[{"data":1,"prerenderedAt":100632},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-integral":1626,"course-stats-imek":2556,"course-topics-imek":2560,"backlinks-integral":100606,"related-integral":100629},{"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":2555},{"id":1628,"title":775,"body":1629,"course":1128,"courses":659,"created":1129,"description":2540,"extension":661,"meta":2541,"navigation":664,"path":2542,"seo":2543,"sources":2544,"stem":2545,"tags":2546,"type":2553,"updated":677,"__hash__":2554},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":1630,"toc":2530},[1631,1634,1645,1649,1707,1794,1798,1879,1925,1934,1938,1942,1978,2038,2088,2126,2130,2181,2234,2286,2330,2333,2336,2412,2415,2487,2494,2498],[12,1632,775],{"id":1633},"integrál",[724,1635,1636,1637,1640,1641,1644],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,1638,1639],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,1642,1643],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,1646,1648],{"id":1647},"neurčitý-integrál","Neurčitý integrál",[724,1650,1651],{},[883,1652,1654],{"className":1653},[886],[888,1655,1656],{"xmlns":890},[892,1657,1658,1704],{},[895,1659,1660,1663,1668,1671,1674,1677,1680,1683,1685,1687,1689,1693,1696,1698,1701],{},[898,1661,1662],{},"F",[1664,1665,1667],"mo",{"stretchy":1666},"false","(",[898,1669,1670],{},"x",[1664,1672,1673],{"stretchy":1666},")",[1664,1675,1676],{},"=",[1664,1678,1679],{},"∫",[898,1681,1682],{},"f",[1664,1684,1667],{"stretchy":1666},[898,1686,1670],{},[1664,1688,1673],{"stretchy":1666},[1690,1691,1692],"mtext",{}," ",[898,1694,1695],{},"d",[898,1697,1670],{},[1664,1699,1700],{},"+",[898,1702,1703],{},"C",[902,1705,1706],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,1708,1709,1710,1748,1749,1762,1763,1766,1767,1343,1780,1793],{},"kde ",[883,1711,1713],{"className":1712},[886],[888,1714,1715],{"xmlns":890},[892,1716,1717,1745],{},[895,1718,1719,1729,1731,1733,1735,1737,1739,1741,1743],{},[1720,1721,1722,1724],"msup",{},[898,1723,1662],{},[1664,1725,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},"normal","0em","′",[1664,1730,1667],{"stretchy":1666},[898,1732,1670],{},[1664,1734,1673],{"stretchy":1666},[1664,1736,1676],{},[898,1738,1682],{},[1664,1740,1667],{"stretchy":1666},[898,1742,1670],{},[1664,1744,1673],{"stretchy":1666},[902,1746,1747],{"encoding":904},"F'(x) = f(x)",". ",[883,1750,1752],{"className":1751},[886],[888,1753,1754],{"xmlns":890},[892,1755,1756,1760],{},[895,1757,1758],{},[898,1759,1662],{},[902,1761,1662],{"encoding":904}," je ",[38,1764,1765],{},"primitivní funkce"," k ",[883,1768,1770],{"className":1769},[886],[888,1771,1772],{"xmlns":890},[892,1773,1774,1778],{},[895,1775,1776],{},[898,1777,1682],{},[902,1779,1682],{"encoding":904},[883,1781,1783],{"className":1782},[886],[888,1784,1785],{"xmlns":890},[892,1786,1787,1791],{},[895,1788,1789],{},[898,1790,1703],{},[902,1792,1703],{"encoding":904}," konstanta.",[115,1795,1797],{"id":1796},"určitý-integrál","Určitý integrál",[724,1799,1800],{},[883,1801,1803],{"className":1802},[886],[888,1804,1805],{"xmlns":890},[892,1806,1807,1876],{},[895,1808,1809,1819,1821,1823,1825,1827,1829,1831,1833,1835,1838,1840,1842,1844,1846,1855,1857,1859,1861,1863,1865,1868,1870,1872,1874],{},[1810,1811,1812,1814,1816],"msubsup",{},[1664,1813,1679],{},[898,1815,207],{},[898,1817,1818],{},"b",[898,1820,1682],{},[1664,1822,1667],{"stretchy":1666},[898,1824,1670],{},[1664,1826,1673],{"stretchy":1666},[1690,1828,1692],{},[898,1830,1695],{},[898,1832,1670],{},[1664,1834,1676],{},[1664,1836,1837],{"stretchy":1666},"[",[898,1839,1662],{},[1664,1841,1667],{"stretchy":1666},[898,1843,1670],{},[1664,1845,1673],{"stretchy":1666},[1810,1847,1848,1851,1853],{},[1664,1849,1850],{"stretchy":1666},"]",[898,1852,207],{},[898,1854,1818],{},[1664,1856,1676],{},[898,1858,1662],{},[1664,1860,1667],{"stretchy":1666},[898,1862,1818],{},[1664,1864,1673],{"stretchy":1666},[1664,1866,1867],{},"−",[898,1869,1662],{},[1664,1871,1667],{"stretchy":1666},[898,1873,207],{},[1664,1875,1673],{"stretchy":1666},[902,1877,1878],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,1880,1881,1882,1885,1886,1899,1900,1924],{},"Geometricky ",[38,1883,1884],{},"plocha pod grafem"," ",[883,1887,1889],{"className":1888},[886],[888,1890,1891],{"xmlns":890},[892,1892,1893,1897],{},[895,1894,1895],{},[898,1896,1682],{},[902,1898,1682],{"encoding":904}," na intervalu ",[883,1901,1903],{"className":1902},[886],[888,1904,1905],{"xmlns":890},[892,1906,1907,1921],{},[895,1908,1909,1911,1913,1917,1919],{},[1664,1910,1837],{"stretchy":1666},[898,1912,207],{},[1664,1914,1916],{"separator":1915},"true",",",[898,1918,1818],{},[1664,1920,1850],{"stretchy":1666},[902,1922,1923],{"encoding":904},"[a, b]"," (orientovaná).",[724,1926,1927],{},[1928,1929],"img",{"alt":1930,"className":1931,"src":1933},"imek-integral-plocha",[210,1932],"wikilink-broken","\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,1935,1937],{"id":1936},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,1939,1941],{"id":1940},"příklad-tr-z-mr","Příklad — TR z MR",[724,1943,1944,1945,1977],{},"Mezní příjem ",[883,1946,1948],{"className":1947},[886],[888,1949,1950],{"xmlns":890},[892,1951,1952,1974],{},[895,1953,1954,1957,1960,1962,1966,1968,1971],{},[898,1955,1956],{},"M",[898,1958,1959],{},"R",[1664,1961,1676],{},[1963,1964,1965],"mn",{},"100",[1664,1967,1867],{},[1963,1969,1970],{},"2",[898,1972,1973],{},"Q",[902,1975,1976],{"encoding":904},"MR = 100 - 2Q",".",[724,1979,1980],{},[883,1981,1983],{"className":1982},[886],[888,1984,1985],{"xmlns":890},[892,1986,1987,2035],{},[895,1988,1989,1992,1994,1996,1998,2000,2002,2004,2006,2008,2010,2012,2014,2016,2018,2020,2022,2024,2030,2032],{},[898,1990,1991],{},"T",[898,1993,1959],{},[1664,1995,1676],{},[1664,1997,1679],{},[1664,1999,1667],{"stretchy":1666},[1963,2001,1965],{},[1664,2003,1867],{},[1963,2005,1970],{},[898,2007,1973],{},[1664,2009,1673],{"stretchy":1666},[1690,2011,1692],{},[898,2013,1695],{},[898,2015,1973],{},[1664,2017,1676],{},[1963,2019,1965],{},[898,2021,1973],{},[1664,2023,1867],{},[1720,2025,2026,2028],{},[898,2027,1973],{},[1963,2029,1970],{},[1664,2031,1700],{},[898,2033,2034],{},"c",[902,2036,2037],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,2039,2040,2041,2068,2069,2087],{},"Okrajová podmínka ",[883,2042,2044],{"className":2043},[886],[888,2045,2046],{"xmlns":890},[892,2047,2048,2065],{},[895,2049,2050,2052,2054,2056,2059,2061,2063],{},[898,2051,1991],{},[898,2053,1959],{},[1664,2055,1667],{"stretchy":1666},[1963,2057,2058],{},"0",[1664,2060,1673],{"stretchy":1666},[1664,2062,1676],{},[1963,2064,2058],{},[902,2066,2067],{"encoding":904},"TR(0) = 0"," ⇒ ",[883,2070,2072],{"className":2071},[886],[888,2073,2074],{"xmlns":890},[892,2075,2076,2084],{},[895,2077,2078,2080,2082],{},[898,2079,2034],{},[1664,2081,1676],{},[1963,2083,2058],{},[902,2085,2086],{"encoding":904},"c = 0",":",[724,2089,2090],{},[883,2091,2093],{"className":2092},[886],[888,2094,2095],{"xmlns":890},[892,2096,2097,2123],{},[895,2098,2099,2101,2103,2105,2107,2109,2111,2113,2115,2117],{},[898,2100,1991],{},[898,2102,1959],{},[1664,2104,1667],{"stretchy":1666},[898,2106,1973],{},[1664,2108,1673],{"stretchy":1666},[1664,2110,1676],{},[1963,2112,1965],{},[898,2114,1973],{},[1664,2116,1867],{},[1720,2118,2119,2121],{},[898,2120,1973],{},[1963,2122,1970],{},[902,2124,2125],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,2127,2129],{"id":2128},"příklad-tc-z-mc","Příklad — TC z MC",[724,2131,2132,2133,2160,2161,1977],{},"Mezní náklady ",[883,2134,2136],{"className":2135},[886],[888,2137,2138],{"xmlns":890},[892,2139,2140,2157],{},[895,2141,2142,2144,2146,2148,2150,2152,2155],{},[898,2143,1956],{},[898,2145,1703],{},[1664,2147,1676],{},[1963,2149,1970],{},[1664,2151,1700],{},[1963,2153,2154],{},"0,2",[898,2156,1973],{},[902,2158,2159],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,2162,2164],{"className":2163},[886],[888,2165,2166],{"xmlns":890},[892,2167,2168,2178],{},[895,2169,2170,2172,2174,2176],{},[898,2171,1662],{},[898,2173,1703],{},[1664,2175,1676],{},[1963,2177,1965],{},[902,2179,2180],{"encoding":904},"FC = 100",[724,2182,2183],{},[883,2184,2186],{"className":2185},[886],[888,2187,2188],{"xmlns":890},[892,2189,2190,2231],{},[895,2191,2192,2194,2196,2198,2200,2202,2204,2206,2208,2210,2212,2214,2216,2218,2221,2227,2229],{},[898,2193,1991],{},[898,2195,1703],{},[1664,2197,1676],{},[1664,2199,1679],{},[898,2201,1956],{},[898,2203,1703],{},[1690,2205,1692],{},[898,2207,1695],{},[898,2209,1973],{},[1664,2211,1676],{},[1963,2213,1970],{},[898,2215,1973],{},[1664,2217,1700],{},[1963,2219,2220],{},"0,1",[1720,2222,2223,2225],{},[898,2224,1973],{},[1963,2226,1970],{},[1664,2228,1700],{},[898,2230,2034],{},[902,2232,2233],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,2235,2040,2236,2068,2268,2087],{},[883,2237,2239],{"className":2238},[886],[888,2240,2241],{"xmlns":890},[892,2242,2243,2265],{},[895,2244,2245,2247,2249,2251,2253,2255,2257,2259,2261,2263],{},[898,2246,1991],{},[898,2248,1703],{},[1664,2250,1667],{"stretchy":1666},[1963,2252,2058],{},[1664,2254,1673],{"stretchy":1666},[1664,2256,1676],{},[898,2258,1662],{},[898,2260,1703],{},[1664,2262,1676],{},[1963,2264,1965],{},[902,2266,2267],{"encoding":904},"TC(0) = FC = 100",[883,2269,2271],{"className":2270},[886],[888,2272,2273],{"xmlns":890},[892,2274,2275,2283],{},[895,2276,2277,2279,2281],{},[898,2278,2034],{},[1664,2280,1676],{},[1963,2282,1965],{},[902,2284,2285],{"encoding":904},"c = 100",[724,2287,2288],{},[883,2289,2291],{"className":2290},[886],[888,2292,2293],{"xmlns":890},[892,2294,2295,2327],{},[895,2296,2297,2299,2301,2303,2305,2307,2309,2311,2313,2315,2317,2319,2321],{},[898,2298,1991],{},[898,2300,1703],{},[1664,2302,1667],{"stretchy":1666},[898,2304,1973],{},[1664,2306,1673],{"stretchy":1666},[1664,2308,1676],{},[1963,2310,1965],{},[1664,2312,1700],{},[1963,2314,1970],{},[898,2316,1973],{},[1664,2318,1700],{},[1963,2320,2220],{},[1720,2322,2323,2325],{},[898,2324,1973],{},[1963,2326,1970],{},[902,2328,2329],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,2331,820],{"id":2332},"přebytek-spotřebitele-a-výrobce",[724,2334,2335],{},"Přebytek spotřebitele:",[724,2337,2338],{},[883,2339,2341],{"className":2340},[886],[888,2342,2343],{"xmlns":890},[892,2344,2345,2409],{},[895,2346,2347,2349,2352,2354,2361,2363,2365,2377,2380,2382,2384,2386,2388,2390,2392,2394,2401,2403],{},[898,2348,1703],{},[898,2350,2351],{},"S",[1664,2353,1667],{"stretchy":1666},[2355,2356,2357,2359],"msub",{},[898,2358,1973],{},[1963,2360,2058],{},[1664,2362,1673],{"stretchy":1666},[1664,2364,1676],{},[1810,2366,2367,2369,2371],{},[1664,2368,1679],{},[1963,2370,2058],{},[2355,2372,2373,2375],{},[898,2374,1973],{},[1963,2376,2058],{},[898,2378,2379],{},"D",[1664,2381,1667],{"stretchy":1666},[898,2383,1973],{},[1664,2385,1673],{"stretchy":1666},[1690,2387,1692],{},[898,2389,1695],{},[898,2391,1973],{},[1664,2393,1867],{},[2355,2395,2396,2399],{},[898,2397,2398],{},"P",[1963,2400,2058],{},[1690,2402,1692],{},[2355,2404,2405,2407],{},[898,2406,1973],{},[1963,2408,2058],{},[902,2410,2411],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,2413,2414],{},"Přebytek výrobce:",[724,2416,2417],{},[883,2418,2420],{"className":2419},[886],[888,2421,2422],{"xmlns":890},[892,2423,2424,2484],{},[895,2425,2426,2428,2430,2432,2438,2440,2442,2448,2450,2456,2458,2470,2472,2474,2476,2478,2480,2482],{},[898,2427,2398],{},[898,2429,2351],{},[1664,2431,1667],{"stretchy":1666},[2355,2433,2434,2436],{},[898,2435,1973],{},[1963,2437,2058],{},[1664,2439,1673],{"stretchy":1666},[1664,2441,1676],{},[2355,2443,2444,2446],{},[898,2445,2398],{},[1963,2447,2058],{},[1690,2449,1692],{},[2355,2451,2452,2454],{},[898,2453,1973],{},[1963,2455,2058],{},[1664,2457,1867],{},[1810,2459,2460,2462,2464],{},[1664,2461,1679],{},[1963,2463,2058],{},[2355,2465,2466,2468],{},[898,2467,1973],{},[1963,2469,2058],{},[898,2471,2351],{},[1664,2473,1667],{"stretchy":1666},[898,2475,1973],{},[1664,2477,1673],{"stretchy":1666},[1690,2479,1692],{},[898,2481,1695],{},[898,2483,1973],{},[902,2485,2486],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,2488,2489,2490,1977],{},"Detailně viz ",[207,2491,2493],{"className":2492,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka",[115,2495,2497],{"id":2496},"navigace","Navigace",[120,2499,2500,2508,2516],{},[123,2501,2502,1885,2505],{},[38,2503,2504],{},"Předchozí:",[207,2506,766],{"className":2507,"dataFsResolvedFilePath":764,"href":765},[210],[123,2509,2510,1885,2513],{},[38,2511,2512],{},"Navazující:",[207,2514,784],{"className":2515,"dataFsResolvedFilePath":782,"href":783},[210],[123,2517,2518,1885,2521,2525,2526,2529],{},[38,2519,2520],{},"Souvislosti:",[207,2522,2524],{"className":2523,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk"," (TR\u002FTC), ",[207,2527,2493],{"className":2528,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":2531},[2532,2533,2534,2539],{"id":1647,"depth":642,"text":1648},{"id":1796,"depth":642,"text":1797},{"id":1936,"depth":642,"text":1937,"children":2535},[2536,2537,2538],{"id":1940,"depth":649,"text":1941},{"id":2128,"depth":649,"text":2129},{"id":2332,"depth":649,"text":820},{"id":2496,"depth":642,"text":2497},"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":2540},[1135],"topics\u002Fintegral",[1128,2547,2548,2549,2550,2551,2552],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","topic","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY","topics",{"zapisku":1625,"topics":2557,"summaries":2558,"outputs":2559},15,5,1,[2561,4427,10131,11686,12494,16778,18385,28265,37259,51326,55618,74962,87074,96033,96321],{"id":2562,"title":2563,"body":2564,"course":1128,"courses":659,"created":1129,"description":4416,"extension":661,"meta":4417,"navigation":664,"path":4418,"seo":4419,"sources":4420,"stem":4421,"tags":4422,"type":2553,"updated":677,"__hash__":4426},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":2565,"toc":4399},[2566,2569,2590,2594,2671,2674,2798,2948,2951,3031,3035,3094,3144,3151,3155,3290,3341,3345,3385,3452,3522,3530,3534,3572,3644,3648,3728,3777,3821,3825,3829,3899,3903,3953,4031,4038,4041,4094,4364,4366],[12,2567,2563],{"id":2568},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,2570,2571,2572,2578,2579,2582,2583,2586,2587,1977],{},"Matematický aparát kurzu ",[207,2573,2577],{"className":2574,"dataFsResolvedFilePath":2575,"href":2576},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","ImeK",". Bez derivace se neobejdou ",[38,2580,2581],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,2584,2585],{},"maximalizace zisku"," ani ",[38,2588,2589],{},"minimalizace nákladů",[115,2591,2593],{"id":2592},"funkce-a-polynomy","Funkce a polynomy",[724,2595,2596,2597,2622,2623,2636,2637,2650,2651,1977],{},"Funkce jedné proměnné ",[883,2598,2600],{"className":2599},[886],[888,2601,2602],{"xmlns":890},[892,2603,2604,2619],{},[895,2605,2606,2609,2611,2613,2615,2617],{},[898,2607,2608],{},"y",[1664,2610,1676],{},[898,2612,1682],{},[1664,2614,1667],{"stretchy":1666},[898,2616,1670],{},[1664,2618,1673],{"stretchy":1666},[902,2620,2621],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,2624,2626],{"className":2625},[886],[888,2627,2628],{"xmlns":890},[892,2629,2630,2634],{},[895,2631,2632],{},[898,2633,1670],{},[902,2635,1670],{"encoding":904}," (nezávislá) → ",[883,2638,2640],{"className":2639},[886],[888,2641,2642],{"xmlns":890},[892,2643,2644,2648],{},[895,2645,2646],{},[898,2647,2608],{},[902,2649,2608],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,2652,2654],{"className":2653},[886],[888,2655,2656],{"xmlns":890},[892,2657,2658,2668],{},[895,2659,2660,2662,2664,2666],{},[898,2661,1682],{},[1664,2663,1667],{"stretchy":1666},[898,2665,207],{},[1664,2667,1673],{"stretchy":1666},[902,2669,2670],{"encoding":904},"f(a)",[724,2672,2673],{},"Polynomy:",[120,2675,2676,2707,2747],{},[123,2677,2678],{},[152,2679,2680],{},[123,2681,2682,2683],{},"stupně: ",[883,2684,2686],{"className":2685},[886],[888,2687,2688],{"xmlns":890},[892,2689,2690,2704],{},[895,2691,2692,2694,2696,2698,2700,2702],{},[898,2693,2608],{},[1664,2695,1676],{},[898,2697,207],{},[898,2699,1670],{},[1664,2701,1700],{},[898,2703,1818],{},[902,2705,2706],{"encoding":904},"y = ax + b",[123,2708,2709],{},[152,2710,2711],{"start":642},[123,2712,2682,2713],{},[883,2714,2716],{"className":2715},[886],[888,2717,2718],{"xmlns":890},[892,2719,2720,2744],{},[895,2721,2722,2724,2726,2728,2734,2736,2738,2740,2742],{},[898,2723,2608],{},[1664,2725,1676],{},[898,2727,207],{},[1720,2729,2730,2732],{},[898,2731,1670],{},[1963,2733,1970],{},[1664,2735,1700],{},[898,2737,1818],{},[898,2739,1670],{},[1664,2741,1700],{},[898,2743,2034],{},[902,2745,2746],{"encoding":904},"y = ax^2 + bx + c",[123,2748,2749],{},[152,2750,2751],{"start":649},[123,2752,2682,2753],{},[883,2754,2756],{"className":2755},[886],[888,2757,2758],{"xmlns":890},[892,2759,2760,2795],{},[895,2761,2762,2764,2766,2768,2775,2777,2779,2785,2787,2789,2791,2793],{},[898,2763,2608],{},[1664,2765,1676],{},[898,2767,207],{},[1720,2769,2770,2772],{},[898,2771,1670],{},[1963,2773,2774],{},"3",[1664,2776,1700],{},[898,2778,1818],{},[1720,2780,2781,2783],{},[898,2782,1670],{},[1963,2784,1970],{},[1664,2786,1700],{},[898,2788,2034],{},[898,2790,1670],{},[1664,2792,1700],{},[898,2794,1695],{},[902,2796,2797],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,2799,2800,1885,2803,2859,2860,2898,2899,1977],{},[38,2801,2802],{},"Příklad rozkladu:",[883,2804,2806],{"className":2805},[886],[888,2807,2808],{"xmlns":890},[892,2809,2810,2856],{},[895,2811,2812,2814,2816,2822,2824,2827,2829,2831,2834,2836,2838,2840,2842,2844,2846,2848,2850,2852,2854],{},[898,2813,2608],{},[1664,2815,1676],{},[1720,2817,2818,2820],{},[898,2819,1670],{},[1963,2821,1970],{},[1664,2823,1867],{},[1963,2825,2826],{},"5",[898,2828,1670],{},[1664,2830,1700],{},[1963,2832,2833],{},"6",[1664,2835,1676],{},[1664,2837,1667],{"stretchy":1666},[898,2839,1670],{},[1664,2841,1867],{},[1963,2843,1970],{},[1664,2845,1673],{"stretchy":1666},[1664,2847,1667],{"stretchy":1666},[898,2849,1670],{},[1664,2851,1867],{},[1963,2853,2774],{},[1664,2855,1673],{"stretchy":1666},[902,2857,2858],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,2861,2863],{"className":2862},[886],[888,2864,2865],{"xmlns":890},[892,2866,2867,2895],{},[895,2868,2869,2876,2878,2880,2882,2885,2891,2893],{},[2355,2870,2871,2873],{},[898,2872,1670],{},[1963,2874,2875],{},"1",[1664,2877,1676],{},[1963,2879,1970],{},[1664,2881,1916],{"separator":1915},[1690,2883,2884],{}," ",[2355,2886,2887,2889],{},[898,2888,1670],{},[1963,2890,1970],{},[1664,2892,1676],{},[1963,2894,2774],{},[902,2896,2897],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,2900,2902],{"className":2901},[886],[888,2903,2904],{"xmlns":890},[892,2905,2906,2945],{},[895,2907,2908,2910,2912,2914,2916,2918,2928,2934,2936],{},[898,2909,2608],{},[1664,2911,1676],{},[1664,2913,1667],{"stretchy":1666},[898,2915,1670],{},[1664,2917,1867],{},[2919,2920,2921],"mstyle",{"scriptlevel":2058,"displaystyle":1666},[2922,2923,2924,2926],"mfrac",{},[1963,2925,2826],{},[1963,2927,1970],{},[1720,2929,2930,2932],{},[1664,2931,1673],{"stretchy":1666},[1963,2933,1970],{},[1664,2935,1867],{},[2919,2937,2938],{"scriptlevel":2058,"displaystyle":1666},[2922,2939,2940,2942],{},[1963,2941,2875],{},[1963,2943,2944],{},"4",[902,2946,2947],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,2949,2950],{"id":1145},"Derivace",[724,2952,2953,2954,1348,2978,3006,3007,1977],{},"Označení ",[883,2955,2957],{"className":2956},[886],[888,2958,2959],{"xmlns":890},[892,2960,2961,2975],{},[895,2962,2963,2969,2971,2973],{},[1720,2964,2965,2967],{},[898,2966,1682],{},[1664,2968,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,2970,1667],{"stretchy":1666},[898,2972,1670],{},[1664,2974,1673],{"stretchy":1666},[902,2976,2977],{"encoding":904},"f'(x)",[883,2979,2981],{"className":2980},[886],[888,2982,2983],{"xmlns":890},[892,2984,2985,3003],{},[895,2986,2987],{},[2919,2988,2989],{"scriptlevel":2058,"displaystyle":1915},[2922,2990,2991,2997],{},[895,2992,2993,2995],{},[898,2994,1695],{},[898,2996,2608],{},[895,2998,2999,3001],{},[898,3000,1695],{},[898,3002,1670],{},[902,3004,3005],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,3008,3010],{"className":3009},[886],[888,3011,3012],{"xmlns":890},[892,3013,3014,3028],{},[895,3015,3016,3022,3024,3026],{},[1720,3017,3018,3020],{},[898,3019,1682],{},[1664,3021,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,3023,1667],{"stretchy":1666},[898,3025,207],{},[1664,3027,1673],{"stretchy":1666},[902,3029,3030],{"encoding":904},"f'(a)",[198,3032,3034],{"id":3033},"geometrická-interpretace","Geometrická interpretace",[724,3036,3037,3060,3061,3064,3065,3093],{},[883,3038,3040],{"className":3039},[886],[888,3041,3042],{"xmlns":890},[892,3043,3044,3058],{},[895,3045,3046,3052,3054,3056],{},[1720,3047,3048,3050],{},[898,3049,1682],{},[1664,3051,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,3053,1667],{"stretchy":1666},[898,3055,207],{},[1664,3057,1673],{"stretchy":1666},[902,3059,3030],{"encoding":904}," = ",[38,3062,3063],{},"sklon tečny"," ke grafu funkce v bodě ",[883,3066,3068],{"className":3067},[886],[888,3069,3070],{"xmlns":890},[892,3071,3072,3090],{},[895,3073,3074,3076,3078,3080,3082,3084,3086,3088],{},[1664,3075,1837],{"stretchy":1666},[898,3077,207],{},[1664,3079,1916],{"separator":1915},[898,3081,1682],{},[1664,3083,1667],{"stretchy":1666},[898,3085,207],{},[1664,3087,1673],{"stretchy":1666},[1664,3089,1850],{"stretchy":1666},[902,3091,3092],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,3095,3096],{},[883,3097,3099],{"className":3098},[886],[888,3100,3101],{"xmlns":890},[892,3102,3103,3141],{},[895,3104,3105,3107,3109,3111,3113,3115,3117,3119,3125,3127,3129,3131,3133,3135,3137,3139],{},[898,3106,2608],{},[1664,3108,1867],{},[898,3110,1682],{},[1664,3112,1667],{"stretchy":1666},[898,3114,207],{},[1664,3116,1673],{"stretchy":1666},[1664,3118,1676],{},[1720,3120,3121,3123],{},[898,3122,1682],{},[1664,3124,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,3126,1667],{"stretchy":1666},[898,3128,207],{},[1664,3130,1673],{"stretchy":1666},[1664,3132,1667],{"stretchy":1666},[898,3134,1670],{},[1664,3136,1867],{},[898,3138,207],{},[1664,3140,1673],{"stretchy":1666},[902,3142,3143],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,3145,3146],{},[1928,3147],{"alt":3148,"className":3149,"src":3150},"imek-derivace-tecna",[210,1932],"\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,3152,3154],{"id":3153},"inženýrská-interpretace","Inženýrská interpretace",[724,3156,3157,3060,3180,1885,3183,3196,3197,3210,3211,3229,3230,3243,3244,3257,3258,3271,3272,2087],{},[883,3158,3160],{"className":3159},[886],[888,3161,3162],{"xmlns":890},[892,3163,3164,3178],{},[895,3165,3166,3172,3174,3176],{},[1720,3167,3168,3170],{},[898,3169,1682],{},[1664,3171,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,3173,1667],{"stretchy":1666},[898,3175,207],{},[1664,3177,1673],{"stretchy":1666},[902,3179,3030],{"encoding":904},[38,3181,3182],{},"rychlost změny",[883,3184,3186],{"className":3185},[886],[888,3187,3188],{"xmlns":890},[892,3189,3190,3194],{},[895,3191,3192],{},[898,3193,2608],{},[902,3195,2608],{"encoding":904}," vzhledem k ",[883,3198,3200],{"className":3199},[886],[888,3201,3202],{"xmlns":890},[892,3203,3204,3208],{},[895,3205,3206],{},[898,3207,1670],{},[902,3209,1670],{"encoding":904}," v bodě ",[883,3212,3214],{"className":3213},[886],[888,3215,3216],{"xmlns":890},[892,3217,3218,3226],{},[895,3219,3220,3222,3224],{},[898,3221,1670],{},[1664,3223,1676],{},[898,3225,207],{},[902,3227,3228],{"encoding":904},"x = a","; přibližná změna ",[883,3231,3233],{"className":3232},[886],[888,3234,3235],{"xmlns":890},[892,3236,3237,3241],{},[895,3238,3239],{},[898,3240,2608],{},[902,3242,2608],{"encoding":904}," při změně ",[883,3245,3247],{"className":3246},[886],[888,3248,3249],{"xmlns":890},[892,3250,3251,3255],{},[895,3252,3253],{},[898,3254,1670],{},[902,3256,1670],{"encoding":904}," z ",[883,3259,3261],{"className":3260},[886],[888,3262,3263],{"xmlns":890},[892,3264,3265,3269],{},[895,3266,3267],{},[898,3268,207],{},[902,3270,207],{"encoding":904}," na ",[883,3273,3275],{"className":3274},[886],[888,3276,3277],{"xmlns":890},[892,3278,3279,3287],{},[895,3280,3281,3283,3285],{},[898,3282,207],{},[1664,3284,1700],{},[1963,3286,2875],{},[902,3288,3289],{"encoding":904},"a+1",[724,3291,3292],{},[883,3293,3295],{"className":3294},[886],[888,3296,3297],{"xmlns":890},[892,3298,3299,3338],{},[895,3300,3301,3303,3305,3307,3309,3311,3313,3316,3318,3320,3322,3324,3326,3332,3334,3336],{},[898,3302,1682],{},[1664,3304,1667],{"stretchy":1666},[898,3306,207],{},[1664,3308,1700],{},[1963,3310,2875],{},[1664,3312,1673],{"stretchy":1666},[1664,3314,3315],{},"≈",[898,3317,1682],{},[1664,3319,1667],{"stretchy":1666},[898,3321,207],{},[1664,3323,1673],{"stretchy":1666},[1664,3325,1700],{},[1720,3327,3328,3330],{},[898,3329,1682],{},[1664,3331,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,3333,1667],{"stretchy":1666},[898,3335,207],{},[1664,3337,1673],{"stretchy":1666},[902,3339,3340],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,3342,3344],{"id":3343},"příklad-mezní-náklady","Příklad — mezní náklady",[724,3346,3347,3348,1977],{},"Celkové náklady ",[883,3349,3351],{"className":3350},[886],[888,3352,3353],{"xmlns":890},[892,3354,3355,3382],{},[895,3356,3357,3359,3361,3363,3366,3368,3370,3372,3374,3376],{},[898,3358,1991],{},[898,3360,1703],{},[1664,3362,1676],{},[1963,3364,3365],{},"1000",[1664,3367,1700],{},[1963,3369,1970],{},[898,3371,1973],{},[1664,3373,1700],{},[1963,3375,2220],{},[1720,3377,3378,3380],{},[898,3379,1973],{},[1963,3381,1970],{},[902,3383,3384],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,3386,3387,3388,3424,3425,1977],{},"Mezní náklady: ",[883,3389,3391],{"className":3390},[886],[888,3392,3393],{"xmlns":890},[892,3394,3395,3421],{},[895,3396,3397,3399,3401,3403,3405,3411,3413,3415,3417,3419],{},[898,3398,1956],{},[898,3400,1703],{},[1664,3402,1676],{},[898,3404,1991],{},[1720,3406,3407,3409],{},[898,3408,1703],{},[1664,3410,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,3412,1676],{},[1963,3414,1970],{},[1664,3416,1700],{},[1963,3418,2154],{},[898,3420,1973],{},[902,3422,3423],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,3426,3428],{"className":3427},[886],[888,3429,3430],{"xmlns":890},[892,3431,3432,3449],{},[895,3433,3434,3436,3438,3440,3443,3445,3447],{},[898,3435,1956],{},[898,3437,1703],{},[1664,3439,1667],{"stretchy":1666},[1963,3441,3442],{},"10",[1664,3444,1673],{"stretchy":1666},[1664,3446,1676],{},[1963,3448,2944],{},[902,3450,3451],{"encoding":904},"MC(10) = 4",[724,3453,3454,1885,3457,1748,3506,1885,3509,1977],{},[38,3455,3456],{},"Skutečný přírůstek:",[883,3458,3460],{"className":3459},[886],[888,3461,3462],{"xmlns":890},[892,3463,3464,3503],{},[895,3465,3466,3469,3471,3473,3475,3477,3479,3481,3484,3486,3488,3490,3492,3494,3496,3498,3500],{},[898,3467,3468],{"mathvariant":1726},"Δ",[898,3470,1991],{},[898,3472,1703],{},[1664,3474,1676],{},[898,3476,1991],{},[898,3478,1703],{},[1664,3480,1667],{"stretchy":1666},[1963,3482,3483],{},"11",[1664,3485,1673],{"stretchy":1666},[1664,3487,1867],{},[898,3489,1991],{},[898,3491,1703],{},[1664,3493,1667],{"stretchy":1666},[1963,3495,3442],{},[1664,3497,1673],{"stretchy":1666},[1664,3499,1676],{},[1963,3501,3502],{},"4,2",[902,3504,3505],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",[38,3507,3508],{},"Přibližný (lineární):",[883,3510,3512],{"className":3511},[886],[888,3513,3514],{"xmlns":890},[892,3515,3516,3520],{},[895,3517,3518],{},[1963,3519,2944],{},[902,3521,2944],{"encoding":904},[724,3523,3524,3525,3529],{},"(Viz aplikace v ",[207,3526,3528],{"className":3527,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk",".)",[115,3531,3533],{"id":3532},"diferenciál","Diferenciál",[724,3535,3536],{},[883,3537,3539],{"className":3538},[886],[888,3540,3541],{"xmlns":890},[892,3542,3543,3569],{},[895,3544,3545,3547,3549,3551,3557,3559,3561,3563,3565,3567],{},[898,3546,1695],{},[898,3548,1682],{},[1664,3550,1676],{},[1720,3552,3553,3555],{},[898,3554,1682],{},[1664,3556,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,3558,1667],{"stretchy":1666},[898,3560,1670],{},[1664,3562,1673],{"stretchy":1666},[1690,3564,1692],{},[898,3566,1695],{},[898,3568,1670],{},[902,3570,3571],{"encoding":904},"df = f'(x)\\, dx",[724,3573,3574,3575,3591,3592,3640,3641,1977],{},"Pro malá ",[883,3576,3578],{"className":3577},[886],[888,3579,3580],{"xmlns":890},[892,3581,3582,3588],{},[895,3583,3584,3586],{},[898,3585,1695],{},[898,3587,1670],{},[902,3589,3590],{"encoding":904},"dx"," platí: ",[883,3593,3595],{"className":3594},[886],[888,3596,3597],{"xmlns":890},[892,3598,3599,3637],{},[895,3600,3601,3603,3605,3607,3609,3611,3613,3615,3617,3619,3621,3623,3625,3627,3629,3631,3633,3635],{},[898,3602,3468],{"mathvariant":1726},[898,3604,1682],{},[1664,3606,1676],{},[898,3608,1682],{},[1664,3610,1667],{"stretchy":1666},[898,3612,1670],{},[1664,3614,1700],{},[898,3616,1695],{},[898,3618,1670],{},[1664,3620,1673],{"stretchy":1666},[1664,3622,1867],{},[898,3624,1682],{},[1664,3626,1667],{"stretchy":1666},[898,3628,1670],{},[1664,3630,1673],{"stretchy":1666},[1664,3632,3315],{},[898,3634,1695],{},[898,3636,1682],{},[902,3638,3639],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,3642,3643],{},"lineární odhad přírůstku",[198,3645,3647],{"id":3646},"příklad","Příklad",[724,3649,3650,3680,3681,3706,3707,3727],{},[883,3651,3653],{"className":3652},[886],[888,3654,3655],{"xmlns":890},[892,3656,3657,3677],{},[895,3658,3659,3661,3663,3665,3667,3669,3671],{},[898,3660,1991],{},[898,3662,1703],{},[1664,3664,1676],{},[1963,3666,1965],{},[1664,3668,1700],{},[1963,3670,2220],{},[1720,3672,3673,3675],{},[898,3674,1973],{},[1963,3676,1970],{},[902,3678,3679],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,3682,3684],{"className":3683},[886],[888,3685,3686],{"xmlns":890},[892,3687,3688,3703],{},[895,3689,3690,3692,3694,3697,3700],{},[898,3691,1973],{},[1664,3693,2087],{},[1963,3695,3696],{},"50",[1664,3698,3699],{},"→",[1963,3701,3702],{},"60",[902,3704,3705],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,3708,3710],{"className":3709},[886],[888,3711,3712],{"xmlns":890},[892,3713,3714,3724],{},[895,3715,3716,3718,3720,3722],{},[898,3717,1695],{},[898,3719,1973],{},[1664,3721,1676],{},[1963,3723,3442],{},[902,3725,3726],{"encoding":904},"dQ = 10","):",[724,3729,3730],{},[883,3731,3733],{"className":3732},[886],[888,3734,3735],{"xmlns":890},[892,3736,3737,3774],{},[895,3738,3739,3741,3743,3745,3747,3749,3751,3754,3756,3758,3760,3762,3764,3766,3768,3770,3772],{},[898,3740,1695],{},[898,3742,1991],{},[898,3744,1703],{},[1664,3746,1676],{},[1963,3748,2154],{},[898,3750,1973],{},[1664,3752,3753],{},"⋅",[898,3755,1695],{},[898,3757,1973],{},[1664,3759,1676],{},[1963,3761,2154],{},[1664,3763,3753],{},[1963,3765,3696],{},[1664,3767,3753],{},[1963,3769,3442],{},[1664,3771,1676],{},[1963,3773,1965],{},[902,3775,3776],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,3778,3779,3780,3803,3804,3820],{},"Přesná změna: ",[883,3781,3783],{"className":3782},[886],[888,3784,3785],{"xmlns":890},[892,3786,3787,3800],{},[895,3788,3789,3791,3793,3795,3797],{},[898,3790,3468],{"mathvariant":1726},[898,3792,1991],{},[898,3794,1703],{},[1664,3796,1676],{},[1963,3798,3799],{},"110",[902,3801,3802],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,3805,3807],{"className":3806},[886],[888,3808,3809],{"xmlns":890},[892,3810,3811,3817],{},[895,3812,3813,3815],{},[898,3814,1991],{},[898,3816,1703],{},[902,3818,3819],{"encoding":904},"TC"," je konvexní.",[115,3822,3824],{"id":3823},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,3826,3828],{"id":3827},"nutná-podmínka","Nutná podmínka",[724,3830,3831,3832,3210,3852,3865,3866,3894,3895,3898],{},"Má-li ",[883,3833,3835],{"className":3834},[886],[888,3836,3837],{"xmlns":890},[892,3838,3839,3849],{},[895,3840,3841,3843,3845,3847],{},[898,3842,1682],{},[1664,3844,1667],{"stretchy":1666},[898,3846,1670],{},[1664,3848,1673],{"stretchy":1666},[902,3850,3851],{"encoding":904},"f(x)",[883,3853,3855],{"className":3854},[886],[888,3856,3857],{"xmlns":890},[892,3858,3859,3863],{},[895,3860,3861],{},[898,3862,207],{},[902,3864,207],{"encoding":904}," extrém, pak ",[883,3867,3869],{"className":3868},[886],[888,3870,3871],{"xmlns":890},[892,3872,3873,3891],{},[895,3874,3875,3881,3883,3885,3887,3889],{},[1720,3876,3877,3879],{},[898,3878,1682],{},[1664,3880,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,3882,1667],{"stretchy":1666},[898,3884,207],{},[1664,3886,1673],{"stretchy":1666},[1664,3888,1676],{},[1963,3890,2058],{},[902,3892,3893],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,3896,3897],{},"stacionární"," (podezřelé) body.",[198,3900,3902],{"id":3901},"postačující-podmínka","Postačující podmínka",[724,3904,3905,3906,3919,3920,2087],{},"Pro stacionární bod ",[883,3907,3909],{"className":3908},[886],[888,3910,3911],{"xmlns":890},[892,3912,3913,3917],{},[895,3914,3915],{},[898,3916,207],{},[902,3918,207],{"encoding":904},", je-li ",[883,3921,3923],{"className":3922},[886],[888,3924,3925],{"xmlns":890},[892,3926,3927,3950],{},[895,3928,3929,3939,3941,3943,3945,3948],{},[1720,3930,3931,3933],{},[898,3932,1682],{},[895,3934,3935,3937],{},[1664,3936,1728],{"mathvariant":1726},[1664,3938,1728],{"mathvariant":1726},[1664,3940,1667],{"stretchy":1666},[898,3942,207],{},[1664,3944,1673],{"stretchy":1666},[1664,3946,3947],{"mathvariant":1726},"≠",[1963,3949,2058],{},[902,3951,3952],{"encoding":904},"f''(a) \\neq 0",[120,3954,3955,3993],{},[123,3956,3957,2068,3990],{},[883,3958,3960],{"className":3959},[886],[888,3961,3962],{"xmlns":890},[892,3963,3964,3987],{},[895,3965,3966,3976,3978,3980,3982,3985],{},[1720,3967,3968,3970],{},[898,3969,1682],{},[895,3971,3972,3974],{},[1664,3973,1728],{"mathvariant":1726},[1664,3975,1728],{"mathvariant":1726},[1664,3977,1667],{"stretchy":1666},[898,3979,207],{},[1664,3981,1673],{"stretchy":1666},[1664,3983,3984],{},">",[1963,3986,2058],{},[902,3988,3989],{"encoding":904},"f''(a) > 0",[38,3991,3992],{},"lokální minimum",[123,3994,3995,2068,4028],{},[883,3996,3998],{"className":3997},[886],[888,3999,4000],{"xmlns":890},[892,4001,4002,4025],{},[895,4003,4004,4014,4016,4018,4020,4023],{},[1720,4005,4006,4008],{},[898,4007,1682],{},[895,4009,4010,4012],{},[1664,4011,1728],{"mathvariant":1726},[1664,4013,1728],{"mathvariant":1726},[1664,4015,1667],{"stretchy":1666},[898,4017,207],{},[1664,4019,1673],{"stretchy":1666},[1664,4021,4022],{},"\u003C",[1963,4024,2058],{},[902,4026,4027],{"encoding":904},"f''(a) \u003C 0",[38,4029,4030],{},"lokální maximum",[724,4032,4033],{},[1928,4034],{"alt":4035,"className":4036,"src":4037},"imek-extremy-1d",[210,1932],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,4039,3647],{"id":4040},"příklad-1",[724,4042,4043],{},[883,4044,4046],{"className":4045},[886],[888,4047,4048],{"xmlns":890},[892,4049,4050,4091],{},[895,4051,4052,4054,4056,4058,4060,4062,4064,4070,4072,4074,4080,4082,4085,4087,4089],{},[898,4053,1682],{},[1664,4055,1667],{"stretchy":1666},[898,4057,1670],{},[1664,4059,1673],{"stretchy":1666},[1664,4061,1676],{},[1963,4063,1970],{},[1720,4065,4066,4068],{},[898,4067,1670],{},[1963,4069,2774],{},[1664,4071,1867],{},[1963,4073,2774],{},[1720,4075,4076,4078],{},[898,4077,1670],{},[1963,4079,1970],{},[1664,4081,1867],{},[1963,4083,4084],{},"12",[898,4086,1670],{},[1664,4088,1700],{},[1963,4090,2774],{},[902,4092,4093],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,4095,4096,4207,4247,4310],{},[123,4097,4098,4170,4171],{},[883,4099,4101],{"className":4100},[886],[888,4102,4103],{"xmlns":890},[892,4104,4105,4167],{},[895,4106,4107,4113,4115,4117,4119,4121,4123,4129,4131,4133,4135,4137,4139,4141,4143,4145,4147,4149,4151,4153,4155,4157,4159,4161,4163,4165],{},[1720,4108,4109,4111],{},[898,4110,1682],{},[1664,4112,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,4114,1667],{"stretchy":1666},[898,4116,1670],{},[1664,4118,1673],{"stretchy":1666},[1664,4120,1676],{},[1963,4122,2833],{},[1720,4124,4125,4127],{},[898,4126,1670],{},[1963,4128,1970],{},[1664,4130,1867],{},[1963,4132,2833],{},[898,4134,1670],{},[1664,4136,1867],{},[1963,4138,4084],{},[1664,4140,1676],{},[1963,4142,2833],{},[1664,4144,1667],{"stretchy":1666},[898,4146,1670],{},[1664,4148,1700],{},[1963,4150,2875],{},[1664,4152,1673],{"stretchy":1666},[1664,4154,1667],{"stretchy":1666},[898,4156,1670],{},[1664,4158,1867],{},[1963,4160,1970],{},[1664,4162,1673],{"stretchy":1666},[1664,4164,1676],{},[1963,4166,2058],{},[902,4168,4169],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,4172,4174],{"className":4173},[886],[888,4175,4176],{"xmlns":890},[892,4177,4178,4204],{},[895,4179,4180,4186,4188,4190,4192,4194,4200,4202],{},[2355,4181,4182,4184],{},[898,4183,1670],{},[1963,4185,2875],{},[1664,4187,1676],{},[1664,4189,1867],{},[1963,4191,2875],{},[1664,4193,1916],{"separator":1915},[2355,4195,4196,4198],{},[898,4197,1670],{},[1963,4199,1970],{},[1664,4201,1676],{},[1963,4203,1970],{},[902,4205,4206],{"encoding":904},"x_1 = -1, x_2 = 2",[123,4208,4209],{},[883,4210,4212],{"className":4211},[886],[888,4213,4214],{"xmlns":890},[892,4215,4216,4244],{},[895,4217,4218,4228,4230,4232,4234,4236,4238,4240,4242],{},[1720,4219,4220,4222],{},[898,4221,1682],{},[895,4223,4224,4226],{},[1664,4225,1728],{"mathvariant":1726},[1664,4227,1728],{"mathvariant":1726},[1664,4229,1667],{"stretchy":1666},[898,4231,1670],{},[1664,4233,1673],{"stretchy":1666},[1664,4235,1676],{},[1963,4237,4084],{},[898,4239,1670],{},[1664,4241,1867],{},[1963,4243,2833],{},[902,4245,4246],{"encoding":904},"f''(x) = 12x - 6",[123,4248,4249,2068,4290,4293,4294],{},[883,4250,4252],{"className":4251},[886],[888,4253,4254],{"xmlns":890},[892,4255,4256,4287],{},[895,4257,4258,4268,4270,4272,4274,4276,4278,4280,4283,4285],{},[1720,4259,4260,4262],{},[898,4261,1682],{},[895,4263,4264,4266],{},[1664,4265,1728],{"mathvariant":1726},[1664,4267,1728],{"mathvariant":1726},[1664,4269,1667],{"stretchy":1666},[1664,4271,1867],{},[1963,4273,2875],{},[1664,4275,1673],{"stretchy":1666},[1664,4277,1676],{},[1664,4279,1867],{},[1963,4281,4282],{},"18",[1664,4284,4022],{},[1963,4286,2058],{},[902,4288,4289],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,4291,4292],{},"maximum"," v ",[883,4295,4297],{"className":4296},[886],[888,4298,4299],{"xmlns":890},[892,4300,4301,4307],{},[895,4302,4303,4305],{},[1664,4304,1867],{},[1963,4306,2875],{},[902,4308,4309],{"encoding":904},"-1",[123,4311,4312,2068,4348,4293,4351],{},[883,4313,4315],{"className":4314},[886],[888,4316,4317],{"xmlns":890},[892,4318,4319,4345],{},[895,4320,4321,4331,4333,4335,4337,4339,4341,4343],{},[1720,4322,4323,4325],{},[898,4324,1682],{},[895,4326,4327,4329],{},[1664,4328,1728],{"mathvariant":1726},[1664,4330,1728],{"mathvariant":1726},[1664,4332,1667],{"stretchy":1666},[1963,4334,1970],{},[1664,4336,1673],{"stretchy":1666},[1664,4338,1676],{},[1963,4340,4282],{},[1664,4342,3984],{},[1963,4344,2058],{},[902,4346,4347],{"encoding":904},"f''(2) = 18 > 0",[38,4349,4350],{},"minimum",[883,4352,4354],{"className":4353},[886],[888,4355,4356],{"xmlns":890},[892,4357,4358,4362],{},[895,4359,4360],{},[1963,4361,1970],{},[902,4363,1970],{"encoding":904},[115,4365,2497],{"id":2496},[120,4367,4368,4375,4382],{},[123,4369,4370,1885,4372],{},[38,4371,2504],{},[207,4373,757],{"className":4374,"dataFsResolvedFilePath":755,"href":756},[210],[123,4376,4377,1885,4379],{},[38,4378,2512],{},[207,4380,775],{"className":4381,"dataFsResolvedFilePath":773,"href":774},[210],[123,4383,4384,1885,4386,4389,4390,4393,4394,4398],{},[38,4385,2520],{},[207,4387,784],{"className":4388,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,4391,2524],{"className":4392,"dataFsResolvedFilePath":827,"href":828},[210]," (aplikace mezních veličin), ",[207,4395,4397],{"className":4396,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita"," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":4400},[4401,4402,4407,4410,4415],{"id":2592,"depth":642,"text":2593},{"id":1145,"depth":642,"text":2950,"children":4403},[4404,4405,4406],{"id":3033,"depth":649,"text":3034},{"id":3153,"depth":649,"text":3154},{"id":3343,"depth":649,"text":3344},{"id":3532,"depth":642,"text":3533,"children":4408},[4409],{"id":3646,"depth":649,"text":3647},{"id":3823,"depth":642,"text":3824,"children":4411},[4412,4413,4414],{"id":3827,"depth":649,"text":3828},{"id":3901,"depth":649,"text":3902},{"id":4040,"depth":649,"text":3647},{"id":2496,"depth":642,"text":2497},"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":2563,"description":4416},[1135],"topics\u002Fderivace",[1128,1145,4423,4424,4425],"diferencial","extremy","mezni-naklady","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":4428,"title":4429,"body":4430,"course":1128,"courses":659,"created":10119,"description":641,"extension":661,"meta":10120,"navigation":664,"path":10121,"seo":10122,"sources":10123,"stem":10124,"tags":10125,"type":2553,"updated":677,"__hash__":10130},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":9,"value":4431,"toc":10092},[4432,4435,4458,4462,4489,4493,4534,4624,4668,4672,4696,4703,4707,4717,4729,4733,4761,4770,4827,4833,4836,4842,4869,4875,4972,5132,5423,5427,5507,5513,5517,5615,5681,5849,5853,5931,5962,5989,5995,6027,6105,6192,6196,6259,6265,6268,6274,6388,6473,6517,6521,6567,6574,6891,6896,6920,6949,7016,7113,7117,7124,7131,7202,7322,7406,7409,7415,7742,7746,7909,7917,8053,8061,8299,8307,8310,8315,8571,8575,8748,8882,8919,8963,8966,9096,9186,9204,9208,9215,9221,9281,9284,9308,9311,9317,9320,9326,9329,9333,9371,9429,9618,9622,9695,9701,9708,9712,9718,9859,9863,9869,9905,9910,10087],[12,4433,4429],{"id":4434},"elasticita-poptávky-a-nabídky",[4436,4437,4438],"blockquote",{},[724,4439,4440,4443,4444,4446,4447,4450,4451,4454,4455,1977],{},[883,4441,4442],{},"!abstract"," TL;DR\n",[38,4445,4397],{}," 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: ",[38,4448,4449],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,4452,4453],{},"křížově-cenovou elasticitu"," a ",[38,4456,4457],{},"důchodovou elasticitu",[115,4459,4461],{"id":4460},"úvod-motivace","Úvod — motivace",[724,4463,4464,4465,4468,4469,4472,4473,4476,4477,4480,4481,4484,4485,4488],{},"Termín ",[614,4466,4467],{},"elasticita"," (alternativně ",[614,4470,4471],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,4474,4475],{},"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 ",[614,4478,4479],{},"cenové elasticity poptávky"," (resp. ",[614,4482,4483],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,4486,2950],{"className":4487,"dataFsResolvedFilePath":764,"href":765},[210],").",[198,4490,4492],{"id":4491},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,4494,4495,4496,4514,4515,4533],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,4497,4499],{"className":4498},[886],[888,4500,4501],{"xmlns":890},[892,4502,4503,4511],{},[895,4504,4505,4507,4509],{},[898,4506,2398],{},[1664,4508,1676],{},[1963,4510,3442],{},[902,4512,4513],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,4516,4518],{"className":4517},[886],[888,4519,4520],{"xmlns":890},[892,4521,4522,4530],{},[895,4523,4524,4526,4528],{},[898,4525,1973],{},[1664,4527,1676],{},[1963,4529,1965],{},[902,4531,4532],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,4535,4536,4581],{},[123,4537,4538,4541,4542,4580],{},[38,4539,4540],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,4543,4545],{"className":4544},[886],[888,4546,4547],{"xmlns":890},[892,4548,4549,4577],{},[895,4550,4551,4554,4557,4559,4561,4563,4565,4568,4570,4572,4574],{},[1690,4552,4553],{},"  ",[1664,4555,4556],{},"⇒",[1690,4558,4553],{},[898,4560,1991],{},[898,4562,1959],{},[1664,4564,1676],{},[1963,4566,4567],{},"9",[1664,4569,3753],{},[1963,4571,3799],{},[1664,4573,1676],{},[1963,4575,4576],{},"990",[902,4578,4579],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,4582,4583,4586,4587,4623],{},[38,4584,4585],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,4588,4590],{"className":4589},[886],[888,4591,4592],{"xmlns":890},[892,4593,4594,4620],{},[895,4595,4596,4598,4600,4602,4604,4606,4608,4610,4612,4615,4617],{},[1690,4597,4553],{},[1664,4599,4556],{},[1690,4601,4553],{},[898,4603,1991],{},[898,4605,1959],{},[1664,4607,1676],{},[1963,4609,4567],{},[1664,4611,3753],{},[1963,4613,4614],{},"120",[1664,4616,1676],{},[1963,4618,4619],{},"1080",[902,4621,4622],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,4625,4626,4627,4630,4631,4634,4635,4638,4639,4642,4643,4646,4647,4663,4664,4667],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,4628,4629],{},"nerozumné",", na Trhu 2 ",[38,4632,4633],{},"rozumné",". Trh 2 je ",[38,4636,4637],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,4640,4641],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,4644,4645],{},"neelastická"," a vyššího ",[883,4648,4650],{"className":4649},[886],[888,4651,4652],{"xmlns":890},[892,4653,4654,4660],{},[895,4655,4656,4658],{},[898,4657,1991],{},[898,4659,1959],{},[902,4661,4662],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,4665,4666],{},"zvýšením"," ceny.",[198,4669,4671],{"id":4670},"hypotéza-41","Hypotéza 4.1",[4436,4673,4674],{},[724,4675,4676,4677],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,4678,4680],{"className":4679},[886],[888,4681,4682],{"xmlns":890},[892,4683,4684,4693],{},[895,4685,4686,4688,4691],{},[1664,4687,1667],{"stretchy":1666},[1963,4689,4690],{},"4.1",[1664,4692,1673],{"stretchy":1666},[902,4694,4695],{"encoding":904},"(4.1)",[724,4697,4698,4699,4702],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,4700,4701],{},"procentní změny"," obou faktorů.",[115,4704,4706],{"id":4705},"pojem-elasticity","Pojem elasticity",[724,4708,4709,4710,4712,4713,4716],{},"Obecně ",[38,4711,4467],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,4714,4715],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[4436,4718,4719],{},[724,4720,4721,4724,4725,4728],{},[883,4722,4723],{},"!info"," Intuice\nElasticitu lze číst jako ",[38,4726,4727],{},"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.",[115,4730,4732],{"id":4731},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,4734,4735,4736,4760],{},"Nechť ",[883,4737,4739],{"className":4738},[886],[888,4740,4741],{"xmlns":890},[892,4742,4743,4757],{},[895,4744,4745,4747,4749,4751,4753,4755],{},[898,4746,1973],{},[1664,4748,1676],{},[898,4750,2379],{},[1664,4752,1667],{"stretchy":1666},[898,4754,2398],{},[1664,4756,1673],{"stretchy":1666},[902,4758,4759],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,4762,4763],{},[883,4764,4769],{"className":4765,"title":4767,"style":4768},[4766],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,4771,4772,4773,4454,4789,4805,4806,4826],{},"Znaménko minus je korekce: změny ",[883,4774,4776],{"className":4775},[886],[888,4777,4778],{"xmlns":890},[892,4779,4780,4786],{},[895,4781,4782,4784],{},[898,4783,3468],{"mathvariant":1726},[898,4785,1973],{},[902,4787,4788],{"encoding":904},"\\Delta Q",[883,4790,4792],{"className":4791},[886],[888,4793,4794],{"xmlns":890},[892,4795,4796,4802],{},[895,4797,4798,4800],{},[898,4799,3468],{"mathvariant":1726},[898,4801,2398],{},[902,4803,4804],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,4807,4809],{"className":4808},[886],[888,4810,4811],{"xmlns":890},[892,4812,4813,4823],{},[895,4814,4815],{},[1720,4816,4817,4820],{},[898,4818,4819],{},"E",[898,4821,4822],{},"A",[902,4824,4825],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,4828,4829],{},[883,4830,4832],{"className":4831,"title":4767,"style":4768},[4766],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,4834,4835],{},"Po dosazení:",[724,4837,4838],{},[883,4839,4841],{"className":4840,"title":4767,"style":4768},[4766],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,4843,4844,4845,4865,4866,4868],{},"Limitním přechodem ",[883,4846,4848],{"className":4847},[886],[888,4849,4850],{"xmlns":890},[892,4851,4852,4862],{},[895,4853,4854,4856,4858,4860],{},[898,4855,3468],{"mathvariant":1726},[898,4857,2398],{},[1664,4859,3699],{},[1963,4861,2058],{},[902,4863,4864],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,4867,4479],{}," (price elasticity of demand):",[724,4870,4871],{},[883,4872,4874],{"className":4873,"title":4767,"style":4768},[4766],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,4876,1709,4877,4900,4901,4924,4925,4949,4950,4971],{},[883,4878,4880],{"className":4879},[886],[888,4881,4882],{"xmlns":890},[892,4883,4884,4898],{},[895,4885,4886,4888,4890,4892,4894,4896],{},[898,4887,1973],{},[1664,4889,1676],{},[898,4891,2379],{},[1664,4893,1667],{"stretchy":1666},[898,4895,2398],{},[1664,4897,1673],{"stretchy":1666},[902,4899,4759],{"encoding":904},". Pro pevnou cenu ",[883,4902,4904],{"className":4903},[886],[888,4905,4906],{"xmlns":890},[892,4907,4908,4921],{},[895,4909,4910,4912,4914],{},[898,4911,2398],{},[1664,4913,1676],{},[1720,4915,4916,4918],{},[898,4917,2398],{},[1664,4919,4920],{},"∗",[902,4922,4923],{"encoding":904},"P = P^*"," se ",[883,4926,4928],{"className":4927},[886],[888,4929,4930],{"xmlns":890},[892,4931,4932,4946],{},[895,4933,4934,4936,4938,4944],{},[898,4935,4819],{},[1664,4937,1667],{"stretchy":1666},[1720,4939,4940,4942],{},[898,4941,2398],{},[1664,4943,4920],{},[1664,4945,1673],{"stretchy":1666},[902,4947,4948],{"encoding":904},"E(P^*)"," nazývá ",[614,4951,4952,4953],{},"elasticita poptávky při ceně ",[883,4954,4956],{"className":4955},[886],[888,4957,4958],{"xmlns":890},[892,4959,4960,4968],{},[895,4961,4962],{},[1720,4963,4964,4966],{},[898,4965,2398],{},[1664,4967,4920],{},[902,4969,4970],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[4436,4973,4974],{},[724,4975,4976,4979,4980,4998,4999,5027,5028,5057,5058,1343,5076,1343,5094,5112,5113,5128,5129,1977],{},[883,4977,4978],{},"!warning"," Pozor na znaménko\nV (4.5) je ",[38,4981,4982,4983],{},"explicitní ",[883,4984,4986],{"className":4985},[886],[888,4987,4988],{"xmlns":890},[892,4989,4990,4996],{},[895,4991,4992,4994],{},[1664,4993,1867],{},[1963,4995,2875],{},[902,4997,4309],{"encoding":904}," právě proto, že ",[883,5000,5002],{"className":5001},[886],[888,5003,5004],{"xmlns":890},[892,5005,5006,5024],{},[895,5007,5008,5014,5016,5018,5020,5022],{},[1720,5009,5010,5012],{},[898,5011,1973],{},[1664,5013,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,5015,1667],{"stretchy":1666},[898,5017,2398],{},[1664,5019,1673],{"stretchy":1666},[1664,5021,4022],{},[1963,5023,2058],{},[902,5025,5026],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,5029,5031],{"className":5030},[886],[888,5032,5033],{"xmlns":890},[892,5034,5035,5054],{},[895,5036,5037,5039,5041,5047,5049,5052],{},[898,5038,4819],{},[1664,5040,1667],{"stretchy":1666},[1720,5042,5043,5045],{},[898,5044,2398],{},[1664,5046,4920],{},[1664,5048,1673],{"stretchy":1666},[1664,5050,5051],{},"≥",[1963,5053,2058],{},[902,5055,5056],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,5059,5061],{"className":5060},[886],[888,5062,5063],{"xmlns":890},[892,5064,5065,5073],{},[895,5066,5067,5069,5071],{},[898,5068,4819],{},[1664,5070,3984],{},[1963,5072,2875],{},[902,5074,5075],{"encoding":904},"E > 1",[883,5077,5079],{"className":5078},[886],[888,5080,5081],{"xmlns":890},[892,5082,5083,5091],{},[895,5084,5085,5087,5089],{},[898,5086,4819],{},[1664,5088,4022],{},[1963,5090,2875],{},[902,5092,5093],{"encoding":904},"E \u003C 1",[883,5095,5097],{"className":5096},[886],[888,5098,5099],{"xmlns":890},[892,5100,5101,5109],{},[895,5102,5103,5105,5107],{},[898,5104,4819],{},[1664,5106,1676],{},[1963,5108,2875],{},[902,5110,5111],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,5114,5116],{"className":5115},[886],[888,5117,5118],{"xmlns":890},[892,5119,5120,5126],{},[895,5121,5122,5124],{},[1664,5123,1867],{},[1963,5125,2875],{},[902,5127,4309],{"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 ",[38,5130,5131],{},"absolutní hodnotou",[4436,5133,5134,5154],{},[724,5135,5136,5139,5140,5153],{},[883,5137,5138],{},"!tip"," Postup: jak spočítat ",[883,5141,5143],{"className":5142},[886],[888,5144,5145],{"xmlns":890},[892,5146,5147,5151],{},[895,5148,5149],{},[898,5150,4819],{},[902,5152,4819],{"encoding":904}," v bodě",[152,5155,5156,5208,5248,5301,5366],{},[123,5157,5158,5159,5182,5183,5207],{},"Zapište ",[883,5160,5162],{"className":5161},[886],[888,5163,5164],{"xmlns":890},[892,5165,5166,5180],{},[895,5167,5168,5170,5172,5174,5176,5178],{},[898,5169,1973],{},[1664,5171,1676],{},[898,5173,2379],{},[1664,5175,1667],{"stretchy":1666},[898,5177,2398],{},[1664,5179,1673],{"stretchy":1666},[902,5181,4759],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,5184,5186],{"className":5185},[886],[888,5187,5188],{"xmlns":890},[892,5189,5190,5204],{},[895,5191,5192,5194,5196,5198,5200,5202],{},[898,5193,2398],{},[1664,5195,1676],{},[898,5197,2379],{},[1664,5199,1667],{"stretchy":1666},[898,5201,1973],{},[1664,5203,1673],{"stretchy":1666},[902,5205,5206],{"encoding":904},"P = D(Q)",", použijte vztah (4.9).",[123,5209,5210,5211,1977],{},"Spočítejte derivaci ",[883,5212,5214],{"className":5213},[886],[888,5215,5216],{"xmlns":890},[892,5217,5218,5245],{},[895,5219,5220,5226,5228,5230,5232,5234,5236,5238,5241,5243],{},[1720,5221,5222,5224],{},[898,5223,1973],{},[1664,5225,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,5227,1667],{"stretchy":1666},[898,5229,2398],{},[1664,5231,1673],{"stretchy":1666},[1664,5233,1676],{},[898,5235,1695],{"mathvariant":1726},[898,5237,1973],{},[898,5239,5240],{"mathvariant":1726},"\u002F",[898,5242,1695],{"mathvariant":1726},[898,5244,2398],{},[902,5246,5247],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,5249,5250,5251,5268,5269,1977],{},"Dosaďte zadanou cenu ",[883,5252,5254],{"className":5253},[886],[888,5255,5256],{"xmlns":890},[892,5257,5258,5266],{},[895,5259,5260],{},[1720,5261,5262,5264],{},[898,5263,2398],{},[1664,5265,4920],{},[902,5267,4970],{"encoding":904}," a dopočítejte odpovídající ",[883,5270,5272],{"className":5271},[886],[888,5273,5274],{"xmlns":890},[892,5275,5276,5298],{},[895,5277,5278,5284,5286,5288,5290,5296],{},[1720,5279,5280,5282],{},[898,5281,1973],{},[1664,5283,4920],{},[1664,5285,1676],{},[898,5287,2379],{},[1664,5289,1667],{"stretchy":1666},[1720,5291,5292,5294],{},[898,5293,2398],{},[1664,5295,4920],{},[1664,5297,1673],{"stretchy":1666},[902,5299,5300],{"encoding":904},"Q^* = D(P^*)",[123,5302,5303,5304,1977],{},"Dosaďte do (4.5): ",[883,5305,5307],{"className":5306},[886],[888,5308,5309],{"xmlns":890},[892,5310,5311,5363],{},[895,5312,5313,5315,5317,5323,5325,5327,5329,5345,5347,5353,5355,5361],{},[898,5314,4819],{},[1664,5316,1667],{"stretchy":1666},[1720,5318,5319,5321],{},[898,5320,2398],{},[1664,5322,4920],{},[1664,5324,1673],{"stretchy":1666},[1664,5326,1676],{},[1664,5328,1867],{},[2919,5330,5331],{"scriptlevel":2058,"displaystyle":1915},[2922,5332,5333,5339],{},[1720,5334,5335,5337],{},[898,5336,2398],{},[1664,5338,4920],{},[1720,5340,5341,5343],{},[898,5342,1973],{},[1664,5344,4920],{},[1690,5346,1692],{},[1720,5348,5349,5351],{},[898,5350,1973],{},[1664,5352,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,5354,1667],{"stretchy":1666},[1720,5356,5357,5359],{},[898,5358,2398],{},[1664,5360,4920],{},[1664,5362,1673],{"stretchy":1666},[902,5364,5365],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,5367,5368,5369,5386,5387,5404,5405,5422],{},"Klasifikujte: ",[883,5370,5372],{"className":5371},[886],[888,5373,5374],{"xmlns":890},[892,5375,5376,5384],{},[895,5377,5378,5380,5382],{},[898,5379,4819],{},[1664,5381,3984],{},[1963,5383,2875],{},[902,5385,5075],{"encoding":904}," elastická, ",[883,5388,5390],{"className":5389},[886],[888,5391,5392],{"xmlns":890},[892,5393,5394,5402],{},[895,5395,5396,5398,5400],{},[898,5397,4819],{},[1664,5399,1676],{},[1963,5401,2875],{},[902,5403,5111],{"encoding":904}," jednotková, ",[883,5406,5408],{"className":5407},[886],[888,5409,5410],{"xmlns":890},[892,5411,5412,5420],{},[895,5413,5414,5416,5418],{},[898,5415,4819],{},[1664,5417,4022],{},[1963,5419,2875],{},[902,5421,5093],{"encoding":904}," neelastická.",[198,5424,5426],{"id":5425},"interpretace-46","Interpretace (4.6)",[4436,5428,5429],{},[724,5430,5431,5432,5455,5456,5469,5470,5487,5488],{},"Číslo ",[883,5433,5435],{"className":5434},[886],[888,5436,5437],{"xmlns":890},[892,5438,5439,5453],{},[895,5440,5441,5443,5445,5451],{},[898,5442,4819],{},[1664,5444,1667],{"stretchy":1666},[1720,5446,5447,5449],{},[898,5448,2398],{},[1664,5450,4920],{},[1664,5452,1673],{"stretchy":1666},[902,5454,4948],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,5457,5459],{"className":5458},[886],[888,5460,5461],{"xmlns":890},[892,5462,5463,5467],{},[895,5464,5465],{},[898,5466,1973],{},[902,5468,1973],{"encoding":904},", jestliže se cena ",[883,5471,5473],{"className":5472},[886],[888,5474,5475],{"xmlns":890},[892,5476,5477,5485],{},[895,5478,5479],{},[1720,5480,5481,5483],{},[898,5482,2398],{},[1664,5484,4920],{},[902,5486,4970],{"encoding":904}," změní o 1 %. ",[883,5489,5491],{"className":5490},[886],[888,5492,5493],{"xmlns":890},[892,5494,5495,5504],{},[895,5496,5497,5499,5502],{},[1664,5498,1667],{"stretchy":1666},[1963,5500,5501],{},"4.6",[1664,5503,1673],{"stretchy":1666},[902,5505,5506],{"encoding":904},"(4.6)",[724,5508,5509,5512],{},[38,5510,5511],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,5514,5516],{"id":5515},"příklad-41","Příklad 4.1",[724,5518,5519,5520,5554,5555,1343,5581,2087],{},"Poptávka ",[883,5521,5523],{"className":5522},[886],[888,5524,5525],{"xmlns":890},[892,5526,5527,5551],{},[895,5528,5529,5531,5533,5535,5537,5539,5541,5543,5545,5547,5549],{},[898,5530,2398],{},[1664,5532,1676],{},[898,5534,2379],{},[1664,5536,1667],{"stretchy":1666},[898,5538,1973],{},[1664,5540,1673],{"stretchy":1666},[1664,5542,1676],{},[1963,5544,3696],{},[1664,5546,1867],{},[1963,5548,1970],{},[898,5550,1973],{},[902,5552,5553],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,5556,5558],{"className":5557},[886],[888,5559,5560],{"xmlns":890},[892,5561,5562,5578],{},[895,5563,5564,5566,5568,5571,5573,5576],{},[898,5565,1973],{},[1664,5567,1676],{},[1963,5569,5570],{},"25",[1664,5572,1867],{},[1963,5574,5575],{},"0,5",[898,5577,2398],{},[902,5579,5580],{"encoding":904},"Q = 25 - 0{,}5P",[883,5582,5584],{"className":5583},[886],[888,5585,5586],{"xmlns":890},[892,5587,5588,5612],{},[895,5589,5590,5606,5608,5610],{},[2919,5591,5592],{"scriptlevel":2058,"displaystyle":1915},[2922,5593,5594,5600],{},[895,5595,5596,5598],{},[898,5597,1695],{"mathvariant":1726},[898,5599,1973],{},[895,5601,5602,5604],{},[898,5603,1695],{"mathvariant":1726},[898,5605,2398],{},[1664,5607,1676],{},[1664,5609,1867],{},[1963,5611,5575],{},[902,5613,5614],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,5616,5617],{},[883,5618,5620],{"className":5619},[886],[888,5621,5622],{"xmlns":890},[892,5623,5624,5678],{},[895,5625,5626,5628,5630,5632,5646,5648,5650,5652,5654,5656,5658,5676],{},[898,5627,4819],{},[1664,5629,1676],{},[1664,5631,1867],{},[2922,5633,5634,5636],{},[898,5635,2398],{},[895,5637,5638,5640,5642,5644],{},[1963,5639,5570],{},[1664,5641,1867],{},[1963,5643,5575],{},[898,5645,2398],{},[1664,5647,3753],{},[1664,5649,1667],{"stretchy":1666},[1664,5651,1867],{},[1963,5653,5575],{},[1664,5655,1673],{"stretchy":1666},[1664,5657,1676],{},[2922,5659,5660,5666],{},[895,5661,5662,5664],{},[1963,5663,5575],{},[898,5665,2398],{},[895,5667,5668,5670,5672,5674],{},[1963,5669,5570],{},[1664,5671,1867],{},[1963,5673,5575],{},[898,5675,2398],{},[898,5677,1977],{"mathvariant":1726},[902,5679,5680],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,5682,5683,5684,1343,5708,1343,5738,1343,5762,5787,5788,5811,5812,3271,5830,4488],{},"Potom ",[883,5685,5687],{"className":5686},[886],[888,5688,5689],{"xmlns":890},[892,5690,5691,5705],{},[895,5692,5693,5695,5697,5699,5701,5703],{},[898,5694,4819],{},[1664,5696,1667],{"stretchy":1666},[1963,5698,2058],{},[1664,5700,1673],{"stretchy":1666},[1664,5702,1676],{},[1963,5704,2058],{},[902,5706,5707],{"encoding":904},"E(0)=0",[883,5709,5711],{"className":5710},[886],[888,5712,5713],{"xmlns":890},[892,5714,5715,5735],{},[895,5716,5717,5719,5721,5723,5725,5727],{},[898,5718,4819],{},[1664,5720,1667],{"stretchy":1666},[1963,5722,3442],{},[1664,5724,1673],{"stretchy":1666},[1664,5726,1676],{},[2919,5728,5729],{"scriptlevel":2058,"displaystyle":1666},[2922,5730,5731,5733],{},[1963,5732,2875],{},[1963,5734,2944],{},[902,5736,5737],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,5739,5741],{"className":5740},[886],[888,5742,5743],{"xmlns":890},[892,5744,5745,5759],{},[895,5746,5747,5749,5751,5753,5755,5757],{},[898,5748,4819],{},[1664,5750,1667],{"stretchy":1666},[1963,5752,5570],{},[1664,5754,1673],{"stretchy":1666},[1664,5756,1676],{},[1963,5758,2875],{},[902,5760,5761],{"encoding":904},"E(25)=1",[883,5763,5765],{"className":5764},[886],[888,5766,5767],{"xmlns":890},[892,5768,5769,5784],{},[895,5770,5771,5773,5775,5778,5780,5782],{},[898,5772,4819],{},[1664,5774,1667],{"stretchy":1666},[1963,5776,5777],{},"40",[1664,5779,1673],{"stretchy":1666},[1664,5781,1676],{},[1963,5783,2944],{},[902,5785,5786],{"encoding":904},"E(40)=4",". Např. ",[883,5789,5791],{"className":5790},[886],[888,5792,5793],{"xmlns":890},[892,5794,5795,5809],{},[895,5796,5797,5799,5801,5803,5805,5807],{},[898,5798,4819],{},[1664,5800,1667],{"stretchy":1666},[1963,5802,5777],{},[1664,5804,1673],{"stretchy":1666},[1664,5806,1676],{},[1963,5808,2944],{},[902,5810,5786],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,5813,5815],{"className":5814},[886],[888,5816,5817],{"xmlns":890},[892,5818,5819,5827],{},[895,5820,5821,5823,5825],{},[898,5822,1973],{},[1664,5824,1676],{},[1963,5826,2826],{},[902,5828,5829],{"encoding":904},"Q=5",[883,5831,5833],{"className":5832},[886],[888,5834,5835],{"xmlns":890},[892,5836,5837,5846],{},[895,5838,5839,5841,5843],{},[898,5840,1973],{},[1664,5842,1676],{},[1963,5844,5845],{},"4,8",[902,5847,5848],{"encoding":904},"Q=4{,}8",[198,5850,5852],{"id":5851},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,5854,5855,5911],{},[123,5856,5857,5860,5861,5878,5879,1977],{},[38,5858,5859],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,5862,5864],{"className":5863},[886],[888,5865,5866],{"xmlns":890},[892,5867,5868,5876],{},[895,5869,5870],{},[1720,5871,5872,5874],{},[898,5873,4819],{},[898,5875,4822],{},[902,5877,4825],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,5880,5882],{"className":5881},[886],[888,5883,5884],{"xmlns":890},[892,5885,5886,5908],{},[895,5887,5888,5891,5893,5895,5897,5899,5901,5903,5905],{},[1664,5889,5890],{"stretchy":1666},"⟨",[898,5892,2398],{},[1664,5894,1916],{"separator":1915},[1690,5896,1692],{},[898,5898,2398],{},[1664,5900,1700],{},[898,5902,3468],{"mathvariant":1726},[898,5904,2398],{},[1664,5906,5907],{"stretchy":1666},"⟩",[902,5909,5910],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,5912,5913,5916,5917,5930],{},[38,5914,5915],{},"Bodová"," (okamžitá) elasticita: ",[883,5918,5920],{"className":5919},[886],[888,5921,5922],{"xmlns":890},[892,5923,5924,5928],{},[895,5925,5926],{},[898,5927,4819],{},[902,5929,4819],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,5932,5934,5935,5948,5949],{"id":5933},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,5936,5938],{"className":5937},[886],[888,5939,5940],{"xmlns":890},[892,5941,5942,5946],{},[895,5943,5944],{},[898,5945,2398],{},[902,5947,2398],{"encoding":904}," jako funkce ",[883,5950,5952],{"className":5951},[886],[888,5953,5954],{"xmlns":890},[892,5955,5956,5960],{},[895,5957,5958],{},[898,5959,1973],{},[902,5961,1973],{"encoding":904},[724,5963,5964,5965,5988],{},"Pokud je poptávka zadaná ve tvaru ",[883,5966,5968],{"className":5967},[886],[888,5969,5970],{"xmlns":890},[892,5971,5972,5986],{},[895,5973,5974,5976,5978,5980,5982,5984],{},[898,5975,2398],{},[1664,5977,1676],{},[898,5979,2379],{},[1664,5981,1667],{"stretchy":1666},[898,5983,1973],{},[1664,5985,1673],{"stretchy":1666},[902,5987,5206],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,5990,5991],{},[883,5992,5994],{"className":5993,"title":4767,"style":4768},[4766],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,5996,5997,1885,6000,6026],{},[38,5998,5999],{},"Příklad 4.3.",[883,6001,6003],{"className":6002},[886],[888,6004,6005],{"xmlns":890},[892,6006,6007,6023],{},[895,6008,6009,6011,6013,6015,6017],{},[898,6010,2398],{},[1664,6012,1676],{},[1963,6014,1965],{},[1664,6016,1867],{},[1720,6018,6019,6021],{},[898,6020,1973],{},[1963,6022,1970],{},[902,6024,6025],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,6028,6029],{},[883,6030,6032],{"className":6031},[886],[888,6033,6034],{"xmlns":890},[892,6035,6036,6102],{},[895,6037,6038,6040,6042,6044,6060,6062,6074,6076,6100],{},[898,6039,4819],{},[1664,6041,1676],{},[1664,6043,1867],{},[2922,6045,6046,6058],{},[895,6047,6048,6050,6052],{},[1963,6049,1965],{},[1664,6051,1867],{},[1720,6053,6054,6056],{},[898,6055,1973],{},[1963,6057,1970],{},[898,6059,1973],{},[1664,6061,3753],{},[2922,6063,6064,6066],{},[1963,6065,2875],{},[895,6067,6068,6070,6072],{},[1664,6069,1867],{},[1963,6071,1970],{},[898,6073,1973],{},[1664,6075,1676],{},[2922,6077,6078,6090],{},[895,6079,6080,6082,6084],{},[1963,6081,1965],{},[1664,6083,1867],{},[1720,6085,6086,6088],{},[898,6087,1973],{},[1963,6089,1970],{},[895,6091,6092,6094],{},[1963,6093,1970],{},[1720,6095,6096,6098],{},[898,6097,1973],{},[1963,6099,1970],{},[898,6101,1977],{"mathvariant":1726},[902,6103,6104],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,6106,6107,6108,6135,6136,6155,6156,1977],{},"Z rovnice ",[883,6109,6111],{"className":6110},[886],[888,6112,6113],{"xmlns":890},[892,6114,6115,6132],{},[895,6116,6117,6119,6121,6127,6129],{},[1963,6118,1965],{},[1664,6120,1867],{},[1720,6122,6123,6125],{},[898,6124,1973],{},[1963,6126,1970],{},[1664,6128,1676],{},[1963,6130,6131],{},"36",[902,6133,6134],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,6137,6139],{"className":6138},[886],[888,6140,6141],{"xmlns":890},[892,6142,6143,6152],{},[895,6144,6145,6147,6149],{},[898,6146,1973],{},[1664,6148,1676],{},[1963,6150,6151],{},"8",[902,6153,6154],{"encoding":904},"Q = 8",", tedy ",[883,6157,6159],{"className":6158},[886],[888,6160,6161],{"xmlns":890},[892,6162,6163,6189],{},[895,6164,6165,6167,6169,6171,6173,6175,6184,6186],{},[898,6166,4819],{},[1664,6168,1667],{"stretchy":1666},[1963,6170,6151],{},[1664,6172,1673],{"stretchy":1666},[1664,6174,1676],{},[2919,6176,6177],{"scriptlevel":2058,"displaystyle":1666},[2922,6178,6179,6181],{},[1963,6180,6131],{},[1963,6182,6183],{},"128",[1664,6185,1676],{},[1963,6187,6188],{},"0,281",[902,6190,6191],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,6193,6195],{"id":6194},"přibližné-změny","Přibližné změny",[724,6197,6198,6199,6235,6236,6258],{},"Diferenciál ",[883,6200,6202],{"className":6201},[886],[888,6203,6204],{"xmlns":890},[892,6205,6206,6232],{},[895,6207,6208,6210,6212,6214,6220,6222,6224,6226,6228,6230],{},[898,6209,1695],{"mathvariant":1726},[898,6211,1973],{},[1664,6213,1676],{},[1720,6215,6216,6218],{},[898,6217,1973],{},[1664,6219,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,6221,1667],{"stretchy":1666},[898,6223,2398],{},[1664,6225,1673],{"stretchy":1666},[1690,6227,1692],{},[898,6229,1695],{"mathvariant":1726},[898,6231,2398],{},[902,6233,6234],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[883,6237,6239],{"className":6238},[886],[888,6240,6241],{"xmlns":890},[892,6242,6243,6255],{},[895,6244,6245,6247,6249,6251,6253],{},[898,6246,1695],{"mathvariant":1726},[898,6248,2398],{},[1664,6250,1676],{},[898,6252,3468],{"mathvariant":1726},[898,6254,2398],{},[902,6256,6257],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,6260,6261],{},[883,6262,6264],{"className":6263,"title":4767,"style":4768},[4766],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,6266,6267],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,6269,6270],{},[883,6271,6273],{"className":6272,"title":4767,"style":4768},[4766],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,6275,6276,1885,6279,6314,6315,6334,6335,6369,6370,6387],{},[38,6277,6278],{},"Příklad 4.5.",[883,6280,6282],{"className":6281},[886],[888,6283,6284],{"xmlns":890},[892,6285,6286,6311],{},[895,6287,6288,6290,6292,6294,6300,6302,6304,6306,6308],{},[898,6289,2398],{},[1664,6291,1676],{},[1664,6293,1867],{},[1720,6295,6296,6298],{},[898,6297,1973],{},[1963,6299,1970],{},[1664,6301,1867],{},[1963,6303,2944],{},[898,6305,1973],{},[1664,6307,1700],{},[1963,6309,6310],{},"96",[902,6312,6313],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,6316,6318],{"className":6317},[886],[888,6319,6320],{"xmlns":890},[892,6321,6322,6331],{},[895,6323,6324,6326,6328],{},[898,6325,2398],{},[1664,6327,1676],{},[1963,6329,6330],{},"51",[902,6332,6333],{"encoding":904},"P=51",". Z rovnice ",[883,6336,6338],{"className":6337},[886],[888,6339,6340],{"xmlns":890},[892,6341,6342,6366],{},[895,6343,6344,6346,6348,6350,6356,6358,6360,6362,6364],{},[1963,6345,6330],{},[1664,6347,1676],{},[1664,6349,1867],{},[1720,6351,6352,6354],{},[898,6353,1973],{},[1963,6355,1970],{},[1664,6357,1867],{},[1963,6359,2944],{},[898,6361,1973],{},[1664,6363,1700],{},[1963,6365,6310],{},[902,6367,6368],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,6371,6373],{"className":6372},[886],[888,6374,6375],{"xmlns":890},[892,6376,6377,6385],{},[895,6378,6379,6381,6383],{},[898,6380,1973],{},[1664,6382,1676],{},[1963,6384,2826],{},[902,6386,5829],{"encoding":904},". Elasticita:",[724,6389,6390],{},[883,6391,6393],{"className":6392},[886],[888,6394,6395],{"xmlns":890},[892,6396,6397,6470],{},[895,6398,6399,6401,6403,6441,6443,6447,6449,6451,6453,6455,6457,6464,6467],{},[898,6400,4819],{},[1664,6402,1676],{},[2922,6404,6405,6425],{},[895,6406,6407,6409,6415,6417,6419,6421,6423],{},[1664,6408,1867],{},[1720,6410,6411,6413],{},[898,6412,1973],{},[1963,6414,1970],{},[1664,6416,1867],{},[1963,6418,2944],{},[898,6420,1973],{},[1664,6422,1700],{},[1963,6424,6310],{},[895,6426,6427,6429,6431,6433,6435,6437,6439],{},[898,6428,1973],{},[1664,6430,1667],{"stretchy":1666},[1963,6432,1970],{},[898,6434,1973],{},[1664,6436,1700],{},[1963,6438,2944],{},[1664,6440,1673],{"stretchy":1666},[1664,6442,1916],{"separator":1915},[6444,6445],"mspace",{"width":6446},"2em",[898,6448,4819],{},[1664,6450,1667],{"stretchy":1666},[1963,6452,2826],{},[1664,6454,1673],{"stretchy":1666},[1664,6456,1676],{},[2922,6458,6459,6461],{},[1963,6460,6330],{},[1963,6462,6463],{},"70",[1664,6465,6466],{},"≐",[1963,6468,6469],{},"0,728.",[902,6471,6472],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,6474,6475,6476,1977],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,6477,6479],{"className":6478},[886],[888,6480,6481],{"xmlns":890},[892,6482,6483,6514],{},[895,6484,6485,6487,6489,6492,6494,6496,6499,6501,6503,6505,6507,6510,6512],{},[898,6486,3468],{"mathvariant":1726},[898,6488,1973],{},[898,6490,6491],{"mathvariant":1726},"%",[1664,6493,3315],{},[1664,6495,1867],{},[1963,6497,6498],{},"0,728",[1664,6500,3753],{},[1963,6502,1970],{},[1664,6504,1676],{},[1664,6506,1867],{},[1963,6508,6509],{},"1,456",[1690,6511,1692],{},[898,6513,6491],{"mathvariant":1726},[902,6515,6516],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,6518,6520],{"id":6519},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,6522,6523,6524,6547,6548,2087],{},"V závislosti na hodnotě ",[883,6525,6527],{"className":6526},[886],[888,6528,6529],{"xmlns":890},[892,6530,6531,6545],{},[895,6532,6533,6535,6537,6543],{},[898,6534,4819],{},[1664,6536,1667],{"stretchy":1666},[1720,6538,6539,6541],{},[898,6540,2398],{},[1664,6542,4920],{},[1664,6544,1673],{"stretchy":1666},[902,6546,4948],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,6549,6551],{"className":6550},[886],[888,6552,6553],{"xmlns":890},[892,6554,6555,6564],{},[895,6556,6557,6559,6562],{},[1664,6558,1667],{"stretchy":1666},[1963,6560,6561],{},"4.7",[1664,6563,1673],{"stretchy":1666},[902,6565,6566],{"encoding":904},"(4.7)",[724,6568,6569],{},[1928,6570],{"alt":6571,"className":6572,"src":6573},"imek-typy-elasticity-5panelu",[210,1932],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,6575,6576,6615],{},[19,6577,6578],{},[22,6579,6580,6606,6609,6612],{},[25,6581,6582,6583],{},"Hodnota ",[883,6584,6586],{"className":6585},[886],[888,6587,6588],{"xmlns":890},[892,6589,6590,6604],{},[895,6591,6592,6594,6596,6602],{},[898,6593,4819],{},[1664,6595,1667],{"stretchy":1666},[1720,6597,6598,6600],{},[898,6599,2398],{},[1664,6601,4920],{},[1664,6603,1673],{"stretchy":1666},[902,6605,4948],{"encoding":904},[25,6607,6608],{},"Typ poptávky",[25,6610,6611],{},"Termín",[25,6613,6614],{},"Význam",[30,6616,6617,6650,6712,6787,6844],{},[22,6618,6619,6639,6644,6647],{},[35,6620,6621],{},[883,6622,6624],{"className":6623},[886],[888,6625,6626],{"xmlns":890},[892,6627,6628,6636],{},[895,6629,6630,6632,6634],{},[898,6631,4819],{},[1664,6633,1676],{},[1963,6635,2058],{},[902,6637,6638],{"encoding":904},"E = 0",[35,6640,6641],{},[38,6642,6643],{},"dokonale neelastická",[35,6645,6646],{},"perfectly inelastic",[35,6648,6649],{},"množství se nemění bez ohledu na cenu",[22,6651,6652,6676,6680,6683],{},[35,6653,6654],{},[883,6655,6657],{"className":6656},[886],[888,6658,6659],{"xmlns":890},[892,6660,6661,6673],{},[895,6662,6663,6665,6667,6669,6671],{},[1963,6664,2058],{},[1664,6666,4022],{},[898,6668,4819],{},[1664,6670,4022],{},[1963,6672,2875],{},[902,6674,6675],{"encoding":904},"0 \u003C E \u003C 1",[35,6677,6678],{},[38,6679,4645],{},[35,6681,6682],{},"inelastic",[35,6684,6685,6698,6699],{},[883,6686,6688],{"className":6687},[886],[888,6689,6690],{"xmlns":890},[892,6691,6692,6696],{},[895,6693,6694],{},[898,6695,1973],{},[902,6697,1973],{"encoding":904}," se mění pomaleji než ",[883,6700,6702],{"className":6701},[886],[888,6703,6704],{"xmlns":890},[892,6705,6706,6710],{},[895,6707,6708],{},[898,6709,2398],{},[902,6711,2398],{"encoding":904},[22,6713,6714,6733,6738,6741],{},[35,6715,6716],{},[883,6717,6719],{"className":6718},[886],[888,6720,6721],{"xmlns":890},[892,6722,6723,6731],{},[895,6724,6725,6727,6729],{},[898,6726,4819],{},[1664,6728,1676],{},[1963,6730,2875],{},[902,6732,5111],{"encoding":904},[35,6734,6735],{},[38,6736,6737],{},"jednotkově elastická",[35,6739,6740],{},"unit elastic",[35,6742,6743,6756,6757,6770,6771,6786],{},[883,6744,6746],{"className":6745},[886],[888,6747,6748],{"xmlns":890},[892,6749,6750,6754],{},[895,6751,6752],{},[898,6753,1973],{},[902,6755,1973],{"encoding":904}," i ",[883,6758,6760],{"className":6759},[886],[888,6761,6762],{"xmlns":890},[892,6763,6764,6768],{},[895,6765,6766],{},[898,6767,2398],{},[902,6769,2398],{"encoding":904}," se mění stejně rychle; ",[883,6772,6774],{"className":6773},[886],[888,6775,6776],{"xmlns":890},[892,6777,6778,6784],{},[895,6779,6780,6782],{},[898,6781,1991],{},[898,6783,1959],{},[902,6785,4662],{"encoding":904}," má maximum",[22,6788,6789,6808,6812,6815],{},[35,6790,6791],{},[883,6792,6794],{"className":6793},[886],[888,6795,6796],{"xmlns":890},[892,6797,6798,6806],{},[895,6799,6800,6802,6804],{},[898,6801,4819],{},[1664,6803,3984],{},[1963,6805,2875],{},[902,6807,5075],{"encoding":904},[35,6809,6810],{},[38,6811,4641],{},[35,6813,6814],{},"elastic",[35,6816,6817,6830,6831],{},[883,6818,6820],{"className":6819},[886],[888,6821,6822],{"xmlns":890},[892,6823,6824,6828],{},[895,6825,6826],{},[898,6827,1973],{},[902,6829,1973],{"encoding":904}," se mění rychleji než ",[883,6832,6834],{"className":6833},[886],[888,6835,6836],{"xmlns":890},[892,6837,6838,6842],{},[895,6839,6840],{},[898,6841,2398],{},[902,6843,2398],{"encoding":904},[22,6845,6846,6867,6872,6875],{},[35,6847,6848],{},[883,6849,6851],{"className":6850},[886],[888,6852,6853],{"xmlns":890},[892,6854,6855,6864],{},[895,6856,6857,6859,6861],{},[898,6858,4819],{},[1664,6860,3699],{},[898,6862,6863],{"mathvariant":1726},"∞",[902,6865,6866],{"encoding":904},"E \\to \\infty",[35,6868,6869],{},[38,6870,6871],{},"dokonale elastická",[35,6873,6874],{},"perfectly elastic",[35,6876,6877,6878],{},"sebemenší změna ceny úplně mění ",[883,6879,6881],{"className":6880},[886],[888,6882,6883],{"xmlns":890},[892,6884,6885,6889],{},[895,6886,6887],{},[898,6888,1973],{},[902,6890,1973],{"encoding":904},[724,6892,6893],{},[38,6894,6895],{},"Pravidlo růstu elasticity s cenou:",[4436,6897,6898],{},[724,6899,6900,6901],{},"S rostoucí cenou elasticita poptávky roste. ",[883,6902,6904],{"className":6903},[886],[888,6905,6906],{"xmlns":890},[892,6907,6908,6917],{},[895,6909,6910,6912,6915],{},[1664,6911,1667],{"stretchy":1666},[1963,6913,6914],{},"4.8",[1664,6916,1673],{"stretchy":1666},[902,6918,6919],{"encoding":904},"(4.8)",[724,6921,6922,6923,6926,6927,6930,6931,6948],{},"Z toho plyne, že při ",[614,6924,6925],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,6928,6929],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,6932,6934],{"className":6933},[886],[888,6935,6936],{"xmlns":890},[892,6937,6938,6946],{},[895,6939,6940],{},[1720,6941,6942,6944],{},[898,6943,2398],{},[1664,6945,4920],{},[902,6947,4970],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[4436,6950,6951,6956],{},[724,6952,6953,6955],{},[883,6954,5138],{}," Postup: jak klasifikovat poptávku",[152,6957,6958,6985,6988],{},[123,6959,6960,6961,6984],{},"Spočítejte ",[883,6962,6964],{"className":6963},[886],[888,6965,6966],{"xmlns":890},[892,6967,6968,6982],{},[895,6969,6970,6972,6974,6980],{},[898,6971,4819],{},[1664,6973,1667],{"stretchy":1666},[1720,6975,6976,6978],{},[898,6977,2398],{},[1664,6979,4920],{},[1664,6981,1673],{"stretchy":1666},[902,6983,4948],{"encoding":904}," dle (4.5).",[123,6986,6987],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,6989,6990,6991,7015],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,6992,6994],{"className":6993},[886],[888,6995,6996],{"xmlns":890},[892,6997,6998,7012],{},[895,6999,7000,7002,7004,7006,7008,7010],{},[898,7001,4819],{},[1664,7003,1667],{"stretchy":1666},[898,7005,2398],{},[1664,7007,1673],{"stretchy":1666},[1664,7009,1676],{},[1963,7011,2875],{},[902,7013,7014],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,7017,7018,7021,7022,7039,7040,7058,7059,7086,7087,1977],{},[38,7019,7020],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,7023,7025],{"className":7024},[886],[888,7026,7027],{"xmlns":890},[892,7028,7029,7037],{},[895,7030,7031,7033,7035],{},[898,7032,4819],{},[1664,7034,1676],{},[1963,7036,2875],{},[902,7038,5111],{"encoding":904}," pro ",[883,7041,7043],{"className":7042},[886],[888,7044,7045],{"xmlns":890},[892,7046,7047,7055],{},[895,7048,7049,7051,7053],{},[898,7050,2398],{},[1664,7052,1676],{},[1963,7054,5570],{},[902,7056,7057],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,7060,7062],{"className":7061},[886],[888,7063,7064],{"xmlns":890},[892,7065,7066,7083],{},[895,7067,7068,7070,7073,7075,7077,7079,7081],{},[898,7069,2398],{},[1664,7071,7072],{},"∈",[1664,7074,5890],{"stretchy":1666},[1963,7076,2058],{},[1664,7078,1916],{"separator":1915},[1963,7080,5570],{},[1664,7082,1673],{"stretchy":1666},[902,7084,7085],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,7088,7090],{"className":7089},[886],[888,7091,7092],{"xmlns":890},[892,7093,7094,7110],{},[895,7095,7096,7098,7100,7102,7104,7106,7108],{},[898,7097,2398],{},[1664,7099,7072],{},[1664,7101,1667],{"stretchy":1666},[1963,7103,5570],{},[1664,7105,1916],{"separator":1915},[1963,7107,3696],{},[1664,7109,5907],{"stretchy":1666},[902,7111,7112],{"encoding":904},"P \\in (25, 50\\rangle",[115,7114,7116],{"id":7115},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,7118,7119],{},[1928,7120],{"alt":7121,"className":7122,"src":7123},"imek-elasticita-tr",[210,1932],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,7125,7126],{},[1928,7127],{"alt":7128,"className":7129,"src":7130},"imek-elasticita-podel-linearni-poptavky",[210,1932],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,7132,7133,7134,7184,7185,7201],{},"Pro celkový příjem platí ",[883,7135,7137],{"className":7136},[886],[888,7138,7139],{"xmlns":890},[892,7140,7141,7181],{},[895,7142,7143,7145,7147,7149,7151,7153,7155,7157,7159,7161,7163,7165,7167,7169,7171,7173,7175,7177,7179],{},[898,7144,1991],{},[898,7146,1959],{},[1664,7148,1676],{},[898,7150,1991],{},[898,7152,1959],{},[1664,7154,1667],{"stretchy":1666},[898,7156,1973],{},[1664,7158,1673],{"stretchy":1666},[1664,7160,1676],{},[898,7162,2398],{},[1664,7164,3753],{},[898,7166,1973],{},[1664,7168,1676],{},[898,7170,1973],{},[1664,7172,3753],{},[898,7174,2379],{},[1664,7176,1667],{"stretchy":1666},[898,7178,1973],{},[1664,7180,1673],{"stretchy":1666},[902,7182,7183],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,7186,7188],{"className":7187},[886],[888,7189,7190],{"xmlns":890},[892,7191,7192,7198],{},[895,7193,7194,7196],{},[898,7195,1956],{},[898,7197,1959],{},[902,7199,7200],{"encoding":904},"MR"," odvodíme:",[724,7203,7204],{},[883,7205,7207],{"className":7206},[886],[888,7208,7209],{"xmlns":890},[892,7210,7211,7319],{},[895,7212,7213,7215,7217,7219,7221,7227,7229,7231,7233,7235,7237,7239,7241,7243,7245,7247,7249,7255,7257,7259,7261,7263,7265,7267,7269,7283,7285,7287],{},[898,7214,1956],{},[898,7216,1959],{},[1664,7218,1676],{},[898,7220,1991],{},[1720,7222,7223,7225],{},[898,7224,1959],{},[1664,7226,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,7228,1667],{"stretchy":1666},[898,7230,1973],{},[1664,7232,1673],{"stretchy":1666},[1664,7234,1676],{},[898,7236,2379],{},[1664,7238,1667],{"stretchy":1666},[898,7240,1973],{},[1664,7242,1673],{"stretchy":1666},[1664,7244,1700],{},[898,7246,1973],{},[1690,7248,1692],{},[1720,7250,7251,7253],{},[898,7252,2379],{},[1664,7254,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,7256,1667],{"stretchy":1666},[898,7258,1973],{},[1664,7260,1673],{"stretchy":1666},[1664,7262,1676],{},[898,7264,2398],{},[1664,7266,1700],{},[898,7268,1973],{},[2922,7270,7271,7277],{},[895,7272,7273,7275],{},[898,7274,1695],{"mathvariant":1726},[898,7276,2398],{},[895,7278,7279,7281],{},[898,7280,1695],{"mathvariant":1726},[898,7282,1973],{},[1664,7284,1676],{},[898,7286,2398],{},[895,7288,7289,7291,7293,7295,7301,7303,7317],{},[1664,7290,1667],{"fence":1915},[1963,7292,2875],{},[1664,7294,1700],{},[2922,7296,7297,7299],{},[898,7298,1973],{},[898,7300,2398],{},[1664,7302,3753],{},[2922,7304,7305,7311],{},[895,7306,7307,7309],{},[898,7308,1695],{"mathvariant":1726},[898,7310,2398],{},[895,7312,7313,7315],{},[898,7314,1695],{"mathvariant":1726},[898,7316,1973],{},[1664,7318,1673],{"fence":1915},[902,7320,7321],{"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)",[724,7323,7324],{},[883,7325,7327],{"className":7326},[886],[888,7328,7329],{"xmlns":890},[892,7330,7331,7403],{},[895,7332,7333,7335,7337,7379,7381,7383],{},[1664,7334,1676],{},[898,7336,2398],{},[895,7338,7339,7341,7343,7345,7377],{},[1664,7340,1667],{"fence":1915},[1963,7342,2875],{},[1664,7344,1700],{},[2922,7346,7347,7349],{},[1963,7348,2875],{},[895,7350,7351,7359,7361],{},[2919,7352,7353],{"scriptlevel":2058,"displaystyle":1666},[2922,7354,7355,7357],{},[898,7356,2398],{},[898,7358,1973],{},[1664,7360,3753],{},[2919,7362,7363],{"scriptlevel":2058,"displaystyle":1666},[2922,7364,7365,7371],{},[895,7366,7367,7369],{},[898,7368,1695],{"mathvariant":1726},[898,7370,1973],{},[895,7372,7373,7375],{},[898,7374,1695],{"mathvariant":1726},[898,7376,2398],{},[1664,7378,1673],{"fence":1915},[1664,7380,1676],{},[898,7382,2398],{},[895,7384,7385,7387,7389,7391,7401],{},[1664,7386,1667],{"fence":1915},[1963,7388,2875],{},[1664,7390,1700],{},[2922,7392,7393,7395],{},[1963,7394,2875],{},[895,7396,7397,7399],{},[1664,7398,1867],{},[898,7400,4819],{},[1664,7402,1673],{"fence":1915},[902,7404,7405],{"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)",[724,7407,7408],{},"a tedy",[724,7410,7411],{},[883,7412,7414],{"className":7413,"title":4767,"style":4768},[4766],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[4436,7416,7417,7486,7736],{},[724,7418,7419,7421,7422,7456,7457,7472,7473,2087],{},[883,7420,4723],{}," Intuice: vztah ",[883,7423,7425],{"className":7424},[886],[888,7426,7427],{"xmlns":890},[892,7428,7429,7453],{},[895,7430,7431,7433,7435,7437,7439,7441,7443,7445,7447,7449,7451],{},[898,7432,1956],{},[898,7434,1959],{},[1664,7436,1676],{},[898,7438,2398],{},[1664,7440,1667],{"stretchy":1666},[1963,7442,2875],{},[1664,7444,1867],{},[1963,7446,2875],{},[898,7448,5240],{"mathvariant":1726},[898,7450,4819],{},[1664,7452,1673],{"stretchy":1666},[902,7454,7455],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,7458,7460],{"className":7459},[886],[888,7461,7462],{"xmlns":890},[892,7463,7464,7470],{},[895,7465,7466,7468],{},[898,7467,1956],{},[898,7469,1959],{},[902,7471,7200],{"encoding":904}," jednoznačně určuje hodnota ",[883,7474,7476],{"className":7475},[886],[888,7477,7478],{"xmlns":890},[892,7479,7480,7484],{},[895,7481,7482],{},[898,7483,4819],{},[902,7485,4819],{"encoding":904},[120,7487,7488,7598,7667],{},[123,7489,7490,7507,7508,1885,7522,1885,7548,1885,7561,7581,7582,7597],{},[883,7491,7493],{"className":7492},[886],[888,7494,7495],{"xmlns":890},[892,7496,7497,7505],{},[895,7498,7499,7501,7503],{},[898,7500,4819],{},[1664,7502,3984],{},[1963,7504,2875],{},[902,7506,5075],{"encoding":904}," (elastická) ",[883,7509,7511],{"className":7510},[886],[888,7512,7513],{"xmlns":890},[892,7514,7515,7519],{},[895,7516,7517],{},[1664,7518,4556],{},[902,7520,7521],{"encoding":904},"\\Rightarrow",[883,7523,7525],{"className":7524},[886],[888,7526,7527],{"xmlns":890},[892,7528,7529,7545],{},[895,7530,7531,7533,7535,7537,7539,7541,7543],{},[1963,7532,2875],{},[1664,7534,1867],{},[1963,7536,2875],{},[898,7538,5240],{"mathvariant":1726},[898,7540,4819],{},[1664,7542,3984],{},[1963,7544,2058],{},[902,7546,7547],{"encoding":904},"1 - 1\u002FE > 0",[883,7549,7551],{"className":7550},[886],[888,7552,7553],{"xmlns":890},[892,7554,7555,7559],{},[895,7556,7557],{},[1664,7558,4556],{},[902,7560,7521],{"encoding":904},[883,7562,7564],{"className":7563},[886],[888,7565,7566],{"xmlns":890},[892,7567,7568,7578],{},[895,7569,7570,7572,7574,7576],{},[898,7571,1956],{},[898,7573,1959],{},[1664,7575,3984],{},[1963,7577,2058],{},[902,7579,7580],{"encoding":904},"MR > 0"," — ",[883,7583,7585],{"className":7584},[886],[888,7586,7587],{"xmlns":890},[892,7588,7589,7595],{},[895,7590,7591,7593],{},[898,7592,1991],{},[898,7594,1959],{},[902,7596,4662],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,7599,7600,7617,7618,1885,7631,7581,7651,7666],{},[883,7601,7603],{"className":7602},[886],[888,7604,7605],{"xmlns":890},[892,7606,7607,7615],{},[895,7608,7609,7611,7613],{},[898,7610,4819],{},[1664,7612,1676],{},[1963,7614,2875],{},[902,7616,5111],{"encoding":904}," (jednotková) ",[883,7619,7621],{"className":7620},[886],[888,7622,7623],{"xmlns":890},[892,7624,7625,7629],{},[895,7626,7627],{},[1664,7628,4556],{},[902,7630,7521],{"encoding":904},[883,7632,7634],{"className":7633},[886],[888,7635,7636],{"xmlns":890},[892,7637,7638,7648],{},[895,7639,7640,7642,7644,7646],{},[898,7641,1956],{},[898,7643,1959],{},[1664,7645,1676],{},[1963,7647,2058],{},[902,7649,7650],{"encoding":904},"MR = 0",[883,7652,7654],{"className":7653},[886],[888,7655,7656],{"xmlns":890},[892,7657,7658,7664],{},[895,7659,7660,7662],{},[898,7661,1991],{},[898,7663,1959],{},[902,7665,4662],{"encoding":904}," je extrém (maximum).",[123,7668,7669,7686,7687,1885,7700,7581,7720,7735],{},[883,7670,7672],{"className":7671},[886],[888,7673,7674],{"xmlns":890},[892,7675,7676,7684],{},[895,7677,7678,7680,7682],{},[898,7679,4819],{},[1664,7681,4022],{},[1963,7683,2875],{},[902,7685,5093],{"encoding":904}," (neelastická) ",[883,7688,7690],{"className":7689},[886],[888,7691,7692],{"xmlns":890},[892,7693,7694,7698],{},[895,7695,7696],{},[1664,7697,4556],{},[902,7699,7521],{"encoding":904},[883,7701,7703],{"className":7702},[886],[888,7704,7705],{"xmlns":890},[892,7706,7707,7717],{},[895,7708,7709,7711,7713,7715],{},[898,7710,1956],{},[898,7712,1959],{},[1664,7714,4022],{},[1963,7716,2058],{},[902,7718,7719],{"encoding":904},"MR \u003C 0",[883,7721,7723],{"className":7722},[886],[888,7724,7725],{"xmlns":890},[892,7726,7727,7733],{},[895,7728,7729,7731],{},[898,7730,1991],{},[898,7732,1959],{},[902,7734,4662],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,7737,7738,7739,1977],{},"Viz také ",[207,7740,2524],{"className":7741,"dataFsResolvedFilePath":827,"href":828},[210],[198,7743,7745],{"id":7744},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,7747,7748,7768,7769,7795,7796,7811,7812,7825,7826,7839,7840,7853,7854,7870,7871,1885,7886,7889,7890,7870,7906,1977],{},[38,7749,7750,7751,4488],{},"(a) Poptávka elastická (",[883,7752,7754],{"className":7753},[886],[888,7755,7756],{"xmlns":890},[892,7757,7758,7766],{},[895,7759,7760,7762,7764],{},[898,7761,4819],{},[1664,7763,3984],{},[1963,7765,2875],{},[902,7767,5075],{"encoding":904}," Z (4.12) plyne ",[883,7770,7772],{"className":7771},[886],[888,7773,7774],{"xmlns":890},[892,7775,7776,7792],{},[895,7777,7778,7780,7782,7784,7786,7788,7790],{},[898,7779,1956],{},[898,7781,1959],{},[1664,7783,1667],{"stretchy":1666},[898,7785,1973],{},[1664,7787,1673],{"stretchy":1666},[1664,7789,3984],{},[1963,7791,2058],{},[902,7793,7794],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,7797,7799],{"className":7798},[886],[888,7800,7801],{"xmlns":890},[892,7802,7803,7809],{},[895,7804,7805,7807],{},[898,7806,1991],{},[898,7808,1959],{},[902,7810,4662],{"encoding":904}," je rostoucí funkcí ",[883,7813,7815],{"className":7814},[886],[888,7816,7817],{"xmlns":890},[892,7818,7819,7823],{},[895,7820,7821],{},[898,7822,1973],{},[902,7824,1973],{"encoding":904},". Avšak růst ",[883,7827,7829],{"className":7828},[886],[888,7830,7831],{"xmlns":890},[892,7832,7833,7837],{},[895,7834,7835],{},[898,7836,1973],{},[902,7838,1973],{"encoding":904}," je odezvou na pokles ceny ",[883,7841,7843],{"className":7842},[886],[888,7844,7845],{"xmlns":890},[892,7846,7847,7851],{},[895,7848,7849],{},[898,7850,2398],{},[902,7852,2398],{"encoding":904},". Tudíž s ",[614,7855,7856,7857],{},"poklesem ceny ",[883,7858,7860],{"className":7859},[886],[888,7861,7862],{"xmlns":890},[892,7863,7864,7868],{},[895,7865,7866],{},[898,7867,2398],{},[902,7869,2398],{"encoding":904}," celkový příjem ",[883,7872,7874],{"className":7873},[886],[888,7875,7876],{"xmlns":890},[892,7877,7878,7884],{},[895,7879,7880,7882],{},[898,7881,1991],{},[898,7883,1959],{},[902,7885,4662],{"encoding":904},[614,7887,7888],{},"roste"," a s ",[614,7891,7892,7893],{},"růstem ceny ",[883,7894,7896],{"className":7895},[886],[888,7897,7898],{"xmlns":890},[892,7899,7900,7904],{},[895,7901,7902],{},[898,7903,2398],{},[902,7905,2398],{"encoding":904},[614,7907,7908],{},"klesá",[4436,7910,7911],{},[724,7912,7913,7916],{},[38,7914,7915],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,7918,7919,7768,7939,1343,7965,7980,7981,7994,7995,8008,8009,8022,8023,7870,8036,1885,8051,1977],{},[38,7920,7921,7922,4488],{},"(b) Poptávka neelastická (",[883,7923,7925],{"className":7924},[886],[888,7926,7927],{"xmlns":890},[892,7928,7929,7937],{},[895,7930,7931,7933,7935],{},[898,7932,4819],{},[1664,7934,4022],{},[1963,7936,2875],{},[902,7938,5093],{"encoding":904},[883,7940,7942],{"className":7941},[886],[888,7943,7944],{"xmlns":890},[892,7945,7946,7962],{},[895,7947,7948,7950,7952,7954,7956,7958,7960],{},[898,7949,1956],{},[898,7951,1959],{},[1664,7953,1667],{"stretchy":1666},[898,7955,1973],{},[1664,7957,1673],{"stretchy":1666},[1664,7959,4022],{},[1963,7961,2058],{},[902,7963,7964],{"encoding":904},"MR(Q) \u003C 0",[883,7966,7968],{"className":7967},[886],[888,7969,7970],{"xmlns":890},[892,7971,7972,7978],{},[895,7973,7974,7976],{},[898,7975,1991],{},[898,7977,1959],{},[902,7979,4662],{"encoding":904}," je klesající funkce ",[883,7982,7984],{"className":7983},[886],[888,7985,7986],{"xmlns":890},[892,7987,7988,7992],{},[895,7989,7990],{},[898,7991,1973],{},[902,7993,1973],{"encoding":904},", tj. s růstem ",[883,7996,7998],{"className":7997},[886],[888,7999,8000],{"xmlns":890},[892,8001,8002,8006],{},[895,8003,8004],{},[898,8005,1973],{},[902,8007,1973],{"encoding":904}," (s poklesem ceny ",[883,8010,8012],{"className":8011},[886],[888,8013,8014],{"xmlns":890},[892,8015,8016,8020],{},[895,8017,8018],{},[898,8019,2398],{},[902,8021,2398],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,8024,8026],{"className":8025},[886],[888,8027,8028],{"xmlns":890},[892,8029,8030,8034],{},[895,8031,8032],{},[898,8033,2398],{},[902,8035,2398],{"encoding":904},[883,8037,8039],{"className":8038},[886],[888,8040,8041],{"xmlns":890},[892,8042,8043,8049],{},[895,8044,8045,8047],{},[898,8046,1991],{},[898,8048,1959],{},[902,8050,4662],{"encoding":904},[614,8052,7888],{},[4436,8054,8055],{},[724,8056,8057,8060],{},[38,8058,8059],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,8062,8063,7768,8083,8102,8103,8118,8119,8189,8190,4454,8218,8251,8252,6155,8280,8295,8296,1977],{},[38,8064,8065,8066,4488],{},"(c) Jednotková elasticita (",[883,8067,8069],{"className":8068},[886],[888,8070,8071],{"xmlns":890},[892,8072,8073,8081],{},[895,8074,8075,8077,8079],{},[898,8076,4819],{},[1664,8078,1676],{},[1963,8080,2875],{},[902,8082,5111],{"encoding":904},[883,8084,8086],{"className":8085},[886],[888,8087,8088],{"xmlns":890},[892,8089,8090,8100],{},[895,8091,8092,8094,8096,8098],{},[898,8093,1956],{},[898,8095,1959],{},[1664,8097,1676],{},[1963,8099,2058],{},[902,8101,7650],{"encoding":904}," — nutná podmínka extrému ",[883,8104,8106],{"className":8105},[886],[888,8107,8108],{"xmlns":890},[892,8109,8110,8116],{},[895,8111,8112,8114],{},[898,8113,1991],{},[898,8115,1959],{},[902,8117,4662],{"encoding":904},". Dále ",[883,8120,8122],{"className":8121},[886],[888,8123,8124],{"xmlns":890},[892,8125,8126,8186],{},[895,8127,8128,8130,8140,8142,8144,8150,8152,8158,8160,8162,8164,8166,8168,8170,8180,8182,8184],{},[898,8129,1991],{},[1720,8131,8132,8134],{},[898,8133,1959],{},[895,8135,8136,8138],{},[1664,8137,1728],{"mathvariant":1726},[1664,8139,1728],{"mathvariant":1726},[1664,8141,1676],{},[898,8143,1956],{},[1720,8145,8146,8148],{},[898,8147,1959],{},[1664,8149,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,8151,1676],{},[1720,8153,8154,8156],{},[898,8155,2379],{},[1664,8157,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,8159,1667],{"stretchy":1666},[898,8161,1973],{},[1664,8163,1673],{"stretchy":1666},[1664,8165,1700],{},[898,8167,1973],{},[1690,8169,1692],{},[1720,8171,8172,8174],{},[898,8173,2379],{},[895,8175,8176,8178],{},[1664,8177,1728],{"mathvariant":1726},[1664,8179,1728],{"mathvariant":1726},[1664,8181,1667],{"stretchy":1666},[898,8183,1973],{},[1664,8185,1673],{"stretchy":1666},[902,8187,8188],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,8191,8193],{"className":8192},[886],[888,8194,8195],{"xmlns":890},[892,8196,8197,8215],{},[895,8198,8199,8205,8207,8209,8211,8213],{},[1720,8200,8201,8203],{},[898,8202,2379],{},[1664,8204,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,8206,1667],{"stretchy":1666},[898,8208,1973],{},[1664,8210,1673],{"stretchy":1666},[1664,8212,4022],{},[1963,8214,2058],{},[902,8216,8217],{"encoding":904},"D'(Q) \u003C 0",[883,8219,8221],{"className":8220},[886],[888,8222,8223],{"xmlns":890},[892,8224,8225,8248],{},[895,8226,8227,8237,8239,8241,8243,8246],{},[1720,8228,8229,8231],{},[898,8230,2379],{},[895,8232,8233,8235],{},[1664,8234,1728],{"mathvariant":1726},[1664,8236,1728],{"mathvariant":1726},[1664,8238,1667],{"stretchy":1666},[898,8240,1973],{},[1664,8242,1673],{"stretchy":1666},[1664,8244,8245],{},"≤",[1963,8247,2058],{},[902,8249,8250],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,8253,8255],{"className":8254},[886],[888,8256,8257],{"xmlns":890},[892,8258,8259,8277],{},[895,8260,8261,8263,8273,8275],{},[898,8262,1991],{},[1720,8264,8265,8267],{},[898,8266,1959],{},[895,8268,8269,8271],{},[1664,8270,1728],{"mathvariant":1726},[1664,8272,1728],{"mathvariant":1726},[1664,8274,4022],{},[1963,8276,2058],{},[902,8278,8279],{"encoding":904},"TR'' \u003C 0",[883,8281,8283],{"className":8282},[886],[888,8284,8285],{"xmlns":890},[892,8286,8287,8293],{},[895,8288,8289,8291],{},[898,8290,1991],{},[898,8292,1959],{},[902,8294,4662],{"encoding":904}," nabývá ",[38,8297,8298],{},"maxima",[4436,8300,8301],{},[724,8302,8303,8306],{},[38,8304,8305],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,8308,8309],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,8311,8312],{},[38,8313,8314],{},"Souhrnná tabulka Pravidel 1–3:",[16,8316,8317,8421],{},[19,8318,8319],{},[22,8320,8321,8324,8339,8356,8387,8418],{},[25,8322,8323],{},"Charakter poptávky",[25,8325,8326],{},[883,8327,8329],{"className":8328},[886],[888,8330,8331],{"xmlns":890},[892,8332,8333,8337],{},[895,8334,8335],{},[898,8336,4819],{},[902,8338,4819],{"encoding":904},[25,8340,8341],{},[883,8342,8344],{"className":8343},[886],[888,8345,8346],{"xmlns":890},[892,8347,8348,8354],{},[895,8349,8350,8352],{},[898,8351,1956],{},[898,8353,1959],{},[902,8355,7200],{"encoding":904},[25,8357,8358,8359,1885,8372],{},"Pokles ceny ",[883,8360,8362],{"className":8361},[886],[888,8363,8364],{"xmlns":890},[892,8365,8366,8370],{},[895,8367,8368],{},[1664,8369,4556],{},[902,8371,7521],{"encoding":904},[883,8373,8375],{"className":8374},[886],[888,8376,8377],{"xmlns":890},[892,8378,8379,8385],{},[895,8380,8381,8383],{},[898,8382,1991],{},[898,8384,1959],{},[902,8386,4662],{"encoding":904},[25,8388,8389,8390,1885,8403],{},"Růst ceny ",[883,8391,8393],{"className":8392},[886],[888,8394,8395],{"xmlns":890},[892,8396,8397,8401],{},[895,8398,8399],{},[1664,8400,4556],{},[902,8402,7521],{"encoding":904},[883,8404,8406],{"className":8405},[886],[888,8407,8408],{"xmlns":890},[892,8409,8410,8416],{},[895,8411,8412,8414],{},[898,8413,1991],{},[898,8415,1959],{},[902,8417,4662],{"encoding":904},[25,8419,8420],{},"Doporučení",[30,8422,8423,8472,8522],{},[22,8424,8425,8427,8445,8463,8465,8467],{},[35,8426,4641],{},[35,8428,8429],{},[883,8430,8432],{"className":8431},[886],[888,8433,8434],{"xmlns":890},[892,8435,8436,8442],{},[895,8437,8438,8440],{},[1664,8439,3984],{},[1963,8441,2875],{},[902,8443,8444],{"encoding":904},"> 1",[35,8446,8447],{},[883,8448,8450],{"className":8449},[886],[888,8451,8452],{"xmlns":890},[892,8453,8454,8460],{},[895,8455,8456,8458],{},[1664,8457,3984],{},[1963,8459,2058],{},[902,8461,8462],{"encoding":904},"> 0",[35,8464,7888],{},[35,8466,7908],{},[35,8468,8469],{},[38,8470,8471],{},"snížit cenu",[22,8473,8474,8477,8495,8513,8515,8517],{},[35,8475,8476],{},"jednotková",[35,8478,8479],{},[883,8480,8482],{"className":8481},[886],[888,8483,8484],{"xmlns":890},[892,8485,8486,8492],{},[895,8487,8488,8490],{},[1664,8489,1676],{},[1963,8491,2875],{},[902,8493,8494],{"encoding":904},"= 1",[35,8496,8497],{},[883,8498,8500],{"className":8499},[886],[888,8501,8502],{"xmlns":890},[892,8503,8504,8510],{},[895,8505,8506,8508],{},[1664,8507,1676],{},[1963,8509,2058],{},[902,8511,8512],{"encoding":904},"= 0",[35,8514,4292],{},[35,8516,4292],{},[35,8518,8519],{},[38,8520,8521],{},"držet cenu",[22,8523,8524,8526,8544,8562,8564,8566],{},[35,8525,4645],{},[35,8527,8528],{},[883,8529,8531],{"className":8530},[886],[888,8532,8533],{"xmlns":890},[892,8534,8535,8541],{},[895,8536,8537,8539],{},[1664,8538,4022],{},[1963,8540,2875],{},[902,8542,8543],{"encoding":904},"\u003C 1",[35,8545,8546],{},[883,8547,8549],{"className":8548},[886],[888,8550,8551],{"xmlns":890},[892,8552,8553,8559],{},[895,8554,8555,8557],{},[1664,8556,4022],{},[1963,8558,2058],{},[902,8560,8561],{"encoding":904},"\u003C 0",[35,8563,7908],{},[35,8565,7888],{},[35,8567,8568],{},[38,8569,8570],{},"zvýšit cenu",[198,8572,8574],{"id":8573},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,8576,8577,8578,8603,8604,8626,8627,8640,8641,8654,8655,1762,8668,6155,8695,8747],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,8579,8581],{"className":8580},[886],[888,8582,8583],{"xmlns":890},[892,8584,8585,8601],{},[895,8586,8587,8589,8591,8593,8595],{},[898,8588,2398],{},[1664,8590,1676],{},[1963,8592,1965],{},[1664,8594,1867],{},[1720,8596,8597,8599],{},[898,8598,1973],{},[1963,8600,1970],{},[902,8602,6025],{"encoding":904},". Reálné cenové rozpětí je ",[883,8605,8607],{"className":8606},[886],[888,8608,8609],{"xmlns":890},[892,8610,8611,8623],{},[895,8612,8613,8615,8617,8619,8621],{},[1664,8614,5890],{"stretchy":1666},[1963,8616,2875],{},[1664,8618,1916],{"separator":1915},[1963,8620,1965],{},[1664,8622,5907],{"stretchy":1666},[902,8624,8625],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,8628,8630],{"className":8629},[886],[888,8631,8632],{"xmlns":890},[892,8633,8634,8638],{},[895,8635,8636],{},[898,8637,1973],{},[902,8639,1973],{"encoding":904}," jako funkci ",[883,8642,8644],{"className":8643},[886],[888,8645,8646],{"xmlns":890},[892,8647,8648,8652],{},[895,8649,8650],{},[898,8651,2398],{},[902,8653,2398],{"encoding":904},"; pro nezáporné ",[883,8656,8658],{"className":8657},[886],[888,8659,8660],{"xmlns":890},[892,8661,8662,8666],{},[895,8663,8664],{},[898,8665,1973],{},[902,8667,1973],{"encoding":904},[883,8669,8671],{"className":8670},[886],[888,8672,8673],{"xmlns":890},[892,8674,8675,8692],{},[895,8676,8677,8679,8681],{},[898,8678,1973],{},[1664,8680,1676],{},[8682,8683,8684],"msqrt",{},[895,8685,8686,8688,8690],{},[1963,8687,1965],{},[1664,8689,1867],{},[898,8691,2398],{},[902,8693,8694],{"encoding":904},"Q = \\sqrt{100 - P}",[883,8696,8698],{"className":8697},[886],[888,8699,8700],{"xmlns":890},[892,8701,8702,8744],{},[895,8703,8704,8720,8722,8724],{},[2919,8705,8706],{"scriptlevel":2058,"displaystyle":1915},[2922,8707,8708,8714],{},[895,8709,8710,8712],{},[898,8711,1695],{"mathvariant":1726},[898,8713,1973],{},[895,8715,8716,8718],{},[898,8717,1695],{"mathvariant":1726},[898,8719,2398],{},[1664,8721,1676],{},[1664,8723,1867],{},[2919,8725,8726],{"scriptlevel":2058,"displaystyle":1915},[2922,8727,8728,8730],{},[1963,8729,2875],{},[895,8731,8732,8734],{},[1963,8733,1970],{},[8682,8735,8736],{},[895,8737,8738,8740,8742],{},[1963,8739,1965],{},[1664,8741,1867],{},[898,8743,2398],{},[902,8745,8746],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,8749,8750],{},[883,8751,8753],{"className":8752},[886],[888,8754,8755],{"xmlns":890},[892,8756,8757,8879],{},[895,8758,8759,8761,8763,8765,8767,8769,8771,8777,8779,8793,8795,8797,8811,8813,8839,8841,8859,8861,8877],{},[898,8760,4819],{},[1664,8762,1667],{"stretchy":1666},[898,8764,2398],{},[1664,8766,1673],{"stretchy":1666},[1664,8768,1676],{},[1664,8770,1867],{},[2922,8772,8773,8775],{},[898,8774,2398],{},[898,8776,1973],{},[1664,8778,3753],{},[2922,8780,8781,8787],{},[895,8782,8783,8785],{},[898,8784,1695],{"mathvariant":1726},[898,8786,1973],{},[895,8788,8789,8791],{},[898,8790,1695],{"mathvariant":1726},[898,8792,2398],{},[1664,8794,1676],{},[1664,8796,1867],{},[2922,8798,8799,8801],{},[898,8800,2398],{},[8682,8802,8803],{},[895,8804,8805,8807,8809],{},[1963,8806,1965],{},[1664,8808,1867],{},[898,8810,2398],{},[1664,8812,3753],{},[895,8814,8815,8817,8819,8837],{},[1664,8816,1667],{"fence":1915},[1664,8818,1867],{},[2922,8820,8821,8823],{},[1963,8822,2875],{},[895,8824,8825,8827],{},[1963,8826,1970],{},[8682,8828,8829],{},[895,8830,8831,8833,8835],{},[1963,8832,1965],{},[1664,8834,1867],{},[898,8836,2398],{},[1664,8838,1673],{"fence":1915},[1664,8840,1676],{},[2922,8842,8843,8845],{},[898,8844,2398],{},[895,8846,8847,8849,8851,8853,8855,8857],{},[1963,8848,1970],{},[1664,8850,1667],{"stretchy":1666},[1963,8852,1965],{},[1664,8854,1867],{},[898,8856,2398],{},[1664,8858,1673],{"stretchy":1666},[1664,8860,1676],{},[2922,8862,8863,8869],{},[895,8864,8865,8867],{},[1963,8866,5575],{},[898,8868,2398],{},[895,8870,8871,8873,8875],{},[1963,8872,1965],{},[1664,8874,1867],{},[898,8876,2398],{},[898,8878,1977],{"mathvariant":1726},[902,8880,8881],{"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}.",[724,8883,8884,8885,2087],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,8886,8888],{"className":8887},[886],[888,8889,8890],{"xmlns":890},[892,8891,8892,8916],{},[895,8893,8894,8912,8914],{},[2919,8895,8896],{"scriptlevel":2058,"displaystyle":1915},[2922,8897,8898,8904],{},[895,8899,8900,8902],{},[1963,8901,5575],{},[898,8903,2398],{},[895,8905,8906,8908,8910],{},[1963,8907,1965],{},[1664,8909,1867],{},[898,8911,2398],{},[1664,8913,1676],{},[1963,8915,2875],{},[902,8917,8918],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,8920,8921],{},[883,8922,8924],{"className":8923},[886],[888,8925,8926],{"xmlns":890},[892,8927,8928,8960],{},[895,8929,8930,8936,8938,8945,8947,8950,8958],{},[1720,8931,8932,8934],{},[898,8933,2398],{},[1664,8935,4920],{},[1664,8937,1676],{},[2922,8939,8940,8943],{},[1963,8941,8942],{},"200",[1963,8944,2774],{},[1664,8946,6466],{},[1963,8948,8949],{},"66,",[8951,8952,8953,8955],"mover",{"accent":1915},[1963,8954,2833],{},[1664,8956,8957],{"stretchy":1915},"‾",[898,8959,1977],{"mathvariant":1726},[902,8961,8962],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,8964,8965],{},"S využitím vlastnosti (4.8):",[120,8967,8968,9014,9056],{},[123,8969,8970,8971,9006,9007,9009,9010,9013],{},"Při cenách ",[883,8972,8974],{"className":8973},[886],[888,8975,8976],{"xmlns":890},[892,8977,8978,9003],{},[895,8979,8980,8982,8984,8986,8988,8991,8993,8995,9001],{},[898,8981,2398],{},[1664,8983,7072],{},[1664,8985,5890],{"stretchy":1666},[1963,8987,2875],{},[1664,8989,8990],{"separator":1915},";",[1690,8992,1692],{},[1963,8994,8949],{},[8951,8996,8997,8999],{"accent":1915},[1963,8998,2833],{},[1664,9000,8957],{"stretchy":1915},[1664,9002,1673],{"stretchy":1666},[902,9004,9005],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,9008,4645],{}," — dle ",[614,9011,9012],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,9015,8970,9016,9006,9050,9009,9052,9055],{},[883,9017,9019],{"className":9018},[886],[888,9020,9021],{"xmlns":890},[892,9022,9023,9047],{},[895,9024,9025,9027,9029,9031,9033,9039,9041,9043,9045],{},[898,9026,2398],{},[1664,9028,7072],{},[1664,9030,1667],{"stretchy":1666},[1963,9032,8949],{},[8951,9034,9035,9037],{"accent":1915},[1963,9036,2833],{},[1664,9038,8957],{"stretchy":1915},[1664,9040,8990],{"separator":1915},[1690,9042,1692],{},[1963,9044,1965],{},[1664,9046,5907],{"stretchy":1666},[902,9048,9049],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,9051,4641],{},[614,9053,9054],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,9057,9058,9059,9062,9063,9091,9092,9095],{},"Dle ",[614,9060,9061],{},"Pravidla 3"," je při ceně ",[883,9064,9066],{"className":9065},[886],[888,9067,9068],{"xmlns":890},[892,9069,9070,9088],{},[895,9071,9072,9078,9080,9082],{},[1720,9073,9074,9076],{},[898,9075,2398],{},[1664,9077,4920],{},[1664,9079,1676],{},[1963,9081,8949],{},[8951,9083,9084,9086],{"accent":1915},[1963,9085,2833],{},[1664,9087,8957],{"stretchy":1915},[902,9089,9090],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,9093,9094],{},"maxima celkového příjmu"," ve výši",[724,9097,9098],{},[883,9099,9101],{"className":9100},[886],[888,9102,9103],{"xmlns":890},[892,9104,9105,9183],{},[895,9106,9107,9109,9111,9113,9119,9121,9123,9129,9131,9145,9147,9153,9155,9163,9165,9178,9180],{},[898,9108,1991],{},[898,9110,1959],{},[1664,9112,1667],{"stretchy":1666},[1720,9114,9115,9117],{},[898,9116,2398],{},[1664,9118,4920],{},[1664,9120,1673],{"stretchy":1666},[1664,9122,1676],{},[1720,9124,9125,9127],{},[898,9126,2398],{},[1664,9128,4920],{},[1664,9130,3753],{},[8682,9132,9133],{},[895,9134,9135,9137,9139],{},[1963,9136,1965],{},[1664,9138,1867],{},[1720,9140,9141,9143],{},[898,9142,2398],{},[1664,9144,4920],{},[1664,9146,1676],{},[2922,9148,9149,9151],{},[1963,9150,8942],{},[1963,9152,2774],{},[1664,9154,3753],{},[8682,9156,9157],{},[2922,9158,9159,9161],{},[1963,9160,1965],{},[1963,9162,2774],{},[1664,9164,1676],{},[2922,9166,9167,9170],{},[1963,9168,9169],{},"2000",[895,9171,9172,9174],{},[1963,9173,2774],{},[8682,9175,9176],{},[1963,9177,2774],{},[1664,9179,6466],{},[1963,9181,9182],{},"384,9.",[902,9184,9185],{"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.",[724,9187,9188,9189,1977],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,9190,9192],{"className":9191},[886],[888,9193,9194],{"xmlns":890},[892,9195,9196,9202],{},[895,9197,9198,9200],{},[898,9199,1991],{},[898,9201,1959],{},[902,9203,4662],{"encoding":904},[115,9205,9207],{"id":9206},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,9209,9210,9211,9214],{},"Analogicky se definuje ",[38,9212,9213],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,9216,9217],{},[883,9218,9220],{"className":9219,"title":4767,"style":4768},[4766],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,9222,1709,9223,9247,9248,9280],{},[883,9224,9226],{"className":9225},[886],[888,9227,9228],{"xmlns":890},[892,9229,9230,9244],{},[895,9231,9232,9234,9236,9238,9240,9242],{},[898,9233,1973],{},[1664,9235,1676],{},[898,9237,2351],{},[1664,9239,1667],{"stretchy":1666},[898,9241,2398],{},[1664,9243,1673],{"stretchy":1666},[902,9245,9246],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,9249,9251],{"className":9250},[886],[888,9252,9253],{"xmlns":890},[892,9254,9255,9277],{},[895,9256,9257,9273,9275],{},[2919,9258,9259],{"scriptlevel":2058,"displaystyle":1915},[2922,9260,9261,9267],{},[895,9262,9263,9265],{},[898,9264,1695],{"mathvariant":1726},[898,9266,1973],{},[895,9268,9269,9271],{},[898,9270,1695],{"mathvariant":1726},[898,9272,2398],{},[1664,9274,3984],{},[1963,9276,2058],{},[902,9278,9279],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,9282,9283],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[4436,9285,9286],{},[724,9287,9288,9289],{},"S rostoucí cenou elasticita nabídky roste. ",[883,9290,9292],{"className":9291},[886],[888,9293,9294],{"xmlns":890},[892,9295,9296,9305],{},[895,9297,9298,9300,9303],{},[1664,9299,1667],{"stretchy":1666},[1963,9301,9302],{},"4.14",[1664,9304,1673],{"stretchy":1666},[902,9306,9307],{"encoding":904},"(4.14)",[724,9309,9310],{},"Pro nominální změny platí",[724,9312,9313],{},[883,9314,9316],{"className":9315,"title":4767,"style":4768},[4766],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,9318,9319],{},"a pro procentní změny",[724,9321,9322],{},[883,9323,9325],{"className":9324,"title":4767,"style":4768},[4766],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,9327,9328],{},"(bez znaménka minus).",[198,9330,9332],{"id":9331},"příklad-47","Příklad 4.7",[724,9334,9335,9336,2087],{},"Nabídka ",[883,9337,9339],{"className":9338},[886],[888,9340,9341],{"xmlns":890},[892,9342,9343,9368],{},[895,9344,9345,9347,9349,9351,9357,9359,9361,9363,9365],{},[898,9346,1973],{},[1664,9348,1676],{},[1963,9350,2220],{},[1720,9352,9353,9355],{},[898,9354,2398],{},[1963,9356,1970],{},[1664,9358,1700],{},[1963,9360,2826],{},[898,9362,2398],{},[1664,9364,1700],{},[1963,9366,9367],{},"150",[902,9369,9370],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,9372,9373],{},[883,9374,9376],{"className":9375},[886],[888,9377,9378],{"xmlns":890},[892,9379,9380,9426],{},[895,9381,9382,9384,9386,9410,9412,9414,9416,9418,9420,9422,9424],{},[898,9383,4819],{},[1664,9385,1676],{},[2922,9387,9388,9390],{},[898,9389,2398],{},[895,9391,9392,9394,9400,9402,9404,9406,9408],{},[1963,9393,2220],{},[1720,9395,9396,9398],{},[898,9397,2398],{},[1963,9399,1970],{},[1664,9401,1700],{},[1963,9403,2826],{},[898,9405,2398],{},[1664,9407,1700],{},[1963,9409,9367],{},[1690,9411,1692],{},[1664,9413,1667],{"stretchy":1666},[1963,9415,2154],{},[898,9417,2398],{},[1664,9419,1700],{},[1963,9421,2826],{},[1664,9423,1673],{"stretchy":1666},[898,9425,1977],{"mathvariant":1726},[902,9427,9428],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,9430,5683,9431,1343,9461,1343,9488,9524,9525,9550,9551,9569,9570,1977],{},[883,9432,9434],{"className":9433},[886],[888,9435,9436],{"xmlns":890},[892,9437,9438,9458],{},[895,9439,9440,9442,9444,9446,9448,9450],{},[898,9441,4819],{},[1664,9443,1667],{"stretchy":1666},[1963,9445,3442],{},[1664,9447,1673],{"stretchy":1666},[1664,9449,1676],{},[2919,9451,9452],{"scriptlevel":2058,"displaystyle":1666},[2922,9453,9454,9456],{},[1963,9455,2875],{},[1963,9457,2774],{},[902,9459,9460],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,9462,9464],{"className":9463},[886],[888,9465,9466],{"xmlns":890},[892,9467,9468,9485],{},[895,9469,9470,9472,9474,9479,9481,9483],{},[898,9471,4819],{},[1664,9473,1667],{"stretchy":1666},[8682,9475,9476],{},[1963,9477,9478],{},"1500",[1664,9480,1673],{"stretchy":1666},[1664,9482,1676],{},[1963,9484,2875],{},[902,9486,9487],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,9489,9491],{"className":9490},[886],[888,9492,9493],{"xmlns":890},[892,9494,9495,9521],{},[895,9496,9497,9499,9501,9503,9505,9507,9516,9518],{},[898,9498,4819],{},[1664,9500,1667],{"stretchy":1666},[1963,9502,1965],{},[1664,9504,1673],{"stretchy":1666},[1664,9506,1676],{},[2919,9508,9509],{"scriptlevel":2058,"displaystyle":1666},[2922,9510,9511,9513],{},[1963,9512,3696],{},[1963,9514,9515],{},"33",[1664,9517,6466],{},[1963,9519,9520],{},"1,515",[902,9522,9523],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,9526,9528],{"className":9527},[886],[888,9529,9530],{"xmlns":890},[892,9531,9532,9547],{},[895,9533,9534,9536,9538,9542,9544],{},[898,9535,2398],{},[1664,9537,3984],{},[8682,9539,9540],{},[1963,9541,9478],{},[1664,9543,3315],{},[1963,9545,9546],{},"38,7",[902,9548,9549],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,9552,9554],{"className":9553},[886],[888,9555,9556],{"xmlns":890},[892,9557,9558,9566],{},[895,9559,9560,9562,9564],{},[898,9561,2398],{},[1664,9563,4022],{},[1963,9565,9546],{},[902,9567,9568],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,9571,9573],{"className":9572},[886],[888,9574,9575],{"xmlns":890},[892,9576,9577,9615],{},[895,9578,9579,9581,9583,9585,9587,9595,9597,9600,9602,9605,9611,9613],{},[898,9580,3468],{"mathvariant":1726},[898,9582,1973],{},[898,9584,6491],{"mathvariant":1726},[1664,9586,3315],{},[2919,9588,9589],{"scriptlevel":2058,"displaystyle":1666},[2922,9590,9591,9593],{},[1963,9592,2875],{},[1963,9594,2774],{},[1664,9596,3753],{},[1963,9598,9599],{},"20",[1664,9601,1676],{},[1963,9603,9604],{},"6,",[8951,9606,9607,9609],{"accent":1915},[1963,9608,2833],{},[1664,9610,8957],{"stretchy":1915},[1690,9612,1692],{},[898,9614,6491],{"mathvariant":1726},[902,9616,9617],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,9619,9621],{"id":9620},"vícefaktorový-model","Vícefaktorový model",[724,9623,9624,9625,9638,9639,1885,9642,9655,9656,1885,9659,9677,9678,1885,9681,2087],{},"Předpokládejme, že poptávané množství ",[883,9626,9628],{"className":9627},[886],[888,9629,9630],{"xmlns":890},[892,9631,9632,9636],{},[895,9633,9634],{},[898,9635,1973],{},[902,9637,1973],{"encoding":904}," závisí na ",[38,9640,9641],{},"ceně základního zboží",[883,9643,9645],{"className":9644},[886],[888,9646,9647],{"xmlns":890},[892,9648,9649,9653],{},[895,9650,9651],{},[898,9652,2398],{},[902,9654,2398],{"encoding":904},", na ",[38,9657,9658],{},"ceně alternativního zboží",[883,9660,9662],{"className":9661},[886],[888,9663,9664],{"xmlns":890},[892,9665,9666,9674],{},[895,9667,9668],{},[2355,9669,9670,9672],{},[898,9671,2398],{},[898,9673,4822],{},[902,9675,9676],{"encoding":904},"P_A"," a na ",[38,9679,9680],{},"důchodu",[883,9682,9684],{"className":9683},[886],[888,9685,9686],{"xmlns":890},[892,9687,9688,9693],{},[895,9689,9690],{},[898,9691,9692],{},"Y",[902,9694,9692],{"encoding":904},[724,9696,9697],{},[883,9698,9700],{"className":9699,"title":4767,"style":4768},[4766],"Q = D(P, P_A, Y). \\tag{4.17}",[724,9702,9703,9704,9707],{},"V analogii jednofaktorového modelu pracujeme s ",[38,9705,9706],{},"parciálními derivacemi"," funkce poptávky.",[198,9709,9711],{"id":9710},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,9713,9714],{},[883,9715,9717],{"className":9716,"title":4767,"style":4768},[4766],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,9719,1709,9720,9740,9741,9754,9755,1748,9777,1885,9780,9826,9827,9840,9841,9858],{},[883,9721,9723],{"className":9722},[886],[888,9724,9725],{"xmlns":890},[892,9726,9727,9737],{},[895,9728,9729],{},[1810,9730,9731,9733,9735],{},[898,9732,1973],{},[898,9734,2398],{},[1664,9736,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,9738,9739],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,9742,9744],{"className":9743},[886],[888,9745,9746],{"xmlns":890},[892,9747,9748,9752],{},[895,9749,9750],{},[898,9751,2398],{},[902,9753,2398],{"encoding":904},". Vždy ",[883,9756,9758],{"className":9757},[886],[888,9759,9760],{"xmlns":890},[892,9761,9762,9774],{},[895,9763,9764,9770,9772],{},[2355,9765,9766,9768],{},[898,9767,4819],{},[898,9769,2398],{},[1664,9771,5051],{},[1963,9773,2058],{},[902,9775,9776],{"encoding":904},"E_P \\ge 0",[614,9778,9779],{},"Interpretace:",[883,9781,9783],{"className":9782},[886],[888,9784,9785],{"xmlns":890},[892,9786,9787,9823],{},[895,9788,9789,9795,9797,9803,9805,9813,9815,9821],{},[2355,9790,9791,9793],{},[898,9792,4819],{},[898,9794,2398],{},[1664,9796,1667],{"stretchy":1666},[1720,9798,9799,9801],{},[898,9800,2398],{},[1664,9802,4920],{},[1664,9804,1916],{"separator":1915},[1810,9806,9807,9809,9811],{},[898,9808,2398],{},[898,9810,4822],{},[1664,9812,4920],{},[1664,9814,1916],{"separator":1915},[1720,9816,9817,9819],{},[898,9818,9692],{},[1664,9820,4920],{},[1664,9822,1673],{"stretchy":1666},[902,9824,9825],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,9828,9830],{"className":9829},[886],[888,9831,9832],{"xmlns":890},[892,9833,9834,9838],{},[895,9835,9836],{},[898,9837,1973],{},[902,9839,1973],{"encoding":904}," při 1% změně ",[883,9842,9844],{"className":9843},[886],[888,9845,9846],{"xmlns":890},[892,9847,9848,9856],{},[895,9849,9850],{},[1720,9851,9852,9854],{},[898,9853,2398],{},[1664,9855,4920],{},[902,9857,4970],{"encoding":904},", ceteris paribus.",[198,9860,9862],{"id":9861},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,9864,9865],{},[883,9866,9868],{"className":9867,"title":4767,"style":4768},[4766],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,9870,9871,9826,9873,9886,9887,9904],{},[614,9872,9779],{},[883,9874,9876],{"className":9875},[886],[888,9877,9878],{"xmlns":890},[892,9879,9880,9884],{},[895,9881,9882],{},[898,9883,1973],{},[902,9885,1973],{"encoding":904}," základního zboží při 1% změně ceny ",[883,9888,9890],{"className":9889},[886],[888,9891,9892],{"xmlns":890},[892,9893,9894,9902],{},[895,9895,9896],{},[2355,9897,9898,9900],{},[898,9899,2398],{},[898,9901,4822],{},[902,9903,9676],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,9906,9907],{},[38,9908,9909],{},"Znaménko závisí na povaze alternativního zboží:",[120,9911,9912,10000],{},[123,9913,9914,9915,9918,9919,9936,9937,1885,9950,1977],{},"Je-li alternativní zboží ",[38,9916,9917],{},"komplement",", růst ",[883,9920,9922],{"className":9921},[886],[888,9923,9924],{"xmlns":890},[892,9925,9926,9934],{},[895,9927,9928],{},[2355,9929,9930,9932],{},[898,9931,2398],{},[898,9933,4822],{},[902,9935,9676],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,9938,9940],{"className":9939},[886],[888,9941,9942],{"xmlns":890},[892,9943,9944,9948],{},[895,9945,9946],{},[898,9947,1973],{},[902,9949,1973],{"encoding":904},[883,9951,9953],{"className":9952},[886],[888,9954,9955],{"xmlns":890},[892,9956,9957,9997],{},[895,9958,9959,9961,9963,9975,9977,9979,9981,9983,9993,9995],{},[1664,9960,4556],{},[1690,9962,4553],{},[1810,9964,9965,9967,9973],{},[898,9966,1973],{},[2355,9968,9969,9971],{},[898,9970,2398],{},[898,9972,4822],{},[1664,9974,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,9976,4022],{},[1963,9978,2058],{},[1664,9980,1916],{"separator":1915},[1690,9982,4553],{},[2355,9984,9985,9987],{},[898,9986,4819],{},[2355,9988,9989,9991],{},[898,9990,2398],{},[898,9992,4822],{},[1664,9994,4022],{},[1963,9996,2058],{},[902,9998,9999],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,10001,9914,10002,9918,10005,10022,10023,10036,10037,1977],{},[38,10003,10004],{},"substitut",[883,10006,10008],{"className":10007},[886],[888,10009,10010],{"xmlns":890},[892,10011,10012,10020],{},[895,10013,10014],{},[2355,10015,10016,10018],{},[898,10017,2398],{},[898,10019,4822],{},[902,10021,9676],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,10024,10026],{"className":10025},[886],[888,10027,10028],{"xmlns":890},[892,10029,10030,10034],{},[895,10031,10032],{},[898,10033,1973],{},[902,10035,1973],{"encoding":904}," roste ",[883,10038,10040],{"className":10039},[886],[888,10041,10042],{"xmlns":890},[892,10043,10044,10084],{},[895,10045,10046,10048,10050,10062,10064,10066,10068,10070,10080,10082],{},[1664,10047,4556],{},[1690,10049,4553],{},[1810,10051,10052,10054,10060],{},[898,10053,1973],{},[2355,10055,10056,10058],{},[898,10057,2398],{},[898,10059,4822],{},[1664,10061,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,10063,3984],{},[1963,10065,2058],{},[1664,10067,1916],{"separator":1915},[1690,10069,4553],{},[2355,10071,10072,10074],{},[898,10073,4819],{},[2355,10075,10076,10078],{},[898,10077,2398],{},[898,10079,4822],{},[1664,10081,3984],{},[1963,10083,2058],{},[902,10085,10086],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,10088,10091],{"className":10089,"title":10090,"style":4768},[4766],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":10093},[10094,10098,10099,10107,10108,10112,10115],{"id":4460,"depth":642,"text":4461,"children":10095},[10096,10097],{"id":4491,"depth":649,"text":4492},{"id":4670,"depth":649,"text":4671},{"id":4705,"depth":642,"text":4706},{"id":4731,"depth":642,"text":4732,"children":10100},[10101,10102,10103,10104,10106],{"id":5425,"depth":649,"text":5426},{"id":5515,"depth":649,"text":5516},{"id":5851,"depth":649,"text":5852},{"id":5933,"depth":649,"text":10105},"Výpočet, je-li dáno PP jako funkce QQ",{"id":6194,"depth":649,"text":6195},{"id":6519,"depth":642,"text":6520},{"id":7115,"depth":642,"text":7116,"children":10109},[10110,10111],{"id":7744,"depth":649,"text":7745},{"id":8573,"depth":649,"text":8574},{"id":9206,"depth":642,"text":9207,"children":10113},[10114],{"id":9331,"depth":649,"text":9332},{"id":9620,"depth":642,"text":9621,"children":10116},[10117,10118],{"id":9710,"depth":649,"text":9711},{"id":9861,"depth":649,"text":9862},"2026-04-22",{},"\u002Ftopics\u002Felasticita",{"title":4429,"description":641},[1138,1136],"topics\u002Felasticita",[1128,4467,10126,10127,10128,10129],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":10132,"title":10133,"body":10134,"course":1128,"courses":659,"created":1129,"description":11674,"extension":661,"meta":11675,"navigation":664,"path":11676,"seo":11677,"sources":11678,"stem":11679,"tags":11680,"type":2553,"updated":677,"__hash__":11685},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":10135,"toc":11659},[10136,10139,10213,10220,10224,10288,10377,10381,10408,10475,10530,10534,10561,10654,10656,10688,10859,10863,10933,10981,10985,11045,11151,11166,11170,11172,11200,11265,11267,11274,11362,11386,11584,11588,11624,11626],[12,10137,10133],{"id":10138},"kalkul-funkcí-více-proměnných",[724,10140,10141,10142,10145,10146,1343,10175,1977],{},"Většina ekonomických veličin závisí na ",[38,10143,10144],{},"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 ",[883,10147,10149],{"className":10148},[886],[888,10150,10151],{"xmlns":890},[892,10152,10153,10172],{},[895,10154,10155,10158,10160,10162,10164,10166,10168,10170],{},[898,10156,10157],{},"z",[1664,10159,1676],{},[898,10161,1682],{},[1664,10163,1667],{"stretchy":1666},[898,10165,1670],{},[1664,10167,1916],{"separator":1915},[898,10169,2608],{},[1664,10171,1673],{"stretchy":1666},[902,10173,10174],{"encoding":904},"z = f(x, y)",[883,10176,10178],{"className":10177},[886],[888,10179,10180],{"xmlns":890},[892,10181,10182,10210],{},[895,10183,10184,10187,10189,10191,10193,10195,10197,10199,10201,10203,10205,10207],{},[898,10185,10186],{},"w",[1664,10188,1676],{},[898,10190,1682],{},[1664,10192,1667],{"stretchy":1666},[898,10194,1670],{},[1664,10196,1916],{"separator":1915},[898,10198,2608],{},[1664,10200,1916],{"separator":1915},[898,10202,10157],{},[1664,10204,1673],{"stretchy":1666},[1664,10206,1916],{"separator":1915},[1664,10208,10209],{},"…",[902,10211,10212],{"encoding":904},"w = f(x, y, z), \\ldots",[724,10214,10215],{},[1928,10216],{"alt":10217,"className":10218,"src":10219},"imek-funkce-2d-vrstevnice",[210,1932],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,10221,10223],{"id":10222},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,10225,10226,10227,10254,10255,10283,10284,10287],{},"Pro ",[883,10228,10230],{"className":10229},[886],[888,10231,10232],{"xmlns":890},[892,10233,10234,10252],{},[895,10235,10236,10238,10240,10242,10244,10246,10248,10250],{},[898,10237,10157],{},[1664,10239,1676],{},[898,10241,1682],{},[1664,10243,1667],{"stretchy":1666},[898,10245,1670],{},[1664,10247,1916],{"separator":1915},[898,10249,2608],{},[1664,10251,1673],{"stretchy":1666},[902,10253,10174],{"encoding":904}," se křivkou s předpisem ",[883,10256,10258],{"className":10257},[886],[888,10259,10260],{"xmlns":890},[892,10261,10262,10280],{},[895,10263,10264,10266,10268,10270,10272,10274,10276,10278],{},[898,10265,1682],{},[1664,10267,1667],{"stretchy":1666},[898,10269,1670],{},[1664,10271,1916],{"separator":1915},[898,10273,2608],{},[1664,10275,1673],{"stretchy":1666},[1664,10277,1676],{},[898,10279,2034],{},[902,10281,10282],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,10285,10286],{},"vrstevnice"," funkce. V ekonomii:",[120,10289,10290,10337],{},[123,10291,10292,10295,10296,10332,10333,1977],{},[38,10293,10294],{},"Indiferenční křivky"," užitečnosti ",[883,10297,10299],{"className":10298},[886],[888,10300,10301],{"xmlns":890},[892,10302,10303,10329],{},[895,10304,10305,10307,10309,10315,10317,10323,10325,10327],{},[898,10306,900],{},[1664,10308,1667],{"stretchy":1666},[2355,10310,10311,10313],{},[898,10312,1973],{},[1963,10314,2875],{},[1664,10316,1916],{"separator":1915},[2355,10318,10319,10321],{},[898,10320,1973],{},[1963,10322,1970],{},[1664,10324,1673],{"stretchy":1666},[1664,10326,1676],{},[898,10328,2034],{},[902,10330,10331],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,10334,10336],{"className":10335,"dataFsResolvedFilePath":878,"href":879},[210],"uzitecnost",[123,10338,10339,10342,10343,10332,10373,1977],{},[38,10340,10341],{},"Izokvanty"," produkce ",[883,10344,10346],{"className":10345},[886],[888,10347,10348],{"xmlns":890},[892,10349,10350,10370],{},[895,10351,10352,10354,10356,10359,10361,10364,10366,10368],{},[898,10353,1973],{},[1664,10355,1667],{"stretchy":1666},[898,10357,10358],{},"L",[1664,10360,1916],{"separator":1915},[898,10362,10363],{},"K",[1664,10365,1673],{"stretchy":1666},[1664,10367,1676],{},[898,10369,2034],{},[902,10371,10372],{"encoding":904},"Q(L, K) = c",[207,10374,10376],{"className":10375,"dataFsResolvedFilePath":857,"href":858},[210],"produkce",[115,10378,10380],{"id":10379},"parciální-derivace","Parciální derivace",[724,10382,10226,10383,10407],{},[883,10384,10386],{"className":10385},[886],[888,10387,10388],{"xmlns":890},[892,10389,10390,10404],{},[895,10391,10392,10394,10396,10398,10400,10402],{},[898,10393,1682],{},[1664,10395,1667],{"stretchy":1666},[898,10397,1670],{},[1664,10399,1916],{"separator":1915},[898,10401,2608],{},[1664,10403,1673],{"stretchy":1666},[902,10405,10406],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,10409,10410],{},[883,10411,10413],{"className":10412},[886],[888,10414,10415],{"xmlns":890},[892,10416,10417,10472],{},[895,10418,10419,10427,10429,10444,10446,10448,10456,10458],{},[1810,10420,10421,10423,10425],{},[898,10422,1682],{},[898,10424,1670],{},[1664,10426,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,10428,1676],{},[2922,10430,10431,10438],{},[895,10432,10433,10436],{},[898,10434,10435],{"mathvariant":1726},"∂",[898,10437,1682],{},[895,10439,10440,10442],{},[898,10441,10435],{"mathvariant":1726},[898,10443,1670],{},[1664,10445,1916],{"separator":1915},[6444,10447],{"width":6446},[1810,10449,10450,10452,10454],{},[898,10451,1682],{},[898,10453,2608],{},[1664,10455,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,10457,1676],{},[2922,10459,10460,10466],{},[895,10461,10462,10464],{},[898,10463,10435],{"mathvariant":1726},[898,10465,1682],{},[895,10467,10468,10470],{},[898,10469,10435],{"mathvariant":1726},[898,10471,2608],{},[902,10473,10474],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,10476,10477,10478,1977],{},"Hodnoty v bodě: ",[883,10479,10481],{"className":10480},[886],[888,10482,10483],{"xmlns":890},[892,10484,10485,10527],{},[895,10486,10487,10495,10497,10499,10501,10503,10505,10507,10509,10517,10519,10521,10523,10525],{},[1810,10488,10489,10491,10493],{},[898,10490,1682],{},[898,10492,1670],{},[1664,10494,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,10496,1667],{"stretchy":1666},[898,10498,207],{},[1664,10500,1916],{"separator":1915},[898,10502,1818],{},[1664,10504,1673],{"stretchy":1666},[1664,10506,1916],{"separator":1915},[1690,10508,2884],{},[1810,10510,10511,10513,10515],{},[898,10512,1682],{},[898,10514,2608],{},[1664,10516,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,10518,1667],{"stretchy":1666},[898,10520,207],{},[1664,10522,1916],{"separator":1915},[898,10524,1818],{},[1664,10526,1673],{"stretchy":1666},[902,10528,10529],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,10531,10533],{"id":10532},"ekonomické-značení","Ekonomické značení",[724,10535,10536,10537,2087],{},"Pro produkční funkci ",[883,10538,10540],{"className":10539},[886],[888,10541,10542],{"xmlns":890},[892,10543,10544,10558],{},[895,10545,10546,10548,10550,10552,10554,10556],{},[898,10547,1973],{},[1664,10549,1667],{"stretchy":1666},[898,10551,10358],{},[1664,10553,1916],{"separator":1915},[898,10555,10363],{},[1664,10557,1673],{"stretchy":1666},[902,10559,10560],{"encoding":904},"Q(L, K)",[120,10562,10563,10609],{},[123,10564,10565,3060,10585,10588,10589,1673],{},[883,10566,10568],{"className":10567},[886],[888,10569,10570],{"xmlns":890},[892,10571,10572,10582],{},[895,10573,10574],{},[1810,10575,10576,10578,10580],{},[898,10577,1973],{},[898,10579,10358],{},[1664,10581,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,10583,10584],{"encoding":904},"Q'_L",[38,10586,10587],{},"mezní produkt práce"," (",[883,10590,10592],{"className":10591},[886],[888,10593,10594],{"xmlns":890},[892,10595,10596,10606],{},[895,10597,10598,10600],{},[898,10599,1956],{},[2355,10601,10602,10604],{},[898,10603,2398],{},[898,10605,10358],{},[902,10607,10608],{"encoding":904},"MP_L",[123,10610,10611,3060,10631,10588,10634,1673],{},[883,10612,10614],{"className":10613},[886],[888,10615,10616],{"xmlns":890},[892,10617,10618,10628],{},[895,10619,10620],{},[1810,10621,10622,10624,10626],{},[898,10623,1973],{},[898,10625,10363],{},[1664,10627,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,10629,10630],{"encoding":904},"Q'_K",[38,10632,10633],{},"mezní produkt kapitálu",[883,10635,10637],{"className":10636},[886],[888,10638,10639],{"xmlns":890},[892,10640,10641,10651],{},[895,10642,10643,10645],{},[898,10644,1956],{},[2355,10646,10647,10649],{},[898,10648,2398],{},[898,10650,10363],{},[902,10652,10653],{"encoding":904},"MP_K",[198,10655,3154],{"id":3153},[724,10657,10658,2087],{},[883,10659,10661],{"className":10660},[886],[888,10662,10663],{"xmlns":890},[892,10664,10665,10685],{},[895,10666,10667,10675,10677,10679,10681,10683],{},[1810,10668,10669,10671,10673],{},[898,10670,1682],{},[898,10672,1670],{},[1664,10674,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,10676,1667],{"stretchy":1666},[898,10678,207],{},[1664,10680,1916],{"separator":1915},[898,10682,1818],{},[1664,10684,1673],{"stretchy":1666},[902,10686,10687],{"encoding":904},"f'_x(a, b)",[120,10689,10690,10748],{},[123,10691,10692,10693,10706,10707,10720,10721,10747],{},"rychlost změny ",[883,10694,10696],{"className":10695},[886],[888,10697,10698],{"xmlns":890},[892,10699,10700,10704],{},[895,10701,10702],{},[898,10703,1682],{},[902,10705,1682],{"encoding":904}," vůči ",[883,10708,10710],{"className":10709},[886],[888,10711,10712],{"xmlns":890},[892,10713,10714,10718],{},[895,10715,10716],{},[898,10717,1670],{},[902,10719,1670],{"encoding":904}," při ",[883,10722,10724],{"className":10723},[886],[888,10725,10726],{"xmlns":890},[892,10727,10728,10744],{},[895,10729,10730,10732,10734,10736,10738,10740,10742],{},[898,10731,1670],{},[1664,10733,1676],{},[898,10735,207],{},[1664,10737,1916],{"separator":1915},[898,10739,2608],{},[1664,10741,1676],{},[898,10743,1818],{},[902,10745,10746],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,10749,10750,10751,3243,10764,10777,10778,10796,10797,1977],{},"přibližná změna ",[883,10752,10754],{"className":10753},[886],[888,10755,10756],{"xmlns":890},[892,10757,10758,10762],{},[895,10759,10760],{},[898,10761,1682],{},[902,10763,1682],{"encoding":904},[883,10765,10767],{"className":10766},[886],[888,10768,10769],{"xmlns":890},[892,10770,10771,10775],{},[895,10772,10773],{},[898,10774,1670],{},[902,10776,1670],{"encoding":904}," o 1 (a pevném ",[883,10779,10781],{"className":10780},[886],[888,10782,10783],{"xmlns":890},[892,10784,10785,10793],{},[895,10786,10787,10789,10791],{},[898,10788,2608],{},[1664,10790,1676],{},[898,10792,1818],{},[902,10794,10795],{"encoding":904},"y = b","): ",[883,10798,10800],{"className":10799},[886],[888,10801,10802],{"xmlns":890},[892,10803,10804,10856],{},[895,10805,10806,10808,10810,10812,10814,10816,10818,10820,10822,10824,10826,10828,10830,10832,10834,10836,10838,10846,10848,10850,10852,10854],{},[898,10807,1682],{},[1664,10809,1667],{"stretchy":1666},[898,10811,207],{},[1664,10813,1700],{},[1963,10815,2875],{},[1664,10817,1916],{"separator":1915},[898,10819,1818],{},[1664,10821,1673],{"stretchy":1666},[1664,10823,3315],{},[898,10825,1682],{},[1664,10827,1667],{"stretchy":1666},[898,10829,207],{},[1664,10831,1916],{"separator":1915},[898,10833,1818],{},[1664,10835,1673],{"stretchy":1666},[1664,10837,1700],{},[1810,10839,10840,10842,10844],{},[898,10841,1682],{},[898,10843,1670],{},[1664,10845,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,10847,1667],{"stretchy":1666},[898,10849,207],{},[1664,10851,1916],{"separator":1915},[898,10853,1818],{},[1664,10855,1673],{"stretchy":1666},[902,10857,10858],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,10860,10862],{"id":10861},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,10864,10865],{},[883,10866,10868],{"className":10867},[886],[888,10869,10870],{"xmlns":890},[892,10871,10872,10930],{},[895,10873,10874,10876,10878,10880,10888,10890,10892,10894,10896,10898,10900,10902,10904,10906,10914,10916,10918,10920,10922,10924,10926,10928],{},[898,10875,1695],{},[898,10877,1682],{},[1664,10879,1676],{},[1810,10881,10882,10884,10886],{},[898,10883,1682],{},[898,10885,1670],{},[1664,10887,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,10889,1667],{"stretchy":1666},[898,10891,1670],{},[1664,10893,1916],{"separator":1915},[898,10895,2608],{},[1664,10897,1673],{"stretchy":1666},[1690,10899,1692],{},[898,10901,1695],{},[898,10903,1670],{},[1664,10905,1700],{},[1810,10907,10908,10910,10912],{},[898,10909,1682],{},[898,10911,2608],{},[1664,10913,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,10915,1667],{"stretchy":1666},[898,10917,1670],{},[1664,10919,1916],{"separator":1915},[898,10921,2608],{},[1664,10923,1673],{"stretchy":1666},[1690,10925,1692],{},[898,10927,1695],{},[898,10929,2608],{},[902,10931,10932],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,10934,3574,10935,10957,10958,10980],{},[883,10936,10938],{"className":10937},[886],[888,10939,10940],{"xmlns":890},[892,10941,10942,10954],{},[895,10943,10944,10946,10948,10950,10952],{},[898,10945,1695],{},[898,10947,1670],{},[1664,10949,1916],{"separator":1915},[898,10951,1695],{},[898,10953,2608],{},[902,10955,10956],{"encoding":904},"dx, dy"," platí ",[883,10959,10961],{"className":10960},[886],[888,10962,10963],{"xmlns":890},[892,10964,10965,10977],{},[895,10966,10967,10969,10971,10973,10975],{},[898,10968,3468],{"mathvariant":1726},[898,10970,1682],{},[1664,10972,3315],{},[898,10974,1695],{},[898,10976,1682],{},[902,10978,10979],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,10982,10984],{"id":10983},"implicitní-funkce","Implicitní funkce",[724,10986,10987,10988,11016,11017,11030,11031,11044],{},"Je-li vztah dán rovnicí ",[883,10989,10991],{"className":10990},[886],[888,10992,10993],{"xmlns":890},[892,10994,10995,11013],{},[895,10996,10997,10999,11001,11003,11005,11007,11009,11011],{},[898,10998,1662],{},[1664,11000,1667],{"stretchy":1666},[898,11002,1670],{},[1664,11004,1916],{"separator":1915},[898,11006,2608],{},[1664,11008,1673],{"stretchy":1666},[1664,11010,1676],{},[1963,11012,2058],{},[902,11014,11015],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,11018,11020],{"className":11019},[886],[888,11021,11022],{"xmlns":890},[892,11023,11024,11028],{},[895,11025,11026],{},[898,11027,2608],{},[902,11029,2608],{"encoding":904}," podle ",[883,11032,11034],{"className":11033},[886],[888,11035,11036],{"xmlns":890},[892,11037,11038,11042],{},[895,11039,11040],{},[898,11041,1670],{},[902,11043,1670],{"encoding":904}," (nebo naopak):",[724,11046,11047],{},[883,11048,11050],{"className":11049},[886],[888,11051,11052],{"xmlns":890},[892,11053,11054,11148],{},[895,11055,11056,11062,11064,11078,11080,11082,11100,11102,11104,11110,11112,11126,11128,11130],{},[1720,11057,11058,11060],{},[898,11059,2608],{},[1664,11061,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,11063,1676],{},[2922,11065,11066,11072],{},[895,11067,11068,11070],{},[898,11069,1695],{},[898,11071,2608],{},[895,11073,11074,11076],{},[898,11075,1695],{},[898,11077,1670],{},[1664,11079,1676],{},[1664,11081,1867],{},[2922,11083,11084,11092],{},[1810,11085,11086,11088,11090],{},[898,11087,1662],{},[898,11089,1670],{},[1664,11091,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1810,11093,11094,11096,11098],{},[898,11095,1662],{},[898,11097,2608],{},[1664,11099,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,11101,1916],{"separator":1915},[6444,11103],{"width":6446},[1720,11105,11106,11108],{},[898,11107,1670],{},[1664,11109,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,11111,1676],{},[2922,11113,11114,11120],{},[895,11115,11116,11118],{},[898,11117,1695],{},[898,11119,1670],{},[895,11121,11122,11124],{},[898,11123,1695],{},[898,11125,2608],{},[1664,11127,1676],{},[1664,11129,1867],{},[2922,11131,11132,11140],{},[1810,11133,11134,11136,11138],{},[898,11135,1662],{},[898,11137,2608],{},[1664,11139,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1810,11141,11142,11144,11146],{},[898,11143,1662],{},[898,11145,1670],{},[1664,11147,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,11149,11150],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,11152,11153,11154,11157,11158,4454,11162,1977],{},"Tato vzorec dává ",[38,11155,11156],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,11159,11161],{"className":11160,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS",[207,11163,11165],{"className":11164,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS",[115,11167,11169],{"id":11168},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,11171,3828],{"id":3827},[724,11173,11174,11175,11199],{},"V bodě extrému ",[883,11176,11178],{"className":11177},[886],[888,11179,11180],{"xmlns":890},[892,11181,11182,11196],{},[895,11183,11184,11186,11188,11190,11192,11194],{},[898,11185,4822],{},[1664,11187,1837],{"stretchy":1666},[898,11189,207],{},[1664,11191,1916],{"separator":1915},[898,11193,1818],{},[1664,11195,1850],{"stretchy":1666},[902,11197,11198],{"encoding":904},"A[a, b]"," musí platit současně:",[724,11201,11202],{},[883,11203,11205],{"className":11204},[886],[888,11206,11207],{"xmlns":890},[892,11208,11209,11262],{},[895,11210,11211,11219,11221,11223,11225,11227,11229,11231,11233,11235,11238,11240,11248,11250,11252,11254,11256,11258,11260],{},[1810,11212,11213,11215,11217],{},[898,11214,1682],{},[898,11216,1670],{},[1664,11218,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,11220,1667],{"stretchy":1666},[898,11222,207],{},[1664,11224,1916],{"separator":1915},[898,11226,1818],{},[1664,11228,1673],{"stretchy":1666},[1664,11230,1676],{},[1963,11232,2058],{},[1690,11234,4553],{},[1664,11236,11237],{},"∧",[1690,11239,4553],{},[1810,11241,11242,11244,11246],{},[898,11243,1682],{},[898,11245,2608],{},[1664,11247,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,11249,1667],{"stretchy":1666},[898,11251,207],{},[1664,11253,1916],{"separator":1915},[898,11255,1818],{},[1664,11257,1673],{"stretchy":1666},[1664,11259,1676],{},[1963,11261,2058],{},[902,11263,11264],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,11266,3902],{"id":3901},[724,11268,11269,11270,11273],{},"Definujeme ",[38,11271,11272],{},"diskriminant"," (Hessián zjednodušeně):",[724,11275,11276],{},[883,11277,11279],{"className":11278},[886],[888,11280,11281],{"xmlns":890},[892,11282,11283,11359],{},[895,11284,11285,11287,11289,11291,11293,11295,11297,11299,11315,11317,11333,11335,11337,11353],{},[898,11286,2379],{},[1664,11288,1667],{"stretchy":1666},[898,11290,1670],{},[1664,11292,1916],{"separator":1915},[898,11294,2608],{},[1664,11296,1673],{"stretchy":1666},[1664,11298,1676],{},[1810,11300,11301,11303,11309],{},[898,11302,1682],{},[895,11304,11305,11307],{},[898,11306,1670],{},[898,11308,1670],{},[895,11310,11311,11313],{},[1664,11312,1728],{"mathvariant":1726},[1664,11314,1728],{"mathvariant":1726},[1664,11316,3753],{},[1810,11318,11319,11321,11327],{},[898,11320,1682],{},[895,11322,11323,11325],{},[898,11324,2608],{},[898,11326,2608],{},[895,11328,11329,11331],{},[1664,11330,1728],{"mathvariant":1726},[1664,11332,1728],{"mathvariant":1726},[1664,11334,1867],{},[1664,11336,1667],{"stretchy":1666},[1810,11338,11339,11341,11347],{},[898,11340,1682],{},[895,11342,11343,11345],{},[898,11344,1670],{},[898,11346,2608],{},[895,11348,11349,11351],{},[1664,11350,1728],{"mathvariant":1726},[1664,11352,1728],{"mathvariant":1726},[1720,11354,11355,11357],{},[1664,11356,1673],{"stretchy":1666},[1963,11358,1970],{},[902,11360,11361],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,11363,11364,11365,2087],{},"V podezřelém bodě ",[883,11366,11368],{"className":11367},[886],[888,11369,11370],{"xmlns":890},[892,11371,11372,11384],{},[895,11373,11374,11376,11378,11380,11382],{},[1664,11375,1837],{"stretchy":1666},[898,11377,207],{},[1664,11379,1916],{"separator":1915},[898,11381,1818],{},[1664,11383,1850],{"stretchy":1666},[902,11385,1923],{"encoding":904},[152,11387,11388,11515,11551],{},[123,11389,11390,11420,11421],{},[38,11391,11392,2087],{},[883,11393,11395],{"className":11394},[886],[888,11396,11397],{"xmlns":890},[892,11398,11399,11417],{},[895,11400,11401,11403,11405,11407,11409,11411,11413,11415],{},[898,11402,2379],{},[1664,11404,1667],{"stretchy":1666},[898,11406,207],{},[1664,11408,1916],{"separator":1915},[898,11410,1818],{},[1664,11412,1673],{"stretchy":1666},[1664,11414,3984],{},[1963,11416,2058],{},[902,11418,11419],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,11422,11423,11469],{},[123,11424,11425,2068,11467],{},[883,11426,11428],{"className":11427},[886],[888,11429,11430],{"xmlns":890},[892,11431,11432,11464],{},[895,11433,11434,11450,11452,11454,11456,11458,11460,11462],{},[1810,11435,11436,11438,11444],{},[898,11437,1682],{},[895,11439,11440,11442],{},[898,11441,1670],{},[898,11443,1670],{},[895,11445,11446,11448],{},[1664,11447,1728],{"mathvariant":1726},[1664,11449,1728],{"mathvariant":1726},[1664,11451,1667],{"stretchy":1666},[898,11453,207],{},[1664,11455,1916],{"separator":1915},[898,11457,1818],{},[1664,11459,1673],{"stretchy":1666},[1664,11461,3984],{},[1963,11463,2058],{},[902,11465,11466],{"encoding":904},"f''_{xx}(a, b) > 0",[38,11468,4350],{},[123,11470,11471,2068,11513],{},[883,11472,11474],{"className":11473},[886],[888,11475,11476],{"xmlns":890},[892,11477,11478,11510],{},[895,11479,11480,11496,11498,11500,11502,11504,11506,11508],{},[1810,11481,11482,11484,11490],{},[898,11483,1682],{},[895,11485,11486,11488],{},[898,11487,1670],{},[898,11489,1670],{},[895,11491,11492,11494],{},[1664,11493,1728],{"mathvariant":1726},[1664,11495,1728],{"mathvariant":1726},[1664,11497,1667],{"stretchy":1666},[898,11499,207],{},[1664,11501,1916],{"separator":1915},[898,11503,1818],{},[1664,11505,1673],{"stretchy":1666},[1664,11507,4022],{},[1963,11509,2058],{},[902,11511,11512],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,11514,4292],{},[123,11516,11517,1885,11547,11550],{},[38,11518,11519,2087],{},[883,11520,11522],{"className":11521},[886],[888,11523,11524],{"xmlns":890},[892,11525,11526,11544],{},[895,11527,11528,11530,11532,11534,11536,11538,11540,11542],{},[898,11529,2379],{},[1664,11531,1667],{"stretchy":1666},[898,11533,207],{},[1664,11535,1916],{"separator":1915},[898,11537,1818],{},[1664,11539,1673],{"stretchy":1666},[1664,11541,4022],{},[1963,11543,2058],{},[902,11545,11546],{"encoding":904},"D(a, b) \u003C 0",[38,11548,11549],{},"sedlo"," (v daném bodě extrém není).",[123,11552,11553,11583],{},[38,11554,11555,2087],{},[883,11556,11558],{"className":11557},[886],[888,11559,11560],{"xmlns":890},[892,11561,11562,11580],{},[895,11563,11564,11566,11568,11570,11572,11574,11576,11578],{},[898,11565,2379],{},[1664,11567,1667],{"stretchy":1666},[898,11569,207],{},[1664,11571,1916],{"separator":1915},[898,11573,1818],{},[1664,11575,1673],{"stretchy":1666},[1664,11577,1676],{},[1963,11579,2058],{},[902,11581,11582],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,11585,11587],{"id":11586},"vázané-extrémy","Vázané extrémy",[724,11589,11590,11591,11620,11621,1977],{},"Pro extrémy s omezující podmínkou ",[883,11592,11594],{"className":11593},[886],[888,11595,11596],{"xmlns":890},[892,11597,11598,11617],{},[895,11599,11600,11603,11605,11607,11609,11611,11613,11615],{},[898,11601,11602],{},"g",[1664,11604,1667],{"stretchy":1666},[898,11606,1670],{},[1664,11608,1916],{"separator":1915},[898,11610,2608],{},[1664,11612,1673],{"stretchy":1666},[1664,11614,1676],{},[1963,11616,2058],{},[902,11618,11619],{"encoding":904},"g(x, y) = 0"," se používá ",[207,11622,793],{"className":11623,"dataFsResolvedFilePath":791,"href":792},[210],[115,11625,2497],{"id":2496},[120,11627,11628,11635,11642],{},[123,11629,11630,1885,11632],{},[38,11631,2504],{},[207,11633,775],{"className":11634,"dataFsResolvedFilePath":773,"href":774},[210],[123,11636,11637,1885,11639],{},[38,11638,2512],{},[207,11640,793],{"className":11641,"dataFsResolvedFilePath":791,"href":792},[210],[123,11643,11644,1885,11646,11650,11651,11654,11655,11658],{},[38,11645,2520],{},[207,11647,11649],{"className":11648,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (parciální derivace = mezní produkty), ",[207,11652,880],{"className":11653,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,11656,4397],{"className":11657,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":11660},[11661,11662,11666,11667,11668,11672,11673],{"id":10222,"depth":642,"text":10223},{"id":10379,"depth":642,"text":10380,"children":11663},[11664,11665],{"id":10532,"depth":649,"text":10533},{"id":3153,"depth":649,"text":3154},{"id":10861,"depth":642,"text":10862},{"id":10983,"depth":642,"text":10984},{"id":11168,"depth":642,"text":11169,"children":11669},[11670,11671],{"id":3827,"depth":649,"text":3828},{"id":3901,"depth":649,"text":3902},{"id":11586,"depth":642,"text":11587},{"id":2496,"depth":642,"text":2497},"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":10133,"description":11674},[1135],"topics\u002Ffunkce-vice-promennych",[1128,11681,4423,11682,11683,11684],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":1628,"title":775,"body":11687,"course":1128,"courses":659,"created":1129,"description":2540,"extension":661,"meta":12490,"navigation":664,"path":2542,"seo":12491,"sources":12492,"stem":2545,"tags":12493,"type":2553,"updated":677,"__hash__":2554},{"type":9,"value":11688,"toc":12480},[11689,11691,11697,11699,11742,11818,11820,11895,11933,11938,11940,11942,11969,12026,12070,12107,12109,12155,12206,12256,12299,12301,12303,12374,12376,12447,12452,12454],[12,11690,775],{"id":1633},[724,11692,1636,11693,1640,11695,1644],{},[38,11694,1639],{},[38,11696,1643],{},[115,11698,1648],{"id":1647},[724,11700,11701],{},[883,11702,11704],{"className":11703},[886],[888,11705,11706],{"xmlns":890},[892,11707,11708,11740],{},[895,11709,11710,11712,11714,11716,11718,11720,11722,11724,11726,11728,11730,11732,11734,11736,11738],{},[898,11711,1662],{},[1664,11713,1667],{"stretchy":1666},[898,11715,1670],{},[1664,11717,1673],{"stretchy":1666},[1664,11719,1676],{},[1664,11721,1679],{},[898,11723,1682],{},[1664,11725,1667],{"stretchy":1666},[898,11727,1670],{},[1664,11729,1673],{"stretchy":1666},[1690,11731,1692],{},[898,11733,1695],{},[898,11735,1670],{},[1664,11737,1700],{},[898,11739,1703],{},[902,11741,1706],{"encoding":904},[724,11743,1709,11744,1748,11777,1762,11790,1766,11792,1343,11805,1793],{},[883,11745,11747],{"className":11746},[886],[888,11748,11749],{"xmlns":890},[892,11750,11751,11775],{},[895,11752,11753,11759,11761,11763,11765,11767,11769,11771,11773],{},[1720,11754,11755,11757],{},[898,11756,1662],{},[1664,11758,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,11760,1667],{"stretchy":1666},[898,11762,1670],{},[1664,11764,1673],{"stretchy":1666},[1664,11766,1676],{},[898,11768,1682],{},[1664,11770,1667],{"stretchy":1666},[898,11772,1670],{},[1664,11774,1673],{"stretchy":1666},[902,11776,1747],{"encoding":904},[883,11778,11780],{"className":11779},[886],[888,11781,11782],{"xmlns":890},[892,11783,11784,11788],{},[895,11785,11786],{},[898,11787,1662],{},[902,11789,1662],{"encoding":904},[38,11791,1765],{},[883,11793,11795],{"className":11794},[886],[888,11796,11797],{"xmlns":890},[892,11798,11799,11803],{},[895,11800,11801],{},[898,11802,1682],{},[902,11804,1682],{"encoding":904},[883,11806,11808],{"className":11807},[886],[888,11809,11810],{"xmlns":890},[892,11811,11812,11816],{},[895,11813,11814],{},[898,11815,1703],{},[902,11817,1703],{"encoding":904},[115,11819,1797],{"id":1796},[724,11821,11822],{},[883,11823,11825],{"className":11824},[886],[888,11826,11827],{"xmlns":890},[892,11828,11829,11893],{},[895,11830,11831,11839,11841,11843,11845,11847,11849,11851,11853,11855,11857,11859,11861,11863,11865,11873,11875,11877,11879,11881,11883,11885,11887,11889,11891],{},[1810,11832,11833,11835,11837],{},[1664,11834,1679],{},[898,11836,207],{},[898,11838,1818],{},[898,11840,1682],{},[1664,11842,1667],{"stretchy":1666},[898,11844,1670],{},[1664,11846,1673],{"stretchy":1666},[1690,11848,1692],{},[898,11850,1695],{},[898,11852,1670],{},[1664,11854,1676],{},[1664,11856,1837],{"stretchy":1666},[898,11858,1662],{},[1664,11860,1667],{"stretchy":1666},[898,11862,1670],{},[1664,11864,1673],{"stretchy":1666},[1810,11866,11867,11869,11871],{},[1664,11868,1850],{"stretchy":1666},[898,11870,207],{},[898,11872,1818],{},[1664,11874,1676],{},[898,11876,1662],{},[1664,11878,1667],{"stretchy":1666},[898,11880,1818],{},[1664,11882,1673],{"stretchy":1666},[1664,11884,1867],{},[898,11886,1662],{},[1664,11888,1667],{"stretchy":1666},[898,11890,207],{},[1664,11892,1673],{"stretchy":1666},[902,11894,1878],{"encoding":904},[724,11896,1881,11897,1885,11899,1899,11912,1924],{},[38,11898,1884],{},[883,11900,11902],{"className":11901},[886],[888,11903,11904],{"xmlns":890},[892,11905,11906,11910],{},[895,11907,11908],{},[898,11909,1682],{},[902,11911,1682],{"encoding":904},[883,11913,11915],{"className":11914},[886],[888,11916,11917],{"xmlns":890},[892,11918,11919,11931],{},[895,11920,11921,11923,11925,11927,11929],{},[1664,11922,1837],{"stretchy":1666},[898,11924,207],{},[1664,11926,1916],{"separator":1915},[898,11928,1818],{},[1664,11930,1850],{"stretchy":1666},[902,11932,1923],{"encoding":904},[724,11934,11935],{},[1928,11936],{"alt":1930,"className":11937,"src":1933},[210,1932],[115,11939,1937],{"id":1936},[198,11941,1941],{"id":1940},[724,11943,1944,11944,1977],{},[883,11945,11947],{"className":11946},[886],[888,11948,11949],{"xmlns":890},[892,11950,11951,11967],{},[895,11952,11953,11955,11957,11959,11961,11963,11965],{},[898,11954,1956],{},[898,11956,1959],{},[1664,11958,1676],{},[1963,11960,1965],{},[1664,11962,1867],{},[1963,11964,1970],{},[898,11966,1973],{},[902,11968,1976],{"encoding":904},[724,11970,11971],{},[883,11972,11974],{"className":11973},[886],[888,11975,11976],{"xmlns":890},[892,11977,11978,12024],{},[895,11979,11980,11982,11984,11986,11988,11990,11992,11994,11996,11998,12000,12002,12004,12006,12008,12010,12012,12014,12020,12022],{},[898,11981,1991],{},[898,11983,1959],{},[1664,11985,1676],{},[1664,11987,1679],{},[1664,11989,1667],{"stretchy":1666},[1963,11991,1965],{},[1664,11993,1867],{},[1963,11995,1970],{},[898,11997,1973],{},[1664,11999,1673],{"stretchy":1666},[1690,12001,1692],{},[898,12003,1695],{},[898,12005,1973],{},[1664,12007,1676],{},[1963,12009,1965],{},[898,12011,1973],{},[1664,12013,1867],{},[1720,12015,12016,12018],{},[898,12017,1973],{},[1963,12019,1970],{},[1664,12021,1700],{},[898,12023,2034],{},[902,12025,2037],{"encoding":904},[724,12027,2040,12028,2068,12053,2087],{},[883,12029,12031],{"className":12030},[886],[888,12032,12033],{"xmlns":890},[892,12034,12035,12051],{},[895,12036,12037,12039,12041,12043,12045,12047,12049],{},[898,12038,1991],{},[898,12040,1959],{},[1664,12042,1667],{"stretchy":1666},[1963,12044,2058],{},[1664,12046,1673],{"stretchy":1666},[1664,12048,1676],{},[1963,12050,2058],{},[902,12052,2067],{"encoding":904},[883,12054,12056],{"className":12055},[886],[888,12057,12058],{"xmlns":890},[892,12059,12060,12068],{},[895,12061,12062,12064,12066],{},[898,12063,2034],{},[1664,12065,1676],{},[1963,12067,2058],{},[902,12069,2086],{"encoding":904},[724,12071,12072],{},[883,12073,12075],{"className":12074},[886],[888,12076,12077],{"xmlns":890},[892,12078,12079,12105],{},[895,12080,12081,12083,12085,12087,12089,12091,12093,12095,12097,12099],{},[898,12082,1991],{},[898,12084,1959],{},[1664,12086,1667],{"stretchy":1666},[898,12088,1973],{},[1664,12090,1673],{"stretchy":1666},[1664,12092,1676],{},[1963,12094,1965],{},[898,12096,1973],{},[1664,12098,1867],{},[1720,12100,12101,12103],{},[898,12102,1973],{},[1963,12104,1970],{},[902,12106,2125],{"encoding":904},[198,12108,2129],{"id":2128},[724,12110,2132,12111,2160,12136,1977],{},[883,12112,12114],{"className":12113},[886],[888,12115,12116],{"xmlns":890},[892,12117,12118,12134],{},[895,12119,12120,12122,12124,12126,12128,12130,12132],{},[898,12121,1956],{},[898,12123,1703],{},[1664,12125,1676],{},[1963,12127,1970],{},[1664,12129,1700],{},[1963,12131,2154],{},[898,12133,1973],{},[902,12135,2159],{"encoding":904},[883,12137,12139],{"className":12138},[886],[888,12140,12141],{"xmlns":890},[892,12142,12143,12153],{},[895,12144,12145,12147,12149,12151],{},[898,12146,1662],{},[898,12148,1703],{},[1664,12150,1676],{},[1963,12152,1965],{},[902,12154,2180],{"encoding":904},[724,12156,12157],{},[883,12158,12160],{"className":12159},[886],[888,12161,12162],{"xmlns":890},[892,12163,12164,12204],{},[895,12165,12166,12168,12170,12172,12174,12176,12178,12180,12182,12184,12186,12188,12190,12192,12194,12200,12202],{},[898,12167,1991],{},[898,12169,1703],{},[1664,12171,1676],{},[1664,12173,1679],{},[898,12175,1956],{},[898,12177,1703],{},[1690,12179,1692],{},[898,12181,1695],{},[898,12183,1973],{},[1664,12185,1676],{},[1963,12187,1970],{},[898,12189,1973],{},[1664,12191,1700],{},[1963,12193,2220],{},[1720,12195,12196,12198],{},[898,12197,1973],{},[1963,12199,1970],{},[1664,12201,1700],{},[898,12203,2034],{},[902,12205,2233],{"encoding":904},[724,12207,2040,12208,2068,12239,2087],{},[883,12209,12211],{"className":12210},[886],[888,12212,12213],{"xmlns":890},[892,12214,12215,12237],{},[895,12216,12217,12219,12221,12223,12225,12227,12229,12231,12233,12235],{},[898,12218,1991],{},[898,12220,1703],{},[1664,12222,1667],{"stretchy":1666},[1963,12224,2058],{},[1664,12226,1673],{"stretchy":1666},[1664,12228,1676],{},[898,12230,1662],{},[898,12232,1703],{},[1664,12234,1676],{},[1963,12236,1965],{},[902,12238,2267],{"encoding":904},[883,12240,12242],{"className":12241},[886],[888,12243,12244],{"xmlns":890},[892,12245,12246,12254],{},[895,12247,12248,12250,12252],{},[898,12249,2034],{},[1664,12251,1676],{},[1963,12253,1965],{},[902,12255,2285],{"encoding":904},[724,12257,12258],{},[883,12259,12261],{"className":12260},[886],[888,12262,12263],{"xmlns":890},[892,12264,12265,12297],{},[895,12266,12267,12269,12271,12273,12275,12277,12279,12281,12283,12285,12287,12289,12291],{},[898,12268,1991],{},[898,12270,1703],{},[1664,12272,1667],{"stretchy":1666},[898,12274,1973],{},[1664,12276,1673],{"stretchy":1666},[1664,12278,1676],{},[1963,12280,1965],{},[1664,12282,1700],{},[1963,12284,1970],{},[898,12286,1973],{},[1664,12288,1700],{},[1963,12290,2220],{},[1720,12292,12293,12295],{},[898,12294,1973],{},[1963,12296,1970],{},[902,12298,2329],{"encoding":904},[198,12300,820],{"id":2332},[724,12302,2335],{},[724,12304,12305],{},[883,12306,12308],{"className":12307},[886],[888,12309,12310],{"xmlns":890},[892,12311,12312,12372],{},[895,12313,12314,12316,12318,12320,12326,12328,12330,12342,12344,12346,12348,12350,12352,12354,12356,12358,12364,12366],{},[898,12315,1703],{},[898,12317,2351],{},[1664,12319,1667],{"stretchy":1666},[2355,12321,12322,12324],{},[898,12323,1973],{},[1963,12325,2058],{},[1664,12327,1673],{"stretchy":1666},[1664,12329,1676],{},[1810,12331,12332,12334,12336],{},[1664,12333,1679],{},[1963,12335,2058],{},[2355,12337,12338,12340],{},[898,12339,1973],{},[1963,12341,2058],{},[898,12343,2379],{},[1664,12345,1667],{"stretchy":1666},[898,12347,1973],{},[1664,12349,1673],{"stretchy":1666},[1690,12351,1692],{},[898,12353,1695],{},[898,12355,1973],{},[1664,12357,1867],{},[2355,12359,12360,12362],{},[898,12361,2398],{},[1963,12363,2058],{},[1690,12365,1692],{},[2355,12367,12368,12370],{},[898,12369,1973],{},[1963,12371,2058],{},[902,12373,2411],{"encoding":904},[724,12375,2414],{},[724,12377,12378],{},[883,12379,12381],{"className":12380},[886],[888,12382,12383],{"xmlns":890},[892,12384,12385,12445],{},[895,12386,12387,12389,12391,12393,12399,12401,12403,12409,12411,12417,12419,12431,12433,12435,12437,12439,12441,12443],{},[898,12388,2398],{},[898,12390,2351],{},[1664,12392,1667],{"stretchy":1666},[2355,12394,12395,12397],{},[898,12396,1973],{},[1963,12398,2058],{},[1664,12400,1673],{"stretchy":1666},[1664,12402,1676],{},[2355,12404,12405,12407],{},[898,12406,2398],{},[1963,12408,2058],{},[1690,12410,1692],{},[2355,12412,12413,12415],{},[898,12414,1973],{},[1963,12416,2058],{},[1664,12418,1867],{},[1810,12420,12421,12423,12425],{},[1664,12422,1679],{},[1963,12424,2058],{},[2355,12426,12427,12429],{},[898,12428,1973],{},[1963,12430,2058],{},[898,12432,2351],{},[1664,12434,1667],{"stretchy":1666},[898,12436,1973],{},[1664,12438,1673],{"stretchy":1666},[1690,12440,1692],{},[898,12442,1695],{},[898,12444,1973],{},[902,12446,2486],{"encoding":904},[724,12448,2489,12449,1977],{},[207,12450,2493],{"className":12451,"dataFsResolvedFilePath":800,"href":801},[210],[115,12453,2497],{"id":2496},[120,12455,12456,12463,12470],{},[123,12457,12458,1885,12460],{},[38,12459,2504],{},[207,12461,766],{"className":12462,"dataFsResolvedFilePath":764,"href":765},[210],[123,12464,12465,1885,12467],{},[38,12466,2512],{},[207,12468,784],{"className":12469,"dataFsResolvedFilePath":782,"href":783},[210],[123,12471,12472,1885,12474,2525,12477,2529],{},[38,12473,2520],{},[207,12475,2524],{"className":12476,"dataFsResolvedFilePath":827,"href":828},[210],[207,12478,2493],{"className":12479,"dataFsResolvedFilePath":800,"href":801},[210],{"title":641,"searchDepth":642,"depth":642,"links":12481},[12482,12483,12484,12489],{"id":1647,"depth":642,"text":1648},{"id":1796,"depth":642,"text":1797},{"id":1936,"depth":642,"text":1937,"children":12485},[12486,12487,12488],{"id":1940,"depth":649,"text":1941},{"id":2128,"depth":649,"text":2129},{"id":2332,"depth":649,"text":820},{"id":2496,"depth":642,"text":2497},{},{"title":775,"description":2540},[1135],[1128,2547,2548,2549,2550,2551,2552],{"id":12495,"title":12496,"body":12497,"course":1128,"courses":659,"created":10119,"description":641,"extension":661,"meta":16766,"navigation":664,"path":16767,"seo":16768,"sources":16769,"stem":16770,"tags":16771,"type":2553,"updated":677,"__hash__":16777},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":12498,"toc":16754},[12499,12502,12506,12650,12657,12661,12731,12769,12872,12876,12906,12972,13019,13022,13091,13094,13129,13165,13169,13217,13224,13270,13316,13319,13398,13495,13578,13582,13626,13656,13662,13691,13713,13763,13816,13882,13885,13951,13980,14039,14055,14142,14240,14371,14375,14532,14681,15061,15065,15068,15127,15130,15216,15244,15282,15285,15322,15362,15396,15398,15435,15467,15565,15570,15694,15746,15828,15967,15971,16091,16098,16209,16216,16220,16695,16697],[12,12500,12496],{"id":12501},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,12503,12505],{"id":12504},"tldr","TL;DR",[724,12507,12508,12511,12512,10588,12515,12528,12529,12543,12544,12547,12548,1343,12551,12554,12555,1343,12558,12561,12562,1885,12565,12595,12596,12599,12600,1343,12614,12627,12628,12631,12632,4488],{},[38,12509,12510],{},"IS-LM"," je makroekonomický model se ",[38,12513,12514],{},"dvěma neznámými",[883,12516,12518],{"className":12517},[886],[888,12519,12520],{"xmlns":890},[892,12521,12522,12526],{},[895,12523,12524],{},[898,12525,9692],{},[902,12527,9692],{"encoding":904}," — národní důchod a ",[883,12530,12532],{"className":12531},[886],[888,12533,12534],{"xmlns":890},[892,12535,12536,12541],{},[895,12537,12538],{},[898,12539,12540],{},"r",[902,12542,12540],{"encoding":904}," — úroková míra) a ",[38,12545,12546],{},"dvěma trhy",": trhem zboží (křivka ",[38,12549,12550],{},"IS",[614,12552,12553],{},"Investment = Savings",") a trhem peněz (křivka ",[38,12556,12557],{},"LM",[614,12559,12560],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,12563,12564],{},"simultánní rovnováhu",[883,12566,12568],{"className":12567},[886],[888,12569,12570],{"xmlns":890},[892,12571,12572,12592],{},[895,12573,12574,12576,12582,12584,12590],{},[1664,12575,1667],{"stretchy":1666},[1720,12577,12578,12580],{},[898,12579,9692],{},[898,12581,4819],{},[1664,12583,1916],{"separator":1915},[1720,12585,12586,12588],{},[898,12587,12540],{},[898,12589,4819],{},[1664,12591,1673],{"stretchy":1666},[902,12593,12594],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,12597,12598],{},"fiskální politiky"," (posun IS změnou ",[883,12601,12603],{"className":12602},[886],[888,12604,12605],{"xmlns":890},[892,12606,12607,12612],{},[895,12608,12609],{},[898,12610,12611],{},"G",[902,12613,12611],{"encoding":904},[883,12615,12617],{"className":12616},[886],[888,12618,12619],{"xmlns":890},[892,12620,12621,12625],{},[895,12622,12623],{},[898,12624,1991],{},[902,12626,1991],{"encoding":904},") a ",[38,12629,12630],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,12633,12635],{"className":12634},[886],[888,12636,12637],{"xmlns":890},[892,12638,12639,12647],{},[895,12640,12641],{},[1720,12642,12643,12645],{},[898,12644,1956],{},[1664,12646,4920],{},[902,12648,12649],{"encoding":904},"M^*",[724,12651,12652],{},[1928,12653],{"alt":12654,"className":12655,"src":12656},"imek-is-lm-model",[210,1932],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,12658,12660],{"id":12659},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,12662,12663,12664,12668,12669,10588,12672,12695,12696,12699,12700,12716,12717,12730],{},"V modelech ",[207,12665,12667],{"className":12666,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,12670,12671],{},"investice pokládány za konstantní",[883,12673,12675],{"className":12674},[886],[888,12676,12677],{"xmlns":890},[892,12678,12679,12692],{},[895,12680,12681,12684,12686],{},[898,12682,12683],{},"I",[1664,12685,1676],{},[1720,12687,12688,12690],{},[898,12689,12683],{},[1664,12691,4920],{},[902,12693,12694],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,12697,12698],{},"ceně peněz",", tedy na ",[38,12701,12702,12703],{},"úrokové míře ",[883,12704,12706],{"className":12705},[886],[888,12707,12708],{"xmlns":890},[892,12709,12710,12714],{},[895,12711,12712],{},[898,12713,12540],{},[902,12715,12540],{"encoding":904},": čím vyšší ",[883,12718,12720],{"className":12719},[886],[888,12721,12722],{"xmlns":890},[892,12723,12724,12728],{},[895,12725,12726],{},[898,12727,12540],{},[902,12729,12540],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,12732,12733,12763],{},[123,12734,12735,1885,12738,12762],{},[38,12736,12737],{},"funkci investic",[883,12739,12741],{"className":12740},[886],[888,12742,12743],{"xmlns":890},[892,12744,12745,12759],{},[895,12746,12747,12749,12751,12753,12755,12757],{},[898,12748,12683],{},[1664,12750,1676],{},[898,12752,12683],{},[1664,12754,1667],{"stretchy":1666},[898,12756,12540],{},[1664,12758,1673],{"stretchy":1666},[902,12760,12761],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,12764,12765,12768],{},[38,12766,12767],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[4436,12770,12771],{},[724,12772,12773,12775,12776,12795,12796,12823,12824,12837,12838,12867,12868,12871],{},[883,12774,4978],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,12777,12779],{"className":12778},[886],[888,12780,12781],{"xmlns":890},[892,12782,12783,12792],{},[895,12784,12785,12787,12790],{},[898,12786,1703],{},[1690,12788,12789],{},"-",[898,12791,12683],{},[902,12793,12794],{"encoding":904},"C\\text{-}I"," až ",[883,12797,12799],{"className":12798},[886],[888,12800,12801],{"xmlns":890},[892,12802,12803,12820],{},[895,12804,12805,12807,12809,12811,12813,12815,12817],{},[898,12806,1703],{},[1690,12808,12789],{},[898,12810,12683],{},[1690,12812,12789],{},[898,12814,12611],{},[1690,12816,12789],{},[898,12818,12819],{},"X",[902,12821,12822],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,12825,12827],{"className":12826},[886],[888,12828,12829],{"xmlns":890},[892,12830,12831,12835],{},[895,12832,12833],{},[898,12834,9692],{},[902,12836,9692],{"encoding":904},". V IS-LM jsou ",[38,12839,12840,12841,4454,12854],{},"dvě neznámé ",[883,12842,12844],{"className":12843},[886],[888,12845,12846],{"xmlns":890},[892,12847,12848,12852],{},[895,12849,12850],{},[898,12851,9692],{},[902,12853,9692],{"encoding":904},[883,12855,12857],{"className":12856},[886],[888,12858,12859],{"xmlns":890},[892,12860,12861,12865],{},[895,12862,12863],{},[898,12864,12540],{},[902,12866,12540],{"encoding":904},", a proto potřebujeme ",[38,12869,12870],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,12873,12875],{"id":12874},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,12877,12878,12879,12892,12893,2087],{},"Lineární závislost investic ",[883,12880,12882],{"className":12881},[886],[888,12883,12884],{"xmlns":890},[892,12885,12886,12890],{},[895,12887,12888],{},[898,12889,12683],{},[902,12891,12683],{"encoding":904}," na úrokové míře ",[883,12894,12896],{"className":12895},[886],[888,12897,12898],{"xmlns":890},[892,12899,12900,12904],{},[895,12901,12902],{},[898,12903,12540],{},[902,12905,12540],{"encoding":904},[724,12907,12908],{},[883,12909,12911],{"className":12910},[886],[888,12912,12913],{"xmlns":890},[892,12914,12915,12969],{},[895,12916,12917,12919,12921,12923,12925,12927,12929,12931,12933,12935,12937,12939,12941,12943,12945,12947,12949,12951,12953,12955,12957,12960,12962,12964,12967],{},[898,12918,12683],{},[1664,12920,1676],{},[898,12922,12683],{},[1664,12924,1667],{"stretchy":1666},[898,12926,12540],{},[1664,12928,1673],{"stretchy":1666},[1664,12930,1676],{},[898,12932,2034],{},[898,12934,12540],{},[1664,12936,1700],{},[898,12938,1695],{},[1664,12940,1916],{"separator":1915},[6444,12942],{"width":6446},[898,12944,2034],{},[1664,12946,4022],{},[1963,12948,2058],{},[1664,12950,1916],{"separator":1915},[1690,12952,2884],{},[898,12954,1695],{},[1664,12956,3984],{},[1963,12958,12959],{},"0.",[6444,12961],{"width":6446},[1664,12963,1667],{"stretchy":1666},[1963,12965,12966],{},"7.11",[1664,12968,1673],{"stretchy":1666},[902,12970,12971],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,12973,12974,12995],{},[123,12975,12976,12994],{},[883,12977,12979],{"className":12978},[886],[888,12980,12981],{"xmlns":890},[892,12982,12983,12991],{},[895,12984,12985,12987,12989],{},[898,12986,1695],{},[1664,12988,3984],{},[1963,12990,2058],{},[902,12992,12993],{"encoding":904},"d > 0"," zřejmé,",[123,12996,12997,13015,13016,1977],{},[883,12998,13000],{"className":12999},[886],[888,13001,13002],{"xmlns":890},[892,13003,13004,13012],{},[895,13005,13006,13008,13010],{},[898,13007,2034],{},[1664,13009,4022],{},[1963,13011,2058],{},[902,13013,13014],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,13017,13018],{},"klesající",[724,13020,13021],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,13023,13024],{},[883,13025,13027],{"className":13026},[886],[888,13028,13029],{"xmlns":890},[892,13030,13031,13088],{},[895,13032,13033,13035,13037,13039,13041,13043,13045,13047,13049,13051,13053,13055,13057,13059,13061,13063,13065,13067,13069,13071,13073,13075,13077,13079,13081,13083,13086],{},[898,13034,1703],{},[1664,13036,1676],{},[898,13038,1703],{},[1664,13040,1667],{"stretchy":1666},[898,13042,9692],{},[1664,13044,1673],{"stretchy":1666},[1664,13046,1676],{},[898,13048,207],{},[898,13050,9692],{},[1664,13052,1700],{},[898,13054,1818],{},[1664,13056,1916],{"separator":1915},[6444,13058],{"width":6446},[1963,13060,2058],{},[1664,13062,4022],{},[898,13064,207],{},[1664,13066,4022],{},[1963,13068,2875],{},[1664,13070,1916],{"separator":1915},[1690,13072,2884],{},[898,13074,1818],{},[1664,13076,3984],{},[1963,13078,12959],{},[6444,13080],{"width":6446},[1664,13082,1667],{"stretchy":1666},[1963,13084,13085],{},"7.12",[1664,13087,1673],{"stretchy":1666},[902,13089,13090],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,13092,13093],{},"Podmínka rovnováhy na trhu zboží:",[724,13095,13096],{},[883,13097,13099],{"className":13098},[886],[888,13100,13101],{"xmlns":890},[892,13102,13103,13126],{},[895,13104,13105,13107,13109,13111,13113,13115,13117,13119,13121,13124],{},[898,13106,9692],{},[1664,13108,1676],{},[898,13110,1703],{},[1664,13112,1700],{},[898,13114,12683],{},[898,13116,1977],{"mathvariant":1726},[6444,13118],{"width":6446},[1664,13120,1667],{"stretchy":1666},[1963,13122,13123],{},"7.13",[1664,13125,1673],{"stretchy":1666},[902,13127,13128],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,13130,13131,13132,1885,13135,13161,13162,1977],{},"To dává ",[38,13133,13134],{},"tři rovnice o čtyřech neznámých",[883,13136,13138],{"className":13137},[886],[888,13139,13140],{"xmlns":890},[892,13141,13142,13158],{},[895,13143,13144,13146,13148,13150,13152,13154,13156],{},[898,13145,9692],{},[1664,13147,1916],{"separator":1915},[898,13149,1703],{},[1664,13151,1916],{"separator":1915},[898,13153,12683],{},[1664,13155,1916],{"separator":1915},[898,13157,12540],{},[902,13159,13160],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,13163,13164],{},"rovnováhy na trhu peněz",[115,13166,13168],{"id":13167},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,13170,13171,13172,6135,13194,13212,13213,13216],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,13173,13175],{"className":13174},[886],[888,13176,13177],{"xmlns":890},[892,13178,13179,13191],{},[895,13180,13181,13183,13185,13187,13189],{},[898,13182,9692],{},[1664,13184,1676],{},[898,13186,1703],{},[1664,13188,1700],{},[898,13190,2351],{},[902,13192,13193],{"encoding":904},"Y = C + S",[883,13195,13197],{"className":13196},[886],[888,13198,13199],{"xmlns":890},[892,13200,13201,13209],{},[895,13202,13203,13205,13207],{},[898,13204,12683],{},[1664,13206,1676],{},[898,13208,2351],{},[902,13210,13211],{"encoding":904},"I = S"," (plánované ",[38,13214,13215],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,13218,13219],{},[1928,13220],{"alt":13221,"className":13222,"src":13223},"imek-odvozeni-is-4panelu",[210,1932],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,13225,13226],{},[883,13227,13229],{"className":13228},[886],[888,13230,13231],{"xmlns":890},[892,13232,13233,13267],{},[895,13234,13235,13237,13239,13241,13243,13245,13247,13249,13251,13253,13255,13257,13259,13261,13263,13265],{},[898,13236,9692],{},[1664,13238,1676],{},[1664,13240,1667],{"stretchy":1666},[898,13242,207],{},[898,13244,9692],{},[1664,13246,1700],{},[898,13248,1818],{},[1664,13250,1673],{"stretchy":1666},[1664,13252,1700],{},[1664,13254,1667],{"stretchy":1666},[898,13256,2034],{},[898,13258,12540],{},[1664,13260,1700],{},[898,13262,1695],{},[1664,13264,1673],{"stretchy":1666},[1664,13266,1916],{"separator":1915},[902,13268,13269],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,13271,13272],{},[883,13273,13275],{"className":13274},[886],[888,13276,13277],{"xmlns":890},[892,13278,13279,13313],{},[895,13280,13281,13283,13285,13287,13289,13291,13293,13295,13297,13299,13301,13303,13305,13307,13309,13311],{},[1664,13282,1667],{"stretchy":1666},[1963,13284,2875],{},[1664,13286,1867],{},[898,13288,207],{},[1664,13290,1673],{"stretchy":1666},[898,13292,9692],{},[1664,13294,1867],{},[898,13296,2034],{},[898,13298,12540],{},[1664,13300,1867],{},[898,13302,1818],{},[1664,13304,1867],{},[898,13306,1695],{},[1664,13308,1676],{},[1963,13310,2058],{},[1664,13312,1916],{"separator":1915},[902,13314,13315],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,13317,13318],{},"odkud",[724,13320,13321],{},[883,13322,13324],{"className":13323},[886],[888,13325,13326],{"xmlns":890},[892,13327,13328,13395],{},[895,13329,13330,13386,13388,13390,13393],{},[13331,13332,13334],"menclose",{"notation":13333},"box",[2919,13335,13336],{"scriptlevel":2058,"displaystyle":1666},[2919,13337,13338],{"scriptlevel":2058,"displaystyle":1666},[2919,13339,13340],{"scriptlevel":2058,"displaystyle":1915},[895,13341,13342,13344,13346,13348,13360,13362,13364,13366,13384],{},[1690,13343,1692],{},[898,13345,9692],{},[1664,13347,1676],{},[2922,13349,13350,13352],{},[898,13351,2034],{},[895,13353,13354,13356,13358],{},[1963,13355,2875],{},[1664,13357,1867],{},[898,13359,207],{},[1690,13361,1692],{},[898,13363,12540],{},[1664,13365,1700],{},[2922,13367,13368,13376],{},[895,13369,13370,13372,13374],{},[898,13371,1818],{},[1664,13373,1700],{},[898,13375,1695],{},[895,13377,13378,13380,13382],{},[1963,13379,2875],{},[1664,13381,1867],{},[898,13383,207],{},[1690,13385,1692],{},[6444,13387],{"width":6446},[1664,13389,1667],{"stretchy":1666},[1963,13391,13392],{},"7.14",[1664,13394,1673],{"stretchy":1666},[902,13396,13397],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,13399,13400,13401,10588,13404,13407,13408,13411,13412,13414,13415,13437,13438,13466,13467,13488,13489,13491,13492,13494],{},"Tento vztah se nazývá ",[38,13402,13403],{},"funkce IS",[614,13405,13406],{},"IS schedule",") a její graf ",[38,13409,13410],{},"křivka IS",". Křivka je ",[38,13413,13018],{}," přímka v rovině ",[883,13416,13418],{"className":13417},[886],[888,13419,13420],{"xmlns":890},[892,13421,13422,13434],{},[895,13423,13424,13426,13428,13430,13432],{},[1664,13425,1667],{"stretchy":1666},[898,13427,12540],{},[1664,13429,1916],{"separator":1915},[898,13431,9692],{},[1664,13433,1673],{"stretchy":1666},[902,13435,13436],{"encoding":904},"(r, Y)",", neboť ",[883,13439,13441],{"className":13440},[886],[888,13442,13443],{"xmlns":890},[892,13444,13445,13463],{},[895,13446,13447,13459,13461],{},[2922,13448,13449,13451],{},[898,13450,2034],{},[895,13452,13453,13455,13457],{},[1963,13454,2875],{},[1664,13456,1867],{},[898,13458,207],{},[1664,13460,4022],{},[1963,13462,2058],{},[902,13464,13465],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,13468,13470],{"className":13469},[886],[888,13471,13472],{"xmlns":890},[892,13473,13474,13486],{},[895,13475,13476,13478,13480,13482,13484],{},[1664,13477,1667],{"stretchy":1666},[898,13479,12540],{},[1664,13481,1916],{"separator":1915},[898,13483,9692],{},[1664,13485,1673],{"stretchy":1666},[902,13487,13436],{"encoding":904},", pro které plánované ",[38,13490,12683],{},"nvestment = ",[38,13493,2351],{},"avings.",[4436,13496,13497],{},[724,13498,13499,13501,13502,13515,13516,1885,13519,13532,13533,13546,13547,4454,13560,13573,13574,13577],{},[883,13500,4723],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,13503,13505],{"className":13504},[886],[888,13506,13507],{"xmlns":890},[892,13508,13509,13513],{},[895,13510,13511],{},[898,13512,12540],{},[902,13514,12540],{"encoding":904}," → levnější úvěr → ",[38,13517,13518],{},"více investic",[883,13520,13522],{"className":13521},[886],[888,13523,13524],{"xmlns":890},[892,13525,13526,13530],{},[895,13527,13528],{},[898,13529,12683],{},[902,13531,12683],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,13534,13536],{"className":13535},[886],[888,13537,13538],{"xmlns":890},[892,13539,13540,13544],{},[895,13541,13542],{},[898,13543,9692],{},[902,13545,9692],{"encoding":904},". Vztah mezi ",[883,13548,13550],{"className":13549},[886],[888,13551,13552],{"xmlns":890},[892,13553,13554,13558],{},[895,13555,13556],{},[898,13557,12540],{},[902,13559,12540],{"encoding":904},[883,13561,13563],{"className":13562},[886],[888,13564,13565],{"xmlns":890},[892,13566,13567,13571],{},[895,13568,13569],{},[898,13570,9692],{},[902,13572,9692],{"encoding":904}," na trhu zboží je proto ",[38,13575,13576],{},"nepřímý"," (klesající křivka).",[115,13579,13581],{"id":13580},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,13583,13584,13585,13603,13604,1748,13622,13625],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,13586,13588],{"className":13587},[886],[888,13589,13590],{"xmlns":890},[892,13591,13592,13600],{},[895,13593,13594],{},[1720,13595,13596,13598],{},[898,13597,1956],{},[898,13599,2379],{},[902,13601,13602],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,13605,13607],{"className":13606},[886],[888,13608,13609],{"xmlns":890},[892,13610,13611,13619],{},[895,13612,13613],{},[1720,13614,13615,13617],{},[898,13616,1956],{},[898,13618,2351],{},[902,13620,13621],{"encoding":904},"M^S",[38,13623,13624],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,13627,13628],{},[883,13629,13631],{"className":13630},[886],[888,13632,13633],{"xmlns":890},[892,13634,13635,13653],{},[895,13636,13637,13643,13645,13651],{},[1720,13638,13639,13641],{},[898,13640,1956],{},[898,13642,2351],{},[1664,13644,1676],{},[1720,13646,13647,13649],{},[898,13648,1956],{},[1664,13650,4920],{},[898,13652,1977],{"mathvariant":1726},[902,13654,13655],{"encoding":904},"M^S = M^*.",[724,13657,13658,13661],{},[38,13659,13660],{},"Poptávka"," po penězích má tři zdroje:",[120,13663,13664,13673,13682],{},[123,13665,13666,10588,13669,13672],{},[38,13667,13668],{},"transakční poptávka",[614,13670,13671],{},"transactions demand",") — peníze pro nákup zboží,",[123,13674,13675,10588,13678,13681],{},[38,13676,13677],{},"opatrnostní poptávka",[614,13679,13680],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,13683,13684,10588,13687,13690],{},[38,13685,13686],{},"spekulační poptávka",[614,13688,13689],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,13692,13693,13694,13712],{},"Součet transakční a opatrnostní poptávky ",[883,13695,13697],{"className":13696},[886],[888,13698,13699],{"xmlns":890},[892,13700,13701,13709],{},[895,13702,13703],{},[2355,13704,13705,13707],{},[898,13706,10358],{},[1963,13708,2875],{},[902,13710,13711],{"encoding":904},"L_1"," je úměrný důchodu:",[724,13714,13715],{},[883,13716,13718],{"className":13717},[886],[888,13719,13720],{"xmlns":890},[892,13721,13722,13760],{},[895,13723,13724,13730,13732,13739,13741,13743,13745,13747,13749,13755,13757],{},[2355,13725,13726,13728],{},[898,13727,10358],{},[1963,13729,2875],{},[1664,13731,1676],{},[2355,13733,13734,13737],{},[898,13735,13736],{},"k",[1963,13738,2875],{},[898,13740,9692],{},[1664,13742,1916],{"separator":1915},[6444,13744],{"width":6446},[1963,13746,2058],{},[1664,13748,4022],{},[2355,13750,13751,13753],{},[898,13752,13736],{},[1963,13754,2875],{},[1664,13756,4022],{},[1963,13758,13759],{},"1.",[902,13761,13762],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,13764,13765,13766,13784,13785,1343,13798,13815],{},"Spekulační poptávka ",[883,13767,13769],{"className":13768},[886],[888,13770,13771],{"xmlns":890},[892,13772,13773,13781],{},[895,13774,13775],{},[2355,13776,13777,13779],{},[898,13778,10358],{},[1963,13780,1970],{},[902,13782,13783],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,13786,13788],{"className":13787},[886],[888,13789,13790],{"xmlns":890},[892,13791,13792,13796],{},[895,13793,13794],{},[898,13795,12540],{},[902,13797,12540],{"encoding":904},[883,13799,13801],{"className":13800},[886],[888,13802,13803],{"xmlns":890},[892,13804,13805,13813],{},[895,13806,13807],{},[2355,13808,13809,13811],{},[898,13810,10358],{},[1963,13812,1970],{},[902,13814,13783],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,13817,13818],{},[883,13819,13821],{"className":13820},[886],[888,13822,13823],{"xmlns":890},[892,13824,13825,13879],{},[895,13826,13827,13833,13835,13841,13843,13845,13851,13853,13855,13861,13863,13865,13867,13869,13875,13877],{},[2355,13828,13829,13831],{},[898,13830,10358],{},[1963,13832,1970],{},[1664,13834,1676],{},[2355,13836,13837,13839],{},[898,13838,13736],{},[1963,13840,1970],{},[898,13842,12540],{},[1664,13844,1700],{},[2355,13846,13847,13849],{},[898,13848,13736],{},[1963,13850,2774],{},[1664,13852,1916],{"separator":1915},[6444,13854],{"width":6446},[2355,13856,13857,13859],{},[898,13858,13736],{},[1963,13860,1970],{},[1664,13862,4022],{},[1963,13864,2058],{},[1664,13866,1916],{"separator":1915},[1690,13868,2884],{},[2355,13870,13871,13873],{},[898,13872,13736],{},[1963,13874,2774],{},[1664,13876,3984],{},[1963,13878,12959],{},[902,13880,13881],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,13883,13884],{},"Celková poptávka po penězích:",[724,13886,13887],{},[883,13888,13890],{"className":13889},[886],[888,13891,13892],{"xmlns":890},[892,13893,13894,13948],{},[895,13895,13896,13902,13904,13910,13912,13918,13920,13926,13928,13930,13936,13938,13940,13946],{},[1720,13897,13898,13900],{},[898,13899,1956],{},[898,13901,2379],{},[1664,13903,1676],{},[2355,13905,13906,13908],{},[898,13907,10358],{},[1963,13909,2875],{},[1664,13911,1700],{},[2355,13913,13914,13916],{},[898,13915,10358],{},[1963,13917,1970],{},[1664,13919,1676],{},[2355,13921,13922,13924],{},[898,13923,13736],{},[1963,13925,2875],{},[898,13927,9692],{},[1664,13929,1700],{},[2355,13931,13932,13934],{},[898,13933,13736],{},[1963,13935,1970],{},[898,13937,12540],{},[1664,13939,1700],{},[2355,13941,13942,13944],{},[898,13943,13736],{},[1963,13945,2774],{},[898,13947,1977],{"mathvariant":1726},[902,13949,13950],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,13952,13953,13954,2087],{},"Podmínka rovnováhy na trhu peněz ",[883,13955,13957],{"className":13956},[886],[888,13958,13959],{"xmlns":890},[892,13960,13961,13977],{},[895,13962,13963,13969,13971],{},[1720,13964,13965,13967],{},[898,13966,1956],{},[898,13968,2379],{},[1664,13970,1676],{},[1720,13972,13973,13975],{},[898,13974,1956],{},[1664,13976,4920],{},[902,13978,13979],{"encoding":904},"M^D = M^*",[724,13981,13982],{},[883,13983,13985],{"className":13984},[886],[888,13986,13987],{"xmlns":890},[892,13988,13989,14036],{},[895,13990,13991,13997,13999,14005,14007,14009,14015,14017,14019,14025,14027,14029,14031,14034],{},[1720,13992,13993,13995],{},[898,13994,1956],{},[1664,13996,4920],{},[1664,13998,1676],{},[2355,14000,14001,14003],{},[898,14002,13736],{},[1963,14004,2875],{},[898,14006,9692],{},[1664,14008,1700],{},[2355,14010,14011,14013],{},[898,14012,13736],{},[1963,14014,1970],{},[898,14016,12540],{},[1664,14018,1700],{},[2355,14020,14021,14023],{},[898,14022,13736],{},[1963,14024,2774],{},[1664,14026,1916],{"separator":1915},[6444,14028],{"width":6446},[1664,14030,1667],{"stretchy":1666},[1963,14032,14033],{},"7.15",[1664,14035,1673],{"stretchy":1666},[902,14037,14038],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,14040,14041,14042,3727],{},"po úpravě (vyjádření ",[883,14043,14045],{"className":14044},[886],[888,14046,14047],{"xmlns":890},[892,14048,14049,14053],{},[895,14050,14051],{},[898,14052,9692],{},[902,14054,9692],{"encoding":904},[724,14056,14057],{},[883,14058,14060],{"className":14059},[886],[888,14061,14062],{"xmlns":890},[892,14063,14064,14139],{},[895,14065,14066,14130,14132,14134,14137],{},[13331,14067,14068],{"notation":13333},[2919,14069,14070],{"scriptlevel":2058,"displaystyle":1666},[2919,14071,14072],{"scriptlevel":2058,"displaystyle":1666},[2919,14073,14074],{"scriptlevel":2058,"displaystyle":1915},[895,14075,14076,14078,14080,14082,14084,14098,14100,14102,14104,14128],{},[1690,14077,1692],{},[898,14079,9692],{},[1664,14081,1676],{},[1664,14083,1867],{},[2922,14085,14086,14092],{},[2355,14087,14088,14090],{},[898,14089,13736],{},[1963,14091,1970],{},[2355,14093,14094,14096],{},[898,14095,13736],{},[1963,14097,2875],{},[1690,14099,1692],{},[898,14101,12540],{},[1664,14103,1700],{},[2922,14105,14106,14122],{},[895,14107,14108,14114,14116],{},[1720,14109,14110,14112],{},[898,14111,1956],{},[1664,14113,4920],{},[1664,14115,1867],{},[2355,14117,14118,14120],{},[898,14119,13736],{},[1963,14121,2774],{},[2355,14123,14124,14126],{},[898,14125,13736],{},[1963,14127,2875],{},[1690,14129,1692],{},[6444,14131],{"width":6446},[1664,14133,1667],{"stretchy":1666},[1963,14135,14136],{},"7.16",[1664,14138,1673],{"stretchy":1666},[902,14140,14141],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,14143,13400,14144,10588,14147,14150,14151,13411,14154,13414,14157,13437,14178,14210,14211,14233,14234,14236,14237,14239],{},[38,14145,14146],{},"funkce LM",[614,14148,14149],{},"LM schedule","), její graf ",[38,14152,14153],{},"křivka LM",[38,14155,14156],{},"rostoucí",[883,14158,14160],{"className":14159},[886],[888,14161,14162],{"xmlns":890},[892,14163,14164,14176],{},[895,14165,14166,14168,14170,14172,14174],{},[1664,14167,1667],{"stretchy":1666},[898,14169,12540],{},[1664,14171,1916],{"separator":1915},[898,14173,9692],{},[1664,14175,1673],{"stretchy":1666},[902,14177,13436],{"encoding":904},[883,14179,14181],{"className":14180},[886],[888,14182,14183],{"xmlns":890},[892,14184,14185,14207],{},[895,14186,14187,14189,14203,14205],{},[1664,14188,1867],{},[2922,14190,14191,14197],{},[2355,14192,14193,14195],{},[898,14194,13736],{},[1963,14196,1970],{},[2355,14198,14199,14201],{},[898,14200,13736],{},[1963,14202,2875],{},[1664,14204,3984],{},[1963,14206,2058],{},[902,14208,14209],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,14212,14214],{"className":14213},[886],[888,14215,14216],{"xmlns":890},[892,14217,14218,14230],{},[895,14219,14220,14226,14228],{},[2355,14221,14222,14224],{},[898,14223,13736],{},[1963,14225,1970],{},[1664,14227,4022],{},[1963,14229,2058],{},[902,14231,14232],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,14235,10358],{},"iquidity of ",[38,14238,1956],{},"oney.",[4436,14241,14242],{},[724,14243,14244,14246,14247,14260,14261,14289,14290,14307,14308,14321,14322,14339,14340,4454,14353,14366,14367,14370],{},[883,14245,4723],{}," Intuice — proč LM roste\nVyšší důchod ",[883,14248,14250],{"className":14249},[886],[888,14251,14252],{"xmlns":890},[892,14253,14254,14258],{},[895,14255,14256],{},[898,14257,9692],{},[902,14259,9692],{"encoding":904}," → větší transakční poptávka po penězích ",[883,14262,14264],{"className":14263},[886],[888,14265,14266],{"xmlns":890},[892,14267,14268,14286],{},[895,14269,14270,14276,14278,14284],{},[2355,14271,14272,14274],{},[898,14273,10358],{},[1963,14275,2875],{},[1664,14277,1676],{},[2355,14279,14280,14282],{},[898,14281,13736],{},[1963,14283,2875],{},[898,14285,9692],{},[902,14287,14288],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,14291,14293],{"className":14292},[886],[888,14294,14295],{"xmlns":890},[892,14296,14297,14305],{},[895,14298,14299],{},[1720,14300,14301,14303],{},[898,14302,1956],{},[1664,14304,4920],{},[902,14306,12649],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,14309,14311],{"className":14310},[886],[888,14312,14313],{"xmlns":890},[892,14314,14315,14319],{},[895,14316,14317],{},[898,14318,12540],{},[902,14320,12540],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,14323,14325],{"className":14324},[886],[888,14326,14327],{"xmlns":890},[892,14328,14329,14337],{},[895,14330,14331],{},[2355,14332,14333,14335],{},[898,14334,10358],{},[1963,14336,1970],{},[902,14338,13783],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,14341,14343],{"className":14342},[886],[888,14344,14345],{"xmlns":890},[892,14346,14347,14351],{},[895,14348,14349],{},[898,14350,9692],{},[902,14352,9692],{"encoding":904},[883,14354,14356],{"className":14355},[886],[888,14357,14358],{"xmlns":890},[892,14359,14360,14364],{},[895,14361,14362],{},[898,14363,12540],{},[902,14365,12540],{"encoding":904}," na trhu peněz je proto ",[38,14368,14369],{},"přímý"," (rostoucí křivka).",[115,14372,14374],{"id":14373},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,14376,14377,14378,14381,14382,1885,14385,4454,14403,1885,14406,14424,14425,14443,14444,14462,14463,14479,14480,4454,14495,14510,14511,1977],{},"Řešením ",[38,14379,14380],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,14383,14384],{},"rovnovážný důchod",[883,14386,14388],{"className":14387},[886],[888,14389,14390],{"xmlns":890},[892,14391,14392,14400],{},[895,14393,14394],{},[1720,14395,14396,14398],{},[898,14397,9692],{},[898,14399,4819],{},[902,14401,14402],{"encoding":904},"Y^E",[38,14404,14405],{},"rovnovážnou úrokovou míru",[883,14407,14409],{"className":14408},[886],[888,14410,14411],{"xmlns":890},[892,14412,14413,14421],{},[895,14414,14415],{},[1720,14416,14417,14419],{},[898,14418,12540],{},[898,14420,4819],{},[902,14422,14423],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,14426,14428],{"className":14427},[886],[888,14429,14430],{"xmlns":890},[892,14431,14432,14440],{},[895,14433,14434],{},[1720,14435,14436,14438],{},[898,14437,12683],{},[898,14439,4819],{},[902,14441,14442],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,14445,14447],{"className":14446},[886],[888,14448,14449],{"xmlns":890},[892,14450,14451,14459],{},[895,14452,14453],{},[1720,14454,14455,14457],{},[898,14456,1703],{},[898,14458,4819],{},[902,14460,14461],{"encoding":904},"C^E",". Graficky jde o ",[38,14464,14465,14466],{},"průsečík ",[883,14467,14469],{"className":14468},[886],[888,14470,14471],{"xmlns":890},[892,14472,14473,14477],{},[895,14474,14475],{},[898,14476,4819],{},[902,14478,4819],{"encoding":904}," křivek ",[883,14481,14483],{"className":14482},[886],[888,14484,14485],{"xmlns":890},[892,14486,14487,14493],{},[895,14488,14489,14491],{},[898,14490,12683],{},[898,14492,2351],{},[902,14494,12550],{"encoding":904},[883,14496,14498],{"className":14497},[886],[888,14499,14500],{"xmlns":890},[892,14501,14502,14508],{},[895,14503,14504,14506],{},[898,14505,10358],{},[898,14507,1956],{},[902,14509,12557],{"encoding":904}," v rovině ",[883,14512,14514],{"className":14513},[886],[888,14515,14516],{"xmlns":890},[892,14517,14518,14530],{},[895,14519,14520,14522,14524,14526,14528],{},[1664,14521,1667],{"stretchy":1666},[898,14523,12540],{},[1664,14525,1916],{"separator":1915},[898,14527,9692],{},[1664,14529,1673],{"stretchy":1666},[902,14531,13436],{"encoding":904},[724,14533,14534],{},[614,14535,14536,14537,14558,14559,14574,14575,14590,14591,14604,14605,14622,14623,12627,14636,14622,14653,14666,14667,14680],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,14538,14540],{"className":14539},[886],[888,14541,14542],{"xmlns":890},[892,14543,14544,14556],{},[895,14545,14546,14548,14550,14552,14554],{},[1664,14547,1667],{"stretchy":1666},[898,14549,12540],{},[1664,14551,1916],{"separator":1915},[898,14553,9692],{},[1664,14555,1673],{"stretchy":1666},[902,14557,13436],{"encoding":904},". Rostoucí přímka ",[883,14560,14562],{"className":14561},[886],[888,14563,14564],{"xmlns":890},[892,14565,14566,14572],{},[895,14567,14568,14570],{},[898,14569,10358],{},[898,14571,1956],{},[902,14573,12557],{"encoding":904}," a klesající přímka ",[883,14576,14578],{"className":14577},[886],[888,14579,14580],{"xmlns":890},[892,14581,14582,14588],{},[895,14583,14584,14586],{},[898,14585,12683],{},[898,14587,2351],{},[902,14589,12550],{"encoding":904}," se protínají v bodě ",[883,14592,14594],{"className":14593},[886],[888,14595,14596],{"xmlns":890},[892,14597,14598,14602],{},[895,14599,14600],{},[898,14601,4819],{},[902,14603,4819],{"encoding":904}," se souřadnicemi ",[883,14606,14608],{"className":14607},[886],[888,14609,14610],{"xmlns":890},[892,14611,14612,14620],{},[895,14613,14614],{},[1720,14615,14616,14618],{},[898,14617,12540],{},[898,14619,4819],{},[902,14621,14423],{"encoding":904}," (na ose ",[883,14624,14626],{"className":14625},[886],[888,14627,14628],{"xmlns":890},[892,14629,14630,14634],{},[895,14631,14632],{},[898,14633,12540],{},[902,14635,12540],{"encoding":904},[883,14637,14639],{"className":14638},[886],[888,14640,14641],{"xmlns":890},[892,14642,14643,14651],{},[895,14644,14645],{},[1720,14646,14647,14649],{},[898,14648,9692],{},[898,14650,4819],{},[902,14652,14402],{"encoding":904},[883,14654,14656],{"className":14655},[886],[888,14657,14658],{"xmlns":890},[892,14659,14660,14664],{},[895,14661,14662],{},[898,14663,9692],{},[902,14665,9692],{"encoding":904},"); tečkované čáry z ",[883,14668,14670],{"className":14669},[886],[888,14671,14672],{"xmlns":890},[892,14673,14674,14678],{},[895,14675,14676],{},[898,14677,4819],{},[902,14679,4819],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[4436,14682,14683,14688],{},[724,14684,14685,14687],{},[883,14686,5138],{}," Postup — jak najít IS-LM rovnováhu",[152,14689,14690,14766,14834,14892,14965],{},[123,14691,14692,14695,14696,4454,14716,14736,14737,4454,14750,14763,14764,1977],{},[38,14693,14694],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,14697,14699],{"className":14698},[886],[888,14700,14701],{"xmlns":890},[892,14702,14703,14713],{},[895,14704,14705,14707,14709,14711],{},[898,14706,1703],{},[1664,14708,1667],{"stretchy":1666},[898,14710,9692],{},[1664,14712,1673],{"stretchy":1666},[902,14714,14715],{"encoding":904},"C(Y)",[883,14717,14719],{"className":14718},[886],[888,14720,14721],{"xmlns":890},[892,14722,14723,14733],{},[895,14724,14725,14727,14729,14731],{},[898,14726,12683],{},[1664,14728,1667],{"stretchy":1666},[898,14730,12540],{},[1664,14732,1673],{"stretchy":1666},[902,14734,14735],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,14738,14740],{"className":14739},[886],[888,14741,14742],{"xmlns":890},[892,14743,14744,14748],{},[895,14745,14746],{},[898,14747,9692],{},[902,14749,9692],{"encoding":904},[883,14751,14753],{"className":14752},[886],[888,14754,14755],{"xmlns":890},[892,14756,14757,14761],{},[895,14758,14759],{},[898,14760,12540],{},[902,14762,12540],{"encoding":904}," — dostaneš rovnici ",[38,14765,12550],{},[123,14767,14768,14771,14772,4454,14789,14806,14807,14763,14832,1977],{},[38,14769,14770],{},"Z trhu peněz (7.15)"," dosaď ",[883,14773,14775],{"className":14774},[886],[888,14776,14777],{"xmlns":890},[892,14778,14779,14787],{},[895,14780,14781],{},[2355,14782,14783,14785],{},[898,14784,10358],{},[1963,14786,2875],{},[902,14788,13711],{"encoding":904},[883,14790,14792],{"className":14791},[886],[888,14793,14794],{"xmlns":890},[892,14795,14796,14804],{},[895,14797,14798],{},[2355,14799,14800,14802],{},[898,14801,10358],{},[1963,14803,1970],{},[902,14805,13783],{"encoding":904}," a vztah ",[883,14808,14810],{"className":14809},[886],[888,14811,14812],{"xmlns":890},[892,14813,14814,14830],{},[895,14815,14816,14822,14824],{},[1720,14817,14818,14820],{},[898,14819,1956],{},[898,14821,2379],{},[1664,14823,1676],{},[1720,14825,14826,14828],{},[898,14827,1956],{},[1664,14829,4920],{},[902,14831,13979],{"encoding":904},[38,14833,12557],{},[123,14835,14836,14839,14840,4454,14853,14866,14867,14891],{},[38,14837,14838],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,14841,14843],{"className":14842},[886],[888,14844,14845],{"xmlns":890},[892,14846,14847,14851],{},[895,14848,14849],{},[898,14850,9692],{},[902,14852,9692],{"encoding":904},[883,14854,14856],{"className":14855},[886],[888,14857,14858],{"xmlns":890},[892,14859,14860,14864],{},[895,14861,14862],{},[898,14863,12540],{},[902,14865,12540],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,14868,14870],{"className":14869},[886],[888,14871,14872],{"xmlns":890},[892,14873,14874,14888],{},[895,14875,14876,14878,14880,14882,14884,14886],{},[898,14877,9692],{},[1664,14879,1676],{},[898,14881,1682],{},[1664,14883,1667],{"stretchy":1666},[898,14885,12540],{},[1664,14887,1673],{"stretchy":1666},[902,14889,14890],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,14893,14894,1885,14897,4454,14931,1977],{},[38,14895,14896],{},"Zpětně dopočítej",[883,14898,14900],{"className":14899},[886],[888,14901,14902],{"xmlns":890},[892,14903,14904,14928],{},[895,14905,14906,14912,14914,14916,14918,14924,14926],{},[1720,14907,14908,14910],{},[898,14909,1703],{},[898,14911,4819],{},[1664,14913,1676],{},[898,14915,207],{},[1690,14917,1692],{},[1720,14919,14920,14922],{},[898,14921,9692],{},[898,14923,4819],{},[1664,14925,1700],{},[898,14927,1818],{},[902,14929,14930],{"encoding":904},"C^E = a\\,Y^E + b",[883,14932,14934],{"className":14933},[886],[888,14935,14936],{"xmlns":890},[892,14937,14938,14962],{},[895,14939,14940,14946,14948,14950,14952,14958,14960],{},[1720,14941,14942,14944],{},[898,14943,12683],{},[898,14945,4819],{},[1664,14947,1676],{},[898,14949,2034],{},[1690,14951,1692],{},[1720,14953,14954,14956],{},[898,14955,12540],{},[898,14957,4819],{},[1664,14959,1700],{},[898,14961,1695],{},[902,14963,14964],{"encoding":904},"I^E = c\\,r^E + d",[123,14966,14967,14970,14971,15005,15006,15060],{},[38,14968,14969],{},"Ověř:"," musí platit ",[883,14972,14974],{"className":14973},[886],[888,14975,14976],{"xmlns":890},[892,14977,14978,15002],{},[895,14979,14980,14986,14988,14994,14996],{},[1720,14981,14982,14984],{},[898,14983,9692],{},[898,14985,4819],{},[1664,14987,1676],{},[1720,14989,14990,14992],{},[898,14991,1703],{},[898,14993,4819],{},[1664,14995,1700],{},[1720,14997,14998,15000],{},[898,14999,12683],{},[898,15001,4819],{},[902,15003,15004],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,15007,15009],{"className":15008},[886],[888,15010,15011],{"xmlns":890},[892,15012,15013,15057],{},[895,15014,15015,15021,15023,15029,15035,15037,15043,15049,15051],{},[1720,15016,15017,15019],{},[898,15018,1956],{},[1664,15020,4920],{},[1664,15022,1676],{},[2355,15024,15025,15027],{},[898,15026,13736],{},[1963,15028,2875],{},[1720,15030,15031,15033],{},[898,15032,9692],{},[898,15034,4819],{},[1664,15036,1700],{},[2355,15038,15039,15041],{},[898,15040,13736],{},[1963,15042,1970],{},[1720,15044,15045,15047],{},[898,15046,12540],{},[898,15048,4819],{},[1664,15050,1700],{},[2355,15052,15053,15055],{},[898,15054,13736],{},[1963,15056,2774],{},[902,15058,15059],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,15062,15064],{"id":15063},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,15066,15067],{},"Pro trh zboží jsou dány:",[120,15069,15070,15098],{},[123,15071,15072,15073,1916],{},"spotřeba ",[883,15074,15076],{"className":15075},[886],[888,15077,15078],{"xmlns":890},[892,15079,15080,15095],{},[895,15081,15082,15084,15086,15089,15091,15093],{},[898,15083,1703],{},[1664,15085,1676],{},[1963,15087,15088],{},"0,8",[898,15090,9692],{},[1664,15092,1700],{},[1963,15094,1965],{},[902,15096,15097],{"encoding":904},"C = 0{,}8Y + 100",[123,15099,15100,15101,1977],{},"investice ",[883,15102,15104],{"className":15103},[886],[888,15105,15106],{"xmlns":890},[892,15107,15108,15124],{},[895,15109,15110,15112,15114,15116,15118,15120,15122],{},[898,15111,12683],{},[1664,15113,1676],{},[1664,15115,1867],{},[1963,15117,9599],{},[898,15119,12540],{},[1664,15121,1700],{},[1963,15123,3365],{},[902,15125,15126],{"encoding":904},"I = -20r + 1000",[724,15128,15129],{},"Pro trh peněz:",[120,15131,15132,15158,15190],{},[123,15133,15134,1916],{},[883,15135,15137],{"className":15136},[886],[888,15138,15139],{"xmlns":890},[892,15140,15141,15155],{},[895,15142,15143,15149,15151,15153],{},[2355,15144,15145,15147],{},[898,15146,10358],{},[1963,15148,2875],{},[1664,15150,1676],{},[1963,15152,2220],{},[898,15154,9692],{},[902,15156,15157],{"encoding":904},"L_1 = 0{,}1Y",[123,15159,15160,1916],{},[883,15161,15163],{"className":15162},[886],[888,15164,15165],{"xmlns":890},[892,15166,15167,15187],{},[895,15168,15169,15175,15177,15179,15181,15183,15185],{},[2355,15170,15171,15173],{},[898,15172,10358],{},[1963,15174,1970],{},[1664,15176,1676],{},[1664,15178,1867],{},[1963,15180,5570],{},[898,15182,12540],{},[1664,15184,1700],{},[1963,15186,9169],{},[902,15188,15189],{"encoding":904},"L_2 = -25r + 2000",[123,15191,15192,15193,1977],{},"nabídka peněz ",[883,15194,15196],{"className":15195},[886],[888,15197,15198],{"xmlns":890},[892,15199,15200,15213],{},[895,15201,15202,15208,15210],{},[1720,15203,15204,15206],{},[898,15205,1956],{},[1664,15207,4920],{},[1664,15209,1676],{},[1963,15211,15212],{},"2375",[902,15214,15215],{"encoding":904},"M^* = 2375",[724,15217,15218,15221,15222,2087],{},[38,15219,15220],{},"Funkce IS"," — dosazením do (7.13) ",[883,15223,15225],{"className":15224},[886],[888,15226,15227],{"xmlns":890},[892,15228,15229,15241],{},[895,15230,15231,15233,15235,15237,15239],{},[898,15232,9692],{},[1664,15234,1676],{},[898,15236,1703],{},[1664,15238,1700],{},[898,15240,12683],{},[902,15242,15243],{"encoding":904},"Y = C + I",[724,15245,15246],{},[883,15247,15249],{"className":15248},[886],[888,15250,15251],{"xmlns":890},[892,15252,15253,15279],{},[895,15254,15255,15257,15259,15261,15263,15265,15267,15269,15271,15273,15275,15277],{},[898,15256,9692],{},[1664,15258,1676],{},[1963,15260,15088],{},[898,15262,9692],{},[1664,15264,1700],{},[1963,15266,1965],{},[1664,15268,1867],{},[1963,15270,9599],{},[898,15272,12540],{},[1664,15274,1700],{},[1963,15276,3365],{},[1664,15278,1916],{"separator":1915},[902,15280,15281],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,15283,15284],{},"tj.",[724,15286,15287],{},[883,15288,15290],{"className":15289},[886],[888,15291,15292],{"xmlns":890},[892,15293,15294,15319],{},[895,15295,15296,15298,15300,15302,15304,15306,15308,15311,15313,15315,15317],{},[1963,15297,2154],{},[898,15299,9692],{},[1664,15301,1700],{},[1963,15303,9599],{},[898,15305,12540],{},[1664,15307,1676],{},[1963,15309,15310],{},"1100.",[6444,15312],{"width":6446},[1664,15314,1667],{"stretchy":1666},[1690,15316,12550],{},[1664,15318,1673],{"stretchy":1666},[902,15320,15321],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,15323,15324,15327,15328,2087],{},[38,15325,15326],{},"Funkce LM"," — dosazením do (7.15) ",[883,15329,15331],{"className":15330},[886],[888,15332,15333],{"xmlns":890},[892,15334,15335,15359],{},[895,15336,15337,15343,15345,15351,15353],{},[1720,15338,15339,15341],{},[898,15340,1956],{},[1664,15342,4920],{},[1664,15344,1676],{},[2355,15346,15347,15349],{},[898,15348,10358],{},[1963,15350,2875],{},[1664,15352,1700],{},[2355,15354,15355,15357],{},[898,15356,10358],{},[1963,15358,1970],{},[902,15360,15361],{"encoding":904},"M^* = L_1 + L_2",[724,15363,15364],{},[883,15365,15367],{"className":15366},[886],[888,15368,15369],{"xmlns":890},[892,15370,15371,15393],{},[895,15372,15373,15375,15377,15379,15381,15383,15385,15387,15389,15391],{},[1963,15374,15212],{},[1664,15376,1676],{},[1963,15378,2220],{},[898,15380,9692],{},[1664,15382,1867],{},[1963,15384,5570],{},[898,15386,12540],{},[1664,15388,1700],{},[1963,15390,9169],{},[1664,15392,1916],{"separator":1915},[902,15394,15395],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,15397,15284],{},[724,15399,15400],{},[883,15401,15403],{"className":15402},[886],[888,15404,15405],{"xmlns":890},[892,15406,15407,15432],{},[895,15408,15409,15411,15413,15415,15417,15419,15421,15424,15426,15428,15430],{},[1963,15410,2220],{},[898,15412,9692],{},[1664,15414,1867],{},[1963,15416,5570],{},[898,15418,12540],{},[1664,15420,1676],{},[1963,15422,15423],{},"375.",[6444,15425],{"width":6446},[1664,15427,1667],{"stretchy":1666},[1690,15429,12557],{},[1664,15431,1673],{"stretchy":1666},[902,15433,15434],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,15436,15437,15440,15441,15466],{},[38,15438,15439],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,15442,15444],{"className":15443},[886],[888,15445,15446],{"xmlns":890},[892,15447,15448,15463],{},[895,15449,15450,15452,15454,15457,15459,15461],{},[898,15451,9692],{},[1664,15453,1676],{},[1963,15455,15456],{},"5500",[1664,15458,1867],{},[1963,15460,1965],{},[898,15462,12540],{},[902,15464,15465],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,15468,15469],{},[883,15470,15472],{"className":15471},[886],[888,15473,15474],{"xmlns":890},[892,15475,15476,15562],{},[895,15477,15478,15480,15482,15484,15486,15488,15490,15492,15494,15496,15498,15500,15503,15505,15508,15510,15513,15515,15517,15519,15521,15523,15525,15527,15529,15531,15533,15535,15538,15540,15542,15545,15547,15549,15551,15557,15559],{},[1963,15479,2220],{},[1664,15481,1667],{"stretchy":1666},[1963,15483,15456],{},[1664,15485,1867],{},[1963,15487,1965],{},[898,15489,12540],{},[1664,15491,1673],{"stretchy":1666},[1664,15493,1867],{},[1963,15495,5570],{},[898,15497,12540],{},[1664,15499,1676],{},[1963,15501,15502],{},"375",[1690,15504,4553],{},[1664,15506,15507],{},"⟹",[1690,15509,4553],{},[1963,15511,15512],{},"550",[1664,15514,1867],{},[1963,15516,3442],{},[898,15518,12540],{},[1664,15520,1867],{},[1963,15522,5570],{},[898,15524,12540],{},[1664,15526,1676],{},[1963,15528,15502],{},[1690,15530,4553],{},[1664,15532,15507],{},[1690,15534,4553],{},[1963,15536,15537],{},"35",[898,15539,12540],{},[1664,15541,1676],{},[1963,15543,15544],{},"175",[1690,15546,4553],{},[1664,15548,15507],{},[1690,15550,4553],{},[1720,15552,15553,15555],{},[898,15554,12540],{},[898,15556,4819],{},[1664,15558,1676],{},[1963,15560,15561],{},"5.",[902,15563,15564],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,15566,15567],{},[38,15568,15569],{},"Zpětné dosazení:",[120,15571,15572,15618,15655],{},[123,15573,15574,1916],{},[883,15575,15577],{"className":15576},[886],[888,15578,15579],{"xmlns":890},[892,15580,15581,15615],{},[895,15582,15583,15589,15591,15593,15595,15597,15599,15601,15603,15605,15607,15610,15612],{},[1720,15584,15585,15587],{},[898,15586,9692],{},[898,15588,4819],{},[1664,15590,1676],{},[1963,15592,15456],{},[1664,15594,1867],{},[1963,15596,1965],{},[1664,15598,3753],{},[1963,15600,2826],{},[1664,15602,1676],{},[1963,15604,15456],{},[1664,15606,1867],{},[1963,15608,15609],{},"500",[1664,15611,1676],{},[1963,15613,15614],{},"5000",[902,15616,15617],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,15619,15620,1916],{},[883,15621,15623],{"className":15622},[886],[888,15624,15625],{"xmlns":890},[892,15626,15627,15652],{},[895,15628,15629,15635,15637,15639,15641,15643,15645,15647,15649],{},[1720,15630,15631,15633],{},[898,15632,1703],{},[898,15634,4819],{},[1664,15636,1676],{},[1963,15638,15088],{},[1664,15640,3753],{},[1963,15642,15614],{},[1664,15644,1700],{},[1963,15646,1965],{},[1664,15648,1676],{},[1963,15650,15651],{},"4100",[902,15653,15654],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,15656,15657,1977],{},[883,15658,15660],{"className":15659},[886],[888,15661,15662],{"xmlns":890},[892,15663,15664,15691],{},[895,15665,15666,15672,15674,15676,15678,15680,15682,15684,15686,15688],{},[1720,15667,15668,15670],{},[898,15669,12683],{},[898,15671,4819],{},[1664,15673,1676],{},[1664,15675,1867],{},[1963,15677,9599],{},[1664,15679,3753],{},[1963,15681,2826],{},[1664,15683,1700],{},[1963,15685,3365],{},[1664,15687,1676],{},[1963,15689,15690],{},"900",[902,15692,15693],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,15695,15696,1885,15699,15745],{},[38,15697,15698],{},"Ověření:",[883,15700,15702],{"className":15701},[886],[888,15703,15704],{"xmlns":890},[892,15705,15706,15742],{},[895,15707,15708,15714,15716,15722,15724,15726,15728,15730,15732,15734,15736],{},[1720,15709,15710,15712],{},[898,15711,1703],{},[898,15713,4819],{},[1664,15715,1700],{},[1720,15717,15718,15720],{},[898,15719,12683],{},[898,15721,4819],{},[1664,15723,1676],{},[1963,15725,15651],{},[1664,15727,1700],{},[1963,15729,15690],{},[1664,15731,1676],{},[1963,15733,15614],{},[1664,15735,1676],{},[1720,15737,15738,15740],{},[898,15739,9692],{},[898,15741,4819],{},[902,15743,15744],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,15747,15748],{},[883,15749,15751],{"className":15750},[886],[888,15752,15753],{"xmlns":890},[892,15754,15755,15825],{},[895,15756,15757],{},[13331,15758,15759],{"notation":13333},[2919,15760,15761],{"scriptlevel":2058,"displaystyle":1666},[2919,15762,15763],{"scriptlevel":2058,"displaystyle":1666},[2919,15764,15765],{"scriptlevel":2058,"displaystyle":1915},[895,15766,15767,15769,15775,15777,15779,15781,15784,15790,15792,15794,15796,15798,15804,15806,15808,15810,15812,15818,15820,15823],{},[1690,15768,1692],{},[1720,15770,15771,15773],{},[898,15772,9692],{},[898,15774,4819],{},[1664,15776,1676],{},[1963,15778,15614],{},[1664,15780,1916],{"separator":1915},[6444,15782],{"width":15783},"1em",[1720,15785,15786,15788],{},[898,15787,12540],{},[898,15789,4819],{},[1664,15791,1676],{},[1963,15793,2826],{},[1664,15795,1916],{"separator":1915},[6444,15797],{"width":15783},[1720,15799,15800,15802],{},[898,15801,1703],{},[898,15803,4819],{},[1664,15805,1676],{},[1963,15807,15651],{},[1664,15809,1916],{"separator":1915},[6444,15811],{"width":15783},[1720,15813,15814,15816],{},[898,15815,12683],{},[898,15817,4819],{},[1664,15819,1676],{},[1963,15821,15822],{},"900.",[1690,15824,1692],{},[902,15826,15827],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,15829,15830],{},[614,15831,15832,15833,15846,15847,15860,15861,15876,15877,15890,15891,15906,15907,15920,15921,15934,15935,1977],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,15834,15836],{"className":15835},[886],[888,15837,15838],{"xmlns":890},[892,15839,15840,15844],{},[895,15841,15842],{},[898,15843,9692],{},[902,15845,9692],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,15848,15850],{"className":15849},[886],[888,15851,15852],{"xmlns":890},[892,15853,15854,15858],{},[895,15855,15856],{},[898,15857,12540],{},[902,15859,12540],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,15862,15864],{"className":15863},[886],[888,15865,15866],{"xmlns":890},[892,15867,15868,15874],{},[895,15869,15870,15872],{},[898,15871,10358],{},[898,15873,1956],{},[902,15875,12557],{"encoding":904}," stoupá z oblasti nízkých ",[883,15878,15880],{"className":15879},[886],[888,15881,15882],{"xmlns":890},[892,15883,15884,15888],{},[895,15885,15886],{},[898,15887,12540],{},[902,15889,12540],{"encoding":904},", přímka ",[883,15892,15894],{"className":15893},[886],[888,15895,15896],{"xmlns":890},[892,15897,15898,15904],{},[895,15899,15900,15902],{},[898,15901,12683],{},[898,15903,2351],{},[902,15905,12550],{"encoding":904}," klesá a protíná osu ",[883,15908,15910],{"className":15909},[886],[888,15911,15912],{"xmlns":890},[892,15913,15914,15918],{},[895,15915,15916],{},[898,15917,12540],{},[902,15919,12540],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,15922,15924],{"className":15923},[886],[888,15925,15926],{"xmlns":890},[892,15927,15928,15932],{},[895,15929,15930],{},[898,15931,4819],{},[902,15933,4819],{"encoding":904}," leží v bodě ",[883,15936,15938],{"className":15937},[886],[888,15939,15940],{"xmlns":890},[892,15941,15942,15964],{},[895,15943,15944,15946,15948,15950,15952,15954,15956,15958,15960,15962],{},[1664,15945,1837],{"stretchy":1666},[898,15947,12540],{},[1664,15949,1676],{},[1963,15951,2826],{},[1664,15953,1916],{"separator":1915},[1690,15955,2884],{},[898,15957,9692],{},[1664,15959,1676],{},[1963,15961,15614],{},[1664,15963,1850],{"stretchy":1666},[902,15965,15966],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,15968,15970],{"id":15969},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,15972,15973,15976,15977,15990,15991,7581,16004,16007,16008,16026,16027,16044,16045,16062,16063,16076,16077,16090],{},[38,15974,15975],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,15978,15980],{"className":15979},[886],[888,15981,15982],{"xmlns":890},[892,15983,15984,15988],{},[895,15985,15986],{},[898,15987,12611],{},[902,15989,12611],{"encoding":904}," nebo snížení daní ",[883,15992,15994],{"className":15993},[886],[888,15995,15996],{"xmlns":890},[892,15997,15998,16002],{},[895,15999,16000],{},[898,16001,1991],{},[902,16003,1991],{"encoding":904},[38,16005,16006],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,16009,16011],{"className":16010},[886],[888,16012,16013],{"xmlns":890},[892,16014,16015,16023],{},[895,16016,16017],{},[1720,16018,16019,16021],{},[898,16020,4819],{},[1664,16022,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,16024,16025],{"encoding":904},"E'"," má vyšší ",[883,16028,16030],{"className":16029},[886],[888,16031,16032],{"xmlns":890},[892,16033,16034,16042],{},[895,16035,16036],{},[1720,16037,16038,16040],{},[898,16039,9692],{},[898,16041,4819],{},[902,16043,14402],{"encoding":904}," i vyšší ",[883,16046,16048],{"className":16047},[886],[888,16049,16050],{"xmlns":890},[892,16051,16052,16060],{},[895,16053,16054],{},[1720,16055,16056,16058],{},[898,16057,12540],{},[898,16059,4819],{},[902,16061,14423],{"encoding":904}," (vyšší ",[883,16064,16066],{"className":16065},[886],[888,16067,16068],{"xmlns":890},[892,16069,16070,16074],{},[895,16071,16072],{},[898,16073,9692],{},[902,16075,9692],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,16078,16080],{"className":16079},[886],[888,16081,16082],{"xmlns":890},[892,16083,16084,16088],{},[895,16085,16086],{},[898,16087,12540],{},[902,16089,12540],{"encoding":904}," nahoru).",[724,16092,16093],{},[1928,16094],{"alt":16095,"className":16096,"src":16097},"imek-posun-is-lm-politiky",[210,1932],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,16099,16100,16103,16104,16121,16122,16125,16126,16143,16144,16161,16162,16175,16176,16195,16196,4488],{},[38,16101,16102],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,16105,16107],{"className":16106},[886],[888,16108,16109],{"xmlns":890},[892,16110,16111,16119],{},[895,16112,16113],{},[1720,16114,16115,16117],{},[898,16116,1956],{},[1664,16118,4920],{},[902,16120,12649],{"encoding":904}," národní bankou — ",[38,16123,16124],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,16127,16129],{"className":16128},[886],[888,16130,16131],{"xmlns":890},[892,16132,16133,16141],{},[895,16134,16135],{},[1720,16136,16137,16139],{},[898,16138,12540],{},[898,16140,4819],{},[902,16142,14423],{"encoding":904}," a vyšší ",[883,16145,16147],{"className":16146},[886],[888,16148,16149],{"xmlns":890},[892,16150,16151,16159],{},[895,16152,16153],{},[1720,16154,16155,16157],{},[898,16156,9692],{},[898,16158,4819],{},[902,16160,14402],{"encoding":904}," (nižší ",[883,16163,16165],{"className":16164},[886],[888,16166,16167],{"xmlns":890},[892,16168,16169,16173],{},[895,16170,16171],{},[898,16172,12540],{},[902,16174,12540],{"encoding":904}," povzbuzuje investice ",[883,16177,16179],{"className":16178},[886],[888,16180,16181],{"xmlns":890},[892,16182,16183,16193],{},[895,16184,16185,16187,16189,16191],{},[898,16186,12683],{},[1664,16188,1667],{"stretchy":1666},[898,16190,12540],{},[1664,16192,1673],{"stretchy":1666},[902,16194,14735],{"encoding":904},", ty zvedají ",[883,16197,16199],{"className":16198},[886],[888,16200,16201],{"xmlns":890},[892,16202,16203,16207],{},[895,16204,16205],{},[898,16206,9692],{},[902,16208,9692],{"encoding":904},[724,16210,16211,16212,16215],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,16213,16214],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,16217,16219],{"id":16218},"klíčové-pojmy","Klíčové pojmy",[120,16221,16222,16295,16341,16423,16473,16540,16597,16638,16671],{},[123,16223,16224,7581,16257,1343,16274,16291,16292,16294],{},[38,16225,16226,16227],{},"Funkce investic ",[883,16228,16230],{"className":16229},[886],[888,16231,16232],{"xmlns":890},[892,16233,16234,16254],{},[895,16235,16236,16238,16240,16242,16244,16246,16248,16250,16252],{},[898,16237,12683],{},[1664,16239,1667],{"stretchy":1666},[898,16241,12540],{},[1664,16243,1673],{"stretchy":1666},[1664,16245,1676],{},[898,16247,2034],{},[898,16249,12540],{},[1664,16251,1700],{},[898,16253,1695],{},[902,16255,16256],{"encoding":904},"I(r) = cr + d",[883,16258,16260],{"className":16259},[886],[888,16261,16262],{"xmlns":890},[892,16263,16264,16272],{},[895,16265,16266,16268,16270],{},[898,16267,2034],{},[1664,16269,4022],{},[1963,16271,2058],{},[902,16273,13014],{"encoding":904},[883,16275,16277],{"className":16276},[886],[888,16278,16279],{"xmlns":890},[892,16280,16281,16289],{},[895,16282,16283,16285,16287],{},[898,16284,1695],{},[1664,16286,3984],{},[1963,16288,2058],{},[902,16290,12993],{"encoding":904},"; ",[38,16293,13018],{}," funkce úrokové míry.",[123,16296,16297,16300,16301,16322,16323,16340],{},[38,16298,16299],{},"Trh zboží"," — rovnováha ",[883,16302,16304],{"className":16303},[886],[888,16305,16306],{"xmlns":890},[892,16307,16308,16320],{},[895,16309,16310,16312,16314,16316,16318],{},[898,16311,9692],{},[1664,16313,1676],{},[898,16315,1703],{},[1664,16317,1700],{},[898,16319,12683],{},[902,16321,15243],{"encoding":904},", ekvivalentně ",[883,16324,16326],{"className":16325},[886],[888,16327,16328],{"xmlns":890},[892,16329,16330,16338],{},[895,16331,16332,16334,16336],{},[898,16333,12683],{},[1664,16335,1676],{},[898,16337,2351],{},[902,16339,13211],{"encoding":904}," (investice = úspory).",[123,16342,16343,10588,16346,16348,16349,16399,16400,13414,16402,1977],{},[38,16344,16345],{},"Křivka IS",[614,16347,12553],{},") — ",[883,16350,16352],{"className":16351},[886],[888,16353,16354],{"xmlns":890},[892,16355,16356,16396],{},[895,16357,16358,16360,16362,16374,16376,16378],{},[898,16359,9692],{},[1664,16361,1676],{},[2922,16363,16364,16366],{},[898,16365,2034],{},[895,16367,16368,16370,16372],{},[1963,16369,2875],{},[1664,16371,1867],{},[898,16373,207],{},[898,16375,12540],{},[1664,16377,1700],{},[2922,16379,16380,16388],{},[895,16381,16382,16384,16386],{},[898,16383,1818],{},[1664,16385,1700],{},[898,16387,1695],{},[895,16389,16390,16392,16394],{},[1963,16391,2875],{},[1664,16393,1867],{},[898,16395,207],{},[902,16397,16398],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,16401,13018],{},[883,16403,16405],{"className":16404},[886],[888,16406,16407],{"xmlns":890},[892,16408,16409,16421],{},[895,16410,16411,16413,16415,16417,16419],{},[1664,16412,1667],{"stretchy":1666},[898,16414,12540],{},[1664,16416,1916],{"separator":1915},[898,16418,9692],{},[1664,16420,1673],{"stretchy":1666},[902,16422,13436],{"encoding":904},[123,16424,16425,16300,16428,16454,16455,1977],{},[38,16426,16427],{},"Trh peněz",[883,16429,16431],{"className":16430},[886],[888,16432,16433],{"xmlns":890},[892,16434,16435,16451],{},[895,16436,16437,16443,16445],{},[1720,16438,16439,16441],{},[898,16440,1956],{},[898,16442,2379],{},[1664,16444,1676],{},[1720,16446,16447,16449],{},[898,16448,1956],{},[898,16450,2351],{},[902,16452,16453],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,16456,16458],{"className":16457},[886],[888,16459,16460],{"xmlns":890},[892,16461,16462,16470],{},[895,16463,16464],{},[1720,16465,16466,16468],{},[898,16467,1956],{},[1664,16469,4920],{},[902,16471,16472],{"encoding":904},"M^* ",[123,16474,16475,7581,16478,1977],{},[38,16476,16477],{},"Transakční, opatrnostní, spekulační poptávka",[883,16479,16481],{"className":16480},[886],[888,16482,16483],{"xmlns":890},[892,16484,16485,16537],{},[895,16486,16487,16493,16495,16501,16503,16509,16511,16517,16519,16521,16527,16529,16531],{},[1720,16488,16489,16491],{},[898,16490,1956],{},[898,16492,2379],{},[1664,16494,1676],{},[2355,16496,16497,16499],{},[898,16498,10358],{},[1963,16500,2875],{},[1664,16502,1700],{},[2355,16504,16505,16507],{},[898,16506,10358],{},[1963,16508,1970],{},[1664,16510,1676],{},[2355,16512,16513,16515],{},[898,16514,13736],{},[1963,16516,2875],{},[898,16518,9692],{},[1664,16520,1700],{},[2355,16522,16523,16525],{},[898,16524,13736],{},[1963,16526,1970],{},[898,16528,12540],{},[1664,16530,1700],{},[2355,16532,16533,16535],{},[898,16534,13736],{},[1963,16536,2774],{},[902,16538,16539],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,16541,16542,10588,16545,16348,16547,16593,16594,16596],{},[38,16543,16544],{},"Křivka LM",[614,16546,12560],{},[883,16548,16550],{"className":16549},[886],[888,16551,16552],{"xmlns":890},[892,16553,16554,16590],{},[895,16555,16556,16562,16564,16570,16572,16574,16580,16582,16584],{},[1720,16557,16558,16560],{},[898,16559,1956],{},[1664,16561,4920],{},[1664,16563,1676],{},[2355,16565,16566,16568],{},[898,16567,13736],{},[1963,16569,2875],{},[898,16571,9692],{},[1664,16573,1700],{},[2355,16575,16576,16578],{},[898,16577,13736],{},[1963,16579,1970],{},[898,16581,12540],{},[1664,16583,1700],{},[2355,16585,16586,16588],{},[898,16587,13736],{},[1963,16589,2774],{},[902,16591,16592],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,16595,14156],{}," přímka.",[123,16598,16599,16602,16603,16637],{},[38,16600,16601],{},"Simultánní rovnováha"," — průsečík ",[883,16604,16606],{"className":16605},[886],[888,16607,16608],{"xmlns":890},[892,16609,16610,16634],{},[895,16611,16612,16614,16616,16618,16624,16626,16632],{},[898,16613,4819],{},[1664,16615,1676],{},[1664,16617,1667],{"stretchy":1666},[1720,16619,16620,16622],{},[898,16621,12540],{},[898,16623,4819],{},[1664,16625,1916],{"separator":1915},[1720,16627,16628,16630],{},[898,16629,9692],{},[898,16631,4819],{},[1664,16633,1673],{"stretchy":1666},[902,16635,16636],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,16639,16640,16643,16644,1343,16657,16670],{},[38,16641,16642],{},"Fiskální politika"," — nástroje ",[883,16645,16647],{"className":16646},[886],[888,16648,16649],{"xmlns":890},[892,16650,16651,16655],{},[895,16652,16653],{},[898,16654,12611],{},[902,16656,12611],{"encoding":904},[883,16658,16660],{"className":16659},[886],[888,16661,16662],{"xmlns":890},[892,16663,16664,16668],{},[895,16665,16666],{},[898,16667,1991],{},[902,16669,1991],{"encoding":904}," posouvající křivku IS.",[123,16672,16673,16676,16677,16694],{},[38,16674,16675],{},"Monetární politika"," — nástroj ",[883,16678,16680],{"className":16679},[886],[888,16681,16682],{"xmlns":890},[892,16683,16684,16692],{},[895,16685,16686],{},[1720,16687,16688,16690],{},[898,16689,1956],{},[1664,16691,4920],{},[902,16693,12649],{"encoding":904}," posouvající křivku LM.",[115,16696,2497],{"id":2496},[120,16698,16699,16708,16717,16727],{},[123,16700,16701,1885,16704],{},[38,16702,16703],{},"Kurz:",[207,16705,16707],{"className":16706,"dataFsResolvedFilePath":2575,"href":2576},[210],"Matematická ekonomie",[123,16709,16710,1885,16713],{},[38,16711,16712],{},"Přednáška:",[207,16714,16716],{"className":16715,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,16718,16719,1885,16722,16726],{},[38,16720,16721],{},"Nadřazené téma:",[207,16723,16725],{"className":16724,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,16728,16729,16732],{},[38,16730,16731],{},"Související:",[120,16733,16734,16741,16747],{},[123,16735,16736,16740],{},[207,16737,16739],{"className":16738,"dataFsResolvedFilePath":800,"href":801},[210],"poptavka-nabidka"," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,16742,16743,16746],{},[207,16744,1145],{"className":16745,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,16748,16749,16753],{},[207,16750,16752],{"className":16751,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":16755},[16756,16757,16758,16759,16760,16761,16762,16763,16764,16765],{"id":12504,"depth":642,"text":12505},{"id":12659,"depth":642,"text":12660},{"id":12874,"depth":642,"text":12875},{"id":13167,"depth":642,"text":13168},{"id":13580,"depth":642,"text":13581},{"id":14373,"depth":642,"text":14374},{"id":15063,"depth":642,"text":15064},{"id":15969,"depth":642,"text":15970},{"id":16218,"depth":642,"text":16219},{"id":2496,"depth":642,"text":2497},{},"\u002Ftopics\u002Fis-lm",{"title":12496,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,16772,1143,16773,16774,16775,16776,16725],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":16779,"title":16780,"body":16781,"course":659,"courses":18374,"created":1129,"description":18375,"extension":661,"meta":18376,"navigation":664,"path":18377,"seo":18378,"sources":18379,"stem":18380,"tags":18381,"type":2553,"updated":677,"__hash__":18384},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":16782,"toc":18362},[16783,16786,16882,16889,16909,16913,16918,16981,17000,17002,17005,17141,17143,17353,17387,17524,17528,17592,17608,17636,17640,17738,17742,17746,17799,17905,18119,18123,18166,18272,18324,18326],[12,16784,16780],{"id":16785},"lagrangeova-metoda-vázané-extrémy",[724,16787,16788,16789,4480,16812,16844,16845,16848,16849,16876,16877,16881],{},"Hledáme extrém funkce ",[883,16790,16792],{"className":16791},[886],[888,16793,16794],{"xmlns":890},[892,16795,16796,16810],{},[895,16797,16798,16800,16802,16804,16806,16808],{},[898,16799,1682],{},[1664,16801,1667],{"stretchy":1666},[898,16803,1670],{},[1664,16805,1916],{"separator":1915},[898,16807,2608],{},[1664,16809,1673],{"stretchy":1666},[902,16811,10406],{"encoding":904},[883,16813,16815],{"className":16814},[886],[888,16816,16817],{"xmlns":890},[892,16818,16819,16841],{},[895,16820,16821,16823,16825,16831,16833,16839],{},[898,16822,900],{},[1664,16824,1667],{"stretchy":1666},[2355,16826,16827,16829],{},[898,16828,1973],{},[1963,16830,2875],{},[1664,16832,1916],{"separator":1915},[2355,16834,16835,16837],{},[898,16836,1973],{},[1963,16838,1970],{},[1664,16840,1673],{"stretchy":1666},[902,16842,16843],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,16846,16847],{},"podmíněný"," rovnicí ",[883,16850,16852],{"className":16851},[886],[888,16853,16854],{"xmlns":890},[892,16855,16856,16874],{},[895,16857,16858,16860,16862,16864,16866,16868,16870,16872],{},[898,16859,11602],{},[1664,16861,1667],{"stretchy":1666},[898,16863,1670],{},[1664,16865,1916],{"separator":1915},[898,16867,2608],{},[1664,16869,1673],{"stretchy":1666},[1664,16871,1676],{},[1963,16873,2058],{},[902,16875,11619],{"encoding":904},". V ",[207,16878,16880],{"className":16879,"dataFsResolvedFilePath":2575,"href":2576},[210],"matematické ekonomii"," se používá pro:",[724,16883,16884],{},[1928,16885],{"alt":16886,"className":16887,"src":16888},"imek-lagrange-tecnost",[210,1932],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,16890,16891,16900,16906],{},[123,16892,16893,16896,16897,1673],{},[38,16894,16895],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,16898,10336],{"className":16899,"dataFsResolvedFilePath":878,"href":879},[210],[123,16901,16902,16905],{},[38,16903,16904],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,16907,16908],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,16910,16912],{"id":16911},"princip","Princip",[724,16914,11269,16915,2087],{},[38,16916,16917],{},"Lagrangeovu funkci",[724,16919,16920],{},[883,16921,16923],{"className":16922},[886],[888,16924,16925],{"xmlns":890},[892,16926,16927,16978],{},[895,16928,16929,16931,16933,16935,16937,16939,16941,16944,16946,16948,16950,16952,16954,16956,16958,16960,16962,16964,16966,16968,16970,16972,16974,16976],{},[898,16930,10358],{},[1664,16932,1667],{"stretchy":1666},[898,16934,1670],{},[1664,16936,1916],{"separator":1915},[898,16938,2608],{},[1664,16940,1916],{"separator":1915},[898,16942,16943],{},"λ",[1664,16945,1673],{"stretchy":1666},[1664,16947,1676],{},[898,16949,1682],{},[1664,16951,1667],{"stretchy":1666},[898,16953,1670],{},[1664,16955,1916],{"separator":1915},[898,16957,2608],{},[1664,16959,1673],{"stretchy":1666},[1664,16961,1700],{},[898,16963,16943],{},[1690,16965,1692],{},[898,16967,11602],{},[1664,16969,1667],{"stretchy":1666},[898,16971,1670],{},[1664,16973,1916],{"separator":1915},[898,16975,2608],{},[1664,16977,1673],{"stretchy":1666},[902,16979,16980],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,16982,1709,16983,1762,16997,1977],{},[883,16984,16986],{"className":16985},[886],[888,16987,16988],{"xmlns":890},[892,16989,16990,16994],{},[895,16991,16992],{},[898,16993,16943],{},[902,16995,16996],{"encoding":904},"\\lambda",[38,16998,16999],{},"Lagrangeův multiplikátor",[115,17001,3828],{"id":3827},[724,17003,17004],{},"Řešíme soustavu:",[724,17006,17007,17055,17103],{},[883,17008,17010],{"className":17009},[886],[888,17011,17012],{"xmlns":890},[892,17013,17014,17052],{},[895,17015,17016,17024,17026,17034,17036,17038,17040,17048,17050],{},[1810,17017,17018,17020,17022],{},[898,17019,10358],{},[898,17021,1670],{},[1664,17023,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,17025,1676],{},[1810,17027,17028,17030,17032],{},[898,17029,1682],{},[898,17031,1670],{},[1664,17033,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,17035,1700],{},[898,17037,16943],{},[1690,17039,1692],{},[1810,17041,17042,17044,17046],{},[898,17043,11602],{},[898,17045,1670],{},[1664,17047,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,17049,1676],{},[1963,17051,2058],{},[902,17053,17054],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,17056,17058],{"className":17057},[886],[888,17059,17060],{"xmlns":890},[892,17061,17062,17100],{},[895,17063,17064,17072,17074,17082,17084,17086,17088,17096,17098],{},[1810,17065,17066,17068,17070],{},[898,17067,10358],{},[898,17069,2608],{},[1664,17071,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,17073,1676],{},[1810,17075,17076,17078,17080],{},[898,17077,1682],{},[898,17079,2608],{},[1664,17081,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,17083,1700],{},[898,17085,16943],{},[1690,17087,1692],{},[1810,17089,17090,17092,17094],{},[898,17091,11602],{},[898,17093,2608],{},[1664,17095,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,17097,1676],{},[1963,17099,2058],{},[902,17101,17102],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,17104,17106],{"className":17105},[886],[888,17107,17108],{"xmlns":890},[892,17109,17110,17138],{},[895,17111,17112,17120,17122,17124,17126,17128,17130,17132,17134,17136],{},[1810,17113,17114,17116,17118],{},[898,17115,10358],{},[898,17117,16943],{},[1664,17119,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,17121,1676],{},[898,17123,11602],{},[1664,17125,1667],{"stretchy":1666},[898,17127,1670],{},[1664,17129,1916],{"separator":1915},[898,17131,2608],{},[1664,17133,1673],{"stretchy":1666},[1664,17135,1676],{},[1963,17137,2058],{},[902,17139,17140],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,17142,3902],{"id":3901},[724,17144,17145],{},[883,17146,17148],{"className":17147},[886],[888,17149,17150],{"xmlns":890},[892,17151,17152,17350],{},[895,17153,17154,17156,17158,17160,17162,17164,17166,17168,17170,17172,17174,17190,17192,17194,17210,17212,17214,17222,17228,17230,17232,17248,17250,17252,17268,17270,17272,17280,17286,17288,17290,17292,17308,17310,17312,17328,17330,17332,17340,17342],{},[898,17155,2379],{},[1664,17157,1667],{"stretchy":1666},[898,17159,1670],{},[1664,17161,1916],{"separator":1915},[898,17163,2608],{},[1664,17165,1916],{"separator":1915},[898,17167,16943],{},[1664,17169,1673],{"stretchy":1666},[1664,17171,1676],{},[1664,17173,1667],{"stretchy":1666},[1810,17175,17176,17178,17184],{},[898,17177,1682],{},[895,17179,17180,17182],{},[898,17181,1670],{},[898,17183,1670],{},[895,17185,17186,17188],{},[1664,17187,1728],{"mathvariant":1726},[1664,17189,1728],{"mathvariant":1726},[1664,17191,1700],{},[898,17193,16943],{},[1810,17195,17196,17198,17204],{},[898,17197,11602],{},[895,17199,17200,17202],{},[898,17201,1670],{},[898,17203,1670],{},[895,17205,17206,17208],{},[1664,17207,1728],{"mathvariant":1726},[1664,17209,1728],{"mathvariant":1726},[1664,17211,1673],{"stretchy":1666},[1664,17213,1667],{"stretchy":1666},[1810,17215,17216,17218,17220],{},[898,17217,11602],{},[898,17219,2608],{},[1664,17221,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1720,17223,17224,17226],{},[1664,17225,1673],{"stretchy":1666},[1963,17227,1970],{},[1664,17229,1700],{},[1664,17231,1667],{"stretchy":1666},[1810,17233,17234,17236,17242],{},[898,17235,1682],{},[895,17237,17238,17240],{},[898,17239,2608],{},[898,17241,2608],{},[895,17243,17244,17246],{},[1664,17245,1728],{"mathvariant":1726},[1664,17247,1728],{"mathvariant":1726},[1664,17249,1700],{},[898,17251,16943],{},[1810,17253,17254,17256,17262],{},[898,17255,11602],{},[895,17257,17258,17260],{},[898,17259,2608],{},[898,17261,2608],{},[895,17263,17264,17266],{},[1664,17265,1728],{"mathvariant":1726},[1664,17267,1728],{"mathvariant":1726},[1664,17269,1673],{"stretchy":1666},[1664,17271,1667],{"stretchy":1666},[1810,17273,17274,17276,17278],{},[898,17275,11602],{},[898,17277,1670],{},[1664,17279,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1720,17281,17282,17284],{},[1664,17283,1673],{"stretchy":1666},[1963,17285,1970],{},[1664,17287,1867],{},[1963,17289,1970],{},[1664,17291,1667],{"stretchy":1666},[1810,17293,17294,17296,17302],{},[898,17295,1682],{},[895,17297,17298,17300],{},[898,17299,1670],{},[898,17301,2608],{},[895,17303,17304,17306],{},[1664,17305,1728],{"mathvariant":1726},[1664,17307,1728],{"mathvariant":1726},[1664,17309,1700],{},[898,17311,16943],{},[1810,17313,17314,17316,17322],{},[898,17315,11602],{},[895,17317,17318,17320],{},[898,17319,1670],{},[898,17321,2608],{},[895,17323,17324,17326],{},[1664,17325,1728],{"mathvariant":1726},[1664,17327,1728],{"mathvariant":1726},[1664,17329,1673],{"stretchy":1666},[1690,17331,1692],{},[1810,17333,17334,17336,17338],{},[898,17335,11602],{},[898,17337,1670],{},[1664,17339,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1690,17341,1692],{},[1810,17343,17344,17346,17348],{},[898,17345,11602],{},[898,17347,2608],{},[1664,17349,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,17351,17352],{"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",[724,17354,17355,17356,17386],{},"Je-li ",[883,17357,17359],{"className":17358},[886],[888,17360,17361],{"xmlns":890},[892,17362,17363,17383],{},[895,17364,17365,17367,17369,17371,17373,17375,17381],{},[1664,17366,1837],{"stretchy":1666},[898,17368,207],{},[1664,17370,1916],{"separator":1915},[898,17372,1818],{},[1664,17374,1916],{"separator":1915},[2355,17376,17377,17379],{},[898,17378,16943],{},[1963,17380,2058],{},[1664,17382,1850],{"stretchy":1666},[902,17384,17385],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,17388,17389,17457],{},[123,17390,17391,2068,17427,17429,17430],{},[883,17392,17394],{"className":17393},[886],[888,17395,17396],{"xmlns":890},[892,17397,17398,17424],{},[895,17399,17400,17402,17404,17406,17408,17410,17412,17418,17420,17422],{},[898,17401,2379],{},[1664,17403,1667],{"stretchy":1666},[898,17405,207],{},[1664,17407,1916],{"separator":1915},[898,17409,1818],{},[1664,17411,1916],{"separator":1915},[2355,17413,17414,17416],{},[898,17415,16943],{},[1963,17417,2058],{},[1664,17419,1673],{"stretchy":1666},[1664,17421,4022],{},[1963,17423,2058],{},[902,17425,17426],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,17428,4292],{}," vázané podmínkou ",[883,17431,17433],{"className":17432},[886],[888,17434,17435],{"xmlns":890},[892,17436,17437,17455],{},[895,17438,17439,17441,17443,17445,17447,17449,17451,17453],{},[898,17440,11602],{},[1664,17442,1667],{"stretchy":1666},[898,17444,1670],{},[1664,17446,1916],{"separator":1915},[898,17448,2608],{},[1664,17450,1673],{"stretchy":1666},[1664,17452,1676],{},[1963,17454,2058],{},[902,17456,11619],{"encoding":904},[123,17458,17459,2068,17495,17429,17497],{},[883,17460,17462],{"className":17461},[886],[888,17463,17464],{"xmlns":890},[892,17465,17466,17492],{},[895,17467,17468,17470,17472,17474,17476,17478,17480,17486,17488,17490],{},[898,17469,2379],{},[1664,17471,1667],{"stretchy":1666},[898,17473,207],{},[1664,17475,1916],{"separator":1915},[898,17477,1818],{},[1664,17479,1916],{"separator":1915},[2355,17481,17482,17484],{},[898,17483,16943],{},[1963,17485,2058],{},[1664,17487,1673],{"stretchy":1666},[1664,17489,3984],{},[1963,17491,2058],{},[902,17493,17494],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,17496,4350],{},[883,17498,17500],{"className":17499},[886],[888,17501,17502],{"xmlns":890},[892,17503,17504,17522],{},[895,17505,17506,17508,17510,17512,17514,17516,17518,17520],{},[898,17507,11602],{},[1664,17509,1667],{"stretchy":1666},[898,17511,1670],{},[1664,17513,1916],{"separator":1915},[898,17515,2608],{},[1664,17517,1673],{"stretchy":1666},[1664,17519,1676],{},[1963,17521,2058],{},[902,17523,11619],{"encoding":904},[115,17525,17527],{"id":17526},"význam-multiplikátoru","Význam multiplikátoru",[724,17529,17530],{},[883,17531,17533],{"className":17532},[886],[888,17534,17535],{"xmlns":890},[892,17536,17537,17589],{},[895,17538,17539,17541,17543,17565,17567],{},[898,17540,16943],{},[1664,17542,1676],{},[2922,17544,17545,17553],{},[1810,17546,17547,17549,17551],{},[898,17548,1682],{},[898,17550,1670],{},[1664,17552,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[895,17554,17555,17557],{},[1664,17556,1867],{},[1810,17558,17559,17561,17563],{},[898,17560,11602],{},[898,17562,1670],{},[1664,17564,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,17566,1676],{},[2922,17568,17569,17577],{},[1810,17570,17571,17573,17575],{},[898,17572,1682],{},[898,17574,2608],{},[1664,17576,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[895,17578,17579,17581],{},[1664,17580,1867],{},[1810,17582,17583,17585,17587],{},[898,17584,11602],{},[898,17586,2608],{},[1664,17588,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,17590,17591],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,17593,17594,17607],{},[883,17595,17597],{"className":17596},[886],[888,17598,17599],{"xmlns":890},[892,17600,17601,17605],{},[895,17602,17603],{},[898,17604,16943],{},[902,17606,16996],{"encoding":904}," udává:",[120,17609,17610,17616],{},[123,17611,17612,17613],{},"konstantní ",[38,17614,17615],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,17617,17618,17621,17622,17635],{},[38,17619,17620],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,17623,17625],{"className":17624},[886],[888,17626,17627],{"xmlns":890},[892,17628,17629,17633],{},[895,17630,17631],{},[898,17632,1682],{},[902,17634,1682],{"encoding":904},", uvolní-li se omezení o jednotku",[115,17637,17639],{"id":17638},"alternativní-postup","Alternativní postup",[724,17641,17642,17643,17670,17671,17695,17696,17720,17721,17734,17735,1977],{},"Lze-li z ",[883,17644,17646],{"className":17645},[886],[888,17647,17648],{"xmlns":890},[892,17649,17650,17668],{},[895,17651,17652,17654,17656,17658,17660,17662,17664,17666],{},[898,17653,11602],{},[1664,17655,1667],{"stretchy":1666},[898,17657,1670],{},[1664,17659,1916],{"separator":1915},[898,17661,2608],{},[1664,17663,1673],{"stretchy":1666},[1664,17665,1676],{},[1963,17667,2058],{},[902,17669,11619],{"encoding":904}," vyjádřit ",[883,17672,17674],{"className":17673},[886],[888,17675,17676],{"xmlns":890},[892,17677,17678,17692],{},[895,17679,17680,17682,17684,17686,17688,17690],{},[898,17681,2608],{},[1664,17683,1676],{},[898,17685,2608],{},[1664,17687,1667],{"stretchy":1666},[898,17689,1670],{},[1664,17691,1673],{"stretchy":1666},[902,17693,17694],{"encoding":904},"y = y(x)"," (nebo ",[883,17697,17699],{"className":17698},[886],[888,17700,17701],{"xmlns":890},[892,17702,17703,17717],{},[895,17704,17705,17707,17709,17711,17713,17715],{},[898,17706,1670],{},[1664,17708,1676],{},[898,17710,1670],{},[1664,17712,1667],{"stretchy":1666},[898,17714,2608],{},[1664,17716,1673],{"stretchy":1666},[902,17718,17719],{"encoding":904},"x = x(y)","), dosadíme do ",[883,17722,17724],{"className":17723},[886],[888,17725,17726],{"xmlns":890},[892,17727,17728,17732],{},[895,17729,17730],{},[898,17731,1682],{},[902,17733,1682],{"encoding":904}," a převedeme na ",[38,17736,17737],{},"extrém funkce jedné proměnné",[115,17739,17741],{"id":17740},"použití-v-imek","Použití v ImeK",[198,17743,17745],{"id":17744},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,17747,17748,17749,1977],{},"Rozpočtové omezení: ",[883,17750,17752],{"className":17751},[886],[888,17753,17754],{"xmlns":890},[892,17755,17756,17796],{},[895,17757,17758,17764,17766,17774,17780,17782,17790],{},[1720,17759,17760,17762],{},[898,17761,9692],{},[1664,17763,4920],{},[1664,17765,1676],{},[1810,17767,17768,17770,17772],{},[898,17769,2398],{},[1963,17771,2875],{},[1664,17773,4920],{},[2355,17775,17776,17778],{},[898,17777,1973],{},[1963,17779,2875],{},[1664,17781,1700],{},[1810,17783,17784,17786,17788],{},[898,17785,2398],{},[1963,17787,1970],{},[1664,17789,4920],{},[2355,17791,17792,17794],{},[898,17793,1973],{},[1963,17795,1970],{},[902,17797,17798],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,17800,17801],{},[883,17802,17804],{"className":17803},[886],[888,17805,17806],{"xmlns":890},[892,17807,17808,17902],{},[895,17809,17810,17812,17814,17820,17822,17828,17830,17832,17834,17836,17838,17840,17846,17848,17854,17856,17858,17860,17862,17868,17870,17878,17884,17886,17894,17900],{},[898,17811,10358],{},[1664,17813,1667],{"stretchy":1666},[2355,17815,17816,17818],{},[898,17817,1973],{},[1963,17819,2875],{},[1664,17821,1916],{"separator":1915},[2355,17823,17824,17826],{},[898,17825,1973],{},[1963,17827,1970],{},[1664,17829,1916],{"separator":1915},[898,17831,16943],{},[1664,17833,1673],{"stretchy":1666},[1664,17835,1676],{},[898,17837,900],{},[1664,17839,1667],{"stretchy":1666},[2355,17841,17842,17844],{},[898,17843,1973],{},[1963,17845,2875],{},[1664,17847,1916],{"separator":1915},[2355,17849,17850,17852],{},[898,17851,1973],{},[1963,17853,1970],{},[1664,17855,1673],{"stretchy":1666},[1664,17857,1700],{},[898,17859,16943],{},[1664,17861,1667],{"stretchy":1666},[1720,17863,17864,17866],{},[898,17865,9692],{},[1664,17867,4920],{},[1664,17869,1867],{},[1810,17871,17872,17874,17876],{},[898,17873,2398],{},[1963,17875,2875],{},[1664,17877,4920],{},[2355,17879,17880,17882],{},[898,17881,1973],{},[1963,17883,2875],{},[1664,17885,1867],{},[1810,17887,17888,17890,17892],{},[898,17889,2398],{},[1963,17891,1970],{},[1664,17893,4920],{},[2355,17895,17896,17898],{},[898,17897,1973],{},[1963,17899,1970],{},[1664,17901,1673],{"stretchy":1666},[902,17903,17904],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,17906,17907,17908,1343,17940,1343,17972,18021,18022,18076,18077,1977],{},"Soustava: ",[883,17909,17911],{"className":17910},[886],[888,17912,17913],{"xmlns":890},[892,17914,17915,17937],{},[895,17916,17917,17925,17927,17929],{},[1810,17918,17919,17921,17923],{},[898,17920,900],{},[1963,17922,2875],{},[1664,17924,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,17926,1676],{},[898,17928,16943],{},[1810,17930,17931,17933,17935],{},[898,17932,2398],{},[1963,17934,2875],{},[1664,17936,4920],{},[902,17938,17939],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,17941,17943],{"className":17942},[886],[888,17944,17945],{"xmlns":890},[892,17946,17947,17969],{},[895,17948,17949,17957,17959,17961],{},[1810,17950,17951,17953,17955],{},[898,17952,900],{},[1963,17954,1970],{},[1664,17956,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,17958,1676],{},[898,17960,16943],{},[1810,17962,17963,17965,17967],{},[898,17964,2398],{},[1963,17966,1970],{},[1664,17968,4920],{},[902,17970,17971],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,17973,17975],{"className":17974},[886],[888,17976,17977],{"xmlns":890},[892,17978,17979,18019],{},[895,17980,17981,17987,17989,17997,18003,18005,18013],{},[1720,17982,17983,17985],{},[898,17984,9692],{},[1664,17986,4920],{},[1664,17988,1676],{},[1810,17990,17991,17993,17995],{},[898,17992,2398],{},[1963,17994,2875],{},[1664,17996,4920],{},[2355,17998,17999,18001],{},[898,18000,1973],{},[1963,18002,2875],{},[1664,18004,1700],{},[1810,18006,18007,18009,18011],{},[898,18008,2398],{},[1963,18010,1970],{},[1664,18012,4920],{},[2355,18014,18015,18017],{},[898,18016,1973],{},[1963,18018,1970],{},[902,18020,17798],{"encoding":904},". Z prvních dvou: ",[883,18023,18025],{"className":18024},[886],[888,18026,18027],{"xmlns":890},[892,18028,18029,18073],{},[895,18030,18031,18051,18053],{},[2919,18032,18033],{"scriptlevel":2058,"displaystyle":1666},[2922,18034,18035,18043],{},[1810,18036,18037,18039,18041],{},[898,18038,900],{},[1963,18040,2875],{},[1664,18042,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1810,18044,18045,18047,18049],{},[898,18046,900],{},[1963,18048,1970],{},[1664,18050,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,18052,1676],{},[2919,18054,18055],{"scriptlevel":2058,"displaystyle":1666},[2922,18056,18057,18065],{},[1810,18058,18059,18061,18063],{},[898,18060,2398],{},[1963,18062,2875],{},[1664,18064,4920],{},[1810,18066,18067,18069,18071],{},[898,18068,2398],{},[1963,18070,1970],{},[1664,18072,4920],{},[902,18074,18075],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,18078,18080],{"className":18079},[886],[888,18081,18082],{"xmlns":890},[892,18083,18084,18116],{},[895,18085,18086,18088,18090,18092,18094,18096],{},[898,18087,1956],{},[898,18089,1959],{},[898,18091,1703],{},[898,18093,2351],{},[1664,18095,1676],{},[2919,18097,18098],{"scriptlevel":2058,"displaystyle":1666},[2922,18099,18100,18108],{},[1810,18101,18102,18104,18106],{},[898,18103,2398],{},[1963,18105,2875],{},[1664,18107,4920],{},[1810,18109,18110,18112,18114],{},[898,18111,2398],{},[1963,18113,1970],{},[1664,18115,4920],{},[902,18117,18118],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,18120,18122],{"id":18121},"minimalizace-výdajů","Minimalizace výdajů",[724,18124,18125,18126,1977],{},"Podmínka dané užitečnosti ",[883,18127,18129],{"className":18128},[886],[888,18130,18131],{"xmlns":890},[892,18132,18133,18163],{},[895,18134,18135,18141,18143,18145,18147,18153,18155,18161],{},[1720,18136,18137,18139],{},[898,18138,900],{},[1664,18140,4920],{},[1664,18142,1676],{},[898,18144,900],{},[1664,18146,1667],{"stretchy":1666},[2355,18148,18149,18151],{},[898,18150,1973],{},[1963,18152,2875],{},[1664,18154,1916],{"separator":1915},[2355,18156,18157,18159],{},[898,18158,1973],{},[1963,18160,1970],{},[1664,18162,1673],{"stretchy":1666},[902,18164,18165],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,18167,18168],{},[883,18169,18171],{"className":18170},[886],[888,18172,18173],{"xmlns":890},[892,18174,18175,18269],{},[895,18176,18177,18179,18181,18187,18189,18195,18197,18199,18201,18203,18211,18217,18219,18227,18233,18235,18237,18239,18245,18247,18249,18251,18257,18259,18265,18267],{},[898,18178,10358],{},[1664,18180,1667],{"stretchy":1666},[2355,18182,18183,18185],{},[898,18184,1973],{},[1963,18186,2875],{},[1664,18188,1916],{"separator":1915},[2355,18190,18191,18193],{},[898,18192,1973],{},[1963,18194,1970],{},[1664,18196,1916],{"separator":1915},[898,18198,16943],{},[1664,18200,1673],{"stretchy":1666},[1664,18202,1676],{},[1810,18204,18205,18207,18209],{},[898,18206,2398],{},[1963,18208,2875],{},[1664,18210,4920],{},[2355,18212,18213,18215],{},[898,18214,1973],{},[1963,18216,2875],{},[1664,18218,1700],{},[1810,18220,18221,18223,18225],{},[898,18222,2398],{},[1963,18224,1970],{},[1664,18226,4920],{},[2355,18228,18229,18231],{},[898,18230,1973],{},[1963,18232,1970],{},[1664,18234,1700],{},[898,18236,16943],{},[1664,18238,1667],{"stretchy":1666},[1720,18240,18241,18243],{},[898,18242,900],{},[1664,18244,4920],{},[1664,18246,1867],{},[898,18248,900],{},[1664,18250,1667],{"stretchy":1666},[2355,18252,18253,18255],{},[898,18254,1973],{},[1963,18256,2875],{},[1664,18258,1916],{"separator":1915},[2355,18260,18261,18263],{},[898,18262,1973],{},[1963,18264,1970],{},[1664,18266,1673],{"stretchy":1666},[1664,18268,1673],{"stretchy":1666},[902,18270,18271],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,18273,18274,18275,1977],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,18276,18278],{"className":18277},[886],[888,18279,18280],{"xmlns":890},[892,18281,18282,18321],{},[895,18283,18284,18291,18293,18299,18301,18307,18309,18315,18317,18319],{},[2355,18285,18286,18288],{},[898,18287,1973],{},[898,18289,18290],{},"i",[1664,18292,1676],{},[2355,18294,18295,18297],{},[898,18296,2379],{},[898,18298,18290],{},[1664,18300,1667],{"stretchy":1666},[2355,18302,18303,18305],{},[898,18304,2398],{},[1963,18306,2875],{},[1664,18308,1916],{"separator":1915},[2355,18310,18311,18313],{},[898,18312,2398],{},[1963,18314,1970],{},[1664,18316,1916],{"separator":1915},[898,18318,900],{},[1664,18320,1673],{"stretchy":1666},[902,18322,18323],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,18325,2497],{"id":2496},[120,18327,18328,18335,18342,18351],{},[123,18329,18330,1885,18332],{},[38,18331,2504],{},[207,18333,784],{"className":18334,"dataFsResolvedFilePath":782,"href":783},[210],[123,18336,18337,1885,18339],{},[38,18338,2512],{},[207,18340,2493],{"className":18341,"dataFsResolvedFilePath":800,"href":801},[210],[123,18343,18344,1885,18347,18350],{},[38,18345,18346],{},"Aplikace v kurzu:",[207,18348,880],{"className":18349,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,18352,18353,1885,18355,1343,18358,18361],{},[38,18354,2520],{},[207,18356,936],{"className":18357,"dataFsResolvedFilePath":934,"href":935},[210],[207,18359,1400],{"className":18360,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":18363},[18364,18365,18366,18367,18368,18369,18373],{"id":16911,"depth":642,"text":16912},{"id":3827,"depth":642,"text":3828},{"id":3901,"depth":642,"text":3902},{"id":17526,"depth":642,"text":17527},{"id":17638,"depth":642,"text":17639},{"id":17740,"depth":642,"text":17741,"children":18370},[18371,18372],{"id":17744,"depth":649,"text":17745},{"id":18121,"depth":649,"text":18122},{"id":2496,"depth":642,"text":2497},[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":16780,"description":18375},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,18382,18383],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":18386,"title":936,"body":18387,"course":1128,"courses":659,"created":10119,"description":641,"extension":661,"meta":28255,"navigation":664,"path":28256,"seo":28257,"sources":28258,"stem":28259,"tags":28260,"type":2553,"updated":677,"__hash__":28264},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":18388,"toc":28217},[18389,18392,18394,18517,18652,18656,18659,18772,18776,18804,18851,18854,18920,18965,18968,18994,19025,19029,19033,19077,19121,19183,19238,19241,19245,19248,19295,19392,19498,19504,19581,19610,19749,19753,19782,19832,19979,20069,20073,20099,20137,20164,20202,20264,20339,20417,20475,20541,20585,20589,20647,20696,20741,20954,21074,21080,21084,21107,21111,21118,21122,21153,21188,21192,21242,21330,21372,21393,21455,21515,21519,21590,21658,21730,21845,21893,21897,21900,21941,21980,22003,22117,22281,22289,22316,22346,22349,22426,22579,22663,23002,23006,23130,23266,23402,23455,23458,23708,23789,23793,23796,23854,23886,23889,23938,23941,24012,24208,24212,24363,24593,24631,24684,24730,24733,24789,24838,25042,25132,25136,25152,25159,25328,25332,25403,25484,25565,25644,25790,25878,25882,26065,26196,26241,26338,26342,27081,27083,28134,28136],[12,18390,936],{"id":18391},"národní-důchod",[115,18393,12505],{"id":12504},[724,18395,18396,18397,1885,18401,18404,18405,1885,18408,18421,18422,18425,18426,18429,18430,18433,18434,18436,18437,1885,18439,18456,18457,18474,18475,18478,18479,4488],{},"Kapitola 7 ",[207,18398,18400],{"className":18399,"dataFsResolvedFilePath":2575,"href":2576},[210],"Matematické ekonomie",[38,18402,18403],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,18406,18407],{},"národním důchodem",[883,18409,18411],{"className":18410},[886],[888,18412,18413],{"xmlns":890},[892,18414,18415,18419],{},[895,18416,18417],{},[898,18418,9692],{},[902,18420,9692],{"encoding":904},". Budují se postupně bohatší modely — ",[38,18423,18424],{},"C-I"," (jen spotřeba a investice) → ",[38,18427,18428],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,18431,18432],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,18435,12510],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,18438,14384],{},[883,18440,18442],{"className":18441},[886],[888,18443,18444],{"xmlns":890},[892,18445,18446,18454],{},[895,18447,18448],{},[1720,18449,18450,18452],{},[898,18451,9692],{},[898,18453,4819],{},[902,18455,14402],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,18458,18460],{"className":18459},[886],[888,18461,18462],{"xmlns":890},[892,18463,18464,18472],{},[895,18465,18466],{},[1720,18467,18468,18470],{},[898,18469,9692],{},[898,18471,4819],{},[902,18473,14402],{"encoding":904}," na exogenní veličiny popisují ",[38,18476,18477],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,18480,18482],{"className":18481},[886],[888,18483,18484],{"xmlns":890},[892,18485,18486,18514],{},[895,18487,18488,18490,18492,18494,18496,18498,18500,18502,18504,18506,18508,18510,18512],{},[1963,18489,2875],{},[898,18491,5240],{"mathvariant":1726},[1664,18493,1667],{"stretchy":1666},[1963,18495,2875],{},[1664,18497,1867],{},[898,18499,207],{},[1664,18501,1673],{"stretchy":1666},[1664,18503,1676],{},[1963,18505,2875],{},[898,18507,5240],{"mathvariant":1726},[898,18509,1956],{},[898,18511,2398],{},[898,18513,2351],{},[902,18515,18516],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[4436,18518,18519],{},[724,18520,18521,18523,18524,18527,18528,18546,18547,18577,18578,18625,18626,18628,18629,18651],{},[883,18522,4723],{}," Intuice\n",[38,18525,18526],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,18529,18531],{"className":18530},[886],[888,18532,18533],{"xmlns":890},[892,18534,18535,18543],{},[895,18536,18537,18539,18541],{},[898,18538,1956],{},[898,18540,2398],{},[898,18542,1703],{},[902,18544,18545],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,18548,18550],{"className":18549},[886],[888,18551,18552],{"xmlns":890},[892,18553,18554,18574],{},[895,18555,18556,18558,18560,18562,18564,18566,18568,18570,18572],{},[898,18557,1956],{},[898,18559,2398],{},[898,18561,2351],{},[1664,18563,1676],{},[1963,18565,2875],{},[1664,18567,1867],{},[898,18569,1956],{},[898,18571,2398],{},[898,18573,1703],{},[902,18575,18576],{"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 ",[883,18579,18581],{"className":18580},[886],[888,18582,18583],{"xmlns":890},[892,18584,18585,18622],{},[895,18586,18587,18589,18591,18593,18595,18601,18603,18606,18608,18610,18612,18614,18616,18618,18620],{},[1963,18588,2875],{},[1664,18590,1700],{},[898,18592,207],{},[1664,18594,1700],{},[1720,18596,18597,18599],{},[898,18598,207],{},[1963,18600,1970],{},[1664,18602,1700],{},[1664,18604,18605],{},"⋯",[1664,18607,1676],{},[1963,18609,2875],{},[898,18611,5240],{"mathvariant":1726},[1664,18613,1667],{"stretchy":1666},[1963,18615,2875],{},[1664,18617,1867],{},[898,18619,207],{},[1664,18621,1673],{"stretchy":1666},[902,18623,18624],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,18627,12510],{}," 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 ",[883,18630,18632],{"className":18631},[886],[888,18633,18634],{"xmlns":890},[892,18635,18636,18648],{},[895,18637,18638,18640,18642,18644,18646],{},[1664,18639,1667],{"stretchy":1666},[898,18641,9692],{},[1664,18643,1916],{"separator":1915},[898,18645,12540],{},[1664,18647,1673],{"stretchy":1666},[902,18649,18650],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,18653,18655],{"id":18654},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,18657,18658],{},"Po prostudování kapitoly by čtenář měl umět:",[120,18660,18661,18664,18667,18670,18673,18676,18679,18769],{},[123,18662,18663],{},"popsat zjednodušený model národní ekonomiky,",[123,18665,18666],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,18668,18669],{},"popsat lineární model spotřeby a úspor,",[123,18671,18672],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,18674,18675],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,18677,18678],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,18680,18681,18682,1343,18699,1343,18721,4454,18746,18768],{},"popsat modely ",[883,18683,18685],{"className":18684},[886],[888,18686,18687],{"xmlns":890},[892,18688,18689,18697],{},[895,18690,18691,18693,18695],{},[898,18692,1703],{},[1690,18694,12789],{},[898,18696,12683],{},[902,18698,12794],{"encoding":904},[883,18700,18702],{"className":18701},[886],[888,18703,18704],{"xmlns":890},[892,18705,18706,18718],{},[895,18707,18708,18710,18712,18714,18716],{},[898,18709,1703],{},[1690,18711,12789],{},[898,18713,12683],{},[1690,18715,12789],{},[898,18717,12611],{},[902,18719,18720],{"encoding":904},"C\\text{-}I\\text{-}G",[883,18722,18724],{"className":18723},[886],[888,18725,18726],{"xmlns":890},[892,18727,18728,18744],{},[895,18729,18730,18732,18734,18736,18738,18740,18742],{},[898,18731,1703],{},[1690,18733,12789],{},[898,18735,12683],{},[1690,18737,12789],{},[898,18739,12611],{},[1690,18741,12789],{},[898,18743,12819],{},[902,18745,12822],{"encoding":904},[883,18747,18749],{"className":18748},[886],[888,18750,18751],{"xmlns":890},[892,18752,18753,18765],{},[895,18754,18755,18757,18759,18761,18763],{},[898,18756,12683],{},[898,18758,2351],{},[1690,18760,12789],{},[898,18762,10358],{},[898,18764,1956],{},[902,18766,18767],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,18770,18771],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,18773,18775],{"id":18774},"gnp-a-národní-důchod","GNP a národní důchod",[724,18777,18778,1885,18781,10588,18800,18803],{},[38,18779,18780],{},"Hrubý národní produkt",[883,18782,18784],{"className":18783},[886],[888,18785,18786],{"xmlns":890},[892,18787,18788,18797],{},[895,18789,18790,18792,18795],{},[898,18791,12611],{},[898,18793,18794],{},"N",[898,18796,2398],{},[902,18798,18799],{"encoding":904},"GNP",[614,18801,18802],{},"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:",[724,18805,18806],{},[883,18807,18809],{"className":18808},[886],[888,18810,18811],{"xmlns":890},[892,18812,18813,18848],{},[895,18814,18815,18817,18819,18821,18823,18825,18827,18829,18831,18833,18835,18837,18839,18841,18843,18846],{},[898,18816,12611],{},[898,18818,18794],{},[898,18820,2398],{},[1664,18822,1676],{},[898,18824,1703],{},[1664,18826,1700],{},[898,18828,12683],{},[1664,18830,1700],{},[898,18832,12611],{},[1664,18834,1700],{},[898,18836,12819],{},[1664,18838,1916],{"separator":1915},[6444,18840],{"width":6446},[1664,18842,1667],{"stretchy":1666},[1963,18844,18845],{},"7.1",[1664,18847,1673],{"stretchy":1666},[902,18849,18850],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,18852,18853],{},"kde",[120,18855,18856,18872,18888,18904],{},[123,18857,18858,18871],{},[883,18859,18861],{"className":18860},[886],[888,18862,18863],{"xmlns":890},[892,18864,18865,18869],{},[895,18866,18867],{},[898,18868,1703],{},[902,18870,1703],{"encoding":904}," — výdaje domácností na spotřebu,",[123,18873,18874,18887],{},[883,18875,18877],{"className":18876},[886],[888,18878,18879],{"xmlns":890},[892,18880,18881,18885],{},[895,18882,18883],{},[898,18884,12683],{},[902,18886,12683],{"encoding":904}," — hrubé domácí investice,",[123,18889,18890,18903],{},[883,18891,18893],{"className":18892},[886],[888,18894,18895],{"xmlns":890},[892,18896,18897,18901],{},[895,18898,18899],{},[898,18900,12611],{},[902,18902,12611],{"encoding":904}," — vládní výdaje,",[123,18905,18906,18919],{},[883,18907,18909],{"className":18908},[886],[888,18910,18911],{"xmlns":890},[892,18912,18913,18917],{},[895,18914,18915],{},[898,18916,12819],{},[902,18918,12819],{"encoding":904}," — čistý export.",[724,18921,18922,18923,18940,18941,18944,18945,1885,18948,10588,18961,18964],{},"K měření ",[883,18924,18926],{"className":18925},[886],[888,18927,18928],{"xmlns":890},[892,18929,18930,18938],{},[895,18931,18932,18934,18936],{},[898,18933,12611],{},[898,18935,18794],{},[898,18937,2398],{},[902,18939,18799],{"encoding":904}," se užívá ",[38,18942,18943],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,18946,18947],{},"národní důchod",[883,18949,18951],{"className":18950},[886],[888,18952,18953],{"xmlns":890},[892,18954,18955,18959],{},[895,18956,18957],{},[898,18958,9692],{},[902,18960,9692],{"encoding":904},[614,18962,18963],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,18966,18967],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,18969,18970],{},[883,18971,18973],{"className":18972},[886],[888,18974,18975],{"xmlns":890},[892,18976,18977,18991],{},[895,18978,18979,18981,18983,18985,18987,18989],{},[898,18980,12611],{},[898,18982,18794],{},[898,18984,2398],{},[1664,18986,3315],{},[898,18988,9692],{},[1664,18990,1916],{"separator":1915},[902,18992,18993],{"encoding":904},"GNP \\approx Y,",[724,18995,18996,18997,10588,19000,19003,19004,19017,19018,19021,19022,1977],{},"a užívá se společného názvu ",[38,18998,18999],{},"důchod",[614,19001,19002],{},"income",") s označením ",[883,19005,19007],{"className":19006},[886],[888,19008,19009],{"xmlns":890},[892,19010,19011,19015],{},[895,19012,19013],{},[898,19014,9692],{},[902,19016,9692],{"encoding":904},". Domácnosti důchod použijí ke ",[38,19019,19020],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,19023,19024],{},"úspor",[115,19026,19028],{"id":19027},"spotřeba-a-úspory","Spotřeba a úspory",[198,19030,19032],{"id":19031},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,19034,19035,19036,19049,19050,19063,19064,2087],{},"Jak spotřeba ",[883,19037,19039],{"className":19038},[886],[888,19040,19041],{"xmlns":890},[892,19042,19043,19047],{},[895,19044,19045],{},[898,19046,1703],{},[902,19048,1703],{"encoding":904},", tak úspory ",[883,19051,19053],{"className":19052},[886],[888,19054,19055],{"xmlns":890},[892,19056,19057,19061],{},[895,19058,19059],{},[898,19060,2351],{},[902,19062,2351],{"encoding":904}," závisejí na důchodu ",[883,19065,19067],{"className":19066},[886],[888,19068,19069],{"xmlns":890},[892,19070,19071,19075],{},[895,19072,19073],{},[898,19074,9692],{},[902,19076,9692],{"encoding":904},[724,19078,19079],{},[883,19080,19082],{"className":19081},[886],[888,19083,19084],{"xmlns":890},[892,19085,19086,19118],{},[895,19087,19088,19090,19092,19094,19096,19098,19100,19102,19104,19106,19108,19110,19112,19114,19116],{},[898,19089,1703],{},[1664,19091,1676],{},[898,19093,1703],{},[1664,19095,1667],{"stretchy":1666},[898,19097,9692],{},[1664,19099,1673],{"stretchy":1666},[1664,19101,1916],{"separator":1915},[6444,19103],{"width":6446},[898,19105,2351],{},[1664,19107,1676],{},[898,19109,2351],{},[1664,19111,1667],{"stretchy":1666},[898,19113,9692],{},[1664,19115,1673],{"stretchy":1666},[898,19117,1977],{"mathvariant":1726},[902,19119,19120],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,19122,19123,1762,19142,10588,19145,19148,19149,1762,19169,10588,19172,19175,19176,4454,19179,19182],{},[883,19124,19126],{"className":19125},[886],[888,19127,19128],{"xmlns":890},[892,19129,19130,19140],{},[895,19131,19132,19134,19136,19138],{},[898,19133,1703],{},[1664,19135,1667],{"stretchy":1666},[898,19137,9692],{},[1664,19139,1673],{"stretchy":1666},[902,19141,14715],{"encoding":904},[38,19143,19144],{},"funkce spotřeby",[614,19146,19147],{},"consumption function","), ",[883,19150,19152],{"className":19151},[886],[888,19153,19154],{"xmlns":890},[892,19155,19156,19166],{},[895,19157,19158,19160,19162,19164],{},[898,19159,2351],{},[1664,19161,1667],{"stretchy":1666},[898,19163,9692],{},[1664,19165,1673],{"stretchy":1666},[902,19167,19168],{"encoding":904},"S(Y)",[38,19170,19171],{},"funkce úspor",[614,19173,19174],{},"savings function","); jejich grafy se nazývají ",[38,19177,19178],{},"křivka spotřeby",[38,19180,19181],{},"křivka úspor",". Platí základní identita",[724,19184,19185],{},[883,19186,19188],{"className":19187},[886],[888,19189,19190],{"xmlns":890},[892,19191,19192,19235],{},[895,19193,19194,19196,19198,19200,19202,19204,19206,19208,19210,19212,19214,19216,19218,19220,19222,19224,19226,19228,19230,19233],{},[898,19195,9692],{},[1664,19197,1676],{},[898,19199,1703],{},[1664,19201,1700],{},[898,19203,2351],{},[1664,19205,1676],{},[898,19207,1703],{},[1664,19209,1667],{"stretchy":1666},[898,19211,9692],{},[1664,19213,1673],{"stretchy":1666},[1664,19215,1700],{},[898,19217,2351],{},[1664,19219,1667],{"stretchy":1666},[898,19221,9692],{},[1664,19223,1673],{"stretchy":1666},[898,19225,1977],{"mathvariant":1726},[6444,19227],{"width":6446},[1664,19229,1667],{"stretchy":1666},[1963,19231,19232],{},"7.2",[1664,19234,1673],{"stretchy":1666},[902,19236,19237],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,19239,19240],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,19242,19244],{"id":19243},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,19246,19247],{},"Nejjednodušší model předpokládá lineární tvar",[724,19249,19250],{},[883,19251,19253],{"className":19252},[886],[888,19254,19255],{"xmlns":890},[892,19256,19257,19292],{},[895,19258,19259,19261,19263,19265,19267,19269,19271,19273,19275,19277,19279,19281,19283,19285,19287,19290],{},[898,19260,1703],{},[1664,19262,1676],{},[898,19264,1703],{},[1664,19266,1667],{"stretchy":1666},[898,19268,9692],{},[1664,19270,1673],{"stretchy":1666},[1664,19272,1676],{},[898,19274,207],{},[898,19276,9692],{},[1664,19278,1700],{},[898,19280,1818],{},[1664,19282,1916],{"separator":1915},[6444,19284],{"width":6446},[1664,19286,1667],{"stretchy":1666},[1963,19288,19289],{},"7.3",[1664,19291,1673],{"stretchy":1666},[902,19293,19294],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,19296,1709,19297,4454,19315,19337,19338,19378,19379,1977],{},[883,19298,19300],{"className":19299},[886],[888,19301,19302],{"xmlns":890},[892,19303,19304,19312],{},[895,19305,19306,19308,19310],{},[898,19307,1818],{},[1664,19309,3984],{},[1963,19311,2058],{},[902,19313,19314],{"encoding":904},"b > 0",[883,19316,19318],{"className":19317},[886],[888,19319,19320],{"xmlns":890},[892,19321,19322,19334],{},[895,19323,19324,19326,19328,19330,19332],{},[1963,19325,2058],{},[1664,19327,4022],{},[898,19329,207],{},[1664,19331,4022],{},[1963,19333,2875],{},[902,19335,19336],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,19339,19341],{"className":19340},[886],[888,19342,19343],{"xmlns":890},[892,19344,19345,19375],{},[895,19346,19347,19349,19351,19358,19360,19363,19365,19367,19369,19371,19373],{},[898,19348,207],{},[1664,19350,1676],{},[895,19352,19353,19356],{},[898,19354,19355],{"mathvariant":1726},"t",[898,19357,11602],{"mathvariant":1726},[1690,19359,1692],{},[898,19361,19362],{},"α",[1664,19364,1676],{},[898,19366,3468],{"mathvariant":1726},[898,19368,1703],{},[898,19370,5240],{"mathvariant":1726},[898,19372,3468],{"mathvariant":1726},[898,19374,9692],{},[902,19376,19377],{"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 ",[883,19380,19382],{"className":19381},[886],[888,19383,19384],{"xmlns":890},[892,19385,19386,19390],{},[895,19387,19388],{},[898,19389,9692],{},[902,19391,9692],{"encoding":904},[724,19393,19394],{},[614,19395,19396,19397,19421,19422,19460,19461,19477,19478,1977],{},"Obrázek 7.1 — Přímka spotřeby ",[883,19398,19400],{"className":19399},[886],[888,19401,19402],{"xmlns":890},[892,19403,19404,19418],{},[895,19405,19406,19408,19410,19412,19414,19416],{},[898,19407,1703],{},[1664,19409,1676],{},[898,19411,207],{},[898,19413,9692],{},[1664,19415,1700],{},[898,19417,1818],{},[902,19419,19420],{"encoding":904},"C = aY + b"," se směrnicí ",[883,19423,19425],{"className":19424},[886],[888,19426,19427],{"xmlns":890},[892,19428,19429,19457],{},[895,19430,19431,19433,19435,19441,19443,19445,19447,19449,19451,19453,19455],{},[898,19432,207],{},[1664,19434,1676],{},[895,19436,19437,19439],{},[898,19438,19355],{"mathvariant":1726},[898,19440,11602],{"mathvariant":1726},[1690,19442,1692],{},[898,19444,19362],{},[1664,19446,1676],{},[898,19448,3468],{"mathvariant":1726},[898,19450,1703],{},[898,19452,5240],{"mathvariant":1726},[898,19454,3468],{"mathvariant":1726},[898,19456,9692],{},[902,19458,19459],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,19462,19464],{"className":19463},[886],[888,19465,19466],{"xmlns":890},[892,19467,19468,19474],{},[895,19469,19470,19472],{},[898,19471,3468],{"mathvariant":1726},[898,19473,1703],{},[902,19475,19476],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,19479,19481],{"className":19480},[886],[888,19482,19483],{"xmlns":890},[892,19484,19485,19495],{},[895,19486,19487,19489,19491,19493],{},[898,19488,3468],{"mathvariant":1726},[898,19490,9692],{},[1664,19492,1676],{},[1963,19494,2875],{},[902,19496,19497],{"encoding":904},"\\Delta Y = 1",[724,19499,19500,19501,2087],{},"Dosazením do (7.2) plyne ",[38,19502,19503],{},"lineární model úspor",[724,19505,19506],{},[883,19507,19509],{"className":19508},[886],[888,19510,19511],{"xmlns":890},[892,19512,19513,19578],{},[895,19514,19515,19517,19519,19521,19523,19525,19527,19529,19531,19533,19535,19537,19539,19541,19543,19545,19547,19549,19551,19553,19555,19557,19559,19561,19563,19565,19567,19569,19571,19573,19576],{},[898,19516,2351],{},[1664,19518,1676],{},[898,19520,9692],{},[1664,19522,1867],{},[898,19524,1703],{},[1664,19526,1667],{"stretchy":1666},[898,19528,9692],{},[1664,19530,1673],{"stretchy":1666},[1664,19532,1676],{},[898,19534,9692],{},[1664,19536,1867],{},[1664,19538,1667],{"stretchy":1666},[898,19540,207],{},[898,19542,9692],{},[1664,19544,1700],{},[898,19546,1818],{},[1664,19548,1673],{"stretchy":1666},[1664,19550,1676],{},[1664,19552,1667],{"stretchy":1666},[1963,19554,2875],{},[1664,19556,1867],{},[898,19558,207],{},[1664,19560,1673],{"stretchy":1666},[898,19562,9692],{},[1664,19564,1867],{},[898,19566,1818],{},[898,19568,1977],{"mathvariant":1726},[6444,19570],{"width":6446},[1664,19572,1667],{"stretchy":1666},[1963,19574,19575],{},"7.4",[1664,19577,1673],{"stretchy":1666},[902,19579,19580],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,19582,19583,19584,4488],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,19585,19587],{"className":19586},[886],[888,19588,19589],{"xmlns":890},[892,19590,19591,19607],{},[895,19592,19593,19595,19597,19599,19601,19603,19605],{},[1963,19594,2058],{},[1664,19596,4022],{},[1963,19598,2875],{},[1664,19600,1867],{},[898,19602,207],{},[1664,19604,4022],{},[1963,19606,2875],{},[902,19608,19609],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,19611,19612],{},[614,19613,19614,19615,4454,19638,19670,19671,3210,19684,19714,19715,3210,19733,1977],{},"Obrázek 7.2 — Přímky ",[883,19616,19618],{"className":19617},[886],[888,19619,19620],{"xmlns":890},[892,19621,19622,19636],{},[895,19623,19624,19626,19628,19630,19632,19634],{},[898,19625,1703],{},[1664,19627,1676],{},[898,19629,207],{},[898,19631,9692],{},[1664,19633,1700],{},[898,19635,1818],{},[902,19637,19420],{"encoding":904},[883,19639,19641],{"className":19640},[886],[888,19642,19643],{"xmlns":890},[892,19644,19645,19667],{},[895,19646,19647,19649,19651,19653,19655,19657,19659,19661,19663,19665],{},[898,19648,2351],{},[1664,19650,1676],{},[1664,19652,1667],{"stretchy":1666},[1963,19654,2875],{},[1664,19656,1867],{},[898,19658,207],{},[1664,19660,1673],{"stretchy":1666},[898,19662,9692],{},[1664,19664,1867],{},[898,19666,1818],{},[902,19668,19669],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,19672,19674],{"className":19673},[886],[888,19675,19676],{"xmlns":890},[892,19677,19678,19682],{},[895,19679,19680],{},[898,19681,9692],{},[902,19683,9692],{"encoding":904},[883,19685,19687],{"className":19686},[886],[888,19688,19689],{"xmlns":890},[892,19690,19691,19711],{},[895,19692,19693,19695,19697,19699,19701,19703,19705,19707,19709],{},[898,19694,9692],{},[1664,19696,1676],{},[898,19698,1818],{},[898,19700,5240],{"mathvariant":1726},[1664,19702,1667],{"stretchy":1666},[1963,19704,2875],{},[1664,19706,1867],{},[898,19708,207],{},[1664,19710,1673],{"stretchy":1666},[902,19712,19713],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,19716,19718],{"className":19717},[886],[888,19719,19720],{"xmlns":890},[892,19721,19722,19730],{},[895,19723,19724,19726,19728],{},[898,19725,1703],{},[1664,19727,1916],{"separator":1915},[898,19729,2351],{},[902,19731,19732],{"encoding":904},"C, S",[883,19734,19736],{"className":19735},[886],[888,19737,19738],{"xmlns":890},[892,19739,19740,19746],{},[895,19741,19742,19744],{},[1664,19743,1867],{},[898,19745,1818],{},[902,19747,19748],{"encoding":904},"-b",[198,19750,19752],{"id":19751},"příklad-71","Příklad 7.1",[724,19754,19755,19756,19781],{},"Pro spotřebu ",[883,19757,19759],{"className":19758},[886],[888,19760,19761],{"xmlns":890},[892,19762,19763,19778],{},[895,19764,19765,19767,19769,19772,19774,19776],{},[898,19766,1703],{},[1664,19768,1676],{},[1963,19770,19771],{},"0,4",[898,19773,9692],{},[1664,19775,1700],{},[1963,19777,3442],{},[902,19779,19780],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,19783,19784],{},[883,19785,19787],{"className":19786},[886],[888,19788,19789],{"xmlns":890},[892,19790,19791,19829],{},[895,19792,19793,19795,19797,19799,19801,19803,19805,19807,19809,19811,19813,19815,19817,19819,19822,19824,19826],{},[898,19794,2351],{},[1664,19796,1676],{},[898,19798,9692],{},[1664,19800,1867],{},[898,19802,1703],{},[1664,19804,1676],{},[898,19806,9692],{},[1664,19808,1867],{},[1963,19810,19771],{},[898,19812,9692],{},[1664,19814,1867],{},[1963,19816,3442],{},[1664,19818,1676],{},[1963,19820,19821],{},"0,6",[898,19823,9692],{},[1664,19825,1867],{},[1963,19827,19828],{},"10.",[902,19830,19831],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,19833,19834],{},[614,19835,19836,19837,4454,19860,19884,19885,1762,19898,19922,19923,1762,19940,19956,19957,1977],{},"Obrázek 7.3 — Přímky ",[883,19838,19840],{"className":19839},[886],[888,19841,19842],{"xmlns":890},[892,19843,19844,19858],{},[895,19845,19846,19848,19850,19852,19854,19856],{},[898,19847,1703],{},[1664,19849,1676],{},[1963,19851,19771],{},[898,19853,9692],{},[1664,19855,1700],{},[1963,19857,3442],{},[902,19859,19780],{"encoding":904},[883,19861,19863],{"className":19862},[886],[888,19864,19865],{"xmlns":890},[892,19866,19867,19881],{},[895,19868,19869,19871,19873,19875,19877,19879],{},[898,19870,2351],{},[1664,19872,1676],{},[1963,19874,19821],{},[898,19876,9692],{},[1664,19878,1867],{},[1963,19880,3442],{},[902,19882,19883],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,19886,19888],{"className":19887},[886],[888,19889,19890],{"xmlns":890},[892,19891,19892,19896],{},[895,19893,19894],{},[898,19895,9692],{},[902,19897,9692],{"encoding":904},[883,19899,19901],{"className":19900},[886],[888,19902,19903],{"xmlns":890},[892,19904,19905,19919],{},[895,19906,19907,19909,19912],{},[1664,19908,3315],{},[1963,19910,19911],{},"16,",[8951,19913,19914,19916],{"accent":1915},[1963,19915,2833],{},[1664,19917,19918],{},"ˉ",[902,19920,19921],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,19924,19926],{"className":19925},[886],[888,19927,19928],{"xmlns":890},[892,19929,19930,19938],{},[895,19931,19932,19934,19936],{},[898,19933,1703],{},[1664,19935,1916],{"separator":1915},[898,19937,2351],{},[902,19939,19732],{"encoding":904},[883,19941,19943],{"className":19942},[886],[888,19944,19945],{"xmlns":890},[892,19946,19947,19953],{},[895,19948,19949,19951],{},[1664,19950,1867],{},[1963,19952,3442],{},[902,19954,19955],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,19958,19960],{"className":19959},[886],[888,19961,19962],{"xmlns":890},[892,19963,19964,19976],{},[895,19965,19966,19968,19970,19972,19974],{},[1664,19967,1667],{"stretchy":1666},[1963,19969,2058],{},[1664,19971,1916],{"separator":1915},[1963,19973,3442],{},[1664,19975,1673],{"stretchy":1666},[902,19977,19978],{"encoding":904},"(0, 10)",[724,19980,19981,19982,1762,20000,20030,20031,10588,20034,20037,20038,1762,20062,10588,20065,20068],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,19983,19985],{"className":19984},[886],[888,19986,19987],{"xmlns":890},[892,19988,19989,19997],{},[895,19990,19991,19993,19995],{},[898,19992,9692],{},[1664,19994,1676],{},[1963,19996,2058],{},[902,19998,19999],{"encoding":904},"Y = 0",[883,20001,20003],{"className":20002},[886],[888,20004,20005],{"xmlns":890},[892,20006,20007,20027],{},[895,20008,20009,20011,20013,20015,20017,20019,20021,20023,20025],{},[898,20010,2351],{},[1664,20012,1667],{"stretchy":1666},[1963,20014,2058],{},[1664,20016,1673],{"stretchy":1666},[1664,20018,1676],{},[1664,20020,1867],{},[898,20022,1818],{},[1664,20024,4022],{},[1963,20026,2058],{},[902,20028,20029],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,20032,20033],{},"autonomních úsporách",[614,20035,20036],{},"autonomous savings","). Analogicky ",[883,20039,20041],{"className":20040},[886],[888,20042,20043],{"xmlns":890},[892,20044,20045,20059],{},[895,20046,20047,20049,20051,20053,20055,20057],{},[898,20048,1703],{},[1664,20050,1667],{"stretchy":1666},[1963,20052,2058],{},[1664,20054,1673],{"stretchy":1666},[1664,20056,1676],{},[898,20058,1818],{},[902,20060,20061],{"encoding":904},"C(0) = b",[38,20063,20064],{},"autonomní spotřeba",[614,20066,20067],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,20070,20072],{"id":20071},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,20074,20075,1885,20078,10588,20095,20098],{},[38,20076,20077],{},"Mezní sklon ke spotřebě",[883,20079,20081],{"className":20080},[886],[888,20082,20083],{"xmlns":890},[892,20084,20085,20093],{},[895,20086,20087,20089,20091],{},[898,20088,1956],{},[898,20090,2398],{},[898,20092,1703],{},[902,20094,18545],{"encoding":904},[614,20096,20097],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,20100,20101],{},[883,20102,20104],{"className":20103},[886],[888,20105,20106],{"xmlns":890},[892,20107,20108,20134],{},[895,20109,20110,20112,20114,20116,20118,20132],{},[898,20111,1956],{},[898,20113,2398],{},[898,20115,1703],{},[1664,20117,1676],{},[2922,20119,20120,20126],{},[895,20121,20122,20124],{},[898,20123,1695],{"mathvariant":1726},[898,20125,1703],{},[895,20127,20128,20130],{},[898,20129,1695],{"mathvariant":1726},[898,20131,9692],{},[898,20133,1977],{"mathvariant":1726},[902,20135,20136],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,20138,20139,1885,20142,10588,20160,20163],{},[38,20140,20141],{},"Mezní sklon k úsporám",[883,20143,20145],{"className":20144},[886],[888,20146,20147],{"xmlns":890},[892,20148,20149,20157],{},[895,20150,20151,20153,20155],{},[898,20152,1956],{},[898,20154,2398],{},[898,20156,2351],{},[902,20158,20159],{"encoding":904},"MPS",[614,20161,20162],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,20165,20166],{},[883,20167,20169],{"className":20168},[886],[888,20170,20171],{"xmlns":890},[892,20172,20173,20199],{},[895,20174,20175,20177,20179,20181,20183,20197],{},[898,20176,1956],{},[898,20178,2398],{},[898,20180,2351],{},[1664,20182,1676],{},[2922,20184,20185,20191],{},[895,20186,20187,20189],{},[898,20188,1695],{"mathvariant":1726},[898,20190,2351],{},[895,20192,20193,20195],{},[898,20194,1695],{"mathvariant":1726},[898,20196,9692],{},[898,20198,1977],{"mathvariant":1726},[902,20200,20201],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,20203,20204,20205,20263],{},"Z (7.2) plyne ",[883,20206,20208],{"className":20207},[886],[888,20209,20210],{"xmlns":890},[892,20211,20212,20260],{},[895,20213,20214,20228,20230,20244,20246],{},[2922,20215,20216,20222],{},[895,20217,20218,20220],{},[898,20219,1695],{"mathvariant":1726},[898,20221,9692],{},[895,20223,20224,20226],{},[898,20225,1695],{"mathvariant":1726},[898,20227,9692],{},[1664,20229,1676],{},[2922,20231,20232,20238],{},[895,20233,20234,20236],{},[898,20235,1695],{"mathvariant":1726},[898,20237,1703],{},[895,20239,20240,20242],{},[898,20241,1695],{"mathvariant":1726},[898,20243,9692],{},[1664,20245,1700],{},[2922,20247,20248,20254],{},[895,20249,20250,20252],{},[898,20251,1695],{"mathvariant":1726},[898,20253,2351],{},[895,20255,20256,20258],{},[898,20257,1695],{"mathvariant":1726},[898,20259,9692],{},[902,20261,20262],{"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",[724,20265,20266],{},[883,20267,20269],{"className":20268},[886],[888,20270,20271],{"xmlns":890},[892,20272,20273,20336],{},[895,20274,20275,20327,20329,20331,20334],{},[13331,20276,20277],{"notation":13333},[2919,20278,20279],{"scriptlevel":2058,"displaystyle":1666},[2919,20280,20281],{"scriptlevel":2058,"displaystyle":1666},[2919,20282,20283],{"scriptlevel":2058,"displaystyle":1915},[895,20284,20285,20287,20289,20291,20293,20295,20297,20299,20301,20303,20305,20307,20309,20311,20313,20315,20317,20319,20321,20323,20325],{},[898,20286,1956],{},[898,20288,2398],{},[898,20290,1703],{},[1664,20292,1700],{},[898,20294,1956],{},[898,20296,2398],{},[898,20298,2351],{},[1664,20300,1676],{},[1963,20302,2875],{},[1664,20304,1916],{"separator":1915},[6444,20306],{"width":6446},[898,20308,1956],{},[898,20310,2398],{},[898,20312,2351],{},[1664,20314,1676],{},[1963,20316,2875],{},[1664,20318,1867],{},[898,20320,1956],{},[898,20322,2398],{},[898,20324,1703],{},[898,20326,1977],{"mathvariant":1726},[6444,20328],{"width":6446},[1664,20330,1667],{"stretchy":1666},[1963,20332,20333],{},"7.5",[1664,20335,1673],{"stretchy":1666},[902,20337,20338],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,20340,20341,1885,20344,20367,20368,4454,20390,20416],{},[38,20342,20343],{},"Pro lineární model",[883,20345,20347],{"className":20346},[886],[888,20348,20349],{"xmlns":890},[892,20350,20351,20365],{},[895,20352,20353,20355,20357,20359,20361,20363],{},[898,20354,1703],{},[1664,20356,1676],{},[898,20358,207],{},[898,20360,9692],{},[1664,20362,1700],{},[898,20364,1818],{},[902,20366,19420],{"encoding":904}," vychází ",[883,20369,20371],{"className":20370},[886],[888,20372,20373],{"xmlns":890},[892,20374,20375,20387],{},[895,20376,20377,20379,20381,20383,20385],{},[898,20378,1956],{},[898,20380,2398],{},[898,20382,1703],{},[1664,20384,1676],{},[898,20386,207],{},[902,20388,20389],{"encoding":904},"MPC = a",[883,20391,20393],{"className":20392},[886],[888,20394,20395],{"xmlns":890},[892,20396,20397,20413],{},[895,20398,20399,20401,20403,20405,20407,20409,20411],{},[898,20400,1956],{},[898,20402,2398],{},[898,20404,2351],{},[1664,20406,1676],{},[1963,20408,2875],{},[1664,20410,1867],{},[898,20412,207],{},[902,20414,20415],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,20418,20419,20422,20423,20445,20446,20474],{},[38,20420,20421],{},"Interpretace diferenciálem."," Pro pevné ",[883,20424,20426],{"className":20425},[886],[888,20427,20428],{"xmlns":890},[892,20429,20430,20442],{},[895,20431,20432,20434,20436],{},[898,20433,9692],{},[1664,20435,1676],{},[1720,20437,20438,20440],{},[898,20439,9692],{},[1664,20441,4920],{},[902,20443,20444],{"encoding":904},"Y = Y^*"," udává ",[883,20447,20449],{"className":20448},[886],[888,20450,20451],{"xmlns":890},[892,20452,20453,20471],{},[895,20454,20455,20457,20459,20461,20463,20469],{},[898,20456,1956],{},[898,20458,2398],{},[898,20460,1703],{},[1664,20462,1667],{"stretchy":1666},[1720,20464,20465,20467],{},[898,20466,9692],{},[1664,20468,4920],{},[1664,20470,1673],{"stretchy":1666},[902,20472,20473],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,20476,20477],{},[883,20478,20480],{"className":20479},[886],[888,20481,20482],{"xmlns":890},[892,20483,20484,20538],{},[895,20485,20486,20488,20490,20492,20494,20496,20498,20504,20506,20508,20510,20512,20514,20516,20518,20520,20522,20524,20526,20528,20530,20532,20534,20536],{},[898,20487,3468],{"mathvariant":1726},[898,20489,1703],{},[1664,20491,3315],{},[898,20493,1695],{"mathvariant":1726},[898,20495,1703],{},[1664,20497,1676],{},[1720,20499,20500,20502],{},[898,20501,1703],{},[1664,20503,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,20505,1667],{"stretchy":1666},[898,20507,9692],{},[1664,20509,1673],{"stretchy":1666},[1690,20511,1692],{},[898,20513,1695],{"mathvariant":1726},[898,20515,9692],{},[1664,20517,1676],{},[898,20519,1956],{},[898,20521,2398],{},[898,20523,1703],{},[1664,20525,1667],{"stretchy":1666},[898,20527,9692],{},[1664,20529,1673],{"stretchy":1666},[1690,20531,1692],{},[898,20533,1695],{"mathvariant":1726},[898,20535,9692],{},[898,20537,1977],{"mathvariant":1726},[902,20539,20540],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,20542,20543,20544,20580,20581,20584],{},"Analogicky ",[883,20545,20547],{"className":20546},[886],[888,20548,20549],{"xmlns":890},[892,20550,20551,20577],{},[895,20552,20553,20555,20557,20559,20561,20563,20565,20567,20569,20571,20573,20575],{},[898,20554,3468],{"mathvariant":1726},[898,20556,2351],{},[1664,20558,3315],{},[898,20560,1956],{},[898,20562,2398],{},[898,20564,2351],{},[1664,20566,1667],{"stretchy":1666},[898,20568,9692],{},[1664,20570,1673],{"stretchy":1666},[1690,20572,1692],{},[898,20574,1695],{"mathvariant":1726},[898,20576,9692],{},[902,20578,20579],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,20582,1145],{"className":20583,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,20586,20588],{"id":20587},"příklad-72","Příklad 7.2",[724,20590,19755,20591,20626,20627,20646],{},[883,20592,20594],{"className":20593},[886],[888,20595,20596],{"xmlns":890},[892,20597,20598,20623],{},[895,20599,20600,20602,20604,20607,20613,20615,20617,20619,20621],{},[898,20601,1703],{},[1664,20603,1676],{},[1963,20605,20606],{},"0,001",[1720,20608,20609,20611],{},[898,20610,9692],{},[1963,20612,1970],{},[1664,20614,1700],{},[1963,20616,2154],{},[898,20618,9692],{},[1664,20620,1700],{},[1963,20622,3696],{},[902,20624,20625],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,20628,20630],{"className":20629},[886],[888,20631,20632],{"xmlns":890},[892,20633,20634,20643],{},[895,20635,20636,20638,20640],{},[898,20637,9692],{},[1664,20639,4022],{},[1963,20641,20642],{},"400",[902,20644,20645],{"encoding":904},"Y \u003C 400",") platí",[724,20648,20649],{},[883,20650,20652],{"className":20651},[886],[888,20653,20654],{"xmlns":890},[892,20655,20656,20693],{},[895,20657,20658,20660,20662,20664,20666,20680,20682,20685,20687,20689,20691],{},[898,20659,1956],{},[898,20661,2398],{},[898,20663,1703],{},[1664,20665,1676],{},[2922,20667,20668,20674],{},[895,20669,20670,20672],{},[898,20671,1695],{"mathvariant":1726},[898,20673,1703],{},[895,20675,20676,20678],{},[898,20677,1695],{"mathvariant":1726},[898,20679,9692],{},[1664,20681,1676],{},[1963,20683,20684],{},"0,002",[898,20686,9692],{},[1664,20688,1700],{},[1963,20690,2154],{},[1664,20692,1916],{"separator":1915},[902,20694,20695],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,20697,20698],{},[883,20699,20701],{"className":20700},[886],[888,20702,20703],{"xmlns":890},[892,20704,20705,20738],{},[895,20706,20707,20709,20711,20713,20715,20717,20719,20721,20723,20725,20727,20729,20731,20733,20735],{},[898,20708,1956],{},[898,20710,2398],{},[898,20712,2351],{},[1664,20714,1676],{},[1963,20716,2875],{},[1664,20718,1867],{},[898,20720,1956],{},[898,20722,2398],{},[898,20724,1703],{},[1664,20726,1676],{},[1664,20728,1867],{},[1963,20730,20684],{},[898,20732,9692],{},[1664,20734,1700],{},[1963,20736,20737],{},"0,8.",[902,20739,20740],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,20742,20743,20823,20902],{},[123,20744,20745,1343,20773,20801,20802,1762,20820,1977],{},[883,20746,20748],{"className":20747},[886],[888,20749,20750],{"xmlns":890},[892,20751,20752,20770],{},[895,20753,20754,20756,20758,20760,20762,20764,20766,20768],{},[898,20755,1956],{},[898,20757,2398],{},[898,20759,1703],{},[1664,20761,1667],{"stretchy":1666},[1963,20763,1965],{},[1664,20765,1673],{"stretchy":1666},[1664,20767,1676],{},[1963,20769,19771],{},[902,20771,20772],{"encoding":904},"MPC(100) = 0{,}4",[883,20774,20776],{"className":20775},[886],[888,20777,20778],{"xmlns":890},[892,20779,20780,20798],{},[895,20781,20782,20784,20786,20788,20790,20792,20794,20796],{},[898,20783,1956],{},[898,20785,2398],{},[898,20787,2351],{},[1664,20789,1667],{"stretchy":1666},[1963,20791,1965],{},[1664,20793,1673],{"stretchy":1666},[1664,20795,1676],{},[1963,20797,19821],{},[902,20799,20800],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,20803,20805],{"className":20804},[886],[888,20806,20807],{"xmlns":890},[892,20808,20809,20817],{},[895,20810,20811,20813,20815],{},[898,20812,9692],{},[1664,20814,1676],{},[1963,20816,1965],{},[902,20818,20819],{"encoding":904},"Y = 100",[38,20821,20822],{},"větší sklon k úsporám",[123,20824,20825,1343,20853,20801,20881,1762,20899,1977],{},[883,20826,20828],{"className":20827},[886],[888,20829,20830],{"xmlns":890},[892,20831,20832,20850],{},[895,20833,20834,20836,20838,20840,20842,20844,20846,20848],{},[898,20835,1956],{},[898,20837,2398],{},[898,20839,1703],{},[1664,20841,1667],{"stretchy":1666},[1963,20843,8942],{},[1664,20845,1673],{"stretchy":1666},[1664,20847,1676],{},[1963,20849,19821],{},[902,20851,20852],{"encoding":904},"MPC(200) = 0{,}6",[883,20854,20856],{"className":20855},[886],[888,20857,20858],{"xmlns":890},[892,20859,20860,20878],{},[895,20861,20862,20864,20866,20868,20870,20872,20874,20876],{},[898,20863,1956],{},[898,20865,2398],{},[898,20867,2351],{},[1664,20869,1667],{"stretchy":1666},[1963,20871,8942],{},[1664,20873,1673],{"stretchy":1666},[1664,20875,1676],{},[1963,20877,19771],{},[902,20879,20880],{"encoding":904},"MPS(200) = 0{,}4",[883,20882,20884],{"className":20883},[886],[888,20885,20886],{"xmlns":890},[892,20887,20888,20896],{},[895,20889,20890,20892,20894],{},[898,20891,9692],{},[1664,20893,1676],{},[1963,20895,8942],{},[902,20897,20898],{"encoding":904},"Y = 200",[38,20900,20901],{},"větší sklon ke spotřebě",[123,20903,20904,20905,20923,20924,4488],{},"Přesně při ",[883,20906,20908],{"className":20907},[886],[888,20909,20910],{"xmlns":890},[892,20911,20912,20920],{},[895,20913,20914,20916,20918],{},[898,20915,9692],{},[1664,20917,1676],{},[1963,20919,9367],{},[902,20921,20922],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,20925,20927],{"className":20926},[886],[888,20928,20929],{"xmlns":890},[892,20930,20931,20951],{},[895,20932,20933,20935,20937,20939,20941,20943,20945,20947,20949],{},[898,20934,1956],{},[898,20936,2398],{},[898,20938,1703],{},[1664,20940,1676],{},[898,20942,1956],{},[898,20944,2398],{},[898,20946,2351],{},[1664,20948,1676],{},[1963,20950,5575],{},[902,20952,20953],{"encoding":904},"MPC = MPS = 0{,}5",[724,20955,20956,20957,20974,20975,20989,20990,3271,21003,21017,21018,21031,21032,21073],{},"Interpretace: při ",[883,20958,20960],{"className":20959},[886],[888,20961,20962],{"xmlns":890},[892,20963,20964,20972],{},[895,20965,20966,20968,20970],{},[898,20967,9692],{},[1664,20969,1676],{},[1963,20971,1965],{},[902,20973,20819],{"encoding":904}," se spotřeba mění ",[883,20976,20978],{"className":20977},[886],[888,20979,20980],{"xmlns":890},[892,20981,20982,20986],{},[895,20983,20984],{},[1963,20985,19771],{},[902,20987,20988],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,20991,20993],{"className":20992},[886],[888,20994,20995],{"xmlns":890},[892,20996,20997,21001],{},[895,20998,20999],{},[1963,21000,1965],{},[902,21002,1965],{"encoding":904},[883,21004,21006],{"className":21005},[886],[888,21007,21008],{"xmlns":890},[892,21009,21010,21015],{},[895,21011,21012],{},[1963,21013,21014],{},"101",[902,21016,21014],{"encoding":904},", změní se spotřeba přibližně o ",[883,21019,21021],{"className":21020},[886],[888,21022,21023],{"xmlns":890},[892,21024,21025,21029],{},[895,21026,21027],{},[1963,21028,19771],{},[902,21030,20988],{"encoding":904},". Skutečná změna ",[883,21033,21035],{"className":21034},[886],[888,21036,21037],{"xmlns":890},[892,21038,21039,21070],{},[895,21040,21041,21043,21045,21047,21049,21051,21053,21055,21057,21059,21061,21063,21065,21067],{},[898,21042,3468],{"mathvariant":1726},[898,21044,1703],{},[1664,21046,1676],{},[898,21048,1703],{},[1664,21050,1667],{"stretchy":1666},[1963,21052,21014],{},[1664,21054,1673],{"stretchy":1666},[1664,21056,1867],{},[898,21058,1703],{},[1664,21060,1667],{"stretchy":1666},[1963,21062,1965],{},[1664,21064,1673],{"stretchy":1666},[1664,21066,1676],{},[1963,21068,21069],{},"0,401",[902,21071,21072],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,21075,21076,21077],{},"Obecný trend: ",[38,21078,21079],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,21081,21083],{"id":21082},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,21085,21086,21087,10588,21090,21093,21094,10588,21097,12627,21100,10588,21103,21106],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,21088,21089],{},"makroekonomická rovnováha",[614,21091,21092],{},"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 ",[38,21095,21096],{},"agregátní poptávky",[614,21098,21099],{},"aggregate demand",[38,21101,21102],{},"agregátní nabídky",[614,21104,21105],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,21108,21110],{"id":21109},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,21112,21113],{},[1928,21114],{"alt":21115,"className":21116,"src":21117},"imek-keynesian-kriz",[210,1932],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,21119,21121],{"id":21120},"zadání-modelu","Zadání modelu",[724,21123,21124,21125,21138,21139,21152],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,21126,21128],{"className":21127},[886],[888,21129,21130],{"xmlns":890},[892,21131,21132,21136],{},[895,21133,21134],{},[898,21135,1703],{},[902,21137,1703],{"encoding":904}," a investice ",[883,21140,21142],{"className":21141},[886],[888,21143,21144],{"xmlns":890},[892,21145,21146,21150],{},[895,21147,21148],{},[898,21149,12683],{},[902,21151,12683],{"encoding":904},". Podmínka rovnováhy:",[724,21154,21155],{},[883,21156,21158],{"className":21157},[886],[888,21159,21160],{"xmlns":890},[892,21161,21162,21185],{},[895,21163,21164,21166,21168,21170,21172,21174,21176,21178,21180,21183],{},[898,21165,9692],{},[1664,21167,1676],{},[898,21169,1703],{},[1664,21171,1700],{},[898,21173,12683],{},[898,21175,1977],{"mathvariant":1726},[6444,21177],{"width":6446},[1664,21179,1667],{"stretchy":1666},[1963,21181,21182],{},"7.6",[1664,21184,1673],{"stretchy":1666},[902,21186,21187],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,21189,21191],{"id":21190},"soustava-rovnic","Soustava rovnic",[724,21193,21194,21195,21216,21217,21241],{},"Pro pevně zadané (plánované) investice ",[883,21196,21198],{"className":21197},[886],[888,21199,21200],{"xmlns":890},[892,21201,21202,21214],{},[895,21203,21204,21206,21208],{},[898,21205,12683],{},[1664,21207,1676],{},[1720,21209,21210,21212],{},[898,21211,12683],{},[1664,21213,4920],{},[902,21215,12694],{"encoding":904}," a funkci spotřeby ",[883,21218,21220],{"className":21219},[886],[888,21221,21222],{"xmlns":890},[892,21223,21224,21238],{},[895,21225,21226,21228,21230,21232,21234,21236],{},[898,21227,1703],{},[1664,21229,1676],{},[898,21231,1703],{},[1664,21233,1667],{"stretchy":1666},[898,21235,9692],{},[1664,21237,1673],{"stretchy":1666},[902,21239,21240],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,21243,21244],{},[883,21245,21247],{"className":21246},[886],[888,21248,21249],{"xmlns":890},[892,21250,21251,21327],{},[895,21252,21253,21318,21320,21322,21325],{},[21254,21255,21258,21290],"mtable",{"rowspacing":21256,"columnalign":21257,"columnspacing":1727},"0.25em","right left",[21259,21260,21261,21268],"mtr",{},[21262,21263,21264],"mtd",{},[2919,21265,21266],{"scriptlevel":2058,"displaystyle":1915},[898,21267,9692],{},[21262,21269,21270],{},[2919,21271,21272],{"scriptlevel":2058,"displaystyle":1915},[895,21273,21274,21276,21278,21280,21282,21288],{},[895,21275],{},[1664,21277,1676],{},[898,21279,1703],{},[1664,21281,1700],{},[1720,21283,21284,21286],{},[898,21285,12683],{},[1664,21287,4920],{},[1664,21289,1916],{"separator":1915},[21259,21291,21292,21298],{},[21262,21293,21294],{},[2919,21295,21296],{"scriptlevel":2058,"displaystyle":1915},[898,21297,1703],{},[21262,21299,21300],{},[2919,21301,21302],{"scriptlevel":2058,"displaystyle":1915},[895,21303,21304,21306,21308,21310,21312,21314,21316],{},[895,21305],{},[1664,21307,1676],{},[898,21309,1703],{},[1664,21311,1667],{"stretchy":1666},[898,21313,9692],{},[1664,21315,1673],{"stretchy":1666},[1664,21317,1916],{"separator":1915},[6444,21319],{"width":6446},[1664,21321,1667],{"stretchy":1666},[1963,21323,21324],{},"7.7",[1664,21326,1673],{"stretchy":1666},[902,21328,21329],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,21331,21332,21333,1885,21335,4454,21352,1885,21355,1977],{},"jejímž řešením jsou ",[38,21334,14384],{},[883,21336,21338],{"className":21337},[886],[888,21339,21340],{"xmlns":890},[892,21341,21342,21350],{},[895,21343,21344],{},[1720,21345,21346,21348],{},[898,21347,9692],{},[898,21349,4819],{},[902,21351,14402],{"encoding":904},[38,21353,21354],{},"rovnovážná spotřeba",[883,21356,21358],{"className":21357},[886],[888,21359,21360],{"xmlns":890},[892,21361,21362,21370],{},[895,21363,21364],{},[1720,21365,21366,21368],{},[898,21367,1703],{},[898,21369,4819],{},[902,21371,14461],{"encoding":904},[198,21373,21375,21376],{"id":21374},"výpočet-yeye","Výpočet ",[883,21377,21379],{"className":21378},[886],[888,21380,21381],{"xmlns":890},[892,21382,21383,21391],{},[895,21384,21385],{},[1720,21386,21387,21389],{},[898,21388,9692],{},[898,21390,4819],{},[902,21392,14402],{"encoding":904},[724,21394,21395,21396,21419,21420,8251,21452],{},"Pro lineární spotřebu ",[883,21397,21399],{"className":21398},[886],[888,21400,21401],{"xmlns":890},[892,21402,21403,21417],{},[895,21404,21405,21407,21409,21411,21413,21415],{},[898,21406,1703],{},[1664,21408,1676],{},[898,21410,207],{},[898,21412,9692],{},[1664,21414,1700],{},[898,21416,1818],{},[902,21418,19420],{"encoding":904}," plyne z (7.7) rovnice ",[883,21421,21423],{"className":21422},[886],[888,21424,21425],{"xmlns":890},[892,21426,21427,21449],{},[895,21428,21429,21431,21433,21435,21437,21439,21441,21443],{},[898,21430,9692],{},[1664,21432,1676],{},[898,21434,207],{},[898,21436,9692],{},[1664,21438,1700],{},[898,21440,1818],{},[1664,21442,1700],{},[1720,21444,21445,21447],{},[898,21446,12683],{},[1664,21448,4920],{},[902,21450,21451],{"encoding":904},"Y = aY + b + I^*",[38,21453,21454],{},"redukovaný tvar",[724,21456,21457],{},[883,21458,21460],{"className":21459},[886],[888,21461,21462],{"xmlns":890},[892,21463,21464,21512],{},[895,21465,21466],{},[13331,21467,21468],{"notation":13333},[2919,21469,21470],{"scriptlevel":2058,"displaystyle":1666},[2919,21471,21472],{"scriptlevel":2058,"displaystyle":1666},[2919,21473,21474],{"scriptlevel":2058,"displaystyle":1915},[895,21475,21476,21478,21484,21486,21508,21510],{},[1690,21477,1692],{},[1720,21479,21480,21482],{},[898,21481,9692],{},[898,21483,4819],{},[1664,21485,1676],{},[2922,21487,21488,21500],{},[895,21489,21490,21492,21494],{},[898,21491,1818],{},[1664,21493,1700],{},[1720,21495,21496,21498],{},[898,21497,12683],{},[1664,21499,4920],{},[895,21501,21502,21504,21506],{},[1963,21503,2875],{},[1664,21505,1867],{},[898,21507,207],{},[898,21509,1977],{"mathvariant":1726},[1690,21511,1692],{},[902,21513,21514],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,21516,21518],{"id":21517},"příklad-73","Příklad 7.3",[724,21520,21521,21522,1762,21539,4454,21563,21589],{},"V modelu ",[883,21523,21525],{"className":21524},[886],[888,21526,21527],{"xmlns":890},[892,21528,21529,21537],{},[895,21530,21531,21533,21535],{},[898,21532,1703],{},[1690,21534,12789],{},[898,21536,12683],{},[902,21538,12794],{"encoding":904},[883,21540,21542],{"className":21541},[886],[888,21543,21544],{"xmlns":890},[892,21545,21546,21560],{},[895,21547,21548,21550,21552,21554,21556,21558],{},[898,21549,1703],{},[1664,21551,1676],{},[1963,21553,19821],{},[898,21555,9692],{},[1664,21557,1700],{},[1963,21559,3442],{},[902,21561,21562],{"encoding":904},"C = 0{,}6Y + 10",[883,21564,21566],{"className":21565},[886],[888,21567,21568],{"xmlns":890},[892,21569,21570,21586],{},[895,21571,21572,21574,21576,21578,21580],{},[898,21573,12683],{},[1664,21575,1676],{},[1963,21577,4084],{},[1664,21579,1676],{},[1720,21581,21582,21584],{},[898,21583,12683],{},[1664,21585,4920],{},[902,21587,21588],{"encoding":904},"I = 12 = I^*",". Soustava",[724,21591,21592],{},[883,21593,21595],{"className":21594},[886],[888,21596,21597],{"xmlns":890},[892,21598,21599,21655],{},[21254,21600,21601,21627],{"rowspacing":21256,"columnalign":21257,"columnspacing":1727},[21259,21602,21603,21609],{},[21262,21604,21605],{},[2919,21606,21607],{"scriptlevel":2058,"displaystyle":1915},[898,21608,9692],{},[21262,21610,21611],{},[2919,21612,21613],{"scriptlevel":2058,"displaystyle":1915},[895,21614,21615,21617,21619,21621,21623,21625],{},[895,21616],{},[1664,21618,1676],{},[898,21620,1703],{},[1664,21622,1700],{},[1963,21624,4084],{},[1664,21626,1916],{"separator":1915},[21259,21628,21629,21635],{},[21262,21630,21631],{},[2919,21632,21633],{"scriptlevel":2058,"displaystyle":1915},[898,21634,1703],{},[21262,21636,21637],{},[2919,21638,21639],{"scriptlevel":2058,"displaystyle":1915},[895,21640,21641,21643,21645,21647,21649,21651,21653],{},[895,21642],{},[1664,21644,1676],{},[1963,21646,19821],{},[898,21648,9692],{},[1664,21650,1700],{},[1963,21652,3442],{},[1664,21654,1916],{"separator":1915},[902,21656,21657],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,21659,21660,21661,1343,21684,21707,21708,4488],{},"má řešení ",[883,21662,21664],{"className":21663},[886],[888,21665,21666],{"xmlns":890},[892,21667,21668,21681],{},[895,21669,21670,21676,21678],{},[1720,21671,21672,21674],{},[898,21673,9692],{},[898,21675,4819],{},[1664,21677,1676],{},[1963,21679,21680],{},"55",[902,21682,21683],{"encoding":904},"Y^E = 55",[883,21685,21687],{"className":21686},[886],[888,21688,21689],{"xmlns":890},[892,21690,21691,21704],{},[895,21692,21693,21699,21701],{},[1720,21694,21695,21697],{},[898,21696,1703],{},[898,21698,4819],{},[1664,21700,1676],{},[1963,21702,21703],{},"43",[902,21705,21706],{"encoding":904},"C^E = 43"," (a ",[883,21709,21711],{"className":21710},[886],[888,21712,21713],{"xmlns":890},[892,21714,21715,21727],{},[895,21716,21717,21723,21725],{},[1720,21718,21719,21721],{},[898,21720,2351],{},[898,21722,4819],{},[1664,21724,1676],{},[1963,21726,4084],{},[902,21728,21729],{"encoding":904},"S^E = 12",[724,21731,21732],{},[614,21733,21734,21735,21757,21758,12627,21779,21802,21803,1977],{},"Obrázek 7.5 — Přímky ",[883,21736,21738],{"className":21737},[886],[888,21739,21740],{"xmlns":890},[892,21741,21742,21754],{},[895,21743,21744,21746,21748,21750,21752],{},[898,21745,1703],{},[1664,21747,1676],{},[898,21749,9692],{},[1664,21751,1867],{},[1963,21753,4084],{},[902,21755,21756],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,21759,21761],{"className":21760},[886],[888,21762,21763],{"xmlns":890},[892,21764,21765,21777],{},[895,21766,21767,21769,21771,21773,21775],{},[898,21768,9692],{},[1664,21770,1676],{},[898,21772,1703],{},[1664,21774,1700],{},[898,21776,12683],{},[902,21778,15243],{"encoding":904},[883,21780,21782],{"className":21781},[886],[888,21783,21784],{"xmlns":890},[892,21785,21786,21800],{},[895,21787,21788,21790,21792,21794,21796,21798],{},[898,21789,1703],{},[1664,21791,1676],{},[1963,21793,19821],{},[898,21795,9692],{},[1664,21797,1700],{},[1963,21799,3442],{},[902,21801,21562],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,21804,21806],{"className":21805},[886],[888,21807,21808],{"xmlns":890},[892,21809,21810,21842],{},[895,21811,21812,21814,21820,21822,21828,21830,21832,21834,21836,21838,21840],{},[1664,21813,1837],{"stretchy":1666},[1720,21815,21816,21818],{},[898,21817,9692],{},[898,21819,4819],{},[1664,21821,1916],{"separator":1915},[1720,21823,21824,21826],{},[898,21825,1703],{},[898,21827,4819],{},[1664,21829,1850],{"stretchy":1666},[1664,21831,1676],{},[1664,21833,1837],{"stretchy":1666},[1963,21835,21680],{},[1664,21837,1916],{"separator":1915},[1963,21839,21703],{},[1664,21841,1850],{"stretchy":1666},[902,21843,21844],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,21846,21847,21850,21851,21868,21869,1977],{},[38,21848,21849],{},"Komentář k přechodu."," Model ",[883,21852,21854],{"className":21853},[886],[888,21855,21856],{"xmlns":890},[892,21857,21858,21866],{},[895,21859,21860,21862,21864],{},[898,21861,1703],{},[1690,21863,12789],{},[898,21865,12683],{},[902,21867,12794],{"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 ",[38,21870,21871,21872],{},"model ",[883,21873,21875],{"className":21874},[886],[888,21876,21877],{"xmlns":890},[892,21878,21879,21891],{},[895,21880,21881,21883,21885,21887,21889],{},[898,21882,1703],{},[1690,21884,12789],{},[898,21886,12683],{},[1690,21888,12789],{},[898,21890,12611],{},[902,21892,18720],{"encoding":904},[115,21894,21896],{"id":21895},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,21898,21121],{"id":21899},"zadání-modelu-1",[724,21901,21902,21903,21920,21921,1885,21924,10588,21937,21940],{},"Rozšíření modelu ",[883,21904,21906],{"className":21905},[886],[888,21907,21908],{"xmlns":890},[892,21909,21910,21918],{},[895,21911,21912,21914,21916],{},[898,21913,1703],{},[1690,21915,12789],{},[898,21917,12683],{},[902,21919,12794],{"encoding":904}," o ",[38,21922,21923],{},"vládní výdaje",[883,21925,21927],{"className":21926},[886],[888,21928,21929],{"xmlns":890},[892,21930,21931,21935],{},[895,21932,21933],{},[898,21934,12611],{},[902,21936,12611],{"encoding":904},[614,21938,21939],{},"government expenditure","). Podmínka rovnováhy:",[724,21942,21943],{},[883,21944,21946],{"className":21945},[886],[888,21947,21948],{"xmlns":890},[892,21949,21950,21977],{},[895,21951,21952,21954,21956,21958,21960,21962,21964,21966,21968,21970,21972,21975],{},[898,21953,9692],{},[1664,21955,1676],{},[898,21957,1703],{},[1664,21959,1700],{},[898,21961,12683],{},[1664,21963,1700],{},[898,21965,12611],{},[898,21967,1977],{"mathvariant":1726},[6444,21969],{"width":6446},[1664,21971,1667],{"stretchy":1666},[1963,21973,21974],{},"7.8",[1664,21976,1673],{"stretchy":1666},[902,21978,21979],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,21981,21982,21983,1885,21986,10588,21999,22002],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,21984,21985],{},"zdaněním domácností",[883,21987,21989],{"className":21988},[886],[888,21990,21991],{"xmlns":890},[892,21992,21993,21997],{},[895,21994,21995],{},[898,21996,1991],{},[902,21998,1991],{"encoding":904},[614,22000,22001],{},"taxation","). Zdanění bývá:",[120,22004,22005,22038,22063],{},[123,22006,22007,22008,1916],{},"úměrné důchodu: ",[883,22009,22011],{"className":22010},[886],[888,22012,22013],{"xmlns":890},[892,22014,22015,22035],{},[895,22016,22017,22019,22021,22023,22025,22027,22029,22031,22033],{},[898,22018,1991],{},[1664,22020,1676],{},[898,22022,1991],{},[1664,22024,1667],{"stretchy":1666},[898,22026,9692],{},[1664,22028,1673],{"stretchy":1666},[1664,22030,1676],{},[898,22032,19355],{},[898,22034,9692],{},[902,22036,22037],{"encoding":904},"T = T(Y) = tY",[123,22039,22040,22041,1916],{},"fixní: ",[883,22042,22044],{"className":22043},[886],[888,22045,22046],{"xmlns":890},[892,22047,22048,22060],{},[895,22049,22050,22052,22054],{},[898,22051,1991],{},[1664,22053,1676],{},[1720,22055,22056,22058],{},[898,22057,1991],{},[1664,22059,4920],{},[902,22061,22062],{"encoding":904},"T = T^*",[123,22064,22065,22066,22094,22095,1977],{},"kombinované: ",[883,22067,22069],{"className":22068},[886],[888,22070,22071],{"xmlns":890},[892,22072,22073,22091],{},[895,22074,22075,22077,22079,22085,22087,22089],{},[898,22076,1991],{},[1664,22078,1676],{},[1720,22080,22081,22083],{},[898,22082,1991],{},[1664,22084,4920],{},[1664,22086,1700],{},[898,22088,19355],{},[898,22090,9692],{},[902,22092,22093],{"encoding":904},"T = T^* + tY",", kde ",[883,22096,22098],{"className":22097},[886],[888,22099,22100],{"xmlns":890},[892,22101,22102,22114],{},[895,22103,22104,22106,22108,22110,22112],{},[1963,22105,2058],{},[1664,22107,8245],{},[898,22109,19355],{},[1664,22111,4022],{},[1963,22113,2875],{},[902,22115,22116],{"encoding":904},"0 \\le t \u003C 1",[4436,22118,22119],{},[724,22120,22121,22123,22124,22145,22146,22149,22150,22163,22164,12627,22190,1885,22193,22219,22220,22248,22249,4454,22262,22280],{},[883,22122,4978],{}," Pozor na disponibilní důchod\nV modelu ",[883,22125,22127],{"className":22126},[886],[888,22128,22129],{"xmlns":890},[892,22130,22131,22143],{},[895,22132,22133,22135,22137,22139,22141],{},[898,22134,1703],{},[1690,22136,12789],{},[898,22138,12683],{},[1690,22140,12789],{},[898,22142,12611],{},[902,22144,18720],{"encoding":904}," je nutné ",[38,22147,22148],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,22151,22153],{"className":22152},[886],[888,22154,22155],{"xmlns":890},[892,22156,22157,22161],{},[895,22158,22159],{},[898,22160,9692],{},[902,22162,9692],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,22165,22167],{"className":22166},[886],[888,22168,22169],{"xmlns":890},[892,22170,22171,22187],{},[895,22172,22173,22175,22177,22179,22181,22183,22185],{},[898,22174,9692],{},[1664,22176,1676],{},[898,22178,1703],{},[1664,22180,1700],{},[898,22182,12683],{},[1664,22184,1700],{},[898,22186,12611],{},[902,22188,22189],{"encoding":904},"Y = C + I + G",[38,22191,22192],{},"disponibilní důchod",[883,22194,22196],{"className":22195},[886],[888,22197,22198],{"xmlns":890},[892,22199,22200,22216],{},[895,22201,22202,22208,22210,22212,22214],{},[2355,22203,22204,22206],{},[898,22205,9692],{},[898,22207,2379],{},[1664,22209,1676],{},[898,22211,9692],{},[1664,22213,1867],{},[898,22215,1991],{},[902,22217,22218],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,22221,22223],{"className":22222},[886],[888,22224,22225],{"xmlns":890},[892,22226,22227,22245],{},[895,22228,22229,22231,22233,22235,22237,22243],{},[898,22230,1703],{},[1664,22232,1676],{},[898,22234,1703],{},[1664,22236,1667],{"stretchy":1666},[2355,22238,22239,22241],{},[898,22240,9692],{},[898,22242,2379],{},[1664,22244,1673],{"stretchy":1666},[902,22246,22247],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,22250,22252],{"className":22251},[886],[888,22253,22254],{"xmlns":890},[892,22255,22256,22260],{},[895,22257,22258],{},[898,22259,9692],{},[902,22261,9692],{"encoding":904},[883,22263,22265],{"className":22264},[886],[888,22266,22267],{"xmlns":890},[892,22268,22269,22277],{},[895,22270,22271],{},[2355,22272,22273,22275],{},[898,22274,9692],{},[898,22276,2379],{},[902,22278,22279],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,22282,22283,10588,22286,1673],{},[38,22284,22285],{},"Disponibilní důchod",[614,22287,22288],{},"disposable income",[724,22290,22291],{},[883,22292,22294],{"className":22293},[886],[888,22295,22296],{"xmlns":890},[892,22297,22298,22314],{},[895,22299,22300,22306,22308,22310,22312],{},[2355,22301,22302,22304],{},[898,22303,9692],{},[898,22305,2379],{},[1664,22307,1676],{},[898,22309,9692],{},[1664,22311,1867],{},[898,22313,1991],{},[902,22315,22218],{"encoding":904},[724,22317,22318,22319,1977],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,22320,22322],{"className":22321},[886],[888,22323,22324],{"xmlns":890},[892,22325,22326,22344],{},[895,22327,22328,22330,22332,22334,22336,22342],{},[898,22329,1703],{},[1664,22331,1676],{},[898,22333,1703],{},[1664,22335,1667],{"stretchy":1666},[2355,22337,22338,22340],{},[898,22339,9692],{},[898,22341,2379],{},[1664,22343,1673],{"stretchy":1666},[902,22345,22247],{"encoding":904},[198,22347,21191],{"id":22348},"soustava-rovnic-1",[724,22350,22351,22352,1343,22373,22395,22396,2087],{},"Pro pevně zadané ",[883,22353,22355],{"className":22354},[886],[888,22356,22357],{"xmlns":890},[892,22358,22359,22371],{},[895,22360,22361,22363,22365],{},[898,22362,12683],{},[1664,22364,1676],{},[1720,22366,22367,22369],{},[898,22368,12683],{},[1664,22370,4920],{},[902,22372,12694],{"encoding":904},[883,22374,22376],{"className":22375},[886],[888,22377,22378],{"xmlns":890},[892,22379,22380,22392],{},[895,22381,22382,22384,22386],{},[898,22383,12611],{},[1664,22385,1676],{},[1720,22387,22388,22390],{},[898,22389,12611],{},[1664,22391,4920],{},[902,22393,22394],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,22397,22399],{"className":22398},[886],[888,22400,22401],{"xmlns":890},[892,22402,22403,22423],{},[895,22404,22405,22407,22409,22411,22413,22419,22421],{},[898,22406,9692],{},[1664,22408,1916],{"separator":1915},[898,22410,1703],{},[1664,22412,1916],{"separator":1915},[2355,22414,22415,22417],{},[898,22416,9692],{},[898,22418,2379],{},[1664,22420,1916],{"separator":1915},[898,22422,1991],{},[902,22424,22425],{"encoding":904},"Y, C, Y_D, T",[724,22427,22428],{},[883,22429,22431],{"className":22430},[886],[888,22432,22433],{"xmlns":890},[892,22434,22435,22576],{},[895,22436,22437,22567,22569,22571,22574],{},[21254,22438,22439,22477,22505,22537],{"rowspacing":21256,"columnalign":21257,"columnspacing":1727},[21259,22440,22441,22447],{},[21262,22442,22443],{},[2919,22444,22445],{"scriptlevel":2058,"displaystyle":1915},[898,22446,9692],{},[21262,22448,22449],{},[2919,22450,22451],{"scriptlevel":2058,"displaystyle":1915},[895,22452,22453,22455,22457,22459,22461,22467,22469,22475],{},[895,22454],{},[1664,22456,1676],{},[898,22458,1703],{},[1664,22460,1700],{},[1720,22462,22463,22465],{},[898,22464,12683],{},[1664,22466,4920],{},[1664,22468,1700],{},[1720,22470,22471,22473],{},[898,22472,12611],{},[1664,22474,4920],{},[1664,22476,1916],{"separator":1915},[21259,22478,22479,22485],{},[21262,22480,22481],{},[2919,22482,22483],{"scriptlevel":2058,"displaystyle":1915},[898,22484,1991],{},[21262,22486,22487],{},[2919,22488,22489],{"scriptlevel":2058,"displaystyle":1915},[895,22490,22491,22493,22495,22497,22499,22501,22503],{},[895,22492],{},[1664,22494,1676],{},[898,22496,1991],{},[1664,22498,1667],{"stretchy":1666},[898,22500,9692],{},[1664,22502,1673],{"stretchy":1666},[1664,22504,1916],{"separator":1915},[21259,22506,22507,22513],{},[21262,22508,22509],{},[2919,22510,22511],{"scriptlevel":2058,"displaystyle":1915},[898,22512,1703],{},[21262,22514,22515],{},[2919,22516,22517],{"scriptlevel":2058,"displaystyle":1915},[895,22518,22519,22521,22523,22525,22527,22533,22535],{},[895,22520],{},[1664,22522,1676],{},[898,22524,1703],{},[1664,22526,1667],{"stretchy":1666},[2355,22528,22529,22531],{},[898,22530,9692],{},[898,22532,2379],{},[1664,22534,1673],{"stretchy":1666},[1664,22536,1916],{"separator":1915},[21259,22538,22539,22549],{},[21262,22540,22541],{},[2919,22542,22543],{"scriptlevel":2058,"displaystyle":1915},[2355,22544,22545,22547],{},[898,22546,9692],{},[898,22548,2379],{},[21262,22550,22551],{},[2919,22552,22553],{"scriptlevel":2058,"displaystyle":1915},[895,22554,22555,22557,22559,22561,22563,22565],{},[895,22556],{},[1664,22558,1676],{},[898,22560,9692],{},[1664,22562,1867],{},[898,22564,1991],{},[1664,22566,1916],{"separator":1915},[6444,22568],{"width":6446},[1664,22570,1667],{"stretchy":1666},[1963,22572,22573],{},"7.9",[1664,22575,1673],{"stretchy":1666},[902,22577,22578],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,22580,22581,22582,22626,22627,1977],{},"s řešeními ",[883,22583,22585],{"className":22584},[886],[888,22586,22587],{"xmlns":890},[892,22588,22589,22623],{},[895,22590,22591,22597,22599,22605,22607,22613,22615],{},[1720,22592,22593,22595],{},[898,22594,9692],{},[898,22596,4819],{},[1664,22598,1916],{"separator":1915},[1720,22600,22601,22603],{},[898,22602,1703],{},[898,22604,4819],{},[1664,22606,1916],{"separator":1915},[1720,22608,22609,22611],{},[898,22610,1991],{},[898,22612,4819],{},[1664,22614,1916],{"separator":1915},[1810,22616,22617,22619,22621],{},[898,22618,9692],{},[898,22620,2379],{},[898,22622,4819],{},[902,22624,22625],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,22628,22630],{"className":22629},[886],[888,22631,22632],{"xmlns":890},[892,22633,22634,22660],{},[895,22635,22636,22642,22644,22652,22654],{},[1720,22637,22638,22640],{},[898,22639,2351],{},[898,22641,4819],{},[1664,22643,1676],{},[1810,22645,22646,22648,22650],{},[898,22647,9692],{},[898,22649,2379],{},[898,22651,4819],{},[1664,22653,1867],{},[1720,22655,22656,22658],{},[898,22657,1703],{},[898,22659,4819],{},[902,22661,22662],{"encoding":904},"S^E = Y_D^E - C^E",[4436,22664,22665,22670],{},[724,22666,22667,22669],{},[883,22668,5138],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,22671,22672,22695,22778,22833,22923],{},[123,22673,22674,22677,22678,1977],{},[38,22675,22676],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,22679,22681],{"className":22680},[886],[888,22682,22683],{"xmlns":890},[892,22684,22685,22693],{},[895,22686,22687],{},[2355,22688,22689,22691],{},[898,22690,9692],{},[898,22692,2379],{},[902,22694,22279],{"encoding":904},[123,22696,22697,22746,22747,22764,22765,1977],{},[38,22698,22699,22700,22720,22721],{},"Dosaď ",[883,22701,22703],{"className":22702},[886],[888,22704,22705],{"xmlns":890},[892,22706,22707,22717],{},[895,22708,22709,22711,22713,22715],{},[898,22710,1991],{},[1664,22712,1667],{"stretchy":1666},[898,22714,9692],{},[1664,22716,1673],{"stretchy":1666},[902,22718,22719],{"encoding":904},"T(Y)"," do ",[883,22722,22724],{"className":22723},[886],[888,22725,22726],{"xmlns":890},[892,22727,22728,22744],{},[895,22729,22730,22736,22738,22740,22742],{},[2355,22731,22732,22734],{},[898,22733,9692],{},[898,22735,2379],{},[1664,22737,1676],{},[898,22739,9692],{},[1664,22741,1867],{},[898,22743,1991],{},[902,22745,22218],{"encoding":904}," — dostaneš ",[883,22748,22750],{"className":22749},[886],[888,22751,22752],{"xmlns":890},[892,22753,22754,22762],{},[895,22755,22756],{},[2355,22757,22758,22760],{},[898,22759,9692],{},[898,22761,2379],{},[902,22763,22279],{"encoding":904}," jako lineární funkci ",[883,22766,22768],{"className":22767},[886],[888,22769,22770],{"xmlns":890},[892,22771,22772,22776],{},[895,22773,22774],{},[898,22775,9692],{},[902,22777,9692],{"encoding":904},[123,22779,22780,22746,22807,22764,22820,1977],{},[38,22781,22699,22782,22806],{},[883,22783,22785],{"className":22784},[886],[888,22786,22787],{"xmlns":890},[892,22788,22789,22803],{},[895,22790,22791,22797,22799,22801],{},[2355,22792,22793,22795],{},[898,22794,9692],{},[898,22796,2379],{},[1664,22798,1667],{"stretchy":1666},[898,22800,9692],{},[1664,22802,1673],{"stretchy":1666},[902,22804,22805],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,22808,22810],{"className":22809},[886],[888,22811,22812],{"xmlns":890},[892,22813,22814,22818],{},[895,22815,22816],{},[898,22817,1703],{},[902,22819,1703],{"encoding":904},[883,22821,22823],{"className":22822},[886],[888,22824,22825],{"xmlns":890},[892,22826,22827,22831],{},[895,22828,22829],{},[898,22830,9692],{},[902,22832,9692],{"encoding":904},[123,22834,22835,1885,22857,22891,22892,22905,22906,1977],{},[38,22836,22699,22837,22856],{},[883,22838,22840],{"className":22839},[886],[888,22841,22842],{"xmlns":890},[892,22843,22844,22854],{},[895,22845,22846,22848,22850,22852],{},[898,22847,1703],{},[1664,22849,1667],{"stretchy":1666},[898,22851,9692],{},[1664,22853,1673],{"stretchy":1666},[902,22855,14715],{"encoding":904}," do podmínky rovnováhy",[883,22858,22860],{"className":22859},[886],[888,22861,22862],{"xmlns":890},[892,22863,22864,22888],{},[895,22865,22866,22868,22870,22872,22874,22880,22882],{},[898,22867,9692],{},[1664,22869,1676],{},[898,22871,1703],{},[1664,22873,1700],{},[1720,22875,22876,22878],{},[898,22877,12683],{},[1664,22879,4920],{},[1664,22881,1700],{},[1720,22883,22884,22886],{},[898,22885,12611],{},[1664,22887,4920],{},[902,22889,22890],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,22893,22895],{"className":22894},[886],[888,22896,22897],{"xmlns":890},[892,22898,22899,22903],{},[895,22900,22901],{},[898,22902,9692],{},[902,22904,9692],{"encoding":904},", odtud ",[883,22907,22909],{"className":22908},[886],[888,22910,22911],{"xmlns":890},[892,22912,22913,22921],{},[895,22914,22915],{},[1720,22916,22917,22919],{},[898,22918,9692],{},[898,22920,4819],{},[902,22922,14402],{"encoding":904},[123,22924,22925,22928,22929,1343,22947,1343,22967,1343,22984,1977],{},[38,22926,22927],{},"Zpětným dosazením"," dopočítej ",[883,22930,22932],{"className":22931},[886],[888,22933,22934],{"xmlns":890},[892,22935,22936,22944],{},[895,22937,22938],{},[1720,22939,22940,22942],{},[898,22941,1991],{},[898,22943,4819],{},[902,22945,22946],{"encoding":904},"T^E",[883,22948,22950],{"className":22949},[886],[888,22951,22952],{"xmlns":890},[892,22953,22954,22964],{},[895,22955,22956],{},[1810,22957,22958,22960,22962],{},[898,22959,9692],{},[898,22961,2379],{},[898,22963,4819],{},[902,22965,22966],{"encoding":904},"Y_D^E",[883,22968,22970],{"className":22969},[886],[888,22971,22972],{"xmlns":890},[892,22973,22974,22982],{},[895,22975,22976],{},[1720,22977,22978,22980],{},[898,22979,1703],{},[898,22981,4819],{},[902,22983,14461],{"encoding":904},[883,22985,22987],{"className":22986},[886],[888,22988,22989],{"xmlns":890},[892,22990,22991,22999],{},[895,22992,22993],{},[1720,22994,22995,22997],{},[898,22996,2351],{},[898,22998,4819],{},[902,23000,23001],{"encoding":904},"S^E",[198,23003,23005],{"id":23004},"příklad-74","Příklad 7.4",[724,23007,21521,23008,23029,23030,1343,23061,1343,23085,1343,23107,23129],{},[883,23009,23011],{"className":23010},[886],[888,23012,23013],{"xmlns":890},[892,23014,23015,23027],{},[895,23016,23017,23019,23021,23023,23025],{},[898,23018,1703],{},[1690,23020,12789],{},[898,23022,12683],{},[1690,23024,12789],{},[898,23026,12611],{},[902,23028,18720],{"encoding":904}," jsou dány ",[883,23031,23033],{"className":23032},[886],[888,23034,23035],{"xmlns":890},[892,23036,23037,23058],{},[895,23038,23039,23041,23043,23046,23048,23054,23056],{},[898,23040,1703],{},[1664,23042,1676],{},[1963,23044,23045],{},"0,9",[1690,23047,1692],{},[2355,23049,23050,23052],{},[898,23051,9692],{},[898,23053,2379],{},[1664,23055,1700],{},[1963,23057,6463],{},[902,23059,23060],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,23062,23064],{"className":23063},[886],[888,23065,23066],{"xmlns":890},[892,23067,23068,23082],{},[895,23069,23070,23072,23074,23076,23078,23080],{},[898,23071,1991],{},[1664,23073,1676],{},[1963,23075,2154],{},[898,23077,9692],{},[1664,23079,1700],{},[1963,23081,5570],{},[902,23083,23084],{"encoding":904},"T = 0{,}2Y + 25",[883,23086,23088],{"className":23087},[886],[888,23089,23090],{"xmlns":890},[892,23091,23092,23104],{},[895,23093,23094,23100,23102],{},[1720,23095,23096,23098],{},[898,23097,12683],{},[1664,23099,4920],{},[1664,23101,1676],{},[1963,23103,15537],{},[902,23105,23106],{"encoding":904},"I^* = 35",[883,23108,23110],{"className":23109},[886],[888,23111,23112],{"xmlns":890},[892,23113,23114,23126],{},[895,23115,23116,23122,23124],{},[1720,23117,23118,23120],{},[898,23119,12611],{},[1664,23121,4920],{},[1664,23123,1676],{},[1963,23125,9599],{},[902,23127,23128],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,23131,23132],{},[883,23133,23135],{"className":23134},[886],[888,23136,23137],{"xmlns":890},[892,23138,23139,23263],{},[21254,23140,23141,23171,23199,23233],{"rowspacing":21256,"columnalign":21257,"columnspacing":1727},[21259,23142,23143,23149],{},[21262,23144,23145],{},[2919,23146,23147],{"scriptlevel":2058,"displaystyle":1915},[898,23148,9692],{},[21262,23150,23151],{},[2919,23152,23153],{"scriptlevel":2058,"displaystyle":1915},[895,23154,23155,23157,23159,23161,23163,23165,23167,23169],{},[895,23156],{},[1664,23158,1676],{},[898,23160,1703],{},[1664,23162,1700],{},[1963,23164,15537],{},[1664,23166,1700],{},[1963,23168,9599],{},[1664,23170,1916],{"separator":1915},[21259,23172,23173,23179],{},[21262,23174,23175],{},[2919,23176,23177],{"scriptlevel":2058,"displaystyle":1915},[898,23178,1991],{},[21262,23180,23181],{},[2919,23182,23183],{"scriptlevel":2058,"displaystyle":1915},[895,23184,23185,23187,23189,23191,23193,23195,23197],{},[895,23186],{},[1664,23188,1676],{},[1963,23190,2154],{},[898,23192,9692],{},[1664,23194,1700],{},[1963,23196,5570],{},[1664,23198,1916],{"separator":1915},[21259,23200,23201,23207],{},[21262,23202,23203],{},[2919,23204,23205],{"scriptlevel":2058,"displaystyle":1915},[898,23206,1703],{},[21262,23208,23209],{},[2919,23210,23211],{"scriptlevel":2058,"displaystyle":1915},[895,23212,23213,23215,23217,23219,23221,23227,23229,23231],{},[895,23214],{},[1664,23216,1676],{},[1963,23218,23045],{},[1690,23220,1692],{},[2355,23222,23223,23225],{},[898,23224,9692],{},[898,23226,2379],{},[1664,23228,1700],{},[1963,23230,6463],{},[1664,23232,1916],{"separator":1915},[21259,23234,23235,23245],{},[21262,23236,23237],{},[2919,23238,23239],{"scriptlevel":2058,"displaystyle":1915},[2355,23240,23241,23243],{},[898,23242,9692],{},[898,23244,2379],{},[21262,23246,23247],{},[2919,23248,23249],{"scriptlevel":2058,"displaystyle":1915},[895,23250,23251,23253,23255,23257,23259,23261],{},[895,23252],{},[1664,23254,1676],{},[898,23256,9692],{},[1664,23258,1867],{},[898,23260,1991],{},[898,23262,1977],{"mathvariant":1726},[902,23264,23265],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,23267,23268,23271,23272,23326,23327,23373,23374,2087],{},[38,23269,23270],{},"Řešení."," Z definice ",[883,23273,23275],{"className":23274},[886],[888,23276,23277],{"xmlns":890},[892,23278,23279,23323],{},[895,23280,23281,23287,23289,23291,23293,23295,23297,23299,23301,23303,23305,23307,23309,23311,23313,23315,23317,23319,23321],{},[2355,23282,23283,23285],{},[898,23284,9692],{},[898,23286,2379],{},[1664,23288,1676],{},[898,23290,9692],{},[1664,23292,1867],{},[898,23294,1991],{},[1664,23296,1676],{},[898,23298,9692],{},[1664,23300,1867],{},[1664,23302,1667],{"stretchy":1666},[1963,23304,2154],{},[898,23306,9692],{},[1664,23308,1700],{},[1963,23310,5570],{},[1664,23312,1673],{"stretchy":1666},[1664,23314,1676],{},[1963,23316,15088],{},[898,23318,9692],{},[1664,23320,1867],{},[1963,23322,5570],{},[902,23324,23325],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,23328,23330],{"className":23329},[886],[888,23331,23332],{"xmlns":890},[892,23333,23334,23370],{},[895,23335,23336,23338,23340,23342,23344,23346,23348,23350,23352,23354,23356,23358,23360,23363,23365,23367],{},[898,23337,1703],{},[1664,23339,1676],{},[1963,23341,23045],{},[1664,23343,1667],{"stretchy":1666},[1963,23345,15088],{},[898,23347,9692],{},[1664,23349,1867],{},[1963,23351,5570],{},[1664,23353,1673],{"stretchy":1666},[1664,23355,1700],{},[1963,23357,6463],{},[1664,23359,1676],{},[1963,23361,23362],{},"0,72",[898,23364,9692],{},[1664,23366,1700],{},[1963,23368,23369],{},"47,5",[902,23371,23372],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,23375,23377],{"className":23376},[886],[888,23378,23379],{"xmlns":890},[892,23380,23381,23399],{},[895,23382,23383,23385,23387,23389,23391,23393,23395,23397],{},[898,23384,9692],{},[1664,23386,1676],{},[1963,23388,23362],{},[898,23390,9692],{},[1664,23392,1700],{},[1963,23394,23369],{},[1664,23396,1700],{},[1963,23398,21680],{},[902,23400,23401],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,23403,23404],{},[883,23405,23407],{"className":23406},[886],[888,23408,23409],{"xmlns":890},[892,23410,23411,23452],{},[895,23412,23413,23416,23418,23420,23423,23425,23427,23429,23435,23437,23447,23449],{},[1963,23414,23415],{},"0,28",[898,23417,9692],{},[1664,23419,1676],{},[1963,23421,23422],{},"102,5",[1690,23424,4553],{},[1664,23426,15507],{},[1690,23428,4553],{},[1720,23430,23431,23433],{},[898,23432,9692],{},[898,23434,4819],{},[1664,23436,1676],{},[2919,23438,23439],{"scriptlevel":2058,"displaystyle":1666},[2922,23440,23441,23444],{},[1963,23442,23443],{},"5125",[1963,23445,23446],{},"14",[1664,23448,6466],{},[1963,23450,23451],{},"366,071.",[902,23453,23454],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,23456,23457],{},"Rovnovážné veličiny:",[120,23459,23460,23495,23547,23601,23649],{},[123,23461,23462,1916],{},[883,23463,23465],{"className":23464},[886],[888,23466,23467],{"xmlns":890},[892,23468,23469,23492],{},[895,23470,23471,23477,23479,23487,23489],{},[1720,23472,23473,23475],{},[898,23474,9692],{},[898,23476,4819],{},[1664,23478,1676],{},[2919,23480,23481],{"scriptlevel":2058,"displaystyle":1666},[2922,23482,23483,23485],{},[1963,23484,23443],{},[1963,23486,23446],{},[1664,23488,6466],{},[1963,23490,23491],{},"366,071",[902,23493,23494],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,23496,23497,1916],{},[883,23498,23500],{"className":23499},[886],[888,23501,23502],{"xmlns":890},[892,23503,23504,23544],{},[895,23505,23506,23512,23514,23516,23518,23524,23526,23528,23530,23539,23541],{},[1720,23507,23508,23510],{},[898,23509,1991],{},[898,23511,4819],{},[1664,23513,1676],{},[1963,23515,2154],{},[1690,23517,1692],{},[1720,23519,23520,23522],{},[898,23521,9692],{},[898,23523,4819],{},[1664,23525,1700],{},[1963,23527,5570],{},[1664,23529,1676],{},[2919,23531,23532],{"scriptlevel":2058,"displaystyle":1666},[2922,23533,23534,23537],{},[1963,23535,23536],{},"1375",[1963,23538,23446],{},[1664,23540,6466],{},[1963,23542,23543],{},"98,214",[902,23545,23546],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,23548,23549,1916],{},[883,23550,23552],{"className":23551},[886],[888,23553,23554],{"xmlns":890},[892,23555,23556,23598],{},[895,23557,23558,23566,23568,23574,23576,23582,23584,23593,23595],{},[1810,23559,23560,23562,23564],{},[898,23561,9692],{},[898,23563,2379],{},[898,23565,4819],{},[1664,23567,1676],{},[1720,23569,23570,23572],{},[898,23571,9692],{},[898,23573,4819],{},[1664,23575,1867],{},[1720,23577,23578,23580],{},[898,23579,1991],{},[898,23581,4819],{},[1664,23583,1676],{},[2919,23585,23586],{"scriptlevel":2058,"displaystyle":1666},[2922,23587,23588,23591],{},[1963,23589,23590],{},"3750",[1963,23592,23446],{},[1664,23594,6466],{},[1963,23596,23597],{},"267,857",[902,23599,23600],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,23602,23603,1916],{},[883,23604,23606],{"className":23605},[886],[888,23607,23608],{"xmlns":890},[892,23609,23610,23646],{},[895,23611,23612,23618,23620,23626,23628,23630,23632,23641,23643],{},[1720,23613,23614,23616],{},[898,23615,1703],{},[898,23617,4819],{},[1664,23619,1676],{},[1720,23621,23622,23624],{},[898,23623,9692],{},[898,23625,4819],{},[1664,23627,1867],{},[1963,23629,21680],{},[1664,23631,1676],{},[2919,23633,23634],{"scriptlevel":2058,"displaystyle":1666},[2922,23635,23636,23639],{},[1963,23637,23638],{},"4355",[1963,23640,23446],{},[1664,23642,6466],{},[1963,23644,23645],{},"311,071",[902,23647,23648],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,23650,23651,23707],{},[883,23652,23654],{"className":23653},[886],[888,23655,23656],{"xmlns":890},[892,23657,23658,23704],{},[895,23659,23660,23666,23668,23676,23678,23684,23686,23688,23697,23699,23701],{},[1720,23661,23662,23664],{},[898,23663,2351],{},[898,23665,4819],{},[1664,23667,1676],{},[1810,23669,23670,23672,23674],{},[898,23671,9692],{},[898,23673,2379],{},[898,23675,4819],{},[1664,23677,1867],{},[1720,23679,23680,23682],{},[898,23681,1703],{},[898,23683,4819],{},[1664,23685,1676],{},[1664,23687,1867],{},[2919,23689,23690],{"scriptlevel":2058,"displaystyle":1666},[2922,23691,23692,23695],{},[1963,23693,23694],{},"605",[1963,23696,23446],{},[1664,23698,6466],{},[1664,23700,1867],{},[1963,23702,23703],{},"43,214",[902,23705,23706],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,23709,23710,21850,23712,23733,23734,23737,23738,23761,23762,1977],{},[38,23711,21849],{},[883,23713,23715],{"className":23714},[886],[888,23716,23717],{"xmlns":890},[892,23718,23719,23731],{},[895,23720,23721,23723,23725,23727,23729],{},[898,23722,1703],{},[1690,23724,12789],{},[898,23726,12683],{},[1690,23728,12789],{},[898,23730,12611],{},[902,23732,18720],{"encoding":904}," stále uvažuje ",[38,23735,23736],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,23739,23741],{"className":23740},[886],[888,23742,23743],{"xmlns":890},[892,23744,23745,23758],{},[895,23746,23747,23749,23751,23754,23756],{},[898,23748,12819],{},[1664,23750,1676],{},[898,23752,23753],{},"B",[1664,23755,1867],{},[898,23757,1956],{},[902,23759,23760],{"encoding":904},"X = B - M"," dává ",[38,23763,21871,23764],{},[883,23765,23767],{"className":23766},[886],[888,23768,23769],{"xmlns":890},[892,23770,23771,23787],{},[895,23772,23773,23775,23777,23779,23781,23783,23785],{},[898,23774,1703],{},[1690,23776,12789],{},[898,23778,12683],{},[1690,23780,12789],{},[898,23782,12611],{},[1690,23784,12789],{},[898,23786,12819],{},[902,23788,12822],{"encoding":904},[115,23790,23792],{"id":23791},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,23794,21121],{"id":23795},"zadání-modelu-2",[724,23797,23798,23799,1885,23802,22094,23823,23836,23837,12627,23840,23853],{},"Rozšíření o ",[38,23800,23801],{},"čistý export",[883,23803,23805],{"className":23804},[886],[888,23806,23807],{"xmlns":890},[892,23808,23809,23821],{},[895,23810,23811,23813,23815,23817,23819],{},[898,23812,12819],{},[1664,23814,1676],{},[898,23816,23753],{},[1664,23818,1867],{},[898,23820,1956],{},[902,23822,23760],{"encoding":904},[883,23824,23826],{"className":23825},[886],[888,23827,23828],{"xmlns":890},[892,23829,23830,23834],{},[895,23831,23832],{},[898,23833,23753],{},[902,23835,23753],{"encoding":904}," je hrubý export (",[614,23838,23839],{},"brutto export",[883,23841,23843],{"className":23842},[886],[888,23844,23845],{"xmlns":890},[892,23846,23847,23851],{},[895,23848,23849],{},[898,23850,1956],{},[902,23852,1956],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,23855,23856],{},[883,23857,23859],{"className":23858},[886],[888,23860,23861],{"xmlns":890},[892,23862,23863,23883],{},[895,23864,23865,23867,23869,23871,23873,23879,23881],{},[898,23866,1956],{},[1664,23868,1676],{},[898,23870,1956],{},[1664,23872,1667],{"stretchy":1666},[2355,23874,23875,23877],{},[898,23876,9692],{},[898,23878,2379],{},[1664,23880,1673],{"stretchy":1666},[898,23882,1977],{"mathvariant":1726},[902,23884,23885],{"encoding":904},"M = M(Y_D).",[724,23887,23888],{},"Podmínka rovnováhy:",[724,23890,23891],{},[883,23892,23894],{"className":23893},[886],[888,23895,23896],{"xmlns":890},[892,23897,23898,23935],{},[895,23899,23900,23902,23904,23906,23908,23910,23912,23914,23916,23918,23920,23922,23924,23926,23928,23931,23933],{},[898,23901,9692],{},[1664,23903,1676],{},[898,23905,1703],{},[1664,23907,1700],{},[898,23909,12683],{},[1664,23911,1700],{},[898,23913,12611],{},[1664,23915,1700],{},[898,23917,23753],{},[1664,23919,1867],{},[898,23921,1956],{},[898,23923,1977],{"mathvariant":1726},[6444,23925],{"width":6446},[1664,23927,1667],{"stretchy":1666},[1963,23929,23930],{},"7.10",[1690,23932,207],{},[1664,23934,1673],{"stretchy":1666},[902,23936,23937],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,23939,21191],{"id":23940},"soustava-rovnic-2",[724,23942,22351,23943,23977,23978,2087],{},[883,23944,23946],{"className":23945},[886],[888,23947,23948],{"xmlns":890},[892,23949,23950,23974],{},[895,23951,23952,23958,23960,23966,23968],{},[1720,23953,23954,23956],{},[898,23955,12683],{},[1664,23957,4920],{},[1664,23959,1916],{"separator":1915},[1720,23961,23962,23964],{},[898,23963,12611],{},[1664,23965,4920],{},[1664,23967,1916],{"separator":1915},[1720,23969,23970,23972],{},[898,23971,23753],{},[1664,23973,4920],{},[902,23975,23976],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,23979,23981],{"className":23980},[886],[888,23982,23983],{"xmlns":890},[892,23984,23985,24009],{},[895,23986,23987,23989,23991,23993,23995,23997,23999,24005,24007],{},[898,23988,9692],{},[1664,23990,1916],{"separator":1915},[898,23992,1703],{},[1664,23994,1916],{"separator":1915},[898,23996,1991],{},[1664,23998,1916],{"separator":1915},[2355,24000,24001,24003],{},[898,24002,9692],{},[898,24004,2379],{},[1664,24006,1916],{"separator":1915},[898,24008,1956],{},[902,24010,24011],{"encoding":904},"Y, C, T, Y_D, M",[724,24013,24014],{},[883,24015,24017],{"className":24016},[886],[888,24018,24019],{"xmlns":890},[892,24020,24021,24205],{},[895,24022,24023,24197,24199,24201,24203],{},[21254,24024,24025,24057,24087,24115,24147],{"rowspacing":21256,"columnalign":21257,"columnspacing":1727},[21259,24026,24027,24033],{},[21262,24028,24029],{},[2919,24030,24031],{"scriptlevel":2058,"displaystyle":1915},[898,24032,1703],{},[21262,24034,24035],{},[2919,24036,24037],{"scriptlevel":2058,"displaystyle":1915},[895,24038,24039,24041,24043,24045,24047,24053,24055],{},[895,24040],{},[1664,24042,1676],{},[898,24044,1703],{},[1664,24046,1667],{"stretchy":1666},[2355,24048,24049,24051],{},[898,24050,9692],{},[898,24052,2379],{},[1664,24054,1673],{"stretchy":1666},[1664,24056,1916],{"separator":1915},[21259,24058,24059,24069],{},[21262,24060,24061],{},[2919,24062,24063],{"scriptlevel":2058,"displaystyle":1915},[2355,24064,24065,24067],{},[898,24066,9692],{},[898,24068,2379],{},[21262,24070,24071],{},[2919,24072,24073],{"scriptlevel":2058,"displaystyle":1915},[895,24074,24075,24077,24079,24081,24083,24085],{},[895,24076],{},[1664,24078,1676],{},[898,24080,9692],{},[1664,24082,1867],{},[898,24084,1991],{},[1664,24086,1916],{"separator":1915},[21259,24088,24089,24095],{},[21262,24090,24091],{},[2919,24092,24093],{"scriptlevel":2058,"displaystyle":1915},[898,24094,1991],{},[21262,24096,24097],{},[2919,24098,24099],{"scriptlevel":2058,"displaystyle":1915},[895,24100,24101,24103,24105,24107,24109,24111,24113],{},[895,24102],{},[1664,24104,1676],{},[898,24106,1991],{},[1664,24108,1667],{"stretchy":1666},[898,24110,9692],{},[1664,24112,1673],{"stretchy":1666},[1664,24114,1916],{"separator":1915},[21259,24116,24117,24123],{},[21262,24118,24119],{},[2919,24120,24121],{"scriptlevel":2058,"displaystyle":1915},[898,24122,1956],{},[21262,24124,24125],{},[2919,24126,24127],{"scriptlevel":2058,"displaystyle":1915},[895,24128,24129,24131,24133,24135,24137,24143,24145],{},[895,24130],{},[1664,24132,1676],{},[898,24134,1956],{},[1664,24136,1667],{"stretchy":1666},[2355,24138,24139,24141],{},[898,24140,9692],{},[898,24142,2379],{},[1664,24144,1673],{"stretchy":1666},[1664,24146,1916],{"separator":1915},[21259,24148,24149,24155],{},[21262,24150,24151],{},[2919,24152,24153],{"scriptlevel":2058,"displaystyle":1915},[898,24154,9692],{},[21262,24156,24157],{},[2919,24158,24159],{"scriptlevel":2058,"displaystyle":1915},[895,24160,24161,24163,24165,24167,24169,24175,24177,24183,24185,24191,24193,24195],{},[895,24162],{},[1664,24164,1676],{},[898,24166,1703],{},[1664,24168,1700],{},[1720,24170,24171,24173],{},[898,24172,12683],{},[1664,24174,4920],{},[1664,24176,1700],{},[1720,24178,24179,24181],{},[898,24180,12611],{},[1664,24182,4920],{},[1664,24184,1700],{},[1720,24186,24187,24189],{},[898,24188,23753],{},[1664,24190,4920],{},[1664,24192,1867],{},[898,24194,1956],{},[898,24196,1977],{"mathvariant":1726},[6444,24198],{"width":6446},[1664,24200,1667],{"stretchy":1666},[1963,24202,23930],{},[1664,24204,1673],{"stretchy":1666},[902,24206,24207],{"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)",[198,24209,24211],{"id":24210},"příklad-75","Příklad 7.5",[724,24213,24214,24215,1343,24247,1343,24274,1343,24295,1343,24317,1343,24339,24362],{},"Dáno: ",[883,24216,24218],{"className":24217},[886],[888,24219,24220],{"xmlns":890},[892,24221,24222,24244],{},[895,24223,24224,24226,24228,24231,24233,24239,24241],{},[898,24225,1703],{},[1664,24227,1676],{},[1963,24229,24230],{},"0,75",[1690,24232,1692],{},[2355,24234,24235,24237],{},[898,24236,9692],{},[898,24238,2379],{},[1664,24240,1700],{},[1963,24242,24243],{},"750",[902,24245,24246],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,24248,24250],{"className":24249},[886],[888,24251,24252],{"xmlns":890},[892,24253,24254,24271],{},[895,24255,24256,24258,24260,24263,24265],{},[898,24257,1956],{},[1664,24259,1676],{},[1963,24261,24262],{},"0,15",[1690,24264,1692],{},[2355,24266,24267,24269],{},[898,24268,9692],{},[898,24270,2379],{},[902,24272,24273],{"encoding":904},"M = 0{,}15\\,Y_D",[883,24275,24277],{"className":24276},[886],[888,24278,24279],{"xmlns":890},[892,24280,24281,24292],{},[895,24282,24283,24285,24287,24290],{},[898,24284,1991],{},[1664,24286,1676],{},[1963,24288,24289],{},"0,25",[898,24291,9692],{},[902,24293,24294],{"encoding":904},"T = 0{,}25Y",[883,24296,24298],{"className":24297},[886],[888,24299,24300],{"xmlns":890},[892,24301,24302,24314],{},[895,24303,24304,24310,24312],{},[1720,24305,24306,24308],{},[898,24307,12683],{},[1664,24309,4920],{},[1664,24311,1676],{},[1963,24313,15609],{},[902,24315,24316],{"encoding":904},"I^* = 500",[883,24318,24320],{"className":24319},[886],[888,24321,24322],{"xmlns":890},[892,24323,24324,24336],{},[895,24325,24326,24332,24334],{},[1720,24327,24328,24330],{},[898,24329,12611],{},[1664,24331,4920],{},[1664,24333,1676],{},[1963,24335,9367],{},[902,24337,24338],{"encoding":904},"G^* = 150",[883,24340,24342],{"className":24341},[886],[888,24343,24344],{"xmlns":890},[892,24345,24346,24359],{},[895,24347,24348,24354,24356],{},[1720,24349,24350,24352],{},[898,24351,23753],{},[1664,24353,4920],{},[1664,24355,1676],{},[1963,24357,24358],{},"800",[902,24360,24361],{"encoding":904},"B^* = 800",". Soustava:",[724,24364,24365],{},[883,24366,24368],{"className":24367},[886],[888,24369,24370],{"xmlns":890},[892,24371,24372,24590],{},[21254,24373,24374,24420,24462,24498,24540],{"rowspacing":21256,"columnalign":21257,"columnspacing":1727},[21259,24375,24376,24392],{},[21262,24377,24378],{},[2919,24379,24380],{"scriptlevel":2058,"displaystyle":1915},[895,24381,24382,24384,24386,24388,24390],{},[1664,24383,1667],{"stretchy":1666},[898,24385,12540],{},[1963,24387,2875],{},[1664,24389,1673],{"stretchy":1666},[1690,24391,2884],{},[21262,24393,24394],{},[2919,24395,24396],{"scriptlevel":2058,"displaystyle":1915},[895,24397,24398,24400,24402,24404,24406,24408,24414,24416,24418],{},[895,24399],{},[898,24401,1703],{},[1664,24403,1676],{},[1963,24405,24230],{},[1690,24407,1692],{},[2355,24409,24410,24412],{},[898,24411,9692],{},[898,24413,2379],{},[1664,24415,1700],{},[1963,24417,24243],{},[1664,24419,1916],{"separator":1915},[21259,24421,24422,24438],{},[21262,24423,24424],{},[2919,24425,24426],{"scriptlevel":2058,"displaystyle":1915},[895,24427,24428,24430,24432,24434,24436],{},[1664,24429,1667],{"stretchy":1666},[898,24431,12540],{},[1963,24433,1970],{},[1664,24435,1673],{"stretchy":1666},[1690,24437,2884],{},[21262,24439,24440],{},[2919,24441,24442],{"scriptlevel":2058,"displaystyle":1915},[895,24443,24444,24446,24452,24454,24456,24458,24460],{},[895,24445],{},[2355,24447,24448,24450],{},[898,24449,9692],{},[898,24451,2379],{},[1664,24453,1676],{},[898,24455,9692],{},[1664,24457,1867],{},[898,24459,1991],{},[1664,24461,1916],{"separator":1915},[21259,24463,24464,24480],{},[21262,24465,24466],{},[2919,24467,24468],{"scriptlevel":2058,"displaystyle":1915},[895,24469,24470,24472,24474,24476,24478],{},[1664,24471,1667],{"stretchy":1666},[898,24473,12540],{},[1963,24475,2774],{},[1664,24477,1673],{"stretchy":1666},[1690,24479,2884],{},[21262,24481,24482],{},[2919,24483,24484],{"scriptlevel":2058,"displaystyle":1915},[895,24485,24486,24488,24490,24492,24494,24496],{},[895,24487],{},[898,24489,1991],{},[1664,24491,1676],{},[1963,24493,24289],{},[898,24495,9692],{},[1664,24497,1916],{"separator":1915},[21259,24499,24500,24516],{},[21262,24501,24502],{},[2919,24503,24504],{"scriptlevel":2058,"displaystyle":1915},[895,24505,24506,24508,24510,24512,24514],{},[1664,24507,1667],{"stretchy":1666},[898,24509,12540],{},[1963,24511,2944],{},[1664,24513,1673],{"stretchy":1666},[1690,24515,2884],{},[21262,24517,24518],{},[2919,24519,24520],{"scriptlevel":2058,"displaystyle":1915},[895,24521,24522,24524,24526,24528,24530,24532,24538],{},[895,24523],{},[898,24525,1956],{},[1664,24527,1676],{},[1963,24529,24262],{},[1690,24531,1692],{},[2355,24533,24534,24536],{},[898,24535,9692],{},[898,24537,2379],{},[1664,24539,1916],{"separator":1915},[21259,24541,24542,24558],{},[21262,24543,24544],{},[2919,24545,24546],{"scriptlevel":2058,"displaystyle":1915},[895,24547,24548,24550,24552,24554,24556],{},[1664,24549,1667],{"stretchy":1666},[898,24551,12540],{},[1963,24553,2826],{},[1664,24555,1673],{"stretchy":1666},[1690,24557,2884],{},[21262,24559,24560],{},[2919,24561,24562],{"scriptlevel":2058,"displaystyle":1915},[895,24563,24564,24566,24568,24570,24572,24574,24576,24578,24580,24582,24584,24586,24588],{},[895,24565],{},[898,24567,9692],{},[1664,24569,1676],{},[898,24571,1703],{},[1664,24573,1700],{},[1963,24575,15609],{},[1664,24577,1700],{},[1963,24579,9367],{},[1664,24581,1700],{},[1963,24583,24358],{},[1664,24585,1867],{},[898,24587,1956],{},[898,24589,1977],{"mathvariant":1726},[902,24591,24592],{"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}",[724,24594,24595,24596,24630],{},"Postupná substituce — z (r3) do (r2): ",[883,24597,24599],{"className":24598},[886],[888,24600,24601],{"xmlns":890},[892,24602,24603,24627],{},[895,24604,24605,24611,24613,24615,24617,24619,24621,24623,24625],{},[2355,24606,24607,24609],{},[898,24608,9692],{},[898,24610,2379],{},[1664,24612,1676],{},[898,24614,9692],{},[1664,24616,1867],{},[1963,24618,24289],{},[898,24620,9692],{},[1664,24622,1676],{},[1963,24624,24230],{},[898,24626,9692],{},[902,24628,24629],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,24632,24633],{},[883,24634,24636],{"className":24635},[886],[888,24637,24638],{"xmlns":890},[892,24639,24640,24681],{},[895,24641,24642,24644,24646,24648,24650,24652,24654,24656,24658,24660,24662,24664,24666,24668,24670,24673,24675,24677,24679],{},[1664,24643,1667],{"stretchy":1666},[898,24645,12540],{},[1963,24647,2833],{},[1664,24649,1673],{"stretchy":1666},[1690,24651,2884],{},[898,24653,1703],{},[1664,24655,1676],{},[1963,24657,24230],{},[1664,24659,3753],{},[1963,24661,24230],{},[898,24663,9692],{},[1664,24665,1700],{},[1963,24667,24243],{},[1664,24669,1676],{},[1963,24671,24672],{},"0,5625",[898,24674,9692],{},[1664,24676,1700],{},[1963,24678,24243],{},[1664,24680,1916],{"separator":1915},[902,24682,24683],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,24685,24686],{},[883,24687,24689],{"className":24688},[886],[888,24690,24691],{"xmlns":890},[892,24692,24693,24727],{},[895,24694,24695,24697,24699,24702,24704,24706,24708,24710,24712,24714,24716,24718,24720,24723,24725],{},[1664,24696,1667],{"stretchy":1666},[898,24698,12540],{},[1963,24700,24701],{},"7",[1664,24703,1673],{"stretchy":1666},[1690,24705,2884],{},[898,24707,1956],{},[1664,24709,1676],{},[1963,24711,24262],{},[1664,24713,3753],{},[1963,24715,24230],{},[898,24717,9692],{},[1664,24719,1676],{},[1963,24721,24722],{},"0,1125",[898,24724,9692],{},[898,24726,1977],{"mathvariant":1726},[902,24728,24729],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,24731,24732],{},"Dosazením do (r5):",[724,24734,24735],{},[883,24736,24738],{"className":24737},[886],[888,24739,24740],{"xmlns":890},[892,24741,24742,24786],{},[895,24743,24744,24746,24748,24750,24752,24754,24756,24758,24760,24762,24764,24766,24768,24770,24772,24774,24776,24779,24781,24783],{},[898,24745,9692],{},[1664,24747,1676],{},[1963,24749,24672],{},[898,24751,9692],{},[1664,24753,1700],{},[1963,24755,24243],{},[1664,24757,1700],{},[1963,24759,15609],{},[1664,24761,1700],{},[1963,24763,9367],{},[1664,24765,1700],{},[1963,24767,24358],{},[1664,24769,1867],{},[1963,24771,24722],{},[898,24773,9692],{},[1664,24775,1676],{},[1963,24777,24778],{},"0,45",[898,24780,9692],{},[1664,24782,1700],{},[1963,24784,24785],{},"2200.",[902,24787,24788],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,24790,24791,24792,6155,24814,24837],{},"Odtud ",[883,24793,24795],{"className":24794},[886],[888,24796,24797],{"xmlns":890},[892,24798,24799,24811],{},[895,24800,24801,24804,24806,24808],{},[1963,24802,24803],{},"0,55",[898,24805,9692],{},[1664,24807,1676],{},[1963,24809,24810],{},"2200",[902,24812,24813],{"encoding":904},"0{,}55Y = 2200",[883,24815,24817],{"className":24816},[886],[888,24818,24819],{"xmlns":890},[892,24820,24821,24834],{},[895,24822,24823,24829,24831],{},[1720,24824,24825,24827],{},[898,24826,9692],{},[898,24828,4819],{},[1664,24830,1676],{},[1963,24832,24833],{},"4000",[902,24835,24836],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,24839,24840,24863,24895,24930,24963,24999],{},[123,24841,24842,1916],{},[883,24843,24845],{"className":24844},[886],[888,24846,24847],{"xmlns":890},[892,24848,24849,24861],{},[895,24850,24851,24857,24859],{},[1720,24852,24853,24855],{},[898,24854,9692],{},[898,24856,4819],{},[1664,24858,1676],{},[1963,24860,24833],{},[902,24862,24836],{"encoding":904},[123,24864,24865,1916],{},[883,24866,24868],{"className":24867},[886],[888,24869,24870],{"xmlns":890},[892,24871,24872,24892],{},[895,24873,24874,24880,24882,24884,24886,24888,24890],{},[1720,24875,24876,24878],{},[898,24877,1991],{},[898,24879,4819],{},[1664,24881,1676],{},[1963,24883,24289],{},[1664,24885,3753],{},[1963,24887,24833],{},[1664,24889,1676],{},[1963,24891,3365],{},[902,24893,24894],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,24896,24897,1916],{},[883,24898,24900],{"className":24899},[886],[888,24901,24902],{"xmlns":890},[892,24903,24904,24927],{},[895,24905,24906,24914,24916,24918,24920,24922,24924],{},[1810,24907,24908,24910,24912],{},[898,24909,9692],{},[898,24911,2379],{},[898,24913,4819],{},[1664,24915,1676],{},[1963,24917,24230],{},[1664,24919,3753],{},[1963,24921,24833],{},[1664,24923,1676],{},[1963,24925,24926],{},"3000",[902,24928,24929],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,24931,24932,1916],{},[883,24933,24935],{"className":24934},[886],[888,24936,24937],{"xmlns":890},[892,24938,24939,24960],{},[895,24940,24941,24947,24949,24951,24953,24955,24957],{},[1720,24942,24943,24945],{},[898,24944,1956],{},[898,24946,4819],{},[1664,24948,1676],{},[1963,24950,24262],{},[1664,24952,3753],{},[1963,24954,24926],{},[1664,24956,1676],{},[1963,24958,24959],{},"450",[902,24961,24962],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,24964,24965,1916],{},[883,24966,24968],{"className":24967},[886],[888,24969,24970],{"xmlns":890},[892,24971,24972,24996],{},[895,24973,24974,24980,24982,24984,24986,24988,24990,24992,24994],{},[1720,24975,24976,24978],{},[898,24977,1703],{},[898,24979,4819],{},[1664,24981,1676],{},[1963,24983,24230],{},[1664,24985,3753],{},[1963,24987,24926],{},[1664,24989,1700],{},[1963,24991,24243],{},[1664,24993,1676],{},[1963,24995,24926],{},[902,24997,24998],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,25000,25001,25041],{},[883,25002,25004],{"className":25003},[886],[888,25005,25006],{"xmlns":890},[892,25007,25008,25038],{},[895,25009,25010,25016,25018,25026,25028,25034,25036],{},[1720,25011,25012,25014],{},[898,25013,2351],{},[898,25015,4819],{},[1664,25017,1676],{},[1810,25019,25020,25022,25024],{},[898,25021,9692],{},[898,25023,2379],{},[898,25025,4819],{},[1664,25027,1867],{},[1720,25029,25030,25032],{},[898,25031,1703],{},[898,25033,4819],{},[1664,25035,1676],{},[1963,25037,2058],{},[902,25039,25040],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,25043,25044,25046,25047,1343,25064,4454,25085,25110,25111,25114,25115,25128,25129,1977],{},[38,25045,21849],{}," Modely ",[883,25048,25050],{"className":25049},[886],[888,25051,25052],{"xmlns":890},[892,25053,25054,25062],{},[895,25055,25056,25058,25060],{},[898,25057,1703],{},[1690,25059,12789],{},[898,25061,12683],{},[902,25063,12794],{"encoding":904},[883,25065,25067],{"className":25066},[886],[888,25068,25069],{"xmlns":890},[892,25070,25071,25083],{},[895,25072,25073,25075,25077,25079,25081],{},[898,25074,1703],{},[1690,25076,12789],{},[898,25078,12683],{},[1690,25080,12789],{},[898,25082,12611],{},[902,25084,18720],{"encoding":904},[883,25086,25088],{"className":25087},[886],[888,25089,25090],{"xmlns":890},[892,25091,25092,25108],{},[895,25093,25094,25096,25098,25100,25102,25104,25106],{},[898,25095,1703],{},[1690,25097,12789],{},[898,25099,12683],{},[1690,25101,12789],{},[898,25103,12611],{},[1690,25105,12789],{},[898,25107,12819],{},[902,25109,12822],{"encoding":904}," pokládají investice za ",[38,25112,25113],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,25116,25118],{"className":25117},[886],[888,25119,25120],{"xmlns":890},[892,25121,25122,25126],{},[895,25123,25124],{},[898,25125,12540],{},[902,25127,12540],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,25130,25131],{},"model IS-LM",[115,25133,25135],{"id":25134},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,25137,25138,25139,25143,25144,25147,25148,25151],{},"V článku ",[207,25140,25142],{"className":25141,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,25145,25146],{},"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 ",[38,25149,25150],{},"výraznější"," než v mikroekonomických modelech.",[724,25153,25154],{},[1928,25155],{"alt":25156,"className":25157,"src":25158},"imek-multiplikatorovy-efekt-chain",[210,1932],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,25160,12663,25161,1343,25178,1343,25199,25224,25225,25228,25229,25247,25248,25266,25267,25285,25286,25289,25290,1343,25307,25324,25325,25327],{},[883,25162,25164],{"className":25163},[886],[888,25165,25166],{"xmlns":890},[892,25167,25168,25176],{},[895,25169,25170,25172,25174],{},[898,25171,1703],{},[1690,25173,12789],{},[898,25175,12683],{},[902,25177,12794],{"encoding":904},[883,25179,25181],{"className":25180},[886],[888,25182,25183],{"xmlns":890},[892,25184,25185,25197],{},[895,25186,25187,25189,25191,25193,25195],{},[898,25188,1703],{},[1690,25190,12789],{},[898,25192,12683],{},[1690,25194,12789],{},[898,25196,12611],{},[902,25198,18720],{"encoding":904},[883,25200,25202],{"className":25201},[886],[888,25203,25204],{"xmlns":890},[892,25205,25206,25222],{},[895,25207,25208,25210,25212,25214,25216,25218,25220],{},[898,25209,1703],{},[1690,25211,12789],{},[898,25213,12683],{},[1690,25215,12789],{},[898,25217,12611],{},[1690,25219,12789],{},[898,25221,12819],{},[902,25223,12822],{"encoding":904}," se vyšetřuje vliv změn ",[38,25226,25227],{},"exogenních"," veličin (plánovaných investic ",[883,25230,25232],{"className":25231},[886],[888,25233,25234],{"xmlns":890},[892,25235,25236,25244],{},[895,25237,25238],{},[1720,25239,25240,25242],{},[898,25241,12683],{},[1664,25243,4920],{},[902,25245,25246],{"encoding":904},"I^*",", vládních výdajů ",[883,25249,25251],{"className":25250},[886],[888,25252,25253],{"xmlns":890},[892,25254,25255,25263],{},[895,25256,25257],{},[1720,25258,25259,25261],{},[898,25260,12611],{},[1664,25262,4920],{},[902,25264,25265],{"encoding":904},"G^*",", exportu ",[883,25268,25270],{"className":25269},[886],[888,25271,25272],{"xmlns":890},[892,25273,25274,25282],{},[895,25275,25276],{},[1720,25277,25278,25280],{},[898,25279,23753],{},[1664,25281,4920],{},[902,25283,25284],{"encoding":904},"B^*",") na změny ",[38,25287,25288],{},"endogenních"," rovnovážných veličin (",[883,25291,25293],{"className":25292},[886],[888,25294,25295],{"xmlns":890},[892,25296,25297,25305],{},[895,25298,25299],{},[1720,25300,25301,25303],{},[898,25302,9692],{},[898,25304,4819],{},[902,25306,14402],{"encoding":904},[883,25308,25310],{"className":25309},[886],[888,25311,25312],{"xmlns":890},[892,25313,25314,25322],{},[895,25315,25316],{},[1720,25317,25318,25320],{},[898,25319,1703],{},[898,25321,4819],{},[902,25323,14461],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,25326,18477],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,25329,25331],{"id":25330},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,25333,21395,25334,25357,25358,25402],{},[883,25335,25337],{"className":25336},[886],[888,25338,25339],{"xmlns":890},[892,25340,25341,25355],{},[895,25342,25343,25345,25347,25349,25351,25353],{},[898,25344,1703],{},[1664,25346,1676],{},[898,25348,207],{},[898,25350,9692],{},[1664,25352,1700],{},[898,25354,1818],{},[902,25356,19420],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,25359,25361],{"className":25360},[886],[888,25362,25363],{"xmlns":890},[892,25364,25365,25399],{},[895,25366,25367,25373,25375],{},[1720,25368,25369,25371],{},[898,25370,9692],{},[898,25372,4819],{},[1664,25374,1676],{},[2919,25376,25377],{"scriptlevel":2058,"displaystyle":1915},[2922,25378,25379,25391],{},[895,25380,25381,25383,25385],{},[898,25382,1818],{},[1664,25384,1700],{},[1720,25386,25387,25389],{},[898,25388,12683],{},[1664,25390,4920],{},[895,25392,25393,25395,25397],{},[1963,25394,2875],{},[1664,25396,1867],{},[898,25398,207],{},[902,25400,25401],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,25404,25405],{},[883,25406,25408],{"className":25407},[886],[888,25409,25410],{"xmlns":890},[892,25411,25412,25481],{},[895,25413,25414,25432,25434,25464,25466],{},[2922,25415,25416,25426],{},[895,25417,25418,25420],{},[898,25419,10435],{"mathvariant":1726},[1720,25421,25422,25424],{},[898,25423,9692],{},[898,25425,4819],{},[895,25427,25428,25430],{},[898,25429,10435],{"mathvariant":1726},[898,25431,207],{},[1664,25433,1676],{},[2922,25435,25436,25448],{},[895,25437,25438,25440,25442],{},[898,25439,1818],{},[1664,25441,1700],{},[1720,25443,25444,25446],{},[898,25445,12683],{},[1664,25447,4920],{},[895,25449,25450,25452,25454,25456,25458],{},[1664,25451,1667],{"stretchy":1666},[1963,25453,2875],{},[1664,25455,1867],{},[898,25457,207],{},[1720,25459,25460,25462],{},[1664,25461,1673],{"stretchy":1666},[1963,25463,1970],{},[6444,25465],{"width":6446},[895,25467,25468,25471,25478],{},[1690,25469,25470],{},"(multiplik",[8951,25472,25473,25475],{"accent":1915},[1690,25474,207],{},[1664,25476,25477],{},"ˊ",[1690,25479,25480],{},"tor MPC)",[902,25482,25483],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,25485,25486],{},[883,25487,25489],{"className":25488},[886],[888,25490,25491],{"xmlns":890},[892,25492,25493,25562],{},[895,25494,25495,25513,25515,25527,25529],{},[2922,25496,25497,25507],{},[895,25498,25499,25501],{},[898,25500,10435],{"mathvariant":1726},[1720,25502,25503,25505],{},[898,25504,9692],{},[898,25506,4819],{},[895,25508,25509,25511],{},[898,25510,10435],{"mathvariant":1726},[898,25512,1818],{},[1664,25514,1676],{},[2922,25516,25517,25519],{},[1963,25518,2875],{},[895,25520,25521,25523,25525],{},[1963,25522,2875],{},[1664,25524,1867],{},[898,25526,207],{},[6444,25528],{"width":6446},[895,25530,25531,25533,25539,25542,25549,25552,25559],{},[1690,25532,25470],{},[8951,25534,25535,25537],{"accent":1915},[1690,25536,207],{},[1664,25538,25477],{},[1690,25540,25541],{},"tor autonomn",[8951,25543,25544,25547],{"accent":1915},[1690,25545,25546],{},"ı",[1664,25548,25477],{},[1690,25550,25551],{}," spot",[8951,25553,25554,25556],{"accent":1915},[1690,25555,12540],{},[1664,25557,25558],{},"ˇ",[1690,25560,25561],{},"eby)",[902,25563,25564],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,25566,25567],{},[883,25568,25570],{"className":25569},[886],[888,25571,25572],{"xmlns":890},[892,25573,25574,25641],{},[895,25575,25576,25598,25600,25612,25614,25626,25628],{},[2922,25577,25578,25588],{},[895,25579,25580,25582],{},[898,25581,10435],{"mathvariant":1726},[1720,25583,25584,25586],{},[898,25585,9692],{},[898,25587,4819],{},[895,25589,25590,25592],{},[898,25591,10435],{"mathvariant":1726},[1720,25593,25594,25596],{},[898,25595,12683],{},[1664,25597,4920],{},[1664,25599,1676],{},[2922,25601,25602,25604],{},[1963,25603,2875],{},[895,25605,25606,25608,25610],{},[1963,25607,2875],{},[1664,25609,1867],{},[898,25611,207],{},[1664,25613,1676],{},[2922,25615,25616,25618],{},[1963,25617,2875],{},[895,25619,25620,25622,25624],{},[898,25621,1956],{},[898,25623,2398],{},[898,25625,2351],{},[6444,25627],{"width":6446},[895,25629,25630,25632,25638],{},[1690,25631,25470],{},[8951,25633,25634,25636],{"accent":1915},[1690,25635,207],{},[1664,25637,25477],{},[1690,25639,25640],{},"tor investic)",[902,25642,25643],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[4436,25645,25646],{},[724,25647,25648,25650,25651,25654,25655,25668,25669,25686,25687,25705,25706,25750,25751,21920,25768,25771,25772,25789],{},[883,25649,4723],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,25652,25653],{},"důchodem","; z něj se utratí ",[883,25656,25658],{"className":25657},[886],[888,25659,25660],{"xmlns":890},[892,25661,25662,25666],{},[895,25663,25664],{},[898,25665,207],{},[902,25667,207],{"encoding":904}," Kč (= ",[883,25670,25672],{"className":25671},[886],[888,25673,25674],{"xmlns":890},[892,25675,25676,25684],{},[895,25677,25678,25680,25682],{},[898,25679,1956],{},[898,25681,2398],{},[898,25683,1703],{},[902,25685,18545],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,25688,25690],{"className":25689},[886],[888,25691,25692],{"xmlns":890},[892,25693,25694,25702],{},[895,25695,25696],{},[1720,25697,25698,25700],{},[898,25699,207],{},[1963,25701,1970],{},[902,25703,25704],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,25707,25709],{"className":25708},[886],[888,25710,25711],{"xmlns":890},[892,25712,25713,25747],{},[895,25714,25715,25717,25719,25721,25723,25729,25731,25733,25735],{},[1963,25716,2875],{},[1664,25718,1700],{},[898,25720,207],{},[1664,25722,1700],{},[1720,25724,25725,25727],{},[898,25726,207],{},[1963,25728,1970],{},[1664,25730,1700],{},[1664,25732,18605],{},[1664,25734,1676],{},[2922,25736,25737,25739],{},[1963,25738,2875],{},[895,25740,25741,25743,25745],{},[1963,25742,2875],{},[1664,25744,1867],{},[898,25746,207],{},[902,25748,25749],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,25752,25754],{"className":25753},[886],[888,25755,25756],{"xmlns":890},[892,25757,25758,25766],{},[895,25759,25760],{},[1720,25761,25762,25764],{},[898,25763,9692],{},[898,25765,4819],{},[902,25767,14402],{"encoding":904},[38,25769,25770],{},"více"," než korunu — čím vyšší ",[883,25773,25775],{"className":25774},[886],[888,25776,25777],{"xmlns":890},[892,25778,25779,25787],{},[895,25780,25781,25783,25785],{},[898,25782,1956],{},[898,25784,2398],{},[898,25786,1703],{},[902,25788,18545],{"encoding":904},", tím silnější multiplikační efekt.",[724,25791,25792,25795,25796,25822,25823,25826,25827,4454,25848,25873,25874,1977],{},[38,25793,25794],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,25797,25799],{"className":25798},[886],[888,25800,25801],{"xmlns":890},[892,25802,25803,25819],{},[895,25804,25805],{},[2919,25806,25807],{"scriptlevel":2058,"displaystyle":1666},[2922,25808,25809,25811],{},[1963,25810,2875],{},[895,25812,25813,25815,25817],{},[1963,25814,2875],{},[1664,25816,1867],{},[898,25818,207],{},[902,25820,25821],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,25824,25825],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,25828,25830],{"className":25829},[886],[888,25831,25832],{"xmlns":890},[892,25833,25834,25846],{},[895,25835,25836,25838,25840,25842,25844],{},[898,25837,1703],{},[1690,25839,12789],{},[898,25841,12683],{},[1690,25843,12789],{},[898,25845,12611],{},[902,25847,18720],{"encoding":904},[883,25849,25851],{"className":25850},[886],[888,25852,25853],{"xmlns":890},[892,25854,25855,25871],{},[895,25856,25857,25859,25861,25863,25865,25867,25869],{},[898,25858,1703],{},[1690,25860,12789],{},[898,25862,12683],{},[1690,25864,12789],{},[898,25866,12611],{},[1690,25868,12789],{},[898,25870,12819],{},[902,25872,12822],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,25875,25877],{"className":25876,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,25879,25881],{"id":25880},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,25883,12663,25884,1343,25901,4454,25922,12668,25947,10588,25950,25971,25972,1885,25975,25988,25989,6235,26018,26035,26036,26039,26040,26042,26043,26064],{},[883,25885,25887],{"className":25886},[886],[888,25888,25889],{"xmlns":890},[892,25890,25891,25899],{},[895,25892,25893,25895,25897],{},[898,25894,1703],{},[1690,25896,12789],{},[898,25898,12683],{},[902,25900,12794],{"encoding":904},[883,25902,25904],{"className":25903},[886],[888,25905,25906],{"xmlns":890},[892,25907,25908,25920],{},[895,25909,25910,25912,25914,25916,25918],{},[898,25911,1703],{},[1690,25913,12789],{},[898,25915,12683],{},[1690,25917,12789],{},[898,25919,12611],{},[902,25921,18720],{"encoding":904},[883,25923,25925],{"className":25924},[886],[888,25926,25927],{"xmlns":890},[892,25928,25929,25945],{},[895,25930,25931,25933,25935,25937,25939,25941,25943],{},[898,25932,1703],{},[1690,25934,12789],{},[898,25936,12683],{},[1690,25938,12789],{},[898,25940,12611],{},[1690,25942,12789],{},[898,25944,12819],{},[902,25946,12822],{"encoding":904},[38,25948,25949],{},"investice konstantní",[883,25951,25953],{"className":25952},[886],[888,25954,25955],{"xmlns":890},[892,25956,25957,25969],{},[895,25958,25959,25961,25963],{},[898,25960,12683],{},[1664,25962,1676],{},[1720,25964,25965,25967],{},[898,25966,12683],{},[1664,25968,4920],{},[902,25970,12694],{"encoding":904},"). Reálnější je předpoklad, že ",[38,25973,25974],{},"investice závisejí na úrokové míře",[883,25976,25978],{"className":25977},[886],[888,25979,25980],{"xmlns":890},[892,25981,25982,25986],{},[895,25983,25984],{},[898,25985,12540],{},[902,25987,12540],{"encoding":904}," — klesající funkce ",[883,25990,25992],{"className":25991},[886],[888,25993,25994],{"xmlns":890},[892,25995,25996,26016],{},[895,25997,25998,26000,26002,26004,26006,26008,26010,26012,26014],{},[898,25999,12683],{},[1664,26001,1667],{"stretchy":1666},[898,26003,12540],{},[1664,26005,1673],{"stretchy":1666},[1664,26007,1676],{},[898,26009,2034],{},[898,26011,12540],{},[1664,26013,1700],{},[898,26015,1695],{},[902,26017,16256],{"encoding":904},[883,26019,26021],{"className":26020},[886],[888,26022,26023],{"xmlns":890},[892,26024,26025,26033],{},[895,26026,26027,26029,26031],{},[898,26028,2034],{},[1664,26030,4022],{},[1963,26032,2058],{},[902,26034,13014],{"encoding":904},". Přidáním ",[38,26037,26038],{},"trhu peněz"," k trhu zboží vzniká model ",[38,26041,12510],{}," se dvěma neznámými ",[883,26044,26046],{"className":26045},[886],[888,26047,26048],{"xmlns":890},[892,26049,26050,26062],{},[895,26051,26052,26054,26056,26058,26060],{},[1664,26053,1667],{"stretchy":1666},[898,26055,9692],{},[1664,26057,1916],{"separator":1915},[898,26059,12540],{},[1664,26061,1673],{"stretchy":1666},[902,26063,18650],{"encoding":904}," a dvěma rovnicemi:",[120,26066,26067,26117],{},[123,26068,26069,10588,26071,26073,26074,26095,26096,1977],{},[38,26070,16345],{},[614,26072,12553],{},") — klesající přímka v rovině ",[883,26075,26077],{"className":26076},[886],[888,26078,26079],{"xmlns":890},[892,26080,26081,26093],{},[895,26082,26083,26085,26087,26089,26091],{},[1664,26084,1667],{"stretchy":1666},[898,26086,12540],{},[1664,26088,1916],{"separator":1915},[898,26090,9692],{},[1664,26092,1673],{"stretchy":1666},[902,26094,13436],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,26097,26099],{"className":26098},[886],[888,26100,26101],{"xmlns":890},[892,26102,26103,26115],{},[895,26104,26105,26107,26109,26111,26113],{},[898,26106,9692],{},[1664,26108,1676],{},[898,26110,1703],{},[1664,26112,1700],{},[898,26114,12683],{},[902,26116,15243],{"encoding":904},[123,26118,26119,10588,26121,26123,26124,22094,26149,26195],{},[38,26120,16544],{},[614,26122,12560],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,26125,26127],{"className":26126},[886],[888,26128,26129],{"xmlns":890},[892,26130,26131,26147],{},[895,26132,26133,26139,26141],{},[1720,26134,26135,26137],{},[898,26136,1956],{},[898,26138,2379],{},[1664,26140,1676],{},[1720,26142,26143,26145],{},[898,26144,1956],{},[1664,26146,4920],{},[902,26148,13979],{"encoding":904},[883,26150,26152],{"className":26151},[886],[888,26153,26154],{"xmlns":890},[892,26155,26156,26192],{},[895,26157,26158,26164,26166,26172,26174,26176,26182,26184,26186],{},[1720,26159,26160,26162],{},[898,26161,1956],{},[898,26163,2379],{},[1664,26165,1676],{},[2355,26167,26168,26170],{},[898,26169,13736],{},[1963,26171,2875],{},[898,26173,9692],{},[1664,26175,1700],{},[2355,26177,26178,26180],{},[898,26179,13736],{},[1963,26181,1970],{},[898,26183,12540],{},[1664,26185,1700],{},[2355,26187,26188,26190],{},[898,26189,13736],{},[1963,26191,2774],{},[902,26193,26194],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,26197,26198,1885,26201,26234,26235,26237,26238,26240],{},[38,26199,26200],{},"Simultánní rovnovážný bod",[883,26202,26204],{"className":26203},[886],[888,26205,26206],{"xmlns":890},[892,26207,26208,26232],{},[895,26209,26210,26212,26214,26216,26222,26224,26230],{},[898,26211,4819],{},[1664,26213,1676],{},[1664,26215,1667],{"stretchy":1666},[1720,26217,26218,26220],{},[898,26219,12540],{},[898,26221,4819],{},[1664,26223,1916],{"separator":1915},[1720,26225,26226,26228],{},[898,26227,9692],{},[898,26229,4819],{},[1664,26231,1673],{"stretchy":1666},[902,26233,16636],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,26236,12598],{}," (posun IS) a ",[38,26239,12630],{}," (posun LM).",[724,26242,26243],{},[38,26244,26245,26246,1343,26268,1343,26290,1343,26312,26334,26335,1977],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,26247,26249],{"className":26248},[886],[888,26250,26251],{"xmlns":890},[892,26252,26253,26265],{},[895,26254,26255,26261,26263],{},[1720,26256,26257,26259],{},[898,26258,9692],{},[898,26260,4819],{},[1664,26262,1676],{},[1963,26264,15614],{},[902,26266,26267],{"encoding":904},"Y^E = 5000",[883,26269,26271],{"className":26270},[886],[888,26272,26273],{"xmlns":890},[892,26274,26275,26287],{},[895,26276,26277,26283,26285],{},[1720,26278,26279,26281],{},[898,26280,12540],{},[898,26282,4819],{},[1664,26284,1676],{},[1963,26286,2826],{},[902,26288,26289],{"encoding":904},"r^E = 5",[883,26291,26293],{"className":26292},[886],[888,26294,26295],{"xmlns":890},[892,26296,26297,26309],{},[895,26298,26299,26305,26307],{},[1720,26300,26301,26303],{},[898,26302,1703],{},[898,26304,4819],{},[1664,26306,1676],{},[1963,26308,15651],{},[902,26310,26311],{"encoding":904},"C^E = 4100",[883,26313,26315],{"className":26314},[886],[888,26316,26317],{"xmlns":890},[892,26318,26319,26331],{},[895,26320,26321,26327,26329],{},[1720,26322,26323,26325],{},[898,26324,12683],{},[898,26326,4819],{},[1664,26328,1676],{},[1963,26330,15690],{},[902,26332,26333],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,26336,945],{"className":26337,"dataFsResolvedFilePath":943,"href":944},[210],[115,26339,26341],{"id":26340},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,26343,26344,26408,26519,26662,26904,26972],{},[123,26345,26346,26349,26350,26372,26373,26407],{},[38,26347,26348],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,26351,26353],{"className":26352},[886],[888,26354,26355],{"xmlns":890},[892,26356,26357,26369],{},[895,26358,26359,26361,26363,26365,26367],{},[898,26360,12611],{},[898,26362,18794],{},[898,26364,2398],{},[1664,26366,3315],{},[898,26368,9692],{},[902,26370,26371],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,26374,26376],{"className":26375},[886],[888,26377,26378],{"xmlns":890},[892,26379,26380,26404],{},[895,26381,26382,26384,26386,26388,26390,26392,26394,26396,26398,26400,26402],{},[898,26383,12611],{},[898,26385,18794],{},[898,26387,2398],{},[1664,26389,1676],{},[898,26391,1703],{},[1664,26393,1700],{},[898,26395,12683],{},[1664,26397,1700],{},[898,26399,12611],{},[1664,26401,1700],{},[898,26403,12819],{},[902,26405,26406],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,26409,26410,26412,26413,26434,26435,1343,26458,26489,26490,26503,26504,1977],{},[38,26411,19028],{}," splňují ",[883,26414,26416],{"className":26415},[886],[888,26417,26418],{"xmlns":890},[892,26419,26420,26432],{},[895,26421,26422,26424,26426,26428,26430],{},[898,26423,9692],{},[1664,26425,1676],{},[898,26427,1703],{},[1664,26429,1700],{},[898,26431,2351],{},[902,26433,13193],{"encoding":904}," (7.2); lineární model ",[883,26436,26438],{"className":26437},[886],[888,26439,26440],{"xmlns":890},[892,26441,26442,26456],{},[895,26443,26444,26446,26448,26450,26452,26454],{},[898,26445,1703],{},[1664,26447,1676],{},[898,26449,207],{},[898,26451,9692],{},[1664,26453,1700],{},[898,26455,1818],{},[902,26457,19420],{"encoding":904},[883,26459,26461],{"className":26460},[886],[888,26462,26463],{"xmlns":890},[892,26464,26465,26487],{},[895,26466,26467,26469,26471,26473,26475,26477,26479,26481,26483,26485],{},[898,26468,2351],{},[1664,26470,1676],{},[1664,26472,1667],{"stretchy":1666},[1963,26474,2875],{},[1664,26476,1867],{},[898,26478,207],{},[1664,26480,1673],{"stretchy":1666},[898,26482,9692],{},[1664,26484,1867],{},[898,26486,1818],{},[902,26488,19669],{"encoding":904}," s autonomní spotřebou ",[883,26491,26493],{"className":26492},[886],[888,26494,26495],{"xmlns":890},[892,26496,26497,26501],{},[895,26498,26499],{},[898,26500,1818],{},[902,26502,1818],{"encoding":904}," a autonomními úsporami ",[883,26505,26507],{"className":26506},[886],[888,26508,26509],{"xmlns":890},[892,26510,26511,26517],{},[895,26512,26513,26515],{},[1664,26514,1867],{},[898,26516,1818],{},[902,26518,19748],{"encoding":904},[123,26520,26521,1885,26524,1343,26554,26584,26585,26615,26616,1343,26637,1977],{},[38,26522,26523],{},"Mezní sklony",[883,26525,26527],{"className":26526},[886],[888,26528,26529],{"xmlns":890},[892,26530,26531,26551],{},[895,26532,26533,26535,26537,26539,26541,26543,26545,26547,26549],{},[898,26534,1956],{},[898,26536,2398],{},[898,26538,1703],{},[1664,26540,1676],{},[898,26542,1695],{"mathvariant":1726},[898,26544,1703],{},[898,26546,5240],{"mathvariant":1726},[898,26548,1695],{"mathvariant":1726},[898,26550,9692],{},[902,26552,26553],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,26555,26557],{"className":26556},[886],[888,26558,26559],{"xmlns":890},[892,26560,26561,26581],{},[895,26562,26563,26565,26567,26569,26571,26573,26575,26577,26579],{},[898,26564,1956],{},[898,26566,2398],{},[898,26568,2351],{},[1664,26570,1676],{},[898,26572,1695],{"mathvariant":1726},[898,26574,2351],{},[898,26576,5240],{"mathvariant":1726},[898,26578,1695],{"mathvariant":1726},[898,26580,9692],{},[902,26582,26583],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,26586,26588],{"className":26587},[886],[888,26589,26590],{"xmlns":890},[892,26591,26592,26612],{},[895,26593,26594,26596,26598,26600,26602,26604,26606,26608,26610],{},[898,26595,1956],{},[898,26597,2398],{},[898,26599,1703],{},[1664,26601,1700],{},[898,26603,1956],{},[898,26605,2398],{},[898,26607,2351],{},[1664,26609,1676],{},[1963,26611,2875],{},[902,26613,26614],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,26617,26619],{"className":26618},[886],[888,26620,26621],{"xmlns":890},[892,26622,26623,26635],{},[895,26624,26625,26627,26629,26631,26633],{},[898,26626,1956],{},[898,26628,2398],{},[898,26630,1703],{},[1664,26632,1676],{},[898,26634,207],{},[902,26636,20389],{"encoding":904},[883,26638,26640],{"className":26639},[886],[888,26641,26642],{"xmlns":890},[892,26643,26644,26660],{},[895,26645,26646,26648,26650,26652,26654,26656,26658],{},[898,26647,1956],{},[898,26649,2398],{},[898,26651,2351],{},[1664,26653,1676],{},[1963,26655,2875],{},[1664,26657,1867],{},[898,26659,207],{},[902,26661,20415],{"encoding":904},[123,26663,26664,26667,26668],{},[38,26665,26666],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,26669,26670,26758,26827],{},[123,26671,26672,26689,26690,26711,26712,1916],{},[883,26673,26675],{"className":26674},[886],[888,26676,26677],{"xmlns":890},[892,26678,26679,26687],{},[895,26680,26681,26683,26685],{},[898,26682,1703],{},[1690,26684,12789],{},[898,26686,12683],{},[902,26688,12794],{"encoding":904},": ",[883,26691,26693],{"className":26692},[886],[888,26694,26695],{"xmlns":890},[892,26696,26697,26709],{},[895,26698,26699,26701,26703,26705,26707],{},[898,26700,9692],{},[1664,26702,1676],{},[898,26704,1703],{},[1664,26706,1700],{},[898,26708,12683],{},[902,26710,15243],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,26713,26715],{"className":26714},[886],[888,26716,26717],{"xmlns":890},[892,26718,26719,26755],{},[895,26720,26721,26727,26729,26731,26733,26735,26741,26743,26745,26747,26749,26751,26753],{},[1720,26722,26723,26725],{},[898,26724,9692],{},[898,26726,4819],{},[1664,26728,1676],{},[1664,26730,1667],{"stretchy":1666},[898,26732,1818],{},[1664,26734,1700],{},[1720,26736,26737,26739],{},[898,26738,12683],{},[1664,26740,4920],{},[1664,26742,1673],{"stretchy":1666},[898,26744,5240],{"mathvariant":1726},[1664,26746,1667],{"stretchy":1666},[1963,26748,2875],{},[1664,26750,1867],{},[898,26752,207],{},[1664,26754,1673],{"stretchy":1666},[902,26756,26757],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,26759,26760,26781,26782,26801,26802,1916],{},[883,26761,26763],{"className":26762},[886],[888,26764,26765],{"xmlns":890},[892,26766,26767,26779],{},[895,26768,26769,26771,26773,26775,26777],{},[898,26770,1703],{},[1690,26772,12789],{},[898,26774,12683],{},[1690,26776,12789],{},[898,26778,12611],{},[902,26780,18720],{"encoding":904},": přidává vládu, zdanění ",[883,26783,26785],{"className":26784},[886],[888,26786,26787],{"xmlns":890},[892,26788,26789,26799],{},[895,26790,26791,26793,26795,26797],{},[898,26792,1991],{},[1664,26794,1667],{"stretchy":1666},[898,26796,9692],{},[1664,26798,1673],{"stretchy":1666},[902,26800,22719],{"encoding":904}," a disponibilní důchod ",[883,26803,26805],{"className":26804},[886],[888,26806,26807],{"xmlns":890},[892,26808,26809,26825],{},[895,26810,26811,26817,26819,26821,26823],{},[2355,26812,26813,26815],{},[898,26814,9692],{},[898,26816,2379],{},[1664,26818,1676],{},[898,26820,9692],{},[1664,26822,1867],{},[898,26824,1991],{},[902,26826,22218],{"encoding":904},[123,26828,26829,26854,26855,22094,26876,1977],{},[883,26830,26832],{"className":26831},[886],[888,26833,26834],{"xmlns":890},[892,26835,26836,26852],{},[895,26837,26838,26840,26842,26844,26846,26848,26850],{},[898,26839,1703],{},[1690,26841,12789],{},[898,26843,12683],{},[1690,26845,12789],{},[898,26847,12611],{},[1690,26849,12789],{},[898,26851,12819],{},[902,26853,12822],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,26856,26858],{"className":26857},[886],[888,26859,26860],{"xmlns":890},[892,26861,26862,26874],{},[895,26863,26864,26866,26868,26870,26872],{},[898,26865,12819],{},[1664,26867,1676],{},[898,26869,23753],{},[1664,26871,1867],{},[898,26873,1956],{},[902,26875,23760],{"encoding":904},[883,26877,26879],{"className":26878},[886],[888,26880,26881],{"xmlns":890},[892,26882,26883,26901],{},[895,26884,26885,26887,26889,26891,26893,26899],{},[898,26886,1956],{},[1664,26888,1676],{},[898,26890,1956],{},[1664,26892,1667],{"stretchy":1666},[2355,26894,26895,26897],{},[898,26896,9692],{},[898,26898,2379],{},[1664,26900,1673],{"stretchy":1666},[902,26902,26903],{"encoding":904},"M = M(Y_D)",[123,26905,26906,26909,26910,1885,26913,26971],{},[38,26907,26908],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,26911,26912],{},"multiplikátor investic",[883,26914,26916],{"className":26915},[886],[888,26917,26918],{"xmlns":890},[892,26919,26920,26968],{},[895,26921,26922,26924,26930,26932,26934,26940,26942,26944,26946,26948,26950,26952,26954,26956,26958,26960,26962,26964,26966],{},[898,26923,10435],{"mathvariant":1726},[1720,26925,26926,26928],{},[898,26927,9692],{},[898,26929,4819],{},[898,26931,5240],{"mathvariant":1726},[898,26933,10435],{"mathvariant":1726},[1720,26935,26936,26938],{},[898,26937,12683],{},[1664,26939,4920],{},[1664,26941,1676],{},[1963,26943,2875],{},[898,26945,5240],{"mathvariant":1726},[1664,26947,1667],{"stretchy":1666},[1963,26949,2875],{},[1664,26951,1867],{},[898,26953,207],{},[1664,26955,1673],{"stretchy":1666},[1664,26957,1676],{},[1963,26959,2875],{},[898,26961,5240],{"mathvariant":1726},[898,26963,1956],{},[898,26965,2398],{},[898,26967,2351],{},[902,26969,26970],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,26973,26974,26976,26977,26992,26993,19148,27010,27025,27026,27051,27052,1977],{},[38,26975,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,26978,26980],{"className":26979},[886],[888,26981,26982],{"xmlns":890},[892,26983,26984,26990],{},[895,26985,26986,26988],{},[898,26987,12683],{},[898,26989,2351],{},[902,26991,12550],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,26994,26996],{"className":26995},[886],[888,26997,26998],{"xmlns":890},[892,26999,27000,27008],{},[895,27001,27002,27004,27006],{},[898,27003,12683],{},[1664,27005,1676],{},[898,27007,2351],{},[902,27009,13211],{"encoding":904},[883,27011,27013],{"className":27012},[886],[888,27014,27015],{"xmlns":890},[892,27016,27017,27023],{},[895,27018,27019,27021],{},[898,27020,10358],{},[898,27022,1956],{},[902,27024,12557],{"encoding":904}," rovnováhu trhu peněz (",[883,27027,27029],{"className":27028},[886],[888,27030,27031],{"xmlns":890},[892,27032,27033,27049],{},[895,27034,27035,27041,27043],{},[1720,27036,27037,27039],{},[898,27038,1956],{},[898,27040,2379],{},[1664,27042,1676],{},[1720,27044,27045,27047],{},[898,27046,1956],{},[1664,27048,4920],{},[902,27050,13979],{"encoding":904},"); průsečík dává ",[883,27053,27055],{"className":27054},[886],[888,27056,27057],{"xmlns":890},[892,27058,27059,27079],{},[895,27060,27061,27063,27069,27071,27077],{},[1664,27062,1667],{"stretchy":1666},[1720,27064,27065,27067],{},[898,27066,9692],{},[898,27068,4819],{},[1664,27070,1916],{"separator":1915},[1720,27072,27073,27075],{},[898,27074,12540],{},[898,27076,4819],{},[1664,27078,1673],{"stretchy":1666},[902,27080,12594],{"encoding":904},[115,27082,16219],{"id":16218},[120,27084,27085,27123,27163,27253,27335,27389,27445,27504,27539,27544,27616,27691,27777,27839,27907,27965,28018,28057],{},[123,27086,27087,7581,27090,26407],{},[38,27088,27089],{},"Hrubý národní produkt (GNP)",[883,27091,27093],{"className":27092},[886],[888,27094,27095],{"xmlns":890},[892,27096,27097,27121],{},[895,27098,27099,27101,27103,27105,27107,27109,27111,27113,27115,27117,27119],{},[898,27100,12611],{},[898,27102,18794],{},[898,27104,2398],{},[1664,27106,1676],{},[898,27108,1703],{},[1664,27110,1700],{},[898,27112,12683],{},[1664,27114,1700],{},[898,27116,12611],{},[1664,27118,1700],{},[898,27120,12819],{},[902,27122,26406],{"encoding":904},[123,27124,27125,27141,27142,1977],{},[38,27126,27127,27128],{},"Národní důchod ",[883,27129,27131],{"className":27130},[886],[888,27132,27133],{"xmlns":890},[892,27134,27135,27139],{},[895,27136,27137],{},[898,27138,9692],{},[902,27140,9692],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,27143,27145],{"className":27144},[886],[888,27146,27147],{"xmlns":890},[892,27148,27149,27161],{},[895,27150,27151,27153,27155,27157,27159],{},[898,27152,12611],{},[898,27154,18794],{},[898,27156,2398],{},[1664,27158,3315],{},[898,27160,9692],{},[902,27162,26371],{"encoding":904},[123,27164,27165,27191,27192,1343,27215,1343,27236,1977],{},[38,27166,27167,27168],{},"Funkce spotřeby ",[883,27169,27171],{"className":27170},[886],[888,27172,27173],{"xmlns":890},[892,27174,27175,27189],{},[895,27176,27177,27179,27181,27183,27185,27187],{},[898,27178,1703],{},[1664,27180,1676],{},[898,27182,1703],{},[1664,27184,1667],{"stretchy":1666},[898,27186,9692],{},[1664,27188,1673],{"stretchy":1666},[902,27190,21240],{"encoding":904}," — lineární model ",[883,27193,27195],{"className":27194},[886],[888,27196,27197],{"xmlns":890},[892,27198,27199,27213],{},[895,27200,27201,27203,27205,27207,27209,27211],{},[898,27202,1703],{},[1664,27204,1676],{},[898,27206,207],{},[898,27208,9692],{},[1664,27210,1700],{},[898,27212,1818],{},[902,27214,19420],{"encoding":904},[883,27216,27218],{"className":27217},[886],[888,27219,27220],{"xmlns":890},[892,27221,27222,27234],{},[895,27223,27224,27226,27228,27230,27232],{},[1963,27225,2058],{},[1664,27227,4022],{},[898,27229,207],{},[1664,27231,4022],{},[1963,27233,2875],{},[902,27235,19336],{"encoding":904},[883,27237,27239],{"className":27238},[886],[888,27240,27241],{"xmlns":890},[892,27242,27243,27251],{},[895,27244,27245,27247,27249],{},[898,27246,1818],{},[1664,27248,3984],{},[1963,27250,2058],{},[902,27252,19314],{"encoding":904},[123,27254,27255,7581,27282,27303,27304,1977],{},[38,27256,27257,27258],{},"Funkce úspor ",[883,27259,27261],{"className":27260},[886],[888,27262,27263],{"xmlns":890},[892,27264,27265,27279],{},[895,27266,27267,27269,27271,27273,27275,27277],{},[898,27268,2351],{},[1664,27270,1676],{},[898,27272,2351],{},[1664,27274,1667],{"stretchy":1666},[898,27276,9692],{},[1664,27278,1673],{"stretchy":1666},[902,27280,27281],{"encoding":904},"S = S(Y)",[883,27283,27285],{"className":27284},[886],[888,27286,27287],{"xmlns":890},[892,27288,27289,27301],{},[895,27290,27291,27293,27295,27297,27299],{},[898,27292,9692],{},[1664,27294,1676],{},[898,27296,1703],{},[1664,27298,1700],{},[898,27300,2351],{},[902,27302,13193],{"encoding":904},"; lineární ",[883,27305,27307],{"className":27306},[886],[888,27308,27309],{"xmlns":890},[892,27310,27311,27333],{},[895,27312,27313,27315,27317,27319,27321,27323,27325,27327,27329,27331],{},[898,27314,2351],{},[1664,27316,1676],{},[1664,27318,1667],{"stretchy":1666},[1963,27320,2875],{},[1664,27322,1867],{},[898,27324,207],{},[1664,27326,1673],{"stretchy":1666},[898,27328,9692],{},[1664,27330,1867],{},[898,27332,1818],{},[902,27334,19669],{"encoding":904},[123,27336,27337,7581,27340,1343,27363,1977],{},[38,27338,27339],{},"Autonomní spotřeba\u002Fúspory",[883,27341,27343],{"className":27342},[886],[888,27344,27345],{"xmlns":890},[892,27346,27347,27361],{},[895,27348,27349,27351,27353,27355,27357,27359],{},[898,27350,1703],{},[1664,27352,1667],{"stretchy":1666},[1963,27354,2058],{},[1664,27356,1673],{"stretchy":1666},[1664,27358,1676],{},[898,27360,1818],{},[902,27362,20061],{"encoding":904},[883,27364,27366],{"className":27365},[886],[888,27367,27368],{"xmlns":890},[892,27369,27370,27386],{},[895,27371,27372,27374,27376,27378,27380,27382,27384],{},[898,27373,2351],{},[1664,27375,1667],{"stretchy":1666},[1963,27377,2058],{},[1664,27379,1673],{"stretchy":1666},[1664,27381,1676],{},[1664,27383,1867],{},[898,27385,1818],{},[902,27387,27388],{"encoding":904},"S(0) = -b",[123,27390,27391,27423,27424,4488],{},[38,27392,27393,27394],{},"Mezní sklon ke spotřebě ",[883,27395,27397],{"className":27396},[886],[888,27398,27399],{"xmlns":890},[892,27400,27401,27421],{},[895,27402,27403,27405,27407,27409,27411,27413,27415,27417,27419],{},[898,27404,1956],{},[898,27406,2398],{},[898,27408,1703],{},[1664,27410,1676],{},[898,27412,1695],{"mathvariant":1726},[898,27414,1703],{},[898,27416,5240],{"mathvariant":1726},[898,27418,1695],{"mathvariant":1726},[898,27420,9692],{},[902,27422,26553],{"encoding":904}," (v lineárním modelu ",[883,27425,27427],{"className":27426},[886],[888,27428,27429],{"xmlns":890},[892,27430,27431,27443],{},[895,27432,27433,27435,27437,27439,27441],{},[898,27434,1956],{},[898,27436,2398],{},[898,27438,1703],{},[1664,27440,1676],{},[898,27442,207],{},[902,27444,20389],{"encoding":904},[123,27446,27447,27423,27479,4488],{},[38,27448,27449,27450],{},"Mezní sklon k úsporám ",[883,27451,27453],{"className":27452},[886],[888,27454,27455],{"xmlns":890},[892,27456,27457,27477],{},[895,27458,27459,27461,27463,27465,27467,27469,27471,27473,27475],{},[898,27460,1956],{},[898,27462,2398],{},[898,27464,2351],{},[1664,27466,1676],{},[898,27468,1695],{"mathvariant":1726},[898,27470,2351],{},[898,27472,5240],{"mathvariant":1726},[898,27474,1695],{"mathvariant":1726},[898,27476,9692],{},[902,27478,26583],{"encoding":904},[883,27480,27482],{"className":27481},[886],[888,27483,27484],{"xmlns":890},[892,27485,27486,27502],{},[895,27487,27488,27490,27492,27494,27496,27498,27500],{},[898,27489,1956],{},[898,27491,2398],{},[898,27493,2351],{},[1664,27495,1676],{},[1963,27497,2875],{},[1664,27499,1867],{},[898,27501,207],{},[902,27503,20415],{"encoding":904},[123,27505,27506,1885,27509,27538],{},[38,27507,27508],{},"Vztah",[883,27510,27512],{"className":27511},[886],[888,27513,27514],{"xmlns":890},[892,27515,27516,27536],{},[895,27517,27518,27520,27522,27524,27526,27528,27530,27532,27534],{},[898,27519,1956],{},[898,27521,2398],{},[898,27523,1703],{},[1664,27525,1700],{},[898,27527,1956],{},[898,27529,2398],{},[898,27531,2351],{},[1664,27533,1676],{},[1963,27535,2875],{},[902,27537,26614],{"encoding":904}," (7.5).",[123,27540,27541,27543],{},[38,27542,21083],{}," — rovnováha agregátní poptávky a nabídky.",[123,27545,27546,27549,27550,16291,27571,1977],{},[38,27547,27548],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,27551,27553],{"className":27552},[886],[888,27554,27555],{"xmlns":890},[892,27556,27557,27569],{},[895,27558,27559,27561,27563,27565,27567],{},[898,27560,9692],{},[1664,27562,1676],{},[898,27564,1703],{},[1664,27566,1700],{},[898,27568,12683],{},[902,27570,15243],{"encoding":904},[883,27572,27574],{"className":27573},[886],[888,27575,27576],{"xmlns":890},[892,27577,27578,27614],{},[895,27579,27580,27586,27588,27590,27592,27594,27600,27602,27604,27606,27608,27610,27612],{},[1720,27581,27582,27584],{},[898,27583,9692],{},[898,27585,4819],{},[1664,27587,1676],{},[1664,27589,1667],{"stretchy":1666},[898,27591,1818],{},[1664,27593,1700],{},[1720,27595,27596,27598],{},[898,27597,12683],{},[1664,27599,4920],{},[1664,27601,1673],{"stretchy":1666},[898,27603,5240],{"mathvariant":1726},[1664,27605,1667],{"stretchy":1666},[1963,27607,2875],{},[1664,27609,1867],{},[898,27611,207],{},[1664,27613,1673],{"stretchy":1666},[902,27615,26757],{"encoding":904},[123,27617,27618,27621,27622,1343,27641,16291,27666,1977],{},[38,27619,27620],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,27623,27625],{"className":27624},[886],[888,27626,27627],{"xmlns":890},[892,27628,27629,27639],{},[895,27630,27631,27633,27635,27637],{},[898,27632,1991],{},[1664,27634,1667],{"stretchy":1666},[898,27636,9692],{},[1664,27638,1673],{"stretchy":1666},[902,27640,22719],{"encoding":904},[883,27642,27644],{"className":27643},[886],[888,27645,27646],{"xmlns":890},[892,27647,27648,27664],{},[895,27649,27650,27656,27658,27660,27662],{},[2355,27651,27652,27654],{},[898,27653,9692],{},[898,27655,2379],{},[1664,27657,1676],{},[898,27659,9692],{},[1664,27661,1867],{},[898,27663,1991],{},[902,27665,22218],{"encoding":904},[883,27667,27669],{"className":27668},[886],[888,27670,27671],{"xmlns":890},[892,27672,27673,27689],{},[895,27674,27675,27677,27679,27681,27683,27685,27687],{},[898,27676,9692],{},[1664,27678,1676],{},[898,27680,1703],{},[1664,27682,1700],{},[898,27684,12683],{},[1664,27686,1700],{},[898,27688,12611],{},[902,27690,22189],{"encoding":904},[123,27692,27693,27696,27697,27718,27719,16291,27743,1977],{},[38,27694,27695],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,27698,27700],{"className":27699},[886],[888,27701,27702],{"xmlns":890},[892,27703,27704,27716],{},[895,27705,27706,27708,27710,27712,27714],{},[898,27707,12819],{},[1664,27709,1676],{},[898,27711,23753],{},[1664,27713,1867],{},[898,27715,1956],{},[902,27717,23760],{"encoding":904},", importem ",[883,27720,27722],{"className":27721},[886],[888,27723,27724],{"xmlns":890},[892,27725,27726,27740],{},[895,27727,27728,27730,27732,27738],{},[898,27729,1956],{},[1664,27731,1667],{"stretchy":1666},[2355,27733,27734,27736],{},[898,27735,9692],{},[898,27737,2379],{},[1664,27739,1673],{"stretchy":1666},[902,27741,27742],{"encoding":904},"M(Y_D)",[883,27744,27746],{"className":27745},[886],[888,27747,27748],{"xmlns":890},[892,27749,27750,27774],{},[895,27751,27752,27754,27756,27758,27760,27762,27764,27766,27768,27770,27772],{},[898,27753,9692],{},[1664,27755,1676],{},[898,27757,1703],{},[1664,27759,1700],{},[898,27761,12683],{},[1664,27763,1700],{},[898,27765,12611],{},[1664,27767,1700],{},[898,27769,23753],{},[1664,27771,1867],{},[898,27773,1956],{},[902,27775,27776],{"encoding":904},"Y = C + I + G + B - M",[123,27778,27779,7581,27782,26971],{},[38,27780,27781],{},"Multiplikátor investic",[883,27783,27785],{"className":27784},[886],[888,27786,27787],{"xmlns":890},[892,27788,27789,27837],{},[895,27790,27791,27793,27799,27801,27803,27809,27811,27813,27815,27817,27819,27821,27823,27825,27827,27829,27831,27833,27835],{},[898,27792,10435],{"mathvariant":1726},[1720,27794,27795,27797],{},[898,27796,9692],{},[898,27798,4819],{},[898,27800,5240],{"mathvariant":1726},[898,27802,10435],{"mathvariant":1726},[1720,27804,27805,27807],{},[898,27806,12683],{},[1664,27808,4920],{},[1664,27810,1676],{},[1963,27812,2875],{},[898,27814,5240],{"mathvariant":1726},[1664,27816,1667],{"stretchy":1666},[1963,27818,2875],{},[1664,27820,1867],{},[898,27822,207],{},[1664,27824,1673],{"stretchy":1666},[1664,27826,1676],{},[1963,27828,2875],{},[898,27830,5240],{"mathvariant":1726},[898,27832,1956],{},[898,27834,2398],{},[898,27836,2351],{},[902,27838,26970],{"encoding":904},[123,27840,27841,7581,27872,1343,27889,27906],{},[38,27842,16226,27843],{},[883,27844,27846],{"className":27845},[886],[888,27847,27848],{"xmlns":890},[892,27849,27850,27870],{},[895,27851,27852,27854,27856,27858,27860,27862,27864,27866,27868],{},[898,27853,12683],{},[1664,27855,1667],{"stretchy":1666},[898,27857,12540],{},[1664,27859,1673],{"stretchy":1666},[1664,27861,1676],{},[898,27863,2034],{},[898,27865,12540],{},[1664,27867,1700],{},[898,27869,1695],{},[902,27871,16256],{"encoding":904},[883,27873,27875],{"className":27874},[886],[888,27876,27877],{"xmlns":890},[892,27878,27879,27887],{},[895,27880,27881,27883,27885],{},[898,27882,2034],{},[1664,27884,4022],{},[1963,27886,2058],{},[902,27888,13014],{"encoding":904},[883,27890,27892],{"className":27891},[886],[888,27893,27894],{"xmlns":890},[892,27895,27896,27904],{},[895,27897,27898,27900,27902],{},[898,27899,1695],{},[1664,27901,3984],{},[1963,27903,2058],{},[902,27905,12993],{"encoding":904},"; klesající.",[123,27908,27909,27911,27912,27914,27915,27964],{},[38,27910,16345],{}," — rovnováha na trhu zboží (",[614,27913,12553],{},"); ",[883,27916,27918],{"className":27917},[886],[888,27919,27920],{"xmlns":890},[892,27921,27922,27962],{},[895,27923,27924,27926,27928,27940,27942,27944],{},[898,27925,9692],{},[1664,27927,1676],{},[2922,27929,27930,27932],{},[898,27931,2034],{},[895,27933,27934,27936,27938],{},[1963,27935,2875],{},[1664,27937,1867],{},[898,27939,207],{},[898,27941,12540],{},[1664,27943,1700],{},[2922,27945,27946,27954],{},[895,27947,27948,27950,27952],{},[898,27949,1818],{},[1664,27951,1700],{},[898,27953,1695],{},[895,27955,27956,27958,27960],{},[1963,27957,2875],{},[1664,27959,1867],{},[898,27961,207],{},[902,27963,16398],{"encoding":904}," (7.14); klesající.",[123,27966,27967,27969,27970,27914,27972,28017],{},[38,27968,16544],{}," — rovnováha na trhu peněz (",[614,27971,12560],{},[883,27973,27975],{"className":27974},[886],[888,27976,27977],{"xmlns":890},[892,27978,27979,28015],{},[895,27980,27981,27987,27989,27995,27997,27999,28005,28007,28009],{},[1720,27982,27983,27985],{},[898,27984,1956],{},[1664,27986,4920],{},[1664,27988,1676],{},[2355,27990,27991,27993],{},[898,27992,13736],{},[1963,27994,2875],{},[898,27996,9692],{},[1664,27998,1700],{},[2355,28000,28001,28003],{},[898,28002,13736],{},[1963,28004,1970],{},[898,28006,12540],{},[1664,28008,1700],{},[2355,28010,28011,28013],{},[898,28012,13736],{},[1963,28014,2774],{},[902,28016,16592],{"encoding":904}," (7.15); rostoucí.",[123,28019,28020,7581,28023,1977],{},[38,28021,28022],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,28024,28026],{"className":28025},[886],[888,28027,28028],{"xmlns":890},[892,28029,28030,28054],{},[895,28031,28032,28038,28040,28046,28048],{},[1720,28033,28034,28036],{},[898,28035,1956],{},[898,28037,2379],{},[1664,28039,1676],{},[2355,28041,28042,28044],{},[898,28043,10358],{},[1963,28045,2875],{},[1664,28047,1700],{},[2355,28049,28050,28052],{},[898,28051,10358],{},[1963,28053,1970],{},[902,28055,28056],{"encoding":904},"M^D = L_1 + L_2",[123,28058,28059,16602,28061,14479,28074,4454,28089,28104,28105,1977],{},[38,28060,945],{},[883,28062,28064],{"className":28063},[886],[888,28065,28066],{"xmlns":890},[892,28067,28068,28072],{},[895,28069,28070],{},[898,28071,4819],{},[902,28073,4819],{"encoding":904},[883,28075,28077],{"className":28076},[886],[888,28078,28079],{"xmlns":890},[892,28080,28081,28087],{},[895,28082,28083,28085],{},[898,28084,12683],{},[898,28086,2351],{},[902,28088,12550],{"encoding":904},[883,28090,28092],{"className":28091},[886],[888,28093,28094],{"xmlns":890},[892,28095,28096,28102],{},[895,28097,28098,28100],{},[898,28099,10358],{},[898,28101,1956],{},[902,28103,12557],{"encoding":904}," určuje ",[883,28106,28108],{"className":28107},[886],[888,28109,28110],{"xmlns":890},[892,28111,28112,28132],{},[895,28113,28114,28116,28122,28124,28130],{},[1664,28115,1667],{"stretchy":1666},[1720,28117,28118,28120],{},[898,28119,9692],{},[898,28121,4819],{},[1664,28123,1916],{"separator":1915},[1720,28125,28126,28128],{},[898,28127,12540],{},[898,28129,4819],{},[1664,28131,1673],{"stretchy":1666},[902,28133,12594],{"encoding":904},[115,28135,2497],{"id":2496},[120,28137,28138,28145,28152],{},[123,28139,28140,1885,28142],{},[38,28141,16703],{},[207,28143,16707],{"className":28144,"dataFsResolvedFilePath":2575,"href":2576},[210],[123,28146,28147,1885,28149],{},[38,28148,16712],{},[207,28150,16716],{"className":28151,"dataFsResolvedFilePath":868,"href":869},[210],[123,28153,28154,28156],{},[38,28155,16731],{},[120,28157,28158,28164,28170,28176],{},[123,28159,28160,28163],{},[207,28161,16772],{"className":28162,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,28165,28166,28169],{},[207,28167,16739],{"className":28168,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,28171,28172,28175],{},[207,28173,3528],{"className":28174,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,28177,28178,28181,28182,1343,28199,28216],{},[207,28179,1145],{"className":28180,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,28183,28185],{"className":28184},[886],[888,28186,28187],{"xmlns":890},[892,28188,28189,28197],{},[895,28190,28191,28193,28195],{},[898,28192,1956],{},[898,28194,2398],{},[898,28196,1703],{},[902,28198,18545],{"encoding":904},[883,28200,28202],{"className":28201},[886],[888,28203,28204],{"xmlns":890},[892,28205,28206,28214],{},[895,28207,28208,28210,28212],{},[898,28209,1956],{},[898,28211,2398],{},[898,28213,2351],{},[902,28215,20159],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":28218},[28219,28220,28221,28222,28227,28230,28231,28238,28243,28248,28251,28252,28253,28254],{"id":12504,"depth":642,"text":12505},{"id":18654,"depth":642,"text":18655},{"id":18774,"depth":642,"text":18775},{"id":19027,"depth":642,"text":19028,"children":28223},[28224,28225,28226],{"id":19031,"depth":649,"text":19032},{"id":19243,"depth":649,"text":19244},{"id":19751,"depth":649,"text":19752},{"id":20071,"depth":642,"text":20072,"children":28228},[28229],{"id":20587,"depth":649,"text":20588},{"id":21082,"depth":642,"text":21083},{"id":21109,"depth":642,"text":21110,"children":28232},[28233,28234,28235,28237],{"id":21120,"depth":649,"text":21121},{"id":21190,"depth":649,"text":21191},{"id":21374,"depth":649,"text":28236},"Výpočet YEY^E",{"id":21517,"depth":649,"text":21518},{"id":21895,"depth":642,"text":21896,"children":28239},[28240,28241,28242],{"id":21899,"depth":649,"text":21121},{"id":22348,"depth":649,"text":21191},{"id":23004,"depth":649,"text":23005},{"id":23791,"depth":642,"text":23792,"children":28244},[28245,28246,28247],{"id":23795,"depth":649,"text":21121},{"id":23940,"depth":649,"text":21191},{"id":24210,"depth":649,"text":24211},{"id":25134,"depth":642,"text":25135,"children":28249},[28250],{"id":25330,"depth":649,"text":25331},{"id":25880,"depth":642,"text":25881},{"id":26340,"depth":642,"text":26341},{"id":16218,"depth":642,"text":16219},{"id":2496,"depth":642,"text":2497},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,16725,1143,28261,28262,28263,16772,18383],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":28266,"title":28267,"body":28268,"course":1128,"courses":659,"created":10119,"description":641,"extension":661,"meta":37248,"navigation":664,"path":37249,"seo":37250,"sources":37251,"stem":37252,"tags":37253,"type":2553,"updated":677,"__hash__":37258},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":28269,"toc":37217},[28270,28273,28275,28504,28508,28561,28631,28743,28902,28906,29022,29026,29029,29151,29154,29347,29371,29439,29603,29621,29687,30065,30069,30076,30320,30376,30380,30445,30563,30695,30727,30847,30929,30932,31054,31247,31468,31472,31512,31617,31674,31774,31951,32081,32134,32137,32224,32228,32404,32408,32411,32496,32499,32556,32661,32665,32786,32789,32972,32975,33083,33292,33612,33660,33733,33807,33809,34033,34268,34536,34540,34543,34648,34705,34739,34786,34819,34903,34905,35137,35270,35347,35469,35624,35628,35769,35776,36000,36011,36015,36019,36124,36266,36376,36475,36479,36638,36748,36750,37143,37145],[12,28271,28267],{"id":28272},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,28274,12505],{"id":12504},[724,28276,28277,28279,28280,28314,28315,28318,28319,28350,28351,28397,28398,28401,28402,28444,28445,28463,28464,28468,28469,28499,28500,28503],{},[38,28278,913],{}," řeší, jaký svazek zboží ",[883,28281,28283],{"className":28282},[886],[888,28284,28285],{"xmlns":890},[892,28286,28287,28311],{},[895,28288,28289,28291,28299,28301,28309],{},[1664,28290,1837],{"stretchy":1666},[1810,28292,28293,28295,28297],{},[898,28294,1973],{},[1963,28296,2875],{},[1664,28298,4920],{},[1664,28300,1916],{"separator":1915},[1810,28302,28303,28305,28307],{},[898,28304,1973],{},[1963,28306,1970],{},[1664,28308,4920],{},[1664,28310,1850],{"stretchy":1666},[902,28312,28313],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,28316,28317],{},"primární úloha"," — maximalizace užitečnosti ",[883,28320,28322],{"className":28321},[886],[888,28323,28324],{"xmlns":890},[892,28325,28326,28348],{},[895,28327,28328,28330,28332,28338,28340,28346],{},[898,28329,900],{},[1664,28331,1667],{"stretchy":1666},[2355,28333,28334,28336],{},[898,28335,1973],{},[1963,28337,2875],{},[1664,28339,1916],{"separator":1915},[2355,28341,28342,28344],{},[898,28343,1973],{},[1963,28345,1970],{},[1664,28347,1673],{"stretchy":1666},[902,28349,16843],{"encoding":904}," při rozpočtovém omezení ",[883,28352,28354],{"className":28353},[886],[888,28355,28356],{"xmlns":890},[892,28357,28358,28394],{},[895,28359,28360,28366,28368,28374,28380,28382,28388],{},[1720,28361,28362,28364],{},[898,28363,9692],{},[1664,28365,4920],{},[1664,28367,1676],{},[2355,28369,28370,28372],{},[898,28371,2398],{},[1963,28373,2875],{},[2355,28375,28376,28378],{},[898,28377,1973],{},[1963,28379,2875],{},[1664,28381,1700],{},[2355,28383,28384,28386],{},[898,28385,2398],{},[1963,28387,1970],{},[2355,28389,28390,28392],{},[898,28391,1973],{},[1963,28393,1970],{},[902,28395,28396],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,28399,28400],{},"duální úloha"," — minimalizace výdajů ",[883,28403,28405],{"className":28404},[886],[888,28406,28407],{"xmlns":890},[892,28408,28409,28441],{},[895,28410,28411,28413,28415,28421,28427,28429,28435],{},[898,28412,4819],{},[1664,28414,1676],{},[2355,28416,28417,28419],{},[898,28418,2398],{},[1963,28420,2875],{},[2355,28422,28423,28425],{},[898,28424,1973],{},[1963,28426,2875],{},[1664,28428,1700],{},[2355,28430,28431,28433],{},[898,28432,2398],{},[1963,28434,1970],{},[2355,28436,28437,28439],{},[898,28438,1973],{},[1963,28440,1970],{},[902,28442,28443],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,28446,28448],{"className":28447},[886],[888,28449,28450],{"xmlns":890},[892,28451,28452,28460],{},[895,28453,28454],{},[1720,28455,28456,28458],{},[898,28457,900],{},[1664,28459,4920],{},[902,28461,28462],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,28465,28467],{"className":28466,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,28470,28472],{"className":28471},[886],[888,28473,28474],{"xmlns":890},[892,28475,28476,28496],{},[895,28477,28478,28480,28482,28488,28490],{},[1690,28479,11165],{},[1664,28481,1676],{},[2355,28483,28484,28486],{},[898,28485,2398],{},[1963,28487,2875],{},[898,28489,5240],{"mathvariant":1726},[2355,28491,28492,28494],{},[898,28493,2398],{},[1963,28495,1970],{},[902,28497,28498],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,28501,28502],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,28505,28507],{"id":28506},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,28509,28510,28511,28529,28530,28560],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,28512,28514],{"className":28513},[886],[888,28515,28516],{"xmlns":890},[892,28517,28518,28526],{},[895,28519,28520],{},[1720,28521,28522,28524],{},[898,28523,9692],{},[1664,28525,4920],{},[902,28527,28528],{"encoding":904},"Y^*"," a ceny ",[883,28531,28533],{"className":28532},[886],[888,28534,28535],{"xmlns":890},[892,28536,28537,28557],{},[895,28538,28539,28547,28549],{},[1810,28540,28541,28543,28545],{},[898,28542,2398],{},[1963,28544,2875],{},[1664,28546,4920],{},[1664,28548,1916],{"separator":1915},[1810,28550,28551,28553,28555],{},[898,28552,2398],{},[1963,28554,1970],{},[1664,28556,4920],{},[902,28558,28559],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,28562,28564],{"className":28563},[886],[888,28565,28567],{"xmlns":890,"display":28566},"block",[892,28568,28569,28628],{},[21254,28570,28572],{"width":28571},"100%",[21259,28573,28574,28577,28621,28623],{},[21262,28575],{"width":28576},"50%",[21262,28578,28579],{},[895,28580,28581,28587,28589,28597,28603,28605,28613,28619],{},[1720,28582,28583,28585],{},[898,28584,9692],{},[1664,28586,4920],{},[1664,28588,1676],{},[1810,28590,28591,28593,28595],{},[898,28592,2398],{},[1963,28594,2875],{},[1664,28596,4920],{},[2355,28598,28599,28601],{},[898,28600,1973],{},[1963,28602,2875],{},[1664,28604,1700],{},[1810,28606,28607,28609,28611],{},[898,28608,2398],{},[1963,28610,1970],{},[1664,28612,4920],{},[2355,28614,28615,28617],{},[898,28616,1973],{},[1963,28618,1970],{},[1664,28620,1916],{"separator":1915},[21262,28622],{"width":28576},[21262,28624,28625],{},[1690,28626,28627],{},"(6.12)",[902,28629,28630],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,28632,28633,28634,28637,28638,4454,28674,28710,28711,28724,28725,28739,28740,1977],{},"geometricky ",[38,28635,28636],{},"rozpočtová přímka (budget line)"," procházející body ",[883,28639,28641],{"className":28640},[886],[888,28642,28643],{"xmlns":890},[892,28644,28645,28671],{},[895,28646,28647,28649,28655,28657,28665,28667,28669],{},[1664,28648,1837],{"stretchy":1666},[1720,28650,28651,28653],{},[898,28652,9692],{},[1664,28654,4920],{},[898,28656,5240],{"mathvariant":1726},[1810,28658,28659,28661,28663],{},[898,28660,2398],{},[1963,28662,2875],{},[1664,28664,4920],{},[1664,28666,1916],{"separator":1915},[1963,28668,2058],{},[1664,28670,1850],{"stretchy":1666},[902,28672,28673],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,28675,28677],{"className":28676},[886],[888,28678,28679],{"xmlns":890},[892,28680,28681,28707],{},[895,28682,28683,28685,28687,28689,28695,28697,28705],{},[1664,28684,1837],{"stretchy":1666},[1963,28686,2058],{},[1664,28688,1916],{"separator":1915},[1720,28690,28691,28693],{},[898,28692,9692],{},[1664,28694,4920],{},[898,28696,5240],{"mathvariant":1726},[1810,28698,28699,28701,28703],{},[898,28700,2398],{},[1963,28702,1970],{},[1664,28704,4920],{},[1664,28706,1850],{"stretchy":1666},[902,28708,28709],{"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 ",[883,28712,28714],{"className":28713},[886],[888,28715,28716],{"xmlns":890},[892,28717,28718,28722],{},[895,28719,28720],{},[898,28721,900],{},[902,28723,900],{"encoding":904},", indiferenční křivky a ",[883,28726,28728],{"className":28727},[886],[888,28729,28730],{"xmlns":890},[892,28731,28732,28736],{},[895,28733,28734],{},[1690,28735,11165],{},[902,28737,28738],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,28741,880],{"className":28742,"dataFsResolvedFilePath":878,"href":879},[210],[4436,28744,28745],{},[724,28746,28747,28749,28750,28753,28754,28767,28768,28770,28771,28784,28785,1885,28788,28828,28829,28846,28847,28864,28865,28882,28883,28901],{},[883,28748,4978],{}," Pozor — dvě úlohy, totéž řešení\n",[38,28751,28752],{},"Primární úloha"," (max ",[883,28755,28757],{"className":28756},[886],[888,28758,28759],{"xmlns":890},[892,28760,28761,28765],{},[895,28762,28763],{},[898,28764,900],{},[902,28766,900],{"encoding":904}," při pevném rozpočtu) a ",[38,28769,28400],{}," (min ",[883,28772,28774],{"className":28773},[886],[888,28775,28776],{"xmlns":890},[892,28777,28778,28782],{},[895,28779,28780],{},[898,28781,4819],{},[902,28783,4819],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,28786,28787],{},"tentýž bod",[883,28789,28791],{"className":28790},[886],[888,28792,28793],{"xmlns":890},[892,28794,28795,28825],{},[895,28796,28797,28803,28805,28813,28815,28823],{},[1720,28798,28799,28801],{},[898,28800,1973],{},[1664,28802,4920],{},[1664,28804,1837],{"stretchy":1666},[1810,28806,28807,28809,28811],{},[898,28808,1973],{},[1963,28810,2875],{},[1664,28812,4920],{},[1664,28814,1916],{"separator":1915},[1810,28816,28817,28819,28821],{},[898,28818,1973],{},[1963,28820,1970],{},[1664,28822,4920],{},[1664,28824,1850],{"stretchy":1666},[902,28826,28827],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,28830,28832],{"className":28831},[886],[888,28833,28834],{"xmlns":890},[892,28835,28836,28844],{},[895,28837,28838],{},[1720,28839,28840,28842],{},[898,28841,9692],{},[1664,28843,4920],{},[902,28845,28528],{"encoding":904}," a hledáme maximální ",[883,28848,28850],{"className":28849},[886],[888,28851,28852],{"xmlns":890},[892,28853,28854,28862],{},[895,28855,28856],{},[1720,28857,28858,28860],{},[898,28859,900],{},[1664,28861,4920],{},[902,28863,28462],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,28866,28868],{"className":28867},[886],[888,28869,28870],{"xmlns":890},[892,28871,28872,28880],{},[895,28873,28874],{},[1720,28875,28876,28878],{},[898,28877,900],{},[1664,28879,4920],{},[902,28881,28462],{"encoding":904}," a hledáme minimální ",[883,28884,28886],{"className":28885},[886],[888,28887,28888],{"xmlns":890},[892,28889,28890,28898],{},[895,28891,28892],{},[1720,28893,28894,28896],{},[898,28895,4819],{},[1664,28897,4920],{},[902,28899,28900],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,28903,28905],{"id":28904},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,28907,28908,28909,28940,28941,29017,29018,1977],{},"Úlohou je najít maximum ",[883,28910,28912],{"className":28911},[886],[888,28913,28914],{"xmlns":890},[892,28915,28916,28938],{},[895,28917,28918,28920,28922,28928,28930,28936],{},[898,28919,900],{},[1664,28921,1667],{"stretchy":1666},[2355,28923,28924,28926],{},[898,28925,1973],{},[1963,28927,2875],{},[1664,28929,1916],{"separator":1915},[2355,28931,28932,28934],{},[898,28933,1973],{},[1963,28935,1970],{},[1664,28937,1673],{"stretchy":1666},[902,28939,16843],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,28942,28944],{"className":28943},[886],[888,28945,28946],{"xmlns":890},[892,28947,28948,29014],{},[895,28949,28950,28952,28954,28960,28962,28968,28970,28972,28978,28980,28988,28994,28996,29004,29010,29012],{},[898,28951,11602],{},[1664,28953,1667],{"stretchy":1666},[2355,28955,28956,28958],{},[898,28957,1973],{},[1963,28959,2875],{},[1664,28961,1916],{"separator":1915},[2355,28963,28964,28966],{},[898,28965,1973],{},[1963,28967,1970],{},[1664,28969,1673],{"stretchy":1666},[1664,28971,1676],{},[1720,28973,28974,28976],{},[898,28975,9692],{},[1664,28977,4920],{},[1664,28979,1867],{},[1810,28981,28982,28984,28986],{},[898,28983,2398],{},[1963,28985,2875],{},[1664,28987,4920],{},[2355,28989,28990,28992],{},[898,28991,1973],{},[1963,28993,2875],{},[1664,28995,1867],{},[1810,28997,28998,29000,29002],{},[898,28999,2398],{},[1963,29001,1970],{},[1664,29003,4920],{},[2355,29005,29006,29008],{},[898,29007,1973],{},[1963,29009,1970],{},[1664,29011,1676],{},[1963,29013,2058],{},[902,29015,29016],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,29019,29021],{"className":29020,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,29023,29025],{"id":29024},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,29027,29028],{},"Sestavíme",[883,29030,29032],{"className":29031},[886],[888,29033,29034],{"xmlns":890,"display":28566},[892,29035,29036,29148],{},[21254,29037,29038],{"width":28571},[21259,29039,29040,29042,29141,29143],{},[21262,29041],{"width":28576},[21262,29043,29044],{},[895,29045,29046,29049,29051,29057,29059,29065,29067,29069,29071,29073,29075,29077,29083,29085,29091,29093,29095,29097,29099,29105,29107,29115,29121,29123,29131,29137,29139],{},[898,29047,10358],{"mathvariant":29048},"script",[1664,29050,1667],{"stretchy":1666},[2355,29052,29053,29055],{},[898,29054,1973],{},[1963,29056,2875],{},[1664,29058,1916],{"separator":1915},[2355,29060,29061,29063],{},[898,29062,1973],{},[1963,29064,1970],{},[1664,29066,1916],{"separator":1915},[898,29068,16943],{},[1664,29070,1673],{"stretchy":1666},[1664,29072,1676],{},[898,29074,900],{},[1664,29076,1667],{"stretchy":1666},[2355,29078,29079,29081],{},[898,29080,1973],{},[1963,29082,2875],{},[1664,29084,1916],{"separator":1915},[2355,29086,29087,29089],{},[898,29088,1973],{},[1963,29090,1970],{},[1664,29092,1673],{"stretchy":1666},[1664,29094,1700],{},[898,29096,16943],{},[1664,29098,1667],{"stretchy":1666},[1720,29100,29101,29103],{},[898,29102,9692],{},[1664,29104,4920],{},[1664,29106,1867],{},[1810,29108,29109,29111,29113],{},[898,29110,2398],{},[1963,29112,2875],{},[1664,29114,4920],{},[2355,29116,29117,29119],{},[898,29118,1973],{},[1963,29120,2875],{},[1664,29122,1867],{},[1810,29124,29125,29127,29129],{},[898,29126,2398],{},[1963,29128,1970],{},[1664,29130,4920],{},[2355,29132,29133,29135],{},[898,29134,1973],{},[1963,29136,1970],{},[1664,29138,1673],{"stretchy":1666},[898,29140,1977],{"mathvariant":1726},[21262,29142],{"width":28576},[21262,29144,29145],{},[1690,29146,29147],{},"(6.13)",[902,29149,29150],{"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}",[724,29152,29153],{},"Soustava prvního řádu:",[883,29155,29157],{"className":29156},[886],[888,29158,29159],{"xmlns":890,"display":28566},[892,29160,29161,29344],{},[21254,29162,29163],{"width":28571},[21259,29164,29165,29167,29337,29339],{},[21262,29166],{"width":28576},[21262,29168,29169],{},[21254,29170,29171,29221,29271],{"rowspacing":21256,"columnalign":21257,"columnspacing":1727},[21259,29172,29173,29185],{},[21262,29174,29175],{},[2919,29176,29177],{"scriptlevel":2058,"displaystyle":1915},[1810,29178,29179,29181,29183],{},[898,29180,10358],{"mathvariant":29048},[1963,29182,2875],{},[1664,29184,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[21262,29186,29187],{},[2919,29188,29189],{"scriptlevel":2058,"displaystyle":1915},[895,29190,29191,29193,29195,29203,29205,29207,29215,29217,29219],{},[895,29192],{},[1664,29194,1676],{},[1810,29196,29197,29199,29201],{},[898,29198,900],{},[1963,29200,2875],{},[1664,29202,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,29204,1867],{},[898,29206,16943],{},[1810,29208,29209,29211,29213],{},[898,29210,2398],{},[1963,29212,2875],{},[1664,29214,4920],{},[1664,29216,1676],{},[1963,29218,2058],{},[1664,29220,1916],{"separator":1915},[21259,29222,29223,29235],{},[21262,29224,29225],{},[2919,29226,29227],{"scriptlevel":2058,"displaystyle":1915},[1810,29228,29229,29231,29233],{},[898,29230,10358],{"mathvariant":29048},[1963,29232,1970],{},[1664,29234,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[21262,29236,29237],{},[2919,29238,29239],{"scriptlevel":2058,"displaystyle":1915},[895,29240,29241,29243,29245,29253,29255,29257,29265,29267,29269],{},[895,29242],{},[1664,29244,1676],{},[1810,29246,29247,29249,29251],{},[898,29248,900],{},[1963,29250,1970],{},[1664,29252,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,29254,1867],{},[898,29256,16943],{},[1810,29258,29259,29261,29263],{},[898,29260,2398],{},[1963,29262,1970],{},[1664,29264,4920],{},[1664,29266,1676],{},[1963,29268,2058],{},[1664,29270,1916],{"separator":1915},[21259,29272,29273,29285],{},[21262,29274,29275],{},[2919,29276,29277],{"scriptlevel":2058,"displaystyle":1915},[1810,29278,29279,29281,29283],{},[898,29280,10358],{"mathvariant":29048},[898,29282,16943],{},[1664,29284,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[21262,29286,29287],{},[2919,29288,29289],{"scriptlevel":2058,"displaystyle":1915},[895,29290,29291,29293,29295,29301,29303,29311,29317,29319,29327,29333,29335],{},[895,29292],{},[1664,29294,1676],{},[1720,29296,29297,29299],{},[898,29298,9692],{},[1664,29300,4920],{},[1664,29302,1867],{},[1810,29304,29305,29307,29309],{},[898,29306,2398],{},[1963,29308,2875],{},[1664,29310,4920],{},[2355,29312,29313,29315],{},[898,29314,1973],{},[1963,29316,2875],{},[1664,29318,1867],{},[1810,29320,29321,29323,29325],{},[898,29322,2398],{},[1963,29324,1970],{},[1664,29326,4920],{},[2355,29328,29329,29331],{},[898,29330,1973],{},[1963,29332,1970],{},[1664,29334,1676],{},[1963,29336,12959],{},[21262,29338],{"width":28576},[21262,29340,29341],{},[1690,29342,29343],{},"(6.14)",[902,29345,29346],{"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}",[724,29348,29349,29350,29353,29354,29367,29368,2087],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,29351,29352],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,29355,29357],{"className":29356},[886],[888,29358,29359],{"xmlns":890},[892,29360,29361,29365],{},[895,29362,29363],{},[898,29364,16943],{},[902,29366,16996],{"encoding":904}," dostáváme ",[38,29369,29370],{},"podmínku optimality",[883,29372,29374],{"className":29373},[886],[888,29375,29376],{"xmlns":890,"display":28566},[892,29377,29378,29436],{},[895,29379,29380],{},[13331,29381,29382],{"notation":13333},[2919,29383,29384],{"scriptlevel":2058,"displaystyle":1666},[2919,29385,29386],{"scriptlevel":2058,"displaystyle":1666},[2919,29387,29388],{"scriptlevel":2058,"displaystyle":1915},[895,29389,29390,29392,29394,29396,29414,29416,29434],{},[1690,29391,4553],{},[1690,29393,11165],{},[1664,29395,1676],{},[2922,29397,29398,29406],{},[1810,29399,29400,29402,29404],{},[898,29401,900],{},[1963,29403,2875],{},[1664,29405,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1810,29407,29408,29410,29412],{},[898,29409,900],{},[1963,29411,1970],{},[1664,29413,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,29415,1676],{},[2922,29417,29418,29426],{},[1810,29419,29420,29422,29424],{},[898,29421,2398],{},[1963,29423,2875],{},[1664,29425,4920],{},[1810,29427,29428,29430,29432],{},[898,29429,2398],{},[1963,29431,1970],{},[1664,29433,4920],{},[1690,29435,4553],{},[902,29437,29438],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[4436,29440,29441],{},[724,29442,29443,29445,29446,29480,29481,29484,29485,29503,29504,29522,29523,29553,29554,29571,29572,29602],{},[883,29444,4723],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,29447,29449],{"className":29448},[886],[888,29450,29451],{"xmlns":890},[892,29452,29453,29477],{},[895,29454,29455,29457,29459,29467,29469],{},[1690,29456,11165],{},[1664,29458,1676],{},[1810,29460,29461,29463,29465],{},[898,29462,2398],{},[1963,29464,2875],{},[1664,29466,4920],{},[898,29468,5240],{"mathvariant":1726},[1810,29470,29471,29473,29475],{},[898,29472,2398],{},[1963,29474,1970],{},[1664,29476,4920],{},[902,29478,29479],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,29482,29483],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,29486,29488],{"className":29487},[886],[888,29489,29490],{"xmlns":890},[892,29491,29492,29500],{},[895,29493,29494],{},[2355,29495,29496,29498],{},[898,29497,1973],{},[1963,29499,2875],{},[902,29501,29502],{"encoding":904},"Q_1"," za ",[883,29505,29507],{"className":29506},[886],[888,29508,29509],{"xmlns":890},[892,29510,29511,29519],{},[895,29512,29513],{},[2355,29514,29515,29517],{},[898,29516,1973],{},[1963,29518,1970],{},[902,29520,29521],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,29524,29526],{"className":29525},[886],[888,29527,29528],{"xmlns":890},[892,29529,29530,29550],{},[895,29531,29532,29534,29536,29542,29544],{},[1690,29533,11165],{},[1664,29535,3984],{},[2355,29537,29538,29540],{},[898,29539,2398],{},[1963,29541,2875],{},[898,29543,5240],{"mathvariant":1726},[2355,29545,29546,29548],{},[898,29547,2398],{},[1963,29549,1970],{},[902,29551,29552],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,29555,29557],{"className":29556},[886],[888,29558,29559],{"xmlns":890},[892,29560,29561,29569],{},[895,29562,29563],{},[2355,29564,29565,29567],{},[898,29566,1973],{},[1963,29568,2875],{},[902,29570,29502],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,29573,29575],{"className":29574},[886],[888,29576,29577],{"xmlns":890},[892,29578,29579,29599],{},[895,29580,29581,29583,29585,29591,29593],{},[1690,29582,11165],{},[1664,29584,4022],{},[2355,29586,29587,29589],{},[898,29588,2398],{},[1963,29590,2875],{},[898,29592,5240],{"mathvariant":1726},[2355,29594,29595,29597],{},[898,29596,2398],{},[1963,29598,1970],{},[902,29600,29601],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,29604,29606,29607,29620],{"id":29605},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,29608,29610],{"className":29609},[886],[888,29611,29612],{"xmlns":890},[892,29613,29614,29618],{},[895,29615,29616],{},[898,29617,16943],{},[902,29619,16996],{"encoding":904}," — mezní užitečnost důchodu",[724,29622,29623,29624,29642,29643,29646,29647,29664,29665,29682,29683,29686],{},"Lagrangeův multiplikátor ",[883,29625,29627],{"className":29626},[886],[888,29628,29629],{"xmlns":890},[892,29630,29631,29639],{},[895,29632,29633],{},[1720,29634,29635,29637],{},[898,29636,16943],{},[1664,29638,4920],{},[902,29640,29641],{"encoding":904},"\\lambda^*"," představuje ",[38,29644,29645],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,29648,29650],{"className":29649},[886],[888,29651,29652],{"xmlns":890},[892,29653,29654,29662],{},[895,29655,29656],{},[1720,29657,29658,29660],{},[898,29659,900],{},[1664,29661,4920],{},[902,29663,28462],{"encoding":904}," při jednotkové změně důchodu ",[883,29666,29668],{"className":29667},[886],[888,29669,29670],{"xmlns":890},[892,29671,29672,29680],{},[895,29673,29674],{},[1720,29675,29676,29678],{},[898,29677,9692],{},[1664,29679,4920],{},[902,29681,28528],{"encoding":904},". Je to ",[38,29684,29685],{},"stínová cena"," rozpočtového omezení.",[4436,29688,29689,29694],{},[724,29690,29691,29693],{},[883,29692,5138],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,29695,29696,29756,29843,29879,29966],{},[123,29697,29698,29701,29702,1977],{},[38,29699,29700],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,29703,29705],{"className":29704},[886],[888,29706,29707],{"xmlns":890},[892,29708,29709,29753],{},[895,29710,29711,29717,29719,29727,29733,29735,29743,29749,29751],{},[1720,29712,29713,29715],{},[898,29714,9692],{},[1664,29716,4920],{},[1664,29718,1867],{},[1810,29720,29721,29723,29725],{},[898,29722,2398],{},[1963,29724,2875],{},[1664,29726,4920],{},[2355,29728,29729,29731],{},[898,29730,1973],{},[1963,29732,2875],{},[1664,29734,1867],{},[1810,29736,29737,29739,29741],{},[898,29738,2398],{},[1963,29740,1970],{},[1664,29742,4920],{},[2355,29744,29745,29747],{},[898,29746,1973],{},[1963,29748,1970],{},[1664,29750,1676],{},[1963,29752,2058],{},[902,29754,29755],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,29757,29758,1885,29761,1977],{},[38,29759,29760],{},"Sestav Lagrangeovu funkci",[883,29762,29764],{"className":29763},[886],[888,29765,29766],{"xmlns":890},[892,29767,29768,29840],{},[895,29769,29770,29772,29774,29776,29778,29784,29786,29792,29794,29796,29798,29800,29806,29808,29816,29822,29824,29832,29838],{},[898,29771,10358],{"mathvariant":29048},[1664,29773,1676],{},[898,29775,900],{},[1664,29777,1667],{"stretchy":1666},[2355,29779,29780,29782],{},[898,29781,1973],{},[1963,29783,2875],{},[1664,29785,1916],{"separator":1915},[2355,29787,29788,29790],{},[898,29789,1973],{},[1963,29791,1970],{},[1664,29793,1673],{"stretchy":1666},[1664,29795,1700],{},[898,29797,16943],{},[1664,29799,1667],{"stretchy":1666},[1720,29801,29802,29804],{},[898,29803,9692],{},[1664,29805,4920],{},[1664,29807,1867],{},[1810,29809,29810,29812,29814],{},[898,29811,2398],{},[1963,29813,2875],{},[1664,29815,4920],{},[2355,29817,29818,29820],{},[898,29819,1973],{},[1963,29821,2875],{},[1664,29823,1867],{},[1810,29825,29826,29828,29830],{},[898,29827,2398],{},[1963,29829,1970],{},[1664,29831,4920],{},[2355,29833,29834,29836],{},[898,29835,1973],{},[1963,29837,1970],{},[1664,29839,1673],{"stretchy":1666},[902,29841,29842],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,29844,29845,11030,29848,29878],{},[38,29846,29847],{},"Spočítej parciální derivace",[883,29849,29851],{"className":29850},[886],[888,29852,29853],{"xmlns":890},[892,29854,29855,29875],{},[895,29856,29857,29863,29865,29871,29873],{},[2355,29858,29859,29861],{},[898,29860,1973],{},[1963,29862,2875],{},[1664,29864,1916],{"separator":1915},[2355,29866,29867,29869],{},[898,29868,1973],{},[1963,29870,1970],{},[1664,29872,1916],{"separator":1915},[898,29874,16943],{},[902,29876,29877],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,29880,29881,29897,29898,29931,29932,4454,29949,1977],{},[38,29882,29883,29884],{},"Vyluč ",[883,29885,29887],{"className":29886},[886],[888,29888,29889],{"xmlns":890},[892,29890,29891,29895],{},[895,29892,29893],{},[898,29894,16943],{},[902,29896,16996],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,29899,29901],{"className":29900},[886],[888,29902,29903],{"xmlns":890},[892,29904,29905,29929],{},[895,29906,29907,29909,29911,29919,29921],{},[1690,29908,11165],{},[1664,29910,1676],{},[1810,29912,29913,29915,29917],{},[898,29914,2398],{},[1963,29916,2875],{},[1664,29918,4920],{},[898,29920,5240],{"mathvariant":1726},[1810,29922,29923,29925,29927],{},[898,29924,2398],{},[1963,29926,1970],{},[1664,29928,4920],{},[902,29930,29479],{"encoding":904},", která dá vztah mezi ",[883,29933,29935],{"className":29934},[886],[888,29936,29937],{"xmlns":890},[892,29938,29939,29947],{},[895,29940,29941],{},[2355,29942,29943,29945],{},[898,29944,1973],{},[1963,29946,2875],{},[902,29948,29502],{"encoding":904},[883,29950,29952],{"className":29951},[886],[888,29953,29954],{"xmlns":890},[892,29955,29956,29964],{},[895,29957,29958],{},[2355,29959,29960,29962],{},[898,29961,1973],{},[1963,29963,1970],{},[902,29965,29521],{"encoding":904},[123,29967,29968,29971,29972,30002,30003,30020,30021,1977],{},[38,29969,29970],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,29973,29975],{"className":29974},[886],[888,29976,29977],{"xmlns":890},[892,29978,29979,29999],{},[895,29980,29981,29989,29991],{},[1810,29982,29983,29985,29987],{},[898,29984,1973],{},[1963,29986,2875],{},[1664,29988,4920],{},[1664,29990,1916],{"separator":1915},[1810,29992,29993,29995,29997],{},[898,29994,1973],{},[1963,29996,1970],{},[1664,29998,4920],{},[902,30000,30001],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,30004,30006],{"className":30005},[886],[888,30007,30008],{"xmlns":890},[892,30009,30010,30018],{},[895,30011,30012],{},[1720,30013,30014,30016],{},[898,30015,16943],{},[1664,30017,4920],{},[902,30019,29641],{"encoding":904}," a maximální užitečnost ",[883,30022,30024],{"className":30023},[886],[888,30025,30026],{"xmlns":890},[892,30027,30028,30062],{},[895,30029,30030,30036,30038,30040,30042,30050,30052,30060],{},[1720,30031,30032,30034],{},[898,30033,900],{},[1664,30035,4920],{},[1664,30037,1676],{},[898,30039,900],{},[1664,30041,1667],{"stretchy":1666},[1810,30043,30044,30046,30048],{},[898,30045,1973],{},[1963,30047,2875],{},[1664,30049,4920],{},[1664,30051,1916],{"separator":1915},[1810,30053,30054,30056,30058],{},[898,30055,1973],{},[1963,30057,1970],{},[1664,30059,4920],{},[1664,30061,1673],{"stretchy":1666},[902,30063,30064],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,30066,30068],{"id":30067},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,30070,30071],{},[1928,30072],{"alt":30073,"className":30074,"src":30075},"imek-uzitecnost-optimum",[210,1932],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,30077,30078],{},[614,30079,30080,30081,30130,30131,4454,30159,30187,30188,30222,30223,30262,30263,30281,30282,30300,30301,30319],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,30082,30084],{"className":30083},[886],[888,30085,30086],{"xmlns":890},[892,30087,30088,30128],{},[895,30089,30090,30096,30098,30106,30112,30114,30122],{},[1720,30091,30092,30094],{},[898,30093,9692],{},[1664,30095,4920],{},[1664,30097,1676],{},[1810,30099,30100,30102,30104],{},[898,30101,2398],{},[1963,30103,2875],{},[1664,30105,4920],{},[2355,30107,30108,30110],{},[898,30109,1973],{},[1963,30111,2875],{},[1664,30113,1700],{},[1810,30115,30116,30118,30120],{},[898,30117,2398],{},[1963,30119,1970],{},[1664,30121,4920],{},[2355,30123,30124,30126],{},[898,30125,1973],{},[1963,30127,1970],{},[902,30129,17798],{"encoding":904}," protíná osy v ",[883,30132,30134],{"className":30133},[886],[888,30135,30136],{"xmlns":890},[892,30137,30138,30156],{},[895,30139,30140,30146,30148],{},[1720,30141,30142,30144],{},[898,30143,9692],{},[1664,30145,4920],{},[898,30147,5240],{"mathvariant":1726},[1810,30149,30150,30152,30154],{},[898,30151,2398],{},[1963,30153,2875],{},[1664,30155,4920],{},[902,30157,30158],{"encoding":904},"Y^*\u002FP_1^*",[883,30160,30162],{"className":30161},[886],[888,30163,30164],{"xmlns":890},[892,30165,30166,30184],{},[895,30167,30168,30174,30176],{},[1720,30169,30170,30172],{},[898,30171,9692],{},[1664,30173,4920],{},[898,30175,5240],{"mathvariant":1726},[1810,30177,30178,30180,30182],{},[898,30179,2398],{},[1963,30181,1970],{},[1664,30183,4920],{},[902,30185,30186],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,30189,30191],{"className":30190},[886],[888,30192,30193],{"xmlns":890},[892,30194,30195,30219],{},[895,30196,30197,30203,30205,30211,30213],{},[2355,30198,30199,30201],{},[898,30200,2034],{},[1963,30202,2875],{},[1664,30204,4022],{},[1720,30206,30207,30209],{},[898,30208,2034],{},[1664,30210,4920],{},[1664,30212,4022],{},[2355,30214,30215,30217],{},[898,30216,2034],{},[1963,30218,1970],{},[902,30220,30221],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,30224,30226],{"className":30225},[886],[888,30227,30228],{"xmlns":890},[892,30229,30230,30260],{},[895,30231,30232,30238,30240,30248,30250,30258],{},[1720,30233,30234,30236],{},[898,30235,1973],{},[1664,30237,4920],{},[1664,30239,1837],{"stretchy":1666},[1810,30241,30242,30244,30246],{},[898,30243,1973],{},[1963,30245,2875],{},[1664,30247,4920],{},[1664,30249,1916],{"separator":1915},[1810,30251,30252,30254,30256],{},[898,30253,1973],{},[1963,30255,1970],{},[1664,30257,4920],{},[1664,30259,1850],{"stretchy":1666},[902,30261,28827],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,30264,30266],{"className":30265},[886],[888,30267,30268],{"xmlns":890},[892,30269,30270,30278],{},[895,30271,30272],{},[1720,30273,30274,30276],{},[898,30275,2034],{},[1664,30277,4920],{},[902,30279,30280],{"encoding":904},"c^*",". Křivka ",[883,30283,30285],{"className":30284},[886],[888,30286,30287],{"xmlns":890},[892,30288,30289,30297],{},[895,30290,30291],{},[2355,30292,30293,30295],{},[898,30294,2034],{},[1963,30296,2875],{},[902,30298,30299],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,30302,30304],{"className":30303},[886],[888,30305,30306],{"xmlns":890},[892,30307,30308,30316],{},[895,30309,30310],{},[2355,30311,30312,30314],{},[898,30313,2034],{},[1963,30315,1970],{},[902,30317,30318],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,30321,30322,30323,30326,30327,30345,30346,30375],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,30324,30325],{},"dotýkají",", tj. mají v bodě ",[883,30328,30330],{"className":30329},[886],[888,30331,30332],{"xmlns":890},[892,30333,30334,30342],{},[895,30335,30336],{},[1720,30337,30338,30340],{},[898,30339,1973],{},[1664,30341,4920],{},[902,30343,30344],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,30347,30349],{"className":30348},[886],[888,30350,30351],{"xmlns":890},[892,30352,30353,30373],{},[895,30354,30355,30357,30359,30365,30367],{},[1690,30356,11165],{},[1664,30358,1676],{},[2355,30360,30361,30363],{},[898,30362,2398],{},[1963,30364,2875],{},[898,30366,5240],{"mathvariant":1726},[2355,30368,30369,30371],{},[898,30370,2398],{},[1963,30372,1970],{},[902,30374,28498],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,30377,30379],{"id":30378},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,30381,10226,30382,30444],{},[883,30383,30385],{"className":30384},[886],[888,30386,30387],{"xmlns":890},[892,30388,30389,30441],{},[895,30390,30391,30393,30395,30401,30403,30409,30411,30413,30427],{},[898,30392,900],{},[1664,30394,1667],{"stretchy":1666},[2355,30396,30397,30399],{},[898,30398,1973],{},[1963,30400,2875],{},[1664,30402,1916],{"separator":1915},[2355,30404,30405,30407],{},[898,30406,1973],{},[1963,30408,1970],{},[1664,30410,1673],{"stretchy":1666},[1664,30412,1676],{},[1810,30414,30415,30417,30419],{},[898,30416,1973],{},[1963,30418,2875],{},[895,30420,30421,30423,30425],{},[1963,30422,2875],{},[898,30424,5240],{"mathvariant":1726},[1963,30426,1970],{},[1810,30428,30429,30431,30433],{},[898,30430,1973],{},[1963,30432,1970],{},[895,30434,30435,30437,30439],{},[1963,30436,2875],{},[898,30438,5240],{"mathvariant":1726},[1963,30440,1970],{},[902,30442,30443],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[724,30446,30447],{},[883,30448,30450],{"className":30449},[886],[888,30451,30452],{"xmlns":890},[892,30453,30454,30560],{},[895,30455,30456,30458,30460,30542,30544,30558],{},[1690,30457,11165],{},[1664,30459,1676],{},[2922,30461,30462,30502],{},[895,30463,30464,30472,30488],{},[2919,30465,30466],{"scriptlevel":2058,"displaystyle":1666},[2922,30467,30468,30470],{},[1963,30469,2875],{},[1963,30471,1970],{},[1810,30473,30474,30476,30478],{},[898,30475,1973],{},[1963,30477,2875],{},[895,30479,30480,30482,30484,30486],{},[1664,30481,1867],{},[1963,30483,2875],{},[898,30485,5240],{"mathvariant":1726},[1963,30487,1970],{},[1810,30489,30490,30492,30494],{},[898,30491,1973],{},[1963,30493,1970],{},[895,30495,30496,30498,30500],{},[1963,30497,2875],{},[898,30499,5240],{"mathvariant":1726},[1963,30501,1970],{},[895,30503,30504,30512,30526],{},[2919,30505,30506],{"scriptlevel":2058,"displaystyle":1666},[2922,30507,30508,30510],{},[1963,30509,2875],{},[1963,30511,1970],{},[1810,30513,30514,30516,30518],{},[898,30515,1973],{},[1963,30517,2875],{},[895,30519,30520,30522,30524],{},[1963,30521,2875],{},[898,30523,5240],{"mathvariant":1726},[1963,30525,1970],{},[1810,30527,30528,30530,30532],{},[898,30529,1973],{},[1963,30531,1970],{},[895,30533,30534,30536,30538,30540],{},[1664,30535,1867],{},[1963,30537,2875],{},[898,30539,5240],{"mathvariant":1726},[1963,30541,1970],{},[1664,30543,1676],{},[2922,30545,30546,30552],{},[2355,30547,30548,30550],{},[898,30549,1973],{},[1963,30551,1970],{},[2355,30553,30554,30556],{},[898,30555,1973],{},[1963,30557,2875],{},[898,30559,1977],{"mathvariant":1726},[902,30561,30562],{"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}.",[724,30564,30565,30566,1748,30611,30613,30614,30634,30635,30665,30666,1977],{},"Tedy ",[883,30567,30569],{"className":30568},[886],[888,30570,30571],{"xmlns":890},[892,30572,30573,30608],{},[895,30574,30575,30577,30579,30582,30584,30586,30588,30590,30598,30600],{},[1690,30576,11165],{},[1664,30578,1667],{"stretchy":1666},[1963,30580,30581],{},"300",[1664,30583,1916],{"separator":1915},[1963,30585,15609],{},[1664,30587,1673],{"stretchy":1666},[1664,30589,1676],{},[2919,30591,30592],{"scriptlevel":2058,"displaystyle":1666},[2922,30593,30594,30596],{},[1963,30595,15609],{},[1963,30597,30581],{},[1664,30599,1676],{},[2919,30601,30602],{"scriptlevel":2058,"displaystyle":1666},[2922,30603,30604,30606],{},[1963,30605,2826],{},[1963,30607,2774],{},[902,30609,30610],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,30612,9779],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,30615,30617],{"className":30616},[886],[888,30618,30619],{"xmlns":890},[892,30620,30621,30631],{},[895,30622,30623],{},[2919,30624,30625],{"scriptlevel":2058,"displaystyle":1666},[2922,30626,30627,30629],{},[1963,30628,2826],{},[1963,30630,2774],{},[902,30632,30633],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,30636,30638],{"className":30637},[886],[888,30639,30640],{"xmlns":890},[892,30641,30642,30662],{},[895,30643,30644,30646,30648,30654,30656],{},[1690,30645,11165],{},[1664,30647,1676],{},[2355,30649,30650,30652],{},[898,30651,1973],{},[1963,30653,1970],{},[898,30655,5240],{"mathvariant":1726},[2355,30657,30658,30660],{},[898,30659,1973],{},[1963,30661,2875],{},[902,30663,30664],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,30667,30669],{"className":30668},[886],[888,30670,30671],{"xmlns":890},[892,30672,30673,30693],{},[895,30674,30675,30677,30679,30685,30687],{},[1690,30676,11165],{},[1664,30678,1676],{},[2355,30680,30681,30683],{},[898,30682,2398],{},[1963,30684,2875],{},[898,30686,5240],{"mathvariant":1726},[2355,30688,30689,30691],{},[898,30690,2398],{},[1963,30692,1970],{},[902,30694,28498],{"encoding":904},[115,30696,30698,30699],{"id":30697},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,30700,30702],{"className":30701},[886],[888,30703,30704],{"xmlns":890},[892,30705,30706,30724],{},[895,30707,30708,30710,30712,30718],{},[898,30709,900],{},[1664,30711,1676],{},[2355,30713,30714,30716],{},[898,30715,1973],{},[1963,30717,2875],{},[2355,30719,30720,30722],{},[898,30721,1973],{},[1963,30723,1970],{},[902,30725,30726],{"encoding":904},"U = Q_1 Q_2",[724,30728,30729,30730,1343,30776,1343,30800,1343,30824,30846],{},"Je dána ",[883,30731,30733],{"className":30732},[886],[888,30734,30735],{"xmlns":890},[892,30736,30737,30773],{},[895,30738,30739,30741,30743,30749,30751,30757,30759,30761,30767],{},[898,30740,900],{},[1664,30742,1667],{"stretchy":1666},[2355,30744,30745,30747],{},[898,30746,1973],{},[1963,30748,2875],{},[1664,30750,1916],{"separator":1915},[2355,30752,30753,30755],{},[898,30754,1973],{},[1963,30756,1970],{},[1664,30758,1673],{"stretchy":1666},[1664,30760,1676],{},[2355,30762,30763,30765],{},[898,30764,1973],{},[1963,30766,2875],{},[2355,30768,30769,30771],{},[898,30770,1973],{},[1963,30772,1970],{},[902,30774,30775],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,30777,30779],{"className":30778},[886],[888,30780,30781],{"xmlns":890},[892,30782,30783,30797],{},[895,30784,30785,30793,30795],{},[1810,30786,30787,30789,30791],{},[898,30788,2398],{},[1963,30790,2875],{},[1664,30792,4920],{},[1664,30794,1676],{},[1963,30796,1970],{},[902,30798,30799],{"encoding":904},"P_1^* = 2",[883,30801,30803],{"className":30802},[886],[888,30804,30805],{"xmlns":890},[892,30806,30807,30821],{},[895,30808,30809,30817,30819],{},[1810,30810,30811,30813,30815],{},[898,30812,2398],{},[1963,30814,1970],{},[1664,30816,4920],{},[1664,30818,1676],{},[1963,30820,2826],{},[902,30822,30823],{"encoding":904},"P_2^* = 5",[883,30825,30827],{"className":30826},[886],[888,30828,30829],{"xmlns":890},[892,30830,30831,30843],{},[895,30832,30833,30839,30841],{},[1720,30834,30835,30837],{},[898,30836,9692],{},[1664,30838,4920],{},[1664,30840,1676],{},[1963,30842,1965],{},[902,30844,30845],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,30848,30850],{"className":30849},[886],[888,30851,30852],{"xmlns":890,"display":28566},[892,30853,30854,30926],{},[895,30855,30856,30858,30860,30866,30868,30874,30876,30878,30880,30882,30888,30894,30896,30898,30900,30902,30904,30906,30912,30914,30916,30922,30924],{},[898,30857,10358],{"mathvariant":29048},[1664,30859,1667],{"stretchy":1666},[2355,30861,30862,30864],{},[898,30863,1973],{},[1963,30865,2875],{},[1664,30867,1916],{"separator":1915},[2355,30869,30870,30872],{},[898,30871,1973],{},[1963,30873,1970],{},[1664,30875,1916],{"separator":1915},[898,30877,16943],{},[1664,30879,1673],{"stretchy":1666},[1664,30881,1676],{},[2355,30883,30884,30886],{},[898,30885,1973],{},[1963,30887,2875],{},[2355,30889,30890,30892],{},[898,30891,1973],{},[1963,30893,1970],{},[1664,30895,1700],{},[898,30897,16943],{},[1664,30899,1667],{"stretchy":1666},[1963,30901,1965],{},[1664,30903,1867],{},[1963,30905,1970],{},[2355,30907,30908,30910],{},[898,30909,1973],{},[1963,30911,2875],{},[1664,30913,1867],{},[1963,30915,2826],{},[2355,30917,30918,30920],{},[898,30919,1973],{},[1963,30921,1970],{},[1664,30923,1673],{"stretchy":1666},[898,30925,1977],{"mathvariant":1726},[902,30927,30928],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,30930,30931],{},"Soustava:",[883,30933,30935],{"className":30934},[886],[888,30936,30937],{"xmlns":890,"display":28566},[892,30938,30939,31051],{},[21254,30940,30941,30975,31009],{"rowspacing":21256,"columnalign":21257,"columnspacing":1727},[21259,30942,30943,30961],{},[21262,30944,30945],{},[2919,30946,30947],{"scriptlevel":2058,"displaystyle":1915},[895,30948,30949,30955,30957,30959],{},[2355,30950,30951,30953],{},[898,30952,1973],{},[1963,30954,1970],{},[1664,30956,1867],{},[1963,30958,1970],{},[898,30960,16943],{},[21262,30962,30963],{},[2919,30964,30965],{"scriptlevel":2058,"displaystyle":1915},[895,30966,30967,30969,30971,30973],{},[895,30968],{},[1664,30970,1676],{},[1963,30972,2058],{},[1664,30974,1916],{"separator":1915},[21259,30976,30977,30995],{},[21262,30978,30979],{},[2919,30980,30981],{"scriptlevel":2058,"displaystyle":1915},[895,30982,30983,30989,30991,30993],{},[2355,30984,30985,30987],{},[898,30986,1973],{},[1963,30988,2875],{},[1664,30990,1867],{},[1963,30992,2826],{},[898,30994,16943],{},[21262,30996,30997],{},[2919,30998,30999],{"scriptlevel":2058,"displaystyle":1915},[895,31000,31001,31003,31005,31007],{},[895,31002],{},[1664,31004,1676],{},[1963,31006,2058],{},[1664,31008,1916],{"separator":1915},[21259,31010,31011,31039],{},[21262,31012,31013],{},[2919,31014,31015],{"scriptlevel":2058,"displaystyle":1915},[895,31016,31017,31019,31021,31023,31029,31031,31033],{},[1963,31018,1965],{},[1664,31020,1867],{},[1963,31022,1970],{},[2355,31024,31025,31027],{},[898,31026,1973],{},[1963,31028,2875],{},[1664,31030,1867],{},[1963,31032,2826],{},[2355,31034,31035,31037],{},[898,31036,1973],{},[1963,31038,1970],{},[21262,31040,31041],{},[2919,31042,31043],{"scriptlevel":2058,"displaystyle":1915},[895,31044,31045,31047,31049],{},[895,31046],{},[1664,31048,1676],{},[1963,31050,12959],{},[902,31052,31053],{"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}",[724,31055,31056,31057,1343,31081,31105,31106,6155,31146,31164,31165,31215,31216,1977],{},"Z prvních dvou rovnic ",[883,31058,31060],{"className":31059},[886],[888,31061,31062],{"xmlns":890},[892,31063,31064,31078],{},[895,31065,31066,31072,31074,31076],{},[2355,31067,31068,31070],{},[898,31069,1973],{},[1963,31071,1970],{},[1664,31073,1676],{},[1963,31075,1970],{},[898,31077,16943],{},[902,31079,31080],{"encoding":904},"Q_2 = 2\\lambda",[883,31082,31084],{"className":31083},[886],[888,31085,31086],{"xmlns":890},[892,31087,31088,31102],{},[895,31089,31090,31096,31098,31100],{},[2355,31091,31092,31094],{},[898,31093,1973],{},[1963,31095,2875],{},[1664,31097,1676],{},[1963,31099,2826],{},[898,31101,16943],{},[902,31103,31104],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,31107,31109],{"className":31108},[886],[888,31110,31111],{"xmlns":890},[892,31112,31113,31143],{},[895,31114,31115,31117,31119,31121,31123,31125,31127,31129,31131,31133,31135,31137,31139,31141],{},[1963,31116,1965],{},[1664,31118,1676],{},[1963,31120,1970],{},[1664,31122,3753],{},[1963,31124,2826],{},[898,31126,16943],{},[1664,31128,1700],{},[1963,31130,2826],{},[1664,31132,3753],{},[1963,31134,1970],{},[898,31136,16943],{},[1664,31138,1676],{},[1963,31140,9599],{},[898,31142,16943],{},[902,31144,31145],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,31147,31149],{"className":31148},[886],[888,31150,31151],{"xmlns":890},[892,31152,31153,31161],{},[895,31154,31155,31157,31159],{},[898,31156,16943],{},[1664,31158,1676],{},[1963,31160,2826],{},[902,31162,31163],{"encoding":904},"\\lambda = 5",". Odtud ",[38,31166,31167,1343,31191],{},[883,31168,31170],{"className":31169},[886],[888,31171,31172],{"xmlns":890},[892,31173,31174,31188],{},[895,31175,31176,31184,31186],{},[1810,31177,31178,31180,31182],{},[898,31179,1973],{},[1963,31181,2875],{},[1664,31183,4920],{},[1664,31185,1676],{},[1963,31187,5570],{},[902,31189,31190],{"encoding":904},"Q_1^* = 25",[883,31192,31194],{"className":31193},[886],[888,31195,31196],{"xmlns":890},[892,31197,31198,31212],{},[895,31199,31200,31208,31210],{},[1810,31201,31202,31204,31206],{},[898,31203,1973],{},[1963,31205,1970],{},[1664,31207,4920],{},[1664,31209,1676],{},[1963,31211,3442],{},[902,31213,31214],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,31217,31219],{"className":31218},[886],[888,31220,31221],{"xmlns":890},[892,31222,31223,31244],{},[895,31224,31225,31231,31233,31235,31237,31239,31241],{},[1720,31226,31227,31229],{},[898,31228,900],{},[1664,31230,4920],{},[1664,31232,1676],{},[1963,31234,5570],{},[1664,31236,3753],{},[1963,31238,3442],{},[1664,31240,1676],{},[1963,31242,31243],{},"250",[902,31245,31246],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,31248,31249],{},[614,31250,31251,31252,28637,31290,4454,31314,31338,31339,31369,31370,31394,31395,31417,31418,1977],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,31253,31255],{"className":31254},[886],[888,31256,31257],{"xmlns":890},[892,31258,31259,31287],{},[895,31260,31261,31263,31265,31267,31273,31275,31277,31283,31285],{},[1963,31262,1965],{},[1664,31264,1867],{},[1963,31266,1970],{},[2355,31268,31269,31271],{},[898,31270,1973],{},[1963,31272,2875],{},[1664,31274,1867],{},[1963,31276,2826],{},[2355,31278,31279,31281],{},[898,31280,1973],{},[1963,31282,1970],{},[1664,31284,1676],{},[1963,31286,2058],{},[902,31288,31289],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,31291,31293],{"className":31292},[886],[888,31294,31295],{"xmlns":890},[892,31296,31297,31311],{},[895,31298,31299,31301,31303,31305,31307,31309],{},[898,31300,4822],{},[1664,31302,1837],{"stretchy":1666},[1963,31304,2058],{},[1664,31306,1916],{"separator":1915},[1963,31308,9599],{},[1664,31310,1850],{"stretchy":1666},[902,31312,31313],{"encoding":904},"A[0, 20]",[883,31315,31317],{"className":31316},[886],[888,31318,31319],{"xmlns":890},[892,31320,31321,31335],{},[895,31322,31323,31325,31327,31329,31331,31333],{},[898,31324,23753],{},[1664,31326,1837],{"stretchy":1666},[1963,31328,3696],{},[1664,31330,1916],{"separator":1915},[1963,31332,2058],{},[1664,31334,1850],{"stretchy":1666},[902,31336,31337],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,31340,31342],{"className":31341},[886],[888,31343,31344],{"xmlns":890},[892,31345,31346,31366],{},[895,31347,31348,31354,31356,31358,31360],{},[2355,31349,31350,31352],{},[898,31351,1973],{},[1963,31353,1970],{},[1664,31355,1676],{},[1963,31357,31243],{},[898,31359,5240],{"mathvariant":1726},[2355,31361,31362,31364],{},[898,31363,1973],{},[1963,31365,2875],{},[902,31367,31368],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,31371,31373],{"className":31372},[886],[888,31374,31375],{"xmlns":890},[892,31376,31377,31391],{},[895,31378,31379,31381,31383,31385,31387,31389],{},[898,31380,4819],{},[1664,31382,1837],{"stretchy":1666},[1963,31384,5570],{},[1664,31386,1916],{"separator":1915},[1963,31388,3442],{},[1664,31390,1850],{"stretchy":1666},[902,31392,31393],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,31396,31398],{"className":31397},[886],[888,31399,31400],{"xmlns":890},[892,31401,31402,31414],{},[895,31403,31404,31406],{},[1664,31405,1867],{},[2919,31407,31408],{"scriptlevel":2058,"displaystyle":1666},[2922,31409,31410,31412],{},[1963,31411,1970],{},[1963,31413,2826],{},[902,31415,31416],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,31419,31421],{"className":31420},[886],[888,31422,31423],{"xmlns":890},[892,31424,31425,31465],{},[895,31426,31427,31429,31431,31433,31435,31437,31439,31441,31443,31445,31453,31455,31457],{},[1664,31428,1867],{},[1690,31430,11165],{},[1664,31432,1667],{"stretchy":1666},[1963,31434,5570],{},[1664,31436,1916],{"separator":1915},[1963,31438,3442],{},[1664,31440,1673],{"stretchy":1666},[1664,31442,1676],{},[1664,31444,1867],{},[2919,31446,31447],{"scriptlevel":2058,"displaystyle":1666},[2922,31448,31449,31451],{},[1963,31450,3442],{},[1963,31452,5570],{},[1664,31454,1676],{},[1664,31456,1867],{},[2919,31458,31459],{"scriptlevel":2058,"displaystyle":1666},[2922,31460,31461,31463],{},[1963,31462,1970],{},[1963,31464,2826],{},[902,31466,31467],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,31469,31471],{"id":31470},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,31473,31474,31475,29503,31505,31508,31509,2087],{},"Považujeme-li v úloze ",[883,31476,31478],{"className":31477},[886],[888,31479,31480],{"xmlns":890},[892,31481,31482,31502],{},[895,31483,31484,31490,31492,31498,31500],{},[2355,31485,31486,31488],{},[898,31487,2398],{},[1963,31489,2875],{},[1664,31491,1916],{"separator":1915},[2355,31493,31494,31496],{},[898,31495,2398],{},[1963,31497,1970],{},[1664,31499,1916],{"separator":1915},[898,31501,9692],{},[902,31503,31504],{"encoding":904},"P_1, P_2, Y",[38,31506,31507],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,31510,31511],{},"Marshallovy poptávkové funkce",[883,31513,31515],{"className":31514},[886],[888,31516,31517],{"xmlns":890,"display":28566},[892,31518,31519,31614],{},[21254,31520,31521],{"width":28571},[21259,31522,31523,31525,31607,31609],{},[21262,31524],{"width":28576},[21262,31526,31527],{},[895,31528,31529,31535,31537,31543,31545,31551,31553,31559,31561,31563,31565,31567,31569,31575,31577,31583,31585,31591,31593,31599,31601,31603,31605],{},[2355,31530,31531,31533],{},[898,31532,1973],{},[1963,31534,2875],{},[1664,31536,1676],{},[2355,31538,31539,31541],{},[898,31540,2379],{},[1963,31542,2875],{},[1664,31544,1667],{"stretchy":1666},[2355,31546,31547,31549],{},[898,31548,2398],{},[1963,31550,2875],{},[1664,31552,1916],{"separator":1915},[2355,31554,31555,31557],{},[898,31556,2398],{},[1963,31558,1970],{},[1664,31560,1916],{"separator":1915},[898,31562,9692],{},[1664,31564,1673],{"stretchy":1666},[1664,31566,1916],{"separator":1915},[6444,31568],{"width":15783},[2355,31570,31571,31573],{},[898,31572,1973],{},[1963,31574,1970],{},[1664,31576,1676],{},[2355,31578,31579,31581],{},[898,31580,2379],{},[1963,31582,1970],{},[1664,31584,1667],{"stretchy":1666},[2355,31586,31587,31589],{},[898,31588,2398],{},[1963,31590,2875],{},[1664,31592,1916],{"separator":1915},[2355,31594,31595,31597],{},[898,31596,2398],{},[1963,31598,1970],{},[1664,31600,1916],{"separator":1915},[898,31602,9692],{},[1664,31604,1673],{"stretchy":1666},[1664,31606,1916],{"separator":1915},[21262,31608],{"width":28576},[21262,31610,31611],{},[1690,31612,31613],{},"(6.15)",[902,31615,31616],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,31618,31620],{"className":31619},[886],[888,31621,31622],{"xmlns":890,"display":28566},[892,31623,31624,31671],{},[21254,31625,31626],{"width":28571},[21259,31627,31628,31630,31664,31666],{},[21262,31629],{"width":28576},[21262,31631,31632],{},[895,31633,31634,31636,31638,31640,31642,31648,31650,31656,31658,31660,31662],{},[898,31635,16943],{},[1664,31637,1676],{},[898,31639,16943],{},[1664,31641,1667],{"stretchy":1666},[2355,31643,31644,31646],{},[898,31645,2398],{},[1963,31647,2875],{},[1664,31649,1916],{"separator":1915},[2355,31651,31652,31654],{},[898,31653,2398],{},[1963,31655,1970],{},[1664,31657,1916],{"separator":1915},[898,31659,9692],{},[1664,31661,1673],{"stretchy":1666},[898,31663,1977],{"mathvariant":1726},[21262,31665],{"width":28576},[21262,31667,31668],{},[1690,31669,31670],{},"(6.16)",[902,31672,31673],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,31675,31676,31706,31707,31773],{},[38,31677,31678,31679,1977],{},"Odvození pro ",[883,31680,31682],{"className":31681},[886],[888,31683,31684],{"xmlns":890},[892,31685,31686,31704],{},[895,31687,31688,31690,31692,31698],{},[898,31689,900],{},[1664,31691,1676],{},[2355,31693,31694,31696],{},[898,31695,1973],{},[1963,31697,2875],{},[2355,31699,31700,31702],{},[898,31701,1973],{},[1963,31703,1970],{},[902,31705,30726],{"encoding":904}," Lagrangeova funkce ",[883,31708,31710],{"className":31709},[886],[888,31711,31712],{"xmlns":890},[892,31713,31714,31770],{},[895,31715,31716,31718,31720,31726,31732,31734,31736,31738,31740,31742,31748,31754,31756,31762,31768],{},[898,31717,10358],{"mathvariant":29048},[1664,31719,1676],{},[2355,31721,31722,31724],{},[898,31723,1973],{},[1963,31725,2875],{},[2355,31727,31728,31730],{},[898,31729,1973],{},[1963,31731,1970],{},[1664,31733,1700],{},[898,31735,16943],{},[1664,31737,1667],{"stretchy":1666},[898,31739,9692],{},[1664,31741,1867],{},[2355,31743,31744,31746],{},[898,31745,2398],{},[1963,31747,2875],{},[2355,31749,31750,31752],{},[898,31751,1973],{},[1963,31753,2875],{},[1664,31755,1867],{},[2355,31757,31758,31760],{},[898,31759,2398],{},[1963,31761,1970],{},[2355,31763,31764,31766],{},[898,31765,1973],{},[1963,31767,1970],{},[1664,31769,1673],{"stretchy":1666},[902,31771,31772],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,31775,31777],{"className":31776},[886],[888,31778,31779],{"xmlns":890,"display":28566},[892,31780,31781,31948],{},[21254,31782,31783],{"width":28571},[21259,31784,31785,31787,31941,31943],{},[21262,31786],{"width":28576},[21262,31788,31789],{},[21254,31790,31791,31837,31883],{"rowspacing":21256,"columnalign":21257,"columnspacing":1727},[21259,31792,31793,31805],{},[21262,31794,31795],{},[2919,31796,31797],{"scriptlevel":2058,"displaystyle":1915},[1810,31798,31799,31801,31803],{},[898,31800,10358],{"mathvariant":29048},[1963,31802,2875],{},[1664,31804,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[21262,31806,31807],{},[2919,31808,31809],{"scriptlevel":2058,"displaystyle":1915},[895,31810,31811,31813,31815,31821,31823,31825,31831,31833,31835],{},[895,31812],{},[1664,31814,1676],{},[2355,31816,31817,31819],{},[898,31818,1973],{},[1963,31820,1970],{},[1664,31822,1867],{},[898,31824,16943],{},[2355,31826,31827,31829],{},[898,31828,2398],{},[1963,31830,2875],{},[1664,31832,1676],{},[1963,31834,2058],{},[1664,31836,1916],{"separator":1915},[21259,31838,31839,31851],{},[21262,31840,31841],{},[2919,31842,31843],{"scriptlevel":2058,"displaystyle":1915},[1810,31844,31845,31847,31849],{},[898,31846,10358],{"mathvariant":29048},[1963,31848,1970],{},[1664,31850,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[21262,31852,31853],{},[2919,31854,31855],{"scriptlevel":2058,"displaystyle":1915},[895,31856,31857,31859,31861,31867,31869,31871,31877,31879,31881],{},[895,31858],{},[1664,31860,1676],{},[2355,31862,31863,31865],{},[898,31864,1973],{},[1963,31866,2875],{},[1664,31868,1867],{},[898,31870,16943],{},[2355,31872,31873,31875],{},[898,31874,2398],{},[1963,31876,1970],{},[1664,31878,1676],{},[1963,31880,2058],{},[1664,31882,1916],{"separator":1915},[21259,31884,31885,31897],{},[21262,31886,31887],{},[2919,31888,31889],{"scriptlevel":2058,"displaystyle":1915},[1810,31890,31891,31893,31895],{},[898,31892,10358],{"mathvariant":29048},[898,31894,16943],{},[1664,31896,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[21262,31898,31899],{},[2919,31900,31901],{"scriptlevel":2058,"displaystyle":1915},[895,31902,31903,31905,31907,31909,31911,31917,31923,31925,31931,31937,31939],{},[895,31904],{},[1664,31906,1676],{},[898,31908,9692],{},[1664,31910,1867],{},[2355,31912,31913,31915],{},[898,31914,2398],{},[1963,31916,2875],{},[2355,31918,31919,31921],{},[898,31920,1973],{},[1963,31922,2875],{},[1664,31924,1867],{},[2355,31926,31927,31929],{},[898,31928,2398],{},[1963,31930,1970],{},[2355,31932,31933,31935],{},[898,31934,1973],{},[1963,31936,1970],{},[1664,31938,1676],{},[1963,31940,12959],{},[21262,31942],{"width":28576},[21262,31944,31945],{},[1690,31946,31947],{},"(6.17)",[902,31949,31950],{"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}",[724,31952,31953,31954,31982,31983,32011,32012,32080],{},"Z prvních dvou: ",[883,31955,31957],{"className":31956},[886],[888,31958,31959],{"xmlns":890},[892,31960,31961,31979],{},[895,31962,31963,31969,31971,31977],{},[2355,31964,31965,31967],{},[898,31966,1973],{},[1963,31968,1970],{},[1664,31970,1676],{},[2355,31972,31973,31975],{},[898,31974,2398],{},[1963,31976,2875],{},[898,31978,16943],{},[902,31980,31981],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,31984,31986],{"className":31985},[886],[888,31987,31988],{"xmlns":890},[892,31989,31990,32008],{},[895,31991,31992,31998,32000,32006],{},[2355,31993,31994,31996],{},[898,31995,1973],{},[1963,31997,2875],{},[1664,31999,1676],{},[2355,32001,32002,32004],{},[898,32003,2398],{},[1963,32005,1970],{},[898,32007,16943],{},[902,32009,32010],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,32013,32015],{"className":32014},[886],[888,32016,32017],{"xmlns":890},[892,32018,32019,32077],{},[895,32020,32021,32023,32025,32031,32033,32039,32041,32043,32049,32051,32057,32059,32061,32063,32069,32075],{},[898,32022,9692],{},[1664,32024,1676],{},[2355,32026,32027,32029],{},[898,32028,2398],{},[1963,32030,2875],{},[1664,32032,3753],{},[2355,32034,32035,32037],{},[898,32036,2398],{},[1963,32038,1970],{},[898,32040,16943],{},[1664,32042,1700],{},[2355,32044,32045,32047],{},[898,32046,2398],{},[1963,32048,1970],{},[1664,32050,3753],{},[2355,32052,32053,32055],{},[898,32054,2398],{},[1963,32056,2875],{},[898,32058,16943],{},[1664,32060,1676],{},[1963,32062,1970],{},[2355,32064,32065,32067],{},[898,32066,2398],{},[1963,32068,2875],{},[2355,32070,32071,32073],{},[898,32072,2398],{},[1963,32074,1970],{},[898,32076,16943],{},[902,32078,32079],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,32082,32084],{"className":32083},[886],[888,32085,32086],{"xmlns":890,"display":28566},[892,32087,32088,32131],{},[21254,32089,32090],{"width":28571},[21259,32091,32092,32094,32124,32126],{},[21262,32093],{"width":28576},[21262,32095,32096],{},[895,32097,32098,32100,32102,32122],{},[898,32099,16943],{},[1664,32101,1676],{},[2922,32103,32104,32106],{},[898,32105,9692],{},[895,32107,32108,32110,32116],{},[1963,32109,1970],{},[2355,32111,32112,32114],{},[898,32113,2398],{},[1963,32115,2875],{},[2355,32117,32118,32120],{},[898,32119,2398],{},[1963,32121,1970],{},[898,32123,1977],{"mathvariant":1726},[21262,32125],{"width":28576},[21262,32127,32128],{},[1690,32129,32130],{},"(6.20)",[902,32132,32133],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,32135,32136],{},"Zpětně:",[883,32138,32140],{"className":32139},[886],[888,32141,32142],{"xmlns":890,"display":28566},[892,32143,32144,32221],{},[21254,32145,32146],{"width":28571},[21259,32147,32148,32150,32214,32216],{},[21262,32149],{"width":28576},[21262,32151,32152],{},[13331,32153,32154],{"notation":13333},[2919,32155,32156],{"scriptlevel":2058,"displaystyle":1666},[2919,32157,32158],{"scriptlevel":2058,"displaystyle":1666},[2919,32159,32160],{"scriptlevel":2058,"displaystyle":1915},[895,32161,32162,32164,32170,32172,32186,32188,32190,32196,32198,32212],{},[1690,32163,4553],{},[2355,32165,32166,32168],{},[898,32167,1973],{},[1963,32169,2875],{},[1664,32171,1676],{},[2922,32173,32174,32176],{},[898,32175,9692],{},[895,32177,32178,32180],{},[1963,32179,1970],{},[2355,32181,32182,32184],{},[898,32183,2398],{},[1963,32185,2875],{},[1664,32187,1916],{"separator":1915},[6444,32189],{"width":15783},[2355,32191,32192,32194],{},[898,32193,1973],{},[1963,32195,1970],{},[1664,32197,1676],{},[2922,32199,32200,32202],{},[898,32201,9692],{},[895,32203,32204,32206],{},[1963,32205,1970],{},[2355,32207,32208,32210],{},[898,32209,2398],{},[1963,32211,1970],{},[1690,32213,4553],{},[21262,32215],{"width":28576},[21262,32217,32218],{},[1690,32219,32220],{},"(6.21)",[902,32222,32223],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,32225,32227],{"id":32226},"engelova-funkce","Engelova funkce",[724,32229,10226,32230,32233,32234,32237,32238,20367,32255,1343,32285,32315,32316,32350,32351,1343,32377,32403],{},[38,32231,32232],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,32235,32236],{},"Engelovou funkcí",": pro ",[883,32239,32241],{"className":32240},[886],[888,32242,32243],{"xmlns":890},[892,32244,32245,32253],{},[895,32246,32247,32249,32251],{},[898,32248,9692],{},[1664,32250,1676],{},[1963,32252,1965],{},[902,32254,20819],{"encoding":904},[883,32256,32258],{"className":32257},[886],[888,32259,32260],{"xmlns":890},[892,32261,32262,32282],{},[895,32263,32264,32270,32272,32274,32276],{},[2355,32265,32266,32268],{},[898,32267,1973],{},[1963,32269,2875],{},[1664,32271,1676],{},[1963,32273,3696],{},[898,32275,5240],{"mathvariant":1726},[2355,32277,32278,32280],{},[898,32279,2398],{},[1963,32281,2875],{},[902,32283,32284],{"encoding":904},"Q_1 = 50\u002FP_1",[883,32286,32288],{"className":32287},[886],[888,32289,32290],{"xmlns":890},[892,32291,32292,32312],{},[895,32293,32294,32300,32302,32304,32306],{},[2355,32295,32296,32298],{},[898,32297,1973],{},[1963,32299,1970],{},[1664,32301,1676],{},[1963,32303,3696],{},[898,32305,5240],{"mathvariant":1726},[2355,32307,32308,32310],{},[898,32309,2398],{},[1963,32311,1970],{},[902,32313,32314],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,32317,32319],{"className":32318},[886],[888,32320,32321],{"xmlns":890},[892,32322,32323,32347],{},[895,32324,32325,32331,32333,32335,32337,32343,32345],{},[2355,32326,32327,32329],{},[898,32328,2398],{},[1963,32330,2875],{},[1664,32332,1676],{},[1963,32334,3442],{},[1664,32336,1916],{"separator":1915},[2355,32338,32339,32341],{},[898,32340,2398],{},[1963,32342,1970],{},[1664,32344,1676],{},[1963,32346,9599],{},[902,32348,32349],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,32352,32354],{"className":32353},[886],[888,32355,32356],{"xmlns":890},[892,32357,32358,32374],{},[895,32359,32360,32366,32368,32370,32372],{},[2355,32361,32362,32364],{},[898,32363,1973],{},[1963,32365,2875],{},[1664,32367,1676],{},[898,32369,9692],{},[898,32371,5240],{"mathvariant":1726},[1963,32373,9599],{},[902,32375,32376],{"encoding":904},"Q_1 = Y\u002F20",[883,32378,32380],{"className":32379},[886],[888,32381,32382],{"xmlns":890},[892,32383,32384,32400],{},[895,32385,32386,32392,32394,32396,32398],{},[2355,32387,32388,32390],{},[898,32389,1973],{},[1963,32391,1970],{},[1664,32393,1676],{},[898,32395,9692],{},[898,32397,5240],{"mathvariant":1726},[1963,32399,5777],{},[902,32401,32402],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,32405,32407],{"id":32406},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,32409,32410],{},"Výdaje spotřebitele jsou",[883,32412,32414],{"className":32413},[886],[888,32415,32416],{"xmlns":890,"display":28566},[892,32417,32418,32493],{},[21254,32419,32420],{"width":28571},[21259,32421,32422,32424,32486,32488],{},[21262,32423],{"width":28576},[21262,32425,32426],{},[895,32427,32428,32430,32432,32434,32436,32442,32444,32450,32452,32454,32462,32468,32470,32478,32484],{},[898,32429,4819],{},[1664,32431,1676],{},[898,32433,4819],{},[1664,32435,1667],{"stretchy":1666},[2355,32437,32438,32440],{},[898,32439,1973],{},[1963,32441,2875],{},[1664,32443,1916],{"separator":1915},[2355,32445,32446,32448],{},[898,32447,1973],{},[1963,32449,1970],{},[1664,32451,1673],{"stretchy":1666},[1664,32453,1676],{},[1810,32455,32456,32458,32460],{},[898,32457,2398],{},[1963,32459,2875],{},[1664,32461,4920],{},[2355,32463,32464,32466],{},[898,32465,1973],{},[1963,32467,2875],{},[1664,32469,1700],{},[1810,32471,32472,32474,32476],{},[898,32473,2398],{},[1963,32475,1970],{},[1664,32477,4920],{},[2355,32479,32480,32482],{},[898,32481,1973],{},[1963,32483,1970],{},[1664,32485,1916],{"separator":1915},[21262,32487],{"width":28576},[21262,32489,32490],{},[1690,32491,32492],{},"(6.22)",[902,32494,32495],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,32497,32498],{},"a je pevně zadána hladina užitečnosti",[883,32500,32502],{"className":32501},[886],[888,32503,32504],{"xmlns":890,"display":28566},[892,32505,32506,32553],{},[21254,32507,32508],{"width":28571},[21259,32509,32510,32512,32546,32548],{},[21262,32511],{"width":28576},[21262,32513,32514],{},[895,32515,32516,32522,32524,32526,32528,32534,32536,32542,32544],{},[1720,32517,32518,32520],{},[898,32519,900],{},[1664,32521,4920],{},[1664,32523,1676],{},[898,32525,900],{},[1664,32527,1667],{"stretchy":1666},[2355,32529,32530,32532],{},[898,32531,1973],{},[1963,32533,2875],{},[1664,32535,1916],{"separator":1915},[2355,32537,32538,32540],{},[898,32539,1973],{},[1963,32541,1970],{},[1664,32543,1673],{"stretchy":1666},[898,32545,1977],{"mathvariant":1726},[21262,32547],{"width":28576},[21262,32549,32550],{},[1690,32551,32552],{},"(6.23)",[902,32554,32555],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,32557,32558,32561,32562,32594,32595,1977],{},[38,32559,32560],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,32563,32565],{"className":32564},[886],[888,32566,32567],{"xmlns":890},[892,32568,32569,32591],{},[895,32570,32571,32573,32575,32581,32583,32589],{},[898,32572,4819],{},[1664,32574,1667],{"stretchy":1666},[2355,32576,32577,32579],{},[898,32578,1973],{},[1963,32580,2875],{},[1664,32582,1916],{"separator":1915},[2355,32584,32585,32587],{},[898,32586,1973],{},[1963,32588,1970],{},[1664,32590,1673],{"stretchy":1666},[902,32592,32593],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,32596,32598],{"className":32597},[886],[888,32599,32600],{"xmlns":890},[892,32601,32602,32658],{},[895,32603,32604,32606,32608,32614,32616,32622,32624,32626,32632,32634,32636,32638,32644,32646,32652,32654,32656],{},[898,32605,11602],{},[1664,32607,1667],{"stretchy":1666},[2355,32609,32610,32612],{},[898,32611,1973],{},[1963,32613,2875],{},[1664,32615,1916],{"separator":1915},[2355,32617,32618,32620],{},[898,32619,1973],{},[1963,32621,1970],{},[1664,32623,1673],{"stretchy":1666},[1664,32625,1676],{},[1720,32627,32628,32630],{},[898,32629,900],{},[1664,32631,4920],{},[1664,32633,1867],{},[898,32635,900],{},[1664,32637,1667],{"stretchy":1666},[2355,32639,32640,32642],{},[898,32641,1973],{},[1963,32643,2875],{},[1664,32645,1916],{"separator":1915},[2355,32647,32648,32650],{},[898,32649,1973],{},[1963,32651,1970],{},[1664,32653,1673],{"stretchy":1666},[1664,32655,1676],{},[1963,32657,2058],{},[902,32659,32660],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,32662,32664],{"id":32663},"lagrangeova-funkce","Lagrangeova funkce",[883,32666,32668],{"className":32667},[886],[888,32669,32670],{"xmlns":890,"display":28566},[892,32671,32672,32783],{},[21254,32673,32674],{"width":28571},[21259,32675,32676,32678,32776,32778],{},[21262,32677],{"width":28576},[21262,32679,32680],{},[895,32681,32682,32684,32686,32692,32694,32700,32702,32704,32706,32708,32716,32722,32724,32732,32738,32740,32742,32744,32750,32752,32754,32756,32762,32764,32770,32772,32774],{},[898,32683,10358],{"mathvariant":29048},[1664,32685,1667],{"stretchy":1666},[2355,32687,32688,32690],{},[898,32689,1973],{},[1963,32691,2875],{},[1664,32693,1916],{"separator":1915},[2355,32695,32696,32698],{},[898,32697,1973],{},[1963,32699,1970],{},[1664,32701,1916],{"separator":1915},[898,32703,16943],{},[1664,32705,1673],{"stretchy":1666},[1664,32707,1676],{},[1810,32709,32710,32712,32714],{},[898,32711,2398],{},[1963,32713,2875],{},[1664,32715,4920],{},[2355,32717,32718,32720],{},[898,32719,1973],{},[1963,32721,2875],{},[1664,32723,1700],{},[1810,32725,32726,32728,32730],{},[898,32727,2398],{},[1963,32729,1970],{},[1664,32731,4920],{},[2355,32733,32734,32736],{},[898,32735,1973],{},[1963,32737,1970],{},[1664,32739,1700],{},[898,32741,16943],{},[1664,32743,1667],{"stretchy":1666},[1720,32745,32746,32748],{},[898,32747,900],{},[1664,32749,4920],{},[1664,32751,1867],{},[898,32753,900],{},[1664,32755,1667],{"stretchy":1666},[2355,32757,32758,32760],{},[898,32759,1973],{},[1963,32761,2875],{},[1664,32763,1916],{"separator":1915},[2355,32765,32766,32768],{},[898,32767,1973],{},[1963,32769,1970],{},[1664,32771,1673],{"stretchy":1666},[1664,32773,1673],{"stretchy":1666},[898,32775,1977],{"mathvariant":1726},[21262,32777],{"width":28576},[21262,32779,32780],{},[1690,32781,32782],{},"(6.24)",[902,32784,32785],{"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}",[724,32787,32788],{},"Soustava podmínek prvního řádu:",[883,32790,32792],{"className":32791},[886],[888,32793,32794],{"xmlns":890,"display":28566},[892,32795,32796,32969],{},[21254,32797,32798],{"width":28571},[21259,32799,32800,32802,32962,32964],{},[21262,32801],{"width":28576},[21262,32803,32804],{},[21254,32805,32806,32856,32906],{"rowspacing":21256,"columnalign":21257,"columnspacing":1727},[21259,32807,32808,32820],{},[21262,32809,32810],{},[2919,32811,32812],{"scriptlevel":2058,"displaystyle":1915},[1810,32813,32814,32816,32818],{},[898,32815,10358],{"mathvariant":29048},[1963,32817,2875],{},[1664,32819,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[21262,32821,32822],{},[2919,32823,32824],{"scriptlevel":2058,"displaystyle":1915},[895,32825,32826,32828,32830,32838,32840,32842,32850,32852,32854],{},[895,32827],{},[1664,32829,1676],{},[1810,32831,32832,32834,32836],{},[898,32833,2398],{},[1963,32835,2875],{},[1664,32837,4920],{},[1664,32839,1867],{},[898,32841,16943],{},[1810,32843,32844,32846,32848],{},[898,32845,900],{},[1963,32847,2875],{},[1664,32849,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,32851,1676],{},[1963,32853,2058],{},[1664,32855,1916],{"separator":1915},[21259,32857,32858,32870],{},[21262,32859,32860],{},[2919,32861,32862],{"scriptlevel":2058,"displaystyle":1915},[1810,32863,32864,32866,32868],{},[898,32865,10358],{"mathvariant":29048},[1963,32867,1970],{},[1664,32869,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[21262,32871,32872],{},[2919,32873,32874],{"scriptlevel":2058,"displaystyle":1915},[895,32875,32876,32878,32880,32888,32890,32892,32900,32902,32904],{},[895,32877],{},[1664,32879,1676],{},[1810,32881,32882,32884,32886],{},[898,32883,2398],{},[1963,32885,1970],{},[1664,32887,4920],{},[1664,32889,1867],{},[898,32891,16943],{},[1810,32893,32894,32896,32898],{},[898,32895,900],{},[1963,32897,1970],{},[1664,32899,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,32901,1676],{},[1963,32903,2058],{},[1664,32905,1916],{"separator":1915},[21259,32907,32908,32920],{},[21262,32909,32910],{},[2919,32911,32912],{"scriptlevel":2058,"displaystyle":1915},[1810,32913,32914,32916,32918],{},[898,32915,10358],{"mathvariant":29048},[898,32917,16943],{},[1664,32919,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[21262,32921,32922],{},[2919,32923,32924],{"scriptlevel":2058,"displaystyle":1915},[895,32925,32926,32928,32930,32936,32938,32940,32942,32948,32950,32956,32958,32960],{},[895,32927],{},[1664,32929,1676],{},[1720,32931,32932,32934],{},[898,32933,900],{},[1664,32935,4920],{},[1664,32937,1867],{},[898,32939,900],{},[1664,32941,1667],{"stretchy":1666},[2355,32943,32944,32946],{},[898,32945,1973],{},[1963,32947,2875],{},[1664,32949,1916],{"separator":1915},[2355,32951,32952,32954],{},[898,32953,1973],{},[1963,32955,1970],{},[1664,32957,1673],{"stretchy":1666},[1664,32959,1676],{},[1963,32961,12959],{},[21262,32963],{"width":28576},[21262,32965,32966],{},[1690,32967,32968],{},"(6.25)",[902,32970,32971],{"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}",[724,32973,32974],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,32976,32978],{"className":32977},[886],[888,32979,32980],{"xmlns":890,"display":28566},[892,32981,32982,33080],{},[21254,32983,32984],{"width":28571},[21259,32985,32986,32988,33073,33075],{},[21262,32987],{"width":28576},[21262,32989,32990],{},[895,32991,32992,32994,32996,33002,33004,33010,33012,33014,33016,33018,33020,33022,33071],{},[898,32993,2379],{},[1664,32995,1667],{"stretchy":1666},[2355,32997,32998,33000],{},[898,32999,1973],{},[1963,33001,2875],{},[1664,33003,1916],{"separator":1915},[2355,33005,33006,33008],{},[898,33007,1973],{},[1963,33009,1970],{},[1664,33011,1916],{"separator":1915},[898,33013,16943],{},[1664,33015,1673],{"stretchy":1666},[1664,33017,1676],{},[1664,33019,1867],{},[898,33021,16943],{},[895,33023,33024,33026,33038,33040,33053,33055,33057,33069],{},[1664,33025,1667],{"fence":1915},[1810,33027,33028,33030,33032],{},[898,33029,900],{},[1963,33031,3483],{},[895,33033,33034,33036],{},[1664,33035,1728],{"mathvariant":1726},[1664,33037,1728],{"mathvariant":1726},[1664,33039,1700],{},[1810,33041,33042,33044,33047],{},[898,33043,900],{},[1963,33045,33046],{},"22",[895,33048,33049,33051],{},[1664,33050,1728],{"mathvariant":1726},[1664,33052,1728],{"mathvariant":1726},[1664,33054,1700],{},[1963,33056,1970],{},[1810,33058,33059,33061,33063],{},[898,33060,900],{},[1963,33062,4084],{},[895,33064,33065,33067],{},[1664,33066,1728],{"mathvariant":1726},[1664,33068,1728],{"mathvariant":1726},[1664,33070,1673],{"fence":1915},[898,33072,1977],{"mathvariant":1726},[21262,33074],{"width":28576},[21262,33076,33077],{},[1690,33078,33079],{},"(6.26)",[902,33081,33082],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,33084,33085,33088,33089,33128,33129,33168,33169,33219,33220,33246,33247,33264,33265,33291],{},[38,33086,33087],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,33090,33092],{"className":33091},[886],[888,33093,33094],{"xmlns":890},[892,33095,33096,33126],{},[895,33097,33098,33104,33106,33114,33116,33124],{},[1720,33099,33100,33102],{},[898,33101,1973],{},[1664,33103,4920],{},[1664,33105,1837],{"stretchy":1666},[1810,33107,33108,33110,33112],{},[898,33109,1973],{},[1963,33111,2875],{},[1664,33113,4920],{},[1664,33115,1916],{"separator":1915},[1810,33117,33118,33120,33122],{},[898,33119,1973],{},[1963,33121,1970],{},[1664,33123,4920],{},[1664,33125,1850],{"stretchy":1666},[902,33127,28827],{"encoding":904}," dotyku křivky užitečnosti ",[883,33130,33132],{"className":33131},[886],[888,33133,33134],{"xmlns":890},[892,33135,33136,33166],{},[895,33137,33138,33144,33146,33148,33150,33156,33158,33164],{},[1720,33139,33140,33142],{},[898,33141,900],{},[1664,33143,4920],{},[1664,33145,1676],{},[898,33147,900],{},[1664,33149,1667],{"stretchy":1666},[2355,33151,33152,33154],{},[898,33153,1973],{},[1963,33155,2875],{},[1664,33157,1916],{"separator":1915},[2355,33159,33160,33162],{},[898,33161,1973],{},[1963,33163,1970],{},[1664,33165,1673],{"stretchy":1666},[902,33167,18165],{"encoding":904}," s přímkou výdajů ",[883,33170,33172],{"className":33171},[886],[888,33173,33174],{"xmlns":890},[892,33175,33176,33216],{},[895,33177,33178,33184,33186,33194,33200,33202,33210],{},[1720,33179,33180,33182],{},[898,33181,4819],{},[1664,33183,4920],{},[1664,33185,1676],{},[1810,33187,33188,33190,33192],{},[898,33189,2398],{},[1963,33191,2875],{},[1664,33193,4920],{},[2355,33195,33196,33198],{},[898,33197,1973],{},[1963,33199,2875],{},[1664,33201,1700],{},[1810,33203,33204,33206,33208],{},[898,33205,2398],{},[1963,33207,1970],{},[1664,33209,4920],{},[2355,33211,33212,33214],{},[898,33213,1973],{},[1963,33215,1970],{},[902,33217,33218],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,33221,33223],{"className":33222},[886],[888,33224,33225],{"xmlns":890},[892,33226,33227,33243],{},[895,33228,33229,33235,33237],{},[2355,33230,33231,33233],{},[898,33232,4819],{},[1963,33234,2058],{},[1664,33236,4022],{},[1720,33238,33239,33241],{},[898,33240,4819],{},[1664,33242,4920],{},[902,33244,33245],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,33248,33250],{"className":33249},[886],[888,33251,33252],{"xmlns":890},[892,33253,33254,33262],{},[895,33255,33256],{},[1720,33257,33258,33260],{},[898,33259,900],{},[1664,33261,4920],{},[902,33263,28462],{"encoding":904},", hladina ",[883,33266,33268],{"className":33267},[886],[888,33269,33270],{"xmlns":890},[892,33271,33272,33288],{},[895,33273,33274,33280,33282],{},[2355,33275,33276,33278],{},[898,33277,4819],{},[1963,33279,2875],{},[1664,33281,3984],{},[1720,33283,33284,33286],{},[898,33285,4819],{},[1664,33287,4920],{},[902,33289,33290],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[4436,33293,33294,33299],{},[724,33295,33296,33298],{},[883,33297,5138],{}," Postup — duální úloha (minimalizace výdajů)",[152,33300,33301,33351,33437,33477,33552],{},[123,33302,33303,1885,33306,33350],{},[38,33304,33305],{},"Zapiš vazbu",[883,33307,33309],{"className":33308},[886],[888,33310,33311],{"xmlns":890},[892,33312,33313,33347],{},[895,33314,33315,33321,33323,33325,33327,33333,33335,33341,33343,33345],{},[1720,33316,33317,33319],{},[898,33318,900],{},[1664,33320,4920],{},[1664,33322,1867],{},[898,33324,900],{},[1664,33326,1667],{"stretchy":1666},[2355,33328,33329,33331],{},[898,33330,1973],{},[1963,33332,2875],{},[1664,33334,1916],{"separator":1915},[2355,33336,33337,33339],{},[898,33338,1973],{},[1963,33340,1970],{},[1664,33342,1673],{"stretchy":1666},[1664,33344,1676],{},[1963,33346,2058],{},[902,33348,33349],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,33352,33353,1885,33355,1977],{},[38,33354,29760],{},[883,33356,33358],{"className":33357},[886],[888,33359,33360],{"xmlns":890},[892,33361,33362,33434],{},[895,33363,33364,33366,33368,33376,33382,33384,33392,33398,33400,33402,33404,33410,33412,33414,33416,33422,33424,33430,33432],{},[898,33365,10358],{"mathvariant":29048},[1664,33367,1676],{},[1810,33369,33370,33372,33374],{},[898,33371,2398],{},[1963,33373,2875],{},[1664,33375,4920],{},[2355,33377,33378,33380],{},[898,33379,1973],{},[1963,33381,2875],{},[1664,33383,1700],{},[1810,33385,33386,33388,33390],{},[898,33387,2398],{},[1963,33389,1970],{},[1664,33391,4920],{},[2355,33393,33394,33396],{},[898,33395,1973],{},[1963,33397,1970],{},[1664,33399,1700],{},[898,33401,16943],{},[1664,33403,1667],{"stretchy":1666},[1720,33405,33406,33408],{},[898,33407,900],{},[1664,33409,4920],{},[1664,33411,1867],{},[898,33413,900],{},[1664,33415,1667],{"stretchy":1666},[2355,33417,33418,33420],{},[898,33419,1973],{},[1963,33421,2875],{},[1664,33423,1916],{"separator":1915},[2355,33425,33426,33428],{},[898,33427,1973],{},[1963,33429,1970],{},[1664,33431,1673],{"stretchy":1666},[1664,33433,1673],{"stretchy":1666},[902,33435,33436],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,33438,33439,33442,33443,33476],{},[38,33440,33441],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,33444,33446],{"className":33445},[886],[888,33447,33448],{"xmlns":890},[892,33449,33450,33474],{},[895,33451,33452,33454,33456,33464,33466],{},[1690,33453,11165],{},[1664,33455,1676],{},[1810,33457,33458,33460,33462],{},[898,33459,2398],{},[1963,33461,2875],{},[1664,33463,4920],{},[898,33465,5240],{"mathvariant":1726},[1810,33467,33468,33470,33472],{},[898,33469,2398],{},[1963,33471,1970],{},[1664,33473,4920],{},[902,33475,29479],{"encoding":904}," (stejná jako u maximalizace!).",[123,33478,33479,1885,33482,33522,33523,1977],{},[38,33480,33481],{},"Dosaď do vazby",[883,33483,33485],{"className":33484},[886],[888,33486,33487],{"xmlns":890},[892,33488,33489,33519],{},[895,33490,33491,33493,33495,33501,33503,33509,33511,33513],{},[898,33492,900],{},[1664,33494,1667],{"stretchy":1666},[2355,33496,33497,33499],{},[898,33498,1973],{},[1963,33500,2875],{},[1664,33502,1916],{"separator":1915},[2355,33504,33505,33507],{},[898,33506,1973],{},[1963,33508,1970],{},[1664,33510,1673],{"stretchy":1666},[1664,33512,1676],{},[1720,33514,33515,33517],{},[898,33516,900],{},[1664,33518,4920],{},[902,33520,33521],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,33524,33526],{"className":33525},[886],[888,33527,33528],{"xmlns":890},[892,33529,33530,33550],{},[895,33531,33532,33540,33542],{},[1810,33533,33534,33536,33538],{},[898,33535,1973],{},[1963,33537,2875],{},[1664,33539,4920],{},[1664,33541,1916],{"separator":1915},[1810,33543,33544,33546,33548],{},[898,33545,1973],{},[1963,33547,1970],{},[1664,33549,4920],{},[902,33551,30001],{"encoding":904},[123,33553,33554,1885,33557,33611],{},[38,33555,33556],{},"Vypočítej minimální výdaje",[883,33558,33560],{"className":33559},[886],[888,33561,33562],{"xmlns":890},[892,33563,33564,33608],{},[895,33565,33566,33572,33574,33582,33590,33592,33600],{},[1720,33567,33568,33570],{},[898,33569,4819],{},[1664,33571,4920],{},[1664,33573,1676],{},[1810,33575,33576,33578,33580],{},[898,33577,2398],{},[1963,33579,2875],{},[1664,33581,4920],{},[1810,33583,33584,33586,33588],{},[898,33585,1973],{},[1963,33587,2875],{},[1664,33589,4920],{},[1664,33591,1700],{},[1810,33593,33594,33596,33598],{},[898,33595,2398],{},[1963,33597,1970],{},[1664,33599,4920],{},[1810,33601,33602,33604,33606],{},[898,33603,1973],{},[1963,33605,1970],{},[1664,33607,4920],{},[902,33609,33610],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,33613,33615,33616],{"id":33614},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,33617,33619],{"className":33618},[886],[888,33620,33621],{"xmlns":890},[892,33622,33623,33657],{},[895,33624,33625,33627,33629,33643],{},[898,33626,900],{},[1664,33628,1676],{},[1810,33630,33631,33633,33635],{},[898,33632,1973],{},[1963,33634,2875],{},[895,33636,33637,33639,33641],{},[1963,33638,2875],{},[898,33640,5240],{"mathvariant":1726},[1963,33642,1970],{},[1810,33644,33645,33647,33649],{},[898,33646,1973],{},[1963,33648,1970],{},[895,33650,33651,33653,33655],{},[1963,33652,2875],{},[898,33654,5240],{"mathvariant":1726},[1963,33656,1970],{},[902,33658,33659],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,33661,33662,33663,1343,33685,1343,33709,30846],{},"Dáno ",[883,33664,33666],{"className":33665},[886],[888,33667,33668],{"xmlns":890},[892,33669,33670,33682],{},[895,33671,33672,33678,33680],{},[1720,33673,33674,33676],{},[898,33675,900],{},[1664,33677,4920],{},[1664,33679,1676],{},[1963,33681,1970],{},[902,33683,33684],{"encoding":904},"U^* = 2",[883,33686,33688],{"className":33687},[886],[888,33689,33690],{"xmlns":890},[892,33691,33692,33706],{},[895,33693,33694,33702,33704],{},[1810,33695,33696,33698,33700],{},[898,33697,2398],{},[1963,33699,2875],{},[1664,33701,4920],{},[1664,33703,1676],{},[1963,33705,24289],{},[902,33707,33708],{"encoding":904},"P_1^* = 0{,}25",[883,33710,33712],{"className":33711},[886],[888,33713,33714],{"xmlns":890},[892,33715,33716,33730],{},[895,33717,33718,33726,33728],{},[1810,33719,33720,33722,33724],{},[898,33721,2398],{},[1963,33723,1970],{},[1664,33725,4920],{},[1664,33727,1676],{},[1963,33729,2875],{},[902,33731,33732],{"encoding":904},"P_2^* = 1",[883,33734,33736],{"className":33735},[886],[888,33737,33738],{"xmlns":890,"display":28566},[892,33739,33740,33804],{},[895,33741,33742,33744,33746,33748,33754,33756,33762,33764,33766,33768,33770,33772,33786,33800,33802],{},[898,33743,10358],{"mathvariant":29048},[1664,33745,1676],{},[1963,33747,24289],{},[2355,33749,33750,33752],{},[898,33751,1973],{},[1963,33753,2875],{},[1664,33755,1700],{},[2355,33757,33758,33760],{},[898,33759,1973],{},[1963,33761,1970],{},[1664,33763,1700],{},[898,33765,16943],{},[1664,33767,1667],{"stretchy":1666},[1963,33769,1970],{},[1664,33771,1867],{},[1810,33773,33774,33776,33778],{},[898,33775,1973],{},[1963,33777,2875],{},[895,33779,33780,33782,33784],{},[1963,33781,2875],{},[898,33783,5240],{"mathvariant":1726},[1963,33785,1970],{},[1810,33787,33788,33790,33792],{},[898,33789,1973],{},[1963,33791,1970],{},[895,33793,33794,33796,33798],{},[1963,33795,2875],{},[898,33797,5240],{"mathvariant":1726},[1963,33799,1970],{},[1664,33801,1673],{"stretchy":1666},[898,33803,1977],{"mathvariant":1726},[902,33805,33806],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,33808,30931],{},[883,33810,33812],{"className":33811},[886],[888,33813,33814],{"xmlns":890,"display":28566},[892,33815,33816,34030],{},[21254,33817,33818,33894,33970],{"rowspacing":21256,"columnalign":21257,"columnspacing":1727},[21259,33819,33820,33832],{},[21262,33821,33822],{},[2919,33823,33824],{"scriptlevel":2058,"displaystyle":1915},[1810,33825,33826,33828,33830],{},[898,33827,10358],{"mathvariant":29048},[1963,33829,2875],{},[1664,33831,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[21262,33833,33834],{},[2919,33835,33836],{"scriptlevel":2058,"displaystyle":1915},[895,33837,33838,33840,33842,33844,33846,33848,33850,33858,33874,33888,33890,33892],{},[895,33839],{},[1664,33841,1676],{},[1963,33843,24289],{},[1664,33845,1867],{},[898,33847,16943],{},[1664,33849,3753],{},[2919,33851,33852],{"scriptlevel":2058,"displaystyle":1666},[2922,33853,33854,33856],{},[1963,33855,2875],{},[1963,33857,1970],{},[1810,33859,33860,33862,33864],{},[898,33861,1973],{},[1963,33863,2875],{},[895,33865,33866,33868,33870,33872],{},[1664,33867,1867],{},[1963,33869,2875],{},[898,33871,5240],{"mathvariant":1726},[1963,33873,1970],{},[1810,33875,33876,33878,33880],{},[898,33877,1973],{},[1963,33879,1970],{},[895,33881,33882,33884,33886],{},[1963,33883,2875],{},[898,33885,5240],{"mathvariant":1726},[1963,33887,1970],{},[1664,33889,1676],{},[1963,33891,2058],{},[1664,33893,1916],{"separator":1915},[21259,33895,33896,33908],{},[21262,33897,33898],{},[2919,33899,33900],{"scriptlevel":2058,"displaystyle":1915},[1810,33901,33902,33904,33906],{},[898,33903,10358],{"mathvariant":29048},[1963,33905,1970],{},[1664,33907,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[21262,33909,33910],{},[2919,33911,33912],{"scriptlevel":2058,"displaystyle":1915},[895,33913,33914,33916,33918,33920,33922,33924,33926,33934,33948,33964,33966,33968],{},[895,33915],{},[1664,33917,1676],{},[1963,33919,2875],{},[1664,33921,1867],{},[898,33923,16943],{},[1664,33925,3753],{},[2919,33927,33928],{"scriptlevel":2058,"displaystyle":1666},[2922,33929,33930,33932],{},[1963,33931,2875],{},[1963,33933,1970],{},[1810,33935,33936,33938,33940],{},[898,33937,1973],{},[1963,33939,2875],{},[895,33941,33942,33944,33946],{},[1963,33943,2875],{},[898,33945,5240],{"mathvariant":1726},[1963,33947,1970],{},[1810,33949,33950,33952,33954],{},[898,33951,1973],{},[1963,33953,1970],{},[895,33955,33956,33958,33960,33962],{},[1664,33957,1867],{},[1963,33959,2875],{},[898,33961,5240],{"mathvariant":1726},[1963,33963,1970],{},[1664,33965,1676],{},[1963,33967,2058],{},[1664,33969,1916],{"separator":1915},[21259,33971,33972,33984],{},[21262,33973,33974],{},[2919,33975,33976],{"scriptlevel":2058,"displaystyle":1915},[1810,33977,33978,33980,33982],{},[898,33979,10358],{"mathvariant":29048},[898,33981,16943],{},[1664,33983,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[21262,33985,33986],{},[2919,33987,33988],{"scriptlevel":2058,"displaystyle":1915},[895,33989,33990,33992,33994,33996,33998,34012,34026,34028],{},[895,33991],{},[1664,33993,1676],{},[1963,33995,1970],{},[1664,33997,1867],{},[1810,33999,34000,34002,34004],{},[898,34001,1973],{},[1963,34003,2875],{},[895,34005,34006,34008,34010],{},[1963,34007,2875],{},[898,34009,5240],{"mathvariant":1726},[1963,34011,1970],{},[1810,34013,34014,34016,34018],{},[898,34015,1973],{},[1963,34017,1970],{},[895,34019,34020,34022,34024],{},[1963,34021,2875],{},[898,34023,5240],{"mathvariant":1726},[1963,34025,1970],{},[1664,34027,1676],{},[1963,34029,12959],{},[902,34031,34032],{"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}",[724,34034,34035,34036,18076,34066,34094,34095,6155,34157,1343,34207,34229,34230,1977],{},"Podílem prvních dvou rovnic: ",[883,34037,34039],{"className":34038},[886],[888,34040,34041],{"xmlns":890},[892,34042,34043,34063],{},[895,34044,34045,34047,34049,34055,34057],{},[1963,34046,24289],{},[1664,34048,1676],{},[2355,34050,34051,34053],{},[898,34052,1973],{},[1963,34054,1970],{},[898,34056,5240],{"mathvariant":1726},[2355,34058,34059,34061],{},[898,34060,1973],{},[1963,34062,2875],{},[902,34064,34065],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,34067,34069],{"className":34068},[886],[888,34070,34071],{"xmlns":890},[892,34072,34073,34091],{},[895,34074,34075,34081,34083,34085],{},[2355,34076,34077,34079],{},[898,34078,1973],{},[1963,34080,1970],{},[1664,34082,1676],{},[1963,34084,24289],{},[2355,34086,34087,34089],{},[898,34088,1973],{},[1963,34090,2875],{},[902,34092,34093],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,34096,34098],{"className":34097},[886],[888,34099,34100],{"xmlns":890},[892,34101,34102,34154],{},[895,34103,34104,34118,34120,34122,34128,34140,34142,34144,34150,34152],{},[1810,34105,34106,34108,34110],{},[898,34107,1973],{},[1963,34109,2875],{},[895,34111,34112,34114,34116],{},[1963,34113,2875],{},[898,34115,5240],{"mathvariant":1726},[1963,34117,1970],{},[1664,34119,1667],{"stretchy":1666},[1963,34121,24289],{},[2355,34123,34124,34126],{},[898,34125,1973],{},[1963,34127,2875],{},[1720,34129,34130,34132],{},[1664,34131,1673],{"stretchy":1666},[895,34133,34134,34136,34138],{},[1963,34135,2875],{},[898,34137,5240],{"mathvariant":1726},[1963,34139,1970],{},[1664,34141,1676],{},[1963,34143,5575],{},[2355,34145,34146,34148],{},[898,34147,1973],{},[1963,34149,2875],{},[1664,34151,1676],{},[1963,34153,1970],{},[902,34155,34156],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,34158,34159,1343,34183],{},[883,34160,34162],{"className":34161},[886],[888,34163,34164],{"xmlns":890},[892,34165,34166,34180],{},[895,34167,34168,34176,34178],{},[1810,34169,34170,34172,34174],{},[898,34171,1973],{},[1963,34173,2875],{},[1664,34175,4920],{},[1664,34177,1676],{},[1963,34179,2944],{},[902,34181,34182],{"encoding":904},"Q_1^* = 4",[883,34184,34186],{"className":34185},[886],[888,34187,34188],{"xmlns":890},[892,34189,34190,34204],{},[895,34191,34192,34200,34202],{},[1810,34193,34194,34196,34198],{},[898,34195,1973],{},[1963,34197,1970],{},[1664,34199,4920],{},[1664,34201,1676],{},[1963,34203,2875],{},[902,34205,34206],{"encoding":904},"Q_2^* = 1",[883,34208,34210],{"className":34209},[886],[888,34211,34212],{"xmlns":890},[892,34213,34214,34226],{},[895,34215,34216,34222,34224],{},[1720,34217,34218,34220],{},[898,34219,16943],{},[1664,34221,4920],{},[1664,34223,1676],{},[1963,34225,2875],{},[902,34227,34228],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,34231,34233],{"className":34232},[886],[888,34234,34235],{"xmlns":890},[892,34236,34237,34265],{},[895,34238,34239,34245,34247,34249,34251,34253,34255,34257,34259,34261,34263],{},[1720,34240,34241,34243],{},[898,34242,4819],{},[1664,34244,4920],{},[1664,34246,1676],{},[1963,34248,24289],{},[1664,34250,3753],{},[1963,34252,2944],{},[1664,34254,1700],{},[1963,34256,2875],{},[1664,34258,3753],{},[1963,34260,2875],{},[1664,34262,1676],{},[1963,34264,1970],{},[902,34266,34267],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,34269,34270,34273,34274,1343,34340,1343,34406,34472,34473,34510,34511,34533,34534,1977],{},[614,34271,34272],{},"Ověření postačující podmínky"," (6.26): ",[883,34275,34277],{"className":34276},[886],[888,34278,34279],{"xmlns":890},[892,34280,34281,34337],{},[895,34282,34283,34295,34297,34299,34307,34323],{},[1810,34284,34285,34287,34289],{},[898,34286,900],{},[1963,34288,3483],{},[895,34290,34291,34293],{},[1664,34292,1728],{"mathvariant":1726},[1664,34294,1728],{"mathvariant":1726},[1664,34296,1676],{},[1664,34298,1867],{},[2919,34300,34301],{"scriptlevel":2058,"displaystyle":1666},[2922,34302,34303,34305],{},[1963,34304,2875],{},[1963,34306,2944],{},[1810,34308,34309,34311,34313],{},[898,34310,1973],{},[1963,34312,2875],{},[895,34314,34315,34317,34319,34321],{},[1664,34316,1867],{},[1963,34318,2774],{},[898,34320,5240],{"mathvariant":1726},[1963,34322,1970],{},[1810,34324,34325,34327,34329],{},[898,34326,1973],{},[1963,34328,1970],{},[895,34330,34331,34333,34335],{},[1963,34332,2875],{},[898,34334,5240],{"mathvariant":1726},[1963,34336,1970],{},[902,34338,34339],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,34341,34343],{"className":34342},[886],[888,34344,34345],{"xmlns":890},[892,34346,34347,34403],{},[895,34348,34349,34361,34363,34365,34373,34387],{},[1810,34350,34351,34353,34355],{},[898,34352,900],{},[1963,34354,33046],{},[895,34356,34357,34359],{},[1664,34358,1728],{"mathvariant":1726},[1664,34360,1728],{"mathvariant":1726},[1664,34362,1676],{},[1664,34364,1867],{},[2919,34366,34367],{"scriptlevel":2058,"displaystyle":1666},[2922,34368,34369,34371],{},[1963,34370,2875],{},[1963,34372,2944],{},[1810,34374,34375,34377,34379],{},[898,34376,1973],{},[1963,34378,2875],{},[895,34380,34381,34383,34385],{},[1963,34382,2875],{},[898,34384,5240],{"mathvariant":1726},[1963,34386,1970],{},[1810,34388,34389,34391,34393],{},[898,34390,1973],{},[1963,34392,1970],{},[895,34394,34395,34397,34399,34401],{},[1664,34396,1867],{},[1963,34398,2774],{},[898,34400,5240],{"mathvariant":1726},[1963,34402,1970],{},[902,34404,34405],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,34407,34409],{"className":34408},[886],[888,34410,34411],{"xmlns":890},[892,34412,34413,34469],{},[895,34414,34415,34427,34429,34437,34453],{},[1810,34416,34417,34419,34421],{},[898,34418,900],{},[1963,34420,4084],{},[895,34422,34423,34425],{},[1664,34424,1728],{"mathvariant":1726},[1664,34426,1728],{"mathvariant":1726},[1664,34428,1676],{},[2919,34430,34431],{"scriptlevel":2058,"displaystyle":1666},[2922,34432,34433,34435],{},[1963,34434,2875],{},[1963,34436,2944],{},[1810,34438,34439,34441,34443],{},[898,34440,1973],{},[1963,34442,2875],{},[895,34444,34445,34447,34449,34451],{},[1664,34446,1867],{},[1963,34448,2875],{},[898,34450,5240],{"mathvariant":1726},[1963,34452,1970],{},[1810,34454,34455,34457,34459],{},[898,34456,1973],{},[1963,34458,1970],{},[895,34460,34461,34463,34465,34467],{},[1664,34462,1867],{},[1963,34464,2875],{},[898,34466,5240],{"mathvariant":1726},[1963,34468,1970],{},[902,34470,34471],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,34474,34476],{"className":34475},[886],[888,34477,34478],{"xmlns":890},[892,34479,34480,34507],{},[895,34481,34482,34484,34486,34488,34490,34492,34494,34496,34498,34500,34503,34505],{},[898,34483,2379],{},[1664,34485,1667],{"stretchy":1666},[1963,34487,2944],{},[1664,34489,1916],{"separator":1915},[1963,34491,2875],{},[1664,34493,1916],{"separator":1915},[1963,34495,2875],{},[1664,34497,1673],{"stretchy":1666},[1664,34499,1676],{},[1963,34501,34502],{},"0,28125",[1664,34504,3984],{},[1963,34506,2058],{},[902,34508,34509],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,34512,34514],{"className":34513},[886],[888,34515,34516],{"xmlns":890},[892,34517,34518,34530],{},[895,34519,34520,34522,34524,34526,34528],{},[1664,34521,1837],{"stretchy":1666},[1963,34523,2944],{},[1664,34525,1916],{"separator":1915},[1963,34527,2875],{},[1664,34529,1850],{"stretchy":1666},[902,34531,34532],{"encoding":904},"[4, 1]"," je vázané ",[38,34535,4350],{},[115,34537,34539],{"id":34538},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,34541,34542],{},"Obecně:",[883,34544,34546],{"className":34545},[886],[888,34547,34548],{"xmlns":890,"display":28566},[892,34549,34550,34645],{},[21254,34551,34552],{"width":28571},[21259,34553,34554,34556,34638,34640],{},[21262,34555],{"width":28576},[21262,34557,34558],{},[895,34559,34560,34566,34568,34574,34576,34582,34584,34590,34592,34594,34596,34598,34600,34606,34608,34614,34616,34622,34624,34630,34632,34634,34636],{},[2355,34561,34562,34564],{},[898,34563,1973],{},[1963,34565,2875],{},[1664,34567,1676],{},[2355,34569,34570,34572],{},[898,34571,2379],{},[1963,34573,2875],{},[1664,34575,1667],{"stretchy":1666},[2355,34577,34578,34580],{},[898,34579,2398],{},[1963,34581,2875],{},[1664,34583,1916],{"separator":1915},[2355,34585,34586,34588],{},[898,34587,2398],{},[1963,34589,1970],{},[1664,34591,1916],{"separator":1915},[898,34593,900],{},[1664,34595,1673],{"stretchy":1666},[1664,34597,1916],{"separator":1915},[6444,34599],{"width":15783},[2355,34601,34602,34604],{},[898,34603,1973],{},[1963,34605,1970],{},[1664,34607,1676],{},[2355,34609,34610,34612],{},[898,34611,2379],{},[1963,34613,1970],{},[1664,34615,1667],{"stretchy":1666},[2355,34617,34618,34620],{},[898,34619,2398],{},[1963,34621,2875],{},[1664,34623,1916],{"separator":1915},[2355,34625,34626,34628],{},[898,34627,2398],{},[1963,34629,1970],{},[1664,34631,1916],{"separator":1915},[898,34633,900],{},[1664,34635,1673],{"stretchy":1666},[1664,34637,1916],{"separator":1915},[21262,34639],{"width":28576},[21262,34641,34642],{},[1690,34643,34644],{},"(6.27)",[902,34646,34647],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,34649,34651],{"className":34650},[886],[888,34652,34653],{"xmlns":890,"display":28566},[892,34654,34655,34702],{},[21254,34656,34657],{"width":28571},[21259,34658,34659,34661,34695,34697],{},[21262,34660],{"width":28576},[21262,34662,34663],{},[895,34664,34665,34667,34669,34671,34673,34679,34681,34687,34689,34691,34693],{},[898,34666,16943],{},[1664,34668,1676],{},[898,34670,16943],{},[1664,34672,1667],{"stretchy":1666},[2355,34674,34675,34677],{},[898,34676,2398],{},[1963,34678,2875],{},[1664,34680,1916],{"separator":1915},[2355,34682,34683,34685],{},[898,34684,2398],{},[1963,34686,1970],{},[1664,34688,1916],{"separator":1915},[898,34690,900],{},[1664,34692,1673],{"stretchy":1666},[898,34694,1977],{"mathvariant":1726},[21262,34696],{"width":28576},[21262,34698,34699],{},[1690,34700,34701],{},"(6.28)",[902,34703,34704],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,34706,34707,34708,1885,34711,34724,34725,34738],{},"Hicksova poptávka závisí na ",[38,34709,34710],{},"hladině užitečnosti",[883,34712,34714],{"className":34713},[886],[888,34715,34716],{"xmlns":890},[892,34717,34718,34722],{},[895,34719,34720],{},[898,34721,900],{},[902,34723,900],{"encoding":904}," (nikoli na důchodu ",[883,34726,34728],{"className":34727},[886],[888,34729,34730],{"xmlns":890},[892,34731,34732,34736],{},[895,34733,34734],{},[898,34735,9692],{},[902,34737,9692],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,34740,34742,34743],{"id":34741},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,34744,34746],{"className":34745},[886],[888,34747,34748],{"xmlns":890},[892,34749,34750,34784],{},[895,34751,34752,34754,34756,34770],{},[898,34753,900],{},[1664,34755,1676],{},[1810,34757,34758,34760,34762],{},[898,34759,1973],{},[1963,34761,2875],{},[895,34763,34764,34766,34768],{},[1963,34765,2875],{},[898,34767,5240],{"mathvariant":1726},[1963,34769,1970],{},[1810,34771,34772,34774,34776],{},[898,34773,1973],{},[1963,34775,1970],{},[895,34777,34778,34780,34782],{},[1963,34779,2875],{},[898,34781,5240],{"mathvariant":1726},[1963,34783,1970],{},[902,34785,33659],{"encoding":904},[724,34787,34788,34818],{},[883,34789,34791],{"className":34790},[886],[888,34792,34793],{"xmlns":890},[892,34794,34795,34815],{},[895,34796,34797,34803,34805,34811,34813],{},[2355,34798,34799,34801],{},[898,34800,2398],{},[1963,34802,2875],{},[1664,34804,1916],{"separator":1915},[2355,34806,34807,34809],{},[898,34808,2398],{},[1963,34810,1970],{},[1664,34812,1916],{"separator":1915},[898,34814,900],{},[902,34816,34817],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,34820,34822],{"className":34821},[886],[888,34823,34824],{"xmlns":890,"display":28566},[892,34825,34826,34900],{},[895,34827,34828,34830,34832,34838,34844,34846,34852,34858,34860,34862,34864,34866,34868,34882,34896,34898],{},[898,34829,10358],{"mathvariant":29048},[1664,34831,1676],{},[2355,34833,34834,34836],{},[898,34835,2398],{},[1963,34837,2875],{},[2355,34839,34840,34842],{},[898,34841,1973],{},[1963,34843,2875],{},[1664,34845,1700],{},[2355,34847,34848,34850],{},[898,34849,2398],{},[1963,34851,1970],{},[2355,34853,34854,34856],{},[898,34855,1973],{},[1963,34857,1970],{},[1664,34859,1700],{},[898,34861,16943],{},[1664,34863,1667],{"stretchy":1666},[898,34865,900],{},[1664,34867,1867],{},[1810,34869,34870,34872,34874],{},[898,34871,1973],{},[1963,34873,2875],{},[895,34875,34876,34878,34880],{},[1963,34877,2875],{},[898,34879,5240],{"mathvariant":1726},[1963,34881,1970],{},[1810,34883,34884,34886,34888],{},[898,34885,1973],{},[1963,34887,1970],{},[895,34889,34890,34892,34894],{},[1963,34891,2875],{},[898,34893,5240],{"mathvariant":1726},[1963,34895,1970],{},[1664,34897,1673],{"stretchy":1666},[898,34899,1977],{"mathvariant":1726},[902,34901,34902],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,34904,30931],{},[883,34906,34908],{"className":34907},[886],[888,34909,34910],{"xmlns":890,"display":28566},[892,34911,34912,35134],{},[21254,34913,34914,34994,35074],{"rowspacing":21256,"columnalign":21257,"columnspacing":1727},[21259,34915,34916,34928],{},[21262,34917,34918],{},[2919,34919,34920],{"scriptlevel":2058,"displaystyle":1915},[1810,34921,34922,34924,34926],{},[898,34923,10358],{"mathvariant":29048},[1963,34925,2875],{},[1664,34927,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[21262,34929,34930],{},[2919,34931,34932],{"scriptlevel":2058,"displaystyle":1915},[895,34933,34934,34936,34938,34944,34946,34948,34950,34958,34974,34988,34990,34992],{},[895,34935],{},[1664,34937,1676],{},[2355,34939,34940,34942],{},[898,34941,2398],{},[1963,34943,2875],{},[1664,34945,1867],{},[898,34947,16943],{},[1664,34949,3753],{},[2919,34951,34952],{"scriptlevel":2058,"displaystyle":1666},[2922,34953,34954,34956],{},[1963,34955,2875],{},[1963,34957,1970],{},[1810,34959,34960,34962,34964],{},[898,34961,1973],{},[1963,34963,2875],{},[895,34965,34966,34968,34970,34972],{},[1664,34967,1867],{},[1963,34969,2875],{},[898,34971,5240],{"mathvariant":1726},[1963,34973,1970],{},[1810,34975,34976,34978,34980],{},[898,34977,1973],{},[1963,34979,1970],{},[895,34981,34982,34984,34986],{},[1963,34983,2875],{},[898,34985,5240],{"mathvariant":1726},[1963,34987,1970],{},[1664,34989,1676],{},[1963,34991,2058],{},[1664,34993,1916],{"separator":1915},[21259,34995,34996,35008],{},[21262,34997,34998],{},[2919,34999,35000],{"scriptlevel":2058,"displaystyle":1915},[1810,35001,35002,35004,35006],{},[898,35003,10358],{"mathvariant":29048},[1963,35005,1970],{},[1664,35007,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[21262,35009,35010],{},[2919,35011,35012],{"scriptlevel":2058,"displaystyle":1915},[895,35013,35014,35016,35018,35024,35026,35028,35030,35038,35052,35068,35070,35072],{},[895,35015],{},[1664,35017,1676],{},[2355,35019,35020,35022],{},[898,35021,2398],{},[1963,35023,1970],{},[1664,35025,1867],{},[898,35027,16943],{},[1664,35029,3753],{},[2919,35031,35032],{"scriptlevel":2058,"displaystyle":1666},[2922,35033,35034,35036],{},[1963,35035,2875],{},[1963,35037,1970],{},[1810,35039,35040,35042,35044],{},[898,35041,1973],{},[1963,35043,2875],{},[895,35045,35046,35048,35050],{},[1963,35047,2875],{},[898,35049,5240],{"mathvariant":1726},[1963,35051,1970],{},[1810,35053,35054,35056,35058],{},[898,35055,1973],{},[1963,35057,1970],{},[895,35059,35060,35062,35064,35066],{},[1664,35061,1867],{},[1963,35063,2875],{},[898,35065,5240],{"mathvariant":1726},[1963,35067,1970],{},[1664,35069,1676],{},[1963,35071,2058],{},[1664,35073,1916],{"separator":1915},[21259,35075,35076,35088],{},[21262,35077,35078],{},[2919,35079,35080],{"scriptlevel":2058,"displaystyle":1915},[1810,35081,35082,35084,35086],{},[898,35083,10358],{"mathvariant":29048},[898,35085,16943],{},[1664,35087,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[21262,35089,35090],{},[2919,35091,35092],{"scriptlevel":2058,"displaystyle":1915},[895,35093,35094,35096,35098,35100,35102,35116,35130,35132],{},[895,35095],{},[1664,35097,1676],{},[898,35099,900],{},[1664,35101,1867],{},[1810,35103,35104,35106,35108],{},[898,35105,1973],{},[1963,35107,2875],{},[895,35109,35110,35112,35114],{},[1963,35111,2875],{},[898,35113,5240],{"mathvariant":1726},[1963,35115,1970],{},[1810,35117,35118,35120,35122],{},[898,35119,1973],{},[1963,35121,1970],{},[895,35123,35124,35126,35128],{},[1963,35125,2875],{},[898,35127,5240],{"mathvariant":1726},[1963,35129,1970],{},[1664,35131,1676],{},[1963,35133,12959],{},[902,35135,35136],{"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}",[724,35138,35139,35140,35210,35211,35269],{},"Podílem rovnic: ",[883,35141,35143],{"className":35142},[886],[888,35144,35145],{"xmlns":890},[892,35146,35147,35207],{},[895,35148,35149,35155,35157,35163,35165,35171,35173,35179,35181,35187,35193,35195,35201],{},[2355,35150,35151,35153],{},[898,35152,2398],{},[1963,35154,2875],{},[898,35156,5240],{"mathvariant":1726},[2355,35158,35159,35161],{},[898,35160,2398],{},[1963,35162,1970],{},[1664,35164,1676],{},[2355,35166,35167,35169],{},[898,35168,1973],{},[1963,35170,1970],{},[898,35172,5240],{"mathvariant":1726},[2355,35174,35175,35177],{},[898,35176,1973],{},[1963,35178,2875],{},[1664,35180,4556],{},[2355,35182,35183,35185],{},[898,35184,2398],{},[1963,35186,2875],{},[2355,35188,35189,35191],{},[898,35190,1973],{},[1963,35192,2875],{},[1664,35194,1676],{},[2355,35196,35197,35199],{},[898,35198,2398],{},[1963,35200,1970],{},[2355,35202,35203,35205],{},[898,35204,1973],{},[1963,35206,1970],{},[902,35208,35209],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,35212,35214],{"className":35213},[886],[888,35215,35216],{"xmlns":890},[892,35217,35218,35266],{},[895,35219,35220,35222,35224,35230,35236,35238,35244,35250,35252,35254,35260],{},[898,35221,4819],{},[1664,35223,1676],{},[2355,35225,35226,35228],{},[898,35227,2398],{},[1963,35229,2875],{},[2355,35231,35232,35234],{},[898,35233,1973],{},[1963,35235,2875],{},[1664,35237,1700],{},[2355,35239,35240,35242],{},[898,35241,2398],{},[1963,35243,1970],{},[2355,35245,35246,35248],{},[898,35247,1973],{},[1963,35249,1970],{},[1664,35251,1676],{},[1963,35253,1970],{},[2355,35255,35256,35258],{},[898,35257,2398],{},[1963,35259,2875],{},[2355,35261,35262,35264],{},[898,35263,1973],{},[1963,35265,2875],{},[902,35267,35268],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,35271,35273],{"className":35272},[886],[888,35274,35275],{"xmlns":890,"display":28566},[892,35276,35277,35344],{},[21254,35278,35279],{"width":28571},[21259,35280,35281,35283,35337,35339],{},[21262,35282],{"width":28576},[21262,35284,35285],{},[895,35286,35287,35293,35295,35309,35311,35313,35319,35321,35335],{},[2355,35288,35289,35291],{},[898,35290,1973],{},[1963,35292,2875],{},[1664,35294,1676],{},[2922,35296,35297,35299],{},[898,35298,4819],{},[895,35300,35301,35303],{},[1963,35302,1970],{},[2355,35304,35305,35307],{},[898,35306,2398],{},[1963,35308,2875],{},[1664,35310,1916],{"separator":1915},[6444,35312],{"width":15783},[2355,35314,35315,35317],{},[898,35316,1973],{},[1963,35318,1970],{},[1664,35320,1676],{},[2922,35322,35323,35325],{},[898,35324,4819],{},[895,35326,35327,35329],{},[1963,35328,1970],{},[2355,35330,35331,35333],{},[898,35332,2398],{},[1963,35334,1970],{},[898,35336,1977],{"mathvariant":1726},[21262,35338],{"width":28576},[21262,35340,35341],{},[1690,35342,35343],{},"(6.29)",[902,35345,35346],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,35348,35349,35350,18076,35432,35468],{},"Ze třetí rovnice ",[883,35351,35353],{"className":35352},[886],[888,35354,35355],{"xmlns":890},[892,35356,35357,35429],{},[895,35358,35359,35361,35363,35401,35403],{},[898,35360,900],{},[1664,35362,1676],{},[8682,35364,35365],{},[895,35366,35367,35383,35385],{},[2919,35368,35369],{"scriptlevel":2058,"displaystyle":1666},[2922,35370,35371,35373],{},[898,35372,4819],{},[895,35374,35375,35377],{},[1963,35376,1970],{},[2355,35378,35379,35381],{},[898,35380,2398],{},[1963,35382,2875],{},[1664,35384,3753],{},[2919,35386,35387],{"scriptlevel":2058,"displaystyle":1666},[2922,35388,35389,35391],{},[898,35390,4819],{},[895,35392,35393,35395],{},[1963,35394,1970],{},[2355,35396,35397,35399],{},[898,35398,2398],{},[1963,35400,1970],{},[1664,35402,1676],{},[2919,35404,35405],{"scriptlevel":2058,"displaystyle":1666},[2922,35406,35407,35409],{},[898,35408,4819],{},[895,35410,35411,35413],{},[1963,35412,1970],{},[8682,35414,35415],{},[895,35416,35417,35423],{},[2355,35418,35419,35421],{},[898,35420,2398],{},[1963,35422,2875],{},[2355,35424,35425,35427],{},[898,35426,2398],{},[1963,35428,1970],{},[902,35430,35431],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,35433,35435],{"className":35434},[886],[888,35436,35437],{"xmlns":890},[892,35438,35439,35465],{},[895,35440,35441,35443,35445,35447,35449],{},[898,35442,4819],{},[1664,35444,1676],{},[1963,35446,1970],{},[898,35448,900],{},[8682,35450,35451],{},[895,35452,35453,35459],{},[2355,35454,35455,35457],{},[898,35456,2398],{},[1963,35458,2875],{},[2355,35460,35461,35463],{},[898,35462,2398],{},[1963,35464,1970],{},[902,35466,35467],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,35470,35472],{"className":35471},[886],[888,35473,35474],{"xmlns":890,"display":28566},[892,35475,35476,35621],{},[21254,35477,35478],{"width":28571},[21259,35479,35480,35482,35614,35616],{},[21262,35481],{"width":28576},[21262,35483,35484],{},[13331,35485,35486],{"notation":13333},[2919,35487,35488],{"scriptlevel":2058,"displaystyle":1666},[2919,35489,35490],{"scriptlevel":2058,"displaystyle":1666},[2919,35491,35492],{"scriptlevel":2058,"displaystyle":1915},[895,35493,35494,35496,35502,35504,35506,35522,35524,35530,35532,35538,35540,35546,35548,35550,35552,35554,35556,35562,35564,35566,35582,35584,35590,35592,35598,35600,35606,35608,35610,35612],{},[1690,35495,4553],{},[2355,35497,35498,35500],{},[898,35499,1973],{},[1963,35501,2875],{},[1664,35503,1676],{},[898,35505,900],{},[8682,35507,35508],{},[2922,35509,35510,35516],{},[2355,35511,35512,35514],{},[898,35513,2398],{},[1963,35515,1970],{},[2355,35517,35518,35520],{},[898,35519,2398],{},[1963,35521,2875],{},[1664,35523,1676],{},[2355,35525,35526,35528],{},[898,35527,2379],{},[1963,35529,2875],{},[1664,35531,1667],{"stretchy":1666},[2355,35533,35534,35536],{},[898,35535,2398],{},[1963,35537,2875],{},[1664,35539,1916],{"separator":1915},[2355,35541,35542,35544],{},[898,35543,2398],{},[1963,35545,1970],{},[1664,35547,1916],{"separator":1915},[898,35549,900],{},[1664,35551,1673],{"stretchy":1666},[1664,35553,1916],{"separator":1915},[6444,35555],{"width":15783},[2355,35557,35558,35560],{},[898,35559,1973],{},[1963,35561,1970],{},[1664,35563,1676],{},[898,35565,900],{},[8682,35567,35568],{},[2922,35569,35570,35576],{},[2355,35571,35572,35574],{},[898,35573,2398],{},[1963,35575,2875],{},[2355,35577,35578,35580],{},[898,35579,2398],{},[1963,35581,1970],{},[1664,35583,1676],{},[2355,35585,35586,35588],{},[898,35587,2379],{},[1963,35589,1970],{},[1664,35591,1667],{"stretchy":1666},[2355,35593,35594,35596],{},[898,35595,2398],{},[1963,35597,2875],{},[1664,35599,1916],{"separator":1915},[2355,35601,35602,35604],{},[898,35603,2398],{},[1963,35605,1970],{},[1664,35607,1916],{"separator":1915},[898,35609,900],{},[1664,35611,1673],{"stretchy":1666},[1690,35613,4553],{},[21262,35615],{"width":28576},[21262,35617,35618],{},[1690,35619,35620],{},"(6.30)",[902,35622,35623],{"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}",[115,35625,35627],{"id":35626},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,35629,35630,35631,35644,35645,35662,35663,35676,35677,35694,35695,35698,35699,35738,35739,35768],{},"Primární (max ",[883,35632,35634],{"className":35633},[886],[888,35635,35636],{"xmlns":890},[892,35637,35638,35642],{},[895,35639,35640],{},[898,35641,900],{},[902,35643,900],{"encoding":904}," při rozpočtu ",[883,35646,35648],{"className":35647},[886],[888,35649,35650],{"xmlns":890},[892,35651,35652,35660],{},[895,35653,35654],{},[1720,35655,35656,35658],{},[898,35657,9692],{},[1664,35659,4920],{},[902,35661,28528],{"encoding":904},") a duální (min ",[883,35664,35666],{"className":35665},[886],[888,35667,35668],{"xmlns":890},[892,35669,35670,35674],{},[895,35671,35672],{},[898,35673,4819],{},[902,35675,4819],{"encoding":904}," při užitečnosti ",[883,35678,35680],{"className":35679},[886],[888,35681,35682],{"xmlns":890},[892,35683,35684,35692],{},[895,35685,35686],{},[1720,35687,35688,35690],{},[898,35689,900],{},[1664,35691,4920],{},[902,35693,28462],{"encoding":904},") úloha jsou ",[38,35696,35697],{},"ekvivalentní",": mají tentýž bod optima ",[883,35700,35702],{"className":35701},[886],[888,35703,35704],{"xmlns":890},[892,35705,35706,35736],{},[895,35707,35708,35714,35716,35724,35726,35734],{},[1720,35709,35710,35712],{},[898,35711,1973],{},[1664,35713,4920],{},[1664,35715,1837],{"stretchy":1666},[1810,35717,35718,35720,35722],{},[898,35719,1973],{},[1963,35721,2875],{},[1664,35723,4920],{},[1664,35725,1916],{"separator":1915},[1810,35727,35728,35730,35732],{},[898,35729,1973],{},[1963,35731,1970],{},[1664,35733,4920],{},[1664,35735,1850],{"stretchy":1666},[902,35737,28827],{"encoding":904}," a v obou platí ",[883,35740,35742],{"className":35741},[886],[888,35743,35744],{"xmlns":890},[892,35745,35746,35766],{},[895,35747,35748,35750,35752,35758,35760],{},[1690,35749,11165],{},[1664,35751,1676],{},[2355,35753,35754,35756],{},[898,35755,2398],{},[1963,35757,2875],{},[898,35759,5240],{"mathvariant":1726},[2355,35761,35762,35764],{},[898,35763,2398],{},[1963,35765,1970],{},[902,35767,28498],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,35770,35771],{},[1928,35772],{"alt":35773,"className":35774,"src":35775},"imek-primarni-vs-dualni",[210,1932],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,35777,35778,35889],{},[123,35779,35780,35783,35784,35797,35798,35838,35839,1977],{},[38,35781,35782],{},"Primární"," (Marshall): zadáno ",[883,35785,35787],{"className":35786},[886],[888,35788,35789],{"xmlns":890},[892,35790,35791,35795],{},[895,35792,35793],{},[898,35794,9692],{},[902,35796,9692],{"encoding":904},", hledáme maximální ",[883,35799,35801],{"className":35800},[886],[888,35802,35803],{"xmlns":890},[892,35804,35805,35835],{},[895,35806,35807,35813,35815,35821,35823,35829,35831,35833],{},[1720,35808,35809,35811],{},[898,35810,900],{},[1664,35812,4920],{},[1664,35814,1667],{"stretchy":1666},[2355,35816,35817,35819],{},[898,35818,2398],{},[1963,35820,2875],{},[1664,35822,1916],{"separator":1915},[2355,35824,35825,35827],{},[898,35826,2398],{},[1963,35828,1970],{},[1664,35830,1916],{"separator":1915},[898,35832,9692],{},[1664,35834,1673],{"stretchy":1666},[902,35836,35837],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,35840,35842],{"className":35841},[886],[888,35843,35844],{"xmlns":890},[892,35845,35846,35886],{},[895,35847,35848,35854,35856,35864,35866,35872,35874,35880,35882,35884],{},[2355,35849,35850,35852],{},[898,35851,1973],{},[898,35853,18290],{},[1664,35855,1676],{},[1810,35857,35858,35860,35862],{},[898,35859,2379],{},[898,35861,18290],{},[898,35863,1956],{},[1664,35865,1667],{"stretchy":1666},[2355,35867,35868,35870],{},[898,35869,2398],{},[1963,35871,2875],{},[1664,35873,1916],{"separator":1915},[2355,35875,35876,35878],{},[898,35877,2398],{},[1963,35879,1970],{},[1664,35881,1916],{"separator":1915},[898,35883,9692],{},[1664,35885,1673],{"stretchy":1666},[902,35887,35888],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,35890,35891,35894,35895,35908,35909,35838,35949,1977],{},[38,35892,35893],{},"Duální"," (Hicks): zadáno ",[883,35896,35898],{"className":35897},[886],[888,35899,35900],{"xmlns":890},[892,35901,35902,35906],{},[895,35903,35904],{},[898,35905,900],{},[902,35907,900],{"encoding":904},", hledáme minimální ",[883,35910,35912],{"className":35911},[886],[888,35913,35914],{"xmlns":890},[892,35915,35916,35946],{},[895,35917,35918,35924,35926,35932,35934,35940,35942,35944],{},[1720,35919,35920,35922],{},[898,35921,4819],{},[1664,35923,4920],{},[1664,35925,1667],{"stretchy":1666},[2355,35927,35928,35930],{},[898,35929,2398],{},[1963,35931,2875],{},[1664,35933,1916],{"separator":1915},[2355,35935,35936,35938],{},[898,35937,2398],{},[1963,35939,1970],{},[1664,35941,1916],{"separator":1915},[898,35943,900],{},[1664,35945,1673],{"stretchy":1666},[902,35947,35948],{"encoding":904},"E^*(P_1, P_2, U)",[883,35950,35952],{"className":35951},[886],[888,35953,35954],{"xmlns":890},[892,35955,35956,35997],{},[895,35957,35958,35964,35966,35975,35977,35983,35985,35991,35993,35995],{},[2355,35959,35960,35962],{},[898,35961,1973],{},[898,35963,18290],{},[1664,35965,1676],{},[1810,35967,35968,35970,35972],{},[898,35969,2379],{},[898,35971,18290],{},[898,35973,35974],{},"H",[1664,35976,1667],{"stretchy":1666},[2355,35978,35979,35981],{},[898,35980,2398],{},[1963,35982,2875],{},[1664,35984,1916],{"separator":1915},[2355,35986,35987,35989],{},[898,35988,2398],{},[1963,35990,1970],{},[1664,35992,1916],{"separator":1915},[898,35994,900],{},[1664,35996,1673],{"stretchy":1666},[902,35998,35999],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,36001,36002,36003,36006,36007,36010],{},"Proč se studují obě? Marshallova poptávka je ",[38,36004,36005],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,36008,36009],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,36012,36014],{"id":36013},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,36016,36018],{"id":36017},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,36020,36021,36024,36025,36057,36058,36096,36097,36123],{},[38,36022,36023],{},"6.8"," Jsou dány užitečnost ",[883,36026,36028],{"className":36027},[886],[888,36029,36030],{"xmlns":890},[892,36031,36032,36054],{},[895,36033,36034,36036,36038,36046],{},[898,36035,900],{},[1664,36037,1676],{},[1810,36039,36040,36042,36044],{},[898,36041,1973],{},[1963,36043,2875],{},[1963,36045,5575],{},[1810,36047,36048,36050,36052],{},[898,36049,1973],{},[1963,36051,1970],{},[1963,36053,5575],{},[902,36055,36056],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,36059,36061],{"className":36060},[886],[888,36062,36063],{"xmlns":890},[892,36064,36065,36093],{},[895,36066,36067,36075,36077,36079,36081,36089,36091],{},[1810,36068,36069,36071,36073],{},[898,36070,2398],{},[1963,36072,2875],{},[1664,36074,4920],{},[1664,36076,1676],{},[1963,36078,2944],{},[1664,36080,1916],{"separator":1915},[1810,36082,36083,36085,36087],{},[898,36084,2398],{},[1963,36086,1970],{},[1664,36088,4920],{},[1664,36090,1676],{},[1963,36092,3442],{},[902,36094,36095],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,36098,36100],{"className":36099},[886],[888,36101,36102],{"xmlns":890},[892,36103,36104,36120],{},[895,36105,36106,36112,36114],{},[2355,36107,36108,36110],{},[898,36109,1973],{},[1963,36111,2875],{},[1664,36113,1916],{"separator":1915},[2355,36115,36116,36118],{},[898,36117,1973],{},[1963,36119,1970],{},[902,36121,36122],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,36125,36126,36129,36130,36172,36173,36204,36205,36227,36228,1977],{},[38,36127,36128],{},"6.9"," Jsou dány rozpočtové omezení ",[883,36131,36133],{"className":36132},[886],[888,36134,36135],{"xmlns":890},[892,36136,36137,36169],{},[895,36138,36139,36141,36143,36149,36155,36157,36163],{},[898,36140,9692],{},[1664,36142,1676],{},[2355,36144,36145,36147],{},[898,36146,2398],{},[1963,36148,2875],{},[2355,36150,36151,36153],{},[898,36152,1973],{},[1963,36154,2875],{},[1664,36156,1700],{},[2355,36158,36159,36161],{},[898,36160,2398],{},[1963,36162,1970],{},[2355,36164,36165,36167],{},[898,36166,1973],{},[1963,36168,1970],{},[902,36170,36171],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,36174,36176],{"className":36175},[886],[888,36177,36178],{"xmlns":890},[892,36179,36180,36202],{},[895,36181,36182,36184,36186,36194],{},[898,36183,900],{},[1664,36185,1676],{},[1810,36187,36188,36190,36192],{},[898,36189,1973],{},[1963,36191,2875],{},[1963,36193,5575],{},[1810,36195,36196,36198,36200],{},[898,36197,1973],{},[1963,36199,1970],{},[1963,36201,5575],{},[902,36203,36056],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,36206,36208],{"className":36207},[886],[888,36209,36210],{"xmlns":890},[892,36211,36212,36224],{},[895,36213,36214,36220,36222],{},[1720,36215,36216,36218],{},[898,36217,9692],{},[1664,36219,4920],{},[1664,36221,1676],{},[1963,36223,15609],{},[902,36225,36226],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,36229,36231],{"className":36230},[886],[888,36232,36233],{"xmlns":890},[892,36234,36235,36263],{},[895,36236,36237,36245,36247,36249,36251,36259,36261],{},[1810,36238,36239,36241,36243],{},[898,36240,2398],{},[1963,36242,2875],{},[1664,36244,4920],{},[1664,36246,1676],{},[1963,36248,2826],{},[1664,36250,1916],{"separator":1915},[1810,36252,36253,36255,36257],{},[898,36254,2398],{},[1963,36256,1970],{},[1664,36258,4920],{},[1664,36260,1676],{},[1963,36262,3442],{},[902,36264,36265],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,36267,36268,36271,36272,22094,36304,36334,36335,1977],{},[38,36269,36270],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,36273,36275],{"className":36274},[886],[888,36276,36277],{"xmlns":890},[892,36278,36279,36301],{},[895,36280,36281,36283,36285,36293],{},[898,36282,900],{},[1664,36284,1676],{},[1810,36286,36287,36289,36291],{},[898,36288,1973],{},[1963,36290,2875],{},[898,36292,207],{},[1810,36294,36295,36297,36299],{},[898,36296,1973],{},[1963,36298,1970],{},[898,36300,1818],{},[902,36302,36303],{"encoding":904},"U = Q_1^a Q_2^b",[883,36305,36307],{"className":36306},[886],[888,36308,36309],{"xmlns":890},[892,36310,36311,36331],{},[895,36312,36313,36315,36317,36319,36321,36323,36325,36327,36329],{},[898,36314,207],{},[1664,36316,1916],{"separator":1915},[898,36318,1818],{},[1664,36320,7072],{},[1664,36322,5890],{"stretchy":1666},[1963,36324,2058],{},[1664,36326,1916],{"separator":1915},[1963,36328,2875],{},[1664,36330,5907],{"stretchy":1666},[902,36332,36333],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,36336,36338],{"className":36337},[886],[888,36339,36340],{"xmlns":890},[892,36341,36342,36374],{},[895,36343,36344,36346,36348,36354,36360,36362,36368],{},[898,36345,9692],{},[1664,36347,1676],{},[2355,36349,36350,36352],{},[898,36351,2398],{},[1963,36353,2875],{},[2355,36355,36356,36358],{},[898,36357,1973],{},[1963,36359,2875],{},[1664,36361,1700],{},[2355,36363,36364,36366],{},[898,36365,2398],{},[1963,36367,1970],{},[2355,36369,36370,36372],{},[898,36371,1973],{},[1963,36373,1970],{},[902,36375,36171],{"encoding":904},[724,36377,36378,36381,36382,22094,36416,36334,36434,1977],{},[38,36379,36380],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,36383,36385],{"className":36384},[886],[888,36386,36387],{"xmlns":890},[892,36388,36389,36413],{},[895,36390,36391,36393,36395,36403,36405],{},[898,36392,900],{},[1664,36394,1676],{},[1810,36396,36397,36399,36401],{},[898,36398,1973],{},[1963,36400,2875],{},[898,36402,207],{},[1664,36404,1700],{},[1810,36406,36407,36409,36411],{},[898,36408,1973],{},[1963,36410,1970],{},[898,36412,207],{},[902,36414,36415],{"encoding":904},"U = Q_1^a + Q_2^a",[883,36417,36419],{"className":36418},[886],[888,36420,36421],{"xmlns":890},[892,36422,36423,36431],{},[895,36424,36425,36427,36429],{},[898,36426,207],{},[1664,36428,3947],{"mathvariant":1726},[1963,36430,2058],{},[902,36432,36433],{"encoding":904},"a \\neq 0",[883,36435,36437],{"className":36436},[886],[888,36438,36439],{"xmlns":890},[892,36440,36441,36473],{},[895,36442,36443,36445,36447,36453,36459,36461,36467],{},[898,36444,9692],{},[1664,36446,1676],{},[2355,36448,36449,36451],{},[898,36450,2398],{},[1963,36452,2875],{},[2355,36454,36455,36457],{},[898,36456,1973],{},[1963,36458,2875],{},[1664,36460,1700],{},[2355,36462,36463,36465],{},[898,36464,2398],{},[1963,36466,1970],{},[2355,36468,36469,36471],{},[898,36470,1973],{},[1963,36472,1970],{},[902,36474,36171],{"encoding":904},[198,36476,36478],{"id":36477},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,36480,36481,36024,36484,1343,36511,36533,36534,1343,36557,36581,36582,36607,36608,1977],{},[38,36482,36483],{},"6.12",[883,36485,36487],{"className":36486},[886],[888,36488,36489],{"xmlns":890},[892,36490,36491,36509],{},[895,36492,36493,36495,36497,36503],{},[898,36494,900],{},[1664,36496,1676],{},[2355,36498,36499,36501],{},[898,36500,1973],{},[1963,36502,2875],{},[2355,36504,36505,36507],{},[898,36506,1973],{},[1963,36508,1970],{},[902,36510,30726],{"encoding":904},[883,36512,36514],{"className":36513},[886],[888,36515,36516],{"xmlns":890},[892,36517,36518,36530],{},[895,36519,36520,36526,36528],{},[1720,36521,36522,36524],{},[898,36523,900],{},[1664,36525,4920],{},[1664,36527,1676],{},[1963,36529,3442],{},[902,36531,36532],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,36535,36537],{"className":36536},[886],[888,36538,36539],{"xmlns":890},[892,36540,36541,36555],{},[895,36542,36543,36551,36553],{},[1810,36544,36545,36547,36549],{},[898,36546,2398],{},[1963,36548,2875],{},[1664,36550,4920],{},[1664,36552,1676],{},[1963,36554,1970],{},[902,36556,30799],{"encoding":904},[883,36558,36560],{"className":36559},[886],[888,36561,36562],{"xmlns":890},[892,36563,36564,36578],{},[895,36565,36566,36574,36576],{},[1810,36567,36568,36570,36572],{},[898,36569,2398],{},[1963,36571,1970],{},[1664,36573,4920],{},[1664,36575,1676],{},[1963,36577,2944],{},[902,36579,36580],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,36583,36585],{"className":36584},[886],[888,36586,36587],{"xmlns":890},[892,36588,36589,36605],{},[895,36590,36591,36597,36599],{},[2355,36592,36593,36595],{},[898,36594,1973],{},[1963,36596,2875],{},[1664,36598,1916],{"separator":1915},[2355,36600,36601,36603],{},[898,36602,1973],{},[1963,36604,1970],{},[902,36606,36122],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,36609,36611],{"className":36610},[886],[888,36612,36613],{"xmlns":890},[892,36614,36615,36635],{},[895,36616,36617,36619,36621,36627,36629],{},[898,36618,900],{},[1664,36620,1676],{},[2355,36622,36623,36625],{},[898,36624,1973],{},[1963,36626,2875],{},[1664,36628,3753],{},[2355,36630,36631,36633],{},[898,36632,1973],{},[1963,36634,1970],{},[902,36636,36637],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,36639,36640,36643,36644,36685,36686,36708,36709,1977],{},[38,36641,36642],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,36645,36647],{"className":36646},[886],[888,36648,36649],{"xmlns":890},[892,36650,36651,36683],{},[895,36652,36653,36655,36657,36663,36669,36671,36677],{},[898,36654,4819],{},[1664,36656,1676],{},[2355,36658,36659,36661],{},[898,36660,2398],{},[1963,36662,2875],{},[2355,36664,36665,36667],{},[898,36666,1973],{},[1963,36668,2875],{},[1664,36670,1700],{},[2355,36672,36673,36675],{},[898,36674,2398],{},[1963,36676,1970],{},[2355,36678,36679,36681],{},[898,36680,1973],{},[1963,36682,1970],{},[902,36684,28443],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,36687,36689],{"className":36688},[886],[888,36690,36691],{"xmlns":890},[892,36692,36693,36705],{},[895,36694,36695,36701,36703],{},[1720,36696,36697,36699],{},[898,36698,900],{},[1664,36700,4920],{},[1664,36702,1676],{},[1963,36704,5570],{},[902,36706,36707],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,36710,36712],{"className":36711},[886],[888,36713,36714],{"xmlns":890},[892,36715,36716,36745],{},[895,36717,36718,36726,36728,36730,36732,36740,36742],{},[1810,36719,36720,36722,36724],{},[898,36721,2398],{},[1963,36723,2875],{},[1664,36725,4920],{},[1664,36727,1676],{},[1963,36729,9599],{},[1664,36731,1916],{"separator":1915},[1810,36733,36734,36736,36738],{},[898,36735,2398],{},[1963,36737,1970],{},[1664,36739,4920],{},[1664,36741,1676],{},[1963,36743,36744],{},"15",[902,36746,36747],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,36749,16219],{"id":16218},[120,36751,36752,36809,36848,36868,36903,36957,36962,36968,37064,37109],{},[123,36753,36754,1885,36757,36806,36807,1977],{},[38,36755,36756],{},"Rozpočtové omezení (budget constraint)",[883,36758,36760],{"className":36759},[886],[888,36761,36762],{"xmlns":890},[892,36763,36764,36804],{},[895,36765,36766,36772,36774,36782,36788,36790,36798],{},[1720,36767,36768,36770],{},[898,36769,9692],{},[1664,36771,4920],{},[1664,36773,1676],{},[1810,36775,36776,36778,36780],{},[898,36777,2398],{},[1963,36779,2875],{},[1664,36781,4920],{},[2355,36783,36784,36786],{},[898,36785,1973],{},[1963,36787,2875],{},[1664,36789,1700],{},[1810,36791,36792,36794,36796],{},[898,36793,2398],{},[1963,36795,1970],{},[1664,36797,4920],{},[2355,36799,36800,36802],{},[898,36801,1973],{},[1963,36803,1970],{},[902,36805,17798],{"encoding":904}," — (6.12); ",[38,36808,28636],{},[123,36810,36811,36814,36815,1977],{},[38,36812,36813],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,36816,36818],{"className":36817},[886],[888,36819,36820],{"xmlns":890},[892,36821,36822,36846],{},[895,36823,36824,36826,36828,36836,36838],{},[1690,36825,11165],{},[1664,36827,1676],{},[1810,36829,36830,36832,36834],{},[898,36831,2398],{},[1963,36833,2875],{},[1664,36835,4920],{},[898,36837,5240],{"mathvariant":1726},[1810,36839,36840,36842,36844],{},[898,36841,2398],{},[1963,36843,1970],{},[1664,36845,4920],{},[902,36847,29479],{"encoding":904},[123,36849,36850,36865,36866,1977],{},[38,36851,29623,36852],{},[883,36853,36855],{"className":36854},[886],[888,36856,36857],{"xmlns":890},[892,36858,36859,36863],{},[895,36860,36861],{},[898,36862,16943],{},[902,36864,16996],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,36867,29645],{},[123,36869,36870,36873,36874,1977],{},[38,36871,36872],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,36875,36877],{"className":36876},[886],[888,36878,36879],{"xmlns":890},[892,36880,36881,36901],{},[895,36882,36883,36885,36887,36893,36895],{},[1690,36884,11165],{},[1664,36886,1676],{},[2355,36888,36889,36891],{},[898,36890,2398],{},[1963,36892,2875],{},[898,36894,5240],{"mathvariant":1726},[2355,36896,36897,36899],{},[898,36898,2398],{},[1963,36900,1970],{},[902,36902,28498],{"encoding":904},[123,36904,36905,7581,36908,36956],{},[38,36906,36907],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,36909,36911],{"className":36910},[886],[888,36912,36913],{"xmlns":890},[892,36914,36915,36953],{},[895,36916,36917,36923,36925,36931,36933,36939,36941,36947,36949,36951],{},[2355,36918,36919,36921],{},[898,36920,1973],{},[898,36922,18290],{},[1664,36924,1676],{},[2355,36926,36927,36929],{},[898,36928,2379],{},[898,36930,18290],{},[1664,36932,1667],{"stretchy":1666},[2355,36934,36935,36937],{},[898,36936,2398],{},[1963,36938,2875],{},[1664,36940,1916],{"separator":1915},[2355,36942,36943,36945],{},[898,36944,2398],{},[1963,36946,1970],{},[1664,36948,1916],{"separator":1915},[898,36950,9692],{},[1664,36952,1673],{"stretchy":1666},[902,36954,36955],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,36958,36959,36961],{},[38,36960,32227],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,36963,36964,36967],{},[38,36965,36966],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,36969,36970,7581,36972,37019,37020,37063],{},[38,36971,34539],{},[883,36973,36975],{"className":36974},[886],[888,36976,36977],{"xmlns":890},[892,36978,36979,37017],{},[895,36980,36981,36987,36989,36995,36997,37003,37005,37011,37013,37015],{},[2355,36982,36983,36985],{},[898,36984,1973],{},[898,36986,18290],{},[1664,36988,1676],{},[2355,36990,36991,36993],{},[898,36992,2379],{},[898,36994,18290],{},[1664,36996,1667],{"stretchy":1666},[2355,36998,36999,37001],{},[898,37000,2398],{},[1963,37002,2875],{},[1664,37004,1916],{"separator":1915},[2355,37006,37007,37009],{},[898,37008,2398],{},[1963,37010,1970],{},[1664,37012,1916],{"separator":1915},[898,37014,900],{},[1664,37016,1673],{"stretchy":1666},[902,37018,18323],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,37021,37023],{"className":37022},[886],[888,37024,37025],{"xmlns":890},[892,37026,37027,37061],{},[895,37028,37029,37031,37033,37047],{},[898,37030,900],{},[1664,37032,1676],{},[1810,37034,37035,37037,37039],{},[898,37036,1973],{},[1963,37038,2875],{},[895,37040,37041,37043,37045],{},[1963,37042,2875],{},[898,37044,5240],{"mathvariant":1726},[1963,37046,1970],{},[1810,37048,37049,37051,37053],{},[898,37050,1973],{},[1963,37052,1970],{},[895,37054,37055,37057,37059],{},[1963,37056,2875],{},[898,37058,5240],{"mathvariant":1726},[1963,37060,1970],{},[902,37062,33659],{"encoding":904},": (6.30).",[123,37065,37066,37108],{},[38,37067,37068,37069],{},"Bod dotyku ",[883,37070,37072],{"className":37071},[886],[888,37073,37074],{"xmlns":890},[892,37075,37076,37106],{},[895,37077,37078,37084,37086,37094,37096,37104],{},[1720,37079,37080,37082],{},[898,37081,1973],{},[1664,37083,4920],{},[1664,37085,1837],{"stretchy":1666},[1810,37087,37088,37090,37092],{},[898,37089,1973],{},[1963,37091,2875],{},[1664,37093,4920],{},[1664,37095,1916],{"separator":1915},[1810,37097,37098,37100,37102],{},[898,37099,1973],{},[1963,37101,1970],{},[1664,37103,4920],{},[1664,37105,1850],{"stretchy":1666},[902,37107,28827],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,37110,37111,37114,37115,37128,37129,37142],{},[38,37112,37113],{},"Dualita"," — ekvivalence max ",[883,37116,37118],{"className":37117},[886],[888,37119,37120],{"xmlns":890},[892,37121,37122,37126],{},[895,37123,37124],{},[898,37125,900],{},[902,37127,900],{"encoding":904}," a min ",[883,37130,37132],{"className":37131},[886],[888,37133,37134],{"xmlns":890},[892,37135,37136,37140],{},[895,37137,37138],{},[898,37139,4819],{},[902,37141,4819],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,37144,2497],{"id":2496},[120,37146,37147,37170,37186,37199,37210],{},[123,37148,37149,1885,37152,37155,37156,37169],{},[38,37150,37151],{},"Teorie před optimalizací:",[207,37153,880],{"className":37154,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,37157,37159],{"className":37158},[886],[888,37160,37161],{"xmlns":890},[892,37162,37163,37167],{},[895,37164,37165],{},[898,37166,900],{},[902,37168,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,37171,37172,1885,37175,37178,37179,37182,37183,1977],{},[38,37173,37174],{},"Matematický aparát:",[207,37176,793],{"className":37177,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,37180,784],{"className":37181,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,37184,2950],{"className":37185,"dataFsResolvedFilePath":764,"href":765},[210],[123,37187,37188,1885,37191,37194,37195,37198],{},[38,37189,37190],{},"Paralely:",[207,37192,11649],{"className":37193,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,37196,2493],{"className":37197,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,37200,37201,1885,37204,1343,37207],{},[38,37202,37203],{},"Přednášky:",[207,37205,1094],{"className":37206,"dataFsResolvedFilePath":838,"href":839},[210],[207,37208,1101],{"className":37209,"dataFsResolvedFilePath":868,"href":869},[210],[123,37211,37212,1885,37214],{},[38,37213,16703],{},[207,37215,16707],{"className":37216,"dataFsResolvedFilePath":2575,"href":2576},[210],{"title":641,"searchDepth":642,"depth":642,"links":37218},[37219,37220,37221,37226,37227,37228,37230,37233,37236,37238,37239,37241,37242,37246,37247],{"id":12504,"depth":642,"text":12505},{"id":28506,"depth":642,"text":28507},{"id":28904,"depth":642,"text":28905,"children":37222},[37223,37224],{"id":29024,"depth":649,"text":29025},{"id":29605,"depth":649,"text":37225},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":30067,"depth":642,"text":30068},{"id":30378,"depth":642,"text":30379},{"id":30697,"depth":642,"text":37229},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":31470,"depth":642,"text":31471,"children":37231},[37232],{"id":32226,"depth":649,"text":32227},{"id":32406,"depth":642,"text":32407,"children":37234},[37235],{"id":32663,"depth":649,"text":32664},{"id":33614,"depth":642,"text":37237},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":34538,"depth":642,"text":34539},{"id":34741,"depth":642,"text":37240},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":35626,"depth":642,"text":35627},{"id":36013,"depth":642,"text":36014,"children":37243},[37244,37245],{"id":36017,"depth":649,"text":36018},{"id":36477,"depth":649,"text":36478},{"id":16218,"depth":642,"text":16219},{"id":2496,"depth":642,"text":2497},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":28267,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,37254,1144,10336,37255,37256,37257],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":37260,"title":802,"body":37261,"course":1128,"courses":659,"created":10119,"description":641,"extension":661,"meta":51314,"navigation":664,"path":51315,"seo":51316,"sources":51317,"stem":51318,"tags":51319,"type":2553,"updated":677,"__hash__":51325},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":37262,"toc":51270},[37263,37266,37292,37296,37303,37455,37469,37472,37474,37561,37565,37601,37674,37695,37820,37830,37843,37847,37852,37882,37944,37953,37957,38019,38026,38047,38165,38243,38247,38250,38309,38424,38429,38461,38523,38571,38626,38630,38651,38675,38723,38727,38739,38743,38853,38857,38873,38914,38925,39084,39094,39099,39103,39225,39235,39242,39246,39324,39335,39415,39421,39428,39567,39574,39577,39634,39638,39716,39762,39806,39812,39925,39929,39932,40127,40131,40368,40371,40525,40678,40680,40682,40762,40765,40870,40939,40948,40952,40955,41016,41025,41029,41062,41140,41179,41183,41232,41286,41290,41319,41348,41400,41407,41461,41539,41543,41586,41653,41697,41801,41820,41822,41826,41934,41938,42006,42055,42062,42147,42151,42223,42228,42276,42465,42469,42474,42650,42655,42714,42819,42823,42850,42854,42861,43025,43112,43117,43119,43122,43222,43372,43444,43518,43520,43524,43538,43542,43675,43730,43842,43919,43923,43980,44083,44142,44303,44307,44382,44454,44552,44610,44704,44757,44778,44832,44837,44915,44963,45050,45088,45176,45329,45365,45419,45422,45424,45426,45475,45482,45490,45577,45586,45673,45680,45682,45686,45911,45913,45917,45921,45990,46041,46244,46250,46261,46329,46335,46757,46761,46825,46849,47045,47051,47065,47133,47136,47176,47400,47468,47770,48179,48256,48422,48428,48431,48506,48959,49010,49416,49521,50184,50187,50264,50272,50346,50377,50379,50383,50427,50429,50431,50435,50665,50669,50760,50765,50859,50864,51037,51041,51159,51164,51213,51215,51217],[12,37264,802],{"id":37265},"poptávka-nabídka-a-tržní-rovnováha",[4436,37267,37268],{},[724,37269,37270,37272,37273,37276,37277,37280,37281,37284,37285,37287,37288,37291],{},[883,37271,4723],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,37274,37275],{},"poptávka",") a výrobce (",[38,37278,37279],{},"nabídka","), jejich interakci v ",[38,37282,37283],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,37286,18477],{},"). Uzavírá ji pojem ",[38,37289,37290],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,37293,37295],{"id":37294},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,37297,37298,37299,37302],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,37300,37301],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,37304,37305,37322,37364,37380],{},[123,37306,37307,37308,37321],{},"cena ",[883,37309,37311],{"className":37310},[886],[888,37312,37313],{"xmlns":890},[892,37314,37315,37319],{},[895,37316,37317],{},[898,37318,2398],{},[902,37320,2398],{"encoding":904}," zkoumaného zboží,",[123,37323,37324,37325,1916],{},"ceny alternativních zboží ",[883,37326,37328],{"className":37327},[886],[888,37329,37330],{"xmlns":890},[892,37331,37332,37361],{},[895,37333,37334,37340,37342,37348,37350,37352,37354],{},[2355,37335,37336,37338],{},[898,37337,2398],{},[1963,37339,2875],{},[1664,37341,1916],{"separator":1915},[2355,37343,37344,37346],{},[898,37345,2398],{},[1963,37347,1970],{},[1664,37349,1916],{"separator":1915},[1664,37351,10209],{},[1664,37353,1916],{"separator":1915},[2355,37355,37356,37358],{},[898,37357,2398],{},[898,37359,37360],{},"n",[902,37362,37363],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,37365,37366,37367,1916],{},"důchod ",[883,37368,37370],{"className":37369},[886],[888,37371,37372],{"xmlns":890},[892,37373,37374,37378],{},[895,37375,37376],{},[898,37377,9692],{},[902,37379,9692],{"encoding":904},[123,37381,37382,37383,37396,37397,37410,37411,37424,37425,37439,37440,37454],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,37384,37386],{"className":37385},[886],[888,37387,37388],{"xmlns":890},[892,37389,37390,37394],{},[895,37391,37392],{},[898,37393,10358],{},[902,37395,10358],{"encoding":904},", kapitál ",[883,37398,37400],{"className":37399},[886],[888,37401,37402],{"xmlns":890},[892,37403,37404,37408],{},[895,37405,37406],{},[898,37407,10363],{},[902,37409,10363],{"encoding":904},", půda ",[883,37412,37414],{"className":37413},[886],[888,37415,37416],{"xmlns":890},[892,37417,37418,37422],{},[895,37419,37420],{},[898,37421,4819],{},[902,37423,4819],{"encoding":904},"), technologie, počet výrobců ",[883,37426,37428],{"className":37427},[886],[888,37429,37430],{"xmlns":890},[892,37431,37432,37437],{},[895,37433,37434],{},[898,37435,37436],{},"O",[902,37438,37436],{"encoding":904},", počasí ",[883,37441,37443],{"className":37442},[886],[888,37444,37445],{"xmlns":890},[892,37446,37447,37452],{},[895,37448,37449],{},[898,37450,37451],{},"W",[902,37453,37451],{"encoding":904}," atd.",[724,37456,37457,37458,37461,37462,37465,37466,1977],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,37459,37460],{},"ceteris paribus","), hovoříme o ",[38,37463,37464],{},"jednofaktorovém modelu","; jinak jde o model ",[38,37467,37468],{},"vícefaktorový",[37470,37471],"hr",{},[115,37473,13660],{"id":37275},[4436,37475,37476],{},[724,37477,37478,37480,37481,37494,37495,37508,37509,37512,37513,37536,37537,1977],{},[883,37479,4723],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,37482,37484],{"className":37483},[886],[888,37485,37486],{"xmlns":890},[892,37487,37488,37492],{},[895,37489,37490],{},[898,37491,1973],{},[902,37493,1973],{"encoding":904}," na ceně ",[883,37496,37498],{"className":37497},[886],[888,37499,37500],{"xmlns":890},[892,37501,37502,37506],{},[895,37503,37504],{},[898,37505,2398],{},[902,37507,2398],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,37510,37511],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,37514,37516],{"className":37515},[886],[888,37517,37518],{"xmlns":890},[892,37519,37520,37534],{},[895,37521,37522,37524,37526,37528,37530,37532],{},[898,37523,1973],{},[1664,37525,1676],{},[898,37527,2379],{},[1664,37529,1667],{"stretchy":1666},[898,37531,2398],{},[1664,37533,1673],{"stretchy":1666},[902,37535,4759],{"encoding":904}," a jeho lineární verzí ",[883,37538,37540],{"className":37539},[886],[888,37541,37542],{"xmlns":890},[892,37543,37544,37558],{},[895,37545,37546,37548,37550,37552,37554,37556],{},[898,37547,2398],{},[1664,37549,1676],{},[898,37551,207],{},[898,37553,1973],{},[1664,37555,1700],{},[898,37557,1818],{},[902,37559,37560],{"encoding":904},"P = aQ + b",[198,37562,37564],{"id":37563},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,37566,37567,37568,37581,37582,37595,37596,10588,37598,3727],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,37569,37571],{"className":37570},[886],[888,37572,37573],{"xmlns":890},[892,37574,37575,37579],{},[895,37576,37577],{},[898,37578,1973],{},[902,37580,1973],{"encoding":904}," závisí na ceně ",[883,37583,37585],{"className":37584},[886],[888,37586,37587],{"xmlns":890},[892,37588,37589,37593],{},[895,37590,37591],{},[898,37592,2398],{},[902,37594,2398],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,37597,28502],{},[614,37599,37600],{},"demand function",[883,37602,37604],{"className":37603},[886],[888,37605,37606],{"xmlns":890,"display":28566},[892,37607,37608,37671],{},[21254,37609,37610],{"width":28571},[21259,37611,37612,37614,37664,37666],{},[21262,37613],{"width":28576},[21262,37615,37616],{},[895,37617,37618,37620,37622,37624,37626,37628,37630,37636,37638,37644,37646,37648,37650,37656,37658,37660,37662],{},[898,37619,1973],{},[1664,37621,1676],{},[898,37623,2379],{},[1664,37625,1667],{"stretchy":1666},[898,37627,2398],{},[1664,37629,1916],{"separator":1915},[2355,37631,37632,37634],{},[898,37633,2398],{},[1963,37635,2875],{},[1664,37637,1916],{"separator":1915},[2355,37639,37640,37642],{},[898,37641,2398],{},[1963,37643,1970],{},[1664,37645,1916],{"separator":1915},[1664,37647,10209],{},[1664,37649,1916],{"separator":1915},[2355,37651,37652,37654],{},[898,37653,2398],{},[898,37655,37360],{},[1664,37657,1916],{"separator":1915},[898,37659,9692],{},[1664,37661,1673],{"stretchy":1666},[898,37663,1977],{"mathvariant":1726},[21262,37665],{"width":28576},[21262,37667,37668],{},[1690,37669,37670],{},"(2.1)",[902,37672,37673],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,37675,37676,37677,37680,37681,37694],{},"Důležitou vlastností je ",[38,37678,37679],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,37682,37684],{"className":37683},[886],[888,37685,37686],{"xmlns":890},[892,37687,37688,37692],{},[895,37689,37690],{},[898,37691,12540],{},[902,37693,12540],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,37696,37698],{"className":37697},[886],[888,37699,37700],{"xmlns":890,"display":28566},[892,37701,37702,37817],{},[21254,37703,37704],{"width":28571},[21259,37705,37706,37708,37810,37812],{},[21262,37707],{"width":28576},[21262,37709,37710],{},[895,37711,37712,37714,37716,37718,37720,37722,37724,37726,37728,37734,37736,37738,37744,37746,37748,37750,37752,37758,37760,37762,37764,37766,37768,37770,37772,37774,37776,37782,37784,37790,37792,37794,37796,37802,37804,37806,37808],{},[898,37713,1973],{},[1664,37715,1676],{},[898,37717,2379],{},[1664,37719,1667],{"stretchy":1666},[898,37721,12540],{},[898,37723,2398],{},[1664,37725,1916],{"separator":1915},[898,37727,12540],{},[2355,37729,37730,37732],{},[898,37731,2398],{},[1963,37733,2875],{},[1664,37735,1916],{"separator":1915},[898,37737,12540],{},[2355,37739,37740,37742],{},[898,37741,2398],{},[1963,37743,1970],{},[1664,37745,1916],{"separator":1915},[1664,37747,10209],{},[1664,37749,1916],{"separator":1915},[898,37751,12540],{},[2355,37753,37754,37756],{},[898,37755,2398],{},[898,37757,37360],{},[1664,37759,1916],{"separator":1915},[898,37761,12540],{},[898,37763,9692],{},[1664,37765,1673],{"stretchy":1666},[1664,37767,1676],{},[898,37769,2379],{},[1664,37771,1667],{"stretchy":1666},[898,37773,2398],{},[1664,37775,1916],{"separator":1915},[2355,37777,37778,37780],{},[898,37779,2398],{},[1963,37781,2875],{},[1664,37783,1916],{"separator":1915},[2355,37785,37786,37788],{},[898,37787,2398],{},[1963,37789,1970],{},[1664,37791,1916],{"separator":1915},[1664,37793,10209],{},[1664,37795,1916],{"separator":1915},[2355,37797,37798,37800],{},[898,37799,2398],{},[898,37801,37360],{},[1664,37803,1916],{"separator":1915},[898,37805,9692],{},[1664,37807,1673],{"stretchy":1666},[898,37809,1977],{"mathvariant":1726},[21262,37811],{"width":28576},[21262,37813,37814],{},[1690,37815,37816],{},"(2.2)",[902,37818,37819],{"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}",[4436,37821,37822],{},[724,37823,37824,37826,37827,1977],{},[883,37825,4978],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,37828,37829],{},"v jednofaktorových modelech neplatí",[724,37831,37832,37833,1343,37836,4454,37839,37842],{},"Rozlišuje se poptávka ",[38,37834,37835],{},"individuální",[38,37837,37838],{},"tržní",[38,37840,37841],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,37844,37846],{"id":37845},"jednofaktorové-modely","Jednofaktorové modely",[37848,37849,37851],"h4",{"id":37850},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,37853,37854,37855,37868,37869,2087],{},"Poptávané množství ",[883,37856,37858],{"className":37857},[886],[888,37859,37860],{"xmlns":890},[892,37861,37862,37866],{},[895,37863,37864],{},[898,37865,1973],{},[902,37867,1973],{"encoding":904}," závisí pouze na ceně ",[883,37870,37872],{"className":37871},[886],[888,37873,37874],{"xmlns":890},[892,37875,37876,37880],{},[895,37877,37878],{},[898,37879,2398],{},[902,37881,2398],{"encoding":904},[883,37883,37885],{"className":37884},[886],[888,37886,37887],{"xmlns":890,"display":28566},[892,37888,37889,37941],{},[21254,37890,37891],{"width":28571},[21259,37892,37893,37895,37934,37936],{},[21262,37894],{"width":28576},[21262,37896,37897],{},[895,37898,37899,37901,37903,37905,37907,37909,37911,37913,37915,37918,37920,37922,37924,37926,37928,37930,37932],{},[898,37900,1973],{},[1664,37902,1676],{},[898,37904,2379],{},[1664,37906,1667],{"stretchy":1666},[898,37908,2398],{},[1664,37910,1673],{"stretchy":1666},[1664,37912,1916],{"separator":1915},[6444,37914],{"width":6446},[1690,37916,37917],{},"resp.",[6444,37919],{"width":6446},[898,37921,2398],{},[1664,37923,1676],{},[898,37925,2379],{},[1664,37927,1667],{"stretchy":1666},[898,37929,1973],{},[1664,37931,1673],{"stretchy":1666},[898,37933,1977],{"mathvariant":1726},[21262,37935],{"width":28576},[21262,37937,37938],{},[1690,37939,37940],{},"(2.3)",[902,37942,37943],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,37945,37946,37947,10588,37950,4488],{},"Graf této funkce se nazývá ",[38,37948,37949],{},"křivka poptávky",[614,37951,37952],{},"demand curve",[37848,37954,37956],{"id":37955},"zákon-klesající-poptávky","Zákon klesající poptávky",[4436,37958,37959],{},[724,37960,37961],{},[38,37962,37963,37964,37977,37978,37991,37992,37977,38005,38018],{},"Roste-li cena ",[883,37965,37967],{"className":37966},[886],[888,37968,37969],{"xmlns":890},[892,37970,37971,37975],{},[895,37972,37973],{},[898,37974,2398],{},[902,37976,2398],{"encoding":904},", pak množství ",[883,37979,37981],{"className":37980},[886],[888,37982,37983],{"xmlns":890},[892,37984,37985,37989],{},[895,37986,37987],{},[898,37988,1973],{},[902,37990,1973],{"encoding":904}," klesá; klesá-li cena ",[883,37993,37995],{"className":37994},[886],[888,37996,37997],{"xmlns":890},[892,37998,37999,38003],{},[895,38000,38001],{},[898,38002,2398],{},[902,38004,2398],{"encoding":904},[883,38006,38008],{"className":38007},[886],[888,38009,38010],{"xmlns":890},[892,38011,38012,38016],{},[895,38013,38014],{},[898,38015,1973],{},[902,38017,1973],{"encoding":904}," roste.",[724,38020,38021,38022,38025],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,38023,38024],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[4436,38027,38028,38033],{},[724,38029,38030,38032],{},[883,38031,4723],{}," Intuice — proč zákon platí",[120,38034,38035,38041],{},[123,38036,38037,38040],{},[38,38038,38039],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,38042,38043,38046],{},[38,38044,38045],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,38048,38049,38050,38063,38064,38077,38078,38104,38105,38131,38132,1762,38158,38161,38162,1977],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,38051,38053],{"className":38052},[886],[888,38054,38055],{"xmlns":890},[892,38056,38057,38061],{},[895,38058,38059],{},[898,38060,2398],{},[902,38062,2398],{"encoding":904}," se vynáší na svislou osu, množství ",[883,38065,38067],{"className":38066},[886],[888,38068,38069],{"xmlns":890},[892,38070,38071,38075],{},[895,38072,38073],{},[898,38074,1973],{},[902,38076,1973],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,38079,38081],{"className":38080},[886],[888,38082,38083],{"xmlns":890},[892,38084,38085,38101],{},[895,38086,38087,38089,38091,38093,38099],{},[1664,38088,1837],{"stretchy":1666},[1963,38090,2058],{},[1664,38092,1916],{"separator":1915},[2355,38094,38095,38097],{},[898,38096,2398],{},[1963,38098,2058],{},[1664,38100,1850],{"stretchy":1666},[902,38102,38103],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,38106,38108],{"className":38107},[886],[888,38109,38110],{"xmlns":890},[892,38111,38112,38128],{},[895,38113,38114,38116,38122,38124,38126],{},[1664,38115,1837],{"stretchy":1666},[2355,38117,38118,38120],{},[898,38119,1973],{},[1963,38121,2058],{},[1664,38123,1916],{"separator":1915},[1963,38125,2058],{},[1664,38127,1850],{"stretchy":1666},[902,38129,38130],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,38133,38135],{"className":38134},[886],[888,38136,38137],{"xmlns":890},[892,38138,38139,38155],{},[895,38140,38141,38143,38145,38147,38153],{},[1664,38142,1667],{"stretchy":1666},[1963,38144,2058],{},[1664,38146,1916],{"separator":1915},[2355,38148,38149,38151],{},[898,38150,2398],{},[1963,38152,2058],{},[1664,38154,1673],{"stretchy":1666},[902,38156,38157],{"encoding":904},"(0, P_0)",[38,38159,38160],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,38163,38164],{},"konvexní",[724,38166,38167],{},[614,38168,38169,38170,38192,38193,4454,38218,1977],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,38171,38173],{"className":38172},[886],[888,38174,38175],{"xmlns":890},[892,38176,38177,38189],{},[895,38178,38179,38181,38183,38185,38187],{},[1664,38180,1667],{"stretchy":1666},[898,38182,1973],{},[1664,38184,1916],{"separator":1915},[898,38186,2398],{},[1664,38188,1673],{"stretchy":1666},[902,38190,38191],{"encoding":904},"(Q, P)"," — klesající, konvexní, procházející body ",[883,38194,38196],{"className":38195},[886],[888,38197,38198],{"xmlns":890},[892,38199,38200,38216],{},[895,38201,38202,38204,38206,38208,38214],{},[1664,38203,1837],{"stretchy":1666},[1963,38205,2058],{},[1664,38207,1916],{"separator":1915},[2355,38209,38210,38212],{},[898,38211,2398],{},[1963,38213,2058],{},[1664,38215,1850],{"stretchy":1666},[902,38217,38103],{"encoding":904},[883,38219,38221],{"className":38220},[886],[888,38222,38223],{"xmlns":890},[892,38224,38225,38241],{},[895,38226,38227,38229,38235,38237,38239],{},[1664,38228,1837],{"stretchy":1666},[2355,38230,38231,38233],{},[898,38232,1973],{},[1963,38234,2058],{},[1664,38236,1916],{"separator":1915},[1963,38238,2058],{},[1664,38240,1850],{"stretchy":1666},[902,38242,38130],{"encoding":904},[37848,38244,38246],{"id":38245},"lineární-model-poptávky","Lineární model poptávky",[724,38248,38249],{},"Nejjednodušší závislostí je",[883,38251,38253],{"className":38252},[886],[888,38254,38255],{"xmlns":890,"display":28566},[892,38256,38257,38306],{},[21254,38258,38259],{"width":28571},[21259,38260,38261,38263,38299,38301],{},[21262,38262],{"width":28576},[21262,38264,38265],{},[895,38266,38267,38269,38271,38273,38275,38277,38279,38281,38283,38285,38287,38289,38291,38293,38295,38297],{},[898,38268,2398],{},[1664,38270,1676],{},[898,38272,207],{},[898,38274,1973],{},[1664,38276,1700],{},[898,38278,1818],{},[1664,38280,1916],{"separator":1915},[6444,38282],{"width":6446},[898,38284,207],{},[1664,38286,4022],{},[1963,38288,2058],{},[1664,38290,1916],{"separator":1915},[1690,38292,2884],{},[898,38294,1818],{},[1664,38296,3984],{},[1963,38298,12959],{},[21262,38300],{"width":28576},[21262,38302,38303],{},[1690,38304,38305],{},"(2.4)",[902,38307,38308],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,38310,38311,38312,22094,38348,4454,38372,8603,38398,38420,38421,1977],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,38313,38315],{"className":38314},[886],[888,38316,38317],{"xmlns":890},[892,38318,38319,38345],{},[895,38320,38321,38323,38325,38333,38335,38337],{},[898,38322,1973],{},[1664,38324,1676],{},[2919,38326,38327],{"scriptlevel":2058,"displaystyle":1666},[2922,38328,38329,38331],{},[1963,38330,2875],{},[898,38332,207],{},[898,38334,2398],{},[1664,38336,1867],{},[2919,38338,38339],{"scriptlevel":2058,"displaystyle":1666},[2922,38340,38341,38343],{},[898,38342,1818],{},[898,38344,207],{},[902,38346,38347],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,38349,38351],{"className":38350},[886],[888,38352,38353],{"xmlns":890},[892,38354,38355,38369],{},[895,38356,38357,38365,38367],{},[2919,38358,38359],{"scriptlevel":2058,"displaystyle":1666},[2922,38360,38361,38363],{},[1963,38362,2875],{},[898,38364,207],{},[1664,38366,4022],{},[1963,38368,2058],{},[902,38370,38371],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,38373,38375],{"className":38374},[886],[888,38376,38377],{"xmlns":890},[892,38378,38379,38395],{},[895,38380,38381,38383,38391,38393],{},[1664,38382,1867],{},[2919,38384,38385],{"scriptlevel":2058,"displaystyle":1666},[2922,38386,38387,38389],{},[898,38388,1818],{},[898,38390,207],{},[1664,38392,3984],{},[1963,38394,2058],{},[902,38396,38397],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,38399,38401],{"className":38400},[886],[888,38402,38403],{"xmlns":890},[892,38404,38405,38417],{},[895,38406,38407,38409,38411,38413,38415],{},[1664,38408,1667],{"stretchy":1666},[1963,38410,2058],{},[1664,38412,1916],{"separator":1915},[898,38414,1818],{},[1664,38416,1673],{"stretchy":1666},[902,38418,38419],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,38422,38423],{},"nedokonalé konkurenci",[38425,38426,38428],"h5",{"id":38427},"příklad-21","Příklad 2.1",[724,38430,38431,38434,38435,1977],{},[38,38432,38433],{},"Zadání:"," Lineární poptávka ",[883,38436,38438],{"className":38437},[886],[888,38439,38440],{"xmlns":890},[892,38441,38442,38458],{},[895,38443,38444,38446,38448,38450,38452,38454,38456],{},[898,38445,2398],{},[1664,38447,1676],{},[1664,38449,1867],{},[1963,38451,1970],{},[898,38453,1973],{},[1664,38455,1700],{},[1963,38457,3702],{},[902,38459,38460],{"encoding":904},"P = -2Q + 60",[724,38462,38463,38466,38467,38489,38490,1977],{},[38,38464,38465],{},"Řešení:"," Reálné cenové rozpětí je ",[883,38468,38470],{"className":38469},[886],[888,38471,38472],{"xmlns":890},[892,38473,38474,38486],{},[895,38475,38476,38478,38480,38482,38484],{},[1664,38477,1667],{"stretchy":1666},[1963,38479,2058],{},[1664,38481,1916],{"separator":1915},[1963,38483,3702],{},[1664,38485,1673],{"stretchy":1666},[902,38487,38488],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,38491,38493],{"className":38492},[886],[888,38494,38495],{"xmlns":890},[892,38496,38497,38520],{},[895,38498,38499,38501,38503,38505,38513,38515,38517],{},[898,38500,1973],{},[1664,38502,1676],{},[1664,38504,1867],{},[2919,38506,38507],{"scriptlevel":2058,"displaystyle":1666},[2922,38508,38509,38511],{},[1963,38510,2875],{},[1963,38512,1970],{},[898,38514,2398],{},[1664,38516,1700],{},[1963,38518,38519],{},"30",[902,38521,38522],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,38524,38525,38548],{},[19,38526,38527],{},[22,38528,38529,38544,38546],{},[25,38530,38531],{},[883,38532,38534],{"className":38533},[886],[888,38535,38536],{"xmlns":890},[892,38537,38538,38542],{},[895,38539,38540],{},[898,38541,2398],{},[902,38543,2398],{"encoding":904},[25,38545,5777],{},[25,38547,9599],{},[30,38549,38550],{},[22,38551,38552,38567,38569],{},[35,38553,38554],{},[883,38555,38557],{"className":38556},[886],[888,38558,38559],{"xmlns":890},[892,38560,38561,38565],{},[895,38562,38563],{},[898,38564,1973],{},[902,38566,1973],{"encoding":904},[35,38568,3442],{},[35,38570,9599],{},[724,38572,38573],{},[614,38574,38575,38576,4454,38598,1977],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,38577,38579],{"className":38578},[886],[888,38580,38581],{"xmlns":890},[892,38582,38583,38595],{},[895,38584,38585,38587,38589,38591,38593],{},[1664,38586,1837],{"stretchy":1666},[1963,38588,2058],{},[1664,38590,1916],{"separator":1915},[898,38592,1818],{},[1664,38594,1850],{"stretchy":1666},[902,38596,38597],{"encoding":904},"[0, b]",[883,38599,38601],{"className":38600},[886],[888,38602,38603],{"xmlns":890},[892,38604,38605,38623],{},[895,38606,38607,38609,38611,38613,38615,38617,38619,38621],{},[1664,38608,1837],{"stretchy":1666},[1664,38610,1867],{},[898,38612,1818],{},[898,38614,5240],{"mathvariant":1726},[898,38616,207],{},[1664,38618,1916],{"separator":1915},[1963,38620,2058],{},[1664,38622,1850],{"stretchy":1666},[902,38624,38625],{"encoding":904},"[-b\u002Fa, 0]",[37848,38627,38629],{"id":38628},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,38631,38632,38633,38650],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,38634,38636],{"className":38635},[886],[888,38637,38638],{"xmlns":890},[892,38639,38640,38648],{},[895,38641,38642],{},[1720,38643,38644,38646],{},[898,38645,2398],{},[1664,38647,4920],{},[902,38649,4970],{"encoding":904},", je funkce poptávky konstantní:",[883,38652,38654],{"className":38653},[886],[888,38655,38656],{"xmlns":890,"display":28566},[892,38657,38658,38672],{},[895,38659,38660,38662,38664,38670],{},[898,38661,2398],{},[1664,38663,1676],{},[1720,38665,38666,38668],{},[898,38667,2398],{},[1664,38669,4920],{},[898,38671,1977],{"mathvariant":1726},[902,38673,38674],{"encoding":904},"P = P^*.",[724,38676,38677],{},[614,38678,38679,38680,38701,38702,1977],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,38681,38683],{"className":38682},[886],[888,38684,38685],{"xmlns":890},[892,38686,38687,38699],{},[895,38688,38689,38691,38693,38695,38697],{},[1664,38690,1667],{"stretchy":1666},[898,38692,1973],{},[1664,38694,1916],{"separator":1915},[898,38696,2398],{},[1664,38698,1673],{"stretchy":1666},[902,38700,38191],{"encoding":904}," na úrovni ",[883,38703,38705],{"className":38704},[886],[888,38706,38707],{"xmlns":890},[892,38708,38709,38721],{},[895,38710,38711,38713,38715],{},[898,38712,2398],{},[1664,38714,1676],{},[1720,38716,38717,38719],{},[898,38718,2398],{},[1664,38720,4920],{},[902,38722,4923],{"encoding":904},[37848,38724,38726],{"id":38725},"giffenův-statek","Giffenův statek",[724,38728,38729,38730,38732,38733,38735,38736,1977],{},"Existují zboží, u nichž je křivka poptávky ",[38,38731,14156],{}," — tzv. ",[38,38734,38726],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,38737,38738],{},"podřadnému zboží",[38425,38740,38742],{"id":38741},"příklad-22","Příklad 2.2",[724,38744,38745,38748,38749,38767,38768,38790,38791,38809,38810,38828,38829,38852],{},[38,38746,38747],{},"Zadání a popis:"," Křivka ",[883,38750,38752],{"className":38751},[886],[888,38753,38754],{"xmlns":890},[892,38755,38756,38764],{},[895,38757,38758],{},[2355,38759,38760,38762],{},[898,38761,2379],{},[1963,38763,2875],{},[902,38765,38766],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,38769,38771],{"className":38770},[886],[888,38772,38773],{"xmlns":890},[892,38774,38775,38787],{},[895,38776,38777,38779,38781,38783,38785],{},[1664,38778,1667],{"stretchy":1666},[1963,38780,2058],{},[1664,38782,1916],{"separator":1915},[1963,38784,36744],{},[1664,38786,1673],{"stretchy":1666},[902,38788,38789],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,38792,38794],{"className":38793},[886],[888,38795,38796],{"xmlns":890},[892,38797,38798,38806],{},[895,38799,38800],{},[2355,38801,38802,38804],{},[898,38803,1973],{},[1963,38805,2058],{},[902,38807,38808],{"encoding":904},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[883,38811,38813],{"className":38812},[886],[888,38814,38815],{"xmlns":890},[892,38816,38817,38825],{},[895,38818,38819],{},[2355,38820,38821,38823],{},[898,38822,2379],{},[1963,38824,1970],{},[902,38826,38827],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,38830,38832],{"className":38831},[886],[888,38833,38834],{"xmlns":890},[892,38835,38836,38849],{},[895,38837,38838,38840,38842,38844,38847],{},[1664,38839,1837],{"stretchy":1666},[1963,38841,2058],{},[1664,38843,1916],{"separator":1915},[1963,38845,38846],{},"21",[1664,38848,1850],{"stretchy":1666},[902,38850,38851],{"encoding":904},"[0, 21]"," centů.",[198,38854,38856],{"id":38855},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,38858,38859,38860,2087],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,38861,38863],{"className":38862},[886],[888,38864,38865],{"xmlns":890},[892,38866,38867,38871],{},[895,38868,38869],{},[898,38870,9692],{},[902,38872,9692],{"encoding":904},[883,38874,38876],{"className":38875},[886],[888,38877,38878],{"xmlns":890,"display":28566},[892,38879,38880,38911],{},[21254,38881,38882],{"width":28571},[21259,38883,38884,38886,38904,38906],{},[21262,38885],{"width":28576},[21262,38887,38888],{},[895,38889,38890,38892,38894,38896,38898,38900,38902],{},[898,38891,1973],{},[1664,38893,1676],{},[898,38895,4819],{},[1664,38897,1667],{"stretchy":1666},[898,38899,9692],{},[1664,38901,1673],{"stretchy":1666},[898,38903,1977],{"mathvariant":1726},[21262,38905],{"width":28576},[21262,38907,38908],{},[1690,38909,38910],{},"(2.5)",[902,38912,38913],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,38915,38916,38917,38920,38921,38924],{},"Funkce se nazývá ",[38,38918,38919],{},"Engelova",", její graf ",[38,38922,38923],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,38926,38927,39059],{},[123,38928,38929,7581,38932,38945,38946,38959,38960,38977,38978],{},[38,38930,38931],{},"Normální (superior) zboží",[883,38933,38935],{"className":38934},[886],[888,38936,38937],{"xmlns":890},[892,38938,38939,38943],{},[895,38940,38941],{},[898,38942,1973],{},[902,38944,1973],{"encoding":904}," roste s ",[883,38947,38949],{"className":38948},[886],[888,38950,38951],{"xmlns":890},[892,38952,38953,38957],{},[895,38954,38955],{},[898,38956,9692],{},[902,38958,9692],{"encoding":904},", nepřesáhne hodnotu ",[883,38961,38963],{"className":38962},[886],[888,38964,38965],{"xmlns":890},[892,38966,38967,38975],{},[895,38968,38969],{},[2355,38970,38971,38973],{},[898,38972,1973],{},[1963,38974,2058],{},[902,38976,38808],{"encoding":904},":\n",[120,38979,38980,39012],{},[123,38981,38982,38985,38986,38989,38990,1977],{},[38,38983,38984],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,38987,38988],{},"konkávní"," křivka, autonomní spotřeba ",[883,38991,38993],{"className":38992},[886],[888,38994,38995],{"xmlns":890},[892,38996,38997,39009],{},[895,38998,38999,39005,39007],{},[2355,39000,39001,39003],{},[898,39002,1973],{},[1963,39004,2875],{},[1664,39006,3984],{},[1963,39008,2058],{},[902,39010,39011],{"encoding":904},"Q_1 > 0",[123,39013,39014,39017,39018,39036,39037,39039,39040,1885,39057,1977],{},[38,39015,39016],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,39019,39021],{"className":39020},[886],[888,39022,39023],{"xmlns":890},[892,39024,39025,39033],{},[895,39026,39027],{},[2355,39028,39029,39031],{},[898,39030,9692],{},[1963,39032,2875],{},[902,39034,39035],{"encoding":904},"Y_1",", křivka je nejprve ",[38,39038,38164],{}," a od ",[883,39041,39043],{"className":39042},[886],[888,39044,39045],{"xmlns":890},[892,39046,39047,39055],{},[895,39048,39049],{},[2355,39050,39051,39053],{},[898,39052,9692],{},[1963,39054,2875],{},[902,39056,39035],{"encoding":904},[38,39058,38988],{},[123,39060,39061,39064,39065,39083],{},[38,39062,39063],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,39066,39068],{"className":39067},[886],[888,39069,39070],{"xmlns":890},[892,39071,39072,39080],{},[895,39073,39074],{},[2355,39075,39076,39078],{},[898,39077,9692],{},[1963,39079,2058],{},[902,39081,39082],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,39085,39086,39087,39090,39091,4488],{},"Mírou citlivosti je ",[614,39088,39089],{},"důchodová elasticita"," (viz ",[207,39092,4467],{"className":39093,"dataFsResolvedFilePath":848,"href":849},[210],[724,39095,39096],{},[614,39097,39098],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[37848,39100,39102],{"id":39101},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[4436,39104,39105,39176,39219],{},[724,39106,39107,39109,39110,1885,39113,1885,39126,6235,39128,39141,39142,39145,39146,1977],{},[883,39108,4978],{}," Pozor — nezbytné ≠ podřadné\n",[38,39111,39112],{},"Nezbytné zboží:",[883,39114,39116],{"className":39115},[886],[888,39117,39118],{"xmlns":890},[892,39119,39120,39124],{},[895,39121,39122],{},[898,39123,1973],{},[902,39125,1973],{"encoding":904},[38,39127,7888],{},[883,39129,39131],{"className":39130},[886],[888,39132,39133],{"xmlns":890},[892,39134,39135,39139],{},[895,39136,39137],{},[898,39138,9692],{},[902,39140,9692],{"encoding":904},", ale ",[38,39143,39144],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,39147,39149],{"className":39148},[886],[888,39150,39151],{"xmlns":890},[892,39152,39153,39173],{},[895,39154,39155,39161,39163,39165,39167,39169,39171],{},[2355,39156,39157,39159],{},[898,39158,4819],{},[898,39160,9692],{},[1664,39162,7072],{},[1664,39164,1667],{"stretchy":1666},[1963,39166,2058],{},[1664,39168,1916],{"separator":1915},[1963,39170,2875],{},[1664,39172,1673],{"stretchy":1666},[902,39174,39175],{"encoding":904},"E_Y \\in (0, 1)",[724,39177,39178,1885,39181,1885,39194,39196,39197,1977],{},[38,39179,39180],{},"Podřadné zboží:",[883,39182,39184],{"className":39183},[886],[888,39185,39186],{"xmlns":890},[892,39187,39188,39192],{},[895,39189,39190],{},[898,39191,1973],{},[902,39193,1973],{"encoding":904},[38,39195,7908],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,39198,39200],{"className":39199},[886],[888,39201,39202],{"xmlns":890},[892,39203,39204,39216],{},[895,39205,39206,39212,39214],{},[2355,39207,39208,39210],{},[898,39209,4819],{},[898,39211,9692],{},[1664,39213,4022],{},[1963,39215,2058],{},[902,39217,39218],{"encoding":904},"E_Y \u003C 0",[724,39220,39221,39222,1977],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,39223,39224],{},"méně kusů, ne jen proporčně méně",[724,39226,39227,39230,39231,39234],{},[38,39228,39229],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,39232,39233],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,39236,39237],{},[1928,39238],{"alt":39239,"className":39240,"src":39241},"imek-engelovy-krivky-3typy",[210,1932],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[38425,39243,39245],{"id":39244},"české-příklady","České příklady",[16,39247,39248,39258],{},[19,39249,39250],{},[22,39251,39252,39255],{},[25,39253,39254],{},"Podřadné",[25,39256,39257],{},"Nahradí se za",[30,39259,39260,39268,39276,39284,39292,39300,39308,39316],{},[22,39261,39262,39265],{},[35,39263,39264],{},"Instantní polévky, ramen",[35,39266,39267],{},"Čerstvé jídlo, restaurace",[22,39269,39270,39273],{},[35,39271,39272],{},"MHD (autobus, tramvaj)",[35,39274,39275],{},"Vlastní auto, Uber, taxi",[22,39277,39278,39281],{},[35,39279,39280],{},"Mražené polotovary, pizza z mrazáku",[35,39282,39283],{},"Čerstvé suroviny, hotovky",[22,39285,39286,39289],{},[35,39287,39288],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,39290,39291],{},"Značkové produkty",[22,39293,39294,39297],{},[35,39295,39296],{},"Paštika Májka, obyčejný měkký salám",[35,39298,39299],{},"Kvalitní uzeniny, šunka od kosti",[22,39301,39302,39305],{},[35,39303,39304],{},"Second hand oblečení",[35,39306,39307],{},"Nové oblečení, značky",[22,39309,39310,39313],{},[35,39311,39312],{},"Krabicové víno, nejlevnější pivo",[35,39314,39315],{},"Lahvové víno, řemeslná piva",[22,39317,39318,39321],{},[35,39319,39320],{},"Ojetá auta nižších tříd",[35,39322,39323],{},"Nová auta, prémiové značky",[4436,39325,39326],{},[724,39327,39328,39330,39331,39334],{},[883,39329,5138],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,39332,39333],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,39336,39337,39340,39341,10588,39344,39366,39367,10588,39370,39391,39392,39410,39411,39414],{},[38,39338,39339],{},"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 ",[38,39342,39343],{},"luxus",[883,39345,39347],{"className":39346},[886],[888,39348,39349],{"xmlns":890},[892,39350,39351,39363],{},[895,39352,39353,39359,39361],{},[2355,39354,39355,39357],{},[898,39356,4819],{},[898,39358,9692],{},[1664,39360,3984],{},[1963,39362,2875],{},[902,39364,39365],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,39368,39369],{},"podřadné",[883,39371,39373],{"className":39372},[886],[888,39374,39375],{"xmlns":890},[892,39376,39377,39389],{},[895,39378,39379,39385,39387],{},[2355,39380,39381,39383],{},[898,39382,4819],{},[898,39384,9692],{},[1664,39386,4022],{},[1963,39388,2058],{},[902,39390,39218],{"encoding":904},"). Proto je ",[883,39393,39395],{"className":39394},[886],[888,39396,39397],{"xmlns":890},[892,39398,39399,39407],{},[895,39400,39401],{},[2355,39402,39403,39405],{},[898,39404,4819],{},[898,39406,9692],{},[902,39408,39409],{"encoding":904},"E_Y"," vždy ",[38,39412,39413],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,39416,39417,39418,39420],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,39419,38726],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,39422,39424,39425,1673],{"id":39423},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,39426,39427],{},"shift of demand",[724,39429,39430,39431,39449,39450,39467,39468,39481,39482,3271,39495,39517,39518,39535,39536,39562,39563,39566],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,39432,39434],{"className":39433},[886],[888,39435,39436],{"xmlns":890},[892,39437,39438,39446],{},[895,39439,39440],{},[2355,39441,39442,39444],{},[898,39443,2398],{},[1963,39445,2058],{},[902,39447,39448],{"encoding":904},"P_0"," odpovídá množství ",[883,39451,39453],{"className":39452},[886],[888,39454,39455],{"xmlns":890},[892,39456,39457,39465],{},[895,39458,39459],{},[2355,39460,39461,39463],{},[898,39462,1973],{},[1963,39464,2058],{},[902,39466,38808],{"encoding":904}," na křivce ",[883,39469,39471],{"className":39470},[886],[888,39472,39473],{"xmlns":890},[892,39474,39475,39479],{},[895,39476,39477],{},[898,39478,2379],{},[902,39480,2379],{"encoding":904},"; vzroste-li důchod z ",[883,39483,39485],{"className":39484},[886],[888,39486,39487],{"xmlns":890},[892,39488,39489,39493],{},[895,39490,39491],{},[898,39492,9692],{},[902,39494,9692],{"encoding":904},[883,39496,39498],{"className":39497},[886],[888,39499,39500],{"xmlns":890},[892,39501,39502,39514],{},[895,39503,39504,39510,39512],{},[2355,39505,39506,39508],{},[898,39507,9692],{},[1963,39509,2875],{},[1664,39511,3984],{},[898,39513,9692],{},[902,39515,39516],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,39519,39521],{"className":39520},[886],[888,39522,39523],{"xmlns":890},[892,39524,39525,39533],{},[895,39526,39527],{},[2355,39528,39529,39531],{},[898,39530,2398],{},[1963,39532,2058],{},[902,39534,39448],{"encoding":904}," odpovídá vyšší ",[883,39537,39539],{"className":39538},[886],[888,39540,39541],{"xmlns":890},[892,39542,39543,39559],{},[895,39544,39545,39551,39553],{},[2355,39546,39547,39549],{},[898,39548,1973],{},[1963,39550,2875],{},[1664,39552,3984],{},[2355,39554,39555,39557],{},[898,39556,1973],{},[1963,39558,2058],{},[902,39560,39561],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,39564,39565],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,39568,39569],{},[1928,39570],{"alt":39571,"className":39572,"src":39573},"imek-posun-vs-pohyb-po-krivce",[210,1932],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,39575,39576],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,39578,39579],{},[614,39580,39581,39582,14510,39612,39633],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,39583,39585],{"className":39584},[886],[888,39586,39587],{"xmlns":890},[892,39588,39589,39609],{},[895,39590,39591,39597,39599,39601,39603],{},[2355,39592,39593,39595],{},[898,39594,2379],{},[1963,39596,1970],{},[1664,39598,1916],{"separator":1915},[898,39600,2379],{},[1664,39602,1916],{"separator":1915},[2355,39604,39605,39607],{},[898,39606,2379],{},[1963,39608,2875],{},[902,39610,39611],{"encoding":904},"D_2, D, D_1",[883,39613,39615],{"className":39614},[886],[888,39616,39617],{"xmlns":890},[892,39618,39619,39631],{},[895,39620,39621,39623,39625,39627,39629],{},[1664,39622,1667],{"stretchy":1666},[898,39624,1973],{},[1664,39626,1916],{"separator":1915},[898,39628,2398],{},[1664,39630,1673],{"stretchy":1666},[902,39632,38191],{"encoding":904},", šipky naznačují posuny.",[38425,39635,39637],{"id":39636},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,39639,39640,39642,39643,39666,39667,39684,39685,39702,39703,1977],{},[38,39641,38433],{}," Poptávce ",[883,39644,39646],{"className":39645},[886],[888,39647,39648],{"xmlns":890},[892,39649,39650,39664],{},[895,39651,39652,39654,39656,39658,39660,39662],{},[898,39653,2398],{},[1664,39655,1676],{},[898,39657,2379],{},[1664,39659,1667],{"stretchy":1666},[898,39661,1973],{},[1664,39663,1673],{"stretchy":1666},[902,39665,5206],{"encoding":904}," odpovídá ceně ",[883,39668,39670],{"className":39669},[886],[888,39671,39672],{"xmlns":890},[892,39673,39674,39682],{},[895,39675,39676],{},[2355,39677,39678,39680],{},[898,39679,2398],{},[1963,39681,2058],{},[902,39683,39448],{"encoding":904}," množství ",[883,39686,39688],{"className":39687},[886],[888,39689,39690],{"xmlns":890},[892,39691,39692,39700],{},[895,39693,39694],{},[2355,39695,39696,39698],{},[898,39697,1973],{},[1963,39699,2058],{},[902,39701,38808],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,39704,39706],{"className":39705},[886],[888,39707,39708],{"xmlns":890},[892,39709,39710,39714],{},[895,39711,39712],{},[898,39713,1991],{},[902,39715,1991],{"encoding":904},[724,39717,39718,39720,39721,39738,39739,39761],{},[38,39719,38465],{}," Kupující nakupuje množství ",[883,39722,39724],{"className":39723},[886],[888,39725,39726],{"xmlns":890},[892,39727,39728,39736],{},[895,39729,39730],{},[2355,39731,39732,39734],{},[898,39733,1973],{},[1963,39735,2875],{},[902,39737,29502],{"encoding":904},", které odpovídá ceně ",[883,39740,39742],{"className":39741},[886],[888,39743,39744],{"xmlns":890},[892,39745,39746,39758],{},[895,39747,39748,39754,39756],{},[2355,39749,39750,39752],{},[898,39751,2398],{},[1963,39753,2058],{},[1664,39755,1700],{},[898,39757,1991],{},[902,39759,39760],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,39763,39765],{"className":39764},[886],[888,39766,39767],{"xmlns":890,"display":28566},[892,39768,39769,39803],{},[895,39770,39771,39773,39775,39781,39783,39785,39787,39789,39791,39793,39795,39797,39799,39801],{},[898,39772,2398],{},[1664,39774,1676],{},[2355,39776,39777,39779],{},[898,39778,2379],{},[1963,39780,2875],{},[1664,39782,1667],{"stretchy":1666},[898,39784,1973],{},[1664,39786,1673],{"stretchy":1666},[1664,39788,1676],{},[898,39790,2379],{},[1664,39792,1667],{"stretchy":1666},[898,39794,1973],{},[1664,39796,1673],{"stretchy":1666},[1664,39798,1867],{},[898,39800,1991],{},[1664,39802,1916],{"separator":1915},[902,39804,39805],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,39807,39808,39809,1977],{},"tj. dojde k ",[38,39810,39811],{},"posunu poptávky doleva",[724,39813,39814],{},[614,39815,39816,39817,39838,39839,1343,39856,1343,39869,39890,39891,4454,39908,1977],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,39818,39820],{"className":39819},[886],[888,39821,39822],{"xmlns":890},[892,39823,39824,39836],{},[895,39825,39826,39828,39830,39832,39834],{},[1664,39827,1667],{"stretchy":1666},[898,39829,1973],{},[1664,39831,1916],{"separator":1915},[898,39833,2398],{},[1664,39835,1673],{"stretchy":1666},[902,39837,38191],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,39840,39842],{"className":39841},[886],[888,39843,39844],{"xmlns":890},[892,39845,39846,39854],{},[895,39847,39848],{},[2355,39849,39850,39852],{},[898,39851,2398],{},[1963,39853,2058],{},[902,39855,39448],{"encoding":904},[883,39857,39859],{"className":39858},[886],[888,39860,39861],{"xmlns":890},[892,39862,39863,39867],{},[895,39864,39865],{},[898,39866,1991],{},[902,39868,1991],{"encoding":904},[883,39870,39872],{"className":39871},[886],[888,39873,39874],{"xmlns":890},[892,39875,39876,39888],{},[895,39877,39878,39884,39886],{},[2355,39879,39880,39882],{},[898,39881,2398],{},[1963,39883,2058],{},[1664,39885,1700],{},[898,39887,1991],{},[902,39889,39760],{"encoding":904},"; na vodorovné ",[883,39892,39894],{"className":39893},[886],[888,39895,39896],{"xmlns":890},[892,39897,39898,39906],{},[895,39899,39900],{},[2355,39901,39902,39904],{},[898,39903,1973],{},[1963,39905,2875],{},[902,39907,29502],{"encoding":904},[883,39909,39911],{"className":39910},[886],[888,39912,39913],{"xmlns":890},[892,39914,39915,39923],{},[895,39916,39917],{},[2355,39918,39919,39921],{},[898,39920,1973],{},[1963,39922,2058],{},[902,39924,38808],{"encoding":904},[198,39926,39928],{"id":39927},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,39930,39931],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,39933,39935],{"className":39934},[886],[888,39936,39937],{"xmlns":890,"display":28566},[892,39938,39939,40124],{},[21254,39940,39941],{"width":28571},[21259,39942,39943,39945,40117,40119],{},[21262,39944],{"width":28576},[21262,39946,39947],{},[21254,39948,39949,40033],{"rowspacing":21256,"columnalign":21257,"columnspacing":1727},[21259,39950,39951,39961],{},[21262,39952,39953],{},[2919,39954,39955],{"scriptlevel":2058,"displaystyle":1915},[2355,39956,39957,39959],{},[898,39958,1973],{},[1963,39960,2875],{},[21262,39962,39963],{},[2919,39964,39965],{"scriptlevel":2058,"displaystyle":1915},[895,39966,39967,39969,39971,39977,39979,39985,39987,39993,39995,39997,40003,40005,40011,40017,40019,40025,40031],{},[895,39968],{},[1664,39970,1676],{},[2355,39972,39973,39975],{},[898,39974,2379],{},[1963,39976,2875],{},[1664,39978,1667],{"stretchy":1666},[2355,39980,39981,39983],{},[898,39982,2398],{},[1963,39984,2875],{},[1664,39986,1916],{"separator":1915},[2355,39988,39989,39991],{},[898,39990,2398],{},[1963,39992,1970],{},[1664,39994,1673],{"stretchy":1666},[1664,39996,1676],{},[2355,39998,39999,40001],{},[898,40000,207],{},[1963,40002,2875],{},[1664,40004,1700],{},[2355,40006,40007,40009],{},[898,40008,1818],{},[1963,40010,2875],{},[2355,40012,40013,40015],{},[898,40014,2398],{},[1963,40016,2875],{},[1664,40018,1700],{},[2355,40020,40021,40023],{},[898,40022,2034],{},[1963,40024,2875],{},[2355,40026,40027,40029],{},[898,40028,2398],{},[1963,40030,1970],{},[1664,40032,1916],{"separator":1915},[21259,40034,40035,40045],{},[21262,40036,40037],{},[2919,40038,40039],{"scriptlevel":2058,"displaystyle":1915},[2355,40040,40041,40043],{},[898,40042,1973],{},[1963,40044,1970],{},[21262,40046,40047],{},[2919,40048,40049],{"scriptlevel":2058,"displaystyle":1915},[895,40050,40051,40053,40055,40061,40063,40069,40071,40077,40079,40081,40087,40089,40095,40101,40103,40109,40115],{},[895,40052],{},[1664,40054,1676],{},[2355,40056,40057,40059],{},[898,40058,2379],{},[1963,40060,1970],{},[1664,40062,1667],{"stretchy":1666},[2355,40064,40065,40067],{},[898,40066,2398],{},[1963,40068,2875],{},[1664,40070,1916],{"separator":1915},[2355,40072,40073,40075],{},[898,40074,2398],{},[1963,40076,1970],{},[1664,40078,1673],{"stretchy":1666},[1664,40080,1676],{},[2355,40082,40083,40085],{},[898,40084,207],{},[1963,40086,1970],{},[1664,40088,1700],{},[2355,40090,40091,40093],{},[898,40092,1818],{},[1963,40094,1970],{},[2355,40096,40097,40099],{},[898,40098,2398],{},[1963,40100,2875],{},[1664,40102,1700],{},[2355,40104,40105,40107],{},[898,40106,2034],{},[1963,40108,1970],{},[2355,40110,40111,40113],{},[898,40112,2398],{},[1963,40114,1970],{},[898,40116,1977],{"mathvariant":1726},[21262,40118],{"width":28576},[21262,40120,40121],{},[1690,40122,40123],{},"(2.6)",[902,40125,40126],{"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}",[37848,40128,40130],{"id":40129},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,40132,40133,40180,40227],{},[123,40134,40135,1343,40157,40179],{},[883,40136,40138],{"className":40137},[886],[888,40139,40140],{"xmlns":890},[892,40141,40142,40154],{},[895,40143,40144,40150,40152],{},[2355,40145,40146,40148],{},[898,40147,207],{},[1963,40149,2875],{},[1664,40151,3984],{},[1963,40153,2058],{},[902,40155,40156],{"encoding":904},"a_1 > 0",[883,40158,40160],{"className":40159},[886],[888,40161,40162],{"xmlns":890},[892,40163,40164,40176],{},[895,40165,40166,40172,40174],{},[2355,40167,40168,40170],{},[898,40169,207],{},[1963,40171,1970],{},[1664,40173,3984],{},[1963,40175,2058],{},[902,40177,40178],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,40181,40182,1343,40204,40226],{},[883,40183,40185],{"className":40184},[886],[888,40186,40187],{"xmlns":890},[892,40188,40189,40201],{},[895,40190,40191,40197,40199],{},[2355,40192,40193,40195],{},[898,40194,1818],{},[1963,40196,2875],{},[1664,40198,4022],{},[1963,40200,2058],{},[902,40202,40203],{"encoding":904},"b_1 \u003C 0",[883,40205,40207],{"className":40206},[886],[888,40208,40209],{"xmlns":890},[892,40210,40211,40223],{},[895,40212,40213,40219,40221],{},[2355,40214,40215,40217],{},[898,40216,2034],{},[1963,40218,1970],{},[1664,40220,4022],{},[1963,40222,2058],{},[902,40224,40225],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,40228,40229,40230,1343,40247,40265,40266],{},"zkřížené koeficienty ",[883,40231,40233],{"className":40232},[886],[888,40234,40235],{"xmlns":890},[892,40236,40237,40245],{},[895,40238,40239],{},[2355,40240,40241,40243],{},[898,40242,2034],{},[1963,40244,2875],{},[902,40246,30299],{"encoding":904},[883,40248,40250],{"className":40249},[886],[888,40251,40252],{"xmlns":890},[892,40253,40254,40262],{},[895,40255,40256],{},[2355,40257,40258,40260],{},[898,40259,1818],{},[1963,40261,1970],{},[902,40263,40264],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,40267,40268,40318],{},[123,40269,40270,40273,40274,1343,40296,1916],{},[38,40271,40272],{},"substituty"," (máslo vs. margarín): ",[883,40275,40277],{"className":40276},[886],[888,40278,40279],{"xmlns":890},[892,40280,40281,40293],{},[895,40282,40283,40289,40291],{},[2355,40284,40285,40287],{},[898,40286,2034],{},[1963,40288,2875],{},[1664,40290,3984],{},[1963,40292,2058],{},[902,40294,40295],{"encoding":904},"c_1 > 0",[883,40297,40299],{"className":40298},[886],[888,40300,40301],{"xmlns":890},[892,40302,40303,40315],{},[895,40304,40305,40311,40313],{},[2355,40306,40307,40309],{},[898,40308,1818],{},[1963,40310,1970],{},[1664,40312,3984],{},[1963,40314,2058],{},[902,40316,40317],{"encoding":904},"b_2 > 0",[123,40319,40320,40323,40324,1343,40346,1977],{},[38,40321,40322],{},"komplementy"," (auto vs. benzín): ",[883,40325,40327],{"className":40326},[886],[888,40328,40329],{"xmlns":890},[892,40330,40331,40343],{},[895,40332,40333,40339,40341],{},[2355,40334,40335,40337],{},[898,40336,2034],{},[1963,40338,2875],{},[1664,40340,4022],{},[1963,40342,2058],{},[902,40344,40345],{"encoding":904},"c_1 \u003C 0",[883,40347,40349],{"className":40348},[886],[888,40350,40351],{"xmlns":890},[892,40352,40353,40365],{},[895,40354,40355,40361,40363],{},[2355,40356,40357,40359],{},[898,40358,1818],{},[1963,40360,1970],{},[1664,40362,4022],{},[1963,40364,2058],{},[902,40366,40367],{"encoding":904},"b_2 \u003C 0",[724,40369,40370],{},"Schematicky:",[724,40372,40373,40376],{},[38,40374,40375],{},"Substituty",[883,40377,40379],{"className":40378},[886],[888,40380,40381],{"xmlns":890},[892,40382,40383,40522],{},[895,40384,40385,40391,40393,40408,40410,40430,40432,40452,40454,40456,40462,40464,40478,40480,40500,40502],{},[2355,40386,40387,40389],{},[898,40388,1973],{},[1963,40390,2875],{},[1664,40392,1676],{},[898,40394,40395],{},[40396,40397,40398,40406],"munder",{},[1664,40399,40400],{},[2355,40401,40402,40404],{},[898,40403,207],{},[1963,40405,2875],{},[1664,40407,1700],{"lspace":1727,"rspace":1727},[1664,40409,1700],{},[898,40411,40412],{},[40396,40413,40414,40428],{},[1664,40415,40416,40422],{},[2355,40417,40418,40420],{},[898,40419,1818],{},[1963,40421,2875],{},[2355,40423,40424,40426],{},[898,40425,2398],{},[1963,40427,2875],{},[1664,40429,1867],{"lspace":1727,"rspace":1727},[1664,40431,1700],{},[898,40433,40434],{},[40396,40435,40436,40450],{},[1664,40437,40438,40444],{},[2355,40439,40440,40442],{},[898,40441,2034],{},[1963,40443,2875],{},[2355,40445,40446,40448],{},[898,40447,2398],{},[1963,40449,1970],{},[1664,40451,1700],{"lspace":1727,"rspace":1727},[1664,40453,1916],{"separator":1915},[6444,40455],{"width":6446},[2355,40457,40458,40460],{},[898,40459,1973],{},[1963,40461,1970],{},[1664,40463,1676],{},[898,40465,40466],{},[40396,40467,40468,40476],{},[1664,40469,40470],{},[2355,40471,40472,40474],{},[898,40473,207],{},[1963,40475,1970],{},[1664,40477,1700],{"lspace":1727,"rspace":1727},[1664,40479,1700],{},[898,40481,40482],{},[40396,40483,40484,40498],{},[1664,40485,40486,40492],{},[2355,40487,40488,40490],{},[898,40489,1818],{},[1963,40491,1970],{},[2355,40493,40494,40496],{},[898,40495,2398],{},[1963,40497,2875],{},[1664,40499,1700],{"lspace":1727,"rspace":1727},[1664,40501,1700],{},[898,40503,40504],{},[40396,40505,40506,40520],{},[1664,40507,40508,40514],{},[2355,40509,40510,40512],{},[898,40511,2034],{},[1963,40513,1970],{},[2355,40515,40516,40518],{},[898,40517,2398],{},[1963,40519,1970],{},[1664,40521,1867],{"lspace":1727,"rspace":1727},[902,40523,40524],{"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}",[724,40526,40527,40530],{},[38,40528,40529],{},"Komplementy",[883,40531,40533],{"className":40532},[886],[888,40534,40535],{"xmlns":890},[892,40536,40537,40675],{},[895,40538,40539,40545,40547,40561,40563,40583,40585,40605,40607,40609,40615,40617,40631,40633,40653,40655],{},[2355,40540,40541,40543],{},[898,40542,1973],{},[1963,40544,2875],{},[1664,40546,1676],{},[898,40548,40549],{},[40396,40550,40551,40559],{},[1664,40552,40553],{},[2355,40554,40555,40557],{},[898,40556,207],{},[1963,40558,2875],{},[1664,40560,1700],{"lspace":1727,"rspace":1727},[1664,40562,1700],{},[898,40564,40565],{},[40396,40566,40567,40581],{},[1664,40568,40569,40575],{},[2355,40570,40571,40573],{},[898,40572,1818],{},[1963,40574,2875],{},[2355,40576,40577,40579],{},[898,40578,2398],{},[1963,40580,2875],{},[1664,40582,1867],{"lspace":1727,"rspace":1727},[1664,40584,1700],{},[898,40586,40587],{},[40396,40588,40589,40603],{},[1664,40590,40591,40597],{},[2355,40592,40593,40595],{},[898,40594,2034],{},[1963,40596,2875],{},[2355,40598,40599,40601],{},[898,40600,2398],{},[1963,40602,1970],{},[1664,40604,1867],{"lspace":1727,"rspace":1727},[1664,40606,1916],{"separator":1915},[6444,40608],{"width":6446},[2355,40610,40611,40613],{},[898,40612,1973],{},[1963,40614,1970],{},[1664,40616,1676],{},[898,40618,40619],{},[40396,40620,40621,40629],{},[1664,40622,40623],{},[2355,40624,40625,40627],{},[898,40626,207],{},[1963,40628,1970],{},[1664,40630,1700],{"lspace":1727,"rspace":1727},[1664,40632,1700],{},[898,40634,40635],{},[40396,40636,40637,40651],{},[1664,40638,40639,40645],{},[2355,40640,40641,40643],{},[898,40642,1818],{},[1963,40644,1970],{},[2355,40646,40647,40649],{},[898,40648,2398],{},[1963,40650,2875],{},[1664,40652,1867],{"lspace":1727,"rspace":1727},[1664,40654,1700],{},[898,40656,40657],{},[40396,40658,40659,40673],{},[1664,40660,40661,40667],{},[2355,40662,40663,40665],{},[898,40664,2034],{},[1963,40666,1970],{},[2355,40668,40669,40671],{},[898,40670,2398],{},[1963,40672,1970],{},[1664,40674,1867],{"lspace":1727,"rspace":1727},[902,40676,40677],{"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}",[37470,40679],{},[115,40681,13624],{"id":37279},[4436,40683,40684],{},[724,40685,40686,40688,40689,37494,40702,37508,40715,40718,40719,6235,40743,40761],{},[883,40687,4723],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,40690,40692],{"className":40691},[886],[888,40693,40694],{"xmlns":890},[892,40695,40696,40700],{},[895,40697,40698],{},[898,40699,1973],{},[902,40701,1973],{"encoding":904},[883,40703,40705],{"className":40704},[886],[888,40706,40707],{"xmlns":890},[892,40708,40709,40713],{},[895,40710,40711],{},[898,40712,2398],{},[902,40714,2398],{"encoding":904},[38,40716,40717],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,40720,40722],{"className":40721},[886],[888,40723,40724],{"xmlns":890},[892,40725,40726,40740],{},[895,40727,40728,40730,40732,40734,40736,40738],{},[898,40729,2398],{},[1664,40731,1676],{},[898,40733,2034],{},[898,40735,1973],{},[1664,40737,1700],{},[898,40739,1695],{},[902,40741,40742],{"encoding":904},"P = cQ + d",[883,40744,40746],{"className":40745},[886],[888,40747,40748],{"xmlns":890},[892,40749,40750,40758],{},[895,40751,40752,40754,40756],{},[898,40753,2034],{},[1664,40755,3984],{},[1963,40757,2058],{},[902,40759,40760],{"encoding":904},"c > 0"," je standardní aproximací.",[198,40763,37564],{"id":40764},"obecný-vícefaktorový-model-1",[724,40766,40767,10588,40770,40773,40774,40787,40788,37396,40801,37410,40814,40827,40828,40842,40843,37439,40856,40869],{},[38,40768,40769],{},"Nabízené množství",[614,40771,40772],{},"quantity supplied",") závisí na ceně ",[883,40775,40777],{"className":40776},[886],[888,40778,40779],{"xmlns":890},[892,40780,40781,40785],{},[895,40782,40783],{},[898,40784,2398],{},[902,40786,2398],{"encoding":904},", cenách výrobních faktorů (práce ",[883,40789,40791],{"className":40790},[886],[888,40792,40793],{"xmlns":890},[892,40794,40795,40799],{},[895,40796,40797],{},[898,40798,10358],{},[902,40800,10358],{"encoding":904},[883,40802,40804],{"className":40803},[886],[888,40805,40806],{"xmlns":890},[892,40807,40808,40812],{},[895,40809,40810],{},[898,40811,10363],{},[902,40813,10363],{"encoding":904},[883,40815,40817],{"className":40816},[886],[888,40818,40819],{"xmlns":890},[892,40820,40821,40825],{},[895,40822,40823],{},[898,40824,4819],{},[902,40826,4819],{"encoding":904},"), očekávání ",[883,40829,40831],{"className":40830},[886],[888,40832,40833],{"xmlns":890},[892,40834,40835,40840],{},[895,40836,40837],{},[898,40838,40839],{},"V",[902,40841,40839],{"encoding":904},", počtu výrobců ",[883,40844,40846],{"className":40845},[886],[888,40847,40848],{"xmlns":890},[892,40849,40850,40854],{},[895,40851,40852],{},[898,40853,37436],{},[902,40855,37436],{"encoding":904},[883,40857,40859],{"className":40858},[886],[888,40860,40861],{"xmlns":890},[892,40862,40863,40867],{},[895,40864,40865],{},[898,40866,37451],{},[902,40868,37451],{"encoding":904}," a dalších:",[883,40871,40873],{"className":40872},[886],[888,40874,40875],{"xmlns":890,"display":28566},[892,40876,40877,40936],{},[21254,40878,40879],{"width":28571},[21259,40880,40881,40883,40929,40931],{},[21262,40882],{"width":28576},[21262,40884,40885],{},[895,40886,40887,40889,40891,40893,40895,40897,40899,40901,40903,40905,40907,40909,40911,40913,40915,40917,40919,40921,40923,40925,40927],{},[898,40888,1973],{},[1664,40890,1676],{},[898,40892,2351],{},[1664,40894,1667],{"stretchy":1666},[898,40896,2398],{},[1664,40898,1916],{"separator":1915},[898,40900,10358],{},[1664,40902,1916],{"separator":1915},[898,40904,10363],{},[1664,40906,1916],{"separator":1915},[898,40908,4819],{},[1664,40910,1916],{"separator":1915},[898,40912,40839],{},[1664,40914,1916],{"separator":1915},[898,40916,37436],{},[1664,40918,1916],{"separator":1915},[898,40920,37451],{},[1664,40922,1916],{"separator":1915},[1664,40924,10209],{},[1664,40926,1673],{"stretchy":1666},[898,40928,1977],{"mathvariant":1726},[21262,40930],{"width":28576},[21262,40932,40933],{},[1690,40934,40935],{},"(2.7)",[902,40937,40938],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,40940,38916,40941,10588,40944,40947],{},[38,40942,40943],{},"funkce nabídky",[614,40945,40946],{},"supply function",") v širším slova smyslu.",[198,40949,40951],{"id":40950},"jednofaktorový-model","Jednofaktorový model",[724,40953,40954],{},"V nejpřirozenějším jednofaktorovém modelu",[883,40956,40958],{"className":40957},[886],[888,40959,40960],{"xmlns":890,"display":28566},[892,40961,40962,41013],{},[21254,40963,40964],{"width":28571},[21259,40965,40966,40968,41006,41008],{},[21262,40967],{"width":28576},[21262,40969,40970],{},[895,40971,40972,40974,40976,40978,40980,40982,40984,40986,40988,40990,40992,40994,40996,40998,41000,41002,41004],{},[898,40973,1973],{},[1664,40975,1676],{},[898,40977,2351],{},[1664,40979,1667],{"stretchy":1666},[898,40981,2398],{},[1664,40983,1673],{"stretchy":1666},[1664,40985,1916],{"separator":1915},[6444,40987],{"width":6446},[1690,40989,37917],{},[6444,40991],{"width":6446},[898,40993,2398],{},[1664,40995,1676],{},[898,40997,2351],{},[1664,40999,1667],{"stretchy":1666},[898,41001,1973],{},[1664,41003,1673],{"stretchy":1666},[898,41005,1977],{"mathvariant":1726},[21262,41007],{"width":28576},[21262,41009,41010],{},[1690,41011,41012],{},"(2.8)",[902,41014,41015],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,41017,41018,41019,10588,41022,4488],{},"Graf je ",[38,41020,41021],{},"křivka nabídky",[614,41023,41024],{},"supply curve",[37848,41026,41028],{"id":41027},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[4436,41030,41031],{},[724,41032,41033],{},[38,41034,37963,41035,41048,41049,38018],{},[883,41036,41038],{"className":41037},[886],[888,41039,41040],{"xmlns":890},[892,41041,41042,41046],{},[895,41043,41044],{},[898,41045,2398],{},[902,41047,2398],{"encoding":904},", pak nabízené množství ",[883,41050,41052],{"className":41051},[886],[888,41053,41054],{"xmlns":890},[892,41055,41056,41060],{},[895,41057,41058],{},[898,41059,1973],{},[902,41061,1973],{"encoding":904},[724,41063,41064,41065,41090,41091,41121,41122,41139],{},"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 ",[883,41066,41068],{"className":41067},[886],[888,41069,41070],{"xmlns":890},[892,41071,41072,41088],{},[895,41073,41074,41076,41078,41080,41086],{},[1664,41075,1837],{"stretchy":1666},[1963,41077,2058],{},[1664,41079,1916],{"separator":1915},[2355,41081,41082,41084],{},[898,41083,2398],{},[1963,41085,2058],{},[1664,41087,1850],{"stretchy":1666},[902,41089,38103],{"encoding":904}," na svislé ose (případně z ",[883,41092,41094],{"className":41093},[886],[888,41095,41096],{"xmlns":890},[892,41097,41098,41118],{},[895,41099,41100,41102,41108,41110,41116],{},[1664,41101,1837],{"stretchy":1666},[2355,41103,41104,41106],{},[898,41105,1973],{},[1963,41107,2875],{},[1664,41109,1916],{"separator":1915},[2355,41111,41112,41114],{},[898,41113,2398],{},[1963,41115,2875],{},[1664,41117,1850],{"stretchy":1666},[902,41119,41120],{"encoding":904},"[Q_1, P_1]","), kde ",[883,41123,41125],{"className":41124},[886],[888,41126,41127],{"xmlns":890},[892,41128,41129,41137],{},[895,41130,41131],{},[2355,41132,41133,41135],{},[898,41134,2398],{},[1963,41136,2058],{},[902,41138,39448],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,41141,41142],{},[614,41143,41144,41145,4293,41158,1977],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,41146,41148],{"className":41147},[886],[888,41149,41150],{"xmlns":890},[892,41151,41152,41156],{},[895,41153,41154],{},[898,41155,2351],{},[902,41157,2351],{"encoding":904},[883,41159,41161],{"className":41160},[886],[888,41162,41163],{"xmlns":890},[892,41164,41165,41177],{},[895,41166,41167,41169,41171,41173,41175],{},[1664,41168,1667],{"stretchy":1666},[898,41170,1973],{},[1664,41172,1916],{"separator":1915},[898,41174,2398],{},[1664,41176,1673],{"stretchy":1666},[902,41178,38191],{"encoding":904},[37848,41180,41182],{"id":41181},"lineární-model-nabídky","Lineární model nabídky",[883,41184,41186],{"className":41185},[886],[888,41187,41188],{"xmlns":890,"display":28566},[892,41189,41190,41229],{},[21254,41191,41192],{"width":28571},[21259,41193,41194,41196,41222,41224],{},[21262,41195],{"width":28576},[21262,41197,41198],{},[895,41199,41200,41202,41204,41206,41208,41210,41212,41214,41216,41218,41220],{},[898,41201,2398],{},[1664,41203,1676],{},[898,41205,2034],{},[898,41207,1973],{},[1664,41209,1700],{},[898,41211,1695],{},[1664,41213,1916],{"separator":1915},[6444,41215],{"width":6446},[898,41217,2034],{},[1664,41219,3984],{},[1963,41221,12959],{},[21262,41223],{"width":28576},[21262,41225,41226],{},[1690,41227,41228],{},"(2.9)",[902,41230,41231],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,41233,41234,41235,41271,41272,41285],{},"Alternativně ",[883,41236,41238],{"className":41237},[886],[888,41239,41240],{"xmlns":890},[892,41241,41242,41268],{},[895,41243,41244,41246,41248,41256,41258,41260],{},[898,41245,1973],{},[1664,41247,1676],{},[2919,41249,41250],{"scriptlevel":2058,"displaystyle":1666},[2922,41251,41252,41254],{},[1963,41253,2875],{},[898,41255,2034],{},[898,41257,2398],{},[1664,41259,1867],{},[2919,41261,41262],{"scriptlevel":2058,"displaystyle":1666},[2922,41263,41264,41266],{},[898,41265,1695],{},[898,41267,2034],{},[902,41269,41270],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,41273,41275],{"className":41274},[886],[888,41276,41277],{"xmlns":890},[892,41278,41279,41283],{},[895,41280,41281],{},[898,41282,2398],{},[902,41284,2398],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[38425,41287,41289],{"id":41288},"příklad-25","Příklad 2.5",[724,41291,41292,41294,41295,1977],{},[38,41293,38433],{}," Lineární nabídka ",[883,41296,41298],{"className":41297},[886],[888,41299,41300],{"xmlns":890},[892,41301,41302,41316],{},[895,41303,41304,41306,41308,41310,41312,41314],{},[898,41305,2398],{},[1664,41307,1676],{},[1963,41309,5575],{},[898,41311,1973],{},[1664,41313,1700],{},[1963,41315,5570],{},[902,41317,41318],{"encoding":904},"P = 0{,}5Q + 25",[724,41320,41321,41323,41324,1977],{},[38,41322,38465],{}," Alternativní tvar ",[883,41325,41327],{"className":41326},[886],[888,41328,41329],{"xmlns":890},[892,41330,41331,41345],{},[895,41332,41333,41335,41337,41339,41341,41343],{},[898,41334,1973],{},[1664,41336,1676],{},[1963,41338,1970],{},[898,41340,2398],{},[1664,41342,1867],{},[1963,41344,3696],{},[902,41346,41347],{"encoding":904},"Q = 2P - 50",[16,41349,41350,41375],{},[19,41351,41352],{},[22,41353,41354,41369,41371,41373],{},[25,41355,41356],{},[883,41357,41359],{"className":41358},[886],[888,41360,41361],{"xmlns":890},[892,41362,41363,41367],{},[895,41364,41365],{},[898,41366,2398],{},[902,41368,2398],{"encoding":904},[25,41370,38519],{},[25,41372,15537],{},[25,41374,5777],{},[30,41376,41377],{},[22,41378,41379,41394,41396,41398],{},[35,41380,41381],{},[883,41382,41384],{"className":41383},[886],[888,41385,41386],{"xmlns":890},[892,41387,41388,41392],{},[895,41389,41390],{},[898,41391,1973],{},[902,41393,1973],{"encoding":904},[35,41395,3442],{},[35,41397,9599],{},[35,41399,38519],{},[198,41401,41403,41404,1673],{"id":41402},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,41405,41406],{},"shift of supply",[724,41408,41409,41410,41413,41414,41431,41432,41457,41458,1977],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,41411,41412],{},"doprava",": při stejné ceně ",[883,41415,41417],{"className":41416},[886],[888,41418,41419],{"xmlns":890},[892,41420,41421,41429],{},[895,41422,41423],{},[2355,41424,41425,41427],{},[898,41426,2398],{},[1963,41428,2058],{},[902,41430,39448],{"encoding":904}," vyrobí výrobce větší ",[883,41433,41435],{"className":41434},[886],[888,41436,41437],{"xmlns":890},[892,41438,41439,41455],{},[895,41440,41441,41447,41449],{},[2355,41442,41443,41445],{},[898,41444,1973],{},[1963,41446,2875],{},[1664,41448,3984],{},[2355,41450,41451,41453],{},[898,41452,1973],{},[1963,41454,2058],{},[902,41456,39561],{"encoding":904},"); zdražení vstupů posune křivku ",[38,41459,41460],{},"doleva",[724,41462,41463],{},[614,41464,41465,41466,41479,41480,41498,41499,41517,41518,1977],{},"Obrázek 2.11: Původní ",[883,41467,41469],{"className":41468},[886],[888,41470,41471],{"xmlns":890},[892,41472,41473,41477],{},[895,41474,41475],{},[898,41476,2351],{},[902,41478,2351],{"encoding":904},", posunuté ",[883,41481,41483],{"className":41482},[886],[888,41484,41485],{"xmlns":890},[892,41486,41487,41495],{},[895,41488,41489],{},[2355,41490,41491,41493],{},[898,41492,2351],{},[1963,41494,2875],{},[902,41496,41497],{"encoding":904},"S_1"," (doprava) a ",[883,41500,41502],{"className":41501},[886],[888,41503,41504],{"xmlns":890},[892,41505,41506,41514],{},[895,41507,41508],{},[2355,41509,41510,41512],{},[898,41511,2351],{},[1963,41513,1970],{},[902,41515,41516],{"encoding":904},"S_2"," (doleva) v ",[883,41519,41521],{"className":41520},[886],[888,41522,41523],{"xmlns":890},[892,41524,41525,41537],{},[895,41526,41527,41529,41531,41533,41535],{},[1664,41528,1667],{"stretchy":1666},[898,41530,1973],{},[1664,41532,1916],{"separator":1915},[898,41534,2398],{},[1664,41536,1673],{"stretchy":1666},[902,41538,38191],{"encoding":904},[38425,41540,41542],{"id":41541},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,41544,41545,41547,41548,41572,41573,1977],{},[38,41546,38433],{}," Nabídka ",[883,41549,41551],{"className":41550},[886],[888,41552,41553],{"xmlns":890},[892,41554,41555,41569],{},[895,41556,41557,41559,41561,41563,41565,41567],{},[898,41558,2398],{},[1664,41560,1676],{},[898,41562,2351],{},[1664,41564,1667],{"stretchy":1666},[898,41566,1973],{},[1664,41568,1673],{"stretchy":1666},[902,41570,41571],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,41574,41576],{"className":41575},[886],[888,41577,41578],{"xmlns":890},[892,41579,41580,41584],{},[895,41581,41582],{},[898,41583,1991],{},[902,41585,1991],{"encoding":904},[724,41587,41588,41590,41591,41604,41605,41623,41624,41652],{},[38,41589,38465],{}," Spotřebitel zaplatí ",[883,41592,41594],{"className":41593},[886],[888,41595,41596],{"xmlns":890},[892,41597,41598,41602],{},[895,41599,41600],{},[898,41601,2398],{},[902,41603,2398],{"encoding":904},", výrobce obdrží ",[883,41606,41608],{"className":41607},[886],[888,41609,41610],{"xmlns":890},[892,41611,41612,41620],{},[895,41613,41614,41616,41618],{},[898,41615,2398],{},[1664,41617,1867],{},[898,41619,1991],{},[902,41621,41622],{"encoding":904},"P - T",". Z podmínky ",[883,41625,41627],{"className":41626},[886],[888,41628,41629],{"xmlns":890},[892,41630,41631,41649],{},[895,41632,41633,41635,41637,41639,41641,41643,41645,41647],{},[898,41634,2398],{},[1664,41636,1867],{},[898,41638,1991],{},[1664,41640,1676],{},[898,41642,2351],{},[1664,41644,1667],{"stretchy":1666},[898,41646,1973],{},[1664,41648,1673],{"stretchy":1666},[902,41650,41651],{"encoding":904},"P - T = S(Q)"," plyne",[883,41654,41656],{"className":41655},[886],[888,41657,41658],{"xmlns":890,"display":28566},[892,41659,41660,41694],{},[895,41661,41662,41664,41666,41672,41674,41676,41678,41680,41682,41684,41686,41688,41690,41692],{},[898,41663,2398],{},[1664,41665,1676],{},[2355,41667,41668,41670],{},[898,41669,2351],{},[1963,41671,2875],{},[1664,41673,1667],{"stretchy":1666},[898,41675,1973],{},[1664,41677,1673],{"stretchy":1666},[1664,41679,1676],{},[898,41681,2351],{},[1664,41683,1667],{"stretchy":1666},[898,41685,1973],{},[1664,41687,1673],{"stretchy":1666},[1664,41689,1700],{},[898,41691,1991],{},[898,41693,1977],{"mathvariant":1726},[902,41695,41696],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,41698,41699,41700,41713,41714,1885,41727,41730,41731,4454,41751,1762,41769,1977],{},"Křivka ",[883,41701,41703],{"className":41702},[886],[888,41704,41705],{"xmlns":890},[892,41706,41707,41711],{},[895,41708,41709],{},[898,41710,2351],{},[902,41712,2351],{"encoding":904}," se tedy posune o ",[883,41715,41717],{"className":41716},[886],[888,41718,41719],{"xmlns":890},[892,41720,41721,41725],{},[895,41722,41723],{},[898,41724,1991],{},[902,41726,1991],{"encoding":904},[38,41728,41729],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,41732,41734],{"className":41733},[886],[888,41735,41736],{"xmlns":890},[892,41737,41738,41748],{},[895,41739,41740,41742,41744,41746],{},[898,41741,2398],{},[1664,41743,1676],{},[1963,41745,1970],{},[898,41747,1973],{},[902,41749,41750],{"encoding":904},"P = 2Q",[883,41752,41754],{"className":41753},[886],[888,41755,41756],{"xmlns":890},[892,41757,41758,41766],{},[895,41759,41760,41762,41764],{},[898,41761,1991],{},[1664,41763,1676],{},[1963,41765,2833],{},[902,41767,41768],{"encoding":904},"T = 6",[883,41770,41772],{"className":41771},[886],[888,41773,41774],{"xmlns":890},[892,41775,41776,41798],{},[895,41777,41778,41784,41786,41788,41790,41792,41794,41796],{},[2355,41779,41780,41782],{},[898,41781,2351],{},[1963,41783,2875],{},[1664,41785,2087],{},[898,41787,2398],{},[1664,41789,1676],{},[1963,41791,1970],{},[898,41793,1973],{},[1664,41795,1700],{},[1963,41797,2833],{},[902,41799,41800],{"encoding":904},"S_1: P = 2Q + 6",[724,41802,41803],{},[614,41804,41805,41806,41819],{},"Obrázek 2.12: Posun nabídky o ",[883,41807,41809],{"className":41808},[886],[888,41810,41811],{"xmlns":890},[892,41812,41813,41817],{},[895,41814,41815],{},[898,41816,1991],{},[902,41818,1991],{"encoding":904}," svisle nahoru.",[37470,41821],{},[115,41823,41825],{"id":41824},"tržní-rovnováha","Tržní rovnováha",[4436,41827,41828],{},[724,41829,41830,41832,41833,1885,41836,41868,41869,1343,41892,41915,41916,41919,41920,41933],{},[883,41831,4723],{}," TL;DR\nV ",[38,41834,41835],{},"rovnovážném bodě",[883,41837,41839],{"className":41838},[886],[888,41840,41841],{"xmlns":890},[892,41842,41843,41865],{},[895,41844,41845,41847,41849,41855,41857,41863],{},[898,41846,4819],{},[1664,41848,1837],{"stretchy":1666},[1720,41850,41851,41853],{},[898,41852,1973],{},[898,41854,4819],{},[1664,41856,1916],{"separator":1915},[1720,41858,41859,41861],{},[898,41860,2398],{},[898,41862,4819],{},[1664,41864,1850],{"stretchy":1666},[902,41866,41867],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,41870,41872],{"className":41871},[886],[888,41873,41874],{"xmlns":890},[892,41875,41876,41890],{},[895,41877,41878,41880,41882,41884,41886,41888],{},[898,41879,2398],{},[1664,41881,1676],{},[898,41883,2379],{},[1664,41885,1667],{"stretchy":1666},[898,41887,1973],{},[1664,41889,1673],{"stretchy":1666},[902,41891,5206],{"encoding":904},[883,41893,41895],{"className":41894},[886],[888,41896,41897],{"xmlns":890},[892,41898,41899,41913],{},[895,41900,41901,41903,41905,41907,41909,41911],{},[898,41902,2398],{},[1664,41904,1676],{},[898,41906,2351],{},[1664,41908,1667],{"stretchy":1666},[898,41910,1973],{},[1664,41912,1673],{"stretchy":1666},[902,41914,41571],{"encoding":904},". Čtyři ",[38,41917,41918],{},"pravidla komparativní statiky"," popisují, jak se ",[883,41921,41923],{"className":41922},[886],[888,41924,41925],{"xmlns":890},[892,41926,41927,41931],{},[895,41928,41929],{},[898,41930,4819],{},[902,41932,4819],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,41935,41937],{"id":41936},"definice","Definice",[724,41939,41940,10588,41942,41945,41946,1885,41949,41967,41968,41999,42000,10588,42003,4488],{},[38,41941,41825],{},[614,41943,41944],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,41947,41948],{},"rovnovážné ceně",[883,41950,41952],{"className":41951},[886],[888,41953,41954],{"xmlns":890},[892,41955,41956,41964],{},[895,41957,41958],{},[1720,41959,41960,41962],{},[898,41961,2398],{},[898,41963,4819],{},[902,41965,41966],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,41969,41971],{"className":41970},[886],[888,41972,41973],{"xmlns":890},[892,41974,41975,41997],{},[895,41976,41977,41979,41981,41987,41989,41995],{},[898,41978,4819],{},[1664,41980,1837],{"stretchy":1666},[1720,41982,41983,41985],{},[898,41984,1973],{},[898,41986,4819],{},[1664,41988,1916],{"separator":1915},[1720,41990,41991,41993],{},[898,41992,2398],{},[898,41994,4819],{},[1664,41996,1850],{"stretchy":1666},[902,41998,41867],{"encoding":904}," se nazývá ",[38,42001,42002],{},"rovnovážný bod",[614,42004,42005],{},"equilibrium point",[724,42007,42008,42009,1343,42032,1977],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,42010,42012],{"className":42011},[886],[888,42013,42014],{"xmlns":890},[892,42015,42016,42030],{},[895,42017,42018,42020,42022,42024,42026,42028],{},[898,42019,2398],{},[1664,42021,1676],{},[898,42023,2379],{},[1664,42025,1667],{"stretchy":1666},[898,42027,1973],{},[1664,42029,1673],{"stretchy":1666},[902,42031,5206],{"encoding":904},[883,42033,42035],{"className":42034},[886],[888,42036,42037],{"xmlns":890},[892,42038,42039,42053],{},[895,42040,42041,42043,42045,42047,42049,42051],{},[898,42042,2398],{},[1664,42044,1676],{},[898,42046,2351],{},[1664,42048,1667],{"stretchy":1666},[898,42050,1973],{},[1664,42052,1673],{"stretchy":1666},[902,42054,41571],{"encoding":904},[724,42056,42057],{},[1928,42058],{"alt":42059,"className":42060,"src":42061},"imek-poptavka-nabidka-rovnovaha",[210,1932],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,42063,42064],{},[614,42065,42066,42067,42080,42081,14510,42094,42115,42116,1977],{},"Obrázek 2.13: Klesající ",[883,42068,42070],{"className":42069},[886],[888,42071,42072],{"xmlns":890},[892,42073,42074,42078],{},[895,42075,42076],{},[898,42077,2379],{},[902,42079,2379],{"encoding":904}," a rostoucí ",[883,42082,42084],{"className":42083},[886],[888,42085,42086],{"xmlns":890},[892,42087,42088,42092],{},[895,42089,42090],{},[898,42091,2351],{},[902,42093,2351],{"encoding":904},[883,42095,42097],{"className":42096},[886],[888,42098,42099],{"xmlns":890},[892,42100,42101,42113],{},[895,42102,42103,42105,42107,42109,42111],{},[1664,42104,1667],{"stretchy":1666},[898,42106,1973],{},[1664,42108,1916],{"separator":1915},[898,42110,2398],{},[1664,42112,1673],{"stretchy":1666},[902,42114,38191],{"encoding":904}," protínající se v ",[883,42117,42119],{"className":42118},[886],[888,42120,42121],{"xmlns":890},[892,42122,42123,42145],{},[895,42124,42125,42127,42129,42135,42137,42143],{},[898,42126,4819],{},[1664,42128,1837],{"stretchy":1666},[1720,42130,42131,42133],{},[898,42132,1973],{},[898,42134,4819],{},[1664,42136,1916],{"separator":1915},[1720,42138,42139,42141],{},[898,42140,2398],{},[898,42142,4819],{},[1664,42144,1850],{"stretchy":1666},[902,42146,41867],{"encoding":904},[198,42148,42150],{"id":42149},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,42152,42153,42155,42156,42190,42191,1977],{},[38,42154,38433],{}," Poptávka ",[883,42157,42159],{"className":42158},[886],[888,42160,42161],{"xmlns":890},[892,42162,42163,42187],{},[895,42164,42165,42167,42169,42171,42177,42179,42181,42183,42185],{},[898,42166,2398],{},[1664,42168,1676],{},[1664,42170,1867],{},[1720,42172,42173,42175],{},[898,42174,1973],{},[1963,42176,1970],{},[1664,42178,1867],{},[1963,42180,3442],{},[898,42182,1973],{},[1664,42184,1700],{},[1963,42186,9367],{},[902,42188,42189],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,42192,42194],{"className":42193},[886],[888,42195,42196],{"xmlns":890},[892,42197,42198,42220],{},[895,42199,42200,42202,42204,42210,42212,42214,42216,42218],{},[898,42201,2398],{},[1664,42203,1676],{},[1720,42205,42206,42208],{},[898,42207,1973],{},[1963,42209,1970],{},[1664,42211,1700],{},[1963,42213,23446],{},[898,42215,1973],{},[1664,42217,1700],{},[1963,42219,33046],{},[902,42221,42222],{"encoding":904},"P = Q^2 + 14Q + 22",[724,42224,42225,42227],{},[38,42226,38465],{}," Z rovnosti",[883,42229,42231],{"className":42230},[886],[888,42232,42233],{"xmlns":890,"display":28566},[892,42234,42235,42273],{},[895,42236,42237,42239,42245,42247,42249,42251,42253,42255,42257,42263,42265,42267,42269,42271],{},[1664,42238,1867],{},[1720,42240,42241,42243],{},[898,42242,1973],{},[1963,42244,1970],{},[1664,42246,1867],{},[1963,42248,3442],{},[898,42250,1973],{},[1664,42252,1700],{},[1963,42254,9367],{},[1664,42256,1676],{},[1720,42258,42259,42261],{},[898,42260,1973],{},[1963,42262,1970],{},[1664,42264,1700],{},[1963,42266,23446],{},[898,42268,1973],{},[1664,42270,1700],{},[1963,42272,33046],{},[902,42274,42275],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,42277,42278,42279,42314,42315,42348,42349,42366,42367,42380,42381,1343,42403,42440,42441,1977],{},"dostaneme ",[883,42280,42282],{"className":42281},[886],[888,42283,42284],{"xmlns":890},[892,42285,42286,42311],{},[895,42287,42288,42290,42296,42298,42301,42303,42305,42307,42309],{},[1963,42289,1970],{},[1720,42291,42292,42294],{},[898,42293,1973],{},[1963,42295,1970],{},[1664,42297,1700],{},[1963,42299,42300],{},"24",[898,42302,1973],{},[1664,42304,1867],{},[1963,42306,6183],{},[1664,42308,1676],{},[1963,42310,2058],{},[902,42312,42313],{"encoding":904},"2Q^2 + 24Q - 128 = 0",", resp. ",[883,42316,42318],{"className":42317},[886],[888,42319,42320],{"xmlns":890},[892,42321,42322,42345],{},[895,42323,42324,42330,42332,42334,42336,42338,42341,42343],{},[1720,42325,42326,42328],{},[898,42327,1973],{},[1963,42329,1970],{},[1664,42331,1700],{},[1963,42333,4084],{},[898,42335,1973],{},[1664,42337,1867],{},[1963,42339,42340],{},"64",[1664,42342,1676],{},[1963,42344,2058],{},[902,42346,42347],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,42350,42352],{"className":42351},[886],[888,42353,42354],{"xmlns":890},[892,42355,42356,42363],{},[895,42357,42358,42360],{},[1664,42359,1867],{},[1963,42361,42362],{},"16",[902,42364,42365],{"encoding":904},"-16"," (nevyhovuje) a ",[883,42368,42370],{"className":42369},[886],[888,42371,42372],{"xmlns":890},[892,42373,42374,42378],{},[895,42375,42376],{},[1963,42377,2944],{},[902,42379,2944],{"encoding":904},". Tedy ",[883,42382,42384],{"className":42383},[886],[888,42385,42386],{"xmlns":890},[892,42387,42388,42400],{},[895,42389,42390,42396,42398],{},[1720,42391,42392,42394],{},[898,42393,1973],{},[898,42395,4819],{},[1664,42397,1676],{},[1963,42399,2944],{},[902,42401,42402],{"encoding":904},"Q^E = 4",[883,42404,42406],{"className":42405},[886],[888,42407,42408],{"xmlns":890},[892,42409,42410,42437],{},[895,42411,42412,42418,42420,42422,42424,42426,42428,42430,42432,42434],{},[1720,42413,42414,42416],{},[898,42415,2398],{},[898,42417,4819],{},[1664,42419,1676],{},[1664,42421,1867],{},[1963,42423,42362],{},[1664,42425,1867],{},[1963,42427,5777],{},[1664,42429,1700],{},[1963,42431,9367],{},[1664,42433,1676],{},[1963,42435,42436],{},"94",[902,42438,42439],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,42442,42444],{"className":42443},[886],[888,42445,42446],{"xmlns":890},[892,42447,42448,42462],{},[895,42449,42450,42452,42454,42456,42458,42460],{},[898,42451,4819],{},[1664,42453,1837],{"stretchy":1666},[1963,42455,2944],{},[1664,42457,1916],{"separator":1915},[1963,42459,42436],{},[1664,42461,1850],{"stretchy":1666},[902,42463,42464],{"encoding":904},"E[4, 94]",[198,42466,42468],{"id":42467},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,42470,42471,42473],{},[38,42472,38433],{}," Poptávky a nabídky dvou zboží",[883,42475,42477],{"className":42476},[886],[888,42478,42479],{"xmlns":890,"display":28566},[892,42480,42481,42647],{},[21254,42482,42485,42573],{"rowspacing":21256,"columnalign":42483,"columnspacing":42484},"right left right left","0em 1em 0em",[21259,42486,42487,42497,42529,42539],{},[21262,42488,42489],{},[2919,42490,42491],{"scriptlevel":2058,"displaystyle":1915},[2355,42492,42493,42495],{},[898,42494,1973],{},[1963,42496,2875],{},[21262,42498,42499],{},[2919,42500,42501],{"scriptlevel":2058,"displaystyle":1915},[895,42502,42503,42505,42507,42509,42511,42513,42519,42521,42527],{},[895,42504],{},[1664,42506,1676],{},[1963,42508,5777],{},[1664,42510,1867],{},[1963,42512,2826],{},[2355,42514,42515,42517],{},[898,42516,2398],{},[1963,42518,2875],{},[1664,42520,1867],{},[2355,42522,42523,42525],{},[898,42524,2398],{},[1963,42526,1970],{},[1664,42528,1916],{"separator":1915},[21262,42530,42531],{},[2919,42532,42533],{"scriptlevel":2058,"displaystyle":1915},[2355,42534,42535,42537],{},[898,42536,1973],{},[1963,42538,1970],{},[21262,42540,42541],{},[2919,42542,42543],{"scriptlevel":2058,"displaystyle":1915},[895,42544,42545,42547,42549,42551,42553,42555,42561,42563,42565,42571],{},[895,42546],{},[1664,42548,1676],{},[1963,42550,3696],{},[1664,42552,1867],{},[1963,42554,1970],{},[2355,42556,42557,42559],{},[898,42558,2398],{},[1963,42560,2875],{},[1664,42562,1867],{},[1963,42564,2944],{},[2355,42566,42567,42569],{},[898,42568,2398],{},[1963,42570,1970],{},[1664,42572,1916],{"separator":1915},[21259,42574,42575,42585,42611,42621],{},[21262,42576,42577],{},[2919,42578,42579],{"scriptlevel":2058,"displaystyle":1915},[2355,42580,42581,42583],{},[898,42582,1973],{},[1963,42584,2875],{},[21262,42586,42587],{},[2919,42588,42589],{"scriptlevel":2058,"displaystyle":1915},[895,42590,42591,42593,42595,42597,42599,42601,42603,42609],{},[895,42592],{},[1664,42594,1676],{},[1664,42596,1867],{},[1963,42598,2774],{},[1664,42600,1700],{},[1963,42602,2944],{},[2355,42604,42605,42607],{},[898,42606,2398],{},[1963,42608,2875],{},[1664,42610,1916],{"separator":1915},[21262,42612,42613],{},[2919,42614,42615],{"scriptlevel":2058,"displaystyle":1915},[2355,42616,42617,42619],{},[898,42618,1973],{},[1963,42620,1970],{},[21262,42622,42623],{},[2919,42624,42625],{"scriptlevel":2058,"displaystyle":1915},[895,42626,42627,42629,42631,42633,42635,42637,42639,42645],{},[895,42628],{},[1664,42630,1676],{},[1664,42632,1867],{},[1963,42634,24701],{},[1664,42636,1700],{},[1963,42638,2774],{},[2355,42640,42641,42643],{},[898,42642,2398],{},[1963,42644,1970],{},[898,42646,1977],{"mathvariant":1726},[902,42648,42649],{"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}",[724,42651,42652,42654],{},[38,42653,38465],{}," Z rovností poptávek a nabídek dostaneme",[883,42656,42658],{"className":42657},[886],[888,42659,42660],{"xmlns":890,"display":28566},[892,42661,42662,42711],{},[895,42663,42664,42666,42672,42674,42680,42682,42684,42686,42688,42690,42696,42698,42700,42706,42708],{},[1963,42665,4567],{},[2355,42667,42668,42670],{},[898,42669,2398],{},[1963,42671,2875],{},[1664,42673,1700],{},[2355,42675,42676,42678],{},[898,42677,2398],{},[1963,42679,1970],{},[1664,42681,1676],{},[1963,42683,21703],{},[1664,42685,1916],{"separator":1915},[6444,42687],{"width":6446},[1963,42689,1970],{},[2355,42691,42692,42694],{},[898,42693,2398],{},[1963,42695,2875],{},[1664,42697,1700],{},[1963,42699,24701],{},[2355,42701,42702,42704],{},[898,42703,2398],{},[1963,42705,1970],{},[1664,42707,1676],{},[1963,42709,42710],{},"57.",[902,42712,42713],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,42715,42716,42717,1343,42741,42765,42766,1343,42791,42815,42816,42818],{},"Řešením je ",[883,42718,42720],{"className":42719},[886],[888,42721,42722],{"xmlns":890},[892,42723,42724,42738],{},[895,42725,42726,42734,42736],{},[1810,42727,42728,42730,42732],{},[898,42729,2398],{},[1963,42731,2875],{},[898,42733,4819],{},[1664,42735,1676],{},[1963,42737,2944],{},[902,42739,42740],{"encoding":904},"P_1^E = 4",[883,42742,42744],{"className":42743},[886],[888,42745,42746],{"xmlns":890},[892,42747,42748,42762],{},[895,42749,42750,42758,42760],{},[1810,42751,42752,42754,42756],{},[898,42753,2398],{},[1963,42755,1970],{},[898,42757,4819],{},[1664,42759,1676],{},[1963,42761,24701],{},[902,42763,42764],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,42767,42769],{"className":42768},[886],[888,42770,42771],{"xmlns":890},[892,42772,42773,42788],{},[895,42774,42775,42783,42785],{},[1810,42776,42777,42779,42781],{},[898,42778,1973],{},[1963,42780,2875],{},[898,42782,4819],{},[1664,42784,1676],{},[1963,42786,42787],{},"13",[902,42789,42790],{"encoding":904},"Q_1^E = 13",[883,42792,42794],{"className":42793},[886],[888,42795,42796],{"xmlns":890},[892,42797,42798,42812],{},[895,42799,42800,42808,42810],{},[1810,42801,42802,42804,42806],{},[898,42803,1973],{},[1963,42805,1970],{},[898,42807,4819],{},[1664,42809,1676],{},[1963,42811,23446],{},[902,42813,42814],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,42817,40322],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,42820,42822],{"id":42821},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,42824,42825,42826,42843,42844,10588,42847,4488],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,42827,42829],{"className":42828},[886],[888,42830,42831],{"xmlns":890},[892,42832,42833,42841],{},[895,42834,42835],{},[1720,42836,42837,42839],{},[898,42838,2398],{},[898,42840,4819],{},[902,42842,41966],{"encoding":904},"; mechanismus popisuje ",[38,42845,42846],{},"teorém pavučiny",[614,42848,42849],{},"cobweb model",[198,42851,42853],{"id":42852},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,42855,42856],{},[1928,42857],{"alt":42858,"className":42859,"src":42860},"imek-komparativni-statika-4pripady",[210,1932],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[4436,42862,42863,42904,42944,42984],{},[724,42864,42865,42868,42869,6756,42886,1977],{},[38,42866,42867],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,42870,42872],{"className":42871},[886],[888,42873,42874],{"xmlns":890},[892,42875,42876,42884],{},[895,42877,42878],{},[1720,42879,42880,42882],{},[898,42881,2398],{},[898,42883,4819],{},[902,42885,41966],{"encoding":904},[883,42887,42889],{"className":42888},[886],[888,42890,42891],{"xmlns":890},[892,42892,42893,42901],{},[895,42894,42895],{},[1720,42896,42897,42899],{},[898,42898,1973],{},[898,42900,4819],{},[902,42902,42903],{"encoding":904},"Q^E",[724,42905,42906,42909,42910,6756,42927,1977],{},[38,42907,42908],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,42911,42913],{"className":42912},[886],[888,42914,42915],{"xmlns":890},[892,42916,42917,42925],{},[895,42918,42919],{},[1720,42920,42921,42923],{},[898,42922,2398],{},[898,42924,4819],{},[902,42926,41966],{"encoding":904},[883,42928,42930],{"className":42929},[886],[888,42931,42932],{"xmlns":890},[892,42933,42934,42942],{},[895,42935,42936],{},[1720,42937,42938,42940],{},[898,42939,1973],{},[898,42941,4819],{},[902,42943,42903],{"encoding":904},[724,42945,42946,42949,42950,9918,42967,1977],{},[38,42947,42948],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,42951,42953],{"className":42952},[886],[888,42954,42955],{"xmlns":890},[892,42956,42957,42965],{},[895,42958,42959],{},[1720,42960,42961,42963],{},[898,42962,2398],{},[898,42964,4819],{},[902,42966,41966],{"encoding":904},[883,42968,42970],{"className":42969},[886],[888,42971,42972],{"xmlns":890},[892,42973,42974,42982],{},[895,42975,42976],{},[1720,42977,42978,42980],{},[898,42979,1973],{},[898,42981,4819],{},[902,42983,42903],{"encoding":904},[724,42985,42986,42989,42990,43007,43008,1977],{},[38,42987,42988],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,42991,42993],{"className":42992},[886],[888,42994,42995],{"xmlns":890},[892,42996,42997,43005],{},[895,42998,42999],{},[1720,43000,43001,43003],{},[898,43002,2398],{},[898,43004,4819],{},[902,43006,41966],{"encoding":904},", pokles ",[883,43009,43011],{"className":43010},[886],[888,43012,43013],{"xmlns":890},[892,43014,43015,43023],{},[895,43016,43017],{},[1720,43018,43019,43021],{},[898,43020,1973],{},[898,43022,4819],{},[902,43024,42903],{"encoding":904},[16,43026,43027,43072],{},[19,43028,43029],{},[22,43030,43031,43034,43053],{},[25,43032,43033],{},"Změna",[25,43035,43036],{},[883,43037,43039],{"className":43038},[886],[888,43040,43041],{"xmlns":890},[892,43042,43043,43051],{},[895,43044,43045],{},[1720,43046,43047,43049],{},[898,43048,2398],{},[898,43050,4819],{},[902,43052,41966],{"encoding":904},[25,43054,43055],{},[883,43056,43058],{"className":43057},[886],[888,43059,43060],{"xmlns":890},[892,43061,43062,43070],{},[895,43063,43064],{},[1720,43065,43066,43068],{},[898,43067,1973],{},[898,43069,4819],{},[902,43071,42903],{"encoding":904},[30,43073,43074,43084,43094,43103],{},[22,43075,43076,43079,43082],{},[35,43077,43078],{},"Růst poptávky",[35,43080,43081],{},"↑",[35,43083,43081],{},[22,43085,43086,43089,43092],{},[35,43087,43088],{},"Pokles poptávky",[35,43090,43091],{},"↓",[35,43093,43091],{},[22,43095,43096,43099,43101],{},[35,43097,43098],{},"Růst nabídky",[35,43100,43091],{},[35,43102,43081],{},[22,43104,43105,43108,43110],{},[35,43106,43107],{},"Pokles nabídky",[35,43109,43081],{},[35,43111,43091],{},[724,43113,43114],{},[614,43115,43116],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[37470,43118],{},[115,43120,811],{"id":43121},"zdanění-trhu",[4436,43123,43124,43213],{},[724,43125,43126,43128,43129,43142,43143,1748,43156,43159,43160,37276,43183,43208,43209,43212],{},[883,43127,4723],{}," TL;DR\nJednotková daň ",[883,43130,43132],{"className":43131},[886],[888,43133,43134],{"xmlns":890},[892,43135,43136,43140],{},[895,43137,43138],{},[898,43139,1991],{},[902,43141,1991],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,43144,43146],{"className":43145},[886],[888,43147,43148],{"xmlns":890},[892,43149,43150,43154],{},[895,43151,43152],{},[898,43153,1991],{},[902,43155,1991],{"encoding":904},[38,43157,43158],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,43161,43163],{"className":43162},[886],[888,43164,43165],{"xmlns":890},[892,43166,43167,43180],{},[895,43168,43169],{},[2355,43170,43171,43173],{},[898,43172,1991],{},[895,43174,43175,43178],{},[898,43176,43177],{},"s",[898,43179,724],{},[902,43181,43182],{"encoding":904},"T_{sp}",[883,43184,43186],{"className":43185},[886],[888,43187,43188],{"xmlns":890},[892,43189,43190,43205],{},[895,43191,43192],{},[2355,43193,43194,43196],{},[898,43195,1991],{},[895,43197,43198,43201,43203],{},[898,43199,43200],{},"v",[898,43202,2608],{},[898,43204,12540],{},[902,43206,43207],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,43210,43211],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,43214,43215],{},[614,43216,43217,43218,1977],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,43219,43221],{"className":43220,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,43223,43224,43225,43228,43229,43255,43256,43259,43260,43286,43287,43304,43305,43345,43346,4454,43359,1977],{},"Existují dvě formy zdanění — daň uložená ",[38,43226,43227],{},"výrobci"," (posun nabídky ",[883,43230,43232],{"className":43231},[886],[888,43233,43234],{"xmlns":890},[892,43235,43236,43252],{},[895,43237,43238,43244,43246,43248,43250],{},[2355,43239,43240,43242],{},[898,43241,2351],{},[1963,43243,2875],{},[1664,43245,1676],{},[898,43247,2351],{},[1664,43249,1700],{},[898,43251,1991],{},[902,43253,43254],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,43257,43258],{},"spotřebiteli"," (posun poptávky ",[883,43261,43263],{"className":43262},[886],[888,43264,43265],{"xmlns":890},[892,43266,43267,43283],{},[895,43268,43269,43275,43277,43279,43281],{},[2355,43270,43271,43273],{},[898,43272,2379],{},[1963,43274,1970],{},[1664,43276,1676],{},[898,43278,2379],{},[1664,43280,1867],{},[898,43282,1991],{},[902,43284,43285],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,43288,43290],{"className":43289},[886],[888,43291,43292],{"xmlns":890},[892,43293,43294,43302],{},[895,43295,43296],{},[1720,43297,43298,43300],{},[898,43299,1973],{},[898,43301,4819],{},[902,43303,42903],{"encoding":904}," klesá a vzniká rozklad daně ",[883,43306,43308],{"className":43307},[886],[888,43309,43310],{"xmlns":890},[892,43311,43312,43342],{},[895,43313,43314,43316,43318,43328,43330],{},[898,43315,1991],{},[1664,43317,1676],{},[2355,43319,43320,43322],{},[898,43321,1991],{},[895,43323,43324,43326],{},[898,43325,43177],{},[898,43327,724],{},[1664,43329,1700],{},[2355,43331,43332,43334],{},[898,43333,1991],{},[895,43335,43336,43338,43340],{},[898,43337,43200],{},[898,43339,2608],{},[898,43341,12540],{},[902,43343,43344],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,43347,43349],{"className":43348},[886],[888,43350,43351],{"xmlns":890},[892,43352,43353,43357],{},[895,43354,43355],{},[898,43356,2379],{},[902,43358,2379],{"encoding":904},[883,43360,43362],{"className":43361},[886],[888,43363,43364],{"xmlns":890},[892,43365,43366,43370],{},[895,43367,43368],{},[898,43369,2351],{},[902,43371,2351],{"encoding":904},[724,43373,43374,43375,43378,43379,4454,43409,43443],{},"Zásadním výsledkem kapitoly je ",[38,43376,43377],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,43380,43382],{"className":43381},[886],[888,43383,43384],{"xmlns":890},[892,43385,43386,43406],{},[895,43387,43388,43396,43398],{},[1810,43389,43390,43392,43394],{},[898,43391,1973],{},[1963,43393,2875],{},[898,43395,4819],{},[1664,43397,1676],{},[1810,43399,43400,43402,43404],{},[898,43401,1973],{},[1963,43403,1970],{},[898,43405,4819],{},[902,43407,43408],{"encoding":904},"Q_1^E = Q_2^E",[883,43410,43412],{"className":43411},[886],[888,43413,43414],{"xmlns":890},[892,43415,43416,43440],{},[895,43417,43418,43426,43428,43430,43432],{},[1810,43419,43420,43422,43424],{},[898,43421,2398],{},[1963,43423,2875],{},[898,43425,4819],{},[1664,43427,1867],{},[898,43429,1991],{},[1664,43431,1676],{},[1810,43433,43434,43436,43438],{},[898,43435,2398],{},[1963,43437,1970],{},[898,43439,4819],{},[902,43441,43442],{"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.",[724,43445,43446,43447,43450,43451,43477,43478,43506,43507,43510,43511,43514,43515,1977],{},"Podrobný výklad, Příklady ",[38,43448,43449],{},"2.9"," (daň výrobci, ",[883,43452,43454],{"className":43453},[886],[888,43455,43456],{"xmlns":890},[892,43457,43458,43474],{},[895,43459,43460,43470,43472],{},[2355,43461,43462,43464],{},[898,43463,1991],{},[895,43465,43466,43468],{},[898,43467,43177],{},[898,43469,724],{},[1664,43471,1676],{},[1963,43473,1970],{},[902,43475,43476],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,43479,43481],{"className":43480},[886],[888,43482,43483],{"xmlns":890},[892,43484,43485,43503],{},[895,43486,43487,43499,43501],{},[2355,43488,43489,43491],{},[898,43490,1991],{},[895,43492,43493,43495,43497],{},[898,43494,43200],{},[898,43496,2608],{},[898,43498,12540],{},[1664,43500,1676],{},[1963,43502,2944],{},[902,43504,43505],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,43508,43509],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,43512,43513],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,43516,43221],{"className":43517,"dataFsResolvedFilePath":809,"href":810},[210],[37470,43519],{},[115,43521,43523],{"id":43522},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[4436,43525,43526],{},[724,43527,43528,43530,43531,43534,43535,43537],{},[883,43529,4723],{}," TL;DR\nMultiplikátory jsou ",[38,43532,43533],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,43536,37460],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,43539,43541],{"id":43540},"redukovaný-tvar","Redukovaný tvar",[724,43543,43544,43545,10588,43568,1343,43586,12627,43603,10588,43626,43643,43644,43674],{},"Pro lineární model ",[883,43546,43548],{"className":43547},[886],[888,43549,43550],{"xmlns":890},[892,43551,43552,43566],{},[895,43553,43554,43556,43558,43560,43562,43564],{},[898,43555,2398],{},[1664,43557,1676],{},[898,43559,207],{},[898,43561,1973],{},[1664,43563,1700],{},[898,43565,1818],{},[902,43567,37560],{"encoding":904},[883,43569,43571],{"className":43570},[886],[888,43572,43573],{"xmlns":890},[892,43574,43575,43583],{},[895,43576,43577,43579,43581],{},[898,43578,207],{},[1664,43580,4022],{},[1963,43582,2058],{},[902,43584,43585],{"encoding":904},"a \u003C 0",[883,43587,43589],{"className":43588},[886],[888,43590,43591],{"xmlns":890},[892,43592,43593,43601],{},[895,43594,43595,43597,43599],{},[898,43596,1818],{},[1664,43598,3984],{},[1963,43600,2058],{},[902,43602,19314],{"encoding":904},[883,43604,43606],{"className":43605},[886],[888,43607,43608],{"xmlns":890},[892,43609,43610,43624],{},[895,43611,43612,43614,43616,43618,43620,43622],{},[898,43613,2398],{},[1664,43615,1676],{},[898,43617,2034],{},[898,43619,1973],{},[1664,43621,1700],{},[898,43623,1695],{},[902,43625,40742],{"encoding":904},[883,43627,43629],{"className":43628},[886],[888,43630,43631],{"xmlns":890},[892,43632,43633,43641],{},[895,43634,43635,43637,43639],{},[898,43636,2034],{},[1664,43638,3984],{},[1963,43640,2058],{},[902,43642,40760],{"encoding":904},") dává podmínka rovnováhy ",[883,43645,43647],{"className":43646},[886],[888,43648,43649],{"xmlns":890},[892,43650,43651,43671],{},[895,43652,43653,43655,43657,43659,43661,43663,43665,43667,43669],{},[898,43654,207],{},[898,43656,1973],{},[1664,43658,1700],{},[898,43660,1818],{},[1664,43662,1676],{},[898,43664,2034],{},[898,43666,1973],{},[1664,43668,1700],{},[898,43670,1695],{},[902,43672,43673],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,43676,43678],{"className":43677},[886],[888,43679,43680],{"xmlns":890,"display":28566},[892,43681,43682,43727],{},[21254,43683,43684],{"width":28571},[21259,43685,43686,43688,43720,43722],{},[21262,43687],{"width":28576},[21262,43689,43690],{},[895,43691,43692,43698,43700,43718],{},[1720,43693,43694,43696],{},[898,43695,1973],{},[898,43697,4819],{},[1664,43699,1676],{},[2922,43701,43702,43710],{},[895,43703,43704,43706,43708],{},[898,43705,1818],{},[1664,43707,1867],{},[898,43709,1695],{},[895,43711,43712,43714,43716],{},[898,43713,2034],{},[1664,43715,1867],{},[898,43717,207],{},[898,43719,1977],{"mathvariant":1726},[21262,43721],{"width":28576},[21262,43723,43724],{},[1690,43725,43726],{},"(2.10)",[902,43728,43729],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,43731,43732,43733,10588,43735,43738,43739,43756,43757,1885,43760,43786,43787,43800,43801,43819,43820,4488],{},"Vztah (2.10) je ",[38,43734,21454],{},[614,43736,43737],{},"reduced form",") pro ",[883,43740,43742],{"className":43741},[886],[888,43743,43744],{"xmlns":890},[892,43745,43746,43754],{},[895,43747,43748],{},[1720,43749,43750,43752],{},[898,43751,1973],{},[898,43753,4819],{},[902,43755,42903],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,43758,43759],{},"parametrů",[883,43761,43763],{"className":43762},[886],[888,43764,43765],{"xmlns":890},[892,43766,43767,43783],{},[895,43768,43769,43771,43773,43775,43777,43779,43781],{},[898,43770,207],{},[1664,43772,1916],{"separator":1915},[898,43774,1818],{},[1664,43776,1916],{"separator":1915},[898,43778,2034],{},[1664,43780,1916],{"separator":1915},[898,43782,1695],{},[902,43784,43785],{"encoding":904},"a, b, c, d",". Aby ",[883,43788,43790],{"className":43789},[886],[888,43791,43792],{"xmlns":890},[892,43793,43794,43798],{},[895,43795,43796],{},[898,43797,4819],{},[902,43799,4819],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,43802,43804],{"className":43803},[886],[888,43805,43806],{"xmlns":890},[892,43807,43808,43816],{},[895,43809,43810,43812,43814],{},[898,43811,1818],{},[1664,43813,3984],{},[898,43815,1695],{},[902,43817,43818],{"encoding":904},"b > d"," (neboť ",[883,43821,43823],{"className":43822},[886],[888,43824,43825],{"xmlns":890},[892,43826,43827,43839],{},[895,43828,43829,43831,43833,43835,43837],{},[898,43830,2034],{},[1664,43832,1867],{},[898,43834,207],{},[1664,43836,3984],{},[1963,43838,2058],{},[902,43840,43841],{"encoding":904},"c - a > 0",[724,43843,43844],{},[614,43845,43846,43847,43860,43861,43874,43875,19148,43888,42440,43905,43918],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,43848,43850],{"className":43849},[886],[888,43851,43852],{"xmlns":890},[892,43853,43854,43858],{},[895,43855,43856],{},[898,43857,1818],{},[902,43859,1818],{"encoding":904}," na ose ",[883,43862,43864],{"className":43863},[886],[888,43865,43866],{"xmlns":890},[892,43867,43868,43872],{},[895,43869,43870],{},[898,43871,2398],{},[902,43873,2398],{"encoding":904},") a nabídka (úsek ",[883,43876,43878],{"className":43877},[886],[888,43879,43880],{"xmlns":890},[892,43881,43882,43886],{},[895,43883,43884],{},[898,43885,1695],{},[902,43887,1695],{"encoding":904},[883,43889,43891],{"className":43890},[886],[888,43892,43893],{"xmlns":890},[892,43894,43895,43903],{},[895,43896,43897,43899,43901],{},[898,43898,1818],{},[1664,43900,3984],{},[898,43902,1695],{},[902,43904,43818],{"encoding":904},[883,43906,43908],{"className":43907},[886],[888,43909,43910],{"xmlns":890},[892,43911,43912,43916],{},[895,43913,43914],{},[898,43915,4819],{},[902,43917,4819],{"encoding":904}," v 1. kvadrantu.",[198,43920,43922],{"id":43921},"definice-multiplikátorů","Definice multiplikátorů",[724,43924,43925,43926,43951,43952,43965,43966,43979],{},"V komparativní statice jsou ",[883,43927,43929],{"className":43928},[886],[888,43930,43931],{"xmlns":890},[892,43932,43933,43949],{},[895,43934,43935,43937,43939,43941,43943,43945,43947],{},[898,43936,207],{},[1664,43938,1916],{"separator":1915},[898,43940,1818],{},[1664,43942,1916],{"separator":1915},[898,43944,2034],{},[1664,43946,1916],{"separator":1915},[898,43948,1695],{},[902,43950,43785],{"encoding":904}," exogenní proměnné a ",[883,43953,43955],{"className":43954},[886],[888,43956,43957],{"xmlns":890},[892,43958,43959,43963],{},[895,43960,43961],{},[898,43962,1973],{},[902,43964,1973],{"encoding":904}," endogenní. Přibližná změna ",[883,43967,43969],{"className":43968},[886],[888,43970,43971],{"xmlns":890},[892,43972,43973,43977],{},[895,43974,43975],{},[898,43976,1973],{},[902,43978,1973],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,43981,43983],{"className":43982},[886],[888,43984,43985],{"xmlns":890,"display":28566},[892,43986,43987,44080],{},[21254,43988,43989],{"width":28571},[21259,43990,43991,43993,44073,44075],{},[21262,43992],{"width":28576},[21262,43994,43995],{},[895,43996,43997,43999,44001,44003,44005,44007,44009,44017,44019,44021,44023,44025,44033,44035,44037,44039,44041,44049,44051,44053,44055,44057,44065,44067,44069,44071],{},[898,43998,3468],{"mathvariant":1726},[898,44000,1973],{},[1664,44002,3315],{},[898,44004,1695],{},[898,44006,1973],{},[1664,44008,1676],{},[1810,44010,44011,44013,44015],{},[898,44012,1973],{},[898,44014,207],{},[1664,44016,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1690,44018,1692],{},[898,44020,1695],{},[898,44022,207],{},[1664,44024,1700],{},[1810,44026,44027,44029,44031],{},[898,44028,1973],{},[898,44030,1818],{},[1664,44032,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1690,44034,1692],{},[898,44036,1695],{},[898,44038,1818],{},[1664,44040,1700],{},[1810,44042,44043,44045,44047],{},[898,44044,1973],{},[898,44046,2034],{},[1664,44048,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1690,44050,1692],{},[898,44052,1695],{},[898,44054,2034],{},[1664,44056,1700],{},[1810,44058,44059,44061,44063],{},[898,44060,1973],{},[898,44062,1695],{},[1664,44064,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1690,44066,1692],{},[898,44068,1695],{},[898,44070,1695],{},[898,44072,1977],{"mathvariant":1726},[21262,44074],{"width":28576},[21262,44076,44077],{},[1690,44078,44079],{},"(2.11)",[902,44081,44082],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,44084,44085,44086,44136,44137,10588,44139,3727],{},"Parciální derivace ",[883,44087,44089],{"className":44088},[886],[888,44090,44091],{"xmlns":890},[892,44092,44093,44133],{},[895,44094,44095,44103,44105,44113,44115,44123,44125],{},[1810,44096,44097,44099,44101],{},[898,44098,1973],{},[898,44100,207],{},[1664,44102,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,44104,1916],{"separator":1915},[1810,44106,44107,44109,44111],{},[898,44108,1973],{},[898,44110,1818],{},[1664,44112,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,44114,1916],{"separator":1915},[1810,44116,44117,44119,44121],{},[898,44118,1973],{},[898,44120,2034],{},[1664,44122,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,44124,1916],{"separator":1915},[1810,44126,44127,44129,44131],{},[898,44128,1973],{},[898,44130,1695],{},[1664,44132,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,44134,44135],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,44138,18477],{},[614,44140,44141],{},"multipliers",[883,44143,44145],{"className":44144},[886],[888,44146,44147],{"xmlns":890,"display":28566},[892,44148,44149,44300],{},[21254,44150,44151],{"width":28571},[21259,44152,44153,44155,44293,44295],{},[21262,44154],{"width":28576},[21262,44156,44157],{},[895,44158,44159,44167,44169,44195,44197,44199,44207,44209,44221,44223,44225,44233,44235,44237,44263,44265,44267,44275,44277,44279,44291],{},[1810,44160,44161,44163,44165],{},[898,44162,1973],{},[898,44164,207],{},[1664,44166,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,44168,1676],{},[2922,44170,44171,44179],{},[895,44172,44173,44175,44177],{},[898,44174,1818],{},[1664,44176,1867],{},[898,44178,1695],{},[895,44180,44181,44183,44185,44187,44189],{},[1664,44182,1667],{"stretchy":1666},[898,44184,2034],{},[1664,44186,1867],{},[898,44188,207],{},[1720,44190,44191,44193],{},[1664,44192,1673],{"stretchy":1666},[1963,44194,1970],{},[1664,44196,1916],{"separator":1915},[6444,44198],{"width":15783},[1810,44200,44201,44203,44205],{},[898,44202,1973],{},[898,44204,1818],{},[1664,44206,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,44208,1676],{},[2922,44210,44211,44213],{},[1963,44212,2875],{},[895,44214,44215,44217,44219],{},[898,44216,2034],{},[1664,44218,1867],{},[898,44220,207],{},[1664,44222,1916],{"separator":1915},[6444,44224],{"width":15783},[1810,44226,44227,44229,44231],{},[898,44228,1973],{},[898,44230,2034],{},[1664,44232,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,44234,1676],{},[1664,44236,1867],{},[2922,44238,44239,44247],{},[895,44240,44241,44243,44245],{},[898,44242,1818],{},[1664,44244,1867],{},[898,44246,1695],{},[895,44248,44249,44251,44253,44255,44257],{},[1664,44250,1667],{"stretchy":1666},[898,44252,2034],{},[1664,44254,1867],{},[898,44256,207],{},[1720,44258,44259,44261],{},[1664,44260,1673],{"stretchy":1666},[1963,44262,1970],{},[1664,44264,1916],{"separator":1915},[6444,44266],{"width":15783},[1810,44268,44269,44271,44273],{},[898,44270,1973],{},[898,44272,1695],{},[1664,44274,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,44276,1676],{},[1664,44278,1867],{},[2922,44280,44281,44283],{},[1963,44282,2875],{},[895,44284,44285,44287,44289],{},[898,44286,2034],{},[1664,44288,1867],{},[898,44290,207],{},[898,44292,1977],{"mathvariant":1726},[21262,44294],{"width":28576},[21262,44296,44297],{},[1690,44298,44299],{},"(2.12)",[902,44301,44302],{"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}",[198,44304,44306],{"id":44305},"znaménka-a-interpretace","Znaménka a interpretace",[724,44308,44309,44310,1343,44327,1343,44344,1343,44361,44378,44379,3727],{},"Za podmínek ",[883,44311,44313],{"className":44312},[886],[888,44314,44315],{"xmlns":890},[892,44316,44317,44325],{},[895,44318,44319,44321,44323],{},[898,44320,207],{},[1664,44322,4022],{},[1963,44324,2058],{},[902,44326,43585],{"encoding":904},[883,44328,44330],{"className":44329},[886],[888,44331,44332],{"xmlns":890},[892,44333,44334,44342],{},[895,44335,44336,44338,44340],{},[898,44337,1818],{},[1664,44339,3984],{},[1963,44341,2058],{},[902,44343,19314],{"encoding":904},[883,44345,44347],{"className":44346},[886],[888,44348,44349],{"xmlns":890},[892,44350,44351,44359],{},[895,44352,44353,44355,44357],{},[898,44354,2034],{},[1664,44356,3984],{},[1963,44358,2058],{},[902,44360,40760],{"encoding":904},[883,44362,44364],{"className":44363},[886],[888,44365,44366],{"xmlns":890},[892,44367,44368,44376],{},[895,44369,44370,44372,44374],{},[898,44371,1818],{},[1664,44373,3984],{},[898,44375,1695],{},[902,44377,43818],{"encoding":904}," platí (znaménka se ",[38,44380,44381],{},"nemění",[883,44383,44385],{"className":44384},[886],[888,44386,44387],{"xmlns":890,"display":28566},[892,44388,44389,44451],{},[895,44390,44391,44399,44401,44403,44405,44407,44415,44417,44419,44421,44423,44431,44433,44435,44437,44439,44447,44449],{},[1810,44392,44393,44395,44397],{},[898,44394,1973],{},[898,44396,207],{},[1664,44398,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,44400,3984],{},[1963,44402,2058],{},[1664,44404,1916],{"separator":1915},[6444,44406],{"width":6446},[1810,44408,44409,44411,44413],{},[898,44410,1973],{},[898,44412,1818],{},[1664,44414,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,44416,3984],{},[1963,44418,2058],{},[1664,44420,1916],{"separator":1915},[6444,44422],{"width":6446},[1810,44424,44425,44427,44429],{},[898,44426,1973],{},[898,44428,2034],{},[1664,44430,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,44432,4022],{},[1963,44434,2058],{},[1664,44436,1916],{"separator":1915},[6444,44438],{"width":6446},[1810,44440,44441,44443,44445],{},[898,44442,1973],{},[898,44444,1695],{},[1664,44446,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,44448,4022],{},[1963,44450,12959],{},[902,44452,44453],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,44455,44456,44515],{},[123,44457,44458,1885,44461,44481,44482,44499,44500,1343,44513,1977],{},[38,44459,44460],{},"Kvantitativní smysl:",[883,44462,44464],{"className":44463},[886],[888,44465,44466],{"xmlns":890},[892,44467,44468,44478],{},[895,44469,44470],{},[1810,44471,44472,44474,44476],{},[898,44473,1973],{},[898,44475,1670],{},[1664,44477,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,44479,44480],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,44483,44485],{"className":44484},[886],[888,44486,44487],{"xmlns":890},[892,44488,44489,44497],{},[895,44490,44491],{},[1720,44492,44493,44495],{},[898,44494,1973],{},[898,44496,4819],{},[902,44498,42903],{"encoding":904}," při jednotkové změně parametru ",[883,44501,44503],{"className":44502},[886],[888,44504,44505],{"xmlns":890},[892,44506,44507,44511],{},[895,44508,44509],{},[898,44510,1670],{},[902,44512,1670],{"encoding":904},[614,44514,37460],{},[123,44516,44517,44520,44521,44538,44539,1977],{},[38,44518,44519],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,44522,44524],{"className":44523},[886],[888,44525,44526],{"xmlns":890},[892,44527,44528,44536],{},[895,44529,44530],{},[1720,44531,44532,44534],{},[898,44533,1973],{},[898,44535,4819],{},[902,44537,42903],{"encoding":904}," na růst ",[883,44540,44542],{"className":44541},[886],[888,44543,44544],{"xmlns":890},[892,44545,44546,44550],{},[895,44547,44548],{},[898,44549,1670],{},[902,44551,1670],{"encoding":904},[724,44553,44554,44555,44568,44569,43819,44586,4488],{},"Např. růst ",[883,44556,44558],{"className":44557},[886],[888,44559,44560],{"xmlns":890},[892,44561,44562,44566],{},[895,44563,44564],{},[898,44565,2034],{},[902,44567,2034],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,44570,44572],{"className":44571},[886],[888,44573,44574],{"xmlns":890},[892,44575,44576,44584],{},[895,44577,44578],{},[1720,44579,44580,44582],{},[898,44581,1973],{},[898,44583,4819],{},[902,44585,42903],{"encoding":904},[883,44587,44589],{"className":44588},[886],[888,44590,44591],{"xmlns":890},[892,44592,44593,44607],{},[895,44594,44595,44603,44605],{},[1810,44596,44597,44599,44601],{},[898,44598,1973],{},[898,44600,2034],{},[1664,44602,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,44604,4022],{},[1963,44606,2058],{},[902,44608,44609],{"encoding":904},"Q'_c \u003C 0",[724,44611,44612],{},[614,44613,44614,44615,44635,44636,44660,44661,44683,44684,1977],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,44616,44618],{"className":44617},[886],[888,44619,44620],{"xmlns":890},[892,44621,44622,44632],{},[895,44623,44624,44626,44628,44630],{},[898,44625,2034],{},[898,44627,1973],{},[1664,44629,1700],{},[898,44631,1695],{},[902,44633,44634],{"encoding":904},"cQ + d"," na strmější ",[883,44637,44639],{"className":44638},[886],[888,44640,44641],{"xmlns":890},[892,44642,44643,44657],{},[895,44644,44645,44651,44653,44655],{},[2355,44646,44647,44649],{},[898,44648,2034],{},[1963,44650,2875],{},[898,44652,1973],{},[1664,44654,1700],{},[898,44656,1695],{},[902,44658,44659],{"encoding":904},"c_1 Q + d"," (při ",[883,44662,44664],{"className":44663},[886],[888,44665,44666],{"xmlns":890},[892,44667,44668,44680],{},[895,44669,44670,44676,44678],{},[2355,44671,44672,44674],{},[898,44673,2034],{},[1963,44675,2875],{},[1664,44677,3984],{},[898,44679,2034],{},[902,44681,44682],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,44685,44687],{"className":44686},[886],[888,44688,44689],{"xmlns":890},[892,44690,44691,44701],{},[895,44692,44693,44699],{},[1720,44694,44695,44697],{},[898,44696,1973],{},[898,44698,4819],{},[1664,44700,43091],{},[902,44702,44703],{"encoding":904},"Q^E \\downarrow",[724,44705,44706,44707,44739,44740,1977],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,44708,44710],{"className":44709},[886],[888,44711,44712],{"xmlns":890},[892,44713,44714,44736],{},[895,44715,44716,44718,44720,44722,44730,44732,44734],{},[898,44717,3468],{"mathvariant":1726},[898,44719,1973],{},[1664,44721,3315],{},[1810,44723,44724,44726,44728],{},[898,44725,1973],{},[898,44727,1818],{},[1664,44729,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1690,44731,1692],{},[898,44733,1695],{},[898,44735,1818],{},[902,44737,44738],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,44741,44743],{"className":44742},[886],[888,44744,44745],{"xmlns":890},[892,44746,44747,44755],{},[895,44748,44749],{},[1720,44750,44751,44753],{},[898,44752,2398],{},[898,44754,4819],{},[902,44756,41966],{"encoding":904},[198,44758,44760,44761],{"id":44759},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,44762,44764],{"className":44763},[886],[888,44765,44766],{"xmlns":890},[892,44767,44768,44776],{},[895,44769,44770],{},[1720,44771,44772,44774],{},[898,44773,1973],{},[898,44775,4819],{},[902,44777,42903],{"encoding":904},[724,44779,44780,42155,44782,42190,44808,1977],{},[38,44781,38433],{},[883,44783,44785],{"className":44784},[886],[888,44786,44787],{"xmlns":890},[892,44788,44789,44805],{},[895,44790,44791,44793,44795,44797,44799,44801,44803],{},[898,44792,2398],{},[1664,44794,1676],{},[1664,44796,1867],{},[1963,44798,2774],{},[898,44800,1973],{},[1664,44802,1700],{},[1963,44804,5777],{},[902,44806,44807],{"encoding":904},"P = -3Q + 40",[883,44809,44811],{"className":44810},[886],[888,44812,44813],{"xmlns":890},[892,44814,44815,44829],{},[895,44816,44817,44819,44821,44823,44825,44827],{},[898,44818,2398],{},[1664,44820,1676],{},[1963,44822,5575],{},[898,44824,1973],{},[1664,44826,1700],{},[1963,44828,3442],{},[902,44830,44831],{"encoding":904},"P = 0{,}5Q + 10",[724,44833,44834,44836],{},[38,44835,38465],{}," Rovnovážné množství",[883,44838,44840],{"className":44839},[886],[888,44841,44842],{"xmlns":890,"display":28566},[892,44843,44844,44912],{},[895,44845,44846,44852,44854,44872,44874,44898,44900,44907,44909],{},[1720,44847,44848,44850],{},[898,44849,1973],{},[898,44851,4819],{},[1664,44853,1676],{},[2922,44855,44856,44864],{},[895,44857,44858,44860,44862],{},[898,44859,1818],{},[1664,44861,1867],{},[898,44863,1695],{},[895,44865,44866,44868,44870],{},[898,44867,2034],{},[1664,44869,1867],{},[898,44871,207],{},[1664,44873,1676],{},[2922,44875,44876,44884],{},[895,44877,44878,44880,44882],{},[1963,44879,5777],{},[1664,44881,1867],{},[1963,44883,3442],{},[895,44885,44886,44888,44890,44892,44894,44896],{},[1963,44887,5575],{},[1664,44889,1867],{},[1664,44891,1667],{"stretchy":1666},[1664,44893,1867],{},[1963,44895,2774],{},[1664,44897,1673],{"stretchy":1666},[1664,44899,1676],{},[2922,44901,44902,44904],{},[1963,44903,38519],{},[1963,44905,44906],{},"3,5",[1664,44908,3315],{},[1963,44910,44911],{},"8,571.",[902,44913,44914],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,44916,44917,44962],{},[38,44918,44919,44920,3257,44933,3271,44947,44961],{},"(a) Změna ",[883,44921,44923],{"className":44922},[886],[888,44924,44925],{"xmlns":890},[892,44926,44927,44931],{},[895,44928,44929],{},[898,44930,2034],{},[902,44932,2034],{"encoding":904},[883,44934,44936],{"className":44935},[886],[888,44937,44938],{"xmlns":890},[892,44939,44940,44944],{},[895,44941,44942],{},[1963,44943,5575],{},[902,44945,44946],{"encoding":904},"0{,}5",[883,44948,44950],{"className":44949},[886],[888,44951,44952],{"xmlns":890},[892,44953,44954,44958],{},[895,44955,44956],{},[1963,44957,19821],{},[902,44959,44960],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,44964,44966],{"className":44965},[886],[888,44967,44968],{"xmlns":890,"display":28566},[892,44969,44970,45047],{},[895,44971,44972,44980,44982,44984,44986,44988,44990,45016,45018,45020,45022,45024,45026,45036,45038,45040,45042,45044],{},[1810,44973,44974,44976,44978],{},[898,44975,1973],{},[898,44977,2034],{},[1664,44979,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1690,44981,1692],{},[898,44983,1695],{},[898,44985,2034],{},[1664,44987,1676],{},[1664,44989,1867],{},[2922,44991,44992,45000],{},[895,44993,44994,44996,44998],{},[898,44995,1818],{},[1664,44997,1867],{},[898,44999,1695],{},[895,45001,45002,45004,45006,45008,45010],{},[1664,45003,1667],{"stretchy":1666},[898,45005,2034],{},[1664,45007,1867],{},[898,45009,207],{},[1720,45011,45012,45014],{},[1664,45013,1673],{"stretchy":1666},[1963,45015,1970],{},[1690,45017,1692],{},[898,45019,1695],{},[898,45021,2034],{},[1664,45023,1676],{},[1664,45025,1867],{},[2922,45027,45028,45030],{},[1963,45029,38519],{},[1720,45031,45032,45034],{},[1963,45033,44906],{},[1963,45035,1970],{},[1664,45037,3753],{},[1963,45039,2220],{},[1664,45041,3315],{},[1664,45043,1867],{},[1963,45045,45046],{},"0,245.",[902,45048,45049],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,45051,45052,45053,1977],{},"Nové rovnovážné množství ",[883,45054,45056],{"className":45055},[886],[888,45057,45058],{"xmlns":890},[892,45059,45060,45085],{},[895,45061,45062,45070,45072,45075,45077,45080,45082],{},[1810,45063,45064,45066,45068],{},[898,45065,1973],{},[1963,45067,2875],{},[898,45069,4819],{},[1664,45071,3315],{},[1963,45073,45074],{},"8,571",[1664,45076,1867],{},[1963,45078,45079],{},"0,245",[1664,45081,1676],{},[1963,45083,45084],{},"8,326",[902,45086,45087],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,45089,45090,45175],{},[38,45091,45092,45093,1343,45113,1343,45135,1343,45155,1977],{},"(b) Současné změny ",[883,45094,45096],{"className":45095},[886],[888,45097,45098],{"xmlns":890},[892,45099,45100,45110],{},[895,45101,45102,45104,45106,45108],{},[898,45103,1695],{},[898,45105,207],{},[1664,45107,1676],{},[1963,45109,5575],{},[902,45111,45112],{"encoding":904},"da = 0{,}5",[883,45114,45116],{"className":45115},[886],[888,45117,45118],{"xmlns":890},[892,45119,45120,45132],{},[895,45121,45122,45124,45126,45128,45130],{},[898,45123,1695],{},[898,45125,1818],{},[1664,45127,1676],{},[1664,45129,1867],{},[1963,45131,2826],{},[902,45133,45134],{"encoding":904},"db = -5",[883,45136,45138],{"className":45137},[886],[888,45139,45140],{"xmlns":890},[892,45141,45142,45152],{},[895,45143,45144,45146,45148,45150],{},[898,45145,1695],{},[898,45147,2034],{},[1664,45149,1676],{},[1963,45151,2220],{},[902,45153,45154],{"encoding":904},"dc = 0{,}1",[883,45156,45158],{"className":45157},[886],[888,45159,45160],{"xmlns":890},[892,45161,45162,45172],{},[895,45163,45164,45166,45168,45170],{},[898,45165,1695],{},[898,45167,1695],{},[1664,45169,1676],{},[1963,45171,2875],{},[902,45173,45174],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,45177,45179],{"className":45178},[886],[888,45180,45181],{"xmlns":890,"display":28566},[892,45182,45183,45326],{},[21254,45184,45185,45267,45303],{"rowspacing":21256,"columnalign":21257,"columnspacing":1727},[21259,45186,45187,45197],{},[21262,45188,45189],{},[2919,45190,45191],{"scriptlevel":2058,"displaystyle":1915},[895,45192,45193,45195],{},[898,45194,3468],{"mathvariant":1726},[898,45196,1973],{},[21262,45198,45199],{},[2919,45200,45201],{"scriptlevel":2058,"displaystyle":1915},[895,45202,45203,45205,45207,45217,45219,45221,45223,45229,45231,45233,45235,45237,45239,45241,45251,45253,45255,45257,45263,45265],{},[895,45204],{},[1664,45206,3315],{},[2922,45208,45209,45211],{},[1963,45210,38519],{},[1720,45212,45213,45215],{},[1963,45214,44906],{},[1963,45216,1970],{},[1664,45218,3753],{},[1963,45220,5575],{},[1664,45222,1700],{},[2922,45224,45225,45227],{},[1963,45226,2875],{},[1963,45228,44906],{},[1664,45230,3753],{},[1664,45232,1667],{"stretchy":1666},[1664,45234,1867],{},[1963,45236,2826],{},[1664,45238,1673],{"stretchy":1666},[1664,45240,1867],{},[2922,45242,45243,45245],{},[1963,45244,38519],{},[1720,45246,45247,45249],{},[1963,45248,44906],{},[1963,45250,1970],{},[1664,45252,3753],{},[1963,45254,2220],{},[1664,45256,1867],{},[2922,45258,45259,45261],{},[1963,45260,2875],{},[1963,45262,44906],{},[1664,45264,3753],{},[1963,45266,2875],{},[21259,45268,45269,45275],{},[21262,45270,45271],{},[2919,45272,45273],{"scriptlevel":2058,"displaystyle":1915},[895,45274],{},[21262,45276,45277],{},[2919,45278,45279],{"scriptlevel":2058,"displaystyle":1915},[895,45280,45281,45283,45285,45288,45290,45293,45295,45298,45300],{},[895,45282],{},[1664,45284,1676],{},[1963,45286,45287],{},"1,2245",[1664,45289,1867],{},[1963,45291,45292],{},"1,4286",[1664,45294,1867],{},[1963,45296,45297],{},"0,2449",[1664,45299,1867],{},[1963,45301,45302],{},"0,2857",[21259,45304,45305,45311],{},[21262,45306,45307],{},[2919,45308,45309],{"scriptlevel":2058,"displaystyle":1915},[895,45310],{},[21262,45312,45313],{},[2919,45314,45315],{"scriptlevel":2058,"displaystyle":1915},[895,45316,45317,45319,45321,45323],{},[895,45318],{},[1664,45320,3315],{},[1664,45322,1867],{},[1963,45324,45325],{},"0,735.",[902,45327,45328],{"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}",[724,45330,30565,45331,1977],{},[883,45332,45334],{"className":45333},[886],[888,45335,45336],{"xmlns":890},[892,45337,45338,45362],{},[895,45339,45340,45348,45350,45352,45354,45357,45359],{},[1810,45341,45342,45344,45346],{},[898,45343,1973],{},[1963,45345,2875],{},[898,45347,4819],{},[1664,45349,3315],{},[1963,45351,45074],{},[1664,45353,1867],{},[1963,45355,45356],{},"0,735",[1664,45358,1676],{},[1963,45360,45361],{},"7,836",[902,45363,45364],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[4436,45366,45367],{},[724,45368,45369,45371,45372,45395,45396,45418],{},[883,45370,4978],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,45373,45375],{"className":45374},[886],[888,45376,45377],{"xmlns":890},[892,45378,45379,45392],{},[895,45380,45381,45383,45385,45387,45389],{},[898,45382,3468],{"mathvariant":1726},[898,45384,1973],{},[1664,45386,3315],{},[1664,45388,1867],{},[1963,45390,45391],{},"2,69",[902,45393,45394],{"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 ",[883,45397,45399],{"className":45398},[886],[888,45400,45401],{"xmlns":890},[892,45402,45403,45415],{},[895,45404,45405,45407,45409,45411,45413],{},[898,45406,3468],{"mathvariant":1726},[898,45408,1973],{},[1664,45410,3315],{},[1664,45412,1867],{},[1963,45414,45356],{},[902,45416,45417],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,45420,45421],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[37470,45423],{},[115,45425,820],{"id":2332},[4436,45427,45428],{},[724,45429,45430,4443,45432,10588,45435,12627,45451,10588,45454,45470,45471,1977],{},[883,45431,4723],{},[38,45433,45434],{},"Přebytek spotřebitele",[883,45436,45438],{"className":45437},[886],[888,45439,45440],{"xmlns":890},[892,45441,45442,45448],{},[895,45443,45444,45446],{},[898,45445,1703],{},[898,45447,2351],{},[902,45449,45450],{"encoding":904},"CS",[38,45452,45453],{},"přebytek výrobce",[883,45455,45457],{"className":45456},[886],[888,45458,45459],{"xmlns":890},[892,45460,45461,45467],{},[895,45462,45463,45465],{},[898,45464,2398],{},[898,45466,2351],{},[902,45468,45469],{"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 ",[207,45472,45474],{"className":45473,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,45476,45477],{},[1928,45478],{"alt":45479,"className":45480,"src":45481},"imek-prebytky-cs-ps",[210,1932],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,45483,45484,10588,45486,45489],{},[38,45485,45434],{},[614,45487,45488],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,45491,45493],{"className":45492},[886],[888,45494,45495],{"xmlns":890,"display":28566},[892,45496,45497,45574],{},[21254,45498,45499],{"width":28571},[21259,45500,45501,45503,45567,45569],{},[21262,45502],{"width":28576},[21262,45504,45505],{},[895,45506,45507,45509,45511,45513,45519,45521,45523,45535,45537,45539,45541,45543,45545,45547,45549,45551,45557,45559,45565],{},[898,45508,1703],{},[898,45510,2351],{},[1664,45512,1667],{"stretchy":1666},[2355,45514,45515,45517],{},[898,45516,1973],{},[1963,45518,2058],{},[1664,45520,1673],{"stretchy":1666},[1664,45522,1676],{},[1810,45524,45525,45527,45529],{},[1664,45526,1679],{},[1963,45528,2058],{},[2355,45530,45531,45533],{},[898,45532,1973],{},[1963,45534,2058],{},[898,45536,2379],{},[1664,45538,1667],{"stretchy":1666},[898,45540,1973],{},[1664,45542,1673],{"stretchy":1666},[1690,45544,1692],{},[898,45546,1695],{},[898,45548,1973],{},[1664,45550,1867],{},[2355,45552,45553,45555],{},[898,45554,2398],{},[1963,45556,2058],{},[1690,45558,1692],{},[2355,45560,45561,45563],{},[898,45562,1973],{},[1963,45564,2058],{},[898,45566,1977],{"mathvariant":1726},[21262,45568],{"width":28576},[21262,45570,45571],{},[1690,45572,45573],{},"(2.14)",[902,45575,45576],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,45578,45579,10588,45582,45585],{},[38,45580,45581],{},"Přebytek výrobce",[614,45583,45584],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,45587,45589],{"className":45588},[886],[888,45590,45591],{"xmlns":890,"display":28566},[892,45592,45593,45670],{},[21254,45594,45595],{"width":28571},[21259,45596,45597,45599,45663,45665],{},[21262,45598],{"width":28576},[21262,45600,45601],{},[895,45602,45603,45605,45607,45609,45615,45617,45619,45625,45627,45633,45635,45647,45649,45651,45653,45655,45657,45659,45661],{},[898,45604,2398],{},[898,45606,2351],{},[1664,45608,1667],{"stretchy":1666},[2355,45610,45611,45613],{},[898,45612,1973],{},[1963,45614,2058],{},[1664,45616,1673],{"stretchy":1666},[1664,45618,1676],{},[2355,45620,45621,45623],{},[898,45622,2398],{},[1963,45624,2058],{},[1690,45626,1692],{},[2355,45628,45629,45631],{},[898,45630,1973],{},[1963,45632,2058],{},[1664,45634,1867],{},[1810,45636,45637,45639,45641],{},[1664,45638,1679],{},[1963,45640,2058],{},[2355,45642,45643,45645],{},[898,45644,1973],{},[1963,45646,2058],{},[898,45648,2351],{},[1664,45650,1667],{"stretchy":1666},[898,45652,1973],{},[1664,45654,1673],{"stretchy":1666},[1690,45656,1692],{},[898,45658,1695],{},[898,45660,1973],{},[898,45662,1977],{"mathvariant":1726},[21262,45664],{"width":28576},[21262,45666,45667],{},[1690,45668,45669],{},"(2.15)",[902,45671,45672],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,45674,45675,45676,1977],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,45677,45679],{"className":45678,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[37470,45681],{},[115,45683,45685],{"id":45684},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,45687,45688,45719,45724,45730,45758,45764,45793,45799,45879,45905],{},[123,45689,45690,45692,45693,45718],{},[38,45691,38428],{}," — lineární poptávka ",[883,45694,45696],{"className":45695},[886],[888,45697,45698],{"xmlns":890},[892,45699,45700,45716],{},[895,45701,45702,45704,45706,45708,45710,45712,45714],{},[898,45703,2398],{},[1664,45705,1676],{},[1664,45707,1867],{},[1963,45709,1970],{},[898,45711,1973],{},[1664,45713,1700],{},[1963,45715,3702],{},[902,45717,38460],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,45720,45721,45723],{},[38,45722,38742],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,45725,45726,45729],{},[38,45727,45728],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,45731,45732,45734,45735,1977],{},[38,45733,41289],{}," — lineární nabídka ",[883,45736,45738],{"className":45737},[886],[888,45739,45740],{"xmlns":890},[892,45741,45742,45756],{},[895,45743,45744,45746,45748,45750,45752,45754],{},[898,45745,2398],{},[1664,45747,1676],{},[1963,45749,5575],{},[898,45751,1973],{},[1664,45753,1700],{},[1963,45755,5570],{},[902,45757,41318],{"encoding":904},[123,45759,45760,45763],{},[38,45761,45762],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,45765,45766,45769,45770,1977],{},[38,45767,45768],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,45771,45773],{"className":45772},[886],[888,45774,45775],{"xmlns":890},[892,45776,45777,45791],{},[895,45778,45779,45781,45783,45785,45787,45789],{},[898,45780,4819],{},[1664,45782,1837],{"stretchy":1666},[1963,45784,2944],{},[1664,45786,1916],{"separator":1915},[1963,45788,42436],{},[1664,45790,1850],{"stretchy":1666},[902,45792,42464],{"encoding":904},[123,45794,45795,45798],{},[38,45796,45797],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,45800,45801,45804,45805,45822,45823,1343,45848,45875,45876,3529],{},[38,45802,45803],{},"Příklad 2.9"," — daň ",[883,45806,45808],{"className":45807},[886],[888,45809,45810],{"xmlns":890},[892,45811,45812,45820],{},[895,45813,45814,45816,45818],{},[898,45815,1991],{},[1664,45817,1676],{},[1963,45819,2833],{},[902,45821,41768],{"encoding":904}," na výrobce; rozklad ",[883,45824,45826],{"className":45825},[886],[888,45827,45828],{"xmlns":890},[892,45829,45830,45846],{},[895,45831,45832,45842,45844],{},[2355,45833,45834,45836],{},[898,45835,1991],{},[895,45837,45838,45840],{},[898,45839,43177],{},[898,45841,724],{},[1664,45843,1676],{},[1963,45845,1970],{},[902,45847,43476],{"encoding":904},[883,45849,45851],{"className":45850},[886],[888,45852,45853],{"xmlns":890},[892,45854,45855,45873],{},[895,45856,45857,45869,45871],{},[2355,45858,45859,45861],{},[898,45860,1991],{},[895,45862,45863,45865,45867],{},[898,45864,43200],{},[898,45866,2608],{},[898,45868,12540],{},[1664,45870,1676],{},[1963,45872,2944],{},[902,45874,43505],{"encoding":904},". (Viz ",[207,45877,43221],{"className":45878,"dataFsResolvedFilePath":809,"href":810},[210],[123,45880,45881,45804,45884,45901,45902,3529],{},[38,45882,45883],{},"Příklad 2.10",[883,45885,45887],{"className":45886},[886],[888,45888,45889],{"xmlns":890},[892,45890,45891,45899],{},[895,45892,45893,45895,45897],{},[898,45894,1991],{},[1664,45896,1676],{},[1963,45898,2833],{},[902,45900,41768],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,45903,43221],{"className":45904,"dataFsResolvedFilePath":809,"href":810},[210],[123,45906,45907,45910],{},[38,45908,45909],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[37470,45912],{},[115,45914,45916],{"id":45915},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,45918,45920],{"id":45919},"základní-analýza-poptávky","Základní analýza poptávky",[724,45922,45923,45926,45927,45962,45963,45989],{},[38,45924,45925],{},"2.1"," Je dána poptávka ",[883,45928,45930],{"className":45929},[886],[888,45931,45932],{"xmlns":890},[892,45933,45934,45959],{},[895,45935,45936,45938,45940,45942,45944,45946,45948,45950,45953,45955,45957],{},[898,45937,1973],{},[1664,45939,1676],{},[898,45941,2379],{},[1664,45943,1667],{"stretchy":1666},[898,45945,2398],{},[1664,45947,1673],{"stretchy":1666},[1664,45949,1676],{},[1963,45951,45952],{},"75",[1664,45954,1867],{},[1963,45956,2826],{},[898,45958,2398],{},[902,45960,45961],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,45964,45966],{"className":45965},[886],[888,45967,45968],{"xmlns":890},[892,45969,45970,45986],{},[895,45971,45972,45974,45976,45978,45980,45982,45984],{},[1963,45973,2058],{},[1664,45975,1916],{"separator":1915},[1963,45977,2826],{},[1664,45979,1916],{"separator":1915},[1963,45981,3442],{},[1664,45983,1916],{"separator":1915},[1963,45985,36744],{},[902,45987,45988],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,45991,45992,45995,45996,46014,46015,3727],{},[38,45993,45994],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,45997,45999],{"className":45998},[886],[888,46000,46001],{"xmlns":890},[892,46002,46003,46011],{},[895,46004,46005,46007,46009],{},[898,46006,2398],{},[1664,46008,1916],{"separator":1915},[898,46010,1973],{},[902,46012,46013],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,46016,46018],{"className":46017},[886],[888,46019,46020],{"xmlns":890},[892,46021,46022,46038],{},[895,46023,46024,46026,46028,46030,46032,46034,46036],{},[898,46025,207],{},[1664,46027,1916],{"separator":1915},[898,46029,1818],{},[1664,46031,1916],{"separator":1915},[898,46033,2034],{},[1664,46035,3984],{},[1963,46037,2058],{},[902,46039,46040],{"encoding":904},"a, b, c > 0",[120,46042,46043,46076,46107,46142,46173,46208],{},[123,46044,46045,46046],{},"(a) ",[883,46047,46049],{"className":46048},[886],[888,46050,46051],{"xmlns":890},[892,46052,46053,46073],{},[895,46054,46055,46057,46059],{},[898,46056,1973],{},[1664,46058,1676],{},[2919,46060,46061],{"scriptlevel":2058,"displaystyle":1915},[2922,46062,46063,46065],{},[898,46064,207],{},[895,46066,46067,46069,46071],{},[898,46068,2398],{},[1664,46070,1700],{},[898,46072,2034],{},[902,46074,46075],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,46077,46078,46079],{},"(b) ",[883,46080,46082],{"className":46081},[886],[888,46083,46084],{"xmlns":890},[892,46085,46086,46104],{},[895,46087,46088,46090,46092],{},[898,46089,1973],{},[1664,46091,1676],{},[8682,46093,46094],{},[895,46095,46096,46098,46100,46102],{},[898,46097,207],{},[1664,46099,1867],{},[898,46101,1818],{},[898,46103,1973],{},[902,46105,46106],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,46108,46109,46110],{},"(c) ",[883,46111,46113],{"className":46112},[886],[888,46114,46115],{"xmlns":890},[892,46116,46117,46139],{},[895,46118,46119,46121,46123],{},[898,46120,1973],{},[1664,46122,1676],{},[2919,46124,46125],{"scriptlevel":2058,"displaystyle":1915},[2922,46126,46127,46137],{},[895,46128,46129,46131,46133],{},[898,46130,207],{},[1664,46132,1867],{},[8682,46134,46135],{},[898,46136,2398],{},[898,46138,1818],{},[902,46140,46141],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,46143,46144,46145],{},"(d) ",[883,46146,46148],{"className":46147},[886],[888,46149,46150],{"xmlns":890},[892,46151,46152,46170],{},[895,46153,46154,46156,46158,46160,46162,46164],{},[898,46155,2398],{},[1664,46157,1676],{},[898,46159,207],{},[1664,46161,1867],{},[898,46163,1818],{},[1720,46165,46166,46168],{},[898,46167,1973],{},[1963,46169,1970],{},[902,46171,46172],{"encoding":904},"P = a - bQ^2",[123,46174,46175,46176],{},"(e) ",[883,46177,46179],{"className":46178},[886],[888,46180,46181],{"xmlns":890},[892,46182,46183,46205],{},[895,46184,46185,46187,46189,46191,46201,46203],{},[898,46186,1973],{},[1664,46188,1676],{},[898,46190,1818],{},[1720,46192,46193,46195],{},[898,46194,2398],{},[895,46196,46197,46199],{},[1664,46198,1867],{},[898,46200,207],{},[1664,46202,1700],{},[898,46204,2034],{},[902,46206,46207],{"encoding":904},"Q = bP^{-a} + c",[123,46209,46210,46211],{},"(f) ",[883,46212,46214],{"className":46213},[886],[888,46215,46216],{"xmlns":890},[892,46217,46218,46241],{},[895,46219,46220,46222,46224,46226,46228],{},[898,46221,1973],{},[1664,46223,1676],{},[898,46225,207],{},[1664,46227,3753],{},[1720,46229,46230,46233],{},[898,46231,46232],{},"e",[895,46234,46235,46237,46239],{},[1664,46236,1867],{},[898,46238,1818],{},[898,46240,2398],{},[902,46242,46243],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,46245,46246,46249],{},[38,46247,46248],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,46251,46252,46255,46258],{},[123,46253,46254],{},"(a) Cena substitutu.",[123,46256,46257],{},"(b) Cena komplementu.",[123,46259,46260],{},"(c) Výdaje na reklamu.",[724,46262,46263,45926,46265,46299,46300,46328],{},[38,46264,25142],{},[883,46266,46268],{"className":46267},[886],[888,46269,46270],{"xmlns":890},[892,46271,46272,46296],{},[895,46273,46274,46276,46278,46280,46282,46284,46286,46288,46290,46292,46294],{},[898,46275,2398],{},[1664,46277,1676],{},[898,46279,2379],{},[1664,46281,1667],{"stretchy":1666},[898,46283,1973],{},[1664,46285,1673],{"stretchy":1666},[1664,46287,1676],{},[1963,46289,4084],{},[1664,46291,1867],{},[1963,46293,1970],{},[898,46295,1973],{},[902,46297,46298],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,46301,46303],{"className":46302},[886],[888,46304,46305],{"xmlns":890},[892,46306,46307,46325],{},[895,46308,46309,46311,46313,46319,46321,46323],{},[898,46310,2398],{},[1664,46312,1676],{},[1720,46314,46315,46317],{},[898,46316,2379],{},[1664,46318,4920],{},[1664,46320,1667],{"stretchy":1666},[898,46322,1973],{},[1664,46324,1673],{"stretchy":1666},[902,46326,46327],{"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.",[724,46330,46331,46334],{},[38,46332,46333],{},"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:",[120,46336,46337,46421,46497,46583,46671],{},[123,46338,46045,46339,1343,46379,1977],{},[883,46340,46342],{"className":46341},[886],[888,46343,46344],{"xmlns":890},[892,46345,46346,46376],{},[895,46347,46348,46354,46356,46358,46360,46362,46368,46370],{},[2355,46349,46350,46352],{},[898,46351,23753],{},[1963,46353,2875],{},[1664,46355,1676],{},[1963,46357,9599],{},[1664,46359,1867],{},[1963,46361,2944],{},[2355,46363,46364,46366],{},[898,46365,4822],{},[1963,46367,2875],{},[1664,46369,1700],{},[2355,46371,46372,46374],{},[898,46373,4822],{},[1963,46375,1970],{},[902,46377,46378],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,46380,46382],{"className":46381},[886],[888,46383,46384],{"xmlns":890},[892,46385,46386,46418],{},[895,46387,46388,46394,46396,46398,46400,46402,46408,46410,46412],{},[2355,46389,46390,46392],{},[898,46391,23753],{},[1963,46393,1970],{},[1664,46395,1676],{},[1963,46397,3442],{},[1664,46399,1700],{},[1963,46401,1970],{},[2355,46403,46404,46406],{},[898,46405,4822],{},[1963,46407,2875],{},[1664,46409,1867],{},[1963,46411,2944],{},[2355,46413,46414,46416],{},[898,46415,4822],{},[1963,46417,1970],{},[902,46419,46420],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,46422,46078,46423,1343,46465,1977],{},[883,46424,46426],{"className":46425},[886],[888,46427,46428],{"xmlns":890},[892,46429,46430,46462],{},[895,46431,46432,46438,46440,46442,46444,46446,46452,46454,46456],{},[2355,46433,46434,46436],{},[898,46435,23753],{},[1963,46437,2875],{},[1664,46439,1676],{},[1963,46441,3696],{},[1664,46443,1867],{},[1963,46445,3442],{},[2355,46447,46448,46450],{},[898,46449,4822],{},[1963,46451,2875],{},[1664,46453,1867],{},[1963,46455,2833],{},[2355,46457,46458,46460],{},[898,46459,4822],{},[1963,46461,1970],{},[902,46463,46464],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,46466,46468],{"className":46467},[886],[888,46469,46470],{"xmlns":890},[892,46471,46472,46494],{},[895,46473,46474,46480,46482,46484,46486,46488],{},[2355,46475,46476,46478],{},[898,46477,23753],{},[1963,46479,1970],{},[1664,46481,1676],{},[1963,46483,36744],{},[1664,46485,1867],{},[1963,46487,3442],{},[2355,46489,46490,46492],{},[898,46491,4822],{},[1963,46493,1970],{},[902,46495,46496],{"encoding":904},"B_2 = 15 - 10A_2",[123,46498,46109,46499,1343,46541,1977],{},[883,46500,46502],{"className":46501},[886],[888,46503,46504],{"xmlns":890},[892,46505,46506,46538],{},[895,46507,46508,46514,46516,46518,46520,46522,46528,46530,46532],{},[2355,46509,46510,46512],{},[898,46511,23753],{},[1963,46513,2875],{},[1664,46515,1676],{},[1963,46517,38519],{},[1664,46519,1867],{},[1963,46521,1970],{},[2355,46523,46524,46526],{},[898,46525,4822],{},[1963,46527,2875],{},[1664,46529,1867],{},[1963,46531,2944],{},[2355,46533,46534,46536],{},[898,46535,4822],{},[1963,46537,1970],{},[902,46539,46540],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,46542,46544],{"className":46543},[886],[888,46545,46546],{"xmlns":890},[892,46547,46548,46580],{},[895,46549,46550,46556,46558,46560,46562,46564,46570,46572,46574],{},[2355,46551,46552,46554],{},[898,46553,23753],{},[1963,46555,1970],{},[1664,46557,1676],{},[1963,46559,36744],{},[1664,46561,1700],{},[1963,46563,1970],{},[2355,46565,46566,46568],{},[898,46567,4822],{},[1963,46569,2875],{},[1664,46571,1867],{},[1963,46573,1970],{},[2355,46575,46576,46578],{},[898,46577,4822],{},[1963,46579,1970],{},[902,46581,46582],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,46584,46144,46585,1343,46629,1977],{},[883,46586,46588],{"className":46587},[886],[888,46589,46590],{"xmlns":890},[892,46591,46592,46626],{},[895,46593,46594,46600,46602,46604,46606,46608,46610,46616,46618,46620],{},[2355,46595,46596,46598],{},[898,46597,23753],{},[1963,46599,2875],{},[1664,46601,1676],{},[1664,46603,1867],{},[1963,46605,9599],{},[1664,46607,1867],{},[1963,46609,1970],{},[2355,46611,46612,46614],{},[898,46613,4822],{},[1963,46615,2875],{},[1664,46617,1700],{},[1963,46619,2774],{},[2355,46621,46622,46624],{},[898,46623,4822],{},[1963,46625,1970],{},[902,46627,46628],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,46630,46632],{"className":46631},[886],[888,46633,46634],{"xmlns":890},[892,46635,46636,46668],{},[895,46637,46638,46644,46646,46648,46650,46652,46658,46660,46662],{},[2355,46639,46640,46642],{},[898,46641,23753],{},[1963,46643,1970],{},[1664,46645,1676],{},[1963,46647,3442],{},[1664,46649,1700],{},[1963,46651,1970],{},[2355,46653,46654,46656],{},[898,46655,4822],{},[1963,46657,2875],{},[1664,46659,1867],{},[1963,46661,1970],{},[2355,46663,46664,46666],{},[898,46665,4822],{},[1963,46667,1970],{},[902,46669,46670],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,46672,46175,46673,1343,46715,1977],{},[883,46674,46676],{"className":46675},[886],[888,46677,46678],{"xmlns":890},[892,46679,46680,46712],{},[895,46681,46682,46688,46690,46692,46694,46696,46702,46704,46706],{},[2355,46683,46684,46686],{},[898,46685,23753],{},[1963,46687,2875],{},[1664,46689,1676],{},[1963,46691,9599],{},[1664,46693,1700],{},[1963,46695,1970],{},[2355,46697,46698,46700],{},[898,46699,4822],{},[1963,46701,2875],{},[1664,46703,1700],{},[1963,46705,2944],{},[2355,46707,46708,46710],{},[898,46709,4822],{},[1963,46711,1970],{},[902,46713,46714],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,46716,46718],{"className":46717},[886],[888,46719,46720],{"xmlns":890},[892,46721,46722,46754],{},[895,46723,46724,46730,46732,46734,46736,46738,46744,46746,46748],{},[2355,46725,46726,46728],{},[898,46727,23753],{},[1963,46729,1970],{},[1664,46731,1676],{},[1963,46733,5777],{},[1664,46735,1867],{},[1963,46737,2774],{},[2355,46739,46740,46742],{},[898,46741,4822],{},[1963,46743,2875],{},[1664,46745,1700],{},[1963,46747,2826],{},[2355,46749,46750,46752],{},[898,46751,4822],{},[1963,46753,1970],{},[902,46755,46756],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,46758,46760],{"id":46759},"základní-analýza-nabídky","Základní analýza nabídky",[724,46762,46763,46766,46767,46801,46802,46824],{},[38,46764,46765],{},"2.6"," Je dána nabídka ",[883,46768,46770],{"className":46769},[886],[888,46771,46772],{"xmlns":890},[892,46773,46774,46798],{},[895,46775,46776,46778,46780,46782,46784,46786,46788,46790,46792,46794,46796],{},[898,46777,2398],{},[1664,46779,1676],{},[898,46781,2351],{},[1664,46783,1667],{"stretchy":1666},[898,46785,1973],{},[1664,46787,1673],{"stretchy":1666},[1664,46789,1676],{},[1963,46791,9599],{},[1664,46793,1700],{},[1963,46795,2154],{},[898,46797,1973],{},[902,46799,46800],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,46803,46805],{"className":46804},[886],[888,46806,46807],{"xmlns":890},[892,46808,46809,46821],{},[895,46810,46811,46813,46815,46817,46819],{},[1963,46812,5570],{},[1664,46814,1916],{"separator":1915},[1963,46816,38519],{},[1664,46818,1916],{"separator":1915},[1963,46820,15537],{},[902,46822,46823],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,46826,46827,46830,46831,46848],{},[38,46828,46829],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,46832,46834],{"className":46833},[886],[888,46835,46836],{"xmlns":890},[892,46837,46838,46846],{},[895,46839,46840,46842,46844],{},[898,46841,2398],{},[1664,46843,1916],{"separator":1915},[898,46845,1973],{},[902,46847,46013],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,46850,46851,46877,46905,46938,46972,47008],{},[123,46852,46045,46853],{},[883,46854,46856],{"className":46855},[886],[888,46857,46858],{"xmlns":890},[892,46859,46860,46874],{},[895,46861,46862,46864,46866,46868,46870,46872],{},[898,46863,2398],{},[1664,46865,1676],{},[1963,46867,38519],{},[1664,46869,1700],{},[1963,46871,1970],{},[898,46873,1973],{},[902,46875,46876],{"encoding":904},"P = 30 + 2Q",[123,46878,46078,46879],{},[883,46880,46882],{"className":46881},[886],[888,46883,46884],{"xmlns":890},[892,46885,46886,46902],{},[895,46887,46888,46890,46892,46894,46896,46898,46900],{},[898,46889,1973],{},[1664,46891,1676],{},[1664,46893,1867],{},[1963,46895,2774],{},[1664,46897,1700],{},[1963,46899,4084],{},[898,46901,2398],{},[902,46903,46904],{"encoding":904},"Q = -3 + 12P",[123,46906,46109,46907],{},[883,46908,46910],{"className":46909},[886],[888,46911,46912],{"xmlns":890},[892,46913,46914,46936],{},[895,46915,46916,46918,46920,46926,46928,46930,46932,46934],{},[898,46917,2398],{},[1664,46919,1676],{},[1720,46921,46922,46924],{},[898,46923,1973],{},[1963,46925,1970],{},[1664,46927,1700],{},[1963,46929,23446],{},[898,46931,1973],{},[1664,46933,1700],{},[1963,46935,33046],{},[902,46937,42222],{"encoding":904},[123,46939,46144,46940],{},[883,46941,46943],{"className":46942},[886],[888,46944,46945],{"xmlns":890},[892,46946,46947,46969],{},[895,46948,46949,46951,46953,46959,46961,46963,46965,46967],{},[898,46950,2398],{},[1664,46952,1676],{},[1720,46954,46955,46957],{},[898,46956,1973],{},[1963,46958,1970],{},[1664,46960,1700],{},[1963,46962,1970],{},[898,46964,1973],{},[1664,46966,1700],{},[1963,46968,4084],{},[902,46970,46971],{"encoding":904},"P = Q^2 + 2Q + 12",[123,46973,46175,46974],{},[883,46975,46977],{"className":46976},[886],[888,46978,46979],{"xmlns":890},[892,46980,46981,47005],{},[895,46982,46983,46985,46987,46989,46991,46993,46995,46997,46999],{},[898,46984,1973],{},[1664,46986,1676],{},[1963,46988,9367],{},[1664,46990,1700],{},[1963,46992,2826],{},[898,46994,2398],{},[1664,46996,1700],{},[1963,46998,2220],{},[1720,47000,47001,47003],{},[898,47002,2398],{},[1963,47004,1970],{},[902,47006,47007],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,47009,46210,47010],{},[883,47011,47013],{"className":47012},[886],[888,47014,47015],{"xmlns":890},[892,47016,47017,47042],{},[895,47018,47019,47021,47023,47025,47027,47029,47031,47033,47036],{},[898,47020,1973],{},[1664,47022,1676],{},[1963,47024,24701],{},[1664,47026,1700],{},[1963,47028,2220],{},[898,47030,2398],{},[1664,47032,1700],{},[1963,47034,47035],{},"0,004",[1720,47037,47038,47040],{},[898,47039,2398],{},[1963,47041,1970],{},[902,47043,47044],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,47046,47047,47050],{},[38,47048,47049],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,47052,47053,47056,47059,47062],{},[123,47054,47055],{},"(a) Sníží ceny surovin — vstupů.",[123,47057,47058],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,47060,47061],{},"(c) Zvýší ceny všech energií.",[123,47063,47064],{},"(d) Sníží daňové odvody státu.",[724,47066,47067,46766,47069,47103,47104,47132],{},[38,47068,43449],{},[883,47070,47072],{"className":47071},[886],[888,47073,47074],{"xmlns":890},[892,47075,47076,47100],{},[895,47077,47078,47080,47082,47084,47086,47088,47090,47092,47094,47096,47098],{},[898,47079,2398],{},[1664,47081,1676],{},[898,47083,2351],{},[1664,47085,1667],{"stretchy":1666},[898,47087,1973],{},[1664,47089,1673],{"stretchy":1666},[1664,47091,1676],{},[1963,47093,5575],{},[898,47095,1973],{},[1664,47097,1700],{},[1963,47099,36744],{},[902,47101,47102],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,47105,47107],{"className":47106},[886],[888,47108,47109],{"xmlns":890},[892,47110,47111,47129],{},[895,47112,47113,47115,47117,47123,47125,47127],{},[898,47114,2398],{},[1664,47116,1676],{},[1720,47118,47119,47121],{},[898,47120,2351],{},[1664,47122,4920],{},[1664,47124,1667],{"stretchy":1666},[898,47126,1973],{},[1664,47128,1673],{"stretchy":1666},[902,47130,47131],{"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.",[198,47134,41825],{"id":47135},"tržní-rovnováha-1",[724,47137,47138,47140,47141,47158,47159,2087],{},[38,47139,43509],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,47142,47144],{"className":47143},[886],[888,47145,47146],{"xmlns":890},[892,47147,47148,47156],{},[895,47149,47150],{},[1720,47151,47152,47154],{},[898,47153,1973],{},[898,47155,4819],{},[902,47157,42903],{"encoding":904}," a rovnovážnou cenu ",[883,47160,47162],{"className":47161},[886],[888,47163,47164],{"xmlns":890},[892,47165,47166,47174],{},[895,47167,47168],{},[1720,47169,47170,47172],{},[898,47171,2398],{},[898,47173,4819],{},[902,47175,41966],{"encoding":904},[120,47177,47178,47231,47282,47341],{},[123,47179,46045,47180,1343,47207,1977],{},[883,47181,47183],{"className":47182},[886],[888,47184,47185],{"xmlns":890},[892,47186,47187,47204],{},[895,47188,47189,47191,47193,47195,47197,47199,47201],{},[898,47190,2398],{},[1664,47192,1676],{},[1664,47194,1867],{},[1963,47196,2826],{},[898,47198,1973],{},[1664,47200,1700],{},[1963,47202,47203],{},"80",[902,47205,47206],{"encoding":904},"P = -5Q + 80",[883,47208,47210],{"className":47209},[886],[888,47211,47212],{"xmlns":890},[892,47213,47214,47228],{},[895,47215,47216,47218,47220,47222,47224,47226],{},[898,47217,2398],{},[1664,47219,1676],{},[1963,47221,1970],{},[898,47223,1973],{},[1664,47225,1700],{},[1963,47227,3442],{},[902,47229,47230],{"encoding":904},"P = 2Q + 10",[123,47232,46078,47233,1343,47259,1977],{},[883,47234,47236],{"className":47235},[886],[888,47237,47238],{"xmlns":890},[892,47239,47240,47256],{},[895,47241,47242,47244,47246,47248,47250,47252,47254],{},[898,47243,1973],{},[1664,47245,1676],{},[1664,47247,1867],{},[1963,47249,5575],{},[898,47251,2398],{},[1664,47253,1700],{},[1963,47255,5570],{},[902,47257,47258],{"encoding":904},"Q = -0{,}5P + 25",[883,47260,47262],{"className":47261},[886],[888,47263,47264],{"xmlns":890},[892,47265,47266,47280],{},[895,47267,47268,47270,47272,47274,47276,47278],{},[898,47269,1973],{},[1664,47271,1676],{},[1963,47273,1970],{},[898,47275,2398],{},[1664,47277,1867],{},[1963,47279,3696],{},[902,47281,41347],{"encoding":904},[123,47283,46109,47284,1343,47310,1977],{},[883,47285,47287],{"className":47286},[886],[888,47288,47289],{"xmlns":890},[892,47290,47291,47307],{},[895,47292,47293,47295,47297,47299,47301,47303,47305],{},[898,47294,2398],{},[1664,47296,1676],{},[1664,47298,1867],{},[1963,47300,2944],{},[898,47302,1973],{},[1664,47304,1700],{},[1963,47306,4614],{},[902,47308,47309],{"encoding":904},"P = -4Q + 120",[883,47311,47313],{"className":47312},[886],[888,47314,47315],{"xmlns":890},[892,47316,47317,47338],{},[895,47318,47319,47321,47323,47331,47333,47335],{},[898,47320,2398],{},[1664,47322,1676],{},[2919,47324,47325],{"scriptlevel":2058,"displaystyle":1666},[2922,47326,47327,47329],{},[1963,47328,2875],{},[1963,47330,2774],{},[898,47332,1973],{},[1664,47334,1700],{},[1963,47336,47337],{},"29",[902,47339,47340],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,47342,46144,47343,1343,47372,1977],{},[883,47344,47346],{"className":47345},[886],[888,47347,47348],{"xmlns":890},[892,47349,47350,47369],{},[895,47351,47352,47354,47356,47358,47364,47366],{},[898,47353,2398],{},[1664,47355,1676],{},[1664,47357,1867],{},[1720,47359,47360,47362],{},[898,47361,1973],{},[1963,47363,1970],{},[1664,47365,1700],{},[1963,47367,47368],{},"52",[902,47370,47371],{"encoding":904},"P = -Q^2 + 52",[883,47373,47375],{"className":47374},[886],[888,47376,47377],{"xmlns":890},[892,47378,47379,47397],{},[895,47380,47381,47383,47385,47387,47393,47395],{},[898,47382,2398],{},[1664,47384,1676],{},[1963,47386,1970],{},[1720,47388,47389,47391],{},[898,47390,1973],{},[1963,47392,1970],{},[1664,47394,1700],{},[1963,47396,3442],{},[902,47398,47399],{"encoding":904},"P = 2Q^2 + 10",[724,47401,47402,47405,47406,47436,47437,47467],{},[38,47403,47404],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,47407,47409],{"className":47408},[886],[888,47410,47411],{"xmlns":890},[892,47412,47413,47433],{},[895,47414,47415,47423,47425],{},[1810,47416,47417,47419,47421],{},[898,47418,1973],{},[1963,47420,2875],{},[898,47422,4819],{},[1664,47424,1916],{"separator":1915},[1810,47426,47427,47429,47431],{},[898,47428,1973],{},[1963,47430,1970],{},[898,47432,4819],{},[902,47434,47435],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,47438,47440],{"className":47439},[886],[888,47441,47442],{"xmlns":890},[892,47443,47444,47464],{},[895,47445,47446,47454,47456],{},[1810,47447,47448,47450,47452],{},[898,47449,2398],{},[1963,47451,2875],{},[898,47453,4819],{},[1664,47455,1916],{"separator":1915},[1810,47457,47458,47460,47462],{},[898,47459,2398],{},[1963,47461,1970],{},[898,47463,4819],{},[902,47465,47466],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,47469,47470,47622],{},[123,47471,46045,47472,1343,47512,1343,47554,1343,47588,1977],{},[883,47473,47475],{"className":47474},[886],[888,47476,47477],{"xmlns":890},[892,47478,47479,47509],{},[895,47480,47481,47487,47489,47491,47493,47495,47501,47503],{},[2355,47482,47483,47485],{},[898,47484,1973],{},[1963,47486,2875],{},[1664,47488,1676],{},[1963,47490,3442],{},[1664,47492,1867],{},[1963,47494,1970],{},[2355,47496,47497,47499],{},[898,47498,2398],{},[1963,47500,2875],{},[1664,47502,1700],{},[2355,47504,47505,47507],{},[898,47506,2398],{},[1963,47508,1970],{},[902,47510,47511],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,47513,47515],{"className":47514},[886],[888,47516,47517],{"xmlns":890},[892,47518,47519,47551],{},[895,47520,47521,47527,47529,47531,47533,47535,47541,47543,47545],{},[2355,47522,47523,47525],{},[898,47524,1973],{},[1963,47526,1970],{},[1664,47528,1676],{},[1963,47530,2826],{},[1664,47532,1700],{},[1963,47534,1970],{},[2355,47536,47537,47539],{},[898,47538,2398],{},[1963,47540,2875],{},[1664,47542,1867],{},[1963,47544,1970],{},[2355,47546,47547,47549],{},[898,47548,2398],{},[1963,47550,1970],{},[902,47552,47553],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,47555,47557],{"className":47556},[886],[888,47558,47559],{"xmlns":890},[892,47560,47561,47585],{},[895,47562,47563,47569,47571,47573,47575,47577,47579],{},[2355,47564,47565,47567],{},[898,47566,1973],{},[1963,47568,2875],{},[1664,47570,1676],{},[1664,47572,1867],{},[1963,47574,2774],{},[1664,47576,1700],{},[1963,47578,1970],{},[2355,47580,47581,47583],{},[898,47582,2398],{},[1963,47584,2875],{},[902,47586,47587],{"encoding":904},"Q_1 = -3 + 2P_1",[883,47589,47591],{"className":47590},[886],[888,47592,47593],{"xmlns":890},[892,47594,47595,47619],{},[895,47596,47597,47603,47605,47607,47609,47611,47613],{},[2355,47598,47599,47601],{},[898,47600,1973],{},[1963,47602,1970],{},[1664,47604,1676],{},[1664,47606,1867],{},[1963,47608,1970],{},[1664,47610,1700],{},[1963,47612,2774],{},[2355,47614,47615,47617],{},[898,47616,2398],{},[1963,47618,1970],{},[902,47620,47621],{"encoding":904},"Q_2 = -2 + 3P_2",[123,47623,46078,47624,1343,47664,1343,47706,1343,47738,1977],{},[883,47625,47627],{"className":47626},[886],[888,47628,47629],{"xmlns":890},[892,47630,47631,47661],{},[895,47632,47633,47639,47641,47643,47645,47647,47653,47655],{},[2355,47634,47635,47637],{},[898,47636,1973],{},[1963,47638,2875],{},[1664,47640,1676],{},[1963,47642,1965],{},[1664,47644,1867],{},[1963,47646,1970],{},[2355,47648,47649,47651],{},[898,47650,2398],{},[1963,47652,2875],{},[1664,47654,1700],{},[2355,47656,47657,47659],{},[898,47658,2398],{},[1963,47660,1970],{},[902,47662,47663],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,47665,47667],{"className":47666},[886],[888,47668,47669],{"xmlns":890},[892,47670,47671,47703],{},[895,47672,47673,47679,47681,47683,47685,47687,47693,47695,47697],{},[2355,47674,47675,47677],{},[898,47676,1973],{},[1963,47678,1970],{},[1664,47680,1676],{},[1963,47682,2826],{},[1664,47684,1700],{},[1963,47686,1970],{},[2355,47688,47689,47691],{},[898,47690,2398],{},[1963,47692,2875],{},[1664,47694,1867],{},[1963,47696,2774],{},[2355,47698,47699,47701],{},[898,47700,2398],{},[1963,47702,1970],{},[902,47704,47705],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,47707,47709],{"className":47708},[886],[888,47710,47711],{"xmlns":890},[892,47712,47713,47735],{},[895,47714,47715,47721,47723,47725,47727,47729],{},[2355,47716,47717,47719],{},[898,47718,1973],{},[1963,47720,2875],{},[1664,47722,1676],{},[1664,47724,1867],{},[1963,47726,3442],{},[1664,47728,1700],{},[2355,47730,47731,47733],{},[898,47732,2398],{},[1963,47734,2875],{},[902,47736,47737],{"encoding":904},"Q_1 = -10 + P_1",[883,47739,47741],{"className":47740},[886],[888,47742,47743],{"xmlns":890},[892,47744,47745,47767],{},[895,47746,47747,47753,47755,47757,47759,47761],{},[2355,47748,47749,47751],{},[898,47750,1973],{},[1963,47752,1970],{},[1664,47754,1676],{},[1963,47756,2826],{},[1664,47758,1700],{},[1963,47760,2833],{},[2355,47762,47763,47765],{},[898,47764,2398],{},[1963,47766,1970],{},[902,47768,47769],{"encoding":904},"Q_2 = 5 + 6P_2",[724,47771,47772,47775,47776,1343,47824,1343,47870,47920,47921,1343,47953,1343,47987,22094,48021,4454,48039,48057,48058,48071,48072,48098,48099,47436,48139,1977],{},[38,47773,47774],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,47777,47779],{"className":47778},[886],[888,47780,47781],{"xmlns":890},[892,47782,47783,47821],{},[895,47784,47785,47791,47793,47795,47797,47803,47805,47807,47813,47815],{},[2355,47786,47787,47789],{},[898,47788,1973],{},[1963,47790,2875],{},[1664,47792,1676],{},[1963,47794,36744],{},[1664,47796,1867],{},[2355,47798,47799,47801],{},[898,47800,2398],{},[1963,47802,2875],{},[1664,47804,1700],{},[1963,47806,1970],{},[2355,47808,47809,47811],{},[898,47810,2398],{},[1963,47812,1970],{},[1664,47814,1700],{},[2355,47816,47817,47819],{},[898,47818,2398],{},[1963,47820,2774],{},[902,47822,47823],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,47825,47827],{"className":47826},[886],[888,47828,47829],{"xmlns":890},[892,47830,47831,47867],{},[895,47832,47833,47839,47841,47843,47845,47851,47853,47859,47861],{},[2355,47834,47835,47837],{},[898,47836,1973],{},[1963,47838,1970],{},[1664,47840,1676],{},[1963,47842,4567],{},[1664,47844,1700],{},[2355,47846,47847,47849],{},[898,47848,2398],{},[1963,47850,2875],{},[1664,47852,1867],{},[2355,47854,47855,47857],{},[898,47856,2398],{},[1963,47858,1970],{},[1664,47860,1867],{},[2355,47862,47863,47865],{},[898,47864,2398],{},[1963,47866,2774],{},[902,47868,47869],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,47871,47873],{"className":47872},[886],[888,47874,47875],{"xmlns":890},[892,47876,47877,47917],{},[895,47878,47879,47885,47887,47889,47891,47893,47899,47901,47907,47909,47911],{},[2355,47880,47881,47883],{},[898,47882,1973],{},[1963,47884,2774],{},[1664,47886,1676],{},[1963,47888,6151],{},[1664,47890,1700],{},[1963,47892,1970],{},[2355,47894,47895,47897],{},[898,47896,2398],{},[1963,47898,2875],{},[1664,47900,1867],{},[2355,47902,47903,47905],{},[898,47904,2398],{},[1963,47906,1970],{},[1664,47908,1867],{},[1963,47910,2944],{},[2355,47912,47913,47915],{},[898,47914,2398],{},[1963,47916,2774],{},[902,47918,47919],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,47922,47924],{"className":47923},[886],[888,47925,47926],{"xmlns":890},[892,47927,47928,47950],{},[895,47929,47930,47936,47938,47940,47942,47944],{},[2355,47931,47932,47934],{},[898,47933,1973],{},[1963,47935,2875],{},[1664,47937,1676],{},[1664,47939,1867],{},[1963,47941,24701],{},[1664,47943,1700],{},[2355,47945,47946,47948],{},[898,47947,2398],{},[1963,47949,2875],{},[902,47951,47952],{"encoding":904},"Q_1 = -7 + P_1",[883,47954,47956],{"className":47955},[886],[888,47957,47958],{"xmlns":890},[892,47959,47960,47984],{},[895,47961,47962,47968,47970,47972,47974,47976,47978],{},[2355,47963,47964,47966],{},[898,47965,1973],{},[1963,47967,1970],{},[1664,47969,1676],{},[1664,47971,1867],{},[1963,47973,2944],{},[1664,47975,1700],{},[1963,47977,2944],{},[2355,47979,47980,47982],{},[898,47981,2398],{},[1963,47983,1970],{},[902,47985,47986],{"encoding":904},"Q_2 = -4 + 4P_2",[883,47988,47990],{"className":47989},[886],[888,47991,47992],{"xmlns":890},[892,47993,47994,48018],{},[895,47995,47996,48002,48004,48006,48008,48010,48012],{},[2355,47997,47998,48000],{},[898,47999,1973],{},[1963,48001,2774],{},[1664,48003,1676],{},[1664,48005,1867],{},[1963,48007,2826],{},[1664,48009,1700],{},[1963,48011,1970],{},[2355,48013,48014,48016],{},[898,48015,2398],{},[1963,48017,2774],{},[902,48019,48020],{"encoding":904},"Q_3 = -5 + 2P_3",[883,48022,48024],{"className":48023},[886],[888,48025,48026],{"xmlns":890},[892,48027,48028,48036],{},[895,48029,48030],{},[2355,48031,48032,48034],{},[898,48033,1973],{},[898,48035,18290],{},[902,48037,48038],{"encoding":904},"Q_i",[883,48040,48042],{"className":48041},[886],[888,48043,48044],{"xmlns":890},[892,48045,48046,48054],{},[895,48047,48048],{},[2355,48049,48050,48052],{},[898,48051,2398],{},[898,48053,18290],{},[902,48055,48056],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,48059,48061],{"className":48060},[886],[888,48062,48063],{"xmlns":890},[892,48064,48065,48069],{},[895,48066,48067],{},[898,48068,18290],{},[902,48070,18290],{"encoding":904},"-tého zboží, ",[883,48073,48075],{"className":48074},[886],[888,48076,48077],{"xmlns":890},[892,48078,48079,48095],{},[895,48080,48081,48083,48085,48087,48089,48091,48093],{},[898,48082,18290],{},[1664,48084,1676],{},[1963,48086,2875],{},[1664,48088,1916],{"separator":1915},[1963,48090,1970],{},[1664,48092,1916],{"separator":1915},[1963,48094,2774],{},[902,48096,48097],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,48100,48102],{"className":48101},[886],[888,48103,48104],{"xmlns":890},[892,48105,48106,48136],{},[895,48107,48108,48116,48118,48126,48128],{},[1810,48109,48110,48112,48114],{},[898,48111,1973],{},[1963,48113,2875],{},[898,48115,4819],{},[1664,48117,1916],{"separator":1915},[1810,48119,48120,48122,48124],{},[898,48121,1973],{},[1963,48123,1970],{},[898,48125,4819],{},[1664,48127,1916],{"separator":1915},[1810,48129,48130,48132,48134],{},[898,48131,1973],{},[1963,48133,2774],{},[898,48135,4819],{},[902,48137,48138],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,48140,48142],{"className":48141},[886],[888,48143,48144],{"xmlns":890},[892,48145,48146,48176],{},[895,48147,48148,48156,48158,48166,48168],{},[1810,48149,48150,48152,48154],{},[898,48151,2398],{},[1963,48153,2875],{},[898,48155,4819],{},[1664,48157,1916],{"separator":1915},[1810,48159,48160,48162,48164],{},[898,48161,2398],{},[1963,48163,1970],{},[898,48165,4819],{},[1664,48167,1916],{"separator":1915},[1810,48169,48170,48172,48174],{},[898,48171,2398],{},[1963,48173,2774],{},[898,48175,4819],{},[902,48177,48178],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,48180,48181,48184,48185,48221,48222,1977],{},[38,48182,48183],{},"2.13"," Jsou dány poptávka ",[883,48186,48188],{"className":48187},[886],[888,48189,48190],{"xmlns":890},[892,48191,48192,48218],{},[895,48193,48194,48196,48198,48200,48202,48204,48206,48208,48210,48212,48214,48216],{},[898,48195,2398],{},[1664,48197,1676],{},[898,48199,2379],{},[1664,48201,1667],{"stretchy":1666},[898,48203,1973],{},[1664,48205,1673],{"stretchy":1666},[1664,48207,1676],{},[1664,48209,1867],{},[1963,48211,2944],{},[898,48213,1973],{},[1664,48215,1700],{},[1963,48217,47203],{},[902,48219,48220],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,48223,48225],{"className":48224},[886],[888,48226,48227],{"xmlns":890},[892,48228,48229,48253],{},[895,48230,48231,48233,48235,48237,48239,48241,48243,48245,48247,48249,48251],{},[898,48232,2398],{},[1664,48234,1676],{},[898,48236,2351],{},[1664,48238,1667],{"stretchy":1666},[898,48240,1973],{},[1664,48242,1673],{"stretchy":1666},[1664,48244,1676],{},[1963,48246,2774],{},[898,48248,1973],{},[1664,48250,1700],{},[1963,48252,3442],{},[902,48254,48255],{"encoding":904},"P = S(Q) = 3Q + 10",[120,48257,48258,48295,48359,48419],{},[123,48259,48260,48261,47158,48278,1977],{},"(a) Určete rovnovážné množství ",[883,48262,48264],{"className":48263},[886],[888,48265,48266],{"xmlns":890},[892,48267,48268,48276],{},[895,48269,48270],{},[1720,48271,48272,48274],{},[898,48273,1973],{},[898,48275,4819],{},[902,48277,42903],{"encoding":904},[883,48279,48281],{"className":48280},[886],[888,48282,48283],{"xmlns":890},[892,48284,48285,48293],{},[895,48286,48287],{},[1720,48288,48289,48291],{},[898,48290,2398],{},[898,48292,4819],{},[902,48294,41966],{"encoding":904},[123,48296,48297,48298,48316,48317,48337,48338,48358],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,48299,48301],{"className":48300},[886],[888,48302,48303],{"xmlns":890},[892,48304,48305,48313],{},[895,48306,48307,48309,48311],{},[898,48308,1991],{},[1664,48310,1676],{},[1963,48312,24701],{},[902,48314,48315],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,48318,48320],{"className":48319},[886],[888,48321,48322],{"xmlns":890},[892,48323,48324,48334],{},[895,48325,48326],{},[1810,48327,48328,48330,48332],{},[898,48329,1973],{},[1963,48331,2875],{},[898,48333,4819],{},[902,48335,48336],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,48339,48341],{"className":48340},[886],[888,48342,48343],{"xmlns":890},[892,48344,48345,48355],{},[895,48346,48347],{},[1810,48348,48349,48351,48353],{},[898,48350,2398],{},[1963,48352,2875],{},[898,48354,4819],{},[902,48356,48357],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,48360,48361,48362,48316,48379,48337,48399,48358],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,48363,48365],{"className":48364},[886],[888,48366,48367],{"xmlns":890},[892,48368,48369,48377],{},[895,48370,48371,48373,48375],{},[898,48372,1991],{},[1664,48374,1676],{},[1963,48376,24701],{},[902,48378,48315],{"encoding":904},[883,48380,48382],{"className":48381},[886],[888,48383,48384],{"xmlns":890},[892,48385,48386,48396],{},[895,48387,48388],{},[1810,48389,48390,48392,48394],{},[898,48391,1973],{},[1963,48393,1970],{},[898,48395,4819],{},[902,48397,48398],{"encoding":904},"Q_2^E",[883,48400,48402],{"className":48401},[886],[888,48403,48404],{"xmlns":890},[892,48405,48406,48416],{},[895,48407,48408],{},[1810,48409,48410,48412,48414],{},[898,48411,2398],{},[1963,48413,1970],{},[898,48415,4819],{},[902,48417,48418],{"encoding":904},"P_2^E",[123,48420,48421],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,48423,48424,48425,1977],{},"Viz též ",[207,48426,43221],{"className":48427,"dataFsResolvedFilePath":809,"href":810},[210],[198,48429,43523],{"id":48430},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,48432,48433,48184,48436,48221,48472,1977],{},[38,48434,48435],{},"2.14",[883,48437,48439],{"className":48438},[886],[888,48440,48441],{"xmlns":890},[892,48442,48443,48469],{},[895,48444,48445,48447,48449,48451,48453,48455,48457,48459,48461,48463,48465,48467],{},[898,48446,2398],{},[1664,48448,1676],{},[898,48450,207],{},[898,48452,1973],{},[1664,48454,1700],{},[898,48456,1818],{},[1664,48458,1676],{},[1664,48460,1867],{},[1963,48462,1970],{},[898,48464,1973],{},[1664,48466,1700],{},[1963,48468,3696],{},[902,48470,48471],{"encoding":904},"P = aQ + b = -2Q + 50",[883,48473,48475],{"className":48474},[886],[888,48476,48477],{"xmlns":890},[892,48478,48479,48503],{},[895,48480,48481,48483,48485,48487,48489,48491,48493,48495,48497,48499,48501],{},[898,48482,2398],{},[1664,48484,1676],{},[898,48486,2034],{},[898,48488,1973],{},[1664,48490,1700],{},[898,48492,1695],{},[1664,48494,1676],{},[1963,48496,19821],{},[898,48498,1973],{},[1664,48500,1700],{},[1963,48502,9599],{},[902,48504,48505],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,48507,48508,48544,48547,48633,48686,48766,48820],{},[123,48509,48260,48510,47158,48527,1977],{},[883,48511,48513],{"className":48512},[886],[888,48514,48515],{"xmlns":890},[892,48516,48517,48525],{},[895,48518,48519],{},[1720,48520,48521,48523],{},[898,48522,1973],{},[898,48524,4819],{},[902,48526,42903],{"encoding":904},[883,48528,48530],{"className":48529},[886],[888,48531,48532],{"xmlns":890},[892,48533,48534,48542],{},[895,48535,48536],{},[1720,48537,48538,48540],{},[898,48539,2398],{},[898,48541,4819],{},[902,48543,41966],{"encoding":904},[123,48545,48546],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,48548,48549,48550,48567,48568,3257,48581,3271,48597,48613,48614,1977],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,48551,48553],{"className":48552},[886],[888,48554,48555],{"xmlns":890},[892,48556,48557,48565],{},[895,48558,48559],{},[1720,48560,48561,48563],{},[898,48562,1973],{},[898,48564,4819],{},[902,48566,42903],{"encoding":904}," odpovídající změně ",[883,48569,48571],{"className":48570},[886],[888,48572,48573],{"xmlns":890},[892,48574,48575,48579],{},[895,48576,48577],{},[898,48578,207],{},[902,48580,207],{"encoding":904},[883,48582,48584],{"className":48583},[886],[888,48585,48586],{"xmlns":890},[892,48587,48588,48594],{},[895,48589,48590,48592],{},[1664,48591,1867],{},[1963,48593,1970],{},[902,48595,48596],{"encoding":904},"-2",[883,48598,48600],{"className":48599},[886],[888,48601,48602],{"xmlns":890},[892,48603,48604,48610],{},[895,48605,48606,48608],{},[1664,48607,1867],{},[1963,48609,2774],{},[902,48611,48612],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48615,48617],{"className":48616},[886],[888,48618,48619],{"xmlns":890},[892,48620,48621,48631],{},[895,48622,48623],{},[1810,48624,48625,48627,48629],{},[898,48626,1973],{},[1963,48628,2875],{},[898,48630,4819],{},[902,48632,48336],{"encoding":904},[123,48634,48635,48636,48567,48653,48666,48667,1977],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,48637,48639],{"className":48638},[886],[888,48640,48641],{"xmlns":890},[892,48642,48643,48651],{},[895,48644,48645],{},[1720,48646,48647,48649],{},[898,48648,1973],{},[898,48650,4819],{},[902,48652,42903],{"encoding":904},[883,48654,48656],{"className":48655},[886],[888,48657,48658],{"xmlns":890},[892,48659,48660,48664],{},[895,48661,48662],{},[898,48663,1818],{},[902,48665,1818],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48668,48670],{"className":48669},[886],[888,48671,48672],{"xmlns":890},[892,48673,48674,48684],{},[895,48675,48676],{},[1810,48677,48678,48680,48682],{},[898,48679,1973],{},[1963,48681,1970],{},[898,48683,4819],{},[902,48685,48398],{"encoding":904},[123,48687,48688,48689,48567,48706,3257,48719,3271,48732,48613,48746,1977],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,48690,48692],{"className":48691},[886],[888,48693,48694],{"xmlns":890},[892,48695,48696,48704],{},[895,48697,48698],{},[1720,48699,48700,48702],{},[898,48701,1973],{},[898,48703,4819],{},[902,48705,42903],{"encoding":904},[883,48707,48709],{"className":48708},[886],[888,48710,48711],{"xmlns":890},[892,48712,48713,48717],{},[895,48714,48715],{},[898,48716,2034],{},[902,48718,2034],{"encoding":904},[883,48720,48722],{"className":48721},[886],[888,48723,48724],{"xmlns":890},[892,48725,48726,48730],{},[895,48727,48728],{},[1963,48729,19821],{},[902,48731,44960],{"encoding":904},[883,48733,48735],{"className":48734},[886],[888,48736,48737],{"xmlns":890},[892,48738,48739,48743],{},[895,48740,48741],{},[1963,48742,15088],{},[902,48744,48745],{"encoding":904},"0{,}8",[883,48747,48749],{"className":48748},[886],[888,48750,48751],{"xmlns":890},[892,48752,48753,48763],{},[895,48754,48755],{},[1810,48756,48757,48759,48761],{},[898,48758,1973],{},[1963,48760,2774],{},[898,48762,4819],{},[902,48764,48765],{"encoding":904},"Q_3^E",[123,48767,48768,48769,48567,48786,48799,48800,1977],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,48770,48772],{"className":48771},[886],[888,48773,48774],{"xmlns":890},[892,48775,48776,48784],{},[895,48777,48778],{},[1720,48779,48780,48782],{},[898,48781,1973],{},[898,48783,4819],{},[902,48785,42903],{"encoding":904},[883,48787,48789],{"className":48788},[886],[888,48790,48791],{"xmlns":890},[892,48792,48793,48797],{},[895,48794,48795],{},[898,48796,1695],{},[902,48798,1695],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48801,48803],{"className":48802},[886],[888,48804,48805],{"xmlns":890},[892,48806,48807,48817],{},[895,48808,48809],{},[1810,48810,48811,48813,48815],{},[898,48812,1973],{},[1963,48814,2944],{},[898,48816,4819],{},[902,48818,48819],{"encoding":904},"Q_4^E",[123,48821,48822,48823,48840,48841,48854,48855,21920,48868,1343,48883,21920,48896,4454,48910,21920,48923,48938,48939,1977],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,48824,48826],{"className":48825},[886],[888,48827,48828],{"xmlns":890},[892,48829,48830,48838],{},[895,48831,48832],{},[1720,48833,48834,48836],{},[898,48835,1973],{},[898,48837,4819],{},[902,48839,42903],{"encoding":904}," odpovídající změnám ",[883,48842,48844],{"className":48843},[886],[888,48845,48846],{"xmlns":890},[892,48847,48848,48852],{},[895,48849,48850],{},[898,48851,207],{},[902,48853,207],{"encoding":904}," o 1, ",[883,48856,48858],{"className":48857},[886],[888,48859,48860],{"xmlns":890},[892,48861,48862,48866],{},[895,48863,48864],{},[898,48865,1818],{},[902,48867,1818],{"encoding":904},[883,48869,48871],{"className":48870},[886],[888,48872,48873],{"xmlns":890},[892,48874,48875,48881],{},[895,48876,48877,48879],{},[1664,48878,1867],{},[1963,48880,3442],{},[902,48882,19955],{"encoding":904},[883,48884,48886],{"className":48885},[886],[888,48887,48888],{"xmlns":890},[892,48889,48890,48894],{},[895,48891,48892],{},[898,48893,2034],{},[902,48895,2034],{"encoding":904},[883,48897,48899],{"className":48898},[886],[888,48900,48901],{"xmlns":890},[892,48902,48903,48907],{},[895,48904,48905],{},[1963,48906,2220],{},[902,48908,48909],{"encoding":904},"0{,}1",[883,48911,48913],{"className":48912},[886],[888,48914,48915],{"xmlns":890},[892,48916,48917,48921],{},[895,48918,48919],{},[898,48920,1695],{},[902,48922,1695],{"encoding":904},[883,48924,48926],{"className":48925},[886],[888,48927,48928],{"xmlns":890},[892,48929,48930,48936],{},[895,48931,48932,48934],{},[1664,48933,1867],{},[1963,48935,3442],{},[902,48937,19955],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,48940,48942],{"className":48941},[886],[888,48943,48944],{"xmlns":890},[892,48945,48946,48956],{},[895,48947,48948],{},[1810,48949,48950,48952,48954],{},[898,48951,1973],{},[1963,48953,2826],{},[898,48955,4819],{},[902,48957,48958],{"encoding":904},"Q_5^E",[724,48960,48961,48184,48964,48221,48987,1977],{},[38,48962,48963],{},"2.15",[883,48965,48967],{"className":48966},[886],[888,48968,48969],{"xmlns":890},[892,48970,48971,48985],{},[895,48972,48973,48975,48977,48979,48981,48983],{},[898,48974,2398],{},[1664,48976,1676],{},[898,48978,207],{},[898,48980,1973],{},[1664,48982,1700],{},[898,48984,1818],{},[902,48986,37560],{"encoding":904},[883,48988,48990],{"className":48989},[886],[888,48991,48992],{"xmlns":890},[892,48993,48994,49008],{},[895,48995,48996,48998,49000,49002,49004,49006],{},[898,48997,2398],{},[1664,48999,1676],{},[898,49001,2034],{},[898,49003,1973],{},[1664,49005,1700],{},[898,49007,1695],{},[902,49009,40742],{"encoding":904},[120,49011,49012,49087,49104,49213,49266,49320],{},[123,49013,49014,49015,49028,49029,49054,49055,49086],{},"(a) Odvoďte redukovaný tvar pro ",[883,49016,49018],{"className":49017},[886],[888,49019,49020],{"xmlns":890},[892,49021,49022,49026],{},[895,49023,49024],{},[898,49025,2398],{},[902,49027,2398],{"encoding":904},". Stanovte podmínky pro ",[883,49030,49032],{"className":49031},[886],[888,49033,49034],{"xmlns":890},[892,49035,49036,49052],{},[895,49037,49038,49040,49042,49044,49046,49048,49050],{},[898,49039,207],{},[1664,49041,1916],{"separator":1915},[898,49043,1818],{},[1664,49045,1916],{"separator":1915},[898,49047,2034],{},[1664,49049,1916],{"separator":1915},[898,49051,1695],{},[902,49053,43785],{"encoding":904}," tak, aby rovnovážný bod ",[883,49056,49058],{"className":49057},[886],[888,49059,49060],{"xmlns":890},[892,49061,49062,49084],{},[895,49063,49064,49066,49068,49074,49076,49082],{},[898,49065,4819],{},[1664,49067,1837],{"stretchy":1666},[1720,49069,49070,49072],{},[898,49071,1973],{},[898,49073,4819],{},[1664,49075,1916],{"separator":1915},[1720,49077,49078,49080],{},[898,49079,2398],{},[898,49081,4819],{},[1664,49083,1850],{"stretchy":1666},[902,49085,41867],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,49088,49089,49090,49103],{},"(b) Vypočtěte multiplikátory pro ",[883,49091,49093],{"className":49092},[886],[888,49094,49095],{"xmlns":890},[892,49096,49097,49101],{},[895,49098,49099],{},[898,49100,2398],{},[902,49102,2398],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,49105,49106,49107,1343,49127,1343,49145,1343,49163,49181,49182,49199,49200,1977],{},"(c) Pro hodnoty parametrů ",[883,49108,49110],{"className":49109},[886],[888,49111,49112],{"xmlns":890},[892,49113,49114,49124],{},[895,49115,49116,49118,49120,49122],{},[898,49117,207],{},[1664,49119,1676],{},[1664,49121,1867],{},[1963,49123,1970],{},[902,49125,49126],{"encoding":904},"a = -2",[883,49128,49130],{"className":49129},[886],[888,49131,49132],{"xmlns":890},[892,49133,49134,49142],{},[895,49135,49136,49138,49140],{},[898,49137,1818],{},[1664,49139,1676],{},[1963,49141,5777],{},[902,49143,49144],{"encoding":904},"b = 40",[883,49146,49148],{"className":49147},[886],[888,49149,49150],{"xmlns":890},[892,49151,49152,49160],{},[895,49153,49154,49156,49158],{},[898,49155,2034],{},[1664,49157,1676],{},[1963,49159,5575],{},[902,49161,49162],{"encoding":904},"c = 0{,}5",[883,49164,49166],{"className":49165},[886],[888,49167,49168],{"xmlns":890},[892,49169,49170,49178],{},[895,49171,49172,49174,49176],{},[898,49173,1695],{},[1664,49175,1676],{},[1963,49177,3442],{},[902,49179,49180],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,49183,49185],{"className":49184},[886],[888,49186,49187],{"xmlns":890},[892,49188,49189,49197],{},[895,49190,49191],{},[1720,49192,49193,49195],{},[898,49194,2398],{},[898,49196,4819],{},[902,49198,41966],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,49201,49203],{"className":49202},[886],[888,49204,49205],{"xmlns":890},[892,49206,49207,49211],{},[895,49208,49209],{},[898,49210,2398],{},[902,49212,2398],{"encoding":904},[123,49214,49215,49216,48567,49233,49246,49247,1977],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,49217,49219],{"className":49218},[886],[888,49220,49221],{"xmlns":890},[892,49222,49223,49231],{},[895,49224,49225],{},[1720,49226,49227,49229],{},[898,49228,2398],{},[898,49230,4819],{},[902,49232,41966],{"encoding":904},[883,49234,49236],{"className":49235},[886],[888,49237,49238],{"xmlns":890},[892,49239,49240,49244],{},[895,49241,49242],{},[898,49243,207],{},[902,49245,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,49248,49250],{"className":49249},[886],[888,49251,49252],{"xmlns":890},[892,49253,49254,49264],{},[895,49255,49256],{},[1810,49257,49258,49260,49262],{},[898,49259,2398],{},[1963,49261,2875],{},[898,49263,4819],{},[902,49265,48357],{"encoding":904},[123,49267,49268,49269,49286,49287,49300,49301,1977],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,49270,49272],{"className":49271},[886],[888,49273,49274],{"xmlns":890},[892,49275,49276,49284],{},[895,49277,49278],{},[1720,49279,49280,49282],{},[898,49281,2398],{},[898,49283,4819],{},[902,49285,41966],{"encoding":904}," odpovídající poklesu ",[883,49288,49290],{"className":49289},[886],[888,49291,49292],{"xmlns":890},[892,49293,49294,49298],{},[895,49295,49296],{},[898,49297,207],{},[902,49299,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,49302,49304],{"className":49303},[886],[888,49305,49306],{"xmlns":890},[892,49307,49308,49318],{},[895,49309,49310],{},[1810,49311,49312,49314,49316],{},[898,49313,2398],{},[1963,49315,1970],{},[898,49317,4819],{},[902,49319,48418],{"encoding":904},[123,49321,49322,49323,48840,49340,49353,49354,3271,49367,4454,49382,49395,49396,1977],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,49324,49326],{"className":49325},[886],[888,49327,49328],{"xmlns":890},[892,49329,49330,49338],{},[895,49331,49332],{},[1720,49333,49334,49336],{},[898,49335,2398],{},[898,49337,4819],{},[902,49339,41966],{"encoding":904},[883,49341,49343],{"className":49342},[886],[888,49344,49345],{"xmlns":890},[892,49346,49347,49351],{},[895,49348,49349],{},[898,49350,207],{},[902,49352,207],{"encoding":904}," na 35, ",[883,49355,49357],{"className":49356},[886],[888,49358,49359],{"xmlns":890},[892,49360,49361,49365],{},[895,49362,49363],{},[898,49364,2034],{},[902,49366,2034],{"encoding":904},[883,49368,49370],{"className":49369},[886],[888,49371,49372],{"xmlns":890},[892,49373,49374,49379],{},[895,49375,49376],{},[1963,49377,49378],{},"0,7",[902,49380,49381],{"encoding":904},"0{,}7",[883,49383,49385],{"className":49384},[886],[888,49386,49387],{"xmlns":890},[892,49388,49389,49393],{},[895,49390,49391],{},[898,49392,1695],{},[902,49394,1695],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,49397,49399],{"className":49398},[886],[888,49400,49401],{"xmlns":890},[892,49402,49403,49413],{},[895,49404,49405],{},[1810,49406,49407,49409,49411],{},[898,49408,2398],{},[1963,49410,2774],{},[898,49412,4819],{},[902,49414,49415],{"encoding":904},"P_3^E",[724,49417,49418,48184,49421,48221,49449,22094,49477,4454,49503,1977],{},[38,49419,49420],{},"2.16",[883,49422,49424],{"className":49423},[886],[888,49425,49426],{"xmlns":890},[892,49427,49428,49446],{},[895,49429,49430,49432,49434,49436,49438,49440],{},[898,49431,2398],{},[1664,49433,1676],{},[898,49435,207],{},[1664,49437,1700],{},[898,49439,1818],{},[1720,49441,49442,49444],{},[898,49443,1973],{},[1963,49445,1970],{},[902,49447,49448],{"encoding":904},"P = a + bQ^2",[883,49450,49452],{"className":49451},[886],[888,49453,49454],{"xmlns":890},[892,49455,49456,49474],{},[895,49457,49458,49460,49462,49464,49466,49468],{},[898,49459,2398],{},[1664,49461,1676],{},[898,49463,2034],{},[1664,49465,1700],{},[898,49467,1695],{},[1720,49469,49470,49472],{},[898,49471,1973],{},[1963,49473,1970],{},[902,49475,49476],{"encoding":904},"P = c + dQ^2",[883,49478,49480],{"className":49479},[886],[888,49481,49482],{"xmlns":890},[892,49483,49484,49500],{},[895,49485,49486,49488,49490,49492,49494,49496,49498],{},[898,49487,207],{},[1664,49489,1916],{"separator":1915},[898,49491,2034],{},[1664,49493,1916],{"separator":1915},[898,49495,1695],{},[1664,49497,3984],{},[1963,49499,2058],{},[902,49501,49502],{"encoding":904},"a, c, d > 0",[883,49504,49506],{"className":49505},[886],[888,49507,49508],{"xmlns":890},[892,49509,49510,49518],{},[895,49511,49512,49514,49516],{},[898,49513,1818],{},[1664,49515,4022],{},[1963,49517,2058],{},[902,49519,49520],{"encoding":904},"b \u003C 0",[120,49522,49523,49571,49587,49694,49746,49798,49907,49923,50022,50075],{},[123,49524,49014,49525,49538,49539,49570],{},[883,49526,49528],{"className":49527},[886],[888,49529,49530],{"xmlns":890},[892,49531,49532,49536],{},[895,49533,49534],{},[898,49535,1973],{},[902,49537,1973],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,49540,49542],{"className":49541},[886],[888,49543,49544],{"xmlns":890},[892,49545,49546,49568],{},[895,49547,49548,49550,49552,49558,49560,49566],{},[898,49549,4819],{},[1664,49551,1837],{"stretchy":1666},[1720,49553,49554,49556],{},[898,49555,1973],{},[898,49557,4819],{},[1664,49559,1916],{"separator":1915},[1720,49561,49562,49564],{},[898,49563,2398],{},[898,49565,4819],{},[1664,49567,1850],{"stretchy":1666},[902,49569,41867],{"encoding":904}," patřil do 1. kvadrantu.",[123,49572,49089,49573,49586],{},[883,49574,49576],{"className":49575},[886],[888,49577,49578],{"xmlns":890},[892,49579,49580,49584],{},[895,49581,49582],{},[898,49583,1973],{},[902,49585,1973],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,49588,49106,49589,1343,49607,1343,49627,1343,49645,49663,49664,49199,49681,1977],{},[883,49590,49592],{"className":49591},[886],[888,49593,49594],{"xmlns":890},[892,49595,49596,49604],{},[895,49597,49598,49600,49602],{},[898,49599,207],{},[1664,49601,1676],{},[1963,49603,1965],{},[902,49605,49606],{"encoding":904},"a = 100",[883,49608,49610],{"className":49609},[886],[888,49611,49612],{"xmlns":890},[892,49613,49614,49624],{},[895,49615,49616,49618,49620,49622],{},[898,49617,1818],{},[1664,49619,1676],{},[1664,49621,1867],{},[1963,49623,2875],{},[902,49625,49626],{"encoding":904},"b = -1",[883,49628,49630],{"className":49629},[886],[888,49631,49632],{"xmlns":890},[892,49633,49634,49642],{},[895,49635,49636,49638,49640],{},[898,49637,2034],{},[1664,49639,1676],{},[1963,49641,9599],{},[902,49643,49644],{"encoding":904},"c = 20",[883,49646,49648],{"className":49647},[886],[888,49649,49650],{"xmlns":890},[892,49651,49652,49660],{},[895,49653,49654,49656,49658],{},[898,49655,1695],{},[1664,49657,1676],{},[1963,49659,2875],{},[902,49661,49662],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,49665,49667],{"className":49666},[886],[888,49668,49669],{"xmlns":890},[892,49670,49671,49679],{},[895,49672,49673],{},[1720,49674,49675,49677],{},[898,49676,1973],{},[898,49678,4819],{},[902,49680,42903],{"encoding":904},[883,49682,49684],{"className":49683},[886],[888,49685,49686],{"xmlns":890},[892,49687,49688,49692],{},[895,49689,49690],{},[898,49691,1973],{},[902,49693,1973],{"encoding":904},[123,49695,48635,49696,48567,49713,49726,49727,1977],{},[883,49697,49699],{"className":49698},[886],[888,49700,49701],{"xmlns":890},[892,49702,49703,49711],{},[895,49704,49705],{},[1720,49706,49707,49709],{},[898,49708,1973],{},[898,49710,4819],{},[902,49712,42903],{"encoding":904},[883,49714,49716],{"className":49715},[886],[888,49717,49718],{"xmlns":890},[892,49719,49720,49724],{},[895,49721,49722],{},[898,49723,207],{},[902,49725,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49728,49730],{"className":49729},[886],[888,49731,49732],{"xmlns":890},[892,49733,49734,49744],{},[895,49735,49736],{},[1810,49737,49738,49740,49742],{},[898,49739,1973],{},[1963,49741,2875],{},[898,49743,4819],{},[902,49745,48336],{"encoding":904},[123,49747,48688,49748,48567,49765,49778,49779,1977],{},[883,49749,49751],{"className":49750},[886],[888,49752,49753],{"xmlns":890},[892,49754,49755,49763],{},[895,49756,49757],{},[1720,49758,49759,49761],{},[898,49760,1973],{},[898,49762,4819],{},[902,49764,42903],{"encoding":904},[883,49766,49768],{"className":49767},[886],[888,49769,49770],{"xmlns":890},[892,49771,49772,49776],{},[895,49773,49774],{},[898,49775,2034],{},[902,49777,2034],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49780,49782],{"className":49781},[886],[888,49783,49784],{"xmlns":890},[892,49785,49786,49796],{},[895,49787,49788],{},[1810,49789,49790,49792,49794],{},[898,49791,1973],{},[1963,49793,1970],{},[898,49795,4819],{},[902,49797,48398],{"encoding":904},[123,49799,48768,49800,48840,49817,49830,49831,3271,49844,49859,49860,49873,49874,49887,49888,1977],{},[883,49801,49803],{"className":49802},[886],[888,49804,49805],{"xmlns":890},[892,49806,49807,49815],{},[895,49808,49809],{},[1720,49810,49811,49813],{},[898,49812,1973],{},[898,49814,4819],{},[902,49816,42903],{"encoding":904},[883,49818,49820],{"className":49819},[886],[888,49821,49822],{"xmlns":890},[892,49823,49824,49828],{},[895,49825,49826],{},[898,49827,207],{},[902,49829,207],{"encoding":904}," na 110, poklesu ",[883,49832,49834],{"className":49833},[886],[888,49835,49836],{"xmlns":890},[892,49837,49838,49842],{},[895,49839,49840],{},[898,49841,1818],{},[902,49843,1818],{"encoding":904},[883,49845,49847],{"className":49846},[886],[888,49848,49849],{"xmlns":890},[892,49850,49851,49857],{},[895,49852,49853,49855],{},[1664,49854,1867],{},[1963,49856,1970],{},[902,49858,48596],{"encoding":904},", růstu ",[883,49861,49863],{"className":49862},[886],[888,49864,49865],{"xmlns":890},[892,49866,49867,49871],{},[895,49868,49869],{},[898,49870,2034],{},[902,49872,2034],{"encoding":904}," na 25 a růstu ",[883,49875,49877],{"className":49876},[886],[888,49878,49879],{"xmlns":890},[892,49880,49881,49885],{},[895,49882,49883],{},[898,49884,1695],{},[902,49886,1695],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,49889,49891],{"className":49890},[886],[888,49892,49893],{"xmlns":890},[892,49894,49895,49905],{},[895,49896,49897],{},[1810,49898,49899,49901,49903],{},[898,49900,1973],{},[1963,49902,2774],{},[898,49904,4819],{},[902,49906,48765],{"encoding":904},[123,49908,49909,49910,49586],{},"(i) Vypočtěte multiplikátory pro ",[883,49911,49913],{"className":49912},[886],[888,49914,49915],{"xmlns":890},[892,49916,49917,49921],{},[895,49918,49919],{},[898,49920,2398],{},[902,49922,2398],{"encoding":904},[123,49924,49925,49926,49199,49943,49956,49957,48567,49974,3271,49987,50002,50003,1977],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,49927,49929],{"className":49928},[886],[888,49930,49931],{"xmlns":890},[892,49932,49933,49941],{},[895,49934,49935],{},[1720,49936,49937,49939],{},[898,49938,2398],{},[898,49940,4819],{},[902,49942,41966],{"encoding":904},[883,49944,49946],{"className":49945},[886],[888,49947,49948],{"xmlns":890},[892,49949,49950,49954],{},[895,49951,49952],{},[898,49953,2398],{},[902,49955,2398],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,49958,49960],{"className":49959},[886],[888,49961,49962],{"xmlns":890},[892,49963,49964,49972],{},[895,49965,49966],{},[1720,49967,49968,49970],{},[898,49969,2398],{},[898,49971,4819],{},[902,49973,41966],{"encoding":904},[883,49975,49977],{"className":49976},[886],[888,49978,49979],{"xmlns":890},[892,49980,49981,49985],{},[895,49982,49983],{},[898,49984,207],{},[902,49986,207],{"encoding":904},[883,49988,49990],{"className":49989},[886],[888,49991,49992],{"xmlns":890},[892,49993,49994,50000],{},[895,49995,49996,49998],{},[1664,49997,1867],{},[1963,49999,2774],{},[902,50001,48612],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,50004,50006],{"className":50005},[886],[888,50007,50008],{"xmlns":890},[892,50009,50010,50020],{},[895,50011,50012],{},[1810,50013,50014,50016,50018],{},[898,50015,2398],{},[1963,50017,2875],{},[898,50019,4819],{},[902,50021,48357],{"encoding":904},[123,50023,50024,50025,48567,50042,50055,50056,1977],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,50026,50028],{"className":50027},[886],[888,50029,50030],{"xmlns":890},[892,50031,50032,50040],{},[895,50033,50034],{},[1720,50035,50036,50038],{},[898,50037,2398],{},[898,50039,4819],{},[902,50041,41966],{"encoding":904},[883,50043,50045],{"className":50044},[886],[888,50046,50047],{"xmlns":890},[892,50048,50049,50053],{},[895,50050,50051],{},[898,50052,207],{},[902,50054,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,50057,50059],{"className":50058},[886],[888,50060,50061],{"xmlns":890},[892,50062,50063,50073],{},[895,50064,50065],{},[1810,50066,50067,50069,50071],{},[898,50068,2398],{},[1963,50070,1970],{},[898,50072,4819],{},[902,50074,48418],{"encoding":904},[123,50076,50077,50078,49286,50095,50108,50109,3271,50122,49859,50137,50150,50151,50164,50165,1977],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,50079,50081],{"className":50080},[886],[888,50082,50083],{"xmlns":890},[892,50084,50085,50093],{},[895,50086,50087],{},[1720,50088,50089,50091],{},[898,50090,2398],{},[898,50092,4819],{},[902,50094,41966],{"encoding":904},[883,50096,50098],{"className":50097},[886],[888,50099,50100],{"xmlns":890},[892,50101,50102,50106],{},[895,50103,50104],{},[898,50105,207],{},[902,50107,207],{"encoding":904}," na 90, poklesu ",[883,50110,50112],{"className":50111},[886],[888,50113,50114],{"xmlns":890},[892,50115,50116,50120],{},[895,50117,50118],{},[898,50119,1818],{},[902,50121,1818],{"encoding":904},[883,50123,50125],{"className":50124},[886],[888,50126,50127],{"xmlns":890},[892,50128,50129,50135],{},[895,50130,50131,50133],{},[1664,50132,1867],{},[1963,50134,2774],{},[902,50136,48612],{"encoding":904},[883,50138,50140],{"className":50139},[886],[888,50141,50142],{"xmlns":890},[892,50143,50144,50148],{},[895,50145,50146],{},[898,50147,2034],{},[902,50149,2034],{"encoding":904}," na 30 a růstu ",[883,50152,50154],{"className":50153},[886],[888,50155,50156],{"xmlns":890},[892,50157,50158,50162],{},[895,50159,50160],{},[898,50161,1695],{},[902,50163,1695],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,50166,50168],{"className":50167},[886],[888,50169,50170],{"xmlns":890},[892,50171,50172,50182],{},[895,50173,50174],{},[1810,50175,50176,50178,50180],{},[898,50177,2398],{},[1963,50179,2774],{},[898,50181,4819],{},[902,50183,49415],{"encoding":904},[198,50185,820],{"id":50186},"přebytek-spotřebitele-a-výrobce-1",[724,50188,50189,48184,50192,48221,50228,1977],{},[38,50190,50191],{},"2.17",[883,50193,50195],{"className":50194},[886],[888,50196,50197],{"xmlns":890},[892,50198,50199,50225],{},[895,50200,50201,50203,50205,50207,50209,50211,50213,50215,50217,50219],{},[898,50202,2398],{},[1664,50204,1676],{},[898,50206,2379],{},[1664,50208,1667],{"stretchy":1666},[898,50210,1973],{},[1664,50212,1673],{"stretchy":1666},[1664,50214,1676],{},[1963,50216,15537],{},[1664,50218,1867],{},[1720,50220,50221,50223],{},[898,50222,1973],{},[1963,50224,1970],{},[902,50226,50227],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,50229,50231],{"className":50230},[886],[888,50232,50233],{"xmlns":890},[892,50234,50235,50261],{},[895,50236,50237,50239,50241,50243,50245,50247,50249,50251,50253,50255],{},[898,50238,2398],{},[1664,50240,1676],{},[898,50242,2351],{},[1664,50244,1667],{"stretchy":1666},[898,50246,1973],{},[1664,50248,1673],{"stretchy":1666},[1664,50250,1676],{},[1963,50252,2774],{},[1664,50254,1700],{},[1720,50256,50257,50259],{},[898,50258,1973],{},[1963,50260,1970],{},[902,50262,50263],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,50265,50266,50269],{},[123,50267,50268],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,50270,50271],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,50273,50274,48184,50277,48221,50311,1977],{},[38,50275,50276],{},"2.18",[883,50278,50280],{"className":50279},[886],[888,50281,50282],{"xmlns":890},[892,50283,50284,50308],{},[895,50285,50286,50288,50290,50292,50294,50296,50298,50300,50302,50304,50306],{},[898,50287,2398],{},[1664,50289,1676],{},[898,50291,2379],{},[1664,50293,1667],{"stretchy":1666},[898,50295,1973],{},[1664,50297,1673],{"stretchy":1666},[1664,50299,1676],{},[1963,50301,4282],{},[1664,50303,1867],{},[1963,50305,1970],{},[898,50307,1973],{},[902,50309,50310],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,50312,50314],{"className":50313},[886],[888,50315,50316],{"xmlns":890},[892,50317,50318,50344],{},[895,50319,50320,50322,50324,50326,50328,50330,50332,50334,50336,50338],{},[898,50321,2398],{},[1664,50323,1676],{},[898,50325,2351],{},[1664,50327,1667],{"stretchy":1666},[898,50329,1973],{},[1664,50331,1673],{"stretchy":1666},[1664,50333,1676],{},[1963,50335,2774],{},[1664,50337,1700],{},[1720,50339,50340,50342],{},[898,50341,1973],{},[1963,50343,1970],{},[902,50345,50263],{"encoding":904},[120,50347,50348,50368,50371,50374],{},[123,50349,50350,50351,1977],{},"(a) Vypočtěte rovnovážné množství ",[883,50352,50354],{"className":50353},[886],[888,50355,50356],{"xmlns":890},[892,50357,50358,50366],{},[895,50359,50360],{},[1720,50361,50362,50364],{},[898,50363,1973],{},[898,50365,4819],{},[902,50367,42903],{"encoding":904},[123,50369,50370],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,50372,50373],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,50375,50376],{},"(c) Graficky interpretujte.",[37470,50378],{},[115,50380,50382],{"id":50381},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,50384,50385,50388,50391,50394,50397,50400,50403,50406,50409,50412,50415,50418,50421,50424],{},[123,50386,50387],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,50389,50390],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,50392,50393],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,50395,50396],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,50398,50399],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,50401,50402],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,50404,50405],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,50407,50408],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,50410,50411],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,50413,50414],{},"K čemu slouží multiplikátory?",[123,50416,50417],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,50419,50420],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,50422,50423],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,50425,50426],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[37470,50428],{},[115,50430,16219],{"id":16218},[724,50432,50433],{},[38,50434,13660],{},[120,50436,50437,50472,50477,50507,50512,50575,50601,50606,50636,50645,50652,50658],{},[123,50438,50439,10588,50442,19148,50445,1885,50447,1343,50470],{},[38,50440,50441],{},"Poptávané množství",[614,50443,50444],{},"quantity demanded",[38,50446,28502],{},[883,50448,50450],{"className":50449},[886],[888,50451,50452],{"xmlns":890},[892,50453,50454,50468],{},[895,50455,50456,50458,50460,50462,50464,50466],{},[898,50457,1973],{},[1664,50459,1676],{},[898,50461,2379],{},[1664,50463,1667],{"stretchy":1666},[898,50465,2398],{},[1664,50467,1673],{"stretchy":1666},[902,50469,4759],{"encoding":904},[38,50471,37949],{},[123,50473,50474,50476],{},[38,50475,37956],{}," — substituční + důchodový efekt",[123,50478,50479,1885,50482],{},[38,50480,50481],{},"Reálné cenové rozpětí",[883,50483,50485],{"className":50484},[886],[888,50486,50487],{"xmlns":890},[892,50488,50489,50505],{},[895,50490,50491,50493,50495,50497,50503],{},[1664,50492,1667],{"stretchy":1666},[1963,50494,2058],{},[1664,50496,1916],{"separator":1915},[2355,50498,50499,50501],{},[898,50500,2398],{},[1963,50502,2058],{},[1664,50504,1673],{"stretchy":1666},[902,50506,38157],{"encoding":904},[123,50508,50509,11658],{},[38,50510,50511],{},"Homogenita poptávky",[123,50513,50514,1885,50517,1343,50540,1343,50557,50574],{},[38,50515,50516],{},"Lineární poptávka",[883,50518,50520],{"className":50519},[886],[888,50521,50522],{"xmlns":890},[892,50523,50524,50538],{},[895,50525,50526,50528,50530,50532,50534,50536],{},[898,50527,2398],{},[1664,50529,1676],{},[898,50531,207],{},[898,50533,1973],{},[1664,50535,1700],{},[898,50537,1818],{},[902,50539,37560],{"encoding":904},[883,50541,50543],{"className":50542},[886],[888,50544,50545],{"xmlns":890},[892,50546,50547,50555],{},[895,50548,50549,50551,50553],{},[898,50550,207],{},[1664,50552,4022],{},[1963,50554,2058],{},[902,50556,43585],{"encoding":904},[883,50558,50560],{"className":50559},[886],[888,50561,50562],{"xmlns":890},[892,50563,50564,50572],{},[895,50565,50566,50568,50570],{},[898,50567,1818],{},[1664,50569,3984],{},[1963,50571,2058],{},[902,50573,19314],{"encoding":904}," — nedokonalá konkurence",[123,50576,50577,7581,50580],{},[38,50578,50579],{},"Dokonalá konkurence",[883,50581,50583],{"className":50582},[886],[888,50584,50585],{"xmlns":890},[892,50586,50587,50599],{},[895,50588,50589,50591,50593],{},[898,50590,2398],{},[1664,50592,1676],{},[1720,50594,50595,50597],{},[898,50596,2398],{},[1664,50598,4920],{},[902,50600,4923],{"encoding":904},[123,50602,50603,50605],{},[38,50604,38726],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,50607,50608,1885,50610,1343,50634],{},[38,50609,32227],{},[883,50611,50613],{"className":50612},[886],[888,50614,50615],{"xmlns":890},[892,50616,50617,50631],{},[895,50618,50619,50621,50623,50625,50627,50629],{},[898,50620,1973],{},[1664,50622,1676],{},[898,50624,4819],{},[1664,50626,1667],{"stretchy":1666},[898,50628,9692],{},[1664,50630,1673],{"stretchy":1666},[902,50632,50633],{"encoding":904},"Q = E(Y)",[38,50635,38923],{},[123,50637,50638,50641,50642,50644],{},[38,50639,50640],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,50643,39369],{}," zboží",[123,50646,50647,4454,50649,50651],{},[38,50648,40375],{},[38,50650,40322],{}," — znaménka zkřížených koeficientů",[123,50653,50654,50657],{},[38,50655,50656],{},"Dvoukomoditní trh"," (2.6)",[123,50659,50660,10588,50663,1673],{},[38,50661,50662],{},"Posun poptávky",[614,50664,39427],{},[724,50666,50667],{},[38,50668,13624],{},[120,50670,50671,50704,50708,50753],{},[123,50672,50673,10588,50675,19148,50677,1885,50679,1343,50702],{},[38,50674,40769],{},[614,50676,40772],{},[38,50678,40943],{},[883,50680,50682],{"className":50681},[886],[888,50683,50684],{"xmlns":890},[892,50685,50686,50700],{},[895,50687,50688,50690,50692,50694,50696,50698],{},[898,50689,1973],{},[1664,50691,1676],{},[898,50693,2351],{},[1664,50695,1667],{"stretchy":1666},[898,50697,2398],{},[1664,50699,1673],{"stretchy":1666},[902,50701,9246],{"encoding":904},[38,50703,41021],{},[123,50705,50706],{},[38,50707,41028],{},[123,50709,50710,1885,50713,1343,50736],{},[38,50711,50712],{},"Lineární nabídka",[883,50714,50716],{"className":50715},[886],[888,50717,50718],{"xmlns":890},[892,50719,50720,50734],{},[895,50721,50722,50724,50726,50728,50730,50732],{},[898,50723,2398],{},[1664,50725,1676],{},[898,50727,2034],{},[898,50729,1973],{},[1664,50731,1700],{},[898,50733,1695],{},[902,50735,40742],{"encoding":904},[883,50737,50739],{"className":50738},[886],[888,50740,50741],{"xmlns":890},[892,50742,50743,50751],{},[895,50744,50745,50747,50749],{},[898,50746,2034],{},[1664,50748,3984],{},[1963,50750,2058],{},[902,50752,40760],{"encoding":904},[123,50754,50755,10588,50758,1673],{},[38,50756,50757],{},"Posun nabídky",[614,50759,41406],{},[724,50761,50762],{},[38,50763,50764],{},"Rovnováha a komparativní statika",[120,50766,50767,50846,50852],{},[123,50768,50769,10588,50771,19148,50773,1885,50776,1343,50793,1885,50796,1343,50813,1885,50815],{},[38,50770,41825],{},[614,50772,41944],{},[38,50774,50775],{},"rovnovážná cena",[883,50777,50779],{"className":50778},[886],[888,50780,50781],{"xmlns":890},[892,50782,50783,50791],{},[895,50784,50785],{},[1720,50786,50787,50789],{},[898,50788,2398],{},[898,50790,4819],{},[902,50792,41966],{"encoding":904},[38,50794,50795],{},"rovnovážné množství",[883,50797,50799],{"className":50798},[886],[888,50800,50801],{"xmlns":890},[892,50802,50803,50811],{},[895,50804,50805],{},[1720,50806,50807,50809],{},[898,50808,1973],{},[898,50810,4819],{},[902,50812,42903],{"encoding":904},[38,50814,42002],{},[883,50816,50818],{"className":50817},[886],[888,50819,50820],{"xmlns":890},[892,50821,50822,50844],{},[895,50823,50824,50826,50828,50834,50836,50842],{},[898,50825,4819],{},[1664,50827,1837],{"stretchy":1666},[1720,50829,50830,50832],{},[898,50831,1973],{},[898,50833,4819],{},[1664,50835,1916],{"separator":1915},[1720,50837,50838,50840],{},[898,50839,2398],{},[898,50841,4819],{},[1664,50843,1850],{"stretchy":1666},[902,50845,41867],{"encoding":904},[123,50847,50848,50851],{},[38,50849,50850],{},"Pravidla 1–4"," komparativní statiky",[123,50853,50854,10588,50857,1673],{},[38,50855,50856],{},"Teorém pavučiny",[614,50858,42849],{},[724,50860,50861],{},[38,50862,50863],{},"Zdanění",[120,50865,50866,50922,50970],{},[123,50867,50868,50870,50871,50896,50897,1673],{},[38,50869,50863],{}," — daň výrobci (",[883,50872,50874],{"className":50873},[886],[888,50875,50876],{"xmlns":890},[892,50877,50878,50894],{},[895,50879,50880,50886,50888,50890,50892],{},[2355,50881,50882,50884],{},[898,50883,2351],{},[1963,50885,2875],{},[1664,50887,1676],{},[898,50889,2351],{},[1664,50891,1700],{},[898,50893,1991],{},[902,50895,43254],{"encoding":904},") vs. daň spotřebiteli (",[883,50898,50900],{"className":50899},[886],[888,50901,50902],{"xmlns":890},[892,50903,50904,50920],{},[895,50905,50906,50912,50914,50916,50918],{},[2355,50907,50908,50910],{},[898,50909,2379],{},[1963,50911,1970],{},[1664,50913,1676],{},[898,50915,2379],{},[1664,50917,1867],{},[898,50919,1991],{},[902,50921,43285],{"encoding":904},[123,50923,50924,1885,50926,1343,50947],{},[38,50925,43158],{},[883,50927,50929],{"className":50928},[886],[888,50930,50931],{"xmlns":890},[892,50932,50933,50945],{},[895,50934,50935],{},[2355,50936,50937,50939],{},[898,50938,1991],{},[895,50940,50941,50943],{},[898,50942,43177],{},[898,50944,724],{},[902,50946,43182],{"encoding":904},[883,50948,50950],{"className":50949},[886],[888,50951,50952],{"xmlns":890},[892,50953,50954,50968],{},[895,50955,50956],{},[2355,50957,50958,50960],{},[898,50959,1991],{},[895,50961,50962,50964,50966],{},[898,50963,43200],{},[898,50965,2608],{},[898,50967,12540],{},[902,50969,43207],{"encoding":904},[123,50971,50972,1885,50975,1343,51004],{},[38,50973,50974],{},"Ekvivalence zdanění",[883,50976,50978],{"className":50977},[886],[888,50979,50980],{"xmlns":890},[892,50981,50982,51002],{},[895,50983,50984,50992,50994],{},[1810,50985,50986,50988,50990],{},[898,50987,1973],{},[1963,50989,2875],{},[898,50991,4819],{},[1664,50993,1676],{},[1810,50995,50996,50998,51000],{},[898,50997,1973],{},[1963,50999,1970],{},[898,51001,4819],{},[902,51003,43408],{"encoding":904},[883,51005,51007],{"className":51006},[886],[888,51008,51009],{"xmlns":890},[892,51010,51011,51035],{},[895,51012,51013,51021,51023,51025,51027],{},[1810,51014,51015,51017,51019],{},[898,51016,2398],{},[1963,51018,2875],{},[898,51020,4819],{},[1664,51022,1867],{},[898,51024,1991],{},[1664,51026,1676],{},[1810,51028,51029,51031,51033],{},[898,51030,2398],{},[1963,51032,1970],{},[898,51034,4819],{},[902,51036,43442],{"encoding":904},[724,51038,51039],{},[38,51040,26908],{},[120,51042,51043,51089,51120,51125,51131,51138],{},[123,51044,51045,1885,51047],{},[38,51046,43541],{},[883,51048,51050],{"className":51049},[886],[888,51051,51052],{"xmlns":890},[892,51053,51054,51086],{},[895,51055,51056,51062,51064,51066,51068,51070,51072,51074,51076,51078,51080,51082,51084],{},[1720,51057,51058,51060],{},[898,51059,1973],{},[898,51061,4819],{},[1664,51063,1676],{},[1664,51065,1667],{"stretchy":1666},[898,51067,1818],{},[1664,51069,1867],{},[898,51071,1695],{},[1664,51073,1673],{"stretchy":1666},[898,51075,5240],{"mathvariant":1726},[1664,51077,1667],{"stretchy":1666},[898,51079,2034],{},[1664,51081,1867],{},[898,51083,207],{},[1664,51085,1673],{"stretchy":1666},[902,51087,51088],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,51090,51091,1885,51094,51119],{},[38,51092,51093],{},"Parametry",[883,51095,51097],{"className":51096},[886],[888,51098,51099],{"xmlns":890},[892,51100,51101,51117],{},[895,51102,51103,51105,51107,51109,51111,51113,51115],{},[898,51104,207],{},[1664,51106,1916],{"separator":1915},[898,51108,1818],{},[1664,51110,1916],{"separator":1915},[898,51112,2034],{},[1664,51114,1916],{"separator":1915},[898,51116,1695],{},[902,51118,43785],{"encoding":904}," — exogenní proměnné",[123,51121,51122],{},[38,51123,51124],{},"Endogenní \u002F exogenní proměnná",[123,51126,51127,51130],{},[38,51128,51129],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,51132,51133,1343,51136],{},[38,51134,51135],{},"Komparativní statika",[38,51137,37460],{},[123,51139,51140,1885,51142,51158],{},[38,51141,3533],{},[883,51143,51145],{"className":51144},[886],[888,51146,51147],{"xmlns":890},[892,51148,51149,51155],{},[895,51150,51151,51153],{},[898,51152,1695],{},[898,51154,1973],{},[902,51156,51157],{"encoding":904},"dQ"," (2.11)",[724,51160,51161],{},[38,51162,51163],{},"Přebytky a ostatní",[120,51165,51166,51204],{},[123,51167,51168,1885,51170,51185,51186,1885,51188,51203],{},[38,51169,45434],{},[883,51171,51173],{"className":51172},[886],[888,51174,51175],{"xmlns":890},[892,51176,51177,51183],{},[895,51178,51179,51181],{},[898,51180,1703],{},[898,51182,2351],{},[902,51184,45450],{"encoding":904}," (2.14), ",[38,51187,45453],{},[883,51189,51191],{"className":51190},[886],[888,51192,51193],{"xmlns":890},[892,51194,51195,51201],{},[895,51196,51197,51199],{},[898,51198,2398],{},[898,51200,2351],{},[902,51202,45469],{"encoding":904}," (2.15)",[123,51205,51206,1343,51209,51212],{},[38,51207,51208],{},"Homo economicus",[38,51210,51211],{},"Marshallova formulace"," (1890)",[37470,51214],{},[115,51216,2497],{"id":2496},[120,51218,51219,51254,51263],{},[123,51220,51221,1885,51224,51227,51228,1343,51231,51234,51235,51238,51239,51242,51243,51246,51247,51250,51251],{},[38,51222,51223],{},"Související témata:",[207,51225,811],{"className":51226,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,51229,820],{"className":51230,"dataFsResolvedFilePath":818,"href":819},[210],[207,51232,2950],{"className":51233,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,51236,775],{"className":51237,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,51240,784],{"className":51241,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,51244,793],{"className":51245,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,51248,4397],{"className":51249,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,51252,2524],{"className":51253,"dataFsResolvedFilePath":827,"href":828},[210],[123,51255,51256,1885,51259],{},[38,51257,51258],{},"Shrnutí přednášek:",[207,51260,51262],{"className":51261,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,51264,51265,1885,51267],{},[38,51266,16703],{},[207,51268,16707],{"className":51269,"dataFsResolvedFilePath":2575,"href":2576},[210],{"title":641,"searchDepth":642,"depth":642,"links":51271},[51272,51273,51281,51287,51294,51295,51302,51303,51304,51311,51312,51313],{"id":37294,"depth":642,"text":37295},{"id":37275,"depth":642,"text":13660,"children":51274},[51275,51276,51277,51278,51280],{"id":37563,"depth":649,"text":37564},{"id":37845,"depth":649,"text":37846},{"id":38855,"depth":649,"text":38856},{"id":39423,"depth":649,"text":51279},"Posun poptávky (shift of demand)",{"id":39927,"depth":649,"text":39928},{"id":37279,"depth":642,"text":13624,"children":51282},[51283,51284,51285],{"id":40764,"depth":649,"text":37564},{"id":40950,"depth":649,"text":40951},{"id":41402,"depth":649,"text":51286},"Posun nabídky (shift of supply)",{"id":41824,"depth":642,"text":41825,"children":51288},[51289,51290,51291,51292,51293],{"id":41936,"depth":649,"text":41937},{"id":42149,"depth":649,"text":42150},{"id":42467,"depth":649,"text":42468},{"id":42821,"depth":649,"text":42822},{"id":42852,"depth":649,"text":42853},{"id":43121,"depth":642,"text":811},{"id":43522,"depth":642,"text":43523,"children":51296},[51297,51298,51299,51300],{"id":43540,"depth":649,"text":43541},{"id":43921,"depth":649,"text":43922},{"id":44305,"depth":649,"text":44306},{"id":44759,"depth":649,"text":51301},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":2332,"depth":642,"text":820},{"id":45684,"depth":642,"text":45685},{"id":45915,"depth":642,"text":45916,"children":51305},[51306,51307,51308,51309,51310],{"id":45919,"depth":649,"text":45920},{"id":46759,"depth":649,"text":46760},{"id":47135,"depth":649,"text":41825},{"id":48430,"depth":649,"text":43523},{"id":50186,"depth":649,"text":820},{"id":50381,"depth":642,"text":50382},{"id":16218,"depth":642,"text":16219},{"id":2496,"depth":642,"text":2497},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,51320,51321,51322,18383,51323,51324],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":51327,"title":820,"body":51328,"course":1128,"courses":659,"created":10119,"description":641,"extension":661,"meta":55607,"navigation":664,"path":55608,"seo":55609,"sources":55610,"stem":55611,"tags":55612,"type":2553,"updated":677,"__hash__":55617},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":51329,"toc":55585},[51330,51332,51400,51450,51452,51455,51713,51789,51794,51796,51815,51819,51895,51980,51982,52296,52389,52391,52410,52414,52488,52573,52576,52752,52757,52759,53179,53181,53185,53189,53425,53469,53569,53635,53638,53671,53847,53909,54039,54117,54228,54262,54460,54479,54498,54563,54567,54570,54615,54618,54736,54782,54784,54788,55136,55138,55140,55418,55420,55424,55459,55466,55539,55541,55543],[12,51331,820],{"id":2332},[4436,51333,51334],{},[724,51335,51336,4443,51338,10588,51340,51355,51356,10588,51358,51373,51374,51396,51397,1977],{},[883,51337,4442],{},[38,51339,45434],{},[883,51341,51343],{"className":51342},[886],[888,51344,51345],{"xmlns":890},[892,51346,51347,51353],{},[895,51348,51349,51351],{},[898,51350,1703],{},[898,51352,2351],{},[902,51354,45450],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,51357,45581],{},[883,51359,51361],{"className":51360},[886],[888,51362,51363],{"xmlns":890},[892,51364,51365,51371],{},[895,51366,51367,51369],{},[898,51368,2398],{},[898,51370,2351],{},[902,51372,45469],{"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 ",[883,51375,51377],{"className":51376},[886],[888,51378,51379],{"xmlns":890},[892,51380,51381,51393],{},[895,51382,51383,51385,51387,51389,51391],{},[898,51384,1703],{},[898,51386,2351],{},[1664,51388,1700],{},[898,51390,2398],{},[898,51392,2351],{},[902,51394,51395],{"encoding":904},"CS + PS"," měří ",[38,51398,51399],{},"celkový blahobyt trhu",[724,51401,51402,10588,51404,1343,51406,12627,51421,10588,51423,1343,51425,51440,51441,51445,51446,1977],{},[38,51403,45434],{},[614,51405,45488],{},[883,51407,51409],{"className":51408},[886],[888,51410,51411],{"xmlns":890},[892,51412,51413,51419],{},[895,51414,51415,51417],{},[898,51416,1703],{},[898,51418,2351],{},[902,51420,45450],{"encoding":904},[38,51422,45453],{},[614,51424,45584],{},[883,51426,51428],{"className":51427},[886],[888,51429,51430],{"xmlns":890},[892,51431,51432,51438],{},[895,51433,51434,51436],{},[898,51435,2398],{},[898,51437,2351],{},[902,51439,45469],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,51442,51444],{"className":51443,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,51447,51449],{"className":51448,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[37470,51451],{},[115,51453,1241],{"id":51454},"úvod",[724,51456,51457,51458,51481,51482,51505,51506,51523,51524,4480,51556,51588,51589,51615,51616,51619,51620,51623,51624,14510,51658,22094,51679,1977],{},"Je dána funkce poptávky ",[883,51459,51461],{"className":51460},[886],[888,51462,51463],{"xmlns":890},[892,51464,51465,51479],{},[895,51466,51467,51469,51471,51473,51475,51477],{},[898,51468,2398],{},[1664,51470,1676],{},[898,51472,2379],{},[1664,51474,1667],{"stretchy":1666},[898,51476,1973],{},[1664,51478,1673],{"stretchy":1666},[902,51480,5206],{"encoding":904},", resp. funkce nabídky ",[883,51483,51485],{"className":51484},[886],[888,51486,51487],{"xmlns":890},[892,51488,51489,51503],{},[895,51490,51491,51493,51495,51497,51499,51501],{},[898,51492,2398],{},[1664,51494,1676],{},[898,51496,2351],{},[1664,51498,1667],{"stretchy":1666},[898,51500,1973],{},[1664,51502,1673],{"stretchy":1666},[902,51504,41571],{"encoding":904},". Pro pevně zadané množství ",[883,51507,51509],{"className":51508},[886],[888,51510,51511],{"xmlns":890},[892,51512,51513,51521],{},[895,51514,51515],{},[2355,51516,51517,51519],{},[898,51518,1973],{},[1963,51520,2058],{},[902,51522,38808],{"encoding":904}," je odpovídající cena ",[883,51525,51527],{"className":51526},[886],[888,51528,51529],{"xmlns":890},[892,51530,51531,51553],{},[895,51532,51533,51539,51541,51543,51545,51551],{},[2355,51534,51535,51537],{},[898,51536,2398],{},[1963,51538,2058],{},[1664,51540,1676],{},[898,51542,2379],{},[1664,51544,1667],{"stretchy":1666},[2355,51546,51547,51549],{},[898,51548,1973],{},[1963,51550,2058],{},[1664,51552,1673],{"stretchy":1666},[902,51554,51555],{"encoding":904},"P_0 = D(Q_0)",[883,51557,51559],{"className":51558},[886],[888,51560,51561],{"xmlns":890},[892,51562,51563,51585],{},[895,51564,51565,51571,51573,51575,51577,51583],{},[2355,51566,51567,51569],{},[898,51568,2398],{},[1963,51570,2058],{},[1664,51572,1676],{},[898,51574,2351],{},[1664,51576,1667],{"stretchy":1666},[2355,51578,51579,51581],{},[898,51580,1973],{},[1963,51582,2058],{},[1664,51584,1673],{"stretchy":1666},[902,51586,51587],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,51590,51592],{"className":51591},[886],[888,51593,51594],{"xmlns":890},[892,51595,51596,51612],{},[895,51597,51598,51604,51606],{},[2355,51599,51600,51602],{},[898,51601,2398],{},[1963,51603,2058],{},[1690,51605,1692],{},[2355,51607,51608,51610],{},[898,51609,1973],{},[1963,51611,2058],{},[902,51613,51614],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,51617,51618],{},"výdaje spotřebitele",", nebo ",[38,51621,51622],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,51625,51627],{"className":51626},[886],[888,51628,51629],{"xmlns":890},[892,51630,51631,51655],{},[895,51632,51633,51635,51637,51643,51645,51647,51649],{},[1963,51634,2058],{},[1690,51636,1692],{},[2355,51638,51639,51641],{},[898,51640,1973],{},[1963,51642,2058],{},[1690,51644,1692],{},[898,51646,4822],{},[1690,51648,1692],{},[2355,51650,51651,51653],{},[898,51652,2398],{},[1963,51654,2058],{},[902,51656,51657],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,51659,51661],{"className":51660},[886],[888,51662,51663],{"xmlns":890},[892,51664,51665,51677],{},[895,51666,51667,51669,51671,51673,51675],{},[1664,51668,1667],{"stretchy":1666},[898,51670,1973],{},[1664,51672,1916],{"separator":1915},[898,51674,2398],{},[1664,51676,1673],{"stretchy":1666},[902,51678,38191],{"encoding":904},[883,51680,51682],{"className":51681},[886],[888,51683,51684],{"xmlns":890},[892,51685,51686,51710],{},[895,51687,51688,51690,51692,51694,51700,51702,51708],{},[898,51689,4822],{},[1664,51691,1676],{},[1664,51693,1837],{"stretchy":1666},[2355,51695,51696,51698],{},[898,51697,1973],{},[1963,51699,2058],{},[1664,51701,1916],{"separator":1915},[2355,51703,51704,51706],{},[898,51705,2398],{},[1963,51707,2058],{},[1664,51709,1850],{"stretchy":1666},[902,51711,51712],{"encoding":904},"A = [Q_0, P_0]",[4436,51714,51715,51720,51778],{},[724,51716,51717,51719],{},[883,51718,4723],{}," Intuice",[120,51721,51722,51750],{},[123,51723,51724,51725,51728,51729,51731,51732,51749],{},"Za jednotky zboží nakoupené ",[38,51726,51727],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,51730,25770],{}," než ",[883,51733,51735],{"className":51734},[886],[888,51736,51737],{"xmlns":890},[892,51738,51739,51747],{},[895,51740,51741],{},[2355,51742,51743,51745],{},[898,51744,2398],{},[1963,51746,2058],{},[902,51748,39448],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,51751,51752,51753,51755,51756,51759,51760,51777],{},"Za jednotky zboží prodané ",[38,51754,51727],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,51757,51758],{},"nižší"," cenu než ",[883,51761,51763],{"className":51762},[886],[888,51764,51765],{"xmlns":890},[892,51766,51767,51775],{},[895,51768,51769],{},[2355,51770,51771,51773],{},[898,51772,2398],{},[1963,51774,2058],{},[902,51776,39448],{"encoding":904}," — rozdíl je jeho přebytek.",[724,51779,51780,51781,51784,51785,51788],{},"Přebytek je tedy rozdíl mezi ",[614,51782,51783],{},"ochotou"," (platit \u002F prodávat) a ",[614,51786,51787],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,51790,51791],{},[1928,51792],{"alt":45479,"className":51793,"src":45481},[210,1932],[37470,51795],{},[115,51797,51799,51800,1673],{"id":51798},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,51801,51803],{"className":51802},[886],[888,51804,51805],{"xmlns":890},[892,51806,51807,51813],{},[895,51808,51809,51811],{},[898,51810,1703],{},[898,51812,2351],{},[902,51814,45450],{"encoding":904},[198,51816,51818],{"id":51817},"definice-vzorec-214","Definice (vzorec 2.14)",[724,51820,51821,51822,51845,51846,51863,51864,2087],{},"Pro poptávku ",[883,51823,51825],{"className":51824},[886],[888,51826,51827],{"xmlns":890},[892,51828,51829,51843],{},[895,51830,51831,51833,51835,51837,51839,51841],{},[898,51832,2398],{},[1664,51834,1676],{},[898,51836,2379],{},[1664,51838,1667],{"stretchy":1666},[898,51840,1973],{},[1664,51842,1673],{"stretchy":1666},[902,51844,5206],{"encoding":904}," a pevně zadané ",[883,51847,51849],{"className":51848},[886],[888,51850,51851],{"xmlns":890},[892,51852,51853,51861],{},[895,51854,51855],{},[2355,51856,51857,51859],{},[898,51858,1973],{},[1963,51860,2058],{},[902,51862,38808],{"encoding":904}," s cenou ",[883,51865,51867],{"className":51866},[886],[888,51868,51869],{"xmlns":890},[892,51870,51871,51893],{},[895,51872,51873,51879,51881,51883,51885,51891],{},[2355,51874,51875,51877],{},[898,51876,2398],{},[1963,51878,2058],{},[1664,51880,1676],{},[898,51882,2379],{},[1664,51884,1667],{"stretchy":1666},[2355,51886,51887,51889],{},[898,51888,1973],{},[1963,51890,2058],{},[1664,51892,1673],{"stretchy":1666},[902,51894,51555],{"encoding":904},[883,51896,51898],{"className":51897},[886],[888,51899,51900],{"xmlns":890,"display":28566},[892,51901,51902,51978],{},[21254,51903,51904],{"width":28571},[21259,51905,51906,51908,51972,51974],{},[21262,51907],{"width":28576},[21262,51909,51910],{},[895,51911,51912,51914,51916,51918,51924,51926,51928,51940,51942,51944,51946,51948,51950,51952,51954,51956,51962,51964,51970],{},[898,51913,1703],{},[898,51915,2351],{},[1664,51917,1667],{"stretchy":1666},[2355,51919,51920,51922],{},[898,51921,1973],{},[1963,51923,2058],{},[1664,51925,1673],{"stretchy":1666},[1664,51927,1676],{},[1810,51929,51930,51932,51934],{},[1664,51931,1679],{},[1963,51933,2058],{},[2355,51935,51936,51938],{},[898,51937,1973],{},[1963,51939,2058],{},[898,51941,2379],{},[1664,51943,1667],{"stretchy":1666},[898,51945,1973],{},[1664,51947,1673],{"stretchy":1666},[1690,51949,1692],{},[898,51951,1695],{},[898,51953,1973],{},[1664,51955,1867],{},[2355,51957,51958,51960],{},[898,51959,2398],{},[1963,51961,2058],{},[1690,51963,1692],{},[2355,51965,51966,51968],{},[898,51967,1973],{},[1963,51969,2058],{},[898,51971,1977],{"mathvariant":1726},[21262,51973],{"width":28576},[21262,51975,51976],{},[1690,51977,45573],{},[902,51979,45576],{"encoding":904},[198,51981,3034],{"id":3033},[120,51983,51984,52076,52138],{},[123,51985,51986,52026,52027,52053,52054,52057,52058,52075],{},[883,51987,51989],{"className":51988},[886],[888,51990,51991],{"xmlns":890},[892,51992,51993,52023],{},[895,51994,51995],{},[2919,51996,51997,52009,52011,52013,52015,52017,52019,52021],{"scriptlevel":2058,"displaystyle":1915},[1810,51998,51999,52001,52003],{},[1664,52000,1679],{},[1963,52002,2058],{},[2355,52004,52005,52007],{},[898,52006,1973],{},[1963,52008,2058],{},[898,52010,2379],{},[1664,52012,1667],{"stretchy":1666},[898,52014,1973],{},[1664,52016,1673],{"stretchy":1666},[1690,52018,1692],{},[898,52020,1695],{},[898,52022,1973],{},[902,52024,52025],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,52028,52030],{"className":52029},[886],[888,52031,52032],{"xmlns":890},[892,52033,52034,52050],{},[895,52035,52036,52038,52040,52042,52048],{},[1664,52037,1837],{"stretchy":1666},[1963,52039,2058],{},[1664,52041,1916],{"separator":1915},[2355,52043,52044,52046],{},[898,52045,1973],{},[1963,52047,2058],{},[1664,52049,1850],{"stretchy":1666},[902,52051,52052],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,52055,52056],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,52059,52061],{"className":52060},[886],[888,52062,52063],{"xmlns":890},[892,52064,52065,52073],{},[895,52066,52067],{},[2355,52068,52069,52071],{},[898,52070,1973],{},[1963,52072,2058],{},[902,52074,38808],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,52077,52078,52104,52105,4488],{},[883,52079,52081],{"className":52080},[886],[888,52082,52083],{"xmlns":890},[892,52084,52085,52101],{},[895,52086,52087,52093,52095],{},[2355,52088,52089,52091],{},[898,52090,2398],{},[1963,52092,2058],{},[1690,52094,1692],{},[2355,52096,52097,52099],{},[898,52098,1973],{},[1963,52100,2058],{},[902,52102,52103],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,52106,52108],{"className":52107},[886],[888,52109,52110],{"xmlns":890},[892,52111,52112,52136],{},[895,52113,52114,52116,52118,52124,52126,52128,52130],{},[1963,52115,2058],{},[1690,52117,1692],{},[2355,52119,52120,52122],{},[898,52121,1973],{},[1963,52123,2058],{},[1690,52125,1692],{},[898,52127,4822],{},[1690,52129,1692],{},[2355,52131,52132,52134],{},[898,52133,2398],{},[1963,52135,2058],{},[902,52137,51657],{"encoding":904},[123,52139,52140,52155,52156,52178,52179,52204,52205,22094,52231,4454,52263,1977],{},[883,52141,52143],{"className":52142},[886],[888,52144,52145],{"xmlns":890},[892,52146,52147,52153],{},[895,52148,52149,52151],{},[898,52150,1703],{},[898,52152,2351],{},[902,52154,45450],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,52157,52159],{"className":52158},[886],[888,52160,52161],{"xmlns":890},[892,52162,52163,52175],{},[895,52164,52165,52167,52169],{},[898,52166,2398],{},[1664,52168,1676],{},[2355,52170,52171,52173],{},[898,52172,2398],{},[1963,52174,2058],{},[902,52176,52177],{"encoding":904},"P = P_0"," v pásu ",[883,52180,52182],{"className":52181},[886],[888,52183,52184],{"xmlns":890},[892,52185,52186,52202],{},[895,52187,52188,52190,52192,52194,52200],{},[1664,52189,1837],{"stretchy":1666},[1963,52191,2058],{},[1664,52193,1916],{"separator":1915},[2355,52195,52196,52198],{},[898,52197,1973],{},[1963,52199,2058],{},[1664,52201,1850],{"stretchy":1666},[902,52203,52052],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,52206,52208],{"className":52207},[886],[888,52209,52210],{"xmlns":890},[892,52211,52212,52228],{},[895,52213,52214,52220,52222,52224,52226],{},[2355,52215,52216,52218],{},[898,52217,2398],{},[1963,52219,2058],{},[1690,52221,1692],{},[898,52223,23753],{},[1690,52225,1692],{},[898,52227,4822],{},[902,52229,52230],{"encoding":904},"P_0\\,B\\,A",[883,52232,52234],{"className":52233},[886],[888,52235,52236],{"xmlns":890},[892,52237,52238,52260],{},[895,52239,52240,52242,52244,52246,52248,52250,52252,52254,52256,52258],{},[898,52241,23753],{},[1664,52243,1676],{},[1664,52245,1837],{"stretchy":1666},[1963,52247,2058],{},[1664,52249,1916],{"separator":1915},[898,52251,2379],{},[1664,52253,1667],{"stretchy":1666},[1963,52255,2058],{},[1664,52257,1673],{"stretchy":1666},[1664,52259,1850],{"stretchy":1666},[902,52261,52262],{"encoding":904},"B = [0, D(0)]",[883,52264,52266],{"className":52265},[886],[888,52267,52268],{"xmlns":890},[892,52269,52270,52294],{},[895,52271,52272,52274,52276,52278,52284,52286,52292],{},[898,52273,4822],{},[1664,52275,1676],{},[1664,52277,1837],{"stretchy":1666},[2355,52279,52280,52282],{},[898,52281,1973],{},[1963,52283,2058],{},[1664,52285,1916],{"separator":1915},[2355,52287,52288,52290],{},[898,52289,2398],{},[1963,52291,2058],{},[1664,52293,1850],{"stretchy":1666},[902,52295,51712],{"encoding":904},[724,52297,52298],{},[614,52299,52300,52301,52314,52315,52348,52349,29642,52374,1977],{},"Obrázek 2.24: Křivka poptávky ",[883,52302,52304],{"className":52303},[886],[888,52305,52306],{"xmlns":890},[892,52307,52308,52312],{},[895,52309,52310],{},[898,52311,2379],{},[902,52313,2379],{"encoding":904},", bod ",[883,52316,52318],{"className":52317},[886],[888,52319,52320],{"xmlns":890},[892,52321,52322,52346],{},[895,52323,52324,52326,52328,52330,52336,52338,52344],{},[898,52325,4822],{},[1664,52327,1676],{},[1664,52329,1837],{"stretchy":1666},[2355,52331,52332,52334],{},[898,52333,1973],{},[1963,52335,2058],{},[1664,52337,1916],{"separator":1915},[2355,52339,52340,52342],{},[898,52341,2398],{},[1963,52343,2058],{},[1664,52345,1850],{"stretchy":1666},[902,52347,51712],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,52350,52352],{"className":52351},[886],[888,52353,52354],{"xmlns":890},[892,52355,52356,52372],{},[895,52357,52358,52364,52366,52368,52370],{},[2355,52359,52360,52362],{},[898,52361,2398],{},[1963,52363,2058],{},[1690,52365,1692],{},[898,52367,23753],{},[1690,52369,1692],{},[898,52371,4822],{},[902,52373,52230],{"encoding":904},[883,52375,52377],{"className":52376},[886],[888,52378,52379],{"xmlns":890},[892,52380,52381,52387],{},[895,52382,52383,52385],{},[898,52384,1703],{},[898,52386,2351],{},[902,52388,45450],{"encoding":904},[37470,52390],{},[115,52392,52394,52395,1673],{"id":52393},"přebytek-výrobce-psps","Přebytek výrobce (",[883,52396,52398],{"className":52397},[886],[888,52399,52400],{"xmlns":890},[892,52401,52402,52408],{},[895,52403,52404,52406],{},[898,52405,2398],{},[898,52407,2351],{},[902,52409,45469],{"encoding":904},[198,52411,52413],{"id":52412},"definice-vzorec-215","Definice (vzorec 2.15)",[724,52415,52416,52417,51845,52440,51863,52457,2087],{},"Analogicky — pro nabídku ",[883,52418,52420],{"className":52419},[886],[888,52421,52422],{"xmlns":890},[892,52423,52424,52438],{},[895,52425,52426,52428,52430,52432,52434,52436],{},[898,52427,2398],{},[1664,52429,1676],{},[898,52431,2351],{},[1664,52433,1667],{"stretchy":1666},[898,52435,1973],{},[1664,52437,1673],{"stretchy":1666},[902,52439,41571],{"encoding":904},[883,52441,52443],{"className":52442},[886],[888,52444,52445],{"xmlns":890},[892,52446,52447,52455],{},[895,52448,52449],{},[2355,52450,52451,52453],{},[898,52452,1973],{},[1963,52454,2058],{},[902,52456,38808],{"encoding":904},[883,52458,52460],{"className":52459},[886],[888,52461,52462],{"xmlns":890},[892,52463,52464,52486],{},[895,52465,52466,52472,52474,52476,52478,52484],{},[2355,52467,52468,52470],{},[898,52469,2398],{},[1963,52471,2058],{},[1664,52473,1676],{},[898,52475,2351],{},[1664,52477,1667],{"stretchy":1666},[2355,52479,52480,52482],{},[898,52481,1973],{},[1963,52483,2058],{},[1664,52485,1673],{"stretchy":1666},[902,52487,51587],{"encoding":904},[883,52489,52491],{"className":52490},[886],[888,52492,52493],{"xmlns":890,"display":28566},[892,52494,52495,52571],{},[21254,52496,52497],{"width":28571},[21259,52498,52499,52501,52565,52567],{},[21262,52500],{"width":28576},[21262,52502,52503],{},[895,52504,52505,52507,52509,52511,52517,52519,52521,52527,52529,52535,52537,52549,52551,52553,52555,52557,52559,52561,52563],{},[898,52506,2398],{},[898,52508,2351],{},[1664,52510,1667],{"stretchy":1666},[2355,52512,52513,52515],{},[898,52514,1973],{},[1963,52516,2058],{},[1664,52518,1673],{"stretchy":1666},[1664,52520,1676],{},[2355,52522,52523,52525],{},[898,52524,2398],{},[1963,52526,2058],{},[1690,52528,1692],{},[2355,52530,52531,52533],{},[898,52532,1973],{},[1963,52534,2058],{},[1664,52536,1867],{},[1810,52538,52539,52541,52543],{},[1664,52540,1679],{},[1963,52542,2058],{},[2355,52544,52545,52547],{},[898,52546,1973],{},[1963,52548,2058],{},[898,52550,2351],{},[1664,52552,1667],{"stretchy":1666},[898,52554,1973],{},[1664,52556,1673],{"stretchy":1666},[1690,52558,1692],{},[898,52560,1695],{},[898,52562,1973],{},[898,52564,1977],{"mathvariant":1726},[21262,52566],{"width":28576},[21262,52568,52569],{},[1690,52570,45669],{},[902,52572,45672],{"encoding":904},[198,52574,3034],{"id":52575},"geometrická-interpretace-1",[120,52577,52578,52626,52687],{},[123,52579,52580,7581,52605,52608,52609,1977],{},[883,52581,52583],{"className":52582},[886],[888,52584,52585],{"xmlns":890},[892,52586,52587,52603],{},[895,52588,52589,52595,52597],{},[2355,52590,52591,52593],{},[898,52592,2398],{},[1963,52594,2058],{},[1690,52596,1692],{},[2355,52598,52599,52601],{},[898,52600,1973],{},[1963,52602,2058],{},[902,52604,52103],{"encoding":904},[38,52606,52607],{},"tržba"," výrobce za prodané množství ",[883,52610,52612],{"className":52611},[886],[888,52613,52614],{"xmlns":890},[892,52615,52616,52624],{},[895,52617,52618],{},[2355,52619,52620,52622],{},[898,52621,1973],{},[1963,52623,2058],{},[902,52625,38808],{"encoding":904},[123,52627,52628,52668,52669,52686],{},[883,52629,52631],{"className":52630},[886],[888,52632,52633],{"xmlns":890},[892,52634,52635,52665],{},[895,52636,52637],{},[2919,52638,52639,52651,52653,52655,52657,52659,52661,52663],{"scriptlevel":2058,"displaystyle":1915},[1810,52640,52641,52643,52645],{},[1664,52642,1679],{},[1963,52644,2058],{},[2355,52646,52647,52649],{},[898,52648,1973],{},[1963,52650,2058],{},[898,52652,2351],{},[1664,52654,1667],{"stretchy":1666},[898,52656,1973],{},[1664,52658,1673],{"stretchy":1666},[1690,52660,1692],{},[898,52662,1695],{},[898,52664,1973],{},[902,52666,52667],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,52670,52672],{"className":52671},[886],[888,52673,52674],{"xmlns":890},[892,52675,52676,52684],{},[895,52677,52678],{},[2355,52679,52680,52682],{},[898,52681,1973],{},[1963,52683,2058],{},[902,52685,38808],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,52688,52689,52704,52705,52726,52727,1977],{},[883,52690,52692],{"className":52691},[886],[888,52693,52694],{"xmlns":890},[892,52695,52696,52702],{},[895,52697,52698,52700],{},[898,52699,2398],{},[898,52701,2351],{},[902,52703,45469],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,52706,52708],{"className":52707},[886],[888,52709,52710],{"xmlns":890},[892,52711,52712,52724],{},[895,52713,52714,52716,52718],{},[898,52715,2398],{},[1664,52717,1676],{},[2355,52719,52720,52722],{},[898,52721,2398],{},[1963,52723,2058],{},[902,52725,52177],{"encoding":904}," a křivkou nabídky v pásu ",[883,52728,52730],{"className":52729},[886],[888,52731,52732],{"xmlns":890},[892,52733,52734,52750],{},[895,52735,52736,52738,52740,52742,52748],{},[1664,52737,1837],{"stretchy":1666},[1963,52739,2058],{},[1664,52741,1916],{"separator":1915},[2355,52743,52744,52746],{},[898,52745,1973],{},[1963,52747,2058],{},[1664,52749,1850],{"stretchy":1666},[902,52751,52052],{"encoding":904},[724,52753,52754],{},[614,52755,52756],{},"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.",[37470,52758],{},[4436,52760,52761,52766],{},[724,52762,52763,52765],{},[883,52764,5138],{}," Postup výpočtu CS a PS",[152,52767,52768,52899,53009,53038,53172],{},[123,52769,52770,52771,52788,52789,52820,52821,52852,52853,1977],{},"Zjisti (nebo si zvol) množství ",[883,52772,52774],{"className":52773},[886],[888,52775,52776],{"xmlns":890},[892,52777,52778,52786],{},[895,52779,52780],{},[2355,52781,52782,52784],{},[898,52783,1973],{},[1963,52785,2058],{},[902,52787,38808],{"encoding":904}," a odpovídající cenu ",[883,52790,52792],{"className":52791},[886],[888,52793,52794],{"xmlns":890},[892,52795,52796,52818],{},[895,52797,52798,52804,52806,52808,52810,52816],{},[2355,52799,52800,52802],{},[898,52801,2398],{},[1963,52803,2058],{},[1664,52805,1676],{},[898,52807,2379],{},[1664,52809,1667],{"stretchy":1666},[2355,52811,52812,52814],{},[898,52813,1973],{},[1963,52815,2058],{},[1664,52817,1673],{"stretchy":1666},[902,52819,51555],{"encoding":904}," resp. ",[883,52822,52824],{"className":52823},[886],[888,52825,52826],{"xmlns":890},[892,52827,52828,52850],{},[895,52829,52830,52836,52838,52840,52842,52848],{},[2355,52831,52832,52834],{},[898,52833,2398],{},[1963,52835,2058],{},[1664,52837,1676],{},[898,52839,2351],{},[1664,52841,1667],{"stretchy":1666},[2355,52843,52844,52846],{},[898,52845,1973],{},[1963,52847,2058],{},[1664,52849,1673],{"stretchy":1666},[902,52851,51587],{"encoding":904},". V rovnováze platí ",[883,52854,52856],{"className":52855},[886],[888,52857,52858],{"xmlns":890},[892,52859,52860,52896],{},[895,52861,52862,52864,52866,52872,52874,52876,52878,52880,52886,52888,52890],{},[898,52863,2379],{},[1664,52865,1667],{"stretchy":1666},[1720,52867,52868,52870],{},[898,52869,1973],{},[898,52871,4819],{},[1664,52873,1673],{"stretchy":1666},[1664,52875,1676],{},[898,52877,2351],{},[1664,52879,1667],{"stretchy":1666},[1720,52881,52882,52884],{},[898,52883,1973],{},[898,52885,4819],{},[1664,52887,1673],{"stretchy":1666},[1664,52889,1676],{},[1720,52891,52892,52894],{},[898,52893,2398],{},[898,52895,4819],{},[902,52897,52898],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,52900,52901,52902,20626,52940,52955,52956,20626,52994,4488],{},"Spočti určitý integrál ",[883,52903,52905],{"className":52904},[886],[888,52906,52907],{"xmlns":890},[892,52908,52909,52937],{},[895,52910,52911,52923,52925,52927,52929,52931,52933,52935],{},[1810,52912,52913,52915,52917],{},[1664,52914,1679],{},[1963,52916,2058],{},[2355,52918,52919,52921],{},[898,52920,1973],{},[1963,52922,2058],{},[898,52924,2379],{},[1664,52926,1667],{"stretchy":1666},[898,52928,1973],{},[1664,52930,1673],{"stretchy":1666},[1690,52932,1692],{},[898,52934,1695],{},[898,52936,1973],{},[902,52938,52939],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,52941,52943],{"className":52942},[886],[888,52944,52945],{"xmlns":890},[892,52946,52947,52953],{},[895,52948,52949,52951],{},[898,52950,1703],{},[898,52952,2351],{},[902,52954,45450],{"encoding":904},") nebo ",[883,52957,52959],{"className":52958},[886],[888,52960,52961],{"xmlns":890},[892,52962,52963,52991],{},[895,52964,52965,52977,52979,52981,52983,52985,52987,52989],{},[1810,52966,52967,52969,52971],{},[1664,52968,1679],{},[1963,52970,2058],{},[2355,52972,52973,52975],{},[898,52974,1973],{},[1963,52976,2058],{},[898,52978,2351],{},[1664,52980,1667],{"stretchy":1666},[898,52982,1973],{},[1664,52984,1673],{"stretchy":1666},[1690,52986,1692],{},[898,52988,1695],{},[898,52990,1973],{},[902,52992,52993],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,52995,52997],{"className":52996},[886],[888,52998,52999],{"xmlns":890},[892,53000,53001,53007],{},[895,53002,53003,53005],{},[898,53004,2398],{},[898,53006,2351],{},[902,53008,45469],{"encoding":904},[123,53010,53011,53012,1977],{},"Sestav obdélník ",[883,53013,53015],{"className":53014},[886],[888,53016,53017],{"xmlns":890},[892,53018,53019,53035],{},[895,53020,53021,53027,53029],{},[2355,53022,53023,53025],{},[898,53024,2398],{},[1963,53026,2058],{},[1664,53028,3753],{},[2355,53030,53031,53033],{},[898,53032,1973],{},[1963,53034,2058],{},[902,53036,53037],{"encoding":904},"P_0 \\cdot Q_0",[123,53039,53040,53041],{},"Dosaď:\n",[120,53042,53043,53108],{},[123,53044,53045,53103,53104,53107],{},[883,53046,53048],{"className":53047},[886],[888,53049,53050],{"xmlns":890},[892,53051,53052,53100],{},[895,53053,53054,53056,53058,53060,53072,53074,53076,53078,53080,53082,53084,53086,53088,53094],{},[898,53055,1703],{},[898,53057,2351],{},[1664,53059,1676],{},[1810,53061,53062,53064,53066],{},[1664,53063,1679],{},[1963,53065,2058],{},[2355,53067,53068,53070],{},[898,53069,1973],{},[1963,53071,2058],{},[898,53073,2379],{},[1664,53075,1667],{"stretchy":1666},[898,53077,1973],{},[1664,53079,1673],{"stretchy":1666},[1690,53081,1692],{},[898,53083,1695],{},[898,53085,1973],{},[1664,53087,1867],{},[2355,53089,53090,53092],{},[898,53091,2398],{},[1963,53093,2058],{},[2355,53095,53096,53098],{},[898,53097,1973],{},[1963,53099,2058],{},[902,53101,53102],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,53105,53106],{},"mínus"," obdélník)",[123,53109,53110,53168,53169,53171],{},[883,53111,53113],{"className":53112},[886],[888,53114,53115],{"xmlns":890},[892,53116,53117,53165],{},[895,53118,53119,53121,53123,53125,53131,53137,53139,53151,53153,53155,53157,53159,53161,53163],{},[898,53120,2398],{},[898,53122,2351],{},[1664,53124,1676],{},[2355,53126,53127,53129],{},[898,53128,2398],{},[1963,53130,2058],{},[2355,53132,53133,53135],{},[898,53134,1973],{},[1963,53136,2058],{},[1664,53138,1867],{},[1810,53140,53141,53143,53145],{},[1664,53142,1679],{},[1963,53144,2058],{},[2355,53146,53147,53149],{},[898,53148,1973],{},[1963,53150,2058],{},[898,53152,2351],{},[1664,53154,1667],{"stretchy":1666},[898,53156,1973],{},[1664,53158,1673],{"stretchy":1666},[1690,53160,1692],{},[898,53162,1695],{},[898,53164,1973],{},[902,53166,53167],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,53170,53106],{}," integrál)",[123,53173,53174,53175,53178],{},"Kontrola znaménka: obě hodnoty musí být ",[38,53176,53177],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[37470,53180],{},[115,53182,53184],{"id":53183},"příklady","Příklady",[198,53186,53188],{"id":53187},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[4436,53190,53191],{},[724,53192,53193,53196,53197,48221,53220,53243,53244,1343,53264,1343,53281,1343,53298,53315,53316,53392,53393,53410,53411,53424],{},[883,53194,53195],{},"!example"," Zadání\nJsou dány poptávka ",[883,53198,53200],{"className":53199},[886],[888,53201,53202],{"xmlns":890},[892,53203,53204,53218],{},[895,53205,53206,53208,53210,53212,53214,53216],{},[898,53207,2398],{},[1664,53209,1676],{},[898,53211,207],{},[898,53213,1973],{},[1664,53215,1700],{},[898,53217,1818],{},[902,53219,37560],{"encoding":904},[883,53221,53223],{"className":53222},[886],[888,53224,53225],{"xmlns":890},[892,53226,53227,53241],{},[895,53228,53229,53231,53233,53235,53237,53239],{},[898,53230,2398],{},[1664,53232,1676],{},[898,53234,2034],{},[898,53236,1973],{},[1664,53238,1700],{},[898,53240,1695],{},[902,53242,40742],{"encoding":904}," s hodnotami ",[883,53245,53247],{"className":53246},[886],[888,53248,53249],{"xmlns":890},[892,53250,53251,53261],{},[895,53252,53253,53255,53257,53259],{},[898,53254,207],{},[1664,53256,1676],{},[1664,53258,1867],{},[1963,53260,2774],{},[902,53262,53263],{"encoding":904},"a = -3",[883,53265,53267],{"className":53266},[886],[888,53268,53269],{"xmlns":890},[892,53270,53271,53279],{},[895,53272,53273,53275,53277],{},[898,53274,1818],{},[1664,53276,1676],{},[1963,53278,5777],{},[902,53280,49144],{"encoding":904},[883,53282,53284],{"className":53283},[886],[888,53285,53286],{"xmlns":890},[892,53287,53288,53296],{},[895,53289,53290,53292,53294],{},[898,53291,2034],{},[1664,53293,1676],{},[1963,53295,5575],{},[902,53297,49162],{"encoding":904},[883,53299,53301],{"className":53300},[886],[888,53302,53303],{"xmlns":890},[892,53304,53305,53313],{},[895,53306,53307,53309,53311],{},[898,53308,1695],{},[1664,53310,1676],{},[1963,53312,3442],{},[902,53314,49180],{"encoding":904},".\nRovnovážné množství:\n",[883,53317,53319],{"className":53318},[886],[888,53320,53321],{"xmlns":890},[892,53322,53323,53389],{},[895,53324,53325,53331,53333,53351,53353,53377,53379,53385,53387],{},[1720,53326,53327,53329],{},[898,53328,1973],{},[898,53330,4819],{},[1664,53332,1676],{},[2922,53334,53335,53343],{},[895,53336,53337,53339,53341],{},[898,53338,1818],{},[1664,53340,1867],{},[898,53342,1695],{},[895,53344,53345,53347,53349],{},[898,53346,2034],{},[1664,53348,1867],{},[898,53350,207],{},[1664,53352,1676],{},[2922,53354,53355,53363],{},[895,53356,53357,53359,53361],{},[1963,53358,5777],{},[1664,53360,1867],{},[1963,53362,3442],{},[895,53364,53365,53367,53369,53371,53373,53375],{},[1963,53366,5575],{},[1664,53368,1867],{},[1664,53370,1667],{"stretchy":1666},[1664,53372,1867],{},[1963,53374,2774],{},[1664,53376,1673],{"stretchy":1666},[1664,53378,1676],{},[2922,53380,53381,53383],{},[1963,53382,38519],{},[1963,53384,44906],{},[1664,53386,6466],{},[1963,53388,44911],{},[902,53390,53391],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,53394,53396],{"className":53395},[886],[888,53397,53398],{"xmlns":890},[892,53399,53400,53408],{},[895,53401,53402],{},[1720,53403,53404,53406],{},[898,53405,1973],{},[898,53407,4819],{},[902,53409,42903],{"encoding":904}," (a) při změně samotného parametru ",[883,53412,53414],{"className":53413},[886],[888,53415,53416],{"xmlns":890},[892,53417,53418,53422],{},[895,53419,53420],{},[898,53421,2034],{},[902,53423,2034],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,53426,53427],{},[38,53428,53429,53430,3257,53443,3271,53456,9858],{},"Řešení (a) — změna ",[883,53431,53433],{"className":53432},[886],[888,53434,53435],{"xmlns":890},[892,53436,53437,53441],{},[895,53438,53439],{},[898,53440,2034],{},[902,53442,2034],{"encoding":904},[883,53444,53446],{"className":53445},[886],[888,53447,53448],{"xmlns":890},[892,53449,53450,53454],{},[895,53451,53452],{},[1963,53453,5575],{},[902,53455,44946],{"encoding":904},[883,53457,53459],{"className":53458},[886],[888,53460,53461],{"xmlns":890},[892,53462,53463,53467],{},[895,53464,53465],{},[1963,53466,19821],{},[902,53468,44960],{"encoding":904},[724,53470,53471,53472,53536,53537,2087],{},"Pomocí vzorce (2.13) pro ",[883,53473,53475],{"className":53474},[886],[888,53476,53477],{"xmlns":890},[892,53478,53479,53533],{},[895,53480,53481,53501,53503,53505],{},[2919,53482,53483],{"scriptlevel":2058,"displaystyle":1915},[2922,53484,53485,53495],{},[895,53486,53487,53489],{},[898,53488,10435],{"mathvariant":1726},[1720,53490,53491,53493],{},[898,53492,1973],{},[898,53494,4819],{},[895,53496,53497,53499],{},[898,53498,10435],{"mathvariant":1726},[898,53500,2034],{},[1664,53502,1676],{},[1664,53504,1867],{},[2919,53506,53507],{"scriptlevel":2058,"displaystyle":1915},[2922,53508,53509,53517],{},[895,53510,53511,53513,53515],{},[898,53512,1818],{},[1664,53514,1867],{},[898,53516,1695],{},[895,53518,53519,53521,53523,53525,53527],{},[1664,53520,1667],{"stretchy":1666},[898,53522,2034],{},[1664,53524,1867],{},[898,53526,207],{},[1720,53528,53529,53531],{},[1664,53530,1673],{"stretchy":1666},[1963,53532,1970],{},[902,53534,53535],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,53538,53540],{"className":53539},[886],[888,53541,53542],{"xmlns":890},[892,53543,53544,53566],{},[895,53545,53546,53548],{},[1664,53547,1867],{},[2919,53549,53550],{"scriptlevel":2058,"displaystyle":1915},[2922,53551,53552,53558],{},[1720,53553,53554,53556],{},[898,53555,1973],{},[898,53557,4819],{},[895,53559,53560,53562,53564],{},[898,53561,2034],{},[1664,53563,1867],{},[898,53565,207],{},[902,53567,53568],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,53570,53572],{"className":53571},[886],[888,53573,53574],{"xmlns":890,"display":28566},[892,53575,53576,53632],{},[895,53577,53578,53580,53586,53588,53590,53606,53608,53610,53612,53614,53616,53622,53624,53626,53628,53630],{},[898,53579,1695],{},[1720,53581,53582,53584],{},[898,53583,1973],{},[898,53585,4819],{},[1664,53587,1676],{},[1664,53589,1867],{},[2922,53591,53592,53598],{},[1720,53593,53594,53596],{},[898,53595,1973],{},[898,53597,4819],{},[895,53599,53600,53602,53604],{},[898,53601,2034],{},[1664,53603,1867],{},[898,53605,207],{},[1690,53607,1692],{},[898,53609,1695],{},[898,53611,2034],{},[1664,53613,1676],{},[1664,53615,1867],{},[2922,53617,53618,53620],{},[1963,53619,45074],{},[1963,53621,44906],{},[1664,53623,3753],{},[1963,53625,2220],{},[1664,53627,6466],{},[1664,53629,1867],{},[1963,53631,45046],{},[902,53633,53634],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,53636,53637],{},"Nové rovnovážné množství:",[883,53639,53641],{"className":53640},[886],[888,53642,53643],{"xmlns":890,"display":28566},[892,53644,53645,53668],{},[895,53646,53647,53655,53657,53659,53661,53663,53665],{},[1810,53648,53649,53651,53653],{},[898,53650,1973],{},[1963,53652,2875],{},[898,53654,4819],{},[1664,53656,3315],{},[1963,53658,45074],{},[1664,53660,1867],{},[1963,53662,45079],{},[1664,53664,1676],{},[1963,53666,53667],{},"8,326.",[902,53669,53670],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,53672,53673,1885,53676,1343,53703,1343,53725,1343,53747,6155,53769,1343,53788,1343,53809,1343,53828,1977],{},[38,53674,53675],{},"Řešení (b) — současná změna všech parametrů:",[883,53677,53679],{"className":53678},[886],[888,53680,53681],{"xmlns":890},[892,53682,53683,53700],{},[895,53684,53685,53687,53689,53691,53693,53695,53697],{},[898,53686,207],{},[1664,53688,2087],{},[1664,53690,1867],{},[1963,53692,2774],{},[1664,53694,3699],{},[1664,53696,1867],{},[1963,53698,53699],{},"2,5",[902,53701,53702],{"encoding":904},"a: -3 \\to -2{,}5",[883,53704,53706],{"className":53705},[886],[888,53707,53708],{"xmlns":890},[892,53709,53710,53722],{},[895,53711,53712,53714,53716,53718,53720],{},[898,53713,1818],{},[1664,53715,2087],{},[1963,53717,5777],{},[1664,53719,3699],{},[1963,53721,15537],{},[902,53723,53724],{"encoding":904},"b: 40 \\to 35",[883,53726,53728],{"className":53727},[886],[888,53729,53730],{"xmlns":890},[892,53731,53732,53744],{},[895,53733,53734,53736,53738,53740,53742],{},[898,53735,2034],{},[1664,53737,2087],{},[1963,53739,5575],{},[1664,53741,3699],{},[1963,53743,19821],{},[902,53745,53746],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,53748,53750],{"className":53749},[886],[888,53751,53752],{"xmlns":890},[892,53753,53754,53766],{},[895,53755,53756,53758,53760,53762,53764],{},[898,53757,1695],{},[1664,53759,2087],{},[1963,53761,3442],{},[1664,53763,3699],{},[1963,53765,3483],{},[902,53767,53768],{"encoding":904},"d: 10 \\to 11",[883,53770,53772],{"className":53771},[886],[888,53773,53774],{"xmlns":890},[892,53775,53776,53786],{},[895,53777,53778,53780,53782,53784],{},[898,53779,1695],{},[898,53781,207],{},[1664,53783,1676],{},[1963,53785,5575],{},[902,53787,45112],{"encoding":904},[883,53789,53791],{"className":53790},[886],[888,53792,53793],{"xmlns":890},[892,53794,53795,53807],{},[895,53796,53797,53799,53801,53803,53805],{},[898,53798,1695],{},[898,53800,1818],{},[1664,53802,1676],{},[1664,53804,1867],{},[1963,53806,2826],{},[902,53808,45134],{"encoding":904},[883,53810,53812],{"className":53811},[886],[888,53813,53814],{"xmlns":890},[892,53815,53816,53826],{},[895,53817,53818,53820,53822,53824],{},[898,53819,1695],{},[898,53821,2034],{},[1664,53823,1676],{},[1963,53825,2220],{},[902,53827,45154],{"encoding":904},[883,53829,53831],{"className":53830},[886],[888,53832,53833],{"xmlns":890},[892,53834,53835,53845],{},[895,53836,53837,53839,53841,53843],{},[898,53838,1695],{},[898,53840,1695],{},[1664,53842,1676],{},[1963,53844,2875],{},[902,53846,45174],{"encoding":904},[724,53848,53849,53850,53908],{},"Totální diferenciál ",[883,53851,53853],{"className":53852},[886],[888,53854,53855],{"xmlns":890},[892,53856,53857,53905],{},[895,53858,53859,53865,53867,53869,53871,53873,53875,53877,53879,53881,53883,53885],{},[1720,53860,53861,53863],{},[898,53862,1973],{},[898,53864,4819],{},[1664,53866,1667],{"stretchy":1666},[898,53868,207],{},[1664,53870,1916],{"separator":1915},[898,53872,1818],{},[1664,53874,1916],{"separator":1915},[898,53876,2034],{},[1664,53878,1916],{"separator":1915},[898,53880,1695],{},[1664,53882,1673],{"stretchy":1666},[1664,53884,1676],{},[2919,53886,53887],{"scriptlevel":2058,"displaystyle":1915},[2922,53888,53889,53897],{},[895,53890,53891,53893,53895],{},[898,53892,1818],{},[1664,53894,1867],{},[898,53896,1695],{},[895,53898,53899,53901,53903],{},[898,53900,2034],{},[1664,53902,1867],{},[898,53904,207],{},[902,53906,53907],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,53910,53912],{"className":53911},[886],[888,53913,53914],{"xmlns":890,"display":28566},[892,53915,53916,54036],{},[895,53917,53918,53920,53926,53928,53954,53956,53958,53960,53962,53974,53976,53978,53980,53982,54008,54010,54012,54014,54016,54028,54030,54032,54034],{},[898,53919,1695],{},[1720,53921,53922,53924],{},[898,53923,1973],{},[898,53925,4819],{},[1664,53927,1676],{},[2922,53929,53930,53938],{},[895,53931,53932,53934,53936],{},[898,53933,1818],{},[1664,53935,1867],{},[898,53937,1695],{},[895,53939,53940,53942,53944,53946,53948],{},[1664,53941,1667],{"stretchy":1666},[898,53943,2034],{},[1664,53945,1867],{},[898,53947,207],{},[1720,53949,53950,53952],{},[1664,53951,1673],{"stretchy":1666},[1963,53953,1970],{},[1690,53955,1692],{},[898,53957,1695],{},[898,53959,207],{},[1664,53961,1700],{},[2922,53963,53964,53966],{},[1963,53965,2875],{},[895,53967,53968,53970,53972],{},[898,53969,2034],{},[1664,53971,1867],{},[898,53973,207],{},[1690,53975,1692],{},[898,53977,1695],{},[898,53979,1818],{},[1664,53981,1867],{},[2922,53983,53984,53992],{},[895,53985,53986,53988,53990],{},[898,53987,1818],{},[1664,53989,1867],{},[898,53991,1695],{},[895,53993,53994,53996,53998,54000,54002],{},[1664,53995,1667],{"stretchy":1666},[898,53997,2034],{},[1664,53999,1867],{},[898,54001,207],{},[1720,54003,54004,54006],{},[1664,54005,1673],{"stretchy":1666},[1963,54007,1970],{},[1690,54009,1692],{},[898,54011,1695],{},[898,54013,2034],{},[1664,54015,1867],{},[2922,54017,54018,54020],{},[1963,54019,2875],{},[895,54021,54022,54024,54026],{},[898,54023,2034],{},[1664,54025,1867],{},[898,54027,207],{},[1690,54029,1692],{},[898,54031,1695],{},[898,54033,1695],{},[898,54035,1977],{"mathvariant":1726},[902,54037,54038],{"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.",[724,54040,54041,54042,1343,54064,1343,54095,3727],{},"Dosazením číselných hodnot (",[883,54043,54045],{"className":54044},[886],[888,54046,54047],{"xmlns":890},[892,54048,54049,54061],{},[895,54050,54051,54053,54055,54057,54059],{},[898,54052,2034],{},[1664,54054,1867],{},[898,54056,207],{},[1664,54058,1676],{},[1963,54060,44906],{},[902,54062,54063],{"encoding":904},"c - a = 3{,}5",[883,54065,54067],{"className":54066},[886],[888,54068,54069],{"xmlns":890},[892,54070,54071,54092],{},[895,54072,54073,54075,54077,54079,54081,54087,54089],{},[1664,54074,1667],{"stretchy":1666},[898,54076,2034],{},[1664,54078,1867],{},[898,54080,207],{},[1720,54082,54083,54085],{},[1664,54084,1673],{"stretchy":1666},[1963,54086,1970],{},[1664,54088,1676],{},[1963,54090,54091],{},"12,25",[902,54093,54094],{"encoding":904},"(c-a)^2 = 12{,}25",[883,54096,54098],{"className":54097},[886],[888,54099,54100],{"xmlns":890},[892,54101,54102,54114],{},[895,54103,54104,54106,54108,54110,54112],{},[898,54105,1818],{},[1664,54107,1867],{},[898,54109,1695],{},[1664,54111,1676],{},[1963,54113,38519],{},[902,54115,54116],{"encoding":904},"b - d = 30",[883,54118,54120],{"className":54119},[886],[888,54121,54122],{"xmlns":890,"display":28566},[892,54123,54124,54225],{},[895,54125,54126,54128,54134,54136,54144,54146,54148,54150,54152,54160,54162,54164,54166,54168,54170,54178,54180,54182,54184,54186,54194,54196,54198,54200,54202,54205,54207,54210,54212,54214,54216,54219,54221,54223],{},[898,54127,1695],{},[1720,54129,54130,54132],{},[898,54131,1973],{},[898,54133,4819],{},[1664,54135,3315],{},[2919,54137,54138],{"scriptlevel":2058,"displaystyle":1666},[2922,54139,54140,54142],{},[1963,54141,38519],{},[1963,54143,54091],{},[1664,54145,1667],{"stretchy":1666},[1963,54147,5575],{},[1664,54149,1673],{"stretchy":1666},[1664,54151,1700],{},[2919,54153,54154],{"scriptlevel":2058,"displaystyle":1666},[2922,54155,54156,54158],{},[1963,54157,2875],{},[1963,54159,44906],{},[1664,54161,1667],{"stretchy":1666},[1664,54163,1867],{},[1963,54165,2826],{},[1664,54167,1673],{"stretchy":1666},[1664,54169,1867],{},[2919,54171,54172],{"scriptlevel":2058,"displaystyle":1666},[2922,54173,54174,54176],{},[1963,54175,38519],{},[1963,54177,54091],{},[1664,54179,1667],{"stretchy":1666},[1963,54181,2220],{},[1664,54183,1673],{"stretchy":1666},[1664,54185,1867],{},[2919,54187,54188],{"scriptlevel":2058,"displaystyle":1666},[2922,54189,54190,54192],{},[1963,54191,2875],{},[1963,54193,44906],{},[1664,54195,1667],{"stretchy":1666},[1963,54197,2875],{},[1664,54199,1673],{"stretchy":1666},[1664,54201,6466],{},[1963,54203,54204],{},"1,224",[1664,54206,1867],{},[1963,54208,54209],{},"1,429",[1664,54211,1867],{},[1963,54213,45079],{},[1664,54215,1867],{},[1963,54217,54218],{},"0,286",[1664,54220,6466],{},[1664,54222,1867],{},[1963,54224,45325],{},[902,54226,54227],{"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.",[724,54229,30565,54230,1977],{},[883,54231,54233],{"className":54232},[886],[888,54234,54235],{"xmlns":890},[892,54236,54237,54259],{},[895,54238,54239,54247,54249,54251,54253,54255,54257],{},[1810,54240,54241,54243,54245],{},[898,54242,1973],{},[1963,54244,2875],{},[898,54246,4819],{},[1664,54248,3315],{},[1963,54250,45074],{},[1664,54252,1867],{},[1963,54254,45356],{},[1664,54256,6466],{},[1963,54258,45361],{},[902,54260,54261],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[4436,54263,54264],{},[724,54265,54266,54268,54269,54290,54291,54317,54318,54321,54322,54418,54419,54442,54443,54459],{},[883,54267,4978],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,54270,54272],{"className":54271},[886],[888,54273,54274],{"xmlns":890},[892,54275,54276,54288],{},[895,54277,54278,54280,54282,54284,54286],{},[898,54279,3468],{"mathvariant":1726},[898,54281,1973],{},[1664,54283,3315],{},[1664,54285,1867],{},[1963,54287,45391],{},[902,54289,45394],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,54292,54294],{"className":54293},[886],[888,54295,54296],{"xmlns":890},[892,54297,54298,54314],{},[895,54299,54300,54302,54308,54310,54312],{},[898,54301,1695],{},[1720,54303,54304,54306],{},[898,54305,1973],{},[898,54307,4819],{},[1664,54309,6466],{},[1664,54311,1867],{},[1963,54313,45356],{},[902,54315,54316],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,54319,54320],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,54323,54325],{"className":54324},[886],[888,54326,54327],{"xmlns":890},[892,54328,54329,54415],{},[895,54330,54331,54339,54341,54375,54377,54401,54403,54410,54412],{},[1810,54332,54333,54335,54337],{},[898,54334,1973],{},[1963,54336,2875],{},[898,54338,4819],{},[1664,54340,1676],{},[2922,54342,54343,54359],{},[895,54344,54345,54351,54353],{},[1720,54346,54347,54349],{},[898,54348,1818],{},[1664,54350,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,54352,1867],{},[1720,54354,54355,54357],{},[898,54356,1695],{},[1664,54358,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[895,54360,54361,54367,54369],{},[1720,54362,54363,54365],{},[898,54364,2034],{},[1664,54366,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,54368,1867],{},[1720,54370,54371,54373],{},[898,54372,207],{},[1664,54374,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,54376,1676],{},[2922,54378,54379,54387],{},[895,54380,54381,54383,54385],{},[1963,54382,15537],{},[1664,54384,1867],{},[1963,54386,3483],{},[895,54388,54389,54391,54393,54395,54397,54399],{},[1963,54390,19821],{},[1664,54392,1867],{},[1664,54394,1667],{"stretchy":1666},[1664,54396,1867],{},[1963,54398,53699],{},[1664,54400,1673],{"stretchy":1666},[1664,54402,1676],{},[2922,54404,54405,54407],{},[1963,54406,42300],{},[1963,54408,54409],{},"3,1",[1664,54411,6466],{},[1963,54413,54414],{},"7,742",[902,54416,54417],{"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 ",[883,54420,54422],{"className":54421},[886],[888,54423,54424],{"xmlns":890},[892,54425,54426,54439],{},[895,54427,54428,54430,54432,54434,54436],{},[898,54429,3468],{"mathvariant":1726},[898,54431,1973],{},[1664,54433,6466],{},[1664,54435,1867],{},[1963,54437,54438],{},"0,829",[902,54440,54441],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,54444,54446],{"className":54445},[886],[888,54447,54448],{"xmlns":890},[892,54449,54450,54456],{},[895,54451,54452,54454],{},[1664,54453,1867],{},[1963,54455,45391],{},[902,54457,54458],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,54461,54462],{},[614,54463,54464,54465,54478],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,54466,54468],{"className":54467},[886],[888,54469,54470],{"xmlns":890},[892,54471,54472,54476],{},[895,54473,54474],{},[898,54475,1973],{},[902,54477,1973],{"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.",[198,54480,54482,54483],{"id":54481},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,54484,54486],{"className":54485},[886],[888,54487,54488],{"xmlns":890},[892,54489,54490,54496],{},[895,54491,54492,54494],{},[898,54493,2398],{},[898,54495,2351],{},[902,54497,45469],{"encoding":904},[4436,54499,54500],{},[724,54501,54502,54504,54505,54539,54540,54562],{},[883,54503,53195],{}," Zadání\nPro nabídku ",[883,54506,54508],{"className":54507},[886],[888,54509,54510],{"xmlns":890},[892,54511,54512,54536],{},[895,54513,54514,54516,54518,54520,54522,54524,54526,54528,54530,54532,54534],{},[898,54515,2398],{},[1664,54517,1676],{},[898,54519,2351],{},[1664,54521,1667],{"stretchy":1666},[898,54523,1973],{},[1664,54525,1673],{"stretchy":1666},[1664,54527,1676],{},[1963,54529,3442],{},[1664,54531,1700],{},[1963,54533,1970],{},[898,54535,1973],{},[902,54537,54538],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,54541,54543],{"className":54542},[886],[888,54544,54545],{"xmlns":890},[892,54546,54547,54559],{},[895,54548,54549,54555,54557],{},[2355,54550,54551,54553],{},[898,54552,1973],{},[1963,54554,2058],{},[1664,54556,1676],{},[1963,54558,3442],{},[902,54560,54561],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,54564,54565],{},[38,54566,23270],{},[724,54568,54569],{},"Odpovídající cena:",[883,54571,54573],{"className":54572},[886],[888,54574,54575],{"xmlns":890,"display":28566},[892,54576,54577,54612],{},[895,54578,54579,54585,54587,54589,54591,54593,54595,54597,54599,54601,54603,54605,54607,54609],{},[2355,54580,54581,54583],{},[898,54582,2398],{},[1963,54584,2058],{},[1664,54586,1676],{},[898,54588,2351],{},[1664,54590,1667],{"stretchy":1666},[1963,54592,3442],{},[1664,54594,1673],{"stretchy":1666},[1664,54596,1676],{},[1963,54598,3442],{},[1664,54600,1700],{},[1963,54602,1970],{},[1664,54604,3753],{},[1963,54606,3442],{},[1664,54608,1676],{},[1963,54610,54611],{},"30.",[902,54613,54614],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,54616,54617],{},"Dle vzorce (2.15):",[883,54619,54621],{"className":54620},[886],[888,54622,54623],{"xmlns":890,"display":28566},[892,54624,54625,54733],{},[895,54626,54627,54629,54631,54633,54635,54637,54639,54645,54651,54653,54661,54663,54665,54667,54669,54671,54673,54675,54677,54679,54681,54683,54685,54687,54689,54692,54694,54696,54698,54704,54712,54714,54716,54718,54720,54722,54724,54726,54728,54730],{},[898,54628,2398],{},[898,54630,2351],{},[1664,54632,1667],{"stretchy":1666},[1963,54634,3442],{},[1664,54636,1673],{"stretchy":1666},[1664,54638,1676],{},[2355,54640,54641,54643],{},[898,54642,2398],{},[1963,54644,2058],{},[2355,54646,54647,54649],{},[898,54648,1973],{},[1963,54650,2058],{},[1664,54652,1867],{},[1810,54654,54655,54657,54659],{},[1664,54656,1679],{},[1963,54658,2058],{},[1963,54660,3442],{},[1664,54662,1667],{"stretchy":1666},[1963,54664,3442],{},[1664,54666,1700],{},[1963,54668,1970],{},[898,54670,1973],{},[1664,54672,1673],{"stretchy":1666},[1690,54674,1692],{},[898,54676,1695],{},[898,54678,1973],{},[1664,54680,1676],{},[1963,54682,3442],{},[1664,54684,3753],{},[1963,54686,38519],{},[1664,54688,1867],{},[1664,54690,1837],{"fence":1666,"stretchy":1915,"minsize":54691,"maxsize":54691},"1.8em",[1963,54693,3442],{},[898,54695,1973],{},[1664,54697,1700],{},[1720,54699,54700,54702],{},[898,54701,1973],{},[1963,54703,1970],{},[1810,54705,54706,54708,54710],{},[1664,54707,1850],{"fence":1666,"stretchy":1915,"minsize":54691,"maxsize":54691},[1963,54709,2058],{},[1963,54711,3442],{},[1664,54713,1676],{},[1963,54715,30581],{},[1664,54717,1867],{},[1664,54719,1667],{"stretchy":1666},[1963,54721,1965],{},[1664,54723,1700],{},[1963,54725,1965],{},[1664,54727,1673],{"stretchy":1666},[1664,54729,1676],{},[1963,54731,54732],{},"100.",[902,54734,54735],{"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.",[724,54737,54738,54739,54760,54761,54781],{},"Přebytek výrobce při množství ",[883,54740,54742],{"className":54741},[886],[888,54743,54744],{"xmlns":890},[892,54745,54746,54758],{},[895,54747,54748,54754,54756],{},[2355,54749,54750,54752],{},[898,54751,1973],{},[1963,54753,2058],{},[1664,54755,1676],{},[1963,54757,3442],{},[902,54759,54561],{"encoding":904}," je tedy ",[883,54762,54764],{"className":54763},[886],[888,54765,54766],{"xmlns":890},[892,54767,54768,54778],{},[895,54769,54770,54772,54774,54776],{},[898,54771,2398],{},[898,54773,2351],{},[1664,54775,1676],{},[1963,54777,1965],{},[902,54779,54780],{"encoding":904},"PS = 100"," (peněžních jednotek).",[37470,54783],{},[115,54785,54787],{"id":54786},"cheat-sheet","Cheat sheet",[16,54789,54790,54803],{},[19,54791,54792],{},[22,54793,54794,54797,54800],{},[25,54795,54796],{},"Veličina",[25,54798,54799],{},"Vzorec",[25,54801,54802],{},"Geometrie",[30,54804,54805,54923,55037,55105],{},[22,54806,54807,54835,54891],{},[35,54808,54809],{},[883,54810,54812],{"className":54811},[886],[888,54813,54814],{"xmlns":890},[892,54815,54816,54832],{},[895,54817,54818,54820,54822,54824,54830],{},[898,54819,1703],{},[898,54821,2351],{},[1664,54823,1667],{"stretchy":1666},[2355,54825,54826,54828],{},[898,54827,1973],{},[1963,54829,2058],{},[1664,54831,1673],{"stretchy":1666},[902,54833,54834],{"encoding":904},"CS(Q_0)",[35,54836,54837],{},[883,54838,54840],{"className":54839},[886],[888,54841,54842],{"xmlns":890},[892,54843,54844,54888],{},[895,54845,54846],{},[2919,54847,54848,54860,54862,54864,54866,54868,54870,54872,54874,54876,54882],{"scriptlevel":2058,"displaystyle":1915},[1810,54849,54850,54852,54854],{},[1664,54851,1679],{},[1963,54853,2058],{},[2355,54855,54856,54858],{},[898,54857,1973],{},[1963,54859,2058],{},[898,54861,2379],{},[1664,54863,1667],{"stretchy":1666},[898,54865,1973],{},[1664,54867,1673],{"stretchy":1666},[1690,54869,1692],{},[898,54871,1695],{},[898,54873,1973],{},[1664,54875,1867],{},[2355,54877,54878,54880],{},[898,54879,2398],{},[1963,54881,2058],{},[2355,54883,54884,54886],{},[898,54885,1973],{},[1963,54887,2058],{},[902,54889,54890],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,54892,54893,54894,54897,54898,54901,54902],{},"plocha ",[38,54895,54896],{},"pod"," křivkou poptávky, ",[38,54899,54900],{},"nad"," čárou ",[883,54903,54905],{"className":54904},[886],[888,54906,54907],{"xmlns":890},[892,54908,54909,54921],{},[895,54910,54911,54913,54915],{},[898,54912,2398],{},[1664,54914,1676],{},[2355,54916,54917,54919],{},[898,54918,2398],{},[1963,54920,2058],{},[902,54922,52177],{"encoding":904},[22,54924,54925,54953,55009],{},[35,54926,54927],{},[883,54928,54930],{"className":54929},[886],[888,54931,54932],{"xmlns":890},[892,54933,54934,54950],{},[895,54935,54936,54938,54940,54942,54948],{},[898,54937,2398],{},[898,54939,2351],{},[1664,54941,1667],{"stretchy":1666},[2355,54943,54944,54946],{},[898,54945,1973],{},[1963,54947,2058],{},[1664,54949,1673],{"stretchy":1666},[902,54951,54952],{"encoding":904},"PS(Q_0)",[35,54954,54955],{},[883,54956,54958],{"className":54957},[886],[888,54959,54960],{"xmlns":890},[892,54961,54962,55006],{},[895,54963,54964],{},[2919,54965,54966,54972,54978,54980,54992,54994,54996,54998,55000,55002,55004],{"scriptlevel":2058,"displaystyle":1915},[2355,54967,54968,54970],{},[898,54969,2398],{},[1963,54971,2058],{},[2355,54973,54974,54976],{},[898,54975,1973],{},[1963,54977,2058],{},[1664,54979,1867],{},[1810,54981,54982,54984,54986],{},[1664,54983,1679],{},[1963,54985,2058],{},[2355,54987,54988,54990],{},[898,54989,1973],{},[1963,54991,2058],{},[898,54993,2351],{},[1664,54995,1667],{"stretchy":1666},[898,54997,1973],{},[1664,54999,1673],{"stretchy":1666},[1690,55001,1692],{},[898,55003,1695],{},[898,55005,1973],{},[902,55007,55008],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,55010,54893,55011,55013,55014,54901,55016],{},[38,55012,54900],{}," křivkou nabídky, ",[38,55015,54896],{},[883,55017,55019],{"className":55018},[886],[888,55020,55021],{"xmlns":890},[892,55022,55023,55035],{},[895,55024,55025,55027,55029],{},[898,55026,2398],{},[1664,55028,1676],{},[2355,55030,55031,55033],{},[898,55032,2398],{},[1963,55034,2058],{},[902,55036,52177],{"encoding":904},[22,55038,55039,55042,55069],{},[35,55040,55041],{},"Výdaje \u002F tržby",[35,55043,55044],{},[883,55045,55047],{"className":55046},[886],[888,55048,55049],{"xmlns":890},[892,55050,55051,55067],{},[895,55052,55053,55059,55061],{},[2355,55054,55055,55057],{},[898,55056,2398],{},[1963,55058,2058],{},[1664,55060,3753],{},[2355,55062,55063,55065],{},[898,55064,1973],{},[1963,55066,2058],{},[902,55068,53037],{"encoding":904},[35,55070,55071,55072],{},"obdélník ",[883,55073,55075],{"className":55074},[886],[888,55076,55077],{"xmlns":890},[892,55078,55079,55103],{},[895,55080,55081,55083,55085,55091,55093,55095,55097],{},[1963,55082,2058],{},[1690,55084,1692],{},[2355,55086,55087,55089],{},[898,55088,1973],{},[1963,55090,2058],{},[1690,55092,1692],{},[898,55094,4822],{},[1690,55096,1692],{},[2355,55098,55099,55101],{},[898,55100,2398],{},[1963,55102,2058],{},[902,55104,51657],{"encoding":904},[22,55106,55107,55110,55133],{},[35,55108,55109],{},"Celkový přebytek",[35,55111,55112],{},[883,55113,55115],{"className":55114},[886],[888,55116,55117],{"xmlns":890},[892,55118,55119,55131],{},[895,55120,55121,55123,55125,55127,55129],{},[898,55122,1703],{},[898,55124,2351],{},[1664,55126,1700],{},[898,55128,2398],{},[898,55130,2351],{},[902,55132,51395],{"encoding":904},[35,55134,55135],{},"součet obou ploch v rovnováze",[37470,55137],{},[115,55139,16219],{"id":16218},[120,55141,55142,55164,55186,55230,55274,55337,55365],{},[123,55143,55144,10588,55146,1343,55161,55163],{},[38,55145,45434],{},[883,55147,55149],{"className":55148},[886],[888,55150,55151],{"xmlns":890},[892,55152,55153,55159],{},[895,55154,55155,55157],{},[898,55156,1703],{},[898,55158,2351],{},[902,55160,45450],{"encoding":904},[614,55162,45488],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,55165,55166,10588,55168,1343,55183,55185],{},[38,55167,45581],{},[883,55169,55171],{"className":55170},[886],[888,55172,55173],{"xmlns":890},[892,55174,55175,55181],{},[895,55176,55177,55179],{},[898,55178,2398],{},[898,55180,2351],{},[902,55182,45469],{"encoding":904},[614,55184,45584],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,55187,55188,7581,55191,1977],{},[38,55189,55190],{},"Ochota platit",[883,55192,55194],{"className":55193},[886],[888,55195,55196],{"xmlns":890},[892,55197,55198,55228],{},[895,55199,55200],{},[2919,55201,55202,55214,55216,55218,55220,55222,55224,55226],{"scriptlevel":2058,"displaystyle":1915},[1810,55203,55204,55206,55208],{},[1664,55205,1679],{},[1963,55207,2058],{},[2355,55209,55210,55212],{},[898,55211,1973],{},[1963,55213,2058],{},[898,55215,2379],{},[1664,55217,1667],{"stretchy":1666},[898,55219,1973],{},[1664,55221,1673],{"stretchy":1666},[1690,55223,1692],{},[898,55225,1695],{},[898,55227,1973],{},[902,55229,52025],{"encoding":904},[123,55231,55232,7581,55235,1977],{},[38,55233,55234],{},"Minimální cena výrobce",[883,55236,55238],{"className":55237},[886],[888,55239,55240],{"xmlns":890},[892,55241,55242,55272],{},[895,55243,55244],{},[2919,55245,55246,55258,55260,55262,55264,55266,55268,55270],{"scriptlevel":2058,"displaystyle":1915},[1810,55247,55248,55250,55252],{},[1664,55249,1679],{},[1963,55251,2058],{},[2355,55253,55254,55256],{},[898,55255,1973],{},[1963,55257,2058],{},[898,55259,2351],{},[1664,55261,1667],{"stretchy":1666},[898,55263,1973],{},[1664,55265,1673],{"stretchy":1666},[1690,55267,1692],{},[898,55269,1695],{},[898,55271,1973],{},[902,55273,52667],{"encoding":904},[123,55275,55276,7581,55279,53168,55304,4488],{},[38,55277,55278],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,55280,55282],{"className":55281},[886],[888,55283,55284],{"xmlns":890},[892,55285,55286,55302],{},[895,55287,55288,55294,55296],{},[2355,55289,55290,55292],{},[898,55291,2398],{},[1963,55293,2058],{},[1690,55295,1692],{},[2355,55297,55298,55300],{},[898,55299,1973],{},[1963,55301,2058],{},[902,55303,52103],{"encoding":904},[883,55305,55307],{"className":55306},[886],[888,55308,55309],{"xmlns":890},[892,55310,55311,55335],{},[895,55312,55313,55315,55317,55323,55325,55327,55329],{},[1963,55314,2058],{},[1690,55316,1692],{},[2355,55318,55319,55321],{},[898,55320,1973],{},[1963,55322,2058],{},[1690,55324,1692],{},[898,55326,4822],{},[1690,55328,1692],{},[2355,55330,55331,55333],{},[898,55332,2398],{},[1963,55334,2058],{},[902,55336,51657],{"encoding":904},[123,55338,55339,55342,55343,55364],{},[38,55340,55341],{},"Celkový přebytek trhu"," — součet ",[883,55344,55346],{"className":55345},[886],[888,55347,55348],{"xmlns":890},[892,55349,55350,55362],{},[895,55351,55352,55354,55356,55358,55360],{},[898,55353,1703],{},[898,55355,2351],{},[1664,55357,1700],{},[898,55359,2398],{},[898,55361,2351],{},[902,55363,51395],{"encoding":904}," v rovnovážném bodě.",[123,55366,55367,55369,55370,1343,55383,55396,55397,1977],{},[38,55368,3034],{}," — plochy ohraničené křivkami ",[883,55371,55373],{"className":55372},[886],[888,55374,55375],{"xmlns":890},[892,55376,55377,55381],{},[895,55378,55379],{},[898,55380,2379],{},[902,55382,2379],{"encoding":904},[883,55384,55386],{"className":55385},[886],[888,55387,55388],{"xmlns":890},[892,55389,55390,55394],{},[895,55391,55392],{},[898,55393,2351],{},[902,55395,2351],{"encoding":904}," a přímkou ",[883,55398,55400],{"className":55399},[886],[888,55401,55402],{"xmlns":890},[892,55403,55404,55416],{},[895,55405,55406,55408,55410],{},[898,55407,2398],{},[1664,55409,1676],{},[2355,55411,55412,55414],{},[898,55413,2398],{},[1963,55415,2058],{},[902,55417,52177],{"encoding":904},[37470,55419],{},[115,55421,55423],{"id":55422},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,55425,55426,55427,55440,55441,55458],{},"Uvalení jednotkové daně ",[883,55428,55430],{"className":55429},[886],[888,55431,55432],{"xmlns":890},[892,55433,55434,55438],{},[895,55435,55436],{},[898,55437,1991],{},[902,55439,1991],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,55442,55444],{"className":55443},[886],[888,55445,55446],{"xmlns":890},[892,55447,55448,55456],{},[895,55449,55450],{},[1720,55451,55452,55454],{},[898,55453,1973],{},[898,55455,4819],{},[902,55457,42903],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,55460,55461],{},[1928,55462],{"alt":55463,"className":55464,"src":55465},"imek-prebytky-s-dani-deadweight",[210,1932],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,55467,55468,55469,55484,55485,55500,55501,53168,55504,55528,55529,10588,55532,55535,55536,1977],{},"Přebytek spotřebitele ",[883,55470,55472],{"className":55471},[886],[888,55473,55474],{"xmlns":890},[892,55475,55476,55482],{},[895,55477,55478,55480],{},[898,55479,1703],{},[898,55481,2351],{},[902,55483,45450],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,55486,55488],{"className":55487},[886],[888,55489,55490],{"xmlns":890},[892,55491,55492,55498],{},[895,55493,55494,55496],{},[898,55495,2398],{},[898,55497,2351],{},[902,55499,45469],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,55502,55503],{},"daňový příjem",[883,55505,55507],{"className":55506},[886],[888,55508,55509],{"xmlns":890},[892,55510,55511,55525],{},[895,55512,55513,55515,55517],{},[898,55514,1991],{},[1664,55516,3753],{},[1810,55518,55519,55521,55523],{},[898,55520,1973],{},[1963,55522,2875],{},[898,55524,4819],{},[902,55526,55527],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,55530,55531],{},"mrtvá ztráta",[614,55533,55534],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,55537,811],{"className":55538,"dataFsResolvedFilePath":809,"href":810},[210],[37470,55540],{},[115,55542,2497],{"id":2496},[120,55544,55545,55552,55564,55571,55578],{},[123,55546,55547,1885,55549],{},[38,55548,16721],{},[207,55550,802],{"className":55551,"dataFsResolvedFilePath":800,"href":801},[210],[123,55553,55554,1885,55556,55559,55560,55563],{},[38,55555,37174],{},[207,55557,775],{"className":55558,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,55561,2950],{"className":55562,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,55565,55566,1885,55568],{},[38,55567,16731],{},[207,55569,2524],{"className":55570,"dataFsResolvedFilePath":827,"href":828},[210],[123,55572,55573,1885,55575],{},[38,55574,51258],{},[207,55576,51262],{"className":55577,"dataFsResolvedFilePath":745,"href":746},[210],[123,55579,55580,1885,55582],{},[38,55581,16703],{},[207,55583,16707],{"className":55584,"dataFsResolvedFilePath":2575,"href":2576},[210],{"title":641,"searchDepth":642,"depth":642,"links":55586},[55587,55588,55593,55598,55603,55604,55605,55606],{"id":51454,"depth":642,"text":1241},{"id":51798,"depth":642,"text":55589,"children":55590},"Přebytek spotřebitele (CSCS)",[55591,55592],{"id":51817,"depth":649,"text":51818},{"id":3033,"depth":649,"text":3034},{"id":52393,"depth":642,"text":55594,"children":55595},"Přebytek výrobce (PSPS)",[55596,55597],{"id":52412,"depth":649,"text":52413},{"id":52575,"depth":649,"text":3034},{"id":53183,"depth":642,"text":53184,"children":55599},[55600,55601],{"id":53187,"depth":649,"text":53188},{"id":54481,"depth":649,"text":55602},"Příklad 2.13 — numerický výpočet PSPS",{"id":54786,"depth":642,"text":54787},{"id":16218,"depth":642,"text":16219},{"id":55422,"depth":642,"text":55423},{"id":2496,"depth":642,"text":2497},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,51324,55613,55614,2547,16739,55615,55616],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":55619,"title":55620,"body":55621,"course":1128,"courses":659,"created":10119,"description":641,"extension":661,"meta":74950,"navigation":664,"path":74951,"seo":74952,"sources":74953,"stem":74954,"tags":74955,"type":2553,"updated":677,"__hash__":74961},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":55622,"toc":74914},[55623,55626,55812,55814,55905,55910,56236,56240,56247,56251,56296,56363,56394,56444,56479,56483,56542,56547,56613,56731,56833,56837,56860,56938,56981,56985,57014,57081,57087,57201,57205,57285,57322,57374,57572,57636,57723,57727,57730,57809,57812,57930,57949,58014,58018,58110,58178,58219,58273,58341,58378,58382,58440,58470,58681,58753,58805,58971,59064,59099,59103,59107,59144,59209,59264,59268,59291,59380,59484,59553,59557,59654,59767,59823,59877,59935,59996,59999,60035,60100,60130,60359,60417,60451,60455,60482,60561,60675,60696,60775,60777,60885,60889,61027,61349,61353,61356,61360,61409,61413,61667,61819,61826,61899,62083,62088,62431,62435,62458,62460,62481,62540,62550,62599,62741,62815,62910,63025,63123,63241,63245,63314,63319,63431,63576,63627,63739,63781,63785,63805,63866,63893,63955,63959,63981,64050,64330,64337,64367,64374,64567,64571,64649,64654,64730,64733,64821,64897,64964,65013,65116,65189,65310,65661,65774,65876,65880,65883,65890,65893,65929,65988,65997,66146,66370,66374,66437,66616,66708,66763,66767,66823,66893,66945,66966,67047,67050,67125,67169,67173,67214,67257,67283,67287,67358,67454,67516,67568,67671,67749,67772,67801,67805,67971,68088,68160,68475,68635,68639,68690,68752,68787,68817,68917,68959,69128,69133,69229,69267,69271,69390,69691,69693,69728,69732,69736,69864,69996,70318,70506,70584,70588,70893,71006,71152,71337,71443,71675,71790,71872,71991,72089,72130,72134,72189,72333,72487,72647,72740,72934,73246,73377,73506,73510,73582,73624,73675,73677,74872,74874],[12,55624,55620],{"id":55625},"příjem-náklady-zisk-a-nabídka-firmy",[4436,55627,55628],{},[724,55629,55630,4443,55632,1885,55635,55650,55651,1885,55654,55669,55670,1885,55673,55701,55702,55724,55725,55749,55750,55772,55773,55776,55777,55793,55794,1977],{},[883,55631,4442],{},[38,55633,55634],{},"Příjem",[883,55636,55638],{"className":55637},[886],[888,55639,55640],{"xmlns":890},[892,55641,55642,55648],{},[895,55643,55644,55646],{},[898,55645,1991],{},[898,55647,1959],{},[902,55649,4662],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,55652,55653],{},"náklady",[883,55655,55657],{"className":55656},[886],[888,55658,55659],{"xmlns":890},[892,55660,55661,55667],{},[895,55662,55663,55665],{},[898,55664,1991],{},[898,55666,1703],{},[902,55668,3819],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,55671,55672],{},"zisk",[883,55674,55676],{"className":55675},[886],[888,55677,55678],{"xmlns":890},[892,55679,55680,55698],{},[895,55681,55682,55684,55686,55688,55690,55692,55694,55696],{},[898,55683,2398],{},[898,55685,1959],{},[1664,55687,1676],{},[898,55689,1991],{},[898,55691,1959],{},[1664,55693,1867],{},[898,55695,1991],{},[898,55697,1703],{},[902,55699,55700],{"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: ",[883,55703,55705],{"className":55704},[886],[888,55706,55707],{"xmlns":890},[892,55708,55709,55721],{},[895,55710,55711,55713,55715,55717,55719],{},[898,55712,4822],{},[898,55714,1703],{},[1664,55716,1676],{},[898,55718,1956],{},[898,55720,1703],{},[902,55722,55723],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,55726,55728],{"className":55727},[886],[888,55729,55730],{"xmlns":890},[892,55731,55732,55746],{},[895,55733,55734,55736,55738,55740,55742,55744],{},[898,55735,4822],{},[898,55737,40839],{},[898,55739,1703],{},[1664,55741,1676],{},[898,55743,1956],{},[898,55745,1703],{},[902,55747,55748],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,55751,55753],{"className":55752},[886],[888,55754,55755],{"xmlns":890},[892,55756,55757,55769],{},[895,55758,55759,55761,55763,55765,55767],{},[898,55760,1956],{},[898,55762,1959],{},[1664,55764,1676],{},[898,55766,1956],{},[898,55768,1703],{},[902,55770,55771],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,55774,55775],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,55778,55780],{"className":55779},[886],[888,55781,55782],{"xmlns":890},[892,55783,55784,55790],{},[895,55785,55786,55788],{},[898,55787,1956],{},[898,55789,1703],{},[902,55791,55792],{"encoding":904},"MC"," nad bodem minima ",[883,55795,55797],{"className":55796},[886],[888,55798,55799],{"xmlns":890},[892,55800,55801,55809],{},[895,55802,55803,55805,55807],{},[898,55804,4822],{},[898,55806,40839],{},[898,55808,1703],{},[902,55810,55811],{"encoding":904},"AVC",[115,55813,1241],{"id":51454},[724,55815,55816,55817,55820,55821,55823,55824,1343,55827,1343,55830,55832,55833,55836,55837,55840,55841,55844,55845,3257,55860,1348,55875,3257,55890,4488],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,55818,55819],{},"příjmem"," (revenue) a ",[38,55822,55653],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,55825,55826],{},"zisku",[38,55828,55829],{},"bodů zvratu",[38,55831,2585],{}," a konstrukcí ",[38,55834,55835],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,55838,1145],{"className":55839,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,55842,1633],{"className":55843,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,55846,55848],{"className":55847},[886],[888,55849,55850],{"xmlns":890},[892,55851,55852,55858],{},[895,55853,55854,55856],{},[898,55855,1991],{},[898,55857,1959],{},[902,55859,4662],{"encoding":904},[883,55861,55863],{"className":55862},[886],[888,55864,55865],{"xmlns":890},[892,55866,55867,55873],{},[895,55868,55869,55871],{},[898,55870,1956],{},[898,55872,1959],{},[902,55874,7200],{"encoding":904},[883,55876,55878],{"className":55877},[886],[888,55879,55880],{"xmlns":890},[892,55881,55882,55888],{},[895,55883,55884,55886],{},[898,55885,1991],{},[898,55887,1703],{},[902,55889,3819],{"encoding":904},[883,55891,55893],{"className":55892},[886],[888,55894,55895],{"xmlns":890},[892,55896,55897,55903],{},[895,55898,55899,55901],{},[898,55900,1956],{},[898,55902,1703],{},[902,55904,55792],{"encoding":904},[724,55906,55907],{},[38,55908,55909],{},"Cílové znalosti:",[120,55911,55912,56076,56079,56082,56175,56222,56229],{},[123,55913,55914,55915,1343,55930,1343,55946,4454,55961,1343,55976,1343,55992,1343,56010,1343,56028,1343,56045,1343,56061,8990],{},"odvodit a interpretovat funkce ",[883,55916,55918],{"className":55917},[886],[888,55919,55920],{"xmlns":890},[892,55921,55922,55928],{},[895,55923,55924,55926],{},[898,55925,1991],{},[898,55927,1959],{},[902,55929,4662],{"encoding":904},[883,55931,55933],{"className":55932},[886],[888,55934,55935],{"xmlns":890},[892,55936,55937,55943],{},[895,55938,55939,55941],{},[898,55940,4822],{},[898,55942,1959],{},[902,55944,55945],{"encoding":904},"AR",[883,55947,55949],{"className":55948},[886],[888,55950,55951],{"xmlns":890},[892,55952,55953,55959],{},[895,55954,55955,55957],{},[898,55956,1956],{},[898,55958,1959],{},[902,55960,7200],{"encoding":904},[883,55962,55964],{"className":55963},[886],[888,55965,55966],{"xmlns":890},[892,55967,55968,55974],{},[895,55969,55970,55972],{},[898,55971,1991],{},[898,55973,1703],{},[902,55975,3819],{"encoding":904},[883,55977,55979],{"className":55978},[886],[888,55980,55981],{"xmlns":890},[892,55982,55983,55989],{},[895,55984,55985,55987],{},[898,55986,1662],{},[898,55988,1703],{},[902,55990,55991],{"encoding":904},"FC",[883,55993,55995],{"className":55994},[886],[888,55996,55997],{"xmlns":890},[892,55998,55999,56007],{},[895,56000,56001,56003,56005],{},[898,56002,1991],{},[898,56004,40839],{},[898,56006,1703],{},[902,56008,56009],{"encoding":904},"TVC",[883,56011,56013],{"className":56012},[886],[888,56014,56015],{"xmlns":890},[892,56016,56017,56025],{},[895,56018,56019,56021,56023],{},[898,56020,4822],{},[898,56022,1662],{},[898,56024,1703],{},[902,56026,56027],{"encoding":904},"AFC",[883,56029,56031],{"className":56030},[886],[888,56032,56033],{"xmlns":890},[892,56034,56035,56043],{},[895,56036,56037,56039,56041],{},[898,56038,4822],{},[898,56040,40839],{},[898,56042,1703],{},[902,56044,55811],{"encoding":904},[883,56046,56048],{"className":56047},[886],[888,56049,56050],{"xmlns":890},[892,56051,56052,56058],{},[895,56053,56054,56056],{},[898,56055,4822],{},[898,56057,1703],{},[902,56059,56060],{"encoding":904},"AC",[883,56062,56064],{"className":56063},[886],[888,56065,56066],{"xmlns":890},[892,56067,56068,56074],{},[895,56069,56070,56072],{},[898,56071,1956],{},[898,56073,1703],{},[902,56075,55792],{"encoding":904},[123,56077,56078],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,56080,56081],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,56083,56084,56085,56088,56089,42314,56131,8990],{},"osvojit si ",[38,56086,56087],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,56090,56092],{"className":56091},[886],[888,56093,56094],{"xmlns":890},[892,56095,56096,56128],{},[895,56097,56098,56100,56102,56104,56110,56112,56114,56116,56118,56120,56126],{},[898,56099,4822],{},[898,56101,1703],{},[1664,56103,1667],{"stretchy":1666},[2355,56105,56106,56108],{},[898,56107,1973],{},[1963,56109,2058],{},[1664,56111,1673],{"stretchy":1666},[1664,56113,1676],{},[898,56115,1956],{},[898,56117,1703],{},[1664,56119,1667],{"stretchy":1666},[2355,56121,56122,56124],{},[898,56123,1973],{},[1963,56125,2058],{},[1664,56127,1673],{"stretchy":1666},[902,56129,56130],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,56132,56134],{"className":56133},[886],[888,56135,56136],{"xmlns":890},[892,56137,56138,56172],{},[895,56139,56140,56142,56144,56146,56148,56154,56156,56158,56160,56162,56164,56170],{},[898,56141,4822],{},[898,56143,40839],{},[898,56145,1703],{},[1664,56147,1667],{"stretchy":1666},[2355,56149,56150,56152],{},[898,56151,1973],{},[1963,56153,2058],{},[1664,56155,1673],{"stretchy":1666},[1664,56157,1676],{},[898,56159,1956],{},[898,56161,1703],{},[1664,56163,1667],{"stretchy":1666},[2355,56165,56166,56168],{},[898,56167,1973],{},[1963,56169,2058],{},[1664,56171,1673],{"stretchy":1666},[902,56173,56174],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,56176,56084,56177,56088,56180,8990],{},[38,56178,56179],{},"princip maximalizace zisku",[883,56181,56183],{"className":56182},[886],[888,56184,56185],{"xmlns":890},[892,56186,56187,56219],{},[895,56188,56189,56191,56193,56195,56201,56203,56205,56207,56209,56211,56217],{},[898,56190,1956],{},[898,56192,1959],{},[1664,56194,1667],{"stretchy":1666},[2355,56196,56197,56199],{},[898,56198,1973],{},[1963,56200,2058],{},[1664,56202,1673],{"stretchy":1666},[1664,56204,1676],{},[898,56206,1956],{},[898,56208,1703],{},[1664,56210,1667],{"stretchy":1666},[2355,56212,56213,56215],{},[898,56214,1973],{},[1963,56216,2058],{},[1664,56218,1673],{"stretchy":1666},[902,56220,56221],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,56223,56224,56225,56228],{},"stanovit ",[38,56226,56227],{},"body zvratu"," a interval zisku;",[123,56230,56231,56232,56235],{},"zkonstruovat ",[38,56233,56234],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,56237,56239],{"id":56238},"příjem-firmy","Příjem firmy",[724,56241,56242],{},[1928,56243],{"alt":56244,"className":56245,"src":56246},"imek-ar-mr-dvojnasobny-sklon",[210,1932],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,56248,56250],{"id":56249},"celkový-příjem","Celkový příjem",[724,56252,56253,56254,10588,56269,56272,56273,30444],{},"Celkový příjem ",[883,56255,56257],{"className":56256},[886],[888,56258,56259],{"xmlns":890},[892,56260,56261,56267],{},[895,56262,56263,56265],{},[898,56264,1991],{},[898,56266,1959],{},[902,56268,4662],{"encoding":904},[38,56270,56271],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,56274,56276],{"className":56275},[886],[888,56277,56278],{"xmlns":890},[892,56279,56280,56294],{},[895,56281,56282,56284,56286,56288,56290,56292],{},[898,56283,2398],{},[1664,56285,1676],{},[898,56287,2379],{},[1664,56289,1667],{"stretchy":1666},[898,56291,1973],{},[1664,56293,1673],{"stretchy":1666},[902,56295,5206],{"encoding":904},[883,56297,56299],{"className":56298},[886],[888,56300,56301],{"xmlns":890,"display":28566},[892,56302,56303,56360],{},[21254,56304,56305],{"width":28571},[21259,56306,56307,56309,56353,56355],{},[21262,56308],{"width":28576},[21262,56310,56311],{},[895,56312,56313,56315,56317,56319,56321,56323,56325,56327,56329,56331,56333,56335,56337,56339,56341,56343,56345,56347,56349,56351],{},[898,56314,1991],{},[898,56316,1959],{},[1664,56318,1676],{},[898,56320,1991],{},[898,56322,1959],{},[1664,56324,1667],{"stretchy":1666},[898,56326,1973],{},[1664,56328,1673],{"stretchy":1666},[1664,56330,1676],{},[898,56332,2398],{},[1664,56334,3753],{},[898,56336,1973],{},[1664,56338,1676],{},[898,56340,2379],{},[1664,56342,1667],{"stretchy":1666},[898,56344,1973],{},[1664,56346,1673],{"stretchy":1666},[1664,56348,3753],{},[898,56350,1973],{},[898,56352,1977],{"mathvariant":1726},[21262,56354],{"width":28576},[21262,56356,56357],{},[1690,56358,56359],{},"(3.1)",[902,56361,56362],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,56364,56365,56366,56369,56370,56393],{},"Graf funkce se nazývá ",[38,56367,56368],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,56371,56373],{"className":56372},[886],[888,56374,56375],{"xmlns":890},[892,56376,56377,56391],{},[895,56378,56379,56381,56383,56385,56387,56389],{},[898,56380,2398],{},[1664,56382,1676],{},[898,56384,207],{},[898,56386,1973],{},[1664,56388,1700],{},[898,56390,1818],{},[902,56392,37560],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,56395,56397],{"className":56396},[886],[888,56398,56399],{"xmlns":890,"display":28566},[892,56400,56401,56441],{},[895,56402,56403,56405,56407,56409,56411,56413,56415,56417,56419,56421,56423,56425,56427,56433,56435,56437,56439],{},[898,56404,1991],{},[898,56406,1959],{},[1664,56408,1676],{},[898,56410,1973],{},[1664,56412,1667],{"stretchy":1666},[898,56414,207],{},[898,56416,1973],{},[1664,56418,1700],{},[898,56420,1818],{},[1664,56422,1673],{"stretchy":1666},[1664,56424,1676],{},[898,56426,207],{},[1720,56428,56429,56431],{},[898,56430,1973],{},[1963,56432,1970],{},[1664,56434,1700],{},[898,56436,1818],{},[898,56438,1973],{},[1664,56440,1916],{"separator":1915},[902,56442,56443],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,56445,56446,56447,56460,56461,56478],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,56448,56450],{"className":56449},[886],[888,56451,56452],{"xmlns":890},[892,56453,56454,56458],{},[895,56455,56456],{},[898,56457,900],{},[902,56459,900],{"encoding":904}," (jelikož ",[883,56462,56464],{"className":56463},[886],[888,56465,56466],{"xmlns":890},[892,56467,56468,56476],{},[895,56469,56470,56472,56474],{},[898,56471,207],{},[1664,56473,4022],{},[1963,56475,2058],{},[902,56477,43585],{"encoding":904},") procházející počátkem.",[37848,56480,56482],{"id":56481},"příklad-31","Příklad 3.1",[724,56484,56485,56488,56489,56525,56526,56541],{},[38,56486,56487],{},"Zadání."," Pro poptávku ",[883,56490,56492],{"className":56491},[886],[888,56493,56494],{"xmlns":890},[892,56495,56496,56522],{},[895,56497,56498,56500,56502,56504,56506,56508,56510,56512,56514,56516,56518,56520],{},[898,56499,2398],{},[1664,56501,1676],{},[898,56503,2379],{},[1664,56505,1667],{"stretchy":1666},[898,56507,1973],{},[1664,56509,1673],{"stretchy":1666},[1664,56511,1676],{},[1664,56513,1867],{},[1963,56515,1970],{},[898,56517,1973],{},[1664,56519,1700],{},[1963,56521,1965],{},[902,56523,56524],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,56527,56529],{"className":56528},[886],[888,56530,56531],{"xmlns":890},[892,56532,56533,56539],{},[895,56534,56535,56537],{},[898,56536,1991],{},[898,56538,1959],{},[902,56540,4662],{"encoding":904}," a charakterizujte jeho křivku.",[724,56543,56544,56546],{},[38,56545,23270],{}," Celkový příjem je",[883,56548,56550],{"className":56549},[886],[888,56551,56552],{"xmlns":890,"display":28566},[892,56553,56554,56610],{},[895,56555,56556,56558,56560,56562,56564,56566,56568,56570,56572,56574,56576,56578,56580,56582,56584,56586,56588,56590,56592,56594,56596,56602,56604,56606,56608],{},[898,56557,1991],{},[898,56559,1959],{},[1664,56561,1676],{},[898,56563,1991],{},[898,56565,1959],{},[1664,56567,1667],{"stretchy":1666},[898,56569,1973],{},[1664,56571,1673],{"stretchy":1666},[1664,56573,1676],{},[898,56575,1973],{},[1664,56577,1667],{"stretchy":1666},[1664,56579,1867],{},[1963,56581,1970],{},[898,56583,1973],{},[1664,56585,1700],{},[1963,56587,1965],{},[1664,56589,1673],{"stretchy":1666},[1664,56591,1676],{},[1664,56593,1867],{},[1963,56595,1970],{},[1720,56597,56598,56600],{},[898,56599,1973],{},[1963,56601,1970],{},[1664,56603,1700],{},[1963,56605,1965],{},[898,56607,1973],{},[898,56609,1977],{"mathvariant":1726},[902,56611,56612],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,56614,56615,56616,4454,56638,56660,56661,56679,56680,1977],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,56617,56619],{"className":56618},[886],[888,56620,56621],{"xmlns":890},[892,56622,56623,56635],{},[895,56624,56625,56631,56633],{},[2355,56626,56627,56629],{},[898,56628,1973],{},[1963,56630,2875],{},[1664,56632,1676],{},[1963,56634,2058],{},[902,56636,56637],{"encoding":904},"Q_1 = 0",[883,56639,56641],{"className":56640},[886],[888,56642,56643],{"xmlns":890},[892,56644,56645,56657],{},[895,56646,56647,56653,56655],{},[2355,56648,56649,56651],{},[898,56650,1973],{},[1963,56652,1970],{},[1664,56654,1676],{},[1963,56656,3696],{},[902,56658,56659],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,56662,56664],{"className":56663},[886],[888,56665,56666],{"xmlns":890},[892,56667,56668,56676],{},[895,56669,56670,56672,56674],{},[898,56671,1973],{},[1664,56673,1676],{},[1963,56675,5570],{},[902,56677,56678],{"encoding":904},"Q = 25"," ve výši ",[883,56681,56683],{"className":56682},[886],[888,56684,56685],{"xmlns":890},[892,56686,56687,56728],{},[895,56688,56689,56691,56701,56703,56705,56707,56709,56712,56714,56716,56718,56720,56722,56724,56726],{},[898,56690,1991],{},[2355,56692,56693,56695,56698],{},[898,56694,1959],{},[898,56696,56697],{},"max",[1664,56699,56700],{},"⁡",[1664,56702,1676],{},[1664,56704,1867],{},[1963,56706,1970],{},[1664,56708,3753],{},[1963,56710,56711],{},"625",[1664,56713,1700],{},[1963,56715,1965],{},[1664,56717,3753],{},[1963,56719,5570],{},[1664,56721,1676],{},[1963,56723,2875],{},[1690,56725,1692],{},[1963,56727,31243],{},[902,56729,56730],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,56732,56733],{},[614,56734,56735,56736,56770,56771,4454,56784,56797,56798,3210,56816,1977],{},"Obrázek 3.1: Parabola ",[883,56737,56739],{"className":56738},[886],[888,56740,56741],{"xmlns":890},[892,56742,56743,56767],{},[895,56744,56745,56747,56749,56751,56753,56755,56761,56763,56765],{},[898,56746,1991],{},[898,56748,1959],{},[1664,56750,1676],{},[1664,56752,1867],{},[1963,56754,1970],{},[1720,56756,56757,56759],{},[898,56758,1973],{},[1963,56760,1970],{},[1664,56762,1700],{},[1963,56764,1965],{},[898,56766,1973],{},[902,56768,56769],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,56772,56774],{"className":56773},[886],[888,56775,56776],{"xmlns":890},[892,56777,56778,56782],{},[895,56779,56780],{},[1963,56781,2058],{},[902,56783,2058],{"encoding":904},[883,56785,56787],{"className":56786},[886],[888,56788,56789],{"xmlns":890},[892,56790,56791,56795],{},[895,56792,56793],{},[1963,56794,3696],{},[902,56796,3696],{"encoding":904}," a maximem ",[883,56799,56801],{"className":56800},[886],[888,56802,56803],{"xmlns":890},[892,56804,56805,56813],{},[895,56806,56807,56809,56811],{},[1963,56808,2875],{},[1690,56810,1692],{},[1963,56812,31243],{},[902,56814,56815],{"encoding":904},"1\\,250",[883,56817,56819],{"className":56818},[886],[888,56820,56821],{"xmlns":890},[892,56822,56823,56831],{},[895,56824,56825,56827,56829],{},[898,56826,1973],{},[1664,56828,1676],{},[1963,56830,5570],{},[902,56832,56678],{"encoding":904},[198,56834,56836],{"id":56835},"průměrný-příjem","Průměrný příjem",[724,56838,56839,1885,56841,10588,56856,56859],{},[38,56840,56836],{},[883,56842,56844],{"className":56843},[886],[888,56845,56846],{"xmlns":890},[892,56847,56848,56854],{},[895,56849,56850,56852],{},[898,56851,4822],{},[898,56853,1959],{},[902,56855,55945],{"encoding":904},[38,56857,56858],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,56861,56863],{"className":56862},[886],[888,56864,56865],{"xmlns":890,"display":28566},[892,56866,56867,56935],{},[895,56868,56869,56871,56873,56875,56877,56879,56881,56883,56885,56887,56903,56905,56923,56925,56927,56929,56931,56933],{},[898,56870,4822],{},[898,56872,1959],{},[1664,56874,1676],{},[898,56876,4822],{},[898,56878,1959],{},[1664,56880,1667],{"stretchy":1666},[898,56882,1973],{},[1664,56884,1673],{"stretchy":1666},[1664,56886,1676],{},[2922,56888,56889,56901],{},[895,56890,56891,56893,56895,56897,56899],{},[898,56892,1991],{},[898,56894,1959],{},[1664,56896,1667],{"stretchy":1666},[898,56898,1973],{},[1664,56900,1673],{"stretchy":1666},[898,56902,1973],{},[1664,56904,1676],{},[2922,56906,56907,56921],{},[895,56908,56909,56911,56913,56915,56917,56919],{},[898,56910,1973],{},[1690,56912,1692],{},[898,56914,2379],{},[1664,56916,1667],{"stretchy":1666},[898,56918,1973],{},[1664,56920,1673],{"stretchy":1666},[898,56922,1973],{},[1664,56924,1676],{},[898,56926,2379],{},[1664,56928,1667],{"stretchy":1666},[898,56930,1973],{},[1664,56932,1673],{"stretchy":1666},[898,56934,1977],{"mathvariant":1726},[902,56936,56937],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[4436,56939,56940],{},[724,56941,56942,56945,56946,1343,56949,1977],{},[883,56943,56944],{},"!note"," Klíčové pozorování\n",[38,56947,56948],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,56950,56952],{"className":56951},[886],[888,56953,56954],{"xmlns":890},[892,56955,56956,56978],{},[895,56957,56958,56960,56962,56964,56966,56968,56970,56972,56974,56976],{},[898,56959,4822],{},[898,56961,1959],{},[1664,56963,1667],{"stretchy":1666},[898,56965,1973],{},[1664,56967,1673],{"stretchy":1666},[1664,56969,1676],{},[898,56971,2379],{},[1664,56973,1667],{"stretchy":1666},[898,56975,1973],{},[1664,56977,1673],{"stretchy":1666},[902,56979,56980],{"encoding":904},"AR(Q) = D(Q)",[198,56982,56984],{"id":56983},"mezní-příjem","Mezní příjem",[724,56986,56987,56988,1885,56991,10588,57006,57009,57010,57013],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,56989,56990],{},"mezní příjem",[883,56992,56994],{"className":56993},[886],[888,56995,56996],{"xmlns":890},[892,56997,56998,57004],{},[895,56999,57000,57002],{},[898,57001,1956],{},[898,57003,1959],{},[902,57005,7200],{"encoding":904},[38,57007,57008],{},"marginal revenue","), definovaný jako ",[207,57011,1145],{"className":57012,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,57015,57017],{"className":57016},[886],[888,57018,57019],{"xmlns":890,"display":28566},[892,57020,57021,57078],{},[21254,57022,57023],{"width":28571},[21259,57024,57025,57027,57071,57073],{},[21262,57026],{"width":28576},[21262,57028,57029],{},[895,57030,57031,57033,57035,57037,57053,57055,57057,57063,57065,57067,57069],{},[898,57032,1956],{},[898,57034,1959],{},[1664,57036,1676],{},[2922,57038,57039,57047],{},[895,57040,57041,57043,57045],{},[898,57042,1695],{"mathvariant":1726},[898,57044,1991],{},[898,57046,1959],{},[895,57048,57049,57051],{},[898,57050,1695],{"mathvariant":1726},[898,57052,1973],{},[1664,57054,1676],{},[898,57056,1991],{},[1720,57058,57059,57061],{},[898,57060,1959],{},[1664,57062,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,57064,1667],{"stretchy":1666},[898,57066,1973],{},[1664,57068,1673],{"stretchy":1666},[898,57070,1977],{"mathvariant":1726},[21262,57072],{"width":28576},[21262,57074,57075],{},[1690,57076,57077],{},"(3.2)",[902,57079,57080],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,57082,57083,57084,57086],{},"Mezní příjem udává ",[38,57085,3182],{}," celkového příjmu vzhledem k množství.",[4436,57088,57089],{},[724,57090,57091,57093,57094,57120,57121,57138,57139,1977],{},[883,57092,4723],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,57095,57097],{"className":57096},[886],[888,57098,57099],{"xmlns":890},[892,57100,57101,57117],{},[895,57102,57103,57105,57107,57109,57115],{},[898,57104,1956],{},[898,57106,1959],{},[1664,57108,1667],{"stretchy":1666},[1720,57110,57111,57113],{},[898,57112,1973],{},[1664,57114,4920],{},[1664,57116,1673],{"stretchy":1666},[902,57118,57119],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,57122,57124],{"className":57123},[886],[888,57125,57126],{"xmlns":890},[892,57127,57128,57136],{},[895,57129,57130],{},[1720,57131,57132,57134],{},[898,57133,1973],{},[1664,57135,4920],{},[902,57137,30344],{"encoding":904},". Jinak řečeno: ",[883,57140,57142],{"className":57141},[886],[888,57143,57144],{"xmlns":890},[892,57145,57146,57198],{},[895,57147,57148,57150,57152,57154,57160,57162,57164,57166,57168,57170,57176,57178,57180,57182,57184,57186,57188,57190,57196],{},[898,57149,1956],{},[898,57151,1959],{},[1664,57153,1667],{"stretchy":1666},[1720,57155,57156,57158],{},[898,57157,1973],{},[1664,57159,4920],{},[1664,57161,1673],{"stretchy":1666},[1664,57163,3315],{},[898,57165,1991],{},[898,57167,1959],{},[1664,57169,1667],{"stretchy":1666},[1720,57171,57172,57174],{},[898,57173,1973],{},[1664,57175,4920],{},[1664,57177,1700],{},[1963,57179,2875],{},[1664,57181,1673],{"stretchy":1666},[1664,57183,1867],{},[898,57185,1991],{},[898,57187,1959],{},[1664,57189,1667],{"stretchy":1666},[1720,57191,57192,57194],{},[898,57193,1973],{},[1664,57195,4920],{},[1664,57197,1673],{"stretchy":1666},[902,57199,57200],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[37848,57202,57204],{"id":57203},"příklad-32","Příklad 3.2",[724,57206,57207,56488,57209,56525,57243,57258,57259,1977],{},[38,57208,56487],{},[883,57210,57212],{"className":57211},[886],[888,57213,57214],{"xmlns":890},[892,57215,57216,57240],{},[895,57217,57218,57220,57222,57224,57226,57228,57230,57232,57234,57236,57238],{},[898,57219,2398],{},[1664,57221,1676],{},[898,57223,2379],{},[1664,57225,1667],{"stretchy":1666},[898,57227,1973],{},[1664,57229,1673],{"stretchy":1666},[1664,57231,1676],{},[1963,57233,1965],{},[1664,57235,1867],{},[1963,57237,1970],{},[898,57239,1973],{},[902,57241,57242],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,57244,57246],{"className":57245},[886],[888,57247,57248],{"xmlns":890},[892,57249,57250,57256],{},[895,57251,57252,57254],{},[898,57253,1956],{},[898,57255,1959],{},[902,57257,7200],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,57260,57262],{"className":57261},[886],[888,57263,57264],{"xmlns":890},[892,57265,57266,57282],{},[895,57267,57268,57270,57272,57274,57276,57278,57280],{},[898,57269,1973],{},[1664,57271,1676],{},[1963,57273,36744],{},[1664,57275,1916],{"separator":1915},[1963,57277,42362],{},[1664,57279,1916],{"separator":1915},[1963,57281,9599],{},[902,57283,57284],{"encoding":904},"Q = 15, 16, 20",[724,57286,57287,1885,57289,57321],{},[38,57288,23270],{},[883,57290,57292],{"className":57291},[886],[888,57293,57294],{"xmlns":890},[892,57295,57296,57318],{},[895,57297,57298,57300,57302,57304,57306,57308,57310,57312],{},[898,57299,1991],{},[898,57301,1959],{},[1664,57303,1676],{},[1963,57305,1965],{},[898,57307,1973],{},[1664,57309,1867],{},[1963,57311,1970],{},[1720,57313,57314,57316],{},[898,57315,1973],{},[1963,57317,1970],{},[902,57319,57320],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,57323,57325],{"className":57324},[886],[888,57326,57327],{"xmlns":890,"display":28566},[892,57328,57329,57371],{},[895,57330,57331,57333,57335,57337,57339,57341,57343,57345,57347,57353,57359,57361,57363,57365,57367,57369],{},[898,57332,1956],{},[898,57334,1959],{},[1664,57336,1676],{},[1664,57338,1667],{"stretchy":1666},[1963,57340,1965],{},[898,57342,1973],{},[1664,57344,1867],{},[1963,57346,1970],{},[1720,57348,57349,57351],{},[898,57350,1973],{},[1963,57352,1970],{},[1720,57354,57355,57357],{},[1664,57356,1673],{"stretchy":1666},[1664,57358,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,57360,1676],{},[1963,57362,1965],{},[1664,57364,1867],{},[1963,57366,2944],{},[898,57368,1973],{},[898,57370,1977],{"mathvariant":1726},[902,57372,57373],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,57375,10226,57376,1762,57394,57420,57421,4924,57434,57449,57450,57463,57464,21920,57477,4924,57490,57505,57506,57519,57520,57551,57552,57571],{},[883,57377,57379],{"className":57378},[886],[888,57380,57381],{"xmlns":890},[892,57382,57383,57391],{},[895,57384,57385,57387,57389],{},[898,57386,1973],{},[1664,57388,1676],{},[1963,57390,36744],{},[902,57392,57393],{"encoding":904},"Q = 15",[883,57395,57397],{"className":57396},[886],[888,57398,57399],{"xmlns":890},[892,57400,57401,57417],{},[895,57402,57403,57405,57407,57409,57411,57413,57415],{},[898,57404,1956],{},[898,57406,1959],{},[1664,57408,1667],{"stretchy":1666},[1963,57410,36744],{},[1664,57412,1673],{"stretchy":1666},[1664,57414,1676],{},[1963,57416,5777],{},[902,57418,57419],{"encoding":904},"MR(15) = 40",": při množství ",[883,57422,57424],{"className":57423},[886],[888,57425,57426],{"xmlns":890},[892,57427,57428,57432],{},[895,57429,57430],{},[1963,57431,36744],{},[902,57433,36744],{"encoding":904},[883,57435,57437],{"className":57436},[886],[888,57438,57439],{"xmlns":890},[892,57440,57441,57447],{},[895,57442,57443,57445],{},[898,57444,1991],{},[898,57446,1959],{},[902,57448,4662],{"encoding":904}," mění asi ",[883,57451,57453],{"className":57452},[886],[888,57454,57455],{"xmlns":890},[892,57456,57457,57461],{},[895,57458,57459],{},[1963,57460,5777],{},[902,57462,5777],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,57465,57467],{"className":57466},[886],[888,57468,57469],{"xmlns":890},[892,57470,57471,57475],{},[895,57472,57473],{},[898,57474,1973],{},[902,57476,1973],{"encoding":904},[883,57478,57480],{"className":57479},[886],[888,57481,57482],{"xmlns":890},[892,57483,57484,57488],{},[895,57485,57486],{},[1963,57487,2875],{},[902,57489,2875],{"encoding":904},[883,57491,57493],{"className":57492},[886],[888,57494,57495],{"xmlns":890},[892,57496,57497,57503],{},[895,57498,57499,57501],{},[898,57500,1991],{},[898,57502,1959],{},[902,57504,4662],{"encoding":904}," zvýší přibližně o ",[883,57507,57509],{"className":57508},[886],[888,57510,57511],{"xmlns":890},[892,57512,57513,57517],{},[895,57514,57515],{},[1963,57516,5777],{},[902,57518,5777],{"encoding":904},", tj. ze skutečné hodnoty ",[883,57521,57523],{"className":57522},[886],[888,57524,57525],{"xmlns":890},[892,57526,57527,57548],{},[895,57528,57529,57531,57533,57535,57537,57539,57541,57543,57545],{},[898,57530,1991],{},[898,57532,1959],{},[1664,57534,1667],{"stretchy":1666},[1963,57536,36744],{},[1664,57538,1673],{"stretchy":1666},[1664,57540,1676],{},[1963,57542,2875],{},[1690,57544,1692],{},[1963,57546,57547],{},"050",[902,57549,57550],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,57553,57555],{"className":57554},[886],[888,57556,57557],{"xmlns":890},[892,57558,57559,57568],{},[895,57560,57561,57563,57565],{},[1963,57562,2875],{},[1690,57564,1692],{},[1963,57566,57567],{},"090",[902,57569,57570],{"encoding":904},"1\\,090",". Skutečná změna je",[883,57573,57575],{"className":57574},[886],[888,57576,57577],{"xmlns":890,"display":28566},[892,57578,57579,57633],{},[895,57580,57581,57583,57585,57587,57589,57591,57593,57595,57597,57599,57601,57603,57605,57607,57609,57611,57613,57615,57617,57620,57622,57624,57626,57628,57630],{},[898,57582,3468],{"mathvariant":1726},[898,57584,1991],{},[898,57586,1959],{},[1664,57588,1676],{},[898,57590,1991],{},[898,57592,1959],{},[1664,57594,1667],{"stretchy":1666},[1963,57596,42362],{},[1664,57598,1673],{"stretchy":1666},[1664,57600,1867],{},[898,57602,1991],{},[898,57604,1959],{},[1664,57606,1667],{"stretchy":1666},[1963,57608,36744],{},[1664,57610,1673],{"stretchy":1666},[1664,57612,1676],{},[1963,57614,2875],{},[1690,57616,1692],{},[1963,57618,57619],{},"088",[1664,57621,1867],{},[1963,57623,2875],{},[1690,57625,1692],{},[1963,57627,57547],{},[1664,57629,1676],{},[1963,57631,57632],{},"38.",[902,57634,57635],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,57637,57638,57639,1343,57665,1748,57691,57706,57707,57722],{},"Podobně ",[883,57640,57642],{"className":57641},[886],[888,57643,57644],{"xmlns":890},[892,57645,57646,57662],{},[895,57647,57648,57650,57652,57654,57656,57658,57660],{},[898,57649,1956],{},[898,57651,1959],{},[1664,57653,1667],{"stretchy":1666},[1963,57655,42362],{},[1664,57657,1673],{"stretchy":1666},[1664,57659,1676],{},[1963,57661,6131],{},[902,57663,57664],{"encoding":904},"MR(16) = 36",[883,57666,57668],{"className":57667},[886],[888,57669,57670],{"xmlns":890},[892,57671,57672,57688],{},[895,57673,57674,57676,57678,57680,57682,57684,57686],{},[898,57675,1956],{},[898,57677,1959],{},[1664,57679,1667],{"stretchy":1666},[1963,57681,9599],{},[1664,57683,1673],{"stretchy":1666},[1664,57685,1676],{},[1963,57687,9599],{},[902,57689,57690],{"encoding":904},"MR(20) = 20",[883,57692,57694],{"className":57693},[886],[888,57695,57696],{"xmlns":890},[892,57697,57698,57704],{},[895,57699,57700,57702],{},[898,57701,1956],{},[898,57703,1959],{},[902,57705,7200],{"encoding":904}," je klesající funkce — rychlost změny ",[883,57708,57710],{"className":57709},[886],[888,57711,57712],{"xmlns":890},[892,57713,57714,57720],{},[895,57715,57716,57718],{},[898,57717,1991],{},[898,57719,1959],{},[902,57721,4662],{"encoding":904}," s růstem množství klesá.",[198,57724,57726],{"id":57725},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,57728,57729],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,57731,57733],{"className":57732},[886],[888,57734,57735],{"xmlns":890,"display":28566},[892,57736,57737,57806],{},[21254,57738,57739],{"width":28571},[21259,57740,57741,57743,57799,57801],{},[21262,57742],{"width":28576},[21262,57744,57745],{},[895,57746,57747,57749,57751,57753,57755,57757,57759,57761,57763,57765,57767,57769,57771,57773,57779,57781,57783,57785,57787,57789,57791,57793,57795,57797],{},[898,57748,3468],{"mathvariant":1726},[898,57750,1991],{},[898,57752,1959],{},[1690,57754,4553],{},[1664,57756,3315],{},[1690,57758,4553],{},[898,57760,1695],{"mathvariant":1726},[898,57762,1991],{},[898,57764,1959],{},[1664,57766,1676],{},[1664,57768,1667],{"stretchy":1666},[898,57770,1991],{},[898,57772,1959],{},[1720,57774,57775,57777],{},[1664,57776,1673],{"stretchy":1666},[1664,57778,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1690,57780,1692],{},[898,57782,1695],{"mathvariant":1726},[898,57784,1973],{},[1664,57786,1676],{},[898,57788,1956],{},[898,57790,1959],{},[1690,57792,1692],{},[898,57794,1695],{"mathvariant":1726},[898,57796,1973],{},[1664,57798,1916],{"separator":1915},[21262,57800],{"width":28576},[21262,57802,57803],{},[1690,57804,57805],{},"(3.3)",[902,57807,57808],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,57810,57811],{},"schematicky:",[883,57813,57815],{"className":57814},[886],[888,57816,57817],{"xmlns":890,"display":28566},[892,57818,57819,57927],{},[895,57820,57821,57859,57861,57863,57865,57894,57897,57925],{},[895,57822,57823,57826,57832,57835,57841,57844,57850,57856],{},[1690,57824,57825],{},"zm",[8951,57827,57828,57830],{"accent":1915},[1690,57829,46232],{},[1664,57831,25558],{},[1690,57833,57834],{},"na celkov",[8951,57836,57837,57839],{"accent":1915},[1690,57838,46232],{},[1664,57840,25477],{},[1690,57842,57843],{},"ho p",[8951,57845,57846,57848],{"accent":1915},[1690,57847,12540],{},[1664,57849,25558],{},[8951,57851,57852,57854],{"accent":1915},[1690,57853,25546],{},[1664,57855,25477],{},[1690,57857,57858],{},"jmu",[1690,57860,4553],{},[1664,57862,3315],{},[1690,57864,4553],{},[895,57866,57867,57870,57876,57879,57885,57891],{},[1690,57868,57869],{},"mezn",[8951,57871,57872,57874],{"accent":1915},[1690,57873,25546],{},[1664,57875,25477],{},[1690,57877,57878],{}," p",[8951,57880,57881,57883],{"accent":1915},[1690,57882,12540],{},[1664,57884,25558],{},[8951,57886,57887,57889],{"accent":1915},[1690,57888,25546],{},[1664,57890,25477],{},[1690,57892,57893],{},"jem",[1664,57895,57896],{},"×",[895,57898,57899,57901,57907,57910,57916,57919],{},[1690,57900,57825],{},[8951,57902,57903,57905],{"accent":1915},[1690,57904,46232],{},[1664,57906,25558],{},[1690,57908,57909],{},"na mno",[8951,57911,57912,57914],{"accent":1915},[1690,57913,10157],{},[1664,57915,25558],{},[1690,57917,57918],{},"stv",[8951,57920,57921,57923],{"accent":1915},[1690,57922,25546],{},[1664,57924,25477],{},[898,57926,1977],{"mathvariant":1726},[902,57928,57929],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,57931,57932,57933,57948],{},"Pro porovnání skutečná změna ",[883,57934,57936],{"className":57935},[886],[888,57937,57938],{"xmlns":890},[892,57939,57940,57946],{},[895,57941,57942,57944],{},[898,57943,1991],{},[898,57945,1959],{},[902,57947,4662],{"encoding":904}," je",[883,57950,57952],{"className":57951},[886],[888,57953,57954],{"xmlns":890,"display":28566},[892,57955,57956,58011],{},[21254,57957,57958],{"width":28571},[21259,57959,57960,57962,58004,58006],{},[21262,57961],{"width":28576},[21262,57963,57964],{},[895,57965,57966,57968,57970,57972,57974,57976,57978,57980,57982,57984,57986,57988,57990,57992,57994,57996,57998,58000,58002],{},[898,57967,3468],{"mathvariant":1726},[898,57969,1991],{},[898,57971,1959],{},[1664,57973,1676],{},[898,57975,1991],{},[898,57977,1959],{},[1664,57979,1667],{"stretchy":1666},[898,57981,1973],{},[1664,57983,1700],{},[898,57985,1695],{"mathvariant":1726},[898,57987,1973],{},[1664,57989,1673],{"stretchy":1666},[1664,57991,1867],{},[898,57993,1991],{},[898,57995,1959],{},[1664,57997,1667],{"stretchy":1666},[898,57999,1973],{},[1664,58001,1673],{"stretchy":1666},[898,58003,1977],{"mathvariant":1726},[21262,58005],{"width":28576},[21262,58007,58008],{},[1690,58009,58010],{},"(3.4)",[902,58012,58013],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[37848,58015,58017],{"id":58016},"příklad-33","Příklad 3.3",[724,58019,58020,58022,58023,58053,58054,3243,58069,3257,58082,3271,58095,58109],{},[38,58021,56487],{}," Pro ",[883,58024,58026],{"className":58025},[886],[888,58027,58028],{"xmlns":890},[892,58029,58030,58050],{},[895,58031,58032,58034,58036,58038,58040,58042,58044],{},[898,58033,1991],{},[898,58035,1959],{},[1664,58037,1676],{},[1963,58039,1965],{},[898,58041,1973],{},[1664,58043,1867],{},[1720,58045,58046,58048],{},[898,58047,1973],{},[1963,58049,1970],{},[902,58051,58052],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,58055,58057],{"className":58056},[886],[888,58058,58059],{"xmlns":890},[892,58060,58061,58067],{},[895,58062,58063,58065],{},[898,58064,1991],{},[898,58066,1959],{},[902,58068,4662],{"encoding":904},[883,58070,58072],{"className":58071},[886],[888,58073,58074],{"xmlns":890},[892,58075,58076,58080],{},[895,58077,58078],{},[898,58079,1973],{},[902,58081,1973],{"encoding":904},[883,58083,58085],{"className":58084},[886],[888,58086,58087],{"xmlns":890},[892,58088,58089,58093],{},[895,58090,58091],{},[1963,58092,3702],{},[902,58094,3702],{"encoding":904},[883,58096,58098],{"className":58097},[886],[888,58099,58100],{"xmlns":890},[892,58101,58102,58107],{},[895,58103,58104],{},[1963,58105,58106],{},"63",[902,58108,58106],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,58111,58112,1885,58114,58139,58140,1343,58158,2087],{},[38,58113,23270],{},[883,58115,58117],{"className":58116},[886],[888,58118,58119],{"xmlns":890},[892,58120,58121,58137],{},[895,58122,58123,58125,58127,58129,58131,58133,58135],{},[898,58124,1956],{},[898,58126,1959],{},[1664,58128,1676],{},[1963,58130,1965],{},[1664,58132,1867],{},[1963,58134,1970],{},[898,58136,1973],{},[902,58138,1976],{"encoding":904},", tedy při ",[883,58141,58143],{"className":58142},[886],[888,58144,58145],{"xmlns":890},[892,58146,58147,58155],{},[895,58148,58149,58151,58153],{},[898,58150,1973],{},[1664,58152,1676],{},[1963,58154,3702],{},[902,58156,58157],{"encoding":904},"Q = 60",[883,58159,58161],{"className":58160},[886],[888,58162,58163],{"xmlns":890},[892,58164,58165,58175],{},[895,58166,58167,58169,58171,58173],{},[898,58168,1695],{"mathvariant":1726},[898,58170,1973],{},[1664,58172,1676],{},[1963,58174,2774],{},[902,58176,58177],{"encoding":904},"\\mathrm{d}Q = 3",[883,58179,58181],{"className":58180},[886],[888,58182,58183],{"xmlns":890,"display":28566},[892,58184,58185,58216],{},[895,58186,58187,58189,58191,58193,58195,58197,58199,58201,58203,58205,58207,58209,58211,58213],{},[898,58188,1695],{"mathvariant":1726},[898,58190,1991],{},[898,58192,1959],{},[1664,58194,1676],{},[1664,58196,1667],{"stretchy":1666},[1963,58198,1965],{},[1664,58200,1867],{},[1963,58202,4614],{},[1664,58204,1673],{"stretchy":1666},[1664,58206,3753],{},[1963,58208,2774],{},[1664,58210,1676],{},[1664,58212,1867],{},[1963,58214,58215],{},"60.",[902,58217,58218],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,58220,58221,58222,58252,58253,58272],{},"Celkový příjem klesne z ",[883,58223,58225],{"className":58224},[886],[888,58226,58227],{"xmlns":890},[892,58228,58229,58249],{},[895,58230,58231,58233,58235,58237,58239,58241,58243,58245,58247],{},[898,58232,1991],{},[898,58234,1959],{},[1664,58236,1667],{"stretchy":1666},[1963,58238,3702],{},[1664,58240,1673],{"stretchy":1666},[1664,58242,1676],{},[1963,58244,1970],{},[1690,58246,1692],{},[1963,58248,20642],{},[902,58250,58251],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,58254,58256],{"className":58255},[886],[888,58257,58258],{"xmlns":890},[892,58259,58260,58269],{},[895,58261,58262,58264,58266],{},[1963,58263,1970],{},[1690,58265,1692],{},[1963,58267,58268],{},"340",[902,58270,58271],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,58274,58276],{"className":58275},[886],[888,58277,58278],{"xmlns":890,"display":28566},[892,58279,58280,58338],{},[895,58281,58282,58284,58286,58288,58290,58292,58294,58296,58298,58300,58302,58304,58306,58308,58310,58312,58314,58316,58318,58321,58323,58325,58327,58329,58331,58333,58336],{},[898,58283,3468],{"mathvariant":1726},[898,58285,1991],{},[898,58287,1959],{},[1664,58289,1676],{},[898,58291,1991],{},[898,58293,1959],{},[1664,58295,1667],{"stretchy":1666},[1963,58297,58106],{},[1664,58299,1673],{"stretchy":1666},[1664,58301,1867],{},[898,58303,1991],{},[898,58305,1959],{},[1664,58307,1667],{"stretchy":1666},[1963,58309,3702],{},[1664,58311,1673],{"stretchy":1666},[1664,58313,1676],{},[1963,58315,1970],{},[1690,58317,1692],{},[1963,58319,58320],{},"331",[1664,58322,1867],{},[1963,58324,1970],{},[1690,58326,1692],{},[1963,58328,20642],{},[1664,58330,1676],{},[1664,58332,1867],{},[1963,58334,58335],{},"69",[1664,58337,1916],{"separator":1915},[902,58339,58340],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,58342,58343,58344,58359,58360,1977],{},"tj. ",[883,58345,58347],{"className":58346},[886],[888,58348,58349],{"xmlns":890},[892,58350,58351,58357],{},[895,58352,58353,58355],{},[898,58354,1991],{},[898,58356,1959],{},[902,58358,4662],{"encoding":904}," klesne na ",[883,58361,58363],{"className":58362},[886],[888,58364,58365],{"xmlns":890},[892,58366,58367,58375],{},[895,58368,58369,58371,58373],{},[1963,58370,1970],{},[1690,58372,1692],{},[1963,58374,58320],{},[902,58376,58377],{"encoding":904},"2\\,331",[198,58379,58381],{"id":58380},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,58383,58384,58385,10957,58408,32080],{},"Obecně pro lineární poptávku ",[883,58386,58388],{"className":58387},[886],[888,58389,58390],{"xmlns":890},[892,58391,58392,58406],{},[895,58393,58394,58396,58398,58400,58402,58404],{},[898,58395,2398],{},[1664,58397,1676],{},[898,58399,207],{},[898,58401,1973],{},[1664,58403,1700],{},[898,58405,1818],{},[902,58407,37560],{"encoding":904},[883,58409,58411],{"className":58410},[886],[888,58412,58413],{"xmlns":890},[892,58414,58415,58437],{},[895,58416,58417,58419,58421,58423,58425,58431,58433,58435],{},[898,58418,1991],{},[898,58420,1959],{},[1664,58422,1676],{},[898,58424,207],{},[1720,58426,58427,58429],{},[898,58428,1973],{},[1963,58430,1970],{},[1664,58432,1700],{},[898,58434,1818],{},[898,58436,1973],{},[902,58438,58439],{"encoding":904},"TR = aQ^2 + bQ",[883,58441,58443],{"className":58442},[886],[888,58444,58445],{"xmlns":890,"display":28566},[892,58446,58447,58467],{},[895,58448,58449,58451,58453,58455,58457,58459,58461,58463,58465],{},[898,58450,1956],{},[898,58452,1959],{},[1664,58454,1676],{},[1963,58456,1970],{},[898,58458,207],{},[898,58460,1973],{},[1664,58462,1700],{},[898,58464,1818],{},[898,58466,1977],{"mathvariant":1726},[902,58468,58469],{"encoding":904},"MR = 2aQ + b.",[724,58471,58472,58473,58488,58489,58504,58505,58518,58519,10588,58522,58538,58539,58552,58553,58568,58569,58584,58585,58600,58601,3210,58614,58644,58645,58664,58665,58680],{},"Křivky ",[883,58474,58476],{"className":58475},[886],[888,58477,58478],{"xmlns":890},[892,58479,58480,58486],{},[895,58481,58482,58484],{},[898,58483,1956],{},[898,58485,1959],{},[902,58487,7200],{"encoding":904}," a poptávky (resp. ",[883,58490,58492],{"className":58491},[886],[888,58493,58494],{"xmlns":890},[892,58495,58496,58502],{},[895,58497,58498,58500],{},[898,58499,4822],{},[898,58501,1959],{},[902,58503,55945],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,58506,58508],{"className":58507},[886],[888,58509,58510],{"xmlns":890},[892,58511,58512,58516],{},[895,58513,58514],{},[898,58515,1818],{},[902,58517,1818],{"encoding":904},", přičemž ",[38,58520,58521],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,58523,58525],{"className":58524},[886],[888,58526,58527],{"xmlns":890},[892,58528,58529,58535],{},[895,58530,58531,58533],{},[1963,58532,1970],{},[898,58534,207],{},[902,58536,58537],{"encoding":904},"2a"," vs. ",[883,58540,58542],{"className":58541},[886],[888,58543,58544],{"xmlns":890},[892,58545,58546,58550],{},[895,58547,58548],{},[898,58549,207],{},[902,58551,207],{"encoding":904},", obrázek 3.2). ",[883,58554,58556],{"className":58555},[886],[888,58557,58558],{"xmlns":890},[892,58559,58560,58566],{},[895,58561,58562,58564],{},[898,58563,1956],{},[898,58565,1959],{},[902,58567,7200],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,58570,58572],{"className":58571},[886],[888,58573,58574],{"xmlns":890},[892,58575,58576,58582],{},[895,58577,58578,58580],{},[898,58579,1991],{},[898,58581,1959],{},[902,58583,4662],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,58586,58588],{"className":58587},[886],[888,58589,58590],{"xmlns":890},[892,58591,58592,58598],{},[895,58593,58594,58596],{},[898,58595,1956],{},[898,58597,1959],{},[902,58599,7200],{"encoding":904}," osu ",[883,58602,58604],{"className":58603},[886],[888,58605,58606],{"xmlns":890},[892,58607,58608,58612],{},[895,58609,58610],{},[898,58611,1973],{},[902,58613,1973],{"encoding":904},[883,58615,58617],{"className":58616},[886],[888,58618,58619],{"xmlns":890},[892,58620,58621,58641],{},[895,58622,58623,58625,58627,58629],{},[898,58624,1973],{},[1664,58626,1676],{},[1664,58628,1867],{},[2919,58630,58631],{"scriptlevel":2058,"displaystyle":1666},[2922,58632,58633,58635],{},[898,58634,1818],{},[895,58636,58637,58639],{},[1963,58638,1970],{},[898,58640,207],{},[902,58642,58643],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,58646,58648],{"className":58647},[886],[888,58649,58650],{"xmlns":890},[892,58651,58652,58662],{},[895,58653,58654,58656,58658,58660],{},[898,58655,1956],{},[898,58657,1959],{},[1664,58659,1676],{},[1963,58661,2058],{},[902,58663,7650],{"encoding":904},", a dále ",[883,58666,58668],{"className":58667},[886],[888,58669,58670],{"xmlns":890},[892,58671,58672,58678],{},[895,58673,58674,58676],{},[898,58675,1991],{},[898,58677,1959],{},[902,58679,4662],{"encoding":904}," klesá.",[724,58682,58683,58684,58690,58691,58723,58724,58752],{},"V případě ",[38,58685,58686],{},[207,58687,58689],{"className":58688,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,58692,58694],{"className":58693},[886],[888,58695,58696],{"xmlns":890},[892,58697,58698,58720],{},[895,58699,58700,58702,58704,58706,58708,58710,58712,58714],{},[898,58701,2398],{},[1664,58703,1676],{},[898,58705,2379],{},[1664,58707,1667],{"stretchy":1666},[898,58709,1973],{},[1664,58711,1673],{"stretchy":1666},[1664,58713,1676],{},[1720,58715,58716,58718],{},[898,58717,2398],{},[1664,58719,4920],{},[902,58721,58722],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,58725,58727],{"className":58726},[886],[888,58728,58729],{"xmlns":890},[892,58730,58731,58749],{},[895,58732,58733,58735,58737,58739,58741,58743],{},[898,58734,1991],{},[898,58736,1959],{},[1664,58738,1676],{},[898,58740,1973],{},[1664,58742,3753],{},[1720,58744,58745,58747],{},[898,58746,2398],{},[1664,58748,4920],{},[902,58750,58751],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,58754,58756],{"className":58755},[886],[888,58757,58758],{"xmlns":890,"display":28566},[892,58759,58760,58802],{},[895,58761,58762,58764,58766,58768,58770,58772,58774,58780,58782,58784,58798,58800],{},[898,58763,1956],{},[898,58765,1959],{},[1664,58767,1676],{},[898,58769,4822],{},[898,58771,1959],{},[1664,58773,1676],{},[1720,58775,58776,58778],{},[898,58777,2398],{},[1664,58779,4920],{},[6444,58781],{"width":15783},[1664,58783,1667],{"stretchy":1666},[895,58785,58786,58789,58795],{},[1690,58787,58788],{},"obr",[8951,58790,58791,58793],{"accent":1915},[1690,58792,207],{},[1664,58794,25477],{},[1690,58796,58797],{},"zek 3.4",[1664,58799,1673],{"stretchy":1666},[898,58801,1977],{"mathvariant":1726},[902,58803,58804],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,58806,58807],{},[614,58808,58809,58810,4454,58836,58864,58865,58878,58879,58894,58895,4293,58908,1343,58934,4293,58949,1977],{},"Obrázek 3.2: Přímky ",[883,58811,58813],{"className":58812},[886],[888,58814,58815],{"xmlns":890},[892,58816,58817,58833],{},[895,58818,58819,58821,58823,58825,58827,58829,58831],{},[898,58820,4822],{},[898,58822,1959],{},[1664,58824,1676],{},[898,58826,207],{},[898,58828,1973],{},[1664,58830,1700],{},[898,58832,1818],{},[902,58834,58835],{"encoding":904},"AR = aQ + b",[883,58837,58839],{"className":58838},[886],[888,58840,58841],{"xmlns":890},[892,58842,58843,58861],{},[895,58844,58845,58847,58849,58851,58853,58855,58857,58859],{},[898,58846,1956],{},[898,58848,1959],{},[1664,58850,1676],{},[1963,58852,1970],{},[898,58854,207],{},[898,58856,1973],{},[1664,58858,1700],{},[898,58860,1818],{},[902,58862,58863],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,58866,58868],{"className":58867},[886],[888,58869,58870],{"xmlns":890},[892,58871,58872,58876],{},[895,58873,58874],{},[898,58875,1818],{},[902,58877,1818],{"encoding":904}," se svislou osou, ",[883,58880,58882],{"className":58881},[886],[888,58883,58884],{"xmlns":890},[892,58885,58886,58892],{},[895,58887,58888,58890],{},[898,58889,1956],{},[898,58891,1959],{},[902,58893,7200],{"encoding":904}," protíná osu ",[883,58896,58898],{"className":58897},[886],[888,58899,58900],{"xmlns":890},[892,58901,58902,58906],{},[895,58903,58904],{},[898,58905,1973],{},[902,58907,1973],{"encoding":904},[883,58909,58911],{"className":58910},[886],[888,58912,58913],{"xmlns":890},[892,58914,58915,58931],{},[895,58916,58917,58919],{},[1664,58918,1867],{},[2919,58920,58921],{"scriptlevel":2058,"displaystyle":1666},[2922,58922,58923,58925],{},[898,58924,1818],{},[895,58926,58927,58929],{},[1963,58928,1970],{},[898,58930,207],{},[902,58932,58933],{"encoding":904},"-\\tfrac{b}{2a}",[883,58935,58937],{"className":58936},[886],[888,58938,58939],{"xmlns":890},[892,58940,58941,58947],{},[895,58942,58943,58945],{},[898,58944,4822],{},[898,58946,1959],{},[902,58948,55945],{"encoding":904},[883,58950,58952],{"className":58951},[886],[888,58953,58954],{"xmlns":890},[892,58955,58956,58968],{},[895,58957,58958,58960],{},[1664,58959,1867],{},[2919,58961,58962],{"scriptlevel":2058,"displaystyle":1666},[2922,58963,58964,58966],{},[898,58965,1818],{},[898,58967,207],{},[902,58969,58970],{"encoding":904},"-\\tfrac{b}{a}",[724,58972,58973],{},[614,58974,58975,58976,59007,59008,59037,59038,1977],{},"Obrázek 3.3: Parabola ",[883,58977,58979],{"className":58978},[886],[888,58980,58981],{"xmlns":890},[892,58982,58983,59005],{},[895,58984,58985,58987,58989,58991,58993,58999,59001,59003],{},[898,58986,1991],{},[898,58988,1959],{},[1664,58990,1676],{},[898,58992,207],{},[1720,58994,58995,58997],{},[898,58996,1973],{},[1963,58998,1970],{},[1664,59000,1700],{},[898,59002,1818],{},[898,59004,1973],{},[902,59006,58439],{"encoding":904}," s maximem v ",[883,59009,59011],{"className":59010},[886],[888,59012,59013],{"xmlns":890},[892,59014,59015,59035],{},[895,59016,59017,59019,59021,59023],{},[898,59018,1973],{},[1664,59020,1676],{},[1664,59022,1867],{},[2919,59024,59025],{"scriptlevel":2058,"displaystyle":1666},[2922,59026,59027,59029],{},[898,59028,1818],{},[895,59030,59031,59033],{},[1963,59032,1970],{},[898,59034,207],{},[902,59036,58643],{"encoding":904}," a nulou v ",[883,59039,59041],{"className":59040},[886],[888,59042,59043],{"xmlns":890},[892,59044,59045,59061],{},[895,59046,59047,59049,59051,59053],{},[898,59048,1973],{},[1664,59050,1676],{},[1664,59052,1867],{},[2919,59054,59055],{"scriptlevel":2058,"displaystyle":1666},[2922,59056,59057,59059],{},[898,59058,1818],{},[898,59060,207],{},[902,59062,59063],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,59065,59066],{},[614,59067,59068,59069,1977],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,59070,59072],{"className":59071},[886],[888,59073,59074],{"xmlns":890},[892,59075,59076,59096],{},[895,59077,59078,59080,59082,59084,59086,59088,59090],{},[898,59079,4822],{},[898,59081,1959],{},[1664,59083,1676],{},[898,59085,1956],{},[898,59087,1959],{},[1664,59089,1676],{},[1720,59091,59092,59094],{},[898,59093,2398],{},[1664,59095,4920],{},[902,59097,59098],{"encoding":904},"AR = MR = P^*",[115,59100,59102],{"id":59101},"náklady-firmy","Náklady firmy",[198,59104,59106],{"id":59105},"celkové-náklady","Celkové náklady",[724,59108,59109,1885,59111,10588,59126,59129,59130,59143],{},[38,59110,59106],{},[883,59112,59114],{"className":59113},[886],[888,59115,59116],{"xmlns":890},[892,59117,59118,59124],{},[895,59119,59120,59122],{},[898,59121,1991],{},[898,59123,1703],{},[902,59125,3819],{"encoding":904},[38,59127,59128],{},"total cost",") jsou veškeré náklady na realizaci ",[883,59131,59133],{"className":59132},[886],[888,59134,59135],{"xmlns":890},[892,59136,59137,59141],{},[895,59138,59139],{},[898,59140,1973],{},[902,59142,1973],{"encoding":904}," jednotek produkce:",[883,59145,59147],{"className":59146},[886],[888,59148,59149],{"xmlns":890,"display":28566},[892,59150,59151,59206],{},[21254,59152,59153],{"width":28571},[21259,59154,59155,59157,59199,59201],{},[21262,59156],{"width":28576},[21262,59158,59159],{},[895,59160,59161,59163,59165,59167,59169,59171,59173,59175,59177,59179,59181,59183,59185,59187,59189,59191,59193,59195,59197],{},[898,59162,1991],{},[898,59164,1703],{},[1664,59166,1676],{},[898,59168,1991],{},[898,59170,1703],{},[1664,59172,1667],{"stretchy":1666},[898,59174,1973],{},[1664,59176,1673],{"stretchy":1666},[1664,59178,1676],{},[898,59180,1662],{},[898,59182,1703],{},[1664,59184,1700],{},[898,59186,1991],{},[898,59188,40839],{},[898,59190,1703],{},[1664,59192,1667],{"stretchy":1666},[898,59194,1973],{},[1664,59196,1673],{"stretchy":1666},[1664,59198,1916],{"separator":1915},[21262,59200],{"width":28576},[21262,59202,59203],{},[1690,59204,59205],{},"(3.5)",[902,59207,59208],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,59210,1709,59211,59226,59227,10588,59230,12627,59233,59226,59257,10588,59260,59263],{},[883,59212,59214],{"className":59213},[886],[888,59215,59216],{"xmlns":890},[892,59217,59218,59224],{},[895,59219,59220,59222],{},[898,59221,1662],{},[898,59223,1703],{},[902,59225,55991],{"encoding":904}," jsou ",[38,59228,59229],{},"fixní náklady",[38,59231,59232],{},"fixed cost",[883,59234,59236],{"className":59235},[886],[888,59237,59238],{"xmlns":890},[892,59239,59240,59254],{},[895,59241,59242,59244,59246,59248,59250,59252],{},[898,59243,1991],{},[898,59245,40839],{},[898,59247,1703],{},[1664,59249,1667],{"stretchy":1666},[898,59251,1973],{},[1664,59253,1673],{"stretchy":1666},[902,59255,59256],{"encoding":904},"TVC(Q)",[38,59258,59259],{},"celkové variabilní náklady",[38,59261,59262],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,59265,59267],{"id":59266},"průměrné-náklady","Průměrné náklady",[724,59269,59270,1885,59272,10588,59287,59290],{},[38,59271,59267],{},[883,59273,59275],{"className":59274},[886],[888,59276,59277],{"xmlns":890},[892,59278,59279,59285],{},[895,59280,59281,59283],{},[898,59282,4822],{},[898,59284,1703],{},[902,59286,56060],{"encoding":904},[38,59288,59289],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,59292,59294],{"className":59293},[886],[888,59295,59296],{"xmlns":890,"display":28566},[892,59297,59298,59377],{},[21254,59299,59300],{"width":28571},[21259,59301,59302,59304,59370,59372],{},[21262,59303],{"width":28576},[21262,59305,59306],{},[895,59307,59308,59310,59312,59314,59316,59318,59320,59322,59324,59326,59336,59338,59348,59350,59368],{},[898,59309,4822],{},[898,59311,1703],{},[1664,59313,1676],{},[898,59315,4822],{},[898,59317,1703],{},[1664,59319,1667],{"stretchy":1666},[898,59321,1973],{},[1664,59323,1673],{"stretchy":1666},[1664,59325,1676],{},[2922,59327,59328,59334],{},[895,59329,59330,59332],{},[898,59331,1991],{},[898,59333,1703],{},[898,59335,1973],{},[1664,59337,1676],{},[2922,59339,59340,59346],{},[895,59341,59342,59344],{},[898,59343,1662],{},[898,59345,1703],{},[898,59347,1973],{},[1664,59349,1700],{},[2922,59351,59352,59366],{},[895,59353,59354,59356,59358,59360,59362,59364],{},[898,59355,1991],{},[898,59357,40839],{},[898,59359,1703],{},[1664,59361,1667],{"stretchy":1666},[898,59363,1973],{},[1664,59365,1673],{"stretchy":1666},[898,59367,1973],{},[1664,59369,1916],{"separator":1915},[21262,59371],{"width":28576},[21262,59373,59374],{},[1690,59375,59376],{},"(3.6)",[902,59378,59379],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,59381,1709,59382,59226,59406,1885,59409,10588,59426,12627,59429,59226,59461,1885,59464,10588,59481,3727],{},[883,59383,59385],{"className":59384},[886],[888,59386,59387],{"xmlns":890},[892,59388,59389,59403],{},[895,59390,59391],{},[2919,59392,59393],{"scriptlevel":2058,"displaystyle":1666},[2922,59394,59395,59401],{},[895,59396,59397,59399],{},[898,59398,1662],{},[898,59400,1703],{},[898,59402,1973],{},[902,59404,59405],{"encoding":904},"\\tfrac{FC}{Q}",[38,59407,59408],{},"průměrné fixní náklady",[883,59410,59412],{"className":59411},[886],[888,59413,59414],{"xmlns":890},[892,59415,59416,59424],{},[895,59417,59418,59420,59422],{},[898,59419,4822],{},[898,59421,1662],{},[898,59423,1703],{},[902,59425,56027],{"encoding":904},[38,59427,59428],{},"average fixed cost",[883,59430,59432],{"className":59431},[886],[888,59433,59434],{"xmlns":890},[892,59435,59436,59458],{},[895,59437,59438],{},[2919,59439,59440],{"scriptlevel":2058,"displaystyle":1666},[2922,59441,59442,59456],{},[895,59443,59444,59446,59448,59450,59452,59454],{},[898,59445,1991],{},[898,59447,40839],{},[898,59449,1703],{},[1664,59451,1667],{"stretchy":1666},[898,59453,1973],{},[1664,59455,1673],{"stretchy":1666},[898,59457,1973],{},[902,59459,59460],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,59462,59463],{},"průměrné variabilní náklady",[883,59465,59467],{"className":59466},[886],[888,59468,59469],{"xmlns":890},[892,59470,59471,59479],{},[895,59472,59473,59475,59477],{},[898,59474,4822],{},[898,59476,40839],{},[898,59478,1703],{},[902,59480,55811],{"encoding":904},[38,59482,59483],{},"average variable cost",[883,59485,59487],{"className":59486},[886],[888,59488,59489],{"xmlns":890,"display":28566},[892,59490,59491,59550],{},[21254,59492,59493],{"width":28571},[21259,59494,59495,59497,59543,59545],{},[21262,59496],{"width":28576},[21262,59498,59499],{},[895,59500,59501,59503,59505,59507,59509,59511,59513,59515,59517,59519,59521,59523,59541],{},[898,59502,4822],{},[898,59504,40839],{},[898,59506,1703],{},[1664,59508,1676],{},[898,59510,4822],{},[898,59512,40839],{},[898,59514,1703],{},[1664,59516,1667],{"stretchy":1666},[898,59518,1973],{},[1664,59520,1673],{"stretchy":1666},[1664,59522,1676],{},[2922,59524,59525,59539],{},[895,59526,59527,59529,59531,59533,59535,59537],{},[898,59528,1991],{},[898,59530,40839],{},[898,59532,1703],{},[1664,59534,1667],{"stretchy":1666},[898,59536,1973],{},[1664,59538,1673],{"stretchy":1666},[898,59540,1973],{},[898,59542,1977],{"mathvariant":1726},[21262,59544],{"width":28576},[21262,59546,59547],{},[1690,59548,59549],{},"(3.7)",[902,59551,59552],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[37848,59554,59556],{"id":59555},"příklad-34","Příklad 3.4",[724,59558,59559,58022,59561,4454,59586,56525,59610,4454,59625,59640,59641,1977],{},[38,59560,56487],{},[883,59562,59564],{"className":59563},[886],[888,59565,59566],{"xmlns":890},[892,59567,59568,59583],{},[895,59569,59570,59572,59574,59576,59578,59580],{},[898,59571,1662],{},[898,59573,1703],{},[1664,59575,1676],{},[1963,59577,2875],{},[1690,59579,1692],{},[1963,59581,59582],{},"000",[902,59584,59585],{"encoding":904},"FC = 1\\,000",[883,59587,59589],{"className":59588},[886],[888,59590,59591],{"xmlns":890},[892,59592,59593,59607],{},[895,59594,59595,59597,59599,59601,59603,59605],{},[898,59596,1991],{},[898,59598,40839],{},[898,59600,1703],{},[1664,59602,1676],{},[1963,59604,2944],{},[898,59606,1973],{},[902,59608,59609],{"encoding":904},"TVC = 4Q",[883,59611,59613],{"className":59612},[886],[888,59614,59615],{"xmlns":890},[892,59616,59617,59623],{},[895,59618,59619,59621],{},[898,59620,1991],{},[898,59622,1703],{},[902,59624,3819],{"encoding":904},[883,59626,59628],{"className":59627},[886],[888,59629,59630],{"xmlns":890},[892,59631,59632,59638],{},[895,59633,59634,59636],{},[898,59635,4822],{},[898,59637,1703],{},[902,59639,56060],{"encoding":904}," a jejich chování s rostoucím ",[883,59642,59644],{"className":59643},[886],[888,59645,59646],{"xmlns":890},[892,59647,59648,59652],{},[895,59649,59650],{},[898,59651,1973],{},[902,59653,1973],{"encoding":904},[724,59655,59656,1885,59658,4454,59688,59724,59725,4924,59738,59753,59754,2087],{},[38,59657,23270],{},[883,59659,59661],{"className":59660},[886],[888,59662,59663],{"xmlns":890},[892,59664,59665,59685],{},[895,59666,59667,59669,59671,59673,59675,59677,59679,59681,59683],{},[898,59668,1991],{},[898,59670,1703],{},[1664,59672,1676],{},[1963,59674,2875],{},[1690,59676,1692],{},[1963,59678,59582],{},[1664,59680,1700],{},[1963,59682,2944],{},[898,59684,1973],{},[902,59686,59687],{"encoding":904},"TC = 1\\,000 + 4Q",[883,59689,59691],{"className":59690},[886],[888,59692,59693],{"xmlns":890},[892,59694,59695,59721],{},[895,59696,59697,59699,59701,59703,59717,59719],{},[898,59698,4822],{},[898,59700,1703],{},[1664,59702,1676],{},[2919,59704,59705],{"scriptlevel":2058,"displaystyle":1666},[2922,59706,59707,59715],{},[895,59708,59709,59711,59713],{},[1963,59710,2875],{},[1690,59712,1692],{},[1963,59714,59582],{},[898,59716,1973],{},[1664,59718,1700],{},[1963,59720,2944],{},[902,59722,59723],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,59726,59728],{"className":59727},[886],[888,59729,59730],{"xmlns":890},[892,59731,59732,59736],{},[895,59733,59734],{},[898,59735,1973],{},[902,59737,1973],{"encoding":904},[883,59739,59741],{"className":59740},[886],[888,59742,59743],{"xmlns":890},[892,59744,59745,59751],{},[895,59746,59747,59749],{},[898,59748,4822],{},[898,59750,1703],{},[902,59752,56060],{"encoding":904}," blíží ",[883,59755,59757],{"className":59756},[886],[888,59758,59759],{"xmlns":890},[892,59760,59761,59765],{},[895,59762,59763],{},[1963,59764,2944],{},[902,59766,2944],{"encoding":904},[883,59768,59770],{"className":59769},[886],[888,59771,59772],{"xmlns":890,"display":28566},[892,59773,59774,59820],{},[895,59775,59776,59793,59815,59817],{},[40396,59777,59778,59785],{},[895,59779,59780,59783],{},[898,59781,59782],{},"lim",[1664,59784,56700],{},[895,59786,59787,59789,59791],{},[898,59788,1973],{},[1664,59790,3699],{},[898,59792,6863],{"mathvariant":1726},[895,59794,59795,59797,59809,59811,59813],{},[1664,59796,1667],{"fence":1915},[2922,59798,59799,59807],{},[895,59800,59801,59803,59805],{},[1963,59802,2875],{},[1690,59804,1692],{},[1963,59806,59582],{},[898,59808,1973],{},[1664,59810,1700],{},[1963,59812,2944],{},[1664,59814,1673],{"fence":1915},[1664,59816,1676],{},[1963,59818,59819],{},"4.",[902,59821,59822],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,59824,59825,59863,59864,1977],{},[883,59826,59828],{"className":59827},[886],[888,59829,59830],{"xmlns":890},[892,59831,59832,59860],{},[895,59833,59834,59836,59838,59840,59842,59856,59858],{},[898,59835,4822],{},[898,59837,1662],{},[898,59839,1703],{},[1664,59841,1676],{},[2919,59843,59844],{"scriptlevel":2058,"displaystyle":1666},[2922,59845,59846,59854],{},[895,59847,59848,59850,59852],{},[1963,59849,2875],{},[1690,59851,1692],{},[1963,59853,59582],{},[898,59855,1973],{},[1664,59857,3699],{},[1963,59859,2058],{},[902,59861,59862],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,59865,59867],{"className":59866},[886],[888,59868,59869],{"xmlns":890},[892,59870,59871,59875],{},[895,59872,59873],{},[898,59874,1973],{},[902,59876,1973],{"encoding":904},[724,59878,59879],{},[614,59880,59881,59882,59911,59912,1977],{},"Obrázek 3.5: Přímka ",[883,59883,59885],{"className":59884},[886],[888,59886,59887],{"xmlns":890},[892,59888,59889,59909],{},[895,59890,59891,59893,59895,59897,59899,59901,59903,59905,59907],{},[898,59892,1991],{},[898,59894,1703],{},[1664,59896,1676],{},[1963,59898,2875],{},[1690,59900,1692],{},[1963,59902,59582],{},[1664,59904,1700],{},[1963,59906,2944],{},[898,59908,1973],{},[902,59910,59687],{"encoding":904}," protínající svislou osu ve výši ",[883,59913,59915],{"className":59914},[886],[888,59916,59917],{"xmlns":890},[892,59918,59919,59933],{},[895,59920,59921,59923,59925,59927,59929,59931],{},[898,59922,1662],{},[898,59924,1703],{},[1664,59926,1676],{},[1963,59928,2875],{},[1690,59930,1692],{},[1963,59932,59582],{},[902,59934,59585],{"encoding":904},[724,59936,59937],{},[614,59938,59939,59940,59975,59976,1977],{},"Obrázek 3.6: Hyperbola ",[883,59941,59943],{"className":59942},[886],[888,59944,59945],{"xmlns":890},[892,59946,59947,59973],{},[895,59948,59949,59951,59953,59955,59969,59971],{},[898,59950,4822],{},[898,59952,1703],{},[1664,59954,1676],{},[2919,59956,59957],{"scriptlevel":2058,"displaystyle":1666},[2922,59958,59959,59967],{},[895,59960,59961,59963,59965],{},[1963,59962,2875],{},[1690,59964,1692],{},[1963,59966,59582],{},[898,59968,1973],{},[1664,59970,1700],{},[1963,59972,2944],{},[902,59974,59723],{"encoding":904}," s vodorovnou asymptotou ",[883,59977,59979],{"className":59978},[886],[888,59980,59981],{"xmlns":890},[892,59982,59983,59993],{},[895,59984,59985,59987,59989,59991],{},[898,59986,4822],{},[898,59988,1703],{},[1664,59990,1676],{},[1963,59992,2944],{},[902,59994,59995],{"encoding":904},"AC = 4",[724,59997,59998],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,60000,60002],{"className":60001},[886],[888,60003,60004],{"xmlns":890,"display":28566},[892,60005,60006,60032],{},[895,60007,60008,60010,60012,60014,60016,60018,60020,60022,60024,60026,60028,60030],{},[898,60009,1991],{},[898,60011,40839],{},[898,60013,1703],{},[1664,60015,1676],{},[898,60017,1973],{},[1664,60019,3753],{},[898,60021,40839],{},[898,60023,1703],{},[1664,60025,1667],{"stretchy":1666},[898,60027,1973],{},[1664,60029,1673],{"stretchy":1666},[1664,60031,1916],{"separator":1915},[902,60033,60034],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,60036,1709,60037,59226,60065,60068,60069,60099],{},[883,60038,60040],{"className":60039},[886],[888,60041,60042],{"xmlns":890},[892,60043,60044,60062],{},[895,60045,60046,60048,60050,60052,60054,60056,60058,60060],{},[898,60047,40839],{},[898,60049,1703],{},[1664,60051,1676],{},[898,60053,40839],{},[898,60055,1703],{},[1664,60057,1667],{"stretchy":1666},[898,60059,1973],{},[1664,60061,1673],{"stretchy":1666},[902,60063,60064],{"encoding":904},"VC = VC(Q)",[38,60066,60067],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,60070,60072],{"className":60071},[886],[888,60073,60074],{"xmlns":890},[892,60075,60076,60096],{},[895,60077,60078,60080,60082,60084,60086,60088,60090,60092,60094],{},[898,60079,1991],{},[898,60081,40839],{},[898,60083,1703],{},[1664,60085,1667],{"stretchy":1666},[898,60087,1973],{},[1664,60089,1673],{"stretchy":1666},[1664,60091,1676],{},[898,60093,207],{},[898,60095,1973],{},[902,60097,60098],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,60101,60103],{"className":60102},[886],[888,60104,60105],{"xmlns":890,"display":28566},[892,60106,60107,60127],{},[895,60108,60109,60111,60113,60115,60117,60119,60121,60123,60125],{},[898,60110,1991],{},[898,60112,1703],{},[1664,60114,1676],{},[898,60116,1662],{},[898,60118,1703],{},[1664,60120,1700],{},[898,60122,207],{},[898,60124,1973],{},[898,60126,1977],{"mathvariant":1726},[902,60128,60129],{"encoding":904},"TC = FC + aQ.",[724,60131,60132,60133,60148,60149,60164,60165,60188,60189,60223,60224,59975,60237,60250,60251,4454,60299,60343,60344,1977],{},"Křivkou ",[883,60134,60136],{"className":60135},[886],[888,60137,60138],{"xmlns":890},[892,60139,60140,60146],{},[895,60141,60142,60144],{},[898,60143,1991],{},[898,60145,1703],{},[902,60147,3819],{"encoding":904}," je přímka se svislým průsečíkem ",[883,60150,60152],{"className":60151},[886],[888,60153,60154],{"xmlns":890},[892,60155,60156,60162],{},[895,60157,60158,60160],{},[898,60159,1662],{},[898,60161,1703],{},[902,60163,55991],{"encoding":904}," a sklonem ",[883,60166,60168],{"className":60167},[886],[888,60169,60170],{"xmlns":890},[892,60171,60172,60185],{},[895,60173,60174,60177,60179,60181,60183],{},[898,60175,60176],{},"tan",[1664,60178,56700],{},[898,60180,19362],{},[1664,60182,1676],{},[898,60184,207],{},[902,60186,60187],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,60190,60192],{"className":60191},[886],[888,60193,60194],{"xmlns":890},[892,60195,60196,60220],{},[895,60197,60198,60200,60202,60204,60216,60218],{},[898,60199,4822],{},[898,60201,1703],{},[1664,60203,1676],{},[2919,60205,60206],{"scriptlevel":2058,"displaystyle":1666},[2922,60207,60208,60214],{},[895,60209,60210,60212],{},[898,60211,1662],{},[898,60213,1703],{},[898,60215,1973],{},[1664,60217,1700],{},[898,60219,207],{},[902,60221,60222],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,60225,60227],{"className":60226},[886],[888,60228,60229],{"xmlns":890},[892,60230,60231,60235],{},[895,60232,60233],{},[898,60234,10358],{},[902,60236,10358],{"encoding":904},[883,60238,60240],{"className":60239},[886],[888,60241,60242],{"xmlns":890},[892,60243,60244,60248],{},[895,60245,60246],{},[898,60247,207],{},[902,60249,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,60252,60254],{"className":60253},[886],[888,60255,60256],{"xmlns":890},[892,60257,60258,60296],{},[895,60259,60260,60280,60292,60294],{},[2355,60261,60262,60268],{},[895,60263,60264,60266],{},[898,60265,59782],{},[1664,60267,56700],{},[895,60269,60270,60272,60274],{},[898,60271,1973],{},[1664,60273,3699],{},[1720,60275,60276,60278],{},[1963,60277,2058],{},[1664,60279,1700],{},[2919,60281,60282],{"scriptlevel":2058,"displaystyle":1666},[2922,60283,60284,60290],{},[895,60285,60286,60288],{},[898,60287,1662],{},[898,60289,1703],{},[898,60291,1973],{},[1664,60293,1676],{},[898,60295,6863],{"mathvariant":1726},[902,60297,60298],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,60300,60302],{"className":60301},[886],[888,60303,60304],{"xmlns":890},[892,60305,60306,60340],{},[895,60307,60308,60324,60336,60338],{},[2355,60309,60310,60316],{},[895,60311,60312,60314],{},[898,60313,59782],{},[1664,60315,56700],{},[895,60317,60318,60320,60322],{},[898,60319,1973],{},[1664,60321,3699],{},[898,60323,6863],{"mathvariant":1726},[2919,60325,60326],{"scriptlevel":2058,"displaystyle":1666},[2922,60327,60328,60334],{},[895,60329,60330,60332],{},[898,60331,1662],{},[898,60333,1703],{},[898,60335,1973],{},[1664,60337,1676],{},[1963,60339,2058],{},[902,60341,60342],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,60345,60347],{"className":60346},[886],[888,60348,60349],{"xmlns":890},[892,60350,60351,60357],{},[895,60352,60353,60355],{},[898,60354,4822],{},[898,60356,1703],{},[902,60358,56060],{"encoding":904},[724,60360,60361],{},[614,60362,60363,60364,60379,60380,60395,60396,1977],{},"Obrázek 3.7: Přímka ",[883,60365,60367],{"className":60366},[886],[888,60368,60369],{"xmlns":890},[892,60370,60371,60377],{},[895,60372,60373,60375],{},[898,60374,1991],{},[898,60376,1703],{},[902,60378,3819],{"encoding":904}," s osovým průsečíkem ve výši ",[883,60381,60383],{"className":60382},[886],[888,60384,60385],{"xmlns":890},[892,60386,60387,60393],{},[895,60388,60389,60391],{},[898,60390,1662],{},[898,60392,1703],{},[902,60394,55991],{"encoding":904}," a se sklonem ",[883,60397,60399],{"className":60398},[886],[888,60400,60401],{"xmlns":890},[892,60402,60403,60415],{},[895,60404,60405,60407,60409,60411,60413],{},[898,60406,60176],{},[1664,60408,56700],{},[898,60410,19362],{},[1664,60412,1676],{},[898,60414,207],{},[902,60416,60187],{"encoding":904},[724,60418,60419],{},[614,60420,60421,60422,60437,60438,1977],{},"Obrázek 3.8: Klesající hyperbola ",[883,60423,60425],{"className":60424},[886],[888,60426,60427],{"xmlns":890},[892,60428,60429,60435],{},[895,60430,60431,60433],{},[898,60432,4822],{},[898,60434,1703],{},[902,60436,56060],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,60439,60441],{"className":60440},[886],[888,60442,60443],{"xmlns":890},[892,60444,60445,60449],{},[895,60446,60447],{},[898,60448,207],{},[902,60450,207],{"encoding":904},[198,60452,60454],{"id":60453},"mezní-náklady","Mezní náklady",[724,60456,60457,1885,60459,10588,60474,60477,60478,60481],{},[38,60458,60454],{},[883,60460,60462],{"className":60461},[886],[888,60463,60464],{"xmlns":890},[892,60465,60466,60472],{},[895,60467,60468,60470],{},[898,60469,1956],{},[898,60471,1703],{},[902,60473,55792],{"encoding":904},[38,60475,60476],{},"marginal cost",") jsou ",[207,60479,1145],{"className":60480,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,60483,60485],{"className":60484},[886],[888,60486,60487],{"xmlns":890,"display":28566},[892,60488,60489,60558],{},[21254,60490,60491],{"width":28571},[21259,60492,60493,60495,60551,60553],{},[21262,60494],{"width":28576},[21262,60496,60497],{},[895,60498,60499,60501,60503,60505,60507,60509,60511,60513,60515,60517,60533,60535,60537,60543,60545,60547,60549],{},[898,60500,1956],{},[898,60502,1703],{},[1664,60504,1676],{},[898,60506,1956],{},[898,60508,1703],{},[1664,60510,1667],{"stretchy":1666},[898,60512,1973],{},[1664,60514,1673],{"stretchy":1666},[1664,60516,1676],{},[2922,60518,60519,60527],{},[895,60520,60521,60523,60525],{},[898,60522,1695],{"mathvariant":1726},[898,60524,1991],{},[898,60526,1703],{},[895,60528,60529,60531],{},[898,60530,1695],{"mathvariant":1726},[898,60532,1973],{},[1664,60534,1676],{},[898,60536,1991],{},[1720,60538,60539,60541],{},[898,60540,1703],{},[1664,60542,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,60544,1667],{"stretchy":1666},[898,60546,1973],{},[1664,60548,1673],{"stretchy":1666},[898,60550,1977],{"mathvariant":1726},[21262,60552],{"width":28576},[21262,60554,60555],{},[1690,60556,60557],{},"(3.8)",[902,60559,60560],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[4436,60562,60563],{},[724,60564,60565,60567,60568,60594,60595,60612,60613,1977],{},[883,60566,4723],{}," Intuice — „kolik stojí další kus\"\n",[883,60569,60571],{"className":60570},[886],[888,60572,60573],{"xmlns":890},[892,60574,60575,60591],{},[895,60576,60577,60579,60581,60583,60589],{},[898,60578,1956],{},[898,60580,1703],{},[1664,60582,1667],{"stretchy":1666},[1720,60584,60585,60587],{},[898,60586,1973],{},[1664,60588,4920],{},[1664,60590,1673],{"stretchy":1666},[902,60592,60593],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,60596,60598],{"className":60597},[886],[888,60599,60600],{"xmlns":890},[892,60601,60602,60610],{},[895,60603,60604],{},[1720,60605,60606,60608],{},[898,60607,1973],{},[1664,60609,4920],{},[902,60611,30344],{"encoding":904},". Formálně ",[883,60614,60616],{"className":60615},[886],[888,60617,60618],{"xmlns":890},[892,60619,60620,60672],{},[895,60621,60622,60624,60626,60628,60634,60636,60638,60640,60642,60644,60650,60652,60654,60656,60658,60660,60662,60664,60670],{},[898,60623,1956],{},[898,60625,1703],{},[1664,60627,1667],{"stretchy":1666},[1720,60629,60630,60632],{},[898,60631,1973],{},[1664,60633,4920],{},[1664,60635,1673],{"stretchy":1666},[1664,60637,3315],{},[898,60639,1991],{},[898,60641,1703],{},[1664,60643,1667],{"stretchy":1666},[1720,60645,60646,60648],{},[898,60647,1973],{},[1664,60649,4920],{},[1664,60651,1700],{},[1963,60653,2875],{},[1664,60655,1673],{"stretchy":1666},[1664,60657,1867],{},[898,60659,1991],{},[898,60661,1703],{},[1664,60663,1667],{"stretchy":1666},[1720,60665,60666,60668],{},[898,60667,1973],{},[1664,60669,4920],{},[1664,60671,1673],{"stretchy":1666},[902,60673,60674],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,60676,60677,60678,2087],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,60679,60681],{"className":60680},[886],[888,60682,60683],{"xmlns":890},[892,60684,60685,60693],{},[895,60686,60687,60689,60691],{},[898,60688,3468],{"mathvariant":1726},[898,60690,1991],{},[898,60692,1703],{},[902,60694,60695],{"encoding":904},"\\Delta TC",[883,60697,60699],{"className":60698},[886],[888,60700,60701],{"xmlns":890,"display":28566},[892,60702,60703,60772],{},[21254,60704,60705],{"width":28571},[21259,60706,60707,60709,60765,60767],{},[21262,60708],{"width":28576},[21262,60710,60711],{},[895,60712,60713,60715,60717,60719,60721,60723,60725,60727,60729,60731,60733,60735,60737,60739,60745,60747,60749,60751,60753,60755,60757,60759,60761,60763],{},[898,60714,3468],{"mathvariant":1726},[898,60716,1991],{},[898,60718,1703],{},[1690,60720,4553],{},[1664,60722,3315],{},[1690,60724,4553],{},[898,60726,1695],{"mathvariant":1726},[898,60728,1991],{},[898,60730,1703],{},[1664,60732,1676],{},[1664,60734,1667],{"stretchy":1666},[898,60736,1991],{},[898,60738,1703],{},[1720,60740,60741,60743],{},[1664,60742,1673],{"stretchy":1666},[1664,60744,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1690,60746,1692],{},[898,60748,1695],{"mathvariant":1726},[898,60750,1973],{},[1664,60752,1676],{},[898,60754,1956],{},[898,60756,1703],{},[1690,60758,1692],{},[898,60760,1695],{"mathvariant":1726},[898,60762,1973],{},[1664,60764,1916],{"separator":1915},[21262,60766],{"width":28576},[21262,60768,60769],{},[1690,60770,60771],{},"(3.9)",[902,60773,60774],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,60776,57811],{},[883,60778,60780],{"className":60779},[886],[888,60781,60782],{"xmlns":890,"display":28566},[892,60783,60784,60882],{},[895,60785,60786,60824,60826,60828,60830,60852,60854,60880],{},[895,60787,60788,60790,60796,60798,60804,60807,60813,60816],{},[1690,60789,57825],{},[8951,60791,60792,60794],{"accent":1915},[1690,60793,46232],{},[1664,60795,25558],{},[1690,60797,57834],{},[8951,60799,60800,60802],{"accent":1915},[1690,60801,2608],{},[1664,60803,25477],{},[1690,60805,60806],{},"ch n",[8951,60808,60809,60811],{"accent":1915},[1690,60810,207],{},[1664,60812,25477],{},[1690,60814,60815],{},"klad",[8951,60817,60818,60821],{"accent":1915},[1690,60819,60820],{},"u",[1664,60822,60823],{},"˚",[1690,60825,4553],{},[1664,60827,3315],{},[1690,60829,4553],{},[895,60831,60832,60834,60840,60843,60849],{},[1690,60833,57869],{},[8951,60835,60836,60838],{"accent":1915},[1690,60837,25546],{},[1664,60839,25477],{},[1690,60841,60842],{}," n",[8951,60844,60845,60847],{"accent":1915},[1690,60846,207],{},[1664,60848,25477],{},[1690,60850,60851],{},"klady",[1664,60853,57896],{},[895,60855,60856,60858,60864,60866,60872,60874],{},[1690,60857,57825],{},[8951,60859,60860,60862],{"accent":1915},[1690,60861,46232],{},[1664,60863,25558],{},[1690,60865,57909],{},[8951,60867,60868,60870],{"accent":1915},[1690,60869,10157],{},[1664,60871,25558],{},[1690,60873,57918],{},[8951,60875,60876,60878],{"accent":1915},[1690,60877,25546],{},[1664,60879,25477],{},[898,60881,1977],{"mathvariant":1726},[902,60883,60884],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[37848,60886,60888],{"id":60887},"příklad-35","Příklad 3.5",[724,60890,60891,58022,60893,56525,60929,60944,60945,60960,60961,3257,60974,3271,60987,61000,61001,3271,61014,1977],{},[38,60892,56487],{},[883,60894,60896],{"className":60895},[886],[888,60897,60898],{"xmlns":890},[892,60899,60900,60926],{},[895,60901,60902,60904,60906,60908,60910,60912,60914,60916,60918,60920],{},[898,60903,1991],{},[898,60905,1703],{},[1664,60907,1676],{},[1963,60909,8942],{},[1664,60911,1700],{},[1963,60913,2833],{},[898,60915,1973],{},[1664,60917,1700],{},[1963,60919,1970],{},[1720,60921,60922,60924],{},[898,60923,1973],{},[1963,60925,1970],{},[902,60927,60928],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,60930,60932],{"className":60931},[886],[888,60933,60934],{"xmlns":890},[892,60935,60936,60942],{},[895,60937,60938,60940],{},[898,60939,1956],{},[898,60941,1703],{},[902,60943,55792],{"encoding":904}," a odhadněte změny ",[883,60946,60948],{"className":60947},[886],[888,60949,60950],{"xmlns":890},[892,60951,60952,60958],{},[895,60953,60954,60956],{},[898,60955,1991],{},[898,60957,1703],{},[902,60959,3819],{"encoding":904}," při změnách ",[883,60962,60964],{"className":60963},[886],[888,60965,60966],{"xmlns":890},[892,60967,60968,60972],{},[895,60969,60970],{},[898,60971,1973],{},[902,60973,1973],{"encoding":904},[883,60975,60977],{"className":60976},[886],[888,60978,60979],{"xmlns":890},[892,60980,60981,60985],{},[895,60982,60983],{},[1963,60984,36744],{},[902,60986,36744],{"encoding":904},[883,60988,60990],{"className":60989},[886],[888,60991,60992],{"xmlns":890},[892,60993,60994,60998],{},[895,60995,60996],{},[1963,60997,42362],{},[902,60999,42362],{"encoding":904}," a z ",[883,61002,61004],{"className":61003},[886],[888,61005,61006],{"xmlns":890},[892,61007,61008,61012],{},[895,61009,61010],{},[1963,61011,36744],{},[902,61013,36744],{"encoding":904},[883,61015,61017],{"className":61016},[886],[888,61018,61019],{"xmlns":890},[892,61020,61021,61025],{},[895,61022,61023],{},[1963,61024,4084],{},[902,61026,4084],{"encoding":904},[724,61028,61029,1885,61031,1748,61057,1343,61084,61111,61112,61127,61128,61143,61144,61171,61172,61192,61193,21031,61214,61270,61271,3257,61284,3271,61297,1762,61310,1977],{},[38,61030,23270],{},[883,61032,61034],{"className":61033},[886],[888,61035,61036],{"xmlns":890},[892,61037,61038,61054],{},[895,61039,61040,61042,61044,61046,61048,61050,61052],{},[898,61041,1956],{},[898,61043,1703],{},[1664,61045,1676],{},[1963,61047,2833],{},[1664,61049,1700],{},[1963,61051,2944],{},[898,61053,1973],{},[902,61055,61056],{"encoding":904},"MC = 6 + 4Q",[883,61058,61060],{"className":61059},[886],[888,61061,61062],{"xmlns":890},[892,61063,61064,61081],{},[895,61065,61066,61068,61070,61072,61074,61076,61078],{},[898,61067,1956],{},[898,61069,1703],{},[1664,61071,1667],{"stretchy":1666},[1963,61073,36744],{},[1664,61075,1673],{"stretchy":1666},[1664,61077,1676],{},[1963,61079,61080],{},"66",[902,61082,61083],{"encoding":904},"MC(15) = 66",[883,61085,61087],{"className":61086},[886],[888,61088,61089],{"xmlns":890},[892,61090,61091,61108],{},[895,61092,61093,61095,61097,61099,61101,61103,61105],{},[898,61094,1956],{},[898,61096,1703],{},[1664,61098,1667],{"stretchy":1666},[1963,61100,9599],{},[1664,61102,1673],{"stretchy":1666},[1664,61104,1676],{},[1963,61106,61107],{},"86",[902,61109,61110],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,61113,61115],{"className":61114},[886],[888,61116,61117],{"xmlns":890},[892,61118,61119,61125],{},[895,61120,61121,61123],{},[898,61122,1991],{},[898,61124,1703],{},[902,61126,3819],{"encoding":904}," zvyšuje (",[883,61129,61131],{"className":61130},[886],[888,61132,61133],{"xmlns":890},[892,61134,61135,61141],{},[895,61136,61137,61139],{},[898,61138,1956],{},[898,61140,1703],{},[902,61142,55792],{"encoding":904}," je rostoucí). Z ",[883,61145,61147],{"className":61146},[886],[888,61148,61149],{"xmlns":890},[892,61150,61151,61168],{},[895,61152,61153,61155,61157,61159,61161,61163,61165],{},[898,61154,1991],{},[898,61156,1703],{},[1664,61158,1667],{"stretchy":1666},[1963,61160,36744],{},[1664,61162,1673],{"stretchy":1666},[1664,61164,1676],{},[1963,61166,61167],{},"740",[902,61169,61170],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,61173,61175],{"className":61174},[886],[888,61176,61177],{"xmlns":890},[892,61178,61179,61189],{},[895,61180,61181,61183,61185,61187],{},[898,61182,1695],{"mathvariant":1726},[898,61184,1973],{},[1664,61186,1676],{},[1963,61188,2875],{},[902,61190,61191],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,61194,61196],{"className":61195},[886],[888,61197,61198],{"xmlns":890},[892,61199,61200,61211],{},[895,61201,61202,61204,61206,61208],{},[898,61203,1991],{},[898,61205,1703],{},[1664,61207,3315],{},[1963,61209,61210],{},"806",[902,61212,61213],{"encoding":904},"TC \\approx 806",[883,61215,61217],{"className":61216},[886],[888,61218,61219],{"xmlns":890},[892,61220,61221,61267],{},[895,61222,61223,61225,61227,61229,61231,61233,61235,61237,61239,61241,61243,61245,61247,61249,61251,61253,61255,61258,61260,61262,61264],{},[898,61224,3468],{"mathvariant":1726},[898,61226,1991],{},[898,61228,1703],{},[1664,61230,1676],{},[898,61232,1991],{},[898,61234,1703],{},[1664,61236,1667],{"stretchy":1666},[1963,61238,42362],{},[1664,61240,1673],{"stretchy":1666},[1664,61242,1867],{},[898,61244,1991],{},[898,61246,1703],{},[1664,61248,1667],{"stretchy":1666},[1963,61250,36744],{},[1664,61252,1673],{"stretchy":1666},[1664,61254,1676],{},[1963,61256,61257],{},"808",[1664,61259,1867],{},[1963,61261,61167],{},[1664,61263,1676],{},[1963,61265,61266],{},"68",[902,61268,61269],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,61272,61274],{"className":61273},[886],[888,61275,61276],{"xmlns":890},[892,61277,61278,61282],{},[895,61279,61280],{},[898,61281,1973],{},[902,61283,1973],{"encoding":904},[883,61285,61287],{"className":61286},[886],[888,61288,61289],{"xmlns":890},[892,61290,61291,61295],{},[895,61292,61293],{},[1963,61294,36744],{},[902,61296,36744],{"encoding":904},[883,61298,61300],{"className":61299},[886],[888,61301,61302],{"xmlns":890},[892,61303,61304,61308],{},[895,61305,61306],{},[1963,61307,4084],{},[902,61309,4084],{"encoding":904},[883,61311,61313],{"className":61312},[886],[888,61314,61315],{"xmlns":890},[892,61316,61317,61346],{},[895,61318,61319,61321,61323,61325,61327,61329,61331,61333,61335,61337,61339,61341,61343],{},[898,61320,3468],{"mathvariant":1726},[898,61322,1991],{},[898,61324,1703],{},[1664,61326,3315],{},[1963,61328,61080],{},[1664,61330,3753],{},[1664,61332,1667],{"stretchy":1666},[1664,61334,1867],{},[1963,61336,2774],{},[1664,61338,1673],{"stretchy":1666},[1664,61340,1676],{},[1664,61342,1867],{},[1963,61344,61345],{},"198",[902,61347,61348],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,61350,61352],{"id":61351},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,61354,61355],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[37848,61357,61359],{"id":61358},"příklad-36","Příklad 3.6",[724,61361,61362,58022,61364,61408],{},[38,61363,56487],{},[883,61365,61367],{"className":61366},[886],[888,61368,61369],{"xmlns":890},[892,61370,61371,61405],{},[895,61372,61373,61375,61377,61379,61381,61383,61385,61387,61389,61391,61397,61399],{},[898,61374,1991],{},[898,61376,1703],{},[1664,61378,1676],{},[1963,61380,1965],{},[1664,61382,1700],{},[1963,61384,5570],{},[898,61386,1973],{},[1664,61388,1867],{},[1963,61390,2826],{},[1720,61392,61393,61395],{},[898,61394,1973],{},[1963,61396,1970],{},[1664,61398,1700],{},[1720,61400,61401,61403],{},[898,61402,1973],{},[1963,61404,2774],{},[902,61406,61407],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,61410,61411],{},[38,61412,23270],{},[883,61414,61416],{"className":61415},[886],[888,61417,61418],{"xmlns":890,"display":28566},[892,61419,61420,61664],{},[21254,61421,61422,61448,61496,61530,61572,61622],{"rowspacing":21256,"columnalign":21257,"columnspacing":1727},[21259,61423,61424,61434],{},[21262,61425,61426],{},[2919,61427,61428],{"scriptlevel":2058,"displaystyle":1915},[895,61429,61430,61432],{},[898,61431,1662],{},[898,61433,1703],{},[21262,61435,61436],{},[2919,61437,61438],{"scriptlevel":2058,"displaystyle":1915},[895,61439,61440,61442,61444,61446],{},[895,61441],{},[1664,61443,1676],{},[1963,61445,1965],{},[1664,61447,1916],{"separator":1915},[21259,61449,61450,61462],{},[21262,61451,61452],{},[2919,61453,61454],{"scriptlevel":2058,"displaystyle":1915},[895,61455,61456,61458,61460],{},[898,61457,1991],{},[898,61459,40839],{},[898,61461,1703],{},[21262,61463,61464],{},[2919,61465,61466],{"scriptlevel":2058,"displaystyle":1915},[895,61467,61468,61470,61472,61474,61476,61478,61480,61486,61488,61494],{},[895,61469],{},[1664,61471,1676],{},[1963,61473,5570],{},[898,61475,1973],{},[1664,61477,1867],{},[1963,61479,2826],{},[1720,61481,61482,61484],{},[898,61483,1973],{},[1963,61485,1970],{},[1664,61487,1700],{},[1720,61489,61490,61492],{},[898,61491,1973],{},[1963,61493,2774],{},[1664,61495,1916],{"separator":1915},[21259,61497,61498,61510],{},[21262,61499,61500],{},[2919,61501,61502],{"scriptlevel":2058,"displaystyle":1915},[895,61503,61504,61506,61508],{},[898,61505,4822],{},[898,61507,1662],{},[898,61509,1703],{},[21262,61511,61512],{},[2919,61513,61514],{"scriptlevel":2058,"displaystyle":1915},[895,61515,61516,61518,61520,61528],{},[895,61517],{},[1664,61519,1676],{},[2919,61521,61522],{"scriptlevel":2058,"displaystyle":1666},[2922,61523,61524,61526],{},[1963,61525,1965],{},[898,61527,1973],{},[1664,61529,1916],{"separator":1915},[21259,61531,61532,61544],{},[21262,61533,61534],{},[2919,61535,61536],{"scriptlevel":2058,"displaystyle":1915},[895,61537,61538,61540,61542],{},[898,61539,4822],{},[898,61541,40839],{},[898,61543,1703],{},[21262,61545,61546],{},[2919,61547,61548],{"scriptlevel":2058,"displaystyle":1915},[895,61549,61550,61552,61554,61556,61558,61560,61562,61564,61570],{},[895,61551],{},[1664,61553,1676],{},[1963,61555,5570],{},[1664,61557,1867],{},[1963,61559,2826],{},[898,61561,1973],{},[1664,61563,1700],{},[1720,61565,61566,61568],{},[898,61567,1973],{},[1963,61569,1970],{},[1664,61571,1916],{"separator":1915},[21259,61573,61574,61584],{},[21262,61575,61576],{},[2919,61577,61578],{"scriptlevel":2058,"displaystyle":1915},[895,61579,61580,61582],{},[898,61581,4822],{},[898,61583,1703],{},[21262,61585,61586],{},[2919,61587,61588],{"scriptlevel":2058,"displaystyle":1915},[895,61589,61590,61592,61594,61602,61604,61606,61608,61610,61612,61614,61620],{},[895,61591],{},[1664,61593,1676],{},[2919,61595,61596],{"scriptlevel":2058,"displaystyle":1666},[2922,61597,61598,61600],{},[1963,61599,1965],{},[898,61601,1973],{},[1664,61603,1700],{},[1963,61605,5570],{},[1664,61607,1867],{},[1963,61609,2826],{},[898,61611,1973],{},[1664,61613,1700],{},[1720,61615,61616,61618],{},[898,61617,1973],{},[1963,61619,1970],{},[1664,61621,1916],{"separator":1915},[21259,61623,61624,61634],{},[21262,61625,61626],{},[2919,61627,61628],{"scriptlevel":2058,"displaystyle":1915},[895,61629,61630,61632],{},[898,61631,1956],{},[898,61633,1703],{},[21262,61635,61636],{},[2919,61637,61638],{"scriptlevel":2058,"displaystyle":1915},[895,61639,61640,61642,61644,61646,61648,61650,61652,61654,61656,61662],{},[895,61641],{},[1664,61643,1676],{},[1963,61645,5570],{},[1664,61647,1867],{},[1963,61649,3442],{},[898,61651,1973],{},[1664,61653,1700],{},[1963,61655,2774],{},[1720,61657,61658,61660],{},[898,61659,1973],{},[1963,61661,1970],{},[898,61663,1977],{"mathvariant":1726},[902,61665,61666],{"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}",[724,61668,61669,61670,16291,61685,16291,61700,61715,61716,61731,61732,1343,61750,61731,61767,1343,61785,61731,61800,61818],{},"Význačné body ",[883,61671,61673],{"className":61672},[886],[888,61674,61675],{"xmlns":890},[892,61676,61677,61682],{},[895,61678,61679],{},[1963,61680,61681],{},"1,67",[902,61683,61684],{"encoding":904},"1{,}67",[883,61686,61688],{"className":61687},[886],[888,61689,61690],{"xmlns":890},[892,61691,61692,61697],{},[895,61693,61694],{},[1963,61695,61696],{},"2,50",[902,61698,61699],{"encoding":904},"2{,}50",[883,61701,61703],{"className":61702},[886],[888,61704,61705],{"xmlns":890},[892,61706,61707,61712],{},[895,61708,61709],{},[1963,61710,61711],{},"4,73",[902,61713,61714],{"encoding":904},"4{,}73"," odpovídají: ",[883,61717,61719],{"className":61718},[886],[888,61720,61721],{"xmlns":890},[892,61722,61723,61729],{},[895,61724,61725,61727],{},[898,61726,1956],{},[898,61728,1703],{},[902,61730,55792],{"encoding":904}," minimum v ",[883,61733,61735],{"className":61734},[886],[888,61736,61737],{"xmlns":890},[892,61738,61739,61747],{},[895,61740,61741,61743,61745],{},[898,61742,1973],{},[1664,61744,6466],{},[1963,61746,61681],{},[902,61748,61749],{"encoding":904},"Q \\doteq 1{,}67",[883,61751,61753],{"className":61752},[886],[888,61754,61755],{"xmlns":890},[892,61756,61757,61765],{},[895,61758,61759,61761,61763],{},[898,61760,4822],{},[898,61762,40839],{},[898,61764,1703],{},[902,61766,55811],{"encoding":904},[883,61768,61770],{"className":61769},[886],[888,61771,61772],{"xmlns":890},[892,61773,61774,61782],{},[895,61775,61776,61778,61780],{},[898,61777,1973],{},[1664,61779,1676],{},[1963,61781,61696],{},[902,61783,61784],{"encoding":904},"Q = 2{,}50",[883,61786,61788],{"className":61787},[886],[888,61789,61790],{"xmlns":890},[892,61791,61792,61798],{},[895,61793,61794,61796],{},[898,61795,4822],{},[898,61797,1703],{},[902,61799,56060],{"encoding":904},[883,61801,61803],{"className":61802},[886],[888,61804,61805],{"xmlns":890},[892,61806,61807,61815],{},[895,61808,61809,61811,61813],{},[898,61810,1973],{},[1664,61812,6466],{},[1963,61814,61711],{},[902,61816,61817],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,61820,61821],{},[1928,61822],{"alt":61823,"className":61824,"src":61825},"imek-ac-avc-mc",[210,1932],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,61827,61828],{},[614,61829,61830,61831,4454,61846,61863,61864,16291,61883,61898],{},"Obrázek 3.9: Kubické křivky ",[883,61832,61834],{"className":61833},[886],[888,61835,61836],{"xmlns":890},[892,61837,61838,61844],{},[895,61839,61840,61842],{},[898,61841,1991],{},[898,61843,1703],{},[902,61845,3819],{"encoding":904},[883,61847,61849],{"className":61848},[886],[888,61850,61851],{"xmlns":890},[892,61852,61853,61861],{},[895,61854,61855,61857,61859],{},[898,61856,1991],{},[898,61858,40839],{},[898,61860,1703],{},[902,61862,56009],{"encoding":904}," rostoucí od bodu ",[883,61865,61867],{"className":61866},[886],[888,61868,61869],{"xmlns":890},[892,61870,61871,61881],{},[895,61872,61873,61875,61877,61879],{},[898,61874,1662],{},[898,61876,1703],{},[1664,61878,1676],{},[1963,61880,1965],{},[902,61882,2180],{"encoding":904},[883,61884,61886],{"className":61885},[886],[888,61887,61888],{"xmlns":890},[892,61889,61890,61896],{},[895,61891,61892,61894],{},[898,61893,1662],{},[898,61895,1703],{},[902,61897,55991],{"encoding":904}," je vodorovná přímka.",[724,61900,61901],{},[614,61902,61903,61904,1343,61919,1343,61936,29701,61951,61964,61965,1748,61982,61997,61998,6756,62015,62030,62031,26689,62044,1343,62057,1343,62070,1977],{},"Obrázek 3.10: Křivky ",[883,61905,61907],{"className":61906},[886],[888,61908,61909],{"xmlns":890},[892,61910,61911,61917],{},[895,61912,61913,61915],{},[898,61914,4822],{},[898,61916,1703],{},[902,61918,56060],{"encoding":904},[883,61920,61922],{"className":61921},[886],[888,61923,61924],{"xmlns":890},[892,61925,61926,61934],{},[895,61927,61928,61930,61932],{},[898,61929,4822],{},[898,61931,40839],{},[898,61933,1703],{},[902,61935,55811],{"encoding":904},[883,61937,61939],{"className":61938},[886],[888,61940,61941],{"xmlns":890},[892,61942,61943,61949],{},[895,61944,61945,61947],{},[898,61946,1956],{},[898,61948,1703],{},[902,61950,55792],{"encoding":904},[883,61952,61954],{"className":61953},[886],[888,61955,61956],{"xmlns":890},[892,61957,61958,61962],{},[895,61959,61960],{},[898,61961,900],{},[902,61963,900],{"encoding":904}," a klesající hyperbola ",[883,61966,61968],{"className":61967},[886],[888,61969,61970],{"xmlns":890},[892,61971,61972,61980],{},[895,61973,61974,61976,61978],{},[898,61975,4822],{},[898,61977,1662],{},[898,61979,1703],{},[902,61981,56027],{"encoding":904},[883,61983,61985],{"className":61984},[886],[888,61986,61987],{"xmlns":890},[892,61988,61989,61995],{},[895,61990,61991,61993],{},[898,61992,1956],{},[898,61994,1703],{},[902,61996,55792],{"encoding":904}," protíná ",[883,61999,62001],{"className":62000},[886],[888,62002,62003],{"xmlns":890},[892,62004,62005,62013],{},[895,62006,62007,62009,62011],{},[898,62008,4822],{},[898,62010,40839],{},[898,62012,1703],{},[902,62014,55811],{"encoding":904},[883,62016,62018],{"className":62017},[886],[888,62019,62020],{"xmlns":890},[892,62021,62022,62028],{},[895,62023,62024,62026],{},[898,62025,4822],{},[898,62027,1703],{},[902,62029,56060],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,62032,62034],{"className":62033},[886],[888,62035,62036],{"xmlns":890},[892,62037,62038,62042],{},[895,62039,62040],{},[898,62041,1973],{},[902,62043,1973],{"encoding":904},[883,62045,62047],{"className":62046},[886],[888,62048,62049],{"xmlns":890},[892,62050,62051,62055],{},[895,62052,62053],{},[1963,62054,61681],{},[902,62056,61684],{"encoding":904},[883,62058,62060],{"className":62059},[886],[888,62061,62062],{"xmlns":890},[892,62063,62064,62068],{},[895,62065,62066],{},[1963,62067,61696],{},[902,62069,61699],{"encoding":904},[883,62071,62073],{"className":62072},[886],[888,62074,62075],{"xmlns":890},[892,62076,62077,62081],{},[895,62078,62079],{},[1963,62080,61711],{},[902,62082,61714],{"encoding":904},[724,62084,62085],{},[38,62086,62087],{},"Standardní vlastnosti:",[120,62089,62090,62125,62189,62257,62307,62327],{},[123,62091,62092,4454,62107,62124],{},[883,62093,62095],{"className":62094},[886],[888,62096,62097],{"xmlns":890},[892,62098,62099,62105],{},[895,62100,62101,62103],{},[898,62102,1991],{},[898,62104,1703],{},[902,62106,3819],{"encoding":904},[883,62108,62110],{"className":62109},[886],[888,62111,62112],{"xmlns":890},[892,62113,62114,62122],{},[895,62115,62116,62118,62120],{},[898,62117,1991],{},[898,62119,40839],{},[898,62121,1703],{},[902,62123,56009],{"encoding":904}," jsou kubické funkce;",[123,62126,62127,1343,62142,1343,62159,62174,62175,62188],{},[883,62128,62130],{"className":62129},[886],[888,62131,62132],{"xmlns":890},[892,62133,62134,62140],{},[895,62135,62136,62138],{},[898,62137,4822],{},[898,62139,1703],{},[902,62141,56060],{"encoding":904},[883,62143,62145],{"className":62144},[886],[888,62146,62147],{"xmlns":890},[892,62148,62149,62157],{},[895,62150,62151,62153,62155],{},[898,62152,4822],{},[898,62154,40839],{},[898,62156,1703],{},[902,62158,55811],{"encoding":904},[883,62160,62162],{"className":62161},[886],[888,62163,62164],{"xmlns":890},[892,62165,62166,62172],{},[895,62167,62168,62170],{},[898,62169,1956],{},[898,62171,1703],{},[902,62173,55792],{"encoding":904}," jsou křivky tvaru ",[883,62176,62178],{"className":62177},[886],[888,62179,62180],{"xmlns":890},[892,62181,62182,62186],{},[895,62183,62184],{},[898,62185,900],{},[902,62187,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,62190,62191,62206,62207,1343,62224,62241,62242,8990],{},[883,62192,62194],{"className":62193},[886],[888,62195,62196],{"xmlns":890},[892,62197,62198,62204],{},[895,62199,62200,62202],{},[898,62201,1956],{},[898,62203,1703],{},[902,62205,55792],{"encoding":904}," nabývá minima před ",[883,62208,62210],{"className":62209},[886],[888,62211,62212],{"xmlns":890},[892,62213,62214,62222],{},[895,62215,62216,62218,62220],{},[898,62217,4822],{},[898,62219,40839],{},[898,62221,1703],{},[902,62223,55811],{"encoding":904},[883,62225,62227],{"className":62226},[886],[888,62228,62229],{"xmlns":890},[892,62230,62231,62239],{},[895,62232,62233,62235,62237],{},[898,62234,4822],{},[898,62236,40839],{},[898,62238,1703],{},[902,62240,55811],{"encoding":904}," před ",[883,62243,62245],{"className":62244},[886],[888,62246,62247],{"xmlns":890},[892,62248,62249,62255],{},[895,62250,62251,62253],{},[898,62252,4822],{},[898,62254,1703],{},[902,62256,56060],{"encoding":904},[123,62258,62259,61997,62274,4454,62289,62306],{},[883,62260,62262],{"className":62261},[886],[888,62263,62264],{"xmlns":890},[892,62265,62266,62272],{},[895,62267,62268,62270],{},[898,62269,1956],{},[898,62271,1703],{},[902,62273,55792],{"encoding":904},[883,62275,62277],{"className":62276},[886],[888,62278,62279],{"xmlns":890},[892,62280,62281,62287],{},[895,62282,62283,62285],{},[898,62284,4822],{},[898,62286,1703],{},[902,62288,56060],{"encoding":904},[883,62290,62292],{"className":62291},[886],[888,62293,62294],{"xmlns":890},[892,62295,62296,62304],{},[895,62297,62298,62300,62302],{},[898,62299,4822],{},[898,62301,40839],{},[898,62303,1703],{},[902,62305,55811],{"encoding":904}," zdola právě v jejich minimech;",[123,62308,62309,62326],{},[883,62310,62312],{"className":62311},[886],[888,62313,62314],{"xmlns":890},[892,62315,62316,62324],{},[895,62317,62318,62320,62322],{},[898,62319,4822],{},[898,62321,1662],{},[898,62323,1703],{},[902,62325,56027],{"encoding":904}," je hyperbola, stále klesající;",[123,62328,62329,62361,62362,4454,62377,62394,62395,62408,62409,4488],{},[883,62330,62332],{"className":62331},[886],[888,62333,62334],{"xmlns":890},[892,62335,62336,62358],{},[895,62337,62338,62340,62342,62344,62346,62348,62350,62352,62354,62356],{},[898,62339,4822],{},[898,62341,1703],{},[1664,62343,1676],{},[898,62345,4822],{},[898,62347,1662],{},[898,62349,1703],{},[1664,62351,1700],{},[898,62353,4822],{},[898,62355,40839],{},[898,62357,1703],{},[902,62359,62360],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,62363,62365],{"className":62364},[886],[888,62366,62367],{"xmlns":890},[892,62368,62369,62375],{},[895,62370,62371,62373],{},[898,62372,4822],{},[898,62374,1703],{},[902,62376,56060],{"encoding":904},[883,62378,62380],{"className":62379},[886],[888,62381,62382],{"xmlns":890},[892,62383,62384,62392],{},[895,62385,62386,62388,62390],{},[898,62387,4822],{},[898,62389,40839],{},[898,62391,1703],{},[902,62393,55811],{"encoding":904}," klesá s rostoucím ",[883,62396,62398],{"className":62397},[886],[888,62399,62400],{"xmlns":890},[892,62401,62402,62406],{},[895,62403,62404],{},[898,62405,1973],{},[902,62407,1973],{"encoding":904}," (protože ",[883,62410,62412],{"className":62411},[886],[888,62413,62414],{"xmlns":890},[892,62415,62416,62428],{},[895,62417,62418,62420,62422,62424,62426],{},[898,62419,4822],{},[898,62421,1662],{},[898,62423,1703],{},[1664,62425,3699],{},[1963,62427,2058],{},[902,62429,62430],{"encoding":904},"AFC \\to 0",[115,62432,62434],{"id":62433},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,62436,62437,62438,62441,62442,62457],{},"Častou optimalizační úlohou je ",[38,62439,62440],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,62443,62445],{"className":62444},[886],[888,62446,62447],{"xmlns":890},[892,62448,62449,62455],{},[895,62450,62451,62453],{},[898,62452,4822],{},[898,62454,1703],{},[902,62456,56060],{"encoding":904}," minimální.",[198,62459,16912],{"id":16911},[724,62461,62462,62463,62480],{},"Mají-li průměrné náklady minimum v bodě ",[883,62464,62466],{"className":62465},[886],[888,62467,62468],{"xmlns":890},[892,62469,62470,62478],{},[895,62471,62472],{},[2355,62473,62474,62476],{},[898,62475,1973],{},[1963,62477,2058],{},[902,62479,38808],{"encoding":904},", pak platí",[883,62482,62484],{"className":62483},[886],[888,62485,62486],{"xmlns":890,"display":28566},[892,62487,62488,62537],{},[21254,62489,62490],{"width":28571},[21259,62491,62492,62494,62530,62532],{},[21262,62493],{"width":28576},[21262,62495,62496],{},[895,62497,62498,62500,62502,62504,62510,62512,62514,62516,62518,62520,62526,62528],{},[898,62499,4822],{},[898,62501,1703],{},[1664,62503,1667],{"stretchy":1666},[2355,62505,62506,62508],{},[898,62507,1973],{},[1963,62509,2058],{},[1664,62511,1673],{"stretchy":1666},[1664,62513,1676],{},[898,62515,1956],{},[898,62517,1703],{},[1664,62519,1667],{"stretchy":1666},[2355,62521,62522,62524],{},[898,62523,1973],{},[1963,62525,2058],{},[1664,62527,1673],{"stretchy":1666},[898,62529,1977],{"mathvariant":1726},[21262,62531],{"width":28576},[21262,62533,62534],{},[1690,62535,62536],{},"(3.10)",[902,62538,62539],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[4436,62541,62542],{},[724,62543,62544,62546,62547],{},[883,62545,56944],{}," Princip\n",[38,62548,62549],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,62551,62552,62555,62556,62598],{},[38,62553,62554],{},"Odvození."," Z ",[883,62557,62559],{"className":62558},[886],[888,62560,62561],{"xmlns":890},[892,62562,62563,62595],{},[895,62564,62565,62567,62569,62571,62573,62575,62577],{},[898,62566,4822],{},[898,62568,1703],{},[1664,62570,1667],{"stretchy":1666},[898,62572,1973],{},[1664,62574,1673],{"stretchy":1666},[1664,62576,1676],{},[2919,62578,62579],{"scriptlevel":2058,"displaystyle":1666},[2922,62580,62581,62593],{},[895,62582,62583,62585,62587,62589,62591],{},[898,62584,1991],{},[898,62586,1703],{},[1664,62588,1667],{"stretchy":1666},[898,62590,1973],{},[1664,62592,1673],{"stretchy":1666},[898,62594,1973],{},[902,62596,62597],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,62600,62602],{"className":62601},[886],[888,62603,62604],{"xmlns":890,"display":28566},[892,62605,62606,62738],{},[895,62607,62608,62610,62616,62618,62620,62622,62624,62664,62666,62706,62708,62736],{},[898,62609,4822],{},[1720,62611,62612,62614],{},[898,62613,1703],{},[1664,62615,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,62617,1667],{"stretchy":1666},[898,62619,1973],{},[1664,62621,1673],{"stretchy":1666},[1664,62623,1676],{},[2922,62625,62626,62658],{},[895,62627,62628,62630,62636,62638,62640,62642,62644,62646,62648,62650,62652,62654,62656],{},[898,62629,1991],{},[1720,62631,62632,62634],{},[898,62633,1703],{},[1664,62635,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,62637,1667],{"stretchy":1666},[898,62639,1973],{},[1664,62641,1673],{"stretchy":1666},[1664,62643,3753],{},[898,62645,1973],{},[1664,62647,1867],{},[898,62649,1991],{},[898,62651,1703],{},[1664,62653,1667],{"stretchy":1666},[898,62655,1973],{},[1664,62657,1673],{"stretchy":1666},[1720,62659,62660,62662],{},[898,62661,1973],{},[1963,62663,1970],{},[1664,62665,1676],{},[2922,62667,62668,62700],{},[895,62669,62670,62672,62674,62676,62678,62680,62682,62684,62686,62688,62690,62692,62694,62696,62698],{},[898,62671,1956],{},[898,62673,1703],{},[1664,62675,1667],{"stretchy":1666},[898,62677,1973],{},[1664,62679,1673],{"stretchy":1666},[1664,62681,3753],{},[898,62683,1973],{},[1664,62685,1867],{},[898,62687,4822],{},[898,62689,1703],{},[1664,62691,1667],{"stretchy":1666},[898,62693,1973],{},[1664,62695,1673],{"stretchy":1666},[1664,62697,3753],{},[898,62699,1973],{},[1720,62701,62702,62704],{},[898,62703,1973],{},[1963,62705,1970],{},[1664,62707,1676],{},[2922,62709,62710,62734],{},[895,62711,62712,62714,62716,62718,62720,62722,62724,62726,62728,62730,62732],{},[898,62713,1956],{},[898,62715,1703],{},[1664,62717,1667],{"stretchy":1666},[898,62719,1973],{},[1664,62721,1673],{"stretchy":1666},[1664,62723,1867],{},[898,62725,4822],{},[898,62727,1703],{},[1664,62729,1667],{"stretchy":1666},[898,62731,1973],{},[1664,62733,1673],{"stretchy":1666},[898,62735,1973],{},[898,62737,1977],{"mathvariant":1726},[902,62739,62740],{"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}.",[724,62742,62743,62744,3210,62759,1762,62781,57321],{},"Nutnou podmínkou minima ",[883,62745,62747],{"className":62746},[886],[888,62748,62749],{"xmlns":890},[892,62750,62751,62757],{},[895,62752,62753,62755],{},[898,62754,4822],{},[898,62756,1703],{},[902,62758,56060],{"encoding":904},[883,62760,62762],{"className":62761},[886],[888,62763,62764],{"xmlns":890},[892,62765,62766,62778],{},[895,62767,62768,62774,62776],{},[2355,62769,62770,62772],{},[898,62771,1973],{},[1963,62773,2058],{},[1664,62775,3984],{},[1963,62777,2058],{},[902,62779,62780],{"encoding":904},"Q_0 > 0",[883,62782,62784],{"className":62783},[886],[888,62785,62786],{"xmlns":890},[892,62787,62788,62812],{},[895,62789,62790,62792,62798,62800,62806,62808,62810],{},[898,62791,4822],{},[1720,62793,62794,62796],{},[898,62795,1703],{},[1664,62797,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,62799,1667],{"stretchy":1666},[2355,62801,62802,62804],{},[898,62803,1973],{},[1963,62805,2058],{},[1664,62807,1673],{"stretchy":1666},[1664,62809,1676],{},[1963,62811,2058],{},[902,62813,62814],{"encoding":904},"AC'(Q_0) = 0",[883,62816,62818],{"className":62817},[886],[888,62819,62820],{"xmlns":890,"display":28566},[892,62821,62822,62907],{},[895,62823,62824,62864,62866,62868,62870,62873,62875,62877,62879,62881,62887,62889,62891,62893,62895,62897,62903,62905],{},[2922,62825,62826,62858],{},[895,62827,62828,62830,62832,62834,62840,62842,62844,62846,62848,62850,62856],{},[898,62829,1956],{},[898,62831,1703],{},[1664,62833,1667],{"stretchy":1666},[2355,62835,62836,62838],{},[898,62837,1973],{},[1963,62839,2058],{},[1664,62841,1673],{"stretchy":1666},[1664,62843,1867],{},[898,62845,4822],{},[898,62847,1703],{},[1664,62849,1667],{"stretchy":1666},[2355,62851,62852,62854],{},[898,62853,1973],{},[1963,62855,2058],{},[1664,62857,1673],{"stretchy":1666},[2355,62859,62860,62862],{},[898,62861,1973],{},[1963,62863,2058],{},[1664,62865,1676],{},[1963,62867,2058],{},[6444,62869],{"width":15783},[1664,62871,62872],{},"⟺",[6444,62874],{"width":15783},[898,62876,1956],{},[898,62878,1703],{},[1664,62880,1667],{"stretchy":1666},[2355,62882,62883,62885],{},[898,62884,1973],{},[1963,62886,2058],{},[1664,62888,1673],{"stretchy":1666},[1664,62890,1676],{},[898,62892,4822],{},[898,62894,1703],{},[1664,62896,1667],{"stretchy":1666},[2355,62898,62899,62901],{},[898,62900,1973],{},[1963,62902,2058],{},[1664,62904,1673],{"stretchy":1666},[898,62906,1977],{"mathvariant":1726},[902,62908,62909],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,62911,62912,1885,62915,61997,62930,62945,62946,62961,62962,1762,62979,63001,63002,63024],{},[38,62913,62914],{},"Geometrická interpretace.",[883,62916,62918],{"className":62917},[886],[888,62919,62920],{"xmlns":890},[892,62921,62922,62928],{},[895,62923,62924,62926],{},[898,62925,1956],{},[898,62927,1703],{},[902,62929,55792],{"encoding":904},[883,62931,62933],{"className":62932},[886],[888,62934,62935],{"xmlns":890},[892,62936,62937,62943],{},[895,62938,62939,62941],{},[898,62940,4822],{},[898,62942,1703],{},[902,62944,56060],{"encoding":904}," právě v bodě minima ",[883,62947,62949],{"className":62948},[886],[888,62950,62951],{"xmlns":890},[892,62952,62953,62959],{},[895,62954,62955,62957],{},[898,62956,4822],{},[898,62958,1703],{},[902,62960,56060],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,62963,62965],{"className":62964},[886],[888,62966,62967],{"xmlns":890},[892,62968,62969,62977],{},[895,62970,62971],{},[2355,62972,62973,62975],{},[898,62974,1973],{},[1963,62976,2058],{},[902,62978,38808],{"encoding":904},[883,62980,62982],{"className":62981},[886],[888,62983,62984],{"xmlns":890},[892,62985,62986,62998],{},[895,62987,62988,62990,62992,62994,62996],{},[898,62989,1956],{},[898,62991,1703],{},[1664,62993,4022],{},[898,62995,4822],{},[898,62997,1703],{},[902,62999,63000],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,63003,63005],{"className":63004},[886],[888,63006,63007],{"xmlns":890},[892,63008,63009,63021],{},[895,63010,63011,63013,63015,63017,63019],{},[898,63012,1956],{},[898,63014,1703],{},[1664,63016,3984],{},[898,63018,4822],{},[898,63020,1703],{},[902,63022,63023],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,63026,63027,63028,63070,63071,63088,63089,1977],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,63029,63031],{"className":63030},[886],[888,63032,63033],{"xmlns":890},[892,63034,63035,63067],{},[895,63036,63037,63039,63041,63043,63049,63051,63053,63055,63057,63059,63065],{},[898,63038,4822],{},[898,63040,1703],{},[1664,63042,1667],{"stretchy":1666},[2355,63044,63045,63047],{},[898,63046,1973],{},[1963,63048,2058],{},[1664,63050,1673],{"stretchy":1666},[1664,63052,1676],{},[898,63054,1956],{},[898,63056,1703],{},[1664,63058,1667],{"stretchy":1666},[2355,63060,63061,63063],{},[898,63062,1973],{},[1963,63064,2058],{},[1664,63066,1673],{"stretchy":1666},[902,63068,63069],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,63072,63074],{"className":63073},[886],[888,63075,63076],{"xmlns":890},[892,63077,63078,63086],{},[895,63079,63080],{},[2355,63081,63082,63084],{},[898,63083,1973],{},[1963,63085,2058],{},[902,63087,38808],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,63090,63092],{"className":63091},[886],[888,63093,63094],{"xmlns":890},[892,63095,63096,63120],{},[895,63097,63098,63100,63102,63104,63106,63108,63110,63112,63114,63116,63118],{},[898,63099,4822],{},[898,63101,1703],{},[1664,63103,1667],{"stretchy":1666},[898,63105,1973],{},[1664,63107,1673],{"stretchy":1666},[1664,63109,1676],{},[898,63111,1956],{},[898,63113,1703],{},[1664,63115,1667],{"stretchy":1666},[898,63117,1973],{},[1664,63119,1673],{"stretchy":1666},[902,63121,63122],{"encoding":904},"AC(Q) = MC(Q)",[4436,63124,63125],{},[724,63126,63127,63129,63130,10957,63148,63169,63170,10957,63173,63194,63195,63210,63211,58538,63226,4488],{},[883,63128,4978],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,63131,63132,63133],{},"minimum ",[883,63134,63136],{"className":63135},[886],[888,63137,63138],{"xmlns":890},[892,63139,63140,63146],{},[895,63141,63142,63144],{},[898,63143,4822],{},[898,63145,1703],{},[902,63147,56060],{"encoding":904},[883,63149,63151],{"className":63150},[886],[888,63152,63153],{"xmlns":890},[892,63154,63155,63167],{},[895,63156,63157,63159,63161,63163,63165],{},[898,63158,4822],{},[898,63160,1703],{},[1664,63162,1676],{},[898,63164,1956],{},[898,63166,1703],{},[902,63168,55723],{"encoding":904},", pro ",[38,63171,63172],{},"maximum zisku",[883,63174,63176],{"className":63175},[886],[888,63177,63178],{"xmlns":890},[892,63179,63180,63192],{},[895,63181,63182,63184,63186,63188,63190],{},[898,63183,1956],{},[898,63185,1959],{},[1664,63187,1676],{},[898,63189,1956],{},[898,63191,1703],{},[902,63193,55771],{"encoding":904},". Obě podmínky využívají ",[883,63196,63198],{"className":63197},[886],[888,63199,63200],{"xmlns":890},[892,63201,63202,63208],{},[895,63203,63204,63206],{},[898,63205,1956],{},[898,63207,1703],{},[902,63209,55792],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,63212,63214],{"className":63213},[886],[888,63215,63216],{"xmlns":890},[892,63217,63218,63224],{},[895,63219,63220,63222],{},[898,63221,4822],{},[898,63223,1703],{},[902,63225,56060],{"encoding":904},[883,63227,63229],{"className":63228},[886],[888,63230,63231],{"xmlns":890},[892,63232,63233,63239],{},[895,63234,63235,63237],{},[898,63236,1956],{},[898,63238,1959],{},[902,63240,7200],{"encoding":904},[37848,63242,63244],{"id":63243},"příklad-37","Příklad 3.7",[724,63246,63247,58022,63249,63283,63284,63297,63298,63313],{},[38,63248,56487],{},[883,63250,63252],{"className":63251},[886],[888,63253,63254],{"xmlns":890},[892,63255,63256,63280],{},[895,63257,63258,63260,63262,63264,63270,63272,63274,63276,63278],{},[898,63259,1991],{},[898,63261,1703],{},[1664,63263,1676],{},[1720,63265,63266,63268],{},[898,63267,1973],{},[1963,63269,1970],{},[1664,63271,1700],{},[1963,63273,2774],{},[898,63275,1973],{},[1664,63277,1700],{},[1963,63279,6131],{},[902,63281,63282],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,63285,63287],{"className":63286},[886],[888,63288,63289],{"xmlns":890},[892,63290,63291,63295],{},[895,63292,63293],{},[898,63294,1973],{},[902,63296,1973],{"encoding":904}," minimalizující ",[883,63299,63301],{"className":63300},[886],[888,63302,63303],{"xmlns":890},[892,63304,63305,63311],{},[895,63306,63307,63309],{},[898,63308,4822],{},[898,63310,1703],{},[902,63312,56060],{"encoding":904}," a ověřte princip (3.10).",[724,63315,63316,63318],{},[38,63317,23270],{}," Přímý výpočet:",[883,63320,63322],{"className":63321},[886],[888,63323,63324],{"xmlns":890,"display":28566},[892,63325,63326,63428],{},[895,63327,63328,63330,63332,63334,63356,63358,63360,63362,63364,63366,63372,63374,63376,63378,63380,63382,63388,63390,63392,63394,63404,63406,63426],{},[898,63329,4822],{},[898,63331,1703],{},[1664,63333,1676],{},[2922,63335,63336,63354],{},[895,63337,63338,63344,63346,63348,63350,63352],{},[1720,63339,63340,63342],{},[898,63341,1973],{},[1963,63343,1970],{},[1664,63345,1700],{},[1963,63347,2774],{},[898,63349,1973],{},[1664,63351,1700],{},[1963,63353,6131],{},[898,63355,1973],{},[1664,63357,1676],{},[898,63359,1973],{},[1664,63361,1700],{},[1963,63363,2774],{},[1664,63365,1700],{},[2922,63367,63368,63370],{},[1963,63369,6131],{},[898,63371,1973],{},[1664,63373,1916],{"separator":1915},[6444,63375],{"width":6446},[1664,63377,1667],{"stretchy":1666},[898,63379,4822],{},[898,63381,1703],{},[1720,63383,63384,63386],{},[1664,63385,1673],{"stretchy":1666},[1664,63387,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,63389,1676],{},[1963,63391,2875],{},[1664,63393,1867],{},[2922,63395,63396,63398],{},[1963,63397,6131],{},[1720,63399,63400,63402],{},[898,63401,1973],{},[1963,63403,1970],{},[1664,63405,1676],{},[2922,63407,63408,63420],{},[895,63409,63410,63416,63418],{},[1720,63411,63412,63414],{},[898,63413,1973],{},[1963,63415,1970],{},[1664,63417,1867],{},[1963,63419,6131],{},[1720,63421,63422,63424],{},[898,63423,1973],{},[1963,63425,1970],{},[898,63427,1977],{"mathvariant":1726},[902,63429,63430],{"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}.",[724,63432,63433,63473,63474,63498,63499,63549,63550,1977],{},[883,63434,63436],{"className":63435},[886],[888,63437,63438],{"xmlns":890},[892,63439,63440,63470],{},[895,63441,63442,63444,63446,63448,63454,63456,63458,63460,63466,63468],{},[1664,63443,1667],{"stretchy":1666},[898,63445,4822],{},[898,63447,1703],{},[1720,63449,63450,63452],{},[1664,63451,1673],{"stretchy":1666},[1664,63453,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,63455,1676],{},[1963,63457,2058],{},[1664,63459,4556],{},[2355,63461,63462,63464],{},[898,63463,1973],{},[1963,63465,2875],{},[1664,63467,1676],{},[1963,63469,2833],{},[902,63471,63472],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,63475,63477],{"className":63476},[886],[888,63478,63479],{"xmlns":890},[892,63480,63481,63495],{},[895,63482,63483,63489,63491,63493],{},[2355,63484,63485,63487],{},[898,63486,1973],{},[1963,63488,1970],{},[1664,63490,1676],{},[1664,63492,1867],{},[1963,63494,2833],{},[902,63496,63497],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,63500,63502],{"className":63501},[886],[888,63503,63504],{"xmlns":890},[892,63505,63506,63546],{},[895,63507,63508,63510,63512,63514,63524,63526,63528,63530,63532,63540,63542,63544],{},[1664,63509,1667],{"stretchy":1666},[898,63511,4822],{},[898,63513,1703],{},[1720,63515,63516,63518],{},[1664,63517,1673],{"stretchy":1666},[895,63519,63520,63522],{},[1664,63521,1728],{"mathvariant":1726},[1664,63523,1728],{"mathvariant":1726},[1664,63525,1667],{"stretchy":1666},[1963,63527,2833],{},[1664,63529,1673],{"stretchy":1666},[1664,63531,1676],{},[2919,63533,63534],{"scriptlevel":2058,"displaystyle":1666},[2922,63535,63536,63538],{},[1963,63537,2875],{},[1963,63539,2774],{},[1664,63541,3984],{},[1963,63543,2058],{},[1664,63545,4556],{},[902,63547,63548],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,63551,63553],{"className":63552},[886],[888,63554,63555],{"xmlns":890},[892,63556,63557,63573],{},[895,63558,63559,63561,63563,63565,63567,63569,63571],{},[898,63560,4822],{},[898,63562,1703],{},[1664,63564,1667],{"stretchy":1666},[1963,63566,2833],{},[1664,63568,1673],{"stretchy":1666},[1664,63570,1676],{},[1963,63572,36744],{},[902,63574,63575],{"encoding":904},"AC(6) = 15",[724,63577,63578,63579,63605,63606,2087],{},"Pomocí principu: ",[883,63580,63582],{"className":63581},[886],[888,63583,63584],{"xmlns":890},[892,63585,63586,63602],{},[895,63587,63588,63590,63592,63594,63596,63598,63600],{},[898,63589,1956],{},[898,63591,1703],{},[1664,63593,1676],{},[1963,63595,1970],{},[898,63597,1973],{},[1664,63599,1700],{},[1963,63601,2774],{},[902,63603,63604],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,63607,63609],{"className":63608},[886],[888,63610,63611],{"xmlns":890},[892,63612,63613,63625],{},[895,63614,63615,63617,63619,63621,63623],{},[898,63616,4822],{},[898,63618,1703],{},[1664,63620,1676],{},[898,63622,1956],{},[898,63624,1703],{},[902,63626,55723],{"encoding":904},[883,63628,63630],{"className":63629},[886],[888,63631,63632],{"xmlns":890,"display":28566},[892,63633,63634,63736],{},[895,63635,63636,63658,63660,63662,63664,63666,63668,63670,63672,63674,63680,63682,63684,63686,63688,63690,63692,63694,63700,63702,63704,63706,63708,63710,63712,63718,63720,63722,63724,63726,63728,63730,63732,63734],{},[2922,63637,63638,63656],{},[895,63639,63640,63646,63648,63650,63652,63654],{},[1720,63641,63642,63644],{},[898,63643,1973],{},[1963,63645,1970],{},[1664,63647,1700],{},[1963,63649,2774],{},[898,63651,1973],{},[1664,63653,1700],{},[1963,63655,6131],{},[898,63657,1973],{},[1664,63659,1676],{},[1963,63661,1970],{},[898,63663,1973],{},[1664,63665,1700],{},[1963,63667,2774],{},[1690,63669,4553],{},[1664,63671,4556],{},[1690,63673,4553],{},[1720,63675,63676,63678],{},[898,63677,1973],{},[1963,63679,1970],{},[1664,63681,1700],{},[1963,63683,2774],{},[898,63685,1973],{},[1664,63687,1700],{},[1963,63689,6131],{},[1664,63691,1676],{},[1963,63693,1970],{},[1720,63695,63696,63698],{},[898,63697,1973],{},[1963,63699,1970],{},[1664,63701,1700],{},[1963,63703,2774],{},[898,63705,1973],{},[1690,63707,4553],{},[1664,63709,4556],{},[1690,63711,4553],{},[1720,63713,63714,63716],{},[898,63715,1973],{},[1963,63717,1970],{},[1664,63719,1676],{},[1963,63721,6131],{},[1690,63723,4553],{},[1664,63725,4556],{},[1690,63727,4553],{},[898,63729,1973],{},[1664,63731,1676],{},[1963,63733,2833],{},[1664,63735,1916],{"separator":1915},[902,63737,63738],{"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,",[724,63740,63741,63742,63780],{},"a ",[883,63743,63745],{"className":63744},[886],[888,63746,63747],{"xmlns":890},[892,63748,63749,63777],{},[895,63750,63751,63753,63755,63757,63759,63761,63763,63765,63767,63769,63771,63773,63775],{},[898,63752,4822],{},[898,63754,1703],{},[1664,63756,1667],{"stretchy":1666},[1963,63758,2833],{},[1664,63760,1673],{"stretchy":1666},[1664,63762,1676],{},[898,63764,1956],{},[898,63766,1703],{},[1664,63768,1667],{"stretchy":1666},[1963,63770,2833],{},[1664,63772,1673],{"stretchy":1666},[1664,63774,1676],{},[1963,63776,36744],{},[902,63778,63779],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,63782,63784],{"id":63783},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,63786,63787,63788,2087],{},"Analogicky pro ",[883,63789,63791],{"className":63790},[886],[888,63792,63793],{"xmlns":890},[892,63794,63795,63803],{},[895,63796,63797,63799,63801],{},[898,63798,4822],{},[898,63800,40839],{},[898,63802,1703],{},[902,63804,55811],{"encoding":904},[883,63806,63808],{"className":63807},[886],[888,63809,63810],{"xmlns":890,"display":28566},[892,63811,63812,63863],{},[21254,63813,63814],{"width":28571},[21259,63815,63816,63818,63856,63858],{},[21262,63817],{"width":28576},[21262,63819,63820],{},[895,63821,63822,63824,63826,63828,63830,63836,63838,63840,63842,63844,63846,63852,63854],{},[898,63823,4822],{},[898,63825,40839],{},[898,63827,1703],{},[1664,63829,1667],{"stretchy":1666},[2355,63831,63832,63834],{},[898,63833,1973],{},[1963,63835,2058],{},[1664,63837,1673],{"stretchy":1666},[1664,63839,1676],{},[898,63841,1956],{},[898,63843,1703],{},[1664,63845,1667],{"stretchy":1666},[2355,63847,63848,63850],{},[898,63849,1973],{},[1963,63851,2058],{},[1664,63853,1673],{"stretchy":1666},[898,63855,1977],{"mathvariant":1726},[21262,63857],{"width":28576},[21262,63859,63860],{},[1690,63861,63862],{},"(3.11)",[902,63864,63865],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[4436,63867,63868],{},[724,63869,63870,62546,63872],{},[883,63871,56944],{},[38,63873,63874,63875,63892],{},"V bodě minima průměrných variabilních nákladů se ",[883,63876,63878],{"className":63877},[886],[888,63879,63880],{"xmlns":890},[892,63881,63882,63890],{},[895,63883,63884,63886,63888],{},[898,63885,4822],{},[898,63887,40839],{},[898,63889,1703],{},[902,63891,55811],{"encoding":904}," rovnají mezním nákladům.",[724,63894,63895,63896,63918,63919,1977],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,63897,63899],{"className":63898},[886],[888,63900,63901],{"xmlns":890},[892,63902,63903,63915],{},[895,63904,63905,63911,63913],{},[2355,63906,63907,63909],{},[898,63908,1973],{},[1963,63910,2058],{},[1664,63912,1676],{},[1963,63914,53699],{},[902,63916,63917],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,63920,63922],{"className":63921},[886],[888,63923,63924],{"xmlns":890},[892,63925,63926,63952],{},[895,63927,63928,63930,63932,63934,63936,63938,63940,63942,63944,63946,63948,63950],{},[898,63929,4822],{},[898,63931,40839],{},[898,63933,1703],{},[1664,63935,1667],{"stretchy":1666},[898,63937,1973],{},[1664,63939,1673],{"stretchy":1666},[1664,63941,1676],{},[898,63943,1956],{},[898,63945,1703],{},[1664,63947,1667],{"stretchy":1666},[898,63949,1973],{},[1664,63951,1673],{"stretchy":1666},[902,63953,63954],{"encoding":904},"AVC(Q) = MC(Q)",[115,63956,63958],{"id":63957},"zisk-a-body-zvratu","Zisk a body zvratu",[724,63960,63961,1885,63964,63980],{},[38,63962,63963],{},"Zisk",[883,63965,63967],{"className":63966},[886],[888,63968,63969],{"xmlns":890},[892,63970,63971,63977],{},[895,63972,63973,63975],{},[898,63974,2398],{},[898,63976,1959],{},[902,63978,63979],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,63982,63984],{"className":63983},[886],[888,63985,63986],{"xmlns":890,"display":28566},[892,63987,63988,64047],{},[21254,63989,63990],{"width":28571},[21259,63991,63992,63994,64040,64042],{},[21262,63993],{"width":28576},[21262,63995,63996],{},[895,63997,63998,64000,64002,64004,64006,64008,64010,64012,64014,64016,64018,64020,64022,64024,64026,64028,64030,64032,64034,64036,64038],{},[898,63999,2398],{},[898,64001,1959],{},[1664,64003,1676],{},[898,64005,2398],{},[898,64007,1959],{},[1664,64009,1667],{"stretchy":1666},[898,64011,1973],{},[1664,64013,1673],{"stretchy":1666},[1664,64015,1676],{},[898,64017,1991],{},[898,64019,1959],{},[1664,64021,1667],{"stretchy":1666},[898,64023,1973],{},[1664,64025,1673],{"stretchy":1666},[1664,64027,1867],{},[898,64029,1991],{},[898,64031,1703],{},[1664,64033,1667],{"stretchy":1666},[898,64035,1973],{},[1664,64037,1673],{"stretchy":1666},[898,64039,1977],{"mathvariant":1726},[21262,64041],{"width":28576},[21262,64043,64044],{},[1690,64045,64046],{},"(3.12)",[902,64048,64049],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,64051,64052,64053,4454,64068,44136,64083,64085,64086,64089,64090,64106,64107,64122,64123,64138,64139,1343,64152,64165,64166,1343,64184,64202,64203,10588,64206,64209,64210,1348,64232,1762,64254,64276,64277,1762,64307,64329],{},"Body rovnosti ",[883,64054,64056],{"className":64055},[886],[888,64057,64058],{"xmlns":890},[892,64059,64060,64066],{},[895,64061,64062,64064],{},[898,64063,1991],{},[898,64065,1959],{},[902,64067,4662],{"encoding":904},[883,64069,64071],{"className":64070},[886],[888,64072,64073],{"xmlns":890},[892,64074,64075,64081],{},[895,64076,64077,64079],{},[898,64078,1991],{},[898,64080,1703],{},[902,64082,3819],{"encoding":904},[38,64084,56227],{}," (též vyrovnání, ",[614,64087,64088],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,64091,64093],{"className":64092},[886],[888,64094,64095],{"xmlns":890},[892,64096,64097,64103],{},[895,64098,64099,64101],{},[898,64100,40839],{},[898,64102,1703],{},[902,64104,64105],{"encoding":904},"VC",") je ",[883,64108,64110],{"className":64109},[886],[888,64111,64112],{"xmlns":890},[892,64113,64114,64120],{},[895,64115,64116,64118],{},[898,64117,1991],{},[898,64119,1959],{},[902,64121,4662],{"encoding":904}," kvadratická a ",[883,64124,64126],{"className":64125},[886],[888,64127,64128],{"xmlns":890},[892,64129,64130,64136],{},[895,64131,64132,64134],{},[898,64133,1991],{},[898,64135,1703],{},[902,64137,3819],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,64140,64142],{"className":64141},[886],[888,64143,64144],{"xmlns":890},[892,64145,64146,64150],{},[895,64147,64148],{},[898,64149,4822],{},[902,64151,4822],{"encoding":904},[883,64153,64155],{"className":64154},[886],[888,64156,64157],{"xmlns":890},[892,64158,64159,64163],{},[895,64160,64161],{},[898,64162,23753],{},[902,64164,23753],{"encoding":904}," odpovídajících množstvím ",[883,64167,64169],{"className":64168},[886],[888,64170,64171],{"xmlns":890},[892,64172,64173,64181],{},[895,64174,64175],{},[2355,64176,64177,64179],{},[898,64178,1973],{},[898,64180,4822],{},[902,64182,64183],{"encoding":904},"Q_A",[883,64185,64187],{"className":64186},[886],[888,64188,64189],{"xmlns":890},[892,64190,64191,64199],{},[895,64192,64193],{},[2355,64194,64195,64197],{},[898,64196,1973],{},[898,64198,23753],{},[902,64200,64201],{"encoding":904},"Q_B"," — firma je na ",[38,64204,64205],{},"prahu rentability",[614,64207,64208],{},"break even","). Pro ",[883,64211,64213],{"className":64212},[886],[888,64214,64215],{"xmlns":890},[892,64216,64217,64229],{},[895,64218,64219,64221,64223],{},[898,64220,1973],{},[1664,64222,4022],{},[2355,64224,64225,64227],{},[898,64226,1973],{},[898,64228,4822],{},[902,64230,64231],{"encoding":904},"Q \u003C Q_A",[883,64233,64235],{"className":64234},[886],[888,64236,64237],{"xmlns":890},[892,64238,64239,64251],{},[895,64240,64241,64243,64245],{},[898,64242,1973],{},[1664,64244,3984],{},[2355,64246,64247,64249],{},[898,64248,1973],{},[898,64250,23753],{},[902,64252,64253],{"encoding":904},"Q > Q_B",[883,64255,64257],{"className":64256},[886],[888,64258,64259],{"xmlns":890},[892,64260,64261,64273],{},[895,64262,64263,64265,64267,64269,64271],{},[898,64264,1991],{},[898,64266,1703],{},[1664,64268,3984],{},[898,64270,1991],{},[898,64272,1959],{},[902,64274,64275],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,64278,64280],{"className":64279},[886],[888,64281,64282],{"xmlns":890},[892,64283,64284,64304],{},[895,64285,64286,64292,64294,64296,64298],{},[2355,64287,64288,64290],{},[898,64289,1973],{},[898,64291,4822],{},[1664,64293,4022],{},[898,64295,1973],{},[1664,64297,4022],{},[2355,64299,64300,64302],{},[898,64301,1973],{},[898,64303,23753],{},[902,64305,64306],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,64308,64310],{"className":64309},[886],[888,64311,64312],{"xmlns":890},[892,64313,64314,64326],{},[895,64315,64316,64318,64320,64322,64324],{},[898,64317,1991],{},[898,64319,1959],{},[1664,64321,3984],{},[898,64323,1991],{},[898,64325,1703],{},[902,64327,64328],{"encoding":904},"TR > TC"," (zisk).",[4436,64331,64332],{},[724,64333,64334,64336],{},[883,64335,4723],{}," 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.",[724,64338,64339,64340,64366],{},"Body zvratu jsou řešení rovnice ",[883,64341,64343],{"className":64342},[886],[888,64344,64345],{"xmlns":890},[892,64346,64347,64363],{},[895,64348,64349,64351,64353,64355,64357,64359,64361],{},[898,64350,2398],{},[898,64352,1959],{},[1664,64354,1667],{"stretchy":1666},[898,64356,1973],{},[1664,64358,1673],{"stretchy":1666},[1664,64360,1676],{},[1963,64362,2058],{},[902,64364,64365],{"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.",[724,64368,64369],{},[1928,64370],{"alt":64371,"className":64372,"src":64373},"imek-tr-tc-body-zvratu",[210,1932],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,64375,64376],{},[614,64377,64378,64379,64394,64395,64410,64411,4454,64424,43860,64437,64450,64451,4454,64468,64485,64486,64506,64507,4454,64522,7039,64537,64566],{},"Obrázek 3.11: Body zvratu — křivky ",[883,64380,64382],{"className":64381},[886],[888,64383,64384],{"xmlns":890},[892,64385,64386,64392],{},[895,64387,64388,64390],{},[898,64389,1991],{},[898,64391,1959],{},[902,64393,4662],{"encoding":904}," (obrácená parabola) a ",[883,64396,64398],{"className":64397},[886],[888,64399,64400],{"xmlns":890},[892,64401,64402,64408],{},[895,64403,64404,64406],{},[898,64405,1991],{},[898,64407,1703],{},[902,64409,3819],{"encoding":904}," (přímka) se protínají v bodech ",[883,64412,64414],{"className":64413},[886],[888,64415,64416],{"xmlns":890},[892,64417,64418,64422],{},[895,64419,64420],{},[898,64421,4822],{},[902,64423,4822],{"encoding":904},[883,64425,64427],{"className":64426},[886],[888,64428,64429],{"xmlns":890},[892,64430,64431,64435],{},[895,64432,64433],{},[898,64434,23753],{},[902,64436,23753],{"encoding":904},[883,64438,64440],{"className":64439},[886],[888,64441,64442],{"xmlns":890},[892,64443,64444,64448],{},[895,64445,64446],{},[898,64447,1973],{},[902,64449,1973],{"encoding":904}," v hodnotách ",[883,64452,64454],{"className":64453},[886],[888,64455,64456],{"xmlns":890},[892,64457,64458,64466],{},[895,64459,64460],{},[2355,64461,64462,64464],{},[898,64463,1973],{},[898,64465,4822],{},[902,64467,64183],{"encoding":904},[883,64469,64471],{"className":64470},[886],[888,64472,64473],{"xmlns":890},[892,64474,64475,64483],{},[895,64476,64477],{},[2355,64478,64479,64481],{},[898,64480,1973],{},[898,64482,23753],{},[902,64484,64201],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,64487,64489],{"className":64488},[886],[888,64490,64491],{"xmlns":890},[892,64492,64493,64503],{},[895,64494,64495],{},[2355,64496,64497,64499,64501],{},[898,64498,1973],{},[898,64500,56697],{},[1664,64502,56700],{},[902,64504,64505],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,64508,64510],{"className":64509},[886],[888,64511,64512],{"xmlns":890},[892,64513,64514,64520],{},[895,64515,64516,64518],{},[898,64517,1991],{},[898,64519,1959],{},[902,64521,4662],{"encoding":904},[883,64523,64525],{"className":64524},[886],[888,64526,64527],{"xmlns":890},[892,64528,64529,64535],{},[895,64530,64531,64533],{},[898,64532,1991],{},[898,64534,1703],{},[902,64536,3819],{"encoding":904},[883,64538,64540],{"className":64539},[886],[888,64541,64542],{"xmlns":890},[892,64543,64544,64564],{},[895,64545,64546,64552,64554,64556,64558],{},[2355,64547,64548,64550],{},[898,64549,1973],{},[898,64551,4822],{},[1664,64553,4022],{},[898,64555,1973],{},[1664,64557,4022],{},[2355,64559,64560,64562],{},[898,64561,1973],{},[898,64563,23753],{},[902,64565,64306],{"encoding":904}," vyznačuje zisk.",[37848,64568,64570],{"id":64569},"příklad-38","Příklad 3.8",[724,64572,64573,64575,64576,1343,64596,1343,64622,64648],{},[38,64574,56487],{}," Dáno ",[883,64577,64579],{"className":64578},[886],[888,64580,64581],{"xmlns":890},[892,64582,64583,64593],{},[895,64584,64585,64587,64589,64591],{},[898,64586,1662],{},[898,64588,1703],{},[1664,64590,1676],{},[1963,64592,2944],{},[902,64594,64595],{"encoding":904},"FC = 4",[883,64597,64599],{"className":64598},[886],[888,64600,64601],{"xmlns":890},[892,64602,64603,64619],{},[895,64604,64605,64607,64609,64611,64613],{},[898,64606,1991],{},[898,64608,40839],{},[898,64610,1703],{},[1664,64612,1676],{},[1720,64614,64615,64617],{},[898,64616,1973],{},[1963,64618,1970],{},[902,64620,64621],{"encoding":904},"TVC = Q^2",[883,64623,64625],{"className":64624},[886],[888,64626,64627],{"xmlns":890},[892,64628,64629,64645],{},[895,64630,64631,64633,64635,64637,64639,64641,64643],{},[898,64632,2398],{},[1664,64634,1676],{},[1664,64636,1867],{},[1963,64638,1970],{},[898,64640,1973],{},[1664,64642,1700],{},[1963,64644,4567],{},[902,64646,64647],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,64650,64651,64653],{},[38,64652,23270],{}," Celkové náklady a příjem:",[883,64655,64657],{"className":64656},[886],[888,64658,64659],{"xmlns":890,"display":28566},[892,64660,64661,64727],{},[895,64662,64663,64665,64667,64669,64671,64673,64679,64681,64683,64685,64687,64689,64691,64693,64695,64697,64699,64701,64703,64705,64707,64709,64711,64713,64719,64721,64723,64725],{},[898,64664,1991],{},[898,64666,1703],{},[1664,64668,1676],{},[1963,64670,2944],{},[1664,64672,1700],{},[1720,64674,64675,64677],{},[898,64676,1973],{},[1963,64678,1970],{},[1664,64680,1916],{"separator":1915},[6444,64682],{"width":6446},[898,64684,1991],{},[898,64686,1959],{},[1664,64688,1676],{},[898,64690,1973],{},[1664,64692,3753],{},[1664,64694,1667],{"stretchy":1666},[1664,64696,1867],{},[1963,64698,1970],{},[898,64700,1973],{},[1664,64702,1700],{},[1963,64704,4567],{},[1664,64706,1673],{"stretchy":1666},[1664,64708,1676],{},[1664,64710,1867],{},[1963,64712,1970],{},[1720,64714,64715,64717],{},[898,64716,1973],{},[1963,64718,1970],{},[1664,64720,1700],{},[1963,64722,4567],{},[898,64724,1973],{},[898,64726,1977],{"mathvariant":1726},[902,64728,64729],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,64731,64732],{},"Zisk dle (3.12):",[883,64734,64736],{"className":64735},[886],[888,64737,64738],{"xmlns":890,"display":28566},[892,64739,64740,64818],{},[895,64741,64742,64744,64746,64748,64750,64752,64754,64756,64758,64760,64762,64764,64766,64772,64774,64776,64778,64780,64782,64784,64786,64788,64794,64796,64798,64800,64802,64808,64810,64812,64814,64816],{},[898,64743,2398],{},[898,64745,1959],{},[1664,64747,1676],{},[898,64749,1991],{},[898,64751,1959],{},[1664,64753,1867],{},[898,64755,1991],{},[898,64757,1703],{},[1664,64759,1676],{},[1664,64761,1667],{"stretchy":1666},[1664,64763,1867],{},[1963,64765,1970],{},[1720,64767,64768,64770],{},[898,64769,1973],{},[1963,64771,1970],{},[1664,64773,1700],{},[1963,64775,4567],{},[898,64777,1973],{},[1664,64779,1673],{"stretchy":1666},[1664,64781,1867],{},[1664,64783,1667],{"stretchy":1666},[1963,64785,2944],{},[1664,64787,1700],{},[1720,64789,64790,64792],{},[898,64791,1973],{},[1963,64793,1970],{},[1664,64795,1673],{"stretchy":1666},[1664,64797,1676],{},[1664,64799,1867],{},[1963,64801,2774],{},[1720,64803,64804,64806],{},[898,64805,1973],{},[1963,64807,1970],{},[1664,64809,1700],{},[1963,64811,4567],{},[898,64813,1973],{},[1664,64815,1867],{},[1963,64817,59819],{},[902,64819,64820],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,64822,64823,64826,64827,18076,64863,2087],{},[38,64824,64825],{},"Body zvratu"," jsou kořeny rovnice ",[883,64828,64830],{"className":64829},[886],[888,64831,64832],{"xmlns":890},[892,64833,64834,64860],{},[895,64835,64836,64838,64840,64846,64848,64850,64852,64854,64856,64858],{},[1664,64837,1867],{},[1963,64839,2774],{},[1720,64841,64842,64844],{},[898,64843,1973],{},[1963,64845,1970],{},[1664,64847,1700],{},[1963,64849,4567],{},[898,64851,1973],{},[1664,64853,1867],{},[1963,64855,2944],{},[1664,64857,1676],{},[1963,64859,2058],{},[902,64861,64862],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,64864,64866],{"className":64865},[886],[888,64867,64868],{"xmlns":890},[892,64869,64870,64894],{},[895,64871,64872,64874,64880,64882,64884,64886,64888,64890,64892],{},[1963,64873,2774],{},[1720,64875,64876,64878],{},[898,64877,1973],{},[1963,64879,1970],{},[1664,64881,1867],{},[1963,64883,4567],{},[898,64885,1973],{},[1664,64887,1700],{},[1963,64889,2944],{},[1664,64891,1676],{},[1963,64893,2058],{},[902,64895,64896],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,64898,64900],{"className":64899},[886],[888,64901,64902],{"xmlns":890,"display":28566},[892,64903,64904,64961],{},[895,64905,64906,64918,64920,64943,64945,64959],{},[2355,64907,64908,64910],{},[898,64909,1973],{},[895,64911,64912,64914,64916],{},[1963,64913,2875],{},[1664,64915,1916],{"separator":1915},[1963,64917,1970],{},[1664,64919,1676],{},[2922,64921,64922,64941],{},[895,64923,64924,64926,64929],{},[1963,64925,4567],{},[1664,64927,64928],{},"±",[8682,64930,64931],{},[895,64932,64933,64936,64938],{},[1963,64934,64935],{},"81",[1664,64937,1867],{},[1963,64939,64940],{},"48",[1963,64942,2833],{},[1664,64944,1676],{},[2922,64946,64947,64957],{},[895,64948,64949,64951,64953],{},[1963,64950,4567],{},[1664,64952,64928],{},[8682,64954,64955],{},[1963,64956,9515],{},[1963,64958,2833],{},[1664,64960,1916],{"separator":1915},[902,64962,64963],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,64965,64966,64967,4454,64990,1977],{},"numericky ",[883,64968,64970],{"className":64969},[886],[888,64971,64972],{"xmlns":890},[892,64973,64974,64987],{},[895,64975,64976,64982,64984],{},[2355,64977,64978,64980],{},[898,64979,1973],{},[1963,64981,2875],{},[1664,64983,6466],{},[1963,64985,64986],{},"0,543",[902,64988,64989],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,64991,64993],{"className":64992},[886],[888,64994,64995],{"xmlns":890},[892,64996,64997,65010],{},[895,64998,64999,65005,65007],{},[2355,65000,65001,65003],{},[898,65002,1973],{},[1963,65004,1970],{},[1664,65006,6466],{},[1963,65008,65009],{},"2,457",[902,65011,65012],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,65014,65015,1885,65018,8118,65063,18076,65097,65115],{},[38,65016,65017],{},"Maximum zisku.",[883,65019,65021],{"className":65020},[886],[888,65022,65023],{"xmlns":890},[892,65024,65025,65060],{},[895,65026,65027,65029,65035,65037,65039,65041,65043,65045,65047,65049,65051,65053,65055,65057],{},[898,65028,2398],{},[1720,65030,65031,65033],{},[898,65032,1959],{},[1664,65034,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,65036,1676],{},[1664,65038,1867],{},[1963,65040,2833],{},[898,65042,1973],{},[1664,65044,1700],{},[1963,65046,4567],{},[1664,65048,1676],{},[1963,65050,2058],{},[1664,65052,4556],{},[898,65054,1973],{},[1664,65056,1676],{},[1963,65058,65059],{},"1,5",[902,65061,65062],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,65064,65066],{"className":65065},[886],[888,65067,65068],{"xmlns":890},[892,65069,65070,65094],{},[895,65071,65072,65074,65084,65086,65088,65090,65092],{},[898,65073,2398],{},[1720,65075,65076,65078],{},[898,65077,1959],{},[895,65079,65080,65082],{},[1664,65081,1728],{"mathvariant":1726},[1664,65083,1728],{"mathvariant":1726},[1664,65085,1676],{},[1664,65087,1867],{},[1963,65089,2833],{},[1664,65091,4022],{},[1963,65093,2058],{},[902,65095,65096],{"encoding":904},"PR'' = -6 \u003C 0",[883,65098,65100],{"className":65099},[886],[888,65101,65102],{"xmlns":890},[892,65103,65104,65112],{},[895,65105,65106,65108,65110],{},[898,65107,1973],{},[1664,65109,1676],{},[1963,65111,65059],{},[902,65113,65114],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,65117,65119],{"className":65118},[886],[888,65120,65121],{"xmlns":890,"display":28566},[892,65122,65123,65186],{},[895,65124,65125,65127,65129,65131,65133,65135,65137,65139,65141,65143,65145,65147,65153,65155,65157,65159,65161,65163,65165,65167,65169,65172,65174,65177,65179,65181,65183],{},[898,65126,2398],{},[898,65128,1959],{},[1664,65130,1667],{"stretchy":1666},[1963,65132,65059],{},[1664,65134,1673],{"stretchy":1666},[1664,65136,1676],{},[1664,65138,1867],{},[1963,65140,2774],{},[1664,65142,3753],{},[1664,65144,1667],{"stretchy":1666},[1963,65146,65059],{},[1720,65148,65149,65151],{},[1664,65150,1673],{"stretchy":1666},[1963,65152,1970],{},[1664,65154,1700],{},[1963,65156,4567],{},[1664,65158,3753],{},[1963,65160,65059],{},[1664,65162,1867],{},[1963,65164,2944],{},[1664,65166,1676],{},[1664,65168,1867],{},[1963,65170,65171],{},"6,75",[1664,65173,1700],{},[1963,65175,65176],{},"13,5",[1664,65178,1867],{},[1963,65180,2944],{},[1664,65182,1676],{},[1963,65184,65185],{},"2,75.",[902,65187,65188],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,65190,65191,65192,1343,65237,65290,65291,65309],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,65193,65195],{"className":65194},[886],[888,65196,65197],{"xmlns":890},[892,65198,65199,65234],{},[895,65200,65201,65203,65209,65211,65213,65215,65217,65219,65221,65223,65225,65227,65229,65231],{},[898,65202,1991],{},[1720,65204,65205,65207],{},[898,65206,1959],{},[1664,65208,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,65210,1676],{},[1664,65212,1867],{},[1963,65214,2944],{},[898,65216,1973],{},[1664,65218,1700],{},[1963,65220,4567],{},[1664,65222,1676],{},[1963,65224,2058],{},[1664,65226,4556],{},[898,65228,1973],{},[1664,65230,1676],{},[1963,65232,65233],{},"2,25",[902,65235,65236],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,65238,65240],{"className":65239},[886],[888,65241,65242],{"xmlns":890},[892,65243,65244,65287],{},[895,65245,65246,65248,65256,65258,65260,65262,65264,65266,65268,65274,65276,65278,65280,65282,65284],{},[898,65247,1991],{},[2355,65249,65250,65252,65254],{},[898,65251,1959],{},[898,65253,56697],{},[1664,65255,56700],{},[1664,65257,1676],{},[1664,65259,1867],{},[1963,65261,1970],{},[1664,65263,3753],{},[1664,65265,1667],{"stretchy":1666},[1963,65267,65233],{},[1720,65269,65270,65272],{},[1664,65271,1673],{"stretchy":1666},[1963,65273,1970],{},[1664,65275,1700],{},[1963,65277,4567],{},[1664,65279,3753],{},[1963,65281,65233],{},[1664,65283,1676],{},[1963,65285,65286],{},"10,125",[902,65288,65289],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,65292,65294],{"className":65293},[886],[888,65295,65296],{"xmlns":890},[892,65297,65298,65306],{},[895,65299,65300,65302,65304],{},[898,65301,1973],{},[1664,65303,1676],{},[1963,65305,65233],{},[902,65307,65308],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[4436,65311,65312],{},[724,65313,65314,65316,65317,1343,65339,65361,65362,1343,65379,65400,65401,65433,65434,65472,65473,3257,65491,65508,65509,4454,65537,65571,65572,8251,65610,4454,65634,1977],{},[883,65315,4978],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,65318,65320],{"className":65319},[886],[888,65321,65322],{"xmlns":890},[892,65323,65324,65336],{},[895,65325,65326,65332,65334],{},[2355,65327,65328,65330],{},[898,65329,1973],{},[1963,65331,2875],{},[1664,65333,1676],{},[1963,65335,5575],{},[902,65337,65338],{"encoding":904},"Q_1 = 0{,}5",[883,65340,65342],{"className":65341},[886],[888,65343,65344],{"xmlns":890},[892,65345,65346,65358],{},[895,65347,65348,65354,65356],{},[2355,65349,65350,65352],{},[898,65351,1973],{},[1963,65353,1970],{},[1664,65355,1676],{},[1963,65357,2944],{},[902,65359,65360],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,65363,65365],{"className":65364},[886],[888,65366,65367],{"xmlns":890},[892,65368,65369,65377],{},[895,65370,65371,65373,65375],{},[898,65372,1973],{},[1664,65374,1676],{},[1963,65376,65233],{},[902,65378,65308],{"encoding":904},[883,65380,65382],{"className":65381},[886],[888,65383,65384],{"xmlns":890},[892,65385,65386,65397],{},[895,65387,65388,65390,65392,65394],{},[898,65389,2398],{},[898,65391,1959],{},[1664,65393,1676],{},[1963,65395,65396],{},"6,125",[902,65398,65399],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,65402,65404],{"className":65403},[886],[888,65405,65406],{"xmlns":890},[892,65407,65408,65430],{},[895,65409,65410,65412,65418,65420,65422,65424,65426,65428],{},[898,65411,2398],{},[1720,65413,65414,65416],{},[898,65415,1959],{},[1664,65417,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,65419,1676],{},[1664,65421,1867],{},[1963,65423,2944],{},[898,65425,1973],{},[1664,65427,1700],{},[1963,65429,4567],{},[902,65431,65432],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,65435,65437],{"className":65436},[886],[888,65438,65439],{"xmlns":890},[892,65440,65441,65469],{},[895,65442,65443,65445,65447,65449,65451,65453,65459,65461,65463,65465,65467],{},[898,65444,2398],{},[898,65446,1959],{},[1664,65448,1676],{},[1664,65450,1867],{},[1963,65452,1970],{},[1720,65454,65455,65457],{},[898,65456,1973],{},[1963,65458,1970],{},[1664,65460,1700],{},[1963,65462,4567],{},[898,65464,1973],{},[1664,65466,1867],{},[1963,65468,2944],{},[902,65470,65471],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,65474,65476],{"className":65475},[886],[888,65477,65478],{"xmlns":890},[892,65479,65480,65488],{},[895,65481,65482],{},[1720,65483,65484,65486],{},[898,65485,1973],{},[1963,65487,1970],{},[902,65489,65490],{"encoding":904},"Q^2",[883,65492,65494],{"className":65493},[886],[888,65495,65496],{"xmlns":890},[892,65497,65498,65506],{},[895,65499,65500,65502,65504],{},[898,65501,1991],{},[898,65503,40839],{},[898,65505,1703],{},[902,65507,56009],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,65510,65512],{"className":65511},[886],[888,65513,65514],{"xmlns":890},[892,65515,65516,65534],{},[895,65517,65518,65520,65522,65524,65526,65528],{},[898,65519,1991],{},[898,65521,1703],{},[1664,65523,1676],{},[1963,65525,2944],{},[1664,65527,1700],{},[1720,65529,65530,65532],{},[898,65531,1973],{},[1963,65533,1970],{},[902,65535,65536],{"encoding":904},"TC = 4 + Q^2",[883,65538,65540],{"className":65539},[886],[888,65541,65542],{"xmlns":890},[892,65543,65544,65568],{},[895,65545,65546,65548,65550,65552,65554,65556,65562,65564,65566],{},[898,65547,1991],{},[898,65549,1959],{},[1664,65551,1676],{},[1664,65553,1867],{},[1963,65555,1970],{},[1720,65557,65558,65560],{},[898,65559,1973],{},[1963,65561,1970],{},[1664,65563,1700],{},[1963,65565,4567],{},[898,65567,1973],{},[902,65569,65570],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,65573,65575],{"className":65574},[886],[888,65576,65577],{"xmlns":890},[892,65578,65579,65607],{},[895,65580,65581,65583,65585,65587,65589,65591,65597,65599,65601,65603,65605],{},[898,65582,2398],{},[898,65584,1959],{},[1664,65586,1676],{},[1664,65588,1867],{},[1963,65590,2774],{},[1720,65592,65593,65595],{},[898,65594,1973],{},[1963,65596,1970],{},[1664,65598,1700],{},[1963,65600,4567],{},[898,65602,1973],{},[1664,65604,1867],{},[1963,65606,2944],{},[902,65608,65609],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,65611,65613],{"className":65612},[886],[888,65614,65615],{"xmlns":890},[892,65616,65617,65631],{},[895,65618,65619,65627,65629],{},[2355,65620,65621,65623,65625],{},[898,65622,1973],{},[898,65624,56697],{},[1664,65626,56700],{},[1664,65628,1676],{},[1963,65630,65059],{},[902,65632,65633],{"encoding":904},"Q_{\\max} = 1{,}5",[883,65635,65637],{"className":65636},[886],[888,65638,65639],{"xmlns":890},[892,65640,65641,65658],{},[895,65642,65643,65645,65653,65655],{},[898,65644,2398],{},[2355,65646,65647,65649,65651],{},[898,65648,1959],{},[898,65650,56697],{},[1664,65652,56700],{},[1664,65654,1676],{},[1963,65656,65657],{},"2,75",[902,65659,65660],{"encoding":904},"PR_{\\max} = 2{,}75",[724,65662,65663],{},[614,65664,65665,65666,65693,65694,65727,65728,1343,65751,1977],{},"Obrázek 3.12: Graf ",[883,65667,65669],{"className":65668},[886],[888,65670,65671],{"xmlns":890},[892,65672,65673,65691],{},[895,65674,65675,65677,65679,65681,65683,65685],{},[898,65676,1991],{},[898,65678,1703],{},[1664,65680,1676],{},[1963,65682,2944],{},[1664,65684,1700],{},[1720,65686,65687,65689],{},[898,65688,1973],{},[1963,65690,1970],{},[902,65692,65536],{"encoding":904}," (parabola) a ",[883,65695,65697],{"className":65696},[886],[888,65698,65699],{"xmlns":890},[892,65700,65701,65725],{},[895,65702,65703,65705,65707,65709,65711,65713,65719,65721,65723],{},[898,65704,1991],{},[898,65706,1959],{},[1664,65708,1676],{},[1664,65710,1867],{},[1963,65712,1970],{},[1720,65714,65715,65717],{},[898,65716,1973],{},[1963,65718,1970],{},[1664,65720,1700],{},[1963,65722,4567],{},[898,65724,1973],{},[902,65726,65570],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,65729,65731],{"className":65730},[886],[888,65732,65733],{"xmlns":890},[892,65734,65735,65748],{},[895,65736,65737,65743,65745],{},[2355,65738,65739,65741],{},[898,65740,1973],{},[1963,65742,2875],{},[1664,65744,6466],{},[1963,65746,65747],{},"0,54",[902,65749,65750],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,65752,65754],{"className":65753},[886],[888,65755,65756],{"xmlns":890},[892,65757,65758,65771],{},[895,65759,65760,65766,65768],{},[2355,65761,65762,65764],{},[898,65763,1973],{},[1963,65765,1970],{},[1664,65767,6466],{},[1963,65769,65770],{},"2,46",[902,65772,65773],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,65775,65776],{},[614,65777,65778,65779,59007,65816,65833,65834,1343,65855,1977],{},"Obrázek 3.13: Graf zisku ",[883,65780,65782],{"className":65781},[886],[888,65783,65784],{"xmlns":890},[892,65785,65786,65814],{},[895,65787,65788,65790,65792,65794,65796,65798,65804,65806,65808,65810,65812],{},[898,65789,2398],{},[898,65791,1959],{},[1664,65793,1676],{},[1664,65795,1867],{},[1963,65797,2774],{},[1720,65799,65800,65802],{},[898,65801,1973],{},[1963,65803,1970],{},[1664,65805,1700],{},[1963,65807,4567],{},[898,65809,1973],{},[1664,65811,1867],{},[1963,65813,2944],{},[902,65815,65609],{"encoding":904},[883,65817,65819],{"className":65818},[886],[888,65820,65821],{"xmlns":890},[892,65822,65823,65831],{},[895,65824,65825,65827,65829],{},[898,65826,1973],{},[1664,65828,1676],{},[1963,65830,65059],{},[902,65832,65114],{"encoding":904}," a nulami ",[883,65835,65837],{"className":65836},[886],[888,65838,65839],{"xmlns":890},[892,65840,65841,65853],{},[895,65842,65843,65849,65851],{},[2355,65844,65845,65847],{},[898,65846,1973],{},[1963,65848,2875],{},[1664,65850,6466],{},[1963,65852,65747],{},[902,65854,65750],{"encoding":904},[883,65856,65858],{"className":65857},[886],[888,65859,65860],{"xmlns":890},[892,65861,65862,65874],{},[895,65863,65864,65870,65872],{},[2355,65865,65866,65868],{},[898,65867,1973],{},[1963,65869,1970],{},[1664,65871,6466],{},[1963,65873,65770],{},[902,65875,65773],{"encoding":904},[115,65877,65879],{"id":65878},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,65881,65882],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,65884,65885],{},[1928,65886],{"alt":65887,"className":65888,"src":65889},"imek-max-zisku-dva-pohledy",[210,1932],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,65891,16912],{"id":65892},"princip-1",[724,65894,65895,65896,3210,65911,65928],{},"Má-li zisk ",[883,65897,65899],{"className":65898},[886],[888,65900,65901],{"xmlns":890},[892,65902,65903,65909],{},[895,65904,65905,65907],{},[898,65906,2398],{},[898,65908,1959],{},[902,65910,63979],{"encoding":904},[883,65912,65914],{"className":65913},[886],[888,65915,65916],{"xmlns":890},[892,65917,65918,65926],{},[895,65919,65920],{},[2355,65921,65922,65924],{},[898,65923,1973],{},[1963,65925,2058],{},[902,65927,38808],{"encoding":904}," maximum, pak platí",[883,65930,65932],{"className":65931},[886],[888,65933,65934],{"xmlns":890,"display":28566},[892,65935,65936,65985],{},[21254,65937,65938],{"width":28571},[21259,65939,65940,65942,65978,65980],{},[21262,65941],{"width":28576},[21262,65943,65944],{},[895,65945,65946,65948,65950,65952,65958,65960,65962,65964,65966,65968,65974,65976],{},[898,65947,1956],{},[898,65949,1959],{},[1664,65951,1667],{"stretchy":1666},[2355,65953,65954,65956],{},[898,65955,1973],{},[1963,65957,2058],{},[1664,65959,1673],{"stretchy":1666},[1664,65961,1676],{},[898,65963,1956],{},[898,65965,1703],{},[1664,65967,1667],{"stretchy":1666},[2355,65969,65970,65972],{},[898,65971,1973],{},[1963,65973,2058],{},[1664,65975,1673],{"stretchy":1666},[898,65977,1977],{"mathvariant":1726},[21262,65979],{"width":28576},[21262,65981,65982],{},[1690,65983,65984],{},"(3.13)",[902,65986,65987],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[4436,65989,65990],{},[724,65991,65992,62546,65994],{},[883,65993,56944],{},[38,65995,65996],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,65998,65999,66002,66003,1762,66030,18076,66104,1977],{},[38,66000,66001],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,66004,66006],{"className":66005},[886],[888,66007,66008],{"xmlns":890},[892,66009,66010,66028],{},[895,66011,66012,66014,66016,66018,66020,66022,66024,66026],{},[898,66013,2398],{},[898,66015,1959],{},[1664,66017,1676],{},[898,66019,1991],{},[898,66021,1959],{},[1664,66023,1867],{},[898,66025,1991],{},[898,66027,1703],{},[902,66029,55700],{"encoding":904},[883,66031,66033],{"className":66032},[886],[888,66034,66035],{"xmlns":890},[892,66036,66037,66101],{},[895,66038,66039,66041,66047,66049,66055,66057,66059,66061,66067,66069,66075,66077,66079,66081,66087,66089,66095,66097,66099],{},[898,66040,2398],{},[1720,66042,66043,66045],{},[898,66044,1959],{},[1664,66046,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,66048,1667],{"stretchy":1666},[2355,66050,66051,66053],{},[898,66052,1973],{},[1963,66054,2058],{},[1664,66056,1673],{"stretchy":1666},[1664,66058,1676],{},[898,66060,1991],{},[1720,66062,66063,66065],{},[898,66064,1959],{},[1664,66066,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,66068,1667],{"stretchy":1666},[2355,66070,66071,66073],{},[898,66072,1973],{},[1963,66074,2058],{},[1664,66076,1673],{"stretchy":1666},[1664,66078,1867],{},[898,66080,1991],{},[1720,66082,66083,66085],{},[898,66084,1703],{},[1664,66086,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,66088,1667],{"stretchy":1666},[2355,66090,66091,66093],{},[898,66092,1973],{},[1963,66094,2058],{},[1664,66096,1673],{"stretchy":1666},[1664,66098,1676],{},[1963,66100,2058],{},[902,66102,66103],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,66105,66107],{"className":66106},[886],[888,66108,66109],{"xmlns":890},[892,66110,66111,66143],{},[895,66112,66113,66115,66117,66119,66125,66127,66129,66131,66133,66135,66141],{},[898,66114,1956],{},[898,66116,1959],{},[1664,66118,1667],{"stretchy":1666},[2355,66120,66121,66123],{},[898,66122,1973],{},[1963,66124,2058],{},[1664,66126,1673],{"stretchy":1666},[1664,66128,1676],{},[898,66130,1956],{},[898,66132,1703],{},[1664,66134,1667],{"stretchy":1666},[2355,66136,66137,66139],{},[898,66138,1973],{},[1963,66140,2058],{},[1664,66142,1673],{"stretchy":1666},[902,66144,66145],{"encoding":904},"MR(Q_0) = MC(Q_0)",[4436,66147,66148,66153],{},[724,66149,66150,66152],{},[883,66151,5138],{}," Postup — jak najít maximum zisku",[152,66154,66155,66219,66274,66311,66339],{},[123,66156,66157,66158,4454,66173,66188,66189,4488],{},"Sestavte ",[883,66159,66161],{"className":66160},[886],[888,66162,66163],{"xmlns":890},[892,66164,66165,66171],{},[895,66166,66167,66169],{},[898,66168,1991],{},[898,66170,1959],{},[902,66172,4662],{"encoding":904},[883,66174,66176],{"className":66175},[886],[888,66177,66178],{"xmlns":890},[892,66179,66180,66186],{},[895,66181,66182,66184],{},[898,66183,1991],{},[898,66185,1703],{},[902,66187,3819],{"encoding":904}," ze zadání (typicky ",[883,66190,66192],{"className":66191},[886],[888,66193,66194],{"xmlns":890},[892,66195,66196,66216],{},[895,66197,66198,66200,66202,66204,66206,66208,66210,66212,66214],{},[898,66199,1991],{},[898,66201,1959],{},[1664,66203,1676],{},[898,66205,2398],{},[1664,66207,1667],{"stretchy":1666},[898,66209,1973],{},[1664,66211,1673],{"stretchy":1666},[1664,66213,3753],{},[898,66215,1973],{},[902,66217,66218],{"encoding":904},"TR = P(Q) \\cdot Q",[123,66220,66221,66222,4454,66248,1977],{},"Vypočtěte ",[883,66223,66225],{"className":66224},[886],[888,66226,66227],{"xmlns":890},[892,66228,66229,66245],{},[895,66230,66231,66233,66235,66237,66239],{},[898,66232,1956],{},[898,66234,1959],{},[1664,66236,1676],{},[898,66238,1991],{},[1720,66240,66241,66243],{},[898,66242,1959],{},[1664,66244,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,66246,66247],{"encoding":904},"MR = TR'",[883,66249,66251],{"className":66250},[886],[888,66252,66253],{"xmlns":890},[892,66254,66255,66271],{},[895,66256,66257,66259,66261,66263,66265],{},[898,66258,1956],{},[898,66260,1703],{},[1664,66262,1676],{},[898,66264,1991],{},[1720,66266,66267,66269],{},[898,66268,1703],{},[1664,66270,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,66272,66273],{"encoding":904},"MC = TC'",[123,66275,66276,66277,1977],{},"Řešte rovnici ",[883,66278,66280],{"className":66279},[886],[888,66281,66282],{"xmlns":890},[892,66283,66284,66308],{},[895,66285,66286,66288,66290,66292,66294,66296,66298,66300,66302,66304,66306],{},[898,66287,1956],{},[898,66289,1959],{},[1664,66291,1667],{"stretchy":1666},[898,66293,1973],{},[1664,66295,1673],{"stretchy":1666},[1664,66297,1676],{},[898,66299,1956],{},[898,66301,1703],{},[1664,66303,1667],{"stretchy":1666},[898,66305,1973],{},[1664,66307,1673],{"stretchy":1666},[902,66309,66310],{"encoding":904},"MR(Q) = MC(Q)",[123,66312,66313,66314,66338],{},"Ověřte druhou derivaci ",[883,66315,66317],{"className":66316},[886],[888,66318,66319],{"xmlns":890},[892,66320,66321,66335],{},[895,66322,66323,66325],{},[898,66324,2398],{},[1720,66326,66327,66329],{},[898,66328,1959],{},[895,66330,66331,66333],{},[1664,66332,1728],{"mathvariant":1726},[1664,66334,1728],{"mathvariant":1726},[902,66336,66337],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,66340,66341,66342,66369],{},"Dosaďte do ",[883,66343,66345],{"className":66344},[886],[888,66346,66347],{"xmlns":890},[892,66348,66349,66367],{},[895,66350,66351,66353,66355,66357,66359,66361,66363,66365],{},[898,66352,2398],{},[898,66354,1959],{},[1664,66356,1676],{},[898,66358,1991],{},[898,66360,1959],{},[1664,66362,1867],{},[898,66364,1991],{},[898,66366,1703],{},[902,66368,55700],{"encoding":904}," pro hodnotu maxima.",[37848,66371,66373],{"id":66372},"příklad-39","Příklad 3.9",[724,66375,66376,56488,66378,4454,66400,66436],{},[38,66377,56487],{},[883,66379,66381],{"className":66380},[886],[888,66382,66383],{"xmlns":890},[892,66384,66385,66397],{},[895,66386,66387,66389,66391,66393,66395],{},[898,66388,2398],{},[1664,66390,1676],{},[1963,66392,38519],{},[1664,66394,1867],{},[898,66396,1973],{},[902,66398,66399],{"encoding":904},"P = 30 - Q",[883,66401,66403],{"className":66402},[886],[888,66404,66405],{"xmlns":890},[892,66406,66407,66433],{},[895,66408,66409,66411,66413,66415,66417,66423,66425,66427,66429,66431],{},[898,66410,1991],{},[898,66412,1703],{},[1664,66414,1676],{},[1963,66416,5575],{},[1720,66418,66419,66421],{},[898,66420,1973],{},[1963,66422,1970],{},[1664,66424,1700],{},[1963,66426,2833],{},[898,66428,1973],{},[1664,66430,1700],{},[1963,66432,24701],{},[902,66434,66435],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,66438,66439,1885,66441,1343,66471,66509,66510,16291,66554,66588,66589,1977],{},[38,66440,23270],{},[883,66442,66444],{"className":66443},[886],[888,66445,66446],{"xmlns":890},[892,66447,66448,66468],{},[895,66449,66450,66452,66454,66456,66458,66460,66462],{},[898,66451,1991],{},[898,66453,1959],{},[1664,66455,1676],{},[1963,66457,38519],{},[898,66459,1973],{},[1664,66461,1867],{},[1720,66463,66464,66466],{},[898,66465,1973],{},[1963,66467,1970],{},[902,66469,66470],{"encoding":904},"TR = 30Q - Q^2",[883,66472,66474],{"className":66473},[886],[888,66475,66476],{"xmlns":890},[892,66477,66478,66506],{},[895,66479,66480,66482,66484,66486,66488,66490,66496,66498,66500,66502,66504],{},[898,66481,2398],{},[898,66483,1959],{},[1664,66485,1676],{},[1664,66487,1867],{},[1963,66489,65059],{},[1720,66491,66492,66494],{},[898,66493,1973],{},[1963,66495,1970],{},[1664,66497,1700],{},[1963,66499,42300],{},[898,66501,1973],{},[1664,66503,1867],{},[1963,66505,24701],{},[902,66507,66508],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,66511,66513],{"className":66512},[886],[888,66514,66515],{"xmlns":890},[892,66516,66517,66551],{},[895,66518,66519,66521,66527,66529,66531,66533,66535,66537,66539,66541,66543,66545,66547,66549],{},[898,66520,2398],{},[1720,66522,66523,66525],{},[898,66524,1959],{},[1664,66526,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,66528,1676],{},[1664,66530,1867],{},[1963,66532,2774],{},[898,66534,1973],{},[1664,66536,1700],{},[1963,66538,42300],{},[1664,66540,1676],{},[1963,66542,2058],{},[1664,66544,4556],{},[898,66546,1973],{},[1664,66548,1676],{},[1963,66550,6151],{},[902,66552,66553],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,66555,66557],{"className":66556},[886],[888,66558,66559],{"xmlns":890},[892,66560,66561,66585],{},[895,66562,66563,66565,66575,66577,66579,66581,66583],{},[898,66564,2398],{},[1720,66566,66567,66569],{},[898,66568,1959],{},[895,66570,66571,66573],{},[1664,66572,1728],{"mathvariant":1726},[1664,66574,1728],{"mathvariant":1726},[1664,66576,1676],{},[1664,66578,1867],{},[1963,66580,2774],{},[1664,66582,4022],{},[1963,66584,2058],{},[902,66586,66587],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,66590,66592],{"className":66591},[886],[888,66593,66594],{"xmlns":890},[892,66595,66596,66613],{},[895,66597,66598,66600,66602,66604,66606,66608,66610],{},[898,66599,2398],{},[898,66601,1959],{},[1664,66603,1667],{"stretchy":1666},[1963,66605,6151],{},[1664,66607,1673],{"stretchy":1666},[1664,66609,1676],{},[1963,66611,66612],{},"89",[902,66614,66615],{"encoding":904},"PR(8) = 89",[724,66617,66618,66619,1343,66645,16291,66669,66707],{},"Ověření principu: ",[883,66620,66622],{"className":66621},[886],[888,66623,66624],{"xmlns":890},[892,66625,66626,66642],{},[895,66627,66628,66630,66632,66634,66636,66638,66640],{},[898,66629,1956],{},[898,66631,1959],{},[1664,66633,1676],{},[1963,66635,38519],{},[1664,66637,1867],{},[1963,66639,1970],{},[898,66641,1973],{},[902,66643,66644],{"encoding":904},"MR = 30 - 2Q",[883,66646,66648],{"className":66647},[886],[888,66649,66650],{"xmlns":890},[892,66651,66652,66666],{},[895,66653,66654,66656,66658,66660,66662,66664],{},[898,66655,1956],{},[898,66657,1703],{},[1664,66659,1676],{},[898,66661,1973],{},[1664,66663,1700],{},[1963,66665,2833],{},[902,66667,66668],{"encoding":904},"MC = Q + 6",[883,66670,66672],{"className":66671},[886],[888,66673,66674],{"xmlns":890},[892,66675,66676,66704],{},[895,66677,66678,66680,66682,66684,66686,66688,66690,66692,66694,66696,66698,66700,66702],{},[898,66679,1956],{},[898,66681,1959],{},[1664,66683,1667],{"stretchy":1666},[1963,66685,6151],{},[1664,66687,1673],{"stretchy":1666},[1664,66689,1676],{},[1963,66691,23446],{},[1664,66693,1676],{},[898,66695,1956],{},[898,66697,1703],{},[1664,66699,1667],{"stretchy":1666},[1963,66701,6151],{},[1664,66703,1673],{"stretchy":1666},[902,66705,66706],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,66709,66710,66711,66744,66745,66762],{},"V řadě případů — má-li rovnice ",[883,66712,66714],{"className":66713},[886],[888,66715,66716],{"xmlns":890},[892,66717,66718,66742],{},[895,66719,66720,66722,66724,66726,66728,66730,66732,66734,66736,66738,66740],{},[898,66721,1956],{},[898,66723,1959],{},[1664,66725,1667],{"stretchy":1666},[898,66727,1973],{},[1664,66729,1673],{"stretchy":1666},[1664,66731,1676],{},[898,66733,1956],{},[898,66735,1703],{},[1664,66737,1667],{"stretchy":1666},[898,66739,1973],{},[1664,66741,1673],{"stretchy":1666},[902,66743,66310],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,66746,66748],{"className":66747},[886],[888,66749,66750],{"xmlns":890},[892,66751,66752,66760],{},[895,66753,66754],{},[2355,66755,66756,66758],{},[898,66757,1973],{},[1963,66759,2058],{},[902,66761,38808],{"encoding":904}," — není třeba provádět test druhé derivace.",[37848,66764,66766],{"id":66765},"příklad-310","Příklad 3.10",[724,66768,66769,66771,66772,66776,66777,66790,66791,66822],{},[38,66770,56487],{}," Firma vyrábí minipočítače v ",[207,66773,66775],{"className":66774,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,66778,66780],{"className":66779},[886],[888,66781,66782],{"xmlns":890},[892,66783,66784,66788],{},[895,66785,66786],{},[1963,66787,15690],{},[902,66789,15690],{"encoding":904}," EUR\u002Fks. ",[883,66792,66794],{"className":66793},[886],[888,66795,66796],{"xmlns":890},[892,66797,66798,66819],{},[895,66799,66800,66802,66804,66806,66808,66810,66813],{},[898,66801,1991],{},[898,66803,1703],{},[1664,66805,1676],{},[1963,66807,3696],{},[1664,66809,1700],{},[1963,66811,66812],{},"28",[1720,66814,66815,66817],{},[898,66816,1973],{},[1963,66818,1970],{},[902,66820,66821],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,66824,66825,1885,66827,1343,66849,1343,66869,66892],{},[38,66826,23270],{},[883,66828,66830],{"className":66829},[886],[888,66831,66832],{"xmlns":890},[892,66833,66834,66846],{},[895,66835,66836,66838,66840,66842,66844],{},[898,66837,1991],{},[898,66839,1959],{},[1664,66841,1676],{},[1963,66843,15690],{},[898,66845,1973],{},[902,66847,66848],{"encoding":904},"TR = 900Q",[883,66850,66852],{"className":66851},[886],[888,66853,66854],{"xmlns":890},[892,66855,66856,66866],{},[895,66857,66858,66860,66862,66864],{},[898,66859,1956],{},[898,66861,1959],{},[1664,66863,1676],{},[1963,66865,15690],{},[902,66867,66868],{"encoding":904},"MR = 900",[883,66870,66872],{"className":66871},[886],[888,66873,66874],{"xmlns":890},[892,66875,66876,66889],{},[895,66877,66878,66880,66882,66884,66887],{},[898,66879,1956],{},[898,66881,1703],{},[1664,66883,1676],{},[1963,66885,66886],{},"56",[898,66888,1973],{},[902,66890,66891],{"encoding":904},"MC = 56Q",". Z principu:",[883,66894,66896],{"className":66895},[886],[888,66897,66898],{"xmlns":890,"display":28566},[892,66899,66900,66942],{},[895,66901,66902,66904,66906,66908,66910,66912,66914,66916,66918,66920,66928,66930,66933,66935,66937,66939],{},[1963,66903,15690],{},[1664,66905,1676],{},[1963,66907,66886],{},[898,66909,1973],{},[1690,66911,4553],{},[1664,66913,4556],{},[1690,66915,4553],{},[898,66917,1973],{},[1664,66919,1676],{},[2919,66921,66922],{"scriptlevel":2058,"displaystyle":1666},[2922,66923,66924,66926],{},[1963,66925,15690],{},[1963,66927,66886],{},[1664,66929,6466],{},[1963,66931,66932],{},"16,07",[1690,66934,4553],{},[1664,66936,3315],{},[1690,66938,4553],{},[1963,66940,66941],{},"16.",[902,66943,66944],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,66946,66947,66948,2087],{},"Zisk při ",[883,66949,66951],{"className":66950},[886],[888,66952,66953],{"xmlns":890},[892,66954,66955,66963],{},[895,66956,66957,66959,66961],{},[898,66958,1973],{},[1664,66960,1676],{},[1963,66962,42362],{},[902,66964,66965],{"encoding":904},"Q = 16",[883,66967,66969],{"className":66968},[886],[888,66970,66971],{"xmlns":890,"display":28566},[892,66972,66973,67044],{},[895,66974,66975,66977,66979,66981,66983,66985,66987,66989,66991,66993,66995,66997,66999,67001,67003,67005,67011,67013,67015,67017,67019,67021,67023,67025,67027,67030,67032,67034,67036,67039,67042],{},[898,66976,2398],{},[898,66978,1959],{},[1664,66980,1667],{"stretchy":1666},[1963,66982,42362],{},[1664,66984,1673],{"stretchy":1666},[1664,66986,1676],{},[1963,66988,15690],{},[1664,66990,3753],{},[1963,66992,42362],{},[1664,66994,1867],{},[1664,66996,1667],{"stretchy":1666},[1963,66998,3696],{},[1664,67000,1700],{},[1963,67002,66812],{},[1664,67004,3753],{},[1720,67006,67007,67009],{},[1963,67008,42362],{},[1963,67010,1970],{},[1664,67012,1673],{"stretchy":1666},[1664,67014,1676],{},[1963,67016,23446],{},[1690,67018,1692],{},[1963,67020,20642],{},[1664,67022,1867],{},[1963,67024,24701],{},[1690,67026,1692],{},[1963,67028,67029],{},"218",[1664,67031,1676],{},[1963,67033,24701],{},[1690,67035,1692],{},[1963,67037,67038],{},"182",[1690,67040,67041],{}," EUR",[898,67043,1977],{"mathvariant":1726},[902,67045,67046],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,67048,67049],{},"Pro srovnání při původních 30 ks:",[883,67051,67053],{"className":67052},[886],[888,67054,67055],{"xmlns":890,"display":28566},[892,67056,67057,67122],{},[895,67058,67059,67061,67063,67065,67067,67069,67071,67073,67075,67077,67079,67081,67083,67085,67087,67089,67091,67093,67095,67098,67100,67102,67104,67106,67108,67110,67112,67114,67116,67118,67120],{},[898,67060,2398],{},[898,67062,1959],{},[1664,67064,1667],{"stretchy":1666},[1963,67066,38519],{},[1664,67068,1673],{"stretchy":1666},[1664,67070,1676],{},[1963,67072,15690],{},[1664,67074,3753],{},[1963,67076,38519],{},[1664,67078,1867],{},[1664,67080,1667],{"stretchy":1666},[1963,67082,3696],{},[1664,67084,1700],{},[1963,67086,66812],{},[1664,67088,3753],{},[1963,67090,15690],{},[1664,67092,1673],{"stretchy":1666},[1664,67094,1676],{},[1963,67096,67097],{},"27",[1690,67099,1692],{},[1963,67101,59582],{},[1664,67103,1867],{},[1963,67105,5570],{},[1690,67107,1692],{},[1963,67109,31243],{},[1664,67111,1676],{},[1963,67113,2875],{},[1690,67115,1692],{},[1963,67117,24243],{},[1690,67119,67041],{},[898,67121,1977],{"mathvariant":1726},[902,67123,67124],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,67126,67127,67130,67131,67149,67150,67168],{},[38,67128,67129],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,67132,67134],{"className":67133},[886],[888,67135,67136],{"xmlns":890},[892,67137,67138,67146],{},[895,67139,67140,67142,67144],{},[1963,67141,24701],{},[1690,67143,1692],{},[1963,67145,67038],{},[902,67147,67148],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,67151,67153],{"className":67152},[886],[888,67154,67155],{"xmlns":890},[892,67156,67157,67165],{},[895,67158,67159,67161,67163],{},[1963,67160,2875],{},[1690,67162,1692],{},[1963,67164,24243],{},[902,67166,67167],{"encoding":904},"1\\,750"," EUR.",[198,67170,67172],{"id":67171},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,67174,67175,67176,63070,67189,67213],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,67177,67179],{"className":67178},[886],[888,67180,67181],{"xmlns":890},[892,67182,67183,67187],{},[895,67184,67185],{},[898,67186,2398],{},[902,67188,2398],{"encoding":904},[883,67190,67192],{"className":67191},[886],[888,67193,67194],{"xmlns":890},[892,67195,67196,67210],{},[895,67197,67198,67200,67202,67204,67206,67208],{},[898,67199,1991],{},[898,67201,1959],{},[1664,67203,1676],{},[898,67205,2398],{},[1664,67207,3753],{},[898,67209,1973],{},[902,67211,67212],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,67215,67217],{"className":67216},[886],[888,67218,67219],{"xmlns":890,"display":28566},[892,67220,67221,67254],{},[21254,67222,67223],{"width":28571},[21259,67224,67225,67227,67247,67249],{},[21262,67226],{"width":28576},[21262,67228,67229],{},[895,67230,67231,67233,67235,67237,67239,67241,67243,67245],{},[898,67232,2398],{},[1664,67234,1676],{},[898,67236,1956],{},[898,67238,1703],{},[1664,67240,1667],{"stretchy":1666},[898,67242,1973],{},[1664,67244,1673],{"stretchy":1666},[898,67246,1977],{"mathvariant":1726},[21262,67248],{"width":28576},[21262,67250,67251],{},[1690,67252,67253],{},"(3.14)",[902,67255,67256],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,67258,67259,67260,1977],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,67261,67263],{"className":67262},[886],[888,67264,67265],{"xmlns":890},[892,67266,67267,67281],{},[895,67268,67269,67271],{},[898,67270,2398],{},[1720,67272,67273,67275],{},[898,67274,1959],{},[895,67276,67277,67279],{},[1664,67278,1728],{"mathvariant":1726},[1664,67280,1728],{"mathvariant":1726},[902,67282,66337],{"encoding":904},[37848,67284,67286],{"id":67285},"příklad-311","Příklad 3.11",[724,67288,67289,58022,67291,67338,67339,67357],{},[38,67290,56487],{},[883,67292,67294],{"className":67293},[886],[888,67295,67296],{"xmlns":890},[892,67297,67298,67335],{},[895,67299,67300,67302,67304,67306,67309,67315,67317,67319,67325,67327,67329,67331,67333],{},[898,67301,1991],{},[898,67303,1703],{},[1664,67305,1676],{},[1963,67307,67308],{},"0,04",[1720,67310,67311,67313],{},[898,67312,1973],{},[1963,67314,2774],{},[1664,67316,1867],{},[1963,67318,23045],{},[1720,67320,67321,67323],{},[898,67322,1973],{},[1963,67324,1970],{},[1664,67326,1700],{},[1963,67328,3442],{},[898,67330,1973],{},[1664,67332,1700],{},[1963,67334,2826],{},[902,67336,67337],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,67340,67342],{"className":67341},[886],[888,67343,67344],{"xmlns":890},[892,67345,67346,67354],{},[895,67347,67348,67350,67352],{},[898,67349,2398],{},[1664,67351,1676],{},[1963,67353,2944],{},[902,67355,67356],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,67359,67360,67362,67363,18076,67405,67439,67440,2087],{},[38,67361,23270],{}," Z (3.14): ",[883,67364,67366],{"className":67365},[886],[888,67367,67368],{"xmlns":890},[892,67369,67370,67402],{},[895,67371,67372,67374,67376,67378,67381,67387,67389,67392,67394,67396,67398,67400],{},[898,67373,1956],{},[898,67375,1703],{},[1664,67377,1676],{},[1963,67379,67380],{},"0,12",[1720,67382,67383,67385],{},[898,67384,1973],{},[1963,67386,1970],{},[1664,67388,1867],{},[1963,67390,67391],{},"1,8",[898,67393,1973],{},[1664,67395,1700],{},[1963,67397,3442],{},[1664,67399,1676],{},[1963,67401,2944],{},[902,67403,67404],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,67406,67408],{"className":67407},[886],[888,67409,67410],{"xmlns":890},[892,67411,67412,67436],{},[895,67413,67414,67416,67422,67424,67426,67428,67430,67432,67434],{},[1963,67415,67380],{},[1720,67417,67418,67420],{},[898,67419,1973],{},[1963,67421,1970],{},[1664,67423,1867],{},[1963,67425,67391],{},[898,67427,1973],{},[1664,67429,1700],{},[1963,67431,2833],{},[1664,67433,1676],{},[1963,67435,2058],{},[902,67437,67438],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,67441,67443],{"className":67442},[886],[888,67444,67445],{"xmlns":890},[892,67446,67447,67451],{},[895,67448,67449],{},[1963,67450,67380],{},[902,67452,67453],{"encoding":904},"0{,}12",[883,67455,67457],{"className":67456},[886],[888,67458,67459],{"xmlns":890,"display":28566},[892,67460,67461,67513],{},[895,67462,67463,67469,67471,67473,67475,67477,67479,67481,67483,67485,67487,67489,67495,67497,67499,67501,67503,67509,67511],{},[1720,67464,67465,67467],{},[898,67466,1973],{},[1963,67468,1970],{},[1664,67470,1867],{},[1963,67472,36744],{},[898,67474,1973],{},[1664,67476,1700],{},[1963,67478,3696],{},[1664,67480,1676],{},[1963,67482,2058],{},[1690,67484,4553],{},[1664,67486,4556],{},[1690,67488,4553],{},[2355,67490,67491,67493],{},[898,67492,1973],{},[1963,67494,2875],{},[1664,67496,1676],{},[1963,67498,2826],{},[1664,67500,1916],{"separator":1915},[1690,67502,4553],{},[2355,67504,67505,67507],{},[898,67506,1973],{},[1963,67508,1970],{},[1664,67510,1676],{},[1963,67512,19828],{},[902,67514,67515],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,67517,67518,67519,2087],{},"Dále ",[883,67520,67522],{"className":67521},[886],[888,67523,67524],{"xmlns":890},[892,67525,67526,67565],{},[895,67527,67528,67530,67540,67542,67544,67546,67552,67554,67556,67559,67561,67563],{},[898,67529,2398],{},[1720,67531,67532,67534],{},[898,67533,1959],{},[895,67535,67536,67538],{},[1664,67537,1728],{"mathvariant":1726},[1664,67539,1728],{"mathvariant":1726},[1664,67541,1676],{},[1664,67543,1867],{},[898,67545,1956],{},[1720,67547,67548,67550],{},[898,67549,1703],{},[1664,67551,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,67553,1676],{},[1664,67555,1867],{},[1963,67557,67558],{},"0,24",[898,67560,1973],{},[1664,67562,1700],{},[1963,67564,67391],{},[902,67566,67567],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,67569,67570,67620],{},[123,67571,67572,67616,67617,67619],{},[883,67573,67575],{"className":67574},[886],[888,67576,67577],{"xmlns":890},[892,67578,67579,67613],{},[895,67580,67581,67583,67593,67595,67597,67599,67601,67603,67605,67607,67609,67611],{},[898,67582,2398],{},[1720,67584,67585,67587],{},[898,67586,1959],{},[895,67588,67589,67591],{},[1664,67590,1728],{"mathvariant":1726},[1664,67592,1728],{"mathvariant":1726},[1664,67594,1667],{"stretchy":1666},[1963,67596,2826],{},[1664,67598,1673],{"stretchy":1666},[1664,67600,1676],{},[1963,67602,19821],{},[1664,67604,3984],{},[1963,67606,2058],{},[1690,67608,4553],{},[1664,67610,4556],{},[1690,67612,4553],{},[902,67614,67615],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,67618,4350],{}," zisku (minimalizace ztráty);",[123,67621,67622,67616,67668,67670],{},[883,67623,67625],{"className":67624},[886],[888,67626,67627],{"xmlns":890},[892,67628,67629,67665],{},[895,67630,67631,67633,67643,67645,67647,67649,67651,67653,67655,67657,67659,67661,67663],{},[898,67632,2398],{},[1720,67634,67635,67637],{},[898,67636,1959],{},[895,67638,67639,67641],{},[1664,67640,1728],{"mathvariant":1726},[1664,67642,1728],{"mathvariant":1726},[1664,67644,1667],{"stretchy":1666},[1963,67646,3442],{},[1664,67648,1673],{"stretchy":1666},[1664,67650,1676],{},[1664,67652,1867],{},[1963,67654,19821],{},[1664,67656,4022],{},[1963,67658,2058],{},[1690,67660,4553],{},[1664,67662,4556],{},[1690,67664,4553],{},[902,67666,67667],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,67669,4292],{}," zisku, avšak",[883,67672,67674],{"className":67673},[886],[888,67675,67676],{"xmlns":890,"display":28566},[892,67677,67678,67746],{},[895,67679,67680,67682,67684,67686,67688,67690,67692,67694,67696,67698,67700,67702,67704,67706,67708,67710,67712,67714,67716,67718,67720,67722,67724,67726,67728,67730,67732,67734,67736,67738,67740,67742,67744],{},[898,67681,2398],{},[898,67683,1959],{},[1664,67685,1667],{"stretchy":1666},[1963,67687,3442],{},[1664,67689,1673],{"stretchy":1666},[1664,67691,1676],{},[1963,67693,2944],{},[1664,67695,3753],{},[1963,67697,3442],{},[1664,67699,1867],{},[1664,67701,1667],{"stretchy":1666},[1963,67703,67308],{},[1664,67705,3753],{},[1963,67707,2875],{},[1690,67709,1692],{},[1963,67711,59582],{},[1664,67713,1867],{},[1963,67715,23045],{},[1664,67717,3753],{},[1963,67719,1965],{},[1664,67721,1700],{},[1963,67723,1965],{},[1664,67725,1700],{},[1963,67727,2826],{},[1664,67729,1673],{"stretchy":1666},[1664,67731,1676],{},[1963,67733,5777],{},[1664,67735,1867],{},[1963,67737,21680],{},[1664,67739,1676],{},[1664,67741,1867],{},[1963,67743,36744],{},[1664,67745,1916],{"separator":1915},[902,67747,67748],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,67750,67751,67752,1977],{},"tj. ztráta větší než ",[883,67753,67755],{"className":67754},[886],[888,67756,67757],{"xmlns":890},[892,67758,67759,67769],{},[895,67760,67761,67763,67765,67767],{},[898,67762,1662],{},[898,67764,1703],{},[1664,67766,1676],{},[1963,67768,2826],{},[902,67770,67771],{"encoding":904},"FC = 5",[724,67773,67774,67777,67778,67781,67782,1977],{},[38,67775,67776],{},"Závěr:"," firma by měla ",[38,67779,67780],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,67783,67785],{"className":67784},[886],[888,67786,67787],{"xmlns":890},[892,67788,67789,67799],{},[895,67790,67791,67793,67795,67797],{},[898,67792,1662],{},[898,67794,1703],{},[1664,67796,1676],{},[1963,67798,2826],{},[902,67800,67771],{"encoding":904},[115,67802,67804],{"id":67803},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,67806,67807,67808,67810,67811,67826,67827,67840,67841,67867,67868,67881,67882,67899,67900,3210,67917,67920,67921,67941,67942,67957,67958,2087],{},"Důležitým završením analýzy je konstrukce ",[38,67809,55775],{},". S nabízeným množstvím rostou mezní náklady ",[883,67812,67814],{"className":67813},[886],[888,67815,67816],{"xmlns":890},[892,67817,67818,67824],{},[895,67819,67820,67822],{},[898,67821,1956],{},[898,67823,1703],{},[902,67825,55792],{"encoding":904}," a tyto určují cenu ",[883,67828,67830],{"className":67829},[886],[888,67831,67832],{"xmlns":890},[892,67833,67834,67838],{},[895,67835,67836],{},[898,67837,2398],{},[902,67839,2398],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,67842,67844],{"className":67843},[886],[888,67845,67846],{"xmlns":890},[892,67847,67848,67864],{},[895,67849,67850,67852,67854,67856,67858,67860,67862],{},[898,67851,2398],{},[1664,67853,1676],{},[898,67855,1956],{},[898,67857,1703],{},[1664,67859,1667],{"stretchy":1666},[898,67861,1973],{},[1664,67863,1673],{"stretchy":1666},[902,67865,67866],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,67869,67871],{"className":67870},[886],[888,67872,67873],{"xmlns":890},[892,67874,67875,67879],{},[895,67876,67877],{},[898,67878,2398],{},[902,67880,2398],{"encoding":904}," však nemůže být nižší než ",[883,67883,67885],{"className":67884},[886],[888,67886,67887],{"xmlns":890},[892,67888,67889,67897],{},[895,67890,67891],{},[1720,67892,67893,67895],{},[898,67894,2398],{},[1664,67896,4920],{},[902,67898,4970],{"encoding":904}," odpovídající množství ",[883,67901,67903],{"className":67902},[886],[888,67904,67905],{"xmlns":890},[892,67906,67907,67915],{},[895,67908,67909],{},[1720,67910,67911,67913],{},[898,67912,1973],{},[1664,67914,4920],{},[902,67916,30344],{"encoding":904},[38,67918,67919],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,67922,67924],{"className":67923},[886],[888,67925,67926],{"xmlns":890},[892,67927,67928,67938],{},[895,67929,67930,67932],{},[1963,67931,2058],{},[1720,67933,67934,67936],{},[898,67935,1973],{},[1664,67937,4920],{},[902,67939,67940],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,67943,67945],{"className":67944},[886],[888,67946,67947],{"xmlns":890},[892,67948,67949,67955],{},[895,67950,67951,67953],{},[898,67952,1956],{},[898,67954,1703],{},[902,67956,55792],{"encoding":904}," nad bodem ",[883,67959,67961],{"className":67960},[886],[888,67962,67963],{"xmlns":890},[892,67964,67965,67969],{},[895,67966,67967],{},[898,67968,4822],{},[902,67970,4822],{"encoding":904},[883,67972,67974],{"className":67973},[886],[888,67975,67976],{"xmlns":890,"display":28566},[892,67977,67978,68085],{},[21254,67979,67980],{"width":28571},[21259,67981,67982,67984,68078,68080],{},[21262,67983],{"width":28576},[21262,67985,67986],{},[895,67987,67988,67990,67992,67994,67996,67998,68000,68002],{},[898,67989,2398],{},[1664,67991,1676],{},[898,67993,2351],{},[1664,67995,1667],{"stretchy":1666},[898,67997,1973],{},[1664,67999,1673],{"stretchy":1666},[1664,68001,1676],{},[895,68003,68004,68007],{},[1664,68005,68006],{"fence":1915},"{",[21254,68008,68011,68050],{"rowspacing":68009,"columnalign":68010,"columnspacing":15783},"0.36em","left left",[21259,68012,68013,68029],{},[21262,68014,68015],{},[2919,68016,68017],{"scriptlevel":2058,"displaystyle":1666},[895,68018,68019,68021,68023,68025,68027],{},[898,68020,1956],{},[898,68022,1703],{},[1664,68024,1667],{"stretchy":1666},[898,68026,1973],{},[1664,68028,1673],{"stretchy":1666},[21262,68030,68031],{},[2919,68032,68033],{"scriptlevel":2058,"displaystyle":1666},[895,68034,68035,68038,68040,68042,68048],{},[1690,68036,68037],{},"pro ",[898,68039,1973],{},[1664,68041,5051],{},[1720,68043,68044,68046],{},[898,68045,1973],{},[1664,68047,4920],{},[1664,68049,1916],{"separator":1915},[21259,68051,68052,68058],{},[21262,68053,68054],{},[2919,68055,68056],{"scriptlevel":2058,"displaystyle":1666},[1963,68057,2058],{},[21262,68059,68060],{},[2919,68061,68062],{"scriptlevel":2058,"displaystyle":1666},[895,68063,68064,68066,68068,68070,68076],{},[1690,68065,68037],{},[898,68067,1973],{},[1664,68069,4022],{},[1720,68071,68072,68074],{},[898,68073,1973],{},[1664,68075,4920],{},[1664,68077,1916],{"separator":1915},[21262,68079],{"width":28576},[21262,68081,68082],{},[1690,68083,68084],{},"(3.15)",[902,68086,68087],{"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}",[724,68089,1709,68090,68107,68108,68125,68126,41999,68156,68159],{},[883,68091,68093],{"className":68092},[886],[888,68094,68095],{"xmlns":890},[892,68096,68097,68105],{},[895,68098,68099],{},[1720,68100,68101,68103],{},[898,68102,1973],{},[1664,68104,4920],{},[902,68106,30344],{"encoding":904}," je bod minima ",[883,68109,68111],{"className":68110},[886],[888,68112,68113],{"xmlns":890},[892,68114,68115,68123],{},[895,68116,68117,68119,68121],{},[898,68118,4822],{},[898,68120,40839],{},[898,68122,1703],{},[902,68124,55811],{"encoding":904},". Bod ",[883,68127,68129],{"className":68128},[886],[888,68130,68131],{"xmlns":890},[892,68132,68133,68153],{},[895,68134,68135,68137,68143,68145,68151],{},[1664,68136,1667],{"stretchy":1666},[1720,68138,68139,68141],{},[898,68140,1973],{},[1664,68142,4920],{},[1664,68144,1916],{"separator":1915},[1720,68146,68147,68149],{},[898,68148,2398],{},[1664,68150,4920],{},[1664,68152,1673],{"stretchy":1666},[902,68154,68155],{"encoding":904},"(Q^*, P^*)",[38,68157,68158],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[4436,68161,68162,68167],{},[724,68163,68164,68166],{},[883,68165,5138],{}," Postup — jak odvodit nabídku firmy",[152,68168,68169,68218,68313,68368,68439],{},[123,68170,68171,68172,4454,68194,1977],{},"Ze zadaných nákladů určete ",[883,68173,68175],{"className":68174},[886],[888,68176,68177],{"xmlns":890},[892,68178,68179,68191],{},[895,68180,68181,68183,68185,68187,68189],{},[898,68182,1956],{},[898,68184,1703],{},[1664,68186,1667],{"stretchy":1666},[898,68188,1973],{},[1664,68190,1673],{"stretchy":1666},[902,68192,68193],{"encoding":904},"MC(Q)",[883,68195,68197],{"className":68196},[886],[888,68198,68199],{"xmlns":890},[892,68200,68201,68215],{},[895,68202,68203,68205,68207,68209,68211,68213],{},[898,68204,4822],{},[898,68206,40839],{},[898,68208,1703],{},[1664,68210,1667],{"stretchy":1666},[898,68212,1973],{},[1664,68214,1673],{"stretchy":1666},[902,68216,68217],{"encoding":904},"AVC(Q)",[123,68219,68220,68221,68238,68239,68256,68257,68289,68290,4488],{},"Najděte ",[883,68222,68224],{"className":68223},[886],[888,68225,68226],{"xmlns":890},[892,68227,68228,68236],{},[895,68229,68230],{},[1720,68231,68232,68234],{},[898,68233,1973],{},[1664,68235,4920],{},[902,68237,30344],{"encoding":904}," jako bod minima ",[883,68240,68242],{"className":68241},[886],[888,68243,68244],{"xmlns":890},[892,68245,68246,68254],{},[895,68247,68248,68250,68252],{},[898,68249,4822],{},[898,68251,40839],{},[898,68253,1703],{},[902,68255,55811],{"encoding":904}," (řešením ",[883,68258,68260],{"className":68259},[886],[888,68261,68262],{"xmlns":890},[892,68263,68264,68286],{},[895,68265,68266,68268,68270,68276,68278,68280,68282,68284],{},[898,68267,4822],{},[898,68269,40839],{},[1720,68271,68272,68274],{},[898,68273,1703],{},[1664,68275,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,68277,1667],{"stretchy":1666},[898,68279,1973],{},[1664,68281,1673],{"stretchy":1666},[1664,68283,1676],{},[1963,68285,2058],{},[902,68287,68288],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,68291,68293],{"className":68292},[886],[888,68294,68295],{"xmlns":890},[892,68296,68297,68311],{},[895,68298,68299,68301,68303,68305,68307,68309],{},[898,68300,4822],{},[898,68302,40839],{},[898,68304,1703],{},[1664,68306,1676],{},[898,68308,1956],{},[898,68310,1703],{},[902,68312,55748],{"encoding":904},[123,68314,66221,68315,68367],{},[883,68316,68318],{"className":68317},[886],[888,68319,68320],{"xmlns":890},[892,68321,68322,68364],{},[895,68323,68324,68330,68332,68334,68336,68338,68344,68346,68348,68350,68352,68354,68356,68362],{},[1720,68325,68326,68328],{},[898,68327,2398],{},[1664,68329,4920],{},[1664,68331,1676],{},[898,68333,1956],{},[898,68335,1703],{},[1664,68337,1667],{"stretchy":1666},[1720,68339,68340,68342],{},[898,68341,1973],{},[1664,68343,4920],{},[1664,68345,1673],{"stretchy":1666},[1664,68347,1676],{},[898,68349,4822],{},[898,68351,40839],{},[898,68353,1703],{},[1664,68355,1667],{"stretchy":1666},[1720,68357,68358,68360],{},[898,68359,1973],{},[1664,68361,4920],{},[1664,68363,1673],{"stretchy":1666},[902,68365,68366],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,68369,68370,68371,7039,68403,68425,68426,1977],{},"Zapište nabídku: ",[883,68372,68374],{"className":68373},[886],[888,68375,68376],{"xmlns":890},[892,68377,68378,68400],{},[895,68379,68380,68382,68384,68386,68388,68390,68392,68394,68396,68398],{},[898,68381,2351],{},[1664,68383,1667],{"stretchy":1666},[898,68385,1973],{},[1664,68387,1673],{"stretchy":1666},[1664,68389,1676],{},[898,68391,1956],{},[898,68393,1703],{},[1664,68395,1667],{"stretchy":1666},[898,68397,1973],{},[1664,68399,1673],{"stretchy":1666},[902,68401,68402],{"encoding":904},"S(Q) = MC(Q)",[883,68404,68406],{"className":68405},[886],[888,68407,68408],{"xmlns":890},[892,68409,68410,68422],{},[895,68411,68412,68414,68416],{},[898,68413,1973],{},[1664,68415,5051],{},[1720,68417,68418,68420],{},[898,68419,1973],{},[1664,68421,4920],{},[902,68423,68424],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,68427,68429],{"className":68428},[886],[888,68430,68431],{"xmlns":890},[892,68432,68433,68437],{},[895,68434,68435],{},[1963,68436,2058],{},[902,68438,2058],{"encoding":904},[123,68440,68441,68442,68474],{},"V případě potřeby vyjádřete inverzi ",[883,68443,68445],{"className":68444},[886],[888,68446,68447],{"xmlns":890},[892,68448,68449,68471],{},[895,68450,68451,68453,68455,68465,68467,68469],{},[898,68452,1973],{},[1664,68454,1676],{},[1720,68456,68457,68459],{},[898,68458,2351],{},[895,68460,68461,68463],{},[1664,68462,1867],{},[1963,68464,2875],{},[1664,68466,1667],{"stretchy":1666},[898,68468,2398],{},[1664,68470,1673],{"stretchy":1666},[902,68472,68473],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,68476,68477],{},[614,68478,68479,68480,1343,68495,4454,68512,29701,68527,68540,68541,68566,68567,68580,68581,68598,68599,68616,68617,68634],{},"Obrázek 3.14: Křivky ",[883,68481,68483],{"className":68482},[886],[888,68484,68485],{"xmlns":890},[892,68486,68487,68493],{},[895,68488,68489,68491],{},[898,68490,4822],{},[898,68492,1703],{},[902,68494,56060],{"encoding":904},[883,68496,68498],{"className":68497},[886],[888,68499,68500],{"xmlns":890},[892,68501,68502,68510],{},[895,68503,68504,68506,68508],{},[898,68505,4822],{},[898,68507,40839],{},[898,68509,1703],{},[902,68511,55811],{"encoding":904},[883,68513,68515],{"className":68514},[886],[888,68516,68517],{"xmlns":890},[892,68518,68519,68525],{},[895,68520,68521,68523],{},[898,68522,1956],{},[898,68524,1703],{},[902,68526,55792],{"encoding":904},[883,68528,68530],{"className":68529},[886],[888,68531,68532],{"xmlns":890},[892,68533,68534,68538],{},[895,68535,68536],{},[898,68537,900],{},[902,68539,900],{"encoding":904},"; křivka nabídky ",[883,68542,68544],{"className":68543},[886],[888,68545,68546],{"xmlns":890},[892,68547,68548,68564],{},[895,68549,68550,68552,68554,68556,68558,68560,68562],{},[898,68551,2398],{},[1664,68553,1676],{},[898,68555,1956],{},[898,68557,1703],{},[1664,68559,1667],{"stretchy":1666},[898,68561,1973],{},[1664,68563,1673],{"stretchy":1666},[902,68565,67866],{"encoding":904}," začíná v bodě ",[883,68568,68570],{"className":68569},[886],[888,68571,68572],{"xmlns":890},[892,68573,68574,68578],{},[895,68575,68576],{},[898,68577,4822],{},[902,68579,4822],{"encoding":904}," odpovídajícím minimu ",[883,68582,68584],{"className":68583},[886],[888,68585,68586],{"xmlns":890},[892,68587,68588,68596],{},[895,68589,68590,68592,68594],{},[898,68591,4822],{},[898,68593,40839],{},[898,68595,1703],{},[902,68597,55811],{"encoding":904}," při ceně ",[883,68600,68602],{"className":68601},[886],[888,68603,68604],{"xmlns":890},[892,68605,68606,68614],{},[895,68607,68608],{},[1720,68609,68610,68612],{},[898,68611,2398],{},[1664,68613,4920],{},[902,68615,4970],{"encoding":904}," (minimální cena nabídky); pod ",[883,68618,68620],{"className":68619},[886],[888,68621,68622],{"xmlns":890},[892,68623,68624,68632],{},[895,68625,68626],{},[1720,68627,68628,68630],{},[898,68629,1973],{},[1664,68631,4920],{},[902,68633,30344],{"encoding":904}," je nabídka nulová.",[37848,68636,68638],{"id":68637},"příklad-312","Příklad 3.12",[724,68640,68641,58022,68643,68689],{},[38,68642,56487],{},[883,68644,68646],{"className":68645},[886],[888,68647,68648],{"xmlns":890},[892,68649,68650,68686],{},[895,68651,68652,68654,68656,68658,68660,68666,68668,68670,68676,68678,68680,68682,68684],{},[898,68653,1991],{},[898,68655,1703],{},[1664,68657,1676],{},[1963,68659,2220],{},[1720,68661,68662,68664],{},[898,68663,1973],{},[1963,68665,2774],{},[1664,68667,1867],{},[1963,68669,1970],{},[1720,68671,68672,68674],{},[898,68673,1973],{},[1963,68675,1970],{},[1664,68677,1700],{},[1963,68679,36744],{},[898,68681,1973],{},[1664,68683,1700],{},[1963,68685,3442],{},[902,68687,68688],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,68691,68692,1885,68694,68731,68732,2087],{},[38,68693,23270],{},[883,68695,68697],{"className":68696},[886],[888,68698,68699],{"xmlns":890},[892,68700,68701,68728],{},[895,68702,68703,68705,68707,68709,68712,68718,68720,68722,68724,68726],{},[898,68704,1956],{},[898,68706,1703],{},[1664,68708,1676],{},[1963,68710,68711],{},"0,3",[1720,68713,68714,68716],{},[898,68715,1973],{},[1963,68717,1970],{},[1664,68719,1867],{},[1963,68721,2944],{},[898,68723,1973],{},[1664,68725,1700],{},[1963,68727,36744],{},[902,68729,68730],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,68733,68735],{"className":68734},[886],[888,68736,68737],{"xmlns":890},[892,68738,68739,68749],{},[895,68740,68741,68743,68745,68747],{},[898,68742,2398],{},[1664,68744,1676],{},[898,68746,1956],{},[898,68748,1703],{},[902,68750,68751],{"encoding":904},"P = MC",[883,68753,68755],{"className":68754},[886],[888,68756,68757],{"xmlns":890,"display":28566},[892,68758,68759,68784],{},[895,68760,68761,68763,68765,68767,68773,68775,68777,68779,68781],{},[898,68762,2398],{},[1664,68764,1676],{},[1963,68766,68711],{},[1720,68768,68769,68771],{},[898,68770,1973],{},[1963,68772,1970],{},[1664,68774,1867],{},[1963,68776,2944],{},[898,68778,1973],{},[1664,68780,1700],{},[1963,68782,68783],{},"15.",[902,68785,68786],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,68788,68789,68790,5948,68803,68816],{},"Vyjádření ",[883,68791,68793],{"className":68792},[886],[888,68794,68795],{"xmlns":890},[892,68796,68797,68801],{},[895,68798,68799],{},[898,68800,1973],{},[902,68802,1973],{"encoding":904},[883,68804,68806],{"className":68805},[886],[888,68807,68808],{"xmlns":890},[892,68809,68810,68814],{},[895,68811,68812],{},[898,68813,2398],{},[902,68815,2398],{"encoding":904}," doplněním na čtverec:",[883,68818,68820],{"className":68819},[886],[888,68821,68822],{"xmlns":890,"display":28566},[892,68823,68824,68914],{},[895,68825,68826,68828,68830,68832,68870,68872,68874,68896,68898,68912],{},[898,68827,2398],{},[1664,68829,1676],{},[1963,68831,68711],{},[895,68833,68834,68836,68858,68860,68868],{},[1664,68835,1667],{"fence":1915},[1720,68837,68838,68856],{},[895,68839,68840,68842,68844,68846,68854],{},[1664,68841,1667],{"fence":1915},[898,68843,1973],{},[1664,68845,1867],{},[2919,68847,68848],{"scriptlevel":2058,"displaystyle":1666},[2922,68849,68850,68852],{},[1963,68851,9599],{},[1963,68853,2774],{},[1664,68855,1673],{"fence":1915},[1963,68857,1970],{},[1664,68859,1700],{},[2919,68861,68862],{"scriptlevel":2058,"displaystyle":1666},[2922,68863,68864,68866],{},[1963,68865,3696],{},[1963,68867,4567],{},[1664,68869,1673],{"fence":1915},[1664,68871,1916],{"separator":1915},[6444,68873],{"width":6446},[1720,68875,68876,68894],{},[895,68877,68878,68880,68882,68884,68892],{},[1664,68879,1667],{"fence":1915},[898,68881,1973],{},[1664,68883,1867],{},[2919,68885,68886],{"scriptlevel":2058,"displaystyle":1666},[2922,68887,68888,68890],{},[1963,68889,9599],{},[1963,68891,2774],{},[1664,68893,1673],{"fence":1915},[1963,68895,1970],{},[1664,68897,1676],{},[2922,68899,68900,68910],{},[895,68901,68902,68904,68906,68908],{},[1963,68903,38519],{},[898,68905,2398],{},[1664,68907,1867],{},[1963,68909,3696],{},[1963,68911,4567],{},[1664,68913,1916],{"separator":1915},[902,68915,68916],{"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},",[883,68918,68920],{"className":68919},[886],[888,68921,68922],{"xmlns":890,"display":28566},[892,68923,68924,68956],{},[895,68925,68926,68928,68930,68936,68938,68954],{},[898,68927,1973],{},[1664,68929,1676],{},[2922,68931,68932,68934],{},[1963,68933,9599],{},[1963,68935,2774],{},[1664,68937,1700],{},[2922,68939,68940,68952],{},[8682,68941,68942],{},[895,68943,68944,68946,68948,68950],{},[1963,68945,38519],{},[898,68947,2398],{},[1664,68949,1867],{},[1963,68951,3696],{},[1963,68953,2774],{},[898,68955,1977],{"mathvariant":1726},[902,68957,68958],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,68960,67518,68961,1343,68999,1343,69047,69081,69082,1977],{},[883,68962,68964],{"className":68963},[886],[888,68965,68966],{"xmlns":890},[892,68967,68968,68996],{},[895,68969,68970,68972,68974,68976,68978,68980,68986,68988,68990,68992,68994],{},[898,68971,4822],{},[898,68973,40839],{},[898,68975,1703],{},[1664,68977,1676],{},[1963,68979,2220],{},[1720,68981,68982,68984],{},[898,68983,1973],{},[1963,68985,1970],{},[1664,68987,1867],{},[1963,68989,1970],{},[898,68991,1973],{},[1664,68993,1700],{},[1963,68995,36744],{},[902,68997,68998],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,69000,69002],{"className":69001},[886],[888,69003,69004],{"xmlns":890},[892,69005,69006,69044],{},[895,69007,69008,69010,69012,69018,69020,69022,69024,69026,69028,69030,69032,69034,69040,69042],{},[898,69009,4822],{},[898,69011,40839],{},[1720,69013,69014,69016],{},[898,69015,1703],{},[1664,69017,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,69019,1676],{},[1963,69021,2154],{},[898,69023,1973],{},[1664,69025,1867],{},[1963,69027,1970],{},[1664,69029,1676],{},[1963,69031,2058],{},[1664,69033,4556],{},[1720,69035,69036,69038],{},[898,69037,1973],{},[1664,69039,4920],{},[1664,69041,1676],{},[1963,69043,3442],{},[902,69045,69046],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,69048,69050],{"className":69049},[886],[888,69051,69052],{"xmlns":890},[892,69053,69054,69078],{},[895,69055,69056,69058,69060,69070,69072,69074,69076],{},[898,69057,4822],{},[898,69059,40839],{},[1720,69061,69062,69064],{},[898,69063,1703],{},[895,69065,69066,69068],{},[1664,69067,1728],{"mathvariant":1726},[1664,69069,1728],{"mathvariant":1726},[1664,69071,1676],{},[1963,69073,2154],{},[1664,69075,3984],{},[1963,69077,2058],{},[902,69079,69080],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,69083,69085],{"className":69084},[886],[888,69086,69087],{"xmlns":890},[892,69088,69089,69125],{},[895,69090,69091,69097,69099,69101,69103,69105,69107,69109,69111,69113,69115,69117,69119,69121,69123],{},[1720,69092,69093,69095],{},[898,69094,2398],{},[1664,69096,4920],{},[1664,69098,1676],{},[898,69100,1956],{},[898,69102,1703],{},[1664,69104,1667],{"stretchy":1666},[1963,69106,3442],{},[1664,69108,1673],{"stretchy":1666},[1664,69110,1676],{},[1963,69112,38519],{},[1664,69114,1867],{},[1963,69116,5777],{},[1664,69118,1700],{},[1963,69120,36744],{},[1664,69122,1676],{},[1963,69124,2826],{},[902,69126,69127],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,69129,69130],{},[38,69131,69132],{},"Závěr.",[883,69134,69136],{"className":69135},[886],[888,69137,69138],{"xmlns":890,"display":28566},[892,69139,69140,69226],{},[895,69141,69142,69144,69146,69148,69150,69152,69154,69156],{},[898,69143,2398],{},[1664,69145,1676],{},[898,69147,2351],{},[1664,69149,1667],{"stretchy":1666},[898,69151,1973],{},[1664,69153,1673],{"stretchy":1666},[1664,69155,1676],{},[895,69157,69158,69160],{},[1664,69159,68006],{"fence":1915},[21254,69161,69162,69204],{"rowspacing":68009,"columnalign":68010,"columnspacing":15783},[21259,69163,69164,69188],{},[21262,69165,69166],{},[2919,69167,69168],{"scriptlevel":2058,"displaystyle":1666},[895,69169,69170,69172,69178,69180,69182,69184,69186],{},[1963,69171,68711],{},[1720,69173,69174,69176],{},[898,69175,1973],{},[1963,69177,1970],{},[1664,69179,1867],{},[1963,69181,2944],{},[898,69183,1973],{},[1664,69185,1700],{},[1963,69187,36744],{},[21262,69189,69190],{},[2919,69191,69192],{"scriptlevel":2058,"displaystyle":1666},[895,69193,69194,69196,69198,69200,69202],{},[1690,69195,68037],{},[898,69197,1973],{},[1664,69199,5051],{},[1963,69201,3442],{},[1664,69203,1916],{"separator":1915},[21259,69205,69206,69212],{},[21262,69207,69208],{},[2919,69209,69210],{"scriptlevel":2058,"displaystyle":1666},[1963,69211,2058],{},[21262,69213,69214],{},[2919,69215,69216],{"scriptlevel":2058,"displaystyle":1666},[895,69217,69218,69220,69222,69224],{},[1690,69219,68037],{},[898,69221,1973],{},[1664,69223,4022],{},[1963,69225,19828],{},[902,69227,69228],{"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}",[724,69230,69231],{},[614,69232,69233,69234,69249,69250,1977],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,69235,69237],{"className":69236},[886],[888,69238,69239],{"xmlns":890},[892,69240,69241,69247],{},[895,69242,69243,69245],{},[898,69244,1956],{},[898,69246,1703],{},[902,69248,55792],{"encoding":904}," ležící nad minimem ",[883,69251,69253],{"className":69252},[886],[888,69254,69255],{"xmlns":890},[892,69256,69257,69265],{},[895,69258,69259,69261,69263],{},[898,69260,4822],{},[898,69262,40839],{},[898,69264,1703],{},[902,69266,55811],{"encoding":904},[115,69268,69270],{"id":69269},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,69272,69273,69274,69278,69279,69294,69295,69315,69316,4454,69319,69322,69323,69325,69326,20445,69348,69350,69351,4454,69353,59226,69356,1885,69359,42314,69374,69389],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,69275,69277],{"className":69276,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,69280,69282],{"className":69281},[886],[888,69283,69284],{"xmlns":890},[892,69285,69286,69292],{},[895,69287,69288,69290],{},[898,69289,1991],{},[898,69291,1959],{},[902,69293,4662],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,69296,69298],{"className":69297},[886],[888,69299,69300],{"xmlns":890},[892,69301,69302,69312],{},[895,69303,69304,69306,69308,69310],{},[898,69305,1991],{},[898,69307,1959],{},[898,69309,5240],{"mathvariant":1726},[898,69311,1973],{},[902,69313,69314],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,69317,69318],{},"fixních",[38,69320,69321],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,69324,64825],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,69327,69329],{"className":69328},[886],[888,69330,69331],{"xmlns":890},[892,69332,69333,69345],{},[895,69334,69335,69337,69339,69341,69343],{},[898,69336,1991],{},[898,69338,1959],{},[1664,69340,1867],{},[898,69342,1991],{},[898,69344,1703],{},[902,69346,69347],{"encoding":904},"TR - TC",[38,69349,55672],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,69352,56984],{},[38,69354,69355],{},"mezní náklady",[207,69357,1145],{"className":69358,"dataFsResolvedFilePath":764,"href":765},[210],[883,69360,69362],{"className":69361},[886],[888,69363,69364],{"xmlns":890},[892,69365,69366,69372],{},[895,69367,69368,69370],{},[898,69369,1991],{},[898,69371,1959],{},[902,69373,4662],{"encoding":904},[883,69375,69377],{"className":69376},[886],[888,69378,69379],{"xmlns":890},[892,69380,69381,69387],{},[895,69382,69383,69385],{},[898,69384,1991],{},[898,69386,1703],{},[902,69388,3819],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,69391,69392,69454,69520,69582],{},[123,69393,69394,69397,69398,10957,69413,1977],{},[38,69395,69396],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,69399,69401],{"className":69400},[886],[888,69402,69403],{"xmlns":890},[892,69404,69405,69411],{},[895,69406,69407,69409],{},[898,69408,4822],{},[898,69410,1703],{},[902,69412,56060],{"encoding":904},[883,69414,69416],{"className":69415},[886],[888,69417,69418],{"xmlns":890},[892,69419,69420,69452],{},[895,69421,69422,69424,69426,69428,69434,69436,69438,69440,69442,69444,69450],{},[898,69423,4822],{},[898,69425,1703],{},[1664,69427,1667],{"stretchy":1666},[2355,69429,69430,69432],{},[898,69431,1973],{},[1963,69433,2058],{},[1664,69435,1673],{"stretchy":1666},[1664,69437,1676],{},[898,69439,1956],{},[898,69441,1703],{},[1664,69443,1667],{"stretchy":1666},[2355,69445,69446,69448],{},[898,69447,1973],{},[1963,69449,2058],{},[1664,69451,1673],{"stretchy":1666},[902,69453,63069],{"encoding":904},[123,69455,69456,69397,69459,10957,69476,1977],{},[38,69457,69458],{},"Princip minimalizace průměrných variabilních nákladů:",[883,69460,69462],{"className":69461},[886],[888,69463,69464],{"xmlns":890},[892,69465,69466,69474],{},[895,69467,69468,69470,69472],{},[898,69469,4822],{},[898,69471,40839],{},[898,69473,1703],{},[902,69475,55811],{"encoding":904},[883,69477,69479],{"className":69478},[886],[888,69480,69481],{"xmlns":890},[892,69482,69483,69517],{},[895,69484,69485,69487,69489,69491,69493,69499,69501,69503,69505,69507,69509,69515],{},[898,69486,4822],{},[898,69488,40839],{},[898,69490,1703],{},[1664,69492,1667],{"stretchy":1666},[2355,69494,69495,69497],{},[898,69496,1973],{},[1963,69498,2058],{},[1664,69500,1673],{"stretchy":1666},[1664,69502,1676],{},[898,69504,1956],{},[898,69506,1703],{},[1664,69508,1667],{"stretchy":1666},[2355,69510,69511,69513],{},[898,69512,1973],{},[1963,69514,2058],{},[1664,69516,1673],{"stretchy":1666},[902,69518,69519],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,69521,69522,69525,69526,10957,69541,1977],{},[38,69523,69524],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,69527,69529],{"className":69528},[886],[888,69530,69531],{"xmlns":890},[892,69532,69533,69539],{},[895,69534,69535,69537],{},[898,69536,2398],{},[898,69538,1959],{},[902,69540,63979],{"encoding":904},[883,69542,69544],{"className":69543},[886],[888,69545,69546],{"xmlns":890},[892,69547,69548,69580],{},[895,69549,69550,69552,69554,69556,69562,69564,69566,69568,69570,69572,69578],{},[898,69551,1956],{},[898,69553,1959],{},[1664,69555,1667],{"stretchy":1666},[2355,69557,69558,69560],{},[898,69559,1973],{},[1963,69561,2058],{},[1664,69563,1673],{"stretchy":1666},[1664,69565,1676],{},[898,69567,1956],{},[898,69569,1703],{},[1664,69571,1667],{"stretchy":1666},[2355,69573,69574,69576],{},[898,69575,1973],{},[1963,69577,2058],{},[1664,69579,1673],{"stretchy":1666},[902,69581,66145],{"encoding":904},[123,69583,69584,1885,69587,7039,69623,68425,69644,22094,69657,68107,69674,1977],{},[38,69585,69586],{},"Funkce nabídky firmy:",[883,69588,69590],{"className":69589},[886],[888,69591,69592],{"xmlns":890},[892,69593,69594,69620],{},[895,69595,69596,69598,69600,69602,69604,69606,69608,69610,69612,69614,69616,69618],{},[898,69597,2398],{},[1664,69599,1676],{},[898,69601,2351],{},[1664,69603,1667],{"stretchy":1666},[898,69605,1973],{},[1664,69607,1673],{"stretchy":1666},[1664,69609,1676],{},[898,69611,1956],{},[898,69613,1703],{},[1664,69615,1667],{"stretchy":1666},[898,69617,1973],{},[1664,69619,1673],{"stretchy":1666},[902,69621,69622],{"encoding":904},"P = S(Q) = MC(Q)",[883,69624,69626],{"className":69625},[886],[888,69627,69628],{"xmlns":890},[892,69629,69630,69642],{},[895,69631,69632,69634,69636],{},[898,69633,1973],{},[1664,69635,5051],{},[1720,69637,69638,69640],{},[898,69639,1973],{},[1664,69641,4920],{},[902,69643,68424],{"encoding":904},[883,69645,69647],{"className":69646},[886],[888,69648,69649],{"xmlns":890},[892,69650,69651,69655],{},[895,69652,69653],{},[1963,69654,2058],{},[902,69656,2058],{"encoding":904},[883,69658,69660],{"className":69659},[886],[888,69661,69662],{"xmlns":890},[892,69663,69664,69672],{},[895,69665,69666],{},[1720,69667,69668,69670],{},[898,69669,1973],{},[1664,69671,4920],{},[902,69673,30344],{"encoding":904},[883,69675,69677],{"className":69676},[886],[888,69678,69679],{"xmlns":890},[892,69680,69681,69689],{},[895,69682,69683,69685,69687],{},[898,69684,4822],{},[898,69686,40839],{},[898,69688,1703],{},[902,69690,55811],{"encoding":904},[115,69692,50382],{"id":50381},[152,69694,69695,69698,69701,69704,69707,69710,69713,69716,69719,69722,69725],{},[123,69696,69697],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,69699,69700],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,69702,69703],{},"Jak se vypočte mezní příjem a co udává?",[123,69705,69706],{},"Z jakých složek se skládají celkové náklady?",[123,69708,69709],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,69711,69712],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,69714,69715],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,69717,69718],{},"Jak se vypočte zisk?",[123,69720,69721],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,69723,69724],{},"Co jsou body zvratu? Jak se najdou?",[123,69726,69727],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,69729,69731],{"id":69730},"úlohy-31328","Úlohy 3.1–3.28",[198,69733,69735],{"id":69734},"příjem-3135","Příjem (3.1–3.5)",[724,69737,69738,45926,69741,69769,69770,69785,69786,69801,69802,69817,69818,1343,69833,1343,69848,69863],{},[38,69739,69740],{},"3.1",[883,69742,69744],{"className":69743},[886],[888,69745,69746],{"xmlns":890},[892,69747,69748,69766],{},[895,69749,69750,69752,69754,69756,69758,69760,69762,69764],{},[898,69751,2398],{},[1664,69753,1676],{},[898,69755,2379],{},[1664,69757,1667],{"stretchy":1666},[898,69759,1973],{},[1664,69761,1673],{"stretchy":1666},[1664,69763,1676],{},[1963,69765,1965],{},[902,69767,69768],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,69771,69773],{"className":69772},[886],[888,69774,69775],{"xmlns":890},[892,69776,69777,69783],{},[895,69778,69779,69781],{},[898,69780,1991],{},[898,69782,1959],{},[902,69784,4662],{"encoding":904},", průměrný příjem ",[883,69787,69789],{"className":69788},[886],[888,69790,69791],{"xmlns":890},[892,69792,69793,69799],{},[895,69794,69795,69797],{},[898,69796,4822],{},[898,69798,1959],{},[902,69800,55945],{"encoding":904}," a mezní příjem ",[883,69803,69805],{"className":69804},[886],[888,69806,69807],{"xmlns":890},[892,69808,69809,69815],{},[895,69810,69811,69813],{},[898,69812,1956],{},[898,69814,1959],{},[902,69816,7200],{"encoding":904},". (c) Vypočtěte ",[883,69819,69821],{"className":69820},[886],[888,69822,69823],{"xmlns":890},[892,69824,69825,69831],{},[895,69826,69827,69829],{},[898,69828,1991],{},[898,69830,1959],{},[902,69832,4662],{"encoding":904},[883,69834,69836],{"className":69835},[886],[888,69837,69838],{"xmlns":890},[892,69839,69840,69846],{},[895,69841,69842,69844],{},[898,69843,4822],{},[898,69845,1959],{},[902,69847,55945],{"encoding":904},[883,69849,69851],{"className":69850},[886],[888,69852,69853],{"xmlns":890},[892,69854,69855,69861],{},[895,69856,69857,69859],{},[898,69858,1956],{},[898,69860,1959],{},[902,69862,7200],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,69865,69866,45926,69869,69769,69905,69785,69920,69801,69935,69817,69950,1343,69965,1343,69980,69995],{},[38,69867,69868],{},"3.2",[883,69870,69872],{"className":69871},[886],[888,69873,69874],{"xmlns":890},[892,69875,69876,69902],{},[895,69877,69878,69880,69882,69884,69886,69888,69890,69892,69894,69896,69898,69900],{},[898,69879,2398],{},[1664,69881,1676],{},[898,69883,2379],{},[1664,69885,1667],{"stretchy":1666},[898,69887,1973],{},[1664,69889,1673],{"stretchy":1666},[1664,69891,1676],{},[1664,69893,1867],{},[1963,69895,5575],{},[898,69897,1973],{},[1664,69899,1700],{},[1963,69901,9599],{},[902,69903,69904],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,69906,69908],{"className":69907},[886],[888,69909,69910],{"xmlns":890},[892,69911,69912,69918],{},[895,69913,69914,69916],{},[898,69915,1991],{},[898,69917,1959],{},[902,69919,4662],{"encoding":904},[883,69921,69923],{"className":69922},[886],[888,69924,69925],{"xmlns":890},[892,69926,69927,69933],{},[895,69928,69929,69931],{},[898,69930,4822],{},[898,69932,1959],{},[902,69934,55945],{"encoding":904},[883,69936,69938],{"className":69937},[886],[888,69939,69940],{"xmlns":890},[892,69941,69942,69948],{},[895,69943,69944,69946],{},[898,69945,1956],{},[898,69947,1959],{},[902,69949,7200],{"encoding":904},[883,69951,69953],{"className":69952},[886],[888,69954,69955],{"xmlns":890},[892,69956,69957,69963],{},[895,69958,69959,69961],{},[898,69960,1991],{},[898,69962,1959],{},[902,69964,4662],{"encoding":904},[883,69966,69968],{"className":69967},[886],[888,69969,69970],{"xmlns":890},[892,69971,69972,69978],{},[895,69973,69974,69976],{},[898,69975,4822],{},[898,69977,1959],{},[902,69979,55945],{"encoding":904},[883,69981,69983],{"className":69982},[886],[888,69984,69985],{"xmlns":890},[892,69986,69987,69993],{},[895,69988,69989,69991],{},[898,69990,1956],{},[898,69992,1959],{},[902,69994,7200],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,69997,69998,45926,70001,70038,70039,69785,70054,69801,70069,70084,70085,7039,70100,70126,70127,70142,70143,1343,70158,7039,70173,70126,70198,70213,70214,70227,70228,70243,70244,70259,70260,1343,70273,1343,70288,1343,70303,1977],{},[38,69999,70000],{},"3.3",[883,70002,70004],{"className":70003},[886],[888,70005,70006],{"xmlns":890},[892,70007,70008,70035],{},[895,70009,70010,70012,70014,70016,70018,70020,70022,70024,70027,70029],{},[898,70011,2398],{},[1664,70013,1676],{},[898,70015,2379],{},[1664,70017,1667],{"stretchy":1666},[898,70019,1973],{},[1664,70021,1673],{"stretchy":1666},[1664,70023,1676],{},[1963,70025,70026],{},"1200",[1664,70028,1867],{},[1720,70030,70031,70033],{},[898,70032,1973],{},[1963,70034,1970],{},[902,70036,70037],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,70040,70042],{"className":70041},[886],[888,70043,70044],{"xmlns":890},[892,70045,70046,70052],{},[895,70047,70048,70050],{},[898,70049,1991],{},[898,70051,1959],{},[902,70053,4662],{"encoding":904},[883,70055,70057],{"className":70056},[886],[888,70058,70059],{"xmlns":890},[892,70060,70061,70067],{},[895,70062,70063,70065],{},[898,70064,4822],{},[898,70066,1959],{},[902,70068,55945],{"encoding":904},[883,70070,70072],{"className":70071},[886],[888,70073,70074],{"xmlns":890},[892,70075,70076,70082],{},[895,70077,70078,70080],{},[898,70079,1956],{},[898,70081,1959],{},[902,70083,7200],{"encoding":904},". (b) Vypočtěte ",[883,70086,70088],{"className":70087},[886],[888,70089,70090],{"xmlns":890},[892,70091,70092,70098],{},[895,70093,70094,70096],{},[898,70095,1991],{},[898,70097,1959],{},[902,70099,4662],{"encoding":904},[883,70101,70103],{"className":70102},[886],[888,70104,70105],{"xmlns":890},[892,70106,70107,70123],{},[895,70108,70109,70111,70113,70115,70117,70119,70121],{},[898,70110,1973],{},[1664,70112,1676],{},[1963,70114,3442],{},[1664,70116,1916],{"separator":1915},[1963,70118,9599],{},[1664,70120,1916],{"separator":1915},[1963,70122,38519],{},[902,70124,70125],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,70128,70130],{"className":70129},[886],[888,70131,70132],{"xmlns":890},[892,70133,70134,70140],{},[895,70135,70136,70138],{},[898,70137,1991],{},[898,70139,1959],{},[902,70141,4662],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,70144,70146],{"className":70145},[886],[888,70147,70148],{"xmlns":890},[892,70149,70150,70156],{},[895,70151,70152,70154],{},[898,70153,4822],{},[898,70155,1959],{},[902,70157,55945],{"encoding":904},[883,70159,70161],{"className":70160},[886],[888,70162,70163],{"xmlns":890},[892,70164,70165,70171],{},[895,70166,70167,70169],{},[898,70168,1956],{},[898,70170,1959],{},[902,70172,7200],{"encoding":904},[883,70174,70176],{"className":70175},[886],[888,70177,70178],{"xmlns":890},[892,70179,70180,70196],{},[895,70181,70182,70184,70186,70188,70190,70192,70194],{},[898,70183,1973],{},[1664,70185,1676],{},[1963,70187,3442],{},[1664,70189,1916],{"separator":1915},[1963,70191,9599],{},[1664,70193,1916],{"separator":1915},[1963,70195,38519],{},[902,70197,70125],{"encoding":904},[883,70199,70201],{"className":70200},[886],[888,70202,70203],{"xmlns":890},[892,70204,70205,70211],{},[895,70206,70207,70209],{},[898,70208,1956],{},[898,70210,1959],{},[902,70212,7200],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,70215,70217],{"className":70216},[886],[888,70218,70219],{"xmlns":890},[892,70220,70221,70225],{},[895,70222,70223],{},[898,70224,1973],{},[902,70226,1973],{"encoding":904},", které maximalizuje ",[883,70229,70231],{"className":70230},[886],[888,70232,70233],{"xmlns":890},[892,70234,70235,70241],{},[895,70236,70237,70239],{},[898,70238,1991],{},[898,70240,1959],{},[902,70242,4662],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,70245,70247],{"className":70246},[886],[888,70248,70249],{"xmlns":890},[892,70250,70251,70257],{},[895,70252,70253,70255],{},[898,70254,1991],{},[898,70256,1959],{},[902,70258,4662],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,70261,70263],{"className":70262},[886],[888,70264,70265],{"xmlns":890},[892,70266,70267,70271],{},[895,70268,70269],{},[898,70270,2379],{},[902,70272,2379],{"encoding":904},[883,70274,70276],{"className":70275},[886],[888,70277,70278],{"xmlns":890},[892,70279,70280,70286],{},[895,70281,70282,70284],{},[898,70283,1991],{},[898,70285,1959],{},[902,70287,4662],{"encoding":904},[883,70289,70291],{"className":70290},[886],[888,70292,70293],{"xmlns":890},[892,70294,70295,70301],{},[895,70296,70297,70299],{},[898,70298,4822],{},[898,70300,1959],{},[902,70302,55945],{"encoding":904},[883,70304,70306],{"className":70305},[886],[888,70307,70308],{"xmlns":890},[892,70309,70310,70316],{},[895,70311,70312,70314],{},[898,70313,1956],{},[898,70315,1959],{},[902,70317,7200],{"encoding":904},[724,70319,70320,70323,70324,70354,70355,70370,70371,10720,70384,1343,70402,1343,70419,70437,70438,70460,70461,70476,70477,70490,70491,1977],{},[38,70321,70322],{},"3.4"," Je dán celkový příjem ",[883,70325,70327],{"className":70326},[886],[888,70328,70329],{"xmlns":890},[892,70330,70331,70351],{},[895,70332,70333,70335,70337,70339,70341,70343,70345],{},[898,70334,1991],{},[898,70336,1959],{},[1664,70338,1676],{},[1963,70340,70026],{},[898,70342,1973],{},[1664,70344,1867],{},[1720,70346,70347,70349],{},[898,70348,1973],{},[1963,70350,2774],{},[902,70352,70353],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,70356,70358],{"className":70357},[886],[888,70359,70360],{"xmlns":890},[892,70361,70362,70368],{},[895,70363,70364,70366],{},[898,70365,1991],{},[898,70367,1959],{},[902,70369,4662],{"encoding":904}," vzhledem ke ",[883,70372,70374],{"className":70373},[886],[888,70375,70376],{"xmlns":890},[892,70377,70378,70382],{},[895,70379,70380],{},[898,70381,1973],{},[902,70383,1973],{"encoding":904},[883,70385,70387],{"className":70386},[886],[888,70388,70389],{"xmlns":890},[892,70390,70391,70399],{},[895,70392,70393,70395,70397],{},[898,70394,1973],{},[1664,70396,1676],{},[1963,70398,2826],{},[902,70400,70401],{"encoding":904},"Q = 5",[883,70403,70405],{"className":70404},[886],[888,70406,70407],{"xmlns":890},[892,70408,70409,70417],{},[895,70410,70411,70413,70415],{},[898,70412,1973],{},[1664,70414,1676],{},[1963,70416,6151],{},[902,70418,6154],{"encoding":904},[883,70420,70422],{"className":70421},[886],[888,70423,70424],{"xmlns":890},[892,70425,70426,70434],{},[895,70427,70428,70430,70432],{},[898,70429,1973],{},[1664,70431,1676],{},[1963,70433,4084],{},[902,70435,70436],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,70439,70441],{"className":70440},[886],[888,70442,70443],{"xmlns":890},[892,70444,70445,70457],{},[895,70446,70447,70449,70451,70453,70455],{},[898,70448,1956],{},[898,70450,1959],{},[1664,70452,1667],{"stretchy":1666},[1963,70454,3442],{},[1664,70456,1673],{"stretchy":1666},[902,70458,70459],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,70462,70464],{"className":70463},[886],[888,70465,70466],{"xmlns":890},[892,70467,70468,70474],{},[895,70469,70470,70472],{},[898,70471,1991],{},[898,70473,1959],{},[902,70475,4662],{"encoding":904},", jestliže se ",[883,70478,70480],{"className":70479},[886],[888,70481,70482],{"xmlns":890},[892,70483,70484,70488],{},[895,70485,70486],{},[898,70487,1973],{},[902,70489,1973],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,70492,70494],{"className":70493},[886],[888,70495,70496],{"xmlns":890},[892,70497,70498,70504],{},[895,70499,70500,70502],{},[898,70501,1991],{},[898,70503,1959],{},[902,70505,4662],{"encoding":904},[724,70507,70508,70511,70512,70538,70539,70554,70555,70476,70570,70583],{},[38,70509,70510],{},"3.5"," Je dán mezní příjem ",[883,70513,70515],{"className":70514},[886],[888,70516,70517],{"xmlns":890},[892,70518,70519,70535],{},[895,70520,70521,70523,70525,70527,70529,70531,70533],{},[898,70522,1956],{},[898,70524,1959],{},[1664,70526,1676],{},[1664,70528,1867],{},[898,70530,1973],{},[1664,70532,1700],{},[1963,70534,9599],{},[902,70536,70537],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,70540,70542],{"className":70541},[886],[888,70543,70544],{"xmlns":890},[892,70545,70546,70552],{},[895,70547,70548,70550],{},[898,70549,1991],{},[898,70551,1959],{},[902,70553,4662],{"encoding":904},". (b) Vypočtěte změnu ",[883,70556,70558],{"className":70557},[886],[888,70559,70560],{"xmlns":890},[892,70561,70562,70568],{},[895,70563,70564,70566],{},[898,70565,1991],{},[898,70567,1959],{},[902,70569,4662],{"encoding":904},[883,70571,70573],{"className":70572},[886],[888,70574,70575],{"xmlns":890},[892,70576,70577,70581],{},[895,70578,70579],{},[898,70580,1973],{},[902,70582,1973],{"encoding":904}," změní z 8 na 12.",[198,70585,70587],{"id":70586},"náklady-36316","Náklady (3.6–3.16)",[724,70589,70590,70593,70594,70634,70635,70650,70651,70668,70669,70686,70687,70702,70703,70718,70719,70084,70734,1343,70749,1343,70766,1343,70783,1343,70798,1343,70813,7039,70828,70846,70847,1343,70862,1343,70877,70892],{},[38,70591,70592],{},"3.6"," Jsou dány celkové náklady ",[883,70595,70597],{"className":70596},[886],[888,70598,70599],{"xmlns":890},[892,70600,70601,70631],{},[895,70602,70603,70605,70607,70609,70611,70613,70615,70617,70619],{},[898,70604,1991],{},[898,70606,1703],{},[1664,70608,1676],{},[1963,70610,1965],{},[1664,70612,1700],{},[1963,70614,1970],{},[898,70616,1973],{},[1664,70618,1700],{},[2919,70620,70621],{"scriptlevel":2058,"displaystyle":1666},[2922,70622,70623,70629],{},[1720,70624,70625,70627],{},[898,70626,1973],{},[1963,70628,1970],{},[1963,70630,3442],{},[902,70632,70633],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,70636,70638],{"className":70637},[886],[888,70639,70640],{"xmlns":890},[892,70641,70642,70648],{},[895,70643,70644,70646],{},[898,70645,1662],{},[898,70647,1703],{},[902,70649,55991],{"encoding":904},", celkové variabilní náklady ",[883,70652,70654],{"className":70653},[886],[888,70655,70656],{"xmlns":890},[892,70657,70658,70666],{},[895,70659,70660,70662,70664],{},[898,70661,1991],{},[898,70663,40839],{},[898,70665,1703],{},[902,70667,56009],{"encoding":904},", průměrné variabilní náklady ",[883,70670,70672],{"className":70671},[886],[888,70673,70674],{"xmlns":890},[892,70675,70676,70684],{},[895,70677,70678,70680,70682],{},[898,70679,4822],{},[898,70681,40839],{},[898,70683,1703],{},[902,70685,55811],{"encoding":904},", variabilní náklady na jednotku ",[883,70688,70690],{"className":70689},[886],[888,70691,70692],{"xmlns":890},[892,70693,70694,70700],{},[895,70695,70696,70698],{},[898,70697,40839],{},[898,70699,1703],{},[902,70701,64105],{"encoding":904},", průměrné náklady ",[883,70704,70706],{"className":70705},[886],[888,70707,70708],{"xmlns":890},[892,70709,70710,70716],{},[895,70711,70712,70714],{},[898,70713,4822],{},[898,70715,1703],{},[902,70717,56060],{"encoding":904}," a mezní náklady ",[883,70720,70722],{"className":70721},[886],[888,70723,70724],{"xmlns":890},[892,70725,70726,70732],{},[895,70727,70728,70730],{},[898,70729,1956],{},[898,70731,1703],{},[902,70733,55792],{"encoding":904},[883,70735,70737],{"className":70736},[886],[888,70738,70739],{"xmlns":890},[892,70740,70741,70747],{},[895,70742,70743,70745],{},[898,70744,1991],{},[898,70746,1703],{},[902,70748,3819],{"encoding":904},[883,70750,70752],{"className":70751},[886],[888,70753,70754],{"xmlns":890},[892,70755,70756,70764],{},[895,70757,70758,70760,70762],{},[898,70759,1991],{},[898,70761,40839],{},[898,70763,1703],{},[902,70765,56009],{"encoding":904},[883,70767,70769],{"className":70768},[886],[888,70770,70771],{"xmlns":890},[892,70772,70773,70781],{},[895,70774,70775,70777,70779],{},[898,70776,4822],{},[898,70778,40839],{},[898,70780,1703],{},[902,70782,55811],{"encoding":904},[883,70784,70786],{"className":70785},[886],[888,70787,70788],{"xmlns":890},[892,70789,70790,70796],{},[895,70791,70792,70794],{},[898,70793,40839],{},[898,70795,1703],{},[902,70797,64105],{"encoding":904},[883,70799,70801],{"className":70800},[886],[888,70802,70803],{"xmlns":890},[892,70804,70805,70811],{},[895,70806,70807,70809],{},[898,70808,4822],{},[898,70810,1703],{},[902,70812,56060],{"encoding":904},[883,70814,70816],{"className":70815},[886],[888,70817,70818],{"xmlns":890},[892,70819,70820,70826],{},[895,70821,70822,70824],{},[898,70823,1956],{},[898,70825,1703],{},[902,70827,55792],{"encoding":904},[883,70829,70831],{"className":70830},[886],[888,70832,70833],{"xmlns":890},[892,70834,70835,70843],{},[895,70836,70837,70839,70841],{},[898,70838,1973],{},[1664,70840,1676],{},[1963,70842,3696],{},[902,70844,70845],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,70848,70850],{"className":70849},[886],[888,70851,70852],{"xmlns":890},[892,70853,70854,70860],{},[895,70855,70856,70858],{},[898,70857,1991],{},[898,70859,1703],{},[902,70861,3819],{"encoding":904},[883,70863,70865],{"className":70864},[886],[888,70866,70867],{"xmlns":890},[892,70868,70869,70875],{},[895,70870,70871,70873],{},[898,70872,4822],{},[898,70874,1703],{},[902,70876,56060],{"encoding":904},[883,70878,70880],{"className":70879},[886],[888,70881,70882],{"xmlns":890},[892,70883,70884,70890],{},[895,70885,70886,70888],{},[898,70887,1956],{},[898,70889,1703],{},[902,70891,55792],{"encoding":904}," rostou, resp. klesají.",[724,70894,70895,70898,70899,70718,70929,70944,70945,70960,70961,1343,70976,1343,70991,1977],{},[38,70896,70897],{},"3.7"," Jsou dány průměrné náklady ",[883,70900,70902],{"className":70901},[886],[888,70903,70904],{"xmlns":890},[892,70905,70906,70926],{},[895,70907,70908,70910,70912,70914,70922,70924],{},[898,70909,4822],{},[898,70911,1703],{},[1664,70913,1676],{},[2919,70915,70916],{"scriptlevel":2058,"displaystyle":1666},[2922,70917,70918,70920],{},[1963,70919,1965],{},[898,70921,1973],{},[1664,70923,1700],{},[1963,70925,9599],{},[902,70927,70928],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,70930,70932],{"className":70931},[886],[888,70933,70934],{"xmlns":890},[892,70935,70936,70942],{},[895,70937,70938,70940],{},[898,70939,1956],{},[898,70941,1703],{},[902,70943,55792],{"encoding":904},". (a) Určete celkové náklady ",[883,70946,70948],{"className":70947},[886],[888,70949,70950],{"xmlns":890},[892,70951,70952,70958],{},[895,70953,70954,70956],{},[898,70955,1991],{},[898,70957,1703],{},[902,70959,3819],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,70962,70964],{"className":70963},[886],[888,70965,70966],{"xmlns":890},[892,70967,70968,70974],{},[895,70969,70970,70972],{},[898,70971,4822],{},[898,70973,1703],{},[902,70975,56060],{"encoding":904},[883,70977,70979],{"className":70978},[886],[888,70980,70981],{"xmlns":890},[892,70982,70983,70989],{},[895,70984,70985,70987],{},[898,70986,1991],{},[898,70988,1703],{},[902,70990,3819],{"encoding":904},[883,70992,70994],{"className":70993},[886],[888,70995,70996],{"xmlns":890},[892,70997,70998,71004],{},[895,70999,71000,71002],{},[898,71001,1956],{},[898,71003,1703],{},[902,71005,55792],{"encoding":904},[724,71007,71008,70593,71011,71055,71056,1343,71073,1343,71088,1343,71105,1343,71120,1343,71137,1977],{},[38,71009,71010],{},"3.8",[883,71012,71014],{"className":71013},[886],[888,71015,71016],{"xmlns":890},[892,71017,71018,71052],{},[895,71019,71020,71022,71024,71026,71028,71030,71032,71034,71036,71038,71044,71046],{},[898,71021,1991],{},[898,71023,1703],{},[1664,71025,1676],{},[1963,71027,47203],{},[1664,71029,1700],{},[1963,71031,38519],{},[898,71033,1973],{},[1664,71035,1867],{},[1963,71037,2833],{},[1720,71039,71040,71042],{},[898,71041,1973],{},[1963,71043,1970],{},[1664,71045,1700],{},[1720,71047,71048,71050],{},[898,71049,1973],{},[1963,71051,2774],{},[902,71053,71054],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,71057,71059],{"className":71058},[886],[888,71060,71061],{"xmlns":890},[892,71062,71063,71071],{},[895,71064,71065,71067,71069],{},[898,71066,1991],{},[898,71068,40839],{},[898,71070,1703],{},[902,71072,56009],{"encoding":904},[883,71074,71076],{"className":71075},[886],[888,71077,71078],{"xmlns":890},[892,71079,71080,71086],{},[895,71081,71082,71084],{},[898,71083,1662],{},[898,71085,1703],{},[902,71087,55991],{"encoding":904},[883,71089,71091],{"className":71090},[886],[888,71092,71093],{"xmlns":890},[892,71094,71095,71103],{},[895,71096,71097,71099,71101],{},[898,71098,4822],{},[898,71100,40839],{},[898,71102,1703],{},[902,71104,55811],{"encoding":904},[883,71106,71108],{"className":71107},[886],[888,71109,71110],{"xmlns":890},[892,71111,71112,71118],{},[895,71113,71114,71116],{},[898,71115,4822],{},[898,71117,1703],{},[902,71119,56060],{"encoding":904},[883,71121,71123],{"className":71122},[886],[888,71124,71125],{"xmlns":890},[892,71126,71127,71135],{},[895,71128,71129,71131,71133],{},[898,71130,4822],{},[898,71132,1662],{},[898,71134,1703],{},[902,71136,56027],{"encoding":904},[883,71138,71140],{"className":71139},[886],[888,71141,71142],{"xmlns":890},[892,71143,71144,71150],{},[895,71145,71146,71148],{},[898,71147,1956],{},[898,71149,1703],{},[902,71151,55792],{"encoding":904},[724,71153,71154,70593,71157,71187,71188,70370,71203,7039,71216,1343,71234,1343,71252,70437,71270,70460,71292,71307,71308,71321,71322,1977],{},[38,71155,71156],{},"3.9",[883,71158,71160],{"className":71159},[886],[888,71161,71162],{"xmlns":890},[892,71163,71164,71184],{},[895,71165,71166,71168,71170,71172,71174,71176,71178],{},[898,71167,1991],{},[898,71169,1703],{},[1664,71171,1676],{},[1963,71173,15609],{},[1664,71175,1700],{},[1963,71177,19821],{},[1720,71179,71180,71182],{},[898,71181,1973],{},[1963,71183,1970],{},[902,71185,71186],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,71189,71191],{"className":71190},[886],[888,71192,71193],{"xmlns":890},[892,71194,71195,71201],{},[895,71196,71197,71199],{},[898,71198,1991],{},[898,71200,1703],{},[902,71202,3819],{"encoding":904},[883,71204,71206],{"className":71205},[886],[888,71207,71208],{"xmlns":890},[892,71209,71210,71214],{},[895,71211,71212],{},[898,71213,1973],{},[902,71215,1973],{"encoding":904},[883,71217,71219],{"className":71218},[886],[888,71220,71221],{"xmlns":890},[892,71222,71223,71231],{},[895,71224,71225,71227,71229],{},[898,71226,1973],{},[1664,71228,1676],{},[1963,71230,3442],{},[902,71232,71233],{"encoding":904},"Q = 10",[883,71235,71237],{"className":71236},[886],[888,71238,71239],{"xmlns":890},[892,71240,71241,71249],{},[895,71242,71243,71245,71247],{},[898,71244,1973],{},[1664,71246,1676],{},[1963,71248,9599],{},[902,71250,71251],{"encoding":904},"Q = 20",[883,71253,71255],{"className":71254},[886],[888,71256,71257],{"xmlns":890},[892,71258,71259,71267],{},[895,71260,71261,71263,71265],{},[898,71262,1973],{},[1664,71264,1676],{},[1963,71266,38519],{},[902,71268,71269],{"encoding":904},"Q = 30",[883,71271,71273],{"className":71272},[886],[888,71274,71275],{"xmlns":890},[892,71276,71277,71289],{},[895,71278,71279,71281,71283,71285,71287],{},[898,71280,1956],{},[898,71282,1703],{},[1664,71284,1667],{"stretchy":1666},[1963,71286,36744],{},[1664,71288,1673],{"stretchy":1666},[902,71290,71291],{"encoding":904},"MC(15)",[883,71293,71295],{"className":71294},[886],[888,71296,71297],{"xmlns":890},[892,71298,71299,71305],{},[895,71300,71301,71303],{},[898,71302,1991],{},[898,71304,1703],{},[902,71306,3819],{"encoding":904}," v důsledku změny ",[883,71309,71311],{"className":71310},[886],[888,71312,71313],{"xmlns":890},[892,71314,71315,71319],{},[895,71316,71317],{},[898,71318,1973],{},[902,71320,1973],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,71323,71325],{"className":71324},[886],[888,71326,71327],{"xmlns":890},[892,71328,71329,71335],{},[895,71330,71331,71333],{},[898,71332,1991],{},[898,71334,1703],{},[902,71336,3819],{"encoding":904},[724,71338,71339,71342,71343,70944,71379,71394,71395,70554,71414,71307,71429,71442],{},[38,71340,71341],{},"3.10"," Jsou dány mezní náklady ",[883,71344,71346],{"className":71345},[886],[888,71347,71348],{"xmlns":890},[892,71349,71350,71376],{},[895,71351,71352,71354,71356,71358,71360,71362,71364,71366,71368,71370],{},[898,71353,1956],{},[898,71355,1703],{},[1664,71357,1676],{},[1963,71359,3702],{},[1664,71361,1867],{},[1963,71363,42362],{},[898,71365,1973],{},[1664,71367,1700],{},[1963,71369,65059],{},[1720,71371,71372,71374],{},[898,71373,1973],{},[1963,71375,1970],{},[902,71377,71378],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,71380,71382],{"className":71381},[886],[888,71383,71384],{"xmlns":890},[892,71385,71386,71392],{},[895,71387,71388,71390],{},[898,71389,1991],{},[898,71391,1703],{},[902,71393,3819],{"encoding":904},", jestliže fixní náklady ",[883,71396,71398],{"className":71397},[886],[888,71399,71400],{"xmlns":890},[892,71401,71402,71412],{},[895,71403,71404,71406,71408,71410],{},[898,71405,1662],{},[898,71407,1703],{},[1664,71409,1676],{},[1963,71411,1965],{},[902,71413,2180],{"encoding":904},[883,71415,71417],{"className":71416},[886],[888,71418,71419],{"xmlns":890},[892,71420,71421,71427],{},[895,71422,71423,71425],{},[898,71424,1991],{},[898,71426,1703],{},[902,71428,3819],{"encoding":904},[883,71430,71432],{"className":71431},[886],[888,71433,71434],{"xmlns":890},[892,71435,71436,71440],{},[895,71437,71438],{},[898,71439,1973],{},[902,71441,1973],{"encoding":904}," z 15 na 20.",[724,71444,71445,70593,71448,71491,71492,71505,71506,71521,71522,71537,71538,71505,71551,71521,71568,71585,71586,71505,71599,71521,71614,71629,71630,71650,71651,71674],{},[38,71446,71447],{},"3.11",[883,71449,71451],{"className":71450},[886],[888,71452,71453],{"xmlns":890},[892,71454,71455,71489],{},[895,71456,71457,71459,71461,71463,71465,71467,71469,71471,71473,71475,71481,71483],{},[898,71458,1991],{},[898,71460,1703],{},[1664,71462,1676],{},[1963,71464,1965],{},[1664,71466,1700],{},[1963,71468,5570],{},[898,71470,1973],{},[1664,71472,1867],{},[1963,71474,2826],{},[1720,71476,71477,71479],{},[898,71478,1973],{},[1963,71480,1970],{},[1664,71482,1700],{},[1720,71484,71485,71487],{},[898,71486,1973],{},[1963,71488,2774],{},[902,71490,61407],{"encoding":904},". (a) Určete ",[883,71493,71495],{"className":71494},[886],[888,71496,71497],{"xmlns":890},[892,71498,71499,71503],{},[895,71500,71501],{},[898,71502,1973],{},[902,71504,1973],{"encoding":904},", které minimalizuje ",[883,71507,71509],{"className":71508},[886],[888,71510,71511],{"xmlns":890},[892,71512,71513,71519],{},[895,71514,71515,71517],{},[898,71516,1956],{},[898,71518,1703],{},[902,71520,55792],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,71523,71525],{"className":71524},[886],[888,71526,71527],{"xmlns":890},[892,71528,71529,71535],{},[895,71530,71531,71533],{},[898,71532,1956],{},[898,71534,1703],{},[902,71536,55792],{"encoding":904},". (b) Určete ",[883,71539,71541],{"className":71540},[886],[888,71542,71543],{"xmlns":890},[892,71544,71545,71549],{},[895,71546,71547],{},[898,71548,1973],{},[902,71550,1973],{"encoding":904},[883,71552,71554],{"className":71553},[886],[888,71555,71556],{"xmlns":890},[892,71557,71558,71566],{},[895,71559,71560,71562,71564],{},[898,71561,4822],{},[898,71563,40839],{},[898,71565,1703],{},[902,71567,55811],{"encoding":904},[883,71569,71571],{"className":71570},[886],[888,71572,71573],{"xmlns":890},[892,71574,71575,71583],{},[895,71576,71577,71579,71581],{},[898,71578,4822],{},[898,71580,40839],{},[898,71582,1703],{},[902,71584,55811],{"encoding":904},". (c) Určete ",[883,71587,71589],{"className":71588},[886],[888,71590,71591],{"xmlns":890},[892,71592,71593,71597],{},[895,71594,71595],{},[898,71596,1973],{},[902,71598,1973],{"encoding":904},[883,71600,71602],{"className":71601},[886],[888,71603,71604],{"xmlns":890},[892,71605,71606,71612],{},[895,71607,71608,71610],{},[898,71609,4822],{},[898,71611,1703],{},[902,71613,56060],{"encoding":904},[883,71615,71617],{"className":71616},[886],[888,71618,71619],{"xmlns":890},[892,71620,71621,71627],{},[895,71622,71623,71625],{},[898,71624,4822],{},[898,71626,1703],{},[902,71628,56060],{"encoding":904}," (rada: hledaný kořen ",[883,71631,71633],{"className":71632},[886],[888,71634,71635],{"xmlns":890},[892,71636,71637,71647],{},[895,71638,71639,71641],{},[898,71640,4822],{},[1720,71642,71643,71645],{},[898,71644,1703],{},[1664,71646,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,71648,71649],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,71652,71654],{"className":71653},[886],[888,71655,71656],{"xmlns":890},[892,71657,71658,71671],{},[895,71659,71660,71662,71665,71667,71669],{},[1664,71661,1667],{"stretchy":1666},[1963,71663,71664],{},"4,7",[1664,71666,8990],{"separator":1915},[1963,71668,5845],{},[1664,71670,1673],{"stretchy":1666},[902,71672,71673],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,71676,71677,71680,71681,3210,71709,71726,71727,22094,71768,71789],{},[38,71678,71679],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,71682,71684],{"className":71683},[886],[888,71685,71686],{"xmlns":890},[892,71687,71688,71706],{},[895,71689,71690,71692,71694,71696,71698,71700,71702,71704],{},[898,71691,4822],{},[898,71693,1703],{},[1664,71695,1676],{},[898,71697,4822],{},[898,71699,1703],{},[1664,71701,1667],{"stretchy":1666},[898,71703,1973],{},[1664,71705,1673],{"stretchy":1666},[902,71707,71708],{"encoding":904},"AC = AC(Q)",[883,71710,71712],{"className":71711},[886],[888,71713,71714],{"xmlns":890},[892,71715,71716,71724],{},[895,71717,71718],{},[2355,71719,71720,71722],{},[898,71721,1973],{},[1963,71723,2058],{},[902,71725,38808],{"encoding":904}," minimum, pak platí ",[883,71728,71730],{"className":71729},[886],[888,71731,71732],{"xmlns":890},[892,71733,71734,71766],{},[895,71735,71736,71738,71740,71742,71748,71750,71752,71754,71756,71758,71764],{},[898,71737,4822],{},[898,71739,1703],{},[1664,71741,1667],{"stretchy":1666},[2355,71743,71744,71746],{},[898,71745,1973],{},[1963,71747,2058],{},[1664,71749,1673],{"stretchy":1666},[1664,71751,1676],{},[898,71753,1956],{},[898,71755,1703],{},[1664,71757,1667],{"stretchy":1666},[2355,71759,71760,71762],{},[898,71761,1973],{},[1963,71763,2058],{},[1664,71765,1673],{"stretchy":1666},[902,71767,63069],{"encoding":904},[883,71769,71771],{"className":71770},[886],[888,71772,71773],{"xmlns":890},[892,71774,71775,71787],{},[895,71776,71777,71779,71781,71783,71785],{},[898,71778,1956],{},[898,71780,1703],{},[1664,71782,1667],{"stretchy":1666},[898,71784,1973],{},[1664,71786,1673],{"stretchy":1666},[902,71788,68193],{"encoding":904}," jsou mezní náklady.",[724,71791,71792,70593,71795,71055,71829,71505,71842,71521,71857,1977],{},[38,71793,71794],{},"3.13",[883,71796,71798],{"className":71797},[886],[888,71799,71800],{"xmlns":890},[892,71801,71802,71826],{},[895,71803,71804,71806,71808,71810,71816,71818,71820,71822,71824],{},[898,71805,1991],{},[898,71807,1703],{},[1664,71809,1676],{},[1720,71811,71812,71814],{},[898,71813,1973],{},[1963,71815,1970],{},[1664,71817,1700],{},[1963,71819,1970],{},[898,71821,1973],{},[1664,71823,1700],{},[1963,71825,5570],{},[902,71827,71828],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,71830,71832],{"className":71831},[886],[888,71833,71834],{"xmlns":890},[892,71835,71836,71840],{},[895,71837,71838],{},[898,71839,1973],{},[902,71841,1973],{"encoding":904},[883,71843,71845],{"className":71844},[886],[888,71846,71847],{"xmlns":890},[892,71848,71849,71855],{},[895,71850,71851,71853],{},[898,71852,4822],{},[898,71854,1703],{},[902,71856,56060],{"encoding":904},[883,71858,71860],{"className":71859},[886],[888,71861,71862],{"xmlns":890},[892,71863,71864,71870],{},[895,71865,71866,71868],{},[898,71867,4822],{},[898,71869,1703],{},[902,71871,56060],{"encoding":904},[724,71873,71874,71877,71878,3210,71910,71726,71927,22094,71970,71789],{},[38,71875,71876],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,71879,71881],{"className":71880},[886],[888,71882,71883],{"xmlns":890},[892,71884,71885,71907],{},[895,71886,71887,71889,71891,71893,71895,71897,71899,71901,71903,71905],{},[898,71888,4822],{},[898,71890,40839],{},[898,71892,1703],{},[1664,71894,1676],{},[898,71896,4822],{},[898,71898,40839],{},[898,71900,1703],{},[1664,71902,1667],{"stretchy":1666},[898,71904,1973],{},[1664,71906,1673],{"stretchy":1666},[902,71908,71909],{"encoding":904},"AVC = AVC(Q)",[883,71911,71913],{"className":71912},[886],[888,71914,71915],{"xmlns":890},[892,71916,71917,71925],{},[895,71918,71919],{},[2355,71920,71921,71923],{},[898,71922,1973],{},[1963,71924,2058],{},[902,71926,38808],{"encoding":904},[883,71928,71930],{"className":71929},[886],[888,71931,71932],{"xmlns":890},[892,71933,71934,71968],{},[895,71935,71936,71938,71940,71942,71944,71950,71952,71954,71956,71958,71960,71966],{},[898,71937,4822],{},[898,71939,40839],{},[898,71941,1703],{},[1664,71943,1667],{"stretchy":1666},[2355,71945,71946,71948],{},[898,71947,1973],{},[1963,71949,2058],{},[1664,71951,1673],{"stretchy":1666},[1664,71953,1676],{},[898,71955,1956],{},[898,71957,1703],{},[1664,71959,1667],{"stretchy":1666},[2355,71961,71962,71964],{},[898,71963,1973],{},[1963,71965,2058],{},[1664,71967,1673],{"stretchy":1666},[902,71969,69519],{"encoding":904},[883,71971,71973],{"className":71972},[886],[888,71974,71975],{"xmlns":890},[892,71976,71977,71989],{},[895,71978,71979,71981,71983,71985,71987],{},[898,71980,1956],{},[898,71982,1703],{},[1664,71984,1667],{"stretchy":1666},[898,71986,1973],{},[1664,71988,1673],{"stretchy":1666},[902,71990,68193],{"encoding":904},[724,71992,71993,70593,71996,71055,72042,71505,72055,71521,72072,1977],{},[38,71994,71995],{},"3.15",[883,71997,71999],{"className":71998},[886],[888,72000,72001],{"xmlns":890},[892,72002,72003,72039],{},[895,72004,72005,72007,72009,72011,72013,72015,72017,72019,72021,72023,72029,72031,72033],{},[898,72006,1991],{},[898,72008,1703],{},[1664,72010,1676],{},[1963,72012,3696],{},[1664,72014,1700],{},[1963,72016,36744],{},[898,72018,1973],{},[1664,72020,1867],{},[1963,72022,1970],{},[1720,72024,72025,72027],{},[898,72026,1973],{},[1963,72028,1970],{},[1664,72030,1700],{},[1963,72032,2154],{},[1720,72034,72035,72037],{},[898,72036,1973],{},[1963,72038,2774],{},[902,72040,72041],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,72043,72045],{"className":72044},[886],[888,72046,72047],{"xmlns":890},[892,72048,72049,72053],{},[895,72050,72051],{},[898,72052,1973],{},[902,72054,1973],{"encoding":904},[883,72056,72058],{"className":72057},[886],[888,72059,72060],{"xmlns":890},[892,72061,72062,72070],{},[895,72063,72064,72066,72068],{},[898,72065,4822],{},[898,72067,40839],{},[898,72069,1703],{},[902,72071,55811],{"encoding":904},[883,72073,72075],{"className":72074},[886],[888,72076,72077],{"xmlns":890},[892,72078,72079,72087],{},[895,72080,72081,72083,72085],{},[898,72082,4822],{},[898,72084,40839],{},[898,72086,1703],{},[902,72088,55811],{"encoding":904},[724,72090,72091,72094,72095,72108,72109,72129],{},[38,72092,72093],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,72096,72098],{"className":72097},[886],[888,72099,72100],{"xmlns":890},[892,72101,72102,72106],{},[895,72103,72104],{},[898,72105,1670],{},[902,72107,1670],{"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 ",[883,72110,72112],{"className":72111},[886],[888,72113,72114],{"xmlns":890},[892,72115,72116,72126],{},[895,72117,72118,72120,72122,72124],{},[1963,72119,3442],{},[1690,72121,1692],{},[1963,72123,59582],{},[898,72125,1670],{},[902,72127,72128],{"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.",[198,72131,72133],{"id":72132},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,72135,72136,72139,72140,4454,72162,72188],{},[38,72137,72138],{},"3.17"," Jsou dány ",[883,72141,72143],{"className":72142},[886],[888,72144,72145],{"xmlns":890},[892,72146,72147,72159],{},[895,72148,72149,72151,72153,72155,72157],{},[898,72150,1991],{},[898,72152,1959],{},[1664,72154,1676],{},[1963,72156,3442],{},[898,72158,1973],{},[902,72160,72161],{"encoding":904},"TR = 10Q",[883,72163,72165],{"className":72164},[886],[888,72166,72167],{"xmlns":890},[892,72168,72169,72185],{},[895,72170,72171,72173,72175,72177,72179,72181,72183],{},[898,72172,1991],{},[898,72174,1703],{},[1664,72176,1676],{},[1963,72178,1965],{},[1664,72180,1700],{},[1963,72182,2826],{},[898,72184,1973],{},[902,72186,72187],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,72190,72191,72194,72195,6756,72210,72225,72226,1343,72248,22094,72275,72297,72298,72332],{},[38,72192,72193],{},"3.18"," Odvoďte, že jestliže ",[883,72196,72198],{"className":72197},[886],[888,72199,72200],{"xmlns":890},[892,72201,72202,72208],{},[895,72203,72204,72206],{},[898,72205,1991],{},[898,72207,1959],{},[902,72209,4662],{"encoding":904},[883,72211,72213],{"className":72212},[886],[888,72214,72215],{"xmlns":890},[892,72216,72217,72223],{},[895,72218,72219,72221],{},[898,72220,1991],{},[898,72222,1703],{},[902,72224,3819],{"encoding":904}," jsou lineární tvaru ",[883,72227,72229],{"className":72228},[886],[888,72230,72231],{"xmlns":890},[892,72232,72233,72245],{},[895,72234,72235,72237,72239,72241,72243],{},[898,72236,1991],{},[898,72238,1959],{},[1664,72240,1676],{},[898,72242,724],{},[898,72244,1973],{},[902,72246,72247],{"encoding":904},"TR = pQ",[883,72249,72251],{"className":72250},[886],[888,72252,72253],{"xmlns":890},[892,72254,72255,72272],{},[895,72256,72257,72259,72261,72263,72266,72268,72270],{},[898,72258,1991],{},[898,72260,1703],{},[1664,72262,1676],{},[898,72264,72265],{},"m",[1664,72267,1700],{},[898,72269,37360],{},[898,72271,1973],{},[902,72273,72274],{"encoding":904},"TC = m + nQ",[883,72276,72278],{"className":72277},[886],[888,72279,72280],{"xmlns":890},[892,72281,72282,72294],{},[895,72283,72284,72286,72288,72290,72292],{},[898,72285,72265],{},[1664,72287,1916],{"separator":1915},[898,72289,37360],{},[1664,72291,1916],{"separator":1915},[898,72293,724],{},[902,72295,72296],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,72299,72301],{"className":72300},[886],[888,72302,72303],{"xmlns":890},[892,72304,72305,72329],{},[895,72306,72307,72313,72315],{},[1720,72308,72309,72311],{},[898,72310,1973],{},[1664,72312,4920],{},[1664,72314,1676],{},[2919,72316,72317],{"scriptlevel":2058,"displaystyle":1666},[2922,72318,72319,72321],{},[898,72320,72265],{},[895,72322,72323,72325,72327],{},[898,72324,724],{},[1664,72326,1867],{},[898,72328,37360],{},[902,72330,72331],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,72334,72335,72139,72338,4454,72372,71491,72398,72411,72412,70243,72427,72442,72443,70227,72456,70243,72471,72486],{},[38,72336,72337],{},"3.19",[883,72339,72341],{"className":72340},[886],[888,72342,72343],{"xmlns":890},[892,72344,72345,72369],{},[895,72346,72347,72349,72351,72353,72355,72357,72363,72365,72367],{},[898,72348,1991],{},[898,72350,1959],{},[1664,72352,1676],{},[1664,72354,1867],{},[1963,72356,1970],{},[1720,72358,72359,72361],{},[898,72360,1973],{},[1963,72362,1970],{},[1664,72364,1700],{},[1963,72366,23446],{},[898,72368,1973],{},[902,72370,72371],{"encoding":904},"TR = -2Q^2 + 14Q",[883,72373,72375],{"className":72374},[886],[888,72376,72377],{"xmlns":890},[892,72378,72379,72395],{},[895,72380,72381,72383,72385,72387,72389,72391,72393],{},[898,72382,1991],{},[898,72384,1703],{},[1664,72386,1676],{},[1963,72388,1970],{},[898,72390,1973],{},[1664,72392,1700],{},[1963,72394,3442],{},[902,72396,72397],{"encoding":904},"TC = 2Q + 10",[883,72399,72401],{"className":72400},[886],[888,72402,72403],{"xmlns":890},[892,72404,72405,72409],{},[895,72406,72407],{},[898,72408,1973],{},[902,72410,1973],{"encoding":904},", které maximalizuje zisk ",[883,72413,72415],{"className":72414},[886],[888,72416,72417],{"xmlns":890},[892,72418,72419,72425],{},[895,72420,72421,72423],{},[898,72422,2398],{},[898,72424,1959],{},[902,72426,63979],{"encoding":904},[883,72428,72430],{"className":72429},[886],[888,72431,72432],{"xmlns":890},[892,72433,72434,72440],{},[895,72435,72436,72438],{},[898,72437,2398],{},[898,72439,1959],{},[902,72441,63979],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,72444,72446],{"className":72445},[886],[888,72447,72448],{"xmlns":890},[892,72449,72450,72454],{},[895,72451,72452],{},[898,72453,1973],{},[902,72455,1973],{"encoding":904},[883,72457,72459],{"className":72458},[886],[888,72460,72461],{"xmlns":890},[892,72462,72463,72469],{},[895,72464,72465,72467],{},[898,72466,1991],{},[898,72468,1959],{},[902,72470,4662],{"encoding":904},[883,72472,72474],{"className":72473},[886],[888,72475,72476],{"xmlns":890},[892,72477,72478,72484],{},[895,72479,72480,72482],{},[898,72481,1991],{},[898,72483,1959],{},[902,72485,4662],{"encoding":904},". (d) Graficky interpretujte.",[724,72488,72489,48184,72492,1343,72518,1343,72537,71491,72557,72411,72570,70243,72585,72600,72601,72623,72624,71674],{},[38,72490,72491],{},"3.20",[883,72493,72495],{"className":72494},[886],[888,72496,72497],{"xmlns":890},[892,72498,72499,72515],{},[895,72500,72501,72503,72505,72507,72509],{},[898,72502,2398],{},[1664,72504,1676],{},[1963,72506,20642],{},[1664,72508,1867],{},[1720,72510,72511,72513],{},[898,72512,1973],{},[1963,72514,1970],{},[902,72516,72517],{"encoding":904},"P = 400 - Q^2",[883,72519,72521],{"className":72520},[886],[888,72522,72523],{"xmlns":890},[892,72524,72525,72535],{},[895,72526,72527,72529,72531,72533],{},[898,72528,1662],{},[898,72530,1703],{},[1664,72532,1676],{},[1963,72534,1965],{},[902,72536,2180],{"encoding":904},[883,72538,72540],{"className":72539},[886],[888,72541,72542],{"xmlns":890},[892,72543,72544,72554],{},[895,72545,72546,72548,72550,72552],{},[898,72547,1956],{},[898,72549,1703],{},[1664,72551,1676],{},[1963,72553,9599],{},[902,72555,72556],{"encoding":904},"MC = 20",[883,72558,72560],{"className":72559},[886],[888,72561,72562],{"xmlns":890},[892,72563,72564,72568],{},[895,72565,72566],{},[898,72567,1973],{},[902,72569,1973],{"encoding":904},[883,72571,72573],{"className":72572},[886],[888,72574,72575],{"xmlns":890},[892,72576,72577,72583],{},[895,72578,72579,72581],{},[898,72580,2398],{},[898,72582,1959],{},[902,72584,63979],{"encoding":904},[883,72586,72588],{"className":72587},[886],[888,72589,72590],{"xmlns":890},[892,72591,72592,72598],{},[895,72593,72594,72596],{},[898,72595,2398],{},[898,72597,1959],{},[902,72599,63979],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,72602,72604],{"className":72603},[886],[888,72605,72606],{"xmlns":890},[892,72607,72608,72620],{},[895,72609,72610,72612,72614,72616,72618],{},[1664,72611,1667],{"stretchy":1666},[1963,72613,2058],{},[1664,72615,1916],{"separator":1915},[1963,72617,2875],{},[1664,72619,1673],{"stretchy":1666},[902,72621,72622],{"encoding":904},"(0, 1)",", druhý do ",[883,72625,72627],{"className":72626},[886],[888,72628,72629],{"xmlns":890},[892,72630,72631,72644],{},[895,72632,72633,72635,72638,72640,72642],{},[1664,72634,1667],{"stretchy":1666},[1963,72636,72637],{},"19",[1664,72639,1916],{"separator":1915},[1963,72641,9599],{},[1664,72643,1673],{"stretchy":1666},[902,72645,72646],{"encoding":904},"(19, 20)",[724,72648,72649,72652,72653,3210,72681,72698,72699,1977],{},[38,72650,72651],{},"3.21"," Dokažte, že má-li zisk ",[883,72654,72656],{"className":72655},[886],[888,72657,72658],{"xmlns":890},[892,72659,72660,72678],{},[895,72661,72662,72664,72666,72668,72670,72672,72674,72676],{},[898,72663,2398],{},[898,72665,1959],{},[1664,72667,1676],{},[898,72669,2398],{},[898,72671,1959],{},[1664,72673,1667],{"stretchy":1666},[898,72675,1973],{},[1664,72677,1673],{"stretchy":1666},[902,72679,72680],{"encoding":904},"PR = PR(Q)",[883,72682,72684],{"className":72683},[886],[888,72685,72686],{"xmlns":890},[892,72687,72688,72696],{},[895,72689,72690],{},[2355,72691,72692,72694],{},[898,72693,1973],{},[1963,72695,2058],{},[902,72697,38808],{"encoding":904}," maximum, pak platí ",[883,72700,72702],{"className":72701},[886],[888,72703,72704],{"xmlns":890},[892,72705,72706,72738],{},[895,72707,72708,72710,72712,72714,72720,72722,72724,72726,72728,72730,72736],{},[898,72709,1956],{},[898,72711,1959],{},[1664,72713,1667],{"stretchy":1666},[2355,72715,72716,72718],{},[898,72717,1973],{},[1963,72719,2058],{},[1664,72721,1673],{"stretchy":1666},[1664,72723,1676],{},[898,72725,1956],{},[898,72727,1703],{},[1664,72729,1667],{"stretchy":1666},[2355,72731,72732,72734],{},[898,72733,1973],{},[1963,72735,2058],{},[1664,72737,1673],{"stretchy":1666},[902,72739,66145],{"encoding":904},[724,72741,72742,72745,72746,4454,72761,56525,72776,72411,72789,72804,72805,1343,72832,72869,72870,1343,72897,1977],{},[38,72743,72744],{},"3.22"," Pro zadané ",[883,72747,72749],{"className":72748},[886],[888,72750,72751],{"xmlns":890},[892,72752,72753,72759],{},[895,72754,72755,72757],{},[898,72756,1956],{},[898,72758,1959],{},[902,72760,7200],{"encoding":904},[883,72762,72764],{"className":72763},[886],[888,72765,72766],{"xmlns":890},[892,72767,72768,72774],{},[895,72769,72770,72772],{},[898,72771,1956],{},[898,72773,1703],{},[902,72775,55792],{"encoding":904},[883,72777,72779],{"className":72778},[886],[888,72780,72781],{"xmlns":890},[892,72782,72783,72787],{},[895,72784,72785],{},[898,72786,1973],{},[902,72788,1973],{"encoding":904},[883,72790,72792],{"className":72791},[886],[888,72793,72794],{"xmlns":890},[892,72795,72796,72802],{},[895,72797,72798,72800],{},[898,72799,2398],{},[898,72801,1959],{},[902,72803,63979],{"encoding":904},". (a) ",[883,72806,72808],{"className":72807},[886],[888,72809,72810],{"xmlns":890},[892,72811,72812,72829],{},[895,72813,72814,72816,72818,72820,72823,72825,72827],{},[898,72815,1956],{},[898,72817,1959],{},[1664,72819,1676],{},[1963,72821,72822],{},"236",[1664,72824,1867],{},[1963,72826,42362],{},[898,72828,1973],{},[902,72830,72831],{"encoding":904},"MR = 236 - 16Q",[883,72833,72835],{"className":72834},[886],[888,72836,72837],{"xmlns":890},[892,72838,72839,72866],{},[895,72840,72841,72843,72845,72847,72849,72855,72857,72860,72862,72864],{},[898,72842,1956],{},[898,72844,1703],{},[1664,72846,1676],{},[1963,72848,2774],{},[1720,72850,72851,72853],{},[898,72852,1973],{},[1963,72854,1970],{},[1664,72856,1867],{},[1963,72858,72859],{},"32",[898,72861,1973],{},[1664,72863,1700],{},[1963,72865,6310],{},[902,72867,72868],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,72871,72873],{"className":72872},[886],[888,72874,72875],{"xmlns":890},[892,72876,72877,72894],{},[895,72878,72879,72881,72883,72885,72888,72890,72892],{},[898,72880,1956],{},[898,72882,1959],{},[1664,72884,1676],{},[1963,72886,72887],{},"280",[1664,72889,1867],{},[1963,72891,9599],{},[898,72893,1973],{},[902,72895,72896],{"encoding":904},"MR = 280 - 20Q",[883,72898,72900],{"className":72899},[886],[888,72901,72902],{"xmlns":890},[892,72903,72904,72931],{},[895,72905,72906,72908,72910,72912,72915,72921,72923,72925,72927,72929],{},[898,72907,1956],{},[898,72909,1703],{},[1664,72911,1676],{},[1963,72913,72914],{},"1,6",[1720,72916,72917,72919],{},[898,72918,1973],{},[1963,72920,1970],{},[1664,72922,1867],{},[1963,72924,36744],{},[898,72926,1973],{},[1664,72928,1700],{},[1963,72930,3702],{},[902,72932,72933],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,72935,72936,72745,72939,4454,72954,56525,72969,70227,72982,70243,72997,72804,73012,1343,73043,72869,73079,1343,73111,73155,73156,1343,73188,1977],{},[38,72937,72938],{},"3.23",[883,72940,72942],{"className":72941},[886],[888,72943,72944],{"xmlns":890},[892,72945,72946,72952],{},[895,72947,72948,72950],{},[898,72949,1991],{},[898,72951,1959],{},[902,72953,4662],{"encoding":904},[883,72955,72957],{"className":72956},[886],[888,72958,72959],{"xmlns":890},[892,72960,72961,72967],{},[895,72962,72963,72965],{},[898,72964,1991],{},[898,72966,1703],{},[902,72968,3819],{"encoding":904},[883,72970,72972],{"className":72971},[886],[888,72973,72974],{"xmlns":890},[892,72975,72976,72980],{},[895,72977,72978],{},[898,72979,1973],{},[902,72981,1973],{"encoding":904},[883,72983,72985],{"className":72984},[886],[888,72986,72987],{"xmlns":890},[892,72988,72989,72995],{},[895,72990,72991,72993],{},[898,72992,2398],{},[898,72994,1959],{},[902,72996,63979],{"encoding":904},[883,72998,73000],{"className":72999},[886],[888,73001,73002],{"xmlns":890},[892,73003,73004,73010],{},[895,73005,73006,73008],{},[898,73007,2398],{},[898,73009,1959],{},[902,73011,63979],{"encoding":904},[883,73013,73015],{"className":73014},[886],[888,73016,73017],{"xmlns":890},[892,73018,73019,73040],{},[895,73020,73021,73023,73025,73027,73030,73032,73034],{},[898,73022,1991],{},[898,73024,1959],{},[1664,73026,1676],{},[1963,73028,73029],{},"125",[898,73031,1973],{},[1664,73033,1867],{},[1720,73035,73036,73038],{},[898,73037,1973],{},[1963,73039,1970],{},[902,73041,73042],{"encoding":904},"TR = 125Q - Q^2",[883,73044,73046],{"className":73045},[886],[888,73047,73048],{"xmlns":890},[892,73049,73050,73076],{},[895,73051,73052,73054,73056,73058,73060,73062,73064,73066,73068,73070],{},[898,73053,1991],{},[898,73055,1703],{},[1664,73057,1676],{},[1963,73059,15609],{},[1664,73061,1700],{},[1963,73063,2826],{},[898,73065,1973],{},[1664,73067,1700],{},[1963,73069,5575],{},[1720,73071,73072,73074],{},[898,73073,1973],{},[1963,73075,1970],{},[902,73077,73078],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,73080,73082],{"className":73081},[886],[888,73083,73084],{"xmlns":890},[892,73085,73086,73108],{},[895,73087,73088,73090,73092,73094,73096,73098,73100,73102],{},[898,73089,1991],{},[898,73091,1959],{},[1664,73093,1676],{},[1963,73095,9599],{},[898,73097,1973],{},[1664,73099,1867],{},[1963,73101,1970],{},[1720,73103,73104,73106],{},[898,73105,1973],{},[1963,73107,1970],{},[902,73109,73110],{"encoding":904},"TR = 20Q - 2Q^2",[883,73112,73114],{"className":73113},[886],[888,73115,73116],{"xmlns":890},[892,73117,73118,73152],{},[895,73119,73120,73122,73124,73126,73128,73130,73132,73134,73136,73138,73144,73146],{},[898,73121,1991],{},[898,73123,1703],{},[1664,73125,1676],{},[1963,73127,1970],{},[1664,73129,1700],{},[1963,73131,9599],{},[898,73133,1973],{},[1664,73135,1867],{},[1963,73137,6151],{},[1720,73139,73140,73142],{},[898,73141,1973],{},[1963,73143,1970],{},[1664,73145,1700],{},[1720,73147,73148,73150],{},[898,73149,1973],{},[1963,73151,2774],{},[902,73153,73154],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,73157,73159],{"className":73158},[886],[888,73160,73161],{"xmlns":890},[892,73162,73163,73185],{},[895,73164,73165,73167,73169,73171,73173,73175,73177,73179],{},[898,73166,1991],{},[898,73168,1959],{},[1664,73170,1676],{},[1963,73172,2944],{},[898,73174,1973],{},[1664,73176,1867],{},[1963,73178,24289],{},[1720,73180,73181,73183],{},[898,73182,1973],{},[1963,73184,1970],{},[902,73186,73187],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,73189,73191],{"className":73190},[886],[888,73192,73193],{"xmlns":890},[892,73194,73195,73243],{},[895,73196,73197,73199,73201,73203,73205,73207,73209,73211,73213,73229,73231],{},[898,73198,1991],{},[898,73200,1703],{},[1664,73202,1676],{},[1963,73204,2944],{},[1664,73206,1700],{},[1963,73208,1970],{},[898,73210,1973],{},[1664,73212,1867],{},[2919,73214,73215],{"scriptlevel":2058,"displaystyle":1666},[2922,73216,73217,73227],{},[895,73218,73219,73221],{},[1963,73220,2774],{},[1720,73222,73223,73225],{},[898,73224,1973],{},[1963,73226,1970],{},[1963,73228,3442],{},[1664,73230,1700],{},[2919,73232,73233],{"scriptlevel":2058,"displaystyle":1666},[2922,73234,73235,73241],{},[1720,73236,73237,73239],{},[898,73238,1973],{},[1963,73240,2774],{},[1963,73242,9599],{},[902,73244,73245],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,73247,73248,73251,73252,73282,73283,73315,73316,22094,73346,73376],{},[38,73249,73250],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,73253,73255],{"className":73254},[886],[888,73256,73257],{"xmlns":890},[892,73258,73259,73279],{},[895,73260,73261,73267,73269,73271,73273],{},[2355,73262,73263,73265],{},[898,73264,2398],{},[1963,73266,2875],{},[1664,73268,1676],{},[1963,73270,15609],{},[1664,73272,1867],{},[2355,73274,73275,73277],{},[898,73276,1973],{},[1963,73278,2875],{},[902,73280,73281],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,73284,73286],{"className":73285},[886],[888,73287,73288],{"xmlns":890},[892,73289,73290,73312],{},[895,73291,73292,73298,73300,73302,73304,73306],{},[2355,73293,73294,73296],{},[898,73295,2398],{},[1963,73297,1970],{},[1664,73299,1676],{},[1963,73301,30581],{},[1664,73303,1867],{},[1963,73305,65059],{},[2355,73307,73308,73310],{},[898,73309,1973],{},[1963,73311,1970],{},[902,73313,73314],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,73317,73319],{"className":73318},[886],[888,73320,73321],{"xmlns":890},[892,73322,73323,73343],{},[895,73324,73325,73327,73329,73331,73333,73335,73337,73339,73341],{},[898,73326,1991],{},[898,73328,1703],{},[1664,73330,1676],{},[1963,73332,3696],{},[1690,73334,1692],{},[1963,73336,59582],{},[1664,73338,1700],{},[1963,73340,9599],{},[898,73342,1973],{},[902,73344,73345],{"encoding":904},"TC = 50\\,000 + 20Q",[883,73347,73349],{"className":73348},[886],[888,73350,73351],{"xmlns":890},[892,73352,73353,73373],{},[895,73354,73355,73357,73359,73365,73367],{},[898,73356,1973],{},[1664,73358,1676],{},[2355,73360,73361,73363],{},[898,73362,1973],{},[1963,73364,2875],{},[1664,73366,1700],{},[2355,73368,73369,73371],{},[898,73370,1973],{},[1963,73372,1970],{},[902,73374,73375],{"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.",[724,73378,73379,73382,73383,73413,73414,73315,73446,22094,73476,73505],{},[38,73380,73381],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,73384,73386],{"className":73385},[886],[888,73387,73388],{"xmlns":890},[892,73389,73390,73410],{},[895,73391,73392,73398,73400,73402,73404],{},[2355,73393,73394,73396],{},[898,73395,2398],{},[1963,73397,2875],{},[1664,73399,1676],{},[1963,73401,30581],{},[1664,73403,1867],{},[2355,73405,73406,73408],{},[898,73407,1973],{},[1963,73409,2875],{},[902,73411,73412],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,73415,73417],{"className":73416},[886],[888,73418,73419],{"xmlns":890},[892,73420,73421,73443],{},[895,73422,73423,73429,73431,73433,73435,73437],{},[2355,73424,73425,73427],{},[898,73426,2398],{},[1963,73428,1970],{},[1664,73430,1676],{},[1963,73432,8942],{},[1664,73434,1867],{},[1963,73436,5575],{},[2355,73438,73439,73441],{},[898,73440,1973],{},[1963,73442,1970],{},[902,73444,73445],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,73447,73449],{"className":73448},[886],[888,73450,73451],{"xmlns":890},[892,73452,73453,73473],{},[895,73454,73455,73457,73459,73461,73463,73465,73467,73469,73471],{},[898,73456,1991],{},[898,73458,1703],{},[1664,73460,1676],{},[1963,73462,2826],{},[1690,73464,1692],{},[1963,73466,59582],{},[1664,73468,1700],{},[1963,73470,1965],{},[898,73472,1973],{},[902,73474,73475],{"encoding":904},"TC = 5\\,000 + 100Q",[883,73477,73479],{"className":73478},[886],[888,73480,73481],{"xmlns":890},[892,73482,73483,73503],{},[895,73484,73485,73487,73489,73495,73497],{},[898,73486,1973],{},[1664,73488,1676],{},[2355,73490,73491,73493],{},[898,73492,1973],{},[1963,73494,2875],{},[1664,73496,1700],{},[2355,73498,73499,73501],{},[898,73500,1973],{},[1963,73502,1970],{},[902,73504,73375],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,73507,73509],{"id":73508},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,73511,73512,73515,73516,73563,73564,73581],{},[38,73513,73514],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,73517,73519],{"className":73518},[886],[888,73520,73521],{"xmlns":890},[892,73522,73523,73560],{},[895,73524,73525,73527,73529,73531,73533,73536,73542,73544,73547,73553,73555,73558],{},[898,73526,1991],{},[898,73528,40839],{},[898,73530,1703],{},[1664,73532,1676],{},[1963,73534,73535],{},"0,85",[1720,73537,73538,73540],{},[898,73539,1973],{},[1963,73541,2774],{},[1664,73543,1867],{},[1963,73545,73546],{},"11,9",[1720,73548,73549,73551],{},[898,73550,1973],{},[1963,73552,1970],{},[1664,73554,1700],{},[1963,73556,73557],{},"102",[898,73559,1973],{},[902,73561,73562],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,73565,73567],{"className":73566},[886],[888,73568,73569],{"xmlns":890},[892,73570,73571,73579],{},[895,73572,73573],{},[1720,73574,73575,73577],{},[898,73576,2398],{},[1664,73578,4920],{},[902,73580,4970],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,73583,73584,71342,73587,73623],{},[38,73585,73586],{},"3.27",[883,73588,73590],{"className":73589},[886],[888,73591,73592],{"xmlns":890},[892,73593,73594,73620],{},[895,73595,73596,73598,73600,73602,73604,73610,73612,73614,73616,73618],{},[898,73597,1956],{},[898,73599,1703],{},[1664,73601,1676],{},[1963,73603,3502],{},[1720,73605,73606,73608],{},[898,73607,1973],{},[1963,73609,1970],{},[1664,73611,1867],{},[1963,73613,64940],{},[898,73615,1973],{},[1664,73617,1700],{},[1963,73619,31243],{},[902,73621,73622],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,73625,73626,70593,73629,73623],{},[38,73627,73628],{},"3.28",[883,73630,73632],{"className":73631},[886],[888,73633,73634],{"xmlns":890},[892,73635,73636,73672],{},[895,73637,73638,73640,73642,73644,73646,73652,73654,73656,73662,73664,73666,73668,73670],{},[898,73639,1991],{},[898,73641,1703],{},[1664,73643,1676],{},[1963,73645,5575],{},[1720,73647,73648,73650],{},[898,73649,1973],{},[1963,73651,2774],{},[1664,73653,1867],{},[1963,73655,24701],{},[1720,73657,73658,73660],{},[898,73659,1973],{},[1963,73661,1970],{},[1664,73663,1700],{},[1963,73665,3702],{},[898,73667,1973],{},[1664,73669,1700],{},[1963,73671,15609],{},[902,73673,73674],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,73676,16219],{"id":16218},[120,73678,73679,73707,73752,73824,73889,73929,74021,74127,74167,74281,74374,74438,74470,74530,74536,74600,74649,74703,74811,74866],{},[123,73680,73681,1885,73683,73706],{},[38,73682,56250],{},[883,73684,73686],{"className":73685},[886],[888,73687,73688],{"xmlns":890},[892,73689,73690,73704],{},[895,73691,73692,73694,73696,73698,73700,73702],{},[898,73693,1991],{},[898,73695,1959],{},[1664,73697,1676],{},[898,73699,2398],{},[1664,73701,3753],{},[898,73703,1973],{},[902,73705,67212],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,73708,73709,1885,73711,73751],{},[38,73710,56836],{},[883,73712,73714],{"className":73713},[886],[888,73715,73716],{"xmlns":890},[892,73717,73718,73748],{},[895,73719,73720,73722,73724,73726,73738,73740,73742,73744,73746],{},[898,73721,4822],{},[898,73723,1959],{},[1664,73725,1676],{},[2919,73727,73728],{"scriptlevel":2058,"displaystyle":1666},[2922,73729,73730,73736],{},[895,73731,73732,73734],{},[898,73733,1991],{},[898,73735,1959],{},[898,73737,1973],{},[1664,73739,1676],{},[898,73741,2379],{},[1664,73743,1667],{"stretchy":1666},[898,73745,1973],{},[1664,73747,1673],{"stretchy":1666},[902,73749,73750],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,73753,73754,1885,73756,73792,73793,73808,73809,1977],{},[38,73755,56984],{},[883,73757,73759],{"className":73758},[886],[888,73760,73761],{"xmlns":890},[892,73762,73763,73789],{},[895,73764,73765,73767,73769,73771],{},[898,73766,1956],{},[898,73768,1959],{},[1664,73770,1676],{},[2919,73772,73773],{"scriptlevel":2058,"displaystyle":1666},[2922,73774,73775,73783],{},[895,73776,73777,73779,73781],{},[898,73778,1695],{"mathvariant":1726},[898,73780,1991],{},[898,73782,1959],{},[895,73784,73785,73787],{},[898,73786,1695],{"mathvariant":1726},[898,73788,1973],{},[902,73790,73791],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,73794,73796],{"className":73795},[886],[888,73797,73798],{"xmlns":890},[892,73799,73800,73806],{},[895,73801,73802,73804],{},[898,73803,1991],{},[898,73805,1959],{},[902,73807,4662],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,73810,73812],{"className":73811},[886],[888,73813,73814],{"xmlns":890},[892,73815,73816,73822],{},[895,73817,73818,73820],{},[898,73819,4822],{},[898,73821,1959],{},[902,73823,55945],{"encoding":904},[123,73825,73826,1885,73829,1343,73859,1977],{},[38,73827,73828],{},"Diferenciál příjmu\u002Fnákladů",[883,73830,73832],{"className":73831},[886],[888,73833,73834],{"xmlns":890},[892,73835,73836,73856],{},[895,73837,73838,73840,73842,73844,73846,73848,73850,73852,73854],{},[898,73839,3468],{"mathvariant":1726},[898,73841,1991],{},[898,73843,1959],{},[1664,73845,3315],{},[898,73847,1956],{},[898,73849,1959],{},[1690,73851,1692],{},[898,73853,1695],{"mathvariant":1726},[898,73855,1973],{},[902,73857,73858],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,73860,73862],{"className":73861},[886],[888,73863,73864],{"xmlns":890},[892,73865,73866,73886],{},[895,73867,73868,73870,73872,73874,73876,73878,73880,73882,73884],{},[898,73869,3468],{"mathvariant":1726},[898,73871,1991],{},[898,73873,1703],{},[1664,73875,3315],{},[898,73877,1956],{},[898,73879,1703],{},[1690,73881,1692],{},[898,73883,1695],{"mathvariant":1726},[898,73885,1973],{},[902,73887,73888],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,73890,73891,1885,73893,1977],{},[38,73892,59106],{},[883,73894,73896],{"className":73895},[886],[888,73897,73898],{"xmlns":890},[892,73899,73900,73926],{},[895,73901,73902,73904,73906,73908,73910,73912,73914,73916,73918,73920,73922,73924],{},[898,73903,1991],{},[898,73905,1703],{},[1664,73907,1676],{},[898,73909,1662],{},[898,73911,1703],{},[1664,73913,1700],{},[898,73915,1991],{},[898,73917,40839],{},[898,73919,1703],{},[1664,73921,1667],{"stretchy":1666},[898,73923,1973],{},[1664,73925,1673],{"stretchy":1666},[902,73927,73928],{"encoding":904},"TC = FC + TVC(Q)",[123,73930,73931,1885,73934,1343,73949,1885,73951,1343,73974,1885,73977,1977],{},[38,73932,73933],{},"Fixní náklady",[883,73935,73937],{"className":73936},[886],[888,73938,73939],{"xmlns":890},[892,73940,73941,73947],{},[895,73942,73943,73945],{},[898,73944,1662],{},[898,73946,1703],{},[902,73948,55991],{"encoding":904},[38,73950,59259],{},[883,73952,73954],{"className":73953},[886],[888,73955,73956],{"xmlns":890},[892,73957,73958,73972],{},[895,73959,73960,73962,73964,73966,73968,73970],{},[898,73961,1991],{},[898,73963,40839],{},[898,73965,1703],{},[1664,73967,1667],{"stretchy":1666},[898,73969,1973],{},[1664,73971,1673],{"stretchy":1666},[902,73973,59256],{"encoding":904},[38,73975,73976],{},"variabilní náklady na jednotku",[883,73978,73980],{"className":73979},[886],[888,73981,73982],{"xmlns":890},[892,73983,73984,74018],{},[895,73985,73986,73988,73990,73992,73994,73996,73998],{},[898,73987,40839],{},[898,73989,1703],{},[1664,73991,1667],{"stretchy":1666},[898,73993,1973],{},[1664,73995,1673],{"stretchy":1666},[1664,73997,1676],{},[2919,73999,74000],{"scriptlevel":2058,"displaystyle":1666},[2922,74001,74002,74016],{},[895,74003,74004,74006,74008,74010,74012,74014],{},[898,74005,1991],{},[898,74007,40839],{},[898,74009,1703],{},[1664,74011,1667],{"stretchy":1666},[898,74013,1973],{},[1664,74015,1673],{"stretchy":1666},[898,74017,1973],{},[902,74019,74020],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,74022,74023,1885,74025,1343,74055,1885,74058,1343,74090,1885,74093,1977],{},[38,74024,59267],{},[883,74026,74028],{"className":74027},[886],[888,74029,74030],{"xmlns":890},[892,74031,74032,74052],{},[895,74033,74034,74036,74038,74040],{},[898,74035,4822],{},[898,74037,1703],{},[1664,74039,1676],{},[2919,74041,74042],{"scriptlevel":2058,"displaystyle":1666},[2922,74043,74044,74050],{},[895,74045,74046,74048],{},[898,74047,1991],{},[898,74049,1703],{},[898,74051,1973],{},[902,74053,74054],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,74056,74057],{},"průměrné fixní",[883,74059,74061],{"className":74060},[886],[888,74062,74063],{"xmlns":890},[892,74064,74065,74087],{},[895,74066,74067,74069,74071,74073,74075],{},[898,74068,4822],{},[898,74070,1662],{},[898,74072,1703],{},[1664,74074,1676],{},[2919,74076,74077],{"scriptlevel":2058,"displaystyle":1666},[2922,74078,74079,74085],{},[895,74080,74081,74083],{},[898,74082,1662],{},[898,74084,1703],{},[898,74086,1973],{},[902,74088,74089],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,74091,74092],{},"průměrné variabilní",[883,74094,74096],{"className":74095},[886],[888,74097,74098],{"xmlns":890},[892,74099,74100,74124],{},[895,74101,74102,74104,74106,74108,74110],{},[898,74103,4822],{},[898,74105,40839],{},[898,74107,1703],{},[1664,74109,1676],{},[2919,74111,74112],{"scriptlevel":2058,"displaystyle":1666},[2922,74113,74114,74122],{},[895,74115,74116,74118,74120],{},[898,74117,1991],{},[898,74119,40839],{},[898,74121,1703],{},[898,74123,1973],{},[902,74125,74126],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,74128,74129,1885,74131,1977],{},[38,74130,60454],{},[883,74132,74134],{"className":74133},[886],[888,74135,74136],{"xmlns":890},[892,74137,74138,74164],{},[895,74139,74140,74142,74144,74146],{},[898,74141,1956],{},[898,74143,1703],{},[1664,74145,1676],{},[2919,74147,74148],{"scriptlevel":2058,"displaystyle":1666},[2922,74149,74150,74158],{},[895,74151,74152,74154,74156],{},[898,74153,1695],{"mathvariant":1726},[898,74155,1991],{},[898,74157,1703],{},[895,74159,74160,74162],{},[898,74161,1695],{"mathvariant":1726},[898,74163,1973],{},[902,74165,74166],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,74168,74169,1885,74171,74219,74220,74233,74234,1343,74249,1343,74266,1977],{},[38,74170,61352],{},[883,74172,74174],{"className":74173},[886],[888,74175,74176],{"xmlns":890},[892,74177,74178,74216],{},[895,74179,74180,74182,74184,74186,74188,74190,74192,74194,74196,74198,74200,74206,74208,74210],{},[898,74181,1991],{},[898,74183,1703],{},[1664,74185,1676],{},[898,74187,1662],{},[898,74189,1703],{},[1664,74191,1700],{},[898,74193,207],{},[898,74195,1973],{},[1664,74197,1700],{},[898,74199,1818],{},[1720,74201,74202,74204],{},[898,74203,1973],{},[1963,74205,1970],{},[1664,74207,1700],{},[898,74209,2034],{},[1720,74211,74212,74214],{},[898,74213,1973],{},[1963,74215,2774],{},[902,74217,74218],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,74221,74223],{"className":74222},[886],[888,74224,74225],{"xmlns":890},[892,74226,74227,74231],{},[895,74228,74229],{},[898,74230,900],{},[902,74232,900],{"encoding":904},"-průběhem ",[883,74235,74237],{"className":74236},[886],[888,74238,74239],{"xmlns":890},[892,74240,74241,74247],{},[895,74242,74243,74245],{},[898,74244,4822],{},[898,74246,1703],{},[902,74248,56060],{"encoding":904},[883,74250,74252],{"className":74251},[886],[888,74253,74254],{"xmlns":890},[892,74255,74256,74264],{},[895,74257,74258,74260,74262],{},[898,74259,4822],{},[898,74261,40839],{},[898,74263,1703],{},[902,74265,55811],{"encoding":904},[883,74267,74269],{"className":74268},[886],[888,74270,74271],{"xmlns":890},[892,74272,74273,74279],{},[895,74274,74275,74277],{},[898,74276,1956],{},[898,74278,1703],{},[902,74280,55792],{"encoding":904},[123,74282,74283,74285,74286,10957,74301,74342,74343,61997,74358,74373],{},[38,74284,62434],{},": v bodě minima ",[883,74287,74289],{"className":74288},[886],[888,74290,74291],{"xmlns":890},[892,74292,74293,74299],{},[895,74294,74295,74297],{},[898,74296,4822],{},[898,74298,1703],{},[902,74300,56060],{"encoding":904},[883,74302,74304],{"className":74303},[886],[888,74305,74306],{"xmlns":890},[892,74307,74308,74340],{},[895,74309,74310,74312,74314,74316,74322,74324,74326,74328,74330,74332,74338],{},[898,74311,4822],{},[898,74313,1703],{},[1664,74315,1667],{"stretchy":1666},[2355,74317,74318,74320],{},[898,74319,1973],{},[1963,74321,2058],{},[1664,74323,1673],{"stretchy":1666},[1664,74325,1676],{},[898,74327,1956],{},[898,74329,1703],{},[1664,74331,1667],{"stretchy":1666},[2355,74333,74334,74336],{},[898,74335,1973],{},[1963,74337,2058],{},[1664,74339,1673],{"stretchy":1666},[902,74341,63069],{"encoding":904},"; geometricky ",[883,74344,74346],{"className":74345},[886],[888,74347,74348],{"xmlns":890},[892,74349,74350,74356],{},[895,74351,74352,74354],{},[898,74353,1956],{},[898,74355,1703],{},[902,74357,55792],{"encoding":904},[883,74359,74361],{"className":74360},[886],[888,74362,74363],{"xmlns":890},[892,74364,74365,74371],{},[895,74366,74367,74369],{},[898,74368,4822],{},[898,74370,1703],{},[902,74372,56060],{"encoding":904}," v jejím minimu.",[123,74375,74376,74285,74378,10957,74395,1977],{},[38,74377,63784],{},[883,74379,74381],{"className":74380},[886],[888,74382,74383],{"xmlns":890},[892,74384,74385,74393],{},[895,74386,74387,74389,74391],{},[898,74388,4822],{},[898,74390,40839],{},[898,74392,1703],{},[902,74394,55811],{"encoding":904},[883,74396,74398],{"className":74397},[886],[888,74399,74400],{"xmlns":890},[892,74401,74402,74436],{},[895,74403,74404,74406,74408,74410,74412,74418,74420,74422,74424,74426,74428,74434],{},[898,74405,4822],{},[898,74407,40839],{},[898,74409,1703],{},[1664,74411,1667],{"stretchy":1666},[2355,74413,74414,74416],{},[898,74415,1973],{},[1963,74417,2058],{},[1664,74419,1673],{"stretchy":1666},[1664,74421,1676],{},[898,74423,1956],{},[898,74425,1703],{},[1664,74427,1667],{"stretchy":1666},[2355,74429,74430,74432],{},[898,74431,1973],{},[1963,74433,2058],{},[1664,74435,1673],{"stretchy":1666},[902,74437,69519],{"encoding":904},[123,74439,74440,1885,74442,74469],{},[38,74441,63963],{},[883,74443,74445],{"className":74444},[886],[888,74446,74447],{"xmlns":890},[892,74448,74449,74467],{},[895,74450,74451,74453,74455,74457,74459,74461,74463,74465],{},[898,74452,2398],{},[898,74454,1959],{},[1664,74456,1676],{},[898,74458,1991],{},[898,74460,1959],{},[1664,74462,1867],{},[898,74464,1991],{},[898,74466,1703],{},[902,74468,55700],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,74471,74472,10588,74474,74476,74477,74503,74504,74529],{},[38,74473,64825],{},[614,74475,64088],{},") — hodnoty ",[883,74478,74480],{"className":74479},[886],[888,74481,74482],{"xmlns":890},[892,74483,74484,74500],{},[895,74485,74486,74492,74494],{},[2355,74487,74488,74490],{},[898,74489,1973],{},[898,74491,4822],{},[1664,74493,1916],{"separator":1915},[2355,74495,74496,74498],{},[898,74497,1973],{},[898,74499,23753],{},[902,74501,74502],{"encoding":904},"Q_A, Q_B"," splňující ",[883,74505,74507],{"className":74506},[886],[888,74508,74509],{"xmlns":890},[892,74510,74511,74527],{},[895,74512,74513,74515,74517,74519,74521,74523,74525],{},[898,74514,2398],{},[898,74516,1959],{},[1664,74518,1667],{"stretchy":1666},[898,74520,1973],{},[1664,74522,1673],{"stretchy":1666},[1664,74524,1676],{},[1963,74526,2058],{},[902,74528,64365],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,74531,74532,74535],{},[38,74533,74534],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,74537,74538,74540,74541,10957,74558,74599],{},[38,74539,65879],{}," — v bodě maxima zisku ",[883,74542,74544],{"className":74543},[886],[888,74545,74546],{"xmlns":890},[892,74547,74548,74556],{},[895,74549,74550],{},[2355,74551,74552,74554],{},[898,74553,1973],{},[1963,74555,2058],{},[902,74557,38808],{"encoding":904},[883,74559,74561],{"className":74560},[886],[888,74562,74563],{"xmlns":890},[892,74564,74565,74597],{},[895,74566,74567,74569,74571,74573,74579,74581,74583,74585,74587,74589,74595],{},[898,74568,1956],{},[898,74570,1959],{},[1664,74572,1667],{"stretchy":1666},[2355,74574,74575,74577],{},[898,74576,1973],{},[1963,74578,2058],{},[1664,74580,1673],{"stretchy":1666},[1664,74582,1676],{},[898,74584,1956],{},[898,74586,1703],{},[1664,74588,1667],{"stretchy":1666},[2355,74590,74591,74593],{},[898,74592,1973],{},[1963,74594,2058],{},[1664,74596,1673],{"stretchy":1666},[902,74598,66145],{"encoding":904}," (3.13).",[123,74601,74602,20801,74604,10957,74623,74648],{},[38,74603,67172],{},[883,74605,74607],{"className":74606},[886],[888,74608,74609],{"xmlns":890},[892,74610,74611,74620],{},[895,74612,74613,74615,74617],{},[898,74614,2398],{},[1664,74616,1676],{},[1690,74618,74619],{},"konst",[902,74621,74622],{"encoding":904},"P = \\text{konst}",[883,74624,74626],{"className":74625},[886],[888,74627,74628],{"xmlns":890},[892,74629,74630,74646],{},[895,74631,74632,74634,74636,74638,74640,74642,74644],{},[898,74633,2398],{},[1664,74635,1676],{},[898,74637,1956],{},[898,74639,1703],{},[1664,74641,1667],{"stretchy":1666},[898,74643,1973],{},[1664,74645,1673],{"stretchy":1666},[902,74647,67866],{"encoding":904}," (3.14).",[123,74650,74651,74654,74655,74684,74685,74702],{},[38,74652,74653],{},"Shutdown point"," — bod ",[883,74656,74658],{"className":74657},[886],[888,74659,74660],{"xmlns":890},[892,74661,74662,74682],{},[895,74663,74664,74666,74672,74674,74680],{},[1664,74665,1667],{"stretchy":1666},[1720,74667,74668,74670],{},[898,74669,1973],{},[1664,74671,4920],{},[1664,74673,1916],{"separator":1915},[1720,74675,74676,74678],{},[898,74677,2398],{},[1664,74679,4920],{},[1664,74681,1673],{"stretchy":1666},[902,74683,68155],{"encoding":904}," v minimu ",[883,74686,74688],{"className":74687},[886],[888,74689,74690],{"xmlns":890},[892,74691,74692,74700],{},[895,74693,74694,74696,74698],{},[898,74695,4822],{},[898,74697,40839],{},[898,74699,1703],{},[902,74701,55811],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,74704,74705,1885,74708,7039,74743,68425,74764,74777,74778,74793,74794,1977],{},[38,74706,74707],{},"Funkce nabídky firmy",[883,74709,74711],{"className":74710},[886],[888,74712,74713],{"xmlns":890},[892,74714,74715,74741],{},[895,74716,74717,74719,74721,74723,74725,74727,74729,74731,74733,74735,74737,74739],{},[898,74718,2398],{},[1664,74720,1676],{},[898,74722,2351],{},[1664,74724,1667],{"stretchy":1666},[898,74726,1973],{},[1664,74728,1673],{"stretchy":1666},[1664,74730,1676],{},[898,74732,1956],{},[898,74734,1703],{},[1664,74736,1667],{"stretchy":1666},[898,74738,1973],{},[1664,74740,1673],{"stretchy":1666},[902,74742,69622],{"encoding":904},[883,74744,74746],{"className":74745},[886],[888,74747,74748],{"xmlns":890},[892,74749,74750,74762],{},[895,74751,74752,74754,74756],{},[898,74753,1973],{},[1664,74755,5051],{},[1720,74757,74758,74760],{},[898,74759,1973],{},[1664,74761,4920],{},[902,74763,68424],{"encoding":904},[883,74765,74767],{"className":74766},[886],[888,74768,74769],{"xmlns":890},[892,74770,74771,74775],{},[895,74772,74773],{},[1963,74774,2058],{},[902,74776,2058],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,74779,74781],{"className":74780},[886],[888,74782,74783],{"xmlns":890},[892,74784,74785,74791],{},[895,74786,74787,74789],{},[898,74788,1956],{},[898,74790,1703],{},[902,74792,55792],{"encoding":904}," nad minimem ",[883,74795,74797],{"className":74796},[886],[888,74798,74799],{"xmlns":890},[892,74800,74801,74809],{},[895,74802,74803,74805,74807],{},[898,74804,4822],{},[898,74806,40839],{},[898,74808,1703],{},[902,74810,55811],{"encoding":904},[123,74812,74813,7581,74815,74836,74837,1977],{},[38,74814,50579],{},[883,74816,74818],{"className":74817},[886],[888,74819,74820],{"xmlns":890},[892,74821,74822,74834],{},[895,74823,74824,74826,74828],{},[898,74825,2398],{},[1664,74827,1676],{},[1720,74829,74830,74832],{},[898,74831,2398],{},[1664,74833,4920],{},[902,74835,4923],{"encoding":904}," konstantní ⇒ ",[883,74838,74840],{"className":74839},[886],[888,74841,74842],{"xmlns":890},[892,74843,74844,74864],{},[895,74845,74846,74848,74850,74852,74854,74856,74858],{},[898,74847,4822],{},[898,74849,1959],{},[1664,74851,1676],{},[898,74853,1956],{},[898,74855,1959],{},[1664,74857,1676],{},[1720,74859,74860,74862],{},[898,74861,2398],{},[1664,74863,4920],{},[902,74865,59098],{"encoding":904},[123,74867,74868,74871],{},[38,74869,74870],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,74873,2497],{"id":2496},[120,74875,74876,74895,74907],{},[123,74877,74878,1885,74880,1343,74883,1343,74886,1343,74889,1343,74892],{},[38,74879,51223],{},[207,74881,2493],{"className":74882,"dataFsResolvedFilePath":800,"href":801},[210],[207,74884,4397],{"className":74885,"dataFsResolvedFilePath":848,"href":849},[210],[207,74887,2950],{"className":74888,"dataFsResolvedFilePath":764,"href":765},[210],[207,74890,775],{"className":74891,"dataFsResolvedFilePath":773,"href":774},[210],[207,74893,859],{"className":74894,"dataFsResolvedFilePath":857,"href":858},[210],[123,74896,74897,1885,74899,1343,74903],{},[38,74898,37203],{},[207,74900,74902],{"className":74901,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,74904,74906],{"className":74905,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,74908,74909,1885,74911],{},[38,74910,16703],{},[207,74912,16707],{"className":74913,"dataFsResolvedFilePath":2575,"href":2576},[210],{"title":641,"searchDepth":642,"depth":642,"links":74915},[74916,74917,74924,74930,74934,74935,74939,74940,74941,74942,74948,74949],{"id":51454,"depth":642,"text":1241},{"id":56238,"depth":642,"text":56239,"children":74918},[74919,74920,74921,74922,74923],{"id":56249,"depth":649,"text":56250},{"id":56835,"depth":649,"text":56836},{"id":56983,"depth":649,"text":56984},{"id":57725,"depth":649,"text":57726},{"id":58380,"depth":649,"text":58381},{"id":59101,"depth":642,"text":59102,"children":74925},[74926,74927,74928,74929],{"id":59105,"depth":649,"text":59106},{"id":59266,"depth":649,"text":59267},{"id":60453,"depth":649,"text":60454},{"id":61351,"depth":649,"text":61352},{"id":62433,"depth":642,"text":62434,"children":74931},[74932,74933],{"id":16911,"depth":649,"text":16912},{"id":63783,"depth":649,"text":63784},{"id":63957,"depth":642,"text":63958},{"id":65878,"depth":642,"text":65879,"children":74936},[74937,74938],{"id":65892,"depth":649,"text":16912},{"id":67171,"depth":649,"text":67172},{"id":67803,"depth":642,"text":67804},{"id":69269,"depth":642,"text":69270},{"id":50381,"depth":642,"text":50382},{"id":69730,"depth":642,"text":69731,"children":74943},[74944,74945,74946,74947],{"id":69734,"depth":649,"text":69735},{"id":70586,"depth":649,"text":70587},{"id":72132,"depth":649,"text":72133},{"id":73508,"depth":649,"text":73509},{"id":16218,"depth":642,"text":16219},{"id":2496,"depth":642,"text":2497},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":55620,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,74956,74957,55672,74958,74959,74960],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":74963,"title":74964,"body":74965,"course":1128,"courses":659,"created":10119,"description":641,"extension":661,"meta":87062,"navigation":664,"path":87063,"seo":87064,"sources":87065,"stem":87066,"tags":87067,"type":2553,"updated":677,"__hash__":87073},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":74966,"toc":87019},[74967,74970,75326,75330,75333,75401,75453,75463,75467,75501,75542,75566,75589,75618,75685,75792,75835,75892,75967,76012,76016,76024,76032,76035,76300,76351,76431,76501,76524,76552,76597,76619,76623,76630,76679,76705,76856,76859,76896,77059,77167,77171,77208,77283,77352,77471,77593,77674,77680,77721,77794,77887,77891,77927,78015,78129,78234,78319,78459,78463,78511,78556,78562,78566,78569,78620,78670,78677,78743,78876,78921,78925,78946,79325,79420,79437,79491,79495,79577,79661,79831,79834,79877,79944,80018,80022,80027,80096,80104,80113,80191,80257,80262,80357,80400,80405,80453,80458,80506,80624,80707,80745,80848,80907,81048,81052,81095,81168,81192,81246,81253,81255,81300,81345,81356,81361,81397,81459,81482,81491,81592,81659,81732,81739,81830,81892,81928,81985,82044,82229,82325,82329,82333,82412,82417,82541,82627,82633,82743,82780,82871,82969,82972,82976,83042,83079,83201,83253,83257,83285,83337,83411,83516,83540,83599,83603,83621,83764,83912,83914,83949,83953,83955,84045,84175,84301,84393,84468,84472,84588,84692,84882,84918,85012,85018,85131,85434,85440,85558,85657,85733,85735,86897,86899],[12,74968,74964],{"id":74969},"produkce-produkční-funkce-cobb-douglas-mrts",[4436,74971,74972],{},[724,74973,74974,4443,74976,74978,74979,37396,74992,75005,75006,16876,75019,10588,75021,75045,75046,1885,75048,4454,75082,1885,75085,75113,75114,10957,75134,75164,75165,10588,75168,75196,75197,75200,75201,75231,75232,75262,75263,1885,75266,75306,75307,75325],{},[883,74975,4442],{},[38,74977,859],{}," popisuje vztah mezi vstupy (práce ",[883,74980,74982],{"className":74981},[886],[888,74983,74984],{"xmlns":890},[892,74985,74986,74990],{},[895,74987,74988],{},[898,74989,10358],{},[902,74991,10358],{"encoding":904},[883,74993,74995],{"className":74994},[886],[888,74996,74997],{"xmlns":890},[892,74998,74999,75003],{},[895,75000,75001],{},[898,75002,10363],{},[902,75004,10363],{"encoding":904},") a výstupem ",[883,75007,75009],{"className":75008},[886],[888,75010,75011],{"xmlns":890},[892,75012,75013,75017],{},[895,75014,75015],{},[898,75016,1973],{},[902,75018,1973],{"encoding":904},[38,75020,37464],{},[883,75022,75024],{"className":75023},[886],[888,75025,75026],{"xmlns":890},[892,75027,75028,75042],{},[895,75029,75030,75032,75034,75036,75038,75040],{},[898,75031,1973],{},[1664,75033,1676],{},[898,75035,1973],{},[1664,75037,1667],{"stretchy":1666},[898,75039,10358],{},[1664,75041,1673],{"stretchy":1666},[902,75043,75044],{"encoding":904},"Q = Q(L)",") studujeme ",[614,75047,10587],{},[883,75049,75051],{"className":75050},[886],[888,75052,75053],{"xmlns":890},[892,75054,75055,75079],{},[895,75056,75057,75059,75065,75067,75073,75075,75077],{},[898,75058,1956],{},[2355,75060,75061,75063],{},[898,75062,2398],{},[898,75064,10358],{},[1664,75066,1676],{},[1720,75068,75069,75071],{},[898,75070,1973],{},[1664,75072,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,75074,1667],{"stretchy":1666},[898,75076,10358],{},[1664,75078,1673],{"stretchy":1666},[902,75080,75081],{"encoding":904},"MP_L = Q'(L)",[614,75083,75084],{},"průměrný produkt",[883,75086,75088],{"className":75087},[886],[888,75089,75090],{"xmlns":890},[892,75091,75092,75110],{},[895,75093,75094,75096,75102,75104,75106,75108],{},[898,75095,4822],{},[2355,75097,75098,75100],{},[898,75099,2398],{},[898,75101,10358],{},[1664,75103,1676],{},[898,75105,1973],{},[898,75107,5240],{"mathvariant":1726},[898,75109,10358],{},[902,75111,75112],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,75115,75117],{"className":75116},[886],[888,75118,75119],{"xmlns":890},[892,75120,75121,75131],{},[895,75122,75123,75125],{},[898,75124,4822],{},[2355,75126,75127,75129],{},[898,75128,2398],{},[898,75130,10358],{},[902,75132,75133],{"encoding":904},"AP_L",[883,75135,75137],{"className":75136},[886],[888,75138,75139],{"xmlns":890},[892,75140,75141,75161],{},[895,75142,75143,75145,75151,75153,75155],{},[898,75144,1956],{},[2355,75146,75147,75149],{},[898,75148,2398],{},[898,75150,10358],{},[1664,75152,1676],{},[898,75154,4822],{},[2355,75156,75157,75159],{},[898,75158,2398],{},[898,75160,10358],{},[902,75162,75163],{"encoding":904},"MP_L = AP_L",". Ve ",[38,75166,75167],{},"dvoufaktorovém modelu",[883,75169,75171],{"className":75170},[886],[888,75172,75173],{"xmlns":890},[892,75174,75175,75193],{},[895,75176,75177,75179,75181,75183,75185,75187,75189,75191],{},[898,75178,1973],{},[1664,75180,1676],{},[898,75182,1973],{},[1664,75184,1667],{"stretchy":1666},[898,75186,10358],{},[1664,75188,1916],{"separator":1915},[898,75190,10363],{},[1664,75192,1673],{"stretchy":1666},[902,75194,75195],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,75198,75199],{},"Cobb-Douglasovy"," funkce ",[883,75202,75204],{"className":75203},[886],[888,75205,75206],{"xmlns":890},[892,75207,75208,75228],{},[895,75209,75210,75212,75214,75216,75222],{},[898,75211,1973],{},[1664,75213,1676],{},[898,75215,4822],{},[1720,75217,75218,75220],{},[898,75219,10358],{},[898,75221,207],{},[1720,75223,75224,75226],{},[898,75225,10363],{},[898,75227,1818],{},[902,75229,75230],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,75233,75235],{"className":75234},[886],[888,75236,75237],{"xmlns":890},[892,75238,75239,75259],{},[895,75240,75241,75243,75249,75251,75253],{},[898,75242,1956],{},[2355,75244,75245,75247],{},[898,75246,2398],{},[898,75248,10358],{},[1664,75250,1916],{"separator":1915},[898,75252,1956],{},[2355,75254,75255,75257],{},[898,75256,2398],{},[898,75258,10363],{},[902,75260,75261],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,75264,75265],{},"mezní míru technické substituce",[883,75267,75269],{"className":75268},[886],[888,75270,75271],{"xmlns":890},[892,75272,75273,75303],{},[895,75274,75275,75277,75279,75281,75283,75285,75287,75293,75295,75297],{},[898,75276,1956],{},[898,75278,1959],{},[898,75280,1991],{},[898,75282,2351],{},[1664,75284,1676],{},[898,75286,1956],{},[2355,75288,75289,75291],{},[898,75290,2398],{},[898,75292,10358],{},[898,75294,5240],{"mathvariant":1726},[898,75296,1956],{},[2355,75298,75299,75301],{},[898,75300,2398],{},[898,75302,10363],{},[902,75304,75305],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,75308,75310],{"className":75309},[886],[888,75311,75312],{"xmlns":890},[892,75313,75314,75322],{},[895,75315,75316,75318,75320],{},[898,75317,207],{},[1664,75319,1700],{},[898,75321,1818],{},[902,75323,75324],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,75327,75329],{"id":75328},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,75331,75332],{},"Po prostudování kapitoly 5 student umí:",[120,75334,75335,75341,75351,75357,75363,75368,75374,75384,75389,75395],{},[123,75336,75337,75338,1916],{},"popsat ",[38,75339,75340],{},"jednofaktorový model produkce",[123,75342,75343,75344,4454,75347,75350],{},"vypočítat ",[38,75345,75346],{},"mezní",[38,75348,75349],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,75352,75353,75354,1916],{},"charakterizovat průběh ",[38,75355,75356],{},"křivky produkce",[123,75358,75359,75360,1916],{},"formulovat ",[38,75361,75362],{},"princip maximalizace průměrného produktu práce",[123,75364,75337,75365,1916],{},[38,75366,75367],{},"dvoufaktorový model produkce",[123,75369,75370,75371,1916],{},"uvést tvar ",[38,75372,75373],{},"Cobb–Douglasových produkčních funkcí",[123,75375,75376,75377,1343,75379,1343,75381,1916],{},"vyložit, co jsou ",[38,75378,25113],{},[38,75380,14156],{},[38,75382,75383],{},"klesající výnosy z rozsahu",[123,75385,75343,75386,75350],{},[38,75387,75388],{},"mezní produkty práce a kapitálu",[123,75390,75391,75392,1916],{},"najít ",[38,75393,75394],{},"izokvanty",[123,75396,75343,75397,75400],{},[38,75398,75399],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,75402,75403,75404,75407,75408,75411,75412,1885,75415,1343,75428,1885,75431,4454,75444,75447,75448,75450,75451,1977],{},"Každý proces produkce je určován ",[38,75405,75406],{},"faktory"," (též ",[38,75409,75410],{},"vstupy",") produkce. K hlavním patří ",[38,75413,75414],{},"práce",[883,75416,75418],{"className":75417},[886],[888,75419,75420],{"xmlns":890},[892,75421,75422,75426],{},[895,75423,75424],{},[898,75425,10358],{},[902,75427,10358],{"encoding":904},[38,75429,75430],{},"kapitál",[883,75432,75434],{"className":75433},[886],[888,75435,75436],{"xmlns":890},[892,75437,75438,75442],{},[895,75439,75440],{},[898,75441,10363],{},[902,75443,10363],{"encoding":904},[38,75445,75446],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,75449,37464],{}," (produkce závisí jen na práci); v opačném případě o ",[38,75452,75167],{},[724,75454,75455,75456,1343,75459,75462],{},"Související matematický aparát: ",[207,75457,2950],{"className":75458,"dataFsResolvedFilePath":764,"href":765},[210],[207,75460,784],{"className":75461,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,75464,75466],{"id":75465},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,75468,75469,75470,75483,75484,75497,75498],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,75471,75473],{"className":75472},[886],[888,75474,75475],{"xmlns":890},[892,75476,75477,75481],{},[895,75478,75479],{},[898,75480,1973],{},[902,75482,1973],{"encoding":904}," na práci ",[883,75485,75487],{"className":75486},[886],[888,75488,75489],{"xmlns":890},[892,75490,75491,75495],{},[895,75492,75493],{},[898,75494,10358],{},[902,75496,10358],{"encoding":904}," vyjadřuje ",[38,75499,75500],{},"produkční funkce",[883,75502,75504],{"className":75503},[886],[888,75505,75506],{"xmlns":890,"display":28566},[892,75507,75508,75539],{},[21254,75509,75510],{"width":28571},[21259,75511,75512,75514,75532,75534],{},[21262,75513],{"width":28576},[21262,75515,75516],{},[895,75517,75518,75520,75522,75524,75526,75528,75530],{},[898,75519,1973],{},[1664,75521,1676],{},[898,75523,1973],{},[1664,75525,1667],{"stretchy":1666},[898,75527,10358],{},[1664,75529,1673],{"stretchy":1666},[1664,75531,1916],{"separator":1915},[21262,75533],{"width":28576},[21262,75535,75536],{},[1690,75537,75538],{},"(5.1)",[902,75540,75541],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,75543,75544,75545,10588,75548,75551,75552,75565],{},"jejíž graf se nazývá ",[38,75546,75547],{},"křivka produkce",[614,75549,75550],{},"production curve","). Práce ",[883,75553,75555],{"className":75554},[886],[888,75556,75557],{"xmlns":890},[892,75558,75559,75563],{},[895,75560,75561],{},[898,75562,10358],{},[902,75564,10358],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,75567,75569,75570,1673],{"id":75568},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,75571,75573],{"className":75572},[886],[888,75574,75575],{"xmlns":890},[892,75576,75577,75587],{},[895,75578,75579,75581],{},[898,75580,1956],{},[2355,75582,75583,75585],{},[898,75584,2398],{},[898,75586,10358],{},[902,75588,10608],{"encoding":904},[724,75590,75591,10588,75594,75597,75598,75617],{},[38,75592,75593],{},"Mezní produkt práce",[614,75595,75596],{},"marginal product of labour",") ",[883,75599,75601],{"className":75600},[886],[888,75602,75603],{"xmlns":890},[892,75604,75605,75615],{},[895,75606,75607,75609],{},[898,75608,1956],{},[2355,75610,75611,75613],{},[898,75612,2398],{},[898,75614,10358],{},[902,75616,10608],{"encoding":904}," je derivace produkce podle práce:",[883,75619,75621],{"className":75620},[886],[888,75622,75623],{"xmlns":890,"display":28566},[892,75624,75625,75682],{},[21254,75626,75627],{"width":28571},[21259,75628,75629,75631,75675,75677],{},[21262,75630],{"width":28576},[21262,75632,75633],{},[895,75634,75635,75637,75643,75645,75659,75661,75667,75669,75671,75673],{},[898,75636,1956],{},[2355,75638,75639,75641],{},[898,75640,2398],{},[898,75642,10358],{},[1664,75644,1676],{},[2922,75646,75647,75653],{},[895,75648,75649,75651],{},[898,75650,1695],{},[898,75652,1973],{},[895,75654,75655,75657],{},[898,75656,1695],{},[898,75658,10358],{},[1664,75660,1676],{},[1720,75662,75663,75665],{},[898,75664,1973],{},[1664,75666,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,75668,1667],{"stretchy":1666},[898,75670,10358],{},[1664,75672,1673],{"stretchy":1666},[898,75674,1977],{"mathvariant":1726},[21262,75676],{"width":28576},[21262,75678,75679],{},[1690,75680,75681],{},"(5.2)",[902,75683,75684],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,75686,75687,75688,20445,75706,75734,75735,75752,75753,3271,75770,4488],{},"Pro pevnou hodnotu ",[883,75689,75691],{"className":75690},[886],[888,75692,75693],{"xmlns":890},[892,75694,75695,75703],{},[895,75696,75697],{},[1720,75698,75699,75701],{},[898,75700,10358],{},[1664,75702,4920],{},[902,75704,75705],{"encoding":904},"L^*",[883,75707,75709],{"className":75708},[886],[888,75710,75711],{"xmlns":890},[892,75712,75713,75731],{},[895,75714,75715,75721,75723,75729],{},[1720,75716,75717,75719],{},[898,75718,1973],{},[1664,75720,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,75722,1667],{"stretchy":1666},[1720,75724,75725,75727],{},[898,75726,10358],{},[1664,75728,4920],{},[1664,75730,1673],{"stretchy":1666},[902,75732,75733],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,75736,75738],{"className":75737},[886],[888,75739,75740],{"xmlns":890},[892,75741,75742,75750],{},[895,75743,75744],{},[1720,75745,75746,75748],{},[898,75747,10358],{},[1664,75749,4920],{},[902,75751,75705],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,75754,75756],{"className":75755},[886],[888,75757,75758],{"xmlns":890},[892,75759,75760,75768],{},[895,75761,75762],{},[1720,75763,75764,75766],{},[898,75765,10358],{},[1664,75767,4920],{},[902,75769,75705],{"encoding":904},[883,75771,75773],{"className":75772},[886],[888,75774,75775],{"xmlns":890},[892,75776,75777,75789],{},[895,75778,75779,75785,75787],{},[1720,75780,75781,75783],{},[898,75782,10358],{},[1664,75784,4920],{},[1664,75786,1700],{},[1963,75788,2875],{},[902,75790,75791],{"encoding":904},"L^*+1",[4436,75793,75794],{},[724,75795,75796,18523,75798,75817,75818,75821,75822,1977],{},[883,75797,4723],{},[883,75799,75801],{"className":75800},[886],[888,75802,75803],{"xmlns":890},[892,75804,75805,75815],{},[895,75806,75807,75809],{},[898,75808,1956],{},[2355,75810,75811,75813],{},[898,75812,2398],{},[898,75814,10358],{},[902,75816,10608],{"encoding":904}," odpovídá na otázku „",[38,75819,75820],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,75823,75825],{"className":75824},[886],[888,75826,75827],{"xmlns":890},[892,75828,75829,75833],{},[895,75830,75831],{},[898,75832,10358],{},[902,75834,10358],{"encoding":904},[724,75836,75837,75840,75841,75857,75858,3271,75871,75891],{},[38,75838,75839],{},"Přibližná změna produkce"," pro změnu práce o ",[883,75842,75844],{"className":75843},[886],[888,75845,75846],{"xmlns":890},[892,75847,75848,75854],{},[895,75849,75850,75852],{},[898,75851,1695],{},[898,75853,10358],{},[902,75855,75856],{"encoding":904},"dL"," (z ",[883,75859,75861],{"className":75860},[886],[888,75862,75863],{"xmlns":890},[892,75864,75865,75869],{},[895,75866,75867],{},[898,75868,10358],{},[902,75870,10358],{"encoding":904},[883,75872,75874],{"className":75873},[886],[888,75875,75876],{"xmlns":890},[892,75877,75878,75888],{},[895,75879,75880,75882,75884,75886],{},[898,75881,10358],{},[1664,75883,1700],{},[898,75885,1695],{},[898,75887,10358],{},[902,75889,75890],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,75893,75895],{"className":75894},[886],[888,75896,75897],{"xmlns":890,"display":28566},[892,75898,75899,75964],{},[21254,75900,75901],{"width":28571},[21259,75902,75903,75905,75957,75959],{},[21262,75904],{"width":28576},[21262,75906,75907],{},[895,75908,75909,75911,75913,75915,75917,75919,75921,75927,75929,75931,75933,75935,75937,75939,75941,75943,75949,75951,75953,75955],{},[898,75910,3468],{"mathvariant":1726},[898,75912,1973],{},[1664,75914,3315],{},[898,75916,1695],{},[898,75918,1973],{},[1664,75920,1676],{},[1720,75922,75923,75925],{},[898,75924,1973],{},[1664,75926,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,75928,1667],{"stretchy":1666},[898,75930,10358],{},[1664,75932,1673],{"stretchy":1666},[1690,75934,1692],{},[898,75936,1695],{},[898,75938,10358],{},[1664,75940,1676],{},[898,75942,1956],{},[2355,75944,75945,75947],{},[898,75946,2398],{},[898,75948,10358],{},[1690,75950,1692],{},[898,75952,1695],{},[898,75954,10358],{},[898,75956,1977],{"mathvariant":1726},[21262,75958],{"width":28576},[21262,75960,75961],{},[1690,75962,75963],{},"(5.3)",[902,75965,75966],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,75968,75969,75970,1977],{},"Skutečná změna je ",[883,75971,75973],{"className":75972},[886],[888,75974,75975],{"xmlns":890},[892,75976,75977,76009],{},[895,75978,75979,75981,75983,75985,75987,75989,75991,75993,75995,75997,75999,76001,76003,76005,76007],{},[898,75980,3468],{"mathvariant":1726},[898,75982,1973],{},[1664,75984,1676],{},[898,75986,1973],{},[1664,75988,1667],{"stretchy":1666},[898,75990,10358],{},[1664,75992,1700],{},[898,75994,1695],{},[898,75996,10358],{},[1664,75998,1673],{"stretchy":1666},[1664,76000,1867],{},[898,76002,1973],{},[1664,76004,1667],{"stretchy":1666},[898,76006,10358],{},[1664,76008,1673],{"stretchy":1666},[902,76010,76011],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,76013,76015],{"id":76014},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,76017,76018,10588,76021,3727],{},[38,76019,76020],{},"Zákon klesajících výnosů",[614,76022,76023],{},"law of diminishing marginal productivity",[4436,76025,76026],{},[724,76027,76028,76029,76031],{},"Roste-li postupně některý ze vstupů (",[614,76030,37460],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,76033,76034],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,76036,76037,76038,1885,76059,76078,76079,76129,76130,76132,76133,1885,76153,76172,76173,76129,76205,1748,76207,76226,76227,22094,76244,76278,76279,1762,76296,76299],{},"1° ",[38,76039,76040,76041,2087],{},"Do bodu ",[883,76042,76044],{"className":76043},[886],[888,76045,76046],{"xmlns":890},[892,76047,76048,76056],{},[895,76049,76050],{},[2355,76051,76052,76054],{},[898,76053,10358],{},[1963,76055,2058],{},[902,76057,76058],{"encoding":904},"L_0",[883,76060,76062],{"className":76061},[886],[888,76063,76064],{"xmlns":890},[892,76065,76066,76076],{},[895,76067,76068,76070],{},[898,76069,1956],{},[2355,76071,76072,76074],{},[898,76073,2398],{},[898,76075,10358],{},[902,76077,10608],{"encoding":904}," roste, tj. ",[883,76080,76082],{"className":76081},[886],[888,76083,76084],{"xmlns":890},[892,76085,76086,76126],{},[895,76087,76088,76090,76092,76098,76104,76106,76116,76118,76120,76122,76124],{},[1664,76089,1667],{"stretchy":1666},[898,76091,1956],{},[2355,76093,76094,76096],{},[898,76095,2398],{},[898,76097,10358],{},[1720,76099,76100,76102],{},[1664,76101,1673],{"stretchy":1666},[1664,76103,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,76105,1676],{},[1720,76107,76108,76110],{},[898,76109,1973],{},[895,76111,76112,76114],{},[1664,76113,1728],{"mathvariant":1726},[1664,76115,1728],{"mathvariant":1726},[1664,76117,1667],{"stretchy":1666},[898,76119,10358],{},[1664,76121,1673],{"stretchy":1666},[1664,76123,3984],{},[1963,76125,2058],{},[902,76127,76128],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,76131,38164],{},".\n2° ",[38,76134,76135,76136,2087],{},"Od bodu ",[883,76137,76139],{"className":76138},[886],[888,76140,76141],{"xmlns":890},[892,76142,76143,76151],{},[895,76144,76145],{},[2355,76146,76147,76149],{},[898,76148,10358],{},[1963,76150,2058],{},[902,76152,76058],{"encoding":904},[883,76154,76156],{"className":76155},[886],[888,76157,76158],{"xmlns":890},[892,76159,76160,76170],{},[895,76161,76162,76164],{},[898,76163,1956],{},[2355,76165,76166,76168],{},[898,76167,2398],{},[898,76169,10358],{},[902,76171,10608],{"encoding":904}," klesá, ",[883,76174,76176],{"className":76175},[886],[888,76177,76178],{"xmlns":890},[892,76179,76180,76202],{},[895,76181,76182,76192,76194,76196,76198,76200],{},[1720,76183,76184,76186],{},[898,76185,1973],{},[895,76187,76188,76190],{},[1664,76189,1728],{"mathvariant":1726},[1664,76191,1728],{"mathvariant":1726},[1664,76193,1667],{"stretchy":1666},[898,76195,10358],{},[1664,76197,1673],{"stretchy":1666},[1664,76199,4022],{},[1963,76201,2058],{},[902,76203,76204],{"encoding":904},"Q''(L) \u003C 0",[38,76206,38988],{},[883,76208,76210],{"className":76209},[886],[888,76211,76212],{"xmlns":890},[892,76213,76214,76224],{},[895,76215,76216,76218],{},[898,76217,1956],{},[2355,76219,76220,76222],{},[898,76221,2398],{},[898,76223,10358],{},[902,76225,10608],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,76228,76230],{"className":76229},[886],[888,76231,76232],{"xmlns":890},[892,76233,76234,76242],{},[895,76235,76236],{},[2355,76237,76238,76240],{},[898,76239,10358],{},[1963,76241,2875],{},[902,76243,13711],{"encoding":904},[883,76245,76247],{"className":76246},[886],[888,76248,76249],{"xmlns":890},[892,76250,76251,76275],{},[895,76252,76253,76255,76261,76263,76269,76271,76273],{},[898,76254,1956],{},[2355,76256,76257,76259],{},[898,76258,2398],{},[898,76260,10358],{},[1664,76262,1667],{"stretchy":1666},[2355,76264,76265,76267],{},[898,76266,10358],{},[1963,76268,2875],{},[1664,76270,1673],{"stretchy":1666},[1664,76272,1676],{},[1963,76274,2058],{},[902,76276,76277],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,76280,76282],{"className":76281},[886],[888,76283,76284],{"xmlns":890},[892,76285,76286,76294],{},[895,76287,76288],{},[2355,76289,76290,76292],{},[898,76291,10358],{},[1963,76293,2058],{},[902,76295,76058],{"encoding":904},[38,76297,76298],{},"inflexním bodem"," produkční funkce.",[724,76301,76302,76303,10957,76320,1977],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,76304,76306],{"className":76305},[886],[888,76307,76308],{"xmlns":890},[892,76309,76310,76318],{},[895,76311,76312],{},[2355,76313,76314,76316],{},[898,76315,10358],{},[1963,76317,2058],{},[902,76319,76058],{"encoding":904},[883,76321,76323],{"className":76322},[886],[888,76324,76325],{"xmlns":890},[892,76326,76327,76349],{},[895,76328,76329,76339,76341,76343,76345,76347],{},[1720,76330,76331,76333],{},[898,76332,1973],{},[895,76334,76335,76337],{},[1664,76336,1728],{"mathvariant":1726},[1664,76338,1728],{"mathvariant":1726},[1664,76340,1667],{"stretchy":1666},[898,76342,10358],{},[1664,76344,1673],{"stretchy":1666},[1664,76346,4022],{},[1963,76348,2058],{},[902,76350,76204],{"encoding":904},[724,76352,76353,1885,76356,6235,76396,1343,76413,76430],{},[38,76354,76355],{},"Typický polynom třetího stupně:",[883,76357,76359],{"className":76358},[886],[888,76360,76361],{"xmlns":890},[892,76362,76363,76393],{},[895,76364,76365,76367,76369,76371,76373,76375,76377,76383,76385,76387],{},[898,76366,1973],{},[1664,76368,1667],{"stretchy":1666},[898,76370,10358],{},[1664,76372,1673],{"stretchy":1666},[1664,76374,1676],{},[898,76376,207],{},[1720,76378,76379,76381],{},[898,76380,10358],{},[1963,76382,2774],{},[1664,76384,1700],{},[898,76386,1818],{},[1720,76388,76389,76391],{},[898,76390,10358],{},[1963,76392,1970],{},[902,76394,76395],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,76397,76399],{"className":76398},[886],[888,76400,76401],{"xmlns":890},[892,76402,76403,76411],{},[895,76404,76405,76407,76409],{},[898,76406,207],{},[1664,76408,4022],{},[1963,76410,2058],{},[902,76412,43585],{"encoding":904},[883,76414,76416],{"className":76415},[886],[888,76417,76418],{"xmlns":890},[892,76419,76420,76428],{},[895,76421,76422,76424,76426],{},[898,76423,1818],{},[1664,76425,3984],{},[1963,76427,2058],{},[902,76429,19314],{"encoding":904},". Pak",[883,76432,76434],{"className":76433},[886],[888,76435,76436],{"xmlns":890,"display":28566},[892,76437,76438,76498],{},[895,76439,76440,76446,76448,76450,76458,76466,76468,76470,76476,76478,76480,76488,76496],{},[2355,76441,76442,76444],{},[898,76443,10358],{},[1963,76445,2058],{},[1664,76447,1676],{},[1664,76449,1867],{},[2919,76451,76452],{"scriptlevel":2058,"displaystyle":1666},[2922,76453,76454,76456],{},[1963,76455,2875],{},[1963,76457,2774],{},[2919,76459,76460],{"scriptlevel":2058,"displaystyle":1666},[2922,76461,76462,76464],{},[898,76463,1818],{},[898,76465,207],{},[1664,76467,1916],{"separator":1915},[6444,76469],{"width":6446},[2355,76471,76472,76474],{},[898,76473,10358],{},[1963,76475,2875],{},[1664,76477,1676],{},[1664,76479,1867],{},[2919,76481,76482],{"scriptlevel":2058,"displaystyle":1666},[2922,76483,76484,76486],{},[1963,76485,1970],{},[1963,76487,2774],{},[2919,76489,76490],{"scriptlevel":2058,"displaystyle":1666},[2922,76491,76492,76494],{},[898,76493,1818],{},[898,76495,207],{},[898,76497,1977],{"mathvariant":1726},[902,76499,76500],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,76502,76504,76505,1673],{"id":76503},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,76506,76508],{"className":76507},[886],[888,76509,76510],{"xmlns":890},[892,76511,76512,76522],{},[895,76513,76514,76516],{},[898,76515,4822],{},[2355,76517,76518,76520],{},[898,76519,2398],{},[898,76521,10358],{},[902,76523,75133],{"encoding":904},[724,76525,76526,10588,76529,75597,76532,76551],{},[38,76527,76528],{},"Průměrný produkt práce",[614,76530,76531],{},"average product of labour",[883,76533,76535],{"className":76534},[886],[888,76536,76537],{"xmlns":890},[892,76538,76539,76549],{},[895,76540,76541,76543],{},[898,76542,4822],{},[2355,76544,76545,76547],{},[898,76546,2398],{},[898,76548,10358],{},[902,76550,75133],{"encoding":904}," je podíl produkce a práce:",[883,76553,76555],{"className":76554},[886],[888,76556,76557],{"xmlns":890,"display":28566},[892,76558,76559,76594],{},[21254,76560,76561],{"width":28571},[21259,76562,76563,76565,76587,76589],{},[21262,76564],{"width":28576},[21262,76566,76567],{},[895,76568,76569,76571,76577,76579,76585],{},[898,76570,4822],{},[2355,76572,76573,76575],{},[898,76574,2398],{},[898,76576,10358],{},[1664,76578,1676],{},[2922,76580,76581,76583],{},[898,76582,1973],{},[898,76584,10358],{},[898,76586,1977],{"mathvariant":1726},[21262,76588],{"width":28576},[21262,76590,76591],{},[1690,76592,76593],{},"(5.4)",[902,76595,76596],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,76598,76599,76600,1977],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,76601,76603],{"className":76602},[886],[888,76604,76605],{"xmlns":890},[892,76606,76607,76617],{},[895,76608,76609,76611],{},[898,76610,4822],{},[2355,76612,76613,76615],{},[898,76614,2398],{},[898,76616,10358],{},[902,76618,75133],{"encoding":904},[115,76620,76622],{"id":76621},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,76624,76625],{},[1928,76626],{"alt":76627,"className":76628,"src":76629},"imek-q-mpl-apl-tripanel",[210,1932],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[4436,76631,76632],{},[724,76633,76634,76637,76638,3210,76657,76674,76675],{},[38,76635,76636],{},"Princip:"," Má-li ",[883,76639,76641],{"className":76640},[886],[888,76642,76643],{"xmlns":890},[892,76644,76645,76655],{},[895,76646,76647,76649],{},[898,76648,4822],{},[2355,76650,76651,76653],{},[898,76652,2398],{},[898,76654,10358],{},[902,76656,75133],{"encoding":904},[883,76658,76660],{"className":76659},[886],[888,76661,76662],{"xmlns":890},[892,76663,76664,76672],{},[895,76665,76666],{},[2355,76667,76668,76670],{},[898,76669,10358],{},[1963,76671,2058],{},[902,76673,76058],{"encoding":904}," maximum, pak platí\n",[883,76676,76678],{"className":76677,"title":4767,"style":4768},[4766],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,76680,76681,76682,76685,76686,1885,76690,1977],{},"Slovně: ",[38,76683,76684],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,76687,76689],{"className":76688,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,76691,76693],{"className":76692},[886],[888,76694,76695],{"xmlns":890},[892,76696,76697,76703],{},[895,76698,76699,76701],{},[898,76700,4822],{},[898,76702,1703],{},[902,76704,56060],{"encoding":904},[4436,76706,76707,76731],{},[724,76708,76709,76711,76712],{},[883,76710,5138],{}," Postup — jak najít max ",[883,76713,76715],{"className":76714},[886],[888,76716,76717],{"xmlns":890},[892,76718,76719,76729],{},[895,76720,76721,76723],{},[898,76722,4822],{},[2355,76724,76725,76727],{},[898,76726,2398],{},[898,76728,10358],{},[902,76730,75133],{"encoding":904},[152,76732,76733,76771,76853],{},[123,76734,76735,76736,76770],{},"Napište ",[883,76737,76739],{"className":76738},[886],[888,76740,76741],{"xmlns":890},[892,76742,76743,76767],{},[895,76744,76745,76747,76753,76755,76757,76759,76761,76763,76765],{},[898,76746,4822],{},[2355,76748,76749,76751],{},[898,76750,2398],{},[898,76752,10358],{},[1664,76754,1676],{},[898,76756,1973],{},[1664,76758,1667],{"stretchy":1666},[898,76760,10358],{},[1664,76762,1673],{"stretchy":1666},[898,76764,5240],{"mathvariant":1726},[898,76766,10358],{},[902,76768,76769],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,76772,76773,76774,76806,76807,76810,76811,1977],{},"Položte ",[883,76775,76777],{"className":76776},[886],[888,76778,76779],{"xmlns":890},[892,76780,76781,76803],{},[895,76782,76783,76785,76787,76793,76799,76801],{},[1664,76784,1667],{"stretchy":1666},[898,76786,4822],{},[2355,76788,76789,76791],{},[898,76790,2398],{},[898,76792,10358],{},[1720,76794,76795,76797],{},[1664,76796,1673],{"stretchy":1666},[1664,76798,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,76800,1676],{},[1963,76802,2058],{},[902,76804,76805],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,76808,76809],{},"Zkratka:"," můžete rovnou řešit ",[883,76812,76814],{"className":76813},[886],[888,76815,76816],{"xmlns":890},[892,76817,76818,76850],{},[895,76819,76820,76822,76828,76830,76832,76834,76836,76838,76844,76846,76848],{},[898,76821,1956],{},[2355,76823,76824,76826],{},[898,76825,2398],{},[898,76827,10358],{},[1664,76829,1667],{"stretchy":1666},[898,76831,10358],{},[1664,76833,1673],{"stretchy":1666},[1664,76835,1676],{},[898,76837,4822],{},[2355,76839,76840,76842],{},[898,76841,2398],{},[898,76843,10358],{},[1664,76845,1667],{"stretchy":1666},[898,76847,10358],{},[1664,76849,1673],{"stretchy":1666},[902,76851,76852],{"encoding":904},"MP_L(L) = AP_L(L)",[123,76854,76855],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,76857,66001],{"id":76858},"odvození",[724,76860,76861,76862,76895],{},"Z ",[883,76863,76865],{"className":76864},[886],[888,76866,76867],{"xmlns":890},[892,76868,76869,76893],{},[895,76870,76871,76873,76879,76881,76883,76885,76887,76889,76891],{},[898,76872,4822],{},[2355,76874,76875,76877],{},[898,76876,2398],{},[898,76878,10358],{},[1664,76880,1676],{},[898,76882,1973],{},[1664,76884,1667],{"stretchy":1666},[898,76886,10358],{},[1664,76888,1673],{"stretchy":1666},[898,76890,5240],{"mathvariant":1726},[898,76892,10358],{},[902,76894,76769],{"encoding":904}," a derivace podílu:",[883,76897,76899],{"className":76898},[886],[888,76900,76901],{"xmlns":890,"display":28566},[892,76902,76903,77056],{},[895,76904,76905,76907,76909,76915,76921,76923,76925,76927,76929,76969,76971,76977,77011,77013,77019,77022,77024,77030,77032,77034,77036,77038,77040,77046,77048,77050,77052,77054],{},[1664,76906,1667],{"stretchy":1666},[898,76908,4822],{},[2355,76910,76911,76913],{},[898,76912,2398],{},[898,76914,10358],{},[1720,76916,76917,76919],{},[1664,76918,1673],{"stretchy":1666},[1664,76920,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,76922,1667],{"stretchy":1666},[898,76924,10358],{},[1664,76926,1673],{"stretchy":1666},[1664,76928,1676],{},[2922,76930,76931,76963],{},[895,76932,76933,76939,76941,76943,76945,76947,76949,76951,76953,76955,76957,76959,76961],{},[1720,76934,76935,76937],{},[898,76936,1973],{},[1664,76938,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,76940,1667],{"stretchy":1666},[898,76942,10358],{},[1664,76944,1673],{"stretchy":1666},[1664,76946,3753],{},[898,76948,10358],{},[1664,76950,1867],{},[898,76952,1973],{},[1664,76954,1667],{"stretchy":1666},[898,76956,10358],{},[1664,76958,1673],{"stretchy":1666},[1664,76960,3753],{},[1963,76962,2875],{},[1720,76964,76965,76967],{},[898,76966,10358],{},[1963,76968,1970],{},[1664,76970,1676],{},[2922,76972,76973,76975],{},[1963,76974,2875],{},[898,76976,10358],{},[895,76978,76979,76981,76987,76989,76991,76993,76995,77009],{},[1664,76980,1667],{"fence":1915},[1720,76982,76983,76985],{},[898,76984,1973],{},[1664,76986,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,76988,1667],{"stretchy":1666},[898,76990,10358],{},[1664,76992,1673],{"stretchy":1666},[1664,76994,1867],{},[2922,76996,76997,77007],{},[895,76998,76999,77001,77003,77005],{},[898,77000,1973],{},[1664,77002,1667],{"stretchy":1666},[898,77004,10358],{},[1664,77006,1673],{"stretchy":1666},[898,77008,10358],{},[1664,77010,1673],{"fence":1915},[1664,77012,1676],{},[2922,77014,77015,77017],{},[1963,77016,2875],{},[898,77018,10358],{},[1664,77020,1667],{"fence":1915,"stretchy":1915,"minsize":77021,"maxsize":77021},"1.2em",[898,77023,1956],{},[2355,77025,77026,77028],{},[898,77027,2398],{},[898,77029,10358],{},[1664,77031,1667],{"stretchy":1666},[898,77033,10358],{},[1664,77035,1673],{"stretchy":1666},[1664,77037,1867],{},[898,77039,4822],{},[2355,77041,77042,77044],{},[898,77043,2398],{},[898,77045,10358],{},[1664,77047,1667],{"stretchy":1666},[898,77049,10358],{},[1664,77051,1673],{"stretchy":1666},[1664,77053,1673],{"fence":1915,"stretchy":1915,"minsize":77021,"maxsize":77021},[898,77055,1977],{"mathvariant":1726},[902,77057,77058],{"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).",[724,77060,10226,77061,1762,77083,77166],{},[883,77062,77064],{"className":77063},[886],[888,77065,77066],{"xmlns":890},[892,77067,77068,77080],{},[895,77069,77070,77076,77078],{},[2355,77071,77072,77074],{},[898,77073,10358],{},[1963,77075,2058],{},[1664,77077,3984],{},[1963,77079,2058],{},[902,77081,77082],{"encoding":904},"L_0 > 0",[883,77084,77086],{"className":77085},[886],[888,77087,77088],{"xmlns":890},[892,77089,77090,77163],{},[895,77091,77092,77094,77096,77102,77108,77110,77116,77118,77120,77122,77125,77127,77133,77135,77141,77143,77145,77147,77153,77155,77161],{},[1664,77093,1667],{"stretchy":1666},[898,77095,4822],{},[2355,77097,77098,77100],{},[898,77099,2398],{},[898,77101,10358],{},[1720,77103,77104,77106],{},[1664,77105,1673],{"stretchy":1666},[1664,77107,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,77109,1667],{"stretchy":1666},[2355,77111,77112,77114],{},[898,77113,10358],{},[1963,77115,2058],{},[1664,77117,1673],{"stretchy":1666},[1664,77119,1676],{},[1963,77121,2058],{},[1664,77123,77124],{},"⇔",[898,77126,1956],{},[2355,77128,77129,77131],{},[898,77130,2398],{},[898,77132,10358],{},[1664,77134,1667],{"stretchy":1666},[2355,77136,77137,77139],{},[898,77138,10358],{},[1963,77140,2058],{},[1664,77142,1673],{"stretchy":1666},[1664,77144,1676],{},[898,77146,4822],{},[2355,77148,77149,77151],{},[898,77150,2398],{},[898,77152,10358],{},[1664,77154,1667],{"stretchy":1666},[2355,77156,77157,77159],{},[898,77158,10358],{},[1963,77160,2058],{},[1664,77162,1673],{"stretchy":1666},[902,77164,77165],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,77168,77170],{"id":77169},"příklad-51","Příklad 5.1",[724,77172,77173,77174,1977],{},"Je dána produkce ",[883,77175,77177],{"className":77176},[886],[888,77178,77179],{"xmlns":890},[892,77180,77181,77205],{},[895,77182,77183,77185,77187,77189,77195,77197,77199],{},[898,77184,1973],{},[1664,77186,1676],{},[1963,77188,2833],{},[1720,77190,77191,77193],{},[898,77192,10358],{},[1963,77194,1970],{},[1664,77196,1867],{},[1963,77198,2154],{},[1720,77200,77201,77203],{},[898,77202,10358],{},[1963,77204,2774],{},[902,77206,77207],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,77209,77210,58022,77213,77263,77264,1977],{},[38,77211,77212],{},"(a)",[883,77214,77216],{"className":77215},[886],[888,77217,77218],{"xmlns":890},[892,77219,77220,77260],{},[895,77221,77222,77224,77226,77228,77230,77232,77234,77236,77238,77240,77242,77244,77246,77248,77250,77252,77254,77256,77258],{},[898,77223,10358],{},[1664,77225,1676],{},[1963,77227,1970],{},[1664,77229,1916],{"separator":1915},[1963,77231,2826],{},[1664,77233,1916],{"separator":1915},[1963,77235,6151],{},[1664,77237,1916],{"separator":1915},[1963,77239,3442],{},[1664,77241,1916],{"separator":1915},[1963,77243,23446],{},[1664,77245,1916],{"separator":1915},[1963,77247,4282],{},[1664,77249,1916],{"separator":1915},[1963,77251,9599],{},[1664,77253,1916],{"separator":1915},[1963,77255,38846],{},[1664,77257,1916],{"separator":1915},[1963,77259,5570],{},[902,77261,77262],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,77265,77267],{"className":77266},[886],[888,77268,77269],{"xmlns":890},[892,77270,77271,77281],{},[895,77272,77273,77275],{},[898,77274,1956],{},[2355,77276,77277,77279],{},[898,77278,2398],{},[898,77280,10358],{},[902,77282,10608],{"encoding":904},[724,77284,77285,77286,35468],{},"Podle (5.2): ",[883,77287,77289],{"className":77288},[886],[888,77290,77291],{"xmlns":890},[892,77292,77293,77349],{},[895,77294,77295,77297,77303,77305,77311,77313,77315,77317,77319,77321,77323,77325,77327,77333,77335,77337,77339,77341,77343,77345,77347],{},[898,77296,1956],{},[2355,77298,77299,77301],{},[898,77300,2398],{},[898,77302,10358],{},[1664,77304,1676],{},[1720,77306,77307,77309],{},[898,77308,1973],{},[1664,77310,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,77312,1667],{"stretchy":1666},[898,77314,10358],{},[1664,77316,1673],{"stretchy":1666},[1664,77318,1676],{},[1963,77320,4084],{},[898,77322,10358],{},[1664,77324,1867],{},[1963,77326,19821],{},[1720,77328,77329,77331],{},[898,77330,10358],{},[1963,77332,1970],{},[1664,77334,1676],{},[898,77336,10358],{},[1664,77338,1667],{"stretchy":1666},[1963,77340,4084],{},[1664,77342,1867],{},[1963,77344,19821],{},[898,77346,10358],{},[1664,77348,1673],{"stretchy":1666},[902,77350,77351],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,77353,77354,77391],{},[19,77355,77356],{},[22,77357,77358,77373,77375,77377,77379,77381,77383,77385,77387,77389],{},[25,77359,77360],{},[883,77361,77363],{"className":77362},[886],[888,77364,77365],{"xmlns":890},[892,77366,77367,77371],{},[895,77368,77369],{},[898,77370,10358],{},[902,77372,10358],{"encoding":904},[25,77374,1970],{},[25,77376,2826],{},[25,77378,6151],{},[25,77380,3442],{},[25,77382,23446],{},[25,77384,4282],{},[25,77386,9599],{},[25,77388,38846],{},[25,77390,5570],{},[30,77392,77393],{},[22,77394,77395,77416,77419,77422,77425,77427,77430,77432,77434,77453],{},[35,77396,77397],{},[883,77398,77400],{"className":77399},[886],[888,77401,77402],{"xmlns":890},[892,77403,77404,77414],{},[895,77405,77406,77408],{},[898,77407,1956],{},[2355,77409,77410,77412],{},[898,77411,2398],{},[898,77413,10358],{},[902,77415,10608],{"encoding":904},[35,77417,77418],{},"21,6",[35,77420,77421],{},"45",[35,77423,77424],{},"57,6",[35,77426,3702],{},[35,77428,77429],{},"50,4",[35,77431,77418],{},[35,77433,2058],{},[35,77435,77436],{},[883,77437,77439],{"className":77438},[886],[888,77440,77441],{"xmlns":890},[892,77442,77443,77450],{},[895,77444,77445,77447],{},[1664,77446,1867],{},[1963,77448,77449],{},"12,6",[902,77451,77452],{"encoding":904},"-12{,}6",[35,77454,77455],{},[883,77456,77458],{"className":77457},[886],[888,77459,77460],{"xmlns":890},[892,77461,77462,77468],{},[895,77463,77464,77466],{},[1664,77465,1867],{},[1963,77467,45952],{},[902,77469,77470],{"encoding":904},"-75",[724,77472,77473,77492,77493,77511,77512,77529,77530,77548,77549,77573,77574,77592],{},[883,77474,77476],{"className":77475},[886],[888,77477,77478],{"xmlns":890},[892,77479,77480,77490],{},[895,77481,77482,77484],{},[898,77483,1956],{},[2355,77485,77486,77488],{},[898,77487,2398],{},[898,77489,10358],{},[902,77491,10608],{"encoding":904}," nabývá maxima pro ",[883,77494,77496],{"className":77495},[886],[888,77497,77498],{"xmlns":890},[892,77499,77500,77508],{},[895,77501,77502,77504,77506],{},[898,77503,10358],{},[1664,77505,1676],{},[1963,77507,3442],{},[902,77509,77510],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,77513,77515],{"className":77514},[886],[888,77516,77517],{"xmlns":890},[892,77518,77519,77527],{},[895,77520,77521,77523,77525],{},[898,77522,10358],{},[1664,77524,1676],{},[1963,77526,3442],{},[902,77528,77510],{"encoding":904}," přírůstky klesají, v ",[883,77531,77533],{"className":77532},[886],[888,77534,77535],{"xmlns":890},[892,77536,77537,77545],{},[895,77538,77539,77541,77543],{},[898,77540,10358],{},[1664,77542,1676],{},[1963,77544,9599],{},[902,77546,77547],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,77550,77552],{"className":77551},[886],[888,77553,77554],{"xmlns":890},[892,77555,77556,77570],{},[895,77557,77558,77560,77562,77564,77566,77568],{},[898,77559,1973],{},[1664,77561,1667],{"stretchy":1666},[1963,77563,9599],{},[1664,77565,1673],{"stretchy":1666},[1664,77567,1676],{},[1963,77569,24358],{},[902,77571,77572],{"encoding":904},"Q(20) = 800","), od ",[883,77575,77577],{"className":77576},[886],[888,77578,77579],{"xmlns":890},[892,77580,77581,77589],{},[895,77582,77583,77585,77587],{},[898,77584,10358],{},[1664,77586,3984],{},[1963,77588,9599],{},[902,77590,77591],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,77594,77595],{},[614,77596,77597,77598,77638,77639,3210,77657,1977],{},"Obrázek 5.1 — graf produkce ",[883,77599,77601],{"className":77600},[886],[888,77602,77603],{"xmlns":890},[892,77604,77605,77635],{},[895,77606,77607,77609,77611,77613,77615,77617,77619,77625,77627,77629],{},[898,77608,1973],{},[1664,77610,1667],{"stretchy":1666},[898,77612,10358],{},[1664,77614,1673],{"stretchy":1666},[1664,77616,1676],{},[1963,77618,2833],{},[1720,77620,77621,77623],{},[898,77622,10358],{},[1963,77624,1970],{},[1664,77626,1867],{},[1963,77628,2154],{},[1720,77630,77631,77633],{},[898,77632,10358],{},[1963,77634,2774],{},[902,77636,77637],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,77640,77642],{"className":77641},[886],[888,77643,77644],{"xmlns":890},[892,77645,77646,77654],{},[895,77647,77648,77650,77652],{},[898,77649,1973],{},[1664,77651,1676],{},[1963,77653,24358],{},[902,77655,77656],{"encoding":904},"Q = 800",[883,77658,77660],{"className":77659},[886],[888,77661,77662],{"xmlns":890},[892,77663,77664,77672],{},[895,77665,77666,77668,77670],{},[898,77667,10358],{},[1664,77669,1676],{},[1963,77671,9599],{},[902,77673,77547],{"encoding":904},[724,77675,77676,77679],{},[38,77677,77678],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,77681,77682,77683,1343,77701,2087],{},"Podle (5.3) s ",[883,77684,77686],{"className":77685},[886],[888,77687,77688],{"xmlns":890},[892,77689,77690,77698],{},[895,77691,77692,77694,77696],{},[898,77693,10358],{},[1664,77695,1676],{},[1963,77697,2833],{},[902,77699,77700],{"encoding":904},"L = 6",[883,77702,77704],{"className":77703},[886],[888,77705,77706],{"xmlns":890},[892,77707,77708,77718],{},[895,77709,77710,77712,77714,77716],{},[898,77711,1695],{},[898,77713,10358],{},[1664,77715,1676],{},[1963,77717,2774],{},[902,77719,77720],{"encoding":904},"dL = 3",[883,77722,77724],{"className":77723},[886],[888,77725,77726],{"xmlns":890,"display":28566},[892,77727,77728,77791],{},[895,77729,77730,77732,77734,77736,77738,77744,77746,77748,77750,77752,77754,77756,77758,77760,77762,77764,77766,77768,77770,77772,77774,77776,77778,77780,77782,77784,77786,77788],{},[898,77731,1695],{},[898,77733,1973],{},[1664,77735,1676],{},[898,77737,1956],{},[2355,77739,77740,77742],{},[898,77741,2398],{},[898,77743,10358],{},[1664,77745,1667],{"stretchy":1666},[1963,77747,2833],{},[1664,77749,1673],{"stretchy":1666},[1664,77751,3753],{},[1963,77753,2774],{},[1664,77755,1676],{},[1664,77757,1667],{"stretchy":1666},[1963,77759,4084],{},[1664,77761,3753],{},[1963,77763,2833],{},[1664,77765,1867],{},[1963,77767,19821],{},[1664,77769,3753],{},[1963,77771,6131],{},[1664,77773,1673],{"stretchy":1666},[1664,77775,3753],{},[1963,77777,2774],{},[1664,77779,1676],{},[1963,77781,77429],{},[1664,77783,3753],{},[1963,77785,2774],{},[1664,77787,1676],{},[1963,77789,77790],{},"151,2.",[902,77792,77793],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,77795,77796,77797,58252,77822,77836,77837,1977],{},"Produkce vzroste z ",[883,77798,77800],{"className":77799},[886],[888,77801,77802],{"xmlns":890},[892,77803,77804,77819],{},[895,77805,77806,77808,77810,77812,77814,77816],{},[898,77807,1973],{},[1664,77809,1667],{"stretchy":1666},[1963,77811,2833],{},[1664,77813,1673],{"stretchy":1666},[1664,77815,1676],{},[1963,77817,77818],{},"172,8",[902,77820,77821],{"encoding":904},"Q(6) = 172{,}8",[883,77823,77825],{"className":77824},[886],[888,77826,77827],{"xmlns":890},[892,77828,77829,77834],{},[895,77830,77831],{},[1963,77832,77833],{},"324",[902,77835,77833],{"encoding":904},". Skutečná hodnota: ",[883,77838,77840],{"className":77839},[886],[888,77841,77842],{"xmlns":890},[892,77843,77844,77884],{},[895,77845,77846,77848,77850,77852,77854,77856,77858,77860,77862,77864,77866,77868,77870,77872,77875,77877,77879,77881],{},[898,77847,3468],{"mathvariant":1726},[898,77849,1973],{},[1664,77851,1676],{},[898,77853,1973],{},[1664,77855,1667],{"stretchy":1666},[1963,77857,4567],{},[1664,77859,1673],{"stretchy":1666},[1664,77861,1867],{},[898,77863,1973],{},[1664,77865,1667],{"stretchy":1666},[1963,77867,2833],{},[1664,77869,1673],{"stretchy":1666},[1664,77871,1676],{},[1963,77873,77874],{},"340,2",[1664,77876,1867],{},[1963,77878,77818],{},[1664,77880,1676],{},[1963,77882,77883],{},"167,4",[902,77885,77886],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,77888,77890],{"id":77889},"příklad-52","Příklad 5.2",[724,77892,77893,77894,1977],{},"Ověříme princip (5.5) pro ",[883,77895,77897],{"className":77896},[886],[888,77898,77899],{"xmlns":890},[892,77900,77901,77925],{},[895,77902,77903,77905,77907,77909,77915,77917,77919],{},[898,77904,1973],{},[1664,77906,1676],{},[1963,77908,2833],{},[1720,77910,77911,77913],{},[898,77912,10358],{},[1963,77914,1970],{},[1664,77916,1867],{},[1963,77918,2154],{},[1720,77920,77921,77923],{},[898,77922,10358],{},[1963,77924,2774],{},[902,77926,77207],{"encoding":904},[883,77928,77930],{"className":77929},[886],[888,77931,77932],{"xmlns":890,"display":28566},[892,77933,77934,78012],{},[895,77935,77936,77938,77944,77946,77952,77954,77956,77958,77960,77962,77968,77970,77972,77974,77982,77984,77986,77988,77990,77992,77994,77996,77998,78000,78002,78008,78010],{},[898,77937,4822],{},[2355,77939,77940,77942],{},[898,77941,2398],{},[898,77943,10358],{},[1664,77945,1676],{},[2922,77947,77948,77950],{},[898,77949,1973],{},[898,77951,10358],{},[1664,77953,1676],{},[1963,77955,2833],{},[898,77957,10358],{},[1664,77959,1867],{},[1963,77961,2154],{},[1720,77963,77964,77966],{},[898,77965,10358],{},[1963,77967,1970],{},[1664,77969,1916],{"separator":1915},[6444,77971],{"width":15783},[898,77973,4822],{},[1810,77975,77976,77978,77980],{},[898,77977,2398],{},[898,77979,10358],{},[1664,77981,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,77983,1676],{},[1963,77985,2833],{},[1664,77987,1867],{},[1963,77989,19771],{},[898,77991,10358],{},[1664,77993,1676],{},[1963,77995,2058],{},[1690,77997,4553],{},[1664,77999,4556],{},[1690,78001,4553],{},[2355,78003,78004,78006],{},[898,78005,10358],{},[1963,78007,2058],{},[1664,78009,1676],{},[1963,78011,68783],{},[902,78013,78014],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,78016,78017,78053,78054,78072,78073,1977],{},[883,78018,78020],{"className":78019},[886],[888,78021,78022],{"xmlns":890},[892,78023,78024,78050],{},[895,78025,78026,78028,78040,78042,78044,78046,78048],{},[898,78027,4822],{},[1810,78029,78030,78032,78034],{},[898,78031,2398],{},[898,78033,10358],{},[895,78035,78036,78038],{},[1664,78037,1728],{"mathvariant":1726},[1664,78039,1728],{"mathvariant":1726},[1664,78041,1676],{},[1664,78043,1867],{},[1963,78045,19771],{},[1664,78047,4022],{},[1963,78049,2058],{},[902,78051,78052],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,78055,78057],{"className":78056},[886],[888,78058,78059],{"xmlns":890},[892,78060,78061,78069],{},[895,78062,78063,78065,78067],{},[898,78064,10358],{},[1664,78066,1676],{},[1963,78068,36744],{},[902,78070,78071],{"encoding":904},"L = 15"," je maximum, ",[883,78074,78076],{"className":78075},[886],[888,78077,78078],{"xmlns":890},[892,78079,78080,78126],{},[895,78081,78082,78084,78090,78092,78094,78096,78098,78100,78102,78104,78106,78108,78110,78113,78115,78118,78120,78122,78124],{},[898,78083,4822],{},[2355,78085,78086,78088],{},[898,78087,2398],{},[898,78089,10358],{},[1664,78091,1667],{"stretchy":1666},[1963,78093,36744],{},[1664,78095,1673],{"stretchy":1666},[1664,78097,1676],{},[1963,78099,2833],{},[1664,78101,3753],{},[1963,78103,36744],{},[1664,78105,1867],{},[1963,78107,2154],{},[1664,78109,3753],{},[1963,78111,78112],{},"225",[1664,78114,1676],{},[1963,78116,78117],{},"90",[1664,78119,1867],{},[1963,78121,77421],{},[1664,78123,1676],{},[1963,78125,77421],{},[902,78127,78128],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,78130,78131,42380,78187,78233],{},[883,78132,78134],{"className":78133},[886],[888,78135,78136],{"xmlns":890},[892,78137,78138,78184],{},[895,78139,78140,78142,78148,78150,78152,78154,78156,78158,78160,78162,78164,78166,78168,78170,78172,78175,78177,78180,78182],{},[898,78141,1956],{},[2355,78143,78144,78146],{},[898,78145,2398],{},[898,78147,10358],{},[1664,78149,1667],{"stretchy":1666},[1963,78151,36744],{},[1664,78153,1673],{"stretchy":1666},[1664,78155,1676],{},[1963,78157,4084],{},[1664,78159,3753],{},[1963,78161,36744],{},[1664,78163,1867],{},[1963,78165,19821],{},[1664,78167,3753],{},[1963,78169,78112],{},[1664,78171,1676],{},[1963,78173,78174],{},"180",[1664,78176,1867],{},[1963,78178,78179],{},"135",[1664,78181,1676],{},[1963,78183,77421],{},[902,78185,78186],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,78188,78190],{"className":78189},[886],[888,78191,78192],{"xmlns":890},[892,78193,78194,78230],{},[895,78195,78196,78198,78204,78206,78208,78210,78212,78214,78220,78222,78224,78226,78228],{},[898,78197,1956],{},[2355,78199,78200,78202],{},[898,78201,2398],{},[898,78203,10358],{},[1664,78205,1667],{"stretchy":1666},[1963,78207,36744],{},[1664,78209,1673],{"stretchy":1666},[1664,78211,1676],{},[898,78213,4822],{},[2355,78215,78216,78218],{},[898,78217,2398],{},[898,78219,10358],{},[1664,78221,1667],{"stretchy":1666},[1963,78223,36744],{},[1664,78225,1673],{"stretchy":1666},[1664,78227,1676],{},[1963,78229,77421],{},[902,78231,78232],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,78235,78236,78239,78240,18076,78269,1977],{},[38,78237,78238],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,78241,78243],{"className":78242},[886],[888,78244,78245],{"xmlns":890},[892,78246,78247,78267],{},[895,78248,78249,78251,78257,78259,78261],{},[898,78250,1956],{},[2355,78252,78253,78255],{},[898,78254,2398],{},[898,78256,10358],{},[1664,78258,1676],{},[898,78260,4822],{},[2355,78262,78263,78265],{},[898,78264,2398],{},[898,78266,10358],{},[902,78268,75163],{"encoding":904},[883,78270,78272],{"className":78271},[886],[888,78273,78274],{"xmlns":890},[892,78275,78276,78316],{},[895,78277,78278,78280,78282,78284,78286,78292,78294,78296,78298,78300,78302,78308,78310,78312,78314],{},[1963,78279,4084],{},[898,78281,10358],{},[1664,78283,1867],{},[1963,78285,19821],{},[1720,78287,78288,78290],{},[898,78289,10358],{},[1963,78291,1970],{},[1664,78293,1676],{},[1963,78295,2833],{},[898,78297,10358],{},[1664,78299,1867],{},[1963,78301,2154],{},[1720,78303,78304,78306],{},[898,78305,10358],{},[1963,78307,1970],{},[1664,78309,4556],{},[898,78311,10358],{},[1664,78313,1676],{},[1963,78315,36744],{},[902,78317,78318],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,78320,78321],{},[614,78322,78323,78324,78343,78344,12627,78362,78381,78382,78400,78401,78418,78419,78438,78439,78458],{},"Obrázek 5.3 — křivky ",[883,78325,78327],{"className":78326},[886],[888,78328,78329],{"xmlns":890},[892,78330,78331,78341],{},[895,78332,78333,78335],{},[898,78334,1956],{},[2355,78336,78337,78339],{},[898,78338,2398],{},[898,78340,10358],{},[902,78342,10608],{"encoding":904}," (max 60 při ",[883,78345,78347],{"className":78346},[886],[888,78348,78349],{"xmlns":890},[892,78350,78351,78359],{},[895,78352,78353,78355,78357],{},[898,78354,10358],{},[1664,78356,1676],{},[1963,78358,3442],{},[902,78360,78361],{"encoding":904},"L=10",[883,78363,78365],{"className":78364},[886],[888,78366,78367],{"xmlns":890},[892,78368,78369,78379],{},[895,78370,78371,78373],{},[898,78372,4822],{},[2355,78374,78375,78377],{},[898,78376,2398],{},[898,78378,10358],{},[902,78380,75133],{"encoding":904}," (max 45 při ",[883,78383,78385],{"className":78384},[886],[888,78386,78387],{"xmlns":890},[892,78388,78389,78397],{},[895,78390,78391,78393,78395],{},[898,78392,10358],{},[1664,78394,1676],{},[1963,78396,36744],{},[902,78398,78399],{"encoding":904},"L=15","), průsečík v ",[883,78402,78404],{"className":78403},[886],[888,78405,78406],{"xmlns":890},[892,78407,78408,78416],{},[895,78409,78410,78412,78414],{},[898,78411,10358],{},[1664,78413,1676],{},[1963,78415,36744],{},[902,78417,78071],{"encoding":904},". Nalevo od 15 leží ",[883,78420,78422],{"className":78421},[886],[888,78423,78424],{"xmlns":890},[892,78425,78426,78436],{},[895,78427,78428,78430],{},[898,78429,1956],{},[2355,78431,78432,78434],{},[898,78433,2398],{},[898,78435,10358],{},[902,78437,10608],{"encoding":904}," nad ",[883,78440,78442],{"className":78441},[886],[888,78443,78444],{"xmlns":890},[892,78445,78446,78456],{},[895,78447,78448,78450],{},[898,78449,4822],{},[2355,78451,78452,78454],{},[898,78453,2398],{},[898,78455,10358],{},[902,78457,75133],{"encoding":904},", napravo pod ní.",[115,78460,78462],{"id":78461},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,78464,78465,78466,3271,78479,1885,78482,6756,78495,1885,78498,2087],{},"V dvoufaktorovém modelu závisí produkce ",[883,78467,78469],{"className":78468},[886],[888,78470,78471],{"xmlns":890},[892,78472,78473,78477],{},[895,78474,78475],{},[898,78476,1973],{},[902,78478,1973],{"encoding":904},[38,78480,78481],{},"práci",[883,78483,78485],{"className":78484},[886],[888,78486,78487],{"xmlns":890},[892,78488,78489,78493],{},[895,78490,78491],{},[898,78492,10358],{},[902,78494,10358],{"encoding":904},[38,78496,78497],{},"kapitálu",[883,78499,78501],{"className":78500},[886],[888,78502,78503],{"xmlns":890},[892,78504,78505,78509],{},[895,78506,78507],{},[898,78508,10363],{},[902,78510,10363],{"encoding":904},[883,78512,78514],{"className":78513},[886],[888,78515,78516],{"xmlns":890,"display":28566},[892,78517,78518,78553],{},[21254,78519,78520],{"width":28571},[21259,78521,78522,78524,78546,78548],{},[21262,78523],{"width":28576},[21262,78525,78526],{},[895,78527,78528,78530,78532,78534,78536,78538,78540,78542,78544],{},[898,78529,1973],{},[1664,78531,1676],{},[898,78533,1973],{},[1664,78535,1667],{"stretchy":1666},[898,78537,10358],{},[1664,78539,1916],{"separator":1915},[898,78541,10363],{},[1664,78543,1673],{"stretchy":1666},[898,78545,1977],{"mathvariant":1726},[21262,78547],{"width":28576},[21262,78549,78550],{},[1690,78551,78552],{},"(5.6)",[902,78554,78555],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,78557,78558,78559,78561],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,78560,75500],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,78563,78565],{"id":78564},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,78567,78568],{},"Široce používané produkční funkce mají tvar",[883,78570,78572],{"className":78571},[886],[888,78573,78574],{"xmlns":890,"display":28566},[892,78575,78576,78617],{},[21254,78577,78578],{"width":28571},[21259,78579,78580,78582,78610,78612],{},[21262,78581],{"width":28576},[21262,78583,78584],{},[895,78585,78586,78588,78590,78592,78594,78600,78602,78608],{},[898,78587,1973],{},[1664,78589,1676],{},[898,78591,4822],{},[1690,78593,1692],{},[1720,78595,78596,78598],{},[898,78597,10358],{},[898,78599,207],{},[1690,78601,1692],{},[1720,78603,78604,78606],{},[898,78605,10363],{},[898,78607,1818],{},[1664,78609,1916],{"separator":1915},[21262,78611],{"width":28576},[21262,78613,78614],{},[1690,78615,78616],{},"(5.7)",[902,78618,78619],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,78621,1709,78622,78644,78645,78647,78648,1977],{},[883,78623,78625],{"className":78624},[886],[888,78626,78627],{"xmlns":890},[892,78628,78629,78641],{},[895,78630,78631,78633,78635,78637,78639],{},[898,78632,4822],{},[1664,78634,1916],{"separator":1915},[898,78636,207],{},[1664,78638,1916],{"separator":1915},[898,78640,1818],{},[902,78642,78643],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,78646,75199],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,78649,78651],{"className":78650},[886],[888,78652,78653],{"xmlns":890},[892,78654,78655,78667],{},[895,78656,78657,78659,78661,78663,78665],{},[898,78658,207],{},[1664,78660,1916],{"separator":1915},[898,78662,1818],{},[1664,78664,4022],{},[1963,78666,2875],{},[902,78668,78669],{"encoding":904},"a, b \u003C 1",[724,78671,78672],{},[1928,78673],{"alt":78674,"className":78675,"src":78676},"imek-vynosy-z-rozsahu-3typy",[210,1932],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,78678,78679,78680,78683,78684,3271,78697,78713,78714,3271,78727,2087],{},"Reflektují ekonomickou zákonitost, že ",[38,78681,78682],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,78685,78687],{"className":78686},[886],[888,78688,78689],{"xmlns":890},[892,78690,78691,78695],{},[895,78692,78693],{},[898,78694,10358],{},[902,78696,10358],{"encoding":904},[883,78698,78700],{"className":78699},[886],[888,78701,78702],{"xmlns":890},[892,78703,78704,78710],{},[895,78705,78706,78708],{},[898,78707,12540],{},[898,78709,10358],{},[902,78711,78712],{"encoding":904},"rL"," a kapitál z ",[883,78715,78717],{"className":78716},[886],[888,78718,78719],{"xmlns":890},[892,78720,78721,78725],{},[895,78722,78723],{},[898,78724,10363],{},[902,78726,10363],{"encoding":904},[883,78728,78730],{"className":78729},[886],[888,78731,78732],{"xmlns":890},[892,78733,78734,78740],{},[895,78735,78736,78738],{},[898,78737,12540],{},[898,78739,10363],{},[902,78741,78742],{"encoding":904},"rK",[883,78744,78746],{"className":78745},[886],[888,78747,78748],{"xmlns":890,"display":28566},[892,78749,78750,78873],{},[21254,78751,78752],{"width":28571},[21259,78753,78754,78756,78866,78868],{},[21262,78755],{"width":28576},[21262,78757,78758],{},[895,78759,78760,78762,78764,78766,78768,78770,78772,78774,78776,78778,78780,78782,78784,78786,78792,78794,78796,78798,78804,78806,78808,78810,78822,78824,78830,78836,78838,78850,78852,78854,78856,78858,78860,78862,78864],{},[898,78761,1973],{},[1664,78763,1667],{"stretchy":1666},[898,78765,12540],{},[898,78767,10358],{},[1664,78769,1916],{"separator":1915},[898,78771,12540],{},[898,78773,10363],{},[1664,78775,1673],{"stretchy":1666},[1664,78777,1676],{},[898,78779,4822],{},[1664,78781,1667],{"stretchy":1666},[898,78783,12540],{},[898,78785,10358],{},[1720,78787,78788,78790],{},[1664,78789,1673],{"stretchy":1666},[898,78791,207],{},[1664,78793,1667],{"stretchy":1666},[898,78795,12540],{},[898,78797,10363],{},[1720,78799,78800,78802],{},[1664,78801,1673],{"stretchy":1666},[898,78803,1818],{},[1664,78805,1676],{},[898,78807,4822],{},[1690,78809,1692],{},[1720,78811,78812,78814],{},[898,78813,12540],{},[895,78815,78816,78818,78820],{},[898,78817,207],{},[1664,78819,1700],{},[898,78821,1818],{},[1690,78823,1692],{},[1720,78825,78826,78828],{},[898,78827,10358],{},[898,78829,207],{},[1720,78831,78832,78834],{},[898,78833,10363],{},[898,78835,1818],{},[1664,78837,1676],{},[1720,78839,78840,78842],{},[898,78841,12540],{},[895,78843,78844,78846,78848],{},[898,78845,207],{},[1664,78847,1700],{},[898,78849,1818],{},[1690,78851,1692],{},[898,78853,1973],{},[1664,78855,1667],{"stretchy":1666},[898,78857,10358],{},[1664,78859,1916],{"separator":1915},[898,78861,10363],{},[1664,78863,1673],{"stretchy":1666},[898,78865,1977],{"mathvariant":1726},[21262,78867],{"width":28576},[21262,78869,78870],{},[1690,78871,78872],{},"(5.8)",[902,78874,78875],{"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}",[724,78877,78878,78879],{},"Volně: ",[38,78880,78881,78882,78895,78896,78920],{},"změní-li se vstupy ",[883,78883,78885],{"className":78884},[886],[888,78886,78887],{"xmlns":890},[892,78888,78889,78893],{},[895,78890,78891],{},[898,78892,12540],{},[902,78894,12540],{"encoding":904},"-krát, změní se výstup ",[883,78897,78899],{"className":78898},[886],[888,78900,78901],{"xmlns":890},[892,78902,78903,78917],{},[895,78904,78905],{},[1720,78906,78907,78909],{},[898,78908,12540],{},[895,78910,78911,78913,78915],{},[898,78912,207],{},[1664,78914,1700],{},[898,78916,1818],{},[902,78918,78919],{"encoding":904},"r^{a+b}","-krát.",[198,78922,78924],{"id":78923},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,78926,78927,78928,78945],{},"Součet exponentů ",[883,78929,78931],{"className":78930},[886],[888,78932,78933],{"xmlns":890},[892,78934,78935,78943],{},[895,78936,78937,78939,78941],{},[898,78938,207],{},[1664,78940,1700],{},[898,78942,1818],{},[902,78944,75324],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,78947,78948,78977],{},[19,78949,78950],{},[22,78951,78952,78955,78958,78975],{},[25,78953,78954],{},"Typ",[25,78956,78957],{},"Podmínka",[25,78959,78960,78961,78974],{},"Chování produkce při ",[883,78962,78964],{"className":78963},[886],[888,78965,78966],{"xmlns":890},[892,78967,78968,78972],{},[895,78969,78970],{},[898,78971,12540],{},[902,78973,12540],{"encoding":904},"-násobném zvýšení vstupů",[25,78976,3647],{},[30,78978,78979,79090,79205],{},[22,78980,78981,78989,79013,79046],{},[35,78982,76037,78983,10588,78986,1673],{},[38,78984,78985],{},"Konstantní",[614,78987,78988],{},"constant returns",[35,78990,78991],{},[883,78992,78994],{"className":78993},[886],[888,78995,78996],{"xmlns":890},[892,78997,78998,79010],{},[895,78999,79000,79002,79004,79006,79008],{},[898,79001,207],{},[1664,79003,1700],{},[898,79005,1818],{},[1664,79007,1676],{},[1963,79009,2875],{},[902,79011,79012],{"encoding":904},"a+b = 1",[35,79014,79015,79028,79029,1885,79032,79045],{},[883,79016,79018],{"className":79017},[886],[888,79019,79020],{"xmlns":890},[892,79021,79022,79026],{},[895,79023,79024],{},[898,79025,1973],{},[902,79027,1973],{"encoding":904}," vzroste ",[38,79030,79031],{},"přesně",[883,79033,79035],{"className":79034},[886],[888,79036,79037],{"xmlns":890},[892,79038,79039,79043],{},[895,79040,79041],{},[898,79042,12540],{},[902,79044,12540],{"encoding":904},"-krát",[35,79047,79048],{},[883,79049,79051],{"className":79050},[886],[888,79052,79053],{"xmlns":890},[892,79054,79055,79087],{},[895,79056,79057,79059,79061,79063,79075],{},[898,79058,1973],{},[1664,79060,1676],{},[1963,79062,1970],{},[1720,79064,79065,79067],{},[898,79066,10358],{},[895,79068,79069,79071,79073],{},[1963,79070,2875],{},[898,79072,5240],{"mathvariant":1726},[1963,79074,2944],{},[1720,79076,79077,79079],{},[898,79078,10363],{},[895,79080,79081,79083,79085],{},[1963,79082,2774],{},[898,79084,5240],{"mathvariant":1726},[1963,79086,2944],{},[902,79088,79089],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,79091,79092,79101,79125,79155],{},[35,79093,79094,79095,10588,79098,1673],{},"2° ",[38,79096,79097],{},"Rostoucí",[614,79099,79100],{},"increasing returns",[35,79102,79103],{},[883,79104,79106],{"className":79105},[886],[888,79107,79108],{"xmlns":890},[892,79109,79110,79122],{},[895,79111,79112,79114,79116,79118,79120],{},[898,79113,207],{},[1664,79115,1700],{},[898,79117,1818],{},[1664,79119,3984],{},[1963,79121,2875],{},[902,79123,79124],{"encoding":904},"a+b > 1",[35,79126,79127,79028,79140,51731,79142,79045],{},[883,79128,79130],{"className":79129},[886],[888,79131,79132],{"xmlns":890},[892,79133,79134,79138],{},[895,79135,79136],{},[898,79137,1973],{},[902,79139,1973],{"encoding":904},[38,79141,25770],{},[883,79143,79145],{"className":79144},[886],[888,79146,79147],{"xmlns":890},[892,79148,79149,79153],{},[895,79150,79151],{},[898,79152,12540],{},[902,79154,12540],{"encoding":904},[35,79156,79157,10588,79183,1673],{},[883,79158,79160],{"className":79159},[886],[888,79161,79162],{"xmlns":890},[892,79163,79164,79180],{},[895,79165,79166,79168,79170,79172,79174],{},[898,79167,1973],{},[1664,79169,1676],{},[1963,79171,24701],{},[898,79173,10358],{},[1720,79175,79176,79178],{},[898,79177,10363],{},[1963,79179,1970],{},[902,79181,79182],{"encoding":904},"Q = 7LK^2",[883,79184,79186],{"className":79185},[886],[888,79187,79188],{"xmlns":890},[892,79189,79190,79202],{},[895,79191,79192,79194,79196,79198,79200],{},[898,79193,207],{},[1664,79195,1700],{},[898,79197,1818],{},[1664,79199,1676],{},[1963,79201,2774],{},[902,79203,79204],{"encoding":904},"a+b = 3",[22,79206,79207,79216,79240,79271],{},[35,79208,79209,79210,10588,79213,1673],{},"3° ",[38,79211,79212],{},"Klesající",[614,79214,79215],{},"decreasing returns",[35,79217,79218],{},[883,79219,79221],{"className":79220},[886],[888,79222,79223],{"xmlns":890},[892,79224,79225,79237],{},[895,79226,79227,79229,79231,79233,79235],{},[898,79228,207],{},[1664,79230,1700],{},[898,79232,1818],{},[1664,79234,4022],{},[1963,79236,2875],{},[902,79238,79239],{"encoding":904},"a+b \u003C 1",[35,79241,79242,79028,79255,51731,79258,79045],{},[883,79243,79245],{"className":79244},[886],[888,79246,79247],{"xmlns":890},[892,79248,79249,79253],{},[895,79250,79251],{},[898,79252,1973],{},[902,79254,1973],{"encoding":904},[38,79256,79257],{},"méně",[883,79259,79261],{"className":79260},[886],[888,79262,79263],{"xmlns":890},[892,79264,79265,79269],{},[895,79266,79267],{},[898,79268,12540],{},[902,79270,12540],{"encoding":904},[35,79272,79273,10588,79303,1673],{},[883,79274,79276],{"className":79275},[886],[888,79277,79278],{"xmlns":890},[892,79279,79280,79300],{},[895,79281,79282,79284,79286,79288,79294],{},[898,79283,1973],{},[1664,79285,1676],{},[1963,79287,3442],{},[1720,79289,79290,79292],{},[898,79291,10358],{},[1963,79293,68711],{},[1720,79295,79296,79298],{},[898,79297,10363],{},[1963,79299,5575],{},[902,79301,79302],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,79304,79306],{"className":79305},[886],[888,79307,79308],{"xmlns":890},[892,79309,79310,79322],{},[895,79311,79312,79314,79316,79318,79320],{},[898,79313,207],{},[1664,79315,1700],{},[898,79317,1818],{},[1664,79319,1676],{},[1963,79321,15088],{},[902,79323,79324],{"encoding":904},"a+b = 0{,}8",[4436,79326,79327],{},[724,79328,79329,79331,79332,79349,79350,79353,79354,1885,79357,79393,79394,79416,79417,1977],{},[883,79330,4978],{}," Pozor\nSoučet ",[883,79333,79335],{"className":79334},[886],[888,79336,79337],{"xmlns":890},[892,79338,79339,79347],{},[895,79340,79341,79343,79345],{},[898,79342,207],{},[1664,79344,1700],{},[898,79346,1818],{},[902,79348,75324],{"encoding":904}," neudává velikost produkce, ale ",[38,79351,79352],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,79355,79356],{},"ryzí Cobb-Douglas",[883,79358,79360],{"className":79359},[886],[888,79361,79362],{"xmlns":890},[892,79363,79364,79390],{},[895,79365,79366,79368,79370,79372,79378],{},[898,79367,1973],{},[1664,79369,1676],{},[898,79371,4822],{},[1720,79373,79374,79376],{},[898,79375,10358],{},[898,79377,207],{},[1720,79379,79380,79382],{},[898,79381,10363],{},[895,79383,79384,79386,79388],{},[1963,79385,2875],{},[1664,79387,1867],{},[898,79389,207],{},[902,79391,79392],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,79395,79397],{"className":79396},[886],[888,79398,79399],{"xmlns":890},[892,79400,79401,79413],{},[895,79402,79403,79405,79407,79409,79411],{},[898,79404,1818],{},[1664,79406,1676],{},[1963,79408,2875],{},[1664,79410,1867],{},[898,79412,207],{},[902,79414,79415],{"encoding":904},"b = 1-a",", tedy vždy ",[38,79418,79419],{},"konstantní výnosy z rozsahu",[198,79421,79423,79424],{"id":79422},"parametr-efektivity-aa","Parametr efektivity ",[883,79425,79427],{"className":79426},[886],[888,79428,79429],{"xmlns":890},[892,79430,79431,79435],{},[895,79432,79433],{},[898,79434,4822],{},[902,79436,4822],{"encoding":904},[724,79438,79439,79440,79453,79454,79467,79468,79486,79487,79490],{},"Konstanta ",[883,79441,79443],{"className":79442},[886],[888,79444,79445],{"xmlns":890},[892,79446,79447,79451],{},[895,79448,79449],{},[898,79450,4822],{},[902,79452,4822],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,79455,79457],{"className":79456},[886],[888,79458,79459],{"xmlns":890},[892,79460,79461,79465],{},[895,79462,79463],{},[898,79464,1973],{},[902,79466,1973],{"encoding":904}," při pevně zadaných ",[883,79469,79471],{"className":79470},[886],[888,79472,79473],{"xmlns":890},[892,79474,79475,79483],{},[895,79476,79477,79479,79481],{},[898,79478,10358],{},[1664,79480,1916],{"separator":1915},[898,79482,10363],{},[902,79484,79485],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,79488,79489],{},"parametr efektivity"," — indikátor stavu technologie.",[198,79492,79494],{"id":79493},"příklad-53","Příklad 5.3",[724,79496,79497,79498,79393,79540,79542,79543,1977],{},"Produkční funkce ",[883,79499,79501],{"className":79500},[886],[888,79502,79503],{"xmlns":890},[892,79504,79505,79537],{},[895,79506,79507,79509,79511,79513,79525],{},[898,79508,1973],{},[1664,79510,1676],{},[1963,79512,1970],{},[1720,79514,79515,79517],{},[898,79516,10358],{},[895,79518,79519,79521,79523],{},[1963,79520,2875],{},[898,79522,5240],{"mathvariant":1726},[1963,79524,2944],{},[1720,79526,79527,79529],{},[898,79528,10363],{},[895,79530,79531,79533,79535],{},[1963,79532,2774],{},[898,79534,5240],{"mathvariant":1726},[1963,79536,2944],{},[902,79538,79539],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,79541,25113],{}," výnosy z rozsahu, neboť ",[883,79544,79546],{"className":79545},[886],[888,79547,79548],{"xmlns":890},[892,79549,79550,79574],{},[895,79551,79552,79560,79562,79570,79572],{},[2919,79553,79554],{"scriptlevel":2058,"displaystyle":1666},[2922,79555,79556,79558],{},[1963,79557,2875],{},[1963,79559,2944],{},[1664,79561,1700],{},[2919,79563,79564],{"scriptlevel":2058,"displaystyle":1666},[2922,79565,79566,79568],{},[1963,79567,2774],{},[1963,79569,2944],{},[1664,79571,1676],{},[1963,79573,2875],{},[902,79575,79576],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,79578,79579,79580,6756,79593,79606,79607,1885,79620,79660],{},"Změní-li se ",[883,79581,79583],{"className":79582},[886],[888,79584,79585],{"xmlns":890},[892,79586,79587,79591],{},[895,79588,79589],{},[898,79590,10358],{},[902,79592,10358],{"encoding":904},[883,79594,79596],{"className":79595},[886],[888,79597,79598],{"xmlns":890},[892,79599,79600,79604],{},[895,79601,79602],{},[898,79603,10363],{},[902,79605,10363],{"encoding":904}," čtyřnásobně, změní se ",[883,79608,79610],{"className":79609},[886],[888,79611,79612],{"xmlns":890},[892,79613,79614,79618],{},[895,79615,79616],{},[898,79617,1973],{},[902,79619,1973],{"encoding":904},[883,79621,79623],{"className":79622},[886],[888,79624,79625],{"xmlns":890},[892,79626,79627,79657],{},[895,79628,79629,79649,79651],{},[1720,79630,79631,79633],{},[1963,79632,2944],{},[895,79634,79635,79637,79639,79641,79643,79645,79647],{},[1963,79636,2875],{},[898,79638,5240],{"mathvariant":1726},[1963,79640,2944],{},[1664,79642,1700],{},[1963,79644,2774],{},[898,79646,5240],{"mathvariant":1726},[1963,79648,2944],{},[1664,79650,1676],{},[1720,79652,79653,79655],{},[1963,79654,2944],{},[1963,79656,2875],{},[902,79658,79659],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,79662,79664],{"className":79663},[886],[888,79665,79666],{"xmlns":890,"display":28566},[892,79667,79668,79828],{},[895,79669,79670,79672,79674,79676,79678,79680,79682,79684,79686,79688,79690,79692,79694,79696,79708,79710,79712,79714,79726,79728,79730,79732,79752,79764,79776,79778,79780,79782,79784,79796,79808,79810,79812,79814,79816,79818,79820,79822,79824,79826],{},[898,79671,1973],{},[1664,79673,1667],{"stretchy":1666},[1963,79675,2944],{},[898,79677,10358],{},[1664,79679,1916],{"separator":1915},[1963,79681,2944],{},[898,79683,10363],{},[1664,79685,1673],{"stretchy":1666},[1664,79687,1676],{},[1963,79689,1970],{},[1664,79691,1667],{"stretchy":1666},[1963,79693,2944],{},[898,79695,10358],{},[1720,79697,79698,79700],{},[1664,79699,1673],{"stretchy":1666},[895,79701,79702,79704,79706],{},[1963,79703,2875],{},[898,79705,5240],{"mathvariant":1726},[1963,79707,2944],{},[1664,79709,1667],{"stretchy":1666},[1963,79711,2944],{},[898,79713,10363],{},[1720,79715,79716,79718],{},[1664,79717,1673],{"stretchy":1666},[895,79719,79720,79722,79724],{},[1963,79721,2774],{},[898,79723,5240],{"mathvariant":1726},[1963,79725,2944],{},[1664,79727,1676],{},[1963,79729,1970],{},[1664,79731,3753],{},[1720,79733,79734,79736],{},[1963,79735,2944],{},[895,79737,79738,79740,79742,79744,79746,79748,79750],{},[1963,79739,2875],{},[898,79741,5240],{"mathvariant":1726},[1963,79743,2944],{},[1664,79745,1700],{},[1963,79747,2774],{},[898,79749,5240],{"mathvariant":1726},[1963,79751,2944],{},[1720,79753,79754,79756],{},[898,79755,10358],{},[895,79757,79758,79760,79762],{},[1963,79759,2875],{},[898,79761,5240],{"mathvariant":1726},[1963,79763,2944],{},[1720,79765,79766,79768],{},[898,79767,10363],{},[895,79769,79770,79772,79774],{},[1963,79771,2774],{},[898,79773,5240],{"mathvariant":1726},[1963,79775,2944],{},[1664,79777,1676],{},[1963,79779,2944],{},[1664,79781,3753],{},[1963,79783,1970],{},[1720,79785,79786,79788],{},[898,79787,10358],{},[895,79789,79790,79792,79794],{},[1963,79791,2875],{},[898,79793,5240],{"mathvariant":1726},[1963,79795,2944],{},[1720,79797,79798,79800],{},[898,79799,10363],{},[895,79801,79802,79804,79806],{},[1963,79803,2774],{},[898,79805,5240],{"mathvariant":1726},[1963,79807,2944],{},[1664,79809,1676],{},[1963,79811,2944],{},[1690,79813,1692],{},[898,79815,1973],{},[1664,79817,1667],{"stretchy":1666},[898,79819,10358],{},[1664,79821,1916],{"separator":1915},[898,79823,10363],{},[1664,79825,1673],{"stretchy":1666},[898,79827,1977],{"mathvariant":1726},[902,79829,79830],{"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).",[198,79832,79833],{"id":37679},"Homogenita",[724,79835,79836,79837,1762,79860,79876],{},"Funkce ",[883,79838,79840],{"className":79839},[886],[888,79841,79842],{"xmlns":890},[892,79843,79844,79858],{},[895,79845,79846,79848,79850,79852,79854,79856],{},[898,79847,1973],{},[1664,79849,1667],{"stretchy":1666},[898,79851,10358],{},[1664,79853,1916],{"separator":1915},[898,79855,10363],{},[1664,79857,1673],{"stretchy":1666},[902,79859,10560],{"encoding":904},[38,79861,79862,79863],{},"homogenní stupně ",[883,79864,79866],{"className":79865},[886],[888,79867,79868],{"xmlns":890},[892,79869,79870,79874],{},[895,79871,79872],{},[898,79873,37360],{},[902,79875,37360],{"encoding":904},", jestliže",[883,79878,79880],{"className":79879},[886],[888,79881,79882],{"xmlns":890,"display":28566},[892,79883,79884,79941],{},[21254,79885,79886],{"width":28571},[21259,79887,79888,79890,79934,79936],{},[21262,79889],{"width":28576},[21262,79891,79892],{},[895,79893,79894,79896,79898,79900,79902,79904,79906,79908,79910,79912,79918,79920,79922,79924,79926,79928,79930,79932],{},[898,79895,1973],{},[1664,79897,1667],{"stretchy":1666},[898,79899,12540],{},[898,79901,10358],{},[1664,79903,1916],{"separator":1915},[898,79905,12540],{},[898,79907,10363],{},[1664,79909,1673],{"stretchy":1666},[1664,79911,1676],{},[1720,79913,79914,79916],{},[898,79915,12540],{},[898,79917,37360],{},[1690,79919,1692],{},[898,79921,1973],{},[1664,79923,1667],{"stretchy":1666},[898,79925,10358],{},[1664,79927,1916],{"separator":1915},[898,79929,10363],{},[1664,79931,1673],{"stretchy":1666},[1664,79933,1916],{"separator":1915},[21262,79935],{"width":28576},[21262,79937,79938],{},[1690,79939,79940],{},"(5.10)",[902,79942,79943],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,79945,1709,79946,79964,79965,79983,79984,44136,79997,80000,80001,1977],{},[883,79947,79949],{"className":79948},[886],[888,79950,79951],{"xmlns":890},[892,79952,79953,79961],{},[895,79954,79955,79957,79959],{},[898,79956,37360],{},[1664,79958,5051],{},[1963,79960,2058],{},[902,79962,79963],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,79966,79968],{"className":79967},[886],[888,79969,79970],{"xmlns":890},[892,79971,79972,79980],{},[895,79973,79974,79976,79978],{},[898,79975,12540],{},[1664,79977,3984],{},[1963,79979,2058],{},[902,79981,79982],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,79985,79987],{"className":79986},[886],[888,79988,79989],{"xmlns":890},[892,79990,79991,79995],{},[895,79992,79993],{},[1963,79994,2875],{},[902,79996,2875],{"encoding":904},[38,79998,79999],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,80002,80004],{"className":80003},[886],[888,80005,80006],{"xmlns":890},[892,80007,80008,80016],{},[895,80009,80010,80012,80014],{},[898,80011,207],{},[1664,80013,1700],{},[898,80015,1818],{},[902,80017,75324],{"encoding":904},[115,80019,80021],{"id":80020},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,80023,80024],{},[38,80025,80026],{},"Ryzí Cobb-Douglasovy funkce:",[883,80028,80030],{"className":80029},[886],[888,80031,80032],{"xmlns":890,"display":28566},[892,80033,80034,80093],{},[21254,80035,80036],{"width":28571},[21259,80037,80038,80040,80086,80088],{},[21262,80039],{"width":28576},[21262,80041,80042],{},[895,80043,80044,80046,80048,80050,80052,80058,80060,80072,80074,80076,80078,80080,80082,80084],{},[898,80045,1973],{},[1664,80047,1676],{},[898,80049,4822],{},[1690,80051,1692],{},[1720,80053,80054,80056],{},[898,80055,10358],{},[898,80057,207],{},[1690,80059,1692],{},[1720,80061,80062,80064],{},[898,80063,10363],{},[895,80065,80066,80068,80070],{},[1963,80067,2875],{},[1664,80069,1867],{},[898,80071,207],{},[1664,80073,1916],{"separator":1915},[6444,80075],{"width":15783},[1963,80077,2058],{},[1664,80079,4022],{},[898,80081,207],{},[1664,80083,4022],{},[1963,80085,13759],{},[21262,80087],{"width":28576},[21262,80089,80090],{},[1690,80091,80092],{},"(5.9)",[902,80094,80095],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,80097,80098,80099,80101,80102,1977],{},"Mají vždy ",[38,80100,79419],{}," a jsou ",[38,80103,79999],{},[724,80105,80106,10588,80109,80112],{},[38,80107,80108],{},"CES produkční funkce",[614,80110,80111],{},"Constant Elasticity of Substitution",", 1961):",[883,80114,80116],{"className":80115},[886],[888,80117,80118],{"xmlns":890,"display":28566},[892,80119,80120,80188],{},[895,80121,80122,80124,80126,80128,80186],{},[898,80123,1973],{},[1664,80125,1676],{},[898,80127,4822],{},[1720,80129,80130,80174],{},[895,80131,80132,80134,80136,80138,80140,80142,80144,80146,80156,80158,80160,80162,80172],{},[1664,80133,1837],{"fence":1915},[1664,80135,1667],{"stretchy":1666},[1963,80137,2875],{},[1664,80139,1867],{},[898,80141,207],{},[1664,80143,1673],{"stretchy":1666},[1690,80145,1692],{},[1720,80147,80148,80150],{},[898,80149,10358],{},[895,80151,80152,80154],{},[1664,80153,1867],{},[898,80155,1818],{},[1664,80157,1700],{},[898,80159,207],{},[1690,80161,1692],{},[1720,80163,80164,80166],{},[898,80165,10363],{},[895,80167,80168,80170],{},[1664,80169,1867],{},[898,80171,1818],{},[1664,80173,1850],{"fence":1915},[895,80175,80176,80178],{},[1664,80177,1867],{},[2919,80179,80180],{"scriptlevel":2058,"displaystyle":1666},[2922,80181,80182,80184],{},[1963,80183,2875],{},[898,80185,1818],{},[1664,80187,1916],{"separator":1915},[902,80189,80190],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,80192,1709,80193,1343,80211,1343,80232,80256],{},[883,80194,80196],{"className":80195},[886],[888,80197,80198],{"xmlns":890},[892,80199,80200,80208],{},[895,80201,80202,80204,80206],{},[898,80203,4822],{},[1664,80205,3984],{},[1963,80207,2058],{},[902,80209,80210],{"encoding":904},"A > 0",[883,80212,80214],{"className":80213},[886],[888,80215,80216],{"xmlns":890},[892,80217,80218,80230],{},[895,80219,80220,80222,80224,80226,80228],{},[1963,80221,2058],{},[1664,80223,4022],{},[898,80225,207],{},[1664,80227,4022],{},[1963,80229,2875],{},[902,80231,19336],{"encoding":904},[883,80233,80235],{"className":80234},[886],[888,80236,80237],{"xmlns":890},[892,80238,80239,80253],{},[895,80240,80241,80243,80245,80247,80249,80251],{},[1664,80242,1867],{},[1963,80244,2875],{},[1664,80246,4022],{},[898,80248,1818],{},[1664,80250,3947],{"mathvariant":1726},[1963,80252,2058],{},[902,80254,80255],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,80258,80259],{},[38,80260,80261],{},"Další typy:",[120,80263,80264,80306],{},[123,80265,80266,1885,80269,80305],{},[38,80267,80268],{},"Lineární:",[883,80270,80272],{"className":80271},[886],[888,80273,80274],{"xmlns":890},[892,80275,80276,80302],{},[895,80277,80278,80280,80282,80284,80286,80288,80290,80292,80294,80296,80298,80300],{},[898,80279,1973],{},[1664,80281,1667],{"stretchy":1666},[898,80283,10358],{},[1664,80285,1916],{"separator":1915},[898,80287,10363],{},[1664,80289,1673],{"stretchy":1666},[1664,80291,1676],{},[898,80293,207],{},[898,80295,10358],{},[1664,80297,1700],{},[898,80299,1818],{},[898,80301,10363],{},[902,80303,80304],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,80307,80308,1885,80311,80356],{},[38,80309,80310],{},"Leontiefova:",[883,80312,80314],{"className":80313},[886],[888,80315,80316],{"xmlns":890},[892,80317,80318,80353],{},[895,80319,80320,80322,80324,80326,80328,80330,80332,80334,80337,80339,80341,80343,80345,80347,80349,80351],{},[898,80321,1973],{},[1664,80323,1667],{"stretchy":1666},[898,80325,10358],{},[1664,80327,1916],{"separator":1915},[898,80329,10363],{},[1664,80331,1673],{"stretchy":1666},[1664,80333,1676],{},[898,80335,80336],{},"min",[1664,80338,56700],{},[1664,80340,1667],{"stretchy":1666},[898,80342,207],{},[898,80344,10358],{},[1664,80346,1916],{"separator":1915},[898,80348,1818],{},[898,80350,10363],{},[1664,80352,1673],{"stretchy":1666},[902,80354,80355],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,80358,80360,80361,1343,80380,80399],{"id":80359},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,80362,80364],{"className":80363},[886],[888,80365,80366],{"xmlns":890},[892,80367,80368,80378],{},[895,80369,80370,80372],{},[898,80371,1956],{},[2355,80373,80374,80376],{},[898,80375,2398],{},[898,80377,10358],{},[902,80379,10608],{"encoding":904},[883,80381,80383],{"className":80382},[886],[888,80384,80385],{"xmlns":890},[892,80386,80387,80397],{},[895,80388,80389,80391],{},[898,80390,1956],{},[2355,80392,80393,80395],{},[898,80394,2398],{},[898,80396,10363],{},[902,80398,10653],{"encoding":904}," a totální diferenciál",[724,80401,80402],{},[38,80403,80404],{},"Mezní produkt práce:",[883,80406,80408],{"className":80407},[886],[888,80409,80410],{"xmlns":890,"display":28566},[892,80411,80412,80450],{},[895,80413,80414,80416,80422,80424,80432,80434,80448],{},[898,80415,1956],{},[2355,80417,80418,80420],{},[898,80419,2398],{},[898,80421,10358],{},[1664,80423,1676],{},[1810,80425,80426,80428,80430],{},[898,80427,1973],{},[898,80429,10358],{},[1664,80431,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,80433,1676],{},[2922,80435,80436,80442],{},[895,80437,80438,80440],{},[898,80439,10435],{"mathvariant":1726},[898,80441,1973],{},[895,80443,80444,80446],{},[898,80445,10435],{"mathvariant":1726},[898,80447,10358],{},[898,80449,1977],{"mathvariant":1726},[902,80451,80452],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,80454,80455],{},[38,80456,80457],{},"Mezní produkt kapitálu:",[883,80459,80461],{"className":80460},[886],[888,80462,80463],{"xmlns":890,"display":28566},[892,80464,80465,80503],{},[895,80466,80467,80469,80475,80477,80485,80487,80501],{},[898,80468,1956],{},[2355,80470,80471,80473],{},[898,80472,2398],{},[898,80474,10363],{},[1664,80476,1676],{},[1810,80478,80479,80481,80483],{},[898,80480,1973],{},[898,80482,10363],{},[1664,80484,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,80486,1676],{},[2922,80488,80489,80495],{},[895,80490,80491,80493],{},[898,80492,10435],{"mathvariant":1726},[898,80494,1973],{},[895,80496,80497,80499],{},[898,80498,10435],{"mathvariant":1726},[898,80500,10363],{},[898,80502,1977],{"mathvariant":1726},[902,80504,80505],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,80507,80508,80538,80539,80560,80561,80579,80580,80593,80594,1977],{},[883,80509,80511],{"className":80510},[886],[888,80512,80513],{"xmlns":890},[892,80514,80515,80535],{},[895,80516,80517,80519,80525,80527,80529,80531,80533],{},[898,80518,1956],{},[2355,80520,80521,80523],{},[898,80522,2398],{},[898,80524,10358],{},[1664,80526,1667],{"stretchy":1666},[898,80528,207],{},[1664,80530,1916],{"separator":1915},[898,80532,1818],{},[1664,80534,1673],{"stretchy":1666},[902,80536,80537],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,80540,80542],{"className":80541},[886],[888,80543,80544],{"xmlns":890},[892,80545,80546,80558],{},[895,80547,80548,80550,80552,80554,80556],{},[1664,80549,1837],{"stretchy":1666},[898,80551,207],{},[1664,80553,1916],{"separator":1915},[898,80555,1818],{},[1664,80557,1850],{"stretchy":1666},[902,80559,1923],{"encoding":904}," (na hladině ",[883,80562,80564],{"className":80563},[886],[888,80565,80566],{"xmlns":890},[892,80567,80568,80576],{},[895,80569,80570,80572,80574],{},[898,80571,10363],{},[1664,80573,1676],{},[898,80575,1818],{},[902,80577,80578],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,80581,80583],{"className":80582},[886],[888,80584,80585],{"xmlns":890},[892,80586,80587,80591],{},[895,80588,80589],{},[898,80590,10358],{},[902,80592,10358],{"encoding":904},". Analogicky ",[883,80595,80597],{"className":80596},[886],[888,80598,80599],{"xmlns":890},[892,80600,80601,80621],{},[895,80602,80603,80605,80611,80613,80615,80617,80619],{},[898,80604,1956],{},[2355,80606,80607,80609],{},[898,80608,2398],{},[898,80610,10363],{},[1664,80612,1667],{"stretchy":1666},[898,80614,207],{},[1664,80616,1916],{"separator":1915},[898,80618,1818],{},[1664,80620,1673],{"stretchy":1666},[902,80622,80623],{"encoding":904},"MP_K(a, b)",[4436,80625,80626,80630],{},[724,80627,80628,51719],{},[883,80629,4723],{},[120,80631,80632,80670],{},[123,80633,80634,26689,80653],{},[883,80635,80637],{"className":80636},[886],[888,80638,80639],{"xmlns":890},[892,80640,80641,80651],{},[895,80642,80643,80645],{},[898,80644,1956],{},[2355,80646,80647,80649],{},[898,80648,2398],{},[898,80650,10358],{},[902,80652,10608],{"encoding":904},[614,80654,80655,80656,80669],{},"„o kolik vzroste ",[883,80657,80659],{"className":80658},[886],[888,80660,80661],{"xmlns":890},[892,80662,80663,80667],{},[895,80664,80665],{},[898,80666,1973],{},[902,80668,1973],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,80671,80672,26689,80691],{},[883,80673,80675],{"className":80674},[886],[888,80676,80677],{"xmlns":890},[892,80678,80679,80689],{},[895,80680,80681,80683],{},[898,80682,1956],{},[2355,80684,80685,80687],{},[898,80686,2398],{},[898,80688,10363],{},[902,80690,10653],{"encoding":904},[614,80692,80655,80693,80706],{},[883,80694,80696],{"className":80695},[886],[888,80697,80698],{"xmlns":890},[892,80699,80700,80704],{},[895,80701,80702],{},[898,80703,1973],{},[902,80705,1973],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,80708,80709,80712,80713,80728,80729,2087],{},[38,80710,80711],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,80714,80716],{"className":80715},[886],[888,80717,80718],{"xmlns":890},[892,80719,80720,80726],{},[895,80721,80722,80724],{},[898,80723,1695],{},[898,80725,10358],{},[902,80727,75856],{"encoding":904}," a kapitálu o ",[883,80730,80732],{"className":80731},[886],[888,80733,80734],{"xmlns":890},[892,80735,80736,80742],{},[895,80737,80738,80740],{},[898,80739,1695],{},[898,80741,10363],{},[902,80743,80744],{"encoding":904},"dK",[883,80746,80748],{"className":80747},[886],[888,80749,80750],{"xmlns":890,"display":28566},[892,80751,80752,80845],{},[21254,80753,80754],{"width":28571},[21259,80755,80756,80758,80838,80840],{},[21262,80757],{"width":28576},[21262,80759,80760],{},[895,80761,80762,80764,80766,80768,80770,80772,80774,80782,80784,80786,80788,80790,80798,80800,80802,80804,80806,80808,80814,80816,80818,80820,80822,80824,80830,80832,80834,80836],{},[898,80763,3468],{"mathvariant":1726},[898,80765,1973],{},[1664,80767,3315],{},[898,80769,1695],{},[898,80771,1973],{},[1664,80773,1676],{},[1810,80775,80776,80778,80780],{},[898,80777,1973],{},[898,80779,10358],{},[1664,80781,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1690,80783,1692],{},[898,80785,1695],{},[898,80787,10358],{},[1664,80789,1700],{},[1810,80791,80792,80794,80796],{},[898,80793,1973],{},[898,80795,10363],{},[1664,80797,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1690,80799,1692],{},[898,80801,1695],{},[898,80803,10363],{},[1664,80805,1676],{},[898,80807,1956],{},[2355,80809,80810,80812],{},[898,80811,2398],{},[898,80813,10358],{},[1690,80815,1692],{},[898,80817,1695],{},[898,80819,10358],{},[1664,80821,1700],{},[898,80823,1956],{},[2355,80825,80826,80828],{},[898,80827,2398],{},[898,80829,10363],{},[1690,80831,1692],{},[898,80833,1695],{},[898,80835,10363],{},[898,80837,1977],{"mathvariant":1726},[21262,80839],{"width":28576},[21262,80841,80842],{},[1690,80843,80844],{},"(5.11)",[902,80846,80847],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,80849,80850,80851,1977],{},"Skutečná změna: ",[883,80852,80854],{"className":80853},[886],[888,80855,80856],{"xmlns":890},[892,80857,80858,80904],{},[895,80859,80860,80862,80864,80866,80868,80870,80872,80874,80876,80878,80880,80882,80884,80886,80888,80890,80892,80894,80896,80898,80900,80902],{},[898,80861,3468],{"mathvariant":1726},[898,80863,1973],{},[1664,80865,1676],{},[898,80867,1973],{},[1664,80869,1667],{"stretchy":1666},[898,80871,10358],{},[1664,80873,1700],{},[898,80875,1695],{},[898,80877,10358],{},[1664,80879,1916],{"separator":1915},[898,80881,10363],{},[1664,80883,1700],{},[898,80885,1695],{},[898,80887,10363],{},[1664,80889,1673],{"stretchy":1666},[1664,80891,1867],{},[898,80893,1973],{},[1664,80895,1667],{"stretchy":1666},[898,80897,10358],{},[1664,80899,1916],{"separator":1915},[898,80901,10363],{},[1664,80903,1673],{"stretchy":1666},[902,80905,80906],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,80908,80909,80911,80912,80930,80931,80944,80945,80964,80965,80997,80998,81030,81031,1977],{},[38,80910,76020],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,80913,80915],{"className":80914},[886],[888,80916,80917],{"xmlns":890},[892,80918,80919,80927],{},[895,80920,80921],{},[2355,80922,80923,80925],{},[898,80924,10363],{},[1963,80926,2058],{},[902,80928,80929],{"encoding":904},"K_0"," se od jistého ",[883,80932,80934],{"className":80933},[886],[888,80935,80936],{"xmlns":890},[892,80937,80938,80942],{},[895,80939,80940],{},[898,80941,10358],{},[902,80943,10358],{"encoding":904}," stane ",[883,80946,80948],{"className":80947},[886],[888,80949,80950],{"xmlns":890},[892,80951,80952,80962],{},[895,80953,80954,80956],{},[898,80955,1956],{},[2355,80957,80958,80960],{},[898,80959,2398],{},[898,80961,10358],{},[902,80963,10608],{"encoding":904}," klesající (",[883,80966,80968],{"className":80967},[886],[888,80969,80970],{"xmlns":890},[892,80971,80972,80994],{},[895,80973,80974,80990,80992],{},[1810,80975,80976,80978,80984],{},[898,80977,1973],{},[895,80979,80980,80982],{},[898,80981,10358],{},[898,80983,10358],{},[895,80985,80986,80988],{},[1664,80987,1728],{"mathvariant":1726},[1664,80989,1728],{"mathvariant":1726},[1664,80991,4022],{},[1963,80993,2058],{},[902,80995,80996],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,80999,81001],{"className":81000},[886],[888,81002,81003],{"xmlns":890},[892,81004,81005,81027],{},[895,81006,81007,81023,81025],{},[1810,81008,81009,81011,81017],{},[898,81010,1973],{},[895,81012,81013,81015],{},[898,81014,10363],{},[898,81016,10363],{},[895,81018,81019,81021],{},[1664,81020,1728],{"mathvariant":1726},[1664,81022,1728],{"mathvariant":1726},[1664,81024,4022],{},[1963,81026,2058],{},[902,81028,81029],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,81032,81034],{"className":81033},[886],[888,81035,81036],{"xmlns":890},[892,81037,81038,81046],{},[895,81039,81040],{},[2355,81041,81042,81044],{},[898,81043,10358],{},[1963,81045,2058],{},[902,81047,76058],{"encoding":904},[115,81049,81051],{"id":81050},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,81053,81054,81057,81058,81081,81082,30444],{},[38,81055,81056],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,81059,81061],{"className":81060},[886],[888,81062,81063],{"xmlns":890},[892,81064,81065,81079],{},[895,81066,81067,81069,81071,81073,81075,81077],{},[898,81068,1973],{},[1664,81070,1667],{"stretchy":1666},[898,81072,10358],{},[1664,81074,1916],{"separator":1915},[898,81076,10363],{},[1664,81078,1673],{"stretchy":1666},[902,81080,10560],{"encoding":904}," stupně ",[883,81083,81085],{"className":81084},[886],[888,81086,81087],{"xmlns":890},[892,81088,81089,81093],{},[895,81090,81091],{},[898,81092,37360],{},[902,81094,37360],{"encoding":904},[883,81096,81098],{"className":81097},[886],[888,81099,81100],{"xmlns":890,"display":28566},[892,81101,81102,81165],{},[21254,81103,81104],{"width":28571},[21259,81105,81106,81108,81158,81160],{},[21262,81107],{"width":28576},[21262,81109,81110],{},[895,81111,81112,81114,81116,81124,81126,81128,81130,81138,81140,81142,81144,81146,81148,81150,81152,81154,81156],{},[898,81113,10358],{},[1690,81115,1692],{},[1810,81117,81118,81120,81122],{},[898,81119,1973],{},[898,81121,10358],{},[1664,81123,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,81125,1700],{},[898,81127,10363],{},[1690,81129,1692],{},[1810,81131,81132,81134,81136],{},[898,81133,1973],{},[898,81135,10363],{},[1664,81137,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,81139,1676],{},[898,81141,37360],{},[1690,81143,1692],{},[898,81145,1973],{},[1664,81147,1667],{"stretchy":1666},[898,81149,10358],{},[1664,81151,1916],{"separator":1915},[898,81153,10363],{},[1664,81155,1673],{"stretchy":1666},[898,81157,1977],{"mathvariant":1726},[21262,81159],{"width":28576},[21262,81161,81162],{},[1690,81163,81164],{},"(5.12)",[902,81166,81167],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,81169,81170,81191],{},[38,81171,81172,81173],{},"Speciální případ ",[883,81174,81176],{"className":81175},[886],[888,81177,81178],{"xmlns":890},[892,81179,81180,81188],{},[895,81181,81182,81184,81186],{},[898,81183,37360],{},[1664,81185,1676],{},[1963,81187,2875],{},[902,81189,81190],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,81193,81195],{"className":81194},[886],[888,81196,81197],{"xmlns":890,"display":28566},[892,81198,81199,81243],{},[895,81200,81201,81203,81205,81207,81213,81215,81217,81219,81221,81227,81229,81231,81233,81235,81237,81239,81241],{},[898,81202,10358],{},[1664,81204,3753],{},[898,81206,1956],{},[2355,81208,81209,81211],{},[898,81210,2398],{},[898,81212,10358],{},[1664,81214,1700],{},[898,81216,10363],{},[1664,81218,3753],{},[898,81220,1956],{},[2355,81222,81223,81225],{},[898,81224,2398],{},[898,81226,10363],{},[1664,81228,1676],{},[898,81230,1973],{},[1664,81232,1667],{"stretchy":1666},[898,81234,10358],{},[1664,81236,1916],{"separator":1915},[898,81238,10363],{},[1664,81240,1673],{"stretchy":1666},[898,81242,1977],{"mathvariant":1726},[902,81244,81245],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,81247,81248,81249,81252],{},"Slovně — ",[38,81250,81251],{},"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).",[115,81254,10341],{"id":75394},[724,81256,81257,10588,81259,81262,81263,81285,81286,2087],{},[38,81258,10341],{},[614,81260,81261],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,81264,81266],{"className":81265},[886],[888,81267,81268],{"xmlns":890},[892,81269,81270,81282],{},[895,81271,81272,81274,81276,81278,81280],{},[1664,81273,1837],{"stretchy":1666},[898,81275,10358],{},[1664,81277,1916],{"separator":1915},[898,81279,10363],{},[1664,81281,1850],{"stretchy":1666},[902,81283,81284],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,81287,81289],{"className":81288},[886],[888,81290,81291],{"xmlns":890},[892,81292,81293,81298],{},[895,81294,81295],{},[898,81296,81297],{},"q",[902,81299,81297],{"encoding":904},[883,81301,81303],{"className":81302},[886],[888,81304,81305],{"xmlns":890,"display":28566},[892,81306,81307,81342],{},[21254,81308,81309],{"width":28571},[21259,81310,81311,81313,81335,81337],{},[21262,81312],{"width":28576},[21262,81314,81315],{},[895,81316,81317,81319,81321,81323,81325,81327,81329,81331,81333],{},[898,81318,1973],{},[1664,81320,1667],{"stretchy":1666},[898,81322,10358],{},[1664,81324,1916],{"separator":1915},[898,81326,10363],{},[1664,81328,1673],{"stretchy":1666},[1664,81330,1676],{},[898,81332,81297],{},[898,81334,1977],{"mathvariant":1726},[21262,81336],{"width":28576},[21262,81338,81339],{},[1690,81340,81341],{},"(5.13)",[902,81343,81344],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,81346,81347,81348,81351,81352,4488],{},"Jsou to ",[38,81349,81350],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,81353,81355],{"className":81354,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,81357,81358],{},[38,81359,81360],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,81362,81363,81368,81373,81378],{},[123,81364,81365,81367],{},[38,81366,13018],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,81369,81370,81372],{},[38,81371,38164],{}," (úloha 5.14);",[123,81374,81375,8990],{},[38,81376,81377],{},"neprotínají se",[123,81379,81380,81381,4924,81394,1977],{},"s rostoucím ",[883,81382,81384],{"className":81383},[886],[888,81385,81386],{"xmlns":890},[892,81387,81388,81392],{},[895,81389,81390],{},[898,81391,81297],{},[902,81393,81297],{"encoding":904},[38,81395,81396],{},"vzdalují od počátku",[724,81398,81399],{},[614,81400,81401,81402,81424,81425,1977],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,81403,81405],{"className":81404},[886],[888,81406,81407],{"xmlns":890},[892,81408,81409,81421],{},[895,81410,81411,81413,81415,81417,81419],{},[1664,81412,1667],{"stretchy":1666},[898,81414,10358],{},[1664,81416,1916],{"separator":1915},[898,81418,10363],{},[1664,81420,1673],{"stretchy":1666},[902,81422,81423],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,81426,81428],{"className":81427},[886],[888,81429,81430],{"xmlns":890},[892,81431,81432,81456],{},[895,81433,81434,81440,81442,81448,81450],{},[2355,81435,81436,81438],{},[898,81437,81297],{},[1963,81439,2875],{},[1664,81441,4022],{},[2355,81443,81444,81446],{},[898,81445,81297],{},[1963,81447,2058],{},[1664,81449,4022],{},[2355,81451,81452,81454],{},[898,81453,81297],{},[1963,81455,1970],{},[902,81457,81458],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,81460,81462,81463,1673],{"id":81461},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,81464,81466],{"className":81465},[886],[888,81467,81468],{"xmlns":890},[892,81469,81470,81480],{},[895,81471,81472,81474,81476,81478],{},[898,81473,1956],{},[898,81475,1959],{},[898,81477,1991],{},[898,81479,2351],{},[902,81481,11161],{"encoding":904},[724,81483,81484,10588,81487,81490],{},[38,81485,81486],{},"Mezní míra technické substituce",[614,81488,81489],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,81492,81494],{"className":81493},[886],[888,81495,81496],{"xmlns":890,"display":28566},[892,81497,81498,81589],{},[21254,81499,81500],{"width":28571},[21259,81501,81502,81504,81582,81584],{},[21262,81503],{"width":28576},[21262,81505,81506],{},[895,81507,81508,81510,81512,81514,81516,81518,81520,81522,81524,81526,81528,81530,81532,81534,81536,81538,81560,81562,81580],{},[898,81509,1956],{},[898,81511,1959],{},[898,81513,1991],{},[898,81515,2351],{},[1664,81517,1676],{},[898,81519,1956],{},[898,81521,1959],{},[898,81523,1991],{},[898,81525,2351],{},[1664,81527,1667],{"stretchy":1666},[898,81529,10358],{},[1664,81531,1916],{"separator":1915},[898,81533,10363],{},[1664,81535,1673],{"stretchy":1666},[1664,81537,1676],{},[2922,81539,81540,81550],{},[895,81541,81542,81544],{},[898,81543,1956],{},[2355,81545,81546,81548],{},[898,81547,2398],{},[898,81549,10358],{},[895,81551,81552,81554],{},[898,81553,1956],{},[2355,81555,81556,81558],{},[898,81557,2398],{},[898,81559,10363],{},[1664,81561,1676],{},[2922,81563,81564,81572],{},[1810,81565,81566,81568,81570],{},[898,81567,1973],{},[898,81569,10358],{},[1664,81571,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1810,81573,81574,81576,81578],{},[898,81575,1973],{},[898,81577,10363],{},[1664,81579,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[898,81581,1977],{"mathvariant":1726},[21262,81583],{"width":28576},[21262,81585,81586],{},[1690,81587,81588],{},"(5.14)",[902,81590,81591],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,81593,81594,1885,81596,81626,81627,81658],{},[38,81595,9779],{},[883,81597,81599],{"className":81598},[886],[888,81600,81601],{"xmlns":890},[892,81602,81603,81623],{},[895,81604,81605,81607,81609,81611,81613,81615,81617,81619,81621],{},[898,81606,1956],{},[898,81608,1959],{},[898,81610,1991],{},[898,81612,2351],{},[1664,81614,1667],{"stretchy":1666},[898,81616,10358],{},[1664,81618,1916],{"separator":1915},[898,81620,10363],{},[1664,81622,1673],{"stretchy":1666},[902,81624,81625],{"encoding":904},"MRTS(L, K)"," udává, ",[38,81628,81629,81630,81643,81644,81657],{},"o kolik se musí přibližně změnit kapitál ",[883,81631,81633],{"className":81632},[886],[888,81634,81635],{"xmlns":890},[892,81636,81637,81641],{},[895,81638,81639],{},[898,81640,10363],{},[902,81642,10363],{"encoding":904},", jestliže se práce ",[883,81645,81647],{"className":81646},[886],[888,81648,81649],{"xmlns":890},[892,81650,81651,81655],{},[895,81652,81653],{},[898,81654,10358],{},[902,81656,10358],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[4436,81660,81661],{},[724,81662,81663,18523,81665,81684,81685,81722,81723,81726,81727,81731],{},[883,81664,4723],{},[883,81666,81668],{"className":81667},[886],[888,81669,81670],{"xmlns":890},[892,81671,81672,81682],{},[895,81673,81674,81676,81678,81680],{},[898,81675,1956],{},[898,81677,1959],{},[898,81679,1991],{},[898,81681,2351],{},[902,81683,11161],{"encoding":904}," říká: ",[614,81686,81687,81688,81707,81708,81721],{},"„jednu jednotku práce musím nahradit přibližně ",[883,81689,81691],{"className":81690},[886],[888,81692,81693],{"xmlns":890},[892,81694,81695,81705],{},[895,81696,81697,81699,81701,81703],{},[898,81698,1956],{},[898,81700,1959],{},[898,81702,1991],{},[898,81704,2351],{},[902,81706,11161],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,81709,81711],{"className":81710},[886],[888,81712,81713],{"xmlns":890},[892,81714,81715,81719],{},[895,81716,81717],{},[898,81718,1973],{},[902,81720,1973],{"encoding":904}," zůstala stejná.\""," Je to ",[38,81724,81725],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,81728,81730],{"className":81729,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,81733,81734],{},[1928,81735],{"alt":81736,"className":81737,"src":81738},"imek-izokvanty-mrts",[210,1932],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,81740,81741,81744,81745,1762,81775,81797,81798,3727],{},[38,81742,81743],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,81746,81748],{"className":81747},[886],[888,81749,81750],{"xmlns":890},[892,81751,81752,81772],{},[895,81753,81754,81756,81762,81764,81770],{},[1664,81755,1837],{"stretchy":1666},[2355,81757,81758,81760],{},[898,81759,10358],{},[1963,81761,2058],{},[1664,81763,1916],{"separator":1915},[2355,81765,81766,81768],{},[898,81767,10363],{},[1963,81769,2058],{},[1664,81771,1850],{"stretchy":1666},[902,81773,81774],{"encoding":904},"[L_0, K_0]",[883,81776,81778],{"className":81777},[886],[888,81779,81780],{"xmlns":890},[892,81781,81782,81794],{},[895,81783,81784,81786,81788,81790,81792],{},[1664,81785,1867],{},[898,81787,1956],{},[898,81789,1959],{},[898,81791,1991],{},[898,81793,2351],{},[902,81795,81796],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,81799,81801],{"className":81800},[886],[888,81802,81803],{"xmlns":890},[892,81804,81805,81827],{},[895,81806,81807,81809,81811,81813,81815,81817,81819,81821],{},[898,81808,1973],{},[1664,81810,1667],{"stretchy":1666},[898,81812,10358],{},[1664,81814,1916],{"separator":1915},[898,81816,10363],{},[1664,81818,1673],{"stretchy":1666},[1664,81820,1676],{},[2355,81822,81823,81825],{},[898,81824,81297],{},[1963,81826,2058],{},[902,81828,81829],{"encoding":904},"Q(L,K) = q_0",[883,81831,81833],{"className":81832},[886],[888,81834,81835],{"xmlns":890,"display":28566},[892,81836,81837,81889],{},[895,81838,81839,81853,81855,81857,81875,81877,81879,81881,81883,81885,81887],{},[2922,81840,81841,81847],{},[895,81842,81843,81845],{},[898,81844,1695],{},[898,81846,10363],{},[895,81848,81849,81851],{},[898,81850,1695],{},[898,81852,10358],{},[1664,81854,1676],{},[1664,81856,1867],{},[2922,81858,81859,81867],{},[1810,81860,81861,81863,81865],{},[898,81862,1973],{},[898,81864,10358],{},[1664,81866,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1810,81868,81869,81871,81873],{},[898,81870,1973],{},[898,81872,10363],{},[1664,81874,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,81876,1676],{},[1664,81878,1867],{},[898,81880,1956],{},[898,81882,1959],{},[898,81884,1991],{},[898,81886,2351],{},[898,81888,1977],{"mathvariant":1726},[902,81890,81891],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,81893,81894,81895,81910,81911,81927],{},"Změní-li se práce o ",[883,81896,81898],{"className":81897},[886],[888,81899,81900],{"xmlns":890},[892,81901,81902,81908],{},[895,81903,81904,81906],{},[898,81905,1695],{},[898,81907,10358],{},[902,81909,75856],{"encoding":904},", lze pro odhad změny kapitálu ",[883,81912,81914],{"className":81913},[886],[888,81915,81916],{"xmlns":890},[892,81917,81918,81924],{},[895,81919,81920,81922],{},[898,81921,3468],{"mathvariant":1726},[898,81923,10363],{},[902,81925,81926],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,81929,81931],{"className":81930},[886],[888,81932,81933],{"xmlns":890,"display":28566},[892,81934,81935,81982],{},[21254,81936,81937],{"width":28571},[21259,81938,81939,81941,81975,81977],{},[21262,81940],{"width":28576},[21262,81942,81943],{},[895,81944,81945,81947,81949,81951,81953,81955,81957,81959,81961,81963,81965,81967,81969,81971,81973],{},[898,81946,3468],{"mathvariant":1726},[898,81948,10363],{},[1664,81950,3315],{},[898,81952,1695],{},[898,81954,10363],{},[1664,81956,1676],{},[1664,81958,1867],{},[898,81960,1956],{},[898,81962,1959],{},[898,81964,1991],{},[898,81966,2351],{},[1690,81968,1692],{},[898,81970,1695],{},[898,81972,10358],{},[1664,81974,1916],{"separator":1915},[21262,81976],{"width":28576},[21262,81978,81979],{},[1690,81980,81981],{},"(5.15)",[902,81983,81984],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,81986,81988],{"className":81987},[886],[888,81989,81990],{"xmlns":890,"display":28566},[892,81991,81992,82041],{},[21254,81993,81994],{"width":28571},[21259,81995,81996,81998,82034,82036],{},[21262,81997],{"width":28576},[21262,81999,82000],{},[895,82001,82002,82004,82006,82008,82026,82028,82030,82032],{},[898,82003,1695],{},[898,82005,10358],{},[1664,82007,1676],{},[2922,82009,82010,82016],{},[895,82011,82012,82014],{},[1664,82013,1867],{},[1963,82015,2875],{},[895,82017,82018,82020,82022,82024],{},[898,82019,1956],{},[898,82021,1959],{},[898,82023,1991],{},[898,82025,2351],{},[1690,82027,1692],{},[898,82029,1695],{},[898,82031,10363],{},[898,82033,1977],{"mathvariant":1726},[21262,82035],{"width":28576},[21262,82037,82038],{},[1690,82039,82040],{},"(5.16)",[902,82042,82043],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[4436,82045,82046,82070],{},[724,82047,82048,82050,82051],{},[883,82049,5138],{}," Postup — jak spočítat ",[883,82052,82054],{"className":82053},[886],[888,82055,82056],{"xmlns":890},[892,82057,82058,82068],{},[895,82059,82060,82062,82064,82066],{},[898,82061,1956],{},[898,82063,1959],{},[898,82065,1991],{},[898,82067,2351],{},[902,82069,11161],{"encoding":904},[152,82071,82072,82113,82156,82188],{},[123,82073,82074,82075,4454,82094,1977],{},"Vypočtěte parciální derivace ",[883,82076,82078],{"className":82077},[886],[888,82079,82080],{"xmlns":890},[892,82081,82082,82092],{},[895,82083,82084],{},[1810,82085,82086,82088,82090],{},[898,82087,1973],{},[898,82089,10358],{},[1664,82091,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,82093,10584],{"encoding":904},[883,82095,82097],{"className":82096},[886],[888,82098,82099],{"xmlns":890},[892,82100,82101,82111],{},[895,82102,82103],{},[1810,82104,82105,82107,82109],{},[898,82106,1973],{},[898,82108,10363],{},[1664,82110,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,82112,10630],{"encoding":904},[123,82114,66341,82115,82155],{},[883,82116,82118],{"className":82117},[886],[888,82119,82120],{"xmlns":890},[892,82121,82122,82152],{},[895,82123,82124,82126,82128,82130,82132,82134,82142,82144],{},[898,82125,1956],{},[898,82127,1959],{},[898,82129,1991],{},[898,82131,2351],{},[1664,82133,1676],{},[1810,82135,82136,82138,82140],{},[898,82137,1973],{},[898,82139,10358],{},[1664,82141,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[898,82143,5240],{"mathvariant":1726},[1810,82145,82146,82148,82150],{},[898,82147,1973],{},[898,82149,10363],{},[1664,82151,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,82153,82154],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,82157,82158,82159,1977],{},"Případně dosaďte konkrétní ",[883,82160,82162],{"className":82161},[886],[888,82163,82164],{"xmlns":890},[892,82165,82166,82186],{},[895,82167,82168,82170,82176,82178,82184],{},[1664,82169,1837],{"stretchy":1666},[2355,82171,82172,82174],{},[898,82173,10358],{},[1963,82175,2058],{},[1664,82177,1916],{"separator":1915},[2355,82179,82180,82182],{},[898,82181,10363],{},[1963,82183,2058],{},[1664,82185,1850],{"stretchy":1666},[902,82187,81774],{"encoding":904},[123,82189,82190,82191,82225,82226,82228],{},"Pro odhad substituce použijte ",[883,82192,82194],{"className":82193},[886],[888,82195,82196],{"xmlns":890},[892,82197,82198,82222],{},[895,82199,82200,82202,82204,82206,82208,82210,82212,82214,82216,82218,82220],{},[898,82201,3468],{"mathvariant":1726},[898,82203,10363],{},[1664,82205,3315],{},[1664,82207,1867],{},[898,82209,1956],{},[898,82211,1959],{},[898,82213,1991],{},[898,82215,2351],{},[1664,82217,3753],{},[898,82219,3468],{"mathvariant":1726},[898,82221,10358],{},[902,82223,82224],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,82227,53106],{}," — substituce, ne doplnění).",[724,82230,82231],{},[614,82232,82233,82234,82266,82267,3210,82280,16291,82309,82324],{},"Obrázek 5.7 — izokvanta ",[883,82235,82237],{"className":82236},[886],[888,82238,82239],{"xmlns":890},[892,82240,82241,82263],{},[895,82242,82243,82249,82251,82253,82255,82257,82259,82261],{},[2355,82244,82245,82247],{},[898,82246,81297],{},[1963,82248,2058],{},[1664,82250,1676],{},[898,82252,1973],{},[1664,82254,1667],{"stretchy":1666},[898,82256,10358],{},[1664,82258,1916],{"separator":1915},[898,82260,10363],{},[1664,82262,1673],{"stretchy":1666},[902,82264,82265],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,82268,82270],{"className":82269},[886],[888,82271,82272],{"xmlns":890},[892,82273,82274,82278],{},[895,82275,82276],{},[898,82277,19355],{},[902,82279,19355],{"encoding":904},[883,82281,82283],{"className":82282},[886],[888,82284,82285],{"xmlns":890},[892,82286,82287,82307],{},[895,82288,82289,82291,82297,82299,82305],{},[1664,82290,1837],{"stretchy":1666},[2355,82292,82293,82295],{},[898,82294,10358],{},[1963,82296,2058],{},[1664,82298,1916],{"separator":1915},[2355,82300,82301,82303],{},[898,82302,10363],{},[1963,82304,2058],{},[1664,82306,1850],{"stretchy":1666},[902,82308,81774],{"encoding":904},[883,82310,82312],{"className":82311},[886],[888,82313,82314],{"xmlns":890},[892,82315,82316,82322],{},[895,82317,82318,82320],{},[898,82319,3468],{"mathvariant":1726},[898,82321,10363],{},[902,82323,81926],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,82326,82328],{"id":82327},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,82330,82332],{"id":82331},"příklad-54","Příklad 5.4",[724,82334,77173,82335,1343,82377,1343,82394,1977],{},[883,82336,82338],{"className":82337},[886],[888,82339,82340],{"xmlns":890},[892,82341,82342,82374],{},[895,82343,82344,82346,82348,82350,82362],{},[898,82345,1973],{},[1664,82347,1676],{},[1963,82349,36744],{},[1720,82351,82352,82354],{},[898,82353,10358],{},[895,82355,82356,82358,82360],{},[1963,82357,2875],{},[898,82359,5240],{"mathvariant":1726},[1963,82361,1970],{},[1720,82363,82364,82366],{},[898,82365,10363],{},[895,82367,82368,82370,82372],{},[1963,82369,2875],{},[898,82371,5240],{"mathvariant":1726},[1963,82373,2774],{},[902,82375,82376],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,82378,82380],{"className":82379},[886],[888,82381,82382],{"xmlns":890},[892,82383,82384,82392],{},[895,82385,82386,82388,82390],{},[898,82387,10358],{},[1664,82389,1676],{},[1963,82391,9599],{},[902,82393,77547],{"encoding":904},[883,82395,82397],{"className":82396},[886],[888,82398,82399],{"xmlns":890},[892,82400,82401,82409],{},[895,82402,82403,82405,82407],{},[898,82404,10363],{},[1664,82406,1676],{},[1963,82408,1965],{},[902,82410,82411],{"encoding":904},"K = 100",[724,82413,82414],{},[38,82415,82416],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,82418,82420],{"className":82419},[886],[888,82421,82422],{"xmlns":890,"display":28566},[892,82423,82424,82538],{},[895,82425,82426,82428,82434,82436,82444,82446,82454,82468,82480,82482,82484,82486,82492,82494,82496,82498,82500,82502,82504,82512,82514,82524,82526,82533,82535],{},[898,82427,1956],{},[2355,82429,82430,82432],{},[898,82431,2398],{},[898,82433,10358],{},[1664,82435,1676],{},[1810,82437,82438,82440,82442],{},[898,82439,1973],{},[898,82441,10358],{},[1664,82443,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,82445,1676],{},[2919,82447,82448],{"scriptlevel":2058,"displaystyle":1666},[2922,82449,82450,82452],{},[1963,82451,36744],{},[1963,82453,1970],{},[1720,82455,82456,82458],{},[898,82457,10358],{},[895,82459,82460,82462,82464,82466],{},[1664,82461,1867],{},[1963,82463,2875],{},[898,82465,5240],{"mathvariant":1726},[1963,82467,1970],{},[1720,82469,82470,82472],{},[898,82471,10363],{},[895,82473,82474,82476,82478],{},[1963,82475,2875],{},[898,82477,5240],{"mathvariant":1726},[1963,82479,2774],{},[1664,82481,1916],{"separator":1915},[6444,82483],{"width":15783},[898,82485,1956],{},[2355,82487,82488,82490],{},[898,82489,2398],{},[898,82491,10358],{},[1664,82493,1667],{"stretchy":1666},[1963,82495,9599],{},[1664,82497,1916],{"separator":1915},[1963,82499,1965],{},[1664,82501,1673],{"stretchy":1666},[1664,82503,1676],{},[2919,82505,82506],{"scriptlevel":2058,"displaystyle":1666},[2922,82507,82508,82510],{},[1963,82509,36744],{},[1963,82511,1970],{},[1664,82513,3753],{},[2919,82515,82516],{"scriptlevel":2058,"displaystyle":1666},[2922,82517,82518,82520],{},[1963,82519,2875],{},[8682,82521,82522],{},[1963,82523,9599],{},[1664,82525,3753],{},[82527,82528,82529,82531],"mroot",{},[1963,82530,1965],{},[1963,82532,2774],{},[1664,82534,3315],{},[1963,82536,82537],{},"7,153.",[902,82539,82540],{"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.",[724,82542,82543,82544,44660,82566,10796,82583,82604,82605,82626],{},"Přibližná změna při ",[883,82545,82547],{"className":82546},[886],[888,82548,82549],{"xmlns":890},[892,82550,82551,82563],{},[895,82552,82553,82555,82557,82559,82561],{},[898,82554,10358],{},[1664,82556,2087],{},[1963,82558,9599],{},[1664,82560,3699],{},[1963,82562,38846],{},[902,82564,82565],{"encoding":904},"L: 20 \\to 21",[883,82567,82569],{"className":82568},[886],[888,82570,82571],{"xmlns":890},[892,82572,82573,82581],{},[895,82574,82575,82577,82579],{},[898,82576,10363],{},[1664,82578,1676],{},[1963,82580,1965],{},[902,82582,82411],{"encoding":904},[883,82584,82586],{"className":82585},[886],[888,82587,82588],{"xmlns":890},[892,82589,82590,82601],{},[895,82591,82592,82594,82596,82598],{},[898,82593,3468],{"mathvariant":1726},[898,82595,1973],{},[1664,82597,3315],{},[1963,82599,82600],{},"7,153",[902,82602,82603],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,82606,82608],{"className":82607},[886],[888,82609,82610],{"xmlns":890},[892,82611,82612,82623],{},[895,82613,82614,82616,82618,82620],{},[898,82615,3468],{"mathvariant":1726},[898,82617,1973],{},[1664,82619,3315],{},[1963,82621,82622],{},"26,888",[902,82624,82625],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,82628,82629,82632],{},[38,82630,82631],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,82634,82636],{"className":82635},[886],[888,82637,82638],{"xmlns":890,"display":28566},[892,82639,82640,82740],{},[895,82641,82642,82644,82650,82652,82660,82662,82664,82676,82690,82692,82694,82696,82702,82704,82706,82708,82710,82712,82714,82716,82720,82722,82735,82737],{},[898,82643,1956],{},[2355,82645,82646,82648],{},[898,82647,2398],{},[898,82649,10363],{},[1664,82651,1676],{},[1810,82653,82654,82656,82658],{},[898,82655,1973],{},[898,82657,10363],{},[1664,82659,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,82661,1676],{},[1963,82663,2826],{},[1720,82665,82666,82668],{},[898,82667,10358],{},[895,82669,82670,82672,82674],{},[1963,82671,2875],{},[898,82673,5240],{"mathvariant":1726},[1963,82675,1970],{},[1720,82677,82678,82680],{},[898,82679,10363],{},[895,82681,82682,82684,82686,82688],{},[1664,82683,1867],{},[1963,82685,1970],{},[898,82687,5240],{"mathvariant":1726},[1963,82689,2774],{},[1664,82691,1916],{"separator":1915},[6444,82693],{"width":15783},[898,82695,1956],{},[2355,82697,82698,82700],{},[898,82699,2398],{},[898,82701,10363],{},[1664,82703,1667],{"stretchy":1666},[1963,82705,9599],{},[1664,82707,1916],{"separator":1915},[1963,82709,1965],{},[1664,82711,1673],{"stretchy":1666},[1664,82713,1676],{},[1963,82715,2826],{},[8682,82717,82718],{},[1963,82719,9599],{},[1664,82721,3753],{},[2919,82723,82724],{"scriptlevel":2058,"displaystyle":1666},[2922,82725,82726,82728],{},[1963,82727,2875],{},[82527,82729,82730,82733],{},[1963,82731,82732],{},"10000",[1963,82734,2774],{},[1664,82736,3315],{},[1963,82738,82739],{},"4,525.",[902,82741,82742],{"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.",[724,82744,82745,82746,3271,82763,4488],{},"Produkce poklesne přibližně o 4,525 (z ",[883,82747,82749],{"className":82748},[886],[888,82750,82751],{"xmlns":890},[892,82752,82753,82760],{},[895,82754,82755,82757],{},[1664,82756,3315],{},[1963,82758,82759],{},"905,126",[902,82761,82762],{"encoding":904},"\\approx 905{,}126",[883,82764,82766],{"className":82765},[886],[888,82767,82768],{"xmlns":890},[892,82769,82770,82777],{},[895,82771,82772,82774],{},[1664,82773,3315],{},[1963,82775,82776],{},"900,601",[902,82778,82779],{"encoding":904},"\\approx 900{,}601",[724,82781,82782,3706,82829,1343,82851,4488],{},[38,82783,82784,82785,4454,82807],{},"(c) Změna ",[883,82786,82788],{"className":82787},[886],[888,82789,82790],{"xmlns":890},[892,82791,82792,82804],{},[895,82793,82794,82796,82798,82800,82802],{},[898,82795,10358],{},[1664,82797,2087],{},[1963,82799,9599],{},[1664,82801,3699],{},[1963,82803,36744],{},[902,82805,82806],{"encoding":904},"L: 20 \\to 15",[883,82808,82810],{"className":82809},[886],[888,82811,82812],{"xmlns":890},[892,82813,82814,82826],{},[895,82815,82816,82818,82820,82822,82824],{},[898,82817,10363],{},[1664,82819,2087],{},[1963,82821,1965],{},[1664,82823,3699],{},[1963,82825,9367],{},[902,82827,82828],{"encoding":904},"K: 100 \\to 150",[883,82830,82832],{"className":82831},[886],[888,82833,82834],{"xmlns":890},[892,82835,82836,82848],{},[895,82837,82838,82840,82842,82844,82846],{},[898,82839,1695],{},[898,82841,10358],{},[1664,82843,1676],{},[1664,82845,1867],{},[1963,82847,2826],{},[902,82849,82850],{"encoding":904},"dL = -5",[883,82852,82854],{"className":82853},[886],[888,82855,82856],{"xmlns":890},[892,82857,82858,82868],{},[895,82859,82860,82862,82864,82866],{},[898,82861,1695],{},[898,82863,10363],{},[1664,82865,1676],{},[1963,82867,3696],{},[902,82869,82870],{"encoding":904},"dK = 50",[883,82872,82874],{"className":82873},[886],[888,82875,82876],{"xmlns":890,"display":28566},[892,82877,82878,82966],{},[895,82879,82880,82882,82884,82886,82888,82894,82896,82898,82900,82902,82904,82906,82908,82910,82912,82914,82916,82918,82924,82926,82928,82930,82932,82934,82936,82938,82940,82942,82944,82946,82948,82950,82952,82954,82957,82959,82961,82963],{},[898,82881,1695],{},[898,82883,1973],{},[1664,82885,1676],{},[898,82887,1956],{},[2355,82889,82890,82892],{},[898,82891,2398],{},[898,82893,10358],{},[1664,82895,1667],{"stretchy":1666},[1963,82897,9599],{},[1664,82899,1916],{"separator":1915},[1963,82901,1965],{},[1664,82903,1673],{"stretchy":1666},[1664,82905,3753],{},[1664,82907,1667],{"stretchy":1666},[1664,82909,1867],{},[1963,82911,2826],{},[1664,82913,1673],{"stretchy":1666},[1664,82915,1700],{},[898,82917,1956],{},[2355,82919,82920,82922],{},[898,82921,2398],{},[898,82923,10363],{},[1664,82925,1667],{"stretchy":1666},[1963,82927,9599],{},[1664,82929,1916],{"separator":1915},[1963,82931,1965],{},[1664,82933,1673],{"stretchy":1666},[1664,82935,3753],{},[1963,82937,3696],{},[1664,82939,1676],{},[1963,82941,82600],{},[1664,82943,3753],{},[1664,82945,1667],{"stretchy":1666},[1664,82947,1867],{},[1963,82949,2826],{},[1664,82951,1673],{"stretchy":1666},[1664,82953,1700],{},[1963,82955,82956],{},"4,525",[1664,82958,3753],{},[1963,82960,3696],{},[1664,82962,3315],{},[1963,82964,82965],{},"190,485.",[902,82967,82968],{"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.",[724,82970,82971],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,82973,82975],{"id":82974},"příklad-55","Příklad 5.5",[724,82977,82978,82979,83015,83016,1977],{},"Pro produkci ",[883,82980,82982],{"className":82981},[886],[888,82983,82984],{"xmlns":890},[892,82985,82986,83012],{},[895,82987,82988,82990,82992,82994,82996,82998,83000,83002,83008],{},[898,82989,1973],{},[1664,82991,1667],{"stretchy":1666},[898,82993,10358],{},[1664,82995,1916],{"separator":1915},[898,82997,10363],{},[1664,82999,1673],{"stretchy":1666},[1664,83001,1676],{},[82527,83003,83004,83006],{},[898,83005,10358],{},[1963,83007,2774],{},[8682,83009,83010],{},[898,83011,10363],{},[902,83013,83014],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,83017,83019],{"className":83018},[886],[888,83020,83021],{"xmlns":890},[892,83022,83023,83039],{},[895,83024,83025,83031,83035,83037],{},[82527,83026,83027,83029],{},[898,83028,10358],{},[1963,83030,2774],{},[8682,83032,83033],{},[898,83034,10363],{},[1664,83036,1676],{},[898,83038,81297],{},[902,83040,83041],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,83043,83044,83045,1977],{},"Umocněním na druhou: ",[883,83046,83048],{"className":83047},[886],[888,83049,83050],{"xmlns":890},[892,83051,83052,83076],{},[895,83053,83054,83056,83058,83064,83066],{},[898,83055,10363],{},[1664,83057,1676],{},[1720,83059,83060,83062],{},[898,83061,81297],{},[1963,83063,1970],{},[898,83065,5240],{"mathvariant":1726},[82527,83067,83068,83074],{},[1720,83069,83070,83072],{},[898,83071,10358],{},[1963,83073,1970],{},[1963,83075,2774],{},[902,83077,83078],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,83080,83081,83121,83161],{},[123,83082,83083],{},[883,83084,83086],{"className":83085},[886],[888,83087,83088],{"xmlns":890},[892,83089,83090,83118],{},[895,83091,83092,83094,83096,83098,83100,83102,83104,83106,83108],{},[898,83093,81297],{},[1664,83095,1676],{},[1963,83097,2875],{},[1664,83099,4556],{},[898,83101,10363],{},[1664,83103,1676],{},[1963,83105,2875],{},[898,83107,5240],{"mathvariant":1726},[82527,83109,83110,83116],{},[1720,83111,83112,83114],{},[898,83113,10358],{},[1963,83115,1970],{},[1963,83117,2774],{},[902,83119,83120],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,83122,83123],{},[883,83124,83126],{"className":83125},[886],[888,83127,83128],{"xmlns":890},[892,83129,83130,83158],{},[895,83131,83132,83134,83136,83138,83140,83142,83144,83146,83148],{},[898,83133,81297],{},[1664,83135,1676],{},[1963,83137,1970],{},[1664,83139,4556],{},[898,83141,10363],{},[1664,83143,1676],{},[1963,83145,2944],{},[898,83147,5240],{"mathvariant":1726},[82527,83149,83150,83156],{},[1720,83151,83152,83154],{},[898,83153,10358],{},[1963,83155,1970],{},[1963,83157,2774],{},[902,83159,83160],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,83162,83163],{},[883,83164,83166],{"className":83165},[886],[888,83167,83168],{"xmlns":890},[892,83169,83170,83198],{},[895,83171,83172,83174,83176,83178,83180,83182,83184,83186,83188],{},[898,83173,81297],{},[1664,83175,1676],{},[1963,83177,2774],{},[1664,83179,4556],{},[898,83181,10363],{},[1664,83183,1676],{},[1963,83185,4567],{},[898,83187,5240],{"mathvariant":1726},[82527,83189,83190,83196],{},[1720,83191,83192,83194],{},[898,83193,10358],{},[1963,83195,1970],{},[1963,83197,2774],{},[902,83199,83200],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,83202,83203],{},[614,83204,83205,83206,7039,83227,1977],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,83207,83209],{"className":83208},[886],[888,83210,83211],{"xmlns":890},[892,83212,83213,83225],{},[895,83214,83215,83217,83219,83221,83223],{},[1664,83216,1667],{"stretchy":1666},[898,83218,10358],{},[1664,83220,1916],{"separator":1915},[898,83222,10363],{},[1664,83224,1673],{"stretchy":1666},[902,83226,81423],{"encoding":904},[883,83228,83230],{"className":83229},[886],[888,83231,83232],{"xmlns":890},[892,83233,83234,83250],{},[895,83235,83236,83238,83240,83242,83244,83246,83248],{},[898,83237,81297],{},[1664,83239,1676],{},[1963,83241,2875],{},[1664,83243,1916],{"separator":1915},[1963,83245,1970],{},[1664,83247,1916],{"separator":1915},[1963,83249,2774],{},[902,83251,83252],{"encoding":904},"q = 1, 2, 3",[198,83254,83256],{"id":83255},"příklad-56","Příklad 5.6",[724,83258,77173,83259,1977],{},[883,83260,83262],{"className":83261},[886],[888,83263,83264],{"xmlns":890},[892,83265,83266,83282],{},[895,83267,83268,83270,83272,83274,83276,83278],{},[898,83269,1973],{},[1664,83271,1676],{},[1963,83273,1970],{},[898,83275,10358],{},[1664,83277,1700],{},[8682,83279,83280],{},[898,83281,10363],{},[902,83283,83284],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,83286,83288],{"className":83287},[886],[888,83289,83290],{"xmlns":890,"display":28566},[892,83291,83292,83334],{},[895,83293,83294,83296,83302,83304,83306,83308,83310,83312,83318,83320,83332],{},[898,83295,1956],{},[2355,83297,83298,83300],{},[898,83299,2398],{},[898,83301,10358],{},[1664,83303,1676],{},[1963,83305,1970],{},[1664,83307,1916],{"separator":1915},[6444,83309],{"width":6446},[898,83311,1956],{},[2355,83313,83314,83316],{},[898,83315,2398],{},[898,83317,10363],{},[1664,83319,1676],{},[2922,83321,83322,83324],{},[1963,83323,2875],{},[895,83325,83326,83328],{},[1963,83327,1970],{},[8682,83329,83330],{},[898,83331,10363],{},[898,83333,1977],{"mathvariant":1726},[902,83335,83336],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,83338,83340],{"className":83339},[886],[888,83341,83342],{"xmlns":890,"display":28566},[892,83343,83344,83408],{},[895,83345,83346,83348,83350,83352,83354,83356,83378,83380,83398,83400,83402,83406],{},[898,83347,1956],{},[898,83349,1959],{},[898,83351,1991],{},[898,83353,2351],{},[1664,83355,1676],{},[2922,83357,83358,83368],{},[895,83359,83360,83362],{},[898,83361,1956],{},[2355,83363,83364,83366],{},[898,83365,2398],{},[898,83367,10358],{},[895,83369,83370,83372],{},[898,83371,1956],{},[2355,83373,83374,83376],{},[898,83375,2398],{},[898,83377,10363],{},[1664,83379,1676],{},[2922,83381,83382,83384],{},[1963,83383,1970],{},[2919,83385,83386],{"scriptlevel":2058,"displaystyle":1666},[2922,83387,83388,83390],{},[1963,83389,2875],{},[895,83391,83392,83394],{},[1963,83393,1970],{},[8682,83395,83396],{},[898,83397,10363],{},[1664,83399,1676],{},[1963,83401,2944],{},[8682,83403,83404],{},[898,83405,10363],{},[898,83407,1977],{"mathvariant":1726},[902,83409,83410],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,83412,83413,83414,83457,83458,83497,83498,1977],{},"Například ",[883,83415,83417],{"className":83416},[886],[888,83418,83419],{"xmlns":890},[892,83420,83421,83454],{},[895,83422,83423,83425,83427,83429,83431,83433,83435,83437,83439,83441,83443,83445,83449,83451],{},[898,83424,1956],{},[898,83426,1959],{},[898,83428,1991],{},[898,83430,2351],{},[1664,83432,1667],{"stretchy":1666},[1963,83434,2944],{},[1664,83436,1916],{"separator":1915},[1963,83438,24701],{},[1664,83440,1673],{"stretchy":1666},[1664,83442,1676],{},[1963,83444,2944],{},[8682,83446,83447],{},[1963,83448,24701],{},[1664,83450,3315],{},[1963,83452,83453],{},"10,58",[902,83455,83456],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,83459,83461],{"className":83460},[886],[888,83462,83463],{"xmlns":890},[892,83464,83465,83494],{},[895,83466,83467,83469,83471,83473,83475,83477,83479,83481,83483,83485,83489,83491],{},[898,83468,1973],{},[1664,83470,1667],{"stretchy":1666},[1963,83472,2944],{},[1664,83474,1916],{"separator":1915},[1963,83476,24701],{},[1664,83478,1673],{"stretchy":1666},[1664,83480,1676],{},[1963,83482,6151],{},[1664,83484,1700],{},[8682,83486,83487],{},[1963,83488,24701],{},[1664,83490,3315],{},[1963,83492,83493],{},"10,646",[902,83495,83496],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,83499,83501],{"className":83500},[886],[888,83502,83503],{"xmlns":890},[892,83504,83505,83513],{},[895,83506,83507,83509],{},[1963,83508,2944],{},[8682,83510,83511],{},[1963,83512,24701],{},[902,83514,83515],{"encoding":904},"4\\sqrt{7}",[724,83517,83518,83519,83539],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,83520,83522],{"className":83521},[886],[888,83523,83524],{"xmlns":890},[892,83525,83526,83536],{},[895,83527,83528,83530,83532,83534],{},[898,83529,1695],{},[898,83531,10358],{},[1664,83533,1676],{},[1963,83535,1970],{},[902,83537,83538],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,83541,83543],{"className":83542},[886],[888,83544,83545],{"xmlns":890,"display":28566},[892,83546,83547,83596],{},[895,83548,83549,83551,83553,83555,83557,83559,83561,83563,83565,83567,83569,83571,83573,83575,83577,83579,83581,83583,83585,83589,83591,83593],{},[898,83550,1695],{},[898,83552,10363],{},[1664,83554,1676],{},[1664,83556,1867],{},[898,83558,1956],{},[898,83560,1959],{},[898,83562,1991],{},[898,83564,2351],{},[1664,83566,1667],{"stretchy":1666},[1963,83568,2944],{},[1664,83570,1916],{"separator":1915},[1963,83572,24701],{},[1664,83574,1673],{"stretchy":1666},[1664,83576,3753],{},[1963,83578,1970],{},[1664,83580,1676],{},[1664,83582,1867],{},[1963,83584,6151],{},[8682,83586,83587],{},[1963,83588,24701],{},[1664,83590,3315],{},[1664,83592,1867],{},[1963,83594,83595],{},"21,17.",[902,83597,83598],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,83600,83602],{"id":83601},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,83604,83605,83606,1343,83608,4454,83610,83612,83613,83616,83617,83620],{},"Hlavními faktory produkce jsou ",[38,83607,75414],{},[38,83609,75430],{},[38,83611,75446],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,83614,83615],{},"jednofaktorový"," (pouze práce) a ",[38,83618,83619],{},"dvoufaktorový"," (práce + kapitál) model.",[724,83622,83623,83624,83627,83628,83630,83631,83633,83634,26689,83637,83656,83657,83674,83675,83692,83693,83715,83716,4924,83735,1977],{},"V ",[38,83625,83626],{},"1F modelu"," se definuje ",[38,83629,10587],{}," (derivace produkce podle práce) a ",[38,83632,75349],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,83635,83636],{},"zákonu klesajících výnosů",[883,83638,83640],{"className":83639},[886],[888,83641,83642],{"xmlns":890},[892,83643,83644,83654],{},[895,83645,83646,83648],{},[898,83647,1956],{},[2355,83649,83650,83652],{},[898,83651,2398],{},[898,83653,10358],{},[902,83655,10608],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,83658,83660],{"className":83659},[886],[888,83661,83662],{"xmlns":890},[892,83663,83664,83672],{},[895,83665,83666],{},[2355,83667,83668,83670],{},[898,83669,10358],{},[1963,83671,2058],{},[902,83673,76058],{"encoding":904}," klesá a v bodě ",[883,83676,83678],{"className":83677},[886],[888,83679,83680],{"xmlns":890},[892,83681,83682,83690],{},[895,83683,83684],{},[2355,83685,83686,83688],{},[898,83687,10358],{},[1963,83689,2875],{},[902,83691,13711],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,83694,83695,83696],{},"princip maximalizace ",[883,83697,83699],{"className":83698},[886],[888,83700,83701],{"xmlns":890},[892,83702,83703,83713],{},[895,83704,83705,83707],{},[898,83706,4822],{},[2355,83708,83709,83711],{},[898,83710,2398],{},[898,83712,10358],{},[902,83714,75133],{"encoding":904},": v bodě maxima ",[883,83717,83719],{"className":83718},[886],[888,83720,83721],{"xmlns":890},[892,83722,83723,83733],{},[895,83724,83725,83727],{},[898,83726,4822],{},[2355,83728,83729,83731],{},[898,83730,2398],{},[898,83732,10358],{},[902,83734,75133],{"encoding":904},[883,83736,83738],{"className":83737},[886],[888,83739,83740],{"xmlns":890},[892,83741,83742,83762],{},[895,83743,83744,83746,83752,83754,83756],{},[898,83745,1956],{},[2355,83747,83748,83750],{},[898,83749,2398],{},[898,83751,10358],{},[1664,83753,1676],{},[898,83755,4822],{},[2355,83757,83758,83760],{},[898,83759,2398],{},[898,83761,10358],{},[902,83763,75163],{"encoding":904},[724,83765,83766,83767,83770,83771,1885,83774,83803,83804,83821,83822,83825,83826,83855,83856,83858,83859,1762,83889,83911],{},"Ve ",[38,83768,83769],{},"2F modelu"," se obvykle používají ",[38,83772,83773],{},"Cobb-Douglasovy funkce",[883,83775,83777],{"className":83776},[886],[888,83778,83779],{"xmlns":890},[892,83780,83781,83801],{},[895,83782,83783,83785,83787,83789,83795],{},[898,83784,1973],{},[1664,83786,1676],{},[898,83788,4822],{},[1720,83790,83791,83793],{},[898,83792,10358],{},[898,83794,207],{},[1720,83796,83797,83799],{},[898,83798,10363],{},[898,83800,1818],{},[902,83802,75230],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,83805,83807],{"className":83806},[886],[888,83808,83809],{"xmlns":890},[892,83810,83811,83819],{},[895,83812,83813,83815,83817],{},[898,83814,207],{},[1664,83816,1700],{},[898,83818,1818],{},[902,83820,75324],{"encoding":904}," rozlišujeme ",[38,83823,83824],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,83827,83829],{"className":83828},[886],[888,83830,83831],{"xmlns":890},[892,83832,83833,83853],{},[895,83834,83835,83837,83843,83845,83847],{},[898,83836,1956],{},[2355,83838,83839,83841],{},[898,83840,2398],{},[898,83842,10358],{},[1664,83844,1916],{"separator":1915},[898,83846,1956],{},[2355,83848,83849,83851],{},[898,83850,2398],{},[898,83852,10363],{},[902,83854,75261],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,83857,10341],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,83860,83862],{"className":83861},[886],[888,83863,83864],{"xmlns":890},[892,83865,83866,83886],{},[895,83867,83868,83870,83876,83878,83880],{},[898,83869,1956],{},[2355,83871,83872,83874],{},[898,83873,2398],{},[898,83875,10358],{},[898,83877,5240],{"mathvariant":1726},[898,83879,1956],{},[2355,83881,83882,83884],{},[898,83883,2398],{},[898,83885,10363],{},[902,83887,83888],{"encoding":904},"MP_L\u002FMP_K",[38,83890,83891,83892,1673],{},"mezní míra technické substituce (",[883,83893,83895],{"className":83894},[886],[888,83896,83897],{"xmlns":890},[892,83898,83899,83909],{},[895,83900,83901,83903,83905,83907],{},[898,83902,1956],{},[898,83904,1959],{},[898,83906,1991],{},[898,83908,2351],{},[902,83910,11161],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,83913,50382],{"id":50381},[152,83915,83916,83919,83922,83925,83928,83931,83934,83937,83940,83943,83946],{},[123,83917,83918],{},"Jaké jsou faktory produkce?",[123,83920,83921],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,83923,83924],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,83926,83927],{},"Co udává mezní produkt práce?",[123,83929,83930],{},"Co musí respektovat průběh křivky produkce?",[123,83932,83933],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,83935,83936],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,83938,83939],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,83941,83942],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,83944,83945],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,83947,83948],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,83950,83952],{"id":83951},"úlohy-51517","Úlohy 5.1–5.17",[198,83954,40951],{"id":40950},[724,83956,83957,83960,83961,83983,83984,1343,84004,1343,84024,84044],{},[38,83958,83959],{},"5.1"," Je dána produkce ",[883,83962,83964],{"className":83963},[886],[888,83965,83966],{"xmlns":890},[892,83967,83968,83980],{},[895,83969,83970,83972,83974,83976],{},[898,83971,1973],{},[1664,83973,1676],{},[1963,83975,3442],{},[8682,83977,83978],{},[898,83979,10358],{},[902,83981,83982],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,83985,83987],{"className":83986},[886],[888,83988,83989],{"xmlns":890},[892,83990,83991,84001],{},[895,83992,83993,83995,83997,83999],{},[898,83994,1973],{},[1664,83996,1667],{"stretchy":1666},[1963,83998,2875],{},[1664,84000,1673],{"stretchy":1666},[902,84002,84003],{"encoding":904},"Q(1)",[883,84005,84007],{"className":84006},[886],[888,84008,84009],{"xmlns":890},[892,84010,84011,84021],{},[895,84012,84013,84015,84017,84019],{},[898,84014,1973],{},[1664,84016,1667],{"stretchy":1666},[1963,84018,2944],{},[1664,84020,1673],{"stretchy":1666},[902,84022,84023],{"encoding":904},"Q(4)",[883,84025,84027],{"className":84026},[886],[888,84028,84029],{"xmlns":890},[892,84030,84031,84041],{},[895,84032,84033,84035,84037,84039],{},[898,84034,1973],{},[1664,84036,1667],{"stretchy":1666},[1963,84038,4567],{},[1664,84040,1673],{"stretchy":1666},[902,84042,84043],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,84046,84047,83960,84050,84086,84087,84100,84101,84120,84121,84147,84148,3271,84161,84174],{},[38,84048,84049],{},"5.2",[883,84051,84053],{"className":84052},[886],[888,84054,84055],{"xmlns":890},[892,84056,84057,84083],{},[895,84058,84059,84061,84063,84065,84067,84073,84075,84077],{},[898,84060,1973],{},[1664,84062,1676],{},[1664,84064,1867],{},[1963,84066,2220],{},[1720,84068,84069,84071],{},[898,84070,10358],{},[1963,84072,2774],{},[1664,84074,1700],{},[1963,84076,4567],{},[1720,84078,84079,84081],{},[898,84080,10358],{},[1963,84082,1970],{},[902,84084,84085],{"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 ",[883,84088,84090],{"className":84089},[886],[888,84091,84092],{"xmlns":890},[892,84093,84094,84098],{},[895,84095,84096],{},[898,84097,10358],{},[902,84099,10358],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,84102,84104],{"className":84103},[886],[888,84105,84106],{"xmlns":890},[892,84107,84108,84118],{},[895,84109,84110,84112],{},[898,84111,1956],{},[2355,84113,84114,84116],{},[898,84115,2398],{},[898,84117,10358],{},[902,84119,10608],{"encoding":904},". (f) Vypočtěte ",[883,84122,84124],{"className":84123},[886],[888,84125,84126],{"xmlns":890},[892,84127,84128,84144],{},[895,84129,84130,84132,84138,84140,84142],{},[898,84131,1956],{},[2355,84133,84134,84136],{},[898,84135,2398],{},[898,84137,10358],{},[1664,84139,1667],{"stretchy":1666},[1963,84141,3442],{},[1664,84143,1673],{"stretchy":1666},[902,84145,84146],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,84149,84151],{"className":84150},[886],[888,84152,84153],{"xmlns":890},[892,84154,84155,84159],{},[895,84156,84157],{},[1963,84158,3442],{},[902,84160,3442],{"encoding":904},[883,84162,84164],{"className":84163},[886],[888,84165,84166],{"xmlns":890},[892,84167,84168,84172],{},[895,84169,84170],{},[1963,84171,42787],{},[902,84173,42787],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,84176,84177,84180,84181,84203,84204,84232,84233,84264,84265,1977],{},[38,84178,84179],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,84182,84184],{"className":84183},[886],[888,84185,84186],{"xmlns":890},[892,84187,84188,84200],{},[895,84189,84190,84192,84194,84196],{},[898,84191,1973],{},[1664,84193,1676],{},[1963,84195,15609],{},[8682,84197,84198],{},[898,84199,10358],{},[902,84201,84202],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,84205,84207],{"className":84206},[886],[888,84208,84209],{"xmlns":890},[892,84210,84211,84229],{},[895,84212,84213,84215,84217,84219,84223,84225,84227],{},[898,84214,1973],{},[1664,84216,1676],{},[1963,84218,30581],{},[8682,84220,84221],{},[898,84222,10358],{},[1664,84224,1867],{},[1963,84226,2944],{},[898,84228,10358],{},[902,84230,84231],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,84234,84236],{"className":84235},[886],[888,84237,84238],{"xmlns":890},[892,84239,84240,84261],{},[895,84241,84242,84244,84246,84248,84250,84252,84255],{},[898,84243,1973],{},[1664,84245,1676],{},[1963,84247,3696],{},[898,84249,10358],{},[1664,84251,1867],{},[1963,84253,84254],{},"0,01",[1720,84256,84257,84259],{},[898,84258,10358],{},[1963,84260,1970],{},[902,84262,84263],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,84266,84268],{"className":84267},[886],[888,84269,84270],{"xmlns":890},[892,84271,84272,84298],{},[895,84273,84274,84276,84278,84280,84282,84288,84290,84292],{},[898,84275,1973],{},[1664,84277,1676],{},[1664,84279,1867],{},[1963,84281,68711],{},[1720,84283,84284,84286],{},[898,84285,10358],{},[1963,84287,2774],{},[1664,84289,1700],{},[1963,84291,4567],{},[1720,84293,84294,84296],{},[898,84295,10358],{},[1963,84297,1970],{},[902,84299,84300],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,84302,84303,84306,84307,3210,84326,72698,84343,1977],{},[38,84304,84305],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,84308,84310],{"className":84309},[886],[888,84311,84312],{"xmlns":890},[892,84313,84314,84324],{},[895,84315,84316,84318],{},[898,84317,4822],{},[2355,84319,84320,84322],{},[898,84321,2398],{},[898,84323,10358],{},[902,84325,75133],{"encoding":904},[883,84327,84329],{"className":84328},[886],[888,84330,84331],{"xmlns":890},[892,84332,84333,84341],{},[895,84334,84335],{},[2355,84336,84337,84339],{},[898,84338,10358],{},[1963,84340,2058],{},[902,84342,76058],{"encoding":904},[883,84344,84346],{"className":84345},[886],[888,84347,84348],{"xmlns":890},[892,84349,84350,84390],{},[895,84351,84352,84354,84360,84362,84368,84370,84372,84374,84380,84382,84388],{},[898,84353,4822],{},[2355,84355,84356,84358],{},[898,84357,2398],{},[898,84359,10358],{},[1664,84361,1667],{"stretchy":1666},[2355,84363,84364,84366],{},[898,84365,10358],{},[1963,84367,2058],{},[1664,84369,1673],{"stretchy":1666},[1664,84371,1676],{},[898,84373,1956],{},[2355,84375,84376,84378],{},[898,84377,2398],{},[898,84379,10358],{},[1664,84381,1667],{"stretchy":1666},[2355,84383,84384,84386],{},[898,84385,10358],{},[1963,84387,2058],{},[1664,84389,1673],{"stretchy":1666},[902,84391,84392],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,84394,84395,83960,84398,22094,84434,84447,84448,84467],{},[38,84396,84397],{},"5.5",[883,84399,84401],{"className":84400},[886],[888,84402,84403],{"xmlns":890},[892,84404,84405,84431],{},[895,84406,84407,84409,84411,84413,84415,84421,84423,84425],{},[898,84408,1973],{},[1664,84410,1676],{},[1664,84412,1867],{},[1963,84414,2154],{},[1720,84416,84417,84419],{},[898,84418,10358],{},[1963,84420,2774],{},[1664,84422,1700],{},[1963,84424,4084],{},[1720,84426,84427,84429],{},[898,84428,10358],{},[1963,84430,1970],{},[902,84432,84433],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,84435,84437],{"className":84436},[886],[888,84438,84439],{"xmlns":890},[892,84440,84441,84445],{},[895,84442,84443],{},[898,84444,10358],{},[902,84446,10358],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,84449,84451],{"className":84450},[886],[888,84452,84453],{"xmlns":890},[892,84454,84455,84465],{},[895,84456,84457,84459],{},[898,84458,4822],{},[2355,84460,84461,84463],{},[898,84462,2398],{},[898,84464,10358],{},[902,84466,75133],{"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.",[198,84469,84471],{"id":84470},"dvoufaktorový-model","Dvoufaktorový model",[724,84473,84474,84477,84478,84203,84504,84232,84546,1977],{},[38,84475,84476],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,84479,84481],{"className":84480},[886],[888,84482,84483],{"xmlns":890},[892,84484,84485,84501],{},[895,84486,84487,84489,84491,84493,84495],{},[898,84488,1973],{},[1664,84490,1676],{},[1963,84492,24701],{},[898,84494,10358],{},[1720,84496,84497,84499],{},[898,84498,10363],{},[1963,84500,1970],{},[902,84502,84503],{"encoding":904},"Q = 7 L K^{2}",[883,84505,84507],{"className":84506},[886],[888,84508,84509],{"xmlns":890},[892,84510,84511,84543],{},[895,84512,84513,84515,84517,84519,84531],{},[898,84514,1973],{},[1664,84516,1676],{},[1963,84518,3696],{},[1720,84520,84521,84523],{},[898,84522,10358],{},[895,84524,84525,84527,84529],{},[1963,84526,1970],{},[898,84528,5240],{"mathvariant":1726},[1963,84530,2774],{},[1720,84532,84533,84535],{},[898,84534,10363],{},[895,84536,84537,84539,84541],{},[1963,84538,2875],{},[898,84540,5240],{"mathvariant":1726},[1963,84542,2774],{},[902,84544,84545],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,84547,84549],{"className":84548},[886],[888,84550,84551],{"xmlns":890},[892,84552,84553,84585],{},[895,84554,84555,84557,84559,84561,84573],{},[898,84556,1973],{},[1664,84558,1676],{},[1963,84560,4282],{},[1720,84562,84563,84565],{},[898,84564,10358],{},[895,84566,84567,84569,84571],{},[1963,84568,2774],{},[898,84570,5240],{"mathvariant":1726},[1963,84572,2826],{},[1720,84574,84575,84577],{},[898,84576,10363],{},[895,84578,84579,84581,84583],{},[1963,84580,1970],{},[898,84582,5240],{"mathvariant":1726},[1963,84584,2826],{},[902,84586,84587],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,84589,84590,83960,84593,84635,84636,1343,84654,84673,84674,84691],{},[38,84591,84592],{},"5.7",[883,84594,84596],{"className":84595},[886],[888,84597,84598],{"xmlns":890},[892,84599,84600,84632],{},[895,84601,84602,84604,84606,84608,84620],{},[898,84603,1973],{},[1664,84605,1676],{},[1963,84607,3442],{},[1720,84609,84610,84612],{},[898,84611,10358],{},[895,84613,84614,84616,84618],{},[1963,84615,2875],{},[898,84617,5240],{"mathvariant":1726},[1963,84619,1970],{},[1720,84621,84622,84624],{},[898,84623,10363],{},[895,84625,84626,84628,84630],{},[1963,84627,2875],{},[898,84629,5240],{"mathvariant":1726},[1963,84631,1970],{},[902,84633,84634],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,84637,84639],{"className":84638},[886],[888,84640,84641],{"xmlns":890},[892,84642,84643,84651],{},[895,84644,84645,84647,84649],{},[898,84646,10358],{},[1664,84648,1676],{},[1963,84650,20642],{},[902,84652,84653],{"encoding":904},"L = 400",[883,84655,84657],{"className":84656},[886],[888,84658,84659],{"xmlns":890},[892,84660,84661,84670],{},[895,84662,84663,84665,84667],{},[898,84664,10363],{},[1664,84666,1676],{},[1963,84668,84669],{},"17576",[902,84671,84672],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,84675,84677],{"className":84676},[886],[888,84678,84679],{"xmlns":890},[892,84680,84681,84689],{},[895,84682,84683,84685,84687],{},[898,84684,10358],{},[1664,84686,1916],{"separator":1915},[898,84688,10363],{},[902,84690,79485],{"encoding":904}," zdvojnásobí.",[724,84693,84694,84697,84698,84635,84729,1343,84747,70084,84765,84795,84796,84826,84827,3271,84840,84854,84855,3271,84868,84881],{},[38,84695,84696],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,84699,84701],{"className":84700},[886],[888,84702,84703],{"xmlns":890},[892,84704,84705,84726],{},[895,84706,84707,84709,84711,84714,84720],{},[898,84708,1973],{},[1664,84710,1676],{},[1963,84712,84713],{},"1,01",[1720,84715,84716,84718],{},[898,84717,10358],{},[1963,84719,24230],{},[1720,84721,84722,84724],{},[898,84723,10363],{},[1963,84725,24289],{},[902,84727,84728],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,84730,84732],{"className":84731},[886],[888,84733,84734],{"xmlns":890},[892,84735,84736,84744],{},[895,84737,84738,84740,84742],{},[898,84739,10358],{},[1664,84741,1676],{},[1963,84743,31243],{},[902,84745,84746],{"encoding":904},"L = 250",[883,84748,84750],{"className":84749},[886],[888,84751,84752],{"xmlns":890},[892,84753,84754,84762],{},[895,84755,84756,84758,84760],{},[898,84757,10363],{},[1664,84759,1676],{},[1963,84761,3365],{},[902,84763,84764],{"encoding":904},"K = 1000",[883,84766,84768],{"className":84767},[886],[888,84769,84770],{"xmlns":890},[892,84771,84772,84792],{},[895,84773,84774,84776,84782,84784,84786,84788,84790],{},[898,84775,1956],{},[2355,84777,84778,84780],{},[898,84779,2398],{},[898,84781,10358],{},[1664,84783,1667],{"stretchy":1666},[1963,84785,31243],{},[1664,84787,1916],{"separator":1915},[1963,84789,3365],{},[1664,84791,1673],{"stretchy":1666},[902,84793,84794],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,84797,84799],{"className":84798},[886],[888,84800,84801],{"xmlns":890},[892,84802,84803,84823],{},[895,84804,84805,84807,84813,84815,84817,84819,84821],{},[898,84806,1956],{},[2355,84808,84809,84811],{},[898,84810,2398],{},[898,84812,10363],{},[1664,84814,1667],{"stretchy":1666},[1963,84816,31243],{},[1664,84818,1916],{"separator":1915},[1963,84820,3365],{},[1664,84822,1673],{"stretchy":1666},[902,84824,84825],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,84828,84830],{"className":84829},[886],[888,84831,84832],{"xmlns":890},[892,84833,84834,84838],{},[895,84835,84836],{},[898,84837,10358],{},[902,84839,10358],{"encoding":904},[883,84841,84843],{"className":84842},[886],[888,84844,84845],{"xmlns":890},[892,84846,84847,84852],{},[895,84848,84849],{},[1963,84850,84851],{},"260",[902,84853,84851],{"encoding":904}," a současném poklesu ",[883,84856,84858],{"className":84857},[886],[888,84859,84860],{"xmlns":890},[892,84861,84862,84866],{},[895,84863,84864],{},[898,84865,10363],{},[902,84867,10363],{"encoding":904},[883,84869,84871],{"className":84870},[886],[888,84872,84873],{"xmlns":890},[892,84874,84875,84879],{},[895,84876,84877],{},[1963,84878,15690],{},[902,84880,15690],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,84883,84884,84887,84888,1977],{},[38,84885,84886],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,84889,84891],{"className":84890},[886],[888,84892,84893],{"xmlns":890},[892,84894,84895,84915],{},[895,84896,84897,84899,84901,84903,84909],{},[898,84898,1973],{},[1664,84900,1676],{},[1963,84902,3442],{},[1720,84904,84905,84907],{},[898,84906,10358],{},[1963,84908,68711],{},[1720,84910,84911,84913],{},[898,84912,10363],{},[1963,84914,5575],{},[902,84916,84917],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,84919,84920,84923,84924,81081,84947,10957,84960,10588,85010,4488],{},[38,84921,84922],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,84925,84927],{"className":84926},[886],[888,84928,84929],{"xmlns":890},[892,84930,84931,84945],{},[895,84932,84933,84935,84937,84939,84941,84943],{},[898,84934,1973],{},[1664,84936,1667],{"stretchy":1666},[898,84938,10358],{},[1664,84940,1916],{"separator":1915},[898,84942,10363],{},[1664,84944,1673],{"stretchy":1666},[902,84946,10560],{"encoding":904},[883,84948,84950],{"className":84949},[886],[888,84951,84952],{"xmlns":890},[892,84953,84954,84958],{},[895,84955,84956],{},[898,84957,37360],{},[902,84959,37360],{"encoding":904},[883,84961,84963],{"className":84962},[886],[888,84964,84965],{"xmlns":890},[892,84966,84967,85007],{},[895,84968,84969,84971,84979,84981,84983,84991,84993,84995,84997,84999,85001,85003,85005],{},[898,84970,10358],{},[1810,84972,84973,84975,84977],{},[898,84974,1973],{},[898,84976,10358],{},[1664,84978,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,84980,1700],{},[898,84982,10363],{},[1810,84984,84985,84987,84989],{},[898,84986,1973],{},[898,84988,10363],{},[1664,84990,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,84992,1676],{},[898,84994,37360],{},[898,84996,1973],{},[1664,84998,1667],{"stretchy":1666},[898,85000,10358],{},[1664,85002,1916],{"separator":1915},[898,85004,10363],{},[1664,85006,1673],{"stretchy":1666},[902,85008,85009],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,85011,81056],{},[724,85013,85014,85017],{},[38,85015,85016],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,85019,85020,83960,85023,85063,85064,1343,85086,1343,85108,85130],{},[38,85021,85022],{},"5.12",[883,85024,85026],{"className":85025},[886],[888,85027,85028],{"xmlns":890},[892,85029,85030,85060],{},[895,85031,85032,85034,85036,85048],{},[898,85033,1973],{},[1664,85035,1676],{},[1720,85037,85038,85040],{},[898,85039,10358],{},[895,85041,85042,85044,85046],{},[1963,85043,2875],{},[898,85045,5240],{"mathvariant":1726},[1963,85047,2774],{},[1720,85049,85050,85052],{},[898,85051,10363],{},[895,85053,85054,85056,85058],{},[1963,85055,2875],{},[898,85057,5240],{"mathvariant":1726},[1963,85059,2944],{},[902,85061,85062],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,85065,85067],{"className":85066},[886],[888,85068,85069],{"xmlns":890},[892,85070,85071,85083],{},[895,85072,85073,85079,85081],{},[2355,85074,85075,85077],{},[898,85076,81297],{},[1963,85078,2058],{},[1664,85080,1676],{},[1963,85082,2875],{},[902,85084,85085],{"encoding":904},"q_0 = 1",[883,85087,85089],{"className":85088},[886],[888,85090,85091],{"xmlns":890},[892,85092,85093,85105],{},[895,85094,85095,85101,85103],{},[2355,85096,85097,85099],{},[898,85098,81297],{},[1963,85100,2875],{},[1664,85102,1676],{},[1963,85104,1970],{},[902,85106,85107],{"encoding":904},"q_1 = 2",[883,85109,85111],{"className":85110},[886],[888,85112,85113],{"xmlns":890},[892,85114,85115,85127],{},[895,85116,85117,85123,85125],{},[2355,85118,85119,85121],{},[898,85120,81297],{},[1963,85122,1970],{},[1664,85124,1676],{},[1963,85126,2774],{},[902,85128,85129],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,85132,85133,83960,85136,85176,85177,1343,85205,1343,85233,1343,85261,1343,85290,1343,85319,1343,85348,1343,85377,1343,85406,1977],{},[38,85134,85135],{},"5.13",[883,85137,85139],{"className":85138},[886],[888,85140,85141],{"xmlns":890},[892,85142,85143,85173],{},[895,85144,85145,85147,85149,85161],{},[898,85146,1973],{},[1664,85148,1676],{},[1720,85150,85151,85153],{},[898,85152,10358],{},[895,85154,85155,85157,85159],{},[1963,85156,2875],{},[898,85158,5240],{"mathvariant":1726},[1963,85160,2774],{},[1720,85162,85163,85165],{},[898,85164,10363],{},[895,85166,85167,85169,85171],{},[1963,85168,2875],{},[898,85170,5240],{"mathvariant":1726},[1963,85172,1970],{},[902,85174,85175],{"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): ",[883,85178,85180],{"className":85179},[886],[888,85181,85182],{"xmlns":890},[892,85183,85184,85202],{},[895,85185,85186,85192,85194,85196,85198,85200],{},[2355,85187,85188,85190],{},[898,85189,4822],{},[1963,85191,2875],{},[1664,85193,1837],{"stretchy":1666},[1963,85195,2875],{},[1664,85197,8990],{"separator":1915},[1963,85199,2875],{},[1664,85201,1850],{"stretchy":1666},[902,85203,85204],{"encoding":904},"A_1[1; 1]",[883,85206,85208],{"className":85207},[886],[888,85209,85210],{"xmlns":890},[892,85211,85212,85230],{},[895,85213,85214,85220,85222,85224,85226,85228],{},[2355,85215,85216,85218],{},[898,85217,4822],{},[1963,85219,1970],{},[1664,85221,1837],{"stretchy":1666},[1963,85223,2875],{},[1664,85225,8990],{"separator":1915},[1963,85227,6151],{},[1664,85229,1850],{"stretchy":1666},[902,85231,85232],{"encoding":904},"A_2[1; 8]",[883,85234,85236],{"className":85235},[886],[888,85237,85238],{"xmlns":890},[892,85239,85240,85258],{},[895,85241,85242,85248,85250,85252,85254,85256],{},[2355,85243,85244,85246],{},[898,85245,4822],{},[1963,85247,2774],{},[1664,85249,1837],{"stretchy":1666},[1963,85251,2875],{},[1664,85253,8990],{"separator":1915},[1963,85255,67097],{},[1664,85257,1850],{"stretchy":1666},[902,85259,85260],{"encoding":904},"A_3[1; 27]",[883,85262,85264],{"className":85263},[886],[888,85265,85266],{"xmlns":890},[892,85267,85268,85287],{},[895,85269,85270,85276,85278,85280,85282,85285],{},[2355,85271,85272,85274],{},[898,85273,4822],{},[1963,85275,2944],{},[1664,85277,1837],{"stretchy":1666},[1963,85279,1970],{},[1664,85281,8990],{"separator":1915},[1963,85283,85284],{},"0,353",[1664,85286,1850],{"stretchy":1666},[902,85288,85289],{"encoding":904},"A_4[2; 0{,}353]",[883,85291,85293],{"className":85292},[886],[888,85294,85295],{"xmlns":890},[892,85296,85297,85316],{},[895,85298,85299,85305,85307,85309,85311,85314],{},[2355,85300,85301,85303],{},[898,85302,4822],{},[1963,85304,2826],{},[1664,85306,1837],{"stretchy":1666},[1963,85308,1970],{},[1664,85310,8990],{"separator":1915},[1963,85312,85313],{},"2,828",[1664,85315,1850],{"stretchy":1666},[902,85317,85318],{"encoding":904},"A_5[2; 2{,}828]",[883,85320,85322],{"className":85321},[886],[888,85323,85324],{"xmlns":890},[892,85325,85326,85345],{},[895,85327,85328,85334,85336,85338,85340,85343],{},[2355,85329,85330,85332],{},[898,85331,4822],{},[1963,85333,2833],{},[1664,85335,1837],{"stretchy":1666},[1963,85337,1970],{},[1664,85339,8990],{"separator":1915},[1963,85341,85342],{},"9,545",[1664,85344,1850],{"stretchy":1666},[902,85346,85347],{"encoding":904},"A_6[2; 9{,}545]",[883,85349,85351],{"className":85350},[886],[888,85352,85353],{"xmlns":890},[892,85354,85355,85374],{},[895,85356,85357,85363,85365,85367,85369,85372],{},[2355,85358,85359,85361],{},[898,85360,4822],{},[1963,85362,24701],{},[1664,85364,1837],{"stretchy":1666},[1963,85366,65059],{},[1664,85368,8990],{"separator":1915},[1963,85370,85371],{},"0,544",[1664,85373,1850],{"stretchy":1666},[902,85375,85376],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,85378,85380],{"className":85379},[886],[888,85381,85382],{"xmlns":890},[892,85383,85384,85403],{},[895,85385,85386,85392,85394,85396,85398,85401],{},[2355,85387,85388,85390],{},[898,85389,4822],{},[1963,85391,6151],{},[1664,85393,1837],{"stretchy":1666},[1963,85395,65059],{},[1664,85397,8990],{"separator":1915},[1963,85399,85400],{},"14,696",[1664,85402,1850],{"stretchy":1666},[902,85404,85405],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,85407,85409],{"className":85408},[886],[888,85410,85411],{"xmlns":890},[892,85412,85413,85431],{},[895,85414,85415,85421,85423,85425,85427,85429],{},[2355,85416,85417,85419],{},[898,85418,4822],{},[1963,85420,4567],{},[1664,85422,1837],{"stretchy":1666},[1963,85424,1970],{},[1664,85426,8990],{"separator":1915},[1963,85428,2826],{},[1664,85430,1850],{"stretchy":1666},[902,85432,85433],{"encoding":904},"A_9[2; 5]",[724,85435,85436,85439],{},[38,85437,85438],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,85441,85442,85445,85446,85476,85477,85490,85491,85504,85505,69817,85524,85543,85544,1977],{},[38,85443,85444],{},"5.15"," Produkce firmy je dána vztahem ",[883,85447,85449],{"className":85448},[886],[888,85450,85451],{"xmlns":890},[892,85452,85453,85473],{},[895,85454,85455,85457,85459,85461,85467],{},[898,85456,1973],{},[1664,85458,1676],{},[1963,85460,1970],{},[1720,85462,85463,85465],{},[898,85464,10358],{},[1963,85466,5575],{},[1720,85468,85469,85471],{},[898,85470,10363],{},[1963,85472,24289],{},[902,85474,85475],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,85478,85480],{"className":85479},[886],[888,85481,85482],{"xmlns":890},[892,85483,85484,85488],{},[895,85485,85486],{},[1963,85487,1965],{},[902,85489,1965],{"encoding":904}," pracovníků a disponuje-li ",[883,85492,85494],{"className":85493},[886],[888,85495,85496],{"xmlns":890},[892,85497,85498,85502],{},[895,85499,85500],{},[1963,85501,64935],{},[902,85503,64935],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,85506,85508],{"className":85507},[886],[888,85509,85510],{"xmlns":890},[892,85511,85512,85522],{},[895,85513,85514,85516,85518,85520],{},[898,85515,1956],{},[898,85517,1959],{},[898,85519,1991],{},[898,85521,2351],{},[902,85523,11161],{"encoding":904},[883,85525,85527],{"className":85526},[886],[888,85528,85529],{"xmlns":890},[892,85530,85531,85541],{},[895,85532,85533,85535,85537,85539],{},[898,85534,1956],{},[898,85536,1959],{},[898,85538,1991],{},[898,85540,2351],{},[902,85542,11161],{"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 ",[883,85545,85547],{"className":85546},[886],[888,85548,85549],{"xmlns":890},[892,85550,85551,85556],{},[895,85552,85553],{},[1963,85554,85555],{},"95",[902,85557,85555],{"encoding":904},[724,85559,85560,83960,85563,71491,85595,85614,85615,85628,85629,85642,85643,85656],{},[38,85561,85562],{},"5.16",[883,85564,85566],{"className":85565},[886],[888,85567,85568],{"xmlns":890},[892,85569,85570,85592],{},[895,85571,85572,85574,85576,85582,85584,85586],{},[898,85573,1973],{},[1664,85575,1676],{},[1720,85577,85578,85580],{},[898,85579,10363],{},[1963,85581,1970],{},[1664,85583,1700],{},[1963,85585,1970],{},[1720,85587,85588,85590],{},[898,85589,10358],{},[1963,85591,1970],{},[902,85593,85594],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,85596,85598],{"className":85597},[886],[888,85599,85600],{"xmlns":890},[892,85601,85602,85612],{},[895,85603,85604,85606,85608,85610],{},[898,85605,1956],{},[898,85607,1959],{},[898,85609,1991],{},[898,85611,2351],{},[902,85613,11161],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,85616,85618],{"className":85617},[886],[888,85619,85620],{"xmlns":890},[892,85621,85622,85626],{},[895,85623,85624],{},[1963,85625,3696],{},[902,85627,3696],{"encoding":904}," pracovníky a ",[883,85630,85632],{"className":85631},[886],[888,85633,85634],{"xmlns":890},[892,85635,85636,85640],{},[895,85637,85638],{},[1963,85639,78117],{},[902,85641,78117],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,85644,85646],{"className":85645},[886],[888,85647,85648],{"xmlns":890},[892,85649,85650,85654],{},[895,85651,85652],{},[1963,85653,47203],{},[902,85655,47203],{"encoding":904}," jednotek.",[724,85658,85659,85662,85663,10957,85693,1977],{},[38,85660,85661],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,85664,85666],{"className":85665},[886],[888,85667,85668],{"xmlns":890},[892,85669,85670,85690],{},[895,85671,85672,85674,85676,85678,85684],{},[898,85673,1973],{},[1664,85675,1676],{},[898,85677,4822],{},[1720,85679,85680,85682],{},[898,85681,10358],{},[898,85683,207],{},[1720,85685,85686,85688],{},[898,85687,10363],{},[898,85689,1818],{},[902,85691,85692],{"encoding":904},"Q = A L^{a} K^{b}",[883,85694,85696],{"className":85695},[886],[888,85697,85698],{"xmlns":890},[892,85699,85700,85730],{},[895,85701,85702,85704,85706,85708,85710,85712,85720,85722],{},[898,85703,1956],{},[898,85705,1959],{},[898,85707,1991],{},[898,85709,2351],{},[1664,85711,1676],{},[2919,85713,85714],{"scriptlevel":2058,"displaystyle":1666},[2922,85715,85716,85718],{},[898,85717,207],{},[898,85719,1818],{},[1664,85721,3753],{},[2919,85723,85724],{"scriptlevel":2058,"displaystyle":1666},[2922,85725,85726,85728],{},[898,85727,10363],{},[898,85729,10358],{},[902,85731,85732],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,85734,16219],{"id":16218},[120,85736,85737,85770,85797,85806,85856,85887,85940,85963,86018,86091,86169,86212,86244,86277,86318,86390,86451,86517,86534,86607,86673,86725,86781,86815,86858],{},[123,85738,85739,85742,85743,37396,85756,85769],{},[38,85740,85741],{},"Faktory (vstupy) produkce:"," práce ",[883,85744,85746],{"className":85745},[886],[888,85747,85748],{"xmlns":890},[892,85749,85750,85754],{},[895,85751,85752],{},[898,85753,10358],{},[902,85755,10358],{"encoding":904},[883,85757,85759],{"className":85758},[886],[888,85760,85761],{"xmlns":890},[892,85762,85763,85767],{},[895,85764,85765],{},[898,85766,10363],{},[902,85768,10363],{"encoding":904},", půda.",[123,85771,85772,7581,85774,1977],{},[38,85773,40951],{},[883,85775,85777],{"className":85776},[886],[888,85778,85779],{"xmlns":890},[892,85780,85781,85795],{},[895,85782,85783,85785,85787,85789,85791,85793],{},[898,85784,1973],{},[1664,85786,1676],{},[898,85788,1973],{},[1664,85790,1667],{"stretchy":1666},[898,85792,10358],{},[1664,85794,1673],{"stretchy":1666},[902,85796,75044],{"encoding":904},[123,85798,85799,10588,85801,12627,85804,1977],{},[38,85800,859],{},[614,85802,85803],{},"production function",[38,85805,75547],{},[123,85807,85808,1885,85810,1977],{},[38,85809,75593],{},[883,85811,85813],{"className":85812},[886],[888,85814,85815],{"xmlns":890},[892,85816,85817,85853],{},[895,85818,85819,85821,85827,85829,85831,85833,85835,85837,85839,85841,85847,85849,85851],{},[898,85820,1956],{},[2355,85822,85823,85825],{},[898,85824,2398],{},[898,85826,10358],{},[1664,85828,1676],{},[898,85830,1695],{},[898,85832,1973],{},[898,85834,5240],{"mathvariant":1726},[898,85836,1695],{},[898,85838,10358],{},[1664,85840,1676],{},[1720,85842,85843,85845],{},[898,85844,1973],{},[1664,85846,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,85848,1667],{"stretchy":1666},[898,85850,10358],{},[1664,85852,1673],{"stretchy":1666},[902,85854,85855],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,85857,85858,1885,85860,1977],{},[38,85859,76528],{},[883,85861,85863],{"className":85862},[886],[888,85864,85865],{"xmlns":890},[892,85866,85867,85885],{},[895,85868,85869,85871,85877,85879,85881,85883],{},[898,85870,4822],{},[2355,85872,85873,85875],{},[898,85874,2398],{},[898,85876,10358],{},[1664,85878,1676],{},[898,85880,1973],{},[898,85882,5240],{"mathvariant":1726},[898,85884,10358],{},[902,85886,75112],{"encoding":904},[123,85888,85889,85891,85892,10957,85909,1977],{},[38,85890,76015],{}," — od určitého ",[883,85893,85895],{"className":85894},[886],[888,85896,85897],{"xmlns":890},[892,85898,85899,85907],{},[895,85900,85901],{},[2355,85902,85903,85905],{},[898,85904,10358],{},[1963,85906,2058],{},[902,85908,76058],{"encoding":904},[883,85910,85912],{"className":85911},[886],[888,85913,85914],{"xmlns":890},[892,85915,85916,85938],{},[895,85917,85918,85928,85930,85932,85934,85936],{},[1720,85919,85920,85922],{},[898,85921,1973],{},[895,85923,85924,85926],{},[1664,85925,1728],{"mathvariant":1726},[1664,85927,1728],{"mathvariant":1726},[1664,85929,1667],{"stretchy":1666},[898,85931,10358],{},[1664,85933,1673],{"stretchy":1666},[1664,85935,4022],{},[1963,85937,2058],{},[902,85939,76204],{"encoding":904},[123,85941,85942,1885,85945,85962],{},[38,85943,85944],{},"Inflexní bod",[883,85946,85948],{"className":85947},[886],[888,85949,85950],{"xmlns":890},[892,85951,85952,85960],{},[895,85953,85954],{},[2355,85955,85956,85958],{},[898,85957,10358],{},[1963,85959,2058],{},[902,85961,76058],{"encoding":904}," — přechod z konvexity do konkavity.",[123,85964,85965,1885,85968,7581,85985,1977],{},[38,85966,85967],{},"Bod maxima produkce",[883,85969,85971],{"className":85970},[886],[888,85972,85973],{"xmlns":890},[892,85974,85975,85983],{},[895,85976,85977],{},[2355,85978,85979,85981],{},[898,85980,10358],{},[1963,85982,2875],{},[902,85984,13711],{"encoding":904},[883,85986,85988],{"className":85987},[886],[888,85989,85990],{"xmlns":890},[892,85991,85992,86016],{},[895,85993,85994,85996,86002,86004,86010,86012,86014],{},[898,85995,1956],{},[2355,85997,85998,86000],{},[898,85999,2398],{},[898,86001,10358],{},[1664,86003,1667],{"stretchy":1666},[2355,86005,86006,86008],{},[898,86007,10358],{},[1963,86009,2875],{},[1664,86011,1673],{"stretchy":1666},[1664,86013,1676],{},[1963,86015,2058],{},[902,86017,76277],{"encoding":904},[123,86019,86020,86042,86043,10957,86062,1977],{},[38,86021,86022,86023],{},"Princip maximalizace ",[883,86024,86026],{"className":86025},[886],[888,86027,86028],{"xmlns":890},[892,86029,86030,86040],{},[895,86031,86032,86034],{},[898,86033,4822],{},[2355,86035,86036,86038],{},[898,86037,2398],{},[898,86039,10358],{},[902,86041,75133],{"encoding":904}," — v bodě maxima ",[883,86044,86046],{"className":86045},[886],[888,86047,86048],{"xmlns":890},[892,86049,86050,86060],{},[895,86051,86052,86054],{},[898,86053,4822],{},[2355,86055,86056,86058],{},[898,86057,2398],{},[898,86059,10358],{},[902,86061,75133],{"encoding":904},[883,86063,86065],{"className":86064},[886],[888,86066,86067],{"xmlns":890},[892,86068,86069,86089],{},[895,86070,86071,86073,86079,86081,86083],{},[898,86072,1956],{},[2355,86074,86075,86077],{},[898,86076,2398],{},[898,86078,10358],{},[1664,86080,1676],{},[898,86082,4822],{},[2355,86084,86085,86087],{},[898,86086,2398],{},[898,86088,10358],{},[902,86090,75163],{"encoding":904},[123,86092,86093,1885,86096,1343,86135,1343,86152,1977],{},[38,86094,86095],{},"Polynomiální produkční funkce",[883,86097,86099],{"className":86098},[886],[888,86100,86101],{"xmlns":890},[892,86102,86103,86133],{},[895,86104,86105,86107,86109,86111,86113,86115,86117,86123,86125,86127],{},[898,86106,1973],{},[1664,86108,1667],{"stretchy":1666},[898,86110,10358],{},[1664,86112,1673],{"stretchy":1666},[1664,86114,1676],{},[898,86116,207],{},[1720,86118,86119,86121],{},[898,86120,10358],{},[1963,86122,2774],{},[1664,86124,1700],{},[898,86126,1818],{},[1720,86128,86129,86131],{},[898,86130,10358],{},[1963,86132,1970],{},[902,86134,76395],{"encoding":904},[883,86136,86138],{"className":86137},[886],[888,86139,86140],{"xmlns":890},[892,86141,86142,86150],{},[895,86143,86144,86146,86148],{},[898,86145,207],{},[1664,86147,4022],{},[1963,86149,2058],{},[902,86151,43585],{"encoding":904},[883,86153,86155],{"className":86154},[886],[888,86156,86157],{"xmlns":890},[892,86158,86159,86167],{},[895,86160,86161,86163,86165],{},[898,86162,1818],{},[1664,86164,3984],{},[1963,86166,2058],{},[902,86168,19314],{"encoding":904},[123,86170,86171,1885,86174,1977],{},[38,86172,86173],{},"Diferenciál produkce",[883,86175,86177],{"className":86176},[886],[888,86178,86179],{"xmlns":890},[892,86180,86181,86209],{},[895,86182,86183,86185,86187,86189,86191,86193,86195,86197,86203,86205,86207],{},[898,86184,3468],{"mathvariant":1726},[898,86186,1973],{},[1664,86188,3315],{},[898,86190,1695],{},[898,86192,1973],{},[1664,86194,1676],{},[898,86196,1956],{},[2355,86198,86199,86201],{},[898,86200,2398],{},[898,86202,10358],{},[1690,86204,1692],{},[898,86206,1695],{},[898,86208,10358],{},[902,86210,86211],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,86213,86214,7581,86216,1977],{},[38,86215,84471],{},[883,86217,86219],{"className":86218},[886],[888,86220,86221],{"xmlns":890},[892,86222,86223,86241],{},[895,86224,86225,86227,86229,86231,86233,86235,86237,86239],{},[898,86226,1973],{},[1664,86228,1676],{},[898,86230,1973],{},[1664,86232,1667],{"stretchy":1666},[898,86234,10358],{},[1664,86236,1916],{"separator":1915},[898,86238,10363],{},[1664,86240,1673],{"stretchy":1666},[902,86242,86243],{"encoding":904},"Q = Q(L, K)",[123,86245,86246,7581,86248,1977],{},[38,86247,78565],{},[883,86249,86251],{"className":86250},[886],[888,86252,86253],{"xmlns":890},[892,86254,86255,86275],{},[895,86256,86257,86259,86261,86263,86269],{},[898,86258,1973],{},[1664,86260,1676],{},[898,86262,4822],{},[1720,86264,86265,86267],{},[898,86266,10358],{},[898,86268,207],{},[1720,86270,86271,86273],{},[898,86272,10363],{},[898,86274,1818],{},[902,86276,75230],{"encoding":904},[123,86278,86279,7581,86282,86317],{},[38,86280,86281],{},"Ryzí Cobb-Douglas",[883,86283,86285],{"className":86284},[886],[888,86286,86287],{"xmlns":890},[892,86288,86289,86315],{},[895,86290,86291,86293,86295,86297,86303],{},[898,86292,1973],{},[1664,86294,1676],{},[898,86296,4822],{},[1720,86298,86299,86301],{},[898,86300,10358],{},[898,86302,207],{},[1720,86304,86305,86307],{},[898,86306,10363],{},[895,86308,86309,86311,86313],{},[1963,86310,2875],{},[1664,86312,1867],{},[898,86314,207],{},[902,86316,79392],{"encoding":904}," (konstantní výnosy).",[123,86319,86320,7581,86322,1977],{},[38,86321,80108],{},[883,86323,86325],{"className":86324},[886],[888,86326,86327],{"xmlns":890},[892,86328,86329,86387],{},[895,86330,86331,86333,86335,86337,86339,86341,86343,86345,86347,86349,86359,86361,86363,86373],{},[898,86332,1973],{},[1664,86334,1676],{},[898,86336,4822],{},[1664,86338,1837],{"stretchy":1666},[1664,86340,1667],{"stretchy":1666},[1963,86342,2875],{},[1664,86344,1867],{},[898,86346,207],{},[1664,86348,1673],{"stretchy":1666},[1720,86350,86351,86353],{},[898,86352,10358],{},[895,86354,86355,86357],{},[1664,86356,1867],{},[898,86358,1818],{},[1664,86360,1700],{},[898,86362,207],{},[1720,86364,86365,86367],{},[898,86366,10363],{},[895,86368,86369,86371],{},[1664,86370,1867],{},[898,86372,1818],{},[1720,86374,86375,86377],{},[1664,86376,1850],{"stretchy":1666},[895,86378,86379,86381,86383,86385],{},[1664,86380,1867],{},[1963,86382,2875],{},[898,86384,5240],{"mathvariant":1726},[898,86386,1818],{},[902,86388,86389],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,86391,86392,10588,86395,12627,86417,10588,86420,86450],{},[38,86393,86394],{},"Lineární",[883,86396,86398],{"className":86397},[886],[888,86399,86400],{"xmlns":890},[892,86401,86402,86414],{},[895,86403,86404,86406,86408,86410,86412],{},[898,86405,207],{},[898,86407,10358],{},[1664,86409,1700],{},[898,86411,1818],{},[898,86413,10363],{},[902,86415,86416],{"encoding":904},"aL + bK",[38,86418,86419],{},"Leontiefova",[883,86421,86423],{"className":86422},[886],[888,86424,86425],{"xmlns":890},[892,86426,86427,86447],{},[895,86428,86429,86431,86433,86435,86437,86439,86441,86443,86445],{},[898,86430,80336],{},[1664,86432,56700],{},[1664,86434,1667],{"stretchy":1666},[898,86436,207],{},[898,86438,10358],{},[1664,86440,1916],{"separator":1915},[898,86442,1818],{},[898,86444,10363],{},[1664,86446,1673],{"stretchy":1666},[902,86448,86449],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,86452,86453,7581,86469,1977],{},[38,86454,86455,86456],{},"Homogenita stupně ",[883,86457,86459],{"className":86458},[886],[888,86460,86461],{"xmlns":890},[892,86462,86463,86467],{},[895,86464,86465],{},[898,86466,37360],{},[902,86468,37360],{"encoding":904},[883,86470,86472],{"className":86471},[886],[888,86473,86474],{"xmlns":890},[892,86475,86476,86514],{},[895,86477,86478,86480,86482,86484,86486,86488,86490,86492,86494,86496,86502,86504,86506,86508,86510,86512],{},[898,86479,1973],{},[1664,86481,1667],{"stretchy":1666},[898,86483,12540],{},[898,86485,10358],{},[1664,86487,1916],{"separator":1915},[898,86489,12540],{},[898,86491,10363],{},[1664,86493,1673],{"stretchy":1666},[1664,86495,1676],{},[1720,86497,86498,86500],{},[898,86499,12540],{},[898,86501,37360],{},[898,86503,1973],{},[1664,86505,1667],{"stretchy":1666},[898,86507,10358],{},[1664,86509,1916],{"separator":1915},[898,86511,10363],{},[1664,86513,1673],{"stretchy":1666},[902,86515,86516],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,86518,86519,79490],{},[38,86520,79423,86521],{},[883,86522,86524],{"className":86523},[886],[888,86525,86526],{"xmlns":890},[892,86527,86528,86532],{},[895,86529,86530],{},[898,86531,4822],{},[902,86533,4822],{"encoding":904},[123,86535,86536,86538,86539,86561,86562,86584,86585,4488],{},[38,86537,78924],{}," — konstantní (",[883,86540,86542],{"className":86541},[886],[888,86543,86544],{"xmlns":890},[892,86545,86546,86558],{},[895,86547,86548,86550,86552,86554,86556],{},[898,86549,207],{},[1664,86551,1700],{},[898,86553,1818],{},[1664,86555,1676],{},[1963,86557,2875],{},[902,86559,86560],{"encoding":904},"a+b=1","), rostoucí (",[883,86563,86565],{"className":86564},[886],[888,86566,86567],{"xmlns":890},[892,86568,86569,86581],{},[895,86570,86571,86573,86575,86577,86579],{},[898,86572,207],{},[1664,86574,1700],{},[898,86576,1818],{},[1664,86578,3984],{},[1963,86580,2875],{},[902,86582,86583],{"encoding":904},"a+b>1","), klesající (",[883,86586,86588],{"className":86587},[886],[888,86589,86590],{"xmlns":890},[892,86591,86592,86604],{},[895,86593,86594,86596,86598,86600,86602],{},[898,86595,207],{},[1664,86597,1700],{},[898,86599,1818],{},[1664,86601,4022],{},[1963,86603,2875],{},[902,86605,86606],{"encoding":904},"a+b\u003C1",[123,86608,86609,1885,86611,1343,86641,1885,86643,1977],{},[38,86610,75593],{},[883,86612,86614],{"className":86613},[886],[888,86615,86616],{"xmlns":890},[892,86617,86618,86638],{},[895,86619,86620,86622,86628,86630],{},[898,86621,1956],{},[2355,86623,86624,86626],{},[898,86625,2398],{},[898,86627,10358],{},[1664,86629,1676],{},[1810,86631,86632,86634,86636],{},[898,86633,1973],{},[898,86635,10358],{},[1664,86637,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,86639,86640],{"encoding":904},"MP_L = Q'_L",[38,86642,78497],{},[883,86644,86646],{"className":86645},[886],[888,86647,86648],{"xmlns":890},[892,86649,86650,86670],{},[895,86651,86652,86654,86660,86662],{},[898,86653,1956],{},[2355,86655,86656,86658],{},[898,86657,2398],{},[898,86659,10363],{},[1664,86661,1676],{},[1810,86663,86664,86666,86668],{},[898,86665,1973],{},[898,86667,10363],{},[1664,86669,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,86671,86672],{"encoding":904},"MP_K = Q'_K",[123,86674,86675,1885,86677,1977],{},[38,86676,80711],{},[883,86678,86680],{"className":86679},[886],[888,86681,86682],{"xmlns":890},[892,86683,86684,86722],{},[895,86685,86686,86688,86690,86692,86694,86700,86702,86704,86706,86708,86710,86716,86718,86720],{},[898,86687,1695],{},[898,86689,1973],{},[1664,86691,1676],{},[898,86693,1956],{},[2355,86695,86696,86698],{},[898,86697,2398],{},[898,86699,10358],{},[1690,86701,1692],{},[898,86703,1695],{},[898,86705,10358],{},[1664,86707,1700],{},[898,86709,1956],{},[2355,86711,86712,86714],{},[898,86713,2398],{},[898,86715,10363],{},[1690,86717,1692],{},[898,86719,1695],{},[898,86721,10363],{},[902,86723,86724],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,86726,86727,7581,86729,1977],{},[38,86728,81056],{},[883,86730,86732],{"className":86731},[886],[888,86733,86734],{"xmlns":890},[892,86735,86736,86778],{},[895,86737,86738,86740,86748,86750,86752,86760,86762,86764,86766,86768,86770,86772,86774,86776],{},[898,86739,10358],{},[1810,86741,86742,86744,86746],{},[898,86743,1973],{},[898,86745,10358],{},[1664,86747,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,86749,1700],{},[898,86751,10363],{},[1810,86753,86754,86756,86758],{},[898,86755,1973],{},[898,86757,10363],{},[1664,86759,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,86761,1676],{},[898,86763,37360],{},[1690,86765,1692],{},[898,86767,1973],{},[1664,86769,1667],{"stretchy":1666},[898,86771,10358],{},[1664,86773,1916],{"separator":1915},[898,86775,10363],{},[1664,86777,1673],{"stretchy":1666},[902,86779,86780],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,86782,86783,86786,86787,1977],{},[38,86784,86785],{},"Izokvanta"," — křivka ",[883,86788,86790],{"className":86789},[886],[888,86791,86792],{"xmlns":890},[892,86793,86794,86812],{},[895,86795,86796,86798,86800,86802,86804,86806,86808,86810],{},[898,86797,1973],{},[1664,86799,1667],{"stretchy":1666},[898,86801,10358],{},[1664,86803,1916],{"separator":1915},[898,86805,10363],{},[1664,86807,1673],{"stretchy":1666},[1664,86809,1676],{},[898,86811,81297],{},[902,86813,86814],{"encoding":904},"Q(L, K) = q",[123,86816,86817,1885,86819,1977],{},[38,86818,81486],{},[883,86820,86822],{"className":86821},[886],[888,86823,86824],{"xmlns":890},[892,86825,86826,86856],{},[895,86827,86828,86830,86832,86834,86836,86838,86840,86846,86848,86850],{},[898,86829,1956],{},[898,86831,1959],{},[898,86833,1991],{},[898,86835,2351],{},[1664,86837,1676],{},[898,86839,1956],{},[2355,86841,86842,86844],{},[898,86843,2398],{},[898,86845,10358],{},[898,86847,5240],{"mathvariant":1726},[898,86849,1956],{},[2355,86851,86852,86854],{},[898,86853,2398],{},[898,86855,10363],{},[902,86857,75305],{"encoding":904},[123,86859,86860,1885,86863,1977],{},[38,86861,86862],{},"Substituční vztah",[883,86864,86866],{"className":86865},[886],[888,86867,86868],{"xmlns":890},[892,86869,86870,86894],{},[895,86871,86872,86874,86876,86878,86880,86882,86884,86886,86888,86890,86892],{},[898,86873,3468],{"mathvariant":1726},[898,86875,10363],{},[1664,86877,3315],{},[1664,86879,1867],{},[898,86881,1956],{},[898,86883,1959],{},[898,86885,1991],{},[898,86887,2351],{},[1690,86889,1692],{},[898,86891,1695],{},[898,86893,10358],{},[902,86895,86896],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,86898,2497],{"id":2496},[120,86900,86901,86998,87005,87012],{},[123,86902,86903,1885,86905,86908,86909,1343,86912,86915,86916,86919,86920,86939,86940,19148,86959,86962,86963,86982,86983,4488],{},[38,86904,51223],{},[207,86906,784],{"className":86907,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,86910,2950],{"className":86911,"dataFsResolvedFilePath":764,"href":765},[210],[207,86913,793],{"className":86914,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,86917,880],{"className":86918,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,86921,86923],{"className":86922},[886],[888,86924,86925],{"xmlns":890},[892,86926,86927,86937],{},[895,86928,86929,86931,86933,86935],{},[898,86930,1956],{},[898,86932,1959],{},[898,86934,1991],{},[898,86936,2351],{},[902,86938,11161],{"encoding":904}," ↔ ",[883,86941,86943],{"className":86942},[886],[888,86944,86945],{"xmlns":890},[892,86946,86947,86957],{},[895,86948,86949,86951,86953,86955],{},[898,86950,1956],{},[898,86952,1959],{},[898,86954,1703],{},[898,86956,2351],{},[902,86958,11165],{"encoding":904},[207,86960,2524],{"className":86961,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,86964,86966],{"className":86965},[886],[888,86967,86968],{"xmlns":890},[892,86969,86970,86980],{},[895,86971,86972,86974],{},[898,86973,4822],{},[2355,86975,86976,86978],{},[898,86977,2398],{},[898,86979,10358],{},[902,86981,75133],{"encoding":904}," ↔ min ",[883,86984,86986],{"className":86985},[886],[888,86987,86988],{"xmlns":890},[892,86989,86990,86996],{},[895,86991,86992,86994],{},[898,86993,4822],{},[898,86995,1703],{},[902,86997,56060],{"encoding":904},[123,86999,87000,1885,87002,1977],{},[38,87001,2504],{},[207,87003,4397],{"className":87004,"dataFsResolvedFilePath":848,"href":849},[210],[123,87006,87007,1885,87009,1977],{},[38,87008,16712],{},[207,87010,1094],{"className":87011,"dataFsResolvedFilePath":838,"href":839},[210],[123,87013,87014,1885,87016,1977],{},[38,87015,16703],{},[207,87017,16707],{"className":87018,"dataFsResolvedFilePath":2575,"href":2576},[210],{"title":641,"searchDepth":642,"depth":642,"links":87020},[87021,87022,87023,87027,87029,87034,87035,87042,87043,87045,87046,87047,87049,87054,87055,87056,87060,87061],{"id":75328,"depth":642,"text":75329},{"id":75465,"depth":642,"text":75466},{"id":75568,"depth":642,"text":87024,"children":87025},"Mezní produkt práce (MPLMP_L)",[87026],{"id":76014,"depth":649,"text":76015},{"id":76503,"depth":642,"text":87028},"Průměrný produkt práce (APLAP_L)",{"id":76621,"depth":642,"text":76622,"children":87030},[87031,87032,87033],{"id":76858,"depth":649,"text":66001},{"id":77169,"depth":649,"text":77170},{"id":77889,"depth":649,"text":77890},{"id":78461,"depth":642,"text":78462},{"id":78564,"depth":642,"text":78565,"children":87036},[87037,87038,87040,87041],{"id":78923,"depth":649,"text":78924},{"id":79422,"depth":649,"text":87039},"Parametr efektivity AA",{"id":79493,"depth":649,"text":79494},{"id":37679,"depth":649,"text":79833},{"id":80020,"depth":642,"text":80021},{"id":80359,"depth":642,"text":87044},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":81050,"depth":642,"text":81051},{"id":75394,"depth":642,"text":10341},{"id":81461,"depth":642,"text":87048},"Mezní míra technické substituce (MRTSMRTS)",{"id":82327,"depth":642,"text":82328,"children":87050},[87051,87052,87053],{"id":82331,"depth":649,"text":82332},{"id":82974,"depth":649,"text":82975},{"id":83255,"depth":649,"text":83256},{"id":83601,"depth":642,"text":83602},{"id":50381,"depth":642,"text":50382},{"id":83951,"depth":642,"text":83952,"children":87057},[87058,87059],{"id":40950,"depth":649,"text":40951},{"id":84470,"depth":649,"text":84471},{"id":16218,"depth":642,"text":16219},{"id":2496,"depth":642,"text":2497},{},"\u002Ftopics\u002Fprodukce",{"title":74964,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,10376,87068,87069,87070,75394,87071,87072],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":87075,"title":87076,"body":87077,"course":1128,"courses":659,"created":10119,"description":641,"extension":661,"meta":96024,"navigation":664,"path":96025,"seo":96026,"sources":96027,"stem":96028,"tags":96029,"type":2553,"updated":677,"__hash__":96032},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":87078,"toc":95998},[87079,87082,87084,87281,87290,87294,87297,87350,87354,87366,87370,87373,87390,87513,87519,87663,87673,87677,87712,87750,87798,87855,87915,87957,88533,88537,88620,88729,88822,89080,89083,89136,89247,89329,89333,89344,89577,89632,89638,89678,89741,89752,89943,90049,90202,90250,90255,90369,90407,90533,90579,90606,90683,90758,90838,90968,91029,91117,91121,91124,91193,91276,91283,91343,91653,91657,91663,91716,91732,91783,91921,91997,92110,92427,92431,92438,92598,92657,92661,92683,92780,92901,93015,93038,93101,93158,93410,93418,93422,93429,93683,93733,93789,93792,93956,93960,94058,94060,94092,94096,94229,94471,94655,94823,95130,95263,95450,95462,95464,95899,95901],[12,87080,87076],{"id":87081},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,87083,12505],{"id":12504},[724,87085,87086,1885,87088,87119,87120,87123,87124,87154,87155,87173,87174,87214,87215,87218,87219,87232,87233,28753,87236,87249,87250,87263,87264,87277,87278,1977],{},[38,87087,880],{},[883,87089,87091],{"className":87090},[886],[888,87092,87093],{"xmlns":890},[892,87094,87095,87117],{},[895,87096,87097,87099,87101,87107,87109,87115],{},[898,87098,900],{},[1664,87100,1667],{"stretchy":1666},[2355,87102,87103,87105],{},[898,87104,1973],{},[1963,87106,2875],{},[1664,87108,1916],{"separator":1915},[2355,87110,87111,87113],{},[898,87112,1973],{},[1963,87114,1970],{},[1664,87116,1673],{"stretchy":1666},[902,87118,16843],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,87121,87122],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,87125,87127],{"className":87126},[886],[888,87128,87129],{"xmlns":890},[892,87130,87131,87151],{},[895,87132,87133,87135,87141,87143],{},[898,87134,1956],{},[2355,87136,87137,87139],{},[898,87138,900],{},[898,87140,18290],{},[1664,87142,1676],{},[1810,87144,87145,87147,87149],{},[898,87146,900],{},[898,87148,18290],{},[1664,87150,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,87152,87153],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,87156,87158],{"className":87157},[886],[888,87159,87160],{"xmlns":890},[892,87161,87162,87170],{},[895,87163,87164,87166,87168],{},[898,87165,900],{},[1664,87167,1676],{},[898,87169,2034],{},[902,87171,87172],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,87175,87177],{"className":87176},[886],[888,87178,87179],{"xmlns":890},[892,87180,87181,87211],{},[895,87182,87183,87185,87187,87189,87191,87193,87195,87201,87203,87205],{},[898,87184,1956],{},[898,87186,1959],{},[898,87188,1703],{},[898,87190,2351],{},[1664,87192,1676],{},[898,87194,1956],{},[2355,87196,87197,87199],{},[898,87198,900],{},[1963,87200,2875],{},[898,87202,5240],{"mathvariant":1726},[898,87204,1956],{},[2355,87206,87207,87209],{},[898,87208,900],{},[1963,87210,1970],{},[902,87212,87213],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,87216,87217],{},"teorii užitečnosti"," — funkce ",[883,87220,87222],{"className":87221},[886],[888,87223,87224],{"xmlns":890},[892,87225,87226,87230],{},[895,87227,87228],{},[898,87229,900],{},[902,87231,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,87234,87235],{},"Optimalizaci spotřebitele",[883,87237,87239],{"className":87238},[886],[888,87240,87241],{"xmlns":890},[892,87242,87243,87247],{},[895,87244,87245],{},[898,87246,900],{},[902,87248,900],{"encoding":904}," při rozpočtu, min ",[883,87251,87253],{"className":87252},[886],[888,87254,87255],{"xmlns":890},[892,87256,87257,87261],{},[895,87258,87259],{},[898,87260,4819],{},[902,87262,4819],{"encoding":904}," při dané ",[883,87265,87267],{"className":87266},[886],[888,87268,87269],{"xmlns":890},[892,87270,87271,87275],{},[895,87272,87273],{},[898,87274,900],{},[902,87276,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,87279,913],{"className":87280,"dataFsResolvedFilePath":911,"href":912},[210],[724,87282,87283,87284,87286,87287,1977],{},"Kapitola 6 knihy ",[614,87285,16707],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,87288,37254],{"className":87289,"dataFsResolvedFilePath":911,"href":912},[210],[115,87291,87293],{"id":87292},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,87295,87296],{},"Po prostudování této kapitoly byste měli umět:",[120,87298,87299,87305,87314,87319,87322,87328,87334,87337,87343],{},[123,87300,87301,87302,1916],{},"vyložit, co se rozumí termínem ",[38,87303,87304],{},"užitečnost",[123,87306,87307,87308,4454,87311,1916],{},"definovat pojmy ",[38,87309,87310],{},"svazek zboží",[38,87312,87313],{},"funkce užitečnosti",[123,87315,75343,87316,75350],{},[38,87317,87318],{},"mezní užitečnosti",[123,87320,87321],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,87323,75370,87324,87327],{},[38,87325,87326],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,87329,75391,87330,87333],{},[38,87331,87332],{},"křivky užitečnosti"," (indiferenční křivky),",[123,87335,87336],{},"vyjmenovat jejich základní vlastnosti,",[123,87338,75343,87339,87342],{},[38,87340,87341],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,87344,87345,87346,87349],{},"řešit ",[38,87347,87348],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,87351,87353],{"id":87352},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,87355,87356,87357,87361,87362,87365],{},"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 ",[207,87358,87360],{"className":87359,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,87363,87364],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,87367,87369],{"id":87368},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,87371,87372],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,87374,87375,87381],{},[123,87376,87377,87380],{},[38,87378,87379],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,87382,87383,87386,87387,87389],{},[38,87384,87385],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,87388,87122],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[4436,87391,87392],{},[724,87393,87394,87396,87397,87400,87401,1885,87414,87417,87418,4454,87431,87450,87451,1343,87477,87504,87505,87508,87509,87512],{},[883,87395,4978],{}," Pozor — ordinalisté užitečnost ",[38,87398,87399],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,87402,87404],{"className":87403},[886],[888,87405,87406],{"xmlns":890},[892,87407,87408,87412],{},[895,87409,87410],{},[898,87411,900],{},[902,87413,900],{"encoding":904},[38,87415,87416],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,87419,87421],{"className":87420},[886],[888,87422,87423],{"xmlns":890},[892,87424,87425,87429],{},[895,87426,87427],{},[898,87428,900],{},[902,87430,900],{"encoding":904},[883,87432,87434],{"className":87433},[886],[888,87435,87436],{"xmlns":890},[892,87437,87438,87447],{},[895,87439,87440],{},[8951,87441,87442,87444],{"accent":1915},[898,87443,900],{},[1664,87445,87446],{},"~",[902,87448,87449],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,87452,87454],{"className":87453},[886],[888,87455,87456],{"xmlns":890},[892,87457,87458,87474],{},[895,87459,87460,87466,87468],{},[8951,87461,87462,87464],{"accent":1915},[898,87463,900],{},[1664,87465,87446],{},[1664,87467,1676],{},[1720,87469,87470,87472],{},[898,87471,900],{},[1963,87473,1970],{},[902,87475,87476],{"encoding":904},"\\tilde U = U^2",[883,87478,87480],{"className":87479},[886],[888,87481,87482],{"xmlns":890},[892,87483,87484,87501],{},[895,87485,87486,87492,87494,87497,87499],{},[8951,87487,87488,87490],{"accent":1915},[898,87489,900],{},[1664,87491,87446],{},[1664,87493,1676],{},[898,87495,87496],{},"ln",[1664,87498,56700],{},[898,87500,900],{},[902,87502,87503],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,87506,87507],{},"porovnání"," mezi svazky a ",[38,87510,87511],{},"poměry"," mezních veličin.",[724,87514,87515,87516,2087],{},"Ordinalistický přístup vychází z ",[38,87517,87518],{},"pěti hlavních předpokladů",[152,87520,87521,87527,87533,87651,87657],{},[123,87522,87523,87526],{},[38,87524,87525],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,87528,87529,87532],{},[38,87530,87531],{},"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.",[123,87534,87535,87538,87539,62241,87552,87565,87566,62241,87579,1748,87592,87595,87596,4454,87615,63070,87633,1977],{},[38,87536,87537],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,87540,87542],{"className":87541},[886],[888,87543,87544],{"xmlns":890},[892,87545,87546,87550],{},[895,87547,87548],{},[898,87549,4822],{},[902,87551,4822],{"encoding":904},[883,87553,87555],{"className":87554},[886],[888,87556,87557],{"xmlns":890},[892,87558,87559,87563],{},[895,87560,87561],{},[898,87562,23753],{},[902,87564,23753],{"encoding":904},", nebude jindy preferovat ",[883,87567,87569],{"className":87568},[886],[888,87570,87571],{"xmlns":890},[892,87572,87573,87577],{},[895,87574,87575],{},[898,87576,23753],{},[902,87578,23753],{"encoding":904},[883,87580,87582],{"className":87581},[886],[888,87583,87584],{"xmlns":890},[892,87585,87586,87590],{},[895,87587,87588],{},[898,87589,4822],{},[902,87591,4822],{"encoding":904},[38,87593,87594],{},"Tranzitivita",": pokud ",[883,87597,87599],{"className":87598},[886],[888,87600,87601],{"xmlns":890},[892,87602,87603,87612],{},[895,87604,87605,87607,87610],{},[898,87606,4822],{},[1664,87608,87609],{},"≻",[898,87611,23753],{},[902,87613,87614],{"encoding":904},"A \\succ B",[883,87616,87618],{"className":87617},[886],[888,87619,87620],{"xmlns":890},[892,87621,87622,87630],{},[895,87623,87624,87626,87628],{},[898,87625,23753],{},[1664,87627,87609],{},[898,87629,1703],{},[902,87631,87632],{"encoding":904},"B \\succ C",[883,87634,87636],{"className":87635},[886],[888,87637,87638],{"xmlns":890},[892,87639,87640,87648],{},[895,87641,87642,87644,87646],{},[898,87643,4822],{},[1664,87645,87609],{},[898,87647,1703],{},[902,87649,87650],{"encoding":904},"A \\succ C",[123,87652,87653,87656],{},[38,87654,87655],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,87658,87659,87662],{},[38,87660,87661],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,87664,87665,87666,87669,87670,1977],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,87667,87668],{},"preference"," a na příbuzné ",[614,87671,87672],{},"funkci užitečnosti",[115,87674,87676],{"id":87675},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,87678,87679,87680,87693,87694,87697,87698,87711],{},"Uvažujme ",[883,87681,87683],{"className":87682},[886],[888,87684,87685],{"xmlns":890},[892,87686,87687,87691],{},[895,87688,87689],{},[898,87690,37360],{},[902,87692,37360],{"encoding":904}," různých zboží. ",[38,87695,87696],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,87699,87701],{"className":87700},[886],[888,87702,87703],{"xmlns":890},[892,87704,87705,87709],{},[895,87706,87707],{},[898,87708,37360],{},[902,87710,37360],{"encoding":904},"-tice",[724,87713,87714],{},[883,87715,87717],{"className":87716},[886],[888,87718,87719],{"xmlns":890},[892,87720,87721,87747],{},[895,87722,87723,87725,87731,87733,87735,87737,87743,87745],{},[1664,87724,1667],{"stretchy":1666},[2355,87726,87727,87729],{},[898,87728,1973],{},[1963,87730,2875],{},[1664,87732,1916],{"separator":1915},[1664,87734,10209],{},[1664,87736,1916],{"separator":1915},[2355,87738,87739,87741],{},[898,87740,1973],{},[898,87742,37360],{},[1664,87744,1673],{"stretchy":1666},[1664,87746,1916],{"separator":1915},[902,87748,87749],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,87751,1709,87752,87769,87770,87783,87784,87787,87788,87791,87792,87795,87796,2087],{},[883,87753,87755],{"className":87754},[886],[888,87756,87757],{"xmlns":890},[892,87758,87759,87767],{},[895,87760,87761],{},[2355,87762,87763,87765],{},[898,87764,1973],{},[898,87766,18290],{},[902,87768,48038],{"encoding":904}," značí množství ",[883,87771,87773],{"className":87772},[886],[888,87774,87775],{"xmlns":890},[892,87776,87777,87781],{},[895,87778,87779],{},[898,87780,18290],{},[902,87782,18290],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,87785,87786],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,87789,87790],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,87793,87794],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,87797,87672],{},[883,87799,87801],{"className":87800},[886],[888,87802,87803],{"xmlns":890,"display":28566},[892,87804,87805,87852],{},[21254,87806,87807],{"width":28571},[21259,87808,87809,87811,87845,87847],{},[21262,87810],{"width":28576},[21262,87812,87813],{},[895,87814,87815,87817,87819,87821,87823,87829,87831,87833,87835,87841,87843],{},[898,87816,900],{},[1664,87818,1676],{},[898,87820,900],{},[1664,87822,1667],{"stretchy":1666},[2355,87824,87825,87827],{},[898,87826,1973],{},[1963,87828,2875],{},[1664,87830,1916],{"separator":1915},[1664,87832,10209],{},[1664,87834,1916],{"separator":1915},[2355,87836,87837,87839],{},[898,87838,1973],{},[898,87840,37360],{},[1664,87842,1673],{"stretchy":1666},[1664,87844,1916],{"separator":1915},[21262,87846],{"width":28576},[21262,87848,87849],{},[1690,87850,87851],{},"(6.1)",[902,87853,87854],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,87856,1709,87857,87887,87888,87910,87911,87914],{},[883,87858,87860],{"className":87859},[886],[888,87861,87862],{"xmlns":890},[892,87863,87864,87884],{},[895,87865,87866,87872,87874,87876,87878],{},[2355,87867,87868,87870],{},[898,87869,1973],{},[1963,87871,2875],{},[1664,87873,1916],{"separator":1915},[1664,87875,10209],{},[1664,87877,1916],{"separator":1915},[2355,87879,87880,87882],{},[898,87881,1973],{},[898,87883,37360],{},[902,87885,87886],{"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 ",[883,87889,87891],{"className":87890},[886],[888,87892,87893],{"xmlns":890},[892,87894,87895,87907],{},[895,87896,87897,87899,87901],{},[898,87898,900],{},[1664,87900,1916],{"separator":1915},[8951,87902,87903,87905],{"accent":1915},[898,87904,900],{},[1664,87906,87446],{},[902,87908,87909],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,87912,87913],{},"monotónní transformace"," zachovávající pořadí.",[724,87916,87917,87918,7581,87921,1977],{},"Dále se omezíme na funkce pro ",[38,87919,87920],{},"dvě zboží",[883,87922,87924],{"className":87923},[886],[888,87925,87926],{"xmlns":890},[892,87927,87928,87954],{},[895,87929,87930,87932,87934,87936,87938,87944,87946,87952],{},[898,87931,900],{},[1664,87933,1676],{},[898,87935,900],{},[1664,87937,1667],{"stretchy":1666},[2355,87939,87940,87942],{},[898,87941,1973],{},[1963,87943,2875],{},[1664,87945,1916],{"separator":1915},[2355,87947,87948,87950],{},[898,87949,1973],{},[1963,87951,1970],{},[1664,87953,1673],{"stretchy":1666},[902,87955,87956],{"encoding":904},"U = U(Q_1, Q_2)",[4436,87958,87959,88034],{},[724,87960,87961,87963,87964,2087],{},[883,87962,53195],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,87965,87967],{"className":87966},[886],[888,87968,87969],{"xmlns":890},[892,87970,87971,88031],{},[895,87972,87973,87975,87977,87979,87981,87987,87989,87995,87997,88003,88005,88007,88009],{},[898,87974,900],{},[1664,87976,1676],{},[898,87978,900],{},[1664,87980,1667],{"stretchy":1666},[2355,87982,87983,87985],{},[898,87984,1973],{},[1963,87986,2875],{},[1664,87988,1916],{"separator":1915},[2355,87990,87991,87993],{},[898,87992,1973],{},[1963,87994,1970],{},[1664,87996,1916],{"separator":1915},[2355,87998,87999,88001],{},[898,88000,1973],{},[1963,88002,2774],{},[1664,88004,1673],{"stretchy":1666},[1664,88006,1676],{},[1963,88008,1970],{},[8682,88010,88011],{},[895,88012,88013,88019,88025],{},[2355,88014,88015,88017],{},[898,88016,1973],{},[1963,88018,2875],{},[2355,88020,88021,88023],{},[898,88022,1973],{},[1963,88024,1970],{},[2355,88026,88027,88029],{},[898,88028,1973],{},[1963,88030,2774],{},[902,88032,88033],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,88035,88036,88229],{},[123,88037,88038,88039,88065,88066,13437,88092,4454,88151,6155,88211,8990],{},"svazek ",[883,88040,88042],{"className":88041},[886],[888,88043,88044],{"xmlns":890},[892,88045,88046,88062],{},[895,88047,88048,88050,88052,88054,88056,88058,88060],{},[1664,88049,1667],{"stretchy":1666},[1963,88051,42362],{},[1664,88053,1916],{"separator":1915},[1963,88055,2944],{},[1664,88057,1916],{"separator":1915},[1963,88059,42340],{},[1664,88061,1673],{"stretchy":1666},[902,88063,88064],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,88067,88069],{"className":88068},[886],[888,88070,88071],{"xmlns":890},[892,88072,88073,88089],{},[895,88074,88075,88077,88079,88081,88083,88085,88087],{},[1664,88076,1667],{"stretchy":1666},[1963,88078,4567],{},[1664,88080,1916],{"separator":1915},[1963,88082,4567],{},[1664,88084,1916],{"separator":1915},[1963,88086,67097],{},[1664,88088,1673],{"stretchy":1666},[902,88090,88091],{"encoding":904},"(9, 9, 27)",[883,88093,88095],{"className":88094},[886],[888,88096,88097],{"xmlns":890},[892,88098,88099,88148],{},[895,88100,88101,88103,88105,88107,88109,88111,88113,88115,88117,88119,88121,88135,88137,88139,88144,88146],{},[898,88102,900],{},[1664,88104,1667],{"stretchy":1666},[1963,88106,42362],{},[1664,88108,1916],{"separator":1915},[1963,88110,2944],{},[1664,88112,1916],{"separator":1915},[1963,88114,42340],{},[1664,88116,1673],{"stretchy":1666},[1664,88118,1676],{},[1963,88120,1970],{},[8682,88122,88123],{},[895,88124,88125,88127,88129,88131,88133],{},[1963,88126,42362],{},[1664,88128,3753],{},[1963,88130,2944],{},[1664,88132,3753],{},[1963,88134,42340],{},[1664,88136,1676],{},[1963,88138,1970],{},[8682,88140,88141],{},[1963,88142,88143],{},"4096",[1664,88145,1676],{},[1963,88147,6183],{},[902,88149,88150],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,88152,88154],{"className":88153},[886],[888,88155,88156],{"xmlns":890},[892,88157,88158,88208],{},[895,88159,88160,88162,88164,88166,88168,88170,88172,88174,88176,88178,88180,88194,88196,88198,88203,88205],{},[898,88161,900],{},[1664,88163,1667],{"stretchy":1666},[1963,88165,4567],{},[1664,88167,1916],{"separator":1915},[1963,88169,4567],{},[1664,88171,1916],{"separator":1915},[1963,88173,67097],{},[1664,88175,1673],{"stretchy":1666},[1664,88177,1676],{},[1963,88179,1970],{},[8682,88181,88182],{},[895,88183,88184,88186,88188,88190,88192],{},[1963,88185,4567],{},[1664,88187,3753],{},[1963,88189,4567],{},[1664,88191,3753],{},[1963,88193,67097],{},[1664,88195,1676],{},[1963,88197,1970],{},[8682,88199,88200],{},[1963,88201,88202],{},"2187",[1664,88204,6466],{},[1963,88206,88207],{},"93,53",[902,88209,88210],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,88212,88214],{"className":88213},[886],[888,88215,88216],{"xmlns":890},[892,88217,88218,88226],{},[895,88219,88220,88222,88224],{},[1963,88221,6183],{},[1664,88223,3984],{},[1963,88225,88207],{},[902,88227,88228],{"encoding":904},"128 > 93{,}53",[123,88230,88231,88232,4454,88258,88284,88285,4454,88325,88366,88367,88413,88414,4454,88440,3424,88466,4454,88484,88502,88503,1977],{},"svazky ",[883,88233,88235],{"className":88234},[886],[888,88236,88237],{"xmlns":890},[892,88238,88239,88255],{},[895,88240,88241,88243,88245,88247,88249,88251,88253],{},[1664,88242,1667],{"stretchy":1666},[1963,88244,2944],{},[1664,88246,1916],{"separator":1915},[1963,88248,6151],{},[1664,88250,1916],{"separator":1915},[1963,88252,1970],{},[1664,88254,1673],{"stretchy":1666},[902,88256,88257],{"encoding":904},"(4, 8, 2)",[883,88259,88261],{"className":88260},[886],[888,88262,88263],{"xmlns":890},[892,88264,88265,88281],{},[895,88266,88267,88269,88271,88273,88275,88277,88279],{},[1664,88268,1667],{"stretchy":1666},[1963,88270,42340],{},[1664,88272,1916],{"separator":1915},[1963,88274,2875],{},[1664,88276,1916],{"separator":1915},[1963,88278,2944],{},[1664,88280,1673],{"stretchy":1666},[902,88282,88283],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,88286,88288],{"className":88287},[886],[888,88289,88290],{"xmlns":890},[892,88291,88292,88322],{},[895,88293,88294,88296,88298,88300,88302,88304,88306,88308,88310,88312,88314,88318,88320],{},[898,88295,900],{},[1664,88297,1667],{"stretchy":1666},[1963,88299,2944],{},[1664,88301,1916],{"separator":1915},[1963,88303,6151],{},[1664,88305,1916],{"separator":1915},[1963,88307,1970],{},[1664,88309,1673],{"stretchy":1666},[1664,88311,1676],{},[1963,88313,1970],{},[8682,88315,88316],{},[1963,88317,42340],{},[1664,88319,1676],{},[1963,88321,42362],{},[902,88323,88324],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,88326,88328],{"className":88327},[886],[888,88329,88330],{"xmlns":890},[892,88331,88332,88363],{},[895,88333,88334,88336,88338,88340,88342,88344,88346,88348,88350,88352,88354,88359,88361],{},[898,88335,900],{},[1664,88337,1667],{"stretchy":1666},[1963,88339,42340],{},[1664,88341,1916],{"separator":1915},[1963,88343,2875],{},[1664,88345,1916],{"separator":1915},[1963,88347,2944],{},[1664,88349,1673],{"stretchy":1666},[1664,88351,1676],{},[1963,88353,1970],{},[8682,88355,88356],{},[1963,88357,88358],{},"256",[1664,88360,1676],{},[1963,88362,72859],{},[902,88364,88365],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,88368,88370],{"className":88369},[886],[888,88371,88372],{"xmlns":890},[892,88373,88374,88410],{},[895,88375,88376,88378,88380,88382,88384,88386,88388,88390,88392,88394,88396,88398,88400,88402,88404,88406,88408],{},[898,88377,900],{},[1664,88379,1667],{"stretchy":1666},[1963,88381,2944],{},[1664,88383,1916],{"separator":1915},[1963,88385,6151],{},[1664,88387,1916],{"separator":1915},[1963,88389,1970],{},[1664,88391,1673],{"stretchy":1666},[1664,88393,1676],{},[898,88395,900],{},[1664,88397,1667],{"stretchy":1666},[1963,88399,42340],{},[1664,88401,1916],{"separator":1915},[1963,88403,2875],{},[1664,88405,1916],{"separator":1915},[1963,88407,2944],{},[1664,88409,1673],{"stretchy":1666},[902,88411,88412],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,88415,88417],{"className":88416},[886],[888,88418,88419],{"xmlns":890},[892,88420,88421,88437],{},[895,88422,88423,88425,88427,88429,88431,88433,88435],{},[1963,88424,2944],{},[1664,88426,3753],{},[1963,88428,6151],{},[1664,88430,3753],{},[1963,88432,1970],{},[1664,88434,1676],{},[1963,88436,42340],{},[902,88438,88439],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,88441,88443],{"className":88442},[886],[888,88444,88445],{"xmlns":890},[892,88446,88447,88463],{},[895,88448,88449,88451,88453,88455,88457,88459,88461],{},[1963,88450,42340],{},[1664,88452,3753],{},[1963,88454,2875],{},[1664,88456,3753],{},[1963,88458,2944],{},[1664,88460,1676],{},[1963,88462,88358],{},[902,88464,88465],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,88467,88469],{"className":88468},[886],[888,88470,88471],{"xmlns":890},[892,88472,88473,88481],{},[895,88474,88475,88477,88479],{},[898,88476,900],{},[1664,88478,1676],{},[1963,88480,42362],{},[902,88482,88483],{"encoding":904},"U = 16",[883,88485,88487],{"className":88486},[886],[888,88488,88489],{"xmlns":890},[892,88490,88491,88499],{},[895,88492,88493,88495,88497],{},[898,88494,900],{},[1664,88496,1676],{},[1963,88498,72859],{},[902,88500,88501],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,88504,88506],{"className":88505},[886],[888,88507,88508],{"xmlns":890},[892,88509,88510,88530],{},[895,88511,88512,88518,88524],{},[2355,88513,88514,88516],{},[898,88515,1973],{},[1963,88517,2875],{},[2355,88519,88520,88522],{},[898,88521,1973],{},[1963,88523,1970],{},[2355,88525,88526,88528],{},[898,88527,1973],{},[1963,88529,2774],{},[902,88531,88532],{"encoding":904},"Q_1 Q_2 Q_3",[115,88534,88536],{"id":88535},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,88538,88539,88540,1762,88575,1885,88578,42314,88595,10588,88612,88615,88616,88619],{},"Pro funkci užitečnosti ",[883,88541,88543],{"className":88542},[886],[888,88544,88545],{"xmlns":890},[892,88546,88547,88573],{},[895,88548,88549,88551,88553,88555,88557,88563,88565,88571],{},[898,88550,900],{},[1664,88552,1676],{},[898,88554,900],{},[1664,88556,1667],{"stretchy":1666},[2355,88558,88559,88561],{},[898,88560,1973],{},[1963,88562,2875],{},[1664,88564,1916],{"separator":1915},[2355,88566,88567,88569],{},[898,88568,1973],{},[1963,88570,1970],{},[1664,88572,1673],{"stretchy":1666},[902,88574,87956],{"encoding":904},[38,88576,88577],{},"mezní užitečnost",[883,88579,88581],{"className":88580},[886],[888,88582,88583],{"xmlns":890},[892,88584,88585,88593],{},[895,88586,88587],{},[2355,88588,88589,88591],{},[898,88590,1973],{},[1963,88592,2875],{},[902,88594,29502],{"encoding":904},[883,88596,88598],{"className":88597},[886],[888,88599,88600],{"xmlns":890},[892,88601,88602,88610],{},[895,88603,88604],{},[2355,88605,88606,88608],{},[898,88607,1973],{},[1963,88609,1970],{},[902,88611,29521],{"encoding":904},[38,88613,88614],{},"marginal utility",") parciální ",[207,88617,1145],{"className":88618,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,88621,88623],{"className":88622},[886],[888,88624,88625],{"xmlns":890,"display":28566},[892,88626,88627,88726],{},[21254,88628,88629],{"width":28571},[21259,88630,88631,88633,88719,88721],{},[21262,88632],{"width":28576},[21262,88634,88635],{},[895,88636,88637,88639,88645,88647,88655,88657,88675,88677,88679,88681,88687,88689,88697,88699,88717],{},[898,88638,1956],{},[2355,88640,88641,88643],{},[898,88642,900],{},[1963,88644,2875],{},[1664,88646,1676],{},[1810,88648,88649,88651,88653],{},[898,88650,900],{},[1963,88652,2875],{},[1664,88654,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,88656,1676],{},[2922,88658,88659,88665],{},[895,88660,88661,88663],{},[898,88662,10435],{"mathvariant":1726},[898,88664,900],{},[895,88666,88667,88669],{},[898,88668,10435],{"mathvariant":1726},[2355,88670,88671,88673],{},[898,88672,1973],{},[1963,88674,2875],{},[1664,88676,1916],{"separator":1915},[6444,88678],{"width":15783},[898,88680,1956],{},[2355,88682,88683,88685],{},[898,88684,900],{},[1963,88686,1970],{},[1664,88688,1676],{},[1810,88690,88691,88693,88695],{},[898,88692,900],{},[1963,88694,1970],{},[1664,88696,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,88698,1676],{},[2922,88700,88701,88707],{},[895,88702,88703,88705],{},[898,88704,10435],{"mathvariant":1726},[898,88706,900],{},[895,88708,88709,88711],{},[898,88710,10435],{"mathvariant":1726},[2355,88712,88713,88715],{},[898,88714,1973],{},[1963,88716,1970],{},[898,88718,1977],{"mathvariant":1726},[21262,88720],{"width":28576},[21262,88722,88723],{},[1690,88724,88725],{},"(6.2)",[902,88727,88728],{"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}",[724,88730,88731,88732,88766,88767,88797,88798,1885,88801,1977],{},"Pro pevné ",[883,88733,88735],{"className":88734},[886],[888,88736,88737],{"xmlns":890},[892,88738,88739,88763],{},[895,88740,88741,88747,88749,88751,88753,88759,88761],{},[2355,88742,88743,88745],{},[898,88744,1973],{},[1963,88746,2875],{},[1664,88748,1676],{},[898,88750,207],{},[1664,88752,1916],{"separator":1915},[2355,88754,88755,88757],{},[898,88756,1973],{},[1963,88758,1970],{},[1664,88760,1676],{},[898,88762,1818],{},[902,88764,88765],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,88768,88770],{"className":88769},[886],[888,88771,88772],{"xmlns":890},[892,88773,88774,88794],{},[895,88775,88776,88778,88784,88786,88788,88790,88792],{},[898,88777,1956],{},[2355,88779,88780,88782],{},[898,88781,900],{},[1963,88783,2875],{},[1664,88785,1667],{"stretchy":1666},[898,88787,207],{},[1664,88789,1916],{"separator":1915},[898,88791,1818],{},[1664,88793,1673],{"stretchy":1666},[902,88795,88796],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,88799,88800],{},"v bodě (na hladině)",[883,88802,88804],{"className":88803},[886],[888,88805,88806],{"xmlns":890},[892,88807,88808,88820],{},[895,88809,88810,88812,88814,88816,88818],{},[1664,88811,1837],{"stretchy":1666},[898,88813,207],{},[1664,88815,1916],{"separator":1915},[898,88817,1818],{},[1664,88819,1850],{"stretchy":1666},[902,88821,1923],{"encoding":904},[4436,88823,88824],{},[724,88825,88826,88828,88829,88859,88888,88889,3196,88902,3210,88919,88940,88941,3257,88958,3271,88971,88988,88989,89011,89012,89041,89042,7039,89062,89079],{},[883,88827,4723],{}," Intuice — co říká ",[883,88830,88832],{"className":88831},[886],[888,88833,88834],{"xmlns":890},[892,88835,88836,88856],{},[895,88837,88838,88840,88846,88848,88850,88852,88854],{},[898,88839,1956],{},[2355,88841,88842,88844],{},[898,88843,900],{},[1963,88845,2875],{},[1664,88847,1667],{"stretchy":1666},[898,88849,207],{},[1664,88851,1916],{"separator":1915},[898,88853,1818],{},[1664,88855,1673],{"stretchy":1666},[902,88857,88858],{"encoding":904},"MU_1(a,b)",[883,88860,88862],{"className":88861},[886],[888,88863,88864],{"xmlns":890},[892,88865,88866,88886],{},[895,88867,88868,88870,88876,88878,88880,88882,88884],{},[898,88869,1956],{},[2355,88871,88872,88874],{},[898,88873,900],{},[1963,88875,2875],{},[1664,88877,1667],{"stretchy":1666},[898,88879,207],{},[1664,88881,1916],{"separator":1915},[898,88883,1818],{},[1664,88885,1673],{"stretchy":1666},[902,88887,88796],{"encoding":904}," je rychlost změny ",[883,88890,88892],{"className":88891},[886],[888,88893,88894],{"xmlns":890},[892,88895,88896,88900],{},[895,88897,88898],{},[898,88899,900],{},[902,88901,900],{"encoding":904},[883,88903,88905],{"className":88904},[886],[888,88906,88907],{"xmlns":890},[892,88908,88909,88917],{},[895,88910,88911],{},[2355,88912,88913,88915],{},[898,88914,1973],{},[1963,88916,2875],{},[902,88918,29502],{"encoding":904},[883,88920,88922],{"className":88921},[886],[888,88923,88924],{"xmlns":890},[892,88925,88926,88938],{},[895,88927,88928,88930,88932,88934,88936],{},[1664,88929,1837],{"stretchy":1666},[898,88931,207],{},[1664,88933,1916],{"separator":1915},[898,88935,1818],{},[1664,88937,1850],{"stretchy":1666},[902,88939,1923],{"encoding":904},". Přibližně: změní-li se ",[883,88942,88944],{"className":88943},[886],[888,88945,88946],{"xmlns":890},[892,88947,88948,88956],{},[895,88949,88950],{},[2355,88951,88952,88954],{},[898,88953,1973],{},[1963,88955,2875],{},[902,88957,29502],{"encoding":904},[883,88959,88961],{"className":88960},[886],[888,88962,88963],{"xmlns":890},[892,88964,88965,88969],{},[895,88966,88967],{},[898,88968,207],{},[902,88970,207],{"encoding":904},[883,88972,88974],{"className":88973},[886],[888,88975,88976],{"xmlns":890},[892,88977,88978,88986],{},[895,88979,88980,88982,88984],{},[898,88981,207],{},[1664,88983,1700],{},[1963,88985,2875],{},[902,88987,3289],{"encoding":904}," při pevném ",[883,88990,88992],{"className":88991},[886],[888,88993,88994],{"xmlns":890},[892,88995,88996,89008],{},[895,88997,88998,89004,89006],{},[2355,88999,89000,89002],{},[898,89001,1973],{},[1963,89003,1970],{},[1664,89005,1676],{},[898,89007,1818],{},[902,89009,89010],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,89013,89015],{"className":89014},[886],[888,89016,89017],{"xmlns":890},[892,89018,89019,89039],{},[895,89020,89021,89023,89029,89031,89033,89035,89037],{},[898,89022,1956],{},[2355,89024,89025,89027],{},[898,89026,900],{},[1963,89028,2875],{},[1664,89030,1667],{"stretchy":1666},[898,89032,207],{},[1664,89034,1916],{"separator":1915},[898,89036,1818],{},[1664,89038,1673],{"stretchy":1666},[902,89040,88796],{"encoding":904},". Stejně tak ",[883,89043,89045],{"className":89044},[886],[888,89046,89047],{"xmlns":890},[892,89048,89049,89059],{},[895,89050,89051,89053],{},[898,89052,1956],{},[2355,89054,89055,89057],{},[898,89056,900],{},[1963,89058,1970],{},[902,89060,89061],{"encoding":904},"MU_2",[883,89063,89065],{"className":89064},[886],[888,89066,89067],{"xmlns":890},[892,89068,89069,89077],{},[895,89070,89071],{},[2355,89072,89073,89075],{},[898,89074,1973],{},[1963,89076,1970],{},[902,89078,29521],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,89081,80711],{"id":89082},"totální-diferenciál",[724,89084,89085,89086,48840,89102,89132,89133,2087],{},"Přibližnou změnu užitečnosti ",[883,89087,89089],{"className":89088},[886],[888,89090,89091],{"xmlns":890},[892,89092,89093,89099],{},[895,89094,89095,89097],{},[898,89096,3468],{"mathvariant":1726},[898,89098,900],{},[902,89100,89101],{"encoding":904},"\\Delta U",[883,89103,89105],{"className":89104},[886],[888,89106,89107],{"xmlns":890},[892,89108,89109,89129],{},[895,89110,89111,89113,89119,89121,89123],{},[898,89112,1695],{"mathvariant":1726},[2355,89114,89115,89117],{},[898,89116,1973],{},[1963,89118,2875],{},[1664,89120,1916],{"separator":1915},[898,89122,1695],{"mathvariant":1726},[2355,89124,89125,89127],{},[898,89126,1973],{},[1963,89128,1970],{},[902,89130,89131],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,89134,89135],{},"totálního diferenciálu",[883,89137,89139],{"className":89138},[886],[888,89140,89141],{"xmlns":890,"display":28566},[892,89142,89143,89244],{},[21254,89144,89145],{"width":28571},[21259,89146,89147,89149,89237,89239],{},[21262,89148],{"width":28576},[21262,89150,89151],{},[895,89152,89153,89155,89157,89159,89161,89163,89165,89173,89175,89181,89183,89191,89193,89199,89201,89203,89209,89211,89217,89219,89221,89227,89229,89235],{},[898,89154,3468],{"mathvariant":1726},[898,89156,900],{},[1664,89158,3315],{},[898,89160,1695],{"mathvariant":1726},[898,89162,900],{},[1664,89164,1676],{},[1810,89166,89167,89169,89171],{},[898,89168,900],{},[1963,89170,2875],{},[1664,89172,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[898,89174,1695],{"mathvariant":1726},[2355,89176,89177,89179],{},[898,89178,1973],{},[1963,89180,2875],{},[1664,89182,1700],{},[1810,89184,89185,89187,89189],{},[898,89186,900],{},[1963,89188,1970],{},[1664,89190,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[898,89192,1695],{"mathvariant":1726},[2355,89194,89195,89197],{},[898,89196,1973],{},[1963,89198,1970],{},[1664,89200,1676],{},[898,89202,1956],{},[2355,89204,89205,89207],{},[898,89206,900],{},[1963,89208,2875],{},[898,89210,1695],{"mathvariant":1726},[2355,89212,89213,89215],{},[898,89214,1973],{},[1963,89216,2875],{},[1664,89218,1700],{},[898,89220,1956],{},[2355,89222,89223,89225],{},[898,89224,900],{},[1963,89226,1970],{},[898,89228,1695],{"mathvariant":1726},[2355,89230,89231,89233],{},[898,89232,1973],{},[1963,89234,1970],{},[898,89236,1977],{"mathvariant":1726},[21262,89238],{"width":28576},[21262,89240,89241],{},[1690,89242,89243],{},"(6.3)",[902,89245,89246],{"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}",[724,89248,75969,89249,1977],{},[883,89250,89252],{"className":89251},[886],[888,89253,89254],{"xmlns":890},[892,89255,89256,89326],{},[895,89257,89258,89260,89262,89264,89266,89268,89274,89276,89278,89284,89286,89292,89294,89296,89302,89304,89306,89308,89310,89316,89318,89324],{},[898,89259,3468],{"mathvariant":1726},[898,89261,900],{},[1664,89263,1676],{},[898,89265,900],{},[1664,89267,1667],{"stretchy":1666},[2355,89269,89270,89272],{},[898,89271,1973],{},[1963,89273,2875],{},[1664,89275,1700],{},[898,89277,1695],{"mathvariant":1726},[2355,89279,89280,89282],{},[898,89281,1973],{},[1963,89283,2875],{},[1664,89285,1916],{"separator":1915},[2355,89287,89288,89290],{},[898,89289,1973],{},[1963,89291,1970],{},[1664,89293,1700],{},[898,89295,1695],{"mathvariant":1726},[2355,89297,89298,89300],{},[898,89299,1973],{},[1963,89301,1970],{},[1664,89303,1673],{"stretchy":1666},[1664,89305,1867],{},[898,89307,900],{},[1664,89309,1667],{"stretchy":1666},[2355,89311,89312,89314],{},[898,89313,1973],{},[1963,89315,2875],{},[1664,89317,1916],{"separator":1915},[2355,89319,89320,89322],{},[898,89321,1973],{},[1963,89323,1970],{},[1664,89325,1673],{"stretchy":1666},[902,89327,89328],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,89330,89332],{"id":89331},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,89334,89335,89336,89339,89340,89343],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,89337,89338],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,89341,89342],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,89345,89346,89349,89350,42314,89376,89402,89403,1343,89435,89467,89468,4454,89522,89576],{},[38,89347,89348],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,89351,89353],{"className":89352},[886],[888,89354,89355],{"xmlns":890},[892,89356,89357,89373],{},[895,89358,89359,89365,89367],{},[2355,89360,89361,89363],{},[898,89362,1973],{},[1963,89364,1970],{},[1664,89366,1676],{},[2355,89368,89369,89371],{},[898,89370,207],{},[1963,89372,2058],{},[902,89374,89375],{"encoding":904},"Q_2 = a_0",[883,89377,89379],{"className":89378},[886],[888,89380,89381],{"xmlns":890},[892,89382,89383,89399],{},[895,89384,89385,89391,89393],{},[2355,89386,89387,89389],{},[898,89388,1973],{},[1963,89390,2875],{},[1664,89392,1676],{},[2355,89394,89395,89397],{},[898,89396,1818],{},[1963,89398,2058],{},[902,89400,89401],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,89404,89406],{"className":89405},[886],[888,89407,89408],{"xmlns":890},[892,89409,89410,89432],{},[895,89411,89412,89414,89416,89422,89424,89430],{},[898,89413,900],{},[1664,89415,1667],{"stretchy":1666},[2355,89417,89418,89420],{},[898,89419,1973],{},[1963,89421,2875],{},[1664,89423,1916],{"separator":1915},[2355,89425,89426,89428],{},[898,89427,207],{},[1963,89429,2058],{},[1664,89431,1673],{"stretchy":1666},[902,89433,89434],{"encoding":904},"U(Q_1, a_0)",[883,89436,89438],{"className":89437},[886],[888,89439,89440],{"xmlns":890},[892,89441,89442,89464],{},[895,89443,89444,89446,89448,89454,89456,89462],{},[898,89445,900],{},[1664,89447,1667],{"stretchy":1666},[2355,89449,89450,89452],{},[898,89451,1818],{},[1963,89453,2058],{},[1664,89455,1916],{"separator":1915},[2355,89457,89458,89460],{},[898,89459,1973],{},[1963,89461,1970],{},[1664,89463,1673],{"stretchy":1666},[902,89465,89466],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,89469,89471],{"className":89470},[886],[888,89472,89473],{"xmlns":890},[892,89474,89475,89519],{},[895,89476,89477,89515,89517],{},[2919,89478,89479],{"scriptlevel":2058,"displaystyle":1915},[2922,89480,89481,89505],{},[895,89482,89483,89485,89487,89489,89495,89497,89503],{},[898,89484,1695],{"mathvariant":1726},[898,89486,900],{},[1664,89488,1667],{"stretchy":1666},[2355,89490,89491,89493],{},[898,89492,1973],{},[1963,89494,2875],{},[1664,89496,1916],{"separator":1915},[2355,89498,89499,89501],{},[898,89500,207],{},[1963,89502,2058],{},[1664,89504,1673],{"stretchy":1666},[895,89506,89507,89509],{},[898,89508,1695],{"mathvariant":1726},[2355,89510,89511,89513],{},[898,89512,1973],{},[1963,89514,2875],{},[1664,89516,3984],{},[1963,89518,2058],{},[902,89520,89521],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,89523,89525],{"className":89524},[886],[888,89526,89527],{"xmlns":890},[892,89528,89529,89573],{},[895,89530,89531,89569,89571],{},[2919,89532,89533],{"scriptlevel":2058,"displaystyle":1915},[2922,89534,89535,89559],{},[895,89536,89537,89539,89541,89543,89549,89551,89557],{},[898,89538,1695],{"mathvariant":1726},[898,89540,900],{},[1664,89542,1667],{"stretchy":1666},[2355,89544,89545,89547],{},[898,89546,1818],{},[1963,89548,2058],{},[1664,89550,1916],{"separator":1915},[2355,89552,89553,89555],{},[898,89554,1973],{},[1963,89556,1970],{},[1664,89558,1673],{"stretchy":1666},[895,89560,89561,89563],{},[898,89562,1695],{"mathvariant":1726},[2355,89564,89565,89567],{},[898,89566,1973],{},[1963,89568,1970],{},[1664,89570,3984],{},[1963,89572,2058],{},[902,89574,89575],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,89578,89580],{"className":89579},[886],[888,89581,89582],{"xmlns":890,"display":28566},[892,89583,89584,89629],{},[21254,89585,89586],{"width":28571},[21259,89587,89588,89590,89622,89624],{},[21262,89589],{"width":28576},[21262,89591,89592],{},[895,89593,89594,89602,89604,89606,89608,89610,89618,89620],{},[1810,89595,89596,89598,89600],{},[898,89597,900],{},[1963,89599,2875],{},[1664,89601,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,89603,3984],{},[1963,89605,2058],{},[1664,89607,1916],{"separator":1915},[6444,89609],{"width":15783},[1810,89611,89612,89614,89616],{},[898,89613,900],{},[1963,89615,1970],{},[1664,89617,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,89619,3984],{},[1963,89621,12959],{},[21262,89623],{"width":28576},[21262,89625,89626],{},[1690,89627,89628],{},"(6.4)",[902,89630,89631],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,89633,89634,89635,89637],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,89636,53177],{}," — užitečnost roste s množstvím každého zboží.",[724,89639,89640,89643,89644,89674,89675,2087],{},[38,89641,89642],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,89645,89647],{"className":89646},[886],[888,89648,89649],{"xmlns":890},[892,89650,89651,89671],{},[895,89652,89653,89661,89663],{},[1810,89654,89655,89657,89659],{},[898,89656,900],{},[1963,89658,2875],{},[1664,89660,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,89662,1916],{"separator":1915},[1810,89664,89665,89667,89669],{},[898,89666,900],{},[1963,89668,1970],{},[1664,89670,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,89672,89673],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,89676,89677],{},"záporné",[883,89679,89681],{"className":89680},[886],[888,89682,89683],{"xmlns":890,"display":28566},[892,89684,89685,89738],{},[21254,89686,89687],{"width":28571},[21259,89688,89689,89691,89731,89733],{},[21262,89690],{"width":28576},[21262,89692,89693],{},[895,89694,89695,89707,89709,89711,89713,89715,89727,89729],{},[1810,89696,89697,89699,89701],{},[898,89698,900],{},[1963,89700,3483],{},[895,89702,89703,89705],{},[1664,89704,1728],{"mathvariant":1726},[1664,89706,1728],{"mathvariant":1726},[1664,89708,4022],{},[1963,89710,2058],{},[1664,89712,1916],{"separator":1915},[6444,89714],{"width":15783},[1810,89716,89717,89719,89721],{},[898,89718,900],{},[1963,89720,33046],{},[895,89722,89723,89725],{},[1664,89724,1728],{"mathvariant":1726},[1664,89726,1728],{"mathvariant":1726},[1664,89728,4022],{},[1963,89730,12959],{},[21262,89732],{"width":28576},[21262,89734,89735],{},[1690,89736,89737],{},"(6.5)",[902,89739,89740],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,89742,89743,89744,89747,89748,1977],{},"Podmínka (6.5) je známa jako ",[38,89745,89746],{},"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 ",[207,89749,89751],{"className":89750,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,89753,89754,89755,4454,89787,89819,89820,4454,89846,89872,89873,89901,89902,4454,89904,89906,89907,89942],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,89756,89758],{"className":89757},[886],[888,89759,89760],{"xmlns":890},[892,89761,89762,89784],{},[895,89763,89764,89766,89768,89774,89776,89782],{},[898,89765,900],{},[1664,89767,1667],{"stretchy":1666},[2355,89769,89770,89772],{},[898,89771,1973],{},[1963,89773,2875],{},[1664,89775,1916],{"separator":1915},[2355,89777,89778,89780],{},[898,89779,1818],{},[1963,89781,2058],{},[1664,89783,1673],{"stretchy":1666},[902,89785,89786],{"encoding":904},"U(Q_1, b_0)",[883,89788,89790],{"className":89789},[886],[888,89791,89792],{"xmlns":890},[892,89793,89794,89816],{},[895,89795,89796,89798,89800,89806,89808,89814],{},[898,89797,900],{},[1664,89799,1667],{"stretchy":1666},[2355,89801,89802,89804],{},[898,89803,207],{},[1963,89805,2058],{},[1664,89807,1916],{"separator":1915},[2355,89809,89810,89812],{},[898,89811,1973],{},[1963,89813,1970],{},[1664,89815,1673],{"stretchy":1666},[902,89817,89818],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,89821,89823],{"className":89822},[886],[888,89824,89825],{"xmlns":890},[892,89826,89827,89843],{},[895,89828,89829,89831,89833,89835,89841],{},[1664,89830,1667],{"stretchy":1666},[898,89832,900],{},[1664,89834,1916],{"separator":1915},[2355,89836,89837,89839],{},[898,89838,1973],{},[1963,89840,2875],{},[1664,89842,1673],{"stretchy":1666},[902,89844,89845],{"encoding":904},"(U, Q_1)",[883,89847,89849],{"className":89848},[886],[888,89850,89851],{"xmlns":890},[892,89852,89853,89869],{},[895,89854,89855,89857,89859,89861,89867],{},[1664,89856,1667],{"stretchy":1666},[898,89858,900],{},[1664,89860,1916],{"separator":1915},[2355,89862,89863,89865],{},[898,89864,1973],{},[1963,89866,1970],{},[1664,89868,1673],{"stretchy":1666},[902,89870,89871],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,89874,89876],{"className":89875},[886],[888,89877,89878],{"xmlns":890},[892,89879,89880,89898],{},[895,89881,89882,89884,89886,89888,89890,89892,89894,89896],{},[898,89883,900],{},[1664,89885,1667],{"stretchy":1666},[1963,89887,2058],{},[1664,89889,1916],{"separator":1915},[1963,89891,2058],{},[1664,89893,1673],{"stretchy":1666},[1664,89895,1676],{},[1963,89897,2058],{},[902,89899,89900],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,89903,14156],{},[38,89905,38988],{},". Typický tvar grafu ",[883,89908,89910],{"className":89909},[886],[888,89911,89912],{"xmlns":890},[892,89913,89914,89940],{},[895,89915,89916,89918,89920,89922,89924,89930,89932,89938],{},[898,89917,900],{},[1664,89919,1676],{},[898,89921,900],{},[1664,89923,1667],{"stretchy":1666},[2355,89925,89926,89928],{},[898,89927,1973],{},[1963,89929,2875],{},[1664,89931,1916],{"separator":1915},[2355,89933,89934,89936],{},[898,89935,1973],{},[1963,89937,1970],{},[1664,89939,1673],{"stretchy":1666},[902,89941,87956],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,89944,89945],{},[614,89946,89947,89948,88988,89976,89997,89998,88988,90026,90048],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,89949,89951],{"className":89950},[886],[888,89952,89953],{"xmlns":890},[892,89954,89955,89973],{},[895,89956,89957,89959,89961,89967,89969,89971],{},[898,89958,900],{},[1664,89960,1667],{"stretchy":1666},[2355,89962,89963,89965],{},[898,89964,1973],{},[1963,89966,2875],{},[1664,89968,1916],{"separator":1915},[898,89970,1818],{},[1664,89972,1673],{"stretchy":1666},[902,89974,89975],{"encoding":904},"U(Q_1, b)",[883,89977,89979],{"className":89978},[886],[888,89980,89981],{"xmlns":890},[892,89982,89983,89995],{},[895,89984,89985,89991,89993],{},[2355,89986,89987,89989],{},[898,89988,1973],{},[1963,89990,1970],{},[1664,89992,1676],{},[898,89994,1818],{},[902,89996,89010],{"encoding":904}," (vlevo) a ",[883,89999,90001],{"className":90000},[886],[888,90002,90003],{"xmlns":890},[892,90004,90005,90023],{},[895,90006,90007,90009,90011,90013,90015,90021],{},[898,90008,900],{},[1664,90010,1667],{"stretchy":1666},[898,90012,207],{},[1664,90014,1916],{"separator":1915},[2355,90016,90017,90019],{},[898,90018,1973],{},[1963,90020,1970],{},[1664,90022,1673],{"stretchy":1666},[902,90024,90025],{"encoding":904},"U(a, Q_2)",[883,90027,90029],{"className":90028},[886],[888,90030,90031],{"xmlns":890},[892,90032,90033,90045],{},[895,90034,90035,90041,90043],{},[2355,90036,90037,90039],{},[898,90038,1973],{},[1963,90040,2875],{},[1664,90042,1676],{},[898,90044,207],{},[902,90046,90047],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,90050,90051],{},[614,90052,90053,90054,90089,90090,90120,90121,4454,90144,90166,90167,1977],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,90055,90057],{"className":90056},[886],[888,90058,90059],{"xmlns":890},[892,90060,90061,90087],{},[895,90062,90063,90065,90067,90069,90071,90077,90079,90085],{},[898,90064,900],{},[1664,90066,1676],{},[898,90068,900],{},[1664,90070,1667],{"stretchy":1666},[2355,90072,90073,90075],{},[898,90074,1973],{},[1963,90076,2875],{},[1664,90078,1916],{"separator":1915},[2355,90080,90081,90083],{},[898,90082,1973],{},[1963,90084,1970],{},[1664,90086,1673],{"stretchy":1666},[902,90088,87956],{"encoding":904}," nad rovinou ",[883,90091,90093],{"className":90092},[886],[888,90094,90095],{"xmlns":890},[892,90096,90097,90117],{},[895,90098,90099,90101,90107,90109,90115],{},[1664,90100,1667],{"stretchy":1666},[2355,90102,90103,90105],{},[898,90104,1973],{},[1963,90106,2875],{},[1664,90108,1916],{"separator":1915},[2355,90110,90111,90113],{},[898,90112,1973],{},[1963,90114,1970],{},[1664,90116,1673],{"stretchy":1666},[902,90118,90119],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,90122,90124],{"className":90123},[886],[888,90125,90126],{"xmlns":890},[892,90127,90128,90141],{},[895,90129,90130,90136,90138],{},[2355,90131,90132,90134],{},[898,90133,1973],{},[1963,90135,2875],{},[1664,90137,1676],{},[1690,90139,90140],{},"const",[902,90142,90143],{"encoding":904},"Q_1 = \\text{const}",[883,90145,90147],{"className":90146},[886],[888,90148,90149],{"xmlns":890},[892,90150,90151,90163],{},[895,90152,90153,90159,90161],{},[2355,90154,90155,90157],{},[898,90156,1973],{},[1963,90158,1970],{},[1664,90160,1676],{},[1690,90162,90140],{},[902,90164,90165],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,90168,90170],{"className":90169},[886],[888,90171,90172],{"xmlns":890},[892,90173,90174,90200],{},[895,90175,90176,90178,90180,90186,90188,90194,90196,90198],{},[898,90177,900],{},[1664,90179,1667],{"stretchy":1666},[2355,90181,90182,90184],{},[898,90183,1973],{},[1963,90185,2875],{},[1664,90187,1916],{"separator":1915},[2355,90189,90190,90192],{},[898,90191,1973],{},[1963,90193,1970],{},[1664,90195,1673],{"stretchy":1666},[1664,90197,1676],{},[898,90199,2034],{},[902,90201,10331],{"encoding":904},[198,90203,90205,90206],{"id":90204},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,90207,90209],{"className":90208},[886],[888,90210,90211],{"xmlns":890},[892,90212,90213,90247],{},[895,90214,90215,90217,90219,90233],{},[898,90216,900],{},[1664,90218,1676],{},[1810,90220,90221,90223,90225],{},[898,90222,1973],{},[1963,90224,2875],{},[895,90226,90227,90229,90231],{},[1963,90228,2875],{},[898,90230,5240],{"mathvariant":1726},[1963,90232,1970],{},[1810,90234,90235,90237,90239],{},[898,90236,1973],{},[1963,90238,1970],{},[895,90240,90241,90243,90245],{},[1963,90242,2875],{},[898,90244,5240],{"mathvariant":1726},[1963,90246,2774],{},[902,90248,90249],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,90251,90252],{},[38,90253,90254],{},"Ověření (6.4) a (6.5).",[883,90256,90258],{"className":90257},[886],[888,90259,90260],{"xmlns":890,"display":28566},[892,90261,90262,90366],{},[895,90263,90264,90272,90274,90282,90298,90312,90314,90316,90324,90326,90334,90348,90364],{},[1810,90265,90266,90268,90270],{},[898,90267,900],{},[1963,90269,2875],{},[1664,90271,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,90273,1676],{},[2919,90275,90276],{"scriptlevel":2058,"displaystyle":1666},[2922,90277,90278,90280],{},[1963,90279,2875],{},[1963,90281,1970],{},[1810,90283,90284,90286,90288],{},[898,90285,1973],{},[1963,90287,2875],{},[895,90289,90290,90292,90294,90296],{},[1664,90291,1867],{},[1963,90293,2875],{},[898,90295,5240],{"mathvariant":1726},[1963,90297,1970],{},[1810,90299,90300,90302,90304],{},[898,90301,1973],{},[1963,90303,1970],{},[895,90305,90306,90308,90310],{},[1963,90307,2875],{},[898,90309,5240],{"mathvariant":1726},[1963,90311,2774],{},[1664,90313,1916],{"separator":1915},[6444,90315],{"width":15783},[1810,90317,90318,90320,90322],{},[898,90319,900],{},[1963,90321,1970],{},[1664,90323,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,90325,1676],{},[2919,90327,90328],{"scriptlevel":2058,"displaystyle":1666},[2922,90329,90330,90332],{},[1963,90331,2875],{},[1963,90333,2774],{},[1810,90335,90336,90338,90340],{},[898,90337,1973],{},[1963,90339,2875],{},[895,90341,90342,90344,90346],{},[1963,90343,2875],{},[898,90345,5240],{"mathvariant":1726},[1963,90347,1970],{},[1810,90349,90350,90352,90354],{},[898,90351,1973],{},[1963,90353,1970],{},[895,90355,90356,90358,90360,90362],{},[1664,90357,1867],{},[1963,90359,1970],{},[898,90361,5240],{"mathvariant":1726},[1963,90363,2774],{},[1664,90365,1916],{"separator":1915},[902,90367,90368],{"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},",[724,90370,90371,90372,90406],{},"zřejmě ",[883,90373,90375],{"className":90374},[886],[888,90376,90377],{"xmlns":890},[892,90378,90379,90403],{},[895,90380,90381,90389,90391,90399,90401],{},[1810,90382,90383,90385,90387],{},[898,90384,900],{},[1963,90386,2875],{},[1664,90388,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,90390,1916],{"separator":1915},[1810,90392,90393,90395,90397],{},[898,90394,900],{},[1963,90396,1970],{},[1664,90398,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,90400,3984],{},[1963,90402,2058],{},[902,90404,90405],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,90408,90410],{"className":90409},[886],[888,90411,90412],{"xmlns":890,"display":28566},[892,90413,90414,90530],{},[895,90415,90416,90428,90430,90432,90440,90456,90470,90472,90474,90486,90488,90490,90498,90512,90528],{},[1810,90417,90418,90420,90422],{},[898,90419,900],{},[1963,90421,3483],{},[895,90423,90424,90426],{},[1664,90425,1728],{"mathvariant":1726},[1664,90427,1728],{"mathvariant":1726},[1664,90429,1676],{},[1664,90431,1867],{},[2919,90433,90434],{"scriptlevel":2058,"displaystyle":1666},[2922,90435,90436,90438],{},[1963,90437,2875],{},[1963,90439,2944],{},[1810,90441,90442,90444,90446],{},[898,90443,1973],{},[1963,90445,2875],{},[895,90447,90448,90450,90452,90454],{},[1664,90449,1867],{},[1963,90451,2774],{},[898,90453,5240],{"mathvariant":1726},[1963,90455,1970],{},[1810,90457,90458,90460,90462],{},[898,90459,1973],{},[1963,90461,1970],{},[895,90463,90464,90466,90468],{},[1963,90465,2875],{},[898,90467,5240],{"mathvariant":1726},[1963,90469,2774],{},[1664,90471,1916],{"separator":1915},[6444,90473],{"width":15783},[1810,90475,90476,90478,90480],{},[898,90477,900],{},[1963,90479,33046],{},[895,90481,90482,90484],{},[1664,90483,1728],{"mathvariant":1726},[1664,90485,1728],{"mathvariant":1726},[1664,90487,1676],{},[1664,90489,1867],{},[2919,90491,90492],{"scriptlevel":2058,"displaystyle":1666},[2922,90493,90494,90496],{},[1963,90495,1970],{},[1963,90497,4567],{},[1810,90499,90500,90502,90504],{},[898,90501,1973],{},[1963,90503,2875],{},[895,90505,90506,90508,90510],{},[1963,90507,2875],{},[898,90509,5240],{"mathvariant":1726},[1963,90511,1970],{},[1810,90513,90514,90516,90518],{},[898,90515,1973],{},[1963,90517,1970],{},[895,90519,90520,90522,90524,90526],{},[1664,90521,1867],{},[1963,90523,2826],{},[898,90525,5240],{"mathvariant":1726},[1963,90527,2774],{},[1664,90529,1916],{"separator":1915},[902,90531,90532],{"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},",[724,90534,90535,90536,90578],{},"opět ",[883,90537,90539],{"className":90538},[886],[888,90540,90541],{"xmlns":890},[892,90542,90543,90575],{},[895,90544,90545,90557,90559,90571,90573],{},[1810,90546,90547,90549,90551],{},[898,90548,900],{},[1963,90550,3483],{},[895,90552,90553,90555],{},[1664,90554,1728],{"mathvariant":1726},[1664,90556,1728],{"mathvariant":1726},[1664,90558,1916],{"separator":1915},[1810,90560,90561,90563,90565],{},[898,90562,900],{},[1963,90564,33046],{},[895,90566,90567,90569],{},[1664,90568,1728],{"mathvariant":1726},[1664,90570,1728],{"mathvariant":1726},[1664,90572,4022],{},[1963,90574,2058],{},[902,90576,90577],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,90580,90581],{},[38,90582,90583,90584,1977],{},"(a) Mezní užitečnosti v bodě ",[883,90585,90587],{"className":90586},[886],[888,90588,90589],{"xmlns":890},[892,90590,90591,90603],{},[895,90592,90593,90595,90597,90599,90601],{},[1664,90594,1837],{"stretchy":1666},[1963,90596,1965],{},[1664,90598,1916],{"separator":1915},[1963,90600,8942],{},[1664,90602,1850],{"stretchy":1666},[902,90604,90605],{"encoding":904},"[100, 200]",[883,90607,90609],{"className":90608},[886],[888,90610,90611],{"xmlns":890,"display":28566},[892,90612,90613,90680],{},[895,90614,90615,90617,90623,90625,90627,90629,90631,90633,90635,90643,90645,90659,90661,90673,90675,90678],{},[898,90616,1956],{},[2355,90618,90619,90621],{},[898,90620,900],{},[1963,90622,2875],{},[1664,90624,1667],{"stretchy":1666},[1963,90626,1965],{},[1664,90628,1916],{"separator":1915},[1963,90630,8942],{},[1664,90632,1673],{"stretchy":1666},[1664,90634,1676],{},[2919,90636,90637],{"scriptlevel":2058,"displaystyle":1666},[2922,90638,90639,90641],{},[1963,90640,2875],{},[1963,90642,1970],{},[1664,90644,3753],{},[1720,90646,90647,90649],{},[1963,90648,1965],{},[895,90650,90651,90653,90655,90657],{},[1664,90652,1867],{},[1963,90654,2875],{},[898,90656,5240],{"mathvariant":1726},[1963,90658,1970],{},[1664,90660,3753],{},[1720,90662,90663,90665],{},[1963,90664,8942],{},[895,90666,90667,90669,90671],{},[1963,90668,2875],{},[898,90670,5240],{"mathvariant":1726},[1963,90672,2774],{},[1664,90674,6466],{},[1963,90676,90677],{},"0,4204",[1664,90679,1916],{"separator":1915},[902,90681,90682],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,90684,90686],{"className":90685},[886],[888,90687,90688],{"xmlns":890,"display":28566},[892,90689,90690,90755],{},[895,90691,90692,90694,90700,90702,90704,90706,90708,90710,90712,90720,90722,90734,90736,90750,90752],{},[898,90693,1956],{},[2355,90695,90696,90698],{},[898,90697,900],{},[1963,90699,1970],{},[1664,90701,1667],{"stretchy":1666},[1963,90703,1965],{},[1664,90705,1916],{"separator":1915},[1963,90707,8942],{},[1664,90709,1673],{"stretchy":1666},[1664,90711,1676],{},[2919,90713,90714],{"scriptlevel":2058,"displaystyle":1666},[2922,90715,90716,90718],{},[1963,90717,2875],{},[1963,90719,2774],{},[1664,90721,3753],{},[1720,90723,90724,90726],{},[1963,90725,1965],{},[895,90727,90728,90730,90732],{},[1963,90729,2875],{},[898,90731,5240],{"mathvariant":1726},[1963,90733,1970],{},[1664,90735,3753],{},[1720,90737,90738,90740],{},[1963,90739,8942],{},[895,90741,90742,90744,90746,90748],{},[1664,90743,1867],{},[1963,90745,1970],{},[898,90747,5240],{"mathvariant":1726},[1963,90749,2774],{},[1664,90751,6466],{},[1963,90753,90754],{},"0,63067.",[902,90756,90757],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,90759,90760,1885,90762,90797,90798,90819,90820,90837],{},[614,90761,9779],{},[883,90763,90765],{"className":90764},[886],[888,90766,90767],{"xmlns":890},[892,90768,90769,90794],{},[895,90770,90771,90773,90779,90781,90783,90785,90787,90789,90791],{},[898,90772,1956],{},[2355,90774,90775,90777],{},[898,90776,900],{},[1963,90778,1970],{},[1664,90780,1667],{"stretchy":1666},[1963,90782,1965],{},[1664,90784,1916],{"separator":1915},[1963,90786,8942],{},[1664,90788,1673],{"stretchy":1666},[1664,90790,6466],{},[1963,90792,90793],{},"0,63067",[902,90795,90796],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,90799,90801],{"className":90800},[886],[888,90802,90803],{"xmlns":890},[892,90804,90805,90817],{},[895,90806,90807,90809,90811,90813,90815],{},[1664,90808,1837],{"stretchy":1666},[1963,90810,1965],{},[1664,90812,1916],{"separator":1915},[1963,90814,8942],{},[1664,90816,1850],{"stretchy":1666},[902,90818,90605],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,90821,90823],{"className":90822},[886],[888,90824,90825],{"xmlns":890},[892,90826,90827,90835],{},[895,90828,90829],{},[2355,90830,90831,90833],{},[898,90832,1973],{},[1963,90834,1970],{},[902,90836,29521],{"encoding":904}," přibližně o 0,63067.",[724,90839,90840,90859,90860,39684,90881,90898,90899,90925,90926,90943,90944,3727],{},[38,90841,90842,90843,90858],{},"(b) Odhad změny ",[883,90844,90846],{"className":90845},[886],[888,90847,90848],{"xmlns":890},[892,90849,90850,90856],{},[895,90851,90852,90854],{},[898,90853,3468],{"mathvariant":1726},[898,90855,900],{},[902,90857,89101],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,90861,90863],{"className":90862},[886],[888,90864,90865],{"xmlns":890},[892,90866,90867,90879],{},[895,90868,90869,90871,90873,90875,90877],{},[1664,90870,1837],{"stretchy":1666},[1963,90872,1965],{},[1664,90874,1916],{"separator":1915},[1963,90876,8942],{},[1664,90878,1850],{"stretchy":1666},[902,90880,90605],{"encoding":904},[883,90882,90884],{"className":90883},[886],[888,90885,90886],{"xmlns":890},[892,90887,90888,90896],{},[895,90889,90890],{},[2355,90891,90892,90894],{},[898,90893,1973],{},[1963,90895,2875],{},[902,90897,29502],{"encoding":904}," na 98 (tj. ",[883,90900,90902],{"className":90901},[886],[888,90903,90904],{"xmlns":890},[892,90905,90906,90922],{},[895,90907,90908,90910,90916,90918,90920],{},[898,90909,1695],{"mathvariant":1726},[2355,90911,90912,90914],{},[898,90913,1973],{},[1963,90915,2875],{},[1664,90917,1676],{},[1664,90919,1867],{},[1963,90921,1970],{},[902,90923,90924],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,90927,90929],{"className":90928},[886],[888,90930,90931],{"xmlns":890},[892,90932,90933,90941],{},[895,90934,90935],{},[2355,90936,90937,90939],{},[898,90938,1973],{},[1963,90940,1970],{},[902,90942,29521],{"encoding":904}," o 3 (tj. ",[883,90945,90947],{"className":90946},[886],[888,90948,90949],{"xmlns":890},[892,90950,90951,90965],{},[895,90952,90953,90955,90961,90963],{},[898,90954,1695],{"mathvariant":1726},[2355,90956,90957,90959],{},[898,90958,1973],{},[1963,90960,1970],{},[1664,90962,1676],{},[1963,90964,2774],{},[902,90966,90967],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,90969,90971],{"className":90970},[886],[888,90972,90973],{"xmlns":890,"display":28566},[892,90974,90975,91026],{},[895,90976,90977,90979,90981,90983,90985,90987,90989,90991,90993,90995,90997,90999,91001,91003,91005,91007,91009,91011,91013,91016,91018,91021,91023],{},[898,90978,3468],{"mathvariant":1726},[898,90980,900],{},[1664,90982,3315],{},[898,90984,1695],{"mathvariant":1726},[898,90986,900],{},[1664,90988,1676],{},[1963,90990,90677],{},[1664,90992,3753],{},[1664,90994,1667],{"stretchy":1666},[1664,90996,1867],{},[1963,90998,1970],{},[1664,91000,1673],{"stretchy":1666},[1664,91002,1700],{},[1963,91004,90793],{},[1664,91006,3753],{},[1963,91008,2774],{},[1664,91010,1676],{},[1664,91012,1867],{},[1963,91014,91015],{},"0,8408",[1664,91017,1700],{},[1963,91019,91020],{},"1,89201",[1664,91022,6466],{},[1963,91024,91025],{},"1,05.",[902,91027,91028],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,91030,91031,91032,91035,91036,91087,91088,1977],{},"Užitečnost se tedy zvýší přibližně o ",[38,91033,91034],{},"1,05",". Skutečná změna je ",[883,91037,91039],{"className":91038},[886],[888,91040,91041],{"xmlns":890},[892,91042,91043,91084],{},[895,91044,91045,91047,91049,91051,91053,91055,91058,91060,91063,91065,91067,91069,91071,91073,91075,91077,91079,91081],{},[898,91046,3468],{"mathvariant":1726},[898,91048,900],{},[1664,91050,1676],{},[898,91052,900],{},[1664,91054,1667],{"stretchy":1666},[1963,91056,91057],{},"98",[1664,91059,1916],{"separator":1915},[1963,91061,91062],{},"203",[1664,91064,1673],{"stretchy":1666},[1664,91066,1867],{},[898,91068,900],{},[1664,91070,1667],{"stretchy":1666},[1963,91072,1965],{},[1664,91074,1916],{"separator":1915},[1963,91076,8942],{},[1664,91078,1673],{"stretchy":1666},[1664,91080,6466],{},[1963,91082,91083],{},"1,031",[902,91085,91086],{"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 ",[883,91089,91091],{"className":91090},[886],[888,91092,91093],{"xmlns":890},[892,91094,91095,91115],{},[895,91096,91097,91099,91105,91107,91109],{},[898,91098,1695],{"mathvariant":1726},[2355,91100,91101,91103],{},[898,91102,1973],{},[1963,91104,2875],{},[1664,91106,1916],{"separator":1915},[898,91108,1695],{"mathvariant":1726},[2355,91110,91111,91113],{},[898,91112,1973],{},[1963,91114,1970],{},[902,91116,89131],{"encoding":904},[115,91118,91120],{"id":91119},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,91122,91123],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,91125,91127],{"className":91126},[886],[888,91128,91129],{"xmlns":890,"display":28566},[892,91130,91131,91190],{},[21254,91132,91133],{"width":28571},[21259,91134,91135,91137,91183,91185],{},[21262,91136],{"width":28576},[21262,91138,91139],{},[895,91140,91141,91143,91145,91151,91153,91159,91161,91163,91171,91173,91181],{},[898,91142,900],{},[1664,91144,1667],{"stretchy":1666},[2355,91146,91147,91149],{},[898,91148,1973],{},[1963,91150,2875],{},[1664,91152,1916],{"separator":1915},[2355,91154,91155,91157],{},[898,91156,1973],{},[1963,91158,1970],{},[1664,91160,1673],{"stretchy":1666},[1664,91162,1676],{},[1810,91164,91165,91167,91169],{},[898,91166,1973],{},[1963,91168,2875],{},[898,91170,207],{},[1664,91172,3753],{},[1810,91174,91175,91177,91179],{},[898,91176,1973],{},[1963,91178,1970],{},[898,91180,1818],{},[1664,91182,1916],{"separator":1915},[21262,91184],{"width":28576},[21262,91186,91187],{},[1690,91188,91189],{},"(6.6)",[902,91191,91192],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,91194,1709,91195,91213,91214,91216,91217,91221,91222,91252,91253,91275],{},[883,91196,91198],{"className":91197},[886],[888,91199,91200],{"xmlns":890},[892,91201,91202,91210],{},[895,91203,91204,91206,91208],{},[898,91205,207],{},[1664,91207,1916],{"separator":1915},[898,91209,1818],{},[902,91211,91212],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,91215,75199],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,91218,91220],{"className":91219,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,91223,91225],{"className":91224},[886],[888,91226,91227],{"xmlns":890},[892,91228,91229,91249],{},[895,91230,91231,91233,91235,91237,91239,91241,91243,91245,91247],{},[898,91232,207],{},[1664,91234,1916],{"separator":1915},[898,91236,1818],{},[1664,91238,7072],{},[1664,91240,1667],{"stretchy":1666},[1963,91242,2058],{},[1664,91244,1916],{"separator":1915},[1963,91246,2875],{},[1664,91248,1673],{"stretchy":1666},[902,91250,91251],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,91254,91256],{"className":91255},[886],[888,91257,91258],{"xmlns":890},[892,91259,91260,91272],{},[895,91261,91262,91264,91266,91268,91270],{},[898,91263,1818],{},[1664,91265,1676],{},[1963,91267,2875],{},[1664,91269,1867],{},[898,91271,207],{},[902,91273,91274],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,91277,91278],{},[1928,91279],{"alt":91280,"className":91281,"src":91282},"imek-cobb-douglas-3d-plus-ic",[210,1932],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,91284,91286],{"className":91285},[886],[888,91287,91288],{"xmlns":890,"display":28566},[892,91289,91290,91340],{},[895,91291,91292,91294,91296,91302,91304,91310,91312,91314,91322,91324,91338],{},[898,91293,900],{},[1664,91295,1667],{"stretchy":1666},[2355,91297,91298,91300],{},[898,91299,1973],{},[1963,91301,2875],{},[1664,91303,1916],{"separator":1915},[2355,91305,91306,91308],{},[898,91307,1973],{},[1963,91309,1970],{},[1664,91311,1673],{"stretchy":1666},[1664,91313,1676],{},[1810,91315,91316,91318,91320],{},[898,91317,1973],{},[1963,91319,2875],{},[898,91321,207],{},[1664,91323,3753],{},[1810,91325,91326,91328,91330],{},[898,91327,1973],{},[1963,91329,1970],{},[895,91331,91332,91334,91336],{},[1963,91333,2875],{},[1664,91335,1867],{},[898,91337,207],{},[898,91339,1977],{"mathvariant":1726},[902,91341,91342],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[4436,91344,91345,91394,91516,91650],{},[724,91346,91347,91349,91350],{},[883,91348,53195],{}," Příklad 6.3 — ověření vlastností pro ",[883,91351,91353],{"className":91352},[886],[888,91354,91355],{"xmlns":890},[892,91356,91357,91391],{},[895,91358,91359,91361,91363,91377],{},[898,91360,900],{},[1664,91362,1676],{},[1810,91364,91365,91367,91369],{},[898,91366,1973],{},[1963,91368,2875],{},[895,91370,91371,91373,91375],{},[1963,91372,2875],{},[898,91374,5240],{"mathvariant":1726},[1963,91376,2944],{},[1810,91378,91379,91381,91383],{},[898,91380,1973],{},[1963,91382,1970],{},[895,91384,91385,91387,91389],{},[1963,91386,2774],{},[898,91388,5240],{"mathvariant":1726},[1963,91390,2944],{},[902,91392,91393],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,91395,91397],{"className":91396},[886],[888,91398,91399],{"xmlns":890,"display":28566},[892,91400,91401,91513],{},[895,91402,91403,91411,91413,91421,91437,91451,91453,91455,91457,91459,91467,91469,91477,91491,91507,91509,91511],{},[1810,91404,91405,91407,91409],{},[898,91406,900],{},[1963,91408,2875],{},[1664,91410,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,91412,1676],{},[2919,91414,91415],{"scriptlevel":2058,"displaystyle":1666},[2922,91416,91417,91419],{},[1963,91418,2875],{},[1963,91420,2944],{},[1810,91422,91423,91425,91427],{},[898,91424,1973],{},[1963,91426,2875],{},[895,91428,91429,91431,91433,91435],{},[1664,91430,1867],{},[1963,91432,2774],{},[898,91434,5240],{"mathvariant":1726},[1963,91436,2944],{},[1810,91438,91439,91441,91443],{},[898,91440,1973],{},[1963,91442,1970],{},[895,91444,91445,91447,91449],{},[1963,91446,2774],{},[898,91448,5240],{"mathvariant":1726},[1963,91450,2944],{},[1664,91452,3984],{},[1963,91454,2058],{},[1664,91456,1916],{"separator":1915},[6444,91458],{"width":15783},[1810,91460,91461,91463,91465],{},[898,91462,900],{},[1963,91464,1970],{},[1664,91466,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,91468,1676],{},[2919,91470,91471],{"scriptlevel":2058,"displaystyle":1666},[2922,91472,91473,91475],{},[1963,91474,2774],{},[1963,91476,2944],{},[1810,91478,91479,91481,91483],{},[898,91480,1973],{},[1963,91482,2875],{},[895,91484,91485,91487,91489],{},[1963,91486,2875],{},[898,91488,5240],{"mathvariant":1726},[1963,91490,2944],{},[1810,91492,91493,91495,91497],{},[898,91494,1973],{},[1963,91496,1970],{},[895,91498,91499,91501,91503,91505],{},[1664,91500,1867],{},[1963,91502,2875],{},[898,91504,5240],{"mathvariant":1726},[1963,91506,2944],{},[1664,91508,3984],{},[1963,91510,2058],{},[1664,91512,1916],{"separator":1915},[902,91514,91515],{"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,",[883,91517,91519],{"className":91518},[886],[888,91520,91521],{"xmlns":890,"display":28566},[892,91522,91523,91647],{},[895,91524,91525,91537,91539,91541,91549,91565,91579,91581,91583,91585,91587,91599,91601,91603,91611,91625,91641,91643,91645],{},[1810,91526,91527,91529,91531],{},[898,91528,900],{},[1963,91530,3483],{},[895,91532,91533,91535],{},[1664,91534,1728],{"mathvariant":1726},[1664,91536,1728],{"mathvariant":1726},[1664,91538,1676],{},[1664,91540,1867],{},[2919,91542,91543],{"scriptlevel":2058,"displaystyle":1666},[2922,91544,91545,91547],{},[1963,91546,2774],{},[1963,91548,42362],{},[1810,91550,91551,91553,91555],{},[898,91552,1973],{},[1963,91554,2875],{},[895,91556,91557,91559,91561,91563],{},[1664,91558,1867],{},[1963,91560,24701],{},[898,91562,5240],{"mathvariant":1726},[1963,91564,2944],{},[1810,91566,91567,91569,91571],{},[898,91568,1973],{},[1963,91570,1970],{},[895,91572,91573,91575,91577],{},[1963,91574,2774],{},[898,91576,5240],{"mathvariant":1726},[1963,91578,2944],{},[1664,91580,4022],{},[1963,91582,2058],{},[1664,91584,1916],{"separator":1915},[6444,91586],{"width":15783},[1810,91588,91589,91591,91593],{},[898,91590,900],{},[1963,91592,33046],{},[895,91594,91595,91597],{},[1664,91596,1728],{"mathvariant":1726},[1664,91598,1728],{"mathvariant":1726},[1664,91600,1676],{},[1664,91602,1867],{},[2919,91604,91605],{"scriptlevel":2058,"displaystyle":1666},[2922,91606,91607,91609],{},[1963,91608,2774],{},[1963,91610,42362],{},[1810,91612,91613,91615,91617],{},[898,91614,1973],{},[1963,91616,2875],{},[895,91618,91619,91621,91623],{},[1963,91620,2875],{},[898,91622,5240],{"mathvariant":1726},[1963,91624,2944],{},[1810,91626,91627,91629,91631],{},[898,91628,1973],{},[1963,91630,1970],{},[895,91632,91633,91635,91637,91639],{},[1664,91634,1867],{},[1963,91636,2826],{},[898,91638,5240],{"mathvariant":1726},[1963,91640,2944],{},[1664,91642,4022],{},[1963,91644,2058],{},[1664,91646,1916],{"separator":1915},[902,91648,91649],{"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,",[724,91651,91652],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,91654,91656],{"id":91655},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,91658,91659,91662],{},[38,91660,91661],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,91664,91666],{"className":91665},[886],[888,91667,91668],{"xmlns":890,"display":28566},[892,91669,91670,91713],{},[21254,91671,91672],{"width":28571},[21259,91673,91674,91676,91706,91708],{},[21262,91675],{"width":28576},[21262,91677,91678],{},[895,91679,91680,91682,91684,91690,91692,91698,91700,91702,91704],{},[898,91681,900],{},[1664,91683,1667],{"stretchy":1666},[2355,91685,91686,91688],{},[898,91687,1973],{},[1963,91689,2875],{},[1664,91691,1916],{"separator":1915},[2355,91693,91694,91696],{},[898,91695,1973],{},[1963,91697,1970],{},[1664,91699,1673],{"stretchy":1666},[1664,91701,1676],{},[898,91703,2034],{},[1664,91705,1916],{"separator":1915},[21262,91707],{"width":28576},[21262,91709,91710],{},[1690,91711,91712],{},"(6.7)",[902,91714,91715],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,91717,1709,91718,91731],{},[883,91719,91721],{"className":91720},[886],[888,91722,91723],{"xmlns":890},[892,91724,91725,91729],{},[895,91726,91727],{},[898,91728,2034],{},[902,91730,2034],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,91733,91735],{"className":91734},[886],[888,91736,91737],{"xmlns":890,"display":28566},[892,91738,91739,91780],{},[21254,91740,91741],{"width":28571},[21259,91742,91743,91745,91773,91775],{},[21262,91744],{"width":28576},[21262,91746,91747],{},[895,91748,91749,91757,91759,91767,91769,91771],{},[1810,91750,91751,91753,91755],{},[898,91752,1973],{},[1963,91754,2875],{},[898,91756,207],{},[1664,91758,3753],{},[1810,91760,91761,91763,91765],{},[898,91762,1973],{},[1963,91764,1970],{},[898,91766,1818],{},[1664,91768,1676],{},[898,91770,2034],{},[898,91772,1977],{"mathvariant":1726},[21262,91774],{"width":28576},[21262,91776,91777],{},[1690,91778,91779],{},"(6.8)",[902,91781,91782],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,91784,91785,91786,4924,91816,1885,91819,91832,91833,91868,91869,91886,91887,91916,91917,91920],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,91787,91789],{"className":91788},[886],[888,91790,91791],{"xmlns":890},[892,91792,91793,91813],{},[895,91794,91795,91797,91803,91805,91811],{},[1664,91796,1837],{"stretchy":1666},[2355,91798,91799,91801],{},[898,91800,1973],{},[1963,91802,2875],{},[1664,91804,1916],{"separator":1915},[2355,91806,91807,91809],{},[898,91808,1973],{},[1963,91810,1970],{},[1664,91812,1850],{"stretchy":1666},[902,91814,91815],{"encoding":904},"[Q_1, Q_2]",[38,91817,91818],{},"stejnou úrovní uspokojení",[883,91820,91822],{"className":91821},[886],[888,91823,91824],{"xmlns":890},[892,91825,91826,91830],{},[895,91827,91828],{},[898,91829,2034],{},[902,91831,2034],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,91834,91836],{"className":91835},[886],[888,91837,91838],{"xmlns":890},[892,91839,91840,91866],{},[895,91841,91842,91844,91846,91848,91850,91856,91858,91864],{},[898,91843,900],{},[1664,91845,1676],{},[898,91847,900],{},[1664,91849,1667],{"stretchy":1666},[2355,91851,91852,91854],{},[898,91853,1973],{},[1963,91855,2875],{},[1664,91857,1916],{"separator":1915},[2355,91859,91860,91862],{},[898,91861,1973],{},[1963,91863,1970],{},[1664,91865,1673],{"stretchy":1666},[902,91867,87956],{"encoding":904}," s rovinami ",[883,91870,91872],{"className":91871},[886],[888,91873,91874],{"xmlns":890},[892,91875,91876,91884],{},[895,91877,91878,91880,91882],{},[898,91879,900],{},[1664,91881,1676],{},[898,91883,2034],{},[902,91885,87172],{"encoding":904}," rovnoběžnými s rovinou ",[883,91888,91890],{"className":91889},[886],[888,91891,91892],{"xmlns":890},[892,91893,91894,91914],{},[895,91895,91896,91898,91904,91906,91912],{},[1664,91897,1667],{"stretchy":1666},[2355,91899,91900,91902],{},[898,91901,1973],{},[1963,91903,2875],{},[1664,91905,1916],{"separator":1915},[2355,91907,91908,91910],{},[898,91909,1973],{},[1963,91911,1970],{},[1664,91913,1673],{"stretchy":1666},[902,91915,90119],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,91918,91919],{},"izokvantami"," produkčních funkcí.",[724,91922,91923],{},[614,91924,91925,91926,89997,91944,91962,91963,1977],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,91927,91929],{"className":91928},[886],[888,91930,91931],{"xmlns":890},[892,91932,91933,91941],{},[895,91934,91935,91937,91939],{},[898,91936,207],{},[1664,91938,4022],{},[898,91940,1818],{},[902,91942,91943],{"encoding":904},"a \u003C b",[883,91945,91947],{"className":91946},[886],[888,91948,91949],{"xmlns":890},[892,91950,91951,91959],{},[895,91952,91953,91955,91957],{},[898,91954,207],{},[1664,91956,3984],{},[898,91958,1818],{},[902,91960,91961],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,91964,91966],{"className":91965},[886],[888,91967,91968],{"xmlns":890},[892,91969,91970,91994],{},[895,91971,91972,91978,91980,91986,91988],{},[2355,91973,91974,91976],{},[898,91975,2034],{},[1963,91977,2058],{},[1664,91979,4022],{},[2355,91981,91982,91984],{},[898,91983,2034],{},[1963,91985,2875],{},[1664,91987,4022],{},[2355,91989,91990,91992],{},[898,91991,2034],{},[1963,91993,1970],{},[902,91995,91996],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,91998,91999],{},[614,92000,92001,92002,92031,92032,92090,92091,92109],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,92003,92005],{"className":92004},[886],[888,92006,92007],{"xmlns":890},[892,92008,92009,92029],{},[895,92010,92011,92013,92019,92021,92027],{},[1664,92012,1667],{"stretchy":1666},[2355,92014,92015,92017],{},[898,92016,1973],{},[1963,92018,2875],{},[1664,92020,1916],{"separator":1915},[2355,92022,92023,92025],{},[898,92024,1973],{},[1963,92026,1970],{},[1664,92028,1673],{"stretchy":1666},[902,92030,90119],{"encoding":904},"; body ",[883,92033,92035],{"className":92034},[886],[888,92036,92037],{"xmlns":890},[892,92038,92039,92087],{},[895,92040,92041,92043,92045,92047,92053,92055,92061,92063,92065,92067,92069,92071,92077,92079,92085],{},[898,92042,4822],{},[1664,92044,1676],{},[1664,92046,1837],{"stretchy":1666},[2355,92048,92049,92051],{},[898,92050,207],{},[1963,92052,2875],{},[1664,92054,1916],{"separator":1915},[2355,92056,92057,92059],{},[898,92058,207],{},[1963,92060,1970],{},[1664,92062,1850],{"stretchy":1666},[1664,92064,1916],{"separator":1915},[898,92066,23753],{},[1664,92068,1676],{},[1664,92070,1837],{"stretchy":1666},[2355,92072,92073,92075],{},[898,92074,1818],{},[1963,92076,2875],{},[1664,92078,1916],{"separator":1915},[2355,92080,92081,92083],{},[898,92082,1818],{},[1963,92084,1970],{},[1664,92086,1850],{"stretchy":1666},[902,92088,92089],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,92092,92094],{"className":92093},[886],[888,92095,92096],{"xmlns":890},[892,92097,92098,92106],{},[895,92099,92100,92102,92104],{},[898,92101,1703],{},[1664,92103,1916],{"separator":1915},[898,92105,2379],{},[902,92107,92108],{"encoding":904},"C, D"," na vyšší hladině.",[4436,92111,92112],{},[724,92113,92114,92116,92117,92179,92180,92224,92225,92259,92260,26689,92278,92259,92332,26689,92350,92426],{},[883,92115,53195],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,92118,92120],{"className":92119},[886],[888,92121,92122],{"xmlns":890},[892,92123,92124,92176],{},[895,92125,92126,92128,92130,92136,92138,92144,92146,92148,92162],{},[898,92127,900],{},[1664,92129,1667],{"stretchy":1666},[2355,92131,92132,92134],{},[898,92133,1973],{},[1963,92135,2875],{},[1664,92137,1916],{"separator":1915},[2355,92139,92140,92142],{},[898,92141,1973],{},[1963,92143,1970],{},[1664,92145,1673],{"stretchy":1666},[1664,92147,1676],{},[1810,92149,92150,92152,92154],{},[898,92151,1973],{},[1963,92153,2875],{},[895,92155,92156,92158,92160],{},[1963,92157,2875],{},[898,92159,5240],{"mathvariant":1726},[1963,92161,2944],{},[1810,92163,92164,92166,92168],{},[898,92165,1973],{},[1963,92167,1970],{},[895,92169,92170,92172,92174],{},[1963,92171,2774],{},[898,92173,5240],{"mathvariant":1726},[1963,92175,2944],{},[902,92177,92178],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,92181,92183],{"className":92182},[886],[888,92184,92185],{"xmlns":890},[892,92186,92187,92221],{},[895,92188,92189,92203,92217,92219],{},[1810,92190,92191,92193,92195],{},[898,92192,1973],{},[1963,92194,2875],{},[895,92196,92197,92199,92201],{},[1963,92198,2875],{},[898,92200,5240],{"mathvariant":1726},[1963,92202,2944],{},[1810,92204,92205,92207,92209],{},[898,92206,1973],{},[1963,92208,1970],{},[895,92210,92211,92213,92215],{},[1963,92212,2774],{},[898,92214,5240],{"mathvariant":1726},[1963,92216,2944],{},[1664,92218,1676],{},[898,92220,2034],{},[902,92222,92223],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,92226,92228],{"className":92227},[886],[888,92229,92230],{"xmlns":890},[892,92231,92232,92256],{},[895,92233,92234,92240,92248,92250],{},[2355,92235,92236,92238],{},[898,92237,1973],{},[1963,92239,2875],{},[1810,92241,92242,92244,92246],{},[898,92243,1973],{},[1963,92245,1970],{},[1963,92247,2774],{},[1664,92249,1676],{},[1720,92251,92252,92254],{},[898,92253,2034],{},[1963,92255,2944],{},[902,92257,92258],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,92261,92263],{"className":92262},[886],[888,92264,92265],{"xmlns":890},[892,92266,92267,92275],{},[895,92268,92269,92271,92273],{},[898,92270,2034],{},[1664,92272,1676],{},[1963,92274,2875],{},[902,92276,92277],{"encoding":904},"c = 1",[883,92279,92281],{"className":92280},[886],[888,92282,92283],{"xmlns":890},[892,92284,92285,92329],{},[895,92286,92287,92293,92295,92311,92313],{},[2355,92288,92289,92291],{},[898,92290,1973],{},[1963,92292,1970],{},[1664,92294,1676],{},[1810,92296,92297,92299,92301],{},[898,92298,1973],{},[1963,92300,2875],{},[895,92302,92303,92305,92307,92309],{},[1664,92304,1867],{},[1963,92306,2875],{},[898,92308,5240],{"mathvariant":1726},[1963,92310,2774],{},[1664,92312,1676],{},[2919,92314,92315],{"scriptlevel":2058,"displaystyle":1915},[2922,92316,92317,92319],{},[1963,92318,2875],{},[82527,92320,92321,92327],{},[2355,92322,92323,92325],{},[898,92324,1973],{},[1963,92326,2875],{},[1963,92328,2774],{},[902,92330,92331],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,92333,92335],{"className":92334},[886],[888,92336,92337],{"xmlns":890},[892,92338,92339,92347],{},[895,92340,92341,92343,92345],{},[898,92342,2034],{},[1664,92344,1676],{},[1963,92346,1970],{},[902,92348,92349],{"encoding":904},"c = 2",[883,92351,92353],{"className":92352},[886],[888,92354,92355],{"xmlns":890},[892,92356,92357,92423],{},[895,92358,92359,92365,92367,92379,92381,92397,92399],{},[2355,92360,92361,92363],{},[898,92362,1973],{},[1963,92364,1970],{},[1664,92366,1676],{},[1720,92368,92369,92371],{},[1963,92370,1970],{},[895,92372,92373,92375,92377],{},[1963,92374,2944],{},[898,92376,5240],{"mathvariant":1726},[1963,92378,2774],{},[1664,92380,3753],{},[1810,92382,92383,92385,92387],{},[898,92384,1973],{},[1963,92386,2875],{},[895,92388,92389,92391,92393,92395],{},[1664,92390,1867],{},[1963,92392,2875],{},[898,92394,5240],{"mathvariant":1726},[1963,92396,2774],{},[1664,92398,1676],{},[2919,92400,92401],{"scriptlevel":2058,"displaystyle":1915},[2922,92402,92403,92413],{},[895,92404,92405,92407],{},[1963,92406,1970],{},[82527,92408,92409,92411],{},[1963,92410,1970],{},[1963,92412,2774],{},[82527,92414,92415,92421],{},[2355,92416,92417,92419],{},[898,92418,1973],{},[1963,92420,2875],{},[1963,92422,2774],{},[902,92424,92425],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,92428,92430],{"id":92429},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,92432,92433],{},[1928,92434],{"alt":92435,"className":92436,"src":92437},"imek-ic-4vlastnosti-anotovane",[210,1932],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[4436,92439,92440,92449,92496,92540,92546,92552],{},[724,92441,92442,92444,92445,92448],{},[883,92443,4978],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,92446,92447],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,92450,92451],{},[883,92452,92454],{"className":92453},[886],[888,92455,92456],{"xmlns":890},[892,92457,92458,92493],{},[895,92459,92460,92463,92465,92467,92469,92471,92489,92491],{},[898,92461,92462],{"mathvariant":1726},"tg",[1664,92464,56700],{},[898,92466,19362],{},[1664,92468,1676],{},[1664,92470,1867],{},[2922,92472,92473,92481],{},[1810,92474,92475,92477,92479],{},[898,92476,900],{},[1963,92478,2875],{},[1664,92480,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1810,92482,92483,92485,92487],{},[898,92484,900],{},[1963,92486,1970],{},[1664,92488,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,92490,4022],{},[1963,92492,2058],{},[902,92494,92495],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,92497,92498,92499,92539],{},"(derivace implicitně zadané funkce ",[883,92500,92502],{"className":92501},[886],[888,92503,92504],{"xmlns":890},[892,92505,92506,92536],{},[895,92507,92508,92510,92512,92518,92520,92526,92528,92530,92532,92534],{},[898,92509,900],{},[1664,92511,1667],{"stretchy":1666},[2355,92513,92514,92516],{},[898,92515,1973],{},[1963,92517,2875],{},[1664,92519,1916],{"separator":1915},[2355,92521,92522,92524],{},[898,92523,1973],{},[1963,92525,1970],{},[1664,92527,1673],{"stretchy":1666},[1664,92529,1867],{},[898,92531,2034],{},[1664,92533,1676],{},[1963,92535,2058],{},[902,92537,92538],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,92541,92542,92545],{},[38,92543,92544],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,92547,92548,92551],{},[38,92549,92550],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,92553,92554,92557,92558,92576,92577,92593,92594,92597],{},[38,92555,92556],{},"4° Konvexní."," Pro každé dva body ",[883,92559,92561],{"className":92560},[886],[888,92562,92563],{"xmlns":890},[892,92564,92565,92573],{},[895,92566,92567,92569,92571],{},[898,92568,4822],{},[1664,92570,1916],{"separator":1915},[898,92572,23753],{},[902,92574,92575],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,92578,92580],{"className":92579},[886],[888,92581,92582],{"xmlns":890},[892,92583,92584,92590],{},[895,92585,92586,92588],{},[898,92587,4822],{},[898,92589,23753],{},[902,92591,92592],{"encoding":904},"AB"," ve ",[38,92595,92596],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,92599,92600],{},[614,92601,92602,92603,92638,92639,1977],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,92604,92606],{"className":92605},[886],[888,92607,92608],{"xmlns":890},[892,92609,92610,92636],{},[895,92611,92612,92614,92616,92622,92624,92630,92632,92634],{},[898,92613,900],{},[1664,92615,1667],{"stretchy":1666},[2355,92617,92618,92620],{},[898,92619,1973],{},[1963,92621,2875],{},[1664,92623,1916],{"separator":1915},[2355,92625,92626,92628],{},[898,92627,1973],{},[1963,92629,1970],{},[1664,92631,1673],{"stretchy":1666},[1664,92633,1676],{},[898,92635,2034],{},[902,92637,10331],{"encoding":904}," s tečnou se sklonem ",[883,92640,92642],{"className":92641},[886],[888,92643,92644],{"xmlns":890},[892,92645,92646,92654],{},[895,92647,92648,92650,92652],{},[898,92649,92462],{"mathvariant":1726},[1664,92651,56700],{},[898,92653,19362],{},[902,92655,92656],{"encoding":904},"\\operatorname{tg}\\alpha",[115,92658,92660],{"id":92659},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,92662,92663,1885,92666,10588,92679,92682],{},[38,92664,92665],{},"Mezní míra komoditní substituce",[883,92667,92669],{"className":92668},[886],[888,92670,92671],{"xmlns":890},[892,92672,92673,92677],{},[895,92674,92675],{},[1690,92676,11165],{},[902,92678,28738],{"encoding":904},[38,92680,92681],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,92684,92686],{"className":92685},[886],[888,92687,92688],{"xmlns":890,"display":28566},[892,92689,92690,92777],{},[21254,92691,92692],{"width":28571},[21259,92693,92694,92696,92770,92772],{},[21262,92695],{"width":28576},[21262,92697,92698],{},[895,92699,92700,92702,92704,92706,92708,92714,92716,92722,92724,92726,92748,92750,92768],{},[1690,92701,11165],{},[1664,92703,1676],{},[1690,92705,11165],{},[1664,92707,1667],{"stretchy":1666},[2355,92709,92710,92712],{},[898,92711,1973],{},[1963,92713,2875],{},[1664,92715,1916],{"separator":1915},[2355,92717,92718,92720],{},[898,92719,1973],{},[1963,92721,1970],{},[1664,92723,1673],{"stretchy":1666},[1664,92725,1676],{},[2922,92727,92728,92738],{},[895,92729,92730,92732],{},[898,92731,1956],{},[2355,92733,92734,92736],{},[898,92735,900],{},[1963,92737,2875],{},[895,92739,92740,92742],{},[898,92741,1956],{},[2355,92743,92744,92746],{},[898,92745,900],{},[1963,92747,1970],{},[1664,92749,1676],{},[2922,92751,92752,92760],{},[1810,92753,92754,92756,92758],{},[898,92755,900],{},[1963,92757,2875],{},[1664,92759,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1810,92761,92762,92764,92766],{},[898,92763,900],{},[1963,92765,1970],{},[1664,92767,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[898,92769,1977],{"mathvariant":1726},[21262,92771],{"width":28576},[21262,92773,92774],{},[1690,92775,92776],{},"(6.9)",[902,92778,92779],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,92781,92782,92783,92817,92818,92850,92851,92886,92887,92900],{},"Geometricky: ",[883,92784,92786],{"className":92785},[886],[888,92787,92788],{"xmlns":890},[892,92789,92790,92814],{},[895,92791,92792,92794],{},[1664,92793,1867],{},[2919,92795,92796],{"scriptlevel":2058,"displaystyle":1666},[2922,92797,92798,92806],{},[1810,92799,92800,92802,92804],{},[898,92801,900],{},[1963,92803,2875],{},[1664,92805,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1810,92807,92808,92810,92812],{},[898,92809,900],{},[1963,92811,1970],{},[1664,92813,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,92815,92816],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,92819,92821],{"className":92820},[886],[888,92822,92823],{"xmlns":890},[892,92824,92825,92847],{},[895,92826,92827,92833,92835,92837,92839,92845],{},[2355,92828,92829,92831],{},[898,92830,1973],{},[1963,92832,1970],{},[1664,92834,1676],{},[898,92836,1682],{},[1664,92838,1667],{"stretchy":1666},[2355,92840,92841,92843],{},[898,92842,1973],{},[1963,92844,2875],{},[1664,92846,1673],{"stretchy":1666},[902,92848,92849],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,92852,92854],{"className":92853},[886],[888,92855,92856],{"xmlns":890},[892,92857,92858,92884],{},[895,92859,92860,92862,92864,92870,92872,92878,92880,92882],{},[898,92861,900],{},[1664,92863,1667],{"stretchy":1666},[2355,92865,92866,92868],{},[898,92867,1973],{},[1963,92869,2875],{},[1664,92871,1916],{"separator":1915},[2355,92873,92874,92876],{},[898,92875,1973],{},[1963,92877,1970],{},[1664,92879,1673],{"stretchy":1666},[1664,92881,1676],{},[898,92883,2034],{},[902,92885,10331],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,92888,92890],{"className":92889},[886],[888,92891,92892],{"xmlns":890},[892,92893,92894,92898],{},[895,92895,92896],{},[1690,92897,11165],{},[902,92899,28738],{"encoding":904}," chápeme jako velikost kompenzace.",[4436,92902,92903],{},[724,92904,92905,92907,92908,1762,92940,92978,92979,92996,92997,93014],{},[883,92906,4723],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,92909,92911],{"className":92910},[886],[888,92912,92913],{"xmlns":890},[892,92914,92915,92937],{},[895,92916,92917,92919,92921,92927,92929,92935],{},[1690,92918,11165],{},[1664,92920,1667],{"stretchy":1666},[2355,92922,92923,92925],{},[898,92924,1973],{},[1963,92926,2875],{},[1664,92928,1916],{"separator":1915},[2355,92930,92931,92933],{},[898,92932,1973],{},[1963,92934,1970],{},[1664,92936,1673],{"stretchy":1666},[902,92938,92939],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,92941,92942,92943,29503,92960,92977],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,92944,92946],{"className":92945},[886],[888,92947,92948],{"xmlns":890},[892,92949,92950,92958],{},[895,92951,92952],{},[2355,92953,92954,92956],{},[898,92955,1973],{},[1963,92957,2875],{},[902,92959,29502],{"encoding":904},[883,92961,92963],{"className":92962},[886],[888,92964,92965],{"xmlns":890},[892,92966,92967,92975],{},[895,92968,92969],{},[2355,92970,92971,92973],{},[898,92972,1973],{},[1963,92974,1970],{},[902,92976,29521],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,92980,92982],{"className":92981},[886],[888,92983,92984],{"xmlns":890},[892,92985,92986,92994],{},[895,92987,92988],{},[2355,92989,92990,92992],{},[898,92991,1973],{},[1963,92993,1970],{},[902,92995,29521],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,92998,93000],{"className":92999},[886],[888,93001,93002],{"xmlns":890},[892,93003,93004,93012],{},[895,93005,93006],{},[2355,93007,93008,93010],{},[898,93009,1973],{},[1963,93011,2875],{},[902,93013,29502],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,93016,93017,93018,30444],{},"Pro obecnou změnu ",[883,93019,93021],{"className":93020},[886],[888,93022,93023],{"xmlns":890},[892,93024,93025,93035],{},[895,93026,93027,93029],{},[898,93028,1695],{"mathvariant":1726},[2355,93030,93031,93033],{},[898,93032,1973],{},[1963,93034,2875],{},[902,93036,93037],{"encoding":904},"\\mathrm{d} Q_1",[883,93039,93041],{"className":93040},[886],[888,93042,93043],{"xmlns":890,"display":28566},[892,93044,93045,93098],{},[21254,93046,93047],{"width":28571},[21259,93048,93049,93051,93091,93093],{},[21262,93050],{"width":28576},[21262,93052,93053],{},[895,93054,93055,93057,93063,93065,93067,93073,93075,93077,93079,93081,93083,93089],{},[898,93056,3468],{"mathvariant":1726},[2355,93058,93059,93061],{},[898,93060,1973],{},[1963,93062,1970],{},[1664,93064,3315],{},[898,93066,1695],{"mathvariant":1726},[2355,93068,93069,93071],{},[898,93070,1973],{},[1963,93072,1970],{},[1664,93074,1676],{},[1664,93076,1867],{},[1690,93078,11165],{},[1664,93080,3753],{},[898,93082,1695],{"mathvariant":1726},[2355,93084,93085,93087],{},[898,93086,1973],{},[1963,93088,2875],{},[1664,93090,1916],{"separator":1915},[21262,93092],{"width":28576},[21262,93094,93095],{},[1690,93096,93097],{},"(6.10)",[902,93099,93100],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,93102,93104],{"className":93103},[886],[888,93105,93106],{"xmlns":890,"display":28566},[892,93107,93108,93155],{},[21254,93109,93110],{"width":28571},[21259,93111,93112,93114,93148,93150],{},[21262,93113],{"width":28576},[21262,93115,93116],{},[895,93117,93118,93120,93126,93128,93130,93136,93138,93140,93146],{},[898,93119,1695],{"mathvariant":1726},[2355,93121,93122,93124],{},[898,93123,1973],{},[1963,93125,2875],{},[1664,93127,1676],{},[1664,93129,1867],{},[2922,93131,93132,93134],{},[1963,93133,2875],{},[1690,93135,11165],{},[1690,93137,1692],{},[898,93139,1695],{"mathvariant":1726},[2355,93141,93142,93144],{},[898,93143,1973],{},[1963,93145,1970],{},[898,93147,1977],{"mathvariant":1726},[21262,93149],{"width":28576},[21262,93151,93152],{},[1690,93153,93154],{},"(6.11)",[902,93156,93157],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[4436,93159,93160,93226,93343],{},[724,93161,93162,93164,93165,30444],{},[883,93163,53195],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,93166,93168],{"className":93167},[886],[888,93169,93170],{"xmlns":890},[892,93171,93172,93224],{},[895,93173,93174,93176,93178,93184,93186,93192,93194,93196,93210],{},[898,93175,900],{},[1664,93177,1667],{"stretchy":1666},[2355,93179,93180,93182],{},[898,93181,1973],{},[1963,93183,2875],{},[1664,93185,1916],{"separator":1915},[2355,93187,93188,93190],{},[898,93189,1973],{},[1963,93191,1970],{},[1664,93193,1673],{"stretchy":1666},[1664,93195,1676],{},[1810,93197,93198,93200,93202],{},[898,93199,1973],{},[1963,93201,2875],{},[895,93203,93204,93206,93208],{},[1963,93205,2875],{},[898,93207,5240],{"mathvariant":1726},[1963,93209,1970],{},[1810,93211,93212,93214,93216],{},[898,93213,1973],{},[1963,93215,1970],{},[895,93217,93218,93220,93222],{},[1963,93219,2875],{},[898,93221,5240],{"mathvariant":1726},[1963,93223,1970],{},[902,93225,30443],{"encoding":904},[724,93227,93228],{},[883,93229,93231],{"className":93230},[886],[888,93232,93233],{"xmlns":890},[892,93234,93235,93341],{},[895,93236,93237,93239,93241,93323,93325,93339],{},[1690,93238,11165],{},[1664,93240,1676],{},[2922,93242,93243,93283],{},[895,93244,93245,93253,93269],{},[2919,93246,93247],{"scriptlevel":2058,"displaystyle":1666},[2922,93248,93249,93251],{},[1963,93250,2875],{},[1963,93252,1970],{},[1810,93254,93255,93257,93259],{},[898,93256,1973],{},[1963,93258,2875],{},[895,93260,93261,93263,93265,93267],{},[1664,93262,1867],{},[1963,93264,2875],{},[898,93266,5240],{"mathvariant":1726},[1963,93268,1970],{},[1810,93270,93271,93273,93275],{},[898,93272,1973],{},[1963,93274,1970],{},[895,93276,93277,93279,93281],{},[1963,93278,2875],{},[898,93280,5240],{"mathvariant":1726},[1963,93282,1970],{},[895,93284,93285,93293,93307],{},[2919,93286,93287],{"scriptlevel":2058,"displaystyle":1666},[2922,93288,93289,93291],{},[1963,93290,2875],{},[1963,93292,1970],{},[1810,93294,93295,93297,93299],{},[898,93296,1973],{},[1963,93298,2875],{},[895,93300,93301,93303,93305],{},[1963,93302,2875],{},[898,93304,5240],{"mathvariant":1726},[1963,93306,1970],{},[1810,93308,93309,93311,93313],{},[898,93310,1973],{},[1963,93312,1970],{},[895,93314,93315,93317,93319,93321],{},[1664,93316,1867],{},[1963,93318,2875],{},[898,93320,5240],{"mathvariant":1726},[1963,93322,1970],{},[1664,93324,1676],{},[2922,93326,93327,93333],{},[2355,93328,93329,93331],{},[898,93330,1973],{},[1963,93332,1970],{},[2355,93334,93335,93337],{},[898,93336,1973],{},[1963,93338,2875],{},[898,93340,1977],{"mathvariant":1726},[902,93342,30562],{"encoding":904},[724,93344,30565,93345,1748,93388,30613,93390,93409],{},[883,93346,93348],{"className":93347},[886],[888,93349,93350],{"xmlns":890},[892,93351,93352,93386],{},[895,93353,93354,93356,93358,93360,93362,93364,93366,93368,93376,93378],{},[1690,93355,11165],{},[1664,93357,1667],{"stretchy":1666},[1963,93359,30581],{},[1664,93361,1916],{"separator":1915},[1963,93363,15609],{},[1664,93365,1673],{"stretchy":1666},[1664,93367,1676],{},[2919,93369,93370],{"scriptlevel":2058,"displaystyle":1666},[2922,93371,93372,93374],{},[1963,93373,15609],{},[1963,93375,30581],{},[1664,93377,1676],{},[2919,93379,93380],{"scriptlevel":2058,"displaystyle":1666},[2922,93381,93382,93384],{},[1963,93383,2826],{},[1963,93385,2774],{},[902,93387,30610],{"encoding":904},[614,93389,9779],{},[883,93391,93393],{"className":93392},[886],[888,93394,93395],{"xmlns":890},[892,93396,93397,93407],{},[895,93398,93399],{},[2919,93400,93401],{"scriptlevel":2058,"displaystyle":1666},[2922,93402,93403,93405],{},[1963,93404,2826],{},[1963,93406,2774],{},[902,93408,30633],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,93411,93412,93413,93417],{},"(Paralelou je ",[207,93414,93416],{"className":93415,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,93419,93421],{"id":93420},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,93423,93424,93425,93428],{},"Rámcově se v kapitole 6 studují ",[38,93426,93427],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,93430,93431,93567],{},[123,93432,93433,93435,93436,10720,93467,1885,93470,93519,93520,1977],{},[38,93434,28752],{}," — maximalizace ",[883,93437,93439],{"className":93438},[886],[888,93440,93441],{"xmlns":890},[892,93442,93443,93465],{},[895,93444,93445,93447,93449,93455,93457,93463],{},[898,93446,900],{},[1664,93448,1667],{"stretchy":1666},[2355,93450,93451,93453],{},[898,93452,1973],{},[1963,93454,2875],{},[1664,93456,1916],{"separator":1915},[2355,93458,93459,93461],{},[898,93460,1973],{},[1963,93462,1970],{},[1664,93464,1673],{"stretchy":1666},[902,93466,16843],{"encoding":904},[38,93468,93469],{},"rozpočtovém omezení",[883,93471,93473],{"className":93472},[886],[888,93474,93475],{"xmlns":890},[892,93476,93477,93517],{},[895,93478,93479,93485,93487,93495,93501,93503,93511],{},[1720,93480,93481,93483],{},[898,93482,9692],{},[1664,93484,4920],{},[1664,93486,1676],{},[1810,93488,93489,93491,93493],{},[898,93490,2398],{},[1963,93492,2875],{},[1664,93494,4920],{},[2355,93496,93497,93499],{},[898,93498,1973],{},[1963,93500,2875],{},[1664,93502,1700],{},[1810,93504,93505,93507,93509],{},[898,93506,2398],{},[1963,93508,1970],{},[1664,93510,4920],{},[2355,93512,93513,93515],{},[898,93514,1973],{},[1963,93516,1970],{},[902,93518,17798],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,93521,93523],{"className":93522},[886],[888,93524,93525],{"xmlns":890},[892,93526,93527,93565],{},[895,93528,93529,93535,93537,93543,93545,93551,93553,93559,93561,93563],{},[2355,93530,93531,93533],{},[898,93532,1973],{},[898,93534,18290],{},[1664,93536,1676],{},[2355,93538,93539,93541],{},[898,93540,2379],{},[898,93542,18290],{},[1664,93544,1667],{"stretchy":1666},[2355,93546,93547,93549],{},[898,93548,2398],{},[1963,93550,2875],{},[1664,93552,1916],{"separator":1915},[2355,93554,93555,93557],{},[898,93556,2398],{},[1963,93558,1970],{},[1664,93560,1916],{"separator":1915},[898,93562,9692],{},[1664,93564,1673],{"stretchy":1666},[902,93566,36955],{"encoding":904},[123,93568,93569,28401,93572,28444,93618,93635,93636,1977],{},[38,93570,93571],{},"Duální úloha",[883,93573,93575],{"className":93574},[886],[888,93576,93577],{"xmlns":890},[892,93578,93579,93615],{},[895,93580,93581,93583,93585,93593,93599,93601,93609],{},[898,93582,4819],{},[1664,93584,1676],{},[1810,93586,93587,93589,93591],{},[898,93588,2398],{},[1963,93590,2875],{},[1664,93592,4920],{},[2355,93594,93595,93597],{},[898,93596,1973],{},[1963,93598,2875],{},[1664,93600,1700],{},[1810,93602,93603,93605,93607],{},[898,93604,2398],{},[1963,93606,1970],{},[1664,93608,4920],{},[2355,93610,93611,93613],{},[898,93612,1973],{},[1963,93614,1970],{},[902,93616,93617],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,93619,93621],{"className":93620},[886],[888,93622,93623],{"xmlns":890},[892,93624,93625,93633],{},[895,93626,93627],{},[1720,93628,93629,93631],{},[898,93630,900],{},[1664,93632,4920],{},[902,93634,28462],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,93637,93639],{"className":93638},[886],[888,93640,93641],{"xmlns":890},[892,93642,93643,93681],{},[895,93644,93645,93651,93653,93659,93661,93667,93669,93675,93677,93679],{},[2355,93646,93647,93649],{},[898,93648,1973],{},[898,93650,18290],{},[1664,93652,1676],{},[2355,93654,93655,93657],{},[898,93656,2379],{},[898,93658,18290],{},[1664,93660,1667],{"stretchy":1666},[2355,93662,93663,93665],{},[898,93664,2398],{},[1963,93666,2875],{},[1664,93668,1916],{"separator":1915},[2355,93670,93671,93673],{},[898,93672,2398],{},[1963,93674,1970],{},[1664,93676,1916],{"separator":1915},[898,93678,900],{},[1664,93680,1673],{"stretchy":1666},[902,93682,18323],{"encoding":904},[724,93684,93685,93686,93689,93690,1885,93693,93732],{},"Obě úlohy se řeší ",[207,93687,28467],{"className":93688,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,93691,93692],{},"tentýž bod dotyku",[883,93694,93696],{"className":93695},[886],[888,93697,93698],{"xmlns":890},[892,93699,93700,93730],{},[895,93701,93702,93708,93710,93718,93720,93728],{},[1720,93703,93704,93706],{},[898,93705,1973],{},[1664,93707,4920],{},[1664,93709,1837],{"stretchy":1666},[1810,93711,93712,93714,93716],{},[898,93713,1973],{},[1963,93715,2875],{},[1664,93717,4920],{},[1664,93719,1916],{"separator":1915},[1810,93721,93722,93724,93726],{},[898,93723,1973],{},[1963,93725,1970],{},[1664,93727,4920],{},[1664,93729,1850],{"stretchy":1666},[902,93731,28827],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,93734,93736],{"className":93735},[886],[888,93737,93738],{"xmlns":890,"display":28566},[892,93739,93740,93786],{},[895,93741,93742,93744,93746,93764,93766,93784],{},[1690,93743,11165],{},[1664,93745,1676],{},[2922,93747,93748,93756],{},[1810,93749,93750,93752,93754],{},[898,93751,900],{},[1963,93753,2875],{},[1664,93755,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1810,93757,93758,93760,93762],{},[898,93759,900],{},[1963,93761,1970],{},[1664,93763,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,93765,1676],{},[2922,93767,93768,93776],{},[1810,93769,93770,93772,93774],{},[898,93771,2398],{},[1963,93773,2875],{},[1664,93775,4920],{},[1810,93777,93778,93780,93782],{},[898,93779,2398],{},[1963,93781,1970],{},[1664,93783,4920],{},[898,93785,1977],{"mathvariant":1726},[902,93787,93788],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,93790,93791],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[4436,93793,93794],{},[724,93795,93796,93798,93799,93802,93803,93806,93807,93834,93835,93869,93870,93904,93905,93948,93949,93952,93953,1977],{},[883,93797,4723],{}," Pro detailní postup viz ",[207,93800,37254],{"className":93801,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,93804,93805],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,93808,93810],{"className":93809},[886],[888,93811,93812],{"xmlns":890},[892,93813,93814,93832],{},[895,93815,93816,93818,93820,93826],{},[898,93817,900],{},[1664,93819,1676],{},[2355,93821,93822,93824],{},[898,93823,1973],{},[1963,93825,2875],{},[2355,93827,93828,93830],{},[898,93829,1973],{},[1963,93831,1970],{},[902,93833,30726],{"encoding":904}," s výsledkem ",[883,93836,93838],{"className":93837},[886],[888,93839,93840],{"xmlns":890},[892,93841,93842,93866],{},[895,93843,93844,93850,93852,93854,93856,93862,93864],{},[2355,93845,93846,93848],{},[898,93847,1973],{},[1963,93849,2875],{},[1664,93851,1676],{},[1963,93853,5570],{},[1664,93855,1916],{"separator":1915},[2355,93857,93858,93860],{},[898,93859,1973],{},[1963,93861,1970],{},[1664,93863,1676],{},[1963,93865,3442],{},[902,93867,93868],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,93871,93873],{"className":93872},[886],[888,93874,93875],{"xmlns":890},[892,93876,93877,93901],{},[895,93878,93879,93885,93887,93889,93891,93897,93899],{},[2355,93880,93881,93883],{},[898,93882,1973],{},[1963,93884,2875],{},[1664,93886,1676],{},[1963,93888,2944],{},[1664,93890,1916],{"separator":1915},[2355,93892,93893,93895],{},[898,93894,1973],{},[1963,93896,1970],{},[1664,93898,1676],{},[1963,93900,2875],{},[902,93902,93903],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,93906,93908],{"className":93907},[886],[888,93909,93910],{"xmlns":890},[892,93911,93912,93946],{},[895,93913,93914,93916,93918,93932],{},[898,93915,900],{},[1664,93917,1676],{},[1810,93919,93920,93922,93924],{},[898,93921,1973],{},[1963,93923,2875],{},[895,93925,93926,93928,93930],{},[1963,93927,2875],{},[898,93929,5240],{"mathvariant":1726},[1963,93931,1970],{},[1810,93933,93934,93936,93938],{},[898,93935,1973],{},[1963,93937,1970],{},[895,93939,93940,93942,93944],{},[1963,93941,2875],{},[898,93943,5240],{"mathvariant":1726},[1963,93945,1970],{},[902,93947,33659],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,93950,93951],{},"6.8–6.13"," jsou na stránce ",[207,93954,28267],{"className":93955,"dataFsResolvedFilePath":911,"href":912},[210],[115,93957,93959],{"id":93958},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,93961,93962,93963,93976,93977,93979,93980,93982,93983,93985,93986,93988,93989,93991,93992,93994,93995,1885,93997,94032,94033,94046,94047,94050,94051,94054,94055,1977],{},"Každá ",[883,93964,93966],{"className":93965},[886],[888,93967,93968],{"xmlns":890},[892,93969,93970,93974],{},[895,93971,93972],{},[898,93973,37360],{},[902,93975,37360],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,93978,87310],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,93981,87794],{}," a současně ",[38,93984,87313],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,93987,87318],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,93990,53177],{}," (6.4) a druhé parciální derivace ",[38,93993,89677],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,93996,10294],{},[883,93998,94000],{"className":93999},[886],[888,94001,94002],{"xmlns":890},[892,94003,94004,94030],{},[895,94005,94006,94008,94010,94016,94018,94024,94026,94028],{},[898,94007,900],{},[1664,94009,1667],{"stretchy":1666},[2355,94011,94012,94014],{},[898,94013,1973],{},[1963,94015,2875],{},[1664,94017,1916],{"separator":1915},[2355,94019,94020,94022],{},[898,94021,1973],{},[1963,94023,1970],{},[1664,94025,1673],{"stretchy":1666},[1664,94027,1676],{},[898,94029,2034],{},[902,94031,10331],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,94034,94036],{"className":94035},[886],[888,94037,94038],{"xmlns":890},[892,94039,94040,94044],{},[895,94041,94042],{},[1690,94043,11165],{},[902,94045,28738],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,94048,94049],{},"maximalizace užitečnosti"," a duální ",[38,94052,94053],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,94056,37254],{"className":94057,"dataFsResolvedFilePath":911,"href":912},[210],[115,94059,50382],{"id":50381},[152,94061,94062,94065,94068,94071,94074,94077,94080,94083,94086,94089],{},[123,94063,94064],{},"Co se zahrnuje pod termín užitečnost?",[123,94066,94067],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,94069,94070],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,94072,94073],{},"Jak se vypočítá mezní užitečnost?",[123,94075,94076],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,94078,94079],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,94081,94082],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,94084,94085],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,94087,94088],{},"Proč mají křivky užitečnosti záporný sklon?",[123,94090,94091],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,94093,94095],{"id":94094},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,94097,94098,94101,94102,83983,94144,1343,94172,1343,94200,94228],{},[38,94099,94100],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,94103,94105],{"className":94104},[886],[888,94106,94107],{"xmlns":890},[892,94108,94109,94141],{},[895,94110,94111,94113,94115,94121,94123,94125,94131,94133,94135],{},[898,94112,900],{},[1664,94114,1676],{},[2355,94116,94117,94119],{},[898,94118,1973],{},[1963,94120,2875],{},[1664,94122,1700],{},[1963,94124,65059],{},[2355,94126,94127,94129],{},[898,94128,1973],{},[1963,94130,1970],{},[1664,94132,1700],{},[1963,94134,1970],{},[2355,94136,94137,94139],{},[898,94138,1973],{},[1963,94140,2774],{},[902,94142,94143],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,94145,94147],{"className":94146},[886],[888,94148,94149],{"xmlns":890},[892,94150,94151,94169],{},[895,94152,94153,94155,94157,94159,94161,94163,94165,94167],{},[898,94154,900],{},[1664,94156,1667],{"stretchy":1666},[1963,94158,2944],{},[1664,94160,1916],{"separator":1915},[1963,94162,1970],{},[1664,94164,1916],{"separator":1915},[1963,94166,1970],{},[1664,94168,1673],{"stretchy":1666},[902,94170,94171],{"encoding":904},"U(4, 2, 2)",[883,94173,94175],{"className":94174},[886],[888,94176,94177],{"xmlns":890},[892,94178,94179,94197],{},[895,94180,94181,94183,94185,94187,94189,94191,94193,94195],{},[898,94182,900],{},[1664,94184,1667],{"stretchy":1666},[1963,94186,2875],{},[1664,94188,1916],{"separator":1915},[1963,94190,2944],{},[1664,94192,1916],{"separator":1915},[1963,94194,1970],{},[1664,94196,1673],{"stretchy":1666},[902,94198,94199],{"encoding":904},"U(1, 4, 2)",[883,94201,94203],{"className":94202},[886],[888,94204,94205],{"xmlns":890},[892,94206,94207,94225],{},[895,94208,94209,94211,94213,94215,94217,94219,94221,94223],{},[898,94210,900],{},[1664,94212,1667],{"stretchy":1666},[1963,94214,1970],{},[1664,94216,1916],{"separator":1915},[1963,94218,2774],{},[1664,94220,1916],{"separator":1915},[1963,94222,2875],{},[1664,94224,1673],{"stretchy":1666},[902,94226,94227],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,94230,94231,94234,94235,94287,94288,1343,94314,1343,94340,1343,94366,1343,94392,1343,94418,1343,94444,94470],{},[38,94232,94233],{},"6.2"," Je dána užitečnost ",[883,94236,94238],{"className":94237},[886],[888,94239,94240],{"xmlns":890},[892,94241,94242,94284],{},[895,94243,94244,94246,94248,94250,94264,94278],{},[898,94245,900],{},[1664,94247,1676],{},[1963,94249,1970],{},[1810,94251,94252,94254,94256],{},[898,94253,1973],{},[1963,94255,2875],{},[895,94257,94258,94260,94262],{},[1963,94259,2875],{},[898,94261,5240],{"mathvariant":1726},[1963,94263,2774],{},[1810,94265,94266,94268,94270],{},[898,94267,1973],{},[1963,94269,1970],{},[895,94271,94272,94274,94276],{},[1963,94273,2875],{},[898,94275,5240],{"mathvariant":1726},[1963,94277,1970],{},[2355,94279,94280,94282],{},[898,94281,1973],{},[1963,94283,2774],{},[902,94285,94286],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,94289,94291],{"className":94290},[886],[888,94292,94293],{"xmlns":890},[892,94294,94295,94311],{},[895,94296,94297,94299,94301,94303,94305,94307,94309],{},[1664,94298,1667],{"stretchy":1666},[1963,94300,6131],{},[1664,94302,1916],{"separator":1915},[1963,94304,67097],{},[1664,94306,1916],{"separator":1915},[1963,94308,3442],{},[1664,94310,1673],{"stretchy":1666},[902,94312,94313],{"encoding":904},"(36, 27, 10)",[883,94315,94317],{"className":94316},[886],[888,94318,94319],{"xmlns":890},[892,94320,94321,94337],{},[895,94322,94323,94325,94327,94329,94331,94333,94335],{},[1664,94324,1667],{"stretchy":1666},[1963,94326,42340],{},[1664,94328,1916],{"separator":1915},[1963,94330,6151],{},[1664,94332,1916],{"separator":1915},[1963,94334,9599],{},[1664,94336,1673],{"stretchy":1666},[902,94338,94339],{"encoding":904},"(64, 8, 20)",[883,94341,94343],{"className":94342},[886],[888,94344,94345],{"xmlns":890},[892,94346,94347,94363],{},[895,94348,94349,94351,94353,94355,94357,94359,94361],{},[1664,94350,1667],{"stretchy":1666},[1963,94352,5570],{},[1664,94354,1916],{"separator":1915},[1963,94356,42340],{},[1664,94358,1916],{"separator":1915},[1963,94360,6151],{},[1664,94362,1673],{"stretchy":1666},[902,94364,94365],{"encoding":904},"(25, 64, 8)",[883,94367,94369],{"className":94368},[886],[888,94370,94371],{"xmlns":890},[892,94372,94373,94389],{},[895,94374,94375,94377,94379,94381,94383,94385,94387],{},[1664,94376,1667],{"stretchy":1666},[1963,94378,2944],{},[1664,94380,1916],{"separator":1915},[1963,94382,73029],{},[1664,94384,1916],{"separator":1915},[1963,94386,2833],{},[1664,94388,1673],{"stretchy":1666},[902,94390,94391],{"encoding":904},"(4, 125, 6)",[883,94393,94395],{"className":94394},[886],[888,94396,94397],{"xmlns":890},[892,94398,94399,94415],{},[895,94400,94401,94403,94405,94407,94409,94411,94413],{},[1664,94402,1667],{"stretchy":1666},[1963,94404,4567],{},[1664,94406,1916],{"separator":1915},[1963,94408,5777],{},[1664,94410,1916],{"separator":1915},[1963,94412,4084],{},[1664,94414,1673],{"stretchy":1666},[902,94416,94417],{"encoding":904},"(9, 40, 12)",[883,94419,94421],{"className":94420},[886],[888,94422,94423],{"xmlns":890},[892,94424,94425,94441],{},[895,94426,94427,94429,94431,94433,94435,94437,94439],{},[1664,94428,1667],{"stretchy":1666},[1963,94430,4567],{},[1664,94432,1916],{"separator":1915},[1963,94434,42340],{},[1664,94436,1916],{"separator":1915},[1963,94438,2826],{},[1664,94440,1673],{"stretchy":1666},[902,94442,94443],{"encoding":904},"(9, 64, 5)",[883,94445,94447],{"className":94446},[886],[888,94448,94449],{"xmlns":890},[892,94450,94451,94467],{},[895,94452,94453,94455,94457,94459,94461,94463,94465],{},[1664,94454,1667],{"stretchy":1666},[1963,94456,42340],{},[1664,94458,1916],{"separator":1915},[1963,94460,6151],{},[1664,94462,1916],{"separator":1915},[1963,94464,3442],{},[1664,94466,1673],{"stretchy":1666},[902,94468,94469],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,94472,94473,94234,94476,94519,94520,94554,94555,7039,94585,94618,94619,94636,94637,94654],{},[38,94474,94475],{},"6.3",[883,94477,94479],{"className":94478},[886],[888,94480,94481],{"xmlns":890},[892,94482,94483,94517],{},[895,94484,94485,94487,94489,94503],{},[898,94486,900],{},[1664,94488,1676],{},[1810,94490,94491,94493,94495],{},[898,94492,1973],{},[1963,94494,2875],{},[895,94496,94497,94499,94501],{},[1963,94498,2875],{},[898,94500,5240],{"mathvariant":1726},[1963,94502,1970],{},[1810,94504,94505,94507,94509],{},[898,94506,1973],{},[1963,94508,1970],{},[895,94510,94511,94513,94515],{},[1963,94512,2875],{},[898,94514,5240],{"mathvariant":1726},[1963,94516,1970],{},[902,94518,33659],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,94521,94523],{"className":94522},[886],[888,94524,94525],{"xmlns":890},[892,94526,94527,94551],{},[895,94528,94529,94535,94537,94539,94541,94547,94549],{},[2355,94530,94531,94533],{},[898,94532,1973],{},[1963,94534,2875],{},[1664,94536,1676],{},[1963,94538,3696],{},[1664,94540,1916],{"separator":1915},[2355,94542,94543,94545],{},[898,94544,1973],{},[1963,94546,1970],{},[1664,94548,1676],{},[1963,94550,47203],{},[902,94552,94553],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,94556,94558],{"className":94557},[886],[888,94559,94560],{"xmlns":890},[892,94561,94562,94582],{},[895,94563,94564,94566,94572,94574,94576],{},[898,94565,1956],{},[2355,94567,94568,94570],{},[898,94569,900],{},[1963,94571,2875],{},[1664,94573,1916],{"separator":1915},[898,94575,1956],{},[2355,94577,94578,94580],{},[898,94579,900],{},[1963,94581,1970],{},[902,94583,94584],{"encoding":904},"MU_1, MU_2",[883,94586,94588],{"className":94587},[886],[888,94589,94590],{"xmlns":890},[892,94591,94592,94616],{},[895,94593,94594,94600,94602,94604,94606,94612,94614],{},[2355,94595,94596,94598],{},[898,94597,1973],{},[1963,94599,2875],{},[1664,94601,1676],{},[1963,94603,3696],{},[1664,94605,1916],{"separator":1915},[2355,94607,94608,94610],{},[898,94609,1973],{},[1963,94611,1970],{},[1664,94613,1676],{},[1963,94615,47203],{},[902,94617,94553],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,94620,94622],{"className":94621},[886],[888,94623,94624],{"xmlns":890},[892,94625,94626,94634],{},[895,94627,94628],{},[2355,94629,94630,94632],{},[898,94631,1973],{},[1963,94633,2875],{},[902,94635,29502],{"encoding":904}," na 60 a poklesu ",[883,94638,94640],{"className":94639},[886],[888,94641,94642],{"xmlns":890},[892,94643,94644,94652],{},[895,94645,94646],{},[2355,94647,94648,94650],{},[898,94649,1973],{},[1963,94651,1970],{},[902,94653,29521],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,94656,94657,94660,94661,94722,94723,1977],{},[38,94658,94659],{},"6.4"," Je dána funkce ",[883,94662,94664],{"className":94663},[886],[888,94665,94666],{"xmlns":890},[892,94667,94668,94720],{},[895,94669,94670,94672,94674,94680,94682,94688,94690,94692,94706],{},[898,94671,900],{},[1664,94673,1667],{"stretchy":1666},[2355,94675,94676,94678],{},[898,94677,1973],{},[1963,94679,2875],{},[1664,94681,1916],{"separator":1915},[2355,94683,94684,94686],{},[898,94685,1973],{},[1963,94687,1970],{},[1664,94689,1673],{"stretchy":1666},[1664,94691,1676],{},[1810,94693,94694,94696,94698],{},[898,94695,1973],{},[1963,94697,2875],{},[895,94699,94700,94702,94704],{},[1963,94701,2875],{},[898,94703,5240],{"mathvariant":1726},[1963,94705,1970],{},[1810,94707,94708,94710,94712],{},[898,94709,1973],{},[1963,94711,1970],{},[895,94713,94714,94716,94718],{},[1963,94715,2875],{},[898,94717,5240],{"mathvariant":1726},[1963,94719,1970],{},[902,94721,30443],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,94724,94726],{"className":94725},[886],[888,94727,94728],{"xmlns":890},[892,94729,94730,94820],{},[895,94731,94732,94734,94736,94742,94744,94746,94748,94750,94752,94754,94760,94762,94764,94766,94768,94770,94772,94774,94776,94782,94784,94786,94788,94790,94792,94794,94800,94802,94804,94806,94808,94810,94812,94818],{},[898,94733,900],{},[1664,94735,1667],{"stretchy":1666},[2355,94737,94738,94740],{},[898,94739,1973],{},[1963,94741,2875],{},[1664,94743,1916],{"separator":1915},[1963,94745,2875],{},[1664,94747,1673],{"stretchy":1666},[1664,94749,1916],{"separator":1915},[898,94751,900],{},[1664,94753,1667],{"stretchy":1666},[2355,94755,94756,94758],{},[898,94757,1973],{},[1963,94759,2875],{},[1664,94761,1916],{"separator":1915},[1963,94763,1970],{},[1664,94765,1673],{"stretchy":1666},[1664,94767,1916],{"separator":1915},[898,94769,900],{},[1664,94771,1667],{"stretchy":1666},[1963,94773,2875],{},[1664,94775,1916],{"separator":1915},[2355,94777,94778,94780],{},[898,94779,1973],{},[1963,94781,1970],{},[1664,94783,1673],{"stretchy":1666},[1664,94785,1916],{"separator":1915},[898,94787,900],{},[1664,94789,1667],{"stretchy":1666},[1963,94791,1970],{},[1664,94793,1916],{"separator":1915},[2355,94795,94796,94798],{},[898,94797,1973],{},[1963,94799,1970],{},[1664,94801,1673],{"stretchy":1666},[1664,94803,1916],{"separator":1915},[898,94805,900],{},[1664,94807,1667],{"stretchy":1666},[1963,94809,2774],{},[1664,94811,1916],{"separator":1915},[2355,94813,94814,94816],{},[898,94815,1973],{},[1963,94817,1970],{},[1664,94819,1673],{"stretchy":1666},[902,94821,94822],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,94824,94825,94234,94828,94872,94873,94981,94982,1343,95007,1343,95032,95074,95075,1343,95104,95129],{},[38,94826,94827],{},"6.5",[883,94829,94831],{"className":94830},[886],[888,94832,94833],{"xmlns":890},[892,94834,94835,94869],{},[895,94836,94837,94839,94841,94855],{},[898,94838,900],{},[1664,94840,1676],{},[1810,94842,94843,94845,94847],{},[898,94844,1973],{},[1963,94846,2875],{},[895,94848,94849,94851,94853],{},[1963,94850,1970],{},[898,94852,5240],{"mathvariant":1726},[1963,94854,2774],{},[1810,94856,94857,94859,94861],{},[898,94858,1973],{},[1963,94860,1970],{},[895,94862,94863,94865,94867],{},[1963,94864,2875],{},[898,94866,5240],{"mathvariant":1726},[1963,94868,2774],{},[902,94870,94871],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,94874,94876],{"className":94875},[886],[888,94877,94878],{"xmlns":890},[892,94879,94880,94978],{},[895,94881,94882,94884,94886,94892,94894,94900,94902,94904,94906,94908,94910,94912,94918,94920,94922,94924,94926,94928,94930,94936,94938,94940,94942,94944,94946,94948,94950,94952,94958,94960,94962,94964,94966,94968,94970,94976],{},[898,94883,900],{},[1664,94885,1667],{"stretchy":1666},[2355,94887,94888,94890],{},[898,94889,1973],{},[1963,94891,2875],{},[1664,94893,1916],{"separator":1915},[2355,94895,94896,94898],{},[898,94897,1973],{},[1963,94899,1970],{},[1664,94901,1673],{"stretchy":1666},[1664,94903,1676],{},[1963,94905,1970],{},[1664,94907,1916],{"separator":1915},[898,94909,900],{},[1664,94911,1667],{"stretchy":1666},[2355,94913,94914,94916],{},[898,94915,1973],{},[1963,94917,2875],{},[1664,94919,1916],{"separator":1915},[1963,94921,2774],{},[1664,94923,1673],{"stretchy":1666},[1664,94925,1916],{"separator":1915},[898,94927,900],{},[1664,94929,1667],{"stretchy":1666},[2355,94931,94932,94934],{},[898,94933,1973],{},[1963,94935,2875],{},[1664,94937,1916],{"separator":1915},[1963,94939,1970],{},[1664,94941,1673],{"stretchy":1666},[1664,94943,1916],{"separator":1915},[898,94945,900],{},[1664,94947,1667],{"stretchy":1666},[1963,94949,1970],{},[1664,94951,1916],{"separator":1915},[2355,94953,94954,94956],{},[898,94955,1973],{},[1963,94957,1970],{},[1664,94959,1673],{"stretchy":1666},[1664,94961,1916],{"separator":1915},[898,94963,900],{},[1664,94965,1667],{"stretchy":1666},[1963,94967,2774],{},[1664,94969,1916],{"separator":1915},[2355,94971,94972,94974],{},[898,94973,1973],{},[1963,94975,1970],{},[1664,94977,1673],{"stretchy":1666},[902,94979,94980],{"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 ",[883,94983,94985],{"className":94984},[886],[888,94986,94987],{"xmlns":890},[892,94988,94989,95004],{},[895,94990,94991,94993,94995,94997,94999,95002],{},[898,94992,4822],{},[1664,94994,1837],{"stretchy":1666},[1963,94996,65059],{},[1664,94998,8990],{"separator":1915},[1963,95000,95001],{},"3,555",[1664,95003,1850],{"stretchy":1666},[902,95005,95006],{"encoding":904},"A[1{,}5; 3{,}555]",[883,95008,95010],{"className":95009},[886],[888,95011,95012],{"xmlns":890},[892,95013,95014,95029],{},[895,95015,95016,95018,95020,95022,95024,95027],{},[898,95017,23753],{},[1664,95019,1837],{"stretchy":1666},[1963,95021,53699],{},[1664,95023,8990],{"separator":1915},[1963,95025,95026],{},"1,28",[1664,95028,1850],{"stretchy":1666},[902,95030,95031],{"encoding":904},"B[2{,}5; 1{,}28]",[883,95033,95035],{"className":95034},[886],[888,95036,95037],{"xmlns":890},[892,95038,95039,95071],{},[895,95040,95041,95043,95045,95047,95049,95051,95053,95059,95061,95063,95065,95067,95069],{},[898,95042,1703],{},[1664,95044,1837],{"stretchy":1666},[1963,95046,1970],{},[1664,95048,8990],{"separator":1915},[898,95050,900],{},[1664,95052,1667],{"stretchy":1666},[2355,95054,95055,95057],{},[898,95056,1973],{},[1963,95058,2875],{},[1664,95060,1916],{"separator":1915},[1963,95062,2774],{},[1664,95064,1673],{"stretchy":1666},[1664,95066,1676],{},[1963,95068,2774],{},[1664,95070,1850],{"stretchy":1666},[902,95072,95073],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,95076,95078],{"className":95077},[886],[888,95079,95080],{"xmlns":890},[892,95081,95082,95101],{},[895,95083,95084,95086,95088,95090,95092,95094,95096,95099],{},[898,95085,2379],{},[1664,95087,1837],{"stretchy":1666},[1963,95089,2774],{},[1664,95091,8990],{"separator":1915},[1963,95093,2875],{},[1664,95095,8990],{"separator":1915},[1963,95097,95098],{},"0,832",[1664,95100,1850],{"stretchy":1666},[902,95102,95103],{"encoding":904},"D[3; 1; 0{,}832]",[883,95105,95107],{"className":95106},[886],[888,95108,95109],{"xmlns":890},[892,95110,95111,95126],{},[895,95112,95113,95115,95117,95119,95121,95124],{},[898,95114,4819],{},[1664,95116,1837],{"stretchy":1666},[1963,95118,53699],{},[1664,95120,8990],{"separator":1915},[1963,95122,95123],{},"4,32",[1664,95125,1850],{"stretchy":1666},[902,95127,95128],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,95131,95132,94234,95135,95178,95179,7039,95192,95226,95227,95244,95245,95262],{},[38,95133,95134],{},"6.6",[883,95136,95138],{"className":95137},[886],[888,95139,95140],{"xmlns":890},[892,95141,95142,95176],{},[895,95143,95144,95146,95148,95162],{},[898,95145,900],{},[1664,95147,1676],{},[1810,95149,95150,95152,95154],{},[898,95151,1973],{},[1963,95153,2875],{},[895,95155,95156,95158,95160],{},[1963,95157,1970],{},[898,95159,5240],{"mathvariant":1726},[1963,95161,2774],{},[1810,95163,95164,95166,95168],{},[898,95165,1973],{},[1963,95167,1970],{},[895,95169,95170,95172,95174],{},[1963,95171,2875],{},[898,95173,5240],{"mathvariant":1726},[1963,95175,2774],{},[902,95177,94871],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,95180,95182],{"className":95181},[886],[888,95183,95184],{"xmlns":890},[892,95185,95186,95190],{},[895,95187,95188],{},[1690,95189,11165],{},[902,95191,28738],{"encoding":904},[883,95193,95195],{"className":95194},[886],[888,95196,95197],{"xmlns":890},[892,95198,95199,95223],{},[895,95200,95201,95207,95209,95211,95213,95219,95221],{},[2355,95202,95203,95205],{},[898,95204,1973],{},[1963,95206,2875],{},[1664,95208,1676],{},[1963,95210,1965],{},[1664,95212,1916],{"separator":1915},[2355,95214,95215,95217],{},[898,95216,1973],{},[1963,95218,1970],{},[1664,95220,1676],{},[1963,95222,8942],{},[902,95224,95225],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,95228,95230],{"className":95229},[886],[888,95231,95232],{"xmlns":890},[892,95233,95234,95242],{},[895,95235,95236],{},[2355,95237,95238,95240],{},[898,95239,1973],{},[1963,95241,2875],{},[902,95243,29502],{"encoding":904},", poklesne-li ",[883,95246,95248],{"className":95247},[886],[888,95249,95250],{"xmlns":890},[892,95251,95252,95260],{},[895,95253,95254],{},[2355,95255,95256,95258],{},[898,95257,1973],{},[1963,95259,1970],{},[902,95261,29521],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,95264,95265,95268,95269,95286,95287,95304,95305,95337,95338,95363,95364,95377,95378,1343,95402,1343,95426,1977],{},[38,95266,95267],{},"6.7"," Míra uspokojení z nákupu množství ",[883,95270,95272],{"className":95271},[886],[888,95273,95274],{"xmlns":890},[892,95275,95276,95284],{},[895,95277,95278],{},[2355,95279,95280,95282],{},[898,95281,1973],{},[1963,95283,2875],{},[902,95285,29502],{"encoding":904}," nealko nápojů a množství ",[883,95288,95290],{"className":95289},[886],[888,95291,95292],{"xmlns":890},[892,95293,95294,95302],{},[895,95295,95296],{},[2355,95297,95298,95300],{},[898,95299,1973],{},[1963,95301,1970],{},[902,95303,29521],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,95306,95308],{"className":95307},[886],[888,95309,95310],{"xmlns":890},[892,95311,95312,95334],{},[895,95313,95314,95316,95318],{},[898,95315,900],{},[1664,95317,1676],{},[8682,95319,95320],{},[895,95321,95322,95328],{},[2355,95323,95324,95326],{},[898,95325,1973],{},[1963,95327,2875],{},[2355,95329,95330,95332],{},[898,95331,1973],{},[1963,95333,1970],{},[902,95335,95336],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,95339,95341],{"className":95340},[886],[888,95342,95343],{"xmlns":890},[892,95344,95345,95361],{},[895,95346,95347,95353,95355],{},[2355,95348,95349,95351],{},[898,95350,1973],{},[1963,95352,2875],{},[1664,95354,1916],{"separator":1915},[2355,95356,95357,95359],{},[898,95358,1973],{},[1963,95360,1970],{},[902,95362,36122],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,95365,95367],{"className":95366},[886],[888,95368,95369],{"xmlns":890},[892,95370,95371,95375],{},[895,95372,95373],{},[1690,95374,11165],{},[902,95376,28738],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,95379,95381],{"className":95380},[886],[888,95382,95383],{"xmlns":890},[892,95384,95385,95399],{},[895,95386,95387,95389,95391,95393,95395,95397],{},[1690,95388,11165],{},[1664,95390,1667],{"stretchy":1666},[1963,95392,2826],{},[1664,95394,1916],{"separator":1915},[1963,95396,9599],{},[1664,95398,1673],{"stretchy":1666},[902,95400,95401],{"encoding":904},"\\text{MRCS}(5, 20)",[883,95403,95405],{"className":95404},[886],[888,95406,95407],{"xmlns":890},[892,95408,95409,95423],{},[895,95410,95411,95413,95415,95417,95419,95421],{},[1690,95412,11165],{},[1664,95414,1667],{"stretchy":1666},[1963,95416,9599],{},[1664,95418,1916],{"separator":1915},[1963,95420,2826],{},[1664,95422,1673],{"stretchy":1666},[902,95424,95425],{"encoding":904},"\\text{MRCS}(20, 5)",[883,95427,95429],{"className":95428},[886],[888,95430,95431],{"xmlns":890},[892,95432,95433,95447],{},[895,95434,95435,95437,95439,95441,95443,95445],{},[1690,95436,11165],{},[1664,95438,1667],{"stretchy":1666},[1963,95440,1970],{},[1664,95442,1916],{"separator":1915},[1963,95444,3696],{},[1664,95446,1673],{"stretchy":1666},[902,95448,95449],{"encoding":904},"\\text{MRCS}(2, 50)",[4436,95451,95452],{},[724,95453,95454,95456,95457,1977],{},[883,95455,5138],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,95458,95461],{"className":95459,"dataFsResolvedFilePath":911,"href":95460},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,95463,16219],{"id":16218},[120,95465,95466,95472,95477,95483,95536,95546,95592,95647,95710,95767,95822,95861],{},[123,95467,95468,95471],{},[38,95469,95470],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,95473,95474,95476],{},[38,95475,87369],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,95478,95479,95482],{},[38,95480,95481],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,95484,95485,95487,95488,95501,95502,1977],{},[38,95486,87696],{}," — uspořádaná ",[883,95489,95491],{"className":95490},[886],[888,95492,95493],{"xmlns":890},[892,95494,95495,95499],{},[895,95496,95497],{},[898,95498,37360],{},[902,95500,37360],{"encoding":904},"-tice ",[883,95503,95505],{"className":95504},[886],[888,95506,95507],{"xmlns":890},[892,95508,95509,95533],{},[895,95510,95511,95513,95519,95521,95523,95525,95531],{},[1664,95512,1667],{"stretchy":1666},[2355,95514,95515,95517],{},[898,95516,1973],{},[1963,95518,2875],{},[1664,95520,1916],{"separator":1915},[1664,95522,10209],{},[1664,95524,1916],{"separator":1915},[2355,95526,95527,95529],{},[898,95528,1973],{},[898,95530,37360],{},[1664,95532,1673],{"stretchy":1666},[902,95534,95535],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,95537,95538,95541,95542,95545],{},[38,95539,95540],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,95543,95544],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,95547,95548,1885,95551,95591],{},[38,95549,95550],{},"Funkce užitečnosti",[883,95552,95554],{"className":95553},[886],[888,95555,95556],{"xmlns":890},[892,95557,95558,95588],{},[895,95559,95560,95562,95564,95566,95568,95574,95576,95578,95580,95586],{},[898,95561,900],{},[1664,95563,1676],{},[898,95565,900],{},[1664,95567,1667],{"stretchy":1666},[2355,95569,95570,95572],{},[898,95571,1973],{},[1963,95573,2875],{},[1664,95575,1916],{"separator":1915},[1664,95577,10209],{},[1664,95579,1916],{"separator":1915},[2355,95581,95582,95584],{},[898,95583,1973],{},[898,95585,37360],{},[1664,95587,1673],{"stretchy":1666},[902,95589,95590],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,95593,95594,1885,95597,95626,95627,1885,95630,95646],{},[38,95595,95596],{},"Mezní užitečnost",[883,95598,95600],{"className":95599},[886],[888,95601,95602],{"xmlns":890},[892,95603,95604,95624],{},[895,95605,95606,95608,95614,95616],{},[898,95607,1956],{},[2355,95609,95610,95612],{},[898,95611,900],{},[898,95613,18290],{},[1664,95615,1676],{},[1810,95617,95618,95620,95622],{},[898,95619,900],{},[898,95621,18290],{},[1664,95623,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[902,95625,87153],{"encoding":904}," — vzorec (6.2); ",[38,95628,95629],{},"totální diferenciál",[883,95631,95633],{"className":95632},[886],[888,95634,95635],{"xmlns":890},[892,95636,95637,95643],{},[895,95638,95639,95641],{},[898,95640,1695],{"mathvariant":1726},[898,95642,900],{},[902,95644,95645],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,95648,95649,95651,95652,95676,95677,95709],{},[38,95650,89332],{}," — (6.4) ",[883,95653,95655],{"className":95654},[886],[888,95656,95657],{"xmlns":890},[892,95658,95659,95673],{},[895,95660,95661,95669,95671],{},[1810,95662,95663,95665,95667],{},[898,95664,900],{},[898,95666,18290],{},[1664,95668,1728],{"mathvariant":1726,"lspace":1727,"rspace":1727},[1664,95670,3984],{},[1963,95672,2058],{},[902,95674,95675],{"encoding":904},"U'_i > 0",", (6.5) ",[883,95678,95680],{"className":95679},[886],[888,95681,95682],{"xmlns":890},[892,95683,95684,95706],{},[895,95685,95686,95702,95704],{},[1810,95687,95688,95690,95696],{},[898,95689,900],{},[895,95691,95692,95694],{},[898,95693,18290],{},[898,95695,18290],{},[895,95697,95698,95700],{},[1664,95699,1728],{"mathvariant":1726},[1664,95701,1728],{"mathvariant":1726},[1664,95703,4022],{},[1963,95705,2058],{},[902,95707,95708],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,95711,95712,1885,95714,95745,95746,1977],{},[38,95713,91120],{},[883,95715,95717],{"className":95716},[886],[888,95718,95719],{"xmlns":890},[892,95720,95721,95743],{},[895,95722,95723,95725,95727,95735],{},[898,95724,900],{},[1664,95726,1676],{},[1810,95728,95729,95731,95733],{},[898,95730,1973],{},[1963,95732,2875],{},[898,95734,207],{},[1810,95736,95737,95739,95741],{},[898,95738,1973],{},[1963,95740,1970],{},[898,95742,1818],{},[902,95744,36303],{"encoding":904}," — (6.6), speciálně ",[883,95747,95749],{"className":95748},[886],[888,95750,95751],{"xmlns":890},[892,95752,95753,95765],{},[895,95754,95755,95757,95759,95761,95763],{},[898,95756,1818],{},[1664,95758,1676],{},[1963,95760,2875],{},[1664,95762,1867],{},[898,95764,207],{},[902,95766,91274],{"encoding":904},[123,95768,95769,1885,95772,95807,95808,95821],{},[38,95770,95771],{},"Křivky užitečnosti (indiferenční)",[883,95773,95775],{"className":95774},[886],[888,95776,95777],{"xmlns":890},[892,95778,95779,95805],{},[895,95780,95781,95783,95785,95791,95793,95799,95801,95803],{},[898,95782,900],{},[1664,95784,1667],{"stretchy":1666},[2355,95786,95787,95789],{},[898,95788,1973],{},[1963,95790,2875],{},[1664,95792,1916],{"separator":1915},[2355,95794,95795,95797],{},[898,95796,1973],{},[1963,95798,1970],{},[1664,95800,1673],{"stretchy":1666},[1664,95802,1676],{},[898,95804,2034],{},[902,95806,10331],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,95809,95811],{"className":95810},[886],[888,95812,95813],{"xmlns":890},[892,95814,95815,95819],{},[895,95816,95817],{},[898,95818,900],{},[902,95820,900],{"encoding":904},", konvexní.",[123,95823,95824,1885,95826,95860],{},[38,95825,92665],{},[883,95827,95829],{"className":95828},[886],[888,95830,95831],{"xmlns":890},[892,95832,95833,95857],{},[895,95834,95835,95837,95839,95841,95847,95849,95851],{},[1690,95836,11165],{},[1664,95838,1676],{},[898,95840,1956],{},[2355,95842,95843,95845],{},[898,95844,900],{},[1963,95846,2875],{},[898,95848,5240],{"mathvariant":1726},[898,95850,1956],{},[2355,95852,95853,95855],{},[898,95854,900],{},[1963,95856,1970],{},[902,95858,95859],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,95862,95863,1885,95866,10332,95895,95898],{},[38,95864,95865],{},"Podmínka optimality",[883,95867,95869],{"className":95868},[886],[888,95870,95871],{"xmlns":890},[892,95872,95873,95893],{},[895,95874,95875,95877,95879,95885,95887],{},[1690,95876,11165],{},[1664,95878,1676],{},[2355,95880,95881,95883],{},[898,95882,2398],{},[1963,95884,2875],{},[898,95886,5240],{"mathvariant":1726},[2355,95888,95889,95891],{},[898,95890,2398],{},[1963,95892,1970],{},[902,95894,28498],{"encoding":904},[207,95896,37254],{"className":95897,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,95900,2497],{"id":2496},[120,95902,95903,95940,95981,95991],{},[123,95904,95905,1885,95908,95911,95912,95925,95926,95939],{},[38,95906,95907],{},"Navazující téma:",[207,95909,913],{"className":95910,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,95913,95915],{"className":95914},[886],[888,95916,95917],{"xmlns":890},[892,95918,95919,95923],{},[895,95920,95921],{},[898,95922,900],{},[902,95924,900],{"encoding":904},", min ",[883,95927,95929],{"className":95928},[886],[888,95930,95931],{"xmlns":890},[892,95932,95933,95937],{},[895,95934,95935],{},[898,95936,4819],{},[902,95938,4819],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,95941,95942,1885,95945,11654,95948,86908,95951,95954,95955,95958,95959,19148,95977,95980],{},[38,95943,95944],{},"Související pojmy:",[207,95946,784],{"className":95947,"dataFsResolvedFilePath":782,"href":783},[210],[207,95949,2950],{"className":95950,"dataFsResolvedFilePath":764,"href":765},[210],[207,95952,11649],{"className":95953,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,95956,2493],{"className":95957,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,95960,95962],{"className":95961},[886],[888,95963,95964],{"xmlns":890},[892,95965,95966,95974],{},[895,95967,95968],{},[2355,95969,95970,95972],{},[898,95971,2379],{},[898,95973,18290],{},[902,95975,95976],{"encoding":904},"D_i",[207,95978,793],{"className":95979,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,95982,95983,1885,95985,1343,95988],{},[38,95984,37203],{},[207,95986,1094],{"className":95987,"dataFsResolvedFilePath":838,"href":839},[210],[207,95989,1101],{"className":95990,"dataFsResolvedFilePath":868,"href":869},[210],[123,95992,95993,1885,95995],{},[38,95994,16703],{},[207,95996,16707],{"className":95997,"dataFsResolvedFilePath":2575,"href":2576},[210],{"title":641,"searchDepth":642,"depth":642,"links":95999},[96000,96001,96002,96005,96006,96009,96013,96014,96017,96018,96019,96020,96021,96022,96023],{"id":12504,"depth":642,"text":12505},{"id":87292,"depth":642,"text":87293},{"id":87352,"depth":642,"text":87353,"children":96003},[96004],{"id":87368,"depth":649,"text":87369},{"id":87675,"depth":642,"text":87676},{"id":88535,"depth":642,"text":88536,"children":96007},[96008],{"id":89082,"depth":649,"text":80711},{"id":89331,"depth":642,"text":89332,"children":96010},[96011],{"id":90204,"depth":649,"text":96012},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":91119,"depth":642,"text":91120},{"id":91655,"depth":642,"text":91656,"children":96015},[96016],{"id":92429,"depth":649,"text":92430},{"id":92659,"depth":642,"text":92660},{"id":93420,"depth":642,"text":93421},{"id":93958,"depth":642,"text":93959},{"id":50381,"depth":642,"text":50382},{"id":94094,"depth":642,"text":94095},{"id":16218,"depth":642,"text":16219},{"id":2496,"depth":642,"text":2497},{},"\u002Ftopics\u002Fuzitecnost",{"title":87076,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,10336,96030,87070,11684,96031],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":96034,"title":757,"body":96035,"course":1128,"courses":659,"created":1129,"description":96308,"extension":661,"meta":96309,"navigation":664,"path":96310,"seo":96311,"sources":96312,"stem":96313,"tags":96314,"type":2553,"updated":677,"__hash__":96320},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":96036,"toc":96300},[96037,96040,96047,96054,96058,96068,96070,96104,96108,96151,96154,96212,96216,96246,96250,96271,96273],[12,96038,757],{"id":96039},"základy-matematické-ekonomie",[724,96041,96042,96043,96046],{},"Úvodní pojmy a princip modelování v ",[207,96044,16880],{"className":96045,"dataFsResolvedFilePath":2575,"href":2576},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,96048,96049],{},[1928,96050],{"alt":96051,"className":96052,"src":96053},"imek-model-promenne",[210,1932],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,96055,96057],{"id":96056},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,96059,96060,96063,96064,96067],{},[38,96061,96062],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,96065,96066],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,96069,16219],{"id":16218},[120,96071,96072,96078,96084,96090,96099],{},[123,96073,96074,96077],{},[38,96075,96076],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,96079,96080,96083],{},[38,96081,96082],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,96085,96086,96089],{},[38,96087,96088],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,96091,96092,7581,96095,96098],{},[38,96093,96094],{},"Ceteris paribus",[614,96096,96097],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,96100,96101,96103],{},[38,96102,51135],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,96105,96107],{"id":96106},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,96109,96110,96150],{},[883,96111,96113],{"className":96112},[886],[888,96114,96115],{"xmlns":890},[892,96116,96117,96147],{},[895,96118,96119,96121,96123,96125,96127,96129,96131,96133,96135,96137,96139,96141,96143,96145],{},[898,96120,1973],{},[1664,96122,1676],{},[898,96124,2379],{},[1664,96126,1667],{"stretchy":1666},[898,96128,2398],{},[1664,96130,1916],{"separator":1915},[898,96132,9692],{},[1664,96134,1916],{"separator":1915},[898,96136,18794],{},[1664,96138,1916],{"separator":1915},[898,96140,900],{},[1664,96142,1916],{"separator":1915},[1664,96144,10209],{},[1664,96146,1673],{"stretchy":1666},[902,96148,96149],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,96152,96153],{},"Zjednodušení:",[120,96155,96156,96184],{},[123,96157,96158,1885,96161],{},[38,96159,96160],{},"Jednofaktorový model:",[883,96162,96164],{"className":96163},[886],[888,96165,96166],{"xmlns":890},[892,96167,96168,96182],{},[895,96169,96170,96172,96174,96176,96178,96180],{},[898,96171,1973],{},[1664,96173,1676],{},[898,96175,2379],{},[1664,96177,1667],{"stretchy":1666},[898,96179,2398],{},[1664,96181,1673],{"stretchy":1666},[902,96183,4759],{"encoding":904},[123,96185,96186,1885,96189],{},[38,96187,96188],{},"Inverzní zápis:",[883,96190,96192],{"className":96191},[886],[888,96193,96194],{"xmlns":890},[892,96195,96196,96210],{},[895,96197,96198,96200,96202,96204,96206,96208],{},[898,96199,2398],{},[1664,96201,1676],{},[898,96203,2379],{},[1664,96205,1667],{"stretchy":1666},[898,96207,1973],{},[1664,96209,1673],{"stretchy":1666},[902,96211,5206],{"encoding":904},[115,96213,96215],{"id":96214},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,96217,96218,96227],{},[123,96219,96220,96223,96224,4488],{},[38,96221,96222],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,96225,16739],{"className":96226,"dataFsResolvedFilePath":800,"href":801},[210],[123,96228,96229,96232,96233,96236,96237,96240,96241,96245],{},[38,96230,96231],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,96234,1145],{"className":96235,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,96238,16752],{"className":96239,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,96242,96244],{"className":96243,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,96247,96249],{"id":96248},"konvence-z-přednášek","Konvence z přednášek",[120,96251,96252,96259,96265],{},[123,96253,96254,96255,96258],{},"Symbol ",[96256,96257,3315],"code",{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,96260,96261,96262,1977],{},"Numerické výsledky ",[38,96263,96264],{},"na 3 desetinná místa",[123,96266,4464,96267,96270],{},[614,96268,96269],{},"jednotková změna"," má standardní význam (změna o 1).",[115,96272,2497],{"id":2496},[120,96274,96275,96280,96288],{},[123,96276,96277,96279],{},[38,96278,2504],{}," —",[123,96281,96282,1885,96284],{},[38,96283,2512],{},[207,96285,96287],{"className":96286,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,96289,96290,1885,96292,1343,96296],{},[38,96291,2520],{},[207,96293,96295],{"className":96294,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,96297,96299],{"className":96298,"dataFsResolvedFilePath":2575,"href":2576},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":96301},[96302,96303,96304,96305,96306,96307],{"id":96056,"depth":642,"text":96057},{"id":16218,"depth":642,"text":16219},{"id":96106,"depth":642,"text":96107},{"id":96214,"depth":642,"text":96215},{"id":96248,"depth":642,"text":96249},{"id":2496,"depth":642,"text":2497},"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":96308},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,96315,96316,96317,96318,96319],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":96322,"title":96323,"body":96324,"course":1128,"courses":659,"created":10119,"description":641,"extension":661,"meta":100596,"navigation":664,"path":100597,"seo":100598,"sources":100599,"stem":100600,"tags":100601,"type":2553,"updated":677,"__hash__":100605},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":96325,"toc":100579},[96326,96329,96423,96427,96449,96463,96515,96517,96521,96584,96627,96646,96809,96908,96911,96978,96982,97111,97150,97180,97292,97337,97403,97456,97532,97588,97590,97594,97658,97702,97722,97883,97886,97970,98067,98070,98136,98140,98189,98215,98320,98384,98389,98485,98532,98534,98537,98559,98601,98608,98641,98643,98714,98768,98877,98881,98970,99046,99310,99348,99350,99354,99357,99364,99675,99678,99736,99916,99945,99947,99951,99957,100095,100104,100106,100108,100533,100535,100537],[12,96327,96323],{"id":96328},"zdanění-trhu-dopady-daně-na-rovnováhu",[4436,96330,96331],{},[724,96332,96333,43128,96335,96348,96349,96352,96353,96355,96356,96359,96360,96381,96382,96405,96406,96409,96410,1977],{},[883,96334,4723],{},[883,96336,96338],{"className":96337},[886],[888,96339,96340],{"xmlns":890},[892,96341,96342,96346],{},[895,96343,96344],{},[898,96345,1991],{},[902,96347,1991],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,96350,96351],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,96354,87360],{}," (je-li uložena spotřebiteli). Výsledné ",[38,96357,96358],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,96361,96363],{"className":96362},[886],[888,96364,96365],{"xmlns":890},[892,96366,96367,96379],{},[895,96368,96369],{},[2355,96370,96371,96373],{},[898,96372,1991],{},[895,96374,96375,96377],{},[898,96376,43177],{},[898,96378,724],{},[902,96380,43182],{"encoding":904}," (spotřebitel) a ",[883,96383,96385],{"className":96384},[886],[888,96386,96387],{"xmlns":890},[892,96388,96389,96403],{},[895,96390,96391],{},[2355,96392,96393,96395],{},[898,96394,1991],{},[895,96396,96397,96399,96401],{},[898,96398,43200],{},[898,96400,2608],{},[898,96402,12540],{},[902,96404,43207],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,96407,96408],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,96411,96413],{"className":96412},[886],[888,96414,96415],{"xmlns":890},[892,96416,96417,96421],{},[895,96418,96419],{},[898,96420,1991],{},[902,96422,1991],{"encoding":904},[115,96424,96426],{"id":96425},"dvě-formy-zdanění","Dvě formy zdanění",[724,96428,96429,96430,96448],{},"Uvažujme jednotkovou daň ",[883,96431,96433],{"className":96432},[886],[888,96434,96435],{"xmlns":890},[892,96436,96437,96445],{},[895,96438,96439,96441,96443],{},[898,96440,1991],{},[1664,96442,3984],{},[1963,96444,2058],{},[902,96446,96447],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,96450,96451,96457],{},[123,96452,96453,96456],{},[38,96454,96455],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,96458,96459,96462],{},[38,96460,96461],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,96464,96465,96466,96479,96480,96483,96484,1977],{},"V obou případech dochází k posunu jedné z křivek o ",[883,96467,96469],{"className":96468},[886],[888,96470,96471],{"xmlns":890},[892,96472,96473,96477],{},[895,96474,96475],{},[898,96476,1991],{},[902,96478,1991],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,96481,96482],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,96485,96487],{"className":96486},[886],[888,96488,96489],{"xmlns":890},[892,96490,96491,96513],{},[895,96492,96493,96495,96497,96503,96505,96511],{},[898,96494,4819],{},[1664,96496,1837],{"stretchy":1666},[1720,96498,96499,96501],{},[898,96500,1973],{},[898,96502,4819],{},[1664,96504,1916],{"separator":1915},[1720,96506,96507,96509],{},[898,96508,2398],{},[898,96510,4819],{},[1664,96512,1850],{"stretchy":1666},[902,96514,41867],{"encoding":904},[37470,96516],{},[115,96518,96520],{"id":96519},"daň-uložená-výrobci","Daň uložená výrobci",[724,96522,96523,96524,96537,96538,96555,96556,96583],{},"Je-li daň ",[883,96525,96527],{"className":96526},[886],[888,96528,96529],{"xmlns":890},[892,96530,96531,96535],{},[895,96532,96533],{},[898,96534,1991],{},[902,96536,1991],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,96539,96541],{"className":96540},[886],[888,96542,96543],{"xmlns":890},[892,96544,96545,96553],{},[895,96546,96547,96549,96551],{},[898,96548,2398],{},[1664,96550,1867],{},[898,96552,1991],{},[902,96554,41622],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,96557,96559],{"className":96558},[886],[888,96560,96561],{"xmlns":890},[892,96562,96563,96581],{},[895,96564,96565,96567,96569,96571,96573,96575,96577,96579],{},[898,96566,2398],{},[1664,96568,1867],{},[898,96570,1991],{},[1664,96572,1676],{},[898,96574,2351],{},[1664,96576,1667],{"stretchy":1666},[898,96578,1973],{},[1664,96580,1673],{"stretchy":1666},[902,96582,41651],{"encoding":904}," nová funkce nabídky:",[883,96585,96587],{"className":96586},[886],[888,96588,96589],{"xmlns":890,"display":28566},[892,96590,96591,96625],{},[895,96592,96593,96595,96597,96603,96605,96607,96609,96611,96613,96615,96617,96619,96621,96623],{},[898,96594,2398],{},[1664,96596,1676],{},[2355,96598,96599,96601],{},[898,96600,2351],{},[1963,96602,2875],{},[1664,96604,1667],{"stretchy":1666},[898,96606,1973],{},[1664,96608,1673],{"stretchy":1666},[1664,96610,1676],{},[898,96612,2351],{},[1664,96614,1667],{"stretchy":1666},[898,96616,1973],{},[1664,96618,1673],{"stretchy":1666},[1664,96620,1700],{},[898,96622,1991],{},[898,96624,1977],{"mathvariant":1726},[902,96626,41696],{"encoding":904},[724,96628,96629,96630,1885,96643,96645],{},"Nabídka se tedy posouvá o ",[883,96631,96633],{"className":96632},[886],[888,96634,96635],{"xmlns":890},[892,96636,96637,96641],{},[895,96638,96639],{},[898,96640,1991],{},[902,96642,1991],{"encoding":904},[38,96644,41729],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,96647,96648,96649,96689,96690,4454,96718,96746,96747,96766,96767,96791,96792,4488],{},"Nový rovnovážný bod ",[883,96650,96652],{"className":96651},[886],[888,96653,96654],{"xmlns":890},[892,96655,96656,96686],{},[895,96657,96658,96664,96666,96674,96676,96684],{},[2355,96659,96660,96662],{},[898,96661,4819],{},[1963,96663,2875],{},[1664,96665,1837],{"stretchy":1666},[1810,96667,96668,96670,96672],{},[898,96669,1973],{},[1963,96671,2875],{},[898,96673,4819],{},[1664,96675,1916],{"separator":1915},[1810,96677,96678,96680,96682],{},[898,96679,2398],{},[1963,96681,2875],{},[898,96683,4819],{},[1664,96685,1850],{"stretchy":1666},[902,96687,96688],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,96691,96693],{"className":96692},[886],[888,96694,96695],{"xmlns":890},[892,96696,96697,96715],{},[895,96698,96699,96707,96709],{},[1810,96700,96701,96703,96705],{},[898,96702,1973],{},[1963,96704,2875],{},[898,96706,4819],{},[1664,96708,4022],{},[1720,96710,96711,96713],{},[898,96712,1973],{},[898,96714,4819],{},[902,96716,96717],{"encoding":904},"Q_1^E \u003C Q^E",[883,96719,96721],{"className":96720},[886],[888,96722,96723],{"xmlns":890},[892,96724,96725,96743],{},[895,96726,96727,96735,96737],{},[1810,96728,96729,96731,96733],{},[898,96730,2398],{},[1963,96732,2875],{},[898,96734,4819],{},[1664,96736,3984],{},[1720,96738,96739,96741],{},[898,96740,2398],{},[898,96742,4819],{},[902,96744,96745],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,96748,96750],{"className":96749},[886],[888,96751,96752],{"xmlns":890},[892,96753,96754,96764],{},[895,96755,96756],{},[1810,96757,96758,96760,96762],{},[898,96759,2398],{},[1963,96761,2875],{},[898,96763,4819],{},[902,96765,48357],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,96768,96770],{"className":96769},[886],[888,96771,96772],{"xmlns":890},[892,96773,96774,96788],{},[895,96775,96776,96784,96786],{},[1810,96777,96778,96780,96782],{},[898,96779,2398],{},[1963,96781,2875],{},[898,96783,4819],{},[1664,96785,1867],{},[898,96787,1991],{},[902,96789,96790],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,96793,96795],{"className":96794},[886],[888,96796,96797],{"xmlns":890},[892,96798,96799,96807],{},[895,96800,96801],{},[1720,96802,96803,96805],{},[898,96804,2398],{},[898,96806,4819],{},[902,96808,41966],{"encoding":904},[724,96810,96811],{},[614,96812,96813,96814,96844,96845,96858,96859,6235,96876,96889,96890,1977],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,96815,96817],{"className":96816},[886],[888,96818,96819],{"xmlns":890},[892,96820,96821,96841],{},[895,96822,96823,96825,96827,96833,96835,96837,96839],{},[898,96824,2351],{},[1664,96826,3699],{},[2355,96828,96829,96831],{},[898,96830,2351],{},[1963,96832,2875],{},[1664,96834,1676],{},[898,96836,2351],{},[1664,96838,1700],{},[898,96840,1991],{},[902,96842,96843],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,96846,96848],{"className":96847},[886],[888,96849,96850],{"xmlns":890},[892,96851,96852,96856],{},[895,96853,96854],{},[898,96855,1991],{},[902,96857,1991],{"encoding":904},". Průsečík ",[883,96860,96862],{"className":96861},[886],[888,96863,96864],{"xmlns":890},[892,96865,96866,96874],{},[895,96867,96868],{},[2355,96869,96870,96872],{},[898,96871,2351],{},[1963,96873,2875],{},[902,96875,41497],{"encoding":904},[883,96877,96879],{"className":96878},[886],[888,96880,96881],{"xmlns":890},[892,96882,96883,96887],{},[895,96884,96885],{},[898,96886,2379],{},[902,96888,2379],{"encoding":904}," je nový rovnovážný bod ",[883,96891,96893],{"className":96892},[886],[888,96894,96895],{"xmlns":890},[892,96896,96897,96905],{},[895,96898,96899],{},[2355,96900,96901,96903],{},[898,96902,4819],{},[1963,96904,2875],{},[902,96906,96907],{"encoding":904},"E_1",[198,96909,45803],{"id":96910},"příklad-29",[724,96912,96913,42155,96915,42190,96939,96959,96960,96977],{},[38,96914,38433],{},[883,96916,96918],{"className":96917},[886],[888,96919,96920],{"xmlns":890},[892,96921,96922,96936],{},[895,96923,96924,96926,96928,96930,96932,96934],{},[898,96925,2398],{},[1664,96927,1676],{},[1963,96929,4084],{},[1664,96931,1867],{},[1963,96933,1970],{},[898,96935,1973],{},[902,96937,96938],{"encoding":904},"P = 12 - 2Q",[883,96940,96942],{"className":96941},[886],[888,96943,96944],{"xmlns":890},[892,96945,96946,96956],{},[895,96947,96948,96950,96952,96954],{},[898,96949,2398],{},[1664,96951,1676],{},[1963,96953,2944],{},[898,96955,1973],{},[902,96957,96958],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,96961,96963],{"className":96962},[886],[888,96964,96965],{"xmlns":890},[892,96966,96967,96975],{},[895,96968,96969,96971,96973],{},[898,96970,1991],{},[1664,96972,1676],{},[1963,96974,2833],{},[902,96976,41768],{"encoding":904}," Kč.",[724,96979,96980],{},[38,96981,38465],{},[724,96983,96984,96987,96988,6135,97014,6155,97034,1343,97056,97086,97087,1977],{},[614,96985,96986],{},"Bez daně."," Z rovnosti ",[883,96989,96991],{"className":96990},[886],[888,96992,96993],{"xmlns":890},[892,96994,96995,97011],{},[895,96996,96997,96999,97001,97003,97005,97007,97009],{},[1963,96998,4084],{},[1664,97000,1867],{},[1963,97002,1970],{},[898,97004,1973],{},[1664,97006,1676],{},[1963,97008,2944],{},[898,97010,1973],{},[902,97012,97013],{"encoding":904},"12 - 2Q = 4Q",[883,97015,97017],{"className":97016},[886],[888,97018,97019],{"xmlns":890},[892,97020,97021,97031],{},[895,97022,97023,97025,97027,97029],{},[1963,97024,2833],{},[898,97026,1973],{},[1664,97028,1676],{},[1963,97030,4084],{},[902,97032,97033],{"encoding":904},"6Q = 12",[883,97035,97037],{"className":97036},[886],[888,97038,97039],{"xmlns":890},[892,97040,97041,97053],{},[895,97042,97043,97049,97051],{},[1720,97044,97045,97047],{},[898,97046,1973],{},[898,97048,4819],{},[1664,97050,1676],{},[1963,97052,1970],{},[902,97054,97055],{"encoding":904},"Q^E = 2",[883,97057,97059],{"className":97058},[886],[888,97060,97061],{"xmlns":890},[892,97062,97063,97083],{},[895,97064,97065,97071,97073,97075,97077,97079,97081],{},[1720,97066,97067,97069],{},[898,97068,2398],{},[898,97070,4819],{},[1664,97072,1676],{},[1963,97074,2944],{},[1664,97076,3753],{},[1963,97078,1970],{},[1664,97080,1676],{},[1963,97082,6151],{},[902,97084,97085],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,97088,97090],{"className":97089},[886],[888,97091,97092],{"xmlns":890},[892,97093,97094,97108],{},[895,97095,97096,97098,97100,97102,97104,97106],{},[898,97097,4819],{},[1664,97099,1837],{"stretchy":1666},[1963,97101,1970],{},[1664,97103,1916],{"separator":1915},[1963,97105,6151],{},[1664,97107,1850],{"stretchy":1666},[902,97109,97110],{"encoding":904},"E[2, 8]",[724,97112,97113,97116,97117,97149],{},[614,97114,97115],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,97118,97120],{"className":97119},[886],[888,97121,97122],{"xmlns":890},[892,97123,97124,97146],{},[895,97125,97126,97132,97134,97136,97138,97140,97142,97144],{},[2355,97127,97128,97130],{},[898,97129,2351],{},[1963,97131,2875],{},[1664,97133,2087],{},[898,97135,2398],{},[1664,97137,1676],{},[1963,97139,2944],{},[898,97141,1973],{},[1664,97143,1700],{},[1963,97145,2833],{},[902,97147,97148],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,97151,97153],{"className":97152},[886],[888,97154,97155],{"xmlns":890,"display":28566},[892,97156,97157,97177],{},[895,97158,97159,97161,97163,97165,97167,97169,97171,97173,97175],{},[1963,97160,4084],{},[1664,97162,1867],{},[1963,97164,1970],{},[898,97166,1973],{},[1664,97168,1676],{},[1963,97170,2944],{},[898,97172,1973],{},[1664,97174,1700],{},[1963,97176,2833],{},[902,97178,97179],{"encoding":904},"12 - 2Q = 4Q + 6",[724,97181,97182,97183,6155,97203,1343,97227,97263,97264,1977],{},"plyne ",[883,97184,97186],{"className":97185},[886],[888,97187,97188],{"xmlns":890},[892,97189,97190,97200],{},[895,97191,97192,97194,97196,97198],{},[1963,97193,2833],{},[898,97195,1973],{},[1664,97197,1676],{},[1963,97199,2833],{},[902,97201,97202],{"encoding":904},"6Q = 6",[883,97204,97206],{"className":97205},[886],[888,97207,97208],{"xmlns":890},[892,97209,97210,97224],{},[895,97211,97212,97220,97222],{},[1810,97213,97214,97216,97218],{},[898,97215,1973],{},[1963,97217,2875],{},[898,97219,4819],{},[1664,97221,1676],{},[1963,97223,2875],{},[902,97225,97226],{"encoding":904},"Q_1^E = 1",[883,97228,97230],{"className":97229},[886],[888,97231,97232],{"xmlns":890},[892,97233,97234,97260],{},[895,97235,97236,97244,97246,97248,97250,97252,97254,97256,97258],{},[1810,97237,97238,97240,97242],{},[898,97239,2398],{},[1963,97241,2875],{},[898,97243,4819],{},[1664,97245,1676],{},[1963,97247,2944],{},[1664,97249,3753],{},[1963,97251,2875],{},[1664,97253,1700],{},[1963,97255,2833],{},[1664,97257,1676],{},[1963,97259,3442],{},[902,97261,97262],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,97265,97267],{"className":97266},[886],[888,97268,97269],{"xmlns":890},[892,97270,97271,97289],{},[895,97272,97273,97279,97281,97283,97285,97287],{},[2355,97274,97275,97277],{},[898,97276,4819],{},[1963,97278,2875],{},[1664,97280,1837],{"stretchy":1666},[1963,97282,2875],{},[1664,97284,1916],{"separator":1915},[1963,97286,3442],{},[1664,97288,1850],{"stretchy":1666},[902,97290,97291],{"encoding":904},"E_1[1, 10]",[724,97293,97294,97297,97298,97322,97323,97336],{},[614,97295,97296],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,97299,97301],{"className":97300},[886],[888,97302,97303],{"xmlns":890},[892,97304,97305,97319],{},[895,97306,97307,97315,97317],{},[1810,97308,97309,97311,97313],{},[898,97310,2398],{},[1963,97312,2875],{},[898,97314,4819],{},[1664,97316,1676],{},[1963,97318,3442],{},[902,97320,97321],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,97324,97326],{"className":97325},[886],[888,97327,97328],{"xmlns":890},[892,97329,97330,97334],{},[895,97331,97332],{},[1963,97333,6151],{},[902,97335,6151],{"encoding":904},", navýšení je",[883,97338,97340],{"className":97339},[886],[888,97341,97342],{"xmlns":890,"display":28566},[892,97343,97344,97400],{},[895,97345,97346,97356,97358,97366,97368,97374,97376,97378,97380,97382,97384,97386,97388,97398],{},[2355,97347,97348,97350],{},[898,97349,1991],{},[895,97351,97352,97354],{},[898,97353,43177],{},[898,97355,724],{},[1664,97357,1676],{},[1810,97359,97360,97362,97364],{},[898,97361,2398],{},[1963,97363,2875],{},[898,97365,4819],{},[1664,97367,1867],{},[1720,97369,97370,97372],{},[898,97371,2398],{},[898,97373,4819],{},[1664,97375,1676],{},[1963,97377,3442],{},[1664,97379,1867],{},[1963,97381,6151],{},[1664,97383,1676],{},[1963,97385,1970],{},[1690,97387,2884],{},[895,97389,97390,97392],{},[1690,97391,10363],{},[8951,97393,97394,97396],{"accent":1915},[1690,97395,2034],{},[1664,97397,25558],{},[898,97399,1977],{"mathvariant":1726},[902,97401,97402],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,97404,97405,97406,97322,97442,97455],{},"Výrobci zůstává čistá cena ",[883,97407,97409],{"className":97408},[886],[888,97410,97411],{"xmlns":890},[892,97412,97413,97439],{},[895,97414,97415,97423,97425,97427,97429,97431,97433,97435,97437],{},[1810,97416,97417,97419,97421],{},[898,97418,2398],{},[1963,97420,2875],{},[898,97422,4819],{},[1664,97424,1867],{},[898,97426,1991],{},[1664,97428,1676],{},[1963,97430,3442],{},[1664,97432,1867],{},[1963,97434,2833],{},[1664,97436,1676],{},[1963,97438,2944],{},[902,97440,97441],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,97443,97445],{"className":97444},[886],[888,97446,97447],{"xmlns":890},[892,97448,97449,97453],{},[895,97450,97451],{},[1963,97452,6151],{},[902,97454,6151],{"encoding":904},", pokles je",[883,97457,97459],{"className":97458},[886],[888,97460,97461],{"xmlns":890,"display":28566},[892,97462,97463,97529],{},[895,97464,97465,97477,97479,97485,97487,97489,97497,97499,97501,97503,97505,97507,97509,97511,97513,97515,97517,97527],{},[2355,97466,97467,97469],{},[898,97468,1991],{},[895,97470,97471,97473,97475],{},[898,97472,43200],{},[898,97474,2608],{},[898,97476,12540],{},[1664,97478,1676],{},[1720,97480,97481,97483],{},[898,97482,2398],{},[898,97484,4819],{},[1664,97486,1867],{},[1664,97488,1667],{"stretchy":1666},[1810,97490,97491,97493,97495],{},[898,97492,2398],{},[1963,97494,2875],{},[898,97496,4819],{},[1664,97498,1867],{},[898,97500,1991],{},[1664,97502,1673],{"stretchy":1666},[1664,97504,1676],{},[1963,97506,6151],{},[1664,97508,1867],{},[1963,97510,2944],{},[1664,97512,1676],{},[1963,97514,2944],{},[1690,97516,2884],{},[895,97518,97519,97521],{},[1690,97520,10363],{},[8951,97522,97523,97525],{"accent":1915},[1690,97524,2034],{},[1664,97526,25558],{},[898,97528,1977],{"mathvariant":1726},[902,97530,97531],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,97533,97534,97535,97587],{},"Kontrola: ",[883,97536,97538],{"className":97537},[886],[888,97539,97540],{"xmlns":890},[892,97541,97542,97584],{},[895,97543,97544,97554,97556,97568,97570,97572,97574,97576,97578,97580,97582],{},[2355,97545,97546,97548],{},[898,97547,1991],{},[895,97549,97550,97552],{},[898,97551,43177],{},[898,97553,724],{},[1664,97555,1700],{},[2355,97557,97558,97560],{},[898,97559,1991],{},[895,97561,97562,97564,97566],{},[898,97563,43200],{},[898,97565,2608],{},[898,97567,12540],{},[1664,97569,1676],{},[1963,97571,1970],{},[1664,97573,1700],{},[1963,97575,2944],{},[1664,97577,1676],{},[1963,97579,2833],{},[1664,97581,1676],{},[898,97583,1991],{},[902,97585,97586],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[37470,97589],{},[115,97591,97593],{"id":97592},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,97595,96523,97596,97609,97610,97628,97629,97657],{},[883,97597,97599],{"className":97598},[886],[888,97600,97601],{"xmlns":890},[892,97602,97603,97607],{},[895,97604,97605],{},[898,97606,1991],{},[902,97608,1991],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,97611,97613],{"className":97612},[886],[888,97614,97615],{"xmlns":890},[892,97616,97617,97625],{},[895,97618,97619,97621,97623],{},[898,97620,2398],{},[1664,97622,1700],{},[898,97624,1991],{},[902,97626,97627],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,97630,97632],{"className":97631},[886],[888,97633,97634],{"xmlns":890},[892,97635,97636,97654],{},[895,97637,97638,97640,97642,97644,97646,97648,97650,97652],{},[898,97639,2398],{},[1664,97641,1700],{},[898,97643,1991],{},[1664,97645,1676],{},[898,97647,2379],{},[1664,97649,1667],{"stretchy":1666},[898,97651,1973],{},[1664,97653,1673],{"stretchy":1666},[902,97655,97656],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,97659,97661],{"className":97660},[886],[888,97662,97663],{"xmlns":890,"display":28566},[892,97664,97665,97699],{},[895,97666,97667,97669,97671,97677,97679,97681,97683,97685,97687,97689,97691,97693,97695,97697],{},[898,97668,2398],{},[1664,97670,1676],{},[2355,97672,97673,97675],{},[898,97674,2379],{},[1963,97676,1970],{},[1664,97678,1667],{"stretchy":1666},[898,97680,1973],{},[1664,97682,1673],{"stretchy":1666},[1664,97684,1676],{},[898,97686,2379],{},[1664,97688,1667],{"stretchy":1666},[898,97690,1973],{},[1664,97692,1673],{"stretchy":1666},[1664,97694,1867],{},[898,97696,1991],{},[898,97698,1977],{"mathvariant":1726},[902,97700,97701],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,97703,97704,97705,1885,97718,97721],{},"Poptávka se tedy posouvá o ",[883,97706,97708],{"className":97707},[886],[888,97709,97710],{"xmlns":890},[892,97711,97712,97716],{},[895,97713,97714],{},[898,97715,1991],{},[902,97717,1991],{"encoding":904},[38,97719,97720],{},"svisle dolů",". Nabídka se nemění.",[724,97723,96648,97724,96689,97764,4454,97792,97820,97821,97840,97841,97865,97866,4488],{},[883,97725,97727],{"className":97726},[886],[888,97728,97729],{"xmlns":890},[892,97730,97731,97761],{},[895,97732,97733,97739,97741,97749,97751,97759],{},[2355,97734,97735,97737],{},[898,97736,4819],{},[1963,97738,1970],{},[1664,97740,1837],{"stretchy":1666},[1810,97742,97743,97745,97747],{},[898,97744,1973],{},[1963,97746,1970],{},[898,97748,4819],{},[1664,97750,1916],{"separator":1915},[1810,97752,97753,97755,97757],{},[898,97754,2398],{},[1963,97756,1970],{},[898,97758,4819],{},[1664,97760,1850],{"stretchy":1666},[902,97762,97763],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,97765,97767],{"className":97766},[886],[888,97768,97769],{"xmlns":890},[892,97770,97771,97789],{},[895,97772,97773,97781,97783],{},[1810,97774,97775,97777,97779],{},[898,97776,1973],{},[1963,97778,1970],{},[898,97780,4819],{},[1664,97782,4022],{},[1720,97784,97785,97787],{},[898,97786,1973],{},[898,97788,4819],{},[902,97790,97791],{"encoding":904},"Q_2^E \u003C Q^E",[883,97793,97795],{"className":97794},[886],[888,97796,97797],{"xmlns":890},[892,97798,97799,97817],{},[895,97800,97801,97809,97811],{},[1810,97802,97803,97805,97807],{},[898,97804,2398],{},[1963,97806,1970],{},[898,97808,4819],{},[1664,97810,4022],{},[1720,97812,97813,97815],{},[898,97814,2398],{},[898,97816,4819],{},[902,97818,97819],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,97822,97824],{"className":97823},[886],[888,97825,97826],{"xmlns":890},[892,97827,97828,97838],{},[895,97829,97830],{},[1810,97831,97832,97834,97836],{},[898,97833,2398],{},[1963,97835,1970],{},[898,97837,4819],{},[902,97839,48418],{"encoding":904},", spotřebitel platí celkem ",[883,97842,97844],{"className":97843},[886],[888,97845,97846],{"xmlns":890},[892,97847,97848,97862],{},[895,97849,97850,97858,97860],{},[1810,97851,97852,97854,97856],{},[898,97853,2398],{},[1963,97855,1970],{},[898,97857,4819],{},[1664,97859,1700],{},[898,97861,1991],{},[902,97863,97864],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,97867,97869],{"className":97868},[886],[888,97870,97871],{"xmlns":890},[892,97872,97873,97881],{},[895,97874,97875],{},[1720,97876,97877,97879],{},[898,97878,2398],{},[898,97880,4819],{},[902,97882,41966],{"encoding":904},[724,97884,97885],{},"Daňové břemeno:",[883,97887,97889],{"className":97888},[886],[888,97890,97891],{"xmlns":890,"display":28566},[892,97892,97893,97967],{},[895,97894,97895,97905,97907,97909,97917,97919,97921,97923,97925,97931,97933,97935,97947,97949,97955,97957,97965],{},[2355,97896,97897,97899],{},[898,97898,1991],{},[895,97900,97901,97903],{},[898,97902,43177],{},[898,97904,724],{},[1664,97906,1676],{},[1664,97908,1667],{"stretchy":1666},[1810,97910,97911,97913,97915],{},[898,97912,2398],{},[1963,97914,1970],{},[898,97916,4819],{},[1664,97918,1700],{},[898,97920,1991],{},[1664,97922,1673],{"stretchy":1666},[1664,97924,1867],{},[1720,97926,97927,97929],{},[898,97928,2398],{},[898,97930,4819],{},[1664,97932,1916],{"separator":1915},[6444,97934],{"width":6446},[2355,97936,97937,97939],{},[898,97938,1991],{},[895,97940,97941,97943,97945],{},[898,97942,43200],{},[898,97944,2608],{},[898,97946,12540],{},[1664,97948,1676],{},[1720,97950,97951,97953],{},[898,97952,2398],{},[898,97954,4819],{},[1664,97956,1867],{},[1810,97958,97959,97961,97963],{},[898,97960,2398],{},[1963,97962,1970],{},[898,97964,4819],{},[898,97966,1977],{"mathvariant":1726},[902,97968,97969],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,97971,97972],{},[614,97973,97974,97975,98005,98006,96858,98019,6235,98036,96889,98049,1977],{},"Obrázek 2.19: Posun ",[883,97976,97978],{"className":97977},[886],[888,97979,97980],{"xmlns":890},[892,97981,97982,98002],{},[895,97983,97984,97986,97988,97994,97996,97998,98000],{},[898,97985,2379],{},[1664,97987,3699],{},[2355,97989,97990,97992],{},[898,97991,2379],{},[1963,97993,1970],{},[1664,97995,1676],{},[898,97997,2379],{},[1664,97999,1867],{},[898,98001,1991],{},[902,98003,98004],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,98007,98009],{"className":98008},[886],[888,98010,98011],{"xmlns":890},[892,98012,98013,98017],{},[895,98014,98015],{},[898,98016,1991],{},[902,98018,1991],{"encoding":904},[883,98020,98022],{"className":98021},[886],[888,98023,98024],{"xmlns":890},[892,98025,98026,98034],{},[895,98027,98028],{},[2355,98029,98030,98032],{},[898,98031,2379],{},[1963,98033,1970],{},[902,98035,38827],{"encoding":904},[883,98037,98039],{"className":98038},[886],[888,98040,98041],{"xmlns":890},[892,98042,98043,98047],{},[895,98044,98045],{},[898,98046,2351],{},[902,98048,2351],{"encoding":904},[883,98050,98052],{"className":98051},[886],[888,98053,98054],{"xmlns":890},[892,98055,98056,98064],{},[895,98057,98058],{},[2355,98059,98060,98062],{},[898,98061,4819],{},[1963,98063,1970],{},[902,98065,98066],{"encoding":904},"E_2",[198,98068,45883],{"id":98069},"příklad-210",[724,98071,98072,98074,98075,42190,98098,98117,98118,98135],{},[38,98073,38433],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,98076,98078],{"className":98077},[886],[888,98079,98080],{"xmlns":890},[892,98081,98082,98096],{},[895,98083,98084,98086,98088,98090,98092,98094],{},[898,98085,2398],{},[1664,98087,1676],{},[1963,98089,4084],{},[1664,98091,1867],{},[1963,98093,1970],{},[898,98095,1973],{},[902,98097,96938],{"encoding":904},[883,98099,98101],{"className":98100},[886],[888,98102,98103],{"xmlns":890},[892,98104,98105,98115],{},[895,98106,98107,98109,98111,98113],{},[898,98108,2398],{},[1664,98110,1676],{},[1963,98112,2944],{},[898,98114,1973],{},[902,98116,96958],{"encoding":904},". Daň ",[883,98119,98121],{"className":98120},[886],[888,98122,98123],{"xmlns":890},[892,98124,98125,98133],{},[895,98126,98127,98129,98131],{},[898,98128,1991],{},[1664,98130,1676],{},[1963,98132,2833],{},[902,98134,41768],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,98137,98138],{},[38,98139,38465],{},[724,98141,98142,98143,97149],{},"Nová poptávka je ",[883,98144,98146],{"className":98145},[886],[888,98147,98148],{"xmlns":890},[892,98149,98150,98186],{},[895,98151,98152,98158,98160,98162,98164,98166,98168,98170,98172,98174,98176,98178,98180,98182,98184],{},[2355,98153,98154,98156],{},[898,98155,2379],{},[1963,98157,1970],{},[1664,98159,2087],{},[898,98161,2398],{},[1664,98163,1676],{},[1963,98165,4084],{},[1664,98167,1867],{},[1963,98169,1970],{},[898,98171,1973],{},[1664,98173,1867],{},[1963,98175,2833],{},[1664,98177,1676],{},[1963,98179,2833],{},[1664,98181,1867],{},[1963,98183,1970],{},[898,98185,1973],{},[902,98187,98188],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,98190,98192],{"className":98191},[886],[888,98193,98194],{"xmlns":890,"display":28566},[892,98195,98196,98212],{},[895,98197,98198,98200,98202,98204,98206,98208,98210],{},[1963,98199,2833],{},[1664,98201,1867],{},[1963,98203,1970],{},[898,98205,1973],{},[1664,98207,1676],{},[1963,98209,2944],{},[898,98211,1973],{},[902,98213,98214],{"encoding":904},"6 - 2Q = 4Q",[724,98216,97182,98217,6155,98236,1343,98260,97263,98292,1977],{},[883,98218,98220],{"className":98219},[886],[888,98221,98222],{"xmlns":890},[892,98223,98224,98234],{},[895,98225,98226,98228,98230,98232],{},[1963,98227,2833],{},[898,98229,1973],{},[1664,98231,1676],{},[1963,98233,2833],{},[902,98235,97202],{"encoding":904},[883,98237,98239],{"className":98238},[886],[888,98240,98241],{"xmlns":890},[892,98242,98243,98257],{},[895,98244,98245,98253,98255],{},[1810,98246,98247,98249,98251],{},[898,98248,1973],{},[1963,98250,1970],{},[898,98252,4819],{},[1664,98254,1676],{},[1963,98256,2875],{},[902,98258,98259],{"encoding":904},"Q_2^E = 1",[883,98261,98263],{"className":98262},[886],[888,98264,98265],{"xmlns":890},[892,98266,98267,98289],{},[895,98268,98269,98277,98279,98281,98283,98285,98287],{},[1810,98270,98271,98273,98275],{},[898,98272,2398],{},[1963,98274,1970],{},[898,98276,4819],{},[1664,98278,1676],{},[1963,98280,2944],{},[1664,98282,3753],{},[1963,98284,2875],{},[1664,98286,1676],{},[1963,98288,2944],{},[902,98290,98291],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,98293,98295],{"className":98294},[886],[888,98296,98297],{"xmlns":890},[892,98298,98299,98317],{},[895,98300,98301,98307,98309,98311,98313,98315],{},[2355,98302,98303,98305],{},[898,98304,4819],{},[1963,98306,1970],{},[1664,98308,1837],{"stretchy":1666},[1963,98310,2875],{},[1664,98312,1916],{"separator":1915},[1963,98314,2944],{},[1664,98316,1850],{"stretchy":1666},[902,98318,98319],{"encoding":904},"E_2[1, 4]",[724,98321,98322,98323,98359,98360,96977],{},"Spotřebitel platí celkem ",[883,98324,98326],{"className":98325},[886],[888,98327,98328],{"xmlns":890},[892,98329,98330,98356],{},[895,98331,98332,98340,98342,98344,98346,98348,98350,98352,98354],{},[1810,98333,98334,98336,98338],{},[898,98335,2398],{},[1963,98337,1970],{},[898,98339,4819],{},[1664,98341,1700],{},[898,98343,1991],{},[1664,98345,1676],{},[1963,98347,2944],{},[1664,98349,1700],{},[1963,98351,2833],{},[1664,98353,1676],{},[1963,98355,3442],{},[902,98357,98358],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,98361,98363],{"className":98362},[886],[888,98364,98365],{"xmlns":890},[892,98366,98367,98381],{},[895,98368,98369,98377,98379],{},[1810,98370,98371,98373,98375],{},[898,98372,2398],{},[1963,98374,1970],{},[898,98376,4819],{},[1664,98378,1676],{},[1963,98380,2944],{},[902,98382,98383],{"encoding":904},"P_2^E = 4",[724,98385,98386],{},[614,98387,98388],{},"Rozklad daňového břemene:",[883,98390,98392],{"className":98391},[886],[888,98393,98394],{"xmlns":890,"display":28566},[892,98395,98396,98482],{},[895,98397,98398,98408,98410,98412,98414,98416,98418,98420,98422,98424,98426,98428,98430,98440,98442,98444,98456,98458,98460,98462,98464,98466,98468,98470,98480],{},[2355,98399,98400,98402],{},[898,98401,1991],{},[895,98403,98404,98406],{},[898,98405,43177],{},[898,98407,724],{},[1664,98409,1676],{},[1664,98411,1667],{"stretchy":1666},[1963,98413,2944],{},[1664,98415,1700],{},[1963,98417,2833],{},[1664,98419,1673],{"stretchy":1666},[1664,98421,1867],{},[1963,98423,6151],{},[1664,98425,1676],{},[1963,98427,1970],{},[1690,98429,2884],{},[895,98431,98432,98434],{},[1690,98433,10363],{},[8951,98435,98436,98438],{"accent":1915},[1690,98437,2034],{},[1664,98439,25558],{},[1664,98441,1916],{"separator":1915},[6444,98443],{"width":6446},[2355,98445,98446,98448],{},[898,98447,1991],{},[895,98449,98450,98452,98454],{},[898,98451,43200],{},[898,98453,2608],{},[898,98455,12540],{},[1664,98457,1676],{},[1963,98459,6151],{},[1664,98461,1867],{},[1963,98463,2944],{},[1664,98465,1676],{},[1963,98467,2944],{},[1690,98469,2884],{},[895,98471,98472,98474],{},[1690,98473,10363],{},[8951,98475,98476,98478],{"accent":1915},[1690,98477,2034],{},[1664,98479,25558],{},[898,98481,1977],{"mathvariant":1726},[902,98483,98484],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,98486,98487,98488,1977],{},"Opět ",[883,98489,98491],{"className":98490},[886],[888,98492,98493],{"xmlns":890},[892,98494,98495,98529],{},[895,98496,98497,98507,98509,98521,98523,98525,98527],{},[2355,98498,98499,98501],{},[898,98500,1991],{},[895,98502,98503,98505],{},[898,98504,43177],{},[898,98506,724],{},[1664,98508,1700],{},[2355,98510,98511,98513],{},[898,98512,1991],{},[895,98514,98515,98517,98519],{},[898,98516,43200],{},[898,98518,2608],{},[898,98520,12540],{},[1664,98522,1676],{},[1963,98524,2833],{},[1664,98526,1676],{},[898,98528,1991],{},[902,98530,98531],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[37470,98533],{},[115,98535,43158],{"id":98536},"daňové-břemeno",[724,98538,98539,10588,98541,98544,98545,98558],{},[38,98540,43158],{},[614,98542,98543],{},"tax burden",") je rozdělení zaplacené daně ",[883,98546,98548],{"className":98547},[886],[888,98549,98550],{"xmlns":890},[892,98551,98552,98556],{},[895,98553,98554],{},[898,98555,1991],{},[902,98557,1991],{"encoding":904}," mezi spotřebitele a výrobce:",[883,98560,98562],{"className":98561},[886],[888,98563,98564],{"xmlns":890,"display":28566},[892,98565,98566,98598],{},[895,98567,98568,98570,98572,98582,98584,98596],{},[898,98569,1991],{},[1664,98571,1676],{},[2355,98573,98574,98576],{},[898,98575,1991],{},[895,98577,98578,98580],{},[898,98579,43177],{},[898,98581,724],{},[1664,98583,1700],{},[2355,98585,98586,98588],{},[898,98587,1991],{},[895,98589,98590,98592,98594],{},[898,98591,43200],{},[898,98593,2608],{},[898,98595,12540],{},[898,98597,1977],{"mathvariant":1726},[902,98599,98600],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,98602,98603],{},[1928,98604],{"alt":98605,"className":98606,"src":98607},"imek-dan-rozklad-bremene-sklony",[210,1932],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[4436,98609,98610],{},[724,98611,98612,98614,98615,4454,98628,1977],{},[883,98613,4723],{}," 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 ",[883,98616,98618],{"className":98617},[886],[888,98619,98620],{"xmlns":890},[892,98621,98622,98626],{},[895,98623,98624],{},[898,98625,2379],{},[902,98627,2379],{"encoding":904},[883,98629,98631],{"className":98630},[886],[888,98632,98633],{"xmlns":890},[892,98634,98635,98639],{},[895,98636,98637],{},[898,98638,2351],{},[902,98640,2351],{"encoding":904},[198,98642,3034],{"id":3033},[724,98644,98645,98646,98667,98668,98681,98682,98699,98700,98713],{},"V grafu ",[883,98647,98649],{"className":98648},[886],[888,98650,98651],{"xmlns":890},[892,98652,98653,98665],{},[895,98654,98655,98657,98659,98661,98663],{},[1664,98656,1667],{"stretchy":1666},[898,98658,1973],{},[1664,98660,1916],{"separator":1915},[898,98662,2398],{},[1664,98664,1673],{"stretchy":1666},[902,98666,38191],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,98669,98671],{"className":98670},[886],[888,98672,98673],{"xmlns":890},[892,98674,98675,98679],{},[895,98676,98677],{},[898,98678,1991],{},[902,98680,1991],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,98683,98685],{"className":98684},[886],[888,98686,98687],{"xmlns":890},[892,98688,98689,98697],{},[895,98690,98691],{},[1720,98692,98693,98695],{},[898,98694,2398],{},[898,98696,4819],{},[902,98698,41966],{"encoding":904},", rozdělí se úsečka ",[883,98701,98703],{"className":98702},[886],[888,98704,98705],{"xmlns":890},[892,98706,98707,98711],{},[895,98708,98709],{},[898,98710,1991],{},[902,98712,1991],{"encoding":904}," na dvě části:",[120,98715,98716,98741],{},[123,98717,98718,98719,98740],{},"horní část odpovídá ",[883,98720,98722],{"className":98721},[886],[888,98723,98724],{"xmlns":890},[892,98725,98726,98738],{},[895,98727,98728],{},[2355,98729,98730,98732],{},[898,98731,1991],{},[895,98733,98734,98736],{},[898,98735,43177],{},[898,98737,724],{},[902,98739,43182],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,98742,98743,98744,98767],{},"dolní část odpovídá ",[883,98745,98747],{"className":98746},[886],[888,98748,98749],{"xmlns":890},[892,98750,98751,98765],{},[895,98752,98753],{},[2355,98754,98755,98757],{},[898,98756,1991],{},[895,98758,98759,98761,98763],{},[898,98760,43200],{},[898,98762,2608],{},[898,98764,12540],{},[902,98766,43207],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,98769,98770],{},[614,98771,98772,98773,3271,98786,98807,98808,98831,98832,4454,98853,98876],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,98774,98776],{"className":98775},[886],[888,98777,98778],{"xmlns":890},[892,98779,98780,98784],{},[895,98781,98782],{},[898,98783,1991],{},[902,98785,1991],{"encoding":904},[883,98787,98789],{"className":98788},[886],[888,98790,98791],{"xmlns":890},[892,98792,98793,98805],{},[895,98794,98795],{},[2355,98796,98797,98799],{},[898,98798,1991],{},[895,98800,98801,98803],{},[898,98802,43177],{},[898,98804,724],{},[902,98806,43182],{"encoding":904}," (nahoře) a ",[883,98809,98811],{"className":98810},[886],[888,98812,98813],{"xmlns":890},[892,98814,98815,98829],{},[895,98816,98817],{},[2355,98818,98819,98821],{},[898,98820,1991],{},[895,98822,98823,98825,98827],{},[898,98824,43200],{},[898,98826,2608],{},[898,98828,12540],{},[902,98830,43207],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,98833,98835],{"className":98834},[886],[888,98836,98837],{"xmlns":890},[892,98838,98839,98851],{},[895,98840,98841],{},[2355,98842,98843,98845],{},[898,98844,1991],{},[895,98846,98847,98849],{},[898,98848,43177],{},[898,98850,724],{},[902,98852,43182],{"encoding":904},[883,98854,98856],{"className":98855},[886],[888,98857,98858],{"xmlns":890},[892,98859,98860,98874],{},[895,98861,98862],{},[2355,98863,98864,98866],{},[898,98865,1991],{},[895,98867,98868,98870,98872],{},[898,98869,43200],{},[898,98871,2608],{},[898,98873,12540],{},[902,98875,43207],{"encoding":904}," je v obou případech stejná.",[198,98878,98880],{"id":98879},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,98882,98883,98884,98887,98888,10588,98911,98928,98929,10588,98952,98969],{},"Platí obecně: ",[38,98885,98886],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,98889,98891],{"className":98890},[886],[888,98892,98893],{"xmlns":890},[892,98894,98895,98909],{},[895,98896,98897,98899,98901,98903,98905,98907],{},[898,98898,2398],{},[1664,98900,1676],{},[898,98902,207],{},[898,98904,1973],{},[1664,98906,1700],{},[898,98908,1818],{},[902,98910,37560],{"encoding":904},[883,98912,98914],{"className":98913},[886],[888,98915,98916],{"xmlns":890},[892,98917,98918,98926],{},[895,98919,98920,98922,98924],{},[898,98921,207],{},[1664,98923,4022],{},[1963,98925,2058],{},[902,98927,43585],{"encoding":904},") a lineární nabídku ",[883,98930,98932],{"className":98931},[886],[888,98933,98934],{"xmlns":890},[892,98935,98936,98950],{},[895,98937,98938,98940,98942,98944,98946,98948],{},[898,98939,2398],{},[1664,98941,1676],{},[898,98943,2034],{},[898,98945,1973],{},[1664,98947,1700],{},[898,98949,1695],{},[902,98951,40742],{"encoding":904},[883,98953,98955],{"className":98954},[886],[888,98956,98957],{"xmlns":890},[892,98958,98959,98967],{},[895,98960,98961,98963,98965],{},[898,98962,2034],{},[1664,98964,3984],{},[1963,98966,2058],{},[902,98968,40760],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,98971,98973],{"className":98972},[886],[888,98974,98975],{"xmlns":890,"display":28566},[892,98976,98977,99043],{},[895,98978,98979,99003,99005,99015,99017,99041],{},[2922,98980,98981,98991],{},[2355,98982,98983,98985],{},[898,98984,1991],{},[895,98986,98987,98989],{},[898,98988,43177],{},[898,98990,724],{},[2355,98992,98993,98995],{},[898,98994,1991],{},[895,98996,98997,98999,99001],{},[898,98998,43200],{},[898,99000,2608],{},[898,99002,12540],{},[1664,99004,1676],{},[2922,99006,99007,99009],{},[898,99008,2034],{},[895,99010,99011,99013],{},[1664,99012,1867],{},[898,99014,207],{},[1664,99016,1676],{},[2922,99018,99019,99031],{},[895,99020,99021,99024,99027,99029],{},[898,99022,99023],{"mathvariant":1726},"∣",[1690,99025,99026],{},"sklon ",[898,99028,2351],{},[898,99030,99023],{"mathvariant":1726},[895,99032,99033,99035,99037,99039],{},[898,99034,99023],{"mathvariant":1726},[1690,99036,99026],{},[898,99038,2379],{},[898,99040,99023],{"mathvariant":1726},[898,99042,1977],{"mathvariant":1726},[902,99044,99045],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[4436,99047,99048,99053],{},[724,99049,99050,99052],{},[883,99051,5138],{}," Postup výpočtu rozkladu",[152,99054,99055,99090,99143,99222],{},[123,99056,99057,99058,99089],{},"Spočti rovnovážný bod ",[883,99059,99061],{"className":99060},[886],[888,99062,99063],{"xmlns":890},[892,99064,99065,99087],{},[895,99066,99067,99069,99071,99077,99079,99085],{},[898,99068,4819],{},[1664,99070,1837],{"stretchy":1666},[1720,99072,99073,99075],{},[898,99074,1973],{},[898,99076,4819],{},[1664,99078,1916],{"separator":1915},[1720,99080,99081,99083],{},[898,99082,2398],{},[898,99084,4819],{},[1664,99086,1850],{"stretchy":1666},[902,99088,41867],{"encoding":904}," bez daně.",[123,99091,99092,99093,1348,99118,4488],{},"Urči posunutou křivku (",[883,99094,99096],{"className":99095},[886],[888,99097,99098],{"xmlns":890},[892,99099,99100,99116],{},[895,99101,99102,99108,99110,99112,99114],{},[2355,99103,99104,99106],{},[898,99105,2351],{},[1963,99107,2875],{},[1664,99109,1676],{},[898,99111,2351],{},[1664,99113,1700],{},[898,99115,1991],{},[902,99117,43254],{"encoding":904},[883,99119,99121],{"className":99120},[886],[888,99122,99123],{"xmlns":890},[892,99124,99125,99141],{},[895,99126,99127,99133,99135,99137,99139],{},[2355,99128,99129,99131],{},[898,99130,2379],{},[1963,99132,1970],{},[1664,99134,1676],{},[898,99136,2379],{},[1664,99138,1867],{},[898,99140,1991],{},[902,99142,43285],{"encoding":904},[123,99144,99145,99146,4480,99165,12627,99184,4480,99203,4488],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,99147,99149],{"className":99148},[886],[888,99150,99151],{"xmlns":890},[892,99152,99153,99163],{},[895,99154,99155],{},[1810,99156,99157,99159,99161],{},[898,99158,1973],{},[1963,99160,2875],{},[898,99162,4819],{},[902,99164,48336],{"encoding":904},[883,99166,99168],{"className":99167},[886],[888,99169,99170],{"xmlns":890},[892,99171,99172,99182],{},[895,99173,99174],{},[1810,99175,99176,99178,99180],{},[898,99177,1973],{},[1963,99179,1970],{},[898,99181,4819],{},[902,99183,48398],{"encoding":904},[883,99185,99187],{"className":99186},[886],[888,99188,99189],{"xmlns":890},[892,99190,99191,99201],{},[895,99192,99193],{},[1810,99194,99195,99197,99199],{},[898,99196,2398],{},[1963,99198,2875],{},[898,99200,4819],{},[902,99202,48357],{"encoding":904},[883,99204,99206],{"className":99205},[886],[888,99207,99208],{"xmlns":890},[892,99209,99210,99220],{},[895,99211,99212],{},[1810,99213,99214,99216,99218],{},[898,99215,2398],{},[1963,99217,1970],{},[898,99219,4819],{},[902,99221,48418],{"encoding":904},[123,99223,99224,99225,4454,99246,99269,99270,1977],{},"Dopočítej ",[883,99226,99228],{"className":99227},[886],[888,99229,99230],{"xmlns":890},[892,99231,99232,99244],{},[895,99233,99234],{},[2355,99235,99236,99238],{},[898,99237,1991],{},[895,99239,99240,99242],{},[898,99241,43177],{},[898,99243,724],{},[902,99245,43182],{"encoding":904},[883,99247,99249],{"className":99248},[886],[888,99250,99251],{"xmlns":890},[892,99252,99253,99267],{},[895,99254,99255],{},[2355,99256,99257,99259],{},[898,99258,1991],{},[895,99260,99261,99263,99265],{},[898,99262,43200],{},[898,99264,2608],{},[898,99266,12540],{},[902,99268,43207],{"encoding":904}," z definice, vždy ověř ",[883,99271,99273],{"className":99272},[886],[888,99274,99275],{"xmlns":890},[892,99276,99277,99307],{},[895,99278,99279,99289,99291,99303,99305],{},[2355,99280,99281,99283],{},[898,99282,1991],{},[895,99284,99285,99287],{},[898,99286,43177],{},[898,99288,724],{},[1664,99290,1700],{},[2355,99292,99293,99295],{},[898,99294,1991],{},[895,99296,99297,99299,99301],{},[898,99298,43200],{},[898,99300,2608],{},[898,99302,12540],{},[1664,99304,1676],{},[898,99306,1991],{},[902,99308,99309],{"encoding":904},"T_{sp} + T_{vyr} = T",[4436,99311,99312],{},[724,99313,99314,99316,99317,99320,99321,4454,99334,99347],{},[883,99315,4978],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,99318,99319],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,99322,99324],{"className":99323},[886],[888,99325,99326],{"xmlns":890},[892,99327,99328,99332],{},[895,99329,99330],{},[898,99331,2379],{},[902,99333,2379],{"encoding":904},[883,99335,99337],{"className":99336},[886],[888,99338,99339],{"xmlns":890},[892,99340,99341,99345],{},[895,99342,99343],{},[898,99344,2351],{},[902,99346,2351],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[37470,99349],{},[115,99351,99353],{"id":99352},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,99355,99356],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,99358,99359],{},[1928,99360],{"alt":99361,"className":99362,"src":99363},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,1932],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,99365,99366,99378],{},[19,99367,99368],{},[22,99369,99370,99372,99375],{},[25,99371,54796],{},[25,99373,99374],{},"(a) daň výrobci",[25,99376,99377],{},"(b) daň spotřebiteli",[30,99379,99380,99435,99502,99562],{},[22,99381,99382,99385,99410],{},[35,99383,99384],{},"Rovnovážné množství",[35,99386,99387],{},[883,99388,99390],{"className":99389},[886],[888,99391,99392],{"xmlns":890},[892,99393,99394,99408],{},[895,99395,99396,99404,99406],{},[1810,99397,99398,99400,99402],{},[898,99399,1973],{},[1963,99401,2875],{},[898,99403,4819],{},[1664,99405,1676],{},[1963,99407,2875],{},[902,99409,97226],{"encoding":904},[35,99411,99412],{},[883,99413,99415],{"className":99414},[886],[888,99416,99417],{"xmlns":890},[892,99418,99419,99433],{},[895,99420,99421,99429,99431],{},[1810,99422,99423,99425,99427],{},[898,99424,1973],{},[1963,99426,1970],{},[898,99428,4819],{},[1664,99430,1676],{},[1963,99432,2875],{},[902,99434,98259],{"encoding":904},[22,99436,99437,99440,99465],{},[35,99438,99439],{},"Cena placená spotřebitelem",[35,99441,99442],{},[883,99443,99445],{"className":99444},[886],[888,99446,99447],{"xmlns":890},[892,99448,99449,99463],{},[895,99450,99451,99459,99461],{},[1810,99452,99453,99455,99457],{},[898,99454,2398],{},[1963,99456,2875],{},[898,99458,4819],{},[1664,99460,1676],{},[1963,99462,3442],{},[902,99464,97321],{"encoding":904},[35,99466,99467],{},[883,99468,99470],{"className":99469},[886],[888,99471,99472],{"xmlns":890},[892,99473,99474,99500],{},[895,99475,99476,99484,99486,99488,99490,99492,99494,99496,99498],{},[1810,99477,99478,99480,99482],{},[898,99479,2398],{},[1963,99481,1970],{},[898,99483,4819],{},[1664,99485,1700],{},[898,99487,1991],{},[1664,99489,1676],{},[1963,99491,2944],{},[1664,99493,1700],{},[1963,99495,2833],{},[1664,99497,1676],{},[1963,99499,3442],{},[902,99501,98358],{"encoding":904},[22,99503,99504,99507,99537],{},[35,99505,99506],{},"Cena přijímaná výrobcem",[35,99508,99509],{},[883,99510,99512],{"className":99511},[886],[888,99513,99514],{"xmlns":890},[892,99515,99516,99534],{},[895,99517,99518,99526,99528,99530,99532],{},[1810,99519,99520,99522,99524],{},[898,99521,2398],{},[1963,99523,2875],{},[898,99525,4819],{},[1664,99527,1867],{},[898,99529,1991],{},[1664,99531,1676],{},[1963,99533,2944],{},[902,99535,99536],{"encoding":904},"P_1^E - T = 4",[35,99538,99539],{},[883,99540,99542],{"className":99541},[886],[888,99543,99544],{"xmlns":890},[892,99545,99546,99560],{},[895,99547,99548,99556,99558],{},[1810,99549,99550,99552,99554],{},[898,99551,2398],{},[1963,99553,1970],{},[898,99555,4819],{},[1664,99557,1676],{},[1963,99559,2944],{},[902,99561,98383],{"encoding":904},[22,99563,99564,99567,99621],{},[35,99565,99566],{},"Rozklad břemene",[35,99568,99569,1343,99594],{},[883,99570,99572],{"className":99571},[886],[888,99573,99574],{"xmlns":890},[892,99575,99576,99592],{},[895,99577,99578,99588,99590],{},[2355,99579,99580,99582],{},[898,99581,1991],{},[895,99583,99584,99586],{},[898,99585,43177],{},[898,99587,724],{},[1664,99589,1676],{},[1963,99591,1970],{},[902,99593,43476],{"encoding":904},[883,99595,99597],{"className":99596},[886],[888,99598,99599],{"xmlns":890},[892,99600,99601,99619],{},[895,99602,99603,99615,99617],{},[2355,99604,99605,99607],{},[898,99606,1991],{},[895,99608,99609,99611,99613],{},[898,99610,43200],{},[898,99612,2608],{},[898,99614,12540],{},[1664,99616,1676],{},[1963,99618,2944],{},[902,99620,43505],{"encoding":904},[35,99622,99623,1343,99648],{},[883,99624,99626],{"className":99625},[886],[888,99627,99628],{"xmlns":890},[892,99629,99630,99646],{},[895,99631,99632,99642,99644],{},[2355,99633,99634,99636],{},[898,99635,1991],{},[895,99637,99638,99640],{},[898,99639,43177],{},[898,99641,724],{},[1664,99643,1676],{},[1963,99645,1970],{},[902,99647,43476],{"encoding":904},[883,99649,99651],{"className":99650},[886],[888,99652,99653],{"xmlns":890},[892,99654,99655,99673],{},[895,99656,99657,99669,99671],{},[2355,99658,99659,99661],{},[898,99660,1991],{},[895,99662,99663,99665,99667],{},[898,99664,43200],{},[898,99666,2608],{},[898,99668,12540],{},[1664,99670,1676],{},[1963,99672,2944],{},[902,99674,43505],{"encoding":904},[724,99676,99677],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,99679,99681],{"className":99680},[886],[888,99682,99683],{"xmlns":890,"display":28566},[892,99684,99685,99733],{},[895,99686,99687,99695,99697,99705,99707,99709,99717,99719,99721,99723,99731],{},[1810,99688,99689,99691,99693],{},[898,99690,1973],{},[1963,99692,2875],{},[898,99694,4819],{},[1664,99696,1676],{},[1810,99698,99699,99701,99703],{},[898,99700,1973],{},[1963,99702,1970],{},[898,99704,4819],{},[1664,99706,1916],{"separator":1915},[6444,99708],{"width":6446},[1810,99710,99711,99713,99715],{},[898,99712,2398],{},[1963,99714,2875],{},[898,99716,4819],{},[1664,99718,1867],{},[898,99720,1991],{},[1664,99722,1676],{},[1810,99724,99725,99727,99729],{},[898,99726,2398],{},[1963,99728,1970],{},[898,99730,4819],{},[898,99732,1977],{"mathvariant":1726},[902,99734,99735],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[4436,99737,99738,99757,99911],{},[724,99739,99740,99742,99743,99756],{},[883,99741,5138],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,99744,99746],{"className":99745},[886],[888,99747,99748],{"xmlns":890},[892,99749,99750,99754],{},[895,99751,99752],{},[898,99753,1991],{},[902,99755,1991],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,99758,99759,99791,99827,99864],{},[123,99760,99761,99762,1916],{},"rovnovážná množství obou režimů, ",[883,99763,99765],{"className":99764},[886],[888,99766,99767],{"xmlns":890},[892,99768,99769,99789],{},[895,99770,99771,99779,99781],{},[1810,99772,99773,99775,99777],{},[898,99774,1973],{},[1963,99776,2875],{},[898,99778,4819],{},[1664,99780,1676],{},[1810,99782,99783,99785,99787],{},[898,99784,1973],{},[1963,99786,1970],{},[898,99788,4819],{},[902,99790,43408],{"encoding":904},[123,99792,99793,99794,1916],{},"čistá cena přijímaná výrobcem, ",[883,99795,99797],{"className":99796},[886],[888,99798,99799],{"xmlns":890},[892,99800,99801,99825],{},[895,99802,99803,99811,99813,99815,99817],{},[1810,99804,99805,99807,99809],{},[898,99806,2398],{},[1963,99808,2875],{},[898,99810,4819],{},[1664,99812,1867],{},[898,99814,1991],{},[1664,99816,1676],{},[1810,99818,99819,99821,99823],{},[898,99820,2398],{},[1963,99822,1970],{},[898,99824,4819],{},[902,99826,43442],{"encoding":904},[123,99828,99829,99830,1916],{},"celková cena placená spotřebitelem, ",[883,99831,99833],{"className":99832},[886],[888,99834,99835],{"xmlns":890},[892,99836,99837,99861],{},[895,99838,99839,99847,99849,99857,99859],{},[1810,99840,99841,99843,99845],{},[898,99842,2398],{},[1963,99844,2875],{},[898,99846,4819],{},[1664,99848,1676],{},[1810,99850,99851,99853,99855],{},[898,99852,2398],{},[1963,99854,1970],{},[898,99856,4819],{},[1664,99858,1700],{},[898,99860,1991],{},[902,99862,99863],{"encoding":904},"P_1^E = P_2^E + T",[123,99865,99866,99867,4454,99888,1977],{},"rozklad daňového břemene ",[883,99868,99870],{"className":99869},[886],[888,99871,99872],{"xmlns":890},[892,99873,99874,99886],{},[895,99875,99876],{},[2355,99877,99878,99880],{},[898,99879,1991],{},[895,99881,99882,99884],{},[898,99883,43177],{},[898,99885,724],{},[902,99887,43182],{"encoding":904},[883,99889,99891],{"className":99890},[886],[888,99892,99893],{"xmlns":890},[892,99894,99895,99909],{},[895,99896,99897],{},[2355,99898,99899,99901],{},[898,99900,1991],{},[895,99902,99903,99905,99907],{},[898,99904,43200],{},[898,99906,2608],{},[898,99908,12540],{},[902,99910,43207],{"encoding":904},[724,99912,99913,99914,1977],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,99915,35697],{},[724,99917,99918,99919,4454,99932,4488],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,99920,99922],{"className":99921},[886],[888,99923,99924],{"xmlns":890},[892,99925,99926,99930],{},[895,99927,99928],{},[898,99929,2379],{},[902,99931,2379],{"encoding":904},[883,99933,99935],{"className":99934},[886],[888,99936,99937],{"xmlns":890},[892,99938,99939,99943],{},[895,99940,99941],{},[898,99942,2351],{},[902,99944,2351],{"encoding":904},[37470,99946],{},[115,99948,99950],{"id":99949},"úlohy","Úlohy",[724,99952,99953,99954,3727],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,99955,16739],{"className":99956,"dataFsResolvedFilePath":800,"href":801},[210],[120,99958,99959,99989,100020],{},[123,99960,99961,99964,99965,99988],{},[38,99962,99963],{},"Úloha 2.4"," — Poptávka ",[883,99966,99968],{"className":99967},[886],[888,99969,99970],{"xmlns":890},[892,99971,99972,99986],{},[895,99973,99974,99976,99978,99980,99982,99984],{},[898,99975,2398],{},[1664,99977,1676],{},[1963,99979,4084],{},[1664,99981,1867],{},[1963,99983,1970],{},[898,99985,1973],{},[902,99987,96938],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,99990,99991,99994,99995,100019],{},[38,99992,99993],{},"Úloha 2.9"," — Nabídka ",[883,99996,99998],{"className":99997},[886],[888,99999,100000],{"xmlns":890},[892,100001,100002,100016],{},[895,100003,100004,100006,100008,100010,100012,100014],{},[898,100005,2398],{},[1664,100007,1676],{},[1963,100009,5575],{},[898,100011,1973],{},[1664,100013,1700],{},[1963,100015,36744],{},[902,100017,100018],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,100021,100022,100025,100026,4454,100052,100076,100077,100094],{},[38,100023,100024],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,100027,100029],{"className":100028},[886],[888,100030,100031],{"xmlns":890},[892,100032,100033,100049],{},[895,100034,100035,100037,100039,100041,100043,100045,100047],{},[898,100036,2398],{},[1664,100038,1676],{},[1664,100040,1867],{},[1963,100042,2944],{},[898,100044,1973],{},[1664,100046,1700],{},[1963,100048,47203],{},[902,100050,100051],{"encoding":904},"P = -4Q + 80",[883,100053,100055],{"className":100054},[886],[888,100056,100057],{"xmlns":890},[892,100058,100059,100073],{},[895,100060,100061,100063,100065,100067,100069,100071],{},[898,100062,2398],{},[1664,100064,1676],{},[1963,100066,2774],{},[898,100068,1973],{},[1664,100070,1700],{},[1963,100072,3442],{},[902,100074,100075],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,100078,100080],{"className":100079},[886],[888,100081,100082],{"xmlns":890},[892,100083,100084,100092],{},[895,100085,100086,100088,100090],{},[898,100087,1991],{},[1664,100089,1676],{},[1963,100091,24701],{},[902,100093,48315],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,100096,100097,100098,100100,100101,100103],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,100099,45728],{}," (posun poptávky při zdanění kupujícího) a ",[38,100102,45762],{}," (posun nabídky při zdanění výrobce).",[37470,100105],{},[115,100107,16219],{"id":16218},[120,100109,100110,100129,100187,100244,100327,100373,100416,100461,100527],{},[123,100111,100112,1885,100115,100128],{},[38,100113,100114],{},"Jednotková daň",[883,100116,100118],{"className":100117},[886],[888,100119,100120],{"xmlns":890},[892,100121,100122,100126],{},[895,100123,100124],{},[898,100125,1991],{},[902,100127,1991],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,100130,100131,100133,100134,100172,100173,100186],{},[38,100132,96520],{}," — posun nabídky ",[883,100135,100137],{"className":100136},[886],[888,100138,100139],{"xmlns":890},[892,100140,100141,100169],{},[895,100142,100143,100149,100151,100153,100155,100157,100159,100161,100163,100165,100167],{},[2355,100144,100145,100147],{},[898,100146,2351],{},[1963,100148,2875],{},[1664,100150,1667],{"stretchy":1666},[898,100152,1973],{},[1664,100154,1673],{"stretchy":1666},[1664,100156,1676],{},[898,100158,2351],{},[1664,100160,1667],{"stretchy":1666},[898,100162,1973],{},[1664,100164,1673],{"stretchy":1666},[1664,100166,1700],{},[898,100168,1991],{},[902,100170,100171],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,100174,100176],{"className":100175},[886],[888,100177,100178],{"xmlns":890},[892,100179,100180,100184],{},[895,100181,100182],{},[898,100183,1991],{},[902,100185,1991],{"encoding":904}," svisle nahoru)",[123,100188,100189,100191,100192,100172,100230,100243],{},[38,100190,97593],{}," — posun poptávky ",[883,100193,100195],{"className":100194},[886],[888,100196,100197],{"xmlns":890},[892,100198,100199,100227],{},[895,100200,100201,100207,100209,100211,100213,100215,100217,100219,100221,100223,100225],{},[2355,100202,100203,100205],{},[898,100204,2379],{},[1963,100206,1970],{},[1664,100208,1667],{"stretchy":1666},[898,100210,1973],{},[1664,100212,1673],{"stretchy":1666},[1664,100214,1676],{},[898,100216,2379],{},[1664,100218,1667],{"stretchy":1666},[898,100220,1973],{},[1664,100222,1673],{"stretchy":1666},[1664,100224,1867],{},[898,100226,1991],{},[902,100228,100229],{"encoding":904},"D_2(Q) = D(Q) - T",[883,100231,100233],{"className":100232},[886],[888,100234,100235],{"xmlns":890},[892,100236,100237,100241],{},[895,100238,100239],{},[898,100240,1991],{},[902,100242,1991],{"encoding":904}," svisle dolů)",[123,100245,100246,7581,100249,42314,100288],{},[38,100247,100248],{},"Rovnovážný bod s daní",[883,100250,100252],{"className":100251},[886],[888,100253,100254],{"xmlns":890},[892,100255,100256,100286],{},[895,100257,100258,100264,100266,100274,100276,100284],{},[2355,100259,100260,100262],{},[898,100261,4819],{},[1963,100263,2875],{},[1664,100265,1837],{"stretchy":1666},[1810,100267,100268,100270,100272],{},[898,100269,1973],{},[1963,100271,2875],{},[898,100273,4819],{},[1664,100275,1916],{"separator":1915},[1810,100277,100278,100280,100282],{},[898,100279,2398],{},[1963,100281,2875],{},[898,100283,4819],{},[1664,100285,1850],{"stretchy":1666},[902,100287,96688],{"encoding":904},[883,100289,100291],{"className":100290},[886],[888,100292,100293],{"xmlns":890},[892,100294,100295,100325],{},[895,100296,100297,100303,100305,100313,100315,100323],{},[2355,100298,100299,100301],{},[898,100300,4819],{},[1963,100302,1970],{},[1664,100304,1837],{"stretchy":1666},[1810,100306,100307,100309,100311],{},[898,100308,1973],{},[1963,100310,1970],{},[898,100312,4819],{},[1664,100314,1916],{"separator":1915},[1810,100316,100317,100319,100321],{},[898,100318,2398],{},[1963,100320,1970],{},[898,100322,4819],{},[1664,100324,1850],{"stretchy":1666},[902,100326,97763],{"encoding":904},[123,100328,100329,10588,100331,100333,100334],{},[38,100330,43158],{},[614,100332,98543],{},") — rozklad ",[883,100335,100337],{"className":100336},[886],[888,100338,100339],{"xmlns":890},[892,100340,100341,100371],{},[895,100342,100343,100345,100347,100357,100359],{},[898,100344,1991],{},[1664,100346,1676],{},[2355,100348,100349,100351],{},[898,100350,1991],{},[895,100352,100353,100355],{},[898,100354,43177],{},[898,100356,724],{},[1664,100358,1700],{},[2355,100360,100361,100363],{},[898,100362,1991],{},[895,100364,100365,100367,100369],{},[898,100366,43200],{},[898,100368,2608],{},[898,100370,12540],{},[902,100372,43344],{"encoding":904},[123,100374,100375,100398,100399,1673],{},[38,100376,100377],{},[883,100378,100380],{"className":100379},[886],[888,100381,100382],{"xmlns":890},[892,100383,100384,100396],{},[895,100385,100386],{},[2355,100387,100388,100390],{},[898,100389,1991],{},[895,100391,100392,100394],{},[898,100393,43177],{},[898,100395,724],{},[902,100397,43182],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,100400,100402],{"className":100401},[886],[888,100403,100404],{"xmlns":890},[892,100405,100406,100414],{},[895,100407,100408],{},[1720,100409,100410,100412],{},[898,100411,2398],{},[898,100413,4819],{},[902,100415,41966],{"encoding":904},[123,100417,100418,100443,100444,1673],{},[38,100419,100420],{},[883,100421,100423],{"className":100422},[886],[888,100424,100425],{"xmlns":890},[892,100426,100427,100441],{},[895,100428,100429],{},[2355,100430,100431,100433],{},[898,100432,1991],{},[895,100434,100435,100437,100439],{},[898,100436,43200],{},[898,100438,2608],{},[898,100440,12540],{},[902,100442,43207],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,100445,100447],{"className":100446},[886],[888,100448,100449],{"xmlns":890},[892,100450,100451,100459],{},[895,100452,100453],{},[1720,100454,100455,100457],{},[898,100456,2398],{},[898,100458,4819],{},[902,100460,41966],{"encoding":904},[123,100462,100463,7581,100465,1343,100494],{},[38,100464,50974],{},[883,100466,100468],{"className":100467},[886],[888,100469,100470],{"xmlns":890},[892,100471,100472,100492],{},[895,100473,100474,100482,100484],{},[1810,100475,100476,100478,100480],{},[898,100477,1973],{},[1963,100479,2875],{},[898,100481,4819],{},[1664,100483,1676],{},[1810,100485,100486,100488,100490],{},[898,100487,1973],{},[1963,100489,1970],{},[898,100491,4819],{},[902,100493,43408],{"encoding":904},[883,100495,100497],{"className":100496},[886],[888,100498,100499],{"xmlns":890},[892,100500,100501,100525],{},[895,100502,100503,100511,100513,100515,100517],{},[1810,100504,100505,100507,100509],{},[898,100506,2398],{},[1963,100508,2875],{},[898,100510,4819],{},[1664,100512,1867],{},[898,100514,1991],{},[1664,100516,1676],{},[1810,100518,100519,100521,100523],{},[898,100520,2398],{},[1963,100522,1970],{},[898,100524,4819],{},[902,100526,43442],{"encoding":904},[123,100528,100529,100532],{},[38,100530,100531],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[37470,100534],{},[115,100536,2497],{"id":2496},[120,100538,100539,100547,100565,100572],{},[123,100540,100541,1885,100544],{},[38,100542,100543],{},"Kontext (hub):",[207,100545,802],{"className":100546,"dataFsResolvedFilePath":800,"href":801},[210],[123,100548,100549,1885,100551,100554,100555,19148,100557,100560,100561,100564],{},[38,100550,51223],{},[207,100552,820],{"className":100553,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,100556,55534],{},[207,100558,2950],{"className":100559,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,100562,4397],{"className":100563,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[123,100566,100567,1885,100569],{},[38,100568,51258],{},[207,100570,51262],{"className":100571,"dataFsResolvedFilePath":745,"href":746},[210],[123,100573,100574,1885,100576],{},[38,100575,16703],{},[207,100577,16707],{"className":100578,"dataFsResolvedFilePath":2575,"href":2576},[210],{"title":641,"searchDepth":642,"depth":642,"links":100580},[100581,100582,100585,100588,100592,100593,100594,100595],{"id":96425,"depth":642,"text":96426},{"id":96519,"depth":642,"text":96520,"children":100583},[100584],{"id":96910,"depth":649,"text":45803},{"id":97592,"depth":642,"text":97593,"children":100586},[100587],{"id":98069,"depth":649,"text":45883},{"id":98536,"depth":642,"text":43158,"children":100589},[100590,100591],{"id":3033,"depth":649,"text":3034},{"id":98879,"depth":649,"text":98880},{"id":99352,"depth":642,"text":99353},{"id":99949,"depth":642,"text":99950},{"id":16218,"depth":642,"text":16219},{"id":2496,"depth":642,"text":2497},{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":96323,"description":641},[1138,1135],"topics\u002Fzdaneni-trhu",[1128,51323,100602,100603,100604,16739],"dane","danove-bremeno","posun-krivek","cFuKqHgzIrqvY-l4jNdqjFEM7_ixjw33HOL0So8cPn0",[100607,100609,100611,100613,100617,100621,100625,100627],{"slug":1145,"path":765,"title":2563,"snippet":100608},"… dchozí:** Základy matematické ekonomie - **Navazující:** \u003C\u003Cintegral>> - **Souvislosti:** Funkce více proměnných (rozšíření na 2D), [ …",{"slug":16752,"path":783,"title":10133,"snippet":100610},"… = 0$ se používá Lagrangeova metoda. ## Navigace - **Předchozí:** \u003C\u003Cintegral>> - **Navazující:** Lagrangeova metoda - **Souvislosti:** [[produkce …",{"slug":1128,"path":2576,"title":681,"snippet":100612},"… ace, diferenciál a extrémy 1D]] — geometrická a inženýrská interpretace, mezní veličiny - \u003C\u003Cintegral>> — neurčitý a určitý, rekonstrukce TR z MR a TC z MC - [[funkce-vice-promennych|Funkce víc …",{"slug":100614,"path":746,"title":100615,"snippet":100616},"imek-blok-01","KS 1. blok — Kalkul a mikroekonomie","… rská interpretace), tečna, diferenciál jako lineární odhad přírůstku, podmínky extrémů 3. \u003C\u003Cintegral>> — primitivní funkce, určitý integrál jako plocha, rekonstrukce TR z MR a TC z MC 4. [[fun …",{"slug":100618,"path":1109,"title":100619,"snippet":100620},"imek-kniha","Kniha — *Úvod do matematické ekonomie pro ekonomy*","… integrály, Lagrange). Teorie je pokryta v zaklady-matematicke-ekonomie, derivace, \u003C\u003Cintegral>>, funkce-vice-promennych, lagrangeova-metoda ze zdrojů ve vysokoškolských blocích. …",{"slug":100622,"path":959,"title":100623,"snippet":100624},"imek-vzorce-prehled","ImeK — kompletní přehled vzorců se zdroji a intuicí","… Mezník — Úvod do matematické ekonomie]] - **Matematický aparát:** Derivace, \u003C\u003Cintegral>>, Funkce více proměnných, [[lagrangeova-metoda|Lagrangeova meto …",{"slug":16739,"path":801,"title":802,"snippet":100626},"… metricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát \u003C\u003Cintegral>>. --- ## Příklady z knihy — přehled - **Příklad 2.1** — lineární poptávka $P = -2Q + 60 …",{"slug":45474,"path":819,"title":820,"snippet":100628},"… ých stran trhu. Navazují na pojmy tržní rovnováhy a využívají aparát \u003C\u003Cintegral>>. --- ## Úvod Je dána funkce poptávky $P = D(Q)$, resp. funkce nabídky $P = S(Q)$. Pro …",[100630,100631],{"slug":100614,"title":100615,"path":746,"sharedTags":642},{"slug":45474,"title":820,"path":819,"sharedTags":642},1777154966090]