,21320,7929],{},[2111,21322,2963],{},[1711,21324,1793],{},[2884,21326,21327,21329],{},[898,21328,6796],{},[2111,21330,2963],{},[1711,21332,2095],{},[898,21334,20041],{},[1711,21336,1714],{"stretchy":1713},[1716,21338,21339,21341],{},[898,21340,900],{},[1711,21342,1793],{},[1711,21344,2460],{},[898,21346,900],{},[1711,21348,1714],{"stretchy":1713},[2884,21350,21351,21353],{},[898,21352,6796],{},[2111,21354,2238],{},[1711,21356,1726],{"separator":1725},[2884,21358,21359,21361],{},[898,21360,6796],{},[2111,21362,2963],{},[1711,21364,1735],{"stretchy":1713},[1711,21366,1735],{"stretchy":1713},[902,21368,21369],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,21371,21372,21373,2186],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,21374,21376],{"className":21375},[886],[888,21377,21378],{"xmlns":890},[892,21379,21380,21419],{},[895,21381,21382,21389,21391,21397,21399,21405,21407,21413,21415,21417],{},[2884,21383,21384,21386],{},[898,21385,6796],{},[898,21387,21388],{},"i",[1711,21390,1836],{},[2884,21392,21393,21395],{},[898,21394,2778],{},[898,21396,21388],{},[1711,21398,1714],{"stretchy":1713},[2884,21400,21401,21403],{},[898,21402,7929],{},[2111,21404,2238],{},[1711,21406,1726],{"separator":1725},[2884,21408,21409,21411],{},[898,21410,7929],{},[2111,21412,2963],{},[1711,21414,1726],{"separator":1725},[898,21416,900],{},[1711,21418,1735],{"stretchy":1713},[902,21420,21421],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,21423,5901],{"id":5900},[120,21425,21426,21433,21440,21449],{},[123,21427,21428,1700,21430],{},[38,21429,7793],{},[207,21431,784],{"className":21432,"dataFsResolvedFilePath":782,"href":783},[210],[123,21434,21435,1700,21437],{},[38,21436,7801],{},[207,21438,15915],{"className":21439,"dataFsResolvedFilePath":800,"href":801},[210],[123,21441,21442,1700,21445,21448],{},[38,21443,21444],{},"Aplikace v kurzu:",[207,21446,880],{"className":21447,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,21450,21451,1700,21453,1343,21456,21459],{},[38,21452,7809],{},[207,21454,936],{"className":21455,"dataFsResolvedFilePath":934,"href":935},[210],[207,21457,1400],{"className":21458,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":21461},[21462,21463,21464,21465,21466,21467,21471],{"id":20009,"depth":642,"text":20010},{"id":7249,"depth":642,"text":7250},{"id":7323,"depth":642,"text":7324},{"id":20624,"depth":642,"text":20625},{"id":20736,"depth":642,"text":20737},{"id":20838,"depth":642,"text":20839,"children":21468},[21469,21470],{"id":20842,"depth":649,"text":20843},{"id":21219,"depth":649,"text":21220},{"id":5900,"depth":642,"text":5901},[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":19878,"description":21473},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,21480,21481],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":21484,"title":936,"body":21485,"course":1128,"courses":659,"created":5973,"description":641,"extension":661,"meta":31353,"navigation":664,"path":31354,"seo":31355,"sources":31356,"stem":31357,"tags":31358,"type":5985,"updated":677,"__hash__":31362},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":21486,"toc":31315},[21487,21490,21492,21615,21750,21754,21757,21870,21874,21902,21949,21952,22018,22063,22066,22092,22123,22127,22131,22175,22219,22281,22336,22339,22343,22346,22393,22490,22596,22602,22679,22708,22847,22851,22880,22930,23077,23167,23171,23197,23235,23262,23300,23362,23437,23515,23573,23639,23683,23687,23745,23794,23839,24052,24172,24178,24182,24205,24209,24216,24220,24251,24286,24290,24340,24428,24470,24491,24553,24613,24617,24688,24756,24828,24943,24991,24995,24998,25039,25078,25101,25215,25379,25387,25414,25444,25447,25524,25677,25761,26100,26104,26228,26364,26500,26553,26556,26806,26887,26891,26894,26952,26984,26987,27036,27039,27110,27306,27310,27461,27691,27729,27782,27828,27831,27887,27936,28140,28230,28234,28250,28257,28426,28430,28501,28582,28663,28742,28888,28976,28980,29163,29294,29339,29436,29440,30179,30181,31232,31234],[12,21488,936],{"id":21489},"národní-důchod",[115,21491,1638],{"id":1637},[724,21493,21494,21495,1700,21499,21502,21503,1700,21506,21519,21520,21523,21524,21527,21528,21531,21532,21534,21535,1700,21537,21554,21555,21572,21573,21576,21577,1797],{},"Kapitola 7 ",[207,21496,21498],{"className":21497,"dataFsResolvedFilePath":5912,"href":5913},[210],"Matematické ekonomie",[38,21500,21501],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,21504,21505],{},"národním důchodem",[883,21507,21509],{"className":21508},[886],[888,21510,21511],{"xmlns":890},[892,21512,21513,21517],{},[895,21514,21515],{},[898,21516,1660],{},[902,21518,1660],{"encoding":904},". Budují se postupně bohatší modely — ",[38,21521,21522],{},"C-I"," (jen spotřeba a investice) → ",[38,21525,21526],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,21529,21530],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,21533,1643],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,21536,3569],{},[883,21538,21540],{"className":21539},[886],[888,21541,21542],{"xmlns":890},[892,21543,21544,21552],{},[895,21545,21546],{},[1716,21547,21548,21550],{},[898,21549,1660],{},[898,21551,1722],{},[902,21553,3587],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,21556,21558],{"className":21557},[886],[888,21559,21560],{"xmlns":890},[892,21561,21562,21570],{},[895,21563,21564],{},[1716,21565,21566,21568],{},[898,21567,1660],{},[898,21569,1722],{},[902,21571,3587],{"encoding":904}," na exogenní veličiny popisují ",[38,21574,21575],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,21578,21580],{"className":21579},[886],[888,21581,21582],{"xmlns":890},[892,21583,21584,21612],{},[895,21585,21586,21588,21590,21592,21594,21596,21598,21600,21602,21604,21606,21608,21610],{},[2111,21587,2238],{},[898,21589,8659],{"mathvariant":2287},[1711,21591,1714],{"stretchy":1713},[2111,21593,2238],{},[1711,21595,2460],{},[898,21597,207],{},[1711,21599,1735],{"stretchy":1713},[1711,21601,1836],{},[2111,21603,2238],{},[898,21605,8659],{"mathvariant":2287},[898,21607,1790],{},[898,21609,7929],{},[898,21611,2362],{},[902,21613,21614],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[1921,21616,21617],{},[724,21618,21619,21621,21622,21625,21626,21644,21645,21675,21676,21723,21724,21726,21727,21749],{},[883,21620,2678],{}," Intuice\n",[38,21623,21624],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,21627,21629],{"className":21628},[886],[888,21630,21631],{"xmlns":890},[892,21632,21633,21641],{},[895,21634,21635,21637,21639],{},[898,21636,1790],{},[898,21638,7929],{},[898,21640,1940],{},[902,21642,21643],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,21646,21648],{"className":21647},[886],[888,21649,21650],{"xmlns":890},[892,21651,21652,21672],{},[895,21653,21654,21656,21658,21660,21662,21664,21666,21668,21670],{},[898,21655,1790],{},[898,21657,7929],{},[898,21659,2362],{},[1711,21661,1836],{},[2111,21663,2238],{},[1711,21665,2460],{},[898,21667,1790],{},[898,21669,7929],{},[898,21671,1940],{},[902,21673,21674],{"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 ",[883,21677,21679],{"className":21678},[886],[888,21680,21681],{"xmlns":890},[892,21682,21683,21720],{},[895,21684,21685,21687,21689,21691,21693,21699,21701,21704,21706,21708,21710,21712,21714,21716,21718],{},[2111,21686,2238],{},[1711,21688,2095],{},[898,21690,207],{},[1711,21692,2095],{},[1716,21694,21695,21697],{},[898,21696,207],{},[2111,21698,2963],{},[1711,21700,2095],{},[1711,21702,21703],{},"⋯",[1711,21705,1836],{},[2111,21707,2238],{},[898,21709,8659],{"mathvariant":2287},[1711,21711,1714],{"stretchy":1713},[2111,21713,2238],{},[1711,21715,2460],{},[898,21717,207],{},[1711,21719,1735],{"stretchy":1713},[902,21721,21722],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,21725,1643],{}," 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 ",[883,21728,21730],{"className":21729},[886],[888,21731,21732],{"xmlns":890},[892,21733,21734,21746],{},[895,21735,21736,21738,21740,21742,21744],{},[1711,21737,1714],{"stretchy":1713},[898,21739,1660],{},[1711,21741,1726],{"separator":1725},[898,21743,1675],{},[1711,21745,1735],{"stretchy":1713},[902,21747,21748],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,21751,21753],{"id":21752},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,21755,21756],{},"Po prostudování kapitoly by čtenář měl umět:",[120,21758,21759,21762,21765,21768,21771,21774,21777,21867],{},[123,21760,21761],{},"popsat zjednodušený model národní ekonomiky,",[123,21763,21764],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,21766,21767],{},"popsat lineární model spotřeby a úspor,",[123,21769,21770],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,21772,21773],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,21775,21776],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,21778,21779,21780,1343,21797,1343,21819,2009,21844,21866],{},"popsat modely ",[883,21781,21783],{"className":21782},[886],[888,21784,21785],{"xmlns":890},[892,21786,21787,21795],{},[895,21788,21789,21791,21793],{},[898,21790,1940],{},[1942,21792,1944],{},[898,21794,1833],{},[902,21796,1949],{"encoding":904},[883,21798,21800],{"className":21799},[886],[888,21801,21802],{"xmlns":890},[892,21803,21804,21816],{},[895,21805,21806,21808,21810,21812,21814],{},[898,21807,1940],{},[1942,21809,1944],{},[898,21811,1833],{},[1942,21813,1944],{},[898,21815,1755],{},[902,21817,21818],{"encoding":904},"C\\text{-}I\\text{-}G",[883,21820,21822],{"className":21821},[886],[888,21823,21824],{"xmlns":890},[892,21825,21826,21842],{},[895,21827,21828,21830,21832,21834,21836,21838,21840],{},[898,21829,1940],{},[1942,21831,1944],{},[898,21833,1833],{},[1942,21835,1944],{},[898,21837,1755],{},[1942,21839,1944],{},[898,21841,1974],{},[902,21843,1977],{"encoding":904},[883,21845,21847],{"className":21846},[886],[888,21848,21849],{"xmlns":890},[892,21850,21851,21863],{},[895,21852,21853,21855,21857,21859,21861],{},[898,21854,1833],{},[898,21856,2362],{},[1942,21858,1944],{},[898,21860,2888],{},[898,21862,1790],{},[902,21864,21865],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,21868,21869],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,21871,21873],{"id":21872},"gnp-a-národní-důchod","GNP a národní důchod",[724,21875,21876,1700,21879,1648,21898,21901],{},[38,21877,21878],{},"Hrubý národní produkt",[883,21880,21882],{"className":21881},[886],[888,21883,21884],{"xmlns":890},[892,21885,21886,21895],{},[895,21887,21888,21890,21893],{},[898,21889,1755],{},[898,21891,21892],{},"N",[898,21894,7929],{},[902,21896,21897],{"encoding":904},"GNP",[614,21899,21900],{},"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:",[724,21903,21904],{},[883,21905,21907],{"className":21906},[886],[888,21908,21909],{"xmlns":890},[892,21910,21911,21946],{},[895,21912,21913,21915,21917,21919,21921,21923,21925,21927,21929,21931,21933,21935,21937,21939,21941,21944],{},[898,21914,1755],{},[898,21916,21892],{},[898,21918,7929],{},[1711,21920,1836],{},[898,21922,1940],{},[1711,21924,2095],{},[898,21926,1833],{},[1711,21928,2095],{},[898,21930,1755],{},[1711,21932,2095],{},[898,21934,1974],{},[1711,21936,1726],{"separator":1725},[2102,21938],{"width":2104},[1711,21940,1714],{"stretchy":1713},[2111,21942,21943],{},"7.1",[1711,21945,1735],{"stretchy":1713},[902,21947,21948],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,21950,21951],{},"kde",[120,21953,21954,21970,21986,22002],{},[123,21955,21956,21969],{},[883,21957,21959],{"className":21958},[886],[888,21960,21961],{"xmlns":890},[892,21962,21963,21967],{},[895,21964,21965],{},[898,21966,1940],{},[902,21968,1940],{"encoding":904}," — výdaje domácností na spotřebu,",[123,21971,21972,21985],{},[883,21973,21975],{"className":21974},[886],[888,21976,21977],{"xmlns":890},[892,21978,21979,21983],{},[895,21980,21981],{},[898,21982,1833],{},[902,21984,1833],{"encoding":904}," — hrubé domácí investice,",[123,21987,21988,22001],{},[883,21989,21991],{"className":21990},[886],[888,21992,21993],{"xmlns":890},[892,21994,21995,21999],{},[895,21996,21997],{},[898,21998,1755],{},[902,22000,1755],{"encoding":904}," — vládní výdaje,",[123,22003,22004,22017],{},[883,22005,22007],{"className":22006},[886],[888,22008,22009],{"xmlns":890},[892,22010,22011,22015],{},[895,22012,22013],{},[898,22014,1974],{},[902,22016,1974],{"encoding":904}," — čistý export.",[724,22019,22020,22021,22038,22039,22042,22043,1700,22046,1648,22059,22062],{},"K měření ",[883,22022,22024],{"className":22023},[886],[888,22025,22026],{"xmlns":890},[892,22027,22028,22036],{},[895,22029,22030,22032,22034],{},[898,22031,1755],{},[898,22033,21892],{},[898,22035,7929],{},[902,22037,21897],{"encoding":904}," se užívá ",[38,22040,22041],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,22044,22045],{},"národní důchod",[883,22047,22049],{"className":22048},[886],[888,22050,22051],{"xmlns":890},[892,22052,22053,22057],{},[895,22054,22055],{},[898,22056,1660],{},[902,22058,1660],{"encoding":904},[614,22060,22061],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,22064,22065],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,22067,22068],{},[883,22069,22071],{"className":22070},[886],[888,22072,22073],{"xmlns":890},[892,22074,22075,22089],{},[895,22076,22077,22079,22081,22083,22085,22087],{},[898,22078,1755],{},[898,22080,21892],{},[898,22082,7929],{},[1711,22084,6740],{},[898,22086,1660],{},[1711,22088,1726],{"separator":1725},[902,22090,22091],{"encoding":904},"GNP \\approx Y,",[724,22093,22094,22095,1648,22098,22101,22102,22115,22116,22119,22120,2186],{},"a užívá se společného názvu ",[38,22096,22097],{},"důchod",[614,22099,22100],{},"income",") s označením ",[883,22103,22105],{"className":22104},[886],[888,22106,22107],{"xmlns":890},[892,22108,22109,22113],{},[895,22110,22111],{},[898,22112,1660],{},[902,22114,1660],{"encoding":904},". Domácnosti důchod použijí ke ",[38,22117,22118],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,22121,22122],{},"úspor",[115,22124,22126],{"id":22125},"spotřeba-a-úspory","Spotřeba a úspory",[198,22128,22130],{"id":22129},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,22132,22133,22134,22147,22148,22161,22162,2062],{},"Jak spotřeba ",[883,22135,22137],{"className":22136},[886],[888,22138,22139],{"xmlns":890},[892,22140,22141,22145],{},[895,22142,22143],{},[898,22144,1940],{},[902,22146,1940],{"encoding":904},", tak úspory ",[883,22149,22151],{"className":22150},[886],[888,22152,22153],{"xmlns":890},[892,22154,22155,22159],{},[895,22156,22157],{},[898,22158,2362],{},[902,22160,2362],{"encoding":904}," závisejí na důchodu ",[883,22163,22165],{"className":22164},[886],[888,22166,22167],{"xmlns":890},[892,22168,22169,22173],{},[895,22170,22171],{},[898,22172,1660],{},[902,22174,1660],{"encoding":904},[724,22176,22177],{},[883,22178,22180],{"className":22179},[886],[888,22181,22182],{"xmlns":890},[892,22183,22184,22216],{},[895,22185,22186,22188,22190,22192,22194,22196,22198,22200,22202,22204,22206,22208,22210,22212,22214],{},[898,22187,1940],{},[1711,22189,1836],{},[898,22191,1940],{},[1711,22193,1714],{"stretchy":1713},[898,22195,1660],{},[1711,22197,1735],{"stretchy":1713},[1711,22199,1726],{"separator":1725},[2102,22201],{"width":2104},[898,22203,2362],{},[1711,22205,1836],{},[898,22207,2362],{},[1711,22209,1714],{"stretchy":1713},[898,22211,1660],{},[1711,22213,1735],{"stretchy":1713},[898,22215,2186],{"mathvariant":2287},[902,22217,22218],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,22220,22221,12082,22240,1648,22243,22246,22247,12082,22267,1648,22270,22273,22274,2009,22277,22280],{},[883,22222,22224],{"className":22223},[886],[888,22225,22226],{"xmlns":890},[892,22227,22228,22238],{},[895,22229,22230,22232,22234,22236],{},[898,22231,1940],{},[1711,22233,1714],{"stretchy":1713},[898,22235,1660],{},[1711,22237,1735],{"stretchy":1713},[902,22239,3901],{"encoding":904},[38,22241,22242],{},"funkce spotřeby",[614,22244,22245],{},"consumption function","), ",[883,22248,22250],{"className":22249},[886],[888,22251,22252],{"xmlns":890},[892,22253,22254,22264],{},[895,22255,22256,22258,22260,22262],{},[898,22257,2362],{},[1711,22259,1714],{"stretchy":1713},[898,22261,1660],{},[1711,22263,1735],{"stretchy":1713},[902,22265,22266],{"encoding":904},"S(Y)",[38,22268,22269],{},"funkce úspor",[614,22271,22272],{},"savings function","); jejich grafy se nazývají ",[38,22275,22276],{},"křivka spotřeby",[38,22278,22279],{},"křivka úspor",". Platí základní identita",[724,22282,22283],{},[883,22284,22286],{"className":22285},[886],[888,22287,22288],{"xmlns":890},[892,22289,22290,22333],{},[895,22291,22292,22294,22296,22298,22300,22302,22304,22306,22308,22310,22312,22314,22316,22318,22320,22322,22324,22326,22328,22331],{},[898,22293,1660],{},[1711,22295,1836],{},[898,22297,1940],{},[1711,22299,2095],{},[898,22301,2362],{},[1711,22303,1836],{},[898,22305,1940],{},[1711,22307,1714],{"stretchy":1713},[898,22309,1660],{},[1711,22311,1735],{"stretchy":1713},[1711,22313,2095],{},[898,22315,2362],{},[1711,22317,1714],{"stretchy":1713},[898,22319,1660],{},[1711,22321,1735],{"stretchy":1713},[898,22323,2186],{"mathvariant":2287},[2102,22325],{"width":2104},[1711,22327,1714],{"stretchy":1713},[2111,22329,22330],{},"7.2",[1711,22332,1735],{"stretchy":1713},[902,22334,22335],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,22337,22338],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,22340,22342],{"id":22341},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,22344,22345],{},"Nejjednodušší model předpokládá lineární tvar",[724,22347,22348],{},[883,22349,22351],{"className":22350},[886],[888,22352,22353],{"xmlns":890},[892,22354,22355,22390],{},[895,22356,22357,22359,22361,22363,22365,22367,22369,22371,22373,22375,22377,22379,22381,22383,22385,22388],{},[898,22358,1940],{},[1711,22360,1836],{},[898,22362,1940],{},[1711,22364,1714],{"stretchy":1713},[898,22366,1660],{},[1711,22368,1735],{"stretchy":1713},[1711,22370,1836],{},[898,22372,207],{},[898,22374,1660],{},[1711,22376,2095],{},[898,22378,2223],{},[1711,22380,1726],{"separator":1725},[2102,22382],{"width":2104},[1711,22384,1714],{"stretchy":1713},[2111,22386,22387],{},"7.3",[1711,22389,1735],{"stretchy":1713},[902,22391,22392],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,22394,8298,22395,2009,22413,22435,22436,22476,22477,2186],{},[883,22396,22398],{"className":22397},[886],[888,22399,22400],{"xmlns":890},[892,22401,22402,22410],{},[895,22403,22404,22406,22408],{},[898,22405,2223],{},[1711,22407,2123],{},[2111,22409,2113],{},[902,22411,22412],{"encoding":904},"b > 0",[883,22414,22416],{"className":22415},[886],[888,22417,22418],{"xmlns":890},[892,22419,22420,22432],{},[895,22421,22422,22424,22426,22428,22430],{},[2111,22423,2113],{},[1711,22425,2109],{},[898,22427,207],{},[1711,22429,2109],{},[2111,22431,2238],{},[902,22433,22434],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,22437,22439],{"className":22438},[886],[888,22440,22441],{"xmlns":890},[892,22442,22443,22473],{},[895,22444,22445,22447,22449,22456,22458,22461,22463,22465,22467,22469,22471],{},[898,22446,207],{},[1711,22448,1836],{},[895,22450,22451,22454],{},[898,22452,22453],{"mathvariant":2287},"t",[898,22455,15014],{"mathvariant":2287},[1942,22457,2519],{},[898,22459,22460],{},"α",[1711,22462,1836],{},[898,22464,6892],{"mathvariant":2287},[898,22466,1940],{},[898,22468,8659],{"mathvariant":2287},[898,22470,6892],{"mathvariant":2287},[898,22472,1660],{},[902,22474,22475],{"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 ",[883,22478,22480],{"className":22479},[886],[888,22481,22482],{"xmlns":890},[892,22483,22484,22488],{},[895,22485,22486],{},[898,22487,1660],{},[902,22489,1660],{"encoding":904},[724,22491,22492],{},[614,22493,22494,22495,22519,22520,22558,22559,22575,22576,2186],{},"Obrázek 7.1 — Přímka spotřeby ",[883,22496,22498],{"className":22497},[886],[888,22499,22500],{"xmlns":890},[892,22501,22502,22516],{},[895,22503,22504,22506,22508,22510,22512,22514],{},[898,22505,1940],{},[1711,22507,1836],{},[898,22509,207],{},[898,22511,1660],{},[1711,22513,2095],{},[898,22515,2223],{},[902,22517,22518],{"encoding":904},"C = aY + b"," se směrnicí ",[883,22521,22523],{"className":22522},[886],[888,22524,22525],{"xmlns":890},[892,22526,22527,22555],{},[895,22528,22529,22531,22533,22539,22541,22543,22545,22547,22549,22551,22553],{},[898,22530,207],{},[1711,22532,1836],{},[895,22534,22535,22537],{},[898,22536,22453],{"mathvariant":2287},[898,22538,15014],{"mathvariant":2287},[1942,22540,2519],{},[898,22542,22460],{},[1711,22544,1836],{},[898,22546,6892],{"mathvariant":2287},[898,22548,1940],{},[898,22550,8659],{"mathvariant":2287},[898,22552,6892],{"mathvariant":2287},[898,22554,1660],{},[902,22556,22557],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,22560,22562],{"className":22561},[886],[888,22563,22564],{"xmlns":890},[892,22565,22566,22572],{},[895,22567,22568,22570],{},[898,22569,6892],{"mathvariant":2287},[898,22571,1940],{},[902,22573,22574],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,22577,22579],{"className":22578},[886],[888,22580,22581],{"xmlns":890},[892,22582,22583,22593],{},[895,22584,22585,22587,22589,22591],{},[898,22586,6892],{"mathvariant":2287},[898,22588,1660],{},[1711,22590,1836],{},[2111,22592,2238],{},[902,22594,22595],{"encoding":904},"\\Delta Y = 1",[724,22597,22598,22599,2062],{},"Dosazením do (7.2) plyne ",[38,22600,22601],{},"lineární model úspor",[724,22603,22604],{},[883,22605,22607],{"className":22606},[886],[888,22608,22609],{"xmlns":890},[892,22610,22611,22676],{},[895,22612,22613,22615,22617,22619,22621,22623,22625,22627,22629,22631,22633,22635,22637,22639,22641,22643,22645,22647,22649,22651,22653,22655,22657,22659,22661,22663,22665,22667,22669,22671,22674],{},[898,22614,2362],{},[1711,22616,1836],{},[898,22618,1660],{},[1711,22620,2460],{},[898,22622,1940],{},[1711,22624,1714],{"stretchy":1713},[898,22626,1660],{},[1711,22628,1735],{"stretchy":1713},[1711,22630,1836],{},[898,22632,1660],{},[1711,22634,2460],{},[1711,22636,1714],{"stretchy":1713},[898,22638,207],{},[898,22640,1660],{},[1711,22642,2095],{},[898,22644,2223],{},[1711,22646,1735],{"stretchy":1713},[1711,22648,1836],{},[1711,22650,1714],{"stretchy":1713},[2111,22652,2238],{},[1711,22654,2460],{},[898,22656,207],{},[1711,22658,1735],{"stretchy":1713},[898,22660,1660],{},[1711,22662,2460],{},[898,22664,2223],{},[898,22666,2186],{"mathvariant":2287},[2102,22668],{"width":2104},[1711,22670,1714],{"stretchy":1713},[2111,22672,22673],{},"7.4",[1711,22675,1735],{"stretchy":1713},[902,22677,22678],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,22680,22681,22682,1797],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,22683,22685],{"className":22684},[886],[888,22686,22687],{"xmlns":890},[892,22688,22689,22705],{},[895,22690,22691,22693,22695,22697,22699,22701,22703],{},[2111,22692,2113],{},[1711,22694,2109],{},[2111,22696,2238],{},[1711,22698,2460],{},[898,22700,207],{},[1711,22702,2109],{},[2111,22704,2238],{},[902,22706,22707],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,22709,22710],{},[614,22711,22712,22713,2009,22736,22768,22769,6635,22782,22812,22813,6635,22831,2186],{},"Obrázek 7.2 — Přímky ",[883,22714,22716],{"className":22715},[886],[888,22717,22718],{"xmlns":890},[892,22719,22720,22734],{},[895,22721,22722,22724,22726,22728,22730,22732],{},[898,22723,1940],{},[1711,22725,1836],{},[898,22727,207],{},[898,22729,1660],{},[1711,22731,2095],{},[898,22733,2223],{},[902,22735,22518],{"encoding":904},[883,22737,22739],{"className":22738},[886],[888,22740,22741],{"xmlns":890},[892,22742,22743,22765],{},[895,22744,22745,22747,22749,22751,22753,22755,22757,22759,22761,22763],{},[898,22746,2362],{},[1711,22748,1836],{},[1711,22750,1714],{"stretchy":1713},[2111,22752,2238],{},[1711,22754,2460],{},[898,22756,207],{},[1711,22758,1735],{"stretchy":1713},[898,22760,1660],{},[1711,22762,2460],{},[898,22764,2223],{},[902,22766,22767],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,22770,22772],{"className":22771},[886],[888,22773,22774],{"xmlns":890},[892,22775,22776,22780],{},[895,22777,22778],{},[898,22779,1660],{},[902,22781,1660],{"encoding":904},[883,22783,22785],{"className":22784},[886],[888,22786,22787],{"xmlns":890},[892,22788,22789,22809],{},[895,22790,22791,22793,22795,22797,22799,22801,22803,22805,22807],{},[898,22792,1660],{},[1711,22794,1836],{},[898,22796,2223],{},[898,22798,8659],{"mathvariant":2287},[1711,22800,1714],{"stretchy":1713},[2111,22802,2238],{},[1711,22804,2460],{},[898,22806,207],{},[1711,22808,1735],{"stretchy":1713},[902,22810,22811],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,22814,22816],{"className":22815},[886],[888,22817,22818],{"xmlns":890},[892,22819,22820,22828],{},[895,22821,22822,22824,22826],{},[898,22823,1940],{},[1711,22825,1726],{"separator":1725},[898,22827,2362],{},[902,22829,22830],{"encoding":904},"C, S",[883,22832,22834],{"className":22833},[886],[888,22835,22836],{"xmlns":890},[892,22837,22838,22844],{},[895,22839,22840,22842],{},[1711,22841,2460],{},[898,22843,2223],{},[902,22845,22846],{"encoding":904},"-b",[198,22848,22850],{"id":22849},"příklad-71","Příklad 7.1",[724,22852,22853,22854,22879],{},"Pro spotřebu ",[883,22855,22857],{"className":22856},[886],[888,22858,22859],{"xmlns":890},[892,22860,22861,22876],{},[895,22862,22863,22865,22867,22870,22872,22874],{},[898,22864,1940],{},[1711,22866,1836],{},[2111,22868,22869],{},"0,4",[898,22871,1660],{},[1711,22873,2095],{},[2111,22875,4712],{},[902,22877,22878],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,22881,22882],{},[883,22883,22885],{"className":22884},[886],[888,22886,22887],{"xmlns":890},[892,22888,22889,22927],{},[895,22890,22891,22893,22895,22897,22899,22901,22903,22905,22907,22909,22911,22913,22915,22917,22920,22922,22924],{},[898,22892,2362],{},[1711,22894,1836],{},[898,22896,1660],{},[1711,22898,2460],{},[898,22900,1940],{},[1711,22902,1836],{},[898,22904,1660],{},[1711,22906,2460],{},[2111,22908,22869],{},[898,22910,1660],{},[1711,22912,2460],{},[2111,22914,4712],{},[1711,22916,1836],{},[2111,22918,22919],{},"0,6",[898,22921,1660],{},[1711,22923,2460],{},[2111,22925,22926],{},"10.",[902,22928,22929],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,22931,22932],{},[614,22933,22934,22935,2009,22958,22982,22983,12082,22996,23020,23021,12082,23038,23054,23055,2186],{},"Obrázek 7.3 — Přímky ",[883,22936,22938],{"className":22937},[886],[888,22939,22940],{"xmlns":890},[892,22941,22942,22956],{},[895,22943,22944,22946,22948,22950,22952,22954],{},[898,22945,1940],{},[1711,22947,1836],{},[2111,22949,22869],{},[898,22951,1660],{},[1711,22953,2095],{},[2111,22955,4712],{},[902,22957,22878],{"encoding":904},[883,22959,22961],{"className":22960},[886],[888,22962,22963],{"xmlns":890},[892,22964,22965,22979],{},[895,22966,22967,22969,22971,22973,22975,22977],{},[898,22968,2362],{},[1711,22970,1836],{},[2111,22972,22919],{},[898,22974,1660],{},[1711,22976,2460],{},[2111,22978,4712],{},[902,22980,22981],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,22984,22986],{"className":22985},[886],[888,22987,22988],{"xmlns":890},[892,22989,22990,22994],{},[895,22991,22992],{},[898,22993,1660],{},[902,22995,1660],{"encoding":904},[883,22997,22999],{"className":22998},[886],[888,23000,23001],{"xmlns":890},[892,23002,23003,23017],{},[895,23004,23005,23007,23010],{},[1711,23006,6740],{},[2111,23008,23009],{},"16,",[12366,23011,23012,23014],{"accent":1725},[2111,23013,6262],{},[1711,23015,23016],{},"ˉ",[902,23018,23019],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,23022,23024],{"className":23023},[886],[888,23025,23026],{"xmlns":890},[892,23027,23028,23036],{},[895,23029,23030,23032,23034],{},[898,23031,1940],{},[1711,23033,1726],{"separator":1725},[898,23035,2362],{},[902,23037,22830],{"encoding":904},[883,23039,23041],{"className":23040},[886],[888,23042,23043],{"xmlns":890},[892,23044,23045,23051],{},[895,23046,23047,23049],{},[1711,23048,2460],{},[2111,23050,4712],{},[902,23052,23053],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,23056,23058],{"className":23057},[886],[888,23059,23060],{"xmlns":890},[892,23061,23062,23074],{},[895,23063,23064,23066,23068,23070,23072],{},[1711,23065,1714],{"stretchy":1713},[2111,23067,2113],{},[1711,23069,1726],{"separator":1725},[2111,23071,4712],{},[1711,23073,1735],{"stretchy":1713},[902,23075,23076],{"encoding":904},"(0, 10)",[724,23078,23079,23080,12082,23098,23128,23129,1648,23132,23135,23136,12082,23160,1648,23163,23166],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,23081,23083],{"className":23082},[886],[888,23084,23085],{"xmlns":890},[892,23086,23087,23095],{},[895,23088,23089,23091,23093],{},[898,23090,1660],{},[1711,23092,1836],{},[2111,23094,2113],{},[902,23096,23097],{"encoding":904},"Y = 0",[883,23099,23101],{"className":23100},[886],[888,23102,23103],{"xmlns":890},[892,23104,23105,23125],{},[895,23106,23107,23109,23111,23113,23115,23117,23119,23121,23123],{},[898,23108,2362],{},[1711,23110,1714],{"stretchy":1713},[2111,23112,2113],{},[1711,23114,1735],{"stretchy":1713},[1711,23116,1836],{},[1711,23118,2460],{},[898,23120,2223],{},[1711,23122,2109],{},[2111,23124,2113],{},[902,23126,23127],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,23130,23131],{},"autonomních úsporách",[614,23133,23134],{},"autonomous savings","). Analogicky ",[883,23137,23139],{"className":23138},[886],[888,23140,23141],{"xmlns":890},[892,23142,23143,23157],{},[895,23144,23145,23147,23149,23151,23153,23155],{},[898,23146,1940],{},[1711,23148,1714],{"stretchy":1713},[2111,23150,2113],{},[1711,23152,1735],{"stretchy":1713},[1711,23154,1836],{},[898,23156,2223],{},[902,23158,23159],{"encoding":904},"C(0) = b",[38,23161,23162],{},"autonomní spotřeba",[614,23164,23165],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,23168,23170],{"id":23169},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,23172,23173,1700,23176,1648,23193,23196],{},[38,23174,23175],{},"Mezní sklon ke spotřebě",[883,23177,23179],{"className":23178},[886],[888,23180,23181],{"xmlns":890},[892,23182,23183,23191],{},[895,23184,23185,23187,23189],{},[898,23186,1790],{},[898,23188,7929],{},[898,23190,1940],{},[902,23192,21643],{"encoding":904},[614,23194,23195],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,23198,23199],{},[883,23200,23202],{"className":23201},[886],[888,23203,23204],{"xmlns":890},[892,23205,23206,23232],{},[895,23207,23208,23210,23212,23214,23216,23230],{},[898,23209,1790],{},[898,23211,7929],{},[898,23213,1940],{},[1711,23215,1836],{},[2525,23217,23218,23224],{},[895,23219,23220,23222],{},[898,23221,2098],{"mathvariant":2287},[898,23223,1940],{},[895,23225,23226,23228],{},[898,23227,2098],{"mathvariant":2287},[898,23229,1660],{},[898,23231,2186],{"mathvariant":2287},[902,23233,23234],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,23236,23237,1700,23240,1648,23258,23261],{},[38,23238,23239],{},"Mezní sklon k úsporám",[883,23241,23243],{"className":23242},[886],[888,23244,23245],{"xmlns":890},[892,23246,23247,23255],{},[895,23248,23249,23251,23253],{},[898,23250,1790],{},[898,23252,7929],{},[898,23254,2362],{},[902,23256,23257],{"encoding":904},"MPS",[614,23259,23260],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,23263,23264],{},[883,23265,23267],{"className":23266},[886],[888,23268,23269],{"xmlns":890},[892,23270,23271,23297],{},[895,23272,23273,23275,23277,23279,23281,23295],{},[898,23274,1790],{},[898,23276,7929],{},[898,23278,2362],{},[1711,23280,1836],{},[2525,23282,23283,23289],{},[895,23284,23285,23287],{},[898,23286,2098],{"mathvariant":2287},[898,23288,2362],{},[895,23290,23291,23293],{},[898,23292,2098],{"mathvariant":2287},[898,23294,1660],{},[898,23296,2186],{"mathvariant":2287},[902,23298,23299],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,23301,23302,23303,23361],{},"Z (7.2) plyne ",[883,23304,23306],{"className":23305},[886],[888,23307,23308],{"xmlns":890},[892,23309,23310,23358],{},[895,23311,23312,23326,23328,23342,23344],{},[2525,23313,23314,23320],{},[895,23315,23316,23318],{},[898,23317,2098],{"mathvariant":2287},[898,23319,1660],{},[895,23321,23322,23324],{},[898,23323,2098],{"mathvariant":2287},[898,23325,1660],{},[1711,23327,1836],{},[2525,23329,23330,23336],{},[895,23331,23332,23334],{},[898,23333,2098],{"mathvariant":2287},[898,23335,1940],{},[895,23337,23338,23340],{},[898,23339,2098],{"mathvariant":2287},[898,23341,1660],{},[1711,23343,2095],{},[2525,23345,23346,23352],{},[895,23347,23348,23350],{},[898,23349,2098],{"mathvariant":2287},[898,23351,2362],{},[895,23353,23354,23356],{},[898,23355,2098],{"mathvariant":2287},[898,23357,1660],{},[902,23359,23360],{"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",[724,23363,23364],{},[883,23365,23367],{"className":23366},[886],[888,23368,23369],{"xmlns":890},[892,23370,23371,23434],{},[895,23372,23373,23425,23427,23429,23432],{},[2505,23374,23375],{"notation":2507},[2509,23376,23377],{"scriptlevel":2113,"displaystyle":1713},[2509,23378,23379],{"scriptlevel":2113,"displaystyle":1713},[2509,23380,23381],{"scriptlevel":2113,"displaystyle":1725},[895,23382,23383,23385,23387,23389,23391,23393,23395,23397,23399,23401,23403,23405,23407,23409,23411,23413,23415,23417,23419,23421,23423],{},[898,23384,1790],{},[898,23386,7929],{},[898,23388,1940],{},[1711,23390,2095],{},[898,23392,1790],{},[898,23394,7929],{},[898,23396,2362],{},[1711,23398,1836],{},[2111,23400,2238],{},[1711,23402,1726],{"separator":1725},[2102,23404],{"width":2104},[898,23406,1790],{},[898,23408,7929],{},[898,23410,2362],{},[1711,23412,1836],{},[2111,23414,2238],{},[1711,23416,2460],{},[898,23418,1790],{},[898,23420,7929],{},[898,23422,1940],{},[898,23424,2186],{"mathvariant":2287},[2102,23426],{"width":2104},[1711,23428,1714],{"stretchy":1713},[2111,23430,23431],{},"7.5",[1711,23433,1735],{"stretchy":1713},[902,23435,23436],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,23438,23439,1700,23442,23465,23466,2009,23488,23514],{},[38,23440,23441],{},"Pro lineární model",[883,23443,23445],{"className":23444},[886],[888,23446,23447],{"xmlns":890},[892,23448,23449,23463],{},[895,23450,23451,23453,23455,23457,23459,23461],{},[898,23452,1940],{},[1711,23454,1836],{},[898,23456,207],{},[898,23458,1660],{},[1711,23460,2095],{},[898,23462,2223],{},[902,23464,22518],{"encoding":904}," vychází ",[883,23467,23469],{"className":23468},[886],[888,23470,23471],{"xmlns":890},[892,23472,23473,23485],{},[895,23474,23475,23477,23479,23481,23483],{},[898,23476,1790],{},[898,23478,7929],{},[898,23480,1940],{},[1711,23482,1836],{},[898,23484,207],{},[902,23486,23487],{"encoding":904},"MPC = a",[883,23489,23491],{"className":23490},[886],[888,23492,23493],{"xmlns":890},[892,23494,23495,23511],{},[895,23496,23497,23499,23501,23503,23505,23507,23509],{},[898,23498,1790],{},[898,23500,7929],{},[898,23502,2362],{},[1711,23504,1836],{},[2111,23506,2238],{},[1711,23508,2460],{},[898,23510,207],{},[902,23512,23513],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,23516,23517,23520,23521,23543,23544,23572],{},[38,23518,23519],{},"Interpretace diferenciálem."," Pro pevné ",[883,23522,23524],{"className":23523},[886],[888,23525,23526],{"xmlns":890},[892,23527,23528,23540],{},[895,23529,23530,23532,23534],{},[898,23531,1660],{},[1711,23533,1836],{},[1716,23535,23536,23538],{},[898,23537,1660],{},[1711,23539,1793],{},[902,23541,23542],{"encoding":904},"Y = Y^*"," udává ",[883,23545,23547],{"className":23546},[886],[888,23548,23549],{"xmlns":890},[892,23550,23551,23569],{},[895,23552,23553,23555,23557,23559,23561,23567],{},[898,23554,1790],{},[898,23556,7929],{},[898,23558,1940],{},[1711,23560,1714],{"stretchy":1713},[1716,23562,23563,23565],{},[898,23564,1660],{},[1711,23566,1793],{},[1711,23568,1735],{"stretchy":1713},[902,23570,23571],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,23574,23575],{},[883,23576,23578],{"className":23577},[886],[888,23579,23580],{"xmlns":890},[892,23581,23582,23636],{},[895,23583,23584,23586,23588,23590,23592,23594,23596,23602,23604,23606,23608,23610,23612,23614,23616,23618,23620,23622,23624,23626,23628,23630,23632,23634],{},[898,23585,6892],{"mathvariant":2287},[898,23587,1940],{},[1711,23589,6740],{},[898,23591,2098],{"mathvariant":2287},[898,23593,1940],{},[1711,23595,1836],{},[1716,23597,23598,23600],{},[898,23599,1940],{},[1711,23601,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,23603,1714],{"stretchy":1713},[898,23605,1660],{},[1711,23607,1735],{"stretchy":1713},[1942,23609,2519],{},[898,23611,2098],{"mathvariant":2287},[898,23613,1660],{},[1711,23615,1836],{},[898,23617,1790],{},[898,23619,7929],{},[898,23621,1940],{},[1711,23623,1714],{"stretchy":1713},[898,23625,1660],{},[1711,23627,1735],{"stretchy":1713},[1942,23629,2519],{},[898,23631,2098],{"mathvariant":2287},[898,23633,1660],{},[898,23635,2186],{"mathvariant":2287},[902,23637,23638],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,23640,23641,23642,23678,23679,23682],{},"Analogicky ",[883,23643,23645],{"className":23644},[886],[888,23646,23647],{"xmlns":890},[892,23648,23649,23675],{},[895,23650,23651,23653,23655,23657,23659,23661,23663,23665,23667,23669,23671,23673],{},[898,23652,6892],{"mathvariant":2287},[898,23654,2362],{},[1711,23656,6740],{},[898,23658,1790],{},[898,23660,7929],{},[898,23662,2362],{},[1711,23664,1714],{"stretchy":1713},[898,23666,1660],{},[1711,23668,1735],{"stretchy":1713},[1942,23670,2519],{},[898,23672,2098],{"mathvariant":2287},[898,23674,1660],{},[902,23676,23677],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,23680,1145],{"className":23681,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,23684,23686],{"id":23685},"příklad-72","Příklad 7.2",[724,23688,22853,23689,23724,23725,23744],{},[883,23690,23692],{"className":23691},[886],[888,23693,23694],{"xmlns":890},[892,23695,23696,23721],{},[895,23697,23698,23700,23702,23705,23711,23713,23715,23717,23719],{},[898,23699,1940],{},[1711,23701,1836],{},[2111,23703,23704],{},"0,001",[1716,23706,23707,23709],{},[898,23708,1660],{},[2111,23710,2963],{},[1711,23712,2095],{},[2111,23714,4491],{},[898,23716,1660],{},[1711,23718,2095],{},[2111,23720,7120],{},[902,23722,23723],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,23726,23728],{"className":23727},[886],[888,23729,23730],{"xmlns":890},[892,23731,23732,23741],{},[895,23733,23734,23736,23738],{},[898,23735,1660],{},[1711,23737,2109],{},[2111,23739,23740],{},"400",[902,23742,23743],{"encoding":904},"Y \u003C 400",") platí",[724,23746,23747],{},[883,23748,23750],{"className":23749},[886],[888,23751,23752],{"xmlns":890},[892,23753,23754,23791],{},[895,23755,23756,23758,23760,23762,23764,23778,23780,23783,23785,23787,23789],{},[898,23757,1790],{},[898,23759,7929],{},[898,23761,1940],{},[1711,23763,1836],{},[2525,23765,23766,23772],{},[895,23767,23768,23770],{},[898,23769,2098],{"mathvariant":2287},[898,23771,1940],{},[895,23773,23774,23776],{},[898,23775,2098],{"mathvariant":2287},[898,23777,1660],{},[1711,23779,1836],{},[2111,23781,23782],{},"0,002",[898,23784,1660],{},[1711,23786,2095],{},[2111,23788,4491],{},[1711,23790,1726],{"separator":1725},[902,23792,23793],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,23795,23796],{},[883,23797,23799],{"className":23798},[886],[888,23800,23801],{"xmlns":890},[892,23802,23803,23836],{},[895,23804,23805,23807,23809,23811,23813,23815,23817,23819,23821,23823,23825,23827,23829,23831,23833],{},[898,23806,1790],{},[898,23808,7929],{},[898,23810,2362],{},[1711,23812,1836],{},[2111,23814,2238],{},[1711,23816,2460],{},[898,23818,1790],{},[898,23820,7929],{},[898,23822,1940],{},[1711,23824,1836],{},[1711,23826,2460],{},[2111,23828,23782],{},[898,23830,1660],{},[1711,23832,2095],{},[2111,23834,23835],{},"0,8.",[902,23837,23838],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,23840,23841,23921,24000],{},[123,23842,23843,1343,23871,23899,23900,12082,23918,2186],{},[883,23844,23846],{"className":23845},[886],[888,23847,23848],{"xmlns":890},[892,23849,23850,23868],{},[895,23851,23852,23854,23856,23858,23860,23862,23864,23866],{},[898,23853,1790],{},[898,23855,7929],{},[898,23857,1940],{},[1711,23859,1714],{"stretchy":1713},[2111,23861,4282],{},[1711,23863,1735],{"stretchy":1713},[1711,23865,1836],{},[2111,23867,22869],{},[902,23869,23870],{"encoding":904},"MPC(100) = 0{,}4",[883,23872,23874],{"className":23873},[886],[888,23875,23876],{"xmlns":890},[892,23877,23878,23896],{},[895,23879,23880,23882,23884,23886,23888,23890,23892,23894],{},[898,23881,1790],{},[898,23883,7929],{},[898,23885,2362],{},[1711,23887,1714],{"stretchy":1713},[2111,23889,4282],{},[1711,23891,1735],{"stretchy":1713},[1711,23893,1836],{},[2111,23895,22919],{},[902,23897,23898],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,23901,23903],{"className":23902},[886],[888,23904,23905],{"xmlns":890},[892,23906,23907,23915],{},[895,23908,23909,23911,23913],{},[898,23910,1660],{},[1711,23912,1836],{},[2111,23914,4282],{},[902,23916,23917],{"encoding":904},"Y = 100",[38,23919,23920],{},"větší sklon k úsporám",[123,23922,23923,1343,23951,23899,23979,12082,23997,2186],{},[883,23924,23926],{"className":23925},[886],[888,23927,23928],{"xmlns":890},[892,23929,23930,23948],{},[895,23931,23932,23934,23936,23938,23940,23942,23944,23946],{},[898,23933,1790],{},[898,23935,7929],{},[898,23937,1940],{},[1711,23939,1714],{"stretchy":1713},[2111,23941,12357],{},[1711,23943,1735],{"stretchy":1713},[1711,23945,1836],{},[2111,23947,22919],{},[902,23949,23950],{"encoding":904},"MPC(200) = 0{,}6",[883,23952,23954],{"className":23953},[886],[888,23955,23956],{"xmlns":890},[892,23957,23958,23976],{},[895,23959,23960,23962,23964,23966,23968,23970,23972,23974],{},[898,23961,1790],{},[898,23963,7929],{},[898,23965,2362],{},[1711,23967,1714],{"stretchy":1713},[2111,23969,12357],{},[1711,23971,1735],{"stretchy":1713},[1711,23973,1836],{},[2111,23975,22869],{},[902,23977,23978],{"encoding":904},"MPS(200) = 0{,}4",[883,23980,23982],{"className":23981},[886],[888,23983,23984],{"xmlns":890},[892,23985,23986,23994],{},[895,23987,23988,23990,23992],{},[898,23989,1660],{},[1711,23991,1836],{},[2111,23993,12357],{},[902,23995,23996],{"encoding":904},"Y = 200",[38,23998,23999],{},"větší sklon ke spotřebě",[123,24001,24002,24003,24021,24022,1797],{},"Přesně při ",[883,24004,24006],{"className":24005},[886],[888,24007,24008],{"xmlns":890},[892,24009,24010,24018],{},[895,24011,24012,24014,24016],{},[898,24013,1660],{},[1711,24015,1836],{},[2111,24017,12781],{},[902,24019,24020],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,24023,24025],{"className":24024},[886],[888,24026,24027],{"xmlns":890},[892,24028,24029,24049],{},[895,24030,24031,24033,24035,24037,24039,24041,24043,24045,24047],{},[898,24032,1790],{},[898,24034,7929],{},[898,24036,1940],{},[1711,24038,1836],{},[898,24040,1790],{},[898,24042,7929],{},[898,24044,2362],{},[1711,24046,1836],{},[2111,24048,8993],{},[902,24050,24051],{"encoding":904},"MPC = MPS = 0{,}5",[724,24053,24054,24055,24072,24073,24087,24088,6696,24101,24115,24116,24129,24130,24171],{},"Interpretace: při ",[883,24056,24058],{"className":24057},[886],[888,24059,24060],{"xmlns":890},[892,24061,24062,24070],{},[895,24063,24064,24066,24068],{},[898,24065,1660],{},[1711,24067,1836],{},[2111,24069,4282],{},[902,24071,23917],{"encoding":904}," se spotřeba mění ",[883,24074,24076],{"className":24075},[886],[888,24077,24078],{"xmlns":890},[892,24079,24080,24084],{},[895,24081,24082],{},[2111,24083,22869],{},[902,24085,24086],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,24089,24091],{"className":24090},[886],[888,24092,24093],{"xmlns":890},[892,24094,24095,24099],{},[895,24096,24097],{},[2111,24098,4282],{},[902,24100,4282],{"encoding":904},[883,24102,24104],{"className":24103},[886],[888,24105,24106],{"xmlns":890},[892,24107,24108,24113],{},[895,24109,24110],{},[2111,24111,24112],{},"101",[902,24114,24112],{"encoding":904},", změní se spotřeba přibližně o ",[883,24117,24119],{"className":24118},[886],[888,24120,24121],{"xmlns":890},[892,24122,24123,24127],{},[895,24124,24125],{},[2111,24126,22869],{},[902,24128,24086],{"encoding":904},". Skutečná změna ",[883,24131,24133],{"className":24132},[886],[888,24134,24135],{"xmlns":890},[892,24136,24137,24168],{},[895,24138,24139,24141,24143,24145,24147,24149,24151,24153,24155,24157,24159,24161,24163,24165],{},[898,24140,6892],{"mathvariant":2287},[898,24142,1940],{},[1711,24144,1836],{},[898,24146,1940],{},[1711,24148,1714],{"stretchy":1713},[2111,24150,24112],{},[1711,24152,1735],{"stretchy":1713},[1711,24154,2460],{},[898,24156,1940],{},[1711,24158,1714],{"stretchy":1713},[2111,24160,4282],{},[1711,24162,1735],{"stretchy":1713},[1711,24164,1836],{},[2111,24166,24167],{},"0,401",[902,24169,24170],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,24173,24174,24175],{},"Obecný trend: ",[38,24176,24177],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,24179,24181],{"id":24180},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,24183,24184,24185,1648,24188,24191,24192,1648,24195,1772,24198,1648,24201,24204],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,24186,24187],{},"makroekonomická rovnováha",[614,24189,24190],{},"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 ",[38,24193,24194],{},"agregátní poptávky",[614,24196,24197],{},"aggregate demand",[38,24199,24200],{},"agregátní nabídky",[614,24202,24203],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,24206,24208],{"id":24207},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,24210,24211],{},[1801,24212],{"alt":24213,"className":24214,"src":24215},"imek-keynesian-kriz",[210,1805],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,24217,24219],{"id":24218},"zadání-modelu","Zadání modelu",[724,24221,24222,24223,24236,24237,24250],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,24224,24226],{"className":24225},[886],[888,24227,24228],{"xmlns":890},[892,24229,24230,24234],{},[895,24231,24232],{},[898,24233,1940],{},[902,24235,1940],{"encoding":904}," a investice ",[883,24238,24240],{"className":24239},[886],[888,24241,24242],{"xmlns":890},[892,24243,24244,24248],{},[895,24245,24246],{},[898,24247,1833],{},[902,24249,1833],{"encoding":904},". Podmínka rovnováhy:",[724,24252,24253],{},[883,24254,24256],{"className":24255},[886],[888,24257,24258],{"xmlns":890},[892,24259,24260,24283],{},[895,24261,24262,24264,24266,24268,24270,24272,24274,24276,24278,24281],{},[898,24263,1660],{},[1711,24265,1836],{},[898,24267,1940],{},[1711,24269,2095],{},[898,24271,1833],{},[898,24273,2186],{"mathvariant":2287},[2102,24275],{"width":2104},[1711,24277,1714],{"stretchy":1713},[2111,24279,24280],{},"7.6",[1711,24282,1735],{"stretchy":1713},[902,24284,24285],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,24287,24289],{"id":24288},"soustava-rovnic","Soustava rovnic",[724,24291,24292,24293,24314,24315,24339],{},"Pro pevně zadané (plánované) investice ",[883,24294,24296],{"className":24295},[886],[888,24297,24298],{"xmlns":890},[892,24299,24300,24312],{},[895,24301,24302,24304,24306],{},[898,24303,1833],{},[1711,24305,1836],{},[1716,24307,24308,24310],{},[898,24309,1833],{},[1711,24311,1793],{},[902,24313,1845],{"encoding":904}," a funkci spotřeby ",[883,24316,24318],{"className":24317},[886],[888,24319,24320],{"xmlns":890},[892,24321,24322,24336],{},[895,24323,24324,24326,24328,24330,24332,24334],{},[898,24325,1940],{},[1711,24327,1836],{},[898,24329,1940],{},[1711,24331,1714],{"stretchy":1713},[898,24333,1660],{},[1711,24335,1735],{"stretchy":1713},[902,24337,24338],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,24341,24342],{},[883,24343,24345],{"className":24344},[886],[888,24346,24347],{"xmlns":890},[892,24348,24349,24425],{},[895,24350,24351,24416,24418,24420,24423],{},[24352,24353,24356,24388],"mtable",{"rowspacing":24354,"columnalign":24355,"columnspacing":5224},"0.25em","right left",[24357,24358,24359,24366],"mtr",{},[24360,24361,24362],"mtd",{},[2509,24363,24364],{"scriptlevel":2113,"displaystyle":1725},[898,24365,1660],{},[24360,24367,24368],{},[2509,24369,24370],{"scriptlevel":2113,"displaystyle":1725},[895,24371,24372,24374,24376,24378,24380,24386],{},[895,24373],{},[1711,24375,1836],{},[898,24377,1940],{},[1711,24379,2095],{},[1716,24381,24382,24384],{},[898,24383,1833],{},[1711,24385,1793],{},[1711,24387,1726],{"separator":1725},[24357,24389,24390,24396],{},[24360,24391,24392],{},[2509,24393,24394],{"scriptlevel":2113,"displaystyle":1725},[898,24395,1940],{},[24360,24397,24398],{},[2509,24399,24400],{"scriptlevel":2113,"displaystyle":1725},[895,24401,24402,24404,24406,24408,24410,24412,24414],{},[895,24403],{},[1711,24405,1836],{},[898,24407,1940],{},[1711,24409,1714],{"stretchy":1713},[898,24411,1660],{},[1711,24413,1735],{"stretchy":1713},[1711,24415,1726],{"separator":1725},[2102,24417],{"width":2104},[1711,24419,1714],{"stretchy":1713},[2111,24421,24422],{},"7.7",[1711,24424,1735],{"stretchy":1713},[902,24426,24427],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,24429,24430,24431,1700,24433,2009,24450,1700,24453,2186],{},"jejímž řešením jsou ",[38,24432,3569],{},[883,24434,24436],{"className":24435},[886],[888,24437,24438],{"xmlns":890},[892,24439,24440,24448],{},[895,24441,24442],{},[1716,24443,24444,24446],{},[898,24445,1660],{},[898,24447,1722],{},[902,24449,3587],{"encoding":904},[38,24451,24452],{},"rovnovážná spotřeba",[883,24454,24456],{"className":24455},[886],[888,24457,24458],{"xmlns":890},[892,24459,24460,24468],{},[895,24461,24462],{},[1716,24463,24464,24466],{},[898,24465,1940],{},[898,24467,1722],{},[902,24469,3646],{"encoding":904},[198,24471,24473,24474],{"id":24472},"výpočet-yeye","Výpočet ",[883,24475,24477],{"className":24476},[886],[888,24478,24479],{"xmlns":890},[892,24480,24481,24489],{},[895,24482,24483],{},[1716,24484,24485,24487],{},[898,24486,1660],{},[898,24488,1722],{},[902,24490,3587],{"encoding":904},[724,24492,24493,24494,24517,24518,11665,24550],{},"Pro lineární spotřebu ",[883,24495,24497],{"className":24496},[886],[888,24498,24499],{"xmlns":890},[892,24500,24501,24515],{},[895,24502,24503,24505,24507,24509,24511,24513],{},[898,24504,1940],{},[1711,24506,1836],{},[898,24508,207],{},[898,24510,1660],{},[1711,24512,2095],{},[898,24514,2223],{},[902,24516,22518],{"encoding":904}," plyne z (7.7) rovnice ",[883,24519,24521],{"className":24520},[886],[888,24522,24523],{"xmlns":890},[892,24524,24525,24547],{},[895,24526,24527,24529,24531,24533,24535,24537,24539,24541],{},[898,24528,1660],{},[1711,24530,1836],{},[898,24532,207],{},[898,24534,1660],{},[1711,24536,2095],{},[898,24538,2223],{},[1711,24540,2095],{},[1716,24542,24543,24545],{},[898,24544,1833],{},[1711,24546,1793],{},[902,24548,24549],{"encoding":904},"Y = aY + b + I^*",[38,24551,24552],{},"redukovaný tvar",[724,24554,24555],{},[883,24556,24558],{"className":24557},[886],[888,24559,24560],{"xmlns":890},[892,24561,24562,24610],{},[895,24563,24564],{},[2505,24565,24566],{"notation":2507},[2509,24567,24568],{"scriptlevel":2113,"displaystyle":1713},[2509,24569,24570],{"scriptlevel":2113,"displaystyle":1713},[2509,24571,24572],{"scriptlevel":2113,"displaystyle":1725},[895,24573,24574,24576,24582,24584,24606,24608],{},[1942,24575,2519],{},[1716,24577,24578,24580],{},[898,24579,1660],{},[898,24581,1722],{},[1711,24583,1836],{},[2525,24585,24586,24598],{},[895,24587,24588,24590,24592],{},[898,24589,2223],{},[1711,24591,2095],{},[1716,24593,24594,24596],{},[898,24595,1833],{},[1711,24597,1793],{},[895,24599,24600,24602,24604],{},[2111,24601,2238],{},[1711,24603,2460],{},[898,24605,207],{},[898,24607,2186],{"mathvariant":2287},[1942,24609,2519],{},[902,24611,24612],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,24614,24616],{"id":24615},"příklad-73","Příklad 7.3",[724,24618,24619,24620,12082,24637,2009,24661,24687],{},"V modelu ",[883,24621,24623],{"className":24622},[886],[888,24624,24625],{"xmlns":890},[892,24626,24627,24635],{},[895,24628,24629,24631,24633],{},[898,24630,1940],{},[1942,24632,1944],{},[898,24634,1833],{},[902,24636,1949],{"encoding":904},[883,24638,24640],{"className":24639},[886],[888,24641,24642],{"xmlns":890},[892,24643,24644,24658],{},[895,24645,24646,24648,24650,24652,24654,24656],{},[898,24647,1940],{},[1711,24649,1836],{},[2111,24651,22919],{},[898,24653,1660],{},[1711,24655,2095],{},[2111,24657,4712],{},[902,24659,24660],{"encoding":904},"C = 0{,}6Y + 10",[883,24662,24664],{"className":24663},[886],[888,24665,24666],{"xmlns":890},[892,24667,24668,24684],{},[895,24669,24670,24672,24674,24676,24678],{},[898,24671,1833],{},[1711,24673,1836],{},[2111,24675,7505],{},[1711,24677,1836],{},[1716,24679,24680,24682],{},[898,24681,1833],{},[1711,24683,1793],{},[902,24685,24686],{"encoding":904},"I = 12 = I^*",". Soustava",[724,24689,24690],{},[883,24691,24693],{"className":24692},[886],[888,24694,24695],{"xmlns":890},[892,24696,24697,24753],{},[24352,24698,24699,24725],{"rowspacing":24354,"columnalign":24355,"columnspacing":5224},[24357,24700,24701,24707],{},[24360,24702,24703],{},[2509,24704,24705],{"scriptlevel":2113,"displaystyle":1725},[898,24706,1660],{},[24360,24708,24709],{},[2509,24710,24711],{"scriptlevel":2113,"displaystyle":1725},[895,24712,24713,24715,24717,24719,24721,24723],{},[895,24714],{},[1711,24716,1836],{},[898,24718,1940],{},[1711,24720,2095],{},[2111,24722,7505],{},[1711,24724,1726],{"separator":1725},[24357,24726,24727,24733],{},[24360,24728,24729],{},[2509,24730,24731],{"scriptlevel":2113,"displaystyle":1725},[898,24732,1940],{},[24360,24734,24735],{},[2509,24736,24737],{"scriptlevel":2113,"displaystyle":1725},[895,24738,24739,24741,24743,24745,24747,24749,24751],{},[895,24740],{},[1711,24742,1836],{},[2111,24744,22919],{},[898,24746,1660],{},[1711,24748,2095],{},[2111,24750,4712],{},[1711,24752,1726],{"separator":1725},[902,24754,24755],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,24757,24758,24759,1343,24782,24805,24806,1797],{},"má řešení ",[883,24760,24762],{"className":24761},[886],[888,24763,24764],{"xmlns":890},[892,24765,24766,24779],{},[895,24767,24768,24774,24776],{},[1716,24769,24770,24772],{},[898,24771,1660],{},[898,24773,1722],{},[1711,24775,1836],{},[2111,24777,24778],{},"55",[902,24780,24781],{"encoding":904},"Y^E = 55",[883,24783,24785],{"className":24784},[886],[888,24786,24787],{"xmlns":890},[892,24788,24789,24802],{},[895,24790,24791,24797,24799],{},[1716,24792,24793,24795],{},[898,24794,1940],{},[898,24796,1722],{},[1711,24798,1836],{},[2111,24800,24801],{},"43",[902,24803,24804],{"encoding":904},"C^E = 43"," (a ",[883,24807,24809],{"className":24808},[886],[888,24810,24811],{"xmlns":890},[892,24812,24813,24825],{},[895,24814,24815,24821,24823],{},[1716,24816,24817,24819],{},[898,24818,2362],{},[898,24820,1722],{},[1711,24822,1836],{},[2111,24824,7505],{},[902,24826,24827],{"encoding":904},"S^E = 12",[724,24829,24830],{},[614,24831,24832,24833,24855,24856,1772,24877,24900,24901,2186],{},"Obrázek 7.5 — Přímky ",[883,24834,24836],{"className":24835},[886],[888,24837,24838],{"xmlns":890},[892,24839,24840,24852],{},[895,24841,24842,24844,24846,24848,24850],{},[898,24843,1940],{},[1711,24845,1836],{},[898,24847,1660],{},[1711,24849,2460],{},[2111,24851,7505],{},[902,24853,24854],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,24857,24859],{"className":24858},[886],[888,24860,24861],{"xmlns":890},[892,24862,24863,24875],{},[895,24864,24865,24867,24869,24871,24873],{},[898,24866,1660],{},[1711,24868,1836],{},[898,24870,1940],{},[1711,24872,2095],{},[898,24874,1833],{},[902,24876,4436],{"encoding":904},[883,24878,24880],{"className":24879},[886],[888,24881,24882],{"xmlns":890},[892,24883,24884,24898],{},[895,24885,24886,24888,24890,24892,24894,24896],{},[898,24887,1940],{},[1711,24889,1836],{},[2111,24891,22919],{},[898,24893,1660],{},[1711,24895,2095],{},[2111,24897,4712],{},[902,24899,24660],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,24902,24904],{"className":24903},[886],[888,24905,24906],{"xmlns":890},[892,24907,24908,24940],{},[895,24909,24910,24912,24918,24920,24926,24928,24930,24932,24934,24936,24938],{},[1711,24911,5144],{"stretchy":1713},[1716,24913,24914,24916],{},[898,24915,1660],{},[898,24917,1722],{},[1711,24919,1726],{"separator":1725},[1716,24921,24922,24924],{},[898,24923,1940],{},[898,24925,1722],{},[1711,24927,5163],{"stretchy":1713},[1711,24929,1836],{},[1711,24931,5144],{"stretchy":1713},[2111,24933,24778],{},[1711,24935,1726],{"separator":1725},[2111,24937,24801],{},[1711,24939,5163],{"stretchy":1713},[902,24941,24942],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,24944,24945,24948,24949,24966,24967,2186],{},[38,24946,24947],{},"Komentář k přechodu."," Model ",[883,24950,24952],{"className":24951},[886],[888,24953,24954],{"xmlns":890},[892,24955,24956,24964],{},[895,24957,24958,24960,24962],{},[898,24959,1940],{},[1942,24961,1944],{},[898,24963,1833],{},[902,24965,1949],{"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 ",[38,24968,24969,24970],{},"model ",[883,24971,24973],{"className":24972},[886],[888,24974,24975],{"xmlns":890},[892,24976,24977,24989],{},[895,24978,24979,24981,24983,24985,24987],{},[898,24980,1940],{},[1942,24982,1944],{},[898,24984,1833],{},[1942,24986,1944],{},[898,24988,1755],{},[902,24990,21818],{"encoding":904},[115,24992,24994],{"id":24993},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,24996,24219],{"id":24997},"zadání-modelu-1",[724,24999,25000,25001,25018,25019,1700,25022,1648,25035,25038],{},"Rozšíření modelu ",[883,25002,25004],{"className":25003},[886],[888,25005,25006],{"xmlns":890},[892,25007,25008,25016],{},[895,25009,25010,25012,25014],{},[898,25011,1940],{},[1942,25013,1944],{},[898,25015,1833],{},[902,25017,1949],{"encoding":904}," o ",[38,25020,25021],{},"vládní výdaje",[883,25023,25025],{"className":25024},[886],[888,25026,25027],{"xmlns":890},[892,25028,25029,25033],{},[895,25030,25031],{},[898,25032,1755],{},[902,25034,1755],{"encoding":904},[614,25036,25037],{},"government expenditure","). Podmínka rovnováhy:",[724,25040,25041],{},[883,25042,25044],{"className":25043},[886],[888,25045,25046],{"xmlns":890},[892,25047,25048,25075],{},[895,25049,25050,25052,25054,25056,25058,25060,25062,25064,25066,25068,25070,25073],{},[898,25051,1660],{},[1711,25053,1836],{},[898,25055,1940],{},[1711,25057,2095],{},[898,25059,1833],{},[1711,25061,2095],{},[898,25063,1755],{},[898,25065,2186],{"mathvariant":2287},[2102,25067],{"width":2104},[1711,25069,1714],{"stretchy":1713},[2111,25071,25072],{},"7.8",[1711,25074,1735],{"stretchy":1713},[902,25076,25077],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,25079,25080,25081,1700,25084,1648,25097,25100],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,25082,25083],{},"zdaněním domácností",[883,25085,25087],{"className":25086},[886],[888,25088,25089],{"xmlns":890},[892,25090,25091,25095],{},[895,25092,25093],{},[898,25094,1769],{},[902,25096,1769],{"encoding":904},[614,25098,25099],{},"taxation","). Zdanění bývá:",[120,25102,25103,25136,25161],{},[123,25104,25105,25106,1726],{},"úměrné důchodu: ",[883,25107,25109],{"className":25108},[886],[888,25110,25111],{"xmlns":890},[892,25112,25113,25133],{},[895,25114,25115,25117,25119,25121,25123,25125,25127,25129,25131],{},[898,25116,1769],{},[1711,25118,1836],{},[898,25120,1769],{},[1711,25122,1714],{"stretchy":1713},[898,25124,1660],{},[1711,25126,1735],{"stretchy":1713},[1711,25128,1836],{},[898,25130,22453],{},[898,25132,1660],{},[902,25134,25135],{"encoding":904},"T = T(Y) = tY",[123,25137,25138,25139,1726],{},"fixní: ",[883,25140,25142],{"className":25141},[886],[888,25143,25144],{"xmlns":890},[892,25145,25146,25158],{},[895,25147,25148,25150,25152],{},[898,25149,1769],{},[1711,25151,1836],{},[1716,25153,25154,25156],{},[898,25155,1769],{},[1711,25157,1793],{},[902,25159,25160],{"encoding":904},"T = T^*",[123,25162,25163,25164,25192,25193,2186],{},"kombinované: ",[883,25165,25167],{"className":25166},[886],[888,25168,25169],{"xmlns":890},[892,25170,25171,25189],{},[895,25172,25173,25175,25177,25183,25185,25187],{},[898,25174,1769],{},[1711,25176,1836],{},[1716,25178,25179,25181],{},[898,25180,1769],{},[1711,25182,1793],{},[1711,25184,2095],{},[898,25186,22453],{},[898,25188,1660],{},[902,25190,25191],{"encoding":904},"T = T^* + tY",", kde ",[883,25194,25196],{"className":25195},[886],[888,25197,25198],{"xmlns":890},[892,25199,25200,25212],{},[895,25201,25202,25204,25206,25208,25210],{},[2111,25203,2113],{},[1711,25205,11659],{},[898,25207,22453],{},[1711,25209,2109],{},[2111,25211,2238],{},[902,25213,25214],{"encoding":904},"0 \\le t \u003C 1",[1921,25216,25217],{},[724,25218,25219,25221,25222,25243,25244,25247,25248,25261,25262,1772,25288,1700,25291,25317,25318,25346,25347,2009,25360,25378],{},[883,25220,1927],{}," Pozor na disponibilní důchod\nV modelu ",[883,25223,25225],{"className":25224},[886],[888,25226,25227],{"xmlns":890},[892,25228,25229,25241],{},[895,25230,25231,25233,25235,25237,25239],{},[898,25232,1940],{},[1942,25234,1944],{},[898,25236,1833],{},[1942,25238,1944],{},[898,25240,1755],{},[902,25242,21818],{"encoding":904}," je nutné ",[38,25245,25246],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,25249,25251],{"className":25250},[886],[888,25252,25253],{"xmlns":890},[892,25254,25255,25259],{},[895,25256,25257],{},[898,25258,1660],{},[902,25260,1660],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,25263,25265],{"className":25264},[886],[888,25266,25267],{"xmlns":890},[892,25268,25269,25285],{},[895,25270,25271,25273,25275,25277,25279,25281,25283],{},[898,25272,1660],{},[1711,25274,1836],{},[898,25276,1940],{},[1711,25278,2095],{},[898,25280,1833],{},[1711,25282,2095],{},[898,25284,1755],{},[902,25286,25287],{"encoding":904},"Y = C + I + G",[38,25289,25290],{},"disponibilní důchod",[883,25292,25294],{"className":25293},[886],[888,25295,25296],{"xmlns":890},[892,25297,25298,25314],{},[895,25299,25300,25306,25308,25310,25312],{},[2884,25301,25302,25304],{},[898,25303,1660],{},[898,25305,2778],{},[1711,25307,1836],{},[898,25309,1660],{},[1711,25311,2460],{},[898,25313,1769],{},[902,25315,25316],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,25319,25321],{"className":25320},[886],[888,25322,25323],{"xmlns":890},[892,25324,25325,25343],{},[895,25326,25327,25329,25331,25333,25335,25341],{},[898,25328,1940],{},[1711,25330,1836],{},[898,25332,1940],{},[1711,25334,1714],{"stretchy":1713},[2884,25336,25337,25339],{},[898,25338,1660],{},[898,25340,2778],{},[1711,25342,1735],{"stretchy":1713},[902,25344,25345],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,25348,25350],{"className":25349},[886],[888,25351,25352],{"xmlns":890},[892,25353,25354,25358],{},[895,25355,25356],{},[898,25357,1660],{},[902,25359,1660],{"encoding":904},[883,25361,25363],{"className":25362},[886],[888,25364,25365],{"xmlns":890},[892,25366,25367,25375],{},[895,25368,25369],{},[2884,25370,25371,25373],{},[898,25372,1660],{},[898,25374,2778],{},[902,25376,25377],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,25380,25381,1648,25384,1735],{},[38,25382,25383],{},"Disponibilní důchod",[614,25385,25386],{},"disposable income",[724,25388,25389],{},[883,25390,25392],{"className":25391},[886],[888,25393,25394],{"xmlns":890},[892,25395,25396,25412],{},[895,25397,25398,25404,25406,25408,25410],{},[2884,25399,25400,25402],{},[898,25401,1660],{},[898,25403,2778],{},[1711,25405,1836],{},[898,25407,1660],{},[1711,25409,2460],{},[898,25411,1769],{},[902,25413,25316],{"encoding":904},[724,25415,25416,25417,2186],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,25418,25420],{"className":25419},[886],[888,25421,25422],{"xmlns":890},[892,25423,25424,25442],{},[895,25425,25426,25428,25430,25432,25434,25440],{},[898,25427,1940],{},[1711,25429,1836],{},[898,25431,1940],{},[1711,25433,1714],{"stretchy":1713},[2884,25435,25436,25438],{},[898,25437,1660],{},[898,25439,2778],{},[1711,25441,1735],{"stretchy":1713},[902,25443,25345],{"encoding":904},[198,25445,24289],{"id":25446},"soustava-rovnic-1",[724,25448,25449,25450,1343,25471,25493,25494,2062],{},"Pro pevně zadané ",[883,25451,25453],{"className":25452},[886],[888,25454,25455],{"xmlns":890},[892,25456,25457,25469],{},[895,25458,25459,25461,25463],{},[898,25460,1833],{},[1711,25462,1836],{},[1716,25464,25465,25467],{},[898,25466,1833],{},[1711,25468,1793],{},[902,25470,1845],{"encoding":904},[883,25472,25474],{"className":25473},[886],[888,25475,25476],{"xmlns":890},[892,25477,25478,25490],{},[895,25479,25480,25482,25484],{},[898,25481,1755],{},[1711,25483,1836],{},[1716,25485,25486,25488],{},[898,25487,1755],{},[1711,25489,1793],{},[902,25491,25492],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,25495,25497],{"className":25496},[886],[888,25498,25499],{"xmlns":890},[892,25500,25501,25521],{},[895,25502,25503,25505,25507,25509,25511,25517,25519],{},[898,25504,1660],{},[1711,25506,1726],{"separator":1725},[898,25508,1940],{},[1711,25510,1726],{"separator":1725},[2884,25512,25513,25515],{},[898,25514,1660],{},[898,25516,2778],{},[1711,25518,1726],{"separator":1725},[898,25520,1769],{},[902,25522,25523],{"encoding":904},"Y, C, Y_D, T",[724,25525,25526],{},[883,25527,25529],{"className":25528},[886],[888,25530,25531],{"xmlns":890},[892,25532,25533,25674],{},[895,25534,25535,25665,25667,25669,25672],{},[24352,25536,25537,25575,25603,25635],{"rowspacing":24354,"columnalign":24355,"columnspacing":5224},[24357,25538,25539,25545],{},[24360,25540,25541],{},[2509,25542,25543],{"scriptlevel":2113,"displaystyle":1725},[898,25544,1660],{},[24360,25546,25547],{},[2509,25548,25549],{"scriptlevel":2113,"displaystyle":1725},[895,25550,25551,25553,25555,25557,25559,25565,25567,25573],{},[895,25552],{},[1711,25554,1836],{},[898,25556,1940],{},[1711,25558,2095],{},[1716,25560,25561,25563],{},[898,25562,1833],{},[1711,25564,1793],{},[1711,25566,2095],{},[1716,25568,25569,25571],{},[898,25570,1755],{},[1711,25572,1793],{},[1711,25574,1726],{"separator":1725},[24357,25576,25577,25583],{},[24360,25578,25579],{},[2509,25580,25581],{"scriptlevel":2113,"displaystyle":1725},[898,25582,1769],{},[24360,25584,25585],{},[2509,25586,25587],{"scriptlevel":2113,"displaystyle":1725},[895,25588,25589,25591,25593,25595,25597,25599,25601],{},[895,25590],{},[1711,25592,1836],{},[898,25594,1769],{},[1711,25596,1714],{"stretchy":1713},[898,25598,1660],{},[1711,25600,1735],{"stretchy":1713},[1711,25602,1726],{"separator":1725},[24357,25604,25605,25611],{},[24360,25606,25607],{},[2509,25608,25609],{"scriptlevel":2113,"displaystyle":1725},[898,25610,1940],{},[24360,25612,25613],{},[2509,25614,25615],{"scriptlevel":2113,"displaystyle":1725},[895,25616,25617,25619,25621,25623,25625,25631,25633],{},[895,25618],{},[1711,25620,1836],{},[898,25622,1940],{},[1711,25624,1714],{"stretchy":1713},[2884,25626,25627,25629],{},[898,25628,1660],{},[898,25630,2778],{},[1711,25632,1735],{"stretchy":1713},[1711,25634,1726],{"separator":1725},[24357,25636,25637,25647],{},[24360,25638,25639],{},[2509,25640,25641],{"scriptlevel":2113,"displaystyle":1725},[2884,25642,25643,25645],{},[898,25644,1660],{},[898,25646,2778],{},[24360,25648,25649],{},[2509,25650,25651],{"scriptlevel":2113,"displaystyle":1725},[895,25652,25653,25655,25657,25659,25661,25663],{},[895,25654],{},[1711,25656,1836],{},[898,25658,1660],{},[1711,25660,2460],{},[898,25662,1769],{},[1711,25664,1726],{"separator":1725},[2102,25666],{"width":2104},[1711,25668,1714],{"stretchy":1713},[2111,25670,25671],{},"7.9",[1711,25673,1735],{"stretchy":1713},[902,25675,25676],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,25678,25679,25680,25724,25725,2186],{},"s řešeními ",[883,25681,25683],{"className":25682},[886],[888,25684,25685],{"xmlns":890},[892,25686,25687,25721],{},[895,25688,25689,25695,25697,25703,25705,25711,25713],{},[1716,25690,25691,25693],{},[898,25692,1660],{},[898,25694,1722],{},[1711,25696,1726],{"separator":1725},[1716,25698,25699,25701],{},[898,25700,1940],{},[898,25702,1722],{},[1711,25704,1726],{"separator":1725},[1716,25706,25707,25709],{},[898,25708,1769],{},[898,25710,1722],{},[1711,25712,1726],{"separator":1725},[13142,25714,25715,25717,25719],{},[898,25716,1660],{},[898,25718,2778],{},[898,25720,1722],{},[902,25722,25723],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,25726,25728],{"className":25727},[886],[888,25729,25730],{"xmlns":890},[892,25731,25732,25758],{},[895,25733,25734,25740,25742,25750,25752],{},[1716,25735,25736,25738],{},[898,25737,2362],{},[898,25739,1722],{},[1711,25741,1836],{},[13142,25743,25744,25746,25748],{},[898,25745,1660],{},[898,25747,2778],{},[898,25749,1722],{},[1711,25751,2460],{},[1716,25753,25754,25756],{},[898,25755,1940],{},[898,25757,1722],{},[902,25759,25760],{"encoding":904},"S^E = Y_D^E - C^E",[1921,25762,25763,25768],{},[724,25764,25765,25767],{},[883,25766,3872],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,25769,25770,25793,25876,25931,26021],{},[123,25771,25772,25775,25776,2186],{},[38,25773,25774],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,25777,25779],{"className":25778},[886],[888,25780,25781],{"xmlns":890},[892,25782,25783,25791],{},[895,25784,25785],{},[2884,25786,25787,25789],{},[898,25788,1660],{},[898,25790,2778],{},[902,25792,25377],{"encoding":904},[123,25794,25795,25844,25845,25862,25863,2186],{},[38,25796,25797,25798,25818,25819],{},"Dosaď ",[883,25799,25801],{"className":25800},[886],[888,25802,25803],{"xmlns":890},[892,25804,25805,25815],{},[895,25806,25807,25809,25811,25813],{},[898,25808,1769],{},[1711,25810,1714],{"stretchy":1713},[898,25812,1660],{},[1711,25814,1735],{"stretchy":1713},[902,25816,25817],{"encoding":904},"T(Y)"," do ",[883,25820,25822],{"className":25821},[886],[888,25823,25824],{"xmlns":890},[892,25825,25826,25842],{},[895,25827,25828,25834,25836,25838,25840],{},[2884,25829,25830,25832],{},[898,25831,1660],{},[898,25833,2778],{},[1711,25835,1836],{},[898,25837,1660],{},[1711,25839,2460],{},[898,25841,1769],{},[902,25843,25316],{"encoding":904}," — dostaneš ",[883,25846,25848],{"className":25847},[886],[888,25849,25850],{"xmlns":890},[892,25851,25852,25860],{},[895,25853,25854],{},[2884,25855,25856,25858],{},[898,25857,1660],{},[898,25859,2778],{},[902,25861,25377],{"encoding":904}," jako lineární funkci ",[883,25864,25866],{"className":25865},[886],[888,25867,25868],{"xmlns":890},[892,25869,25870,25874],{},[895,25871,25872],{},[898,25873,1660],{},[902,25875,1660],{"encoding":904},[123,25877,25878,25844,25905,25862,25918,2186],{},[38,25879,25797,25880,25904],{},[883,25881,25883],{"className":25882},[886],[888,25884,25885],{"xmlns":890},[892,25886,25887,25901],{},[895,25888,25889,25895,25897,25899],{},[2884,25890,25891,25893],{},[898,25892,1660],{},[898,25894,2778],{},[1711,25896,1714],{"stretchy":1713},[898,25898,1660],{},[1711,25900,1735],{"stretchy":1713},[902,25902,25903],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,25906,25908],{"className":25907},[886],[888,25909,25910],{"xmlns":890},[892,25911,25912,25916],{},[895,25913,25914],{},[898,25915,1940],{},[902,25917,1940],{"encoding":904},[883,25919,25921],{"className":25920},[886],[888,25922,25923],{"xmlns":890},[892,25924,25925,25929],{},[895,25926,25927],{},[898,25928,1660],{},[902,25930,1660],{"encoding":904},[123,25932,25933,1700,25955,25989,25990,26003,26004,2186],{},[38,25934,25797,25935,25954],{},[883,25936,25938],{"className":25937},[886],[888,25939,25940],{"xmlns":890},[892,25941,25942,25952],{},[895,25943,25944,25946,25948,25950],{},[898,25945,1940],{},[1711,25947,1714],{"stretchy":1713},[898,25949,1660],{},[1711,25951,1735],{"stretchy":1713},[902,25953,3901],{"encoding":904}," do podmínky rovnováhy",[883,25956,25958],{"className":25957},[886],[888,25959,25960],{"xmlns":890},[892,25961,25962,25986],{},[895,25963,25964,25966,25968,25970,25972,25978,25980],{},[898,25965,1660],{},[1711,25967,1836],{},[898,25969,1940],{},[1711,25971,2095],{},[1716,25973,25974,25976],{},[898,25975,1833],{},[1711,25977,1793],{},[1711,25979,2095],{},[1716,25981,25982,25984],{},[898,25983,1755],{},[1711,25985,1793],{},[902,25987,25988],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,25991,25993],{"className":25992},[886],[888,25994,25995],{"xmlns":890},[892,25996,25997,26001],{},[895,25998,25999],{},[898,26000,1660],{},[902,26002,1660],{"encoding":904},", odtud ",[883,26005,26007],{"className":26006},[886],[888,26008,26009],{"xmlns":890},[892,26010,26011,26019],{},[895,26012,26013],{},[1716,26014,26015,26017],{},[898,26016,1660],{},[898,26018,1722],{},[902,26020,3587],{"encoding":904},[123,26022,26023,26026,26027,1343,26045,1343,26065,1343,26082,2186],{},[38,26024,26025],{},"Zpětným dosazením"," dopočítej ",[883,26028,26030],{"className":26029},[886],[888,26031,26032],{"xmlns":890},[892,26033,26034,26042],{},[895,26035,26036],{},[1716,26037,26038,26040],{},[898,26039,1769],{},[898,26041,1722],{},[902,26043,26044],{"encoding":904},"T^E",[883,26046,26048],{"className":26047},[886],[888,26049,26050],{"xmlns":890},[892,26051,26052,26062],{},[895,26053,26054],{},[13142,26055,26056,26058,26060],{},[898,26057,1660],{},[898,26059,2778],{},[898,26061,1722],{},[902,26063,26064],{"encoding":904},"Y_D^E",[883,26066,26068],{"className":26067},[886],[888,26069,26070],{"xmlns":890},[892,26071,26072,26080],{},[895,26073,26074],{},[1716,26075,26076,26078],{},[898,26077,1940],{},[898,26079,1722],{},[902,26081,3646],{"encoding":904},[883,26083,26085],{"className":26084},[886],[888,26086,26087],{"xmlns":890},[892,26088,26089,26097],{},[895,26090,26091],{},[1716,26092,26093,26095],{},[898,26094,2362],{},[898,26096,1722],{},[902,26098,26099],{"encoding":904},"S^E",[198,26101,26103],{"id":26102},"příklad-74","Příklad 7.4",[724,26105,24619,26106,26127,26128,1343,26159,1343,26183,1343,26205,26227],{},[883,26107,26109],{"className":26108},[886],[888,26110,26111],{"xmlns":890},[892,26112,26113,26125],{},[895,26114,26115,26117,26119,26121,26123],{},[898,26116,1940],{},[1942,26118,1944],{},[898,26120,1833],{},[1942,26122,1944],{},[898,26124,1755],{},[902,26126,21818],{"encoding":904}," jsou dány ",[883,26129,26131],{"className":26130},[886],[888,26132,26133],{"xmlns":890},[892,26134,26135,26156],{},[895,26136,26137,26139,26141,26144,26146,26152,26154],{},[898,26138,1940],{},[1711,26140,1836],{},[2111,26142,26143],{},"0,9",[1942,26145,2519],{},[2884,26147,26148,26150],{},[898,26149,1660],{},[898,26151,2778],{},[1711,26153,2095],{},[2111,26155,9878],{},[902,26157,26158],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,26160,26162],{"className":26161},[886],[888,26163,26164],{"xmlns":890},[892,26165,26166,26180],{},[895,26167,26168,26170,26172,26174,26176,26178],{},[898,26169,1769],{},[1711,26171,1836],{},[2111,26173,4491],{},[898,26175,1660],{},[1711,26177,2095],{},[2111,26179,4372],{},[902,26181,26182],{"encoding":904},"T = 0{,}2Y + 25",[883,26184,26186],{"className":26185},[886],[888,26187,26188],{"xmlns":890},[892,26189,26190,26202],{},[895,26191,26192,26198,26200],{},[1716,26193,26194,26196],{},[898,26195,1833],{},[1711,26197,1793],{},[1711,26199,1836],{},[2111,26201,4733],{},[902,26203,26204],{"encoding":904},"I^* = 35",[883,26206,26208],{"className":26207},[886],[888,26209,26210],{"xmlns":890},[892,26211,26212,26224],{},[895,26213,26214,26220,26222],{},[1716,26215,26216,26218],{},[898,26217,1755],{},[1711,26219,1793],{},[1711,26221,1836],{},[2111,26223,4306],{},[902,26225,26226],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,26229,26230],{},[883,26231,26233],{"className":26232},[886],[888,26234,26235],{"xmlns":890},[892,26236,26237,26361],{},[24352,26238,26239,26269,26297,26331],{"rowspacing":24354,"columnalign":24355,"columnspacing":5224},[24357,26240,26241,26247],{},[24360,26242,26243],{},[2509,26244,26245],{"scriptlevel":2113,"displaystyle":1725},[898,26246,1660],{},[24360,26248,26249],{},[2509,26250,26251],{"scriptlevel":2113,"displaystyle":1725},[895,26252,26253,26255,26257,26259,26261,26263,26265,26267],{},[895,26254],{},[1711,26256,1836],{},[898,26258,1940],{},[1711,26260,2095],{},[2111,26262,4733],{},[1711,26264,2095],{},[2111,26266,4306],{},[1711,26268,1726],{"separator":1725},[24357,26270,26271,26277],{},[24360,26272,26273],{},[2509,26274,26275],{"scriptlevel":2113,"displaystyle":1725},[898,26276,1769],{},[24360,26278,26279],{},[2509,26280,26281],{"scriptlevel":2113,"displaystyle":1725},[895,26282,26283,26285,26287,26289,26291,26293,26295],{},[895,26284],{},[1711,26286,1836],{},[2111,26288,4491],{},[898,26290,1660],{},[1711,26292,2095],{},[2111,26294,4372],{},[1711,26296,1726],{"separator":1725},[24357,26298,26299,26305],{},[24360,26300,26301],{},[2509,26302,26303],{"scriptlevel":2113,"displaystyle":1725},[898,26304,1940],{},[24360,26306,26307],{},[2509,26308,26309],{"scriptlevel":2113,"displaystyle":1725},[895,26310,26311,26313,26315,26317,26319,26325,26327,26329],{},[895,26312],{},[1711,26314,1836],{},[2111,26316,26143],{},[1942,26318,2519],{},[2884,26320,26321,26323],{},[898,26322,1660],{},[898,26324,2778],{},[1711,26326,2095],{},[2111,26328,9878],{},[1711,26330,1726],{"separator":1725},[24357,26332,26333,26343],{},[24360,26334,26335],{},[2509,26336,26337],{"scriptlevel":2113,"displaystyle":1725},[2884,26338,26339,26341],{},[898,26340,1660],{},[898,26342,2778],{},[24360,26344,26345],{},[2509,26346,26347],{"scriptlevel":2113,"displaystyle":1725},[895,26348,26349,26351,26353,26355,26357,26359],{},[895,26350],{},[1711,26352,1836],{},[898,26354,1660],{},[1711,26356,2460],{},[898,26358,1769],{},[898,26360,2186],{"mathvariant":2287},[902,26362,26363],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,26365,26366,26369,26370,26424,26425,26471,26472,2062],{},[38,26367,26368],{},"Řešení."," Z definice ",[883,26371,26373],{"className":26372},[886],[888,26374,26375],{"xmlns":890},[892,26376,26377,26421],{},[895,26378,26379,26385,26387,26389,26391,26393,26395,26397,26399,26401,26403,26405,26407,26409,26411,26413,26415,26417,26419],{},[2884,26380,26381,26383],{},[898,26382,1660],{},[898,26384,2778],{},[1711,26386,1836],{},[898,26388,1660],{},[1711,26390,2460],{},[898,26392,1769],{},[1711,26394,1836],{},[898,26396,1660],{},[1711,26398,2460],{},[1711,26400,1714],{"stretchy":1713},[2111,26402,4491],{},[898,26404,1660],{},[1711,26406,2095],{},[2111,26408,4372],{},[1711,26410,1735],{"stretchy":1713},[1711,26412,1836],{},[2111,26414,4275],{},[898,26416,1660],{},[1711,26418,2460],{},[2111,26420,4372],{},[902,26422,26423],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,26426,26428],{"className":26427},[886],[888,26429,26430],{"xmlns":890},[892,26431,26432,26468],{},[895,26433,26434,26436,26438,26440,26442,26444,26446,26448,26450,26452,26454,26456,26458,26461,26463,26465],{},[898,26435,1940],{},[1711,26437,1836],{},[2111,26439,26143],{},[1711,26441,1714],{"stretchy":1713},[2111,26443,4275],{},[898,26445,1660],{},[1711,26447,2460],{},[2111,26449,4372],{},[1711,26451,1735],{"stretchy":1713},[1711,26453,2095],{},[2111,26455,9878],{},[1711,26457,1836],{},[2111,26459,26460],{},"0,72",[898,26462,1660],{},[1711,26464,2095],{},[2111,26466,26467],{},"47,5",[902,26469,26470],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,26473,26475],{"className":26474},[886],[888,26476,26477],{"xmlns":890},[892,26478,26479,26497],{},[895,26480,26481,26483,26485,26487,26489,26491,26493,26495],{},[898,26482,1660],{},[1711,26484,1836],{},[2111,26486,26460],{},[898,26488,1660],{},[1711,26490,2095],{},[2111,26492,26467],{},[1711,26494,2095],{},[2111,26496,24778],{},[902,26498,26499],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,26501,26502],{},[883,26503,26505],{"className":26504},[886],[888,26506,26507],{"xmlns":890},[892,26508,26509,26550],{},[895,26510,26511,26514,26516,26518,26521,26523,26525,26527,26533,26535,26545,26547],{},[2111,26512,26513],{},"0,28",[898,26515,1660],{},[1711,26517,1836],{},[2111,26519,26520],{},"102,5",[1942,26522,4699],{},[1711,26524,4702],{},[1942,26526,4699],{},[1716,26528,26529,26531],{},[898,26530,1660],{},[898,26532,1722],{},[1711,26534,1836],{},[2509,26536,26537],{"scriptlevel":2113,"displaystyle":1713},[2525,26538,26539,26542],{},[2111,26540,26541],{},"5125",[2111,26543,26544],{},"14",[1711,26546,9881],{},[2111,26548,26549],{},"366,071.",[902,26551,26552],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,26554,26555],{},"Rovnovážné veličiny:",[120,26557,26558,26593,26645,26699,26747],{},[123,26559,26560,1726],{},[883,26561,26563],{"className":26562},[886],[888,26564,26565],{"xmlns":890},[892,26566,26567,26590],{},[895,26568,26569,26575,26577,26585,26587],{},[1716,26570,26571,26573],{},[898,26572,1660],{},[898,26574,1722],{},[1711,26576,1836],{},[2509,26578,26579],{"scriptlevel":2113,"displaystyle":1713},[2525,26580,26581,26583],{},[2111,26582,26541],{},[2111,26584,26544],{},[1711,26586,9881],{},[2111,26588,26589],{},"366,071",[902,26591,26592],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,26594,26595,1726],{},[883,26596,26598],{"className":26597},[886],[888,26599,26600],{"xmlns":890},[892,26601,26602,26642],{},[895,26603,26604,26610,26612,26614,26616,26622,26624,26626,26628,26637,26639],{},[1716,26605,26606,26608],{},[898,26607,1769],{},[898,26609,1722],{},[1711,26611,1836],{},[2111,26613,4491],{},[1942,26615,2519],{},[1716,26617,26618,26620],{},[898,26619,1660],{},[898,26621,1722],{},[1711,26623,2095],{},[2111,26625,4372],{},[1711,26627,1836],{},[2509,26629,26630],{"scriptlevel":2113,"displaystyle":1713},[2525,26631,26632,26635],{},[2111,26633,26634],{},"1375",[2111,26636,26544],{},[1711,26638,9881],{},[2111,26640,26641],{},"98,214",[902,26643,26644],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,26646,26647,1726],{},[883,26648,26650],{"className":26649},[886],[888,26651,26652],{"xmlns":890},[892,26653,26654,26696],{},[895,26655,26656,26664,26666,26672,26674,26680,26682,26691,26693],{},[13142,26657,26658,26660,26662],{},[898,26659,1660],{},[898,26661,2778],{},[898,26663,1722],{},[1711,26665,1836],{},[1716,26667,26668,26670],{},[898,26669,1660],{},[898,26671,1722],{},[1711,26673,2460],{},[1716,26675,26676,26678],{},[898,26677,1769],{},[898,26679,1722],{},[1711,26681,1836],{},[2509,26683,26684],{"scriptlevel":2113,"displaystyle":1713},[2525,26685,26686,26689],{},[2111,26687,26688],{},"3750",[2111,26690,26544],{},[1711,26692,9881],{},[2111,26694,26695],{},"267,857",[902,26697,26698],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,26700,26701,1726],{},[883,26702,26704],{"className":26703},[886],[888,26705,26706],{"xmlns":890},[892,26707,26708,26744],{},[895,26709,26710,26716,26718,26724,26726,26728,26730,26739,26741],{},[1716,26711,26712,26714],{},[898,26713,1940],{},[898,26715,1722],{},[1711,26717,1836],{},[1716,26719,26720,26722],{},[898,26721,1660],{},[898,26723,1722],{},[1711,26725,2460],{},[2111,26727,24778],{},[1711,26729,1836],{},[2509,26731,26732],{"scriptlevel":2113,"displaystyle":1713},[2525,26733,26734,26737],{},[2111,26735,26736],{},"4355",[2111,26738,26544],{},[1711,26740,9881],{},[2111,26742,26743],{},"311,071",[902,26745,26746],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,26748,26749,26805],{},[883,26750,26752],{"className":26751},[886],[888,26753,26754],{"xmlns":890},[892,26755,26756,26802],{},[895,26757,26758,26764,26766,26774,26776,26782,26784,26786,26795,26797,26799],{},[1716,26759,26760,26762],{},[898,26761,2362],{},[898,26763,1722],{},[1711,26765,1836],{},[13142,26767,26768,26770,26772],{},[898,26769,1660],{},[898,26771,2778],{},[898,26773,1722],{},[1711,26775,2460],{},[1716,26777,26778,26780],{},[898,26779,1940],{},[898,26781,1722],{},[1711,26783,1836],{},[1711,26785,2460],{},[2509,26787,26788],{"scriptlevel":2113,"displaystyle":1713},[2525,26789,26790,26793],{},[2111,26791,26792],{},"605",[2111,26794,26544],{},[1711,26796,9881],{},[1711,26798,2460],{},[2111,26800,26801],{},"43,214",[902,26803,26804],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,26807,26808,24948,26810,26831,26832,26835,26836,26859,26860,2186],{},[38,26809,24947],{},[883,26811,26813],{"className":26812},[886],[888,26814,26815],{"xmlns":890},[892,26816,26817,26829],{},[895,26818,26819,26821,26823,26825,26827],{},[898,26820,1940],{},[1942,26822,1944],{},[898,26824,1833],{},[1942,26826,1944],{},[898,26828,1755],{},[902,26830,21818],{"encoding":904}," stále uvažuje ",[38,26833,26834],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,26837,26839],{"className":26838},[886],[888,26840,26841],{"xmlns":890},[892,26842,26843,26856],{},[895,26844,26845,26847,26849,26852,26854],{},[898,26846,1974],{},[1711,26848,1836],{},[898,26850,26851],{},"B",[1711,26853,2460],{},[898,26855,1790],{},[902,26857,26858],{"encoding":904},"X = B - M"," dává ",[38,26861,24969,26862],{},[883,26863,26865],{"className":26864},[886],[888,26866,26867],{"xmlns":890},[892,26868,26869,26885],{},[895,26870,26871,26873,26875,26877,26879,26881,26883],{},[898,26872,1940],{},[1942,26874,1944],{},[898,26876,1833],{},[1942,26878,1944],{},[898,26880,1755],{},[1942,26882,1944],{},[898,26884,1974],{},[902,26886,1977],{"encoding":904},[115,26888,26890],{"id":26889},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,26892,24219],{"id":26893},"zadání-modelu-2",[724,26895,26896,26897,1700,26900,25192,26921,26934,26935,1772,26938,26951],{},"Rozšíření o ",[38,26898,26899],{},"čistý export",[883,26901,26903],{"className":26902},[886],[888,26904,26905],{"xmlns":890},[892,26906,26907,26919],{},[895,26908,26909,26911,26913,26915,26917],{},[898,26910,1974],{},[1711,26912,1836],{},[898,26914,26851],{},[1711,26916,2460],{},[898,26918,1790],{},[902,26920,26858],{"encoding":904},[883,26922,26924],{"className":26923},[886],[888,26925,26926],{"xmlns":890},[892,26927,26928,26932],{},[895,26929,26930],{},[898,26931,26851],{},[902,26933,26851],{"encoding":904}," je hrubý export (",[614,26936,26937],{},"brutto export",[883,26939,26941],{"className":26940},[886],[888,26942,26943],{"xmlns":890},[892,26944,26945,26949],{},[895,26946,26947],{},[898,26948,1790],{},[902,26950,1790],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,26953,26954],{},[883,26955,26957],{"className":26956},[886],[888,26958,26959],{"xmlns":890},[892,26960,26961,26981],{},[895,26962,26963,26965,26967,26969,26971,26977,26979],{},[898,26964,1790],{},[1711,26966,1836],{},[898,26968,1790],{},[1711,26970,1714],{"stretchy":1713},[2884,26972,26973,26975],{},[898,26974,1660],{},[898,26976,2778],{},[1711,26978,1735],{"stretchy":1713},[898,26980,2186],{"mathvariant":2287},[902,26982,26983],{"encoding":904},"M = M(Y_D).",[724,26985,26986],{},"Podmínka rovnováhy:",[724,26988,26989],{},[883,26990,26992],{"className":26991},[886],[888,26993,26994],{"xmlns":890},[892,26995,26996,27033],{},[895,26997,26998,27000,27002,27004,27006,27008,27010,27012,27014,27016,27018,27020,27022,27024,27026,27029,27031],{},[898,26999,1660],{},[1711,27001,1836],{},[898,27003,1940],{},[1711,27005,2095],{},[898,27007,1833],{},[1711,27009,2095],{},[898,27011,1755],{},[1711,27013,2095],{},[898,27015,26851],{},[1711,27017,2460],{},[898,27019,1790],{},[898,27021,2186],{"mathvariant":2287},[2102,27023],{"width":2104},[1711,27025,1714],{"stretchy":1713},[2111,27027,27028],{},"7.10",[1942,27030,207],{},[1711,27032,1735],{"stretchy":1713},[902,27034,27035],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,27037,24289],{"id":27038},"soustava-rovnic-2",[724,27040,25449,27041,27075,27076,2062],{},[883,27042,27044],{"className":27043},[886],[888,27045,27046],{"xmlns":890},[892,27047,27048,27072],{},[895,27049,27050,27056,27058,27064,27066],{},[1716,27051,27052,27054],{},[898,27053,1833],{},[1711,27055,1793],{},[1711,27057,1726],{"separator":1725},[1716,27059,27060,27062],{},[898,27061,1755],{},[1711,27063,1793],{},[1711,27065,1726],{"separator":1725},[1716,27067,27068,27070],{},[898,27069,26851],{},[1711,27071,1793],{},[902,27073,27074],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,27077,27079],{"className":27078},[886],[888,27080,27081],{"xmlns":890},[892,27082,27083,27107],{},[895,27084,27085,27087,27089,27091,27093,27095,27097,27103,27105],{},[898,27086,1660],{},[1711,27088,1726],{"separator":1725},[898,27090,1940],{},[1711,27092,1726],{"separator":1725},[898,27094,1769],{},[1711,27096,1726],{"separator":1725},[2884,27098,27099,27101],{},[898,27100,1660],{},[898,27102,2778],{},[1711,27104,1726],{"separator":1725},[898,27106,1790],{},[902,27108,27109],{"encoding":904},"Y, C, T, Y_D, M",[724,27111,27112],{},[883,27113,27115],{"className":27114},[886],[888,27116,27117],{"xmlns":890},[892,27118,27119,27303],{},[895,27120,27121,27295,27297,27299,27301],{},[24352,27122,27123,27155,27185,27213,27245],{"rowspacing":24354,"columnalign":24355,"columnspacing":5224},[24357,27124,27125,27131],{},[24360,27126,27127],{},[2509,27128,27129],{"scriptlevel":2113,"displaystyle":1725},[898,27130,1940],{},[24360,27132,27133],{},[2509,27134,27135],{"scriptlevel":2113,"displaystyle":1725},[895,27136,27137,27139,27141,27143,27145,27151,27153],{},[895,27138],{},[1711,27140,1836],{},[898,27142,1940],{},[1711,27144,1714],{"stretchy":1713},[2884,27146,27147,27149],{},[898,27148,1660],{},[898,27150,2778],{},[1711,27152,1735],{"stretchy":1713},[1711,27154,1726],{"separator":1725},[24357,27156,27157,27167],{},[24360,27158,27159],{},[2509,27160,27161],{"scriptlevel":2113,"displaystyle":1725},[2884,27162,27163,27165],{},[898,27164,1660],{},[898,27166,2778],{},[24360,27168,27169],{},[2509,27170,27171],{"scriptlevel":2113,"displaystyle":1725},[895,27172,27173,27175,27177,27179,27181,27183],{},[895,27174],{},[1711,27176,1836],{},[898,27178,1660],{},[1711,27180,2460],{},[898,27182,1769],{},[1711,27184,1726],{"separator":1725},[24357,27186,27187,27193],{},[24360,27188,27189],{},[2509,27190,27191],{"scriptlevel":2113,"displaystyle":1725},[898,27192,1769],{},[24360,27194,27195],{},[2509,27196,27197],{"scriptlevel":2113,"displaystyle":1725},[895,27198,27199,27201,27203,27205,27207,27209,27211],{},[895,27200],{},[1711,27202,1836],{},[898,27204,1769],{},[1711,27206,1714],{"stretchy":1713},[898,27208,1660],{},[1711,27210,1735],{"stretchy":1713},[1711,27212,1726],{"separator":1725},[24357,27214,27215,27221],{},[24360,27216,27217],{},[2509,27218,27219],{"scriptlevel":2113,"displaystyle":1725},[898,27220,1790],{},[24360,27222,27223],{},[2509,27224,27225],{"scriptlevel":2113,"displaystyle":1725},[895,27226,27227,27229,27231,27233,27235,27241,27243],{},[895,27228],{},[1711,27230,1836],{},[898,27232,1790],{},[1711,27234,1714],{"stretchy":1713},[2884,27236,27237,27239],{},[898,27238,1660],{},[898,27240,2778],{},[1711,27242,1735],{"stretchy":1713},[1711,27244,1726],{"separator":1725},[24357,27246,27247,27253],{},[24360,27248,27249],{},[2509,27250,27251],{"scriptlevel":2113,"displaystyle":1725},[898,27252,1660],{},[24360,27254,27255],{},[2509,27256,27257],{"scriptlevel":2113,"displaystyle":1725},[895,27258,27259,27261,27263,27265,27267,27273,27275,27281,27283,27289,27291,27293],{},[895,27260],{},[1711,27262,1836],{},[898,27264,1940],{},[1711,27266,2095],{},[1716,27268,27269,27271],{},[898,27270,1833],{},[1711,27272,1793],{},[1711,27274,2095],{},[1716,27276,27277,27279],{},[898,27278,1755],{},[1711,27280,1793],{},[1711,27282,2095],{},[1716,27284,27285,27287],{},[898,27286,26851],{},[1711,27288,1793],{},[1711,27290,2460],{},[898,27292,1790],{},[898,27294,2186],{"mathvariant":2287},[2102,27296],{"width":2104},[1711,27298,1714],{"stretchy":1713},[2111,27300,27028],{},[1711,27302,1735],{"stretchy":1713},[902,27304,27305],{"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)",[198,27307,27309],{"id":27308},"příklad-75","Příklad 7.5",[724,27311,27312,27313,1343,27345,1343,27372,1343,27393,1343,27415,1343,27437,27460],{},"Dáno: ",[883,27314,27316],{"className":27315},[886],[888,27317,27318],{"xmlns":890},[892,27319,27320,27342],{},[895,27321,27322,27324,27326,27329,27331,27337,27339],{},[898,27323,1940],{},[1711,27325,1836],{},[2111,27327,27328],{},"0,75",[1942,27330,2519],{},[2884,27332,27333,27335],{},[898,27334,1660],{},[898,27336,2778],{},[1711,27338,2095],{},[2111,27340,27341],{},"750",[902,27343,27344],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,27346,27348],{"className":27347},[886],[888,27349,27350],{"xmlns":890},[892,27351,27352,27369],{},[895,27353,27354,27356,27358,27361,27363],{},[898,27355,1790],{},[1711,27357,1836],{},[2111,27359,27360],{},"0,15",[1942,27362,2519],{},[2884,27364,27365,27367],{},[898,27366,1660],{},[898,27368,2778],{},[902,27370,27371],{"encoding":904},"M = 0{,}15\\,Y_D",[883,27373,27375],{"className":27374},[886],[888,27376,27377],{"xmlns":890},[892,27378,27379,27390],{},[895,27380,27381,27383,27385,27388],{},[898,27382,1769],{},[1711,27384,1836],{},[2111,27386,27387],{},"0,25",[898,27389,1660],{},[902,27391,27392],{"encoding":904},"T = 0{,}25Y",[883,27394,27396],{"className":27395},[886],[888,27397,27398],{"xmlns":890},[892,27399,27400,27412],{},[895,27401,27402,27408,27410],{},[1716,27403,27404,27406],{},[898,27405,1833],{},[1711,27407,1793],{},[1711,27409,1836],{},[2111,27411,4807],{},[902,27413,27414],{"encoding":904},"I^* = 500",[883,27416,27418],{"className":27417},[886],[888,27419,27420],{"xmlns":890},[892,27421,27422,27434],{},[895,27423,27424,27430,27432],{},[1716,27425,27426,27428],{},[898,27427,1755],{},[1711,27429,1793],{},[1711,27431,1836],{},[2111,27433,12781],{},[902,27435,27436],{"encoding":904},"G^* = 150",[883,27438,27440],{"className":27439},[886],[888,27441,27442],{"xmlns":890},[892,27443,27444,27457],{},[895,27445,27446,27452,27454],{},[1716,27447,27448,27450],{},[898,27449,26851],{},[1711,27451,1793],{},[1711,27453,1836],{},[2111,27455,27456],{},"800",[902,27458,27459],{"encoding":904},"B^* = 800",". Soustava:",[724,27462,27463],{},[883,27464,27466],{"className":27465},[886],[888,27467,27468],{"xmlns":890},[892,27469,27470,27688],{},[24352,27471,27472,27518,27560,27596,27638],{"rowspacing":24354,"columnalign":24355,"columnspacing":5224},[24357,27473,27474,27490],{},[24360,27475,27476],{},[2509,27477,27478],{"scriptlevel":2113,"displaystyle":1725},[895,27479,27480,27482,27484,27486,27488],{},[1711,27481,1714],{"stretchy":1713},[898,27483,1675],{},[2111,27485,2238],{},[1711,27487,1735],{"stretchy":1713},[1942,27489,2118],{},[24360,27491,27492],{},[2509,27493,27494],{"scriptlevel":2113,"displaystyle":1725},[895,27495,27496,27498,27500,27502,27504,27506,27512,27514,27516],{},[895,27497],{},[898,27499,1940],{},[1711,27501,1836],{},[2111,27503,27328],{},[1942,27505,2519],{},[2884,27507,27508,27510],{},[898,27509,1660],{},[898,27511,2778],{},[1711,27513,2095],{},[2111,27515,27341],{},[1711,27517,1726],{"separator":1725},[24357,27519,27520,27536],{},[24360,27521,27522],{},[2509,27523,27524],{"scriptlevel":2113,"displaystyle":1725},[895,27525,27526,27528,27530,27532,27534],{},[1711,27527,1714],{"stretchy":1713},[898,27529,1675],{},[2111,27531,2963],{},[1711,27533,1735],{"stretchy":1713},[1942,27535,2118],{},[24360,27537,27538],{},[2509,27539,27540],{"scriptlevel":2113,"displaystyle":1725},[895,27541,27542,27544,27550,27552,27554,27556,27558],{},[895,27543],{},[2884,27545,27546,27548],{},[898,27547,1660],{},[898,27549,2778],{},[1711,27551,1836],{},[898,27553,1660],{},[1711,27555,2460],{},[898,27557,1769],{},[1711,27559,1726],{"separator":1725},[24357,27561,27562,27578],{},[24360,27563,27564],{},[2509,27565,27566],{"scriptlevel":2113,"displaystyle":1725},[895,27567,27568,27570,27572,27574,27576],{},[1711,27569,1714],{"stretchy":1713},[898,27571,1675],{},[2111,27573,3034],{},[1711,27575,1735],{"stretchy":1713},[1942,27577,2118],{},[24360,27579,27580],{},[2509,27581,27582],{"scriptlevel":2113,"displaystyle":1725},[895,27583,27584,27586,27588,27590,27592,27594],{},[895,27585],{},[898,27587,1769],{},[1711,27589,1836],{},[2111,27591,27387],{},[898,27593,1660],{},[1711,27595,1726],{"separator":1725},[24357,27597,27598,27614],{},[24360,27599,27600],{},[2509,27601,27602],{"scriptlevel":2113,"displaystyle":1725},[895,27603,27604,27606,27608,27610,27612],{},[1711,27605,1714],{"stretchy":1713},[898,27607,1675],{},[2111,27609,6369],{},[1711,27611,1735],{"stretchy":1713},[1942,27613,2118],{},[24360,27615,27616],{},[2509,27617,27618],{"scriptlevel":2113,"displaystyle":1725},[895,27619,27620,27622,27624,27626,27628,27630,27636],{},[895,27621],{},[898,27623,1790],{},[1711,27625,1836],{},[2111,27627,27360],{},[1942,27629,2519],{},[2884,27631,27632,27634],{},[898,27633,1660],{},[898,27635,2778],{},[1711,27637,1726],{"separator":1725},[24357,27639,27640,27656],{},[24360,27641,27642],{},[2509,27643,27644],{"scriptlevel":2113,"displaystyle":1725},[895,27645,27646,27648,27650,27652,27654],{},[1711,27647,1714],{"stretchy":1713},[898,27649,1675],{},[2111,27651,4798],{},[1711,27653,1735],{"stretchy":1713},[1942,27655,2118],{},[24360,27657,27658],{},[2509,27659,27660],{"scriptlevel":2113,"displaystyle":1725},[895,27661,27662,27664,27666,27668,27670,27672,27674,27676,27678,27680,27682,27684,27686],{},[895,27663],{},[898,27665,1660],{},[1711,27667,1836],{},[898,27669,1940],{},[1711,27671,2095],{},[2111,27673,4807],{},[1711,27675,2095],{},[2111,27677,12781],{},[1711,27679,2095],{},[2111,27681,27456],{},[1711,27683,2460],{},[898,27685,1790],{},[898,27687,2186],{"mathvariant":2287},[902,27689,27690],{"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}",[724,27692,27693,27694,27728],{},"Postupná substituce — z (r3) do (r2): ",[883,27695,27697],{"className":27696},[886],[888,27698,27699],{"xmlns":890},[892,27700,27701,27725],{},[895,27702,27703,27709,27711,27713,27715,27717,27719,27721,27723],{},[2884,27704,27705,27707],{},[898,27706,1660],{},[898,27708,2778],{},[1711,27710,1836],{},[898,27712,1660],{},[1711,27714,2460],{},[2111,27716,27387],{},[898,27718,1660],{},[1711,27720,1836],{},[2111,27722,27328],{},[898,27724,1660],{},[902,27726,27727],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,27730,27731],{},[883,27732,27734],{"className":27733},[886],[888,27735,27736],{"xmlns":890},[892,27737,27738,27779],{},[895,27739,27740,27742,27744,27746,27748,27750,27752,27754,27756,27758,27760,27762,27764,27766,27768,27771,27773,27775,27777],{},[1711,27741,1714],{"stretchy":1713},[898,27743,1675],{},[2111,27745,6262],{},[1711,27747,1735],{"stretchy":1713},[1942,27749,2118],{},[898,27751,1940],{},[1711,27753,1836],{},[2111,27755,27328],{},[1711,27757,4795],{},[2111,27759,27328],{},[898,27761,1660],{},[1711,27763,2095],{},[2111,27765,27341],{},[1711,27767,1836],{},[2111,27769,27770],{},"0,5625",[898,27772,1660],{},[1711,27774,2095],{},[2111,27776,27341],{},[1711,27778,1726],{"separator":1725},[902,27780,27781],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,27783,27784],{},[883,27785,27787],{"className":27786},[886],[888,27788,27789],{"xmlns":890},[892,27790,27791,27825],{},[895,27792,27793,27795,27797,27800,27802,27804,27806,27808,27810,27812,27814,27816,27818,27821,27823],{},[1711,27794,1714],{"stretchy":1713},[898,27796,1675],{},[2111,27798,27799],{},"7",[1711,27801,1735],{"stretchy":1713},[1942,27803,2118],{},[898,27805,1790],{},[1711,27807,1836],{},[2111,27809,27360],{},[1711,27811,4795],{},[2111,27813,27328],{},[898,27815,1660],{},[1711,27817,1836],{},[2111,27819,27820],{},"0,1125",[898,27822,1660],{},[898,27824,2186],{"mathvariant":2287},[902,27826,27827],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,27829,27830],{},"Dosazením do (r5):",[724,27832,27833],{},[883,27834,27836],{"className":27835},[886],[888,27837,27838],{"xmlns":890},[892,27839,27840,27884],{},[895,27841,27842,27844,27846,27848,27850,27852,27854,27856,27858,27860,27862,27864,27866,27868,27870,27872,27874,27877,27879,27881],{},[898,27843,1660],{},[1711,27845,1836],{},[2111,27847,27770],{},[898,27849,1660],{},[1711,27851,2095],{},[2111,27853,27341],{},[1711,27855,2095],{},[2111,27857,4807],{},[1711,27859,2095],{},[2111,27861,12781],{},[1711,27863,2095],{},[2111,27865,27456],{},[1711,27867,2460],{},[2111,27869,27820],{},[898,27871,1660],{},[1711,27873,1836],{},[2111,27875,27876],{},"0,45",[898,27878,1660],{},[1711,27880,2095],{},[2111,27882,27883],{},"2200.",[902,27885,27886],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,27888,27889,27890,9572,27912,27935],{},"Odtud ",[883,27891,27893],{"className":27892},[886],[888,27894,27895],{"xmlns":890},[892,27896,27897,27909],{},[895,27898,27899,27902,27904,27906],{},[2111,27900,27901],{},"0,55",[898,27903,1660],{},[1711,27905,1836],{},[2111,27907,27908],{},"2200",[902,27910,27911],{"encoding":904},"0{,}55Y = 2200",[883,27913,27915],{"className":27914},[886],[888,27916,27917],{"xmlns":890},[892,27918,27919,27932],{},[895,27920,27921,27927,27929],{},[1716,27922,27923,27925],{},[898,27924,1660],{},[898,27926,1722],{},[1711,27928,1836],{},[2111,27930,27931],{},"4000",[902,27933,27934],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,27937,27938,27961,27993,28028,28061,28097],{},[123,27939,27940,1726],{},[883,27941,27943],{"className":27942},[886],[888,27944,27945],{"xmlns":890},[892,27946,27947,27959],{},[895,27948,27949,27955,27957],{},[1716,27950,27951,27953],{},[898,27952,1660],{},[898,27954,1722],{},[1711,27956,1836],{},[2111,27958,27931],{},[902,27960,27934],{"encoding":904},[123,27962,27963,1726],{},[883,27964,27966],{"className":27965},[886],[888,27967,27968],{"xmlns":890},[892,27969,27970,27990],{},[895,27971,27972,27978,27980,27982,27984,27986,27988],{},[1716,27973,27974,27976],{},[898,27975,1769],{},[898,27977,1722],{},[1711,27979,1836],{},[2111,27981,27387],{},[1711,27983,4795],{},[2111,27985,27931],{},[1711,27987,1836],{},[2111,27989,4313],{},[902,27991,27992],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,27994,27995,1726],{},[883,27996,27998],{"className":27997},[886],[888,27999,28000],{"xmlns":890},[892,28001,28002,28025],{},[895,28003,28004,28012,28014,28016,28018,28020,28022],{},[13142,28005,28006,28008,28010],{},[898,28007,1660],{},[898,28009,2778],{},[898,28011,1722],{},[1711,28013,1836],{},[2111,28015,27328],{},[1711,28017,4795],{},[2111,28019,27931],{},[1711,28021,1836],{},[2111,28023,28024],{},"3000",[902,28026,28027],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,28029,28030,1726],{},[883,28031,28033],{"className":28032},[886],[888,28034,28035],{"xmlns":890},[892,28036,28037,28058],{},[895,28038,28039,28045,28047,28049,28051,28053,28055],{},[1716,28040,28041,28043],{},[898,28042,1790],{},[898,28044,1722],{},[1711,28046,1836],{},[2111,28048,27360],{},[1711,28050,4795],{},[2111,28052,28024],{},[1711,28054,1836],{},[2111,28056,28057],{},"450",[902,28059,28060],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,28062,28063,1726],{},[883,28064,28066],{"className":28065},[886],[888,28067,28068],{"xmlns":890},[892,28069,28070,28094],{},[895,28071,28072,28078,28080,28082,28084,28086,28088,28090,28092],{},[1716,28073,28074,28076],{},[898,28075,1940],{},[898,28077,1722],{},[1711,28079,1836],{},[2111,28081,27328],{},[1711,28083,4795],{},[2111,28085,28024],{},[1711,28087,2095],{},[2111,28089,27341],{},[1711,28091,1836],{},[2111,28093,28024],{},[902,28095,28096],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,28098,28099,28139],{},[883,28100,28102],{"className":28101},[886],[888,28103,28104],{"xmlns":890},[892,28105,28106,28136],{},[895,28107,28108,28114,28116,28124,28126,28132,28134],{},[1716,28109,28110,28112],{},[898,28111,2362],{},[898,28113,1722],{},[1711,28115,1836],{},[13142,28117,28118,28120,28122],{},[898,28119,1660],{},[898,28121,2778],{},[898,28123,1722],{},[1711,28125,2460],{},[1716,28127,28128,28130],{},[898,28129,1940],{},[898,28131,1722],{},[1711,28133,1836],{},[2111,28135,2113],{},[902,28137,28138],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,28141,28142,28144,28145,1343,28162,2009,28183,28208,28209,28212,28213,28226,28227,2186],{},[38,28143,24947],{}," Modely ",[883,28146,28148],{"className":28147},[886],[888,28149,28150],{"xmlns":890},[892,28151,28152,28160],{},[895,28153,28154,28156,28158],{},[898,28155,1940],{},[1942,28157,1944],{},[898,28159,1833],{},[902,28161,1949],{"encoding":904},[883,28163,28165],{"className":28164},[886],[888,28166,28167],{"xmlns":890},[892,28168,28169,28181],{},[895,28170,28171,28173,28175,28177,28179],{},[898,28172,1940],{},[1942,28174,1944],{},[898,28176,1833],{},[1942,28178,1944],{},[898,28180,1755],{},[902,28182,21818],{"encoding":904},[883,28184,28186],{"className":28185},[886],[888,28187,28188],{"xmlns":890},[892,28189,28190,28206],{},[895,28191,28192,28194,28196,28198,28200,28202,28204],{},[898,28193,1940],{},[1942,28195,1944],{},[898,28197,1833],{},[1942,28199,1944],{},[898,28201,1755],{},[1942,28203,1944],{},[898,28205,1974],{},[902,28207,1977],{"encoding":904}," pokládají investice za ",[38,28210,28211],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,28214,28216],{"className":28215},[886],[888,28217,28218],{"xmlns":890},[892,28219,28220,28224],{},[895,28221,28222],{},[898,28223,1675],{},[902,28225,1675],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,28228,28229],{},"model IS-LM",[115,28231,28233],{"id":28232},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,28235,28236,28237,28241,28242,28245,28246,28249],{},"V článku ",[207,28238,28240],{"className":28239,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,28243,28244],{},"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 ",[38,28247,28248],{},"výraznější"," než v mikroekonomických modelech.",[724,28251,28252],{},[1801,28253],{"alt":28254,"className":28255,"src":28256},"imek-multiplikatorovy-efekt-chain",[210,1805],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,28258,1813,28259,1343,28276,1343,28297,28322,28323,28326,28327,28345,28346,28364,28365,28383,28384,28387,28388,1343,28405,28422,28423,28425],{},[883,28260,28262],{"className":28261},[886],[888,28263,28264],{"xmlns":890},[892,28265,28266,28274],{},[895,28267,28268,28270,28272],{},[898,28269,1940],{},[1942,28271,1944],{},[898,28273,1833],{},[902,28275,1949],{"encoding":904},[883,28277,28279],{"className":28278},[886],[888,28280,28281],{"xmlns":890},[892,28282,28283,28295],{},[895,28284,28285,28287,28289,28291,28293],{},[898,28286,1940],{},[1942,28288,1944],{},[898,28290,1833],{},[1942,28292,1944],{},[898,28294,1755],{},[902,28296,21818],{"encoding":904},[883,28298,28300],{"className":28299},[886],[888,28301,28302],{"xmlns":890},[892,28303,28304,28320],{},[895,28305,28306,28308,28310,28312,28314,28316,28318],{},[898,28307,1940],{},[1942,28309,1944],{},[898,28311,1833],{},[1942,28313,1944],{},[898,28315,1755],{},[1942,28317,1944],{},[898,28319,1974],{},[902,28321,1977],{"encoding":904}," se vyšetřuje vliv změn ",[38,28324,28325],{},"exogenních"," veličin (plánovaných investic ",[883,28328,28330],{"className":28329},[886],[888,28331,28332],{"xmlns":890},[892,28333,28334,28342],{},[895,28335,28336],{},[1716,28337,28338,28340],{},[898,28339,1833],{},[1711,28341,1793],{},[902,28343,28344],{"encoding":904},"I^*",", vládních výdajů ",[883,28347,28349],{"className":28348},[886],[888,28350,28351],{"xmlns":890},[892,28352,28353,28361],{},[895,28354,28355],{},[1716,28356,28357,28359],{},[898,28358,1755],{},[1711,28360,1793],{},[902,28362,28363],{"encoding":904},"G^*",", exportu ",[883,28366,28368],{"className":28367},[886],[888,28369,28370],{"xmlns":890},[892,28371,28372,28380],{},[895,28373,28374],{},[1716,28375,28376,28378],{},[898,28377,26851],{},[1711,28379,1793],{},[902,28381,28382],{"encoding":904},"B^*",") na změny ",[38,28385,28386],{},"endogenních"," rovnovážných veličin (",[883,28389,28391],{"className":28390},[886],[888,28392,28393],{"xmlns":890},[892,28394,28395,28403],{},[895,28396,28397],{},[1716,28398,28399,28401],{},[898,28400,1660],{},[898,28402,1722],{},[902,28404,3587],{"encoding":904},[883,28406,28408],{"className":28407},[886],[888,28409,28410],{"xmlns":890},[892,28411,28412,28420],{},[895,28413,28414],{},[1716,28415,28416,28418],{},[898,28417,1940],{},[898,28419,1722],{},[902,28421,3646],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,28424,21575],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,28427,28429],{"id":28428},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,28431,24493,28432,28455,28456,28500],{},[883,28433,28435],{"className":28434},[886],[888,28436,28437],{"xmlns":890},[892,28438,28439,28453],{},[895,28440,28441,28443,28445,28447,28449,28451],{},[898,28442,1940],{},[1711,28444,1836],{},[898,28446,207],{},[898,28448,1660],{},[1711,28450,2095],{},[898,28452,2223],{},[902,28454,22518],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,28457,28459],{"className":28458},[886],[888,28460,28461],{"xmlns":890},[892,28462,28463,28497],{},[895,28464,28465,28471,28473],{},[1716,28466,28467,28469],{},[898,28468,1660],{},[898,28470,1722],{},[1711,28472,1836],{},[2509,28474,28475],{"scriptlevel":2113,"displaystyle":1725},[2525,28476,28477,28489],{},[895,28478,28479,28481,28483],{},[898,28480,2223],{},[1711,28482,2095],{},[1716,28484,28485,28487],{},[898,28486,1833],{},[1711,28488,1793],{},[895,28490,28491,28493,28495],{},[2111,28492,2238],{},[1711,28494,2460],{},[898,28496,207],{},[902,28498,28499],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,28502,28503],{},[883,28504,28506],{"className":28505},[886],[888,28507,28508],{"xmlns":890},[892,28509,28510,28579],{},[895,28511,28512,28530,28532,28562,28564],{},[2525,28513,28514,28524],{},[895,28515,28516,28518],{},[898,28517,13846],{"mathvariant":2287},[1716,28519,28520,28522],{},[898,28521,1660],{},[898,28523,1722],{},[895,28525,28526,28528],{},[898,28527,13846],{"mathvariant":2287},[898,28529,207],{},[1711,28531,1836],{},[2525,28533,28534,28546],{},[895,28535,28536,28538,28540],{},[898,28537,2223],{},[1711,28539,2095],{},[1716,28541,28542,28544],{},[898,28543,1833],{},[1711,28545,1793],{},[895,28547,28548,28550,28552,28554,28556],{},[1711,28549,1714],{"stretchy":1713},[2111,28551,2238],{},[1711,28553,2460],{},[898,28555,207],{},[1716,28557,28558,28560],{},[1711,28559,1735],{"stretchy":1713},[2111,28561,2963],{},[2102,28563],{"width":2104},[895,28565,28566,28569,28576],{},[1942,28567,28568],{},"(multiplik",[12366,28570,28571,28573],{"accent":1725},[1942,28572,207],{},[1711,28574,28575],{},"ˊ",[1942,28577,28578],{},"tor MPC)",[902,28580,28581],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,28583,28584],{},[883,28585,28587],{"className":28586},[886],[888,28588,28589],{"xmlns":890},[892,28590,28591,28660],{},[895,28592,28593,28611,28613,28625,28627],{},[2525,28594,28595,28605],{},[895,28596,28597,28599],{},[898,28598,13846],{"mathvariant":2287},[1716,28600,28601,28603],{},[898,28602,1660],{},[898,28604,1722],{},[895,28606,28607,28609],{},[898,28608,13846],{"mathvariant":2287},[898,28610,2223],{},[1711,28612,1836],{},[2525,28614,28615,28617],{},[2111,28616,2238],{},[895,28618,28619,28621,28623],{},[2111,28620,2238],{},[1711,28622,2460],{},[898,28624,207],{},[2102,28626],{"width":2104},[895,28628,28629,28631,28637,28640,28647,28650,28657],{},[1942,28630,28568],{},[12366,28632,28633,28635],{"accent":1725},[1942,28634,207],{},[1711,28636,28575],{},[1942,28638,28639],{},"tor autonomn",[12366,28641,28642,28645],{"accent":1725},[1942,28643,28644],{},"ı",[1711,28646,28575],{},[1942,28648,28649],{}," spot",[12366,28651,28652,28654],{"accent":1725},[1942,28653,1675],{},[1711,28655,28656],{},"ˇ",[1942,28658,28659],{},"eby)",[902,28661,28662],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,28664,28665],{},[883,28666,28668],{"className":28667},[886],[888,28669,28670],{"xmlns":890},[892,28671,28672,28739],{},[895,28673,28674,28696,28698,28710,28712,28724,28726],{},[2525,28675,28676,28686],{},[895,28677,28678,28680],{},[898,28679,13846],{"mathvariant":2287},[1716,28681,28682,28684],{},[898,28683,1660],{},[898,28685,1722],{},[895,28687,28688,28690],{},[898,28689,13846],{"mathvariant":2287},[1716,28691,28692,28694],{},[898,28693,1833],{},[1711,28695,1793],{},[1711,28697,1836],{},[2525,28699,28700,28702],{},[2111,28701,2238],{},[895,28703,28704,28706,28708],{},[2111,28705,2238],{},[1711,28707,2460],{},[898,28709,207],{},[1711,28711,1836],{},[2525,28713,28714,28716],{},[2111,28715,2238],{},[895,28717,28718,28720,28722],{},[898,28719,1790],{},[898,28721,7929],{},[898,28723,2362],{},[2102,28725],{"width":2104},[895,28727,28728,28730,28736],{},[1942,28729,28568],{},[12366,28731,28732,28734],{"accent":1725},[1942,28733,207],{},[1711,28735,28575],{},[1942,28737,28738],{},"tor investic)",[902,28740,28741],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[1921,28743,28744],{},[724,28745,28746,28748,28749,28752,28753,28766,28767,28784,28785,28803,28804,28848,28849,25018,28866,28869,28870,28887],{},[883,28747,2678],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,28750,28751],{},"důchodem","; z něj se utratí ",[883,28754,28756],{"className":28755},[886],[888,28757,28758],{"xmlns":890},[892,28759,28760,28764],{},[895,28761,28762],{},[898,28763,207],{},[902,28765,207],{"encoding":904}," Kč (= ",[883,28768,28770],{"className":28769},[886],[888,28771,28772],{"xmlns":890},[892,28773,28774,28782],{},[895,28775,28776,28778,28780],{},[898,28777,1790],{},[898,28779,7929],{},[898,28781,1940],{},[902,28783,21643],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,28786,28788],{"className":28787},[886],[888,28789,28790],{"xmlns":890},[892,28791,28792,28800],{},[895,28793,28794],{},[1716,28795,28796,28798],{},[898,28797,207],{},[2111,28799,2963],{},[902,28801,28802],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,28805,28807],{"className":28806},[886],[888,28808,28809],{"xmlns":890},[892,28810,28811,28845],{},[895,28812,28813,28815,28817,28819,28821,28827,28829,28831,28833],{},[2111,28814,2238],{},[1711,28816,2095],{},[898,28818,207],{},[1711,28820,2095],{},[1716,28822,28823,28825],{},[898,28824,207],{},[2111,28826,2963],{},[1711,28828,2095],{},[1711,28830,21703],{},[1711,28832,1836],{},[2525,28834,28835,28837],{},[2111,28836,2238],{},[895,28838,28839,28841,28843],{},[2111,28840,2238],{},[1711,28842,2460],{},[898,28844,207],{},[902,28846,28847],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,28850,28852],{"className":28851},[886],[888,28853,28854],{"xmlns":890},[892,28855,28856,28864],{},[895,28857,28858],{},[1716,28859,28860,28862],{},[898,28861,1660],{},[898,28863,1722],{},[902,28865,3587],{"encoding":904},[38,28867,28868],{},"více"," než korunu — čím vyšší ",[883,28871,28873],{"className":28872},[886],[888,28874,28875],{"xmlns":890},[892,28876,28877,28885],{},[895,28878,28879,28881,28883],{},[898,28880,1790],{},[898,28882,7929],{},[898,28884,1940],{},[902,28886,21643],{"encoding":904},", tím silnější multiplikační efekt.",[724,28889,28890,28893,28894,28920,28921,28924,28925,2009,28946,28971,28972,2186],{},[38,28891,28892],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,28895,28897],{"className":28896},[886],[888,28898,28899],{"xmlns":890},[892,28900,28901,28917],{},[895,28902,28903],{},[2509,28904,28905],{"scriptlevel":2113,"displaystyle":1713},[2525,28906,28907,28909],{},[2111,28908,2238],{},[895,28910,28911,28913,28915],{},[2111,28912,2238],{},[1711,28914,2460],{},[898,28916,207],{},[902,28918,28919],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,28922,28923],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,28926,28928],{"className":28927},[886],[888,28929,28930],{"xmlns":890},[892,28931,28932,28944],{},[895,28933,28934,28936,28938,28940,28942],{},[898,28935,1940],{},[1942,28937,1944],{},[898,28939,1833],{},[1942,28941,1944],{},[898,28943,1755],{},[902,28945,21818],{"encoding":904},[883,28947,28949],{"className":28948},[886],[888,28950,28951],{"xmlns":890},[892,28952,28953,28969],{},[895,28954,28955,28957,28959,28961,28963,28965,28967],{},[898,28956,1940],{},[1942,28958,1944],{},[898,28960,1833],{},[1942,28962,1944],{},[898,28964,1755],{},[1942,28966,1944],{},[898,28968,1974],{},[902,28970,1977],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,28973,28975],{"className":28974,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,28977,28979],{"id":28978},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,28981,1813,28982,1343,28999,2009,29020,1818,29045,1648,29048,29069,29070,1700,29073,29086,29087,9652,29116,29133,29134,29137,29138,29140,29141,29162],{},[883,28983,28985],{"className":28984},[886],[888,28986,28987],{"xmlns":890},[892,28988,28989,28997],{},[895,28990,28991,28993,28995],{},[898,28992,1940],{},[1942,28994,1944],{},[898,28996,1833],{},[902,28998,1949],{"encoding":904},[883,29000,29002],{"className":29001},[886],[888,29003,29004],{"xmlns":890},[892,29005,29006,29018],{},[895,29007,29008,29010,29012,29014,29016],{},[898,29009,1940],{},[1942,29011,1944],{},[898,29013,1833],{},[1942,29015,1944],{},[898,29017,1755],{},[902,29019,21818],{"encoding":904},[883,29021,29023],{"className":29022},[886],[888,29024,29025],{"xmlns":890},[892,29026,29027,29043],{},[895,29028,29029,29031,29033,29035,29037,29039,29041],{},[898,29030,1940],{},[1942,29032,1944],{},[898,29034,1833],{},[1942,29036,1944],{},[898,29038,1755],{},[1942,29040,1944],{},[898,29042,1974],{},[902,29044,1977],{"encoding":904},[38,29046,29047],{},"investice konstantní",[883,29049,29051],{"className":29050},[886],[888,29052,29053],{"xmlns":890},[892,29054,29055,29067],{},[895,29056,29057,29059,29061],{},[898,29058,1833],{},[1711,29060,1836],{},[1716,29062,29063,29065],{},[898,29064,1833],{},[1711,29066,1793],{},[902,29068,1845],{"encoding":904},"). Reálnější je předpoklad, že ",[38,29071,29072],{},"investice závisejí na úrokové míře",[883,29074,29076],{"className":29075},[886],[888,29077,29078],{"xmlns":890},[892,29079,29080,29084],{},[895,29081,29082],{},[898,29083,1675],{},[902,29085,1675],{"encoding":904}," — klesající funkce ",[883,29088,29090],{"className":29089},[886],[888,29091,29092],{"xmlns":890},[892,29093,29094,29114],{},[895,29095,29096,29098,29100,29102,29104,29106,29108,29110,29112],{},[898,29097,1833],{},[1711,29099,1714],{"stretchy":1713},[898,29101,1675],{},[1711,29103,1735],{"stretchy":1713},[1711,29105,1836],{},[898,29107,2090],{},[898,29109,1675],{},[1711,29111,2095],{},[898,29113,2098],{},[902,29115,5459],{"encoding":904},[883,29117,29119],{"className":29118},[886],[888,29120,29121],{"xmlns":890},[892,29122,29123,29131],{},[895,29124,29125,29127,29129],{},[898,29126,2090],{},[1711,29128,2109],{},[2111,29130,2113],{},[902,29132,2181],{"encoding":904},". Přidáním ",[38,29135,29136],{},"trhu peněz"," k trhu zboží vzniká model ",[38,29139,1643],{}," se dvěma neznámými ",[883,29142,29144],{"className":29143},[886],[888,29145,29146],{"xmlns":890},[892,29147,29148,29160],{},[895,29149,29150,29152,29154,29156,29158],{},[1711,29151,1714],{"stretchy":1713},[898,29153,1660],{},[1711,29155,1726],{"separator":1725},[898,29157,1675],{},[1711,29159,1735],{"stretchy":1713},[902,29161,21748],{"encoding":904}," a dvěma rovnicemi:",[120,29164,29165,29215],{},[123,29166,29167,1648,29169,29171,29172,29193,29194,2186],{},[38,29168,5548],{},[614,29170,1688],{},") — klesající přímka v rovině ",[883,29173,29175],{"className":29174},[886],[888,29176,29177],{"xmlns":890},[892,29178,29179,29191],{},[895,29180,29181,29183,29185,29187,29189],{},[1711,29182,1714],{"stretchy":1713},[898,29184,1675],{},[1711,29186,1726],{"separator":1725},[898,29188,1660],{},[1711,29190,1735],{"stretchy":1713},[902,29192,2613],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,29195,29197],{"className":29196},[886],[888,29198,29199],{"xmlns":890},[892,29200,29201,29213],{},[895,29202,29203,29205,29207,29209,29211],{},[898,29204,1660],{},[1711,29206,1836],{},[898,29208,1940],{},[1711,29210,2095],{},[898,29212,1833],{},[902,29214,4436],{"encoding":904},[123,29216,29217,1648,29219,29221,29222,25192,29247,29293],{},[38,29218,5747],{},[614,29220,1695],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,29223,29225],{"className":29224},[886],[888,29226,29227],{"xmlns":890},[892,29228,29229,29245],{},[895,29230,29231,29237,29239],{},[1716,29232,29233,29235],{},[898,29234,1790],{},[898,29236,2778],{},[1711,29238,1836],{},[1716,29240,29241,29243],{},[898,29242,1790],{},[1711,29244,1793],{},[902,29246,3163],{"encoding":904},[883,29248,29250],{"className":29249},[886],[888,29251,29252],{"xmlns":890},[892,29253,29254,29290],{},[895,29255,29256,29262,29264,29270,29272,29274,29280,29282,29284],{},[1716,29257,29258,29260],{},[898,29259,1790],{},[898,29261,2778],{},[1711,29263,1836],{},[2884,29265,29266,29268],{},[898,29267,2918],{},[2111,29269,2238],{},[898,29271,1660],{},[1711,29273,2095],{},[2884,29275,29276,29278],{},[898,29277,2918],{},[2111,29279,2963],{},[898,29281,1675],{},[1711,29283,2095],{},[2884,29285,29286,29288],{},[898,29287,2918],{},[2111,29289,3034],{},[902,29291,29292],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,29295,29296,1700,29299,29332,29333,29335,29336,29338],{},[38,29297,29298],{},"Simultánní rovnovážný bod",[883,29300,29302],{"className":29301},[886],[888,29303,29304],{"xmlns":890},[892,29305,29306,29330],{},[895,29307,29308,29310,29312,29314,29320,29322,29328],{},[898,29309,1722],{},[1711,29311,1836],{},[1711,29313,1714],{"stretchy":1713},[1716,29315,29316,29318],{},[898,29317,1675],{},[898,29319,1722],{},[1711,29321,1726],{"separator":1725},[1716,29323,29324,29326],{},[898,29325,1660],{},[898,29327,1722],{},[1711,29329,1735],{"stretchy":1713},[902,29331,5839],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,29334,1742],{}," (posun IS) a ",[38,29337,1775],{}," (posun LM).",[724,29340,29341],{},[38,29342,29343,29344,1343,29366,1343,29388,1343,29410,29432,29433,2186],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,29345,29347],{"className":29346},[886],[888,29348,29349],{"xmlns":890},[892,29350,29351,29363],{},[895,29352,29353,29359,29361],{},[1716,29354,29355,29357],{},[898,29356,1660],{},[898,29358,1722],{},[1711,29360,1836],{},[2111,29362,4812],{},[902,29364,29365],{"encoding":904},"Y^E = 5000",[883,29367,29369],{"className":29368},[886],[888,29370,29371],{"xmlns":890},[892,29372,29373,29385],{},[895,29374,29375,29381,29383],{},[1716,29376,29377,29379],{},[898,29378,1675],{},[898,29380,1722],{},[1711,29382,1836],{},[2111,29384,4798],{},[902,29386,29387],{"encoding":904},"r^E = 5",[883,29389,29391],{"className":29390},[886],[888,29392,29393],{"xmlns":890},[892,29394,29395,29407],{},[895,29396,29397,29403,29405],{},[1716,29398,29399,29401],{},[898,29400,1940],{},[898,29402,1722],{},[1711,29404,1836],{},[2111,29406,4849],{},[902,29408,29409],{"encoding":904},"C^E = 4100",[883,29411,29413],{"className":29412},[886],[888,29414,29415],{"xmlns":890},[892,29416,29417,29429],{},[895,29418,29419,29425,29427],{},[1716,29420,29421,29423],{},[898,29422,1833],{},[898,29424,1722],{},[1711,29426,1836],{},[2111,29428,4888],{},[902,29430,29431],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,29434,945],{"className":29435,"dataFsResolvedFilePath":943,"href":944},[210],[115,29437,29439],{"id":29438},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,29441,29442,29506,29617,29760,30002,30070],{},[123,29443,29444,29447,29448,29470,29471,29505],{},[38,29445,29446],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,29449,29451],{"className":29450},[886],[888,29452,29453],{"xmlns":890},[892,29454,29455,29467],{},[895,29456,29457,29459,29461,29463,29465],{},[898,29458,1755],{},[898,29460,21892],{},[898,29462,7929],{},[1711,29464,6740],{},[898,29466,1660],{},[902,29468,29469],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,29472,29474],{"className":29473},[886],[888,29475,29476],{"xmlns":890},[892,29477,29478,29502],{},[895,29479,29480,29482,29484,29486,29488,29490,29492,29494,29496,29498,29500],{},[898,29481,1755],{},[898,29483,21892],{},[898,29485,7929],{},[1711,29487,1836],{},[898,29489,1940],{},[1711,29491,2095],{},[898,29493,1833],{},[1711,29495,2095],{},[898,29497,1755],{},[1711,29499,2095],{},[898,29501,1974],{},[902,29503,29504],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,29507,29508,29510,29511,29532,29533,1343,29556,29587,29588,29601,29602,2186],{},[38,29509,22126],{}," splňují ",[883,29512,29514],{"className":29513},[886],[888,29515,29516],{"xmlns":890},[892,29517,29518,29530],{},[895,29519,29520,29522,29524,29526,29528],{},[898,29521,1660],{},[1711,29523,1836],{},[898,29525,1940],{},[1711,29527,2095],{},[898,29529,2362],{},[902,29531,2365],{"encoding":904}," (7.2); lineární model ",[883,29534,29536],{"className":29535},[886],[888,29537,29538],{"xmlns":890},[892,29539,29540,29554],{},[895,29541,29542,29544,29546,29548,29550,29552],{},[898,29543,1940],{},[1711,29545,1836],{},[898,29547,207],{},[898,29549,1660],{},[1711,29551,2095],{},[898,29553,2223],{},[902,29555,22518],{"encoding":904},[883,29557,29559],{"className":29558},[886],[888,29560,29561],{"xmlns":890},[892,29562,29563,29585],{},[895,29564,29565,29567,29569,29571,29573,29575,29577,29579,29581,29583],{},[898,29566,2362],{},[1711,29568,1836],{},[1711,29570,1714],{"stretchy":1713},[2111,29572,2238],{},[1711,29574,2460],{},[898,29576,207],{},[1711,29578,1735],{"stretchy":1713},[898,29580,1660],{},[1711,29582,2460],{},[898,29584,2223],{},[902,29586,22767],{"encoding":904}," s autonomní spotřebou ",[883,29589,29591],{"className":29590},[886],[888,29592,29593],{"xmlns":890},[892,29594,29595,29599],{},[895,29596,29597],{},[898,29598,2223],{},[902,29600,2223],{"encoding":904}," a autonomními úsporami ",[883,29603,29605],{"className":29604},[886],[888,29606,29607],{"xmlns":890},[892,29608,29609,29615],{},[895,29610,29611,29613],{},[1711,29612,2460],{},[898,29614,2223],{},[902,29616,22846],{"encoding":904},[123,29618,29619,1700,29622,1343,29652,29682,29683,29713,29714,1343,29735,2186],{},[38,29620,29621],{},"Mezní sklony",[883,29623,29625],{"className":29624},[886],[888,29626,29627],{"xmlns":890},[892,29628,29629,29649],{},[895,29630,29631,29633,29635,29637,29639,29641,29643,29645,29647],{},[898,29632,1790],{},[898,29634,7929],{},[898,29636,1940],{},[1711,29638,1836],{},[898,29640,2098],{"mathvariant":2287},[898,29642,1940],{},[898,29644,8659],{"mathvariant":2287},[898,29646,2098],{"mathvariant":2287},[898,29648,1660],{},[902,29650,29651],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,29653,29655],{"className":29654},[886],[888,29656,29657],{"xmlns":890},[892,29658,29659,29679],{},[895,29660,29661,29663,29665,29667,29669,29671,29673,29675,29677],{},[898,29662,1790],{},[898,29664,7929],{},[898,29666,2362],{},[1711,29668,1836],{},[898,29670,2098],{"mathvariant":2287},[898,29672,2362],{},[898,29674,8659],{"mathvariant":2287},[898,29676,2098],{"mathvariant":2287},[898,29678,1660],{},[902,29680,29681],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,29684,29686],{"className":29685},[886],[888,29687,29688],{"xmlns":890},[892,29689,29690,29710],{},[895,29691,29692,29694,29696,29698,29700,29702,29704,29706,29708],{},[898,29693,1790],{},[898,29695,7929],{},[898,29697,1940],{},[1711,29699,2095],{},[898,29701,1790],{},[898,29703,7929],{},[898,29705,2362],{},[1711,29707,1836],{},[2111,29709,2238],{},[902,29711,29712],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,29715,29717],{"className":29716},[886],[888,29718,29719],{"xmlns":890},[892,29720,29721,29733],{},[895,29722,29723,29725,29727,29729,29731],{},[898,29724,1790],{},[898,29726,7929],{},[898,29728,1940],{},[1711,29730,1836],{},[898,29732,207],{},[902,29734,23487],{"encoding":904},[883,29736,29738],{"className":29737},[886],[888,29739,29740],{"xmlns":890},[892,29741,29742,29758],{},[895,29743,29744,29746,29748,29750,29752,29754,29756],{},[898,29745,1790],{},[898,29747,7929],{},[898,29749,2362],{},[1711,29751,1836],{},[2111,29753,2238],{},[1711,29755,2460],{},[898,29757,207],{},[902,29759,23513],{"encoding":904},[123,29761,29762,29765,29766],{},[38,29763,29764],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,29767,29768,29856,29925],{},[123,29769,29770,29787,29788,29809,29810,1726],{},[883,29771,29773],{"className":29772},[886],[888,29774,29775],{"xmlns":890},[892,29776,29777,29785],{},[895,29778,29779,29781,29783],{},[898,29780,1940],{},[1942,29782,1944],{},[898,29784,1833],{},[902,29786,1949],{"encoding":904},": ",[883,29789,29791],{"className":29790},[886],[888,29792,29793],{"xmlns":890},[892,29794,29795,29807],{},[895,29796,29797,29799,29801,29803,29805],{},[898,29798,1660],{},[1711,29800,1836],{},[898,29802,1940],{},[1711,29804,2095],{},[898,29806,1833],{},[902,29808,4436],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,29811,29813],{"className":29812},[886],[888,29814,29815],{"xmlns":890},[892,29816,29817,29853],{},[895,29818,29819,29825,29827,29829,29831,29833,29839,29841,29843,29845,29847,29849,29851],{},[1716,29820,29821,29823],{},[898,29822,1660],{},[898,29824,1722],{},[1711,29826,1836],{},[1711,29828,1714],{"stretchy":1713},[898,29830,2223],{},[1711,29832,2095],{},[1716,29834,29835,29837],{},[898,29836,1833],{},[1711,29838,1793],{},[1711,29840,1735],{"stretchy":1713},[898,29842,8659],{"mathvariant":2287},[1711,29844,1714],{"stretchy":1713},[2111,29846,2238],{},[1711,29848,2460],{},[898,29850,207],{},[1711,29852,1735],{"stretchy":1713},[902,29854,29855],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,29857,29858,29879,29880,29899,29900,1726],{},[883,29859,29861],{"className":29860},[886],[888,29862,29863],{"xmlns":890},[892,29864,29865,29877],{},[895,29866,29867,29869,29871,29873,29875],{},[898,29868,1940],{},[1942,29870,1944],{},[898,29872,1833],{},[1942,29874,1944],{},[898,29876,1755],{},[902,29878,21818],{"encoding":904},": přidává vládu, zdanění ",[883,29881,29883],{"className":29882},[886],[888,29884,29885],{"xmlns":890},[892,29886,29887,29897],{},[895,29888,29889,29891,29893,29895],{},[898,29890,1769],{},[1711,29892,1714],{"stretchy":1713},[898,29894,1660],{},[1711,29896,1735],{"stretchy":1713},[902,29898,25817],{"encoding":904}," a disponibilní důchod ",[883,29901,29903],{"className":29902},[886],[888,29904,29905],{"xmlns":890},[892,29906,29907,29923],{},[895,29908,29909,29915,29917,29919,29921],{},[2884,29910,29911,29913],{},[898,29912,1660],{},[898,29914,2778],{},[1711,29916,1836],{},[898,29918,1660],{},[1711,29920,2460],{},[898,29922,1769],{},[902,29924,25316],{"encoding":904},[123,29926,29927,29952,29953,25192,29974,2186],{},[883,29928,29930],{"className":29929},[886],[888,29931,29932],{"xmlns":890},[892,29933,29934,29950],{},[895,29935,29936,29938,29940,29942,29944,29946,29948],{},[898,29937,1940],{},[1942,29939,1944],{},[898,29941,1833],{},[1942,29943,1944],{},[898,29945,1755],{},[1942,29947,1944],{},[898,29949,1974],{},[902,29951,1977],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,29954,29956],{"className":29955},[886],[888,29957,29958],{"xmlns":890},[892,29959,29960,29972],{},[895,29961,29962,29964,29966,29968,29970],{},[898,29963,1974],{},[1711,29965,1836],{},[898,29967,26851],{},[1711,29969,2460],{},[898,29971,1790],{},[902,29973,26858],{"encoding":904},[883,29975,29977],{"className":29976},[886],[888,29978,29979],{"xmlns":890},[892,29980,29981,29999],{},[895,29982,29983,29985,29987,29989,29991,29997],{},[898,29984,1790],{},[1711,29986,1836],{},[898,29988,1790],{},[1711,29990,1714],{"stretchy":1713},[2884,29992,29993,29995],{},[898,29994,1660],{},[898,29996,2778],{},[1711,29998,1735],{"stretchy":1713},[902,30000,30001],{"encoding":904},"M = M(Y_D)",[123,30003,30004,30007,30008,1700,30011,30069],{},[38,30005,30006],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,30009,30010],{},"multiplikátor investic",[883,30012,30014],{"className":30013},[886],[888,30015,30016],{"xmlns":890},[892,30017,30018,30066],{},[895,30019,30020,30022,30028,30030,30032,30038,30040,30042,30044,30046,30048,30050,30052,30054,30056,30058,30060,30062,30064],{},[898,30021,13846],{"mathvariant":2287},[1716,30023,30024,30026],{},[898,30025,1660],{},[898,30027,1722],{},[898,30029,8659],{"mathvariant":2287},[898,30031,13846],{"mathvariant":2287},[1716,30033,30034,30036],{},[898,30035,1833],{},[1711,30037,1793],{},[1711,30039,1836],{},[2111,30041,2238],{},[898,30043,8659],{"mathvariant":2287},[1711,30045,1714],{"stretchy":1713},[2111,30047,2238],{},[1711,30049,2460],{},[898,30051,207],{},[1711,30053,1735],{"stretchy":1713},[1711,30055,1836],{},[2111,30057,2238],{},[898,30059,8659],{"mathvariant":2287},[898,30061,1790],{},[898,30063,7929],{},[898,30065,2362],{},[902,30067,30068],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,30071,30072,30074,30075,30090,30091,22246,30108,30123,30124,30149,30150,2186],{},[38,30073,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,30076,30078],{"className":30077},[886],[888,30079,30080],{"xmlns":890},[892,30081,30082,30088],{},[895,30083,30084,30086],{},[898,30085,1833],{},[898,30087,2362],{},[902,30089,1685],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,30092,30094],{"className":30093},[886],[888,30095,30096],{"xmlns":890},[892,30097,30098,30106],{},[895,30099,30100,30102,30104],{},[898,30101,1833],{},[1711,30103,1836],{},[898,30105,2362],{},[902,30107,2384],{"encoding":904},[883,30109,30111],{"className":30110},[886],[888,30112,30113],{"xmlns":890},[892,30114,30115,30121],{},[895,30116,30117,30119],{},[898,30118,2888],{},[898,30120,1790],{},[902,30122,1692],{"encoding":904}," rovnováhu trhu peněz (",[883,30125,30127],{"className":30126},[886],[888,30128,30129],{"xmlns":890},[892,30130,30131,30147],{},[895,30132,30133,30139,30141],{},[1716,30134,30135,30137],{},[898,30136,1790],{},[898,30138,2778],{},[1711,30140,1836],{},[1716,30142,30143,30145],{},[898,30144,1790],{},[1711,30146,1793],{},[902,30148,3163],{"encoding":904},"); průsečík dává ",[883,30151,30153],{"className":30152},[886],[888,30154,30155],{"xmlns":890},[892,30156,30157,30177],{},[895,30158,30159,30161,30167,30169,30175],{},[1711,30160,1714],{"stretchy":1713},[1716,30162,30163,30165],{},[898,30164,1660],{},[898,30166,1722],{},[1711,30168,1726],{"separator":1725},[1716,30170,30171,30173],{},[898,30172,1675],{},[898,30174,1722],{},[1711,30176,1735],{"stretchy":1713},[902,30178,1738],{"encoding":904},[115,30180,5422],{"id":5421},[120,30182,30183,30221,30261,30351,30433,30487,30543,30602,30637,30642,30714,30789,30875,30937,31005,31063,31116,31155],{},[123,30184,30185,5204,30188,29505],{},[38,30186,30187],{},"Hrubý národní produkt (GNP)",[883,30189,30191],{"className":30190},[886],[888,30192,30193],{"xmlns":890},[892,30194,30195,30219],{},[895,30196,30197,30199,30201,30203,30205,30207,30209,30211,30213,30215,30217],{},[898,30198,1755],{},[898,30200,21892],{},[898,30202,7929],{},[1711,30204,1836],{},[898,30206,1940],{},[1711,30208,2095],{},[898,30210,1833],{},[1711,30212,2095],{},[898,30214,1755],{},[1711,30216,2095],{},[898,30218,1974],{},[902,30220,29504],{"encoding":904},[123,30222,30223,30239,30240,2186],{},[38,30224,30225,30226],{},"Národní důchod ",[883,30227,30229],{"className":30228},[886],[888,30230,30231],{"xmlns":890},[892,30232,30233,30237],{},[895,30234,30235],{},[898,30236,1660],{},[902,30238,1660],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,30241,30243],{"className":30242},[886],[888,30244,30245],{"xmlns":890},[892,30246,30247,30259],{},[895,30248,30249,30251,30253,30255,30257],{},[898,30250,1755],{},[898,30252,21892],{},[898,30254,7929],{},[1711,30256,6740],{},[898,30258,1660],{},[902,30260,29469],{"encoding":904},[123,30262,30263,30289,30290,1343,30313,1343,30334,2186],{},[38,30264,30265,30266],{},"Funkce spotřeby ",[883,30267,30269],{"className":30268},[886],[888,30270,30271],{"xmlns":890},[892,30272,30273,30287],{},[895,30274,30275,30277,30279,30281,30283,30285],{},[898,30276,1940],{},[1711,30278,1836],{},[898,30280,1940],{},[1711,30282,1714],{"stretchy":1713},[898,30284,1660],{},[1711,30286,1735],{"stretchy":1713},[902,30288,24338],{"encoding":904}," — lineární model ",[883,30291,30293],{"className":30292},[886],[888,30294,30295],{"xmlns":890},[892,30296,30297,30311],{},[895,30298,30299,30301,30303,30305,30307,30309],{},[898,30300,1940],{},[1711,30302,1836],{},[898,30304,207],{},[898,30306,1660],{},[1711,30308,2095],{},[898,30310,2223],{},[902,30312,22518],{"encoding":904},[883,30314,30316],{"className":30315},[886],[888,30317,30318],{"xmlns":890},[892,30319,30320,30332],{},[895,30321,30322,30324,30326,30328,30330],{},[2111,30323,2113],{},[1711,30325,2109],{},[898,30327,207],{},[1711,30329,2109],{},[2111,30331,2238],{},[902,30333,22434],{"encoding":904},[883,30335,30337],{"className":30336},[886],[888,30338,30339],{"xmlns":890},[892,30340,30341,30349],{},[895,30342,30343,30345,30347],{},[898,30344,2223],{},[1711,30346,2123],{},[2111,30348,2113],{},[902,30350,22412],{"encoding":904},[123,30352,30353,5204,30380,30401,30402,2186],{},[38,30354,30355,30356],{},"Funkce úspor ",[883,30357,30359],{"className":30358},[886],[888,30360,30361],{"xmlns":890},[892,30362,30363,30377],{},[895,30364,30365,30367,30369,30371,30373,30375],{},[898,30366,2362],{},[1711,30368,1836],{},[898,30370,2362],{},[1711,30372,1714],{"stretchy":1713},[898,30374,1660],{},[1711,30376,1735],{"stretchy":1713},[902,30378,30379],{"encoding":904},"S = S(Y)",[883,30381,30383],{"className":30382},[886],[888,30384,30385],{"xmlns":890},[892,30386,30387,30399],{},[895,30388,30389,30391,30393,30395,30397],{},[898,30390,1660],{},[1711,30392,1836],{},[898,30394,1940],{},[1711,30396,2095],{},[898,30398,2362],{},[902,30400,2365],{"encoding":904},"; lineární ",[883,30403,30405],{"className":30404},[886],[888,30406,30407],{"xmlns":890},[892,30408,30409,30431],{},[895,30410,30411,30413,30415,30417,30419,30421,30423,30425,30427,30429],{},[898,30412,2362],{},[1711,30414,1836],{},[1711,30416,1714],{"stretchy":1713},[2111,30418,2238],{},[1711,30420,2460],{},[898,30422,207],{},[1711,30424,1735],{"stretchy":1713},[898,30426,1660],{},[1711,30428,2460],{},[898,30430,2223],{},[902,30432,22767],{"encoding":904},[123,30434,30435,5204,30438,1343,30461,2186],{},[38,30436,30437],{},"Autonomní spotřeba\u002Fúspory",[883,30439,30441],{"className":30440},[886],[888,30442,30443],{"xmlns":890},[892,30444,30445,30459],{},[895,30446,30447,30449,30451,30453,30455,30457],{},[898,30448,1940],{},[1711,30450,1714],{"stretchy":1713},[2111,30452,2113],{},[1711,30454,1735],{"stretchy":1713},[1711,30456,1836],{},[898,30458,2223],{},[902,30460,23159],{"encoding":904},[883,30462,30464],{"className":30463},[886],[888,30465,30466],{"xmlns":890},[892,30467,30468,30484],{},[895,30469,30470,30472,30474,30476,30478,30480,30482],{},[898,30471,2362],{},[1711,30473,1714],{"stretchy":1713},[2111,30475,2113],{},[1711,30477,1735],{"stretchy":1713},[1711,30479,1836],{},[1711,30481,2460],{},[898,30483,2223],{},[902,30485,30486],{"encoding":904},"S(0) = -b",[123,30488,30489,30521,30522,1797],{},[38,30490,30491,30492],{},"Mezní sklon ke spotřebě ",[883,30493,30495],{"className":30494},[886],[888,30496,30497],{"xmlns":890},[892,30498,30499,30519],{},[895,30500,30501,30503,30505,30507,30509,30511,30513,30515,30517],{},[898,30502,1790],{},[898,30504,7929],{},[898,30506,1940],{},[1711,30508,1836],{},[898,30510,2098],{"mathvariant":2287},[898,30512,1940],{},[898,30514,8659],{"mathvariant":2287},[898,30516,2098],{"mathvariant":2287},[898,30518,1660],{},[902,30520,29651],{"encoding":904}," (v lineárním modelu ",[883,30523,30525],{"className":30524},[886],[888,30526,30527],{"xmlns":890},[892,30528,30529,30541],{},[895,30530,30531,30533,30535,30537,30539],{},[898,30532,1790],{},[898,30534,7929],{},[898,30536,1940],{},[1711,30538,1836],{},[898,30540,207],{},[902,30542,23487],{"encoding":904},[123,30544,30545,30521,30577,1797],{},[38,30546,30547,30548],{},"Mezní sklon k úsporám ",[883,30549,30551],{"className":30550},[886],[888,30552,30553],{"xmlns":890},[892,30554,30555,30575],{},[895,30556,30557,30559,30561,30563,30565,30567,30569,30571,30573],{},[898,30558,1790],{},[898,30560,7929],{},[898,30562,2362],{},[1711,30564,1836],{},[898,30566,2098],{"mathvariant":2287},[898,30568,2362],{},[898,30570,8659],{"mathvariant":2287},[898,30572,2098],{"mathvariant":2287},[898,30574,1660],{},[902,30576,29681],{"encoding":904},[883,30578,30580],{"className":30579},[886],[888,30581,30582],{"xmlns":890},[892,30583,30584,30600],{},[895,30585,30586,30588,30590,30592,30594,30596,30598],{},[898,30587,1790],{},[898,30589,7929],{},[898,30591,2362],{},[1711,30593,1836],{},[2111,30595,2238],{},[1711,30597,2460],{},[898,30599,207],{},[902,30601,23513],{"encoding":904},[123,30603,30604,1700,30607,30636],{},[38,30605,30606],{},"Vztah",[883,30608,30610],{"className":30609},[886],[888,30611,30612],{"xmlns":890},[892,30613,30614,30634],{},[895,30615,30616,30618,30620,30622,30624,30626,30628,30630,30632],{},[898,30617,1790],{},[898,30619,7929],{},[898,30621,1940],{},[1711,30623,2095],{},[898,30625,1790],{},[898,30627,7929],{},[898,30629,2362],{},[1711,30631,1836],{},[2111,30633,2238],{},[902,30635,29712],{"encoding":904}," (7.5).",[123,30638,30639,30641],{},[38,30640,24181],{}," — rovnováha agregátní poptávky a nabídky.",[123,30643,30644,30647,30648,5494,30669,2186],{},[38,30645,30646],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,30649,30651],{"className":30650},[886],[888,30652,30653],{"xmlns":890},[892,30654,30655,30667],{},[895,30656,30657,30659,30661,30663,30665],{},[898,30658,1660],{},[1711,30660,1836],{},[898,30662,1940],{},[1711,30664,2095],{},[898,30666,1833],{},[902,30668,4436],{"encoding":904},[883,30670,30672],{"className":30671},[886],[888,30673,30674],{"xmlns":890},[892,30675,30676,30712],{},[895,30677,30678,30684,30686,30688,30690,30692,30698,30700,30702,30704,30706,30708,30710],{},[1716,30679,30680,30682],{},[898,30681,1660],{},[898,30683,1722],{},[1711,30685,1836],{},[1711,30687,1714],{"stretchy":1713},[898,30689,2223],{},[1711,30691,2095],{},[1716,30693,30694,30696],{},[898,30695,1833],{},[1711,30697,1793],{},[1711,30699,1735],{"stretchy":1713},[898,30701,8659],{"mathvariant":2287},[1711,30703,1714],{"stretchy":1713},[2111,30705,2238],{},[1711,30707,2460],{},[898,30709,207],{},[1711,30711,1735],{"stretchy":1713},[902,30713,29855],{"encoding":904},[123,30715,30716,30719,30720,1343,30739,5494,30764,2186],{},[38,30717,30718],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,30721,30723],{"className":30722},[886],[888,30724,30725],{"xmlns":890},[892,30726,30727,30737],{},[895,30728,30729,30731,30733,30735],{},[898,30730,1769],{},[1711,30732,1714],{"stretchy":1713},[898,30734,1660],{},[1711,30736,1735],{"stretchy":1713},[902,30738,25817],{"encoding":904},[883,30740,30742],{"className":30741},[886],[888,30743,30744],{"xmlns":890},[892,30745,30746,30762],{},[895,30747,30748,30754,30756,30758,30760],{},[2884,30749,30750,30752],{},[898,30751,1660],{},[898,30753,2778],{},[1711,30755,1836],{},[898,30757,1660],{},[1711,30759,2460],{},[898,30761,1769],{},[902,30763,25316],{"encoding":904},[883,30765,30767],{"className":30766},[886],[888,30768,30769],{"xmlns":890},[892,30770,30771,30787],{},[895,30772,30773,30775,30777,30779,30781,30783,30785],{},[898,30774,1660],{},[1711,30776,1836],{},[898,30778,1940],{},[1711,30780,2095],{},[898,30782,1833],{},[1711,30784,2095],{},[898,30786,1755],{},[902,30788,25287],{"encoding":904},[123,30790,30791,30794,30795,30816,30817,5494,30841,2186],{},[38,30792,30793],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,30796,30798],{"className":30797},[886],[888,30799,30800],{"xmlns":890},[892,30801,30802,30814],{},[895,30803,30804,30806,30808,30810,30812],{},[898,30805,1974],{},[1711,30807,1836],{},[898,30809,26851],{},[1711,30811,2460],{},[898,30813,1790],{},[902,30815,26858],{"encoding":904},", importem ",[883,30818,30820],{"className":30819},[886],[888,30821,30822],{"xmlns":890},[892,30823,30824,30838],{},[895,30825,30826,30828,30830,30836],{},[898,30827,1790],{},[1711,30829,1714],{"stretchy":1713},[2884,30831,30832,30834],{},[898,30833,1660],{},[898,30835,2778],{},[1711,30837,1735],{"stretchy":1713},[902,30839,30840],{"encoding":904},"M(Y_D)",[883,30842,30844],{"className":30843},[886],[888,30845,30846],{"xmlns":890},[892,30847,30848,30872],{},[895,30849,30850,30852,30854,30856,30858,30860,30862,30864,30866,30868,30870],{},[898,30851,1660],{},[1711,30853,1836],{},[898,30855,1940],{},[1711,30857,2095],{},[898,30859,1833],{},[1711,30861,2095],{},[898,30863,1755],{},[1711,30865,2095],{},[898,30867,26851],{},[1711,30869,2460],{},[898,30871,1790],{},[902,30873,30874],{"encoding":904},"Y = C + I + G + B - M",[123,30876,30877,5204,30880,30069],{},[38,30878,30879],{},"Multiplikátor investic",[883,30881,30883],{"className":30882},[886],[888,30884,30885],{"xmlns":890},[892,30886,30887,30935],{},[895,30888,30889,30891,30897,30899,30901,30907,30909,30911,30913,30915,30917,30919,30921,30923,30925,30927,30929,30931,30933],{},[898,30890,13846],{"mathvariant":2287},[1716,30892,30893,30895],{},[898,30894,1660],{},[898,30896,1722],{},[898,30898,8659],{"mathvariant":2287},[898,30900,13846],{"mathvariant":2287},[1716,30902,30903,30905],{},[898,30904,1833],{},[1711,30906,1793],{},[1711,30908,1836],{},[2111,30910,2238],{},[898,30912,8659],{"mathvariant":2287},[1711,30914,1714],{"stretchy":1713},[2111,30916,2238],{},[1711,30918,2460],{},[898,30920,207],{},[1711,30922,1735],{"stretchy":1713},[1711,30924,1836],{},[2111,30926,2238],{},[898,30928,8659],{"mathvariant":2287},[898,30930,1790],{},[898,30932,7929],{},[898,30934,2362],{},[902,30936,30068],{"encoding":904},[123,30938,30939,5204,30970,1343,30987,31004],{},[38,30940,5429,30941],{},[883,30942,30944],{"className":30943},[886],[888,30945,30946],{"xmlns":890},[892,30947,30948,30968],{},[895,30949,30950,30952,30954,30956,30958,30960,30962,30964,30966],{},[898,30951,1833],{},[1711,30953,1714],{"stretchy":1713},[898,30955,1675],{},[1711,30957,1735],{"stretchy":1713},[1711,30959,1836],{},[898,30961,2090],{},[898,30963,1675],{},[1711,30965,2095],{},[898,30967,2098],{},[902,30969,5459],{"encoding":904},[883,30971,30973],{"className":30972},[886],[888,30974,30975],{"xmlns":890},[892,30976,30977,30985],{},[895,30978,30979,30981,30983],{},[898,30980,2090],{},[1711,30982,2109],{},[2111,30984,2113],{},[902,30986,2181],{"encoding":904},[883,30988,30990],{"className":30989},[886],[888,30991,30992],{"xmlns":890},[892,30993,30994,31002],{},[895,30995,30996,30998,31000],{},[898,30997,2098],{},[1711,30999,2123],{},[2111,31001,2113],{},[902,31003,2160],{"encoding":904},"; klesající.",[123,31006,31007,31009,31010,31012,31013,31062],{},[38,31008,5548],{}," — rovnováha na trhu zboží (",[614,31011,1688],{},"); ",[883,31014,31016],{"className":31015},[886],[888,31017,31018],{"xmlns":890},[892,31019,31020,31060],{},[895,31021,31022,31024,31026,31038,31040,31042],{},[898,31023,1660],{},[1711,31025,1836],{},[2525,31027,31028,31030],{},[898,31029,2090],{},[895,31031,31032,31034,31036],{},[2111,31033,2238],{},[1711,31035,2460],{},[898,31037,207],{},[898,31039,1675],{},[1711,31041,2095],{},[2525,31043,31044,31052],{},[895,31045,31046,31048,31050],{},[898,31047,2223],{},[1711,31049,2095],{},[898,31051,2098],{},[895,31053,31054,31056,31058],{},[2111,31055,2238],{},[1711,31057,2460],{},[898,31059,207],{},[902,31061,5601],{"encoding":904}," (7.14); klesající.",[123,31064,31065,31067,31068,31012,31070,31115],{},[38,31066,5747],{}," — rovnováha na trhu peněz (",[614,31069,1695],{},[883,31071,31073],{"className":31072},[886],[888,31074,31075],{"xmlns":890},[892,31076,31077,31113],{},[895,31078,31079,31085,31087,31093,31095,31097,31103,31105,31107],{},[1716,31080,31081,31083],{},[898,31082,1790],{},[1711,31084,1793],{},[1711,31086,1836],{},[2884,31088,31089,31091],{},[898,31090,2918],{},[2111,31092,2238],{},[898,31094,1660],{},[1711,31096,2095],{},[2884,31098,31099,31101],{},[898,31100,2918],{},[2111,31102,2963],{},[898,31104,1675],{},[1711,31106,2095],{},[2884,31108,31109,31111],{},[898,31110,2918],{},[2111,31112,3034],{},[902,31114,5795],{"encoding":904}," (7.15); rostoucí.",[123,31117,31118,5204,31121,2186],{},[38,31119,31120],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,31122,31124],{"className":31123},[886],[888,31125,31126],{"xmlns":890},[892,31127,31128,31152],{},[895,31129,31130,31136,31138,31144,31146],{},[1716,31131,31132,31134],{},[898,31133,1790],{},[898,31135,2778],{},[1711,31137,1836],{},[2884,31139,31140,31142],{},[898,31141,2888],{},[2111,31143,2238],{},[1711,31145,2095],{},[2884,31147,31148,31150],{},[898,31149,2888],{},[2111,31151,2963],{},[902,31153,31154],{"encoding":904},"M^D = L_1 + L_2",[123,31156,31157,5805,31159,3664,31172,2009,31187,31202,31203,2186],{},[38,31158,945],{},[883,31160,31162],{"className":31161},[886],[888,31163,31164],{"xmlns":890},[892,31165,31166,31170],{},[895,31167,31168],{},[898,31169,1722],{},[902,31171,1722],{"encoding":904},[883,31173,31175],{"className":31174},[886],[888,31176,31177],{"xmlns":890},[892,31178,31179,31185],{},[895,31180,31181,31183],{},[898,31182,1833],{},[898,31184,2362],{},[902,31186,1685],{"encoding":904},[883,31188,31190],{"className":31189},[886],[888,31191,31192],{"xmlns":890},[892,31193,31194,31200],{},[895,31195,31196,31198],{},[898,31197,2888],{},[898,31199,1790],{},[902,31201,1692],{"encoding":904}," určuje ",[883,31204,31206],{"className":31205},[886],[888,31207,31208],{"xmlns":890},[892,31209,31210,31230],{},[895,31211,31212,31214,31220,31222,31228],{},[1711,31213,1714],{"stretchy":1713},[1716,31215,31216,31218],{},[898,31217,1660],{},[898,31219,1722],{},[1711,31221,1726],{"separator":1725},[1716,31223,31224,31226],{},[898,31225,1675],{},[898,31227,1722],{},[1711,31229,1735],{"stretchy":1713},[902,31231,1738],{"encoding":904},[115,31233,5901],{"id":5900},[120,31235,31236,31243,31250],{},[123,31237,31238,1700,31240],{},[38,31239,5908],{},[207,31241,5914],{"className":31242,"dataFsResolvedFilePath":5912,"href":5913},[210],[123,31244,31245,1700,31247],{},[38,31246,5919],{},[207,31248,5923],{"className":31249,"dataFsResolvedFilePath":868,"href":869},[210],[123,31251,31252,31254],{},[38,31253,5938],{},[120,31255,31256,31262,31268,31274],{},[123,31257,31258,31261],{},[207,31259,5980],{"className":31260,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,31263,31264,31267],{},[207,31265,5946],{"className":31266,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,31269,31270,31273],{},[207,31271,6952],{"className":31272,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,31275,31276,31279,31280,1343,31297,31314],{},[207,31277,1145],{"className":31278,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,31281,31283],{"className":31282},[886],[888,31284,31285],{"xmlns":890},[892,31286,31287,31295],{},[895,31288,31289,31291,31293],{},[898,31290,1790],{},[898,31292,7929],{},[898,31294,1940],{},[902,31296,21643],{"encoding":904},[883,31298,31300],{"className":31299},[886],[888,31301,31302],{"xmlns":890},[892,31303,31304,31312],{},[895,31305,31306,31308,31310],{},[898,31307,1790],{},[898,31309,7929],{},[898,31311,2362],{},[902,31313,23257],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":31316},[31317,31318,31319,31320,31325,31328,31329,31336,31341,31346,31349,31350,31351,31352],{"id":1637,"depth":642,"text":1638},{"id":21752,"depth":642,"text":21753},{"id":21872,"depth":642,"text":21873},{"id":22125,"depth":642,"text":22126,"children":31321},[31322,31323,31324],{"id":22129,"depth":649,"text":22130},{"id":22341,"depth":649,"text":22342},{"id":22849,"depth":649,"text":22850},{"id":23169,"depth":642,"text":23170,"children":31326},[31327],{"id":23685,"depth":649,"text":23686},{"id":24180,"depth":642,"text":24181},{"id":24207,"depth":642,"text":24208,"children":31330},[31331,31332,31333,31335],{"id":24218,"depth":649,"text":24219},{"id":24288,"depth":649,"text":24289},{"id":24472,"depth":649,"text":31334},"Výpočet YEY^E",{"id":24615,"depth":649,"text":24616},{"id":24993,"depth":642,"text":24994,"children":31337},[31338,31339,31340],{"id":24997,"depth":649,"text":24219},{"id":25446,"depth":649,"text":24289},{"id":26102,"depth":649,"text":26103},{"id":26889,"depth":642,"text":26890,"children":31342},[31343,31344,31345],{"id":26893,"depth":649,"text":24219},{"id":27038,"depth":649,"text":24289},{"id":27308,"depth":649,"text":27309},{"id":28232,"depth":642,"text":28233,"children":31347},[31348],{"id":28428,"depth":649,"text":28429},{"id":28978,"depth":642,"text":28979},{"id":29438,"depth":642,"text":29439},{"id":5421,"depth":642,"text":5422},{"id":5900,"depth":642,"text":5901},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,5932,1143,31359,31360,31361,5980,21481],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":31364,"title":31365,"body":31366,"course":1128,"courses":659,"created":5973,"description":641,"extension":661,"meta":40346,"navigation":664,"path":40347,"seo":40348,"sources":40349,"stem":40350,"tags":40351,"type":5985,"updated":677,"__hash__":40356},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":31367,"toc":40315},[31368,31371,31373,31602,31606,31659,31729,31841,32000,32004,32120,32124,32127,32249,32252,32445,32469,32537,32701,32719,32785,33163,33167,33174,33418,33474,33478,33543,33661,33793,33825,33945,34027,34030,34152,34345,34566,34570,34610,34715,34772,34872,35049,35179,35232,35235,35322,35326,35502,35506,35509,35594,35597,35654,35759,35763,35884,35887,36070,36073,36181,36390,36710,36758,36831,36905,36907,37131,37366,37634,37638,37641,37746,37803,37837,37884,37917,38001,38003,38235,38368,38445,38567,38722,38726,38867,38874,39098,39109,39113,39117,39222,39364,39474,39573,39577,39736,39846,39848,40241,40243],[12,31369,31365],{"id":31370},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,31372,1638],{"id":1637},[724,31374,31375,31377,31378,31412,31413,31416,31417,31448,31449,31495,31496,31499,31500,31542,31543,31561,31562,31566,31567,31597,31598,31601],{},[38,31376,913],{}," řeší, jaký svazek zboží ",[883,31379,31381],{"className":31380},[886],[888,31382,31383],{"xmlns":890},[892,31384,31385,31409],{},[895,31386,31387,31389,31397,31399,31407],{},[1711,31388,5144],{"stretchy":1713},[13142,31390,31391,31393,31395],{},[898,31392,6796],{},[2111,31394,2238],{},[1711,31396,1793],{},[1711,31398,1726],{"separator":1725},[13142,31400,31401,31403,31405],{},[898,31402,6796],{},[2111,31404,2963],{},[1711,31406,1793],{},[1711,31408,5163],{"stretchy":1713},[902,31410,31411],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,31414,31415],{},"primární úloha"," — maximalizace užitečnosti ",[883,31418,31420],{"className":31419},[886],[888,31421,31422],{"xmlns":890},[892,31423,31424,31446],{},[895,31425,31426,31428,31430,31436,31438,31444],{},[898,31427,900],{},[1711,31429,1714],{"stretchy":1713},[2884,31431,31432,31434],{},[898,31433,6796],{},[2111,31435,2238],{},[1711,31437,1726],{"separator":1725},[2884,31439,31440,31442],{},[898,31441,6796],{},[2111,31443,2963],{},[1711,31445,1735],{"stretchy":1713},[902,31447,19941],{"encoding":904}," při rozpočtovém omezení ",[883,31450,31452],{"className":31451},[886],[888,31453,31454],{"xmlns":890},[892,31455,31456,31492],{},[895,31457,31458,31464,31466,31472,31478,31480,31486],{},[1716,31459,31460,31462],{},[898,31461,1660],{},[1711,31463,1793],{},[1711,31465,1836],{},[2884,31467,31468,31470],{},[898,31469,7929],{},[2111,31471,2238],{},[2884,31473,31474,31476],{},[898,31475,6796],{},[2111,31477,2238],{},[1711,31479,2095],{},[2884,31481,31482,31484],{},[898,31483,7929],{},[2111,31485,2963],{},[2884,31487,31488,31490],{},[898,31489,6796],{},[2111,31491,2963],{},[902,31493,31494],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,31497,31498],{},"duální úloha"," — minimalizace výdajů ",[883,31501,31503],{"className":31502},[886],[888,31504,31505],{"xmlns":890},[892,31506,31507,31539],{},[895,31508,31509,31511,31513,31519,31525,31527,31533],{},[898,31510,1722],{},[1711,31512,1836],{},[2884,31514,31515,31517],{},[898,31516,7929],{},[2111,31518,2238],{},[2884,31520,31521,31523],{},[898,31522,6796],{},[2111,31524,2238],{},[1711,31526,2095],{},[2884,31528,31529,31531],{},[898,31530,7929],{},[2111,31532,2963],{},[2884,31534,31535,31537],{},[898,31536,6796],{},[2111,31538,2963],{},[902,31540,31541],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,31544,31546],{"className":31545},[886],[888,31547,31548],{"xmlns":890},[892,31549,31550,31558],{},[895,31551,31552],{},[1716,31553,31554,31556],{},[898,31555,900],{},[1711,31557,1793],{},[902,31559,31560],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,31563,31565],{"className":31564,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,31568,31570],{"className":31569},[886],[888,31571,31572],{"xmlns":890},[892,31573,31574,31594],{},[895,31575,31576,31578,31580,31586,31588],{},[1942,31577,14576],{},[1711,31579,1836],{},[2884,31581,31582,31584],{},[898,31583,7929],{},[2111,31585,2238],{},[898,31587,8659],{"mathvariant":2287},[2884,31589,31590,31592],{},[898,31591,7929],{},[2111,31593,2963],{},[902,31595,31596],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,31599,31600],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,31603,31605],{"id":31604},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,31607,31608,31609,31627,31628,31658],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,31610,31612],{"className":31611},[886],[888,31613,31614],{"xmlns":890},[892,31615,31616,31624],{},[895,31617,31618],{},[1716,31619,31620,31622],{},[898,31621,1660],{},[1711,31623,1793],{},[902,31625,31626],{"encoding":904},"Y^*"," a ceny ",[883,31629,31631],{"className":31630},[886],[888,31632,31633],{"xmlns":890},[892,31634,31635,31655],{},[895,31636,31637,31645,31647],{},[13142,31638,31639,31641,31643],{},[898,31640,7929],{},[2111,31642,2238],{},[1711,31644,1793],{},[1711,31646,1726],{"separator":1725},[13142,31648,31649,31651,31653],{},[898,31650,7929],{},[2111,31652,2963],{},[1711,31654,1793],{},[902,31656,31657],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,31660,31662],{"className":31661},[886],[888,31663,31665],{"xmlns":890,"display":31664},"block",[892,31666,31667,31726],{},[24352,31668,31670],{"width":31669},"100%",[24357,31671,31672,31675,31719,31721],{},[24360,31673],{"width":31674},"50%",[24360,31676,31677],{},[895,31678,31679,31685,31687,31695,31701,31703,31711,31717],{},[1716,31680,31681,31683],{},[898,31682,1660],{},[1711,31684,1793],{},[1711,31686,1836],{},[13142,31688,31689,31691,31693],{},[898,31690,7929],{},[2111,31692,2238],{},[1711,31694,1793],{},[2884,31696,31697,31699],{},[898,31698,6796],{},[2111,31700,2238],{},[1711,31702,2095],{},[13142,31704,31705,31707,31709],{},[898,31706,7929],{},[2111,31708,2963],{},[1711,31710,1793],{},[2884,31712,31713,31715],{},[898,31714,6796],{},[2111,31716,2963],{},[1711,31718,1726],{"separator":1725},[24360,31720],{"width":31674},[24360,31722,31723],{},[1942,31724,31725],{},"(6.12)",[902,31727,31728],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,31730,31731,31732,31735,31736,2009,31772,31808,31809,31822,31823,31837,31838,2186],{},"geometricky ",[38,31733,31734],{},"rozpočtová přímka (budget line)"," procházející body ",[883,31737,31739],{"className":31738},[886],[888,31740,31741],{"xmlns":890},[892,31742,31743,31769],{},[895,31744,31745,31747,31753,31755,31763,31765,31767],{},[1711,31746,5144],{"stretchy":1713},[1716,31748,31749,31751],{},[898,31750,1660],{},[1711,31752,1793],{},[898,31754,8659],{"mathvariant":2287},[13142,31756,31757,31759,31761],{},[898,31758,7929],{},[2111,31760,2238],{},[1711,31762,1793],{},[1711,31764,1726],{"separator":1725},[2111,31766,2113],{},[1711,31768,5163],{"stretchy":1713},[902,31770,31771],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,31773,31775],{"className":31774},[886],[888,31776,31777],{"xmlns":890},[892,31778,31779,31805],{},[895,31780,31781,31783,31785,31787,31793,31795,31803],{},[1711,31782,5144],{"stretchy":1713},[2111,31784,2113],{},[1711,31786,1726],{"separator":1725},[1716,31788,31789,31791],{},[898,31790,1660],{},[1711,31792,1793],{},[898,31794,8659],{"mathvariant":2287},[13142,31796,31797,31799,31801],{},[898,31798,7929],{},[2111,31800,2963],{},[1711,31802,1793],{},[1711,31804,5163],{"stretchy":1713},[902,31806,31807],{"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 ",[883,31810,31812],{"className":31811},[886],[888,31813,31814],{"xmlns":890},[892,31815,31816,31820],{},[895,31817,31818],{},[898,31819,900],{},[902,31821,900],{"encoding":904},", indiferenční křivky a ",[883,31824,31826],{"className":31825},[886],[888,31827,31828],{"xmlns":890},[892,31829,31830,31834],{},[895,31831,31832],{},[1942,31833,14576],{},[902,31835,31836],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,31839,880],{"className":31840,"dataFsResolvedFilePath":878,"href":879},[210],[1921,31842,31843],{},[724,31844,31845,31847,31848,31851,31852,31865,31866,31868,31869,31882,31883,1700,31886,31926,31927,31944,31945,31962,31963,31980,31981,31999],{},[883,31846,1927],{}," Pozor — dvě úlohy, totéž řešení\n",[38,31849,31850],{},"Primární úloha"," (max ",[883,31853,31855],{"className":31854},[886],[888,31856,31857],{"xmlns":890},[892,31858,31859,31863],{},[895,31860,31861],{},[898,31862,900],{},[902,31864,900],{"encoding":904}," při pevném rozpočtu) a ",[38,31867,31498],{}," (min ",[883,31870,31872],{"className":31871},[886],[888,31873,31874],{"xmlns":890},[892,31875,31876,31880],{},[895,31877,31878],{},[898,31879,1722],{},[902,31881,1722],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,31884,31885],{},"tentýž bod",[883,31887,31889],{"className":31888},[886],[888,31890,31891],{"xmlns":890},[892,31892,31893,31923],{},[895,31894,31895,31901,31903,31911,31913,31921],{},[1716,31896,31897,31899],{},[898,31898,6796],{},[1711,31900,1793],{},[1711,31902,5144],{"stretchy":1713},[13142,31904,31905,31907,31909],{},[898,31906,6796],{},[2111,31908,2238],{},[1711,31910,1793],{},[1711,31912,1726],{"separator":1725},[13142,31914,31915,31917,31919],{},[898,31916,6796],{},[2111,31918,2963],{},[1711,31920,1793],{},[1711,31922,5163],{"stretchy":1713},[902,31924,31925],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,31928,31930],{"className":31929},[886],[888,31931,31932],{"xmlns":890},[892,31933,31934,31942],{},[895,31935,31936],{},[1716,31937,31938,31940],{},[898,31939,1660],{},[1711,31941,1793],{},[902,31943,31626],{"encoding":904}," a hledáme maximální ",[883,31946,31948],{"className":31947},[886],[888,31949,31950],{"xmlns":890},[892,31951,31952,31960],{},[895,31953,31954],{},[1716,31955,31956,31958],{},[898,31957,900],{},[1711,31959,1793],{},[902,31961,31560],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,31964,31966],{"className":31965},[886],[888,31967,31968],{"xmlns":890},[892,31969,31970,31978],{},[895,31971,31972],{},[1716,31973,31974,31976],{},[898,31975,900],{},[1711,31977,1793],{},[902,31979,31560],{"encoding":904}," a hledáme minimální ",[883,31982,31984],{"className":31983},[886],[888,31985,31986],{"xmlns":890},[892,31987,31988,31996],{},[895,31989,31990],{},[1716,31991,31992,31994],{},[898,31993,1722],{},[1711,31995,1793],{},[902,31997,31998],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,32001,32003],{"id":32002},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,32005,32006,32007,32038,32039,32115,32116,2186],{},"Úlohou je najít maximum ",[883,32008,32010],{"className":32009},[886],[888,32011,32012],{"xmlns":890},[892,32013,32014,32036],{},[895,32015,32016,32018,32020,32026,32028,32034],{},[898,32017,900],{},[1711,32019,1714],{"stretchy":1713},[2884,32021,32022,32024],{},[898,32023,6796],{},[2111,32025,2238],{},[1711,32027,1726],{"separator":1725},[2884,32029,32030,32032],{},[898,32031,6796],{},[2111,32033,2963],{},[1711,32035,1735],{"stretchy":1713},[902,32037,19941],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,32040,32042],{"className":32041},[886],[888,32043,32044],{"xmlns":890},[892,32045,32046,32112],{},[895,32047,32048,32050,32052,32058,32060,32066,32068,32070,32076,32078,32086,32092,32094,32102,32108,32110],{},[898,32049,15014],{},[1711,32051,1714],{"stretchy":1713},[2884,32053,32054,32056],{},[898,32055,6796],{},[2111,32057,2238],{},[1711,32059,1726],{"separator":1725},[2884,32061,32062,32064],{},[898,32063,6796],{},[2111,32065,2963],{},[1711,32067,1735],{"stretchy":1713},[1711,32069,1836],{},[1716,32071,32072,32074],{},[898,32073,1660],{},[1711,32075,1793],{},[1711,32077,2460],{},[13142,32079,32080,32082,32084],{},[898,32081,7929],{},[2111,32083,2238],{},[1711,32085,1793],{},[2884,32087,32088,32090],{},[898,32089,6796],{},[2111,32091,2238],{},[1711,32093,2460],{},[13142,32095,32096,32098,32100],{},[898,32097,7929],{},[2111,32099,2963],{},[1711,32101,1793],{},[2884,32103,32104,32106],{},[898,32105,6796],{},[2111,32107,2963],{},[1711,32109,1836],{},[2111,32111,2113],{},[902,32113,32114],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,32117,32119],{"className":32118,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,32121,32123],{"id":32122},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,32125,32126],{},"Sestavíme",[883,32128,32130],{"className":32129},[886],[888,32131,32132],{"xmlns":890,"display":31664},[892,32133,32134,32246],{},[24352,32135,32136],{"width":31669},[24357,32137,32138,32140,32239,32241],{},[24360,32139],{"width":31674},[24360,32141,32142],{},[895,32143,32144,32147,32149,32155,32157,32163,32165,32167,32169,32171,32173,32175,32181,32183,32189,32191,32193,32195,32197,32203,32205,32213,32219,32221,32229,32235,32237],{},[898,32145,2888],{"mathvariant":32146},"script",[1711,32148,1714],{"stretchy":1713},[2884,32150,32151,32153],{},[898,32152,6796],{},[2111,32154,2238],{},[1711,32156,1726],{"separator":1725},[2884,32158,32159,32161],{},[898,32160,6796],{},[2111,32162,2963],{},[1711,32164,1726],{"separator":1725},[898,32166,20041],{},[1711,32168,1735],{"stretchy":1713},[1711,32170,1836],{},[898,32172,900],{},[1711,32174,1714],{"stretchy":1713},[2884,32176,32177,32179],{},[898,32178,6796],{},[2111,32180,2238],{},[1711,32182,1726],{"separator":1725},[2884,32184,32185,32187],{},[898,32186,6796],{},[2111,32188,2963],{},[1711,32190,1735],{"stretchy":1713},[1711,32192,2095],{},[898,32194,20041],{},[1711,32196,1714],{"stretchy":1713},[1716,32198,32199,32201],{},[898,32200,1660],{},[1711,32202,1793],{},[1711,32204,2460],{},[13142,32206,32207,32209,32211],{},[898,32208,7929],{},[2111,32210,2238],{},[1711,32212,1793],{},[2884,32214,32215,32217],{},[898,32216,6796],{},[2111,32218,2238],{},[1711,32220,2460],{},[13142,32222,32223,32225,32227],{},[898,32224,7929],{},[2111,32226,2963],{},[1711,32228,1793],{},[2884,32230,32231,32233],{},[898,32232,6796],{},[2111,32234,2963],{},[1711,32236,1735],{"stretchy":1713},[898,32238,2186],{"mathvariant":2287},[24360,32240],{"width":31674},[24360,32242,32243],{},[1942,32244,32245],{},"(6.13)",[902,32247,32248],{"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}",[724,32250,32251],{},"Soustava prvního řádu:",[883,32253,32255],{"className":32254},[886],[888,32256,32257],{"xmlns":890,"display":31664},[892,32258,32259,32442],{},[24352,32260,32261],{"width":31669},[24357,32262,32263,32265,32435,32437],{},[24360,32264],{"width":31674},[24360,32266,32267],{},[24352,32268,32269,32319,32369],{"rowspacing":24354,"columnalign":24355,"columnspacing":5224},[24357,32270,32271,32283],{},[24360,32272,32273],{},[2509,32274,32275],{"scriptlevel":2113,"displaystyle":1725},[13142,32276,32277,32279,32281],{},[898,32278,2888],{"mathvariant":32146},[2111,32280,2238],{},[1711,32282,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[24360,32284,32285],{},[2509,32286,32287],{"scriptlevel":2113,"displaystyle":1725},[895,32288,32289,32291,32293,32301,32303,32305,32313,32315,32317],{},[895,32290],{},[1711,32292,1836],{},[13142,32294,32295,32297,32299],{},[898,32296,900],{},[2111,32298,2238],{},[1711,32300,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,32302,2460],{},[898,32304,20041],{},[13142,32306,32307,32309,32311],{},[898,32308,7929],{},[2111,32310,2238],{},[1711,32312,1793],{},[1711,32314,1836],{},[2111,32316,2113],{},[1711,32318,1726],{"separator":1725},[24357,32320,32321,32333],{},[24360,32322,32323],{},[2509,32324,32325],{"scriptlevel":2113,"displaystyle":1725},[13142,32326,32327,32329,32331],{},[898,32328,2888],{"mathvariant":32146},[2111,32330,2963],{},[1711,32332,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[24360,32334,32335],{},[2509,32336,32337],{"scriptlevel":2113,"displaystyle":1725},[895,32338,32339,32341,32343,32351,32353,32355,32363,32365,32367],{},[895,32340],{},[1711,32342,1836],{},[13142,32344,32345,32347,32349],{},[898,32346,900],{},[2111,32348,2963],{},[1711,32350,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,32352,2460],{},[898,32354,20041],{},[13142,32356,32357,32359,32361],{},[898,32358,7929],{},[2111,32360,2963],{},[1711,32362,1793],{},[1711,32364,1836],{},[2111,32366,2113],{},[1711,32368,1726],{"separator":1725},[24357,32370,32371,32383],{},[24360,32372,32373],{},[2509,32374,32375],{"scriptlevel":2113,"displaystyle":1725},[13142,32376,32377,32379,32381],{},[898,32378,2888],{"mathvariant":32146},[898,32380,20041],{},[1711,32382,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[24360,32384,32385],{},[2509,32386,32387],{"scriptlevel":2113,"displaystyle":1725},[895,32388,32389,32391,32393,32399,32401,32409,32415,32417,32425,32431,32433],{},[895,32390],{},[1711,32392,1836],{},[1716,32394,32395,32397],{},[898,32396,1660],{},[1711,32398,1793],{},[1711,32400,2460],{},[13142,32402,32403,32405,32407],{},[898,32404,7929],{},[2111,32406,2238],{},[1711,32408,1793],{},[2884,32410,32411,32413],{},[898,32412,6796],{},[2111,32414,2238],{},[1711,32416,2460],{},[13142,32418,32419,32421,32423],{},[898,32420,7929],{},[2111,32422,2963],{},[1711,32424,1793],{},[2884,32426,32427,32429],{},[898,32428,6796],{},[2111,32430,2963],{},[1711,32432,1836],{},[2111,32434,2126],{},[24360,32436],{"width":31674},[24360,32438,32439],{},[1942,32440,32441],{},"(6.14)",[902,32443,32444],{"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}",[724,32446,32447,32448,32451,32452,32465,32466,2062],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,32449,32450],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,32453,32455],{"className":32454},[886],[888,32456,32457],{"xmlns":890},[892,32458,32459,32463],{},[895,32460,32461],{},[898,32462,20041],{},[902,32464,20094],{"encoding":904}," dostáváme ",[38,32467,32468],{},"podmínku optimality",[883,32470,32472],{"className":32471},[886],[888,32473,32474],{"xmlns":890,"display":31664},[892,32475,32476,32534],{},[895,32477,32478],{},[2505,32479,32480],{"notation":2507},[2509,32481,32482],{"scriptlevel":2113,"displaystyle":1713},[2509,32483,32484],{"scriptlevel":2113,"displaystyle":1713},[2509,32485,32486],{"scriptlevel":2113,"displaystyle":1725},[895,32487,32488,32490,32492,32494,32512,32514,32532],{},[1942,32489,4699],{},[1942,32491,14576],{},[1711,32493,1836],{},[2525,32495,32496,32504],{},[13142,32497,32498,32500,32502],{},[898,32499,900],{},[2111,32501,2238],{},[1711,32503,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[13142,32505,32506,32508,32510],{},[898,32507,900],{},[2111,32509,2963],{},[1711,32511,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,32513,1836],{},[2525,32515,32516,32524],{},[13142,32517,32518,32520,32522],{},[898,32519,7929],{},[2111,32521,2238],{},[1711,32523,1793],{},[13142,32525,32526,32528,32530],{},[898,32527,7929],{},[2111,32529,2963],{},[1711,32531,1793],{},[1942,32533,4699],{},[902,32535,32536],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[1921,32538,32539],{},[724,32540,32541,32543,32544,32578,32579,32582,32583,32601,32602,32620,32621,32651,32652,32669,32670,32700],{},[883,32542,2678],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,32545,32547],{"className":32546},[886],[888,32548,32549],{"xmlns":890},[892,32550,32551,32575],{},[895,32552,32553,32555,32557,32565,32567],{},[1942,32554,14576],{},[1711,32556,1836],{},[13142,32558,32559,32561,32563],{},[898,32560,7929],{},[2111,32562,2238],{},[1711,32564,1793],{},[898,32566,8659],{"mathvariant":2287},[13142,32568,32569,32571,32573],{},[898,32570,7929],{},[2111,32572,2963],{},[1711,32574,1793],{},[902,32576,32577],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,32580,32581],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,32584,32586],{"className":32585},[886],[888,32587,32588],{"xmlns":890},[892,32589,32590,32598],{},[895,32591,32592],{},[2884,32593,32594,32596],{},[898,32595,6796],{},[2111,32597,2238],{},[902,32599,32600],{"encoding":904},"Q_1"," za ",[883,32603,32605],{"className":32604},[886],[888,32606,32607],{"xmlns":890},[892,32608,32609,32617],{},[895,32610,32611],{},[2884,32612,32613,32615],{},[898,32614,6796],{},[2111,32616,2963],{},[902,32618,32619],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,32622,32624],{"className":32623},[886],[888,32625,32626],{"xmlns":890},[892,32627,32628,32648],{},[895,32629,32630,32632,32634,32640,32642],{},[1942,32631,14576],{},[1711,32633,2123],{},[2884,32635,32636,32638],{},[898,32637,7929],{},[2111,32639,2238],{},[898,32641,8659],{"mathvariant":2287},[2884,32643,32644,32646],{},[898,32645,7929],{},[2111,32647,2963],{},[902,32649,32650],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,32653,32655],{"className":32654},[886],[888,32656,32657],{"xmlns":890},[892,32658,32659,32667],{},[895,32660,32661],{},[2884,32662,32663,32665],{},[898,32664,6796],{},[2111,32666,2238],{},[902,32668,32600],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,32671,32673],{"className":32672},[886],[888,32674,32675],{"xmlns":890},[892,32676,32677,32697],{},[895,32678,32679,32681,32683,32689,32691],{},[1942,32680,14576],{},[1711,32682,2109],{},[2884,32684,32685,32687],{},[898,32686,7929],{},[2111,32688,2238],{},[898,32690,8659],{"mathvariant":2287},[2884,32692,32693,32695],{},[898,32694,7929],{},[2111,32696,2963],{},[902,32698,32699],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,32702,32704,32705,32718],{"id":32703},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,32706,32708],{"className":32707},[886],[888,32709,32710],{"xmlns":890},[892,32711,32712,32716],{},[895,32713,32714],{},[898,32715,20041],{},[902,32717,20094],{"encoding":904}," — mezní užitečnost důchodu",[724,32720,32721,32722,32740,32741,32744,32745,32762,32763,32780,32781,32784],{},"Lagrangeův multiplikátor ",[883,32723,32725],{"className":32724},[886],[888,32726,32727],{"xmlns":890},[892,32728,32729,32737],{},[895,32730,32731],{},[1716,32732,32733,32735],{},[898,32734,20041],{},[1711,32736,1793],{},[902,32738,32739],{"encoding":904},"\\lambda^*"," představuje ",[38,32742,32743],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,32746,32748],{"className":32747},[886],[888,32749,32750],{"xmlns":890},[892,32751,32752,32760],{},[895,32753,32754],{},[1716,32755,32756,32758],{},[898,32757,900],{},[1711,32759,1793],{},[902,32761,31560],{"encoding":904}," při jednotkové změně důchodu ",[883,32764,32766],{"className":32765},[886],[888,32767,32768],{"xmlns":890},[892,32769,32770,32778],{},[895,32771,32772],{},[1716,32773,32774,32776],{},[898,32775,1660],{},[1711,32777,1793],{},[902,32779,31626],{"encoding":904},". Je to ",[38,32782,32783],{},"stínová cena"," rozpočtového omezení.",[1921,32786,32787,32792],{},[724,32788,32789,32791],{},[883,32790,3872],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,32793,32794,32854,32941,32977,33064],{},[123,32795,32796,32799,32800,2186],{},[38,32797,32798],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,32801,32803],{"className":32802},[886],[888,32804,32805],{"xmlns":890},[892,32806,32807,32851],{},[895,32808,32809,32815,32817,32825,32831,32833,32841,32847,32849],{},[1716,32810,32811,32813],{},[898,32812,1660],{},[1711,32814,1793],{},[1711,32816,2460],{},[13142,32818,32819,32821,32823],{},[898,32820,7929],{},[2111,32822,2238],{},[1711,32824,1793],{},[2884,32826,32827,32829],{},[898,32828,6796],{},[2111,32830,2238],{},[1711,32832,2460],{},[13142,32834,32835,32837,32839],{},[898,32836,7929],{},[2111,32838,2963],{},[1711,32840,1793],{},[2884,32842,32843,32845],{},[898,32844,6796],{},[2111,32846,2963],{},[1711,32848,1836],{},[2111,32850,2113],{},[902,32852,32853],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,32855,32856,1700,32859,2186],{},[38,32857,32858],{},"Sestav Lagrangeovu funkci",[883,32860,32862],{"className":32861},[886],[888,32863,32864],{"xmlns":890},[892,32865,32866,32938],{},[895,32867,32868,32870,32872,32874,32876,32882,32884,32890,32892,32894,32896,32898,32904,32906,32914,32920,32922,32930,32936],{},[898,32869,2888],{"mathvariant":32146},[1711,32871,1836],{},[898,32873,900],{},[1711,32875,1714],{"stretchy":1713},[2884,32877,32878,32880],{},[898,32879,6796],{},[2111,32881,2238],{},[1711,32883,1726],{"separator":1725},[2884,32885,32886,32888],{},[898,32887,6796],{},[2111,32889,2963],{},[1711,32891,1735],{"stretchy":1713},[1711,32893,2095],{},[898,32895,20041],{},[1711,32897,1714],{"stretchy":1713},[1716,32899,32900,32902],{},[898,32901,1660],{},[1711,32903,1793],{},[1711,32905,2460],{},[13142,32907,32908,32910,32912],{},[898,32909,7929],{},[2111,32911,2238],{},[1711,32913,1793],{},[2884,32915,32916,32918],{},[898,32917,6796],{},[2111,32919,2238],{},[1711,32921,2460],{},[13142,32923,32924,32926,32928],{},[898,32925,7929],{},[2111,32927,2963],{},[1711,32929,1793],{},[2884,32931,32932,32934],{},[898,32933,6796],{},[2111,32935,2963],{},[1711,32937,1735],{"stretchy":1713},[902,32939,32940],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,32942,32943,14441,32946,32976],{},[38,32944,32945],{},"Spočítej parciální derivace",[883,32947,32949],{"className":32948},[886],[888,32950,32951],{"xmlns":890},[892,32952,32953,32973],{},[895,32954,32955,32961,32963,32969,32971],{},[2884,32956,32957,32959],{},[898,32958,6796],{},[2111,32960,2238],{},[1711,32962,1726],{"separator":1725},[2884,32964,32965,32967],{},[898,32966,6796],{},[2111,32968,2963],{},[1711,32970,1726],{"separator":1725},[898,32972,20041],{},[902,32974,32975],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,32978,32979,32995,32996,33029,33030,2009,33047,2186],{},[38,32980,32981,32982],{},"Vyluč ",[883,32983,32985],{"className":32984},[886],[888,32986,32987],{"xmlns":890},[892,32988,32989,32993],{},[895,32990,32991],{},[898,32992,20041],{},[902,32994,20094],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,32997,32999],{"className":32998},[886],[888,33000,33001],{"xmlns":890},[892,33002,33003,33027],{},[895,33004,33005,33007,33009,33017,33019],{},[1942,33006,14576],{},[1711,33008,1836],{},[13142,33010,33011,33013,33015],{},[898,33012,7929],{},[2111,33014,2238],{},[1711,33016,1793],{},[898,33018,8659],{"mathvariant":2287},[13142,33020,33021,33023,33025],{},[898,33022,7929],{},[2111,33024,2963],{},[1711,33026,1793],{},[902,33028,32577],{"encoding":904},", která dá vztah mezi ",[883,33031,33033],{"className":33032},[886],[888,33034,33035],{"xmlns":890},[892,33036,33037,33045],{},[895,33038,33039],{},[2884,33040,33041,33043],{},[898,33042,6796],{},[2111,33044,2238],{},[902,33046,32600],{"encoding":904},[883,33048,33050],{"className":33049},[886],[888,33051,33052],{"xmlns":890},[892,33053,33054,33062],{},[895,33055,33056],{},[2884,33057,33058,33060],{},[898,33059,6796],{},[2111,33061,2963],{},[902,33063,32619],{"encoding":904},[123,33065,33066,33069,33070,33100,33101,33118,33119,2186],{},[38,33067,33068],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,33071,33073],{"className":33072},[886],[888,33074,33075],{"xmlns":890},[892,33076,33077,33097],{},[895,33078,33079,33087,33089],{},[13142,33080,33081,33083,33085],{},[898,33082,6796],{},[2111,33084,2238],{},[1711,33086,1793],{},[1711,33088,1726],{"separator":1725},[13142,33090,33091,33093,33095],{},[898,33092,6796],{},[2111,33094,2963],{},[1711,33096,1793],{},[902,33098,33099],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,33102,33104],{"className":33103},[886],[888,33105,33106],{"xmlns":890},[892,33107,33108,33116],{},[895,33109,33110],{},[1716,33111,33112,33114],{},[898,33113,20041],{},[1711,33115,1793],{},[902,33117,32739],{"encoding":904}," a maximální užitečnost ",[883,33120,33122],{"className":33121},[886],[888,33123,33124],{"xmlns":890},[892,33125,33126,33160],{},[895,33127,33128,33134,33136,33138,33140,33148,33150,33158],{},[1716,33129,33130,33132],{},[898,33131,900],{},[1711,33133,1793],{},[1711,33135,1836],{},[898,33137,900],{},[1711,33139,1714],{"stretchy":1713},[13142,33141,33142,33144,33146],{},[898,33143,6796],{},[2111,33145,2238],{},[1711,33147,1793],{},[1711,33149,1726],{"separator":1725},[13142,33151,33152,33154,33156],{},[898,33153,6796],{},[2111,33155,2963],{},[1711,33157,1793],{},[1711,33159,1735],{"stretchy":1713},[902,33161,33162],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,33164,33166],{"id":33165},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,33168,33169],{},[1801,33170],{"alt":33171,"className":33172,"src":33173},"imek-uzitecnost-optimum",[210,1805],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,33175,33176],{},[614,33177,33178,33179,33228,33229,2009,33257,33285,33286,33320,33321,33360,33361,33379,33380,33398,33399,33417],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,33180,33182],{"className":33181},[886],[888,33183,33184],{"xmlns":890},[892,33185,33186,33226],{},[895,33187,33188,33194,33196,33204,33210,33212,33220],{},[1716,33189,33190,33192],{},[898,33191,1660],{},[1711,33193,1793],{},[1711,33195,1836],{},[13142,33197,33198,33200,33202],{},[898,33199,7929],{},[2111,33201,2238],{},[1711,33203,1793],{},[2884,33205,33206,33208],{},[898,33207,6796],{},[2111,33209,2238],{},[1711,33211,2095],{},[13142,33213,33214,33216,33218],{},[898,33215,7929],{},[2111,33217,2963],{},[1711,33219,1793],{},[2884,33221,33222,33224],{},[898,33223,6796],{},[2111,33225,2963],{},[902,33227,20896],{"encoding":904}," protíná osy v ",[883,33230,33232],{"className":33231},[886],[888,33233,33234],{"xmlns":890},[892,33235,33236,33254],{},[895,33237,33238,33244,33246],{},[1716,33239,33240,33242],{},[898,33241,1660],{},[1711,33243,1793],{},[898,33245,8659],{"mathvariant":2287},[13142,33247,33248,33250,33252],{},[898,33249,7929],{},[2111,33251,2238],{},[1711,33253,1793],{},[902,33255,33256],{"encoding":904},"Y^*\u002FP_1^*",[883,33258,33260],{"className":33259},[886],[888,33261,33262],{"xmlns":890},[892,33263,33264,33282],{},[895,33265,33266,33272,33274],{},[1716,33267,33268,33270],{},[898,33269,1660],{},[1711,33271,1793],{},[898,33273,8659],{"mathvariant":2287},[13142,33275,33276,33278,33280],{},[898,33277,7929],{},[2111,33279,2963],{},[1711,33281,1793],{},[902,33283,33284],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,33287,33289],{"className":33288},[886],[888,33290,33291],{"xmlns":890},[892,33292,33293,33317],{},[895,33294,33295,33301,33303,33309,33311],{},[2884,33296,33297,33299],{},[898,33298,2090],{},[2111,33300,2238],{},[1711,33302,2109],{},[1716,33304,33305,33307],{},[898,33306,2090],{},[1711,33308,1793],{},[1711,33310,2109],{},[2884,33312,33313,33315],{},[898,33314,2090],{},[2111,33316,2963],{},[902,33318,33319],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,33322,33324],{"className":33323},[886],[888,33325,33326],{"xmlns":890},[892,33327,33328,33358],{},[895,33329,33330,33336,33338,33346,33348,33356],{},[1716,33331,33332,33334],{},[898,33333,6796],{},[1711,33335,1793],{},[1711,33337,5144],{"stretchy":1713},[13142,33339,33340,33342,33344],{},[898,33341,6796],{},[2111,33343,2238],{},[1711,33345,1793],{},[1711,33347,1726],{"separator":1725},[13142,33349,33350,33352,33354],{},[898,33351,6796],{},[2111,33353,2963],{},[1711,33355,1793],{},[1711,33357,5163],{"stretchy":1713},[902,33359,31925],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,33362,33364],{"className":33363},[886],[888,33365,33366],{"xmlns":890},[892,33367,33368,33376],{},[895,33369,33370],{},[1716,33371,33372,33374],{},[898,33373,2090],{},[1711,33375,1793],{},[902,33377,33378],{"encoding":904},"c^*",". Křivka ",[883,33381,33383],{"className":33382},[886],[888,33384,33385],{"xmlns":890},[892,33386,33387,33395],{},[895,33388,33389],{},[2884,33390,33391,33393],{},[898,33392,2090],{},[2111,33394,2238],{},[902,33396,33397],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,33400,33402],{"className":33401},[886],[888,33403,33404],{"xmlns":890},[892,33405,33406,33414],{},[895,33407,33408],{},[2884,33409,33410,33412],{},[898,33411,2090],{},[2111,33413,2963],{},[902,33415,33416],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,33419,33420,33421,33424,33425,33443,33444,33473],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,33422,33423],{},"dotýkají",", tj. mají v bodě ",[883,33426,33428],{"className":33427},[886],[888,33429,33430],{"xmlns":890},[892,33431,33432,33440],{},[895,33433,33434],{},[1716,33435,33436,33438],{},[898,33437,6796],{},[1711,33439,1793],{},[902,33441,33442],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,33445,33447],{"className":33446},[886],[888,33448,33449],{"xmlns":890},[892,33450,33451,33471],{},[895,33452,33453,33455,33457,33463,33465],{},[1942,33454,14576],{},[1711,33456,1836],{},[2884,33458,33459,33461],{},[898,33460,7929],{},[2111,33462,2238],{},[898,33464,8659],{"mathvariant":2287},[2884,33466,33467,33469],{},[898,33468,7929],{},[2111,33470,2963],{},[902,33472,31596],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,33475,33477],{"id":33476},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,33479,13638,33480,33542],{},[883,33481,33483],{"className":33482},[886],[888,33484,33485],{"xmlns":890},[892,33486,33487,33539],{},[895,33488,33489,33491,33493,33499,33501,33507,33509,33511,33525],{},[898,33490,900],{},[1711,33492,1714],{"stretchy":1713},[2884,33494,33495,33497],{},[898,33496,6796],{},[2111,33498,2238],{},[1711,33500,1726],{"separator":1725},[2884,33502,33503,33505],{},[898,33504,6796],{},[2111,33506,2963],{},[1711,33508,1735],{"stretchy":1713},[1711,33510,1836],{},[13142,33512,33513,33515,33517],{},[898,33514,6796],{},[2111,33516,2238],{},[895,33518,33519,33521,33523],{},[2111,33520,2238],{},[898,33522,8659],{"mathvariant":2287},[2111,33524,2963],{},[13142,33526,33527,33529,33531],{},[898,33528,6796],{},[2111,33530,2963],{},[895,33532,33533,33535,33537],{},[2111,33534,2238],{},[898,33536,8659],{"mathvariant":2287},[2111,33538,2963],{},[902,33540,33541],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[724,33544,33545],{},[883,33546,33548],{"className":33547},[886],[888,33549,33550],{"xmlns":890},[892,33551,33552,33658],{},[895,33553,33554,33556,33558,33640,33642,33656],{},[1942,33555,14576],{},[1711,33557,1836],{},[2525,33559,33560,33600],{},[895,33561,33562,33570,33586],{},[2509,33563,33564],{"scriptlevel":2113,"displaystyle":1713},[2525,33565,33566,33568],{},[2111,33567,2238],{},[2111,33569,2963],{},[13142,33571,33572,33574,33576],{},[898,33573,6796],{},[2111,33575,2238],{},[895,33577,33578,33580,33582,33584],{},[1711,33579,2460],{},[2111,33581,2238],{},[898,33583,8659],{"mathvariant":2287},[2111,33585,2963],{},[13142,33587,33588,33590,33592],{},[898,33589,6796],{},[2111,33591,2963],{},[895,33593,33594,33596,33598],{},[2111,33595,2238],{},[898,33597,8659],{"mathvariant":2287},[2111,33599,2963],{},[895,33601,33602,33610,33624],{},[2509,33603,33604],{"scriptlevel":2113,"displaystyle":1713},[2525,33605,33606,33608],{},[2111,33607,2238],{},[2111,33609,2963],{},[13142,33611,33612,33614,33616],{},[898,33613,6796],{},[2111,33615,2238],{},[895,33617,33618,33620,33622],{},[2111,33619,2238],{},[898,33621,8659],{"mathvariant":2287},[2111,33623,2963],{},[13142,33625,33626,33628,33630],{},[898,33627,6796],{},[2111,33629,2963],{},[895,33631,33632,33634,33636,33638],{},[1711,33633,2460],{},[2111,33635,2238],{},[898,33637,8659],{"mathvariant":2287},[2111,33639,2963],{},[1711,33641,1836],{},[2525,33643,33644,33650],{},[2884,33645,33646,33648],{},[898,33647,6796],{},[2111,33649,2963],{},[2884,33651,33652,33654],{},[898,33653,6796],{},[2111,33655,2238],{},[898,33657,2186],{"mathvariant":2287},[902,33659,33660],{"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}.",[724,33662,33663,33664,2801,33709,33711,33712,33732,33733,33763,33764,2186],{},"Tedy ",[883,33665,33667],{"className":33666},[886],[888,33668,33669],{"xmlns":890},[892,33670,33671,33706],{},[895,33672,33673,33675,33677,33680,33682,33684,33686,33688,33696,33698],{},[1942,33674,14576],{},[1711,33676,1714],{"stretchy":1713},[2111,33678,33679],{},"300",[1711,33681,1726],{"separator":1725},[2111,33683,4807],{},[1711,33685,1735],{"stretchy":1713},[1711,33687,1836],{},[2509,33689,33690],{"scriptlevel":2113,"displaystyle":1713},[2525,33691,33692,33694],{},[2111,33693,4807],{},[2111,33695,33679],{},[1711,33697,1836],{},[2509,33699,33700],{"scriptlevel":2113,"displaystyle":1713},[2525,33701,33702,33704],{},[2111,33703,4798],{},[2111,33705,3034],{},[902,33707,33708],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,33710,13192],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,33713,33715],{"className":33714},[886],[888,33716,33717],{"xmlns":890},[892,33718,33719,33729],{},[895,33720,33721],{},[2509,33722,33723],{"scriptlevel":2113,"displaystyle":1713},[2525,33724,33725,33727],{},[2111,33726,4798],{},[2111,33728,3034],{},[902,33730,33731],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,33734,33736],{"className":33735},[886],[888,33737,33738],{"xmlns":890},[892,33739,33740,33760],{},[895,33741,33742,33744,33746,33752,33754],{},[1942,33743,14576],{},[1711,33745,1836],{},[2884,33747,33748,33750],{},[898,33749,6796],{},[2111,33751,2963],{},[898,33753,8659],{"mathvariant":2287},[2884,33755,33756,33758],{},[898,33757,6796],{},[2111,33759,2238],{},[902,33761,33762],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,33765,33767],{"className":33766},[886],[888,33768,33769],{"xmlns":890},[892,33770,33771,33791],{},[895,33772,33773,33775,33777,33783,33785],{},[1942,33774,14576],{},[1711,33776,1836],{},[2884,33778,33779,33781],{},[898,33780,7929],{},[2111,33782,2238],{},[898,33784,8659],{"mathvariant":2287},[2884,33786,33787,33789],{},[898,33788,7929],{},[2111,33790,2963],{},[902,33792,31596],{"encoding":904},[115,33794,33796,33797],{"id":33795},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,33798,33800],{"className":33799},[886],[888,33801,33802],{"xmlns":890},[892,33803,33804,33822],{},[895,33805,33806,33808,33810,33816],{},[898,33807,900],{},[1711,33809,1836],{},[2884,33811,33812,33814],{},[898,33813,6796],{},[2111,33815,2238],{},[2884,33817,33818,33820],{},[898,33819,6796],{},[2111,33821,2963],{},[902,33823,33824],{"encoding":904},"U = Q_1 Q_2",[724,33826,33827,33828,1343,33874,1343,33898,1343,33922,33944],{},"Je dána ",[883,33829,33831],{"className":33830},[886],[888,33832,33833],{"xmlns":890},[892,33834,33835,33871],{},[895,33836,33837,33839,33841,33847,33849,33855,33857,33859,33865],{},[898,33838,900],{},[1711,33840,1714],{"stretchy":1713},[2884,33842,33843,33845],{},[898,33844,6796],{},[2111,33846,2238],{},[1711,33848,1726],{"separator":1725},[2884,33850,33851,33853],{},[898,33852,6796],{},[2111,33854,2963],{},[1711,33856,1735],{"stretchy":1713},[1711,33858,1836],{},[2884,33860,33861,33863],{},[898,33862,6796],{},[2111,33864,2238],{},[2884,33866,33867,33869],{},[898,33868,6796],{},[2111,33870,2963],{},[902,33872,33873],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,33875,33877],{"className":33876},[886],[888,33878,33879],{"xmlns":890},[892,33880,33881,33895],{},[895,33882,33883,33891,33893],{},[13142,33884,33885,33887,33889],{},[898,33886,7929],{},[2111,33888,2238],{},[1711,33890,1793],{},[1711,33892,1836],{},[2111,33894,2963],{},[902,33896,33897],{"encoding":904},"P_1^* = 2",[883,33899,33901],{"className":33900},[886],[888,33902,33903],{"xmlns":890},[892,33904,33905,33919],{},[895,33906,33907,33915,33917],{},[13142,33908,33909,33911,33913],{},[898,33910,7929],{},[2111,33912,2963],{},[1711,33914,1793],{},[1711,33916,1836],{},[2111,33918,4798],{},[902,33920,33921],{"encoding":904},"P_2^* = 5",[883,33923,33925],{"className":33924},[886],[888,33926,33927],{"xmlns":890},[892,33928,33929,33941],{},[895,33930,33931,33937,33939],{},[1716,33932,33933,33935],{},[898,33934,1660],{},[1711,33936,1793],{},[1711,33938,1836],{},[2111,33940,4282],{},[902,33942,33943],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,33946,33948],{"className":33947},[886],[888,33949,33950],{"xmlns":890,"display":31664},[892,33951,33952,34024],{},[895,33953,33954,33956,33958,33964,33966,33972,33974,33976,33978,33980,33986,33992,33994,33996,33998,34000,34002,34004,34010,34012,34014,34020,34022],{},[898,33955,2888],{"mathvariant":32146},[1711,33957,1714],{"stretchy":1713},[2884,33959,33960,33962],{},[898,33961,6796],{},[2111,33963,2238],{},[1711,33965,1726],{"separator":1725},[2884,33967,33968,33970],{},[898,33969,6796],{},[2111,33971,2963],{},[1711,33973,1726],{"separator":1725},[898,33975,20041],{},[1711,33977,1735],{"stretchy":1713},[1711,33979,1836],{},[2884,33981,33982,33984],{},[898,33983,6796],{},[2111,33985,2238],{},[2884,33987,33988,33990],{},[898,33989,6796],{},[2111,33991,2963],{},[1711,33993,2095],{},[898,33995,20041],{},[1711,33997,1714],{"stretchy":1713},[2111,33999,4282],{},[1711,34001,2460],{},[2111,34003,2963],{},[2884,34005,34006,34008],{},[898,34007,6796],{},[2111,34009,2238],{},[1711,34011,2460],{},[2111,34013,4798],{},[2884,34015,34016,34018],{},[898,34017,6796],{},[2111,34019,2963],{},[1711,34021,1735],{"stretchy":1713},[898,34023,2186],{"mathvariant":2287},[902,34025,34026],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,34028,34029],{},"Soustava:",[883,34031,34033],{"className":34032},[886],[888,34034,34035],{"xmlns":890,"display":31664},[892,34036,34037,34149],{},[24352,34038,34039,34073,34107],{"rowspacing":24354,"columnalign":24355,"columnspacing":5224},[24357,34040,34041,34059],{},[24360,34042,34043],{},[2509,34044,34045],{"scriptlevel":2113,"displaystyle":1725},[895,34046,34047,34053,34055,34057],{},[2884,34048,34049,34051],{},[898,34050,6796],{},[2111,34052,2963],{},[1711,34054,2460],{},[2111,34056,2963],{},[898,34058,20041],{},[24360,34060,34061],{},[2509,34062,34063],{"scriptlevel":2113,"displaystyle":1725},[895,34064,34065,34067,34069,34071],{},[895,34066],{},[1711,34068,1836],{},[2111,34070,2113],{},[1711,34072,1726],{"separator":1725},[24357,34074,34075,34093],{},[24360,34076,34077],{},[2509,34078,34079],{"scriptlevel":2113,"displaystyle":1725},[895,34080,34081,34087,34089,34091],{},[2884,34082,34083,34085],{},[898,34084,6796],{},[2111,34086,2238],{},[1711,34088,2460],{},[2111,34090,4798],{},[898,34092,20041],{},[24360,34094,34095],{},[2509,34096,34097],{"scriptlevel":2113,"displaystyle":1725},[895,34098,34099,34101,34103,34105],{},[895,34100],{},[1711,34102,1836],{},[2111,34104,2113],{},[1711,34106,1726],{"separator":1725},[24357,34108,34109,34137],{},[24360,34110,34111],{},[2509,34112,34113],{"scriptlevel":2113,"displaystyle":1725},[895,34114,34115,34117,34119,34121,34127,34129,34131],{},[2111,34116,4282],{},[1711,34118,2460],{},[2111,34120,2963],{},[2884,34122,34123,34125],{},[898,34124,6796],{},[2111,34126,2238],{},[1711,34128,2460],{},[2111,34130,4798],{},[2884,34132,34133,34135],{},[898,34134,6796],{},[2111,34136,2963],{},[24360,34138,34139],{},[2509,34140,34141],{"scriptlevel":2113,"displaystyle":1725},[895,34142,34143,34145,34147],{},[895,34144],{},[1711,34146,1836],{},[2111,34148,2126],{},[902,34150,34151],{"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}",[724,34153,34154,34155,1343,34179,34203,34204,9572,34244,34262,34263,34313,34314,2186],{},"Z prvních dvou rovnic ",[883,34156,34158],{"className":34157},[886],[888,34159,34160],{"xmlns":890},[892,34161,34162,34176],{},[895,34163,34164,34170,34172,34174],{},[2884,34165,34166,34168],{},[898,34167,6796],{},[2111,34169,2963],{},[1711,34171,1836],{},[2111,34173,2963],{},[898,34175,20041],{},[902,34177,34178],{"encoding":904},"Q_2 = 2\\lambda",[883,34180,34182],{"className":34181},[886],[888,34183,34184],{"xmlns":890},[892,34185,34186,34200],{},[895,34187,34188,34194,34196,34198],{},[2884,34189,34190,34192],{},[898,34191,6796],{},[2111,34193,2238],{},[1711,34195,1836],{},[2111,34197,4798],{},[898,34199,20041],{},[902,34201,34202],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,34205,34207],{"className":34206},[886],[888,34208,34209],{"xmlns":890},[892,34210,34211,34241],{},[895,34212,34213,34215,34217,34219,34221,34223,34225,34227,34229,34231,34233,34235,34237,34239],{},[2111,34214,4282],{},[1711,34216,1836],{},[2111,34218,2963],{},[1711,34220,4795],{},[2111,34222,4798],{},[898,34224,20041],{},[1711,34226,2095],{},[2111,34228,4798],{},[1711,34230,4795],{},[2111,34232,2963],{},[898,34234,20041],{},[1711,34236,1836],{},[2111,34238,4306],{},[898,34240,20041],{},[902,34242,34243],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,34245,34247],{"className":34246},[886],[888,34248,34249],{"xmlns":890},[892,34250,34251,34259],{},[895,34252,34253,34255,34257],{},[898,34254,20041],{},[1711,34256,1836],{},[2111,34258,4798],{},[902,34260,34261],{"encoding":904},"\\lambda = 5",". Odtud ",[38,34264,34265,1343,34289],{},[883,34266,34268],{"className":34267},[886],[888,34269,34270],{"xmlns":890},[892,34271,34272,34286],{},[895,34273,34274,34282,34284],{},[13142,34275,34276,34278,34280],{},[898,34277,6796],{},[2111,34279,2238],{},[1711,34281,1793],{},[1711,34283,1836],{},[2111,34285,4372],{},[902,34287,34288],{"encoding":904},"Q_1^* = 25",[883,34290,34292],{"className":34291},[886],[888,34293,34294],{"xmlns":890},[892,34295,34296,34310],{},[895,34297,34298,34306,34308],{},[13142,34299,34300,34302,34304],{},[898,34301,6796],{},[2111,34303,2963],{},[1711,34305,1793],{},[1711,34307,1836],{},[2111,34309,4712],{},[902,34311,34312],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,34315,34317],{"className":34316},[886],[888,34318,34319],{"xmlns":890},[892,34320,34321,34342],{},[895,34322,34323,34329,34331,34333,34335,34337,34339],{},[1716,34324,34325,34327],{},[898,34326,900],{},[1711,34328,1793],{},[1711,34330,1836],{},[2111,34332,4372],{},[1711,34334,4795],{},[2111,34336,4712],{},[1711,34338,1836],{},[2111,34340,34341],{},"250",[902,34343,34344],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,34346,34347],{},[614,34348,34349,34350,31735,34388,2009,34412,34436,34437,34467,34468,34492,34493,34515,34516,2186],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,34351,34353],{"className":34352},[886],[888,34354,34355],{"xmlns":890},[892,34356,34357,34385],{},[895,34358,34359,34361,34363,34365,34371,34373,34375,34381,34383],{},[2111,34360,4282],{},[1711,34362,2460],{},[2111,34364,2963],{},[2884,34366,34367,34369],{},[898,34368,6796],{},[2111,34370,2238],{},[1711,34372,2460],{},[2111,34374,4798],{},[2884,34376,34377,34379],{},[898,34378,6796],{},[2111,34380,2963],{},[1711,34382,1836],{},[2111,34384,2113],{},[902,34386,34387],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,34389,34391],{"className":34390},[886],[888,34392,34393],{"xmlns":890},[892,34394,34395,34409],{},[895,34396,34397,34399,34401,34403,34405,34407],{},[898,34398,8243],{},[1711,34400,5144],{"stretchy":1713},[2111,34402,2113],{},[1711,34404,1726],{"separator":1725},[2111,34406,4306],{},[1711,34408,5163],{"stretchy":1713},[902,34410,34411],{"encoding":904},"A[0, 20]",[883,34413,34415],{"className":34414},[886],[888,34416,34417],{"xmlns":890},[892,34418,34419,34433],{},[895,34420,34421,34423,34425,34427,34429,34431],{},[898,34422,26851],{},[1711,34424,5144],{"stretchy":1713},[2111,34426,7120],{},[1711,34428,1726],{"separator":1725},[2111,34430,2113],{},[1711,34432,5163],{"stretchy":1713},[902,34434,34435],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,34438,34440],{"className":34439},[886],[888,34441,34442],{"xmlns":890},[892,34443,34444,34464],{},[895,34445,34446,34452,34454,34456,34458],{},[2884,34447,34448,34450],{},[898,34449,6796],{},[2111,34451,2963],{},[1711,34453,1836],{},[2111,34455,34341],{},[898,34457,8659],{"mathvariant":2287},[2884,34459,34460,34462],{},[898,34461,6796],{},[2111,34463,2238],{},[902,34465,34466],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,34469,34471],{"className":34470},[886],[888,34472,34473],{"xmlns":890},[892,34474,34475,34489],{},[895,34476,34477,34479,34481,34483,34485,34487],{},[898,34478,1722],{},[1711,34480,5144],{"stretchy":1713},[2111,34482,4372],{},[1711,34484,1726],{"separator":1725},[2111,34486,4712],{},[1711,34488,5163],{"stretchy":1713},[902,34490,34491],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,34494,34496],{"className":34495},[886],[888,34497,34498],{"xmlns":890},[892,34499,34500,34512],{},[895,34501,34502,34504],{},[1711,34503,2460],{},[2509,34505,34506],{"scriptlevel":2113,"displaystyle":1713},[2525,34507,34508,34510],{},[2111,34509,2963],{},[2111,34511,4798],{},[902,34513,34514],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,34517,34519],{"className":34518},[886],[888,34520,34521],{"xmlns":890},[892,34522,34523,34563],{},[895,34524,34525,34527,34529,34531,34533,34535,34537,34539,34541,34543,34551,34553,34555],{},[1711,34526,2460],{},[1942,34528,14576],{},[1711,34530,1714],{"stretchy":1713},[2111,34532,4372],{},[1711,34534,1726],{"separator":1725},[2111,34536,4712],{},[1711,34538,1735],{"stretchy":1713},[1711,34540,1836],{},[1711,34542,2460],{},[2509,34544,34545],{"scriptlevel":2113,"displaystyle":1713},[2525,34546,34547,34549],{},[2111,34548,4712],{},[2111,34550,4372],{},[1711,34552,1836],{},[1711,34554,2460],{},[2509,34556,34557],{"scriptlevel":2113,"displaystyle":1713},[2525,34558,34559,34561],{},[2111,34560,2963],{},[2111,34562,4798],{},[902,34564,34565],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,34567,34569],{"id":34568},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,34571,34572,34573,32601,34603,34606,34607,2062],{},"Považujeme-li v úloze ",[883,34574,34576],{"className":34575},[886],[888,34577,34578],{"xmlns":890},[892,34579,34580,34600],{},[895,34581,34582,34588,34590,34596,34598],{},[2884,34583,34584,34586],{},[898,34585,7929],{},[2111,34587,2238],{},[1711,34589,1726],{"separator":1725},[2884,34591,34592,34594],{},[898,34593,7929],{},[2111,34595,2963],{},[1711,34597,1726],{"separator":1725},[898,34599,1660],{},[902,34601,34602],{"encoding":904},"P_1, P_2, Y",[38,34604,34605],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,34608,34609],{},"Marshallovy poptávkové funkce",[883,34611,34613],{"className":34612},[886],[888,34614,34615],{"xmlns":890,"display":31664},[892,34616,34617,34712],{},[24352,34618,34619],{"width":31669},[24357,34620,34621,34623,34705,34707],{},[24360,34622],{"width":31674},[24360,34624,34625],{},[895,34626,34627,34633,34635,34641,34643,34649,34651,34657,34659,34661,34663,34665,34667,34673,34675,34681,34683,34689,34691,34697,34699,34701,34703],{},[2884,34628,34629,34631],{},[898,34630,6796],{},[2111,34632,2238],{},[1711,34634,1836],{},[2884,34636,34637,34639],{},[898,34638,2778],{},[2111,34640,2238],{},[1711,34642,1714],{"stretchy":1713},[2884,34644,34645,34647],{},[898,34646,7929],{},[2111,34648,2238],{},[1711,34650,1726],{"separator":1725},[2884,34652,34653,34655],{},[898,34654,7929],{},[2111,34656,2963],{},[1711,34658,1726],{"separator":1725},[898,34660,1660],{},[1711,34662,1735],{"stretchy":1713},[1711,34664,1726],{"separator":1725},[2102,34666],{"width":4981},[2884,34668,34669,34671],{},[898,34670,6796],{},[2111,34672,2963],{},[1711,34674,1836],{},[2884,34676,34677,34679],{},[898,34678,2778],{},[2111,34680,2963],{},[1711,34682,1714],{"stretchy":1713},[2884,34684,34685,34687],{},[898,34686,7929],{},[2111,34688,2238],{},[1711,34690,1726],{"separator":1725},[2884,34692,34693,34695],{},[898,34694,7929],{},[2111,34696,2963],{},[1711,34698,1726],{"separator":1725},[898,34700,1660],{},[1711,34702,1735],{"stretchy":1713},[1711,34704,1726],{"separator":1725},[24360,34706],{"width":31674},[24360,34708,34709],{},[1942,34710,34711],{},"(6.15)",[902,34713,34714],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,34716,34718],{"className":34717},[886],[888,34719,34720],{"xmlns":890,"display":31664},[892,34721,34722,34769],{},[24352,34723,34724],{"width":31669},[24357,34725,34726,34728,34762,34764],{},[24360,34727],{"width":31674},[24360,34729,34730],{},[895,34731,34732,34734,34736,34738,34740,34746,34748,34754,34756,34758,34760],{},[898,34733,20041],{},[1711,34735,1836],{},[898,34737,20041],{},[1711,34739,1714],{"stretchy":1713},[2884,34741,34742,34744],{},[898,34743,7929],{},[2111,34745,2238],{},[1711,34747,1726],{"separator":1725},[2884,34749,34750,34752],{},[898,34751,7929],{},[2111,34753,2963],{},[1711,34755,1726],{"separator":1725},[898,34757,1660],{},[1711,34759,1735],{"stretchy":1713},[898,34761,2186],{"mathvariant":2287},[24360,34763],{"width":31674},[24360,34765,34766],{},[1942,34767,34768],{},"(6.16)",[902,34770,34771],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,34773,34774,34804,34805,34871],{},[38,34775,34776,34777,2186],{},"Odvození pro ",[883,34778,34780],{"className":34779},[886],[888,34781,34782],{"xmlns":890},[892,34783,34784,34802],{},[895,34785,34786,34788,34790,34796],{},[898,34787,900],{},[1711,34789,1836],{},[2884,34791,34792,34794],{},[898,34793,6796],{},[2111,34795,2238],{},[2884,34797,34798,34800],{},[898,34799,6796],{},[2111,34801,2963],{},[902,34803,33824],{"encoding":904}," Lagrangeova funkce ",[883,34806,34808],{"className":34807},[886],[888,34809,34810],{"xmlns":890},[892,34811,34812,34868],{},[895,34813,34814,34816,34818,34824,34830,34832,34834,34836,34838,34840,34846,34852,34854,34860,34866],{},[898,34815,2888],{"mathvariant":32146},[1711,34817,1836],{},[2884,34819,34820,34822],{},[898,34821,6796],{},[2111,34823,2238],{},[2884,34825,34826,34828],{},[898,34827,6796],{},[2111,34829,2963],{},[1711,34831,2095],{},[898,34833,20041],{},[1711,34835,1714],{"stretchy":1713},[898,34837,1660],{},[1711,34839,2460],{},[2884,34841,34842,34844],{},[898,34843,7929],{},[2111,34845,2238],{},[2884,34847,34848,34850],{},[898,34849,6796],{},[2111,34851,2238],{},[1711,34853,2460],{},[2884,34855,34856,34858],{},[898,34857,7929],{},[2111,34859,2963],{},[2884,34861,34862,34864],{},[898,34863,6796],{},[2111,34865,2963],{},[1711,34867,1735],{"stretchy":1713},[902,34869,34870],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,34873,34875],{"className":34874},[886],[888,34876,34877],{"xmlns":890,"display":31664},[892,34878,34879,35046],{},[24352,34880,34881],{"width":31669},[24357,34882,34883,34885,35039,35041],{},[24360,34884],{"width":31674},[24360,34886,34887],{},[24352,34888,34889,34935,34981],{"rowspacing":24354,"columnalign":24355,"columnspacing":5224},[24357,34890,34891,34903],{},[24360,34892,34893],{},[2509,34894,34895],{"scriptlevel":2113,"displaystyle":1725},[13142,34896,34897,34899,34901],{},[898,34898,2888],{"mathvariant":32146},[2111,34900,2238],{},[1711,34902,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[24360,34904,34905],{},[2509,34906,34907],{"scriptlevel":2113,"displaystyle":1725},[895,34908,34909,34911,34913,34919,34921,34923,34929,34931,34933],{},[895,34910],{},[1711,34912,1836],{},[2884,34914,34915,34917],{},[898,34916,6796],{},[2111,34918,2963],{},[1711,34920,2460],{},[898,34922,20041],{},[2884,34924,34925,34927],{},[898,34926,7929],{},[2111,34928,2238],{},[1711,34930,1836],{},[2111,34932,2113],{},[1711,34934,1726],{"separator":1725},[24357,34936,34937,34949],{},[24360,34938,34939],{},[2509,34940,34941],{"scriptlevel":2113,"displaystyle":1725},[13142,34942,34943,34945,34947],{},[898,34944,2888],{"mathvariant":32146},[2111,34946,2963],{},[1711,34948,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[24360,34950,34951],{},[2509,34952,34953],{"scriptlevel":2113,"displaystyle":1725},[895,34954,34955,34957,34959,34965,34967,34969,34975,34977,34979],{},[895,34956],{},[1711,34958,1836],{},[2884,34960,34961,34963],{},[898,34962,6796],{},[2111,34964,2238],{},[1711,34966,2460],{},[898,34968,20041],{},[2884,34970,34971,34973],{},[898,34972,7929],{},[2111,34974,2963],{},[1711,34976,1836],{},[2111,34978,2113],{},[1711,34980,1726],{"separator":1725},[24357,34982,34983,34995],{},[24360,34984,34985],{},[2509,34986,34987],{"scriptlevel":2113,"displaystyle":1725},[13142,34988,34989,34991,34993],{},[898,34990,2888],{"mathvariant":32146},[898,34992,20041],{},[1711,34994,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[24360,34996,34997],{},[2509,34998,34999],{"scriptlevel":2113,"displaystyle":1725},[895,35000,35001,35003,35005,35007,35009,35015,35021,35023,35029,35035,35037],{},[895,35002],{},[1711,35004,1836],{},[898,35006,1660],{},[1711,35008,2460],{},[2884,35010,35011,35013],{},[898,35012,7929],{},[2111,35014,2238],{},[2884,35016,35017,35019],{},[898,35018,6796],{},[2111,35020,2238],{},[1711,35022,2460],{},[2884,35024,35025,35027],{},[898,35026,7929],{},[2111,35028,2963],{},[2884,35030,35031,35033],{},[898,35032,6796],{},[2111,35034,2963],{},[1711,35036,1836],{},[2111,35038,2126],{},[24360,35040],{"width":31674},[24360,35042,35043],{},[1942,35044,35045],{},"(6.17)",[902,35047,35048],{"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}",[724,35050,35051,35052,35080,35081,35109,35110,35178],{},"Z prvních dvou: ",[883,35053,35055],{"className":35054},[886],[888,35056,35057],{"xmlns":890},[892,35058,35059,35077],{},[895,35060,35061,35067,35069,35075],{},[2884,35062,35063,35065],{},[898,35064,6796],{},[2111,35066,2963],{},[1711,35068,1836],{},[2884,35070,35071,35073],{},[898,35072,7929],{},[2111,35074,2238],{},[898,35076,20041],{},[902,35078,35079],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,35082,35084],{"className":35083},[886],[888,35085,35086],{"xmlns":890},[892,35087,35088,35106],{},[895,35089,35090,35096,35098,35104],{},[2884,35091,35092,35094],{},[898,35093,6796],{},[2111,35095,2238],{},[1711,35097,1836],{},[2884,35099,35100,35102],{},[898,35101,7929],{},[2111,35103,2963],{},[898,35105,20041],{},[902,35107,35108],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,35111,35113],{"className":35112},[886],[888,35114,35115],{"xmlns":890},[892,35116,35117,35175],{},[895,35118,35119,35121,35123,35129,35131,35137,35139,35141,35147,35149,35155,35157,35159,35161,35167,35173],{},[898,35120,1660],{},[1711,35122,1836],{},[2884,35124,35125,35127],{},[898,35126,7929],{},[2111,35128,2238],{},[1711,35130,4795],{},[2884,35132,35133,35135],{},[898,35134,7929],{},[2111,35136,2963],{},[898,35138,20041],{},[1711,35140,2095],{},[2884,35142,35143,35145],{},[898,35144,7929],{},[2111,35146,2963],{},[1711,35148,4795],{},[2884,35150,35151,35153],{},[898,35152,7929],{},[2111,35154,2238],{},[898,35156,20041],{},[1711,35158,1836],{},[2111,35160,2963],{},[2884,35162,35163,35165],{},[898,35164,7929],{},[2111,35166,2238],{},[2884,35168,35169,35171],{},[898,35170,7929],{},[2111,35172,2963],{},[898,35174,20041],{},[902,35176,35177],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,35180,35182],{"className":35181},[886],[888,35183,35184],{"xmlns":890,"display":31664},[892,35185,35186,35229],{},[24352,35187,35188],{"width":31669},[24357,35189,35190,35192,35222,35224],{},[24360,35191],{"width":31674},[24360,35193,35194],{},[895,35195,35196,35198,35200,35220],{},[898,35197,20041],{},[1711,35199,1836],{},[2525,35201,35202,35204],{},[898,35203,1660],{},[895,35205,35206,35208,35214],{},[2111,35207,2963],{},[2884,35209,35210,35212],{},[898,35211,7929],{},[2111,35213,2238],{},[2884,35215,35216,35218],{},[898,35217,7929],{},[2111,35219,2963],{},[898,35221,2186],{"mathvariant":2287},[24360,35223],{"width":31674},[24360,35225,35226],{},[1942,35227,35228],{},"(6.20)",[902,35230,35231],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,35233,35234],{},"Zpětně:",[883,35236,35238],{"className":35237},[886],[888,35239,35240],{"xmlns":890,"display":31664},[892,35241,35242,35319],{},[24352,35243,35244],{"width":31669},[24357,35245,35246,35248,35312,35314],{},[24360,35247],{"width":31674},[24360,35249,35250],{},[2505,35251,35252],{"notation":2507},[2509,35253,35254],{"scriptlevel":2113,"displaystyle":1713},[2509,35255,35256],{"scriptlevel":2113,"displaystyle":1713},[2509,35257,35258],{"scriptlevel":2113,"displaystyle":1725},[895,35259,35260,35262,35268,35270,35284,35286,35288,35294,35296,35310],{},[1942,35261,4699],{},[2884,35263,35264,35266],{},[898,35265,6796],{},[2111,35267,2238],{},[1711,35269,1836],{},[2525,35271,35272,35274],{},[898,35273,1660],{},[895,35275,35276,35278],{},[2111,35277,2963],{},[2884,35279,35280,35282],{},[898,35281,7929],{},[2111,35283,2238],{},[1711,35285,1726],{"separator":1725},[2102,35287],{"width":4981},[2884,35289,35290,35292],{},[898,35291,6796],{},[2111,35293,2963],{},[1711,35295,1836],{},[2525,35297,35298,35300],{},[898,35299,1660],{},[895,35301,35302,35304],{},[2111,35303,2963],{},[2884,35305,35306,35308],{},[898,35307,7929],{},[2111,35309,2963],{},[1942,35311,4699],{},[24360,35313],{"width":31674},[24360,35315,35316],{},[1942,35317,35318],{},"(6.21)",[902,35320,35321],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,35323,35325],{"id":35324},"engelova-funkce","Engelova funkce",[724,35327,13638,35328,35331,35332,35335,35336,23465,35353,1343,35383,35413,35414,35448,35449,1343,35475,35501],{},[38,35329,35330],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,35333,35334],{},"Engelovou funkcí",": pro ",[883,35337,35339],{"className":35338},[886],[888,35340,35341],{"xmlns":890},[892,35342,35343,35351],{},[895,35344,35345,35347,35349],{},[898,35346,1660],{},[1711,35348,1836],{},[2111,35350,4282],{},[902,35352,23917],{"encoding":904},[883,35354,35356],{"className":35355},[886],[888,35357,35358],{"xmlns":890},[892,35359,35360,35380],{},[895,35361,35362,35368,35370,35372,35374],{},[2884,35363,35364,35366],{},[898,35365,6796],{},[2111,35367,2238],{},[1711,35369,1836],{},[2111,35371,7120],{},[898,35373,8659],{"mathvariant":2287},[2884,35375,35376,35378],{},[898,35377,7929],{},[2111,35379,2238],{},[902,35381,35382],{"encoding":904},"Q_1 = 50\u002FP_1",[883,35384,35386],{"className":35385},[886],[888,35387,35388],{"xmlns":890},[892,35389,35390,35410],{},[895,35391,35392,35398,35400,35402,35404],{},[2884,35393,35394,35396],{},[898,35395,6796],{},[2111,35397,2963],{},[1711,35399,1836],{},[2111,35401,7120],{},[898,35403,8659],{"mathvariant":2287},[2884,35405,35406,35408],{},[898,35407,7929],{},[2111,35409,2963],{},[902,35411,35412],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,35415,35417],{"className":35416},[886],[888,35418,35419],{"xmlns":890},[892,35420,35421,35445],{},[895,35422,35423,35429,35431,35433,35435,35441,35443],{},[2884,35424,35425,35427],{},[898,35426,7929],{},[2111,35428,2238],{},[1711,35430,1836],{},[2111,35432,4712],{},[1711,35434,1726],{"separator":1725},[2884,35436,35437,35439],{},[898,35438,7929],{},[2111,35440,2963],{},[1711,35442,1836],{},[2111,35444,4306],{},[902,35446,35447],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,35450,35452],{"className":35451},[886],[888,35453,35454],{"xmlns":890},[892,35455,35456,35472],{},[895,35457,35458,35464,35466,35468,35470],{},[2884,35459,35460,35462],{},[898,35461,6796],{},[2111,35463,2238],{},[1711,35465,1836],{},[898,35467,1660],{},[898,35469,8659],{"mathvariant":2287},[2111,35471,4306],{},[902,35473,35474],{"encoding":904},"Q_1 = Y\u002F20",[883,35476,35478],{"className":35477},[886],[888,35479,35480],{"xmlns":890},[892,35481,35482,35498],{},[895,35483,35484,35490,35492,35494,35496],{},[2884,35485,35486,35488],{},[898,35487,6796],{},[2111,35489,2963],{},[1711,35491,1836],{},[898,35493,1660],{},[898,35495,8659],{"mathvariant":2287},[2111,35497,9195],{},[902,35499,35500],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,35503,35505],{"id":35504},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,35507,35508],{},"Výdaje spotřebitele jsou",[883,35510,35512],{"className":35511},[886],[888,35513,35514],{"xmlns":890,"display":31664},[892,35515,35516,35591],{},[24352,35517,35518],{"width":31669},[24357,35519,35520,35522,35584,35586],{},[24360,35521],{"width":31674},[24360,35523,35524],{},[895,35525,35526,35528,35530,35532,35534,35540,35542,35548,35550,35552,35560,35566,35568,35576,35582],{},[898,35527,1722],{},[1711,35529,1836],{},[898,35531,1722],{},[1711,35533,1714],{"stretchy":1713},[2884,35535,35536,35538],{},[898,35537,6796],{},[2111,35539,2238],{},[1711,35541,1726],{"separator":1725},[2884,35543,35544,35546],{},[898,35545,6796],{},[2111,35547,2963],{},[1711,35549,1735],{"stretchy":1713},[1711,35551,1836],{},[13142,35553,35554,35556,35558],{},[898,35555,7929],{},[2111,35557,2238],{},[1711,35559,1793],{},[2884,35561,35562,35564],{},[898,35563,6796],{},[2111,35565,2238],{},[1711,35567,2095],{},[13142,35569,35570,35572,35574],{},[898,35571,7929],{},[2111,35573,2963],{},[1711,35575,1793],{},[2884,35577,35578,35580],{},[898,35579,6796],{},[2111,35581,2963],{},[1711,35583,1726],{"separator":1725},[24360,35585],{"width":31674},[24360,35587,35588],{},[1942,35589,35590],{},"(6.22)",[902,35592,35593],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,35595,35596],{},"a je pevně zadána hladina užitečnosti",[883,35598,35600],{"className":35599},[886],[888,35601,35602],{"xmlns":890,"display":31664},[892,35603,35604,35651],{},[24352,35605,35606],{"width":31669},[24357,35607,35608,35610,35644,35646],{},[24360,35609],{"width":31674},[24360,35611,35612],{},[895,35613,35614,35620,35622,35624,35626,35632,35634,35640,35642],{},[1716,35615,35616,35618],{},[898,35617,900],{},[1711,35619,1793],{},[1711,35621,1836],{},[898,35623,900],{},[1711,35625,1714],{"stretchy":1713},[2884,35627,35628,35630],{},[898,35629,6796],{},[2111,35631,2238],{},[1711,35633,1726],{"separator":1725},[2884,35635,35636,35638],{},[898,35637,6796],{},[2111,35639,2963],{},[1711,35641,1735],{"stretchy":1713},[898,35643,2186],{"mathvariant":2287},[24360,35645],{"width":31674},[24360,35647,35648],{},[1942,35649,35650],{},"(6.23)",[902,35652,35653],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,35655,35656,35659,35660,35692,35693,2186],{},[38,35657,35658],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,35661,35663],{"className":35662},[886],[888,35664,35665],{"xmlns":890},[892,35666,35667,35689],{},[895,35668,35669,35671,35673,35679,35681,35687],{},[898,35670,1722],{},[1711,35672,1714],{"stretchy":1713},[2884,35674,35675,35677],{},[898,35676,6796],{},[2111,35678,2238],{},[1711,35680,1726],{"separator":1725},[2884,35682,35683,35685],{},[898,35684,6796],{},[2111,35686,2963],{},[1711,35688,1735],{"stretchy":1713},[902,35690,35691],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,35694,35696],{"className":35695},[886],[888,35697,35698],{"xmlns":890},[892,35699,35700,35756],{},[895,35701,35702,35704,35706,35712,35714,35720,35722,35724,35730,35732,35734,35736,35742,35744,35750,35752,35754],{},[898,35703,15014],{},[1711,35705,1714],{"stretchy":1713},[2884,35707,35708,35710],{},[898,35709,6796],{},[2111,35711,2238],{},[1711,35713,1726],{"separator":1725},[2884,35715,35716,35718],{},[898,35717,6796],{},[2111,35719,2963],{},[1711,35721,1735],{"stretchy":1713},[1711,35723,1836],{},[1716,35725,35726,35728],{},[898,35727,900],{},[1711,35729,1793],{},[1711,35731,2460],{},[898,35733,900],{},[1711,35735,1714],{"stretchy":1713},[2884,35737,35738,35740],{},[898,35739,6796],{},[2111,35741,2238],{},[1711,35743,1726],{"separator":1725},[2884,35745,35746,35748],{},[898,35747,6796],{},[2111,35749,2963],{},[1711,35751,1735],{"stretchy":1713},[1711,35753,1836],{},[2111,35755,2113],{},[902,35757,35758],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,35760,35762],{"id":35761},"lagrangeova-funkce","Lagrangeova funkce",[883,35764,35766],{"className":35765},[886],[888,35767,35768],{"xmlns":890,"display":31664},[892,35769,35770,35881],{},[24352,35771,35772],{"width":31669},[24357,35773,35774,35776,35874,35876],{},[24360,35775],{"width":31674},[24360,35777,35778],{},[895,35779,35780,35782,35784,35790,35792,35798,35800,35802,35804,35806,35814,35820,35822,35830,35836,35838,35840,35842,35848,35850,35852,35854,35860,35862,35868,35870,35872],{},[898,35781,2888],{"mathvariant":32146},[1711,35783,1714],{"stretchy":1713},[2884,35785,35786,35788],{},[898,35787,6796],{},[2111,35789,2238],{},[1711,35791,1726],{"separator":1725},[2884,35793,35794,35796],{},[898,35795,6796],{},[2111,35797,2963],{},[1711,35799,1726],{"separator":1725},[898,35801,20041],{},[1711,35803,1735],{"stretchy":1713},[1711,35805,1836],{},[13142,35807,35808,35810,35812],{},[898,35809,7929],{},[2111,35811,2238],{},[1711,35813,1793],{},[2884,35815,35816,35818],{},[898,35817,6796],{},[2111,35819,2238],{},[1711,35821,2095],{},[13142,35823,35824,35826,35828],{},[898,35825,7929],{},[2111,35827,2963],{},[1711,35829,1793],{},[2884,35831,35832,35834],{},[898,35833,6796],{},[2111,35835,2963],{},[1711,35837,2095],{},[898,35839,20041],{},[1711,35841,1714],{"stretchy":1713},[1716,35843,35844,35846],{},[898,35845,900],{},[1711,35847,1793],{},[1711,35849,2460],{},[898,35851,900],{},[1711,35853,1714],{"stretchy":1713},[2884,35855,35856,35858],{},[898,35857,6796],{},[2111,35859,2238],{},[1711,35861,1726],{"separator":1725},[2884,35863,35864,35866],{},[898,35865,6796],{},[2111,35867,2963],{},[1711,35869,1735],{"stretchy":1713},[1711,35871,1735],{"stretchy":1713},[898,35873,2186],{"mathvariant":2287},[24360,35875],{"width":31674},[24360,35877,35878],{},[1942,35879,35880],{},"(6.24)",[902,35882,35883],{"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}",[724,35885,35886],{},"Soustava podmínek prvního řádu:",[883,35888,35890],{"className":35889},[886],[888,35891,35892],{"xmlns":890,"display":31664},[892,35893,35894,36067],{},[24352,35895,35896],{"width":31669},[24357,35897,35898,35900,36060,36062],{},[24360,35899],{"width":31674},[24360,35901,35902],{},[24352,35903,35904,35954,36004],{"rowspacing":24354,"columnalign":24355,"columnspacing":5224},[24357,35905,35906,35918],{},[24360,35907,35908],{},[2509,35909,35910],{"scriptlevel":2113,"displaystyle":1725},[13142,35911,35912,35914,35916],{},[898,35913,2888],{"mathvariant":32146},[2111,35915,2238],{},[1711,35917,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[24360,35919,35920],{},[2509,35921,35922],{"scriptlevel":2113,"displaystyle":1725},[895,35923,35924,35926,35928,35936,35938,35940,35948,35950,35952],{},[895,35925],{},[1711,35927,1836],{},[13142,35929,35930,35932,35934],{},[898,35931,7929],{},[2111,35933,2238],{},[1711,35935,1793],{},[1711,35937,2460],{},[898,35939,20041],{},[13142,35941,35942,35944,35946],{},[898,35943,900],{},[2111,35945,2238],{},[1711,35947,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,35949,1836],{},[2111,35951,2113],{},[1711,35953,1726],{"separator":1725},[24357,35955,35956,35968],{},[24360,35957,35958],{},[2509,35959,35960],{"scriptlevel":2113,"displaystyle":1725},[13142,35961,35962,35964,35966],{},[898,35963,2888],{"mathvariant":32146},[2111,35965,2963],{},[1711,35967,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[24360,35969,35970],{},[2509,35971,35972],{"scriptlevel":2113,"displaystyle":1725},[895,35973,35974,35976,35978,35986,35988,35990,35998,36000,36002],{},[895,35975],{},[1711,35977,1836],{},[13142,35979,35980,35982,35984],{},[898,35981,7929],{},[2111,35983,2963],{},[1711,35985,1793],{},[1711,35987,2460],{},[898,35989,20041],{},[13142,35991,35992,35994,35996],{},[898,35993,900],{},[2111,35995,2963],{},[1711,35997,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,35999,1836],{},[2111,36001,2113],{},[1711,36003,1726],{"separator":1725},[24357,36005,36006,36018],{},[24360,36007,36008],{},[2509,36009,36010],{"scriptlevel":2113,"displaystyle":1725},[13142,36011,36012,36014,36016],{},[898,36013,2888],{"mathvariant":32146},[898,36015,20041],{},[1711,36017,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[24360,36019,36020],{},[2509,36021,36022],{"scriptlevel":2113,"displaystyle":1725},[895,36023,36024,36026,36028,36034,36036,36038,36040,36046,36048,36054,36056,36058],{},[895,36025],{},[1711,36027,1836],{},[1716,36029,36030,36032],{},[898,36031,900],{},[1711,36033,1793],{},[1711,36035,2460],{},[898,36037,900],{},[1711,36039,1714],{"stretchy":1713},[2884,36041,36042,36044],{},[898,36043,6796],{},[2111,36045,2238],{},[1711,36047,1726],{"separator":1725},[2884,36049,36050,36052],{},[898,36051,6796],{},[2111,36053,2963],{},[1711,36055,1735],{"stretchy":1713},[1711,36057,1836],{},[2111,36059,2126],{},[24360,36061],{"width":31674},[24360,36063,36064],{},[1942,36065,36066],{},"(6.25)",[902,36068,36069],{"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}",[724,36071,36072],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,36074,36076],{"className":36075},[886],[888,36077,36078],{"xmlns":890,"display":31664},[892,36079,36080,36178],{},[24352,36081,36082],{"width":31669},[24357,36083,36084,36086,36171,36173],{},[24360,36085],{"width":31674},[24360,36087,36088],{},[895,36089,36090,36092,36094,36100,36102,36108,36110,36112,36114,36116,36118,36120,36169],{},[898,36091,2778],{},[1711,36093,1714],{"stretchy":1713},[2884,36095,36096,36098],{},[898,36097,6796],{},[2111,36099,2238],{},[1711,36101,1726],{"separator":1725},[2884,36103,36104,36106],{},[898,36105,6796],{},[2111,36107,2963],{},[1711,36109,1726],{"separator":1725},[898,36111,20041],{},[1711,36113,1735],{"stretchy":1713},[1711,36115,1836],{},[1711,36117,2460],{},[898,36119,20041],{},[895,36121,36122,36124,36136,36138,36151,36153,36155,36167],{},[1711,36123,1714],{"fence":1725},[13142,36125,36126,36128,36130],{},[898,36127,900],{},[2111,36129,6907],{},[895,36131,36132,36134],{},[1711,36133,5225],{"mathvariant":2287},[1711,36135,5225],{"mathvariant":2287},[1711,36137,2095],{},[13142,36139,36140,36142,36145],{},[898,36141,900],{},[2111,36143,36144],{},"22",[895,36146,36147,36149],{},[1711,36148,5225],{"mathvariant":2287},[1711,36150,5225],{"mathvariant":2287},[1711,36152,2095],{},[2111,36154,2963],{},[13142,36156,36157,36159,36161],{},[898,36158,900],{},[2111,36160,7505],{},[895,36162,36163,36165],{},[1711,36164,5225],{"mathvariant":2287},[1711,36166,5225],{"mathvariant":2287},[1711,36168,1735],{"fence":1725},[898,36170,2186],{"mathvariant":2287},[24360,36172],{"width":31674},[24360,36174,36175],{},[1942,36176,36177],{},"(6.26)",[902,36179,36180],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,36182,36183,36186,36187,36226,36227,36266,36267,36317,36318,36344,36345,36362,36363,36389],{},[38,36184,36185],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,36188,36190],{"className":36189},[886],[888,36191,36192],{"xmlns":890},[892,36193,36194,36224],{},[895,36195,36196,36202,36204,36212,36214,36222],{},[1716,36197,36198,36200],{},[898,36199,6796],{},[1711,36201,1793],{},[1711,36203,5144],{"stretchy":1713},[13142,36205,36206,36208,36210],{},[898,36207,6796],{},[2111,36209,2238],{},[1711,36211,1793],{},[1711,36213,1726],{"separator":1725},[13142,36215,36216,36218,36220],{},[898,36217,6796],{},[2111,36219,2963],{},[1711,36221,1793],{},[1711,36223,5163],{"stretchy":1713},[902,36225,31925],{"encoding":904}," dotyku křivky užitečnosti ",[883,36228,36230],{"className":36229},[886],[888,36231,36232],{"xmlns":890},[892,36233,36234,36264],{},[895,36235,36236,36242,36244,36246,36248,36254,36256,36262],{},[1716,36237,36238,36240],{},[898,36239,900],{},[1711,36241,1793],{},[1711,36243,1836],{},[898,36245,900],{},[1711,36247,1714],{"stretchy":1713},[2884,36249,36250,36252],{},[898,36251,6796],{},[2111,36253,2238],{},[1711,36255,1726],{"separator":1725},[2884,36257,36258,36260],{},[898,36259,6796],{},[2111,36261,2963],{},[1711,36263,1735],{"stretchy":1713},[902,36265,21263],{"encoding":904}," s přímkou výdajů ",[883,36268,36270],{"className":36269},[886],[888,36271,36272],{"xmlns":890},[892,36273,36274,36314],{},[895,36275,36276,36282,36284,36292,36298,36300,36308],{},[1716,36277,36278,36280],{},[898,36279,1722],{},[1711,36281,1793],{},[1711,36283,1836],{},[13142,36285,36286,36288,36290],{},[898,36287,7929],{},[2111,36289,2238],{},[1711,36291,1793],{},[2884,36293,36294,36296],{},[898,36295,6796],{},[2111,36297,2238],{},[1711,36299,2095],{},[13142,36301,36302,36304,36306],{},[898,36303,7929],{},[2111,36305,2963],{},[1711,36307,1793],{},[2884,36309,36310,36312],{},[898,36311,6796],{},[2111,36313,2963],{},[902,36315,36316],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,36319,36321],{"className":36320},[886],[888,36322,36323],{"xmlns":890},[892,36324,36325,36341],{},[895,36326,36327,36333,36335],{},[2884,36328,36329,36331],{},[898,36330,1722],{},[2111,36332,2113],{},[1711,36334,2109],{},[1716,36336,36337,36339],{},[898,36338,1722],{},[1711,36340,1793],{},[902,36342,36343],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,36346,36348],{"className":36347},[886],[888,36349,36350],{"xmlns":890},[892,36351,36352,36360],{},[895,36353,36354],{},[1716,36355,36356,36358],{},[898,36357,900],{},[1711,36359,1793],{},[902,36361,31560],{"encoding":904},", hladina ",[883,36364,36366],{"className":36365},[886],[888,36367,36368],{"xmlns":890},[892,36369,36370,36386],{},[895,36371,36372,36378,36380],{},[2884,36373,36374,36376],{},[898,36375,1722],{},[2111,36377,2238],{},[1711,36379,2123],{},[1716,36381,36382,36384],{},[898,36383,1722],{},[1711,36385,1793],{},[902,36387,36388],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[1921,36391,36392,36397],{},[724,36393,36394,36396],{},[883,36395,3872],{}," Postup — duální úloha (minimalizace výdajů)",[152,36398,36399,36449,36535,36575,36650],{},[123,36400,36401,1700,36404,36448],{},[38,36402,36403],{},"Zapiš vazbu",[883,36405,36407],{"className":36406},[886],[888,36408,36409],{"xmlns":890},[892,36410,36411,36445],{},[895,36412,36413,36419,36421,36423,36425,36431,36433,36439,36441,36443],{},[1716,36414,36415,36417],{},[898,36416,900],{},[1711,36418,1793],{},[1711,36420,2460],{},[898,36422,900],{},[1711,36424,1714],{"stretchy":1713},[2884,36426,36427,36429],{},[898,36428,6796],{},[2111,36430,2238],{},[1711,36432,1726],{"separator":1725},[2884,36434,36435,36437],{},[898,36436,6796],{},[2111,36438,2963],{},[1711,36440,1735],{"stretchy":1713},[1711,36442,1836],{},[2111,36444,2113],{},[902,36446,36447],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,36450,36451,1700,36453,2186],{},[38,36452,32858],{},[883,36454,36456],{"className":36455},[886],[888,36457,36458],{"xmlns":890},[892,36459,36460,36532],{},[895,36461,36462,36464,36466,36474,36480,36482,36490,36496,36498,36500,36502,36508,36510,36512,36514,36520,36522,36528,36530],{},[898,36463,2888],{"mathvariant":32146},[1711,36465,1836],{},[13142,36467,36468,36470,36472],{},[898,36469,7929],{},[2111,36471,2238],{},[1711,36473,1793],{},[2884,36475,36476,36478],{},[898,36477,6796],{},[2111,36479,2238],{},[1711,36481,2095],{},[13142,36483,36484,36486,36488],{},[898,36485,7929],{},[2111,36487,2963],{},[1711,36489,1793],{},[2884,36491,36492,36494],{},[898,36493,6796],{},[2111,36495,2963],{},[1711,36497,2095],{},[898,36499,20041],{},[1711,36501,1714],{"stretchy":1713},[1716,36503,36504,36506],{},[898,36505,900],{},[1711,36507,1793],{},[1711,36509,2460],{},[898,36511,900],{},[1711,36513,1714],{"stretchy":1713},[2884,36515,36516,36518],{},[898,36517,6796],{},[2111,36519,2238],{},[1711,36521,1726],{"separator":1725},[2884,36523,36524,36526],{},[898,36525,6796],{},[2111,36527,2963],{},[1711,36529,1735],{"stretchy":1713},[1711,36531,1735],{"stretchy":1713},[902,36533,36534],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,36536,36537,36540,36541,36574],{},[38,36538,36539],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,36542,36544],{"className":36543},[886],[888,36545,36546],{"xmlns":890},[892,36547,36548,36572],{},[895,36549,36550,36552,36554,36562,36564],{},[1942,36551,14576],{},[1711,36553,1836],{},[13142,36555,36556,36558,36560],{},[898,36557,7929],{},[2111,36559,2238],{},[1711,36561,1793],{},[898,36563,8659],{"mathvariant":2287},[13142,36565,36566,36568,36570],{},[898,36567,7929],{},[2111,36569,2963],{},[1711,36571,1793],{},[902,36573,32577],{"encoding":904}," (stejná jako u maximalizace!).",[123,36576,36577,1700,36580,36620,36621,2186],{},[38,36578,36579],{},"Dosaď do vazby",[883,36581,36583],{"className":36582},[886],[888,36584,36585],{"xmlns":890},[892,36586,36587,36617],{},[895,36588,36589,36591,36593,36599,36601,36607,36609,36611],{},[898,36590,900],{},[1711,36592,1714],{"stretchy":1713},[2884,36594,36595,36597],{},[898,36596,6796],{},[2111,36598,2238],{},[1711,36600,1726],{"separator":1725},[2884,36602,36603,36605],{},[898,36604,6796],{},[2111,36606,2963],{},[1711,36608,1735],{"stretchy":1713},[1711,36610,1836],{},[1716,36612,36613,36615],{},[898,36614,900],{},[1711,36616,1793],{},[902,36618,36619],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,36622,36624],{"className":36623},[886],[888,36625,36626],{"xmlns":890},[892,36627,36628,36648],{},[895,36629,36630,36638,36640],{},[13142,36631,36632,36634,36636],{},[898,36633,6796],{},[2111,36635,2238],{},[1711,36637,1793],{},[1711,36639,1726],{"separator":1725},[13142,36641,36642,36644,36646],{},[898,36643,6796],{},[2111,36645,2963],{},[1711,36647,1793],{},[902,36649,33099],{"encoding":904},[123,36651,36652,1700,36655,36709],{},[38,36653,36654],{},"Vypočítej minimální výdaje",[883,36656,36658],{"className":36657},[886],[888,36659,36660],{"xmlns":890},[892,36661,36662,36706],{},[895,36663,36664,36670,36672,36680,36688,36690,36698],{},[1716,36665,36666,36668],{},[898,36667,1722],{},[1711,36669,1793],{},[1711,36671,1836],{},[13142,36673,36674,36676,36678],{},[898,36675,7929],{},[2111,36677,2238],{},[1711,36679,1793],{},[13142,36681,36682,36684,36686],{},[898,36683,6796],{},[2111,36685,2238],{},[1711,36687,1793],{},[1711,36689,2095],{},[13142,36691,36692,36694,36696],{},[898,36693,7929],{},[2111,36695,2963],{},[1711,36697,1793],{},[13142,36699,36700,36702,36704],{},[898,36701,6796],{},[2111,36703,2963],{},[1711,36705,1793],{},[902,36707,36708],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,36711,36713,36714],{"id":36712},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,36715,36717],{"className":36716},[886],[888,36718,36719],{"xmlns":890},[892,36720,36721,36755],{},[895,36722,36723,36725,36727,36741],{},[898,36724,900],{},[1711,36726,1836],{},[13142,36728,36729,36731,36733],{},[898,36730,6796],{},[2111,36732,2238],{},[895,36734,36735,36737,36739],{},[2111,36736,2238],{},[898,36738,8659],{"mathvariant":2287},[2111,36740,2963],{},[13142,36742,36743,36745,36747],{},[898,36744,6796],{},[2111,36746,2963],{},[895,36748,36749,36751,36753],{},[2111,36750,2238],{},[898,36752,8659],{"mathvariant":2287},[2111,36754,2963],{},[902,36756,36757],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,36759,36760,36761,1343,36783,1343,36807,33944],{},"Dáno ",[883,36762,36764],{"className":36763},[886],[888,36765,36766],{"xmlns":890},[892,36767,36768,36780],{},[895,36769,36770,36776,36778],{},[1716,36771,36772,36774],{},[898,36773,900],{},[1711,36775,1793],{},[1711,36777,1836],{},[2111,36779,2963],{},[902,36781,36782],{"encoding":904},"U^* = 2",[883,36784,36786],{"className":36785},[886],[888,36787,36788],{"xmlns":890},[892,36789,36790,36804],{},[895,36791,36792,36800,36802],{},[13142,36793,36794,36796,36798],{},[898,36795,7929],{},[2111,36797,2238],{},[1711,36799,1793],{},[1711,36801,1836],{},[2111,36803,27387],{},[902,36805,36806],{"encoding":904},"P_1^* = 0{,}25",[883,36808,36810],{"className":36809},[886],[888,36811,36812],{"xmlns":890},[892,36813,36814,36828],{},[895,36815,36816,36824,36826],{},[13142,36817,36818,36820,36822],{},[898,36819,7929],{},[2111,36821,2963],{},[1711,36823,1793],{},[1711,36825,1836],{},[2111,36827,2238],{},[902,36829,36830],{"encoding":904},"P_2^* = 1",[883,36832,36834],{"className":36833},[886],[888,36835,36836],{"xmlns":890,"display":31664},[892,36837,36838,36902],{},[895,36839,36840,36842,36844,36846,36852,36854,36860,36862,36864,36866,36868,36870,36884,36898,36900],{},[898,36841,2888],{"mathvariant":32146},[1711,36843,1836],{},[2111,36845,27387],{},[2884,36847,36848,36850],{},[898,36849,6796],{},[2111,36851,2238],{},[1711,36853,2095],{},[2884,36855,36856,36858],{},[898,36857,6796],{},[2111,36859,2963],{},[1711,36861,2095],{},[898,36863,20041],{},[1711,36865,1714],{"stretchy":1713},[2111,36867,2963],{},[1711,36869,2460],{},[13142,36871,36872,36874,36876],{},[898,36873,6796],{},[2111,36875,2238],{},[895,36877,36878,36880,36882],{},[2111,36879,2238],{},[898,36881,8659],{"mathvariant":2287},[2111,36883,2963],{},[13142,36885,36886,36888,36890],{},[898,36887,6796],{},[2111,36889,2963],{},[895,36891,36892,36894,36896],{},[2111,36893,2238],{},[898,36895,8659],{"mathvariant":2287},[2111,36897,2963],{},[1711,36899,1735],{"stretchy":1713},[898,36901,2186],{"mathvariant":2287},[902,36903,36904],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,36906,34029],{},[883,36908,36910],{"className":36909},[886],[888,36911,36912],{"xmlns":890,"display":31664},[892,36913,36914,37128],{},[24352,36915,36916,36992,37068],{"rowspacing":24354,"columnalign":24355,"columnspacing":5224},[24357,36917,36918,36930],{},[24360,36919,36920],{},[2509,36921,36922],{"scriptlevel":2113,"displaystyle":1725},[13142,36923,36924,36926,36928],{},[898,36925,2888],{"mathvariant":32146},[2111,36927,2238],{},[1711,36929,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[24360,36931,36932],{},[2509,36933,36934],{"scriptlevel":2113,"displaystyle":1725},[895,36935,36936,36938,36940,36942,36944,36946,36948,36956,36972,36986,36988,36990],{},[895,36937],{},[1711,36939,1836],{},[2111,36941,27387],{},[1711,36943,2460],{},[898,36945,20041],{},[1711,36947,4795],{},[2509,36949,36950],{"scriptlevel":2113,"displaystyle":1713},[2525,36951,36952,36954],{},[2111,36953,2238],{},[2111,36955,2963],{},[13142,36957,36958,36960,36962],{},[898,36959,6796],{},[2111,36961,2238],{},[895,36963,36964,36966,36968,36970],{},[1711,36965,2460],{},[2111,36967,2238],{},[898,36969,8659],{"mathvariant":2287},[2111,36971,2963],{},[13142,36973,36974,36976,36978],{},[898,36975,6796],{},[2111,36977,2963],{},[895,36979,36980,36982,36984],{},[2111,36981,2238],{},[898,36983,8659],{"mathvariant":2287},[2111,36985,2963],{},[1711,36987,1836],{},[2111,36989,2113],{},[1711,36991,1726],{"separator":1725},[24357,36993,36994,37006],{},[24360,36995,36996],{},[2509,36997,36998],{"scriptlevel":2113,"displaystyle":1725},[13142,36999,37000,37002,37004],{},[898,37001,2888],{"mathvariant":32146},[2111,37003,2963],{},[1711,37005,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[24360,37007,37008],{},[2509,37009,37010],{"scriptlevel":2113,"displaystyle":1725},[895,37011,37012,37014,37016,37018,37020,37022,37024,37032,37046,37062,37064,37066],{},[895,37013],{},[1711,37015,1836],{},[2111,37017,2238],{},[1711,37019,2460],{},[898,37021,20041],{},[1711,37023,4795],{},[2509,37025,37026],{"scriptlevel":2113,"displaystyle":1713},[2525,37027,37028,37030],{},[2111,37029,2238],{},[2111,37031,2963],{},[13142,37033,37034,37036,37038],{},[898,37035,6796],{},[2111,37037,2238],{},[895,37039,37040,37042,37044],{},[2111,37041,2238],{},[898,37043,8659],{"mathvariant":2287},[2111,37045,2963],{},[13142,37047,37048,37050,37052],{},[898,37049,6796],{},[2111,37051,2963],{},[895,37053,37054,37056,37058,37060],{},[1711,37055,2460],{},[2111,37057,2238],{},[898,37059,8659],{"mathvariant":2287},[2111,37061,2963],{},[1711,37063,1836],{},[2111,37065,2113],{},[1711,37067,1726],{"separator":1725},[24357,37069,37070,37082],{},[24360,37071,37072],{},[2509,37073,37074],{"scriptlevel":2113,"displaystyle":1725},[13142,37075,37076,37078,37080],{},[898,37077,2888],{"mathvariant":32146},[898,37079,20041],{},[1711,37081,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[24360,37083,37084],{},[2509,37085,37086],{"scriptlevel":2113,"displaystyle":1725},[895,37087,37088,37090,37092,37094,37096,37110,37124,37126],{},[895,37089],{},[1711,37091,1836],{},[2111,37093,2963],{},[1711,37095,2460],{},[13142,37097,37098,37100,37102],{},[898,37099,6796],{},[2111,37101,2238],{},[895,37103,37104,37106,37108],{},[2111,37105,2238],{},[898,37107,8659],{"mathvariant":2287},[2111,37109,2963],{},[13142,37111,37112,37114,37116],{},[898,37113,6796],{},[2111,37115,2963],{},[895,37117,37118,37120,37122],{},[2111,37119,2238],{},[898,37121,8659],{"mathvariant":2287},[2111,37123,2963],{},[1711,37125,1836],{},[2111,37127,2126],{},[902,37129,37130],{"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}",[724,37132,37133,37134,21174,37164,37192,37193,9572,37255,1343,37305,37327,37328,2186],{},"Podílem prvních dvou rovnic: ",[883,37135,37137],{"className":37136},[886],[888,37138,37139],{"xmlns":890},[892,37140,37141,37161],{},[895,37142,37143,37145,37147,37153,37155],{},[2111,37144,27387],{},[1711,37146,1836],{},[2884,37148,37149,37151],{},[898,37150,6796],{},[2111,37152,2963],{},[898,37154,8659],{"mathvariant":2287},[2884,37156,37157,37159],{},[898,37158,6796],{},[2111,37160,2238],{},[902,37162,37163],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,37165,37167],{"className":37166},[886],[888,37168,37169],{"xmlns":890},[892,37170,37171,37189],{},[895,37172,37173,37179,37181,37183],{},[2884,37174,37175,37177],{},[898,37176,6796],{},[2111,37178,2963],{},[1711,37180,1836],{},[2111,37182,27387],{},[2884,37184,37185,37187],{},[898,37186,6796],{},[2111,37188,2238],{},[902,37190,37191],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,37194,37196],{"className":37195},[886],[888,37197,37198],{"xmlns":890},[892,37199,37200,37252],{},[895,37201,37202,37216,37218,37220,37226,37238,37240,37242,37248,37250],{},[13142,37203,37204,37206,37208],{},[898,37205,6796],{},[2111,37207,2238],{},[895,37209,37210,37212,37214],{},[2111,37211,2238],{},[898,37213,8659],{"mathvariant":2287},[2111,37215,2963],{},[1711,37217,1714],{"stretchy":1713},[2111,37219,27387],{},[2884,37221,37222,37224],{},[898,37223,6796],{},[2111,37225,2238],{},[1716,37227,37228,37230],{},[1711,37229,1735],{"stretchy":1713},[895,37231,37232,37234,37236],{},[2111,37233,2238],{},[898,37235,8659],{"mathvariant":2287},[2111,37237,2963],{},[1711,37239,1836],{},[2111,37241,8993],{},[2884,37243,37244,37246],{},[898,37245,6796],{},[2111,37247,2238],{},[1711,37249,1836],{},[2111,37251,2963],{},[902,37253,37254],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,37256,37257,1343,37281],{},[883,37258,37260],{"className":37259},[886],[888,37261,37262],{"xmlns":890},[892,37263,37264,37278],{},[895,37265,37266,37274,37276],{},[13142,37267,37268,37270,37272],{},[898,37269,6796],{},[2111,37271,2238],{},[1711,37273,1793],{},[1711,37275,1836],{},[2111,37277,6369],{},[902,37279,37280],{"encoding":904},"Q_1^* = 4",[883,37282,37284],{"className":37283},[886],[888,37285,37286],{"xmlns":890},[892,37287,37288,37302],{},[895,37289,37290,37298,37300],{},[13142,37291,37292,37294,37296],{},[898,37293,6796],{},[2111,37295,2963],{},[1711,37297,1793],{},[1711,37299,1836],{},[2111,37301,2238],{},[902,37303,37304],{"encoding":904},"Q_2^* = 1",[883,37306,37308],{"className":37307},[886],[888,37309,37310],{"xmlns":890},[892,37311,37312,37324],{},[895,37313,37314,37320,37322],{},[1716,37315,37316,37318],{},[898,37317,20041],{},[1711,37319,1793],{},[1711,37321,1836],{},[2111,37323,2238],{},[902,37325,37326],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,37329,37331],{"className":37330},[886],[888,37332,37333],{"xmlns":890},[892,37334,37335,37363],{},[895,37336,37337,37343,37345,37347,37349,37351,37353,37355,37357,37359,37361],{},[1716,37338,37339,37341],{},[898,37340,1722],{},[1711,37342,1793],{},[1711,37344,1836],{},[2111,37346,27387],{},[1711,37348,4795],{},[2111,37350,6369],{},[1711,37352,2095],{},[2111,37354,2238],{},[1711,37356,4795],{},[2111,37358,2238],{},[1711,37360,1836],{},[2111,37362,2963],{},[902,37364,37365],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,37367,37368,37371,37372,1343,37438,1343,37504,37570,37571,37608,37609,37631,37632,2186],{},[614,37369,37370],{},"Ověření postačující podmínky"," (6.26): ",[883,37373,37375],{"className":37374},[886],[888,37376,37377],{"xmlns":890},[892,37378,37379,37435],{},[895,37380,37381,37393,37395,37397,37405,37421],{},[13142,37382,37383,37385,37387],{},[898,37384,900],{},[2111,37386,6907],{},[895,37388,37389,37391],{},[1711,37390,5225],{"mathvariant":2287},[1711,37392,5225],{"mathvariant":2287},[1711,37394,1836],{},[1711,37396,2460],{},[2509,37398,37399],{"scriptlevel":2113,"displaystyle":1713},[2525,37400,37401,37403],{},[2111,37402,2238],{},[2111,37404,6369],{},[13142,37406,37407,37409,37411],{},[898,37408,6796],{},[2111,37410,2238],{},[895,37412,37413,37415,37417,37419],{},[1711,37414,2460],{},[2111,37416,3034],{},[898,37418,8659],{"mathvariant":2287},[2111,37420,2963],{},[13142,37422,37423,37425,37427],{},[898,37424,6796],{},[2111,37426,2963],{},[895,37428,37429,37431,37433],{},[2111,37430,2238],{},[898,37432,8659],{"mathvariant":2287},[2111,37434,2963],{},[902,37436,37437],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,37439,37441],{"className":37440},[886],[888,37442,37443],{"xmlns":890},[892,37444,37445,37501],{},[895,37446,37447,37459,37461,37463,37471,37485],{},[13142,37448,37449,37451,37453],{},[898,37450,900],{},[2111,37452,36144],{},[895,37454,37455,37457],{},[1711,37456,5225],{"mathvariant":2287},[1711,37458,5225],{"mathvariant":2287},[1711,37460,1836],{},[1711,37462,2460],{},[2509,37464,37465],{"scriptlevel":2113,"displaystyle":1713},[2525,37466,37467,37469],{},[2111,37468,2238],{},[2111,37470,6369],{},[13142,37472,37473,37475,37477],{},[898,37474,6796],{},[2111,37476,2238],{},[895,37478,37479,37481,37483],{},[2111,37480,2238],{},[898,37482,8659],{"mathvariant":2287},[2111,37484,2963],{},[13142,37486,37487,37489,37491],{},[898,37488,6796],{},[2111,37490,2963],{},[895,37492,37493,37495,37497,37499],{},[1711,37494,2460],{},[2111,37496,3034],{},[898,37498,8659],{"mathvariant":2287},[2111,37500,2963],{},[902,37502,37503],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,37505,37507],{"className":37506},[886],[888,37508,37509],{"xmlns":890},[892,37510,37511,37567],{},[895,37512,37513,37525,37527,37535,37551],{},[13142,37514,37515,37517,37519],{},[898,37516,900],{},[2111,37518,7505],{},[895,37520,37521,37523],{},[1711,37522,5225],{"mathvariant":2287},[1711,37524,5225],{"mathvariant":2287},[1711,37526,1836],{},[2509,37528,37529],{"scriptlevel":2113,"displaystyle":1713},[2525,37530,37531,37533],{},[2111,37532,2238],{},[2111,37534,6369],{},[13142,37536,37537,37539,37541],{},[898,37538,6796],{},[2111,37540,2238],{},[895,37542,37543,37545,37547,37549],{},[1711,37544,2460],{},[2111,37546,2238],{},[898,37548,8659],{"mathvariant":2287},[2111,37550,2963],{},[13142,37552,37553,37555,37557],{},[898,37554,6796],{},[2111,37556,2963],{},[895,37558,37559,37561,37563,37565],{},[1711,37560,2460],{},[2111,37562,2238],{},[898,37564,8659],{"mathvariant":2287},[2111,37566,2963],{},[902,37568,37569],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,37572,37574],{"className":37573},[886],[888,37575,37576],{"xmlns":890},[892,37577,37578,37605],{},[895,37579,37580,37582,37584,37586,37588,37590,37592,37594,37596,37598,37601,37603],{},[898,37581,2778],{},[1711,37583,1714],{"stretchy":1713},[2111,37585,6369],{},[1711,37587,1726],{"separator":1725},[2111,37589,2238],{},[1711,37591,1726],{"separator":1725},[2111,37593,2238],{},[1711,37595,1735],{"stretchy":1713},[1711,37597,1836],{},[2111,37599,37600],{},"0,28125",[1711,37602,2123],{},[2111,37604,2113],{},[902,37606,37607],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,37610,37612],{"className":37611},[886],[888,37613,37614],{"xmlns":890},[892,37615,37616,37628],{},[895,37617,37618,37620,37622,37624,37626],{},[1711,37619,5144],{"stretchy":1713},[2111,37621,6369],{},[1711,37623,1726],{"separator":1725},[2111,37625,2238],{},[1711,37627,5163],{"stretchy":1713},[902,37629,37630],{"encoding":904},"[4, 1]"," je vázané ",[38,37633,7771],{},[115,37635,37637],{"id":37636},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,37639,37640],{},"Obecně:",[883,37642,37644],{"className":37643},[886],[888,37645,37646],{"xmlns":890,"display":31664},[892,37647,37648,37743],{},[24352,37649,37650],{"width":31669},[24357,37651,37652,37654,37736,37738],{},[24360,37653],{"width":31674},[24360,37655,37656],{},[895,37657,37658,37664,37666,37672,37674,37680,37682,37688,37690,37692,37694,37696,37698,37704,37706,37712,37714,37720,37722,37728,37730,37732,37734],{},[2884,37659,37660,37662],{},[898,37661,6796],{},[2111,37663,2238],{},[1711,37665,1836],{},[2884,37667,37668,37670],{},[898,37669,2778],{},[2111,37671,2238],{},[1711,37673,1714],{"stretchy":1713},[2884,37675,37676,37678],{},[898,37677,7929],{},[2111,37679,2238],{},[1711,37681,1726],{"separator":1725},[2884,37683,37684,37686],{},[898,37685,7929],{},[2111,37687,2963],{},[1711,37689,1726],{"separator":1725},[898,37691,900],{},[1711,37693,1735],{"stretchy":1713},[1711,37695,1726],{"separator":1725},[2102,37697],{"width":4981},[2884,37699,37700,37702],{},[898,37701,6796],{},[2111,37703,2963],{},[1711,37705,1836],{},[2884,37707,37708,37710],{},[898,37709,2778],{},[2111,37711,2963],{},[1711,37713,1714],{"stretchy":1713},[2884,37715,37716,37718],{},[898,37717,7929],{},[2111,37719,2238],{},[1711,37721,1726],{"separator":1725},[2884,37723,37724,37726],{},[898,37725,7929],{},[2111,37727,2963],{},[1711,37729,1726],{"separator":1725},[898,37731,900],{},[1711,37733,1735],{"stretchy":1713},[1711,37735,1726],{"separator":1725},[24360,37737],{"width":31674},[24360,37739,37740],{},[1942,37741,37742],{},"(6.27)",[902,37744,37745],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,37747,37749],{"className":37748},[886],[888,37750,37751],{"xmlns":890,"display":31664},[892,37752,37753,37800],{},[24352,37754,37755],{"width":31669},[24357,37756,37757,37759,37793,37795],{},[24360,37758],{"width":31674},[24360,37760,37761],{},[895,37762,37763,37765,37767,37769,37771,37777,37779,37785,37787,37789,37791],{},[898,37764,20041],{},[1711,37766,1836],{},[898,37768,20041],{},[1711,37770,1714],{"stretchy":1713},[2884,37772,37773,37775],{},[898,37774,7929],{},[2111,37776,2238],{},[1711,37778,1726],{"separator":1725},[2884,37780,37781,37783],{},[898,37782,7929],{},[2111,37784,2963],{},[1711,37786,1726],{"separator":1725},[898,37788,900],{},[1711,37790,1735],{"stretchy":1713},[898,37792,2186],{"mathvariant":2287},[24360,37794],{"width":31674},[24360,37796,37797],{},[1942,37798,37799],{},"(6.28)",[902,37801,37802],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,37804,37805,37806,1700,37809,37822,37823,37836],{},"Hicksova poptávka závisí na ",[38,37807,37808],{},"hladině užitečnosti",[883,37810,37812],{"className":37811},[886],[888,37813,37814],{"xmlns":890},[892,37815,37816,37820],{},[895,37817,37818],{},[898,37819,900],{},[902,37821,900],{"encoding":904}," (nikoli na důchodu ",[883,37824,37826],{"className":37825},[886],[888,37827,37828],{"xmlns":890},[892,37829,37830,37834],{},[895,37831,37832],{},[898,37833,1660],{},[902,37835,1660],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,37838,37840,37841],{"id":37839},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,37842,37844],{"className":37843},[886],[888,37845,37846],{"xmlns":890},[892,37847,37848,37882],{},[895,37849,37850,37852,37854,37868],{},[898,37851,900],{},[1711,37853,1836],{},[13142,37855,37856,37858,37860],{},[898,37857,6796],{},[2111,37859,2238],{},[895,37861,37862,37864,37866],{},[2111,37863,2238],{},[898,37865,8659],{"mathvariant":2287},[2111,37867,2963],{},[13142,37869,37870,37872,37874],{},[898,37871,6796],{},[2111,37873,2963],{},[895,37875,37876,37878,37880],{},[2111,37877,2238],{},[898,37879,8659],{"mathvariant":2287},[2111,37881,2963],{},[902,37883,36757],{"encoding":904},[724,37885,37886,37916],{},[883,37887,37889],{"className":37888},[886],[888,37890,37891],{"xmlns":890},[892,37892,37893,37913],{},[895,37894,37895,37901,37903,37909,37911],{},[2884,37896,37897,37899],{},[898,37898,7929],{},[2111,37900,2238],{},[1711,37902,1726],{"separator":1725},[2884,37904,37905,37907],{},[898,37906,7929],{},[2111,37908,2963],{},[1711,37910,1726],{"separator":1725},[898,37912,900],{},[902,37914,37915],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,37918,37920],{"className":37919},[886],[888,37921,37922],{"xmlns":890,"display":31664},[892,37923,37924,37998],{},[895,37925,37926,37928,37930,37936,37942,37944,37950,37956,37958,37960,37962,37964,37966,37980,37994,37996],{},[898,37927,2888],{"mathvariant":32146},[1711,37929,1836],{},[2884,37931,37932,37934],{},[898,37933,7929],{},[2111,37935,2238],{},[2884,37937,37938,37940],{},[898,37939,6796],{},[2111,37941,2238],{},[1711,37943,2095],{},[2884,37945,37946,37948],{},[898,37947,7929],{},[2111,37949,2963],{},[2884,37951,37952,37954],{},[898,37953,6796],{},[2111,37955,2963],{},[1711,37957,2095],{},[898,37959,20041],{},[1711,37961,1714],{"stretchy":1713},[898,37963,900],{},[1711,37965,2460],{},[13142,37967,37968,37970,37972],{},[898,37969,6796],{},[2111,37971,2238],{},[895,37973,37974,37976,37978],{},[2111,37975,2238],{},[898,37977,8659],{"mathvariant":2287},[2111,37979,2963],{},[13142,37981,37982,37984,37986],{},[898,37983,6796],{},[2111,37985,2963],{},[895,37987,37988,37990,37992],{},[2111,37989,2238],{},[898,37991,8659],{"mathvariant":2287},[2111,37993,2963],{},[1711,37995,1735],{"stretchy":1713},[898,37997,2186],{"mathvariant":2287},[902,37999,38000],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,38002,34029],{},[883,38004,38006],{"className":38005},[886],[888,38007,38008],{"xmlns":890,"display":31664},[892,38009,38010,38232],{},[24352,38011,38012,38092,38172],{"rowspacing":24354,"columnalign":24355,"columnspacing":5224},[24357,38013,38014,38026],{},[24360,38015,38016],{},[2509,38017,38018],{"scriptlevel":2113,"displaystyle":1725},[13142,38019,38020,38022,38024],{},[898,38021,2888],{"mathvariant":32146},[2111,38023,2238],{},[1711,38025,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[24360,38027,38028],{},[2509,38029,38030],{"scriptlevel":2113,"displaystyle":1725},[895,38031,38032,38034,38036,38042,38044,38046,38048,38056,38072,38086,38088,38090],{},[895,38033],{},[1711,38035,1836],{},[2884,38037,38038,38040],{},[898,38039,7929],{},[2111,38041,2238],{},[1711,38043,2460],{},[898,38045,20041],{},[1711,38047,4795],{},[2509,38049,38050],{"scriptlevel":2113,"displaystyle":1713},[2525,38051,38052,38054],{},[2111,38053,2238],{},[2111,38055,2963],{},[13142,38057,38058,38060,38062],{},[898,38059,6796],{},[2111,38061,2238],{},[895,38063,38064,38066,38068,38070],{},[1711,38065,2460],{},[2111,38067,2238],{},[898,38069,8659],{"mathvariant":2287},[2111,38071,2963],{},[13142,38073,38074,38076,38078],{},[898,38075,6796],{},[2111,38077,2963],{},[895,38079,38080,38082,38084],{},[2111,38081,2238],{},[898,38083,8659],{"mathvariant":2287},[2111,38085,2963],{},[1711,38087,1836],{},[2111,38089,2113],{},[1711,38091,1726],{"separator":1725},[24357,38093,38094,38106],{},[24360,38095,38096],{},[2509,38097,38098],{"scriptlevel":2113,"displaystyle":1725},[13142,38099,38100,38102,38104],{},[898,38101,2888],{"mathvariant":32146},[2111,38103,2963],{},[1711,38105,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[24360,38107,38108],{},[2509,38109,38110],{"scriptlevel":2113,"displaystyle":1725},[895,38111,38112,38114,38116,38122,38124,38126,38128,38136,38150,38166,38168,38170],{},[895,38113],{},[1711,38115,1836],{},[2884,38117,38118,38120],{},[898,38119,7929],{},[2111,38121,2963],{},[1711,38123,2460],{},[898,38125,20041],{},[1711,38127,4795],{},[2509,38129,38130],{"scriptlevel":2113,"displaystyle":1713},[2525,38131,38132,38134],{},[2111,38133,2238],{},[2111,38135,2963],{},[13142,38137,38138,38140,38142],{},[898,38139,6796],{},[2111,38141,2238],{},[895,38143,38144,38146,38148],{},[2111,38145,2238],{},[898,38147,8659],{"mathvariant":2287},[2111,38149,2963],{},[13142,38151,38152,38154,38156],{},[898,38153,6796],{},[2111,38155,2963],{},[895,38157,38158,38160,38162,38164],{},[1711,38159,2460],{},[2111,38161,2238],{},[898,38163,8659],{"mathvariant":2287},[2111,38165,2963],{},[1711,38167,1836],{},[2111,38169,2113],{},[1711,38171,1726],{"separator":1725},[24357,38173,38174,38186],{},[24360,38175,38176],{},[2509,38177,38178],{"scriptlevel":2113,"displaystyle":1725},[13142,38179,38180,38182,38184],{},[898,38181,2888],{"mathvariant":32146},[898,38183,20041],{},[1711,38185,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[24360,38187,38188],{},[2509,38189,38190],{"scriptlevel":2113,"displaystyle":1725},[895,38191,38192,38194,38196,38198,38200,38214,38228,38230],{},[895,38193],{},[1711,38195,1836],{},[898,38197,900],{},[1711,38199,2460],{},[13142,38201,38202,38204,38206],{},[898,38203,6796],{},[2111,38205,2238],{},[895,38207,38208,38210,38212],{},[2111,38209,2238],{},[898,38211,8659],{"mathvariant":2287},[2111,38213,2963],{},[13142,38215,38216,38218,38220],{},[898,38217,6796],{},[2111,38219,2963],{},[895,38221,38222,38224,38226],{},[2111,38223,2238],{},[898,38225,8659],{"mathvariant":2287},[2111,38227,2963],{},[1711,38229,1836],{},[2111,38231,2126],{},[902,38233,38234],{"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}",[724,38236,38237,38238,38308,38309,38367],{},"Podílem rovnic: ",[883,38239,38241],{"className":38240},[886],[888,38242,38243],{"xmlns":890},[892,38244,38245,38305],{},[895,38246,38247,38253,38255,38261,38263,38269,38271,38277,38279,38285,38291,38293,38299],{},[2884,38248,38249,38251],{},[898,38250,7929],{},[2111,38252,2238],{},[898,38254,8659],{"mathvariant":2287},[2884,38256,38257,38259],{},[898,38258,7929],{},[2111,38260,2963],{},[1711,38262,1836],{},[2884,38264,38265,38267],{},[898,38266,6796],{},[2111,38268,2963],{},[898,38270,8659],{"mathvariant":2287},[2884,38272,38273,38275],{},[898,38274,6796],{},[2111,38276,2238],{},[1711,38278,7978],{},[2884,38280,38281,38283],{},[898,38282,7929],{},[2111,38284,2238],{},[2884,38286,38287,38289],{},[898,38288,6796],{},[2111,38290,2238],{},[1711,38292,1836],{},[2884,38294,38295,38297],{},[898,38296,7929],{},[2111,38298,2963],{},[2884,38300,38301,38303],{},[898,38302,6796],{},[2111,38304,2963],{},[902,38306,38307],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,38310,38312],{"className":38311},[886],[888,38313,38314],{"xmlns":890},[892,38315,38316,38364],{},[895,38317,38318,38320,38322,38328,38334,38336,38342,38348,38350,38352,38358],{},[898,38319,1722],{},[1711,38321,1836],{},[2884,38323,38324,38326],{},[898,38325,7929],{},[2111,38327,2238],{},[2884,38329,38330,38332],{},[898,38331,6796],{},[2111,38333,2238],{},[1711,38335,2095],{},[2884,38337,38338,38340],{},[898,38339,7929],{},[2111,38341,2963],{},[2884,38343,38344,38346],{},[898,38345,6796],{},[2111,38347,2963],{},[1711,38349,1836],{},[2111,38351,2963],{},[2884,38353,38354,38356],{},[898,38355,7929],{},[2111,38357,2238],{},[2884,38359,38360,38362],{},[898,38361,6796],{},[2111,38363,2238],{},[902,38365,38366],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,38369,38371],{"className":38370},[886],[888,38372,38373],{"xmlns":890,"display":31664},[892,38374,38375,38442],{},[24352,38376,38377],{"width":31669},[24357,38378,38379,38381,38435,38437],{},[24360,38380],{"width":31674},[24360,38382,38383],{},[895,38384,38385,38391,38393,38407,38409,38411,38417,38419,38433],{},[2884,38386,38387,38389],{},[898,38388,6796],{},[2111,38390,2238],{},[1711,38392,1836],{},[2525,38394,38395,38397],{},[898,38396,1722],{},[895,38398,38399,38401],{},[2111,38400,2963],{},[2884,38402,38403,38405],{},[898,38404,7929],{},[2111,38406,2238],{},[1711,38408,1726],{"separator":1725},[2102,38410],{"width":4981},[2884,38412,38413,38415],{},[898,38414,6796],{},[2111,38416,2963],{},[1711,38418,1836],{},[2525,38420,38421,38423],{},[898,38422,1722],{},[895,38424,38425,38427],{},[2111,38426,2963],{},[2884,38428,38429,38431],{},[898,38430,7929],{},[2111,38432,2963],{},[898,38434,2186],{"mathvariant":2287},[24360,38436],{"width":31674},[24360,38438,38439],{},[1942,38440,38441],{},"(6.29)",[902,38443,38444],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,38446,38447,38448,21174,38530,38566],{},"Ze třetí rovnice ",[883,38449,38451],{"className":38450},[886],[888,38452,38453],{"xmlns":890},[892,38454,38455,38527],{},[895,38456,38457,38459,38461,38499,38501],{},[898,38458,900],{},[1711,38460,1836],{},[12097,38462,38463],{},[895,38464,38465,38481,38483],{},[2509,38466,38467],{"scriptlevel":2113,"displaystyle":1713},[2525,38468,38469,38471],{},[898,38470,1722],{},[895,38472,38473,38475],{},[2111,38474,2963],{},[2884,38476,38477,38479],{},[898,38478,7929],{},[2111,38480,2238],{},[1711,38482,4795],{},[2509,38484,38485],{"scriptlevel":2113,"displaystyle":1713},[2525,38486,38487,38489],{},[898,38488,1722],{},[895,38490,38491,38493],{},[2111,38492,2963],{},[2884,38494,38495,38497],{},[898,38496,7929],{},[2111,38498,2963],{},[1711,38500,1836],{},[2509,38502,38503],{"scriptlevel":2113,"displaystyle":1713},[2525,38504,38505,38507],{},[898,38506,1722],{},[895,38508,38509,38511],{},[2111,38510,2963],{},[12097,38512,38513],{},[895,38514,38515,38521],{},[2884,38516,38517,38519],{},[898,38518,7929],{},[2111,38520,2238],{},[2884,38522,38523,38525],{},[898,38524,7929],{},[2111,38526,2963],{},[902,38528,38529],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,38531,38533],{"className":38532},[886],[888,38534,38535],{"xmlns":890},[892,38536,38537,38563],{},[895,38538,38539,38541,38543,38545,38547],{},[898,38540,1722],{},[1711,38542,1836],{},[2111,38544,2963],{},[898,38546,900],{},[12097,38548,38549],{},[895,38550,38551,38557],{},[2884,38552,38553,38555],{},[898,38554,7929],{},[2111,38556,2238],{},[2884,38558,38559,38561],{},[898,38560,7929],{},[2111,38562,2963],{},[902,38564,38565],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,38568,38570],{"className":38569},[886],[888,38571,38572],{"xmlns":890,"display":31664},[892,38573,38574,38719],{},[24352,38575,38576],{"width":31669},[24357,38577,38578,38580,38712,38714],{},[24360,38579],{"width":31674},[24360,38581,38582],{},[2505,38583,38584],{"notation":2507},[2509,38585,38586],{"scriptlevel":2113,"displaystyle":1713},[2509,38587,38588],{"scriptlevel":2113,"displaystyle":1713},[2509,38589,38590],{"scriptlevel":2113,"displaystyle":1725},[895,38591,38592,38594,38600,38602,38604,38620,38622,38628,38630,38636,38638,38644,38646,38648,38650,38652,38654,38660,38662,38664,38680,38682,38688,38690,38696,38698,38704,38706,38708,38710],{},[1942,38593,4699],{},[2884,38595,38596,38598],{},[898,38597,6796],{},[2111,38599,2238],{},[1711,38601,1836],{},[898,38603,900],{},[12097,38605,38606],{},[2525,38607,38608,38614],{},[2884,38609,38610,38612],{},[898,38611,7929],{},[2111,38613,2963],{},[2884,38615,38616,38618],{},[898,38617,7929],{},[2111,38619,2238],{},[1711,38621,1836],{},[2884,38623,38624,38626],{},[898,38625,2778],{},[2111,38627,2238],{},[1711,38629,1714],{"stretchy":1713},[2884,38631,38632,38634],{},[898,38633,7929],{},[2111,38635,2238],{},[1711,38637,1726],{"separator":1725},[2884,38639,38640,38642],{},[898,38641,7929],{},[2111,38643,2963],{},[1711,38645,1726],{"separator":1725},[898,38647,900],{},[1711,38649,1735],{"stretchy":1713},[1711,38651,1726],{"separator":1725},[2102,38653],{"width":4981},[2884,38655,38656,38658],{},[898,38657,6796],{},[2111,38659,2963],{},[1711,38661,1836],{},[898,38663,900],{},[12097,38665,38666],{},[2525,38667,38668,38674],{},[2884,38669,38670,38672],{},[898,38671,7929],{},[2111,38673,2238],{},[2884,38675,38676,38678],{},[898,38677,7929],{},[2111,38679,2963],{},[1711,38681,1836],{},[2884,38683,38684,38686],{},[898,38685,2778],{},[2111,38687,2963],{},[1711,38689,1714],{"stretchy":1713},[2884,38691,38692,38694],{},[898,38693,7929],{},[2111,38695,2238],{},[1711,38697,1726],{"separator":1725},[2884,38699,38700,38702],{},[898,38701,7929],{},[2111,38703,2963],{},[1711,38705,1726],{"separator":1725},[898,38707,900],{},[1711,38709,1735],{"stretchy":1713},[1942,38711,4699],{},[24360,38713],{"width":31674},[24360,38715,38716],{},[1942,38717,38718],{},"(6.30)",[902,38720,38721],{"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}",[115,38723,38725],{"id":38724},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,38727,38728,38729,38742,38743,38760,38761,38774,38775,38792,38793,38796,38797,38836,38837,38866],{},"Primární (max ",[883,38730,38732],{"className":38731},[886],[888,38733,38734],{"xmlns":890},[892,38735,38736,38740],{},[895,38737,38738],{},[898,38739,900],{},[902,38741,900],{"encoding":904}," při rozpočtu ",[883,38744,38746],{"className":38745},[886],[888,38747,38748],{"xmlns":890},[892,38749,38750,38758],{},[895,38751,38752],{},[1716,38753,38754,38756],{},[898,38755,1660],{},[1711,38757,1793],{},[902,38759,31626],{"encoding":904},") a duální (min ",[883,38762,38764],{"className":38763},[886],[888,38765,38766],{"xmlns":890},[892,38767,38768,38772],{},[895,38769,38770],{},[898,38771,1722],{},[902,38773,1722],{"encoding":904}," při užitečnosti ",[883,38776,38778],{"className":38777},[886],[888,38779,38780],{"xmlns":890},[892,38781,38782,38790],{},[895,38783,38784],{},[1716,38785,38786,38788],{},[898,38787,900],{},[1711,38789,1793],{},[902,38791,31560],{"encoding":904},") úloha jsou ",[38,38794,38795],{},"ekvivalentní",": mají tentýž bod optima ",[883,38798,38800],{"className":38799},[886],[888,38801,38802],{"xmlns":890},[892,38803,38804,38834],{},[895,38805,38806,38812,38814,38822,38824,38832],{},[1716,38807,38808,38810],{},[898,38809,6796],{},[1711,38811,1793],{},[1711,38813,5144],{"stretchy":1713},[13142,38815,38816,38818,38820],{},[898,38817,6796],{},[2111,38819,2238],{},[1711,38821,1793],{},[1711,38823,1726],{"separator":1725},[13142,38825,38826,38828,38830],{},[898,38827,6796],{},[2111,38829,2963],{},[1711,38831,1793],{},[1711,38833,5163],{"stretchy":1713},[902,38835,31925],{"encoding":904}," a v obou platí ",[883,38838,38840],{"className":38839},[886],[888,38841,38842],{"xmlns":890},[892,38843,38844,38864],{},[895,38845,38846,38848,38850,38856,38858],{},[1942,38847,14576],{},[1711,38849,1836],{},[2884,38851,38852,38854],{},[898,38853,7929],{},[2111,38855,2238],{},[898,38857,8659],{"mathvariant":2287},[2884,38859,38860,38862],{},[898,38861,7929],{},[2111,38863,2963],{},[902,38865,31596],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,38868,38869],{},[1801,38870],{"alt":38871,"className":38872,"src":38873},"imek-primarni-vs-dualni",[210,1805],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,38875,38876,38987],{},[123,38877,38878,38881,38882,38895,38896,38936,38937,2186],{},[38,38879,38880],{},"Primární"," (Marshall): zadáno ",[883,38883,38885],{"className":38884},[886],[888,38886,38887],{"xmlns":890},[892,38888,38889,38893],{},[895,38890,38891],{},[898,38892,1660],{},[902,38894,1660],{"encoding":904},", hledáme maximální ",[883,38897,38899],{"className":38898},[886],[888,38900,38901],{"xmlns":890},[892,38902,38903,38933],{},[895,38904,38905,38911,38913,38919,38921,38927,38929,38931],{},[1716,38906,38907,38909],{},[898,38908,900],{},[1711,38910,1793],{},[1711,38912,1714],{"stretchy":1713},[2884,38914,38915,38917],{},[898,38916,7929],{},[2111,38918,2238],{},[1711,38920,1726],{"separator":1725},[2884,38922,38923,38925],{},[898,38924,7929],{},[2111,38926,2963],{},[1711,38928,1726],{"separator":1725},[898,38930,1660],{},[1711,38932,1735],{"stretchy":1713},[902,38934,38935],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,38938,38940],{"className":38939},[886],[888,38941,38942],{"xmlns":890},[892,38943,38944,38984],{},[895,38945,38946,38952,38954,38962,38964,38970,38972,38978,38980,38982],{},[2884,38947,38948,38950],{},[898,38949,6796],{},[898,38951,21388],{},[1711,38953,1836],{},[13142,38955,38956,38958,38960],{},[898,38957,2778],{},[898,38959,21388],{},[898,38961,1790],{},[1711,38963,1714],{"stretchy":1713},[2884,38965,38966,38968],{},[898,38967,7929],{},[2111,38969,2238],{},[1711,38971,1726],{"separator":1725},[2884,38973,38974,38976],{},[898,38975,7929],{},[2111,38977,2963],{},[1711,38979,1726],{"separator":1725},[898,38981,1660],{},[1711,38983,1735],{"stretchy":1713},[902,38985,38986],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,38988,38989,38992,38993,39006,39007,38936,39047,2186],{},[38,38990,38991],{},"Duální"," (Hicks): zadáno ",[883,38994,38996],{"className":38995},[886],[888,38997,38998],{"xmlns":890},[892,38999,39000,39004],{},[895,39001,39002],{},[898,39003,900],{},[902,39005,900],{"encoding":904},", hledáme minimální ",[883,39008,39010],{"className":39009},[886],[888,39011,39012],{"xmlns":890},[892,39013,39014,39044],{},[895,39015,39016,39022,39024,39030,39032,39038,39040,39042],{},[1716,39017,39018,39020],{},[898,39019,1722],{},[1711,39021,1793],{},[1711,39023,1714],{"stretchy":1713},[2884,39025,39026,39028],{},[898,39027,7929],{},[2111,39029,2238],{},[1711,39031,1726],{"separator":1725},[2884,39033,39034,39036],{},[898,39035,7929],{},[2111,39037,2963],{},[1711,39039,1726],{"separator":1725},[898,39041,900],{},[1711,39043,1735],{"stretchy":1713},[902,39045,39046],{"encoding":904},"E^*(P_1, P_2, U)",[883,39048,39050],{"className":39049},[886],[888,39051,39052],{"xmlns":890},[892,39053,39054,39095],{},[895,39055,39056,39062,39064,39073,39075,39081,39083,39089,39091,39093],{},[2884,39057,39058,39060],{},[898,39059,6796],{},[898,39061,21388],{},[1711,39063,1836],{},[13142,39065,39066,39068,39070],{},[898,39067,2778],{},[898,39069,21388],{},[898,39071,39072],{},"H",[1711,39074,1714],{"stretchy":1713},[2884,39076,39077,39079],{},[898,39078,7929],{},[2111,39080,2238],{},[1711,39082,1726],{"separator":1725},[2884,39084,39085,39087],{},[898,39086,7929],{},[2111,39088,2963],{},[1711,39090,1726],{"separator":1725},[898,39092,900],{},[1711,39094,1735],{"stretchy":1713},[902,39096,39097],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,39099,39100,39101,39104,39105,39108],{},"Proč se studují obě? Marshallova poptávka je ",[38,39102,39103],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,39106,39107],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,39110,39112],{"id":39111},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,39114,39116],{"id":39115},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,39118,39119,39122,39123,39155,39156,39194,39195,39221],{},[38,39120,39121],{},"6.8"," Jsou dány užitečnost ",[883,39124,39126],{"className":39125},[886],[888,39127,39128],{"xmlns":890},[892,39129,39130,39152],{},[895,39131,39132,39134,39136,39144],{},[898,39133,900],{},[1711,39135,1836],{},[13142,39137,39138,39140,39142],{},[898,39139,6796],{},[2111,39141,2238],{},[2111,39143,8993],{},[13142,39145,39146,39148,39150],{},[898,39147,6796],{},[2111,39149,2963],{},[2111,39151,8993],{},[902,39153,39154],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,39157,39159],{"className":39158},[886],[888,39160,39161],{"xmlns":890},[892,39162,39163,39191],{},[895,39164,39165,39173,39175,39177,39179,39187,39189],{},[13142,39166,39167,39169,39171],{},[898,39168,7929],{},[2111,39170,2238],{},[1711,39172,1793],{},[1711,39174,1836],{},[2111,39176,6369],{},[1711,39178,1726],{"separator":1725},[13142,39180,39181,39183,39185],{},[898,39182,7929],{},[2111,39184,2963],{},[1711,39186,1793],{},[1711,39188,1836],{},[2111,39190,4712],{},[902,39192,39193],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,39196,39198],{"className":39197},[886],[888,39199,39200],{"xmlns":890},[892,39201,39202,39218],{},[895,39203,39204,39210,39212],{},[2884,39205,39206,39208],{},[898,39207,6796],{},[2111,39209,2238],{},[1711,39211,1726],{"separator":1725},[2884,39213,39214,39216],{},[898,39215,6796],{},[2111,39217,2963],{},[902,39219,39220],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,39223,39224,39227,39228,39270,39271,39302,39303,39325,39326,2186],{},[38,39225,39226],{},"6.9"," Jsou dány rozpočtové omezení ",[883,39229,39231],{"className":39230},[886],[888,39232,39233],{"xmlns":890},[892,39234,39235,39267],{},[895,39236,39237,39239,39241,39247,39253,39255,39261],{},[898,39238,1660],{},[1711,39240,1836],{},[2884,39242,39243,39245],{},[898,39244,7929],{},[2111,39246,2238],{},[2884,39248,39249,39251],{},[898,39250,6796],{},[2111,39252,2238],{},[1711,39254,2095],{},[2884,39256,39257,39259],{},[898,39258,7929],{},[2111,39260,2963],{},[2884,39262,39263,39265],{},[898,39264,6796],{},[2111,39266,2963],{},[902,39268,39269],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,39272,39274],{"className":39273},[886],[888,39275,39276],{"xmlns":890},[892,39277,39278,39300],{},[895,39279,39280,39282,39284,39292],{},[898,39281,900],{},[1711,39283,1836],{},[13142,39285,39286,39288,39290],{},[898,39287,6796],{},[2111,39289,2238],{},[2111,39291,8993],{},[13142,39293,39294,39296,39298],{},[898,39295,6796],{},[2111,39297,2963],{},[2111,39299,8993],{},[902,39301,39154],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,39304,39306],{"className":39305},[886],[888,39307,39308],{"xmlns":890},[892,39309,39310,39322],{},[895,39311,39312,39318,39320],{},[1716,39313,39314,39316],{},[898,39315,1660],{},[1711,39317,1793],{},[1711,39319,1836],{},[2111,39321,4807],{},[902,39323,39324],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,39327,39329],{"className":39328},[886],[888,39330,39331],{"xmlns":890},[892,39332,39333,39361],{},[895,39334,39335,39343,39345,39347,39349,39357,39359],{},[13142,39336,39337,39339,39341],{},[898,39338,7929],{},[2111,39340,2238],{},[1711,39342,1793],{},[1711,39344,1836],{},[2111,39346,4798],{},[1711,39348,1726],{"separator":1725},[13142,39350,39351,39353,39355],{},[898,39352,7929],{},[2111,39354,2963],{},[1711,39356,1793],{},[1711,39358,1836],{},[2111,39360,4712],{},[902,39362,39363],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,39365,39366,39369,39370,25192,39402,39432,39433,2186],{},[38,39367,39368],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,39371,39373],{"className":39372},[886],[888,39374,39375],{"xmlns":890},[892,39376,39377,39399],{},[895,39378,39379,39381,39383,39391],{},[898,39380,900],{},[1711,39382,1836],{},[13142,39384,39385,39387,39389],{},[898,39386,6796],{},[2111,39388,2238],{},[898,39390,207],{},[13142,39392,39393,39395,39397],{},[898,39394,6796],{},[2111,39396,2963],{},[898,39398,2223],{},[902,39400,39401],{"encoding":904},"U = Q_1^a Q_2^b",[883,39403,39405],{"className":39404},[886],[888,39406,39407],{"xmlns":890},[892,39408,39409,39429],{},[895,39410,39411,39413,39415,39417,39419,39421,39423,39425,39427],{},[898,39412,207],{},[1711,39414,1726],{"separator":1725},[898,39416,2223],{},[1711,39418,10487],{},[1711,39420,9308],{"stretchy":1713},[2111,39422,2113],{},[1711,39424,1726],{"separator":1725},[2111,39426,2238],{},[1711,39428,9325],{"stretchy":1713},[902,39430,39431],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,39434,39436],{"className":39435},[886],[888,39437,39438],{"xmlns":890},[892,39439,39440,39472],{},[895,39441,39442,39444,39446,39452,39458,39460,39466],{},[898,39443,1660],{},[1711,39445,1836],{},[2884,39447,39448,39450],{},[898,39449,7929],{},[2111,39451,2238],{},[2884,39453,39454,39456],{},[898,39455,6796],{},[2111,39457,2238],{},[1711,39459,2095],{},[2884,39461,39462,39464],{},[898,39463,7929],{},[2111,39465,2963],{},[2884,39467,39468,39470],{},[898,39469,6796],{},[2111,39471,2963],{},[902,39473,39269],{"encoding":904},[724,39475,39476,39479,39480,25192,39514,39432,39532,2186],{},[38,39477,39478],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,39481,39483],{"className":39482},[886],[888,39484,39485],{"xmlns":890},[892,39486,39487,39511],{},[895,39488,39489,39491,39493,39501,39503],{},[898,39490,900],{},[1711,39492,1836],{},[13142,39494,39495,39497,39499],{},[898,39496,6796],{},[2111,39498,2238],{},[898,39500,207],{},[1711,39502,2095],{},[13142,39504,39505,39507,39509],{},[898,39506,6796],{},[2111,39508,2963],{},[898,39510,207],{},[902,39512,39513],{"encoding":904},"U = Q_1^a + Q_2^a",[883,39515,39517],{"className":39516},[886],[888,39518,39519],{"xmlns":890},[892,39520,39521,39529],{},[895,39522,39523,39525,39527],{},[898,39524,207],{},[1711,39526,7369],{"mathvariant":2287},[2111,39528,2113],{},[902,39530,39531],{"encoding":904},"a \\neq 0",[883,39533,39535],{"className":39534},[886],[888,39536,39537],{"xmlns":890},[892,39538,39539,39571],{},[895,39540,39541,39543,39545,39551,39557,39559,39565],{},[898,39542,1660],{},[1711,39544,1836],{},[2884,39546,39547,39549],{},[898,39548,7929],{},[2111,39550,2238],{},[2884,39552,39553,39555],{},[898,39554,6796],{},[2111,39556,2238],{},[1711,39558,2095],{},[2884,39560,39561,39563],{},[898,39562,7929],{},[2111,39564,2963],{},[2884,39566,39567,39569],{},[898,39568,6796],{},[2111,39570,2963],{},[902,39572,39269],{"encoding":904},[198,39574,39576],{"id":39575},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,39578,39579,39122,39582,1343,39609,39631,39632,1343,39655,39679,39680,39705,39706,2186],{},[38,39580,39581],{},"6.12",[883,39583,39585],{"className":39584},[886],[888,39586,39587],{"xmlns":890},[892,39588,39589,39607],{},[895,39590,39591,39593,39595,39601],{},[898,39592,900],{},[1711,39594,1836],{},[2884,39596,39597,39599],{},[898,39598,6796],{},[2111,39600,2238],{},[2884,39602,39603,39605],{},[898,39604,6796],{},[2111,39606,2963],{},[902,39608,33824],{"encoding":904},[883,39610,39612],{"className":39611},[886],[888,39613,39614],{"xmlns":890},[892,39615,39616,39628],{},[895,39617,39618,39624,39626],{},[1716,39619,39620,39622],{},[898,39621,900],{},[1711,39623,1793],{},[1711,39625,1836],{},[2111,39627,4712],{},[902,39629,39630],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,39633,39635],{"className":39634},[886],[888,39636,39637],{"xmlns":890},[892,39638,39639,39653],{},[895,39640,39641,39649,39651],{},[13142,39642,39643,39645,39647],{},[898,39644,7929],{},[2111,39646,2238],{},[1711,39648,1793],{},[1711,39650,1836],{},[2111,39652,2963],{},[902,39654,33897],{"encoding":904},[883,39656,39658],{"className":39657},[886],[888,39659,39660],{"xmlns":890},[892,39661,39662,39676],{},[895,39663,39664,39672,39674],{},[13142,39665,39666,39668,39670],{},[898,39667,7929],{},[2111,39669,2963],{},[1711,39671,1793],{},[1711,39673,1836],{},[2111,39675,6369],{},[902,39677,39678],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,39681,39683],{"className":39682},[886],[888,39684,39685],{"xmlns":890},[892,39686,39687,39703],{},[895,39688,39689,39695,39697],{},[2884,39690,39691,39693],{},[898,39692,6796],{},[2111,39694,2238],{},[1711,39696,1726],{"separator":1725},[2884,39698,39699,39701],{},[898,39700,6796],{},[2111,39702,2963],{},[902,39704,39220],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,39707,39709],{"className":39708},[886],[888,39710,39711],{"xmlns":890},[892,39712,39713,39733],{},[895,39714,39715,39717,39719,39725,39727],{},[898,39716,900],{},[1711,39718,1836],{},[2884,39720,39721,39723],{},[898,39722,6796],{},[2111,39724,2238],{},[1711,39726,4795],{},[2884,39728,39729,39731],{},[898,39730,6796],{},[2111,39732,2963],{},[902,39734,39735],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,39737,39738,39741,39742,39783,39784,39806,39807,2186],{},[38,39739,39740],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,39743,39745],{"className":39744},[886],[888,39746,39747],{"xmlns":890},[892,39748,39749,39781],{},[895,39750,39751,39753,39755,39761,39767,39769,39775],{},[898,39752,1722],{},[1711,39754,1836],{},[2884,39756,39757,39759],{},[898,39758,7929],{},[2111,39760,2238],{},[2884,39762,39763,39765],{},[898,39764,6796],{},[2111,39766,2238],{},[1711,39768,2095],{},[2884,39770,39771,39773],{},[898,39772,7929],{},[2111,39774,2963],{},[2884,39776,39777,39779],{},[898,39778,6796],{},[2111,39780,2963],{},[902,39782,31541],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,39785,39787],{"className":39786},[886],[888,39788,39789],{"xmlns":890},[892,39790,39791,39803],{},[895,39792,39793,39799,39801],{},[1716,39794,39795,39797],{},[898,39796,900],{},[1711,39798,1793],{},[1711,39800,1836],{},[2111,39802,4372],{},[902,39804,39805],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,39808,39810],{"className":39809},[886],[888,39811,39812],{"xmlns":890},[892,39813,39814,39843],{},[895,39815,39816,39824,39826,39828,39830,39838,39840],{},[13142,39817,39818,39820,39822],{},[898,39819,7929],{},[2111,39821,2238],{},[1711,39823,1793],{},[1711,39825,1836],{},[2111,39827,4306],{},[1711,39829,1726],{"separator":1725},[13142,39831,39832,39834,39836],{},[898,39833,7929],{},[2111,39835,2963],{},[1711,39837,1793],{},[1711,39839,1836],{},[2111,39841,39842],{},"15",[902,39844,39845],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,39847,5422],{"id":5421},[120,39849,39850,39907,39946,39966,40001,40055,40060,40066,40162,40207],{},[123,39851,39852,1700,39855,39904,39905,2186],{},[38,39853,39854],{},"Rozpočtové omezení (budget constraint)",[883,39856,39858],{"className":39857},[886],[888,39859,39860],{"xmlns":890},[892,39861,39862,39902],{},[895,39863,39864,39870,39872,39880,39886,39888,39896],{},[1716,39865,39866,39868],{},[898,39867,1660],{},[1711,39869,1793],{},[1711,39871,1836],{},[13142,39873,39874,39876,39878],{},[898,39875,7929],{},[2111,39877,2238],{},[1711,39879,1793],{},[2884,39881,39882,39884],{},[898,39883,6796],{},[2111,39885,2238],{},[1711,39887,2095],{},[13142,39889,39890,39892,39894],{},[898,39891,7929],{},[2111,39893,2963],{},[1711,39895,1793],{},[2884,39897,39898,39900],{},[898,39899,6796],{},[2111,39901,2963],{},[902,39903,20896],{"encoding":904}," — (6.12); ",[38,39906,31734],{},[123,39908,39909,39912,39913,2186],{},[38,39910,39911],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,39914,39916],{"className":39915},[886],[888,39917,39918],{"xmlns":890},[892,39919,39920,39944],{},[895,39921,39922,39924,39926,39934,39936],{},[1942,39923,14576],{},[1711,39925,1836],{},[13142,39927,39928,39930,39932],{},[898,39929,7929],{},[2111,39931,2238],{},[1711,39933,1793],{},[898,39935,8659],{"mathvariant":2287},[13142,39937,39938,39940,39942],{},[898,39939,7929],{},[2111,39941,2963],{},[1711,39943,1793],{},[902,39945,32577],{"encoding":904},[123,39947,39948,39963,39964,2186],{},[38,39949,32721,39950],{},[883,39951,39953],{"className":39952},[886],[888,39954,39955],{"xmlns":890},[892,39956,39957,39961],{},[895,39958,39959],{},[898,39960,20041],{},[902,39962,20094],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,39965,32743],{},[123,39967,39968,39971,39972,2186],{},[38,39969,39970],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,39973,39975],{"className":39974},[886],[888,39976,39977],{"xmlns":890},[892,39978,39979,39999],{},[895,39980,39981,39983,39985,39991,39993],{},[1942,39982,14576],{},[1711,39984,1836],{},[2884,39986,39987,39989],{},[898,39988,7929],{},[2111,39990,2238],{},[898,39992,8659],{"mathvariant":2287},[2884,39994,39995,39997],{},[898,39996,7929],{},[2111,39998,2963],{},[902,40000,31596],{"encoding":904},[123,40002,40003,5204,40006,40054],{},[38,40004,40005],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,40007,40009],{"className":40008},[886],[888,40010,40011],{"xmlns":890},[892,40012,40013,40051],{},[895,40014,40015,40021,40023,40029,40031,40037,40039,40045,40047,40049],{},[2884,40016,40017,40019],{},[898,40018,6796],{},[898,40020,21388],{},[1711,40022,1836],{},[2884,40024,40025,40027],{},[898,40026,2778],{},[898,40028,21388],{},[1711,40030,1714],{"stretchy":1713},[2884,40032,40033,40035],{},[898,40034,7929],{},[2111,40036,2238],{},[1711,40038,1726],{"separator":1725},[2884,40040,40041,40043],{},[898,40042,7929],{},[2111,40044,2963],{},[1711,40046,1726],{"separator":1725},[898,40048,1660],{},[1711,40050,1735],{"stretchy":1713},[902,40052,40053],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,40056,40057,40059],{},[38,40058,35325],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,40061,40062,40065],{},[38,40063,40064],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,40067,40068,5204,40070,40117,40118,40161],{},[38,40069,37637],{},[883,40071,40073],{"className":40072},[886],[888,40074,40075],{"xmlns":890},[892,40076,40077,40115],{},[895,40078,40079,40085,40087,40093,40095,40101,40103,40109,40111,40113],{},[2884,40080,40081,40083],{},[898,40082,6796],{},[898,40084,21388],{},[1711,40086,1836],{},[2884,40088,40089,40091],{},[898,40090,2778],{},[898,40092,21388],{},[1711,40094,1714],{"stretchy":1713},[2884,40096,40097,40099],{},[898,40098,7929],{},[2111,40100,2238],{},[1711,40102,1726],{"separator":1725},[2884,40104,40105,40107],{},[898,40106,7929],{},[2111,40108,2963],{},[1711,40110,1726],{"separator":1725},[898,40112,900],{},[1711,40114,1735],{"stretchy":1713},[902,40116,21421],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,40119,40121],{"className":40120},[886],[888,40122,40123],{"xmlns":890},[892,40124,40125,40159],{},[895,40126,40127,40129,40131,40145],{},[898,40128,900],{},[1711,40130,1836],{},[13142,40132,40133,40135,40137],{},[898,40134,6796],{},[2111,40136,2238],{},[895,40138,40139,40141,40143],{},[2111,40140,2238],{},[898,40142,8659],{"mathvariant":2287},[2111,40144,2963],{},[13142,40146,40147,40149,40151],{},[898,40148,6796],{},[2111,40150,2963],{},[895,40152,40153,40155,40157],{},[2111,40154,2238],{},[898,40156,8659],{"mathvariant":2287},[2111,40158,2963],{},[902,40160,36757],{"encoding":904},": (6.30).",[123,40163,40164,40206],{},[38,40165,40166,40167],{},"Bod dotyku ",[883,40168,40170],{"className":40169},[886],[888,40171,40172],{"xmlns":890},[892,40173,40174,40204],{},[895,40175,40176,40182,40184,40192,40194,40202],{},[1716,40177,40178,40180],{},[898,40179,6796],{},[1711,40181,1793],{},[1711,40183,5144],{"stretchy":1713},[13142,40185,40186,40188,40190],{},[898,40187,6796],{},[2111,40189,2238],{},[1711,40191,1793],{},[1711,40193,1726],{"separator":1725},[13142,40195,40196,40198,40200],{},[898,40197,6796],{},[2111,40199,2963],{},[1711,40201,1793],{},[1711,40203,5163],{"stretchy":1713},[902,40205,31925],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,40208,40209,40212,40213,40226,40227,40240],{},[38,40210,40211],{},"Dualita"," — ekvivalence max ",[883,40214,40216],{"className":40215},[886],[888,40217,40218],{"xmlns":890},[892,40219,40220,40224],{},[895,40221,40222],{},[898,40223,900],{},[902,40225,900],{"encoding":904}," a min ",[883,40228,40230],{"className":40229},[886],[888,40231,40232],{"xmlns":890},[892,40233,40234,40238],{},[895,40235,40236],{},[898,40237,1722],{},[902,40239,1722],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,40242,5901],{"id":5900},[120,40244,40245,40268,40284,40297,40308],{},[123,40246,40247,1700,40250,40253,40254,40267],{},[38,40248,40249],{},"Teorie před optimalizací:",[207,40251,880],{"className":40252,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,40255,40257],{"className":40256},[886],[888,40258,40259],{"xmlns":890},[892,40260,40261,40265],{},[895,40262,40263],{},[898,40264,900],{},[902,40266,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,40269,40270,1700,40273,40276,40277,40280,40281,2186],{},[38,40271,40272],{},"Matematický aparát:",[207,40274,793],{"className":40275,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,40278,784],{"className":40279,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,40282,6375],{"className":40283,"dataFsResolvedFilePath":764,"href":765},[210],[123,40285,40286,1700,40289,40292,40293,40296],{},[38,40287,40288],{},"Paralely:",[207,40290,15061],{"className":40291,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,40294,15915],{"className":40295,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,40298,40299,1700,40302,1343,40305],{},[38,40300,40301],{},"Přednášky:",[207,40303,1094],{"className":40304,"dataFsResolvedFilePath":838,"href":839},[210],[207,40306,1101],{"className":40307,"dataFsResolvedFilePath":868,"href":869},[210],[123,40309,40310,1700,40312],{},[38,40311,5908],{},[207,40313,5914],{"className":40314,"dataFsResolvedFilePath":5912,"href":5913},[210],{"title":641,"searchDepth":642,"depth":642,"links":40316},[40317,40318,40319,40324,40325,40326,40328,40331,40334,40336,40337,40339,40340,40344,40345],{"id":1637,"depth":642,"text":1638},{"id":31604,"depth":642,"text":31605},{"id":32002,"depth":642,"text":32003,"children":40320},[40321,40322],{"id":32122,"depth":649,"text":32123},{"id":32703,"depth":649,"text":40323},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":33165,"depth":642,"text":33166},{"id":33476,"depth":642,"text":33477},{"id":33795,"depth":642,"text":40327},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":34568,"depth":642,"text":34569,"children":40329},[40330],{"id":35324,"depth":649,"text":35325},{"id":35504,"depth":642,"text":35505,"children":40332},[40333],{"id":35761,"depth":649,"text":35762},{"id":36712,"depth":642,"text":40335},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":37636,"depth":642,"text":37637},{"id":37839,"depth":642,"text":40338},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":38724,"depth":642,"text":38725},{"id":39111,"depth":642,"text":39112,"children":40341},[40342,40343],{"id":39115,"depth":649,"text":39116},{"id":39575,"depth":649,"text":39576},{"id":5421,"depth":642,"text":5422},{"id":5900,"depth":642,"text":5901},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":31365,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,40352,1144,13748,40353,40354,40355],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":40358,"title":802,"body":40359,"course":1128,"courses":659,"created":5973,"description":641,"extension":661,"meta":54412,"navigation":664,"path":54413,"seo":54414,"sources":54415,"stem":54416,"tags":54417,"type":5985,"updated":677,"__hash__":54423},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":40360,"toc":54368},[40361,40364,40390,40394,40401,40553,40567,40570,40572,40659,40663,40699,40772,40793,40918,40928,40941,40945,40950,40980,41042,41051,41055,41117,41124,41145,41263,41341,41345,41348,41407,41522,41527,41559,41621,41669,41724,41728,41749,41773,41821,41825,41837,41841,41951,41955,41971,42012,42023,42182,42192,42197,42201,42323,42333,42340,42344,42422,42433,42513,42519,42526,42665,42672,42675,42732,42736,42814,42860,42904,42910,43023,43027,43030,43225,43229,43466,43469,43623,43776,43778,43780,43860,43863,43968,44037,44046,44050,44053,44114,44123,44127,44160,44238,44277,44281,44330,44384,44388,44417,44446,44498,44505,44559,44637,44641,44684,44751,44795,44899,44918,44920,44924,45032,45036,45104,45153,45160,45245,45249,45321,45326,45374,45563,45567,45572,45748,45753,45812,45917,45921,45948,45952,45959,46123,46210,46215,46217,46220,46320,46470,46542,46616,46618,46622,46636,46640,46773,46828,46940,47017,47021,47078,47181,47240,47401,47405,47480,47552,47650,47708,47802,47855,47876,47930,47935,48013,48061,48148,48186,48274,48427,48463,48517,48520,48522,48524,48573,48580,48588,48675,48684,48771,48778,48780,48784,49009,49011,49015,49019,49088,49139,49342,49348,49359,49427,49433,49855,49859,49923,49947,50143,50149,50163,50231,50234,50274,50498,50566,50868,51277,51354,51520,51526,51529,51604,52057,52108,52514,52619,53282,53285,53362,53370,53444,53475,53477,53481,53525,53527,53529,53533,53763,53767,53858,53863,53957,53962,54135,54139,54257,54262,54311,54313,54315],[12,40362,802],{"id":40363},"poptávka-nabídka-a-tržní-rovnováha",[1921,40365,40366],{},[724,40367,40368,40370,40371,40374,40375,40378,40379,40382,40383,40385,40386,40389],{},[883,40369,2678],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,40372,40373],{},"poptávka",") a výrobce (",[38,40376,40377],{},"nabídka","), jejich interakci v ",[38,40380,40381],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,40384,21575],{},"). Uzavírá ji pojem ",[38,40387,40388],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,40391,40393],{"id":40392},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,40395,40396,40397,40400],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,40398,40399],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,40402,40403,40420,40462,40478],{},[123,40404,40405,40406,40419],{},"cena ",[883,40407,40409],{"className":40408},[886],[888,40410,40411],{"xmlns":890},[892,40412,40413,40417],{},[895,40414,40415],{},[898,40416,7929],{},[902,40418,7929],{"encoding":904}," zkoumaného zboží,",[123,40421,40422,40423,1726],{},"ceny alternativních zboží ",[883,40424,40426],{"className":40425},[886],[888,40427,40428],{"xmlns":890},[892,40429,40430,40459],{},[895,40431,40432,40438,40440,40446,40448,40450,40452],{},[2884,40433,40434,40436],{},[898,40435,7929],{},[2111,40437,2238],{},[1711,40439,1726],{"separator":1725},[2884,40441,40442,40444],{},[898,40443,7929],{},[2111,40445,2963],{},[1711,40447,1726],{"separator":1725},[1711,40449,13621],{},[1711,40451,1726],{"separator":1725},[2884,40453,40454,40456],{},[898,40455,7929],{},[898,40457,40458],{},"n",[902,40460,40461],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,40463,40464,40465,1726],{},"důchod ",[883,40466,40468],{"className":40467},[886],[888,40469,40470],{"xmlns":890},[892,40471,40472,40476],{},[895,40473,40474],{},[898,40475,1660],{},[902,40477,1660],{"encoding":904},[123,40479,40480,40481,40494,40495,40508,40509,40522,40523,40537,40538,40552],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,40482,40484],{"className":40483},[886],[888,40485,40486],{"xmlns":890},[892,40487,40488,40492],{},[895,40489,40490],{},[898,40491,2888],{},[902,40493,2888],{"encoding":904},", kapitál ",[883,40496,40498],{"className":40497},[886],[888,40499,40500],{"xmlns":890},[892,40501,40502,40506],{},[895,40503,40504],{},[898,40505,13774],{},[902,40507,13774],{"encoding":904},", půda ",[883,40510,40512],{"className":40511},[886],[888,40513,40514],{"xmlns":890},[892,40515,40516,40520],{},[895,40517,40518],{},[898,40519,1722],{},[902,40521,1722],{"encoding":904},"), technologie, počet výrobců ",[883,40524,40526],{"className":40525},[886],[888,40527,40528],{"xmlns":890},[892,40529,40530,40535],{},[895,40531,40532],{},[898,40533,40534],{},"O",[902,40536,40534],{"encoding":904},", počasí ",[883,40539,40541],{"className":40540},[886],[888,40542,40543],{"xmlns":890},[892,40544,40545,40550],{},[895,40546,40547],{},[898,40548,40549],{},"W",[902,40551,40549],{"encoding":904}," atd.",[724,40554,40555,40556,40559,40560,40563,40564,2186],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,40557,40558],{},"ceteris paribus","), hovoříme o ",[38,40561,40562],{},"jednofaktorovém modelu","; jinak jde o model ",[38,40565,40566],{},"vícefaktorový",[40568,40569],"hr",{},[115,40571,2840],{"id":40373},[1921,40573,40574],{},[724,40575,40576,40578,40579,40592,40593,40606,40607,40610,40611,40634,40635,2186],{},[883,40577,2678],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,40580,40582],{"className":40581},[886],[888,40583,40584],{"xmlns":890},[892,40585,40586,40590],{},[895,40587,40588],{},[898,40589,6796],{},[902,40591,6796],{"encoding":904}," na ceně ",[883,40594,40596],{"className":40595},[886],[888,40597,40598],{"xmlns":890},[892,40599,40600,40604],{},[895,40601,40602],{},[898,40603,7929],{},[902,40605,7929],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,40608,40609],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,40612,40614],{"className":40613},[886],[888,40615,40616],{"xmlns":890},[892,40617,40618,40632],{},[895,40619,40620,40622,40624,40626,40628,40630],{},[898,40621,6796],{},[1711,40623,1836],{},[898,40625,2778],{},[1711,40627,1714],{"stretchy":1713},[898,40629,7929],{},[1711,40631,1735],{"stretchy":1713},[902,40633,8181],{"encoding":904}," a jeho lineární verzí ",[883,40636,40638],{"className":40637},[886],[888,40639,40640],{"xmlns":890},[892,40641,40642,40656],{},[895,40643,40644,40646,40648,40650,40652,40654],{},[898,40645,7929],{},[1711,40647,1836],{},[898,40649,207],{},[898,40651,6796],{},[1711,40653,2095],{},[898,40655,2223],{},[902,40657,40658],{"encoding":904},"P = aQ + b",[198,40660,40662],{"id":40661},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,40664,40665,40666,40679,40680,40693,40694,1648,40696,3239],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,40667,40669],{"className":40668},[886],[888,40670,40671],{"xmlns":890},[892,40672,40673,40677],{},[895,40674,40675],{},[898,40676,6796],{},[902,40678,6796],{"encoding":904}," závisí na ceně ",[883,40681,40683],{"className":40682},[886],[888,40684,40685],{"xmlns":890},[892,40686,40687,40691],{},[895,40688,40689],{},[898,40690,7929],{},[902,40692,7929],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,40695,31600],{},[614,40697,40698],{},"demand function",[883,40700,40702],{"className":40701},[886],[888,40703,40704],{"xmlns":890,"display":31664},[892,40705,40706,40769],{},[24352,40707,40708],{"width":31669},[24357,40709,40710,40712,40762,40764],{},[24360,40711],{"width":31674},[24360,40713,40714],{},[895,40715,40716,40718,40720,40722,40724,40726,40728,40734,40736,40742,40744,40746,40748,40754,40756,40758,40760],{},[898,40717,6796],{},[1711,40719,1836],{},[898,40721,2778],{},[1711,40723,1714],{"stretchy":1713},[898,40725,7929],{},[1711,40727,1726],{"separator":1725},[2884,40729,40730,40732],{},[898,40731,7929],{},[2111,40733,2238],{},[1711,40735,1726],{"separator":1725},[2884,40737,40738,40740],{},[898,40739,7929],{},[2111,40741,2963],{},[1711,40743,1726],{"separator":1725},[1711,40745,13621],{},[1711,40747,1726],{"separator":1725},[2884,40749,40750,40752],{},[898,40751,7929],{},[898,40753,40458],{},[1711,40755,1726],{"separator":1725},[898,40757,1660],{},[1711,40759,1735],{"stretchy":1713},[898,40761,2186],{"mathvariant":2287},[24360,40763],{"width":31674},[24360,40765,40766],{},[1942,40767,40768],{},"(2.1)",[902,40770,40771],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,40773,40774,40775,40778,40779,40792],{},"Důležitou vlastností je ",[38,40776,40777],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,40780,40782],{"className":40781},[886],[888,40783,40784],{"xmlns":890},[892,40785,40786,40790],{},[895,40787,40788],{},[898,40789,1675],{},[902,40791,1675],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,40794,40796],{"className":40795},[886],[888,40797,40798],{"xmlns":890,"display":31664},[892,40799,40800,40915],{},[24352,40801,40802],{"width":31669},[24357,40803,40804,40806,40908,40910],{},[24360,40805],{"width":31674},[24360,40807,40808],{},[895,40809,40810,40812,40814,40816,40818,40820,40822,40824,40826,40832,40834,40836,40842,40844,40846,40848,40850,40856,40858,40860,40862,40864,40866,40868,40870,40872,40874,40880,40882,40888,40890,40892,40894,40900,40902,40904,40906],{},[898,40811,6796],{},[1711,40813,1836],{},[898,40815,2778],{},[1711,40817,1714],{"stretchy":1713},[898,40819,1675],{},[898,40821,7929],{},[1711,40823,1726],{"separator":1725},[898,40825,1675],{},[2884,40827,40828,40830],{},[898,40829,7929],{},[2111,40831,2238],{},[1711,40833,1726],{"separator":1725},[898,40835,1675],{},[2884,40837,40838,40840],{},[898,40839,7929],{},[2111,40841,2963],{},[1711,40843,1726],{"separator":1725},[1711,40845,13621],{},[1711,40847,1726],{"separator":1725},[898,40849,1675],{},[2884,40851,40852,40854],{},[898,40853,7929],{},[898,40855,40458],{},[1711,40857,1726],{"separator":1725},[898,40859,1675],{},[898,40861,1660],{},[1711,40863,1735],{"stretchy":1713},[1711,40865,1836],{},[898,40867,2778],{},[1711,40869,1714],{"stretchy":1713},[898,40871,7929],{},[1711,40873,1726],{"separator":1725},[2884,40875,40876,40878],{},[898,40877,7929],{},[2111,40879,2238],{},[1711,40881,1726],{"separator":1725},[2884,40883,40884,40886],{},[898,40885,7929],{},[2111,40887,2963],{},[1711,40889,1726],{"separator":1725},[1711,40891,13621],{},[1711,40893,1726],{"separator":1725},[2884,40895,40896,40898],{},[898,40897,7929],{},[898,40899,40458],{},[1711,40901,1726],{"separator":1725},[898,40903,1660],{},[1711,40905,1735],{"stretchy":1713},[898,40907,2186],{"mathvariant":2287},[24360,40909],{"width":31674},[24360,40911,40912],{},[1942,40913,40914],{},"(2.2)",[902,40916,40917],{"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}",[1921,40919,40920],{},[724,40921,40922,40924,40925,2186],{},[883,40923,1927],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,40926,40927],{},"v jednofaktorových modelech neplatí",[724,40929,40930,40931,1343,40934,2009,40937,40940],{},"Rozlišuje se poptávka ",[38,40932,40933],{},"individuální",[38,40935,40936],{},"tržní",[38,40938,40939],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,40942,40944],{"id":40943},"jednofaktorové-modely","Jednofaktorové modely",[40946,40947,40949],"h4",{"id":40948},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,40951,40952,40953,40966,40967,2062],{},"Poptávané množství ",[883,40954,40956],{"className":40955},[886],[888,40957,40958],{"xmlns":890},[892,40959,40960,40964],{},[895,40961,40962],{},[898,40963,6796],{},[902,40965,6796],{"encoding":904}," závisí pouze na ceně ",[883,40968,40970],{"className":40969},[886],[888,40971,40972],{"xmlns":890},[892,40973,40974,40978],{},[895,40975,40976],{},[898,40977,7929],{},[902,40979,7929],{"encoding":904},[883,40981,40983],{"className":40982},[886],[888,40984,40985],{"xmlns":890,"display":31664},[892,40986,40987,41039],{},[24352,40988,40989],{"width":31669},[24357,40990,40991,40993,41032,41034],{},[24360,40992],{"width":31674},[24360,40994,40995],{},[895,40996,40997,40999,41001,41003,41005,41007,41009,41011,41013,41016,41018,41020,41022,41024,41026,41028,41030],{},[898,40998,6796],{},[1711,41000,1836],{},[898,41002,2778],{},[1711,41004,1714],{"stretchy":1713},[898,41006,7929],{},[1711,41008,1735],{"stretchy":1713},[1711,41010,1726],{"separator":1725},[2102,41012],{"width":2104},[1942,41014,41015],{},"resp.",[2102,41017],{"width":2104},[898,41019,7929],{},[1711,41021,1836],{},[898,41023,2778],{},[1711,41025,1714],{"stretchy":1713},[898,41027,6796],{},[1711,41029,1735],{"stretchy":1713},[898,41031,2186],{"mathvariant":2287},[24360,41033],{"width":31674},[24360,41035,41036],{},[1942,41037,41038],{},"(2.3)",[902,41040,41041],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,41043,41044,41045,1648,41048,1797],{},"Graf této funkce se nazývá ",[38,41046,41047],{},"křivka poptávky",[614,41049,41050],{},"demand curve",[40946,41052,41054],{"id":41053},"zákon-klesající-poptávky","Zákon klesající poptávky",[1921,41056,41057],{},[724,41058,41059],{},[38,41060,41061,41062,41075,41076,41089,41090,41075,41103,41116],{},"Roste-li cena ",[883,41063,41065],{"className":41064},[886],[888,41066,41067],{"xmlns":890},[892,41068,41069,41073],{},[895,41070,41071],{},[898,41072,7929],{},[902,41074,7929],{"encoding":904},", pak množství ",[883,41077,41079],{"className":41078},[886],[888,41080,41081],{"xmlns":890},[892,41082,41083,41087],{},[895,41084,41085],{},[898,41086,6796],{},[902,41088,6796],{"encoding":904}," klesá; klesá-li cena ",[883,41091,41093],{"className":41092},[886],[888,41094,41095],{"xmlns":890},[892,41096,41097,41101],{},[895,41098,41099],{},[898,41100,7929],{},[902,41102,7929],{"encoding":904},[883,41104,41106],{"className":41105},[886],[888,41107,41108],{"xmlns":890},[892,41109,41110,41114],{},[895,41111,41112],{},[898,41113,6796],{},[902,41115,6796],{"encoding":904}," roste.",[724,41118,41119,41120,41123],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,41121,41122],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[1921,41125,41126,41131],{},[724,41127,41128,41130],{},[883,41129,2678],{}," Intuice — proč zákon platí",[120,41132,41133,41139],{},[123,41134,41135,41138],{},[38,41136,41137],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,41140,41141,41144],{},[38,41142,41143],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,41146,41147,41148,41161,41162,41175,41176,41202,41203,41229,41230,12082,41256,41259,41260,2186],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,41149,41151],{"className":41150},[886],[888,41152,41153],{"xmlns":890},[892,41154,41155,41159],{},[895,41156,41157],{},[898,41158,7929],{},[902,41160,7929],{"encoding":904}," se vynáší na svislou osu, množství ",[883,41163,41165],{"className":41164},[886],[888,41166,41167],{"xmlns":890},[892,41168,41169,41173],{},[895,41170,41171],{},[898,41172,6796],{},[902,41174,6796],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,41177,41179],{"className":41178},[886],[888,41180,41181],{"xmlns":890},[892,41182,41183,41199],{},[895,41184,41185,41187,41189,41191,41197],{},[1711,41186,5144],{"stretchy":1713},[2111,41188,2113],{},[1711,41190,1726],{"separator":1725},[2884,41192,41193,41195],{},[898,41194,7929],{},[2111,41196,2113],{},[1711,41198,5163],{"stretchy":1713},[902,41200,41201],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,41204,41206],{"className":41205},[886],[888,41207,41208],{"xmlns":890},[892,41209,41210,41226],{},[895,41211,41212,41214,41220,41222,41224],{},[1711,41213,5144],{"stretchy":1713},[2884,41215,41216,41218],{},[898,41217,6796],{},[2111,41219,2113],{},[1711,41221,1726],{"separator":1725},[2111,41223,2113],{},[1711,41225,5163],{"stretchy":1713},[902,41227,41228],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,41231,41233],{"className":41232},[886],[888,41234,41235],{"xmlns":890},[892,41236,41237,41253],{},[895,41238,41239,41241,41243,41245,41251],{},[1711,41240,1714],{"stretchy":1713},[2111,41242,2113],{},[1711,41244,1726],{"separator":1725},[2884,41246,41247,41249],{},[898,41248,7929],{},[2111,41250,2113],{},[1711,41252,1735],{"stretchy":1713},[902,41254,41255],{"encoding":904},"(0, P_0)",[38,41257,41258],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,41261,41262],{},"konvexní",[724,41264,41265],{},[614,41266,41267,41268,41290,41291,2009,41316,2186],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,41269,41271],{"className":41270},[886],[888,41272,41273],{"xmlns":890},[892,41274,41275,41287],{},[895,41276,41277,41279,41281,41283,41285],{},[1711,41278,1714],{"stretchy":1713},[898,41280,6796],{},[1711,41282,1726],{"separator":1725},[898,41284,7929],{},[1711,41286,1735],{"stretchy":1713},[902,41288,41289],{"encoding":904},"(Q, P)"," — klesající, konvexní, procházející body ",[883,41292,41294],{"className":41293},[886],[888,41295,41296],{"xmlns":890},[892,41297,41298,41314],{},[895,41299,41300,41302,41304,41306,41312],{},[1711,41301,5144],{"stretchy":1713},[2111,41303,2113],{},[1711,41305,1726],{"separator":1725},[2884,41307,41308,41310],{},[898,41309,7929],{},[2111,41311,2113],{},[1711,41313,5163],{"stretchy":1713},[902,41315,41201],{"encoding":904},[883,41317,41319],{"className":41318},[886],[888,41320,41321],{"xmlns":890},[892,41322,41323,41339],{},[895,41324,41325,41327,41333,41335,41337],{},[1711,41326,5144],{"stretchy":1713},[2884,41328,41329,41331],{},[898,41330,6796],{},[2111,41332,2113],{},[1711,41334,1726],{"separator":1725},[2111,41336,2113],{},[1711,41338,5163],{"stretchy":1713},[902,41340,41228],{"encoding":904},[40946,41342,41344],{"id":41343},"lineární-model-poptávky","Lineární model poptávky",[724,41346,41347],{},"Nejjednodušší závislostí je",[883,41349,41351],{"className":41350},[886],[888,41352,41353],{"xmlns":890,"display":31664},[892,41354,41355,41404],{},[24352,41356,41357],{"width":31669},[24357,41358,41359,41361,41397,41399],{},[24360,41360],{"width":31674},[24360,41362,41363],{},[895,41364,41365,41367,41369,41371,41373,41375,41377,41379,41381,41383,41385,41387,41389,41391,41393,41395],{},[898,41366,7929],{},[1711,41368,1836],{},[898,41370,207],{},[898,41372,6796],{},[1711,41374,2095],{},[898,41376,2223],{},[1711,41378,1726],{"separator":1725},[2102,41380],{"width":2104},[898,41382,207],{},[1711,41384,2109],{},[2111,41386,2113],{},[1711,41388,1726],{"separator":1725},[1942,41390,2118],{},[898,41392,2223],{},[1711,41394,2123],{},[2111,41396,2126],{},[24360,41398],{"width":31674},[24360,41400,41401],{},[1942,41402,41403],{},"(2.4)",[902,41405,41406],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,41408,41409,41410,25192,41446,2009,41470,12017,41496,41518,41519,2186],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,41411,41413],{"className":41412},[886],[888,41414,41415],{"xmlns":890},[892,41416,41417,41443],{},[895,41418,41419,41421,41423,41431,41433,41435],{},[898,41420,6796],{},[1711,41422,1836],{},[2509,41424,41425],{"scriptlevel":2113,"displaystyle":1713},[2525,41426,41427,41429],{},[2111,41428,2238],{},[898,41430,207],{},[898,41432,7929],{},[1711,41434,2460],{},[2509,41436,41437],{"scriptlevel":2113,"displaystyle":1713},[2525,41438,41439,41441],{},[898,41440,2223],{},[898,41442,207],{},[902,41444,41445],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,41447,41449],{"className":41448},[886],[888,41450,41451],{"xmlns":890},[892,41452,41453,41467],{},[895,41454,41455,41463,41465],{},[2509,41456,41457],{"scriptlevel":2113,"displaystyle":1713},[2525,41458,41459,41461],{},[2111,41460,2238],{},[898,41462,207],{},[1711,41464,2109],{},[2111,41466,2113],{},[902,41468,41469],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,41471,41473],{"className":41472},[886],[888,41474,41475],{"xmlns":890},[892,41476,41477,41493],{},[895,41478,41479,41481,41489,41491],{},[1711,41480,2460],{},[2509,41482,41483],{"scriptlevel":2113,"displaystyle":1713},[2525,41484,41485,41487],{},[898,41486,2223],{},[898,41488,207],{},[1711,41490,2123],{},[2111,41492,2113],{},[902,41494,41495],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,41497,41499],{"className":41498},[886],[888,41500,41501],{"xmlns":890},[892,41502,41503,41515],{},[895,41504,41505,41507,41509,41511,41513],{},[1711,41506,1714],{"stretchy":1713},[2111,41508,2113],{},[1711,41510,1726],{"separator":1725},[898,41512,2223],{},[1711,41514,1735],{"stretchy":1713},[902,41516,41517],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,41520,41521],{},"nedokonalé konkurenci",[41523,41524,41526],"h5",{"id":41525},"příklad-21","Příklad 2.1",[724,41528,41529,41532,41533,2186],{},[38,41530,41531],{},"Zadání:"," Lineární poptávka ",[883,41534,41536],{"className":41535},[886],[888,41537,41538],{"xmlns":890},[892,41539,41540,41556],{},[895,41541,41542,41544,41546,41548,41550,41552,41554],{},[898,41543,7929],{},[1711,41545,1836],{},[1711,41547,2460],{},[2111,41549,2963],{},[898,41551,6796],{},[1711,41553,2095],{},[2111,41555,7126],{},[902,41557,41558],{"encoding":904},"P = -2Q + 60",[724,41560,41561,41564,41565,41587,41588,2186],{},[38,41562,41563],{},"Řešení:"," Reálné cenové rozpětí je ",[883,41566,41568],{"className":41567},[886],[888,41569,41570],{"xmlns":890},[892,41571,41572,41584],{},[895,41573,41574,41576,41578,41580,41582],{},[1711,41575,1714],{"stretchy":1713},[2111,41577,2113],{},[1711,41579,1726],{"separator":1725},[2111,41581,7126],{},[1711,41583,1735],{"stretchy":1713},[902,41585,41586],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,41589,41591],{"className":41590},[886],[888,41592,41593],{"xmlns":890},[892,41594,41595,41618],{},[895,41596,41597,41599,41601,41603,41611,41613,41615],{},[898,41598,6796],{},[1711,41600,1836],{},[1711,41602,2460],{},[2509,41604,41605],{"scriptlevel":2113,"displaystyle":1713},[2525,41606,41607,41609],{},[2111,41608,2238],{},[2111,41610,2963],{},[898,41612,7929],{},[1711,41614,2095],{},[2111,41616,41617],{},"30",[902,41619,41620],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,41622,41623,41646],{},[19,41624,41625],{},[22,41626,41627,41642,41644],{},[25,41628,41629],{},[883,41630,41632],{"className":41631},[886],[888,41633,41634],{"xmlns":890},[892,41635,41636,41640],{},[895,41637,41638],{},[898,41639,7929],{},[902,41641,7929],{"encoding":904},[25,41643,9195],{},[25,41645,4306],{},[30,41647,41648],{},[22,41649,41650,41665,41667],{},[35,41651,41652],{},[883,41653,41655],{"className":41654},[886],[888,41656,41657],{"xmlns":890},[892,41658,41659,41663],{},[895,41660,41661],{},[898,41662,6796],{},[902,41664,6796],{"encoding":904},[35,41666,4712],{},[35,41668,4306],{},[724,41670,41671],{},[614,41672,41673,41674,2009,41696,2186],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,41675,41677],{"className":41676},[886],[888,41678,41679],{"xmlns":890},[892,41680,41681,41693],{},[895,41682,41683,41685,41687,41689,41691],{},[1711,41684,5144],{"stretchy":1713},[2111,41686,2113],{},[1711,41688,1726],{"separator":1725},[898,41690,2223],{},[1711,41692,5163],{"stretchy":1713},[902,41694,41695],{"encoding":904},"[0, b]",[883,41697,41699],{"className":41698},[886],[888,41700,41701],{"xmlns":890},[892,41702,41703,41721],{},[895,41704,41705,41707,41709,41711,41713,41715,41717,41719],{},[1711,41706,5144],{"stretchy":1713},[1711,41708,2460],{},[898,41710,2223],{},[898,41712,8659],{"mathvariant":2287},[898,41714,207],{},[1711,41716,1726],{"separator":1725},[2111,41718,2113],{},[1711,41720,5163],{"stretchy":1713},[902,41722,41723],{"encoding":904},"[-b\u002Fa, 0]",[40946,41725,41727],{"id":41726},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,41729,41730,41731,41748],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,41732,41734],{"className":41733},[886],[888,41735,41736],{"xmlns":890},[892,41737,41738,41746],{},[895,41739,41740],{},[1716,41741,41742,41744],{},[898,41743,7929],{},[1711,41745,1793],{},[902,41747,8391],{"encoding":904},", je funkce poptávky konstantní:",[883,41750,41752],{"className":41751},[886],[888,41753,41754],{"xmlns":890,"display":31664},[892,41755,41756,41770],{},[895,41757,41758,41760,41762,41768],{},[898,41759,7929],{},[1711,41761,1836],{},[1716,41763,41764,41766],{},[898,41765,7929],{},[1711,41767,1793],{},[898,41769,2186],{"mathvariant":2287},[902,41771,41772],{"encoding":904},"P = P^*.",[724,41774,41775],{},[614,41776,41777,41778,41799,41800,2186],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,41779,41781],{"className":41780},[886],[888,41782,41783],{"xmlns":890},[892,41784,41785,41797],{},[895,41786,41787,41789,41791,41793,41795],{},[1711,41788,1714],{"stretchy":1713},[898,41790,6796],{},[1711,41792,1726],{"separator":1725},[898,41794,7929],{},[1711,41796,1735],{"stretchy":1713},[902,41798,41289],{"encoding":904}," na úrovni ",[883,41801,41803],{"className":41802},[886],[888,41804,41805],{"xmlns":890},[892,41806,41807,41819],{},[895,41808,41809,41811,41813],{},[898,41810,7929],{},[1711,41812,1836],{},[1716,41814,41815,41817],{},[898,41816,7929],{},[1711,41818,1793],{},[902,41820,8344],{"encoding":904},[40946,41822,41824],{"id":41823},"giffenův-statek","Giffenův statek",[724,41826,41827,41828,41830,41831,41833,41834,2186],{},"Existují zboží, u nichž je křivka poptávky ",[38,41829,3341],{}," — tzv. ",[38,41832,41824],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,41835,41836],{},"podřadnému zboží",[41523,41838,41840],{"id":41839},"příklad-22","Příklad 2.2",[724,41842,41843,41846,41847,41865,41866,41888,41889,41907,41908,41926,41927,41950],{},[38,41844,41845],{},"Zadání a popis:"," Křivka ",[883,41848,41850],{"className":41849},[886],[888,41851,41852],{"xmlns":890},[892,41853,41854,41862],{},[895,41855,41856],{},[2884,41857,41858,41860],{},[898,41859,2778],{},[2111,41861,2238],{},[902,41863,41864],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,41867,41869],{"className":41868},[886],[888,41870,41871],{"xmlns":890},[892,41872,41873,41885],{},[895,41874,41875,41877,41879,41881,41883],{},[1711,41876,1714],{"stretchy":1713},[2111,41878,2113],{},[1711,41880,1726],{"separator":1725},[2111,41882,39842],{},[1711,41884,1735],{"stretchy":1713},[902,41886,41887],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,41890,41892],{"className":41891},[886],[888,41893,41894],{"xmlns":890},[892,41895,41896,41904],{},[895,41897,41898],{},[2884,41899,41900,41902],{},[898,41901,6796],{},[2111,41903,2113],{},[902,41905,41906],{"encoding":904},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[883,41909,41911],{"className":41910},[886],[888,41912,41913],{"xmlns":890},[892,41914,41915,41923],{},[895,41916,41917],{},[2884,41918,41919,41921],{},[898,41920,2778],{},[2111,41922,2963],{},[902,41924,41925],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,41928,41930],{"className":41929},[886],[888,41931,41932],{"xmlns":890},[892,41933,41934,41947],{},[895,41935,41936,41938,41940,41942,41945],{},[1711,41937,5144],{"stretchy":1713},[2111,41939,2113],{},[1711,41941,1726],{"separator":1725},[2111,41943,41944],{},"21",[1711,41946,5163],{"stretchy":1713},[902,41948,41949],{"encoding":904},"[0, 21]"," centů.",[198,41952,41954],{"id":41953},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,41956,41957,41958,2062],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,41959,41961],{"className":41960},[886],[888,41962,41963],{"xmlns":890},[892,41964,41965,41969],{},[895,41966,41967],{},[898,41968,1660],{},[902,41970,1660],{"encoding":904},[883,41972,41974],{"className":41973},[886],[888,41975,41976],{"xmlns":890,"display":31664},[892,41977,41978,42009],{},[24352,41979,41980],{"width":31669},[24357,41981,41982,41984,42002,42004],{},[24360,41983],{"width":31674},[24360,41985,41986],{},[895,41987,41988,41990,41992,41994,41996,41998,42000],{},[898,41989,6796],{},[1711,41991,1836],{},[898,41993,1722],{},[1711,41995,1714],{"stretchy":1713},[898,41997,1660],{},[1711,41999,1735],{"stretchy":1713},[898,42001,2186],{"mathvariant":2287},[24360,42003],{"width":31674},[24360,42005,42006],{},[1942,42007,42008],{},"(2.5)",[902,42010,42011],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,42013,42014,42015,42018,42019,42022],{},"Funkce se nazývá ",[38,42016,42017],{},"Engelova",", její graf ",[38,42020,42021],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,42024,42025,42157],{},[123,42026,42027,5204,42030,42043,42044,42057,42058,42075,42076],{},[38,42028,42029],{},"Normální (superior) zboží",[883,42031,42033],{"className":42032},[886],[888,42034,42035],{"xmlns":890},[892,42036,42037,42041],{},[895,42038,42039],{},[898,42040,6796],{},[902,42042,6796],{"encoding":904}," roste s ",[883,42045,42047],{"className":42046},[886],[888,42048,42049],{"xmlns":890},[892,42050,42051,42055],{},[895,42052,42053],{},[898,42054,1660],{},[902,42056,1660],{"encoding":904},", nepřesáhne hodnotu ",[883,42059,42061],{"className":42060},[886],[888,42062,42063],{"xmlns":890},[892,42064,42065,42073],{},[895,42066,42067],{},[2884,42068,42069,42071],{},[898,42070,6796],{},[2111,42072,2113],{},[902,42074,41906],{"encoding":904},":\n",[120,42077,42078,42110],{},[123,42079,42080,42083,42084,42087,42088,2186],{},[38,42081,42082],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,42085,42086],{},"konkávní"," křivka, autonomní spotřeba ",[883,42089,42091],{"className":42090},[886],[888,42092,42093],{"xmlns":890},[892,42094,42095,42107],{},[895,42096,42097,42103,42105],{},[2884,42098,42099,42101],{},[898,42100,6796],{},[2111,42102,2238],{},[1711,42104,2123],{},[2111,42106,2113],{},[902,42108,42109],{"encoding":904},"Q_1 > 0",[123,42111,42112,42115,42116,42134,42135,42137,42138,1700,42155,2186],{},[38,42113,42114],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,42117,42119],{"className":42118},[886],[888,42120,42121],{"xmlns":890},[892,42122,42123,42131],{},[895,42124,42125],{},[2884,42126,42127,42129],{},[898,42128,1660],{},[2111,42130,2238],{},[902,42132,42133],{"encoding":904},"Y_1",", křivka je nejprve ",[38,42136,41262],{}," a od ",[883,42139,42141],{"className":42140},[886],[888,42142,42143],{"xmlns":890},[892,42144,42145,42153],{},[895,42146,42147],{},[2884,42148,42149,42151],{},[898,42150,1660],{},[2111,42152,2238],{},[902,42154,42133],{"encoding":904},[38,42156,42086],{},[123,42158,42159,42162,42163,42181],{},[38,42160,42161],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,42164,42166],{"className":42165},[886],[888,42167,42168],{"xmlns":890},[892,42169,42170,42178],{},[895,42171,42172],{},[2884,42173,42174,42176],{},[898,42175,1660],{},[2111,42177,2113],{},[902,42179,42180],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,42183,42184,42185,42188,42189,1797],{},"Mírou citlivosti je ",[614,42186,42187],{},"důchodová elasticita"," (viz ",[207,42190,7890],{"className":42191,"dataFsResolvedFilePath":848,"href":849},[210],[724,42193,42194],{},[614,42195,42196],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[40946,42198,42200],{"id":42199},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[1921,42202,42203,42274,42317],{},[724,42204,42205,42207,42208,1700,42211,1700,42224,9652,42226,42239,42240,42243,42244,2186],{},[883,42206,1927],{}," Pozor — nezbytné ≠ podřadné\n",[38,42209,42210],{},"Nezbytné zboží:",[883,42212,42214],{"className":42213},[886],[888,42215,42216],{"xmlns":890},[892,42217,42218,42222],{},[895,42219,42220],{},[898,42221,6796],{},[902,42223,6796],{"encoding":904},[38,42225,11302],{},[883,42227,42229],{"className":42228},[886],[888,42230,42231],{"xmlns":890},[892,42232,42233,42237],{},[895,42234,42235],{},[898,42236,1660],{},[902,42238,1660],{"encoding":904},", ale ",[38,42241,42242],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,42245,42247],{"className":42246},[886],[888,42248,42249],{"xmlns":890},[892,42250,42251,42271],{},[895,42252,42253,42259,42261,42263,42265,42267,42269],{},[2884,42254,42255,42257],{},[898,42256,1722],{},[898,42258,1660],{},[1711,42260,10487],{},[1711,42262,1714],{"stretchy":1713},[2111,42264,2113],{},[1711,42266,1726],{"separator":1725},[2111,42268,2238],{},[1711,42270,1735],{"stretchy":1713},[902,42272,42273],{"encoding":904},"E_Y \\in (0, 1)",[724,42275,42276,1700,42279,1700,42292,42294,42295,2186],{},[38,42277,42278],{},"Podřadné zboží:",[883,42280,42282],{"className":42281},[886],[888,42283,42284],{"xmlns":890},[892,42285,42286,42290],{},[895,42287,42288],{},[898,42289,6796],{},[902,42291,6796],{"encoding":904},[38,42293,11322],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,42296,42298],{"className":42297},[886],[888,42299,42300],{"xmlns":890},[892,42301,42302,42314],{},[895,42303,42304,42310,42312],{},[2884,42305,42306,42308],{},[898,42307,1722],{},[898,42309,1660],{},[1711,42311,2109],{},[2111,42313,2113],{},[902,42315,42316],{"encoding":904},"E_Y \u003C 0",[724,42318,42319,42320,2186],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,42321,42322],{},"méně kusů, ne jen proporčně méně",[724,42324,42325,42328,42329,42332],{},[38,42326,42327],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,42330,42331],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,42334,42335],{},[1801,42336],{"alt":42337,"className":42338,"src":42339},"imek-engelovy-krivky-3typy",[210,1805],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[41523,42341,42343],{"id":42342},"české-příklady","České příklady",[16,42345,42346,42356],{},[19,42347,42348],{},[22,42349,42350,42353],{},[25,42351,42352],{},"Podřadné",[25,42354,42355],{},"Nahradí se za",[30,42357,42358,42366,42374,42382,42390,42398,42406,42414],{},[22,42359,42360,42363],{},[35,42361,42362],{},"Instantní polévky, ramen",[35,42364,42365],{},"Čerstvé jídlo, restaurace",[22,42367,42368,42371],{},[35,42369,42370],{},"MHD (autobus, tramvaj)",[35,42372,42373],{},"Vlastní auto, Uber, taxi",[22,42375,42376,42379],{},[35,42377,42378],{},"Mražené polotovary, pizza z mrazáku",[35,42380,42381],{},"Čerstvé suroviny, hotovky",[22,42383,42384,42387],{},[35,42385,42386],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,42388,42389],{},"Značkové produkty",[22,42391,42392,42395],{},[35,42393,42394],{},"Paštika Májka, obyčejný měkký salám",[35,42396,42397],{},"Kvalitní uzeniny, šunka od kosti",[22,42399,42400,42403],{},[35,42401,42402],{},"Second hand oblečení",[35,42404,42405],{},"Nové oblečení, značky",[22,42407,42408,42411],{},[35,42409,42410],{},"Krabicové víno, nejlevnější pivo",[35,42412,42413],{},"Lahvové víno, řemeslná piva",[22,42415,42416,42419],{},[35,42417,42418],{},"Ojetá auta nižších tříd",[35,42420,42421],{},"Nová auta, prémiové značky",[1921,42423,42424],{},[724,42425,42426,42428,42429,42432],{},[883,42427,3872],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,42430,42431],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,42434,42435,42438,42439,1648,42442,42464,42465,1648,42468,42489,42490,42508,42509,42512],{},[38,42436,42437],{},"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 ",[38,42440,42441],{},"luxus",[883,42443,42445],{"className":42444},[886],[888,42446,42447],{"xmlns":890},[892,42448,42449,42461],{},[895,42450,42451,42457,42459],{},[2884,42452,42453,42455],{},[898,42454,1722],{},[898,42456,1660],{},[1711,42458,2123],{},[2111,42460,2238],{},[902,42462,42463],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,42466,42467],{},"podřadné",[883,42469,42471],{"className":42470},[886],[888,42472,42473],{"xmlns":890},[892,42474,42475,42487],{},[895,42476,42477,42483,42485],{},[2884,42478,42479,42481],{},[898,42480,1722],{},[898,42482,1660],{},[1711,42484,2109],{},[2111,42486,2113],{},[902,42488,42316],{"encoding":904},"). Proto je ",[883,42491,42493],{"className":42492},[886],[888,42494,42495],{"xmlns":890},[892,42496,42497,42505],{},[895,42498,42499],{},[2884,42500,42501,42503],{},[898,42502,1722],{},[898,42504,1660],{},[902,42506,42507],{"encoding":904},"E_Y"," vždy ",[38,42510,42511],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,42514,42515,42516,42518],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,42517,41824],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,42520,42522,42523,1735],{"id":42521},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,42524,42525],{},"shift of demand",[724,42527,42528,42529,42547,42548,42565,42566,42579,42580,6696,42593,42615,42616,42633,42634,42660,42661,42664],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,42530,42532],{"className":42531},[886],[888,42533,42534],{"xmlns":890},[892,42535,42536,42544],{},[895,42537,42538],{},[2884,42539,42540,42542],{},[898,42541,7929],{},[2111,42543,2113],{},[902,42545,42546],{"encoding":904},"P_0"," odpovídá množství ",[883,42549,42551],{"className":42550},[886],[888,42552,42553],{"xmlns":890},[892,42554,42555,42563],{},[895,42556,42557],{},[2884,42558,42559,42561],{},[898,42560,6796],{},[2111,42562,2113],{},[902,42564,41906],{"encoding":904}," na křivce ",[883,42567,42569],{"className":42568},[886],[888,42570,42571],{"xmlns":890},[892,42572,42573,42577],{},[895,42574,42575],{},[898,42576,2778],{},[902,42578,2778],{"encoding":904},"; vzroste-li důchod z ",[883,42581,42583],{"className":42582},[886],[888,42584,42585],{"xmlns":890},[892,42586,42587,42591],{},[895,42588,42589],{},[898,42590,1660],{},[902,42592,1660],{"encoding":904},[883,42594,42596],{"className":42595},[886],[888,42597,42598],{"xmlns":890},[892,42599,42600,42612],{},[895,42601,42602,42608,42610],{},[2884,42603,42604,42606],{},[898,42605,1660],{},[2111,42607,2238],{},[1711,42609,2123],{},[898,42611,1660],{},[902,42613,42614],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,42617,42619],{"className":42618},[886],[888,42620,42621],{"xmlns":890},[892,42622,42623,42631],{},[895,42624,42625],{},[2884,42626,42627,42629],{},[898,42628,7929],{},[2111,42630,2113],{},[902,42632,42546],{"encoding":904}," odpovídá vyšší ",[883,42635,42637],{"className":42636},[886],[888,42638,42639],{"xmlns":890},[892,42640,42641,42657],{},[895,42642,42643,42649,42651],{},[2884,42644,42645,42647],{},[898,42646,6796],{},[2111,42648,2238],{},[1711,42650,2123],{},[2884,42652,42653,42655],{},[898,42654,6796],{},[2111,42656,2113],{},[902,42658,42659],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,42662,42663],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,42666,42667],{},[1801,42668],{"alt":42669,"className":42670,"src":42671},"imek-posun-vs-pohyb-po-krivce",[210,1805],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,42673,42674],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,42676,42677],{},[614,42678,42679,42680,3695,42710,42731],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,42681,42683],{"className":42682},[886],[888,42684,42685],{"xmlns":890},[892,42686,42687,42707],{},[895,42688,42689,42695,42697,42699,42701],{},[2884,42690,42691,42693],{},[898,42692,2778],{},[2111,42694,2963],{},[1711,42696,1726],{"separator":1725},[898,42698,2778],{},[1711,42700,1726],{"separator":1725},[2884,42702,42703,42705],{},[898,42704,2778],{},[2111,42706,2238],{},[902,42708,42709],{"encoding":904},"D_2, D, D_1",[883,42711,42713],{"className":42712},[886],[888,42714,42715],{"xmlns":890},[892,42716,42717,42729],{},[895,42718,42719,42721,42723,42725,42727],{},[1711,42720,1714],{"stretchy":1713},[898,42722,6796],{},[1711,42724,1726],{"separator":1725},[898,42726,7929],{},[1711,42728,1735],{"stretchy":1713},[902,42730,41289],{"encoding":904},", šipky naznačují posuny.",[41523,42733,42735],{"id":42734},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,42737,42738,42740,42741,42764,42765,42782,42783,42800,42801,2186],{},[38,42739,41531],{}," Poptávce ",[883,42742,42744],{"className":42743},[886],[888,42745,42746],{"xmlns":890},[892,42747,42748,42762],{},[895,42749,42750,42752,42754,42756,42758,42760],{},[898,42751,7929],{},[1711,42753,1836],{},[898,42755,2778],{},[1711,42757,1714],{"stretchy":1713},[898,42759,6796],{},[1711,42761,1735],{"stretchy":1713},[902,42763,8625],{"encoding":904}," odpovídá ceně ",[883,42766,42768],{"className":42767},[886],[888,42769,42770],{"xmlns":890},[892,42771,42772,42780],{},[895,42773,42774],{},[2884,42775,42776,42778],{},[898,42777,7929],{},[2111,42779,2113],{},[902,42781,42546],{"encoding":904}," množství ",[883,42784,42786],{"className":42785},[886],[888,42787,42788],{"xmlns":890},[892,42789,42790,42798],{},[895,42791,42792],{},[2884,42793,42794,42796],{},[898,42795,6796],{},[2111,42797,2113],{},[902,42799,41906],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,42802,42804],{"className":42803},[886],[888,42805,42806],{"xmlns":890},[892,42807,42808,42812],{},[895,42809,42810],{},[898,42811,1769],{},[902,42813,1769],{"encoding":904},[724,42815,42816,42818,42819,42836,42837,42859],{},[38,42817,41563],{}," Kupující nakupuje množství ",[883,42820,42822],{"className":42821},[886],[888,42823,42824],{"xmlns":890},[892,42825,42826,42834],{},[895,42827,42828],{},[2884,42829,42830,42832],{},[898,42831,6796],{},[2111,42833,2238],{},[902,42835,32600],{"encoding":904},", které odpovídá ceně ",[883,42838,42840],{"className":42839},[886],[888,42841,42842],{"xmlns":890},[892,42843,42844,42856],{},[895,42845,42846,42852,42854],{},[2884,42847,42848,42850],{},[898,42849,7929],{},[2111,42851,2113],{},[1711,42853,2095],{},[898,42855,1769],{},[902,42857,42858],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,42861,42863],{"className":42862},[886],[888,42864,42865],{"xmlns":890,"display":31664},[892,42866,42867,42901],{},[895,42868,42869,42871,42873,42879,42881,42883,42885,42887,42889,42891,42893,42895,42897,42899],{},[898,42870,7929],{},[1711,42872,1836],{},[2884,42874,42875,42877],{},[898,42876,2778],{},[2111,42878,2238],{},[1711,42880,1714],{"stretchy":1713},[898,42882,6796],{},[1711,42884,1735],{"stretchy":1713},[1711,42886,1836],{},[898,42888,2778],{},[1711,42890,1714],{"stretchy":1713},[898,42892,6796],{},[1711,42894,1735],{"stretchy":1713},[1711,42896,2460],{},[898,42898,1769],{},[1711,42900,1726],{"separator":1725},[902,42902,42903],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,42905,42906,42907,2186],{},"tj. dojde k ",[38,42908,42909],{},"posunu poptávky doleva",[724,42911,42912],{},[614,42913,42914,42915,42936,42937,1343,42954,1343,42967,42988,42989,2009,43006,2186],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,42916,42918],{"className":42917},[886],[888,42919,42920],{"xmlns":890},[892,42921,42922,42934],{},[895,42923,42924,42926,42928,42930,42932],{},[1711,42925,1714],{"stretchy":1713},[898,42927,6796],{},[1711,42929,1726],{"separator":1725},[898,42931,7929],{},[1711,42933,1735],{"stretchy":1713},[902,42935,41289],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,42938,42940],{"className":42939},[886],[888,42941,42942],{"xmlns":890},[892,42943,42944,42952],{},[895,42945,42946],{},[2884,42947,42948,42950],{},[898,42949,7929],{},[2111,42951,2113],{},[902,42953,42546],{"encoding":904},[883,42955,42957],{"className":42956},[886],[888,42958,42959],{"xmlns":890},[892,42960,42961,42965],{},[895,42962,42963],{},[898,42964,1769],{},[902,42966,1769],{"encoding":904},[883,42968,42970],{"className":42969},[886],[888,42971,42972],{"xmlns":890},[892,42973,42974,42986],{},[895,42975,42976,42982,42984],{},[2884,42977,42978,42980],{},[898,42979,7929],{},[2111,42981,2113],{},[1711,42983,2095],{},[898,42985,1769],{},[902,42987,42858],{"encoding":904},"; na vodorovné ",[883,42990,42992],{"className":42991},[886],[888,42993,42994],{"xmlns":890},[892,42995,42996,43004],{},[895,42997,42998],{},[2884,42999,43000,43002],{},[898,43001,6796],{},[2111,43003,2238],{},[902,43005,32600],{"encoding":904},[883,43007,43009],{"className":43008},[886],[888,43010,43011],{"xmlns":890},[892,43012,43013,43021],{},[895,43014,43015],{},[2884,43016,43017,43019],{},[898,43018,6796],{},[2111,43020,2113],{},[902,43022,41906],{"encoding":904},[198,43024,43026],{"id":43025},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,43028,43029],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,43031,43033],{"className":43032},[886],[888,43034,43035],{"xmlns":890,"display":31664},[892,43036,43037,43222],{},[24352,43038,43039],{"width":31669},[24357,43040,43041,43043,43215,43217],{},[24360,43042],{"width":31674},[24360,43044,43045],{},[24352,43046,43047,43131],{"rowspacing":24354,"columnalign":24355,"columnspacing":5224},[24357,43048,43049,43059],{},[24360,43050,43051],{},[2509,43052,43053],{"scriptlevel":2113,"displaystyle":1725},[2884,43054,43055,43057],{},[898,43056,6796],{},[2111,43058,2238],{},[24360,43060,43061],{},[2509,43062,43063],{"scriptlevel":2113,"displaystyle":1725},[895,43064,43065,43067,43069,43075,43077,43083,43085,43091,43093,43095,43101,43103,43109,43115,43117,43123,43129],{},[895,43066],{},[1711,43068,1836],{},[2884,43070,43071,43073],{},[898,43072,2778],{},[2111,43074,2238],{},[1711,43076,1714],{"stretchy":1713},[2884,43078,43079,43081],{},[898,43080,7929],{},[2111,43082,2238],{},[1711,43084,1726],{"separator":1725},[2884,43086,43087,43089],{},[898,43088,7929],{},[2111,43090,2963],{},[1711,43092,1735],{"stretchy":1713},[1711,43094,1836],{},[2884,43096,43097,43099],{},[898,43098,207],{},[2111,43100,2238],{},[1711,43102,2095],{},[2884,43104,43105,43107],{},[898,43106,2223],{},[2111,43108,2238],{},[2884,43110,43111,43113],{},[898,43112,7929],{},[2111,43114,2238],{},[1711,43116,2095],{},[2884,43118,43119,43121],{},[898,43120,2090],{},[2111,43122,2238],{},[2884,43124,43125,43127],{},[898,43126,7929],{},[2111,43128,2963],{},[1711,43130,1726],{"separator":1725},[24357,43132,43133,43143],{},[24360,43134,43135],{},[2509,43136,43137],{"scriptlevel":2113,"displaystyle":1725},[2884,43138,43139,43141],{},[898,43140,6796],{},[2111,43142,2963],{},[24360,43144,43145],{},[2509,43146,43147],{"scriptlevel":2113,"displaystyle":1725},[895,43148,43149,43151,43153,43159,43161,43167,43169,43175,43177,43179,43185,43187,43193,43199,43201,43207,43213],{},[895,43150],{},[1711,43152,1836],{},[2884,43154,43155,43157],{},[898,43156,2778],{},[2111,43158,2963],{},[1711,43160,1714],{"stretchy":1713},[2884,43162,43163,43165],{},[898,43164,7929],{},[2111,43166,2238],{},[1711,43168,1726],{"separator":1725},[2884,43170,43171,43173],{},[898,43172,7929],{},[2111,43174,2963],{},[1711,43176,1735],{"stretchy":1713},[1711,43178,1836],{},[2884,43180,43181,43183],{},[898,43182,207],{},[2111,43184,2963],{},[1711,43186,2095],{},[2884,43188,43189,43191],{},[898,43190,2223],{},[2111,43192,2963],{},[2884,43194,43195,43197],{},[898,43196,7929],{},[2111,43198,2238],{},[1711,43200,2095],{},[2884,43202,43203,43205],{},[898,43204,2090],{},[2111,43206,2963],{},[2884,43208,43209,43211],{},[898,43210,7929],{},[2111,43212,2963],{},[898,43214,2186],{"mathvariant":2287},[24360,43216],{"width":31674},[24360,43218,43219],{},[1942,43220,43221],{},"(2.6)",[902,43223,43224],{"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}",[40946,43226,43228],{"id":43227},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,43230,43231,43278,43325],{},[123,43232,43233,1343,43255,43277],{},[883,43234,43236],{"className":43235},[886],[888,43237,43238],{"xmlns":890},[892,43239,43240,43252],{},[895,43241,43242,43248,43250],{},[2884,43243,43244,43246],{},[898,43245,207],{},[2111,43247,2238],{},[1711,43249,2123],{},[2111,43251,2113],{},[902,43253,43254],{"encoding":904},"a_1 > 0",[883,43256,43258],{"className":43257},[886],[888,43259,43260],{"xmlns":890},[892,43261,43262,43274],{},[895,43263,43264,43270,43272],{},[2884,43265,43266,43268],{},[898,43267,207],{},[2111,43269,2963],{},[1711,43271,2123],{},[2111,43273,2113],{},[902,43275,43276],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,43279,43280,1343,43302,43324],{},[883,43281,43283],{"className":43282},[886],[888,43284,43285],{"xmlns":890},[892,43286,43287,43299],{},[895,43288,43289,43295,43297],{},[2884,43290,43291,43293],{},[898,43292,2223],{},[2111,43294,2238],{},[1711,43296,2109],{},[2111,43298,2113],{},[902,43300,43301],{"encoding":904},"b_1 \u003C 0",[883,43303,43305],{"className":43304},[886],[888,43306,43307],{"xmlns":890},[892,43308,43309,43321],{},[895,43310,43311,43317,43319],{},[2884,43312,43313,43315],{},[898,43314,2090],{},[2111,43316,2963],{},[1711,43318,2109],{},[2111,43320,2113],{},[902,43322,43323],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,43326,43327,43328,1343,43345,43363,43364],{},"zkřížené koeficienty ",[883,43329,43331],{"className":43330},[886],[888,43332,43333],{"xmlns":890},[892,43334,43335,43343],{},[895,43336,43337],{},[2884,43338,43339,43341],{},[898,43340,2090],{},[2111,43342,2238],{},[902,43344,33397],{"encoding":904},[883,43346,43348],{"className":43347},[886],[888,43349,43350],{"xmlns":890},[892,43351,43352,43360],{},[895,43353,43354],{},[2884,43355,43356,43358],{},[898,43357,2223],{},[2111,43359,2963],{},[902,43361,43362],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,43365,43366,43416],{},[123,43367,43368,43371,43372,1343,43394,1726],{},[38,43369,43370],{},"substituty"," (máslo vs. margarín): ",[883,43373,43375],{"className":43374},[886],[888,43376,43377],{"xmlns":890},[892,43378,43379,43391],{},[895,43380,43381,43387,43389],{},[2884,43382,43383,43385],{},[898,43384,2090],{},[2111,43386,2238],{},[1711,43388,2123],{},[2111,43390,2113],{},[902,43392,43393],{"encoding":904},"c_1 > 0",[883,43395,43397],{"className":43396},[886],[888,43398,43399],{"xmlns":890},[892,43400,43401,43413],{},[895,43402,43403,43409,43411],{},[2884,43404,43405,43407],{},[898,43406,2223],{},[2111,43408,2963],{},[1711,43410,2123],{},[2111,43412,2113],{},[902,43414,43415],{"encoding":904},"b_2 > 0",[123,43417,43418,43421,43422,1343,43444,2186],{},[38,43419,43420],{},"komplementy"," (auto vs. benzín): ",[883,43423,43425],{"className":43424},[886],[888,43426,43427],{"xmlns":890},[892,43428,43429,43441],{},[895,43430,43431,43437,43439],{},[2884,43432,43433,43435],{},[898,43434,2090],{},[2111,43436,2238],{},[1711,43438,2109],{},[2111,43440,2113],{},[902,43442,43443],{"encoding":904},"c_1 \u003C 0",[883,43445,43447],{"className":43446},[886],[888,43448,43449],{"xmlns":890},[892,43450,43451,43463],{},[895,43452,43453,43459,43461],{},[2884,43454,43455,43457],{},[898,43456,2223],{},[2111,43458,2963],{},[1711,43460,2109],{},[2111,43462,2113],{},[902,43464,43465],{"encoding":904},"b_2 \u003C 0",[724,43467,43468],{},"Schematicky:",[724,43470,43471,43474],{},[38,43472,43473],{},"Substituty",[883,43475,43477],{"className":43476},[886],[888,43478,43479],{"xmlns":890},[892,43480,43481,43620],{},[895,43482,43483,43489,43491,43506,43508,43528,43530,43550,43552,43554,43560,43562,43576,43578,43598,43600],{},[2884,43484,43485,43487],{},[898,43486,6796],{},[2111,43488,2238],{},[1711,43490,1836],{},[898,43492,43493],{},[43494,43495,43496,43504],"munder",{},[1711,43497,43498],{},[2884,43499,43500,43502],{},[898,43501,207],{},[2111,43503,2238],{},[1711,43505,2095],{"lspace":5224,"rspace":5224},[1711,43507,2095],{},[898,43509,43510],{},[43494,43511,43512,43526],{},[1711,43513,43514,43520],{},[2884,43515,43516,43518],{},[898,43517,2223],{},[2111,43519,2238],{},[2884,43521,43522,43524],{},[898,43523,7929],{},[2111,43525,2238],{},[1711,43527,2460],{"lspace":5224,"rspace":5224},[1711,43529,2095],{},[898,43531,43532],{},[43494,43533,43534,43548],{},[1711,43535,43536,43542],{},[2884,43537,43538,43540],{},[898,43539,2090],{},[2111,43541,2238],{},[2884,43543,43544,43546],{},[898,43545,7929],{},[2111,43547,2963],{},[1711,43549,2095],{"lspace":5224,"rspace":5224},[1711,43551,1726],{"separator":1725},[2102,43553],{"width":2104},[2884,43555,43556,43558],{},[898,43557,6796],{},[2111,43559,2963],{},[1711,43561,1836],{},[898,43563,43564],{},[43494,43565,43566,43574],{},[1711,43567,43568],{},[2884,43569,43570,43572],{},[898,43571,207],{},[2111,43573,2963],{},[1711,43575,2095],{"lspace":5224,"rspace":5224},[1711,43577,2095],{},[898,43579,43580],{},[43494,43581,43582,43596],{},[1711,43583,43584,43590],{},[2884,43585,43586,43588],{},[898,43587,2223],{},[2111,43589,2963],{},[2884,43591,43592,43594],{},[898,43593,7929],{},[2111,43595,2238],{},[1711,43597,2095],{"lspace":5224,"rspace":5224},[1711,43599,2095],{},[898,43601,43602],{},[43494,43603,43604,43618],{},[1711,43605,43606,43612],{},[2884,43607,43608,43610],{},[898,43609,2090],{},[2111,43611,2963],{},[2884,43613,43614,43616],{},[898,43615,7929],{},[2111,43617,2963],{},[1711,43619,2460],{"lspace":5224,"rspace":5224},[902,43621,43622],{"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}",[724,43624,43625,43628],{},[38,43626,43627],{},"Komplementy",[883,43629,43631],{"className":43630},[886],[888,43632,43633],{"xmlns":890},[892,43634,43635,43773],{},[895,43636,43637,43643,43645,43659,43661,43681,43683,43703,43705,43707,43713,43715,43729,43731,43751,43753],{},[2884,43638,43639,43641],{},[898,43640,6796],{},[2111,43642,2238],{},[1711,43644,1836],{},[898,43646,43647],{},[43494,43648,43649,43657],{},[1711,43650,43651],{},[2884,43652,43653,43655],{},[898,43654,207],{},[2111,43656,2238],{},[1711,43658,2095],{"lspace":5224,"rspace":5224},[1711,43660,2095],{},[898,43662,43663],{},[43494,43664,43665,43679],{},[1711,43666,43667,43673],{},[2884,43668,43669,43671],{},[898,43670,2223],{},[2111,43672,2238],{},[2884,43674,43675,43677],{},[898,43676,7929],{},[2111,43678,2238],{},[1711,43680,2460],{"lspace":5224,"rspace":5224},[1711,43682,2095],{},[898,43684,43685],{},[43494,43686,43687,43701],{},[1711,43688,43689,43695],{},[2884,43690,43691,43693],{},[898,43692,2090],{},[2111,43694,2238],{},[2884,43696,43697,43699],{},[898,43698,7929],{},[2111,43700,2963],{},[1711,43702,2460],{"lspace":5224,"rspace":5224},[1711,43704,1726],{"separator":1725},[2102,43706],{"width":2104},[2884,43708,43709,43711],{},[898,43710,6796],{},[2111,43712,2963],{},[1711,43714,1836],{},[898,43716,43717],{},[43494,43718,43719,43727],{},[1711,43720,43721],{},[2884,43722,43723,43725],{},[898,43724,207],{},[2111,43726,2963],{},[1711,43728,2095],{"lspace":5224,"rspace":5224},[1711,43730,2095],{},[898,43732,43733],{},[43494,43734,43735,43749],{},[1711,43736,43737,43743],{},[2884,43738,43739,43741],{},[898,43740,2223],{},[2111,43742,2963],{},[2884,43744,43745,43747],{},[898,43746,7929],{},[2111,43748,2238],{},[1711,43750,2460],{"lspace":5224,"rspace":5224},[1711,43752,2095],{},[898,43754,43755],{},[43494,43756,43757,43771],{},[1711,43758,43759,43765],{},[2884,43760,43761,43763],{},[898,43762,2090],{},[2111,43764,2963],{},[2884,43766,43767,43769],{},[898,43768,7929],{},[2111,43770,2963],{},[1711,43772,2460],{"lspace":5224,"rspace":5224},[902,43774,43775],{"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}",[40568,43777],{},[115,43779,2804],{"id":40377},[1921,43781,43782],{},[724,43783,43784,43786,43787,40592,43800,40606,43813,43816,43817,9652,43841,43859],{},[883,43785,2678],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,43788,43790],{"className":43789},[886],[888,43791,43792],{"xmlns":890},[892,43793,43794,43798],{},[895,43795,43796],{},[898,43797,6796],{},[902,43799,6796],{"encoding":904},[883,43801,43803],{"className":43802},[886],[888,43804,43805],{"xmlns":890},[892,43806,43807,43811],{},[895,43808,43809],{},[898,43810,7929],{},[902,43812,7929],{"encoding":904},[38,43814,43815],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,43818,43820],{"className":43819},[886],[888,43821,43822],{"xmlns":890},[892,43823,43824,43838],{},[895,43825,43826,43828,43830,43832,43834,43836],{},[898,43827,7929],{},[1711,43829,1836],{},[898,43831,2090],{},[898,43833,6796],{},[1711,43835,2095],{},[898,43837,2098],{},[902,43839,43840],{"encoding":904},"P = cQ + d",[883,43842,43844],{"className":43843},[886],[888,43845,43846],{"xmlns":890},[892,43847,43848,43856],{},[895,43849,43850,43852,43854],{},[898,43851,2090],{},[1711,43853,2123],{},[2111,43855,2113],{},[902,43857,43858],{"encoding":904},"c > 0"," je standardní aproximací.",[198,43861,40662],{"id":43862},"obecný-vícefaktorový-model-1",[724,43864,43865,1648,43868,43871,43872,43885,43886,40494,43899,40508,43912,43925,43926,43940,43941,40537,43954,43967],{},[38,43866,43867],{},"Nabízené množství",[614,43869,43870],{},"quantity supplied",") závisí na ceně ",[883,43873,43875],{"className":43874},[886],[888,43876,43877],{"xmlns":890},[892,43878,43879,43883],{},[895,43880,43881],{},[898,43882,7929],{},[902,43884,7929],{"encoding":904},", cenách výrobních faktorů (práce ",[883,43887,43889],{"className":43888},[886],[888,43890,43891],{"xmlns":890},[892,43892,43893,43897],{},[895,43894,43895],{},[898,43896,2888],{},[902,43898,2888],{"encoding":904},[883,43900,43902],{"className":43901},[886],[888,43903,43904],{"xmlns":890},[892,43905,43906,43910],{},[895,43907,43908],{},[898,43909,13774],{},[902,43911,13774],{"encoding":904},[883,43913,43915],{"className":43914},[886],[888,43916,43917],{"xmlns":890},[892,43918,43919,43923],{},[895,43920,43921],{},[898,43922,1722],{},[902,43924,1722],{"encoding":904},"), očekávání ",[883,43927,43929],{"className":43928},[886],[888,43930,43931],{"xmlns":890},[892,43932,43933,43938],{},[895,43934,43935],{},[898,43936,43937],{},"V",[902,43939,43937],{"encoding":904},", počtu výrobců ",[883,43942,43944],{"className":43943},[886],[888,43945,43946],{"xmlns":890},[892,43947,43948,43952],{},[895,43949,43950],{},[898,43951,40534],{},[902,43953,40534],{"encoding":904},[883,43955,43957],{"className":43956},[886],[888,43958,43959],{"xmlns":890},[892,43960,43961,43965],{},[895,43962,43963],{},[898,43964,40549],{},[902,43966,40549],{"encoding":904}," a dalších:",[883,43969,43971],{"className":43970},[886],[888,43972,43973],{"xmlns":890,"display":31664},[892,43974,43975,44034],{},[24352,43976,43977],{"width":31669},[24357,43978,43979,43981,44027,44029],{},[24360,43980],{"width":31674},[24360,43982,43983],{},[895,43984,43985,43987,43989,43991,43993,43995,43997,43999,44001,44003,44005,44007,44009,44011,44013,44015,44017,44019,44021,44023,44025],{},[898,43986,6796],{},[1711,43988,1836],{},[898,43990,2362],{},[1711,43992,1714],{"stretchy":1713},[898,43994,7929],{},[1711,43996,1726],{"separator":1725},[898,43998,2888],{},[1711,44000,1726],{"separator":1725},[898,44002,13774],{},[1711,44004,1726],{"separator":1725},[898,44006,1722],{},[1711,44008,1726],{"separator":1725},[898,44010,43937],{},[1711,44012,1726],{"separator":1725},[898,44014,40534],{},[1711,44016,1726],{"separator":1725},[898,44018,40549],{},[1711,44020,1726],{"separator":1725},[1711,44022,13621],{},[1711,44024,1735],{"stretchy":1713},[898,44026,2186],{"mathvariant":2287},[24360,44028],{"width":31674},[24360,44030,44031],{},[1942,44032,44033],{},"(2.7)",[902,44035,44036],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,44038,42014,44039,1648,44042,44045],{},[38,44040,44041],{},"funkce nabídky",[614,44043,44044],{},"supply function",") v širším slova smyslu.",[198,44047,44049],{"id":44048},"jednofaktorový-model","Jednofaktorový model",[724,44051,44052],{},"V nejpřirozenějším jednofaktorovém modelu",[883,44054,44056],{"className":44055},[886],[888,44057,44058],{"xmlns":890,"display":31664},[892,44059,44060,44111],{},[24352,44061,44062],{"width":31669},[24357,44063,44064,44066,44104,44106],{},[24360,44065],{"width":31674},[24360,44067,44068],{},[895,44069,44070,44072,44074,44076,44078,44080,44082,44084,44086,44088,44090,44092,44094,44096,44098,44100,44102],{},[898,44071,6796],{},[1711,44073,1836],{},[898,44075,2362],{},[1711,44077,1714],{"stretchy":1713},[898,44079,7929],{},[1711,44081,1735],{"stretchy":1713},[1711,44083,1726],{"separator":1725},[2102,44085],{"width":2104},[1942,44087,41015],{},[2102,44089],{"width":2104},[898,44091,7929],{},[1711,44093,1836],{},[898,44095,2362],{},[1711,44097,1714],{"stretchy":1713},[898,44099,6796],{},[1711,44101,1735],{"stretchy":1713},[898,44103,2186],{"mathvariant":2287},[24360,44105],{"width":31674},[24360,44107,44108],{},[1942,44109,44110],{},"(2.8)",[902,44112,44113],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,44115,44116,44117,1648,44120,1797],{},"Graf je ",[38,44118,44119],{},"křivka nabídky",[614,44121,44122],{},"supply curve",[40946,44124,44126],{"id":44125},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[1921,44128,44129],{},[724,44130,44131],{},[38,44132,41061,44133,44146,44147,41116],{},[883,44134,44136],{"className":44135},[886],[888,44137,44138],{"xmlns":890},[892,44139,44140,44144],{},[895,44141,44142],{},[898,44143,7929],{},[902,44145,7929],{"encoding":904},", pak nabízené množství ",[883,44148,44150],{"className":44149},[886],[888,44151,44152],{"xmlns":890},[892,44153,44154,44158],{},[895,44155,44156],{},[898,44157,6796],{},[902,44159,6796],{"encoding":904},[724,44161,44162,44163,44188,44189,44219,44220,44237],{},"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 ",[883,44164,44166],{"className":44165},[886],[888,44167,44168],{"xmlns":890},[892,44169,44170,44186],{},[895,44171,44172,44174,44176,44178,44184],{},[1711,44173,5144],{"stretchy":1713},[2111,44175,2113],{},[1711,44177,1726],{"separator":1725},[2884,44179,44180,44182],{},[898,44181,7929],{},[2111,44183,2113],{},[1711,44185,5163],{"stretchy":1713},[902,44187,41201],{"encoding":904}," na svislé ose (případně z ",[883,44190,44192],{"className":44191},[886],[888,44193,44194],{"xmlns":890},[892,44195,44196,44216],{},[895,44197,44198,44200,44206,44208,44214],{},[1711,44199,5144],{"stretchy":1713},[2884,44201,44202,44204],{},[898,44203,6796],{},[2111,44205,2238],{},[1711,44207,1726],{"separator":1725},[2884,44209,44210,44212],{},[898,44211,7929],{},[2111,44213,2238],{},[1711,44215,5163],{"stretchy":1713},[902,44217,44218],{"encoding":904},"[Q_1, P_1]","), kde ",[883,44221,44223],{"className":44222},[886],[888,44224,44225],{"xmlns":890},[892,44226,44227,44235],{},[895,44228,44229],{},[2884,44230,44231,44233],{},[898,44232,7929],{},[2111,44234,2113],{},[902,44236,42546],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,44239,44240],{},[614,44241,44242,44243,7714,44256,2186],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,44244,44246],{"className":44245},[886],[888,44247,44248],{"xmlns":890},[892,44249,44250,44254],{},[895,44251,44252],{},[898,44253,2362],{},[902,44255,2362],{"encoding":904},[883,44257,44259],{"className":44258},[886],[888,44260,44261],{"xmlns":890},[892,44262,44263,44275],{},[895,44264,44265,44267,44269,44271,44273],{},[1711,44266,1714],{"stretchy":1713},[898,44268,6796],{},[1711,44270,1726],{"separator":1725},[898,44272,7929],{},[1711,44274,1735],{"stretchy":1713},[902,44276,41289],{"encoding":904},[40946,44278,44280],{"id":44279},"lineární-model-nabídky","Lineární model nabídky",[883,44282,44284],{"className":44283},[886],[888,44285,44286],{"xmlns":890,"display":31664},[892,44287,44288,44327],{},[24352,44289,44290],{"width":31669},[24357,44291,44292,44294,44320,44322],{},[24360,44293],{"width":31674},[24360,44295,44296],{},[895,44297,44298,44300,44302,44304,44306,44308,44310,44312,44314,44316,44318],{},[898,44299,7929],{},[1711,44301,1836],{},[898,44303,2090],{},[898,44305,6796],{},[1711,44307,2095],{},[898,44309,2098],{},[1711,44311,1726],{"separator":1725},[2102,44313],{"width":2104},[898,44315,2090],{},[1711,44317,2123],{},[2111,44319,2126],{},[24360,44321],{"width":31674},[24360,44323,44324],{},[1942,44325,44326],{},"(2.9)",[902,44328,44329],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,44331,44332,44333,44369,44370,44383],{},"Alternativně ",[883,44334,44336],{"className":44335},[886],[888,44337,44338],{"xmlns":890},[892,44339,44340,44366],{},[895,44341,44342,44344,44346,44354,44356,44358],{},[898,44343,6796],{},[1711,44345,1836],{},[2509,44347,44348],{"scriptlevel":2113,"displaystyle":1713},[2525,44349,44350,44352],{},[2111,44351,2238],{},[898,44353,2090],{},[898,44355,7929],{},[1711,44357,2460],{},[2509,44359,44360],{"scriptlevel":2113,"displaystyle":1713},[2525,44361,44362,44364],{},[898,44363,2098],{},[898,44365,2090],{},[902,44367,44368],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,44371,44373],{"className":44372},[886],[888,44374,44375],{"xmlns":890},[892,44376,44377,44381],{},[895,44378,44379],{},[898,44380,7929],{},[902,44382,7929],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[41523,44385,44387],{"id":44386},"příklad-25","Příklad 2.5",[724,44389,44390,44392,44393,2186],{},[38,44391,41531],{}," Lineární nabídka ",[883,44394,44396],{"className":44395},[886],[888,44397,44398],{"xmlns":890},[892,44399,44400,44414],{},[895,44401,44402,44404,44406,44408,44410,44412],{},[898,44403,7929],{},[1711,44405,1836],{},[2111,44407,8993],{},[898,44409,6796],{},[1711,44411,2095],{},[2111,44413,4372],{},[902,44415,44416],{"encoding":904},"P = 0{,}5Q + 25",[724,44418,44419,44421,44422,2186],{},[38,44420,41563],{}," Alternativní tvar ",[883,44423,44425],{"className":44424},[886],[888,44426,44427],{"xmlns":890},[892,44428,44429,44443],{},[895,44430,44431,44433,44435,44437,44439,44441],{},[898,44432,6796],{},[1711,44434,1836],{},[2111,44436,2963],{},[898,44438,7929],{},[1711,44440,2460],{},[2111,44442,7120],{},[902,44444,44445],{"encoding":904},"Q = 2P - 50",[16,44447,44448,44473],{},[19,44449,44450],{},[22,44451,44452,44467,44469,44471],{},[25,44453,44454],{},[883,44455,44457],{"className":44456},[886],[888,44458,44459],{"xmlns":890},[892,44460,44461,44465],{},[895,44462,44463],{},[898,44464,7929],{},[902,44466,7929],{"encoding":904},[25,44468,41617],{},[25,44470,4733],{},[25,44472,9195],{},[30,44474,44475],{},[22,44476,44477,44492,44494,44496],{},[35,44478,44479],{},[883,44480,44482],{"className":44481},[886],[888,44483,44484],{"xmlns":890},[892,44485,44486,44490],{},[895,44487,44488],{},[898,44489,6796],{},[902,44491,6796],{"encoding":904},[35,44493,4712],{},[35,44495,4306],{},[35,44497,41617],{},[198,44499,44501,44502,1735],{"id":44500},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,44503,44504],{},"shift of supply",[724,44506,44507,44508,44511,44512,44529,44530,44555,44556,2186],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,44509,44510],{},"doprava",": při stejné ceně ",[883,44513,44515],{"className":44514},[886],[888,44516,44517],{"xmlns":890},[892,44518,44519,44527],{},[895,44520,44521],{},[2884,44522,44523,44525],{},[898,44524,7929],{},[2111,44526,2113],{},[902,44528,42546],{"encoding":904}," vyrobí výrobce větší ",[883,44531,44533],{"className":44532},[886],[888,44534,44535],{"xmlns":890},[892,44536,44537,44553],{},[895,44538,44539,44545,44547],{},[2884,44540,44541,44543],{},[898,44542,6796],{},[2111,44544,2238],{},[1711,44546,2123],{},[2884,44548,44549,44551],{},[898,44550,6796],{},[2111,44552,2113],{},[902,44554,42659],{"encoding":904},"); zdražení vstupů posune křivku ",[38,44557,44558],{},"doleva",[724,44560,44561],{},[614,44562,44563,44564,44577,44578,44596,44597,44615,44616,2186],{},"Obrázek 2.11: Původní ",[883,44565,44567],{"className":44566},[886],[888,44568,44569],{"xmlns":890},[892,44570,44571,44575],{},[895,44572,44573],{},[898,44574,2362],{},[902,44576,2362],{"encoding":904},", posunuté ",[883,44579,44581],{"className":44580},[886],[888,44582,44583],{"xmlns":890},[892,44584,44585,44593],{},[895,44586,44587],{},[2884,44588,44589,44591],{},[898,44590,2362],{},[2111,44592,2238],{},[902,44594,44595],{"encoding":904},"S_1"," (doprava) a ",[883,44598,44600],{"className":44599},[886],[888,44601,44602],{"xmlns":890},[892,44603,44604,44612],{},[895,44605,44606],{},[2884,44607,44608,44610],{},[898,44609,2362],{},[2111,44611,2963],{},[902,44613,44614],{"encoding":904},"S_2"," (doleva) v ",[883,44617,44619],{"className":44618},[886],[888,44620,44621],{"xmlns":890},[892,44622,44623,44635],{},[895,44624,44625,44627,44629,44631,44633],{},[1711,44626,1714],{"stretchy":1713},[898,44628,6796],{},[1711,44630,1726],{"separator":1725},[898,44632,7929],{},[1711,44634,1735],{"stretchy":1713},[902,44636,41289],{"encoding":904},[41523,44638,44640],{"id":44639},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,44642,44643,44645,44646,44670,44671,2186],{},[38,44644,41531],{}," Nabídka ",[883,44647,44649],{"className":44648},[886],[888,44650,44651],{"xmlns":890},[892,44652,44653,44667],{},[895,44654,44655,44657,44659,44661,44663,44665],{},[898,44656,7929],{},[1711,44658,1836],{},[898,44660,2362],{},[1711,44662,1714],{"stretchy":1713},[898,44664,6796],{},[1711,44666,1735],{"stretchy":1713},[902,44668,44669],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,44672,44674],{"className":44673},[886],[888,44675,44676],{"xmlns":890},[892,44677,44678,44682],{},[895,44679,44680],{},[898,44681,1769],{},[902,44683,1769],{"encoding":904},[724,44685,44686,44688,44689,44702,44703,44721,44722,44750],{},[38,44687,41563],{}," Spotřebitel zaplatí ",[883,44690,44692],{"className":44691},[886],[888,44693,44694],{"xmlns":890},[892,44695,44696,44700],{},[895,44697,44698],{},[898,44699,7929],{},[902,44701,7929],{"encoding":904},", výrobce obdrží ",[883,44704,44706],{"className":44705},[886],[888,44707,44708],{"xmlns":890},[892,44709,44710,44718],{},[895,44711,44712,44714,44716],{},[898,44713,7929],{},[1711,44715,2460],{},[898,44717,1769],{},[902,44719,44720],{"encoding":904},"P - T",". Z podmínky ",[883,44723,44725],{"className":44724},[886],[888,44726,44727],{"xmlns":890},[892,44728,44729,44747],{},[895,44730,44731,44733,44735,44737,44739,44741,44743,44745],{},[898,44732,7929],{},[1711,44734,2460],{},[898,44736,1769],{},[1711,44738,1836],{},[898,44740,2362],{},[1711,44742,1714],{"stretchy":1713},[898,44744,6796],{},[1711,44746,1735],{"stretchy":1713},[902,44748,44749],{"encoding":904},"P - T = S(Q)"," plyne",[883,44752,44754],{"className":44753},[886],[888,44755,44756],{"xmlns":890,"display":31664},[892,44757,44758,44792],{},[895,44759,44760,44762,44764,44770,44772,44774,44776,44778,44780,44782,44784,44786,44788,44790],{},[898,44761,7929],{},[1711,44763,1836],{},[2884,44765,44766,44768],{},[898,44767,2362],{},[2111,44769,2238],{},[1711,44771,1714],{"stretchy":1713},[898,44773,6796],{},[1711,44775,1735],{"stretchy":1713},[1711,44777,1836],{},[898,44779,2362],{},[1711,44781,1714],{"stretchy":1713},[898,44783,6796],{},[1711,44785,1735],{"stretchy":1713},[1711,44787,2095],{},[898,44789,1769],{},[898,44791,2186],{"mathvariant":2287},[902,44793,44794],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,44796,44797,44798,44811,44812,1700,44825,44828,44829,2009,44849,12082,44867,2186],{},"Křivka ",[883,44799,44801],{"className":44800},[886],[888,44802,44803],{"xmlns":890},[892,44804,44805,44809],{},[895,44806,44807],{},[898,44808,2362],{},[902,44810,2362],{"encoding":904}," se tedy posune o ",[883,44813,44815],{"className":44814},[886],[888,44816,44817],{"xmlns":890},[892,44818,44819,44823],{},[895,44820,44821],{},[898,44822,1769],{},[902,44824,1769],{"encoding":904},[38,44826,44827],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,44830,44832],{"className":44831},[886],[888,44833,44834],{"xmlns":890},[892,44835,44836,44846],{},[895,44837,44838,44840,44842,44844],{},[898,44839,7929],{},[1711,44841,1836],{},[2111,44843,2963],{},[898,44845,6796],{},[902,44847,44848],{"encoding":904},"P = 2Q",[883,44850,44852],{"className":44851},[886],[888,44853,44854],{"xmlns":890},[892,44855,44856,44864],{},[895,44857,44858,44860,44862],{},[898,44859,1769],{},[1711,44861,1836],{},[2111,44863,6262],{},[902,44865,44866],{"encoding":904},"T = 6",[883,44868,44870],{"className":44869},[886],[888,44871,44872],{"xmlns":890},[892,44873,44874,44896],{},[895,44875,44876,44882,44884,44886,44888,44890,44892,44894],{},[2884,44877,44878,44880],{},[898,44879,2362],{},[2111,44881,2238],{},[1711,44883,2062],{},[898,44885,7929],{},[1711,44887,1836],{},[2111,44889,2963],{},[898,44891,6796],{},[1711,44893,2095],{},[2111,44895,6262],{},[902,44897,44898],{"encoding":904},"S_1: P = 2Q + 6",[724,44900,44901],{},[614,44902,44903,44904,44917],{},"Obrázek 2.12: Posun nabídky o ",[883,44905,44907],{"className":44906},[886],[888,44908,44909],{"xmlns":890},[892,44910,44911,44915],{},[895,44912,44913],{},[898,44914,1769],{},[902,44916,1769],{"encoding":904}," svisle nahoru.",[40568,44919],{},[115,44921,44923],{"id":44922},"tržní-rovnováha","Tržní rovnováha",[1921,44925,44926],{},[724,44927,44928,44930,44931,1700,44934,44966,44967,1343,44990,45013,45014,45017,45018,45031],{},[883,44929,2678],{}," TL;DR\nV ",[38,44932,44933],{},"rovnovážném bodě",[883,44935,44937],{"className":44936},[886],[888,44938,44939],{"xmlns":890},[892,44940,44941,44963],{},[895,44942,44943,44945,44947,44953,44955,44961],{},[898,44944,1722],{},[1711,44946,5144],{"stretchy":1713},[1716,44948,44949,44951],{},[898,44950,6796],{},[898,44952,1722],{},[1711,44954,1726],{"separator":1725},[1716,44956,44957,44959],{},[898,44958,7929],{},[898,44960,1722],{},[1711,44962,5163],{"stretchy":1713},[902,44964,44965],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,44968,44970],{"className":44969},[886],[888,44971,44972],{"xmlns":890},[892,44973,44974,44988],{},[895,44975,44976,44978,44980,44982,44984,44986],{},[898,44977,7929],{},[1711,44979,1836],{},[898,44981,2778],{},[1711,44983,1714],{"stretchy":1713},[898,44985,6796],{},[1711,44987,1735],{"stretchy":1713},[902,44989,8625],{"encoding":904},[883,44991,44993],{"className":44992},[886],[888,44994,44995],{"xmlns":890},[892,44996,44997,45011],{},[895,44998,44999,45001,45003,45005,45007,45009],{},[898,45000,7929],{},[1711,45002,1836],{},[898,45004,2362],{},[1711,45006,1714],{"stretchy":1713},[898,45008,6796],{},[1711,45010,1735],{"stretchy":1713},[902,45012,44669],{"encoding":904},". Čtyři ",[38,45015,45016],{},"pravidla komparativní statiky"," popisují, jak se ",[883,45019,45021],{"className":45020},[886],[888,45022,45023],{"xmlns":890},[892,45024,45025,45029],{},[895,45026,45027],{},[898,45028,1722],{},[902,45030,1722],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,45033,45035],{"id":45034},"definice","Definice",[724,45037,45038,1648,45040,45043,45044,1700,45047,45065,45066,45097,45098,1648,45101,1797],{},[38,45039,44923],{},[614,45041,45042],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,45045,45046],{},"rovnovážné ceně",[883,45048,45050],{"className":45049},[886],[888,45051,45052],{"xmlns":890},[892,45053,45054,45062],{},[895,45055,45056],{},[1716,45057,45058,45060],{},[898,45059,7929],{},[898,45061,1722],{},[902,45063,45064],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,45067,45069],{"className":45068},[886],[888,45070,45071],{"xmlns":890},[892,45072,45073,45095],{},[895,45074,45075,45077,45079,45085,45087,45093],{},[898,45076,1722],{},[1711,45078,5144],{"stretchy":1713},[1716,45080,45081,45083],{},[898,45082,6796],{},[898,45084,1722],{},[1711,45086,1726],{"separator":1725},[1716,45088,45089,45091],{},[898,45090,7929],{},[898,45092,1722],{},[1711,45094,5163],{"stretchy":1713},[902,45096,44965],{"encoding":904}," se nazývá ",[38,45099,45100],{},"rovnovážný bod",[614,45102,45103],{},"equilibrium point",[724,45105,45106,45107,1343,45130,2186],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,45108,45110],{"className":45109},[886],[888,45111,45112],{"xmlns":890},[892,45113,45114,45128],{},[895,45115,45116,45118,45120,45122,45124,45126],{},[898,45117,7929],{},[1711,45119,1836],{},[898,45121,2778],{},[1711,45123,1714],{"stretchy":1713},[898,45125,6796],{},[1711,45127,1735],{"stretchy":1713},[902,45129,8625],{"encoding":904},[883,45131,45133],{"className":45132},[886],[888,45134,45135],{"xmlns":890},[892,45136,45137,45151],{},[895,45138,45139,45141,45143,45145,45147,45149],{},[898,45140,7929],{},[1711,45142,1836],{},[898,45144,2362],{},[1711,45146,1714],{"stretchy":1713},[898,45148,6796],{},[1711,45150,1735],{"stretchy":1713},[902,45152,44669],{"encoding":904},[724,45154,45155],{},[1801,45156],{"alt":45157,"className":45158,"src":45159},"imek-poptavka-nabidka-rovnovaha",[210,1805],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,45161,45162],{},[614,45163,45164,45165,45178,45179,3695,45192,45213,45214,2186],{},"Obrázek 2.13: Klesající ",[883,45166,45168],{"className":45167},[886],[888,45169,45170],{"xmlns":890},[892,45171,45172,45176],{},[895,45173,45174],{},[898,45175,2778],{},[902,45177,2778],{"encoding":904}," a rostoucí ",[883,45180,45182],{"className":45181},[886],[888,45183,45184],{"xmlns":890},[892,45185,45186,45190],{},[895,45187,45188],{},[898,45189,2362],{},[902,45191,2362],{"encoding":904},[883,45193,45195],{"className":45194},[886],[888,45196,45197],{"xmlns":890},[892,45198,45199,45211],{},[895,45200,45201,45203,45205,45207,45209],{},[1711,45202,1714],{"stretchy":1713},[898,45204,6796],{},[1711,45206,1726],{"separator":1725},[898,45208,7929],{},[1711,45210,1735],{"stretchy":1713},[902,45212,41289],{"encoding":904}," protínající se v ",[883,45215,45217],{"className":45216},[886],[888,45218,45219],{"xmlns":890},[892,45220,45221,45243],{},[895,45222,45223,45225,45227,45233,45235,45241],{},[898,45224,1722],{},[1711,45226,5144],{"stretchy":1713},[1716,45228,45229,45231],{},[898,45230,6796],{},[898,45232,1722],{},[1711,45234,1726],{"separator":1725},[1716,45236,45237,45239],{},[898,45238,7929],{},[898,45240,1722],{},[1711,45242,5163],{"stretchy":1713},[902,45244,44965],{"encoding":904},[198,45246,45248],{"id":45247},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,45250,45251,45253,45254,45288,45289,2186],{},[38,45252,41531],{}," Poptávka ",[883,45255,45257],{"className":45256},[886],[888,45258,45259],{"xmlns":890},[892,45260,45261,45285],{},[895,45262,45263,45265,45267,45269,45275,45277,45279,45281,45283],{},[898,45264,7929],{},[1711,45266,1836],{},[1711,45268,2460],{},[1716,45270,45271,45273],{},[898,45272,6796],{},[2111,45274,2963],{},[1711,45276,2460],{},[2111,45278,4712],{},[898,45280,6796],{},[1711,45282,2095],{},[2111,45284,12781],{},[902,45286,45287],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,45290,45292],{"className":45291},[886],[888,45293,45294],{"xmlns":890},[892,45295,45296,45318],{},[895,45297,45298,45300,45302,45308,45310,45312,45314,45316],{},[898,45299,7929],{},[1711,45301,1836],{},[1716,45303,45304,45306],{},[898,45305,6796],{},[2111,45307,2963],{},[1711,45309,2095],{},[2111,45311,26544],{},[898,45313,6796],{},[1711,45315,2095],{},[2111,45317,36144],{},[902,45319,45320],{"encoding":904},"P = Q^2 + 14Q + 22",[724,45322,45323,45325],{},[38,45324,41563],{}," Z rovnosti",[883,45327,45329],{"className":45328},[886],[888,45330,45331],{"xmlns":890,"display":31664},[892,45332,45333,45371],{},[895,45334,45335,45337,45343,45345,45347,45349,45351,45353,45355,45361,45363,45365,45367,45369],{},[1711,45336,2460],{},[1716,45338,45339,45341],{},[898,45340,6796],{},[2111,45342,2963],{},[1711,45344,2460],{},[2111,45346,4712],{},[898,45348,6796],{},[1711,45350,2095],{},[2111,45352,12781],{},[1711,45354,1836],{},[1716,45356,45357,45359],{},[898,45358,6796],{},[2111,45360,2963],{},[1711,45362,2095],{},[2111,45364,26544],{},[898,45366,6796],{},[1711,45368,2095],{},[2111,45370,36144],{},[902,45372,45373],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,45375,45376,45377,45412,45413,45446,45447,45464,45465,45478,45479,1343,45501,45538,45539,2186],{},"dostaneme ",[883,45378,45380],{"className":45379},[886],[888,45381,45382],{"xmlns":890},[892,45383,45384,45409],{},[895,45385,45386,45388,45394,45396,45399,45401,45403,45405,45407],{},[2111,45387,2963],{},[1716,45389,45390,45392],{},[898,45391,6796],{},[2111,45393,2963],{},[1711,45395,2095],{},[2111,45397,45398],{},"24",[898,45400,6796],{},[1711,45402,2460],{},[2111,45404,9600],{},[1711,45406,1836],{},[2111,45408,2113],{},[902,45410,45411],{"encoding":904},"2Q^2 + 24Q - 128 = 0",", resp. ",[883,45414,45416],{"className":45415},[886],[888,45417,45418],{"xmlns":890},[892,45419,45420,45443],{},[895,45421,45422,45428,45430,45432,45434,45436,45439,45441],{},[1716,45423,45424,45426],{},[898,45425,6796],{},[2111,45427,2963],{},[1711,45429,2095],{},[2111,45431,7505],{},[898,45433,6796],{},[1711,45435,2460],{},[2111,45437,45438],{},"64",[1711,45440,1836],{},[2111,45442,2113],{},[902,45444,45445],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,45448,45450],{"className":45449},[886],[888,45451,45452],{"xmlns":890},[892,45453,45454,45461],{},[895,45455,45456,45458],{},[1711,45457,2460],{},[2111,45459,45460],{},"16",[902,45462,45463],{"encoding":904},"-16"," (nevyhovuje) a ",[883,45466,45468],{"className":45467},[886],[888,45469,45470],{"xmlns":890},[892,45471,45472,45476],{},[895,45473,45474],{},[2111,45475,6369],{},[902,45477,6369],{"encoding":904},". Tedy ",[883,45480,45482],{"className":45481},[886],[888,45483,45484],{"xmlns":890},[892,45485,45486,45498],{},[895,45487,45488,45494,45496],{},[1716,45489,45490,45492],{},[898,45491,6796],{},[898,45493,1722],{},[1711,45495,1836],{},[2111,45497,6369],{},[902,45499,45500],{"encoding":904},"Q^E = 4",[883,45502,45504],{"className":45503},[886],[888,45505,45506],{"xmlns":890},[892,45507,45508,45535],{},[895,45509,45510,45516,45518,45520,45522,45524,45526,45528,45530,45532],{},[1716,45511,45512,45514],{},[898,45513,7929],{},[898,45515,1722],{},[1711,45517,1836],{},[1711,45519,2460],{},[2111,45521,45460],{},[1711,45523,2460],{},[2111,45525,9195],{},[1711,45527,2095],{},[2111,45529,12781],{},[1711,45531,1836],{},[2111,45533,45534],{},"94",[902,45536,45537],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,45540,45542],{"className":45541},[886],[888,45543,45544],{"xmlns":890},[892,45545,45546,45560],{},[895,45547,45548,45550,45552,45554,45556,45558],{},[898,45549,1722],{},[1711,45551,5144],{"stretchy":1713},[2111,45553,6369],{},[1711,45555,1726],{"separator":1725},[2111,45557,45534],{},[1711,45559,5163],{"stretchy":1713},[902,45561,45562],{"encoding":904},"E[4, 94]",[198,45564,45566],{"id":45565},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,45568,45569,45571],{},[38,45570,41531],{}," Poptávky a nabídky dvou zboží",[883,45573,45575],{"className":45574},[886],[888,45576,45577],{"xmlns":890,"display":31664},[892,45578,45579,45745],{},[24352,45580,45583,45671],{"rowspacing":24354,"columnalign":45581,"columnspacing":45582},"right left right left","0em 1em 0em",[24357,45584,45585,45595,45627,45637],{},[24360,45586,45587],{},[2509,45588,45589],{"scriptlevel":2113,"displaystyle":1725},[2884,45590,45591,45593],{},[898,45592,6796],{},[2111,45594,2238],{},[24360,45596,45597],{},[2509,45598,45599],{"scriptlevel":2113,"displaystyle":1725},[895,45600,45601,45603,45605,45607,45609,45611,45617,45619,45625],{},[895,45602],{},[1711,45604,1836],{},[2111,45606,9195],{},[1711,45608,2460],{},[2111,45610,4798],{},[2884,45612,45613,45615],{},[898,45614,7929],{},[2111,45616,2238],{},[1711,45618,2460],{},[2884,45620,45621,45623],{},[898,45622,7929],{},[2111,45624,2963],{},[1711,45626,1726],{"separator":1725},[24360,45628,45629],{},[2509,45630,45631],{"scriptlevel":2113,"displaystyle":1725},[2884,45632,45633,45635],{},[898,45634,6796],{},[2111,45636,2963],{},[24360,45638,45639],{},[2509,45640,45641],{"scriptlevel":2113,"displaystyle":1725},[895,45642,45643,45645,45647,45649,45651,45653,45659,45661,45663,45669],{},[895,45644],{},[1711,45646,1836],{},[2111,45648,7120],{},[1711,45650,2460],{},[2111,45652,2963],{},[2884,45654,45655,45657],{},[898,45656,7929],{},[2111,45658,2238],{},[1711,45660,2460],{},[2111,45662,6369],{},[2884,45664,45665,45667],{},[898,45666,7929],{},[2111,45668,2963],{},[1711,45670,1726],{"separator":1725},[24357,45672,45673,45683,45709,45719],{},[24360,45674,45675],{},[2509,45676,45677],{"scriptlevel":2113,"displaystyle":1725},[2884,45678,45679,45681],{},[898,45680,6796],{},[2111,45682,2238],{},[24360,45684,45685],{},[2509,45686,45687],{"scriptlevel":2113,"displaystyle":1725},[895,45688,45689,45691,45693,45695,45697,45699,45701,45707],{},[895,45690],{},[1711,45692,1836],{},[1711,45694,2460],{},[2111,45696,3034],{},[1711,45698,2095],{},[2111,45700,6369],{},[2884,45702,45703,45705],{},[898,45704,7929],{},[2111,45706,2238],{},[1711,45708,1726],{"separator":1725},[24360,45710,45711],{},[2509,45712,45713],{"scriptlevel":2113,"displaystyle":1725},[2884,45714,45715,45717],{},[898,45716,6796],{},[2111,45718,2963],{},[24360,45720,45721],{},[2509,45722,45723],{"scriptlevel":2113,"displaystyle":1725},[895,45724,45725,45727,45729,45731,45733,45735,45737,45743],{},[895,45726],{},[1711,45728,1836],{},[1711,45730,2460],{},[2111,45732,27799],{},[1711,45734,2095],{},[2111,45736,3034],{},[2884,45738,45739,45741],{},[898,45740,7929],{},[2111,45742,2963],{},[898,45744,2186],{"mathvariant":2287},[902,45746,45747],{"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}",[724,45749,45750,45752],{},[38,45751,41563],{}," Z rovností poptávek a nabídek dostaneme",[883,45754,45756],{"className":45755},[886],[888,45757,45758],{"xmlns":890,"display":31664},[892,45759,45760,45809],{},[895,45761,45762,45764,45770,45772,45778,45780,45782,45784,45786,45788,45794,45796,45798,45804,45806],{},[2111,45763,7990],{},[2884,45765,45766,45768],{},[898,45767,7929],{},[2111,45769,2238],{},[1711,45771,2095],{},[2884,45773,45774,45776],{},[898,45775,7929],{},[2111,45777,2963],{},[1711,45779,1836],{},[2111,45781,24801],{},[1711,45783,1726],{"separator":1725},[2102,45785],{"width":2104},[2111,45787,2963],{},[2884,45789,45790,45792],{},[898,45791,7929],{},[2111,45793,2238],{},[1711,45795,2095],{},[2111,45797,27799],{},[2884,45799,45800,45802],{},[898,45801,7929],{},[2111,45803,2963],{},[1711,45805,1836],{},[2111,45807,45808],{},"57.",[902,45810,45811],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,45813,45814,45815,1343,45839,45863,45864,1343,45889,45913,45914,45916],{},"Řešením je ",[883,45816,45818],{"className":45817},[886],[888,45819,45820],{"xmlns":890},[892,45821,45822,45836],{},[895,45823,45824,45832,45834],{},[13142,45825,45826,45828,45830],{},[898,45827,7929],{},[2111,45829,2238],{},[898,45831,1722],{},[1711,45833,1836],{},[2111,45835,6369],{},[902,45837,45838],{"encoding":904},"P_1^E = 4",[883,45840,45842],{"className":45841},[886],[888,45843,45844],{"xmlns":890},[892,45845,45846,45860],{},[895,45847,45848,45856,45858],{},[13142,45849,45850,45852,45854],{},[898,45851,7929],{},[2111,45853,2963],{},[898,45855,1722],{},[1711,45857,1836],{},[2111,45859,27799],{},[902,45861,45862],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,45865,45867],{"className":45866},[886],[888,45868,45869],{"xmlns":890},[892,45870,45871,45886],{},[895,45872,45873,45881,45883],{},[13142,45874,45875,45877,45879],{},[898,45876,6796],{},[2111,45878,2238],{},[898,45880,1722],{},[1711,45882,1836],{},[2111,45884,45885],{},"13",[902,45887,45888],{"encoding":904},"Q_1^E = 13",[883,45890,45892],{"className":45891},[886],[888,45893,45894],{"xmlns":890},[892,45895,45896,45910],{},[895,45897,45898,45906,45908],{},[13142,45899,45900,45902,45904],{},[898,45901,6796],{},[2111,45903,2963],{},[898,45905,1722],{},[1711,45907,1836],{},[2111,45909,26544],{},[902,45911,45912],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,45915,43420],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,45918,45920],{"id":45919},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,45922,45923,45924,45941,45942,1648,45945,1797],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,45925,45927],{"className":45926},[886],[888,45928,45929],{"xmlns":890},[892,45930,45931,45939],{},[895,45932,45933],{},[1716,45934,45935,45937],{},[898,45936,7929],{},[898,45938,1722],{},[902,45940,45064],{"encoding":904},"; mechanismus popisuje ",[38,45943,45944],{},"teorém pavučiny",[614,45946,45947],{},"cobweb model",[198,45949,45951],{"id":45950},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,45953,45954],{},[1801,45955],{"alt":45956,"className":45957,"src":45958},"imek-komparativni-statika-4pripady",[210,1805],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[1921,45960,45961,46002,46042,46082],{},[724,45962,45963,45966,45967,10171,45984,2186],{},[38,45964,45965],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,45968,45970],{"className":45969},[886],[888,45971,45972],{"xmlns":890},[892,45973,45974,45982],{},[895,45975,45976],{},[1716,45977,45978,45980],{},[898,45979,7929],{},[898,45981,1722],{},[902,45983,45064],{"encoding":904},[883,45985,45987],{"className":45986},[886],[888,45988,45989],{"xmlns":890},[892,45990,45991,45999],{},[895,45992,45993],{},[1716,45994,45995,45997],{},[898,45996,6796],{},[898,45998,1722],{},[902,46000,46001],{"encoding":904},"Q^E",[724,46003,46004,46007,46008,10171,46025,2186],{},[38,46005,46006],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,46009,46011],{"className":46010},[886],[888,46012,46013],{"xmlns":890},[892,46014,46015,46023],{},[895,46016,46017],{},[1716,46018,46019,46021],{},[898,46020,7929],{},[898,46022,1722],{},[902,46024,45064],{"encoding":904},[883,46026,46028],{"className":46027},[886],[888,46029,46030],{"xmlns":890},[892,46031,46032,46040],{},[895,46033,46034],{},[1716,46035,46036,46038],{},[898,46037,6796],{},[898,46039,1722],{},[902,46041,46001],{"encoding":904},[724,46043,46044,46047,46048,13331,46065,2186],{},[38,46045,46046],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,46049,46051],{"className":46050},[886],[888,46052,46053],{"xmlns":890},[892,46054,46055,46063],{},[895,46056,46057],{},[1716,46058,46059,46061],{},[898,46060,7929],{},[898,46062,1722],{},[902,46064,45064],{"encoding":904},[883,46066,46068],{"className":46067},[886],[888,46069,46070],{"xmlns":890},[892,46071,46072,46080],{},[895,46073,46074],{},[1716,46075,46076,46078],{},[898,46077,6796],{},[898,46079,1722],{},[902,46081,46001],{"encoding":904},[724,46083,46084,46087,46088,46105,46106,2186],{},[38,46085,46086],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,46089,46091],{"className":46090},[886],[888,46092,46093],{"xmlns":890},[892,46094,46095,46103],{},[895,46096,46097],{},[1716,46098,46099,46101],{},[898,46100,7929],{},[898,46102,1722],{},[902,46104,45064],{"encoding":904},", pokles ",[883,46107,46109],{"className":46108},[886],[888,46110,46111],{"xmlns":890},[892,46112,46113,46121],{},[895,46114,46115],{},[1716,46116,46117,46119],{},[898,46118,6796],{},[898,46120,1722],{},[902,46122,46001],{"encoding":904},[16,46124,46125,46170],{},[19,46126,46127],{},[22,46128,46129,46132,46151],{},[25,46130,46131],{},"Změna",[25,46133,46134],{},[883,46135,46137],{"className":46136},[886],[888,46138,46139],{"xmlns":890},[892,46140,46141,46149],{},[895,46142,46143],{},[1716,46144,46145,46147],{},[898,46146,7929],{},[898,46148,1722],{},[902,46150,45064],{"encoding":904},[25,46152,46153],{},[883,46154,46156],{"className":46155},[886],[888,46157,46158],{"xmlns":890},[892,46159,46160,46168],{},[895,46161,46162],{},[1716,46163,46164,46166],{},[898,46165,6796],{},[898,46167,1722],{},[902,46169,46001],{"encoding":904},[30,46171,46172,46182,46192,46201],{},[22,46173,46174,46177,46180],{},[35,46175,46176],{},"Růst poptávky",[35,46178,46179],{},"↑",[35,46181,46179],{},[22,46183,46184,46187,46190],{},[35,46185,46186],{},"Pokles poptávky",[35,46188,46189],{},"↓",[35,46191,46189],{},[22,46193,46194,46197,46199],{},[35,46195,46196],{},"Růst nabídky",[35,46198,46189],{},[35,46200,46179],{},[22,46202,46203,46206,46208],{},[35,46204,46205],{},"Pokles nabídky",[35,46207,46179],{},[35,46209,46189],{},[724,46211,46212],{},[614,46213,46214],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[40568,46216],{},[115,46218,811],{"id":46219},"zdanění-trhu",[1921,46221,46222,46311],{},[724,46223,46224,46226,46227,46240,46241,2801,46254,46257,46258,40374,46281,46306,46307,46310],{},[883,46225,2678],{}," TL;DR\nJednotková daň ",[883,46228,46230],{"className":46229},[886],[888,46231,46232],{"xmlns":890},[892,46233,46234,46238],{},[895,46235,46236],{},[898,46237,1769],{},[902,46239,1769],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,46242,46244],{"className":46243},[886],[888,46245,46246],{"xmlns":890},[892,46247,46248,46252],{},[895,46249,46250],{},[898,46251,1769],{},[902,46253,1769],{"encoding":904},[38,46255,46256],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,46259,46261],{"className":46260},[886],[888,46262,46263],{"xmlns":890},[892,46264,46265,46278],{},[895,46266,46267],{},[2884,46268,46269,46271],{},[898,46270,1769],{},[895,46272,46273,46276],{},[898,46274,46275],{},"s",[898,46277,724],{},[902,46279,46280],{"encoding":904},"T_{sp}",[883,46282,46284],{"className":46283},[886],[888,46285,46286],{"xmlns":890},[892,46287,46288,46303],{},[895,46289,46290],{},[2884,46291,46292,46294],{},[898,46293,1769],{},[895,46295,46296,46299,46301],{},[898,46297,46298],{},"v",[898,46300,6038],{},[898,46302,1675],{},[902,46304,46305],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,46308,46309],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,46312,46313],{},[614,46314,46315,46316,2186],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,46317,46319],{"className":46318,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,46321,46322,46323,46326,46327,46353,46354,46357,46358,46384,46385,46402,46403,46443,46444,2009,46457,2186],{},"Existují dvě formy zdanění — daň uložená ",[38,46324,46325],{},"výrobci"," (posun nabídky ",[883,46328,46330],{"className":46329},[886],[888,46331,46332],{"xmlns":890},[892,46333,46334,46350],{},[895,46335,46336,46342,46344,46346,46348],{},[2884,46337,46338,46340],{},[898,46339,2362],{},[2111,46341,2238],{},[1711,46343,1836],{},[898,46345,2362],{},[1711,46347,2095],{},[898,46349,1769],{},[902,46351,46352],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,46355,46356],{},"spotřebiteli"," (posun poptávky ",[883,46359,46361],{"className":46360},[886],[888,46362,46363],{"xmlns":890},[892,46364,46365,46381],{},[895,46366,46367,46373,46375,46377,46379],{},[2884,46368,46369,46371],{},[898,46370,2778],{},[2111,46372,2963],{},[1711,46374,1836],{},[898,46376,2778],{},[1711,46378,2460],{},[898,46380,1769],{},[902,46382,46383],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,46386,46388],{"className":46387},[886],[888,46389,46390],{"xmlns":890},[892,46391,46392,46400],{},[895,46393,46394],{},[1716,46395,46396,46398],{},[898,46397,6796],{},[898,46399,1722],{},[902,46401,46001],{"encoding":904}," klesá a vzniká rozklad daně ",[883,46404,46406],{"className":46405},[886],[888,46407,46408],{"xmlns":890},[892,46409,46410,46440],{},[895,46411,46412,46414,46416,46426,46428],{},[898,46413,1769],{},[1711,46415,1836],{},[2884,46417,46418,46420],{},[898,46419,1769],{},[895,46421,46422,46424],{},[898,46423,46275],{},[898,46425,724],{},[1711,46427,2095],{},[2884,46429,46430,46432],{},[898,46431,1769],{},[895,46433,46434,46436,46438],{},[898,46435,46298],{},[898,46437,6038],{},[898,46439,1675],{},[902,46441,46442],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,46445,46447],{"className":46446},[886],[888,46448,46449],{"xmlns":890},[892,46450,46451,46455],{},[895,46452,46453],{},[898,46454,2778],{},[902,46456,2778],{"encoding":904},[883,46458,46460],{"className":46459},[886],[888,46461,46462],{"xmlns":890},[892,46463,46464,46468],{},[895,46465,46466],{},[898,46467,2362],{},[902,46469,2362],{"encoding":904},[724,46471,46472,46473,46476,46477,2009,46507,46541],{},"Zásadním výsledkem kapitoly je ",[38,46474,46475],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,46478,46480],{"className":46479},[886],[888,46481,46482],{"xmlns":890},[892,46483,46484,46504],{},[895,46485,46486,46494,46496],{},[13142,46487,46488,46490,46492],{},[898,46489,6796],{},[2111,46491,2238],{},[898,46493,1722],{},[1711,46495,1836],{},[13142,46497,46498,46500,46502],{},[898,46499,6796],{},[2111,46501,2963],{},[898,46503,1722],{},[902,46505,46506],{"encoding":904},"Q_1^E = Q_2^E",[883,46508,46510],{"className":46509},[886],[888,46511,46512],{"xmlns":890},[892,46513,46514,46538],{},[895,46515,46516,46524,46526,46528,46530],{},[13142,46517,46518,46520,46522],{},[898,46519,7929],{},[2111,46521,2238],{},[898,46523,1722],{},[1711,46525,2460],{},[898,46527,1769],{},[1711,46529,1836],{},[13142,46531,46532,46534,46536],{},[898,46533,7929],{},[2111,46535,2963],{},[898,46537,1722],{},[902,46539,46540],{"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.",[724,46543,46544,46545,46548,46549,46575,46576,46604,46605,46608,46609,46612,46613,2186],{},"Podrobný výklad, Příklady ",[38,46546,46547],{},"2.9"," (daň výrobci, ",[883,46550,46552],{"className":46551},[886],[888,46553,46554],{"xmlns":890},[892,46555,46556,46572],{},[895,46557,46558,46568,46570],{},[2884,46559,46560,46562],{},[898,46561,1769],{},[895,46563,46564,46566],{},[898,46565,46275],{},[898,46567,724],{},[1711,46569,1836],{},[2111,46571,2963],{},[902,46573,46574],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,46577,46579],{"className":46578},[886],[888,46580,46581],{"xmlns":890},[892,46582,46583,46601],{},[895,46584,46585,46597,46599],{},[2884,46586,46587,46589],{},[898,46588,1769],{},[895,46590,46591,46593,46595],{},[898,46592,46298],{},[898,46594,6038],{},[898,46596,1675],{},[1711,46598,1836],{},[2111,46600,6369],{},[902,46602,46603],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,46606,46607],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,46610,46611],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,46614,46319],{"className":46615,"dataFsResolvedFilePath":809,"href":810},[210],[40568,46617],{},[115,46619,46621],{"id":46620},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[1921,46623,46624],{},[724,46625,46626,46628,46629,46632,46633,46635],{},[883,46627,2678],{}," TL;DR\nMultiplikátory jsou ",[38,46630,46631],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,46634,40558],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,46637,46639],{"id":46638},"redukovaný-tvar","Redukovaný tvar",[724,46641,46642,46643,1648,46666,1343,46684,1772,46701,1648,46724,46741,46742,46772],{},"Pro lineární model ",[883,46644,46646],{"className":46645},[886],[888,46647,46648],{"xmlns":890},[892,46649,46650,46664],{},[895,46651,46652,46654,46656,46658,46660,46662],{},[898,46653,7929],{},[1711,46655,1836],{},[898,46657,207],{},[898,46659,6796],{},[1711,46661,2095],{},[898,46663,2223],{},[902,46665,40658],{"encoding":904},[883,46667,46669],{"className":46668},[886],[888,46670,46671],{"xmlns":890},[892,46672,46673,46681],{},[895,46674,46675,46677,46679],{},[898,46676,207],{},[1711,46678,2109],{},[2111,46680,2113],{},[902,46682,46683],{"encoding":904},"a \u003C 0",[883,46685,46687],{"className":46686},[886],[888,46688,46689],{"xmlns":890},[892,46690,46691,46699],{},[895,46692,46693,46695,46697],{},[898,46694,2223],{},[1711,46696,2123],{},[2111,46698,2113],{},[902,46700,22412],{"encoding":904},[883,46702,46704],{"className":46703},[886],[888,46705,46706],{"xmlns":890},[892,46707,46708,46722],{},[895,46709,46710,46712,46714,46716,46718,46720],{},[898,46711,7929],{},[1711,46713,1836],{},[898,46715,2090],{},[898,46717,6796],{},[1711,46719,2095],{},[898,46721,2098],{},[902,46723,43840],{"encoding":904},[883,46725,46727],{"className":46726},[886],[888,46728,46729],{"xmlns":890},[892,46730,46731,46739],{},[895,46732,46733,46735,46737],{},[898,46734,2090],{},[1711,46736,2123],{},[2111,46738,2113],{},[902,46740,43858],{"encoding":904},") dává podmínka rovnováhy ",[883,46743,46745],{"className":46744},[886],[888,46746,46747],{"xmlns":890},[892,46748,46749,46769],{},[895,46750,46751,46753,46755,46757,46759,46761,46763,46765,46767],{},[898,46752,207],{},[898,46754,6796],{},[1711,46756,2095],{},[898,46758,2223],{},[1711,46760,1836],{},[898,46762,2090],{},[898,46764,6796],{},[1711,46766,2095],{},[898,46768,2098],{},[902,46770,46771],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,46774,46776],{"className":46775},[886],[888,46777,46778],{"xmlns":890,"display":31664},[892,46779,46780,46825],{},[24352,46781,46782],{"width":31669},[24357,46783,46784,46786,46818,46820],{},[24360,46785],{"width":31674},[24360,46787,46788],{},[895,46789,46790,46796,46798,46816],{},[1716,46791,46792,46794],{},[898,46793,6796],{},[898,46795,1722],{},[1711,46797,1836],{},[2525,46799,46800,46808],{},[895,46801,46802,46804,46806],{},[898,46803,2223],{},[1711,46805,2460],{},[898,46807,2098],{},[895,46809,46810,46812,46814],{},[898,46811,2090],{},[1711,46813,2460],{},[898,46815,207],{},[898,46817,2186],{"mathvariant":2287},[24360,46819],{"width":31674},[24360,46821,46822],{},[1942,46823,46824],{},"(2.10)",[902,46826,46827],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,46829,46830,46831,1648,46833,46836,46837,46854,46855,1700,46858,46884,46885,46898,46899,46917,46918,1797],{},"Vztah (2.10) je ",[38,46832,24552],{},[614,46834,46835],{},"reduced form",") pro ",[883,46838,46840],{"className":46839},[886],[888,46841,46842],{"xmlns":890},[892,46843,46844,46852],{},[895,46845,46846],{},[1716,46847,46848,46850],{},[898,46849,6796],{},[898,46851,1722],{},[902,46853,46001],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,46856,46857],{},"parametrů",[883,46859,46861],{"className":46860},[886],[888,46862,46863],{"xmlns":890},[892,46864,46865,46881],{},[895,46866,46867,46869,46871,46873,46875,46877,46879],{},[898,46868,207],{},[1711,46870,1726],{"separator":1725},[898,46872,2223],{},[1711,46874,1726],{"separator":1725},[898,46876,2090],{},[1711,46878,1726],{"separator":1725},[898,46880,2098],{},[902,46882,46883],{"encoding":904},"a, b, c, d",". Aby ",[883,46886,46888],{"className":46887},[886],[888,46889,46890],{"xmlns":890},[892,46891,46892,46896],{},[895,46893,46894],{},[898,46895,1722],{},[902,46897,1722],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,46900,46902],{"className":46901},[886],[888,46903,46904],{"xmlns":890},[892,46905,46906,46914],{},[895,46907,46908,46910,46912],{},[898,46909,2223],{},[1711,46911,2123],{},[898,46913,2098],{},[902,46915,46916],{"encoding":904},"b > d"," (neboť ",[883,46919,46921],{"className":46920},[886],[888,46922,46923],{"xmlns":890},[892,46924,46925,46937],{},[895,46926,46927,46929,46931,46933,46935],{},[898,46928,2090],{},[1711,46930,2460],{},[898,46932,207],{},[1711,46934,2123],{},[2111,46936,2113],{},[902,46938,46939],{"encoding":904},"c - a > 0",[724,46941,46942],{},[614,46943,46944,46945,46958,46959,46972,46973,22246,46986,45538,47003,47016],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,46946,46948],{"className":46947},[886],[888,46949,46950],{"xmlns":890},[892,46951,46952,46956],{},[895,46953,46954],{},[898,46955,2223],{},[902,46957,2223],{"encoding":904}," na ose ",[883,46960,46962],{"className":46961},[886],[888,46963,46964],{"xmlns":890},[892,46965,46966,46970],{},[895,46967,46968],{},[898,46969,7929],{},[902,46971,7929],{"encoding":904},") a nabídka (úsek ",[883,46974,46976],{"className":46975},[886],[888,46977,46978],{"xmlns":890},[892,46979,46980,46984],{},[895,46981,46982],{},[898,46983,2098],{},[902,46985,2098],{"encoding":904},[883,46987,46989],{"className":46988},[886],[888,46990,46991],{"xmlns":890},[892,46992,46993,47001],{},[895,46994,46995,46997,46999],{},[898,46996,2223],{},[1711,46998,2123],{},[898,47000,2098],{},[902,47002,46916],{"encoding":904},[883,47004,47006],{"className":47005},[886],[888,47007,47008],{"xmlns":890},[892,47009,47010,47014],{},[895,47011,47012],{},[898,47013,1722],{},[902,47015,1722],{"encoding":904}," v 1. kvadrantu.",[198,47018,47020],{"id":47019},"definice-multiplikátorů","Definice multiplikátorů",[724,47022,47023,47024,47049,47050,47063,47064,47077],{},"V komparativní statice jsou ",[883,47025,47027],{"className":47026},[886],[888,47028,47029],{"xmlns":890},[892,47030,47031,47047],{},[895,47032,47033,47035,47037,47039,47041,47043,47045],{},[898,47034,207],{},[1711,47036,1726],{"separator":1725},[898,47038,2223],{},[1711,47040,1726],{"separator":1725},[898,47042,2090],{},[1711,47044,1726],{"separator":1725},[898,47046,2098],{},[902,47048,46883],{"encoding":904}," exogenní proměnné a ",[883,47051,47053],{"className":47052},[886],[888,47054,47055],{"xmlns":890},[892,47056,47057,47061],{},[895,47058,47059],{},[898,47060,6796],{},[902,47062,6796],{"encoding":904}," endogenní. Přibližná změna ",[883,47065,47067],{"className":47066},[886],[888,47068,47069],{"xmlns":890},[892,47070,47071,47075],{},[895,47072,47073],{},[898,47074,6796],{},[902,47076,6796],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,47079,47081],{"className":47080},[886],[888,47082,47083],{"xmlns":890,"display":31664},[892,47084,47085,47178],{},[24352,47086,47087],{"width":31669},[24357,47088,47089,47091,47171,47173],{},[24360,47090],{"width":31674},[24360,47092,47093],{},[895,47094,47095,47097,47099,47101,47103,47105,47107,47115,47117,47119,47121,47123,47131,47133,47135,47137,47139,47147,47149,47151,47153,47155,47163,47165,47167,47169],{},[898,47096,6892],{"mathvariant":2287},[898,47098,6796],{},[1711,47100,6740],{},[898,47102,2098],{},[898,47104,6796],{},[1711,47106,1836],{},[13142,47108,47109,47111,47113],{},[898,47110,6796],{},[898,47112,207],{},[1711,47114,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1942,47116,2519],{},[898,47118,2098],{},[898,47120,207],{},[1711,47122,2095],{},[13142,47124,47125,47127,47129],{},[898,47126,6796],{},[898,47128,2223],{},[1711,47130,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1942,47132,2519],{},[898,47134,2098],{},[898,47136,2223],{},[1711,47138,2095],{},[13142,47140,47141,47143,47145],{},[898,47142,6796],{},[898,47144,2090],{},[1711,47146,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1942,47148,2519],{},[898,47150,2098],{},[898,47152,2090],{},[1711,47154,2095],{},[13142,47156,47157,47159,47161],{},[898,47158,6796],{},[898,47160,2098],{},[1711,47162,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1942,47164,2519],{},[898,47166,2098],{},[898,47168,2098],{},[898,47170,2186],{"mathvariant":2287},[24360,47172],{"width":31674},[24360,47174,47175],{},[1942,47176,47177],{},"(2.11)",[902,47179,47180],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,47182,47183,47184,47234,47235,1648,47237,3239],{},"Parciální derivace ",[883,47185,47187],{"className":47186},[886],[888,47188,47189],{"xmlns":890},[892,47190,47191,47231],{},[895,47192,47193,47201,47203,47211,47213,47221,47223],{},[13142,47194,47195,47197,47199],{},[898,47196,6796],{},[898,47198,207],{},[1711,47200,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,47202,1726],{"separator":1725},[13142,47204,47205,47207,47209],{},[898,47206,6796],{},[898,47208,2223],{},[1711,47210,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,47212,1726],{"separator":1725},[13142,47214,47215,47217,47219],{},[898,47216,6796],{},[898,47218,2090],{},[1711,47220,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,47222,1726],{"separator":1725},[13142,47224,47225,47227,47229],{},[898,47226,6796],{},[898,47228,2098],{},[1711,47230,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,47232,47233],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,47236,21575],{},[614,47238,47239],{},"multipliers",[883,47241,47243],{"className":47242},[886],[888,47244,47245],{"xmlns":890,"display":31664},[892,47246,47247,47398],{},[24352,47248,47249],{"width":31669},[24357,47250,47251,47253,47391,47393],{},[24360,47252],{"width":31674},[24360,47254,47255],{},[895,47256,47257,47265,47267,47293,47295,47297,47305,47307,47319,47321,47323,47331,47333,47335,47361,47363,47365,47373,47375,47377,47389],{},[13142,47258,47259,47261,47263],{},[898,47260,6796],{},[898,47262,207],{},[1711,47264,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,47266,1836],{},[2525,47268,47269,47277],{},[895,47270,47271,47273,47275],{},[898,47272,2223],{},[1711,47274,2460],{},[898,47276,2098],{},[895,47278,47279,47281,47283,47285,47287],{},[1711,47280,1714],{"stretchy":1713},[898,47282,2090],{},[1711,47284,2460],{},[898,47286,207],{},[1716,47288,47289,47291],{},[1711,47290,1735],{"stretchy":1713},[2111,47292,2963],{},[1711,47294,1726],{"separator":1725},[2102,47296],{"width":4981},[13142,47298,47299,47301,47303],{},[898,47300,6796],{},[898,47302,2223],{},[1711,47304,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,47306,1836],{},[2525,47308,47309,47311],{},[2111,47310,2238],{},[895,47312,47313,47315,47317],{},[898,47314,2090],{},[1711,47316,2460],{},[898,47318,207],{},[1711,47320,1726],{"separator":1725},[2102,47322],{"width":4981},[13142,47324,47325,47327,47329],{},[898,47326,6796],{},[898,47328,2090],{},[1711,47330,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,47332,1836],{},[1711,47334,2460],{},[2525,47336,47337,47345],{},[895,47338,47339,47341,47343],{},[898,47340,2223],{},[1711,47342,2460],{},[898,47344,2098],{},[895,47346,47347,47349,47351,47353,47355],{},[1711,47348,1714],{"stretchy":1713},[898,47350,2090],{},[1711,47352,2460],{},[898,47354,207],{},[1716,47356,47357,47359],{},[1711,47358,1735],{"stretchy":1713},[2111,47360,2963],{},[1711,47362,1726],{"separator":1725},[2102,47364],{"width":4981},[13142,47366,47367,47369,47371],{},[898,47368,6796],{},[898,47370,2098],{},[1711,47372,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,47374,1836],{},[1711,47376,2460],{},[2525,47378,47379,47381],{},[2111,47380,2238],{},[895,47382,47383,47385,47387],{},[898,47384,2090],{},[1711,47386,2460],{},[898,47388,207],{},[898,47390,2186],{"mathvariant":2287},[24360,47392],{"width":31674},[24360,47394,47395],{},[1942,47396,47397],{},"(2.12)",[902,47399,47400],{"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}",[198,47402,47404],{"id":47403},"znaménka-a-interpretace","Znaménka a interpretace",[724,47406,47407,47408,1343,47425,1343,47442,1343,47459,47476,47477,3239],{},"Za podmínek ",[883,47409,47411],{"className":47410},[886],[888,47412,47413],{"xmlns":890},[892,47414,47415,47423],{},[895,47416,47417,47419,47421],{},[898,47418,207],{},[1711,47420,2109],{},[2111,47422,2113],{},[902,47424,46683],{"encoding":904},[883,47426,47428],{"className":47427},[886],[888,47429,47430],{"xmlns":890},[892,47431,47432,47440],{},[895,47433,47434,47436,47438],{},[898,47435,2223],{},[1711,47437,2123],{},[2111,47439,2113],{},[902,47441,22412],{"encoding":904},[883,47443,47445],{"className":47444},[886],[888,47446,47447],{"xmlns":890},[892,47448,47449,47457],{},[895,47450,47451,47453,47455],{},[898,47452,2090],{},[1711,47454,2123],{},[2111,47456,2113],{},[902,47458,43858],{"encoding":904},[883,47460,47462],{"className":47461},[886],[888,47463,47464],{"xmlns":890},[892,47465,47466,47474],{},[895,47467,47468,47470,47472],{},[898,47469,2223],{},[1711,47471,2123],{},[898,47473,2098],{},[902,47475,46916],{"encoding":904}," platí (znaménka se ",[38,47478,47479],{},"nemění",[883,47481,47483],{"className":47482},[886],[888,47484,47485],{"xmlns":890,"display":31664},[892,47486,47487,47549],{},[895,47488,47489,47497,47499,47501,47503,47505,47513,47515,47517,47519,47521,47529,47531,47533,47535,47537,47545,47547],{},[13142,47490,47491,47493,47495],{},[898,47492,6796],{},[898,47494,207],{},[1711,47496,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,47498,2123],{},[2111,47500,2113],{},[1711,47502,1726],{"separator":1725},[2102,47504],{"width":2104},[13142,47506,47507,47509,47511],{},[898,47508,6796],{},[898,47510,2223],{},[1711,47512,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,47514,2123],{},[2111,47516,2113],{},[1711,47518,1726],{"separator":1725},[2102,47520],{"width":2104},[13142,47522,47523,47525,47527],{},[898,47524,6796],{},[898,47526,2090],{},[1711,47528,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,47530,2109],{},[2111,47532,2113],{},[1711,47534,1726],{"separator":1725},[2102,47536],{"width":2104},[13142,47538,47539,47541,47543],{},[898,47540,6796],{},[898,47542,2098],{},[1711,47544,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,47546,2109],{},[2111,47548,2126],{},[902,47550,47551],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,47553,47554,47613],{},[123,47555,47556,1700,47559,47579,47580,47597,47598,1343,47611,2186],{},[38,47557,47558],{},"Kvantitativní smysl:",[883,47560,47562],{"className":47561},[886],[888,47563,47564],{"xmlns":890},[892,47565,47566,47576],{},[895,47567,47568],{},[13142,47569,47570,47572,47574],{},[898,47571,6796],{},[898,47573,6047],{},[1711,47575,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,47577,47578],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,47581,47583],{"className":47582},[886],[888,47584,47585],{"xmlns":890},[892,47586,47587,47595],{},[895,47588,47589],{},[1716,47590,47591,47593],{},[898,47592,6796],{},[898,47594,1722],{},[902,47596,46001],{"encoding":904}," při jednotkové změně parametru ",[883,47599,47601],{"className":47600},[886],[888,47602,47603],{"xmlns":890},[892,47604,47605,47609],{},[895,47606,47607],{},[898,47608,6047],{},[902,47610,6047],{"encoding":904},[614,47612,40558],{},[123,47614,47615,47618,47619,47636,47637,2186],{},[38,47616,47617],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,47620,47622],{"className":47621},[886],[888,47623,47624],{"xmlns":890},[892,47625,47626,47634],{},[895,47627,47628],{},[1716,47629,47630,47632],{},[898,47631,6796],{},[898,47633,1722],{},[902,47635,46001],{"encoding":904}," na růst ",[883,47638,47640],{"className":47639},[886],[888,47641,47642],{"xmlns":890},[892,47643,47644,47648],{},[895,47645,47646],{},[898,47647,6047],{},[902,47649,6047],{"encoding":904},[724,47651,47652,47653,47666,47667,46917,47684,1797],{},"Např. růst ",[883,47654,47656],{"className":47655},[886],[888,47657,47658],{"xmlns":890},[892,47659,47660,47664],{},[895,47661,47662],{},[898,47663,2090],{},[902,47665,2090],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,47668,47670],{"className":47669},[886],[888,47671,47672],{"xmlns":890},[892,47673,47674,47682],{},[895,47675,47676],{},[1716,47677,47678,47680],{},[898,47679,6796],{},[898,47681,1722],{},[902,47683,46001],{"encoding":904},[883,47685,47687],{"className":47686},[886],[888,47688,47689],{"xmlns":890},[892,47690,47691,47705],{},[895,47692,47693,47701,47703],{},[13142,47694,47695,47697,47699],{},[898,47696,6796],{},[898,47698,2090],{},[1711,47700,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,47702,2109],{},[2111,47704,2113],{},[902,47706,47707],{"encoding":904},"Q'_c \u003C 0",[724,47709,47710],{},[614,47711,47712,47713,47733,47734,47758,47759,47781,47782,2186],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,47714,47716],{"className":47715},[886],[888,47717,47718],{"xmlns":890},[892,47719,47720,47730],{},[895,47721,47722,47724,47726,47728],{},[898,47723,2090],{},[898,47725,6796],{},[1711,47727,2095],{},[898,47729,2098],{},[902,47731,47732],{"encoding":904},"cQ + d"," na strmější ",[883,47735,47737],{"className":47736},[886],[888,47738,47739],{"xmlns":890},[892,47740,47741,47755],{},[895,47742,47743,47749,47751,47753],{},[2884,47744,47745,47747],{},[898,47746,2090],{},[2111,47748,2238],{},[898,47750,6796],{},[1711,47752,2095],{},[898,47754,2098],{},[902,47756,47757],{"encoding":904},"c_1 Q + d"," (při ",[883,47760,47762],{"className":47761},[886],[888,47763,47764],{"xmlns":890},[892,47765,47766,47778],{},[895,47767,47768,47774,47776],{},[2884,47769,47770,47772],{},[898,47771,2090],{},[2111,47773,2238],{},[1711,47775,2123],{},[898,47777,2090],{},[902,47779,47780],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,47783,47785],{"className":47784},[886],[888,47786,47787],{"xmlns":890},[892,47788,47789,47799],{},[895,47790,47791,47797],{},[1716,47792,47793,47795],{},[898,47794,6796],{},[898,47796,1722],{},[1711,47798,46189],{},[902,47800,47801],{"encoding":904},"Q^E \\downarrow",[724,47803,47804,47805,47837,47838,2186],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,47806,47808],{"className":47807},[886],[888,47809,47810],{"xmlns":890},[892,47811,47812,47834],{},[895,47813,47814,47816,47818,47820,47828,47830,47832],{},[898,47815,6892],{"mathvariant":2287},[898,47817,6796],{},[1711,47819,6740],{},[13142,47821,47822,47824,47826],{},[898,47823,6796],{},[898,47825,2223],{},[1711,47827,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1942,47829,2519],{},[898,47831,2098],{},[898,47833,2223],{},[902,47835,47836],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,47839,47841],{"className":47840},[886],[888,47842,47843],{"xmlns":890},[892,47844,47845,47853],{},[895,47846,47847],{},[1716,47848,47849,47851],{},[898,47850,7929],{},[898,47852,1722],{},[902,47854,45064],{"encoding":904},[198,47856,47858,47859],{"id":47857},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,47860,47862],{"className":47861},[886],[888,47863,47864],{"xmlns":890},[892,47865,47866,47874],{},[895,47867,47868],{},[1716,47869,47870,47872],{},[898,47871,6796],{},[898,47873,1722],{},[902,47875,46001],{"encoding":904},[724,47877,47878,45253,47880,45288,47906,2186],{},[38,47879,41531],{},[883,47881,47883],{"className":47882},[886],[888,47884,47885],{"xmlns":890},[892,47886,47887,47903],{},[895,47888,47889,47891,47893,47895,47897,47899,47901],{},[898,47890,7929],{},[1711,47892,1836],{},[1711,47894,2460],{},[2111,47896,3034],{},[898,47898,6796],{},[1711,47900,2095],{},[2111,47902,9195],{},[902,47904,47905],{"encoding":904},"P = -3Q + 40",[883,47907,47909],{"className":47908},[886],[888,47910,47911],{"xmlns":890},[892,47912,47913,47927],{},[895,47914,47915,47917,47919,47921,47923,47925],{},[898,47916,7929],{},[1711,47918,1836],{},[2111,47920,8993],{},[898,47922,6796],{},[1711,47924,2095],{},[2111,47926,4712],{},[902,47928,47929],{"encoding":904},"P = 0{,}5Q + 10",[724,47931,47932,47934],{},[38,47933,41563],{}," Rovnovážné množství",[883,47936,47938],{"className":47937},[886],[888,47939,47940],{"xmlns":890,"display":31664},[892,47941,47942,48010],{},[895,47943,47944,47950,47952,47970,47972,47996,47998,48005,48007],{},[1716,47945,47946,47948],{},[898,47947,6796],{},[898,47949,1722],{},[1711,47951,1836],{},[2525,47953,47954,47962],{},[895,47955,47956,47958,47960],{},[898,47957,2223],{},[1711,47959,2460],{},[898,47961,2098],{},[895,47963,47964,47966,47968],{},[898,47965,2090],{},[1711,47967,2460],{},[898,47969,207],{},[1711,47971,1836],{},[2525,47973,47974,47982],{},[895,47975,47976,47978,47980],{},[2111,47977,9195],{},[1711,47979,2460],{},[2111,47981,4712],{},[895,47983,47984,47986,47988,47990,47992,47994],{},[2111,47985,8993],{},[1711,47987,2460],{},[1711,47989,1714],{"stretchy":1713},[1711,47991,2460],{},[2111,47993,3034],{},[1711,47995,1735],{"stretchy":1713},[1711,47997,1836],{},[2525,47999,48000,48002],{},[2111,48001,41617],{},[2111,48003,48004],{},"3,5",[1711,48006,6740],{},[2111,48008,48009],{},"8,571.",[902,48011,48012],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,48014,48015,48060],{},[38,48016,48017,48018,6682,48031,6696,48045,48059],{},"(a) Změna ",[883,48019,48021],{"className":48020},[886],[888,48022,48023],{"xmlns":890},[892,48024,48025,48029],{},[895,48026,48027],{},[898,48028,2090],{},[902,48030,2090],{"encoding":904},[883,48032,48034],{"className":48033},[886],[888,48035,48036],{"xmlns":890},[892,48037,48038,48042],{},[895,48039,48040],{},[2111,48041,8993],{},[902,48043,48044],{"encoding":904},"0{,}5",[883,48046,48048],{"className":48047},[886],[888,48049,48050],{"xmlns":890},[892,48051,48052,48056],{},[895,48053,48054],{},[2111,48055,22919],{},[902,48057,48058],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,48062,48064],{"className":48063},[886],[888,48065,48066],{"xmlns":890,"display":31664},[892,48067,48068,48145],{},[895,48069,48070,48078,48080,48082,48084,48086,48088,48114,48116,48118,48120,48122,48124,48134,48136,48138,48140,48142],{},[13142,48071,48072,48074,48076],{},[898,48073,6796],{},[898,48075,2090],{},[1711,48077,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1942,48079,2519],{},[898,48081,2098],{},[898,48083,2090],{},[1711,48085,1836],{},[1711,48087,2460],{},[2525,48089,48090,48098],{},[895,48091,48092,48094,48096],{},[898,48093,2223],{},[1711,48095,2460],{},[898,48097,2098],{},[895,48099,48100,48102,48104,48106,48108],{},[1711,48101,1714],{"stretchy":1713},[898,48103,2090],{},[1711,48105,2460],{},[898,48107,207],{},[1716,48109,48110,48112],{},[1711,48111,1735],{"stretchy":1713},[2111,48113,2963],{},[1942,48115,2519],{},[898,48117,2098],{},[898,48119,2090],{},[1711,48121,1836],{},[1711,48123,2460],{},[2525,48125,48126,48128],{},[2111,48127,41617],{},[1716,48129,48130,48132],{},[2111,48131,48004],{},[2111,48133,2963],{},[1711,48135,4795],{},[2111,48137,4343],{},[1711,48139,6740],{},[1711,48141,2460],{},[2111,48143,48144],{},"0,245.",[902,48146,48147],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,48149,48150,48151,2186],{},"Nové rovnovážné množství ",[883,48152,48154],{"className":48153},[886],[888,48155,48156],{"xmlns":890},[892,48157,48158,48183],{},[895,48159,48160,48168,48170,48173,48175,48178,48180],{},[13142,48161,48162,48164,48166],{},[898,48163,6796],{},[2111,48165,2238],{},[898,48167,1722],{},[1711,48169,6740],{},[2111,48171,48172],{},"8,571",[1711,48174,2460],{},[2111,48176,48177],{},"0,245",[1711,48179,1836],{},[2111,48181,48182],{},"8,326",[902,48184,48185],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,48187,48188,48273],{},[38,48189,48190,48191,1343,48211,1343,48233,1343,48253,2186],{},"(b) Současné změny ",[883,48192,48194],{"className":48193},[886],[888,48195,48196],{"xmlns":890},[892,48197,48198,48208],{},[895,48199,48200,48202,48204,48206],{},[898,48201,2098],{},[898,48203,207],{},[1711,48205,1836],{},[2111,48207,8993],{},[902,48209,48210],{"encoding":904},"da = 0{,}5",[883,48212,48214],{"className":48213},[886],[888,48215,48216],{"xmlns":890},[892,48217,48218,48230],{},[895,48219,48220,48222,48224,48226,48228],{},[898,48221,2098],{},[898,48223,2223],{},[1711,48225,1836],{},[1711,48227,2460],{},[2111,48229,4798],{},[902,48231,48232],{"encoding":904},"db = -5",[883,48234,48236],{"className":48235},[886],[888,48237,48238],{"xmlns":890},[892,48239,48240,48250],{},[895,48241,48242,48244,48246,48248],{},[898,48243,2098],{},[898,48245,2090],{},[1711,48247,1836],{},[2111,48249,4343],{},[902,48251,48252],{"encoding":904},"dc = 0{,}1",[883,48254,48256],{"className":48255},[886],[888,48257,48258],{"xmlns":890},[892,48259,48260,48270],{},[895,48261,48262,48264,48266,48268],{},[898,48263,2098],{},[898,48265,2098],{},[1711,48267,1836],{},[2111,48269,2238],{},[902,48271,48272],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,48275,48277],{"className":48276},[886],[888,48278,48279],{"xmlns":890,"display":31664},[892,48280,48281,48424],{},[24352,48282,48283,48365,48401],{"rowspacing":24354,"columnalign":24355,"columnspacing":5224},[24357,48284,48285,48295],{},[24360,48286,48287],{},[2509,48288,48289],{"scriptlevel":2113,"displaystyle":1725},[895,48290,48291,48293],{},[898,48292,6892],{"mathvariant":2287},[898,48294,6796],{},[24360,48296,48297],{},[2509,48298,48299],{"scriptlevel":2113,"displaystyle":1725},[895,48300,48301,48303,48305,48315,48317,48319,48321,48327,48329,48331,48333,48335,48337,48339,48349,48351,48353,48355,48361,48363],{},[895,48302],{},[1711,48304,6740],{},[2525,48306,48307,48309],{},[2111,48308,41617],{},[1716,48310,48311,48313],{},[2111,48312,48004],{},[2111,48314,2963],{},[1711,48316,4795],{},[2111,48318,8993],{},[1711,48320,2095],{},[2525,48322,48323,48325],{},[2111,48324,2238],{},[2111,48326,48004],{},[1711,48328,4795],{},[1711,48330,1714],{"stretchy":1713},[1711,48332,2460],{},[2111,48334,4798],{},[1711,48336,1735],{"stretchy":1713},[1711,48338,2460],{},[2525,48340,48341,48343],{},[2111,48342,41617],{},[1716,48344,48345,48347],{},[2111,48346,48004],{},[2111,48348,2963],{},[1711,48350,4795],{},[2111,48352,4343],{},[1711,48354,2460],{},[2525,48356,48357,48359],{},[2111,48358,2238],{},[2111,48360,48004],{},[1711,48362,4795],{},[2111,48364,2238],{},[24357,48366,48367,48373],{},[24360,48368,48369],{},[2509,48370,48371],{"scriptlevel":2113,"displaystyle":1725},[895,48372],{},[24360,48374,48375],{},[2509,48376,48377],{"scriptlevel":2113,"displaystyle":1725},[895,48378,48379,48381,48383,48386,48388,48391,48393,48396,48398],{},[895,48380],{},[1711,48382,1836],{},[2111,48384,48385],{},"1,2245",[1711,48387,2460],{},[2111,48389,48390],{},"1,4286",[1711,48392,2460],{},[2111,48394,48395],{},"0,2449",[1711,48397,2460],{},[2111,48399,48400],{},"0,2857",[24357,48402,48403,48409],{},[24360,48404,48405],{},[2509,48406,48407],{"scriptlevel":2113,"displaystyle":1725},[895,48408],{},[24360,48410,48411],{},[2509,48412,48413],{"scriptlevel":2113,"displaystyle":1725},[895,48414,48415,48417,48419,48421],{},[895,48416],{},[1711,48418,6740],{},[1711,48420,2460],{},[2111,48422,48423],{},"0,735.",[902,48425,48426],{"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}",[724,48428,33663,48429,2186],{},[883,48430,48432],{"className":48431},[886],[888,48433,48434],{"xmlns":890},[892,48435,48436,48460],{},[895,48437,48438,48446,48448,48450,48452,48455,48457],{},[13142,48439,48440,48442,48444],{},[898,48441,6796],{},[2111,48443,2238],{},[898,48445,1722],{},[1711,48447,6740],{},[2111,48449,48172],{},[1711,48451,2460],{},[2111,48453,48454],{},"0,735",[1711,48456,1836],{},[2111,48458,48459],{},"7,836",[902,48461,48462],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[1921,48464,48465],{},[724,48466,48467,48469,48470,48493,48494,48516],{},[883,48468,1927],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,48471,48473],{"className":48472},[886],[888,48474,48475],{"xmlns":890},[892,48476,48477,48490],{},[895,48478,48479,48481,48483,48485,48487],{},[898,48480,6892],{"mathvariant":2287},[898,48482,6796],{},[1711,48484,6740],{},[1711,48486,2460],{},[2111,48488,48489],{},"2,69",[902,48491,48492],{"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 ",[883,48495,48497],{"className":48496},[886],[888,48498,48499],{"xmlns":890},[892,48500,48501,48513],{},[895,48502,48503,48505,48507,48509,48511],{},[898,48504,6892],{"mathvariant":2287},[898,48506,6796],{},[1711,48508,6740],{},[1711,48510,2460],{},[2111,48512,48454],{},[902,48514,48515],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,48518,48519],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[40568,48521],{},[115,48523,820],{"id":15758},[1921,48525,48526],{},[724,48527,48528,7867,48530,1648,48533,1772,48549,1648,48552,48568,48569,2186],{},[883,48529,2678],{},[38,48531,48532],{},"Přebytek spotřebitele",[883,48534,48536],{"className":48535},[886],[888,48537,48538],{"xmlns":890},[892,48539,48540,48546],{},[895,48541,48542,48544],{},[898,48543,1940],{},[898,48545,2362],{},[902,48547,48548],{"encoding":904},"CS",[38,48550,48551],{},"přebytek výrobce",[883,48553,48555],{"className":48554},[886],[888,48556,48557],{"xmlns":890},[892,48558,48559,48565],{},[895,48560,48561,48563],{},[898,48562,7929],{},[898,48564,2362],{},[902,48566,48567],{"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 ",[207,48570,48572],{"className":48571,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,48574,48575],{},[1801,48576],{"alt":48577,"className":48578,"src":48579},"imek-prebytky-cs-ps",[210,1805],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,48581,48582,1648,48584,48587],{},[38,48583,48532],{},[614,48585,48586],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,48589,48591],{"className":48590},[886],[888,48592,48593],{"xmlns":890,"display":31664},[892,48594,48595,48672],{},[24352,48596,48597],{"width":31669},[24357,48598,48599,48601,48665,48667],{},[24360,48600],{"width":31674},[24360,48602,48603],{},[895,48604,48605,48607,48609,48611,48617,48619,48621,48633,48635,48637,48639,48641,48643,48645,48647,48649,48655,48657,48663],{},[898,48606,1940],{},[898,48608,2362],{},[1711,48610,1714],{"stretchy":1713},[2884,48612,48613,48615],{},[898,48614,6796],{},[2111,48616,2113],{},[1711,48618,1735],{"stretchy":1713},[1711,48620,1836],{},[13142,48622,48623,48625,48627],{},[1711,48624,15143],{},[2111,48626,2113],{},[2884,48628,48629,48631],{},[898,48630,6796],{},[2111,48632,2113],{},[898,48634,2778],{},[1711,48636,1714],{"stretchy":1713},[898,48638,6796],{},[1711,48640,1735],{"stretchy":1713},[1942,48642,2519],{},[898,48644,2098],{},[898,48646,6796],{},[1711,48648,2460],{},[2884,48650,48651,48653],{},[898,48652,7929],{},[2111,48654,2113],{},[1942,48656,2519],{},[2884,48658,48659,48661],{},[898,48660,6796],{},[2111,48662,2113],{},[898,48664,2186],{"mathvariant":2287},[24360,48666],{"width":31674},[24360,48668,48669],{},[1942,48670,48671],{},"(2.14)",[902,48673,48674],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,48676,48677,1648,48680,48683],{},[38,48678,48679],{},"Přebytek výrobce",[614,48681,48682],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,48685,48687],{"className":48686},[886],[888,48688,48689],{"xmlns":890,"display":31664},[892,48690,48691,48768],{},[24352,48692,48693],{"width":31669},[24357,48694,48695,48697,48761,48763],{},[24360,48696],{"width":31674},[24360,48698,48699],{},[895,48700,48701,48703,48705,48707,48713,48715,48717,48723,48725,48731,48733,48745,48747,48749,48751,48753,48755,48757,48759],{},[898,48702,7929],{},[898,48704,2362],{},[1711,48706,1714],{"stretchy":1713},[2884,48708,48709,48711],{},[898,48710,6796],{},[2111,48712,2113],{},[1711,48714,1735],{"stretchy":1713},[1711,48716,1836],{},[2884,48718,48719,48721],{},[898,48720,7929],{},[2111,48722,2113],{},[1942,48724,2519],{},[2884,48726,48727,48729],{},[898,48728,6796],{},[2111,48730,2113],{},[1711,48732,2460],{},[13142,48734,48735,48737,48739],{},[1711,48736,15143],{},[2111,48738,2113],{},[2884,48740,48741,48743],{},[898,48742,6796],{},[2111,48744,2113],{},[898,48746,2362],{},[1711,48748,1714],{"stretchy":1713},[898,48750,6796],{},[1711,48752,1735],{"stretchy":1713},[1942,48754,2519],{},[898,48756,2098],{},[898,48758,6796],{},[898,48760,2186],{"mathvariant":2287},[24360,48762],{"width":31674},[24360,48764,48765],{},[1942,48766,48767],{},"(2.15)",[902,48769,48770],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,48772,48773,48774,2186],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,48775,48777],{"className":48776,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[40568,48779],{},[115,48781,48783],{"id":48782},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,48785,48786,48817,48822,48828,48856,48862,48891,48897,48977,49003],{},[123,48787,48788,48790,48791,48816],{},[38,48789,41526],{}," — lineární poptávka ",[883,48792,48794],{"className":48793},[886],[888,48795,48796],{"xmlns":890},[892,48797,48798,48814],{},[895,48799,48800,48802,48804,48806,48808,48810,48812],{},[898,48801,7929],{},[1711,48803,1836],{},[1711,48805,2460],{},[2111,48807,2963],{},[898,48809,6796],{},[1711,48811,2095],{},[2111,48813,7126],{},[902,48815,41558],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,48818,48819,48821],{},[38,48820,41840],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,48823,48824,48827],{},[38,48825,48826],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,48829,48830,48832,48833,2186],{},[38,48831,44387],{}," — lineární nabídka ",[883,48834,48836],{"className":48835},[886],[888,48837,48838],{"xmlns":890},[892,48839,48840,48854],{},[895,48841,48842,48844,48846,48848,48850,48852],{},[898,48843,7929],{},[1711,48845,1836],{},[2111,48847,8993],{},[898,48849,6796],{},[1711,48851,2095],{},[2111,48853,4372],{},[902,48855,44416],{"encoding":904},[123,48857,48858,48861],{},[38,48859,48860],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,48863,48864,48867,48868,2186],{},[38,48865,48866],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,48869,48871],{"className":48870},[886],[888,48872,48873],{"xmlns":890},[892,48874,48875,48889],{},[895,48876,48877,48879,48881,48883,48885,48887],{},[898,48878,1722],{},[1711,48880,5144],{"stretchy":1713},[2111,48882,6369],{},[1711,48884,1726],{"separator":1725},[2111,48886,45534],{},[1711,48888,5163],{"stretchy":1713},[902,48890,45562],{"encoding":904},[123,48892,48893,48896],{},[38,48894,48895],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,48898,48899,48902,48903,48920,48921,1343,48946,48973,48974,6953],{},[38,48900,48901],{},"Příklad 2.9"," — daň ",[883,48904,48906],{"className":48905},[886],[888,48907,48908],{"xmlns":890},[892,48909,48910,48918],{},[895,48911,48912,48914,48916],{},[898,48913,1769],{},[1711,48915,1836],{},[2111,48917,6262],{},[902,48919,44866],{"encoding":904}," na výrobce; rozklad ",[883,48922,48924],{"className":48923},[886],[888,48925,48926],{"xmlns":890},[892,48927,48928,48944],{},[895,48929,48930,48940,48942],{},[2884,48931,48932,48934],{},[898,48933,1769],{},[895,48935,48936,48938],{},[898,48937,46275],{},[898,48939,724],{},[1711,48941,1836],{},[2111,48943,2963],{},[902,48945,46574],{"encoding":904},[883,48947,48949],{"className":48948},[886],[888,48950,48951],{"xmlns":890},[892,48952,48953,48971],{},[895,48954,48955,48967,48969],{},[2884,48956,48957,48959],{},[898,48958,1769],{},[895,48960,48961,48963,48965],{},[898,48962,46298],{},[898,48964,6038],{},[898,48966,1675],{},[1711,48968,1836],{},[2111,48970,6369],{},[902,48972,46603],{"encoding":904},". (Viz ",[207,48975,46319],{"className":48976,"dataFsResolvedFilePath":809,"href":810},[210],[123,48978,48979,48902,48982,48999,49000,6953],{},[38,48980,48981],{},"Příklad 2.10",[883,48983,48985],{"className":48984},[886],[888,48986,48987],{"xmlns":890},[892,48988,48989,48997],{},[895,48990,48991,48993,48995],{},[898,48992,1769],{},[1711,48994,1836],{},[2111,48996,6262],{},[902,48998,44866],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,49001,46319],{"className":49002,"dataFsResolvedFilePath":809,"href":810},[210],[123,49004,49005,49008],{},[38,49006,49007],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[40568,49010],{},[115,49012,49014],{"id":49013},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,49016,49018],{"id":49017},"základní-analýza-poptávky","Základní analýza poptávky",[724,49020,49021,49024,49025,49060,49061,49087],{},[38,49022,49023],{},"2.1"," Je dána poptávka ",[883,49026,49028],{"className":49027},[886],[888,49029,49030],{"xmlns":890},[892,49031,49032,49057],{},[895,49033,49034,49036,49038,49040,49042,49044,49046,49048,49051,49053,49055],{},[898,49035,6796],{},[1711,49037,1836],{},[898,49039,2778],{},[1711,49041,1714],{"stretchy":1713},[898,49043,7929],{},[1711,49045,1735],{"stretchy":1713},[1711,49047,1836],{},[2111,49049,49050],{},"75",[1711,49052,2460],{},[2111,49054,4798],{},[898,49056,7929],{},[902,49058,49059],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,49062,49064],{"className":49063},[886],[888,49065,49066],{"xmlns":890},[892,49067,49068,49084],{},[895,49069,49070,49072,49074,49076,49078,49080,49082],{},[2111,49071,2113],{},[1711,49073,1726],{"separator":1725},[2111,49075,4798],{},[1711,49077,1726],{"separator":1725},[2111,49079,4712],{},[1711,49081,1726],{"separator":1725},[2111,49083,39842],{},[902,49085,49086],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,49089,49090,49093,49094,49112,49113,3239],{},[38,49091,49092],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,49095,49097],{"className":49096},[886],[888,49098,49099],{"xmlns":890},[892,49100,49101,49109],{},[895,49102,49103,49105,49107],{},[898,49104,7929],{},[1711,49106,1726],{"separator":1725},[898,49108,6796],{},[902,49110,49111],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,49114,49116],{"className":49115},[886],[888,49117,49118],{"xmlns":890},[892,49119,49120,49136],{},[895,49121,49122,49124,49126,49128,49130,49132,49134],{},[898,49123,207],{},[1711,49125,1726],{"separator":1725},[898,49127,2223],{},[1711,49129,1726],{"separator":1725},[898,49131,2090],{},[1711,49133,2123],{},[2111,49135,2113],{},[902,49137,49138],{"encoding":904},"a, b, c > 0",[120,49140,49141,49174,49205,49240,49271,49306],{},[123,49142,49143,49144],{},"(a) ",[883,49145,49147],{"className":49146},[886],[888,49148,49149],{"xmlns":890},[892,49150,49151,49171],{},[895,49152,49153,49155,49157],{},[898,49154,6796],{},[1711,49156,1836],{},[2509,49158,49159],{"scriptlevel":2113,"displaystyle":1725},[2525,49160,49161,49163],{},[898,49162,207],{},[895,49164,49165,49167,49169],{},[898,49166,7929],{},[1711,49168,2095],{},[898,49170,2090],{},[902,49172,49173],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,49175,49176,49177],{},"(b) ",[883,49178,49180],{"className":49179},[886],[888,49181,49182],{"xmlns":890},[892,49183,49184,49202],{},[895,49185,49186,49188,49190],{},[898,49187,6796],{},[1711,49189,1836],{},[12097,49191,49192],{},[895,49193,49194,49196,49198,49200],{},[898,49195,207],{},[1711,49197,2460],{},[898,49199,2223],{},[898,49201,6796],{},[902,49203,49204],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,49206,49207,49208],{},"(c) ",[883,49209,49211],{"className":49210},[886],[888,49212,49213],{"xmlns":890},[892,49214,49215,49237],{},[895,49216,49217,49219,49221],{},[898,49218,6796],{},[1711,49220,1836],{},[2509,49222,49223],{"scriptlevel":2113,"displaystyle":1725},[2525,49224,49225,49235],{},[895,49226,49227,49229,49231],{},[898,49228,207],{},[1711,49230,2460],{},[12097,49232,49233],{},[898,49234,7929],{},[898,49236,2223],{},[902,49238,49239],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,49241,49242,49243],{},"(d) ",[883,49244,49246],{"className":49245},[886],[888,49247,49248],{"xmlns":890},[892,49249,49250,49268],{},[895,49251,49252,49254,49256,49258,49260,49262],{},[898,49253,7929],{},[1711,49255,1836],{},[898,49257,207],{},[1711,49259,2460],{},[898,49261,2223],{},[1716,49263,49264,49266],{},[898,49265,6796],{},[2111,49267,2963],{},[902,49269,49270],{"encoding":904},"P = a - bQ^2",[123,49272,49273,49274],{},"(e) ",[883,49275,49277],{"className":49276},[886],[888,49278,49279],{"xmlns":890},[892,49280,49281,49303],{},[895,49282,49283,49285,49287,49289,49299,49301],{},[898,49284,6796],{},[1711,49286,1836],{},[898,49288,2223],{},[1716,49290,49291,49293],{},[898,49292,7929],{},[895,49294,49295,49297],{},[1711,49296,2460],{},[898,49298,207],{},[1711,49300,2095],{},[898,49302,2090],{},[902,49304,49305],{"encoding":904},"Q = bP^{-a} + c",[123,49307,49308,49309],{},"(f) ",[883,49310,49312],{"className":49311},[886],[888,49313,49314],{"xmlns":890},[892,49315,49316,49339],{},[895,49317,49318,49320,49322,49324,49326],{},[898,49319,6796],{},[1711,49321,1836],{},[898,49323,207],{},[1711,49325,4795],{},[1716,49327,49328,49331],{},[898,49329,49330],{},"e",[895,49332,49333,49335,49337],{},[1711,49334,2460],{},[898,49336,2223],{},[898,49338,7929],{},[902,49340,49341],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,49343,49344,49347],{},[38,49345,49346],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,49349,49350,49353,49356],{},[123,49351,49352],{},"(a) Cena substitutu.",[123,49354,49355],{},"(b) Cena komplementu.",[123,49357,49358],{},"(c) Výdaje na reklamu.",[724,49360,49361,49024,49363,49397,49398,49426],{},[38,49362,28240],{},[883,49364,49366],{"className":49365},[886],[888,49367,49368],{"xmlns":890},[892,49369,49370,49394],{},[895,49371,49372,49374,49376,49378,49380,49382,49384,49386,49388,49390,49392],{},[898,49373,7929],{},[1711,49375,1836],{},[898,49377,2778],{},[1711,49379,1714],{"stretchy":1713},[898,49381,6796],{},[1711,49383,1735],{"stretchy":1713},[1711,49385,1836],{},[2111,49387,7505],{},[1711,49389,2460],{},[2111,49391,2963],{},[898,49393,6796],{},[902,49395,49396],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,49399,49401],{"className":49400},[886],[888,49402,49403],{"xmlns":890},[892,49404,49405,49423],{},[895,49406,49407,49409,49411,49417,49419,49421],{},[898,49408,7929],{},[1711,49410,1836],{},[1716,49412,49413,49415],{},[898,49414,2778],{},[1711,49416,1793],{},[1711,49418,1714],{"stretchy":1713},[898,49420,6796],{},[1711,49422,1735],{"stretchy":1713},[902,49424,49425],{"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.",[724,49428,49429,49432],{},[38,49430,49431],{},"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:",[120,49434,49435,49519,49595,49681,49769],{},[123,49436,49143,49437,1343,49477,2186],{},[883,49438,49440],{"className":49439},[886],[888,49441,49442],{"xmlns":890},[892,49443,49444,49474],{},[895,49445,49446,49452,49454,49456,49458,49460,49466,49468],{},[2884,49447,49448,49450],{},[898,49449,26851],{},[2111,49451,2238],{},[1711,49453,1836],{},[2111,49455,4306],{},[1711,49457,2460],{},[2111,49459,6369],{},[2884,49461,49462,49464],{},[898,49463,8243],{},[2111,49465,2238],{},[1711,49467,2095],{},[2884,49469,49470,49472],{},[898,49471,8243],{},[2111,49473,2963],{},[902,49475,49476],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,49478,49480],{"className":49479},[886],[888,49481,49482],{"xmlns":890},[892,49483,49484,49516],{},[895,49485,49486,49492,49494,49496,49498,49500,49506,49508,49510],{},[2884,49487,49488,49490],{},[898,49489,26851],{},[2111,49491,2963],{},[1711,49493,1836],{},[2111,49495,4712],{},[1711,49497,2095],{},[2111,49499,2963],{},[2884,49501,49502,49504],{},[898,49503,8243],{},[2111,49505,2238],{},[1711,49507,2460],{},[2111,49509,6369],{},[2884,49511,49512,49514],{},[898,49513,8243],{},[2111,49515,2963],{},[902,49517,49518],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,49520,49176,49521,1343,49563,2186],{},[883,49522,49524],{"className":49523},[886],[888,49525,49526],{"xmlns":890},[892,49527,49528,49560],{},[895,49529,49530,49536,49538,49540,49542,49544,49550,49552,49554],{},[2884,49531,49532,49534],{},[898,49533,26851],{},[2111,49535,2238],{},[1711,49537,1836],{},[2111,49539,7120],{},[1711,49541,2460],{},[2111,49543,4712],{},[2884,49545,49546,49548],{},[898,49547,8243],{},[2111,49549,2238],{},[1711,49551,2460],{},[2111,49553,6262],{},[2884,49555,49556,49558],{},[898,49557,8243],{},[2111,49559,2963],{},[902,49561,49562],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,49564,49566],{"className":49565},[886],[888,49567,49568],{"xmlns":890},[892,49569,49570,49592],{},[895,49571,49572,49578,49580,49582,49584,49586],{},[2884,49573,49574,49576],{},[898,49575,26851],{},[2111,49577,2963],{},[1711,49579,1836],{},[2111,49581,39842],{},[1711,49583,2460],{},[2111,49585,4712],{},[2884,49587,49588,49590],{},[898,49589,8243],{},[2111,49591,2963],{},[902,49593,49594],{"encoding":904},"B_2 = 15 - 10A_2",[123,49596,49207,49597,1343,49639,2186],{},[883,49598,49600],{"className":49599},[886],[888,49601,49602],{"xmlns":890},[892,49603,49604,49636],{},[895,49605,49606,49612,49614,49616,49618,49620,49626,49628,49630],{},[2884,49607,49608,49610],{},[898,49609,26851],{},[2111,49611,2238],{},[1711,49613,1836],{},[2111,49615,41617],{},[1711,49617,2460],{},[2111,49619,2963],{},[2884,49621,49622,49624],{},[898,49623,8243],{},[2111,49625,2238],{},[1711,49627,2460],{},[2111,49629,6369],{},[2884,49631,49632,49634],{},[898,49633,8243],{},[2111,49635,2963],{},[902,49637,49638],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,49640,49642],{"className":49641},[886],[888,49643,49644],{"xmlns":890},[892,49645,49646,49678],{},[895,49647,49648,49654,49656,49658,49660,49662,49668,49670,49672],{},[2884,49649,49650,49652],{},[898,49651,26851],{},[2111,49653,2963],{},[1711,49655,1836],{},[2111,49657,39842],{},[1711,49659,2095],{},[2111,49661,2963],{},[2884,49663,49664,49666],{},[898,49665,8243],{},[2111,49667,2238],{},[1711,49669,2460],{},[2111,49671,2963],{},[2884,49673,49674,49676],{},[898,49675,8243],{},[2111,49677,2963],{},[902,49679,49680],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,49682,49242,49683,1343,49727,2186],{},[883,49684,49686],{"className":49685},[886],[888,49687,49688],{"xmlns":890},[892,49689,49690,49724],{},[895,49691,49692,49698,49700,49702,49704,49706,49708,49714,49716,49718],{},[2884,49693,49694,49696],{},[898,49695,26851],{},[2111,49697,2238],{},[1711,49699,1836],{},[1711,49701,2460],{},[2111,49703,4306],{},[1711,49705,2460],{},[2111,49707,2963],{},[2884,49709,49710,49712],{},[898,49711,8243],{},[2111,49713,2238],{},[1711,49715,2095],{},[2111,49717,3034],{},[2884,49719,49720,49722],{},[898,49721,8243],{},[2111,49723,2963],{},[902,49725,49726],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,49728,49730],{"className":49729},[886],[888,49731,49732],{"xmlns":890},[892,49733,49734,49766],{},[895,49735,49736,49742,49744,49746,49748,49750,49756,49758,49760],{},[2884,49737,49738,49740],{},[898,49739,26851],{},[2111,49741,2963],{},[1711,49743,1836],{},[2111,49745,4712],{},[1711,49747,2095],{},[2111,49749,2963],{},[2884,49751,49752,49754],{},[898,49753,8243],{},[2111,49755,2238],{},[1711,49757,2460],{},[2111,49759,2963],{},[2884,49761,49762,49764],{},[898,49763,8243],{},[2111,49765,2963],{},[902,49767,49768],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,49770,49273,49771,1343,49813,2186],{},[883,49772,49774],{"className":49773},[886],[888,49775,49776],{"xmlns":890},[892,49777,49778,49810],{},[895,49779,49780,49786,49788,49790,49792,49794,49800,49802,49804],{},[2884,49781,49782,49784],{},[898,49783,26851],{},[2111,49785,2238],{},[1711,49787,1836],{},[2111,49789,4306],{},[1711,49791,2095],{},[2111,49793,2963],{},[2884,49795,49796,49798],{},[898,49797,8243],{},[2111,49799,2238],{},[1711,49801,2095],{},[2111,49803,6369],{},[2884,49805,49806,49808],{},[898,49807,8243],{},[2111,49809,2963],{},[902,49811,49812],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,49814,49816],{"className":49815},[886],[888,49817,49818],{"xmlns":890},[892,49819,49820,49852],{},[895,49821,49822,49828,49830,49832,49834,49836,49842,49844,49846],{},[2884,49823,49824,49826],{},[898,49825,26851],{},[2111,49827,2963],{},[1711,49829,1836],{},[2111,49831,9195],{},[1711,49833,2460],{},[2111,49835,3034],{},[2884,49837,49838,49840],{},[898,49839,8243],{},[2111,49841,2238],{},[1711,49843,2095],{},[2111,49845,4798],{},[2884,49847,49848,49850],{},[898,49849,8243],{},[2111,49851,2963],{},[902,49853,49854],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,49856,49858],{"id":49857},"základní-analýza-nabídky","Základní analýza nabídky",[724,49860,49861,49864,49865,49899,49900,49922],{},[38,49862,49863],{},"2.6"," Je dána nabídka ",[883,49866,49868],{"className":49867},[886],[888,49869,49870],{"xmlns":890},[892,49871,49872,49896],{},[895,49873,49874,49876,49878,49880,49882,49884,49886,49888,49890,49892,49894],{},[898,49875,7929],{},[1711,49877,1836],{},[898,49879,2362],{},[1711,49881,1714],{"stretchy":1713},[898,49883,6796],{},[1711,49885,1735],{"stretchy":1713},[1711,49887,1836],{},[2111,49889,4306],{},[1711,49891,2095],{},[2111,49893,4491],{},[898,49895,6796],{},[902,49897,49898],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,49901,49903],{"className":49902},[886],[888,49904,49905],{"xmlns":890},[892,49906,49907,49919],{},[895,49908,49909,49911,49913,49915,49917],{},[2111,49910,4372],{},[1711,49912,1726],{"separator":1725},[2111,49914,41617],{},[1711,49916,1726],{"separator":1725},[2111,49918,4733],{},[902,49920,49921],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,49924,49925,49928,49929,49946],{},[38,49926,49927],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,49930,49932],{"className":49931},[886],[888,49933,49934],{"xmlns":890},[892,49935,49936,49944],{},[895,49937,49938,49940,49942],{},[898,49939,7929],{},[1711,49941,1726],{"separator":1725},[898,49943,6796],{},[902,49945,49111],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,49948,49949,49975,50003,50036,50070,50106],{},[123,49950,49143,49951],{},[883,49952,49954],{"className":49953},[886],[888,49955,49956],{"xmlns":890},[892,49957,49958,49972],{},[895,49959,49960,49962,49964,49966,49968,49970],{},[898,49961,7929],{},[1711,49963,1836],{},[2111,49965,41617],{},[1711,49967,2095],{},[2111,49969,2963],{},[898,49971,6796],{},[902,49973,49974],{"encoding":904},"P = 30 + 2Q",[123,49976,49176,49977],{},[883,49978,49980],{"className":49979},[886],[888,49981,49982],{"xmlns":890},[892,49983,49984,50000],{},[895,49985,49986,49988,49990,49992,49994,49996,49998],{},[898,49987,6796],{},[1711,49989,1836],{},[1711,49991,2460],{},[2111,49993,3034],{},[1711,49995,2095],{},[2111,49997,7505],{},[898,49999,7929],{},[902,50001,50002],{"encoding":904},"Q = -3 + 12P",[123,50004,49207,50005],{},[883,50006,50008],{"className":50007},[886],[888,50009,50010],{"xmlns":890},[892,50011,50012,50034],{},[895,50013,50014,50016,50018,50024,50026,50028,50030,50032],{},[898,50015,7929],{},[1711,50017,1836],{},[1716,50019,50020,50022],{},[898,50021,6796],{},[2111,50023,2963],{},[1711,50025,2095],{},[2111,50027,26544],{},[898,50029,6796],{},[1711,50031,2095],{},[2111,50033,36144],{},[902,50035,45320],{"encoding":904},[123,50037,49242,50038],{},[883,50039,50041],{"className":50040},[886],[888,50042,50043],{"xmlns":890},[892,50044,50045,50067],{},[895,50046,50047,50049,50051,50057,50059,50061,50063,50065],{},[898,50048,7929],{},[1711,50050,1836],{},[1716,50052,50053,50055],{},[898,50054,6796],{},[2111,50056,2963],{},[1711,50058,2095],{},[2111,50060,2963],{},[898,50062,6796],{},[1711,50064,2095],{},[2111,50066,7505],{},[902,50068,50069],{"encoding":904},"P = Q^2 + 2Q + 12",[123,50071,49273,50072],{},[883,50073,50075],{"className":50074},[886],[888,50076,50077],{"xmlns":890},[892,50078,50079,50103],{},[895,50080,50081,50083,50085,50087,50089,50091,50093,50095,50097],{},[898,50082,6796],{},[1711,50084,1836],{},[2111,50086,12781],{},[1711,50088,2095],{},[2111,50090,4798],{},[898,50092,7929],{},[1711,50094,2095],{},[2111,50096,4343],{},[1716,50098,50099,50101],{},[898,50100,7929],{},[2111,50102,2963],{},[902,50104,50105],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,50107,49308,50108],{},[883,50109,50111],{"className":50110},[886],[888,50112,50113],{"xmlns":890},[892,50114,50115,50140],{},[895,50116,50117,50119,50121,50123,50125,50127,50129,50131,50134],{},[898,50118,6796],{},[1711,50120,1836],{},[2111,50122,27799],{},[1711,50124,2095],{},[2111,50126,4343],{},[898,50128,7929],{},[1711,50130,2095],{},[2111,50132,50133],{},"0,004",[1716,50135,50136,50138],{},[898,50137,7929],{},[2111,50139,2963],{},[902,50141,50142],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,50144,50145,50148],{},[38,50146,50147],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,50150,50151,50154,50157,50160],{},[123,50152,50153],{},"(a) Sníží ceny surovin — vstupů.",[123,50155,50156],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,50158,50159],{},"(c) Zvýší ceny všech energií.",[123,50161,50162],{},"(d) Sníží daňové odvody státu.",[724,50164,50165,49864,50167,50201,50202,50230],{},[38,50166,46547],{},[883,50168,50170],{"className":50169},[886],[888,50171,50172],{"xmlns":890},[892,50173,50174,50198],{},[895,50175,50176,50178,50180,50182,50184,50186,50188,50190,50192,50194,50196],{},[898,50177,7929],{},[1711,50179,1836],{},[898,50181,2362],{},[1711,50183,1714],{"stretchy":1713},[898,50185,6796],{},[1711,50187,1735],{"stretchy":1713},[1711,50189,1836],{},[2111,50191,8993],{},[898,50193,6796],{},[1711,50195,2095],{},[2111,50197,39842],{},[902,50199,50200],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,50203,50205],{"className":50204},[886],[888,50206,50207],{"xmlns":890},[892,50208,50209,50227],{},[895,50210,50211,50213,50215,50221,50223,50225],{},[898,50212,7929],{},[1711,50214,1836],{},[1716,50216,50217,50219],{},[898,50218,2362],{},[1711,50220,1793],{},[1711,50222,1714],{"stretchy":1713},[898,50224,6796],{},[1711,50226,1735],{"stretchy":1713},[902,50228,50229],{"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.",[198,50232,44923],{"id":50233},"tržní-rovnováha-1",[724,50235,50236,50238,50239,50256,50257,2062],{},[38,50237,46607],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,50240,50242],{"className":50241},[886],[888,50243,50244],{"xmlns":890},[892,50245,50246,50254],{},[895,50247,50248],{},[1716,50249,50250,50252],{},[898,50251,6796],{},[898,50253,1722],{},[902,50255,46001],{"encoding":904}," a rovnovážnou cenu ",[883,50258,50260],{"className":50259},[886],[888,50261,50262],{"xmlns":890},[892,50263,50264,50272],{},[895,50265,50266],{},[1716,50267,50268,50270],{},[898,50269,7929],{},[898,50271,1722],{},[902,50273,45064],{"encoding":904},[120,50275,50276,50329,50380,50439],{},[123,50277,49143,50278,1343,50305,2186],{},[883,50279,50281],{"className":50280},[886],[888,50282,50283],{"xmlns":890},[892,50284,50285,50302],{},[895,50286,50287,50289,50291,50293,50295,50297,50299],{},[898,50288,7929],{},[1711,50290,1836],{},[1711,50292,2460],{},[2111,50294,4798],{},[898,50296,6796],{},[1711,50298,2095],{},[2111,50300,50301],{},"80",[902,50303,50304],{"encoding":904},"P = -5Q + 80",[883,50306,50308],{"className":50307},[886],[888,50309,50310],{"xmlns":890},[892,50311,50312,50326],{},[895,50313,50314,50316,50318,50320,50322,50324],{},[898,50315,7929],{},[1711,50317,1836],{},[2111,50319,2963],{},[898,50321,6796],{},[1711,50323,2095],{},[2111,50325,4712],{},[902,50327,50328],{"encoding":904},"P = 2Q + 10",[123,50330,49176,50331,1343,50357,2186],{},[883,50332,50334],{"className":50333},[886],[888,50335,50336],{"xmlns":890},[892,50337,50338,50354],{},[895,50339,50340,50342,50344,50346,50348,50350,50352],{},[898,50341,6796],{},[1711,50343,1836],{},[1711,50345,2460],{},[2111,50347,8993],{},[898,50349,7929],{},[1711,50351,2095],{},[2111,50353,4372],{},[902,50355,50356],{"encoding":904},"Q = -0{,}5P + 25",[883,50358,50360],{"className":50359},[886],[888,50361,50362],{"xmlns":890},[892,50363,50364,50378],{},[895,50365,50366,50368,50370,50372,50374,50376],{},[898,50367,6796],{},[1711,50369,1836],{},[2111,50371,2963],{},[898,50373,7929],{},[1711,50375,2460],{},[2111,50377,7120],{},[902,50379,44445],{"encoding":904},[123,50381,49207,50382,1343,50408,2186],{},[883,50383,50385],{"className":50384},[886],[888,50386,50387],{"xmlns":890},[892,50388,50389,50405],{},[895,50390,50391,50393,50395,50397,50399,50401,50403],{},[898,50392,7929],{},[1711,50394,1836],{},[1711,50396,2460],{},[2111,50398,6369],{},[898,50400,6796],{},[1711,50402,2095],{},[2111,50404,8037],{},[902,50406,50407],{"encoding":904},"P = -4Q + 120",[883,50409,50411],{"className":50410},[886],[888,50412,50413],{"xmlns":890},[892,50414,50415,50436],{},[895,50416,50417,50419,50421,50429,50431,50433],{},[898,50418,7929],{},[1711,50420,1836],{},[2509,50422,50423],{"scriptlevel":2113,"displaystyle":1713},[2525,50424,50425,50427],{},[2111,50426,2238],{},[2111,50428,3034],{},[898,50430,6796],{},[1711,50432,2095],{},[2111,50434,50435],{},"29",[902,50437,50438],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,50440,49242,50441,1343,50470,2186],{},[883,50442,50444],{"className":50443},[886],[888,50445,50446],{"xmlns":890},[892,50447,50448,50467],{},[895,50449,50450,50452,50454,50456,50462,50464],{},[898,50451,7929],{},[1711,50453,1836],{},[1711,50455,2460],{},[1716,50457,50458,50460],{},[898,50459,6796],{},[2111,50461,2963],{},[1711,50463,2095],{},[2111,50465,50466],{},"52",[902,50468,50469],{"encoding":904},"P = -Q^2 + 52",[883,50471,50473],{"className":50472},[886],[888,50474,50475],{"xmlns":890},[892,50476,50477,50495],{},[895,50478,50479,50481,50483,50485,50491,50493],{},[898,50480,7929],{},[1711,50482,1836],{},[2111,50484,2963],{},[1716,50486,50487,50489],{},[898,50488,6796],{},[2111,50490,2963],{},[1711,50492,2095],{},[2111,50494,4712],{},[902,50496,50497],{"encoding":904},"P = 2Q^2 + 10",[724,50499,50500,50503,50504,50534,50535,50565],{},[38,50501,50502],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,50505,50507],{"className":50506},[886],[888,50508,50509],{"xmlns":890},[892,50510,50511,50531],{},[895,50512,50513,50521,50523],{},[13142,50514,50515,50517,50519],{},[898,50516,6796],{},[2111,50518,2238],{},[898,50520,1722],{},[1711,50522,1726],{"separator":1725},[13142,50524,50525,50527,50529],{},[898,50526,6796],{},[2111,50528,2963],{},[898,50530,1722],{},[902,50532,50533],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,50536,50538],{"className":50537},[886],[888,50539,50540],{"xmlns":890},[892,50541,50542,50562],{},[895,50543,50544,50552,50554],{},[13142,50545,50546,50548,50550],{},[898,50547,7929],{},[2111,50549,2238],{},[898,50551,1722],{},[1711,50553,1726],{"separator":1725},[13142,50555,50556,50558,50560],{},[898,50557,7929],{},[2111,50559,2963],{},[898,50561,1722],{},[902,50563,50564],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,50567,50568,50720],{},[123,50569,49143,50570,1343,50610,1343,50652,1343,50686,2186],{},[883,50571,50573],{"className":50572},[886],[888,50574,50575],{"xmlns":890},[892,50576,50577,50607],{},[895,50578,50579,50585,50587,50589,50591,50593,50599,50601],{},[2884,50580,50581,50583],{},[898,50582,6796],{},[2111,50584,2238],{},[1711,50586,1836],{},[2111,50588,4712],{},[1711,50590,2460],{},[2111,50592,2963],{},[2884,50594,50595,50597],{},[898,50596,7929],{},[2111,50598,2238],{},[1711,50600,2095],{},[2884,50602,50603,50605],{},[898,50604,7929],{},[2111,50606,2963],{},[902,50608,50609],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,50611,50613],{"className":50612},[886],[888,50614,50615],{"xmlns":890},[892,50616,50617,50649],{},[895,50618,50619,50625,50627,50629,50631,50633,50639,50641,50643],{},[2884,50620,50621,50623],{},[898,50622,6796],{},[2111,50624,2963],{},[1711,50626,1836],{},[2111,50628,4798],{},[1711,50630,2095],{},[2111,50632,2963],{},[2884,50634,50635,50637],{},[898,50636,7929],{},[2111,50638,2238],{},[1711,50640,2460],{},[2111,50642,2963],{},[2884,50644,50645,50647],{},[898,50646,7929],{},[2111,50648,2963],{},[902,50650,50651],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,50653,50655],{"className":50654},[886],[888,50656,50657],{"xmlns":890},[892,50658,50659,50683],{},[895,50660,50661,50667,50669,50671,50673,50675,50677],{},[2884,50662,50663,50665],{},[898,50664,6796],{},[2111,50666,2238],{},[1711,50668,1836],{},[1711,50670,2460],{},[2111,50672,3034],{},[1711,50674,2095],{},[2111,50676,2963],{},[2884,50678,50679,50681],{},[898,50680,7929],{},[2111,50682,2238],{},[902,50684,50685],{"encoding":904},"Q_1 = -3 + 2P_1",[883,50687,50689],{"className":50688},[886],[888,50690,50691],{"xmlns":890},[892,50692,50693,50717],{},[895,50694,50695,50701,50703,50705,50707,50709,50711],{},[2884,50696,50697,50699],{},[898,50698,6796],{},[2111,50700,2963],{},[1711,50702,1836],{},[1711,50704,2460],{},[2111,50706,2963],{},[1711,50708,2095],{},[2111,50710,3034],{},[2884,50712,50713,50715],{},[898,50714,7929],{},[2111,50716,2963],{},[902,50718,50719],{"encoding":904},"Q_2 = -2 + 3P_2",[123,50721,49176,50722,1343,50762,1343,50804,1343,50836,2186],{},[883,50723,50725],{"className":50724},[886],[888,50726,50727],{"xmlns":890},[892,50728,50729,50759],{},[895,50730,50731,50737,50739,50741,50743,50745,50751,50753],{},[2884,50732,50733,50735],{},[898,50734,6796],{},[2111,50736,2238],{},[1711,50738,1836],{},[2111,50740,4282],{},[1711,50742,2460],{},[2111,50744,2963],{},[2884,50746,50747,50749],{},[898,50748,7929],{},[2111,50750,2238],{},[1711,50752,2095],{},[2884,50754,50755,50757],{},[898,50756,7929],{},[2111,50758,2963],{},[902,50760,50761],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,50763,50765],{"className":50764},[886],[888,50766,50767],{"xmlns":890},[892,50768,50769,50801],{},[895,50770,50771,50777,50779,50781,50783,50785,50791,50793,50795],{},[2884,50772,50773,50775],{},[898,50774,6796],{},[2111,50776,2963],{},[1711,50778,1836],{},[2111,50780,4798],{},[1711,50782,2095],{},[2111,50784,2963],{},[2884,50786,50787,50789],{},[898,50788,7929],{},[2111,50790,2238],{},[1711,50792,2460],{},[2111,50794,3034],{},[2884,50796,50797,50799],{},[898,50798,7929],{},[2111,50800,2963],{},[902,50802,50803],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,50805,50807],{"className":50806},[886],[888,50808,50809],{"xmlns":890},[892,50810,50811,50833],{},[895,50812,50813,50819,50821,50823,50825,50827],{},[2884,50814,50815,50817],{},[898,50816,6796],{},[2111,50818,2238],{},[1711,50820,1836],{},[1711,50822,2460],{},[2111,50824,4712],{},[1711,50826,2095],{},[2884,50828,50829,50831],{},[898,50830,7929],{},[2111,50832,2238],{},[902,50834,50835],{"encoding":904},"Q_1 = -10 + P_1",[883,50837,50839],{"className":50838},[886],[888,50840,50841],{"xmlns":890},[892,50842,50843,50865],{},[895,50844,50845,50851,50853,50855,50857,50859],{},[2884,50846,50847,50849],{},[898,50848,6796],{},[2111,50850,2963],{},[1711,50852,1836],{},[2111,50854,4798],{},[1711,50856,2095],{},[2111,50858,6262],{},[2884,50860,50861,50863],{},[898,50862,7929],{},[2111,50864,2963],{},[902,50866,50867],{"encoding":904},"Q_2 = 5 + 6P_2",[724,50869,50870,50873,50874,1343,50922,1343,50968,51018,51019,1343,51051,1343,51085,25192,51119,2009,51137,51155,51156,51169,51170,51196,51197,50534,51237,2186],{},[38,50871,50872],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,50875,50877],{"className":50876},[886],[888,50878,50879],{"xmlns":890},[892,50880,50881,50919],{},[895,50882,50883,50889,50891,50893,50895,50901,50903,50905,50911,50913],{},[2884,50884,50885,50887],{},[898,50886,6796],{},[2111,50888,2238],{},[1711,50890,1836],{},[2111,50892,39842],{},[1711,50894,2460],{},[2884,50896,50897,50899],{},[898,50898,7929],{},[2111,50900,2238],{},[1711,50902,2095],{},[2111,50904,2963],{},[2884,50906,50907,50909],{},[898,50908,7929],{},[2111,50910,2963],{},[1711,50912,2095],{},[2884,50914,50915,50917],{},[898,50916,7929],{},[2111,50918,3034],{},[902,50920,50921],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,50923,50925],{"className":50924},[886],[888,50926,50927],{"xmlns":890},[892,50928,50929,50965],{},[895,50930,50931,50937,50939,50941,50943,50949,50951,50957,50959],{},[2884,50932,50933,50935],{},[898,50934,6796],{},[2111,50936,2963],{},[1711,50938,1836],{},[2111,50940,7990],{},[1711,50942,2095],{},[2884,50944,50945,50947],{},[898,50946,7929],{},[2111,50948,2238],{},[1711,50950,2460],{},[2884,50952,50953,50955],{},[898,50954,7929],{},[2111,50956,2963],{},[1711,50958,2460],{},[2884,50960,50961,50963],{},[898,50962,7929],{},[2111,50964,3034],{},[902,50966,50967],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,50969,50971],{"className":50970},[886],[888,50972,50973],{"xmlns":890},[892,50974,50975,51015],{},[895,50976,50977,50983,50985,50987,50989,50991,50997,50999,51005,51007,51009],{},[2884,50978,50979,50981],{},[898,50980,6796],{},[2111,50982,3034],{},[1711,50984,1836],{},[2111,50986,9568],{},[1711,50988,2095],{},[2111,50990,2963],{},[2884,50992,50993,50995],{},[898,50994,7929],{},[2111,50996,2238],{},[1711,50998,2460],{},[2884,51000,51001,51003],{},[898,51002,7929],{},[2111,51004,2963],{},[1711,51006,2460],{},[2111,51008,6369],{},[2884,51010,51011,51013],{},[898,51012,7929],{},[2111,51014,3034],{},[902,51016,51017],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,51020,51022],{"className":51021},[886],[888,51023,51024],{"xmlns":890},[892,51025,51026,51048],{},[895,51027,51028,51034,51036,51038,51040,51042],{},[2884,51029,51030,51032],{},[898,51031,6796],{},[2111,51033,2238],{},[1711,51035,1836],{},[1711,51037,2460],{},[2111,51039,27799],{},[1711,51041,2095],{},[2884,51043,51044,51046],{},[898,51045,7929],{},[2111,51047,2238],{},[902,51049,51050],{"encoding":904},"Q_1 = -7 + P_1",[883,51052,51054],{"className":51053},[886],[888,51055,51056],{"xmlns":890},[892,51057,51058,51082],{},[895,51059,51060,51066,51068,51070,51072,51074,51076],{},[2884,51061,51062,51064],{},[898,51063,6796],{},[2111,51065,2963],{},[1711,51067,1836],{},[1711,51069,2460],{},[2111,51071,6369],{},[1711,51073,2095],{},[2111,51075,6369],{},[2884,51077,51078,51080],{},[898,51079,7929],{},[2111,51081,2963],{},[902,51083,51084],{"encoding":904},"Q_2 = -4 + 4P_2",[883,51086,51088],{"className":51087},[886],[888,51089,51090],{"xmlns":890},[892,51091,51092,51116],{},[895,51093,51094,51100,51102,51104,51106,51108,51110],{},[2884,51095,51096,51098],{},[898,51097,6796],{},[2111,51099,3034],{},[1711,51101,1836],{},[1711,51103,2460],{},[2111,51105,4798],{},[1711,51107,2095],{},[2111,51109,2963],{},[2884,51111,51112,51114],{},[898,51113,7929],{},[2111,51115,3034],{},[902,51117,51118],{"encoding":904},"Q_3 = -5 + 2P_3",[883,51120,51122],{"className":51121},[886],[888,51123,51124],{"xmlns":890},[892,51125,51126,51134],{},[895,51127,51128],{},[2884,51129,51130,51132],{},[898,51131,6796],{},[898,51133,21388],{},[902,51135,51136],{"encoding":904},"Q_i",[883,51138,51140],{"className":51139},[886],[888,51141,51142],{"xmlns":890},[892,51143,51144,51152],{},[895,51145,51146],{},[2884,51147,51148,51150],{},[898,51149,7929],{},[898,51151,21388],{},[902,51153,51154],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,51157,51159],{"className":51158},[886],[888,51160,51161],{"xmlns":890},[892,51162,51163,51167],{},[895,51164,51165],{},[898,51166,21388],{},[902,51168,21388],{"encoding":904},"-tého zboží, ",[883,51171,51173],{"className":51172},[886],[888,51174,51175],{"xmlns":890},[892,51176,51177,51193],{},[895,51178,51179,51181,51183,51185,51187,51189,51191],{},[898,51180,21388],{},[1711,51182,1836],{},[2111,51184,2238],{},[1711,51186,1726],{"separator":1725},[2111,51188,2963],{},[1711,51190,1726],{"separator":1725},[2111,51192,3034],{},[902,51194,51195],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,51198,51200],{"className":51199},[886],[888,51201,51202],{"xmlns":890},[892,51203,51204,51234],{},[895,51205,51206,51214,51216,51224,51226],{},[13142,51207,51208,51210,51212],{},[898,51209,6796],{},[2111,51211,2238],{},[898,51213,1722],{},[1711,51215,1726],{"separator":1725},[13142,51217,51218,51220,51222],{},[898,51219,6796],{},[2111,51221,2963],{},[898,51223,1722],{},[1711,51225,1726],{"separator":1725},[13142,51227,51228,51230,51232],{},[898,51229,6796],{},[2111,51231,3034],{},[898,51233,1722],{},[902,51235,51236],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,51238,51240],{"className":51239},[886],[888,51241,51242],{"xmlns":890},[892,51243,51244,51274],{},[895,51245,51246,51254,51256,51264,51266],{},[13142,51247,51248,51250,51252],{},[898,51249,7929],{},[2111,51251,2238],{},[898,51253,1722],{},[1711,51255,1726],{"separator":1725},[13142,51257,51258,51260,51262],{},[898,51259,7929],{},[2111,51261,2963],{},[898,51263,1722],{},[1711,51265,1726],{"separator":1725},[13142,51267,51268,51270,51272],{},[898,51269,7929],{},[2111,51271,3034],{},[898,51273,1722],{},[902,51275,51276],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,51278,51279,51282,51283,51319,51320,2186],{},[38,51280,51281],{},"2.13"," Jsou dány poptávka ",[883,51284,51286],{"className":51285},[886],[888,51287,51288],{"xmlns":890},[892,51289,51290,51316],{},[895,51291,51292,51294,51296,51298,51300,51302,51304,51306,51308,51310,51312,51314],{},[898,51293,7929],{},[1711,51295,1836],{},[898,51297,2778],{},[1711,51299,1714],{"stretchy":1713},[898,51301,6796],{},[1711,51303,1735],{"stretchy":1713},[1711,51305,1836],{},[1711,51307,2460],{},[2111,51309,6369],{},[898,51311,6796],{},[1711,51313,2095],{},[2111,51315,50301],{},[902,51317,51318],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,51321,51323],{"className":51322},[886],[888,51324,51325],{"xmlns":890},[892,51326,51327,51351],{},[895,51328,51329,51331,51333,51335,51337,51339,51341,51343,51345,51347,51349],{},[898,51330,7929],{},[1711,51332,1836],{},[898,51334,2362],{},[1711,51336,1714],{"stretchy":1713},[898,51338,6796],{},[1711,51340,1735],{"stretchy":1713},[1711,51342,1836],{},[2111,51344,3034],{},[898,51346,6796],{},[1711,51348,2095],{},[2111,51350,4712],{},[902,51352,51353],{"encoding":904},"P = S(Q) = 3Q + 10",[120,51355,51356,51393,51457,51517],{},[123,51357,51358,51359,50256,51376,2186],{},"(a) Určete rovnovážné množství ",[883,51360,51362],{"className":51361},[886],[888,51363,51364],{"xmlns":890},[892,51365,51366,51374],{},[895,51367,51368],{},[1716,51369,51370,51372],{},[898,51371,6796],{},[898,51373,1722],{},[902,51375,46001],{"encoding":904},[883,51377,51379],{"className":51378},[886],[888,51380,51381],{"xmlns":890},[892,51382,51383,51391],{},[895,51384,51385],{},[1716,51386,51387,51389],{},[898,51388,7929],{},[898,51390,1722],{},[902,51392,45064],{"encoding":904},[123,51394,51395,51396,51414,51415,51435,51436,51456],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,51397,51399],{"className":51398},[886],[888,51400,51401],{"xmlns":890},[892,51402,51403,51411],{},[895,51404,51405,51407,51409],{},[898,51406,1769],{},[1711,51408,1836],{},[2111,51410,27799],{},[902,51412,51413],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,51416,51418],{"className":51417},[886],[888,51419,51420],{"xmlns":890},[892,51421,51422,51432],{},[895,51423,51424],{},[13142,51425,51426,51428,51430],{},[898,51427,6796],{},[2111,51429,2238],{},[898,51431,1722],{},[902,51433,51434],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,51437,51439],{"className":51438},[886],[888,51440,51441],{"xmlns":890},[892,51442,51443,51453],{},[895,51444,51445],{},[13142,51446,51447,51449,51451],{},[898,51448,7929],{},[2111,51450,2238],{},[898,51452,1722],{},[902,51454,51455],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,51458,51459,51460,51414,51477,51435,51497,51456],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,51461,51463],{"className":51462},[886],[888,51464,51465],{"xmlns":890},[892,51466,51467,51475],{},[895,51468,51469,51471,51473],{},[898,51470,1769],{},[1711,51472,1836],{},[2111,51474,27799],{},[902,51476,51413],{"encoding":904},[883,51478,51480],{"className":51479},[886],[888,51481,51482],{"xmlns":890},[892,51483,51484,51494],{},[895,51485,51486],{},[13142,51487,51488,51490,51492],{},[898,51489,6796],{},[2111,51491,2963],{},[898,51493,1722],{},[902,51495,51496],{"encoding":904},"Q_2^E",[883,51498,51500],{"className":51499},[886],[888,51501,51502],{"xmlns":890},[892,51503,51504,51514],{},[895,51505,51506],{},[13142,51507,51508,51510,51512],{},[898,51509,7929],{},[2111,51511,2963],{},[898,51513,1722],{},[902,51515,51516],{"encoding":904},"P_2^E",[123,51518,51519],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,51521,51522,51523,2186],{},"Viz též ",[207,51524,46319],{"className":51525,"dataFsResolvedFilePath":809,"href":810},[210],[198,51527,46621],{"id":51528},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,51530,51531,51282,51534,51319,51570,2186],{},[38,51532,51533],{},"2.14",[883,51535,51537],{"className":51536},[886],[888,51538,51539],{"xmlns":890},[892,51540,51541,51567],{},[895,51542,51543,51545,51547,51549,51551,51553,51555,51557,51559,51561,51563,51565],{},[898,51544,7929],{},[1711,51546,1836],{},[898,51548,207],{},[898,51550,6796],{},[1711,51552,2095],{},[898,51554,2223],{},[1711,51556,1836],{},[1711,51558,2460],{},[2111,51560,2963],{},[898,51562,6796],{},[1711,51564,2095],{},[2111,51566,7120],{},[902,51568,51569],{"encoding":904},"P = aQ + b = -2Q + 50",[883,51571,51573],{"className":51572},[886],[888,51574,51575],{"xmlns":890},[892,51576,51577,51601],{},[895,51578,51579,51581,51583,51585,51587,51589,51591,51593,51595,51597,51599],{},[898,51580,7929],{},[1711,51582,1836],{},[898,51584,2090],{},[898,51586,6796],{},[1711,51588,2095],{},[898,51590,2098],{},[1711,51592,1836],{},[2111,51594,22919],{},[898,51596,6796],{},[1711,51598,2095],{},[2111,51600,4306],{},[902,51602,51603],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,51605,51606,51642,51645,51731,51784,51864,51918],{},[123,51607,51358,51608,50256,51625,2186],{},[883,51609,51611],{"className":51610},[886],[888,51612,51613],{"xmlns":890},[892,51614,51615,51623],{},[895,51616,51617],{},[1716,51618,51619,51621],{},[898,51620,6796],{},[898,51622,1722],{},[902,51624,46001],{"encoding":904},[883,51626,51628],{"className":51627},[886],[888,51629,51630],{"xmlns":890},[892,51631,51632,51640],{},[895,51633,51634],{},[1716,51635,51636,51638],{},[898,51637,7929],{},[898,51639,1722],{},[902,51641,45064],{"encoding":904},[123,51643,51644],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,51646,51647,51648,51665,51666,6682,51679,6696,51695,51711,51712,2186],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,51649,51651],{"className":51650},[886],[888,51652,51653],{"xmlns":890},[892,51654,51655,51663],{},[895,51656,51657],{},[1716,51658,51659,51661],{},[898,51660,6796],{},[898,51662,1722],{},[902,51664,46001],{"encoding":904}," odpovídající změně ",[883,51667,51669],{"className":51668},[886],[888,51670,51671],{"xmlns":890},[892,51672,51673,51677],{},[895,51674,51675],{},[898,51676,207],{},[902,51678,207],{"encoding":904},[883,51680,51682],{"className":51681},[886],[888,51683,51684],{"xmlns":890},[892,51685,51686,51692],{},[895,51687,51688,51690],{},[1711,51689,2460],{},[2111,51691,2963],{},[902,51693,51694],{"encoding":904},"-2",[883,51696,51698],{"className":51697},[886],[888,51699,51700],{"xmlns":890},[892,51701,51702,51708],{},[895,51703,51704,51706],{},[1711,51705,2460],{},[2111,51707,3034],{},[902,51709,51710],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,51713,51715],{"className":51714},[886],[888,51716,51717],{"xmlns":890},[892,51718,51719,51729],{},[895,51720,51721],{},[13142,51722,51723,51725,51727],{},[898,51724,6796],{},[2111,51726,2238],{},[898,51728,1722],{},[902,51730,51434],{"encoding":904},[123,51732,51733,51734,51665,51751,51764,51765,2186],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,51735,51737],{"className":51736},[886],[888,51738,51739],{"xmlns":890},[892,51740,51741,51749],{},[895,51742,51743],{},[1716,51744,51745,51747],{},[898,51746,6796],{},[898,51748,1722],{},[902,51750,46001],{"encoding":904},[883,51752,51754],{"className":51753},[886],[888,51755,51756],{"xmlns":890},[892,51757,51758,51762],{},[895,51759,51760],{},[898,51761,2223],{},[902,51763,2223],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,51766,51768],{"className":51767},[886],[888,51769,51770],{"xmlns":890},[892,51771,51772,51782],{},[895,51773,51774],{},[13142,51775,51776,51778,51780],{},[898,51777,6796],{},[2111,51779,2963],{},[898,51781,1722],{},[902,51783,51496],{"encoding":904},[123,51785,51786,51787,51665,51804,6682,51817,6696,51830,51711,51844,2186],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,51788,51790],{"className":51789},[886],[888,51791,51792],{"xmlns":890},[892,51793,51794,51802],{},[895,51795,51796],{},[1716,51797,51798,51800],{},[898,51799,6796],{},[898,51801,1722],{},[902,51803,46001],{"encoding":904},[883,51805,51807],{"className":51806},[886],[888,51808,51809],{"xmlns":890},[892,51810,51811,51815],{},[895,51812,51813],{},[898,51814,2090],{},[902,51816,2090],{"encoding":904},[883,51818,51820],{"className":51819},[886],[888,51821,51822],{"xmlns":890},[892,51823,51824,51828],{},[895,51825,51826],{},[2111,51827,22919],{},[902,51829,48058],{"encoding":904},[883,51831,51833],{"className":51832},[886],[888,51834,51835],{"xmlns":890},[892,51836,51837,51841],{},[895,51838,51839],{},[2111,51840,4275],{},[902,51842,51843],{"encoding":904},"0{,}8",[883,51845,51847],{"className":51846},[886],[888,51848,51849],{"xmlns":890},[892,51850,51851,51861],{},[895,51852,51853],{},[13142,51854,51855,51857,51859],{},[898,51856,6796],{},[2111,51858,3034],{},[898,51860,1722],{},[902,51862,51863],{"encoding":904},"Q_3^E",[123,51865,51866,51867,51665,51884,51897,51898,2186],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,51868,51870],{"className":51869},[886],[888,51871,51872],{"xmlns":890},[892,51873,51874,51882],{},[895,51875,51876],{},[1716,51877,51878,51880],{},[898,51879,6796],{},[898,51881,1722],{},[902,51883,46001],{"encoding":904},[883,51885,51887],{"className":51886},[886],[888,51888,51889],{"xmlns":890},[892,51890,51891,51895],{},[895,51892,51893],{},[898,51894,2098],{},[902,51896,2098],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,51899,51901],{"className":51900},[886],[888,51902,51903],{"xmlns":890},[892,51904,51905,51915],{},[895,51906,51907],{},[13142,51908,51909,51911,51913],{},[898,51910,6796],{},[2111,51912,6369],{},[898,51914,1722],{},[902,51916,51917],{"encoding":904},"Q_4^E",[123,51919,51920,51921,51938,51939,51952,51953,25018,51966,1343,51981,25018,51994,2009,52008,25018,52021,52036,52037,2186],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,51922,51924],{"className":51923},[886],[888,51925,51926],{"xmlns":890},[892,51927,51928,51936],{},[895,51929,51930],{},[1716,51931,51932,51934],{},[898,51933,6796],{},[898,51935,1722],{},[902,51937,46001],{"encoding":904}," odpovídající změnám ",[883,51940,51942],{"className":51941},[886],[888,51943,51944],{"xmlns":890},[892,51945,51946,51950],{},[895,51947,51948],{},[898,51949,207],{},[902,51951,207],{"encoding":904}," o 1, ",[883,51954,51956],{"className":51955},[886],[888,51957,51958],{"xmlns":890},[892,51959,51960,51964],{},[895,51961,51962],{},[898,51963,2223],{},[902,51965,2223],{"encoding":904},[883,51967,51969],{"className":51968},[886],[888,51970,51971],{"xmlns":890},[892,51972,51973,51979],{},[895,51974,51975,51977],{},[1711,51976,2460],{},[2111,51978,4712],{},[902,51980,23053],{"encoding":904},[883,51982,51984],{"className":51983},[886],[888,51985,51986],{"xmlns":890},[892,51987,51988,51992],{},[895,51989,51990],{},[898,51991,2090],{},[902,51993,2090],{"encoding":904},[883,51995,51997],{"className":51996},[886],[888,51998,51999],{"xmlns":890},[892,52000,52001,52005],{},[895,52002,52003],{},[2111,52004,4343],{},[902,52006,52007],{"encoding":904},"0{,}1",[883,52009,52011],{"className":52010},[886],[888,52012,52013],{"xmlns":890},[892,52014,52015,52019],{},[895,52016,52017],{},[898,52018,2098],{},[902,52020,2098],{"encoding":904},[883,52022,52024],{"className":52023},[886],[888,52025,52026],{"xmlns":890},[892,52027,52028,52034],{},[895,52029,52030,52032],{},[1711,52031,2460],{},[2111,52033,4712],{},[902,52035,23053],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,52038,52040],{"className":52039},[886],[888,52041,52042],{"xmlns":890},[892,52043,52044,52054],{},[895,52045,52046],{},[13142,52047,52048,52050,52052],{},[898,52049,6796],{},[2111,52051,4798],{},[898,52053,1722],{},[902,52055,52056],{"encoding":904},"Q_5^E",[724,52058,52059,51282,52062,51319,52085,2186],{},[38,52060,52061],{},"2.15",[883,52063,52065],{"className":52064},[886],[888,52066,52067],{"xmlns":890},[892,52068,52069,52083],{},[895,52070,52071,52073,52075,52077,52079,52081],{},[898,52072,7929],{},[1711,52074,1836],{},[898,52076,207],{},[898,52078,6796],{},[1711,52080,2095],{},[898,52082,2223],{},[902,52084,40658],{"encoding":904},[883,52086,52088],{"className":52087},[886],[888,52089,52090],{"xmlns":890},[892,52091,52092,52106],{},[895,52093,52094,52096,52098,52100,52102,52104],{},[898,52095,7929],{},[1711,52097,1836],{},[898,52099,2090],{},[898,52101,6796],{},[1711,52103,2095],{},[898,52105,2098],{},[902,52107,43840],{"encoding":904},[120,52109,52110,52185,52202,52311,52364,52418],{},[123,52111,52112,52113,52126,52127,52152,52153,52184],{},"(a) Odvoďte redukovaný tvar pro ",[883,52114,52116],{"className":52115},[886],[888,52117,52118],{"xmlns":890},[892,52119,52120,52124],{},[895,52121,52122],{},[898,52123,7929],{},[902,52125,7929],{"encoding":904},". Stanovte podmínky pro ",[883,52128,52130],{"className":52129},[886],[888,52131,52132],{"xmlns":890},[892,52133,52134,52150],{},[895,52135,52136,52138,52140,52142,52144,52146,52148],{},[898,52137,207],{},[1711,52139,1726],{"separator":1725},[898,52141,2223],{},[1711,52143,1726],{"separator":1725},[898,52145,2090],{},[1711,52147,1726],{"separator":1725},[898,52149,2098],{},[902,52151,46883],{"encoding":904}," tak, aby rovnovážný bod ",[883,52154,52156],{"className":52155},[886],[888,52157,52158],{"xmlns":890},[892,52159,52160,52182],{},[895,52161,52162,52164,52166,52172,52174,52180],{},[898,52163,1722],{},[1711,52165,5144],{"stretchy":1713},[1716,52167,52168,52170],{},[898,52169,6796],{},[898,52171,1722],{},[1711,52173,1726],{"separator":1725},[1716,52175,52176,52178],{},[898,52177,7929],{},[898,52179,1722],{},[1711,52181,5163],{"stretchy":1713},[902,52183,44965],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,52186,52187,52188,52201],{},"(b) Vypočtěte multiplikátory pro ",[883,52189,52191],{"className":52190},[886],[888,52192,52193],{"xmlns":890},[892,52194,52195,52199],{},[895,52196,52197],{},[898,52198,7929],{},[902,52200,7929],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,52203,52204,52205,1343,52225,1343,52243,1343,52261,52279,52280,52297,52298,2186],{},"(c) Pro hodnoty parametrů ",[883,52206,52208],{"className":52207},[886],[888,52209,52210],{"xmlns":890},[892,52211,52212,52222],{},[895,52213,52214,52216,52218,52220],{},[898,52215,207],{},[1711,52217,1836],{},[1711,52219,2460],{},[2111,52221,2963],{},[902,52223,52224],{"encoding":904},"a = -2",[883,52226,52228],{"className":52227},[886],[888,52229,52230],{"xmlns":890},[892,52231,52232,52240],{},[895,52233,52234,52236,52238],{},[898,52235,2223],{},[1711,52237,1836],{},[2111,52239,9195],{},[902,52241,52242],{"encoding":904},"b = 40",[883,52244,52246],{"className":52245},[886],[888,52247,52248],{"xmlns":890},[892,52249,52250,52258],{},[895,52251,52252,52254,52256],{},[898,52253,2090],{},[1711,52255,1836],{},[2111,52257,8993],{},[902,52259,52260],{"encoding":904},"c = 0{,}5",[883,52262,52264],{"className":52263},[886],[888,52265,52266],{"xmlns":890},[892,52267,52268,52276],{},[895,52269,52270,52272,52274],{},[898,52271,2098],{},[1711,52273,1836],{},[2111,52275,4712],{},[902,52277,52278],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,52281,52283],{"className":52282},[886],[888,52284,52285],{"xmlns":890},[892,52286,52287,52295],{},[895,52288,52289],{},[1716,52290,52291,52293],{},[898,52292,7929],{},[898,52294,1722],{},[902,52296,45064],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,52299,52301],{"className":52300},[886],[888,52302,52303],{"xmlns":890},[892,52304,52305,52309],{},[895,52306,52307],{},[898,52308,7929],{},[902,52310,7929],{"encoding":904},[123,52312,52313,52314,51665,52331,52344,52345,2186],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,52315,52317],{"className":52316},[886],[888,52318,52319],{"xmlns":890},[892,52320,52321,52329],{},[895,52322,52323],{},[1716,52324,52325,52327],{},[898,52326,7929],{},[898,52328,1722],{},[902,52330,45064],{"encoding":904},[883,52332,52334],{"className":52333},[886],[888,52335,52336],{"xmlns":890},[892,52337,52338,52342],{},[895,52339,52340],{},[898,52341,207],{},[902,52343,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,52346,52348],{"className":52347},[886],[888,52349,52350],{"xmlns":890},[892,52351,52352,52362],{},[895,52353,52354],{},[13142,52355,52356,52358,52360],{},[898,52357,7929],{},[2111,52359,2238],{},[898,52361,1722],{},[902,52363,51455],{"encoding":904},[123,52365,52366,52367,52384,52385,52398,52399,2186],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,52368,52370],{"className":52369},[886],[888,52371,52372],{"xmlns":890},[892,52373,52374,52382],{},[895,52375,52376],{},[1716,52377,52378,52380],{},[898,52379,7929],{},[898,52381,1722],{},[902,52383,45064],{"encoding":904}," odpovídající poklesu ",[883,52386,52388],{"className":52387},[886],[888,52389,52390],{"xmlns":890},[892,52391,52392,52396],{},[895,52393,52394],{},[898,52395,207],{},[902,52397,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,52400,52402],{"className":52401},[886],[888,52403,52404],{"xmlns":890},[892,52405,52406,52416],{},[895,52407,52408],{},[13142,52409,52410,52412,52414],{},[898,52411,7929],{},[2111,52413,2963],{},[898,52415,1722],{},[902,52417,51516],{"encoding":904},[123,52419,52420,52421,51938,52438,52451,52452,6696,52465,2009,52480,52493,52494,2186],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,52422,52424],{"className":52423},[886],[888,52425,52426],{"xmlns":890},[892,52427,52428,52436],{},[895,52429,52430],{},[1716,52431,52432,52434],{},[898,52433,7929],{},[898,52435,1722],{},[902,52437,45064],{"encoding":904},[883,52439,52441],{"className":52440},[886],[888,52442,52443],{"xmlns":890},[892,52444,52445,52449],{},[895,52446,52447],{},[898,52448,207],{},[902,52450,207],{"encoding":904}," na 35, ",[883,52453,52455],{"className":52454},[886],[888,52456,52457],{"xmlns":890},[892,52458,52459,52463],{},[895,52460,52461],{},[898,52462,2090],{},[902,52464,2090],{"encoding":904},[883,52466,52468],{"className":52467},[886],[888,52469,52470],{"xmlns":890},[892,52471,52472,52477],{},[895,52473,52474],{},[2111,52475,52476],{},"0,7",[902,52478,52479],{"encoding":904},"0{,}7",[883,52481,52483],{"className":52482},[886],[888,52484,52485],{"xmlns":890},[892,52486,52487,52491],{},[895,52488,52489],{},[898,52490,2098],{},[902,52492,2098],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,52495,52497],{"className":52496},[886],[888,52498,52499],{"xmlns":890},[892,52500,52501,52511],{},[895,52502,52503],{},[13142,52504,52505,52507,52509],{},[898,52506,7929],{},[2111,52508,3034],{},[898,52510,1722],{},[902,52512,52513],{"encoding":904},"P_3^E",[724,52515,52516,51282,52519,51319,52547,25192,52575,2009,52601,2186],{},[38,52517,52518],{},"2.16",[883,52520,52522],{"className":52521},[886],[888,52523,52524],{"xmlns":890},[892,52525,52526,52544],{},[895,52527,52528,52530,52532,52534,52536,52538],{},[898,52529,7929],{},[1711,52531,1836],{},[898,52533,207],{},[1711,52535,2095],{},[898,52537,2223],{},[1716,52539,52540,52542],{},[898,52541,6796],{},[2111,52543,2963],{},[902,52545,52546],{"encoding":904},"P = a + bQ^2",[883,52548,52550],{"className":52549},[886],[888,52551,52552],{"xmlns":890},[892,52553,52554,52572],{},[895,52555,52556,52558,52560,52562,52564,52566],{},[898,52557,7929],{},[1711,52559,1836],{},[898,52561,2090],{},[1711,52563,2095],{},[898,52565,2098],{},[1716,52567,52568,52570],{},[898,52569,6796],{},[2111,52571,2963],{},[902,52573,52574],{"encoding":904},"P = c + dQ^2",[883,52576,52578],{"className":52577},[886],[888,52579,52580],{"xmlns":890},[892,52581,52582,52598],{},[895,52583,52584,52586,52588,52590,52592,52594,52596],{},[898,52585,207],{},[1711,52587,1726],{"separator":1725},[898,52589,2090],{},[1711,52591,1726],{"separator":1725},[898,52593,2098],{},[1711,52595,2123],{},[2111,52597,2113],{},[902,52599,52600],{"encoding":904},"a, c, d > 0",[883,52602,52604],{"className":52603},[886],[888,52605,52606],{"xmlns":890},[892,52607,52608,52616],{},[895,52609,52610,52612,52614],{},[898,52611,2223],{},[1711,52613,2109],{},[2111,52615,2113],{},[902,52617,52618],{"encoding":904},"b \u003C 0",[120,52620,52621,52669,52685,52792,52844,52896,53005,53021,53120,53173],{},[123,52622,52112,52623,52636,52637,52668],{},[883,52624,52626],{"className":52625},[886],[888,52627,52628],{"xmlns":890},[892,52629,52630,52634],{},[895,52631,52632],{},[898,52633,6796],{},[902,52635,6796],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,52638,52640],{"className":52639},[886],[888,52641,52642],{"xmlns":890},[892,52643,52644,52666],{},[895,52645,52646,52648,52650,52656,52658,52664],{},[898,52647,1722],{},[1711,52649,5144],{"stretchy":1713},[1716,52651,52652,52654],{},[898,52653,6796],{},[898,52655,1722],{},[1711,52657,1726],{"separator":1725},[1716,52659,52660,52662],{},[898,52661,7929],{},[898,52663,1722],{},[1711,52665,5163],{"stretchy":1713},[902,52667,44965],{"encoding":904}," patřil do 1. kvadrantu.",[123,52670,52187,52671,52684],{},[883,52672,52674],{"className":52673},[886],[888,52675,52676],{"xmlns":890},[892,52677,52678,52682],{},[895,52679,52680],{},[898,52681,6796],{},[902,52683,6796],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,52686,52204,52687,1343,52705,1343,52725,1343,52743,52761,52762,52297,52779,2186],{},[883,52688,52690],{"className":52689},[886],[888,52691,52692],{"xmlns":890},[892,52693,52694,52702],{},[895,52695,52696,52698,52700],{},[898,52697,207],{},[1711,52699,1836],{},[2111,52701,4282],{},[902,52703,52704],{"encoding":904},"a = 100",[883,52706,52708],{"className":52707},[886],[888,52709,52710],{"xmlns":890},[892,52711,52712,52722],{},[895,52713,52714,52716,52718,52720],{},[898,52715,2223],{},[1711,52717,1836],{},[1711,52719,2460],{},[2111,52721,2238],{},[902,52723,52724],{"encoding":904},"b = -1",[883,52726,52728],{"className":52727},[886],[888,52729,52730],{"xmlns":890},[892,52731,52732,52740],{},[895,52733,52734,52736,52738],{},[898,52735,2090],{},[1711,52737,1836],{},[2111,52739,4306],{},[902,52741,52742],{"encoding":904},"c = 20",[883,52744,52746],{"className":52745},[886],[888,52747,52748],{"xmlns":890},[892,52749,52750,52758],{},[895,52751,52752,52754,52756],{},[898,52753,2098],{},[1711,52755,1836],{},[2111,52757,2238],{},[902,52759,52760],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,52763,52765],{"className":52764},[886],[888,52766,52767],{"xmlns":890},[892,52768,52769,52777],{},[895,52770,52771],{},[1716,52772,52773,52775],{},[898,52774,6796],{},[898,52776,1722],{},[902,52778,46001],{"encoding":904},[883,52780,52782],{"className":52781},[886],[888,52783,52784],{"xmlns":890},[892,52785,52786,52790],{},[895,52787,52788],{},[898,52789,6796],{},[902,52791,6796],{"encoding":904},[123,52793,51733,52794,51665,52811,52824,52825,2186],{},[883,52795,52797],{"className":52796},[886],[888,52798,52799],{"xmlns":890},[892,52800,52801,52809],{},[895,52802,52803],{},[1716,52804,52805,52807],{},[898,52806,6796],{},[898,52808,1722],{},[902,52810,46001],{"encoding":904},[883,52812,52814],{"className":52813},[886],[888,52815,52816],{"xmlns":890},[892,52817,52818,52822],{},[895,52819,52820],{},[898,52821,207],{},[902,52823,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,52826,52828],{"className":52827},[886],[888,52829,52830],{"xmlns":890},[892,52831,52832,52842],{},[895,52833,52834],{},[13142,52835,52836,52838,52840],{},[898,52837,6796],{},[2111,52839,2238],{},[898,52841,1722],{},[902,52843,51434],{"encoding":904},[123,52845,51786,52846,51665,52863,52876,52877,2186],{},[883,52847,52849],{"className":52848},[886],[888,52850,52851],{"xmlns":890},[892,52852,52853,52861],{},[895,52854,52855],{},[1716,52856,52857,52859],{},[898,52858,6796],{},[898,52860,1722],{},[902,52862,46001],{"encoding":904},[883,52864,52866],{"className":52865},[886],[888,52867,52868],{"xmlns":890},[892,52869,52870,52874],{},[895,52871,52872],{},[898,52873,2090],{},[902,52875,2090],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,52878,52880],{"className":52879},[886],[888,52881,52882],{"xmlns":890},[892,52883,52884,52894],{},[895,52885,52886],{},[13142,52887,52888,52890,52892],{},[898,52889,6796],{},[2111,52891,2963],{},[898,52893,1722],{},[902,52895,51496],{"encoding":904},[123,52897,51866,52898,51938,52915,52928,52929,6696,52942,52957,52958,52971,52972,52985,52986,2186],{},[883,52899,52901],{"className":52900},[886],[888,52902,52903],{"xmlns":890},[892,52904,52905,52913],{},[895,52906,52907],{},[1716,52908,52909,52911],{},[898,52910,6796],{},[898,52912,1722],{},[902,52914,46001],{"encoding":904},[883,52916,52918],{"className":52917},[886],[888,52919,52920],{"xmlns":890},[892,52921,52922,52926],{},[895,52923,52924],{},[898,52925,207],{},[902,52927,207],{"encoding":904}," na 110, poklesu ",[883,52930,52932],{"className":52931},[886],[888,52933,52934],{"xmlns":890},[892,52935,52936,52940],{},[895,52937,52938],{},[898,52939,2223],{},[902,52941,2223],{"encoding":904},[883,52943,52945],{"className":52944},[886],[888,52946,52947],{"xmlns":890},[892,52948,52949,52955],{},[895,52950,52951,52953],{},[1711,52952,2460],{},[2111,52954,2963],{},[902,52956,51694],{"encoding":904},", růstu ",[883,52959,52961],{"className":52960},[886],[888,52962,52963],{"xmlns":890},[892,52964,52965,52969],{},[895,52966,52967],{},[898,52968,2090],{},[902,52970,2090],{"encoding":904}," na 25 a růstu ",[883,52973,52975],{"className":52974},[886],[888,52976,52977],{"xmlns":890},[892,52978,52979,52983],{},[895,52980,52981],{},[898,52982,2098],{},[902,52984,2098],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,52987,52989],{"className":52988},[886],[888,52990,52991],{"xmlns":890},[892,52992,52993,53003],{},[895,52994,52995],{},[13142,52996,52997,52999,53001],{},[898,52998,6796],{},[2111,53000,3034],{},[898,53002,1722],{},[902,53004,51863],{"encoding":904},[123,53006,53007,53008,52684],{},"(i) Vypočtěte multiplikátory pro ",[883,53009,53011],{"className":53010},[886],[888,53012,53013],{"xmlns":890},[892,53014,53015,53019],{},[895,53016,53017],{},[898,53018,7929],{},[902,53020,7929],{"encoding":904},[123,53022,53023,53024,52297,53041,53054,53055,51665,53072,6696,53085,53100,53101,2186],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,53025,53027],{"className":53026},[886],[888,53028,53029],{"xmlns":890},[892,53030,53031,53039],{},[895,53032,53033],{},[1716,53034,53035,53037],{},[898,53036,7929],{},[898,53038,1722],{},[902,53040,45064],{"encoding":904},[883,53042,53044],{"className":53043},[886],[888,53045,53046],{"xmlns":890},[892,53047,53048,53052],{},[895,53049,53050],{},[898,53051,7929],{},[902,53053,7929],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,53056,53058],{"className":53057},[886],[888,53059,53060],{"xmlns":890},[892,53061,53062,53070],{},[895,53063,53064],{},[1716,53065,53066,53068],{},[898,53067,7929],{},[898,53069,1722],{},[902,53071,45064],{"encoding":904},[883,53073,53075],{"className":53074},[886],[888,53076,53077],{"xmlns":890},[892,53078,53079,53083],{},[895,53080,53081],{},[898,53082,207],{},[902,53084,207],{"encoding":904},[883,53086,53088],{"className":53087},[886],[888,53089,53090],{"xmlns":890},[892,53091,53092,53098],{},[895,53093,53094,53096],{},[1711,53095,2460],{},[2111,53097,3034],{},[902,53099,51710],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,53102,53104],{"className":53103},[886],[888,53105,53106],{"xmlns":890},[892,53107,53108,53118],{},[895,53109,53110],{},[13142,53111,53112,53114,53116],{},[898,53113,7929],{},[2111,53115,2238],{},[898,53117,1722],{},[902,53119,51455],{"encoding":904},[123,53121,53122,53123,51665,53140,53153,53154,2186],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,53124,53126],{"className":53125},[886],[888,53127,53128],{"xmlns":890},[892,53129,53130,53138],{},[895,53131,53132],{},[1716,53133,53134,53136],{},[898,53135,7929],{},[898,53137,1722],{},[902,53139,45064],{"encoding":904},[883,53141,53143],{"className":53142},[886],[888,53144,53145],{"xmlns":890},[892,53146,53147,53151],{},[895,53148,53149],{},[898,53150,207],{},[902,53152,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,53155,53157],{"className":53156},[886],[888,53158,53159],{"xmlns":890},[892,53160,53161,53171],{},[895,53162,53163],{},[13142,53164,53165,53167,53169],{},[898,53166,7929],{},[2111,53168,2963],{},[898,53170,1722],{},[902,53172,51516],{"encoding":904},[123,53174,53175,53176,52384,53193,53206,53207,6696,53220,52957,53235,53248,53249,53262,53263,2186],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,53177,53179],{"className":53178},[886],[888,53180,53181],{"xmlns":890},[892,53182,53183,53191],{},[895,53184,53185],{},[1716,53186,53187,53189],{},[898,53188,7929],{},[898,53190,1722],{},[902,53192,45064],{"encoding":904},[883,53194,53196],{"className":53195},[886],[888,53197,53198],{"xmlns":890},[892,53199,53200,53204],{},[895,53201,53202],{},[898,53203,207],{},[902,53205,207],{"encoding":904}," na 90, poklesu ",[883,53208,53210],{"className":53209},[886],[888,53211,53212],{"xmlns":890},[892,53213,53214,53218],{},[895,53215,53216],{},[898,53217,2223],{},[902,53219,2223],{"encoding":904},[883,53221,53223],{"className":53222},[886],[888,53224,53225],{"xmlns":890},[892,53226,53227,53233],{},[895,53228,53229,53231],{},[1711,53230,2460],{},[2111,53232,3034],{},[902,53234,51710],{"encoding":904},[883,53236,53238],{"className":53237},[886],[888,53239,53240],{"xmlns":890},[892,53241,53242,53246],{},[895,53243,53244],{},[898,53245,2090],{},[902,53247,2090],{"encoding":904}," na 30 a růstu ",[883,53250,53252],{"className":53251},[886],[888,53253,53254],{"xmlns":890},[892,53255,53256,53260],{},[895,53257,53258],{},[898,53259,2098],{},[902,53261,2098],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,53264,53266],{"className":53265},[886],[888,53267,53268],{"xmlns":890},[892,53269,53270,53280],{},[895,53271,53272],{},[13142,53273,53274,53276,53278],{},[898,53275,7929],{},[2111,53277,3034],{},[898,53279,1722],{},[902,53281,52513],{"encoding":904},[198,53283,820],{"id":53284},"přebytek-spotřebitele-a-výrobce-1",[724,53286,53287,51282,53290,51319,53326,2186],{},[38,53288,53289],{},"2.17",[883,53291,53293],{"className":53292},[886],[888,53294,53295],{"xmlns":890},[892,53296,53297,53323],{},[895,53298,53299,53301,53303,53305,53307,53309,53311,53313,53315,53317],{},[898,53300,7929],{},[1711,53302,1836],{},[898,53304,2778],{},[1711,53306,1714],{"stretchy":1713},[898,53308,6796],{},[1711,53310,1735],{"stretchy":1713},[1711,53312,1836],{},[2111,53314,4733],{},[1711,53316,2460],{},[1716,53318,53319,53321],{},[898,53320,6796],{},[2111,53322,2963],{},[902,53324,53325],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,53327,53329],{"className":53328},[886],[888,53330,53331],{"xmlns":890},[892,53332,53333,53359],{},[895,53334,53335,53337,53339,53341,53343,53345,53347,53349,53351,53353],{},[898,53336,7929],{},[1711,53338,1836],{},[898,53340,2362],{},[1711,53342,1714],{"stretchy":1713},[898,53344,6796],{},[1711,53346,1735],{"stretchy":1713},[1711,53348,1836],{},[2111,53350,3034],{},[1711,53352,2095],{},[1716,53354,53355,53357],{},[898,53356,6796],{},[2111,53358,2963],{},[902,53360,53361],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,53363,53364,53367],{},[123,53365,53366],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,53368,53369],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,53371,53372,51282,53375,51319,53409,2186],{},[38,53373,53374],{},"2.18",[883,53376,53378],{"className":53377},[886],[888,53379,53380],{"xmlns":890},[892,53381,53382,53406],{},[895,53383,53384,53386,53388,53390,53392,53394,53396,53398,53400,53402,53404],{},[898,53385,7929],{},[1711,53387,1836],{},[898,53389,2778],{},[1711,53391,1714],{"stretchy":1713},[898,53393,6796],{},[1711,53395,1735],{"stretchy":1713},[1711,53397,1836],{},[2111,53399,7703],{},[1711,53401,2460],{},[2111,53403,2963],{},[898,53405,6796],{},[902,53407,53408],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,53410,53412],{"className":53411},[886],[888,53413,53414],{"xmlns":890},[892,53415,53416,53442],{},[895,53417,53418,53420,53422,53424,53426,53428,53430,53432,53434,53436],{},[898,53419,7929],{},[1711,53421,1836],{},[898,53423,2362],{},[1711,53425,1714],{"stretchy":1713},[898,53427,6796],{},[1711,53429,1735],{"stretchy":1713},[1711,53431,1836],{},[2111,53433,3034],{},[1711,53435,2095],{},[1716,53437,53438,53440],{},[898,53439,6796],{},[2111,53441,2963],{},[902,53443,53361],{"encoding":904},[120,53445,53446,53466,53469,53472],{},[123,53447,53448,53449,2186],{},"(a) Vypočtěte rovnovážné množství ",[883,53450,53452],{"className":53451},[886],[888,53453,53454],{"xmlns":890},[892,53455,53456,53464],{},[895,53457,53458],{},[1716,53459,53460,53462],{},[898,53461,6796],{},[898,53463,1722],{},[902,53465,46001],{"encoding":904},[123,53467,53468],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,53470,53471],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,53473,53474],{},"(c) Graficky interpretujte.",[40568,53476],{},[115,53478,53480],{"id":53479},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,53482,53483,53486,53489,53492,53495,53498,53501,53504,53507,53510,53513,53516,53519,53522],{},[123,53484,53485],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,53487,53488],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,53490,53491],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,53493,53494],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,53496,53497],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,53499,53500],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,53502,53503],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,53505,53506],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,53508,53509],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,53511,53512],{},"K čemu slouží multiplikátory?",[123,53514,53515],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,53517,53518],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,53520,53521],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,53523,53524],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[40568,53526],{},[115,53528,5422],{"id":5421},[724,53530,53531],{},[38,53532,2840],{},[120,53534,53535,53570,53575,53605,53610,53673,53699,53704,53734,53743,53750,53756],{},[123,53536,53537,1648,53540,22246,53543,1700,53545,1343,53568],{},[38,53538,53539],{},"Poptávané množství",[614,53541,53542],{},"quantity demanded",[38,53544,31600],{},[883,53546,53548],{"className":53547},[886],[888,53549,53550],{"xmlns":890},[892,53551,53552,53566],{},[895,53553,53554,53556,53558,53560,53562,53564],{},[898,53555,6796],{},[1711,53557,1836],{},[898,53559,2778],{},[1711,53561,1714],{"stretchy":1713},[898,53563,7929],{},[1711,53565,1735],{"stretchy":1713},[902,53567,8181],{"encoding":904},[38,53569,41047],{},[123,53571,53572,53574],{},[38,53573,41054],{}," — substituční + důchodový efekt",[123,53576,53577,1700,53580],{},[38,53578,53579],{},"Reálné cenové rozpětí",[883,53581,53583],{"className":53582},[886],[888,53584,53585],{"xmlns":890},[892,53586,53587,53603],{},[895,53588,53589,53591,53593,53595,53601],{},[1711,53590,1714],{"stretchy":1713},[2111,53592,2113],{},[1711,53594,1726],{"separator":1725},[2884,53596,53597,53599],{},[898,53598,7929],{},[2111,53600,2113],{},[1711,53602,1735],{"stretchy":1713},[902,53604,41255],{"encoding":904},[123,53606,53607,15070],{},[38,53608,53609],{},"Homogenita poptávky",[123,53611,53612,1700,53615,1343,53638,1343,53655,53672],{},[38,53613,53614],{},"Lineární poptávka",[883,53616,53618],{"className":53617},[886],[888,53619,53620],{"xmlns":890},[892,53621,53622,53636],{},[895,53623,53624,53626,53628,53630,53632,53634],{},[898,53625,7929],{},[1711,53627,1836],{},[898,53629,207],{},[898,53631,6796],{},[1711,53633,2095],{},[898,53635,2223],{},[902,53637,40658],{"encoding":904},[883,53639,53641],{"className":53640},[886],[888,53642,53643],{"xmlns":890},[892,53644,53645,53653],{},[895,53646,53647,53649,53651],{},[898,53648,207],{},[1711,53650,2109],{},[2111,53652,2113],{},[902,53654,46683],{"encoding":904},[883,53656,53658],{"className":53657},[886],[888,53659,53660],{"xmlns":890},[892,53661,53662,53670],{},[895,53663,53664,53666,53668],{},[898,53665,2223],{},[1711,53667,2123],{},[2111,53669,2113],{},[902,53671,22412],{"encoding":904}," — nedokonalá konkurence",[123,53674,53675,5204,53678],{},[38,53676,53677],{},"Dokonalá konkurence",[883,53679,53681],{"className":53680},[886],[888,53682,53683],{"xmlns":890},[892,53684,53685,53697],{},[895,53686,53687,53689,53691],{},[898,53688,7929],{},[1711,53690,1836],{},[1716,53692,53693,53695],{},[898,53694,7929],{},[1711,53696,1793],{},[902,53698,8344],{"encoding":904},[123,53700,53701,53703],{},[38,53702,41824],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,53705,53706,1700,53708,1343,53732],{},[38,53707,35325],{},[883,53709,53711],{"className":53710},[886],[888,53712,53713],{"xmlns":890},[892,53714,53715,53729],{},[895,53716,53717,53719,53721,53723,53725,53727],{},[898,53718,6796],{},[1711,53720,1836],{},[898,53722,1722],{},[1711,53724,1714],{"stretchy":1713},[898,53726,1660],{},[1711,53728,1735],{"stretchy":1713},[902,53730,53731],{"encoding":904},"Q = E(Y)",[38,53733,42021],{},[123,53735,53736,53739,53740,53742],{},[38,53737,53738],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,53741,42467],{}," zboží",[123,53744,53745,2009,53747,53749],{},[38,53746,43473],{},[38,53748,43420],{}," — znaménka zkřížených koeficientů",[123,53751,53752,53755],{},[38,53753,53754],{},"Dvoukomoditní trh"," (2.6)",[123,53757,53758,1648,53761,1735],{},[38,53759,53760],{},"Posun poptávky",[614,53762,42525],{},[724,53764,53765],{},[38,53766,2804],{},[120,53768,53769,53802,53806,53851],{},[123,53770,53771,1648,53773,22246,53775,1700,53777,1343,53800],{},[38,53772,43867],{},[614,53774,43870],{},[38,53776,44041],{},[883,53778,53780],{"className":53779},[886],[888,53781,53782],{"xmlns":890},[892,53783,53784,53798],{},[895,53785,53786,53788,53790,53792,53794,53796],{},[898,53787,6796],{},[1711,53789,1836],{},[898,53791,2362],{},[1711,53793,1714],{"stretchy":1713},[898,53795,7929],{},[1711,53797,1735],{"stretchy":1713},[902,53799,12660],{"encoding":904},[38,53801,44119],{},[123,53803,53804],{},[38,53805,44126],{},[123,53807,53808,1700,53811,1343,53834],{},[38,53809,53810],{},"Lineární nabídka",[883,53812,53814],{"className":53813},[886],[888,53815,53816],{"xmlns":890},[892,53817,53818,53832],{},[895,53819,53820,53822,53824,53826,53828,53830],{},[898,53821,7929],{},[1711,53823,1836],{},[898,53825,2090],{},[898,53827,6796],{},[1711,53829,2095],{},[898,53831,2098],{},[902,53833,43840],{"encoding":904},[883,53835,53837],{"className":53836},[886],[888,53838,53839],{"xmlns":890},[892,53840,53841,53849],{},[895,53842,53843,53845,53847],{},[898,53844,2090],{},[1711,53846,2123],{},[2111,53848,2113],{},[902,53850,43858],{"encoding":904},[123,53852,53853,1648,53856,1735],{},[38,53854,53855],{},"Posun nabídky",[614,53857,44504],{},[724,53859,53860],{},[38,53861,53862],{},"Rovnováha a komparativní statika",[120,53864,53865,53944,53950],{},[123,53866,53867,1648,53869,22246,53871,1700,53874,1343,53891,1700,53894,1343,53911,1700,53913],{},[38,53868,44923],{},[614,53870,45042],{},[38,53872,53873],{},"rovnovážná cena",[883,53875,53877],{"className":53876},[886],[888,53878,53879],{"xmlns":890},[892,53880,53881,53889],{},[895,53882,53883],{},[1716,53884,53885,53887],{},[898,53886,7929],{},[898,53888,1722],{},[902,53890,45064],{"encoding":904},[38,53892,53893],{},"rovnovážné množství",[883,53895,53897],{"className":53896},[886],[888,53898,53899],{"xmlns":890},[892,53900,53901,53909],{},[895,53902,53903],{},[1716,53904,53905,53907],{},[898,53906,6796],{},[898,53908,1722],{},[902,53910,46001],{"encoding":904},[38,53912,45100],{},[883,53914,53916],{"className":53915},[886],[888,53917,53918],{"xmlns":890},[892,53919,53920,53942],{},[895,53921,53922,53924,53926,53932,53934,53940],{},[898,53923,1722],{},[1711,53925,5144],{"stretchy":1713},[1716,53927,53928,53930],{},[898,53929,6796],{},[898,53931,1722],{},[1711,53933,1726],{"separator":1725},[1716,53935,53936,53938],{},[898,53937,7929],{},[898,53939,1722],{},[1711,53941,5163],{"stretchy":1713},[902,53943,44965],{"encoding":904},[123,53945,53946,53949],{},[38,53947,53948],{},"Pravidla 1–4"," komparativní statiky",[123,53951,53952,1648,53955,1735],{},[38,53953,53954],{},"Teorém pavučiny",[614,53956,45947],{},[724,53958,53959],{},[38,53960,53961],{},"Zdanění",[120,53963,53964,54020,54068],{},[123,53965,53966,53968,53969,53994,53995,1735],{},[38,53967,53961],{}," — daň výrobci (",[883,53970,53972],{"className":53971},[886],[888,53973,53974],{"xmlns":890},[892,53975,53976,53992],{},[895,53977,53978,53984,53986,53988,53990],{},[2884,53979,53980,53982],{},[898,53981,2362],{},[2111,53983,2238],{},[1711,53985,1836],{},[898,53987,2362],{},[1711,53989,2095],{},[898,53991,1769],{},[902,53993,46352],{"encoding":904},") vs. daň spotřebiteli (",[883,53996,53998],{"className":53997},[886],[888,53999,54000],{"xmlns":890},[892,54001,54002,54018],{},[895,54003,54004,54010,54012,54014,54016],{},[2884,54005,54006,54008],{},[898,54007,2778],{},[2111,54009,2963],{},[1711,54011,1836],{},[898,54013,2778],{},[1711,54015,2460],{},[898,54017,1769],{},[902,54019,46383],{"encoding":904},[123,54021,54022,1700,54024,1343,54045],{},[38,54023,46256],{},[883,54025,54027],{"className":54026},[886],[888,54028,54029],{"xmlns":890},[892,54030,54031,54043],{},[895,54032,54033],{},[2884,54034,54035,54037],{},[898,54036,1769],{},[895,54038,54039,54041],{},[898,54040,46275],{},[898,54042,724],{},[902,54044,46280],{"encoding":904},[883,54046,54048],{"className":54047},[886],[888,54049,54050],{"xmlns":890},[892,54051,54052,54066],{},[895,54053,54054],{},[2884,54055,54056,54058],{},[898,54057,1769],{},[895,54059,54060,54062,54064],{},[898,54061,46298],{},[898,54063,6038],{},[898,54065,1675],{},[902,54067,46305],{"encoding":904},[123,54069,54070,1700,54073,1343,54102],{},[38,54071,54072],{},"Ekvivalence zdanění",[883,54074,54076],{"className":54075},[886],[888,54077,54078],{"xmlns":890},[892,54079,54080,54100],{},[895,54081,54082,54090,54092],{},[13142,54083,54084,54086,54088],{},[898,54085,6796],{},[2111,54087,2238],{},[898,54089,1722],{},[1711,54091,1836],{},[13142,54093,54094,54096,54098],{},[898,54095,6796],{},[2111,54097,2963],{},[898,54099,1722],{},[902,54101,46506],{"encoding":904},[883,54103,54105],{"className":54104},[886],[888,54106,54107],{"xmlns":890},[892,54108,54109,54133],{},[895,54110,54111,54119,54121,54123,54125],{},[13142,54112,54113,54115,54117],{},[898,54114,7929],{},[2111,54116,2238],{},[898,54118,1722],{},[1711,54120,2460],{},[898,54122,1769],{},[1711,54124,1836],{},[13142,54126,54127,54129,54131],{},[898,54128,7929],{},[2111,54130,2963],{},[898,54132,1722],{},[902,54134,46540],{"encoding":904},[724,54136,54137],{},[38,54138,30006],{},[120,54140,54141,54187,54218,54223,54229,54236],{},[123,54142,54143,1700,54145],{},[38,54144,46639],{},[883,54146,54148],{"className":54147},[886],[888,54149,54150],{"xmlns":890},[892,54151,54152,54184],{},[895,54153,54154,54160,54162,54164,54166,54168,54170,54172,54174,54176,54178,54180,54182],{},[1716,54155,54156,54158],{},[898,54157,6796],{},[898,54159,1722],{},[1711,54161,1836],{},[1711,54163,1714],{"stretchy":1713},[898,54165,2223],{},[1711,54167,2460],{},[898,54169,2098],{},[1711,54171,1735],{"stretchy":1713},[898,54173,8659],{"mathvariant":2287},[1711,54175,1714],{"stretchy":1713},[898,54177,2090],{},[1711,54179,2460],{},[898,54181,207],{},[1711,54183,1735],{"stretchy":1713},[902,54185,54186],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,54188,54189,1700,54192,54217],{},[38,54190,54191],{},"Parametry",[883,54193,54195],{"className":54194},[886],[888,54196,54197],{"xmlns":890},[892,54198,54199,54215],{},[895,54200,54201,54203,54205,54207,54209,54211,54213],{},[898,54202,207],{},[1711,54204,1726],{"separator":1725},[898,54206,2223],{},[1711,54208,1726],{"separator":1725},[898,54210,2090],{},[1711,54212,1726],{"separator":1725},[898,54214,2098],{},[902,54216,46883],{"encoding":904}," — exogenní proměnné",[123,54219,54220],{},[38,54221,54222],{},"Endogenní \u002F exogenní proměnná",[123,54224,54225,54228],{},[38,54226,54227],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,54230,54231,1343,54234],{},[38,54232,54233],{},"Komparativní statika",[38,54235,40558],{},[123,54237,54238,1700,54240,54256],{},[38,54239,6957],{},[883,54241,54243],{"className":54242},[886],[888,54244,54245],{"xmlns":890},[892,54246,54247,54253],{},[895,54248,54249,54251],{},[898,54250,2098],{},[898,54252,6796],{},[902,54254,54255],{"encoding":904},"dQ"," (2.11)",[724,54258,54259],{},[38,54260,54261],{},"Přebytky a ostatní",[120,54263,54264,54302],{},[123,54265,54266,1700,54268,54283,54284,1700,54286,54301],{},[38,54267,48532],{},[883,54269,54271],{"className":54270},[886],[888,54272,54273],{"xmlns":890},[892,54274,54275,54281],{},[895,54276,54277,54279],{},[898,54278,1940],{},[898,54280,2362],{},[902,54282,48548],{"encoding":904}," (2.14), ",[38,54285,48551],{},[883,54287,54289],{"className":54288},[886],[888,54290,54291],{"xmlns":890},[892,54292,54293,54299],{},[895,54294,54295,54297],{},[898,54296,7929],{},[898,54298,2362],{},[902,54300,48567],{"encoding":904}," (2.15)",[123,54303,54304,1343,54307,54310],{},[38,54305,54306],{},"Homo economicus",[38,54308,54309],{},"Marshallova formulace"," (1890)",[40568,54312],{},[115,54314,5901],{"id":5900},[120,54316,54317,54352,54361],{},[123,54318,54319,1700,54322,54325,54326,1343,54329,54332,54333,54336,54337,54340,54341,54344,54345,54348,54349],{},[38,54320,54321],{},"Související témata:",[207,54323,811],{"className":54324,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,54327,820],{"className":54328,"dataFsResolvedFilePath":818,"href":819},[210],[207,54330,6375],{"className":54331,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,54334,775],{"className":54335,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,54338,784],{"className":54339,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,54342,793],{"className":54343,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,54346,7822],{"className":54347,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,54350,7817],{"className":54351,"dataFsResolvedFilePath":827,"href":828},[210],[123,54353,54354,1700,54357],{},[38,54355,54356],{},"Shrnutí přednášek:",[207,54358,54360],{"className":54359,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,54362,54363,1700,54365],{},[38,54364,5908],{},[207,54366,5914],{"className":54367,"dataFsResolvedFilePath":5912,"href":5913},[210],{"title":641,"searchDepth":642,"depth":642,"links":54369},[54370,54371,54379,54385,54392,54393,54400,54401,54402,54409,54410,54411],{"id":40392,"depth":642,"text":40393},{"id":40373,"depth":642,"text":2840,"children":54372},[54373,54374,54375,54376,54378],{"id":40661,"depth":649,"text":40662},{"id":40943,"depth":649,"text":40944},{"id":41953,"depth":649,"text":41954},{"id":42521,"depth":649,"text":54377},"Posun poptávky (shift of demand)",{"id":43025,"depth":649,"text":43026},{"id":40377,"depth":642,"text":2804,"children":54380},[54381,54382,54383],{"id":43862,"depth":649,"text":40662},{"id":44048,"depth":649,"text":44049},{"id":44500,"depth":649,"text":54384},"Posun nabídky (shift of supply)",{"id":44922,"depth":642,"text":44923,"children":54386},[54387,54388,54389,54390,54391],{"id":45034,"depth":649,"text":45035},{"id":45247,"depth":649,"text":45248},{"id":45565,"depth":649,"text":45566},{"id":45919,"depth":649,"text":45920},{"id":45950,"depth":649,"text":45951},{"id":46219,"depth":642,"text":811},{"id":46620,"depth":642,"text":46621,"children":54394},[54395,54396,54397,54398],{"id":46638,"depth":649,"text":46639},{"id":47019,"depth":649,"text":47020},{"id":47403,"depth":649,"text":47404},{"id":47857,"depth":649,"text":54399},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":15758,"depth":642,"text":820},{"id":48782,"depth":642,"text":48783},{"id":49013,"depth":642,"text":49014,"children":54403},[54404,54405,54406,54407,54408],{"id":49017,"depth":649,"text":49018},{"id":49857,"depth":649,"text":49858},{"id":50233,"depth":649,"text":44923},{"id":51528,"depth":649,"text":46621},{"id":53284,"depth":649,"text":820},{"id":53479,"depth":642,"text":53480},{"id":5421,"depth":642,"text":5422},{"id":5900,"depth":642,"text":5901},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,54418,54419,54420,21481,54421,54422],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":54425,"title":820,"body":54426,"course":1128,"courses":659,"created":5973,"description":641,"extension":661,"meta":58705,"navigation":664,"path":58706,"seo":58707,"sources":58708,"stem":58709,"tags":58710,"type":5985,"updated":677,"__hash__":58715},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":54427,"toc":58683},[54428,54430,54498,54548,54550,54553,54811,54887,54892,54894,54913,54917,54993,55078,55080,55394,55487,55489,55508,55512,55586,55671,55674,55850,55855,55857,56277,56279,56283,56287,56523,56567,56667,56733,56736,56769,56945,57007,57137,57215,57326,57360,57558,57577,57596,57661,57665,57668,57713,57716,57834,57880,57882,57886,58234,58236,58238,58516,58518,58522,58557,58564,58637,58639,58641],[12,54429,820],{"id":15758},[1921,54431,54432],{},[724,54433,54434,7867,54436,1648,54438,54453,54454,1648,54456,54471,54472,54494,54495,2186],{},[883,54435,7866],{},[38,54437,48532],{},[883,54439,54441],{"className":54440},[886],[888,54442,54443],{"xmlns":890},[892,54444,54445,54451],{},[895,54446,54447,54449],{},[898,54448,1940],{},[898,54450,2362],{},[902,54452,48548],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,54455,48679],{},[883,54457,54459],{"className":54458},[886],[888,54460,54461],{"xmlns":890},[892,54462,54463,54469],{},[895,54464,54465,54467],{},[898,54466,7929],{},[898,54468,2362],{},[902,54470,48567],{"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 ",[883,54473,54475],{"className":54474},[886],[888,54476,54477],{"xmlns":890},[892,54478,54479,54491],{},[895,54480,54481,54483,54485,54487,54489],{},[898,54482,1940],{},[898,54484,2362],{},[1711,54486,2095],{},[898,54488,7929],{},[898,54490,2362],{},[902,54492,54493],{"encoding":904},"CS + PS"," měří ",[38,54496,54497],{},"celkový blahobyt trhu",[724,54499,54500,1648,54502,1343,54504,1772,54519,1648,54521,1343,54523,54538,54539,54543,54544,2186],{},[38,54501,48532],{},[614,54503,48586],{},[883,54505,54507],{"className":54506},[886],[888,54508,54509],{"xmlns":890},[892,54510,54511,54517],{},[895,54512,54513,54515],{},[898,54514,1940],{},[898,54516,2362],{},[902,54518,48548],{"encoding":904},[38,54520,48551],{},[614,54522,48682],{},[883,54524,54526],{"className":54525},[886],[888,54527,54528],{"xmlns":890},[892,54529,54530,54536],{},[895,54531,54532,54534],{},[898,54533,7929],{},[898,54535,2362],{},[902,54537,48567],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,54540,54542],{"className":54541,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,54545,54547],{"className":54546,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[40568,54549],{},[115,54551,1241],{"id":54552},"úvod",[724,54554,54555,54556,54579,54580,54603,54604,54621,54622,7903,54654,54686,54687,54713,54714,54717,54718,54721,54722,3695,54756,25192,54777,2186],{},"Je dána funkce poptávky ",[883,54557,54559],{"className":54558},[886],[888,54560,54561],{"xmlns":890},[892,54562,54563,54577],{},[895,54564,54565,54567,54569,54571,54573,54575],{},[898,54566,7929],{},[1711,54568,1836],{},[898,54570,2778],{},[1711,54572,1714],{"stretchy":1713},[898,54574,6796],{},[1711,54576,1735],{"stretchy":1713},[902,54578,8625],{"encoding":904},", resp. funkce nabídky ",[883,54581,54583],{"className":54582},[886],[888,54584,54585],{"xmlns":890},[892,54586,54587,54601],{},[895,54588,54589,54591,54593,54595,54597,54599],{},[898,54590,7929],{},[1711,54592,1836],{},[898,54594,2362],{},[1711,54596,1714],{"stretchy":1713},[898,54598,6796],{},[1711,54600,1735],{"stretchy":1713},[902,54602,44669],{"encoding":904},". Pro pevně zadané množství ",[883,54605,54607],{"className":54606},[886],[888,54608,54609],{"xmlns":890},[892,54610,54611,54619],{},[895,54612,54613],{},[2884,54614,54615,54617],{},[898,54616,6796],{},[2111,54618,2113],{},[902,54620,41906],{"encoding":904}," je odpovídající cena ",[883,54623,54625],{"className":54624},[886],[888,54626,54627],{"xmlns":890},[892,54628,54629,54651],{},[895,54630,54631,54637,54639,54641,54643,54649],{},[2884,54632,54633,54635],{},[898,54634,7929],{},[2111,54636,2113],{},[1711,54638,1836],{},[898,54640,2778],{},[1711,54642,1714],{"stretchy":1713},[2884,54644,54645,54647],{},[898,54646,6796],{},[2111,54648,2113],{},[1711,54650,1735],{"stretchy":1713},[902,54652,54653],{"encoding":904},"P_0 = D(Q_0)",[883,54655,54657],{"className":54656},[886],[888,54658,54659],{"xmlns":890},[892,54660,54661,54683],{},[895,54662,54663,54669,54671,54673,54675,54681],{},[2884,54664,54665,54667],{},[898,54666,7929],{},[2111,54668,2113],{},[1711,54670,1836],{},[898,54672,2362],{},[1711,54674,1714],{"stretchy":1713},[2884,54676,54677,54679],{},[898,54678,6796],{},[2111,54680,2113],{},[1711,54682,1735],{"stretchy":1713},[902,54684,54685],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,54688,54690],{"className":54689},[886],[888,54691,54692],{"xmlns":890},[892,54693,54694,54710],{},[895,54695,54696,54702,54704],{},[2884,54697,54698,54700],{},[898,54699,7929],{},[2111,54701,2113],{},[1942,54703,2519],{},[2884,54705,54706,54708],{},[898,54707,6796],{},[2111,54709,2113],{},[902,54711,54712],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,54715,54716],{},"výdaje spotřebitele",", nebo ",[38,54719,54720],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,54723,54725],{"className":54724},[886],[888,54726,54727],{"xmlns":890},[892,54728,54729,54753],{},[895,54730,54731,54733,54735,54741,54743,54745,54747],{},[2111,54732,2113],{},[1942,54734,2519],{},[2884,54736,54737,54739],{},[898,54738,6796],{},[2111,54740,2113],{},[1942,54742,2519],{},[898,54744,8243],{},[1942,54746,2519],{},[2884,54748,54749,54751],{},[898,54750,7929],{},[2111,54752,2113],{},[902,54754,54755],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,54757,54759],{"className":54758},[886],[888,54760,54761],{"xmlns":890},[892,54762,54763,54775],{},[895,54764,54765,54767,54769,54771,54773],{},[1711,54766,1714],{"stretchy":1713},[898,54768,6796],{},[1711,54770,1726],{"separator":1725},[898,54772,7929],{},[1711,54774,1735],{"stretchy":1713},[902,54776,41289],{"encoding":904},[883,54778,54780],{"className":54779},[886],[888,54781,54782],{"xmlns":890},[892,54783,54784,54808],{},[895,54785,54786,54788,54790,54792,54798,54800,54806],{},[898,54787,8243],{},[1711,54789,1836],{},[1711,54791,5144],{"stretchy":1713},[2884,54793,54794,54796],{},[898,54795,6796],{},[2111,54797,2113],{},[1711,54799,1726],{"separator":1725},[2884,54801,54802,54804],{},[898,54803,7929],{},[2111,54805,2113],{},[1711,54807,5163],{"stretchy":1713},[902,54809,54810],{"encoding":904},"A = [Q_0, P_0]",[1921,54812,54813,54818,54876],{},[724,54814,54815,54817],{},[883,54816,2678],{}," Intuice",[120,54819,54820,54848],{},[123,54821,54822,54823,54826,54827,54829,54830,54847],{},"Za jednotky zboží nakoupené ",[38,54824,54825],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,54828,28868],{}," než ",[883,54831,54833],{"className":54832},[886],[888,54834,54835],{"xmlns":890},[892,54836,54837,54845],{},[895,54838,54839],{},[2884,54840,54841,54843],{},[898,54842,7929],{},[2111,54844,2113],{},[902,54846,42546],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,54849,54850,54851,54853,54854,54857,54858,54875],{},"Za jednotky zboží prodané ",[38,54852,54825],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,54855,54856],{},"nižší"," cenu než ",[883,54859,54861],{"className":54860},[886],[888,54862,54863],{"xmlns":890},[892,54864,54865,54873],{},[895,54866,54867],{},[2884,54868,54869,54871],{},[898,54870,7929],{},[2111,54872,2113],{},[902,54874,42546],{"encoding":904}," — rozdíl je jeho přebytek.",[724,54877,54878,54879,54882,54883,54886],{},"Přebytek je tedy rozdíl mezi ",[614,54880,54881],{},"ochotou"," (platit \u002F prodávat) a ",[614,54884,54885],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,54888,54889],{},[1801,54890],{"alt":48577,"className":54891,"src":48579},[210,1805],[40568,54893],{},[115,54895,54897,54898,1735],{"id":54896},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,54899,54901],{"className":54900},[886],[888,54902,54903],{"xmlns":890},[892,54904,54905,54911],{},[895,54906,54907,54909],{},[898,54908,1940],{},[898,54910,2362],{},[902,54912,48548],{"encoding":904},[198,54914,54916],{"id":54915},"definice-vzorec-214","Definice (vzorec 2.14)",[724,54918,54919,54920,54943,54944,54961,54962,2062],{},"Pro poptávku ",[883,54921,54923],{"className":54922},[886],[888,54924,54925],{"xmlns":890},[892,54926,54927,54941],{},[895,54928,54929,54931,54933,54935,54937,54939],{},[898,54930,7929],{},[1711,54932,1836],{},[898,54934,2778],{},[1711,54936,1714],{"stretchy":1713},[898,54938,6796],{},[1711,54940,1735],{"stretchy":1713},[902,54942,8625],{"encoding":904}," a pevně zadané ",[883,54945,54947],{"className":54946},[886],[888,54948,54949],{"xmlns":890},[892,54950,54951,54959],{},[895,54952,54953],{},[2884,54954,54955,54957],{},[898,54956,6796],{},[2111,54958,2113],{},[902,54960,41906],{"encoding":904}," s cenou ",[883,54963,54965],{"className":54964},[886],[888,54966,54967],{"xmlns":890},[892,54968,54969,54991],{},[895,54970,54971,54977,54979,54981,54983,54989],{},[2884,54972,54973,54975],{},[898,54974,7929],{},[2111,54976,2113],{},[1711,54978,1836],{},[898,54980,2778],{},[1711,54982,1714],{"stretchy":1713},[2884,54984,54985,54987],{},[898,54986,6796],{},[2111,54988,2113],{},[1711,54990,1735],{"stretchy":1713},[902,54992,54653],{"encoding":904},[883,54994,54996],{"className":54995},[886],[888,54997,54998],{"xmlns":890,"display":31664},[892,54999,55000,55076],{},[24352,55001,55002],{"width":31669},[24357,55003,55004,55006,55070,55072],{},[24360,55005],{"width":31674},[24360,55007,55008],{},[895,55009,55010,55012,55014,55016,55022,55024,55026,55038,55040,55042,55044,55046,55048,55050,55052,55054,55060,55062,55068],{},[898,55011,1940],{},[898,55013,2362],{},[1711,55015,1714],{"stretchy":1713},[2884,55017,55018,55020],{},[898,55019,6796],{},[2111,55021,2113],{},[1711,55023,1735],{"stretchy":1713},[1711,55025,1836],{},[13142,55027,55028,55030,55032],{},[1711,55029,15143],{},[2111,55031,2113],{},[2884,55033,55034,55036],{},[898,55035,6796],{},[2111,55037,2113],{},[898,55039,2778],{},[1711,55041,1714],{"stretchy":1713},[898,55043,6796],{},[1711,55045,1735],{"stretchy":1713},[1942,55047,2519],{},[898,55049,2098],{},[898,55051,6796],{},[1711,55053,2460],{},[2884,55055,55056,55058],{},[898,55057,7929],{},[2111,55059,2113],{},[1942,55061,2519],{},[2884,55063,55064,55066],{},[898,55065,6796],{},[2111,55067,2113],{},[898,55069,2186],{"mathvariant":2287},[24360,55071],{"width":31674},[24360,55073,55074],{},[1942,55075,48671],{},[902,55077,48674],{"encoding":904},[198,55079,6459],{"id":6458},[120,55081,55082,55174,55236],{},[123,55083,55084,55124,55125,55151,55152,55155,55156,55173],{},[883,55085,55087],{"className":55086},[886],[888,55088,55089],{"xmlns":890},[892,55090,55091,55121],{},[895,55092,55093],{},[2509,55094,55095,55107,55109,55111,55113,55115,55117,55119],{"scriptlevel":2113,"displaystyle":1725},[13142,55096,55097,55099,55101],{},[1711,55098,15143],{},[2111,55100,2113],{},[2884,55102,55103,55105],{},[898,55104,6796],{},[2111,55106,2113],{},[898,55108,2778],{},[1711,55110,1714],{"stretchy":1713},[898,55112,6796],{},[1711,55114,1735],{"stretchy":1713},[1942,55116,2519],{},[898,55118,2098],{},[898,55120,6796],{},[902,55122,55123],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,55126,55128],{"className":55127},[886],[888,55129,55130],{"xmlns":890},[892,55131,55132,55148],{},[895,55133,55134,55136,55138,55140,55146],{},[1711,55135,5144],{"stretchy":1713},[2111,55137,2113],{},[1711,55139,1726],{"separator":1725},[2884,55141,55142,55144],{},[898,55143,6796],{},[2111,55145,2113],{},[1711,55147,5163],{"stretchy":1713},[902,55149,55150],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,55153,55154],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,55157,55159],{"className":55158},[886],[888,55160,55161],{"xmlns":890},[892,55162,55163,55171],{},[895,55164,55165],{},[2884,55166,55167,55169],{},[898,55168,6796],{},[2111,55170,2113],{},[902,55172,41906],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,55175,55176,55202,55203,1797],{},[883,55177,55179],{"className":55178},[886],[888,55180,55181],{"xmlns":890},[892,55182,55183,55199],{},[895,55184,55185,55191,55193],{},[2884,55186,55187,55189],{},[898,55188,7929],{},[2111,55190,2113],{},[1942,55192,2519],{},[2884,55194,55195,55197],{},[898,55196,6796],{},[2111,55198,2113],{},[902,55200,55201],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,55204,55206],{"className":55205},[886],[888,55207,55208],{"xmlns":890},[892,55209,55210,55234],{},[895,55211,55212,55214,55216,55222,55224,55226,55228],{},[2111,55213,2113],{},[1942,55215,2519],{},[2884,55217,55218,55220],{},[898,55219,6796],{},[2111,55221,2113],{},[1942,55223,2519],{},[898,55225,8243],{},[1942,55227,2519],{},[2884,55229,55230,55232],{},[898,55231,7929],{},[2111,55233,2113],{},[902,55235,54755],{"encoding":904},[123,55237,55238,55253,55254,55276,55277,55302,55303,25192,55329,2009,55361,2186],{},[883,55239,55241],{"className":55240},[886],[888,55242,55243],{"xmlns":890},[892,55244,55245,55251],{},[895,55246,55247,55249],{},[898,55248,1940],{},[898,55250,2362],{},[902,55252,48548],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,55255,55257],{"className":55256},[886],[888,55258,55259],{"xmlns":890},[892,55260,55261,55273],{},[895,55262,55263,55265,55267],{},[898,55264,7929],{},[1711,55266,1836],{},[2884,55268,55269,55271],{},[898,55270,7929],{},[2111,55272,2113],{},[902,55274,55275],{"encoding":904},"P = P_0"," v pásu ",[883,55278,55280],{"className":55279},[886],[888,55281,55282],{"xmlns":890},[892,55283,55284,55300],{},[895,55285,55286,55288,55290,55292,55298],{},[1711,55287,5144],{"stretchy":1713},[2111,55289,2113],{},[1711,55291,1726],{"separator":1725},[2884,55293,55294,55296],{},[898,55295,6796],{},[2111,55297,2113],{},[1711,55299,5163],{"stretchy":1713},[902,55301,55150],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,55304,55306],{"className":55305},[886],[888,55307,55308],{"xmlns":890},[892,55309,55310,55326],{},[895,55311,55312,55318,55320,55322,55324],{},[2884,55313,55314,55316],{},[898,55315,7929],{},[2111,55317,2113],{},[1942,55319,2519],{},[898,55321,26851],{},[1942,55323,2519],{},[898,55325,8243],{},[902,55327,55328],{"encoding":904},"P_0\\,B\\,A",[883,55330,55332],{"className":55331},[886],[888,55333,55334],{"xmlns":890},[892,55335,55336,55358],{},[895,55337,55338,55340,55342,55344,55346,55348,55350,55352,55354,55356],{},[898,55339,26851],{},[1711,55341,1836],{},[1711,55343,5144],{"stretchy":1713},[2111,55345,2113],{},[1711,55347,1726],{"separator":1725},[898,55349,2778],{},[1711,55351,1714],{"stretchy":1713},[2111,55353,2113],{},[1711,55355,1735],{"stretchy":1713},[1711,55357,5163],{"stretchy":1713},[902,55359,55360],{"encoding":904},"B = [0, D(0)]",[883,55362,55364],{"className":55363},[886],[888,55365,55366],{"xmlns":890},[892,55367,55368,55392],{},[895,55369,55370,55372,55374,55376,55382,55384,55390],{},[898,55371,8243],{},[1711,55373,1836],{},[1711,55375,5144],{"stretchy":1713},[2884,55377,55378,55380],{},[898,55379,6796],{},[2111,55381,2113],{},[1711,55383,1726],{"separator":1725},[2884,55385,55386,55388],{},[898,55387,7929],{},[2111,55389,2113],{},[1711,55391,5163],{"stretchy":1713},[902,55393,54810],{"encoding":904},[724,55395,55396],{},[614,55397,55398,55399,55412,55413,55446,55447,32740,55472,2186],{},"Obrázek 2.24: Křivka poptávky ",[883,55400,55402],{"className":55401},[886],[888,55403,55404],{"xmlns":890},[892,55405,55406,55410],{},[895,55407,55408],{},[898,55409,2778],{},[902,55411,2778],{"encoding":904},", bod ",[883,55414,55416],{"className":55415},[886],[888,55417,55418],{"xmlns":890},[892,55419,55420,55444],{},[895,55421,55422,55424,55426,55428,55434,55436,55442],{},[898,55423,8243],{},[1711,55425,1836],{},[1711,55427,5144],{"stretchy":1713},[2884,55429,55430,55432],{},[898,55431,6796],{},[2111,55433,2113],{},[1711,55435,1726],{"separator":1725},[2884,55437,55438,55440],{},[898,55439,7929],{},[2111,55441,2113],{},[1711,55443,5163],{"stretchy":1713},[902,55445,54810],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,55448,55450],{"className":55449},[886],[888,55451,55452],{"xmlns":890},[892,55453,55454,55470],{},[895,55455,55456,55462,55464,55466,55468],{},[2884,55457,55458,55460],{},[898,55459,7929],{},[2111,55461,2113],{},[1942,55463,2519],{},[898,55465,26851],{},[1942,55467,2519],{},[898,55469,8243],{},[902,55471,55328],{"encoding":904},[883,55473,55475],{"className":55474},[886],[888,55476,55477],{"xmlns":890},[892,55478,55479,55485],{},[895,55480,55481,55483],{},[898,55482,1940],{},[898,55484,2362],{},[902,55486,48548],{"encoding":904},[40568,55488],{},[115,55490,55492,55493,1735],{"id":55491},"přebytek-výrobce-psps","Přebytek výrobce (",[883,55494,55496],{"className":55495},[886],[888,55497,55498],{"xmlns":890},[892,55499,55500,55506],{},[895,55501,55502,55504],{},[898,55503,7929],{},[898,55505,2362],{},[902,55507,48567],{"encoding":904},[198,55509,55511],{"id":55510},"definice-vzorec-215","Definice (vzorec 2.15)",[724,55513,55514,55515,54943,55538,54961,55555,2062],{},"Analogicky — pro nabídku ",[883,55516,55518],{"className":55517},[886],[888,55519,55520],{"xmlns":890},[892,55521,55522,55536],{},[895,55523,55524,55526,55528,55530,55532,55534],{},[898,55525,7929],{},[1711,55527,1836],{},[898,55529,2362],{},[1711,55531,1714],{"stretchy":1713},[898,55533,6796],{},[1711,55535,1735],{"stretchy":1713},[902,55537,44669],{"encoding":904},[883,55539,55541],{"className":55540},[886],[888,55542,55543],{"xmlns":890},[892,55544,55545,55553],{},[895,55546,55547],{},[2884,55548,55549,55551],{},[898,55550,6796],{},[2111,55552,2113],{},[902,55554,41906],{"encoding":904},[883,55556,55558],{"className":55557},[886],[888,55559,55560],{"xmlns":890},[892,55561,55562,55584],{},[895,55563,55564,55570,55572,55574,55576,55582],{},[2884,55565,55566,55568],{},[898,55567,7929],{},[2111,55569,2113],{},[1711,55571,1836],{},[898,55573,2362],{},[1711,55575,1714],{"stretchy":1713},[2884,55577,55578,55580],{},[898,55579,6796],{},[2111,55581,2113],{},[1711,55583,1735],{"stretchy":1713},[902,55585,54685],{"encoding":904},[883,55587,55589],{"className":55588},[886],[888,55590,55591],{"xmlns":890,"display":31664},[892,55592,55593,55669],{},[24352,55594,55595],{"width":31669},[24357,55596,55597,55599,55663,55665],{},[24360,55598],{"width":31674},[24360,55600,55601],{},[895,55602,55603,55605,55607,55609,55615,55617,55619,55625,55627,55633,55635,55647,55649,55651,55653,55655,55657,55659,55661],{},[898,55604,7929],{},[898,55606,2362],{},[1711,55608,1714],{"stretchy":1713},[2884,55610,55611,55613],{},[898,55612,6796],{},[2111,55614,2113],{},[1711,55616,1735],{"stretchy":1713},[1711,55618,1836],{},[2884,55620,55621,55623],{},[898,55622,7929],{},[2111,55624,2113],{},[1942,55626,2519],{},[2884,55628,55629,55631],{},[898,55630,6796],{},[2111,55632,2113],{},[1711,55634,2460],{},[13142,55636,55637,55639,55641],{},[1711,55638,15143],{},[2111,55640,2113],{},[2884,55642,55643,55645],{},[898,55644,6796],{},[2111,55646,2113],{},[898,55648,2362],{},[1711,55650,1714],{"stretchy":1713},[898,55652,6796],{},[1711,55654,1735],{"stretchy":1713},[1942,55656,2519],{},[898,55658,2098],{},[898,55660,6796],{},[898,55662,2186],{"mathvariant":2287},[24360,55664],{"width":31674},[24360,55666,55667],{},[1942,55668,48767],{},[902,55670,48770],{"encoding":904},[198,55672,6459],{"id":55673},"geometrická-interpretace-1",[120,55675,55676,55724,55785],{},[123,55677,55678,5204,55703,55706,55707,2186],{},[883,55679,55681],{"className":55680},[886],[888,55682,55683],{"xmlns":890},[892,55684,55685,55701],{},[895,55686,55687,55693,55695],{},[2884,55688,55689,55691],{},[898,55690,7929],{},[2111,55692,2113],{},[1942,55694,2519],{},[2884,55696,55697,55699],{},[898,55698,6796],{},[2111,55700,2113],{},[902,55702,55201],{"encoding":904},[38,55704,55705],{},"tržba"," výrobce za prodané množství ",[883,55708,55710],{"className":55709},[886],[888,55711,55712],{"xmlns":890},[892,55713,55714,55722],{},[895,55715,55716],{},[2884,55717,55718,55720],{},[898,55719,6796],{},[2111,55721,2113],{},[902,55723,41906],{"encoding":904},[123,55725,55726,55766,55767,55784],{},[883,55727,55729],{"className":55728},[886],[888,55730,55731],{"xmlns":890},[892,55732,55733,55763],{},[895,55734,55735],{},[2509,55736,55737,55749,55751,55753,55755,55757,55759,55761],{"scriptlevel":2113,"displaystyle":1725},[13142,55738,55739,55741,55743],{},[1711,55740,15143],{},[2111,55742,2113],{},[2884,55744,55745,55747],{},[898,55746,6796],{},[2111,55748,2113],{},[898,55750,2362],{},[1711,55752,1714],{"stretchy":1713},[898,55754,6796],{},[1711,55756,1735],{"stretchy":1713},[1942,55758,2519],{},[898,55760,2098],{},[898,55762,6796],{},[902,55764,55765],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,55768,55770],{"className":55769},[886],[888,55771,55772],{"xmlns":890},[892,55773,55774,55782],{},[895,55775,55776],{},[2884,55777,55778,55780],{},[898,55779,6796],{},[2111,55781,2113],{},[902,55783,41906],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,55786,55787,55802,55803,55824,55825,2186],{},[883,55788,55790],{"className":55789},[886],[888,55791,55792],{"xmlns":890},[892,55793,55794,55800],{},[895,55795,55796,55798],{},[898,55797,7929],{},[898,55799,2362],{},[902,55801,48567],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,55804,55806],{"className":55805},[886],[888,55807,55808],{"xmlns":890},[892,55809,55810,55822],{},[895,55811,55812,55814,55816],{},[898,55813,7929],{},[1711,55815,1836],{},[2884,55817,55818,55820],{},[898,55819,7929],{},[2111,55821,2113],{},[902,55823,55275],{"encoding":904}," a křivkou nabídky v pásu ",[883,55826,55828],{"className":55827},[886],[888,55829,55830],{"xmlns":890},[892,55831,55832,55848],{},[895,55833,55834,55836,55838,55840,55846],{},[1711,55835,5144],{"stretchy":1713},[2111,55837,2113],{},[1711,55839,1726],{"separator":1725},[2884,55841,55842,55844],{},[898,55843,6796],{},[2111,55845,2113],{},[1711,55847,5163],{"stretchy":1713},[902,55849,55150],{"encoding":904},[724,55851,55852],{},[614,55853,55854],{},"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.",[40568,55856],{},[1921,55858,55859,55864],{},[724,55860,55861,55863],{},[883,55862,3872],{}," Postup výpočtu CS a PS",[152,55865,55866,55997,56107,56136,56270],{},[123,55867,55868,55869,55886,55887,55918,55919,55950,55951,2186],{},"Zjisti (nebo si zvol) množství ",[883,55870,55872],{"className":55871},[886],[888,55873,55874],{"xmlns":890},[892,55875,55876,55884],{},[895,55877,55878],{},[2884,55879,55880,55882],{},[898,55881,6796],{},[2111,55883,2113],{},[902,55885,41906],{"encoding":904}," a odpovídající cenu ",[883,55888,55890],{"className":55889},[886],[888,55891,55892],{"xmlns":890},[892,55893,55894,55916],{},[895,55895,55896,55902,55904,55906,55908,55914],{},[2884,55897,55898,55900],{},[898,55899,7929],{},[2111,55901,2113],{},[1711,55903,1836],{},[898,55905,2778],{},[1711,55907,1714],{"stretchy":1713},[2884,55909,55910,55912],{},[898,55911,6796],{},[2111,55913,2113],{},[1711,55915,1735],{"stretchy":1713},[902,55917,54653],{"encoding":904}," resp. ",[883,55920,55922],{"className":55921},[886],[888,55923,55924],{"xmlns":890},[892,55925,55926,55948],{},[895,55927,55928,55934,55936,55938,55940,55946],{},[2884,55929,55930,55932],{},[898,55931,7929],{},[2111,55933,2113],{},[1711,55935,1836],{},[898,55937,2362],{},[1711,55939,1714],{"stretchy":1713},[2884,55941,55942,55944],{},[898,55943,6796],{},[2111,55945,2113],{},[1711,55947,1735],{"stretchy":1713},[902,55949,54685],{"encoding":904},". V rovnováze platí ",[883,55952,55954],{"className":55953},[886],[888,55955,55956],{"xmlns":890},[892,55957,55958,55994],{},[895,55959,55960,55962,55964,55970,55972,55974,55976,55978,55984,55986,55988],{},[898,55961,2778],{},[1711,55963,1714],{"stretchy":1713},[1716,55965,55966,55968],{},[898,55967,6796],{},[898,55969,1722],{},[1711,55971,1735],{"stretchy":1713},[1711,55973,1836],{},[898,55975,2362],{},[1711,55977,1714],{"stretchy":1713},[1716,55979,55980,55982],{},[898,55981,6796],{},[898,55983,1722],{},[1711,55985,1735],{"stretchy":1713},[1711,55987,1836],{},[1716,55989,55990,55992],{},[898,55991,7929],{},[898,55993,1722],{},[902,55995,55996],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,55998,55999,56000,23724,56038,56053,56054,23724,56092,1797],{},"Spočti určitý integrál ",[883,56001,56003],{"className":56002},[886],[888,56004,56005],{"xmlns":890},[892,56006,56007,56035],{},[895,56008,56009,56021,56023,56025,56027,56029,56031,56033],{},[13142,56010,56011,56013,56015],{},[1711,56012,15143],{},[2111,56014,2113],{},[2884,56016,56017,56019],{},[898,56018,6796],{},[2111,56020,2113],{},[898,56022,2778],{},[1711,56024,1714],{"stretchy":1713},[898,56026,6796],{},[1711,56028,1735],{"stretchy":1713},[1942,56030,2519],{},[898,56032,2098],{},[898,56034,6796],{},[902,56036,56037],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,56039,56041],{"className":56040},[886],[888,56042,56043],{"xmlns":890},[892,56044,56045,56051],{},[895,56046,56047,56049],{},[898,56048,1940],{},[898,56050,2362],{},[902,56052,48548],{"encoding":904},") nebo ",[883,56055,56057],{"className":56056},[886],[888,56058,56059],{"xmlns":890},[892,56060,56061,56089],{},[895,56062,56063,56075,56077,56079,56081,56083,56085,56087],{},[13142,56064,56065,56067,56069],{},[1711,56066,15143],{},[2111,56068,2113],{},[2884,56070,56071,56073],{},[898,56072,6796],{},[2111,56074,2113],{},[898,56076,2362],{},[1711,56078,1714],{"stretchy":1713},[898,56080,6796],{},[1711,56082,1735],{"stretchy":1713},[1942,56084,2519],{},[898,56086,2098],{},[898,56088,6796],{},[902,56090,56091],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,56093,56095],{"className":56094},[886],[888,56096,56097],{"xmlns":890},[892,56098,56099,56105],{},[895,56100,56101,56103],{},[898,56102,7929],{},[898,56104,2362],{},[902,56106,48567],{"encoding":904},[123,56108,56109,56110,2186],{},"Sestav obdélník ",[883,56111,56113],{"className":56112},[886],[888,56114,56115],{"xmlns":890},[892,56116,56117,56133],{},[895,56118,56119,56125,56127],{},[2884,56120,56121,56123],{},[898,56122,7929],{},[2111,56124,2113],{},[1711,56126,4795],{},[2884,56128,56129,56131],{},[898,56130,6796],{},[2111,56132,2113],{},[902,56134,56135],{"encoding":904},"P_0 \\cdot Q_0",[123,56137,56138,56139],{},"Dosaď:\n",[120,56140,56141,56206],{},[123,56142,56143,56201,56202,56205],{},[883,56144,56146],{"className":56145},[886],[888,56147,56148],{"xmlns":890},[892,56149,56150,56198],{},[895,56151,56152,56154,56156,56158,56170,56172,56174,56176,56178,56180,56182,56184,56186,56192],{},[898,56153,1940],{},[898,56155,2362],{},[1711,56157,1836],{},[13142,56159,56160,56162,56164],{},[1711,56161,15143],{},[2111,56163,2113],{},[2884,56165,56166,56168],{},[898,56167,6796],{},[2111,56169,2113],{},[898,56171,2778],{},[1711,56173,1714],{"stretchy":1713},[898,56175,6796],{},[1711,56177,1735],{"stretchy":1713},[1942,56179,2519],{},[898,56181,2098],{},[898,56183,6796],{},[1711,56185,2460],{},[2884,56187,56188,56190],{},[898,56189,7929],{},[2111,56191,2113],{},[2884,56193,56194,56196],{},[898,56195,6796],{},[2111,56197,2113],{},[902,56199,56200],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,56203,56204],{},"mínus"," obdélník)",[123,56207,56208,56266,56267,56269],{},[883,56209,56211],{"className":56210},[886],[888,56212,56213],{"xmlns":890},[892,56214,56215,56263],{},[895,56216,56217,56219,56221,56223,56229,56235,56237,56249,56251,56253,56255,56257,56259,56261],{},[898,56218,7929],{},[898,56220,2362],{},[1711,56222,1836],{},[2884,56224,56225,56227],{},[898,56226,7929],{},[2111,56228,2113],{},[2884,56230,56231,56233],{},[898,56232,6796],{},[2111,56234,2113],{},[1711,56236,2460],{},[13142,56238,56239,56241,56243],{},[1711,56240,15143],{},[2111,56242,2113],{},[2884,56244,56245,56247],{},[898,56246,6796],{},[2111,56248,2113],{},[898,56250,2362],{},[1711,56252,1714],{"stretchy":1713},[898,56254,6796],{},[1711,56256,1735],{"stretchy":1713},[1942,56258,2519],{},[898,56260,2098],{},[898,56262,6796],{},[902,56264,56265],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,56268,56204],{}," integrál)",[123,56271,56272,56273,56276],{},"Kontrola znaménka: obě hodnoty musí být ",[38,56274,56275],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[40568,56278],{},[115,56280,56282],{"id":56281},"příklady","Příklady",[198,56284,56286],{"id":56285},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[1921,56288,56289],{},[724,56290,56291,56294,56295,51319,56318,56341,56342,1343,56362,1343,56379,1343,56396,56413,56414,56490,56491,56508,56509,56522],{},[883,56292,56293],{},"!example"," Zadání\nJsou dány poptávka ",[883,56296,56298],{"className":56297},[886],[888,56299,56300],{"xmlns":890},[892,56301,56302,56316],{},[895,56303,56304,56306,56308,56310,56312,56314],{},[898,56305,7929],{},[1711,56307,1836],{},[898,56309,207],{},[898,56311,6796],{},[1711,56313,2095],{},[898,56315,2223],{},[902,56317,40658],{"encoding":904},[883,56319,56321],{"className":56320},[886],[888,56322,56323],{"xmlns":890},[892,56324,56325,56339],{},[895,56326,56327,56329,56331,56333,56335,56337],{},[898,56328,7929],{},[1711,56330,1836],{},[898,56332,2090],{},[898,56334,6796],{},[1711,56336,2095],{},[898,56338,2098],{},[902,56340,43840],{"encoding":904}," s hodnotami ",[883,56343,56345],{"className":56344},[886],[888,56346,56347],{"xmlns":890},[892,56348,56349,56359],{},[895,56350,56351,56353,56355,56357],{},[898,56352,207],{},[1711,56354,1836],{},[1711,56356,2460],{},[2111,56358,3034],{},[902,56360,56361],{"encoding":904},"a = -3",[883,56363,56365],{"className":56364},[886],[888,56366,56367],{"xmlns":890},[892,56368,56369,56377],{},[895,56370,56371,56373,56375],{},[898,56372,2223],{},[1711,56374,1836],{},[2111,56376,9195],{},[902,56378,52242],{"encoding":904},[883,56380,56382],{"className":56381},[886],[888,56383,56384],{"xmlns":890},[892,56385,56386,56394],{},[895,56387,56388,56390,56392],{},[898,56389,2090],{},[1711,56391,1836],{},[2111,56393,8993],{},[902,56395,52260],{"encoding":904},[883,56397,56399],{"className":56398},[886],[888,56400,56401],{"xmlns":890},[892,56402,56403,56411],{},[895,56404,56405,56407,56409],{},[898,56406,2098],{},[1711,56408,1836],{},[2111,56410,4712],{},[902,56412,52278],{"encoding":904},".\nRovnovážné množství:\n",[883,56415,56417],{"className":56416},[886],[888,56418,56419],{"xmlns":890},[892,56420,56421,56487],{},[895,56422,56423,56429,56431,56449,56451,56475,56477,56483,56485],{},[1716,56424,56425,56427],{},[898,56426,6796],{},[898,56428,1722],{},[1711,56430,1836],{},[2525,56432,56433,56441],{},[895,56434,56435,56437,56439],{},[898,56436,2223],{},[1711,56438,2460],{},[898,56440,2098],{},[895,56442,56443,56445,56447],{},[898,56444,2090],{},[1711,56446,2460],{},[898,56448,207],{},[1711,56450,1836],{},[2525,56452,56453,56461],{},[895,56454,56455,56457,56459],{},[2111,56456,9195],{},[1711,56458,2460],{},[2111,56460,4712],{},[895,56462,56463,56465,56467,56469,56471,56473],{},[2111,56464,8993],{},[1711,56466,2460],{},[1711,56468,1714],{"stretchy":1713},[1711,56470,2460],{},[2111,56472,3034],{},[1711,56474,1735],{"stretchy":1713},[1711,56476,1836],{},[2525,56478,56479,56481],{},[2111,56480,41617],{},[2111,56482,48004],{},[1711,56484,9881],{},[2111,56486,48009],{},[902,56488,56489],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,56492,56494],{"className":56493},[886],[888,56495,56496],{"xmlns":890},[892,56497,56498,56506],{},[895,56499,56500],{},[1716,56501,56502,56504],{},[898,56503,6796],{},[898,56505,1722],{},[902,56507,46001],{"encoding":904}," (a) při změně samotného parametru ",[883,56510,56512],{"className":56511},[886],[888,56513,56514],{"xmlns":890},[892,56515,56516,56520],{},[895,56517,56518],{},[898,56519,2090],{},[902,56521,2090],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,56524,56525],{},[38,56526,56527,56528,6682,56541,6696,56554,13271],{},"Řešení (a) — změna ",[883,56529,56531],{"className":56530},[886],[888,56532,56533],{"xmlns":890},[892,56534,56535,56539],{},[895,56536,56537],{},[898,56538,2090],{},[902,56540,2090],{"encoding":904},[883,56542,56544],{"className":56543},[886],[888,56545,56546],{"xmlns":890},[892,56547,56548,56552],{},[895,56549,56550],{},[2111,56551,8993],{},[902,56553,48044],{"encoding":904},[883,56555,56557],{"className":56556},[886],[888,56558,56559],{"xmlns":890},[892,56560,56561,56565],{},[895,56562,56563],{},[2111,56564,22919],{},[902,56566,48058],{"encoding":904},[724,56568,56569,56570,56634,56635,2062],{},"Pomocí vzorce (2.13) pro ",[883,56571,56573],{"className":56572},[886],[888,56574,56575],{"xmlns":890},[892,56576,56577,56631],{},[895,56578,56579,56599,56601,56603],{},[2509,56580,56581],{"scriptlevel":2113,"displaystyle":1725},[2525,56582,56583,56593],{},[895,56584,56585,56587],{},[898,56586,13846],{"mathvariant":2287},[1716,56588,56589,56591],{},[898,56590,6796],{},[898,56592,1722],{},[895,56594,56595,56597],{},[898,56596,13846],{"mathvariant":2287},[898,56598,2090],{},[1711,56600,1836],{},[1711,56602,2460],{},[2509,56604,56605],{"scriptlevel":2113,"displaystyle":1725},[2525,56606,56607,56615],{},[895,56608,56609,56611,56613],{},[898,56610,2223],{},[1711,56612,2460],{},[898,56614,2098],{},[895,56616,56617,56619,56621,56623,56625],{},[1711,56618,1714],{"stretchy":1713},[898,56620,2090],{},[1711,56622,2460],{},[898,56624,207],{},[1716,56626,56627,56629],{},[1711,56628,1735],{"stretchy":1713},[2111,56630,2963],{},[902,56632,56633],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,56636,56638],{"className":56637},[886],[888,56639,56640],{"xmlns":890},[892,56641,56642,56664],{},[895,56643,56644,56646],{},[1711,56645,2460],{},[2509,56647,56648],{"scriptlevel":2113,"displaystyle":1725},[2525,56649,56650,56656],{},[1716,56651,56652,56654],{},[898,56653,6796],{},[898,56655,1722],{},[895,56657,56658,56660,56662],{},[898,56659,2090],{},[1711,56661,2460],{},[898,56663,207],{},[902,56665,56666],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,56668,56670],{"className":56669},[886],[888,56671,56672],{"xmlns":890,"display":31664},[892,56673,56674,56730],{},[895,56675,56676,56678,56684,56686,56688,56704,56706,56708,56710,56712,56714,56720,56722,56724,56726,56728],{},[898,56677,2098],{},[1716,56679,56680,56682],{},[898,56681,6796],{},[898,56683,1722],{},[1711,56685,1836],{},[1711,56687,2460],{},[2525,56689,56690,56696],{},[1716,56691,56692,56694],{},[898,56693,6796],{},[898,56695,1722],{},[895,56697,56698,56700,56702],{},[898,56699,2090],{},[1711,56701,2460],{},[898,56703,207],{},[1942,56705,2519],{},[898,56707,2098],{},[898,56709,2090],{},[1711,56711,1836],{},[1711,56713,2460],{},[2525,56715,56716,56718],{},[2111,56717,48172],{},[2111,56719,48004],{},[1711,56721,4795],{},[2111,56723,4343],{},[1711,56725,9881],{},[1711,56727,2460],{},[2111,56729,48144],{},[902,56731,56732],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,56734,56735],{},"Nové rovnovážné množství:",[883,56737,56739],{"className":56738},[886],[888,56740,56741],{"xmlns":890,"display":31664},[892,56742,56743,56766],{},[895,56744,56745,56753,56755,56757,56759,56761,56763],{},[13142,56746,56747,56749,56751],{},[898,56748,6796],{},[2111,56750,2238],{},[898,56752,1722],{},[1711,56754,6740],{},[2111,56756,48172],{},[1711,56758,2460],{},[2111,56760,48177],{},[1711,56762,1836],{},[2111,56764,56765],{},"8,326.",[902,56767,56768],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,56770,56771,1700,56774,1343,56801,1343,56823,1343,56845,9572,56867,1343,56886,1343,56907,1343,56926,2186],{},[38,56772,56773],{},"Řešení (b) — současná změna všech parametrů:",[883,56775,56777],{"className":56776},[886],[888,56778,56779],{"xmlns":890},[892,56780,56781,56798],{},[895,56782,56783,56785,56787,56789,56791,56793,56795],{},[898,56784,207],{},[1711,56786,2062],{},[1711,56788,2460],{},[2111,56790,3034],{},[1711,56792,7123],{},[1711,56794,2460],{},[2111,56796,56797],{},"2,5",[902,56799,56800],{"encoding":904},"a: -3 \\to -2{,}5",[883,56802,56804],{"className":56803},[886],[888,56805,56806],{"xmlns":890},[892,56807,56808,56820],{},[895,56809,56810,56812,56814,56816,56818],{},[898,56811,2223],{},[1711,56813,2062],{},[2111,56815,9195],{},[1711,56817,7123],{},[2111,56819,4733],{},[902,56821,56822],{"encoding":904},"b: 40 \\to 35",[883,56824,56826],{"className":56825},[886],[888,56827,56828],{"xmlns":890},[892,56829,56830,56842],{},[895,56831,56832,56834,56836,56838,56840],{},[898,56833,2090],{},[1711,56835,2062],{},[2111,56837,8993],{},[1711,56839,7123],{},[2111,56841,22919],{},[902,56843,56844],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,56846,56848],{"className":56847},[886],[888,56849,56850],{"xmlns":890},[892,56851,56852,56864],{},[895,56853,56854,56856,56858,56860,56862],{},[898,56855,2098],{},[1711,56857,2062],{},[2111,56859,4712],{},[1711,56861,7123],{},[2111,56863,6907],{},[902,56865,56866],{"encoding":904},"d: 10 \\to 11",[883,56868,56870],{"className":56869},[886],[888,56871,56872],{"xmlns":890},[892,56873,56874,56884],{},[895,56875,56876,56878,56880,56882],{},[898,56877,2098],{},[898,56879,207],{},[1711,56881,1836],{},[2111,56883,8993],{},[902,56885,48210],{"encoding":904},[883,56887,56889],{"className":56888},[886],[888,56890,56891],{"xmlns":890},[892,56892,56893,56905],{},[895,56894,56895,56897,56899,56901,56903],{},[898,56896,2098],{},[898,56898,2223],{},[1711,56900,1836],{},[1711,56902,2460],{},[2111,56904,4798],{},[902,56906,48232],{"encoding":904},[883,56908,56910],{"className":56909},[886],[888,56911,56912],{"xmlns":890},[892,56913,56914,56924],{},[895,56915,56916,56918,56920,56922],{},[898,56917,2098],{},[898,56919,2090],{},[1711,56921,1836],{},[2111,56923,4343],{},[902,56925,48252],{"encoding":904},[883,56927,56929],{"className":56928},[886],[888,56930,56931],{"xmlns":890},[892,56932,56933,56943],{},[895,56934,56935,56937,56939,56941],{},[898,56936,2098],{},[898,56938,2098],{},[1711,56940,1836],{},[2111,56942,2238],{},[902,56944,48272],{"encoding":904},[724,56946,56947,56948,57006],{},"Totální diferenciál ",[883,56949,56951],{"className":56950},[886],[888,56952,56953],{"xmlns":890},[892,56954,56955,57003],{},[895,56956,56957,56963,56965,56967,56969,56971,56973,56975,56977,56979,56981,56983],{},[1716,56958,56959,56961],{},[898,56960,6796],{},[898,56962,1722],{},[1711,56964,1714],{"stretchy":1713},[898,56966,207],{},[1711,56968,1726],{"separator":1725},[898,56970,2223],{},[1711,56972,1726],{"separator":1725},[898,56974,2090],{},[1711,56976,1726],{"separator":1725},[898,56978,2098],{},[1711,56980,1735],{"stretchy":1713},[1711,56982,1836],{},[2509,56984,56985],{"scriptlevel":2113,"displaystyle":1725},[2525,56986,56987,56995],{},[895,56988,56989,56991,56993],{},[898,56990,2223],{},[1711,56992,2460],{},[898,56994,2098],{},[895,56996,56997,56999,57001],{},[898,56998,2090],{},[1711,57000,2460],{},[898,57002,207],{},[902,57004,57005],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,57008,57010],{"className":57009},[886],[888,57011,57012],{"xmlns":890,"display":31664},[892,57013,57014,57134],{},[895,57015,57016,57018,57024,57026,57052,57054,57056,57058,57060,57072,57074,57076,57078,57080,57106,57108,57110,57112,57114,57126,57128,57130,57132],{},[898,57017,2098],{},[1716,57019,57020,57022],{},[898,57021,6796],{},[898,57023,1722],{},[1711,57025,1836],{},[2525,57027,57028,57036],{},[895,57029,57030,57032,57034],{},[898,57031,2223],{},[1711,57033,2460],{},[898,57035,2098],{},[895,57037,57038,57040,57042,57044,57046],{},[1711,57039,1714],{"stretchy":1713},[898,57041,2090],{},[1711,57043,2460],{},[898,57045,207],{},[1716,57047,57048,57050],{},[1711,57049,1735],{"stretchy":1713},[2111,57051,2963],{},[1942,57053,2519],{},[898,57055,2098],{},[898,57057,207],{},[1711,57059,2095],{},[2525,57061,57062,57064],{},[2111,57063,2238],{},[895,57065,57066,57068,57070],{},[898,57067,2090],{},[1711,57069,2460],{},[898,57071,207],{},[1942,57073,2519],{},[898,57075,2098],{},[898,57077,2223],{},[1711,57079,2460],{},[2525,57081,57082,57090],{},[895,57083,57084,57086,57088],{},[898,57085,2223],{},[1711,57087,2460],{},[898,57089,2098],{},[895,57091,57092,57094,57096,57098,57100],{},[1711,57093,1714],{"stretchy":1713},[898,57095,2090],{},[1711,57097,2460],{},[898,57099,207],{},[1716,57101,57102,57104],{},[1711,57103,1735],{"stretchy":1713},[2111,57105,2963],{},[1942,57107,2519],{},[898,57109,2098],{},[898,57111,2090],{},[1711,57113,2460],{},[2525,57115,57116,57118],{},[2111,57117,2238],{},[895,57119,57120,57122,57124],{},[898,57121,2090],{},[1711,57123,2460],{},[898,57125,207],{},[1942,57127,2519],{},[898,57129,2098],{},[898,57131,2098],{},[898,57133,2186],{"mathvariant":2287},[902,57135,57136],{"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.",[724,57138,57139,57140,1343,57162,1343,57193,3239],{},"Dosazením číselných hodnot (",[883,57141,57143],{"className":57142},[886],[888,57144,57145],{"xmlns":890},[892,57146,57147,57159],{},[895,57148,57149,57151,57153,57155,57157],{},[898,57150,2090],{},[1711,57152,2460],{},[898,57154,207],{},[1711,57156,1836],{},[2111,57158,48004],{},[902,57160,57161],{"encoding":904},"c - a = 3{,}5",[883,57163,57165],{"className":57164},[886],[888,57166,57167],{"xmlns":890},[892,57168,57169,57190],{},[895,57170,57171,57173,57175,57177,57179,57185,57187],{},[1711,57172,1714],{"stretchy":1713},[898,57174,2090],{},[1711,57176,2460],{},[898,57178,207],{},[1716,57180,57181,57183],{},[1711,57182,1735],{"stretchy":1713},[2111,57184,2963],{},[1711,57186,1836],{},[2111,57188,57189],{},"12,25",[902,57191,57192],{"encoding":904},"(c-a)^2 = 12{,}25",[883,57194,57196],{"className":57195},[886],[888,57197,57198],{"xmlns":890},[892,57199,57200,57212],{},[895,57201,57202,57204,57206,57208,57210],{},[898,57203,2223],{},[1711,57205,2460],{},[898,57207,2098],{},[1711,57209,1836],{},[2111,57211,41617],{},[902,57213,57214],{"encoding":904},"b - d = 30",[883,57216,57218],{"className":57217},[886],[888,57219,57220],{"xmlns":890,"display":31664},[892,57221,57222,57323],{},[895,57223,57224,57226,57232,57234,57242,57244,57246,57248,57250,57258,57260,57262,57264,57266,57268,57276,57278,57280,57282,57284,57292,57294,57296,57298,57300,57303,57305,57308,57310,57312,57314,57317,57319,57321],{},[898,57225,2098],{},[1716,57227,57228,57230],{},[898,57229,6796],{},[898,57231,1722],{},[1711,57233,6740],{},[2509,57235,57236],{"scriptlevel":2113,"displaystyle":1713},[2525,57237,57238,57240],{},[2111,57239,41617],{},[2111,57241,57189],{},[1711,57243,1714],{"stretchy":1713},[2111,57245,8993],{},[1711,57247,1735],{"stretchy":1713},[1711,57249,2095],{},[2509,57251,57252],{"scriptlevel":2113,"displaystyle":1713},[2525,57253,57254,57256],{},[2111,57255,2238],{},[2111,57257,48004],{},[1711,57259,1714],{"stretchy":1713},[1711,57261,2460],{},[2111,57263,4798],{},[1711,57265,1735],{"stretchy":1713},[1711,57267,2460],{},[2509,57269,57270],{"scriptlevel":2113,"displaystyle":1713},[2525,57271,57272,57274],{},[2111,57273,41617],{},[2111,57275,57189],{},[1711,57277,1714],{"stretchy":1713},[2111,57279,4343],{},[1711,57281,1735],{"stretchy":1713},[1711,57283,2460],{},[2509,57285,57286],{"scriptlevel":2113,"displaystyle":1713},[2525,57287,57288,57290],{},[2111,57289,2238],{},[2111,57291,48004],{},[1711,57293,1714],{"stretchy":1713},[2111,57295,2238],{},[1711,57297,1735],{"stretchy":1713},[1711,57299,9881],{},[2111,57301,57302],{},"1,224",[1711,57304,2460],{},[2111,57306,57307],{},"1,429",[1711,57309,2460],{},[2111,57311,48177],{},[1711,57313,2460],{},[2111,57315,57316],{},"0,286",[1711,57318,9881],{},[1711,57320,2460],{},[2111,57322,48423],{},[902,57324,57325],{"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.",[724,57327,33663,57328,2186],{},[883,57329,57331],{"className":57330},[886],[888,57332,57333],{"xmlns":890},[892,57334,57335,57357],{},[895,57336,57337,57345,57347,57349,57351,57353,57355],{},[13142,57338,57339,57341,57343],{},[898,57340,6796],{},[2111,57342,2238],{},[898,57344,1722],{},[1711,57346,6740],{},[2111,57348,48172],{},[1711,57350,2460],{},[2111,57352,48454],{},[1711,57354,9881],{},[2111,57356,48459],{},[902,57358,57359],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[1921,57361,57362],{},[724,57363,57364,57366,57367,57388,57389,57415,57416,57419,57420,57516,57517,57540,57541,57557],{},[883,57365,1927],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,57368,57370],{"className":57369},[886],[888,57371,57372],{"xmlns":890},[892,57373,57374,57386],{},[895,57375,57376,57378,57380,57382,57384],{},[898,57377,6892],{"mathvariant":2287},[898,57379,6796],{},[1711,57381,6740],{},[1711,57383,2460],{},[2111,57385,48489],{},[902,57387,48492],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,57390,57392],{"className":57391},[886],[888,57393,57394],{"xmlns":890},[892,57395,57396,57412],{},[895,57397,57398,57400,57406,57408,57410],{},[898,57399,2098],{},[1716,57401,57402,57404],{},[898,57403,6796],{},[898,57405,1722],{},[1711,57407,9881],{},[1711,57409,2460],{},[2111,57411,48454],{},[902,57413,57414],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,57417,57418],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,57421,57423],{"className":57422},[886],[888,57424,57425],{"xmlns":890},[892,57426,57427,57513],{},[895,57428,57429,57437,57439,57473,57475,57499,57501,57508,57510],{},[13142,57430,57431,57433,57435],{},[898,57432,6796],{},[2111,57434,2238],{},[898,57436,1722],{},[1711,57438,1836],{},[2525,57440,57441,57457],{},[895,57442,57443,57449,57451],{},[1716,57444,57445,57447],{},[898,57446,2223],{},[1711,57448,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,57450,2460],{},[1716,57452,57453,57455],{},[898,57454,2098],{},[1711,57456,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[895,57458,57459,57465,57467],{},[1716,57460,57461,57463],{},[898,57462,2090],{},[1711,57464,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,57466,2460],{},[1716,57468,57469,57471],{},[898,57470,207],{},[1711,57472,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,57474,1836],{},[2525,57476,57477,57485],{},[895,57478,57479,57481,57483],{},[2111,57480,4733],{},[1711,57482,2460],{},[2111,57484,6907],{},[895,57486,57487,57489,57491,57493,57495,57497],{},[2111,57488,22919],{},[1711,57490,2460],{},[1711,57492,1714],{"stretchy":1713},[1711,57494,2460],{},[2111,57496,56797],{},[1711,57498,1735],{"stretchy":1713},[1711,57500,1836],{},[2525,57502,57503,57505],{},[2111,57504,45398],{},[2111,57506,57507],{},"3,1",[1711,57509,9881],{},[2111,57511,57512],{},"7,742",[902,57514,57515],{"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 ",[883,57518,57520],{"className":57519},[886],[888,57521,57522],{"xmlns":890},[892,57523,57524,57537],{},[895,57525,57526,57528,57530,57532,57534],{},[898,57527,6892],{"mathvariant":2287},[898,57529,6796],{},[1711,57531,9881],{},[1711,57533,2460],{},[2111,57535,57536],{},"0,829",[902,57538,57539],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,57542,57544],{"className":57543},[886],[888,57545,57546],{"xmlns":890},[892,57547,57548,57554],{},[895,57549,57550,57552],{},[1711,57551,2460],{},[2111,57553,48489],{},[902,57555,57556],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,57559,57560],{},[614,57561,57562,57563,57576],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,57564,57566],{"className":57565},[886],[888,57567,57568],{"xmlns":890},[892,57569,57570,57574],{},[895,57571,57572],{},[898,57573,6796],{},[902,57575,6796],{"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.",[198,57578,57580,57581],{"id":57579},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,57582,57584],{"className":57583},[886],[888,57585,57586],{"xmlns":890},[892,57587,57588,57594],{},[895,57589,57590,57592],{},[898,57591,7929],{},[898,57593,2362],{},[902,57595,48567],{"encoding":904},[1921,57597,57598],{},[724,57599,57600,57602,57603,57637,57638,57660],{},[883,57601,56293],{}," Zadání\nPro nabídku ",[883,57604,57606],{"className":57605},[886],[888,57607,57608],{"xmlns":890},[892,57609,57610,57634],{},[895,57611,57612,57614,57616,57618,57620,57622,57624,57626,57628,57630,57632],{},[898,57613,7929],{},[1711,57615,1836],{},[898,57617,2362],{},[1711,57619,1714],{"stretchy":1713},[898,57621,6796],{},[1711,57623,1735],{"stretchy":1713},[1711,57625,1836],{},[2111,57627,4712],{},[1711,57629,2095],{},[2111,57631,2963],{},[898,57633,6796],{},[902,57635,57636],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,57639,57641],{"className":57640},[886],[888,57642,57643],{"xmlns":890},[892,57644,57645,57657],{},[895,57646,57647,57653,57655],{},[2884,57648,57649,57651],{},[898,57650,6796],{},[2111,57652,2113],{},[1711,57654,1836],{},[2111,57656,4712],{},[902,57658,57659],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,57662,57663],{},[38,57664,26368],{},[724,57666,57667],{},"Odpovídající cena:",[883,57669,57671],{"className":57670},[886],[888,57672,57673],{"xmlns":890,"display":31664},[892,57674,57675,57710],{},[895,57676,57677,57683,57685,57687,57689,57691,57693,57695,57697,57699,57701,57703,57705,57707],{},[2884,57678,57679,57681],{},[898,57680,7929],{},[2111,57682,2113],{},[1711,57684,1836],{},[898,57686,2362],{},[1711,57688,1714],{"stretchy":1713},[2111,57690,4712],{},[1711,57692,1735],{"stretchy":1713},[1711,57694,1836],{},[2111,57696,4712],{},[1711,57698,2095],{},[2111,57700,2963],{},[1711,57702,4795],{},[2111,57704,4712],{},[1711,57706,1836],{},[2111,57708,57709],{},"30.",[902,57711,57712],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,57714,57715],{},"Dle vzorce (2.15):",[883,57717,57719],{"className":57718},[886],[888,57720,57721],{"xmlns":890,"display":31664},[892,57722,57723,57831],{},[895,57724,57725,57727,57729,57731,57733,57735,57737,57743,57749,57751,57759,57761,57763,57765,57767,57769,57771,57773,57775,57777,57779,57781,57783,57785,57787,57790,57792,57794,57796,57802,57810,57812,57814,57816,57818,57820,57822,57824,57826,57828],{},[898,57726,7929],{},[898,57728,2362],{},[1711,57730,1714],{"stretchy":1713},[2111,57732,4712],{},[1711,57734,1735],{"stretchy":1713},[1711,57736,1836],{},[2884,57738,57739,57741],{},[898,57740,7929],{},[2111,57742,2113],{},[2884,57744,57745,57747],{},[898,57746,6796],{},[2111,57748,2113],{},[1711,57750,2460],{},[13142,57752,57753,57755,57757],{},[1711,57754,15143],{},[2111,57756,2113],{},[2111,57758,4712],{},[1711,57760,1714],{"stretchy":1713},[2111,57762,4712],{},[1711,57764,2095],{},[2111,57766,2963],{},[898,57768,6796],{},[1711,57770,1735],{"stretchy":1713},[1942,57772,2519],{},[898,57774,2098],{},[898,57776,6796],{},[1711,57778,1836],{},[2111,57780,4712],{},[1711,57782,4795],{},[2111,57784,41617],{},[1711,57786,2460],{},[1711,57788,5144],{"fence":1713,"stretchy":1725,"minsize":57789,"maxsize":57789},"1.8em",[2111,57791,4712],{},[898,57793,6796],{},[1711,57795,2095],{},[1716,57797,57798,57800],{},[898,57799,6796],{},[2111,57801,2963],{},[13142,57803,57804,57806,57808],{},[1711,57805,5163],{"fence":1713,"stretchy":1725,"minsize":57789,"maxsize":57789},[2111,57807,2113],{},[2111,57809,4712],{},[1711,57811,1836],{},[2111,57813,33679],{},[1711,57815,2460],{},[1711,57817,1714],{"stretchy":1713},[2111,57819,4282],{},[1711,57821,2095],{},[2111,57823,4282],{},[1711,57825,1735],{"stretchy":1713},[1711,57827,1836],{},[2111,57829,57830],{},"100.",[902,57832,57833],{"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.",[724,57835,57836,57837,57858,57859,57879],{},"Přebytek výrobce při množství ",[883,57838,57840],{"className":57839},[886],[888,57841,57842],{"xmlns":890},[892,57843,57844,57856],{},[895,57845,57846,57852,57854],{},[2884,57847,57848,57850],{},[898,57849,6796],{},[2111,57851,2113],{},[1711,57853,1836],{},[2111,57855,4712],{},[902,57857,57659],{"encoding":904}," je tedy ",[883,57860,57862],{"className":57861},[886],[888,57863,57864],{"xmlns":890},[892,57865,57866,57876],{},[895,57867,57868,57870,57872,57874],{},[898,57869,7929],{},[898,57871,2362],{},[1711,57873,1836],{},[2111,57875,4282],{},[902,57877,57878],{"encoding":904},"PS = 100"," (peněžních jednotek).",[40568,57881],{},[115,57883,57885],{"id":57884},"cheat-sheet","Cheat sheet",[16,57887,57888,57901],{},[19,57889,57890],{},[22,57891,57892,57895,57898],{},[25,57893,57894],{},"Veličina",[25,57896,57897],{},"Vzorec",[25,57899,57900],{},"Geometrie",[30,57902,57903,58021,58135,58203],{},[22,57904,57905,57933,57989],{},[35,57906,57907],{},[883,57908,57910],{"className":57909},[886],[888,57911,57912],{"xmlns":890},[892,57913,57914,57930],{},[895,57915,57916,57918,57920,57922,57928],{},[898,57917,1940],{},[898,57919,2362],{},[1711,57921,1714],{"stretchy":1713},[2884,57923,57924,57926],{},[898,57925,6796],{},[2111,57927,2113],{},[1711,57929,1735],{"stretchy":1713},[902,57931,57932],{"encoding":904},"CS(Q_0)",[35,57934,57935],{},[883,57936,57938],{"className":57937},[886],[888,57939,57940],{"xmlns":890},[892,57941,57942,57986],{},[895,57943,57944],{},[2509,57945,57946,57958,57960,57962,57964,57966,57968,57970,57972,57974,57980],{"scriptlevel":2113,"displaystyle":1725},[13142,57947,57948,57950,57952],{},[1711,57949,15143],{},[2111,57951,2113],{},[2884,57953,57954,57956],{},[898,57955,6796],{},[2111,57957,2113],{},[898,57959,2778],{},[1711,57961,1714],{"stretchy":1713},[898,57963,6796],{},[1711,57965,1735],{"stretchy":1713},[1942,57967,2519],{},[898,57969,2098],{},[898,57971,6796],{},[1711,57973,2460],{},[2884,57975,57976,57978],{},[898,57977,7929],{},[2111,57979,2113],{},[2884,57981,57982,57984],{},[898,57983,6796],{},[2111,57985,2113],{},[902,57987,57988],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,57990,57991,57992,57995,57996,57999,58000],{},"plocha ",[38,57993,57994],{},"pod"," křivkou poptávky, ",[38,57997,57998],{},"nad"," čárou ",[883,58001,58003],{"className":58002},[886],[888,58004,58005],{"xmlns":890},[892,58006,58007,58019],{},[895,58008,58009,58011,58013],{},[898,58010,7929],{},[1711,58012,1836],{},[2884,58014,58015,58017],{},[898,58016,7929],{},[2111,58018,2113],{},[902,58020,55275],{"encoding":904},[22,58022,58023,58051,58107],{},[35,58024,58025],{},[883,58026,58028],{"className":58027},[886],[888,58029,58030],{"xmlns":890},[892,58031,58032,58048],{},[895,58033,58034,58036,58038,58040,58046],{},[898,58035,7929],{},[898,58037,2362],{},[1711,58039,1714],{"stretchy":1713},[2884,58041,58042,58044],{},[898,58043,6796],{},[2111,58045,2113],{},[1711,58047,1735],{"stretchy":1713},[902,58049,58050],{"encoding":904},"PS(Q_0)",[35,58052,58053],{},[883,58054,58056],{"className":58055},[886],[888,58057,58058],{"xmlns":890},[892,58059,58060,58104],{},[895,58061,58062],{},[2509,58063,58064,58070,58076,58078,58090,58092,58094,58096,58098,58100,58102],{"scriptlevel":2113,"displaystyle":1725},[2884,58065,58066,58068],{},[898,58067,7929],{},[2111,58069,2113],{},[2884,58071,58072,58074],{},[898,58073,6796],{},[2111,58075,2113],{},[1711,58077,2460],{},[13142,58079,58080,58082,58084],{},[1711,58081,15143],{},[2111,58083,2113],{},[2884,58085,58086,58088],{},[898,58087,6796],{},[2111,58089,2113],{},[898,58091,2362],{},[1711,58093,1714],{"stretchy":1713},[898,58095,6796],{},[1711,58097,1735],{"stretchy":1713},[1942,58099,2519],{},[898,58101,2098],{},[898,58103,6796],{},[902,58105,58106],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,58108,57991,58109,58111,58112,57999,58114],{},[38,58110,57998],{}," křivkou nabídky, ",[38,58113,57994],{},[883,58115,58117],{"className":58116},[886],[888,58118,58119],{"xmlns":890},[892,58120,58121,58133],{},[895,58122,58123,58125,58127],{},[898,58124,7929],{},[1711,58126,1836],{},[2884,58128,58129,58131],{},[898,58130,7929],{},[2111,58132,2113],{},[902,58134,55275],{"encoding":904},[22,58136,58137,58140,58167],{},[35,58138,58139],{},"Výdaje \u002F tržby",[35,58141,58142],{},[883,58143,58145],{"className":58144},[886],[888,58146,58147],{"xmlns":890},[892,58148,58149,58165],{},[895,58150,58151,58157,58159],{},[2884,58152,58153,58155],{},[898,58154,7929],{},[2111,58156,2113],{},[1711,58158,4795],{},[2884,58160,58161,58163],{},[898,58162,6796],{},[2111,58164,2113],{},[902,58166,56135],{"encoding":904},[35,58168,58169,58170],{},"obdélník ",[883,58171,58173],{"className":58172},[886],[888,58174,58175],{"xmlns":890},[892,58176,58177,58201],{},[895,58178,58179,58181,58183,58189,58191,58193,58195],{},[2111,58180,2113],{},[1942,58182,2519],{},[2884,58184,58185,58187],{},[898,58186,6796],{},[2111,58188,2113],{},[1942,58190,2519],{},[898,58192,8243],{},[1942,58194,2519],{},[2884,58196,58197,58199],{},[898,58198,7929],{},[2111,58200,2113],{},[902,58202,54755],{"encoding":904},[22,58204,58205,58208,58231],{},[35,58206,58207],{},"Celkový přebytek",[35,58209,58210],{},[883,58211,58213],{"className":58212},[886],[888,58214,58215],{"xmlns":890},[892,58216,58217,58229],{},[895,58218,58219,58221,58223,58225,58227],{},[898,58220,1940],{},[898,58222,2362],{},[1711,58224,2095],{},[898,58226,7929],{},[898,58228,2362],{},[902,58230,54493],{"encoding":904},[35,58232,58233],{},"součet obou ploch v rovnováze",[40568,58235],{},[115,58237,5422],{"id":5421},[120,58239,58240,58262,58284,58328,58372,58435,58463],{},[123,58241,58242,1648,58244,1343,58259,58261],{},[38,58243,48532],{},[883,58245,58247],{"className":58246},[886],[888,58248,58249],{"xmlns":890},[892,58250,58251,58257],{},[895,58252,58253,58255],{},[898,58254,1940],{},[898,58256,2362],{},[902,58258,48548],{"encoding":904},[614,58260,48586],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,58263,58264,1648,58266,1343,58281,58283],{},[38,58265,48679],{},[883,58267,58269],{"className":58268},[886],[888,58270,58271],{"xmlns":890},[892,58272,58273,58279],{},[895,58274,58275,58277],{},[898,58276,7929],{},[898,58278,2362],{},[902,58280,48567],{"encoding":904},[614,58282,48682],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,58285,58286,5204,58289,2186],{},[38,58287,58288],{},"Ochota platit",[883,58290,58292],{"className":58291},[886],[888,58293,58294],{"xmlns":890},[892,58295,58296,58326],{},[895,58297,58298],{},[2509,58299,58300,58312,58314,58316,58318,58320,58322,58324],{"scriptlevel":2113,"displaystyle":1725},[13142,58301,58302,58304,58306],{},[1711,58303,15143],{},[2111,58305,2113],{},[2884,58307,58308,58310],{},[898,58309,6796],{},[2111,58311,2113],{},[898,58313,2778],{},[1711,58315,1714],{"stretchy":1713},[898,58317,6796],{},[1711,58319,1735],{"stretchy":1713},[1942,58321,2519],{},[898,58323,2098],{},[898,58325,6796],{},[902,58327,55123],{"encoding":904},[123,58329,58330,5204,58333,2186],{},[38,58331,58332],{},"Minimální cena výrobce",[883,58334,58336],{"className":58335},[886],[888,58337,58338],{"xmlns":890},[892,58339,58340,58370],{},[895,58341,58342],{},[2509,58343,58344,58356,58358,58360,58362,58364,58366,58368],{"scriptlevel":2113,"displaystyle":1725},[13142,58345,58346,58348,58350],{},[1711,58347,15143],{},[2111,58349,2113],{},[2884,58351,58352,58354],{},[898,58353,6796],{},[2111,58355,2113],{},[898,58357,2362],{},[1711,58359,1714],{"stretchy":1713},[898,58361,6796],{},[1711,58363,1735],{"stretchy":1713},[1942,58365,2519],{},[898,58367,2098],{},[898,58369,6796],{},[902,58371,55765],{"encoding":904},[123,58373,58374,5204,58377,56266,58402,1797],{},[38,58375,58376],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,58378,58380],{"className":58379},[886],[888,58381,58382],{"xmlns":890},[892,58383,58384,58400],{},[895,58385,58386,58392,58394],{},[2884,58387,58388,58390],{},[898,58389,7929],{},[2111,58391,2113],{},[1942,58393,2519],{},[2884,58395,58396,58398],{},[898,58397,6796],{},[2111,58399,2113],{},[902,58401,55201],{"encoding":904},[883,58403,58405],{"className":58404},[886],[888,58406,58407],{"xmlns":890},[892,58408,58409,58433],{},[895,58410,58411,58413,58415,58421,58423,58425,58427],{},[2111,58412,2113],{},[1942,58414,2519],{},[2884,58416,58417,58419],{},[898,58418,6796],{},[2111,58420,2113],{},[1942,58422,2519],{},[898,58424,8243],{},[1942,58426,2519],{},[2884,58428,58429,58431],{},[898,58430,7929],{},[2111,58432,2113],{},[902,58434,54755],{"encoding":904},[123,58436,58437,58440,58441,58462],{},[38,58438,58439],{},"Celkový přebytek trhu"," — součet ",[883,58442,58444],{"className":58443},[886],[888,58445,58446],{"xmlns":890},[892,58447,58448,58460],{},[895,58449,58450,58452,58454,58456,58458],{},[898,58451,1940],{},[898,58453,2362],{},[1711,58455,2095],{},[898,58457,7929],{},[898,58459,2362],{},[902,58461,54493],{"encoding":904}," v rovnovážném bodě.",[123,58464,58465,58467,58468,1343,58481,58494,58495,2186],{},[38,58466,6459],{}," — plochy ohraničené křivkami ",[883,58469,58471],{"className":58470},[886],[888,58472,58473],{"xmlns":890},[892,58474,58475,58479],{},[895,58476,58477],{},[898,58478,2778],{},[902,58480,2778],{"encoding":904},[883,58482,58484],{"className":58483},[886],[888,58485,58486],{"xmlns":890},[892,58487,58488,58492],{},[895,58489,58490],{},[898,58491,2362],{},[902,58493,2362],{"encoding":904}," a přímkou ",[883,58496,58498],{"className":58497},[886],[888,58499,58500],{"xmlns":890},[892,58501,58502,58514],{},[895,58503,58504,58506,58508],{},[898,58505,7929],{},[1711,58507,1836],{},[2884,58509,58510,58512],{},[898,58511,7929],{},[2111,58513,2113],{},[902,58515,55275],{"encoding":904},[40568,58517],{},[115,58519,58521],{"id":58520},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,58523,58524,58525,58538,58539,58556],{},"Uvalení jednotkové daně ",[883,58526,58528],{"className":58527},[886],[888,58529,58530],{"xmlns":890},[892,58531,58532,58536],{},[895,58533,58534],{},[898,58535,1769],{},[902,58537,1769],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,58540,58542],{"className":58541},[886],[888,58543,58544],{"xmlns":890},[892,58545,58546,58554],{},[895,58547,58548],{},[1716,58549,58550,58552],{},[898,58551,6796],{},[898,58553,1722],{},[902,58555,46001],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,58558,58559],{},[1801,58560],{"alt":58561,"className":58562,"src":58563},"imek-prebytky-s-dani-deadweight",[210,1805],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,58565,58566,58567,58582,58583,58598,58599,56266,58602,58626,58627,1648,58630,58633,58634,2186],{},"Přebytek spotřebitele ",[883,58568,58570],{"className":58569},[886],[888,58571,58572],{"xmlns":890},[892,58573,58574,58580],{},[895,58575,58576,58578],{},[898,58577,1940],{},[898,58579,2362],{},[902,58581,48548],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,58584,58586],{"className":58585},[886],[888,58587,58588],{"xmlns":890},[892,58589,58590,58596],{},[895,58591,58592,58594],{},[898,58593,7929],{},[898,58595,2362],{},[902,58597,48567],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,58600,58601],{},"daňový příjem",[883,58603,58605],{"className":58604},[886],[888,58606,58607],{"xmlns":890},[892,58608,58609,58623],{},[895,58610,58611,58613,58615],{},[898,58612,1769],{},[1711,58614,4795],{},[13142,58616,58617,58619,58621],{},[898,58618,6796],{},[2111,58620,2238],{},[898,58622,1722],{},[902,58624,58625],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,58628,58629],{},"mrtvá ztráta",[614,58631,58632],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,58635,811],{"className":58636,"dataFsResolvedFilePath":809,"href":810},[210],[40568,58638],{},[115,58640,5901],{"id":5900},[120,58642,58643,58650,58662,58669,58676],{},[123,58644,58645,1700,58647],{},[38,58646,5928],{},[207,58648,802],{"className":58649,"dataFsResolvedFilePath":800,"href":801},[210],[123,58651,58652,1700,58654,58657,58658,58661],{},[38,58653,40272],{},[207,58655,775],{"className":58656,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,58659,6375],{"className":58660,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,58663,58664,1700,58666],{},[38,58665,5938],{},[207,58667,7817],{"className":58668,"dataFsResolvedFilePath":827,"href":828},[210],[123,58670,58671,1700,58673],{},[38,58672,54356],{},[207,58674,54360],{"className":58675,"dataFsResolvedFilePath":745,"href":746},[210],[123,58677,58678,1700,58680],{},[38,58679,5908],{},[207,58681,5914],{"className":58682,"dataFsResolvedFilePath":5912,"href":5913},[210],{"title":641,"searchDepth":642,"depth":642,"links":58684},[58685,58686,58691,58696,58701,58702,58703,58704],{"id":54552,"depth":642,"text":1241},{"id":54896,"depth":642,"text":58687,"children":58688},"Přebytek spotřebitele (CSCS)",[58689,58690],{"id":54915,"depth":649,"text":54916},{"id":6458,"depth":649,"text":6459},{"id":55491,"depth":642,"text":58692,"children":58693},"Přebytek výrobce (PSPS)",[58694,58695],{"id":55510,"depth":649,"text":55511},{"id":55673,"depth":649,"text":6459},{"id":56281,"depth":642,"text":56282,"children":58697},[58698,58699],{"id":56285,"depth":649,"text":56286},{"id":57579,"depth":649,"text":58700},"Příklad 2.13 — numerický výpočet PSPS",{"id":57884,"depth":642,"text":57885},{"id":5421,"depth":642,"text":5422},{"id":58520,"depth":642,"text":58521},{"id":5900,"depth":642,"text":5901},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,54422,58711,58712,15963,5946,58713,58714],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":58717,"title":58718,"body":58719,"course":1128,"courses":659,"created":5973,"description":641,"extension":661,"meta":78048,"navigation":664,"path":78049,"seo":78050,"sources":78051,"stem":78052,"tags":78053,"type":5985,"updated":677,"__hash__":78059},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":58720,"toc":78012},[58721,58724,58910,58912,59003,59008,59334,59338,59345,59349,59394,59461,59492,59542,59577,59581,59640,59645,59711,59829,59931,59935,59958,60036,60079,60083,60112,60179,60185,60299,60303,60383,60420,60472,60670,60734,60821,60825,60828,60907,60910,61028,61047,61112,61116,61208,61276,61317,61371,61439,61476,61480,61538,61568,61779,61851,61903,62069,62162,62197,62201,62205,62242,62307,62362,62366,62389,62478,62582,62651,62655,62752,62865,62921,62975,63033,63094,63097,63133,63198,63228,63457,63515,63549,63553,63580,63659,63773,63794,63873,63875,63983,63987,64125,64447,64451,64454,64458,64507,64511,64765,64917,64924,64997,65181,65186,65529,65533,65556,65558,65579,65638,65648,65697,65839,65913,66008,66123,66221,66339,66343,66412,66417,66529,66674,66725,66837,66879,66883,66903,66964,66991,67053,67057,67079,67148,67428,67435,67465,67472,67665,67669,67747,67752,67828,67831,67919,67995,68062,68111,68214,68287,68408,68759,68872,68974,68978,68981,68988,68991,69027,69086,69095,69244,69468,69472,69535,69714,69806,69861,69865,69921,69991,70043,70064,70145,70148,70223,70267,70271,70312,70355,70381,70385,70456,70552,70614,70666,70769,70847,70870,70899,70903,71069,71186,71258,71573,71733,71737,71788,71850,71885,71915,72015,72057,72226,72231,72327,72365,72369,72488,72789,72791,72826,72830,72834,72962,73094,73416,73604,73682,73686,73991,74104,74250,74435,74541,74773,74888,74970,75089,75187,75228,75232,75287,75431,75585,75745,75838,76032,76344,76475,76604,76608,76680,76722,76773,76775,77970,77972],[12,58722,58718],{"id":58723},"příjem-náklady-zisk-a-nabídka-firmy",[1921,58725,58726],{},[724,58727,58728,7867,58730,1700,58733,58748,58749,1700,58752,58767,58768,1700,58771,58799,58800,58822,58823,58847,58848,58870,58871,58874,58875,58891,58892,2186],{},[883,58729,7866],{},[38,58731,58732],{},"Příjem",[883,58734,58736],{"className":58735},[886],[888,58737,58738],{"xmlns":890},[892,58739,58740,58746],{},[895,58741,58742,58744],{},[898,58743,1769],{},[898,58745,7985],{},[902,58747,8085],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,58750,58751],{},"náklady",[883,58753,58755],{"className":58754},[886],[888,58756,58757],{"xmlns":890},[892,58758,58759,58765],{},[895,58760,58761,58763],{},[898,58762,1769],{},[898,58764,1940],{},[902,58766,7241],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,58769,58770],{},"zisk",[883,58772,58774],{"className":58773},[886],[888,58775,58776],{"xmlns":890},[892,58777,58778,58796],{},[895,58779,58780,58782,58784,58786,58788,58790,58792,58794],{},[898,58781,7929],{},[898,58783,7985],{},[1711,58785,1836],{},[898,58787,1769],{},[898,58789,7985],{},[1711,58791,2460],{},[898,58793,1769],{},[898,58795,1940],{},[902,58797,58798],{"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: ",[883,58801,58803],{"className":58802},[886],[888,58804,58805],{"xmlns":890},[892,58806,58807,58819],{},[895,58808,58809,58811,58813,58815,58817],{},[898,58810,8243],{},[898,58812,1940],{},[1711,58814,1836],{},[898,58816,1790],{},[898,58818,1940],{},[902,58820,58821],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,58824,58826],{"className":58825},[886],[888,58827,58828],{"xmlns":890},[892,58829,58830,58844],{},[895,58831,58832,58834,58836,58838,58840,58842],{},[898,58833,8243],{},[898,58835,43937],{},[898,58837,1940],{},[1711,58839,1836],{},[898,58841,1790],{},[898,58843,1940],{},[902,58845,58846],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,58849,58851],{"className":58850},[886],[888,58852,58853],{"xmlns":890},[892,58854,58855,58867],{},[895,58856,58857,58859,58861,58863,58865],{},[898,58858,1790],{},[898,58860,7985],{},[1711,58862,1836],{},[898,58864,1790],{},[898,58866,1940],{},[902,58868,58869],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,58872,58873],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,58876,58878],{"className":58877},[886],[888,58879,58880],{"xmlns":890},[892,58881,58882,58888],{},[895,58883,58884,58886],{},[898,58885,1790],{},[898,58887,1940],{},[902,58889,58890],{"encoding":904},"MC"," nad bodem minima ",[883,58893,58895],{"className":58894},[886],[888,58896,58897],{"xmlns":890},[892,58898,58899,58907],{},[895,58900,58901,58903,58905],{},[898,58902,8243],{},[898,58904,43937],{},[898,58906,1940],{},[902,58908,58909],{"encoding":904},"AVC",[115,58911,1241],{"id":54552},[724,58913,58914,58915,58918,58919,58921,58922,1343,58925,1343,58928,58930,58931,58934,58935,58938,58939,58942,58943,6682,58958,1348,58973,6682,58988,1797],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,58916,58917],{},"příjmem"," (revenue) a ",[38,58920,58751],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,58923,58924],{},"zisku",[38,58926,58927],{},"bodů zvratu",[38,58929,6015],{}," a konstrukcí ",[38,58932,58933],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,58936,1145],{"className":58937,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,58940,15104],{"className":58941,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,58944,58946],{"className":58945},[886],[888,58947,58948],{"xmlns":890},[892,58949,58950,58956],{},[895,58951,58952,58954],{},[898,58953,1769],{},[898,58955,7985],{},[902,58957,8085],{"encoding":904},[883,58959,58961],{"className":58960},[886],[888,58962,58963],{"xmlns":890},[892,58964,58965,58971],{},[895,58966,58967,58969],{},[898,58968,1790],{},[898,58970,7985],{},[902,58972,10615],{"encoding":904},[883,58974,58976],{"className":58975},[886],[888,58977,58978],{"xmlns":890},[892,58979,58980,58986],{},[895,58981,58982,58984],{},[898,58983,1769],{},[898,58985,1940],{},[902,58987,7241],{"encoding":904},[883,58989,58991],{"className":58990},[886],[888,58992,58993],{"xmlns":890},[892,58994,58995,59001],{},[895,58996,58997,58999],{},[898,58998,1790],{},[898,59000,1940],{},[902,59002,58890],{"encoding":904},[724,59004,59005],{},[38,59006,59007],{},"Cílové znalosti:",[120,59009,59010,59174,59177,59180,59273,59320,59327],{},[123,59011,59012,59013,1343,59028,1343,59044,2009,59059,1343,59074,1343,59090,1343,59108,1343,59126,1343,59143,1343,59159,12405],{},"odvodit a interpretovat funkce ",[883,59014,59016],{"className":59015},[886],[888,59017,59018],{"xmlns":890},[892,59019,59020,59026],{},[895,59021,59022,59024],{},[898,59023,1769],{},[898,59025,7985],{},[902,59027,8085],{"encoding":904},[883,59029,59031],{"className":59030},[886],[888,59032,59033],{"xmlns":890},[892,59034,59035,59041],{},[895,59036,59037,59039],{},[898,59038,8243],{},[898,59040,7985],{},[902,59042,59043],{"encoding":904},"AR",[883,59045,59047],{"className":59046},[886],[888,59048,59049],{"xmlns":890},[892,59050,59051,59057],{},[895,59052,59053,59055],{},[898,59054,1790],{},[898,59056,7985],{},[902,59058,10615],{"encoding":904},[883,59060,59062],{"className":59061},[886],[888,59063,59064],{"xmlns":890},[892,59065,59066,59072],{},[895,59067,59068,59070],{},[898,59069,1769],{},[898,59071,1940],{},[902,59073,7241],{"encoding":904},[883,59075,59077],{"className":59076},[886],[888,59078,59079],{"xmlns":890},[892,59080,59081,59087],{},[895,59082,59083,59085],{},[898,59084,14409],{},[898,59086,1940],{},[902,59088,59089],{"encoding":904},"FC",[883,59091,59093],{"className":59092},[886],[888,59094,59095],{"xmlns":890},[892,59096,59097,59105],{},[895,59098,59099,59101,59103],{},[898,59100,1769],{},[898,59102,43937],{},[898,59104,1940],{},[902,59106,59107],{"encoding":904},"TVC",[883,59109,59111],{"className":59110},[886],[888,59112,59113],{"xmlns":890},[892,59114,59115,59123],{},[895,59116,59117,59119,59121],{},[898,59118,8243],{},[898,59120,14409],{},[898,59122,1940],{},[902,59124,59125],{"encoding":904},"AFC",[883,59127,59129],{"className":59128},[886],[888,59130,59131],{"xmlns":890},[892,59132,59133,59141],{},[895,59134,59135,59137,59139],{},[898,59136,8243],{},[898,59138,43937],{},[898,59140,1940],{},[902,59142,58909],{"encoding":904},[883,59144,59146],{"className":59145},[886],[888,59147,59148],{"xmlns":890},[892,59149,59150,59156],{},[895,59151,59152,59154],{},[898,59153,8243],{},[898,59155,1940],{},[902,59157,59158],{"encoding":904},"AC",[883,59160,59162],{"className":59161},[886],[888,59163,59164],{"xmlns":890},[892,59165,59166,59172],{},[895,59167,59168,59170],{},[898,59169,1790],{},[898,59171,1940],{},[902,59173,58890],{"encoding":904},[123,59175,59176],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,59178,59179],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,59181,59182,59183,59186,59187,45412,59229,12405],{},"osvojit si ",[38,59184,59185],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,59188,59190],{"className":59189},[886],[888,59191,59192],{"xmlns":890},[892,59193,59194,59226],{},[895,59195,59196,59198,59200,59202,59208,59210,59212,59214,59216,59218,59224],{},[898,59197,8243],{},[898,59199,1940],{},[1711,59201,1714],{"stretchy":1713},[2884,59203,59204,59206],{},[898,59205,6796],{},[2111,59207,2113],{},[1711,59209,1735],{"stretchy":1713},[1711,59211,1836],{},[898,59213,1790],{},[898,59215,1940],{},[1711,59217,1714],{"stretchy":1713},[2884,59219,59220,59222],{},[898,59221,6796],{},[2111,59223,2113],{},[1711,59225,1735],{"stretchy":1713},[902,59227,59228],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,59230,59232],{"className":59231},[886],[888,59233,59234],{"xmlns":890},[892,59235,59236,59270],{},[895,59237,59238,59240,59242,59244,59246,59252,59254,59256,59258,59260,59262,59268],{},[898,59239,8243],{},[898,59241,43937],{},[898,59243,1940],{},[1711,59245,1714],{"stretchy":1713},[2884,59247,59248,59250],{},[898,59249,6796],{},[2111,59251,2113],{},[1711,59253,1735],{"stretchy":1713},[1711,59255,1836],{},[898,59257,1790],{},[898,59259,1940],{},[1711,59261,1714],{"stretchy":1713},[2884,59263,59264,59266],{},[898,59265,6796],{},[2111,59267,2113],{},[1711,59269,1735],{"stretchy":1713},[902,59271,59272],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,59274,59182,59275,59186,59278,12405],{},[38,59276,59277],{},"princip maximalizace zisku",[883,59279,59281],{"className":59280},[886],[888,59282,59283],{"xmlns":890},[892,59284,59285,59317],{},[895,59286,59287,59289,59291,59293,59299,59301,59303,59305,59307,59309,59315],{},[898,59288,1790],{},[898,59290,7985],{},[1711,59292,1714],{"stretchy":1713},[2884,59294,59295,59297],{},[898,59296,6796],{},[2111,59298,2113],{},[1711,59300,1735],{"stretchy":1713},[1711,59302,1836],{},[898,59304,1790],{},[898,59306,1940],{},[1711,59308,1714],{"stretchy":1713},[2884,59310,59311,59313],{},[898,59312,6796],{},[2111,59314,2113],{},[1711,59316,1735],{"stretchy":1713},[902,59318,59319],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,59321,59322,59323,59326],{},"stanovit ",[38,59324,59325],{},"body zvratu"," a interval zisku;",[123,59328,59329,59330,59333],{},"zkonstruovat ",[38,59331,59332],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,59335,59337],{"id":59336},"příjem-firmy","Příjem firmy",[724,59339,59340],{},[1801,59341],{"alt":59342,"className":59343,"src":59344},"imek-ar-mr-dvojnasobny-sklon",[210,1805],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,59346,59348],{"id":59347},"celkový-příjem","Celkový příjem",[724,59350,59351,59352,1648,59367,59370,59371,33542],{},"Celkový příjem ",[883,59353,59355],{"className":59354},[886],[888,59356,59357],{"xmlns":890},[892,59358,59359,59365],{},[895,59360,59361,59363],{},[898,59362,1769],{},[898,59364,7985],{},[902,59366,8085],{"encoding":904},[38,59368,59369],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,59372,59374],{"className":59373},[886],[888,59375,59376],{"xmlns":890},[892,59377,59378,59392],{},[895,59379,59380,59382,59384,59386,59388,59390],{},[898,59381,7929],{},[1711,59383,1836],{},[898,59385,2778],{},[1711,59387,1714],{"stretchy":1713},[898,59389,6796],{},[1711,59391,1735],{"stretchy":1713},[902,59393,8625],{"encoding":904},[883,59395,59397],{"className":59396},[886],[888,59398,59399],{"xmlns":890,"display":31664},[892,59400,59401,59458],{},[24352,59402,59403],{"width":31669},[24357,59404,59405,59407,59451,59453],{},[24360,59406],{"width":31674},[24360,59408,59409],{},[895,59410,59411,59413,59415,59417,59419,59421,59423,59425,59427,59429,59431,59433,59435,59437,59439,59441,59443,59445,59447,59449],{},[898,59412,1769],{},[898,59414,7985],{},[1711,59416,1836],{},[898,59418,1769],{},[898,59420,7985],{},[1711,59422,1714],{"stretchy":1713},[898,59424,6796],{},[1711,59426,1735],{"stretchy":1713},[1711,59428,1836],{},[898,59430,7929],{},[1711,59432,4795],{},[898,59434,6796],{},[1711,59436,1836],{},[898,59438,2778],{},[1711,59440,1714],{"stretchy":1713},[898,59442,6796],{},[1711,59444,1735],{"stretchy":1713},[1711,59446,4795],{},[898,59448,6796],{},[898,59450,2186],{"mathvariant":2287},[24360,59452],{"width":31674},[24360,59454,59455],{},[1942,59456,59457],{},"(3.1)",[902,59459,59460],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,59462,59463,59464,59467,59468,59491],{},"Graf funkce se nazývá ",[38,59465,59466],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,59469,59471],{"className":59470},[886],[888,59472,59473],{"xmlns":890},[892,59474,59475,59489],{},[895,59476,59477,59479,59481,59483,59485,59487],{},[898,59478,7929],{},[1711,59480,1836],{},[898,59482,207],{},[898,59484,6796],{},[1711,59486,2095],{},[898,59488,2223],{},[902,59490,40658],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,59493,59495],{"className":59494},[886],[888,59496,59497],{"xmlns":890,"display":31664},[892,59498,59499,59539],{},[895,59500,59501,59503,59505,59507,59509,59511,59513,59515,59517,59519,59521,59523,59525,59531,59533,59535,59537],{},[898,59502,1769],{},[898,59504,7985],{},[1711,59506,1836],{},[898,59508,6796],{},[1711,59510,1714],{"stretchy":1713},[898,59512,207],{},[898,59514,6796],{},[1711,59516,2095],{},[898,59518,2223],{},[1711,59520,1735],{"stretchy":1713},[1711,59522,1836],{},[898,59524,207],{},[1716,59526,59527,59529],{},[898,59528,6796],{},[2111,59530,2963],{},[1711,59532,2095],{},[898,59534,2223],{},[898,59536,6796],{},[1711,59538,1726],{"separator":1725},[902,59540,59541],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,59543,59544,59545,59558,59559,59576],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,59546,59548],{"className":59547},[886],[888,59549,59550],{"xmlns":890},[892,59551,59552,59556],{},[895,59553,59554],{},[898,59555,900],{},[902,59557,900],{"encoding":904}," (jelikož ",[883,59560,59562],{"className":59561},[886],[888,59563,59564],{"xmlns":890},[892,59565,59566,59574],{},[895,59567,59568,59570,59572],{},[898,59569,207],{},[1711,59571,2109],{},[2111,59573,2113],{},[902,59575,46683],{"encoding":904},") procházející počátkem.",[40946,59578,59580],{"id":59579},"příklad-31","Příklad 3.1",[724,59582,59583,59586,59587,59623,59624,59639],{},[38,59584,59585],{},"Zadání."," Pro poptávku ",[883,59588,59590],{"className":59589},[886],[888,59591,59592],{"xmlns":890},[892,59593,59594,59620],{},[895,59595,59596,59598,59600,59602,59604,59606,59608,59610,59612,59614,59616,59618],{},[898,59597,7929],{},[1711,59599,1836],{},[898,59601,2778],{},[1711,59603,1714],{"stretchy":1713},[898,59605,6796],{},[1711,59607,1735],{"stretchy":1713},[1711,59609,1836],{},[1711,59611,2460],{},[2111,59613,2963],{},[898,59615,6796],{},[1711,59617,2095],{},[2111,59619,4282],{},[902,59621,59622],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,59625,59627],{"className":59626},[886],[888,59628,59629],{"xmlns":890},[892,59630,59631,59637],{},[895,59632,59633,59635],{},[898,59634,1769],{},[898,59636,7985],{},[902,59638,8085],{"encoding":904}," a charakterizujte jeho křivku.",[724,59641,59642,59644],{},[38,59643,26368],{}," Celkový příjem je",[883,59646,59648],{"className":59647},[886],[888,59649,59650],{"xmlns":890,"display":31664},[892,59651,59652,59708],{},[895,59653,59654,59656,59658,59660,59662,59664,59666,59668,59670,59672,59674,59676,59678,59680,59682,59684,59686,59688,59690,59692,59694,59700,59702,59704,59706],{},[898,59655,1769],{},[898,59657,7985],{},[1711,59659,1836],{},[898,59661,1769],{},[898,59663,7985],{},[1711,59665,1714],{"stretchy":1713},[898,59667,6796],{},[1711,59669,1735],{"stretchy":1713},[1711,59671,1836],{},[898,59673,6796],{},[1711,59675,1714],{"stretchy":1713},[1711,59677,2460],{},[2111,59679,2963],{},[898,59681,6796],{},[1711,59683,2095],{},[2111,59685,4282],{},[1711,59687,1735],{"stretchy":1713},[1711,59689,1836],{},[1711,59691,2460],{},[2111,59693,2963],{},[1716,59695,59696,59698],{},[898,59697,6796],{},[2111,59699,2963],{},[1711,59701,2095],{},[2111,59703,4282],{},[898,59705,6796],{},[898,59707,2186],{"mathvariant":2287},[902,59709,59710],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,59712,59713,59714,2009,59736,59758,59759,59777,59778,2186],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,59715,59717],{"className":59716},[886],[888,59718,59719],{"xmlns":890},[892,59720,59721,59733],{},[895,59722,59723,59729,59731],{},[2884,59724,59725,59727],{},[898,59726,6796],{},[2111,59728,2238],{},[1711,59730,1836],{},[2111,59732,2113],{},[902,59734,59735],{"encoding":904},"Q_1 = 0",[883,59737,59739],{"className":59738},[886],[888,59740,59741],{"xmlns":890},[892,59742,59743,59755],{},[895,59744,59745,59751,59753],{},[2884,59746,59747,59749],{},[898,59748,6796],{},[2111,59750,2963],{},[1711,59752,1836],{},[2111,59754,7120],{},[902,59756,59757],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,59760,59762],{"className":59761},[886],[888,59763,59764],{"xmlns":890},[892,59765,59766,59774],{},[895,59767,59768,59770,59772],{},[898,59769,6796],{},[1711,59771,1836],{},[2111,59773,4372],{},[902,59775,59776],{"encoding":904},"Q = 25"," ve výši ",[883,59779,59781],{"className":59780},[886],[888,59782,59783],{"xmlns":890},[892,59784,59785,59826],{},[895,59786,59787,59789,59799,59801,59803,59805,59807,59810,59812,59814,59816,59818,59820,59822,59824],{},[898,59788,1769],{},[2884,59790,59791,59793,59796],{},[898,59792,7985],{},[898,59794,59795],{},"max",[1711,59797,59798],{},"⁡",[1711,59800,1836],{},[1711,59802,2460],{},[2111,59804,2963],{},[1711,59806,4795],{},[2111,59808,59809],{},"625",[1711,59811,2095],{},[2111,59813,4282],{},[1711,59815,4795],{},[2111,59817,4372],{},[1711,59819,1836],{},[2111,59821,2238],{},[1942,59823,2519],{},[2111,59825,34341],{},[902,59827,59828],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,59830,59831],{},[614,59832,59833,59834,59868,59869,2009,59882,59895,59896,6635,59914,2186],{},"Obrázek 3.1: Parabola ",[883,59835,59837],{"className":59836},[886],[888,59838,59839],{"xmlns":890},[892,59840,59841,59865],{},[895,59842,59843,59845,59847,59849,59851,59853,59859,59861,59863],{},[898,59844,1769],{},[898,59846,7985],{},[1711,59848,1836],{},[1711,59850,2460],{},[2111,59852,2963],{},[1716,59854,59855,59857],{},[898,59856,6796],{},[2111,59858,2963],{},[1711,59860,2095],{},[2111,59862,4282],{},[898,59864,6796],{},[902,59866,59867],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,59870,59872],{"className":59871},[886],[888,59873,59874],{"xmlns":890},[892,59875,59876,59880],{},[895,59877,59878],{},[2111,59879,2113],{},[902,59881,2113],{"encoding":904},[883,59883,59885],{"className":59884},[886],[888,59886,59887],{"xmlns":890},[892,59888,59889,59893],{},[895,59890,59891],{},[2111,59892,7120],{},[902,59894,7120],{"encoding":904}," a maximem ",[883,59897,59899],{"className":59898},[886],[888,59900,59901],{"xmlns":890},[892,59902,59903,59911],{},[895,59904,59905,59907,59909],{},[2111,59906,2238],{},[1942,59908,2519],{},[2111,59910,34341],{},[902,59912,59913],{"encoding":904},"1\\,250",[883,59915,59917],{"className":59916},[886],[888,59918,59919],{"xmlns":890},[892,59920,59921,59929],{},[895,59922,59923,59925,59927],{},[898,59924,6796],{},[1711,59926,1836],{},[2111,59928,4372],{},[902,59930,59776],{"encoding":904},[198,59932,59934],{"id":59933},"průměrný-příjem","Průměrný příjem",[724,59936,59937,1700,59939,1648,59954,59957],{},[38,59938,59934],{},[883,59940,59942],{"className":59941},[886],[888,59943,59944],{"xmlns":890},[892,59945,59946,59952],{},[895,59947,59948,59950],{},[898,59949,8243],{},[898,59951,7985],{},[902,59953,59043],{"encoding":904},[38,59955,59956],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,59959,59961],{"className":59960},[886],[888,59962,59963],{"xmlns":890,"display":31664},[892,59964,59965,60033],{},[895,59966,59967,59969,59971,59973,59975,59977,59979,59981,59983,59985,60001,60003,60021,60023,60025,60027,60029,60031],{},[898,59968,8243],{},[898,59970,7985],{},[1711,59972,1836],{},[898,59974,8243],{},[898,59976,7985],{},[1711,59978,1714],{"stretchy":1713},[898,59980,6796],{},[1711,59982,1735],{"stretchy":1713},[1711,59984,1836],{},[2525,59986,59987,59999],{},[895,59988,59989,59991,59993,59995,59997],{},[898,59990,1769],{},[898,59992,7985],{},[1711,59994,1714],{"stretchy":1713},[898,59996,6796],{},[1711,59998,1735],{"stretchy":1713},[898,60000,6796],{},[1711,60002,1836],{},[2525,60004,60005,60019],{},[895,60006,60007,60009,60011,60013,60015,60017],{},[898,60008,6796],{},[1942,60010,2519],{},[898,60012,2778],{},[1711,60014,1714],{"stretchy":1713},[898,60016,6796],{},[1711,60018,1735],{"stretchy":1713},[898,60020,6796],{},[1711,60022,1836],{},[898,60024,2778],{},[1711,60026,1714],{"stretchy":1713},[898,60028,6796],{},[1711,60030,1735],{"stretchy":1713},[898,60032,2186],{"mathvariant":2287},[902,60034,60035],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[1921,60037,60038],{},[724,60039,60040,60043,60044,1343,60047,2186],{},[883,60041,60042],{},"!note"," Klíčové pozorování\n",[38,60045,60046],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,60048,60050],{"className":60049},[886],[888,60051,60052],{"xmlns":890},[892,60053,60054,60076],{},[895,60055,60056,60058,60060,60062,60064,60066,60068,60070,60072,60074],{},[898,60057,8243],{},[898,60059,7985],{},[1711,60061,1714],{"stretchy":1713},[898,60063,6796],{},[1711,60065,1735],{"stretchy":1713},[1711,60067,1836],{},[898,60069,2778],{},[1711,60071,1714],{"stretchy":1713},[898,60073,6796],{},[1711,60075,1735],{"stretchy":1713},[902,60077,60078],{"encoding":904},"AR(Q) = D(Q)",[198,60080,60082],{"id":60081},"mezní-příjem","Mezní příjem",[724,60084,60085,60086,1700,60089,1648,60104,60107,60108,60111],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,60087,60088],{},"mezní příjem",[883,60090,60092],{"className":60091},[886],[888,60093,60094],{"xmlns":890},[892,60095,60096,60102],{},[895,60097,60098,60100],{},[898,60099,1790],{},[898,60101,7985],{},[902,60103,10615],{"encoding":904},[38,60105,60106],{},"marginal revenue","), definovaný jako ",[207,60109,1145],{"className":60110,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,60113,60115],{"className":60114},[886],[888,60116,60117],{"xmlns":890,"display":31664},[892,60118,60119,60176],{},[24352,60120,60121],{"width":31669},[24357,60122,60123,60125,60169,60171],{},[24360,60124],{"width":31674},[24360,60126,60127],{},[895,60128,60129,60131,60133,60135,60151,60153,60155,60161,60163,60165,60167],{},[898,60130,1790],{},[898,60132,7985],{},[1711,60134,1836],{},[2525,60136,60137,60145],{},[895,60138,60139,60141,60143],{},[898,60140,2098],{"mathvariant":2287},[898,60142,1769],{},[898,60144,7985],{},[895,60146,60147,60149],{},[898,60148,2098],{"mathvariant":2287},[898,60150,6796],{},[1711,60152,1836],{},[898,60154,1769],{},[1716,60156,60157,60159],{},[898,60158,7985],{},[1711,60160,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,60162,1714],{"stretchy":1713},[898,60164,6796],{},[1711,60166,1735],{"stretchy":1713},[898,60168,2186],{"mathvariant":2287},[24360,60170],{"width":31674},[24360,60172,60173],{},[1942,60174,60175],{},"(3.2)",[902,60177,60178],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,60180,60181,60182,60184],{},"Mezní příjem udává ",[38,60183,6607],{}," celkového příjmu vzhledem k množství.",[1921,60186,60187],{},[724,60188,60189,60191,60192,60218,60219,60236,60237,2186],{},[883,60190,2678],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,60193,60195],{"className":60194},[886],[888,60196,60197],{"xmlns":890},[892,60198,60199,60215],{},[895,60200,60201,60203,60205,60207,60213],{},[898,60202,1790],{},[898,60204,7985],{},[1711,60206,1714],{"stretchy":1713},[1716,60208,60209,60211],{},[898,60210,6796],{},[1711,60212,1793],{},[1711,60214,1735],{"stretchy":1713},[902,60216,60217],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,60220,60222],{"className":60221},[886],[888,60223,60224],{"xmlns":890},[892,60225,60226,60234],{},[895,60227,60228],{},[1716,60229,60230,60232],{},[898,60231,6796],{},[1711,60233,1793],{},[902,60235,33442],{"encoding":904},". Jinak řečeno: ",[883,60238,60240],{"className":60239},[886],[888,60241,60242],{"xmlns":890},[892,60243,60244,60296],{},[895,60245,60246,60248,60250,60252,60258,60260,60262,60264,60266,60268,60274,60276,60278,60280,60282,60284,60286,60288,60294],{},[898,60247,1790],{},[898,60249,7985],{},[1711,60251,1714],{"stretchy":1713},[1716,60253,60254,60256],{},[898,60255,6796],{},[1711,60257,1793],{},[1711,60259,1735],{"stretchy":1713},[1711,60261,6740],{},[898,60263,1769],{},[898,60265,7985],{},[1711,60267,1714],{"stretchy":1713},[1716,60269,60270,60272],{},[898,60271,6796],{},[1711,60273,1793],{},[1711,60275,2095],{},[2111,60277,2238],{},[1711,60279,1735],{"stretchy":1713},[1711,60281,2460],{},[898,60283,1769],{},[898,60285,7985],{},[1711,60287,1714],{"stretchy":1713},[1716,60289,60290,60292],{},[898,60291,6796],{},[1711,60293,1793],{},[1711,60295,1735],{"stretchy":1713},[902,60297,60298],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[40946,60300,60302],{"id":60301},"příklad-32","Příklad 3.2",[724,60304,60305,59586,60307,59623,60341,60356,60357,2186],{},[38,60306,59585],{},[883,60308,60310],{"className":60309},[886],[888,60311,60312],{"xmlns":890},[892,60313,60314,60338],{},[895,60315,60316,60318,60320,60322,60324,60326,60328,60330,60332,60334,60336],{},[898,60317,7929],{},[1711,60319,1836],{},[898,60321,2778],{},[1711,60323,1714],{"stretchy":1713},[898,60325,6796],{},[1711,60327,1735],{"stretchy":1713},[1711,60329,1836],{},[2111,60331,4282],{},[1711,60333,2460],{},[2111,60335,2963],{},[898,60337,6796],{},[902,60339,60340],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,60342,60344],{"className":60343},[886],[888,60345,60346],{"xmlns":890},[892,60347,60348,60354],{},[895,60349,60350,60352],{},[898,60351,1790],{},[898,60353,7985],{},[902,60355,10615],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,60358,60360],{"className":60359},[886],[888,60361,60362],{"xmlns":890},[892,60363,60364,60380],{},[895,60365,60366,60368,60370,60372,60374,60376,60378],{},[898,60367,6796],{},[1711,60369,1836],{},[2111,60371,39842],{},[1711,60373,1726],{"separator":1725},[2111,60375,45460],{},[1711,60377,1726],{"separator":1725},[2111,60379,4306],{},[902,60381,60382],{"encoding":904},"Q = 15, 16, 20",[724,60384,60385,1700,60387,60419],{},[38,60386,26368],{},[883,60388,60390],{"className":60389},[886],[888,60391,60392],{"xmlns":890},[892,60393,60394,60416],{},[895,60395,60396,60398,60400,60402,60404,60406,60408,60410],{},[898,60397,1769],{},[898,60399,7985],{},[1711,60401,1836],{},[2111,60403,4282],{},[898,60405,6796],{},[1711,60407,2460],{},[2111,60409,2963],{},[1716,60411,60412,60414],{},[898,60413,6796],{},[2111,60415,2963],{},[902,60417,60418],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,60421,60423],{"className":60422},[886],[888,60424,60425],{"xmlns":890,"display":31664},[892,60426,60427,60469],{},[895,60428,60429,60431,60433,60435,60437,60439,60441,60443,60445,60451,60457,60459,60461,60463,60465,60467],{},[898,60430,1790],{},[898,60432,7985],{},[1711,60434,1836],{},[1711,60436,1714],{"stretchy":1713},[2111,60438,4282],{},[898,60440,6796],{},[1711,60442,2460],{},[2111,60444,2963],{},[1716,60446,60447,60449],{},[898,60448,6796],{},[2111,60450,2963],{},[1716,60452,60453,60455],{},[1711,60454,1735],{"stretchy":1713},[1711,60456,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,60458,1836],{},[2111,60460,4282],{},[1711,60462,2460],{},[2111,60464,6369],{},[898,60466,6796],{},[898,60468,2186],{"mathvariant":2287},[902,60470,60471],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,60473,13638,60474,12082,60492,60518,60519,8345,60532,60547,60548,60561,60562,25018,60575,8345,60588,60603,60604,60617,60618,60649,60650,60669],{},[883,60475,60477],{"className":60476},[886],[888,60478,60479],{"xmlns":890},[892,60480,60481,60489],{},[895,60482,60483,60485,60487],{},[898,60484,6796],{},[1711,60486,1836],{},[2111,60488,39842],{},[902,60490,60491],{"encoding":904},"Q = 15",[883,60493,60495],{"className":60494},[886],[888,60496,60497],{"xmlns":890},[892,60498,60499,60515],{},[895,60500,60501,60503,60505,60507,60509,60511,60513],{},[898,60502,1790],{},[898,60504,7985],{},[1711,60506,1714],{"stretchy":1713},[2111,60508,39842],{},[1711,60510,1735],{"stretchy":1713},[1711,60512,1836],{},[2111,60514,9195],{},[902,60516,60517],{"encoding":904},"MR(15) = 40",": při množství ",[883,60520,60522],{"className":60521},[886],[888,60523,60524],{"xmlns":890},[892,60525,60526,60530],{},[895,60527,60528],{},[2111,60529,39842],{},[902,60531,39842],{"encoding":904},[883,60533,60535],{"className":60534},[886],[888,60536,60537],{"xmlns":890},[892,60538,60539,60545],{},[895,60540,60541,60543],{},[898,60542,1769],{},[898,60544,7985],{},[902,60546,8085],{"encoding":904}," mění asi ",[883,60549,60551],{"className":60550},[886],[888,60552,60553],{"xmlns":890},[892,60554,60555,60559],{},[895,60556,60557],{},[2111,60558,9195],{},[902,60560,9195],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,60563,60565],{"className":60564},[886],[888,60566,60567],{"xmlns":890},[892,60568,60569,60573],{},[895,60570,60571],{},[898,60572,6796],{},[902,60574,6796],{"encoding":904},[883,60576,60578],{"className":60577},[886],[888,60579,60580],{"xmlns":890},[892,60581,60582,60586],{},[895,60583,60584],{},[2111,60585,2238],{},[902,60587,2238],{"encoding":904},[883,60589,60591],{"className":60590},[886],[888,60592,60593],{"xmlns":890},[892,60594,60595,60601],{},[895,60596,60597,60599],{},[898,60598,1769],{},[898,60600,7985],{},[902,60602,8085],{"encoding":904}," zvýší přibližně o ",[883,60605,60607],{"className":60606},[886],[888,60608,60609],{"xmlns":890},[892,60610,60611,60615],{},[895,60612,60613],{},[2111,60614,9195],{},[902,60616,9195],{"encoding":904},", tj. ze skutečné hodnoty ",[883,60619,60621],{"className":60620},[886],[888,60622,60623],{"xmlns":890},[892,60624,60625,60646],{},[895,60626,60627,60629,60631,60633,60635,60637,60639,60641,60643],{},[898,60628,1769],{},[898,60630,7985],{},[1711,60632,1714],{"stretchy":1713},[2111,60634,39842],{},[1711,60636,1735],{"stretchy":1713},[1711,60638,1836],{},[2111,60640,2238],{},[1942,60642,2519],{},[2111,60644,60645],{},"050",[902,60647,60648],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,60651,60653],{"className":60652},[886],[888,60654,60655],{"xmlns":890},[892,60656,60657,60666],{},[895,60658,60659,60661,60663],{},[2111,60660,2238],{},[1942,60662,2519],{},[2111,60664,60665],{},"090",[902,60667,60668],{"encoding":904},"1\\,090",". Skutečná změna je",[883,60671,60673],{"className":60672},[886],[888,60674,60675],{"xmlns":890,"display":31664},[892,60676,60677,60731],{},[895,60678,60679,60681,60683,60685,60687,60689,60691,60693,60695,60697,60699,60701,60703,60705,60707,60709,60711,60713,60715,60718,60720,60722,60724,60726,60728],{},[898,60680,6892],{"mathvariant":2287},[898,60682,1769],{},[898,60684,7985],{},[1711,60686,1836],{},[898,60688,1769],{},[898,60690,7985],{},[1711,60692,1714],{"stretchy":1713},[2111,60694,45460],{},[1711,60696,1735],{"stretchy":1713},[1711,60698,2460],{},[898,60700,1769],{},[898,60702,7985],{},[1711,60704,1714],{"stretchy":1713},[2111,60706,39842],{},[1711,60708,1735],{"stretchy":1713},[1711,60710,1836],{},[2111,60712,2238],{},[1942,60714,2519],{},[2111,60716,60717],{},"088",[1711,60719,2460],{},[2111,60721,2238],{},[1942,60723,2519],{},[2111,60725,60645],{},[1711,60727,1836],{},[2111,60729,60730],{},"38.",[902,60732,60733],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,60735,60736,60737,1343,60763,2801,60789,60804,60805,60820],{},"Podobně ",[883,60738,60740],{"className":60739},[886],[888,60741,60742],{"xmlns":890},[892,60743,60744,60760],{},[895,60745,60746,60748,60750,60752,60754,60756,60758],{},[898,60747,1790],{},[898,60749,7985],{},[1711,60751,1714],{"stretchy":1713},[2111,60753,45460],{},[1711,60755,1735],{"stretchy":1713},[1711,60757,1836],{},[2111,60759,9549],{},[902,60761,60762],{"encoding":904},"MR(16) = 36",[883,60764,60766],{"className":60765},[886],[888,60767,60768],{"xmlns":890},[892,60769,60770,60786],{},[895,60771,60772,60774,60776,60778,60780,60782,60784],{},[898,60773,1790],{},[898,60775,7985],{},[1711,60777,1714],{"stretchy":1713},[2111,60779,4306],{},[1711,60781,1735],{"stretchy":1713},[1711,60783,1836],{},[2111,60785,4306],{},[902,60787,60788],{"encoding":904},"MR(20) = 20",[883,60790,60792],{"className":60791},[886],[888,60793,60794],{"xmlns":890},[892,60795,60796,60802],{},[895,60797,60798,60800],{},[898,60799,1790],{},[898,60801,7985],{},[902,60803,10615],{"encoding":904}," je klesající funkce — rychlost změny ",[883,60806,60808],{"className":60807},[886],[888,60809,60810],{"xmlns":890},[892,60811,60812,60818],{},[895,60813,60814,60816],{},[898,60815,1769],{},[898,60817,7985],{},[902,60819,8085],{"encoding":904}," s růstem množství klesá.",[198,60822,60824],{"id":60823},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,60826,60827],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,60829,60831],{"className":60830},[886],[888,60832,60833],{"xmlns":890,"display":31664},[892,60834,60835,60904],{},[24352,60836,60837],{"width":31669},[24357,60838,60839,60841,60897,60899],{},[24360,60840],{"width":31674},[24360,60842,60843],{},[895,60844,60845,60847,60849,60851,60853,60855,60857,60859,60861,60863,60865,60867,60869,60871,60877,60879,60881,60883,60885,60887,60889,60891,60893,60895],{},[898,60846,6892],{"mathvariant":2287},[898,60848,1769],{},[898,60850,7985],{},[1942,60852,4699],{},[1711,60854,6740],{},[1942,60856,4699],{},[898,60858,2098],{"mathvariant":2287},[898,60860,1769],{},[898,60862,7985],{},[1711,60864,1836],{},[1711,60866,1714],{"stretchy":1713},[898,60868,1769],{},[898,60870,7985],{},[1716,60872,60873,60875],{},[1711,60874,1735],{"stretchy":1713},[1711,60876,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1942,60878,2519],{},[898,60880,2098],{"mathvariant":2287},[898,60882,6796],{},[1711,60884,1836],{},[898,60886,1790],{},[898,60888,7985],{},[1942,60890,2519],{},[898,60892,2098],{"mathvariant":2287},[898,60894,6796],{},[1711,60896,1726],{"separator":1725},[24360,60898],{"width":31674},[24360,60900,60901],{},[1942,60902,60903],{},"(3.3)",[902,60905,60906],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,60908,60909],{},"schematicky:",[883,60911,60913],{"className":60912},[886],[888,60914,60915],{"xmlns":890,"display":31664},[892,60916,60917,61025],{},[895,60918,60919,60957,60959,60961,60963,60992,60995,61023],{},[895,60920,60921,60924,60930,60933,60939,60942,60948,60954],{},[1942,60922,60923],{},"zm",[12366,60925,60926,60928],{"accent":1725},[1942,60927,49330],{},[1711,60929,28656],{},[1942,60931,60932],{},"na celkov",[12366,60934,60935,60937],{"accent":1725},[1942,60936,49330],{},[1711,60938,28575],{},[1942,60940,60941],{},"ho p",[12366,60943,60944,60946],{"accent":1725},[1942,60945,1675],{},[1711,60947,28656],{},[12366,60949,60950,60952],{"accent":1725},[1942,60951,28644],{},[1711,60953,28575],{},[1942,60955,60956],{},"jmu",[1942,60958,4699],{},[1711,60960,6740],{},[1942,60962,4699],{},[895,60964,60965,60968,60974,60977,60983,60989],{},[1942,60966,60967],{},"mezn",[12366,60969,60970,60972],{"accent":1725},[1942,60971,28644],{},[1711,60973,28575],{},[1942,60975,60976],{}," p",[12366,60978,60979,60981],{"accent":1725},[1942,60980,1675],{},[1711,60982,28656],{},[12366,60984,60985,60987],{"accent":1725},[1942,60986,28644],{},[1711,60988,28575],{},[1942,60990,60991],{},"jem",[1711,60993,60994],{},"×",[895,60996,60997,60999,61005,61008,61014,61017],{},[1942,60998,60923],{},[12366,61000,61001,61003],{"accent":1725},[1942,61002,49330],{},[1711,61004,28656],{},[1942,61006,61007],{},"na mno",[12366,61009,61010,61012],{"accent":1725},[1942,61011,13569],{},[1711,61013,28656],{},[1942,61015,61016],{},"stv",[12366,61018,61019,61021],{"accent":1725},[1942,61020,28644],{},[1711,61022,28575],{},[898,61024,2186],{"mathvariant":2287},[902,61026,61027],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,61029,61030,61031,61046],{},"Pro porovnání skutečná změna ",[883,61032,61034],{"className":61033},[886],[888,61035,61036],{"xmlns":890},[892,61037,61038,61044],{},[895,61039,61040,61042],{},[898,61041,1769],{},[898,61043,7985],{},[902,61045,8085],{"encoding":904}," je",[883,61048,61050],{"className":61049},[886],[888,61051,61052],{"xmlns":890,"display":31664},[892,61053,61054,61109],{},[24352,61055,61056],{"width":31669},[24357,61057,61058,61060,61102,61104],{},[24360,61059],{"width":31674},[24360,61061,61062],{},[895,61063,61064,61066,61068,61070,61072,61074,61076,61078,61080,61082,61084,61086,61088,61090,61092,61094,61096,61098,61100],{},[898,61065,6892],{"mathvariant":2287},[898,61067,1769],{},[898,61069,7985],{},[1711,61071,1836],{},[898,61073,1769],{},[898,61075,7985],{},[1711,61077,1714],{"stretchy":1713},[898,61079,6796],{},[1711,61081,2095],{},[898,61083,2098],{"mathvariant":2287},[898,61085,6796],{},[1711,61087,1735],{"stretchy":1713},[1711,61089,2460],{},[898,61091,1769],{},[898,61093,7985],{},[1711,61095,1714],{"stretchy":1713},[898,61097,6796],{},[1711,61099,1735],{"stretchy":1713},[898,61101,2186],{"mathvariant":2287},[24360,61103],{"width":31674},[24360,61105,61106],{},[1942,61107,61108],{},"(3.4)",[902,61110,61111],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[40946,61113,61115],{"id":61114},"příklad-33","Příklad 3.3",[724,61117,61118,61120,61121,61151,61152,6668,61167,6682,61180,6696,61193,61207],{},[38,61119,59585],{}," Pro ",[883,61122,61124],{"className":61123},[886],[888,61125,61126],{"xmlns":890},[892,61127,61128,61148],{},[895,61129,61130,61132,61134,61136,61138,61140,61142],{},[898,61131,1769],{},[898,61133,7985],{},[1711,61135,1836],{},[2111,61137,4282],{},[898,61139,6796],{},[1711,61141,2460],{},[1716,61143,61144,61146],{},[898,61145,6796],{},[2111,61147,2963],{},[902,61149,61150],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,61153,61155],{"className":61154},[886],[888,61156,61157],{"xmlns":890},[892,61158,61159,61165],{},[895,61160,61161,61163],{},[898,61162,1769],{},[898,61164,7985],{},[902,61166,8085],{"encoding":904},[883,61168,61170],{"className":61169},[886],[888,61171,61172],{"xmlns":890},[892,61173,61174,61178],{},[895,61175,61176],{},[898,61177,6796],{},[902,61179,6796],{"encoding":904},[883,61181,61183],{"className":61182},[886],[888,61184,61185],{"xmlns":890},[892,61186,61187,61191],{},[895,61188,61189],{},[2111,61190,7126],{},[902,61192,7126],{"encoding":904},[883,61194,61196],{"className":61195},[886],[888,61197,61198],{"xmlns":890},[892,61199,61200,61205],{},[895,61201,61202],{},[2111,61203,61204],{},"63",[902,61206,61204],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,61209,61210,1700,61212,61237,61238,1343,61256,2062],{},[38,61211,26368],{},[883,61213,61215],{"className":61214},[886],[888,61216,61217],{"xmlns":890},[892,61218,61219,61235],{},[895,61220,61221,61223,61225,61227,61229,61231,61233],{},[898,61222,1790],{},[898,61224,7985],{},[1711,61226,1836],{},[2111,61228,4282],{},[1711,61230,2460],{},[2111,61232,2963],{},[898,61234,6796],{},[902,61236,15410],{"encoding":904},", tedy při ",[883,61239,61241],{"className":61240},[886],[888,61242,61243],{"xmlns":890},[892,61244,61245,61253],{},[895,61246,61247,61249,61251],{},[898,61248,6796],{},[1711,61250,1836],{},[2111,61252,7126],{},[902,61254,61255],{"encoding":904},"Q = 60",[883,61257,61259],{"className":61258},[886],[888,61260,61261],{"xmlns":890},[892,61262,61263,61273],{},[895,61264,61265,61267,61269,61271],{},[898,61266,2098],{"mathvariant":2287},[898,61268,6796],{},[1711,61270,1836],{},[2111,61272,3034],{},[902,61274,61275],{"encoding":904},"\\mathrm{d}Q = 3",[883,61277,61279],{"className":61278},[886],[888,61280,61281],{"xmlns":890,"display":31664},[892,61282,61283,61314],{},[895,61284,61285,61287,61289,61291,61293,61295,61297,61299,61301,61303,61305,61307,61309,61311],{},[898,61286,2098],{"mathvariant":2287},[898,61288,1769],{},[898,61290,7985],{},[1711,61292,1836],{},[1711,61294,1714],{"stretchy":1713},[2111,61296,4282],{},[1711,61298,2460],{},[2111,61300,8037],{},[1711,61302,1735],{"stretchy":1713},[1711,61304,4795],{},[2111,61306,3034],{},[1711,61308,1836],{},[1711,61310,2460],{},[2111,61312,61313],{},"60.",[902,61315,61316],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,61318,61319,61320,61350,61351,61370],{},"Celkový příjem klesne z ",[883,61321,61323],{"className":61322},[886],[888,61324,61325],{"xmlns":890},[892,61326,61327,61347],{},[895,61328,61329,61331,61333,61335,61337,61339,61341,61343,61345],{},[898,61330,1769],{},[898,61332,7985],{},[1711,61334,1714],{"stretchy":1713},[2111,61336,7126],{},[1711,61338,1735],{"stretchy":1713},[1711,61340,1836],{},[2111,61342,2963],{},[1942,61344,2519],{},[2111,61346,23740],{},[902,61348,61349],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,61352,61354],{"className":61353},[886],[888,61355,61356],{"xmlns":890},[892,61357,61358,61367],{},[895,61359,61360,61362,61364],{},[2111,61361,2963],{},[1942,61363,2519],{},[2111,61365,61366],{},"340",[902,61368,61369],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,61372,61374],{"className":61373},[886],[888,61375,61376],{"xmlns":890,"display":31664},[892,61377,61378,61436],{},[895,61379,61380,61382,61384,61386,61388,61390,61392,61394,61396,61398,61400,61402,61404,61406,61408,61410,61412,61414,61416,61419,61421,61423,61425,61427,61429,61431,61434],{},[898,61381,6892],{"mathvariant":2287},[898,61383,1769],{},[898,61385,7985],{},[1711,61387,1836],{},[898,61389,1769],{},[898,61391,7985],{},[1711,61393,1714],{"stretchy":1713},[2111,61395,61204],{},[1711,61397,1735],{"stretchy":1713},[1711,61399,2460],{},[898,61401,1769],{},[898,61403,7985],{},[1711,61405,1714],{"stretchy":1713},[2111,61407,7126],{},[1711,61409,1735],{"stretchy":1713},[1711,61411,1836],{},[2111,61413,2963],{},[1942,61415,2519],{},[2111,61417,61418],{},"331",[1711,61420,2460],{},[2111,61422,2963],{},[1942,61424,2519],{},[2111,61426,23740],{},[1711,61428,1836],{},[1711,61430,2460],{},[2111,61432,61433],{},"69",[1711,61435,1726],{"separator":1725},[902,61437,61438],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,61440,61441,61442,61457,61458,2186],{},"tj. ",[883,61443,61445],{"className":61444},[886],[888,61446,61447],{"xmlns":890},[892,61448,61449,61455],{},[895,61450,61451,61453],{},[898,61452,1769],{},[898,61454,7985],{},[902,61456,8085],{"encoding":904}," klesne na ",[883,61459,61461],{"className":61460},[886],[888,61462,61463],{"xmlns":890},[892,61464,61465,61473],{},[895,61466,61467,61469,61471],{},[2111,61468,2963],{},[1942,61470,2519],{},[2111,61472,61418],{},[902,61474,61475],{"encoding":904},"2\\,331",[198,61477,61479],{"id":61478},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,61481,61482,61483,14367,61506,35178],{},"Obecně pro lineární poptávku ",[883,61484,61486],{"className":61485},[886],[888,61487,61488],{"xmlns":890},[892,61489,61490,61504],{},[895,61491,61492,61494,61496,61498,61500,61502],{},[898,61493,7929],{},[1711,61495,1836],{},[898,61497,207],{},[898,61499,6796],{},[1711,61501,2095],{},[898,61503,2223],{},[902,61505,40658],{"encoding":904},[883,61507,61509],{"className":61508},[886],[888,61510,61511],{"xmlns":890},[892,61512,61513,61535],{},[895,61514,61515,61517,61519,61521,61523,61529,61531,61533],{},[898,61516,1769],{},[898,61518,7985],{},[1711,61520,1836],{},[898,61522,207],{},[1716,61524,61525,61527],{},[898,61526,6796],{},[2111,61528,2963],{},[1711,61530,2095],{},[898,61532,2223],{},[898,61534,6796],{},[902,61536,61537],{"encoding":904},"TR = aQ^2 + bQ",[883,61539,61541],{"className":61540},[886],[888,61542,61543],{"xmlns":890,"display":31664},[892,61544,61545,61565],{},[895,61546,61547,61549,61551,61553,61555,61557,61559,61561,61563],{},[898,61548,1790],{},[898,61550,7985],{},[1711,61552,1836],{},[2111,61554,2963],{},[898,61556,207],{},[898,61558,6796],{},[1711,61560,2095],{},[898,61562,2223],{},[898,61564,2186],{"mathvariant":2287},[902,61566,61567],{"encoding":904},"MR = 2aQ + b.",[724,61569,61570,61571,61586,61587,61602,61603,61616,61617,1648,61620,61636,61637,61650,61651,61666,61667,61682,61683,61698,61699,6635,61712,61742,61743,61762,61763,61778],{},"Křivky ",[883,61572,61574],{"className":61573},[886],[888,61575,61576],{"xmlns":890},[892,61577,61578,61584],{},[895,61579,61580,61582],{},[898,61581,1790],{},[898,61583,7985],{},[902,61585,10615],{"encoding":904}," a poptávky (resp. ",[883,61588,61590],{"className":61589},[886],[888,61591,61592],{"xmlns":890},[892,61593,61594,61600],{},[895,61595,61596,61598],{},[898,61597,8243],{},[898,61599,7985],{},[902,61601,59043],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,61604,61606],{"className":61605},[886],[888,61607,61608],{"xmlns":890},[892,61609,61610,61614],{},[895,61611,61612],{},[898,61613,2223],{},[902,61615,2223],{"encoding":904},", přičemž ",[38,61618,61619],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,61621,61623],{"className":61622},[886],[888,61624,61625],{"xmlns":890},[892,61626,61627,61633],{},[895,61628,61629,61631],{},[2111,61630,2963],{},[898,61632,207],{},[902,61634,61635],{"encoding":904},"2a"," vs. ",[883,61638,61640],{"className":61639},[886],[888,61641,61642],{"xmlns":890},[892,61643,61644,61648],{},[895,61645,61646],{},[898,61647,207],{},[902,61649,207],{"encoding":904},", obrázek 3.2). ",[883,61652,61654],{"className":61653},[886],[888,61655,61656],{"xmlns":890},[892,61657,61658,61664],{},[895,61659,61660,61662],{},[898,61661,1790],{},[898,61663,7985],{},[902,61665,10615],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,61668,61670],{"className":61669},[886],[888,61671,61672],{"xmlns":890},[892,61673,61674,61680],{},[895,61675,61676,61678],{},[898,61677,1769],{},[898,61679,7985],{},[902,61681,8085],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,61684,61686],{"className":61685},[886],[888,61687,61688],{"xmlns":890},[892,61689,61690,61696],{},[895,61691,61692,61694],{},[898,61693,1790],{},[898,61695,7985],{},[902,61697,10615],{"encoding":904}," osu ",[883,61700,61702],{"className":61701},[886],[888,61703,61704],{"xmlns":890},[892,61705,61706,61710],{},[895,61707,61708],{},[898,61709,6796],{},[902,61711,6796],{"encoding":904},[883,61713,61715],{"className":61714},[886],[888,61716,61717],{"xmlns":890},[892,61718,61719,61739],{},[895,61720,61721,61723,61725,61727],{},[898,61722,6796],{},[1711,61724,1836],{},[1711,61726,2460],{},[2509,61728,61729],{"scriptlevel":2113,"displaystyle":1713},[2525,61730,61731,61733],{},[898,61732,2223],{},[895,61734,61735,61737],{},[2111,61736,2963],{},[898,61738,207],{},[902,61740,61741],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,61744,61746],{"className":61745},[886],[888,61747,61748],{"xmlns":890},[892,61749,61750,61760],{},[895,61751,61752,61754,61756,61758],{},[898,61753,1790],{},[898,61755,7985],{},[1711,61757,1836],{},[2111,61759,2113],{},[902,61761,11064],{"encoding":904},", a dále ",[883,61764,61766],{"className":61765},[886],[888,61767,61768],{"xmlns":890},[892,61769,61770,61776],{},[895,61771,61772,61774],{},[898,61773,1769],{},[898,61775,7985],{},[902,61777,8085],{"encoding":904}," klesá.",[724,61780,61781,61782,61788,61789,61821,61822,61850],{},"V případě ",[38,61783,61784],{},[207,61785,61787],{"className":61786,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,61790,61792],{"className":61791},[886],[888,61793,61794],{"xmlns":890},[892,61795,61796,61818],{},[895,61797,61798,61800,61802,61804,61806,61808,61810,61812],{},[898,61799,7929],{},[1711,61801,1836],{},[898,61803,2778],{},[1711,61805,1714],{"stretchy":1713},[898,61807,6796],{},[1711,61809,1735],{"stretchy":1713},[1711,61811,1836],{},[1716,61813,61814,61816],{},[898,61815,7929],{},[1711,61817,1793],{},[902,61819,61820],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,61823,61825],{"className":61824},[886],[888,61826,61827],{"xmlns":890},[892,61828,61829,61847],{},[895,61830,61831,61833,61835,61837,61839,61841],{},[898,61832,1769],{},[898,61834,7985],{},[1711,61836,1836],{},[898,61838,6796],{},[1711,61840,4795],{},[1716,61842,61843,61845],{},[898,61844,7929],{},[1711,61846,1793],{},[902,61848,61849],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,61852,61854],{"className":61853},[886],[888,61855,61856],{"xmlns":890,"display":31664},[892,61857,61858,61900],{},[895,61859,61860,61862,61864,61866,61868,61870,61872,61878,61880,61882,61896,61898],{},[898,61861,1790],{},[898,61863,7985],{},[1711,61865,1836],{},[898,61867,8243],{},[898,61869,7985],{},[1711,61871,1836],{},[1716,61873,61874,61876],{},[898,61875,7929],{},[1711,61877,1793],{},[2102,61879],{"width":4981},[1711,61881,1714],{"stretchy":1713},[895,61883,61884,61887,61893],{},[1942,61885,61886],{},"obr",[12366,61888,61889,61891],{"accent":1725},[1942,61890,207],{},[1711,61892,28575],{},[1942,61894,61895],{},"zek 3.4",[1711,61897,1735],{"stretchy":1713},[898,61899,2186],{"mathvariant":2287},[902,61901,61902],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,61904,61905],{},[614,61906,61907,61908,2009,61934,61962,61963,61976,61977,61992,61993,7714,62006,1343,62032,7714,62047,2186],{},"Obrázek 3.2: Přímky ",[883,61909,61911],{"className":61910},[886],[888,61912,61913],{"xmlns":890},[892,61914,61915,61931],{},[895,61916,61917,61919,61921,61923,61925,61927,61929],{},[898,61918,8243],{},[898,61920,7985],{},[1711,61922,1836],{},[898,61924,207],{},[898,61926,6796],{},[1711,61928,2095],{},[898,61930,2223],{},[902,61932,61933],{"encoding":904},"AR = aQ + b",[883,61935,61937],{"className":61936},[886],[888,61938,61939],{"xmlns":890},[892,61940,61941,61959],{},[895,61942,61943,61945,61947,61949,61951,61953,61955,61957],{},[898,61944,1790],{},[898,61946,7985],{},[1711,61948,1836],{},[2111,61950,2963],{},[898,61952,207],{},[898,61954,6796],{},[1711,61956,2095],{},[898,61958,2223],{},[902,61960,61961],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,61964,61966],{"className":61965},[886],[888,61967,61968],{"xmlns":890},[892,61969,61970,61974],{},[895,61971,61972],{},[898,61973,2223],{},[902,61975,2223],{"encoding":904}," se svislou osou, ",[883,61978,61980],{"className":61979},[886],[888,61981,61982],{"xmlns":890},[892,61983,61984,61990],{},[895,61985,61986,61988],{},[898,61987,1790],{},[898,61989,7985],{},[902,61991,10615],{"encoding":904}," protíná osu ",[883,61994,61996],{"className":61995},[886],[888,61997,61998],{"xmlns":890},[892,61999,62000,62004],{},[895,62001,62002],{},[898,62003,6796],{},[902,62005,6796],{"encoding":904},[883,62007,62009],{"className":62008},[886],[888,62010,62011],{"xmlns":890},[892,62012,62013,62029],{},[895,62014,62015,62017],{},[1711,62016,2460],{},[2509,62018,62019],{"scriptlevel":2113,"displaystyle":1713},[2525,62020,62021,62023],{},[898,62022,2223],{},[895,62024,62025,62027],{},[2111,62026,2963],{},[898,62028,207],{},[902,62030,62031],{"encoding":904},"-\\tfrac{b}{2a}",[883,62033,62035],{"className":62034},[886],[888,62036,62037],{"xmlns":890},[892,62038,62039,62045],{},[895,62040,62041,62043],{},[898,62042,8243],{},[898,62044,7985],{},[902,62046,59043],{"encoding":904},[883,62048,62050],{"className":62049},[886],[888,62051,62052],{"xmlns":890},[892,62053,62054,62066],{},[895,62055,62056,62058],{},[1711,62057,2460],{},[2509,62059,62060],{"scriptlevel":2113,"displaystyle":1713},[2525,62061,62062,62064],{},[898,62063,2223],{},[898,62065,207],{},[902,62067,62068],{"encoding":904},"-\\tfrac{b}{a}",[724,62070,62071],{},[614,62072,62073,62074,62105,62106,62135,62136,2186],{},"Obrázek 3.3: Parabola ",[883,62075,62077],{"className":62076},[886],[888,62078,62079],{"xmlns":890},[892,62080,62081,62103],{},[895,62082,62083,62085,62087,62089,62091,62097,62099,62101],{},[898,62084,1769],{},[898,62086,7985],{},[1711,62088,1836],{},[898,62090,207],{},[1716,62092,62093,62095],{},[898,62094,6796],{},[2111,62096,2963],{},[1711,62098,2095],{},[898,62100,2223],{},[898,62102,6796],{},[902,62104,61537],{"encoding":904}," s maximem v ",[883,62107,62109],{"className":62108},[886],[888,62110,62111],{"xmlns":890},[892,62112,62113,62133],{},[895,62114,62115,62117,62119,62121],{},[898,62116,6796],{},[1711,62118,1836],{},[1711,62120,2460],{},[2509,62122,62123],{"scriptlevel":2113,"displaystyle":1713},[2525,62124,62125,62127],{},[898,62126,2223],{},[895,62128,62129,62131],{},[2111,62130,2963],{},[898,62132,207],{},[902,62134,61741],{"encoding":904}," a nulou v ",[883,62137,62139],{"className":62138},[886],[888,62140,62141],{"xmlns":890},[892,62142,62143,62159],{},[895,62144,62145,62147,62149,62151],{},[898,62146,6796],{},[1711,62148,1836],{},[1711,62150,2460],{},[2509,62152,62153],{"scriptlevel":2113,"displaystyle":1713},[2525,62154,62155,62157],{},[898,62156,2223],{},[898,62158,207],{},[902,62160,62161],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,62163,62164],{},[614,62165,62166,62167,2186],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,62168,62170],{"className":62169},[886],[888,62171,62172],{"xmlns":890},[892,62173,62174,62194],{},[895,62175,62176,62178,62180,62182,62184,62186,62188],{},[898,62177,8243],{},[898,62179,7985],{},[1711,62181,1836],{},[898,62183,1790],{},[898,62185,7985],{},[1711,62187,1836],{},[1716,62189,62190,62192],{},[898,62191,7929],{},[1711,62193,1793],{},[902,62195,62196],{"encoding":904},"AR = MR = P^*",[115,62198,62200],{"id":62199},"náklady-firmy","Náklady firmy",[198,62202,62204],{"id":62203},"celkové-náklady","Celkové náklady",[724,62206,62207,1700,62209,1648,62224,62227,62228,62241],{},[38,62208,62204],{},[883,62210,62212],{"className":62211},[886],[888,62213,62214],{"xmlns":890},[892,62215,62216,62222],{},[895,62217,62218,62220],{},[898,62219,1769],{},[898,62221,1940],{},[902,62223,7241],{"encoding":904},[38,62225,62226],{},"total cost",") jsou veškeré náklady na realizaci ",[883,62229,62231],{"className":62230},[886],[888,62232,62233],{"xmlns":890},[892,62234,62235,62239],{},[895,62236,62237],{},[898,62238,6796],{},[902,62240,6796],{"encoding":904}," jednotek produkce:",[883,62243,62245],{"className":62244},[886],[888,62246,62247],{"xmlns":890,"display":31664},[892,62248,62249,62304],{},[24352,62250,62251],{"width":31669},[24357,62252,62253,62255,62297,62299],{},[24360,62254],{"width":31674},[24360,62256,62257],{},[895,62258,62259,62261,62263,62265,62267,62269,62271,62273,62275,62277,62279,62281,62283,62285,62287,62289,62291,62293,62295],{},[898,62260,1769],{},[898,62262,1940],{},[1711,62264,1836],{},[898,62266,1769],{},[898,62268,1940],{},[1711,62270,1714],{"stretchy":1713},[898,62272,6796],{},[1711,62274,1735],{"stretchy":1713},[1711,62276,1836],{},[898,62278,14409],{},[898,62280,1940],{},[1711,62282,2095],{},[898,62284,1769],{},[898,62286,43937],{},[898,62288,1940],{},[1711,62290,1714],{"stretchy":1713},[898,62292,6796],{},[1711,62294,1735],{"stretchy":1713},[1711,62296,1726],{"separator":1725},[24360,62298],{"width":31674},[24360,62300,62301],{},[1942,62302,62303],{},"(3.5)",[902,62305,62306],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,62308,8298,62309,62324,62325,1648,62328,1772,62331,62324,62355,1648,62358,62361],{},[883,62310,62312],{"className":62311},[886],[888,62313,62314],{"xmlns":890},[892,62315,62316,62322],{},[895,62317,62318,62320],{},[898,62319,14409],{},[898,62321,1940],{},[902,62323,59089],{"encoding":904}," jsou ",[38,62326,62327],{},"fixní náklady",[38,62329,62330],{},"fixed cost",[883,62332,62334],{"className":62333},[886],[888,62335,62336],{"xmlns":890},[892,62337,62338,62352],{},[895,62339,62340,62342,62344,62346,62348,62350],{},[898,62341,1769],{},[898,62343,43937],{},[898,62345,1940],{},[1711,62347,1714],{"stretchy":1713},[898,62349,6796],{},[1711,62351,1735],{"stretchy":1713},[902,62353,62354],{"encoding":904},"TVC(Q)",[38,62356,62357],{},"celkové variabilní náklady",[38,62359,62360],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,62363,62365],{"id":62364},"průměrné-náklady","Průměrné náklady",[724,62367,62368,1700,62370,1648,62385,62388],{},[38,62369,62365],{},[883,62371,62373],{"className":62372},[886],[888,62374,62375],{"xmlns":890},[892,62376,62377,62383],{},[895,62378,62379,62381],{},[898,62380,8243],{},[898,62382,1940],{},[902,62384,59158],{"encoding":904},[38,62386,62387],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,62390,62392],{"className":62391},[886],[888,62393,62394],{"xmlns":890,"display":31664},[892,62395,62396,62475],{},[24352,62397,62398],{"width":31669},[24357,62399,62400,62402,62468,62470],{},[24360,62401],{"width":31674},[24360,62403,62404],{},[895,62405,62406,62408,62410,62412,62414,62416,62418,62420,62422,62424,62434,62436,62446,62448,62466],{},[898,62407,8243],{},[898,62409,1940],{},[1711,62411,1836],{},[898,62413,8243],{},[898,62415,1940],{},[1711,62417,1714],{"stretchy":1713},[898,62419,6796],{},[1711,62421,1735],{"stretchy":1713},[1711,62423,1836],{},[2525,62425,62426,62432],{},[895,62427,62428,62430],{},[898,62429,1769],{},[898,62431,1940],{},[898,62433,6796],{},[1711,62435,1836],{},[2525,62437,62438,62444],{},[895,62439,62440,62442],{},[898,62441,14409],{},[898,62443,1940],{},[898,62445,6796],{},[1711,62447,2095],{},[2525,62449,62450,62464],{},[895,62451,62452,62454,62456,62458,62460,62462],{},[898,62453,1769],{},[898,62455,43937],{},[898,62457,1940],{},[1711,62459,1714],{"stretchy":1713},[898,62461,6796],{},[1711,62463,1735],{"stretchy":1713},[898,62465,6796],{},[1711,62467,1726],{"separator":1725},[24360,62469],{"width":31674},[24360,62471,62472],{},[1942,62473,62474],{},"(3.6)",[902,62476,62477],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,62479,8298,62480,62324,62504,1700,62507,1648,62524,1772,62527,62324,62559,1700,62562,1648,62579,3239],{},[883,62481,62483],{"className":62482},[886],[888,62484,62485],{"xmlns":890},[892,62486,62487,62501],{},[895,62488,62489],{},[2509,62490,62491],{"scriptlevel":2113,"displaystyle":1713},[2525,62492,62493,62499],{},[895,62494,62495,62497],{},[898,62496,14409],{},[898,62498,1940],{},[898,62500,6796],{},[902,62502,62503],{"encoding":904},"\\tfrac{FC}{Q}",[38,62505,62506],{},"průměrné fixní náklady",[883,62508,62510],{"className":62509},[886],[888,62511,62512],{"xmlns":890},[892,62513,62514,62522],{},[895,62515,62516,62518,62520],{},[898,62517,8243],{},[898,62519,14409],{},[898,62521,1940],{},[902,62523,59125],{"encoding":904},[38,62525,62526],{},"average fixed cost",[883,62528,62530],{"className":62529},[886],[888,62531,62532],{"xmlns":890},[892,62533,62534,62556],{},[895,62535,62536],{},[2509,62537,62538],{"scriptlevel":2113,"displaystyle":1713},[2525,62539,62540,62554],{},[895,62541,62542,62544,62546,62548,62550,62552],{},[898,62543,1769],{},[898,62545,43937],{},[898,62547,1940],{},[1711,62549,1714],{"stretchy":1713},[898,62551,6796],{},[1711,62553,1735],{"stretchy":1713},[898,62555,6796],{},[902,62557,62558],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,62560,62561],{},"průměrné variabilní náklady",[883,62563,62565],{"className":62564},[886],[888,62566,62567],{"xmlns":890},[892,62568,62569,62577],{},[895,62570,62571,62573,62575],{},[898,62572,8243],{},[898,62574,43937],{},[898,62576,1940],{},[902,62578,58909],{"encoding":904},[38,62580,62581],{},"average variable cost",[883,62583,62585],{"className":62584},[886],[888,62586,62587],{"xmlns":890,"display":31664},[892,62588,62589,62648],{},[24352,62590,62591],{"width":31669},[24357,62592,62593,62595,62641,62643],{},[24360,62594],{"width":31674},[24360,62596,62597],{},[895,62598,62599,62601,62603,62605,62607,62609,62611,62613,62615,62617,62619,62621,62639],{},[898,62600,8243],{},[898,62602,43937],{},[898,62604,1940],{},[1711,62606,1836],{},[898,62608,8243],{},[898,62610,43937],{},[898,62612,1940],{},[1711,62614,1714],{"stretchy":1713},[898,62616,6796],{},[1711,62618,1735],{"stretchy":1713},[1711,62620,1836],{},[2525,62622,62623,62637],{},[895,62624,62625,62627,62629,62631,62633,62635],{},[898,62626,1769],{},[898,62628,43937],{},[898,62630,1940],{},[1711,62632,1714],{"stretchy":1713},[898,62634,6796],{},[1711,62636,1735],{"stretchy":1713},[898,62638,6796],{},[898,62640,2186],{"mathvariant":2287},[24360,62642],{"width":31674},[24360,62644,62645],{},[1942,62646,62647],{},"(3.7)",[902,62649,62650],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[40946,62652,62654],{"id":62653},"příklad-34","Příklad 3.4",[724,62656,62657,61120,62659,2009,62684,59623,62708,2009,62723,62738,62739,2186],{},[38,62658,59585],{},[883,62660,62662],{"className":62661},[886],[888,62663,62664],{"xmlns":890},[892,62665,62666,62681],{},[895,62667,62668,62670,62672,62674,62676,62678],{},[898,62669,14409],{},[898,62671,1940],{},[1711,62673,1836],{},[2111,62675,2238],{},[1942,62677,2519],{},[2111,62679,62680],{},"000",[902,62682,62683],{"encoding":904},"FC = 1\\,000",[883,62685,62687],{"className":62686},[886],[888,62688,62689],{"xmlns":890},[892,62690,62691,62705],{},[895,62692,62693,62695,62697,62699,62701,62703],{},[898,62694,1769],{},[898,62696,43937],{},[898,62698,1940],{},[1711,62700,1836],{},[2111,62702,6369],{},[898,62704,6796],{},[902,62706,62707],{"encoding":904},"TVC = 4Q",[883,62709,62711],{"className":62710},[886],[888,62712,62713],{"xmlns":890},[892,62714,62715,62721],{},[895,62716,62717,62719],{},[898,62718,1769],{},[898,62720,1940],{},[902,62722,7241],{"encoding":904},[883,62724,62726],{"className":62725},[886],[888,62727,62728],{"xmlns":890},[892,62729,62730,62736],{},[895,62731,62732,62734],{},[898,62733,8243],{},[898,62735,1940],{},[902,62737,59158],{"encoding":904}," a jejich chování s rostoucím ",[883,62740,62742],{"className":62741},[886],[888,62743,62744],{"xmlns":890},[892,62745,62746,62750],{},[895,62747,62748],{},[898,62749,6796],{},[902,62751,6796],{"encoding":904},[724,62753,62754,1700,62756,2009,62786,62822,62823,8345,62836,62851,62852,2062],{},[38,62755,26368],{},[883,62757,62759],{"className":62758},[886],[888,62760,62761],{"xmlns":890},[892,62762,62763,62783],{},[895,62764,62765,62767,62769,62771,62773,62775,62777,62779,62781],{},[898,62766,1769],{},[898,62768,1940],{},[1711,62770,1836],{},[2111,62772,2238],{},[1942,62774,2519],{},[2111,62776,62680],{},[1711,62778,2095],{},[2111,62780,6369],{},[898,62782,6796],{},[902,62784,62785],{"encoding":904},"TC = 1\\,000 + 4Q",[883,62787,62789],{"className":62788},[886],[888,62790,62791],{"xmlns":890},[892,62792,62793,62819],{},[895,62794,62795,62797,62799,62801,62815,62817],{},[898,62796,8243],{},[898,62798,1940],{},[1711,62800,1836],{},[2509,62802,62803],{"scriptlevel":2113,"displaystyle":1713},[2525,62804,62805,62813],{},[895,62806,62807,62809,62811],{},[2111,62808,2238],{},[1942,62810,2519],{},[2111,62812,62680],{},[898,62814,6796],{},[1711,62816,2095],{},[2111,62818,6369],{},[902,62820,62821],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,62824,62826],{"className":62825},[886],[888,62827,62828],{"xmlns":890},[892,62829,62830,62834],{},[895,62831,62832],{},[898,62833,6796],{},[902,62835,6796],{"encoding":904},[883,62837,62839],{"className":62838},[886],[888,62840,62841],{"xmlns":890},[892,62842,62843,62849],{},[895,62844,62845,62847],{},[898,62846,8243],{},[898,62848,1940],{},[902,62850,59158],{"encoding":904}," blíží ",[883,62853,62855],{"className":62854},[886],[888,62856,62857],{"xmlns":890},[892,62858,62859,62863],{},[895,62860,62861],{},[2111,62862,6369],{},[902,62864,6369],{"encoding":904},[883,62866,62868],{"className":62867},[886],[888,62869,62870],{"xmlns":890,"display":31664},[892,62871,62872,62918],{},[895,62873,62874,62891,62913,62915],{},[43494,62875,62876,62883],{},[895,62877,62878,62881],{},[898,62879,62880],{},"lim",[1711,62882,59798],{},[895,62884,62885,62887,62889],{},[898,62886,6796],{},[1711,62888,7123],{},[898,62890,10278],{"mathvariant":2287},[895,62892,62893,62895,62907,62909,62911],{},[1711,62894,1714],{"fence":1725},[2525,62896,62897,62905],{},[895,62898,62899,62901,62903],{},[2111,62900,2238],{},[1942,62902,2519],{},[2111,62904,62680],{},[898,62906,6796],{},[1711,62908,2095],{},[2111,62910,6369],{},[1711,62912,1735],{"fence":1725},[1711,62914,1836],{},[2111,62916,62917],{},"4.",[902,62919,62920],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,62922,62923,62961,62962,2186],{},[883,62924,62926],{"className":62925},[886],[888,62927,62928],{"xmlns":890},[892,62929,62930,62958],{},[895,62931,62932,62934,62936,62938,62940,62954,62956],{},[898,62933,8243],{},[898,62935,14409],{},[898,62937,1940],{},[1711,62939,1836],{},[2509,62941,62942],{"scriptlevel":2113,"displaystyle":1713},[2525,62943,62944,62952],{},[895,62945,62946,62948,62950],{},[2111,62947,2238],{},[1942,62949,2519],{},[2111,62951,62680],{},[898,62953,6796],{},[1711,62955,7123],{},[2111,62957,2113],{},[902,62959,62960],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,62963,62965],{"className":62964},[886],[888,62966,62967],{"xmlns":890},[892,62968,62969,62973],{},[895,62970,62971],{},[898,62972,6796],{},[902,62974,6796],{"encoding":904},[724,62976,62977],{},[614,62978,62979,62980,63009,63010,2186],{},"Obrázek 3.5: Přímka ",[883,62981,62983],{"className":62982},[886],[888,62984,62985],{"xmlns":890},[892,62986,62987,63007],{},[895,62988,62989,62991,62993,62995,62997,62999,63001,63003,63005],{},[898,62990,1769],{},[898,62992,1940],{},[1711,62994,1836],{},[2111,62996,2238],{},[1942,62998,2519],{},[2111,63000,62680],{},[1711,63002,2095],{},[2111,63004,6369],{},[898,63006,6796],{},[902,63008,62785],{"encoding":904}," protínající svislou osu ve výši ",[883,63011,63013],{"className":63012},[886],[888,63014,63015],{"xmlns":890},[892,63016,63017,63031],{},[895,63018,63019,63021,63023,63025,63027,63029],{},[898,63020,14409],{},[898,63022,1940],{},[1711,63024,1836],{},[2111,63026,2238],{},[1942,63028,2519],{},[2111,63030,62680],{},[902,63032,62683],{"encoding":904},[724,63034,63035],{},[614,63036,63037,63038,63073,63074,2186],{},"Obrázek 3.6: Hyperbola ",[883,63039,63041],{"className":63040},[886],[888,63042,63043],{"xmlns":890},[892,63044,63045,63071],{},[895,63046,63047,63049,63051,63053,63067,63069],{},[898,63048,8243],{},[898,63050,1940],{},[1711,63052,1836],{},[2509,63054,63055],{"scriptlevel":2113,"displaystyle":1713},[2525,63056,63057,63065],{},[895,63058,63059,63061,63063],{},[2111,63060,2238],{},[1942,63062,2519],{},[2111,63064,62680],{},[898,63066,6796],{},[1711,63068,2095],{},[2111,63070,6369],{},[902,63072,62821],{"encoding":904}," s vodorovnou asymptotou ",[883,63075,63077],{"className":63076},[886],[888,63078,63079],{"xmlns":890},[892,63080,63081,63091],{},[895,63082,63083,63085,63087,63089],{},[898,63084,8243],{},[898,63086,1940],{},[1711,63088,1836],{},[2111,63090,6369],{},[902,63092,63093],{"encoding":904},"AC = 4",[724,63095,63096],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,63098,63100],{"className":63099},[886],[888,63101,63102],{"xmlns":890,"display":31664},[892,63103,63104,63130],{},[895,63105,63106,63108,63110,63112,63114,63116,63118,63120,63122,63124,63126,63128],{},[898,63107,1769],{},[898,63109,43937],{},[898,63111,1940],{},[1711,63113,1836],{},[898,63115,6796],{},[1711,63117,4795],{},[898,63119,43937],{},[898,63121,1940],{},[1711,63123,1714],{"stretchy":1713},[898,63125,6796],{},[1711,63127,1735],{"stretchy":1713},[1711,63129,1726],{"separator":1725},[902,63131,63132],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,63134,8298,63135,62324,63163,63166,63167,63197],{},[883,63136,63138],{"className":63137},[886],[888,63139,63140],{"xmlns":890},[892,63141,63142,63160],{},[895,63143,63144,63146,63148,63150,63152,63154,63156,63158],{},[898,63145,43937],{},[898,63147,1940],{},[1711,63149,1836],{},[898,63151,43937],{},[898,63153,1940],{},[1711,63155,1714],{"stretchy":1713},[898,63157,6796],{},[1711,63159,1735],{"stretchy":1713},[902,63161,63162],{"encoding":904},"VC = VC(Q)",[38,63164,63165],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,63168,63170],{"className":63169},[886],[888,63171,63172],{"xmlns":890},[892,63173,63174,63194],{},[895,63175,63176,63178,63180,63182,63184,63186,63188,63190,63192],{},[898,63177,1769],{},[898,63179,43937],{},[898,63181,1940],{},[1711,63183,1714],{"stretchy":1713},[898,63185,6796],{},[1711,63187,1735],{"stretchy":1713},[1711,63189,1836],{},[898,63191,207],{},[898,63193,6796],{},[902,63195,63196],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,63199,63201],{"className":63200},[886],[888,63202,63203],{"xmlns":890,"display":31664},[892,63204,63205,63225],{},[895,63206,63207,63209,63211,63213,63215,63217,63219,63221,63223],{},[898,63208,1769],{},[898,63210,1940],{},[1711,63212,1836],{},[898,63214,14409],{},[898,63216,1940],{},[1711,63218,2095],{},[898,63220,207],{},[898,63222,6796],{},[898,63224,2186],{"mathvariant":2287},[902,63226,63227],{"encoding":904},"TC = FC + aQ.",[724,63229,63230,63231,63246,63247,63262,63263,63286,63287,63321,63322,63073,63335,63348,63349,2009,63397,63441,63442,2186],{},"Křivkou ",[883,63232,63234],{"className":63233},[886],[888,63235,63236],{"xmlns":890},[892,63237,63238,63244],{},[895,63239,63240,63242],{},[898,63241,1769],{},[898,63243,1940],{},[902,63245,7241],{"encoding":904}," je přímka se svislým průsečíkem ",[883,63248,63250],{"className":63249},[886],[888,63251,63252],{"xmlns":890},[892,63253,63254,63260],{},[895,63255,63256,63258],{},[898,63257,14409],{},[898,63259,1940],{},[902,63261,59089],{"encoding":904}," a sklonem ",[883,63264,63266],{"className":63265},[886],[888,63267,63268],{"xmlns":890},[892,63269,63270,63283],{},[895,63271,63272,63275,63277,63279,63281],{},[898,63273,63274],{},"tan",[1711,63276,59798],{},[898,63278,22460],{},[1711,63280,1836],{},[898,63282,207],{},[902,63284,63285],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,63288,63290],{"className":63289},[886],[888,63291,63292],{"xmlns":890},[892,63293,63294,63318],{},[895,63295,63296,63298,63300,63302,63314,63316],{},[898,63297,8243],{},[898,63299,1940],{},[1711,63301,1836],{},[2509,63303,63304],{"scriptlevel":2113,"displaystyle":1713},[2525,63305,63306,63312],{},[895,63307,63308,63310],{},[898,63309,14409],{},[898,63311,1940],{},[898,63313,6796],{},[1711,63315,2095],{},[898,63317,207],{},[902,63319,63320],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,63323,63325],{"className":63324},[886],[888,63326,63327],{"xmlns":890},[892,63328,63329,63333],{},[895,63330,63331],{},[898,63332,2888],{},[902,63334,2888],{"encoding":904},[883,63336,63338],{"className":63337},[886],[888,63339,63340],{"xmlns":890},[892,63341,63342,63346],{},[895,63343,63344],{},[898,63345,207],{},[902,63347,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,63350,63352],{"className":63351},[886],[888,63353,63354],{"xmlns":890},[892,63355,63356,63394],{},[895,63357,63358,63378,63390,63392],{},[2884,63359,63360,63366],{},[895,63361,63362,63364],{},[898,63363,62880],{},[1711,63365,59798],{},[895,63367,63368,63370,63372],{},[898,63369,6796],{},[1711,63371,7123],{},[1716,63373,63374,63376],{},[2111,63375,2113],{},[1711,63377,2095],{},[2509,63379,63380],{"scriptlevel":2113,"displaystyle":1713},[2525,63381,63382,63388],{},[895,63383,63384,63386],{},[898,63385,14409],{},[898,63387,1940],{},[898,63389,6796],{},[1711,63391,1836],{},[898,63393,10278],{"mathvariant":2287},[902,63395,63396],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,63398,63400],{"className":63399},[886],[888,63401,63402],{"xmlns":890},[892,63403,63404,63438],{},[895,63405,63406,63422,63434,63436],{},[2884,63407,63408,63414],{},[895,63409,63410,63412],{},[898,63411,62880],{},[1711,63413,59798],{},[895,63415,63416,63418,63420],{},[898,63417,6796],{},[1711,63419,7123],{},[898,63421,10278],{"mathvariant":2287},[2509,63423,63424],{"scriptlevel":2113,"displaystyle":1713},[2525,63425,63426,63432],{},[895,63427,63428,63430],{},[898,63429,14409],{},[898,63431,1940],{},[898,63433,6796],{},[1711,63435,1836],{},[2111,63437,2113],{},[902,63439,63440],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,63443,63445],{"className":63444},[886],[888,63446,63447],{"xmlns":890},[892,63448,63449,63455],{},[895,63450,63451,63453],{},[898,63452,8243],{},[898,63454,1940],{},[902,63456,59158],{"encoding":904},[724,63458,63459],{},[614,63460,63461,63462,63477,63478,63493,63494,2186],{},"Obrázek 3.7: Přímka ",[883,63463,63465],{"className":63464},[886],[888,63466,63467],{"xmlns":890},[892,63468,63469,63475],{},[895,63470,63471,63473],{},[898,63472,1769],{},[898,63474,1940],{},[902,63476,7241],{"encoding":904}," s osovým průsečíkem ve výši ",[883,63479,63481],{"className":63480},[886],[888,63482,63483],{"xmlns":890},[892,63484,63485,63491],{},[895,63486,63487,63489],{},[898,63488,14409],{},[898,63490,1940],{},[902,63492,59089],{"encoding":904}," a se sklonem ",[883,63495,63497],{"className":63496},[886],[888,63498,63499],{"xmlns":890},[892,63500,63501,63513],{},[895,63502,63503,63505,63507,63509,63511],{},[898,63504,63274],{},[1711,63506,59798],{},[898,63508,22460],{},[1711,63510,1836],{},[898,63512,207],{},[902,63514,63285],{"encoding":904},[724,63516,63517],{},[614,63518,63519,63520,63535,63536,2186],{},"Obrázek 3.8: Klesající hyperbola ",[883,63521,63523],{"className":63522},[886],[888,63524,63525],{"xmlns":890},[892,63526,63527,63533],{},[895,63528,63529,63531],{},[898,63530,8243],{},[898,63532,1940],{},[902,63534,59158],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,63537,63539],{"className":63538},[886],[888,63540,63541],{"xmlns":890},[892,63542,63543,63547],{},[895,63544,63545],{},[898,63546,207],{},[902,63548,207],{"encoding":904},[198,63550,63552],{"id":63551},"mezní-náklady","Mezní náklady",[724,63554,63555,1700,63557,1648,63572,63575,63576,63579],{},[38,63556,63552],{},[883,63558,63560],{"className":63559},[886],[888,63561,63562],{"xmlns":890},[892,63563,63564,63570],{},[895,63565,63566,63568],{},[898,63567,1790],{},[898,63569,1940],{},[902,63571,58890],{"encoding":904},[38,63573,63574],{},"marginal cost",") jsou ",[207,63577,1145],{"className":63578,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,63581,63583],{"className":63582},[886],[888,63584,63585],{"xmlns":890,"display":31664},[892,63586,63587,63656],{},[24352,63588,63589],{"width":31669},[24357,63590,63591,63593,63649,63651],{},[24360,63592],{"width":31674},[24360,63594,63595],{},[895,63596,63597,63599,63601,63603,63605,63607,63609,63611,63613,63615,63631,63633,63635,63641,63643,63645,63647],{},[898,63598,1790],{},[898,63600,1940],{},[1711,63602,1836],{},[898,63604,1790],{},[898,63606,1940],{},[1711,63608,1714],{"stretchy":1713},[898,63610,6796],{},[1711,63612,1735],{"stretchy":1713},[1711,63614,1836],{},[2525,63616,63617,63625],{},[895,63618,63619,63621,63623],{},[898,63620,2098],{"mathvariant":2287},[898,63622,1769],{},[898,63624,1940],{},[895,63626,63627,63629],{},[898,63628,2098],{"mathvariant":2287},[898,63630,6796],{},[1711,63632,1836],{},[898,63634,1769],{},[1716,63636,63637,63639],{},[898,63638,1940],{},[1711,63640,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,63642,1714],{"stretchy":1713},[898,63644,6796],{},[1711,63646,1735],{"stretchy":1713},[898,63648,2186],{"mathvariant":2287},[24360,63650],{"width":31674},[24360,63652,63653],{},[1942,63654,63655],{},"(3.8)",[902,63657,63658],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[1921,63660,63661],{},[724,63662,63663,63665,63666,63692,63693,63710,63711,2186],{},[883,63664,2678],{}," Intuice — „kolik stojí další kus\"\n",[883,63667,63669],{"className":63668},[886],[888,63670,63671],{"xmlns":890},[892,63672,63673,63689],{},[895,63674,63675,63677,63679,63681,63687],{},[898,63676,1790],{},[898,63678,1940],{},[1711,63680,1714],{"stretchy":1713},[1716,63682,63683,63685],{},[898,63684,6796],{},[1711,63686,1793],{},[1711,63688,1735],{"stretchy":1713},[902,63690,63691],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,63694,63696],{"className":63695},[886],[888,63697,63698],{"xmlns":890},[892,63699,63700,63708],{},[895,63701,63702],{},[1716,63703,63704,63706],{},[898,63705,6796],{},[1711,63707,1793],{},[902,63709,33442],{"encoding":904},". Formálně ",[883,63712,63714],{"className":63713},[886],[888,63715,63716],{"xmlns":890},[892,63717,63718,63770],{},[895,63719,63720,63722,63724,63726,63732,63734,63736,63738,63740,63742,63748,63750,63752,63754,63756,63758,63760,63762,63768],{},[898,63721,1790],{},[898,63723,1940],{},[1711,63725,1714],{"stretchy":1713},[1716,63727,63728,63730],{},[898,63729,6796],{},[1711,63731,1793],{},[1711,63733,1735],{"stretchy":1713},[1711,63735,6740],{},[898,63737,1769],{},[898,63739,1940],{},[1711,63741,1714],{"stretchy":1713},[1716,63743,63744,63746],{},[898,63745,6796],{},[1711,63747,1793],{},[1711,63749,2095],{},[2111,63751,2238],{},[1711,63753,1735],{"stretchy":1713},[1711,63755,2460],{},[898,63757,1769],{},[898,63759,1940],{},[1711,63761,1714],{"stretchy":1713},[1716,63763,63764,63766],{},[898,63765,6796],{},[1711,63767,1793],{},[1711,63769,1735],{"stretchy":1713},[902,63771,63772],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,63774,63775,63776,2062],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,63777,63779],{"className":63778},[886],[888,63780,63781],{"xmlns":890},[892,63782,63783,63791],{},[895,63784,63785,63787,63789],{},[898,63786,6892],{"mathvariant":2287},[898,63788,1769],{},[898,63790,1940],{},[902,63792,63793],{"encoding":904},"\\Delta TC",[883,63795,63797],{"className":63796},[886],[888,63798,63799],{"xmlns":890,"display":31664},[892,63800,63801,63870],{},[24352,63802,63803],{"width":31669},[24357,63804,63805,63807,63863,63865],{},[24360,63806],{"width":31674},[24360,63808,63809],{},[895,63810,63811,63813,63815,63817,63819,63821,63823,63825,63827,63829,63831,63833,63835,63837,63843,63845,63847,63849,63851,63853,63855,63857,63859,63861],{},[898,63812,6892],{"mathvariant":2287},[898,63814,1769],{},[898,63816,1940],{},[1942,63818,4699],{},[1711,63820,6740],{},[1942,63822,4699],{},[898,63824,2098],{"mathvariant":2287},[898,63826,1769],{},[898,63828,1940],{},[1711,63830,1836],{},[1711,63832,1714],{"stretchy":1713},[898,63834,1769],{},[898,63836,1940],{},[1716,63838,63839,63841],{},[1711,63840,1735],{"stretchy":1713},[1711,63842,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1942,63844,2519],{},[898,63846,2098],{"mathvariant":2287},[898,63848,6796],{},[1711,63850,1836],{},[898,63852,1790],{},[898,63854,1940],{},[1942,63856,2519],{},[898,63858,2098],{"mathvariant":2287},[898,63860,6796],{},[1711,63862,1726],{"separator":1725},[24360,63864],{"width":31674},[24360,63866,63867],{},[1942,63868,63869],{},"(3.9)",[902,63871,63872],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,63874,60909],{},[883,63876,63878],{"className":63877},[886],[888,63879,63880],{"xmlns":890,"display":31664},[892,63881,63882,63980],{},[895,63883,63884,63922,63924,63926,63928,63950,63952,63978],{},[895,63885,63886,63888,63894,63896,63902,63905,63911,63914],{},[1942,63887,60923],{},[12366,63889,63890,63892],{"accent":1725},[1942,63891,49330],{},[1711,63893,28656],{},[1942,63895,60932],{},[12366,63897,63898,63900],{"accent":1725},[1942,63899,6038],{},[1711,63901,28575],{},[1942,63903,63904],{},"ch n",[12366,63906,63907,63909],{"accent":1725},[1942,63908,207],{},[1711,63910,28575],{},[1942,63912,63913],{},"klad",[12366,63915,63916,63919],{"accent":1725},[1942,63917,63918],{},"u",[1711,63920,63921],{},"˚",[1942,63923,4699],{},[1711,63925,6740],{},[1942,63927,4699],{},[895,63929,63930,63932,63938,63941,63947],{},[1942,63931,60967],{},[12366,63933,63934,63936],{"accent":1725},[1942,63935,28644],{},[1711,63937,28575],{},[1942,63939,63940],{}," n",[12366,63942,63943,63945],{"accent":1725},[1942,63944,207],{},[1711,63946,28575],{},[1942,63948,63949],{},"klady",[1711,63951,60994],{},[895,63953,63954,63956,63962,63964,63970,63972],{},[1942,63955,60923],{},[12366,63957,63958,63960],{"accent":1725},[1942,63959,49330],{},[1711,63961,28656],{},[1942,63963,61007],{},[12366,63965,63966,63968],{"accent":1725},[1942,63967,13569],{},[1711,63969,28656],{},[1942,63971,61016],{},[12366,63973,63974,63976],{"accent":1725},[1942,63975,28644],{},[1711,63977,28575],{},[898,63979,2186],{"mathvariant":2287},[902,63981,63982],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[40946,63984,63986],{"id":63985},"příklad-35","Příklad 3.5",[724,63988,63989,61120,63991,59623,64027,64042,64043,64058,64059,6682,64072,6696,64085,64098,64099,6696,64112,2186],{},[38,63990,59585],{},[883,63992,63994],{"className":63993},[886],[888,63995,63996],{"xmlns":890},[892,63997,63998,64024],{},[895,63999,64000,64002,64004,64006,64008,64010,64012,64014,64016,64018],{},[898,64001,1769],{},[898,64003,1940],{},[1711,64005,1836],{},[2111,64007,12357],{},[1711,64009,2095],{},[2111,64011,6262],{},[898,64013,6796],{},[1711,64015,2095],{},[2111,64017,2963],{},[1716,64019,64020,64022],{},[898,64021,6796],{},[2111,64023,2963],{},[902,64025,64026],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,64028,64030],{"className":64029},[886],[888,64031,64032],{"xmlns":890},[892,64033,64034,64040],{},[895,64035,64036,64038],{},[898,64037,1790],{},[898,64039,1940],{},[902,64041,58890],{"encoding":904}," a odhadněte změny ",[883,64044,64046],{"className":64045},[886],[888,64047,64048],{"xmlns":890},[892,64049,64050,64056],{},[895,64051,64052,64054],{},[898,64053,1769],{},[898,64055,1940],{},[902,64057,7241],{"encoding":904}," při změnách ",[883,64060,64062],{"className":64061},[886],[888,64063,64064],{"xmlns":890},[892,64065,64066,64070],{},[895,64067,64068],{},[898,64069,6796],{},[902,64071,6796],{"encoding":904},[883,64073,64075],{"className":64074},[886],[888,64076,64077],{"xmlns":890},[892,64078,64079,64083],{},[895,64080,64081],{},[2111,64082,39842],{},[902,64084,39842],{"encoding":904},[883,64086,64088],{"className":64087},[886],[888,64089,64090],{"xmlns":890},[892,64091,64092,64096],{},[895,64093,64094],{},[2111,64095,45460],{},[902,64097,45460],{"encoding":904}," a z ",[883,64100,64102],{"className":64101},[886],[888,64103,64104],{"xmlns":890},[892,64105,64106,64110],{},[895,64107,64108],{},[2111,64109,39842],{},[902,64111,39842],{"encoding":904},[883,64113,64115],{"className":64114},[886],[888,64116,64117],{"xmlns":890},[892,64118,64119,64123],{},[895,64120,64121],{},[2111,64122,7505],{},[902,64124,7505],{"encoding":904},[724,64126,64127,1700,64129,2801,64155,1343,64182,64209,64210,64225,64226,64241,64242,64269,64270,64290,64291,24129,64312,64368,64369,6682,64382,6696,64395,12082,64408,2186],{},[38,64128,26368],{},[883,64130,64132],{"className":64131},[886],[888,64133,64134],{"xmlns":890},[892,64135,64136,64152],{},[895,64137,64138,64140,64142,64144,64146,64148,64150],{},[898,64139,1790],{},[898,64141,1940],{},[1711,64143,1836],{},[2111,64145,6262],{},[1711,64147,2095],{},[2111,64149,6369],{},[898,64151,6796],{},[902,64153,64154],{"encoding":904},"MC = 6 + 4Q",[883,64156,64158],{"className":64157},[886],[888,64159,64160],{"xmlns":890},[892,64161,64162,64179],{},[895,64163,64164,64166,64168,64170,64172,64174,64176],{},[898,64165,1790],{},[898,64167,1940],{},[1711,64169,1714],{"stretchy":1713},[2111,64171,39842],{},[1711,64173,1735],{"stretchy":1713},[1711,64175,1836],{},[2111,64177,64178],{},"66",[902,64180,64181],{"encoding":904},"MC(15) = 66",[883,64183,64185],{"className":64184},[886],[888,64186,64187],{"xmlns":890},[892,64188,64189,64206],{},[895,64190,64191,64193,64195,64197,64199,64201,64203],{},[898,64192,1790],{},[898,64194,1940],{},[1711,64196,1714],{"stretchy":1713},[2111,64198,4306],{},[1711,64200,1735],{"stretchy":1713},[1711,64202,1836],{},[2111,64204,64205],{},"86",[902,64207,64208],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,64211,64213],{"className":64212},[886],[888,64214,64215],{"xmlns":890},[892,64216,64217,64223],{},[895,64218,64219,64221],{},[898,64220,1769],{},[898,64222,1940],{},[902,64224,7241],{"encoding":904}," zvyšuje (",[883,64227,64229],{"className":64228},[886],[888,64230,64231],{"xmlns":890},[892,64232,64233,64239],{},[895,64234,64235,64237],{},[898,64236,1790],{},[898,64238,1940],{},[902,64240,58890],{"encoding":904}," je rostoucí). Z ",[883,64243,64245],{"className":64244},[886],[888,64246,64247],{"xmlns":890},[892,64248,64249,64266],{},[895,64250,64251,64253,64255,64257,64259,64261,64263],{},[898,64252,1769],{},[898,64254,1940],{},[1711,64256,1714],{"stretchy":1713},[2111,64258,39842],{},[1711,64260,1735],{"stretchy":1713},[1711,64262,1836],{},[2111,64264,64265],{},"740",[902,64267,64268],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,64271,64273],{"className":64272},[886],[888,64274,64275],{"xmlns":890},[892,64276,64277,64287],{},[895,64278,64279,64281,64283,64285],{},[898,64280,2098],{"mathvariant":2287},[898,64282,6796],{},[1711,64284,1836],{},[2111,64286,2238],{},[902,64288,64289],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,64292,64294],{"className":64293},[886],[888,64295,64296],{"xmlns":890},[892,64297,64298,64309],{},[895,64299,64300,64302,64304,64306],{},[898,64301,1769],{},[898,64303,1940],{},[1711,64305,6740],{},[2111,64307,64308],{},"806",[902,64310,64311],{"encoding":904},"TC \\approx 806",[883,64313,64315],{"className":64314},[886],[888,64316,64317],{"xmlns":890},[892,64318,64319,64365],{},[895,64320,64321,64323,64325,64327,64329,64331,64333,64335,64337,64339,64341,64343,64345,64347,64349,64351,64353,64356,64358,64360,64362],{},[898,64322,6892],{"mathvariant":2287},[898,64324,1769],{},[898,64326,1940],{},[1711,64328,1836],{},[898,64330,1769],{},[898,64332,1940],{},[1711,64334,1714],{"stretchy":1713},[2111,64336,45460],{},[1711,64338,1735],{"stretchy":1713},[1711,64340,2460],{},[898,64342,1769],{},[898,64344,1940],{},[1711,64346,1714],{"stretchy":1713},[2111,64348,39842],{},[1711,64350,1735],{"stretchy":1713},[1711,64352,1836],{},[2111,64354,64355],{},"808",[1711,64357,2460],{},[2111,64359,64265],{},[1711,64361,1836],{},[2111,64363,64364],{},"68",[902,64366,64367],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,64370,64372],{"className":64371},[886],[888,64373,64374],{"xmlns":890},[892,64375,64376,64380],{},[895,64377,64378],{},[898,64379,6796],{},[902,64381,6796],{"encoding":904},[883,64383,64385],{"className":64384},[886],[888,64386,64387],{"xmlns":890},[892,64388,64389,64393],{},[895,64390,64391],{},[2111,64392,39842],{},[902,64394,39842],{"encoding":904},[883,64396,64398],{"className":64397},[886],[888,64399,64400],{"xmlns":890},[892,64401,64402,64406],{},[895,64403,64404],{},[2111,64405,7505],{},[902,64407,7505],{"encoding":904},[883,64409,64411],{"className":64410},[886],[888,64412,64413],{"xmlns":890},[892,64414,64415,64444],{},[895,64416,64417,64419,64421,64423,64425,64427,64429,64431,64433,64435,64437,64439,64441],{},[898,64418,6892],{"mathvariant":2287},[898,64420,1769],{},[898,64422,1940],{},[1711,64424,6740],{},[2111,64426,64178],{},[1711,64428,4795],{},[1711,64430,1714],{"stretchy":1713},[1711,64432,2460],{},[2111,64434,3034],{},[1711,64436,1735],{"stretchy":1713},[1711,64438,1836],{},[1711,64440,2460],{},[2111,64442,64443],{},"198",[902,64445,64446],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,64448,64450],{"id":64449},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,64452,64453],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[40946,64455,64457],{"id":64456},"příklad-36","Příklad 3.6",[724,64459,64460,61120,64462,64506],{},[38,64461,59585],{},[883,64463,64465],{"className":64464},[886],[888,64466,64467],{"xmlns":890},[892,64468,64469,64503],{},[895,64470,64471,64473,64475,64477,64479,64481,64483,64485,64487,64489,64495,64497],{},[898,64472,1769],{},[898,64474,1940],{},[1711,64476,1836],{},[2111,64478,4282],{},[1711,64480,2095],{},[2111,64482,4372],{},[898,64484,6796],{},[1711,64486,2460],{},[2111,64488,4798],{},[1716,64490,64491,64493],{},[898,64492,6796],{},[2111,64494,2963],{},[1711,64496,2095],{},[1716,64498,64499,64501],{},[898,64500,6796],{},[2111,64502,3034],{},[902,64504,64505],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,64508,64509],{},[38,64510,26368],{},[883,64512,64514],{"className":64513},[886],[888,64515,64516],{"xmlns":890,"display":31664},[892,64517,64518,64762],{},[24352,64519,64520,64546,64594,64628,64670,64720],{"rowspacing":24354,"columnalign":24355,"columnspacing":5224},[24357,64521,64522,64532],{},[24360,64523,64524],{},[2509,64525,64526],{"scriptlevel":2113,"displaystyle":1725},[895,64527,64528,64530],{},[898,64529,14409],{},[898,64531,1940],{},[24360,64533,64534],{},[2509,64535,64536],{"scriptlevel":2113,"displaystyle":1725},[895,64537,64538,64540,64542,64544],{},[895,64539],{},[1711,64541,1836],{},[2111,64543,4282],{},[1711,64545,1726],{"separator":1725},[24357,64547,64548,64560],{},[24360,64549,64550],{},[2509,64551,64552],{"scriptlevel":2113,"displaystyle":1725},[895,64553,64554,64556,64558],{},[898,64555,1769],{},[898,64557,43937],{},[898,64559,1940],{},[24360,64561,64562],{},[2509,64563,64564],{"scriptlevel":2113,"displaystyle":1725},[895,64565,64566,64568,64570,64572,64574,64576,64578,64584,64586,64592],{},[895,64567],{},[1711,64569,1836],{},[2111,64571,4372],{},[898,64573,6796],{},[1711,64575,2460],{},[2111,64577,4798],{},[1716,64579,64580,64582],{},[898,64581,6796],{},[2111,64583,2963],{},[1711,64585,2095],{},[1716,64587,64588,64590],{},[898,64589,6796],{},[2111,64591,3034],{},[1711,64593,1726],{"separator":1725},[24357,64595,64596,64608],{},[24360,64597,64598],{},[2509,64599,64600],{"scriptlevel":2113,"displaystyle":1725},[895,64601,64602,64604,64606],{},[898,64603,8243],{},[898,64605,14409],{},[898,64607,1940],{},[24360,64609,64610],{},[2509,64611,64612],{"scriptlevel":2113,"displaystyle":1725},[895,64613,64614,64616,64618,64626],{},[895,64615],{},[1711,64617,1836],{},[2509,64619,64620],{"scriptlevel":2113,"displaystyle":1713},[2525,64621,64622,64624],{},[2111,64623,4282],{},[898,64625,6796],{},[1711,64627,1726],{"separator":1725},[24357,64629,64630,64642],{},[24360,64631,64632],{},[2509,64633,64634],{"scriptlevel":2113,"displaystyle":1725},[895,64635,64636,64638,64640],{},[898,64637,8243],{},[898,64639,43937],{},[898,64641,1940],{},[24360,64643,64644],{},[2509,64645,64646],{"scriptlevel":2113,"displaystyle":1725},[895,64647,64648,64650,64652,64654,64656,64658,64660,64662,64668],{},[895,64649],{},[1711,64651,1836],{},[2111,64653,4372],{},[1711,64655,2460],{},[2111,64657,4798],{},[898,64659,6796],{},[1711,64661,2095],{},[1716,64663,64664,64666],{},[898,64665,6796],{},[2111,64667,2963],{},[1711,64669,1726],{"separator":1725},[24357,64671,64672,64682],{},[24360,64673,64674],{},[2509,64675,64676],{"scriptlevel":2113,"displaystyle":1725},[895,64677,64678,64680],{},[898,64679,8243],{},[898,64681,1940],{},[24360,64683,64684],{},[2509,64685,64686],{"scriptlevel":2113,"displaystyle":1725},[895,64687,64688,64690,64692,64700,64702,64704,64706,64708,64710,64712,64718],{},[895,64689],{},[1711,64691,1836],{},[2509,64693,64694],{"scriptlevel":2113,"displaystyle":1713},[2525,64695,64696,64698],{},[2111,64697,4282],{},[898,64699,6796],{},[1711,64701,2095],{},[2111,64703,4372],{},[1711,64705,2460],{},[2111,64707,4798],{},[898,64709,6796],{},[1711,64711,2095],{},[1716,64713,64714,64716],{},[898,64715,6796],{},[2111,64717,2963],{},[1711,64719,1726],{"separator":1725},[24357,64721,64722,64732],{},[24360,64723,64724],{},[2509,64725,64726],{"scriptlevel":2113,"displaystyle":1725},[895,64727,64728,64730],{},[898,64729,1790],{},[898,64731,1940],{},[24360,64733,64734],{},[2509,64735,64736],{"scriptlevel":2113,"displaystyle":1725},[895,64737,64738,64740,64742,64744,64746,64748,64750,64752,64754,64760],{},[895,64739],{},[1711,64741,1836],{},[2111,64743,4372],{},[1711,64745,2460],{},[2111,64747,4712],{},[898,64749,6796],{},[1711,64751,2095],{},[2111,64753,3034],{},[1716,64755,64756,64758],{},[898,64757,6796],{},[2111,64759,2963],{},[898,64761,2186],{"mathvariant":2287},[902,64763,64764],{"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}",[724,64766,64767,64768,5494,64783,5494,64798,64813,64814,64829,64830,1343,64848,64829,64865,1343,64883,64829,64898,64916],{},"Význačné body ",[883,64769,64771],{"className":64770},[886],[888,64772,64773],{"xmlns":890},[892,64774,64775,64780],{},[895,64776,64777],{},[2111,64778,64779],{},"1,67",[902,64781,64782],{"encoding":904},"1{,}67",[883,64784,64786],{"className":64785},[886],[888,64787,64788],{"xmlns":890},[892,64789,64790,64795],{},[895,64791,64792],{},[2111,64793,64794],{},"2,50",[902,64796,64797],{"encoding":904},"2{,}50",[883,64799,64801],{"className":64800},[886],[888,64802,64803],{"xmlns":890},[892,64804,64805,64810],{},[895,64806,64807],{},[2111,64808,64809],{},"4,73",[902,64811,64812],{"encoding":904},"4{,}73"," odpovídají: ",[883,64815,64817],{"className":64816},[886],[888,64818,64819],{"xmlns":890},[892,64820,64821,64827],{},[895,64822,64823,64825],{},[898,64824,1790],{},[898,64826,1940],{},[902,64828,58890],{"encoding":904}," minimum v ",[883,64831,64833],{"className":64832},[886],[888,64834,64835],{"xmlns":890},[892,64836,64837,64845],{},[895,64838,64839,64841,64843],{},[898,64840,6796],{},[1711,64842,9881],{},[2111,64844,64779],{},[902,64846,64847],{"encoding":904},"Q \\doteq 1{,}67",[883,64849,64851],{"className":64850},[886],[888,64852,64853],{"xmlns":890},[892,64854,64855,64863],{},[895,64856,64857,64859,64861],{},[898,64858,8243],{},[898,64860,43937],{},[898,64862,1940],{},[902,64864,58909],{"encoding":904},[883,64866,64868],{"className":64867},[886],[888,64869,64870],{"xmlns":890},[892,64871,64872,64880],{},[895,64873,64874,64876,64878],{},[898,64875,6796],{},[1711,64877,1836],{},[2111,64879,64794],{},[902,64881,64882],{"encoding":904},"Q = 2{,}50",[883,64884,64886],{"className":64885},[886],[888,64887,64888],{"xmlns":890},[892,64889,64890,64896],{},[895,64891,64892,64894],{},[898,64893,8243],{},[898,64895,1940],{},[902,64897,59158],{"encoding":904},[883,64899,64901],{"className":64900},[886],[888,64902,64903],{"xmlns":890},[892,64904,64905,64913],{},[895,64906,64907,64909,64911],{},[898,64908,6796],{},[1711,64910,9881],{},[2111,64912,64809],{},[902,64914,64915],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,64918,64919],{},[1801,64920],{"alt":64921,"className":64922,"src":64923},"imek-ac-avc-mc",[210,1805],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,64925,64926],{},[614,64927,64928,64929,2009,64944,64961,64962,5494,64981,64996],{},"Obrázek 3.9: Kubické křivky ",[883,64930,64932],{"className":64931},[886],[888,64933,64934],{"xmlns":890},[892,64935,64936,64942],{},[895,64937,64938,64940],{},[898,64939,1769],{},[898,64941,1940],{},[902,64943,7241],{"encoding":904},[883,64945,64947],{"className":64946},[886],[888,64948,64949],{"xmlns":890},[892,64950,64951,64959],{},[895,64952,64953,64955,64957],{},[898,64954,1769],{},[898,64956,43937],{},[898,64958,1940],{},[902,64960,59107],{"encoding":904}," rostoucí od bodu ",[883,64963,64965],{"className":64964},[886],[888,64966,64967],{"xmlns":890},[892,64968,64969,64979],{},[895,64970,64971,64973,64975,64977],{},[898,64972,14409],{},[898,64974,1940],{},[1711,64976,1836],{},[2111,64978,4282],{},[902,64980,15607],{"encoding":904},[883,64982,64984],{"className":64983},[886],[888,64985,64986],{"xmlns":890},[892,64987,64988,64994],{},[895,64989,64990,64992],{},[898,64991,14409],{},[898,64993,1940],{},[902,64995,59089],{"encoding":904}," je vodorovná přímka.",[724,64998,64999],{},[614,65000,65001,65002,1343,65017,1343,65034,32799,65049,65062,65063,2801,65080,65095,65096,10171,65113,65128,65129,29787,65142,1343,65155,1343,65168,2186],{},"Obrázek 3.10: Křivky ",[883,65003,65005],{"className":65004},[886],[888,65006,65007],{"xmlns":890},[892,65008,65009,65015],{},[895,65010,65011,65013],{},[898,65012,8243],{},[898,65014,1940],{},[902,65016,59158],{"encoding":904},[883,65018,65020],{"className":65019},[886],[888,65021,65022],{"xmlns":890},[892,65023,65024,65032],{},[895,65025,65026,65028,65030],{},[898,65027,8243],{},[898,65029,43937],{},[898,65031,1940],{},[902,65033,58909],{"encoding":904},[883,65035,65037],{"className":65036},[886],[888,65038,65039],{"xmlns":890},[892,65040,65041,65047],{},[895,65042,65043,65045],{},[898,65044,1790],{},[898,65046,1940],{},[902,65048,58890],{"encoding":904},[883,65050,65052],{"className":65051},[886],[888,65053,65054],{"xmlns":890},[892,65055,65056,65060],{},[895,65057,65058],{},[898,65059,900],{},[902,65061,900],{"encoding":904}," a klesající hyperbola ",[883,65064,65066],{"className":65065},[886],[888,65067,65068],{"xmlns":890},[892,65069,65070,65078],{},[895,65071,65072,65074,65076],{},[898,65073,8243],{},[898,65075,14409],{},[898,65077,1940],{},[902,65079,59125],{"encoding":904},[883,65081,65083],{"className":65082},[886],[888,65084,65085],{"xmlns":890},[892,65086,65087,65093],{},[895,65088,65089,65091],{},[898,65090,1790],{},[898,65092,1940],{},[902,65094,58890],{"encoding":904}," protíná ",[883,65097,65099],{"className":65098},[886],[888,65100,65101],{"xmlns":890},[892,65102,65103,65111],{},[895,65104,65105,65107,65109],{},[898,65106,8243],{},[898,65108,43937],{},[898,65110,1940],{},[902,65112,58909],{"encoding":904},[883,65114,65116],{"className":65115},[886],[888,65117,65118],{"xmlns":890},[892,65119,65120,65126],{},[895,65121,65122,65124],{},[898,65123,8243],{},[898,65125,1940],{},[902,65127,59158],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,65130,65132],{"className":65131},[886],[888,65133,65134],{"xmlns":890},[892,65135,65136,65140],{},[895,65137,65138],{},[898,65139,6796],{},[902,65141,6796],{"encoding":904},[883,65143,65145],{"className":65144},[886],[888,65146,65147],{"xmlns":890},[892,65148,65149,65153],{},[895,65150,65151],{},[2111,65152,64779],{},[902,65154,64782],{"encoding":904},[883,65156,65158],{"className":65157},[886],[888,65159,65160],{"xmlns":890},[892,65161,65162,65166],{},[895,65163,65164],{},[2111,65165,64794],{},[902,65167,64797],{"encoding":904},[883,65169,65171],{"className":65170},[886],[888,65172,65173],{"xmlns":890},[892,65174,65175,65179],{},[895,65176,65177],{},[2111,65178,64809],{},[902,65180,64812],{"encoding":904},[724,65182,65183],{},[38,65184,65185],{},"Standardní vlastnosti:",[120,65187,65188,65223,65287,65355,65405,65425],{},[123,65189,65190,2009,65205,65222],{},[883,65191,65193],{"className":65192},[886],[888,65194,65195],{"xmlns":890},[892,65196,65197,65203],{},[895,65198,65199,65201],{},[898,65200,1769],{},[898,65202,1940],{},[902,65204,7241],{"encoding":904},[883,65206,65208],{"className":65207},[886],[888,65209,65210],{"xmlns":890},[892,65211,65212,65220],{},[895,65213,65214,65216,65218],{},[898,65215,1769],{},[898,65217,43937],{},[898,65219,1940],{},[902,65221,59107],{"encoding":904}," jsou kubické funkce;",[123,65224,65225,1343,65240,1343,65257,65272,65273,65286],{},[883,65226,65228],{"className":65227},[886],[888,65229,65230],{"xmlns":890},[892,65231,65232,65238],{},[895,65233,65234,65236],{},[898,65235,8243],{},[898,65237,1940],{},[902,65239,59158],{"encoding":904},[883,65241,65243],{"className":65242},[886],[888,65244,65245],{"xmlns":890},[892,65246,65247,65255],{},[895,65248,65249,65251,65253],{},[898,65250,8243],{},[898,65252,43937],{},[898,65254,1940],{},[902,65256,58909],{"encoding":904},[883,65258,65260],{"className":65259},[886],[888,65261,65262],{"xmlns":890},[892,65263,65264,65270],{},[895,65265,65266,65268],{},[898,65267,1790],{},[898,65269,1940],{},[902,65271,58890],{"encoding":904}," jsou křivky tvaru ",[883,65274,65276],{"className":65275},[886],[888,65277,65278],{"xmlns":890},[892,65279,65280,65284],{},[895,65281,65282],{},[898,65283,900],{},[902,65285,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,65288,65289,65304,65305,1343,65322,65339,65340,12405],{},[883,65290,65292],{"className":65291},[886],[888,65293,65294],{"xmlns":890},[892,65295,65296,65302],{},[895,65297,65298,65300],{},[898,65299,1790],{},[898,65301,1940],{},[902,65303,58890],{"encoding":904}," nabývá minima před ",[883,65306,65308],{"className":65307},[886],[888,65309,65310],{"xmlns":890},[892,65311,65312,65320],{},[895,65313,65314,65316,65318],{},[898,65315,8243],{},[898,65317,43937],{},[898,65319,1940],{},[902,65321,58909],{"encoding":904},[883,65323,65325],{"className":65324},[886],[888,65326,65327],{"xmlns":890},[892,65328,65329,65337],{},[895,65330,65331,65333,65335],{},[898,65332,8243],{},[898,65334,43937],{},[898,65336,1940],{},[902,65338,58909],{"encoding":904}," před ",[883,65341,65343],{"className":65342},[886],[888,65344,65345],{"xmlns":890},[892,65346,65347,65353],{},[895,65348,65349,65351],{},[898,65350,8243],{},[898,65352,1940],{},[902,65354,59158],{"encoding":904},[123,65356,65357,65095,65372,2009,65387,65404],{},[883,65358,65360],{"className":65359},[886],[888,65361,65362],{"xmlns":890},[892,65363,65364,65370],{},[895,65365,65366,65368],{},[898,65367,1790],{},[898,65369,1940],{},[902,65371,58890],{"encoding":904},[883,65373,65375],{"className":65374},[886],[888,65376,65377],{"xmlns":890},[892,65378,65379,65385],{},[895,65380,65381,65383],{},[898,65382,8243],{},[898,65384,1940],{},[902,65386,59158],{"encoding":904},[883,65388,65390],{"className":65389},[886],[888,65391,65392],{"xmlns":890},[892,65393,65394,65402],{},[895,65395,65396,65398,65400],{},[898,65397,8243],{},[898,65399,43937],{},[898,65401,1940],{},[902,65403,58909],{"encoding":904}," zdola právě v jejich minimech;",[123,65406,65407,65424],{},[883,65408,65410],{"className":65409},[886],[888,65411,65412],{"xmlns":890},[892,65413,65414,65422],{},[895,65415,65416,65418,65420],{},[898,65417,8243],{},[898,65419,14409],{},[898,65421,1940],{},[902,65423,59125],{"encoding":904}," je hyperbola, stále klesající;",[123,65426,65427,65459,65460,2009,65475,65492,65493,65506,65507,1797],{},[883,65428,65430],{"className":65429},[886],[888,65431,65432],{"xmlns":890},[892,65433,65434,65456],{},[895,65435,65436,65438,65440,65442,65444,65446,65448,65450,65452,65454],{},[898,65437,8243],{},[898,65439,1940],{},[1711,65441,1836],{},[898,65443,8243],{},[898,65445,14409],{},[898,65447,1940],{},[1711,65449,2095],{},[898,65451,8243],{},[898,65453,43937],{},[898,65455,1940],{},[902,65457,65458],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,65461,65463],{"className":65462},[886],[888,65464,65465],{"xmlns":890},[892,65466,65467,65473],{},[895,65468,65469,65471],{},[898,65470,8243],{},[898,65472,1940],{},[902,65474,59158],{"encoding":904},[883,65476,65478],{"className":65477},[886],[888,65479,65480],{"xmlns":890},[892,65481,65482,65490],{},[895,65483,65484,65486,65488],{},[898,65485,8243],{},[898,65487,43937],{},[898,65489,1940],{},[902,65491,58909],{"encoding":904}," klesá s rostoucím ",[883,65494,65496],{"className":65495},[886],[888,65497,65498],{"xmlns":890},[892,65499,65500,65504],{},[895,65501,65502],{},[898,65503,6796],{},[902,65505,6796],{"encoding":904}," (protože ",[883,65508,65510],{"className":65509},[886],[888,65511,65512],{"xmlns":890},[892,65513,65514,65526],{},[895,65515,65516,65518,65520,65522,65524],{},[898,65517,8243],{},[898,65519,14409],{},[898,65521,1940],{},[1711,65523,7123],{},[2111,65525,2113],{},[902,65527,65528],{"encoding":904},"AFC \\to 0",[115,65530,65532],{"id":65531},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,65534,65535,65536,65539,65540,65555],{},"Častou optimalizační úlohou je ",[38,65537,65538],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,65541,65543],{"className":65542},[886],[888,65544,65545],{"xmlns":890},[892,65546,65547,65553],{},[895,65548,65549,65551],{},[898,65550,8243],{},[898,65552,1940],{},[902,65554,59158],{"encoding":904}," minimální.",[198,65557,20010],{"id":20009},[724,65559,65560,65561,65578],{},"Mají-li průměrné náklady minimum v bodě ",[883,65562,65564],{"className":65563},[886],[888,65565,65566],{"xmlns":890},[892,65567,65568,65576],{},[895,65569,65570],{},[2884,65571,65572,65574],{},[898,65573,6796],{},[2111,65575,2113],{},[902,65577,41906],{"encoding":904},", pak platí",[883,65580,65582],{"className":65581},[886],[888,65583,65584],{"xmlns":890,"display":31664},[892,65585,65586,65635],{},[24352,65587,65588],{"width":31669},[24357,65589,65590,65592,65628,65630],{},[24360,65591],{"width":31674},[24360,65593,65594],{},[895,65595,65596,65598,65600,65602,65608,65610,65612,65614,65616,65618,65624,65626],{},[898,65597,8243],{},[898,65599,1940],{},[1711,65601,1714],{"stretchy":1713},[2884,65603,65604,65606],{},[898,65605,6796],{},[2111,65607,2113],{},[1711,65609,1735],{"stretchy":1713},[1711,65611,1836],{},[898,65613,1790],{},[898,65615,1940],{},[1711,65617,1714],{"stretchy":1713},[2884,65619,65620,65622],{},[898,65621,6796],{},[2111,65623,2113],{},[1711,65625,1735],{"stretchy":1713},[898,65627,2186],{"mathvariant":2287},[24360,65629],{"width":31674},[24360,65631,65632],{},[1942,65633,65634],{},"(3.10)",[902,65636,65637],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[1921,65639,65640],{},[724,65641,65642,65644,65645],{},[883,65643,60042],{}," Princip\n",[38,65646,65647],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,65649,65650,65653,65654,65696],{},[38,65651,65652],{},"Odvození."," Z ",[883,65655,65657],{"className":65656},[886],[888,65658,65659],{"xmlns":890},[892,65660,65661,65693],{},[895,65662,65663,65665,65667,65669,65671,65673,65675],{},[898,65664,8243],{},[898,65666,1940],{},[1711,65668,1714],{"stretchy":1713},[898,65670,6796],{},[1711,65672,1735],{"stretchy":1713},[1711,65674,1836],{},[2509,65676,65677],{"scriptlevel":2113,"displaystyle":1713},[2525,65678,65679,65691],{},[895,65680,65681,65683,65685,65687,65689],{},[898,65682,1769],{},[898,65684,1940],{},[1711,65686,1714],{"stretchy":1713},[898,65688,6796],{},[1711,65690,1735],{"stretchy":1713},[898,65692,6796],{},[902,65694,65695],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,65698,65700],{"className":65699},[886],[888,65701,65702],{"xmlns":890,"display":31664},[892,65703,65704,65836],{},[895,65705,65706,65708,65714,65716,65718,65720,65722,65762,65764,65804,65806,65834],{},[898,65707,8243],{},[1716,65709,65710,65712],{},[898,65711,1940],{},[1711,65713,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,65715,1714],{"stretchy":1713},[898,65717,6796],{},[1711,65719,1735],{"stretchy":1713},[1711,65721,1836],{},[2525,65723,65724,65756],{},[895,65725,65726,65728,65734,65736,65738,65740,65742,65744,65746,65748,65750,65752,65754],{},[898,65727,1769],{},[1716,65729,65730,65732],{},[898,65731,1940],{},[1711,65733,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,65735,1714],{"stretchy":1713},[898,65737,6796],{},[1711,65739,1735],{"stretchy":1713},[1711,65741,4795],{},[898,65743,6796],{},[1711,65745,2460],{},[898,65747,1769],{},[898,65749,1940],{},[1711,65751,1714],{"stretchy":1713},[898,65753,6796],{},[1711,65755,1735],{"stretchy":1713},[1716,65757,65758,65760],{},[898,65759,6796],{},[2111,65761,2963],{},[1711,65763,1836],{},[2525,65765,65766,65798],{},[895,65767,65768,65770,65772,65774,65776,65778,65780,65782,65784,65786,65788,65790,65792,65794,65796],{},[898,65769,1790],{},[898,65771,1940],{},[1711,65773,1714],{"stretchy":1713},[898,65775,6796],{},[1711,65777,1735],{"stretchy":1713},[1711,65779,4795],{},[898,65781,6796],{},[1711,65783,2460],{},[898,65785,8243],{},[898,65787,1940],{},[1711,65789,1714],{"stretchy":1713},[898,65791,6796],{},[1711,65793,1735],{"stretchy":1713},[1711,65795,4795],{},[898,65797,6796],{},[1716,65799,65800,65802],{},[898,65801,6796],{},[2111,65803,2963],{},[1711,65805,1836],{},[2525,65807,65808,65832],{},[895,65809,65810,65812,65814,65816,65818,65820,65822,65824,65826,65828,65830],{},[898,65811,1790],{},[898,65813,1940],{},[1711,65815,1714],{"stretchy":1713},[898,65817,6796],{},[1711,65819,1735],{"stretchy":1713},[1711,65821,2460],{},[898,65823,8243],{},[898,65825,1940],{},[1711,65827,1714],{"stretchy":1713},[898,65829,6796],{},[1711,65831,1735],{"stretchy":1713},[898,65833,6796],{},[898,65835,2186],{"mathvariant":2287},[902,65837,65838],{"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}.",[724,65840,65841,65842,6635,65857,12082,65879,60419],{},"Nutnou podmínkou minima ",[883,65843,65845],{"className":65844},[886],[888,65846,65847],{"xmlns":890},[892,65848,65849,65855],{},[895,65850,65851,65853],{},[898,65852,8243],{},[898,65854,1940],{},[902,65856,59158],{"encoding":904},[883,65858,65860],{"className":65859},[886],[888,65861,65862],{"xmlns":890},[892,65863,65864,65876],{},[895,65865,65866,65872,65874],{},[2884,65867,65868,65870],{},[898,65869,6796],{},[2111,65871,2113],{},[1711,65873,2123],{},[2111,65875,2113],{},[902,65877,65878],{"encoding":904},"Q_0 > 0",[883,65880,65882],{"className":65881},[886],[888,65883,65884],{"xmlns":890},[892,65885,65886,65910],{},[895,65887,65888,65890,65896,65898,65904,65906,65908],{},[898,65889,8243],{},[1716,65891,65892,65894],{},[898,65893,1940],{},[1711,65895,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,65897,1714],{"stretchy":1713},[2884,65899,65900,65902],{},[898,65901,6796],{},[2111,65903,2113],{},[1711,65905,1735],{"stretchy":1713},[1711,65907,1836],{},[2111,65909,2113],{},[902,65911,65912],{"encoding":904},"AC'(Q_0) = 0",[883,65914,65916],{"className":65915},[886],[888,65917,65918],{"xmlns":890,"display":31664},[892,65919,65920,66005],{},[895,65921,65922,65962,65964,65966,65968,65971,65973,65975,65977,65979,65985,65987,65989,65991,65993,65995,66001,66003],{},[2525,65923,65924,65956],{},[895,65925,65926,65928,65930,65932,65938,65940,65942,65944,65946,65948,65954],{},[898,65927,1790],{},[898,65929,1940],{},[1711,65931,1714],{"stretchy":1713},[2884,65933,65934,65936],{},[898,65935,6796],{},[2111,65937,2113],{},[1711,65939,1735],{"stretchy":1713},[1711,65941,2460],{},[898,65943,8243],{},[898,65945,1940],{},[1711,65947,1714],{"stretchy":1713},[2884,65949,65950,65952],{},[898,65951,6796],{},[2111,65953,2113],{},[1711,65955,1735],{"stretchy":1713},[2884,65957,65958,65960],{},[898,65959,6796],{},[2111,65961,2113],{},[1711,65963,1836],{},[2111,65965,2113],{},[2102,65967],{"width":4981},[1711,65969,65970],{},"⟺",[2102,65972],{"width":4981},[898,65974,1790],{},[898,65976,1940],{},[1711,65978,1714],{"stretchy":1713},[2884,65980,65981,65983],{},[898,65982,6796],{},[2111,65984,2113],{},[1711,65986,1735],{"stretchy":1713},[1711,65988,1836],{},[898,65990,8243],{},[898,65992,1940],{},[1711,65994,1714],{"stretchy":1713},[2884,65996,65997,65999],{},[898,65998,6796],{},[2111,66000,2113],{},[1711,66002,1735],{"stretchy":1713},[898,66004,2186],{"mathvariant":2287},[902,66006,66007],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,66009,66010,1700,66013,65095,66028,66043,66044,66059,66060,12082,66077,66099,66100,66122],{},[38,66011,66012],{},"Geometrická interpretace.",[883,66014,66016],{"className":66015},[886],[888,66017,66018],{"xmlns":890},[892,66019,66020,66026],{},[895,66021,66022,66024],{},[898,66023,1790],{},[898,66025,1940],{},[902,66027,58890],{"encoding":904},[883,66029,66031],{"className":66030},[886],[888,66032,66033],{"xmlns":890},[892,66034,66035,66041],{},[895,66036,66037,66039],{},[898,66038,8243],{},[898,66040,1940],{},[902,66042,59158],{"encoding":904}," právě v bodě minima ",[883,66045,66047],{"className":66046},[886],[888,66048,66049],{"xmlns":890},[892,66050,66051,66057],{},[895,66052,66053,66055],{},[898,66054,8243],{},[898,66056,1940],{},[902,66058,59158],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,66061,66063],{"className":66062},[886],[888,66064,66065],{"xmlns":890},[892,66066,66067,66075],{},[895,66068,66069],{},[2884,66070,66071,66073],{},[898,66072,6796],{},[2111,66074,2113],{},[902,66076,41906],{"encoding":904},[883,66078,66080],{"className":66079},[886],[888,66081,66082],{"xmlns":890},[892,66083,66084,66096],{},[895,66085,66086,66088,66090,66092,66094],{},[898,66087,1790],{},[898,66089,1940],{},[1711,66091,2109],{},[898,66093,8243],{},[898,66095,1940],{},[902,66097,66098],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,66101,66103],{"className":66102},[886],[888,66104,66105],{"xmlns":890},[892,66106,66107,66119],{},[895,66108,66109,66111,66113,66115,66117],{},[898,66110,1790],{},[898,66112,1940],{},[1711,66114,2123],{},[898,66116,8243],{},[898,66118,1940],{},[902,66120,66121],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,66124,66125,66126,66168,66169,66186,66187,2186],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,66127,66129],{"className":66128},[886],[888,66130,66131],{"xmlns":890},[892,66132,66133,66165],{},[895,66134,66135,66137,66139,66141,66147,66149,66151,66153,66155,66157,66163],{},[898,66136,8243],{},[898,66138,1940],{},[1711,66140,1714],{"stretchy":1713},[2884,66142,66143,66145],{},[898,66144,6796],{},[2111,66146,2113],{},[1711,66148,1735],{"stretchy":1713},[1711,66150,1836],{},[898,66152,1790],{},[898,66154,1940],{},[1711,66156,1714],{"stretchy":1713},[2884,66158,66159,66161],{},[898,66160,6796],{},[2111,66162,2113],{},[1711,66164,1735],{"stretchy":1713},[902,66166,66167],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,66170,66172],{"className":66171},[886],[888,66173,66174],{"xmlns":890},[892,66175,66176,66184],{},[895,66177,66178],{},[2884,66179,66180,66182],{},[898,66181,6796],{},[2111,66183,2113],{},[902,66185,41906],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,66188,66190],{"className":66189},[886],[888,66191,66192],{"xmlns":890},[892,66193,66194,66218],{},[895,66195,66196,66198,66200,66202,66204,66206,66208,66210,66212,66214,66216],{},[898,66197,8243],{},[898,66199,1940],{},[1711,66201,1714],{"stretchy":1713},[898,66203,6796],{},[1711,66205,1735],{"stretchy":1713},[1711,66207,1836],{},[898,66209,1790],{},[898,66211,1940],{},[1711,66213,1714],{"stretchy":1713},[898,66215,6796],{},[1711,66217,1735],{"stretchy":1713},[902,66219,66220],{"encoding":904},"AC(Q) = MC(Q)",[1921,66222,66223],{},[724,66224,66225,66227,66228,14367,66246,66267,66268,14367,66271,66292,66293,66308,66309,61636,66324,1797],{},[883,66226,1927],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,66229,66230,66231],{},"minimum ",[883,66232,66234],{"className":66233},[886],[888,66235,66236],{"xmlns":890},[892,66237,66238,66244],{},[895,66239,66240,66242],{},[898,66241,8243],{},[898,66243,1940],{},[902,66245,59158],{"encoding":904},[883,66247,66249],{"className":66248},[886],[888,66250,66251],{"xmlns":890},[892,66252,66253,66265],{},[895,66254,66255,66257,66259,66261,66263],{},[898,66256,8243],{},[898,66258,1940],{},[1711,66260,1836],{},[898,66262,1790],{},[898,66264,1940],{},[902,66266,58821],{"encoding":904},", pro ",[38,66269,66270],{},"maximum zisku",[883,66272,66274],{"className":66273},[886],[888,66275,66276],{"xmlns":890},[892,66277,66278,66290],{},[895,66279,66280,66282,66284,66286,66288],{},[898,66281,1790],{},[898,66283,7985],{},[1711,66285,1836],{},[898,66287,1790],{},[898,66289,1940],{},[902,66291,58869],{"encoding":904},". Obě podmínky využívají ",[883,66294,66296],{"className":66295},[886],[888,66297,66298],{"xmlns":890},[892,66299,66300,66306],{},[895,66301,66302,66304],{},[898,66303,1790],{},[898,66305,1940],{},[902,66307,58890],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,66310,66312],{"className":66311},[886],[888,66313,66314],{"xmlns":890},[892,66315,66316,66322],{},[895,66317,66318,66320],{},[898,66319,8243],{},[898,66321,1940],{},[902,66323,59158],{"encoding":904},[883,66325,66327],{"className":66326},[886],[888,66328,66329],{"xmlns":890},[892,66330,66331,66337],{},[895,66332,66333,66335],{},[898,66334,1790],{},[898,66336,7985],{},[902,66338,10615],{"encoding":904},[40946,66340,66342],{"id":66341},"příklad-37","Příklad 3.7",[724,66344,66345,61120,66347,66381,66382,66395,66396,66411],{},[38,66346,59585],{},[883,66348,66350],{"className":66349},[886],[888,66351,66352],{"xmlns":890},[892,66353,66354,66378],{},[895,66355,66356,66358,66360,66362,66368,66370,66372,66374,66376],{},[898,66357,1769],{},[898,66359,1940],{},[1711,66361,1836],{},[1716,66363,66364,66366],{},[898,66365,6796],{},[2111,66367,2963],{},[1711,66369,2095],{},[2111,66371,3034],{},[898,66373,6796],{},[1711,66375,2095],{},[2111,66377,9549],{},[902,66379,66380],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,66383,66385],{"className":66384},[886],[888,66386,66387],{"xmlns":890},[892,66388,66389,66393],{},[895,66390,66391],{},[898,66392,6796],{},[902,66394,6796],{"encoding":904}," minimalizující ",[883,66397,66399],{"className":66398},[886],[888,66400,66401],{"xmlns":890},[892,66402,66403,66409],{},[895,66404,66405,66407],{},[898,66406,8243],{},[898,66408,1940],{},[902,66410,59158],{"encoding":904}," a ověřte princip (3.10).",[724,66413,66414,66416],{},[38,66415,26368],{}," Přímý výpočet:",[883,66418,66420],{"className":66419},[886],[888,66421,66422],{"xmlns":890,"display":31664},[892,66423,66424,66526],{},[895,66425,66426,66428,66430,66432,66454,66456,66458,66460,66462,66464,66470,66472,66474,66476,66478,66480,66486,66488,66490,66492,66502,66504,66524],{},[898,66427,8243],{},[898,66429,1940],{},[1711,66431,1836],{},[2525,66433,66434,66452],{},[895,66435,66436,66442,66444,66446,66448,66450],{},[1716,66437,66438,66440],{},[898,66439,6796],{},[2111,66441,2963],{},[1711,66443,2095],{},[2111,66445,3034],{},[898,66447,6796],{},[1711,66449,2095],{},[2111,66451,9549],{},[898,66453,6796],{},[1711,66455,1836],{},[898,66457,6796],{},[1711,66459,2095],{},[2111,66461,3034],{},[1711,66463,2095],{},[2525,66465,66466,66468],{},[2111,66467,9549],{},[898,66469,6796],{},[1711,66471,1726],{"separator":1725},[2102,66473],{"width":2104},[1711,66475,1714],{"stretchy":1713},[898,66477,8243],{},[898,66479,1940],{},[1716,66481,66482,66484],{},[1711,66483,1735],{"stretchy":1713},[1711,66485,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,66487,1836],{},[2111,66489,2238],{},[1711,66491,2460],{},[2525,66493,66494,66496],{},[2111,66495,9549],{},[1716,66497,66498,66500],{},[898,66499,6796],{},[2111,66501,2963],{},[1711,66503,1836],{},[2525,66505,66506,66518],{},[895,66507,66508,66514,66516],{},[1716,66509,66510,66512],{},[898,66511,6796],{},[2111,66513,2963],{},[1711,66515,2460],{},[2111,66517,9549],{},[1716,66519,66520,66522],{},[898,66521,6796],{},[2111,66523,2963],{},[898,66525,2186],{"mathvariant":2287},[902,66527,66528],{"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}.",[724,66530,66531,66571,66572,66596,66597,66647,66648,2186],{},[883,66532,66534],{"className":66533},[886],[888,66535,66536],{"xmlns":890},[892,66537,66538,66568],{},[895,66539,66540,66542,66544,66546,66552,66554,66556,66558,66564,66566],{},[1711,66541,1714],{"stretchy":1713},[898,66543,8243],{},[898,66545,1940],{},[1716,66547,66548,66550],{},[1711,66549,1735],{"stretchy":1713},[1711,66551,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,66553,1836],{},[2111,66555,2113],{},[1711,66557,7978],{},[2884,66559,66560,66562],{},[898,66561,6796],{},[2111,66563,2238],{},[1711,66565,1836],{},[2111,66567,6262],{},[902,66569,66570],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,66573,66575],{"className":66574},[886],[888,66576,66577],{"xmlns":890},[892,66578,66579,66593],{},[895,66580,66581,66587,66589,66591],{},[2884,66582,66583,66585],{},[898,66584,6796],{},[2111,66586,2963],{},[1711,66588,1836],{},[1711,66590,2460],{},[2111,66592,6262],{},[902,66594,66595],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,66598,66600],{"className":66599},[886],[888,66601,66602],{"xmlns":890},[892,66603,66604,66644],{},[895,66605,66606,66608,66610,66612,66622,66624,66626,66628,66630,66638,66640,66642],{},[1711,66607,1714],{"stretchy":1713},[898,66609,8243],{},[898,66611,1940],{},[1716,66613,66614,66616],{},[1711,66615,1735],{"stretchy":1713},[895,66617,66618,66620],{},[1711,66619,5225],{"mathvariant":2287},[1711,66621,5225],{"mathvariant":2287},[1711,66623,1714],{"stretchy":1713},[2111,66625,6262],{},[1711,66627,1735],{"stretchy":1713},[1711,66629,1836],{},[2509,66631,66632],{"scriptlevel":2113,"displaystyle":1713},[2525,66633,66634,66636],{},[2111,66635,2238],{},[2111,66637,3034],{},[1711,66639,2123],{},[2111,66641,2113],{},[1711,66643,7978],{},[902,66645,66646],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,66649,66651],{"className":66650},[886],[888,66652,66653],{"xmlns":890},[892,66654,66655,66671],{},[895,66656,66657,66659,66661,66663,66665,66667,66669],{},[898,66658,8243],{},[898,66660,1940],{},[1711,66662,1714],{"stretchy":1713},[2111,66664,6262],{},[1711,66666,1735],{"stretchy":1713},[1711,66668,1836],{},[2111,66670,39842],{},[902,66672,66673],{"encoding":904},"AC(6) = 15",[724,66675,66676,66677,66703,66704,2062],{},"Pomocí principu: ",[883,66678,66680],{"className":66679},[886],[888,66681,66682],{"xmlns":890},[892,66683,66684,66700],{},[895,66685,66686,66688,66690,66692,66694,66696,66698],{},[898,66687,1790],{},[898,66689,1940],{},[1711,66691,1836],{},[2111,66693,2963],{},[898,66695,6796],{},[1711,66697,2095],{},[2111,66699,3034],{},[902,66701,66702],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,66705,66707],{"className":66706},[886],[888,66708,66709],{"xmlns":890},[892,66710,66711,66723],{},[895,66712,66713,66715,66717,66719,66721],{},[898,66714,8243],{},[898,66716,1940],{},[1711,66718,1836],{},[898,66720,1790],{},[898,66722,1940],{},[902,66724,58821],{"encoding":904},[883,66726,66728],{"className":66727},[886],[888,66729,66730],{"xmlns":890,"display":31664},[892,66731,66732,66834],{},[895,66733,66734,66756,66758,66760,66762,66764,66766,66768,66770,66772,66778,66780,66782,66784,66786,66788,66790,66792,66798,66800,66802,66804,66806,66808,66810,66816,66818,66820,66822,66824,66826,66828,66830,66832],{},[2525,66735,66736,66754],{},[895,66737,66738,66744,66746,66748,66750,66752],{},[1716,66739,66740,66742],{},[898,66741,6796],{},[2111,66743,2963],{},[1711,66745,2095],{},[2111,66747,3034],{},[898,66749,6796],{},[1711,66751,2095],{},[2111,66753,9549],{},[898,66755,6796],{},[1711,66757,1836],{},[2111,66759,2963],{},[898,66761,6796],{},[1711,66763,2095],{},[2111,66765,3034],{},[1942,66767,4699],{},[1711,66769,7978],{},[1942,66771,4699],{},[1716,66773,66774,66776],{},[898,66775,6796],{},[2111,66777,2963],{},[1711,66779,2095],{},[2111,66781,3034],{},[898,66783,6796],{},[1711,66785,2095],{},[2111,66787,9549],{},[1711,66789,1836],{},[2111,66791,2963],{},[1716,66793,66794,66796],{},[898,66795,6796],{},[2111,66797,2963],{},[1711,66799,2095],{},[2111,66801,3034],{},[898,66803,6796],{},[1942,66805,4699],{},[1711,66807,7978],{},[1942,66809,4699],{},[1716,66811,66812,66814],{},[898,66813,6796],{},[2111,66815,2963],{},[1711,66817,1836],{},[2111,66819,9549],{},[1942,66821,4699],{},[1711,66823,7978],{},[1942,66825,4699],{},[898,66827,6796],{},[1711,66829,1836],{},[2111,66831,6262],{},[1711,66833,1726],{"separator":1725},[902,66835,66836],{"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,",[724,66838,66839,66840,66878],{},"a ",[883,66841,66843],{"className":66842},[886],[888,66844,66845],{"xmlns":890},[892,66846,66847,66875],{},[895,66848,66849,66851,66853,66855,66857,66859,66861,66863,66865,66867,66869,66871,66873],{},[898,66850,8243],{},[898,66852,1940],{},[1711,66854,1714],{"stretchy":1713},[2111,66856,6262],{},[1711,66858,1735],{"stretchy":1713},[1711,66860,1836],{},[898,66862,1790],{},[898,66864,1940],{},[1711,66866,1714],{"stretchy":1713},[2111,66868,6262],{},[1711,66870,1735],{"stretchy":1713},[1711,66872,1836],{},[2111,66874,39842],{},[902,66876,66877],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,66880,66882],{"id":66881},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,66884,66885,66886,2062],{},"Analogicky pro ",[883,66887,66889],{"className":66888},[886],[888,66890,66891],{"xmlns":890},[892,66892,66893,66901],{},[895,66894,66895,66897,66899],{},[898,66896,8243],{},[898,66898,43937],{},[898,66900,1940],{},[902,66902,58909],{"encoding":904},[883,66904,66906],{"className":66905},[886],[888,66907,66908],{"xmlns":890,"display":31664},[892,66909,66910,66961],{},[24352,66911,66912],{"width":31669},[24357,66913,66914,66916,66954,66956],{},[24360,66915],{"width":31674},[24360,66917,66918],{},[895,66919,66920,66922,66924,66926,66928,66934,66936,66938,66940,66942,66944,66950,66952],{},[898,66921,8243],{},[898,66923,43937],{},[898,66925,1940],{},[1711,66927,1714],{"stretchy":1713},[2884,66929,66930,66932],{},[898,66931,6796],{},[2111,66933,2113],{},[1711,66935,1735],{"stretchy":1713},[1711,66937,1836],{},[898,66939,1790],{},[898,66941,1940],{},[1711,66943,1714],{"stretchy":1713},[2884,66945,66946,66948],{},[898,66947,6796],{},[2111,66949,2113],{},[1711,66951,1735],{"stretchy":1713},[898,66953,2186],{"mathvariant":2287},[24360,66955],{"width":31674},[24360,66957,66958],{},[1942,66959,66960],{},"(3.11)",[902,66962,66963],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[1921,66965,66966],{},[724,66967,66968,65644,66970],{},[883,66969,60042],{},[38,66971,66972,66973,66990],{},"V bodě minima průměrných variabilních nákladů se ",[883,66974,66976],{"className":66975},[886],[888,66977,66978],{"xmlns":890},[892,66979,66980,66988],{},[895,66981,66982,66984,66986],{},[898,66983,8243],{},[898,66985,43937],{},[898,66987,1940],{},[902,66989,58909],{"encoding":904}," rovnají mezním nákladům.",[724,66992,66993,66994,67016,67017,2186],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,66995,66997],{"className":66996},[886],[888,66998,66999],{"xmlns":890},[892,67000,67001,67013],{},[895,67002,67003,67009,67011],{},[2884,67004,67005,67007],{},[898,67006,6796],{},[2111,67008,2113],{},[1711,67010,1836],{},[2111,67012,56797],{},[902,67014,67015],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,67018,67020],{"className":67019},[886],[888,67021,67022],{"xmlns":890},[892,67023,67024,67050],{},[895,67025,67026,67028,67030,67032,67034,67036,67038,67040,67042,67044,67046,67048],{},[898,67027,8243],{},[898,67029,43937],{},[898,67031,1940],{},[1711,67033,1714],{"stretchy":1713},[898,67035,6796],{},[1711,67037,1735],{"stretchy":1713},[1711,67039,1836],{},[898,67041,1790],{},[898,67043,1940],{},[1711,67045,1714],{"stretchy":1713},[898,67047,6796],{},[1711,67049,1735],{"stretchy":1713},[902,67051,67052],{"encoding":904},"AVC(Q) = MC(Q)",[115,67054,67056],{"id":67055},"zisk-a-body-zvratu","Zisk a body zvratu",[724,67058,67059,1700,67062,67078],{},[38,67060,67061],{},"Zisk",[883,67063,67065],{"className":67064},[886],[888,67066,67067],{"xmlns":890},[892,67068,67069,67075],{},[895,67070,67071,67073],{},[898,67072,7929],{},[898,67074,7985],{},[902,67076,67077],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,67080,67082],{"className":67081},[886],[888,67083,67084],{"xmlns":890,"display":31664},[892,67085,67086,67145],{},[24352,67087,67088],{"width":31669},[24357,67089,67090,67092,67138,67140],{},[24360,67091],{"width":31674},[24360,67093,67094],{},[895,67095,67096,67098,67100,67102,67104,67106,67108,67110,67112,67114,67116,67118,67120,67122,67124,67126,67128,67130,67132,67134,67136],{},[898,67097,7929],{},[898,67099,7985],{},[1711,67101,1836],{},[898,67103,7929],{},[898,67105,7985],{},[1711,67107,1714],{"stretchy":1713},[898,67109,6796],{},[1711,67111,1735],{"stretchy":1713},[1711,67113,1836],{},[898,67115,1769],{},[898,67117,7985],{},[1711,67119,1714],{"stretchy":1713},[898,67121,6796],{},[1711,67123,1735],{"stretchy":1713},[1711,67125,2460],{},[898,67127,1769],{},[898,67129,1940],{},[1711,67131,1714],{"stretchy":1713},[898,67133,6796],{},[1711,67135,1735],{"stretchy":1713},[898,67137,2186],{"mathvariant":2287},[24360,67139],{"width":31674},[24360,67141,67142],{},[1942,67143,67144],{},"(3.12)",[902,67146,67147],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,67149,67150,67151,2009,67166,47234,67181,67183,67184,67187,67188,67204,67205,67220,67221,67236,67237,1343,67250,67263,67264,1343,67282,67300,67301,1648,67304,67307,67308,1348,67330,12082,67352,67374,67375,12082,67405,67427],{},"Body rovnosti ",[883,67152,67154],{"className":67153},[886],[888,67155,67156],{"xmlns":890},[892,67157,67158,67164],{},[895,67159,67160,67162],{},[898,67161,1769],{},[898,67163,7985],{},[902,67165,8085],{"encoding":904},[883,67167,67169],{"className":67168},[886],[888,67170,67171],{"xmlns":890},[892,67172,67173,67179],{},[895,67174,67175,67177],{},[898,67176,1769],{},[898,67178,1940],{},[902,67180,7241],{"encoding":904},[38,67182,59325],{}," (též vyrovnání, ",[614,67185,67186],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,67189,67191],{"className":67190},[886],[888,67192,67193],{"xmlns":890},[892,67194,67195,67201],{},[895,67196,67197,67199],{},[898,67198,43937],{},[898,67200,1940],{},[902,67202,67203],{"encoding":904},"VC",") je ",[883,67206,67208],{"className":67207},[886],[888,67209,67210],{"xmlns":890},[892,67211,67212,67218],{},[895,67213,67214,67216],{},[898,67215,1769],{},[898,67217,7985],{},[902,67219,8085],{"encoding":904}," kvadratická a ",[883,67222,67224],{"className":67223},[886],[888,67225,67226],{"xmlns":890},[892,67227,67228,67234],{},[895,67229,67230,67232],{},[898,67231,1769],{},[898,67233,1940],{},[902,67235,7241],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,67238,67240],{"className":67239},[886],[888,67241,67242],{"xmlns":890},[892,67243,67244,67248],{},[895,67245,67246],{},[898,67247,8243],{},[902,67249,8243],{"encoding":904},[883,67251,67253],{"className":67252},[886],[888,67254,67255],{"xmlns":890},[892,67256,67257,67261],{},[895,67258,67259],{},[898,67260,26851],{},[902,67262,26851],{"encoding":904}," odpovídajících množstvím ",[883,67265,67267],{"className":67266},[886],[888,67268,67269],{"xmlns":890},[892,67270,67271,67279],{},[895,67272,67273],{},[2884,67274,67275,67277],{},[898,67276,6796],{},[898,67278,8243],{},[902,67280,67281],{"encoding":904},"Q_A",[883,67283,67285],{"className":67284},[886],[888,67286,67287],{"xmlns":890},[892,67288,67289,67297],{},[895,67290,67291],{},[2884,67292,67293,67295],{},[898,67294,6796],{},[898,67296,26851],{},[902,67298,67299],{"encoding":904},"Q_B"," — firma je na ",[38,67302,67303],{},"prahu rentability",[614,67305,67306],{},"break even","). Pro ",[883,67309,67311],{"className":67310},[886],[888,67312,67313],{"xmlns":890},[892,67314,67315,67327],{},[895,67316,67317,67319,67321],{},[898,67318,6796],{},[1711,67320,2109],{},[2884,67322,67323,67325],{},[898,67324,6796],{},[898,67326,8243],{},[902,67328,67329],{"encoding":904},"Q \u003C Q_A",[883,67331,67333],{"className":67332},[886],[888,67334,67335],{"xmlns":890},[892,67336,67337,67349],{},[895,67338,67339,67341,67343],{},[898,67340,6796],{},[1711,67342,2123],{},[2884,67344,67345,67347],{},[898,67346,6796],{},[898,67348,26851],{},[902,67350,67351],{"encoding":904},"Q > Q_B",[883,67353,67355],{"className":67354},[886],[888,67356,67357],{"xmlns":890},[892,67358,67359,67371],{},[895,67360,67361,67363,67365,67367,67369],{},[898,67362,1769],{},[898,67364,1940],{},[1711,67366,2123],{},[898,67368,1769],{},[898,67370,7985],{},[902,67372,67373],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,67376,67378],{"className":67377},[886],[888,67379,67380],{"xmlns":890},[892,67381,67382,67402],{},[895,67383,67384,67390,67392,67394,67396],{},[2884,67385,67386,67388],{},[898,67387,6796],{},[898,67389,8243],{},[1711,67391,2109],{},[898,67393,6796],{},[1711,67395,2109],{},[2884,67397,67398,67400],{},[898,67399,6796],{},[898,67401,26851],{},[902,67403,67404],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,67406,67408],{"className":67407},[886],[888,67409,67410],{"xmlns":890},[892,67411,67412,67424],{},[895,67413,67414,67416,67418,67420,67422],{},[898,67415,1769],{},[898,67417,7985],{},[1711,67419,2123],{},[898,67421,1769],{},[898,67423,1940],{},[902,67425,67426],{"encoding":904},"TR > TC"," (zisk).",[1921,67429,67430],{},[724,67431,67432,67434],{},[883,67433,2678],{}," 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.",[724,67436,67437,67438,67464],{},"Body zvratu jsou řešení rovnice ",[883,67439,67441],{"className":67440},[886],[888,67442,67443],{"xmlns":890},[892,67444,67445,67461],{},[895,67446,67447,67449,67451,67453,67455,67457,67459],{},[898,67448,7929],{},[898,67450,7985],{},[1711,67452,1714],{"stretchy":1713},[898,67454,6796],{},[1711,67456,1735],{"stretchy":1713},[1711,67458,1836],{},[2111,67460,2113],{},[902,67462,67463],{"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.",[724,67466,67467],{},[1801,67468],{"alt":67469,"className":67470,"src":67471},"imek-tr-tc-body-zvratu",[210,1805],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,67473,67474],{},[614,67475,67476,67477,67492,67493,67508,67509,2009,67522,46958,67535,67548,67549,2009,67566,67583,67584,67604,67605,2009,67620,10454,67635,67664],{},"Obrázek 3.11: Body zvratu — křivky ",[883,67478,67480],{"className":67479},[886],[888,67481,67482],{"xmlns":890},[892,67483,67484,67490],{},[895,67485,67486,67488],{},[898,67487,1769],{},[898,67489,7985],{},[902,67491,8085],{"encoding":904}," (obrácená parabola) a ",[883,67494,67496],{"className":67495},[886],[888,67497,67498],{"xmlns":890},[892,67499,67500,67506],{},[895,67501,67502,67504],{},[898,67503,1769],{},[898,67505,1940],{},[902,67507,7241],{"encoding":904}," (přímka) se protínají v bodech ",[883,67510,67512],{"className":67511},[886],[888,67513,67514],{"xmlns":890},[892,67515,67516,67520],{},[895,67517,67518],{},[898,67519,8243],{},[902,67521,8243],{"encoding":904},[883,67523,67525],{"className":67524},[886],[888,67526,67527],{"xmlns":890},[892,67528,67529,67533],{},[895,67530,67531],{},[898,67532,26851],{},[902,67534,26851],{"encoding":904},[883,67536,67538],{"className":67537},[886],[888,67539,67540],{"xmlns":890},[892,67541,67542,67546],{},[895,67543,67544],{},[898,67545,6796],{},[902,67547,6796],{"encoding":904}," v hodnotách ",[883,67550,67552],{"className":67551},[886],[888,67553,67554],{"xmlns":890},[892,67555,67556,67564],{},[895,67557,67558],{},[2884,67559,67560,67562],{},[898,67561,6796],{},[898,67563,8243],{},[902,67565,67281],{"encoding":904},[883,67567,67569],{"className":67568},[886],[888,67570,67571],{"xmlns":890},[892,67572,67573,67581],{},[895,67574,67575],{},[2884,67576,67577,67579],{},[898,67578,6796],{},[898,67580,26851],{},[902,67582,67299],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,67585,67587],{"className":67586},[886],[888,67588,67589],{"xmlns":890},[892,67590,67591,67601],{},[895,67592,67593],{},[2884,67594,67595,67597,67599],{},[898,67596,6796],{},[898,67598,59795],{},[1711,67600,59798],{},[902,67602,67603],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,67606,67608],{"className":67607},[886],[888,67609,67610],{"xmlns":890},[892,67611,67612,67618],{},[895,67613,67614,67616],{},[898,67615,1769],{},[898,67617,7985],{},[902,67619,8085],{"encoding":904},[883,67621,67623],{"className":67622},[886],[888,67624,67625],{"xmlns":890},[892,67626,67627,67633],{},[895,67628,67629,67631],{},[898,67630,1769],{},[898,67632,1940],{},[902,67634,7241],{"encoding":904},[883,67636,67638],{"className":67637},[886],[888,67639,67640],{"xmlns":890},[892,67641,67642,67662],{},[895,67643,67644,67650,67652,67654,67656],{},[2884,67645,67646,67648],{},[898,67647,6796],{},[898,67649,8243],{},[1711,67651,2109],{},[898,67653,6796],{},[1711,67655,2109],{},[2884,67657,67658,67660],{},[898,67659,6796],{},[898,67661,26851],{},[902,67663,67404],{"encoding":904}," vyznačuje zisk.",[40946,67666,67668],{"id":67667},"příklad-38","Příklad 3.8",[724,67670,67671,67673,67674,1343,67694,1343,67720,67746],{},[38,67672,59585],{}," Dáno ",[883,67675,67677],{"className":67676},[886],[888,67678,67679],{"xmlns":890},[892,67680,67681,67691],{},[895,67682,67683,67685,67687,67689],{},[898,67684,14409],{},[898,67686,1940],{},[1711,67688,1836],{},[2111,67690,6369],{},[902,67692,67693],{"encoding":904},"FC = 4",[883,67695,67697],{"className":67696},[886],[888,67698,67699],{"xmlns":890},[892,67700,67701,67717],{},[895,67702,67703,67705,67707,67709,67711],{},[898,67704,1769],{},[898,67706,43937],{},[898,67708,1940],{},[1711,67710,1836],{},[1716,67712,67713,67715],{},[898,67714,6796],{},[2111,67716,2963],{},[902,67718,67719],{"encoding":904},"TVC = Q^2",[883,67721,67723],{"className":67722},[886],[888,67724,67725],{"xmlns":890},[892,67726,67727,67743],{},[895,67728,67729,67731,67733,67735,67737,67739,67741],{},[898,67730,7929],{},[1711,67732,1836],{},[1711,67734,2460],{},[2111,67736,2963],{},[898,67738,6796],{},[1711,67740,2095],{},[2111,67742,7990],{},[902,67744,67745],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,67748,67749,67751],{},[38,67750,26368],{}," Celkové náklady a příjem:",[883,67753,67755],{"className":67754},[886],[888,67756,67757],{"xmlns":890,"display":31664},[892,67758,67759,67825],{},[895,67760,67761,67763,67765,67767,67769,67771,67777,67779,67781,67783,67785,67787,67789,67791,67793,67795,67797,67799,67801,67803,67805,67807,67809,67811,67817,67819,67821,67823],{},[898,67762,1769],{},[898,67764,1940],{},[1711,67766,1836],{},[2111,67768,6369],{},[1711,67770,2095],{},[1716,67772,67773,67775],{},[898,67774,6796],{},[2111,67776,2963],{},[1711,67778,1726],{"separator":1725},[2102,67780],{"width":2104},[898,67782,1769],{},[898,67784,7985],{},[1711,67786,1836],{},[898,67788,6796],{},[1711,67790,4795],{},[1711,67792,1714],{"stretchy":1713},[1711,67794,2460],{},[2111,67796,2963],{},[898,67798,6796],{},[1711,67800,2095],{},[2111,67802,7990],{},[1711,67804,1735],{"stretchy":1713},[1711,67806,1836],{},[1711,67808,2460],{},[2111,67810,2963],{},[1716,67812,67813,67815],{},[898,67814,6796],{},[2111,67816,2963],{},[1711,67818,2095],{},[2111,67820,7990],{},[898,67822,6796],{},[898,67824,2186],{"mathvariant":2287},[902,67826,67827],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,67829,67830],{},"Zisk dle (3.12):",[883,67832,67834],{"className":67833},[886],[888,67835,67836],{"xmlns":890,"display":31664},[892,67837,67838,67916],{},[895,67839,67840,67842,67844,67846,67848,67850,67852,67854,67856,67858,67860,67862,67864,67870,67872,67874,67876,67878,67880,67882,67884,67886,67892,67894,67896,67898,67900,67906,67908,67910,67912,67914],{},[898,67841,7929],{},[898,67843,7985],{},[1711,67845,1836],{},[898,67847,1769],{},[898,67849,7985],{},[1711,67851,2460],{},[898,67853,1769],{},[898,67855,1940],{},[1711,67857,1836],{},[1711,67859,1714],{"stretchy":1713},[1711,67861,2460],{},[2111,67863,2963],{},[1716,67865,67866,67868],{},[898,67867,6796],{},[2111,67869,2963],{},[1711,67871,2095],{},[2111,67873,7990],{},[898,67875,6796],{},[1711,67877,1735],{"stretchy":1713},[1711,67879,2460],{},[1711,67881,1714],{"stretchy":1713},[2111,67883,6369],{},[1711,67885,2095],{},[1716,67887,67888,67890],{},[898,67889,6796],{},[2111,67891,2963],{},[1711,67893,1735],{"stretchy":1713},[1711,67895,1836],{},[1711,67897,2460],{},[2111,67899,3034],{},[1716,67901,67902,67904],{},[898,67903,6796],{},[2111,67905,2963],{},[1711,67907,2095],{},[2111,67909,7990],{},[898,67911,6796],{},[1711,67913,2460],{},[2111,67915,62917],{},[902,67917,67918],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,67920,67921,67924,67925,21174,67961,2062],{},[38,67922,67923],{},"Body zvratu"," jsou kořeny rovnice ",[883,67926,67928],{"className":67927},[886],[888,67929,67930],{"xmlns":890},[892,67931,67932,67958],{},[895,67933,67934,67936,67938,67944,67946,67948,67950,67952,67954,67956],{},[1711,67935,2460],{},[2111,67937,3034],{},[1716,67939,67940,67942],{},[898,67941,6796],{},[2111,67943,2963],{},[1711,67945,2095],{},[2111,67947,7990],{},[898,67949,6796],{},[1711,67951,2460],{},[2111,67953,6369],{},[1711,67955,1836],{},[2111,67957,2113],{},[902,67959,67960],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,67962,67964],{"className":67963},[886],[888,67965,67966],{"xmlns":890},[892,67967,67968,67992],{},[895,67969,67970,67972,67978,67980,67982,67984,67986,67988,67990],{},[2111,67971,3034],{},[1716,67973,67974,67976],{},[898,67975,6796],{},[2111,67977,2963],{},[1711,67979,2460],{},[2111,67981,7990],{},[898,67983,6796],{},[1711,67985,2095],{},[2111,67987,6369],{},[1711,67989,1836],{},[2111,67991,2113],{},[902,67993,67994],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,67996,67998],{"className":67997},[886],[888,67999,68000],{"xmlns":890,"display":31664},[892,68001,68002,68059],{},[895,68003,68004,68016,68018,68041,68043,68057],{},[2884,68005,68006,68008],{},[898,68007,6796],{},[895,68009,68010,68012,68014],{},[2111,68011,2238],{},[1711,68013,1726],{"separator":1725},[2111,68015,2963],{},[1711,68017,1836],{},[2525,68019,68020,68039],{},[895,68021,68022,68024,68027],{},[2111,68023,7990],{},[1711,68025,68026],{},"±",[12097,68028,68029],{},[895,68030,68031,68034,68036],{},[2111,68032,68033],{},"81",[1711,68035,2460],{},[2111,68037,68038],{},"48",[2111,68040,6262],{},[1711,68042,1836],{},[2525,68044,68045,68055],{},[895,68046,68047,68049,68051],{},[2111,68048,7990],{},[1711,68050,68026],{},[12097,68052,68053],{},[2111,68054,12929],{},[2111,68056,6262],{},[1711,68058,1726],{"separator":1725},[902,68060,68061],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,68063,68064,68065,2009,68088,2186],{},"numericky ",[883,68066,68068],{"className":68067},[886],[888,68069,68070],{"xmlns":890},[892,68071,68072,68085],{},[895,68073,68074,68080,68082],{},[2884,68075,68076,68078],{},[898,68077,6796],{},[2111,68079,2238],{},[1711,68081,9881],{},[2111,68083,68084],{},"0,543",[902,68086,68087],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,68089,68091],{"className":68090},[886],[888,68092,68093],{"xmlns":890},[892,68094,68095,68108],{},[895,68096,68097,68103,68105],{},[2884,68098,68099,68101],{},[898,68100,6796],{},[2111,68102,2963],{},[1711,68104,9881],{},[2111,68106,68107],{},"2,457",[902,68109,68110],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,68112,68113,1700,68116,11532,68161,21174,68195,68213],{},[38,68114,68115],{},"Maximum zisku.",[883,68117,68119],{"className":68118},[886],[888,68120,68121],{"xmlns":890},[892,68122,68123,68158],{},[895,68124,68125,68127,68133,68135,68137,68139,68141,68143,68145,68147,68149,68151,68153,68155],{},[898,68126,7929],{},[1716,68128,68129,68131],{},[898,68130,7985],{},[1711,68132,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,68134,1836],{},[1711,68136,2460],{},[2111,68138,6262],{},[898,68140,6796],{},[1711,68142,2095],{},[2111,68144,7990],{},[1711,68146,1836],{},[2111,68148,2113],{},[1711,68150,7978],{},[898,68152,6796],{},[1711,68154,1836],{},[2111,68156,68157],{},"1,5",[902,68159,68160],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,68162,68164],{"className":68163},[886],[888,68165,68166],{"xmlns":890},[892,68167,68168,68192],{},[895,68169,68170,68172,68182,68184,68186,68188,68190],{},[898,68171,7929],{},[1716,68173,68174,68176],{},[898,68175,7985],{},[895,68177,68178,68180],{},[1711,68179,5225],{"mathvariant":2287},[1711,68181,5225],{"mathvariant":2287},[1711,68183,1836],{},[1711,68185,2460],{},[2111,68187,6262],{},[1711,68189,2109],{},[2111,68191,2113],{},[902,68193,68194],{"encoding":904},"PR'' = -6 \u003C 0",[883,68196,68198],{"className":68197},[886],[888,68199,68200],{"xmlns":890},[892,68201,68202,68210],{},[895,68203,68204,68206,68208],{},[898,68205,6796],{},[1711,68207,1836],{},[2111,68209,68157],{},[902,68211,68212],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,68215,68217],{"className":68216},[886],[888,68218,68219],{"xmlns":890,"display":31664},[892,68220,68221,68284],{},[895,68222,68223,68225,68227,68229,68231,68233,68235,68237,68239,68241,68243,68245,68251,68253,68255,68257,68259,68261,68263,68265,68267,68270,68272,68275,68277,68279,68281],{},[898,68224,7929],{},[898,68226,7985],{},[1711,68228,1714],{"stretchy":1713},[2111,68230,68157],{},[1711,68232,1735],{"stretchy":1713},[1711,68234,1836],{},[1711,68236,2460],{},[2111,68238,3034],{},[1711,68240,4795],{},[1711,68242,1714],{"stretchy":1713},[2111,68244,68157],{},[1716,68246,68247,68249],{},[1711,68248,1735],{"stretchy":1713},[2111,68250,2963],{},[1711,68252,2095],{},[2111,68254,7990],{},[1711,68256,4795],{},[2111,68258,68157],{},[1711,68260,2460],{},[2111,68262,6369],{},[1711,68264,1836],{},[1711,68266,2460],{},[2111,68268,68269],{},"6,75",[1711,68271,2095],{},[2111,68273,68274],{},"13,5",[1711,68276,2460],{},[2111,68278,6369],{},[1711,68280,1836],{},[2111,68282,68283],{},"2,75.",[902,68285,68286],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,68288,68289,68290,1343,68335,68388,68389,68407],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,68291,68293],{"className":68292},[886],[888,68294,68295],{"xmlns":890},[892,68296,68297,68332],{},[895,68298,68299,68301,68307,68309,68311,68313,68315,68317,68319,68321,68323,68325,68327,68329],{},[898,68300,1769],{},[1716,68302,68303,68305],{},[898,68304,7985],{},[1711,68306,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,68308,1836],{},[1711,68310,2460],{},[2111,68312,6369],{},[898,68314,6796],{},[1711,68316,2095],{},[2111,68318,7990],{},[1711,68320,1836],{},[2111,68322,2113],{},[1711,68324,7978],{},[898,68326,6796],{},[1711,68328,1836],{},[2111,68330,68331],{},"2,25",[902,68333,68334],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,68336,68338],{"className":68337},[886],[888,68339,68340],{"xmlns":890},[892,68341,68342,68385],{},[895,68343,68344,68346,68354,68356,68358,68360,68362,68364,68366,68372,68374,68376,68378,68380,68382],{},[898,68345,1769],{},[2884,68347,68348,68350,68352],{},[898,68349,7985],{},[898,68351,59795],{},[1711,68353,59798],{},[1711,68355,1836],{},[1711,68357,2460],{},[2111,68359,2963],{},[1711,68361,4795],{},[1711,68363,1714],{"stretchy":1713},[2111,68365,68331],{},[1716,68367,68368,68370],{},[1711,68369,1735],{"stretchy":1713},[2111,68371,2963],{},[1711,68373,2095],{},[2111,68375,7990],{},[1711,68377,4795],{},[2111,68379,68331],{},[1711,68381,1836],{},[2111,68383,68384],{},"10,125",[902,68386,68387],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,68390,68392],{"className":68391},[886],[888,68393,68394],{"xmlns":890},[892,68395,68396,68404],{},[895,68397,68398,68400,68402],{},[898,68399,6796],{},[1711,68401,1836],{},[2111,68403,68331],{},[902,68405,68406],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[1921,68409,68410],{},[724,68411,68412,68414,68415,1343,68437,68459,68460,1343,68477,68498,68499,68531,68532,68570,68571,6682,68589,68606,68607,2009,68635,68669,68670,11665,68708,2009,68732,2186],{},[883,68413,1927],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,68416,68418],{"className":68417},[886],[888,68419,68420],{"xmlns":890},[892,68421,68422,68434],{},[895,68423,68424,68430,68432],{},[2884,68425,68426,68428],{},[898,68427,6796],{},[2111,68429,2238],{},[1711,68431,1836],{},[2111,68433,8993],{},[902,68435,68436],{"encoding":904},"Q_1 = 0{,}5",[883,68438,68440],{"className":68439},[886],[888,68441,68442],{"xmlns":890},[892,68443,68444,68456],{},[895,68445,68446,68452,68454],{},[2884,68447,68448,68450],{},[898,68449,6796],{},[2111,68451,2963],{},[1711,68453,1836],{},[2111,68455,6369],{},[902,68457,68458],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,68461,68463],{"className":68462},[886],[888,68464,68465],{"xmlns":890},[892,68466,68467,68475],{},[895,68468,68469,68471,68473],{},[898,68470,6796],{},[1711,68472,1836],{},[2111,68474,68331],{},[902,68476,68406],{"encoding":904},[883,68478,68480],{"className":68479},[886],[888,68481,68482],{"xmlns":890},[892,68483,68484,68495],{},[895,68485,68486,68488,68490,68492],{},[898,68487,7929],{},[898,68489,7985],{},[1711,68491,1836],{},[2111,68493,68494],{},"6,125",[902,68496,68497],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,68500,68502],{"className":68501},[886],[888,68503,68504],{"xmlns":890},[892,68505,68506,68528],{},[895,68507,68508,68510,68516,68518,68520,68522,68524,68526],{},[898,68509,7929],{},[1716,68511,68512,68514],{},[898,68513,7985],{},[1711,68515,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,68517,1836],{},[1711,68519,2460],{},[2111,68521,6369],{},[898,68523,6796],{},[1711,68525,2095],{},[2111,68527,7990],{},[902,68529,68530],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,68533,68535],{"className":68534},[886],[888,68536,68537],{"xmlns":890},[892,68538,68539,68567],{},[895,68540,68541,68543,68545,68547,68549,68551,68557,68559,68561,68563,68565],{},[898,68542,7929],{},[898,68544,7985],{},[1711,68546,1836],{},[1711,68548,2460],{},[2111,68550,2963],{},[1716,68552,68553,68555],{},[898,68554,6796],{},[2111,68556,2963],{},[1711,68558,2095],{},[2111,68560,7990],{},[898,68562,6796],{},[1711,68564,2460],{},[2111,68566,6369],{},[902,68568,68569],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,68572,68574],{"className":68573},[886],[888,68575,68576],{"xmlns":890},[892,68577,68578,68586],{},[895,68579,68580],{},[1716,68581,68582,68584],{},[898,68583,6796],{},[2111,68585,2963],{},[902,68587,68588],{"encoding":904},"Q^2",[883,68590,68592],{"className":68591},[886],[888,68593,68594],{"xmlns":890},[892,68595,68596,68604],{},[895,68597,68598,68600,68602],{},[898,68599,1769],{},[898,68601,43937],{},[898,68603,1940],{},[902,68605,59107],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,68608,68610],{"className":68609},[886],[888,68611,68612],{"xmlns":890},[892,68613,68614,68632],{},[895,68615,68616,68618,68620,68622,68624,68626],{},[898,68617,1769],{},[898,68619,1940],{},[1711,68621,1836],{},[2111,68623,6369],{},[1711,68625,2095],{},[1716,68627,68628,68630],{},[898,68629,6796],{},[2111,68631,2963],{},[902,68633,68634],{"encoding":904},"TC = 4 + Q^2",[883,68636,68638],{"className":68637},[886],[888,68639,68640],{"xmlns":890},[892,68641,68642,68666],{},[895,68643,68644,68646,68648,68650,68652,68654,68660,68662,68664],{},[898,68645,1769],{},[898,68647,7985],{},[1711,68649,1836],{},[1711,68651,2460],{},[2111,68653,2963],{},[1716,68655,68656,68658],{},[898,68657,6796],{},[2111,68659,2963],{},[1711,68661,2095],{},[2111,68663,7990],{},[898,68665,6796],{},[902,68667,68668],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,68671,68673],{"className":68672},[886],[888,68674,68675],{"xmlns":890},[892,68676,68677,68705],{},[895,68678,68679,68681,68683,68685,68687,68689,68695,68697,68699,68701,68703],{},[898,68680,7929],{},[898,68682,7985],{},[1711,68684,1836],{},[1711,68686,2460],{},[2111,68688,3034],{},[1716,68690,68691,68693],{},[898,68692,6796],{},[2111,68694,2963],{},[1711,68696,2095],{},[2111,68698,7990],{},[898,68700,6796],{},[1711,68702,2460],{},[2111,68704,6369],{},[902,68706,68707],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,68709,68711],{"className":68710},[886],[888,68712,68713],{"xmlns":890},[892,68714,68715,68729],{},[895,68716,68717,68725,68727],{},[2884,68718,68719,68721,68723],{},[898,68720,6796],{},[898,68722,59795],{},[1711,68724,59798],{},[1711,68726,1836],{},[2111,68728,68157],{},[902,68730,68731],{"encoding":904},"Q_{\\max} = 1{,}5",[883,68733,68735],{"className":68734},[886],[888,68736,68737],{"xmlns":890},[892,68738,68739,68756],{},[895,68740,68741,68743,68751,68753],{},[898,68742,7929],{},[2884,68744,68745,68747,68749],{},[898,68746,7985],{},[898,68748,59795],{},[1711,68750,59798],{},[1711,68752,1836],{},[2111,68754,68755],{},"2,75",[902,68757,68758],{"encoding":904},"PR_{\\max} = 2{,}75",[724,68760,68761],{},[614,68762,68763,68764,68791,68792,68825,68826,1343,68849,2186],{},"Obrázek 3.12: Graf ",[883,68765,68767],{"className":68766},[886],[888,68768,68769],{"xmlns":890},[892,68770,68771,68789],{},[895,68772,68773,68775,68777,68779,68781,68783],{},[898,68774,1769],{},[898,68776,1940],{},[1711,68778,1836],{},[2111,68780,6369],{},[1711,68782,2095],{},[1716,68784,68785,68787],{},[898,68786,6796],{},[2111,68788,2963],{},[902,68790,68634],{"encoding":904}," (parabola) a ",[883,68793,68795],{"className":68794},[886],[888,68796,68797],{"xmlns":890},[892,68798,68799,68823],{},[895,68800,68801,68803,68805,68807,68809,68811,68817,68819,68821],{},[898,68802,1769],{},[898,68804,7985],{},[1711,68806,1836],{},[1711,68808,2460],{},[2111,68810,2963],{},[1716,68812,68813,68815],{},[898,68814,6796],{},[2111,68816,2963],{},[1711,68818,2095],{},[2111,68820,7990],{},[898,68822,6796],{},[902,68824,68668],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,68827,68829],{"className":68828},[886],[888,68830,68831],{"xmlns":890},[892,68832,68833,68846],{},[895,68834,68835,68841,68843],{},[2884,68836,68837,68839],{},[898,68838,6796],{},[2111,68840,2238],{},[1711,68842,9881],{},[2111,68844,68845],{},"0,54",[902,68847,68848],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,68850,68852],{"className":68851},[886],[888,68853,68854],{"xmlns":890},[892,68855,68856,68869],{},[895,68857,68858,68864,68866],{},[2884,68859,68860,68862],{},[898,68861,6796],{},[2111,68863,2963],{},[1711,68865,9881],{},[2111,68867,68868],{},"2,46",[902,68870,68871],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,68873,68874],{},[614,68875,68876,68877,62105,68914,68931,68932,1343,68953,2186],{},"Obrázek 3.13: Graf zisku ",[883,68878,68880],{"className":68879},[886],[888,68881,68882],{"xmlns":890},[892,68883,68884,68912],{},[895,68885,68886,68888,68890,68892,68894,68896,68902,68904,68906,68908,68910],{},[898,68887,7929],{},[898,68889,7985],{},[1711,68891,1836],{},[1711,68893,2460],{},[2111,68895,3034],{},[1716,68897,68898,68900],{},[898,68899,6796],{},[2111,68901,2963],{},[1711,68903,2095],{},[2111,68905,7990],{},[898,68907,6796],{},[1711,68909,2460],{},[2111,68911,6369],{},[902,68913,68707],{"encoding":904},[883,68915,68917],{"className":68916},[886],[888,68918,68919],{"xmlns":890},[892,68920,68921,68929],{},[895,68922,68923,68925,68927],{},[898,68924,6796],{},[1711,68926,1836],{},[2111,68928,68157],{},[902,68930,68212],{"encoding":904}," a nulami ",[883,68933,68935],{"className":68934},[886],[888,68936,68937],{"xmlns":890},[892,68938,68939,68951],{},[895,68940,68941,68947,68949],{},[2884,68942,68943,68945],{},[898,68944,6796],{},[2111,68946,2238],{},[1711,68948,9881],{},[2111,68950,68845],{},[902,68952,68848],{"encoding":904},[883,68954,68956],{"className":68955},[886],[888,68957,68958],{"xmlns":890},[892,68959,68960,68972],{},[895,68961,68962,68968,68970],{},[2884,68963,68964,68966],{},[898,68965,6796],{},[2111,68967,2963],{},[1711,68969,9881],{},[2111,68971,68868],{},[902,68973,68871],{"encoding":904},[115,68975,68977],{"id":68976},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,68979,68980],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,68982,68983],{},[1801,68984],{"alt":68985,"className":68986,"src":68987},"imek-max-zisku-dva-pohledy",[210,1805],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,68989,20010],{"id":68990},"princip-1",[724,68992,68993,68994,6635,69009,69026],{},"Má-li zisk ",[883,68995,68997],{"className":68996},[886],[888,68998,68999],{"xmlns":890},[892,69000,69001,69007],{},[895,69002,69003,69005],{},[898,69004,7929],{},[898,69006,7985],{},[902,69008,67077],{"encoding":904},[883,69010,69012],{"className":69011},[886],[888,69013,69014],{"xmlns":890},[892,69015,69016,69024],{},[895,69017,69018],{},[2884,69019,69020,69022],{},[898,69021,6796],{},[2111,69023,2113],{},[902,69025,41906],{"encoding":904}," maximum, pak platí",[883,69028,69030],{"className":69029},[886],[888,69031,69032],{"xmlns":890,"display":31664},[892,69033,69034,69083],{},[24352,69035,69036],{"width":31669},[24357,69037,69038,69040,69076,69078],{},[24360,69039],{"width":31674},[24360,69041,69042],{},[895,69043,69044,69046,69048,69050,69056,69058,69060,69062,69064,69066,69072,69074],{},[898,69045,1790],{},[898,69047,7985],{},[1711,69049,1714],{"stretchy":1713},[2884,69051,69052,69054],{},[898,69053,6796],{},[2111,69055,2113],{},[1711,69057,1735],{"stretchy":1713},[1711,69059,1836],{},[898,69061,1790],{},[898,69063,1940],{},[1711,69065,1714],{"stretchy":1713},[2884,69067,69068,69070],{},[898,69069,6796],{},[2111,69071,2113],{},[1711,69073,1735],{"stretchy":1713},[898,69075,2186],{"mathvariant":2287},[24360,69077],{"width":31674},[24360,69079,69080],{},[1942,69081,69082],{},"(3.13)",[902,69084,69085],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[1921,69087,69088],{},[724,69089,69090,65644,69092],{},[883,69091,60042],{},[38,69093,69094],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,69096,69097,69100,69101,12082,69128,21174,69202,2186],{},[38,69098,69099],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,69102,69104],{"className":69103},[886],[888,69105,69106],{"xmlns":890},[892,69107,69108,69126],{},[895,69109,69110,69112,69114,69116,69118,69120,69122,69124],{},[898,69111,7929],{},[898,69113,7985],{},[1711,69115,1836],{},[898,69117,1769],{},[898,69119,7985],{},[1711,69121,2460],{},[898,69123,1769],{},[898,69125,1940],{},[902,69127,58798],{"encoding":904},[883,69129,69131],{"className":69130},[886],[888,69132,69133],{"xmlns":890},[892,69134,69135,69199],{},[895,69136,69137,69139,69145,69147,69153,69155,69157,69159,69165,69167,69173,69175,69177,69179,69185,69187,69193,69195,69197],{},[898,69138,7929],{},[1716,69140,69141,69143],{},[898,69142,7985],{},[1711,69144,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,69146,1714],{"stretchy":1713},[2884,69148,69149,69151],{},[898,69150,6796],{},[2111,69152,2113],{},[1711,69154,1735],{"stretchy":1713},[1711,69156,1836],{},[898,69158,1769],{},[1716,69160,69161,69163],{},[898,69162,7985],{},[1711,69164,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,69166,1714],{"stretchy":1713},[2884,69168,69169,69171],{},[898,69170,6796],{},[2111,69172,2113],{},[1711,69174,1735],{"stretchy":1713},[1711,69176,2460],{},[898,69178,1769],{},[1716,69180,69181,69183],{},[898,69182,1940],{},[1711,69184,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,69186,1714],{"stretchy":1713},[2884,69188,69189,69191],{},[898,69190,6796],{},[2111,69192,2113],{},[1711,69194,1735],{"stretchy":1713},[1711,69196,1836],{},[2111,69198,2113],{},[902,69200,69201],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,69203,69205],{"className":69204},[886],[888,69206,69207],{"xmlns":890},[892,69208,69209,69241],{},[895,69210,69211,69213,69215,69217,69223,69225,69227,69229,69231,69233,69239],{},[898,69212,1790],{},[898,69214,7985],{},[1711,69216,1714],{"stretchy":1713},[2884,69218,69219,69221],{},[898,69220,6796],{},[2111,69222,2113],{},[1711,69224,1735],{"stretchy":1713},[1711,69226,1836],{},[898,69228,1790],{},[898,69230,1940],{},[1711,69232,1714],{"stretchy":1713},[2884,69234,69235,69237],{},[898,69236,6796],{},[2111,69238,2113],{},[1711,69240,1735],{"stretchy":1713},[902,69242,69243],{"encoding":904},"MR(Q_0) = MC(Q_0)",[1921,69245,69246,69251],{},[724,69247,69248,69250],{},[883,69249,3872],{}," Postup — jak najít maximum zisku",[152,69252,69253,69317,69372,69409,69437],{},[123,69254,69255,69256,2009,69271,69286,69287,1797],{},"Sestavte ",[883,69257,69259],{"className":69258},[886],[888,69260,69261],{"xmlns":890},[892,69262,69263,69269],{},[895,69264,69265,69267],{},[898,69266,1769],{},[898,69268,7985],{},[902,69270,8085],{"encoding":904},[883,69272,69274],{"className":69273},[886],[888,69275,69276],{"xmlns":890},[892,69277,69278,69284],{},[895,69279,69280,69282],{},[898,69281,1769],{},[898,69283,1940],{},[902,69285,7241],{"encoding":904}," ze zadání (typicky ",[883,69288,69290],{"className":69289},[886],[888,69291,69292],{"xmlns":890},[892,69293,69294,69314],{},[895,69295,69296,69298,69300,69302,69304,69306,69308,69310,69312],{},[898,69297,1769],{},[898,69299,7985],{},[1711,69301,1836],{},[898,69303,7929],{},[1711,69305,1714],{"stretchy":1713},[898,69307,6796],{},[1711,69309,1735],{"stretchy":1713},[1711,69311,4795],{},[898,69313,6796],{},[902,69315,69316],{"encoding":904},"TR = P(Q) \\cdot Q",[123,69318,69319,69320,2009,69346,2186],{},"Vypočtěte ",[883,69321,69323],{"className":69322},[886],[888,69324,69325],{"xmlns":890},[892,69326,69327,69343],{},[895,69328,69329,69331,69333,69335,69337],{},[898,69330,1790],{},[898,69332,7985],{},[1711,69334,1836],{},[898,69336,1769],{},[1716,69338,69339,69341],{},[898,69340,7985],{},[1711,69342,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,69344,69345],{"encoding":904},"MR = TR'",[883,69347,69349],{"className":69348},[886],[888,69350,69351],{"xmlns":890},[892,69352,69353,69369],{},[895,69354,69355,69357,69359,69361,69363],{},[898,69356,1790],{},[898,69358,1940],{},[1711,69360,1836],{},[898,69362,1769],{},[1716,69364,69365,69367],{},[898,69366,1940],{},[1711,69368,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,69370,69371],{"encoding":904},"MC = TC'",[123,69373,69374,69375,2186],{},"Řešte rovnici ",[883,69376,69378],{"className":69377},[886],[888,69379,69380],{"xmlns":890},[892,69381,69382,69406],{},[895,69383,69384,69386,69388,69390,69392,69394,69396,69398,69400,69402,69404],{},[898,69385,1790],{},[898,69387,7985],{},[1711,69389,1714],{"stretchy":1713},[898,69391,6796],{},[1711,69393,1735],{"stretchy":1713},[1711,69395,1836],{},[898,69397,1790],{},[898,69399,1940],{},[1711,69401,1714],{"stretchy":1713},[898,69403,6796],{},[1711,69405,1735],{"stretchy":1713},[902,69407,69408],{"encoding":904},"MR(Q) = MC(Q)",[123,69410,69411,69412,69436],{},"Ověřte druhou derivaci ",[883,69413,69415],{"className":69414},[886],[888,69416,69417],{"xmlns":890},[892,69418,69419,69433],{},[895,69420,69421,69423],{},[898,69422,7929],{},[1716,69424,69425,69427],{},[898,69426,7985],{},[895,69428,69429,69431],{},[1711,69430,5225],{"mathvariant":2287},[1711,69432,5225],{"mathvariant":2287},[902,69434,69435],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,69438,69439,69440,69467],{},"Dosaďte do ",[883,69441,69443],{"className":69442},[886],[888,69444,69445],{"xmlns":890},[892,69446,69447,69465],{},[895,69448,69449,69451,69453,69455,69457,69459,69461,69463],{},[898,69450,7929],{},[898,69452,7985],{},[1711,69454,1836],{},[898,69456,1769],{},[898,69458,7985],{},[1711,69460,2460],{},[898,69462,1769],{},[898,69464,1940],{},[902,69466,58798],{"encoding":904}," pro hodnotu maxima.",[40946,69469,69471],{"id":69470},"příklad-39","Příklad 3.9",[724,69473,69474,59586,69476,2009,69498,69534],{},[38,69475,59585],{},[883,69477,69479],{"className":69478},[886],[888,69480,69481],{"xmlns":890},[892,69482,69483,69495],{},[895,69484,69485,69487,69489,69491,69493],{},[898,69486,7929],{},[1711,69488,1836],{},[2111,69490,41617],{},[1711,69492,2460],{},[898,69494,6796],{},[902,69496,69497],{"encoding":904},"P = 30 - Q",[883,69499,69501],{"className":69500},[886],[888,69502,69503],{"xmlns":890},[892,69504,69505,69531],{},[895,69506,69507,69509,69511,69513,69515,69521,69523,69525,69527,69529],{},[898,69508,1769],{},[898,69510,1940],{},[1711,69512,1836],{},[2111,69514,8993],{},[1716,69516,69517,69519],{},[898,69518,6796],{},[2111,69520,2963],{},[1711,69522,2095],{},[2111,69524,6262],{},[898,69526,6796],{},[1711,69528,2095],{},[2111,69530,27799],{},[902,69532,69533],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,69536,69537,1700,69539,1343,69569,69607,69608,5494,69652,69686,69687,2186],{},[38,69538,26368],{},[883,69540,69542],{"className":69541},[886],[888,69543,69544],{"xmlns":890},[892,69545,69546,69566],{},[895,69547,69548,69550,69552,69554,69556,69558,69560],{},[898,69549,1769],{},[898,69551,7985],{},[1711,69553,1836],{},[2111,69555,41617],{},[898,69557,6796],{},[1711,69559,2460],{},[1716,69561,69562,69564],{},[898,69563,6796],{},[2111,69565,2963],{},[902,69567,69568],{"encoding":904},"TR = 30Q - Q^2",[883,69570,69572],{"className":69571},[886],[888,69573,69574],{"xmlns":890},[892,69575,69576,69604],{},[895,69577,69578,69580,69582,69584,69586,69588,69594,69596,69598,69600,69602],{},[898,69579,7929],{},[898,69581,7985],{},[1711,69583,1836],{},[1711,69585,2460],{},[2111,69587,68157],{},[1716,69589,69590,69592],{},[898,69591,6796],{},[2111,69593,2963],{},[1711,69595,2095],{},[2111,69597,45398],{},[898,69599,6796],{},[1711,69601,2460],{},[2111,69603,27799],{},[902,69605,69606],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,69609,69611],{"className":69610},[886],[888,69612,69613],{"xmlns":890},[892,69614,69615,69649],{},[895,69616,69617,69619,69625,69627,69629,69631,69633,69635,69637,69639,69641,69643,69645,69647],{},[898,69618,7929],{},[1716,69620,69621,69623],{},[898,69622,7985],{},[1711,69624,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,69626,1836],{},[1711,69628,2460],{},[2111,69630,3034],{},[898,69632,6796],{},[1711,69634,2095],{},[2111,69636,45398],{},[1711,69638,1836],{},[2111,69640,2113],{},[1711,69642,7978],{},[898,69644,6796],{},[1711,69646,1836],{},[2111,69648,9568],{},[902,69650,69651],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,69653,69655],{"className":69654},[886],[888,69656,69657],{"xmlns":890},[892,69658,69659,69683],{},[895,69660,69661,69663,69673,69675,69677,69679,69681],{},[898,69662,7929],{},[1716,69664,69665,69667],{},[898,69666,7985],{},[895,69668,69669,69671],{},[1711,69670,5225],{"mathvariant":2287},[1711,69672,5225],{"mathvariant":2287},[1711,69674,1836],{},[1711,69676,2460],{},[2111,69678,3034],{},[1711,69680,2109],{},[2111,69682,2113],{},[902,69684,69685],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,69688,69690],{"className":69689},[886],[888,69691,69692],{"xmlns":890},[892,69693,69694,69711],{},[895,69695,69696,69698,69700,69702,69704,69706,69708],{},[898,69697,7929],{},[898,69699,7985],{},[1711,69701,1714],{"stretchy":1713},[2111,69703,9568],{},[1711,69705,1735],{"stretchy":1713},[1711,69707,1836],{},[2111,69709,69710],{},"89",[902,69712,69713],{"encoding":904},"PR(8) = 89",[724,69715,69716,69717,1343,69743,5494,69767,69805],{},"Ověření principu: ",[883,69718,69720],{"className":69719},[886],[888,69721,69722],{"xmlns":890},[892,69723,69724,69740],{},[895,69725,69726,69728,69730,69732,69734,69736,69738],{},[898,69727,1790],{},[898,69729,7985],{},[1711,69731,1836],{},[2111,69733,41617],{},[1711,69735,2460],{},[2111,69737,2963],{},[898,69739,6796],{},[902,69741,69742],{"encoding":904},"MR = 30 - 2Q",[883,69744,69746],{"className":69745},[886],[888,69747,69748],{"xmlns":890},[892,69749,69750,69764],{},[895,69751,69752,69754,69756,69758,69760,69762],{},[898,69753,1790],{},[898,69755,1940],{},[1711,69757,1836],{},[898,69759,6796],{},[1711,69761,2095],{},[2111,69763,6262],{},[902,69765,69766],{"encoding":904},"MC = Q + 6",[883,69768,69770],{"className":69769},[886],[888,69771,69772],{"xmlns":890},[892,69773,69774,69802],{},[895,69775,69776,69778,69780,69782,69784,69786,69788,69790,69792,69794,69796,69798,69800],{},[898,69777,1790],{},[898,69779,7985],{},[1711,69781,1714],{"stretchy":1713},[2111,69783,9568],{},[1711,69785,1735],{"stretchy":1713},[1711,69787,1836],{},[2111,69789,26544],{},[1711,69791,1836],{},[898,69793,1790],{},[898,69795,1940],{},[1711,69797,1714],{"stretchy":1713},[2111,69799,9568],{},[1711,69801,1735],{"stretchy":1713},[902,69803,69804],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,69807,69808,69809,69842,69843,69860],{},"V řadě případů — má-li rovnice ",[883,69810,69812],{"className":69811},[886],[888,69813,69814],{"xmlns":890},[892,69815,69816,69840],{},[895,69817,69818,69820,69822,69824,69826,69828,69830,69832,69834,69836,69838],{},[898,69819,1790],{},[898,69821,7985],{},[1711,69823,1714],{"stretchy":1713},[898,69825,6796],{},[1711,69827,1735],{"stretchy":1713},[1711,69829,1836],{},[898,69831,1790],{},[898,69833,1940],{},[1711,69835,1714],{"stretchy":1713},[898,69837,6796],{},[1711,69839,1735],{"stretchy":1713},[902,69841,69408],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,69844,69846],{"className":69845},[886],[888,69847,69848],{"xmlns":890},[892,69849,69850,69858],{},[895,69851,69852],{},[2884,69853,69854,69856],{},[898,69855,6796],{},[2111,69857,2113],{},[902,69859,41906],{"encoding":904}," — není třeba provádět test druhé derivace.",[40946,69862,69864],{"id":69863},"příklad-310","Příklad 3.10",[724,69866,69867,69869,69870,69874,69875,69888,69889,69920],{},[38,69868,59585],{}," Firma vyrábí minipočítače v ",[207,69871,69873],{"className":69872,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,69876,69878],{"className":69877},[886],[888,69879,69880],{"xmlns":890},[892,69881,69882,69886],{},[895,69883,69884],{},[2111,69885,4888],{},[902,69887,4888],{"encoding":904}," EUR\u002Fks. ",[883,69890,69892],{"className":69891},[886],[888,69893,69894],{"xmlns":890},[892,69895,69896,69917],{},[895,69897,69898,69900,69902,69904,69906,69908,69911],{},[898,69899,1769],{},[898,69901,1940],{},[1711,69903,1836],{},[2111,69905,7120],{},[1711,69907,2095],{},[2111,69909,69910],{},"28",[1716,69912,69913,69915],{},[898,69914,6796],{},[2111,69916,2963],{},[902,69918,69919],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,69922,69923,1700,69925,1343,69947,1343,69967,69990],{},[38,69924,26368],{},[883,69926,69928],{"className":69927},[886],[888,69929,69930],{"xmlns":890},[892,69931,69932,69944],{},[895,69933,69934,69936,69938,69940,69942],{},[898,69935,1769],{},[898,69937,7985],{},[1711,69939,1836],{},[2111,69941,4888],{},[898,69943,6796],{},[902,69945,69946],{"encoding":904},"TR = 900Q",[883,69948,69950],{"className":69949},[886],[888,69951,69952],{"xmlns":890},[892,69953,69954,69964],{},[895,69955,69956,69958,69960,69962],{},[898,69957,1790],{},[898,69959,7985],{},[1711,69961,1836],{},[2111,69963,4888],{},[902,69965,69966],{"encoding":904},"MR = 900",[883,69968,69970],{"className":69969},[886],[888,69971,69972],{"xmlns":890},[892,69973,69974,69987],{},[895,69975,69976,69978,69980,69982,69985],{},[898,69977,1790],{},[898,69979,1940],{},[1711,69981,1836],{},[2111,69983,69984],{},"56",[898,69986,6796],{},[902,69988,69989],{"encoding":904},"MC = 56Q",". Z principu:",[883,69992,69994],{"className":69993},[886],[888,69995,69996],{"xmlns":890,"display":31664},[892,69997,69998,70040],{},[895,69999,70000,70002,70004,70006,70008,70010,70012,70014,70016,70018,70026,70028,70031,70033,70035,70037],{},[2111,70001,4888],{},[1711,70003,1836],{},[2111,70005,69984],{},[898,70007,6796],{},[1942,70009,4699],{},[1711,70011,7978],{},[1942,70013,4699],{},[898,70015,6796],{},[1711,70017,1836],{},[2509,70019,70020],{"scriptlevel":2113,"displaystyle":1713},[2525,70021,70022,70024],{},[2111,70023,4888],{},[2111,70025,69984],{},[1711,70027,9881],{},[2111,70029,70030],{},"16,07",[1942,70032,4699],{},[1711,70034,6740],{},[1942,70036,4699],{},[2111,70038,70039],{},"16.",[902,70041,70042],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,70044,70045,70046,2062],{},"Zisk při ",[883,70047,70049],{"className":70048},[886],[888,70050,70051],{"xmlns":890},[892,70052,70053,70061],{},[895,70054,70055,70057,70059],{},[898,70056,6796],{},[1711,70058,1836],{},[2111,70060,45460],{},[902,70062,70063],{"encoding":904},"Q = 16",[883,70065,70067],{"className":70066},[886],[888,70068,70069],{"xmlns":890,"display":31664},[892,70070,70071,70142],{},[895,70072,70073,70075,70077,70079,70081,70083,70085,70087,70089,70091,70093,70095,70097,70099,70101,70103,70109,70111,70113,70115,70117,70119,70121,70123,70125,70128,70130,70132,70134,70137,70140],{},[898,70074,7929],{},[898,70076,7985],{},[1711,70078,1714],{"stretchy":1713},[2111,70080,45460],{},[1711,70082,1735],{"stretchy":1713},[1711,70084,1836],{},[2111,70086,4888],{},[1711,70088,4795],{},[2111,70090,45460],{},[1711,70092,2460],{},[1711,70094,1714],{"stretchy":1713},[2111,70096,7120],{},[1711,70098,2095],{},[2111,70100,69910],{},[1711,70102,4795],{},[1716,70104,70105,70107],{},[2111,70106,45460],{},[2111,70108,2963],{},[1711,70110,1735],{"stretchy":1713},[1711,70112,1836],{},[2111,70114,26544],{},[1942,70116,2519],{},[2111,70118,23740],{},[1711,70120,2460],{},[2111,70122,27799],{},[1942,70124,2519],{},[2111,70126,70127],{},"218",[1711,70129,1836],{},[2111,70131,27799],{},[1942,70133,2519],{},[2111,70135,70136],{},"182",[1942,70138,70139],{}," EUR",[898,70141,2186],{"mathvariant":2287},[902,70143,70144],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,70146,70147],{},"Pro srovnání při původních 30 ks:",[883,70149,70151],{"className":70150},[886],[888,70152,70153],{"xmlns":890,"display":31664},[892,70154,70155,70220],{},[895,70156,70157,70159,70161,70163,70165,70167,70169,70171,70173,70175,70177,70179,70181,70183,70185,70187,70189,70191,70193,70196,70198,70200,70202,70204,70206,70208,70210,70212,70214,70216,70218],{},[898,70158,7929],{},[898,70160,7985],{},[1711,70162,1714],{"stretchy":1713},[2111,70164,41617],{},[1711,70166,1735],{"stretchy":1713},[1711,70168,1836],{},[2111,70170,4888],{},[1711,70172,4795],{},[2111,70174,41617],{},[1711,70176,2460],{},[1711,70178,1714],{"stretchy":1713},[2111,70180,7120],{},[1711,70182,2095],{},[2111,70184,69910],{},[1711,70186,4795],{},[2111,70188,4888],{},[1711,70190,1735],{"stretchy":1713},[1711,70192,1836],{},[2111,70194,70195],{},"27",[1942,70197,2519],{},[2111,70199,62680],{},[1711,70201,2460],{},[2111,70203,4372],{},[1942,70205,2519],{},[2111,70207,34341],{},[1711,70209,1836],{},[2111,70211,2238],{},[1942,70213,2519],{},[2111,70215,27341],{},[1942,70217,70139],{},[898,70219,2186],{"mathvariant":2287},[902,70221,70222],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,70224,70225,70228,70229,70247,70248,70266],{},[38,70226,70227],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,70230,70232],{"className":70231},[886],[888,70233,70234],{"xmlns":890},[892,70235,70236,70244],{},[895,70237,70238,70240,70242],{},[2111,70239,27799],{},[1942,70241,2519],{},[2111,70243,70136],{},[902,70245,70246],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,70249,70251],{"className":70250},[886],[888,70252,70253],{"xmlns":890},[892,70254,70255,70263],{},[895,70256,70257,70259,70261],{},[2111,70258,2238],{},[1942,70260,2519],{},[2111,70262,27341],{},[902,70264,70265],{"encoding":904},"1\\,750"," EUR.",[198,70268,70270],{"id":70269},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,70272,70273,70274,66168,70287,70311],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,70275,70277],{"className":70276},[886],[888,70278,70279],{"xmlns":890},[892,70280,70281,70285],{},[895,70282,70283],{},[898,70284,7929],{},[902,70286,7929],{"encoding":904},[883,70288,70290],{"className":70289},[886],[888,70291,70292],{"xmlns":890},[892,70293,70294,70308],{},[895,70295,70296,70298,70300,70302,70304,70306],{},[898,70297,1769],{},[898,70299,7985],{},[1711,70301,1836],{},[898,70303,7929],{},[1711,70305,4795],{},[898,70307,6796],{},[902,70309,70310],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,70313,70315],{"className":70314},[886],[888,70316,70317],{"xmlns":890,"display":31664},[892,70318,70319,70352],{},[24352,70320,70321],{"width":31669},[24357,70322,70323,70325,70345,70347],{},[24360,70324],{"width":31674},[24360,70326,70327],{},[895,70328,70329,70331,70333,70335,70337,70339,70341,70343],{},[898,70330,7929],{},[1711,70332,1836],{},[898,70334,1790],{},[898,70336,1940],{},[1711,70338,1714],{"stretchy":1713},[898,70340,6796],{},[1711,70342,1735],{"stretchy":1713},[898,70344,2186],{"mathvariant":2287},[24360,70346],{"width":31674},[24360,70348,70349],{},[1942,70350,70351],{},"(3.14)",[902,70353,70354],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,70356,70357,70358,2186],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,70359,70361],{"className":70360},[886],[888,70362,70363],{"xmlns":890},[892,70364,70365,70379],{},[895,70366,70367,70369],{},[898,70368,7929],{},[1716,70370,70371,70373],{},[898,70372,7985],{},[895,70374,70375,70377],{},[1711,70376,5225],{"mathvariant":2287},[1711,70378,5225],{"mathvariant":2287},[902,70380,69435],{"encoding":904},[40946,70382,70384],{"id":70383},"příklad-311","Příklad 3.11",[724,70386,70387,61120,70389,70436,70437,70455],{},[38,70388,59585],{},[883,70390,70392],{"className":70391},[886],[888,70393,70394],{"xmlns":890},[892,70395,70396,70433],{},[895,70397,70398,70400,70402,70404,70407,70413,70415,70417,70423,70425,70427,70429,70431],{},[898,70399,1769],{},[898,70401,1940],{},[1711,70403,1836],{},[2111,70405,70406],{},"0,04",[1716,70408,70409,70411],{},[898,70410,6796],{},[2111,70412,3034],{},[1711,70414,2460],{},[2111,70416,26143],{},[1716,70418,70419,70421],{},[898,70420,6796],{},[2111,70422,2963],{},[1711,70424,2095],{},[2111,70426,4712],{},[898,70428,6796],{},[1711,70430,2095],{},[2111,70432,4798],{},[902,70434,70435],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,70438,70440],{"className":70439},[886],[888,70441,70442],{"xmlns":890},[892,70443,70444,70452],{},[895,70445,70446,70448,70450],{},[898,70447,7929],{},[1711,70449,1836],{},[2111,70451,6369],{},[902,70453,70454],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,70457,70458,70460,70461,21174,70503,70537,70538,2062],{},[38,70459,26368],{}," Z (3.14): ",[883,70462,70464],{"className":70463},[886],[888,70465,70466],{"xmlns":890},[892,70467,70468,70500],{},[895,70469,70470,70472,70474,70476,70479,70485,70487,70490,70492,70494,70496,70498],{},[898,70471,1790],{},[898,70473,1940],{},[1711,70475,1836],{},[2111,70477,70478],{},"0,12",[1716,70480,70481,70483],{},[898,70482,6796],{},[2111,70484,2963],{},[1711,70486,2460],{},[2111,70488,70489],{},"1,8",[898,70491,6796],{},[1711,70493,2095],{},[2111,70495,4712],{},[1711,70497,1836],{},[2111,70499,6369],{},[902,70501,70502],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,70504,70506],{"className":70505},[886],[888,70507,70508],{"xmlns":890},[892,70509,70510,70534],{},[895,70511,70512,70514,70520,70522,70524,70526,70528,70530,70532],{},[2111,70513,70478],{},[1716,70515,70516,70518],{},[898,70517,6796],{},[2111,70519,2963],{},[1711,70521,2460],{},[2111,70523,70489],{},[898,70525,6796],{},[1711,70527,2095],{},[2111,70529,6262],{},[1711,70531,1836],{},[2111,70533,2113],{},[902,70535,70536],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,70539,70541],{"className":70540},[886],[888,70542,70543],{"xmlns":890},[892,70544,70545,70549],{},[895,70546,70547],{},[2111,70548,70478],{},[902,70550,70551],{"encoding":904},"0{,}12",[883,70553,70555],{"className":70554},[886],[888,70556,70557],{"xmlns":890,"display":31664},[892,70558,70559,70611],{},[895,70560,70561,70567,70569,70571,70573,70575,70577,70579,70581,70583,70585,70587,70593,70595,70597,70599,70601,70607,70609],{},[1716,70562,70563,70565],{},[898,70564,6796],{},[2111,70566,2963],{},[1711,70568,2460],{},[2111,70570,39842],{},[898,70572,6796],{},[1711,70574,2095],{},[2111,70576,7120],{},[1711,70578,1836],{},[2111,70580,2113],{},[1942,70582,4699],{},[1711,70584,7978],{},[1942,70586,4699],{},[2884,70588,70589,70591],{},[898,70590,6796],{},[2111,70592,2238],{},[1711,70594,1836],{},[2111,70596,4798],{},[1711,70598,1726],{"separator":1725},[1942,70600,4699],{},[2884,70602,70603,70605],{},[898,70604,6796],{},[2111,70606,2963],{},[1711,70608,1836],{},[2111,70610,22926],{},[902,70612,70613],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,70615,70616,70617,2062],{},"Dále ",[883,70618,70620],{"className":70619},[886],[888,70621,70622],{"xmlns":890},[892,70623,70624,70663],{},[895,70625,70626,70628,70638,70640,70642,70644,70650,70652,70654,70657,70659,70661],{},[898,70627,7929],{},[1716,70629,70630,70632],{},[898,70631,7985],{},[895,70633,70634,70636],{},[1711,70635,5225],{"mathvariant":2287},[1711,70637,5225],{"mathvariant":2287},[1711,70639,1836],{},[1711,70641,2460],{},[898,70643,1790],{},[1716,70645,70646,70648],{},[898,70647,1940],{},[1711,70649,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,70651,1836],{},[1711,70653,2460],{},[2111,70655,70656],{},"0,24",[898,70658,6796],{},[1711,70660,2095],{},[2111,70662,70489],{},[902,70664,70665],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,70667,70668,70718],{},[123,70669,70670,70714,70715,70717],{},[883,70671,70673],{"className":70672},[886],[888,70674,70675],{"xmlns":890},[892,70676,70677,70711],{},[895,70678,70679,70681,70691,70693,70695,70697,70699,70701,70703,70705,70707,70709],{},[898,70680,7929],{},[1716,70682,70683,70685],{},[898,70684,7985],{},[895,70686,70687,70689],{},[1711,70688,5225],{"mathvariant":2287},[1711,70690,5225],{"mathvariant":2287},[1711,70692,1714],{"stretchy":1713},[2111,70694,4798],{},[1711,70696,1735],{"stretchy":1713},[1711,70698,1836],{},[2111,70700,22919],{},[1711,70702,2123],{},[2111,70704,2113],{},[1942,70706,4699],{},[1711,70708,7978],{},[1942,70710,4699],{},[902,70712,70713],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,70716,7771],{}," zisku (minimalizace ztráty);",[123,70719,70720,70714,70766,70768],{},[883,70721,70723],{"className":70722},[886],[888,70724,70725],{"xmlns":890},[892,70726,70727,70763],{},[895,70728,70729,70731,70741,70743,70745,70747,70749,70751,70753,70755,70757,70759,70761],{},[898,70730,7929],{},[1716,70732,70733,70735],{},[898,70734,7985],{},[895,70736,70737,70739],{},[1711,70738,5225],{"mathvariant":2287},[1711,70740,5225],{"mathvariant":2287},[1711,70742,1714],{"stretchy":1713},[2111,70744,4712],{},[1711,70746,1735],{"stretchy":1713},[1711,70748,1836],{},[1711,70750,2460],{},[2111,70752,22919],{},[1711,70754,2109],{},[2111,70756,2113],{},[1942,70758,4699],{},[1711,70760,7978],{},[1942,70762,4699],{},[902,70764,70765],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,70767,7713],{}," zisku, avšak",[883,70770,70772],{"className":70771},[886],[888,70773,70774],{"xmlns":890,"display":31664},[892,70775,70776,70844],{},[895,70777,70778,70780,70782,70784,70786,70788,70790,70792,70794,70796,70798,70800,70802,70804,70806,70808,70810,70812,70814,70816,70818,70820,70822,70824,70826,70828,70830,70832,70834,70836,70838,70840,70842],{},[898,70779,7929],{},[898,70781,7985],{},[1711,70783,1714],{"stretchy":1713},[2111,70785,4712],{},[1711,70787,1735],{"stretchy":1713},[1711,70789,1836],{},[2111,70791,6369],{},[1711,70793,4795],{},[2111,70795,4712],{},[1711,70797,2460],{},[1711,70799,1714],{"stretchy":1713},[2111,70801,70406],{},[1711,70803,4795],{},[2111,70805,2238],{},[1942,70807,2519],{},[2111,70809,62680],{},[1711,70811,2460],{},[2111,70813,26143],{},[1711,70815,4795],{},[2111,70817,4282],{},[1711,70819,2095],{},[2111,70821,4282],{},[1711,70823,2095],{},[2111,70825,4798],{},[1711,70827,1735],{"stretchy":1713},[1711,70829,1836],{},[2111,70831,9195],{},[1711,70833,2460],{},[2111,70835,24778],{},[1711,70837,1836],{},[1711,70839,2460],{},[2111,70841,39842],{},[1711,70843,1726],{"separator":1725},[902,70845,70846],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,70848,70849,70850,2186],{},"tj. ztráta větší než ",[883,70851,70853],{"className":70852},[886],[888,70854,70855],{"xmlns":890},[892,70856,70857,70867],{},[895,70858,70859,70861,70863,70865],{},[898,70860,14409],{},[898,70862,1940],{},[1711,70864,1836],{},[2111,70866,4798],{},[902,70868,70869],{"encoding":904},"FC = 5",[724,70871,70872,70875,70876,70879,70880,2186],{},[38,70873,70874],{},"Závěr:"," firma by měla ",[38,70877,70878],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,70881,70883],{"className":70882},[886],[888,70884,70885],{"xmlns":890},[892,70886,70887,70897],{},[895,70888,70889,70891,70893,70895],{},[898,70890,14409],{},[898,70892,1940],{},[1711,70894,1836],{},[2111,70896,4798],{},[902,70898,70869],{"encoding":904},[115,70900,70902],{"id":70901},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,70904,70905,70906,70908,70909,70924,70925,70938,70939,70965,70966,70979,70980,70997,70998,6635,71015,71018,71019,71039,71040,71055,71056,2062],{},"Důležitým završením analýzy je konstrukce ",[38,70907,58873],{},". S nabízeným množstvím rostou mezní náklady ",[883,70910,70912],{"className":70911},[886],[888,70913,70914],{"xmlns":890},[892,70915,70916,70922],{},[895,70917,70918,70920],{},[898,70919,1790],{},[898,70921,1940],{},[902,70923,58890],{"encoding":904}," a tyto určují cenu ",[883,70926,70928],{"className":70927},[886],[888,70929,70930],{"xmlns":890},[892,70931,70932,70936],{},[895,70933,70934],{},[898,70935,7929],{},[902,70937,7929],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,70940,70942],{"className":70941},[886],[888,70943,70944],{"xmlns":890},[892,70945,70946,70962],{},[895,70947,70948,70950,70952,70954,70956,70958,70960],{},[898,70949,7929],{},[1711,70951,1836],{},[898,70953,1790],{},[898,70955,1940],{},[1711,70957,1714],{"stretchy":1713},[898,70959,6796],{},[1711,70961,1735],{"stretchy":1713},[902,70963,70964],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,70967,70969],{"className":70968},[886],[888,70970,70971],{"xmlns":890},[892,70972,70973,70977],{},[895,70974,70975],{},[898,70976,7929],{},[902,70978,7929],{"encoding":904}," však nemůže být nižší než ",[883,70981,70983],{"className":70982},[886],[888,70984,70985],{"xmlns":890},[892,70986,70987,70995],{},[895,70988,70989],{},[1716,70990,70991,70993],{},[898,70992,7929],{},[1711,70994,1793],{},[902,70996,8391],{"encoding":904}," odpovídající množství ",[883,70999,71001],{"className":71000},[886],[888,71002,71003],{"xmlns":890},[892,71004,71005,71013],{},[895,71006,71007],{},[1716,71008,71009,71011],{},[898,71010,6796],{},[1711,71012,1793],{},[902,71014,33442],{"encoding":904},[38,71016,71017],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,71020,71022],{"className":71021},[886],[888,71023,71024],{"xmlns":890},[892,71025,71026,71036],{},[895,71027,71028,71030],{},[2111,71029,2113],{},[1716,71031,71032,71034],{},[898,71033,6796],{},[1711,71035,1793],{},[902,71037,71038],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,71041,71043],{"className":71042},[886],[888,71044,71045],{"xmlns":890},[892,71046,71047,71053],{},[895,71048,71049,71051],{},[898,71050,1790],{},[898,71052,1940],{},[902,71054,58890],{"encoding":904}," nad bodem ",[883,71057,71059],{"className":71058},[886],[888,71060,71061],{"xmlns":890},[892,71062,71063,71067],{},[895,71064,71065],{},[898,71066,8243],{},[902,71068,8243],{"encoding":904},[883,71070,71072],{"className":71071},[886],[888,71073,71074],{"xmlns":890,"display":31664},[892,71075,71076,71183],{},[24352,71077,71078],{"width":31669},[24357,71079,71080,71082,71176,71178],{},[24360,71081],{"width":31674},[24360,71083,71084],{},[895,71085,71086,71088,71090,71092,71094,71096,71098,71100],{},[898,71087,7929],{},[1711,71089,1836],{},[898,71091,2362],{},[1711,71093,1714],{"stretchy":1713},[898,71095,6796],{},[1711,71097,1735],{"stretchy":1713},[1711,71099,1836],{},[895,71101,71102,71105],{},[1711,71103,71104],{"fence":1725},"{",[24352,71106,71109,71148],{"rowspacing":71107,"columnalign":71108,"columnspacing":4981},"0.36em","left left",[24357,71110,71111,71127],{},[24360,71112,71113],{},[2509,71114,71115],{"scriptlevel":2113,"displaystyle":1713},[895,71116,71117,71119,71121,71123,71125],{},[898,71118,1790],{},[898,71120,1940],{},[1711,71122,1714],{"stretchy":1713},[898,71124,6796],{},[1711,71126,1735],{"stretchy":1713},[24360,71128,71129],{},[2509,71130,71131],{"scriptlevel":2113,"displaystyle":1713},[895,71132,71133,71136,71138,71140,71146],{},[1942,71134,71135],{},"pro ",[898,71137,6796],{},[1711,71139,8471],{},[1716,71141,71142,71144],{},[898,71143,6796],{},[1711,71145,1793],{},[1711,71147,1726],{"separator":1725},[24357,71149,71150,71156],{},[24360,71151,71152],{},[2509,71153,71154],{"scriptlevel":2113,"displaystyle":1713},[2111,71155,2113],{},[24360,71157,71158],{},[2509,71159,71160],{"scriptlevel":2113,"displaystyle":1713},[895,71161,71162,71164,71166,71168,71174],{},[1942,71163,71135],{},[898,71165,6796],{},[1711,71167,2109],{},[1716,71169,71170,71172],{},[898,71171,6796],{},[1711,71173,1793],{},[1711,71175,1726],{"separator":1725},[24360,71177],{"width":31674},[24360,71179,71180],{},[1942,71181,71182],{},"(3.15)",[902,71184,71185],{"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}",[724,71187,8298,71188,71205,71206,71223,71224,45097,71254,71257],{},[883,71189,71191],{"className":71190},[886],[888,71192,71193],{"xmlns":890},[892,71194,71195,71203],{},[895,71196,71197],{},[1716,71198,71199,71201],{},[898,71200,6796],{},[1711,71202,1793],{},[902,71204,33442],{"encoding":904}," je bod minima ",[883,71207,71209],{"className":71208},[886],[888,71210,71211],{"xmlns":890},[892,71212,71213,71221],{},[895,71214,71215,71217,71219],{},[898,71216,8243],{},[898,71218,43937],{},[898,71220,1940],{},[902,71222,58909],{"encoding":904},". Bod ",[883,71225,71227],{"className":71226},[886],[888,71228,71229],{"xmlns":890},[892,71230,71231,71251],{},[895,71232,71233,71235,71241,71243,71249],{},[1711,71234,1714],{"stretchy":1713},[1716,71236,71237,71239],{},[898,71238,6796],{},[1711,71240,1793],{},[1711,71242,1726],{"separator":1725},[1716,71244,71245,71247],{},[898,71246,7929],{},[1711,71248,1793],{},[1711,71250,1735],{"stretchy":1713},[902,71252,71253],{"encoding":904},"(Q^*, P^*)",[38,71255,71256],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[1921,71259,71260,71265],{},[724,71261,71262,71264],{},[883,71263,3872],{}," Postup — jak odvodit nabídku firmy",[152,71266,71267,71316,71411,71466,71537],{},[123,71268,71269,71270,2009,71292,2186],{},"Ze zadaných nákladů určete ",[883,71271,71273],{"className":71272},[886],[888,71274,71275],{"xmlns":890},[892,71276,71277,71289],{},[895,71278,71279,71281,71283,71285,71287],{},[898,71280,1790],{},[898,71282,1940],{},[1711,71284,1714],{"stretchy":1713},[898,71286,6796],{},[1711,71288,1735],{"stretchy":1713},[902,71290,71291],{"encoding":904},"MC(Q)",[883,71293,71295],{"className":71294},[886],[888,71296,71297],{"xmlns":890},[892,71298,71299,71313],{},[895,71300,71301,71303,71305,71307,71309,71311],{},[898,71302,8243],{},[898,71304,43937],{},[898,71306,1940],{},[1711,71308,1714],{"stretchy":1713},[898,71310,6796],{},[1711,71312,1735],{"stretchy":1713},[902,71314,71315],{"encoding":904},"AVC(Q)",[123,71317,71318,71319,71336,71337,71354,71355,71387,71388,1797],{},"Najděte ",[883,71320,71322],{"className":71321},[886],[888,71323,71324],{"xmlns":890},[892,71325,71326,71334],{},[895,71327,71328],{},[1716,71329,71330,71332],{},[898,71331,6796],{},[1711,71333,1793],{},[902,71335,33442],{"encoding":904}," jako bod minima ",[883,71338,71340],{"className":71339},[886],[888,71341,71342],{"xmlns":890},[892,71343,71344,71352],{},[895,71345,71346,71348,71350],{},[898,71347,8243],{},[898,71349,43937],{},[898,71351,1940],{},[902,71353,58909],{"encoding":904}," (řešením ",[883,71356,71358],{"className":71357},[886],[888,71359,71360],{"xmlns":890},[892,71361,71362,71384],{},[895,71363,71364,71366,71368,71374,71376,71378,71380,71382],{},[898,71365,8243],{},[898,71367,43937],{},[1716,71369,71370,71372],{},[898,71371,1940],{},[1711,71373,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,71375,1714],{"stretchy":1713},[898,71377,6796],{},[1711,71379,1735],{"stretchy":1713},[1711,71381,1836],{},[2111,71383,2113],{},[902,71385,71386],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,71389,71391],{"className":71390},[886],[888,71392,71393],{"xmlns":890},[892,71394,71395,71409],{},[895,71396,71397,71399,71401,71403,71405,71407],{},[898,71398,8243],{},[898,71400,43937],{},[898,71402,1940],{},[1711,71404,1836],{},[898,71406,1790],{},[898,71408,1940],{},[902,71410,58846],{"encoding":904},[123,71412,69319,71413,71465],{},[883,71414,71416],{"className":71415},[886],[888,71417,71418],{"xmlns":890},[892,71419,71420,71462],{},[895,71421,71422,71428,71430,71432,71434,71436,71442,71444,71446,71448,71450,71452,71454,71460],{},[1716,71423,71424,71426],{},[898,71425,7929],{},[1711,71427,1793],{},[1711,71429,1836],{},[898,71431,1790],{},[898,71433,1940],{},[1711,71435,1714],{"stretchy":1713},[1716,71437,71438,71440],{},[898,71439,6796],{},[1711,71441,1793],{},[1711,71443,1735],{"stretchy":1713},[1711,71445,1836],{},[898,71447,8243],{},[898,71449,43937],{},[898,71451,1940],{},[1711,71453,1714],{"stretchy":1713},[1716,71455,71456,71458],{},[898,71457,6796],{},[1711,71459,1793],{},[1711,71461,1735],{"stretchy":1713},[902,71463,71464],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,71467,71468,71469,10454,71501,71523,71524,2186],{},"Zapište nabídku: ",[883,71470,71472],{"className":71471},[886],[888,71473,71474],{"xmlns":890},[892,71475,71476,71498],{},[895,71477,71478,71480,71482,71484,71486,71488,71490,71492,71494,71496],{},[898,71479,2362],{},[1711,71481,1714],{"stretchy":1713},[898,71483,6796],{},[1711,71485,1735],{"stretchy":1713},[1711,71487,1836],{},[898,71489,1790],{},[898,71491,1940],{},[1711,71493,1714],{"stretchy":1713},[898,71495,6796],{},[1711,71497,1735],{"stretchy":1713},[902,71499,71500],{"encoding":904},"S(Q) = MC(Q)",[883,71502,71504],{"className":71503},[886],[888,71505,71506],{"xmlns":890},[892,71507,71508,71520],{},[895,71509,71510,71512,71514],{},[898,71511,6796],{},[1711,71513,8471],{},[1716,71515,71516,71518],{},[898,71517,6796],{},[1711,71519,1793],{},[902,71521,71522],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,71525,71527],{"className":71526},[886],[888,71528,71529],{"xmlns":890},[892,71530,71531,71535],{},[895,71532,71533],{},[2111,71534,2113],{},[902,71536,2113],{"encoding":904},[123,71538,71539,71540,71572],{},"V případě potřeby vyjádřete inverzi ",[883,71541,71543],{"className":71542},[886],[888,71544,71545],{"xmlns":890},[892,71546,71547,71569],{},[895,71548,71549,71551,71553,71563,71565,71567],{},[898,71550,6796],{},[1711,71552,1836],{},[1716,71554,71555,71557],{},[898,71556,2362],{},[895,71558,71559,71561],{},[1711,71560,2460],{},[2111,71562,2238],{},[1711,71564,1714],{"stretchy":1713},[898,71566,7929],{},[1711,71568,1735],{"stretchy":1713},[902,71570,71571],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,71574,71575],{},[614,71576,71577,71578,1343,71593,2009,71610,32799,71625,71638,71639,71664,71665,71678,71679,71696,71697,71714,71715,71732],{},"Obrázek 3.14: Křivky ",[883,71579,71581],{"className":71580},[886],[888,71582,71583],{"xmlns":890},[892,71584,71585,71591],{},[895,71586,71587,71589],{},[898,71588,8243],{},[898,71590,1940],{},[902,71592,59158],{"encoding":904},[883,71594,71596],{"className":71595},[886],[888,71597,71598],{"xmlns":890},[892,71599,71600,71608],{},[895,71601,71602,71604,71606],{},[898,71603,8243],{},[898,71605,43937],{},[898,71607,1940],{},[902,71609,58909],{"encoding":904},[883,71611,71613],{"className":71612},[886],[888,71614,71615],{"xmlns":890},[892,71616,71617,71623],{},[895,71618,71619,71621],{},[898,71620,1790],{},[898,71622,1940],{},[902,71624,58890],{"encoding":904},[883,71626,71628],{"className":71627},[886],[888,71629,71630],{"xmlns":890},[892,71631,71632,71636],{},[895,71633,71634],{},[898,71635,900],{},[902,71637,900],{"encoding":904},"; křivka nabídky ",[883,71640,71642],{"className":71641},[886],[888,71643,71644],{"xmlns":890},[892,71645,71646,71662],{},[895,71647,71648,71650,71652,71654,71656,71658,71660],{},[898,71649,7929],{},[1711,71651,1836],{},[898,71653,1790],{},[898,71655,1940],{},[1711,71657,1714],{"stretchy":1713},[898,71659,6796],{},[1711,71661,1735],{"stretchy":1713},[902,71663,70964],{"encoding":904}," začíná v bodě ",[883,71666,71668],{"className":71667},[886],[888,71669,71670],{"xmlns":890},[892,71671,71672,71676],{},[895,71673,71674],{},[898,71675,8243],{},[902,71677,8243],{"encoding":904}," odpovídajícím minimu ",[883,71680,71682],{"className":71681},[886],[888,71683,71684],{"xmlns":890},[892,71685,71686,71694],{},[895,71687,71688,71690,71692],{},[898,71689,8243],{},[898,71691,43937],{},[898,71693,1940],{},[902,71695,58909],{"encoding":904}," při ceně ",[883,71698,71700],{"className":71699},[886],[888,71701,71702],{"xmlns":890},[892,71703,71704,71712],{},[895,71705,71706],{},[1716,71707,71708,71710],{},[898,71709,7929],{},[1711,71711,1793],{},[902,71713,8391],{"encoding":904}," (minimální cena nabídky); pod ",[883,71716,71718],{"className":71717},[886],[888,71719,71720],{"xmlns":890},[892,71721,71722,71730],{},[895,71723,71724],{},[1716,71725,71726,71728],{},[898,71727,6796],{},[1711,71729,1793],{},[902,71731,33442],{"encoding":904}," je nabídka nulová.",[40946,71734,71736],{"id":71735},"příklad-312","Příklad 3.12",[724,71738,71739,61120,71741,71787],{},[38,71740,59585],{},[883,71742,71744],{"className":71743},[886],[888,71745,71746],{"xmlns":890},[892,71747,71748,71784],{},[895,71749,71750,71752,71754,71756,71758,71764,71766,71768,71774,71776,71778,71780,71782],{},[898,71751,1769],{},[898,71753,1940],{},[1711,71755,1836],{},[2111,71757,4343],{},[1716,71759,71760,71762],{},[898,71761,6796],{},[2111,71763,3034],{},[1711,71765,2460],{},[2111,71767,2963],{},[1716,71769,71770,71772],{},[898,71771,6796],{},[2111,71773,2963],{},[1711,71775,2095],{},[2111,71777,39842],{},[898,71779,6796],{},[1711,71781,2095],{},[2111,71783,4712],{},[902,71785,71786],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,71789,71790,1700,71792,71829,71830,2062],{},[38,71791,26368],{},[883,71793,71795],{"className":71794},[886],[888,71796,71797],{"xmlns":890},[892,71798,71799,71826],{},[895,71800,71801,71803,71805,71807,71810,71816,71818,71820,71822,71824],{},[898,71802,1790],{},[898,71804,1940],{},[1711,71806,1836],{},[2111,71808,71809],{},"0,3",[1716,71811,71812,71814],{},[898,71813,6796],{},[2111,71815,2963],{},[1711,71817,2460],{},[2111,71819,6369],{},[898,71821,6796],{},[1711,71823,2095],{},[2111,71825,39842],{},[902,71827,71828],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,71831,71833],{"className":71832},[886],[888,71834,71835],{"xmlns":890},[892,71836,71837,71847],{},[895,71838,71839,71841,71843,71845],{},[898,71840,7929],{},[1711,71842,1836],{},[898,71844,1790],{},[898,71846,1940],{},[902,71848,71849],{"encoding":904},"P = MC",[883,71851,71853],{"className":71852},[886],[888,71854,71855],{"xmlns":890,"display":31664},[892,71856,71857,71882],{},[895,71858,71859,71861,71863,71865,71871,71873,71875,71877,71879],{},[898,71860,7929],{},[1711,71862,1836],{},[2111,71864,71809],{},[1716,71866,71867,71869],{},[898,71868,6796],{},[2111,71870,2963],{},[1711,71872,2460],{},[2111,71874,6369],{},[898,71876,6796],{},[1711,71878,2095],{},[2111,71880,71881],{},"15.",[902,71883,71884],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,71886,71887,71888,9366,71901,71914],{},"Vyjádření ",[883,71889,71891],{"className":71890},[886],[888,71892,71893],{"xmlns":890},[892,71894,71895,71899],{},[895,71896,71897],{},[898,71898,6796],{},[902,71900,6796],{"encoding":904},[883,71902,71904],{"className":71903},[886],[888,71905,71906],{"xmlns":890},[892,71907,71908,71912],{},[895,71909,71910],{},[898,71911,7929],{},[902,71913,7929],{"encoding":904}," doplněním na čtverec:",[883,71916,71918],{"className":71917},[886],[888,71919,71920],{"xmlns":890,"display":31664},[892,71921,71922,72012],{},[895,71923,71924,71926,71928,71930,71968,71970,71972,71994,71996,72010],{},[898,71925,7929],{},[1711,71927,1836],{},[2111,71929,71809],{},[895,71931,71932,71934,71956,71958,71966],{},[1711,71933,1714],{"fence":1725},[1716,71935,71936,71954],{},[895,71937,71938,71940,71942,71944,71952],{},[1711,71939,1714],{"fence":1725},[898,71941,6796],{},[1711,71943,2460],{},[2509,71945,71946],{"scriptlevel":2113,"displaystyle":1713},[2525,71947,71948,71950],{},[2111,71949,4306],{},[2111,71951,3034],{},[1711,71953,1735],{"fence":1725},[2111,71955,2963],{},[1711,71957,2095],{},[2509,71959,71960],{"scriptlevel":2113,"displaystyle":1713},[2525,71961,71962,71964],{},[2111,71963,7120],{},[2111,71965,7990],{},[1711,71967,1735],{"fence":1725},[1711,71969,1726],{"separator":1725},[2102,71971],{"width":2104},[1716,71973,71974,71992],{},[895,71975,71976,71978,71980,71982,71990],{},[1711,71977,1714],{"fence":1725},[898,71979,6796],{},[1711,71981,2460],{},[2509,71983,71984],{"scriptlevel":2113,"displaystyle":1713},[2525,71985,71986,71988],{},[2111,71987,4306],{},[2111,71989,3034],{},[1711,71991,1735],{"fence":1725},[2111,71993,2963],{},[1711,71995,1836],{},[2525,71997,71998,72008],{},[895,71999,72000,72002,72004,72006],{},[2111,72001,41617],{},[898,72003,7929],{},[1711,72005,2460],{},[2111,72007,7120],{},[2111,72009,7990],{},[1711,72011,1726],{"separator":1725},[902,72013,72014],{"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},",[883,72016,72018],{"className":72017},[886],[888,72019,72020],{"xmlns":890,"display":31664},[892,72021,72022,72054],{},[895,72023,72024,72026,72028,72034,72036,72052],{},[898,72025,6796],{},[1711,72027,1836],{},[2525,72029,72030,72032],{},[2111,72031,4306],{},[2111,72033,3034],{},[1711,72035,2095],{},[2525,72037,72038,72050],{},[12097,72039,72040],{},[895,72041,72042,72044,72046,72048],{},[2111,72043,41617],{},[898,72045,7929],{},[1711,72047,2460],{},[2111,72049,7120],{},[2111,72051,3034],{},[898,72053,2186],{"mathvariant":2287},[902,72055,72056],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,72058,70616,72059,1343,72097,1343,72145,72179,72180,2186],{},[883,72060,72062],{"className":72061},[886],[888,72063,72064],{"xmlns":890},[892,72065,72066,72094],{},[895,72067,72068,72070,72072,72074,72076,72078,72084,72086,72088,72090,72092],{},[898,72069,8243],{},[898,72071,43937],{},[898,72073,1940],{},[1711,72075,1836],{},[2111,72077,4343],{},[1716,72079,72080,72082],{},[898,72081,6796],{},[2111,72083,2963],{},[1711,72085,2460],{},[2111,72087,2963],{},[898,72089,6796],{},[1711,72091,2095],{},[2111,72093,39842],{},[902,72095,72096],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,72098,72100],{"className":72099},[886],[888,72101,72102],{"xmlns":890},[892,72103,72104,72142],{},[895,72105,72106,72108,72110,72116,72118,72120,72122,72124,72126,72128,72130,72132,72138,72140],{},[898,72107,8243],{},[898,72109,43937],{},[1716,72111,72112,72114],{},[898,72113,1940],{},[1711,72115,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,72117,1836],{},[2111,72119,4491],{},[898,72121,6796],{},[1711,72123,2460],{},[2111,72125,2963],{},[1711,72127,1836],{},[2111,72129,2113],{},[1711,72131,7978],{},[1716,72133,72134,72136],{},[898,72135,6796],{},[1711,72137,1793],{},[1711,72139,1836],{},[2111,72141,4712],{},[902,72143,72144],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,72146,72148],{"className":72147},[886],[888,72149,72150],{"xmlns":890},[892,72151,72152,72176],{},[895,72153,72154,72156,72158,72168,72170,72172,72174],{},[898,72155,8243],{},[898,72157,43937],{},[1716,72159,72160,72162],{},[898,72161,1940],{},[895,72163,72164,72166],{},[1711,72165,5225],{"mathvariant":2287},[1711,72167,5225],{"mathvariant":2287},[1711,72169,1836],{},[2111,72171,4491],{},[1711,72173,2123],{},[2111,72175,2113],{},[902,72177,72178],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,72181,72183],{"className":72182},[886],[888,72184,72185],{"xmlns":890},[892,72186,72187,72223],{},[895,72188,72189,72195,72197,72199,72201,72203,72205,72207,72209,72211,72213,72215,72217,72219,72221],{},[1716,72190,72191,72193],{},[898,72192,7929],{},[1711,72194,1793],{},[1711,72196,1836],{},[898,72198,1790],{},[898,72200,1940],{},[1711,72202,1714],{"stretchy":1713},[2111,72204,4712],{},[1711,72206,1735],{"stretchy":1713},[1711,72208,1836],{},[2111,72210,41617],{},[1711,72212,2460],{},[2111,72214,9195],{},[1711,72216,2095],{},[2111,72218,39842],{},[1711,72220,1836],{},[2111,72222,4798],{},[902,72224,72225],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,72227,72228],{},[38,72229,72230],{},"Závěr.",[883,72232,72234],{"className":72233},[886],[888,72235,72236],{"xmlns":890,"display":31664},[892,72237,72238,72324],{},[895,72239,72240,72242,72244,72246,72248,72250,72252,72254],{},[898,72241,7929],{},[1711,72243,1836],{},[898,72245,2362],{},[1711,72247,1714],{"stretchy":1713},[898,72249,6796],{},[1711,72251,1735],{"stretchy":1713},[1711,72253,1836],{},[895,72255,72256,72258],{},[1711,72257,71104],{"fence":1725},[24352,72259,72260,72302],{"rowspacing":71107,"columnalign":71108,"columnspacing":4981},[24357,72261,72262,72286],{},[24360,72263,72264],{},[2509,72265,72266],{"scriptlevel":2113,"displaystyle":1713},[895,72267,72268,72270,72276,72278,72280,72282,72284],{},[2111,72269,71809],{},[1716,72271,72272,72274],{},[898,72273,6796],{},[2111,72275,2963],{},[1711,72277,2460],{},[2111,72279,6369],{},[898,72281,6796],{},[1711,72283,2095],{},[2111,72285,39842],{},[24360,72287,72288],{},[2509,72289,72290],{"scriptlevel":2113,"displaystyle":1713},[895,72291,72292,72294,72296,72298,72300],{},[1942,72293,71135],{},[898,72295,6796],{},[1711,72297,8471],{},[2111,72299,4712],{},[1711,72301,1726],{"separator":1725},[24357,72303,72304,72310],{},[24360,72305,72306],{},[2509,72307,72308],{"scriptlevel":2113,"displaystyle":1713},[2111,72309,2113],{},[24360,72311,72312],{},[2509,72313,72314],{"scriptlevel":2113,"displaystyle":1713},[895,72315,72316,72318,72320,72322],{},[1942,72317,71135],{},[898,72319,6796],{},[1711,72321,2109],{},[2111,72323,22926],{},[902,72325,72326],{"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}",[724,72328,72329],{},[614,72330,72331,72332,72347,72348,2186],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,72333,72335],{"className":72334},[886],[888,72336,72337],{"xmlns":890},[892,72338,72339,72345],{},[895,72340,72341,72343],{},[898,72342,1790],{},[898,72344,1940],{},[902,72346,58890],{"encoding":904}," ležící nad minimem ",[883,72349,72351],{"className":72350},[886],[888,72352,72353],{"xmlns":890},[892,72354,72355,72363],{},[895,72356,72357,72359,72361],{},[898,72358,8243],{},[898,72360,43937],{},[898,72362,1940],{},[902,72364,58909],{"encoding":904},[115,72366,72368],{"id":72367},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,72370,72371,72372,72376,72377,72392,72393,72413,72414,2009,72417,72420,72421,72423,72424,23543,72446,72448,72449,2009,72451,62324,72454,1700,72457,45412,72472,72487],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,72373,72375],{"className":72374,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,72378,72380],{"className":72379},[886],[888,72381,72382],{"xmlns":890},[892,72383,72384,72390],{},[895,72385,72386,72388],{},[898,72387,1769],{},[898,72389,7985],{},[902,72391,8085],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,72394,72396],{"className":72395},[886],[888,72397,72398],{"xmlns":890},[892,72399,72400,72410],{},[895,72401,72402,72404,72406,72408],{},[898,72403,1769],{},[898,72405,7985],{},[898,72407,8659],{"mathvariant":2287},[898,72409,6796],{},[902,72411,72412],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,72415,72416],{},"fixních",[38,72418,72419],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,72422,67923],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,72425,72427],{"className":72426},[886],[888,72428,72429],{"xmlns":890},[892,72430,72431,72443],{},[895,72432,72433,72435,72437,72439,72441],{},[898,72434,1769],{},[898,72436,7985],{},[1711,72438,2460],{},[898,72440,1769],{},[898,72442,1940],{},[902,72444,72445],{"encoding":904},"TR - TC",[38,72447,58770],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,72450,60082],{},[38,72452,72453],{},"mezní náklady",[207,72455,1145],{"className":72456,"dataFsResolvedFilePath":764,"href":765},[210],[883,72458,72460],{"className":72459},[886],[888,72461,72462],{"xmlns":890},[892,72463,72464,72470],{},[895,72465,72466,72468],{},[898,72467,1769],{},[898,72469,7985],{},[902,72471,8085],{"encoding":904},[883,72473,72475],{"className":72474},[886],[888,72476,72477],{"xmlns":890},[892,72478,72479,72485],{},[895,72480,72481,72483],{},[898,72482,1769],{},[898,72484,1940],{},[902,72486,7241],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,72489,72490,72552,72618,72680],{},[123,72491,72492,72495,72496,14367,72511,2186],{},[38,72493,72494],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,72497,72499],{"className":72498},[886],[888,72500,72501],{"xmlns":890},[892,72502,72503,72509],{},[895,72504,72505,72507],{},[898,72506,8243],{},[898,72508,1940],{},[902,72510,59158],{"encoding":904},[883,72512,72514],{"className":72513},[886],[888,72515,72516],{"xmlns":890},[892,72517,72518,72550],{},[895,72519,72520,72522,72524,72526,72532,72534,72536,72538,72540,72542,72548],{},[898,72521,8243],{},[898,72523,1940],{},[1711,72525,1714],{"stretchy":1713},[2884,72527,72528,72530],{},[898,72529,6796],{},[2111,72531,2113],{},[1711,72533,1735],{"stretchy":1713},[1711,72535,1836],{},[898,72537,1790],{},[898,72539,1940],{},[1711,72541,1714],{"stretchy":1713},[2884,72543,72544,72546],{},[898,72545,6796],{},[2111,72547,2113],{},[1711,72549,1735],{"stretchy":1713},[902,72551,66167],{"encoding":904},[123,72553,72554,72495,72557,14367,72574,2186],{},[38,72555,72556],{},"Princip minimalizace průměrných variabilních nákladů:",[883,72558,72560],{"className":72559},[886],[888,72561,72562],{"xmlns":890},[892,72563,72564,72572],{},[895,72565,72566,72568,72570],{},[898,72567,8243],{},[898,72569,43937],{},[898,72571,1940],{},[902,72573,58909],{"encoding":904},[883,72575,72577],{"className":72576},[886],[888,72578,72579],{"xmlns":890},[892,72580,72581,72615],{},[895,72582,72583,72585,72587,72589,72591,72597,72599,72601,72603,72605,72607,72613],{},[898,72584,8243],{},[898,72586,43937],{},[898,72588,1940],{},[1711,72590,1714],{"stretchy":1713},[2884,72592,72593,72595],{},[898,72594,6796],{},[2111,72596,2113],{},[1711,72598,1735],{"stretchy":1713},[1711,72600,1836],{},[898,72602,1790],{},[898,72604,1940],{},[1711,72606,1714],{"stretchy":1713},[2884,72608,72609,72611],{},[898,72610,6796],{},[2111,72612,2113],{},[1711,72614,1735],{"stretchy":1713},[902,72616,72617],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,72619,72620,72623,72624,14367,72639,2186],{},[38,72621,72622],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,72625,72627],{"className":72626},[886],[888,72628,72629],{"xmlns":890},[892,72630,72631,72637],{},[895,72632,72633,72635],{},[898,72634,7929],{},[898,72636,7985],{},[902,72638,67077],{"encoding":904},[883,72640,72642],{"className":72641},[886],[888,72643,72644],{"xmlns":890},[892,72645,72646,72678],{},[895,72647,72648,72650,72652,72654,72660,72662,72664,72666,72668,72670,72676],{},[898,72649,1790],{},[898,72651,7985],{},[1711,72653,1714],{"stretchy":1713},[2884,72655,72656,72658],{},[898,72657,6796],{},[2111,72659,2113],{},[1711,72661,1735],{"stretchy":1713},[1711,72663,1836],{},[898,72665,1790],{},[898,72667,1940],{},[1711,72669,1714],{"stretchy":1713},[2884,72671,72672,72674],{},[898,72673,6796],{},[2111,72675,2113],{},[1711,72677,1735],{"stretchy":1713},[902,72679,69243],{"encoding":904},[123,72681,72682,1700,72685,10454,72721,71523,72742,25192,72755,71205,72772,2186],{},[38,72683,72684],{},"Funkce nabídky firmy:",[883,72686,72688],{"className":72687},[886],[888,72689,72690],{"xmlns":890},[892,72691,72692,72718],{},[895,72693,72694,72696,72698,72700,72702,72704,72706,72708,72710,72712,72714,72716],{},[898,72695,7929],{},[1711,72697,1836],{},[898,72699,2362],{},[1711,72701,1714],{"stretchy":1713},[898,72703,6796],{},[1711,72705,1735],{"stretchy":1713},[1711,72707,1836],{},[898,72709,1790],{},[898,72711,1940],{},[1711,72713,1714],{"stretchy":1713},[898,72715,6796],{},[1711,72717,1735],{"stretchy":1713},[902,72719,72720],{"encoding":904},"P = S(Q) = MC(Q)",[883,72722,72724],{"className":72723},[886],[888,72725,72726],{"xmlns":890},[892,72727,72728,72740],{},[895,72729,72730,72732,72734],{},[898,72731,6796],{},[1711,72733,8471],{},[1716,72735,72736,72738],{},[898,72737,6796],{},[1711,72739,1793],{},[902,72741,71522],{"encoding":904},[883,72743,72745],{"className":72744},[886],[888,72746,72747],{"xmlns":890},[892,72748,72749,72753],{},[895,72750,72751],{},[2111,72752,2113],{},[902,72754,2113],{"encoding":904},[883,72756,72758],{"className":72757},[886],[888,72759,72760],{"xmlns":890},[892,72761,72762,72770],{},[895,72763,72764],{},[1716,72765,72766,72768],{},[898,72767,6796],{},[1711,72769,1793],{},[902,72771,33442],{"encoding":904},[883,72773,72775],{"className":72774},[886],[888,72776,72777],{"xmlns":890},[892,72778,72779,72787],{},[895,72780,72781,72783,72785],{},[898,72782,8243],{},[898,72784,43937],{},[898,72786,1940],{},[902,72788,58909],{"encoding":904},[115,72790,53480],{"id":53479},[152,72792,72793,72796,72799,72802,72805,72808,72811,72814,72817,72820,72823],{},[123,72794,72795],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,72797,72798],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,72800,72801],{},"Jak se vypočte mezní příjem a co udává?",[123,72803,72804],{},"Z jakých složek se skládají celkové náklady?",[123,72806,72807],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,72809,72810],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,72812,72813],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,72815,72816],{},"Jak se vypočte zisk?",[123,72818,72819],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,72821,72822],{},"Co jsou body zvratu? Jak se najdou?",[123,72824,72825],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,72827,72829],{"id":72828},"úlohy-31328","Úlohy 3.1–3.28",[198,72831,72833],{"id":72832},"příjem-3135","Příjem (3.1–3.5)",[724,72835,72836,49024,72839,72867,72868,72883,72884,72899,72900,72915,72916,1343,72931,1343,72946,72961],{},[38,72837,72838],{},"3.1",[883,72840,72842],{"className":72841},[886],[888,72843,72844],{"xmlns":890},[892,72845,72846,72864],{},[895,72847,72848,72850,72852,72854,72856,72858,72860,72862],{},[898,72849,7929],{},[1711,72851,1836],{},[898,72853,2778],{},[1711,72855,1714],{"stretchy":1713},[898,72857,6796],{},[1711,72859,1735],{"stretchy":1713},[1711,72861,1836],{},[2111,72863,4282],{},[902,72865,72866],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,72869,72871],{"className":72870},[886],[888,72872,72873],{"xmlns":890},[892,72874,72875,72881],{},[895,72876,72877,72879],{},[898,72878,1769],{},[898,72880,7985],{},[902,72882,8085],{"encoding":904},", průměrný příjem ",[883,72885,72887],{"className":72886},[886],[888,72888,72889],{"xmlns":890},[892,72890,72891,72897],{},[895,72892,72893,72895],{},[898,72894,8243],{},[898,72896,7985],{},[902,72898,59043],{"encoding":904}," a mezní příjem ",[883,72901,72903],{"className":72902},[886],[888,72904,72905],{"xmlns":890},[892,72906,72907,72913],{},[895,72908,72909,72911],{},[898,72910,1790],{},[898,72912,7985],{},[902,72914,10615],{"encoding":904},". (c) Vypočtěte ",[883,72917,72919],{"className":72918},[886],[888,72920,72921],{"xmlns":890},[892,72922,72923,72929],{},[895,72924,72925,72927],{},[898,72926,1769],{},[898,72928,7985],{},[902,72930,8085],{"encoding":904},[883,72932,72934],{"className":72933},[886],[888,72935,72936],{"xmlns":890},[892,72937,72938,72944],{},[895,72939,72940,72942],{},[898,72941,8243],{},[898,72943,7985],{},[902,72945,59043],{"encoding":904},[883,72947,72949],{"className":72948},[886],[888,72950,72951],{"xmlns":890},[892,72952,72953,72959],{},[895,72954,72955,72957],{},[898,72956,1790],{},[898,72958,7985],{},[902,72960,10615],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,72963,72964,49024,72967,72867,73003,72883,73018,72899,73033,72915,73048,1343,73063,1343,73078,73093],{},[38,72965,72966],{},"3.2",[883,72968,72970],{"className":72969},[886],[888,72971,72972],{"xmlns":890},[892,72973,72974,73000],{},[895,72975,72976,72978,72980,72982,72984,72986,72988,72990,72992,72994,72996,72998],{},[898,72977,7929],{},[1711,72979,1836],{},[898,72981,2778],{},[1711,72983,1714],{"stretchy":1713},[898,72985,6796],{},[1711,72987,1735],{"stretchy":1713},[1711,72989,1836],{},[1711,72991,2460],{},[2111,72993,8993],{},[898,72995,6796],{},[1711,72997,2095],{},[2111,72999,4306],{},[902,73001,73002],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,73004,73006],{"className":73005},[886],[888,73007,73008],{"xmlns":890},[892,73009,73010,73016],{},[895,73011,73012,73014],{},[898,73013,1769],{},[898,73015,7985],{},[902,73017,8085],{"encoding":904},[883,73019,73021],{"className":73020},[886],[888,73022,73023],{"xmlns":890},[892,73024,73025,73031],{},[895,73026,73027,73029],{},[898,73028,8243],{},[898,73030,7985],{},[902,73032,59043],{"encoding":904},[883,73034,73036],{"className":73035},[886],[888,73037,73038],{"xmlns":890},[892,73039,73040,73046],{},[895,73041,73042,73044],{},[898,73043,1790],{},[898,73045,7985],{},[902,73047,10615],{"encoding":904},[883,73049,73051],{"className":73050},[886],[888,73052,73053],{"xmlns":890},[892,73054,73055,73061],{},[895,73056,73057,73059],{},[898,73058,1769],{},[898,73060,7985],{},[902,73062,8085],{"encoding":904},[883,73064,73066],{"className":73065},[886],[888,73067,73068],{"xmlns":890},[892,73069,73070,73076],{},[895,73071,73072,73074],{},[898,73073,8243],{},[898,73075,7985],{},[902,73077,59043],{"encoding":904},[883,73079,73081],{"className":73080},[886],[888,73082,73083],{"xmlns":890},[892,73084,73085,73091],{},[895,73086,73087,73089],{},[898,73088,1790],{},[898,73090,7985],{},[902,73092,10615],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,73095,73096,49024,73099,73136,73137,72883,73152,72899,73167,73182,73183,10454,73198,73224,73225,73240,73241,1343,73256,10454,73271,73224,73296,73311,73312,73325,73326,73341,73342,73357,73358,1343,73371,1343,73386,1343,73401,2186],{},[38,73097,73098],{},"3.3",[883,73100,73102],{"className":73101},[886],[888,73103,73104],{"xmlns":890},[892,73105,73106,73133],{},[895,73107,73108,73110,73112,73114,73116,73118,73120,73122,73125,73127],{},[898,73109,7929],{},[1711,73111,1836],{},[898,73113,2778],{},[1711,73115,1714],{"stretchy":1713},[898,73117,6796],{},[1711,73119,1735],{"stretchy":1713},[1711,73121,1836],{},[2111,73123,73124],{},"1200",[1711,73126,2460],{},[1716,73128,73129,73131],{},[898,73130,6796],{},[2111,73132,2963],{},[902,73134,73135],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,73138,73140],{"className":73139},[886],[888,73141,73142],{"xmlns":890},[892,73143,73144,73150],{},[895,73145,73146,73148],{},[898,73147,1769],{},[898,73149,7985],{},[902,73151,8085],{"encoding":904},[883,73153,73155],{"className":73154},[886],[888,73156,73157],{"xmlns":890},[892,73158,73159,73165],{},[895,73160,73161,73163],{},[898,73162,8243],{},[898,73164,7985],{},[902,73166,59043],{"encoding":904},[883,73168,73170],{"className":73169},[886],[888,73171,73172],{"xmlns":890},[892,73173,73174,73180],{},[895,73175,73176,73178],{},[898,73177,1790],{},[898,73179,7985],{},[902,73181,10615],{"encoding":904},". (b) Vypočtěte ",[883,73184,73186],{"className":73185},[886],[888,73187,73188],{"xmlns":890},[892,73189,73190,73196],{},[895,73191,73192,73194],{},[898,73193,1769],{},[898,73195,7985],{},[902,73197,8085],{"encoding":904},[883,73199,73201],{"className":73200},[886],[888,73202,73203],{"xmlns":890},[892,73204,73205,73221],{},[895,73206,73207,73209,73211,73213,73215,73217,73219],{},[898,73208,6796],{},[1711,73210,1836],{},[2111,73212,4712],{},[1711,73214,1726],{"separator":1725},[2111,73216,4306],{},[1711,73218,1726],{"separator":1725},[2111,73220,41617],{},[902,73222,73223],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,73226,73228],{"className":73227},[886],[888,73229,73230],{"xmlns":890},[892,73231,73232,73238],{},[895,73233,73234,73236],{},[898,73235,1769],{},[898,73237,7985],{},[902,73239,8085],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,73242,73244],{"className":73243},[886],[888,73245,73246],{"xmlns":890},[892,73247,73248,73254],{},[895,73249,73250,73252],{},[898,73251,8243],{},[898,73253,7985],{},[902,73255,59043],{"encoding":904},[883,73257,73259],{"className":73258},[886],[888,73260,73261],{"xmlns":890},[892,73262,73263,73269],{},[895,73264,73265,73267],{},[898,73266,1790],{},[898,73268,7985],{},[902,73270,10615],{"encoding":904},[883,73272,73274],{"className":73273},[886],[888,73275,73276],{"xmlns":890},[892,73277,73278,73294],{},[895,73279,73280,73282,73284,73286,73288,73290,73292],{},[898,73281,6796],{},[1711,73283,1836],{},[2111,73285,4712],{},[1711,73287,1726],{"separator":1725},[2111,73289,4306],{},[1711,73291,1726],{"separator":1725},[2111,73293,41617],{},[902,73295,73223],{"encoding":904},[883,73297,73299],{"className":73298},[886],[888,73300,73301],{"xmlns":890},[892,73302,73303,73309],{},[895,73304,73305,73307],{},[898,73306,1790],{},[898,73308,7985],{},[902,73310,10615],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,73313,73315],{"className":73314},[886],[888,73316,73317],{"xmlns":890},[892,73318,73319,73323],{},[895,73320,73321],{},[898,73322,6796],{},[902,73324,6796],{"encoding":904},", které maximalizuje ",[883,73327,73329],{"className":73328},[886],[888,73330,73331],{"xmlns":890},[892,73332,73333,73339],{},[895,73334,73335,73337],{},[898,73336,1769],{},[898,73338,7985],{},[902,73340,8085],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,73343,73345],{"className":73344},[886],[888,73346,73347],{"xmlns":890},[892,73348,73349,73355],{},[895,73350,73351,73353],{},[898,73352,1769],{},[898,73354,7985],{},[902,73356,8085],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,73359,73361],{"className":73360},[886],[888,73362,73363],{"xmlns":890},[892,73364,73365,73369],{},[895,73366,73367],{},[898,73368,2778],{},[902,73370,2778],{"encoding":904},[883,73372,73374],{"className":73373},[886],[888,73375,73376],{"xmlns":890},[892,73377,73378,73384],{},[895,73379,73380,73382],{},[898,73381,1769],{},[898,73383,7985],{},[902,73385,8085],{"encoding":904},[883,73387,73389],{"className":73388},[886],[888,73390,73391],{"xmlns":890},[892,73392,73393,73399],{},[895,73394,73395,73397],{},[898,73396,8243],{},[898,73398,7985],{},[902,73400,59043],{"encoding":904},[883,73402,73404],{"className":73403},[886],[888,73405,73406],{"xmlns":890},[892,73407,73408,73414],{},[895,73409,73410,73412],{},[898,73411,1790],{},[898,73413,7985],{},[902,73415,10615],{"encoding":904},[724,73417,73418,73421,73422,73452,73453,73468,73469,14130,73482,1343,73500,1343,73517,73535,73536,73558,73559,73574,73575,73588,73589,2186],{},[38,73419,73420],{},"3.4"," Je dán celkový příjem ",[883,73423,73425],{"className":73424},[886],[888,73426,73427],{"xmlns":890},[892,73428,73429,73449],{},[895,73430,73431,73433,73435,73437,73439,73441,73443],{},[898,73432,1769],{},[898,73434,7985],{},[1711,73436,1836],{},[2111,73438,73124],{},[898,73440,6796],{},[1711,73442,2460],{},[1716,73444,73445,73447],{},[898,73446,6796],{},[2111,73448,3034],{},[902,73450,73451],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,73454,73456],{"className":73455},[886],[888,73457,73458],{"xmlns":890},[892,73459,73460,73466],{},[895,73461,73462,73464],{},[898,73463,1769],{},[898,73465,7985],{},[902,73467,8085],{"encoding":904}," vzhledem ke ",[883,73470,73472],{"className":73471},[886],[888,73473,73474],{"xmlns":890},[892,73475,73476,73480],{},[895,73477,73478],{},[898,73479,6796],{},[902,73481,6796],{"encoding":904},[883,73483,73485],{"className":73484},[886],[888,73486,73487],{"xmlns":890},[892,73488,73489,73497],{},[895,73490,73491,73493,73495],{},[898,73492,6796],{},[1711,73494,1836],{},[2111,73496,4798],{},[902,73498,73499],{"encoding":904},"Q = 5",[883,73501,73503],{"className":73502},[886],[888,73504,73505],{"xmlns":890},[892,73506,73507,73515],{},[895,73508,73509,73511,73513],{},[898,73510,6796],{},[1711,73512,1836],{},[2111,73514,9568],{},[902,73516,9571],{"encoding":904},[883,73518,73520],{"className":73519},[886],[888,73521,73522],{"xmlns":890},[892,73523,73524,73532],{},[895,73525,73526,73528,73530],{},[898,73527,6796],{},[1711,73529,1836],{},[2111,73531,7505],{},[902,73533,73534],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,73537,73539],{"className":73538},[886],[888,73540,73541],{"xmlns":890},[892,73542,73543,73555],{},[895,73544,73545,73547,73549,73551,73553],{},[898,73546,1790],{},[898,73548,7985],{},[1711,73550,1714],{"stretchy":1713},[2111,73552,4712],{},[1711,73554,1735],{"stretchy":1713},[902,73556,73557],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,73560,73562],{"className":73561},[886],[888,73563,73564],{"xmlns":890},[892,73565,73566,73572],{},[895,73567,73568,73570],{},[898,73569,1769],{},[898,73571,7985],{},[902,73573,8085],{"encoding":904},", jestliže se ",[883,73576,73578],{"className":73577},[886],[888,73579,73580],{"xmlns":890},[892,73581,73582,73586],{},[895,73583,73584],{},[898,73585,6796],{},[902,73587,6796],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,73590,73592],{"className":73591},[886],[888,73593,73594],{"xmlns":890},[892,73595,73596,73602],{},[895,73597,73598,73600],{},[898,73599,1769],{},[898,73601,7985],{},[902,73603,8085],{"encoding":904},[724,73605,73606,73609,73610,73636,73637,73652,73653,73574,73668,73681],{},[38,73607,73608],{},"3.5"," Je dán mezní příjem ",[883,73611,73613],{"className":73612},[886],[888,73614,73615],{"xmlns":890},[892,73616,73617,73633],{},[895,73618,73619,73621,73623,73625,73627,73629,73631],{},[898,73620,1790],{},[898,73622,7985],{},[1711,73624,1836],{},[1711,73626,2460],{},[898,73628,6796],{},[1711,73630,2095],{},[2111,73632,4306],{},[902,73634,73635],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,73638,73640],{"className":73639},[886],[888,73641,73642],{"xmlns":890},[892,73643,73644,73650],{},[895,73645,73646,73648],{},[898,73647,1769],{},[898,73649,7985],{},[902,73651,8085],{"encoding":904},". (b) Vypočtěte změnu ",[883,73654,73656],{"className":73655},[886],[888,73657,73658],{"xmlns":890},[892,73659,73660,73666],{},[895,73661,73662,73664],{},[898,73663,1769],{},[898,73665,7985],{},[902,73667,8085],{"encoding":904},[883,73669,73671],{"className":73670},[886],[888,73672,73673],{"xmlns":890},[892,73674,73675,73679],{},[895,73676,73677],{},[898,73678,6796],{},[902,73680,6796],{"encoding":904}," změní z 8 na 12.",[198,73683,73685],{"id":73684},"náklady-36316","Náklady (3.6–3.16)",[724,73687,73688,73691,73692,73732,73733,73748,73749,73766,73767,73784,73785,73800,73801,73816,73817,73182,73832,1343,73847,1343,73864,1343,73881,1343,73896,1343,73911,10454,73926,73944,73945,1343,73960,1343,73975,73990],{},[38,73689,73690],{},"3.6"," Jsou dány celkové náklady ",[883,73693,73695],{"className":73694},[886],[888,73696,73697],{"xmlns":890},[892,73698,73699,73729],{},[895,73700,73701,73703,73705,73707,73709,73711,73713,73715,73717],{},[898,73702,1769],{},[898,73704,1940],{},[1711,73706,1836],{},[2111,73708,4282],{},[1711,73710,2095],{},[2111,73712,2963],{},[898,73714,6796],{},[1711,73716,2095],{},[2509,73718,73719],{"scriptlevel":2113,"displaystyle":1713},[2525,73720,73721,73727],{},[1716,73722,73723,73725],{},[898,73724,6796],{},[2111,73726,2963],{},[2111,73728,4712],{},[902,73730,73731],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,73734,73736],{"className":73735},[886],[888,73737,73738],{"xmlns":890},[892,73739,73740,73746],{},[895,73741,73742,73744],{},[898,73743,14409],{},[898,73745,1940],{},[902,73747,59089],{"encoding":904},", celkové variabilní náklady ",[883,73750,73752],{"className":73751},[886],[888,73753,73754],{"xmlns":890},[892,73755,73756,73764],{},[895,73757,73758,73760,73762],{},[898,73759,1769],{},[898,73761,43937],{},[898,73763,1940],{},[902,73765,59107],{"encoding":904},", průměrné variabilní náklady ",[883,73768,73770],{"className":73769},[886],[888,73771,73772],{"xmlns":890},[892,73773,73774,73782],{},[895,73775,73776,73778,73780],{},[898,73777,8243],{},[898,73779,43937],{},[898,73781,1940],{},[902,73783,58909],{"encoding":904},", variabilní náklady na jednotku ",[883,73786,73788],{"className":73787},[886],[888,73789,73790],{"xmlns":890},[892,73791,73792,73798],{},[895,73793,73794,73796],{},[898,73795,43937],{},[898,73797,1940],{},[902,73799,67203],{"encoding":904},", průměrné náklady ",[883,73802,73804],{"className":73803},[886],[888,73805,73806],{"xmlns":890},[892,73807,73808,73814],{},[895,73809,73810,73812],{},[898,73811,8243],{},[898,73813,1940],{},[902,73815,59158],{"encoding":904}," a mezní náklady ",[883,73818,73820],{"className":73819},[886],[888,73821,73822],{"xmlns":890},[892,73823,73824,73830],{},[895,73825,73826,73828],{},[898,73827,1790],{},[898,73829,1940],{},[902,73831,58890],{"encoding":904},[883,73833,73835],{"className":73834},[886],[888,73836,73837],{"xmlns":890},[892,73838,73839,73845],{},[895,73840,73841,73843],{},[898,73842,1769],{},[898,73844,1940],{},[902,73846,7241],{"encoding":904},[883,73848,73850],{"className":73849},[886],[888,73851,73852],{"xmlns":890},[892,73853,73854,73862],{},[895,73855,73856,73858,73860],{},[898,73857,1769],{},[898,73859,43937],{},[898,73861,1940],{},[902,73863,59107],{"encoding":904},[883,73865,73867],{"className":73866},[886],[888,73868,73869],{"xmlns":890},[892,73870,73871,73879],{},[895,73872,73873,73875,73877],{},[898,73874,8243],{},[898,73876,43937],{},[898,73878,1940],{},[902,73880,58909],{"encoding":904},[883,73882,73884],{"className":73883},[886],[888,73885,73886],{"xmlns":890},[892,73887,73888,73894],{},[895,73889,73890,73892],{},[898,73891,43937],{},[898,73893,1940],{},[902,73895,67203],{"encoding":904},[883,73897,73899],{"className":73898},[886],[888,73900,73901],{"xmlns":890},[892,73902,73903,73909],{},[895,73904,73905,73907],{},[898,73906,8243],{},[898,73908,1940],{},[902,73910,59158],{"encoding":904},[883,73912,73914],{"className":73913},[886],[888,73915,73916],{"xmlns":890},[892,73917,73918,73924],{},[895,73919,73920,73922],{},[898,73921,1790],{},[898,73923,1940],{},[902,73925,58890],{"encoding":904},[883,73927,73929],{"className":73928},[886],[888,73930,73931],{"xmlns":890},[892,73932,73933,73941],{},[895,73934,73935,73937,73939],{},[898,73936,6796],{},[1711,73938,1836],{},[2111,73940,7120],{},[902,73942,73943],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,73946,73948],{"className":73947},[886],[888,73949,73950],{"xmlns":890},[892,73951,73952,73958],{},[895,73953,73954,73956],{},[898,73955,1769],{},[898,73957,1940],{},[902,73959,7241],{"encoding":904},[883,73961,73963],{"className":73962},[886],[888,73964,73965],{"xmlns":890},[892,73966,73967,73973],{},[895,73968,73969,73971],{},[898,73970,8243],{},[898,73972,1940],{},[902,73974,59158],{"encoding":904},[883,73976,73978],{"className":73977},[886],[888,73979,73980],{"xmlns":890},[892,73981,73982,73988],{},[895,73983,73984,73986],{},[898,73985,1790],{},[898,73987,1940],{},[902,73989,58890],{"encoding":904}," rostou, resp. klesají.",[724,73992,73993,73996,73997,73816,74027,74042,74043,74058,74059,1343,74074,1343,74089,2186],{},[38,73994,73995],{},"3.7"," Jsou dány průměrné náklady ",[883,73998,74000],{"className":73999},[886],[888,74001,74002],{"xmlns":890},[892,74003,74004,74024],{},[895,74005,74006,74008,74010,74012,74020,74022],{},[898,74007,8243],{},[898,74009,1940],{},[1711,74011,1836],{},[2509,74013,74014],{"scriptlevel":2113,"displaystyle":1713},[2525,74015,74016,74018],{},[2111,74017,4282],{},[898,74019,6796],{},[1711,74021,2095],{},[2111,74023,4306],{},[902,74025,74026],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,74028,74030],{"className":74029},[886],[888,74031,74032],{"xmlns":890},[892,74033,74034,74040],{},[895,74035,74036,74038],{},[898,74037,1790],{},[898,74039,1940],{},[902,74041,58890],{"encoding":904},". (a) Určete celkové náklady ",[883,74044,74046],{"className":74045},[886],[888,74047,74048],{"xmlns":890},[892,74049,74050,74056],{},[895,74051,74052,74054],{},[898,74053,1769],{},[898,74055,1940],{},[902,74057,7241],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,74060,74062],{"className":74061},[886],[888,74063,74064],{"xmlns":890},[892,74065,74066,74072],{},[895,74067,74068,74070],{},[898,74069,8243],{},[898,74071,1940],{},[902,74073,59158],{"encoding":904},[883,74075,74077],{"className":74076},[886],[888,74078,74079],{"xmlns":890},[892,74080,74081,74087],{},[895,74082,74083,74085],{},[898,74084,1769],{},[898,74086,1940],{},[902,74088,7241],{"encoding":904},[883,74090,74092],{"className":74091},[886],[888,74093,74094],{"xmlns":890},[892,74095,74096,74102],{},[895,74097,74098,74100],{},[898,74099,1790],{},[898,74101,1940],{},[902,74103,58890],{"encoding":904},[724,74105,74106,73691,74109,74153,74154,1343,74171,1343,74186,1343,74203,1343,74218,1343,74235,2186],{},[38,74107,74108],{},"3.8",[883,74110,74112],{"className":74111},[886],[888,74113,74114],{"xmlns":890},[892,74115,74116,74150],{},[895,74117,74118,74120,74122,74124,74126,74128,74130,74132,74134,74136,74142,74144],{},[898,74119,1769],{},[898,74121,1940],{},[1711,74123,1836],{},[2111,74125,50301],{},[1711,74127,2095],{},[2111,74129,41617],{},[898,74131,6796],{},[1711,74133,2460],{},[2111,74135,6262],{},[1716,74137,74138,74140],{},[898,74139,6796],{},[2111,74141,2963],{},[1711,74143,2095],{},[1716,74145,74146,74148],{},[898,74147,6796],{},[2111,74149,3034],{},[902,74151,74152],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,74155,74157],{"className":74156},[886],[888,74158,74159],{"xmlns":890},[892,74160,74161,74169],{},[895,74162,74163,74165,74167],{},[898,74164,1769],{},[898,74166,43937],{},[898,74168,1940],{},[902,74170,59107],{"encoding":904},[883,74172,74174],{"className":74173},[886],[888,74175,74176],{"xmlns":890},[892,74177,74178,74184],{},[895,74179,74180,74182],{},[898,74181,14409],{},[898,74183,1940],{},[902,74185,59089],{"encoding":904},[883,74187,74189],{"className":74188},[886],[888,74190,74191],{"xmlns":890},[892,74192,74193,74201],{},[895,74194,74195,74197,74199],{},[898,74196,8243],{},[898,74198,43937],{},[898,74200,1940],{},[902,74202,58909],{"encoding":904},[883,74204,74206],{"className":74205},[886],[888,74207,74208],{"xmlns":890},[892,74209,74210,74216],{},[895,74211,74212,74214],{},[898,74213,8243],{},[898,74215,1940],{},[902,74217,59158],{"encoding":904},[883,74219,74221],{"className":74220},[886],[888,74222,74223],{"xmlns":890},[892,74224,74225,74233],{},[895,74226,74227,74229,74231],{},[898,74228,8243],{},[898,74230,14409],{},[898,74232,1940],{},[902,74234,59125],{"encoding":904},[883,74236,74238],{"className":74237},[886],[888,74239,74240],{"xmlns":890},[892,74241,74242,74248],{},[895,74243,74244,74246],{},[898,74245,1790],{},[898,74247,1940],{},[902,74249,58890],{"encoding":904},[724,74251,74252,73691,74255,74285,74286,73468,74301,10454,74314,1343,74332,1343,74350,73535,74368,73558,74390,74405,74406,74419,74420,2186],{},[38,74253,74254],{},"3.9",[883,74256,74258],{"className":74257},[886],[888,74259,74260],{"xmlns":890},[892,74261,74262,74282],{},[895,74263,74264,74266,74268,74270,74272,74274,74276],{},[898,74265,1769],{},[898,74267,1940],{},[1711,74269,1836],{},[2111,74271,4807],{},[1711,74273,2095],{},[2111,74275,22919],{},[1716,74277,74278,74280],{},[898,74279,6796],{},[2111,74281,2963],{},[902,74283,74284],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,74287,74289],{"className":74288},[886],[888,74290,74291],{"xmlns":890},[892,74292,74293,74299],{},[895,74294,74295,74297],{},[898,74296,1769],{},[898,74298,1940],{},[902,74300,7241],{"encoding":904},[883,74302,74304],{"className":74303},[886],[888,74305,74306],{"xmlns":890},[892,74307,74308,74312],{},[895,74309,74310],{},[898,74311,6796],{},[902,74313,6796],{"encoding":904},[883,74315,74317],{"className":74316},[886],[888,74318,74319],{"xmlns":890},[892,74320,74321,74329],{},[895,74322,74323,74325,74327],{},[898,74324,6796],{},[1711,74326,1836],{},[2111,74328,4712],{},[902,74330,74331],{"encoding":904},"Q = 10",[883,74333,74335],{"className":74334},[886],[888,74336,74337],{"xmlns":890},[892,74338,74339,74347],{},[895,74340,74341,74343,74345],{},[898,74342,6796],{},[1711,74344,1836],{},[2111,74346,4306],{},[902,74348,74349],{"encoding":904},"Q = 20",[883,74351,74353],{"className":74352},[886],[888,74354,74355],{"xmlns":890},[892,74356,74357,74365],{},[895,74358,74359,74361,74363],{},[898,74360,6796],{},[1711,74362,1836],{},[2111,74364,41617],{},[902,74366,74367],{"encoding":904},"Q = 30",[883,74369,74371],{"className":74370},[886],[888,74372,74373],{"xmlns":890},[892,74374,74375,74387],{},[895,74376,74377,74379,74381,74383,74385],{},[898,74378,1790],{},[898,74380,1940],{},[1711,74382,1714],{"stretchy":1713},[2111,74384,39842],{},[1711,74386,1735],{"stretchy":1713},[902,74388,74389],{"encoding":904},"MC(15)",[883,74391,74393],{"className":74392},[886],[888,74394,74395],{"xmlns":890},[892,74396,74397,74403],{},[895,74398,74399,74401],{},[898,74400,1769],{},[898,74402,1940],{},[902,74404,7241],{"encoding":904}," v důsledku změny ",[883,74407,74409],{"className":74408},[886],[888,74410,74411],{"xmlns":890},[892,74412,74413,74417],{},[895,74414,74415],{},[898,74416,6796],{},[902,74418,6796],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,74421,74423],{"className":74422},[886],[888,74424,74425],{"xmlns":890},[892,74426,74427,74433],{},[895,74428,74429,74431],{},[898,74430,1769],{},[898,74432,1940],{},[902,74434,7241],{"encoding":904},[724,74436,74437,74440,74441,74042,74477,74492,74493,73652,74512,74405,74527,74540],{},[38,74438,74439],{},"3.10"," Jsou dány mezní náklady ",[883,74442,74444],{"className":74443},[886],[888,74445,74446],{"xmlns":890},[892,74447,74448,74474],{},[895,74449,74450,74452,74454,74456,74458,74460,74462,74464,74466,74468],{},[898,74451,1790],{},[898,74453,1940],{},[1711,74455,1836],{},[2111,74457,7126],{},[1711,74459,2460],{},[2111,74461,45460],{},[898,74463,6796],{},[1711,74465,2095],{},[2111,74467,68157],{},[1716,74469,74470,74472],{},[898,74471,6796],{},[2111,74473,2963],{},[902,74475,74476],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,74478,74480],{"className":74479},[886],[888,74481,74482],{"xmlns":890},[892,74483,74484,74490],{},[895,74485,74486,74488],{},[898,74487,1769],{},[898,74489,1940],{},[902,74491,7241],{"encoding":904},", jestliže fixní náklady ",[883,74494,74496],{"className":74495},[886],[888,74497,74498],{"xmlns":890},[892,74499,74500,74510],{},[895,74501,74502,74504,74506,74508],{},[898,74503,14409],{},[898,74505,1940],{},[1711,74507,1836],{},[2111,74509,4282],{},[902,74511,15607],{"encoding":904},[883,74513,74515],{"className":74514},[886],[888,74516,74517],{"xmlns":890},[892,74518,74519,74525],{},[895,74520,74521,74523],{},[898,74522,1769],{},[898,74524,1940],{},[902,74526,7241],{"encoding":904},[883,74528,74530],{"className":74529},[886],[888,74531,74532],{"xmlns":890},[892,74533,74534,74538],{},[895,74535,74536],{},[898,74537,6796],{},[902,74539,6796],{"encoding":904}," z 15 na 20.",[724,74542,74543,73691,74546,74589,74590,74603,74604,74619,74620,74635,74636,74603,74649,74619,74666,74683,74684,74603,74697,74619,74712,74727,74728,74748,74749,74772],{},[38,74544,74545],{},"3.11",[883,74547,74549],{"className":74548},[886],[888,74550,74551],{"xmlns":890},[892,74552,74553,74587],{},[895,74554,74555,74557,74559,74561,74563,74565,74567,74569,74571,74573,74579,74581],{},[898,74556,1769],{},[898,74558,1940],{},[1711,74560,1836],{},[2111,74562,4282],{},[1711,74564,2095],{},[2111,74566,4372],{},[898,74568,6796],{},[1711,74570,2460],{},[2111,74572,4798],{},[1716,74574,74575,74577],{},[898,74576,6796],{},[2111,74578,2963],{},[1711,74580,2095],{},[1716,74582,74583,74585],{},[898,74584,6796],{},[2111,74586,3034],{},[902,74588,64505],{"encoding":904},". (a) Určete ",[883,74591,74593],{"className":74592},[886],[888,74594,74595],{"xmlns":890},[892,74596,74597,74601],{},[895,74598,74599],{},[898,74600,6796],{},[902,74602,6796],{"encoding":904},", které minimalizuje ",[883,74605,74607],{"className":74606},[886],[888,74608,74609],{"xmlns":890},[892,74610,74611,74617],{},[895,74612,74613,74615],{},[898,74614,1790],{},[898,74616,1940],{},[902,74618,58890],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,74621,74623],{"className":74622},[886],[888,74624,74625],{"xmlns":890},[892,74626,74627,74633],{},[895,74628,74629,74631],{},[898,74630,1790],{},[898,74632,1940],{},[902,74634,58890],{"encoding":904},". (b) Určete ",[883,74637,74639],{"className":74638},[886],[888,74640,74641],{"xmlns":890},[892,74642,74643,74647],{},[895,74644,74645],{},[898,74646,6796],{},[902,74648,6796],{"encoding":904},[883,74650,74652],{"className":74651},[886],[888,74653,74654],{"xmlns":890},[892,74655,74656,74664],{},[895,74657,74658,74660,74662],{},[898,74659,8243],{},[898,74661,43937],{},[898,74663,1940],{},[902,74665,58909],{"encoding":904},[883,74667,74669],{"className":74668},[886],[888,74670,74671],{"xmlns":890},[892,74672,74673,74681],{},[895,74674,74675,74677,74679],{},[898,74676,8243],{},[898,74678,43937],{},[898,74680,1940],{},[902,74682,58909],{"encoding":904},". (c) Určete ",[883,74685,74687],{"className":74686},[886],[888,74688,74689],{"xmlns":890},[892,74690,74691,74695],{},[895,74692,74693],{},[898,74694,6796],{},[902,74696,6796],{"encoding":904},[883,74698,74700],{"className":74699},[886],[888,74701,74702],{"xmlns":890},[892,74703,74704,74710],{},[895,74705,74706,74708],{},[898,74707,8243],{},[898,74709,1940],{},[902,74711,59158],{"encoding":904},[883,74713,74715],{"className":74714},[886],[888,74716,74717],{"xmlns":890},[892,74718,74719,74725],{},[895,74720,74721,74723],{},[898,74722,8243],{},[898,74724,1940],{},[902,74726,59158],{"encoding":904}," (rada: hledaný kořen ",[883,74729,74731],{"className":74730},[886],[888,74732,74733],{"xmlns":890},[892,74734,74735,74745],{},[895,74736,74737,74739],{},[898,74738,8243],{},[1716,74740,74741,74743],{},[898,74742,1940],{},[1711,74744,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,74746,74747],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,74750,74752],{"className":74751},[886],[888,74753,74754],{"xmlns":890},[892,74755,74756,74769],{},[895,74757,74758,74760,74763,74765,74767],{},[1711,74759,1714],{"stretchy":1713},[2111,74761,74762],{},"4,7",[1711,74764,12405],{"separator":1725},[2111,74766,9263],{},[1711,74768,1735],{"stretchy":1713},[902,74770,74771],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,74774,74775,74778,74779,6635,74807,74824,74825,25192,74866,74887],{},[38,74776,74777],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,74780,74782],{"className":74781},[886],[888,74783,74784],{"xmlns":890},[892,74785,74786,74804],{},[895,74787,74788,74790,74792,74794,74796,74798,74800,74802],{},[898,74789,8243],{},[898,74791,1940],{},[1711,74793,1836],{},[898,74795,8243],{},[898,74797,1940],{},[1711,74799,1714],{"stretchy":1713},[898,74801,6796],{},[1711,74803,1735],{"stretchy":1713},[902,74805,74806],{"encoding":904},"AC = AC(Q)",[883,74808,74810],{"className":74809},[886],[888,74811,74812],{"xmlns":890},[892,74813,74814,74822],{},[895,74815,74816],{},[2884,74817,74818,74820],{},[898,74819,6796],{},[2111,74821,2113],{},[902,74823,41906],{"encoding":904}," minimum, pak platí ",[883,74826,74828],{"className":74827},[886],[888,74829,74830],{"xmlns":890},[892,74831,74832,74864],{},[895,74833,74834,74836,74838,74840,74846,74848,74850,74852,74854,74856,74862],{},[898,74835,8243],{},[898,74837,1940],{},[1711,74839,1714],{"stretchy":1713},[2884,74841,74842,74844],{},[898,74843,6796],{},[2111,74845,2113],{},[1711,74847,1735],{"stretchy":1713},[1711,74849,1836],{},[898,74851,1790],{},[898,74853,1940],{},[1711,74855,1714],{"stretchy":1713},[2884,74857,74858,74860],{},[898,74859,6796],{},[2111,74861,2113],{},[1711,74863,1735],{"stretchy":1713},[902,74865,66167],{"encoding":904},[883,74867,74869],{"className":74868},[886],[888,74870,74871],{"xmlns":890},[892,74872,74873,74885],{},[895,74874,74875,74877,74879,74881,74883],{},[898,74876,1790],{},[898,74878,1940],{},[1711,74880,1714],{"stretchy":1713},[898,74882,6796],{},[1711,74884,1735],{"stretchy":1713},[902,74886,71291],{"encoding":904}," jsou mezní náklady.",[724,74889,74890,73691,74893,74153,74927,74603,74940,74619,74955,2186],{},[38,74891,74892],{},"3.13",[883,74894,74896],{"className":74895},[886],[888,74897,74898],{"xmlns":890},[892,74899,74900,74924],{},[895,74901,74902,74904,74906,74908,74914,74916,74918,74920,74922],{},[898,74903,1769],{},[898,74905,1940],{},[1711,74907,1836],{},[1716,74909,74910,74912],{},[898,74911,6796],{},[2111,74913,2963],{},[1711,74915,2095],{},[2111,74917,2963],{},[898,74919,6796],{},[1711,74921,2095],{},[2111,74923,4372],{},[902,74925,74926],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,74928,74930],{"className":74929},[886],[888,74931,74932],{"xmlns":890},[892,74933,74934,74938],{},[895,74935,74936],{},[898,74937,6796],{},[902,74939,6796],{"encoding":904},[883,74941,74943],{"className":74942},[886],[888,74944,74945],{"xmlns":890},[892,74946,74947,74953],{},[895,74948,74949,74951],{},[898,74950,8243],{},[898,74952,1940],{},[902,74954,59158],{"encoding":904},[883,74956,74958],{"className":74957},[886],[888,74959,74960],{"xmlns":890},[892,74961,74962,74968],{},[895,74963,74964,74966],{},[898,74965,8243],{},[898,74967,1940],{},[902,74969,59158],{"encoding":904},[724,74971,74972,74975,74976,6635,75008,74824,75025,25192,75068,74887],{},[38,74973,74974],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,74977,74979],{"className":74978},[886],[888,74980,74981],{"xmlns":890},[892,74982,74983,75005],{},[895,74984,74985,74987,74989,74991,74993,74995,74997,74999,75001,75003],{},[898,74986,8243],{},[898,74988,43937],{},[898,74990,1940],{},[1711,74992,1836],{},[898,74994,8243],{},[898,74996,43937],{},[898,74998,1940],{},[1711,75000,1714],{"stretchy":1713},[898,75002,6796],{},[1711,75004,1735],{"stretchy":1713},[902,75006,75007],{"encoding":904},"AVC = AVC(Q)",[883,75009,75011],{"className":75010},[886],[888,75012,75013],{"xmlns":890},[892,75014,75015,75023],{},[895,75016,75017],{},[2884,75018,75019,75021],{},[898,75020,6796],{},[2111,75022,2113],{},[902,75024,41906],{"encoding":904},[883,75026,75028],{"className":75027},[886],[888,75029,75030],{"xmlns":890},[892,75031,75032,75066],{},[895,75033,75034,75036,75038,75040,75042,75048,75050,75052,75054,75056,75058,75064],{},[898,75035,8243],{},[898,75037,43937],{},[898,75039,1940],{},[1711,75041,1714],{"stretchy":1713},[2884,75043,75044,75046],{},[898,75045,6796],{},[2111,75047,2113],{},[1711,75049,1735],{"stretchy":1713},[1711,75051,1836],{},[898,75053,1790],{},[898,75055,1940],{},[1711,75057,1714],{"stretchy":1713},[2884,75059,75060,75062],{},[898,75061,6796],{},[2111,75063,2113],{},[1711,75065,1735],{"stretchy":1713},[902,75067,72617],{"encoding":904},[883,75069,75071],{"className":75070},[886],[888,75072,75073],{"xmlns":890},[892,75074,75075,75087],{},[895,75076,75077,75079,75081,75083,75085],{},[898,75078,1790],{},[898,75080,1940],{},[1711,75082,1714],{"stretchy":1713},[898,75084,6796],{},[1711,75086,1735],{"stretchy":1713},[902,75088,71291],{"encoding":904},[724,75090,75091,73691,75094,74153,75140,74603,75153,74619,75170,2186],{},[38,75092,75093],{},"3.15",[883,75095,75097],{"className":75096},[886],[888,75098,75099],{"xmlns":890},[892,75100,75101,75137],{},[895,75102,75103,75105,75107,75109,75111,75113,75115,75117,75119,75121,75127,75129,75131],{},[898,75104,1769],{},[898,75106,1940],{},[1711,75108,1836],{},[2111,75110,7120],{},[1711,75112,2095],{},[2111,75114,39842],{},[898,75116,6796],{},[1711,75118,2460],{},[2111,75120,2963],{},[1716,75122,75123,75125],{},[898,75124,6796],{},[2111,75126,2963],{},[1711,75128,2095],{},[2111,75130,4491],{},[1716,75132,75133,75135],{},[898,75134,6796],{},[2111,75136,3034],{},[902,75138,75139],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,75141,75143],{"className":75142},[886],[888,75144,75145],{"xmlns":890},[892,75146,75147,75151],{},[895,75148,75149],{},[898,75150,6796],{},[902,75152,6796],{"encoding":904},[883,75154,75156],{"className":75155},[886],[888,75157,75158],{"xmlns":890},[892,75159,75160,75168],{},[895,75161,75162,75164,75166],{},[898,75163,8243],{},[898,75165,43937],{},[898,75167,1940],{},[902,75169,58909],{"encoding":904},[883,75171,75173],{"className":75172},[886],[888,75174,75175],{"xmlns":890},[892,75176,75177,75185],{},[895,75178,75179,75181,75183],{},[898,75180,8243],{},[898,75182,43937],{},[898,75184,1940],{},[902,75186,58909],{"encoding":904},[724,75188,75189,75192,75193,75206,75207,75227],{},[38,75190,75191],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,75194,75196],{"className":75195},[886],[888,75197,75198],{"xmlns":890},[892,75199,75200,75204],{},[895,75201,75202],{},[898,75203,6047],{},[902,75205,6047],{"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 ",[883,75208,75210],{"className":75209},[886],[888,75211,75212],{"xmlns":890},[892,75213,75214,75224],{},[895,75215,75216,75218,75220,75222],{},[2111,75217,4712],{},[1942,75219,2519],{},[2111,75221,62680],{},[898,75223,6047],{},[902,75225,75226],{"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.",[198,75229,75231],{"id":75230},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,75233,75234,75237,75238,2009,75260,75286],{},[38,75235,75236],{},"3.17"," Jsou dány ",[883,75239,75241],{"className":75240},[886],[888,75242,75243],{"xmlns":890},[892,75244,75245,75257],{},[895,75246,75247,75249,75251,75253,75255],{},[898,75248,1769],{},[898,75250,7985],{},[1711,75252,1836],{},[2111,75254,4712],{},[898,75256,6796],{},[902,75258,75259],{"encoding":904},"TR = 10Q",[883,75261,75263],{"className":75262},[886],[888,75264,75265],{"xmlns":890},[892,75266,75267,75283],{},[895,75268,75269,75271,75273,75275,75277,75279,75281],{},[898,75270,1769],{},[898,75272,1940],{},[1711,75274,1836],{},[2111,75276,4282],{},[1711,75278,2095],{},[2111,75280,4798],{},[898,75282,6796],{},[902,75284,75285],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,75288,75289,75292,75293,10171,75308,75323,75324,1343,75346,25192,75373,75395,75396,75430],{},[38,75290,75291],{},"3.18"," Odvoďte, že jestliže ",[883,75294,75296],{"className":75295},[886],[888,75297,75298],{"xmlns":890},[892,75299,75300,75306],{},[895,75301,75302,75304],{},[898,75303,1769],{},[898,75305,7985],{},[902,75307,8085],{"encoding":904},[883,75309,75311],{"className":75310},[886],[888,75312,75313],{"xmlns":890},[892,75314,75315,75321],{},[895,75316,75317,75319],{},[898,75318,1769],{},[898,75320,1940],{},[902,75322,7241],{"encoding":904}," jsou lineární tvaru ",[883,75325,75327],{"className":75326},[886],[888,75328,75329],{"xmlns":890},[892,75330,75331,75343],{},[895,75332,75333,75335,75337,75339,75341],{},[898,75334,1769],{},[898,75336,7985],{},[1711,75338,1836],{},[898,75340,724],{},[898,75342,6796],{},[902,75344,75345],{"encoding":904},"TR = pQ",[883,75347,75349],{"className":75348},[886],[888,75350,75351],{"xmlns":890},[892,75352,75353,75370],{},[895,75354,75355,75357,75359,75361,75364,75366,75368],{},[898,75356,1769],{},[898,75358,1940],{},[1711,75360,1836],{},[898,75362,75363],{},"m",[1711,75365,2095],{},[898,75367,40458],{},[898,75369,6796],{},[902,75371,75372],{"encoding":904},"TC = m + nQ",[883,75374,75376],{"className":75375},[886],[888,75377,75378],{"xmlns":890},[892,75379,75380,75392],{},[895,75381,75382,75384,75386,75388,75390],{},[898,75383,75363],{},[1711,75385,1726],{"separator":1725},[898,75387,40458],{},[1711,75389,1726],{"separator":1725},[898,75391,724],{},[902,75393,75394],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,75397,75399],{"className":75398},[886],[888,75400,75401],{"xmlns":890},[892,75402,75403,75427],{},[895,75404,75405,75411,75413],{},[1716,75406,75407,75409],{},[898,75408,6796],{},[1711,75410,1793],{},[1711,75412,1836],{},[2509,75414,75415],{"scriptlevel":2113,"displaystyle":1713},[2525,75416,75417,75419],{},[898,75418,75363],{},[895,75420,75421,75423,75425],{},[898,75422,724],{},[1711,75424,2460],{},[898,75426,40458],{},[902,75428,75429],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,75432,75433,75237,75436,2009,75470,74589,75496,75509,75510,73341,75525,75540,75541,73325,75554,73341,75569,75584],{},[38,75434,75435],{},"3.19",[883,75437,75439],{"className":75438},[886],[888,75440,75441],{"xmlns":890},[892,75442,75443,75467],{},[895,75444,75445,75447,75449,75451,75453,75455,75461,75463,75465],{},[898,75446,1769],{},[898,75448,7985],{},[1711,75450,1836],{},[1711,75452,2460],{},[2111,75454,2963],{},[1716,75456,75457,75459],{},[898,75458,6796],{},[2111,75460,2963],{},[1711,75462,2095],{},[2111,75464,26544],{},[898,75466,6796],{},[902,75468,75469],{"encoding":904},"TR = -2Q^2 + 14Q",[883,75471,75473],{"className":75472},[886],[888,75474,75475],{"xmlns":890},[892,75476,75477,75493],{},[895,75478,75479,75481,75483,75485,75487,75489,75491],{},[898,75480,1769],{},[898,75482,1940],{},[1711,75484,1836],{},[2111,75486,2963],{},[898,75488,6796],{},[1711,75490,2095],{},[2111,75492,4712],{},[902,75494,75495],{"encoding":904},"TC = 2Q + 10",[883,75497,75499],{"className":75498},[886],[888,75500,75501],{"xmlns":890},[892,75502,75503,75507],{},[895,75504,75505],{},[898,75506,6796],{},[902,75508,6796],{"encoding":904},", které maximalizuje zisk ",[883,75511,75513],{"className":75512},[886],[888,75514,75515],{"xmlns":890},[892,75516,75517,75523],{},[895,75518,75519,75521],{},[898,75520,7929],{},[898,75522,7985],{},[902,75524,67077],{"encoding":904},[883,75526,75528],{"className":75527},[886],[888,75529,75530],{"xmlns":890},[892,75531,75532,75538],{},[895,75533,75534,75536],{},[898,75535,7929],{},[898,75537,7985],{},[902,75539,67077],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,75542,75544],{"className":75543},[886],[888,75545,75546],{"xmlns":890},[892,75547,75548,75552],{},[895,75549,75550],{},[898,75551,6796],{},[902,75553,6796],{"encoding":904},[883,75555,75557],{"className":75556},[886],[888,75558,75559],{"xmlns":890},[892,75560,75561,75567],{},[895,75562,75563,75565],{},[898,75564,1769],{},[898,75566,7985],{},[902,75568,8085],{"encoding":904},[883,75570,75572],{"className":75571},[886],[888,75573,75574],{"xmlns":890},[892,75575,75576,75582],{},[895,75577,75578,75580],{},[898,75579,1769],{},[898,75581,7985],{},[902,75583,8085],{"encoding":904},". (d) Graficky interpretujte.",[724,75586,75587,51282,75590,1343,75616,1343,75635,74589,75655,75509,75668,73341,75683,75698,75699,75721,75722,74772],{},[38,75588,75589],{},"3.20",[883,75591,75593],{"className":75592},[886],[888,75594,75595],{"xmlns":890},[892,75596,75597,75613],{},[895,75598,75599,75601,75603,75605,75607],{},[898,75600,7929],{},[1711,75602,1836],{},[2111,75604,23740],{},[1711,75606,2460],{},[1716,75608,75609,75611],{},[898,75610,6796],{},[2111,75612,2963],{},[902,75614,75615],{"encoding":904},"P = 400 - Q^2",[883,75617,75619],{"className":75618},[886],[888,75620,75621],{"xmlns":890},[892,75622,75623,75633],{},[895,75624,75625,75627,75629,75631],{},[898,75626,14409],{},[898,75628,1940],{},[1711,75630,1836],{},[2111,75632,4282],{},[902,75634,15607],{"encoding":904},[883,75636,75638],{"className":75637},[886],[888,75639,75640],{"xmlns":890},[892,75641,75642,75652],{},[895,75643,75644,75646,75648,75650],{},[898,75645,1790],{},[898,75647,1940],{},[1711,75649,1836],{},[2111,75651,4306],{},[902,75653,75654],{"encoding":904},"MC = 20",[883,75656,75658],{"className":75657},[886],[888,75659,75660],{"xmlns":890},[892,75661,75662,75666],{},[895,75663,75664],{},[898,75665,6796],{},[902,75667,6796],{"encoding":904},[883,75669,75671],{"className":75670},[886],[888,75672,75673],{"xmlns":890},[892,75674,75675,75681],{},[895,75676,75677,75679],{},[898,75678,7929],{},[898,75680,7985],{},[902,75682,67077],{"encoding":904},[883,75684,75686],{"className":75685},[886],[888,75687,75688],{"xmlns":890},[892,75689,75690,75696],{},[895,75691,75692,75694],{},[898,75693,7929],{},[898,75695,7985],{},[902,75697,67077],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,75700,75702],{"className":75701},[886],[888,75703,75704],{"xmlns":890},[892,75705,75706,75718],{},[895,75707,75708,75710,75712,75714,75716],{},[1711,75709,1714],{"stretchy":1713},[2111,75711,2113],{},[1711,75713,1726],{"separator":1725},[2111,75715,2238],{},[1711,75717,1735],{"stretchy":1713},[902,75719,75720],{"encoding":904},"(0, 1)",", druhý do ",[883,75723,75725],{"className":75724},[886],[888,75726,75727],{"xmlns":890},[892,75728,75729,75742],{},[895,75730,75731,75733,75736,75738,75740],{},[1711,75732,1714],{"stretchy":1713},[2111,75734,75735],{},"19",[1711,75737,1726],{"separator":1725},[2111,75739,4306],{},[1711,75741,1735],{"stretchy":1713},[902,75743,75744],{"encoding":904},"(19, 20)",[724,75746,75747,75750,75751,6635,75779,75796,75797,2186],{},[38,75748,75749],{},"3.21"," Dokažte, že má-li zisk ",[883,75752,75754],{"className":75753},[886],[888,75755,75756],{"xmlns":890},[892,75757,75758,75776],{},[895,75759,75760,75762,75764,75766,75768,75770,75772,75774],{},[898,75761,7929],{},[898,75763,7985],{},[1711,75765,1836],{},[898,75767,7929],{},[898,75769,7985],{},[1711,75771,1714],{"stretchy":1713},[898,75773,6796],{},[1711,75775,1735],{"stretchy":1713},[902,75777,75778],{"encoding":904},"PR = PR(Q)",[883,75780,75782],{"className":75781},[886],[888,75783,75784],{"xmlns":890},[892,75785,75786,75794],{},[895,75787,75788],{},[2884,75789,75790,75792],{},[898,75791,6796],{},[2111,75793,2113],{},[902,75795,41906],{"encoding":904}," maximum, pak platí ",[883,75798,75800],{"className":75799},[886],[888,75801,75802],{"xmlns":890},[892,75803,75804,75836],{},[895,75805,75806,75808,75810,75812,75818,75820,75822,75824,75826,75828,75834],{},[898,75807,1790],{},[898,75809,7985],{},[1711,75811,1714],{"stretchy":1713},[2884,75813,75814,75816],{},[898,75815,6796],{},[2111,75817,2113],{},[1711,75819,1735],{"stretchy":1713},[1711,75821,1836],{},[898,75823,1790],{},[898,75825,1940],{},[1711,75827,1714],{"stretchy":1713},[2884,75829,75830,75832],{},[898,75831,6796],{},[2111,75833,2113],{},[1711,75835,1735],{"stretchy":1713},[902,75837,69243],{"encoding":904},[724,75839,75840,75843,75844,2009,75859,59623,75874,75509,75887,75902,75903,1343,75930,75967,75968,1343,75995,2186],{},[38,75841,75842],{},"3.22"," Pro zadané ",[883,75845,75847],{"className":75846},[886],[888,75848,75849],{"xmlns":890},[892,75850,75851,75857],{},[895,75852,75853,75855],{},[898,75854,1790],{},[898,75856,7985],{},[902,75858,10615],{"encoding":904},[883,75860,75862],{"className":75861},[886],[888,75863,75864],{"xmlns":890},[892,75865,75866,75872],{},[895,75867,75868,75870],{},[898,75869,1790],{},[898,75871,1940],{},[902,75873,58890],{"encoding":904},[883,75875,75877],{"className":75876},[886],[888,75878,75879],{"xmlns":890},[892,75880,75881,75885],{},[895,75882,75883],{},[898,75884,6796],{},[902,75886,6796],{"encoding":904},[883,75888,75890],{"className":75889},[886],[888,75891,75892],{"xmlns":890},[892,75893,75894,75900],{},[895,75895,75896,75898],{},[898,75897,7929],{},[898,75899,7985],{},[902,75901,67077],{"encoding":904},". (a) ",[883,75904,75906],{"className":75905},[886],[888,75907,75908],{"xmlns":890},[892,75909,75910,75927],{},[895,75911,75912,75914,75916,75918,75921,75923,75925],{},[898,75913,1790],{},[898,75915,7985],{},[1711,75917,1836],{},[2111,75919,75920],{},"236",[1711,75922,2460],{},[2111,75924,45460],{},[898,75926,6796],{},[902,75928,75929],{"encoding":904},"MR = 236 - 16Q",[883,75931,75933],{"className":75932},[886],[888,75934,75935],{"xmlns":890},[892,75936,75937,75964],{},[895,75938,75939,75941,75943,75945,75947,75953,75955,75958,75960,75962],{},[898,75940,1790],{},[898,75942,1940],{},[1711,75944,1836],{},[2111,75946,3034],{},[1716,75948,75949,75951],{},[898,75950,6796],{},[2111,75952,2963],{},[1711,75954,2460],{},[2111,75956,75957],{},"32",[898,75959,6796],{},[1711,75961,2095],{},[2111,75963,9727],{},[902,75965,75966],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,75969,75971],{"className":75970},[886],[888,75972,75973],{"xmlns":890},[892,75974,75975,75992],{},[895,75976,75977,75979,75981,75983,75986,75988,75990],{},[898,75978,1790],{},[898,75980,7985],{},[1711,75982,1836],{},[2111,75984,75985],{},"280",[1711,75987,2460],{},[2111,75989,4306],{},[898,75991,6796],{},[902,75993,75994],{"encoding":904},"MR = 280 - 20Q",[883,75996,75998],{"className":75997},[886],[888,75999,76000],{"xmlns":890},[892,76001,76002,76029],{},[895,76003,76004,76006,76008,76010,76013,76019,76021,76023,76025,76027],{},[898,76005,1790],{},[898,76007,1940],{},[1711,76009,1836],{},[2111,76011,76012],{},"1,6",[1716,76014,76015,76017],{},[898,76016,6796],{},[2111,76018,2963],{},[1711,76020,2460],{},[2111,76022,39842],{},[898,76024,6796],{},[1711,76026,2095],{},[2111,76028,7126],{},[902,76030,76031],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,76033,76034,75843,76037,2009,76052,59623,76067,73325,76080,73341,76095,75902,76110,1343,76141,75967,76177,1343,76209,76253,76254,1343,76286,2186],{},[38,76035,76036],{},"3.23",[883,76038,76040],{"className":76039},[886],[888,76041,76042],{"xmlns":890},[892,76043,76044,76050],{},[895,76045,76046,76048],{},[898,76047,1769],{},[898,76049,7985],{},[902,76051,8085],{"encoding":904},[883,76053,76055],{"className":76054},[886],[888,76056,76057],{"xmlns":890},[892,76058,76059,76065],{},[895,76060,76061,76063],{},[898,76062,1769],{},[898,76064,1940],{},[902,76066,7241],{"encoding":904},[883,76068,76070],{"className":76069},[886],[888,76071,76072],{"xmlns":890},[892,76073,76074,76078],{},[895,76075,76076],{},[898,76077,6796],{},[902,76079,6796],{"encoding":904},[883,76081,76083],{"className":76082},[886],[888,76084,76085],{"xmlns":890},[892,76086,76087,76093],{},[895,76088,76089,76091],{},[898,76090,7929],{},[898,76092,7985],{},[902,76094,67077],{"encoding":904},[883,76096,76098],{"className":76097},[886],[888,76099,76100],{"xmlns":890},[892,76101,76102,76108],{},[895,76103,76104,76106],{},[898,76105,7929],{},[898,76107,7985],{},[902,76109,67077],{"encoding":904},[883,76111,76113],{"className":76112},[886],[888,76114,76115],{"xmlns":890},[892,76116,76117,76138],{},[895,76118,76119,76121,76123,76125,76128,76130,76132],{},[898,76120,1769],{},[898,76122,7985],{},[1711,76124,1836],{},[2111,76126,76127],{},"125",[898,76129,6796],{},[1711,76131,2460],{},[1716,76133,76134,76136],{},[898,76135,6796],{},[2111,76137,2963],{},[902,76139,76140],{"encoding":904},"TR = 125Q - Q^2",[883,76142,76144],{"className":76143},[886],[888,76145,76146],{"xmlns":890},[892,76147,76148,76174],{},[895,76149,76150,76152,76154,76156,76158,76160,76162,76164,76166,76168],{},[898,76151,1769],{},[898,76153,1940],{},[1711,76155,1836],{},[2111,76157,4807],{},[1711,76159,2095],{},[2111,76161,4798],{},[898,76163,6796],{},[1711,76165,2095],{},[2111,76167,8993],{},[1716,76169,76170,76172],{},[898,76171,6796],{},[2111,76173,2963],{},[902,76175,76176],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,76178,76180],{"className":76179},[886],[888,76181,76182],{"xmlns":890},[892,76183,76184,76206],{},[895,76185,76186,76188,76190,76192,76194,76196,76198,76200],{},[898,76187,1769],{},[898,76189,7985],{},[1711,76191,1836],{},[2111,76193,4306],{},[898,76195,6796],{},[1711,76197,2460],{},[2111,76199,2963],{},[1716,76201,76202,76204],{},[898,76203,6796],{},[2111,76205,2963],{},[902,76207,76208],{"encoding":904},"TR = 20Q - 2Q^2",[883,76210,76212],{"className":76211},[886],[888,76213,76214],{"xmlns":890},[892,76215,76216,76250],{},[895,76217,76218,76220,76222,76224,76226,76228,76230,76232,76234,76236,76242,76244],{},[898,76219,1769],{},[898,76221,1940],{},[1711,76223,1836],{},[2111,76225,2963],{},[1711,76227,2095],{},[2111,76229,4306],{},[898,76231,6796],{},[1711,76233,2460],{},[2111,76235,9568],{},[1716,76237,76238,76240],{},[898,76239,6796],{},[2111,76241,2963],{},[1711,76243,2095],{},[1716,76245,76246,76248],{},[898,76247,6796],{},[2111,76249,3034],{},[902,76251,76252],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,76255,76257],{"className":76256},[886],[888,76258,76259],{"xmlns":890},[892,76260,76261,76283],{},[895,76262,76263,76265,76267,76269,76271,76273,76275,76277],{},[898,76264,1769],{},[898,76266,7985],{},[1711,76268,1836],{},[2111,76270,6369],{},[898,76272,6796],{},[1711,76274,2460],{},[2111,76276,27387],{},[1716,76278,76279,76281],{},[898,76280,6796],{},[2111,76282,2963],{},[902,76284,76285],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,76287,76289],{"className":76288},[886],[888,76290,76291],{"xmlns":890},[892,76292,76293,76341],{},[895,76294,76295,76297,76299,76301,76303,76305,76307,76309,76311,76327,76329],{},[898,76296,1769],{},[898,76298,1940],{},[1711,76300,1836],{},[2111,76302,6369],{},[1711,76304,2095],{},[2111,76306,2963],{},[898,76308,6796],{},[1711,76310,2460],{},[2509,76312,76313],{"scriptlevel":2113,"displaystyle":1713},[2525,76314,76315,76325],{},[895,76316,76317,76319],{},[2111,76318,3034],{},[1716,76320,76321,76323],{},[898,76322,6796],{},[2111,76324,2963],{},[2111,76326,4712],{},[1711,76328,2095],{},[2509,76330,76331],{"scriptlevel":2113,"displaystyle":1713},[2525,76332,76333,76339],{},[1716,76334,76335,76337],{},[898,76336,6796],{},[2111,76338,3034],{},[2111,76340,4306],{},[902,76342,76343],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,76345,76346,76349,76350,76380,76381,76413,76414,25192,76444,76474],{},[38,76347,76348],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,76351,76353],{"className":76352},[886],[888,76354,76355],{"xmlns":890},[892,76356,76357,76377],{},[895,76358,76359,76365,76367,76369,76371],{},[2884,76360,76361,76363],{},[898,76362,7929],{},[2111,76364,2238],{},[1711,76366,1836],{},[2111,76368,4807],{},[1711,76370,2460],{},[2884,76372,76373,76375],{},[898,76374,6796],{},[2111,76376,2238],{},[902,76378,76379],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,76382,76384],{"className":76383},[886],[888,76385,76386],{"xmlns":890},[892,76387,76388,76410],{},[895,76389,76390,76396,76398,76400,76402,76404],{},[2884,76391,76392,76394],{},[898,76393,7929],{},[2111,76395,2963],{},[1711,76397,1836],{},[2111,76399,33679],{},[1711,76401,2460],{},[2111,76403,68157],{},[2884,76405,76406,76408],{},[898,76407,6796],{},[2111,76409,2963],{},[902,76411,76412],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,76415,76417],{"className":76416},[886],[888,76418,76419],{"xmlns":890},[892,76420,76421,76441],{},[895,76422,76423,76425,76427,76429,76431,76433,76435,76437,76439],{},[898,76424,1769],{},[898,76426,1940],{},[1711,76428,1836],{},[2111,76430,7120],{},[1942,76432,2519],{},[2111,76434,62680],{},[1711,76436,2095],{},[2111,76438,4306],{},[898,76440,6796],{},[902,76442,76443],{"encoding":904},"TC = 50\\,000 + 20Q",[883,76445,76447],{"className":76446},[886],[888,76448,76449],{"xmlns":890},[892,76450,76451,76471],{},[895,76452,76453,76455,76457,76463,76465],{},[898,76454,6796],{},[1711,76456,1836],{},[2884,76458,76459,76461],{},[898,76460,6796],{},[2111,76462,2238],{},[1711,76464,2095],{},[2884,76466,76467,76469],{},[898,76468,6796],{},[2111,76470,2963],{},[902,76472,76473],{"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.",[724,76476,76477,76480,76481,76511,76512,76413,76544,25192,76574,76603],{},[38,76478,76479],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,76482,76484],{"className":76483},[886],[888,76485,76486],{"xmlns":890},[892,76487,76488,76508],{},[895,76489,76490,76496,76498,76500,76502],{},[2884,76491,76492,76494],{},[898,76493,7929],{},[2111,76495,2238],{},[1711,76497,1836],{},[2111,76499,33679],{},[1711,76501,2460],{},[2884,76503,76504,76506],{},[898,76505,6796],{},[2111,76507,2238],{},[902,76509,76510],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,76513,76515],{"className":76514},[886],[888,76516,76517],{"xmlns":890},[892,76518,76519,76541],{},[895,76520,76521,76527,76529,76531,76533,76535],{},[2884,76522,76523,76525],{},[898,76524,7929],{},[2111,76526,2963],{},[1711,76528,1836],{},[2111,76530,12357],{},[1711,76532,2460],{},[2111,76534,8993],{},[2884,76536,76537,76539],{},[898,76538,6796],{},[2111,76540,2963],{},[902,76542,76543],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,76545,76547],{"className":76546},[886],[888,76548,76549],{"xmlns":890},[892,76550,76551,76571],{},[895,76552,76553,76555,76557,76559,76561,76563,76565,76567,76569],{},[898,76554,1769],{},[898,76556,1940],{},[1711,76558,1836],{},[2111,76560,4798],{},[1942,76562,2519],{},[2111,76564,62680],{},[1711,76566,2095],{},[2111,76568,4282],{},[898,76570,6796],{},[902,76572,76573],{"encoding":904},"TC = 5\\,000 + 100Q",[883,76575,76577],{"className":76576},[886],[888,76578,76579],{"xmlns":890},[892,76580,76581,76601],{},[895,76582,76583,76585,76587,76593,76595],{},[898,76584,6796],{},[1711,76586,1836],{},[2884,76588,76589,76591],{},[898,76590,6796],{},[2111,76592,2238],{},[1711,76594,2095],{},[2884,76596,76597,76599],{},[898,76598,6796],{},[2111,76600,2963],{},[902,76602,76473],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,76605,76607],{"id":76606},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,76609,76610,76613,76614,76661,76662,76679],{},[38,76611,76612],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,76615,76617],{"className":76616},[886],[888,76618,76619],{"xmlns":890},[892,76620,76621,76658],{},[895,76622,76623,76625,76627,76629,76631,76634,76640,76642,76645,76651,76653,76656],{},[898,76624,1769],{},[898,76626,43937],{},[898,76628,1940],{},[1711,76630,1836],{},[2111,76632,76633],{},"0,85",[1716,76635,76636,76638],{},[898,76637,6796],{},[2111,76639,3034],{},[1711,76641,2460],{},[2111,76643,76644],{},"11,9",[1716,76646,76647,76649],{},[898,76648,6796],{},[2111,76650,2963],{},[1711,76652,2095],{},[2111,76654,76655],{},"102",[898,76657,6796],{},[902,76659,76660],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,76663,76665],{"className":76664},[886],[888,76666,76667],{"xmlns":890},[892,76668,76669,76677],{},[895,76670,76671],{},[1716,76672,76673,76675],{},[898,76674,7929],{},[1711,76676,1793],{},[902,76678,8391],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,76681,76682,74440,76685,76721],{},[38,76683,76684],{},"3.27",[883,76686,76688],{"className":76687},[886],[888,76689,76690],{"xmlns":890},[892,76691,76692,76718],{},[895,76693,76694,76696,76698,76700,76702,76708,76710,76712,76714,76716],{},[898,76695,1790],{},[898,76697,1940],{},[1711,76699,1836],{},[2111,76701,6926],{},[1716,76703,76704,76706],{},[898,76705,6796],{},[2111,76707,2963],{},[1711,76709,2460],{},[2111,76711,68038],{},[898,76713,6796],{},[1711,76715,2095],{},[2111,76717,34341],{},[902,76719,76720],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,76723,76724,73691,76727,76721],{},[38,76725,76726],{},"3.28",[883,76728,76730],{"className":76729},[886],[888,76731,76732],{"xmlns":890},[892,76733,76734,76770],{},[895,76735,76736,76738,76740,76742,76744,76750,76752,76754,76760,76762,76764,76766,76768],{},[898,76737,1769],{},[898,76739,1940],{},[1711,76741,1836],{},[2111,76743,8993],{},[1716,76745,76746,76748],{},[898,76747,6796],{},[2111,76749,3034],{},[1711,76751,2460],{},[2111,76753,27799],{},[1716,76755,76756,76758],{},[898,76757,6796],{},[2111,76759,2963],{},[1711,76761,2095],{},[2111,76763,7126],{},[898,76765,6796],{},[1711,76767,2095],{},[2111,76769,4807],{},[902,76771,76772],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,76774,5422],{"id":5421},[120,76776,76777,76805,76850,76922,76987,77027,77119,77225,77265,77379,77472,77536,77568,77628,77634,77698,77747,77801,77909,77964],{},[123,76778,76779,1700,76781,76804],{},[38,76780,59348],{},[883,76782,76784],{"className":76783},[886],[888,76785,76786],{"xmlns":890},[892,76787,76788,76802],{},[895,76789,76790,76792,76794,76796,76798,76800],{},[898,76791,1769],{},[898,76793,7985],{},[1711,76795,1836],{},[898,76797,7929],{},[1711,76799,4795],{},[898,76801,6796],{},[902,76803,70310],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,76806,76807,1700,76809,76849],{},[38,76808,59934],{},[883,76810,76812],{"className":76811},[886],[888,76813,76814],{"xmlns":890},[892,76815,76816,76846],{},[895,76817,76818,76820,76822,76824,76836,76838,76840,76842,76844],{},[898,76819,8243],{},[898,76821,7985],{},[1711,76823,1836],{},[2509,76825,76826],{"scriptlevel":2113,"displaystyle":1713},[2525,76827,76828,76834],{},[895,76829,76830,76832],{},[898,76831,1769],{},[898,76833,7985],{},[898,76835,6796],{},[1711,76837,1836],{},[898,76839,2778],{},[1711,76841,1714],{"stretchy":1713},[898,76843,6796],{},[1711,76845,1735],{"stretchy":1713},[902,76847,76848],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,76851,76852,1700,76854,76890,76891,76906,76907,2186],{},[38,76853,60082],{},[883,76855,76857],{"className":76856},[886],[888,76858,76859],{"xmlns":890},[892,76860,76861,76887],{},[895,76862,76863,76865,76867,76869],{},[898,76864,1790],{},[898,76866,7985],{},[1711,76868,1836],{},[2509,76870,76871],{"scriptlevel":2113,"displaystyle":1713},[2525,76872,76873,76881],{},[895,76874,76875,76877,76879],{},[898,76876,2098],{"mathvariant":2287},[898,76878,1769],{},[898,76880,7985],{},[895,76882,76883,76885],{},[898,76884,2098],{"mathvariant":2287},[898,76886,6796],{},[902,76888,76889],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,76892,76894],{"className":76893},[886],[888,76895,76896],{"xmlns":890},[892,76897,76898,76904],{},[895,76899,76900,76902],{},[898,76901,1769],{},[898,76903,7985],{},[902,76905,8085],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,76908,76910],{"className":76909},[886],[888,76911,76912],{"xmlns":890},[892,76913,76914,76920],{},[895,76915,76916,76918],{},[898,76917,8243],{},[898,76919,7985],{},[902,76921,59043],{"encoding":904},[123,76923,76924,1700,76927,1343,76957,2186],{},[38,76925,76926],{},"Diferenciál příjmu\u002Fnákladů",[883,76928,76930],{"className":76929},[886],[888,76931,76932],{"xmlns":890},[892,76933,76934,76954],{},[895,76935,76936,76938,76940,76942,76944,76946,76948,76950,76952],{},[898,76937,6892],{"mathvariant":2287},[898,76939,1769],{},[898,76941,7985],{},[1711,76943,6740],{},[898,76945,1790],{},[898,76947,7985],{},[1942,76949,2519],{},[898,76951,2098],{"mathvariant":2287},[898,76953,6796],{},[902,76955,76956],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,76958,76960],{"className":76959},[886],[888,76961,76962],{"xmlns":890},[892,76963,76964,76984],{},[895,76965,76966,76968,76970,76972,76974,76976,76978,76980,76982],{},[898,76967,6892],{"mathvariant":2287},[898,76969,1769],{},[898,76971,1940],{},[1711,76973,6740],{},[898,76975,1790],{},[898,76977,1940],{},[1942,76979,2519],{},[898,76981,2098],{"mathvariant":2287},[898,76983,6796],{},[902,76985,76986],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,76988,76989,1700,76991,2186],{},[38,76990,62204],{},[883,76992,76994],{"className":76993},[886],[888,76995,76996],{"xmlns":890},[892,76997,76998,77024],{},[895,76999,77000,77002,77004,77006,77008,77010,77012,77014,77016,77018,77020,77022],{},[898,77001,1769],{},[898,77003,1940],{},[1711,77005,1836],{},[898,77007,14409],{},[898,77009,1940],{},[1711,77011,2095],{},[898,77013,1769],{},[898,77015,43937],{},[898,77017,1940],{},[1711,77019,1714],{"stretchy":1713},[898,77021,6796],{},[1711,77023,1735],{"stretchy":1713},[902,77025,77026],{"encoding":904},"TC = FC + TVC(Q)",[123,77028,77029,1700,77032,1343,77047,1700,77049,1343,77072,1700,77075,2186],{},[38,77030,77031],{},"Fixní náklady",[883,77033,77035],{"className":77034},[886],[888,77036,77037],{"xmlns":890},[892,77038,77039,77045],{},[895,77040,77041,77043],{},[898,77042,14409],{},[898,77044,1940],{},[902,77046,59089],{"encoding":904},[38,77048,62357],{},[883,77050,77052],{"className":77051},[886],[888,77053,77054],{"xmlns":890},[892,77055,77056,77070],{},[895,77057,77058,77060,77062,77064,77066,77068],{},[898,77059,1769],{},[898,77061,43937],{},[898,77063,1940],{},[1711,77065,1714],{"stretchy":1713},[898,77067,6796],{},[1711,77069,1735],{"stretchy":1713},[902,77071,62354],{"encoding":904},[38,77073,77074],{},"variabilní náklady na jednotku",[883,77076,77078],{"className":77077},[886],[888,77079,77080],{"xmlns":890},[892,77081,77082,77116],{},[895,77083,77084,77086,77088,77090,77092,77094,77096],{},[898,77085,43937],{},[898,77087,1940],{},[1711,77089,1714],{"stretchy":1713},[898,77091,6796],{},[1711,77093,1735],{"stretchy":1713},[1711,77095,1836],{},[2509,77097,77098],{"scriptlevel":2113,"displaystyle":1713},[2525,77099,77100,77114],{},[895,77101,77102,77104,77106,77108,77110,77112],{},[898,77103,1769],{},[898,77105,43937],{},[898,77107,1940],{},[1711,77109,1714],{"stretchy":1713},[898,77111,6796],{},[1711,77113,1735],{"stretchy":1713},[898,77115,6796],{},[902,77117,77118],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,77120,77121,1700,77123,1343,77153,1700,77156,1343,77188,1700,77191,2186],{},[38,77122,62365],{},[883,77124,77126],{"className":77125},[886],[888,77127,77128],{"xmlns":890},[892,77129,77130,77150],{},[895,77131,77132,77134,77136,77138],{},[898,77133,8243],{},[898,77135,1940],{},[1711,77137,1836],{},[2509,77139,77140],{"scriptlevel":2113,"displaystyle":1713},[2525,77141,77142,77148],{},[895,77143,77144,77146],{},[898,77145,1769],{},[898,77147,1940],{},[898,77149,6796],{},[902,77151,77152],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,77154,77155],{},"průměrné fixní",[883,77157,77159],{"className":77158},[886],[888,77160,77161],{"xmlns":890},[892,77162,77163,77185],{},[895,77164,77165,77167,77169,77171,77173],{},[898,77166,8243],{},[898,77168,14409],{},[898,77170,1940],{},[1711,77172,1836],{},[2509,77174,77175],{"scriptlevel":2113,"displaystyle":1713},[2525,77176,77177,77183],{},[895,77178,77179,77181],{},[898,77180,14409],{},[898,77182,1940],{},[898,77184,6796],{},[902,77186,77187],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,77189,77190],{},"průměrné variabilní",[883,77192,77194],{"className":77193},[886],[888,77195,77196],{"xmlns":890},[892,77197,77198,77222],{},[895,77199,77200,77202,77204,77206,77208],{},[898,77201,8243],{},[898,77203,43937],{},[898,77205,1940],{},[1711,77207,1836],{},[2509,77209,77210],{"scriptlevel":2113,"displaystyle":1713},[2525,77211,77212,77220],{},[895,77213,77214,77216,77218],{},[898,77215,1769],{},[898,77217,43937],{},[898,77219,1940],{},[898,77221,6796],{},[902,77223,77224],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,77226,77227,1700,77229,2186],{},[38,77228,63552],{},[883,77230,77232],{"className":77231},[886],[888,77233,77234],{"xmlns":890},[892,77235,77236,77262],{},[895,77237,77238,77240,77242,77244],{},[898,77239,1790],{},[898,77241,1940],{},[1711,77243,1836],{},[2509,77245,77246],{"scriptlevel":2113,"displaystyle":1713},[2525,77247,77248,77256],{},[895,77249,77250,77252,77254],{},[898,77251,2098],{"mathvariant":2287},[898,77253,1769],{},[898,77255,1940],{},[895,77257,77258,77260],{},[898,77259,2098],{"mathvariant":2287},[898,77261,6796],{},[902,77263,77264],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,77266,77267,1700,77269,77317,77318,77331,77332,1343,77347,1343,77364,2186],{},[38,77268,64450],{},[883,77270,77272],{"className":77271},[886],[888,77273,77274],{"xmlns":890},[892,77275,77276,77314],{},[895,77277,77278,77280,77282,77284,77286,77288,77290,77292,77294,77296,77298,77304,77306,77308],{},[898,77279,1769],{},[898,77281,1940],{},[1711,77283,1836],{},[898,77285,14409],{},[898,77287,1940],{},[1711,77289,2095],{},[898,77291,207],{},[898,77293,6796],{},[1711,77295,2095],{},[898,77297,2223],{},[1716,77299,77300,77302],{},[898,77301,6796],{},[2111,77303,2963],{},[1711,77305,2095],{},[898,77307,2090],{},[1716,77309,77310,77312],{},[898,77311,6796],{},[2111,77313,3034],{},[902,77315,77316],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,77319,77321],{"className":77320},[886],[888,77322,77323],{"xmlns":890},[892,77324,77325,77329],{},[895,77326,77327],{},[898,77328,900],{},[902,77330,900],{"encoding":904},"-průběhem ",[883,77333,77335],{"className":77334},[886],[888,77336,77337],{"xmlns":890},[892,77338,77339,77345],{},[895,77340,77341,77343],{},[898,77342,8243],{},[898,77344,1940],{},[902,77346,59158],{"encoding":904},[883,77348,77350],{"className":77349},[886],[888,77351,77352],{"xmlns":890},[892,77353,77354,77362],{},[895,77355,77356,77358,77360],{},[898,77357,8243],{},[898,77359,43937],{},[898,77361,1940],{},[902,77363,58909],{"encoding":904},[883,77365,77367],{"className":77366},[886],[888,77368,77369],{"xmlns":890},[892,77370,77371,77377],{},[895,77372,77373,77375],{},[898,77374,1790],{},[898,77376,1940],{},[902,77378,58890],{"encoding":904},[123,77380,77381,77383,77384,14367,77399,77440,77441,65095,77456,77471],{},[38,77382,65532],{},": v bodě minima ",[883,77385,77387],{"className":77386},[886],[888,77388,77389],{"xmlns":890},[892,77390,77391,77397],{},[895,77392,77393,77395],{},[898,77394,8243],{},[898,77396,1940],{},[902,77398,59158],{"encoding":904},[883,77400,77402],{"className":77401},[886],[888,77403,77404],{"xmlns":890},[892,77405,77406,77438],{},[895,77407,77408,77410,77412,77414,77420,77422,77424,77426,77428,77430,77436],{},[898,77409,8243],{},[898,77411,1940],{},[1711,77413,1714],{"stretchy":1713},[2884,77415,77416,77418],{},[898,77417,6796],{},[2111,77419,2113],{},[1711,77421,1735],{"stretchy":1713},[1711,77423,1836],{},[898,77425,1790],{},[898,77427,1940],{},[1711,77429,1714],{"stretchy":1713},[2884,77431,77432,77434],{},[898,77433,6796],{},[2111,77435,2113],{},[1711,77437,1735],{"stretchy":1713},[902,77439,66167],{"encoding":904},"; geometricky ",[883,77442,77444],{"className":77443},[886],[888,77445,77446],{"xmlns":890},[892,77447,77448,77454],{},[895,77449,77450,77452],{},[898,77451,1790],{},[898,77453,1940],{},[902,77455,58890],{"encoding":904},[883,77457,77459],{"className":77458},[886],[888,77460,77461],{"xmlns":890},[892,77462,77463,77469],{},[895,77464,77465,77467],{},[898,77466,8243],{},[898,77468,1940],{},[902,77470,59158],{"encoding":904}," v jejím minimu.",[123,77473,77474,77383,77476,14367,77493,2186],{},[38,77475,66882],{},[883,77477,77479],{"className":77478},[886],[888,77480,77481],{"xmlns":890},[892,77482,77483,77491],{},[895,77484,77485,77487,77489],{},[898,77486,8243],{},[898,77488,43937],{},[898,77490,1940],{},[902,77492,58909],{"encoding":904},[883,77494,77496],{"className":77495},[886],[888,77497,77498],{"xmlns":890},[892,77499,77500,77534],{},[895,77501,77502,77504,77506,77508,77510,77516,77518,77520,77522,77524,77526,77532],{},[898,77503,8243],{},[898,77505,43937],{},[898,77507,1940],{},[1711,77509,1714],{"stretchy":1713},[2884,77511,77512,77514],{},[898,77513,6796],{},[2111,77515,2113],{},[1711,77517,1735],{"stretchy":1713},[1711,77519,1836],{},[898,77521,1790],{},[898,77523,1940],{},[1711,77525,1714],{"stretchy":1713},[2884,77527,77528,77530],{},[898,77529,6796],{},[2111,77531,2113],{},[1711,77533,1735],{"stretchy":1713},[902,77535,72617],{"encoding":904},[123,77537,77538,1700,77540,77567],{},[38,77539,67061],{},[883,77541,77543],{"className":77542},[886],[888,77544,77545],{"xmlns":890},[892,77546,77547,77565],{},[895,77548,77549,77551,77553,77555,77557,77559,77561,77563],{},[898,77550,7929],{},[898,77552,7985],{},[1711,77554,1836],{},[898,77556,1769],{},[898,77558,7985],{},[1711,77560,2460],{},[898,77562,1769],{},[898,77564,1940],{},[902,77566,58798],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,77569,77570,1648,77572,77574,77575,77601,77602,77627],{},[38,77571,67923],{},[614,77573,67186],{},") — hodnoty ",[883,77576,77578],{"className":77577},[886],[888,77579,77580],{"xmlns":890},[892,77581,77582,77598],{},[895,77583,77584,77590,77592],{},[2884,77585,77586,77588],{},[898,77587,6796],{},[898,77589,8243],{},[1711,77591,1726],{"separator":1725},[2884,77593,77594,77596],{},[898,77595,6796],{},[898,77597,26851],{},[902,77599,77600],{"encoding":904},"Q_A, Q_B"," splňující ",[883,77603,77605],{"className":77604},[886],[888,77606,77607],{"xmlns":890},[892,77608,77609,77625],{},[895,77610,77611,77613,77615,77617,77619,77621,77623],{},[898,77612,7929],{},[898,77614,7985],{},[1711,77616,1714],{"stretchy":1713},[898,77618,6796],{},[1711,77620,1735],{"stretchy":1713},[1711,77622,1836],{},[2111,77624,2113],{},[902,77626,67463],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,77629,77630,77633],{},[38,77631,77632],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,77635,77636,77638,77639,14367,77656,77697],{},[38,77637,68977],{}," — v bodě maxima zisku ",[883,77640,77642],{"className":77641},[886],[888,77643,77644],{"xmlns":890},[892,77645,77646,77654],{},[895,77647,77648],{},[2884,77649,77650,77652],{},[898,77651,6796],{},[2111,77653,2113],{},[902,77655,41906],{"encoding":904},[883,77657,77659],{"className":77658},[886],[888,77660,77661],{"xmlns":890},[892,77662,77663,77695],{},[895,77664,77665,77667,77669,77671,77677,77679,77681,77683,77685,77687,77693],{},[898,77666,1790],{},[898,77668,7985],{},[1711,77670,1714],{"stretchy":1713},[2884,77672,77673,77675],{},[898,77674,6796],{},[2111,77676,2113],{},[1711,77678,1735],{"stretchy":1713},[1711,77680,1836],{},[898,77682,1790],{},[898,77684,1940],{},[1711,77686,1714],{"stretchy":1713},[2884,77688,77689,77691],{},[898,77690,6796],{},[2111,77692,2113],{},[1711,77694,1735],{"stretchy":1713},[902,77696,69243],{"encoding":904}," (3.13).",[123,77699,77700,23899,77702,14367,77721,77746],{},[38,77701,70270],{},[883,77703,77705],{"className":77704},[886],[888,77706,77707],{"xmlns":890},[892,77708,77709,77718],{},[895,77710,77711,77713,77715],{},[898,77712,7929],{},[1711,77714,1836],{},[1942,77716,77717],{},"konst",[902,77719,77720],{"encoding":904},"P = \\text{konst}",[883,77722,77724],{"className":77723},[886],[888,77725,77726],{"xmlns":890},[892,77727,77728,77744],{},[895,77729,77730,77732,77734,77736,77738,77740,77742],{},[898,77731,7929],{},[1711,77733,1836],{},[898,77735,1790],{},[898,77737,1940],{},[1711,77739,1714],{"stretchy":1713},[898,77741,6796],{},[1711,77743,1735],{"stretchy":1713},[902,77745,70964],{"encoding":904}," (3.14).",[123,77748,77749,77752,77753,77782,77783,77800],{},[38,77750,77751],{},"Shutdown point"," — bod ",[883,77754,77756],{"className":77755},[886],[888,77757,77758],{"xmlns":890},[892,77759,77760,77780],{},[895,77761,77762,77764,77770,77772,77778],{},[1711,77763,1714],{"stretchy":1713},[1716,77765,77766,77768],{},[898,77767,6796],{},[1711,77769,1793],{},[1711,77771,1726],{"separator":1725},[1716,77773,77774,77776],{},[898,77775,7929],{},[1711,77777,1793],{},[1711,77779,1735],{"stretchy":1713},[902,77781,71253],{"encoding":904}," v minimu ",[883,77784,77786],{"className":77785},[886],[888,77787,77788],{"xmlns":890},[892,77789,77790,77798],{},[895,77791,77792,77794,77796],{},[898,77793,8243],{},[898,77795,43937],{},[898,77797,1940],{},[902,77799,58909],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,77802,77803,1700,77806,10454,77841,71523,77862,77875,77876,77891,77892,2186],{},[38,77804,77805],{},"Funkce nabídky firmy",[883,77807,77809],{"className":77808},[886],[888,77810,77811],{"xmlns":890},[892,77812,77813,77839],{},[895,77814,77815,77817,77819,77821,77823,77825,77827,77829,77831,77833,77835,77837],{},[898,77816,7929],{},[1711,77818,1836],{},[898,77820,2362],{},[1711,77822,1714],{"stretchy":1713},[898,77824,6796],{},[1711,77826,1735],{"stretchy":1713},[1711,77828,1836],{},[898,77830,1790],{},[898,77832,1940],{},[1711,77834,1714],{"stretchy":1713},[898,77836,6796],{},[1711,77838,1735],{"stretchy":1713},[902,77840,72720],{"encoding":904},[883,77842,77844],{"className":77843},[886],[888,77845,77846],{"xmlns":890},[892,77847,77848,77860],{},[895,77849,77850,77852,77854],{},[898,77851,6796],{},[1711,77853,8471],{},[1716,77855,77856,77858],{},[898,77857,6796],{},[1711,77859,1793],{},[902,77861,71522],{"encoding":904},[883,77863,77865],{"className":77864},[886],[888,77866,77867],{"xmlns":890},[892,77868,77869,77873],{},[895,77870,77871],{},[2111,77872,2113],{},[902,77874,2113],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,77877,77879],{"className":77878},[886],[888,77880,77881],{"xmlns":890},[892,77882,77883,77889],{},[895,77884,77885,77887],{},[898,77886,1790],{},[898,77888,1940],{},[902,77890,58890],{"encoding":904}," nad minimem ",[883,77893,77895],{"className":77894},[886],[888,77896,77897],{"xmlns":890},[892,77898,77899,77907],{},[895,77900,77901,77903,77905],{},[898,77902,8243],{},[898,77904,43937],{},[898,77906,1940],{},[902,77908,58909],{"encoding":904},[123,77910,77911,5204,77913,77934,77935,2186],{},[38,77912,53677],{},[883,77914,77916],{"className":77915},[886],[888,77917,77918],{"xmlns":890},[892,77919,77920,77932],{},[895,77921,77922,77924,77926],{},[898,77923,7929],{},[1711,77925,1836],{},[1716,77927,77928,77930],{},[898,77929,7929],{},[1711,77931,1793],{},[902,77933,8344],{"encoding":904}," konstantní ⇒ ",[883,77936,77938],{"className":77937},[886],[888,77939,77940],{"xmlns":890},[892,77941,77942,77962],{},[895,77943,77944,77946,77948,77950,77952,77954,77956],{},[898,77945,8243],{},[898,77947,7985],{},[1711,77949,1836],{},[898,77951,1790],{},[898,77953,7985],{},[1711,77955,1836],{},[1716,77957,77958,77960],{},[898,77959,7929],{},[1711,77961,1793],{},[902,77963,62196],{"encoding":904},[123,77965,77966,77969],{},[38,77967,77968],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,77971,5901],{"id":5900},[120,77973,77974,77993,78005],{},[123,77975,77976,1700,77978,1343,77981,1343,77984,1343,77987,1343,77990],{},[38,77977,54321],{},[207,77979,15915],{"className":77980,"dataFsResolvedFilePath":800,"href":801},[210],[207,77982,7822],{"className":77983,"dataFsResolvedFilePath":848,"href":849},[210],[207,77985,6375],{"className":77986,"dataFsResolvedFilePath":764,"href":765},[210],[207,77988,775],{"className":77989,"dataFsResolvedFilePath":773,"href":774},[210],[207,77991,859],{"className":77992,"dataFsResolvedFilePath":857,"href":858},[210],[123,77994,77995,1700,77997,1343,78001],{},[38,77996,40301],{},[207,77998,78000],{"className":77999,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,78002,78004],{"className":78003,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,78006,78007,1700,78009],{},[38,78008,5908],{},[207,78010,5914],{"className":78011,"dataFsResolvedFilePath":5912,"href":5913},[210],{"title":641,"searchDepth":642,"depth":642,"links":78013},[78014,78015,78022,78028,78032,78033,78037,78038,78039,78040,78046,78047],{"id":54552,"depth":642,"text":1241},{"id":59336,"depth":642,"text":59337,"children":78016},[78017,78018,78019,78020,78021],{"id":59347,"depth":649,"text":59348},{"id":59933,"depth":649,"text":59934},{"id":60081,"depth":649,"text":60082},{"id":60823,"depth":649,"text":60824},{"id":61478,"depth":649,"text":61479},{"id":62199,"depth":642,"text":62200,"children":78023},[78024,78025,78026,78027],{"id":62203,"depth":649,"text":62204},{"id":62364,"depth":649,"text":62365},{"id":63551,"depth":649,"text":63552},{"id":64449,"depth":649,"text":64450},{"id":65531,"depth":642,"text":65532,"children":78029},[78030,78031],{"id":20009,"depth":649,"text":20010},{"id":66881,"depth":649,"text":66882},{"id":67055,"depth":642,"text":67056},{"id":68976,"depth":642,"text":68977,"children":78034},[78035,78036],{"id":68990,"depth":649,"text":20010},{"id":70269,"depth":649,"text":70270},{"id":70901,"depth":642,"text":70902},{"id":72367,"depth":642,"text":72368},{"id":53479,"depth":642,"text":53480},{"id":72828,"depth":642,"text":72829,"children":78041},[78042,78043,78044,78045],{"id":72832,"depth":649,"text":72833},{"id":73684,"depth":649,"text":73685},{"id":75230,"depth":649,"text":75231},{"id":76606,"depth":649,"text":76607},{"id":5421,"depth":642,"text":5422},{"id":5900,"depth":642,"text":5901},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":58718,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,78054,78055,58770,78056,78057,78058],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":78061,"title":78062,"body":78063,"course":1128,"courses":659,"created":5973,"description":641,"extension":661,"meta":90160,"navigation":664,"path":90161,"seo":90162,"sources":90163,"stem":90164,"tags":90165,"type":5985,"updated":677,"__hash__":90171},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":78064,"toc":90117},[78065,78068,78424,78428,78431,78499,78551,78561,78565,78599,78640,78664,78687,78716,78783,78890,78933,78990,79065,79110,79114,79122,79130,79133,79398,79449,79529,79599,79622,79650,79695,79717,79721,79728,79777,79803,79954,79957,79994,80157,80265,80269,80306,80381,80450,80569,80691,80772,80778,80819,80892,80985,80989,81025,81113,81227,81332,81417,81557,81561,81609,81654,81660,81664,81667,81718,81768,81775,81841,81974,82019,82023,82044,82423,82518,82535,82589,82593,82675,82759,82929,82932,82975,83042,83116,83120,83125,83194,83202,83211,83289,83355,83360,83455,83498,83503,83551,83556,83604,83722,83805,83843,83946,84005,84146,84150,84193,84266,84290,84344,84351,84353,84398,84443,84454,84459,84495,84557,84580,84589,84690,84757,84830,84837,84928,84990,85026,85083,85142,85327,85423,85427,85431,85510,85515,85639,85725,85731,85841,85878,85969,86067,86070,86074,86140,86177,86299,86351,86355,86383,86435,86509,86614,86638,86697,86701,86719,86862,87010,87012,87047,87051,87053,87143,87273,87399,87491,87566,87570,87686,87790,87980,88016,88110,88116,88229,88532,88538,88656,88755,88831,88833,89995,89997],[12,78066,78062],{"id":78067},"produkce-produkční-funkce-cobb-douglas-mrts",[1921,78069,78070],{},[724,78071,78072,7867,78074,78076,78077,40494,78090,78103,78104,19974,78117,1648,78119,78143,78144,1700,78146,2009,78180,1700,78183,78211,78212,14367,78232,78262,78263,1648,78266,78294,78295,78298,78299,78329,78330,78360,78361,1700,78364,78404,78405,78423],{},[883,78073,7866],{},[38,78075,859],{}," popisuje vztah mezi vstupy (práce ",[883,78078,78080],{"className":78079},[886],[888,78081,78082],{"xmlns":890},[892,78083,78084,78088],{},[895,78085,78086],{},[898,78087,2888],{},[902,78089,2888],{"encoding":904},[883,78091,78093],{"className":78092},[886],[888,78094,78095],{"xmlns":890},[892,78096,78097,78101],{},[895,78098,78099],{},[898,78100,13774],{},[902,78102,13774],{"encoding":904},") a výstupem ",[883,78105,78107],{"className":78106},[886],[888,78108,78109],{"xmlns":890},[892,78110,78111,78115],{},[895,78112,78113],{},[898,78114,6796],{},[902,78116,6796],{"encoding":904},[38,78118,40562],{},[883,78120,78122],{"className":78121},[886],[888,78123,78124],{"xmlns":890},[892,78125,78126,78140],{},[895,78127,78128,78130,78132,78134,78136,78138],{},[898,78129,6796],{},[1711,78131,1836],{},[898,78133,6796],{},[1711,78135,1714],{"stretchy":1713},[898,78137,2888],{},[1711,78139,1735],{"stretchy":1713},[902,78141,78142],{"encoding":904},"Q = Q(L)",") studujeme ",[614,78145,13998],{},[883,78147,78149],{"className":78148},[886],[888,78150,78151],{"xmlns":890},[892,78152,78153,78177],{},[895,78154,78155,78157,78163,78165,78171,78173,78175],{},[898,78156,1790],{},[2884,78158,78159,78161],{},[898,78160,7929],{},[898,78162,2888],{},[1711,78164,1836],{},[1716,78166,78167,78169],{},[898,78168,6796],{},[1711,78170,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,78172,1714],{"stretchy":1713},[898,78174,2888],{},[1711,78176,1735],{"stretchy":1713},[902,78178,78179],{"encoding":904},"MP_L = Q'(L)",[614,78181,78182],{},"průměrný produkt",[883,78184,78186],{"className":78185},[886],[888,78187,78188],{"xmlns":890},[892,78189,78190,78208],{},[895,78191,78192,78194,78200,78202,78204,78206],{},[898,78193,8243],{},[2884,78195,78196,78198],{},[898,78197,7929],{},[898,78199,2888],{},[1711,78201,1836],{},[898,78203,6796],{},[898,78205,8659],{"mathvariant":2287},[898,78207,2888],{},[902,78209,78210],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,78213,78215],{"className":78214},[886],[888,78216,78217],{"xmlns":890},[892,78218,78219,78229],{},[895,78220,78221,78223],{},[898,78222,8243],{},[2884,78224,78225,78227],{},[898,78226,7929],{},[898,78228,2888],{},[902,78230,78231],{"encoding":904},"AP_L",[883,78233,78235],{"className":78234},[886],[888,78236,78237],{"xmlns":890},[892,78238,78239,78259],{},[895,78240,78241,78243,78249,78251,78253],{},[898,78242,1790],{},[2884,78244,78245,78247],{},[898,78246,7929],{},[898,78248,2888],{},[1711,78250,1836],{},[898,78252,8243],{},[2884,78254,78255,78257],{},[898,78256,7929],{},[898,78258,2888],{},[902,78260,78261],{"encoding":904},"MP_L = AP_L",". Ve ",[38,78264,78265],{},"dvoufaktorovém modelu",[883,78267,78269],{"className":78268},[886],[888,78270,78271],{"xmlns":890},[892,78272,78273,78291],{},[895,78274,78275,78277,78279,78281,78283,78285,78287,78289],{},[898,78276,6796],{},[1711,78278,1836],{},[898,78280,6796],{},[1711,78282,1714],{"stretchy":1713},[898,78284,2888],{},[1711,78286,1726],{"separator":1725},[898,78288,13774],{},[1711,78290,1735],{"stretchy":1713},[902,78292,78293],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,78296,78297],{},"Cobb-Douglasovy"," funkce ",[883,78300,78302],{"className":78301},[886],[888,78303,78304],{"xmlns":890},[892,78305,78306,78326],{},[895,78307,78308,78310,78312,78314,78320],{},[898,78309,6796],{},[1711,78311,1836],{},[898,78313,8243],{},[1716,78315,78316,78318],{},[898,78317,2888],{},[898,78319,207],{},[1716,78321,78322,78324],{},[898,78323,13774],{},[898,78325,2223],{},[902,78327,78328],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,78331,78333],{"className":78332},[886],[888,78334,78335],{"xmlns":890},[892,78336,78337,78357],{},[895,78338,78339,78341,78347,78349,78351],{},[898,78340,1790],{},[2884,78342,78343,78345],{},[898,78344,7929],{},[898,78346,2888],{},[1711,78348,1726],{"separator":1725},[898,78350,1790],{},[2884,78352,78353,78355],{},[898,78354,7929],{},[898,78356,13774],{},[902,78358,78359],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,78362,78363],{},"mezní míru technické substituce",[883,78365,78367],{"className":78366},[886],[888,78368,78369],{"xmlns":890},[892,78370,78371,78401],{},[895,78372,78373,78375,78377,78379,78381,78383,78385,78391,78393,78395],{},[898,78374,1790],{},[898,78376,7985],{},[898,78378,1769],{},[898,78380,2362],{},[1711,78382,1836],{},[898,78384,1790],{},[2884,78386,78387,78389],{},[898,78388,7929],{},[898,78390,2888],{},[898,78392,8659],{"mathvariant":2287},[898,78394,1790],{},[2884,78396,78397,78399],{},[898,78398,7929],{},[898,78400,13774],{},[902,78402,78403],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,78406,78408],{"className":78407},[886],[888,78409,78410],{"xmlns":890},[892,78411,78412,78420],{},[895,78413,78414,78416,78418],{},[898,78415,207],{},[1711,78417,2095],{},[898,78419,2223],{},[902,78421,78422],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,78425,78427],{"id":78426},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,78429,78430],{},"Po prostudování kapitoly 5 student umí:",[120,78432,78433,78439,78449,78455,78461,78466,78472,78482,78487,78493],{},[123,78434,78435,78436,1726],{},"popsat ",[38,78437,78438],{},"jednofaktorový model produkce",[123,78440,78441,78442,2009,78445,78448],{},"vypočítat ",[38,78443,78444],{},"mezní",[38,78446,78447],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,78450,78451,78452,1726],{},"charakterizovat průběh ",[38,78453,78454],{},"křivky produkce",[123,78456,78457,78458,1726],{},"formulovat ",[38,78459,78460],{},"princip maximalizace průměrného produktu práce",[123,78462,78435,78463,1726],{},[38,78464,78465],{},"dvoufaktorový model produkce",[123,78467,78468,78469,1726],{},"uvést tvar ",[38,78470,78471],{},"Cobb–Douglasových produkčních funkcí",[123,78473,78474,78475,1343,78477,1343,78479,1726],{},"vyložit, co jsou ",[38,78476,28211],{},[38,78478,3341],{},[38,78480,78481],{},"klesající výnosy z rozsahu",[123,78483,78441,78484,78448],{},[38,78485,78486],{},"mezní produkty práce a kapitálu",[123,78488,78489,78490,1726],{},"najít ",[38,78491,78492],{},"izokvanty",[123,78494,78441,78495,78498],{},[38,78496,78497],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,78500,78501,78502,78505,78506,78509,78510,1700,78513,1343,78526,1700,78529,2009,78542,78545,78546,78548,78549,2186],{},"Každý proces produkce je určován ",[38,78503,78504],{},"faktory"," (též ",[38,78507,78508],{},"vstupy",") produkce. K hlavním patří ",[38,78511,78512],{},"práce",[883,78514,78516],{"className":78515},[886],[888,78517,78518],{"xmlns":890},[892,78519,78520,78524],{},[895,78521,78522],{},[898,78523,2888],{},[902,78525,2888],{"encoding":904},[38,78527,78528],{},"kapitál",[883,78530,78532],{"className":78531},[886],[888,78533,78534],{"xmlns":890},[892,78535,78536,78540],{},[895,78537,78538],{},[898,78539,13774],{},[902,78541,13774],{"encoding":904},[38,78543,78544],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,78547,40562],{}," (produkce závisí jen na práci); v opačném případě o ",[38,78550,78265],{},[724,78552,78553,78554,1343,78557,78560],{},"Související matematický aparát: ",[207,78555,6375],{"className":78556,"dataFsResolvedFilePath":764,"href":765},[210],[207,78558,784],{"className":78559,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,78562,78564],{"id":78563},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,78566,78567,78568,78581,78582,78595,78596],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,78569,78571],{"className":78570},[886],[888,78572,78573],{"xmlns":890},[892,78574,78575,78579],{},[895,78576,78577],{},[898,78578,6796],{},[902,78580,6796],{"encoding":904}," na práci ",[883,78583,78585],{"className":78584},[886],[888,78586,78587],{"xmlns":890},[892,78588,78589,78593],{},[895,78590,78591],{},[898,78592,2888],{},[902,78594,2888],{"encoding":904}," vyjadřuje ",[38,78597,78598],{},"produkční funkce",[883,78600,78602],{"className":78601},[886],[888,78603,78604],{"xmlns":890,"display":31664},[892,78605,78606,78637],{},[24352,78607,78608],{"width":31669},[24357,78609,78610,78612,78630,78632],{},[24360,78611],{"width":31674},[24360,78613,78614],{},[895,78615,78616,78618,78620,78622,78624,78626,78628],{},[898,78617,6796],{},[1711,78619,1836],{},[898,78621,6796],{},[1711,78623,1714],{"stretchy":1713},[898,78625,2888],{},[1711,78627,1735],{"stretchy":1713},[1711,78629,1726],{"separator":1725},[24360,78631],{"width":31674},[24360,78633,78634],{},[1942,78635,78636],{},"(5.1)",[902,78638,78639],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,78641,78642,78643,1648,78646,78649,78650,78663],{},"jejíž graf se nazývá ",[38,78644,78645],{},"křivka produkce",[614,78647,78648],{},"production curve","). Práce ",[883,78651,78653],{"className":78652},[886],[888,78654,78655],{"xmlns":890},[892,78656,78657,78661],{},[895,78658,78659],{},[898,78660,2888],{},[902,78662,2888],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,78665,78667,78668,1735],{"id":78666},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,78669,78671],{"className":78670},[886],[888,78672,78673],{"xmlns":890},[892,78674,78675,78685],{},[895,78676,78677,78679],{},[898,78678,1790],{},[2884,78680,78681,78683],{},[898,78682,7929],{},[898,78684,2888],{},[902,78686,14018],{"encoding":904},[724,78688,78689,1648,78692,78695,78696,78715],{},[38,78690,78691],{},"Mezní produkt práce",[614,78693,78694],{},"marginal product of labour",") ",[883,78697,78699],{"className":78698},[886],[888,78700,78701],{"xmlns":890},[892,78702,78703,78713],{},[895,78704,78705,78707],{},[898,78706,1790],{},[2884,78708,78709,78711],{},[898,78710,7929],{},[898,78712,2888],{},[902,78714,14018],{"encoding":904}," je derivace produkce podle práce:",[883,78717,78719],{"className":78718},[886],[888,78720,78721],{"xmlns":890,"display":31664},[892,78722,78723,78780],{},[24352,78724,78725],{"width":31669},[24357,78726,78727,78729,78773,78775],{},[24360,78728],{"width":31674},[24360,78730,78731],{},[895,78732,78733,78735,78741,78743,78757,78759,78765,78767,78769,78771],{},[898,78734,1790],{},[2884,78736,78737,78739],{},[898,78738,7929],{},[898,78740,2888],{},[1711,78742,1836],{},[2525,78744,78745,78751],{},[895,78746,78747,78749],{},[898,78748,2098],{},[898,78750,6796],{},[895,78752,78753,78755],{},[898,78754,2098],{},[898,78756,2888],{},[1711,78758,1836],{},[1716,78760,78761,78763],{},[898,78762,6796],{},[1711,78764,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,78766,1714],{"stretchy":1713},[898,78768,2888],{},[1711,78770,1735],{"stretchy":1713},[898,78772,2186],{"mathvariant":2287},[24360,78774],{"width":31674},[24360,78776,78777],{},[1942,78778,78779],{},"(5.2)",[902,78781,78782],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,78784,78785,78786,23543,78804,78832,78833,78850,78851,6696,78868,1797],{},"Pro pevnou hodnotu ",[883,78787,78789],{"className":78788},[886],[888,78790,78791],{"xmlns":890},[892,78792,78793,78801],{},[895,78794,78795],{},[1716,78796,78797,78799],{},[898,78798,2888],{},[1711,78800,1793],{},[902,78802,78803],{"encoding":904},"L^*",[883,78805,78807],{"className":78806},[886],[888,78808,78809],{"xmlns":890},[892,78810,78811,78829],{},[895,78812,78813,78819,78821,78827],{},[1716,78814,78815,78817],{},[898,78816,6796],{},[1711,78818,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,78820,1714],{"stretchy":1713},[1716,78822,78823,78825],{},[898,78824,2888],{},[1711,78826,1793],{},[1711,78828,1735],{"stretchy":1713},[902,78830,78831],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,78834,78836],{"className":78835},[886],[888,78837,78838],{"xmlns":890},[892,78839,78840,78848],{},[895,78841,78842],{},[1716,78843,78844,78846],{},[898,78845,2888],{},[1711,78847,1793],{},[902,78849,78803],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,78852,78854],{"className":78853},[886],[888,78855,78856],{"xmlns":890},[892,78857,78858,78866],{},[895,78859,78860],{},[1716,78861,78862,78864],{},[898,78863,2888],{},[1711,78865,1793],{},[902,78867,78803],{"encoding":904},[883,78869,78871],{"className":78870},[886],[888,78872,78873],{"xmlns":890},[892,78874,78875,78887],{},[895,78876,78877,78883,78885],{},[1716,78878,78879,78881],{},[898,78880,2888],{},[1711,78882,1793],{},[1711,78884,2095],{},[2111,78886,2238],{},[902,78888,78889],{"encoding":904},"L^*+1",[1921,78891,78892],{},[724,78893,78894,21621,78896,78915,78916,78919,78920,2186],{},[883,78895,2678],{},[883,78897,78899],{"className":78898},[886],[888,78900,78901],{"xmlns":890},[892,78902,78903,78913],{},[895,78904,78905,78907],{},[898,78906,1790],{},[2884,78908,78909,78911],{},[898,78910,7929],{},[898,78912,2888],{},[902,78914,14018],{"encoding":904}," odpovídá na otázku „",[38,78917,78918],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,78921,78923],{"className":78922},[886],[888,78924,78925],{"xmlns":890},[892,78926,78927,78931],{},[895,78928,78929],{},[898,78930,2888],{},[902,78932,2888],{"encoding":904},[724,78934,78935,78938,78939,78955,78956,6696,78969,78989],{},[38,78936,78937],{},"Přibližná změna produkce"," pro změnu práce o ",[883,78940,78942],{"className":78941},[886],[888,78943,78944],{"xmlns":890},[892,78945,78946,78952],{},[895,78947,78948,78950],{},[898,78949,2098],{},[898,78951,2888],{},[902,78953,78954],{"encoding":904},"dL"," (z ",[883,78957,78959],{"className":78958},[886],[888,78960,78961],{"xmlns":890},[892,78962,78963,78967],{},[895,78964,78965],{},[898,78966,2888],{},[902,78968,2888],{"encoding":904},[883,78970,78972],{"className":78971},[886],[888,78973,78974],{"xmlns":890},[892,78975,78976,78986],{},[895,78977,78978,78980,78982,78984],{},[898,78979,2888],{},[1711,78981,2095],{},[898,78983,2098],{},[898,78985,2888],{},[902,78987,78988],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,78991,78993],{"className":78992},[886],[888,78994,78995],{"xmlns":890,"display":31664},[892,78996,78997,79062],{},[24352,78998,78999],{"width":31669},[24357,79000,79001,79003,79055,79057],{},[24360,79002],{"width":31674},[24360,79004,79005],{},[895,79006,79007,79009,79011,79013,79015,79017,79019,79025,79027,79029,79031,79033,79035,79037,79039,79041,79047,79049,79051,79053],{},[898,79008,6892],{"mathvariant":2287},[898,79010,6796],{},[1711,79012,6740],{},[898,79014,2098],{},[898,79016,6796],{},[1711,79018,1836],{},[1716,79020,79021,79023],{},[898,79022,6796],{},[1711,79024,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,79026,1714],{"stretchy":1713},[898,79028,2888],{},[1711,79030,1735],{"stretchy":1713},[1942,79032,2519],{},[898,79034,2098],{},[898,79036,2888],{},[1711,79038,1836],{},[898,79040,1790],{},[2884,79042,79043,79045],{},[898,79044,7929],{},[898,79046,2888],{},[1942,79048,2519],{},[898,79050,2098],{},[898,79052,2888],{},[898,79054,2186],{"mathvariant":2287},[24360,79056],{"width":31674},[24360,79058,79059],{},[1942,79060,79061],{},"(5.3)",[902,79063,79064],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,79066,79067,79068,2186],{},"Skutečná změna je ",[883,79069,79071],{"className":79070},[886],[888,79072,79073],{"xmlns":890},[892,79074,79075,79107],{},[895,79076,79077,79079,79081,79083,79085,79087,79089,79091,79093,79095,79097,79099,79101,79103,79105],{},[898,79078,6892],{"mathvariant":2287},[898,79080,6796],{},[1711,79082,1836],{},[898,79084,6796],{},[1711,79086,1714],{"stretchy":1713},[898,79088,2888],{},[1711,79090,2095],{},[898,79092,2098],{},[898,79094,2888],{},[1711,79096,1735],{"stretchy":1713},[1711,79098,2460],{},[898,79100,6796],{},[1711,79102,1714],{"stretchy":1713},[898,79104,2888],{},[1711,79106,1735],{"stretchy":1713},[902,79108,79109],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,79111,79113],{"id":79112},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,79115,79116,1648,79119,3239],{},[38,79117,79118],{},"Zákon klesajících výnosů",[614,79120,79121],{},"law of diminishing marginal productivity",[1921,79123,79124],{},[724,79125,79126,79127,79129],{},"Roste-li postupně některý ze vstupů (",[614,79128,40558],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,79131,79132],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,79134,79135,79136,1700,79157,79176,79177,79227,79228,79230,79231,1700,79251,79270,79271,79227,79303,2801,79305,79324,79325,25192,79342,79376,79377,12082,79394,79397],{},"1° ",[38,79137,79138,79139,2062],{},"Do bodu ",[883,79140,79142],{"className":79141},[886],[888,79143,79144],{"xmlns":890},[892,79145,79146,79154],{},[895,79147,79148],{},[2884,79149,79150,79152],{},[898,79151,2888],{},[2111,79153,2113],{},[902,79155,79156],{"encoding":904},"L_0",[883,79158,79160],{"className":79159},[886],[888,79161,79162],{"xmlns":890},[892,79163,79164,79174],{},[895,79165,79166,79168],{},[898,79167,1790],{},[2884,79169,79170,79172],{},[898,79171,7929],{},[898,79173,2888],{},[902,79175,14018],{"encoding":904}," roste, tj. ",[883,79178,79180],{"className":79179},[886],[888,79181,79182],{"xmlns":890},[892,79183,79184,79224],{},[895,79185,79186,79188,79190,79196,79202,79204,79214,79216,79218,79220,79222],{},[1711,79187,1714],{"stretchy":1713},[898,79189,1790],{},[2884,79191,79192,79194],{},[898,79193,7929],{},[898,79195,2888],{},[1716,79197,79198,79200],{},[1711,79199,1735],{"stretchy":1713},[1711,79201,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,79203,1836],{},[1716,79205,79206,79208],{},[898,79207,6796],{},[895,79209,79210,79212],{},[1711,79211,5225],{"mathvariant":2287},[1711,79213,5225],{"mathvariant":2287},[1711,79215,1714],{"stretchy":1713},[898,79217,2888],{},[1711,79219,1735],{"stretchy":1713},[1711,79221,2123],{},[2111,79223,2113],{},[902,79225,79226],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,79229,41262],{},".\n2° ",[38,79232,79233,79234,2062],{},"Od bodu ",[883,79235,79237],{"className":79236},[886],[888,79238,79239],{"xmlns":890},[892,79240,79241,79249],{},[895,79242,79243],{},[2884,79244,79245,79247],{},[898,79246,2888],{},[2111,79248,2113],{},[902,79250,79156],{"encoding":904},[883,79252,79254],{"className":79253},[886],[888,79255,79256],{"xmlns":890},[892,79257,79258,79268],{},[895,79259,79260,79262],{},[898,79261,1790],{},[2884,79263,79264,79266],{},[898,79265,7929],{},[898,79267,2888],{},[902,79269,14018],{"encoding":904}," klesá, ",[883,79272,79274],{"className":79273},[886],[888,79275,79276],{"xmlns":890},[892,79277,79278,79300],{},[895,79279,79280,79290,79292,79294,79296,79298],{},[1716,79281,79282,79284],{},[898,79283,6796],{},[895,79285,79286,79288],{},[1711,79287,5225],{"mathvariant":2287},[1711,79289,5225],{"mathvariant":2287},[1711,79291,1714],{"stretchy":1713},[898,79293,2888],{},[1711,79295,1735],{"stretchy":1713},[1711,79297,2109],{},[2111,79299,2113],{},[902,79301,79302],{"encoding":904},"Q''(L) \u003C 0",[38,79304,42086],{},[883,79306,79308],{"className":79307},[886],[888,79309,79310],{"xmlns":890},[892,79311,79312,79322],{},[895,79313,79314,79316],{},[898,79315,1790],{},[2884,79317,79318,79320],{},[898,79319,7929],{},[898,79321,2888],{},[902,79323,14018],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,79326,79328],{"className":79327},[886],[888,79329,79330],{"xmlns":890},[892,79331,79332,79340],{},[895,79333,79334],{},[2884,79335,79336,79338],{},[898,79337,2888],{},[2111,79339,2238],{},[902,79341,2893],{"encoding":904},[883,79343,79345],{"className":79344},[886],[888,79346,79347],{"xmlns":890},[892,79348,79349,79373],{},[895,79350,79351,79353,79359,79361,79367,79369,79371],{},[898,79352,1790],{},[2884,79354,79355,79357],{},[898,79356,7929],{},[898,79358,2888],{},[1711,79360,1714],{"stretchy":1713},[2884,79362,79363,79365],{},[898,79364,2888],{},[2111,79366,2238],{},[1711,79368,1735],{"stretchy":1713},[1711,79370,1836],{},[2111,79372,2113],{},[902,79374,79375],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,79378,79380],{"className":79379},[886],[888,79381,79382],{"xmlns":890},[892,79383,79384,79392],{},[895,79385,79386],{},[2884,79387,79388,79390],{},[898,79389,2888],{},[2111,79391,2113],{},[902,79393,79156],{"encoding":904},[38,79395,79396],{},"inflexním bodem"," produkční funkce.",[724,79399,79400,79401,14367,79418,2186],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,79402,79404],{"className":79403},[886],[888,79405,79406],{"xmlns":890},[892,79407,79408,79416],{},[895,79409,79410],{},[2884,79411,79412,79414],{},[898,79413,2888],{},[2111,79415,2113],{},[902,79417,79156],{"encoding":904},[883,79419,79421],{"className":79420},[886],[888,79422,79423],{"xmlns":890},[892,79424,79425,79447],{},[895,79426,79427,79437,79439,79441,79443,79445],{},[1716,79428,79429,79431],{},[898,79430,6796],{},[895,79432,79433,79435],{},[1711,79434,5225],{"mathvariant":2287},[1711,79436,5225],{"mathvariant":2287},[1711,79438,1714],{"stretchy":1713},[898,79440,2888],{},[1711,79442,1735],{"stretchy":1713},[1711,79444,2109],{},[2111,79446,2113],{},[902,79448,79302],{"encoding":904},[724,79450,79451,1700,79454,9652,79494,1343,79511,79528],{},[38,79452,79453],{},"Typický polynom třetího stupně:",[883,79455,79457],{"className":79456},[886],[888,79458,79459],{"xmlns":890},[892,79460,79461,79491],{},[895,79462,79463,79465,79467,79469,79471,79473,79475,79481,79483,79485],{},[898,79464,6796],{},[1711,79466,1714],{"stretchy":1713},[898,79468,2888],{},[1711,79470,1735],{"stretchy":1713},[1711,79472,1836],{},[898,79474,207],{},[1716,79476,79477,79479],{},[898,79478,2888],{},[2111,79480,3034],{},[1711,79482,2095],{},[898,79484,2223],{},[1716,79486,79487,79489],{},[898,79488,2888],{},[2111,79490,2963],{},[902,79492,79493],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,79495,79497],{"className":79496},[886],[888,79498,79499],{"xmlns":890},[892,79500,79501,79509],{},[895,79502,79503,79505,79507],{},[898,79504,207],{},[1711,79506,2109],{},[2111,79508,2113],{},[902,79510,46683],{"encoding":904},[883,79512,79514],{"className":79513},[886],[888,79515,79516],{"xmlns":890},[892,79517,79518,79526],{},[895,79519,79520,79522,79524],{},[898,79521,2223],{},[1711,79523,2123],{},[2111,79525,2113],{},[902,79527,22412],{"encoding":904},". Pak",[883,79530,79532],{"className":79531},[886],[888,79533,79534],{"xmlns":890,"display":31664},[892,79535,79536,79596],{},[895,79537,79538,79544,79546,79548,79556,79564,79566,79568,79574,79576,79578,79586,79594],{},[2884,79539,79540,79542],{},[898,79541,2888],{},[2111,79543,2113],{},[1711,79545,1836],{},[1711,79547,2460],{},[2509,79549,79550],{"scriptlevel":2113,"displaystyle":1713},[2525,79551,79552,79554],{},[2111,79553,2238],{},[2111,79555,3034],{},[2509,79557,79558],{"scriptlevel":2113,"displaystyle":1713},[2525,79559,79560,79562],{},[898,79561,2223],{},[898,79563,207],{},[1711,79565,1726],{"separator":1725},[2102,79567],{"width":2104},[2884,79569,79570,79572],{},[898,79571,2888],{},[2111,79573,2238],{},[1711,79575,1836],{},[1711,79577,2460],{},[2509,79579,79580],{"scriptlevel":2113,"displaystyle":1713},[2525,79581,79582,79584],{},[2111,79583,2963],{},[2111,79585,3034],{},[2509,79587,79588],{"scriptlevel":2113,"displaystyle":1713},[2525,79589,79590,79592],{},[898,79591,2223],{},[898,79593,207],{},[898,79595,2186],{"mathvariant":2287},[902,79597,79598],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,79600,79602,79603,1735],{"id":79601},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,79604,79606],{"className":79605},[886],[888,79607,79608],{"xmlns":890},[892,79609,79610,79620],{},[895,79611,79612,79614],{},[898,79613,8243],{},[2884,79615,79616,79618],{},[898,79617,7929],{},[898,79619,2888],{},[902,79621,78231],{"encoding":904},[724,79623,79624,1648,79627,78695,79630,79649],{},[38,79625,79626],{},"Průměrný produkt práce",[614,79628,79629],{},"average product of labour",[883,79631,79633],{"className":79632},[886],[888,79634,79635],{"xmlns":890},[892,79636,79637,79647],{},[895,79638,79639,79641],{},[898,79640,8243],{},[2884,79642,79643,79645],{},[898,79644,7929],{},[898,79646,2888],{},[902,79648,78231],{"encoding":904}," je podíl produkce a práce:",[883,79651,79653],{"className":79652},[886],[888,79654,79655],{"xmlns":890,"display":31664},[892,79656,79657,79692],{},[24352,79658,79659],{"width":31669},[24357,79660,79661,79663,79685,79687],{},[24360,79662],{"width":31674},[24360,79664,79665],{},[895,79666,79667,79669,79675,79677,79683],{},[898,79668,8243],{},[2884,79670,79671,79673],{},[898,79672,7929],{},[898,79674,2888],{},[1711,79676,1836],{},[2525,79678,79679,79681],{},[898,79680,6796],{},[898,79682,2888],{},[898,79684,2186],{"mathvariant":2287},[24360,79686],{"width":31674},[24360,79688,79689],{},[1942,79690,79691],{},"(5.4)",[902,79693,79694],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,79696,79697,79698,2186],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,79699,79701],{"className":79700},[886],[888,79702,79703],{"xmlns":890},[892,79704,79705,79715],{},[895,79706,79707,79709],{},[898,79708,8243],{},[2884,79710,79711,79713],{},[898,79712,7929],{},[898,79714,2888],{},[902,79716,78231],{"encoding":904},[115,79718,79720],{"id":79719},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,79722,79723],{},[1801,79724],{"alt":79725,"className":79726,"src":79727},"imek-q-mpl-apl-tripanel",[210,1805],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[1921,79729,79730],{},[724,79731,79732,79735,79736,6635,79755,79772,79773],{},[38,79733,79734],{},"Princip:"," Má-li ",[883,79737,79739],{"className":79738},[886],[888,79740,79741],{"xmlns":890},[892,79742,79743,79753],{},[895,79744,79745,79747],{},[898,79746,8243],{},[2884,79748,79749,79751],{},[898,79750,7929],{},[898,79752,2888],{},[902,79754,78231],{"encoding":904},[883,79756,79758],{"className":79757},[886],[888,79759,79760],{"xmlns":890},[892,79761,79762,79770],{},[895,79763,79764],{},[2884,79765,79766,79768],{},[898,79767,2888],{},[2111,79769,2113],{},[902,79771,79156],{"encoding":904}," maximum, pak platí\n",[883,79774,79776],{"className":79775,"title":8189,"style":8190},[8188],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,79778,79779,79780,79783,79784,1700,79788,2186],{},"Slovně: ",[38,79781,79782],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,79785,79787],{"className":79786,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,79789,79791],{"className":79790},[886],[888,79792,79793],{"xmlns":890},[892,79794,79795,79801],{},[895,79796,79797,79799],{},[898,79798,8243],{},[898,79800,1940],{},[902,79802,59158],{"encoding":904},[1921,79804,79805,79829],{},[724,79806,79807,79809,79810],{},[883,79808,3872],{}," Postup — jak najít max ",[883,79811,79813],{"className":79812},[886],[888,79814,79815],{"xmlns":890},[892,79816,79817,79827],{},[895,79818,79819,79821],{},[898,79820,8243],{},[2884,79822,79823,79825],{},[898,79824,7929],{},[898,79826,2888],{},[902,79828,78231],{"encoding":904},[152,79830,79831,79869,79951],{},[123,79832,79833,79834,79868],{},"Napište ",[883,79835,79837],{"className":79836},[886],[888,79838,79839],{"xmlns":890},[892,79840,79841,79865],{},[895,79842,79843,79845,79851,79853,79855,79857,79859,79861,79863],{},[898,79844,8243],{},[2884,79846,79847,79849],{},[898,79848,7929],{},[898,79850,2888],{},[1711,79852,1836],{},[898,79854,6796],{},[1711,79856,1714],{"stretchy":1713},[898,79858,2888],{},[1711,79860,1735],{"stretchy":1713},[898,79862,8659],{"mathvariant":2287},[898,79864,2888],{},[902,79866,79867],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,79870,79871,79872,79904,79905,79908,79909,2186],{},"Položte ",[883,79873,79875],{"className":79874},[886],[888,79876,79877],{"xmlns":890},[892,79878,79879,79901],{},[895,79880,79881,79883,79885,79891,79897,79899],{},[1711,79882,1714],{"stretchy":1713},[898,79884,8243],{},[2884,79886,79887,79889],{},[898,79888,7929],{},[898,79890,2888],{},[1716,79892,79893,79895],{},[1711,79894,1735],{"stretchy":1713},[1711,79896,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,79898,1836],{},[2111,79900,2113],{},[902,79902,79903],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,79906,79907],{},"Zkratka:"," můžete rovnou řešit ",[883,79910,79912],{"className":79911},[886],[888,79913,79914],{"xmlns":890},[892,79915,79916,79948],{},[895,79917,79918,79920,79926,79928,79930,79932,79934,79936,79942,79944,79946],{},[898,79919,1790],{},[2884,79921,79922,79924],{},[898,79923,7929],{},[898,79925,2888],{},[1711,79927,1714],{"stretchy":1713},[898,79929,2888],{},[1711,79931,1735],{"stretchy":1713},[1711,79933,1836],{},[898,79935,8243],{},[2884,79937,79938,79940],{},[898,79939,7929],{},[898,79941,2888],{},[1711,79943,1714],{"stretchy":1713},[898,79945,2888],{},[1711,79947,1735],{"stretchy":1713},[902,79949,79950],{"encoding":904},"MP_L(L) = AP_L(L)",[123,79952,79953],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,79955,69099],{"id":79956},"odvození",[724,79958,79959,79960,79993],{},"Z ",[883,79961,79963],{"className":79962},[886],[888,79964,79965],{"xmlns":890},[892,79966,79967,79991],{},[895,79968,79969,79971,79977,79979,79981,79983,79985,79987,79989],{},[898,79970,8243],{},[2884,79972,79973,79975],{},[898,79974,7929],{},[898,79976,2888],{},[1711,79978,1836],{},[898,79980,6796],{},[1711,79982,1714],{"stretchy":1713},[898,79984,2888],{},[1711,79986,1735],{"stretchy":1713},[898,79988,8659],{"mathvariant":2287},[898,79990,2888],{},[902,79992,79867],{"encoding":904}," a derivace podílu:",[883,79995,79997],{"className":79996},[886],[888,79998,79999],{"xmlns":890,"display":31664},[892,80000,80001,80154],{},[895,80002,80003,80005,80007,80013,80019,80021,80023,80025,80027,80067,80069,80075,80109,80111,80117,80120,80122,80128,80130,80132,80134,80136,80138,80144,80146,80148,80150,80152],{},[1711,80004,1714],{"stretchy":1713},[898,80006,8243],{},[2884,80008,80009,80011],{},[898,80010,7929],{},[898,80012,2888],{},[1716,80014,80015,80017],{},[1711,80016,1735],{"stretchy":1713},[1711,80018,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,80020,1714],{"stretchy":1713},[898,80022,2888],{},[1711,80024,1735],{"stretchy":1713},[1711,80026,1836],{},[2525,80028,80029,80061],{},[895,80030,80031,80037,80039,80041,80043,80045,80047,80049,80051,80053,80055,80057,80059],{},[1716,80032,80033,80035],{},[898,80034,6796],{},[1711,80036,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,80038,1714],{"stretchy":1713},[898,80040,2888],{},[1711,80042,1735],{"stretchy":1713},[1711,80044,4795],{},[898,80046,2888],{},[1711,80048,2460],{},[898,80050,6796],{},[1711,80052,1714],{"stretchy":1713},[898,80054,2888],{},[1711,80056,1735],{"stretchy":1713},[1711,80058,4795],{},[2111,80060,2238],{},[1716,80062,80063,80065],{},[898,80064,2888],{},[2111,80066,2963],{},[1711,80068,1836],{},[2525,80070,80071,80073],{},[2111,80072,2238],{},[898,80074,2888],{},[895,80076,80077,80079,80085,80087,80089,80091,80093,80107],{},[1711,80078,1714],{"fence":1725},[1716,80080,80081,80083],{},[898,80082,6796],{},[1711,80084,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,80086,1714],{"stretchy":1713},[898,80088,2888],{},[1711,80090,1735],{"stretchy":1713},[1711,80092,2460],{},[2525,80094,80095,80105],{},[895,80096,80097,80099,80101,80103],{},[898,80098,6796],{},[1711,80100,1714],{"stretchy":1713},[898,80102,2888],{},[1711,80104,1735],{"stretchy":1713},[898,80106,2888],{},[1711,80108,1735],{"fence":1725},[1711,80110,1836],{},[2525,80112,80113,80115],{},[2111,80114,2238],{},[898,80116,2888],{},[1711,80118,1714],{"fence":1725,"stretchy":1725,"minsize":80119,"maxsize":80119},"1.2em",[898,80121,1790],{},[2884,80123,80124,80126],{},[898,80125,7929],{},[898,80127,2888],{},[1711,80129,1714],{"stretchy":1713},[898,80131,2888],{},[1711,80133,1735],{"stretchy":1713},[1711,80135,2460],{},[898,80137,8243],{},[2884,80139,80140,80142],{},[898,80141,7929],{},[898,80143,2888],{},[1711,80145,1714],{"stretchy":1713},[898,80147,2888],{},[1711,80149,1735],{"stretchy":1713},[1711,80151,1735],{"fence":1725,"stretchy":1725,"minsize":80119,"maxsize":80119},[898,80153,2186],{"mathvariant":2287},[902,80155,80156],{"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).",[724,80158,13638,80159,12082,80181,80264],{},[883,80160,80162],{"className":80161},[886],[888,80163,80164],{"xmlns":890},[892,80165,80166,80178],{},[895,80167,80168,80174,80176],{},[2884,80169,80170,80172],{},[898,80171,2888],{},[2111,80173,2113],{},[1711,80175,2123],{},[2111,80177,2113],{},[902,80179,80180],{"encoding":904},"L_0 > 0",[883,80182,80184],{"className":80183},[886],[888,80185,80186],{"xmlns":890},[892,80187,80188,80261],{},[895,80189,80190,80192,80194,80200,80206,80208,80214,80216,80218,80220,80223,80225,80231,80233,80239,80241,80243,80245,80251,80253,80259],{},[1711,80191,1714],{"stretchy":1713},[898,80193,8243],{},[2884,80195,80196,80198],{},[898,80197,7929],{},[898,80199,2888],{},[1716,80201,80202,80204],{},[1711,80203,1735],{"stretchy":1713},[1711,80205,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,80207,1714],{"stretchy":1713},[2884,80209,80210,80212],{},[898,80211,2888],{},[2111,80213,2113],{},[1711,80215,1735],{"stretchy":1713},[1711,80217,1836],{},[2111,80219,2113],{},[1711,80221,80222],{},"⇔",[898,80224,1790],{},[2884,80226,80227,80229],{},[898,80228,7929],{},[898,80230,2888],{},[1711,80232,1714],{"stretchy":1713},[2884,80234,80235,80237],{},[898,80236,2888],{},[2111,80238,2113],{},[1711,80240,1735],{"stretchy":1713},[1711,80242,1836],{},[898,80244,8243],{},[2884,80246,80247,80249],{},[898,80248,7929],{},[898,80250,2888],{},[1711,80252,1714],{"stretchy":1713},[2884,80254,80255,80257],{},[898,80256,2888],{},[2111,80258,2113],{},[1711,80260,1735],{"stretchy":1713},[902,80262,80263],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,80266,80268],{"id":80267},"příklad-51","Příklad 5.1",[724,80270,80271,80272,2186],{},"Je dána produkce ",[883,80273,80275],{"className":80274},[886],[888,80276,80277],{"xmlns":890},[892,80278,80279,80303],{},[895,80280,80281,80283,80285,80287,80293,80295,80297],{},[898,80282,6796],{},[1711,80284,1836],{},[2111,80286,6262],{},[1716,80288,80289,80291],{},[898,80290,2888],{},[2111,80292,2963],{},[1711,80294,2460],{},[2111,80296,4491],{},[1716,80298,80299,80301],{},[898,80300,2888],{},[2111,80302,3034],{},[902,80304,80305],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,80307,80308,61120,80311,80361,80362,2186],{},[38,80309,80310],{},"(a)",[883,80312,80314],{"className":80313},[886],[888,80315,80316],{"xmlns":890},[892,80317,80318,80358],{},[895,80319,80320,80322,80324,80326,80328,80330,80332,80334,80336,80338,80340,80342,80344,80346,80348,80350,80352,80354,80356],{},[898,80321,2888],{},[1711,80323,1836],{},[2111,80325,2963],{},[1711,80327,1726],{"separator":1725},[2111,80329,4798],{},[1711,80331,1726],{"separator":1725},[2111,80333,9568],{},[1711,80335,1726],{"separator":1725},[2111,80337,4712],{},[1711,80339,1726],{"separator":1725},[2111,80341,26544],{},[1711,80343,1726],{"separator":1725},[2111,80345,7703],{},[1711,80347,1726],{"separator":1725},[2111,80349,4306],{},[1711,80351,1726],{"separator":1725},[2111,80353,41944],{},[1711,80355,1726],{"separator":1725},[2111,80357,4372],{},[902,80359,80360],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,80363,80365],{"className":80364},[886],[888,80366,80367],{"xmlns":890},[892,80368,80369,80379],{},[895,80370,80371,80373],{},[898,80372,1790],{},[2884,80374,80375,80377],{},[898,80376,7929],{},[898,80378,2888],{},[902,80380,14018],{"encoding":904},[724,80382,80383,80384,38566],{},"Podle (5.2): ",[883,80385,80387],{"className":80386},[886],[888,80388,80389],{"xmlns":890},[892,80390,80391,80447],{},[895,80392,80393,80395,80401,80403,80409,80411,80413,80415,80417,80419,80421,80423,80425,80431,80433,80435,80437,80439,80441,80443,80445],{},[898,80394,1790],{},[2884,80396,80397,80399],{},[898,80398,7929],{},[898,80400,2888],{},[1711,80402,1836],{},[1716,80404,80405,80407],{},[898,80406,6796],{},[1711,80408,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,80410,1714],{"stretchy":1713},[898,80412,2888],{},[1711,80414,1735],{"stretchy":1713},[1711,80416,1836],{},[2111,80418,7505],{},[898,80420,2888],{},[1711,80422,2460],{},[2111,80424,22919],{},[1716,80426,80427,80429],{},[898,80428,2888],{},[2111,80430,2963],{},[1711,80432,1836],{},[898,80434,2888],{},[1711,80436,1714],{"stretchy":1713},[2111,80438,7505],{},[1711,80440,2460],{},[2111,80442,22919],{},[898,80444,2888],{},[1711,80446,1735],{"stretchy":1713},[902,80448,80449],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,80451,80452,80489],{},[19,80453,80454],{},[22,80455,80456,80471,80473,80475,80477,80479,80481,80483,80485,80487],{},[25,80457,80458],{},[883,80459,80461],{"className":80460},[886],[888,80462,80463],{"xmlns":890},[892,80464,80465,80469],{},[895,80466,80467],{},[898,80468,2888],{},[902,80470,2888],{"encoding":904},[25,80472,2963],{},[25,80474,4798],{},[25,80476,9568],{},[25,80478,4712],{},[25,80480,26544],{},[25,80482,7703],{},[25,80484,4306],{},[25,80486,41944],{},[25,80488,4372],{},[30,80490,80491],{},[22,80492,80493,80514,80517,80520,80523,80525,80528,80530,80532,80551],{},[35,80494,80495],{},[883,80496,80498],{"className":80497},[886],[888,80499,80500],{"xmlns":890},[892,80501,80502,80512],{},[895,80503,80504,80506],{},[898,80505,1790],{},[2884,80507,80508,80510],{},[898,80509,7929],{},[898,80511,2888],{},[902,80513,14018],{"encoding":904},[35,80515,80516],{},"21,6",[35,80518,80519],{},"45",[35,80521,80522],{},"57,6",[35,80524,7126],{},[35,80526,80527],{},"50,4",[35,80529,80516],{},[35,80531,2113],{},[35,80533,80534],{},[883,80535,80537],{"className":80536},[886],[888,80538,80539],{"xmlns":890},[892,80540,80541,80548],{},[895,80542,80543,80545],{},[1711,80544,2460],{},[2111,80546,80547],{},"12,6",[902,80549,80550],{"encoding":904},"-12{,}6",[35,80552,80553],{},[883,80554,80556],{"className":80555},[886],[888,80557,80558],{"xmlns":890},[892,80559,80560,80566],{},[895,80561,80562,80564],{},[1711,80563,2460],{},[2111,80565,49050],{},[902,80567,80568],{"encoding":904},"-75",[724,80570,80571,80590,80591,80609,80610,80627,80628,80646,80647,80671,80672,80690],{},[883,80572,80574],{"className":80573},[886],[888,80575,80576],{"xmlns":890},[892,80577,80578,80588],{},[895,80579,80580,80582],{},[898,80581,1790],{},[2884,80583,80584,80586],{},[898,80585,7929],{},[898,80587,2888],{},[902,80589,14018],{"encoding":904}," nabývá maxima pro ",[883,80592,80594],{"className":80593},[886],[888,80595,80596],{"xmlns":890},[892,80597,80598,80606],{},[895,80599,80600,80602,80604],{},[898,80601,2888],{},[1711,80603,1836],{},[2111,80605,4712],{},[902,80607,80608],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,80611,80613],{"className":80612},[886],[888,80614,80615],{"xmlns":890},[892,80616,80617,80625],{},[895,80618,80619,80621,80623],{},[898,80620,2888],{},[1711,80622,1836],{},[2111,80624,4712],{},[902,80626,80608],{"encoding":904}," přírůstky klesají, v ",[883,80629,80631],{"className":80630},[886],[888,80632,80633],{"xmlns":890},[892,80634,80635,80643],{},[895,80636,80637,80639,80641],{},[898,80638,2888],{},[1711,80640,1836],{},[2111,80642,4306],{},[902,80644,80645],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,80648,80650],{"className":80649},[886],[888,80651,80652],{"xmlns":890},[892,80653,80654,80668],{},[895,80655,80656,80658,80660,80662,80664,80666],{},[898,80657,6796],{},[1711,80659,1714],{"stretchy":1713},[2111,80661,4306],{},[1711,80663,1735],{"stretchy":1713},[1711,80665,1836],{},[2111,80667,27456],{},[902,80669,80670],{"encoding":904},"Q(20) = 800","), od ",[883,80673,80675],{"className":80674},[886],[888,80676,80677],{"xmlns":890},[892,80678,80679,80687],{},[895,80680,80681,80683,80685],{},[898,80682,2888],{},[1711,80684,2123],{},[2111,80686,4306],{},[902,80688,80689],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,80692,80693],{},[614,80694,80695,80696,80736,80737,6635,80755,2186],{},"Obrázek 5.1 — graf produkce ",[883,80697,80699],{"className":80698},[886],[888,80700,80701],{"xmlns":890},[892,80702,80703,80733],{},[895,80704,80705,80707,80709,80711,80713,80715,80717,80723,80725,80727],{},[898,80706,6796],{},[1711,80708,1714],{"stretchy":1713},[898,80710,2888],{},[1711,80712,1735],{"stretchy":1713},[1711,80714,1836],{},[2111,80716,6262],{},[1716,80718,80719,80721],{},[898,80720,2888],{},[2111,80722,2963],{},[1711,80724,2460],{},[2111,80726,4491],{},[1716,80728,80729,80731],{},[898,80730,2888],{},[2111,80732,3034],{},[902,80734,80735],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,80738,80740],{"className":80739},[886],[888,80741,80742],{"xmlns":890},[892,80743,80744,80752],{},[895,80745,80746,80748,80750],{},[898,80747,6796],{},[1711,80749,1836],{},[2111,80751,27456],{},[902,80753,80754],{"encoding":904},"Q = 800",[883,80756,80758],{"className":80757},[886],[888,80759,80760],{"xmlns":890},[892,80761,80762,80770],{},[895,80763,80764,80766,80768],{},[898,80765,2888],{},[1711,80767,1836],{},[2111,80769,4306],{},[902,80771,80645],{"encoding":904},[724,80773,80774,80777],{},[38,80775,80776],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,80779,80780,80781,1343,80799,2062],{},"Podle (5.3) s ",[883,80782,80784],{"className":80783},[886],[888,80785,80786],{"xmlns":890},[892,80787,80788,80796],{},[895,80789,80790,80792,80794],{},[898,80791,2888],{},[1711,80793,1836],{},[2111,80795,6262],{},[902,80797,80798],{"encoding":904},"L = 6",[883,80800,80802],{"className":80801},[886],[888,80803,80804],{"xmlns":890},[892,80805,80806,80816],{},[895,80807,80808,80810,80812,80814],{},[898,80809,2098],{},[898,80811,2888],{},[1711,80813,1836],{},[2111,80815,3034],{},[902,80817,80818],{"encoding":904},"dL = 3",[883,80820,80822],{"className":80821},[886],[888,80823,80824],{"xmlns":890,"display":31664},[892,80825,80826,80889],{},[895,80827,80828,80830,80832,80834,80836,80842,80844,80846,80848,80850,80852,80854,80856,80858,80860,80862,80864,80866,80868,80870,80872,80874,80876,80878,80880,80882,80884,80886],{},[898,80829,2098],{},[898,80831,6796],{},[1711,80833,1836],{},[898,80835,1790],{},[2884,80837,80838,80840],{},[898,80839,7929],{},[898,80841,2888],{},[1711,80843,1714],{"stretchy":1713},[2111,80845,6262],{},[1711,80847,1735],{"stretchy":1713},[1711,80849,4795],{},[2111,80851,3034],{},[1711,80853,1836],{},[1711,80855,1714],{"stretchy":1713},[2111,80857,7505],{},[1711,80859,4795],{},[2111,80861,6262],{},[1711,80863,2460],{},[2111,80865,22919],{},[1711,80867,4795],{},[2111,80869,9549],{},[1711,80871,1735],{"stretchy":1713},[1711,80873,4795],{},[2111,80875,3034],{},[1711,80877,1836],{},[2111,80879,80527],{},[1711,80881,4795],{},[2111,80883,3034],{},[1711,80885,1836],{},[2111,80887,80888],{},"151,2.",[902,80890,80891],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,80893,80894,80895,61350,80920,80934,80935,2186],{},"Produkce vzroste z ",[883,80896,80898],{"className":80897},[886],[888,80899,80900],{"xmlns":890},[892,80901,80902,80917],{},[895,80903,80904,80906,80908,80910,80912,80914],{},[898,80905,6796],{},[1711,80907,1714],{"stretchy":1713},[2111,80909,6262],{},[1711,80911,1735],{"stretchy":1713},[1711,80913,1836],{},[2111,80915,80916],{},"172,8",[902,80918,80919],{"encoding":904},"Q(6) = 172{,}8",[883,80921,80923],{"className":80922},[886],[888,80924,80925],{"xmlns":890},[892,80926,80927,80932],{},[895,80928,80929],{},[2111,80930,80931],{},"324",[902,80933,80931],{"encoding":904},". Skutečná hodnota: ",[883,80936,80938],{"className":80937},[886],[888,80939,80940],{"xmlns":890},[892,80941,80942,80982],{},[895,80943,80944,80946,80948,80950,80952,80954,80956,80958,80960,80962,80964,80966,80968,80970,80973,80975,80977,80979],{},[898,80945,6892],{"mathvariant":2287},[898,80947,6796],{},[1711,80949,1836],{},[898,80951,6796],{},[1711,80953,1714],{"stretchy":1713},[2111,80955,7990],{},[1711,80957,1735],{"stretchy":1713},[1711,80959,2460],{},[898,80961,6796],{},[1711,80963,1714],{"stretchy":1713},[2111,80965,6262],{},[1711,80967,1735],{"stretchy":1713},[1711,80969,1836],{},[2111,80971,80972],{},"340,2",[1711,80974,2460],{},[2111,80976,80916],{},[1711,80978,1836],{},[2111,80980,80981],{},"167,4",[902,80983,80984],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,80986,80988],{"id":80987},"příklad-52","Příklad 5.2",[724,80990,80991,80992,2186],{},"Ověříme princip (5.5) pro ",[883,80993,80995],{"className":80994},[886],[888,80996,80997],{"xmlns":890},[892,80998,80999,81023],{},[895,81000,81001,81003,81005,81007,81013,81015,81017],{},[898,81002,6796],{},[1711,81004,1836],{},[2111,81006,6262],{},[1716,81008,81009,81011],{},[898,81010,2888],{},[2111,81012,2963],{},[1711,81014,2460],{},[2111,81016,4491],{},[1716,81018,81019,81021],{},[898,81020,2888],{},[2111,81022,3034],{},[902,81024,80305],{"encoding":904},[883,81026,81028],{"className":81027},[886],[888,81029,81030],{"xmlns":890,"display":31664},[892,81031,81032,81110],{},[895,81033,81034,81036,81042,81044,81050,81052,81054,81056,81058,81060,81066,81068,81070,81072,81080,81082,81084,81086,81088,81090,81092,81094,81096,81098,81100,81106,81108],{},[898,81035,8243],{},[2884,81037,81038,81040],{},[898,81039,7929],{},[898,81041,2888],{},[1711,81043,1836],{},[2525,81045,81046,81048],{},[898,81047,6796],{},[898,81049,2888],{},[1711,81051,1836],{},[2111,81053,6262],{},[898,81055,2888],{},[1711,81057,2460],{},[2111,81059,4491],{},[1716,81061,81062,81064],{},[898,81063,2888],{},[2111,81065,2963],{},[1711,81067,1726],{"separator":1725},[2102,81069],{"width":4981},[898,81071,8243],{},[13142,81073,81074,81076,81078],{},[898,81075,7929],{},[898,81077,2888],{},[1711,81079,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,81081,1836],{},[2111,81083,6262],{},[1711,81085,2460],{},[2111,81087,22869],{},[898,81089,2888],{},[1711,81091,1836],{},[2111,81093,2113],{},[1942,81095,4699],{},[1711,81097,7978],{},[1942,81099,4699],{},[2884,81101,81102,81104],{},[898,81103,2888],{},[2111,81105,2113],{},[1711,81107,1836],{},[2111,81109,71881],{},[902,81111,81112],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,81114,81115,81151,81152,81170,81171,2186],{},[883,81116,81118],{"className":81117},[886],[888,81119,81120],{"xmlns":890},[892,81121,81122,81148],{},[895,81123,81124,81126,81138,81140,81142,81144,81146],{},[898,81125,8243],{},[13142,81127,81128,81130,81132],{},[898,81129,7929],{},[898,81131,2888],{},[895,81133,81134,81136],{},[1711,81135,5225],{"mathvariant":2287},[1711,81137,5225],{"mathvariant":2287},[1711,81139,1836],{},[1711,81141,2460],{},[2111,81143,22869],{},[1711,81145,2109],{},[2111,81147,2113],{},[902,81149,81150],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,81153,81155],{"className":81154},[886],[888,81156,81157],{"xmlns":890},[892,81158,81159,81167],{},[895,81160,81161,81163,81165],{},[898,81162,2888],{},[1711,81164,1836],{},[2111,81166,39842],{},[902,81168,81169],{"encoding":904},"L = 15"," je maximum, ",[883,81172,81174],{"className":81173},[886],[888,81175,81176],{"xmlns":890},[892,81177,81178,81224],{},[895,81179,81180,81182,81188,81190,81192,81194,81196,81198,81200,81202,81204,81206,81208,81211,81213,81216,81218,81220,81222],{},[898,81181,8243],{},[2884,81183,81184,81186],{},[898,81185,7929],{},[898,81187,2888],{},[1711,81189,1714],{"stretchy":1713},[2111,81191,39842],{},[1711,81193,1735],{"stretchy":1713},[1711,81195,1836],{},[2111,81197,6262],{},[1711,81199,4795],{},[2111,81201,39842],{},[1711,81203,2460],{},[2111,81205,4491],{},[1711,81207,4795],{},[2111,81209,81210],{},"225",[1711,81212,1836],{},[2111,81214,81215],{},"90",[1711,81217,2460],{},[2111,81219,80519],{},[1711,81221,1836],{},[2111,81223,80519],{},[902,81225,81226],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,81228,81229,45478,81285,81331],{},[883,81230,81232],{"className":81231},[886],[888,81233,81234],{"xmlns":890},[892,81235,81236,81282],{},[895,81237,81238,81240,81246,81248,81250,81252,81254,81256,81258,81260,81262,81264,81266,81268,81270,81273,81275,81278,81280],{},[898,81239,1790],{},[2884,81241,81242,81244],{},[898,81243,7929],{},[898,81245,2888],{},[1711,81247,1714],{"stretchy":1713},[2111,81249,39842],{},[1711,81251,1735],{"stretchy":1713},[1711,81253,1836],{},[2111,81255,7505],{},[1711,81257,4795],{},[2111,81259,39842],{},[1711,81261,2460],{},[2111,81263,22919],{},[1711,81265,4795],{},[2111,81267,81210],{},[1711,81269,1836],{},[2111,81271,81272],{},"180",[1711,81274,2460],{},[2111,81276,81277],{},"135",[1711,81279,1836],{},[2111,81281,80519],{},[902,81283,81284],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,81286,81288],{"className":81287},[886],[888,81289,81290],{"xmlns":890},[892,81291,81292,81328],{},[895,81293,81294,81296,81302,81304,81306,81308,81310,81312,81318,81320,81322,81324,81326],{},[898,81295,1790],{},[2884,81297,81298,81300],{},[898,81299,7929],{},[898,81301,2888],{},[1711,81303,1714],{"stretchy":1713},[2111,81305,39842],{},[1711,81307,1735],{"stretchy":1713},[1711,81309,1836],{},[898,81311,8243],{},[2884,81313,81314,81316],{},[898,81315,7929],{},[898,81317,2888],{},[1711,81319,1714],{"stretchy":1713},[2111,81321,39842],{},[1711,81323,1735],{"stretchy":1713},[1711,81325,1836],{},[2111,81327,80519],{},[902,81329,81330],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,81333,81334,81337,81338,21174,81367,2186],{},[38,81335,81336],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,81339,81341],{"className":81340},[886],[888,81342,81343],{"xmlns":890},[892,81344,81345,81365],{},[895,81346,81347,81349,81355,81357,81359],{},[898,81348,1790],{},[2884,81350,81351,81353],{},[898,81352,7929],{},[898,81354,2888],{},[1711,81356,1836],{},[898,81358,8243],{},[2884,81360,81361,81363],{},[898,81362,7929],{},[898,81364,2888],{},[902,81366,78261],{"encoding":904},[883,81368,81370],{"className":81369},[886],[888,81371,81372],{"xmlns":890},[892,81373,81374,81414],{},[895,81375,81376,81378,81380,81382,81384,81390,81392,81394,81396,81398,81400,81406,81408,81410,81412],{},[2111,81377,7505],{},[898,81379,2888],{},[1711,81381,2460],{},[2111,81383,22919],{},[1716,81385,81386,81388],{},[898,81387,2888],{},[2111,81389,2963],{},[1711,81391,1836],{},[2111,81393,6262],{},[898,81395,2888],{},[1711,81397,2460],{},[2111,81399,4491],{},[1716,81401,81402,81404],{},[898,81403,2888],{},[2111,81405,2963],{},[1711,81407,7978],{},[898,81409,2888],{},[1711,81411,1836],{},[2111,81413,39842],{},[902,81415,81416],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,81418,81419],{},[614,81420,81421,81422,81441,81442,1772,81460,81479,81480,81498,81499,81516,81517,81536,81537,81556],{},"Obrázek 5.3 — křivky ",[883,81423,81425],{"className":81424},[886],[888,81426,81427],{"xmlns":890},[892,81428,81429,81439],{},[895,81430,81431,81433],{},[898,81432,1790],{},[2884,81434,81435,81437],{},[898,81436,7929],{},[898,81438,2888],{},[902,81440,14018],{"encoding":904}," (max 60 při ",[883,81443,81445],{"className":81444},[886],[888,81446,81447],{"xmlns":890},[892,81448,81449,81457],{},[895,81450,81451,81453,81455],{},[898,81452,2888],{},[1711,81454,1836],{},[2111,81456,4712],{},[902,81458,81459],{"encoding":904},"L=10",[883,81461,81463],{"className":81462},[886],[888,81464,81465],{"xmlns":890},[892,81466,81467,81477],{},[895,81468,81469,81471],{},[898,81470,8243],{},[2884,81472,81473,81475],{},[898,81474,7929],{},[898,81476,2888],{},[902,81478,78231],{"encoding":904}," (max 45 při ",[883,81481,81483],{"className":81482},[886],[888,81484,81485],{"xmlns":890},[892,81486,81487,81495],{},[895,81488,81489,81491,81493],{},[898,81490,2888],{},[1711,81492,1836],{},[2111,81494,39842],{},[902,81496,81497],{"encoding":904},"L=15","), průsečík v ",[883,81500,81502],{"className":81501},[886],[888,81503,81504],{"xmlns":890},[892,81505,81506,81514],{},[895,81507,81508,81510,81512],{},[898,81509,2888],{},[1711,81511,1836],{},[2111,81513,39842],{},[902,81515,81169],{"encoding":904},". Nalevo od 15 leží ",[883,81518,81520],{"className":81519},[886],[888,81521,81522],{"xmlns":890},[892,81523,81524,81534],{},[895,81525,81526,81528],{},[898,81527,1790],{},[2884,81529,81530,81532],{},[898,81531,7929],{},[898,81533,2888],{},[902,81535,14018],{"encoding":904}," nad ",[883,81538,81540],{"className":81539},[886],[888,81541,81542],{"xmlns":890},[892,81543,81544,81554],{},[895,81545,81546,81548],{},[898,81547,8243],{},[2884,81549,81550,81552],{},[898,81551,7929],{},[898,81553,2888],{},[902,81555,78231],{"encoding":904},", napravo pod ní.",[115,81558,81560],{"id":81559},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,81562,81563,81564,6696,81577,1700,81580,10171,81593,1700,81596,2062],{},"V dvoufaktorovém modelu závisí produkce ",[883,81565,81567],{"className":81566},[886],[888,81568,81569],{"xmlns":890},[892,81570,81571,81575],{},[895,81572,81573],{},[898,81574,6796],{},[902,81576,6796],{"encoding":904},[38,81578,81579],{},"práci",[883,81581,81583],{"className":81582},[886],[888,81584,81585],{"xmlns":890},[892,81586,81587,81591],{},[895,81588,81589],{},[898,81590,2888],{},[902,81592,2888],{"encoding":904},[38,81594,81595],{},"kapitálu",[883,81597,81599],{"className":81598},[886],[888,81600,81601],{"xmlns":890},[892,81602,81603,81607],{},[895,81604,81605],{},[898,81606,13774],{},[902,81608,13774],{"encoding":904},[883,81610,81612],{"className":81611},[886],[888,81613,81614],{"xmlns":890,"display":31664},[892,81615,81616,81651],{},[24352,81617,81618],{"width":31669},[24357,81619,81620,81622,81644,81646],{},[24360,81621],{"width":31674},[24360,81623,81624],{},[895,81625,81626,81628,81630,81632,81634,81636,81638,81640,81642],{},[898,81627,6796],{},[1711,81629,1836],{},[898,81631,6796],{},[1711,81633,1714],{"stretchy":1713},[898,81635,2888],{},[1711,81637,1726],{"separator":1725},[898,81639,13774],{},[1711,81641,1735],{"stretchy":1713},[898,81643,2186],{"mathvariant":2287},[24360,81645],{"width":31674},[24360,81647,81648],{},[1942,81649,81650],{},"(5.6)",[902,81652,81653],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,81655,81656,81657,81659],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,81658,78598],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,81661,81663],{"id":81662},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,81665,81666],{},"Široce používané produkční funkce mají tvar",[883,81668,81670],{"className":81669},[886],[888,81671,81672],{"xmlns":890,"display":31664},[892,81673,81674,81715],{},[24352,81675,81676],{"width":31669},[24357,81677,81678,81680,81708,81710],{},[24360,81679],{"width":31674},[24360,81681,81682],{},[895,81683,81684,81686,81688,81690,81692,81698,81700,81706],{},[898,81685,6796],{},[1711,81687,1836],{},[898,81689,8243],{},[1942,81691,2519],{},[1716,81693,81694,81696],{},[898,81695,2888],{},[898,81697,207],{},[1942,81699,2519],{},[1716,81701,81702,81704],{},[898,81703,13774],{},[898,81705,2223],{},[1711,81707,1726],{"separator":1725},[24360,81709],{"width":31674},[24360,81711,81712],{},[1942,81713,81714],{},"(5.7)",[902,81716,81717],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,81719,8298,81720,81742,81743,81745,81746,2186],{},[883,81721,81723],{"className":81722},[886],[888,81724,81725],{"xmlns":890},[892,81726,81727,81739],{},[895,81728,81729,81731,81733,81735,81737],{},[898,81730,8243],{},[1711,81732,1726],{"separator":1725},[898,81734,207],{},[1711,81736,1726],{"separator":1725},[898,81738,2223],{},[902,81740,81741],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,81744,78297],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,81747,81749],{"className":81748},[886],[888,81750,81751],{"xmlns":890},[892,81752,81753,81765],{},[895,81754,81755,81757,81759,81761,81763],{},[898,81756,207],{},[1711,81758,1726],{"separator":1725},[898,81760,2223],{},[1711,81762,2109],{},[2111,81764,2238],{},[902,81766,81767],{"encoding":904},"a, b \u003C 1",[724,81769,81770],{},[1801,81771],{"alt":81772,"className":81773,"src":81774},"imek-vynosy-z-rozsahu-3typy",[210,1805],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,81776,81777,81778,81781,81782,6696,81795,81811,81812,6696,81825,2062],{},"Reflektují ekonomickou zákonitost, že ",[38,81779,81780],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,81783,81785],{"className":81784},[886],[888,81786,81787],{"xmlns":890},[892,81788,81789,81793],{},[895,81790,81791],{},[898,81792,2888],{},[902,81794,2888],{"encoding":904},[883,81796,81798],{"className":81797},[886],[888,81799,81800],{"xmlns":890},[892,81801,81802,81808],{},[895,81803,81804,81806],{},[898,81805,1675],{},[898,81807,2888],{},[902,81809,81810],{"encoding":904},"rL"," a kapitál z ",[883,81813,81815],{"className":81814},[886],[888,81816,81817],{"xmlns":890},[892,81818,81819,81823],{},[895,81820,81821],{},[898,81822,13774],{},[902,81824,13774],{"encoding":904},[883,81826,81828],{"className":81827},[886],[888,81829,81830],{"xmlns":890},[892,81831,81832,81838],{},[895,81833,81834,81836],{},[898,81835,1675],{},[898,81837,13774],{},[902,81839,81840],{"encoding":904},"rK",[883,81842,81844],{"className":81843},[886],[888,81845,81846],{"xmlns":890,"display":31664},[892,81847,81848,81971],{},[24352,81849,81850],{"width":31669},[24357,81851,81852,81854,81964,81966],{},[24360,81853],{"width":31674},[24360,81855,81856],{},[895,81857,81858,81860,81862,81864,81866,81868,81870,81872,81874,81876,81878,81880,81882,81884,81890,81892,81894,81896,81902,81904,81906,81908,81920,81922,81928,81934,81936,81948,81950,81952,81954,81956,81958,81960,81962],{},[898,81859,6796],{},[1711,81861,1714],{"stretchy":1713},[898,81863,1675],{},[898,81865,2888],{},[1711,81867,1726],{"separator":1725},[898,81869,1675],{},[898,81871,13774],{},[1711,81873,1735],{"stretchy":1713},[1711,81875,1836],{},[898,81877,8243],{},[1711,81879,1714],{"stretchy":1713},[898,81881,1675],{},[898,81883,2888],{},[1716,81885,81886,81888],{},[1711,81887,1735],{"stretchy":1713},[898,81889,207],{},[1711,81891,1714],{"stretchy":1713},[898,81893,1675],{},[898,81895,13774],{},[1716,81897,81898,81900],{},[1711,81899,1735],{"stretchy":1713},[898,81901,2223],{},[1711,81903,1836],{},[898,81905,8243],{},[1942,81907,2519],{},[1716,81909,81910,81912],{},[898,81911,1675],{},[895,81913,81914,81916,81918],{},[898,81915,207],{},[1711,81917,2095],{},[898,81919,2223],{},[1942,81921,2519],{},[1716,81923,81924,81926],{},[898,81925,2888],{},[898,81927,207],{},[1716,81929,81930,81932],{},[898,81931,13774],{},[898,81933,2223],{},[1711,81935,1836],{},[1716,81937,81938,81940],{},[898,81939,1675],{},[895,81941,81942,81944,81946],{},[898,81943,207],{},[1711,81945,2095],{},[898,81947,2223],{},[1942,81949,2519],{},[898,81951,6796],{},[1711,81953,1714],{"stretchy":1713},[898,81955,2888],{},[1711,81957,1726],{"separator":1725},[898,81959,13774],{},[1711,81961,1735],{"stretchy":1713},[898,81963,2186],{"mathvariant":2287},[24360,81965],{"width":31674},[24360,81967,81968],{},[1942,81969,81970],{},"(5.8)",[902,81972,81973],{"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}",[724,81975,81976,81977],{},"Volně: ",[38,81978,81979,81980,81993,81994,82018],{},"změní-li se vstupy ",[883,81981,81983],{"className":81982},[886],[888,81984,81985],{"xmlns":890},[892,81986,81987,81991],{},[895,81988,81989],{},[898,81990,1675],{},[902,81992,1675],{"encoding":904},"-krát, změní se výstup ",[883,81995,81997],{"className":81996},[886],[888,81998,81999],{"xmlns":890},[892,82000,82001,82015],{},[895,82002,82003],{},[1716,82004,82005,82007],{},[898,82006,1675],{},[895,82008,82009,82011,82013],{},[898,82010,207],{},[1711,82012,2095],{},[898,82014,2223],{},[902,82016,82017],{"encoding":904},"r^{a+b}","-krát.",[198,82020,82022],{"id":82021},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,82024,82025,82026,82043],{},"Součet exponentů ",[883,82027,82029],{"className":82028},[886],[888,82030,82031],{"xmlns":890},[892,82032,82033,82041],{},[895,82034,82035,82037,82039],{},[898,82036,207],{},[1711,82038,2095],{},[898,82040,2223],{},[902,82042,78422],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,82045,82046,82075],{},[19,82047,82048],{},[22,82049,82050,82053,82056,82073],{},[25,82051,82052],{},"Typ",[25,82054,82055],{},"Podmínka",[25,82057,82058,82059,82072],{},"Chování produkce při ",[883,82060,82062],{"className":82061},[886],[888,82063,82064],{"xmlns":890},[892,82065,82066,82070],{},[895,82067,82068],{},[898,82069,1675],{},[902,82071,1675],{"encoding":904},"-násobném zvýšení vstupů",[25,82074,7071],{},[30,82076,82077,82188,82303],{},[22,82078,82079,82087,82111,82144],{},[35,82080,79135,82081,1648,82084,1735],{},[38,82082,82083],{},"Konstantní",[614,82085,82086],{},"constant returns",[35,82088,82089],{},[883,82090,82092],{"className":82091},[886],[888,82093,82094],{"xmlns":890},[892,82095,82096,82108],{},[895,82097,82098,82100,82102,82104,82106],{},[898,82099,207],{},[1711,82101,2095],{},[898,82103,2223],{},[1711,82105,1836],{},[2111,82107,2238],{},[902,82109,82110],{"encoding":904},"a+b = 1",[35,82112,82113,82126,82127,1700,82130,82143],{},[883,82114,82116],{"className":82115},[886],[888,82117,82118],{"xmlns":890},[892,82119,82120,82124],{},[895,82121,82122],{},[898,82123,6796],{},[902,82125,6796],{"encoding":904}," vzroste ",[38,82128,82129],{},"přesně",[883,82131,82133],{"className":82132},[886],[888,82134,82135],{"xmlns":890},[892,82136,82137,82141],{},[895,82138,82139],{},[898,82140,1675],{},[902,82142,1675],{"encoding":904},"-krát",[35,82145,82146],{},[883,82147,82149],{"className":82148},[886],[888,82150,82151],{"xmlns":890},[892,82152,82153,82185],{},[895,82154,82155,82157,82159,82161,82173],{},[898,82156,6796],{},[1711,82158,1836],{},[2111,82160,2963],{},[1716,82162,82163,82165],{},[898,82164,2888],{},[895,82166,82167,82169,82171],{},[2111,82168,2238],{},[898,82170,8659],{"mathvariant":2287},[2111,82172,6369],{},[1716,82174,82175,82177],{},[898,82176,13774],{},[895,82178,82179,82181,82183],{},[2111,82180,3034],{},[898,82182,8659],{"mathvariant":2287},[2111,82184,6369],{},[902,82186,82187],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,82189,82190,82199,82223,82253],{},[35,82191,82192,82193,1648,82196,1735],{},"2° ",[38,82194,82195],{},"Rostoucí",[614,82197,82198],{},"increasing returns",[35,82200,82201],{},[883,82202,82204],{"className":82203},[886],[888,82205,82206],{"xmlns":890},[892,82207,82208,82220],{},[895,82209,82210,82212,82214,82216,82218],{},[898,82211,207],{},[1711,82213,2095],{},[898,82215,2223],{},[1711,82217,2123],{},[2111,82219,2238],{},[902,82221,82222],{"encoding":904},"a+b > 1",[35,82224,82225,82126,82238,54829,82240,82143],{},[883,82226,82228],{"className":82227},[886],[888,82229,82230],{"xmlns":890},[892,82231,82232,82236],{},[895,82233,82234],{},[898,82235,6796],{},[902,82237,6796],{"encoding":904},[38,82239,28868],{},[883,82241,82243],{"className":82242},[886],[888,82244,82245],{"xmlns":890},[892,82246,82247,82251],{},[895,82248,82249],{},[898,82250,1675],{},[902,82252,1675],{"encoding":904},[35,82254,82255,1648,82281,1735],{},[883,82256,82258],{"className":82257},[886],[888,82259,82260],{"xmlns":890},[892,82261,82262,82278],{},[895,82263,82264,82266,82268,82270,82272],{},[898,82265,6796],{},[1711,82267,1836],{},[2111,82269,27799],{},[898,82271,2888],{},[1716,82273,82274,82276],{},[898,82275,13774],{},[2111,82277,2963],{},[902,82279,82280],{"encoding":904},"Q = 7LK^2",[883,82282,82284],{"className":82283},[886],[888,82285,82286],{"xmlns":890},[892,82287,82288,82300],{},[895,82289,82290,82292,82294,82296,82298],{},[898,82291,207],{},[1711,82293,2095],{},[898,82295,2223],{},[1711,82297,1836],{},[2111,82299,3034],{},[902,82301,82302],{"encoding":904},"a+b = 3",[22,82304,82305,82314,82338,82369],{},[35,82306,82307,82308,1648,82311,1735],{},"3° ",[38,82309,82310],{},"Klesající",[614,82312,82313],{},"decreasing returns",[35,82315,82316],{},[883,82317,82319],{"className":82318},[886],[888,82320,82321],{"xmlns":890},[892,82322,82323,82335],{},[895,82324,82325,82327,82329,82331,82333],{},[898,82326,207],{},[1711,82328,2095],{},[898,82330,2223],{},[1711,82332,2109],{},[2111,82334,2238],{},[902,82336,82337],{"encoding":904},"a+b \u003C 1",[35,82339,82340,82126,82353,54829,82356,82143],{},[883,82341,82343],{"className":82342},[886],[888,82344,82345],{"xmlns":890},[892,82346,82347,82351],{},[895,82348,82349],{},[898,82350,6796],{},[902,82352,6796],{"encoding":904},[38,82354,82355],{},"méně",[883,82357,82359],{"className":82358},[886],[888,82360,82361],{"xmlns":890},[892,82362,82363,82367],{},[895,82364,82365],{},[898,82366,1675],{},[902,82368,1675],{"encoding":904},[35,82370,82371,1648,82401,1735],{},[883,82372,82374],{"className":82373},[886],[888,82375,82376],{"xmlns":890},[892,82377,82378,82398],{},[895,82379,82380,82382,82384,82386,82392],{},[898,82381,6796],{},[1711,82383,1836],{},[2111,82385,4712],{},[1716,82387,82388,82390],{},[898,82389,2888],{},[2111,82391,71809],{},[1716,82393,82394,82396],{},[898,82395,13774],{},[2111,82397,8993],{},[902,82399,82400],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,82402,82404],{"className":82403},[886],[888,82405,82406],{"xmlns":890},[892,82407,82408,82420],{},[895,82409,82410,82412,82414,82416,82418],{},[898,82411,207],{},[1711,82413,2095],{},[898,82415,2223],{},[1711,82417,1836],{},[2111,82419,4275],{},[902,82421,82422],{"encoding":904},"a+b = 0{,}8",[1921,82424,82425],{},[724,82426,82427,82429,82430,82447,82448,82451,82452,1700,82455,82491,82492,82514,82515,2186],{},[883,82428,1927],{}," Pozor\nSoučet ",[883,82431,82433],{"className":82432},[886],[888,82434,82435],{"xmlns":890},[892,82436,82437,82445],{},[895,82438,82439,82441,82443],{},[898,82440,207],{},[1711,82442,2095],{},[898,82444,2223],{},[902,82446,78422],{"encoding":904}," neudává velikost produkce, ale ",[38,82449,82450],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,82453,82454],{},"ryzí Cobb-Douglas",[883,82456,82458],{"className":82457},[886],[888,82459,82460],{"xmlns":890},[892,82461,82462,82488],{},[895,82463,82464,82466,82468,82470,82476],{},[898,82465,6796],{},[1711,82467,1836],{},[898,82469,8243],{},[1716,82471,82472,82474],{},[898,82473,2888],{},[898,82475,207],{},[1716,82477,82478,82480],{},[898,82479,13774],{},[895,82481,82482,82484,82486],{},[2111,82483,2238],{},[1711,82485,2460],{},[898,82487,207],{},[902,82489,82490],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,82493,82495],{"className":82494},[886],[888,82496,82497],{"xmlns":890},[892,82498,82499,82511],{},[895,82500,82501,82503,82505,82507,82509],{},[898,82502,2223],{},[1711,82504,1836],{},[2111,82506,2238],{},[1711,82508,2460],{},[898,82510,207],{},[902,82512,82513],{"encoding":904},"b = 1-a",", tedy vždy ",[38,82516,82517],{},"konstantní výnosy z rozsahu",[198,82519,82521,82522],{"id":82520},"parametr-efektivity-aa","Parametr efektivity ",[883,82523,82525],{"className":82524},[886],[888,82526,82527],{"xmlns":890},[892,82528,82529,82533],{},[895,82530,82531],{},[898,82532,8243],{},[902,82534,8243],{"encoding":904},[724,82536,82537,82538,82551,82552,82565,82566,82584,82585,82588],{},"Konstanta ",[883,82539,82541],{"className":82540},[886],[888,82542,82543],{"xmlns":890},[892,82544,82545,82549],{},[895,82546,82547],{},[898,82548,8243],{},[902,82550,8243],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,82553,82555],{"className":82554},[886],[888,82556,82557],{"xmlns":890},[892,82558,82559,82563],{},[895,82560,82561],{},[898,82562,6796],{},[902,82564,6796],{"encoding":904}," při pevně zadaných ",[883,82567,82569],{"className":82568},[886],[888,82570,82571],{"xmlns":890},[892,82572,82573,82581],{},[895,82574,82575,82577,82579],{},[898,82576,2888],{},[1711,82578,1726],{"separator":1725},[898,82580,13774],{},[902,82582,82583],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,82586,82587],{},"parametr efektivity"," — indikátor stavu technologie.",[198,82590,82592],{"id":82591},"příklad-53","Příklad 5.3",[724,82594,82595,82596,82491,82638,82640,82641,2186],{},"Produkční funkce ",[883,82597,82599],{"className":82598},[886],[888,82600,82601],{"xmlns":890},[892,82602,82603,82635],{},[895,82604,82605,82607,82609,82611,82623],{},[898,82606,6796],{},[1711,82608,1836],{},[2111,82610,2963],{},[1716,82612,82613,82615],{},[898,82614,2888],{},[895,82616,82617,82619,82621],{},[2111,82618,2238],{},[898,82620,8659],{"mathvariant":2287},[2111,82622,6369],{},[1716,82624,82625,82627],{},[898,82626,13774],{},[895,82628,82629,82631,82633],{},[2111,82630,3034],{},[898,82632,8659],{"mathvariant":2287},[2111,82634,6369],{},[902,82636,82637],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,82639,28211],{}," výnosy z rozsahu, neboť ",[883,82642,82644],{"className":82643},[886],[888,82645,82646],{"xmlns":890},[892,82647,82648,82672],{},[895,82649,82650,82658,82660,82668,82670],{},[2509,82651,82652],{"scriptlevel":2113,"displaystyle":1713},[2525,82653,82654,82656],{},[2111,82655,2238],{},[2111,82657,6369],{},[1711,82659,2095],{},[2509,82661,82662],{"scriptlevel":2113,"displaystyle":1713},[2525,82663,82664,82666],{},[2111,82665,3034],{},[2111,82667,6369],{},[1711,82669,1836],{},[2111,82671,2238],{},[902,82673,82674],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,82676,82677,82678,10171,82691,82704,82705,1700,82718,82758],{},"Změní-li se ",[883,82679,82681],{"className":82680},[886],[888,82682,82683],{"xmlns":890},[892,82684,82685,82689],{},[895,82686,82687],{},[898,82688,2888],{},[902,82690,2888],{"encoding":904},[883,82692,82694],{"className":82693},[886],[888,82695,82696],{"xmlns":890},[892,82697,82698,82702],{},[895,82699,82700],{},[898,82701,13774],{},[902,82703,13774],{"encoding":904}," čtyřnásobně, změní se ",[883,82706,82708],{"className":82707},[886],[888,82709,82710],{"xmlns":890},[892,82711,82712,82716],{},[895,82713,82714],{},[898,82715,6796],{},[902,82717,6796],{"encoding":904},[883,82719,82721],{"className":82720},[886],[888,82722,82723],{"xmlns":890},[892,82724,82725,82755],{},[895,82726,82727,82747,82749],{},[1716,82728,82729,82731],{},[2111,82730,6369],{},[895,82732,82733,82735,82737,82739,82741,82743,82745],{},[2111,82734,2238],{},[898,82736,8659],{"mathvariant":2287},[2111,82738,6369],{},[1711,82740,2095],{},[2111,82742,3034],{},[898,82744,8659],{"mathvariant":2287},[2111,82746,6369],{},[1711,82748,1836],{},[1716,82750,82751,82753],{},[2111,82752,6369],{},[2111,82754,2238],{},[902,82756,82757],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,82760,82762],{"className":82761},[886],[888,82763,82764],{"xmlns":890,"display":31664},[892,82765,82766,82926],{},[895,82767,82768,82770,82772,82774,82776,82778,82780,82782,82784,82786,82788,82790,82792,82794,82806,82808,82810,82812,82824,82826,82828,82830,82850,82862,82874,82876,82878,82880,82882,82894,82906,82908,82910,82912,82914,82916,82918,82920,82922,82924],{},[898,82769,6796],{},[1711,82771,1714],{"stretchy":1713},[2111,82773,6369],{},[898,82775,2888],{},[1711,82777,1726],{"separator":1725},[2111,82779,6369],{},[898,82781,13774],{},[1711,82783,1735],{"stretchy":1713},[1711,82785,1836],{},[2111,82787,2963],{},[1711,82789,1714],{"stretchy":1713},[2111,82791,6369],{},[898,82793,2888],{},[1716,82795,82796,82798],{},[1711,82797,1735],{"stretchy":1713},[895,82799,82800,82802,82804],{},[2111,82801,2238],{},[898,82803,8659],{"mathvariant":2287},[2111,82805,6369],{},[1711,82807,1714],{"stretchy":1713},[2111,82809,6369],{},[898,82811,13774],{},[1716,82813,82814,82816],{},[1711,82815,1735],{"stretchy":1713},[895,82817,82818,82820,82822],{},[2111,82819,3034],{},[898,82821,8659],{"mathvariant":2287},[2111,82823,6369],{},[1711,82825,1836],{},[2111,82827,2963],{},[1711,82829,4795],{},[1716,82831,82832,82834],{},[2111,82833,6369],{},[895,82835,82836,82838,82840,82842,82844,82846,82848],{},[2111,82837,2238],{},[898,82839,8659],{"mathvariant":2287},[2111,82841,6369],{},[1711,82843,2095],{},[2111,82845,3034],{},[898,82847,8659],{"mathvariant":2287},[2111,82849,6369],{},[1716,82851,82852,82854],{},[898,82853,2888],{},[895,82855,82856,82858,82860],{},[2111,82857,2238],{},[898,82859,8659],{"mathvariant":2287},[2111,82861,6369],{},[1716,82863,82864,82866],{},[898,82865,13774],{},[895,82867,82868,82870,82872],{},[2111,82869,3034],{},[898,82871,8659],{"mathvariant":2287},[2111,82873,6369],{},[1711,82875,1836],{},[2111,82877,6369],{},[1711,82879,4795],{},[2111,82881,2963],{},[1716,82883,82884,82886],{},[898,82885,2888],{},[895,82887,82888,82890,82892],{},[2111,82889,2238],{},[898,82891,8659],{"mathvariant":2287},[2111,82893,6369],{},[1716,82895,82896,82898],{},[898,82897,13774],{},[895,82899,82900,82902,82904],{},[2111,82901,3034],{},[898,82903,8659],{"mathvariant":2287},[2111,82905,6369],{},[1711,82907,1836],{},[2111,82909,6369],{},[1942,82911,2519],{},[898,82913,6796],{},[1711,82915,1714],{"stretchy":1713},[898,82917,2888],{},[1711,82919,1726],{"separator":1725},[898,82921,13774],{},[1711,82923,1735],{"stretchy":1713},[898,82925,2186],{"mathvariant":2287},[902,82927,82928],{"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).",[198,82930,82931],{"id":40777},"Homogenita",[724,82933,82934,82935,12082,82958,82974],{},"Funkce ",[883,82936,82938],{"className":82937},[886],[888,82939,82940],{"xmlns":890},[892,82941,82942,82956],{},[895,82943,82944,82946,82948,82950,82952,82954],{},[898,82945,6796],{},[1711,82947,1714],{"stretchy":1713},[898,82949,2888],{},[1711,82951,1726],{"separator":1725},[898,82953,13774],{},[1711,82955,1735],{"stretchy":1713},[902,82957,13971],{"encoding":904},[38,82959,82960,82961],{},"homogenní stupně ",[883,82962,82964],{"className":82963},[886],[888,82965,82966],{"xmlns":890},[892,82967,82968,82972],{},[895,82969,82970],{},[898,82971,40458],{},[902,82973,40458],{"encoding":904},", jestliže",[883,82976,82978],{"className":82977},[886],[888,82979,82980],{"xmlns":890,"display":31664},[892,82981,82982,83039],{},[24352,82983,82984],{"width":31669},[24357,82985,82986,82988,83032,83034],{},[24360,82987],{"width":31674},[24360,82989,82990],{},[895,82991,82992,82994,82996,82998,83000,83002,83004,83006,83008,83010,83016,83018,83020,83022,83024,83026,83028,83030],{},[898,82993,6796],{},[1711,82995,1714],{"stretchy":1713},[898,82997,1675],{},[898,82999,2888],{},[1711,83001,1726],{"separator":1725},[898,83003,1675],{},[898,83005,13774],{},[1711,83007,1735],{"stretchy":1713},[1711,83009,1836],{},[1716,83011,83012,83014],{},[898,83013,1675],{},[898,83015,40458],{},[1942,83017,2519],{},[898,83019,6796],{},[1711,83021,1714],{"stretchy":1713},[898,83023,2888],{},[1711,83025,1726],{"separator":1725},[898,83027,13774],{},[1711,83029,1735],{"stretchy":1713},[1711,83031,1726],{"separator":1725},[24360,83033],{"width":31674},[24360,83035,83036],{},[1942,83037,83038],{},"(5.10)",[902,83040,83041],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,83043,8298,83044,83062,83063,83081,83082,47234,83095,83098,83099,2186],{},[883,83045,83047],{"className":83046},[886],[888,83048,83049],{"xmlns":890},[892,83050,83051,83059],{},[895,83052,83053,83055,83057],{},[898,83054,40458],{},[1711,83056,8471],{},[2111,83058,2113],{},[902,83060,83061],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,83064,83066],{"className":83065},[886],[888,83067,83068],{"xmlns":890},[892,83069,83070,83078],{},[895,83071,83072,83074,83076],{},[898,83073,1675],{},[1711,83075,2123],{},[2111,83077,2113],{},[902,83079,83080],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,83083,83085],{"className":83084},[886],[888,83086,83087],{"xmlns":890},[892,83088,83089,83093],{},[895,83090,83091],{},[2111,83092,2238],{},[902,83094,2238],{"encoding":904},[38,83096,83097],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,83100,83102],{"className":83101},[886],[888,83103,83104],{"xmlns":890},[892,83105,83106,83114],{},[895,83107,83108,83110,83112],{},[898,83109,207],{},[1711,83111,2095],{},[898,83113,2223],{},[902,83115,78422],{"encoding":904},[115,83117,83119],{"id":83118},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,83121,83122],{},[38,83123,83124],{},"Ryzí Cobb-Douglasovy funkce:",[883,83126,83128],{"className":83127},[886],[888,83129,83130],{"xmlns":890,"display":31664},[892,83131,83132,83191],{},[24352,83133,83134],{"width":31669},[24357,83135,83136,83138,83184,83186],{},[24360,83137],{"width":31674},[24360,83139,83140],{},[895,83141,83142,83144,83146,83148,83150,83156,83158,83170,83172,83174,83176,83178,83180,83182],{},[898,83143,6796],{},[1711,83145,1836],{},[898,83147,8243],{},[1942,83149,2519],{},[1716,83151,83152,83154],{},[898,83153,2888],{},[898,83155,207],{},[1942,83157,2519],{},[1716,83159,83160,83162],{},[898,83161,13774],{},[895,83163,83164,83166,83168],{},[2111,83165,2238],{},[1711,83167,2460],{},[898,83169,207],{},[1711,83171,1726],{"separator":1725},[2102,83173],{"width":4981},[2111,83175,2113],{},[1711,83177,2109],{},[898,83179,207],{},[1711,83181,2109],{},[2111,83183,2941],{},[24360,83185],{"width":31674},[24360,83187,83188],{},[1942,83189,83190],{},"(5.9)",[902,83192,83193],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,83195,83196,83197,83199,83200,2186],{},"Mají vždy ",[38,83198,82517],{}," a jsou ",[38,83201,83097],{},[724,83203,83204,1648,83207,83210],{},[38,83205,83206],{},"CES produkční funkce",[614,83208,83209],{},"Constant Elasticity of Substitution",", 1961):",[883,83212,83214],{"className":83213},[886],[888,83215,83216],{"xmlns":890,"display":31664},[892,83217,83218,83286],{},[895,83219,83220,83222,83224,83226,83284],{},[898,83221,6796],{},[1711,83223,1836],{},[898,83225,8243],{},[1716,83227,83228,83272],{},[895,83229,83230,83232,83234,83236,83238,83240,83242,83244,83254,83256,83258,83260,83270],{},[1711,83231,5144],{"fence":1725},[1711,83233,1714],{"stretchy":1713},[2111,83235,2238],{},[1711,83237,2460],{},[898,83239,207],{},[1711,83241,1735],{"stretchy":1713},[1942,83243,2519],{},[1716,83245,83246,83248],{},[898,83247,2888],{},[895,83249,83250,83252],{},[1711,83251,2460],{},[898,83253,2223],{},[1711,83255,2095],{},[898,83257,207],{},[1942,83259,2519],{},[1716,83261,83262,83264],{},[898,83263,13774],{},[895,83265,83266,83268],{},[1711,83267,2460],{},[898,83269,2223],{},[1711,83271,5163],{"fence":1725},[895,83273,83274,83276],{},[1711,83275,2460],{},[2509,83277,83278],{"scriptlevel":2113,"displaystyle":1713},[2525,83279,83280,83282],{},[2111,83281,2238],{},[898,83283,2223],{},[1711,83285,1726],{"separator":1725},[902,83287,83288],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,83290,8298,83291,1343,83309,1343,83330,83354],{},[883,83292,83294],{"className":83293},[886],[888,83295,83296],{"xmlns":890},[892,83297,83298,83306],{},[895,83299,83300,83302,83304],{},[898,83301,8243],{},[1711,83303,2123],{},[2111,83305,2113],{},[902,83307,83308],{"encoding":904},"A > 0",[883,83310,83312],{"className":83311},[886],[888,83313,83314],{"xmlns":890},[892,83315,83316,83328],{},[895,83317,83318,83320,83322,83324,83326],{},[2111,83319,2113],{},[1711,83321,2109],{},[898,83323,207],{},[1711,83325,2109],{},[2111,83327,2238],{},[902,83329,22434],{"encoding":904},[883,83331,83333],{"className":83332},[886],[888,83334,83335],{"xmlns":890},[892,83336,83337,83351],{},[895,83338,83339,83341,83343,83345,83347,83349],{},[1711,83340,2460],{},[2111,83342,2238],{},[1711,83344,2109],{},[898,83346,2223],{},[1711,83348,7369],{"mathvariant":2287},[2111,83350,2113],{},[902,83352,83353],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,83356,83357],{},[38,83358,83359],{},"Další typy:",[120,83361,83362,83404],{},[123,83363,83364,1700,83367,83403],{},[38,83365,83366],{},"Lineární:",[883,83368,83370],{"className":83369},[886],[888,83371,83372],{"xmlns":890},[892,83373,83374,83400],{},[895,83375,83376,83378,83380,83382,83384,83386,83388,83390,83392,83394,83396,83398],{},[898,83377,6796],{},[1711,83379,1714],{"stretchy":1713},[898,83381,2888],{},[1711,83383,1726],{"separator":1725},[898,83385,13774],{},[1711,83387,1735],{"stretchy":1713},[1711,83389,1836],{},[898,83391,207],{},[898,83393,2888],{},[1711,83395,2095],{},[898,83397,2223],{},[898,83399,13774],{},[902,83401,83402],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,83405,83406,1700,83409,83454],{},[38,83407,83408],{},"Leontiefova:",[883,83410,83412],{"className":83411},[886],[888,83413,83414],{"xmlns":890},[892,83415,83416,83451],{},[895,83417,83418,83420,83422,83424,83426,83428,83430,83432,83435,83437,83439,83441,83443,83445,83447,83449],{},[898,83419,6796],{},[1711,83421,1714],{"stretchy":1713},[898,83423,2888],{},[1711,83425,1726],{"separator":1725},[898,83427,13774],{},[1711,83429,1735],{"stretchy":1713},[1711,83431,1836],{},[898,83433,83434],{},"min",[1711,83436,59798],{},[1711,83438,1714],{"stretchy":1713},[898,83440,207],{},[898,83442,2888],{},[1711,83444,1726],{"separator":1725},[898,83446,2223],{},[898,83448,13774],{},[1711,83450,1735],{"stretchy":1713},[902,83452,83453],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,83456,83458,83459,1343,83478,83497],{"id":83457},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,83460,83462],{"className":83461},[886],[888,83463,83464],{"xmlns":890},[892,83465,83466,83476],{},[895,83467,83468,83470],{},[898,83469,1790],{},[2884,83471,83472,83474],{},[898,83473,7929],{},[898,83475,2888],{},[902,83477,14018],{"encoding":904},[883,83479,83481],{"className":83480},[886],[888,83482,83483],{"xmlns":890},[892,83484,83485,83495],{},[895,83486,83487,83489],{},[898,83488,1790],{},[2884,83490,83491,83493],{},[898,83492,7929],{},[898,83494,13774],{},[902,83496,14063],{"encoding":904}," a totální diferenciál",[724,83499,83500],{},[38,83501,83502],{},"Mezní produkt práce:",[883,83504,83506],{"className":83505},[886],[888,83507,83508],{"xmlns":890,"display":31664},[892,83509,83510,83548],{},[895,83511,83512,83514,83520,83522,83530,83532,83546],{},[898,83513,1790],{},[2884,83515,83516,83518],{},[898,83517,7929],{},[898,83519,2888],{},[1711,83521,1836],{},[13142,83523,83524,83526,83528],{},[898,83525,6796],{},[898,83527,2888],{},[1711,83529,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,83531,1836],{},[2525,83533,83534,83540],{},[895,83535,83536,83538],{},[898,83537,13846],{"mathvariant":2287},[898,83539,6796],{},[895,83541,83542,83544],{},[898,83543,13846],{"mathvariant":2287},[898,83545,2888],{},[898,83547,2186],{"mathvariant":2287},[902,83549,83550],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,83552,83553],{},[38,83554,83555],{},"Mezní produkt kapitálu:",[883,83557,83559],{"className":83558},[886],[888,83560,83561],{"xmlns":890,"display":31664},[892,83562,83563,83601],{},[895,83564,83565,83567,83573,83575,83583,83585,83599],{},[898,83566,1790],{},[2884,83568,83569,83571],{},[898,83570,7929],{},[898,83572,13774],{},[1711,83574,1836],{},[13142,83576,83577,83579,83581],{},[898,83578,6796],{},[898,83580,13774],{},[1711,83582,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,83584,1836],{},[2525,83586,83587,83593],{},[895,83588,83589,83591],{},[898,83590,13846],{"mathvariant":2287},[898,83592,6796],{},[895,83594,83595,83597],{},[898,83596,13846],{"mathvariant":2287},[898,83598,13774],{},[898,83600,2186],{"mathvariant":2287},[902,83602,83603],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,83605,83606,83636,83637,83658,83659,83677,83678,83691,83692,2186],{},[883,83607,83609],{"className":83608},[886],[888,83610,83611],{"xmlns":890},[892,83612,83613,83633],{},[895,83614,83615,83617,83623,83625,83627,83629,83631],{},[898,83616,1790],{},[2884,83618,83619,83621],{},[898,83620,7929],{},[898,83622,2888],{},[1711,83624,1714],{"stretchy":1713},[898,83626,207],{},[1711,83628,1726],{"separator":1725},[898,83630,2223],{},[1711,83632,1735],{"stretchy":1713},[902,83634,83635],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,83638,83640],{"className":83639},[886],[888,83641,83642],{"xmlns":890},[892,83643,83644,83656],{},[895,83645,83646,83648,83650,83652,83654],{},[1711,83647,5144],{"stretchy":1713},[898,83649,207],{},[1711,83651,1726],{"separator":1725},[898,83653,2223],{},[1711,83655,5163],{"stretchy":1713},[902,83657,14797],{"encoding":904}," (na hladině ",[883,83660,83662],{"className":83661},[886],[888,83663,83664],{"xmlns":890},[892,83665,83666,83674],{},[895,83667,83668,83670,83672],{},[898,83669,13774],{},[1711,83671,1836],{},[898,83673,2223],{},[902,83675,83676],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,83679,83681],{"className":83680},[886],[888,83682,83683],{"xmlns":890},[892,83684,83685,83689],{},[895,83686,83687],{},[898,83688,2888],{},[902,83690,2888],{"encoding":904},". Analogicky ",[883,83693,83695],{"className":83694},[886],[888,83696,83697],{"xmlns":890},[892,83698,83699,83719],{},[895,83700,83701,83703,83709,83711,83713,83715,83717],{},[898,83702,1790],{},[2884,83704,83705,83707],{},[898,83706,7929],{},[898,83708,13774],{},[1711,83710,1714],{"stretchy":1713},[898,83712,207],{},[1711,83714,1726],{"separator":1725},[898,83716,2223],{},[1711,83718,1735],{"stretchy":1713},[902,83720,83721],{"encoding":904},"MP_K(a, b)",[1921,83723,83724,83728],{},[724,83725,83726,54817],{},[883,83727,2678],{},[120,83729,83730,83768],{},[123,83731,83732,29787,83751],{},[883,83733,83735],{"className":83734},[886],[888,83736,83737],{"xmlns":890},[892,83738,83739,83749],{},[895,83740,83741,83743],{},[898,83742,1790],{},[2884,83744,83745,83747],{},[898,83746,7929],{},[898,83748,2888],{},[902,83750,14018],{"encoding":904},[614,83752,83753,83754,83767],{},"„o kolik vzroste ",[883,83755,83757],{"className":83756},[886],[888,83758,83759],{"xmlns":890},[892,83760,83761,83765],{},[895,83762,83763],{},[898,83764,6796],{},[902,83766,6796],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,83769,83770,29787,83789],{},[883,83771,83773],{"className":83772},[886],[888,83774,83775],{"xmlns":890},[892,83776,83777,83787],{},[895,83778,83779,83781],{},[898,83780,1790],{},[2884,83782,83783,83785],{},[898,83784,7929],{},[898,83786,13774],{},[902,83788,14063],{"encoding":904},[614,83790,83753,83791,83804],{},[883,83792,83794],{"className":83793},[886],[888,83795,83796],{"xmlns":890},[892,83797,83798,83802],{},[895,83799,83800],{},[898,83801,6796],{},[902,83803,6796],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,83806,83807,83810,83811,83826,83827,2062],{},[38,83808,83809],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,83812,83814],{"className":83813},[886],[888,83815,83816],{"xmlns":890},[892,83817,83818,83824],{},[895,83819,83820,83822],{},[898,83821,2098],{},[898,83823,2888],{},[902,83825,78954],{"encoding":904}," a kapitálu o ",[883,83828,83830],{"className":83829},[886],[888,83831,83832],{"xmlns":890},[892,83833,83834,83840],{},[895,83835,83836,83838],{},[898,83837,2098],{},[898,83839,13774],{},[902,83841,83842],{"encoding":904},"dK",[883,83844,83846],{"className":83845},[886],[888,83847,83848],{"xmlns":890,"display":31664},[892,83849,83850,83943],{},[24352,83851,83852],{"width":31669},[24357,83853,83854,83856,83936,83938],{},[24360,83855],{"width":31674},[24360,83857,83858],{},[895,83859,83860,83862,83864,83866,83868,83870,83872,83880,83882,83884,83886,83888,83896,83898,83900,83902,83904,83906,83912,83914,83916,83918,83920,83922,83928,83930,83932,83934],{},[898,83861,6892],{"mathvariant":2287},[898,83863,6796],{},[1711,83865,6740],{},[898,83867,2098],{},[898,83869,6796],{},[1711,83871,1836],{},[13142,83873,83874,83876,83878],{},[898,83875,6796],{},[898,83877,2888],{},[1711,83879,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1942,83881,2519],{},[898,83883,2098],{},[898,83885,2888],{},[1711,83887,2095],{},[13142,83889,83890,83892,83894],{},[898,83891,6796],{},[898,83893,13774],{},[1711,83895,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1942,83897,2519],{},[898,83899,2098],{},[898,83901,13774],{},[1711,83903,1836],{},[898,83905,1790],{},[2884,83907,83908,83910],{},[898,83909,7929],{},[898,83911,2888],{},[1942,83913,2519],{},[898,83915,2098],{},[898,83917,2888],{},[1711,83919,2095],{},[898,83921,1790],{},[2884,83923,83924,83926],{},[898,83925,7929],{},[898,83927,13774],{},[1942,83929,2519],{},[898,83931,2098],{},[898,83933,13774],{},[898,83935,2186],{"mathvariant":2287},[24360,83937],{"width":31674},[24360,83939,83940],{},[1942,83941,83942],{},"(5.11)",[902,83944,83945],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,83947,83948,83949,2186],{},"Skutečná změna: ",[883,83950,83952],{"className":83951},[886],[888,83953,83954],{"xmlns":890},[892,83955,83956,84002],{},[895,83957,83958,83960,83962,83964,83966,83968,83970,83972,83974,83976,83978,83980,83982,83984,83986,83988,83990,83992,83994,83996,83998,84000],{},[898,83959,6892],{"mathvariant":2287},[898,83961,6796],{},[1711,83963,1836],{},[898,83965,6796],{},[1711,83967,1714],{"stretchy":1713},[898,83969,2888],{},[1711,83971,2095],{},[898,83973,2098],{},[898,83975,2888],{},[1711,83977,1726],{"separator":1725},[898,83979,13774],{},[1711,83981,2095],{},[898,83983,2098],{},[898,83985,13774],{},[1711,83987,1735],{"stretchy":1713},[1711,83989,2460],{},[898,83991,6796],{},[1711,83993,1714],{"stretchy":1713},[898,83995,2888],{},[1711,83997,1726],{"separator":1725},[898,83999,13774],{},[1711,84001,1735],{"stretchy":1713},[902,84003,84004],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,84006,84007,84009,84010,84028,84029,84042,84043,84062,84063,84095,84096,84128,84129,2186],{},[38,84008,79118],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,84011,84013],{"className":84012},[886],[888,84014,84015],{"xmlns":890},[892,84016,84017,84025],{},[895,84018,84019],{},[2884,84020,84021,84023],{},[898,84022,13774],{},[2111,84024,2113],{},[902,84026,84027],{"encoding":904},"K_0"," se od jistého ",[883,84030,84032],{"className":84031},[886],[888,84033,84034],{"xmlns":890},[892,84035,84036,84040],{},[895,84037,84038],{},[898,84039,2888],{},[902,84041,2888],{"encoding":904}," stane ",[883,84044,84046],{"className":84045},[886],[888,84047,84048],{"xmlns":890},[892,84049,84050,84060],{},[895,84051,84052,84054],{},[898,84053,1790],{},[2884,84055,84056,84058],{},[898,84057,7929],{},[898,84059,2888],{},[902,84061,14018],{"encoding":904}," klesající (",[883,84064,84066],{"className":84065},[886],[888,84067,84068],{"xmlns":890},[892,84069,84070,84092],{},[895,84071,84072,84088,84090],{},[13142,84073,84074,84076,84082],{},[898,84075,6796],{},[895,84077,84078,84080],{},[898,84079,2888],{},[898,84081,2888],{},[895,84083,84084,84086],{},[1711,84085,5225],{"mathvariant":2287},[1711,84087,5225],{"mathvariant":2287},[1711,84089,2109],{},[2111,84091,2113],{},[902,84093,84094],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,84097,84099],{"className":84098},[886],[888,84100,84101],{"xmlns":890},[892,84102,84103,84125],{},[895,84104,84105,84121,84123],{},[13142,84106,84107,84109,84115],{},[898,84108,6796],{},[895,84110,84111,84113],{},[898,84112,13774],{},[898,84114,13774],{},[895,84116,84117,84119],{},[1711,84118,5225],{"mathvariant":2287},[1711,84120,5225],{"mathvariant":2287},[1711,84122,2109],{},[2111,84124,2113],{},[902,84126,84127],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,84130,84132],{"className":84131},[886],[888,84133,84134],{"xmlns":890},[892,84135,84136,84144],{},[895,84137,84138],{},[2884,84139,84140,84142],{},[898,84141,2888],{},[2111,84143,2113],{},[902,84145,79156],{"encoding":904},[115,84147,84149],{"id":84148},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,84151,84152,84155,84156,84179,84180,33542],{},[38,84153,84154],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,84157,84159],{"className":84158},[886],[888,84160,84161],{"xmlns":890},[892,84162,84163,84177],{},[895,84164,84165,84167,84169,84171,84173,84175],{},[898,84166,6796],{},[1711,84168,1714],{"stretchy":1713},[898,84170,2888],{},[1711,84172,1726],{"separator":1725},[898,84174,13774],{},[1711,84176,1735],{"stretchy":1713},[902,84178,13971],{"encoding":904}," stupně ",[883,84181,84183],{"className":84182},[886],[888,84184,84185],{"xmlns":890},[892,84186,84187,84191],{},[895,84188,84189],{},[898,84190,40458],{},[902,84192,40458],{"encoding":904},[883,84194,84196],{"className":84195},[886],[888,84197,84198],{"xmlns":890,"display":31664},[892,84199,84200,84263],{},[24352,84201,84202],{"width":31669},[24357,84203,84204,84206,84256,84258],{},[24360,84205],{"width":31674},[24360,84207,84208],{},[895,84209,84210,84212,84214,84222,84224,84226,84228,84236,84238,84240,84242,84244,84246,84248,84250,84252,84254],{},[898,84211,2888],{},[1942,84213,2519],{},[13142,84215,84216,84218,84220],{},[898,84217,6796],{},[898,84219,2888],{},[1711,84221,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,84223,2095],{},[898,84225,13774],{},[1942,84227,2519],{},[13142,84229,84230,84232,84234],{},[898,84231,6796],{},[898,84233,13774],{},[1711,84235,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,84237,1836],{},[898,84239,40458],{},[1942,84241,2519],{},[898,84243,6796],{},[1711,84245,1714],{"stretchy":1713},[898,84247,2888],{},[1711,84249,1726],{"separator":1725},[898,84251,13774],{},[1711,84253,1735],{"stretchy":1713},[898,84255,2186],{"mathvariant":2287},[24360,84257],{"width":31674},[24360,84259,84260],{},[1942,84261,84262],{},"(5.12)",[902,84264,84265],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,84267,84268,84289],{},[38,84269,84270,84271],{},"Speciální případ ",[883,84272,84274],{"className":84273},[886],[888,84275,84276],{"xmlns":890},[892,84277,84278,84286],{},[895,84279,84280,84282,84284],{},[898,84281,40458],{},[1711,84283,1836],{},[2111,84285,2238],{},[902,84287,84288],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,84291,84293],{"className":84292},[886],[888,84294,84295],{"xmlns":890,"display":31664},[892,84296,84297,84341],{},[895,84298,84299,84301,84303,84305,84311,84313,84315,84317,84319,84325,84327,84329,84331,84333,84335,84337,84339],{},[898,84300,2888],{},[1711,84302,4795],{},[898,84304,1790],{},[2884,84306,84307,84309],{},[898,84308,7929],{},[898,84310,2888],{},[1711,84312,2095],{},[898,84314,13774],{},[1711,84316,4795],{},[898,84318,1790],{},[2884,84320,84321,84323],{},[898,84322,7929],{},[898,84324,13774],{},[1711,84326,1836],{},[898,84328,6796],{},[1711,84330,1714],{"stretchy":1713},[898,84332,2888],{},[1711,84334,1726],{"separator":1725},[898,84336,13774],{},[1711,84338,1735],{"stretchy":1713},[898,84340,2186],{"mathvariant":2287},[902,84342,84343],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,84345,84346,84347,84350],{},"Slovně — ",[38,84348,84349],{},"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).",[115,84352,13753],{"id":78492},[724,84354,84355,1648,84357,84360,84361,84383,84384,2062],{},[38,84356,13753],{},[614,84358,84359],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,84362,84364],{"className":84363},[886],[888,84365,84366],{"xmlns":890},[892,84367,84368,84380],{},[895,84369,84370,84372,84374,84376,84378],{},[1711,84371,5144],{"stretchy":1713},[898,84373,2888],{},[1711,84375,1726],{"separator":1725},[898,84377,13774],{},[1711,84379,5163],{"stretchy":1713},[902,84381,84382],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,84385,84387],{"className":84386},[886],[888,84388,84389],{"xmlns":890},[892,84390,84391,84396],{},[895,84392,84393],{},[898,84394,84395],{},"q",[902,84397,84395],{"encoding":904},[883,84399,84401],{"className":84400},[886],[888,84402,84403],{"xmlns":890,"display":31664},[892,84404,84405,84440],{},[24352,84406,84407],{"width":31669},[24357,84408,84409,84411,84433,84435],{},[24360,84410],{"width":31674},[24360,84412,84413],{},[895,84414,84415,84417,84419,84421,84423,84425,84427,84429,84431],{},[898,84416,6796],{},[1711,84418,1714],{"stretchy":1713},[898,84420,2888],{},[1711,84422,1726],{"separator":1725},[898,84424,13774],{},[1711,84426,1735],{"stretchy":1713},[1711,84428,1836],{},[898,84430,84395],{},[898,84432,2186],{"mathvariant":2287},[24360,84434],{"width":31674},[24360,84436,84437],{},[1942,84438,84439],{},"(5.13)",[902,84441,84442],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,84444,84445,84446,84449,84450,1797],{},"Jsou to ",[38,84447,84448],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,84451,84453],{"className":84452,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,84455,84456],{},[38,84457,84458],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,84460,84461,84466,84471,84476],{},[123,84462,84463,84465],{},[38,84464,2185],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,84467,84468,84470],{},[38,84469,41262],{}," (úloha 5.14);",[123,84472,84473,12405],{},[38,84474,84475],{},"neprotínají se",[123,84477,84478,84479,8345,84492,2186],{},"s rostoucím ",[883,84480,84482],{"className":84481},[886],[888,84483,84484],{"xmlns":890},[892,84485,84486,84490],{},[895,84487,84488],{},[898,84489,84395],{},[902,84491,84395],{"encoding":904},[38,84493,84494],{},"vzdalují od počátku",[724,84496,84497],{},[614,84498,84499,84500,84522,84523,2186],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,84501,84503],{"className":84502},[886],[888,84504,84505],{"xmlns":890},[892,84506,84507,84519],{},[895,84508,84509,84511,84513,84515,84517],{},[1711,84510,1714],{"stretchy":1713},[898,84512,2888],{},[1711,84514,1726],{"separator":1725},[898,84516,13774],{},[1711,84518,1735],{"stretchy":1713},[902,84520,84521],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,84524,84526],{"className":84525},[886],[888,84527,84528],{"xmlns":890},[892,84529,84530,84554],{},[895,84531,84532,84538,84540,84546,84548],{},[2884,84533,84534,84536],{},[898,84535,84395],{},[2111,84537,2238],{},[1711,84539,2109],{},[2884,84541,84542,84544],{},[898,84543,84395],{},[2111,84545,2113],{},[1711,84547,2109],{},[2884,84549,84550,84552],{},[898,84551,84395],{},[2111,84553,2963],{},[902,84555,84556],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,84558,84560,84561,1735],{"id":84559},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,84562,84564],{"className":84563},[886],[888,84565,84566],{"xmlns":890},[892,84567,84568,84578],{},[895,84569,84570,84572,84574,84576],{},[898,84571,1790],{},[898,84573,7985],{},[898,84575,1769],{},[898,84577,2362],{},[902,84579,14572],{"encoding":904},[724,84581,84582,1648,84585,84588],{},[38,84583,84584],{},"Mezní míra technické substituce",[614,84586,84587],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,84590,84592],{"className":84591},[886],[888,84593,84594],{"xmlns":890,"display":31664},[892,84595,84596,84687],{},[24352,84597,84598],{"width":31669},[24357,84599,84600,84602,84680,84682],{},[24360,84601],{"width":31674},[24360,84603,84604],{},[895,84605,84606,84608,84610,84612,84614,84616,84618,84620,84622,84624,84626,84628,84630,84632,84634,84636,84658,84660,84678],{},[898,84607,1790],{},[898,84609,7985],{},[898,84611,1769],{},[898,84613,2362],{},[1711,84615,1836],{},[898,84617,1790],{},[898,84619,7985],{},[898,84621,1769],{},[898,84623,2362],{},[1711,84625,1714],{"stretchy":1713},[898,84627,2888],{},[1711,84629,1726],{"separator":1725},[898,84631,13774],{},[1711,84633,1735],{"stretchy":1713},[1711,84635,1836],{},[2525,84637,84638,84648],{},[895,84639,84640,84642],{},[898,84641,1790],{},[2884,84643,84644,84646],{},[898,84645,7929],{},[898,84647,2888],{},[895,84649,84650,84652],{},[898,84651,1790],{},[2884,84653,84654,84656],{},[898,84655,7929],{},[898,84657,13774],{},[1711,84659,1836],{},[2525,84661,84662,84670],{},[13142,84663,84664,84666,84668],{},[898,84665,6796],{},[898,84667,2888],{},[1711,84669,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[13142,84671,84672,84674,84676],{},[898,84673,6796],{},[898,84675,13774],{},[1711,84677,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[898,84679,2186],{"mathvariant":2287},[24360,84681],{"width":31674},[24360,84683,84684],{},[1942,84685,84686],{},"(5.14)",[902,84688,84689],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,84691,84692,1700,84694,84724,84725,84756],{},[38,84693,13192],{},[883,84695,84697],{"className":84696},[886],[888,84698,84699],{"xmlns":890},[892,84700,84701,84721],{},[895,84702,84703,84705,84707,84709,84711,84713,84715,84717,84719],{},[898,84704,1790],{},[898,84706,7985],{},[898,84708,1769],{},[898,84710,2362],{},[1711,84712,1714],{"stretchy":1713},[898,84714,2888],{},[1711,84716,1726],{"separator":1725},[898,84718,13774],{},[1711,84720,1735],{"stretchy":1713},[902,84722,84723],{"encoding":904},"MRTS(L, K)"," udává, ",[38,84726,84727,84728,84741,84742,84755],{},"o kolik se musí přibližně změnit kapitál ",[883,84729,84731],{"className":84730},[886],[888,84732,84733],{"xmlns":890},[892,84734,84735,84739],{},[895,84736,84737],{},[898,84738,13774],{},[902,84740,13774],{"encoding":904},", jestliže se práce ",[883,84743,84745],{"className":84744},[886],[888,84746,84747],{"xmlns":890},[892,84748,84749,84753],{},[895,84750,84751],{},[898,84752,2888],{},[902,84754,2888],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[1921,84758,84759],{},[724,84760,84761,21621,84763,84782,84783,84820,84821,84824,84825,84829],{},[883,84762,2678],{},[883,84764,84766],{"className":84765},[886],[888,84767,84768],{"xmlns":890},[892,84769,84770,84780],{},[895,84771,84772,84774,84776,84778],{},[898,84773,1790],{},[898,84775,7985],{},[898,84777,1769],{},[898,84779,2362],{},[902,84781,14572],{"encoding":904}," říká: ",[614,84784,84785,84786,84805,84806,84819],{},"„jednu jednotku práce musím nahradit přibližně ",[883,84787,84789],{"className":84788},[886],[888,84790,84791],{"xmlns":890},[892,84792,84793,84803],{},[895,84794,84795,84797,84799,84801],{},[898,84796,1790],{},[898,84798,7985],{},[898,84800,1769],{},[898,84802,2362],{},[902,84804,14572],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,84807,84809],{"className":84808},[886],[888,84810,84811],{"xmlns":890},[892,84812,84813,84817],{},[895,84814,84815],{},[898,84816,6796],{},[902,84818,6796],{"encoding":904}," zůstala stejná.\""," Je to ",[38,84822,84823],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,84826,84828],{"className":84827,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,84831,84832],{},[1801,84833],{"alt":84834,"className":84835,"src":84836},"imek-izokvanty-mrts",[210,1805],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,84838,84839,84842,84843,12082,84873,84895,84896,3239],{},[38,84840,84841],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,84844,84846],{"className":84845},[886],[888,84847,84848],{"xmlns":890},[892,84849,84850,84870],{},[895,84851,84852,84854,84860,84862,84868],{},[1711,84853,5144],{"stretchy":1713},[2884,84855,84856,84858],{},[898,84857,2888],{},[2111,84859,2113],{},[1711,84861,1726],{"separator":1725},[2884,84863,84864,84866],{},[898,84865,13774],{},[2111,84867,2113],{},[1711,84869,5163],{"stretchy":1713},[902,84871,84872],{"encoding":904},"[L_0, K_0]",[883,84874,84876],{"className":84875},[886],[888,84877,84878],{"xmlns":890},[892,84879,84880,84892],{},[895,84881,84882,84884,84886,84888,84890],{},[1711,84883,2460],{},[898,84885,1790],{},[898,84887,7985],{},[898,84889,1769],{},[898,84891,2362],{},[902,84893,84894],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,84897,84899],{"className":84898},[886],[888,84900,84901],{"xmlns":890},[892,84902,84903,84925],{},[895,84904,84905,84907,84909,84911,84913,84915,84917,84919],{},[898,84906,6796],{},[1711,84908,1714],{"stretchy":1713},[898,84910,2888],{},[1711,84912,1726],{"separator":1725},[898,84914,13774],{},[1711,84916,1735],{"stretchy":1713},[1711,84918,1836],{},[2884,84920,84921,84923],{},[898,84922,84395],{},[2111,84924,2113],{},[902,84926,84927],{"encoding":904},"Q(L,K) = q_0",[883,84929,84931],{"className":84930},[886],[888,84932,84933],{"xmlns":890,"display":31664},[892,84934,84935,84987],{},[895,84936,84937,84951,84953,84955,84973,84975,84977,84979,84981,84983,84985],{},[2525,84938,84939,84945],{},[895,84940,84941,84943],{},[898,84942,2098],{},[898,84944,13774],{},[895,84946,84947,84949],{},[898,84948,2098],{},[898,84950,2888],{},[1711,84952,1836],{},[1711,84954,2460],{},[2525,84956,84957,84965],{},[13142,84958,84959,84961,84963],{},[898,84960,6796],{},[898,84962,2888],{},[1711,84964,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[13142,84966,84967,84969,84971],{},[898,84968,6796],{},[898,84970,13774],{},[1711,84972,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,84974,1836],{},[1711,84976,2460],{},[898,84978,1790],{},[898,84980,7985],{},[898,84982,1769],{},[898,84984,2362],{},[898,84986,2186],{"mathvariant":2287},[902,84988,84989],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,84991,84992,84993,85008,85009,85025],{},"Změní-li se práce o ",[883,84994,84996],{"className":84995},[886],[888,84997,84998],{"xmlns":890},[892,84999,85000,85006],{},[895,85001,85002,85004],{},[898,85003,2098],{},[898,85005,2888],{},[902,85007,78954],{"encoding":904},", lze pro odhad změny kapitálu ",[883,85010,85012],{"className":85011},[886],[888,85013,85014],{"xmlns":890},[892,85015,85016,85022],{},[895,85017,85018,85020],{},[898,85019,6892],{"mathvariant":2287},[898,85021,13774],{},[902,85023,85024],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,85027,85029],{"className":85028},[886],[888,85030,85031],{"xmlns":890,"display":31664},[892,85032,85033,85080],{},[24352,85034,85035],{"width":31669},[24357,85036,85037,85039,85073,85075],{},[24360,85038],{"width":31674},[24360,85040,85041],{},[895,85042,85043,85045,85047,85049,85051,85053,85055,85057,85059,85061,85063,85065,85067,85069,85071],{},[898,85044,6892],{"mathvariant":2287},[898,85046,13774],{},[1711,85048,6740],{},[898,85050,2098],{},[898,85052,13774],{},[1711,85054,1836],{},[1711,85056,2460],{},[898,85058,1790],{},[898,85060,7985],{},[898,85062,1769],{},[898,85064,2362],{},[1942,85066,2519],{},[898,85068,2098],{},[898,85070,2888],{},[1711,85072,1726],{"separator":1725},[24360,85074],{"width":31674},[24360,85076,85077],{},[1942,85078,85079],{},"(5.15)",[902,85081,85082],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,85084,85086],{"className":85085},[886],[888,85087,85088],{"xmlns":890,"display":31664},[892,85089,85090,85139],{},[24352,85091,85092],{"width":31669},[24357,85093,85094,85096,85132,85134],{},[24360,85095],{"width":31674},[24360,85097,85098],{},[895,85099,85100,85102,85104,85106,85124,85126,85128,85130],{},[898,85101,2098],{},[898,85103,2888],{},[1711,85105,1836],{},[2525,85107,85108,85114],{},[895,85109,85110,85112],{},[1711,85111,2460],{},[2111,85113,2238],{},[895,85115,85116,85118,85120,85122],{},[898,85117,1790],{},[898,85119,7985],{},[898,85121,1769],{},[898,85123,2362],{},[1942,85125,2519],{},[898,85127,2098],{},[898,85129,13774],{},[898,85131,2186],{"mathvariant":2287},[24360,85133],{"width":31674},[24360,85135,85136],{},[1942,85137,85138],{},"(5.16)",[902,85140,85141],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[1921,85143,85144,85168],{},[724,85145,85146,85148,85149],{},[883,85147,3872],{}," Postup — jak spočítat ",[883,85150,85152],{"className":85151},[886],[888,85153,85154],{"xmlns":890},[892,85155,85156,85166],{},[895,85157,85158,85160,85162,85164],{},[898,85159,1790],{},[898,85161,7985],{},[898,85163,1769],{},[898,85165,2362],{},[902,85167,14572],{"encoding":904},[152,85169,85170,85211,85254,85286],{},[123,85171,85172,85173,2009,85192,2186],{},"Vypočtěte parciální derivace ",[883,85174,85176],{"className":85175},[886],[888,85177,85178],{"xmlns":890},[892,85179,85180,85190],{},[895,85181,85182],{},[13142,85183,85184,85186,85188],{},[898,85185,6796],{},[898,85187,2888],{},[1711,85189,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,85191,13995],{"encoding":904},[883,85193,85195],{"className":85194},[886],[888,85196,85197],{"xmlns":890},[892,85198,85199,85209],{},[895,85200,85201],{},[13142,85202,85203,85205,85207],{},[898,85204,6796],{},[898,85206,13774],{},[1711,85208,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,85210,14040],{"encoding":904},[123,85212,69439,85213,85253],{},[883,85214,85216],{"className":85215},[886],[888,85217,85218],{"xmlns":890},[892,85219,85220,85250],{},[895,85221,85222,85224,85226,85228,85230,85232,85240,85242],{},[898,85223,1790],{},[898,85225,7985],{},[898,85227,1769],{},[898,85229,2362],{},[1711,85231,1836],{},[13142,85233,85234,85236,85238],{},[898,85235,6796],{},[898,85237,2888],{},[1711,85239,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[898,85241,8659],{"mathvariant":2287},[13142,85243,85244,85246,85248],{},[898,85245,6796],{},[898,85247,13774],{},[1711,85249,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,85251,85252],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,85255,85256,85257,2186],{},"Případně dosaďte konkrétní ",[883,85258,85260],{"className":85259},[886],[888,85261,85262],{"xmlns":890},[892,85263,85264,85284],{},[895,85265,85266,85268,85274,85276,85282],{},[1711,85267,5144],{"stretchy":1713},[2884,85269,85270,85272],{},[898,85271,2888],{},[2111,85273,2113],{},[1711,85275,1726],{"separator":1725},[2884,85277,85278,85280],{},[898,85279,13774],{},[2111,85281,2113],{},[1711,85283,5163],{"stretchy":1713},[902,85285,84872],{"encoding":904},[123,85287,85288,85289,85323,85324,85326],{},"Pro odhad substituce použijte ",[883,85290,85292],{"className":85291},[886],[888,85293,85294],{"xmlns":890},[892,85295,85296,85320],{},[895,85297,85298,85300,85302,85304,85306,85308,85310,85312,85314,85316,85318],{},[898,85299,6892],{"mathvariant":2287},[898,85301,13774],{},[1711,85303,6740],{},[1711,85305,2460],{},[898,85307,1790],{},[898,85309,7985],{},[898,85311,1769],{},[898,85313,2362],{},[1711,85315,4795],{},[898,85317,6892],{"mathvariant":2287},[898,85319,2888],{},[902,85321,85322],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,85325,56204],{}," — substituce, ne doplnění).",[724,85328,85329],{},[614,85330,85331,85332,85364,85365,6635,85378,5494,85407,85422],{},"Obrázek 5.7 — izokvanta ",[883,85333,85335],{"className":85334},[886],[888,85336,85337],{"xmlns":890},[892,85338,85339,85361],{},[895,85340,85341,85347,85349,85351,85353,85355,85357,85359],{},[2884,85342,85343,85345],{},[898,85344,84395],{},[2111,85346,2113],{},[1711,85348,1836],{},[898,85350,6796],{},[1711,85352,1714],{"stretchy":1713},[898,85354,2888],{},[1711,85356,1726],{"separator":1725},[898,85358,13774],{},[1711,85360,1735],{"stretchy":1713},[902,85362,85363],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,85366,85368],{"className":85367},[886],[888,85369,85370],{"xmlns":890},[892,85371,85372,85376],{},[895,85373,85374],{},[898,85375,22453],{},[902,85377,22453],{"encoding":904},[883,85379,85381],{"className":85380},[886],[888,85382,85383],{"xmlns":890},[892,85384,85385,85405],{},[895,85386,85387,85389,85395,85397,85403],{},[1711,85388,5144],{"stretchy":1713},[2884,85390,85391,85393],{},[898,85392,2888],{},[2111,85394,2113],{},[1711,85396,1726],{"separator":1725},[2884,85398,85399,85401],{},[898,85400,13774],{},[2111,85402,2113],{},[1711,85404,5163],{"stretchy":1713},[902,85406,84872],{"encoding":904},[883,85408,85410],{"className":85409},[886],[888,85411,85412],{"xmlns":890},[892,85413,85414,85420],{},[895,85415,85416,85418],{},[898,85417,6892],{"mathvariant":2287},[898,85419,13774],{},[902,85421,85024],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,85424,85426],{"id":85425},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,85428,85430],{"id":85429},"příklad-54","Příklad 5.4",[724,85432,80271,85433,1343,85475,1343,85492,2186],{},[883,85434,85436],{"className":85435},[886],[888,85437,85438],{"xmlns":890},[892,85439,85440,85472],{},[895,85441,85442,85444,85446,85448,85460],{},[898,85443,6796],{},[1711,85445,1836],{},[2111,85447,39842],{},[1716,85449,85450,85452],{},[898,85451,2888],{},[895,85453,85454,85456,85458],{},[2111,85455,2238],{},[898,85457,8659],{"mathvariant":2287},[2111,85459,2963],{},[1716,85461,85462,85464],{},[898,85463,13774],{},[895,85465,85466,85468,85470],{},[2111,85467,2238],{},[898,85469,8659],{"mathvariant":2287},[2111,85471,3034],{},[902,85473,85474],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,85476,85478],{"className":85477},[886],[888,85479,85480],{"xmlns":890},[892,85481,85482,85490],{},[895,85483,85484,85486,85488],{},[898,85485,2888],{},[1711,85487,1836],{},[2111,85489,4306],{},[902,85491,80645],{"encoding":904},[883,85493,85495],{"className":85494},[886],[888,85496,85497],{"xmlns":890},[892,85498,85499,85507],{},[895,85500,85501,85503,85505],{},[898,85502,13774],{},[1711,85504,1836],{},[2111,85506,4282],{},[902,85508,85509],{"encoding":904},"K = 100",[724,85511,85512],{},[38,85513,85514],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,85516,85518],{"className":85517},[886],[888,85519,85520],{"xmlns":890,"display":31664},[892,85521,85522,85636],{},[895,85523,85524,85526,85532,85534,85542,85544,85552,85566,85578,85580,85582,85584,85590,85592,85594,85596,85598,85600,85602,85610,85612,85622,85624,85631,85633],{},[898,85525,1790],{},[2884,85527,85528,85530],{},[898,85529,7929],{},[898,85531,2888],{},[1711,85533,1836],{},[13142,85535,85536,85538,85540],{},[898,85537,6796],{},[898,85539,2888],{},[1711,85541,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,85543,1836],{},[2509,85545,85546],{"scriptlevel":2113,"displaystyle":1713},[2525,85547,85548,85550],{},[2111,85549,39842],{},[2111,85551,2963],{},[1716,85553,85554,85556],{},[898,85555,2888],{},[895,85557,85558,85560,85562,85564],{},[1711,85559,2460],{},[2111,85561,2238],{},[898,85563,8659],{"mathvariant":2287},[2111,85565,2963],{},[1716,85567,85568,85570],{},[898,85569,13774],{},[895,85571,85572,85574,85576],{},[2111,85573,2238],{},[898,85575,8659],{"mathvariant":2287},[2111,85577,3034],{},[1711,85579,1726],{"separator":1725},[2102,85581],{"width":4981},[898,85583,1790],{},[2884,85585,85586,85588],{},[898,85587,7929],{},[898,85589,2888],{},[1711,85591,1714],{"stretchy":1713},[2111,85593,4306],{},[1711,85595,1726],{"separator":1725},[2111,85597,4282],{},[1711,85599,1735],{"stretchy":1713},[1711,85601,1836],{},[2509,85603,85604],{"scriptlevel":2113,"displaystyle":1713},[2525,85605,85606,85608],{},[2111,85607,39842],{},[2111,85609,2963],{},[1711,85611,4795],{},[2509,85613,85614],{"scriptlevel":2113,"displaystyle":1713},[2525,85615,85616,85618],{},[2111,85617,2238],{},[12097,85619,85620],{},[2111,85621,4306],{},[1711,85623,4795],{},[85625,85626,85627,85629],"mroot",{},[2111,85628,4282],{},[2111,85630,3034],{},[1711,85632,6740],{},[2111,85634,85635],{},"7,153.",[902,85637,85638],{"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.",[724,85640,85641,85642,47758,85664,14206,85681,85702,85703,85724],{},"Přibližná změna při ",[883,85643,85645],{"className":85644},[886],[888,85646,85647],{"xmlns":890},[892,85648,85649,85661],{},[895,85650,85651,85653,85655,85657,85659],{},[898,85652,2888],{},[1711,85654,2062],{},[2111,85656,4306],{},[1711,85658,7123],{},[2111,85660,41944],{},[902,85662,85663],{"encoding":904},"L: 20 \\to 21",[883,85665,85667],{"className":85666},[886],[888,85668,85669],{"xmlns":890},[892,85670,85671,85679],{},[895,85672,85673,85675,85677],{},[898,85674,13774],{},[1711,85676,1836],{},[2111,85678,4282],{},[902,85680,85509],{"encoding":904},[883,85682,85684],{"className":85683},[886],[888,85685,85686],{"xmlns":890},[892,85687,85688,85699],{},[895,85689,85690,85692,85694,85696],{},[898,85691,6892],{"mathvariant":2287},[898,85693,6796],{},[1711,85695,6740],{},[2111,85697,85698],{},"7,153",[902,85700,85701],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,85704,85706],{"className":85705},[886],[888,85707,85708],{"xmlns":890},[892,85709,85710,85721],{},[895,85711,85712,85714,85716,85718],{},[898,85713,6892],{"mathvariant":2287},[898,85715,6796],{},[1711,85717,6740],{},[2111,85719,85720],{},"26,888",[902,85722,85723],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,85726,85727,85730],{},[38,85728,85729],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,85732,85734],{"className":85733},[886],[888,85735,85736],{"xmlns":890,"display":31664},[892,85737,85738,85838],{},[895,85739,85740,85742,85748,85750,85758,85760,85762,85774,85788,85790,85792,85794,85800,85802,85804,85806,85808,85810,85812,85814,85818,85820,85833,85835],{},[898,85741,1790],{},[2884,85743,85744,85746],{},[898,85745,7929],{},[898,85747,13774],{},[1711,85749,1836],{},[13142,85751,85752,85754,85756],{},[898,85753,6796],{},[898,85755,13774],{},[1711,85757,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,85759,1836],{},[2111,85761,4798],{},[1716,85763,85764,85766],{},[898,85765,2888],{},[895,85767,85768,85770,85772],{},[2111,85769,2238],{},[898,85771,8659],{"mathvariant":2287},[2111,85773,2963],{},[1716,85775,85776,85778],{},[898,85777,13774],{},[895,85779,85780,85782,85784,85786],{},[1711,85781,2460],{},[2111,85783,2963],{},[898,85785,8659],{"mathvariant":2287},[2111,85787,3034],{},[1711,85789,1726],{"separator":1725},[2102,85791],{"width":4981},[898,85793,1790],{},[2884,85795,85796,85798],{},[898,85797,7929],{},[898,85799,13774],{},[1711,85801,1714],{"stretchy":1713},[2111,85803,4306],{},[1711,85805,1726],{"separator":1725},[2111,85807,4282],{},[1711,85809,1735],{"stretchy":1713},[1711,85811,1836],{},[2111,85813,4798],{},[12097,85815,85816],{},[2111,85817,4306],{},[1711,85819,4795],{},[2509,85821,85822],{"scriptlevel":2113,"displaystyle":1713},[2525,85823,85824,85826],{},[2111,85825,2238],{},[85625,85827,85828,85831],{},[2111,85829,85830],{},"10000",[2111,85832,3034],{},[1711,85834,6740],{},[2111,85836,85837],{},"4,525.",[902,85839,85840],{"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.",[724,85842,85843,85844,6696,85861,1797],{},"Produkce poklesne přibližně o 4,525 (z ",[883,85845,85847],{"className":85846},[886],[888,85848,85849],{"xmlns":890},[892,85850,85851,85858],{},[895,85852,85853,85855],{},[1711,85854,6740],{},[2111,85856,85857],{},"905,126",[902,85859,85860],{"encoding":904},"\\approx 905{,}126",[883,85862,85864],{"className":85863},[886],[888,85865,85866],{"xmlns":890},[892,85867,85868,85875],{},[895,85869,85870,85872],{},[1711,85871,6740],{},[2111,85873,85874],{},"900,601",[902,85876,85877],{"encoding":904},"\\approx 900{,}601",[724,85879,85880,7130,85927,1343,85949,1797],{},[38,85881,85882,85883,2009,85905],{},"(c) Změna ",[883,85884,85886],{"className":85885},[886],[888,85887,85888],{"xmlns":890},[892,85889,85890,85902],{},[895,85891,85892,85894,85896,85898,85900],{},[898,85893,2888],{},[1711,85895,2062],{},[2111,85897,4306],{},[1711,85899,7123],{},[2111,85901,39842],{},[902,85903,85904],{"encoding":904},"L: 20 \\to 15",[883,85906,85908],{"className":85907},[886],[888,85909,85910],{"xmlns":890},[892,85911,85912,85924],{},[895,85913,85914,85916,85918,85920,85922],{},[898,85915,13774],{},[1711,85917,2062],{},[2111,85919,4282],{},[1711,85921,7123],{},[2111,85923,12781],{},[902,85925,85926],{"encoding":904},"K: 100 \\to 150",[883,85928,85930],{"className":85929},[886],[888,85931,85932],{"xmlns":890},[892,85933,85934,85946],{},[895,85935,85936,85938,85940,85942,85944],{},[898,85937,2098],{},[898,85939,2888],{},[1711,85941,1836],{},[1711,85943,2460],{},[2111,85945,4798],{},[902,85947,85948],{"encoding":904},"dL = -5",[883,85950,85952],{"className":85951},[886],[888,85953,85954],{"xmlns":890},[892,85955,85956,85966],{},[895,85957,85958,85960,85962,85964],{},[898,85959,2098],{},[898,85961,13774],{},[1711,85963,1836],{},[2111,85965,7120],{},[902,85967,85968],{"encoding":904},"dK = 50",[883,85970,85972],{"className":85971},[886],[888,85973,85974],{"xmlns":890,"display":31664},[892,85975,85976,86064],{},[895,85977,85978,85980,85982,85984,85986,85992,85994,85996,85998,86000,86002,86004,86006,86008,86010,86012,86014,86016,86022,86024,86026,86028,86030,86032,86034,86036,86038,86040,86042,86044,86046,86048,86050,86052,86055,86057,86059,86061],{},[898,85979,2098],{},[898,85981,6796],{},[1711,85983,1836],{},[898,85985,1790],{},[2884,85987,85988,85990],{},[898,85989,7929],{},[898,85991,2888],{},[1711,85993,1714],{"stretchy":1713},[2111,85995,4306],{},[1711,85997,1726],{"separator":1725},[2111,85999,4282],{},[1711,86001,1735],{"stretchy":1713},[1711,86003,4795],{},[1711,86005,1714],{"stretchy":1713},[1711,86007,2460],{},[2111,86009,4798],{},[1711,86011,1735],{"stretchy":1713},[1711,86013,2095],{},[898,86015,1790],{},[2884,86017,86018,86020],{},[898,86019,7929],{},[898,86021,13774],{},[1711,86023,1714],{"stretchy":1713},[2111,86025,4306],{},[1711,86027,1726],{"separator":1725},[2111,86029,4282],{},[1711,86031,1735],{"stretchy":1713},[1711,86033,4795],{},[2111,86035,7120],{},[1711,86037,1836],{},[2111,86039,85698],{},[1711,86041,4795],{},[1711,86043,1714],{"stretchy":1713},[1711,86045,2460],{},[2111,86047,4798],{},[1711,86049,1735],{"stretchy":1713},[1711,86051,2095],{},[2111,86053,86054],{},"4,525",[1711,86056,4795],{},[2111,86058,7120],{},[1711,86060,6740],{},[2111,86062,86063],{},"190,485.",[902,86065,86066],{"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.",[724,86068,86069],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,86071,86073],{"id":86072},"příklad-55","Příklad 5.5",[724,86075,86076,86077,86113,86114,2186],{},"Pro produkci ",[883,86078,86080],{"className":86079},[886],[888,86081,86082],{"xmlns":890},[892,86083,86084,86110],{},[895,86085,86086,86088,86090,86092,86094,86096,86098,86100,86106],{},[898,86087,6796],{},[1711,86089,1714],{"stretchy":1713},[898,86091,2888],{},[1711,86093,1726],{"separator":1725},[898,86095,13774],{},[1711,86097,1735],{"stretchy":1713},[1711,86099,1836],{},[85625,86101,86102,86104],{},[898,86103,2888],{},[2111,86105,3034],{},[12097,86107,86108],{},[898,86109,13774],{},[902,86111,86112],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,86115,86117],{"className":86116},[886],[888,86118,86119],{"xmlns":890},[892,86120,86121,86137],{},[895,86122,86123,86129,86133,86135],{},[85625,86124,86125,86127],{},[898,86126,2888],{},[2111,86128,3034],{},[12097,86130,86131],{},[898,86132,13774],{},[1711,86134,1836],{},[898,86136,84395],{},[902,86138,86139],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,86141,86142,86143,2186],{},"Umocněním na druhou: ",[883,86144,86146],{"className":86145},[886],[888,86147,86148],{"xmlns":890},[892,86149,86150,86174],{},[895,86151,86152,86154,86156,86162,86164],{},[898,86153,13774],{},[1711,86155,1836],{},[1716,86157,86158,86160],{},[898,86159,84395],{},[2111,86161,2963],{},[898,86163,8659],{"mathvariant":2287},[85625,86165,86166,86172],{},[1716,86167,86168,86170],{},[898,86169,2888],{},[2111,86171,2963],{},[2111,86173,3034],{},[902,86175,86176],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,86178,86179,86219,86259],{},[123,86180,86181],{},[883,86182,86184],{"className":86183},[886],[888,86185,86186],{"xmlns":890},[892,86187,86188,86216],{},[895,86189,86190,86192,86194,86196,86198,86200,86202,86204,86206],{},[898,86191,84395],{},[1711,86193,1836],{},[2111,86195,2238],{},[1711,86197,7978],{},[898,86199,13774],{},[1711,86201,1836],{},[2111,86203,2238],{},[898,86205,8659],{"mathvariant":2287},[85625,86207,86208,86214],{},[1716,86209,86210,86212],{},[898,86211,2888],{},[2111,86213,2963],{},[2111,86215,3034],{},[902,86217,86218],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,86220,86221],{},[883,86222,86224],{"className":86223},[886],[888,86225,86226],{"xmlns":890},[892,86227,86228,86256],{},[895,86229,86230,86232,86234,86236,86238,86240,86242,86244,86246],{},[898,86231,84395],{},[1711,86233,1836],{},[2111,86235,2963],{},[1711,86237,7978],{},[898,86239,13774],{},[1711,86241,1836],{},[2111,86243,6369],{},[898,86245,8659],{"mathvariant":2287},[85625,86247,86248,86254],{},[1716,86249,86250,86252],{},[898,86251,2888],{},[2111,86253,2963],{},[2111,86255,3034],{},[902,86257,86258],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,86260,86261],{},[883,86262,86264],{"className":86263},[886],[888,86265,86266],{"xmlns":890},[892,86267,86268,86296],{},[895,86269,86270,86272,86274,86276,86278,86280,86282,86284,86286],{},[898,86271,84395],{},[1711,86273,1836],{},[2111,86275,3034],{},[1711,86277,7978],{},[898,86279,13774],{},[1711,86281,1836],{},[2111,86283,7990],{},[898,86285,8659],{"mathvariant":2287},[85625,86287,86288,86294],{},[1716,86289,86290,86292],{},[898,86291,2888],{},[2111,86293,2963],{},[2111,86295,3034],{},[902,86297,86298],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,86300,86301],{},[614,86302,86303,86304,10454,86325,2186],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,86305,86307],{"className":86306},[886],[888,86308,86309],{"xmlns":890},[892,86310,86311,86323],{},[895,86312,86313,86315,86317,86319,86321],{},[1711,86314,1714],{"stretchy":1713},[898,86316,2888],{},[1711,86318,1726],{"separator":1725},[898,86320,13774],{},[1711,86322,1735],{"stretchy":1713},[902,86324,84521],{"encoding":904},[883,86326,86328],{"className":86327},[886],[888,86329,86330],{"xmlns":890},[892,86331,86332,86348],{},[895,86333,86334,86336,86338,86340,86342,86344,86346],{},[898,86335,84395],{},[1711,86337,1836],{},[2111,86339,2238],{},[1711,86341,1726],{"separator":1725},[2111,86343,2963],{},[1711,86345,1726],{"separator":1725},[2111,86347,3034],{},[902,86349,86350],{"encoding":904},"q = 1, 2, 3",[198,86352,86354],{"id":86353},"příklad-56","Příklad 5.6",[724,86356,80271,86357,2186],{},[883,86358,86360],{"className":86359},[886],[888,86361,86362],{"xmlns":890},[892,86363,86364,86380],{},[895,86365,86366,86368,86370,86372,86374,86376],{},[898,86367,6796],{},[1711,86369,1836],{},[2111,86371,2963],{},[898,86373,2888],{},[1711,86375,2095],{},[12097,86377,86378],{},[898,86379,13774],{},[902,86381,86382],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,86384,86386],{"className":86385},[886],[888,86387,86388],{"xmlns":890,"display":31664},[892,86389,86390,86432],{},[895,86391,86392,86394,86400,86402,86404,86406,86408,86410,86416,86418,86430],{},[898,86393,1790],{},[2884,86395,86396,86398],{},[898,86397,7929],{},[898,86399,2888],{},[1711,86401,1836],{},[2111,86403,2963],{},[1711,86405,1726],{"separator":1725},[2102,86407],{"width":2104},[898,86409,1790],{},[2884,86411,86412,86414],{},[898,86413,7929],{},[898,86415,13774],{},[1711,86417,1836],{},[2525,86419,86420,86422],{},[2111,86421,2238],{},[895,86423,86424,86426],{},[2111,86425,2963],{},[12097,86427,86428],{},[898,86429,13774],{},[898,86431,2186],{"mathvariant":2287},[902,86433,86434],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,86436,86438],{"className":86437},[886],[888,86439,86440],{"xmlns":890,"display":31664},[892,86441,86442,86506],{},[895,86443,86444,86446,86448,86450,86452,86454,86476,86478,86496,86498,86500,86504],{},[898,86445,1790],{},[898,86447,7985],{},[898,86449,1769],{},[898,86451,2362],{},[1711,86453,1836],{},[2525,86455,86456,86466],{},[895,86457,86458,86460],{},[898,86459,1790],{},[2884,86461,86462,86464],{},[898,86463,7929],{},[898,86465,2888],{},[895,86467,86468,86470],{},[898,86469,1790],{},[2884,86471,86472,86474],{},[898,86473,7929],{},[898,86475,13774],{},[1711,86477,1836],{},[2525,86479,86480,86482],{},[2111,86481,2963],{},[2509,86483,86484],{"scriptlevel":2113,"displaystyle":1713},[2525,86485,86486,86488],{},[2111,86487,2238],{},[895,86489,86490,86492],{},[2111,86491,2963],{},[12097,86493,86494],{},[898,86495,13774],{},[1711,86497,1836],{},[2111,86499,6369],{},[12097,86501,86502],{},[898,86503,13774],{},[898,86505,2186],{"mathvariant":2287},[902,86507,86508],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,86510,86511,86512,86555,86556,86595,86596,2186],{},"Například ",[883,86513,86515],{"className":86514},[886],[888,86516,86517],{"xmlns":890},[892,86518,86519,86552],{},[895,86520,86521,86523,86525,86527,86529,86531,86533,86535,86537,86539,86541,86543,86547,86549],{},[898,86522,1790],{},[898,86524,7985],{},[898,86526,1769],{},[898,86528,2362],{},[1711,86530,1714],{"stretchy":1713},[2111,86532,6369],{},[1711,86534,1726],{"separator":1725},[2111,86536,27799],{},[1711,86538,1735],{"stretchy":1713},[1711,86540,1836],{},[2111,86542,6369],{},[12097,86544,86545],{},[2111,86546,27799],{},[1711,86548,6740],{},[2111,86550,86551],{},"10,58",[902,86553,86554],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,86557,86559],{"className":86558},[886],[888,86560,86561],{"xmlns":890},[892,86562,86563,86592],{},[895,86564,86565,86567,86569,86571,86573,86575,86577,86579,86581,86583,86587,86589],{},[898,86566,6796],{},[1711,86568,1714],{"stretchy":1713},[2111,86570,6369],{},[1711,86572,1726],{"separator":1725},[2111,86574,27799],{},[1711,86576,1735],{"stretchy":1713},[1711,86578,1836],{},[2111,86580,9568],{},[1711,86582,2095],{},[12097,86584,86585],{},[2111,86586,27799],{},[1711,86588,6740],{},[2111,86590,86591],{},"10,646",[902,86593,86594],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,86597,86599],{"className":86598},[886],[888,86600,86601],{"xmlns":890},[892,86602,86603,86611],{},[895,86604,86605,86607],{},[2111,86606,6369],{},[12097,86608,86609],{},[2111,86610,27799],{},[902,86612,86613],{"encoding":904},"4\\sqrt{7}",[724,86615,86616,86617,86637],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,86618,86620],{"className":86619},[886],[888,86621,86622],{"xmlns":890},[892,86623,86624,86634],{},[895,86625,86626,86628,86630,86632],{},[898,86627,2098],{},[898,86629,2888],{},[1711,86631,1836],{},[2111,86633,2963],{},[902,86635,86636],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,86639,86641],{"className":86640},[886],[888,86642,86643],{"xmlns":890,"display":31664},[892,86644,86645,86694],{},[895,86646,86647,86649,86651,86653,86655,86657,86659,86661,86663,86665,86667,86669,86671,86673,86675,86677,86679,86681,86683,86687,86689,86691],{},[898,86648,2098],{},[898,86650,13774],{},[1711,86652,1836],{},[1711,86654,2460],{},[898,86656,1790],{},[898,86658,7985],{},[898,86660,1769],{},[898,86662,2362],{},[1711,86664,1714],{"stretchy":1713},[2111,86666,6369],{},[1711,86668,1726],{"separator":1725},[2111,86670,27799],{},[1711,86672,1735],{"stretchy":1713},[1711,86674,4795],{},[2111,86676,2963],{},[1711,86678,1836],{},[1711,86680,2460],{},[2111,86682,9568],{},[12097,86684,86685],{},[2111,86686,27799],{},[1711,86688,6740],{},[1711,86690,2460],{},[2111,86692,86693],{},"21,17.",[902,86695,86696],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,86698,86700],{"id":86699},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,86702,86703,86704,1343,86706,2009,86708,86710,86711,86714,86715,86718],{},"Hlavními faktory produkce jsou ",[38,86705,78512],{},[38,86707,78528],{},[38,86709,78544],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,86712,86713],{},"jednofaktorový"," (pouze práce) a ",[38,86716,86717],{},"dvoufaktorový"," (práce + kapitál) model.",[724,86720,86721,86722,86725,86726,86728,86729,86731,86732,29787,86735,86754,86755,86772,86773,86790,86791,86813,86814,8345,86833,2186],{},"V ",[38,86723,86724],{},"1F modelu"," se definuje ",[38,86727,13998],{}," (derivace produkce podle práce) a ",[38,86730,78447],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,86733,86734],{},"zákonu klesajících výnosů",[883,86736,86738],{"className":86737},[886],[888,86739,86740],{"xmlns":890},[892,86741,86742,86752],{},[895,86743,86744,86746],{},[898,86745,1790],{},[2884,86747,86748,86750],{},[898,86749,7929],{},[898,86751,2888],{},[902,86753,14018],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,86756,86758],{"className":86757},[886],[888,86759,86760],{"xmlns":890},[892,86761,86762,86770],{},[895,86763,86764],{},[2884,86765,86766,86768],{},[898,86767,2888],{},[2111,86769,2113],{},[902,86771,79156],{"encoding":904}," klesá a v bodě ",[883,86774,86776],{"className":86775},[886],[888,86777,86778],{"xmlns":890},[892,86779,86780,86788],{},[895,86781,86782],{},[2884,86783,86784,86786],{},[898,86785,2888],{},[2111,86787,2238],{},[902,86789,2893],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,86792,86793,86794],{},"princip maximalizace ",[883,86795,86797],{"className":86796},[886],[888,86798,86799],{"xmlns":890},[892,86800,86801,86811],{},[895,86802,86803,86805],{},[898,86804,8243],{},[2884,86806,86807,86809],{},[898,86808,7929],{},[898,86810,2888],{},[902,86812,78231],{"encoding":904},": v bodě maxima ",[883,86815,86817],{"className":86816},[886],[888,86818,86819],{"xmlns":890},[892,86820,86821,86831],{},[895,86822,86823,86825],{},[898,86824,8243],{},[2884,86826,86827,86829],{},[898,86828,7929],{},[898,86830,2888],{},[902,86832,78231],{"encoding":904},[883,86834,86836],{"className":86835},[886],[888,86837,86838],{"xmlns":890},[892,86839,86840,86860],{},[895,86841,86842,86844,86850,86852,86854],{},[898,86843,1790],{},[2884,86845,86846,86848],{},[898,86847,7929],{},[898,86849,2888],{},[1711,86851,1836],{},[898,86853,8243],{},[2884,86855,86856,86858],{},[898,86857,7929],{},[898,86859,2888],{},[902,86861,78261],{"encoding":904},[724,86863,86864,86865,86868,86869,1700,86872,86901,86902,86919,86920,86923,86924,86953,86954,86956,86957,12082,86987,87009],{},"Ve ",[38,86866,86867],{},"2F modelu"," se obvykle používají ",[38,86870,86871],{},"Cobb-Douglasovy funkce",[883,86873,86875],{"className":86874},[886],[888,86876,86877],{"xmlns":890},[892,86878,86879,86899],{},[895,86880,86881,86883,86885,86887,86893],{},[898,86882,6796],{},[1711,86884,1836],{},[898,86886,8243],{},[1716,86888,86889,86891],{},[898,86890,2888],{},[898,86892,207],{},[1716,86894,86895,86897],{},[898,86896,13774],{},[898,86898,2223],{},[902,86900,78328],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,86903,86905],{"className":86904},[886],[888,86906,86907],{"xmlns":890},[892,86908,86909,86917],{},[895,86910,86911,86913,86915],{},[898,86912,207],{},[1711,86914,2095],{},[898,86916,2223],{},[902,86918,78422],{"encoding":904}," rozlišujeme ",[38,86921,86922],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,86925,86927],{"className":86926},[886],[888,86928,86929],{"xmlns":890},[892,86930,86931,86951],{},[895,86932,86933,86935,86941,86943,86945],{},[898,86934,1790],{},[2884,86936,86937,86939],{},[898,86938,7929],{},[898,86940,2888],{},[1711,86942,1726],{"separator":1725},[898,86944,1790],{},[2884,86946,86947,86949],{},[898,86948,7929],{},[898,86950,13774],{},[902,86952,78359],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,86955,13753],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,86958,86960],{"className":86959},[886],[888,86961,86962],{"xmlns":890},[892,86963,86964,86984],{},[895,86965,86966,86968,86974,86976,86978],{},[898,86967,1790],{},[2884,86969,86970,86972],{},[898,86971,7929],{},[898,86973,2888],{},[898,86975,8659],{"mathvariant":2287},[898,86977,1790],{},[2884,86979,86980,86982],{},[898,86981,7929],{},[898,86983,13774],{},[902,86985,86986],{"encoding":904},"MP_L\u002FMP_K",[38,86988,86989,86990,1735],{},"mezní míra technické substituce (",[883,86991,86993],{"className":86992},[886],[888,86994,86995],{"xmlns":890},[892,86996,86997,87007],{},[895,86998,86999,87001,87003,87005],{},[898,87000,1790],{},[898,87002,7985],{},[898,87004,1769],{},[898,87006,2362],{},[902,87008,14572],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,87011,53480],{"id":53479},[152,87013,87014,87017,87020,87023,87026,87029,87032,87035,87038,87041,87044],{},[123,87015,87016],{},"Jaké jsou faktory produkce?",[123,87018,87019],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,87021,87022],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,87024,87025],{},"Co udává mezní produkt práce?",[123,87027,87028],{},"Co musí respektovat průběh křivky produkce?",[123,87030,87031],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,87033,87034],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,87036,87037],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,87039,87040],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,87042,87043],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,87045,87046],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,87048,87050],{"id":87049},"úlohy-51517","Úlohy 5.1–5.17",[198,87052,44049],{"id":44048},[724,87054,87055,87058,87059,87081,87082,1343,87102,1343,87122,87142],{},[38,87056,87057],{},"5.1"," Je dána produkce ",[883,87060,87062],{"className":87061},[886],[888,87063,87064],{"xmlns":890},[892,87065,87066,87078],{},[895,87067,87068,87070,87072,87074],{},[898,87069,6796],{},[1711,87071,1836],{},[2111,87073,4712],{},[12097,87075,87076],{},[898,87077,2888],{},[902,87079,87080],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,87083,87085],{"className":87084},[886],[888,87086,87087],{"xmlns":890},[892,87088,87089,87099],{},[895,87090,87091,87093,87095,87097],{},[898,87092,6796],{},[1711,87094,1714],{"stretchy":1713},[2111,87096,2238],{},[1711,87098,1735],{"stretchy":1713},[902,87100,87101],{"encoding":904},"Q(1)",[883,87103,87105],{"className":87104},[886],[888,87106,87107],{"xmlns":890},[892,87108,87109,87119],{},[895,87110,87111,87113,87115,87117],{},[898,87112,6796],{},[1711,87114,1714],{"stretchy":1713},[2111,87116,6369],{},[1711,87118,1735],{"stretchy":1713},[902,87120,87121],{"encoding":904},"Q(4)",[883,87123,87125],{"className":87124},[886],[888,87126,87127],{"xmlns":890},[892,87128,87129,87139],{},[895,87130,87131,87133,87135,87137],{},[898,87132,6796],{},[1711,87134,1714],{"stretchy":1713},[2111,87136,7990],{},[1711,87138,1735],{"stretchy":1713},[902,87140,87141],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,87144,87145,87058,87148,87184,87185,87198,87199,87218,87219,87245,87246,6696,87259,87272],{},[38,87146,87147],{},"5.2",[883,87149,87151],{"className":87150},[886],[888,87152,87153],{"xmlns":890},[892,87154,87155,87181],{},[895,87156,87157,87159,87161,87163,87165,87171,87173,87175],{},[898,87158,6796],{},[1711,87160,1836],{},[1711,87162,2460],{},[2111,87164,4343],{},[1716,87166,87167,87169],{},[898,87168,2888],{},[2111,87170,3034],{},[1711,87172,2095],{},[2111,87174,7990],{},[1716,87176,87177,87179],{},[898,87178,2888],{},[2111,87180,2963],{},[902,87182,87183],{"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 ",[883,87186,87188],{"className":87187},[886],[888,87189,87190],{"xmlns":890},[892,87191,87192,87196],{},[895,87193,87194],{},[898,87195,2888],{},[902,87197,2888],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,87200,87202],{"className":87201},[886],[888,87203,87204],{"xmlns":890},[892,87205,87206,87216],{},[895,87207,87208,87210],{},[898,87209,1790],{},[2884,87211,87212,87214],{},[898,87213,7929],{},[898,87215,2888],{},[902,87217,14018],{"encoding":904},". (f) Vypočtěte ",[883,87220,87222],{"className":87221},[886],[888,87223,87224],{"xmlns":890},[892,87225,87226,87242],{},[895,87227,87228,87230,87236,87238,87240],{},[898,87229,1790],{},[2884,87231,87232,87234],{},[898,87233,7929],{},[898,87235,2888],{},[1711,87237,1714],{"stretchy":1713},[2111,87239,4712],{},[1711,87241,1735],{"stretchy":1713},[902,87243,87244],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,87247,87249],{"className":87248},[886],[888,87250,87251],{"xmlns":890},[892,87252,87253,87257],{},[895,87254,87255],{},[2111,87256,4712],{},[902,87258,4712],{"encoding":904},[883,87260,87262],{"className":87261},[886],[888,87263,87264],{"xmlns":890},[892,87265,87266,87270],{},[895,87267,87268],{},[2111,87269,45885],{},[902,87271,45885],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,87274,87275,87278,87279,87301,87302,87330,87331,87362,87363,2186],{},[38,87276,87277],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,87280,87282],{"className":87281},[886],[888,87283,87284],{"xmlns":890},[892,87285,87286,87298],{},[895,87287,87288,87290,87292,87294],{},[898,87289,6796],{},[1711,87291,1836],{},[2111,87293,4807],{},[12097,87295,87296],{},[898,87297,2888],{},[902,87299,87300],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,87303,87305],{"className":87304},[886],[888,87306,87307],{"xmlns":890},[892,87308,87309,87327],{},[895,87310,87311,87313,87315,87317,87321,87323,87325],{},[898,87312,6796],{},[1711,87314,1836],{},[2111,87316,33679],{},[12097,87318,87319],{},[898,87320,2888],{},[1711,87322,2460],{},[2111,87324,6369],{},[898,87326,2888],{},[902,87328,87329],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,87332,87334],{"className":87333},[886],[888,87335,87336],{"xmlns":890},[892,87337,87338,87359],{},[895,87339,87340,87342,87344,87346,87348,87350,87353],{},[898,87341,6796],{},[1711,87343,1836],{},[2111,87345,7120],{},[898,87347,2888],{},[1711,87349,2460],{},[2111,87351,87352],{},"0,01",[1716,87354,87355,87357],{},[898,87356,2888],{},[2111,87358,2963],{},[902,87360,87361],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,87364,87366],{"className":87365},[886],[888,87367,87368],{"xmlns":890},[892,87369,87370,87396],{},[895,87371,87372,87374,87376,87378,87380,87386,87388,87390],{},[898,87373,6796],{},[1711,87375,1836],{},[1711,87377,2460],{},[2111,87379,71809],{},[1716,87381,87382,87384],{},[898,87383,2888],{},[2111,87385,3034],{},[1711,87387,2095],{},[2111,87389,7990],{},[1716,87391,87392,87394],{},[898,87393,2888],{},[2111,87395,2963],{},[902,87397,87398],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,87400,87401,87404,87405,6635,87424,75796,87441,2186],{},[38,87402,87403],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,87406,87408],{"className":87407},[886],[888,87409,87410],{"xmlns":890},[892,87411,87412,87422],{},[895,87413,87414,87416],{},[898,87415,8243],{},[2884,87417,87418,87420],{},[898,87419,7929],{},[898,87421,2888],{},[902,87423,78231],{"encoding":904},[883,87425,87427],{"className":87426},[886],[888,87428,87429],{"xmlns":890},[892,87430,87431,87439],{},[895,87432,87433],{},[2884,87434,87435,87437],{},[898,87436,2888],{},[2111,87438,2113],{},[902,87440,79156],{"encoding":904},[883,87442,87444],{"className":87443},[886],[888,87445,87446],{"xmlns":890},[892,87447,87448,87488],{},[895,87449,87450,87452,87458,87460,87466,87468,87470,87472,87478,87480,87486],{},[898,87451,8243],{},[2884,87453,87454,87456],{},[898,87455,7929],{},[898,87457,2888],{},[1711,87459,1714],{"stretchy":1713},[2884,87461,87462,87464],{},[898,87463,2888],{},[2111,87465,2113],{},[1711,87467,1735],{"stretchy":1713},[1711,87469,1836],{},[898,87471,1790],{},[2884,87473,87474,87476],{},[898,87475,7929],{},[898,87477,2888],{},[1711,87479,1714],{"stretchy":1713},[2884,87481,87482,87484],{},[898,87483,2888],{},[2111,87485,2113],{},[1711,87487,1735],{"stretchy":1713},[902,87489,87490],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,87492,87493,87058,87496,25192,87532,87545,87546,87565],{},[38,87494,87495],{},"5.5",[883,87497,87499],{"className":87498},[886],[888,87500,87501],{"xmlns":890},[892,87502,87503,87529],{},[895,87504,87505,87507,87509,87511,87513,87519,87521,87523],{},[898,87506,6796],{},[1711,87508,1836],{},[1711,87510,2460],{},[2111,87512,4491],{},[1716,87514,87515,87517],{},[898,87516,2888],{},[2111,87518,3034],{},[1711,87520,2095],{},[2111,87522,7505],{},[1716,87524,87525,87527],{},[898,87526,2888],{},[2111,87528,2963],{},[902,87530,87531],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,87533,87535],{"className":87534},[886],[888,87536,87537],{"xmlns":890},[892,87538,87539,87543],{},[895,87540,87541],{},[898,87542,2888],{},[902,87544,2888],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,87547,87549],{"className":87548},[886],[888,87550,87551],{"xmlns":890},[892,87552,87553,87563],{},[895,87554,87555,87557],{},[898,87556,8243],{},[2884,87558,87559,87561],{},[898,87560,7929],{},[898,87562,2888],{},[902,87564,78231],{"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.",[198,87567,87569],{"id":87568},"dvoufaktorový-model","Dvoufaktorový model",[724,87571,87572,87575,87576,87301,87602,87330,87644,2186],{},[38,87573,87574],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,87577,87579],{"className":87578},[886],[888,87580,87581],{"xmlns":890},[892,87582,87583,87599],{},[895,87584,87585,87587,87589,87591,87593],{},[898,87586,6796],{},[1711,87588,1836],{},[2111,87590,27799],{},[898,87592,2888],{},[1716,87594,87595,87597],{},[898,87596,13774],{},[2111,87598,2963],{},[902,87600,87601],{"encoding":904},"Q = 7 L K^{2}",[883,87603,87605],{"className":87604},[886],[888,87606,87607],{"xmlns":890},[892,87608,87609,87641],{},[895,87610,87611,87613,87615,87617,87629],{},[898,87612,6796],{},[1711,87614,1836],{},[2111,87616,7120],{},[1716,87618,87619,87621],{},[898,87620,2888],{},[895,87622,87623,87625,87627],{},[2111,87624,2963],{},[898,87626,8659],{"mathvariant":2287},[2111,87628,3034],{},[1716,87630,87631,87633],{},[898,87632,13774],{},[895,87634,87635,87637,87639],{},[2111,87636,2238],{},[898,87638,8659],{"mathvariant":2287},[2111,87640,3034],{},[902,87642,87643],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,87645,87647],{"className":87646},[886],[888,87648,87649],{"xmlns":890},[892,87650,87651,87683],{},[895,87652,87653,87655,87657,87659,87671],{},[898,87654,6796],{},[1711,87656,1836],{},[2111,87658,7703],{},[1716,87660,87661,87663],{},[898,87662,2888],{},[895,87664,87665,87667,87669],{},[2111,87666,3034],{},[898,87668,8659],{"mathvariant":2287},[2111,87670,4798],{},[1716,87672,87673,87675],{},[898,87674,13774],{},[895,87676,87677,87679,87681],{},[2111,87678,2963],{},[898,87680,8659],{"mathvariant":2287},[2111,87682,4798],{},[902,87684,87685],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,87687,87688,87058,87691,87733,87734,1343,87752,87771,87772,87789],{},[38,87689,87690],{},"5.7",[883,87692,87694],{"className":87693},[886],[888,87695,87696],{"xmlns":890},[892,87697,87698,87730],{},[895,87699,87700,87702,87704,87706,87718],{},[898,87701,6796],{},[1711,87703,1836],{},[2111,87705,4712],{},[1716,87707,87708,87710],{},[898,87709,2888],{},[895,87711,87712,87714,87716],{},[2111,87713,2238],{},[898,87715,8659],{"mathvariant":2287},[2111,87717,2963],{},[1716,87719,87720,87722],{},[898,87721,13774],{},[895,87723,87724,87726,87728],{},[2111,87725,2238],{},[898,87727,8659],{"mathvariant":2287},[2111,87729,2963],{},[902,87731,87732],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,87735,87737],{"className":87736},[886],[888,87738,87739],{"xmlns":890},[892,87740,87741,87749],{},[895,87742,87743,87745,87747],{},[898,87744,2888],{},[1711,87746,1836],{},[2111,87748,23740],{},[902,87750,87751],{"encoding":904},"L = 400",[883,87753,87755],{"className":87754},[886],[888,87756,87757],{"xmlns":890},[892,87758,87759,87768],{},[895,87760,87761,87763,87765],{},[898,87762,13774],{},[1711,87764,1836],{},[2111,87766,87767],{},"17576",[902,87769,87770],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,87773,87775],{"className":87774},[886],[888,87776,87777],{"xmlns":890},[892,87778,87779,87787],{},[895,87780,87781,87783,87785],{},[898,87782,2888],{},[1711,87784,1726],{"separator":1725},[898,87786,13774],{},[902,87788,82583],{"encoding":904}," zdvojnásobí.",[724,87791,87792,87795,87796,87733,87827,1343,87845,73182,87863,87893,87894,87924,87925,6696,87938,87952,87953,6696,87966,87979],{},[38,87793,87794],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,87797,87799],{"className":87798},[886],[888,87800,87801],{"xmlns":890},[892,87802,87803,87824],{},[895,87804,87805,87807,87809,87812,87818],{},[898,87806,6796],{},[1711,87808,1836],{},[2111,87810,87811],{},"1,01",[1716,87813,87814,87816],{},[898,87815,2888],{},[2111,87817,27328],{},[1716,87819,87820,87822],{},[898,87821,13774],{},[2111,87823,27387],{},[902,87825,87826],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,87828,87830],{"className":87829},[886],[888,87831,87832],{"xmlns":890},[892,87833,87834,87842],{},[895,87835,87836,87838,87840],{},[898,87837,2888],{},[1711,87839,1836],{},[2111,87841,34341],{},[902,87843,87844],{"encoding":904},"L = 250",[883,87846,87848],{"className":87847},[886],[888,87849,87850],{"xmlns":890},[892,87851,87852,87860],{},[895,87853,87854,87856,87858],{},[898,87855,13774],{},[1711,87857,1836],{},[2111,87859,4313],{},[902,87861,87862],{"encoding":904},"K = 1000",[883,87864,87866],{"className":87865},[886],[888,87867,87868],{"xmlns":890},[892,87869,87870,87890],{},[895,87871,87872,87874,87880,87882,87884,87886,87888],{},[898,87873,1790],{},[2884,87875,87876,87878],{},[898,87877,7929],{},[898,87879,2888],{},[1711,87881,1714],{"stretchy":1713},[2111,87883,34341],{},[1711,87885,1726],{"separator":1725},[2111,87887,4313],{},[1711,87889,1735],{"stretchy":1713},[902,87891,87892],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,87895,87897],{"className":87896},[886],[888,87898,87899],{"xmlns":890},[892,87900,87901,87921],{},[895,87902,87903,87905,87911,87913,87915,87917,87919],{},[898,87904,1790],{},[2884,87906,87907,87909],{},[898,87908,7929],{},[898,87910,13774],{},[1711,87912,1714],{"stretchy":1713},[2111,87914,34341],{},[1711,87916,1726],{"separator":1725},[2111,87918,4313],{},[1711,87920,1735],{"stretchy":1713},[902,87922,87923],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,87926,87928],{"className":87927},[886],[888,87929,87930],{"xmlns":890},[892,87931,87932,87936],{},[895,87933,87934],{},[898,87935,2888],{},[902,87937,2888],{"encoding":904},[883,87939,87941],{"className":87940},[886],[888,87942,87943],{"xmlns":890},[892,87944,87945,87950],{},[895,87946,87947],{},[2111,87948,87949],{},"260",[902,87951,87949],{"encoding":904}," a současném poklesu ",[883,87954,87956],{"className":87955},[886],[888,87957,87958],{"xmlns":890},[892,87959,87960,87964],{},[895,87961,87962],{},[898,87963,13774],{},[902,87965,13774],{"encoding":904},[883,87967,87969],{"className":87968},[886],[888,87970,87971],{"xmlns":890},[892,87972,87973,87977],{},[895,87974,87975],{},[2111,87976,4888],{},[902,87978,4888],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,87981,87982,87985,87986,2186],{},[38,87983,87984],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,87987,87989],{"className":87988},[886],[888,87990,87991],{"xmlns":890},[892,87992,87993,88013],{},[895,87994,87995,87997,87999,88001,88007],{},[898,87996,6796],{},[1711,87998,1836],{},[2111,88000,4712],{},[1716,88002,88003,88005],{},[898,88004,2888],{},[2111,88006,71809],{},[1716,88008,88009,88011],{},[898,88010,13774],{},[2111,88012,8993],{},[902,88014,88015],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,88017,88018,88021,88022,84179,88045,14367,88058,1648,88108,1797],{},[38,88019,88020],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,88023,88025],{"className":88024},[886],[888,88026,88027],{"xmlns":890},[892,88028,88029,88043],{},[895,88030,88031,88033,88035,88037,88039,88041],{},[898,88032,6796],{},[1711,88034,1714],{"stretchy":1713},[898,88036,2888],{},[1711,88038,1726],{"separator":1725},[898,88040,13774],{},[1711,88042,1735],{"stretchy":1713},[902,88044,13971],{"encoding":904},[883,88046,88048],{"className":88047},[886],[888,88049,88050],{"xmlns":890},[892,88051,88052,88056],{},[895,88053,88054],{},[898,88055,40458],{},[902,88057,40458],{"encoding":904},[883,88059,88061],{"className":88060},[886],[888,88062,88063],{"xmlns":890},[892,88064,88065,88105],{},[895,88066,88067,88069,88077,88079,88081,88089,88091,88093,88095,88097,88099,88101,88103],{},[898,88068,2888],{},[13142,88070,88071,88073,88075],{},[898,88072,6796],{},[898,88074,2888],{},[1711,88076,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,88078,2095],{},[898,88080,13774],{},[13142,88082,88083,88085,88087],{},[898,88084,6796],{},[898,88086,13774],{},[1711,88088,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,88090,1836],{},[898,88092,40458],{},[898,88094,6796],{},[1711,88096,1714],{"stretchy":1713},[898,88098,2888],{},[1711,88100,1726],{"separator":1725},[898,88102,13774],{},[1711,88104,1735],{"stretchy":1713},[902,88106,88107],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,88109,84154],{},[724,88111,88112,88115],{},[38,88113,88114],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,88117,88118,87058,88121,88161,88162,1343,88184,1343,88206,88228],{},[38,88119,88120],{},"5.12",[883,88122,88124],{"className":88123},[886],[888,88125,88126],{"xmlns":890},[892,88127,88128,88158],{},[895,88129,88130,88132,88134,88146],{},[898,88131,6796],{},[1711,88133,1836],{},[1716,88135,88136,88138],{},[898,88137,2888],{},[895,88139,88140,88142,88144],{},[2111,88141,2238],{},[898,88143,8659],{"mathvariant":2287},[2111,88145,3034],{},[1716,88147,88148,88150],{},[898,88149,13774],{},[895,88151,88152,88154,88156],{},[2111,88153,2238],{},[898,88155,8659],{"mathvariant":2287},[2111,88157,6369],{},[902,88159,88160],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,88163,88165],{"className":88164},[886],[888,88166,88167],{"xmlns":890},[892,88168,88169,88181],{},[895,88170,88171,88177,88179],{},[2884,88172,88173,88175],{},[898,88174,84395],{},[2111,88176,2113],{},[1711,88178,1836],{},[2111,88180,2238],{},[902,88182,88183],{"encoding":904},"q_0 = 1",[883,88185,88187],{"className":88186},[886],[888,88188,88189],{"xmlns":890},[892,88190,88191,88203],{},[895,88192,88193,88199,88201],{},[2884,88194,88195,88197],{},[898,88196,84395],{},[2111,88198,2238],{},[1711,88200,1836],{},[2111,88202,2963],{},[902,88204,88205],{"encoding":904},"q_1 = 2",[883,88207,88209],{"className":88208},[886],[888,88210,88211],{"xmlns":890},[892,88212,88213,88225],{},[895,88214,88215,88221,88223],{},[2884,88216,88217,88219],{},[898,88218,84395],{},[2111,88220,2963],{},[1711,88222,1836],{},[2111,88224,3034],{},[902,88226,88227],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,88230,88231,87058,88234,88274,88275,1343,88303,1343,88331,1343,88359,1343,88388,1343,88417,1343,88446,1343,88475,1343,88504,2186],{},[38,88232,88233],{},"5.13",[883,88235,88237],{"className":88236},[886],[888,88238,88239],{"xmlns":890},[892,88240,88241,88271],{},[895,88242,88243,88245,88247,88259],{},[898,88244,6796],{},[1711,88246,1836],{},[1716,88248,88249,88251],{},[898,88250,2888],{},[895,88252,88253,88255,88257],{},[2111,88254,2238],{},[898,88256,8659],{"mathvariant":2287},[2111,88258,3034],{},[1716,88260,88261,88263],{},[898,88262,13774],{},[895,88264,88265,88267,88269],{},[2111,88266,2238],{},[898,88268,8659],{"mathvariant":2287},[2111,88270,2963],{},[902,88272,88273],{"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): ",[883,88276,88278],{"className":88277},[886],[888,88279,88280],{"xmlns":890},[892,88281,88282,88300],{},[895,88283,88284,88290,88292,88294,88296,88298],{},[2884,88285,88286,88288],{},[898,88287,8243],{},[2111,88289,2238],{},[1711,88291,5144],{"stretchy":1713},[2111,88293,2238],{},[1711,88295,12405],{"separator":1725},[2111,88297,2238],{},[1711,88299,5163],{"stretchy":1713},[902,88301,88302],{"encoding":904},"A_1[1; 1]",[883,88304,88306],{"className":88305},[886],[888,88307,88308],{"xmlns":890},[892,88309,88310,88328],{},[895,88311,88312,88318,88320,88322,88324,88326],{},[2884,88313,88314,88316],{},[898,88315,8243],{},[2111,88317,2963],{},[1711,88319,5144],{"stretchy":1713},[2111,88321,2238],{},[1711,88323,12405],{"separator":1725},[2111,88325,9568],{},[1711,88327,5163],{"stretchy":1713},[902,88329,88330],{"encoding":904},"A_2[1; 8]",[883,88332,88334],{"className":88333},[886],[888,88335,88336],{"xmlns":890},[892,88337,88338,88356],{},[895,88339,88340,88346,88348,88350,88352,88354],{},[2884,88341,88342,88344],{},[898,88343,8243],{},[2111,88345,3034],{},[1711,88347,5144],{"stretchy":1713},[2111,88349,2238],{},[1711,88351,12405],{"separator":1725},[2111,88353,70195],{},[1711,88355,5163],{"stretchy":1713},[902,88357,88358],{"encoding":904},"A_3[1; 27]",[883,88360,88362],{"className":88361},[886],[888,88363,88364],{"xmlns":890},[892,88365,88366,88385],{},[895,88367,88368,88374,88376,88378,88380,88383],{},[2884,88369,88370,88372],{},[898,88371,8243],{},[2111,88373,6369],{},[1711,88375,5144],{"stretchy":1713},[2111,88377,2963],{},[1711,88379,12405],{"separator":1725},[2111,88381,88382],{},"0,353",[1711,88384,5163],{"stretchy":1713},[902,88386,88387],{"encoding":904},"A_4[2; 0{,}353]",[883,88389,88391],{"className":88390},[886],[888,88392,88393],{"xmlns":890},[892,88394,88395,88414],{},[895,88396,88397,88403,88405,88407,88409,88412],{},[2884,88398,88399,88401],{},[898,88400,8243],{},[2111,88402,4798],{},[1711,88404,5144],{"stretchy":1713},[2111,88406,2963],{},[1711,88408,12405],{"separator":1725},[2111,88410,88411],{},"2,828",[1711,88413,5163],{"stretchy":1713},[902,88415,88416],{"encoding":904},"A_5[2; 2{,}828]",[883,88418,88420],{"className":88419},[886],[888,88421,88422],{"xmlns":890},[892,88423,88424,88443],{},[895,88425,88426,88432,88434,88436,88438,88441],{},[2884,88427,88428,88430],{},[898,88429,8243],{},[2111,88431,6262],{},[1711,88433,5144],{"stretchy":1713},[2111,88435,2963],{},[1711,88437,12405],{"separator":1725},[2111,88439,88440],{},"9,545",[1711,88442,5163],{"stretchy":1713},[902,88444,88445],{"encoding":904},"A_6[2; 9{,}545]",[883,88447,88449],{"className":88448},[886],[888,88450,88451],{"xmlns":890},[892,88452,88453,88472],{},[895,88454,88455,88461,88463,88465,88467,88470],{},[2884,88456,88457,88459],{},[898,88458,8243],{},[2111,88460,27799],{},[1711,88462,5144],{"stretchy":1713},[2111,88464,68157],{},[1711,88466,12405],{"separator":1725},[2111,88468,88469],{},"0,544",[1711,88471,5163],{"stretchy":1713},[902,88473,88474],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,88476,88478],{"className":88477},[886],[888,88479,88480],{"xmlns":890},[892,88481,88482,88501],{},[895,88483,88484,88490,88492,88494,88496,88499],{},[2884,88485,88486,88488],{},[898,88487,8243],{},[2111,88489,9568],{},[1711,88491,5144],{"stretchy":1713},[2111,88493,68157],{},[1711,88495,12405],{"separator":1725},[2111,88497,88498],{},"14,696",[1711,88500,5163],{"stretchy":1713},[902,88502,88503],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,88505,88507],{"className":88506},[886],[888,88508,88509],{"xmlns":890},[892,88510,88511,88529],{},[895,88512,88513,88519,88521,88523,88525,88527],{},[2884,88514,88515,88517],{},[898,88516,8243],{},[2111,88518,7990],{},[1711,88520,5144],{"stretchy":1713},[2111,88522,2963],{},[1711,88524,12405],{"separator":1725},[2111,88526,4798],{},[1711,88528,5163],{"stretchy":1713},[902,88530,88531],{"encoding":904},"A_9[2; 5]",[724,88533,88534,88537],{},[38,88535,88536],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,88539,88540,88543,88544,88574,88575,88588,88589,88602,88603,72915,88622,88641,88642,2186],{},[38,88541,88542],{},"5.15"," Produkce firmy je dána vztahem ",[883,88545,88547],{"className":88546},[886],[888,88548,88549],{"xmlns":890},[892,88550,88551,88571],{},[895,88552,88553,88555,88557,88559,88565],{},[898,88554,6796],{},[1711,88556,1836],{},[2111,88558,2963],{},[1716,88560,88561,88563],{},[898,88562,2888],{},[2111,88564,8993],{},[1716,88566,88567,88569],{},[898,88568,13774],{},[2111,88570,27387],{},[902,88572,88573],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,88576,88578],{"className":88577},[886],[888,88579,88580],{"xmlns":890},[892,88581,88582,88586],{},[895,88583,88584],{},[2111,88585,4282],{},[902,88587,4282],{"encoding":904}," pracovníků a disponuje-li ",[883,88590,88592],{"className":88591},[886],[888,88593,88594],{"xmlns":890},[892,88595,88596,88600],{},[895,88597,88598],{},[2111,88599,68033],{},[902,88601,68033],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,88604,88606],{"className":88605},[886],[888,88607,88608],{"xmlns":890},[892,88609,88610,88620],{},[895,88611,88612,88614,88616,88618],{},[898,88613,1790],{},[898,88615,7985],{},[898,88617,1769],{},[898,88619,2362],{},[902,88621,14572],{"encoding":904},[883,88623,88625],{"className":88624},[886],[888,88626,88627],{"xmlns":890},[892,88628,88629,88639],{},[895,88630,88631,88633,88635,88637],{},[898,88632,1790],{},[898,88634,7985],{},[898,88636,1769],{},[898,88638,2362],{},[902,88640,14572],{"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 ",[883,88643,88645],{"className":88644},[886],[888,88646,88647],{"xmlns":890},[892,88648,88649,88654],{},[895,88650,88651],{},[2111,88652,88653],{},"95",[902,88655,88653],{"encoding":904},[724,88657,88658,87058,88661,74589,88693,88712,88713,88726,88727,88740,88741,88754],{},[38,88659,88660],{},"5.16",[883,88662,88664],{"className":88663},[886],[888,88665,88666],{"xmlns":890},[892,88667,88668,88690],{},[895,88669,88670,88672,88674,88680,88682,88684],{},[898,88671,6796],{},[1711,88673,1836],{},[1716,88675,88676,88678],{},[898,88677,13774],{},[2111,88679,2963],{},[1711,88681,2095],{},[2111,88683,2963],{},[1716,88685,88686,88688],{},[898,88687,2888],{},[2111,88689,2963],{},[902,88691,88692],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,88694,88696],{"className":88695},[886],[888,88697,88698],{"xmlns":890},[892,88699,88700,88710],{},[895,88701,88702,88704,88706,88708],{},[898,88703,1790],{},[898,88705,7985],{},[898,88707,1769],{},[898,88709,2362],{},[902,88711,14572],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,88714,88716],{"className":88715},[886],[888,88717,88718],{"xmlns":890},[892,88719,88720,88724],{},[895,88721,88722],{},[2111,88723,7120],{},[902,88725,7120],{"encoding":904}," pracovníky a ",[883,88728,88730],{"className":88729},[886],[888,88731,88732],{"xmlns":890},[892,88733,88734,88738],{},[895,88735,88736],{},[2111,88737,81215],{},[902,88739,81215],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,88742,88744],{"className":88743},[886],[888,88745,88746],{"xmlns":890},[892,88747,88748,88752],{},[895,88749,88750],{},[2111,88751,50301],{},[902,88753,50301],{"encoding":904}," jednotek.",[724,88756,88757,88760,88761,14367,88791,2186],{},[38,88758,88759],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,88762,88764],{"className":88763},[886],[888,88765,88766],{"xmlns":890},[892,88767,88768,88788],{},[895,88769,88770,88772,88774,88776,88782],{},[898,88771,6796],{},[1711,88773,1836],{},[898,88775,8243],{},[1716,88777,88778,88780],{},[898,88779,2888],{},[898,88781,207],{},[1716,88783,88784,88786],{},[898,88785,13774],{},[898,88787,2223],{},[902,88789,88790],{"encoding":904},"Q = A L^{a} K^{b}",[883,88792,88794],{"className":88793},[886],[888,88795,88796],{"xmlns":890},[892,88797,88798,88828],{},[895,88799,88800,88802,88804,88806,88808,88810,88818,88820],{},[898,88801,1790],{},[898,88803,7985],{},[898,88805,1769],{},[898,88807,2362],{},[1711,88809,1836],{},[2509,88811,88812],{"scriptlevel":2113,"displaystyle":1713},[2525,88813,88814,88816],{},[898,88815,207],{},[898,88817,2223],{},[1711,88819,4795],{},[2509,88821,88822],{"scriptlevel":2113,"displaystyle":1713},[2525,88823,88824,88826],{},[898,88825,13774],{},[898,88827,2888],{},[902,88829,88830],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,88832,5422],{"id":5421},[120,88834,88835,88868,88895,88904,88954,88985,89038,89061,89116,89189,89267,89310,89342,89375,89416,89488,89549,89615,89632,89705,89771,89823,89879,89913,89956],{},[123,88836,88837,88840,88841,40494,88854,88867],{},[38,88838,88839],{},"Faktory (vstupy) produkce:"," práce ",[883,88842,88844],{"className":88843},[886],[888,88845,88846],{"xmlns":890},[892,88847,88848,88852],{},[895,88849,88850],{},[898,88851,2888],{},[902,88853,2888],{"encoding":904},[883,88855,88857],{"className":88856},[886],[888,88858,88859],{"xmlns":890},[892,88860,88861,88865],{},[895,88862,88863],{},[898,88864,13774],{},[902,88866,13774],{"encoding":904},", půda.",[123,88869,88870,5204,88872,2186],{},[38,88871,44049],{},[883,88873,88875],{"className":88874},[886],[888,88876,88877],{"xmlns":890},[892,88878,88879,88893],{},[895,88880,88881,88883,88885,88887,88889,88891],{},[898,88882,6796],{},[1711,88884,1836],{},[898,88886,6796],{},[1711,88888,1714],{"stretchy":1713},[898,88890,2888],{},[1711,88892,1735],{"stretchy":1713},[902,88894,78142],{"encoding":904},[123,88896,88897,1648,88899,1772,88902,2186],{},[38,88898,859],{},[614,88900,88901],{},"production function",[38,88903,78645],{},[123,88905,88906,1700,88908,2186],{},[38,88907,78691],{},[883,88909,88911],{"className":88910},[886],[888,88912,88913],{"xmlns":890},[892,88914,88915,88951],{},[895,88916,88917,88919,88925,88927,88929,88931,88933,88935,88937,88939,88945,88947,88949],{},[898,88918,1790],{},[2884,88920,88921,88923],{},[898,88922,7929],{},[898,88924,2888],{},[1711,88926,1836],{},[898,88928,2098],{},[898,88930,6796],{},[898,88932,8659],{"mathvariant":2287},[898,88934,2098],{},[898,88936,2888],{},[1711,88938,1836],{},[1716,88940,88941,88943],{},[898,88942,6796],{},[1711,88944,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,88946,1714],{"stretchy":1713},[898,88948,2888],{},[1711,88950,1735],{"stretchy":1713},[902,88952,88953],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,88955,88956,1700,88958,2186],{},[38,88957,79626],{},[883,88959,88961],{"className":88960},[886],[888,88962,88963],{"xmlns":890},[892,88964,88965,88983],{},[895,88966,88967,88969,88975,88977,88979,88981],{},[898,88968,8243],{},[2884,88970,88971,88973],{},[898,88972,7929],{},[898,88974,2888],{},[1711,88976,1836],{},[898,88978,6796],{},[898,88980,8659],{"mathvariant":2287},[898,88982,2888],{},[902,88984,78210],{"encoding":904},[123,88986,88987,88989,88990,14367,89007,2186],{},[38,88988,79113],{}," — od určitého ",[883,88991,88993],{"className":88992},[886],[888,88994,88995],{"xmlns":890},[892,88996,88997,89005],{},[895,88998,88999],{},[2884,89000,89001,89003],{},[898,89002,2888],{},[2111,89004,2113],{},[902,89006,79156],{"encoding":904},[883,89008,89010],{"className":89009},[886],[888,89011,89012],{"xmlns":890},[892,89013,89014,89036],{},[895,89015,89016,89026,89028,89030,89032,89034],{},[1716,89017,89018,89020],{},[898,89019,6796],{},[895,89021,89022,89024],{},[1711,89023,5225],{"mathvariant":2287},[1711,89025,5225],{"mathvariant":2287},[1711,89027,1714],{"stretchy":1713},[898,89029,2888],{},[1711,89031,1735],{"stretchy":1713},[1711,89033,2109],{},[2111,89035,2113],{},[902,89037,79302],{"encoding":904},[123,89039,89040,1700,89043,89060],{},[38,89041,89042],{},"Inflexní bod",[883,89044,89046],{"className":89045},[886],[888,89047,89048],{"xmlns":890},[892,89049,89050,89058],{},[895,89051,89052],{},[2884,89053,89054,89056],{},[898,89055,2888],{},[2111,89057,2113],{},[902,89059,79156],{"encoding":904}," — přechod z konvexity do konkavity.",[123,89062,89063,1700,89066,5204,89083,2186],{},[38,89064,89065],{},"Bod maxima produkce",[883,89067,89069],{"className":89068},[886],[888,89070,89071],{"xmlns":890},[892,89072,89073,89081],{},[895,89074,89075],{},[2884,89076,89077,89079],{},[898,89078,2888],{},[2111,89080,2238],{},[902,89082,2893],{"encoding":904},[883,89084,89086],{"className":89085},[886],[888,89087,89088],{"xmlns":890},[892,89089,89090,89114],{},[895,89091,89092,89094,89100,89102,89108,89110,89112],{},[898,89093,1790],{},[2884,89095,89096,89098],{},[898,89097,7929],{},[898,89099,2888],{},[1711,89101,1714],{"stretchy":1713},[2884,89103,89104,89106],{},[898,89105,2888],{},[2111,89107,2238],{},[1711,89109,1735],{"stretchy":1713},[1711,89111,1836],{},[2111,89113,2113],{},[902,89115,79375],{"encoding":904},[123,89117,89118,89140,89141,14367,89160,2186],{},[38,89119,89120,89121],{},"Princip maximalizace ",[883,89122,89124],{"className":89123},[886],[888,89125,89126],{"xmlns":890},[892,89127,89128,89138],{},[895,89129,89130,89132],{},[898,89131,8243],{},[2884,89133,89134,89136],{},[898,89135,7929],{},[898,89137,2888],{},[902,89139,78231],{"encoding":904}," — v bodě maxima ",[883,89142,89144],{"className":89143},[886],[888,89145,89146],{"xmlns":890},[892,89147,89148,89158],{},[895,89149,89150,89152],{},[898,89151,8243],{},[2884,89153,89154,89156],{},[898,89155,7929],{},[898,89157,2888],{},[902,89159,78231],{"encoding":904},[883,89161,89163],{"className":89162},[886],[888,89164,89165],{"xmlns":890},[892,89166,89167,89187],{},[895,89168,89169,89171,89177,89179,89181],{},[898,89170,1790],{},[2884,89172,89173,89175],{},[898,89174,7929],{},[898,89176,2888],{},[1711,89178,1836],{},[898,89180,8243],{},[2884,89182,89183,89185],{},[898,89184,7929],{},[898,89186,2888],{},[902,89188,78261],{"encoding":904},[123,89190,89191,1700,89194,1343,89233,1343,89250,2186],{},[38,89192,89193],{},"Polynomiální produkční funkce",[883,89195,89197],{"className":89196},[886],[888,89198,89199],{"xmlns":890},[892,89200,89201,89231],{},[895,89202,89203,89205,89207,89209,89211,89213,89215,89221,89223,89225],{},[898,89204,6796],{},[1711,89206,1714],{"stretchy":1713},[898,89208,2888],{},[1711,89210,1735],{"stretchy":1713},[1711,89212,1836],{},[898,89214,207],{},[1716,89216,89217,89219],{},[898,89218,2888],{},[2111,89220,3034],{},[1711,89222,2095],{},[898,89224,2223],{},[1716,89226,89227,89229],{},[898,89228,2888],{},[2111,89230,2963],{},[902,89232,79493],{"encoding":904},[883,89234,89236],{"className":89235},[886],[888,89237,89238],{"xmlns":890},[892,89239,89240,89248],{},[895,89241,89242,89244,89246],{},[898,89243,207],{},[1711,89245,2109],{},[2111,89247,2113],{},[902,89249,46683],{"encoding":904},[883,89251,89253],{"className":89252},[886],[888,89254,89255],{"xmlns":890},[892,89256,89257,89265],{},[895,89258,89259,89261,89263],{},[898,89260,2223],{},[1711,89262,2123],{},[2111,89264,2113],{},[902,89266,22412],{"encoding":904},[123,89268,89269,1700,89272,2186],{},[38,89270,89271],{},"Diferenciál produkce",[883,89273,89275],{"className":89274},[886],[888,89276,89277],{"xmlns":890},[892,89278,89279,89307],{},[895,89280,89281,89283,89285,89287,89289,89291,89293,89295,89301,89303,89305],{},[898,89282,6892],{"mathvariant":2287},[898,89284,6796],{},[1711,89286,6740],{},[898,89288,2098],{},[898,89290,6796],{},[1711,89292,1836],{},[898,89294,1790],{},[2884,89296,89297,89299],{},[898,89298,7929],{},[898,89300,2888],{},[1942,89302,2519],{},[898,89304,2098],{},[898,89306,2888],{},[902,89308,89309],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,89311,89312,5204,89314,2186],{},[38,89313,87569],{},[883,89315,89317],{"className":89316},[886],[888,89318,89319],{"xmlns":890},[892,89320,89321,89339],{},[895,89322,89323,89325,89327,89329,89331,89333,89335,89337],{},[898,89324,6796],{},[1711,89326,1836],{},[898,89328,6796],{},[1711,89330,1714],{"stretchy":1713},[898,89332,2888],{},[1711,89334,1726],{"separator":1725},[898,89336,13774],{},[1711,89338,1735],{"stretchy":1713},[902,89340,89341],{"encoding":904},"Q = Q(L, K)",[123,89343,89344,5204,89346,2186],{},[38,89345,81663],{},[883,89347,89349],{"className":89348},[886],[888,89350,89351],{"xmlns":890},[892,89352,89353,89373],{},[895,89354,89355,89357,89359,89361,89367],{},[898,89356,6796],{},[1711,89358,1836],{},[898,89360,8243],{},[1716,89362,89363,89365],{},[898,89364,2888],{},[898,89366,207],{},[1716,89368,89369,89371],{},[898,89370,13774],{},[898,89372,2223],{},[902,89374,78328],{"encoding":904},[123,89376,89377,5204,89380,89415],{},[38,89378,89379],{},"Ryzí Cobb-Douglas",[883,89381,89383],{"className":89382},[886],[888,89384,89385],{"xmlns":890},[892,89386,89387,89413],{},[895,89388,89389,89391,89393,89395,89401],{},[898,89390,6796],{},[1711,89392,1836],{},[898,89394,8243],{},[1716,89396,89397,89399],{},[898,89398,2888],{},[898,89400,207],{},[1716,89402,89403,89405],{},[898,89404,13774],{},[895,89406,89407,89409,89411],{},[2111,89408,2238],{},[1711,89410,2460],{},[898,89412,207],{},[902,89414,82490],{"encoding":904}," (konstantní výnosy).",[123,89417,89418,5204,89420,2186],{},[38,89419,83206],{},[883,89421,89423],{"className":89422},[886],[888,89424,89425],{"xmlns":890},[892,89426,89427,89485],{},[895,89428,89429,89431,89433,89435,89437,89439,89441,89443,89445,89447,89457,89459,89461,89471],{},[898,89430,6796],{},[1711,89432,1836],{},[898,89434,8243],{},[1711,89436,5144],{"stretchy":1713},[1711,89438,1714],{"stretchy":1713},[2111,89440,2238],{},[1711,89442,2460],{},[898,89444,207],{},[1711,89446,1735],{"stretchy":1713},[1716,89448,89449,89451],{},[898,89450,2888],{},[895,89452,89453,89455],{},[1711,89454,2460],{},[898,89456,2223],{},[1711,89458,2095],{},[898,89460,207],{},[1716,89462,89463,89465],{},[898,89464,13774],{},[895,89466,89467,89469],{},[1711,89468,2460],{},[898,89470,2223],{},[1716,89472,89473,89475],{},[1711,89474,5163],{"stretchy":1713},[895,89476,89477,89479,89481,89483],{},[1711,89478,2460],{},[2111,89480,2238],{},[898,89482,8659],{"mathvariant":2287},[898,89484,2223],{},[902,89486,89487],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,89489,89490,1648,89493,1772,89515,1648,89518,89548],{},[38,89491,89492],{},"Lineární",[883,89494,89496],{"className":89495},[886],[888,89497,89498],{"xmlns":890},[892,89499,89500,89512],{},[895,89501,89502,89504,89506,89508,89510],{},[898,89503,207],{},[898,89505,2888],{},[1711,89507,2095],{},[898,89509,2223],{},[898,89511,13774],{},[902,89513,89514],{"encoding":904},"aL + bK",[38,89516,89517],{},"Leontiefova",[883,89519,89521],{"className":89520},[886],[888,89522,89523],{"xmlns":890},[892,89524,89525,89545],{},[895,89526,89527,89529,89531,89533,89535,89537,89539,89541,89543],{},[898,89528,83434],{},[1711,89530,59798],{},[1711,89532,1714],{"stretchy":1713},[898,89534,207],{},[898,89536,2888],{},[1711,89538,1726],{"separator":1725},[898,89540,2223],{},[898,89542,13774],{},[1711,89544,1735],{"stretchy":1713},[902,89546,89547],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,89550,89551,5204,89567,2186],{},[38,89552,89553,89554],{},"Homogenita stupně ",[883,89555,89557],{"className":89556},[886],[888,89558,89559],{"xmlns":890},[892,89560,89561,89565],{},[895,89562,89563],{},[898,89564,40458],{},[902,89566,40458],{"encoding":904},[883,89568,89570],{"className":89569},[886],[888,89571,89572],{"xmlns":890},[892,89573,89574,89612],{},[895,89575,89576,89578,89580,89582,89584,89586,89588,89590,89592,89594,89600,89602,89604,89606,89608,89610],{},[898,89577,6796],{},[1711,89579,1714],{"stretchy":1713},[898,89581,1675],{},[898,89583,2888],{},[1711,89585,1726],{"separator":1725},[898,89587,1675],{},[898,89589,13774],{},[1711,89591,1735],{"stretchy":1713},[1711,89593,1836],{},[1716,89595,89596,89598],{},[898,89597,1675],{},[898,89599,40458],{},[898,89601,6796],{},[1711,89603,1714],{"stretchy":1713},[898,89605,2888],{},[1711,89607,1726],{"separator":1725},[898,89609,13774],{},[1711,89611,1735],{"stretchy":1713},[902,89613,89614],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,89616,89617,82588],{},[38,89618,82521,89619],{},[883,89620,89622],{"className":89621},[886],[888,89623,89624],{"xmlns":890},[892,89625,89626,89630],{},[895,89627,89628],{},[898,89629,8243],{},[902,89631,8243],{"encoding":904},[123,89633,89634,89636,89637,89659,89660,89682,89683,1797],{},[38,89635,82022],{}," — konstantní (",[883,89638,89640],{"className":89639},[886],[888,89641,89642],{"xmlns":890},[892,89643,89644,89656],{},[895,89645,89646,89648,89650,89652,89654],{},[898,89647,207],{},[1711,89649,2095],{},[898,89651,2223],{},[1711,89653,1836],{},[2111,89655,2238],{},[902,89657,89658],{"encoding":904},"a+b=1","), rostoucí (",[883,89661,89663],{"className":89662},[886],[888,89664,89665],{"xmlns":890},[892,89666,89667,89679],{},[895,89668,89669,89671,89673,89675,89677],{},[898,89670,207],{},[1711,89672,2095],{},[898,89674,2223],{},[1711,89676,2123],{},[2111,89678,2238],{},[902,89680,89681],{"encoding":904},"a+b>1","), klesající (",[883,89684,89686],{"className":89685},[886],[888,89687,89688],{"xmlns":890},[892,89689,89690,89702],{},[895,89691,89692,89694,89696,89698,89700],{},[898,89693,207],{},[1711,89695,2095],{},[898,89697,2223],{},[1711,89699,2109],{},[2111,89701,2238],{},[902,89703,89704],{"encoding":904},"a+b\u003C1",[123,89706,89707,1700,89709,1343,89739,1700,89741,2186],{},[38,89708,78691],{},[883,89710,89712],{"className":89711},[886],[888,89713,89714],{"xmlns":890},[892,89715,89716,89736],{},[895,89717,89718,89720,89726,89728],{},[898,89719,1790],{},[2884,89721,89722,89724],{},[898,89723,7929],{},[898,89725,2888],{},[1711,89727,1836],{},[13142,89729,89730,89732,89734],{},[898,89731,6796],{},[898,89733,2888],{},[1711,89735,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,89737,89738],{"encoding":904},"MP_L = Q'_L",[38,89740,81595],{},[883,89742,89744],{"className":89743},[886],[888,89745,89746],{"xmlns":890},[892,89747,89748,89768],{},[895,89749,89750,89752,89758,89760],{},[898,89751,1790],{},[2884,89753,89754,89756],{},[898,89755,7929],{},[898,89757,13774],{},[1711,89759,1836],{},[13142,89761,89762,89764,89766],{},[898,89763,6796],{},[898,89765,13774],{},[1711,89767,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,89769,89770],{"encoding":904},"MP_K = Q'_K",[123,89772,89773,1700,89775,2186],{},[38,89774,83809],{},[883,89776,89778],{"className":89777},[886],[888,89779,89780],{"xmlns":890},[892,89781,89782,89820],{},[895,89783,89784,89786,89788,89790,89792,89798,89800,89802,89804,89806,89808,89814,89816,89818],{},[898,89785,2098],{},[898,89787,6796],{},[1711,89789,1836],{},[898,89791,1790],{},[2884,89793,89794,89796],{},[898,89795,7929],{},[898,89797,2888],{},[1942,89799,2519],{},[898,89801,2098],{},[898,89803,2888],{},[1711,89805,2095],{},[898,89807,1790],{},[2884,89809,89810,89812],{},[898,89811,7929],{},[898,89813,13774],{},[1942,89815,2519],{},[898,89817,2098],{},[898,89819,13774],{},[902,89821,89822],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,89824,89825,5204,89827,2186],{},[38,89826,84154],{},[883,89828,89830],{"className":89829},[886],[888,89831,89832],{"xmlns":890},[892,89833,89834,89876],{},[895,89835,89836,89838,89846,89848,89850,89858,89860,89862,89864,89866,89868,89870,89872,89874],{},[898,89837,2888],{},[13142,89839,89840,89842,89844],{},[898,89841,6796],{},[898,89843,2888],{},[1711,89845,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,89847,2095],{},[898,89849,13774],{},[13142,89851,89852,89854,89856],{},[898,89853,6796],{},[898,89855,13774],{},[1711,89857,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,89859,1836],{},[898,89861,40458],{},[1942,89863,2519],{},[898,89865,6796],{},[1711,89867,1714],{"stretchy":1713},[898,89869,2888],{},[1711,89871,1726],{"separator":1725},[898,89873,13774],{},[1711,89875,1735],{"stretchy":1713},[902,89877,89878],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,89880,89881,89884,89885,2186],{},[38,89882,89883],{},"Izokvanta"," — křivka ",[883,89886,89888],{"className":89887},[886],[888,89889,89890],{"xmlns":890},[892,89891,89892,89910],{},[895,89893,89894,89896,89898,89900,89902,89904,89906,89908],{},[898,89895,6796],{},[1711,89897,1714],{"stretchy":1713},[898,89899,2888],{},[1711,89901,1726],{"separator":1725},[898,89903,13774],{},[1711,89905,1735],{"stretchy":1713},[1711,89907,1836],{},[898,89909,84395],{},[902,89911,89912],{"encoding":904},"Q(L, K) = q",[123,89914,89915,1700,89917,2186],{},[38,89916,84584],{},[883,89918,89920],{"className":89919},[886],[888,89921,89922],{"xmlns":890},[892,89923,89924,89954],{},[895,89925,89926,89928,89930,89932,89934,89936,89938,89944,89946,89948],{},[898,89927,1790],{},[898,89929,7985],{},[898,89931,1769],{},[898,89933,2362],{},[1711,89935,1836],{},[898,89937,1790],{},[2884,89939,89940,89942],{},[898,89941,7929],{},[898,89943,2888],{},[898,89945,8659],{"mathvariant":2287},[898,89947,1790],{},[2884,89949,89950,89952],{},[898,89951,7929],{},[898,89953,13774],{},[902,89955,78403],{"encoding":904},[123,89957,89958,1700,89961,2186],{},[38,89959,89960],{},"Substituční vztah",[883,89962,89964],{"className":89963},[886],[888,89965,89966],{"xmlns":890},[892,89967,89968,89992],{},[895,89969,89970,89972,89974,89976,89978,89980,89982,89984,89986,89988,89990],{},[898,89971,6892],{"mathvariant":2287},[898,89973,13774],{},[1711,89975,6740],{},[1711,89977,2460],{},[898,89979,1790],{},[898,89981,7985],{},[898,89983,1769],{},[898,89985,2362],{},[1942,89987,2519],{},[898,89989,2098],{},[898,89991,2888],{},[902,89993,89994],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,89996,5901],{"id":5900},[120,89998,89999,90096,90103,90110],{},[123,90000,90001,1700,90003,90006,90007,1343,90010,90013,90014,90017,90018,90037,90038,22246,90057,90060,90061,90080,90081,1797],{},[38,90002,54321],{},[207,90004,784],{"className":90005,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,90008,6375],{"className":90009,"dataFsResolvedFilePath":764,"href":765},[210],[207,90011,793],{"className":90012,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,90015,880],{"className":90016,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,90019,90021],{"className":90020},[886],[888,90022,90023],{"xmlns":890},[892,90024,90025,90035],{},[895,90026,90027,90029,90031,90033],{},[898,90028,1790],{},[898,90030,7985],{},[898,90032,1769],{},[898,90034,2362],{},[902,90036,14572],{"encoding":904}," ↔ ",[883,90039,90041],{"className":90040},[886],[888,90042,90043],{"xmlns":890},[892,90044,90045,90055],{},[895,90046,90047,90049,90051,90053],{},[898,90048,1790],{},[898,90050,7985],{},[898,90052,1940],{},[898,90054,2362],{},[902,90056,14576],{"encoding":904},[207,90058,7817],{"className":90059,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,90062,90064],{"className":90063},[886],[888,90065,90066],{"xmlns":890},[892,90067,90068,90078],{},[895,90069,90070,90072],{},[898,90071,8243],{},[2884,90073,90074,90076],{},[898,90075,7929],{},[898,90077,2888],{},[902,90079,78231],{"encoding":904}," ↔ min ",[883,90082,90084],{"className":90083},[886],[888,90085,90086],{"xmlns":890},[892,90087,90088,90094],{},[895,90089,90090,90092],{},[898,90091,8243],{},[898,90093,1940],{},[902,90095,59158],{"encoding":904},[123,90097,90098,1700,90100,2186],{},[38,90099,7793],{},[207,90101,7822],{"className":90102,"dataFsResolvedFilePath":848,"href":849},[210],[123,90104,90105,1700,90107,2186],{},[38,90106,5919],{},[207,90108,1094],{"className":90109,"dataFsResolvedFilePath":838,"href":839},[210],[123,90111,90112,1700,90114,2186],{},[38,90113,5908],{},[207,90115,5914],{"className":90116,"dataFsResolvedFilePath":5912,"href":5913},[210],{"title":641,"searchDepth":642,"depth":642,"links":90118},[90119,90120,90121,90125,90127,90132,90133,90140,90141,90143,90144,90145,90147,90152,90153,90154,90158,90159],{"id":78426,"depth":642,"text":78427},{"id":78563,"depth":642,"text":78564},{"id":78666,"depth":642,"text":90122,"children":90123},"Mezní produkt práce (MPLMP_L)",[90124],{"id":79112,"depth":649,"text":79113},{"id":79601,"depth":642,"text":90126},"Průměrný produkt práce (APLAP_L)",{"id":79719,"depth":642,"text":79720,"children":90128},[90129,90130,90131],{"id":79956,"depth":649,"text":69099},{"id":80267,"depth":649,"text":80268},{"id":80987,"depth":649,"text":80988},{"id":81559,"depth":642,"text":81560},{"id":81662,"depth":642,"text":81663,"children":90134},[90135,90136,90138,90139],{"id":82021,"depth":649,"text":82022},{"id":82520,"depth":649,"text":90137},"Parametr efektivity AA",{"id":82591,"depth":649,"text":82592},{"id":40777,"depth":649,"text":82931},{"id":83118,"depth":642,"text":83119},{"id":83457,"depth":642,"text":90142},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":84148,"depth":642,"text":84149},{"id":78492,"depth":642,"text":13753},{"id":84559,"depth":642,"text":90146},"Mezní míra technické substituce (MRTSMRTS)",{"id":85425,"depth":642,"text":85426,"children":90148},[90149,90150,90151],{"id":85429,"depth":649,"text":85430},{"id":86072,"depth":649,"text":86073},{"id":86353,"depth":649,"text":86354},{"id":86699,"depth":642,"text":86700},{"id":53479,"depth":642,"text":53480},{"id":87049,"depth":642,"text":87050,"children":90155},[90156,90157],{"id":44048,"depth":649,"text":44049},{"id":87568,"depth":649,"text":87569},{"id":5421,"depth":642,"text":5422},{"id":5900,"depth":642,"text":5901},{},"\u002Ftopics\u002Fprodukce",{"title":78062,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,13787,90166,90167,90168,78492,90169,90170],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":90173,"title":90174,"body":90175,"course":1128,"courses":659,"created":5973,"description":641,"extension":661,"meta":99122,"navigation":664,"path":99123,"seo":99124,"sources":99125,"stem":99126,"tags":99127,"type":5985,"updated":677,"__hash__":99130},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":90176,"toc":99096},[90177,90180,90182,90379,90388,90392,90395,90448,90452,90464,90468,90471,90488,90611,90617,90761,90771,90775,90810,90848,90896,90953,91013,91055,91631,91635,91718,91827,91920,92178,92181,92234,92345,92427,92431,92442,92675,92730,92736,92776,92839,92850,93041,93147,93300,93348,93353,93467,93505,93631,93677,93704,93781,93856,93936,94066,94127,94215,94219,94222,94291,94374,94381,94441,94751,94755,94761,94814,94830,94881,95019,95095,95208,95525,95529,95536,95696,95755,95759,95781,95878,95999,96113,96136,96199,96256,96508,96516,96520,96527,96781,96831,96887,96890,97054,97058,97156,97158,97190,97194,97327,97569,97753,97921,98228,98361,98548,98560,98562,98997,98999],[12,90178,90174],{"id":90179},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,90181,1638],{"id":1637},[724,90183,90184,1700,90186,90217,90218,90221,90222,90252,90253,90271,90272,90312,90313,90316,90317,90330,90331,31851,90334,90347,90348,90361,90362,90375,90376,2186],{},[38,90185,880],{},[883,90187,90189],{"className":90188},[886],[888,90190,90191],{"xmlns":890},[892,90192,90193,90215],{},[895,90194,90195,90197,90199,90205,90207,90213],{},[898,90196,900],{},[1711,90198,1714],{"stretchy":1713},[2884,90200,90201,90203],{},[898,90202,6796],{},[2111,90204,2238],{},[1711,90206,1726],{"separator":1725},[2884,90208,90209,90211],{},[898,90210,6796],{},[2111,90212,2963],{},[1711,90214,1735],{"stretchy":1713},[902,90216,19941],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,90219,90220],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,90223,90225],{"className":90224},[886],[888,90226,90227],{"xmlns":890},[892,90228,90229,90249],{},[895,90230,90231,90233,90239,90241],{},[898,90232,1790],{},[2884,90234,90235,90237],{},[898,90236,900],{},[898,90238,21388],{},[1711,90240,1836],{},[13142,90242,90243,90245,90247],{},[898,90244,900],{},[898,90246,21388],{},[1711,90248,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,90250,90251],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,90254,90256],{"className":90255},[886],[888,90257,90258],{"xmlns":890},[892,90259,90260,90268],{},[895,90261,90262,90264,90266],{},[898,90263,900],{},[1711,90265,1836],{},[898,90267,2090],{},[902,90269,90270],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,90273,90275],{"className":90274},[886],[888,90276,90277],{"xmlns":890},[892,90278,90279,90309],{},[895,90280,90281,90283,90285,90287,90289,90291,90293,90299,90301,90303],{},[898,90282,1790],{},[898,90284,7985],{},[898,90286,1940],{},[898,90288,2362],{},[1711,90290,1836],{},[898,90292,1790],{},[2884,90294,90295,90297],{},[898,90296,900],{},[2111,90298,2238],{},[898,90300,8659],{"mathvariant":2287},[898,90302,1790],{},[2884,90304,90305,90307],{},[898,90306,900],{},[2111,90308,2963],{},[902,90310,90311],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,90314,90315],{},"teorii užitečnosti"," — funkce ",[883,90318,90320],{"className":90319},[886],[888,90321,90322],{"xmlns":890},[892,90323,90324,90328],{},[895,90325,90326],{},[898,90327,900],{},[902,90329,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,90332,90333],{},"Optimalizaci spotřebitele",[883,90335,90337],{"className":90336},[886],[888,90338,90339],{"xmlns":890},[892,90340,90341,90345],{},[895,90342,90343],{},[898,90344,900],{},[902,90346,900],{"encoding":904}," při rozpočtu, min ",[883,90349,90351],{"className":90350},[886],[888,90352,90353],{"xmlns":890},[892,90354,90355,90359],{},[895,90356,90357],{},[898,90358,1722],{},[902,90360,1722],{"encoding":904}," při dané ",[883,90363,90365],{"className":90364},[886],[888,90366,90367],{"xmlns":890},[892,90368,90369,90373],{},[895,90370,90371],{},[898,90372,900],{},[902,90374,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,90377,913],{"className":90378,"dataFsResolvedFilePath":911,"href":912},[210],[724,90380,90381,90382,90384,90385,2186],{},"Kapitola 6 knihy ",[614,90383,5914],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,90386,40352],{"className":90387,"dataFsResolvedFilePath":911,"href":912},[210],[115,90389,90391],{"id":90390},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,90393,90394],{},"Po prostudování této kapitoly byste měli umět:",[120,90396,90397,90403,90412,90417,90420,90426,90432,90435,90441],{},[123,90398,90399,90400,1726],{},"vyložit, co se rozumí termínem ",[38,90401,90402],{},"užitečnost",[123,90404,90405,90406,2009,90409,1726],{},"definovat pojmy ",[38,90407,90408],{},"svazek zboží",[38,90410,90411],{},"funkce užitečnosti",[123,90413,78441,90414,78448],{},[38,90415,90416],{},"mezní užitečnosti",[123,90418,90419],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,90421,78468,90422,90425],{},[38,90423,90424],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,90427,78489,90428,90431],{},[38,90429,90430],{},"křivky užitečnosti"," (indiferenční křivky),",[123,90433,90434],{},"vyjmenovat jejich základní vlastnosti,",[123,90436,78441,90437,90440],{},[38,90438,90439],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,90442,90443,90444,90447],{},"řešit ",[38,90445,90446],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,90449,90451],{"id":90450},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,90453,90454,90455,90459,90460,90463],{},"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 ",[207,90456,90458],{"className":90457,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,90461,90462],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,90465,90467],{"id":90466},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,90469,90470],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,90472,90473,90479],{},[123,90474,90475,90478],{},[38,90476,90477],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,90480,90481,90484,90485,90487],{},[38,90482,90483],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,90486,90220],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[1921,90489,90490],{},[724,90491,90492,90494,90495,90498,90499,1700,90512,90515,90516,2009,90529,90548,90549,1343,90575,90602,90603,90606,90607,90610],{},[883,90493,1927],{}," Pozor — ordinalisté užitečnost ",[38,90496,90497],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,90500,90502],{"className":90501},[886],[888,90503,90504],{"xmlns":890},[892,90505,90506,90510],{},[895,90507,90508],{},[898,90509,900],{},[902,90511,900],{"encoding":904},[38,90513,90514],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,90517,90519],{"className":90518},[886],[888,90520,90521],{"xmlns":890},[892,90522,90523,90527],{},[895,90524,90525],{},[898,90526,900],{},[902,90528,900],{"encoding":904},[883,90530,90532],{"className":90531},[886],[888,90533,90534],{"xmlns":890},[892,90535,90536,90545],{},[895,90537,90538],{},[12366,90539,90540,90542],{"accent":1725},[898,90541,900],{},[1711,90543,90544],{},"~",[902,90546,90547],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,90550,90552],{"className":90551},[886],[888,90553,90554],{"xmlns":890},[892,90555,90556,90572],{},[895,90557,90558,90564,90566],{},[12366,90559,90560,90562],{"accent":1725},[898,90561,900],{},[1711,90563,90544],{},[1711,90565,1836],{},[1716,90567,90568,90570],{},[898,90569,900],{},[2111,90571,2963],{},[902,90573,90574],{"encoding":904},"\\tilde U = U^2",[883,90576,90578],{"className":90577},[886],[888,90579,90580],{"xmlns":890},[892,90581,90582,90599],{},[895,90583,90584,90590,90592,90595,90597],{},[12366,90585,90586,90588],{"accent":1725},[898,90587,900],{},[1711,90589,90544],{},[1711,90591,1836],{},[898,90593,90594],{},"ln",[1711,90596,59798],{},[898,90598,900],{},[902,90600,90601],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,90604,90605],{},"porovnání"," mezi svazky a ",[38,90608,90609],{},"poměry"," mezních veličin.",[724,90612,90613,90614,2062],{},"Ordinalistický přístup vychází z ",[38,90615,90616],{},"pěti hlavních předpokladů",[152,90618,90619,90625,90631,90749,90755],{},[123,90620,90621,90624],{},[38,90622,90623],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,90626,90627,90630],{},[38,90628,90629],{},"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.",[123,90632,90633,90636,90637,65339,90650,90663,90664,65339,90677,2801,90690,90693,90694,2009,90713,66168,90731,2186],{},[38,90634,90635],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,90638,90640],{"className":90639},[886],[888,90641,90642],{"xmlns":890},[892,90643,90644,90648],{},[895,90645,90646],{},[898,90647,8243],{},[902,90649,8243],{"encoding":904},[883,90651,90653],{"className":90652},[886],[888,90654,90655],{"xmlns":890},[892,90656,90657,90661],{},[895,90658,90659],{},[898,90660,26851],{},[902,90662,26851],{"encoding":904},", nebude jindy preferovat ",[883,90665,90667],{"className":90666},[886],[888,90668,90669],{"xmlns":890},[892,90670,90671,90675],{},[895,90672,90673],{},[898,90674,26851],{},[902,90676,26851],{"encoding":904},[883,90678,90680],{"className":90679},[886],[888,90681,90682],{"xmlns":890},[892,90683,90684,90688],{},[895,90685,90686],{},[898,90687,8243],{},[902,90689,8243],{"encoding":904},[38,90691,90692],{},"Tranzitivita",": pokud ",[883,90695,90697],{"className":90696},[886],[888,90698,90699],{"xmlns":890},[892,90700,90701,90710],{},[895,90702,90703,90705,90708],{},[898,90704,8243],{},[1711,90706,90707],{},"≻",[898,90709,26851],{},[902,90711,90712],{"encoding":904},"A \\succ B",[883,90714,90716],{"className":90715},[886],[888,90717,90718],{"xmlns":890},[892,90719,90720,90728],{},[895,90721,90722,90724,90726],{},[898,90723,26851],{},[1711,90725,90707],{},[898,90727,1940],{},[902,90729,90730],{"encoding":904},"B \\succ C",[883,90732,90734],{"className":90733},[886],[888,90735,90736],{"xmlns":890},[892,90737,90738,90746],{},[895,90739,90740,90742,90744],{},[898,90741,8243],{},[1711,90743,90707],{},[898,90745,1940],{},[902,90747,90748],{"encoding":904},"A \\succ C",[123,90750,90751,90754],{},[38,90752,90753],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,90756,90757,90760],{},[38,90758,90759],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,90762,90763,90764,90767,90768,2186],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,90765,90766],{},"preference"," a na příbuzné ",[614,90769,90770],{},"funkci užitečnosti",[115,90772,90774],{"id":90773},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,90776,90777,90778,90791,90792,90795,90796,90809],{},"Uvažujme ",[883,90779,90781],{"className":90780},[886],[888,90782,90783],{"xmlns":890},[892,90784,90785,90789],{},[895,90786,90787],{},[898,90788,40458],{},[902,90790,40458],{"encoding":904}," různých zboží. ",[38,90793,90794],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,90797,90799],{"className":90798},[886],[888,90800,90801],{"xmlns":890},[892,90802,90803,90807],{},[895,90804,90805],{},[898,90806,40458],{},[902,90808,40458],{"encoding":904},"-tice",[724,90811,90812],{},[883,90813,90815],{"className":90814},[886],[888,90816,90817],{"xmlns":890},[892,90818,90819,90845],{},[895,90820,90821,90823,90829,90831,90833,90835,90841,90843],{},[1711,90822,1714],{"stretchy":1713},[2884,90824,90825,90827],{},[898,90826,6796],{},[2111,90828,2238],{},[1711,90830,1726],{"separator":1725},[1711,90832,13621],{},[1711,90834,1726],{"separator":1725},[2884,90836,90837,90839],{},[898,90838,6796],{},[898,90840,40458],{},[1711,90842,1735],{"stretchy":1713},[1711,90844,1726],{"separator":1725},[902,90846,90847],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,90849,8298,90850,90867,90868,90881,90882,90885,90886,90889,90890,90893,90894,2062],{},[883,90851,90853],{"className":90852},[886],[888,90854,90855],{"xmlns":890},[892,90856,90857,90865],{},[895,90858,90859],{},[2884,90860,90861,90863],{},[898,90862,6796],{},[898,90864,21388],{},[902,90866,51136],{"encoding":904}," značí množství ",[883,90869,90871],{"className":90870},[886],[888,90872,90873],{"xmlns":890},[892,90874,90875,90879],{},[895,90876,90877],{},[898,90878,21388],{},[902,90880,21388],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,90883,90884],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,90887,90888],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,90891,90892],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,90895,90770],{},[883,90897,90899],{"className":90898},[886],[888,90900,90901],{"xmlns":890,"display":31664},[892,90902,90903,90950],{},[24352,90904,90905],{"width":31669},[24357,90906,90907,90909,90943,90945],{},[24360,90908],{"width":31674},[24360,90910,90911],{},[895,90912,90913,90915,90917,90919,90921,90927,90929,90931,90933,90939,90941],{},[898,90914,900],{},[1711,90916,1836],{},[898,90918,900],{},[1711,90920,1714],{"stretchy":1713},[2884,90922,90923,90925],{},[898,90924,6796],{},[2111,90926,2238],{},[1711,90928,1726],{"separator":1725},[1711,90930,13621],{},[1711,90932,1726],{"separator":1725},[2884,90934,90935,90937],{},[898,90936,6796],{},[898,90938,40458],{},[1711,90940,1735],{"stretchy":1713},[1711,90942,1726],{"separator":1725},[24360,90944],{"width":31674},[24360,90946,90947],{},[1942,90948,90949],{},"(6.1)",[902,90951,90952],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,90954,8298,90955,90985,90986,91008,91009,91012],{},[883,90956,90958],{"className":90957},[886],[888,90959,90960],{"xmlns":890},[892,90961,90962,90982],{},[895,90963,90964,90970,90972,90974,90976],{},[2884,90965,90966,90968],{},[898,90967,6796],{},[2111,90969,2238],{},[1711,90971,1726],{"separator":1725},[1711,90973,13621],{},[1711,90975,1726],{"separator":1725},[2884,90977,90978,90980],{},[898,90979,6796],{},[898,90981,40458],{},[902,90983,90984],{"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 ",[883,90987,90989],{"className":90988},[886],[888,90990,90991],{"xmlns":890},[892,90992,90993,91005],{},[895,90994,90995,90997,90999],{},[898,90996,900],{},[1711,90998,1726],{"separator":1725},[12366,91000,91001,91003],{"accent":1725},[898,91002,900],{},[1711,91004,90544],{},[902,91006,91007],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,91010,91011],{},"monotónní transformace"," zachovávající pořadí.",[724,91014,91015,91016,5204,91019,2186],{},"Dále se omezíme na funkce pro ",[38,91017,91018],{},"dvě zboží",[883,91020,91022],{"className":91021},[886],[888,91023,91024],{"xmlns":890},[892,91025,91026,91052],{},[895,91027,91028,91030,91032,91034,91036,91042,91044,91050],{},[898,91029,900],{},[1711,91031,1836],{},[898,91033,900],{},[1711,91035,1714],{"stretchy":1713},[2884,91037,91038,91040],{},[898,91039,6796],{},[2111,91041,2238],{},[1711,91043,1726],{"separator":1725},[2884,91045,91046,91048],{},[898,91047,6796],{},[2111,91049,2963],{},[1711,91051,1735],{"stretchy":1713},[902,91053,91054],{"encoding":904},"U = U(Q_1, Q_2)",[1921,91056,91057,91132],{},[724,91058,91059,91061,91062,2062],{},[883,91060,56293],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,91063,91065],{"className":91064},[886],[888,91066,91067],{"xmlns":890},[892,91068,91069,91129],{},[895,91070,91071,91073,91075,91077,91079,91085,91087,91093,91095,91101,91103,91105,91107],{},[898,91072,900],{},[1711,91074,1836],{},[898,91076,900],{},[1711,91078,1714],{"stretchy":1713},[2884,91080,91081,91083],{},[898,91082,6796],{},[2111,91084,2238],{},[1711,91086,1726],{"separator":1725},[2884,91088,91089,91091],{},[898,91090,6796],{},[2111,91092,2963],{},[1711,91094,1726],{"separator":1725},[2884,91096,91097,91099],{},[898,91098,6796],{},[2111,91100,3034],{},[1711,91102,1735],{"stretchy":1713},[1711,91104,1836],{},[2111,91106,2963],{},[12097,91108,91109],{},[895,91110,91111,91117,91123],{},[2884,91112,91113,91115],{},[898,91114,6796],{},[2111,91116,2238],{},[2884,91118,91119,91121],{},[898,91120,6796],{},[2111,91122,2963],{},[2884,91124,91125,91127],{},[898,91126,6796],{},[2111,91128,3034],{},[902,91130,91131],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,91133,91134,91327],{},[123,91135,91136,91137,91163,91164,2614,91190,2009,91249,9572,91309,12405],{},"svazek ",[883,91138,91140],{"className":91139},[886],[888,91141,91142],{"xmlns":890},[892,91143,91144,91160],{},[895,91145,91146,91148,91150,91152,91154,91156,91158],{},[1711,91147,1714],{"stretchy":1713},[2111,91149,45460],{},[1711,91151,1726],{"separator":1725},[2111,91153,6369],{},[1711,91155,1726],{"separator":1725},[2111,91157,45438],{},[1711,91159,1735],{"stretchy":1713},[902,91161,91162],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,91165,91167],{"className":91166},[886],[888,91168,91169],{"xmlns":890},[892,91170,91171,91187],{},[895,91172,91173,91175,91177,91179,91181,91183,91185],{},[1711,91174,1714],{"stretchy":1713},[2111,91176,7990],{},[1711,91178,1726],{"separator":1725},[2111,91180,7990],{},[1711,91182,1726],{"separator":1725},[2111,91184,70195],{},[1711,91186,1735],{"stretchy":1713},[902,91188,91189],{"encoding":904},"(9, 9, 27)",[883,91191,91193],{"className":91192},[886],[888,91194,91195],{"xmlns":890},[892,91196,91197,91246],{},[895,91198,91199,91201,91203,91205,91207,91209,91211,91213,91215,91217,91219,91233,91235,91237,91242,91244],{},[898,91200,900],{},[1711,91202,1714],{"stretchy":1713},[2111,91204,45460],{},[1711,91206,1726],{"separator":1725},[2111,91208,6369],{},[1711,91210,1726],{"separator":1725},[2111,91212,45438],{},[1711,91214,1735],{"stretchy":1713},[1711,91216,1836],{},[2111,91218,2963],{},[12097,91220,91221],{},[895,91222,91223,91225,91227,91229,91231],{},[2111,91224,45460],{},[1711,91226,4795],{},[2111,91228,6369],{},[1711,91230,4795],{},[2111,91232,45438],{},[1711,91234,1836],{},[2111,91236,2963],{},[12097,91238,91239],{},[2111,91240,91241],{},"4096",[1711,91243,1836],{},[2111,91245,9600],{},[902,91247,91248],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,91250,91252],{"className":91251},[886],[888,91253,91254],{"xmlns":890},[892,91255,91256,91306],{},[895,91257,91258,91260,91262,91264,91266,91268,91270,91272,91274,91276,91278,91292,91294,91296,91301,91303],{},[898,91259,900],{},[1711,91261,1714],{"stretchy":1713},[2111,91263,7990],{},[1711,91265,1726],{"separator":1725},[2111,91267,7990],{},[1711,91269,1726],{"separator":1725},[2111,91271,70195],{},[1711,91273,1735],{"stretchy":1713},[1711,91275,1836],{},[2111,91277,2963],{},[12097,91279,91280],{},[895,91281,91282,91284,91286,91288,91290],{},[2111,91283,7990],{},[1711,91285,4795],{},[2111,91287,7990],{},[1711,91289,4795],{},[2111,91291,70195],{},[1711,91293,1836],{},[2111,91295,2963],{},[12097,91297,91298],{},[2111,91299,91300],{},"2187",[1711,91302,9881],{},[2111,91304,91305],{},"93,53",[902,91307,91308],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,91310,91312],{"className":91311},[886],[888,91313,91314],{"xmlns":890},[892,91315,91316,91324],{},[895,91317,91318,91320,91322],{},[2111,91319,9600],{},[1711,91321,2123],{},[2111,91323,91305],{},[902,91325,91326],{"encoding":904},"128 > 93{,}53",[123,91328,91329,91330,2009,91356,91382,91383,2009,91423,91464,91465,91511,91512,2009,91538,6849,91564,2009,91582,91600,91601,2186],{},"svazky ",[883,91331,91333],{"className":91332},[886],[888,91334,91335],{"xmlns":890},[892,91336,91337,91353],{},[895,91338,91339,91341,91343,91345,91347,91349,91351],{},[1711,91340,1714],{"stretchy":1713},[2111,91342,6369],{},[1711,91344,1726],{"separator":1725},[2111,91346,9568],{},[1711,91348,1726],{"separator":1725},[2111,91350,2963],{},[1711,91352,1735],{"stretchy":1713},[902,91354,91355],{"encoding":904},"(4, 8, 2)",[883,91357,91359],{"className":91358},[886],[888,91360,91361],{"xmlns":890},[892,91362,91363,91379],{},[895,91364,91365,91367,91369,91371,91373,91375,91377],{},[1711,91366,1714],{"stretchy":1713},[2111,91368,45438],{},[1711,91370,1726],{"separator":1725},[2111,91372,2238],{},[1711,91374,1726],{"separator":1725},[2111,91376,6369],{},[1711,91378,1735],{"stretchy":1713},[902,91380,91381],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,91384,91386],{"className":91385},[886],[888,91387,91388],{"xmlns":890},[892,91389,91390,91420],{},[895,91391,91392,91394,91396,91398,91400,91402,91404,91406,91408,91410,91412,91416,91418],{},[898,91393,900],{},[1711,91395,1714],{"stretchy":1713},[2111,91397,6369],{},[1711,91399,1726],{"separator":1725},[2111,91401,9568],{},[1711,91403,1726],{"separator":1725},[2111,91405,2963],{},[1711,91407,1735],{"stretchy":1713},[1711,91409,1836],{},[2111,91411,2963],{},[12097,91413,91414],{},[2111,91415,45438],{},[1711,91417,1836],{},[2111,91419,45460],{},[902,91421,91422],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,91424,91426],{"className":91425},[886],[888,91427,91428],{"xmlns":890},[892,91429,91430,91461],{},[895,91431,91432,91434,91436,91438,91440,91442,91444,91446,91448,91450,91452,91457,91459],{},[898,91433,900],{},[1711,91435,1714],{"stretchy":1713},[2111,91437,45438],{},[1711,91439,1726],{"separator":1725},[2111,91441,2238],{},[1711,91443,1726],{"separator":1725},[2111,91445,6369],{},[1711,91447,1735],{"stretchy":1713},[1711,91449,1836],{},[2111,91451,2963],{},[12097,91453,91454],{},[2111,91455,91456],{},"256",[1711,91458,1836],{},[2111,91460,75957],{},[902,91462,91463],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,91466,91468],{"className":91467},[886],[888,91469,91470],{"xmlns":890},[892,91471,91472,91508],{},[895,91473,91474,91476,91478,91480,91482,91484,91486,91488,91490,91492,91494,91496,91498,91500,91502,91504,91506],{},[898,91475,900],{},[1711,91477,1714],{"stretchy":1713},[2111,91479,6369],{},[1711,91481,1726],{"separator":1725},[2111,91483,9568],{},[1711,91485,1726],{"separator":1725},[2111,91487,2963],{},[1711,91489,1735],{"stretchy":1713},[1711,91491,1836],{},[898,91493,900],{},[1711,91495,1714],{"stretchy":1713},[2111,91497,45438],{},[1711,91499,1726],{"separator":1725},[2111,91501,2238],{},[1711,91503,1726],{"separator":1725},[2111,91505,6369],{},[1711,91507,1735],{"stretchy":1713},[902,91509,91510],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,91513,91515],{"className":91514},[886],[888,91516,91517],{"xmlns":890},[892,91518,91519,91535],{},[895,91520,91521,91523,91525,91527,91529,91531,91533],{},[2111,91522,6369],{},[1711,91524,4795],{},[2111,91526,9568],{},[1711,91528,4795],{},[2111,91530,2963],{},[1711,91532,1836],{},[2111,91534,45438],{},[902,91536,91537],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,91539,91541],{"className":91540},[886],[888,91542,91543],{"xmlns":890},[892,91544,91545,91561],{},[895,91546,91547,91549,91551,91553,91555,91557,91559],{},[2111,91548,45438],{},[1711,91550,4795],{},[2111,91552,2238],{},[1711,91554,4795],{},[2111,91556,6369],{},[1711,91558,1836],{},[2111,91560,91456],{},[902,91562,91563],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,91565,91567],{"className":91566},[886],[888,91568,91569],{"xmlns":890},[892,91570,91571,91579],{},[895,91572,91573,91575,91577],{},[898,91574,900],{},[1711,91576,1836],{},[2111,91578,45460],{},[902,91580,91581],{"encoding":904},"U = 16",[883,91583,91585],{"className":91584},[886],[888,91586,91587],{"xmlns":890},[892,91588,91589,91597],{},[895,91590,91591,91593,91595],{},[898,91592,900],{},[1711,91594,1836],{},[2111,91596,75957],{},[902,91598,91599],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,91602,91604],{"className":91603},[886],[888,91605,91606],{"xmlns":890},[892,91607,91608,91628],{},[895,91609,91610,91616,91622],{},[2884,91611,91612,91614],{},[898,91613,6796],{},[2111,91615,2238],{},[2884,91617,91618,91620],{},[898,91619,6796],{},[2111,91621,2963],{},[2884,91623,91624,91626],{},[898,91625,6796],{},[2111,91627,3034],{},[902,91629,91630],{"encoding":904},"Q_1 Q_2 Q_3",[115,91632,91634],{"id":91633},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,91636,91637,91638,12082,91673,1700,91676,45412,91693,1648,91710,91713,91714,91717],{},"Pro funkci užitečnosti ",[883,91639,91641],{"className":91640},[886],[888,91642,91643],{"xmlns":890},[892,91644,91645,91671],{},[895,91646,91647,91649,91651,91653,91655,91661,91663,91669],{},[898,91648,900],{},[1711,91650,1836],{},[898,91652,900],{},[1711,91654,1714],{"stretchy":1713},[2884,91656,91657,91659],{},[898,91658,6796],{},[2111,91660,2238],{},[1711,91662,1726],{"separator":1725},[2884,91664,91665,91667],{},[898,91666,6796],{},[2111,91668,2963],{},[1711,91670,1735],{"stretchy":1713},[902,91672,91054],{"encoding":904},[38,91674,91675],{},"mezní užitečnost",[883,91677,91679],{"className":91678},[886],[888,91680,91681],{"xmlns":890},[892,91682,91683,91691],{},[895,91684,91685],{},[2884,91686,91687,91689],{},[898,91688,6796],{},[2111,91690,2238],{},[902,91692,32600],{"encoding":904},[883,91694,91696],{"className":91695},[886],[888,91697,91698],{"xmlns":890},[892,91699,91700,91708],{},[895,91701,91702],{},[2884,91703,91704,91706],{},[898,91705,6796],{},[2111,91707,2963],{},[902,91709,32619],{"encoding":904},[38,91711,91712],{},"marginal utility",") parciální ",[207,91715,1145],{"className":91716,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,91719,91721],{"className":91720},[886],[888,91722,91723],{"xmlns":890,"display":31664},[892,91724,91725,91824],{},[24352,91726,91727],{"width":31669},[24357,91728,91729,91731,91817,91819],{},[24360,91730],{"width":31674},[24360,91732,91733],{},[895,91734,91735,91737,91743,91745,91753,91755,91773,91775,91777,91779,91785,91787,91795,91797,91815],{},[898,91736,1790],{},[2884,91738,91739,91741],{},[898,91740,900],{},[2111,91742,2238],{},[1711,91744,1836],{},[13142,91746,91747,91749,91751],{},[898,91748,900],{},[2111,91750,2238],{},[1711,91752,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,91754,1836],{},[2525,91756,91757,91763],{},[895,91758,91759,91761],{},[898,91760,13846],{"mathvariant":2287},[898,91762,900],{},[895,91764,91765,91767],{},[898,91766,13846],{"mathvariant":2287},[2884,91768,91769,91771],{},[898,91770,6796],{},[2111,91772,2238],{},[1711,91774,1726],{"separator":1725},[2102,91776],{"width":4981},[898,91778,1790],{},[2884,91780,91781,91783],{},[898,91782,900],{},[2111,91784,2963],{},[1711,91786,1836],{},[13142,91788,91789,91791,91793],{},[898,91790,900],{},[2111,91792,2963],{},[1711,91794,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,91796,1836],{},[2525,91798,91799,91805],{},[895,91800,91801,91803],{},[898,91802,13846],{"mathvariant":2287},[898,91804,900],{},[895,91806,91807,91809],{},[898,91808,13846],{"mathvariant":2287},[2884,91810,91811,91813],{},[898,91812,6796],{},[2111,91814,2963],{},[898,91816,2186],{"mathvariant":2287},[24360,91818],{"width":31674},[24360,91820,91821],{},[1942,91822,91823],{},"(6.2)",[902,91825,91826],{"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}",[724,91828,91829,91830,91864,91865,91895,91896,1700,91899,2186],{},"Pro pevné ",[883,91831,91833],{"className":91832},[886],[888,91834,91835],{"xmlns":890},[892,91836,91837,91861],{},[895,91838,91839,91845,91847,91849,91851,91857,91859],{},[2884,91840,91841,91843],{},[898,91842,6796],{},[2111,91844,2238],{},[1711,91846,1836],{},[898,91848,207],{},[1711,91850,1726],{"separator":1725},[2884,91852,91853,91855],{},[898,91854,6796],{},[2111,91856,2963],{},[1711,91858,1836],{},[898,91860,2223],{},[902,91862,91863],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,91866,91868],{"className":91867},[886],[888,91869,91870],{"xmlns":890},[892,91871,91872,91892],{},[895,91873,91874,91876,91882,91884,91886,91888,91890],{},[898,91875,1790],{},[2884,91877,91878,91880],{},[898,91879,900],{},[2111,91881,2238],{},[1711,91883,1714],{"stretchy":1713},[898,91885,207],{},[1711,91887,1726],{"separator":1725},[898,91889,2223],{},[1711,91891,1735],{"stretchy":1713},[902,91893,91894],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,91897,91898],{},"v bodě (na hladině)",[883,91900,91902],{"className":91901},[886],[888,91903,91904],{"xmlns":890},[892,91905,91906,91918],{},[895,91907,91908,91910,91912,91914,91916],{},[1711,91909,5144],{"stretchy":1713},[898,91911,207],{},[1711,91913,1726],{"separator":1725},[898,91915,2223],{},[1711,91917,5163],{"stretchy":1713},[902,91919,14797],{"encoding":904},[1921,91921,91922],{},[724,91923,91924,91926,91927,91957,91986,91987,6621,92000,6635,92017,92038,92039,6682,92056,6696,92069,92086,92087,92109,92110,92139,92140,10454,92160,92177],{},[883,91925,2678],{}," Intuice — co říká ",[883,91928,91930],{"className":91929},[886],[888,91931,91932],{"xmlns":890},[892,91933,91934,91954],{},[895,91935,91936,91938,91944,91946,91948,91950,91952],{},[898,91937,1790],{},[2884,91939,91940,91942],{},[898,91941,900],{},[2111,91943,2238],{},[1711,91945,1714],{"stretchy":1713},[898,91947,207],{},[1711,91949,1726],{"separator":1725},[898,91951,2223],{},[1711,91953,1735],{"stretchy":1713},[902,91955,91956],{"encoding":904},"MU_1(a,b)",[883,91958,91960],{"className":91959},[886],[888,91961,91962],{"xmlns":890},[892,91963,91964,91984],{},[895,91965,91966,91968,91974,91976,91978,91980,91982],{},[898,91967,1790],{},[2884,91969,91970,91972],{},[898,91971,900],{},[2111,91973,2238],{},[1711,91975,1714],{"stretchy":1713},[898,91977,207],{},[1711,91979,1726],{"separator":1725},[898,91981,2223],{},[1711,91983,1735],{"stretchy":1713},[902,91985,91894],{"encoding":904}," je rychlost změny ",[883,91988,91990],{"className":91989},[886],[888,91991,91992],{"xmlns":890},[892,91993,91994,91998],{},[895,91995,91996],{},[898,91997,900],{},[902,91999,900],{"encoding":904},[883,92001,92003],{"className":92002},[886],[888,92004,92005],{"xmlns":890},[892,92006,92007,92015],{},[895,92008,92009],{},[2884,92010,92011,92013],{},[898,92012,6796],{},[2111,92014,2238],{},[902,92016,32600],{"encoding":904},[883,92018,92020],{"className":92019},[886],[888,92021,92022],{"xmlns":890},[892,92023,92024,92036],{},[895,92025,92026,92028,92030,92032,92034],{},[1711,92027,5144],{"stretchy":1713},[898,92029,207],{},[1711,92031,1726],{"separator":1725},[898,92033,2223],{},[1711,92035,5163],{"stretchy":1713},[902,92037,14797],{"encoding":904},". Přibližně: změní-li se ",[883,92040,92042],{"className":92041},[886],[888,92043,92044],{"xmlns":890},[892,92045,92046,92054],{},[895,92047,92048],{},[2884,92049,92050,92052],{},[898,92051,6796],{},[2111,92053,2238],{},[902,92055,32600],{"encoding":904},[883,92057,92059],{"className":92058},[886],[888,92060,92061],{"xmlns":890},[892,92062,92063,92067],{},[895,92064,92065],{},[898,92066,207],{},[902,92068,207],{"encoding":904},[883,92070,92072],{"className":92071},[886],[888,92073,92074],{"xmlns":890},[892,92075,92076,92084],{},[895,92077,92078,92080,92082],{},[898,92079,207],{},[1711,92081,2095],{},[2111,92083,2238],{},[902,92085,6714],{"encoding":904}," při pevném ",[883,92088,92090],{"className":92089},[886],[888,92091,92092],{"xmlns":890},[892,92093,92094,92106],{},[895,92095,92096,92102,92104],{},[2884,92097,92098,92100],{},[898,92099,6796],{},[2111,92101,2963],{},[1711,92103,1836],{},[898,92105,2223],{},[902,92107,92108],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,92111,92113],{"className":92112},[886],[888,92114,92115],{"xmlns":890},[892,92116,92117,92137],{},[895,92118,92119,92121,92127,92129,92131,92133,92135],{},[898,92120,1790],{},[2884,92122,92123,92125],{},[898,92124,900],{},[2111,92126,2238],{},[1711,92128,1714],{"stretchy":1713},[898,92130,207],{},[1711,92132,1726],{"separator":1725},[898,92134,2223],{},[1711,92136,1735],{"stretchy":1713},[902,92138,91894],{"encoding":904},". Stejně tak ",[883,92141,92143],{"className":92142},[886],[888,92144,92145],{"xmlns":890},[892,92146,92147,92157],{},[895,92148,92149,92151],{},[898,92150,1790],{},[2884,92152,92153,92155],{},[898,92154,900],{},[2111,92156,2963],{},[902,92158,92159],{"encoding":904},"MU_2",[883,92161,92163],{"className":92162},[886],[888,92164,92165],{"xmlns":890},[892,92166,92167,92175],{},[895,92168,92169],{},[2884,92170,92171,92173],{},[898,92172,6796],{},[2111,92174,2963],{},[902,92176,32619],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,92179,83809],{"id":92180},"totální-diferenciál",[724,92182,92183,92184,51938,92200,92230,92231,2062],{},"Přibližnou změnu užitečnosti ",[883,92185,92187],{"className":92186},[886],[888,92188,92189],{"xmlns":890},[892,92190,92191,92197],{},[895,92192,92193,92195],{},[898,92194,6892],{"mathvariant":2287},[898,92196,900],{},[902,92198,92199],{"encoding":904},"\\Delta U",[883,92201,92203],{"className":92202},[886],[888,92204,92205],{"xmlns":890},[892,92206,92207,92227],{},[895,92208,92209,92211,92217,92219,92221],{},[898,92210,2098],{"mathvariant":2287},[2884,92212,92213,92215],{},[898,92214,6796],{},[2111,92216,2238],{},[1711,92218,1726],{"separator":1725},[898,92220,2098],{"mathvariant":2287},[2884,92222,92223,92225],{},[898,92224,6796],{},[2111,92226,2963],{},[902,92228,92229],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,92232,92233],{},"totálního diferenciálu",[883,92235,92237],{"className":92236},[886],[888,92238,92239],{"xmlns":890,"display":31664},[892,92240,92241,92342],{},[24352,92242,92243],{"width":31669},[24357,92244,92245,92247,92335,92337],{},[24360,92246],{"width":31674},[24360,92248,92249],{},[895,92250,92251,92253,92255,92257,92259,92261,92263,92271,92273,92279,92281,92289,92291,92297,92299,92301,92307,92309,92315,92317,92319,92325,92327,92333],{},[898,92252,6892],{"mathvariant":2287},[898,92254,900],{},[1711,92256,6740],{},[898,92258,2098],{"mathvariant":2287},[898,92260,900],{},[1711,92262,1836],{},[13142,92264,92265,92267,92269],{},[898,92266,900],{},[2111,92268,2238],{},[1711,92270,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[898,92272,2098],{"mathvariant":2287},[2884,92274,92275,92277],{},[898,92276,6796],{},[2111,92278,2238],{},[1711,92280,2095],{},[13142,92282,92283,92285,92287],{},[898,92284,900],{},[2111,92286,2963],{},[1711,92288,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[898,92290,2098],{"mathvariant":2287},[2884,92292,92293,92295],{},[898,92294,6796],{},[2111,92296,2963],{},[1711,92298,1836],{},[898,92300,1790],{},[2884,92302,92303,92305],{},[898,92304,900],{},[2111,92306,2238],{},[898,92308,2098],{"mathvariant":2287},[2884,92310,92311,92313],{},[898,92312,6796],{},[2111,92314,2238],{},[1711,92316,2095],{},[898,92318,1790],{},[2884,92320,92321,92323],{},[898,92322,900],{},[2111,92324,2963],{},[898,92326,2098],{"mathvariant":2287},[2884,92328,92329,92331],{},[898,92330,6796],{},[2111,92332,2963],{},[898,92334,2186],{"mathvariant":2287},[24360,92336],{"width":31674},[24360,92338,92339],{},[1942,92340,92341],{},"(6.3)",[902,92343,92344],{"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}",[724,92346,79067,92347,2186],{},[883,92348,92350],{"className":92349},[886],[888,92351,92352],{"xmlns":890},[892,92353,92354,92424],{},[895,92355,92356,92358,92360,92362,92364,92366,92372,92374,92376,92382,92384,92390,92392,92394,92400,92402,92404,92406,92408,92414,92416,92422],{},[898,92357,6892],{"mathvariant":2287},[898,92359,900],{},[1711,92361,1836],{},[898,92363,900],{},[1711,92365,1714],{"stretchy":1713},[2884,92367,92368,92370],{},[898,92369,6796],{},[2111,92371,2238],{},[1711,92373,2095],{},[898,92375,2098],{"mathvariant":2287},[2884,92377,92378,92380],{},[898,92379,6796],{},[2111,92381,2238],{},[1711,92383,1726],{"separator":1725},[2884,92385,92386,92388],{},[898,92387,6796],{},[2111,92389,2963],{},[1711,92391,2095],{},[898,92393,2098],{"mathvariant":2287},[2884,92395,92396,92398],{},[898,92397,6796],{},[2111,92399,2963],{},[1711,92401,1735],{"stretchy":1713},[1711,92403,2460],{},[898,92405,900],{},[1711,92407,1714],{"stretchy":1713},[2884,92409,92410,92412],{},[898,92411,6796],{},[2111,92413,2238],{},[1711,92415,1726],{"separator":1725},[2884,92417,92418,92420],{},[898,92419,6796],{},[2111,92421,2963],{},[1711,92423,1735],{"stretchy":1713},[902,92425,92426],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,92428,92430],{"id":92429},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,92432,92433,92434,92437,92438,92441],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,92435,92436],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,92439,92440],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,92443,92444,92447,92448,45412,92474,92500,92501,1343,92533,92565,92566,2009,92620,92674],{},[38,92445,92446],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,92449,92451],{"className":92450},[886],[888,92452,92453],{"xmlns":890},[892,92454,92455,92471],{},[895,92456,92457,92463,92465],{},[2884,92458,92459,92461],{},[898,92460,6796],{},[2111,92462,2963],{},[1711,92464,1836],{},[2884,92466,92467,92469],{},[898,92468,207],{},[2111,92470,2113],{},[902,92472,92473],{"encoding":904},"Q_2 = a_0",[883,92475,92477],{"className":92476},[886],[888,92478,92479],{"xmlns":890},[892,92480,92481,92497],{},[895,92482,92483,92489,92491],{},[2884,92484,92485,92487],{},[898,92486,6796],{},[2111,92488,2238],{},[1711,92490,1836],{},[2884,92492,92493,92495],{},[898,92494,2223],{},[2111,92496,2113],{},[902,92498,92499],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,92502,92504],{"className":92503},[886],[888,92505,92506],{"xmlns":890},[892,92507,92508,92530],{},[895,92509,92510,92512,92514,92520,92522,92528],{},[898,92511,900],{},[1711,92513,1714],{"stretchy":1713},[2884,92515,92516,92518],{},[898,92517,6796],{},[2111,92519,2238],{},[1711,92521,1726],{"separator":1725},[2884,92523,92524,92526],{},[898,92525,207],{},[2111,92527,2113],{},[1711,92529,1735],{"stretchy":1713},[902,92531,92532],{"encoding":904},"U(Q_1, a_0)",[883,92534,92536],{"className":92535},[886],[888,92537,92538],{"xmlns":890},[892,92539,92540,92562],{},[895,92541,92542,92544,92546,92552,92554,92560],{},[898,92543,900],{},[1711,92545,1714],{"stretchy":1713},[2884,92547,92548,92550],{},[898,92549,2223],{},[2111,92551,2113],{},[1711,92553,1726],{"separator":1725},[2884,92555,92556,92558],{},[898,92557,6796],{},[2111,92559,2963],{},[1711,92561,1735],{"stretchy":1713},[902,92563,92564],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,92567,92569],{"className":92568},[886],[888,92570,92571],{"xmlns":890},[892,92572,92573,92617],{},[895,92574,92575,92613,92615],{},[2509,92576,92577],{"scriptlevel":2113,"displaystyle":1725},[2525,92578,92579,92603],{},[895,92580,92581,92583,92585,92587,92593,92595,92601],{},[898,92582,2098],{"mathvariant":2287},[898,92584,900],{},[1711,92586,1714],{"stretchy":1713},[2884,92588,92589,92591],{},[898,92590,6796],{},[2111,92592,2238],{},[1711,92594,1726],{"separator":1725},[2884,92596,92597,92599],{},[898,92598,207],{},[2111,92600,2113],{},[1711,92602,1735],{"stretchy":1713},[895,92604,92605,92607],{},[898,92606,2098],{"mathvariant":2287},[2884,92608,92609,92611],{},[898,92610,6796],{},[2111,92612,2238],{},[1711,92614,2123],{},[2111,92616,2113],{},[902,92618,92619],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,92621,92623],{"className":92622},[886],[888,92624,92625],{"xmlns":890},[892,92626,92627,92671],{},[895,92628,92629,92667,92669],{},[2509,92630,92631],{"scriptlevel":2113,"displaystyle":1725},[2525,92632,92633,92657],{},[895,92634,92635,92637,92639,92641,92647,92649,92655],{},[898,92636,2098],{"mathvariant":2287},[898,92638,900],{},[1711,92640,1714],{"stretchy":1713},[2884,92642,92643,92645],{},[898,92644,2223],{},[2111,92646,2113],{},[1711,92648,1726],{"separator":1725},[2884,92650,92651,92653],{},[898,92652,6796],{},[2111,92654,2963],{},[1711,92656,1735],{"stretchy":1713},[895,92658,92659,92661],{},[898,92660,2098],{"mathvariant":2287},[2884,92662,92663,92665],{},[898,92664,6796],{},[2111,92666,2963],{},[1711,92668,2123],{},[2111,92670,2113],{},[902,92672,92673],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,92676,92678],{"className":92677},[886],[888,92679,92680],{"xmlns":890,"display":31664},[892,92681,92682,92727],{},[24352,92683,92684],{"width":31669},[24357,92685,92686,92688,92720,92722],{},[24360,92687],{"width":31674},[24360,92689,92690],{},[895,92691,92692,92700,92702,92704,92706,92708,92716,92718],{},[13142,92693,92694,92696,92698],{},[898,92695,900],{},[2111,92697,2238],{},[1711,92699,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,92701,2123],{},[2111,92703,2113],{},[1711,92705,1726],{"separator":1725},[2102,92707],{"width":4981},[13142,92709,92710,92712,92714],{},[898,92711,900],{},[2111,92713,2963],{},[1711,92715,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,92717,2123],{},[2111,92719,2126],{},[24360,92721],{"width":31674},[24360,92723,92724],{},[1942,92725,92726],{},"(6.4)",[902,92728,92729],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,92731,92732,92733,92735],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,92734,56275],{}," — užitečnost roste s množstvím každého zboží.",[724,92737,92738,92741,92742,92772,92773,2062],{},[38,92739,92740],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,92743,92745],{"className":92744},[886],[888,92746,92747],{"xmlns":890},[892,92748,92749,92769],{},[895,92750,92751,92759,92761],{},[13142,92752,92753,92755,92757],{},[898,92754,900],{},[2111,92756,2238],{},[1711,92758,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,92760,1726],{"separator":1725},[13142,92762,92763,92765,92767],{},[898,92764,900],{},[2111,92766,2963],{},[1711,92768,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,92770,92771],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,92774,92775],{},"záporné",[883,92777,92779],{"className":92778},[886],[888,92780,92781],{"xmlns":890,"display":31664},[892,92782,92783,92836],{},[24352,92784,92785],{"width":31669},[24357,92786,92787,92789,92829,92831],{},[24360,92788],{"width":31674},[24360,92790,92791],{},[895,92792,92793,92805,92807,92809,92811,92813,92825,92827],{},[13142,92794,92795,92797,92799],{},[898,92796,900],{},[2111,92798,6907],{},[895,92800,92801,92803],{},[1711,92802,5225],{"mathvariant":2287},[1711,92804,5225],{"mathvariant":2287},[1711,92806,2109],{},[2111,92808,2113],{},[1711,92810,1726],{"separator":1725},[2102,92812],{"width":4981},[13142,92814,92815,92817,92819],{},[898,92816,900],{},[2111,92818,36144],{},[895,92820,92821,92823],{},[1711,92822,5225],{"mathvariant":2287},[1711,92824,5225],{"mathvariant":2287},[1711,92826,2109],{},[2111,92828,2126],{},[24360,92830],{"width":31674},[24360,92832,92833],{},[1942,92834,92835],{},"(6.5)",[902,92837,92838],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,92840,92841,92842,92845,92846,2186],{},"Podmínka (6.5) je známa jako ",[38,92843,92844],{},"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 ",[207,92847,92849],{"className":92848,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,92851,92852,92853,2009,92885,92917,92918,2009,92944,92970,92971,92999,93000,2009,93002,93004,93005,93040],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,92854,92856],{"className":92855},[886],[888,92857,92858],{"xmlns":890},[892,92859,92860,92882],{},[895,92861,92862,92864,92866,92872,92874,92880],{},[898,92863,900],{},[1711,92865,1714],{"stretchy":1713},[2884,92867,92868,92870],{},[898,92869,6796],{},[2111,92871,2238],{},[1711,92873,1726],{"separator":1725},[2884,92875,92876,92878],{},[898,92877,2223],{},[2111,92879,2113],{},[1711,92881,1735],{"stretchy":1713},[902,92883,92884],{"encoding":904},"U(Q_1, b_0)",[883,92886,92888],{"className":92887},[886],[888,92889,92890],{"xmlns":890},[892,92891,92892,92914],{},[895,92893,92894,92896,92898,92904,92906,92912],{},[898,92895,900],{},[1711,92897,1714],{"stretchy":1713},[2884,92899,92900,92902],{},[898,92901,207],{},[2111,92903,2113],{},[1711,92905,1726],{"separator":1725},[2884,92907,92908,92910],{},[898,92909,6796],{},[2111,92911,2963],{},[1711,92913,1735],{"stretchy":1713},[902,92915,92916],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,92919,92921],{"className":92920},[886],[888,92922,92923],{"xmlns":890},[892,92924,92925,92941],{},[895,92926,92927,92929,92931,92933,92939],{},[1711,92928,1714],{"stretchy":1713},[898,92930,900],{},[1711,92932,1726],{"separator":1725},[2884,92934,92935,92937],{},[898,92936,6796],{},[2111,92938,2238],{},[1711,92940,1735],{"stretchy":1713},[902,92942,92943],{"encoding":904},"(U, Q_1)",[883,92945,92947],{"className":92946},[886],[888,92948,92949],{"xmlns":890},[892,92950,92951,92967],{},[895,92952,92953,92955,92957,92959,92965],{},[1711,92954,1714],{"stretchy":1713},[898,92956,900],{},[1711,92958,1726],{"separator":1725},[2884,92960,92961,92963],{},[898,92962,6796],{},[2111,92964,2963],{},[1711,92966,1735],{"stretchy":1713},[902,92968,92969],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,92972,92974],{"className":92973},[886],[888,92975,92976],{"xmlns":890},[892,92977,92978,92996],{},[895,92979,92980,92982,92984,92986,92988,92990,92992,92994],{},[898,92981,900],{},[1711,92983,1714],{"stretchy":1713},[2111,92985,2113],{},[1711,92987,1726],{"separator":1725},[2111,92989,2113],{},[1711,92991,1735],{"stretchy":1713},[1711,92993,1836],{},[2111,92995,2113],{},[902,92997,92998],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,93001,3341],{},[38,93003,42086],{},". Typický tvar grafu ",[883,93006,93008],{"className":93007},[886],[888,93009,93010],{"xmlns":890},[892,93011,93012,93038],{},[895,93013,93014,93016,93018,93020,93022,93028,93030,93036],{},[898,93015,900],{},[1711,93017,1836],{},[898,93019,900],{},[1711,93021,1714],{"stretchy":1713},[2884,93023,93024,93026],{},[898,93025,6796],{},[2111,93027,2238],{},[1711,93029,1726],{"separator":1725},[2884,93031,93032,93034],{},[898,93033,6796],{},[2111,93035,2963],{},[1711,93037,1735],{"stretchy":1713},[902,93039,91054],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,93042,93043],{},[614,93044,93045,93046,92086,93074,93095,93096,92086,93124,93146],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,93047,93049],{"className":93048},[886],[888,93050,93051],{"xmlns":890},[892,93052,93053,93071],{},[895,93054,93055,93057,93059,93065,93067,93069],{},[898,93056,900],{},[1711,93058,1714],{"stretchy":1713},[2884,93060,93061,93063],{},[898,93062,6796],{},[2111,93064,2238],{},[1711,93066,1726],{"separator":1725},[898,93068,2223],{},[1711,93070,1735],{"stretchy":1713},[902,93072,93073],{"encoding":904},"U(Q_1, b)",[883,93075,93077],{"className":93076},[886],[888,93078,93079],{"xmlns":890},[892,93080,93081,93093],{},[895,93082,93083,93089,93091],{},[2884,93084,93085,93087],{},[898,93086,6796],{},[2111,93088,2963],{},[1711,93090,1836],{},[898,93092,2223],{},[902,93094,92108],{"encoding":904}," (vlevo) a ",[883,93097,93099],{"className":93098},[886],[888,93100,93101],{"xmlns":890},[892,93102,93103,93121],{},[895,93104,93105,93107,93109,93111,93113,93119],{},[898,93106,900],{},[1711,93108,1714],{"stretchy":1713},[898,93110,207],{},[1711,93112,1726],{"separator":1725},[2884,93114,93115,93117],{},[898,93116,6796],{},[2111,93118,2963],{},[1711,93120,1735],{"stretchy":1713},[902,93122,93123],{"encoding":904},"U(a, Q_2)",[883,93125,93127],{"className":93126},[886],[888,93128,93129],{"xmlns":890},[892,93130,93131,93143],{},[895,93132,93133,93139,93141],{},[2884,93134,93135,93137],{},[898,93136,6796],{},[2111,93138,2238],{},[1711,93140,1836],{},[898,93142,207],{},[902,93144,93145],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,93148,93149],{},[614,93150,93151,93152,93187,93188,93218,93219,2009,93242,93264,93265,2186],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,93153,93155],{"className":93154},[886],[888,93156,93157],{"xmlns":890},[892,93158,93159,93185],{},[895,93160,93161,93163,93165,93167,93169,93175,93177,93183],{},[898,93162,900],{},[1711,93164,1836],{},[898,93166,900],{},[1711,93168,1714],{"stretchy":1713},[2884,93170,93171,93173],{},[898,93172,6796],{},[2111,93174,2238],{},[1711,93176,1726],{"separator":1725},[2884,93178,93179,93181],{},[898,93180,6796],{},[2111,93182,2963],{},[1711,93184,1735],{"stretchy":1713},[902,93186,91054],{"encoding":904}," nad rovinou ",[883,93189,93191],{"className":93190},[886],[888,93192,93193],{"xmlns":890},[892,93194,93195,93215],{},[895,93196,93197,93199,93205,93207,93213],{},[1711,93198,1714],{"stretchy":1713},[2884,93200,93201,93203],{},[898,93202,6796],{},[2111,93204,2238],{},[1711,93206,1726],{"separator":1725},[2884,93208,93209,93211],{},[898,93210,6796],{},[2111,93212,2963],{},[1711,93214,1735],{"stretchy":1713},[902,93216,93217],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,93220,93222],{"className":93221},[886],[888,93223,93224],{"xmlns":890},[892,93225,93226,93239],{},[895,93227,93228,93234,93236],{},[2884,93229,93230,93232],{},[898,93231,6796],{},[2111,93233,2238],{},[1711,93235,1836],{},[1942,93237,93238],{},"const",[902,93240,93241],{"encoding":904},"Q_1 = \\text{const}",[883,93243,93245],{"className":93244},[886],[888,93246,93247],{"xmlns":890},[892,93248,93249,93261],{},[895,93250,93251,93257,93259],{},[2884,93252,93253,93255],{},[898,93254,6796],{},[2111,93256,2963],{},[1711,93258,1836],{},[1942,93260,93238],{},[902,93262,93263],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,93266,93268],{"className":93267},[886],[888,93269,93270],{"xmlns":890},[892,93271,93272,93298],{},[895,93273,93274,93276,93278,93284,93286,93292,93294,93296],{},[898,93275,900],{},[1711,93277,1714],{"stretchy":1713},[2884,93279,93280,93282],{},[898,93281,6796],{},[2111,93283,2238],{},[1711,93285,1726],{"separator":1725},[2884,93287,93288,93290],{},[898,93289,6796],{},[2111,93291,2963],{},[1711,93293,1735],{"stretchy":1713},[1711,93295,1836],{},[898,93297,2090],{},[902,93299,13743],{"encoding":904},[198,93301,93303,93304],{"id":93302},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,93305,93307],{"className":93306},[886],[888,93308,93309],{"xmlns":890},[892,93310,93311,93345],{},[895,93312,93313,93315,93317,93331],{},[898,93314,900],{},[1711,93316,1836],{},[13142,93318,93319,93321,93323],{},[898,93320,6796],{},[2111,93322,2238],{},[895,93324,93325,93327,93329],{},[2111,93326,2238],{},[898,93328,8659],{"mathvariant":2287},[2111,93330,2963],{},[13142,93332,93333,93335,93337],{},[898,93334,6796],{},[2111,93336,2963],{},[895,93338,93339,93341,93343],{},[2111,93340,2238],{},[898,93342,8659],{"mathvariant":2287},[2111,93344,3034],{},[902,93346,93347],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,93349,93350],{},[38,93351,93352],{},"Ověření (6.4) a (6.5).",[883,93354,93356],{"className":93355},[886],[888,93357,93358],{"xmlns":890,"display":31664},[892,93359,93360,93464],{},[895,93361,93362,93370,93372,93380,93396,93410,93412,93414,93422,93424,93432,93446,93462],{},[13142,93363,93364,93366,93368],{},[898,93365,900],{},[2111,93367,2238],{},[1711,93369,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,93371,1836],{},[2509,93373,93374],{"scriptlevel":2113,"displaystyle":1713},[2525,93375,93376,93378],{},[2111,93377,2238],{},[2111,93379,2963],{},[13142,93381,93382,93384,93386],{},[898,93383,6796],{},[2111,93385,2238],{},[895,93387,93388,93390,93392,93394],{},[1711,93389,2460],{},[2111,93391,2238],{},[898,93393,8659],{"mathvariant":2287},[2111,93395,2963],{},[13142,93397,93398,93400,93402],{},[898,93399,6796],{},[2111,93401,2963],{},[895,93403,93404,93406,93408],{},[2111,93405,2238],{},[898,93407,8659],{"mathvariant":2287},[2111,93409,3034],{},[1711,93411,1726],{"separator":1725},[2102,93413],{"width":4981},[13142,93415,93416,93418,93420],{},[898,93417,900],{},[2111,93419,2963],{},[1711,93421,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,93423,1836],{},[2509,93425,93426],{"scriptlevel":2113,"displaystyle":1713},[2525,93427,93428,93430],{},[2111,93429,2238],{},[2111,93431,3034],{},[13142,93433,93434,93436,93438],{},[898,93435,6796],{},[2111,93437,2238],{},[895,93439,93440,93442,93444],{},[2111,93441,2238],{},[898,93443,8659],{"mathvariant":2287},[2111,93445,2963],{},[13142,93447,93448,93450,93452],{},[898,93449,6796],{},[2111,93451,2963],{},[895,93453,93454,93456,93458,93460],{},[1711,93455,2460],{},[2111,93457,2963],{},[898,93459,8659],{"mathvariant":2287},[2111,93461,3034],{},[1711,93463,1726],{"separator":1725},[902,93465,93466],{"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},",[724,93468,93469,93470,93504],{},"zřejmě ",[883,93471,93473],{"className":93472},[886],[888,93474,93475],{"xmlns":890},[892,93476,93477,93501],{},[895,93478,93479,93487,93489,93497,93499],{},[13142,93480,93481,93483,93485],{},[898,93482,900],{},[2111,93484,2238],{},[1711,93486,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,93488,1726],{"separator":1725},[13142,93490,93491,93493,93495],{},[898,93492,900],{},[2111,93494,2963],{},[1711,93496,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,93498,2123],{},[2111,93500,2113],{},[902,93502,93503],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,93506,93508],{"className":93507},[886],[888,93509,93510],{"xmlns":890,"display":31664},[892,93511,93512,93628],{},[895,93513,93514,93526,93528,93530,93538,93554,93568,93570,93572,93584,93586,93588,93596,93610,93626],{},[13142,93515,93516,93518,93520],{},[898,93517,900],{},[2111,93519,6907],{},[895,93521,93522,93524],{},[1711,93523,5225],{"mathvariant":2287},[1711,93525,5225],{"mathvariant":2287},[1711,93527,1836],{},[1711,93529,2460],{},[2509,93531,93532],{"scriptlevel":2113,"displaystyle":1713},[2525,93533,93534,93536],{},[2111,93535,2238],{},[2111,93537,6369],{},[13142,93539,93540,93542,93544],{},[898,93541,6796],{},[2111,93543,2238],{},[895,93545,93546,93548,93550,93552],{},[1711,93547,2460],{},[2111,93549,3034],{},[898,93551,8659],{"mathvariant":2287},[2111,93553,2963],{},[13142,93555,93556,93558,93560],{},[898,93557,6796],{},[2111,93559,2963],{},[895,93561,93562,93564,93566],{},[2111,93563,2238],{},[898,93565,8659],{"mathvariant":2287},[2111,93567,3034],{},[1711,93569,1726],{"separator":1725},[2102,93571],{"width":4981},[13142,93573,93574,93576,93578],{},[898,93575,900],{},[2111,93577,36144],{},[895,93579,93580,93582],{},[1711,93581,5225],{"mathvariant":2287},[1711,93583,5225],{"mathvariant":2287},[1711,93585,1836],{},[1711,93587,2460],{},[2509,93589,93590],{"scriptlevel":2113,"displaystyle":1713},[2525,93591,93592,93594],{},[2111,93593,2963],{},[2111,93595,7990],{},[13142,93597,93598,93600,93602],{},[898,93599,6796],{},[2111,93601,2238],{},[895,93603,93604,93606,93608],{},[2111,93605,2238],{},[898,93607,8659],{"mathvariant":2287},[2111,93609,2963],{},[13142,93611,93612,93614,93616],{},[898,93613,6796],{},[2111,93615,2963],{},[895,93617,93618,93620,93622,93624],{},[1711,93619,2460],{},[2111,93621,4798],{},[898,93623,8659],{"mathvariant":2287},[2111,93625,3034],{},[1711,93627,1726],{"separator":1725},[902,93629,93630],{"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},",[724,93632,93633,93634,93676],{},"opět ",[883,93635,93637],{"className":93636},[886],[888,93638,93639],{"xmlns":890},[892,93640,93641,93673],{},[895,93642,93643,93655,93657,93669,93671],{},[13142,93644,93645,93647,93649],{},[898,93646,900],{},[2111,93648,6907],{},[895,93650,93651,93653],{},[1711,93652,5225],{"mathvariant":2287},[1711,93654,5225],{"mathvariant":2287},[1711,93656,1726],{"separator":1725},[13142,93658,93659,93661,93663],{},[898,93660,900],{},[2111,93662,36144],{},[895,93664,93665,93667],{},[1711,93666,5225],{"mathvariant":2287},[1711,93668,5225],{"mathvariant":2287},[1711,93670,2109],{},[2111,93672,2113],{},[902,93674,93675],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,93678,93679],{},[38,93680,93681,93682,2186],{},"(a) Mezní užitečnosti v bodě ",[883,93683,93685],{"className":93684},[886],[888,93686,93687],{"xmlns":890},[892,93688,93689,93701],{},[895,93690,93691,93693,93695,93697,93699],{},[1711,93692,5144],{"stretchy":1713},[2111,93694,4282],{},[1711,93696,1726],{"separator":1725},[2111,93698,12357],{},[1711,93700,5163],{"stretchy":1713},[902,93702,93703],{"encoding":904},"[100, 200]",[883,93705,93707],{"className":93706},[886],[888,93708,93709],{"xmlns":890,"display":31664},[892,93710,93711,93778],{},[895,93712,93713,93715,93721,93723,93725,93727,93729,93731,93733,93741,93743,93757,93759,93771,93773,93776],{},[898,93714,1790],{},[2884,93716,93717,93719],{},[898,93718,900],{},[2111,93720,2238],{},[1711,93722,1714],{"stretchy":1713},[2111,93724,4282],{},[1711,93726,1726],{"separator":1725},[2111,93728,12357],{},[1711,93730,1735],{"stretchy":1713},[1711,93732,1836],{},[2509,93734,93735],{"scriptlevel":2113,"displaystyle":1713},[2525,93736,93737,93739],{},[2111,93738,2238],{},[2111,93740,2963],{},[1711,93742,4795],{},[1716,93744,93745,93747],{},[2111,93746,4282],{},[895,93748,93749,93751,93753,93755],{},[1711,93750,2460],{},[2111,93752,2238],{},[898,93754,8659],{"mathvariant":2287},[2111,93756,2963],{},[1711,93758,4795],{},[1716,93760,93761,93763],{},[2111,93762,12357],{},[895,93764,93765,93767,93769],{},[2111,93766,2238],{},[898,93768,8659],{"mathvariant":2287},[2111,93770,3034],{},[1711,93772,9881],{},[2111,93774,93775],{},"0,4204",[1711,93777,1726],{"separator":1725},[902,93779,93780],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,93782,93784],{"className":93783},[886],[888,93785,93786],{"xmlns":890,"display":31664},[892,93787,93788,93853],{},[895,93789,93790,93792,93798,93800,93802,93804,93806,93808,93810,93818,93820,93832,93834,93848,93850],{},[898,93791,1790],{},[2884,93793,93794,93796],{},[898,93795,900],{},[2111,93797,2963],{},[1711,93799,1714],{"stretchy":1713},[2111,93801,4282],{},[1711,93803,1726],{"separator":1725},[2111,93805,12357],{},[1711,93807,1735],{"stretchy":1713},[1711,93809,1836],{},[2509,93811,93812],{"scriptlevel":2113,"displaystyle":1713},[2525,93813,93814,93816],{},[2111,93815,2238],{},[2111,93817,3034],{},[1711,93819,4795],{},[1716,93821,93822,93824],{},[2111,93823,4282],{},[895,93825,93826,93828,93830],{},[2111,93827,2238],{},[898,93829,8659],{"mathvariant":2287},[2111,93831,2963],{},[1711,93833,4795],{},[1716,93835,93836,93838],{},[2111,93837,12357],{},[895,93839,93840,93842,93844,93846],{},[1711,93841,2460],{},[2111,93843,2963],{},[898,93845,8659],{"mathvariant":2287},[2111,93847,3034],{},[1711,93849,9881],{},[2111,93851,93852],{},"0,63067.",[902,93854,93855],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,93857,93858,1700,93860,93895,93896,93917,93918,93935],{},[614,93859,13192],{},[883,93861,93863],{"className":93862},[886],[888,93864,93865],{"xmlns":890},[892,93866,93867,93892],{},[895,93868,93869,93871,93877,93879,93881,93883,93885,93887,93889],{},[898,93870,1790],{},[2884,93872,93873,93875],{},[898,93874,900],{},[2111,93876,2963],{},[1711,93878,1714],{"stretchy":1713},[2111,93880,4282],{},[1711,93882,1726],{"separator":1725},[2111,93884,12357],{},[1711,93886,1735],{"stretchy":1713},[1711,93888,9881],{},[2111,93890,93891],{},"0,63067",[902,93893,93894],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,93897,93899],{"className":93898},[886],[888,93900,93901],{"xmlns":890},[892,93902,93903,93915],{},[895,93904,93905,93907,93909,93911,93913],{},[1711,93906,5144],{"stretchy":1713},[2111,93908,4282],{},[1711,93910,1726],{"separator":1725},[2111,93912,12357],{},[1711,93914,5163],{"stretchy":1713},[902,93916,93703],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,93919,93921],{"className":93920},[886],[888,93922,93923],{"xmlns":890},[892,93924,93925,93933],{},[895,93926,93927],{},[2884,93928,93929,93931],{},[898,93930,6796],{},[2111,93932,2963],{},[902,93934,32619],{"encoding":904}," přibližně o 0,63067.",[724,93937,93938,93957,93958,42782,93979,93996,93997,94023,94024,94041,94042,3239],{},[38,93939,93940,93941,93956],{},"(b) Odhad změny ",[883,93942,93944],{"className":93943},[886],[888,93945,93946],{"xmlns":890},[892,93947,93948,93954],{},[895,93949,93950,93952],{},[898,93951,6892],{"mathvariant":2287},[898,93953,900],{},[902,93955,92199],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,93959,93961],{"className":93960},[886],[888,93962,93963],{"xmlns":890},[892,93964,93965,93977],{},[895,93966,93967,93969,93971,93973,93975],{},[1711,93968,5144],{"stretchy":1713},[2111,93970,4282],{},[1711,93972,1726],{"separator":1725},[2111,93974,12357],{},[1711,93976,5163],{"stretchy":1713},[902,93978,93703],{"encoding":904},[883,93980,93982],{"className":93981},[886],[888,93983,93984],{"xmlns":890},[892,93985,93986,93994],{},[895,93987,93988],{},[2884,93989,93990,93992],{},[898,93991,6796],{},[2111,93993,2238],{},[902,93995,32600],{"encoding":904}," na 98 (tj. ",[883,93998,94000],{"className":93999},[886],[888,94001,94002],{"xmlns":890},[892,94003,94004,94020],{},[895,94005,94006,94008,94014,94016,94018],{},[898,94007,2098],{"mathvariant":2287},[2884,94009,94010,94012],{},[898,94011,6796],{},[2111,94013,2238],{},[1711,94015,1836],{},[1711,94017,2460],{},[2111,94019,2963],{},[902,94021,94022],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,94025,94027],{"className":94026},[886],[888,94028,94029],{"xmlns":890},[892,94030,94031,94039],{},[895,94032,94033],{},[2884,94034,94035,94037],{},[898,94036,6796],{},[2111,94038,2963],{},[902,94040,32619],{"encoding":904}," o 3 (tj. ",[883,94043,94045],{"className":94044},[886],[888,94046,94047],{"xmlns":890},[892,94048,94049,94063],{},[895,94050,94051,94053,94059,94061],{},[898,94052,2098],{"mathvariant":2287},[2884,94054,94055,94057],{},[898,94056,6796],{},[2111,94058,2963],{},[1711,94060,1836],{},[2111,94062,3034],{},[902,94064,94065],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,94067,94069],{"className":94068},[886],[888,94070,94071],{"xmlns":890,"display":31664},[892,94072,94073,94124],{},[895,94074,94075,94077,94079,94081,94083,94085,94087,94089,94091,94093,94095,94097,94099,94101,94103,94105,94107,94109,94111,94114,94116,94119,94121],{},[898,94076,6892],{"mathvariant":2287},[898,94078,900],{},[1711,94080,6740],{},[898,94082,2098],{"mathvariant":2287},[898,94084,900],{},[1711,94086,1836],{},[2111,94088,93775],{},[1711,94090,4795],{},[1711,94092,1714],{"stretchy":1713},[1711,94094,2460],{},[2111,94096,2963],{},[1711,94098,1735],{"stretchy":1713},[1711,94100,2095],{},[2111,94102,93891],{},[1711,94104,4795],{},[2111,94106,3034],{},[1711,94108,1836],{},[1711,94110,2460],{},[2111,94112,94113],{},"0,8408",[1711,94115,2095],{},[2111,94117,94118],{},"1,89201",[1711,94120,9881],{},[2111,94122,94123],{},"1,05.",[902,94125,94126],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,94128,94129,94130,94133,94134,94185,94186,2186],{},"Užitečnost se tedy zvýší přibližně o ",[38,94131,94132],{},"1,05",". Skutečná změna je ",[883,94135,94137],{"className":94136},[886],[888,94138,94139],{"xmlns":890},[892,94140,94141,94182],{},[895,94142,94143,94145,94147,94149,94151,94153,94156,94158,94161,94163,94165,94167,94169,94171,94173,94175,94177,94179],{},[898,94144,6892],{"mathvariant":2287},[898,94146,900],{},[1711,94148,1836],{},[898,94150,900],{},[1711,94152,1714],{"stretchy":1713},[2111,94154,94155],{},"98",[1711,94157,1726],{"separator":1725},[2111,94159,94160],{},"203",[1711,94162,1735],{"stretchy":1713},[1711,94164,2460],{},[898,94166,900],{},[1711,94168,1714],{"stretchy":1713},[2111,94170,4282],{},[1711,94172,1726],{"separator":1725},[2111,94174,12357],{},[1711,94176,1735],{"stretchy":1713},[1711,94178,9881],{},[2111,94180,94181],{},"1,031",[902,94183,94184],{"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 ",[883,94187,94189],{"className":94188},[886],[888,94190,94191],{"xmlns":890},[892,94192,94193,94213],{},[895,94194,94195,94197,94203,94205,94207],{},[898,94196,2098],{"mathvariant":2287},[2884,94198,94199,94201],{},[898,94200,6796],{},[2111,94202,2238],{},[1711,94204,1726],{"separator":1725},[898,94206,2098],{"mathvariant":2287},[2884,94208,94209,94211],{},[898,94210,6796],{},[2111,94212,2963],{},[902,94214,92229],{"encoding":904},[115,94216,94218],{"id":94217},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,94220,94221],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,94223,94225],{"className":94224},[886],[888,94226,94227],{"xmlns":890,"display":31664},[892,94228,94229,94288],{},[24352,94230,94231],{"width":31669},[24357,94232,94233,94235,94281,94283],{},[24360,94234],{"width":31674},[24360,94236,94237],{},[895,94238,94239,94241,94243,94249,94251,94257,94259,94261,94269,94271,94279],{},[898,94240,900],{},[1711,94242,1714],{"stretchy":1713},[2884,94244,94245,94247],{},[898,94246,6796],{},[2111,94248,2238],{},[1711,94250,1726],{"separator":1725},[2884,94252,94253,94255],{},[898,94254,6796],{},[2111,94256,2963],{},[1711,94258,1735],{"stretchy":1713},[1711,94260,1836],{},[13142,94262,94263,94265,94267],{},[898,94264,6796],{},[2111,94266,2238],{},[898,94268,207],{},[1711,94270,4795],{},[13142,94272,94273,94275,94277],{},[898,94274,6796],{},[2111,94276,2963],{},[898,94278,2223],{},[1711,94280,1726],{"separator":1725},[24360,94282],{"width":31674},[24360,94284,94285],{},[1942,94286,94287],{},"(6.6)",[902,94289,94290],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,94292,8298,94293,94311,94312,94314,94315,94319,94320,94350,94351,94373],{},[883,94294,94296],{"className":94295},[886],[888,94297,94298],{"xmlns":890},[892,94299,94300,94308],{},[895,94301,94302,94304,94306],{},[898,94303,207],{},[1711,94305,1726],{"separator":1725},[898,94307,2223],{},[902,94309,94310],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,94313,78297],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,94316,94318],{"className":94317,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,94321,94323],{"className":94322},[886],[888,94324,94325],{"xmlns":890},[892,94326,94327,94347],{},[895,94328,94329,94331,94333,94335,94337,94339,94341,94343,94345],{},[898,94330,207],{},[1711,94332,1726],{"separator":1725},[898,94334,2223],{},[1711,94336,10487],{},[1711,94338,1714],{"stretchy":1713},[2111,94340,2113],{},[1711,94342,1726],{"separator":1725},[2111,94344,2238],{},[1711,94346,1735],{"stretchy":1713},[902,94348,94349],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,94352,94354],{"className":94353},[886],[888,94355,94356],{"xmlns":890},[892,94357,94358,94370],{},[895,94359,94360,94362,94364,94366,94368],{},[898,94361,2223],{},[1711,94363,1836],{},[2111,94365,2238],{},[1711,94367,2460],{},[898,94369,207],{},[902,94371,94372],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,94375,94376],{},[1801,94377],{"alt":94378,"className":94379,"src":94380},"imek-cobb-douglas-3d-plus-ic",[210,1805],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,94382,94384],{"className":94383},[886],[888,94385,94386],{"xmlns":890,"display":31664},[892,94387,94388,94438],{},[895,94389,94390,94392,94394,94400,94402,94408,94410,94412,94420,94422,94436],{},[898,94391,900],{},[1711,94393,1714],{"stretchy":1713},[2884,94395,94396,94398],{},[898,94397,6796],{},[2111,94399,2238],{},[1711,94401,1726],{"separator":1725},[2884,94403,94404,94406],{},[898,94405,6796],{},[2111,94407,2963],{},[1711,94409,1735],{"stretchy":1713},[1711,94411,1836],{},[13142,94413,94414,94416,94418],{},[898,94415,6796],{},[2111,94417,2238],{},[898,94419,207],{},[1711,94421,4795],{},[13142,94423,94424,94426,94428],{},[898,94425,6796],{},[2111,94427,2963],{},[895,94429,94430,94432,94434],{},[2111,94431,2238],{},[1711,94433,2460],{},[898,94435,207],{},[898,94437,2186],{"mathvariant":2287},[902,94439,94440],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[1921,94442,94443,94492,94614,94748],{},[724,94444,94445,94447,94448],{},[883,94446,56293],{}," Příklad 6.3 — ověření vlastností pro ",[883,94449,94451],{"className":94450},[886],[888,94452,94453],{"xmlns":890},[892,94454,94455,94489],{},[895,94456,94457,94459,94461,94475],{},[898,94458,900],{},[1711,94460,1836],{},[13142,94462,94463,94465,94467],{},[898,94464,6796],{},[2111,94466,2238],{},[895,94468,94469,94471,94473],{},[2111,94470,2238],{},[898,94472,8659],{"mathvariant":2287},[2111,94474,6369],{},[13142,94476,94477,94479,94481],{},[898,94478,6796],{},[2111,94480,2963],{},[895,94482,94483,94485,94487],{},[2111,94484,3034],{},[898,94486,8659],{"mathvariant":2287},[2111,94488,6369],{},[902,94490,94491],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,94493,94495],{"className":94494},[886],[888,94496,94497],{"xmlns":890,"display":31664},[892,94498,94499,94611],{},[895,94500,94501,94509,94511,94519,94535,94549,94551,94553,94555,94557,94565,94567,94575,94589,94605,94607,94609],{},[13142,94502,94503,94505,94507],{},[898,94504,900],{},[2111,94506,2238],{},[1711,94508,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,94510,1836],{},[2509,94512,94513],{"scriptlevel":2113,"displaystyle":1713},[2525,94514,94515,94517],{},[2111,94516,2238],{},[2111,94518,6369],{},[13142,94520,94521,94523,94525],{},[898,94522,6796],{},[2111,94524,2238],{},[895,94526,94527,94529,94531,94533],{},[1711,94528,2460],{},[2111,94530,3034],{},[898,94532,8659],{"mathvariant":2287},[2111,94534,6369],{},[13142,94536,94537,94539,94541],{},[898,94538,6796],{},[2111,94540,2963],{},[895,94542,94543,94545,94547],{},[2111,94544,3034],{},[898,94546,8659],{"mathvariant":2287},[2111,94548,6369],{},[1711,94550,2123],{},[2111,94552,2113],{},[1711,94554,1726],{"separator":1725},[2102,94556],{"width":4981},[13142,94558,94559,94561,94563],{},[898,94560,900],{},[2111,94562,2963],{},[1711,94564,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,94566,1836],{},[2509,94568,94569],{"scriptlevel":2113,"displaystyle":1713},[2525,94570,94571,94573],{},[2111,94572,3034],{},[2111,94574,6369],{},[13142,94576,94577,94579,94581],{},[898,94578,6796],{},[2111,94580,2238],{},[895,94582,94583,94585,94587],{},[2111,94584,2238],{},[898,94586,8659],{"mathvariant":2287},[2111,94588,6369],{},[13142,94590,94591,94593,94595],{},[898,94592,6796],{},[2111,94594,2963],{},[895,94596,94597,94599,94601,94603],{},[1711,94598,2460],{},[2111,94600,2238],{},[898,94602,8659],{"mathvariant":2287},[2111,94604,6369],{},[1711,94606,2123],{},[2111,94608,2113],{},[1711,94610,1726],{"separator":1725},[902,94612,94613],{"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,",[883,94615,94617],{"className":94616},[886],[888,94618,94619],{"xmlns":890,"display":31664},[892,94620,94621,94745],{},[895,94622,94623,94635,94637,94639,94647,94663,94677,94679,94681,94683,94685,94697,94699,94701,94709,94723,94739,94741,94743],{},[13142,94624,94625,94627,94629],{},[898,94626,900],{},[2111,94628,6907],{},[895,94630,94631,94633],{},[1711,94632,5225],{"mathvariant":2287},[1711,94634,5225],{"mathvariant":2287},[1711,94636,1836],{},[1711,94638,2460],{},[2509,94640,94641],{"scriptlevel":2113,"displaystyle":1713},[2525,94642,94643,94645],{},[2111,94644,3034],{},[2111,94646,45460],{},[13142,94648,94649,94651,94653],{},[898,94650,6796],{},[2111,94652,2238],{},[895,94654,94655,94657,94659,94661],{},[1711,94656,2460],{},[2111,94658,27799],{},[898,94660,8659],{"mathvariant":2287},[2111,94662,6369],{},[13142,94664,94665,94667,94669],{},[898,94666,6796],{},[2111,94668,2963],{},[895,94670,94671,94673,94675],{},[2111,94672,3034],{},[898,94674,8659],{"mathvariant":2287},[2111,94676,6369],{},[1711,94678,2109],{},[2111,94680,2113],{},[1711,94682,1726],{"separator":1725},[2102,94684],{"width":4981},[13142,94686,94687,94689,94691],{},[898,94688,900],{},[2111,94690,36144],{},[895,94692,94693,94695],{},[1711,94694,5225],{"mathvariant":2287},[1711,94696,5225],{"mathvariant":2287},[1711,94698,1836],{},[1711,94700,2460],{},[2509,94702,94703],{"scriptlevel":2113,"displaystyle":1713},[2525,94704,94705,94707],{},[2111,94706,3034],{},[2111,94708,45460],{},[13142,94710,94711,94713,94715],{},[898,94712,6796],{},[2111,94714,2238],{},[895,94716,94717,94719,94721],{},[2111,94718,2238],{},[898,94720,8659],{"mathvariant":2287},[2111,94722,6369],{},[13142,94724,94725,94727,94729],{},[898,94726,6796],{},[2111,94728,2963],{},[895,94730,94731,94733,94735,94737],{},[1711,94732,2460],{},[2111,94734,4798],{},[898,94736,8659],{"mathvariant":2287},[2111,94738,6369],{},[1711,94740,2109],{},[2111,94742,2113],{},[1711,94744,1726],{"separator":1725},[902,94746,94747],{"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,",[724,94749,94750],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,94752,94754],{"id":94753},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,94756,94757,94760],{},[38,94758,94759],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,94762,94764],{"className":94763},[886],[888,94765,94766],{"xmlns":890,"display":31664},[892,94767,94768,94811],{},[24352,94769,94770],{"width":31669},[24357,94771,94772,94774,94804,94806],{},[24360,94773],{"width":31674},[24360,94775,94776],{},[895,94777,94778,94780,94782,94788,94790,94796,94798,94800,94802],{},[898,94779,900],{},[1711,94781,1714],{"stretchy":1713},[2884,94783,94784,94786],{},[898,94785,6796],{},[2111,94787,2238],{},[1711,94789,1726],{"separator":1725},[2884,94791,94792,94794],{},[898,94793,6796],{},[2111,94795,2963],{},[1711,94797,1735],{"stretchy":1713},[1711,94799,1836],{},[898,94801,2090],{},[1711,94803,1726],{"separator":1725},[24360,94805],{"width":31674},[24360,94807,94808],{},[1942,94809,94810],{},"(6.7)",[902,94812,94813],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,94815,8298,94816,94829],{},[883,94817,94819],{"className":94818},[886],[888,94820,94821],{"xmlns":890},[892,94822,94823,94827],{},[895,94824,94825],{},[898,94826,2090],{},[902,94828,2090],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,94831,94833],{"className":94832},[886],[888,94834,94835],{"xmlns":890,"display":31664},[892,94836,94837,94878],{},[24352,94838,94839],{"width":31669},[24357,94840,94841,94843,94871,94873],{},[24360,94842],{"width":31674},[24360,94844,94845],{},[895,94846,94847,94855,94857,94865,94867,94869],{},[13142,94848,94849,94851,94853],{},[898,94850,6796],{},[2111,94852,2238],{},[898,94854,207],{},[1711,94856,4795],{},[13142,94858,94859,94861,94863],{},[898,94860,6796],{},[2111,94862,2963],{},[898,94864,2223],{},[1711,94866,1836],{},[898,94868,2090],{},[898,94870,2186],{"mathvariant":2287},[24360,94872],{"width":31674},[24360,94874,94875],{},[1942,94876,94877],{},"(6.8)",[902,94879,94880],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,94882,94883,94884,8345,94914,1700,94917,94930,94931,94966,94967,94984,94985,95014,95015,95018],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,94885,94887],{"className":94886},[886],[888,94888,94889],{"xmlns":890},[892,94890,94891,94911],{},[895,94892,94893,94895,94901,94903,94909],{},[1711,94894,5144],{"stretchy":1713},[2884,94896,94897,94899],{},[898,94898,6796],{},[2111,94900,2238],{},[1711,94902,1726],{"separator":1725},[2884,94904,94905,94907],{},[898,94906,6796],{},[2111,94908,2963],{},[1711,94910,5163],{"stretchy":1713},[902,94912,94913],{"encoding":904},"[Q_1, Q_2]",[38,94915,94916],{},"stejnou úrovní uspokojení",[883,94918,94920],{"className":94919},[886],[888,94921,94922],{"xmlns":890},[892,94923,94924,94928],{},[895,94925,94926],{},[898,94927,2090],{},[902,94929,2090],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,94932,94934],{"className":94933},[886],[888,94935,94936],{"xmlns":890},[892,94937,94938,94964],{},[895,94939,94940,94942,94944,94946,94948,94954,94956,94962],{},[898,94941,900],{},[1711,94943,1836],{},[898,94945,900],{},[1711,94947,1714],{"stretchy":1713},[2884,94949,94950,94952],{},[898,94951,6796],{},[2111,94953,2238],{},[1711,94955,1726],{"separator":1725},[2884,94957,94958,94960],{},[898,94959,6796],{},[2111,94961,2963],{},[1711,94963,1735],{"stretchy":1713},[902,94965,91054],{"encoding":904}," s rovinami ",[883,94968,94970],{"className":94969},[886],[888,94971,94972],{"xmlns":890},[892,94973,94974,94982],{},[895,94975,94976,94978,94980],{},[898,94977,900],{},[1711,94979,1836],{},[898,94981,2090],{},[902,94983,90270],{"encoding":904}," rovnoběžnými s rovinou ",[883,94986,94988],{"className":94987},[886],[888,94989,94990],{"xmlns":890},[892,94991,94992,95012],{},[895,94993,94994,94996,95002,95004,95010],{},[1711,94995,1714],{"stretchy":1713},[2884,94997,94998,95000],{},[898,94999,6796],{},[2111,95001,2238],{},[1711,95003,1726],{"separator":1725},[2884,95005,95006,95008],{},[898,95007,6796],{},[2111,95009,2963],{},[1711,95011,1735],{"stretchy":1713},[902,95013,93217],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,95016,95017],{},"izokvantami"," produkčních funkcí.",[724,95020,95021],{},[614,95022,95023,95024,93095,95042,95060,95061,2186],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,95025,95027],{"className":95026},[886],[888,95028,95029],{"xmlns":890},[892,95030,95031,95039],{},[895,95032,95033,95035,95037],{},[898,95034,207],{},[1711,95036,2109],{},[898,95038,2223],{},[902,95040,95041],{"encoding":904},"a \u003C b",[883,95043,95045],{"className":95044},[886],[888,95046,95047],{"xmlns":890},[892,95048,95049,95057],{},[895,95050,95051,95053,95055],{},[898,95052,207],{},[1711,95054,2123],{},[898,95056,2223],{},[902,95058,95059],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,95062,95064],{"className":95063},[886],[888,95065,95066],{"xmlns":890},[892,95067,95068,95092],{},[895,95069,95070,95076,95078,95084,95086],{},[2884,95071,95072,95074],{},[898,95073,2090],{},[2111,95075,2113],{},[1711,95077,2109],{},[2884,95079,95080,95082],{},[898,95081,2090],{},[2111,95083,2238],{},[1711,95085,2109],{},[2884,95087,95088,95090],{},[898,95089,2090],{},[2111,95091,2963],{},[902,95093,95094],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,95096,95097],{},[614,95098,95099,95100,95129,95130,95188,95189,95207],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,95101,95103],{"className":95102},[886],[888,95104,95105],{"xmlns":890},[892,95106,95107,95127],{},[895,95108,95109,95111,95117,95119,95125],{},[1711,95110,1714],{"stretchy":1713},[2884,95112,95113,95115],{},[898,95114,6796],{},[2111,95116,2238],{},[1711,95118,1726],{"separator":1725},[2884,95120,95121,95123],{},[898,95122,6796],{},[2111,95124,2963],{},[1711,95126,1735],{"stretchy":1713},[902,95128,93217],{"encoding":904},"; body ",[883,95131,95133],{"className":95132},[886],[888,95134,95135],{"xmlns":890},[892,95136,95137,95185],{},[895,95138,95139,95141,95143,95145,95151,95153,95159,95161,95163,95165,95167,95169,95175,95177,95183],{},[898,95140,8243],{},[1711,95142,1836],{},[1711,95144,5144],{"stretchy":1713},[2884,95146,95147,95149],{},[898,95148,207],{},[2111,95150,2238],{},[1711,95152,1726],{"separator":1725},[2884,95154,95155,95157],{},[898,95156,207],{},[2111,95158,2963],{},[1711,95160,5163],{"stretchy":1713},[1711,95162,1726],{"separator":1725},[898,95164,26851],{},[1711,95166,1836],{},[1711,95168,5144],{"stretchy":1713},[2884,95170,95171,95173],{},[898,95172,2223],{},[2111,95174,2238],{},[1711,95176,1726],{"separator":1725},[2884,95178,95179,95181],{},[898,95180,2223],{},[2111,95182,2963],{},[1711,95184,5163],{"stretchy":1713},[902,95186,95187],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,95190,95192],{"className":95191},[886],[888,95193,95194],{"xmlns":890},[892,95195,95196,95204],{},[895,95197,95198,95200,95202],{},[898,95199,1940],{},[1711,95201,1726],{"separator":1725},[898,95203,2778],{},[902,95205,95206],{"encoding":904},"C, D"," na vyšší hladině.",[1921,95209,95210],{},[724,95211,95212,95214,95215,95277,95278,95322,95323,95357,95358,29787,95376,95357,95430,29787,95448,95524],{},[883,95213,56293],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,95216,95218],{"className":95217},[886],[888,95219,95220],{"xmlns":890},[892,95221,95222,95274],{},[895,95223,95224,95226,95228,95234,95236,95242,95244,95246,95260],{},[898,95225,900],{},[1711,95227,1714],{"stretchy":1713},[2884,95229,95230,95232],{},[898,95231,6796],{},[2111,95233,2238],{},[1711,95235,1726],{"separator":1725},[2884,95237,95238,95240],{},[898,95239,6796],{},[2111,95241,2963],{},[1711,95243,1735],{"stretchy":1713},[1711,95245,1836],{},[13142,95247,95248,95250,95252],{},[898,95249,6796],{},[2111,95251,2238],{},[895,95253,95254,95256,95258],{},[2111,95255,2238],{},[898,95257,8659],{"mathvariant":2287},[2111,95259,6369],{},[13142,95261,95262,95264,95266],{},[898,95263,6796],{},[2111,95265,2963],{},[895,95267,95268,95270,95272],{},[2111,95269,3034],{},[898,95271,8659],{"mathvariant":2287},[2111,95273,6369],{},[902,95275,95276],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,95279,95281],{"className":95280},[886],[888,95282,95283],{"xmlns":890},[892,95284,95285,95319],{},[895,95286,95287,95301,95315,95317],{},[13142,95288,95289,95291,95293],{},[898,95290,6796],{},[2111,95292,2238],{},[895,95294,95295,95297,95299],{},[2111,95296,2238],{},[898,95298,8659],{"mathvariant":2287},[2111,95300,6369],{},[13142,95302,95303,95305,95307],{},[898,95304,6796],{},[2111,95306,2963],{},[895,95308,95309,95311,95313],{},[2111,95310,3034],{},[898,95312,8659],{"mathvariant":2287},[2111,95314,6369],{},[1711,95316,1836],{},[898,95318,2090],{},[902,95320,95321],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,95324,95326],{"className":95325},[886],[888,95327,95328],{"xmlns":890},[892,95329,95330,95354],{},[895,95331,95332,95338,95346,95348],{},[2884,95333,95334,95336],{},[898,95335,6796],{},[2111,95337,2238],{},[13142,95339,95340,95342,95344],{},[898,95341,6796],{},[2111,95343,2963],{},[2111,95345,3034],{},[1711,95347,1836],{},[1716,95349,95350,95352],{},[898,95351,2090],{},[2111,95353,6369],{},[902,95355,95356],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,95359,95361],{"className":95360},[886],[888,95362,95363],{"xmlns":890},[892,95364,95365,95373],{},[895,95366,95367,95369,95371],{},[898,95368,2090],{},[1711,95370,1836],{},[2111,95372,2238],{},[902,95374,95375],{"encoding":904},"c = 1",[883,95377,95379],{"className":95378},[886],[888,95380,95381],{"xmlns":890},[892,95382,95383,95427],{},[895,95384,95385,95391,95393,95409,95411],{},[2884,95386,95387,95389],{},[898,95388,6796],{},[2111,95390,2963],{},[1711,95392,1836],{},[13142,95394,95395,95397,95399],{},[898,95396,6796],{},[2111,95398,2238],{},[895,95400,95401,95403,95405,95407],{},[1711,95402,2460],{},[2111,95404,2238],{},[898,95406,8659],{"mathvariant":2287},[2111,95408,3034],{},[1711,95410,1836],{},[2509,95412,95413],{"scriptlevel":2113,"displaystyle":1725},[2525,95414,95415,95417],{},[2111,95416,2238],{},[85625,95418,95419,95425],{},[2884,95420,95421,95423],{},[898,95422,6796],{},[2111,95424,2238],{},[2111,95426,3034],{},[902,95428,95429],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,95431,95433],{"className":95432},[886],[888,95434,95435],{"xmlns":890},[892,95436,95437,95445],{},[895,95438,95439,95441,95443],{},[898,95440,2090],{},[1711,95442,1836],{},[2111,95444,2963],{},[902,95446,95447],{"encoding":904},"c = 2",[883,95449,95451],{"className":95450},[886],[888,95452,95453],{"xmlns":890},[892,95454,95455,95521],{},[895,95456,95457,95463,95465,95477,95479,95495,95497],{},[2884,95458,95459,95461],{},[898,95460,6796],{},[2111,95462,2963],{},[1711,95464,1836],{},[1716,95466,95467,95469],{},[2111,95468,2963],{},[895,95470,95471,95473,95475],{},[2111,95472,6369],{},[898,95474,8659],{"mathvariant":2287},[2111,95476,3034],{},[1711,95478,4795],{},[13142,95480,95481,95483,95485],{},[898,95482,6796],{},[2111,95484,2238],{},[895,95486,95487,95489,95491,95493],{},[1711,95488,2460],{},[2111,95490,2238],{},[898,95492,8659],{"mathvariant":2287},[2111,95494,3034],{},[1711,95496,1836],{},[2509,95498,95499],{"scriptlevel":2113,"displaystyle":1725},[2525,95500,95501,95511],{},[895,95502,95503,95505],{},[2111,95504,2963],{},[85625,95506,95507,95509],{},[2111,95508,2963],{},[2111,95510,3034],{},[85625,95512,95513,95519],{},[2884,95514,95515,95517],{},[898,95516,6796],{},[2111,95518,2238],{},[2111,95520,3034],{},[902,95522,95523],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,95526,95528],{"id":95527},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,95530,95531],{},[1801,95532],{"alt":95533,"className":95534,"src":95535},"imek-ic-4vlastnosti-anotovane",[210,1805],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[1921,95537,95538,95547,95594,95638,95644,95650],{},[724,95539,95540,95542,95543,95546],{},[883,95541,1927],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,95544,95545],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,95548,95549],{},[883,95550,95552],{"className":95551},[886],[888,95553,95554],{"xmlns":890},[892,95555,95556,95591],{},[895,95557,95558,95561,95563,95565,95567,95569,95587,95589],{},[898,95559,95560],{"mathvariant":2287},"tg",[1711,95562,59798],{},[898,95564,22460],{},[1711,95566,1836],{},[1711,95568,2460],{},[2525,95570,95571,95579],{},[13142,95572,95573,95575,95577],{},[898,95574,900],{},[2111,95576,2238],{},[1711,95578,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[13142,95580,95581,95583,95585],{},[898,95582,900],{},[2111,95584,2963],{},[1711,95586,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,95588,2109],{},[2111,95590,2113],{},[902,95592,95593],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,95595,95596,95597,95637],{},"(derivace implicitně zadané funkce ",[883,95598,95600],{"className":95599},[886],[888,95601,95602],{"xmlns":890},[892,95603,95604,95634],{},[895,95605,95606,95608,95610,95616,95618,95624,95626,95628,95630,95632],{},[898,95607,900],{},[1711,95609,1714],{"stretchy":1713},[2884,95611,95612,95614],{},[898,95613,6796],{},[2111,95615,2238],{},[1711,95617,1726],{"separator":1725},[2884,95619,95620,95622],{},[898,95621,6796],{},[2111,95623,2963],{},[1711,95625,1735],{"stretchy":1713},[1711,95627,2460],{},[898,95629,2090],{},[1711,95631,1836],{},[2111,95633,2113],{},[902,95635,95636],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,95639,95640,95643],{},[38,95641,95642],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,95645,95646,95649],{},[38,95647,95648],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,95651,95652,95655,95656,95674,95675,95691,95692,95695],{},[38,95653,95654],{},"4° Konvexní."," Pro každé dva body ",[883,95657,95659],{"className":95658},[886],[888,95660,95661],{"xmlns":890},[892,95662,95663,95671],{},[895,95664,95665,95667,95669],{},[898,95666,8243],{},[1711,95668,1726],{"separator":1725},[898,95670,26851],{},[902,95672,95673],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,95676,95678],{"className":95677},[886],[888,95679,95680],{"xmlns":890},[892,95681,95682,95688],{},[895,95683,95684,95686],{},[898,95685,8243],{},[898,95687,26851],{},[902,95689,95690],{"encoding":904},"AB"," ve ",[38,95693,95694],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,95697,95698],{},[614,95699,95700,95701,95736,95737,2186],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,95702,95704],{"className":95703},[886],[888,95705,95706],{"xmlns":890},[892,95707,95708,95734],{},[895,95709,95710,95712,95714,95720,95722,95728,95730,95732],{},[898,95711,900],{},[1711,95713,1714],{"stretchy":1713},[2884,95715,95716,95718],{},[898,95717,6796],{},[2111,95719,2238],{},[1711,95721,1726],{"separator":1725},[2884,95723,95724,95726],{},[898,95725,6796],{},[2111,95727,2963],{},[1711,95729,1735],{"stretchy":1713},[1711,95731,1836],{},[898,95733,2090],{},[902,95735,13743],{"encoding":904}," s tečnou se sklonem ",[883,95738,95740],{"className":95739},[886],[888,95741,95742],{"xmlns":890},[892,95743,95744,95752],{},[895,95745,95746,95748,95750],{},[898,95747,95560],{"mathvariant":2287},[1711,95749,59798],{},[898,95751,22460],{},[902,95753,95754],{"encoding":904},"\\operatorname{tg}\\alpha",[115,95756,95758],{"id":95757},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,95760,95761,1700,95764,1648,95777,95780],{},[38,95762,95763],{},"Mezní míra komoditní substituce",[883,95765,95767],{"className":95766},[886],[888,95768,95769],{"xmlns":890},[892,95770,95771,95775],{},[895,95772,95773],{},[1942,95774,14576],{},[902,95776,31836],{"encoding":904},[38,95778,95779],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,95782,95784],{"className":95783},[886],[888,95785,95786],{"xmlns":890,"display":31664},[892,95787,95788,95875],{},[24352,95789,95790],{"width":31669},[24357,95791,95792,95794,95868,95870],{},[24360,95793],{"width":31674},[24360,95795,95796],{},[895,95797,95798,95800,95802,95804,95806,95812,95814,95820,95822,95824,95846,95848,95866],{},[1942,95799,14576],{},[1711,95801,1836],{},[1942,95803,14576],{},[1711,95805,1714],{"stretchy":1713},[2884,95807,95808,95810],{},[898,95809,6796],{},[2111,95811,2238],{},[1711,95813,1726],{"separator":1725},[2884,95815,95816,95818],{},[898,95817,6796],{},[2111,95819,2963],{},[1711,95821,1735],{"stretchy":1713},[1711,95823,1836],{},[2525,95825,95826,95836],{},[895,95827,95828,95830],{},[898,95829,1790],{},[2884,95831,95832,95834],{},[898,95833,900],{},[2111,95835,2238],{},[895,95837,95838,95840],{},[898,95839,1790],{},[2884,95841,95842,95844],{},[898,95843,900],{},[2111,95845,2963],{},[1711,95847,1836],{},[2525,95849,95850,95858],{},[13142,95851,95852,95854,95856],{},[898,95853,900],{},[2111,95855,2238],{},[1711,95857,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[13142,95859,95860,95862,95864],{},[898,95861,900],{},[2111,95863,2963],{},[1711,95865,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[898,95867,2186],{"mathvariant":2287},[24360,95869],{"width":31674},[24360,95871,95872],{},[1942,95873,95874],{},"(6.9)",[902,95876,95877],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,95879,95880,95881,95915,95916,95948,95949,95984,95985,95998],{},"Geometricky: ",[883,95882,95884],{"className":95883},[886],[888,95885,95886],{"xmlns":890},[892,95887,95888,95912],{},[895,95889,95890,95892],{},[1711,95891,2460],{},[2509,95893,95894],{"scriptlevel":2113,"displaystyle":1713},[2525,95895,95896,95904],{},[13142,95897,95898,95900,95902],{},[898,95899,900],{},[2111,95901,2238],{},[1711,95903,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[13142,95905,95906,95908,95910],{},[898,95907,900],{},[2111,95909,2963],{},[1711,95911,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,95913,95914],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,95917,95919],{"className":95918},[886],[888,95920,95921],{"xmlns":890},[892,95922,95923,95945],{},[895,95924,95925,95931,95933,95935,95937,95943],{},[2884,95926,95927,95929],{},[898,95928,6796],{},[2111,95930,2963],{},[1711,95932,1836],{},[898,95934,4068],{},[1711,95936,1714],{"stretchy":1713},[2884,95938,95939,95941],{},[898,95940,6796],{},[2111,95942,2238],{},[1711,95944,1735],{"stretchy":1713},[902,95946,95947],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,95950,95952],{"className":95951},[886],[888,95953,95954],{"xmlns":890},[892,95955,95956,95982],{},[895,95957,95958,95960,95962,95968,95970,95976,95978,95980],{},[898,95959,900],{},[1711,95961,1714],{"stretchy":1713},[2884,95963,95964,95966],{},[898,95965,6796],{},[2111,95967,2238],{},[1711,95969,1726],{"separator":1725},[2884,95971,95972,95974],{},[898,95973,6796],{},[2111,95975,2963],{},[1711,95977,1735],{"stretchy":1713},[1711,95979,1836],{},[898,95981,2090],{},[902,95983,13743],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,95986,95988],{"className":95987},[886],[888,95989,95990],{"xmlns":890},[892,95991,95992,95996],{},[895,95993,95994],{},[1942,95995,14576],{},[902,95997,31836],{"encoding":904}," chápeme jako velikost kompenzace.",[1921,96000,96001],{},[724,96002,96003,96005,96006,12082,96038,96076,96077,96094,96095,96112],{},[883,96004,2678],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,96007,96009],{"className":96008},[886],[888,96010,96011],{"xmlns":890},[892,96012,96013,96035],{},[895,96014,96015,96017,96019,96025,96027,96033],{},[1942,96016,14576],{},[1711,96018,1714],{"stretchy":1713},[2884,96020,96021,96023],{},[898,96022,6796],{},[2111,96024,2238],{},[1711,96026,1726],{"separator":1725},[2884,96028,96029,96031],{},[898,96030,6796],{},[2111,96032,2963],{},[1711,96034,1735],{"stretchy":1713},[902,96036,96037],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,96039,96040,96041,32601,96058,96075],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,96042,96044],{"className":96043},[886],[888,96045,96046],{"xmlns":890},[892,96047,96048,96056],{},[895,96049,96050],{},[2884,96051,96052,96054],{},[898,96053,6796],{},[2111,96055,2238],{},[902,96057,32600],{"encoding":904},[883,96059,96061],{"className":96060},[886],[888,96062,96063],{"xmlns":890},[892,96064,96065,96073],{},[895,96066,96067],{},[2884,96068,96069,96071],{},[898,96070,6796],{},[2111,96072,2963],{},[902,96074,32619],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,96078,96080],{"className":96079},[886],[888,96081,96082],{"xmlns":890},[892,96083,96084,96092],{},[895,96085,96086],{},[2884,96087,96088,96090],{},[898,96089,6796],{},[2111,96091,2963],{},[902,96093,32619],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,96096,96098],{"className":96097},[886],[888,96099,96100],{"xmlns":890},[892,96101,96102,96110],{},[895,96103,96104],{},[2884,96105,96106,96108],{},[898,96107,6796],{},[2111,96109,2238],{},[902,96111,32600],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,96114,96115,96116,33542],{},"Pro obecnou změnu ",[883,96117,96119],{"className":96118},[886],[888,96120,96121],{"xmlns":890},[892,96122,96123,96133],{},[895,96124,96125,96127],{},[898,96126,2098],{"mathvariant":2287},[2884,96128,96129,96131],{},[898,96130,6796],{},[2111,96132,2238],{},[902,96134,96135],{"encoding":904},"\\mathrm{d} Q_1",[883,96137,96139],{"className":96138},[886],[888,96140,96141],{"xmlns":890,"display":31664},[892,96142,96143,96196],{},[24352,96144,96145],{"width":31669},[24357,96146,96147,96149,96189,96191],{},[24360,96148],{"width":31674},[24360,96150,96151],{},[895,96152,96153,96155,96161,96163,96165,96171,96173,96175,96177,96179,96181,96187],{},[898,96154,6892],{"mathvariant":2287},[2884,96156,96157,96159],{},[898,96158,6796],{},[2111,96160,2963],{},[1711,96162,6740],{},[898,96164,2098],{"mathvariant":2287},[2884,96166,96167,96169],{},[898,96168,6796],{},[2111,96170,2963],{},[1711,96172,1836],{},[1711,96174,2460],{},[1942,96176,14576],{},[1711,96178,4795],{},[898,96180,2098],{"mathvariant":2287},[2884,96182,96183,96185],{},[898,96184,6796],{},[2111,96186,2238],{},[1711,96188,1726],{"separator":1725},[24360,96190],{"width":31674},[24360,96192,96193],{},[1942,96194,96195],{},"(6.10)",[902,96197,96198],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,96200,96202],{"className":96201},[886],[888,96203,96204],{"xmlns":890,"display":31664},[892,96205,96206,96253],{},[24352,96207,96208],{"width":31669},[24357,96209,96210,96212,96246,96248],{},[24360,96211],{"width":31674},[24360,96213,96214],{},[895,96215,96216,96218,96224,96226,96228,96234,96236,96238,96244],{},[898,96217,2098],{"mathvariant":2287},[2884,96219,96220,96222],{},[898,96221,6796],{},[2111,96223,2238],{},[1711,96225,1836],{},[1711,96227,2460],{},[2525,96229,96230,96232],{},[2111,96231,2238],{},[1942,96233,14576],{},[1942,96235,2519],{},[898,96237,2098],{"mathvariant":2287},[2884,96239,96240,96242],{},[898,96241,6796],{},[2111,96243,2963],{},[898,96245,2186],{"mathvariant":2287},[24360,96247],{"width":31674},[24360,96249,96250],{},[1942,96251,96252],{},"(6.11)",[902,96254,96255],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[1921,96257,96258,96324,96441],{},[724,96259,96260,96262,96263,33542],{},[883,96261,56293],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,96264,96266],{"className":96265},[886],[888,96267,96268],{"xmlns":890},[892,96269,96270,96322],{},[895,96271,96272,96274,96276,96282,96284,96290,96292,96294,96308],{},[898,96273,900],{},[1711,96275,1714],{"stretchy":1713},[2884,96277,96278,96280],{},[898,96279,6796],{},[2111,96281,2238],{},[1711,96283,1726],{"separator":1725},[2884,96285,96286,96288],{},[898,96287,6796],{},[2111,96289,2963],{},[1711,96291,1735],{"stretchy":1713},[1711,96293,1836],{},[13142,96295,96296,96298,96300],{},[898,96297,6796],{},[2111,96299,2238],{},[895,96301,96302,96304,96306],{},[2111,96303,2238],{},[898,96305,8659],{"mathvariant":2287},[2111,96307,2963],{},[13142,96309,96310,96312,96314],{},[898,96311,6796],{},[2111,96313,2963],{},[895,96315,96316,96318,96320],{},[2111,96317,2238],{},[898,96319,8659],{"mathvariant":2287},[2111,96321,2963],{},[902,96323,33541],{"encoding":904},[724,96325,96326],{},[883,96327,96329],{"className":96328},[886],[888,96330,96331],{"xmlns":890},[892,96332,96333,96439],{},[895,96334,96335,96337,96339,96421,96423,96437],{},[1942,96336,14576],{},[1711,96338,1836],{},[2525,96340,96341,96381],{},[895,96342,96343,96351,96367],{},[2509,96344,96345],{"scriptlevel":2113,"displaystyle":1713},[2525,96346,96347,96349],{},[2111,96348,2238],{},[2111,96350,2963],{},[13142,96352,96353,96355,96357],{},[898,96354,6796],{},[2111,96356,2238],{},[895,96358,96359,96361,96363,96365],{},[1711,96360,2460],{},[2111,96362,2238],{},[898,96364,8659],{"mathvariant":2287},[2111,96366,2963],{},[13142,96368,96369,96371,96373],{},[898,96370,6796],{},[2111,96372,2963],{},[895,96374,96375,96377,96379],{},[2111,96376,2238],{},[898,96378,8659],{"mathvariant":2287},[2111,96380,2963],{},[895,96382,96383,96391,96405],{},[2509,96384,96385],{"scriptlevel":2113,"displaystyle":1713},[2525,96386,96387,96389],{},[2111,96388,2238],{},[2111,96390,2963],{},[13142,96392,96393,96395,96397],{},[898,96394,6796],{},[2111,96396,2238],{},[895,96398,96399,96401,96403],{},[2111,96400,2238],{},[898,96402,8659],{"mathvariant":2287},[2111,96404,2963],{},[13142,96406,96407,96409,96411],{},[898,96408,6796],{},[2111,96410,2963],{},[895,96412,96413,96415,96417,96419],{},[1711,96414,2460],{},[2111,96416,2238],{},[898,96418,8659],{"mathvariant":2287},[2111,96420,2963],{},[1711,96422,1836],{},[2525,96424,96425,96431],{},[2884,96426,96427,96429],{},[898,96428,6796],{},[2111,96430,2963],{},[2884,96432,96433,96435],{},[898,96434,6796],{},[2111,96436,2238],{},[898,96438,2186],{"mathvariant":2287},[902,96440,33660],{"encoding":904},[724,96442,33663,96443,2801,96486,33711,96488,96507],{},[883,96444,96446],{"className":96445},[886],[888,96447,96448],{"xmlns":890},[892,96449,96450,96484],{},[895,96451,96452,96454,96456,96458,96460,96462,96464,96466,96474,96476],{},[1942,96453,14576],{},[1711,96455,1714],{"stretchy":1713},[2111,96457,33679],{},[1711,96459,1726],{"separator":1725},[2111,96461,4807],{},[1711,96463,1735],{"stretchy":1713},[1711,96465,1836],{},[2509,96467,96468],{"scriptlevel":2113,"displaystyle":1713},[2525,96469,96470,96472],{},[2111,96471,4807],{},[2111,96473,33679],{},[1711,96475,1836],{},[2509,96477,96478],{"scriptlevel":2113,"displaystyle":1713},[2525,96479,96480,96482],{},[2111,96481,4798],{},[2111,96483,3034],{},[902,96485,33708],{"encoding":904},[614,96487,13192],{},[883,96489,96491],{"className":96490},[886],[888,96492,96493],{"xmlns":890},[892,96494,96495,96505],{},[895,96496,96497],{},[2509,96498,96499],{"scriptlevel":2113,"displaystyle":1713},[2525,96500,96501,96503],{},[2111,96502,4798],{},[2111,96504,3034],{},[902,96506,33731],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,96509,96510,96511,96515],{},"(Paralelou je ",[207,96512,96514],{"className":96513,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,96517,96519],{"id":96518},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,96521,96522,96523,96526],{},"Rámcově se v kapitole 6 studují ",[38,96524,96525],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,96528,96529,96665],{},[123,96530,96531,96533,96534,14130,96565,1700,96568,96617,96618,2186],{},[38,96532,31850],{}," — maximalizace ",[883,96535,96537],{"className":96536},[886],[888,96538,96539],{"xmlns":890},[892,96540,96541,96563],{},[895,96542,96543,96545,96547,96553,96555,96561],{},[898,96544,900],{},[1711,96546,1714],{"stretchy":1713},[2884,96548,96549,96551],{},[898,96550,6796],{},[2111,96552,2238],{},[1711,96554,1726],{"separator":1725},[2884,96556,96557,96559],{},[898,96558,6796],{},[2111,96560,2963],{},[1711,96562,1735],{"stretchy":1713},[902,96564,19941],{"encoding":904},[38,96566,96567],{},"rozpočtovém omezení",[883,96569,96571],{"className":96570},[886],[888,96572,96573],{"xmlns":890},[892,96574,96575,96615],{},[895,96576,96577,96583,96585,96593,96599,96601,96609],{},[1716,96578,96579,96581],{},[898,96580,1660],{},[1711,96582,1793],{},[1711,96584,1836],{},[13142,96586,96587,96589,96591],{},[898,96588,7929],{},[2111,96590,2238],{},[1711,96592,1793],{},[2884,96594,96595,96597],{},[898,96596,6796],{},[2111,96598,2238],{},[1711,96600,2095],{},[13142,96602,96603,96605,96607],{},[898,96604,7929],{},[2111,96606,2963],{},[1711,96608,1793],{},[2884,96610,96611,96613],{},[898,96612,6796],{},[2111,96614,2963],{},[902,96616,20896],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,96619,96621],{"className":96620},[886],[888,96622,96623],{"xmlns":890},[892,96624,96625,96663],{},[895,96626,96627,96633,96635,96641,96643,96649,96651,96657,96659,96661],{},[2884,96628,96629,96631],{},[898,96630,6796],{},[898,96632,21388],{},[1711,96634,1836],{},[2884,96636,96637,96639],{},[898,96638,2778],{},[898,96640,21388],{},[1711,96642,1714],{"stretchy":1713},[2884,96644,96645,96647],{},[898,96646,7929],{},[2111,96648,2238],{},[1711,96650,1726],{"separator":1725},[2884,96652,96653,96655],{},[898,96654,7929],{},[2111,96656,2963],{},[1711,96658,1726],{"separator":1725},[898,96660,1660],{},[1711,96662,1735],{"stretchy":1713},[902,96664,40053],{"encoding":904},[123,96666,96667,31499,96670,31542,96716,96733,96734,2186],{},[38,96668,96669],{},"Duální úloha",[883,96671,96673],{"className":96672},[886],[888,96674,96675],{"xmlns":890},[892,96676,96677,96713],{},[895,96678,96679,96681,96683,96691,96697,96699,96707],{},[898,96680,1722],{},[1711,96682,1836],{},[13142,96684,96685,96687,96689],{},[898,96686,7929],{},[2111,96688,2238],{},[1711,96690,1793],{},[2884,96692,96693,96695],{},[898,96694,6796],{},[2111,96696,2238],{},[1711,96698,2095],{},[13142,96700,96701,96703,96705],{},[898,96702,7929],{},[2111,96704,2963],{},[1711,96706,1793],{},[2884,96708,96709,96711],{},[898,96710,6796],{},[2111,96712,2963],{},[902,96714,96715],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,96717,96719],{"className":96718},[886],[888,96720,96721],{"xmlns":890},[892,96722,96723,96731],{},[895,96724,96725],{},[1716,96726,96727,96729],{},[898,96728,900],{},[1711,96730,1793],{},[902,96732,31560],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,96735,96737],{"className":96736},[886],[888,96738,96739],{"xmlns":890},[892,96740,96741,96779],{},[895,96742,96743,96749,96751,96757,96759,96765,96767,96773,96775,96777],{},[2884,96744,96745,96747],{},[898,96746,6796],{},[898,96748,21388],{},[1711,96750,1836],{},[2884,96752,96753,96755],{},[898,96754,2778],{},[898,96756,21388],{},[1711,96758,1714],{"stretchy":1713},[2884,96760,96761,96763],{},[898,96762,7929],{},[2111,96764,2238],{},[1711,96766,1726],{"separator":1725},[2884,96768,96769,96771],{},[898,96770,7929],{},[2111,96772,2963],{},[1711,96774,1726],{"separator":1725},[898,96776,900],{},[1711,96778,1735],{"stretchy":1713},[902,96780,21421],{"encoding":904},[724,96782,96783,96784,96787,96788,1700,96791,96830],{},"Obě úlohy se řeší ",[207,96785,31565],{"className":96786,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,96789,96790],{},"tentýž bod dotyku",[883,96792,96794],{"className":96793},[886],[888,96795,96796],{"xmlns":890},[892,96797,96798,96828],{},[895,96799,96800,96806,96808,96816,96818,96826],{},[1716,96801,96802,96804],{},[898,96803,6796],{},[1711,96805,1793],{},[1711,96807,5144],{"stretchy":1713},[13142,96809,96810,96812,96814],{},[898,96811,6796],{},[2111,96813,2238],{},[1711,96815,1793],{},[1711,96817,1726],{"separator":1725},[13142,96819,96820,96822,96824],{},[898,96821,6796],{},[2111,96823,2963],{},[1711,96825,1793],{},[1711,96827,5163],{"stretchy":1713},[902,96829,31925],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,96832,96834],{"className":96833},[886],[888,96835,96836],{"xmlns":890,"display":31664},[892,96837,96838,96884],{},[895,96839,96840,96842,96844,96862,96864,96882],{},[1942,96841,14576],{},[1711,96843,1836],{},[2525,96845,96846,96854],{},[13142,96847,96848,96850,96852],{},[898,96849,900],{},[2111,96851,2238],{},[1711,96853,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[13142,96855,96856,96858,96860],{},[898,96857,900],{},[2111,96859,2963],{},[1711,96861,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,96863,1836],{},[2525,96865,96866,96874],{},[13142,96867,96868,96870,96872],{},[898,96869,7929],{},[2111,96871,2238],{},[1711,96873,1793],{},[13142,96875,96876,96878,96880],{},[898,96877,7929],{},[2111,96879,2963],{},[1711,96881,1793],{},[898,96883,2186],{"mathvariant":2287},[902,96885,96886],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,96888,96889],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[1921,96891,96892],{},[724,96893,96894,96896,96897,96900,96901,96904,96905,96932,96933,96967,96968,97002,97003,97046,97047,97050,97051,2186],{},[883,96895,2678],{}," Pro detailní postup viz ",[207,96898,40352],{"className":96899,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,96902,96903],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,96906,96908],{"className":96907},[886],[888,96909,96910],{"xmlns":890},[892,96911,96912,96930],{},[895,96913,96914,96916,96918,96924],{},[898,96915,900],{},[1711,96917,1836],{},[2884,96919,96920,96922],{},[898,96921,6796],{},[2111,96923,2238],{},[2884,96925,96926,96928],{},[898,96927,6796],{},[2111,96929,2963],{},[902,96931,33824],{"encoding":904}," s výsledkem ",[883,96934,96936],{"className":96935},[886],[888,96937,96938],{"xmlns":890},[892,96939,96940,96964],{},[895,96941,96942,96948,96950,96952,96954,96960,96962],{},[2884,96943,96944,96946],{},[898,96945,6796],{},[2111,96947,2238],{},[1711,96949,1836],{},[2111,96951,4372],{},[1711,96953,1726],{"separator":1725},[2884,96955,96956,96958],{},[898,96957,6796],{},[2111,96959,2963],{},[1711,96961,1836],{},[2111,96963,4712],{},[902,96965,96966],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,96969,96971],{"className":96970},[886],[888,96972,96973],{"xmlns":890},[892,96974,96975,96999],{},[895,96976,96977,96983,96985,96987,96989,96995,96997],{},[2884,96978,96979,96981],{},[898,96980,6796],{},[2111,96982,2238],{},[1711,96984,1836],{},[2111,96986,6369],{},[1711,96988,1726],{"separator":1725},[2884,96990,96991,96993],{},[898,96992,6796],{},[2111,96994,2963],{},[1711,96996,1836],{},[2111,96998,2238],{},[902,97000,97001],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,97004,97006],{"className":97005},[886],[888,97007,97008],{"xmlns":890},[892,97009,97010,97044],{},[895,97011,97012,97014,97016,97030],{},[898,97013,900],{},[1711,97015,1836],{},[13142,97017,97018,97020,97022],{},[898,97019,6796],{},[2111,97021,2238],{},[895,97023,97024,97026,97028],{},[2111,97025,2238],{},[898,97027,8659],{"mathvariant":2287},[2111,97029,2963],{},[13142,97031,97032,97034,97036],{},[898,97033,6796],{},[2111,97035,2963],{},[895,97037,97038,97040,97042],{},[2111,97039,2238],{},[898,97041,8659],{"mathvariant":2287},[2111,97043,2963],{},[902,97045,36757],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,97048,97049],{},"6.8–6.13"," jsou na stránce ",[207,97052,31365],{"className":97053,"dataFsResolvedFilePath":911,"href":912},[210],[115,97055,97057],{"id":97056},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,97059,97060,97061,97074,97075,97077,97078,97080,97081,97083,97084,97086,97087,97089,97090,97092,97093,1700,97095,97130,97131,97144,97145,97148,97149,97152,97153,2186],{},"Každá ",[883,97062,97064],{"className":97063},[886],[888,97065,97066],{"xmlns":890},[892,97067,97068,97072],{},[895,97069,97070],{},[898,97071,40458],{},[902,97073,40458],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,97076,90408],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,97079,90892],{}," a současně ",[38,97082,90411],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,97085,90416],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,97088,56275],{}," (6.4) a druhé parciální derivace ",[38,97091,92775],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,97094,13706],{},[883,97096,97098],{"className":97097},[886],[888,97099,97100],{"xmlns":890},[892,97101,97102,97128],{},[895,97103,97104,97106,97108,97114,97116,97122,97124,97126],{},[898,97105,900],{},[1711,97107,1714],{"stretchy":1713},[2884,97109,97110,97112],{},[898,97111,6796],{},[2111,97113,2238],{},[1711,97115,1726],{"separator":1725},[2884,97117,97118,97120],{},[898,97119,6796],{},[2111,97121,2963],{},[1711,97123,1735],{"stretchy":1713},[1711,97125,1836],{},[898,97127,2090],{},[902,97129,13743],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,97132,97134],{"className":97133},[886],[888,97135,97136],{"xmlns":890},[892,97137,97138,97142],{},[895,97139,97140],{},[1942,97141,14576],{},[902,97143,31836],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,97146,97147],{},"maximalizace užitečnosti"," a duální ",[38,97150,97151],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,97154,40352],{"className":97155,"dataFsResolvedFilePath":911,"href":912},[210],[115,97157,53480],{"id":53479},[152,97159,97160,97163,97166,97169,97172,97175,97178,97181,97184,97187],{},[123,97161,97162],{},"Co se zahrnuje pod termín užitečnost?",[123,97164,97165],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,97167,97168],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,97170,97171],{},"Jak se vypočítá mezní užitečnost?",[123,97173,97174],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,97176,97177],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,97179,97180],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,97182,97183],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,97185,97186],{},"Proč mají křivky užitečnosti záporný sklon?",[123,97188,97189],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,97191,97193],{"id":97192},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,97195,97196,97199,97200,87081,97242,1343,97270,1343,97298,97326],{},[38,97197,97198],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,97201,97203],{"className":97202},[886],[888,97204,97205],{"xmlns":890},[892,97206,97207,97239],{},[895,97208,97209,97211,97213,97219,97221,97223,97229,97231,97233],{},[898,97210,900],{},[1711,97212,1836],{},[2884,97214,97215,97217],{},[898,97216,6796],{},[2111,97218,2238],{},[1711,97220,2095],{},[2111,97222,68157],{},[2884,97224,97225,97227],{},[898,97226,6796],{},[2111,97228,2963],{},[1711,97230,2095],{},[2111,97232,2963],{},[2884,97234,97235,97237],{},[898,97236,6796],{},[2111,97238,3034],{},[902,97240,97241],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,97243,97245],{"className":97244},[886],[888,97246,97247],{"xmlns":890},[892,97248,97249,97267],{},[895,97250,97251,97253,97255,97257,97259,97261,97263,97265],{},[898,97252,900],{},[1711,97254,1714],{"stretchy":1713},[2111,97256,6369],{},[1711,97258,1726],{"separator":1725},[2111,97260,2963],{},[1711,97262,1726],{"separator":1725},[2111,97264,2963],{},[1711,97266,1735],{"stretchy":1713},[902,97268,97269],{"encoding":904},"U(4, 2, 2)",[883,97271,97273],{"className":97272},[886],[888,97274,97275],{"xmlns":890},[892,97276,97277,97295],{},[895,97278,97279,97281,97283,97285,97287,97289,97291,97293],{},[898,97280,900],{},[1711,97282,1714],{"stretchy":1713},[2111,97284,2238],{},[1711,97286,1726],{"separator":1725},[2111,97288,6369],{},[1711,97290,1726],{"separator":1725},[2111,97292,2963],{},[1711,97294,1735],{"stretchy":1713},[902,97296,97297],{"encoding":904},"U(1, 4, 2)",[883,97299,97301],{"className":97300},[886],[888,97302,97303],{"xmlns":890},[892,97304,97305,97323],{},[895,97306,97307,97309,97311,97313,97315,97317,97319,97321],{},[898,97308,900],{},[1711,97310,1714],{"stretchy":1713},[2111,97312,2963],{},[1711,97314,1726],{"separator":1725},[2111,97316,3034],{},[1711,97318,1726],{"separator":1725},[2111,97320,2238],{},[1711,97322,1735],{"stretchy":1713},[902,97324,97325],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,97328,97329,97332,97333,97385,97386,1343,97412,1343,97438,1343,97464,1343,97490,1343,97516,1343,97542,97568],{},[38,97330,97331],{},"6.2"," Je dána užitečnost ",[883,97334,97336],{"className":97335},[886],[888,97337,97338],{"xmlns":890},[892,97339,97340,97382],{},[895,97341,97342,97344,97346,97348,97362,97376],{},[898,97343,900],{},[1711,97345,1836],{},[2111,97347,2963],{},[13142,97349,97350,97352,97354],{},[898,97351,6796],{},[2111,97353,2238],{},[895,97355,97356,97358,97360],{},[2111,97357,2238],{},[898,97359,8659],{"mathvariant":2287},[2111,97361,3034],{},[13142,97363,97364,97366,97368],{},[898,97365,6796],{},[2111,97367,2963],{},[895,97369,97370,97372,97374],{},[2111,97371,2238],{},[898,97373,8659],{"mathvariant":2287},[2111,97375,2963],{},[2884,97377,97378,97380],{},[898,97379,6796],{},[2111,97381,3034],{},[902,97383,97384],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,97387,97389],{"className":97388},[886],[888,97390,97391],{"xmlns":890},[892,97392,97393,97409],{},[895,97394,97395,97397,97399,97401,97403,97405,97407],{},[1711,97396,1714],{"stretchy":1713},[2111,97398,9549],{},[1711,97400,1726],{"separator":1725},[2111,97402,70195],{},[1711,97404,1726],{"separator":1725},[2111,97406,4712],{},[1711,97408,1735],{"stretchy":1713},[902,97410,97411],{"encoding":904},"(36, 27, 10)",[883,97413,97415],{"className":97414},[886],[888,97416,97417],{"xmlns":890},[892,97418,97419,97435],{},[895,97420,97421,97423,97425,97427,97429,97431,97433],{},[1711,97422,1714],{"stretchy":1713},[2111,97424,45438],{},[1711,97426,1726],{"separator":1725},[2111,97428,9568],{},[1711,97430,1726],{"separator":1725},[2111,97432,4306],{},[1711,97434,1735],{"stretchy":1713},[902,97436,97437],{"encoding":904},"(64, 8, 20)",[883,97439,97441],{"className":97440},[886],[888,97442,97443],{"xmlns":890},[892,97444,97445,97461],{},[895,97446,97447,97449,97451,97453,97455,97457,97459],{},[1711,97448,1714],{"stretchy":1713},[2111,97450,4372],{},[1711,97452,1726],{"separator":1725},[2111,97454,45438],{},[1711,97456,1726],{"separator":1725},[2111,97458,9568],{},[1711,97460,1735],{"stretchy":1713},[902,97462,97463],{"encoding":904},"(25, 64, 8)",[883,97465,97467],{"className":97466},[886],[888,97468,97469],{"xmlns":890},[892,97470,97471,97487],{},[895,97472,97473,97475,97477,97479,97481,97483,97485],{},[1711,97474,1714],{"stretchy":1713},[2111,97476,6369],{},[1711,97478,1726],{"separator":1725},[2111,97480,76127],{},[1711,97482,1726],{"separator":1725},[2111,97484,6262],{},[1711,97486,1735],{"stretchy":1713},[902,97488,97489],{"encoding":904},"(4, 125, 6)",[883,97491,97493],{"className":97492},[886],[888,97494,97495],{"xmlns":890},[892,97496,97497,97513],{},[895,97498,97499,97501,97503,97505,97507,97509,97511],{},[1711,97500,1714],{"stretchy":1713},[2111,97502,7990],{},[1711,97504,1726],{"separator":1725},[2111,97506,9195],{},[1711,97508,1726],{"separator":1725},[2111,97510,7505],{},[1711,97512,1735],{"stretchy":1713},[902,97514,97515],{"encoding":904},"(9, 40, 12)",[883,97517,97519],{"className":97518},[886],[888,97520,97521],{"xmlns":890},[892,97522,97523,97539],{},[895,97524,97525,97527,97529,97531,97533,97535,97537],{},[1711,97526,1714],{"stretchy":1713},[2111,97528,7990],{},[1711,97530,1726],{"separator":1725},[2111,97532,45438],{},[1711,97534,1726],{"separator":1725},[2111,97536,4798],{},[1711,97538,1735],{"stretchy":1713},[902,97540,97541],{"encoding":904},"(9, 64, 5)",[883,97543,97545],{"className":97544},[886],[888,97546,97547],{"xmlns":890},[892,97548,97549,97565],{},[895,97550,97551,97553,97555,97557,97559,97561,97563],{},[1711,97552,1714],{"stretchy":1713},[2111,97554,45438],{},[1711,97556,1726],{"separator":1725},[2111,97558,9568],{},[1711,97560,1726],{"separator":1725},[2111,97562,4712],{},[1711,97564,1735],{"stretchy":1713},[902,97566,97567],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,97570,97571,97332,97574,97617,97618,97652,97653,10454,97683,97716,97717,97734,97735,97752],{},[38,97572,97573],{},"6.3",[883,97575,97577],{"className":97576},[886],[888,97578,97579],{"xmlns":890},[892,97580,97581,97615],{},[895,97582,97583,97585,97587,97601],{},[898,97584,900],{},[1711,97586,1836],{},[13142,97588,97589,97591,97593],{},[898,97590,6796],{},[2111,97592,2238],{},[895,97594,97595,97597,97599],{},[2111,97596,2238],{},[898,97598,8659],{"mathvariant":2287},[2111,97600,2963],{},[13142,97602,97603,97605,97607],{},[898,97604,6796],{},[2111,97606,2963],{},[895,97608,97609,97611,97613],{},[2111,97610,2238],{},[898,97612,8659],{"mathvariant":2287},[2111,97614,2963],{},[902,97616,36757],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,97619,97621],{"className":97620},[886],[888,97622,97623],{"xmlns":890},[892,97624,97625,97649],{},[895,97626,97627,97633,97635,97637,97639,97645,97647],{},[2884,97628,97629,97631],{},[898,97630,6796],{},[2111,97632,2238],{},[1711,97634,1836],{},[2111,97636,7120],{},[1711,97638,1726],{"separator":1725},[2884,97640,97641,97643],{},[898,97642,6796],{},[2111,97644,2963],{},[1711,97646,1836],{},[2111,97648,50301],{},[902,97650,97651],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,97654,97656],{"className":97655},[886],[888,97657,97658],{"xmlns":890},[892,97659,97660,97680],{},[895,97661,97662,97664,97670,97672,97674],{},[898,97663,1790],{},[2884,97665,97666,97668],{},[898,97667,900],{},[2111,97669,2238],{},[1711,97671,1726],{"separator":1725},[898,97673,1790],{},[2884,97675,97676,97678],{},[898,97677,900],{},[2111,97679,2963],{},[902,97681,97682],{"encoding":904},"MU_1, MU_2",[883,97684,97686],{"className":97685},[886],[888,97687,97688],{"xmlns":890},[892,97689,97690,97714],{},[895,97691,97692,97698,97700,97702,97704,97710,97712],{},[2884,97693,97694,97696],{},[898,97695,6796],{},[2111,97697,2238],{},[1711,97699,1836],{},[2111,97701,7120],{},[1711,97703,1726],{"separator":1725},[2884,97705,97706,97708],{},[898,97707,6796],{},[2111,97709,2963],{},[1711,97711,1836],{},[2111,97713,50301],{},[902,97715,97651],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,97718,97720],{"className":97719},[886],[888,97721,97722],{"xmlns":890},[892,97723,97724,97732],{},[895,97725,97726],{},[2884,97727,97728,97730],{},[898,97729,6796],{},[2111,97731,2238],{},[902,97733,32600],{"encoding":904}," na 60 a poklesu ",[883,97736,97738],{"className":97737},[886],[888,97739,97740],{"xmlns":890},[892,97741,97742,97750],{},[895,97743,97744],{},[2884,97745,97746,97748],{},[898,97747,6796],{},[2111,97749,2963],{},[902,97751,32619],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,97754,97755,97758,97759,97820,97821,2186],{},[38,97756,97757],{},"6.4"," Je dána funkce ",[883,97760,97762],{"className":97761},[886],[888,97763,97764],{"xmlns":890},[892,97765,97766,97818],{},[895,97767,97768,97770,97772,97778,97780,97786,97788,97790,97804],{},[898,97769,900],{},[1711,97771,1714],{"stretchy":1713},[2884,97773,97774,97776],{},[898,97775,6796],{},[2111,97777,2238],{},[1711,97779,1726],{"separator":1725},[2884,97781,97782,97784],{},[898,97783,6796],{},[2111,97785,2963],{},[1711,97787,1735],{"stretchy":1713},[1711,97789,1836],{},[13142,97791,97792,97794,97796],{},[898,97793,6796],{},[2111,97795,2238],{},[895,97797,97798,97800,97802],{},[2111,97799,2238],{},[898,97801,8659],{"mathvariant":2287},[2111,97803,2963],{},[13142,97805,97806,97808,97810],{},[898,97807,6796],{},[2111,97809,2963],{},[895,97811,97812,97814,97816],{},[2111,97813,2238],{},[898,97815,8659],{"mathvariant":2287},[2111,97817,2963],{},[902,97819,33541],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,97822,97824],{"className":97823},[886],[888,97825,97826],{"xmlns":890},[892,97827,97828,97918],{},[895,97829,97830,97832,97834,97840,97842,97844,97846,97848,97850,97852,97858,97860,97862,97864,97866,97868,97870,97872,97874,97880,97882,97884,97886,97888,97890,97892,97898,97900,97902,97904,97906,97908,97910,97916],{},[898,97831,900],{},[1711,97833,1714],{"stretchy":1713},[2884,97835,97836,97838],{},[898,97837,6796],{},[2111,97839,2238],{},[1711,97841,1726],{"separator":1725},[2111,97843,2238],{},[1711,97845,1735],{"stretchy":1713},[1711,97847,1726],{"separator":1725},[898,97849,900],{},[1711,97851,1714],{"stretchy":1713},[2884,97853,97854,97856],{},[898,97855,6796],{},[2111,97857,2238],{},[1711,97859,1726],{"separator":1725},[2111,97861,2963],{},[1711,97863,1735],{"stretchy":1713},[1711,97865,1726],{"separator":1725},[898,97867,900],{},[1711,97869,1714],{"stretchy":1713},[2111,97871,2238],{},[1711,97873,1726],{"separator":1725},[2884,97875,97876,97878],{},[898,97877,6796],{},[2111,97879,2963],{},[1711,97881,1735],{"stretchy":1713},[1711,97883,1726],{"separator":1725},[898,97885,900],{},[1711,97887,1714],{"stretchy":1713},[2111,97889,2963],{},[1711,97891,1726],{"separator":1725},[2884,97893,97894,97896],{},[898,97895,6796],{},[2111,97897,2963],{},[1711,97899,1735],{"stretchy":1713},[1711,97901,1726],{"separator":1725},[898,97903,900],{},[1711,97905,1714],{"stretchy":1713},[2111,97907,3034],{},[1711,97909,1726],{"separator":1725},[2884,97911,97912,97914],{},[898,97913,6796],{},[2111,97915,2963],{},[1711,97917,1735],{"stretchy":1713},[902,97919,97920],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,97922,97923,97332,97926,97970,97971,98079,98080,1343,98105,1343,98130,98172,98173,1343,98202,98227],{},[38,97924,97925],{},"6.5",[883,97927,97929],{"className":97928},[886],[888,97930,97931],{"xmlns":890},[892,97932,97933,97967],{},[895,97934,97935,97937,97939,97953],{},[898,97936,900],{},[1711,97938,1836],{},[13142,97940,97941,97943,97945],{},[898,97942,6796],{},[2111,97944,2238],{},[895,97946,97947,97949,97951],{},[2111,97948,2963],{},[898,97950,8659],{"mathvariant":2287},[2111,97952,3034],{},[13142,97954,97955,97957,97959],{},[898,97956,6796],{},[2111,97958,2963],{},[895,97960,97961,97963,97965],{},[2111,97962,2238],{},[898,97964,8659],{"mathvariant":2287},[2111,97966,3034],{},[902,97968,97969],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,97972,97974],{"className":97973},[886],[888,97975,97976],{"xmlns":890},[892,97977,97978,98076],{},[895,97979,97980,97982,97984,97990,97992,97998,98000,98002,98004,98006,98008,98010,98016,98018,98020,98022,98024,98026,98028,98034,98036,98038,98040,98042,98044,98046,98048,98050,98056,98058,98060,98062,98064,98066,98068,98074],{},[898,97981,900],{},[1711,97983,1714],{"stretchy":1713},[2884,97985,97986,97988],{},[898,97987,6796],{},[2111,97989,2238],{},[1711,97991,1726],{"separator":1725},[2884,97993,97994,97996],{},[898,97995,6796],{},[2111,97997,2963],{},[1711,97999,1735],{"stretchy":1713},[1711,98001,1836],{},[2111,98003,2963],{},[1711,98005,1726],{"separator":1725},[898,98007,900],{},[1711,98009,1714],{"stretchy":1713},[2884,98011,98012,98014],{},[898,98013,6796],{},[2111,98015,2238],{},[1711,98017,1726],{"separator":1725},[2111,98019,3034],{},[1711,98021,1735],{"stretchy":1713},[1711,98023,1726],{"separator":1725},[898,98025,900],{},[1711,98027,1714],{"stretchy":1713},[2884,98029,98030,98032],{},[898,98031,6796],{},[2111,98033,2238],{},[1711,98035,1726],{"separator":1725},[2111,98037,2963],{},[1711,98039,1735],{"stretchy":1713},[1711,98041,1726],{"separator":1725},[898,98043,900],{},[1711,98045,1714],{"stretchy":1713},[2111,98047,2963],{},[1711,98049,1726],{"separator":1725},[2884,98051,98052,98054],{},[898,98053,6796],{},[2111,98055,2963],{},[1711,98057,1735],{"stretchy":1713},[1711,98059,1726],{"separator":1725},[898,98061,900],{},[1711,98063,1714],{"stretchy":1713},[2111,98065,3034],{},[1711,98067,1726],{"separator":1725},[2884,98069,98070,98072],{},[898,98071,6796],{},[2111,98073,2963],{},[1711,98075,1735],{"stretchy":1713},[902,98077,98078],{"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 ",[883,98081,98083],{"className":98082},[886],[888,98084,98085],{"xmlns":890},[892,98086,98087,98102],{},[895,98088,98089,98091,98093,98095,98097,98100],{},[898,98090,8243],{},[1711,98092,5144],{"stretchy":1713},[2111,98094,68157],{},[1711,98096,12405],{"separator":1725},[2111,98098,98099],{},"3,555",[1711,98101,5163],{"stretchy":1713},[902,98103,98104],{"encoding":904},"A[1{,}5; 3{,}555]",[883,98106,98108],{"className":98107},[886],[888,98109,98110],{"xmlns":890},[892,98111,98112,98127],{},[895,98113,98114,98116,98118,98120,98122,98125],{},[898,98115,26851],{},[1711,98117,5144],{"stretchy":1713},[2111,98119,56797],{},[1711,98121,12405],{"separator":1725},[2111,98123,98124],{},"1,28",[1711,98126,5163],{"stretchy":1713},[902,98128,98129],{"encoding":904},"B[2{,}5; 1{,}28]",[883,98131,98133],{"className":98132},[886],[888,98134,98135],{"xmlns":890},[892,98136,98137,98169],{},[895,98138,98139,98141,98143,98145,98147,98149,98151,98157,98159,98161,98163,98165,98167],{},[898,98140,1940],{},[1711,98142,5144],{"stretchy":1713},[2111,98144,2963],{},[1711,98146,12405],{"separator":1725},[898,98148,900],{},[1711,98150,1714],{"stretchy":1713},[2884,98152,98153,98155],{},[898,98154,6796],{},[2111,98156,2238],{},[1711,98158,1726],{"separator":1725},[2111,98160,3034],{},[1711,98162,1735],{"stretchy":1713},[1711,98164,1836],{},[2111,98166,3034],{},[1711,98168,5163],{"stretchy":1713},[902,98170,98171],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,98174,98176],{"className":98175},[886],[888,98177,98178],{"xmlns":890},[892,98179,98180,98199],{},[895,98181,98182,98184,98186,98188,98190,98192,98194,98197],{},[898,98183,2778],{},[1711,98185,5144],{"stretchy":1713},[2111,98187,3034],{},[1711,98189,12405],{"separator":1725},[2111,98191,2238],{},[1711,98193,12405],{"separator":1725},[2111,98195,98196],{},"0,832",[1711,98198,5163],{"stretchy":1713},[902,98200,98201],{"encoding":904},"D[3; 1; 0{,}832]",[883,98203,98205],{"className":98204},[886],[888,98206,98207],{"xmlns":890},[892,98208,98209,98224],{},[895,98210,98211,98213,98215,98217,98219,98222],{},[898,98212,1722],{},[1711,98214,5144],{"stretchy":1713},[2111,98216,56797],{},[1711,98218,12405],{"separator":1725},[2111,98220,98221],{},"4,32",[1711,98223,5163],{"stretchy":1713},[902,98225,98226],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,98229,98230,97332,98233,98276,98277,10454,98290,98324,98325,98342,98343,98360],{},[38,98231,98232],{},"6.6",[883,98234,98236],{"className":98235},[886],[888,98237,98238],{"xmlns":890},[892,98239,98240,98274],{},[895,98241,98242,98244,98246,98260],{},[898,98243,900],{},[1711,98245,1836],{},[13142,98247,98248,98250,98252],{},[898,98249,6796],{},[2111,98251,2238],{},[895,98253,98254,98256,98258],{},[2111,98255,2963],{},[898,98257,8659],{"mathvariant":2287},[2111,98259,3034],{},[13142,98261,98262,98264,98266],{},[898,98263,6796],{},[2111,98265,2963],{},[895,98267,98268,98270,98272],{},[2111,98269,2238],{},[898,98271,8659],{"mathvariant":2287},[2111,98273,3034],{},[902,98275,97969],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,98278,98280],{"className":98279},[886],[888,98281,98282],{"xmlns":890},[892,98283,98284,98288],{},[895,98285,98286],{},[1942,98287,14576],{},[902,98289,31836],{"encoding":904},[883,98291,98293],{"className":98292},[886],[888,98294,98295],{"xmlns":890},[892,98296,98297,98321],{},[895,98298,98299,98305,98307,98309,98311,98317,98319],{},[2884,98300,98301,98303],{},[898,98302,6796],{},[2111,98304,2238],{},[1711,98306,1836],{},[2111,98308,4282],{},[1711,98310,1726],{"separator":1725},[2884,98312,98313,98315],{},[898,98314,6796],{},[2111,98316,2963],{},[1711,98318,1836],{},[2111,98320,12357],{},[902,98322,98323],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,98326,98328],{"className":98327},[886],[888,98329,98330],{"xmlns":890},[892,98331,98332,98340],{},[895,98333,98334],{},[2884,98335,98336,98338],{},[898,98337,6796],{},[2111,98339,2238],{},[902,98341,32600],{"encoding":904},", poklesne-li ",[883,98344,98346],{"className":98345},[886],[888,98347,98348],{"xmlns":890},[892,98349,98350,98358],{},[895,98351,98352],{},[2884,98353,98354,98356],{},[898,98355,6796],{},[2111,98357,2963],{},[902,98359,32619],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,98362,98363,98366,98367,98384,98385,98402,98403,98435,98436,98461,98462,98475,98476,1343,98500,1343,98524,2186],{},[38,98364,98365],{},"6.7"," Míra uspokojení z nákupu množství ",[883,98368,98370],{"className":98369},[886],[888,98371,98372],{"xmlns":890},[892,98373,98374,98382],{},[895,98375,98376],{},[2884,98377,98378,98380],{},[898,98379,6796],{},[2111,98381,2238],{},[902,98383,32600],{"encoding":904}," nealko nápojů a množství ",[883,98386,98388],{"className":98387},[886],[888,98389,98390],{"xmlns":890},[892,98391,98392,98400],{},[895,98393,98394],{},[2884,98395,98396,98398],{},[898,98397,6796],{},[2111,98399,2963],{},[902,98401,32619],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,98404,98406],{"className":98405},[886],[888,98407,98408],{"xmlns":890},[892,98409,98410,98432],{},[895,98411,98412,98414,98416],{},[898,98413,900],{},[1711,98415,1836],{},[12097,98417,98418],{},[895,98419,98420,98426],{},[2884,98421,98422,98424],{},[898,98423,6796],{},[2111,98425,2238],{},[2884,98427,98428,98430],{},[898,98429,6796],{},[2111,98431,2963],{},[902,98433,98434],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,98437,98439],{"className":98438},[886],[888,98440,98441],{"xmlns":890},[892,98442,98443,98459],{},[895,98444,98445,98451,98453],{},[2884,98446,98447,98449],{},[898,98448,6796],{},[2111,98450,2238],{},[1711,98452,1726],{"separator":1725},[2884,98454,98455,98457],{},[898,98456,6796],{},[2111,98458,2963],{},[902,98460,39220],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,98463,98465],{"className":98464},[886],[888,98466,98467],{"xmlns":890},[892,98468,98469,98473],{},[895,98470,98471],{},[1942,98472,14576],{},[902,98474,31836],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,98477,98479],{"className":98478},[886],[888,98480,98481],{"xmlns":890},[892,98482,98483,98497],{},[895,98484,98485,98487,98489,98491,98493,98495],{},[1942,98486,14576],{},[1711,98488,1714],{"stretchy":1713},[2111,98490,4798],{},[1711,98492,1726],{"separator":1725},[2111,98494,4306],{},[1711,98496,1735],{"stretchy":1713},[902,98498,98499],{"encoding":904},"\\text{MRCS}(5, 20)",[883,98501,98503],{"className":98502},[886],[888,98504,98505],{"xmlns":890},[892,98506,98507,98521],{},[895,98508,98509,98511,98513,98515,98517,98519],{},[1942,98510,14576],{},[1711,98512,1714],{"stretchy":1713},[2111,98514,4306],{},[1711,98516,1726],{"separator":1725},[2111,98518,4798],{},[1711,98520,1735],{"stretchy":1713},[902,98522,98523],{"encoding":904},"\\text{MRCS}(20, 5)",[883,98525,98527],{"className":98526},[886],[888,98528,98529],{"xmlns":890},[892,98530,98531,98545],{},[895,98532,98533,98535,98537,98539,98541,98543],{},[1942,98534,14576],{},[1711,98536,1714],{"stretchy":1713},[2111,98538,2963],{},[1711,98540,1726],{"separator":1725},[2111,98542,7120],{},[1711,98544,1735],{"stretchy":1713},[902,98546,98547],{"encoding":904},"\\text{MRCS}(2, 50)",[1921,98549,98550],{},[724,98551,98552,98554,98555,2186],{},[883,98553,3872],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,98556,98559],{"className":98557,"dataFsResolvedFilePath":911,"href":98558},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,98561,5422],{"id":5421},[120,98563,98564,98570,98575,98581,98634,98644,98690,98745,98808,98865,98920,98959],{},[123,98565,98566,98569],{},[38,98567,98568],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,98571,98572,98574],{},[38,98573,90467],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,98576,98577,98580],{},[38,98578,98579],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,98582,98583,98585,98586,98599,98600,2186],{},[38,98584,90794],{}," — uspořádaná ",[883,98587,98589],{"className":98588},[886],[888,98590,98591],{"xmlns":890},[892,98592,98593,98597],{},[895,98594,98595],{},[898,98596,40458],{},[902,98598,40458],{"encoding":904},"-tice ",[883,98601,98603],{"className":98602},[886],[888,98604,98605],{"xmlns":890},[892,98606,98607,98631],{},[895,98608,98609,98611,98617,98619,98621,98623,98629],{},[1711,98610,1714],{"stretchy":1713},[2884,98612,98613,98615],{},[898,98614,6796],{},[2111,98616,2238],{},[1711,98618,1726],{"separator":1725},[1711,98620,13621],{},[1711,98622,1726],{"separator":1725},[2884,98624,98625,98627],{},[898,98626,6796],{},[898,98628,40458],{},[1711,98630,1735],{"stretchy":1713},[902,98632,98633],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,98635,98636,98639,98640,98643],{},[38,98637,98638],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,98641,98642],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,98645,98646,1700,98649,98689],{},[38,98647,98648],{},"Funkce užitečnosti",[883,98650,98652],{"className":98651},[886],[888,98653,98654],{"xmlns":890},[892,98655,98656,98686],{},[895,98657,98658,98660,98662,98664,98666,98672,98674,98676,98678,98684],{},[898,98659,900],{},[1711,98661,1836],{},[898,98663,900],{},[1711,98665,1714],{"stretchy":1713},[2884,98667,98668,98670],{},[898,98669,6796],{},[2111,98671,2238],{},[1711,98673,1726],{"separator":1725},[1711,98675,13621],{},[1711,98677,1726],{"separator":1725},[2884,98679,98680,98682],{},[898,98681,6796],{},[898,98683,40458],{},[1711,98685,1735],{"stretchy":1713},[902,98687,98688],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,98691,98692,1700,98695,98724,98725,1700,98728,98744],{},[38,98693,98694],{},"Mezní užitečnost",[883,98696,98698],{"className":98697},[886],[888,98699,98700],{"xmlns":890},[892,98701,98702,98722],{},[895,98703,98704,98706,98712,98714],{},[898,98705,1790],{},[2884,98707,98708,98710],{},[898,98709,900],{},[898,98711,21388],{},[1711,98713,1836],{},[13142,98715,98716,98718,98720],{},[898,98717,900],{},[898,98719,21388],{},[1711,98721,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[902,98723,90251],{"encoding":904}," — vzorec (6.2); ",[38,98726,98727],{},"totální diferenciál",[883,98729,98731],{"className":98730},[886],[888,98732,98733],{"xmlns":890},[892,98734,98735,98741],{},[895,98736,98737,98739],{},[898,98738,2098],{"mathvariant":2287},[898,98740,900],{},[902,98742,98743],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,98746,98747,98749,98750,98774,98775,98807],{},[38,98748,92430],{}," — (6.4) ",[883,98751,98753],{"className":98752},[886],[888,98754,98755],{"xmlns":890},[892,98756,98757,98771],{},[895,98758,98759,98767,98769],{},[13142,98760,98761,98763,98765],{},[898,98762,900],{},[898,98764,21388],{},[1711,98766,5225],{"mathvariant":2287,"lspace":5224,"rspace":5224},[1711,98768,2123],{},[2111,98770,2113],{},[902,98772,98773],{"encoding":904},"U'_i > 0",", (6.5) ",[883,98776,98778],{"className":98777},[886],[888,98779,98780],{"xmlns":890},[892,98781,98782,98804],{},[895,98783,98784,98800,98802],{},[13142,98785,98786,98788,98794],{},[898,98787,900],{},[895,98789,98790,98792],{},[898,98791,21388],{},[898,98793,21388],{},[895,98795,98796,98798],{},[1711,98797,5225],{"mathvariant":2287},[1711,98799,5225],{"mathvariant":2287},[1711,98801,2109],{},[2111,98803,2113],{},[902,98805,98806],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,98809,98810,1700,98812,98843,98844,2186],{},[38,98811,94218],{},[883,98813,98815],{"className":98814},[886],[888,98816,98817],{"xmlns":890},[892,98818,98819,98841],{},[895,98820,98821,98823,98825,98833],{},[898,98822,900],{},[1711,98824,1836],{},[13142,98826,98827,98829,98831],{},[898,98828,6796],{},[2111,98830,2238],{},[898,98832,207],{},[13142,98834,98835,98837,98839],{},[898,98836,6796],{},[2111,98838,2963],{},[898,98840,2223],{},[902,98842,39401],{"encoding":904}," — (6.6), speciálně ",[883,98845,98847],{"className":98846},[886],[888,98848,98849],{"xmlns":890},[892,98850,98851,98863],{},[895,98852,98853,98855,98857,98859,98861],{},[898,98854,2223],{},[1711,98856,1836],{},[2111,98858,2238],{},[1711,98860,2460],{},[898,98862,207],{},[902,98864,94372],{"encoding":904},[123,98866,98867,1700,98870,98905,98906,98919],{},[38,98868,98869],{},"Křivky užitečnosti (indiferenční)",[883,98871,98873],{"className":98872},[886],[888,98874,98875],{"xmlns":890},[892,98876,98877,98903],{},[895,98878,98879,98881,98883,98889,98891,98897,98899,98901],{},[898,98880,900],{},[1711,98882,1714],{"stretchy":1713},[2884,98884,98885,98887],{},[898,98886,6796],{},[2111,98888,2238],{},[1711,98890,1726],{"separator":1725},[2884,98892,98893,98895],{},[898,98894,6796],{},[2111,98896,2963],{},[1711,98898,1735],{"stretchy":1713},[1711,98900,1836],{},[898,98902,2090],{},[902,98904,13743],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,98907,98909],{"className":98908},[886],[888,98910,98911],{"xmlns":890},[892,98912,98913,98917],{},[895,98914,98915],{},[898,98916,900],{},[902,98918,900],{"encoding":904},", konvexní.",[123,98921,98922,1700,98924,98958],{},[38,98923,95763],{},[883,98925,98927],{"className":98926},[886],[888,98928,98929],{"xmlns":890},[892,98930,98931,98955],{},[895,98932,98933,98935,98937,98939,98945,98947,98949],{},[1942,98934,14576],{},[1711,98936,1836],{},[898,98938,1790],{},[2884,98940,98941,98943],{},[898,98942,900],{},[2111,98944,2238],{},[898,98946,8659],{"mathvariant":2287},[898,98948,1790],{},[2884,98950,98951,98953],{},[898,98952,900],{},[2111,98954,2963],{},[902,98956,98957],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,98960,98961,1700,98964,13744,98993,98996],{},[38,98962,98963],{},"Podmínka optimality",[883,98965,98967],{"className":98966},[886],[888,98968,98969],{"xmlns":890},[892,98970,98971,98991],{},[895,98972,98973,98975,98977,98983,98985],{},[1942,98974,14576],{},[1711,98976,1836],{},[2884,98978,98979,98981],{},[898,98980,7929],{},[2111,98982,2238],{},[898,98984,8659],{"mathvariant":2287},[2884,98986,98987,98989],{},[898,98988,7929],{},[2111,98990,2963],{},[902,98992,31596],{"encoding":904},[207,98994,40352],{"className":98995,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,98998,5901],{"id":5900},[120,99000,99001,99038,99079,99089],{},[123,99002,99003,1700,99006,99009,99010,99023,99024,99037],{},[38,99004,99005],{},"Navazující téma:",[207,99007,913],{"className":99008,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,99011,99013],{"className":99012},[886],[888,99014,99015],{"xmlns":890},[892,99016,99017,99021],{},[895,99018,99019],{},[898,99020,900],{},[902,99022,900],{"encoding":904},", min ",[883,99025,99027],{"className":99026},[886],[888,99028,99029],{"xmlns":890},[892,99030,99031,99035],{},[895,99032,99033],{},[898,99034,1722],{},[902,99036,1722],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,99039,99040,1700,99043,15066,99046,90006,99049,99052,99053,99056,99057,22246,99075,99078],{},[38,99041,99042],{},"Související pojmy:",[207,99044,784],{"className":99045,"dataFsResolvedFilePath":782,"href":783},[210],[207,99047,6375],{"className":99048,"dataFsResolvedFilePath":764,"href":765},[210],[207,99050,15061],{"className":99051,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,99054,15915],{"className":99055,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,99058,99060],{"className":99059},[886],[888,99061,99062],{"xmlns":890},[892,99063,99064,99072],{},[895,99065,99066],{},[2884,99067,99068,99070],{},[898,99069,2778],{},[898,99071,21388],{},[902,99073,99074],{"encoding":904},"D_i",[207,99076,793],{"className":99077,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,99080,99081,1700,99083,1343,99086],{},[38,99082,40301],{},[207,99084,1094],{"className":99085,"dataFsResolvedFilePath":838,"href":839},[210],[207,99087,1101],{"className":99088,"dataFsResolvedFilePath":868,"href":869},[210],[123,99090,99091,1700,99093],{},[38,99092,5908],{},[207,99094,5914],{"className":99095,"dataFsResolvedFilePath":5912,"href":5913},[210],{"title":641,"searchDepth":642,"depth":642,"links":99097},[99098,99099,99100,99103,99104,99107,99111,99112,99115,99116,99117,99118,99119,99120,99121],{"id":1637,"depth":642,"text":1638},{"id":90390,"depth":642,"text":90391},{"id":90450,"depth":642,"text":90451,"children":99101},[99102],{"id":90466,"depth":649,"text":90467},{"id":90773,"depth":642,"text":90774},{"id":91633,"depth":642,"text":91634,"children":99105},[99106],{"id":92180,"depth":649,"text":83809},{"id":92429,"depth":642,"text":92430,"children":99108},[99109],{"id":93302,"depth":649,"text":99110},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":94217,"depth":642,"text":94218},{"id":94753,"depth":642,"text":94754,"children":99113},[99114],{"id":95527,"depth":649,"text":95528},{"id":95757,"depth":642,"text":95758},{"id":96518,"depth":642,"text":96519},{"id":97056,"depth":642,"text":97057},{"id":53479,"depth":642,"text":53480},{"id":97192,"depth":642,"text":97193},{"id":5421,"depth":642,"text":5422},{"id":5900,"depth":642,"text":5901},{},"\u002Ftopics\u002Fuzitecnost",{"title":90174,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,13748,99128,90168,15096,99129],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":99132,"title":757,"body":99133,"course":1128,"courses":659,"created":1129,"description":99406,"extension":661,"meta":99407,"navigation":664,"path":99408,"seo":99409,"sources":99410,"stem":99411,"tags":99412,"type":5985,"updated":677,"__hash__":99418},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":99134,"toc":99398},[99135,99138,99145,99152,99156,99166,99168,99202,99206,99249,99252,99310,99314,99344,99348,99369,99371],[12,99136,757],{"id":99137},"základy-matematické-ekonomie",[724,99139,99140,99141,99144],{},"Úvodní pojmy a princip modelování v ",[207,99142,19978],{"className":99143,"dataFsResolvedFilePath":5912,"href":5913},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,99146,99147],{},[1801,99148],{"alt":99149,"className":99150,"src":99151},"imek-model-promenne",[210,1805],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,99153,99155],{"id":99154},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,99157,99158,99161,99162,99165],{},[38,99159,99160],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,99163,99164],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,99167,5422],{"id":5421},[120,99169,99170,99176,99182,99188,99197],{},[123,99171,99172,99175],{},[38,99173,99174],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,99177,99178,99181],{},[38,99179,99180],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,99183,99184,99187],{},[38,99185,99186],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,99189,99190,5204,99193,99196],{},[38,99191,99192],{},"Ceteris paribus",[614,99194,99195],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,99198,99199,99201],{},[38,99200,54233],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,99203,99205],{"id":99204},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,99207,99208,99248],{},[883,99209,99211],{"className":99210},[886],[888,99212,99213],{"xmlns":890},[892,99214,99215,99245],{},[895,99216,99217,99219,99221,99223,99225,99227,99229,99231,99233,99235,99237,99239,99241,99243],{},[898,99218,6796],{},[1711,99220,1836],{},[898,99222,2778],{},[1711,99224,1714],{"stretchy":1713},[898,99226,7929],{},[1711,99228,1726],{"separator":1725},[898,99230,1660],{},[1711,99232,1726],{"separator":1725},[898,99234,21892],{},[1711,99236,1726],{"separator":1725},[898,99238,900],{},[1711,99240,1726],{"separator":1725},[1711,99242,13621],{},[1711,99244,1735],{"stretchy":1713},[902,99246,99247],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,99250,99251],{},"Zjednodušení:",[120,99253,99254,99282],{},[123,99255,99256,1700,99259],{},[38,99257,99258],{},"Jednofaktorový model:",[883,99260,99262],{"className":99261},[886],[888,99263,99264],{"xmlns":890},[892,99265,99266,99280],{},[895,99267,99268,99270,99272,99274,99276,99278],{},[898,99269,6796],{},[1711,99271,1836],{},[898,99273,2778],{},[1711,99275,1714],{"stretchy":1713},[898,99277,7929],{},[1711,99279,1735],{"stretchy":1713},[902,99281,8181],{"encoding":904},[123,99283,99284,1700,99287],{},[38,99285,99286],{},"Inverzní zápis:",[883,99288,99290],{"className":99289},[886],[888,99291,99292],{"xmlns":890},[892,99293,99294,99308],{},[895,99295,99296,99298,99300,99302,99304,99306],{},[898,99297,7929],{},[1711,99299,1836],{},[898,99301,2778],{},[1711,99303,1714],{"stretchy":1713},[898,99305,6796],{},[1711,99307,1735],{"stretchy":1713},[902,99309,8625],{"encoding":904},[115,99311,99313],{"id":99312},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,99315,99316,99325],{},[123,99317,99318,99321,99322,1797],{},[38,99319,99320],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,99323,5946],{"className":99324,"dataFsResolvedFilePath":800,"href":801},[210],[123,99326,99327,99330,99331,99334,99335,99338,99339,99343],{},[38,99328,99329],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,99332,1145],{"className":99333,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,99336,5959],{"className":99337,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,99340,99342],{"className":99341,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,99345,99347],{"id":99346},"konvence-z-přednášek","Konvence z přednášek",[120,99349,99350,99357,99363],{},[123,99351,99352,99353,99356],{},"Symbol ",[99354,99355,6740],"code",{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,99358,99359,99360,2186],{},"Numerické výsledky ",[38,99361,99362],{},"na 3 desetinná místa",[123,99364,7887,99365,99368],{},[614,99366,99367],{},"jednotková změna"," má standardní význam (změna o 1).",[115,99370,5901],{"id":5900},[120,99372,99373,99378,99386],{},[123,99374,99375,99377],{},[38,99376,7793],{}," —",[123,99379,99380,1700,99382],{},[38,99381,7801],{},[207,99383,99385],{"className":99384,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,99387,99388,1700,99390,1343,99394],{},[38,99389,7809],{},[207,99391,99393],{"className":99392,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,99395,99397],{"className":99396,"dataFsResolvedFilePath":5912,"href":5913},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":99399},[99400,99401,99402,99403,99404,99405],{"id":99154,"depth":642,"text":99155},{"id":5421,"depth":642,"text":5422},{"id":99204,"depth":642,"text":99205},{"id":99312,"depth":642,"text":99313},{"id":99346,"depth":642,"text":99347},{"id":5900,"depth":642,"text":5901},"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":99406},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,99413,99414,99415,99416,99417],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":99420,"title":99421,"body":99422,"course":1128,"courses":659,"created":5973,"description":641,"extension":661,"meta":103694,"navigation":664,"path":103695,"seo":103696,"sources":103697,"stem":103698,"tags":103699,"type":5985,"updated":677,"__hash__":103703},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":99423,"toc":103677},[99424,99427,99521,99525,99547,99561,99613,99615,99619,99682,99725,99744,99907,100006,100009,100076,100080,100209,100248,100278,100390,100435,100501,100554,100630,100686,100688,100692,100756,100800,100820,100981,100984,101068,101165,101168,101234,101238,101287,101313,101418,101482,101487,101583,101630,101632,101635,101657,101699,101706,101739,101741,101812,101866,101975,101979,102068,102144,102408,102446,102448,102452,102455,102462,102773,102776,102834,103014,103043,103045,103049,103055,103193,103202,103204,103206,103631,103633,103635],[12,99425,99421],{"id":99426},"zdanění-trhu-dopady-daně-na-rovnováhu",[1921,99428,99429],{},[724,99430,99431,46226,99433,99446,99447,99450,99451,99453,99454,99457,99458,99479,99480,99503,99504,99507,99508,2186],{},[883,99432,2678],{},[883,99434,99436],{"className":99435},[886],[888,99437,99438],{"xmlns":890},[892,99439,99440,99444],{},[895,99441,99442],{},[898,99443,1769],{},[902,99445,1769],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,99448,99449],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,99452,90458],{}," (je-li uložena spotřebiteli). Výsledné ",[38,99455,99456],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,99459,99461],{"className":99460},[886],[888,99462,99463],{"xmlns":890},[892,99464,99465,99477],{},[895,99466,99467],{},[2884,99468,99469,99471],{},[898,99470,1769],{},[895,99472,99473,99475],{},[898,99474,46275],{},[898,99476,724],{},[902,99478,46280],{"encoding":904}," (spotřebitel) a ",[883,99481,99483],{"className":99482},[886],[888,99484,99485],{"xmlns":890},[892,99486,99487,99501],{},[895,99488,99489],{},[2884,99490,99491,99493],{},[898,99492,1769],{},[895,99494,99495,99497,99499],{},[898,99496,46298],{},[898,99498,6038],{},[898,99500,1675],{},[902,99502,46305],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,99505,99506],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,99509,99511],{"className":99510},[886],[888,99512,99513],{"xmlns":890},[892,99514,99515,99519],{},[895,99516,99517],{},[898,99518,1769],{},[902,99520,1769],{"encoding":904},[115,99522,99524],{"id":99523},"dvě-formy-zdanění","Dvě formy zdanění",[724,99526,99527,99528,99546],{},"Uvažujme jednotkovou daň ",[883,99529,99531],{"className":99530},[886],[888,99532,99533],{"xmlns":890},[892,99534,99535,99543],{},[895,99536,99537,99539,99541],{},[898,99538,1769],{},[1711,99540,2123],{},[2111,99542,2113],{},[902,99544,99545],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,99548,99549,99555],{},[123,99550,99551,99554],{},[38,99552,99553],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,99556,99557,99560],{},[38,99558,99559],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,99562,99563,99564,99577,99578,99581,99582,2186],{},"V obou případech dochází k posunu jedné z křivek o ",[883,99565,99567],{"className":99566},[886],[888,99568,99569],{"xmlns":890},[892,99570,99571,99575],{},[895,99572,99573],{},[898,99574,1769],{},[902,99576,1769],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,99579,99580],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,99583,99585],{"className":99584},[886],[888,99586,99587],{"xmlns":890},[892,99588,99589,99611],{},[895,99590,99591,99593,99595,99601,99603,99609],{},[898,99592,1722],{},[1711,99594,5144],{"stretchy":1713},[1716,99596,99597,99599],{},[898,99598,6796],{},[898,99600,1722],{},[1711,99602,1726],{"separator":1725},[1716,99604,99605,99607],{},[898,99606,7929],{},[898,99608,1722],{},[1711,99610,5163],{"stretchy":1713},[902,99612,44965],{"encoding":904},[40568,99614],{},[115,99616,99618],{"id":99617},"daň-uložená-výrobci","Daň uložená výrobci",[724,99620,99621,99622,99635,99636,99653,99654,99681],{},"Je-li daň ",[883,99623,99625],{"className":99624},[886],[888,99626,99627],{"xmlns":890},[892,99628,99629,99633],{},[895,99630,99631],{},[898,99632,1769],{},[902,99634,1769],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,99637,99639],{"className":99638},[886],[888,99640,99641],{"xmlns":890},[892,99642,99643,99651],{},[895,99644,99645,99647,99649],{},[898,99646,7929],{},[1711,99648,2460],{},[898,99650,1769],{},[902,99652,44720],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,99655,99657],{"className":99656},[886],[888,99658,99659],{"xmlns":890},[892,99660,99661,99679],{},[895,99662,99663,99665,99667,99669,99671,99673,99675,99677],{},[898,99664,7929],{},[1711,99666,2460],{},[898,99668,1769],{},[1711,99670,1836],{},[898,99672,2362],{},[1711,99674,1714],{"stretchy":1713},[898,99676,6796],{},[1711,99678,1735],{"stretchy":1713},[902,99680,44749],{"encoding":904}," nová funkce nabídky:",[883,99683,99685],{"className":99684},[886],[888,99686,99687],{"xmlns":890,"display":31664},[892,99688,99689,99723],{},[895,99690,99691,99693,99695,99701,99703,99705,99707,99709,99711,99713,99715,99717,99719,99721],{},[898,99692,7929],{},[1711,99694,1836],{},[2884,99696,99697,99699],{},[898,99698,2362],{},[2111,99700,2238],{},[1711,99702,1714],{"stretchy":1713},[898,99704,6796],{},[1711,99706,1735],{"stretchy":1713},[1711,99708,1836],{},[898,99710,2362],{},[1711,99712,1714],{"stretchy":1713},[898,99714,6796],{},[1711,99716,1735],{"stretchy":1713},[1711,99718,2095],{},[898,99720,1769],{},[898,99722,2186],{"mathvariant":2287},[902,99724,44794],{"encoding":904},[724,99726,99727,99728,1700,99741,99743],{},"Nabídka se tedy posouvá o ",[883,99729,99731],{"className":99730},[886],[888,99732,99733],{"xmlns":890},[892,99734,99735,99739],{},[895,99736,99737],{},[898,99738,1769],{},[902,99740,1769],{"encoding":904},[38,99742,44827],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,99745,99746,99747,99787,99788,2009,99816,99844,99845,99864,99865,99889,99890,1797],{},"Nový rovnovážný bod ",[883,99748,99750],{"className":99749},[886],[888,99751,99752],{"xmlns":890},[892,99753,99754,99784],{},[895,99755,99756,99762,99764,99772,99774,99782],{},[2884,99757,99758,99760],{},[898,99759,1722],{},[2111,99761,2238],{},[1711,99763,5144],{"stretchy":1713},[13142,99765,99766,99768,99770],{},[898,99767,6796],{},[2111,99769,2238],{},[898,99771,1722],{},[1711,99773,1726],{"separator":1725},[13142,99775,99776,99778,99780],{},[898,99777,7929],{},[2111,99779,2238],{},[898,99781,1722],{},[1711,99783,5163],{"stretchy":1713},[902,99785,99786],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,99789,99791],{"className":99790},[886],[888,99792,99793],{"xmlns":890},[892,99794,99795,99813],{},[895,99796,99797,99805,99807],{},[13142,99798,99799,99801,99803],{},[898,99800,6796],{},[2111,99802,2238],{},[898,99804,1722],{},[1711,99806,2109],{},[1716,99808,99809,99811],{},[898,99810,6796],{},[898,99812,1722],{},[902,99814,99815],{"encoding":904},"Q_1^E \u003C Q^E",[883,99817,99819],{"className":99818},[886],[888,99820,99821],{"xmlns":890},[892,99822,99823,99841],{},[895,99824,99825,99833,99835],{},[13142,99826,99827,99829,99831],{},[898,99828,7929],{},[2111,99830,2238],{},[898,99832,1722],{},[1711,99834,2123],{},[1716,99836,99837,99839],{},[898,99838,7929],{},[898,99840,1722],{},[902,99842,99843],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,99846,99848],{"className":99847},[886],[888,99849,99850],{"xmlns":890},[892,99851,99852,99862],{},[895,99853,99854],{},[13142,99855,99856,99858,99860],{},[898,99857,7929],{},[2111,99859,2238],{},[898,99861,1722],{},[902,99863,51455],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,99866,99868],{"className":99867},[886],[888,99869,99870],{"xmlns":890},[892,99871,99872,99886],{},[895,99873,99874,99882,99884],{},[13142,99875,99876,99878,99880],{},[898,99877,7929],{},[2111,99879,2238],{},[898,99881,1722],{},[1711,99883,2460],{},[898,99885,1769],{},[902,99887,99888],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,99891,99893],{"className":99892},[886],[888,99894,99895],{"xmlns":890},[892,99896,99897,99905],{},[895,99898,99899],{},[1716,99900,99901,99903],{},[898,99902,7929],{},[898,99904,1722],{},[902,99906,45064],{"encoding":904},[724,99908,99909],{},[614,99910,99911,99912,99942,99943,99956,99957,9652,99974,99987,99988,2186],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,99913,99915],{"className":99914},[886],[888,99916,99917],{"xmlns":890},[892,99918,99919,99939],{},[895,99920,99921,99923,99925,99931,99933,99935,99937],{},[898,99922,2362],{},[1711,99924,7123],{},[2884,99926,99927,99929],{},[898,99928,2362],{},[2111,99930,2238],{},[1711,99932,1836],{},[898,99934,2362],{},[1711,99936,2095],{},[898,99938,1769],{},[902,99940,99941],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,99944,99946],{"className":99945},[886],[888,99947,99948],{"xmlns":890},[892,99949,99950,99954],{},[895,99951,99952],{},[898,99953,1769],{},[902,99955,1769],{"encoding":904},". Průsečík ",[883,99958,99960],{"className":99959},[886],[888,99961,99962],{"xmlns":890},[892,99963,99964,99972],{},[895,99965,99966],{},[2884,99967,99968,99970],{},[898,99969,2362],{},[2111,99971,2238],{},[902,99973,44595],{"encoding":904},[883,99975,99977],{"className":99976},[886],[888,99978,99979],{"xmlns":890},[892,99980,99981,99985],{},[895,99982,99983],{},[898,99984,2778],{},[902,99986,2778],{"encoding":904}," je nový rovnovážný bod ",[883,99989,99991],{"className":99990},[886],[888,99992,99993],{"xmlns":890},[892,99994,99995,100003],{},[895,99996,99997],{},[2884,99998,99999,100001],{},[898,100000,1722],{},[2111,100002,2238],{},[902,100004,100005],{"encoding":904},"E_1",[198,100007,48901],{"id":100008},"příklad-29",[724,100010,100011,45253,100013,45288,100037,100057,100058,100075],{},[38,100012,41531],{},[883,100014,100016],{"className":100015},[886],[888,100017,100018],{"xmlns":890},[892,100019,100020,100034],{},[895,100021,100022,100024,100026,100028,100030,100032],{},[898,100023,7929],{},[1711,100025,1836],{},[2111,100027,7505],{},[1711,100029,2460],{},[2111,100031,2963],{},[898,100033,6796],{},[902,100035,100036],{"encoding":904},"P = 12 - 2Q",[883,100038,100040],{"className":100039},[886],[888,100041,100042],{"xmlns":890},[892,100043,100044,100054],{},[895,100045,100046,100048,100050,100052],{},[898,100047,7929],{},[1711,100049,1836],{},[2111,100051,6369],{},[898,100053,6796],{},[902,100055,100056],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,100059,100061],{"className":100060},[886],[888,100062,100063],{"xmlns":890},[892,100064,100065,100073],{},[895,100066,100067,100069,100071],{},[898,100068,1769],{},[1711,100070,1836],{},[2111,100072,6262],{},[902,100074,44866],{"encoding":904}," Kč.",[724,100077,100078],{},[38,100079,41563],{},[724,100081,100082,100085,100086,2366,100112,9572,100132,1343,100154,100184,100185,2186],{},[614,100083,100084],{},"Bez daně."," Z rovnosti ",[883,100087,100089],{"className":100088},[886],[888,100090,100091],{"xmlns":890},[892,100092,100093,100109],{},[895,100094,100095,100097,100099,100101,100103,100105,100107],{},[2111,100096,7505],{},[1711,100098,2460],{},[2111,100100,2963],{},[898,100102,6796],{},[1711,100104,1836],{},[2111,100106,6369],{},[898,100108,6796],{},[902,100110,100111],{"encoding":904},"12 - 2Q = 4Q",[883,100113,100115],{"className":100114},[886],[888,100116,100117],{"xmlns":890},[892,100118,100119,100129],{},[895,100120,100121,100123,100125,100127],{},[2111,100122,6262],{},[898,100124,6796],{},[1711,100126,1836],{},[2111,100128,7505],{},[902,100130,100131],{"encoding":904},"6Q = 12",[883,100133,100135],{"className":100134},[886],[888,100136,100137],{"xmlns":890},[892,100138,100139,100151],{},[895,100140,100141,100147,100149],{},[1716,100142,100143,100145],{},[898,100144,6796],{},[898,100146,1722],{},[1711,100148,1836],{},[2111,100150,2963],{},[902,100152,100153],{"encoding":904},"Q^E = 2",[883,100155,100157],{"className":100156},[886],[888,100158,100159],{"xmlns":890},[892,100160,100161,100181],{},[895,100162,100163,100169,100171,100173,100175,100177,100179],{},[1716,100164,100165,100167],{},[898,100166,7929],{},[898,100168,1722],{},[1711,100170,1836],{},[2111,100172,6369],{},[1711,100174,4795],{},[2111,100176,2963],{},[1711,100178,1836],{},[2111,100180,9568],{},[902,100182,100183],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,100186,100188],{"className":100187},[886],[888,100189,100190],{"xmlns":890},[892,100191,100192,100206],{},[895,100193,100194,100196,100198,100200,100202,100204],{},[898,100195,1722],{},[1711,100197,5144],{"stretchy":1713},[2111,100199,2963],{},[1711,100201,1726],{"separator":1725},[2111,100203,9568],{},[1711,100205,5163],{"stretchy":1713},[902,100207,100208],{"encoding":904},"E[2, 8]",[724,100210,100211,100214,100215,100247],{},[614,100212,100213],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,100216,100218],{"className":100217},[886],[888,100219,100220],{"xmlns":890},[892,100221,100222,100244],{},[895,100223,100224,100230,100232,100234,100236,100238,100240,100242],{},[2884,100225,100226,100228],{},[898,100227,2362],{},[2111,100229,2238],{},[1711,100231,2062],{},[898,100233,7929],{},[1711,100235,1836],{},[2111,100237,6369],{},[898,100239,6796],{},[1711,100241,2095],{},[2111,100243,6262],{},[902,100245,100246],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,100249,100251],{"className":100250},[886],[888,100252,100253],{"xmlns":890,"display":31664},[892,100254,100255,100275],{},[895,100256,100257,100259,100261,100263,100265,100267,100269,100271,100273],{},[2111,100258,7505],{},[1711,100260,2460],{},[2111,100262,2963],{},[898,100264,6796],{},[1711,100266,1836],{},[2111,100268,6369],{},[898,100270,6796],{},[1711,100272,2095],{},[2111,100274,6262],{},[902,100276,100277],{"encoding":904},"12 - 2Q = 4Q + 6",[724,100279,100280,100281,9572,100301,1343,100325,100361,100362,2186],{},"plyne ",[883,100282,100284],{"className":100283},[886],[888,100285,100286],{"xmlns":890},[892,100287,100288,100298],{},[895,100289,100290,100292,100294,100296],{},[2111,100291,6262],{},[898,100293,6796],{},[1711,100295,1836],{},[2111,100297,6262],{},[902,100299,100300],{"encoding":904},"6Q = 6",[883,100302,100304],{"className":100303},[886],[888,100305,100306],{"xmlns":890},[892,100307,100308,100322],{},[895,100309,100310,100318,100320],{},[13142,100311,100312,100314,100316],{},[898,100313,6796],{},[2111,100315,2238],{},[898,100317,1722],{},[1711,100319,1836],{},[2111,100321,2238],{},[902,100323,100324],{"encoding":904},"Q_1^E = 1",[883,100326,100328],{"className":100327},[886],[888,100329,100330],{"xmlns":890},[892,100331,100332,100358],{},[895,100333,100334,100342,100344,100346,100348,100350,100352,100354,100356],{},[13142,100335,100336,100338,100340],{},[898,100337,7929],{},[2111,100339,2238],{},[898,100341,1722],{},[1711,100343,1836],{},[2111,100345,6369],{},[1711,100347,4795],{},[2111,100349,2238],{},[1711,100351,2095],{},[2111,100353,6262],{},[1711,100355,1836],{},[2111,100357,4712],{},[902,100359,100360],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,100363,100365],{"className":100364},[886],[888,100366,100367],{"xmlns":890},[892,100368,100369,100387],{},[895,100370,100371,100377,100379,100381,100383,100385],{},[2884,100372,100373,100375],{},[898,100374,1722],{},[2111,100376,2238],{},[1711,100378,5144],{"stretchy":1713},[2111,100380,2238],{},[1711,100382,1726],{"separator":1725},[2111,100384,4712],{},[1711,100386,5163],{"stretchy":1713},[902,100388,100389],{"encoding":904},"E_1[1, 10]",[724,100391,100392,100395,100396,100420,100421,100434],{},[614,100393,100394],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,100397,100399],{"className":100398},[886],[888,100400,100401],{"xmlns":890},[892,100402,100403,100417],{},[895,100404,100405,100413,100415],{},[13142,100406,100407,100409,100411],{},[898,100408,7929],{},[2111,100410,2238],{},[898,100412,1722],{},[1711,100414,1836],{},[2111,100416,4712],{},[902,100418,100419],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,100422,100424],{"className":100423},[886],[888,100425,100426],{"xmlns":890},[892,100427,100428,100432],{},[895,100429,100430],{},[2111,100431,9568],{},[902,100433,9568],{"encoding":904},", navýšení je",[883,100436,100438],{"className":100437},[886],[888,100439,100440],{"xmlns":890,"display":31664},[892,100441,100442,100498],{},[895,100443,100444,100454,100456,100464,100466,100472,100474,100476,100478,100480,100482,100484,100486,100496],{},[2884,100445,100446,100448],{},[898,100447,1769],{},[895,100449,100450,100452],{},[898,100451,46275],{},[898,100453,724],{},[1711,100455,1836],{},[13142,100457,100458,100460,100462],{},[898,100459,7929],{},[2111,100461,2238],{},[898,100463,1722],{},[1711,100465,2460],{},[1716,100467,100468,100470],{},[898,100469,7929],{},[898,100471,1722],{},[1711,100473,1836],{},[2111,100475,4712],{},[1711,100477,2460],{},[2111,100479,9568],{},[1711,100481,1836],{},[2111,100483,2963],{},[1942,100485,2118],{},[895,100487,100488,100490],{},[1942,100489,13774],{},[12366,100491,100492,100494],{"accent":1725},[1942,100493,2090],{},[1711,100495,28656],{},[898,100497,2186],{"mathvariant":2287},[902,100499,100500],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,100502,100503,100504,100420,100540,100553],{},"Výrobci zůstává čistá cena ",[883,100505,100507],{"className":100506},[886],[888,100508,100509],{"xmlns":890},[892,100510,100511,100537],{},[895,100512,100513,100521,100523,100525,100527,100529,100531,100533,100535],{},[13142,100514,100515,100517,100519],{},[898,100516,7929],{},[2111,100518,2238],{},[898,100520,1722],{},[1711,100522,2460],{},[898,100524,1769],{},[1711,100526,1836],{},[2111,100528,4712],{},[1711,100530,2460],{},[2111,100532,6262],{},[1711,100534,1836],{},[2111,100536,6369],{},[902,100538,100539],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,100541,100543],{"className":100542},[886],[888,100544,100545],{"xmlns":890},[892,100546,100547,100551],{},[895,100548,100549],{},[2111,100550,9568],{},[902,100552,9568],{"encoding":904},", pokles je",[883,100555,100557],{"className":100556},[886],[888,100558,100559],{"xmlns":890,"display":31664},[892,100560,100561,100627],{},[895,100562,100563,100575,100577,100583,100585,100587,100595,100597,100599,100601,100603,100605,100607,100609,100611,100613,100615,100625],{},[2884,100564,100565,100567],{},[898,100566,1769],{},[895,100568,100569,100571,100573],{},[898,100570,46298],{},[898,100572,6038],{},[898,100574,1675],{},[1711,100576,1836],{},[1716,100578,100579,100581],{},[898,100580,7929],{},[898,100582,1722],{},[1711,100584,2460],{},[1711,100586,1714],{"stretchy":1713},[13142,100588,100589,100591,100593],{},[898,100590,7929],{},[2111,100592,2238],{},[898,100594,1722],{},[1711,100596,2460],{},[898,100598,1769],{},[1711,100600,1735],{"stretchy":1713},[1711,100602,1836],{},[2111,100604,9568],{},[1711,100606,2460],{},[2111,100608,6369],{},[1711,100610,1836],{},[2111,100612,6369],{},[1942,100614,2118],{},[895,100616,100617,100619],{},[1942,100618,13774],{},[12366,100620,100621,100623],{"accent":1725},[1942,100622,2090],{},[1711,100624,28656],{},[898,100626,2186],{"mathvariant":2287},[902,100628,100629],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,100631,100632,100633,100685],{},"Kontrola: ",[883,100634,100636],{"className":100635},[886],[888,100637,100638],{"xmlns":890},[892,100639,100640,100682],{},[895,100641,100642,100652,100654,100666,100668,100670,100672,100674,100676,100678,100680],{},[2884,100643,100644,100646],{},[898,100645,1769],{},[895,100647,100648,100650],{},[898,100649,46275],{},[898,100651,724],{},[1711,100653,2095],{},[2884,100655,100656,100658],{},[898,100657,1769],{},[895,100659,100660,100662,100664],{},[898,100661,46298],{},[898,100663,6038],{},[898,100665,1675],{},[1711,100667,1836],{},[2111,100669,2963],{},[1711,100671,2095],{},[2111,100673,6369],{},[1711,100675,1836],{},[2111,100677,6262],{},[1711,100679,1836],{},[898,100681,1769],{},[902,100683,100684],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[40568,100687],{},[115,100689,100691],{"id":100690},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,100693,99621,100694,100707,100708,100726,100727,100755],{},[883,100695,100697],{"className":100696},[886],[888,100698,100699],{"xmlns":890},[892,100700,100701,100705],{},[895,100702,100703],{},[898,100704,1769],{},[902,100706,1769],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,100709,100711],{"className":100710},[886],[888,100712,100713],{"xmlns":890},[892,100714,100715,100723],{},[895,100716,100717,100719,100721],{},[898,100718,7929],{},[1711,100720,2095],{},[898,100722,1769],{},[902,100724,100725],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,100728,100730],{"className":100729},[886],[888,100731,100732],{"xmlns":890},[892,100733,100734,100752],{},[895,100735,100736,100738,100740,100742,100744,100746,100748,100750],{},[898,100737,7929],{},[1711,100739,2095],{},[898,100741,1769],{},[1711,100743,1836],{},[898,100745,2778],{},[1711,100747,1714],{"stretchy":1713},[898,100749,6796],{},[1711,100751,1735],{"stretchy":1713},[902,100753,100754],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,100757,100759],{"className":100758},[886],[888,100760,100761],{"xmlns":890,"display":31664},[892,100762,100763,100797],{},[895,100764,100765,100767,100769,100775,100777,100779,100781,100783,100785,100787,100789,100791,100793,100795],{},[898,100766,7929],{},[1711,100768,1836],{},[2884,100770,100771,100773],{},[898,100772,2778],{},[2111,100774,2963],{},[1711,100776,1714],{"stretchy":1713},[898,100778,6796],{},[1711,100780,1735],{"stretchy":1713},[1711,100782,1836],{},[898,100784,2778],{},[1711,100786,1714],{"stretchy":1713},[898,100788,6796],{},[1711,100790,1735],{"stretchy":1713},[1711,100792,2460],{},[898,100794,1769],{},[898,100796,2186],{"mathvariant":2287},[902,100798,100799],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,100801,100802,100803,1700,100816,100819],{},"Poptávka se tedy posouvá o ",[883,100804,100806],{"className":100805},[886],[888,100807,100808],{"xmlns":890},[892,100809,100810,100814],{},[895,100811,100812],{},[898,100813,1769],{},[902,100815,1769],{"encoding":904},[38,100817,100818],{},"svisle dolů",". Nabídka se nemění.",[724,100821,99746,100822,99787,100862,2009,100890,100918,100919,100938,100939,100963,100964,1797],{},[883,100823,100825],{"className":100824},[886],[888,100826,100827],{"xmlns":890},[892,100828,100829,100859],{},[895,100830,100831,100837,100839,100847,100849,100857],{},[2884,100832,100833,100835],{},[898,100834,1722],{},[2111,100836,2963],{},[1711,100838,5144],{"stretchy":1713},[13142,100840,100841,100843,100845],{},[898,100842,6796],{},[2111,100844,2963],{},[898,100846,1722],{},[1711,100848,1726],{"separator":1725},[13142,100850,100851,100853,100855],{},[898,100852,7929],{},[2111,100854,2963],{},[898,100856,1722],{},[1711,100858,5163],{"stretchy":1713},[902,100860,100861],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,100863,100865],{"className":100864},[886],[888,100866,100867],{"xmlns":890},[892,100868,100869,100887],{},[895,100870,100871,100879,100881],{},[13142,100872,100873,100875,100877],{},[898,100874,6796],{},[2111,100876,2963],{},[898,100878,1722],{},[1711,100880,2109],{},[1716,100882,100883,100885],{},[898,100884,6796],{},[898,100886,1722],{},[902,100888,100889],{"encoding":904},"Q_2^E \u003C Q^E",[883,100891,100893],{"className":100892},[886],[888,100894,100895],{"xmlns":890},[892,100896,100897,100915],{},[895,100898,100899,100907,100909],{},[13142,100900,100901,100903,100905],{},[898,100902,7929],{},[2111,100904,2963],{},[898,100906,1722],{},[1711,100908,2109],{},[1716,100910,100911,100913],{},[898,100912,7929],{},[898,100914,1722],{},[902,100916,100917],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,100920,100922],{"className":100921},[886],[888,100923,100924],{"xmlns":890},[892,100925,100926,100936],{},[895,100927,100928],{},[13142,100929,100930,100932,100934],{},[898,100931,7929],{},[2111,100933,2963],{},[898,100935,1722],{},[902,100937,51516],{"encoding":904},", spotřebitel platí celkem ",[883,100940,100942],{"className":100941},[886],[888,100943,100944],{"xmlns":890},[892,100945,100946,100960],{},[895,100947,100948,100956,100958],{},[13142,100949,100950,100952,100954],{},[898,100951,7929],{},[2111,100953,2963],{},[898,100955,1722],{},[1711,100957,2095],{},[898,100959,1769],{},[902,100961,100962],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,100965,100967],{"className":100966},[886],[888,100968,100969],{"xmlns":890},[892,100970,100971,100979],{},[895,100972,100973],{},[1716,100974,100975,100977],{},[898,100976,7929],{},[898,100978,1722],{},[902,100980,45064],{"encoding":904},[724,100982,100983],{},"Daňové břemeno:",[883,100985,100987],{"className":100986},[886],[888,100988,100989],{"xmlns":890,"display":31664},[892,100990,100991,101065],{},[895,100992,100993,101003,101005,101007,101015,101017,101019,101021,101023,101029,101031,101033,101045,101047,101053,101055,101063],{},[2884,100994,100995,100997],{},[898,100996,1769],{},[895,100998,100999,101001],{},[898,101000,46275],{},[898,101002,724],{},[1711,101004,1836],{},[1711,101006,1714],{"stretchy":1713},[13142,101008,101009,101011,101013],{},[898,101010,7929],{},[2111,101012,2963],{},[898,101014,1722],{},[1711,101016,2095],{},[898,101018,1769],{},[1711,101020,1735],{"stretchy":1713},[1711,101022,2460],{},[1716,101024,101025,101027],{},[898,101026,7929],{},[898,101028,1722],{},[1711,101030,1726],{"separator":1725},[2102,101032],{"width":2104},[2884,101034,101035,101037],{},[898,101036,1769],{},[895,101038,101039,101041,101043],{},[898,101040,46298],{},[898,101042,6038],{},[898,101044,1675],{},[1711,101046,1836],{},[1716,101048,101049,101051],{},[898,101050,7929],{},[898,101052,1722],{},[1711,101054,2460],{},[13142,101056,101057,101059,101061],{},[898,101058,7929],{},[2111,101060,2963],{},[898,101062,1722],{},[898,101064,2186],{"mathvariant":2287},[902,101066,101067],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,101069,101070],{},[614,101071,101072,101073,101103,101104,99956,101117,9652,101134,99987,101147,2186],{},"Obrázek 2.19: Posun ",[883,101074,101076],{"className":101075},[886],[888,101077,101078],{"xmlns":890},[892,101079,101080,101100],{},[895,101081,101082,101084,101086,101092,101094,101096,101098],{},[898,101083,2778],{},[1711,101085,7123],{},[2884,101087,101088,101090],{},[898,101089,2778],{},[2111,101091,2963],{},[1711,101093,1836],{},[898,101095,2778],{},[1711,101097,2460],{},[898,101099,1769],{},[902,101101,101102],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,101105,101107],{"className":101106},[886],[888,101108,101109],{"xmlns":890},[892,101110,101111,101115],{},[895,101112,101113],{},[898,101114,1769],{},[902,101116,1769],{"encoding":904},[883,101118,101120],{"className":101119},[886],[888,101121,101122],{"xmlns":890},[892,101123,101124,101132],{},[895,101125,101126],{},[2884,101127,101128,101130],{},[898,101129,2778],{},[2111,101131,2963],{},[902,101133,41925],{"encoding":904},[883,101135,101137],{"className":101136},[886],[888,101138,101139],{"xmlns":890},[892,101140,101141,101145],{},[895,101142,101143],{},[898,101144,2362],{},[902,101146,2362],{"encoding":904},[883,101148,101150],{"className":101149},[886],[888,101151,101152],{"xmlns":890},[892,101153,101154,101162],{},[895,101155,101156],{},[2884,101157,101158,101160],{},[898,101159,1722],{},[2111,101161,2963],{},[902,101163,101164],{"encoding":904},"E_2",[198,101166,48981],{"id":101167},"příklad-210",[724,101169,101170,101172,101173,45288,101196,101215,101216,101233],{},[38,101171,41531],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,101174,101176],{"className":101175},[886],[888,101177,101178],{"xmlns":890},[892,101179,101180,101194],{},[895,101181,101182,101184,101186,101188,101190,101192],{},[898,101183,7929],{},[1711,101185,1836],{},[2111,101187,7505],{},[1711,101189,2460],{},[2111,101191,2963],{},[898,101193,6796],{},[902,101195,100036],{"encoding":904},[883,101197,101199],{"className":101198},[886],[888,101200,101201],{"xmlns":890},[892,101202,101203,101213],{},[895,101204,101205,101207,101209,101211],{},[898,101206,7929],{},[1711,101208,1836],{},[2111,101210,6369],{},[898,101212,6796],{},[902,101214,100056],{"encoding":904},". Daň ",[883,101217,101219],{"className":101218},[886],[888,101220,101221],{"xmlns":890},[892,101222,101223,101231],{},[895,101224,101225,101227,101229],{},[898,101226,1769],{},[1711,101228,1836],{},[2111,101230,6262],{},[902,101232,44866],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,101235,101236],{},[38,101237,41563],{},[724,101239,101240,101241,100247],{},"Nová poptávka je ",[883,101242,101244],{"className":101243},[886],[888,101245,101246],{"xmlns":890},[892,101247,101248,101284],{},[895,101249,101250,101256,101258,101260,101262,101264,101266,101268,101270,101272,101274,101276,101278,101280,101282],{},[2884,101251,101252,101254],{},[898,101253,2778],{},[2111,101255,2963],{},[1711,101257,2062],{},[898,101259,7929],{},[1711,101261,1836],{},[2111,101263,7505],{},[1711,101265,2460],{},[2111,101267,2963],{},[898,101269,6796],{},[1711,101271,2460],{},[2111,101273,6262],{},[1711,101275,1836],{},[2111,101277,6262],{},[1711,101279,2460],{},[2111,101281,2963],{},[898,101283,6796],{},[902,101285,101286],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,101288,101290],{"className":101289},[886],[888,101291,101292],{"xmlns":890,"display":31664},[892,101293,101294,101310],{},[895,101295,101296,101298,101300,101302,101304,101306,101308],{},[2111,101297,6262],{},[1711,101299,2460],{},[2111,101301,2963],{},[898,101303,6796],{},[1711,101305,1836],{},[2111,101307,6369],{},[898,101309,6796],{},[902,101311,101312],{"encoding":904},"6 - 2Q = 4Q",[724,101314,100280,101315,9572,101334,1343,101358,100361,101390,2186],{},[883,101316,101318],{"className":101317},[886],[888,101319,101320],{"xmlns":890},[892,101321,101322,101332],{},[895,101323,101324,101326,101328,101330],{},[2111,101325,6262],{},[898,101327,6796],{},[1711,101329,1836],{},[2111,101331,6262],{},[902,101333,100300],{"encoding":904},[883,101335,101337],{"className":101336},[886],[888,101338,101339],{"xmlns":890},[892,101340,101341,101355],{},[895,101342,101343,101351,101353],{},[13142,101344,101345,101347,101349],{},[898,101346,6796],{},[2111,101348,2963],{},[898,101350,1722],{},[1711,101352,1836],{},[2111,101354,2238],{},[902,101356,101357],{"encoding":904},"Q_2^E = 1",[883,101359,101361],{"className":101360},[886],[888,101362,101363],{"xmlns":890},[892,101364,101365,101387],{},[895,101366,101367,101375,101377,101379,101381,101383,101385],{},[13142,101368,101369,101371,101373],{},[898,101370,7929],{},[2111,101372,2963],{},[898,101374,1722],{},[1711,101376,1836],{},[2111,101378,6369],{},[1711,101380,4795],{},[2111,101382,2238],{},[1711,101384,1836],{},[2111,101386,6369],{},[902,101388,101389],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,101391,101393],{"className":101392},[886],[888,101394,101395],{"xmlns":890},[892,101396,101397,101415],{},[895,101398,101399,101405,101407,101409,101411,101413],{},[2884,101400,101401,101403],{},[898,101402,1722],{},[2111,101404,2963],{},[1711,101406,5144],{"stretchy":1713},[2111,101408,2238],{},[1711,101410,1726],{"separator":1725},[2111,101412,6369],{},[1711,101414,5163],{"stretchy":1713},[902,101416,101417],{"encoding":904},"E_2[1, 4]",[724,101419,101420,101421,101457,101458,100075],{},"Spotřebitel platí celkem ",[883,101422,101424],{"className":101423},[886],[888,101425,101426],{"xmlns":890},[892,101427,101428,101454],{},[895,101429,101430,101438,101440,101442,101444,101446,101448,101450,101452],{},[13142,101431,101432,101434,101436],{},[898,101433,7929],{},[2111,101435,2963],{},[898,101437,1722],{},[1711,101439,2095],{},[898,101441,1769],{},[1711,101443,1836],{},[2111,101445,6369],{},[1711,101447,2095],{},[2111,101449,6262],{},[1711,101451,1836],{},[2111,101453,4712],{},[902,101455,101456],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,101459,101461],{"className":101460},[886],[888,101462,101463],{"xmlns":890},[892,101464,101465,101479],{},[895,101466,101467,101475,101477],{},[13142,101468,101469,101471,101473],{},[898,101470,7929],{},[2111,101472,2963],{},[898,101474,1722],{},[1711,101476,1836],{},[2111,101478,6369],{},[902,101480,101481],{"encoding":904},"P_2^E = 4",[724,101483,101484],{},[614,101485,101486],{},"Rozklad daňového břemene:",[883,101488,101490],{"className":101489},[886],[888,101491,101492],{"xmlns":890,"display":31664},[892,101493,101494,101580],{},[895,101495,101496,101506,101508,101510,101512,101514,101516,101518,101520,101522,101524,101526,101528,101538,101540,101542,101554,101556,101558,101560,101562,101564,101566,101568,101578],{},[2884,101497,101498,101500],{},[898,101499,1769],{},[895,101501,101502,101504],{},[898,101503,46275],{},[898,101505,724],{},[1711,101507,1836],{},[1711,101509,1714],{"stretchy":1713},[2111,101511,6369],{},[1711,101513,2095],{},[2111,101515,6262],{},[1711,101517,1735],{"stretchy":1713},[1711,101519,2460],{},[2111,101521,9568],{},[1711,101523,1836],{},[2111,101525,2963],{},[1942,101527,2118],{},[895,101529,101530,101532],{},[1942,101531,13774],{},[12366,101533,101534,101536],{"accent":1725},[1942,101535,2090],{},[1711,101537,28656],{},[1711,101539,1726],{"separator":1725},[2102,101541],{"width":2104},[2884,101543,101544,101546],{},[898,101545,1769],{},[895,101547,101548,101550,101552],{},[898,101549,46298],{},[898,101551,6038],{},[898,101553,1675],{},[1711,101555,1836],{},[2111,101557,9568],{},[1711,101559,2460],{},[2111,101561,6369],{},[1711,101563,1836],{},[2111,101565,6369],{},[1942,101567,2118],{},[895,101569,101570,101572],{},[1942,101571,13774],{},[12366,101573,101574,101576],{"accent":1725},[1942,101575,2090],{},[1711,101577,28656],{},[898,101579,2186],{"mathvariant":2287},[902,101581,101582],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,101584,101585,101586,2186],{},"Opět ",[883,101587,101589],{"className":101588},[886],[888,101590,101591],{"xmlns":890},[892,101592,101593,101627],{},[895,101594,101595,101605,101607,101619,101621,101623,101625],{},[2884,101596,101597,101599],{},[898,101598,1769],{},[895,101600,101601,101603],{},[898,101602,46275],{},[898,101604,724],{},[1711,101606,2095],{},[2884,101608,101609,101611],{},[898,101610,1769],{},[895,101612,101613,101615,101617],{},[898,101614,46298],{},[898,101616,6038],{},[898,101618,1675],{},[1711,101620,1836],{},[2111,101622,6262],{},[1711,101624,1836],{},[898,101626,1769],{},[902,101628,101629],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[40568,101631],{},[115,101633,46256],{"id":101634},"daňové-břemeno",[724,101636,101637,1648,101639,101642,101643,101656],{},[38,101638,46256],{},[614,101640,101641],{},"tax burden",") je rozdělení zaplacené daně ",[883,101644,101646],{"className":101645},[886],[888,101647,101648],{"xmlns":890},[892,101649,101650,101654],{},[895,101651,101652],{},[898,101653,1769],{},[902,101655,1769],{"encoding":904}," mezi spotřebitele a výrobce:",[883,101658,101660],{"className":101659},[886],[888,101661,101662],{"xmlns":890,"display":31664},[892,101663,101664,101696],{},[895,101665,101666,101668,101670,101680,101682,101694],{},[898,101667,1769],{},[1711,101669,1836],{},[2884,101671,101672,101674],{},[898,101673,1769],{},[895,101675,101676,101678],{},[898,101677,46275],{},[898,101679,724],{},[1711,101681,2095],{},[2884,101683,101684,101686],{},[898,101685,1769],{},[895,101687,101688,101690,101692],{},[898,101689,46298],{},[898,101691,6038],{},[898,101693,1675],{},[898,101695,2186],{"mathvariant":2287},[902,101697,101698],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,101700,101701],{},[1801,101702],{"alt":101703,"className":101704,"src":101705},"imek-dan-rozklad-bremene-sklony",[210,1805],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[1921,101707,101708],{},[724,101709,101710,101712,101713,2009,101726,2186],{},[883,101711,2678],{}," 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 ",[883,101714,101716],{"className":101715},[886],[888,101717,101718],{"xmlns":890},[892,101719,101720,101724],{},[895,101721,101722],{},[898,101723,2778],{},[902,101725,2778],{"encoding":904},[883,101727,101729],{"className":101728},[886],[888,101730,101731],{"xmlns":890},[892,101732,101733,101737],{},[895,101734,101735],{},[898,101736,2362],{},[902,101738,2362],{"encoding":904},[198,101740,6459],{"id":6458},[724,101742,101743,101744,101765,101766,101779,101780,101797,101798,101811],{},"V grafu ",[883,101745,101747],{"className":101746},[886],[888,101748,101749],{"xmlns":890},[892,101750,101751,101763],{},[895,101752,101753,101755,101757,101759,101761],{},[1711,101754,1714],{"stretchy":1713},[898,101756,6796],{},[1711,101758,1726],{"separator":1725},[898,101760,7929],{},[1711,101762,1735],{"stretchy":1713},[902,101764,41289],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,101767,101769],{"className":101768},[886],[888,101770,101771],{"xmlns":890},[892,101772,101773,101777],{},[895,101774,101775],{},[898,101776,1769],{},[902,101778,1769],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,101781,101783],{"className":101782},[886],[888,101784,101785],{"xmlns":890},[892,101786,101787,101795],{},[895,101788,101789],{},[1716,101790,101791,101793],{},[898,101792,7929],{},[898,101794,1722],{},[902,101796,45064],{"encoding":904},", rozdělí se úsečka ",[883,101799,101801],{"className":101800},[886],[888,101802,101803],{"xmlns":890},[892,101804,101805,101809],{},[895,101806,101807],{},[898,101808,1769],{},[902,101810,1769],{"encoding":904}," na dvě části:",[120,101813,101814,101839],{},[123,101815,101816,101817,101838],{},"horní část odpovídá ",[883,101818,101820],{"className":101819},[886],[888,101821,101822],{"xmlns":890},[892,101823,101824,101836],{},[895,101825,101826],{},[2884,101827,101828,101830],{},[898,101829,1769],{},[895,101831,101832,101834],{},[898,101833,46275],{},[898,101835,724],{},[902,101837,46280],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,101840,101841,101842,101865],{},"dolní část odpovídá ",[883,101843,101845],{"className":101844},[886],[888,101846,101847],{"xmlns":890},[892,101848,101849,101863],{},[895,101850,101851],{},[2884,101852,101853,101855],{},[898,101854,1769],{},[895,101856,101857,101859,101861],{},[898,101858,46298],{},[898,101860,6038],{},[898,101862,1675],{},[902,101864,46305],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,101867,101868],{},[614,101869,101870,101871,6696,101884,101905,101906,101929,101930,2009,101951,101974],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,101872,101874],{"className":101873},[886],[888,101875,101876],{"xmlns":890},[892,101877,101878,101882],{},[895,101879,101880],{},[898,101881,1769],{},[902,101883,1769],{"encoding":904},[883,101885,101887],{"className":101886},[886],[888,101888,101889],{"xmlns":890},[892,101890,101891,101903],{},[895,101892,101893],{},[2884,101894,101895,101897],{},[898,101896,1769],{},[895,101898,101899,101901],{},[898,101900,46275],{},[898,101902,724],{},[902,101904,46280],{"encoding":904}," (nahoře) a ",[883,101907,101909],{"className":101908},[886],[888,101910,101911],{"xmlns":890},[892,101912,101913,101927],{},[895,101914,101915],{},[2884,101916,101917,101919],{},[898,101918,1769],{},[895,101920,101921,101923,101925],{},[898,101922,46298],{},[898,101924,6038],{},[898,101926,1675],{},[902,101928,46305],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,101931,101933],{"className":101932},[886],[888,101934,101935],{"xmlns":890},[892,101936,101937,101949],{},[895,101938,101939],{},[2884,101940,101941,101943],{},[898,101942,1769],{},[895,101944,101945,101947],{},[898,101946,46275],{},[898,101948,724],{},[902,101950,46280],{"encoding":904},[883,101952,101954],{"className":101953},[886],[888,101955,101956],{"xmlns":890},[892,101957,101958,101972],{},[895,101959,101960],{},[2884,101961,101962,101964],{},[898,101963,1769],{},[895,101965,101966,101968,101970],{},[898,101967,46298],{},[898,101969,6038],{},[898,101971,1675],{},[902,101973,46305],{"encoding":904}," je v obou případech stejná.",[198,101976,101978],{"id":101977},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,101980,101981,101982,101985,101986,1648,102009,102026,102027,1648,102050,102067],{},"Platí obecně: ",[38,101983,101984],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,101987,101989],{"className":101988},[886],[888,101990,101991],{"xmlns":890},[892,101992,101993,102007],{},[895,101994,101995,101997,101999,102001,102003,102005],{},[898,101996,7929],{},[1711,101998,1836],{},[898,102000,207],{},[898,102002,6796],{},[1711,102004,2095],{},[898,102006,2223],{},[902,102008,40658],{"encoding":904},[883,102010,102012],{"className":102011},[886],[888,102013,102014],{"xmlns":890},[892,102015,102016,102024],{},[895,102017,102018,102020,102022],{},[898,102019,207],{},[1711,102021,2109],{},[2111,102023,2113],{},[902,102025,46683],{"encoding":904},") a lineární nabídku ",[883,102028,102030],{"className":102029},[886],[888,102031,102032],{"xmlns":890},[892,102033,102034,102048],{},[895,102035,102036,102038,102040,102042,102044,102046],{},[898,102037,7929],{},[1711,102039,1836],{},[898,102041,2090],{},[898,102043,6796],{},[1711,102045,2095],{},[898,102047,2098],{},[902,102049,43840],{"encoding":904},[883,102051,102053],{"className":102052},[886],[888,102054,102055],{"xmlns":890},[892,102056,102057,102065],{},[895,102058,102059,102061,102063],{},[898,102060,2090],{},[1711,102062,2123],{},[2111,102064,2113],{},[902,102066,43858],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,102069,102071],{"className":102070},[886],[888,102072,102073],{"xmlns":890,"display":31664},[892,102074,102075,102141],{},[895,102076,102077,102101,102103,102113,102115,102139],{},[2525,102078,102079,102089],{},[2884,102080,102081,102083],{},[898,102082,1769],{},[895,102084,102085,102087],{},[898,102086,46275],{},[898,102088,724],{},[2884,102090,102091,102093],{},[898,102092,1769],{},[895,102094,102095,102097,102099],{},[898,102096,46298],{},[898,102098,6038],{},[898,102100,1675],{},[1711,102102,1836],{},[2525,102104,102105,102107],{},[898,102106,2090],{},[895,102108,102109,102111],{},[1711,102110,2460],{},[898,102112,207],{},[1711,102114,1836],{},[2525,102116,102117,102129],{},[895,102118,102119,102122,102125,102127],{},[898,102120,102121],{"mathvariant":2287},"∣",[1942,102123,102124],{},"sklon ",[898,102126,2362],{},[898,102128,102121],{"mathvariant":2287},[895,102130,102131,102133,102135,102137],{},[898,102132,102121],{"mathvariant":2287},[1942,102134,102124],{},[898,102136,2778],{},[898,102138,102121],{"mathvariant":2287},[898,102140,2186],{"mathvariant":2287},[902,102142,102143],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[1921,102145,102146,102151],{},[724,102147,102148,102150],{},[883,102149,3872],{}," Postup výpočtu rozkladu",[152,102152,102153,102188,102241,102320],{},[123,102154,102155,102156,102187],{},"Spočti rovnovážný bod ",[883,102157,102159],{"className":102158},[886],[888,102160,102161],{"xmlns":890},[892,102162,102163,102185],{},[895,102164,102165,102167,102169,102175,102177,102183],{},[898,102166,1722],{},[1711,102168,5144],{"stretchy":1713},[1716,102170,102171,102173],{},[898,102172,6796],{},[898,102174,1722],{},[1711,102176,1726],{"separator":1725},[1716,102178,102179,102181],{},[898,102180,7929],{},[898,102182,1722],{},[1711,102184,5163],{"stretchy":1713},[902,102186,44965],{"encoding":904}," bez daně.",[123,102189,102190,102191,1348,102216,1797],{},"Urči posunutou křivku (",[883,102192,102194],{"className":102193},[886],[888,102195,102196],{"xmlns":890},[892,102197,102198,102214],{},[895,102199,102200,102206,102208,102210,102212],{},[2884,102201,102202,102204],{},[898,102203,2362],{},[2111,102205,2238],{},[1711,102207,1836],{},[898,102209,2362],{},[1711,102211,2095],{},[898,102213,1769],{},[902,102215,46352],{"encoding":904},[883,102217,102219],{"className":102218},[886],[888,102220,102221],{"xmlns":890},[892,102222,102223,102239],{},[895,102224,102225,102231,102233,102235,102237],{},[2884,102226,102227,102229],{},[898,102228,2778],{},[2111,102230,2963],{},[1711,102232,1836],{},[898,102234,2778],{},[1711,102236,2460],{},[898,102238,1769],{},[902,102240,46383],{"encoding":904},[123,102242,102243,102244,7903,102263,1772,102282,7903,102301,1797],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,102245,102247],{"className":102246},[886],[888,102248,102249],{"xmlns":890},[892,102250,102251,102261],{},[895,102252,102253],{},[13142,102254,102255,102257,102259],{},[898,102256,6796],{},[2111,102258,2238],{},[898,102260,1722],{},[902,102262,51434],{"encoding":904},[883,102264,102266],{"className":102265},[886],[888,102267,102268],{"xmlns":890},[892,102269,102270,102280],{},[895,102271,102272],{},[13142,102273,102274,102276,102278],{},[898,102275,6796],{},[2111,102277,2963],{},[898,102279,1722],{},[902,102281,51496],{"encoding":904},[883,102283,102285],{"className":102284},[886],[888,102286,102287],{"xmlns":890},[892,102288,102289,102299],{},[895,102290,102291],{},[13142,102292,102293,102295,102297],{},[898,102294,7929],{},[2111,102296,2238],{},[898,102298,1722],{},[902,102300,51455],{"encoding":904},[883,102302,102304],{"className":102303},[886],[888,102305,102306],{"xmlns":890},[892,102307,102308,102318],{},[895,102309,102310],{},[13142,102311,102312,102314,102316],{},[898,102313,7929],{},[2111,102315,2963],{},[898,102317,1722],{},[902,102319,51516],{"encoding":904},[123,102321,102322,102323,2009,102344,102367,102368,2186],{},"Dopočítej ",[883,102324,102326],{"className":102325},[886],[888,102327,102328],{"xmlns":890},[892,102329,102330,102342],{},[895,102331,102332],{},[2884,102333,102334,102336],{},[898,102335,1769],{},[895,102337,102338,102340],{},[898,102339,46275],{},[898,102341,724],{},[902,102343,46280],{"encoding":904},[883,102345,102347],{"className":102346},[886],[888,102348,102349],{"xmlns":890},[892,102350,102351,102365],{},[895,102352,102353],{},[2884,102354,102355,102357],{},[898,102356,1769],{},[895,102358,102359,102361,102363],{},[898,102360,46298],{},[898,102362,6038],{},[898,102364,1675],{},[902,102366,46305],{"encoding":904}," z definice, vždy ověř ",[883,102369,102371],{"className":102370},[886],[888,102372,102373],{"xmlns":890},[892,102374,102375,102405],{},[895,102376,102377,102387,102389,102401,102403],{},[2884,102378,102379,102381],{},[898,102380,1769],{},[895,102382,102383,102385],{},[898,102384,46275],{},[898,102386,724],{},[1711,102388,2095],{},[2884,102390,102391,102393],{},[898,102392,1769],{},[895,102394,102395,102397,102399],{},[898,102396,46298],{},[898,102398,6038],{},[898,102400,1675],{},[1711,102402,1836],{},[898,102404,1769],{},[902,102406,102407],{"encoding":904},"T_{sp} + T_{vyr} = T",[1921,102409,102410],{},[724,102411,102412,102414,102415,102418,102419,2009,102432,102445],{},[883,102413,1927],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,102416,102417],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,102420,102422],{"className":102421},[886],[888,102423,102424],{"xmlns":890},[892,102425,102426,102430],{},[895,102427,102428],{},[898,102429,2778],{},[902,102431,2778],{"encoding":904},[883,102433,102435],{"className":102434},[886],[888,102436,102437],{"xmlns":890},[892,102438,102439,102443],{},[895,102440,102441],{},[898,102442,2362],{},[902,102444,2362],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[40568,102447],{},[115,102449,102451],{"id":102450},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,102453,102454],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,102456,102457],{},[1801,102458],{"alt":102459,"className":102460,"src":102461},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,1805],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,102463,102464,102476],{},[19,102465,102466],{},[22,102467,102468,102470,102473],{},[25,102469,57894],{},[25,102471,102472],{},"(a) daň výrobci",[25,102474,102475],{},"(b) daň spotřebiteli",[30,102477,102478,102533,102600,102660],{},[22,102479,102480,102483,102508],{},[35,102481,102482],{},"Rovnovážné množství",[35,102484,102485],{},[883,102486,102488],{"className":102487},[886],[888,102489,102490],{"xmlns":890},[892,102491,102492,102506],{},[895,102493,102494,102502,102504],{},[13142,102495,102496,102498,102500],{},[898,102497,6796],{},[2111,102499,2238],{},[898,102501,1722],{},[1711,102503,1836],{},[2111,102505,2238],{},[902,102507,100324],{"encoding":904},[35,102509,102510],{},[883,102511,102513],{"className":102512},[886],[888,102514,102515],{"xmlns":890},[892,102516,102517,102531],{},[895,102518,102519,102527,102529],{},[13142,102520,102521,102523,102525],{},[898,102522,6796],{},[2111,102524,2963],{},[898,102526,1722],{},[1711,102528,1836],{},[2111,102530,2238],{},[902,102532,101357],{"encoding":904},[22,102534,102535,102538,102563],{},[35,102536,102537],{},"Cena placená spotřebitelem",[35,102539,102540],{},[883,102541,102543],{"className":102542},[886],[888,102544,102545],{"xmlns":890},[892,102546,102547,102561],{},[895,102548,102549,102557,102559],{},[13142,102550,102551,102553,102555],{},[898,102552,7929],{},[2111,102554,2238],{},[898,102556,1722],{},[1711,102558,1836],{},[2111,102560,4712],{},[902,102562,100419],{"encoding":904},[35,102564,102565],{},[883,102566,102568],{"className":102567},[886],[888,102569,102570],{"xmlns":890},[892,102571,102572,102598],{},[895,102573,102574,102582,102584,102586,102588,102590,102592,102594,102596],{},[13142,102575,102576,102578,102580],{},[898,102577,7929],{},[2111,102579,2963],{},[898,102581,1722],{},[1711,102583,2095],{},[898,102585,1769],{},[1711,102587,1836],{},[2111,102589,6369],{},[1711,102591,2095],{},[2111,102593,6262],{},[1711,102595,1836],{},[2111,102597,4712],{},[902,102599,101456],{"encoding":904},[22,102601,102602,102605,102635],{},[35,102603,102604],{},"Cena přijímaná výrobcem",[35,102606,102607],{},[883,102608,102610],{"className":102609},[886],[888,102611,102612],{"xmlns":890},[892,102613,102614,102632],{},[895,102615,102616,102624,102626,102628,102630],{},[13142,102617,102618,102620,102622],{},[898,102619,7929],{},[2111,102621,2238],{},[898,102623,1722],{},[1711,102625,2460],{},[898,102627,1769],{},[1711,102629,1836],{},[2111,102631,6369],{},[902,102633,102634],{"encoding":904},"P_1^E - T = 4",[35,102636,102637],{},[883,102638,102640],{"className":102639},[886],[888,102641,102642],{"xmlns":890},[892,102643,102644,102658],{},[895,102645,102646,102654,102656],{},[13142,102647,102648,102650,102652],{},[898,102649,7929],{},[2111,102651,2963],{},[898,102653,1722],{},[1711,102655,1836],{},[2111,102657,6369],{},[902,102659,101481],{"encoding":904},[22,102661,102662,102665,102719],{},[35,102663,102664],{},"Rozklad břemene",[35,102666,102667,1343,102692],{},[883,102668,102670],{"className":102669},[886],[888,102671,102672],{"xmlns":890},[892,102673,102674,102690],{},[895,102675,102676,102686,102688],{},[2884,102677,102678,102680],{},[898,102679,1769],{},[895,102681,102682,102684],{},[898,102683,46275],{},[898,102685,724],{},[1711,102687,1836],{},[2111,102689,2963],{},[902,102691,46574],{"encoding":904},[883,102693,102695],{"className":102694},[886],[888,102696,102697],{"xmlns":890},[892,102698,102699,102717],{},[895,102700,102701,102713,102715],{},[2884,102702,102703,102705],{},[898,102704,1769],{},[895,102706,102707,102709,102711],{},[898,102708,46298],{},[898,102710,6038],{},[898,102712,1675],{},[1711,102714,1836],{},[2111,102716,6369],{},[902,102718,46603],{"encoding":904},[35,102720,102721,1343,102746],{},[883,102722,102724],{"className":102723},[886],[888,102725,102726],{"xmlns":890},[892,102727,102728,102744],{},[895,102729,102730,102740,102742],{},[2884,102731,102732,102734],{},[898,102733,1769],{},[895,102735,102736,102738],{},[898,102737,46275],{},[898,102739,724],{},[1711,102741,1836],{},[2111,102743,2963],{},[902,102745,46574],{"encoding":904},[883,102747,102749],{"className":102748},[886],[888,102750,102751],{"xmlns":890},[892,102752,102753,102771],{},[895,102754,102755,102767,102769],{},[2884,102756,102757,102759],{},[898,102758,1769],{},[895,102760,102761,102763,102765],{},[898,102762,46298],{},[898,102764,6038],{},[898,102766,1675],{},[1711,102768,1836],{},[2111,102770,6369],{},[902,102772,46603],{"encoding":904},[724,102774,102775],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,102777,102779],{"className":102778},[886],[888,102780,102781],{"xmlns":890,"display":31664},[892,102782,102783,102831],{},[895,102784,102785,102793,102795,102803,102805,102807,102815,102817,102819,102821,102829],{},[13142,102786,102787,102789,102791],{},[898,102788,6796],{},[2111,102790,2238],{},[898,102792,1722],{},[1711,102794,1836],{},[13142,102796,102797,102799,102801],{},[898,102798,6796],{},[2111,102800,2963],{},[898,102802,1722],{},[1711,102804,1726],{"separator":1725},[2102,102806],{"width":2104},[13142,102808,102809,102811,102813],{},[898,102810,7929],{},[2111,102812,2238],{},[898,102814,1722],{},[1711,102816,2460],{},[898,102818,1769],{},[1711,102820,1836],{},[13142,102822,102823,102825,102827],{},[898,102824,7929],{},[2111,102826,2963],{},[898,102828,1722],{},[898,102830,2186],{"mathvariant":2287},[902,102832,102833],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[1921,102835,102836,102855,103009],{},[724,102837,102838,102840,102841,102854],{},[883,102839,3872],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,102842,102844],{"className":102843},[886],[888,102845,102846],{"xmlns":890},[892,102847,102848,102852],{},[895,102849,102850],{},[898,102851,1769],{},[902,102853,1769],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,102856,102857,102889,102925,102962],{},[123,102858,102859,102860,1726],{},"rovnovážná množství obou režimů, ",[883,102861,102863],{"className":102862},[886],[888,102864,102865],{"xmlns":890},[892,102866,102867,102887],{},[895,102868,102869,102877,102879],{},[13142,102870,102871,102873,102875],{},[898,102872,6796],{},[2111,102874,2238],{},[898,102876,1722],{},[1711,102878,1836],{},[13142,102880,102881,102883,102885],{},[898,102882,6796],{},[2111,102884,2963],{},[898,102886,1722],{},[902,102888,46506],{"encoding":904},[123,102890,102891,102892,1726],{},"čistá cena přijímaná výrobcem, ",[883,102893,102895],{"className":102894},[886],[888,102896,102897],{"xmlns":890},[892,102898,102899,102923],{},[895,102900,102901,102909,102911,102913,102915],{},[13142,102902,102903,102905,102907],{},[898,102904,7929],{},[2111,102906,2238],{},[898,102908,1722],{},[1711,102910,2460],{},[898,102912,1769],{},[1711,102914,1836],{},[13142,102916,102917,102919,102921],{},[898,102918,7929],{},[2111,102920,2963],{},[898,102922,1722],{},[902,102924,46540],{"encoding":904},[123,102926,102927,102928,1726],{},"celková cena placená spotřebitelem, ",[883,102929,102931],{"className":102930},[886],[888,102932,102933],{"xmlns":890},[892,102934,102935,102959],{},[895,102936,102937,102945,102947,102955,102957],{},[13142,102938,102939,102941,102943],{},[898,102940,7929],{},[2111,102942,2238],{},[898,102944,1722],{},[1711,102946,1836],{},[13142,102948,102949,102951,102953],{},[898,102950,7929],{},[2111,102952,2963],{},[898,102954,1722],{},[1711,102956,2095],{},[898,102958,1769],{},[902,102960,102961],{"encoding":904},"P_1^E = P_2^E + T",[123,102963,102964,102965,2009,102986,2186],{},"rozklad daňového břemene ",[883,102966,102968],{"className":102967},[886],[888,102969,102970],{"xmlns":890},[892,102971,102972,102984],{},[895,102973,102974],{},[2884,102975,102976,102978],{},[898,102977,1769],{},[895,102979,102980,102982],{},[898,102981,46275],{},[898,102983,724],{},[902,102985,46280],{"encoding":904},[883,102987,102989],{"className":102988},[886],[888,102990,102991],{"xmlns":890},[892,102992,102993,103007],{},[895,102994,102995],{},[2884,102996,102997,102999],{},[898,102998,1769],{},[895,103000,103001,103003,103005],{},[898,103002,46298],{},[898,103004,6038],{},[898,103006,1675],{},[902,103008,46305],{"encoding":904},[724,103010,103011,103012,2186],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,103013,38795],{},[724,103015,103016,103017,2009,103030,1797],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,103018,103020],{"className":103019},[886],[888,103021,103022],{"xmlns":890},[892,103023,103024,103028],{},[895,103025,103026],{},[898,103027,2778],{},[902,103029,2778],{"encoding":904},[883,103031,103033],{"className":103032},[886],[888,103034,103035],{"xmlns":890},[892,103036,103037,103041],{},[895,103038,103039],{},[898,103040,2362],{},[902,103042,2362],{"encoding":904},[40568,103044],{},[115,103046,103048],{"id":103047},"úlohy","Úlohy",[724,103050,103051,103052,3239],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,103053,5946],{"className":103054,"dataFsResolvedFilePath":800,"href":801},[210],[120,103056,103057,103087,103118],{},[123,103058,103059,103062,103063,103086],{},[38,103060,103061],{},"Úloha 2.4"," — Poptávka ",[883,103064,103066],{"className":103065},[886],[888,103067,103068],{"xmlns":890},[892,103069,103070,103084],{},[895,103071,103072,103074,103076,103078,103080,103082],{},[898,103073,7929],{},[1711,103075,1836],{},[2111,103077,7505],{},[1711,103079,2460],{},[2111,103081,2963],{},[898,103083,6796],{},[902,103085,100036],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,103088,103089,103092,103093,103117],{},[38,103090,103091],{},"Úloha 2.9"," — Nabídka ",[883,103094,103096],{"className":103095},[886],[888,103097,103098],{"xmlns":890},[892,103099,103100,103114],{},[895,103101,103102,103104,103106,103108,103110,103112],{},[898,103103,7929],{},[1711,103105,1836],{},[2111,103107,8993],{},[898,103109,6796],{},[1711,103111,2095],{},[2111,103113,39842],{},[902,103115,103116],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,103119,103120,103123,103124,2009,103150,103174,103175,103192],{},[38,103121,103122],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,103125,103127],{"className":103126},[886],[888,103128,103129],{"xmlns":890},[892,103130,103131,103147],{},[895,103132,103133,103135,103137,103139,103141,103143,103145],{},[898,103134,7929],{},[1711,103136,1836],{},[1711,103138,2460],{},[2111,103140,6369],{},[898,103142,6796],{},[1711,103144,2095],{},[2111,103146,50301],{},[902,103148,103149],{"encoding":904},"P = -4Q + 80",[883,103151,103153],{"className":103152},[886],[888,103154,103155],{"xmlns":890},[892,103156,103157,103171],{},[895,103158,103159,103161,103163,103165,103167,103169],{},[898,103160,7929],{},[1711,103162,1836],{},[2111,103164,3034],{},[898,103166,6796],{},[1711,103168,2095],{},[2111,103170,4712],{},[902,103172,103173],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,103176,103178],{"className":103177},[886],[888,103179,103180],{"xmlns":890},[892,103181,103182,103190],{},[895,103183,103184,103186,103188],{},[898,103185,1769],{},[1711,103187,1836],{},[2111,103189,27799],{},[902,103191,51413],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,103194,103195,103196,103198,103199,103201],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,103197,48826],{}," (posun poptávky při zdanění kupujícího) a ",[38,103200,48860],{}," (posun nabídky při zdanění výrobce).",[40568,103203],{},[115,103205,5422],{"id":5421},[120,103207,103208,103227,103285,103342,103425,103471,103514,103559,103625],{},[123,103209,103210,1700,103213,103226],{},[38,103211,103212],{},"Jednotková daň",[883,103214,103216],{"className":103215},[886],[888,103217,103218],{"xmlns":890},[892,103219,103220,103224],{},[895,103221,103222],{},[898,103223,1769],{},[902,103225,1769],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,103228,103229,103231,103232,103270,103271,103284],{},[38,103230,99618],{}," — posun nabídky ",[883,103233,103235],{"className":103234},[886],[888,103236,103237],{"xmlns":890},[892,103238,103239,103267],{},[895,103240,103241,103247,103249,103251,103253,103255,103257,103259,103261,103263,103265],{},[2884,103242,103243,103245],{},[898,103244,2362],{},[2111,103246,2238],{},[1711,103248,1714],{"stretchy":1713},[898,103250,6796],{},[1711,103252,1735],{"stretchy":1713},[1711,103254,1836],{},[898,103256,2362],{},[1711,103258,1714],{"stretchy":1713},[898,103260,6796],{},[1711,103262,1735],{"stretchy":1713},[1711,103264,2095],{},[898,103266,1769],{},[902,103268,103269],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,103272,103274],{"className":103273},[886],[888,103275,103276],{"xmlns":890},[892,103277,103278,103282],{},[895,103279,103280],{},[898,103281,1769],{},[902,103283,1769],{"encoding":904}," svisle nahoru)",[123,103286,103287,103289,103290,103270,103328,103341],{},[38,103288,100691],{}," — posun poptávky ",[883,103291,103293],{"className":103292},[886],[888,103294,103295],{"xmlns":890},[892,103296,103297,103325],{},[895,103298,103299,103305,103307,103309,103311,103313,103315,103317,103319,103321,103323],{},[2884,103300,103301,103303],{},[898,103302,2778],{},[2111,103304,2963],{},[1711,103306,1714],{"stretchy":1713},[898,103308,6796],{},[1711,103310,1735],{"stretchy":1713},[1711,103312,1836],{},[898,103314,2778],{},[1711,103316,1714],{"stretchy":1713},[898,103318,6796],{},[1711,103320,1735],{"stretchy":1713},[1711,103322,2460],{},[898,103324,1769],{},[902,103326,103327],{"encoding":904},"D_2(Q) = D(Q) - T",[883,103329,103331],{"className":103330},[886],[888,103332,103333],{"xmlns":890},[892,103334,103335,103339],{},[895,103336,103337],{},[898,103338,1769],{},[902,103340,1769],{"encoding":904}," svisle dolů)",[123,103343,103344,5204,103347,45412,103386],{},[38,103345,103346],{},"Rovnovážný bod s daní",[883,103348,103350],{"className":103349},[886],[888,103351,103352],{"xmlns":890},[892,103353,103354,103384],{},[895,103355,103356,103362,103364,103372,103374,103382],{},[2884,103357,103358,103360],{},[898,103359,1722],{},[2111,103361,2238],{},[1711,103363,5144],{"stretchy":1713},[13142,103365,103366,103368,103370],{},[898,103367,6796],{},[2111,103369,2238],{},[898,103371,1722],{},[1711,103373,1726],{"separator":1725},[13142,103375,103376,103378,103380],{},[898,103377,7929],{},[2111,103379,2238],{},[898,103381,1722],{},[1711,103383,5163],{"stretchy":1713},[902,103385,99786],{"encoding":904},[883,103387,103389],{"className":103388},[886],[888,103390,103391],{"xmlns":890},[892,103392,103393,103423],{},[895,103394,103395,103401,103403,103411,103413,103421],{},[2884,103396,103397,103399],{},[898,103398,1722],{},[2111,103400,2963],{},[1711,103402,5144],{"stretchy":1713},[13142,103404,103405,103407,103409],{},[898,103406,6796],{},[2111,103408,2963],{},[898,103410,1722],{},[1711,103412,1726],{"separator":1725},[13142,103414,103415,103417,103419],{},[898,103416,7929],{},[2111,103418,2963],{},[898,103420,1722],{},[1711,103422,5163],{"stretchy":1713},[902,103424,100861],{"encoding":904},[123,103426,103427,1648,103429,103431,103432],{},[38,103428,46256],{},[614,103430,101641],{},") — rozklad ",[883,103433,103435],{"className":103434},[886],[888,103436,103437],{"xmlns":890},[892,103438,103439,103469],{},[895,103440,103441,103443,103445,103455,103457],{},[898,103442,1769],{},[1711,103444,1836],{},[2884,103446,103447,103449],{},[898,103448,1769],{},[895,103450,103451,103453],{},[898,103452,46275],{},[898,103454,724],{},[1711,103456,2095],{},[2884,103458,103459,103461],{},[898,103460,1769],{},[895,103462,103463,103465,103467],{},[898,103464,46298],{},[898,103466,6038],{},[898,103468,1675],{},[902,103470,46442],{"encoding":904},[123,103472,103473,103496,103497,1735],{},[38,103474,103475],{},[883,103476,103478],{"className":103477},[886],[888,103479,103480],{"xmlns":890},[892,103481,103482,103494],{},[895,103483,103484],{},[2884,103485,103486,103488],{},[898,103487,1769],{},[895,103489,103490,103492],{},[898,103491,46275],{},[898,103493,724],{},[902,103495,46280],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,103498,103500],{"className":103499},[886],[888,103501,103502],{"xmlns":890},[892,103503,103504,103512],{},[895,103505,103506],{},[1716,103507,103508,103510],{},[898,103509,7929],{},[898,103511,1722],{},[902,103513,45064],{"encoding":904},[123,103515,103516,103541,103542,1735],{},[38,103517,103518],{},[883,103519,103521],{"className":103520},[886],[888,103522,103523],{"xmlns":890},[892,103524,103525,103539],{},[895,103526,103527],{},[2884,103528,103529,103531],{},[898,103530,1769],{},[895,103532,103533,103535,103537],{},[898,103534,46298],{},[898,103536,6038],{},[898,103538,1675],{},[902,103540,46305],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,103543,103545],{"className":103544},[886],[888,103546,103547],{"xmlns":890},[892,103548,103549,103557],{},[895,103550,103551],{},[1716,103552,103553,103555],{},[898,103554,7929],{},[898,103556,1722],{},[902,103558,45064],{"encoding":904},[123,103560,103561,5204,103563,1343,103592],{},[38,103562,54072],{},[883,103564,103566],{"className":103565},[886],[888,103567,103568],{"xmlns":890},[892,103569,103570,103590],{},[895,103571,103572,103580,103582],{},[13142,103573,103574,103576,103578],{},[898,103575,6796],{},[2111,103577,2238],{},[898,103579,1722],{},[1711,103581,1836],{},[13142,103583,103584,103586,103588],{},[898,103585,6796],{},[2111,103587,2963],{},[898,103589,1722],{},[902,103591,46506],{"encoding":904},[883,103593,103595],{"className":103594},[886],[888,103596,103597],{"xmlns":890},[892,103598,103599,103623],{},[895,103600,103601,103609,103611,103613,103615],{},[13142,103602,103603,103605,103607],{},[898,103604,7929],{},[2111,103606,2238],{},[898,103608,1722],{},[1711,103610,2460],{},[898,103612,1769],{},[1711,103614,1836],{},[13142,103616,103617,103619,103621],{},[898,103618,7929],{},[2111,103620,2963],{},[898,103622,1722],{},[902,103624,46540],{"encoding":904},[123,103626,103627,103630],{},[38,103628,103629],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[40568,103632],{},[115,103634,5901],{"id":5900},[120,103636,103637,103645,103663,103670],{},[123,103638,103639,1700,103642],{},[38,103640,103641],{},"Kontext (hub):",[207,103643,802],{"className":103644,"dataFsResolvedFilePath":800,"href":801},[210],[123,103646,103647,1700,103649,103652,103653,22246,103655,103658,103659,103662],{},[38,103648,54321],{},[207,103650,820],{"className":103651,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,103654,58632],{},[207,103656,6375],{"className":103657,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,103660,7822],{"className":103661,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[123,103664,103665,1700,103667],{},[38,103666,54356],{},[207,103668,54360],{"className":103669,"dataFsResolvedFilePath":745,"href":746},[210],[123,103671,103672,1700,103674],{},[38,103673,5908],{},[207,103675,5914],{"className":103676,"dataFsResolvedFilePath":5912,"href":5913},[210],{"title":641,"searchDepth":642,"depth":642,"links":103678},[103679,103680,103683,103686,103690,103691,103692,103693],{"id":99523,"depth":642,"text":99524},{"id":99617,"depth":642,"text":99618,"children":103681},[103682],{"id":100008,"depth":649,"text":48901},{"id":100690,"depth":642,"text":100691,"children":103684},[103685],{"id":101167,"depth":649,"text":48981},{"id":101634,"depth":642,"text":46256,"children":103687},[103688,103689],{"id":6458,"depth":649,"text":6459},{"id":101977,"depth":649,"text":101978},{"id":102450,"depth":642,"text":102451},{"id":103047,"depth":642,"text":103048},{"id":5421,"depth":642,"text":5422},{"id":5900,"depth":642,"text":5901},{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":99421,"description":641},[1138,1135],"topics\u002Fzdaneni-trhu",[1128,54421,103700,103701,103702,5946],"dane","danove-bremeno","posun-krivek","cFuKqHgzIrqvY-l4jNdqjFEM7_ixjw33HOL0So8cPn0",[103705,103707,103711],{"slug":1128,"path":5913,"title":681,"snippet":103706},"… dni-duchod|Národní důchod]] — GNP, spotřeba\u002Fúspory, MPC\u002FMPS, modely C-I, C-I-G, C-I-G-X - \u003C\u003Cis-lm>> — simultánní rovnováha trhu zboží a peněz, fiskální\u002Fmonetární politika ## Reference a př …",{"slug":103708,"path":959,"title":103709,"snippet":103710},"imek-vzorce-prehled","ImeK — kompletní přehled vzorců se zdroji a intuicí","… $. Čím vyšší $MPC$, tím silnější násobení. --- ## 14. IS-LM analýza **Základní téma:** \u003C\u003Cis-lm>> ### Funkce investic $$I = I(r) = cr + d, \\qquad c \u003C 0, \\; d > 0$$ **Původ:** lineární …",{"slug":5932,"path":935,"title":936,"snippet":103712},"… $Y^E = 5000$, $r^E = 5$, $C^E = 4100$, $I^E = 900$) a ekonomickou interpretaci posunů viz \u003C\u003Cis-lm>>.** ## Shrnutí kapitoly 7 1. **Zjednodušený makroekonomický model** ztotožňuje $GNP \\app …",[103714,103716,103717,103720],{"slug":5932,"title":936,"path":935,"sharedTags":103715},4,{"slug":103708,"title":103709,"path":959,"sharedTags":642},{"slug":103718,"title":103719,"path":1109,"sharedTags":642},"imek-kniha","Kniha — *Úvod do matematické ekonomie pro ekonomy*",{"slug":5923,"title":103721,"path":869,"sharedTags":642},"KS 3. blok — Užitečnost a národní důchod",1777154966349]