[{"data":1,"prerenderedAt":118089},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-prijem-naklady-zisk":1626,"course-stats-imek":21184,"course-topics-imek":21188,"backlinks-prijem-naklady-zisk":118065,"related-prijem-naklady-zisk":118088},{"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":21183},{"id":1628,"title":1629,"body":1630,"course":1128,"courses":659,"created":21169,"description":641,"extension":661,"meta":21170,"navigation":664,"path":21171,"seo":21172,"sources":21173,"stem":21174,"tags":21175,"type":21181,"updated":677,"__hash__":21182},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":1631,"toc":21133},[1632,1635,1838,1841,1937,1942,2279,2283,2292,2296,2345,2421,2455,2509,2546,2551,2611,2617,2683,2806,2909,2913,2936,3015,3058,3062,3091,3161,3168,3286,3290,3373,3410,3463,3666,3731,3820,3824,3827,3907,3910,4035,4054,4119,4123,4218,4289,4331,4386,4454,4491,4495,4555,4585,4798,4870,4924,5091,5184,5219,5223,5227,5264,5329,5386,5390,5413,5502,5607,5676,5680,5777,5890,5949,6003,6061,6122,6125,6161,6226,6256,6487,6545,6579,6583,6610,6689,6803,6824,6903,6905,7014,7018,7159,7482,7486,7489,7493,7543,7547,7804,7958,7965,8039,8226,8231,8574,8578,8601,8605,8627,8686,8696,8745,8887,8962,9057,9172,9270,9389,9393,9462,9467,9580,9726,9777,9889,9931,9935,9955,10016,10043,10106,10110,10132,10201,10483,10490,10520,10527,10722,10726,10805,10810,10886,10889,10977,11054,11123,11172,11276,11349,11470,11823,11936,12038,12042,12045,12052,12055,12091,12150,12159,12308,12533,12537,12602,12783,12876,12931,12935,12992,13062,13114,13135,13216,13219,13295,13339,13343,13384,13427,13453,13457,13529,13625,13688,13740,13846,13925,13948,13977,13981,14148,14267,14340,14655,14815,14819,14871,14933,14968,14999,15099,15141,15311,15316,15412,15450,15454,15575,15877,15881,15916,15920,15924,16053,16185,16507,16697,16775,16779,17084,17197,17344,17530,17636,17869,17984,18066,18185,18283,18325,18329,18384,18529,18683,18844,18937,19132,19445,19577,19706,19710,19782,19825,19876,19880,21080,21084],[12,1633,1629],{"id":1634},"příjem-náklady-zisk-a-nabídka-firmy",[1636,1637,1638],"blockquote",{},[724,1639,1640,1643,1644,1647,1648,1666,1667,1647,1670,1687,1688,1647,1691,1723,1724,1748,1749,1774,1775,1797,1798,1801,1802,1818,1819,1837],{},[883,1641,1642],{},"!abstract"," TL;DR\n",[38,1645,1646],{},"Příjem"," ",[883,1649,1651],{"className":1650},[886],[888,1652,1653],{"xmlns":890},[892,1654,1655,1663],{},[895,1656,1657,1660],{},[898,1658,1659],{},"T",[898,1661,1662],{},"R",[902,1664,1665],{"encoding":904},"TR"," je to, co firma inkasuje (cena krát množství), ",[38,1668,1669],{},"náklady",[883,1671,1673],{"className":1672},[886],[888,1674,1675],{"xmlns":890},[892,1676,1677,1684],{},[895,1678,1679,1681],{},[898,1680,1659],{},[898,1682,1683],{},"C",[902,1685,1686],{"encoding":904},"TC"," to, co vynaloží (fixní plus variabilní), a ",[38,1689,1690],{},"zisk",[883,1692,1694],{"className":1693},[886],[888,1695,1696],{"xmlns":890},[892,1697,1698,1720],{},[895,1699,1700,1703,1705,1709,1711,1713,1716,1718],{},[898,1701,1702],{},"P",[898,1704,1662],{},[1706,1707,1708],"mo",{},"=",[898,1710,1659],{},[898,1712,1662],{},[1706,1714,1715],{},"−",[898,1717,1659],{},[898,1719,1683],{},[902,1721,1722],{"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: ",[883,1725,1727],{"className":1726},[886],[888,1728,1729],{"xmlns":890},[892,1730,1731,1745],{},[895,1732,1733,1736,1738,1740,1743],{},[898,1734,1735],{},"A",[898,1737,1683],{},[1706,1739,1708],{},[898,1741,1742],{},"M",[898,1744,1683],{},[902,1746,1747],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,1750,1752],{"className":1751},[886],[888,1753,1754],{"xmlns":890},[892,1755,1756,1771],{},[895,1757,1758,1760,1763,1765,1767,1769],{},[898,1759,1735],{},[898,1761,1762],{},"V",[898,1764,1683],{},[1706,1766,1708],{},[898,1768,1742],{},[898,1770,1683],{},[902,1772,1773],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,1776,1778],{"className":1777},[886],[888,1779,1780],{"xmlns":890},[892,1781,1782,1794],{},[895,1783,1784,1786,1788,1790,1792],{},[898,1785,1742],{},[898,1787,1662],{},[1706,1789,1708],{},[898,1791,1742],{},[898,1793,1683],{},[902,1795,1796],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,1799,1800],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,1803,1805],{"className":1804},[886],[888,1806,1807],{"xmlns":890},[892,1808,1809,1815],{},[895,1810,1811,1813],{},[898,1812,1742],{},[898,1814,1683],{},[902,1816,1817],{"encoding":904},"MC"," nad bodem minima ",[883,1820,1822],{"className":1821},[886],[888,1823,1824],{"xmlns":890},[892,1825,1826,1834],{},[895,1827,1828,1830,1832],{},[898,1829,1735],{},[898,1831,1762],{},[898,1833,1683],{},[902,1835,1836],{"encoding":904},"AVC",".",[115,1839,1241],{"id":1840},"úvod",[724,1842,1843,1844,1847,1848,1850,1851,1343,1854,1343,1857,1860,1861,1864,1865,1868,1869,1873,1874,1889,1890,1348,1906,1889,1921,1936],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,1845,1846],{},"příjmem"," (revenue) a ",[38,1849,1669],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,1852,1853],{},"zisku",[38,1855,1856],{},"bodů zvratu",[38,1858,1859],{},"maximalizace zisku"," a konstrukcí ",[38,1862,1863],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,1866,1145],{"className":1867,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,1870,1872],{"className":1871,"dataFsResolvedFilePath":773,"href":774},[210],"integrál"," (pro zpětnou rekonstrukci ",[883,1875,1877],{"className":1876},[886],[888,1878,1879],{"xmlns":890},[892,1880,1881,1887],{},[895,1882,1883,1885],{},[898,1884,1659],{},[898,1886,1662],{},[902,1888,1665],{"encoding":904}," z ",[883,1891,1893],{"className":1892},[886],[888,1894,1895],{"xmlns":890},[892,1896,1897,1903],{},[895,1898,1899,1901],{},[898,1900,1742],{},[898,1902,1662],{},[902,1904,1905],{"encoding":904},"MR",[883,1907,1909],{"className":1908},[886],[888,1910,1911],{"xmlns":890},[892,1912,1913,1919],{},[895,1914,1915,1917],{},[898,1916,1659],{},[898,1918,1683],{},[902,1920,1686],{"encoding":904},[883,1922,1924],{"className":1923},[886],[888,1925,1926],{"xmlns":890},[892,1927,1928,1934],{},[895,1929,1930,1932],{},[898,1931,1742],{},[898,1933,1683],{},[902,1935,1817],{"encoding":904},").",[724,1938,1939],{},[38,1940,1941],{},"Cílové znalosti:",[120,1943,1944,2111,2114,2117,2218,2265,2272],{},[123,1945,1946,1947,1343,1962,1343,1978,1993,1994,1343,2009,1343,2026,1343,2044,1343,2062,1343,2079,1343,2095,2110],{},"odvodit a interpretovat funkce ",[883,1948,1950],{"className":1949},[886],[888,1951,1952],{"xmlns":890},[892,1953,1954,1960],{},[895,1955,1956,1958],{},[898,1957,1659],{},[898,1959,1662],{},[902,1961,1665],{"encoding":904},[883,1963,1965],{"className":1964},[886],[888,1966,1967],{"xmlns":890},[892,1968,1969,1975],{},[895,1970,1971,1973],{},[898,1972,1735],{},[898,1974,1662],{},[902,1976,1977],{"encoding":904},"AR",[883,1979,1981],{"className":1980},[886],[888,1982,1983],{"xmlns":890},[892,1984,1985,1991],{},[895,1986,1987,1989],{},[898,1988,1742],{},[898,1990,1662],{},[902,1992,1905],{"encoding":904}," a ",[883,1995,1997],{"className":1996},[886],[888,1998,1999],{"xmlns":890},[892,2000,2001,2007],{},[895,2002,2003,2005],{},[898,2004,1659],{},[898,2006,1683],{},[902,2008,1686],{"encoding":904},[883,2010,2012],{"className":2011},[886],[888,2013,2014],{"xmlns":890},[892,2015,2016,2023],{},[895,2017,2018,2021],{},[898,2019,2020],{},"F",[898,2022,1683],{},[902,2024,2025],{"encoding":904},"FC",[883,2027,2029],{"className":2028},[886],[888,2030,2031],{"xmlns":890},[892,2032,2033,2041],{},[895,2034,2035,2037,2039],{},[898,2036,1659],{},[898,2038,1762],{},[898,2040,1683],{},[902,2042,2043],{"encoding":904},"TVC",[883,2045,2047],{"className":2046},[886],[888,2048,2049],{"xmlns":890},[892,2050,2051,2059],{},[895,2052,2053,2055,2057],{},[898,2054,1735],{},[898,2056,2020],{},[898,2058,1683],{},[902,2060,2061],{"encoding":904},"AFC",[883,2063,2065],{"className":2064},[886],[888,2066,2067],{"xmlns":890},[892,2068,2069,2077],{},[895,2070,2071,2073,2075],{},[898,2072,1735],{},[898,2074,1762],{},[898,2076,1683],{},[902,2078,1836],{"encoding":904},[883,2080,2082],{"className":2081},[886],[888,2083,2084],{"xmlns":890},[892,2085,2086,2092],{},[895,2087,2088,2090],{},[898,2089,1735],{},[898,2091,1683],{},[902,2093,2094],{"encoding":904},"AC",[883,2096,2098],{"className":2097},[886],[888,2099,2100],{"xmlns":890},[892,2101,2102,2108],{},[895,2103,2104,2106],{},[898,2105,1742],{},[898,2107,1683],{},[902,2109,1817],{"encoding":904},";",[123,2112,2113],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,2115,2116],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,2118,2119,2120,2123,2124,2173,2174,2110],{},"osvojit si ",[38,2121,2122],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,2125,2127],{"className":2126},[886],[888,2128,2129],{"xmlns":890},[892,2130,2131,2170],{},[895,2132,2133,2135,2137,2141,2151,2154,2156,2158,2160,2162,2168],{},[898,2134,1735],{},[898,2136,1683],{},[1706,2138,2140],{"stretchy":2139},"false","(",[2142,2143,2144,2147],"msub",{},[898,2145,2146],{},"Q",[2148,2149,2150],"mn",{},"0",[1706,2152,2153],{"stretchy":2139},")",[1706,2155,1708],{},[898,2157,1742],{},[898,2159,1683],{},[1706,2161,2140],{"stretchy":2139},[2142,2163,2164,2166],{},[898,2165,2146],{},[2148,2167,2150],{},[1706,2169,2153],{"stretchy":2139},[902,2171,2172],{"encoding":904},"AC(Q_0)=MC(Q_0)",", resp. ",[883,2175,2177],{"className":2176},[886],[888,2178,2179],{"xmlns":890},[892,2180,2181,2215],{},[895,2182,2183,2185,2187,2189,2191,2197,2199,2201,2203,2205,2207,2213],{},[898,2184,1735],{},[898,2186,1762],{},[898,2188,1683],{},[1706,2190,2140],{"stretchy":2139},[2142,2192,2193,2195],{},[898,2194,2146],{},[2148,2196,2150],{},[1706,2198,2153],{"stretchy":2139},[1706,2200,1708],{},[898,2202,1742],{},[898,2204,1683],{},[1706,2206,2140],{"stretchy":2139},[2142,2208,2209,2211],{},[898,2210,2146],{},[2148,2212,2150],{},[1706,2214,2153],{"stretchy":2139},[902,2216,2217],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,2219,2119,2220,2123,2223,2110],{},[38,2221,2222],{},"princip maximalizace zisku",[883,2224,2226],{"className":2225},[886],[888,2227,2228],{"xmlns":890},[892,2229,2230,2262],{},[895,2231,2232,2234,2236,2238,2244,2246,2248,2250,2252,2254,2260],{},[898,2233,1742],{},[898,2235,1662],{},[1706,2237,2140],{"stretchy":2139},[2142,2239,2240,2242],{},[898,2241,2146],{},[2148,2243,2150],{},[1706,2245,2153],{"stretchy":2139},[1706,2247,1708],{},[898,2249,1742],{},[898,2251,1683],{},[1706,2253,2140],{"stretchy":2139},[2142,2255,2256,2258],{},[898,2257,2146],{},[2148,2259,2150],{},[1706,2261,2153],{"stretchy":2139},[902,2263,2264],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,2266,2267,2268,2271],{},"stanovit ",[38,2269,2270],{},"body zvratu"," a interval zisku;",[123,2273,2274,2275,2278],{},"zkonstruovat ",[38,2276,2277],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,2280,2282],{"id":2281},"příjem-firmy","Příjem firmy",[724,2284,2285],{},[2286,2287],"img",{"alt":2288,"className":2289,"src":2291},"imek-ar-mr-dvojnasobny-sklon",[210,2290],"wikilink-broken","\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,2293,2295],{"id":2294},"celkový-příjem","Celkový příjem",[724,2297,2298,2299,2314,2315,2318,2319,2344],{},"Celkový příjem ",[883,2300,2302],{"className":2301},[886],[888,2303,2304],{"xmlns":890},[892,2305,2306,2312],{},[895,2307,2308,2310],{},[898,2309,1659],{},[898,2311,1662],{},[902,2313,1665],{"encoding":904}," (",[38,2316,2317],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,2320,2322],{"className":2321},[886],[888,2323,2324],{"xmlns":890},[892,2325,2326,2341],{},[895,2327,2328,2330,2332,2335,2337,2339],{},[898,2329,1702],{},[1706,2331,1708],{},[898,2333,2334],{},"D",[1706,2336,2140],{"stretchy":2139},[898,2338,2146],{},[1706,2340,2153],{"stretchy":2139},[902,2342,2343],{"encoding":904},"P = D(Q)"," platí",[883,2346,2348],{"className":2347},[886],[888,2349,2351],{"xmlns":890,"display":2350},"block",[892,2352,2353,2418],{},[2354,2355,2357],"mtable",{"width":2356},"100%",[2358,2359,2360,2364,2410,2412],"mtr",{},[2361,2362],"mtd",{"width":2363},"50%",[2361,2365,2366],{},[895,2367,2368,2370,2372,2374,2376,2378,2380,2382,2384,2386,2388,2391,2393,2395,2397,2399,2401,2403,2405,2407],{},[898,2369,1659],{},[898,2371,1662],{},[1706,2373,1708],{},[898,2375,1659],{},[898,2377,1662],{},[1706,2379,2140],{"stretchy":2139},[898,2381,2146],{},[1706,2383,2153],{"stretchy":2139},[1706,2385,1708],{},[898,2387,1702],{},[1706,2389,2390],{},"⋅",[898,2392,2146],{},[1706,2394,1708],{},[898,2396,2334],{},[1706,2398,2140],{"stretchy":2139},[898,2400,2146],{},[1706,2402,2153],{"stretchy":2139},[1706,2404,2390],{},[898,2406,2146],{},[898,2408,1837],{"mathvariant":2409},"normal",[2361,2411],{"width":2363},[2361,2413,2414],{},[2415,2416,2417],"mtext",{},"(3.1)",[902,2419,2420],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,2422,2423,2424,2427,2428,2454],{},"Graf funkce se nazývá ",[38,2425,2426],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,2429,2431],{"className":2430},[886],[888,2432,2433],{"xmlns":890},[892,2434,2435,2451],{},[895,2436,2437,2439,2441,2443,2445,2448],{},[898,2438,1702],{},[1706,2440,1708],{},[898,2442,207],{},[898,2444,2146],{},[1706,2446,2447],{},"+",[898,2449,2450],{},"b",[902,2452,2453],{"encoding":904},"P = aQ + b",", je celkový příjem kvadratickou funkcí, neboť",[883,2456,2458],{"className":2457},[886],[888,2459,2460],{"xmlns":890,"display":2350},[892,2461,2462,2506],{},[895,2463,2464,2466,2468,2470,2472,2474,2476,2478,2480,2482,2484,2486,2488,2496,2498,2500,2502],{},[898,2465,1659],{},[898,2467,1662],{},[1706,2469,1708],{},[898,2471,2146],{},[1706,2473,2140],{"stretchy":2139},[898,2475,207],{},[898,2477,2146],{},[1706,2479,2447],{},[898,2481,2450],{},[1706,2483,2153],{"stretchy":2139},[1706,2485,1708],{},[898,2487,207],{},[2489,2490,2491,2493],"msup",{},[898,2492,2146],{},[2148,2494,2495],{},"2",[1706,2497,2447],{},[898,2499,2450],{},[898,2501,2146],{},[1706,2503,2505],{"separator":2504},"true",",",[902,2507,2508],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,2510,2511,2512,2525,2526,2545],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,2513,2515],{"className":2514},[886],[888,2516,2517],{"xmlns":890},[892,2518,2519,2523],{},[895,2520,2521],{},[898,2522,900],{},[902,2524,900],{"encoding":904}," (jelikož ",[883,2527,2529],{"className":2528},[886],[888,2530,2531],{"xmlns":890},[892,2532,2533,2542],{},[895,2534,2535,2537,2540],{},[898,2536,207],{},[1706,2538,2539],{},"\u003C",[2148,2541,2150],{},[902,2543,2544],{"encoding":904},"a \u003C 0",") procházející počátkem.",[2547,2548,2550],"h4",{"id":2549},"příklad-31","Příklad 3.1",[724,2552,2553,2556,2557,2594,2595,2610],{},[38,2554,2555],{},"Zadání."," Pro poptávku ",[883,2558,2560],{"className":2559},[886],[888,2561,2562],{"xmlns":890},[892,2563,2564,2591],{},[895,2565,2566,2568,2570,2572,2574,2576,2578,2580,2582,2584,2586,2588],{},[898,2567,1702],{},[1706,2569,1708],{},[898,2571,2334],{},[1706,2573,2140],{"stretchy":2139},[898,2575,2146],{},[1706,2577,2153],{"stretchy":2139},[1706,2579,1708],{},[1706,2581,1715],{},[2148,2583,2495],{},[898,2585,2146],{},[1706,2587,2447],{},[2148,2589,2590],{},"100",[902,2592,2593],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,2596,2598],{"className":2597},[886],[888,2599,2600],{"xmlns":890},[892,2601,2602,2608],{},[895,2603,2604,2606],{},[898,2605,1659],{},[898,2607,1662],{},[902,2609,1665],{"encoding":904}," a charakterizujte jeho křivku.",[724,2612,2613,2616],{},[38,2614,2615],{},"Řešení."," Celkový příjem je",[883,2618,2620],{"className":2619},[886],[888,2621,2622],{"xmlns":890,"display":2350},[892,2623,2624,2680],{},[895,2625,2626,2628,2630,2632,2634,2636,2638,2640,2642,2644,2646,2648,2650,2652,2654,2656,2658,2660,2662,2664,2666,2672,2674,2676,2678],{},[898,2627,1659],{},[898,2629,1662],{},[1706,2631,1708],{},[898,2633,1659],{},[898,2635,1662],{},[1706,2637,2140],{"stretchy":2139},[898,2639,2146],{},[1706,2641,2153],{"stretchy":2139},[1706,2643,1708],{},[898,2645,2146],{},[1706,2647,2140],{"stretchy":2139},[1706,2649,1715],{},[2148,2651,2495],{},[898,2653,2146],{},[1706,2655,2447],{},[2148,2657,2590],{},[1706,2659,2153],{"stretchy":2139},[1706,2661,1708],{},[1706,2663,1715],{},[2148,2665,2495],{},[2489,2667,2668,2670],{},[898,2669,2146],{},[2148,2671,2495],{},[1706,2673,2447],{},[2148,2675,2590],{},[898,2677,2146],{},[898,2679,1837],{"mathvariant":2409},[902,2681,2682],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,2684,2685,2686,1993,2709,2732,2733,2752,2753,1837],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,2687,2689],{"className":2688},[886],[888,2690,2691],{"xmlns":890},[892,2692,2693,2706],{},[895,2694,2695,2702,2704],{},[2142,2696,2697,2699],{},[898,2698,2146],{},[2148,2700,2701],{},"1",[1706,2703,1708],{},[2148,2705,2150],{},[902,2707,2708],{"encoding":904},"Q_1 = 0",[883,2710,2712],{"className":2711},[886],[888,2713,2714],{"xmlns":890},[892,2715,2716,2729],{},[895,2717,2718,2724,2726],{},[2142,2719,2720,2722],{},[898,2721,2146],{},[2148,2723,2495],{},[1706,2725,1708],{},[2148,2727,2728],{},"50",[902,2730,2731],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,2734,2736],{"className":2735},[886],[888,2737,2738],{"xmlns":890},[892,2739,2740,2749],{},[895,2741,2742,2744,2746],{},[898,2743,2146],{},[1706,2745,1708],{},[2148,2747,2748],{},"25",[902,2750,2751],{"encoding":904},"Q = 25"," ve výši ",[883,2754,2756],{"className":2755},[886],[888,2757,2758],{"xmlns":890},[892,2759,2760,2803],{},[895,2761,2762,2764,2774,2776,2778,2780,2782,2785,2787,2789,2791,2793,2795,2797,2800],{},[898,2763,1659],{},[2142,2765,2766,2768,2771],{},[898,2767,1662],{},[898,2769,2770],{},"max",[1706,2772,2773],{},"⁡",[1706,2775,1708],{},[1706,2777,1715],{},[2148,2779,2495],{},[1706,2781,2390],{},[2148,2783,2784],{},"625",[1706,2786,2447],{},[2148,2788,2590],{},[1706,2790,2390],{},[2148,2792,2748],{},[1706,2794,1708],{},[2148,2796,2701],{},[2415,2798,2799],{}," ",[2148,2801,2802],{},"250",[902,2804,2805],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,2807,2808],{},[614,2809,2810,2811,2845,2846,1993,2859,2872,2873,2891,2892,1837],{},"Obrázek 3.1: Parabola ",[883,2812,2814],{"className":2813},[886],[888,2815,2816],{"xmlns":890},[892,2817,2818,2842],{},[895,2819,2820,2822,2824,2826,2828,2830,2836,2838,2840],{},[898,2821,1659],{},[898,2823,1662],{},[1706,2825,1708],{},[1706,2827,1715],{},[2148,2829,2495],{},[2489,2831,2832,2834],{},[898,2833,2146],{},[2148,2835,2495],{},[1706,2837,2447],{},[2148,2839,2590],{},[898,2841,2146],{},[902,2843,2844],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,2847,2849],{"className":2848},[886],[888,2850,2851],{"xmlns":890},[892,2852,2853,2857],{},[895,2854,2855],{},[2148,2856,2150],{},[902,2858,2150],{"encoding":904},[883,2860,2862],{"className":2861},[886],[888,2863,2864],{"xmlns":890},[892,2865,2866,2870],{},[895,2867,2868],{},[2148,2869,2728],{},[902,2871,2728],{"encoding":904}," a maximem ",[883,2874,2876],{"className":2875},[886],[888,2877,2878],{"xmlns":890},[892,2879,2880,2888],{},[895,2881,2882,2884,2886],{},[2148,2883,2701],{},[2415,2885,2799],{},[2148,2887,2802],{},[902,2889,2890],{"encoding":904},"1\\,250"," v bodě ",[883,2893,2895],{"className":2894},[886],[888,2896,2897],{"xmlns":890},[892,2898,2899,2907],{},[895,2900,2901,2903,2905],{},[898,2902,2146],{},[1706,2904,1708],{},[2148,2906,2748],{},[902,2908,2751],{"encoding":904},[198,2910,2912],{"id":2911},"průměrný-příjem","Průměrný příjem",[724,2914,2915,1647,2917,2314,2932,2935],{},[38,2916,2912],{},[883,2918,2920],{"className":2919},[886],[888,2921,2922],{"xmlns":890},[892,2923,2924,2930],{},[895,2925,2926,2928],{},[898,2927,1735],{},[898,2929,1662],{},[902,2931,1977],{"encoding":904},[38,2933,2934],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,2937,2939],{"className":2938},[886],[888,2940,2941],{"xmlns":890,"display":2350},[892,2942,2943,3012],{},[895,2944,2945,2947,2949,2951,2953,2955,2957,2959,2961,2963,2980,2982,3000,3002,3004,3006,3008,3010],{},[898,2946,1735],{},[898,2948,1662],{},[1706,2950,1708],{},[898,2952,1735],{},[898,2954,1662],{},[1706,2956,2140],{"stretchy":2139},[898,2958,2146],{},[1706,2960,2153],{"stretchy":2139},[1706,2962,1708],{},[2964,2965,2966,2978],"mfrac",{},[895,2967,2968,2970,2972,2974,2976],{},[898,2969,1659],{},[898,2971,1662],{},[1706,2973,2140],{"stretchy":2139},[898,2975,2146],{},[1706,2977,2153],{"stretchy":2139},[898,2979,2146],{},[1706,2981,1708],{},[2964,2983,2984,2998],{},[895,2985,2986,2988,2990,2992,2994,2996],{},[898,2987,2146],{},[2415,2989,2799],{},[898,2991,2334],{},[1706,2993,2140],{"stretchy":2139},[898,2995,2146],{},[1706,2997,2153],{"stretchy":2139},[898,2999,2146],{},[1706,3001,1708],{},[898,3003,2334],{},[1706,3005,2140],{"stretchy":2139},[898,3007,2146],{},[1706,3009,2153],{"stretchy":2139},[898,3011,1837],{"mathvariant":2409},[902,3013,3014],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[1636,3016,3017],{},[724,3018,3019,3022,3023,1343,3026,1837],{},[883,3020,3021],{},"!note"," Klíčové pozorování\n",[38,3024,3025],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,3027,3029],{"className":3028},[886],[888,3030,3031],{"xmlns":890},[892,3032,3033,3055],{},[895,3034,3035,3037,3039,3041,3043,3045,3047,3049,3051,3053],{},[898,3036,1735],{},[898,3038,1662],{},[1706,3040,2140],{"stretchy":2139},[898,3042,2146],{},[1706,3044,2153],{"stretchy":2139},[1706,3046,1708],{},[898,3048,2334],{},[1706,3050,2140],{"stretchy":2139},[898,3052,2146],{},[1706,3054,2153],{"stretchy":2139},[902,3056,3057],{"encoding":904},"AR(Q) = D(Q)",[198,3059,3061],{"id":3060},"mezní-příjem","Mezní příjem",[724,3063,3064,3065,1647,3068,2314,3083,3086,3087,3090],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,3066,3067],{},"mezní příjem",[883,3069,3071],{"className":3070},[886],[888,3072,3073],{"xmlns":890},[892,3074,3075,3081],{},[895,3076,3077,3079],{},[898,3078,1742],{},[898,3080,1662],{},[902,3082,1905],{"encoding":904},[38,3084,3085],{},"marginal revenue","), definovaný jako ",[207,3088,1145],{"className":3089,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,3092,3094],{"className":3093},[886],[888,3095,3096],{"xmlns":890,"display":2350},[892,3097,3098,3158],{},[2354,3099,3100],{"width":2356},[2358,3101,3102,3104,3151,3153],{},[2361,3103],{"width":2363},[2361,3105,3106],{},[895,3107,3108,3110,3112,3114,3131,3133,3135,3143,3145,3147,3149],{},[898,3109,1742],{},[898,3111,1662],{},[1706,3113,1708],{},[2964,3115,3116,3125],{},[895,3117,3118,3121,3123],{},[898,3119,3120],{"mathvariant":2409},"d",[898,3122,1659],{},[898,3124,1662],{},[895,3126,3127,3129],{},[898,3128,3120],{"mathvariant":2409},[898,3130,2146],{},[1706,3132,1708],{},[898,3134,1659],{},[2489,3136,3137,3139],{},[898,3138,1662],{},[1706,3140,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},"0em","′",[1706,3144,2140],{"stretchy":2139},[898,3146,2146],{},[1706,3148,2153],{"stretchy":2139},[898,3150,1837],{"mathvariant":2409},[2361,3152],{"width":2363},[2361,3154,3155],{},[2415,3156,3157],{},"(3.2)",[902,3159,3160],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,3162,3163,3164,3167],{},"Mezní příjem udává ",[38,3165,3166],{},"rychlost změny"," celkového příjmu vzhledem k množství.",[1636,3169,3170],{},[724,3171,3172,3175,3176,3203,3204,3222,3223,1837],{},[883,3173,3174],{},"!info"," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,3177,3179],{"className":3178},[886],[888,3180,3181],{"xmlns":890},[892,3182,3183,3200],{},[895,3184,3185,3187,3189,3191,3198],{},[898,3186,1742],{},[898,3188,1662],{},[1706,3190,2140],{"stretchy":2139},[2489,3192,3193,3195],{},[898,3194,2146],{},[1706,3196,3197],{},"∗",[1706,3199,2153],{"stretchy":2139},[902,3201,3202],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,3205,3207],{"className":3206},[886],[888,3208,3209],{"xmlns":890},[892,3210,3211,3219],{},[895,3212,3213],{},[2489,3214,3215,3217],{},[898,3216,2146],{},[1706,3218,3197],{},[902,3220,3221],{"encoding":904},"Q^*",". Jinak řečeno: ",[883,3224,3226],{"className":3225},[886],[888,3227,3228],{"xmlns":890},[892,3229,3230,3283],{},[895,3231,3232,3234,3236,3238,3244,3246,3249,3251,3253,3255,3261,3263,3265,3267,3269,3271,3273,3275,3281],{},[898,3233,1742],{},[898,3235,1662],{},[1706,3237,2140],{"stretchy":2139},[2489,3239,3240,3242],{},[898,3241,2146],{},[1706,3243,3197],{},[1706,3245,2153],{"stretchy":2139},[1706,3247,3248],{},"≈",[898,3250,1659],{},[898,3252,1662],{},[1706,3254,2140],{"stretchy":2139},[2489,3256,3257,3259],{},[898,3258,2146],{},[1706,3260,3197],{},[1706,3262,2447],{},[2148,3264,2701],{},[1706,3266,2153],{"stretchy":2139},[1706,3268,1715],{},[898,3270,1659],{},[898,3272,1662],{},[1706,3274,2140],{"stretchy":2139},[2489,3276,3277,3279],{},[898,3278,2146],{},[1706,3280,3197],{},[1706,3282,2153],{"stretchy":2139},[902,3284,3285],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[2547,3287,3289],{"id":3288},"příklad-32","Příklad 3.2",[724,3291,3292,2556,3294,2594,3328,3343,3344,1837],{},[38,3293,2555],{},[883,3295,3297],{"className":3296},[886],[888,3298,3299],{"xmlns":890},[892,3300,3301,3325],{},[895,3302,3303,3305,3307,3309,3311,3313,3315,3317,3319,3321,3323],{},[898,3304,1702],{},[1706,3306,1708],{},[898,3308,2334],{},[1706,3310,2140],{"stretchy":2139},[898,3312,2146],{},[1706,3314,2153],{"stretchy":2139},[1706,3316,1708],{},[2148,3318,2590],{},[1706,3320,1715],{},[2148,3322,2495],{},[898,3324,2146],{},[902,3326,3327],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,3329,3331],{"className":3330},[886],[888,3332,3333],{"xmlns":890},[892,3334,3335,3341],{},[895,3336,3337,3339],{},[898,3338,1742],{},[898,3340,1662],{},[902,3342,1905],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,3345,3347],{"className":3346},[886],[888,3348,3349],{"xmlns":890},[892,3350,3351,3370],{},[895,3352,3353,3355,3357,3360,3362,3365,3367],{},[898,3354,2146],{},[1706,3356,1708],{},[2148,3358,3359],{},"15",[1706,3361,2505],{"separator":2504},[2148,3363,3364],{},"16",[1706,3366,2505],{"separator":2504},[2148,3368,3369],{},"20",[902,3371,3372],{"encoding":904},"Q = 15, 16, 20",[724,3374,3375,1647,3377,3409],{},[38,3376,2615],{},[883,3378,3380],{"className":3379},[886],[888,3381,3382],{"xmlns":890},[892,3383,3384,3406],{},[895,3385,3386,3388,3390,3392,3394,3396,3398,3400],{},[898,3387,1659],{},[898,3389,1662],{},[1706,3391,1708],{},[2148,3393,2590],{},[898,3395,2146],{},[1706,3397,1715],{},[2148,3399,2495],{},[2489,3401,3402,3404],{},[898,3403,2146],{},[2148,3405,2495],{},[902,3407,3408],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,3411,3413],{"className":3412},[886],[888,3414,3415],{"xmlns":890,"display":2350},[892,3416,3417,3460],{},[895,3418,3419,3421,3423,3425,3427,3429,3431,3433,3435,3441,3447,3449,3451,3453,3456,3458],{},[898,3420,1742],{},[898,3422,1662],{},[1706,3424,1708],{},[1706,3426,2140],{"stretchy":2139},[2148,3428,2590],{},[898,3430,2146],{},[1706,3432,1715],{},[2148,3434,2495],{},[2489,3436,3437,3439],{},[898,3438,2146],{},[2148,3440,2495],{},[2489,3442,3443,3445],{},[1706,3444,2153],{"stretchy":2139},[1706,3446,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,3448,1708],{},[2148,3450,2590],{},[1706,3452,1715],{},[2148,3454,3455],{},"4",[898,3457,2146],{},[898,3459,1837],{"mathvariant":2409},[902,3461,3462],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,3464,3465,3466,3484,3485,3512,3513,3526,3527,3542,3543,3556,3557,3570,3571,3526,3584,3599,3600,3613,3614,3645,3646,3665],{},"Pro ",[883,3467,3469],{"className":3468},[886],[888,3470,3471],{"xmlns":890},[892,3472,3473,3481],{},[895,3474,3475,3477,3479],{},[898,3476,2146],{},[1706,3478,1708],{},[2148,3480,3359],{},[902,3482,3483],{"encoding":904},"Q = 15"," je ",[883,3486,3488],{"className":3487},[886],[888,3489,3490],{"xmlns":890},[892,3491,3492,3509],{},[895,3493,3494,3496,3498,3500,3502,3504,3506],{},[898,3495,1742],{},[898,3497,1662],{},[1706,3499,2140],{"stretchy":2139},[2148,3501,3359],{},[1706,3503,2153],{"stretchy":2139},[1706,3505,1708],{},[2148,3507,3508],{},"40",[902,3510,3511],{"encoding":904},"MR(15) = 40",": při množství ",[883,3514,3516],{"className":3515},[886],[888,3517,3518],{"xmlns":890},[892,3519,3520,3524],{},[895,3521,3522],{},[2148,3523,3359],{},[902,3525,3359],{"encoding":904}," se ",[883,3528,3530],{"className":3529},[886],[888,3531,3532],{"xmlns":890},[892,3533,3534,3540],{},[895,3535,3536,3538],{},[898,3537,1659],{},[898,3539,1662],{},[902,3541,1665],{"encoding":904}," mění asi ",[883,3544,3546],{"className":3545},[886],[888,3547,3548],{"xmlns":890},[892,3549,3550,3554],{},[895,3551,3552],{},[2148,3553,3508],{},[902,3555,3508],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,3558,3560],{"className":3559},[886],[888,3561,3562],{"xmlns":890},[892,3563,3564,3568],{},[895,3565,3566],{},[898,3567,2146],{},[902,3569,2146],{"encoding":904}," o ",[883,3572,3574],{"className":3573},[886],[888,3575,3576],{"xmlns":890},[892,3577,3578,3582],{},[895,3579,3580],{},[2148,3581,2701],{},[902,3583,2701],{"encoding":904},[883,3585,3587],{"className":3586},[886],[888,3588,3589],{"xmlns":890},[892,3590,3591,3597],{},[895,3592,3593,3595],{},[898,3594,1659],{},[898,3596,1662],{},[902,3598,1665],{"encoding":904}," zvýší přibližně o ",[883,3601,3603],{"className":3602},[886],[888,3604,3605],{"xmlns":890},[892,3606,3607,3611],{},[895,3608,3609],{},[2148,3610,3508],{},[902,3612,3508],{"encoding":904},", tj. ze skutečné hodnoty ",[883,3615,3617],{"className":3616},[886],[888,3618,3619],{"xmlns":890},[892,3620,3621,3642],{},[895,3622,3623,3625,3627,3629,3631,3633,3635,3637,3639],{},[898,3624,1659],{},[898,3626,1662],{},[1706,3628,2140],{"stretchy":2139},[2148,3630,3359],{},[1706,3632,2153],{"stretchy":2139},[1706,3634,1708],{},[2148,3636,2701],{},[2415,3638,2799],{},[2148,3640,3641],{},"050",[902,3643,3644],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,3647,3649],{"className":3648},[886],[888,3650,3651],{"xmlns":890},[892,3652,3653,3662],{},[895,3654,3655,3657,3659],{},[2148,3656,2701],{},[2415,3658,2799],{},[2148,3660,3661],{},"090",[902,3663,3664],{"encoding":904},"1\\,090",". Skutečná změna je",[883,3667,3669],{"className":3668},[886],[888,3670,3671],{"xmlns":890,"display":2350},[892,3672,3673,3728],{},[895,3674,3675,3678,3680,3682,3684,3686,3688,3690,3692,3694,3696,3698,3700,3702,3704,3706,3708,3710,3712,3715,3717,3719,3721,3723,3725],{},[898,3676,3677],{"mathvariant":2409},"Δ",[898,3679,1659],{},[898,3681,1662],{},[1706,3683,1708],{},[898,3685,1659],{},[898,3687,1662],{},[1706,3689,2140],{"stretchy":2139},[2148,3691,3364],{},[1706,3693,2153],{"stretchy":2139},[1706,3695,1715],{},[898,3697,1659],{},[898,3699,1662],{},[1706,3701,2140],{"stretchy":2139},[2148,3703,3359],{},[1706,3705,2153],{"stretchy":2139},[1706,3707,1708],{},[2148,3709,2701],{},[2415,3711,2799],{},[2148,3713,3714],{},"088",[1706,3716,1715],{},[2148,3718,2701],{},[2415,3720,2799],{},[2148,3722,3641],{},[1706,3724,1708],{},[2148,3726,3727],{},"38.",[902,3729,3730],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,3732,3733,3734,1343,3761,3787,3788,3803,3804,3819],{},"Podobně ",[883,3735,3737],{"className":3736},[886],[888,3738,3739],{"xmlns":890},[892,3740,3741,3758],{},[895,3742,3743,3745,3747,3749,3751,3753,3755],{},[898,3744,1742],{},[898,3746,1662],{},[1706,3748,2140],{"stretchy":2139},[2148,3750,3364],{},[1706,3752,2153],{"stretchy":2139},[1706,3754,1708],{},[2148,3756,3757],{},"36",[902,3759,3760],{"encoding":904},"MR(16) = 36",[883,3762,3764],{"className":3763},[886],[888,3765,3766],{"xmlns":890},[892,3767,3768,3784],{},[895,3769,3770,3772,3774,3776,3778,3780,3782],{},[898,3771,1742],{},[898,3773,1662],{},[1706,3775,2140],{"stretchy":2139},[2148,3777,3369],{},[1706,3779,2153],{"stretchy":2139},[1706,3781,1708],{},[2148,3783,3369],{},[902,3785,3786],{"encoding":904},"MR(20) = 20",". ",[883,3789,3791],{"className":3790},[886],[888,3792,3793],{"xmlns":890},[892,3794,3795,3801],{},[895,3796,3797,3799],{},[898,3798,1742],{},[898,3800,1662],{},[902,3802,1905],{"encoding":904}," je klesající funkce — rychlost změny ",[883,3805,3807],{"className":3806},[886],[888,3808,3809],{"xmlns":890},[892,3810,3811,3817],{},[895,3812,3813,3815],{},[898,3814,1659],{},[898,3816,1662],{},[902,3818,1665],{"encoding":904}," s růstem množství klesá.",[198,3821,3823],{"id":3822},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,3825,3826],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,3828,3830],{"className":3829},[886],[888,3831,3832],{"xmlns":890,"display":2350},[892,3833,3834,3904],{},[2354,3835,3836],{"width":2356},[2358,3837,3838,3840,3897,3899],{},[2361,3839],{"width":2363},[2361,3841,3842],{},[895,3843,3844,3846,3848,3850,3853,3855,3857,3859,3861,3863,3865,3867,3869,3871,3877,3879,3881,3883,3885,3887,3889,3891,3893,3895],{},[898,3845,3677],{"mathvariant":2409},[898,3847,1659],{},[898,3849,1662],{},[2415,3851,3852],{},"  ",[1706,3854,3248],{},[2415,3856,3852],{},[898,3858,3120],{"mathvariant":2409},[898,3860,1659],{},[898,3862,1662],{},[1706,3864,1708],{},[1706,3866,2140],{"stretchy":2139},[898,3868,1659],{},[898,3870,1662],{},[2489,3872,3873,3875],{},[1706,3874,2153],{"stretchy":2139},[1706,3876,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2415,3878,2799],{},[898,3880,3120],{"mathvariant":2409},[898,3882,2146],{},[1706,3884,1708],{},[898,3886,1742],{},[898,3888,1662],{},[2415,3890,2799],{},[898,3892,3120],{"mathvariant":2409},[898,3894,2146],{},[1706,3896,2505],{"separator":2504},[2361,3898],{"width":2363},[2361,3900,3901],{},[2415,3902,3903],{},"(3.3)",[902,3905,3906],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,3908,3909],{},"schematicky:",[883,3911,3913],{"className":3912},[886],[888,3914,3915],{"xmlns":890,"display":2350},[892,3916,3917,4032],{},[895,3918,3919,3963,3965,3967,3969,3998,4001,4030],{},[895,3920,3921,3924,3933,3936,3943,3946,3953,3960],{},[2415,3922,3923],{},"zm",[3925,3926,3927,3930],"mover",{"accent":2504},[2415,3928,3929],{},"e",[1706,3931,3932],{},"ˇ",[2415,3934,3935],{},"na celkov",[3925,3937,3938,3940],{"accent":2504},[2415,3939,3929],{},[1706,3941,3942],{},"ˊ",[2415,3944,3945],{},"ho p",[3925,3947,3948,3951],{"accent":2504},[2415,3949,3950],{},"r",[1706,3952,3932],{},[3925,3954,3955,3958],{"accent":2504},[2415,3956,3957],{},"ı",[1706,3959,3942],{},[2415,3961,3962],{},"jmu",[2415,3964,3852],{},[1706,3966,3248],{},[2415,3968,3852],{},[895,3970,3971,3974,3980,3983,3989,3995],{},[2415,3972,3973],{},"mezn",[3925,3975,3976,3978],{"accent":2504},[2415,3977,3957],{},[1706,3979,3942],{},[2415,3981,3982],{}," p",[3925,3984,3985,3987],{"accent":2504},[2415,3986,3950],{},[1706,3988,3932],{},[3925,3990,3991,3993],{"accent":2504},[2415,3992,3957],{},[1706,3994,3942],{},[2415,3996,3997],{},"jem",[1706,3999,4000],{},"×",[895,4002,4003,4005,4011,4014,4021,4024],{},[2415,4004,3923],{},[3925,4006,4007,4009],{"accent":2504},[2415,4008,3929],{},[1706,4010,3932],{},[2415,4012,4013],{},"na mno",[3925,4015,4016,4019],{"accent":2504},[2415,4017,4018],{},"z",[1706,4020,3932],{},[2415,4022,4023],{},"stv",[3925,4025,4026,4028],{"accent":2504},[2415,4027,3957],{},[1706,4029,3942],{},[898,4031,1837],{"mathvariant":2409},[902,4033,4034],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,4036,4037,4038,4053],{},"Pro porovnání skutečná změna ",[883,4039,4041],{"className":4040},[886],[888,4042,4043],{"xmlns":890},[892,4044,4045,4051],{},[895,4046,4047,4049],{},[898,4048,1659],{},[898,4050,1662],{},[902,4052,1665],{"encoding":904}," je",[883,4055,4057],{"className":4056},[886],[888,4058,4059],{"xmlns":890,"display":2350},[892,4060,4061,4116],{},[2354,4062,4063],{"width":2356},[2358,4064,4065,4067,4109,4111],{},[2361,4066],{"width":2363},[2361,4068,4069],{},[895,4070,4071,4073,4075,4077,4079,4081,4083,4085,4087,4089,4091,4093,4095,4097,4099,4101,4103,4105,4107],{},[898,4072,3677],{"mathvariant":2409},[898,4074,1659],{},[898,4076,1662],{},[1706,4078,1708],{},[898,4080,1659],{},[898,4082,1662],{},[1706,4084,2140],{"stretchy":2139},[898,4086,2146],{},[1706,4088,2447],{},[898,4090,3120],{"mathvariant":2409},[898,4092,2146],{},[1706,4094,2153],{"stretchy":2139},[1706,4096,1715],{},[898,4098,1659],{},[898,4100,1662],{},[1706,4102,2140],{"stretchy":2139},[898,4104,2146],{},[1706,4106,2153],{"stretchy":2139},[898,4108,1837],{"mathvariant":2409},[2361,4110],{"width":2363},[2361,4112,4113],{},[2415,4114,4115],{},"(3.4)",[902,4117,4118],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[2547,4120,4122],{"id":4121},"příklad-33","Příklad 3.3",[724,4124,4125,4127,4128,4158,4159,4174,4175,1889,4188,4202,4203,4217],{},[38,4126,2555],{}," Pro ",[883,4129,4131],{"className":4130},[886],[888,4132,4133],{"xmlns":890},[892,4134,4135,4155],{},[895,4136,4137,4139,4141,4143,4145,4147,4149],{},[898,4138,1659],{},[898,4140,1662],{},[1706,4142,1708],{},[2148,4144,2590],{},[898,4146,2146],{},[1706,4148,1715],{},[2489,4150,4151,4153],{},[898,4152,2146],{},[2148,4154,2495],{},[902,4156,4157],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,4160,4162],{"className":4161},[886],[888,4163,4164],{"xmlns":890},[892,4165,4166,4172],{},[895,4167,4168,4170],{},[898,4169,1659],{},[898,4171,1662],{},[902,4173,1665],{"encoding":904}," při změně ",[883,4176,4178],{"className":4177},[886],[888,4179,4180],{"xmlns":890},[892,4181,4182,4186],{},[895,4183,4184],{},[898,4185,2146],{},[902,4187,2146],{"encoding":904},[883,4189,4191],{"className":4190},[886],[888,4192,4193],{"xmlns":890},[892,4194,4195,4200],{},[895,4196,4197],{},[2148,4198,4199],{},"60",[902,4201,4199],{"encoding":904}," na ",[883,4204,4206],{"className":4205},[886],[888,4207,4208],{"xmlns":890},[892,4209,4210,4215],{},[895,4211,4212],{},[2148,4213,4214],{},"63",[902,4216,4214],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,4219,4220,1647,4222,4248,4249,1343,4267,4288],{},[38,4221,2615],{},[883,4223,4225],{"className":4224},[886],[888,4226,4227],{"xmlns":890},[892,4228,4229,4245],{},[895,4230,4231,4233,4235,4237,4239,4241,4243],{},[898,4232,1742],{},[898,4234,1662],{},[1706,4236,1708],{},[2148,4238,2590],{},[1706,4240,1715],{},[2148,4242,2495],{},[898,4244,2146],{},[902,4246,4247],{"encoding":904},"MR = 100 - 2Q",", tedy při ",[883,4250,4252],{"className":4251},[886],[888,4253,4254],{"xmlns":890},[892,4255,4256,4264],{},[895,4257,4258,4260,4262],{},[898,4259,2146],{},[1706,4261,1708],{},[2148,4263,4199],{},[902,4265,4266],{"encoding":904},"Q = 60",[883,4268,4270],{"className":4269},[886],[888,4271,4272],{"xmlns":890},[892,4273,4274,4285],{},[895,4275,4276,4278,4280,4282],{},[898,4277,3120],{"mathvariant":2409},[898,4279,2146],{},[1706,4281,1708],{},[2148,4283,4284],{},"3",[902,4286,4287],{"encoding":904},"\\mathrm{d}Q = 3",":",[883,4290,4292],{"className":4291},[886],[888,4293,4294],{"xmlns":890,"display":2350},[892,4295,4296,4328],{},[895,4297,4298,4300,4302,4304,4306,4308,4310,4312,4315,4317,4319,4321,4323,4325],{},[898,4299,3120],{"mathvariant":2409},[898,4301,1659],{},[898,4303,1662],{},[1706,4305,1708],{},[1706,4307,2140],{"stretchy":2139},[2148,4309,2590],{},[1706,4311,1715],{},[2148,4313,4314],{},"120",[1706,4316,2153],{"stretchy":2139},[1706,4318,2390],{},[2148,4320,4284],{},[1706,4322,1708],{},[1706,4324,1715],{},[2148,4326,4327],{},"60.",[902,4329,4330],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,4332,4333,4334,4365,4366,4385],{},"Celkový příjem klesne z ",[883,4335,4337],{"className":4336},[886],[888,4338,4339],{"xmlns":890},[892,4340,4341,4362],{},[895,4342,4343,4345,4347,4349,4351,4353,4355,4357,4359],{},[898,4344,1659],{},[898,4346,1662],{},[1706,4348,2140],{"stretchy":2139},[2148,4350,4199],{},[1706,4352,2153],{"stretchy":2139},[1706,4354,1708],{},[2148,4356,2495],{},[2415,4358,2799],{},[2148,4360,4361],{},"400",[902,4363,4364],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,4367,4369],{"className":4368},[886],[888,4370,4371],{"xmlns":890},[892,4372,4373,4382],{},[895,4374,4375,4377,4379],{},[2148,4376,2495],{},[2415,4378,2799],{},[2148,4380,4381],{},"340",[902,4383,4384],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,4387,4389],{"className":4388},[886],[888,4390,4391],{"xmlns":890,"display":2350},[892,4392,4393,4451],{},[895,4394,4395,4397,4399,4401,4403,4405,4407,4409,4411,4413,4415,4417,4419,4421,4423,4425,4427,4429,4431,4434,4436,4438,4440,4442,4444,4446,4449],{},[898,4396,3677],{"mathvariant":2409},[898,4398,1659],{},[898,4400,1662],{},[1706,4402,1708],{},[898,4404,1659],{},[898,4406,1662],{},[1706,4408,2140],{"stretchy":2139},[2148,4410,4214],{},[1706,4412,2153],{"stretchy":2139},[1706,4414,1715],{},[898,4416,1659],{},[898,4418,1662],{},[1706,4420,2140],{"stretchy":2139},[2148,4422,4199],{},[1706,4424,2153],{"stretchy":2139},[1706,4426,1708],{},[2148,4428,2495],{},[2415,4430,2799],{},[2148,4432,4433],{},"331",[1706,4435,1715],{},[2148,4437,2495],{},[2415,4439,2799],{},[2148,4441,4361],{},[1706,4443,1708],{},[1706,4445,1715],{},[2148,4447,4448],{},"69",[1706,4450,2505],{"separator":2504},[902,4452,4453],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,4455,4456,4457,4472,4473,1837],{},"tj. ",[883,4458,4460],{"className":4459},[886],[888,4461,4462],{"xmlns":890},[892,4463,4464,4470],{},[895,4465,4466,4468],{},[898,4467,1659],{},[898,4469,1662],{},[902,4471,1665],{"encoding":904}," klesne na ",[883,4474,4476],{"className":4475},[886],[888,4477,4478],{"xmlns":890},[892,4479,4480,4488],{},[895,4481,4482,4484,4486],{},[2148,4483,2495],{},[2415,4485,2799],{},[2148,4487,4433],{},[902,4489,4490],{"encoding":904},"2\\,331",[198,4492,4494],{"id":4493},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,4496,4497,4498,4521,4522,4554],{},"Obecně pro lineární poptávku ",[883,4499,4501],{"className":4500},[886],[888,4502,4503],{"xmlns":890},[892,4504,4505,4519],{},[895,4506,4507,4509,4511,4513,4515,4517],{},[898,4508,1702],{},[1706,4510,1708],{},[898,4512,207],{},[898,4514,2146],{},[1706,4516,2447],{},[898,4518,2450],{},[902,4520,2453],{"encoding":904}," platí ",[883,4523,4525],{"className":4524},[886],[888,4526,4527],{"xmlns":890},[892,4528,4529,4551],{},[895,4530,4531,4533,4535,4537,4539,4545,4547,4549],{},[898,4532,1659],{},[898,4534,1662],{},[1706,4536,1708],{},[898,4538,207],{},[2489,4540,4541,4543],{},[898,4542,2146],{},[2148,4544,2495],{},[1706,4546,2447],{},[898,4548,2450],{},[898,4550,2146],{},[902,4552,4553],{"encoding":904},"TR = aQ^2 + bQ",", odtud",[883,4556,4558],{"className":4557},[886],[888,4559,4560],{"xmlns":890,"display":2350},[892,4561,4562,4582],{},[895,4563,4564,4566,4568,4570,4572,4574,4576,4578,4580],{},[898,4565,1742],{},[898,4567,1662],{},[1706,4569,1708],{},[2148,4571,2495],{},[898,4573,207],{},[898,4575,2146],{},[1706,4577,2447],{},[898,4579,2450],{},[898,4581,1837],{"mathvariant":2409},[902,4583,4584],{"encoding":904},"MR = 2aQ + b.",[724,4586,4587,4588,4603,4604,4619,4620,4633,4634,2314,4637,4653,4654,4667,4668,4683,4684,4699,4700,4715,4716,2891,4729,4760,4761,4781,4782,4797],{},"Křivky ",[883,4589,4591],{"className":4590},[886],[888,4592,4593],{"xmlns":890},[892,4594,4595,4601],{},[895,4596,4597,4599],{},[898,4598,1742],{},[898,4600,1662],{},[902,4602,1905],{"encoding":904}," a poptávky (resp. ",[883,4605,4607],{"className":4606},[886],[888,4608,4609],{"xmlns":890},[892,4610,4611,4617],{},[895,4612,4613,4615],{},[898,4614,1735],{},[898,4616,1662],{},[902,4618,1977],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,4621,4623],{"className":4622},[886],[888,4624,4625],{"xmlns":890},[892,4626,4627,4631],{},[895,4628,4629],{},[898,4630,2450],{},[902,4632,2450],{"encoding":904},", přičemž ",[38,4635,4636],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,4638,4640],{"className":4639},[886],[888,4641,4642],{"xmlns":890},[892,4643,4644,4650],{},[895,4645,4646,4648],{},[2148,4647,2495],{},[898,4649,207],{},[902,4651,4652],{"encoding":904},"2a"," vs. ",[883,4655,4657],{"className":4656},[886],[888,4658,4659],{"xmlns":890},[892,4660,4661,4665],{},[895,4662,4663],{},[898,4664,207],{},[902,4666,207],{"encoding":904},", obrázek 3.2). ",[883,4669,4671],{"className":4670},[886],[888,4672,4673],{"xmlns":890},[892,4674,4675,4681],{},[895,4676,4677,4679],{},[898,4678,1742],{},[898,4680,1662],{},[902,4682,1905],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,4685,4687],{"className":4686},[886],[888,4688,4689],{"xmlns":890},[892,4690,4691,4697],{},[895,4692,4693,4695],{},[898,4694,1659],{},[898,4696,1662],{},[902,4698,1665],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,4701,4703],{"className":4702},[886],[888,4704,4705],{"xmlns":890},[892,4706,4707,4713],{},[895,4708,4709,4711],{},[898,4710,1742],{},[898,4712,1662],{},[902,4714,1905],{"encoding":904}," osu ",[883,4717,4719],{"className":4718},[886],[888,4720,4721],{"xmlns":890},[892,4722,4723,4727],{},[895,4724,4725],{},[898,4726,2146],{},[902,4728,2146],{"encoding":904},[883,4730,4732],{"className":4731},[886],[888,4733,4734],{"xmlns":890},[892,4735,4736,4757],{},[895,4737,4738,4740,4742,4744],{},[898,4739,2146],{},[1706,4741,1708],{},[1706,4743,1715],{},[4745,4746,4747],"mstyle",{"scriptlevel":2150,"displaystyle":2139},[2964,4748,4749,4751],{},[898,4750,2450],{},[895,4752,4753,4755],{},[2148,4754,2495],{},[898,4756,207],{},[902,4758,4759],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,4762,4764],{"className":4763},[886],[888,4765,4766],{"xmlns":890},[892,4767,4768,4778],{},[895,4769,4770,4772,4774,4776],{},[898,4771,1742],{},[898,4773,1662],{},[1706,4775,1708],{},[2148,4777,2150],{},[902,4779,4780],{"encoding":904},"MR = 0",", a dále ",[883,4783,4785],{"className":4784},[886],[888,4786,4787],{"xmlns":890},[892,4788,4789,4795],{},[895,4790,4791,4793],{},[898,4792,1659],{},[898,4794,1662],{},[902,4796,1665],{"encoding":904}," klesá.",[724,4799,4800,4801,4807,4808,4840,4841,4869],{},"V případě ",[38,4802,4803],{},[207,4804,4806],{"className":4805,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,4809,4811],{"className":4810},[886],[888,4812,4813],{"xmlns":890},[892,4814,4815,4837],{},[895,4816,4817,4819,4821,4823,4825,4827,4829,4831],{},[898,4818,1702],{},[1706,4820,1708],{},[898,4822,2334],{},[1706,4824,2140],{"stretchy":2139},[898,4826,2146],{},[1706,4828,2153],{"stretchy":2139},[1706,4830,1708],{},[2489,4832,4833,4835],{},[898,4834,1702],{},[1706,4836,3197],{},[902,4838,4839],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,4842,4844],{"className":4843},[886],[888,4845,4846],{"xmlns":890},[892,4847,4848,4866],{},[895,4849,4850,4852,4854,4856,4858,4860],{},[898,4851,1659],{},[898,4853,1662],{},[1706,4855,1708],{},[898,4857,2146],{},[1706,4859,2390],{},[2489,4861,4862,4864],{},[898,4863,1702],{},[1706,4865,3197],{},[902,4867,4868],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,4871,4873],{"className":4872},[886],[888,4874,4875],{"xmlns":890,"display":2350},[892,4876,4877,4921],{},[895,4878,4879,4881,4883,4885,4887,4889,4891,4897,4901,4903,4917,4919],{},[898,4880,1742],{},[898,4882,1662],{},[1706,4884,1708],{},[898,4886,1735],{},[898,4888,1662],{},[1706,4890,1708],{},[2489,4892,4893,4895],{},[898,4894,1702],{},[1706,4896,3197],{},[4898,4899],"mspace",{"width":4900},"1em",[1706,4902,2140],{"stretchy":2139},[895,4904,4905,4908,4914],{},[2415,4906,4907],{},"obr",[3925,4909,4910,4912],{"accent":2504},[2415,4911,207],{},[1706,4913,3942],{},[2415,4915,4916],{},"zek 3.4",[1706,4918,2153],{"stretchy":2139},[898,4920,1837],{"mathvariant":2409},[902,4922,4923],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,4925,4926],{},[614,4927,4928,4929,1993,4955,4983,4984,4997,4998,5013,5014,5027,5028,1343,5054,5027,5069,1837],{},"Obrázek 3.2: Přímky ",[883,4930,4932],{"className":4931},[886],[888,4933,4934],{"xmlns":890},[892,4935,4936,4952],{},[895,4937,4938,4940,4942,4944,4946,4948,4950],{},[898,4939,1735],{},[898,4941,1662],{},[1706,4943,1708],{},[898,4945,207],{},[898,4947,2146],{},[1706,4949,2447],{},[898,4951,2450],{},[902,4953,4954],{"encoding":904},"AR = aQ + b",[883,4956,4958],{"className":4957},[886],[888,4959,4960],{"xmlns":890},[892,4961,4962,4980],{},[895,4963,4964,4966,4968,4970,4972,4974,4976,4978],{},[898,4965,1742],{},[898,4967,1662],{},[1706,4969,1708],{},[2148,4971,2495],{},[898,4973,207],{},[898,4975,2146],{},[1706,4977,2447],{},[898,4979,2450],{},[902,4981,4982],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,4985,4987],{"className":4986},[886],[888,4988,4989],{"xmlns":890},[892,4990,4991,4995],{},[895,4992,4993],{},[898,4994,2450],{},[902,4996,2450],{"encoding":904}," se svislou osou, ",[883,4999,5001],{"className":5000},[886],[888,5002,5003],{"xmlns":890},[892,5004,5005,5011],{},[895,5006,5007,5009],{},[898,5008,1742],{},[898,5010,1662],{},[902,5012,1905],{"encoding":904}," protíná osu ",[883,5015,5017],{"className":5016},[886],[888,5018,5019],{"xmlns":890},[892,5020,5021,5025],{},[895,5022,5023],{},[898,5024,2146],{},[902,5026,2146],{"encoding":904}," v ",[883,5029,5031],{"className":5030},[886],[888,5032,5033],{"xmlns":890},[892,5034,5035,5051],{},[895,5036,5037,5039],{},[1706,5038,1715],{},[4745,5040,5041],{"scriptlevel":2150,"displaystyle":2139},[2964,5042,5043,5045],{},[898,5044,2450],{},[895,5046,5047,5049],{},[2148,5048,2495],{},[898,5050,207],{},[902,5052,5053],{"encoding":904},"-\\tfrac{b}{2a}",[883,5055,5057],{"className":5056},[886],[888,5058,5059],{"xmlns":890},[892,5060,5061,5067],{},[895,5062,5063,5065],{},[898,5064,1735],{},[898,5066,1662],{},[902,5068,1977],{"encoding":904},[883,5070,5072],{"className":5071},[886],[888,5073,5074],{"xmlns":890},[892,5075,5076,5088],{},[895,5077,5078,5080],{},[1706,5079,1715],{},[4745,5081,5082],{"scriptlevel":2150,"displaystyle":2139},[2964,5083,5084,5086],{},[898,5085,2450],{},[898,5087,207],{},[902,5089,5090],{"encoding":904},"-\\tfrac{b}{a}",[724,5092,5093],{},[614,5094,5095,5096,5127,5128,5157,5158,1837],{},"Obrázek 3.3: Parabola ",[883,5097,5099],{"className":5098},[886],[888,5100,5101],{"xmlns":890},[892,5102,5103,5125],{},[895,5104,5105,5107,5109,5111,5113,5119,5121,5123],{},[898,5106,1659],{},[898,5108,1662],{},[1706,5110,1708],{},[898,5112,207],{},[2489,5114,5115,5117],{},[898,5116,2146],{},[2148,5118,2495],{},[1706,5120,2447],{},[898,5122,2450],{},[898,5124,2146],{},[902,5126,4553],{"encoding":904}," s maximem v ",[883,5129,5131],{"className":5130},[886],[888,5132,5133],{"xmlns":890},[892,5134,5135,5155],{},[895,5136,5137,5139,5141,5143],{},[898,5138,2146],{},[1706,5140,1708],{},[1706,5142,1715],{},[4745,5144,5145],{"scriptlevel":2150,"displaystyle":2139},[2964,5146,5147,5149],{},[898,5148,2450],{},[895,5150,5151,5153],{},[2148,5152,2495],{},[898,5154,207],{},[902,5156,4759],{"encoding":904}," a nulou v ",[883,5159,5161],{"className":5160},[886],[888,5162,5163],{"xmlns":890},[892,5164,5165,5181],{},[895,5166,5167,5169,5171,5173],{},[898,5168,2146],{},[1706,5170,1708],{},[1706,5172,1715],{},[4745,5174,5175],{"scriptlevel":2150,"displaystyle":2139},[2964,5176,5177,5179],{},[898,5178,2450],{},[898,5180,207],{},[902,5182,5183],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,5185,5186],{},[614,5187,5188,5189,1837],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,5190,5192],{"className":5191},[886],[888,5193,5194],{"xmlns":890},[892,5195,5196,5216],{},[895,5197,5198,5200,5202,5204,5206,5208,5210],{},[898,5199,1735],{},[898,5201,1662],{},[1706,5203,1708],{},[898,5205,1742],{},[898,5207,1662],{},[1706,5209,1708],{},[2489,5211,5212,5214],{},[898,5213,1702],{},[1706,5215,3197],{},[902,5217,5218],{"encoding":904},"AR = MR = P^*",[115,5220,5222],{"id":5221},"náklady-firmy","Náklady firmy",[198,5224,5226],{"id":5225},"celkové-náklady","Celkové náklady",[724,5228,5229,1647,5231,2314,5246,5249,5250,5263],{},[38,5230,5226],{},[883,5232,5234],{"className":5233},[886],[888,5235,5236],{"xmlns":890},[892,5237,5238,5244],{},[895,5239,5240,5242],{},[898,5241,1659],{},[898,5243,1683],{},[902,5245,1686],{"encoding":904},[38,5247,5248],{},"total cost",") jsou veškeré náklady na realizaci ",[883,5251,5253],{"className":5252},[886],[888,5254,5255],{"xmlns":890},[892,5256,5257,5261],{},[895,5258,5259],{},[898,5260,2146],{},[902,5262,2146],{"encoding":904}," jednotek produkce:",[883,5265,5267],{"className":5266},[886],[888,5268,5269],{"xmlns":890,"display":2350},[892,5270,5271,5326],{},[2354,5272,5273],{"width":2356},[2358,5274,5275,5277,5319,5321],{},[2361,5276],{"width":2363},[2361,5278,5279],{},[895,5280,5281,5283,5285,5287,5289,5291,5293,5295,5297,5299,5301,5303,5305,5307,5309,5311,5313,5315,5317],{},[898,5282,1659],{},[898,5284,1683],{},[1706,5286,1708],{},[898,5288,1659],{},[898,5290,1683],{},[1706,5292,2140],{"stretchy":2139},[898,5294,2146],{},[1706,5296,2153],{"stretchy":2139},[1706,5298,1708],{},[898,5300,2020],{},[898,5302,1683],{},[1706,5304,2447],{},[898,5306,1659],{},[898,5308,1762],{},[898,5310,1683],{},[1706,5312,2140],{"stretchy":2139},[898,5314,2146],{},[1706,5316,2153],{"stretchy":2139},[1706,5318,2505],{"separator":2504},[2361,5320],{"width":2363},[2361,5322,5323],{},[2415,5324,5325],{},"(3.5)",[902,5327,5328],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,5330,5331,5332,5347,5348,2314,5351,5354,5355,5347,5379,2314,5382,5385],{},"kde ",[883,5333,5335],{"className":5334},[886],[888,5336,5337],{"xmlns":890},[892,5338,5339,5345],{},[895,5340,5341,5343],{},[898,5342,2020],{},[898,5344,1683],{},[902,5346,2025],{"encoding":904}," jsou ",[38,5349,5350],{},"fixní náklady",[38,5352,5353],{},"fixed cost",") a ",[883,5356,5358],{"className":5357},[886],[888,5359,5360],{"xmlns":890},[892,5361,5362,5376],{},[895,5363,5364,5366,5368,5370,5372,5374],{},[898,5365,1659],{},[898,5367,1762],{},[898,5369,1683],{},[1706,5371,2140],{"stretchy":2139},[898,5373,2146],{},[1706,5375,2153],{"stretchy":2139},[902,5377,5378],{"encoding":904},"TVC(Q)",[38,5380,5381],{},"celkové variabilní náklady",[38,5383,5384],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,5387,5389],{"id":5388},"průměrné-náklady","Průměrné náklady",[724,5391,5392,1647,5394,2314,5409,5412],{},[38,5393,5389],{},[883,5395,5397],{"className":5396},[886],[888,5398,5399],{"xmlns":890},[892,5400,5401,5407],{},[895,5402,5403,5405],{},[898,5404,1735],{},[898,5406,1683],{},[902,5408,2094],{"encoding":904},[38,5410,5411],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,5414,5416],{"className":5415},[886],[888,5417,5418],{"xmlns":890,"display":2350},[892,5419,5420,5499],{},[2354,5421,5422],{"width":2356},[2358,5423,5424,5426,5492,5494],{},[2361,5425],{"width":2363},[2361,5427,5428],{},[895,5429,5430,5432,5434,5436,5438,5440,5442,5444,5446,5448,5458,5460,5470,5472,5490],{},[898,5431,1735],{},[898,5433,1683],{},[1706,5435,1708],{},[898,5437,1735],{},[898,5439,1683],{},[1706,5441,2140],{"stretchy":2139},[898,5443,2146],{},[1706,5445,2153],{"stretchy":2139},[1706,5447,1708],{},[2964,5449,5450,5456],{},[895,5451,5452,5454],{},[898,5453,1659],{},[898,5455,1683],{},[898,5457,2146],{},[1706,5459,1708],{},[2964,5461,5462,5468],{},[895,5463,5464,5466],{},[898,5465,2020],{},[898,5467,1683],{},[898,5469,2146],{},[1706,5471,2447],{},[2964,5473,5474,5488],{},[895,5475,5476,5478,5480,5482,5484,5486],{},[898,5477,1659],{},[898,5479,1762],{},[898,5481,1683],{},[1706,5483,2140],{"stretchy":2139},[898,5485,2146],{},[1706,5487,2153],{"stretchy":2139},[898,5489,2146],{},[1706,5491,2505],{"separator":2504},[2361,5493],{"width":2363},[2361,5495,5496],{},[2415,5497,5498],{},"(3.6)",[902,5500,5501],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,5503,5331,5504,5347,5528,1647,5531,2314,5548,5354,5551,5347,5583,1647,5586,2314,5603,5606],{},[883,5505,5507],{"className":5506},[886],[888,5508,5509],{"xmlns":890},[892,5510,5511,5525],{},[895,5512,5513],{},[4745,5514,5515],{"scriptlevel":2150,"displaystyle":2139},[2964,5516,5517,5523],{},[895,5518,5519,5521],{},[898,5520,2020],{},[898,5522,1683],{},[898,5524,2146],{},[902,5526,5527],{"encoding":904},"\\tfrac{FC}{Q}",[38,5529,5530],{},"průměrné fixní náklady",[883,5532,5534],{"className":5533},[886],[888,5535,5536],{"xmlns":890},[892,5537,5538,5546],{},[895,5539,5540,5542,5544],{},[898,5541,1735],{},[898,5543,2020],{},[898,5545,1683],{},[902,5547,2061],{"encoding":904},[38,5549,5550],{},"average fixed cost",[883,5552,5554],{"className":5553},[886],[888,5555,5556],{"xmlns":890},[892,5557,5558,5580],{},[895,5559,5560],{},[4745,5561,5562],{"scriptlevel":2150,"displaystyle":2139},[2964,5563,5564,5578],{},[895,5565,5566,5568,5570,5572,5574,5576],{},[898,5567,1659],{},[898,5569,1762],{},[898,5571,1683],{},[1706,5573,2140],{"stretchy":2139},[898,5575,2146],{},[1706,5577,2153],{"stretchy":2139},[898,5579,2146],{},[902,5581,5582],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,5584,5585],{},"průměrné variabilní náklady",[883,5587,5589],{"className":5588},[886],[888,5590,5591],{"xmlns":890},[892,5592,5593,5601],{},[895,5594,5595,5597,5599],{},[898,5596,1735],{},[898,5598,1762],{},[898,5600,1683],{},[902,5602,1836],{"encoding":904},[38,5604,5605],{},"average variable cost","):",[883,5608,5610],{"className":5609},[886],[888,5611,5612],{"xmlns":890,"display":2350},[892,5613,5614,5673],{},[2354,5615,5616],{"width":2356},[2358,5617,5618,5620,5666,5668],{},[2361,5619],{"width":2363},[2361,5621,5622],{},[895,5623,5624,5626,5628,5630,5632,5634,5636,5638,5640,5642,5644,5646,5664],{},[898,5625,1735],{},[898,5627,1762],{},[898,5629,1683],{},[1706,5631,1708],{},[898,5633,1735],{},[898,5635,1762],{},[898,5637,1683],{},[1706,5639,2140],{"stretchy":2139},[898,5641,2146],{},[1706,5643,2153],{"stretchy":2139},[1706,5645,1708],{},[2964,5647,5648,5662],{},[895,5649,5650,5652,5654,5656,5658,5660],{},[898,5651,1659],{},[898,5653,1762],{},[898,5655,1683],{},[1706,5657,2140],{"stretchy":2139},[898,5659,2146],{},[1706,5661,2153],{"stretchy":2139},[898,5663,2146],{},[898,5665,1837],{"mathvariant":2409},[2361,5667],{"width":2363},[2361,5669,5670],{},[2415,5671,5672],{},"(3.7)",[902,5674,5675],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[2547,5677,5679],{"id":5678},"příklad-34","Příklad 3.4",[724,5681,5682,4127,5684,1993,5709,2594,5733,1993,5748,5763,5764,1837],{},[38,5683,2555],{},[883,5685,5687],{"className":5686},[886],[888,5688,5689],{"xmlns":890},[892,5690,5691,5706],{},[895,5692,5693,5695,5697,5699,5701,5703],{},[898,5694,2020],{},[898,5696,1683],{},[1706,5698,1708],{},[2148,5700,2701],{},[2415,5702,2799],{},[2148,5704,5705],{},"000",[902,5707,5708],{"encoding":904},"FC = 1\\,000",[883,5710,5712],{"className":5711},[886],[888,5713,5714],{"xmlns":890},[892,5715,5716,5730],{},[895,5717,5718,5720,5722,5724,5726,5728],{},[898,5719,1659],{},[898,5721,1762],{},[898,5723,1683],{},[1706,5725,1708],{},[2148,5727,3455],{},[898,5729,2146],{},[902,5731,5732],{"encoding":904},"TVC = 4Q",[883,5734,5736],{"className":5735},[886],[888,5737,5738],{"xmlns":890},[892,5739,5740,5746],{},[895,5741,5742,5744],{},[898,5743,1659],{},[898,5745,1683],{},[902,5747,1686],{"encoding":904},[883,5749,5751],{"className":5750},[886],[888,5752,5753],{"xmlns":890},[892,5754,5755,5761],{},[895,5756,5757,5759],{},[898,5758,1735],{},[898,5760,1683],{},[902,5762,2094],{"encoding":904}," a jejich chování s rostoucím ",[883,5765,5767],{"className":5766},[886],[888,5768,5769],{"xmlns":890},[892,5770,5771,5775],{},[895,5772,5773],{},[898,5774,2146],{},[902,5776,2146],{"encoding":904},[724,5778,5779,1647,5781,1993,5811,5847,5848,3526,5861,5876,5877,4288],{},[38,5780,2615],{},[883,5782,5784],{"className":5783},[886],[888,5785,5786],{"xmlns":890},[892,5787,5788,5808],{},[895,5789,5790,5792,5794,5796,5798,5800,5802,5804,5806],{},[898,5791,1659],{},[898,5793,1683],{},[1706,5795,1708],{},[2148,5797,2701],{},[2415,5799,2799],{},[2148,5801,5705],{},[1706,5803,2447],{},[2148,5805,3455],{},[898,5807,2146],{},[902,5809,5810],{"encoding":904},"TC = 1\\,000 + 4Q",[883,5812,5814],{"className":5813},[886],[888,5815,5816],{"xmlns":890},[892,5817,5818,5844],{},[895,5819,5820,5822,5824,5826,5840,5842],{},[898,5821,1735],{},[898,5823,1683],{},[1706,5825,1708],{},[4745,5827,5828],{"scriptlevel":2150,"displaystyle":2139},[2964,5829,5830,5838],{},[895,5831,5832,5834,5836],{},[2148,5833,2701],{},[2415,5835,2799],{},[2148,5837,5705],{},[898,5839,2146],{},[1706,5841,2447],{},[2148,5843,3455],{},[902,5845,5846],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,5849,5851],{"className":5850},[886],[888,5852,5853],{"xmlns":890},[892,5854,5855,5859],{},[895,5856,5857],{},[898,5858,2146],{},[902,5860,2146],{"encoding":904},[883,5862,5864],{"className":5863},[886],[888,5865,5866],{"xmlns":890},[892,5867,5868,5874],{},[895,5869,5870,5872],{},[898,5871,1735],{},[898,5873,1683],{},[902,5875,2094],{"encoding":904}," blíží ",[883,5878,5880],{"className":5879},[886],[888,5881,5882],{"xmlns":890},[892,5883,5884,5888],{},[895,5885,5886],{},[2148,5887,3455],{},[902,5889,3455],{"encoding":904},[883,5891,5893],{"className":5892},[886],[888,5894,5895],{"xmlns":890,"display":2350},[892,5896,5897,5946],{},[895,5898,5899,5919,5941,5943],{},[5900,5901,5902,5909],"munder",{},[895,5903,5904,5907],{},[898,5905,5906],{},"lim",[1706,5908,2773],{},[895,5910,5911,5913,5916],{},[898,5912,2146],{},[1706,5914,5915],{},"→",[898,5917,5918],{"mathvariant":2409},"∞",[895,5920,5921,5923,5935,5937,5939],{},[1706,5922,2140],{"fence":2504},[2964,5924,5925,5933],{},[895,5926,5927,5929,5931],{},[2148,5928,2701],{},[2415,5930,2799],{},[2148,5932,5705],{},[898,5934,2146],{},[1706,5936,2447],{},[2148,5938,3455],{},[1706,5940,2153],{"fence":2504},[1706,5942,1708],{},[2148,5944,5945],{},"4.",[902,5947,5948],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,5950,5951,5989,5990,1837],{},[883,5952,5954],{"className":5953},[886],[888,5955,5956],{"xmlns":890},[892,5957,5958,5986],{},[895,5959,5960,5962,5964,5966,5968,5982,5984],{},[898,5961,1735],{},[898,5963,2020],{},[898,5965,1683],{},[1706,5967,1708],{},[4745,5969,5970],{"scriptlevel":2150,"displaystyle":2139},[2964,5971,5972,5980],{},[895,5973,5974,5976,5978],{},[2148,5975,2701],{},[2415,5977,2799],{},[2148,5979,5705],{},[898,5981,2146],{},[1706,5983,5915],{},[2148,5985,2150],{},[902,5987,5988],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,5991,5993],{"className":5992},[886],[888,5994,5995],{"xmlns":890},[892,5996,5997,6001],{},[895,5998,5999],{},[898,6000,2146],{},[902,6002,2146],{"encoding":904},[724,6004,6005],{},[614,6006,6007,6008,6037,6038,1837],{},"Obrázek 3.5: Přímka ",[883,6009,6011],{"className":6010},[886],[888,6012,6013],{"xmlns":890},[892,6014,6015,6035],{},[895,6016,6017,6019,6021,6023,6025,6027,6029,6031,6033],{},[898,6018,1659],{},[898,6020,1683],{},[1706,6022,1708],{},[2148,6024,2701],{},[2415,6026,2799],{},[2148,6028,5705],{},[1706,6030,2447],{},[2148,6032,3455],{},[898,6034,2146],{},[902,6036,5810],{"encoding":904}," protínající svislou osu ve výši ",[883,6039,6041],{"className":6040},[886],[888,6042,6043],{"xmlns":890},[892,6044,6045,6059],{},[895,6046,6047,6049,6051,6053,6055,6057],{},[898,6048,2020],{},[898,6050,1683],{},[1706,6052,1708],{},[2148,6054,2701],{},[2415,6056,2799],{},[2148,6058,5705],{},[902,6060,5708],{"encoding":904},[724,6062,6063],{},[614,6064,6065,6066,6101,6102,1837],{},"Obrázek 3.6: Hyperbola ",[883,6067,6069],{"className":6068},[886],[888,6070,6071],{"xmlns":890},[892,6072,6073,6099],{},[895,6074,6075,6077,6079,6081,6095,6097],{},[898,6076,1735],{},[898,6078,1683],{},[1706,6080,1708],{},[4745,6082,6083],{"scriptlevel":2150,"displaystyle":2139},[2964,6084,6085,6093],{},[895,6086,6087,6089,6091],{},[2148,6088,2701],{},[2415,6090,2799],{},[2148,6092,5705],{},[898,6094,2146],{},[1706,6096,2447],{},[2148,6098,3455],{},[902,6100,5846],{"encoding":904}," s vodorovnou asymptotou ",[883,6103,6105],{"className":6104},[886],[888,6106,6107],{"xmlns":890},[892,6108,6109,6119],{},[895,6110,6111,6113,6115,6117],{},[898,6112,1735],{},[898,6114,1683],{},[1706,6116,1708],{},[2148,6118,3455],{},[902,6120,6121],{"encoding":904},"AC = 4",[724,6123,6124],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,6126,6128],{"className":6127},[886],[888,6129,6130],{"xmlns":890,"display":2350},[892,6131,6132,6158],{},[895,6133,6134,6136,6138,6140,6142,6144,6146,6148,6150,6152,6154,6156],{},[898,6135,1659],{},[898,6137,1762],{},[898,6139,1683],{},[1706,6141,1708],{},[898,6143,2146],{},[1706,6145,2390],{},[898,6147,1762],{},[898,6149,1683],{},[1706,6151,2140],{"stretchy":2139},[898,6153,2146],{},[1706,6155,2153],{"stretchy":2139},[1706,6157,2505],{"separator":2504},[902,6159,6160],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,6162,5331,6163,5347,6191,6194,6195,6225],{},[883,6164,6166],{"className":6165},[886],[888,6167,6168],{"xmlns":890},[892,6169,6170,6188],{},[895,6171,6172,6174,6176,6178,6180,6182,6184,6186],{},[898,6173,1762],{},[898,6175,1683],{},[1706,6177,1708],{},[898,6179,1762],{},[898,6181,1683],{},[1706,6183,2140],{"stretchy":2139},[898,6185,2146],{},[1706,6187,2153],{"stretchy":2139},[902,6189,6190],{"encoding":904},"VC = VC(Q)",[38,6192,6193],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,6196,6198],{"className":6197},[886],[888,6199,6200],{"xmlns":890},[892,6201,6202,6222],{},[895,6203,6204,6206,6208,6210,6212,6214,6216,6218,6220],{},[898,6205,1659],{},[898,6207,1762],{},[898,6209,1683],{},[1706,6211,2140],{"stretchy":2139},[898,6213,2146],{},[1706,6215,2153],{"stretchy":2139},[1706,6217,1708],{},[898,6219,207],{},[898,6221,2146],{},[902,6223,6224],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,6227,6229],{"className":6228},[886],[888,6230,6231],{"xmlns":890,"display":2350},[892,6232,6233,6253],{},[895,6234,6235,6237,6239,6241,6243,6245,6247,6249,6251],{},[898,6236,1659],{},[898,6238,1683],{},[1706,6240,1708],{},[898,6242,2020],{},[898,6244,1683],{},[1706,6246,2447],{},[898,6248,207],{},[898,6250,2146],{},[898,6252,1837],{"mathvariant":2409},[902,6254,6255],{"encoding":904},"TC = FC + aQ.",[724,6257,6258,6259,6274,6275,6290,6291,6315,6316,6350,6351,6101,6365,6378,6379,1993,6427,6471,6472,1837],{},"Křivkou ",[883,6260,6262],{"className":6261},[886],[888,6263,6264],{"xmlns":890},[892,6265,6266,6272],{},[895,6267,6268,6270],{},[898,6269,1659],{},[898,6271,1683],{},[902,6273,1686],{"encoding":904}," je přímka se svislým průsečíkem ",[883,6276,6278],{"className":6277},[886],[888,6279,6280],{"xmlns":890},[892,6281,6282,6288],{},[895,6283,6284,6286],{},[898,6285,2020],{},[898,6287,1683],{},[902,6289,2025],{"encoding":904}," a sklonem ",[883,6292,6294],{"className":6293},[886],[888,6295,6296],{"xmlns":890},[892,6297,6298,6312],{},[895,6299,6300,6303,6305,6308,6310],{},[898,6301,6302],{},"tan",[1706,6304,2773],{},[898,6306,6307],{},"α",[1706,6309,1708],{},[898,6311,207],{},[902,6313,6314],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,6317,6319],{"className":6318},[886],[888,6320,6321],{"xmlns":890},[892,6322,6323,6347],{},[895,6324,6325,6327,6329,6331,6343,6345],{},[898,6326,1735],{},[898,6328,1683],{},[1706,6330,1708],{},[4745,6332,6333],{"scriptlevel":2150,"displaystyle":2139},[2964,6334,6335,6341],{},[895,6336,6337,6339],{},[898,6338,2020],{},[898,6340,1683],{},[898,6342,2146],{},[1706,6344,2447],{},[898,6346,207],{},[902,6348,6349],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,6352,6354],{"className":6353},[886],[888,6355,6356],{"xmlns":890},[892,6357,6358,6363],{},[895,6359,6360],{},[898,6361,6362],{},"L",[902,6364,6362],{"encoding":904},[883,6366,6368],{"className":6367},[886],[888,6369,6370],{"xmlns":890},[892,6371,6372,6376],{},[895,6373,6374],{},[898,6375,207],{},[902,6377,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,6380,6382],{"className":6381},[886],[888,6383,6384],{"xmlns":890},[892,6385,6386,6424],{},[895,6387,6388,6408,6420,6422],{},[2142,6389,6390,6396],{},[895,6391,6392,6394],{},[898,6393,5906],{},[1706,6395,2773],{},[895,6397,6398,6400,6402],{},[898,6399,2146],{},[1706,6401,5915],{},[2489,6403,6404,6406],{},[2148,6405,2150],{},[1706,6407,2447],{},[4745,6409,6410],{"scriptlevel":2150,"displaystyle":2139},[2964,6411,6412,6418],{},[895,6413,6414,6416],{},[898,6415,2020],{},[898,6417,1683],{},[898,6419,2146],{},[1706,6421,1708],{},[898,6423,5918],{"mathvariant":2409},[902,6425,6426],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,6428,6430],{"className":6429},[886],[888,6431,6432],{"xmlns":890},[892,6433,6434,6468],{},[895,6435,6436,6452,6464,6466],{},[2142,6437,6438,6444],{},[895,6439,6440,6442],{},[898,6441,5906],{},[1706,6443,2773],{},[895,6445,6446,6448,6450],{},[898,6447,2146],{},[1706,6449,5915],{},[898,6451,5918],{"mathvariant":2409},[4745,6453,6454],{"scriptlevel":2150,"displaystyle":2139},[2964,6455,6456,6462],{},[895,6457,6458,6460],{},[898,6459,2020],{},[898,6461,1683],{},[898,6463,2146],{},[1706,6465,1708],{},[2148,6467,2150],{},[902,6469,6470],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,6473,6475],{"className":6474},[886],[888,6476,6477],{"xmlns":890},[892,6478,6479,6485],{},[895,6480,6481,6483],{},[898,6482,1735],{},[898,6484,1683],{},[902,6486,2094],{"encoding":904},[724,6488,6489],{},[614,6490,6491,6492,6507,6508,6523,6524,1837],{},"Obrázek 3.7: Přímka ",[883,6493,6495],{"className":6494},[886],[888,6496,6497],{"xmlns":890},[892,6498,6499,6505],{},[895,6500,6501,6503],{},[898,6502,1659],{},[898,6504,1683],{},[902,6506,1686],{"encoding":904}," s osovým průsečíkem ve výši ",[883,6509,6511],{"className":6510},[886],[888,6512,6513],{"xmlns":890},[892,6514,6515,6521],{},[895,6516,6517,6519],{},[898,6518,2020],{},[898,6520,1683],{},[902,6522,2025],{"encoding":904}," a se sklonem ",[883,6525,6527],{"className":6526},[886],[888,6528,6529],{"xmlns":890},[892,6530,6531,6543],{},[895,6532,6533,6535,6537,6539,6541],{},[898,6534,6302],{},[1706,6536,2773],{},[898,6538,6307],{},[1706,6540,1708],{},[898,6542,207],{},[902,6544,6314],{"encoding":904},[724,6546,6547],{},[614,6548,6549,6550,6565,6566,1837],{},"Obrázek 3.8: Klesající hyperbola ",[883,6551,6553],{"className":6552},[886],[888,6554,6555],{"xmlns":890},[892,6556,6557,6563],{},[895,6558,6559,6561],{},[898,6560,1735],{},[898,6562,1683],{},[902,6564,2094],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,6567,6569],{"className":6568},[886],[888,6570,6571],{"xmlns":890},[892,6572,6573,6577],{},[895,6574,6575],{},[898,6576,207],{},[902,6578,207],{"encoding":904},[198,6580,6582],{"id":6581},"mezní-náklady","Mezní náklady",[724,6584,6585,1647,6587,2314,6602,6605,6606,6609],{},[38,6586,6582],{},[883,6588,6590],{"className":6589},[886],[888,6591,6592],{"xmlns":890},[892,6593,6594,6600],{},[895,6595,6596,6598],{},[898,6597,1742],{},[898,6599,1683],{},[902,6601,1817],{"encoding":904},[38,6603,6604],{},"marginal cost",") jsou ",[207,6607,1145],{"className":6608,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,6611,6613],{"className":6612},[886],[888,6614,6615],{"xmlns":890,"display":2350},[892,6616,6617,6686],{},[2354,6618,6619],{"width":2356},[2358,6620,6621,6623,6679,6681],{},[2361,6622],{"width":2363},[2361,6624,6625],{},[895,6626,6627,6629,6631,6633,6635,6637,6639,6641,6643,6645,6661,6663,6665,6671,6673,6675,6677],{},[898,6628,1742],{},[898,6630,1683],{},[1706,6632,1708],{},[898,6634,1742],{},[898,6636,1683],{},[1706,6638,2140],{"stretchy":2139},[898,6640,2146],{},[1706,6642,2153],{"stretchy":2139},[1706,6644,1708],{},[2964,6646,6647,6655],{},[895,6648,6649,6651,6653],{},[898,6650,3120],{"mathvariant":2409},[898,6652,1659],{},[898,6654,1683],{},[895,6656,6657,6659],{},[898,6658,3120],{"mathvariant":2409},[898,6660,2146],{},[1706,6662,1708],{},[898,6664,1659],{},[2489,6666,6667,6669],{},[898,6668,1683],{},[1706,6670,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,6672,2140],{"stretchy":2139},[898,6674,2146],{},[1706,6676,2153],{"stretchy":2139},[898,6678,1837],{"mathvariant":2409},[2361,6680],{"width":2363},[2361,6682,6683],{},[2415,6684,6685],{},"(3.8)",[902,6687,6688],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[1636,6690,6691],{},[724,6692,6693,6695,6696,6722,6723,6740,6741,1837],{},[883,6694,3174],{}," Intuice — „kolik stojí další kus\"\n",[883,6697,6699],{"className":6698},[886],[888,6700,6701],{"xmlns":890},[892,6702,6703,6719],{},[895,6704,6705,6707,6709,6711,6717],{},[898,6706,1742],{},[898,6708,1683],{},[1706,6710,2140],{"stretchy":2139},[2489,6712,6713,6715],{},[898,6714,2146],{},[1706,6716,3197],{},[1706,6718,2153],{"stretchy":2139},[902,6720,6721],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,6724,6726],{"className":6725},[886],[888,6727,6728],{"xmlns":890},[892,6729,6730,6738],{},[895,6731,6732],{},[2489,6733,6734,6736],{},[898,6735,2146],{},[1706,6737,3197],{},[902,6739,3221],{"encoding":904},". Formálně ",[883,6742,6744],{"className":6743},[886],[888,6745,6746],{"xmlns":890},[892,6747,6748,6800],{},[895,6749,6750,6752,6754,6756,6762,6764,6766,6768,6770,6772,6778,6780,6782,6784,6786,6788,6790,6792,6798],{},[898,6751,1742],{},[898,6753,1683],{},[1706,6755,2140],{"stretchy":2139},[2489,6757,6758,6760],{},[898,6759,2146],{},[1706,6761,3197],{},[1706,6763,2153],{"stretchy":2139},[1706,6765,3248],{},[898,6767,1659],{},[898,6769,1683],{},[1706,6771,2140],{"stretchy":2139},[2489,6773,6774,6776],{},[898,6775,2146],{},[1706,6777,3197],{},[1706,6779,2447],{},[2148,6781,2701],{},[1706,6783,2153],{"stretchy":2139},[1706,6785,1715],{},[898,6787,1659],{},[898,6789,1683],{},[1706,6791,2140],{"stretchy":2139},[2489,6793,6794,6796],{},[898,6795,2146],{},[1706,6797,3197],{},[1706,6799,2153],{"stretchy":2139},[902,6801,6802],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,6804,6805,6806,4288],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,6807,6809],{"className":6808},[886],[888,6810,6811],{"xmlns":890},[892,6812,6813,6821],{},[895,6814,6815,6817,6819],{},[898,6816,3677],{"mathvariant":2409},[898,6818,1659],{},[898,6820,1683],{},[902,6822,6823],{"encoding":904},"\\Delta TC",[883,6825,6827],{"className":6826},[886],[888,6828,6829],{"xmlns":890,"display":2350},[892,6830,6831,6900],{},[2354,6832,6833],{"width":2356},[2358,6834,6835,6837,6893,6895],{},[2361,6836],{"width":2363},[2361,6838,6839],{},[895,6840,6841,6843,6845,6847,6849,6851,6853,6855,6857,6859,6861,6863,6865,6867,6873,6875,6877,6879,6881,6883,6885,6887,6889,6891],{},[898,6842,3677],{"mathvariant":2409},[898,6844,1659],{},[898,6846,1683],{},[2415,6848,3852],{},[1706,6850,3248],{},[2415,6852,3852],{},[898,6854,3120],{"mathvariant":2409},[898,6856,1659],{},[898,6858,1683],{},[1706,6860,1708],{},[1706,6862,2140],{"stretchy":2139},[898,6864,1659],{},[898,6866,1683],{},[2489,6868,6869,6871],{},[1706,6870,2153],{"stretchy":2139},[1706,6872,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2415,6874,2799],{},[898,6876,3120],{"mathvariant":2409},[898,6878,2146],{},[1706,6880,1708],{},[898,6882,1742],{},[898,6884,1683],{},[2415,6886,2799],{},[898,6888,3120],{"mathvariant":2409},[898,6890,2146],{},[1706,6892,2505],{"separator":2504},[2361,6894],{"width":2363},[2361,6896,6897],{},[2415,6898,6899],{},"(3.9)",[902,6901,6902],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,6904,3909],{},[883,6906,6908],{"className":6907},[886],[888,6909,6910],{"xmlns":890,"display":2350},[892,6911,6912,7011],{},[895,6913,6914,6953,6955,6957,6959,6981,6983,7009],{},[895,6915,6916,6918,6924,6926,6933,6936,6942,6945],{},[2415,6917,3923],{},[3925,6919,6920,6922],{"accent":2504},[2415,6921,3929],{},[1706,6923,3932],{},[2415,6925,3935],{},[3925,6927,6928,6931],{"accent":2504},[2415,6929,6930],{},"y",[1706,6932,3942],{},[2415,6934,6935],{},"ch n",[3925,6937,6938,6940],{"accent":2504},[2415,6939,207],{},[1706,6941,3942],{},[2415,6943,6944],{},"klad",[3925,6946,6947,6950],{"accent":2504},[2415,6948,6949],{},"u",[1706,6951,6952],{},"˚",[2415,6954,3852],{},[1706,6956,3248],{},[2415,6958,3852],{},[895,6960,6961,6963,6969,6972,6978],{},[2415,6962,3973],{},[3925,6964,6965,6967],{"accent":2504},[2415,6966,3957],{},[1706,6968,3942],{},[2415,6970,6971],{}," n",[3925,6973,6974,6976],{"accent":2504},[2415,6975,207],{},[1706,6977,3942],{},[2415,6979,6980],{},"klady",[1706,6982,4000],{},[895,6984,6985,6987,6993,6995,7001,7003],{},[2415,6986,3923],{},[3925,6988,6989,6991],{"accent":2504},[2415,6990,3929],{},[1706,6992,3932],{},[2415,6994,4013],{},[3925,6996,6997,6999],{"accent":2504},[2415,6998,4018],{},[1706,7000,3932],{},[2415,7002,4023],{},[3925,7004,7005,7007],{"accent":2504},[2415,7006,3957],{},[1706,7008,3942],{},[898,7010,1837],{"mathvariant":2409},[902,7012,7013],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[2547,7015,7017],{"id":7016},"příklad-35","Příklad 3.5",[724,7019,7020,4127,7022,2594,7060,7075,7076,7091,7092,1889,7105,4202,7118,7131,7132,4202,7145,1837],{},[38,7021,2555],{},[883,7023,7025],{"className":7024},[886],[888,7026,7027],{"xmlns":890},[892,7028,7029,7057],{},[895,7030,7031,7033,7035,7037,7040,7042,7045,7047,7049,7051],{},[898,7032,1659],{},[898,7034,1683],{},[1706,7036,1708],{},[2148,7038,7039],{},"200",[1706,7041,2447],{},[2148,7043,7044],{},"6",[898,7046,2146],{},[1706,7048,2447],{},[2148,7050,2495],{},[2489,7052,7053,7055],{},[898,7054,2146],{},[2148,7056,2495],{},[902,7058,7059],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,7061,7063],{"className":7062},[886],[888,7064,7065],{"xmlns":890},[892,7066,7067,7073],{},[895,7068,7069,7071],{},[898,7070,1742],{},[898,7072,1683],{},[902,7074,1817],{"encoding":904}," a odhadněte změny ",[883,7077,7079],{"className":7078},[886],[888,7080,7081],{"xmlns":890},[892,7082,7083,7089],{},[895,7084,7085,7087],{},[898,7086,1659],{},[898,7088,1683],{},[902,7090,1686],{"encoding":904}," při změnách ",[883,7093,7095],{"className":7094},[886],[888,7096,7097],{"xmlns":890},[892,7098,7099,7103],{},[895,7100,7101],{},[898,7102,2146],{},[902,7104,2146],{"encoding":904},[883,7106,7108],{"className":7107},[886],[888,7109,7110],{"xmlns":890},[892,7111,7112,7116],{},[895,7113,7114],{},[2148,7115,3359],{},[902,7117,3359],{"encoding":904},[883,7119,7121],{"className":7120},[886],[888,7122,7123],{"xmlns":890},[892,7124,7125,7129],{},[895,7126,7127],{},[2148,7128,3364],{},[902,7130,3364],{"encoding":904}," a z ",[883,7133,7135],{"className":7134},[886],[888,7136,7137],{"xmlns":890},[892,7138,7139,7143],{},[895,7140,7141],{},[2148,7142,3359],{},[902,7144,3359],{"encoding":904},[883,7146,7148],{"className":7147},[886],[888,7149,7150],{"xmlns":890},[892,7151,7152,7157],{},[895,7153,7154],{},[2148,7155,7156],{},"12",[902,7158,7156],{"encoding":904},[724,7160,7161,1647,7163,3787,7189,1343,7216,7243,7244,7259,7260,7275,7276,7303,7304,7324,7325,7346,7347,7403,7404,1889,7417,4202,7430,3484,7443,1837],{},[38,7162,2615],{},[883,7164,7166],{"className":7165},[886],[888,7167,7168],{"xmlns":890},[892,7169,7170,7186],{},[895,7171,7172,7174,7176,7178,7180,7182,7184],{},[898,7173,1742],{},[898,7175,1683],{},[1706,7177,1708],{},[2148,7179,7044],{},[1706,7181,2447],{},[2148,7183,3455],{},[898,7185,2146],{},[902,7187,7188],{"encoding":904},"MC = 6 + 4Q",[883,7190,7192],{"className":7191},[886],[888,7193,7194],{"xmlns":890},[892,7195,7196,7213],{},[895,7197,7198,7200,7202,7204,7206,7208,7210],{},[898,7199,1742],{},[898,7201,1683],{},[1706,7203,2140],{"stretchy":2139},[2148,7205,3359],{},[1706,7207,2153],{"stretchy":2139},[1706,7209,1708],{},[2148,7211,7212],{},"66",[902,7214,7215],{"encoding":904},"MC(15) = 66",[883,7217,7219],{"className":7218},[886],[888,7220,7221],{"xmlns":890},[892,7222,7223,7240],{},[895,7224,7225,7227,7229,7231,7233,7235,7237],{},[898,7226,1742],{},[898,7228,1683],{},[1706,7230,2140],{"stretchy":2139},[2148,7232,3369],{},[1706,7234,2153],{"stretchy":2139},[1706,7236,1708],{},[2148,7238,7239],{},"86",[902,7241,7242],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,7245,7247],{"className":7246},[886],[888,7248,7249],{"xmlns":890},[892,7250,7251,7257],{},[895,7252,7253,7255],{},[898,7254,1659],{},[898,7256,1683],{},[902,7258,1686],{"encoding":904}," zvyšuje (",[883,7261,7263],{"className":7262},[886],[888,7264,7265],{"xmlns":890},[892,7266,7267,7273],{},[895,7268,7269,7271],{},[898,7270,1742],{},[898,7272,1683],{},[902,7274,1817],{"encoding":904}," je rostoucí). Z ",[883,7277,7279],{"className":7278},[886],[888,7280,7281],{"xmlns":890},[892,7282,7283,7300],{},[895,7284,7285,7287,7289,7291,7293,7295,7297],{},[898,7286,1659],{},[898,7288,1683],{},[1706,7290,2140],{"stretchy":2139},[2148,7292,3359],{},[1706,7294,2153],{"stretchy":2139},[1706,7296,1708],{},[2148,7298,7299],{},"740",[902,7301,7302],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,7305,7307],{"className":7306},[886],[888,7308,7309],{"xmlns":890},[892,7310,7311,7321],{},[895,7312,7313,7315,7317,7319],{},[898,7314,3120],{"mathvariant":2409},[898,7316,2146],{},[1706,7318,1708],{},[2148,7320,2701],{},[902,7322,7323],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,7326,7328],{"className":7327},[886],[888,7329,7330],{"xmlns":890},[892,7331,7332,7343],{},[895,7333,7334,7336,7338,7340],{},[898,7335,1659],{},[898,7337,1683],{},[1706,7339,3248],{},[2148,7341,7342],{},"806",[902,7344,7345],{"encoding":904},"TC \\approx 806",". Skutečná změna ",[883,7348,7350],{"className":7349},[886],[888,7351,7352],{"xmlns":890},[892,7353,7354,7400],{},[895,7355,7356,7358,7360,7362,7364,7366,7368,7370,7372,7374,7376,7378,7380,7382,7384,7386,7388,7391,7393,7395,7397],{},[898,7357,3677],{"mathvariant":2409},[898,7359,1659],{},[898,7361,1683],{},[1706,7363,1708],{},[898,7365,1659],{},[898,7367,1683],{},[1706,7369,2140],{"stretchy":2139},[2148,7371,3364],{},[1706,7373,2153],{"stretchy":2139},[1706,7375,1715],{},[898,7377,1659],{},[898,7379,1683],{},[1706,7381,2140],{"stretchy":2139},[2148,7383,3359],{},[1706,7385,2153],{"stretchy":2139},[1706,7387,1708],{},[2148,7389,7390],{},"808",[1706,7392,1715],{},[2148,7394,7299],{},[1706,7396,1708],{},[2148,7398,7399],{},"68",[902,7401,7402],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,7405,7407],{"className":7406},[886],[888,7408,7409],{"xmlns":890},[892,7410,7411,7415],{},[895,7412,7413],{},[898,7414,2146],{},[902,7416,2146],{"encoding":904},[883,7418,7420],{"className":7419},[886],[888,7421,7422],{"xmlns":890},[892,7423,7424,7428],{},[895,7425,7426],{},[2148,7427,3359],{},[902,7429,3359],{"encoding":904},[883,7431,7433],{"className":7432},[886],[888,7434,7435],{"xmlns":890},[892,7436,7437,7441],{},[895,7438,7439],{},[2148,7440,7156],{},[902,7442,7156],{"encoding":904},[883,7444,7446],{"className":7445},[886],[888,7447,7448],{"xmlns":890},[892,7449,7450,7479],{},[895,7451,7452,7454,7456,7458,7460,7462,7464,7466,7468,7470,7472,7474,7476],{},[898,7453,3677],{"mathvariant":2409},[898,7455,1659],{},[898,7457,1683],{},[1706,7459,3248],{},[2148,7461,7212],{},[1706,7463,2390],{},[1706,7465,2140],{"stretchy":2139},[1706,7467,1715],{},[2148,7469,4284],{},[1706,7471,2153],{"stretchy":2139},[1706,7473,1708],{},[1706,7475,1715],{},[2148,7477,7478],{},"198",[902,7480,7481],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,7483,7485],{"id":7484},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,7487,7488],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[2547,7490,7492],{"id":7491},"příklad-36","Příklad 3.6",[724,7494,7495,4127,7497,7542],{},[38,7496,2555],{},[883,7498,7500],{"className":7499},[886],[888,7501,7502],{"xmlns":890},[892,7503,7504,7539],{},[895,7505,7506,7508,7510,7512,7514,7516,7518,7520,7522,7525,7531,7533],{},[898,7507,1659],{},[898,7509,1683],{},[1706,7511,1708],{},[2148,7513,2590],{},[1706,7515,2447],{},[2148,7517,2748],{},[898,7519,2146],{},[1706,7521,1715],{},[2148,7523,7524],{},"5",[2489,7526,7527,7529],{},[898,7528,2146],{},[2148,7530,2495],{},[1706,7532,2447],{},[2489,7534,7535,7537],{},[898,7536,2146],{},[2148,7538,4284],{},[902,7540,7541],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,7544,7545],{},[38,7546,2615],{},[883,7548,7550],{"className":7549},[886],[888,7551,7552],{"xmlns":890,"display":2350},[892,7553,7554,7801],{},[2354,7555,7558,7584,7632,7666,7708,7758],{"rowspacing":7556,"columnalign":7557,"columnspacing":3141},"0.25em","right left",[2358,7559,7560,7570],{},[2361,7561,7562],{},[4745,7563,7564],{"scriptlevel":2150,"displaystyle":2504},[895,7565,7566,7568],{},[898,7567,2020],{},[898,7569,1683],{},[2361,7571,7572],{},[4745,7573,7574],{"scriptlevel":2150,"displaystyle":2504},[895,7575,7576,7578,7580,7582],{},[895,7577],{},[1706,7579,1708],{},[2148,7581,2590],{},[1706,7583,2505],{"separator":2504},[2358,7585,7586,7598],{},[2361,7587,7588],{},[4745,7589,7590],{"scriptlevel":2150,"displaystyle":2504},[895,7591,7592,7594,7596],{},[898,7593,1659],{},[898,7595,1762],{},[898,7597,1683],{},[2361,7599,7600],{},[4745,7601,7602],{"scriptlevel":2150,"displaystyle":2504},[895,7603,7604,7606,7608,7610,7612,7614,7616,7622,7624,7630],{},[895,7605],{},[1706,7607,1708],{},[2148,7609,2748],{},[898,7611,2146],{},[1706,7613,1715],{},[2148,7615,7524],{},[2489,7617,7618,7620],{},[898,7619,2146],{},[2148,7621,2495],{},[1706,7623,2447],{},[2489,7625,7626,7628],{},[898,7627,2146],{},[2148,7629,4284],{},[1706,7631,2505],{"separator":2504},[2358,7633,7634,7646],{},[2361,7635,7636],{},[4745,7637,7638],{"scriptlevel":2150,"displaystyle":2504},[895,7639,7640,7642,7644],{},[898,7641,1735],{},[898,7643,2020],{},[898,7645,1683],{},[2361,7647,7648],{},[4745,7649,7650],{"scriptlevel":2150,"displaystyle":2504},[895,7651,7652,7654,7656,7664],{},[895,7653],{},[1706,7655,1708],{},[4745,7657,7658],{"scriptlevel":2150,"displaystyle":2139},[2964,7659,7660,7662],{},[2148,7661,2590],{},[898,7663,2146],{},[1706,7665,2505],{"separator":2504},[2358,7667,7668,7680],{},[2361,7669,7670],{},[4745,7671,7672],{"scriptlevel":2150,"displaystyle":2504},[895,7673,7674,7676,7678],{},[898,7675,1735],{},[898,7677,1762],{},[898,7679,1683],{},[2361,7681,7682],{},[4745,7683,7684],{"scriptlevel":2150,"displaystyle":2504},[895,7685,7686,7688,7690,7692,7694,7696,7698,7700,7706],{},[895,7687],{},[1706,7689,1708],{},[2148,7691,2748],{},[1706,7693,1715],{},[2148,7695,7524],{},[898,7697,2146],{},[1706,7699,2447],{},[2489,7701,7702,7704],{},[898,7703,2146],{},[2148,7705,2495],{},[1706,7707,2505],{"separator":2504},[2358,7709,7710,7720],{},[2361,7711,7712],{},[4745,7713,7714],{"scriptlevel":2150,"displaystyle":2504},[895,7715,7716,7718],{},[898,7717,1735],{},[898,7719,1683],{},[2361,7721,7722],{},[4745,7723,7724],{"scriptlevel":2150,"displaystyle":2504},[895,7725,7726,7728,7730,7738,7740,7742,7744,7746,7748,7750,7756],{},[895,7727],{},[1706,7729,1708],{},[4745,7731,7732],{"scriptlevel":2150,"displaystyle":2139},[2964,7733,7734,7736],{},[2148,7735,2590],{},[898,7737,2146],{},[1706,7739,2447],{},[2148,7741,2748],{},[1706,7743,1715],{},[2148,7745,7524],{},[898,7747,2146],{},[1706,7749,2447],{},[2489,7751,7752,7754],{},[898,7753,2146],{},[2148,7755,2495],{},[1706,7757,2505],{"separator":2504},[2358,7759,7760,7770],{},[2361,7761,7762],{},[4745,7763,7764],{"scriptlevel":2150,"displaystyle":2504},[895,7765,7766,7768],{},[898,7767,1742],{},[898,7769,1683],{},[2361,7771,7772],{},[4745,7773,7774],{"scriptlevel":2150,"displaystyle":2504},[895,7775,7776,7778,7780,7782,7784,7787,7789,7791,7793,7799],{},[895,7777],{},[1706,7779,1708],{},[2148,7781,2748],{},[1706,7783,1715],{},[2148,7785,7786],{},"10",[898,7788,2146],{},[1706,7790,2447],{},[2148,7792,4284],{},[2489,7794,7795,7797],{},[898,7796,2146],{},[2148,7798,2495],{},[898,7800,1837],{"mathvariant":2409},[902,7802,7803],{"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}",[724,7805,7806,7807,7822,7823,7822,7838,7853,7854,7869,7870,1343,7889,7869,7906,1343,7924,7869,7939,7957],{},"Význačné body ",[883,7808,7810],{"className":7809},[886],[888,7811,7812],{"xmlns":890},[892,7813,7814,7819],{},[895,7815,7816],{},[2148,7817,7818],{},"1,67",[902,7820,7821],{"encoding":904},"1{,}67","; ",[883,7824,7826],{"className":7825},[886],[888,7827,7828],{"xmlns":890},[892,7829,7830,7835],{},[895,7831,7832],{},[2148,7833,7834],{},"2,50",[902,7836,7837],{"encoding":904},"2{,}50",[883,7839,7841],{"className":7840},[886],[888,7842,7843],{"xmlns":890},[892,7844,7845,7850],{},[895,7846,7847],{},[2148,7848,7849],{},"4,73",[902,7851,7852],{"encoding":904},"4{,}73"," odpovídají: ",[883,7855,7857],{"className":7856},[886],[888,7858,7859],{"xmlns":890},[892,7860,7861,7867],{},[895,7862,7863,7865],{},[898,7864,1742],{},[898,7866,1683],{},[902,7868,1817],{"encoding":904}," minimum v ",[883,7871,7873],{"className":7872},[886],[888,7874,7875],{"xmlns":890},[892,7876,7877,7886],{},[895,7878,7879,7881,7884],{},[898,7880,2146],{},[1706,7882,7883],{},"≐",[2148,7885,7818],{},[902,7887,7888],{"encoding":904},"Q \\doteq 1{,}67",[883,7890,7892],{"className":7891},[886],[888,7893,7894],{"xmlns":890},[892,7895,7896,7904],{},[895,7897,7898,7900,7902],{},[898,7899,1735],{},[898,7901,1762],{},[898,7903,1683],{},[902,7905,1836],{"encoding":904},[883,7907,7909],{"className":7908},[886],[888,7910,7911],{"xmlns":890},[892,7912,7913,7921],{},[895,7914,7915,7917,7919],{},[898,7916,2146],{},[1706,7918,1708],{},[2148,7920,7834],{},[902,7922,7923],{"encoding":904},"Q = 2{,}50",[883,7925,7927],{"className":7926},[886],[888,7928,7929],{"xmlns":890},[892,7930,7931,7937],{},[895,7932,7933,7935],{},[898,7934,1735],{},[898,7936,1683],{},[902,7938,2094],{"encoding":904},[883,7940,7942],{"className":7941},[886],[888,7943,7944],{"xmlns":890},[892,7945,7946,7954],{},[895,7947,7948,7950,7952],{},[898,7949,2146],{},[1706,7951,7883],{},[2148,7953,7849],{},[902,7955,7956],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,7959,7960],{},[2286,7961],{"alt":7962,"className":7963,"src":7964},"imek-ac-avc-mc",[210,2290],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,7966,7967],{},[614,7968,7969,7970,1993,7985,8002,8003,7822,8023,8038],{},"Obrázek 3.9: Kubické křivky ",[883,7971,7973],{"className":7972},[886],[888,7974,7975],{"xmlns":890},[892,7976,7977,7983],{},[895,7978,7979,7981],{},[898,7980,1659],{},[898,7982,1683],{},[902,7984,1686],{"encoding":904},[883,7986,7988],{"className":7987},[886],[888,7989,7990],{"xmlns":890},[892,7991,7992,8000],{},[895,7993,7994,7996,7998],{},[898,7995,1659],{},[898,7997,1762],{},[898,7999,1683],{},[902,8001,2043],{"encoding":904}," rostoucí od bodu ",[883,8004,8006],{"className":8005},[886],[888,8007,8008],{"xmlns":890},[892,8009,8010,8020],{},[895,8011,8012,8014,8016,8018],{},[898,8013,2020],{},[898,8015,1683],{},[1706,8017,1708],{},[2148,8019,2590],{},[902,8021,8022],{"encoding":904},"FC = 100",[883,8024,8026],{"className":8025},[886],[888,8027,8028],{"xmlns":890},[892,8029,8030,8036],{},[895,8031,8032,8034],{},[898,8033,2020],{},[898,8035,1683],{},[902,8037,2025],{"encoding":904}," je vodorovná přímka.",[724,8040,8041],{},[614,8042,8043,8044,1343,8059,1343,8076,8091,8092,8105,8106,3787,8123,8138,8139,8156,8157,8172,8173,8186,8187,1343,8200,1343,8213,1837],{},"Obrázek 3.10: Křivky ",[883,8045,8047],{"className":8046},[886],[888,8048,8049],{"xmlns":890},[892,8050,8051,8057],{},[895,8052,8053,8055],{},[898,8054,1735],{},[898,8056,1683],{},[902,8058,2094],{"encoding":904},[883,8060,8062],{"className":8061},[886],[888,8063,8064],{"xmlns":890},[892,8065,8066,8074],{},[895,8067,8068,8070,8072],{},[898,8069,1735],{},[898,8071,1762],{},[898,8073,1683],{},[902,8075,1836],{"encoding":904},[883,8077,8079],{"className":8078},[886],[888,8080,8081],{"xmlns":890},[892,8082,8083,8089],{},[895,8084,8085,8087],{},[898,8086,1742],{},[898,8088,1683],{},[902,8090,1817],{"encoding":904}," ve tvaru ",[883,8093,8095],{"className":8094},[886],[888,8096,8097],{"xmlns":890},[892,8098,8099,8103],{},[895,8100,8101],{},[898,8102,900],{},[902,8104,900],{"encoding":904}," a klesající hyperbola ",[883,8107,8109],{"className":8108},[886],[888,8110,8111],{"xmlns":890},[892,8112,8113,8121],{},[895,8114,8115,8117,8119],{},[898,8116,1735],{},[898,8118,2020],{},[898,8120,1683],{},[902,8122,2061],{"encoding":904},[883,8124,8126],{"className":8125},[886],[888,8127,8128],{"xmlns":890},[892,8129,8130,8136],{},[895,8131,8132,8134],{},[898,8133,1742],{},[898,8135,1683],{},[902,8137,1817],{"encoding":904}," protíná ",[883,8140,8142],{"className":8141},[886],[888,8143,8144],{"xmlns":890},[892,8145,8146,8154],{},[895,8147,8148,8150,8152],{},[898,8149,1735],{},[898,8151,1762],{},[898,8153,1683],{},[902,8155,1836],{"encoding":904}," i ",[883,8158,8160],{"className":8159},[886],[888,8161,8162],{"xmlns":890},[892,8163,8164,8170],{},[895,8165,8166,8168],{},[898,8167,1735],{},[898,8169,1683],{},[902,8171,2094],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,8174,8176],{"className":8175},[886],[888,8177,8178],{"xmlns":890},[892,8179,8180,8184],{},[895,8181,8182],{},[898,8183,2146],{},[902,8185,2146],{"encoding":904},": ",[883,8188,8190],{"className":8189},[886],[888,8191,8192],{"xmlns":890},[892,8193,8194,8198],{},[895,8195,8196],{},[2148,8197,7818],{},[902,8199,7821],{"encoding":904},[883,8201,8203],{"className":8202},[886],[888,8204,8205],{"xmlns":890},[892,8206,8207,8211],{},[895,8208,8209],{},[2148,8210,7834],{},[902,8212,7837],{"encoding":904},[883,8214,8216],{"className":8215},[886],[888,8217,8218],{"xmlns":890},[892,8219,8220,8224],{},[895,8221,8222],{},[2148,8223,7849],{},[902,8225,7852],{"encoding":904},[724,8227,8228],{},[38,8229,8230],{},"Standardní vlastnosti:",[120,8232,8233,8268,8332,8400,8450,8470],{},[123,8234,8235,1993,8250,8267],{},[883,8236,8238],{"className":8237},[886],[888,8239,8240],{"xmlns":890},[892,8241,8242,8248],{},[895,8243,8244,8246],{},[898,8245,1659],{},[898,8247,1683],{},[902,8249,1686],{"encoding":904},[883,8251,8253],{"className":8252},[886],[888,8254,8255],{"xmlns":890},[892,8256,8257,8265],{},[895,8258,8259,8261,8263],{},[898,8260,1659],{},[898,8262,1762],{},[898,8264,1683],{},[902,8266,2043],{"encoding":904}," jsou kubické funkce;",[123,8269,8270,1343,8285,1343,8302,8317,8318,8331],{},[883,8271,8273],{"className":8272},[886],[888,8274,8275],{"xmlns":890},[892,8276,8277,8283],{},[895,8278,8279,8281],{},[898,8280,1735],{},[898,8282,1683],{},[902,8284,2094],{"encoding":904},[883,8286,8288],{"className":8287},[886],[888,8289,8290],{"xmlns":890},[892,8291,8292,8300],{},[895,8293,8294,8296,8298],{},[898,8295,1735],{},[898,8297,1762],{},[898,8299,1683],{},[902,8301,1836],{"encoding":904},[883,8303,8305],{"className":8304},[886],[888,8306,8307],{"xmlns":890},[892,8308,8309,8315],{},[895,8310,8311,8313],{},[898,8312,1742],{},[898,8314,1683],{},[902,8316,1817],{"encoding":904}," jsou křivky tvaru ",[883,8319,8321],{"className":8320},[886],[888,8322,8323],{"xmlns":890},[892,8324,8325,8329],{},[895,8326,8327],{},[898,8328,900],{},[902,8330,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,8333,8334,8349,8350,1343,8367,8384,8385,2110],{},[883,8335,8337],{"className":8336},[886],[888,8338,8339],{"xmlns":890},[892,8340,8341,8347],{},[895,8342,8343,8345],{},[898,8344,1742],{},[898,8346,1683],{},[902,8348,1817],{"encoding":904}," nabývá minima před ",[883,8351,8353],{"className":8352},[886],[888,8354,8355],{"xmlns":890},[892,8356,8357,8365],{},[895,8358,8359,8361,8363],{},[898,8360,1735],{},[898,8362,1762],{},[898,8364,1683],{},[902,8366,1836],{"encoding":904},[883,8368,8370],{"className":8369},[886],[888,8371,8372],{"xmlns":890},[892,8373,8374,8382],{},[895,8375,8376,8378,8380],{},[898,8377,1735],{},[898,8379,1762],{},[898,8381,1683],{},[902,8383,1836],{"encoding":904}," před ",[883,8386,8388],{"className":8387},[886],[888,8389,8390],{"xmlns":890},[892,8391,8392,8398],{},[895,8393,8394,8396],{},[898,8395,1735],{},[898,8397,1683],{},[902,8399,2094],{"encoding":904},[123,8401,8402,8138,8417,1993,8432,8449],{},[883,8403,8405],{"className":8404},[886],[888,8406,8407],{"xmlns":890},[892,8408,8409,8415],{},[895,8410,8411,8413],{},[898,8412,1742],{},[898,8414,1683],{},[902,8416,1817],{"encoding":904},[883,8418,8420],{"className":8419},[886],[888,8421,8422],{"xmlns":890},[892,8423,8424,8430],{},[895,8425,8426,8428],{},[898,8427,1735],{},[898,8429,1683],{},[902,8431,2094],{"encoding":904},[883,8433,8435],{"className":8434},[886],[888,8436,8437],{"xmlns":890},[892,8438,8439,8447],{},[895,8440,8441,8443,8445],{},[898,8442,1735],{},[898,8444,1762],{},[898,8446,1683],{},[902,8448,1836],{"encoding":904}," zdola právě v jejich minimech;",[123,8451,8452,8469],{},[883,8453,8455],{"className":8454},[886],[888,8456,8457],{"xmlns":890},[892,8458,8459,8467],{},[895,8460,8461,8463,8465],{},[898,8462,1735],{},[898,8464,2020],{},[898,8466,1683],{},[902,8468,2061],{"encoding":904}," je hyperbola, stále klesající;",[123,8471,8472,8504,8505,1993,8520,8537,8538,8551,8552,1936],{},[883,8473,8475],{"className":8474},[886],[888,8476,8477],{"xmlns":890},[892,8478,8479,8501],{},[895,8480,8481,8483,8485,8487,8489,8491,8493,8495,8497,8499],{},[898,8482,1735],{},[898,8484,1683],{},[1706,8486,1708],{},[898,8488,1735],{},[898,8490,2020],{},[898,8492,1683],{},[1706,8494,2447],{},[898,8496,1735],{},[898,8498,1762],{},[898,8500,1683],{},[902,8502,8503],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,8506,8508],{"className":8507},[886],[888,8509,8510],{"xmlns":890},[892,8511,8512,8518],{},[895,8513,8514,8516],{},[898,8515,1735],{},[898,8517,1683],{},[902,8519,2094],{"encoding":904},[883,8521,8523],{"className":8522},[886],[888,8524,8525],{"xmlns":890},[892,8526,8527,8535],{},[895,8528,8529,8531,8533],{},[898,8530,1735],{},[898,8532,1762],{},[898,8534,1683],{},[902,8536,1836],{"encoding":904}," klesá s rostoucím ",[883,8539,8541],{"className":8540},[886],[888,8542,8543],{"xmlns":890},[892,8544,8545,8549],{},[895,8546,8547],{},[898,8548,2146],{},[902,8550,2146],{"encoding":904}," (protože ",[883,8553,8555],{"className":8554},[886],[888,8556,8557],{"xmlns":890},[892,8558,8559,8571],{},[895,8560,8561,8563,8565,8567,8569],{},[898,8562,1735],{},[898,8564,2020],{},[898,8566,1683],{},[1706,8568,5915],{},[2148,8570,2150],{},[902,8572,8573],{"encoding":904},"AFC \\to 0",[115,8575,8577],{"id":8576},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,8579,8580,8581,8584,8585,8600],{},"Častou optimalizační úlohou je ",[38,8582,8583],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,8586,8588],{"className":8587},[886],[888,8589,8590],{"xmlns":890},[892,8591,8592,8598],{},[895,8593,8594,8596],{},[898,8595,1735],{},[898,8597,1683],{},[902,8599,2094],{"encoding":904}," minimální.",[198,8602,8604],{"id":8603},"princip","Princip",[724,8606,8607,8608,8626],{},"Mají-li průměrné náklady minimum v bodě ",[883,8609,8611],{"className":8610},[886],[888,8612,8613],{"xmlns":890},[892,8614,8615,8623],{},[895,8616,8617],{},[2142,8618,8619,8621],{},[898,8620,2146],{},[2148,8622,2150],{},[902,8624,8625],{"encoding":904},"Q_0",", pak platí",[883,8628,8630],{"className":8629},[886],[888,8631,8632],{"xmlns":890,"display":2350},[892,8633,8634,8683],{},[2354,8635,8636],{"width":2356},[2358,8637,8638,8640,8676,8678],{},[2361,8639],{"width":2363},[2361,8641,8642],{},[895,8643,8644,8646,8648,8650,8656,8658,8660,8662,8664,8666,8672,8674],{},[898,8645,1735],{},[898,8647,1683],{},[1706,8649,2140],{"stretchy":2139},[2142,8651,8652,8654],{},[898,8653,2146],{},[2148,8655,2150],{},[1706,8657,2153],{"stretchy":2139},[1706,8659,1708],{},[898,8661,1742],{},[898,8663,1683],{},[1706,8665,2140],{"stretchy":2139},[2142,8667,8668,8670],{},[898,8669,2146],{},[2148,8671,2150],{},[1706,8673,2153],{"stretchy":2139},[898,8675,1837],{"mathvariant":2409},[2361,8677],{"width":2363},[2361,8679,8680],{},[2415,8681,8682],{},"(3.10)",[902,8684,8685],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[1636,8687,8688],{},[724,8689,8690,8692,8693],{},[883,8691,3021],{}," Princip\n",[38,8694,8695],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,8697,8698,8701,8702,8744],{},[38,8699,8700],{},"Odvození."," Z ",[883,8703,8705],{"className":8704},[886],[888,8706,8707],{"xmlns":890},[892,8708,8709,8741],{},[895,8710,8711,8713,8715,8717,8719,8721,8723],{},[898,8712,1735],{},[898,8714,1683],{},[1706,8716,2140],{"stretchy":2139},[898,8718,2146],{},[1706,8720,2153],{"stretchy":2139},[1706,8722,1708],{},[4745,8724,8725],{"scriptlevel":2150,"displaystyle":2139},[2964,8726,8727,8739],{},[895,8728,8729,8731,8733,8735,8737],{},[898,8730,1659],{},[898,8732,1683],{},[1706,8734,2140],{"stretchy":2139},[898,8736,2146],{},[1706,8738,2153],{"stretchy":2139},[898,8740,2146],{},[902,8742,8743],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,8746,8748],{"className":8747},[886],[888,8749,8750],{"xmlns":890,"display":2350},[892,8751,8752,8884],{},[895,8753,8754,8756,8762,8764,8766,8768,8770,8810,8812,8852,8854,8882],{},[898,8755,1735],{},[2489,8757,8758,8760],{},[898,8759,1683],{},[1706,8761,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,8763,2140],{"stretchy":2139},[898,8765,2146],{},[1706,8767,2153],{"stretchy":2139},[1706,8769,1708],{},[2964,8771,8772,8804],{},[895,8773,8774,8776,8782,8784,8786,8788,8790,8792,8794,8796,8798,8800,8802],{},[898,8775,1659],{},[2489,8777,8778,8780],{},[898,8779,1683],{},[1706,8781,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,8783,2140],{"stretchy":2139},[898,8785,2146],{},[1706,8787,2153],{"stretchy":2139},[1706,8789,2390],{},[898,8791,2146],{},[1706,8793,1715],{},[898,8795,1659],{},[898,8797,1683],{},[1706,8799,2140],{"stretchy":2139},[898,8801,2146],{},[1706,8803,2153],{"stretchy":2139},[2489,8805,8806,8808],{},[898,8807,2146],{},[2148,8809,2495],{},[1706,8811,1708],{},[2964,8813,8814,8846],{},[895,8815,8816,8818,8820,8822,8824,8826,8828,8830,8832,8834,8836,8838,8840,8842,8844],{},[898,8817,1742],{},[898,8819,1683],{},[1706,8821,2140],{"stretchy":2139},[898,8823,2146],{},[1706,8825,2153],{"stretchy":2139},[1706,8827,2390],{},[898,8829,2146],{},[1706,8831,1715],{},[898,8833,1735],{},[898,8835,1683],{},[1706,8837,2140],{"stretchy":2139},[898,8839,2146],{},[1706,8841,2153],{"stretchy":2139},[1706,8843,2390],{},[898,8845,2146],{},[2489,8847,8848,8850],{},[898,8849,2146],{},[2148,8851,2495],{},[1706,8853,1708],{},[2964,8855,8856,8880],{},[895,8857,8858,8860,8862,8864,8866,8868,8870,8872,8874,8876,8878],{},[898,8859,1742],{},[898,8861,1683],{},[1706,8863,2140],{"stretchy":2139},[898,8865,2146],{},[1706,8867,2153],{"stretchy":2139},[1706,8869,1715],{},[898,8871,1735],{},[898,8873,1683],{},[1706,8875,2140],{"stretchy":2139},[898,8877,2146],{},[1706,8879,2153],{"stretchy":2139},[898,8881,2146],{},[898,8883,1837],{"mathvariant":2409},[902,8885,8886],{"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}.",[724,8888,8889,8890,2891,8905,3484,8928,3409],{},"Nutnou podmínkou minima ",[883,8891,8893],{"className":8892},[886],[888,8894,8895],{"xmlns":890},[892,8896,8897,8903],{},[895,8898,8899,8901],{},[898,8900,1735],{},[898,8902,1683],{},[902,8904,2094],{"encoding":904},[883,8906,8908],{"className":8907},[886],[888,8909,8910],{"xmlns":890},[892,8911,8912,8925],{},[895,8913,8914,8920,8923],{},[2142,8915,8916,8918],{},[898,8917,2146],{},[2148,8919,2150],{},[1706,8921,8922],{},">",[2148,8924,2150],{},[902,8926,8927],{"encoding":904},"Q_0 > 0",[883,8929,8931],{"className":8930},[886],[888,8932,8933],{"xmlns":890},[892,8934,8935,8959],{},[895,8936,8937,8939,8945,8947,8953,8955,8957],{},[898,8938,1735],{},[2489,8940,8941,8943],{},[898,8942,1683],{},[1706,8944,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,8946,2140],{"stretchy":2139},[2142,8948,8949,8951],{},[898,8950,2146],{},[2148,8952,2150],{},[1706,8954,2153],{"stretchy":2139},[1706,8956,1708],{},[2148,8958,2150],{},[902,8960,8961],{"encoding":904},"AC'(Q_0) = 0",[883,8963,8965],{"className":8964},[886],[888,8966,8967],{"xmlns":890,"display":2350},[892,8968,8969,9054],{},[895,8970,8971,9011,9013,9015,9017,9020,9022,9024,9026,9028,9034,9036,9038,9040,9042,9044,9050,9052],{},[2964,8972,8973,9005],{},[895,8974,8975,8977,8979,8981,8987,8989,8991,8993,8995,8997,9003],{},[898,8976,1742],{},[898,8978,1683],{},[1706,8980,2140],{"stretchy":2139},[2142,8982,8983,8985],{},[898,8984,2146],{},[2148,8986,2150],{},[1706,8988,2153],{"stretchy":2139},[1706,8990,1715],{},[898,8992,1735],{},[898,8994,1683],{},[1706,8996,2140],{"stretchy":2139},[2142,8998,8999,9001],{},[898,9000,2146],{},[2148,9002,2150],{},[1706,9004,2153],{"stretchy":2139},[2142,9006,9007,9009],{},[898,9008,2146],{},[2148,9010,2150],{},[1706,9012,1708],{},[2148,9014,2150],{},[4898,9016],{"width":4900},[1706,9018,9019],{},"⟺",[4898,9021],{"width":4900},[898,9023,1742],{},[898,9025,1683],{},[1706,9027,2140],{"stretchy":2139},[2142,9029,9030,9032],{},[898,9031,2146],{},[2148,9033,2150],{},[1706,9035,2153],{"stretchy":2139},[1706,9037,1708],{},[898,9039,1735],{},[898,9041,1683],{},[1706,9043,2140],{"stretchy":2139},[2142,9045,9046,9048],{},[898,9047,2146],{},[2148,9049,2150],{},[1706,9051,2153],{"stretchy":2139},[898,9053,1837],{"mathvariant":2409},[902,9055,9056],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,9058,9059,1647,9062,8138,9077,9092,9093,9108,9109,3484,9126,9148,9149,9171],{},[38,9060,9061],{},"Geometrická interpretace.",[883,9063,9065],{"className":9064},[886],[888,9066,9067],{"xmlns":890},[892,9068,9069,9075],{},[895,9070,9071,9073],{},[898,9072,1742],{},[898,9074,1683],{},[902,9076,1817],{"encoding":904},[883,9078,9080],{"className":9079},[886],[888,9081,9082],{"xmlns":890},[892,9083,9084,9090],{},[895,9085,9086,9088],{},[898,9087,1735],{},[898,9089,1683],{},[902,9091,2094],{"encoding":904}," právě v bodě minima ",[883,9094,9096],{"className":9095},[886],[888,9097,9098],{"xmlns":890},[892,9099,9100,9106],{},[895,9101,9102,9104],{},[898,9103,1735],{},[898,9105,1683],{},[902,9107,2094],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,9110,9112],{"className":9111},[886],[888,9113,9114],{"xmlns":890},[892,9115,9116,9124],{},[895,9117,9118],{},[2142,9119,9120,9122],{},[898,9121,2146],{},[2148,9123,2150],{},[902,9125,8625],{"encoding":904},[883,9127,9129],{"className":9128},[886],[888,9130,9131],{"xmlns":890},[892,9132,9133,9145],{},[895,9134,9135,9137,9139,9141,9143],{},[898,9136,1742],{},[898,9138,1683],{},[1706,9140,2539],{},[898,9142,1735],{},[898,9144,1683],{},[902,9146,9147],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,9150,9152],{"className":9151},[886],[888,9153,9154],{"xmlns":890},[892,9155,9156,9168],{},[895,9157,9158,9160,9162,9164,9166],{},[898,9159,1742],{},[898,9161,1683],{},[1706,9163,8922],{},[898,9165,1735],{},[898,9167,1683],{},[902,9169,9170],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,9173,9174,9175,9217,9218,9235,9236,1837],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,9176,9178],{"className":9177},[886],[888,9179,9180],{"xmlns":890},[892,9181,9182,9214],{},[895,9183,9184,9186,9188,9190,9196,9198,9200,9202,9204,9206,9212],{},[898,9185,1735],{},[898,9187,1683],{},[1706,9189,2140],{"stretchy":2139},[2142,9191,9192,9194],{},[898,9193,2146],{},[2148,9195,2150],{},[1706,9197,2153],{"stretchy":2139},[1706,9199,1708],{},[898,9201,1742],{},[898,9203,1683],{},[1706,9205,2140],{"stretchy":2139},[2142,9207,9208,9210],{},[898,9209,2146],{},[2148,9211,2150],{},[1706,9213,2153],{"stretchy":2139},[902,9215,9216],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,9219,9221],{"className":9220},[886],[888,9222,9223],{"xmlns":890},[892,9224,9225,9233],{},[895,9226,9227],{},[2142,9228,9229,9231],{},[898,9230,2146],{},[2148,9232,2150],{},[902,9234,8625],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,9237,9239],{"className":9238},[886],[888,9240,9241],{"xmlns":890},[892,9242,9243,9267],{},[895,9244,9245,9247,9249,9251,9253,9255,9257,9259,9261,9263,9265],{},[898,9246,1735],{},[898,9248,1683],{},[1706,9250,2140],{"stretchy":2139},[898,9252,2146],{},[1706,9254,2153],{"stretchy":2139},[1706,9256,1708],{},[898,9258,1742],{},[898,9260,1683],{},[1706,9262,2140],{"stretchy":2139},[898,9264,2146],{},[1706,9266,2153],{"stretchy":2139},[902,9268,9269],{"encoding":904},"AC(Q) = MC(Q)",[1636,9271,9272],{},[724,9273,9274,9277,9278,4521,9296,9317,9318,4521,9321,9342,9343,9358,9359,4653,9374,1936],{},[883,9275,9276],{},"!warning"," Pozor — neplést s principem maxima zisku\nPro ",[38,9279,9280,9281],{},"minimum ",[883,9282,9284],{"className":9283},[886],[888,9285,9286],{"xmlns":890},[892,9287,9288,9294],{},[895,9289,9290,9292],{},[898,9291,1735],{},[898,9293,1683],{},[902,9295,2094],{"encoding":904},[883,9297,9299],{"className":9298},[886],[888,9300,9301],{"xmlns":890},[892,9302,9303,9315],{},[895,9304,9305,9307,9309,9311,9313],{},[898,9306,1735],{},[898,9308,1683],{},[1706,9310,1708],{},[898,9312,1742],{},[898,9314,1683],{},[902,9316,1747],{"encoding":904},", pro ",[38,9319,9320],{},"maximum zisku",[883,9322,9324],{"className":9323},[886],[888,9325,9326],{"xmlns":890},[892,9327,9328,9340],{},[895,9329,9330,9332,9334,9336,9338],{},[898,9331,1742],{},[898,9333,1662],{},[1706,9335,1708],{},[898,9337,1742],{},[898,9339,1683],{},[902,9341,1796],{"encoding":904},". Obě podmínky využívají ",[883,9344,9346],{"className":9345},[886],[888,9347,9348],{"xmlns":890},[892,9349,9350,9356],{},[895,9351,9352,9354],{},[898,9353,1742],{},[898,9355,1683],{},[902,9357,1817],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,9360,9362],{"className":9361},[886],[888,9363,9364],{"xmlns":890},[892,9365,9366,9372],{},[895,9367,9368,9370],{},[898,9369,1735],{},[898,9371,1683],{},[902,9373,2094],{"encoding":904},[883,9375,9377],{"className":9376},[886],[888,9378,9379],{"xmlns":890},[892,9380,9381,9387],{},[895,9382,9383,9385],{},[898,9384,1742],{},[898,9386,1662],{},[902,9388,1905],{"encoding":904},[2547,9390,9392],{"id":9391},"příklad-37","Příklad 3.7",[724,9394,9395,4127,9397,9431,9432,9445,9446,9461],{},[38,9396,2555],{},[883,9398,9400],{"className":9399},[886],[888,9401,9402],{"xmlns":890},[892,9403,9404,9428],{},[895,9405,9406,9408,9410,9412,9418,9420,9422,9424,9426],{},[898,9407,1659],{},[898,9409,1683],{},[1706,9411,1708],{},[2489,9413,9414,9416],{},[898,9415,2146],{},[2148,9417,2495],{},[1706,9419,2447],{},[2148,9421,4284],{},[898,9423,2146],{},[1706,9425,2447],{},[2148,9427,3757],{},[902,9429,9430],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,9433,9435],{"className":9434},[886],[888,9436,9437],{"xmlns":890},[892,9438,9439,9443],{},[895,9440,9441],{},[898,9442,2146],{},[902,9444,2146],{"encoding":904}," minimalizující ",[883,9447,9449],{"className":9448},[886],[888,9450,9451],{"xmlns":890},[892,9452,9453,9459],{},[895,9454,9455,9457],{},[898,9456,1735],{},[898,9458,1683],{},[902,9460,2094],{"encoding":904}," a ověřte princip (3.10).",[724,9463,9464,9466],{},[38,9465,2615],{}," Přímý výpočet:",[883,9468,9470],{"className":9469},[886],[888,9471,9472],{"xmlns":890,"display":2350},[892,9473,9474,9577],{},[895,9475,9476,9478,9480,9482,9504,9506,9508,9510,9512,9514,9520,9522,9525,9527,9529,9531,9537,9539,9541,9543,9553,9555,9575],{},[898,9477,1735],{},[898,9479,1683],{},[1706,9481,1708],{},[2964,9483,9484,9502],{},[895,9485,9486,9492,9494,9496,9498,9500],{},[2489,9487,9488,9490],{},[898,9489,2146],{},[2148,9491,2495],{},[1706,9493,2447],{},[2148,9495,4284],{},[898,9497,2146],{},[1706,9499,2447],{},[2148,9501,3757],{},[898,9503,2146],{},[1706,9505,1708],{},[898,9507,2146],{},[1706,9509,2447],{},[2148,9511,4284],{},[1706,9513,2447],{},[2964,9515,9516,9518],{},[2148,9517,3757],{},[898,9519,2146],{},[1706,9521,2505],{"separator":2504},[4898,9523],{"width":9524},"2em",[1706,9526,2140],{"stretchy":2139},[898,9528,1735],{},[898,9530,1683],{},[2489,9532,9533,9535],{},[1706,9534,2153],{"stretchy":2139},[1706,9536,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,9538,1708],{},[2148,9540,2701],{},[1706,9542,1715],{},[2964,9544,9545,9547],{},[2148,9546,3757],{},[2489,9548,9549,9551],{},[898,9550,2146],{},[2148,9552,2495],{},[1706,9554,1708],{},[2964,9556,9557,9569],{},[895,9558,9559,9565,9567],{},[2489,9560,9561,9563],{},[898,9562,2146],{},[2148,9564,2495],{},[1706,9566,1715],{},[2148,9568,3757],{},[2489,9570,9571,9573],{},[898,9572,2146],{},[2148,9574,2495],{},[898,9576,1837],{"mathvariant":2409},[902,9578,9579],{"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}.",[724,9581,9582,9623,9624,9648,9649,9699,9700,1837],{},[883,9583,9585],{"className":9584},[886],[888,9586,9587],{"xmlns":890},[892,9588,9589,9620],{},[895,9590,9591,9593,9595,9597,9603,9605,9607,9610,9616,9618],{},[1706,9592,2140],{"stretchy":2139},[898,9594,1735],{},[898,9596,1683],{},[2489,9598,9599,9601],{},[1706,9600,2153],{"stretchy":2139},[1706,9602,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,9604,1708],{},[2148,9606,2150],{},[1706,9608,9609],{},"⇒",[2142,9611,9612,9614],{},[898,9613,2146],{},[2148,9615,2701],{},[1706,9617,1708],{},[2148,9619,7044],{},[902,9621,9622],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,9625,9627],{"className":9626},[886],[888,9628,9629],{"xmlns":890},[892,9630,9631,9645],{},[895,9632,9633,9639,9641,9643],{},[2142,9634,9635,9637],{},[898,9636,2146],{},[2148,9638,2495],{},[1706,9640,1708],{},[1706,9642,1715],{},[2148,9644,7044],{},[902,9646,9647],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,9650,9652],{"className":9651},[886],[888,9653,9654],{"xmlns":890},[892,9655,9656,9696],{},[895,9657,9658,9660,9662,9664,9674,9676,9678,9680,9682,9690,9692,9694],{},[1706,9659,2140],{"stretchy":2139},[898,9661,1735],{},[898,9663,1683],{},[2489,9665,9666,9668],{},[1706,9667,2153],{"stretchy":2139},[895,9669,9670,9672],{},[1706,9671,3142],{"mathvariant":2409},[1706,9673,3142],{"mathvariant":2409},[1706,9675,2140],{"stretchy":2139},[2148,9677,7044],{},[1706,9679,2153],{"stretchy":2139},[1706,9681,1708],{},[4745,9683,9684],{"scriptlevel":2150,"displaystyle":2139},[2964,9685,9686,9688],{},[2148,9687,2701],{},[2148,9689,4284],{},[1706,9691,8922],{},[2148,9693,2150],{},[1706,9695,9609],{},[902,9697,9698],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,9701,9703],{"className":9702},[886],[888,9704,9705],{"xmlns":890},[892,9706,9707,9723],{},[895,9708,9709,9711,9713,9715,9717,9719,9721],{},[898,9710,1735],{},[898,9712,1683],{},[1706,9714,2140],{"stretchy":2139},[2148,9716,7044],{},[1706,9718,2153],{"stretchy":2139},[1706,9720,1708],{},[2148,9722,3359],{},[902,9724,9725],{"encoding":904},"AC(6) = 15",[724,9727,9728,9729,9755,9756,4288],{},"Pomocí principu: ",[883,9730,9732],{"className":9731},[886],[888,9733,9734],{"xmlns":890},[892,9735,9736,9752],{},[895,9737,9738,9740,9742,9744,9746,9748,9750],{},[898,9739,1742],{},[898,9741,1683],{},[1706,9743,1708],{},[2148,9745,2495],{},[898,9747,2146],{},[1706,9749,2447],{},[2148,9751,4284],{},[902,9753,9754],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,9757,9759],{"className":9758},[886],[888,9760,9761],{"xmlns":890},[892,9762,9763,9775],{},[895,9764,9765,9767,9769,9771,9773],{},[898,9766,1735],{},[898,9768,1683],{},[1706,9770,1708],{},[898,9772,1742],{},[898,9774,1683],{},[902,9776,1747],{"encoding":904},[883,9778,9780],{"className":9779},[886],[888,9781,9782],{"xmlns":890,"display":2350},[892,9783,9784,9886],{},[895,9785,9786,9808,9810,9812,9814,9816,9818,9820,9822,9824,9830,9832,9834,9836,9838,9840,9842,9844,9850,9852,9854,9856,9858,9860,9862,9868,9870,9872,9874,9876,9878,9880,9882,9884],{},[2964,9787,9788,9806],{},[895,9789,9790,9796,9798,9800,9802,9804],{},[2489,9791,9792,9794],{},[898,9793,2146],{},[2148,9795,2495],{},[1706,9797,2447],{},[2148,9799,4284],{},[898,9801,2146],{},[1706,9803,2447],{},[2148,9805,3757],{},[898,9807,2146],{},[1706,9809,1708],{},[2148,9811,2495],{},[898,9813,2146],{},[1706,9815,2447],{},[2148,9817,4284],{},[2415,9819,3852],{},[1706,9821,9609],{},[2415,9823,3852],{},[2489,9825,9826,9828],{},[898,9827,2146],{},[2148,9829,2495],{},[1706,9831,2447],{},[2148,9833,4284],{},[898,9835,2146],{},[1706,9837,2447],{},[2148,9839,3757],{},[1706,9841,1708],{},[2148,9843,2495],{},[2489,9845,9846,9848],{},[898,9847,2146],{},[2148,9849,2495],{},[1706,9851,2447],{},[2148,9853,4284],{},[898,9855,2146],{},[2415,9857,3852],{},[1706,9859,9609],{},[2415,9861,3852],{},[2489,9863,9864,9866],{},[898,9865,2146],{},[2148,9867,2495],{},[1706,9869,1708],{},[2148,9871,3757],{},[2415,9873,3852],{},[1706,9875,9609],{},[2415,9877,3852],{},[898,9879,2146],{},[1706,9881,1708],{},[2148,9883,7044],{},[1706,9885,2505],{"separator":2504},[902,9887,9888],{"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,",[724,9890,9891,9892,9930],{},"a ",[883,9893,9895],{"className":9894},[886],[888,9896,9897],{"xmlns":890},[892,9898,9899,9927],{},[895,9900,9901,9903,9905,9907,9909,9911,9913,9915,9917,9919,9921,9923,9925],{},[898,9902,1735],{},[898,9904,1683],{},[1706,9906,2140],{"stretchy":2139},[2148,9908,7044],{},[1706,9910,2153],{"stretchy":2139},[1706,9912,1708],{},[898,9914,1742],{},[898,9916,1683],{},[1706,9918,2140],{"stretchy":2139},[2148,9920,7044],{},[1706,9922,2153],{"stretchy":2139},[1706,9924,1708],{},[2148,9926,3359],{},[902,9928,9929],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,9932,9934],{"id":9933},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,9936,9937,9938,4288],{},"Analogicky pro ",[883,9939,9941],{"className":9940},[886],[888,9942,9943],{"xmlns":890},[892,9944,9945,9953],{},[895,9946,9947,9949,9951],{},[898,9948,1735],{},[898,9950,1762],{},[898,9952,1683],{},[902,9954,1836],{"encoding":904},[883,9956,9958],{"className":9957},[886],[888,9959,9960],{"xmlns":890,"display":2350},[892,9961,9962,10013],{},[2354,9963,9964],{"width":2356},[2358,9965,9966,9968,10006,10008],{},[2361,9967],{"width":2363},[2361,9969,9970],{},[895,9971,9972,9974,9976,9978,9980,9986,9988,9990,9992,9994,9996,10002,10004],{},[898,9973,1735],{},[898,9975,1762],{},[898,9977,1683],{},[1706,9979,2140],{"stretchy":2139},[2142,9981,9982,9984],{},[898,9983,2146],{},[2148,9985,2150],{},[1706,9987,2153],{"stretchy":2139},[1706,9989,1708],{},[898,9991,1742],{},[898,9993,1683],{},[1706,9995,2140],{"stretchy":2139},[2142,9997,9998,10000],{},[898,9999,2146],{},[2148,10001,2150],{},[1706,10003,2153],{"stretchy":2139},[898,10005,1837],{"mathvariant":2409},[2361,10007],{"width":2363},[2361,10009,10010],{},[2415,10011,10012],{},"(3.11)",[902,10014,10015],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[1636,10017,10018],{},[724,10019,10020,8692,10022],{},[883,10021,3021],{},[38,10023,10024,10025,10042],{},"V bodě minima průměrných variabilních nákladů se ",[883,10026,10028],{"className":10027},[886],[888,10029,10030],{"xmlns":890},[892,10031,10032,10040],{},[895,10033,10034,10036,10038],{},[898,10035,1735],{},[898,10037,1762],{},[898,10039,1683],{},[902,10041,1836],{"encoding":904}," rovnají mezním nákladům.",[724,10044,10045,10046,10069,10070,1837],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,10047,10049],{"className":10048},[886],[888,10050,10051],{"xmlns":890},[892,10052,10053,10066],{},[895,10054,10055,10061,10063],{},[2142,10056,10057,10059],{},[898,10058,2146],{},[2148,10060,2150],{},[1706,10062,1708],{},[2148,10064,10065],{},"2,5",[902,10067,10068],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,10071,10073],{"className":10072},[886],[888,10074,10075],{"xmlns":890},[892,10076,10077,10103],{},[895,10078,10079,10081,10083,10085,10087,10089,10091,10093,10095,10097,10099,10101],{},[898,10080,1735],{},[898,10082,1762],{},[898,10084,1683],{},[1706,10086,2140],{"stretchy":2139},[898,10088,2146],{},[1706,10090,2153],{"stretchy":2139},[1706,10092,1708],{},[898,10094,1742],{},[898,10096,1683],{},[1706,10098,2140],{"stretchy":2139},[898,10100,2146],{},[1706,10102,2153],{"stretchy":2139},[902,10104,10105],{"encoding":904},"AVC(Q) = MC(Q)",[115,10107,10109],{"id":10108},"zisk-a-body-zvratu","Zisk a body zvratu",[724,10111,10112,1647,10115,10131],{},[38,10113,10114],{},"Zisk",[883,10116,10118],{"className":10117},[886],[888,10119,10120],{"xmlns":890},[892,10121,10122,10128],{},[895,10123,10124,10126],{},[898,10125,1702],{},[898,10127,1662],{},[902,10129,10130],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,10133,10135],{"className":10134},[886],[888,10136,10137],{"xmlns":890,"display":2350},[892,10138,10139,10198],{},[2354,10140,10141],{"width":2356},[2358,10142,10143,10145,10191,10193],{},[2361,10144],{"width":2363},[2361,10146,10147],{},[895,10148,10149,10151,10153,10155,10157,10159,10161,10163,10165,10167,10169,10171,10173,10175,10177,10179,10181,10183,10185,10187,10189],{},[898,10150,1702],{},[898,10152,1662],{},[1706,10154,1708],{},[898,10156,1702],{},[898,10158,1662],{},[1706,10160,2140],{"stretchy":2139},[898,10162,2146],{},[1706,10164,2153],{"stretchy":2139},[1706,10166,1708],{},[898,10168,1659],{},[898,10170,1662],{},[1706,10172,2140],{"stretchy":2139},[898,10174,2146],{},[1706,10176,2153],{"stretchy":2139},[1706,10178,1715],{},[898,10180,1659],{},[898,10182,1683],{},[1706,10184,2140],{"stretchy":2139},[898,10186,2146],{},[1706,10188,2153],{"stretchy":2139},[898,10190,1837],{"mathvariant":2409},[2361,10192],{"width":2363},[2361,10194,10195],{},[2415,10196,10197],{},"(3.12)",[902,10199,10200],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,10202,10203,10204,1993,10219,10234,10235,10237,10238,10241,10242,10258,10259,10274,10275,10290,10291,1343,10304,10318,10319,1343,10337,10355,10356,2314,10359,10362,10363,1348,10385,3484,10407,10429,10430,3484,10460,10482],{},"Body rovnosti ",[883,10205,10207],{"className":10206},[886],[888,10208,10209],{"xmlns":890},[892,10210,10211,10217],{},[895,10212,10213,10215],{},[898,10214,1659],{},[898,10216,1662],{},[902,10218,1665],{"encoding":904},[883,10220,10222],{"className":10221},[886],[888,10223,10224],{"xmlns":890},[892,10225,10226,10232],{},[895,10227,10228,10230],{},[898,10229,1659],{},[898,10231,1683],{},[902,10233,1686],{"encoding":904}," se nazývají ",[38,10236,2270],{}," (též vyrovnání, ",[614,10239,10240],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,10243,10245],{"className":10244},[886],[888,10246,10247],{"xmlns":890},[892,10248,10249,10255],{},[895,10250,10251,10253],{},[898,10252,1762],{},[898,10254,1683],{},[902,10256,10257],{"encoding":904},"VC",") je ",[883,10260,10262],{"className":10261},[886],[888,10263,10264],{"xmlns":890},[892,10265,10266,10272],{},[895,10267,10268,10270],{},[898,10269,1659],{},[898,10271,1662],{},[902,10273,1665],{"encoding":904}," kvadratická a ",[883,10276,10278],{"className":10277},[886],[888,10279,10280],{"xmlns":890},[892,10281,10282,10288],{},[895,10283,10284,10286],{},[898,10285,1659],{},[898,10287,1683],{},[902,10289,1686],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,10292,10294],{"className":10293},[886],[888,10295,10296],{"xmlns":890},[892,10297,10298,10302],{},[895,10299,10300],{},[898,10301,1735],{},[902,10303,1735],{"encoding":904},[883,10305,10307],{"className":10306},[886],[888,10308,10309],{"xmlns":890},[892,10310,10311,10316],{},[895,10312,10313],{},[898,10314,10315],{},"B",[902,10317,10315],{"encoding":904}," odpovídajících množstvím ",[883,10320,10322],{"className":10321},[886],[888,10323,10324],{"xmlns":890},[892,10325,10326,10334],{},[895,10327,10328],{},[2142,10329,10330,10332],{},[898,10331,2146],{},[898,10333,1735],{},[902,10335,10336],{"encoding":904},"Q_A",[883,10338,10340],{"className":10339},[886],[888,10341,10342],{"xmlns":890},[892,10343,10344,10352],{},[895,10345,10346],{},[2142,10347,10348,10350],{},[898,10349,2146],{},[898,10351,10315],{},[902,10353,10354],{"encoding":904},"Q_B"," — firma je na ",[38,10357,10358],{},"prahu rentability",[614,10360,10361],{},"break even","). Pro ",[883,10364,10366],{"className":10365},[886],[888,10367,10368],{"xmlns":890},[892,10369,10370,10382],{},[895,10371,10372,10374,10376],{},[898,10373,2146],{},[1706,10375,2539],{},[2142,10377,10378,10380],{},[898,10379,2146],{},[898,10381,1735],{},[902,10383,10384],{"encoding":904},"Q \u003C Q_A",[883,10386,10388],{"className":10387},[886],[888,10389,10390],{"xmlns":890},[892,10391,10392,10404],{},[895,10393,10394,10396,10398],{},[898,10395,2146],{},[1706,10397,8922],{},[2142,10399,10400,10402],{},[898,10401,2146],{},[898,10403,10315],{},[902,10405,10406],{"encoding":904},"Q > Q_B",[883,10408,10410],{"className":10409},[886],[888,10411,10412],{"xmlns":890},[892,10413,10414,10426],{},[895,10415,10416,10418,10420,10422,10424],{},[898,10417,1659],{},[898,10419,1683],{},[1706,10421,8922],{},[898,10423,1659],{},[898,10425,1662],{},[902,10427,10428],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,10431,10433],{"className":10432},[886],[888,10434,10435],{"xmlns":890},[892,10436,10437,10457],{},[895,10438,10439,10445,10447,10449,10451],{},[2142,10440,10441,10443],{},[898,10442,2146],{},[898,10444,1735],{},[1706,10446,2539],{},[898,10448,2146],{},[1706,10450,2539],{},[2142,10452,10453,10455],{},[898,10454,2146],{},[898,10456,10315],{},[902,10458,10459],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,10461,10463],{"className":10462},[886],[888,10464,10465],{"xmlns":890},[892,10466,10467,10479],{},[895,10468,10469,10471,10473,10475,10477],{},[898,10470,1659],{},[898,10472,1662],{},[1706,10474,8922],{},[898,10476,1659],{},[898,10478,1683],{},[902,10480,10481],{"encoding":904},"TR > TC"," (zisk).",[1636,10484,10485],{},[724,10486,10487,10489],{},[883,10488,3174],{}," 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.",[724,10491,10492,10493,10519],{},"Body zvratu jsou řešení rovnice ",[883,10494,10496],{"className":10495},[886],[888,10497,10498],{"xmlns":890},[892,10499,10500,10516],{},[895,10501,10502,10504,10506,10508,10510,10512,10514],{},[898,10503,1702],{},[898,10505,1662],{},[1706,10507,2140],{"stretchy":2139},[898,10509,2146],{},[1706,10511,2153],{"stretchy":2139},[1706,10513,1708],{},[2148,10515,2150],{},[902,10517,10518],{"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.",[724,10521,10522],{},[2286,10523],{"alt":10524,"className":10525,"src":10526},"imek-tr-tc-body-zvratu",[210,2290],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,10528,10529],{},[614,10530,10531,10532,10547,10548,10563,10564,1993,10577,10590,10591,10604,10605,1993,10622,10639,10640,10660,10661,1993,10676,10691,10692,10721],{},"Obrázek 3.11: Body zvratu — křivky ",[883,10533,10535],{"className":10534},[886],[888,10536,10537],{"xmlns":890},[892,10538,10539,10545],{},[895,10540,10541,10543],{},[898,10542,1659],{},[898,10544,1662],{},[902,10546,1665],{"encoding":904}," (obrácená parabola) a ",[883,10549,10551],{"className":10550},[886],[888,10552,10553],{"xmlns":890},[892,10554,10555,10561],{},[895,10556,10557,10559],{},[898,10558,1659],{},[898,10560,1683],{},[902,10562,1686],{"encoding":904}," (přímka) se protínají v bodech ",[883,10565,10567],{"className":10566},[886],[888,10568,10569],{"xmlns":890},[892,10570,10571,10575],{},[895,10572,10573],{},[898,10574,1735],{},[902,10576,1735],{"encoding":904},[883,10578,10580],{"className":10579},[886],[888,10581,10582],{"xmlns":890},[892,10583,10584,10588],{},[895,10585,10586],{},[898,10587,10315],{},[902,10589,10315],{"encoding":904}," na ose ",[883,10592,10594],{"className":10593},[886],[888,10595,10596],{"xmlns":890},[892,10597,10598,10602],{},[895,10599,10600],{},[898,10601,2146],{},[902,10603,2146],{"encoding":904}," v hodnotách ",[883,10606,10608],{"className":10607},[886],[888,10609,10610],{"xmlns":890},[892,10611,10612,10620],{},[895,10613,10614],{},[2142,10615,10616,10618],{},[898,10617,2146],{},[898,10619,1735],{},[902,10621,10336],{"encoding":904},[883,10623,10625],{"className":10624},[886],[888,10626,10627],{"xmlns":890},[892,10628,10629,10637],{},[895,10630,10631],{},[2142,10632,10633,10635],{},[898,10634,2146],{},[898,10636,10315],{},[902,10638,10354],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,10641,10643],{"className":10642},[886],[888,10644,10645],{"xmlns":890},[892,10646,10647,10657],{},[895,10648,10649],{},[2142,10650,10651,10653,10655],{},[898,10652,2146],{},[898,10654,2770],{},[1706,10656,2773],{},[902,10658,10659],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,10662,10664],{"className":10663},[886],[888,10665,10666],{"xmlns":890},[892,10667,10668,10674],{},[895,10669,10670,10672],{},[898,10671,1659],{},[898,10673,1662],{},[902,10675,1665],{"encoding":904},[883,10677,10679],{"className":10678},[886],[888,10680,10681],{"xmlns":890},[892,10682,10683,10689],{},[895,10684,10685,10687],{},[898,10686,1659],{},[898,10688,1683],{},[902,10690,1686],{"encoding":904}," pro ",[883,10693,10695],{"className":10694},[886],[888,10696,10697],{"xmlns":890},[892,10698,10699,10719],{},[895,10700,10701,10707,10709,10711,10713],{},[2142,10702,10703,10705],{},[898,10704,2146],{},[898,10706,1735],{},[1706,10708,2539],{},[898,10710,2146],{},[1706,10712,2539],{},[2142,10714,10715,10717],{},[898,10716,2146],{},[898,10718,10315],{},[902,10720,10459],{"encoding":904}," vyznačuje zisk.",[2547,10723,10725],{"id":10724},"příklad-38","Příklad 3.8",[724,10727,10728,10730,10731,1343,10751,1343,10777,10804],{},[38,10729,2555],{}," Dáno ",[883,10732,10734],{"className":10733},[886],[888,10735,10736],{"xmlns":890},[892,10737,10738,10748],{},[895,10739,10740,10742,10744,10746],{},[898,10741,2020],{},[898,10743,1683],{},[1706,10745,1708],{},[2148,10747,3455],{},[902,10749,10750],{"encoding":904},"FC = 4",[883,10752,10754],{"className":10753},[886],[888,10755,10756],{"xmlns":890},[892,10757,10758,10774],{},[895,10759,10760,10762,10764,10766,10768],{},[898,10761,1659],{},[898,10763,1762],{},[898,10765,1683],{},[1706,10767,1708],{},[2489,10769,10770,10772],{},[898,10771,2146],{},[2148,10773,2495],{},[902,10775,10776],{"encoding":904},"TVC = Q^2",[883,10778,10780],{"className":10779},[886],[888,10781,10782],{"xmlns":890},[892,10783,10784,10801],{},[895,10785,10786,10788,10790,10792,10794,10796,10798],{},[898,10787,1702],{},[1706,10789,1708],{},[1706,10791,1715],{},[2148,10793,2495],{},[898,10795,2146],{},[1706,10797,2447],{},[2148,10799,10800],{},"9",[902,10802,10803],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,10806,10807,10809],{},[38,10808,2615],{}," Celkové náklady a příjem:",[883,10811,10813],{"className":10812},[886],[888,10814,10815],{"xmlns":890,"display":2350},[892,10816,10817,10883],{},[895,10818,10819,10821,10823,10825,10827,10829,10835,10837,10839,10841,10843,10845,10847,10849,10851,10853,10855,10857,10859,10861,10863,10865,10867,10869,10875,10877,10879,10881],{},[898,10820,1659],{},[898,10822,1683],{},[1706,10824,1708],{},[2148,10826,3455],{},[1706,10828,2447],{},[2489,10830,10831,10833],{},[898,10832,2146],{},[2148,10834,2495],{},[1706,10836,2505],{"separator":2504},[4898,10838],{"width":9524},[898,10840,1659],{},[898,10842,1662],{},[1706,10844,1708],{},[898,10846,2146],{},[1706,10848,2390],{},[1706,10850,2140],{"stretchy":2139},[1706,10852,1715],{},[2148,10854,2495],{},[898,10856,2146],{},[1706,10858,2447],{},[2148,10860,10800],{},[1706,10862,2153],{"stretchy":2139},[1706,10864,1708],{},[1706,10866,1715],{},[2148,10868,2495],{},[2489,10870,10871,10873],{},[898,10872,2146],{},[2148,10874,2495],{},[1706,10876,2447],{},[2148,10878,10800],{},[898,10880,2146],{},[898,10882,1837],{"mathvariant":2409},[902,10884,10885],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,10887,10888],{},"Zisk dle (3.12):",[883,10890,10892],{"className":10891},[886],[888,10893,10894],{"xmlns":890,"display":2350},[892,10895,10896,10974],{},[895,10897,10898,10900,10902,10904,10906,10908,10910,10912,10914,10916,10918,10920,10922,10928,10930,10932,10934,10936,10938,10940,10942,10944,10950,10952,10954,10956,10958,10964,10966,10968,10970,10972],{},[898,10899,1702],{},[898,10901,1662],{},[1706,10903,1708],{},[898,10905,1659],{},[898,10907,1662],{},[1706,10909,1715],{},[898,10911,1659],{},[898,10913,1683],{},[1706,10915,1708],{},[1706,10917,2140],{"stretchy":2139},[1706,10919,1715],{},[2148,10921,2495],{},[2489,10923,10924,10926],{},[898,10925,2146],{},[2148,10927,2495],{},[1706,10929,2447],{},[2148,10931,10800],{},[898,10933,2146],{},[1706,10935,2153],{"stretchy":2139},[1706,10937,1715],{},[1706,10939,2140],{"stretchy":2139},[2148,10941,3455],{},[1706,10943,2447],{},[2489,10945,10946,10948],{},[898,10947,2146],{},[2148,10949,2495],{},[1706,10951,2153],{"stretchy":2139},[1706,10953,1708],{},[1706,10955,1715],{},[2148,10957,4284],{},[2489,10959,10960,10962],{},[898,10961,2146],{},[2148,10963,2495],{},[1706,10965,2447],{},[2148,10967,10800],{},[898,10969,2146],{},[1706,10971,1715],{},[2148,10973,5945],{},[902,10975,10976],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,10978,10979,10982,10983,11019,11020,4288],{},[38,10980,10981],{},"Body zvratu"," jsou kořeny rovnice ",[883,10984,10986],{"className":10985},[886],[888,10987,10988],{"xmlns":890},[892,10989,10990,11016],{},[895,10991,10992,10994,10996,11002,11004,11006,11008,11010,11012,11014],{},[1706,10993,1715],{},[2148,10995,4284],{},[2489,10997,10998,11000],{},[898,10999,2146],{},[2148,11001,2495],{},[1706,11003,2447],{},[2148,11005,10800],{},[898,11007,2146],{},[1706,11009,1715],{},[2148,11011,3455],{},[1706,11013,1708],{},[2148,11015,2150],{},[902,11017,11018],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",", tj. ",[883,11021,11023],{"className":11022},[886],[888,11024,11025],{"xmlns":890},[892,11026,11027,11051],{},[895,11028,11029,11031,11037,11039,11041,11043,11045,11047,11049],{},[2148,11030,4284],{},[2489,11032,11033,11035],{},[898,11034,2146],{},[2148,11036,2495],{},[1706,11038,1715],{},[2148,11040,10800],{},[898,11042,2146],{},[1706,11044,2447],{},[2148,11046,3455],{},[1706,11048,1708],{},[2148,11050,2150],{},[902,11052,11053],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,11055,11057],{"className":11056},[886],[888,11058,11059],{"xmlns":890,"display":2350},[892,11060,11061,11120],{},[895,11062,11063,11075,11077,11101,11103,11118],{},[2142,11064,11065,11067],{},[898,11066,2146],{},[895,11068,11069,11071,11073],{},[2148,11070,2701],{},[1706,11072,2505],{"separator":2504},[2148,11074,2495],{},[1706,11076,1708],{},[2964,11078,11079,11099],{},[895,11080,11081,11083,11086],{},[2148,11082,10800],{},[1706,11084,11085],{},"±",[11087,11088,11089],"msqrt",{},[895,11090,11091,11094,11096],{},[2148,11092,11093],{},"81",[1706,11095,1715],{},[2148,11097,11098],{},"48",[2148,11100,7044],{},[1706,11102,1708],{},[2964,11104,11105,11116],{},[895,11106,11107,11109,11111],{},[2148,11108,10800],{},[1706,11110,11085],{},[11087,11112,11113],{},[2148,11114,11115],{},"33",[2148,11117,7044],{},[1706,11119,2505],{"separator":2504},[902,11121,11122],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,11124,11125,11126,1993,11149,1837],{},"numericky ",[883,11127,11129],{"className":11128},[886],[888,11130,11131],{"xmlns":890},[892,11132,11133,11146],{},[895,11134,11135,11141,11143],{},[2142,11136,11137,11139],{},[898,11138,2146],{},[2148,11140,2701],{},[1706,11142,7883],{},[2148,11144,11145],{},"0,543",[902,11147,11148],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,11150,11152],{"className":11151},[886],[888,11153,11154],{"xmlns":890},[892,11155,11156,11169],{},[895,11157,11158,11164,11166],{},[2142,11159,11160,11162],{},[898,11161,2146],{},[2148,11163,2495],{},[1706,11165,7883],{},[2148,11167,11168],{},"2,457",[902,11170,11171],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,11173,11174,1647,11177,11222,11223,11019,11257,11275],{},[38,11175,11176],{},"Maximum zisku.",[883,11178,11180],{"className":11179},[886],[888,11181,11182],{"xmlns":890},[892,11183,11184,11219],{},[895,11185,11186,11188,11194,11196,11198,11200,11202,11204,11206,11208,11210,11212,11214,11216],{},[898,11187,1702],{},[2489,11189,11190,11192],{},[898,11191,1662],{},[1706,11193,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,11195,1708],{},[1706,11197,1715],{},[2148,11199,7044],{},[898,11201,2146],{},[1706,11203,2447],{},[2148,11205,10800],{},[1706,11207,1708],{},[2148,11209,2150],{},[1706,11211,9609],{},[898,11213,2146],{},[1706,11215,1708],{},[2148,11217,11218],{},"1,5",[902,11220,11221],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",". Dále ",[883,11224,11226],{"className":11225},[886],[888,11227,11228],{"xmlns":890},[892,11229,11230,11254],{},[895,11231,11232,11234,11244,11246,11248,11250,11252],{},[898,11233,1702],{},[2489,11235,11236,11238],{},[898,11237,1662],{},[895,11239,11240,11242],{},[1706,11241,3142],{"mathvariant":2409},[1706,11243,3142],{"mathvariant":2409},[1706,11245,1708],{},[1706,11247,1715],{},[2148,11249,7044],{},[1706,11251,2539],{},[2148,11253,2150],{},[902,11255,11256],{"encoding":904},"PR'' = -6 \u003C 0",[883,11258,11260],{"className":11259},[886],[888,11261,11262],{"xmlns":890},[892,11263,11264,11272],{},[895,11265,11266,11268,11270],{},[898,11267,2146],{},[1706,11269,1708],{},[2148,11271,11218],{},[902,11273,11274],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,11277,11279],{"className":11278},[886],[888,11280,11281],{"xmlns":890,"display":2350},[892,11282,11283,11346],{},[895,11284,11285,11287,11289,11291,11293,11295,11297,11299,11301,11303,11305,11307,11313,11315,11317,11319,11321,11323,11325,11327,11329,11332,11334,11337,11339,11341,11343],{},[898,11286,1702],{},[898,11288,1662],{},[1706,11290,2140],{"stretchy":2139},[2148,11292,11218],{},[1706,11294,2153],{"stretchy":2139},[1706,11296,1708],{},[1706,11298,1715],{},[2148,11300,4284],{},[1706,11302,2390],{},[1706,11304,2140],{"stretchy":2139},[2148,11306,11218],{},[2489,11308,11309,11311],{},[1706,11310,2153],{"stretchy":2139},[2148,11312,2495],{},[1706,11314,2447],{},[2148,11316,10800],{},[1706,11318,2390],{},[2148,11320,11218],{},[1706,11322,1715],{},[2148,11324,3455],{},[1706,11326,1708],{},[1706,11328,1715],{},[2148,11330,11331],{},"6,75",[1706,11333,2447],{},[2148,11335,11336],{},"13,5",[1706,11338,1715],{},[2148,11340,3455],{},[1706,11342,1708],{},[2148,11344,11345],{},"2,75.",[902,11347,11348],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,11350,11351,11352,1343,11397,11450,11451,11469],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,11353,11355],{"className":11354},[886],[888,11356,11357],{"xmlns":890},[892,11358,11359,11394],{},[895,11360,11361,11363,11369,11371,11373,11375,11377,11379,11381,11383,11385,11387,11389,11391],{},[898,11362,1659],{},[2489,11364,11365,11367],{},[898,11366,1662],{},[1706,11368,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,11370,1708],{},[1706,11372,1715],{},[2148,11374,3455],{},[898,11376,2146],{},[1706,11378,2447],{},[2148,11380,10800],{},[1706,11382,1708],{},[2148,11384,2150],{},[1706,11386,9609],{},[898,11388,2146],{},[1706,11390,1708],{},[2148,11392,11393],{},"2,25",[902,11395,11396],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,11398,11400],{"className":11399},[886],[888,11401,11402],{"xmlns":890},[892,11403,11404,11447],{},[895,11405,11406,11408,11416,11418,11420,11422,11424,11426,11428,11434,11436,11438,11440,11442,11444],{},[898,11407,1659],{},[2142,11409,11410,11412,11414],{},[898,11411,1662],{},[898,11413,2770],{},[1706,11415,2773],{},[1706,11417,1708],{},[1706,11419,1715],{},[2148,11421,2495],{},[1706,11423,2390],{},[1706,11425,2140],{"stretchy":2139},[2148,11427,11393],{},[2489,11429,11430,11432],{},[1706,11431,2153],{"stretchy":2139},[2148,11433,2495],{},[1706,11435,2447],{},[2148,11437,10800],{},[1706,11439,2390],{},[2148,11441,11393],{},[1706,11443,1708],{},[2148,11445,11446],{},"10,125",[902,11448,11449],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,11452,11454],{"className":11453},[886],[888,11455,11456],{"xmlns":890},[892,11457,11458,11466],{},[895,11459,11460,11462,11464],{},[898,11461,2146],{},[1706,11463,1708],{},[2148,11465,11393],{},[902,11467,11468],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[1636,11471,11472],{},[724,11473,11474,11476,11477,1343,11500,11522,11523,1343,11540,11561,11562,11594,11595,11633,11634,1889,11652,11669,11670,1993,11698,11732,11733,11771,11772,1993,11796,1837],{},[883,11475,9276],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,11478,11480],{"className":11479},[886],[888,11481,11482],{"xmlns":890},[892,11483,11484,11497],{},[895,11485,11486,11492,11494],{},[2142,11487,11488,11490],{},[898,11489,2146],{},[2148,11491,2701],{},[1706,11493,1708],{},[2148,11495,11496],{},"0,5",[902,11498,11499],{"encoding":904},"Q_1 = 0{,}5",[883,11501,11503],{"className":11502},[886],[888,11504,11505],{"xmlns":890},[892,11506,11507,11519],{},[895,11508,11509,11515,11517],{},[2142,11510,11511,11513],{},[898,11512,2146],{},[2148,11514,2495],{},[1706,11516,1708],{},[2148,11518,3455],{},[902,11520,11521],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,11524,11526],{"className":11525},[886],[888,11527,11528],{"xmlns":890},[892,11529,11530,11538],{},[895,11531,11532,11534,11536],{},[898,11533,2146],{},[1706,11535,1708],{},[2148,11537,11393],{},[902,11539,11468],{"encoding":904},[883,11541,11543],{"className":11542},[886],[888,11544,11545],{"xmlns":890},[892,11546,11547,11558],{},[895,11548,11549,11551,11553,11555],{},[898,11550,1702],{},[898,11552,1662],{},[1706,11554,1708],{},[2148,11556,11557],{},"6,125",[902,11559,11560],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,11563,11565],{"className":11564},[886],[888,11566,11567],{"xmlns":890},[892,11568,11569,11591],{},[895,11570,11571,11573,11579,11581,11583,11585,11587,11589],{},[898,11572,1702],{},[2489,11574,11575,11577],{},[898,11576,1662],{},[1706,11578,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,11580,1708],{},[1706,11582,1715],{},[2148,11584,3455],{},[898,11586,2146],{},[1706,11588,2447],{},[2148,11590,10800],{},[902,11592,11593],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,11596,11598],{"className":11597},[886],[888,11599,11600],{"xmlns":890},[892,11601,11602,11630],{},[895,11603,11604,11606,11608,11610,11612,11614,11620,11622,11624,11626,11628],{},[898,11605,1702],{},[898,11607,1662],{},[1706,11609,1708],{},[1706,11611,1715],{},[2148,11613,2495],{},[2489,11615,11616,11618],{},[898,11617,2146],{},[2148,11619,2495],{},[1706,11621,2447],{},[2148,11623,10800],{},[898,11625,2146],{},[1706,11627,1715],{},[2148,11629,3455],{},[902,11631,11632],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,11635,11637],{"className":11636},[886],[888,11638,11639],{"xmlns":890},[892,11640,11641,11649],{},[895,11642,11643],{},[2489,11644,11645,11647],{},[898,11646,2146],{},[2148,11648,2495],{},[902,11650,11651],{"encoding":904},"Q^2",[883,11653,11655],{"className":11654},[886],[888,11656,11657],{"xmlns":890},[892,11658,11659,11667],{},[895,11660,11661,11663,11665],{},[898,11662,1659],{},[898,11664,1762],{},[898,11666,1683],{},[902,11668,2043],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,11671,11673],{"className":11672},[886],[888,11674,11675],{"xmlns":890},[892,11676,11677,11695],{},[895,11678,11679,11681,11683,11685,11687,11689],{},[898,11680,1659],{},[898,11682,1683],{},[1706,11684,1708],{},[2148,11686,3455],{},[1706,11688,2447],{},[2489,11690,11691,11693],{},[898,11692,2146],{},[2148,11694,2495],{},[902,11696,11697],{"encoding":904},"TC = 4 + Q^2",[883,11699,11701],{"className":11700},[886],[888,11702,11703],{"xmlns":890},[892,11704,11705,11729],{},[895,11706,11707,11709,11711,11713,11715,11717,11723,11725,11727],{},[898,11708,1659],{},[898,11710,1662],{},[1706,11712,1708],{},[1706,11714,1715],{},[2148,11716,2495],{},[2489,11718,11719,11721],{},[898,11720,2146],{},[2148,11722,2495],{},[1706,11724,2447],{},[2148,11726,10800],{},[898,11728,2146],{},[902,11730,11731],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,11734,11736],{"className":11735},[886],[888,11737,11738],{"xmlns":890},[892,11739,11740,11768],{},[895,11741,11742,11744,11746,11748,11750,11752,11758,11760,11762,11764,11766],{},[898,11743,1702],{},[898,11745,1662],{},[1706,11747,1708],{},[1706,11749,1715],{},[2148,11751,4284],{},[2489,11753,11754,11756],{},[898,11755,2146],{},[2148,11757,2495],{},[1706,11759,2447],{},[2148,11761,10800],{},[898,11763,2146],{},[1706,11765,1715],{},[2148,11767,3455],{},[902,11769,11770],{"encoding":904},"PR = -3Q^2 + 9Q - 4",", odkud ",[883,11773,11775],{"className":11774},[886],[888,11776,11777],{"xmlns":890},[892,11778,11779,11793],{},[895,11780,11781,11789,11791],{},[2142,11782,11783,11785,11787],{},[898,11784,2146],{},[898,11786,2770],{},[1706,11788,2773],{},[1706,11790,1708],{},[2148,11792,11218],{},[902,11794,11795],{"encoding":904},"Q_{\\max} = 1{,}5",[883,11797,11799],{"className":11798},[886],[888,11800,11801],{"xmlns":890},[892,11802,11803,11820],{},[895,11804,11805,11807,11815,11817],{},[898,11806,1702],{},[2142,11808,11809,11811,11813],{},[898,11810,1662],{},[898,11812,2770],{},[1706,11814,2773],{},[1706,11816,1708],{},[2148,11818,11819],{},"2,75",[902,11821,11822],{"encoding":904},"PR_{\\max} = 2{,}75",[724,11824,11825],{},[614,11826,11827,11828,11855,11856,11889,11890,1343,11913,1837],{},"Obrázek 3.12: Graf ",[883,11829,11831],{"className":11830},[886],[888,11832,11833],{"xmlns":890},[892,11834,11835,11853],{},[895,11836,11837,11839,11841,11843,11845,11847],{},[898,11838,1659],{},[898,11840,1683],{},[1706,11842,1708],{},[2148,11844,3455],{},[1706,11846,2447],{},[2489,11848,11849,11851],{},[898,11850,2146],{},[2148,11852,2495],{},[902,11854,11697],{"encoding":904}," (parabola) a ",[883,11857,11859],{"className":11858},[886],[888,11860,11861],{"xmlns":890},[892,11862,11863,11887],{},[895,11864,11865,11867,11869,11871,11873,11875,11881,11883,11885],{},[898,11866,1659],{},[898,11868,1662],{},[1706,11870,1708],{},[1706,11872,1715],{},[2148,11874,2495],{},[2489,11876,11877,11879],{},[898,11878,2146],{},[2148,11880,2495],{},[1706,11882,2447],{},[2148,11884,10800],{},[898,11886,2146],{},[902,11888,11731],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,11891,11893],{"className":11892},[886],[888,11894,11895],{"xmlns":890},[892,11896,11897,11910],{},[895,11898,11899,11905,11907],{},[2142,11900,11901,11903],{},[898,11902,2146],{},[2148,11904,2701],{},[1706,11906,7883],{},[2148,11908,11909],{},"0,54",[902,11911,11912],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,11914,11916],{"className":11915},[886],[888,11917,11918],{"xmlns":890},[892,11919,11920,11933],{},[895,11921,11922,11928,11930],{},[2142,11923,11924,11926],{},[898,11925,2146],{},[2148,11927,2495],{},[1706,11929,7883],{},[2148,11931,11932],{},"2,46",[902,11934,11935],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,11937,11938],{},[614,11939,11940,11941,5127,11978,11995,11996,1343,12017,1837],{},"Obrázek 3.13: Graf zisku ",[883,11942,11944],{"className":11943},[886],[888,11945,11946],{"xmlns":890},[892,11947,11948,11976],{},[895,11949,11950,11952,11954,11956,11958,11960,11966,11968,11970,11972,11974],{},[898,11951,1702],{},[898,11953,1662],{},[1706,11955,1708],{},[1706,11957,1715],{},[2148,11959,4284],{},[2489,11961,11962,11964],{},[898,11963,2146],{},[2148,11965,2495],{},[1706,11967,2447],{},[2148,11969,10800],{},[898,11971,2146],{},[1706,11973,1715],{},[2148,11975,3455],{},[902,11977,11770],{"encoding":904},[883,11979,11981],{"className":11980},[886],[888,11982,11983],{"xmlns":890},[892,11984,11985,11993],{},[895,11986,11987,11989,11991],{},[898,11988,2146],{},[1706,11990,1708],{},[2148,11992,11218],{},[902,11994,11274],{"encoding":904}," a nulami ",[883,11997,11999],{"className":11998},[886],[888,12000,12001],{"xmlns":890},[892,12002,12003,12015],{},[895,12004,12005,12011,12013],{},[2142,12006,12007,12009],{},[898,12008,2146],{},[2148,12010,2701],{},[1706,12012,7883],{},[2148,12014,11909],{},[902,12016,11912],{"encoding":904},[883,12018,12020],{"className":12019},[886],[888,12021,12022],{"xmlns":890},[892,12023,12024,12036],{},[895,12025,12026,12032,12034],{},[2142,12027,12028,12030],{},[898,12029,2146],{},[2148,12031,2495],{},[1706,12033,7883],{},[2148,12035,11932],{},[902,12037,11935],{"encoding":904},[115,12039,12041],{"id":12040},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,12043,12044],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,12046,12047],{},[2286,12048],{"alt":12049,"className":12050,"src":12051},"imek-max-zisku-dva-pohledy",[210,2290],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,12053,8604],{"id":12054},"princip-1",[724,12056,12057,12058,2891,12073,12090],{},"Má-li zisk ",[883,12059,12061],{"className":12060},[886],[888,12062,12063],{"xmlns":890},[892,12064,12065,12071],{},[895,12066,12067,12069],{},[898,12068,1702],{},[898,12070,1662],{},[902,12072,10130],{"encoding":904},[883,12074,12076],{"className":12075},[886],[888,12077,12078],{"xmlns":890},[892,12079,12080,12088],{},[895,12081,12082],{},[2142,12083,12084,12086],{},[898,12085,2146],{},[2148,12087,2150],{},[902,12089,8625],{"encoding":904}," maximum, pak platí",[883,12092,12094],{"className":12093},[886],[888,12095,12096],{"xmlns":890,"display":2350},[892,12097,12098,12147],{},[2354,12099,12100],{"width":2356},[2358,12101,12102,12104,12140,12142],{},[2361,12103],{"width":2363},[2361,12105,12106],{},[895,12107,12108,12110,12112,12114,12120,12122,12124,12126,12128,12130,12136,12138],{},[898,12109,1742],{},[898,12111,1662],{},[1706,12113,2140],{"stretchy":2139},[2142,12115,12116,12118],{},[898,12117,2146],{},[2148,12119,2150],{},[1706,12121,2153],{"stretchy":2139},[1706,12123,1708],{},[898,12125,1742],{},[898,12127,1683],{},[1706,12129,2140],{"stretchy":2139},[2142,12131,12132,12134],{},[898,12133,2146],{},[2148,12135,2150],{},[1706,12137,2153],{"stretchy":2139},[898,12139,1837],{"mathvariant":2409},[2361,12141],{"width":2363},[2361,12143,12144],{},[2415,12145,12146],{},"(3.13)",[902,12148,12149],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[1636,12151,12152],{},[724,12153,12154,8692,12156],{},[883,12155,3021],{},[38,12157,12158],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,12160,12161,12164,12165,3484,12192,11019,12266,1837],{},[38,12162,12163],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,12166,12168],{"className":12167},[886],[888,12169,12170],{"xmlns":890},[892,12171,12172,12190],{},[895,12173,12174,12176,12178,12180,12182,12184,12186,12188],{},[898,12175,1702],{},[898,12177,1662],{},[1706,12179,1708],{},[898,12181,1659],{},[898,12183,1662],{},[1706,12185,1715],{},[898,12187,1659],{},[898,12189,1683],{},[902,12191,1722],{"encoding":904},[883,12193,12195],{"className":12194},[886],[888,12196,12197],{"xmlns":890},[892,12198,12199,12263],{},[895,12200,12201,12203,12209,12211,12217,12219,12221,12223,12229,12231,12237,12239,12241,12243,12249,12251,12257,12259,12261],{},[898,12202,1702],{},[2489,12204,12205,12207],{},[898,12206,1662],{},[1706,12208,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,12210,2140],{"stretchy":2139},[2142,12212,12213,12215],{},[898,12214,2146],{},[2148,12216,2150],{},[1706,12218,2153],{"stretchy":2139},[1706,12220,1708],{},[898,12222,1659],{},[2489,12224,12225,12227],{},[898,12226,1662],{},[1706,12228,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,12230,2140],{"stretchy":2139},[2142,12232,12233,12235],{},[898,12234,2146],{},[2148,12236,2150],{},[1706,12238,2153],{"stretchy":2139},[1706,12240,1715],{},[898,12242,1659],{},[2489,12244,12245,12247],{},[898,12246,1683],{},[1706,12248,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,12250,2140],{"stretchy":2139},[2142,12252,12253,12255],{},[898,12254,2146],{},[2148,12256,2150],{},[1706,12258,2153],{"stretchy":2139},[1706,12260,1708],{},[2148,12262,2150],{},[902,12264,12265],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,12267,12269],{"className":12268},[886],[888,12270,12271],{"xmlns":890},[892,12272,12273,12305],{},[895,12274,12275,12277,12279,12281,12287,12289,12291,12293,12295,12297,12303],{},[898,12276,1742],{},[898,12278,1662],{},[1706,12280,2140],{"stretchy":2139},[2142,12282,12283,12285],{},[898,12284,2146],{},[2148,12286,2150],{},[1706,12288,2153],{"stretchy":2139},[1706,12290,1708],{},[898,12292,1742],{},[898,12294,1683],{},[1706,12296,2140],{"stretchy":2139},[2142,12298,12299,12301],{},[898,12300,2146],{},[2148,12302,2150],{},[1706,12304,2153],{"stretchy":2139},[902,12306,12307],{"encoding":904},"MR(Q_0) = MC(Q_0)",[1636,12309,12310,12316],{},[724,12311,12312,12315],{},[883,12313,12314],{},"!tip"," Postup — jak najít maximum zisku",[152,12317,12318,12382,12437,12474,12502],{},[123,12319,12320,12321,1993,12336,12351,12352,1936],{},"Sestavte ",[883,12322,12324],{"className":12323},[886],[888,12325,12326],{"xmlns":890},[892,12327,12328,12334],{},[895,12329,12330,12332],{},[898,12331,1659],{},[898,12333,1662],{},[902,12335,1665],{"encoding":904},[883,12337,12339],{"className":12338},[886],[888,12340,12341],{"xmlns":890},[892,12342,12343,12349],{},[895,12344,12345,12347],{},[898,12346,1659],{},[898,12348,1683],{},[902,12350,1686],{"encoding":904}," ze zadání (typicky ",[883,12353,12355],{"className":12354},[886],[888,12356,12357],{"xmlns":890},[892,12358,12359,12379],{},[895,12360,12361,12363,12365,12367,12369,12371,12373,12375,12377],{},[898,12362,1659],{},[898,12364,1662],{},[1706,12366,1708],{},[898,12368,1702],{},[1706,12370,2140],{"stretchy":2139},[898,12372,2146],{},[1706,12374,2153],{"stretchy":2139},[1706,12376,2390],{},[898,12378,2146],{},[902,12380,12381],{"encoding":904},"TR = P(Q) \\cdot Q",[123,12383,12384,12385,1993,12411,1837],{},"Vypočtěte ",[883,12386,12388],{"className":12387},[886],[888,12389,12390],{"xmlns":890},[892,12391,12392,12408],{},[895,12393,12394,12396,12398,12400,12402],{},[898,12395,1742],{},[898,12397,1662],{},[1706,12399,1708],{},[898,12401,1659],{},[2489,12403,12404,12406],{},[898,12405,1662],{},[1706,12407,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,12409,12410],{"encoding":904},"MR = TR'",[883,12412,12414],{"className":12413},[886],[888,12415,12416],{"xmlns":890},[892,12417,12418,12434],{},[895,12419,12420,12422,12424,12426,12428],{},[898,12421,1742],{},[898,12423,1683],{},[1706,12425,1708],{},[898,12427,1659],{},[2489,12429,12430,12432],{},[898,12431,1683],{},[1706,12433,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,12435,12436],{"encoding":904},"MC = TC'",[123,12438,12439,12440,1837],{},"Řešte rovnici ",[883,12441,12443],{"className":12442},[886],[888,12444,12445],{"xmlns":890},[892,12446,12447,12471],{},[895,12448,12449,12451,12453,12455,12457,12459,12461,12463,12465,12467,12469],{},[898,12450,1742],{},[898,12452,1662],{},[1706,12454,2140],{"stretchy":2139},[898,12456,2146],{},[1706,12458,2153],{"stretchy":2139},[1706,12460,1708],{},[898,12462,1742],{},[898,12464,1683],{},[1706,12466,2140],{"stretchy":2139},[898,12468,2146],{},[1706,12470,2153],{"stretchy":2139},[902,12472,12473],{"encoding":904},"MR(Q) = MC(Q)",[123,12475,12476,12477,12501],{},"Ověřte druhou derivaci ",[883,12478,12480],{"className":12479},[886],[888,12481,12482],{"xmlns":890},[892,12483,12484,12498],{},[895,12485,12486,12488],{},[898,12487,1702],{},[2489,12489,12490,12492],{},[898,12491,1662],{},[895,12493,12494,12496],{},[1706,12495,3142],{"mathvariant":2409},[1706,12497,3142],{"mathvariant":2409},[902,12499,12500],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,12503,12504,12505,12532],{},"Dosaďte do ",[883,12506,12508],{"className":12507},[886],[888,12509,12510],{"xmlns":890},[892,12511,12512,12530],{},[895,12513,12514,12516,12518,12520,12522,12524,12526,12528],{},[898,12515,1702],{},[898,12517,1662],{},[1706,12519,1708],{},[898,12521,1659],{},[898,12523,1662],{},[1706,12525,1715],{},[898,12527,1659],{},[898,12529,1683],{},[902,12531,1722],{"encoding":904}," pro hodnotu maxima.",[2547,12534,12536],{"id":12535},"příklad-39","Příklad 3.9",[724,12538,12539,2556,12541,1993,12564,12601],{},[38,12540,2555],{},[883,12542,12544],{"className":12543},[886],[888,12545,12546],{"xmlns":890},[892,12547,12548,12561],{},[895,12549,12550,12552,12554,12557,12559],{},[898,12551,1702],{},[1706,12553,1708],{},[2148,12555,12556],{},"30",[1706,12558,1715],{},[898,12560,2146],{},[902,12562,12563],{"encoding":904},"P = 30 - Q",[883,12565,12567],{"className":12566},[886],[888,12568,12569],{"xmlns":890},[892,12570,12571,12598],{},[895,12572,12573,12575,12577,12579,12581,12587,12589,12591,12593,12595],{},[898,12574,1659],{},[898,12576,1683],{},[1706,12578,1708],{},[2148,12580,11496],{},[2489,12582,12583,12585],{},[898,12584,2146],{},[2148,12586,2495],{},[1706,12588,2447],{},[2148,12590,7044],{},[898,12592,2146],{},[1706,12594,2447],{},[2148,12596,12597],{},"7",[902,12599,12600],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,12603,12604,1647,12606,1343,12636,12675,12676,7822,12721,12755,12756,1837],{},[38,12605,2615],{},[883,12607,12609],{"className":12608},[886],[888,12610,12611],{"xmlns":890},[892,12612,12613,12633],{},[895,12614,12615,12617,12619,12621,12623,12625,12627],{},[898,12616,1659],{},[898,12618,1662],{},[1706,12620,1708],{},[2148,12622,12556],{},[898,12624,2146],{},[1706,12626,1715],{},[2489,12628,12629,12631],{},[898,12630,2146],{},[2148,12632,2495],{},[902,12634,12635],{"encoding":904},"TR = 30Q - Q^2",[883,12637,12639],{"className":12638},[886],[888,12640,12641],{"xmlns":890},[892,12642,12643,12672],{},[895,12644,12645,12647,12649,12651,12653,12655,12661,12663,12666,12668,12670],{},[898,12646,1702],{},[898,12648,1662],{},[1706,12650,1708],{},[1706,12652,1715],{},[2148,12654,11218],{},[2489,12656,12657,12659],{},[898,12658,2146],{},[2148,12660,2495],{},[1706,12662,2447],{},[2148,12664,12665],{},"24",[898,12667,2146],{},[1706,12669,1715],{},[2148,12671,12597],{},[902,12673,12674],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,12677,12679],{"className":12678},[886],[888,12680,12681],{"xmlns":890},[892,12682,12683,12718],{},[895,12684,12685,12687,12693,12695,12697,12699,12701,12703,12705,12707,12709,12711,12713,12715],{},[898,12686,1702],{},[2489,12688,12689,12691],{},[898,12690,1662],{},[1706,12692,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,12694,1708],{},[1706,12696,1715],{},[2148,12698,4284],{},[898,12700,2146],{},[1706,12702,2447],{},[2148,12704,12665],{},[1706,12706,1708],{},[2148,12708,2150],{},[1706,12710,9609],{},[898,12712,2146],{},[1706,12714,1708],{},[2148,12716,12717],{},"8",[902,12719,12720],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,12722,12724],{"className":12723},[886],[888,12725,12726],{"xmlns":890},[892,12727,12728,12752],{},[895,12729,12730,12732,12742,12744,12746,12748,12750],{},[898,12731,1702],{},[2489,12733,12734,12736],{},[898,12735,1662],{},[895,12737,12738,12740],{},[1706,12739,3142],{"mathvariant":2409},[1706,12741,3142],{"mathvariant":2409},[1706,12743,1708],{},[1706,12745,1715],{},[2148,12747,4284],{},[1706,12749,2539],{},[2148,12751,2150],{},[902,12753,12754],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,12757,12759],{"className":12758},[886],[888,12760,12761],{"xmlns":890},[892,12762,12763,12780],{},[895,12764,12765,12767,12769,12771,12773,12775,12777],{},[898,12766,1702],{},[898,12768,1662],{},[1706,12770,2140],{"stretchy":2139},[2148,12772,12717],{},[1706,12774,2153],{"stretchy":2139},[1706,12776,1708],{},[2148,12778,12779],{},"89",[902,12781,12782],{"encoding":904},"PR(8) = 89",[724,12784,12785,12786,1343,12812,7822,12836,12875],{},"Ověření principu: ",[883,12787,12789],{"className":12788},[886],[888,12790,12791],{"xmlns":890},[892,12792,12793,12809],{},[895,12794,12795,12797,12799,12801,12803,12805,12807],{},[898,12796,1742],{},[898,12798,1662],{},[1706,12800,1708],{},[2148,12802,12556],{},[1706,12804,1715],{},[2148,12806,2495],{},[898,12808,2146],{},[902,12810,12811],{"encoding":904},"MR = 30 - 2Q",[883,12813,12815],{"className":12814},[886],[888,12816,12817],{"xmlns":890},[892,12818,12819,12833],{},[895,12820,12821,12823,12825,12827,12829,12831],{},[898,12822,1742],{},[898,12824,1683],{},[1706,12826,1708],{},[898,12828,2146],{},[1706,12830,2447],{},[2148,12832,7044],{},[902,12834,12835],{"encoding":904},"MC = Q + 6",[883,12837,12839],{"className":12838},[886],[888,12840,12841],{"xmlns":890},[892,12842,12843,12872],{},[895,12844,12845,12847,12849,12851,12853,12855,12857,12860,12862,12864,12866,12868,12870],{},[898,12846,1742],{},[898,12848,1662],{},[1706,12850,2140],{"stretchy":2139},[2148,12852,12717],{},[1706,12854,2153],{"stretchy":2139},[1706,12856,1708],{},[2148,12858,12859],{},"14",[1706,12861,1708],{},[898,12863,1742],{},[898,12865,1683],{},[1706,12867,2140],{"stretchy":2139},[2148,12869,12717],{},[1706,12871,2153],{"stretchy":2139},[902,12873,12874],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,12877,12878,12879,12912,12913,12930],{},"V řadě případů — má-li rovnice ",[883,12880,12882],{"className":12881},[886],[888,12883,12884],{"xmlns":890},[892,12885,12886,12910],{},[895,12887,12888,12890,12892,12894,12896,12898,12900,12902,12904,12906,12908],{},[898,12889,1742],{},[898,12891,1662],{},[1706,12893,2140],{"stretchy":2139},[898,12895,2146],{},[1706,12897,2153],{"stretchy":2139},[1706,12899,1708],{},[898,12901,1742],{},[898,12903,1683],{},[1706,12905,2140],{"stretchy":2139},[898,12907,2146],{},[1706,12909,2153],{"stretchy":2139},[902,12911,12473],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,12914,12916],{"className":12915},[886],[888,12917,12918],{"xmlns":890},[892,12919,12920,12928],{},[895,12921,12922],{},[2142,12923,12924,12926],{},[898,12925,2146],{},[2148,12927,2150],{},[902,12929,8625],{"encoding":904}," — není třeba provádět test druhé derivace.",[2547,12932,12934],{"id":12933},"příklad-310","Příklad 3.10",[724,12936,12937,12939,12940,12944,12945,12959,12960,12991],{},[38,12938,2555],{}," Firma vyrábí minipočítače v ",[207,12941,12943],{"className":12942,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,12946,12948],{"className":12947},[886],[888,12949,12950],{"xmlns":890},[892,12951,12952,12957],{},[895,12953,12954],{},[2148,12955,12956],{},"900",[902,12958,12956],{"encoding":904}," EUR\u002Fks. ",[883,12961,12963],{"className":12962},[886],[888,12964,12965],{"xmlns":890},[892,12966,12967,12988],{},[895,12968,12969,12971,12973,12975,12977,12979,12982],{},[898,12970,1659],{},[898,12972,1683],{},[1706,12974,1708],{},[2148,12976,2728],{},[1706,12978,2447],{},[2148,12980,12981],{},"28",[2489,12983,12984,12986],{},[898,12985,2146],{},[2148,12987,2495],{},[902,12989,12990],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,12993,12994,1647,12996,1343,13018,1343,13038,13061],{},[38,12995,2615],{},[883,12997,12999],{"className":12998},[886],[888,13000,13001],{"xmlns":890},[892,13002,13003,13015],{},[895,13004,13005,13007,13009,13011,13013],{},[898,13006,1659],{},[898,13008,1662],{},[1706,13010,1708],{},[2148,13012,12956],{},[898,13014,2146],{},[902,13016,13017],{"encoding":904},"TR = 900Q",[883,13019,13021],{"className":13020},[886],[888,13022,13023],{"xmlns":890},[892,13024,13025,13035],{},[895,13026,13027,13029,13031,13033],{},[898,13028,1742],{},[898,13030,1662],{},[1706,13032,1708],{},[2148,13034,12956],{},[902,13036,13037],{"encoding":904},"MR = 900",[883,13039,13041],{"className":13040},[886],[888,13042,13043],{"xmlns":890},[892,13044,13045,13058],{},[895,13046,13047,13049,13051,13053,13056],{},[898,13048,1742],{},[898,13050,1683],{},[1706,13052,1708],{},[2148,13054,13055],{},"56",[898,13057,2146],{},[902,13059,13060],{"encoding":904},"MC = 56Q",". Z principu:",[883,13063,13065],{"className":13064},[886],[888,13066,13067],{"xmlns":890,"display":2350},[892,13068,13069,13111],{},[895,13070,13071,13073,13075,13077,13079,13081,13083,13085,13087,13089,13097,13099,13102,13104,13106,13108],{},[2148,13072,12956],{},[1706,13074,1708],{},[2148,13076,13055],{},[898,13078,2146],{},[2415,13080,3852],{},[1706,13082,9609],{},[2415,13084,3852],{},[898,13086,2146],{},[1706,13088,1708],{},[4745,13090,13091],{"scriptlevel":2150,"displaystyle":2139},[2964,13092,13093,13095],{},[2148,13094,12956],{},[2148,13096,13055],{},[1706,13098,7883],{},[2148,13100,13101],{},"16,07",[2415,13103,3852],{},[1706,13105,3248],{},[2415,13107,3852],{},[2148,13109,13110],{},"16.",[902,13112,13113],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,13115,13116,13117,4288],{},"Zisk při ",[883,13118,13120],{"className":13119},[886],[888,13121,13122],{"xmlns":890},[892,13123,13124,13132],{},[895,13125,13126,13128,13130],{},[898,13127,2146],{},[1706,13129,1708],{},[2148,13131,3364],{},[902,13133,13134],{"encoding":904},"Q = 16",[883,13136,13138],{"className":13137},[886],[888,13139,13140],{"xmlns":890,"display":2350},[892,13141,13142,13213],{},[895,13143,13144,13146,13148,13150,13152,13154,13156,13158,13160,13162,13164,13166,13168,13170,13172,13174,13180,13182,13184,13186,13188,13190,13192,13194,13196,13199,13201,13203,13205,13208,13211],{},[898,13145,1702],{},[898,13147,1662],{},[1706,13149,2140],{"stretchy":2139},[2148,13151,3364],{},[1706,13153,2153],{"stretchy":2139},[1706,13155,1708],{},[2148,13157,12956],{},[1706,13159,2390],{},[2148,13161,3364],{},[1706,13163,1715],{},[1706,13165,2140],{"stretchy":2139},[2148,13167,2728],{},[1706,13169,2447],{},[2148,13171,12981],{},[1706,13173,2390],{},[2489,13175,13176,13178],{},[2148,13177,3364],{},[2148,13179,2495],{},[1706,13181,2153],{"stretchy":2139},[1706,13183,1708],{},[2148,13185,12859],{},[2415,13187,2799],{},[2148,13189,4361],{},[1706,13191,1715],{},[2148,13193,12597],{},[2415,13195,2799],{},[2148,13197,13198],{},"218",[1706,13200,1708],{},[2148,13202,12597],{},[2415,13204,2799],{},[2148,13206,13207],{},"182",[2415,13209,13210],{}," EUR",[898,13212,1837],{"mathvariant":2409},[902,13214,13215],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,13217,13218],{},"Pro srovnání při původních 30 ks:",[883,13220,13222],{"className":13221},[886],[888,13223,13224],{"xmlns":890,"display":2350},[892,13225,13226,13292],{},[895,13227,13228,13230,13232,13234,13236,13238,13240,13242,13244,13246,13248,13250,13252,13254,13256,13258,13260,13262,13264,13267,13269,13271,13273,13275,13277,13279,13281,13283,13285,13288,13290],{},[898,13229,1702],{},[898,13231,1662],{},[1706,13233,2140],{"stretchy":2139},[2148,13235,12556],{},[1706,13237,2153],{"stretchy":2139},[1706,13239,1708],{},[2148,13241,12956],{},[1706,13243,2390],{},[2148,13245,12556],{},[1706,13247,1715],{},[1706,13249,2140],{"stretchy":2139},[2148,13251,2728],{},[1706,13253,2447],{},[2148,13255,12981],{},[1706,13257,2390],{},[2148,13259,12956],{},[1706,13261,2153],{"stretchy":2139},[1706,13263,1708],{},[2148,13265,13266],{},"27",[2415,13268,2799],{},[2148,13270,5705],{},[1706,13272,1715],{},[2148,13274,2748],{},[2415,13276,2799],{},[2148,13278,2802],{},[1706,13280,1708],{},[2148,13282,2701],{},[2415,13284,2799],{},[2148,13286,13287],{},"750",[2415,13289,13210],{},[898,13291,1837],{"mathvariant":2409},[902,13293,13294],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,13296,13297,13300,13301,13319,13320,13338],{},[38,13298,13299],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,13302,13304],{"className":13303},[886],[888,13305,13306],{"xmlns":890},[892,13307,13308,13316],{},[895,13309,13310,13312,13314],{},[2148,13311,12597],{},[2415,13313,2799],{},[2148,13315,13207],{},[902,13317,13318],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,13321,13323],{"className":13322},[886],[888,13324,13325],{"xmlns":890},[892,13326,13327,13335],{},[895,13328,13329,13331,13333],{},[2148,13330,2701],{},[2415,13332,2799],{},[2148,13334,13287],{},[902,13336,13337],{"encoding":904},"1\\,750"," EUR.",[198,13340,13342],{"id":13341},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,13344,13345,13346,9217,13359,13383],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,13347,13349],{"className":13348},[886],[888,13350,13351],{"xmlns":890},[892,13352,13353,13357],{},[895,13354,13355],{},[898,13356,1702],{},[902,13358,1702],{"encoding":904},[883,13360,13362],{"className":13361},[886],[888,13363,13364],{"xmlns":890},[892,13365,13366,13380],{},[895,13367,13368,13370,13372,13374,13376,13378],{},[898,13369,1659],{},[898,13371,1662],{},[1706,13373,1708],{},[898,13375,1702],{},[1706,13377,2390],{},[898,13379,2146],{},[902,13381,13382],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,13385,13387],{"className":13386},[886],[888,13388,13389],{"xmlns":890,"display":2350},[892,13390,13391,13424],{},[2354,13392,13393],{"width":2356},[2358,13394,13395,13397,13417,13419],{},[2361,13396],{"width":2363},[2361,13398,13399],{},[895,13400,13401,13403,13405,13407,13409,13411,13413,13415],{},[898,13402,1702],{},[1706,13404,1708],{},[898,13406,1742],{},[898,13408,1683],{},[1706,13410,2140],{"stretchy":2139},[898,13412,2146],{},[1706,13414,2153],{"stretchy":2139},[898,13416,1837],{"mathvariant":2409},[2361,13418],{"width":2363},[2361,13420,13421],{},[2415,13422,13423],{},"(3.14)",[902,13425,13426],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,13428,13429,13430,1837],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,13431,13433],{"className":13432},[886],[888,13434,13435],{"xmlns":890},[892,13436,13437,13451],{},[895,13438,13439,13441],{},[898,13440,1702],{},[2489,13442,13443,13445],{},[898,13444,1662],{},[895,13446,13447,13449],{},[1706,13448,3142],{"mathvariant":2409},[1706,13450,3142],{"mathvariant":2409},[902,13452,12500],{"encoding":904},[2547,13454,13456],{"id":13455},"příklad-311","Příklad 3.11",[724,13458,13459,4127,13461,13509,13510,13528],{},[38,13460,2555],{},[883,13462,13464],{"className":13463},[886],[888,13465,13466],{"xmlns":890},[892,13467,13468,13506],{},[895,13469,13470,13472,13474,13476,13479,13485,13487,13490,13496,13498,13500,13502,13504],{},[898,13471,1659],{},[898,13473,1683],{},[1706,13475,1708],{},[2148,13477,13478],{},"0,04",[2489,13480,13481,13483],{},[898,13482,2146],{},[2148,13484,4284],{},[1706,13486,1715],{},[2148,13488,13489],{},"0,9",[2489,13491,13492,13494],{},[898,13493,2146],{},[2148,13495,2495],{},[1706,13497,2447],{},[2148,13499,7786],{},[898,13501,2146],{},[1706,13503,2447],{},[2148,13505,7524],{},[902,13507,13508],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,13511,13513],{"className":13512},[886],[888,13514,13515],{"xmlns":890},[892,13516,13517,13525],{},[895,13518,13519,13521,13523],{},[898,13520,1702],{},[1706,13522,1708],{},[2148,13524,3455],{},[902,13526,13527],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,13530,13531,13533,13534,11019,13576,13610,13611,4288],{},[38,13532,2615],{}," Z (3.14): ",[883,13535,13537],{"className":13536},[886],[888,13538,13539],{"xmlns":890},[892,13540,13541,13573],{},[895,13542,13543,13545,13547,13549,13552,13558,13560,13563,13565,13567,13569,13571],{},[898,13544,1742],{},[898,13546,1683],{},[1706,13548,1708],{},[2148,13550,13551],{},"0,12",[2489,13553,13554,13556],{},[898,13555,2146],{},[2148,13557,2495],{},[1706,13559,1715],{},[2148,13561,13562],{},"1,8",[898,13564,2146],{},[1706,13566,2447],{},[2148,13568,7786],{},[1706,13570,1708],{},[2148,13572,3455],{},[902,13574,13575],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,13577,13579],{"className":13578},[886],[888,13580,13581],{"xmlns":890},[892,13582,13583,13607],{},[895,13584,13585,13587,13593,13595,13597,13599,13601,13603,13605],{},[2148,13586,13551],{},[2489,13588,13589,13591],{},[898,13590,2146],{},[2148,13592,2495],{},[1706,13594,1715],{},[2148,13596,13562],{},[898,13598,2146],{},[1706,13600,2447],{},[2148,13602,7044],{},[1706,13604,1708],{},[2148,13606,2150],{},[902,13608,13609],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,13612,13614],{"className":13613},[886],[888,13615,13616],{"xmlns":890},[892,13617,13618,13622],{},[895,13619,13620],{},[2148,13621,13551],{},[902,13623,13624],{"encoding":904},"0{,}12",[883,13626,13628],{"className":13627},[886],[888,13629,13630],{"xmlns":890,"display":2350},[892,13631,13632,13685],{},[895,13633,13634,13640,13642,13644,13646,13648,13650,13652,13654,13656,13658,13660,13666,13668,13670,13672,13674,13680,13682],{},[2489,13635,13636,13638],{},[898,13637,2146],{},[2148,13639,2495],{},[1706,13641,1715],{},[2148,13643,3359],{},[898,13645,2146],{},[1706,13647,2447],{},[2148,13649,2728],{},[1706,13651,1708],{},[2148,13653,2150],{},[2415,13655,3852],{},[1706,13657,9609],{},[2415,13659,3852],{},[2142,13661,13662,13664],{},[898,13663,2146],{},[2148,13665,2701],{},[1706,13667,1708],{},[2148,13669,7524],{},[1706,13671,2505],{"separator":2504},[2415,13673,3852],{},[2142,13675,13676,13678],{},[898,13677,2146],{},[2148,13679,2495],{},[1706,13681,1708],{},[2148,13683,13684],{},"10.",[902,13686,13687],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,13689,13690,13691,4288],{},"Dále ",[883,13692,13694],{"className":13693},[886],[888,13695,13696],{"xmlns":890},[892,13697,13698,13737],{},[895,13699,13700,13702,13712,13714,13716,13718,13724,13726,13728,13731,13733,13735],{},[898,13701,1702],{},[2489,13703,13704,13706],{},[898,13705,1662],{},[895,13707,13708,13710],{},[1706,13709,3142],{"mathvariant":2409},[1706,13711,3142],{"mathvariant":2409},[1706,13713,1708],{},[1706,13715,1715],{},[898,13717,1742],{},[2489,13719,13720,13722],{},[898,13721,1683],{},[1706,13723,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,13725,1708],{},[1706,13727,1715],{},[2148,13729,13730],{},"0,24",[898,13732,2146],{},[1706,13734,2447],{},[2148,13736,13562],{},[902,13738,13739],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,13741,13742,13794],{},[123,13743,13744,13789,13790,13793],{},[883,13745,13747],{"className":13746},[886],[888,13748,13749],{"xmlns":890},[892,13750,13751,13786],{},[895,13752,13753,13755,13765,13767,13769,13771,13773,13776,13778,13780,13782,13784],{},[898,13754,1702],{},[2489,13756,13757,13759],{},[898,13758,1662],{},[895,13760,13761,13763],{},[1706,13762,3142],{"mathvariant":2409},[1706,13764,3142],{"mathvariant":2409},[1706,13766,2140],{"stretchy":2139},[2148,13768,7524],{},[1706,13770,2153],{"stretchy":2139},[1706,13772,1708],{},[2148,13774,13775],{},"0,6",[1706,13777,8922],{},[2148,13779,2150],{},[2415,13781,3852],{},[1706,13783,9609],{},[2415,13785,3852],{},[902,13787,13788],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,13791,13792],{},"minimum"," zisku (minimalizace ztráty);",[123,13795,13796,13789,13842,13845],{},[883,13797,13799],{"className":13798},[886],[888,13800,13801],{"xmlns":890},[892,13802,13803,13839],{},[895,13804,13805,13807,13817,13819,13821,13823,13825,13827,13829,13831,13833,13835,13837],{},[898,13806,1702],{},[2489,13808,13809,13811],{},[898,13810,1662],{},[895,13812,13813,13815],{},[1706,13814,3142],{"mathvariant":2409},[1706,13816,3142],{"mathvariant":2409},[1706,13818,2140],{"stretchy":2139},[2148,13820,7786],{},[1706,13822,2153],{"stretchy":2139},[1706,13824,1708],{},[1706,13826,1715],{},[2148,13828,13775],{},[1706,13830,2539],{},[2148,13832,2150],{},[2415,13834,3852],{},[1706,13836,9609],{},[2415,13838,3852],{},[902,13840,13841],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,13843,13844],{},"maximum"," zisku, avšak",[883,13847,13849],{"className":13848},[886],[888,13850,13851],{"xmlns":890,"display":2350},[892,13852,13853,13922],{},[895,13854,13855,13857,13859,13861,13863,13865,13867,13869,13871,13873,13875,13877,13879,13881,13883,13885,13887,13889,13891,13893,13895,13897,13899,13901,13903,13905,13907,13909,13911,13914,13916,13918,13920],{},[898,13856,1702],{},[898,13858,1662],{},[1706,13860,2140],{"stretchy":2139},[2148,13862,7786],{},[1706,13864,2153],{"stretchy":2139},[1706,13866,1708],{},[2148,13868,3455],{},[1706,13870,2390],{},[2148,13872,7786],{},[1706,13874,1715],{},[1706,13876,2140],{"stretchy":2139},[2148,13878,13478],{},[1706,13880,2390],{},[2148,13882,2701],{},[2415,13884,2799],{},[2148,13886,5705],{},[1706,13888,1715],{},[2148,13890,13489],{},[1706,13892,2390],{},[2148,13894,2590],{},[1706,13896,2447],{},[2148,13898,2590],{},[1706,13900,2447],{},[2148,13902,7524],{},[1706,13904,2153],{"stretchy":2139},[1706,13906,1708],{},[2148,13908,3508],{},[1706,13910,1715],{},[2148,13912,13913],{},"55",[1706,13915,1708],{},[1706,13917,1715],{},[2148,13919,3359],{},[1706,13921,2505],{"separator":2504},[902,13923,13924],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,13926,13927,13928,1837],{},"tj. ztráta větší než ",[883,13929,13931],{"className":13930},[886],[888,13932,13933],{"xmlns":890},[892,13934,13935,13945],{},[895,13936,13937,13939,13941,13943],{},[898,13938,2020],{},[898,13940,1683],{},[1706,13942,1708],{},[2148,13944,7524],{},[902,13946,13947],{"encoding":904},"FC = 5",[724,13949,13950,13953,13954,13957,13958,1837],{},[38,13951,13952],{},"Závěr:"," firma by měla ",[38,13955,13956],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,13959,13961],{"className":13960},[886],[888,13962,13963],{"xmlns":890},[892,13964,13965,13975],{},[895,13966,13967,13969,13971,13973],{},[898,13968,2020],{},[898,13970,1683],{},[1706,13972,1708],{},[2148,13974,7524],{},[902,13976,13947],{"encoding":904},[115,13978,13980],{"id":13979},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,13982,13983,13984,13986,13987,14002,14003,14016,14017,14043,14044,14057,14058,14076,14077,2891,14094,14097,14098,14118,14119,14134,14135,4288],{},"Důležitým završením analýzy je konstrukce ",[38,13985,1800],{},". S nabízeným množstvím rostou mezní náklady ",[883,13988,13990],{"className":13989},[886],[888,13991,13992],{"xmlns":890},[892,13993,13994,14000],{},[895,13995,13996,13998],{},[898,13997,1742],{},[898,13999,1683],{},[902,14001,1817],{"encoding":904}," a tyto určují cenu ",[883,14004,14006],{"className":14005},[886],[888,14007,14008],{"xmlns":890},[892,14009,14010,14014],{},[895,14011,14012],{},[898,14013,1702],{},[902,14015,1702],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,14018,14020],{"className":14019},[886],[888,14021,14022],{"xmlns":890},[892,14023,14024,14040],{},[895,14025,14026,14028,14030,14032,14034,14036,14038],{},[898,14027,1702],{},[1706,14029,1708],{},[898,14031,1742],{},[898,14033,1683],{},[1706,14035,2140],{"stretchy":2139},[898,14037,2146],{},[1706,14039,2153],{"stretchy":2139},[902,14041,14042],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,14045,14047],{"className":14046},[886],[888,14048,14049],{"xmlns":890},[892,14050,14051,14055],{},[895,14052,14053],{},[898,14054,1702],{},[902,14056,1702],{"encoding":904}," však nemůže být nižší než ",[883,14059,14061],{"className":14060},[886],[888,14062,14063],{"xmlns":890},[892,14064,14065,14073],{},[895,14066,14067],{},[2489,14068,14069,14071],{},[898,14070,1702],{},[1706,14072,3197],{},[902,14074,14075],{"encoding":904},"P^*"," odpovídající množství ",[883,14078,14080],{"className":14079},[886],[888,14081,14082],{"xmlns":890},[892,14083,14084,14092],{},[895,14085,14086],{},[2489,14087,14088,14090],{},[898,14089,2146],{},[1706,14091,3197],{},[902,14093,3221],{"encoding":904},[38,14095,14096],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,14099,14101],{"className":14100},[886],[888,14102,14103],{"xmlns":890},[892,14104,14105,14115],{},[895,14106,14107,14109],{},[2148,14108,2150],{},[2489,14110,14111,14113],{},[898,14112,2146],{},[1706,14114,3197],{},[902,14116,14117],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,14120,14122],{"className":14121},[886],[888,14123,14124],{"xmlns":890},[892,14125,14126,14132],{},[895,14127,14128,14130],{},[898,14129,1742],{},[898,14131,1683],{},[902,14133,1817],{"encoding":904}," nad bodem ",[883,14136,14138],{"className":14137},[886],[888,14139,14140],{"xmlns":890},[892,14141,14142,14146],{},[895,14143,14144],{},[898,14145,1735],{},[902,14147,1735],{"encoding":904},[883,14149,14151],{"className":14150},[886],[888,14152,14153],{"xmlns":890,"display":2350},[892,14154,14155,14264],{},[2354,14156,14157],{"width":2356},[2358,14158,14159,14161,14257,14259],{},[2361,14160],{"width":2363},[2361,14162,14163],{},[895,14164,14165,14167,14169,14172,14174,14176,14178,14180],{},[898,14166,1702],{},[1706,14168,1708],{},[898,14170,14171],{},"S",[1706,14173,2140],{"stretchy":2139},[898,14175,2146],{},[1706,14177,2153],{"stretchy":2139},[1706,14179,1708],{},[895,14181,14182,14185],{},[1706,14183,14184],{"fence":2504},"{",[2354,14186,14189,14229],{"rowspacing":14187,"columnalign":14188,"columnspacing":4900},"0.36em","left left",[2358,14190,14191,14207],{},[2361,14192,14193],{},[4745,14194,14195],{"scriptlevel":2150,"displaystyle":2139},[895,14196,14197,14199,14201,14203,14205],{},[898,14198,1742],{},[898,14200,1683],{},[1706,14202,2140],{"stretchy":2139},[898,14204,2146],{},[1706,14206,2153],{"stretchy":2139},[2361,14208,14209],{},[4745,14210,14211],{"scriptlevel":2150,"displaystyle":2139},[895,14212,14213,14216,14218,14221,14227],{},[2415,14214,14215],{},"pro ",[898,14217,2146],{},[1706,14219,14220],{},"≥",[2489,14222,14223,14225],{},[898,14224,2146],{},[1706,14226,3197],{},[1706,14228,2505],{"separator":2504},[2358,14230,14231,14237],{},[2361,14232,14233],{},[4745,14234,14235],{"scriptlevel":2150,"displaystyle":2139},[2148,14236,2150],{},[2361,14238,14239],{},[4745,14240,14241],{"scriptlevel":2150,"displaystyle":2139},[895,14242,14243,14245,14247,14249,14255],{},[2415,14244,14215],{},[898,14246,2146],{},[1706,14248,2539],{},[2489,14250,14251,14253],{},[898,14252,2146],{},[1706,14254,3197],{},[1706,14256,2505],{"separator":2504},[2361,14258],{"width":2363},[2361,14260,14261],{},[2415,14262,14263],{},"(3.15)",[902,14265,14266],{"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}",[724,14268,5331,14269,14286,14287,14304,14305,14335,14336,14339],{},[883,14270,14272],{"className":14271},[886],[888,14273,14274],{"xmlns":890},[892,14275,14276,14284],{},[895,14277,14278],{},[2489,14279,14280,14282],{},[898,14281,2146],{},[1706,14283,3197],{},[902,14285,3221],{"encoding":904}," je bod minima ",[883,14288,14290],{"className":14289},[886],[888,14291,14292],{"xmlns":890},[892,14293,14294,14302],{},[895,14295,14296,14298,14300],{},[898,14297,1735],{},[898,14299,1762],{},[898,14301,1683],{},[902,14303,1836],{"encoding":904},". Bod ",[883,14306,14308],{"className":14307},[886],[888,14309,14310],{"xmlns":890},[892,14311,14312,14332],{},[895,14313,14314,14316,14322,14324,14330],{},[1706,14315,2140],{"stretchy":2139},[2489,14317,14318,14320],{},[898,14319,2146],{},[1706,14321,3197],{},[1706,14323,2505],{"separator":2504},[2489,14325,14326,14328],{},[898,14327,1702],{},[1706,14329,3197],{},[1706,14331,2153],{"stretchy":2139},[902,14333,14334],{"encoding":904},"(Q^*, P^*)"," se nazývá ",[38,14337,14338],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[1636,14341,14342,14347],{},[724,14343,14344,14346],{},[883,14345,12314],{}," Postup — jak odvodit nabídku firmy",[152,14348,14349,14398,14493,14548,14619],{},[123,14350,14351,14352,1993,14374,1837],{},"Ze zadaných nákladů určete ",[883,14353,14355],{"className":14354},[886],[888,14356,14357],{"xmlns":890},[892,14358,14359,14371],{},[895,14360,14361,14363,14365,14367,14369],{},[898,14362,1742],{},[898,14364,1683],{},[1706,14366,2140],{"stretchy":2139},[898,14368,2146],{},[1706,14370,2153],{"stretchy":2139},[902,14372,14373],{"encoding":904},"MC(Q)",[883,14375,14377],{"className":14376},[886],[888,14378,14379],{"xmlns":890},[892,14380,14381,14395],{},[895,14382,14383,14385,14387,14389,14391,14393],{},[898,14384,1735],{},[898,14386,1762],{},[898,14388,1683],{},[1706,14390,2140],{"stretchy":2139},[898,14392,2146],{},[1706,14394,2153],{"stretchy":2139},[902,14396,14397],{"encoding":904},"AVC(Q)",[123,14399,14400,14401,14418,14419,14436,14437,14469,14470,1936],{},"Najděte ",[883,14402,14404],{"className":14403},[886],[888,14405,14406],{"xmlns":890},[892,14407,14408,14416],{},[895,14409,14410],{},[2489,14411,14412,14414],{},[898,14413,2146],{},[1706,14415,3197],{},[902,14417,3221],{"encoding":904}," jako bod minima ",[883,14420,14422],{"className":14421},[886],[888,14423,14424],{"xmlns":890},[892,14425,14426,14434],{},[895,14427,14428,14430,14432],{},[898,14429,1735],{},[898,14431,1762],{},[898,14433,1683],{},[902,14435,1836],{"encoding":904}," (řešením ",[883,14438,14440],{"className":14439},[886],[888,14441,14442],{"xmlns":890},[892,14443,14444,14466],{},[895,14445,14446,14448,14450,14456,14458,14460,14462,14464],{},[898,14447,1735],{},[898,14449,1762],{},[2489,14451,14452,14454],{},[898,14453,1683],{},[1706,14455,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,14457,2140],{"stretchy":2139},[898,14459,2146],{},[1706,14461,2153],{"stretchy":2139},[1706,14463,1708],{},[2148,14465,2150],{},[902,14467,14468],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,14471,14473],{"className":14472},[886],[888,14474,14475],{"xmlns":890},[892,14476,14477,14491],{},[895,14478,14479,14481,14483,14485,14487,14489],{},[898,14480,1735],{},[898,14482,1762],{},[898,14484,1683],{},[1706,14486,1708],{},[898,14488,1742],{},[898,14490,1683],{},[902,14492,1773],{"encoding":904},[123,14494,12384,14495,14547],{},[883,14496,14498],{"className":14497},[886],[888,14499,14500],{"xmlns":890},[892,14501,14502,14544],{},[895,14503,14504,14510,14512,14514,14516,14518,14524,14526,14528,14530,14532,14534,14536,14542],{},[2489,14505,14506,14508],{},[898,14507,1702],{},[1706,14509,3197],{},[1706,14511,1708],{},[898,14513,1742],{},[898,14515,1683],{},[1706,14517,2140],{"stretchy":2139},[2489,14519,14520,14522],{},[898,14521,2146],{},[1706,14523,3197],{},[1706,14525,2153],{"stretchy":2139},[1706,14527,1708],{},[898,14529,1735],{},[898,14531,1762],{},[898,14533,1683],{},[1706,14535,2140],{"stretchy":2139},[2489,14537,14538,14540],{},[898,14539,2146],{},[1706,14541,3197],{},[1706,14543,2153],{"stretchy":2139},[902,14545,14546],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,14549,14550,14551,10691,14583,14605,14606,1837],{},"Zapište nabídku: ",[883,14552,14554],{"className":14553},[886],[888,14555,14556],{"xmlns":890},[892,14557,14558,14580],{},[895,14559,14560,14562,14564,14566,14568,14570,14572,14574,14576,14578],{},[898,14561,14171],{},[1706,14563,2140],{"stretchy":2139},[898,14565,2146],{},[1706,14567,2153],{"stretchy":2139},[1706,14569,1708],{},[898,14571,1742],{},[898,14573,1683],{},[1706,14575,2140],{"stretchy":2139},[898,14577,2146],{},[1706,14579,2153],{"stretchy":2139},[902,14581,14582],{"encoding":904},"S(Q) = MC(Q)",[883,14584,14586],{"className":14585},[886],[888,14587,14588],{"xmlns":890},[892,14589,14590,14602],{},[895,14591,14592,14594,14596],{},[898,14593,2146],{},[1706,14595,14220],{},[2489,14597,14598,14600],{},[898,14599,2146],{},[1706,14601,3197],{},[902,14603,14604],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,14607,14609],{"className":14608},[886],[888,14610,14611],{"xmlns":890},[892,14612,14613,14617],{},[895,14614,14615],{},[2148,14616,2150],{},[902,14618,2150],{"encoding":904},[123,14620,14621,14622,14654],{},"V případě potřeby vyjádřete inverzi ",[883,14623,14625],{"className":14624},[886],[888,14626,14627],{"xmlns":890},[892,14628,14629,14651],{},[895,14630,14631,14633,14635,14645,14647,14649],{},[898,14632,2146],{},[1706,14634,1708],{},[2489,14636,14637,14639],{},[898,14638,14171],{},[895,14640,14641,14643],{},[1706,14642,1715],{},[2148,14644,2701],{},[1706,14646,2140],{"stretchy":2139},[898,14648,1702],{},[1706,14650,2153],{"stretchy":2139},[902,14652,14653],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,14656,14657],{},[614,14658,14659,14660,1343,14675,1993,14692,8091,14707,14720,14721,14746,14747,14760,14761,14778,14779,14796,14797,14814],{},"Obrázek 3.14: Křivky ",[883,14661,14663],{"className":14662},[886],[888,14664,14665],{"xmlns":890},[892,14666,14667,14673],{},[895,14668,14669,14671],{},[898,14670,1735],{},[898,14672,1683],{},[902,14674,2094],{"encoding":904},[883,14676,14678],{"className":14677},[886],[888,14679,14680],{"xmlns":890},[892,14681,14682,14690],{},[895,14683,14684,14686,14688],{},[898,14685,1735],{},[898,14687,1762],{},[898,14689,1683],{},[902,14691,1836],{"encoding":904},[883,14693,14695],{"className":14694},[886],[888,14696,14697],{"xmlns":890},[892,14698,14699,14705],{},[895,14700,14701,14703],{},[898,14702,1742],{},[898,14704,1683],{},[902,14706,1817],{"encoding":904},[883,14708,14710],{"className":14709},[886],[888,14711,14712],{"xmlns":890},[892,14713,14714,14718],{},[895,14715,14716],{},[898,14717,900],{},[902,14719,900],{"encoding":904},"; křivka nabídky ",[883,14722,14724],{"className":14723},[886],[888,14725,14726],{"xmlns":890},[892,14727,14728,14744],{},[895,14729,14730,14732,14734,14736,14738,14740,14742],{},[898,14731,1702],{},[1706,14733,1708],{},[898,14735,1742],{},[898,14737,1683],{},[1706,14739,2140],{"stretchy":2139},[898,14741,2146],{},[1706,14743,2153],{"stretchy":2139},[902,14745,14042],{"encoding":904}," začíná v bodě ",[883,14748,14750],{"className":14749},[886],[888,14751,14752],{"xmlns":890},[892,14753,14754,14758],{},[895,14755,14756],{},[898,14757,1735],{},[902,14759,1735],{"encoding":904}," odpovídajícím minimu ",[883,14762,14764],{"className":14763},[886],[888,14765,14766],{"xmlns":890},[892,14767,14768,14776],{},[895,14769,14770,14772,14774],{},[898,14771,1735],{},[898,14773,1762],{},[898,14775,1683],{},[902,14777,1836],{"encoding":904}," při ceně ",[883,14780,14782],{"className":14781},[886],[888,14783,14784],{"xmlns":890},[892,14785,14786,14794],{},[895,14787,14788],{},[2489,14789,14790,14792],{},[898,14791,1702],{},[1706,14793,3197],{},[902,14795,14075],{"encoding":904}," (minimální cena nabídky); pod ",[883,14798,14800],{"className":14799},[886],[888,14801,14802],{"xmlns":890},[892,14803,14804,14812],{},[895,14805,14806],{},[2489,14807,14808,14810],{},[898,14809,2146],{},[1706,14811,3197],{},[902,14813,3221],{"encoding":904}," je nabídka nulová.",[2547,14816,14818],{"id":14817},"příklad-312","Příklad 3.12",[724,14820,14821,4127,14823,14870],{},[38,14822,2555],{},[883,14824,14826],{"className":14825},[886],[888,14827,14828],{"xmlns":890},[892,14829,14830,14867],{},[895,14831,14832,14834,14836,14838,14841,14847,14849,14851,14857,14859,14861,14863,14865],{},[898,14833,1659],{},[898,14835,1683],{},[1706,14837,1708],{},[2148,14839,14840],{},"0,1",[2489,14842,14843,14845],{},[898,14844,2146],{},[2148,14846,4284],{},[1706,14848,1715],{},[2148,14850,2495],{},[2489,14852,14853,14855],{},[898,14854,2146],{},[2148,14856,2495],{},[1706,14858,2447],{},[2148,14860,3359],{},[898,14862,2146],{},[1706,14864,2447],{},[2148,14866,7786],{},[902,14868,14869],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,14872,14873,1647,14875,14912,14913,4288],{},[38,14874,2615],{},[883,14876,14878],{"className":14877},[886],[888,14879,14880],{"xmlns":890},[892,14881,14882,14909],{},[895,14883,14884,14886,14888,14890,14893,14899,14901,14903,14905,14907],{},[898,14885,1742],{},[898,14887,1683],{},[1706,14889,1708],{},[2148,14891,14892],{},"0,3",[2489,14894,14895,14897],{},[898,14896,2146],{},[2148,14898,2495],{},[1706,14900,1715],{},[2148,14902,3455],{},[898,14904,2146],{},[1706,14906,2447],{},[2148,14908,3359],{},[902,14910,14911],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,14914,14916],{"className":14915},[886],[888,14917,14918],{"xmlns":890},[892,14919,14920,14930],{},[895,14921,14922,14924,14926,14928],{},[898,14923,1702],{},[1706,14925,1708],{},[898,14927,1742],{},[898,14929,1683],{},[902,14931,14932],{"encoding":904},"P = MC",[883,14934,14936],{"className":14935},[886],[888,14937,14938],{"xmlns":890,"display":2350},[892,14939,14940,14965],{},[895,14941,14942,14944,14946,14948,14954,14956,14958,14960,14962],{},[898,14943,1702],{},[1706,14945,1708],{},[2148,14947,14892],{},[2489,14949,14950,14952],{},[898,14951,2146],{},[2148,14953,2495],{},[1706,14955,1715],{},[2148,14957,3455],{},[898,14959,2146],{},[1706,14961,2447],{},[2148,14963,14964],{},"15.",[902,14966,14967],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,14969,14970,14971,14984,14985,14998],{},"Vyjádření ",[883,14972,14974],{"className":14973},[886],[888,14975,14976],{"xmlns":890},[892,14977,14978,14982],{},[895,14979,14980],{},[898,14981,2146],{},[902,14983,2146],{"encoding":904}," jako funkce ",[883,14986,14988],{"className":14987},[886],[888,14989,14990],{"xmlns":890},[892,14991,14992,14996],{},[895,14993,14994],{},[898,14995,1702],{},[902,14997,1702],{"encoding":904}," doplněním na čtverec:",[883,15000,15002],{"className":15001},[886],[888,15003,15004],{"xmlns":890,"display":2350},[892,15005,15006,15096],{},[895,15007,15008,15010,15012,15014,15052,15054,15056,15078,15080,15094],{},[898,15009,1702],{},[1706,15011,1708],{},[2148,15013,14892],{},[895,15015,15016,15018,15040,15042,15050],{},[1706,15017,2140],{"fence":2504},[2489,15019,15020,15038],{},[895,15021,15022,15024,15026,15028,15036],{},[1706,15023,2140],{"fence":2504},[898,15025,2146],{},[1706,15027,1715],{},[4745,15029,15030],{"scriptlevel":2150,"displaystyle":2139},[2964,15031,15032,15034],{},[2148,15033,3369],{},[2148,15035,4284],{},[1706,15037,2153],{"fence":2504},[2148,15039,2495],{},[1706,15041,2447],{},[4745,15043,15044],{"scriptlevel":2150,"displaystyle":2139},[2964,15045,15046,15048],{},[2148,15047,2728],{},[2148,15049,10800],{},[1706,15051,2153],{"fence":2504},[1706,15053,2505],{"separator":2504},[4898,15055],{"width":9524},[2489,15057,15058,15076],{},[895,15059,15060,15062,15064,15066,15074],{},[1706,15061,2140],{"fence":2504},[898,15063,2146],{},[1706,15065,1715],{},[4745,15067,15068],{"scriptlevel":2150,"displaystyle":2139},[2964,15069,15070,15072],{},[2148,15071,3369],{},[2148,15073,4284],{},[1706,15075,2153],{"fence":2504},[2148,15077,2495],{},[1706,15079,1708],{},[2964,15081,15082,15092],{},[895,15083,15084,15086,15088,15090],{},[2148,15085,12556],{},[898,15087,1702],{},[1706,15089,1715],{},[2148,15091,2728],{},[2148,15093,10800],{},[1706,15095,2505],{"separator":2504},[902,15097,15098],{"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},",[883,15100,15102],{"className":15101},[886],[888,15103,15104],{"xmlns":890,"display":2350},[892,15105,15106,15138],{},[895,15107,15108,15110,15112,15118,15120,15136],{},[898,15109,2146],{},[1706,15111,1708],{},[2964,15113,15114,15116],{},[2148,15115,3369],{},[2148,15117,4284],{},[1706,15119,2447],{},[2964,15121,15122,15134],{},[11087,15123,15124],{},[895,15125,15126,15128,15130,15132],{},[2148,15127,12556],{},[898,15129,1702],{},[1706,15131,1715],{},[2148,15133,2728],{},[2148,15135,4284],{},[898,15137,1837],{"mathvariant":2409},[902,15139,15140],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,15142,13690,15143,1343,15181,1343,15230,15264,15265,1837],{},[883,15144,15146],{"className":15145},[886],[888,15147,15148],{"xmlns":890},[892,15149,15150,15178],{},[895,15151,15152,15154,15156,15158,15160,15162,15168,15170,15172,15174,15176],{},[898,15153,1735],{},[898,15155,1762],{},[898,15157,1683],{},[1706,15159,1708],{},[2148,15161,14840],{},[2489,15163,15164,15166],{},[898,15165,2146],{},[2148,15167,2495],{},[1706,15169,1715],{},[2148,15171,2495],{},[898,15173,2146],{},[1706,15175,2447],{},[2148,15177,3359],{},[902,15179,15180],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,15182,15184],{"className":15183},[886],[888,15185,15186],{"xmlns":890},[892,15187,15188,15227],{},[895,15189,15190,15192,15194,15200,15202,15205,15207,15209,15211,15213,15215,15217,15223,15225],{},[898,15191,1735],{},[898,15193,1762],{},[2489,15195,15196,15198],{},[898,15197,1683],{},[1706,15199,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,15201,1708],{},[2148,15203,15204],{},"0,2",[898,15206,2146],{},[1706,15208,1715],{},[2148,15210,2495],{},[1706,15212,1708],{},[2148,15214,2150],{},[1706,15216,9609],{},[2489,15218,15219,15221],{},[898,15220,2146],{},[1706,15222,3197],{},[1706,15224,1708],{},[2148,15226,7786],{},[902,15228,15229],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,15231,15233],{"className":15232},[886],[888,15234,15235],{"xmlns":890},[892,15236,15237,15261],{},[895,15238,15239,15241,15243,15253,15255,15257,15259],{},[898,15240,1735],{},[898,15242,1762],{},[2489,15244,15245,15247],{},[898,15246,1683],{},[895,15248,15249,15251],{},[1706,15250,3142],{"mathvariant":2409},[1706,15252,3142],{"mathvariant":2409},[1706,15254,1708],{},[2148,15256,15204],{},[1706,15258,8922],{},[2148,15260,2150],{},[902,15262,15263],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,15266,15268],{"className":15267},[886],[888,15269,15270],{"xmlns":890},[892,15271,15272,15308],{},[895,15273,15274,15280,15282,15284,15286,15288,15290,15292,15294,15296,15298,15300,15302,15304,15306],{},[2489,15275,15276,15278],{},[898,15277,1702],{},[1706,15279,3197],{},[1706,15281,1708],{},[898,15283,1742],{},[898,15285,1683],{},[1706,15287,2140],{"stretchy":2139},[2148,15289,7786],{},[1706,15291,2153],{"stretchy":2139},[1706,15293,1708],{},[2148,15295,12556],{},[1706,15297,1715],{},[2148,15299,3508],{},[1706,15301,2447],{},[2148,15303,3359],{},[1706,15305,1708],{},[2148,15307,7524],{},[902,15309,15310],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,15312,15313],{},[38,15314,15315],{},"Závěr.",[883,15317,15319],{"className":15318},[886],[888,15320,15321],{"xmlns":890,"display":2350},[892,15322,15323,15409],{},[895,15324,15325,15327,15329,15331,15333,15335,15337,15339],{},[898,15326,1702],{},[1706,15328,1708],{},[898,15330,14171],{},[1706,15332,2140],{"stretchy":2139},[898,15334,2146],{},[1706,15336,2153],{"stretchy":2139},[1706,15338,1708],{},[895,15340,15341,15343],{},[1706,15342,14184],{"fence":2504},[2354,15344,15345,15387],{"rowspacing":14187,"columnalign":14188,"columnspacing":4900},[2358,15346,15347,15371],{},[2361,15348,15349],{},[4745,15350,15351],{"scriptlevel":2150,"displaystyle":2139},[895,15352,15353,15355,15361,15363,15365,15367,15369],{},[2148,15354,14892],{},[2489,15356,15357,15359],{},[898,15358,2146],{},[2148,15360,2495],{},[1706,15362,1715],{},[2148,15364,3455],{},[898,15366,2146],{},[1706,15368,2447],{},[2148,15370,3359],{},[2361,15372,15373],{},[4745,15374,15375],{"scriptlevel":2150,"displaystyle":2139},[895,15376,15377,15379,15381,15383,15385],{},[2415,15378,14215],{},[898,15380,2146],{},[1706,15382,14220],{},[2148,15384,7786],{},[1706,15386,2505],{"separator":2504},[2358,15388,15389,15395],{},[2361,15390,15391],{},[4745,15392,15393],{"scriptlevel":2150,"displaystyle":2139},[2148,15394,2150],{},[2361,15396,15397],{},[4745,15398,15399],{"scriptlevel":2150,"displaystyle":2139},[895,15400,15401,15403,15405,15407],{},[2415,15402,14215],{},[898,15404,2146],{},[1706,15406,2539],{},[2148,15408,13684],{},[902,15410,15411],{"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}",[724,15413,15414],{},[614,15415,15416,15417,15432,15433,1837],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,15418,15420],{"className":15419},[886],[888,15421,15422],{"xmlns":890},[892,15423,15424,15430],{},[895,15425,15426,15428],{},[898,15427,1742],{},[898,15429,1683],{},[902,15431,1817],{"encoding":904}," ležící nad minimem ",[883,15434,15436],{"className":15435},[886],[888,15437,15438],{"xmlns":890},[892,15439,15440,15448],{},[895,15441,15442,15444,15446],{},[898,15443,1735],{},[898,15445,1762],{},[898,15447,1683],{},[902,15449,1836],{"encoding":904},[115,15451,15453],{"id":15452},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,15455,15456,15457,15461,15462,15477,15478,15499,15500,1993,15503,15506,15507,15509,15510,15532,15533,15535,15536,1993,15538,5347,15541,1647,15544,2173,15559,15574],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,15458,15460],{"className":15459,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,15463,15465],{"className":15464},[886],[888,15466,15467],{"xmlns":890},[892,15468,15469,15475],{},[895,15470,15471,15473],{},[898,15472,1659],{},[898,15474,1662],{},[902,15476,1665],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,15479,15481],{"className":15480},[886],[888,15482,15483],{"xmlns":890},[892,15484,15485,15496],{},[895,15486,15487,15489,15491,15494],{},[898,15488,1659],{},[898,15490,1662],{},[898,15492,15493],{"mathvariant":2409},"\u002F",[898,15495,2146],{},[902,15497,15498],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,15501,15502],{},"fixních",[38,15504,15505],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,15508,10981],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,15511,15513],{"className":15512},[886],[888,15514,15515],{"xmlns":890},[892,15516,15517,15529],{},[895,15518,15519,15521,15523,15525,15527],{},[898,15520,1659],{},[898,15522,1662],{},[1706,15524,1715],{},[898,15526,1659],{},[898,15528,1683],{},[902,15530,15531],{"encoding":904},"TR - TC"," udává ",[38,15534,1690],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,15537,3061],{},[38,15539,15540],{},"mezní náklady",[207,15542,1145],{"className":15543,"dataFsResolvedFilePath":764,"href":765},[210],[883,15545,15547],{"className":15546},[886],[888,15548,15549],{"xmlns":890},[892,15550,15551,15557],{},[895,15552,15553,15555],{},[898,15554,1659],{},[898,15556,1662],{},[902,15558,1665],{"encoding":904},[883,15560,15562],{"className":15561},[886],[888,15563,15564],{"xmlns":890},[892,15565,15566,15572],{},[895,15567,15568,15570],{},[898,15569,1659],{},[898,15571,1683],{},[902,15573,1686],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,15576,15577,15639,15705,15767],{},[123,15578,15579,15582,15583,4521,15598,1837],{},[38,15580,15581],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,15584,15586],{"className":15585},[886],[888,15587,15588],{"xmlns":890},[892,15589,15590,15596],{},[895,15591,15592,15594],{},[898,15593,1735],{},[898,15595,1683],{},[902,15597,2094],{"encoding":904},[883,15599,15601],{"className":15600},[886],[888,15602,15603],{"xmlns":890},[892,15604,15605,15637],{},[895,15606,15607,15609,15611,15613,15619,15621,15623,15625,15627,15629,15635],{},[898,15608,1735],{},[898,15610,1683],{},[1706,15612,2140],{"stretchy":2139},[2142,15614,15615,15617],{},[898,15616,2146],{},[2148,15618,2150],{},[1706,15620,2153],{"stretchy":2139},[1706,15622,1708],{},[898,15624,1742],{},[898,15626,1683],{},[1706,15628,2140],{"stretchy":2139},[2142,15630,15631,15633],{},[898,15632,2146],{},[2148,15634,2150],{},[1706,15636,2153],{"stretchy":2139},[902,15638,9216],{"encoding":904},[123,15640,15641,15582,15644,4521,15661,1837],{},[38,15642,15643],{},"Princip minimalizace průměrných variabilních nákladů:",[883,15645,15647],{"className":15646},[886],[888,15648,15649],{"xmlns":890},[892,15650,15651,15659],{},[895,15652,15653,15655,15657],{},[898,15654,1735],{},[898,15656,1762],{},[898,15658,1683],{},[902,15660,1836],{"encoding":904},[883,15662,15664],{"className":15663},[886],[888,15665,15666],{"xmlns":890},[892,15667,15668,15702],{},[895,15669,15670,15672,15674,15676,15678,15684,15686,15688,15690,15692,15694,15700],{},[898,15671,1735],{},[898,15673,1762],{},[898,15675,1683],{},[1706,15677,2140],{"stretchy":2139},[2142,15679,15680,15682],{},[898,15681,2146],{},[2148,15683,2150],{},[1706,15685,2153],{"stretchy":2139},[1706,15687,1708],{},[898,15689,1742],{},[898,15691,1683],{},[1706,15693,2140],{"stretchy":2139},[2142,15695,15696,15698],{},[898,15697,2146],{},[2148,15699,2150],{},[1706,15701,2153],{"stretchy":2139},[902,15703,15704],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,15706,15707,15710,15711,4521,15726,1837],{},[38,15708,15709],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,15712,15714],{"className":15713},[886],[888,15715,15716],{"xmlns":890},[892,15717,15718,15724],{},[895,15719,15720,15722],{},[898,15721,1702],{},[898,15723,1662],{},[902,15725,10130],{"encoding":904},[883,15727,15729],{"className":15728},[886],[888,15730,15731],{"xmlns":890},[892,15732,15733,15765],{},[895,15734,15735,15737,15739,15741,15747,15749,15751,15753,15755,15757,15763],{},[898,15736,1742],{},[898,15738,1662],{},[1706,15740,2140],{"stretchy":2139},[2142,15742,15743,15745],{},[898,15744,2146],{},[2148,15746,2150],{},[1706,15748,2153],{"stretchy":2139},[1706,15750,1708],{},[898,15752,1742],{},[898,15754,1683],{},[1706,15756,2140],{"stretchy":2139},[2142,15758,15759,15761],{},[898,15760,2146],{},[2148,15762,2150],{},[1706,15764,2153],{"stretchy":2139},[902,15766,12307],{"encoding":904},[123,15768,15769,1647,15772,10691,15808,14605,15829,15842,15843,14286,15860,1837],{},[38,15770,15771],{},"Funkce nabídky firmy:",[883,15773,15775],{"className":15774},[886],[888,15776,15777],{"xmlns":890},[892,15778,15779,15805],{},[895,15780,15781,15783,15785,15787,15789,15791,15793,15795,15797,15799,15801,15803],{},[898,15782,1702],{},[1706,15784,1708],{},[898,15786,14171],{},[1706,15788,2140],{"stretchy":2139},[898,15790,2146],{},[1706,15792,2153],{"stretchy":2139},[1706,15794,1708],{},[898,15796,1742],{},[898,15798,1683],{},[1706,15800,2140],{"stretchy":2139},[898,15802,2146],{},[1706,15804,2153],{"stretchy":2139},[902,15806,15807],{"encoding":904},"P = S(Q) = MC(Q)",[883,15809,15811],{"className":15810},[886],[888,15812,15813],{"xmlns":890},[892,15814,15815,15827],{},[895,15816,15817,15819,15821],{},[898,15818,2146],{},[1706,15820,14220],{},[2489,15822,15823,15825],{},[898,15824,2146],{},[1706,15826,3197],{},[902,15828,14604],{"encoding":904},[883,15830,15832],{"className":15831},[886],[888,15833,15834],{"xmlns":890},[892,15835,15836,15840],{},[895,15837,15838],{},[2148,15839,2150],{},[902,15841,2150],{"encoding":904},", kde ",[883,15844,15846],{"className":15845},[886],[888,15847,15848],{"xmlns":890},[892,15849,15850,15858],{},[895,15851,15852],{},[2489,15853,15854,15856],{},[898,15855,2146],{},[1706,15857,3197],{},[902,15859,3221],{"encoding":904},[883,15861,15863],{"className":15862},[886],[888,15864,15865],{"xmlns":890},[892,15866,15867,15875],{},[895,15868,15869,15871,15873],{},[898,15870,1735],{},[898,15872,1762],{},[898,15874,1683],{},[902,15876,1836],{"encoding":904},[115,15878,15880],{"id":15879},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,15882,15883,15886,15889,15892,15895,15898,15901,15904,15907,15910,15913],{},[123,15884,15885],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,15887,15888],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,15890,15891],{},"Jak se vypočte mezní příjem a co udává?",[123,15893,15894],{},"Z jakých složek se skládají celkové náklady?",[123,15896,15897],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,15899,15900],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,15902,15903],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,15905,15906],{},"Jak se vypočte zisk?",[123,15908,15909],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,15911,15912],{},"Co jsou body zvratu? Jak se najdou?",[123,15914,15915],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,15917,15919],{"id":15918},"úlohy-31328","Úlohy 3.1–3.28",[198,15921,15923],{"id":15922},"příjem-3135","Příjem (3.1–3.5)",[724,15925,15926,15929,15930,15958,15959,15974,15975,15990,15991,16006,16007,1343,16022,1343,16037,16052],{},[38,15927,15928],{},"3.1"," Je dána poptávka ",[883,15931,15933],{"className":15932},[886],[888,15934,15935],{"xmlns":890},[892,15936,15937,15955],{},[895,15938,15939,15941,15943,15945,15947,15949,15951,15953],{},[898,15940,1702],{},[1706,15942,1708],{},[898,15944,2334],{},[1706,15946,2140],{"stretchy":2139},[898,15948,2146],{},[1706,15950,2153],{"stretchy":2139},[1706,15952,1708],{},[2148,15954,2590],{},[902,15956,15957],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,15960,15962],{"className":15961},[886],[888,15963,15964],{"xmlns":890},[892,15965,15966,15972],{},[895,15967,15968,15970],{},[898,15969,1659],{},[898,15971,1662],{},[902,15973,1665],{"encoding":904},", průměrný příjem ",[883,15976,15978],{"className":15977},[886],[888,15979,15980],{"xmlns":890},[892,15981,15982,15988],{},[895,15983,15984,15986],{},[898,15985,1735],{},[898,15987,1662],{},[902,15989,1977],{"encoding":904}," a mezní příjem ",[883,15992,15994],{"className":15993},[886],[888,15995,15996],{"xmlns":890},[892,15997,15998,16004],{},[895,15999,16000,16002],{},[898,16001,1742],{},[898,16003,1662],{},[902,16005,1905],{"encoding":904},". (c) Vypočtěte ",[883,16008,16010],{"className":16009},[886],[888,16011,16012],{"xmlns":890},[892,16013,16014,16020],{},[895,16015,16016,16018],{},[898,16017,1659],{},[898,16019,1662],{},[902,16021,1665],{"encoding":904},[883,16023,16025],{"className":16024},[886],[888,16026,16027],{"xmlns":890},[892,16028,16029,16035],{},[895,16030,16031,16033],{},[898,16032,1735],{},[898,16034,1662],{},[902,16036,1977],{"encoding":904},[883,16038,16040],{"className":16039},[886],[888,16041,16042],{"xmlns":890},[892,16043,16044,16050],{},[895,16045,16046,16048],{},[898,16047,1742],{},[898,16049,1662],{},[902,16051,1905],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,16054,16055,15929,16058,15958,16094,15974,16109,15990,16124,16006,16139,1343,16154,1343,16169,16184],{},[38,16056,16057],{},"3.2",[883,16059,16061],{"className":16060},[886],[888,16062,16063],{"xmlns":890},[892,16064,16065,16091],{},[895,16066,16067,16069,16071,16073,16075,16077,16079,16081,16083,16085,16087,16089],{},[898,16068,1702],{},[1706,16070,1708],{},[898,16072,2334],{},[1706,16074,2140],{"stretchy":2139},[898,16076,2146],{},[1706,16078,2153],{"stretchy":2139},[1706,16080,1708],{},[1706,16082,1715],{},[2148,16084,11496],{},[898,16086,2146],{},[1706,16088,2447],{},[2148,16090,3369],{},[902,16092,16093],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,16095,16097],{"className":16096},[886],[888,16098,16099],{"xmlns":890},[892,16100,16101,16107],{},[895,16102,16103,16105],{},[898,16104,1659],{},[898,16106,1662],{},[902,16108,1665],{"encoding":904},[883,16110,16112],{"className":16111},[886],[888,16113,16114],{"xmlns":890},[892,16115,16116,16122],{},[895,16117,16118,16120],{},[898,16119,1735],{},[898,16121,1662],{},[902,16123,1977],{"encoding":904},[883,16125,16127],{"className":16126},[886],[888,16128,16129],{"xmlns":890},[892,16130,16131,16137],{},[895,16132,16133,16135],{},[898,16134,1742],{},[898,16136,1662],{},[902,16138,1905],{"encoding":904},[883,16140,16142],{"className":16141},[886],[888,16143,16144],{"xmlns":890},[892,16145,16146,16152],{},[895,16147,16148,16150],{},[898,16149,1659],{},[898,16151,1662],{},[902,16153,1665],{"encoding":904},[883,16155,16157],{"className":16156},[886],[888,16158,16159],{"xmlns":890},[892,16160,16161,16167],{},[895,16162,16163,16165],{},[898,16164,1735],{},[898,16166,1662],{},[902,16168,1977],{"encoding":904},[883,16170,16172],{"className":16171},[886],[888,16173,16174],{"xmlns":890},[892,16175,16176,16182],{},[895,16177,16178,16180],{},[898,16179,1742],{},[898,16181,1662],{},[902,16183,1905],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,16186,16187,15929,16190,16227,16228,15974,16243,15990,16258,16273,16274,10691,16289,16315,16316,16331,16332,1343,16347,10691,16362,16315,16387,16402,16403,16416,16417,16432,16433,16448,16449,1343,16462,1343,16477,1343,16492,1837],{},[38,16188,16189],{},"3.3",[883,16191,16193],{"className":16192},[886],[888,16194,16195],{"xmlns":890},[892,16196,16197,16224],{},[895,16198,16199,16201,16203,16205,16207,16209,16211,16213,16216,16218],{},[898,16200,1702],{},[1706,16202,1708],{},[898,16204,2334],{},[1706,16206,2140],{"stretchy":2139},[898,16208,2146],{},[1706,16210,2153],{"stretchy":2139},[1706,16212,1708],{},[2148,16214,16215],{},"1200",[1706,16217,1715],{},[2489,16219,16220,16222],{},[898,16221,2146],{},[2148,16223,2495],{},[902,16225,16226],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,16229,16231],{"className":16230},[886],[888,16232,16233],{"xmlns":890},[892,16234,16235,16241],{},[895,16236,16237,16239],{},[898,16238,1659],{},[898,16240,1662],{},[902,16242,1665],{"encoding":904},[883,16244,16246],{"className":16245},[886],[888,16247,16248],{"xmlns":890},[892,16249,16250,16256],{},[895,16251,16252,16254],{},[898,16253,1735],{},[898,16255,1662],{},[902,16257,1977],{"encoding":904},[883,16259,16261],{"className":16260},[886],[888,16262,16263],{"xmlns":890},[892,16264,16265,16271],{},[895,16266,16267,16269],{},[898,16268,1742],{},[898,16270,1662],{},[902,16272,1905],{"encoding":904},". (b) Vypočtěte ",[883,16275,16277],{"className":16276},[886],[888,16278,16279],{"xmlns":890},[892,16280,16281,16287],{},[895,16282,16283,16285],{},[898,16284,1659],{},[898,16286,1662],{},[902,16288,1665],{"encoding":904},[883,16290,16292],{"className":16291},[886],[888,16293,16294],{"xmlns":890},[892,16295,16296,16312],{},[895,16297,16298,16300,16302,16304,16306,16308,16310],{},[898,16299,2146],{},[1706,16301,1708],{},[2148,16303,7786],{},[1706,16305,2505],{"separator":2504},[2148,16307,3369],{},[1706,16309,2505],{"separator":2504},[2148,16311,12556],{},[902,16313,16314],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,16317,16319],{"className":16318},[886],[888,16320,16321],{"xmlns":890},[892,16322,16323,16329],{},[895,16324,16325,16327],{},[898,16326,1659],{},[898,16328,1662],{},[902,16330,1665],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,16333,16335],{"className":16334},[886],[888,16336,16337],{"xmlns":890},[892,16338,16339,16345],{},[895,16340,16341,16343],{},[898,16342,1735],{},[898,16344,1662],{},[902,16346,1977],{"encoding":904},[883,16348,16350],{"className":16349},[886],[888,16351,16352],{"xmlns":890},[892,16353,16354,16360],{},[895,16355,16356,16358],{},[898,16357,1742],{},[898,16359,1662],{},[902,16361,1905],{"encoding":904},[883,16363,16365],{"className":16364},[886],[888,16366,16367],{"xmlns":890},[892,16368,16369,16385],{},[895,16370,16371,16373,16375,16377,16379,16381,16383],{},[898,16372,2146],{},[1706,16374,1708],{},[2148,16376,7786],{},[1706,16378,2505],{"separator":2504},[2148,16380,3369],{},[1706,16382,2505],{"separator":2504},[2148,16384,12556],{},[902,16386,16314],{"encoding":904},[883,16388,16390],{"className":16389},[886],[888,16391,16392],{"xmlns":890},[892,16393,16394,16400],{},[895,16395,16396,16398],{},[898,16397,1742],{},[898,16399,1662],{},[902,16401,1905],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,16404,16406],{"className":16405},[886],[888,16407,16408],{"xmlns":890},[892,16409,16410,16414],{},[895,16411,16412],{},[898,16413,2146],{},[902,16415,2146],{"encoding":904},", které maximalizuje ",[883,16418,16420],{"className":16419},[886],[888,16421,16422],{"xmlns":890},[892,16423,16424,16430],{},[895,16425,16426,16428],{},[898,16427,1659],{},[898,16429,1662],{},[902,16431,1665],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,16434,16436],{"className":16435},[886],[888,16437,16438],{"xmlns":890},[892,16439,16440,16446],{},[895,16441,16442,16444],{},[898,16443,1659],{},[898,16445,1662],{},[902,16447,1665],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,16450,16452],{"className":16451},[886],[888,16453,16454],{"xmlns":890},[892,16455,16456,16460],{},[895,16457,16458],{},[898,16459,2334],{},[902,16461,2334],{"encoding":904},[883,16463,16465],{"className":16464},[886],[888,16466,16467],{"xmlns":890},[892,16468,16469,16475],{},[895,16470,16471,16473],{},[898,16472,1659],{},[898,16474,1662],{},[902,16476,1665],{"encoding":904},[883,16478,16480],{"className":16479},[886],[888,16481,16482],{"xmlns":890},[892,16483,16484,16490],{},[895,16485,16486,16488],{},[898,16487,1735],{},[898,16489,1662],{},[902,16491,1977],{"encoding":904},[883,16493,16495],{"className":16494},[886],[888,16496,16497],{"xmlns":890},[892,16498,16499,16505],{},[895,16500,16501,16503],{},[898,16502,1742],{},[898,16504,1662],{},[902,16506,1905],{"encoding":904},[724,16508,16509,16512,16513,16543,16544,16559,16560,16573,16574,1343,16592,1343,16610,16628,16629,16651,16652,16667,16668,16681,16682,1837],{},[38,16510,16511],{},"3.4"," Je dán celkový příjem ",[883,16514,16516],{"className":16515},[886],[888,16517,16518],{"xmlns":890},[892,16519,16520,16540],{},[895,16521,16522,16524,16526,16528,16530,16532,16534],{},[898,16523,1659],{},[898,16525,1662],{},[1706,16527,1708],{},[2148,16529,16215],{},[898,16531,2146],{},[1706,16533,1715],{},[2489,16535,16536,16538],{},[898,16537,2146],{},[2148,16539,4284],{},[902,16541,16542],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,16545,16547],{"className":16546},[886],[888,16548,16549],{"xmlns":890},[892,16550,16551,16557],{},[895,16552,16553,16555],{},[898,16554,1659],{},[898,16556,1662],{},[902,16558,1665],{"encoding":904}," vzhledem ke ",[883,16561,16563],{"className":16562},[886],[888,16564,16565],{"xmlns":890},[892,16566,16567,16571],{},[895,16568,16569],{},[898,16570,2146],{},[902,16572,2146],{"encoding":904}," při ",[883,16575,16577],{"className":16576},[886],[888,16578,16579],{"xmlns":890},[892,16580,16581,16589],{},[895,16582,16583,16585,16587],{},[898,16584,2146],{},[1706,16586,1708],{},[2148,16588,7524],{},[902,16590,16591],{"encoding":904},"Q = 5",[883,16593,16595],{"className":16594},[886],[888,16596,16597],{"xmlns":890},[892,16598,16599,16607],{},[895,16600,16601,16603,16605],{},[898,16602,2146],{},[1706,16604,1708],{},[2148,16606,12717],{},[902,16608,16609],{"encoding":904},"Q = 8",[883,16611,16613],{"className":16612},[886],[888,16614,16615],{"xmlns":890},[892,16616,16617,16625],{},[895,16618,16619,16621,16623],{},[898,16620,2146],{},[1706,16622,1708],{},[2148,16624,7156],{},[902,16626,16627],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,16630,16632],{"className":16631},[886],[888,16633,16634],{"xmlns":890},[892,16635,16636,16648],{},[895,16637,16638,16640,16642,16644,16646],{},[898,16639,1742],{},[898,16641,1662],{},[1706,16643,2140],{"stretchy":2139},[2148,16645,7786],{},[1706,16647,2153],{"stretchy":2139},[902,16649,16650],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,16653,16655],{"className":16654},[886],[888,16656,16657],{"xmlns":890},[892,16658,16659,16665],{},[895,16660,16661,16663],{},[898,16662,1659],{},[898,16664,1662],{},[902,16666,1665],{"encoding":904},", jestliže se ",[883,16669,16671],{"className":16670},[886],[888,16672,16673],{"xmlns":890},[892,16674,16675,16679],{},[895,16676,16677],{},[898,16678,2146],{},[902,16680,2146],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,16683,16685],{"className":16684},[886],[888,16686,16687],{"xmlns":890},[892,16688,16689,16695],{},[895,16690,16691,16693],{},[898,16692,1659],{},[898,16694,1662],{},[902,16696,1665],{"encoding":904},[724,16698,16699,16702,16703,16729,16730,16745,16746,16667,16761,16774],{},[38,16700,16701],{},"3.5"," Je dán mezní příjem ",[883,16704,16706],{"className":16705},[886],[888,16707,16708],{"xmlns":890},[892,16709,16710,16726],{},[895,16711,16712,16714,16716,16718,16720,16722,16724],{},[898,16713,1742],{},[898,16715,1662],{},[1706,16717,1708],{},[1706,16719,1715],{},[898,16721,2146],{},[1706,16723,2447],{},[2148,16725,3369],{},[902,16727,16728],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,16731,16733],{"className":16732},[886],[888,16734,16735],{"xmlns":890},[892,16736,16737,16743],{},[895,16738,16739,16741],{},[898,16740,1659],{},[898,16742,1662],{},[902,16744,1665],{"encoding":904},". (b) Vypočtěte změnu ",[883,16747,16749],{"className":16748},[886],[888,16750,16751],{"xmlns":890},[892,16752,16753,16759],{},[895,16754,16755,16757],{},[898,16756,1659],{},[898,16758,1662],{},[902,16760,1665],{"encoding":904},[883,16762,16764],{"className":16763},[886],[888,16765,16766],{"xmlns":890},[892,16767,16768,16772],{},[895,16769,16770],{},[898,16771,2146],{},[902,16773,2146],{"encoding":904}," změní z 8 na 12.",[198,16776,16778],{"id":16777},"náklady-36316","Náklady (3.6–3.16)",[724,16780,16781,16784,16785,16825,16826,16841,16842,16859,16860,16877,16878,16893,16894,16909,16910,16273,16925,1343,16940,1343,16957,1343,16974,1343,16989,1343,17004,10691,17019,17037,17038,1343,17053,1343,17068,17083],{},[38,16782,16783],{},"3.6"," Jsou dány celkové náklady ",[883,16786,16788],{"className":16787},[886],[888,16789,16790],{"xmlns":890},[892,16791,16792,16822],{},[895,16793,16794,16796,16798,16800,16802,16804,16806,16808,16810],{},[898,16795,1659],{},[898,16797,1683],{},[1706,16799,1708],{},[2148,16801,2590],{},[1706,16803,2447],{},[2148,16805,2495],{},[898,16807,2146],{},[1706,16809,2447],{},[4745,16811,16812],{"scriptlevel":2150,"displaystyle":2139},[2964,16813,16814,16820],{},[2489,16815,16816,16818],{},[898,16817,2146],{},[2148,16819,2495],{},[2148,16821,7786],{},[902,16823,16824],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,16827,16829],{"className":16828},[886],[888,16830,16831],{"xmlns":890},[892,16832,16833,16839],{},[895,16834,16835,16837],{},[898,16836,2020],{},[898,16838,1683],{},[902,16840,2025],{"encoding":904},", celkové variabilní náklady ",[883,16843,16845],{"className":16844},[886],[888,16846,16847],{"xmlns":890},[892,16848,16849,16857],{},[895,16850,16851,16853,16855],{},[898,16852,1659],{},[898,16854,1762],{},[898,16856,1683],{},[902,16858,2043],{"encoding":904},", průměrné variabilní náklady ",[883,16861,16863],{"className":16862},[886],[888,16864,16865],{"xmlns":890},[892,16866,16867,16875],{},[895,16868,16869,16871,16873],{},[898,16870,1735],{},[898,16872,1762],{},[898,16874,1683],{},[902,16876,1836],{"encoding":904},", variabilní náklady na jednotku ",[883,16879,16881],{"className":16880},[886],[888,16882,16883],{"xmlns":890},[892,16884,16885,16891],{},[895,16886,16887,16889],{},[898,16888,1762],{},[898,16890,1683],{},[902,16892,10257],{"encoding":904},", průměrné náklady ",[883,16895,16897],{"className":16896},[886],[888,16898,16899],{"xmlns":890},[892,16900,16901,16907],{},[895,16902,16903,16905],{},[898,16904,1735],{},[898,16906,1683],{},[902,16908,2094],{"encoding":904}," a mezní náklady ",[883,16911,16913],{"className":16912},[886],[888,16914,16915],{"xmlns":890},[892,16916,16917,16923],{},[895,16918,16919,16921],{},[898,16920,1742],{},[898,16922,1683],{},[902,16924,1817],{"encoding":904},[883,16926,16928],{"className":16927},[886],[888,16929,16930],{"xmlns":890},[892,16931,16932,16938],{},[895,16933,16934,16936],{},[898,16935,1659],{},[898,16937,1683],{},[902,16939,1686],{"encoding":904},[883,16941,16943],{"className":16942},[886],[888,16944,16945],{"xmlns":890},[892,16946,16947,16955],{},[895,16948,16949,16951,16953],{},[898,16950,1659],{},[898,16952,1762],{},[898,16954,1683],{},[902,16956,2043],{"encoding":904},[883,16958,16960],{"className":16959},[886],[888,16961,16962],{"xmlns":890},[892,16963,16964,16972],{},[895,16965,16966,16968,16970],{},[898,16967,1735],{},[898,16969,1762],{},[898,16971,1683],{},[902,16973,1836],{"encoding":904},[883,16975,16977],{"className":16976},[886],[888,16978,16979],{"xmlns":890},[892,16980,16981,16987],{},[895,16982,16983,16985],{},[898,16984,1762],{},[898,16986,1683],{},[902,16988,10257],{"encoding":904},[883,16990,16992],{"className":16991},[886],[888,16993,16994],{"xmlns":890},[892,16995,16996,17002],{},[895,16997,16998,17000],{},[898,16999,1735],{},[898,17001,1683],{},[902,17003,2094],{"encoding":904},[883,17005,17007],{"className":17006},[886],[888,17008,17009],{"xmlns":890},[892,17010,17011,17017],{},[895,17012,17013,17015],{},[898,17014,1742],{},[898,17016,1683],{},[902,17018,1817],{"encoding":904},[883,17020,17022],{"className":17021},[886],[888,17023,17024],{"xmlns":890},[892,17025,17026,17034],{},[895,17027,17028,17030,17032],{},[898,17029,2146],{},[1706,17031,1708],{},[2148,17033,2728],{},[902,17035,17036],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,17039,17041],{"className":17040},[886],[888,17042,17043],{"xmlns":890},[892,17044,17045,17051],{},[895,17046,17047,17049],{},[898,17048,1659],{},[898,17050,1683],{},[902,17052,1686],{"encoding":904},[883,17054,17056],{"className":17055},[886],[888,17057,17058],{"xmlns":890},[892,17059,17060,17066],{},[895,17061,17062,17064],{},[898,17063,1735],{},[898,17065,1683],{},[902,17067,2094],{"encoding":904},[883,17069,17071],{"className":17070},[886],[888,17072,17073],{"xmlns":890},[892,17074,17075,17081],{},[895,17076,17077,17079],{},[898,17078,1742],{},[898,17080,1683],{},[902,17082,1817],{"encoding":904}," rostou, resp. klesají.",[724,17085,17086,17089,17090,16909,17120,17135,17136,17151,17152,1343,17167,1343,17182,1837],{},[38,17087,17088],{},"3.7"," Jsou dány průměrné náklady ",[883,17091,17093],{"className":17092},[886],[888,17094,17095],{"xmlns":890},[892,17096,17097,17117],{},[895,17098,17099,17101,17103,17105,17113,17115],{},[898,17100,1735],{},[898,17102,1683],{},[1706,17104,1708],{},[4745,17106,17107],{"scriptlevel":2150,"displaystyle":2139},[2964,17108,17109,17111],{},[2148,17110,2590],{},[898,17112,2146],{},[1706,17114,2447],{},[2148,17116,3369],{},[902,17118,17119],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,17121,17123],{"className":17122},[886],[888,17124,17125],{"xmlns":890},[892,17126,17127,17133],{},[895,17128,17129,17131],{},[898,17130,1742],{},[898,17132,1683],{},[902,17134,1817],{"encoding":904},". (a) Určete celkové náklady ",[883,17137,17139],{"className":17138},[886],[888,17140,17141],{"xmlns":890},[892,17142,17143,17149],{},[895,17144,17145,17147],{},[898,17146,1659],{},[898,17148,1683],{},[902,17150,1686],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,17153,17155],{"className":17154},[886],[888,17156,17157],{"xmlns":890},[892,17158,17159,17165],{},[895,17160,17161,17163],{},[898,17162,1735],{},[898,17164,1683],{},[902,17166,2094],{"encoding":904},[883,17168,17170],{"className":17169},[886],[888,17171,17172],{"xmlns":890},[892,17173,17174,17180],{},[895,17175,17176,17178],{},[898,17177,1659],{},[898,17179,1683],{},[902,17181,1686],{"encoding":904},[883,17183,17185],{"className":17184},[886],[888,17186,17187],{"xmlns":890},[892,17188,17189,17195],{},[895,17190,17191,17193],{},[898,17192,1742],{},[898,17194,1683],{},[902,17196,1817],{"encoding":904},[724,17198,17199,16784,17202,17247,17248,1343,17265,1343,17280,1343,17297,1343,17312,1343,17329,1837],{},[38,17200,17201],{},"3.8",[883,17203,17205],{"className":17204},[886],[888,17206,17207],{"xmlns":890},[892,17208,17209,17244],{},[895,17210,17211,17213,17215,17217,17220,17222,17224,17226,17228,17230,17236,17238],{},[898,17212,1659],{},[898,17214,1683],{},[1706,17216,1708],{},[2148,17218,17219],{},"80",[1706,17221,2447],{},[2148,17223,12556],{},[898,17225,2146],{},[1706,17227,1715],{},[2148,17229,7044],{},[2489,17231,17232,17234],{},[898,17233,2146],{},[2148,17235,2495],{},[1706,17237,2447],{},[2489,17239,17240,17242],{},[898,17241,2146],{},[2148,17243,4284],{},[902,17245,17246],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,17249,17251],{"className":17250},[886],[888,17252,17253],{"xmlns":890},[892,17254,17255,17263],{},[895,17256,17257,17259,17261],{},[898,17258,1659],{},[898,17260,1762],{},[898,17262,1683],{},[902,17264,2043],{"encoding":904},[883,17266,17268],{"className":17267},[886],[888,17269,17270],{"xmlns":890},[892,17271,17272,17278],{},[895,17273,17274,17276],{},[898,17275,2020],{},[898,17277,1683],{},[902,17279,2025],{"encoding":904},[883,17281,17283],{"className":17282},[886],[888,17284,17285],{"xmlns":890},[892,17286,17287,17295],{},[895,17288,17289,17291,17293],{},[898,17290,1735],{},[898,17292,1762],{},[898,17294,1683],{},[902,17296,1836],{"encoding":904},[883,17298,17300],{"className":17299},[886],[888,17301,17302],{"xmlns":890},[892,17303,17304,17310],{},[895,17305,17306,17308],{},[898,17307,1735],{},[898,17309,1683],{},[902,17311,2094],{"encoding":904},[883,17313,17315],{"className":17314},[886],[888,17316,17317],{"xmlns":890},[892,17318,17319,17327],{},[895,17320,17321,17323,17325],{},[898,17322,1735],{},[898,17324,2020],{},[898,17326,1683],{},[902,17328,2061],{"encoding":904},[883,17330,17332],{"className":17331},[886],[888,17333,17334],{"xmlns":890},[892,17335,17336,17342],{},[895,17337,17338,17340],{},[898,17339,1742],{},[898,17341,1683],{},[902,17343,1817],{"encoding":904},[724,17345,17346,16784,17349,17380,17381,16559,17396,10691,17409,1343,17427,1343,17445,16628,17463,16651,17485,17500,17501,17514,17515,1837],{},[38,17347,17348],{},"3.9",[883,17350,17352],{"className":17351},[886],[888,17353,17354],{"xmlns":890},[892,17355,17356,17377],{},[895,17357,17358,17360,17362,17364,17367,17369,17371],{},[898,17359,1659],{},[898,17361,1683],{},[1706,17363,1708],{},[2148,17365,17366],{},"500",[1706,17368,2447],{},[2148,17370,13775],{},[2489,17372,17373,17375],{},[898,17374,2146],{},[2148,17376,2495],{},[902,17378,17379],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,17382,17384],{"className":17383},[886],[888,17385,17386],{"xmlns":890},[892,17387,17388,17394],{},[895,17389,17390,17392],{},[898,17391,1659],{},[898,17393,1683],{},[902,17395,1686],{"encoding":904},[883,17397,17399],{"className":17398},[886],[888,17400,17401],{"xmlns":890},[892,17402,17403,17407],{},[895,17404,17405],{},[898,17406,2146],{},[902,17408,2146],{"encoding":904},[883,17410,17412],{"className":17411},[886],[888,17413,17414],{"xmlns":890},[892,17415,17416,17424],{},[895,17417,17418,17420,17422],{},[898,17419,2146],{},[1706,17421,1708],{},[2148,17423,7786],{},[902,17425,17426],{"encoding":904},"Q = 10",[883,17428,17430],{"className":17429},[886],[888,17431,17432],{"xmlns":890},[892,17433,17434,17442],{},[895,17435,17436,17438,17440],{},[898,17437,2146],{},[1706,17439,1708],{},[2148,17441,3369],{},[902,17443,17444],{"encoding":904},"Q = 20",[883,17446,17448],{"className":17447},[886],[888,17449,17450],{"xmlns":890},[892,17451,17452,17460],{},[895,17453,17454,17456,17458],{},[898,17455,2146],{},[1706,17457,1708],{},[2148,17459,12556],{},[902,17461,17462],{"encoding":904},"Q = 30",[883,17464,17466],{"className":17465},[886],[888,17467,17468],{"xmlns":890},[892,17469,17470,17482],{},[895,17471,17472,17474,17476,17478,17480],{},[898,17473,1742],{},[898,17475,1683],{},[1706,17477,2140],{"stretchy":2139},[2148,17479,3359],{},[1706,17481,2153],{"stretchy":2139},[902,17483,17484],{"encoding":904},"MC(15)",[883,17486,17488],{"className":17487},[886],[888,17489,17490],{"xmlns":890},[892,17491,17492,17498],{},[895,17493,17494,17496],{},[898,17495,1659],{},[898,17497,1683],{},[902,17499,1686],{"encoding":904}," v důsledku změny ",[883,17502,17504],{"className":17503},[886],[888,17505,17506],{"xmlns":890},[892,17507,17508,17512],{},[895,17509,17510],{},[898,17511,2146],{},[902,17513,2146],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,17516,17518],{"className":17517},[886],[888,17519,17520],{"xmlns":890},[892,17521,17522,17528],{},[895,17523,17524,17526],{},[898,17525,1659],{},[898,17527,1683],{},[902,17529,1686],{"encoding":904},[724,17531,17532,17535,17536,17135,17572,17587,17588,16745,17607,17500,17622,17635],{},[38,17533,17534],{},"3.10"," Jsou dány mezní náklady ",[883,17537,17539],{"className":17538},[886],[888,17540,17541],{"xmlns":890},[892,17542,17543,17569],{},[895,17544,17545,17547,17549,17551,17553,17555,17557,17559,17561,17563],{},[898,17546,1742],{},[898,17548,1683],{},[1706,17550,1708],{},[2148,17552,4199],{},[1706,17554,1715],{},[2148,17556,3364],{},[898,17558,2146],{},[1706,17560,2447],{},[2148,17562,11218],{},[2489,17564,17565,17567],{},[898,17566,2146],{},[2148,17568,2495],{},[902,17570,17571],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,17573,17575],{"className":17574},[886],[888,17576,17577],{"xmlns":890},[892,17578,17579,17585],{},[895,17580,17581,17583],{},[898,17582,1659],{},[898,17584,1683],{},[902,17586,1686],{"encoding":904},", jestliže fixní náklady ",[883,17589,17591],{"className":17590},[886],[888,17592,17593],{"xmlns":890},[892,17594,17595,17605],{},[895,17596,17597,17599,17601,17603],{},[898,17598,2020],{},[898,17600,1683],{},[1706,17602,1708],{},[2148,17604,2590],{},[902,17606,8022],{"encoding":904},[883,17608,17610],{"className":17609},[886],[888,17611,17612],{"xmlns":890},[892,17613,17614,17620],{},[895,17615,17616,17618],{},[898,17617,1659],{},[898,17619,1683],{},[902,17621,1686],{"encoding":904},[883,17623,17625],{"className":17624},[886],[888,17626,17627],{"xmlns":890},[892,17628,17629,17633],{},[895,17630,17631],{},[898,17632,2146],{},[902,17634,2146],{"encoding":904}," z 15 na 20.",[724,17637,17638,16784,17641,17684,17685,17698,17699,17714,17715,17730,17731,17698,17744,17714,17761,17778,17779,17698,17792,17714,17807,17822,17823,17843,17844,17868],{},[38,17639,17640],{},"3.11",[883,17642,17644],{"className":17643},[886],[888,17645,17646],{"xmlns":890},[892,17647,17648,17682],{},[895,17649,17650,17652,17654,17656,17658,17660,17662,17664,17666,17668,17674,17676],{},[898,17651,1659],{},[898,17653,1683],{},[1706,17655,1708],{},[2148,17657,2590],{},[1706,17659,2447],{},[2148,17661,2748],{},[898,17663,2146],{},[1706,17665,1715],{},[2148,17667,7524],{},[2489,17669,17670,17672],{},[898,17671,2146],{},[2148,17673,2495],{},[1706,17675,2447],{},[2489,17677,17678,17680],{},[898,17679,2146],{},[2148,17681,4284],{},[902,17683,7541],{"encoding":904},". (a) Určete ",[883,17686,17688],{"className":17687},[886],[888,17689,17690],{"xmlns":890},[892,17691,17692,17696],{},[895,17693,17694],{},[898,17695,2146],{},[902,17697,2146],{"encoding":904},", které minimalizuje ",[883,17700,17702],{"className":17701},[886],[888,17703,17704],{"xmlns":890},[892,17705,17706,17712],{},[895,17707,17708,17710],{},[898,17709,1742],{},[898,17711,1683],{},[902,17713,1817],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,17716,17718],{"className":17717},[886],[888,17719,17720],{"xmlns":890},[892,17721,17722,17728],{},[895,17723,17724,17726],{},[898,17725,1742],{},[898,17727,1683],{},[902,17729,1817],{"encoding":904},". (b) Určete ",[883,17732,17734],{"className":17733},[886],[888,17735,17736],{"xmlns":890},[892,17737,17738,17742],{},[895,17739,17740],{},[898,17741,2146],{},[902,17743,2146],{"encoding":904},[883,17745,17747],{"className":17746},[886],[888,17748,17749],{"xmlns":890},[892,17750,17751,17759],{},[895,17752,17753,17755,17757],{},[898,17754,1735],{},[898,17756,1762],{},[898,17758,1683],{},[902,17760,1836],{"encoding":904},[883,17762,17764],{"className":17763},[886],[888,17765,17766],{"xmlns":890},[892,17767,17768,17776],{},[895,17769,17770,17772,17774],{},[898,17771,1735],{},[898,17773,1762],{},[898,17775,1683],{},[902,17777,1836],{"encoding":904},". (c) Určete ",[883,17780,17782],{"className":17781},[886],[888,17783,17784],{"xmlns":890},[892,17785,17786,17790],{},[895,17787,17788],{},[898,17789,2146],{},[902,17791,2146],{"encoding":904},[883,17793,17795],{"className":17794},[886],[888,17796,17797],{"xmlns":890},[892,17798,17799,17805],{},[895,17800,17801,17803],{},[898,17802,1735],{},[898,17804,1683],{},[902,17806,2094],{"encoding":904},[883,17808,17810],{"className":17809},[886],[888,17811,17812],{"xmlns":890},[892,17813,17814,17820],{},[895,17815,17816,17818],{},[898,17817,1735],{},[898,17819,1683],{},[902,17821,2094],{"encoding":904}," (rada: hledaný kořen ",[883,17824,17826],{"className":17825},[886],[888,17827,17828],{"xmlns":890},[892,17829,17830,17840],{},[895,17831,17832,17834],{},[898,17833,1735],{},[2489,17835,17836,17838],{},[898,17837,1683],{},[1706,17839,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,17841,17842],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,17845,17847],{"className":17846},[886],[888,17848,17849],{"xmlns":890},[892,17850,17851,17865],{},[895,17852,17853,17855,17858,17860,17863],{},[1706,17854,2140],{"stretchy":2139},[2148,17856,17857],{},"4,7",[1706,17859,2110],{"separator":2504},[2148,17861,17862],{},"4,8",[1706,17864,2153],{"stretchy":2139},[902,17866,17867],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,17870,17871,17874,17875,2891,17903,17920,17921,15842,17962,17983],{},[38,17872,17873],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,17876,17878],{"className":17877},[886],[888,17879,17880],{"xmlns":890},[892,17881,17882,17900],{},[895,17883,17884,17886,17888,17890,17892,17894,17896,17898],{},[898,17885,1735],{},[898,17887,1683],{},[1706,17889,1708],{},[898,17891,1735],{},[898,17893,1683],{},[1706,17895,2140],{"stretchy":2139},[898,17897,2146],{},[1706,17899,2153],{"stretchy":2139},[902,17901,17902],{"encoding":904},"AC = AC(Q)",[883,17904,17906],{"className":17905},[886],[888,17907,17908],{"xmlns":890},[892,17909,17910,17918],{},[895,17911,17912],{},[2142,17913,17914,17916],{},[898,17915,2146],{},[2148,17917,2150],{},[902,17919,8625],{"encoding":904}," minimum, pak platí ",[883,17922,17924],{"className":17923},[886],[888,17925,17926],{"xmlns":890},[892,17927,17928,17960],{},[895,17929,17930,17932,17934,17936,17942,17944,17946,17948,17950,17952,17958],{},[898,17931,1735],{},[898,17933,1683],{},[1706,17935,2140],{"stretchy":2139},[2142,17937,17938,17940],{},[898,17939,2146],{},[2148,17941,2150],{},[1706,17943,2153],{"stretchy":2139},[1706,17945,1708],{},[898,17947,1742],{},[898,17949,1683],{},[1706,17951,2140],{"stretchy":2139},[2142,17953,17954,17956],{},[898,17955,2146],{},[2148,17957,2150],{},[1706,17959,2153],{"stretchy":2139},[902,17961,9216],{"encoding":904},[883,17963,17965],{"className":17964},[886],[888,17966,17967],{"xmlns":890},[892,17968,17969,17981],{},[895,17970,17971,17973,17975,17977,17979],{},[898,17972,1742],{},[898,17974,1683],{},[1706,17976,2140],{"stretchy":2139},[898,17978,2146],{},[1706,17980,2153],{"stretchy":2139},[902,17982,14373],{"encoding":904}," jsou mezní náklady.",[724,17985,17986,16784,17989,17247,18023,17698,18036,17714,18051,1837],{},[38,17987,17988],{},"3.13",[883,17990,17992],{"className":17991},[886],[888,17993,17994],{"xmlns":890},[892,17995,17996,18020],{},[895,17997,17998,18000,18002,18004,18010,18012,18014,18016,18018],{},[898,17999,1659],{},[898,18001,1683],{},[1706,18003,1708],{},[2489,18005,18006,18008],{},[898,18007,2146],{},[2148,18009,2495],{},[1706,18011,2447],{},[2148,18013,2495],{},[898,18015,2146],{},[1706,18017,2447],{},[2148,18019,2748],{},[902,18021,18022],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,18024,18026],{"className":18025},[886],[888,18027,18028],{"xmlns":890},[892,18029,18030,18034],{},[895,18031,18032],{},[898,18033,2146],{},[902,18035,2146],{"encoding":904},[883,18037,18039],{"className":18038},[886],[888,18040,18041],{"xmlns":890},[892,18042,18043,18049],{},[895,18044,18045,18047],{},[898,18046,1735],{},[898,18048,1683],{},[902,18050,2094],{"encoding":904},[883,18052,18054],{"className":18053},[886],[888,18055,18056],{"xmlns":890},[892,18057,18058,18064],{},[895,18059,18060,18062],{},[898,18061,1735],{},[898,18063,1683],{},[902,18065,2094],{"encoding":904},[724,18067,18068,18071,18072,2891,18104,17920,18121,15842,18164,17983],{},[38,18069,18070],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,18073,18075],{"className":18074},[886],[888,18076,18077],{"xmlns":890},[892,18078,18079,18101],{},[895,18080,18081,18083,18085,18087,18089,18091,18093,18095,18097,18099],{},[898,18082,1735],{},[898,18084,1762],{},[898,18086,1683],{},[1706,18088,1708],{},[898,18090,1735],{},[898,18092,1762],{},[898,18094,1683],{},[1706,18096,2140],{"stretchy":2139},[898,18098,2146],{},[1706,18100,2153],{"stretchy":2139},[902,18102,18103],{"encoding":904},"AVC = AVC(Q)",[883,18105,18107],{"className":18106},[886],[888,18108,18109],{"xmlns":890},[892,18110,18111,18119],{},[895,18112,18113],{},[2142,18114,18115,18117],{},[898,18116,2146],{},[2148,18118,2150],{},[902,18120,8625],{"encoding":904},[883,18122,18124],{"className":18123},[886],[888,18125,18126],{"xmlns":890},[892,18127,18128,18162],{},[895,18129,18130,18132,18134,18136,18138,18144,18146,18148,18150,18152,18154,18160],{},[898,18131,1735],{},[898,18133,1762],{},[898,18135,1683],{},[1706,18137,2140],{"stretchy":2139},[2142,18139,18140,18142],{},[898,18141,2146],{},[2148,18143,2150],{},[1706,18145,2153],{"stretchy":2139},[1706,18147,1708],{},[898,18149,1742],{},[898,18151,1683],{},[1706,18153,2140],{"stretchy":2139},[2142,18155,18156,18158],{},[898,18157,2146],{},[2148,18159,2150],{},[1706,18161,2153],{"stretchy":2139},[902,18163,15704],{"encoding":904},[883,18165,18167],{"className":18166},[886],[888,18168,18169],{"xmlns":890},[892,18170,18171,18183],{},[895,18172,18173,18175,18177,18179,18181],{},[898,18174,1742],{},[898,18176,1683],{},[1706,18178,2140],{"stretchy":2139},[898,18180,2146],{},[1706,18182,2153],{"stretchy":2139},[902,18184,14373],{"encoding":904},[724,18186,18187,16784,18190,17247,18236,17698,18249,17714,18266,1837],{},[38,18188,18189],{},"3.15",[883,18191,18193],{"className":18192},[886],[888,18194,18195],{"xmlns":890},[892,18196,18197,18233],{},[895,18198,18199,18201,18203,18205,18207,18209,18211,18213,18215,18217,18223,18225,18227],{},[898,18200,1659],{},[898,18202,1683],{},[1706,18204,1708],{},[2148,18206,2728],{},[1706,18208,2447],{},[2148,18210,3359],{},[898,18212,2146],{},[1706,18214,1715],{},[2148,18216,2495],{},[2489,18218,18219,18221],{},[898,18220,2146],{},[2148,18222,2495],{},[1706,18224,2447],{},[2148,18226,15204],{},[2489,18228,18229,18231],{},[898,18230,2146],{},[2148,18232,4284],{},[902,18234,18235],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,18237,18239],{"className":18238},[886],[888,18240,18241],{"xmlns":890},[892,18242,18243,18247],{},[895,18244,18245],{},[898,18246,2146],{},[902,18248,2146],{"encoding":904},[883,18250,18252],{"className":18251},[886],[888,18253,18254],{"xmlns":890},[892,18255,18256,18264],{},[895,18257,18258,18260,18262],{},[898,18259,1735],{},[898,18261,1762],{},[898,18263,1683],{},[902,18265,1836],{"encoding":904},[883,18267,18269],{"className":18268},[886],[888,18270,18271],{"xmlns":890},[892,18272,18273,18281],{},[895,18274,18275,18277,18279],{},[898,18276,1735],{},[898,18278,1762],{},[898,18280,1683],{},[902,18282,1836],{"encoding":904},[724,18284,18285,18288,18289,18303,18304,18324],{},[38,18286,18287],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,18290,18292],{"className":18291},[886],[888,18293,18294],{"xmlns":890},[892,18295,18296,18301],{},[895,18297,18298],{},[898,18299,18300],{},"x",[902,18302,18300],{"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 ",[883,18305,18307],{"className":18306},[886],[888,18308,18309],{"xmlns":890},[892,18310,18311,18321],{},[895,18312,18313,18315,18317,18319],{},[2148,18314,7786],{},[2415,18316,2799],{},[2148,18318,5705],{},[898,18320,18300],{},[902,18322,18323],{"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.",[198,18326,18328],{"id":18327},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,18330,18331,18334,18335,1993,18357,18383],{},[38,18332,18333],{},"3.17"," Jsou dány ",[883,18336,18338],{"className":18337},[886],[888,18339,18340],{"xmlns":890},[892,18341,18342,18354],{},[895,18343,18344,18346,18348,18350,18352],{},[898,18345,1659],{},[898,18347,1662],{},[1706,18349,1708],{},[2148,18351,7786],{},[898,18353,2146],{},[902,18355,18356],{"encoding":904},"TR = 10Q",[883,18358,18360],{"className":18359},[886],[888,18361,18362],{"xmlns":890},[892,18363,18364,18380],{},[895,18365,18366,18368,18370,18372,18374,18376,18378],{},[898,18367,1659],{},[898,18369,1683],{},[1706,18371,1708],{},[2148,18373,2590],{},[1706,18375,2447],{},[2148,18377,7524],{},[898,18379,2146],{},[902,18381,18382],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,18385,18386,18389,18390,8156,18405,18420,18421,1343,18443,15842,18471,18493,18494,18528],{},[38,18387,18388],{},"3.18"," Odvoďte, že jestliže ",[883,18391,18393],{"className":18392},[886],[888,18394,18395],{"xmlns":890},[892,18396,18397,18403],{},[895,18398,18399,18401],{},[898,18400,1659],{},[898,18402,1662],{},[902,18404,1665],{"encoding":904},[883,18406,18408],{"className":18407},[886],[888,18409,18410],{"xmlns":890},[892,18411,18412,18418],{},[895,18413,18414,18416],{},[898,18415,1659],{},[898,18417,1683],{},[902,18419,1686],{"encoding":904}," jsou lineární tvaru ",[883,18422,18424],{"className":18423},[886],[888,18425,18426],{"xmlns":890},[892,18427,18428,18440],{},[895,18429,18430,18432,18434,18436,18438],{},[898,18431,1659],{},[898,18433,1662],{},[1706,18435,1708],{},[898,18437,724],{},[898,18439,2146],{},[902,18441,18442],{"encoding":904},"TR = pQ",[883,18444,18446],{"className":18445},[886],[888,18447,18448],{"xmlns":890},[892,18449,18450,18468],{},[895,18451,18452,18454,18456,18458,18461,18463,18466],{},[898,18453,1659],{},[898,18455,1683],{},[1706,18457,1708],{},[898,18459,18460],{},"m",[1706,18462,2447],{},[898,18464,18465],{},"n",[898,18467,2146],{},[902,18469,18470],{"encoding":904},"TC = m + nQ",[883,18472,18474],{"className":18473},[886],[888,18475,18476],{"xmlns":890},[892,18477,18478,18490],{},[895,18479,18480,18482,18484,18486,18488],{},[898,18481,18460],{},[1706,18483,2505],{"separator":2504},[898,18485,18465],{},[1706,18487,2505],{"separator":2504},[898,18489,724],{},[902,18491,18492],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,18495,18497],{"className":18496},[886],[888,18498,18499],{"xmlns":890},[892,18500,18501,18525],{},[895,18502,18503,18509,18511],{},[2489,18504,18505,18507],{},[898,18506,2146],{},[1706,18508,3197],{},[1706,18510,1708],{},[4745,18512,18513],{"scriptlevel":2150,"displaystyle":2139},[2964,18514,18515,18517],{},[898,18516,18460],{},[895,18518,18519,18521,18523],{},[898,18520,724],{},[1706,18522,1715],{},[898,18524,18465],{},[902,18526,18527],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,18530,18531,18334,18534,1993,18568,17684,18594,18607,18608,16432,18623,18638,18639,16416,18652,16432,18667,18682],{},[38,18532,18533],{},"3.19",[883,18535,18537],{"className":18536},[886],[888,18538,18539],{"xmlns":890},[892,18540,18541,18565],{},[895,18542,18543,18545,18547,18549,18551,18553,18559,18561,18563],{},[898,18544,1659],{},[898,18546,1662],{},[1706,18548,1708],{},[1706,18550,1715],{},[2148,18552,2495],{},[2489,18554,18555,18557],{},[898,18556,2146],{},[2148,18558,2495],{},[1706,18560,2447],{},[2148,18562,12859],{},[898,18564,2146],{},[902,18566,18567],{"encoding":904},"TR = -2Q^2 + 14Q",[883,18569,18571],{"className":18570},[886],[888,18572,18573],{"xmlns":890},[892,18574,18575,18591],{},[895,18576,18577,18579,18581,18583,18585,18587,18589],{},[898,18578,1659],{},[898,18580,1683],{},[1706,18582,1708],{},[2148,18584,2495],{},[898,18586,2146],{},[1706,18588,2447],{},[2148,18590,7786],{},[902,18592,18593],{"encoding":904},"TC = 2Q + 10",[883,18595,18597],{"className":18596},[886],[888,18598,18599],{"xmlns":890},[892,18600,18601,18605],{},[895,18602,18603],{},[898,18604,2146],{},[902,18606,2146],{"encoding":904},", které maximalizuje zisk ",[883,18609,18611],{"className":18610},[886],[888,18612,18613],{"xmlns":890},[892,18614,18615,18621],{},[895,18616,18617,18619],{},[898,18618,1702],{},[898,18620,1662],{},[902,18622,10130],{"encoding":904},[883,18624,18626],{"className":18625},[886],[888,18627,18628],{"xmlns":890},[892,18629,18630,18636],{},[895,18631,18632,18634],{},[898,18633,1702],{},[898,18635,1662],{},[902,18637,10130],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,18640,18642],{"className":18641},[886],[888,18643,18644],{"xmlns":890},[892,18645,18646,18650],{},[895,18647,18648],{},[898,18649,2146],{},[902,18651,2146],{"encoding":904},[883,18653,18655],{"className":18654},[886],[888,18656,18657],{"xmlns":890},[892,18658,18659,18665],{},[895,18660,18661,18663],{},[898,18662,1659],{},[898,18664,1662],{},[902,18666,1665],{"encoding":904},[883,18668,18670],{"className":18669},[886],[888,18671,18672],{"xmlns":890},[892,18673,18674,18680],{},[895,18675,18676,18678],{},[898,18677,1659],{},[898,18679,1662],{},[902,18681,1665],{"encoding":904},". (d) Graficky interpretujte.",[724,18684,18685,18688,18689,1343,18715,1343,18734,17684,18754,18607,18767,16432,18782,18797,18798,18820,18821,17868],{},[38,18686,18687],{},"3.20"," Jsou dány poptávka ",[883,18690,18692],{"className":18691},[886],[888,18693,18694],{"xmlns":890},[892,18695,18696,18712],{},[895,18697,18698,18700,18702,18704,18706],{},[898,18699,1702],{},[1706,18701,1708],{},[2148,18703,4361],{},[1706,18705,1715],{},[2489,18707,18708,18710],{},[898,18709,2146],{},[2148,18711,2495],{},[902,18713,18714],{"encoding":904},"P = 400 - Q^2",[883,18716,18718],{"className":18717},[886],[888,18719,18720],{"xmlns":890},[892,18721,18722,18732],{},[895,18723,18724,18726,18728,18730],{},[898,18725,2020],{},[898,18727,1683],{},[1706,18729,1708],{},[2148,18731,2590],{},[902,18733,8022],{"encoding":904},[883,18735,18737],{"className":18736},[886],[888,18738,18739],{"xmlns":890},[892,18740,18741,18751],{},[895,18742,18743,18745,18747,18749],{},[898,18744,1742],{},[898,18746,1683],{},[1706,18748,1708],{},[2148,18750,3369],{},[902,18752,18753],{"encoding":904},"MC = 20",[883,18755,18757],{"className":18756},[886],[888,18758,18759],{"xmlns":890},[892,18760,18761,18765],{},[895,18762,18763],{},[898,18764,2146],{},[902,18766,2146],{"encoding":904},[883,18768,18770],{"className":18769},[886],[888,18771,18772],{"xmlns":890},[892,18773,18774,18780],{},[895,18775,18776,18778],{},[898,18777,1702],{},[898,18779,1662],{},[902,18781,10130],{"encoding":904},[883,18783,18785],{"className":18784},[886],[888,18786,18787],{"xmlns":890},[892,18788,18789,18795],{},[895,18790,18791,18793],{},[898,18792,1702],{},[898,18794,1662],{},[902,18796,10130],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,18799,18801],{"className":18800},[886],[888,18802,18803],{"xmlns":890},[892,18804,18805,18817],{},[895,18806,18807,18809,18811,18813,18815],{},[1706,18808,2140],{"stretchy":2139},[2148,18810,2150],{},[1706,18812,2505],{"separator":2504},[2148,18814,2701],{},[1706,18816,2153],{"stretchy":2139},[902,18818,18819],{"encoding":904},"(0, 1)",", druhý do ",[883,18822,18824],{"className":18823},[886],[888,18825,18826],{"xmlns":890},[892,18827,18828,18841],{},[895,18829,18830,18832,18835,18837,18839],{},[1706,18831,2140],{"stretchy":2139},[2148,18833,18834],{},"19",[1706,18836,2505],{"separator":2504},[2148,18838,3369],{},[1706,18840,2153],{"stretchy":2139},[902,18842,18843],{"encoding":904},"(19, 20)",[724,18845,18846,18849,18850,2891,18878,18895,18896,1837],{},[38,18847,18848],{},"3.21"," Dokažte, že má-li zisk ",[883,18851,18853],{"className":18852},[886],[888,18854,18855],{"xmlns":890},[892,18856,18857,18875],{},[895,18858,18859,18861,18863,18865,18867,18869,18871,18873],{},[898,18860,1702],{},[898,18862,1662],{},[1706,18864,1708],{},[898,18866,1702],{},[898,18868,1662],{},[1706,18870,2140],{"stretchy":2139},[898,18872,2146],{},[1706,18874,2153],{"stretchy":2139},[902,18876,18877],{"encoding":904},"PR = PR(Q)",[883,18879,18881],{"className":18880},[886],[888,18882,18883],{"xmlns":890},[892,18884,18885,18893],{},[895,18886,18887],{},[2142,18888,18889,18891],{},[898,18890,2146],{},[2148,18892,2150],{},[902,18894,8625],{"encoding":904}," maximum, pak platí ",[883,18897,18899],{"className":18898},[886],[888,18900,18901],{"xmlns":890},[892,18902,18903,18935],{},[895,18904,18905,18907,18909,18911,18917,18919,18921,18923,18925,18927,18933],{},[898,18906,1742],{},[898,18908,1662],{},[1706,18910,2140],{"stretchy":2139},[2142,18912,18913,18915],{},[898,18914,2146],{},[2148,18916,2150],{},[1706,18918,2153],{"stretchy":2139},[1706,18920,1708],{},[898,18922,1742],{},[898,18924,1683],{},[1706,18926,2140],{"stretchy":2139},[2142,18928,18929,18931],{},[898,18930,2146],{},[2148,18932,2150],{},[1706,18934,2153],{"stretchy":2139},[902,18936,12307],{"encoding":904},[724,18938,18939,18942,18943,1993,18958,2594,18973,18607,18986,19001,19002,1343,19029,19067,19068,1343,19095,1837],{},[38,18940,18941],{},"3.22"," Pro zadané ",[883,18944,18946],{"className":18945},[886],[888,18947,18948],{"xmlns":890},[892,18949,18950,18956],{},[895,18951,18952,18954],{},[898,18953,1742],{},[898,18955,1662],{},[902,18957,1905],{"encoding":904},[883,18959,18961],{"className":18960},[886],[888,18962,18963],{"xmlns":890},[892,18964,18965,18971],{},[895,18966,18967,18969],{},[898,18968,1742],{},[898,18970,1683],{},[902,18972,1817],{"encoding":904},[883,18974,18976],{"className":18975},[886],[888,18977,18978],{"xmlns":890},[892,18979,18980,18984],{},[895,18981,18982],{},[898,18983,2146],{},[902,18985,2146],{"encoding":904},[883,18987,18989],{"className":18988},[886],[888,18990,18991],{"xmlns":890},[892,18992,18993,18999],{},[895,18994,18995,18997],{},[898,18996,1702],{},[898,18998,1662],{},[902,19000,10130],{"encoding":904},". (a) ",[883,19003,19005],{"className":19004},[886],[888,19006,19007],{"xmlns":890},[892,19008,19009,19026],{},[895,19010,19011,19013,19015,19017,19020,19022,19024],{},[898,19012,1742],{},[898,19014,1662],{},[1706,19016,1708],{},[2148,19018,19019],{},"236",[1706,19021,1715],{},[2148,19023,3364],{},[898,19025,2146],{},[902,19027,19028],{"encoding":904},"MR = 236 - 16Q",[883,19030,19032],{"className":19031},[886],[888,19033,19034],{"xmlns":890},[892,19035,19036,19064],{},[895,19037,19038,19040,19042,19044,19046,19052,19054,19057,19059,19061],{},[898,19039,1742],{},[898,19041,1683],{},[1706,19043,1708],{},[2148,19045,4284],{},[2489,19047,19048,19050],{},[898,19049,2146],{},[2148,19051,2495],{},[1706,19053,1715],{},[2148,19055,19056],{},"32",[898,19058,2146],{},[1706,19060,2447],{},[2148,19062,19063],{},"96",[902,19065,19066],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,19069,19071],{"className":19070},[886],[888,19072,19073],{"xmlns":890},[892,19074,19075,19092],{},[895,19076,19077,19079,19081,19083,19086,19088,19090],{},[898,19078,1742],{},[898,19080,1662],{},[1706,19082,1708],{},[2148,19084,19085],{},"280",[1706,19087,1715],{},[2148,19089,3369],{},[898,19091,2146],{},[902,19093,19094],{"encoding":904},"MR = 280 - 20Q",[883,19096,19098],{"className":19097},[886],[888,19099,19100],{"xmlns":890},[892,19101,19102,19129],{},[895,19103,19104,19106,19108,19110,19113,19119,19121,19123,19125,19127],{},[898,19105,1742],{},[898,19107,1683],{},[1706,19109,1708],{},[2148,19111,19112],{},"1,6",[2489,19114,19115,19117],{},[898,19116,2146],{},[2148,19118,2495],{},[1706,19120,1715],{},[2148,19122,3359],{},[898,19124,2146],{},[1706,19126,2447],{},[2148,19128,4199],{},[902,19130,19131],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,19133,19134,18942,19137,1993,19152,2594,19167,16416,19180,16432,19195,19001,19210,1343,19241,19067,19277,1343,19309,19353,19354,1343,19387,1837],{},[38,19135,19136],{},"3.23",[883,19138,19140],{"className":19139},[886],[888,19141,19142],{"xmlns":890},[892,19143,19144,19150],{},[895,19145,19146,19148],{},[898,19147,1659],{},[898,19149,1662],{},[902,19151,1665],{"encoding":904},[883,19153,19155],{"className":19154},[886],[888,19156,19157],{"xmlns":890},[892,19158,19159,19165],{},[895,19160,19161,19163],{},[898,19162,1659],{},[898,19164,1683],{},[902,19166,1686],{"encoding":904},[883,19168,19170],{"className":19169},[886],[888,19171,19172],{"xmlns":890},[892,19173,19174,19178],{},[895,19175,19176],{},[898,19177,2146],{},[902,19179,2146],{"encoding":904},[883,19181,19183],{"className":19182},[886],[888,19184,19185],{"xmlns":890},[892,19186,19187,19193],{},[895,19188,19189,19191],{},[898,19190,1702],{},[898,19192,1662],{},[902,19194,10130],{"encoding":904},[883,19196,19198],{"className":19197},[886],[888,19199,19200],{"xmlns":890},[892,19201,19202,19208],{},[895,19203,19204,19206],{},[898,19205,1702],{},[898,19207,1662],{},[902,19209,10130],{"encoding":904},[883,19211,19213],{"className":19212},[886],[888,19214,19215],{"xmlns":890},[892,19216,19217,19238],{},[895,19218,19219,19221,19223,19225,19228,19230,19232],{},[898,19220,1659],{},[898,19222,1662],{},[1706,19224,1708],{},[2148,19226,19227],{},"125",[898,19229,2146],{},[1706,19231,1715],{},[2489,19233,19234,19236],{},[898,19235,2146],{},[2148,19237,2495],{},[902,19239,19240],{"encoding":904},"TR = 125Q - Q^2",[883,19242,19244],{"className":19243},[886],[888,19245,19246],{"xmlns":890},[892,19247,19248,19274],{},[895,19249,19250,19252,19254,19256,19258,19260,19262,19264,19266,19268],{},[898,19251,1659],{},[898,19253,1683],{},[1706,19255,1708],{},[2148,19257,17366],{},[1706,19259,2447],{},[2148,19261,7524],{},[898,19263,2146],{},[1706,19265,2447],{},[2148,19267,11496],{},[2489,19269,19270,19272],{},[898,19271,2146],{},[2148,19273,2495],{},[902,19275,19276],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,19278,19280],{"className":19279},[886],[888,19281,19282],{"xmlns":890},[892,19283,19284,19306],{},[895,19285,19286,19288,19290,19292,19294,19296,19298,19300],{},[898,19287,1659],{},[898,19289,1662],{},[1706,19291,1708],{},[2148,19293,3369],{},[898,19295,2146],{},[1706,19297,1715],{},[2148,19299,2495],{},[2489,19301,19302,19304],{},[898,19303,2146],{},[2148,19305,2495],{},[902,19307,19308],{"encoding":904},"TR = 20Q - 2Q^2",[883,19310,19312],{"className":19311},[886],[888,19313,19314],{"xmlns":890},[892,19315,19316,19350],{},[895,19317,19318,19320,19322,19324,19326,19328,19330,19332,19334,19336,19342,19344],{},[898,19319,1659],{},[898,19321,1683],{},[1706,19323,1708],{},[2148,19325,2495],{},[1706,19327,2447],{},[2148,19329,3369],{},[898,19331,2146],{},[1706,19333,1715],{},[2148,19335,12717],{},[2489,19337,19338,19340],{},[898,19339,2146],{},[2148,19341,2495],{},[1706,19343,2447],{},[2489,19345,19346,19348],{},[898,19347,2146],{},[2148,19349,4284],{},[902,19351,19352],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,19355,19357],{"className":19356},[886],[888,19358,19359],{"xmlns":890},[892,19360,19361,19384],{},[895,19362,19363,19365,19367,19369,19371,19373,19375,19378],{},[898,19364,1659],{},[898,19366,1662],{},[1706,19368,1708],{},[2148,19370,3455],{},[898,19372,2146],{},[1706,19374,1715],{},[2148,19376,19377],{},"0,25",[2489,19379,19380,19382],{},[898,19381,2146],{},[2148,19383,2495],{},[902,19385,19386],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,19388,19390],{"className":19389},[886],[888,19391,19392],{"xmlns":890},[892,19393,19394,19442],{},[895,19395,19396,19398,19400,19402,19404,19406,19408,19410,19412,19428,19430],{},[898,19397,1659],{},[898,19399,1683],{},[1706,19401,1708],{},[2148,19403,3455],{},[1706,19405,2447],{},[2148,19407,2495],{},[898,19409,2146],{},[1706,19411,1715],{},[4745,19413,19414],{"scriptlevel":2150,"displaystyle":2139},[2964,19415,19416,19426],{},[895,19417,19418,19420],{},[2148,19419,4284],{},[2489,19421,19422,19424],{},[898,19423,2146],{},[2148,19425,2495],{},[2148,19427,7786],{},[1706,19429,2447],{},[4745,19431,19432],{"scriptlevel":2150,"displaystyle":2139},[2964,19433,19434,19440],{},[2489,19435,19436,19438],{},[898,19437,2146],{},[2148,19439,4284],{},[2148,19441,3369],{},[902,19443,19444],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,19446,19447,19450,19451,19481,19482,19515,19516,15842,19546,19576],{},[38,19448,19449],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,19452,19454],{"className":19453},[886],[888,19455,19456],{"xmlns":890},[892,19457,19458,19478],{},[895,19459,19460,19466,19468,19470,19472],{},[2142,19461,19462,19464],{},[898,19463,1702],{},[2148,19465,2701],{},[1706,19467,1708],{},[2148,19469,17366],{},[1706,19471,1715],{},[2142,19473,19474,19476],{},[898,19475,2146],{},[2148,19477,2701],{},[902,19479,19480],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,19483,19485],{"className":19484},[886],[888,19486,19487],{"xmlns":890},[892,19488,19489,19512],{},[895,19490,19491,19497,19499,19502,19504,19506],{},[2142,19492,19493,19495],{},[898,19494,1702],{},[2148,19496,2495],{},[1706,19498,1708],{},[2148,19500,19501],{},"300",[1706,19503,1715],{},[2148,19505,11218],{},[2142,19507,19508,19510],{},[898,19509,2146],{},[2148,19511,2495],{},[902,19513,19514],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,19517,19519],{"className":19518},[886],[888,19520,19521],{"xmlns":890},[892,19522,19523,19543],{},[895,19524,19525,19527,19529,19531,19533,19535,19537,19539,19541],{},[898,19526,1659],{},[898,19528,1683],{},[1706,19530,1708],{},[2148,19532,2728],{},[2415,19534,2799],{},[2148,19536,5705],{},[1706,19538,2447],{},[2148,19540,3369],{},[898,19542,2146],{},[902,19544,19545],{"encoding":904},"TC = 50\\,000 + 20Q",[883,19547,19549],{"className":19548},[886],[888,19550,19551],{"xmlns":890},[892,19552,19553,19573],{},[895,19554,19555,19557,19559,19565,19567],{},[898,19556,2146],{},[1706,19558,1708],{},[2142,19560,19561,19563],{},[898,19562,2146],{},[2148,19564,2701],{},[1706,19566,2447],{},[2142,19568,19569,19571],{},[898,19570,2146],{},[2148,19572,2495],{},[902,19574,19575],{"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.",[724,19578,19579,19582,19583,19613,19614,19515,19646,15842,19676,19705],{},[38,19580,19581],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,19584,19586],{"className":19585},[886],[888,19587,19588],{"xmlns":890},[892,19589,19590,19610],{},[895,19591,19592,19598,19600,19602,19604],{},[2142,19593,19594,19596],{},[898,19595,1702],{},[2148,19597,2701],{},[1706,19599,1708],{},[2148,19601,19501],{},[1706,19603,1715],{},[2142,19605,19606,19608],{},[898,19607,2146],{},[2148,19609,2701],{},[902,19611,19612],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,19615,19617],{"className":19616},[886],[888,19618,19619],{"xmlns":890},[892,19620,19621,19643],{},[895,19622,19623,19629,19631,19633,19635,19637],{},[2142,19624,19625,19627],{},[898,19626,1702],{},[2148,19628,2495],{},[1706,19630,1708],{},[2148,19632,7039],{},[1706,19634,1715],{},[2148,19636,11496],{},[2142,19638,19639,19641],{},[898,19640,2146],{},[2148,19642,2495],{},[902,19644,19645],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,19647,19649],{"className":19648},[886],[888,19650,19651],{"xmlns":890},[892,19652,19653,19673],{},[895,19654,19655,19657,19659,19661,19663,19665,19667,19669,19671],{},[898,19656,1659],{},[898,19658,1683],{},[1706,19660,1708],{},[2148,19662,7524],{},[2415,19664,2799],{},[2148,19666,5705],{},[1706,19668,2447],{},[2148,19670,2590],{},[898,19672,2146],{},[902,19674,19675],{"encoding":904},"TC = 5\\,000 + 100Q",[883,19677,19679],{"className":19678},[886],[888,19680,19681],{"xmlns":890},[892,19682,19683,19703],{},[895,19684,19685,19687,19689,19695,19697],{},[898,19686,2146],{},[1706,19688,1708],{},[2142,19690,19691,19693],{},[898,19692,2146],{},[2148,19694,2701],{},[1706,19696,2447],{},[2142,19698,19699,19701],{},[898,19700,2146],{},[2148,19702,2495],{},[902,19704,19575],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,19707,19709],{"id":19708},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,19711,19712,19715,19716,19763,19764,19781],{},[38,19713,19714],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,19717,19719],{"className":19718},[886],[888,19720,19721],{"xmlns":890},[892,19722,19723,19760],{},[895,19724,19725,19727,19729,19731,19733,19736,19742,19744,19747,19753,19755,19758],{},[898,19726,1659],{},[898,19728,1762],{},[898,19730,1683],{},[1706,19732,1708],{},[2148,19734,19735],{},"0,85",[2489,19737,19738,19740],{},[898,19739,2146],{},[2148,19741,4284],{},[1706,19743,1715],{},[2148,19745,19746],{},"11,9",[2489,19748,19749,19751],{},[898,19750,2146],{},[2148,19752,2495],{},[1706,19754,2447],{},[2148,19756,19757],{},"102",[898,19759,2146],{},[902,19761,19762],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,19765,19767],{"className":19766},[886],[888,19768,19769],{"xmlns":890},[892,19770,19771,19779],{},[895,19772,19773],{},[2489,19774,19775,19777],{},[898,19776,1702],{},[1706,19778,3197],{},[902,19780,14075],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,19783,19784,17535,19787,19824],{},[38,19785,19786],{},"3.27",[883,19788,19790],{"className":19789},[886],[888,19791,19792],{"xmlns":890},[892,19793,19794,19821],{},[895,19795,19796,19798,19800,19802,19805,19811,19813,19815,19817,19819],{},[898,19797,1742],{},[898,19799,1683],{},[1706,19801,1708],{},[2148,19803,19804],{},"4,2",[2489,19806,19807,19809],{},[898,19808,2146],{},[2148,19810,2495],{},[1706,19812,1715],{},[2148,19814,11098],{},[898,19816,2146],{},[1706,19818,2447],{},[2148,19820,2802],{},[902,19822,19823],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,19826,19827,16784,19830,19824],{},[38,19828,19829],{},"3.28",[883,19831,19833],{"className":19832},[886],[888,19834,19835],{"xmlns":890},[892,19836,19837,19873],{},[895,19838,19839,19841,19843,19845,19847,19853,19855,19857,19863,19865,19867,19869,19871],{},[898,19840,1659],{},[898,19842,1683],{},[1706,19844,1708],{},[2148,19846,11496],{},[2489,19848,19849,19851],{},[898,19850,2146],{},[2148,19852,4284],{},[1706,19854,1715],{},[2148,19856,12597],{},[2489,19858,19859,19861],{},[898,19860,2146],{},[2148,19862,2495],{},[1706,19864,2447],{},[2148,19866,4199],{},[898,19868,2146],{},[1706,19870,2447],{},[2148,19872,17366],{},[902,19874,19875],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,19877,19879],{"id":19878},"klíčové-pojmy","Klíčové pojmy",[120,19881,19882,19910,19955,20027,20092,20132,20224,20330,20370,20485,20578,20642,20674,20734,20740,20804,20854,20908,21016,21074],{},[123,19883,19884,1647,19886,19909],{},[38,19885,2295],{},[883,19887,19889],{"className":19888},[886],[888,19890,19891],{"xmlns":890},[892,19892,19893,19907],{},[895,19894,19895,19897,19899,19901,19903,19905],{},[898,19896,1659],{},[898,19898,1662],{},[1706,19900,1708],{},[898,19902,1702],{},[1706,19904,2390],{},[898,19906,2146],{},[902,19908,13382],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,19911,19912,1647,19914,19954],{},[38,19913,2912],{},[883,19915,19917],{"className":19916},[886],[888,19918,19919],{"xmlns":890},[892,19920,19921,19951],{},[895,19922,19923,19925,19927,19929,19941,19943,19945,19947,19949],{},[898,19924,1735],{},[898,19926,1662],{},[1706,19928,1708],{},[4745,19930,19931],{"scriptlevel":2150,"displaystyle":2139},[2964,19932,19933,19939],{},[895,19934,19935,19937],{},[898,19936,1659],{},[898,19938,1662],{},[898,19940,2146],{},[1706,19942,1708],{},[898,19944,2334],{},[1706,19946,2140],{"stretchy":2139},[898,19948,2146],{},[1706,19950,2153],{"stretchy":2139},[902,19952,19953],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,19956,19957,1647,19959,19995,19996,20011,20012,1837],{},[38,19958,3061],{},[883,19960,19962],{"className":19961},[886],[888,19963,19964],{"xmlns":890},[892,19965,19966,19992],{},[895,19967,19968,19970,19972,19974],{},[898,19969,1742],{},[898,19971,1662],{},[1706,19973,1708],{},[4745,19975,19976],{"scriptlevel":2150,"displaystyle":2139},[2964,19977,19978,19986],{},[895,19979,19980,19982,19984],{},[898,19981,3120],{"mathvariant":2409},[898,19983,1659],{},[898,19985,1662],{},[895,19987,19988,19990],{},[898,19989,3120],{"mathvariant":2409},[898,19991,2146],{},[902,19993,19994],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,19997,19999],{"className":19998},[886],[888,20000,20001],{"xmlns":890},[892,20002,20003,20009],{},[895,20004,20005,20007],{},[898,20006,1659],{},[898,20008,1662],{},[902,20010,1665],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,20013,20015],{"className":20014},[886],[888,20016,20017],{"xmlns":890},[892,20018,20019,20025],{},[895,20020,20021,20023],{},[898,20022,1735],{},[898,20024,1662],{},[902,20026,1977],{"encoding":904},[123,20028,20029,1647,20032,1343,20062,1837],{},[38,20030,20031],{},"Diferenciál příjmu\u002Fnákladů",[883,20033,20035],{"className":20034},[886],[888,20036,20037],{"xmlns":890},[892,20038,20039,20059],{},[895,20040,20041,20043,20045,20047,20049,20051,20053,20055,20057],{},[898,20042,3677],{"mathvariant":2409},[898,20044,1659],{},[898,20046,1662],{},[1706,20048,3248],{},[898,20050,1742],{},[898,20052,1662],{},[2415,20054,2799],{},[898,20056,3120],{"mathvariant":2409},[898,20058,2146],{},[902,20060,20061],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,20063,20065],{"className":20064},[886],[888,20066,20067],{"xmlns":890},[892,20068,20069,20089],{},[895,20070,20071,20073,20075,20077,20079,20081,20083,20085,20087],{},[898,20072,3677],{"mathvariant":2409},[898,20074,1659],{},[898,20076,1683],{},[1706,20078,3248],{},[898,20080,1742],{},[898,20082,1683],{},[2415,20084,2799],{},[898,20086,3120],{"mathvariant":2409},[898,20088,2146],{},[902,20090,20091],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,20093,20094,1647,20096,1837],{},[38,20095,5226],{},[883,20097,20099],{"className":20098},[886],[888,20100,20101],{"xmlns":890},[892,20102,20103,20129],{},[895,20104,20105,20107,20109,20111,20113,20115,20117,20119,20121,20123,20125,20127],{},[898,20106,1659],{},[898,20108,1683],{},[1706,20110,1708],{},[898,20112,2020],{},[898,20114,1683],{},[1706,20116,2447],{},[898,20118,1659],{},[898,20120,1762],{},[898,20122,1683],{},[1706,20124,2140],{"stretchy":2139},[898,20126,2146],{},[1706,20128,2153],{"stretchy":2139},[902,20130,20131],{"encoding":904},"TC = FC + TVC(Q)",[123,20133,20134,1647,20137,1343,20152,1647,20154,1343,20177,1647,20180,1837],{},[38,20135,20136],{},"Fixní náklady",[883,20138,20140],{"className":20139},[886],[888,20141,20142],{"xmlns":890},[892,20143,20144,20150],{},[895,20145,20146,20148],{},[898,20147,2020],{},[898,20149,1683],{},[902,20151,2025],{"encoding":904},[38,20153,5381],{},[883,20155,20157],{"className":20156},[886],[888,20158,20159],{"xmlns":890},[892,20160,20161,20175],{},[895,20162,20163,20165,20167,20169,20171,20173],{},[898,20164,1659],{},[898,20166,1762],{},[898,20168,1683],{},[1706,20170,2140],{"stretchy":2139},[898,20172,2146],{},[1706,20174,2153],{"stretchy":2139},[902,20176,5378],{"encoding":904},[38,20178,20179],{},"variabilní náklady na jednotku",[883,20181,20183],{"className":20182},[886],[888,20184,20185],{"xmlns":890},[892,20186,20187,20221],{},[895,20188,20189,20191,20193,20195,20197,20199,20201],{},[898,20190,1762],{},[898,20192,1683],{},[1706,20194,2140],{"stretchy":2139},[898,20196,2146],{},[1706,20198,2153],{"stretchy":2139},[1706,20200,1708],{},[4745,20202,20203],{"scriptlevel":2150,"displaystyle":2139},[2964,20204,20205,20219],{},[895,20206,20207,20209,20211,20213,20215,20217],{},[898,20208,1659],{},[898,20210,1762],{},[898,20212,1683],{},[1706,20214,2140],{"stretchy":2139},[898,20216,2146],{},[1706,20218,2153],{"stretchy":2139},[898,20220,2146],{},[902,20222,20223],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,20225,20226,1647,20228,1343,20258,1647,20261,1343,20293,1647,20296,1837],{},[38,20227,5389],{},[883,20229,20231],{"className":20230},[886],[888,20232,20233],{"xmlns":890},[892,20234,20235,20255],{},[895,20236,20237,20239,20241,20243],{},[898,20238,1735],{},[898,20240,1683],{},[1706,20242,1708],{},[4745,20244,20245],{"scriptlevel":2150,"displaystyle":2139},[2964,20246,20247,20253],{},[895,20248,20249,20251],{},[898,20250,1659],{},[898,20252,1683],{},[898,20254,2146],{},[902,20256,20257],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,20259,20260],{},"průměrné fixní",[883,20262,20264],{"className":20263},[886],[888,20265,20266],{"xmlns":890},[892,20267,20268,20290],{},[895,20269,20270,20272,20274,20276,20278],{},[898,20271,1735],{},[898,20273,2020],{},[898,20275,1683],{},[1706,20277,1708],{},[4745,20279,20280],{"scriptlevel":2150,"displaystyle":2139},[2964,20281,20282,20288],{},[895,20283,20284,20286],{},[898,20285,2020],{},[898,20287,1683],{},[898,20289,2146],{},[902,20291,20292],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,20294,20295],{},"průměrné variabilní",[883,20297,20299],{"className":20298},[886],[888,20300,20301],{"xmlns":890},[892,20302,20303,20327],{},[895,20304,20305,20307,20309,20311,20313],{},[898,20306,1735],{},[898,20308,1762],{},[898,20310,1683],{},[1706,20312,1708],{},[4745,20314,20315],{"scriptlevel":2150,"displaystyle":2139},[2964,20316,20317,20325],{},[895,20318,20319,20321,20323],{},[898,20320,1659],{},[898,20322,1762],{},[898,20324,1683],{},[898,20326,2146],{},[902,20328,20329],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,20331,20332,1647,20334,1837],{},[38,20333,6582],{},[883,20335,20337],{"className":20336},[886],[888,20338,20339],{"xmlns":890},[892,20340,20341,20367],{},[895,20342,20343,20345,20347,20349],{},[898,20344,1742],{},[898,20346,1683],{},[1706,20348,1708],{},[4745,20350,20351],{"scriptlevel":2150,"displaystyle":2139},[2964,20352,20353,20361],{},[895,20354,20355,20357,20359],{},[898,20356,3120],{"mathvariant":2409},[898,20358,1659],{},[898,20360,1683],{},[895,20362,20363,20365],{},[898,20364,3120],{"mathvariant":2409},[898,20366,2146],{},[902,20368,20369],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,20371,20372,1647,20374,20423,20424,20437,20438,1343,20453,1343,20470,1837],{},[38,20373,7485],{},[883,20375,20377],{"className":20376},[886],[888,20378,20379],{"xmlns":890},[892,20380,20381,20420],{},[895,20382,20383,20385,20387,20389,20391,20393,20395,20397,20399,20401,20403,20409,20411,20414],{},[898,20384,1659],{},[898,20386,1683],{},[1706,20388,1708],{},[898,20390,2020],{},[898,20392,1683],{},[1706,20394,2447],{},[898,20396,207],{},[898,20398,2146],{},[1706,20400,2447],{},[898,20402,2450],{},[2489,20404,20405,20407],{},[898,20406,2146],{},[2148,20408,2495],{},[1706,20410,2447],{},[898,20412,20413],{},"c",[2489,20415,20416,20418],{},[898,20417,2146],{},[2148,20419,4284],{},[902,20421,20422],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,20425,20427],{"className":20426},[886],[888,20428,20429],{"xmlns":890},[892,20430,20431,20435],{},[895,20432,20433],{},[898,20434,900],{},[902,20436,900],{"encoding":904},"-průběhem ",[883,20439,20441],{"className":20440},[886],[888,20442,20443],{"xmlns":890},[892,20444,20445,20451],{},[895,20446,20447,20449],{},[898,20448,1735],{},[898,20450,1683],{},[902,20452,2094],{"encoding":904},[883,20454,20456],{"className":20455},[886],[888,20457,20458],{"xmlns":890},[892,20459,20460,20468],{},[895,20461,20462,20464,20466],{},[898,20463,1735],{},[898,20465,1762],{},[898,20467,1683],{},[902,20469,1836],{"encoding":904},[883,20471,20473],{"className":20472},[886],[888,20474,20475],{"xmlns":890},[892,20476,20477,20483],{},[895,20478,20479,20481],{},[898,20480,1742],{},[898,20482,1683],{},[902,20484,1817],{"encoding":904},[123,20486,20487,20489,20490,4521,20505,20546,20547,8138,20562,20577],{},[38,20488,8577],{},": v bodě minima ",[883,20491,20493],{"className":20492},[886],[888,20494,20495],{"xmlns":890},[892,20496,20497,20503],{},[895,20498,20499,20501],{},[898,20500,1735],{},[898,20502,1683],{},[902,20504,2094],{"encoding":904},[883,20506,20508],{"className":20507},[886],[888,20509,20510],{"xmlns":890},[892,20511,20512,20544],{},[895,20513,20514,20516,20518,20520,20526,20528,20530,20532,20534,20536,20542],{},[898,20515,1735],{},[898,20517,1683],{},[1706,20519,2140],{"stretchy":2139},[2142,20521,20522,20524],{},[898,20523,2146],{},[2148,20525,2150],{},[1706,20527,2153],{"stretchy":2139},[1706,20529,1708],{},[898,20531,1742],{},[898,20533,1683],{},[1706,20535,2140],{"stretchy":2139},[2142,20537,20538,20540],{},[898,20539,2146],{},[2148,20541,2150],{},[1706,20543,2153],{"stretchy":2139},[902,20545,9216],{"encoding":904},"; geometricky ",[883,20548,20550],{"className":20549},[886],[888,20551,20552],{"xmlns":890},[892,20553,20554,20560],{},[895,20555,20556,20558],{},[898,20557,1742],{},[898,20559,1683],{},[902,20561,1817],{"encoding":904},[883,20563,20565],{"className":20564},[886],[888,20566,20567],{"xmlns":890},[892,20568,20569,20575],{},[895,20570,20571,20573],{},[898,20572,1735],{},[898,20574,1683],{},[902,20576,2094],{"encoding":904}," v jejím minimu.",[123,20579,20580,20489,20582,4521,20599,1837],{},[38,20581,9934],{},[883,20583,20585],{"className":20584},[886],[888,20586,20587],{"xmlns":890},[892,20588,20589,20597],{},[895,20590,20591,20593,20595],{},[898,20592,1735],{},[898,20594,1762],{},[898,20596,1683],{},[902,20598,1836],{"encoding":904},[883,20600,20602],{"className":20601},[886],[888,20603,20604],{"xmlns":890},[892,20605,20606,20640],{},[895,20607,20608,20610,20612,20614,20616,20622,20624,20626,20628,20630,20632,20638],{},[898,20609,1735],{},[898,20611,1762],{},[898,20613,1683],{},[1706,20615,2140],{"stretchy":2139},[2142,20617,20618,20620],{},[898,20619,2146],{},[2148,20621,2150],{},[1706,20623,2153],{"stretchy":2139},[1706,20625,1708],{},[898,20627,1742],{},[898,20629,1683],{},[1706,20631,2140],{"stretchy":2139},[2142,20633,20634,20636],{},[898,20635,2146],{},[2148,20637,2150],{},[1706,20639,2153],{"stretchy":2139},[902,20641,15704],{"encoding":904},[123,20643,20644,1647,20646,20673],{},[38,20645,10114],{},[883,20647,20649],{"className":20648},[886],[888,20650,20651],{"xmlns":890},[892,20652,20653,20671],{},[895,20654,20655,20657,20659,20661,20663,20665,20667,20669],{},[898,20656,1702],{},[898,20658,1662],{},[1706,20660,1708],{},[898,20662,1659],{},[898,20664,1662],{},[1706,20666,1715],{},[898,20668,1659],{},[898,20670,1683],{},[902,20672,1722],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,20675,20676,2314,20678,20680,20681,20707,20708,20733],{},[38,20677,10981],{},[614,20679,10240],{},") — hodnoty ",[883,20682,20684],{"className":20683},[886],[888,20685,20686],{"xmlns":890},[892,20687,20688,20704],{},[895,20689,20690,20696,20698],{},[2142,20691,20692,20694],{},[898,20693,2146],{},[898,20695,1735],{},[1706,20697,2505],{"separator":2504},[2142,20699,20700,20702],{},[898,20701,2146],{},[898,20703,10315],{},[902,20705,20706],{"encoding":904},"Q_A, Q_B"," splňující ",[883,20709,20711],{"className":20710},[886],[888,20712,20713],{"xmlns":890},[892,20714,20715,20731],{},[895,20716,20717,20719,20721,20723,20725,20727,20729],{},[898,20718,1702],{},[898,20720,1662],{},[1706,20722,2140],{"stretchy":2139},[898,20724,2146],{},[1706,20726,2153],{"stretchy":2139},[1706,20728,1708],{},[2148,20730,2150],{},[902,20732,10518],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,20735,20736,20739],{},[38,20737,20738],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,20741,20742,20744,20745,4521,20762,20803],{},[38,20743,12041],{}," — v bodě maxima zisku ",[883,20746,20748],{"className":20747},[886],[888,20749,20750],{"xmlns":890},[892,20751,20752,20760],{},[895,20753,20754],{},[2142,20755,20756,20758],{},[898,20757,2146],{},[2148,20759,2150],{},[902,20761,8625],{"encoding":904},[883,20763,20765],{"className":20764},[886],[888,20766,20767],{"xmlns":890},[892,20768,20769,20801],{},[895,20770,20771,20773,20775,20777,20783,20785,20787,20789,20791,20793,20799],{},[898,20772,1742],{},[898,20774,1662],{},[1706,20776,2140],{"stretchy":2139},[2142,20778,20779,20781],{},[898,20780,2146],{},[2148,20782,2150],{},[1706,20784,2153],{"stretchy":2139},[1706,20786,1708],{},[898,20788,1742],{},[898,20790,1683],{},[1706,20792,2140],{"stretchy":2139},[2142,20794,20795,20797],{},[898,20796,2146],{},[2148,20798,2150],{},[1706,20800,2153],{"stretchy":2139},[902,20802,12307],{"encoding":904}," (3.13).",[123,20805,20806,20808,20809,4521,20828,20853],{},[38,20807,13342],{}," — při ",[883,20810,20812],{"className":20811},[886],[888,20813,20814],{"xmlns":890},[892,20815,20816,20825],{},[895,20817,20818,20820,20822],{},[898,20819,1702],{},[1706,20821,1708],{},[2415,20823,20824],{},"konst",[902,20826,20827],{"encoding":904},"P = \\text{konst}",[883,20829,20831],{"className":20830},[886],[888,20832,20833],{"xmlns":890},[892,20834,20835,20851],{},[895,20836,20837,20839,20841,20843,20845,20847,20849],{},[898,20838,1702],{},[1706,20840,1708],{},[898,20842,1742],{},[898,20844,1683],{},[1706,20846,2140],{"stretchy":2139},[898,20848,2146],{},[1706,20850,2153],{"stretchy":2139},[902,20852,14042],{"encoding":904}," (3.14).",[123,20855,20856,20859,20860,20889,20890,20907],{},[38,20857,20858],{},"Shutdown point"," — bod ",[883,20861,20863],{"className":20862},[886],[888,20864,20865],{"xmlns":890},[892,20866,20867,20887],{},[895,20868,20869,20871,20877,20879,20885],{},[1706,20870,2140],{"stretchy":2139},[2489,20872,20873,20875],{},[898,20874,2146],{},[1706,20876,3197],{},[1706,20878,2505],{"separator":2504},[2489,20880,20881,20883],{},[898,20882,1702],{},[1706,20884,3197],{},[1706,20886,2153],{"stretchy":2139},[902,20888,14334],{"encoding":904}," v minimu ",[883,20891,20893],{"className":20892},[886],[888,20894,20895],{"xmlns":890},[892,20896,20897,20905],{},[895,20898,20899,20901,20903],{},[898,20900,1735],{},[898,20902,1762],{},[898,20904,1683],{},[902,20906,1836],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,20909,20910,1647,20913,10691,20948,14605,20969,20982,20983,20998,20999,1837],{},[38,20911,20912],{},"Funkce nabídky firmy",[883,20914,20916],{"className":20915},[886],[888,20917,20918],{"xmlns":890},[892,20919,20920,20946],{},[895,20921,20922,20924,20926,20928,20930,20932,20934,20936,20938,20940,20942,20944],{},[898,20923,1702],{},[1706,20925,1708],{},[898,20927,14171],{},[1706,20929,2140],{"stretchy":2139},[898,20931,2146],{},[1706,20933,2153],{"stretchy":2139},[1706,20935,1708],{},[898,20937,1742],{},[898,20939,1683],{},[1706,20941,2140],{"stretchy":2139},[898,20943,2146],{},[1706,20945,2153],{"stretchy":2139},[902,20947,15807],{"encoding":904},[883,20949,20951],{"className":20950},[886],[888,20952,20953],{"xmlns":890},[892,20954,20955,20967],{},[895,20956,20957,20959,20961],{},[898,20958,2146],{},[1706,20960,14220],{},[2489,20962,20963,20965],{},[898,20964,2146],{},[1706,20966,3197],{},[902,20968,14604],{"encoding":904},[883,20970,20972],{"className":20971},[886],[888,20973,20974],{"xmlns":890},[892,20975,20976,20980],{},[895,20977,20978],{},[2148,20979,2150],{},[902,20981,2150],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,20984,20986],{"className":20985},[886],[888,20987,20988],{"xmlns":890},[892,20989,20990,20996],{},[895,20991,20992,20994],{},[898,20993,1742],{},[898,20995,1683],{},[902,20997,1817],{"encoding":904}," nad minimem ",[883,21000,21002],{"className":21001},[886],[888,21003,21004],{"xmlns":890},[892,21005,21006,21014],{},[895,21007,21008,21010,21012],{},[898,21009,1735],{},[898,21011,1762],{},[898,21013,1683],{},[902,21015,1836],{"encoding":904},[123,21017,21018,21021,21022,21044,21045,1837],{},[38,21019,21020],{},"Dokonalá konkurence"," — ",[883,21023,21025],{"className":21024},[886],[888,21026,21027],{"xmlns":890},[892,21028,21029,21041],{},[895,21030,21031,21033,21035],{},[898,21032,1702],{},[1706,21034,1708],{},[2489,21036,21037,21039],{},[898,21038,1702],{},[1706,21040,3197],{},[902,21042,21043],{"encoding":904},"P = P^*"," konstantní ⇒ ",[883,21046,21048],{"className":21047},[886],[888,21049,21050],{"xmlns":890},[892,21051,21052,21072],{},[895,21053,21054,21056,21058,21060,21062,21064,21066],{},[898,21055,1735],{},[898,21057,1662],{},[1706,21059,1708],{},[898,21061,1742],{},[898,21063,1662],{},[1706,21065,1708],{},[2489,21067,21068,21070],{},[898,21069,1702],{},[1706,21071,3197],{},[902,21073,5218],{"encoding":904},[123,21075,21076,21079],{},[38,21077,21078],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,21081,21083],{"id":21082},"navigace","Navigace",[120,21085,21086,21109,21122],{},[123,21087,21088,1647,21091,1343,21095,1343,21099,1343,21103,1343,21106],{},[38,21089,21090],{},"Související témata:",[207,21092,21094],{"className":21093,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka",[207,21096,21098],{"className":21097,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita",[207,21100,21102],{"className":21101,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace",[207,21104,775],{"className":21105,"dataFsResolvedFilePath":773,"href":774},[210],[207,21107,859],{"className":21108,"dataFsResolvedFilePath":857,"href":858},[210],[123,21110,21111,1647,21114,1343,21118],{},[38,21112,21113],{},"Přednášky:",[207,21115,21117],{"className":21116,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,21119,21121],{"className":21120,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,21123,21124,1647,21127],{},[38,21125,21126],{},"Kurz:",[207,21128,21132],{"className":21129,"dataFsResolvedFilePath":21130,"href":21131},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","Matematická ekonomie",{"title":641,"searchDepth":642,"depth":642,"links":21134},[21135,21136,21143,21149,21153,21154,21158,21159,21160,21161,21167,21168],{"id":1840,"depth":642,"text":1241},{"id":2281,"depth":642,"text":2282,"children":21137},[21138,21139,21140,21141,21142],{"id":2294,"depth":649,"text":2295},{"id":2911,"depth":649,"text":2912},{"id":3060,"depth":649,"text":3061},{"id":3822,"depth":649,"text":3823},{"id":4493,"depth":649,"text":4494},{"id":5221,"depth":642,"text":5222,"children":21144},[21145,21146,21147,21148],{"id":5225,"depth":649,"text":5226},{"id":5388,"depth":649,"text":5389},{"id":6581,"depth":649,"text":6582},{"id":7484,"depth":649,"text":7485},{"id":8576,"depth":642,"text":8577,"children":21150},[21151,21152],{"id":8603,"depth":649,"text":8604},{"id":9933,"depth":649,"text":9934},{"id":10108,"depth":642,"text":10109},{"id":12040,"depth":642,"text":12041,"children":21155},[21156,21157],{"id":12054,"depth":649,"text":8604},{"id":13341,"depth":649,"text":13342},{"id":13979,"depth":642,"text":13980},{"id":15452,"depth":642,"text":15453},{"id":15879,"depth":642,"text":15880},{"id":15918,"depth":642,"text":15919,"children":21162},[21163,21164,21165,21166],{"id":15922,"depth":649,"text":15923},{"id":16777,"depth":649,"text":16778},{"id":18327,"depth":649,"text":18328},{"id":19708,"depth":649,"text":19709},{"id":19878,"depth":642,"text":19879},{"id":21082,"depth":642,"text":21083},"2026-04-22",{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":1629,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,21176,21177,1690,21178,21179,21180],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","topic","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI","topics",{"zapisku":1625,"topics":21185,"summaries":21186,"outputs":21187},15,5,1,[21189,23029,28686,30236,31104,35378,36982,46836,55819,69864,74154,92421,104533,113492,113780],{"id":21190,"title":21191,"body":21192,"course":1128,"courses":659,"created":1129,"description":23018,"extension":661,"meta":23019,"navigation":664,"path":23020,"seo":23021,"sources":23022,"stem":23023,"tags":23024,"type":21181,"updated":677,"__hash__":23028},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":21193,"toc":23001},[21194,21197,21215,21219,21296,21299,21422,21566,21568,21648,21652,21713,21763,21770,21774,21904,21954,21958,21998,22064,22132,22140,22144,22182,22254,22258,22334,22382,22425,22429,22433,22503,22507,22557,22634,22641,22644,22696,22963,22965],[12,21195,21191],{"id":21196},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,21198,21199,21200,21204,21205,21208,21209,21211,21212,1837],{},"Matematický aparát kurzu ",[207,21201,21203],{"className":21202,"dataFsResolvedFilePath":21130,"href":21131},[210],"ImeK",". Bez derivace se neobejdou ",[38,21206,21207],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,21210,1859],{}," ani ",[38,21213,21214],{},"minimalizace nákladů",[115,21216,21218],{"id":21217},"funkce-a-polynomy","Funkce a polynomy",[724,21220,21221,21222,21247,21248,21261,21262,21275,21276,1837],{},"Funkce jedné proměnné ",[883,21223,21225],{"className":21224},[886],[888,21226,21227],{"xmlns":890},[892,21228,21229,21244],{},[895,21230,21231,21233,21235,21238,21240,21242],{},[898,21232,6930],{},[1706,21234,1708],{},[898,21236,21237],{},"f",[1706,21239,2140],{"stretchy":2139},[898,21241,18300],{},[1706,21243,2153],{"stretchy":2139},[902,21245,21246],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,21249,21251],{"className":21250},[886],[888,21252,21253],{"xmlns":890},[892,21254,21255,21259],{},[895,21256,21257],{},[898,21258,18300],{},[902,21260,18300],{"encoding":904}," (nezávislá) → ",[883,21263,21265],{"className":21264},[886],[888,21266,21267],{"xmlns":890},[892,21268,21269,21273],{},[895,21270,21271],{},[898,21272,6930],{},[902,21274,6930],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,21277,21279],{"className":21278},[886],[888,21280,21281],{"xmlns":890},[892,21282,21283,21293],{},[895,21284,21285,21287,21289,21291],{},[898,21286,21237],{},[1706,21288,2140],{"stretchy":2139},[898,21290,207],{},[1706,21292,2153],{"stretchy":2139},[902,21294,21295],{"encoding":904},"f(a)",[724,21297,21298],{},"Polynomy:",[120,21300,21301,21332,21372],{},[123,21302,21303],{},[152,21304,21305],{},[123,21306,21307,21308],{},"stupně: ",[883,21309,21311],{"className":21310},[886],[888,21312,21313],{"xmlns":890},[892,21314,21315,21329],{},[895,21316,21317,21319,21321,21323,21325,21327],{},[898,21318,6930],{},[1706,21320,1708],{},[898,21322,207],{},[898,21324,18300],{},[1706,21326,2447],{},[898,21328,2450],{},[902,21330,21331],{"encoding":904},"y = ax + b",[123,21333,21334],{},[152,21335,21336],{"start":642},[123,21337,21307,21338],{},[883,21339,21341],{"className":21340},[886],[888,21342,21343],{"xmlns":890},[892,21344,21345,21369],{},[895,21346,21347,21349,21351,21353,21359,21361,21363,21365,21367],{},[898,21348,6930],{},[1706,21350,1708],{},[898,21352,207],{},[2489,21354,21355,21357],{},[898,21356,18300],{},[2148,21358,2495],{},[1706,21360,2447],{},[898,21362,2450],{},[898,21364,18300],{},[1706,21366,2447],{},[898,21368,20413],{},[902,21370,21371],{"encoding":904},"y = ax^2 + bx + c",[123,21373,21374],{},[152,21375,21376],{"start":649},[123,21377,21307,21378],{},[883,21379,21381],{"className":21380},[886],[888,21382,21383],{"xmlns":890},[892,21384,21385,21419],{},[895,21386,21387,21389,21391,21393,21399,21401,21403,21409,21411,21413,21415,21417],{},[898,21388,6930],{},[1706,21390,1708],{},[898,21392,207],{},[2489,21394,21395,21397],{},[898,21396,18300],{},[2148,21398,4284],{},[1706,21400,2447],{},[898,21402,2450],{},[2489,21404,21405,21407],{},[898,21406,18300],{},[2148,21408,2495],{},[1706,21410,2447],{},[898,21412,20413],{},[898,21414,18300],{},[1706,21416,2447],{},[898,21418,3120],{},[902,21420,21421],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,21423,21424,1647,21427,21481,21482,21519,21520,1837],{},[38,21425,21426],{},"Příklad rozkladu:",[883,21428,21430],{"className":21429},[886],[888,21431,21432],{"xmlns":890},[892,21433,21434,21478],{},[895,21435,21436,21438,21440,21446,21448,21450,21452,21454,21456,21458,21460,21462,21464,21466,21468,21470,21472,21474,21476],{},[898,21437,6930],{},[1706,21439,1708],{},[2489,21441,21442,21444],{},[898,21443,18300],{},[2148,21445,2495],{},[1706,21447,1715],{},[2148,21449,7524],{},[898,21451,18300],{},[1706,21453,2447],{},[2148,21455,7044],{},[1706,21457,1708],{},[1706,21459,2140],{"stretchy":2139},[898,21461,18300],{},[1706,21463,1715],{},[2148,21465,2495],{},[1706,21467,2153],{"stretchy":2139},[1706,21469,2140],{"stretchy":2139},[898,21471,18300],{},[1706,21473,1715],{},[2148,21475,4284],{},[1706,21477,2153],{"stretchy":2139},[902,21479,21480],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,21483,21485],{"className":21484},[886],[888,21486,21487],{"xmlns":890},[892,21488,21489,21516],{},[895,21490,21491,21497,21499,21501,21503,21506,21512,21514],{},[2142,21492,21493,21495],{},[898,21494,18300],{},[2148,21496,2701],{},[1706,21498,1708],{},[2148,21500,2495],{},[1706,21502,2505],{"separator":2504},[2415,21504,21505],{}," ",[2142,21507,21508,21510],{},[898,21509,18300],{},[2148,21511,2495],{},[1706,21513,1708],{},[2148,21515,4284],{},[902,21517,21518],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,21521,21523],{"className":21522},[886],[888,21524,21525],{"xmlns":890},[892,21526,21527,21563],{},[895,21528,21529,21531,21533,21535,21537,21539,21547,21553,21555],{},[898,21530,6930],{},[1706,21532,1708],{},[1706,21534,2140],{"stretchy":2139},[898,21536,18300],{},[1706,21538,1715],{},[4745,21540,21541],{"scriptlevel":2150,"displaystyle":2139},[2964,21542,21543,21545],{},[2148,21544,7524],{},[2148,21546,2495],{},[2489,21548,21549,21551],{},[1706,21550,2153],{"stretchy":2139},[2148,21552,2495],{},[1706,21554,1715],{},[4745,21556,21557],{"scriptlevel":2150,"displaystyle":2139},[2964,21558,21559,21561],{},[2148,21560,2701],{},[2148,21562,3455],{},[902,21564,21565],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,21567,21102],{"id":1145},[724,21569,21570,21571,1348,21595,21623,21624,1837],{},"Označení ",[883,21572,21574],{"className":21573},[886],[888,21575,21576],{"xmlns":890},[892,21577,21578,21592],{},[895,21579,21580,21586,21588,21590],{},[2489,21581,21582,21584],{},[898,21583,21237],{},[1706,21585,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,21587,2140],{"stretchy":2139},[898,21589,18300],{},[1706,21591,2153],{"stretchy":2139},[902,21593,21594],{"encoding":904},"f'(x)",[883,21596,21598],{"className":21597},[886],[888,21599,21600],{"xmlns":890},[892,21601,21602,21620],{},[895,21603,21604],{},[4745,21605,21606],{"scriptlevel":2150,"displaystyle":2504},[2964,21607,21608,21614],{},[895,21609,21610,21612],{},[898,21611,3120],{},[898,21613,6930],{},[895,21615,21616,21618],{},[898,21617,3120],{},[898,21619,18300],{},[902,21621,21622],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,21625,21627],{"className":21626},[886],[888,21628,21629],{"xmlns":890},[892,21630,21631,21645],{},[895,21632,21633,21639,21641,21643],{},[2489,21634,21635,21637],{},[898,21636,21237],{},[1706,21638,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,21640,2140],{"stretchy":2139},[898,21642,207],{},[1706,21644,2153],{"stretchy":2139},[902,21646,21647],{"encoding":904},"f'(a)",[198,21649,21651],{"id":21650},"geometrická-interpretace","Geometrická interpretace",[724,21653,21654,21677,21678,21681,21682,21712],{},[883,21655,21657],{"className":21656},[886],[888,21658,21659],{"xmlns":890},[892,21660,21661,21675],{},[895,21662,21663,21669,21671,21673],{},[2489,21664,21665,21667],{},[898,21666,21237],{},[1706,21668,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,21670,2140],{"stretchy":2139},[898,21672,207],{},[1706,21674,2153],{"stretchy":2139},[902,21676,21647],{"encoding":904}," = ",[38,21679,21680],{},"sklon tečny"," ke grafu funkce v bodě ",[883,21683,21685],{"className":21684},[886],[888,21686,21687],{"xmlns":890},[892,21688,21689,21709],{},[895,21690,21691,21694,21696,21698,21700,21702,21704,21706],{},[1706,21692,21693],{"stretchy":2139},"[",[898,21695,207],{},[1706,21697,2505],{"separator":2504},[898,21699,21237],{},[1706,21701,2140],{"stretchy":2139},[898,21703,207],{},[1706,21705,2153],{"stretchy":2139},[1706,21707,21708],{"stretchy":2139},"]",[902,21710,21711],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,21714,21715],{},[883,21716,21718],{"className":21717},[886],[888,21719,21720],{"xmlns":890},[892,21721,21722,21760],{},[895,21723,21724,21726,21728,21730,21732,21734,21736,21738,21744,21746,21748,21750,21752,21754,21756,21758],{},[898,21725,6930],{},[1706,21727,1715],{},[898,21729,21237],{},[1706,21731,2140],{"stretchy":2139},[898,21733,207],{},[1706,21735,2153],{"stretchy":2139},[1706,21737,1708],{},[2489,21739,21740,21742],{},[898,21741,21237],{},[1706,21743,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,21745,2140],{"stretchy":2139},[898,21747,207],{},[1706,21749,2153],{"stretchy":2139},[1706,21751,2140],{"stretchy":2139},[898,21753,18300],{},[1706,21755,1715],{},[898,21757,207],{},[1706,21759,2153],{"stretchy":2139},[902,21761,21762],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,21764,21765],{},[2286,21766],{"alt":21767,"className":21768,"src":21769},"imek-derivace-tecna",[210,2290],"\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,21771,21773],{"id":21772},"inženýrská-interpretace","Inženýrská interpretace",[724,21775,21776,21677,21799,1647,21801,21814,21815,2891,21828,21846,21847,4174,21860,1889,21873,4202,21886,4288],{},[883,21777,21779],{"className":21778},[886],[888,21780,21781],{"xmlns":890},[892,21782,21783,21797],{},[895,21784,21785,21791,21793,21795],{},[2489,21786,21787,21789],{},[898,21788,21237],{},[1706,21790,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,21792,2140],{"stretchy":2139},[898,21794,207],{},[1706,21796,2153],{"stretchy":2139},[902,21798,21647],{"encoding":904},[38,21800,3166],{},[883,21802,21804],{"className":21803},[886],[888,21805,21806],{"xmlns":890},[892,21807,21808,21812],{},[895,21809,21810],{},[898,21811,6930],{},[902,21813,6930],{"encoding":904}," vzhledem k ",[883,21816,21818],{"className":21817},[886],[888,21819,21820],{"xmlns":890},[892,21821,21822,21826],{},[895,21823,21824],{},[898,21825,18300],{},[902,21827,18300],{"encoding":904},[883,21829,21831],{"className":21830},[886],[888,21832,21833],{"xmlns":890},[892,21834,21835,21843],{},[895,21836,21837,21839,21841],{},[898,21838,18300],{},[1706,21840,1708],{},[898,21842,207],{},[902,21844,21845],{"encoding":904},"x = a","; přibližná změna ",[883,21848,21850],{"className":21849},[886],[888,21851,21852],{"xmlns":890},[892,21853,21854,21858],{},[895,21855,21856],{},[898,21857,6930],{},[902,21859,6930],{"encoding":904},[883,21861,21863],{"className":21862},[886],[888,21864,21865],{"xmlns":890},[892,21866,21867,21871],{},[895,21868,21869],{},[898,21870,18300],{},[902,21872,18300],{"encoding":904},[883,21874,21876],{"className":21875},[886],[888,21877,21878],{"xmlns":890},[892,21879,21880,21884],{},[895,21881,21882],{},[898,21883,207],{},[902,21885,207],{"encoding":904},[883,21887,21889],{"className":21888},[886],[888,21890,21891],{"xmlns":890},[892,21892,21893,21901],{},[895,21894,21895,21897,21899],{},[898,21896,207],{},[1706,21898,2447],{},[2148,21900,2701],{},[902,21902,21903],{"encoding":904},"a+1",[724,21905,21906],{},[883,21907,21909],{"className":21908},[886],[888,21910,21911],{"xmlns":890},[892,21912,21913,21951],{},[895,21914,21915,21917,21919,21921,21923,21925,21927,21929,21931,21933,21935,21937,21939,21945,21947,21949],{},[898,21916,21237],{},[1706,21918,2140],{"stretchy":2139},[898,21920,207],{},[1706,21922,2447],{},[2148,21924,2701],{},[1706,21926,2153],{"stretchy":2139},[1706,21928,3248],{},[898,21930,21237],{},[1706,21932,2140],{"stretchy":2139},[898,21934,207],{},[1706,21936,2153],{"stretchy":2139},[1706,21938,2447],{},[2489,21940,21941,21943],{},[898,21942,21237],{},[1706,21944,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,21946,2140],{"stretchy":2139},[898,21948,207],{},[1706,21950,2153],{"stretchy":2139},[902,21952,21953],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,21955,21957],{"id":21956},"příklad-mezní-náklady","Příklad — mezní náklady",[724,21959,21960,21961,1837],{},"Celkové náklady ",[883,21962,21964],{"className":21963},[886],[888,21965,21966],{"xmlns":890},[892,21967,21968,21995],{},[895,21969,21970,21972,21974,21976,21979,21981,21983,21985,21987,21989],{},[898,21971,1659],{},[898,21973,1683],{},[1706,21975,1708],{},[2148,21977,21978],{},"1000",[1706,21980,2447],{},[2148,21982,2495],{},[898,21984,2146],{},[1706,21986,2447],{},[2148,21988,14840],{},[2489,21990,21991,21993],{},[898,21992,2146],{},[2148,21994,2495],{},[902,21996,21997],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,21999,22000,22001,22037,22038,1837],{},"Mezní náklady: ",[883,22002,22004],{"className":22003},[886],[888,22005,22006],{"xmlns":890},[892,22007,22008,22034],{},[895,22009,22010,22012,22014,22016,22018,22024,22026,22028,22030,22032],{},[898,22011,1742],{},[898,22013,1683],{},[1706,22015,1708],{},[898,22017,1659],{},[2489,22019,22020,22022],{},[898,22021,1683],{},[1706,22023,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,22025,1708],{},[2148,22027,2495],{},[1706,22029,2447],{},[2148,22031,15204],{},[898,22033,2146],{},[902,22035,22036],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,22039,22041],{"className":22040},[886],[888,22042,22043],{"xmlns":890},[892,22044,22045,22061],{},[895,22046,22047,22049,22051,22053,22055,22057,22059],{},[898,22048,1742],{},[898,22050,1683],{},[1706,22052,2140],{"stretchy":2139},[2148,22054,7786],{},[1706,22056,2153],{"stretchy":2139},[1706,22058,1708],{},[2148,22060,3455],{},[902,22062,22063],{"encoding":904},"MC(10) = 4",[724,22065,22066,1647,22069,3787,22116,1647,22119,1837],{},[38,22067,22068],{},"Skutečný přírůstek:",[883,22070,22072],{"className":22071},[886],[888,22073,22074],{"xmlns":890},[892,22075,22076,22113],{},[895,22077,22078,22080,22082,22084,22086,22088,22090,22092,22095,22097,22099,22101,22103,22105,22107,22109,22111],{},[898,22079,3677],{"mathvariant":2409},[898,22081,1659],{},[898,22083,1683],{},[1706,22085,1708],{},[898,22087,1659],{},[898,22089,1683],{},[1706,22091,2140],{"stretchy":2139},[2148,22093,22094],{},"11",[1706,22096,2153],{"stretchy":2139},[1706,22098,1715],{},[898,22100,1659],{},[898,22102,1683],{},[1706,22104,2140],{"stretchy":2139},[2148,22106,7786],{},[1706,22108,2153],{"stretchy":2139},[1706,22110,1708],{},[2148,22112,19804],{},[902,22114,22115],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",[38,22117,22118],{},"Přibližný (lineární):",[883,22120,22122],{"className":22121},[886],[888,22123,22124],{"xmlns":890},[892,22125,22126,22130],{},[895,22127,22128],{},[2148,22129,3455],{},[902,22131,3455],{"encoding":904},[724,22133,22134,22135,22139],{},"(Viz aplikace v ",[207,22136,22138],{"className":22137,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk",".)",[115,22141,22143],{"id":22142},"diferenciál","Diferenciál",[724,22145,22146],{},[883,22147,22149],{"className":22148},[886],[888,22150,22151],{"xmlns":890},[892,22152,22153,22179],{},[895,22154,22155,22157,22159,22161,22167,22169,22171,22173,22175,22177],{},[898,22156,3120],{},[898,22158,21237],{},[1706,22160,1708],{},[2489,22162,22163,22165],{},[898,22164,21237],{},[1706,22166,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,22168,2140],{"stretchy":2139},[898,22170,18300],{},[1706,22172,2153],{"stretchy":2139},[2415,22174,2799],{},[898,22176,3120],{},[898,22178,18300],{},[902,22180,22181],{"encoding":904},"df = f'(x)\\, dx",[724,22183,22184,22185,22201,22202,22250,22251,1837],{},"Pro malá ",[883,22186,22188],{"className":22187},[886],[888,22189,22190],{"xmlns":890},[892,22191,22192,22198],{},[895,22193,22194,22196],{},[898,22195,3120],{},[898,22197,18300],{},[902,22199,22200],{"encoding":904},"dx"," platí: ",[883,22203,22205],{"className":22204},[886],[888,22206,22207],{"xmlns":890},[892,22208,22209,22247],{},[895,22210,22211,22213,22215,22217,22219,22221,22223,22225,22227,22229,22231,22233,22235,22237,22239,22241,22243,22245],{},[898,22212,3677],{"mathvariant":2409},[898,22214,21237],{},[1706,22216,1708],{},[898,22218,21237],{},[1706,22220,2140],{"stretchy":2139},[898,22222,18300],{},[1706,22224,2447],{},[898,22226,3120],{},[898,22228,18300],{},[1706,22230,2153],{"stretchy":2139},[1706,22232,1715],{},[898,22234,21237],{},[1706,22236,2140],{"stretchy":2139},[898,22238,18300],{},[1706,22240,2153],{"stretchy":2139},[1706,22242,3248],{},[898,22244,3120],{},[898,22246,21237],{},[902,22248,22249],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,22252,22253],{},"lineární odhad přírůstku",[198,22255,22257],{"id":22256},"příklad","Příklad",[724,22259,22260,22290,22291,22313,22314,5606],{},[883,22261,22263],{"className":22262},[886],[888,22264,22265],{"xmlns":890},[892,22266,22267,22287],{},[895,22268,22269,22271,22273,22275,22277,22279,22281],{},[898,22270,1659],{},[898,22272,1683],{},[1706,22274,1708],{},[2148,22276,2590],{},[1706,22278,2447],{},[2148,22280,14840],{},[2489,22282,22283,22285],{},[898,22284,2146],{},[2148,22286,2495],{},[902,22288,22289],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,22292,22294],{"className":22293},[886],[888,22295,22296],{"xmlns":890},[892,22297,22298,22310],{},[895,22299,22300,22302,22304,22306,22308],{},[898,22301,2146],{},[1706,22303,4288],{},[2148,22305,2728],{},[1706,22307,5915],{},[2148,22309,4199],{},[902,22311,22312],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,22315,22317],{"className":22316},[886],[888,22318,22319],{"xmlns":890},[892,22320,22321,22331],{},[895,22322,22323,22325,22327,22329],{},[898,22324,3120],{},[898,22326,2146],{},[1706,22328,1708],{},[2148,22330,7786],{},[902,22332,22333],{"encoding":904},"dQ = 10",[724,22335,22336],{},[883,22337,22339],{"className":22338},[886],[888,22340,22341],{"xmlns":890},[892,22342,22343,22379],{},[895,22344,22345,22347,22349,22351,22353,22355,22357,22359,22361,22363,22365,22367,22369,22371,22373,22375,22377],{},[898,22346,3120],{},[898,22348,1659],{},[898,22350,1683],{},[1706,22352,1708],{},[2148,22354,15204],{},[898,22356,2146],{},[1706,22358,2390],{},[898,22360,3120],{},[898,22362,2146],{},[1706,22364,1708],{},[2148,22366,15204],{},[1706,22368,2390],{},[2148,22370,2728],{},[1706,22372,2390],{},[2148,22374,7786],{},[1706,22376,1708],{},[2148,22378,2590],{},[902,22380,22381],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,22383,22384,22385,22408,22409,22424],{},"Přesná změna: ",[883,22386,22388],{"className":22387},[886],[888,22389,22390],{"xmlns":890},[892,22391,22392,22405],{},[895,22393,22394,22396,22398,22400,22402],{},[898,22395,3677],{"mathvariant":2409},[898,22397,1659],{},[898,22399,1683],{},[1706,22401,1708],{},[2148,22403,22404],{},"110",[902,22406,22407],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,22410,22412],{"className":22411},[886],[888,22413,22414],{"xmlns":890},[892,22415,22416,22422],{},[895,22417,22418,22420],{},[898,22419,1659],{},[898,22421,1683],{},[902,22423,1686],{"encoding":904}," je konvexní.",[115,22426,22428],{"id":22427},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,22430,22432],{"id":22431},"nutná-podmínka","Nutná podmínka",[724,22434,22435,22436,2891,22456,22469,22470,22498,22499,22502],{},"Má-li ",[883,22437,22439],{"className":22438},[886],[888,22440,22441],{"xmlns":890},[892,22442,22443,22453],{},[895,22444,22445,22447,22449,22451],{},[898,22446,21237],{},[1706,22448,2140],{"stretchy":2139},[898,22450,18300],{},[1706,22452,2153],{"stretchy":2139},[902,22454,22455],{"encoding":904},"f(x)",[883,22457,22459],{"className":22458},[886],[888,22460,22461],{"xmlns":890},[892,22462,22463,22467],{},[895,22464,22465],{},[898,22466,207],{},[902,22468,207],{"encoding":904}," extrém, pak ",[883,22471,22473],{"className":22472},[886],[888,22474,22475],{"xmlns":890},[892,22476,22477,22495],{},[895,22478,22479,22485,22487,22489,22491,22493],{},[2489,22480,22481,22483],{},[898,22482,21237],{},[1706,22484,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,22486,2140],{"stretchy":2139},[898,22488,207],{},[1706,22490,2153],{"stretchy":2139},[1706,22492,1708],{},[2148,22494,2150],{},[902,22496,22497],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,22500,22501],{},"stacionární"," (podezřelé) body.",[198,22504,22506],{"id":22505},"postačující-podmínka","Postačující podmínka",[724,22508,22509,22510,22523,22524,4288],{},"Pro stacionární bod ",[883,22511,22513],{"className":22512},[886],[888,22514,22515],{"xmlns":890},[892,22516,22517,22521],{},[895,22518,22519],{},[898,22520,207],{},[902,22522,207],{"encoding":904},", je-li ",[883,22525,22527],{"className":22526},[886],[888,22528,22529],{"xmlns":890},[892,22530,22531,22554],{},[895,22532,22533,22543,22545,22547,22549,22552],{},[2489,22534,22535,22537],{},[898,22536,21237],{},[895,22538,22539,22541],{},[1706,22540,3142],{"mathvariant":2409},[1706,22542,3142],{"mathvariant":2409},[1706,22544,2140],{"stretchy":2139},[898,22546,207],{},[1706,22548,2153],{"stretchy":2139},[1706,22550,22551],{"mathvariant":2409},"≠",[2148,22553,2150],{},[902,22555,22556],{"encoding":904},"f''(a) \\neq 0",[120,22558,22559,22597],{},[123,22560,22561,22593,22594],{},[883,22562,22564],{"className":22563},[886],[888,22565,22566],{"xmlns":890},[892,22567,22568,22590],{},[895,22569,22570,22580,22582,22584,22586,22588],{},[2489,22571,22572,22574],{},[898,22573,21237],{},[895,22575,22576,22578],{},[1706,22577,3142],{"mathvariant":2409},[1706,22579,3142],{"mathvariant":2409},[1706,22581,2140],{"stretchy":2139},[898,22583,207],{},[1706,22585,2153],{"stretchy":2139},[1706,22587,8922],{},[2148,22589,2150],{},[902,22591,22592],{"encoding":904},"f''(a) > 0"," ⇒ ",[38,22595,22596],{},"lokální minimum",[123,22598,22599,22593,22631],{},[883,22600,22602],{"className":22601},[886],[888,22603,22604],{"xmlns":890},[892,22605,22606,22628],{},[895,22607,22608,22618,22620,22622,22624,22626],{},[2489,22609,22610,22612],{},[898,22611,21237],{},[895,22613,22614,22616],{},[1706,22615,3142],{"mathvariant":2409},[1706,22617,3142],{"mathvariant":2409},[1706,22619,2140],{"stretchy":2139},[898,22621,207],{},[1706,22623,2153],{"stretchy":2139},[1706,22625,2539],{},[2148,22627,2150],{},[902,22629,22630],{"encoding":904},"f''(a) \u003C 0",[38,22632,22633],{},"lokální maximum",[724,22635,22636],{},[2286,22637],{"alt":22638,"className":22639,"src":22640},"imek-extremy-1d",[210,2290],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,22642,22257],{"id":22643},"příklad-1",[724,22645,22646],{},[883,22647,22649],{"className":22648},[886],[888,22650,22651],{"xmlns":890},[892,22652,22653,22693],{},[895,22654,22655,22657,22659,22661,22663,22665,22667,22673,22675,22677,22683,22685,22687,22689,22691],{},[898,22656,21237],{},[1706,22658,2140],{"stretchy":2139},[898,22660,18300],{},[1706,22662,2153],{"stretchy":2139},[1706,22664,1708],{},[2148,22666,2495],{},[2489,22668,22669,22671],{},[898,22670,18300],{},[2148,22672,4284],{},[1706,22674,1715],{},[2148,22676,4284],{},[2489,22678,22679,22681],{},[898,22680,18300],{},[2148,22682,2495],{},[1706,22684,1715],{},[2148,22686,7156],{},[898,22688,18300],{},[1706,22690,2447],{},[2148,22692,4284],{},[902,22694,22695],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,22697,22698,22809,22849,22910],{},[123,22699,22700,22772,22773],{},[883,22701,22703],{"className":22702},[886],[888,22704,22705],{"xmlns":890},[892,22706,22707,22769],{},[895,22708,22709,22715,22717,22719,22721,22723,22725,22731,22733,22735,22737,22739,22741,22743,22745,22747,22749,22751,22753,22755,22757,22759,22761,22763,22765,22767],{},[2489,22710,22711,22713],{},[898,22712,21237],{},[1706,22714,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,22716,2140],{"stretchy":2139},[898,22718,18300],{},[1706,22720,2153],{"stretchy":2139},[1706,22722,1708],{},[2148,22724,7044],{},[2489,22726,22727,22729],{},[898,22728,18300],{},[2148,22730,2495],{},[1706,22732,1715],{},[2148,22734,7044],{},[898,22736,18300],{},[1706,22738,1715],{},[2148,22740,7156],{},[1706,22742,1708],{},[2148,22744,7044],{},[1706,22746,2140],{"stretchy":2139},[898,22748,18300],{},[1706,22750,2447],{},[2148,22752,2701],{},[1706,22754,2153],{"stretchy":2139},[1706,22756,2140],{"stretchy":2139},[898,22758,18300],{},[1706,22760,1715],{},[2148,22762,2495],{},[1706,22764,2153],{"stretchy":2139},[1706,22766,1708],{},[2148,22768,2150],{},[902,22770,22771],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,22774,22776],{"className":22775},[886],[888,22777,22778],{"xmlns":890},[892,22779,22780,22806],{},[895,22781,22782,22788,22790,22792,22794,22796,22802,22804],{},[2142,22783,22784,22786],{},[898,22785,18300],{},[2148,22787,2701],{},[1706,22789,1708],{},[1706,22791,1715],{},[2148,22793,2701],{},[1706,22795,2505],{"separator":2504},[2142,22797,22798,22800],{},[898,22799,18300],{},[2148,22801,2495],{},[1706,22803,1708],{},[2148,22805,2495],{},[902,22807,22808],{"encoding":904},"x_1 = -1, x_2 = 2",[123,22810,22811],{},[883,22812,22814],{"className":22813},[886],[888,22815,22816],{"xmlns":890},[892,22817,22818,22846],{},[895,22819,22820,22830,22832,22834,22836,22838,22840,22842,22844],{},[2489,22821,22822,22824],{},[898,22823,21237],{},[895,22825,22826,22828],{},[1706,22827,3142],{"mathvariant":2409},[1706,22829,3142],{"mathvariant":2409},[1706,22831,2140],{"stretchy":2139},[898,22833,18300],{},[1706,22835,2153],{"stretchy":2139},[1706,22837,1708],{},[2148,22839,7156],{},[898,22841,18300],{},[1706,22843,1715],{},[2148,22845,7044],{},[902,22847,22848],{"encoding":904},"f''(x) = 12x - 6",[123,22850,22851,22593,22892,5027,22894],{},[883,22852,22854],{"className":22853},[886],[888,22855,22856],{"xmlns":890},[892,22857,22858,22889],{},[895,22859,22860,22870,22872,22874,22876,22878,22880,22882,22885,22887],{},[2489,22861,22862,22864],{},[898,22863,21237],{},[895,22865,22866,22868],{},[1706,22867,3142],{"mathvariant":2409},[1706,22869,3142],{"mathvariant":2409},[1706,22871,2140],{"stretchy":2139},[1706,22873,1715],{},[2148,22875,2701],{},[1706,22877,2153],{"stretchy":2139},[1706,22879,1708],{},[1706,22881,1715],{},[2148,22883,22884],{},"18",[1706,22886,2539],{},[2148,22888,2150],{},[902,22890,22891],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,22893,13844],{},[883,22895,22897],{"className":22896},[886],[888,22898,22899],{"xmlns":890},[892,22900,22901,22907],{},[895,22902,22903,22905],{},[1706,22904,1715],{},[2148,22906,2701],{},[902,22908,22909],{"encoding":904},"-1",[123,22911,22912,22593,22948,5027,22950],{},[883,22913,22915],{"className":22914},[886],[888,22916,22917],{"xmlns":890},[892,22918,22919,22945],{},[895,22920,22921,22931,22933,22935,22937,22939,22941,22943],{},[2489,22922,22923,22925],{},[898,22924,21237],{},[895,22926,22927,22929],{},[1706,22928,3142],{"mathvariant":2409},[1706,22930,3142],{"mathvariant":2409},[1706,22932,2140],{"stretchy":2139},[2148,22934,2495],{},[1706,22936,2153],{"stretchy":2139},[1706,22938,1708],{},[2148,22940,22884],{},[1706,22942,8922],{},[2148,22944,2150],{},[902,22946,22947],{"encoding":904},"f''(2) = 18 > 0",[38,22949,13792],{},[883,22951,22953],{"className":22952},[886],[888,22954,22955],{"xmlns":890},[892,22956,22957,22961],{},[895,22958,22959],{},[2148,22960,2495],{},[902,22962,2495],{"encoding":904},[115,22964,21083],{"id":21082},[120,22966,22967,22975,22983],{},[123,22968,22969,1647,22972],{},[38,22970,22971],{},"Předchozí:",[207,22973,757],{"className":22974,"dataFsResolvedFilePath":755,"href":756},[210],[123,22976,22977,1647,22980],{},[38,22978,22979],{},"Navazující:",[207,22981,775],{"className":22982,"dataFsResolvedFilePath":773,"href":774},[210],[123,22984,22985,1647,22988,22991,22992,22996,22997,23000],{},[38,22986,22987],{},"Souvislosti:",[207,22989,784],{"className":22990,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,22993,22995],{"className":22994,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk"," (aplikace mezních veličin), ",[207,22998,21098],{"className":22999,"dataFsResolvedFilePath":848,"href":849},[210]," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":23002},[23003,23004,23009,23012,23017],{"id":21217,"depth":642,"text":21218},{"id":1145,"depth":642,"text":21102,"children":23005},[23006,23007,23008],{"id":21650,"depth":649,"text":21651},{"id":21772,"depth":649,"text":21773},{"id":21956,"depth":649,"text":21957},{"id":22142,"depth":642,"text":22143,"children":23010},[23011],{"id":22256,"depth":649,"text":22257},{"id":22427,"depth":642,"text":22428,"children":23013},[23014,23015,23016],{"id":22431,"depth":649,"text":22432},{"id":22505,"depth":649,"text":22506},{"id":22643,"depth":649,"text":22257},{"id":21082,"depth":642,"text":21083},"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":21191,"description":23018},[1135],"topics\u002Fderivace",[1128,1145,23025,23026,23027],"diferencial","extremy","mezni-naklady","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":23030,"title":23031,"body":23032,"course":1128,"courses":659,"created":21169,"description":641,"extension":661,"meta":28675,"navigation":664,"path":28676,"seo":28677,"sources":28678,"stem":28679,"tags":28680,"type":21181,"updated":677,"__hash__":28685},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":9,"value":23033,"toc":28648},[23034,23037,23056,23060,23086,23090,23131,23217,23260,23264,23288,23295,23299,23309,23320,23324,23352,23361,23417,23423,23426,23432,23459,23465,23558,23716,24004,24008,24088,24094,24098,24194,24260,24426,24430,24508,24538,24565,24571,24603,24681,24765,24769,24832,24838,24841,24847,24960,25042,25086,25090,25136,25143,25458,25463,25487,25516,25583,25679,25683,25690,25697,25767,25887,25971,25974,25980,26305,26309,26472,26480,26616,26624,26860,26868,26871,26876,27132,27136,27308,27442,27479,27521,27524,27653,27743,27761,27765,27772,27778,27838,27841,27865,27868,27874,27877,27883,27886,27890,27928,27986,28173,28177,28250,28256,28263,28267,28273,28415,28419,28425,28461,28466,28643],[12,23035,23031],{"id":23036},"elasticita-poptávky-a-nabídky",[1636,23038,23039],{},[724,23040,23041,1643,23043,23045,23046,23049,23050,1993,23053,1837],{},[883,23042,1642],{},[38,23044,21098],{}," 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: ",[38,23047,23048],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,23051,23052],{},"křížově-cenovou elasticitu",[38,23054,23055],{},"důchodovou elasticitu",[115,23057,23059],{"id":23058},"úvod-motivace","Úvod — motivace",[724,23061,23062,23063,23066,23067,23070,23071,23074,23075,23078,23079,23082,23083,1936],{},"Termín ",[614,23064,23065],{},"elasticita"," (alternativně ",[614,23068,23069],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,23072,23073],{},"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 ",[614,23076,23077],{},"cenové elasticity poptávky"," (resp. ",[614,23080,23081],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,23084,21102],{"className":23085,"dataFsResolvedFilePath":764,"href":765},[210],[198,23087,23089],{"id":23088},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,23091,23092,23093,23111,23112,23130],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,23094,23096],{"className":23095},[886],[888,23097,23098],{"xmlns":890},[892,23099,23100,23108],{},[895,23101,23102,23104,23106],{},[898,23103,1702],{},[1706,23105,1708],{},[2148,23107,7786],{},[902,23109,23110],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,23113,23115],{"className":23114},[886],[888,23116,23117],{"xmlns":890},[892,23118,23119,23127],{},[895,23120,23121,23123,23125],{},[898,23122,2146],{},[1706,23124,1708],{},[2148,23126,2590],{},[902,23128,23129],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,23132,23133,23175],{},[123,23134,23135,23138,23139,23174],{},[38,23136,23137],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,23140,23142],{"className":23141},[886],[888,23143,23144],{"xmlns":890},[892,23145,23146,23171],{},[895,23147,23148,23150,23152,23154,23156,23158,23160,23162,23164,23166,23168],{},[2415,23149,3852],{},[1706,23151,9609],{},[2415,23153,3852],{},[898,23155,1659],{},[898,23157,1662],{},[1706,23159,1708],{},[2148,23161,10800],{},[1706,23163,2390],{},[2148,23165,22404],{},[1706,23167,1708],{},[2148,23169,23170],{},"990",[902,23172,23173],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,23176,23177,23180,23181,23216],{},[38,23178,23179],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,23182,23184],{"className":23183},[886],[888,23185,23186],{"xmlns":890},[892,23187,23188,23213],{},[895,23189,23190,23192,23194,23196,23198,23200,23202,23204,23206,23208,23210],{},[2415,23191,3852],{},[1706,23193,9609],{},[2415,23195,3852],{},[898,23197,1659],{},[898,23199,1662],{},[1706,23201,1708],{},[2148,23203,10800],{},[1706,23205,2390],{},[2148,23207,4314],{},[1706,23209,1708],{},[2148,23211,23212],{},"1080",[902,23214,23215],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,23218,23219,23220,23223,23224,23227,23228,23231,23232,23235,23236,23239,23240,23255,23256,23259],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,23221,23222],{},"nerozumné",", na Trhu 2 ",[38,23225,23226],{},"rozumné",". Trh 2 je ",[38,23229,23230],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,23233,23234],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,23237,23238],{},"neelastická"," a vyššího ",[883,23241,23243],{"className":23242},[886],[888,23244,23245],{"xmlns":890},[892,23246,23247,23253],{},[895,23248,23249,23251],{},[898,23250,1659],{},[898,23252,1662],{},[902,23254,1665],{"encoding":904}," lze naopak dosáhnout ",[614,23257,23258],{},"zvýšením"," ceny.",[198,23261,23263],{"id":23262},"hypotéza-41","Hypotéza 4.1",[1636,23265,23266],{},[724,23267,23268,23269],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,23270,23272],{"className":23271},[886],[888,23273,23274],{"xmlns":890},[892,23275,23276,23285],{},[895,23277,23278,23280,23283],{},[1706,23279,2140],{"stretchy":2139},[2148,23281,23282],{},"4.1",[1706,23284,2153],{"stretchy":2139},[902,23286,23287],{"encoding":904},"(4.1)",[724,23289,23290,23291,23294],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,23292,23293],{},"procentní změny"," obou faktorů.",[115,23296,23298],{"id":23297},"pojem-elasticity","Pojem elasticity",[724,23300,23301,23302,23304,23305,23308],{},"Obecně ",[38,23303,23065],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,23306,23307],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[1636,23310,23311],{},[724,23312,23313,23315,23316,23319],{},[883,23314,3174],{}," Intuice\nElasticitu lze číst jako ",[38,23317,23318],{},"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.",[115,23321,23323],{"id":23322},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,23325,23326,23327,23351],{},"Nechť ",[883,23328,23330],{"className":23329},[886],[888,23331,23332],{"xmlns":890},[892,23333,23334,23348],{},[895,23335,23336,23338,23340,23342,23344,23346],{},[898,23337,2146],{},[1706,23339,1708],{},[898,23341,2334],{},[1706,23343,2140],{"stretchy":2139},[898,23345,1702],{},[1706,23347,2153],{"stretchy":2139},[902,23349,23350],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,23353,23354],{},[883,23355,23360],{"className":23356,"title":23358,"style":23359},[23357],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,23362,23363,23364,1993,23380,23396,23397,23416],{},"Znaménko minus je korekce: změny ",[883,23365,23367],{"className":23366},[886],[888,23368,23369],{"xmlns":890},[892,23370,23371,23377],{},[895,23372,23373,23375],{},[898,23374,3677],{"mathvariant":2409},[898,23376,2146],{},[902,23378,23379],{"encoding":904},"\\Delta Q",[883,23381,23383],{"className":23382},[886],[888,23384,23385],{"xmlns":890},[892,23386,23387,23393],{},[895,23388,23389,23391],{},[898,23390,3677],{"mathvariant":2409},[898,23392,1702],{},[902,23394,23395],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,23398,23400],{"className":23399},[886],[888,23401,23402],{"xmlns":890},[892,23403,23404,23413],{},[895,23405,23406],{},[2489,23407,23408,23411],{},[898,23409,23410],{},"E",[898,23412,1735],{},[902,23414,23415],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,23418,23419],{},[883,23420,23422],{"className":23421,"title":23358,"style":23359},[23357],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,23424,23425],{},"Po dosazení:",[724,23427,23428],{},[883,23429,23431],{"className":23430,"title":23358,"style":23359},[23357],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,23433,23434,23435,23455,23456,23458],{},"Limitním přechodem ",[883,23436,23438],{"className":23437},[886],[888,23439,23440],{"xmlns":890},[892,23441,23442,23452],{},[895,23443,23444,23446,23448,23450],{},[898,23445,3677],{"mathvariant":2409},[898,23447,1702],{},[1706,23449,5915],{},[2148,23451,2150],{},[902,23453,23454],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,23457,23077],{}," (price elasticity of demand):",[724,23460,23461],{},[883,23462,23464],{"className":23463,"title":23358,"style":23359},[23357],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,23466,5331,23467,23490,23491,3526,23512,23536,23537,23557],{},[883,23468,23470],{"className":23469},[886],[888,23471,23472],{"xmlns":890},[892,23473,23474,23488],{},[895,23475,23476,23478,23480,23482,23484,23486],{},[898,23477,2146],{},[1706,23479,1708],{},[898,23481,2334],{},[1706,23483,2140],{"stretchy":2139},[898,23485,1702],{},[1706,23487,2153],{"stretchy":2139},[902,23489,23350],{"encoding":904},". Pro pevnou cenu ",[883,23492,23494],{"className":23493},[886],[888,23495,23496],{"xmlns":890},[892,23497,23498,23510],{},[895,23499,23500,23502,23504],{},[898,23501,1702],{},[1706,23503,1708],{},[2489,23505,23506,23508],{},[898,23507,1702],{},[1706,23509,3197],{},[902,23511,21043],{"encoding":904},[883,23513,23515],{"className":23514},[886],[888,23516,23517],{"xmlns":890},[892,23518,23519,23533],{},[895,23520,23521,23523,23525,23531],{},[898,23522,23410],{},[1706,23524,2140],{"stretchy":2139},[2489,23526,23527,23529],{},[898,23528,1702],{},[1706,23530,3197],{},[1706,23532,2153],{"stretchy":2139},[902,23534,23535],{"encoding":904},"E(P^*)"," nazývá ",[614,23538,23539,23540],{},"elasticita poptávky při ceně ",[883,23541,23543],{"className":23542},[886],[888,23544,23545],{"xmlns":890},[892,23546,23547,23555],{},[895,23548,23549],{},[2489,23550,23551,23553],{},[898,23552,1702],{},[1706,23554,3197],{},[902,23556,14075],{"encoding":904}," a je to vždy nezáporné číslo.",[1636,23559,23560],{},[724,23561,23562,23564,23565,23583,23584,23612,23613,23641,23642,1343,23660,1343,23678,23696,23697,23712,23713,1837],{},[883,23563,9276],{}," Pozor na znaménko\nV (4.5) je ",[38,23566,23567,23568],{},"explicitní ",[883,23569,23571],{"className":23570},[886],[888,23572,23573],{"xmlns":890},[892,23574,23575,23581],{},[895,23576,23577,23579],{},[1706,23578,1715],{},[2148,23580,2701],{},[902,23582,22909],{"encoding":904}," právě proto, že ",[883,23585,23587],{"className":23586},[886],[888,23588,23589],{"xmlns":890},[892,23590,23591,23609],{},[895,23592,23593,23599,23601,23603,23605,23607],{},[2489,23594,23595,23597],{},[898,23596,2146],{},[1706,23598,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,23600,2140],{"stretchy":2139},[898,23602,1702],{},[1706,23604,2153],{"stretchy":2139},[1706,23606,2539],{},[2148,23608,2150],{},[902,23610,23611],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,23614,23616],{"className":23615},[886],[888,23617,23618],{"xmlns":890},[892,23619,23620,23638],{},[895,23621,23622,23624,23626,23632,23634,23636],{},[898,23623,23410],{},[1706,23625,2140],{"stretchy":2139},[2489,23627,23628,23630],{},[898,23629,1702],{},[1706,23631,3197],{},[1706,23633,2153],{"stretchy":2139},[1706,23635,14220],{},[2148,23637,2150],{},[902,23639,23640],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,23643,23645],{"className":23644},[886],[888,23646,23647],{"xmlns":890},[892,23648,23649,23657],{},[895,23650,23651,23653,23655],{},[898,23652,23410],{},[1706,23654,8922],{},[2148,23656,2701],{},[902,23658,23659],{"encoding":904},"E > 1",[883,23661,23663],{"className":23662},[886],[888,23664,23665],{"xmlns":890},[892,23666,23667,23675],{},[895,23668,23669,23671,23673],{},[898,23670,23410],{},[1706,23672,2539],{},[2148,23674,2701],{},[902,23676,23677],{"encoding":904},"E \u003C 1",[883,23679,23681],{"className":23680},[886],[888,23682,23683],{"xmlns":890},[892,23684,23685,23693],{},[895,23686,23687,23689,23691],{},[898,23688,23410],{},[1706,23690,1708],{},[2148,23692,2701],{},[902,23694,23695],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,23698,23700],{"className":23699},[886],[888,23701,23702],{"xmlns":890},[892,23703,23704,23710],{},[895,23705,23706,23708],{},[1706,23707,1715],{},[2148,23709,2701],{},[902,23711,22909],{"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 ",[38,23714,23715],{},"absolutní hodnotou",[1636,23717,23718,23737],{},[724,23719,23720,23722,23723,23736],{},[883,23721,12314],{}," Postup: jak spočítat ",[883,23724,23726],{"className":23725},[886],[888,23727,23728],{"xmlns":890},[892,23729,23730,23734],{},[895,23731,23732],{},[898,23733,23410],{},[902,23735,23410],{"encoding":904}," v bodě",[152,23738,23739,23790,23829,23882,23947],{},[123,23740,23741,23742,23765,23766,23789],{},"Zapište ",[883,23743,23745],{"className":23744},[886],[888,23746,23747],{"xmlns":890},[892,23748,23749,23763],{},[895,23750,23751,23753,23755,23757,23759,23761],{},[898,23752,2146],{},[1706,23754,1708],{},[898,23756,2334],{},[1706,23758,2140],{"stretchy":2139},[898,23760,1702],{},[1706,23762,2153],{"stretchy":2139},[902,23764,23350],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,23767,23769],{"className":23768},[886],[888,23770,23771],{"xmlns":890},[892,23772,23773,23787],{},[895,23774,23775,23777,23779,23781,23783,23785],{},[898,23776,1702],{},[1706,23778,1708],{},[898,23780,2334],{},[1706,23782,2140],{"stretchy":2139},[898,23784,2146],{},[1706,23786,2153],{"stretchy":2139},[902,23788,2343],{"encoding":904},", použijte vztah (4.9).",[123,23791,23792,23793,1837],{},"Spočítejte derivaci ",[883,23794,23796],{"className":23795},[886],[888,23797,23798],{"xmlns":890},[892,23799,23800,23826],{},[895,23801,23802,23808,23810,23812,23814,23816,23818,23820,23822,23824],{},[2489,23803,23804,23806],{},[898,23805,2146],{},[1706,23807,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,23809,2140],{"stretchy":2139},[898,23811,1702],{},[1706,23813,2153],{"stretchy":2139},[1706,23815,1708],{},[898,23817,3120],{"mathvariant":2409},[898,23819,2146],{},[898,23821,15493],{"mathvariant":2409},[898,23823,3120],{"mathvariant":2409},[898,23825,1702],{},[902,23827,23828],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,23830,23831,23832,23849,23850,1837],{},"Dosaďte zadanou cenu ",[883,23833,23835],{"className":23834},[886],[888,23836,23837],{"xmlns":890},[892,23838,23839,23847],{},[895,23840,23841],{},[2489,23842,23843,23845],{},[898,23844,1702],{},[1706,23846,3197],{},[902,23848,14075],{"encoding":904}," a dopočítejte odpovídající ",[883,23851,23853],{"className":23852},[886],[888,23854,23855],{"xmlns":890},[892,23856,23857,23879],{},[895,23858,23859,23865,23867,23869,23871,23877],{},[2489,23860,23861,23863],{},[898,23862,2146],{},[1706,23864,3197],{},[1706,23866,1708],{},[898,23868,2334],{},[1706,23870,2140],{"stretchy":2139},[2489,23872,23873,23875],{},[898,23874,1702],{},[1706,23876,3197],{},[1706,23878,2153],{"stretchy":2139},[902,23880,23881],{"encoding":904},"Q^* = D(P^*)",[123,23883,23884,23885,1837],{},"Dosaďte do (4.5): ",[883,23886,23888],{"className":23887},[886],[888,23889,23890],{"xmlns":890},[892,23891,23892,23944],{},[895,23893,23894,23896,23898,23904,23906,23908,23910,23926,23928,23934,23936,23942],{},[898,23895,23410],{},[1706,23897,2140],{"stretchy":2139},[2489,23899,23900,23902],{},[898,23901,1702],{},[1706,23903,3197],{},[1706,23905,2153],{"stretchy":2139},[1706,23907,1708],{},[1706,23909,1715],{},[4745,23911,23912],{"scriptlevel":2150,"displaystyle":2504},[2964,23913,23914,23920],{},[2489,23915,23916,23918],{},[898,23917,1702],{},[1706,23919,3197],{},[2489,23921,23922,23924],{},[898,23923,2146],{},[1706,23925,3197],{},[2415,23927,2799],{},[2489,23929,23930,23932],{},[898,23931,2146],{},[1706,23933,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,23935,2140],{"stretchy":2139},[2489,23937,23938,23940],{},[898,23939,1702],{},[1706,23941,3197],{},[1706,23943,2153],{"stretchy":2139},[902,23945,23946],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,23948,23949,23950,23967,23968,23985,23986,24003],{},"Klasifikujte: ",[883,23951,23953],{"className":23952},[886],[888,23954,23955],{"xmlns":890},[892,23956,23957,23965],{},[895,23958,23959,23961,23963],{},[898,23960,23410],{},[1706,23962,8922],{},[2148,23964,2701],{},[902,23966,23659],{"encoding":904}," elastická, ",[883,23969,23971],{"className":23970},[886],[888,23972,23973],{"xmlns":890},[892,23974,23975,23983],{},[895,23976,23977,23979,23981],{},[898,23978,23410],{},[1706,23980,1708],{},[2148,23982,2701],{},[902,23984,23695],{"encoding":904}," jednotková, ",[883,23987,23989],{"className":23988},[886],[888,23990,23991],{"xmlns":890},[892,23992,23993,24001],{},[895,23994,23995,23997,23999],{},[898,23996,23410],{},[1706,23998,2539],{},[2148,24000,2701],{},[902,24002,23677],{"encoding":904}," neelastická.",[198,24005,24007],{"id":24006},"interpretace-46","Interpretace (4.6)",[1636,24009,24010],{},[724,24011,24012,24013,24036,24037,24050,24051,24068,24069],{},"Číslo ",[883,24014,24016],{"className":24015},[886],[888,24017,24018],{"xmlns":890},[892,24019,24020,24034],{},[895,24021,24022,24024,24026,24032],{},[898,24023,23410],{},[1706,24025,2140],{"stretchy":2139},[2489,24027,24028,24030],{},[898,24029,1702],{},[1706,24031,3197],{},[1706,24033,2153],{"stretchy":2139},[902,24035,23535],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,24038,24040],{"className":24039},[886],[888,24041,24042],{"xmlns":890},[892,24043,24044,24048],{},[895,24045,24046],{},[898,24047,2146],{},[902,24049,2146],{"encoding":904},", jestliže se cena ",[883,24052,24054],{"className":24053},[886],[888,24055,24056],{"xmlns":890},[892,24057,24058,24066],{},[895,24059,24060],{},[2489,24061,24062,24064],{},[898,24063,1702],{},[1706,24065,3197],{},[902,24067,14075],{"encoding":904}," změní o 1 %. ",[883,24070,24072],{"className":24071},[886],[888,24073,24074],{"xmlns":890},[892,24075,24076,24085],{},[895,24077,24078,24080,24083],{},[1706,24079,2140],{"stretchy":2139},[2148,24081,24082],{},"4.6",[1706,24084,2153],{"stretchy":2139},[902,24086,24087],{"encoding":904},"(4.6)",[724,24089,24090,24093],{},[38,24091,24092],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,24095,24097],{"id":24096},"příklad-41","Příklad 4.1",[724,24099,24100,24101,24135,24136,1343,24160,4288],{},"Poptávka ",[883,24102,24104],{"className":24103},[886],[888,24105,24106],{"xmlns":890},[892,24107,24108,24132],{},[895,24109,24110,24112,24114,24116,24118,24120,24122,24124,24126,24128,24130],{},[898,24111,1702],{},[1706,24113,1708],{},[898,24115,2334],{},[1706,24117,2140],{"stretchy":2139},[898,24119,2146],{},[1706,24121,2153],{"stretchy":2139},[1706,24123,1708],{},[2148,24125,2728],{},[1706,24127,1715],{},[2148,24129,2495],{},[898,24131,2146],{},[902,24133,24134],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,24137,24139],{"className":24138},[886],[888,24140,24141],{"xmlns":890},[892,24142,24143,24157],{},[895,24144,24145,24147,24149,24151,24153,24155],{},[898,24146,2146],{},[1706,24148,1708],{},[2148,24150,2748],{},[1706,24152,1715],{},[2148,24154,11496],{},[898,24156,1702],{},[902,24158,24159],{"encoding":904},"Q = 25 - 0{,}5P",[883,24161,24163],{"className":24162},[886],[888,24164,24165],{"xmlns":890},[892,24166,24167,24191],{},[895,24168,24169,24185,24187,24189],{},[4745,24170,24171],{"scriptlevel":2150,"displaystyle":2504},[2964,24172,24173,24179],{},[895,24174,24175,24177],{},[898,24176,3120],{"mathvariant":2409},[898,24178,2146],{},[895,24180,24181,24183],{},[898,24182,3120],{"mathvariant":2409},[898,24184,1702],{},[1706,24186,1708],{},[1706,24188,1715],{},[2148,24190,11496],{},[902,24192,24193],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,24195,24196],{},[883,24197,24199],{"className":24198},[886],[888,24200,24201],{"xmlns":890},[892,24202,24203,24257],{},[895,24204,24205,24207,24209,24211,24225,24227,24229,24231,24233,24235,24237,24255],{},[898,24206,23410],{},[1706,24208,1708],{},[1706,24210,1715],{},[2964,24212,24213,24215],{},[898,24214,1702],{},[895,24216,24217,24219,24221,24223],{},[2148,24218,2748],{},[1706,24220,1715],{},[2148,24222,11496],{},[898,24224,1702],{},[1706,24226,2390],{},[1706,24228,2140],{"stretchy":2139},[1706,24230,1715],{},[2148,24232,11496],{},[1706,24234,2153],{"stretchy":2139},[1706,24236,1708],{},[2964,24238,24239,24245],{},[895,24240,24241,24243],{},[2148,24242,11496],{},[898,24244,1702],{},[895,24246,24247,24249,24251,24253],{},[2148,24248,2748],{},[1706,24250,1715],{},[2148,24252,11496],{},[898,24254,1702],{},[898,24256,1837],{"mathvariant":2409},[902,24258,24259],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,24261,24262,24263,1343,24287,1343,24317,1343,24341,24365,24366,24389,24390,4202,24408,1936],{},"Potom ",[883,24264,24266],{"className":24265},[886],[888,24267,24268],{"xmlns":890},[892,24269,24270,24284],{},[895,24271,24272,24274,24276,24278,24280,24282],{},[898,24273,23410],{},[1706,24275,2140],{"stretchy":2139},[2148,24277,2150],{},[1706,24279,2153],{"stretchy":2139},[1706,24281,1708],{},[2148,24283,2150],{},[902,24285,24286],{"encoding":904},"E(0)=0",[883,24288,24290],{"className":24289},[886],[888,24291,24292],{"xmlns":890},[892,24293,24294,24314],{},[895,24295,24296,24298,24300,24302,24304,24306],{},[898,24297,23410],{},[1706,24299,2140],{"stretchy":2139},[2148,24301,7786],{},[1706,24303,2153],{"stretchy":2139},[1706,24305,1708],{},[4745,24307,24308],{"scriptlevel":2150,"displaystyle":2139},[2964,24309,24310,24312],{},[2148,24311,2701],{},[2148,24313,3455],{},[902,24315,24316],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,24318,24320],{"className":24319},[886],[888,24321,24322],{"xmlns":890},[892,24323,24324,24338],{},[895,24325,24326,24328,24330,24332,24334,24336],{},[898,24327,23410],{},[1706,24329,2140],{"stretchy":2139},[2148,24331,2748],{},[1706,24333,2153],{"stretchy":2139},[1706,24335,1708],{},[2148,24337,2701],{},[902,24339,24340],{"encoding":904},"E(25)=1",[883,24342,24344],{"className":24343},[886],[888,24345,24346],{"xmlns":890},[892,24347,24348,24362],{},[895,24349,24350,24352,24354,24356,24358,24360],{},[898,24351,23410],{},[1706,24353,2140],{"stretchy":2139},[2148,24355,3508],{},[1706,24357,2153],{"stretchy":2139},[1706,24359,1708],{},[2148,24361,3455],{},[902,24363,24364],{"encoding":904},"E(40)=4",". Např. ",[883,24367,24369],{"className":24368},[886],[888,24370,24371],{"xmlns":890},[892,24372,24373,24387],{},[895,24374,24375,24377,24379,24381,24383,24385],{},[898,24376,23410],{},[1706,24378,2140],{"stretchy":2139},[2148,24380,3508],{},[1706,24382,2153],{"stretchy":2139},[1706,24384,1708],{},[2148,24386,3455],{},[902,24388,24364],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,24391,24393],{"className":24392},[886],[888,24394,24395],{"xmlns":890},[892,24396,24397,24405],{},[895,24398,24399,24401,24403],{},[898,24400,2146],{},[1706,24402,1708],{},[2148,24404,7524],{},[902,24406,24407],{"encoding":904},"Q=5",[883,24409,24411],{"className":24410},[886],[888,24412,24413],{"xmlns":890},[892,24414,24415,24423],{},[895,24416,24417,24419,24421],{},[898,24418,2146],{},[1706,24420,1708],{},[2148,24422,17862],{},[902,24424,24425],{"encoding":904},"Q=4{,}8",[198,24427,24429],{"id":24428},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,24431,24432,24488],{},[123,24433,24434,24437,24438,24455,24456,1837],{},[38,24435,24436],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,24439,24441],{"className":24440},[886],[888,24442,24443],{"xmlns":890},[892,24444,24445,24453],{},[895,24446,24447],{},[2489,24448,24449,24451],{},[898,24450,23410],{},[898,24452,1735],{},[902,24454,23415],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,24457,24459],{"className":24458},[886],[888,24460,24461],{"xmlns":890},[892,24462,24463,24485],{},[895,24464,24465,24468,24470,24472,24474,24476,24478,24480,24482],{},[1706,24466,24467],{"stretchy":2139},"⟨",[898,24469,1702],{},[1706,24471,2505],{"separator":2504},[2415,24473,2799],{},[898,24475,1702],{},[1706,24477,2447],{},[898,24479,3677],{"mathvariant":2409},[898,24481,1702],{},[1706,24483,24484],{"stretchy":2139},"⟩",[902,24486,24487],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,24489,24490,24493,24494,24507],{},[38,24491,24492],{},"Bodová"," (okamžitá) elasticita: ",[883,24495,24497],{"className":24496},[886],[888,24498,24499],{"xmlns":890},[892,24500,24501,24505],{},[895,24502,24503],{},[898,24504,23410],{},[902,24506,23410],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,24509,24511,24512,14984,24525],{"id":24510},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,24513,24515],{"className":24514},[886],[888,24516,24517],{"xmlns":890},[892,24518,24519,24523],{},[895,24520,24521],{},[898,24522,1702],{},[902,24524,1702],{"encoding":904},[883,24526,24528],{"className":24527},[886],[888,24529,24530],{"xmlns":890},[892,24531,24532,24536],{},[895,24533,24534],{},[898,24535,2146],{},[902,24537,2146],{"encoding":904},[724,24539,24540,24541,24564],{},"Pokud je poptávka zadaná ve tvaru ",[883,24542,24544],{"className":24543},[886],[888,24545,24546],{"xmlns":890},[892,24547,24548,24562],{},[895,24549,24550,24552,24554,24556,24558,24560],{},[898,24551,1702],{},[1706,24553,1708],{},[898,24555,2334],{},[1706,24557,2140],{"stretchy":2139},[898,24559,2146],{},[1706,24561,2153],{"stretchy":2139},[902,24563,2343],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,24566,24567],{},[883,24568,24570],{"className":24569,"title":23358,"style":23359},[23357],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,24572,24573,1647,24576,24602],{},[38,24574,24575],{},"Příklad 4.3.",[883,24577,24579],{"className":24578},[886],[888,24580,24581],{"xmlns":890},[892,24582,24583,24599],{},[895,24584,24585,24587,24589,24591,24593],{},[898,24586,1702],{},[1706,24588,1708],{},[2148,24590,2590],{},[1706,24592,1715],{},[2489,24594,24595,24597],{},[898,24596,2146],{},[2148,24598,2495],{},[902,24600,24601],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,24604,24605],{},[883,24606,24608],{"className":24607},[886],[888,24609,24610],{"xmlns":890},[892,24611,24612,24678],{},[895,24613,24614,24616,24618,24620,24636,24638,24650,24652,24676],{},[898,24615,23410],{},[1706,24617,1708],{},[1706,24619,1715],{},[2964,24621,24622,24634],{},[895,24623,24624,24626,24628],{},[2148,24625,2590],{},[1706,24627,1715],{},[2489,24629,24630,24632],{},[898,24631,2146],{},[2148,24633,2495],{},[898,24635,2146],{},[1706,24637,2390],{},[2964,24639,24640,24642],{},[2148,24641,2701],{},[895,24643,24644,24646,24648],{},[1706,24645,1715],{},[2148,24647,2495],{},[898,24649,2146],{},[1706,24651,1708],{},[2964,24653,24654,24666],{},[895,24655,24656,24658,24660],{},[2148,24657,2590],{},[1706,24659,1715],{},[2489,24661,24662,24664],{},[898,24663,2146],{},[2148,24665,2495],{},[895,24667,24668,24670],{},[2148,24669,2495],{},[2489,24671,24672,24674],{},[898,24673,2146],{},[2148,24675,2495],{},[898,24677,1837],{"mathvariant":2409},[902,24679,24680],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,24682,24683,24684,24710,24711,24728,24729,1837],{},"Z rovnice ",[883,24685,24687],{"className":24686},[886],[888,24688,24689],{"xmlns":890},[892,24690,24691,24707],{},[895,24692,24693,24695,24697,24703,24705],{},[2148,24694,2590],{},[1706,24696,1715],{},[2489,24698,24699,24701],{},[898,24700,2146],{},[2148,24702,2495],{},[1706,24704,1708],{},[2148,24706,3757],{},[902,24708,24709],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,24712,24714],{"className":24713},[886],[888,24715,24716],{"xmlns":890},[892,24717,24718,24726],{},[895,24719,24720,24722,24724],{},[898,24721,2146],{},[1706,24723,1708],{},[2148,24725,12717],{},[902,24727,16609],{"encoding":904},", tedy ",[883,24730,24732],{"className":24731},[886],[888,24733,24734],{"xmlns":890},[892,24735,24736,24762],{},[895,24737,24738,24740,24742,24744,24746,24748,24757,24759],{},[898,24739,23410],{},[1706,24741,2140],{"stretchy":2139},[2148,24743,12717],{},[1706,24745,2153],{"stretchy":2139},[1706,24747,1708],{},[4745,24749,24750],{"scriptlevel":2150,"displaystyle":2139},[2964,24751,24752,24754],{},[2148,24753,3757],{},[2148,24755,24756],{},"128",[1706,24758,1708],{},[2148,24760,24761],{},"0,281",[902,24763,24764],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,24766,24768],{"id":24767},"přibližné-změny","Přibližné změny",[724,24770,24771,24772,24808,24809,24831],{},"Diferenciál ",[883,24773,24775],{"className":24774},[886],[888,24776,24777],{"xmlns":890},[892,24778,24779,24805],{},[895,24780,24781,24783,24785,24787,24793,24795,24797,24799,24801,24803],{},[898,24782,3120],{"mathvariant":2409},[898,24784,2146],{},[1706,24786,1708],{},[2489,24788,24789,24791],{},[898,24790,2146],{},[1706,24792,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,24794,2140],{"stretchy":2139},[898,24796,1702],{},[1706,24798,2153],{"stretchy":2139},[2415,24800,2799],{},[898,24802,3120],{"mathvariant":2409},[898,24804,1702],{},[902,24806,24807],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[883,24810,24812],{"className":24811},[886],[888,24813,24814],{"xmlns":890},[892,24815,24816,24828],{},[895,24817,24818,24820,24822,24824,24826],{},[898,24819,3120],{"mathvariant":2409},[898,24821,1702],{},[1706,24823,1708],{},[898,24825,3677],{"mathvariant":2409},[898,24827,1702],{},[902,24829,24830],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,24833,24834],{},[883,24835,24837],{"className":24836,"title":23358,"style":23359},[23357],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,24839,24840],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,24842,24843],{},[883,24844,24846],{"className":24845,"title":23358,"style":23359},[23357],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,24848,24849,1647,24852,24886,24887,24906,24907,24941,24942,24959],{},[38,24850,24851],{},"Příklad 4.5.",[883,24853,24855],{"className":24854},[886],[888,24856,24857],{"xmlns":890},[892,24858,24859,24883],{},[895,24860,24861,24863,24865,24867,24873,24875,24877,24879,24881],{},[898,24862,1702],{},[1706,24864,1708],{},[1706,24866,1715],{},[2489,24868,24869,24871],{},[898,24870,2146],{},[2148,24872,2495],{},[1706,24874,1715],{},[2148,24876,3455],{},[898,24878,2146],{},[1706,24880,2447],{},[2148,24882,19063],{},[902,24884,24885],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,24888,24890],{"className":24889},[886],[888,24891,24892],{"xmlns":890},[892,24893,24894,24903],{},[895,24895,24896,24898,24900],{},[898,24897,1702],{},[1706,24899,1708],{},[2148,24901,24902],{},"51",[902,24904,24905],{"encoding":904},"P=51",". Z rovnice ",[883,24908,24910],{"className":24909},[886],[888,24911,24912],{"xmlns":890},[892,24913,24914,24938],{},[895,24915,24916,24918,24920,24922,24928,24930,24932,24934,24936],{},[2148,24917,24902],{},[1706,24919,1708],{},[1706,24921,1715],{},[2489,24923,24924,24926],{},[898,24925,2146],{},[2148,24927,2495],{},[1706,24929,1715],{},[2148,24931,3455],{},[898,24933,2146],{},[1706,24935,2447],{},[2148,24937,19063],{},[902,24939,24940],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,24943,24945],{"className":24944},[886],[888,24946,24947],{"xmlns":890},[892,24948,24949,24957],{},[895,24950,24951,24953,24955],{},[898,24952,2146],{},[1706,24954,1708],{},[2148,24956,7524],{},[902,24958,24407],{"encoding":904},". Elasticita:",[724,24961,24962],{},[883,24963,24965],{"className":24964},[886],[888,24966,24967],{"xmlns":890},[892,24968,24969,25039],{},[895,24970,24971,24973,24975,25013,25015,25017,25019,25021,25023,25025,25027,25034,25036],{},[898,24972,23410],{},[1706,24974,1708],{},[2964,24976,24977,24997],{},[895,24978,24979,24981,24987,24989,24991,24993,24995],{},[1706,24980,1715],{},[2489,24982,24983,24985],{},[898,24984,2146],{},[2148,24986,2495],{},[1706,24988,1715],{},[2148,24990,3455],{},[898,24992,2146],{},[1706,24994,2447],{},[2148,24996,19063],{},[895,24998,24999,25001,25003,25005,25007,25009,25011],{},[898,25000,2146],{},[1706,25002,2140],{"stretchy":2139},[2148,25004,2495],{},[898,25006,2146],{},[1706,25008,2447],{},[2148,25010,3455],{},[1706,25012,2153],{"stretchy":2139},[1706,25014,2505],{"separator":2504},[4898,25016],{"width":9524},[898,25018,23410],{},[1706,25020,2140],{"stretchy":2139},[2148,25022,7524],{},[1706,25024,2153],{"stretchy":2139},[1706,25026,1708],{},[2964,25028,25029,25031],{},[2148,25030,24902],{},[2148,25032,25033],{},"70",[1706,25035,7883],{},[2148,25037,25038],{},"0,728.",[902,25040,25041],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,25043,25044,25045,1837],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,25046,25048],{"className":25047},[886],[888,25049,25050],{"xmlns":890},[892,25051,25052,25083],{},[895,25053,25054,25056,25058,25061,25063,25065,25068,25070,25072,25074,25076,25079,25081],{},[898,25055,3677],{"mathvariant":2409},[898,25057,2146],{},[898,25059,25060],{"mathvariant":2409},"%",[1706,25062,3248],{},[1706,25064,1715],{},[2148,25066,25067],{},"0,728",[1706,25069,2390],{},[2148,25071,2495],{},[1706,25073,1708],{},[1706,25075,1715],{},[2148,25077,25078],{},"1,456",[2415,25080,2799],{},[898,25082,25060],{"mathvariant":2409},[902,25084,25085],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,25087,25089],{"id":25088},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,25091,25092,25093,25116,25117,4288],{},"V závislosti na hodnotě ",[883,25094,25096],{"className":25095},[886],[888,25097,25098],{"xmlns":890},[892,25099,25100,25114],{},[895,25101,25102,25104,25106,25112],{},[898,25103,23410],{},[1706,25105,2140],{"stretchy":2139},[2489,25107,25108,25110],{},[898,25109,1702],{},[1706,25111,3197],{},[1706,25113,2153],{"stretchy":2139},[902,25115,23535],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,25118,25120],{"className":25119},[886],[888,25121,25122],{"xmlns":890},[892,25123,25124,25133],{},[895,25125,25126,25128,25131],{},[1706,25127,2140],{"stretchy":2139},[2148,25129,25130],{},"4.7",[1706,25132,2153],{"stretchy":2139},[902,25134,25135],{"encoding":904},"(4.7)",[724,25137,25138],{},[2286,25139],{"alt":25140,"className":25141,"src":25142},"imek-typy-elasticity-5panelu",[210,2290],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,25144,25145,25184],{},[19,25146,25147],{},[22,25148,25149,25175,25178,25181],{},[25,25150,25151,25152],{},"Hodnota ",[883,25153,25155],{"className":25154},[886],[888,25156,25157],{"xmlns":890},[892,25158,25159,25173],{},[895,25160,25161,25163,25165,25171],{},[898,25162,23410],{},[1706,25164,2140],{"stretchy":2139},[2489,25166,25167,25169],{},[898,25168,1702],{},[1706,25170,3197],{},[1706,25172,2153],{"stretchy":2139},[902,25174,23535],{"encoding":904},[25,25176,25177],{},"Typ poptávky",[25,25179,25180],{},"Termín",[25,25182,25183],{},"Význam",[30,25185,25186,25219,25281,25355,25412],{},[22,25187,25188,25208,25213,25216],{},[35,25189,25190],{},[883,25191,25193],{"className":25192},[886],[888,25194,25195],{"xmlns":890},[892,25196,25197,25205],{},[895,25198,25199,25201,25203],{},[898,25200,23410],{},[1706,25202,1708],{},[2148,25204,2150],{},[902,25206,25207],{"encoding":904},"E = 0",[35,25209,25210],{},[38,25211,25212],{},"dokonale neelastická",[35,25214,25215],{},"perfectly inelastic",[35,25217,25218],{},"množství se nemění bez ohledu na cenu",[22,25220,25221,25245,25249,25252],{},[35,25222,25223],{},[883,25224,25226],{"className":25225},[886],[888,25227,25228],{"xmlns":890},[892,25229,25230,25242],{},[895,25231,25232,25234,25236,25238,25240],{},[2148,25233,2150],{},[1706,25235,2539],{},[898,25237,23410],{},[1706,25239,2539],{},[2148,25241,2701],{},[902,25243,25244],{"encoding":904},"0 \u003C E \u003C 1",[35,25246,25247],{},[38,25248,23238],{},[35,25250,25251],{},"inelastic",[35,25253,25254,25267,25268],{},[883,25255,25257],{"className":25256},[886],[888,25258,25259],{"xmlns":890},[892,25260,25261,25265],{},[895,25262,25263],{},[898,25264,2146],{},[902,25266,2146],{"encoding":904}," se mění pomaleji než ",[883,25269,25271],{"className":25270},[886],[888,25272,25273],{"xmlns":890},[892,25274,25275,25279],{},[895,25276,25277],{},[898,25278,1702],{},[902,25280,1702],{"encoding":904},[22,25282,25283,25302,25307,25310],{},[35,25284,25285],{},[883,25286,25288],{"className":25287},[886],[888,25289,25290],{"xmlns":890},[892,25291,25292,25300],{},[895,25293,25294,25296,25298],{},[898,25295,23410],{},[1706,25297,1708],{},[2148,25299,2701],{},[902,25301,23695],{"encoding":904},[35,25303,25304],{},[38,25305,25306],{},"jednotkově elastická",[35,25308,25309],{},"unit elastic",[35,25311,25312,8156,25325,25338,25339,25354],{},[883,25313,25315],{"className":25314},[886],[888,25316,25317],{"xmlns":890},[892,25318,25319,25323],{},[895,25320,25321],{},[898,25322,2146],{},[902,25324,2146],{"encoding":904},[883,25326,25328],{"className":25327},[886],[888,25329,25330],{"xmlns":890},[892,25331,25332,25336],{},[895,25333,25334],{},[898,25335,1702],{},[902,25337,1702],{"encoding":904}," se mění stejně rychle; ",[883,25340,25342],{"className":25341},[886],[888,25343,25344],{"xmlns":890},[892,25345,25346,25352],{},[895,25347,25348,25350],{},[898,25349,1659],{},[898,25351,1662],{},[902,25353,1665],{"encoding":904}," má maximum",[22,25356,25357,25376,25380,25383],{},[35,25358,25359],{},[883,25360,25362],{"className":25361},[886],[888,25363,25364],{"xmlns":890},[892,25365,25366,25374],{},[895,25367,25368,25370,25372],{},[898,25369,23410],{},[1706,25371,8922],{},[2148,25373,2701],{},[902,25375,23659],{"encoding":904},[35,25377,25378],{},[38,25379,23234],{},[35,25381,25382],{},"elastic",[35,25384,25385,25398,25399],{},[883,25386,25388],{"className":25387},[886],[888,25389,25390],{"xmlns":890},[892,25391,25392,25396],{},[895,25393,25394],{},[898,25395,2146],{},[902,25397,2146],{"encoding":904}," se mění rychleji než ",[883,25400,25402],{"className":25401},[886],[888,25403,25404],{"xmlns":890},[892,25405,25406,25410],{},[895,25407,25408],{},[898,25409,1702],{},[902,25411,1702],{"encoding":904},[22,25413,25414,25434,25439,25442],{},[35,25415,25416],{},[883,25417,25419],{"className":25418},[886],[888,25420,25421],{"xmlns":890},[892,25422,25423,25431],{},[895,25424,25425,25427,25429],{},[898,25426,23410],{},[1706,25428,5915],{},[898,25430,5918],{"mathvariant":2409},[902,25432,25433],{"encoding":904},"E \\to \\infty",[35,25435,25436],{},[38,25437,25438],{},"dokonale elastická",[35,25440,25441],{},"perfectly elastic",[35,25443,25444,25445],{},"sebemenší změna ceny úplně mění ",[883,25446,25448],{"className":25447},[886],[888,25449,25450],{"xmlns":890},[892,25451,25452,25456],{},[895,25453,25454],{},[898,25455,2146],{},[902,25457,2146],{"encoding":904},[724,25459,25460],{},[38,25461,25462],{},"Pravidlo růstu elasticity s cenou:",[1636,25464,25465],{},[724,25466,25467,25468],{},"S rostoucí cenou elasticita poptávky roste. ",[883,25469,25471],{"className":25470},[886],[888,25472,25473],{"xmlns":890},[892,25474,25475,25484],{},[895,25476,25477,25479,25482],{},[1706,25478,2140],{"stretchy":2139},[2148,25480,25481],{},"4.8",[1706,25483,2153],{"stretchy":2139},[902,25485,25486],{"encoding":904},"(4.8)",[724,25488,25489,25490,25493,25494,25497,25498,25515],{},"Z toho plyne, že při ",[614,25491,25492],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,25495,25496],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,25499,25501],{"className":25500},[886],[888,25502,25503],{"xmlns":890},[892,25504,25505,25513],{},[895,25506,25507],{},[2489,25508,25509,25511],{},[898,25510,1702],{},[1706,25512,3197],{},[902,25514,14075],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[1636,25517,25518,25523],{},[724,25519,25520,25522],{},[883,25521,12314],{}," Postup: jak klasifikovat poptávku",[152,25524,25525,25552,25555],{},[123,25526,25527,25528,25551],{},"Spočítejte ",[883,25529,25531],{"className":25530},[886],[888,25532,25533],{"xmlns":890},[892,25534,25535,25549],{},[895,25536,25537,25539,25541,25547],{},[898,25538,23410],{},[1706,25540,2140],{"stretchy":2139},[2489,25542,25543,25545],{},[898,25544,1702],{},[1706,25546,3197],{},[1706,25548,2153],{"stretchy":2139},[902,25550,23535],{"encoding":904}," dle (4.5).",[123,25553,25554],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,25556,25557,25558,25582],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,25559,25561],{"className":25560},[886],[888,25562,25563],{"xmlns":890},[892,25564,25565,25579],{},[895,25566,25567,25569,25571,25573,25575,25577],{},[898,25568,23410],{},[1706,25570,2140],{"stretchy":2139},[898,25572,1702],{},[1706,25574,2153],{"stretchy":2139},[1706,25576,1708],{},[2148,25578,2701],{},[902,25580,25581],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,25584,25585,25588,25589,10691,25606,25624,25625,25652,25653,1837],{},[38,25586,25587],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,25590,25592],{"className":25591},[886],[888,25593,25594],{"xmlns":890},[892,25595,25596,25604],{},[895,25597,25598,25600,25602],{},[898,25599,23410],{},[1706,25601,1708],{},[2148,25603,2701],{},[902,25605,23695],{"encoding":904},[883,25607,25609],{"className":25608},[886],[888,25610,25611],{"xmlns":890},[892,25612,25613,25621],{},[895,25614,25615,25617,25619],{},[898,25616,1702],{},[1706,25618,1708],{},[2148,25620,2748],{},[902,25622,25623],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,25626,25628],{"className":25627},[886],[888,25629,25630],{"xmlns":890},[892,25631,25632,25649],{},[895,25633,25634,25636,25639,25641,25643,25645,25647],{},[898,25635,1702],{},[1706,25637,25638],{},"∈",[1706,25640,24467],{"stretchy":2139},[2148,25642,2150],{},[1706,25644,2505],{"separator":2504},[2148,25646,2748],{},[1706,25648,2153],{"stretchy":2139},[902,25650,25651],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,25654,25656],{"className":25655},[886],[888,25657,25658],{"xmlns":890},[892,25659,25660,25676],{},[895,25661,25662,25664,25666,25668,25670,25672,25674],{},[898,25663,1702],{},[1706,25665,25638],{},[1706,25667,2140],{"stretchy":2139},[2148,25669,2748],{},[1706,25671,2505],{"separator":2504},[2148,25673,2728],{},[1706,25675,24484],{"stretchy":2139},[902,25677,25678],{"encoding":904},"P \\in (25, 50\\rangle",[115,25680,25682],{"id":25681},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,25684,25685],{},[2286,25686],{"alt":25687,"className":25688,"src":25689},"imek-elasticita-tr",[210,2290],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,25691,25692],{},[2286,25693],{"alt":25694,"className":25695,"src":25696},"imek-elasticita-podel-linearni-poptavky",[210,2290],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,25698,25699,25700,25750,25751,25766],{},"Pro celkový příjem platí ",[883,25701,25703],{"className":25702},[886],[888,25704,25705],{"xmlns":890},[892,25706,25707,25747],{},[895,25708,25709,25711,25713,25715,25717,25719,25721,25723,25725,25727,25729,25731,25733,25735,25737,25739,25741,25743,25745],{},[898,25710,1659],{},[898,25712,1662],{},[1706,25714,1708],{},[898,25716,1659],{},[898,25718,1662],{},[1706,25720,2140],{"stretchy":2139},[898,25722,2146],{},[1706,25724,2153],{"stretchy":2139},[1706,25726,1708],{},[898,25728,1702],{},[1706,25730,2390],{},[898,25732,2146],{},[1706,25734,1708],{},[898,25736,2146],{},[1706,25738,2390],{},[898,25740,2334],{},[1706,25742,2140],{"stretchy":2139},[898,25744,2146],{},[1706,25746,2153],{"stretchy":2139},[902,25748,25749],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,25752,25754],{"className":25753},[886],[888,25755,25756],{"xmlns":890},[892,25757,25758,25764],{},[895,25759,25760,25762],{},[898,25761,1742],{},[898,25763,1662],{},[902,25765,1905],{"encoding":904}," odvodíme:",[724,25768,25769],{},[883,25770,25772],{"className":25771},[886],[888,25773,25774],{"xmlns":890},[892,25775,25776,25884],{},[895,25777,25778,25780,25782,25784,25786,25792,25794,25796,25798,25800,25802,25804,25806,25808,25810,25812,25814,25820,25822,25824,25826,25828,25830,25832,25834,25848,25850,25852],{},[898,25779,1742],{},[898,25781,1662],{},[1706,25783,1708],{},[898,25785,1659],{},[2489,25787,25788,25790],{},[898,25789,1662],{},[1706,25791,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,25793,2140],{"stretchy":2139},[898,25795,2146],{},[1706,25797,2153],{"stretchy":2139},[1706,25799,1708],{},[898,25801,2334],{},[1706,25803,2140],{"stretchy":2139},[898,25805,2146],{},[1706,25807,2153],{"stretchy":2139},[1706,25809,2447],{},[898,25811,2146],{},[2415,25813,2799],{},[2489,25815,25816,25818],{},[898,25817,2334],{},[1706,25819,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,25821,2140],{"stretchy":2139},[898,25823,2146],{},[1706,25825,2153],{"stretchy":2139},[1706,25827,1708],{},[898,25829,1702],{},[1706,25831,2447],{},[898,25833,2146],{},[2964,25835,25836,25842],{},[895,25837,25838,25840],{},[898,25839,3120],{"mathvariant":2409},[898,25841,1702],{},[895,25843,25844,25846],{},[898,25845,3120],{"mathvariant":2409},[898,25847,2146],{},[1706,25849,1708],{},[898,25851,1702],{},[895,25853,25854,25856,25858,25860,25866,25868,25882],{},[1706,25855,2140],{"fence":2504},[2148,25857,2701],{},[1706,25859,2447],{},[2964,25861,25862,25864],{},[898,25863,2146],{},[898,25865,1702],{},[1706,25867,2390],{},[2964,25869,25870,25876],{},[895,25871,25872,25874],{},[898,25873,3120],{"mathvariant":2409},[898,25875,1702],{},[895,25877,25878,25880],{},[898,25879,3120],{"mathvariant":2409},[898,25881,2146],{},[1706,25883,2153],{"fence":2504},[902,25885,25886],{"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)",[724,25888,25889],{},[883,25890,25892],{"className":25891},[886],[888,25893,25894],{"xmlns":890},[892,25895,25896,25968],{},[895,25897,25898,25900,25902,25944,25946,25948],{},[1706,25899,1708],{},[898,25901,1702],{},[895,25903,25904,25906,25908,25910,25942],{},[1706,25905,2140],{"fence":2504},[2148,25907,2701],{},[1706,25909,2447],{},[2964,25911,25912,25914],{},[2148,25913,2701],{},[895,25915,25916,25924,25926],{},[4745,25917,25918],{"scriptlevel":2150,"displaystyle":2139},[2964,25919,25920,25922],{},[898,25921,1702],{},[898,25923,2146],{},[1706,25925,2390],{},[4745,25927,25928],{"scriptlevel":2150,"displaystyle":2139},[2964,25929,25930,25936],{},[895,25931,25932,25934],{},[898,25933,3120],{"mathvariant":2409},[898,25935,2146],{},[895,25937,25938,25940],{},[898,25939,3120],{"mathvariant":2409},[898,25941,1702],{},[1706,25943,2153],{"fence":2504},[1706,25945,1708],{},[898,25947,1702],{},[895,25949,25950,25952,25954,25956,25966],{},[1706,25951,2140],{"fence":2504},[2148,25953,2701],{},[1706,25955,2447],{},[2964,25957,25958,25960],{},[2148,25959,2701],{},[895,25961,25962,25964],{},[1706,25963,1715],{},[898,25965,23410],{},[1706,25967,2153],{"fence":2504},[902,25969,25970],{"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)",[724,25972,25973],{},"a tedy",[724,25975,25976],{},[883,25977,25979],{"className":25978,"title":23358,"style":23359},[23357],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[1636,25981,25982,26051,26299],{},[724,25983,25984,25986,25987,26021,26022,26037,26038,4288],{},[883,25985,3174],{}," Intuice: vztah ",[883,25988,25990],{"className":25989},[886],[888,25991,25992],{"xmlns":890},[892,25993,25994,26018],{},[895,25995,25996,25998,26000,26002,26004,26006,26008,26010,26012,26014,26016],{},[898,25997,1742],{},[898,25999,1662],{},[1706,26001,1708],{},[898,26003,1702],{},[1706,26005,2140],{"stretchy":2139},[2148,26007,2701],{},[1706,26009,1715],{},[2148,26011,2701],{},[898,26013,15493],{"mathvariant":2409},[898,26015,23410],{},[1706,26017,2153],{"stretchy":2139},[902,26019,26020],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,26023,26025],{"className":26024},[886],[888,26026,26027],{"xmlns":890},[892,26028,26029,26035],{},[895,26030,26031,26033],{},[898,26032,1742],{},[898,26034,1662],{},[902,26036,1905],{"encoding":904}," jednoznačně určuje hodnota ",[883,26039,26041],{"className":26040},[886],[888,26042,26043],{"xmlns":890},[892,26044,26045,26049],{},[895,26046,26047],{},[898,26048,23410],{},[902,26050,23410],{"encoding":904},[120,26052,26053,26162,26230],{},[123,26054,26055,26072,26073,1647,26087,1647,26113,1647,26126,21021,26146,26161],{},[883,26056,26058],{"className":26057},[886],[888,26059,26060],{"xmlns":890},[892,26061,26062,26070],{},[895,26063,26064,26066,26068],{},[898,26065,23410],{},[1706,26067,8922],{},[2148,26069,2701],{},[902,26071,23659],{"encoding":904}," (elastická) ",[883,26074,26076],{"className":26075},[886],[888,26077,26078],{"xmlns":890},[892,26079,26080,26084],{},[895,26081,26082],{},[1706,26083,9609],{},[902,26085,26086],{"encoding":904},"\\Rightarrow",[883,26088,26090],{"className":26089},[886],[888,26091,26092],{"xmlns":890},[892,26093,26094,26110],{},[895,26095,26096,26098,26100,26102,26104,26106,26108],{},[2148,26097,2701],{},[1706,26099,1715],{},[2148,26101,2701],{},[898,26103,15493],{"mathvariant":2409},[898,26105,23410],{},[1706,26107,8922],{},[2148,26109,2150],{},[902,26111,26112],{"encoding":904},"1 - 1\u002FE > 0",[883,26114,26116],{"className":26115},[886],[888,26117,26118],{"xmlns":890},[892,26119,26120,26124],{},[895,26121,26122],{},[1706,26123,9609],{},[902,26125,26086],{"encoding":904},[883,26127,26129],{"className":26128},[886],[888,26130,26131],{"xmlns":890},[892,26132,26133,26143],{},[895,26134,26135,26137,26139,26141],{},[898,26136,1742],{},[898,26138,1662],{},[1706,26140,8922],{},[2148,26142,2150],{},[902,26144,26145],{"encoding":904},"MR > 0",[883,26147,26149],{"className":26148},[886],[888,26150,26151],{"xmlns":890},[892,26152,26153,26159],{},[895,26154,26155,26157],{},[898,26156,1659],{},[898,26158,1662],{},[902,26160,1665],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,26163,26164,26181,26182,1647,26195,21021,26214,26229],{},[883,26165,26167],{"className":26166},[886],[888,26168,26169],{"xmlns":890},[892,26170,26171,26179],{},[895,26172,26173,26175,26177],{},[898,26174,23410],{},[1706,26176,1708],{},[2148,26178,2701],{},[902,26180,23695],{"encoding":904}," (jednotková) ",[883,26183,26185],{"className":26184},[886],[888,26186,26187],{"xmlns":890},[892,26188,26189,26193],{},[895,26190,26191],{},[1706,26192,9609],{},[902,26194,26086],{"encoding":904},[883,26196,26198],{"className":26197},[886],[888,26199,26200],{"xmlns":890},[892,26201,26202,26212],{},[895,26203,26204,26206,26208,26210],{},[898,26205,1742],{},[898,26207,1662],{},[1706,26209,1708],{},[2148,26211,2150],{},[902,26213,4780],{"encoding":904},[883,26215,26217],{"className":26216},[886],[888,26218,26219],{"xmlns":890},[892,26220,26221,26227],{},[895,26222,26223,26225],{},[898,26224,1659],{},[898,26226,1662],{},[902,26228,1665],{"encoding":904}," je extrém (maximum).",[123,26231,26232,26249,26250,1647,26263,21021,26283,26298],{},[883,26233,26235],{"className":26234},[886],[888,26236,26237],{"xmlns":890},[892,26238,26239,26247],{},[895,26240,26241,26243,26245],{},[898,26242,23410],{},[1706,26244,2539],{},[2148,26246,2701],{},[902,26248,23677],{"encoding":904}," (neelastická) ",[883,26251,26253],{"className":26252},[886],[888,26254,26255],{"xmlns":890},[892,26256,26257,26261],{},[895,26258,26259],{},[1706,26260,9609],{},[902,26262,26086],{"encoding":904},[883,26264,26266],{"className":26265},[886],[888,26267,26268],{"xmlns":890},[892,26269,26270,26280],{},[895,26271,26272,26274,26276,26278],{},[898,26273,1742],{},[898,26275,1662],{},[1706,26277,2539],{},[2148,26279,2150],{},[902,26281,26282],{"encoding":904},"MR \u003C 0",[883,26284,26286],{"className":26285},[886],[888,26287,26288],{"xmlns":890},[892,26289,26290,26296],{},[895,26291,26292,26294],{},[898,26293,1659],{},[898,26295,1662],{},[902,26297,1665],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,26300,26301,26302,1837],{},"Viz také ",[207,26303,22995],{"className":26304,"dataFsResolvedFilePath":827,"href":828},[210],[198,26306,26308],{"id":26307},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,26310,26311,26331,26332,26358,26359,26374,26375,26388,26389,26402,26403,26416,26417,26433,26434,1647,26449,26452,26453,26433,26469,1837],{},[38,26312,26313,26314,1936],{},"(a) Poptávka elastická (",[883,26315,26317],{"className":26316},[886],[888,26318,26319],{"xmlns":890},[892,26320,26321,26329],{},[895,26322,26323,26325,26327],{},[898,26324,23410],{},[1706,26326,8922],{},[2148,26328,2701],{},[902,26330,23659],{"encoding":904}," Z (4.12) plyne ",[883,26333,26335],{"className":26334},[886],[888,26336,26337],{"xmlns":890},[892,26338,26339,26355],{},[895,26340,26341,26343,26345,26347,26349,26351,26353],{},[898,26342,1742],{},[898,26344,1662],{},[1706,26346,2140],{"stretchy":2139},[898,26348,2146],{},[1706,26350,2153],{"stretchy":2139},[1706,26352,8922],{},[2148,26354,2150],{},[902,26356,26357],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,26360,26362],{"className":26361},[886],[888,26363,26364],{"xmlns":890},[892,26365,26366,26372],{},[895,26367,26368,26370],{},[898,26369,1659],{},[898,26371,1662],{},[902,26373,1665],{"encoding":904}," je rostoucí funkcí ",[883,26376,26378],{"className":26377},[886],[888,26379,26380],{"xmlns":890},[892,26381,26382,26386],{},[895,26383,26384],{},[898,26385,2146],{},[902,26387,2146],{"encoding":904},". Avšak růst ",[883,26390,26392],{"className":26391},[886],[888,26393,26394],{"xmlns":890},[892,26395,26396,26400],{},[895,26397,26398],{},[898,26399,2146],{},[902,26401,2146],{"encoding":904}," je odezvou na pokles ceny ",[883,26404,26406],{"className":26405},[886],[888,26407,26408],{"xmlns":890},[892,26409,26410,26414],{},[895,26411,26412],{},[898,26413,1702],{},[902,26415,1702],{"encoding":904},". Tudíž s ",[614,26418,26419,26420],{},"poklesem ceny ",[883,26421,26423],{"className":26422},[886],[888,26424,26425],{"xmlns":890},[892,26426,26427,26431],{},[895,26428,26429],{},[898,26430,1702],{},[902,26432,1702],{"encoding":904}," celkový příjem ",[883,26435,26437],{"className":26436},[886],[888,26438,26439],{"xmlns":890},[892,26440,26441,26447],{},[895,26442,26443,26445],{},[898,26444,1659],{},[898,26446,1662],{},[902,26448,1665],{"encoding":904},[614,26450,26451],{},"roste"," a s ",[614,26454,26455,26456],{},"růstem ceny ",[883,26457,26459],{"className":26458},[886],[888,26460,26461],{"xmlns":890},[892,26462,26463,26467],{},[895,26464,26465],{},[898,26466,1702],{},[902,26468,1702],{"encoding":904},[614,26470,26471],{},"klesá",[1636,26473,26474],{},[724,26475,26476,26479],{},[38,26477,26478],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,26481,26482,26331,26502,1343,26528,26543,26544,26557,26558,26571,26572,26585,26586,26433,26599,1647,26614,1837],{},[38,26483,26484,26485,1936],{},"(b) Poptávka neelastická (",[883,26486,26488],{"className":26487},[886],[888,26489,26490],{"xmlns":890},[892,26491,26492,26500],{},[895,26493,26494,26496,26498],{},[898,26495,23410],{},[1706,26497,2539],{},[2148,26499,2701],{},[902,26501,23677],{"encoding":904},[883,26503,26505],{"className":26504},[886],[888,26506,26507],{"xmlns":890},[892,26508,26509,26525],{},[895,26510,26511,26513,26515,26517,26519,26521,26523],{},[898,26512,1742],{},[898,26514,1662],{},[1706,26516,2140],{"stretchy":2139},[898,26518,2146],{},[1706,26520,2153],{"stretchy":2139},[1706,26522,2539],{},[2148,26524,2150],{},[902,26526,26527],{"encoding":904},"MR(Q) \u003C 0",[883,26529,26531],{"className":26530},[886],[888,26532,26533],{"xmlns":890},[892,26534,26535,26541],{},[895,26536,26537,26539],{},[898,26538,1659],{},[898,26540,1662],{},[902,26542,1665],{"encoding":904}," je klesající funkce ",[883,26545,26547],{"className":26546},[886],[888,26548,26549],{"xmlns":890},[892,26550,26551,26555],{},[895,26552,26553],{},[898,26554,2146],{},[902,26556,2146],{"encoding":904},", tj. s růstem ",[883,26559,26561],{"className":26560},[886],[888,26562,26563],{"xmlns":890},[892,26564,26565,26569],{},[895,26566,26567],{},[898,26568,2146],{},[902,26570,2146],{"encoding":904}," (s poklesem ceny ",[883,26573,26575],{"className":26574},[886],[888,26576,26577],{"xmlns":890},[892,26578,26579,26583],{},[895,26580,26581],{},[898,26582,1702],{},[902,26584,1702],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,26587,26589],{"className":26588},[886],[888,26590,26591],{"xmlns":890},[892,26592,26593,26597],{},[895,26594,26595],{},[898,26596,1702],{},[902,26598,1702],{"encoding":904},[883,26600,26602],{"className":26601},[886],[888,26603,26604],{"xmlns":890},[892,26605,26606,26612],{},[895,26607,26608,26610],{},[898,26609,1659],{},[898,26611,1662],{},[902,26613,1665],{"encoding":904},[614,26615,26451],{},[1636,26617,26618],{},[724,26619,26620,26623],{},[38,26621,26622],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,26625,26626,26331,26646,26665,26666,11222,26681,26751,26752,1993,26780,11771,26813,24728,26841,26856,26857,1837],{},[38,26627,26628,26629,1936],{},"(c) Jednotková elasticita (",[883,26630,26632],{"className":26631},[886],[888,26633,26634],{"xmlns":890},[892,26635,26636,26644],{},[895,26637,26638,26640,26642],{},[898,26639,23410],{},[1706,26641,1708],{},[2148,26643,2701],{},[902,26645,23695],{"encoding":904},[883,26647,26649],{"className":26648},[886],[888,26650,26651],{"xmlns":890},[892,26652,26653,26663],{},[895,26654,26655,26657,26659,26661],{},[898,26656,1742],{},[898,26658,1662],{},[1706,26660,1708],{},[2148,26662,2150],{},[902,26664,4780],{"encoding":904}," — nutná podmínka extrému ",[883,26667,26669],{"className":26668},[886],[888,26670,26671],{"xmlns":890},[892,26672,26673,26679],{},[895,26674,26675,26677],{},[898,26676,1659],{},[898,26678,1662],{},[902,26680,1665],{"encoding":904},[883,26682,26684],{"className":26683},[886],[888,26685,26686],{"xmlns":890},[892,26687,26688,26748],{},[895,26689,26690,26692,26702,26704,26706,26712,26714,26720,26722,26724,26726,26728,26730,26732,26742,26744,26746],{},[898,26691,1659],{},[2489,26693,26694,26696],{},[898,26695,1662],{},[895,26697,26698,26700],{},[1706,26699,3142],{"mathvariant":2409},[1706,26701,3142],{"mathvariant":2409},[1706,26703,1708],{},[898,26705,1742],{},[2489,26707,26708,26710],{},[898,26709,1662],{},[1706,26711,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,26713,1708],{},[2489,26715,26716,26718],{},[898,26717,2334],{},[1706,26719,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,26721,2140],{"stretchy":2139},[898,26723,2146],{},[1706,26725,2153],{"stretchy":2139},[1706,26727,2447],{},[898,26729,2146],{},[2415,26731,2799],{},[2489,26733,26734,26736],{},[898,26735,2334],{},[895,26737,26738,26740],{},[1706,26739,3142],{"mathvariant":2409},[1706,26741,3142],{"mathvariant":2409},[1706,26743,2140],{"stretchy":2139},[898,26745,2146],{},[1706,26747,2153],{"stretchy":2139},[902,26749,26750],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,26753,26755],{"className":26754},[886],[888,26756,26757],{"xmlns":890},[892,26758,26759,26777],{},[895,26760,26761,26767,26769,26771,26773,26775],{},[2489,26762,26763,26765],{},[898,26764,2334],{},[1706,26766,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,26768,2140],{"stretchy":2139},[898,26770,2146],{},[1706,26772,2153],{"stretchy":2139},[1706,26774,2539],{},[2148,26776,2150],{},[902,26778,26779],{"encoding":904},"D'(Q) \u003C 0",[883,26781,26783],{"className":26782},[886],[888,26784,26785],{"xmlns":890},[892,26786,26787,26810],{},[895,26788,26789,26799,26801,26803,26805,26808],{},[2489,26790,26791,26793],{},[898,26792,2334],{},[895,26794,26795,26797],{},[1706,26796,3142],{"mathvariant":2409},[1706,26798,3142],{"mathvariant":2409},[1706,26800,2140],{"stretchy":2139},[898,26802,2146],{},[1706,26804,2153],{"stretchy":2139},[1706,26806,26807],{},"≤",[2148,26809,2150],{},[902,26811,26812],{"encoding":904},"D''(Q) \\le 0",[883,26814,26816],{"className":26815},[886],[888,26817,26818],{"xmlns":890},[892,26819,26820,26838],{},[895,26821,26822,26824,26834,26836],{},[898,26823,1659],{},[2489,26825,26826,26828],{},[898,26827,1662],{},[895,26829,26830,26832],{},[1706,26831,3142],{"mathvariant":2409},[1706,26833,3142],{"mathvariant":2409},[1706,26835,2539],{},[2148,26837,2150],{},[902,26839,26840],{"encoding":904},"TR'' \u003C 0",[883,26842,26844],{"className":26843},[886],[888,26845,26846],{"xmlns":890},[892,26847,26848,26854],{},[895,26849,26850,26852],{},[898,26851,1659],{},[898,26853,1662],{},[902,26855,1665],{"encoding":904}," nabývá ",[38,26858,26859],{},"maxima",[1636,26861,26862],{},[724,26863,26864,26867],{},[38,26865,26866],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,26869,26870],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,26872,26873],{},[38,26874,26875],{},"Souhrnná tabulka Pravidel 1–3:",[16,26877,26878,26982],{},[19,26879,26880],{},[22,26881,26882,26885,26900,26917,26948,26979],{},[25,26883,26884],{},"Charakter poptávky",[25,26886,26887],{},[883,26888,26890],{"className":26889},[886],[888,26891,26892],{"xmlns":890},[892,26893,26894,26898],{},[895,26895,26896],{},[898,26897,23410],{},[902,26899,23410],{"encoding":904},[25,26901,26902],{},[883,26903,26905],{"className":26904},[886],[888,26906,26907],{"xmlns":890},[892,26908,26909,26915],{},[895,26910,26911,26913],{},[898,26912,1742],{},[898,26914,1662],{},[902,26916,1905],{"encoding":904},[25,26918,26919,26920,1647,26933],{},"Pokles ceny ",[883,26921,26923],{"className":26922},[886],[888,26924,26925],{"xmlns":890},[892,26926,26927,26931],{},[895,26928,26929],{},[1706,26930,9609],{},[902,26932,26086],{"encoding":904},[883,26934,26936],{"className":26935},[886],[888,26937,26938],{"xmlns":890},[892,26939,26940,26946],{},[895,26941,26942,26944],{},[898,26943,1659],{},[898,26945,1662],{},[902,26947,1665],{"encoding":904},[25,26949,26950,26951,1647,26964],{},"Růst ceny ",[883,26952,26954],{"className":26953},[886],[888,26955,26956],{"xmlns":890},[892,26957,26958,26962],{},[895,26959,26960],{},[1706,26961,9609],{},[902,26963,26086],{"encoding":904},[883,26965,26967],{"className":26966},[886],[888,26968,26969],{"xmlns":890},[892,26970,26971,26977],{},[895,26972,26973,26975],{},[898,26974,1659],{},[898,26976,1662],{},[902,26978,1665],{"encoding":904},[25,26980,26981],{},"Doporučení",[30,26983,26984,27033,27083],{},[22,26985,26986,26988,27006,27024,27026,27028],{},[35,26987,23234],{},[35,26989,26990],{},[883,26991,26993],{"className":26992},[886],[888,26994,26995],{"xmlns":890},[892,26996,26997,27003],{},[895,26998,26999,27001],{},[1706,27000,8922],{},[2148,27002,2701],{},[902,27004,27005],{"encoding":904},"> 1",[35,27007,27008],{},[883,27009,27011],{"className":27010},[886],[888,27012,27013],{"xmlns":890},[892,27014,27015,27021],{},[895,27016,27017,27019],{},[1706,27018,8922],{},[2148,27020,2150],{},[902,27022,27023],{"encoding":904},"> 0",[35,27025,26451],{},[35,27027,26471],{},[35,27029,27030],{},[38,27031,27032],{},"snížit cenu",[22,27034,27035,27038,27056,27074,27076,27078],{},[35,27036,27037],{},"jednotková",[35,27039,27040],{},[883,27041,27043],{"className":27042},[886],[888,27044,27045],{"xmlns":890},[892,27046,27047,27053],{},[895,27048,27049,27051],{},[1706,27050,1708],{},[2148,27052,2701],{},[902,27054,27055],{"encoding":904},"= 1",[35,27057,27058],{},[883,27059,27061],{"className":27060},[886],[888,27062,27063],{"xmlns":890},[892,27064,27065,27071],{},[895,27066,27067,27069],{},[1706,27068,1708],{},[2148,27070,2150],{},[902,27072,27073],{"encoding":904},"= 0",[35,27075,13844],{},[35,27077,13844],{},[35,27079,27080],{},[38,27081,27082],{},"držet cenu",[22,27084,27085,27087,27105,27123,27125,27127],{},[35,27086,23238],{},[35,27088,27089],{},[883,27090,27092],{"className":27091},[886],[888,27093,27094],{"xmlns":890},[892,27095,27096,27102],{},[895,27097,27098,27100],{},[1706,27099,2539],{},[2148,27101,2701],{},[902,27103,27104],{"encoding":904},"\u003C 1",[35,27106,27107],{},[883,27108,27110],{"className":27109},[886],[888,27111,27112],{"xmlns":890},[892,27113,27114,27120],{},[895,27115,27116,27118],{},[1706,27117,2539],{},[2148,27119,2150],{},[902,27121,27122],{"encoding":904},"\u003C 0",[35,27124,26471],{},[35,27126,26451],{},[35,27128,27129],{},[38,27130,27131],{},"zvýšit cenu",[198,27133,27135],{"id":27134},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,27137,27138,27139,27164,27165,27187,27188,27201,27202,27215,27216,3484,27229,24728,27255,27307],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,27140,27142],{"className":27141},[886],[888,27143,27144],{"xmlns":890},[892,27145,27146,27162],{},[895,27147,27148,27150,27152,27154,27156],{},[898,27149,1702],{},[1706,27151,1708],{},[2148,27153,2590],{},[1706,27155,1715],{},[2489,27157,27158,27160],{},[898,27159,2146],{},[2148,27161,2495],{},[902,27163,24601],{"encoding":904},". Reálné cenové rozpětí je ",[883,27166,27168],{"className":27167},[886],[888,27169,27170],{"xmlns":890},[892,27171,27172,27184],{},[895,27173,27174,27176,27178,27180,27182],{},[1706,27175,24467],{"stretchy":2139},[2148,27177,2701],{},[1706,27179,2505],{"separator":2504},[2148,27181,2590],{},[1706,27183,24484],{"stretchy":2139},[902,27185,27186],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,27189,27191],{"className":27190},[886],[888,27192,27193],{"xmlns":890},[892,27194,27195,27199],{},[895,27196,27197],{},[898,27198,2146],{},[902,27200,2146],{"encoding":904}," jako funkci ",[883,27203,27205],{"className":27204},[886],[888,27206,27207],{"xmlns":890},[892,27208,27209,27213],{},[895,27210,27211],{},[898,27212,1702],{},[902,27214,1702],{"encoding":904},"; pro nezáporné ",[883,27217,27219],{"className":27218},[886],[888,27220,27221],{"xmlns":890},[892,27222,27223,27227],{},[895,27224,27225],{},[898,27226,2146],{},[902,27228,2146],{"encoding":904},[883,27230,27232],{"className":27231},[886],[888,27233,27234],{"xmlns":890},[892,27235,27236,27252],{},[895,27237,27238,27240,27242],{},[898,27239,2146],{},[1706,27241,1708],{},[11087,27243,27244],{},[895,27245,27246,27248,27250],{},[2148,27247,2590],{},[1706,27249,1715],{},[898,27251,1702],{},[902,27253,27254],{"encoding":904},"Q = \\sqrt{100 - P}",[883,27256,27258],{"className":27257},[886],[888,27259,27260],{"xmlns":890},[892,27261,27262,27304],{},[895,27263,27264,27280,27282,27284],{},[4745,27265,27266],{"scriptlevel":2150,"displaystyle":2504},[2964,27267,27268,27274],{},[895,27269,27270,27272],{},[898,27271,3120],{"mathvariant":2409},[898,27273,2146],{},[895,27275,27276,27278],{},[898,27277,3120],{"mathvariant":2409},[898,27279,1702],{},[1706,27281,1708],{},[1706,27283,1715],{},[4745,27285,27286],{"scriptlevel":2150,"displaystyle":2504},[2964,27287,27288,27290],{},[2148,27289,2701],{},[895,27291,27292,27294],{},[2148,27293,2495],{},[11087,27295,27296],{},[895,27297,27298,27300,27302],{},[2148,27299,2590],{},[1706,27301,1715],{},[898,27303,1702],{},[902,27305,27306],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,27309,27310],{},[883,27311,27313],{"className":27312},[886],[888,27314,27315],{"xmlns":890},[892,27316,27317,27439],{},[895,27318,27319,27321,27323,27325,27327,27329,27331,27337,27339,27353,27355,27357,27371,27373,27399,27401,27419,27421,27437],{},[898,27320,23410],{},[1706,27322,2140],{"stretchy":2139},[898,27324,1702],{},[1706,27326,2153],{"stretchy":2139},[1706,27328,1708],{},[1706,27330,1715],{},[2964,27332,27333,27335],{},[898,27334,1702],{},[898,27336,2146],{},[1706,27338,2390],{},[2964,27340,27341,27347],{},[895,27342,27343,27345],{},[898,27344,3120],{"mathvariant":2409},[898,27346,2146],{},[895,27348,27349,27351],{},[898,27350,3120],{"mathvariant":2409},[898,27352,1702],{},[1706,27354,1708],{},[1706,27356,1715],{},[2964,27358,27359,27361],{},[898,27360,1702],{},[11087,27362,27363],{},[895,27364,27365,27367,27369],{},[2148,27366,2590],{},[1706,27368,1715],{},[898,27370,1702],{},[1706,27372,2390],{},[895,27374,27375,27377,27379,27397],{},[1706,27376,2140],{"fence":2504},[1706,27378,1715],{},[2964,27380,27381,27383],{},[2148,27382,2701],{},[895,27384,27385,27387],{},[2148,27386,2495],{},[11087,27388,27389],{},[895,27390,27391,27393,27395],{},[2148,27392,2590],{},[1706,27394,1715],{},[898,27396,1702],{},[1706,27398,2153],{"fence":2504},[1706,27400,1708],{},[2964,27402,27403,27405],{},[898,27404,1702],{},[895,27406,27407,27409,27411,27413,27415,27417],{},[2148,27408,2495],{},[1706,27410,2140],{"stretchy":2139},[2148,27412,2590],{},[1706,27414,1715],{},[898,27416,1702],{},[1706,27418,2153],{"stretchy":2139},[1706,27420,1708],{},[2964,27422,27423,27429],{},[895,27424,27425,27427],{},[2148,27426,11496],{},[898,27428,1702],{},[895,27430,27431,27433,27435],{},[2148,27432,2590],{},[1706,27434,1715],{},[898,27436,1702],{},[898,27438,1837],{"mathvariant":2409},[902,27440,27441],{"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}.",[724,27443,27444,27445,4288],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,27446,27448],{"className":27447},[886],[888,27449,27450],{"xmlns":890},[892,27451,27452,27476],{},[895,27453,27454,27472,27474],{},[4745,27455,27456],{"scriptlevel":2150,"displaystyle":2504},[2964,27457,27458,27464],{},[895,27459,27460,27462],{},[2148,27461,11496],{},[898,27463,1702],{},[895,27465,27466,27468,27470],{},[2148,27467,2590],{},[1706,27469,1715],{},[898,27471,1702],{},[1706,27473,1708],{},[2148,27475,2701],{},[902,27477,27478],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,27480,27481],{},[883,27482,27484],{"className":27483},[886],[888,27485,27486],{"xmlns":890},[892,27487,27488,27518],{},[895,27489,27490,27496,27498,27504,27506,27509,27516],{},[2489,27491,27492,27494],{},[898,27493,1702],{},[1706,27495,3197],{},[1706,27497,1708],{},[2964,27499,27500,27502],{},[2148,27501,7039],{},[2148,27503,4284],{},[1706,27505,7883],{},[2148,27507,27508],{},"66,",[3925,27510,27511,27513],{"accent":2504},[2148,27512,7044],{},[1706,27514,27515],{"stretchy":2504},"‾",[898,27517,1837],{"mathvariant":2409},[902,27519,27520],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,27522,27523],{},"S využitím vlastnosti (4.8):",[120,27525,27526,27571,27613],{},[123,27527,27528,27529,27563,27564,27566,27567,27570],{},"Při cenách ",[883,27530,27532],{"className":27531},[886],[888,27533,27534],{"xmlns":890},[892,27535,27536,27560],{},[895,27537,27538,27540,27542,27544,27546,27548,27550,27552,27558],{},[898,27539,1702],{},[1706,27541,25638],{},[1706,27543,24467],{"stretchy":2139},[2148,27545,2701],{},[1706,27547,2110],{"separator":2504},[2415,27549,2799],{},[2148,27551,27508],{},[3925,27553,27554,27556],{"accent":2504},[2148,27555,7044],{},[1706,27557,27515],{"stretchy":2504},[1706,27559,2153],{"stretchy":2139},[902,27561,27562],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,27565,23238],{}," — dle ",[614,27568,27569],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,27572,27528,27573,27563,27607,27566,27609,27612],{},[883,27574,27576],{"className":27575},[886],[888,27577,27578],{"xmlns":890},[892,27579,27580,27604],{},[895,27581,27582,27584,27586,27588,27590,27596,27598,27600,27602],{},[898,27583,1702],{},[1706,27585,25638],{},[1706,27587,2140],{"stretchy":2139},[2148,27589,27508],{},[3925,27591,27592,27594],{"accent":2504},[2148,27593,7044],{},[1706,27595,27515],{"stretchy":2504},[1706,27597,2110],{"separator":2504},[2415,27599,2799],{},[2148,27601,2590],{},[1706,27603,24484],{"stretchy":2139},[902,27605,27606],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,27608,23234],{},[614,27610,27611],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,27614,27615,27616,27619,27620,27648,27649,27652],{},"Dle ",[614,27617,27618],{},"Pravidla 3"," je při ceně ",[883,27621,27623],{"className":27622},[886],[888,27624,27625],{"xmlns":890},[892,27626,27627,27645],{},[895,27628,27629,27635,27637,27639],{},[2489,27630,27631,27633],{},[898,27632,1702],{},[1706,27634,3197],{},[1706,27636,1708],{},[2148,27638,27508],{},[3925,27640,27641,27643],{"accent":2504},[2148,27642,7044],{},[1706,27644,27515],{"stretchy":2504},[902,27646,27647],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,27650,27651],{},"maxima celkového příjmu"," ve výši",[724,27654,27655],{},[883,27656,27658],{"className":27657},[886],[888,27659,27660],{"xmlns":890},[892,27661,27662,27740],{},[895,27663,27664,27666,27668,27670,27676,27678,27680,27686,27688,27702,27704,27710,27712,27720,27722,27735,27737],{},[898,27665,1659],{},[898,27667,1662],{},[1706,27669,2140],{"stretchy":2139},[2489,27671,27672,27674],{},[898,27673,1702],{},[1706,27675,3197],{},[1706,27677,2153],{"stretchy":2139},[1706,27679,1708],{},[2489,27681,27682,27684],{},[898,27683,1702],{},[1706,27685,3197],{},[1706,27687,2390],{},[11087,27689,27690],{},[895,27691,27692,27694,27696],{},[2148,27693,2590],{},[1706,27695,1715],{},[2489,27697,27698,27700],{},[898,27699,1702],{},[1706,27701,3197],{},[1706,27703,1708],{},[2964,27705,27706,27708],{},[2148,27707,7039],{},[2148,27709,4284],{},[1706,27711,2390],{},[11087,27713,27714],{},[2964,27715,27716,27718],{},[2148,27717,2590],{},[2148,27719,4284],{},[1706,27721,1708],{},[2964,27723,27724,27727],{},[2148,27725,27726],{},"2000",[895,27728,27729,27731],{},[2148,27730,4284],{},[11087,27732,27733],{},[2148,27734,4284],{},[1706,27736,7883],{},[2148,27738,27739],{},"384,9.",[902,27741,27742],{"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.",[724,27744,27745,27746,1837],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,27747,27749],{"className":27748},[886],[888,27750,27751],{"xmlns":890},[892,27752,27753,27759],{},[895,27754,27755,27757],{},[898,27756,1659],{},[898,27758,1662],{},[902,27760,1665],{"encoding":904},[115,27762,27764],{"id":27763},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,27766,27767,27768,27771],{},"Analogicky se definuje ",[38,27769,27770],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,27773,27774],{},[883,27775,27777],{"className":27776,"title":23358,"style":23359},[23357],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,27779,5331,27780,27804,27805,27837],{},[883,27781,27783],{"className":27782},[886],[888,27784,27785],{"xmlns":890},[892,27786,27787,27801],{},[895,27788,27789,27791,27793,27795,27797,27799],{},[898,27790,2146],{},[1706,27792,1708],{},[898,27794,14171],{},[1706,27796,2140],{"stretchy":2139},[898,27798,1702],{},[1706,27800,2153],{"stretchy":2139},[902,27802,27803],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,27806,27808],{"className":27807},[886],[888,27809,27810],{"xmlns":890},[892,27811,27812,27834],{},[895,27813,27814,27830,27832],{},[4745,27815,27816],{"scriptlevel":2150,"displaystyle":2504},[2964,27817,27818,27824],{},[895,27819,27820,27822],{},[898,27821,3120],{"mathvariant":2409},[898,27823,2146],{},[895,27825,27826,27828],{},[898,27827,3120],{"mathvariant":2409},[898,27829,1702],{},[1706,27831,8922],{},[2148,27833,2150],{},[902,27835,27836],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,27839,27840],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[1636,27842,27843],{},[724,27844,27845,27846],{},"S rostoucí cenou elasticita nabídky roste. ",[883,27847,27849],{"className":27848},[886],[888,27850,27851],{"xmlns":890},[892,27852,27853,27862],{},[895,27854,27855,27857,27860],{},[1706,27856,2140],{"stretchy":2139},[2148,27858,27859],{},"4.14",[1706,27861,2153],{"stretchy":2139},[902,27863,27864],{"encoding":904},"(4.14)",[724,27866,27867],{},"Pro nominální změny platí",[724,27869,27870],{},[883,27871,27873],{"className":27872,"title":23358,"style":23359},[23357],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,27875,27876],{},"a pro procentní změny",[724,27878,27879],{},[883,27880,27882],{"className":27881,"title":23358,"style":23359},[23357],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,27884,27885],{},"(bez znaménka minus).",[198,27887,27889],{"id":27888},"příklad-47","Příklad 4.7",[724,27891,27892,27893,4288],{},"Nabídka ",[883,27894,27896],{"className":27895},[886],[888,27897,27898],{"xmlns":890},[892,27899,27900,27925],{},[895,27901,27902,27904,27906,27908,27914,27916,27918,27920,27922],{},[898,27903,2146],{},[1706,27905,1708],{},[2148,27907,14840],{},[2489,27909,27910,27912],{},[898,27911,1702],{},[2148,27913,2495],{},[1706,27915,2447],{},[2148,27917,7524],{},[898,27919,1702],{},[1706,27921,2447],{},[2148,27923,27924],{},"150",[902,27926,27927],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,27929,27930],{},[883,27931,27933],{"className":27932},[886],[888,27934,27935],{"xmlns":890},[892,27936,27937,27983],{},[895,27938,27939,27941,27943,27967,27969,27971,27973,27975,27977,27979,27981],{},[898,27940,23410],{},[1706,27942,1708],{},[2964,27944,27945,27947],{},[898,27946,1702],{},[895,27948,27949,27951,27957,27959,27961,27963,27965],{},[2148,27950,14840],{},[2489,27952,27953,27955],{},[898,27954,1702],{},[2148,27956,2495],{},[1706,27958,2447],{},[2148,27960,7524],{},[898,27962,1702],{},[1706,27964,2447],{},[2148,27966,27924],{},[2415,27968,2799],{},[1706,27970,2140],{"stretchy":2139},[2148,27972,15204],{},[898,27974,1702],{},[1706,27976,2447],{},[2148,27978,7524],{},[1706,27980,2153],{"stretchy":2139},[898,27982,1837],{"mathvariant":2409},[902,27984,27985],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,27987,24262,27988,1343,28018,1343,28045,28080,28081,28106,28107,28125,28126,1837],{},[883,27989,27991],{"className":27990},[886],[888,27992,27993],{"xmlns":890},[892,27994,27995,28015],{},[895,27996,27997,27999,28001,28003,28005,28007],{},[898,27998,23410],{},[1706,28000,2140],{"stretchy":2139},[2148,28002,7786],{},[1706,28004,2153],{"stretchy":2139},[1706,28006,1708],{},[4745,28008,28009],{"scriptlevel":2150,"displaystyle":2139},[2964,28010,28011,28013],{},[2148,28012,2701],{},[2148,28014,4284],{},[902,28016,28017],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,28019,28021],{"className":28020},[886],[888,28022,28023],{"xmlns":890},[892,28024,28025,28042],{},[895,28026,28027,28029,28031,28036,28038,28040],{},[898,28028,23410],{},[1706,28030,2140],{"stretchy":2139},[11087,28032,28033],{},[2148,28034,28035],{},"1500",[1706,28037,2153],{"stretchy":2139},[1706,28039,1708],{},[2148,28041,2701],{},[902,28043,28044],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,28046,28048],{"className":28047},[886],[888,28049,28050],{"xmlns":890},[892,28051,28052,28077],{},[895,28053,28054,28056,28058,28060,28062,28064,28072,28074],{},[898,28055,23410],{},[1706,28057,2140],{"stretchy":2139},[2148,28059,2590],{},[1706,28061,2153],{"stretchy":2139},[1706,28063,1708],{},[4745,28065,28066],{"scriptlevel":2150,"displaystyle":2139},[2964,28067,28068,28070],{},[2148,28069,2728],{},[2148,28071,11115],{},[1706,28073,7883],{},[2148,28075,28076],{},"1,515",[902,28078,28079],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,28082,28084],{"className":28083},[886],[888,28085,28086],{"xmlns":890},[892,28087,28088,28103],{},[895,28089,28090,28092,28094,28098,28100],{},[898,28091,1702],{},[1706,28093,8922],{},[11087,28095,28096],{},[2148,28097,28035],{},[1706,28099,3248],{},[2148,28101,28102],{},"38,7",[902,28104,28105],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,28108,28110],{"className":28109},[886],[888,28111,28112],{"xmlns":890},[892,28113,28114,28122],{},[895,28115,28116,28118,28120],{},[898,28117,1702],{},[1706,28119,2539],{},[2148,28121,28102],{},[902,28123,28124],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,28127,28129],{"className":28128},[886],[888,28130,28131],{"xmlns":890},[892,28132,28133,28170],{},[895,28134,28135,28137,28139,28141,28143,28151,28153,28155,28157,28160,28166,28168],{},[898,28136,3677],{"mathvariant":2409},[898,28138,2146],{},[898,28140,25060],{"mathvariant":2409},[1706,28142,3248],{},[4745,28144,28145],{"scriptlevel":2150,"displaystyle":2139},[2964,28146,28147,28149],{},[2148,28148,2701],{},[2148,28150,4284],{},[1706,28152,2390],{},[2148,28154,3369],{},[1706,28156,1708],{},[2148,28158,28159],{},"6,",[3925,28161,28162,28164],{"accent":2504},[2148,28163,7044],{},[1706,28165,27515],{"stretchy":2504},[2415,28167,2799],{},[898,28169,25060],{"mathvariant":2409},[902,28171,28172],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,28174,28176],{"id":28175},"vícefaktorový-model","Vícefaktorový model",[724,28178,28179,28180,28193,28194,1647,28197,28210,28211,1647,28214,28232,28233,1647,28236,4288],{},"Předpokládejme, že poptávané množství ",[883,28181,28183],{"className":28182},[886],[888,28184,28185],{"xmlns":890},[892,28186,28187,28191],{},[895,28188,28189],{},[898,28190,2146],{},[902,28192,2146],{"encoding":904}," závisí na ",[38,28195,28196],{},"ceně základního zboží",[883,28198,28200],{"className":28199},[886],[888,28201,28202],{"xmlns":890},[892,28203,28204,28208],{},[895,28205,28206],{},[898,28207,1702],{},[902,28209,1702],{"encoding":904},", na ",[38,28212,28213],{},"ceně alternativního zboží",[883,28215,28217],{"className":28216},[886],[888,28218,28219],{"xmlns":890},[892,28220,28221,28229],{},[895,28222,28223],{},[2142,28224,28225,28227],{},[898,28226,1702],{},[898,28228,1735],{},[902,28230,28231],{"encoding":904},"P_A"," a na ",[38,28234,28235],{},"důchodu",[883,28237,28239],{"className":28238},[886],[888,28240,28241],{"xmlns":890},[892,28242,28243,28248],{},[895,28244,28245],{},[898,28246,28247],{},"Y",[902,28249,28247],{"encoding":904},[724,28251,28252],{},[883,28253,28255],{"className":28254,"title":23358,"style":23359},[23357],"Q = D(P, P_A, Y). \\tag{4.17}",[724,28257,28258,28259,28262],{},"V analogii jednofaktorového modelu pracujeme s ",[38,28260,28261],{},"parciálními derivacemi"," funkce poptávky.",[198,28264,28266],{"id":28265},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,28268,28269],{},[883,28270,28272],{"className":28271,"title":23358,"style":23359},[23357],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,28274,5331,28275,28296,28297,28310,28311,3787,28333,1647,28336,28382,28383,28396,28397,28414],{},[883,28276,28278],{"className":28277},[886],[888,28279,28280],{"xmlns":890},[892,28281,28282,28293],{},[895,28283,28284],{},[28285,28286,28287,28289,28291],"msubsup",{},[898,28288,2146],{},[898,28290,1702],{},[1706,28292,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,28294,28295],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,28298,28300],{"className":28299},[886],[888,28301,28302],{"xmlns":890},[892,28303,28304,28308],{},[895,28305,28306],{},[898,28307,1702],{},[902,28309,1702],{"encoding":904},". Vždy ",[883,28312,28314],{"className":28313},[886],[888,28315,28316],{"xmlns":890},[892,28317,28318,28330],{},[895,28319,28320,28326,28328],{},[2142,28321,28322,28324],{},[898,28323,23410],{},[898,28325,1702],{},[1706,28327,14220],{},[2148,28329,2150],{},[902,28331,28332],{"encoding":904},"E_P \\ge 0",[614,28334,28335],{},"Interpretace:",[883,28337,28339],{"className":28338},[886],[888,28340,28341],{"xmlns":890},[892,28342,28343,28379],{},[895,28344,28345,28351,28353,28359,28361,28369,28371,28377],{},[2142,28346,28347,28349],{},[898,28348,23410],{},[898,28350,1702],{},[1706,28352,2140],{"stretchy":2139},[2489,28354,28355,28357],{},[898,28356,1702],{},[1706,28358,3197],{},[1706,28360,2505],{"separator":2504},[28285,28362,28363,28365,28367],{},[898,28364,1702],{},[898,28366,1735],{},[1706,28368,3197],{},[1706,28370,2505],{"separator":2504},[2489,28372,28373,28375],{},[898,28374,28247],{},[1706,28376,3197],{},[1706,28378,2153],{"stretchy":2139},[902,28380,28381],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,28384,28386],{"className":28385},[886],[888,28387,28388],{"xmlns":890},[892,28389,28390,28394],{},[895,28391,28392],{},[898,28393,2146],{},[902,28395,2146],{"encoding":904}," při 1% změně ",[883,28398,28400],{"className":28399},[886],[888,28401,28402],{"xmlns":890},[892,28403,28404,28412],{},[895,28405,28406],{},[2489,28407,28408,28410],{},[898,28409,1702],{},[1706,28411,3197],{},[902,28413,14075],{"encoding":904},", ceteris paribus.",[198,28416,28418],{"id":28417},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,28420,28421],{},[883,28422,28424],{"className":28423,"title":23358,"style":23359},[23357],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,28426,28427,28382,28429,28442,28443,28460],{},[614,28428,28335],{},[883,28430,28432],{"className":28431},[886],[888,28433,28434],{"xmlns":890},[892,28435,28436,28440],{},[895,28437,28438],{},[898,28439,2146],{},[902,28441,2146],{"encoding":904}," základního zboží při 1% změně ceny ",[883,28444,28446],{"className":28445},[886],[888,28447,28448],{"xmlns":890},[892,28449,28450,28458],{},[895,28451,28452],{},[2142,28453,28454,28456],{},[898,28455,1702],{},[898,28457,1735],{},[902,28459,28231],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,28462,28463],{},[38,28464,28465],{},"Znaménko závisí na povaze alternativního zboží:",[120,28467,28468,28556],{},[123,28469,28470,28471,28474,28475,28492,28493,1647,28506,1837],{},"Je-li alternativní zboží ",[38,28472,28473],{},"komplement",", růst ",[883,28476,28478],{"className":28477},[886],[888,28479,28480],{"xmlns":890},[892,28481,28482,28490],{},[895,28483,28484],{},[2142,28485,28486,28488],{},[898,28487,1702],{},[898,28489,1735],{},[902,28491,28231],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,28494,28496],{"className":28495},[886],[888,28497,28498],{"xmlns":890},[892,28499,28500,28504],{},[895,28501,28502],{},[898,28503,2146],{},[902,28505,2146],{"encoding":904},[883,28507,28509],{"className":28508},[886],[888,28510,28511],{"xmlns":890},[892,28512,28513,28553],{},[895,28514,28515,28517,28519,28531,28533,28535,28537,28539,28549,28551],{},[1706,28516,9609],{},[2415,28518,3852],{},[28285,28520,28521,28523,28529],{},[898,28522,2146],{},[2142,28524,28525,28527],{},[898,28526,1702],{},[898,28528,1735],{},[1706,28530,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,28532,2539],{},[2148,28534,2150],{},[1706,28536,2505],{"separator":2504},[2415,28538,3852],{},[2142,28540,28541,28543],{},[898,28542,23410],{},[2142,28544,28545,28547],{},[898,28546,1702],{},[898,28548,1735],{},[1706,28550,2539],{},[2148,28552,2150],{},[902,28554,28555],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,28557,28470,28558,28474,28561,28578,28579,28592,28593,1837],{},[38,28559,28560],{},"substitut",[883,28562,28564],{"className":28563},[886],[888,28565,28566],{"xmlns":890},[892,28567,28568,28576],{},[895,28569,28570],{},[2142,28571,28572,28574],{},[898,28573,1702],{},[898,28575,1735],{},[902,28577,28231],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,28580,28582],{"className":28581},[886],[888,28583,28584],{"xmlns":890},[892,28585,28586,28590],{},[895,28587,28588],{},[898,28589,2146],{},[902,28591,2146],{"encoding":904}," roste ",[883,28594,28596],{"className":28595},[886],[888,28597,28598],{"xmlns":890},[892,28599,28600,28640],{},[895,28601,28602,28604,28606,28618,28620,28622,28624,28626,28636,28638],{},[1706,28603,9609],{},[2415,28605,3852],{},[28285,28607,28608,28610,28616],{},[898,28609,2146],{},[2142,28611,28612,28614],{},[898,28613,1702],{},[898,28615,1735],{},[1706,28617,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,28619,8922],{},[2148,28621,2150],{},[1706,28623,2505],{"separator":2504},[2415,28625,3852],{},[2142,28627,28628,28630],{},[898,28629,23410],{},[2142,28631,28632,28634],{},[898,28633,1702],{},[898,28635,1735],{},[1706,28637,8922],{},[2148,28639,2150],{},[902,28641,28642],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,28644,28647],{"className":28645,"title":28646,"style":23359},[23357],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":28649},[28650,28654,28655,28663,28664,28668,28671],{"id":23058,"depth":642,"text":23059,"children":28651},[28652,28653],{"id":23088,"depth":649,"text":23089},{"id":23262,"depth":649,"text":23263},{"id":23297,"depth":642,"text":23298},{"id":23322,"depth":642,"text":23323,"children":28656},[28657,28658,28659,28660,28662],{"id":24006,"depth":649,"text":24007},{"id":24096,"depth":649,"text":24097},{"id":24428,"depth":649,"text":24429},{"id":24510,"depth":649,"text":28661},"Výpočet, je-li dáno PP jako funkce QQ",{"id":24767,"depth":649,"text":24768},{"id":25088,"depth":642,"text":25089},{"id":25681,"depth":642,"text":25682,"children":28665},[28666,28667],{"id":26307,"depth":649,"text":26308},{"id":27134,"depth":649,"text":27135},{"id":27763,"depth":642,"text":27764,"children":28669},[28670],{"id":27888,"depth":649,"text":27889},{"id":28175,"depth":642,"text":28176,"children":28672},[28673,28674],{"id":28265,"depth":649,"text":28266},{"id":28417,"depth":649,"text":28418},{},"\u002Ftopics\u002Felasticita",{"title":23031,"description":641},[1138,1136],"topics\u002Felasticita",[1128,23065,28681,28682,28683,28684],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":28687,"title":28688,"body":28689,"course":1128,"courses":659,"created":1129,"description":30224,"extension":661,"meta":30225,"navigation":664,"path":30226,"seo":30227,"sources":30228,"stem":30229,"tags":30230,"type":21181,"updated":677,"__hash__":30235},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":28690,"toc":30209},[28691,28694,28767,28774,28778,28841,28929,28933,28960,29027,29082,29086,29113,29205,29207,29239,29409,29413,29483,29530,29534,29594,29700,29715,29719,29721,29749,29814,29816,29823,29911,29936,30134,30138,30174,30176],[12,28692,28688],{"id":28693},"kalkul-funkcí-více-proměnných",[724,28695,28696,28697,28700,28701,1343,28729,1837],{},"Většina ekonomických veličin závisí na ",[38,28698,28699],{},"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 ",[883,28702,28704],{"className":28703},[886],[888,28705,28706],{"xmlns":890},[892,28707,28708,28726],{},[895,28709,28710,28712,28714,28716,28718,28720,28722,28724],{},[898,28711,4018],{},[1706,28713,1708],{},[898,28715,21237],{},[1706,28717,2140],{"stretchy":2139},[898,28719,18300],{},[1706,28721,2505],{"separator":2504},[898,28723,6930],{},[1706,28725,2153],{"stretchy":2139},[902,28727,28728],{"encoding":904},"z = f(x, y)",[883,28730,28732],{"className":28731},[886],[888,28733,28734],{"xmlns":890},[892,28735,28736,28764],{},[895,28737,28738,28741,28743,28745,28747,28749,28751,28753,28755,28757,28759,28761],{},[898,28739,28740],{},"w",[1706,28742,1708],{},[898,28744,21237],{},[1706,28746,2140],{"stretchy":2139},[898,28748,18300],{},[1706,28750,2505],{"separator":2504},[898,28752,6930],{},[1706,28754,2505],{"separator":2504},[898,28756,4018],{},[1706,28758,2153],{"stretchy":2139},[1706,28760,2505],{"separator":2504},[1706,28762,28763],{},"…",[902,28765,28766],{"encoding":904},"w = f(x, y, z), \\ldots",[724,28768,28769],{},[2286,28770],{"alt":28771,"className":28772,"src":28773},"imek-funkce-2d-vrstevnice",[210,2290],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,28775,28777],{"id":28776},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,28779,3465,28780,28807,28808,28836,28837,28840],{},[883,28781,28783],{"className":28782},[886],[888,28784,28785],{"xmlns":890},[892,28786,28787,28805],{},[895,28788,28789,28791,28793,28795,28797,28799,28801,28803],{},[898,28790,4018],{},[1706,28792,1708],{},[898,28794,21237],{},[1706,28796,2140],{"stretchy":2139},[898,28798,18300],{},[1706,28800,2505],{"separator":2504},[898,28802,6930],{},[1706,28804,2153],{"stretchy":2139},[902,28806,28728],{"encoding":904}," se křivkou s předpisem ",[883,28809,28811],{"className":28810},[886],[888,28812,28813],{"xmlns":890},[892,28814,28815,28833],{},[895,28816,28817,28819,28821,28823,28825,28827,28829,28831],{},[898,28818,21237],{},[1706,28820,2140],{"stretchy":2139},[898,28822,18300],{},[1706,28824,2505],{"separator":2504},[898,28826,6930],{},[1706,28828,2153],{"stretchy":2139},[1706,28830,1708],{},[898,28832,20413],{},[902,28834,28835],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,28838,28839],{},"vrstevnice"," funkce. V ekonomii:",[120,28842,28843,28890],{},[123,28844,28845,28848,28849,28885,28886,1837],{},[38,28846,28847],{},"Indiferenční křivky"," užitečnosti ",[883,28850,28852],{"className":28851},[886],[888,28853,28854],{"xmlns":890},[892,28855,28856,28882],{},[895,28857,28858,28860,28862,28868,28870,28876,28878,28880],{},[898,28859,900],{},[1706,28861,2140],{"stretchy":2139},[2142,28863,28864,28866],{},[898,28865,2146],{},[2148,28867,2701],{},[1706,28869,2505],{"separator":2504},[2142,28871,28872,28874],{},[898,28873,2146],{},[2148,28875,2495],{},[1706,28877,2153],{"stretchy":2139},[1706,28879,1708],{},[898,28881,20413],{},[902,28883,28884],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,28887,28889],{"className":28888,"dataFsResolvedFilePath":878,"href":879},[210],"uzitecnost",[123,28891,28892,28895,28896,28885,28925,1837],{},[38,28893,28894],{},"Izokvanty"," produkce ",[883,28897,28899],{"className":28898},[886],[888,28900,28901],{"xmlns":890},[892,28902,28903,28922],{},[895,28904,28905,28907,28909,28911,28913,28916,28918,28920],{},[898,28906,2146],{},[1706,28908,2140],{"stretchy":2139},[898,28910,6362],{},[1706,28912,2505],{"separator":2504},[898,28914,28915],{},"K",[1706,28917,2153],{"stretchy":2139},[1706,28919,1708],{},[898,28921,20413],{},[902,28923,28924],{"encoding":904},"Q(L, K) = c",[207,28926,28928],{"className":28927,"dataFsResolvedFilePath":857,"href":858},[210],"produkce",[115,28930,28932],{"id":28931},"parciální-derivace","Parciální derivace",[724,28934,3465,28935,28959],{},[883,28936,28938],{"className":28937},[886],[888,28939,28940],{"xmlns":890},[892,28941,28942,28956],{},[895,28943,28944,28946,28948,28950,28952,28954],{},[898,28945,21237],{},[1706,28947,2140],{"stretchy":2139},[898,28949,18300],{},[1706,28951,2505],{"separator":2504},[898,28953,6930],{},[1706,28955,2153],{"stretchy":2139},[902,28957,28958],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,28961,28962],{},[883,28963,28965],{"className":28964},[886],[888,28966,28967],{"xmlns":890},[892,28968,28969,29024],{},[895,28970,28971,28979,28981,28996,28998,29000,29008,29010],{},[28285,28972,28973,28975,28977],{},[898,28974,21237],{},[898,28976,18300],{},[1706,28978,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,28980,1708],{},[2964,28982,28983,28990],{},[895,28984,28985,28988],{},[898,28986,28987],{"mathvariant":2409},"∂",[898,28989,21237],{},[895,28991,28992,28994],{},[898,28993,28987],{"mathvariant":2409},[898,28995,18300],{},[1706,28997,2505],{"separator":2504},[4898,28999],{"width":9524},[28285,29001,29002,29004,29006],{},[898,29003,21237],{},[898,29005,6930],{},[1706,29007,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,29009,1708],{},[2964,29011,29012,29018],{},[895,29013,29014,29016],{},[898,29015,28987],{"mathvariant":2409},[898,29017,21237],{},[895,29019,29020,29022],{},[898,29021,28987],{"mathvariant":2409},[898,29023,6930],{},[902,29025,29026],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,29028,29029,29030,1837],{},"Hodnoty v bodě: ",[883,29031,29033],{"className":29032},[886],[888,29034,29035],{"xmlns":890},[892,29036,29037,29079],{},[895,29038,29039,29047,29049,29051,29053,29055,29057,29059,29061,29069,29071,29073,29075,29077],{},[28285,29040,29041,29043,29045],{},[898,29042,21237],{},[898,29044,18300],{},[1706,29046,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,29048,2140],{"stretchy":2139},[898,29050,207],{},[1706,29052,2505],{"separator":2504},[898,29054,2450],{},[1706,29056,2153],{"stretchy":2139},[1706,29058,2505],{"separator":2504},[2415,29060,21505],{},[28285,29062,29063,29065,29067],{},[898,29064,21237],{},[898,29066,6930],{},[1706,29068,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,29070,2140],{"stretchy":2139},[898,29072,207],{},[1706,29074,2505],{"separator":2504},[898,29076,2450],{},[1706,29078,2153],{"stretchy":2139},[902,29080,29081],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,29083,29085],{"id":29084},"ekonomické-značení","Ekonomické značení",[724,29087,29088,29089,4288],{},"Pro produkční funkci ",[883,29090,29092],{"className":29091},[886],[888,29093,29094],{"xmlns":890},[892,29095,29096,29110],{},[895,29097,29098,29100,29102,29104,29106,29108],{},[898,29099,2146],{},[1706,29101,2140],{"stretchy":2139},[898,29103,6362],{},[1706,29105,2505],{"separator":2504},[898,29107,28915],{},[1706,29109,2153],{"stretchy":2139},[902,29111,29112],{"encoding":904},"Q(L, K)",[120,29114,29115,29160],{},[123,29116,29117,21677,29137,2314,29140,2153],{},[883,29118,29120],{"className":29119},[886],[888,29121,29122],{"xmlns":890},[892,29123,29124,29134],{},[895,29125,29126],{},[28285,29127,29128,29130,29132],{},[898,29129,2146],{},[898,29131,6362],{},[1706,29133,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,29135,29136],{"encoding":904},"Q'_L",[38,29138,29139],{},"mezní produkt práce",[883,29141,29143],{"className":29142},[886],[888,29144,29145],{"xmlns":890},[892,29146,29147,29157],{},[895,29148,29149,29151],{},[898,29150,1742],{},[2142,29152,29153,29155],{},[898,29154,1702],{},[898,29156,6362],{},[902,29158,29159],{"encoding":904},"MP_L",[123,29161,29162,21677,29182,2314,29185,2153],{},[883,29163,29165],{"className":29164},[886],[888,29166,29167],{"xmlns":890},[892,29168,29169,29179],{},[895,29170,29171],{},[28285,29172,29173,29175,29177],{},[898,29174,2146],{},[898,29176,28915],{},[1706,29178,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,29180,29181],{"encoding":904},"Q'_K",[38,29183,29184],{},"mezní produkt kapitálu",[883,29186,29188],{"className":29187},[886],[888,29189,29190],{"xmlns":890},[892,29191,29192,29202],{},[895,29193,29194,29196],{},[898,29195,1742],{},[2142,29197,29198,29200],{},[898,29199,1702],{},[898,29201,28915],{},[902,29203,29204],{"encoding":904},"MP_K",[198,29206,21773],{"id":21772},[724,29208,29209,4288],{},[883,29210,29212],{"className":29211},[886],[888,29213,29214],{"xmlns":890},[892,29215,29216,29236],{},[895,29217,29218,29226,29228,29230,29232,29234],{},[28285,29219,29220,29222,29224],{},[898,29221,21237],{},[898,29223,18300],{},[1706,29225,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,29227,2140],{"stretchy":2139},[898,29229,207],{},[1706,29231,2505],{"separator":2504},[898,29233,2450],{},[1706,29235,2153],{"stretchy":2139},[902,29237,29238],{"encoding":904},"f'_x(a, b)",[120,29240,29241,29298],{},[123,29242,29243,29244,29257,29258,16573,29271,29297],{},"rychlost změny ",[883,29245,29247],{"className":29246},[886],[888,29248,29249],{"xmlns":890},[892,29250,29251,29255],{},[895,29252,29253],{},[898,29254,21237],{},[902,29256,21237],{"encoding":904}," vůči ",[883,29259,29261],{"className":29260},[886],[888,29262,29263],{"xmlns":890},[892,29264,29265,29269],{},[895,29266,29267],{},[898,29268,18300],{},[902,29270,18300],{"encoding":904},[883,29272,29274],{"className":29273},[886],[888,29275,29276],{"xmlns":890},[892,29277,29278,29294],{},[895,29279,29280,29282,29284,29286,29288,29290,29292],{},[898,29281,18300],{},[1706,29283,1708],{},[898,29285,207],{},[1706,29287,2505],{"separator":2504},[898,29289,6930],{},[1706,29291,1708],{},[898,29293,2450],{},[902,29295,29296],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,29299,29300,29301,4174,29314,29327,29328,29346,29347,1837],{},"přibližná změna ",[883,29302,29304],{"className":29303},[886],[888,29305,29306],{"xmlns":890},[892,29307,29308,29312],{},[895,29309,29310],{},[898,29311,21237],{},[902,29313,21237],{"encoding":904},[883,29315,29317],{"className":29316},[886],[888,29318,29319],{"xmlns":890},[892,29320,29321,29325],{},[895,29322,29323],{},[898,29324,18300],{},[902,29326,18300],{"encoding":904}," o 1 (a pevném ",[883,29329,29331],{"className":29330},[886],[888,29332,29333],{"xmlns":890},[892,29334,29335,29343],{},[895,29336,29337,29339,29341],{},[898,29338,6930],{},[1706,29340,1708],{},[898,29342,2450],{},[902,29344,29345],{"encoding":904},"y = b","): ",[883,29348,29350],{"className":29349},[886],[888,29351,29352],{"xmlns":890},[892,29353,29354,29406],{},[895,29355,29356,29358,29360,29362,29364,29366,29368,29370,29372,29374,29376,29378,29380,29382,29384,29386,29388,29396,29398,29400,29402,29404],{},[898,29357,21237],{},[1706,29359,2140],{"stretchy":2139},[898,29361,207],{},[1706,29363,2447],{},[2148,29365,2701],{},[1706,29367,2505],{"separator":2504},[898,29369,2450],{},[1706,29371,2153],{"stretchy":2139},[1706,29373,3248],{},[898,29375,21237],{},[1706,29377,2140],{"stretchy":2139},[898,29379,207],{},[1706,29381,2505],{"separator":2504},[898,29383,2450],{},[1706,29385,2153],{"stretchy":2139},[1706,29387,2447],{},[28285,29389,29390,29392,29394],{},[898,29391,21237],{},[898,29393,18300],{},[1706,29395,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,29397,2140],{"stretchy":2139},[898,29399,207],{},[1706,29401,2505],{"separator":2504},[898,29403,2450],{},[1706,29405,2153],{"stretchy":2139},[902,29407,29408],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,29410,29412],{"id":29411},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,29414,29415],{},[883,29416,29418],{"className":29417},[886],[888,29419,29420],{"xmlns":890},[892,29421,29422,29480],{},[895,29423,29424,29426,29428,29430,29438,29440,29442,29444,29446,29448,29450,29452,29454,29456,29464,29466,29468,29470,29472,29474,29476,29478],{},[898,29425,3120],{},[898,29427,21237],{},[1706,29429,1708],{},[28285,29431,29432,29434,29436],{},[898,29433,21237],{},[898,29435,18300],{},[1706,29437,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,29439,2140],{"stretchy":2139},[898,29441,18300],{},[1706,29443,2505],{"separator":2504},[898,29445,6930],{},[1706,29447,2153],{"stretchy":2139},[2415,29449,2799],{},[898,29451,3120],{},[898,29453,18300],{},[1706,29455,2447],{},[28285,29457,29458,29460,29462],{},[898,29459,21237],{},[898,29461,6930],{},[1706,29463,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,29465,2140],{"stretchy":2139},[898,29467,18300],{},[1706,29469,2505],{"separator":2504},[898,29471,6930],{},[1706,29473,2153],{"stretchy":2139},[2415,29475,2799],{},[898,29477,3120],{},[898,29479,6930],{},[902,29481,29482],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,29484,22184,29485,4521,29507,29529],{},[883,29486,29488],{"className":29487},[886],[888,29489,29490],{"xmlns":890},[892,29491,29492,29504],{},[895,29493,29494,29496,29498,29500,29502],{},[898,29495,3120],{},[898,29497,18300],{},[1706,29499,2505],{"separator":2504},[898,29501,3120],{},[898,29503,6930],{},[902,29505,29506],{"encoding":904},"dx, dy",[883,29508,29510],{"className":29509},[886],[888,29511,29512],{"xmlns":890},[892,29513,29514,29526],{},[895,29515,29516,29518,29520,29522,29524],{},[898,29517,3677],{"mathvariant":2409},[898,29519,21237],{},[1706,29521,3248],{},[898,29523,3120],{},[898,29525,21237],{},[902,29527,29528],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,29531,29533],{"id":29532},"implicitní-funkce","Implicitní funkce",[724,29535,29536,29537,29565,29566,29579,29580,29593],{},"Je-li vztah dán rovnicí ",[883,29538,29540],{"className":29539},[886],[888,29541,29542],{"xmlns":890},[892,29543,29544,29562],{},[895,29545,29546,29548,29550,29552,29554,29556,29558,29560],{},[898,29547,2020],{},[1706,29549,2140],{"stretchy":2139},[898,29551,18300],{},[1706,29553,2505],{"separator":2504},[898,29555,6930],{},[1706,29557,2153],{"stretchy":2139},[1706,29559,1708],{},[2148,29561,2150],{},[902,29563,29564],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,29567,29569],{"className":29568},[886],[888,29570,29571],{"xmlns":890},[892,29572,29573,29577],{},[895,29574,29575],{},[898,29576,6930],{},[902,29578,6930],{"encoding":904}," podle ",[883,29581,29583],{"className":29582},[886],[888,29584,29585],{"xmlns":890},[892,29586,29587,29591],{},[895,29588,29589],{},[898,29590,18300],{},[902,29592,18300],{"encoding":904}," (nebo naopak):",[724,29595,29596],{},[883,29597,29599],{"className":29598},[886],[888,29600,29601],{"xmlns":890},[892,29602,29603,29697],{},[895,29604,29605,29611,29613,29627,29629,29631,29649,29651,29653,29659,29661,29675,29677,29679],{},[2489,29606,29607,29609],{},[898,29608,6930],{},[1706,29610,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,29612,1708],{},[2964,29614,29615,29621],{},[895,29616,29617,29619],{},[898,29618,3120],{},[898,29620,6930],{},[895,29622,29623,29625],{},[898,29624,3120],{},[898,29626,18300],{},[1706,29628,1708],{},[1706,29630,1715],{},[2964,29632,29633,29641],{},[28285,29634,29635,29637,29639],{},[898,29636,2020],{},[898,29638,18300],{},[1706,29640,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[28285,29642,29643,29645,29647],{},[898,29644,2020],{},[898,29646,6930],{},[1706,29648,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,29650,2505],{"separator":2504},[4898,29652],{"width":9524},[2489,29654,29655,29657],{},[898,29656,18300],{},[1706,29658,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,29660,1708],{},[2964,29662,29663,29669],{},[895,29664,29665,29667],{},[898,29666,3120],{},[898,29668,18300],{},[895,29670,29671,29673],{},[898,29672,3120],{},[898,29674,6930],{},[1706,29676,1708],{},[1706,29678,1715],{},[2964,29680,29681,29689],{},[28285,29682,29683,29685,29687],{},[898,29684,2020],{},[898,29686,6930],{},[1706,29688,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[28285,29690,29691,29693,29695],{},[898,29692,2020],{},[898,29694,18300],{},[1706,29696,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,29698,29699],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,29701,29702,29703,29706,29707,1993,29711,1837],{},"Tato vzorec dává ",[38,29704,29705],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,29708,29710],{"className":29709,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS",[207,29712,29714],{"className":29713,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS",[115,29716,29718],{"id":29717},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,29720,22432],{"id":22431},[724,29722,29723,29724,29748],{},"V bodě extrému ",[883,29725,29727],{"className":29726},[886],[888,29728,29729],{"xmlns":890},[892,29730,29731,29745],{},[895,29732,29733,29735,29737,29739,29741,29743],{},[898,29734,1735],{},[1706,29736,21693],{"stretchy":2139},[898,29738,207],{},[1706,29740,2505],{"separator":2504},[898,29742,2450],{},[1706,29744,21708],{"stretchy":2139},[902,29746,29747],{"encoding":904},"A[a, b]"," musí platit současně:",[724,29750,29751],{},[883,29752,29754],{"className":29753},[886],[888,29755,29756],{"xmlns":890},[892,29757,29758,29811],{},[895,29759,29760,29768,29770,29772,29774,29776,29778,29780,29782,29784,29787,29789,29797,29799,29801,29803,29805,29807,29809],{},[28285,29761,29762,29764,29766],{},[898,29763,21237],{},[898,29765,18300],{},[1706,29767,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,29769,2140],{"stretchy":2139},[898,29771,207],{},[1706,29773,2505],{"separator":2504},[898,29775,2450],{},[1706,29777,2153],{"stretchy":2139},[1706,29779,1708],{},[2148,29781,2150],{},[2415,29783,3852],{},[1706,29785,29786],{},"∧",[2415,29788,3852],{},[28285,29790,29791,29793,29795],{},[898,29792,21237],{},[898,29794,6930],{},[1706,29796,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,29798,2140],{"stretchy":2139},[898,29800,207],{},[1706,29802,2505],{"separator":2504},[898,29804,2450],{},[1706,29806,2153],{"stretchy":2139},[1706,29808,1708],{},[2148,29810,2150],{},[902,29812,29813],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,29815,22506],{"id":22505},[724,29817,29818,29819,29822],{},"Definujeme ",[38,29820,29821],{},"diskriminant"," (Hessián zjednodušeně):",[724,29824,29825],{},[883,29826,29828],{"className":29827},[886],[888,29829,29830],{"xmlns":890},[892,29831,29832,29908],{},[895,29833,29834,29836,29838,29840,29842,29844,29846,29848,29864,29866,29882,29884,29886,29902],{},[898,29835,2334],{},[1706,29837,2140],{"stretchy":2139},[898,29839,18300],{},[1706,29841,2505],{"separator":2504},[898,29843,6930],{},[1706,29845,2153],{"stretchy":2139},[1706,29847,1708],{},[28285,29849,29850,29852,29858],{},[898,29851,21237],{},[895,29853,29854,29856],{},[898,29855,18300],{},[898,29857,18300],{},[895,29859,29860,29862],{},[1706,29861,3142],{"mathvariant":2409},[1706,29863,3142],{"mathvariant":2409},[1706,29865,2390],{},[28285,29867,29868,29870,29876],{},[898,29869,21237],{},[895,29871,29872,29874],{},[898,29873,6930],{},[898,29875,6930],{},[895,29877,29878,29880],{},[1706,29879,3142],{"mathvariant":2409},[1706,29881,3142],{"mathvariant":2409},[1706,29883,1715],{},[1706,29885,2140],{"stretchy":2139},[28285,29887,29888,29890,29896],{},[898,29889,21237],{},[895,29891,29892,29894],{},[898,29893,18300],{},[898,29895,6930],{},[895,29897,29898,29900],{},[1706,29899,3142],{"mathvariant":2409},[1706,29901,3142],{"mathvariant":2409},[2489,29903,29904,29906],{},[1706,29905,2153],{"stretchy":2139},[2148,29907,2495],{},[902,29909,29910],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,29912,29913,29914,4288],{},"V podezřelém bodě ",[883,29915,29917],{"className":29916},[886],[888,29918,29919],{"xmlns":890},[892,29920,29921,29933],{},[895,29922,29923,29925,29927,29929,29931],{},[1706,29924,21693],{"stretchy":2139},[898,29926,207],{},[1706,29928,2505],{"separator":2504},[898,29930,2450],{},[1706,29932,21708],{"stretchy":2139},[902,29934,29935],{"encoding":904},"[a, b]",[152,29937,29938,30065,30101],{},[123,29939,29940,29970,29971],{},[38,29941,29942,4288],{},[883,29943,29945],{"className":29944},[886],[888,29946,29947],{"xmlns":890},[892,29948,29949,29967],{},[895,29950,29951,29953,29955,29957,29959,29961,29963,29965],{},[898,29952,2334],{},[1706,29954,2140],{"stretchy":2139},[898,29956,207],{},[1706,29958,2505],{"separator":2504},[898,29960,2450],{},[1706,29962,2153],{"stretchy":2139},[1706,29964,8922],{},[2148,29966,2150],{},[902,29968,29969],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,29972,29973,30019],{},[123,29974,29975,22593,30017],{},[883,29976,29978],{"className":29977},[886],[888,29979,29980],{"xmlns":890},[892,29981,29982,30014],{},[895,29983,29984,30000,30002,30004,30006,30008,30010,30012],{},[28285,29985,29986,29988,29994],{},[898,29987,21237],{},[895,29989,29990,29992],{},[898,29991,18300],{},[898,29993,18300],{},[895,29995,29996,29998],{},[1706,29997,3142],{"mathvariant":2409},[1706,29999,3142],{"mathvariant":2409},[1706,30001,2140],{"stretchy":2139},[898,30003,207],{},[1706,30005,2505],{"separator":2504},[898,30007,2450],{},[1706,30009,2153],{"stretchy":2139},[1706,30011,8922],{},[2148,30013,2150],{},[902,30015,30016],{"encoding":904},"f''_{xx}(a, b) > 0",[38,30018,13792],{},[123,30020,30021,22593,30063],{},[883,30022,30024],{"className":30023},[886],[888,30025,30026],{"xmlns":890},[892,30027,30028,30060],{},[895,30029,30030,30046,30048,30050,30052,30054,30056,30058],{},[28285,30031,30032,30034,30040],{},[898,30033,21237],{},[895,30035,30036,30038],{},[898,30037,18300],{},[898,30039,18300],{},[895,30041,30042,30044],{},[1706,30043,3142],{"mathvariant":2409},[1706,30045,3142],{"mathvariant":2409},[1706,30047,2140],{"stretchy":2139},[898,30049,207],{},[1706,30051,2505],{"separator":2504},[898,30053,2450],{},[1706,30055,2153],{"stretchy":2139},[1706,30057,2539],{},[2148,30059,2150],{},[902,30061,30062],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,30064,13844],{},[123,30066,30067,1647,30097,30100],{},[38,30068,30069,4288],{},[883,30070,30072],{"className":30071},[886],[888,30073,30074],{"xmlns":890},[892,30075,30076,30094],{},[895,30077,30078,30080,30082,30084,30086,30088,30090,30092],{},[898,30079,2334],{},[1706,30081,2140],{"stretchy":2139},[898,30083,207],{},[1706,30085,2505],{"separator":2504},[898,30087,2450],{},[1706,30089,2153],{"stretchy":2139},[1706,30091,2539],{},[2148,30093,2150],{},[902,30095,30096],{"encoding":904},"D(a, b) \u003C 0",[38,30098,30099],{},"sedlo"," (v daném bodě extrém není).",[123,30102,30103,30133],{},[38,30104,30105,4288],{},[883,30106,30108],{"className":30107},[886],[888,30109,30110],{"xmlns":890},[892,30111,30112,30130],{},[895,30113,30114,30116,30118,30120,30122,30124,30126,30128],{},[898,30115,2334],{},[1706,30117,2140],{"stretchy":2139},[898,30119,207],{},[1706,30121,2505],{"separator":2504},[898,30123,2450],{},[1706,30125,2153],{"stretchy":2139},[1706,30127,1708],{},[2148,30129,2150],{},[902,30131,30132],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,30135,30137],{"id":30136},"vázané-extrémy","Vázané extrémy",[724,30139,30140,30141,30170,30171,1837],{},"Pro extrémy s omezující podmínkou ",[883,30142,30144],{"className":30143},[886],[888,30145,30146],{"xmlns":890},[892,30147,30148,30167],{},[895,30149,30150,30153,30155,30157,30159,30161,30163,30165],{},[898,30151,30152],{},"g",[1706,30154,2140],{"stretchy":2139},[898,30156,18300],{},[1706,30158,2505],{"separator":2504},[898,30160,6930],{},[1706,30162,2153],{"stretchy":2139},[1706,30164,1708],{},[2148,30166,2150],{},[902,30168,30169],{"encoding":904},"g(x, y) = 0"," se používá ",[207,30172,793],{"className":30173,"dataFsResolvedFilePath":791,"href":792},[210],[115,30175,21083],{"id":21082},[120,30177,30178,30185,30192],{},[123,30179,30180,1647,30182],{},[38,30181,22971],{},[207,30183,775],{"className":30184,"dataFsResolvedFilePath":773,"href":774},[210],[123,30186,30187,1647,30189],{},[38,30188,22979],{},[207,30190,793],{"className":30191,"dataFsResolvedFilePath":791,"href":792},[210],[123,30193,30194,1647,30196,30200,30201,30204,30205,30208],{},[38,30195,22987],{},[207,30197,30199],{"className":30198,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (parciální derivace = mezní produkty), ",[207,30202,880],{"className":30203,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,30206,21098],{"className":30207,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":30210},[30211,30212,30216,30217,30218,30222,30223],{"id":28776,"depth":642,"text":28777},{"id":28931,"depth":642,"text":28932,"children":30213},[30214,30215],{"id":29084,"depth":649,"text":29085},{"id":21772,"depth":649,"text":21773},{"id":29411,"depth":642,"text":29412},{"id":29532,"depth":642,"text":29533},{"id":29717,"depth":642,"text":29718,"children":30219},[30220,30221],{"id":22431,"depth":649,"text":22432},{"id":22505,"depth":649,"text":22506},{"id":30136,"depth":642,"text":30137},{"id":21082,"depth":642,"text":21083},"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":28688,"description":30224},[1135],"topics\u002Ffunkce-vice-promennych",[1128,30231,23025,30232,30233,30234],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":30237,"title":775,"body":30238,"course":1128,"courses":659,"created":1129,"description":31090,"extension":661,"meta":31091,"navigation":664,"path":31092,"seo":31093,"sources":31094,"stem":31095,"tags":31096,"type":21181,"updated":677,"__hash__":31103},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":30239,"toc":31080},[30240,30242,30253,30257,30302,30382,30386,30462,30504,30511,30515,30519,30547,30605,30652,30690,30694,30743,30795,30847,30891,30894,30897,30969,30972,31044,31050,31052],[12,30241,775],{"id":1872},[724,30243,30244,30245,30248,30249,30252],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,30246,30247],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,30250,30251],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,30254,30256],{"id":30255},"neurčitý-integrál","Neurčitý integrál",[724,30258,30259],{},[883,30260,30262],{"className":30261},[886],[888,30263,30264],{"xmlns":890},[892,30265,30266,30299],{},[895,30267,30268,30270,30272,30274,30276,30278,30281,30283,30285,30287,30289,30291,30293,30295,30297],{},[898,30269,2020],{},[1706,30271,2140],{"stretchy":2139},[898,30273,18300],{},[1706,30275,2153],{"stretchy":2139},[1706,30277,1708],{},[1706,30279,30280],{},"∫",[898,30282,21237],{},[1706,30284,2140],{"stretchy":2139},[898,30286,18300],{},[1706,30288,2153],{"stretchy":2139},[2415,30290,2799],{},[898,30292,3120],{},[898,30294,18300],{},[1706,30296,2447],{},[898,30298,1683],{},[902,30300,30301],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,30303,5331,30304,3787,30338,3484,30351,30354,30355,1343,30368,30381],{},[883,30305,30307],{"className":30306},[886],[888,30308,30309],{"xmlns":890},[892,30310,30311,30335],{},[895,30312,30313,30319,30321,30323,30325,30327,30329,30331,30333],{},[2489,30314,30315,30317],{},[898,30316,2020],{},[1706,30318,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,30320,2140],{"stretchy":2139},[898,30322,18300],{},[1706,30324,2153],{"stretchy":2139},[1706,30326,1708],{},[898,30328,21237],{},[1706,30330,2140],{"stretchy":2139},[898,30332,18300],{},[1706,30334,2153],{"stretchy":2139},[902,30336,30337],{"encoding":904},"F'(x) = f(x)",[883,30339,30341],{"className":30340},[886],[888,30342,30343],{"xmlns":890},[892,30344,30345,30349],{},[895,30346,30347],{},[898,30348,2020],{},[902,30350,2020],{"encoding":904},[38,30352,30353],{},"primitivní funkce"," k ",[883,30356,30358],{"className":30357},[886],[888,30359,30360],{"xmlns":890},[892,30361,30362,30366],{},[895,30363,30364],{},[898,30365,21237],{},[902,30367,21237],{"encoding":904},[883,30369,30371],{"className":30370},[886],[888,30372,30373],{"xmlns":890},[892,30374,30375,30379],{},[895,30376,30377],{},[898,30378,1683],{},[902,30380,1683],{"encoding":904}," konstanta.",[115,30383,30385],{"id":30384},"určitý-integrál","Určitý integrál",[724,30387,30388],{},[883,30389,30391],{"className":30390},[886],[888,30392,30393],{"xmlns":890},[892,30394,30395,30459],{},[895,30396,30397,30405,30407,30409,30411,30413,30415,30417,30419,30421,30423,30425,30427,30429,30431,30439,30441,30443,30445,30447,30449,30451,30453,30455,30457],{},[28285,30398,30399,30401,30403],{},[1706,30400,30280],{},[898,30402,207],{},[898,30404,2450],{},[898,30406,21237],{},[1706,30408,2140],{"stretchy":2139},[898,30410,18300],{},[1706,30412,2153],{"stretchy":2139},[2415,30414,2799],{},[898,30416,3120],{},[898,30418,18300],{},[1706,30420,1708],{},[1706,30422,21693],{"stretchy":2139},[898,30424,2020],{},[1706,30426,2140],{"stretchy":2139},[898,30428,18300],{},[1706,30430,2153],{"stretchy":2139},[28285,30432,30433,30435,30437],{},[1706,30434,21708],{"stretchy":2139},[898,30436,207],{},[898,30438,2450],{},[1706,30440,1708],{},[898,30442,2020],{},[1706,30444,2140],{"stretchy":2139},[898,30446,2450],{},[1706,30448,2153],{"stretchy":2139},[1706,30450,1715],{},[898,30452,2020],{},[1706,30454,2140],{"stretchy":2139},[898,30456,207],{},[1706,30458,2153],{"stretchy":2139},[902,30460,30461],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,30463,30464,30465,1647,30468,30481,30482,30503],{},"Geometricky ",[38,30466,30467],{},"plocha pod grafem",[883,30469,30471],{"className":30470},[886],[888,30472,30473],{"xmlns":890},[892,30474,30475,30479],{},[895,30476,30477],{},[898,30478,21237],{},[902,30480,21237],{"encoding":904}," na intervalu ",[883,30483,30485],{"className":30484},[886],[888,30486,30487],{"xmlns":890},[892,30488,30489,30501],{},[895,30490,30491,30493,30495,30497,30499],{},[1706,30492,21693],{"stretchy":2139},[898,30494,207],{},[1706,30496,2505],{"separator":2504},[898,30498,2450],{},[1706,30500,21708],{"stretchy":2139},[902,30502,29935],{"encoding":904}," (orientovaná).",[724,30505,30506],{},[2286,30507],{"alt":30508,"className":30509,"src":30510},"imek-integral-plocha",[210,2290],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,30512,30514],{"id":30513},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,30516,30518],{"id":30517},"příklad-tr-z-mr","Příklad — TR z MR",[724,30520,30521,30522,1837],{},"Mezní příjem ",[883,30523,30525],{"className":30524},[886],[888,30526,30527],{"xmlns":890},[892,30528,30529,30545],{},[895,30530,30531,30533,30535,30537,30539,30541,30543],{},[898,30532,1742],{},[898,30534,1662],{},[1706,30536,1708],{},[2148,30538,2590],{},[1706,30540,1715],{},[2148,30542,2495],{},[898,30544,2146],{},[902,30546,4247],{"encoding":904},[724,30548,30549],{},[883,30550,30552],{"className":30551},[886],[888,30553,30554],{"xmlns":890},[892,30555,30556,30602],{},[895,30557,30558,30560,30562,30564,30566,30568,30570,30572,30574,30576,30578,30580,30582,30584,30586,30588,30590,30592,30598,30600],{},[898,30559,1659],{},[898,30561,1662],{},[1706,30563,1708],{},[1706,30565,30280],{},[1706,30567,2140],{"stretchy":2139},[2148,30569,2590],{},[1706,30571,1715],{},[2148,30573,2495],{},[898,30575,2146],{},[1706,30577,2153],{"stretchy":2139},[2415,30579,2799],{},[898,30581,3120],{},[898,30583,2146],{},[1706,30585,1708],{},[2148,30587,2590],{},[898,30589,2146],{},[1706,30591,1715],{},[2489,30593,30594,30596],{},[898,30595,2146],{},[2148,30597,2495],{},[1706,30599,2447],{},[898,30601,20413],{},[902,30603,30604],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,30606,30607,30608,22593,30634,4288],{},"Okrajová podmínka ",[883,30609,30611],{"className":30610},[886],[888,30612,30613],{"xmlns":890},[892,30614,30615,30631],{},[895,30616,30617,30619,30621,30623,30625,30627,30629],{},[898,30618,1659],{},[898,30620,1662],{},[1706,30622,2140],{"stretchy":2139},[2148,30624,2150],{},[1706,30626,2153],{"stretchy":2139},[1706,30628,1708],{},[2148,30630,2150],{},[902,30632,30633],{"encoding":904},"TR(0) = 0",[883,30635,30637],{"className":30636},[886],[888,30638,30639],{"xmlns":890},[892,30640,30641,30649],{},[895,30642,30643,30645,30647],{},[898,30644,20413],{},[1706,30646,1708],{},[2148,30648,2150],{},[902,30650,30651],{"encoding":904},"c = 0",[724,30653,30654],{},[883,30655,30657],{"className":30656},[886],[888,30658,30659],{"xmlns":890},[892,30660,30661,30687],{},[895,30662,30663,30665,30667,30669,30671,30673,30675,30677,30679,30681],{},[898,30664,1659],{},[898,30666,1662],{},[1706,30668,2140],{"stretchy":2139},[898,30670,2146],{},[1706,30672,2153],{"stretchy":2139},[1706,30674,1708],{},[2148,30676,2590],{},[898,30678,2146],{},[1706,30680,1715],{},[2489,30682,30683,30685],{},[898,30684,2146],{},[2148,30686,2495],{},[902,30688,30689],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,30691,30693],{"id":30692},"příklad-tc-z-mc","Příklad — TC z MC",[724,30695,30696,30697,30723,30724,1837],{},"Mezní náklady ",[883,30698,30700],{"className":30699},[886],[888,30701,30702],{"xmlns":890},[892,30703,30704,30720],{},[895,30705,30706,30708,30710,30712,30714,30716,30718],{},[898,30707,1742],{},[898,30709,1683],{},[1706,30711,1708],{},[2148,30713,2495],{},[1706,30715,2447],{},[2148,30717,15204],{},[898,30719,2146],{},[902,30721,30722],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,30725,30727],{"className":30726},[886],[888,30728,30729],{"xmlns":890},[892,30730,30731,30741],{},[895,30732,30733,30735,30737,30739],{},[898,30734,2020],{},[898,30736,1683],{},[1706,30738,1708],{},[2148,30740,2590],{},[902,30742,8022],{"encoding":904},[724,30744,30745],{},[883,30746,30748],{"className":30747},[886],[888,30749,30750],{"xmlns":890},[892,30751,30752,30792],{},[895,30753,30754,30756,30758,30760,30762,30764,30766,30768,30770,30772,30774,30776,30778,30780,30782,30788,30790],{},[898,30755,1659],{},[898,30757,1683],{},[1706,30759,1708],{},[1706,30761,30280],{},[898,30763,1742],{},[898,30765,1683],{},[2415,30767,2799],{},[898,30769,3120],{},[898,30771,2146],{},[1706,30773,1708],{},[2148,30775,2495],{},[898,30777,2146],{},[1706,30779,2447],{},[2148,30781,14840],{},[2489,30783,30784,30786],{},[898,30785,2146],{},[2148,30787,2495],{},[1706,30789,2447],{},[898,30791,20413],{},[902,30793,30794],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,30796,30607,30797,22593,30829,4288],{},[883,30798,30800],{"className":30799},[886],[888,30801,30802],{"xmlns":890},[892,30803,30804,30826],{},[895,30805,30806,30808,30810,30812,30814,30816,30818,30820,30822,30824],{},[898,30807,1659],{},[898,30809,1683],{},[1706,30811,2140],{"stretchy":2139},[2148,30813,2150],{},[1706,30815,2153],{"stretchy":2139},[1706,30817,1708],{},[898,30819,2020],{},[898,30821,1683],{},[1706,30823,1708],{},[2148,30825,2590],{},[902,30827,30828],{"encoding":904},"TC(0) = FC = 100",[883,30830,30832],{"className":30831},[886],[888,30833,30834],{"xmlns":890},[892,30835,30836,30844],{},[895,30837,30838,30840,30842],{},[898,30839,20413],{},[1706,30841,1708],{},[2148,30843,2590],{},[902,30845,30846],{"encoding":904},"c = 100",[724,30848,30849],{},[883,30850,30852],{"className":30851},[886],[888,30853,30854],{"xmlns":890},[892,30855,30856,30888],{},[895,30857,30858,30860,30862,30864,30866,30868,30870,30872,30874,30876,30878,30880,30882],{},[898,30859,1659],{},[898,30861,1683],{},[1706,30863,2140],{"stretchy":2139},[898,30865,2146],{},[1706,30867,2153],{"stretchy":2139},[1706,30869,1708],{},[2148,30871,2590],{},[1706,30873,2447],{},[2148,30875,2495],{},[898,30877,2146],{},[1706,30879,2447],{},[2148,30881,14840],{},[2489,30883,30884,30886],{},[898,30885,2146],{},[2148,30887,2495],{},[902,30889,30890],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,30892,820],{"id":30893},"přebytek-spotřebitele-a-výrobce",[724,30895,30896],{},"Přebytek spotřebitele:",[724,30898,30899],{},[883,30900,30902],{"className":30901},[886],[888,30903,30904],{"xmlns":890},[892,30905,30906,30966],{},[895,30907,30908,30910,30912,30914,30920,30922,30924,30936,30938,30940,30942,30944,30946,30948,30950,30952,30958,30960],{},[898,30909,1683],{},[898,30911,14171],{},[1706,30913,2140],{"stretchy":2139},[2142,30915,30916,30918],{},[898,30917,2146],{},[2148,30919,2150],{},[1706,30921,2153],{"stretchy":2139},[1706,30923,1708],{},[28285,30925,30926,30928,30930],{},[1706,30927,30280],{},[2148,30929,2150],{},[2142,30931,30932,30934],{},[898,30933,2146],{},[2148,30935,2150],{},[898,30937,2334],{},[1706,30939,2140],{"stretchy":2139},[898,30941,2146],{},[1706,30943,2153],{"stretchy":2139},[2415,30945,2799],{},[898,30947,3120],{},[898,30949,2146],{},[1706,30951,1715],{},[2142,30953,30954,30956],{},[898,30955,1702],{},[2148,30957,2150],{},[2415,30959,2799],{},[2142,30961,30962,30964],{},[898,30963,2146],{},[2148,30965,2150],{},[902,30967,30968],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,30970,30971],{},"Přebytek výrobce:",[724,30973,30974],{},[883,30975,30977],{"className":30976},[886],[888,30978,30979],{"xmlns":890},[892,30980,30981,31041],{},[895,30982,30983,30985,30987,30989,30995,30997,30999,31005,31007,31013,31015,31027,31029,31031,31033,31035,31037,31039],{},[898,30984,1702],{},[898,30986,14171],{},[1706,30988,2140],{"stretchy":2139},[2142,30990,30991,30993],{},[898,30992,2146],{},[2148,30994,2150],{},[1706,30996,2153],{"stretchy":2139},[1706,30998,1708],{},[2142,31000,31001,31003],{},[898,31002,1702],{},[2148,31004,2150],{},[2415,31006,2799],{},[2142,31008,31009,31011],{},[898,31010,2146],{},[2148,31012,2150],{},[1706,31014,1715],{},[28285,31016,31017,31019,31021],{},[1706,31018,30280],{},[2148,31020,2150],{},[2142,31022,31023,31025],{},[898,31024,2146],{},[2148,31026,2150],{},[898,31028,14171],{},[1706,31030,2140],{"stretchy":2139},[898,31032,2146],{},[1706,31034,2153],{"stretchy":2139},[2415,31036,2799],{},[898,31038,3120],{},[898,31040,2146],{},[902,31042,31043],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,31045,31046,31047,1837],{},"Detailně viz ",[207,31048,21094],{"className":31049,"dataFsResolvedFilePath":800,"href":801},[210],[115,31051,21083],{"id":21082},[120,31053,31054,31061,31068],{},[123,31055,31056,1647,31058],{},[38,31057,22971],{},[207,31059,766],{"className":31060,"dataFsResolvedFilePath":764,"href":765},[210],[123,31062,31063,1647,31065],{},[38,31064,22979],{},[207,31066,784],{"className":31067,"dataFsResolvedFilePath":782,"href":783},[210],[123,31069,31070,1647,31072,31075,31076,31079],{},[38,31071,22987],{},[207,31073,22995],{"className":31074,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,31077,21094],{"className":31078,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":31081},[31082,31083,31084,31089],{"id":30255,"depth":642,"text":30256},{"id":30384,"depth":642,"text":30385},{"id":30513,"depth":642,"text":30514,"children":31085},[31086,31087,31088],{"id":30517,"depth":649,"text":30518},{"id":30692,"depth":649,"text":30693},{"id":30893,"depth":649,"text":820},{"id":21082,"depth":642,"text":21083},"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":31090},[1135],"topics\u002Fintegral",[1128,31097,31098,31099,31100,31101,31102],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":31105,"title":31106,"body":31107,"course":1128,"courses":659,"created":21169,"description":641,"extension":661,"meta":35366,"navigation":664,"path":35367,"seo":35368,"sources":35369,"stem":35370,"tags":35371,"type":21181,"updated":677,"__hash__":35377},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":31108,"toc":35354},[31109,31112,31116,31258,31265,31269,31339,31377,31480,31484,31514,31580,31627,31630,31699,31702,31737,31773,31777,31825,31832,31878,31924,31927,32006,32103,32186,32190,32234,32264,32270,32299,32321,32371,32424,32490,32493,32559,32588,32647,32663,32750,32848,32979,32983,33140,33289,33669,33673,33676,33735,33738,33824,33852,33890,33893,33930,33970,34004,34006,34043,34075,34173,34178,34300,34352,34433,34572,34576,34696,34703,34814,34821,34823,35297,35299],[12,31110,31106],{"id":31111},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,31113,31115],{"id":31114},"tldr","TL;DR",[724,31117,31118,31121,31122,2314,31125,31138,31139,31152,31153,31156,31157,1343,31160,31163,31164,1343,31167,31170,31171,1647,31174,31204,31205,31208,31209,1343,31223,5354,31236,31239,31240,1936],{},[38,31119,31120],{},"IS-LM"," je makroekonomický model se ",[38,31123,31124],{},"dvěma neznámými",[883,31126,31128],{"className":31127},[886],[888,31129,31130],{"xmlns":890},[892,31131,31132,31136],{},[895,31133,31134],{},[898,31135,28247],{},[902,31137,28247],{"encoding":904}," — národní důchod a ",[883,31140,31142],{"className":31141},[886],[888,31143,31144],{"xmlns":890},[892,31145,31146,31150],{},[895,31147,31148],{},[898,31149,3950],{},[902,31151,3950],{"encoding":904}," — úroková míra) a ",[38,31154,31155],{},"dvěma trhy",": trhem zboží (křivka ",[38,31158,31159],{},"IS",[614,31161,31162],{},"Investment = Savings",") a trhem peněz (křivka ",[38,31165,31166],{},"LM",[614,31168,31169],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,31172,31173],{},"simultánní rovnováhu",[883,31175,31177],{"className":31176},[886],[888,31178,31179],{"xmlns":890},[892,31180,31181,31201],{},[895,31182,31183,31185,31191,31193,31199],{},[1706,31184,2140],{"stretchy":2139},[2489,31186,31187,31189],{},[898,31188,28247],{},[898,31190,23410],{},[1706,31192,2505],{"separator":2504},[2489,31194,31195,31197],{},[898,31196,3950],{},[898,31198,23410],{},[1706,31200,2153],{"stretchy":2139},[902,31202,31203],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,31206,31207],{},"fiskální politiky"," (posun IS změnou ",[883,31210,31212],{"className":31211},[886],[888,31213,31214],{"xmlns":890},[892,31215,31216,31221],{},[895,31217,31218],{},[898,31219,31220],{},"G",[902,31222,31220],{"encoding":904},[883,31224,31226],{"className":31225},[886],[888,31227,31228],{"xmlns":890},[892,31229,31230,31234],{},[895,31231,31232],{},[898,31233,1659],{},[902,31235,1659],{"encoding":904},[38,31237,31238],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,31241,31243],{"className":31242},[886],[888,31244,31245],{"xmlns":890},[892,31246,31247,31255],{},[895,31248,31249],{},[2489,31250,31251,31253],{},[898,31252,1742],{},[1706,31254,3197],{},[902,31256,31257],{"encoding":904},"M^*",[724,31259,31260],{},[2286,31261],{"alt":31262,"className":31263,"src":31264},"imek-is-lm-model",[210,2290],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,31266,31268],{"id":31267},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,31270,31271,31272,31276,31277,2314,31280,31303,31304,31307,31308,31324,31325,31338],{},"V modelech ",[207,31273,31275],{"className":31274,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,31278,31279],{},"investice pokládány za konstantní",[883,31281,31283],{"className":31282},[886],[888,31284,31285],{"xmlns":890},[892,31286,31287,31300],{},[895,31288,31289,31292,31294],{},[898,31290,31291],{},"I",[1706,31293,1708],{},[2489,31295,31296,31298],{},[898,31297,31291],{},[1706,31299,3197],{},[902,31301,31302],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,31305,31306],{},"ceně peněz",", tedy na ",[38,31309,31310,31311],{},"úrokové míře ",[883,31312,31314],{"className":31313},[886],[888,31315,31316],{"xmlns":890},[892,31317,31318,31322],{},[895,31319,31320],{},[898,31321,3950],{},[902,31323,3950],{"encoding":904},": čím vyšší ",[883,31326,31328],{"className":31327},[886],[888,31329,31330],{"xmlns":890},[892,31331,31332,31336],{},[895,31333,31334],{},[898,31335,3950],{},[902,31337,3950],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,31340,31341,31371],{},[123,31342,31343,1647,31346,31370],{},[38,31344,31345],{},"funkci investic",[883,31347,31349],{"className":31348},[886],[888,31350,31351],{"xmlns":890},[892,31352,31353,31367],{},[895,31354,31355,31357,31359,31361,31363,31365],{},[898,31356,31291],{},[1706,31358,1708],{},[898,31360,31291],{},[1706,31362,2140],{"stretchy":2139},[898,31364,3950],{},[1706,31366,2153],{"stretchy":2139},[902,31368,31369],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,31372,31373,31376],{},[38,31374,31375],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[1636,31378,31379],{},[724,31380,31381,31383,31384,31403,31404,31431,31432,31445,31446,31475,31476,31479],{},[883,31382,9276],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,31385,31387],{"className":31386},[886],[888,31388,31389],{"xmlns":890},[892,31390,31391,31400],{},[895,31392,31393,31395,31398],{},[898,31394,1683],{},[2415,31396,31397],{},"-",[898,31399,31291],{},[902,31401,31402],{"encoding":904},"C\\text{-}I"," až ",[883,31405,31407],{"className":31406},[886],[888,31408,31409],{"xmlns":890},[892,31410,31411,31428],{},[895,31412,31413,31415,31417,31419,31421,31423,31425],{},[898,31414,1683],{},[2415,31416,31397],{},[898,31418,31291],{},[2415,31420,31397],{},[898,31422,31220],{},[2415,31424,31397],{},[898,31426,31427],{},"X",[902,31429,31430],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,31433,31435],{"className":31434},[886],[888,31436,31437],{"xmlns":890},[892,31438,31439,31443],{},[895,31440,31441],{},[898,31442,28247],{},[902,31444,28247],{"encoding":904},". V IS-LM jsou ",[38,31447,31448,31449,1993,31462],{},"dvě neznámé ",[883,31450,31452],{"className":31451},[886],[888,31453,31454],{"xmlns":890},[892,31455,31456,31460],{},[895,31457,31458],{},[898,31459,28247],{},[902,31461,28247],{"encoding":904},[883,31463,31465],{"className":31464},[886],[888,31466,31467],{"xmlns":890},[892,31468,31469,31473],{},[895,31470,31471],{},[898,31472,3950],{},[902,31474,3950],{"encoding":904},", a proto potřebujeme ",[38,31477,31478],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,31481,31483],{"id":31482},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,31485,31486,31487,31500,31501,4288],{},"Lineární závislost investic ",[883,31488,31490],{"className":31489},[886],[888,31491,31492],{"xmlns":890},[892,31493,31494,31498],{},[895,31495,31496],{},[898,31497,31291],{},[902,31499,31291],{"encoding":904}," na úrokové míře ",[883,31502,31504],{"className":31503},[886],[888,31505,31506],{"xmlns":890},[892,31507,31508,31512],{},[895,31509,31510],{},[898,31511,3950],{},[902,31513,3950],{"encoding":904},[724,31515,31516],{},[883,31517,31519],{"className":31518},[886],[888,31520,31521],{"xmlns":890},[892,31522,31523,31577],{},[895,31524,31525,31527,31529,31531,31533,31535,31537,31539,31541,31543,31545,31547,31549,31551,31553,31555,31557,31559,31561,31563,31565,31568,31570,31572,31575],{},[898,31526,31291],{},[1706,31528,1708],{},[898,31530,31291],{},[1706,31532,2140],{"stretchy":2139},[898,31534,3950],{},[1706,31536,2153],{"stretchy":2139},[1706,31538,1708],{},[898,31540,20413],{},[898,31542,3950],{},[1706,31544,2447],{},[898,31546,3120],{},[1706,31548,2505],{"separator":2504},[4898,31550],{"width":9524},[898,31552,20413],{},[1706,31554,2539],{},[2148,31556,2150],{},[1706,31558,2505],{"separator":2504},[2415,31560,21505],{},[898,31562,3120],{},[1706,31564,8922],{},[2148,31566,31567],{},"0.",[4898,31569],{"width":9524},[1706,31571,2140],{"stretchy":2139},[2148,31573,31574],{},"7.11",[1706,31576,2153],{"stretchy":2139},[902,31578,31579],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,31581,31582,31603],{},[123,31583,31584,31602],{},[883,31585,31587],{"className":31586},[886],[888,31588,31589],{"xmlns":890},[892,31590,31591,31599],{},[895,31592,31593,31595,31597],{},[898,31594,3120],{},[1706,31596,8922],{},[2148,31598,2150],{},[902,31600,31601],{"encoding":904},"d > 0"," zřejmé,",[123,31604,31605,31623,31624,1837],{},[883,31606,31608],{"className":31607},[886],[888,31609,31610],{"xmlns":890},[892,31611,31612,31620],{},[895,31613,31614,31616,31618],{},[898,31615,20413],{},[1706,31617,2539],{},[2148,31619,2150],{},[902,31621,31622],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,31625,31626],{},"klesající",[724,31628,31629],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,31631,31632],{},[883,31633,31635],{"className":31634},[886],[888,31636,31637],{"xmlns":890},[892,31638,31639,31696],{},[895,31640,31641,31643,31645,31647,31649,31651,31653,31655,31657,31659,31661,31663,31665,31667,31669,31671,31673,31675,31677,31679,31681,31683,31685,31687,31689,31691,31694],{},[898,31642,1683],{},[1706,31644,1708],{},[898,31646,1683],{},[1706,31648,2140],{"stretchy":2139},[898,31650,28247],{},[1706,31652,2153],{"stretchy":2139},[1706,31654,1708],{},[898,31656,207],{},[898,31658,28247],{},[1706,31660,2447],{},[898,31662,2450],{},[1706,31664,2505],{"separator":2504},[4898,31666],{"width":9524},[2148,31668,2150],{},[1706,31670,2539],{},[898,31672,207],{},[1706,31674,2539],{},[2148,31676,2701],{},[1706,31678,2505],{"separator":2504},[2415,31680,21505],{},[898,31682,2450],{},[1706,31684,8922],{},[2148,31686,31567],{},[4898,31688],{"width":9524},[1706,31690,2140],{"stretchy":2139},[2148,31692,31693],{},"7.12",[1706,31695,2153],{"stretchy":2139},[902,31697,31698],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,31700,31701],{},"Podmínka rovnováhy na trhu zboží:",[724,31703,31704],{},[883,31705,31707],{"className":31706},[886],[888,31708,31709],{"xmlns":890},[892,31710,31711,31734],{},[895,31712,31713,31715,31717,31719,31721,31723,31725,31727,31729,31732],{},[898,31714,28247],{},[1706,31716,1708],{},[898,31718,1683],{},[1706,31720,2447],{},[898,31722,31291],{},[898,31724,1837],{"mathvariant":2409},[4898,31726],{"width":9524},[1706,31728,2140],{"stretchy":2139},[2148,31730,31731],{},"7.13",[1706,31733,2153],{"stretchy":2139},[902,31735,31736],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,31738,31739,31740,1647,31743,31769,31770,1837],{},"To dává ",[38,31741,31742],{},"tři rovnice o čtyřech neznámých",[883,31744,31746],{"className":31745},[886],[888,31747,31748],{"xmlns":890},[892,31749,31750,31766],{},[895,31751,31752,31754,31756,31758,31760,31762,31764],{},[898,31753,28247],{},[1706,31755,2505],{"separator":2504},[898,31757,1683],{},[1706,31759,2505],{"separator":2504},[898,31761,31291],{},[1706,31763,2505],{"separator":2504},[898,31765,3950],{},[902,31767,31768],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,31771,31772],{},"rovnováhy na trhu peněz",[115,31774,31776],{"id":31775},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,31778,31779,31780,24710,31802,31820,31821,31824],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,31781,31783],{"className":31782},[886],[888,31784,31785],{"xmlns":890},[892,31786,31787,31799],{},[895,31788,31789,31791,31793,31795,31797],{},[898,31790,28247],{},[1706,31792,1708],{},[898,31794,1683],{},[1706,31796,2447],{},[898,31798,14171],{},[902,31800,31801],{"encoding":904},"Y = C + S",[883,31803,31805],{"className":31804},[886],[888,31806,31807],{"xmlns":890},[892,31808,31809,31817],{},[895,31810,31811,31813,31815],{},[898,31812,31291],{},[1706,31814,1708],{},[898,31816,14171],{},[902,31818,31819],{"encoding":904},"I = S"," (plánované ",[38,31822,31823],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,31826,31827],{},[2286,31828],{"alt":31829,"className":31830,"src":31831},"imek-odvozeni-is-4panelu",[210,2290],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,31833,31834],{},[883,31835,31837],{"className":31836},[886],[888,31838,31839],{"xmlns":890},[892,31840,31841,31875],{},[895,31842,31843,31845,31847,31849,31851,31853,31855,31857,31859,31861,31863,31865,31867,31869,31871,31873],{},[898,31844,28247],{},[1706,31846,1708],{},[1706,31848,2140],{"stretchy":2139},[898,31850,207],{},[898,31852,28247],{},[1706,31854,2447],{},[898,31856,2450],{},[1706,31858,2153],{"stretchy":2139},[1706,31860,2447],{},[1706,31862,2140],{"stretchy":2139},[898,31864,20413],{},[898,31866,3950],{},[1706,31868,2447],{},[898,31870,3120],{},[1706,31872,2153],{"stretchy":2139},[1706,31874,2505],{"separator":2504},[902,31876,31877],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,31879,31880],{},[883,31881,31883],{"className":31882},[886],[888,31884,31885],{"xmlns":890},[892,31886,31887,31921],{},[895,31888,31889,31891,31893,31895,31897,31899,31901,31903,31905,31907,31909,31911,31913,31915,31917,31919],{},[1706,31890,2140],{"stretchy":2139},[2148,31892,2701],{},[1706,31894,1715],{},[898,31896,207],{},[1706,31898,2153],{"stretchy":2139},[898,31900,28247],{},[1706,31902,1715],{},[898,31904,20413],{},[898,31906,3950],{},[1706,31908,1715],{},[898,31910,2450],{},[1706,31912,1715],{},[898,31914,3120],{},[1706,31916,1708],{},[2148,31918,2150],{},[1706,31920,2505],{"separator":2504},[902,31922,31923],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,31925,31926],{},"odkud",[724,31928,31929],{},[883,31930,31932],{"className":31931},[886],[888,31933,31934],{"xmlns":890},[892,31935,31936,32003],{},[895,31937,31938,31994,31996,31998,32001],{},[31939,31940,31942],"menclose",{"notation":31941},"box",[4745,31943,31944],{"scriptlevel":2150,"displaystyle":2139},[4745,31945,31946],{"scriptlevel":2150,"displaystyle":2139},[4745,31947,31948],{"scriptlevel":2150,"displaystyle":2504},[895,31949,31950,31952,31954,31956,31968,31970,31972,31974,31992],{},[2415,31951,2799],{},[898,31953,28247],{},[1706,31955,1708],{},[2964,31957,31958,31960],{},[898,31959,20413],{},[895,31961,31962,31964,31966],{},[2148,31963,2701],{},[1706,31965,1715],{},[898,31967,207],{},[2415,31969,2799],{},[898,31971,3950],{},[1706,31973,2447],{},[2964,31975,31976,31984],{},[895,31977,31978,31980,31982],{},[898,31979,2450],{},[1706,31981,2447],{},[898,31983,3120],{},[895,31985,31986,31988,31990],{},[2148,31987,2701],{},[1706,31989,1715],{},[898,31991,207],{},[2415,31993,2799],{},[4898,31995],{"width":9524},[1706,31997,2140],{"stretchy":2139},[2148,31999,32000],{},"7.14",[1706,32002,2153],{"stretchy":2139},[902,32004,32005],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,32007,32008,32009,2314,32012,32015,32016,32019,32020,32022,32023,32045,32046,32074,32075,32096,32097,32099,32100,32102],{},"Tento vztah se nazývá ",[38,32010,32011],{},"funkce IS",[614,32013,32014],{},"IS schedule",") a její graf ",[38,32017,32018],{},"křivka IS",". Křivka je ",[38,32021,31626],{}," přímka v rovině ",[883,32024,32026],{"className":32025},[886],[888,32027,32028],{"xmlns":890},[892,32029,32030,32042],{},[895,32031,32032,32034,32036,32038,32040],{},[1706,32033,2140],{"stretchy":2139},[898,32035,3950],{},[1706,32037,2505],{"separator":2504},[898,32039,28247],{},[1706,32041,2153],{"stretchy":2139},[902,32043,32044],{"encoding":904},"(r, Y)",", neboť ",[883,32047,32049],{"className":32048},[886],[888,32050,32051],{"xmlns":890},[892,32052,32053,32071],{},[895,32054,32055,32067,32069],{},[2964,32056,32057,32059],{},[898,32058,20413],{},[895,32060,32061,32063,32065],{},[2148,32062,2701],{},[1706,32064,1715],{},[898,32066,207],{},[1706,32068,2539],{},[2148,32070,2150],{},[902,32072,32073],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,32076,32078],{"className":32077},[886],[888,32079,32080],{"xmlns":890},[892,32081,32082,32094],{},[895,32083,32084,32086,32088,32090,32092],{},[1706,32085,2140],{"stretchy":2139},[898,32087,3950],{},[1706,32089,2505],{"separator":2504},[898,32091,28247],{},[1706,32093,2153],{"stretchy":2139},[902,32095,32044],{"encoding":904},", pro které plánované ",[38,32098,31291],{},"nvestment = ",[38,32101,14171],{},"avings.",[1636,32104,32105],{},[724,32106,32107,32109,32110,32123,32124,1647,32127,32140,32141,32154,32155,1993,32168,32181,32182,32185],{},[883,32108,3174],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,32111,32113],{"className":32112},[886],[888,32114,32115],{"xmlns":890},[892,32116,32117,32121],{},[895,32118,32119],{},[898,32120,3950],{},[902,32122,3950],{"encoding":904}," → levnější úvěr → ",[38,32125,32126],{},"více investic",[883,32128,32130],{"className":32129},[886],[888,32131,32132],{"xmlns":890},[892,32133,32134,32138],{},[895,32135,32136],{},[898,32137,31291],{},[902,32139,31291],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,32142,32144],{"className":32143},[886],[888,32145,32146],{"xmlns":890},[892,32147,32148,32152],{},[895,32149,32150],{},[898,32151,28247],{},[902,32153,28247],{"encoding":904},". Vztah mezi ",[883,32156,32158],{"className":32157},[886],[888,32159,32160],{"xmlns":890},[892,32161,32162,32166],{},[895,32163,32164],{},[898,32165,3950],{},[902,32167,3950],{"encoding":904},[883,32169,32171],{"className":32170},[886],[888,32172,32173],{"xmlns":890},[892,32174,32175,32179],{},[895,32176,32177],{},[898,32178,28247],{},[902,32180,28247],{"encoding":904}," na trhu zboží je proto ",[38,32183,32184],{},"nepřímý"," (klesající křivka).",[115,32187,32189],{"id":32188},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,32191,32192,32193,32211,32212,3787,32230,32233],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,32194,32196],{"className":32195},[886],[888,32197,32198],{"xmlns":890},[892,32199,32200,32208],{},[895,32201,32202],{},[2489,32203,32204,32206],{},[898,32205,1742],{},[898,32207,2334],{},[902,32209,32210],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,32213,32215],{"className":32214},[886],[888,32216,32217],{"xmlns":890},[892,32218,32219,32227],{},[895,32220,32221],{},[2489,32222,32223,32225],{},[898,32224,1742],{},[898,32226,14171],{},[902,32228,32229],{"encoding":904},"M^S",[38,32231,32232],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,32235,32236],{},[883,32237,32239],{"className":32238},[886],[888,32240,32241],{"xmlns":890},[892,32242,32243,32261],{},[895,32244,32245,32251,32253,32259],{},[2489,32246,32247,32249],{},[898,32248,1742],{},[898,32250,14171],{},[1706,32252,1708],{},[2489,32254,32255,32257],{},[898,32256,1742],{},[1706,32258,3197],{},[898,32260,1837],{"mathvariant":2409},[902,32262,32263],{"encoding":904},"M^S = M^*.",[724,32265,32266,32269],{},[38,32267,32268],{},"Poptávka"," po penězích má tři zdroje:",[120,32271,32272,32281,32290],{},[123,32273,32274,2314,32277,32280],{},[38,32275,32276],{},"transakční poptávka",[614,32278,32279],{},"transactions demand",") — peníze pro nákup zboží,",[123,32282,32283,2314,32286,32289],{},[38,32284,32285],{},"opatrnostní poptávka",[614,32287,32288],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,32291,32292,2314,32295,32298],{},[38,32293,32294],{},"spekulační poptávka",[614,32296,32297],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,32300,32301,32302,32320],{},"Součet transakční a opatrnostní poptávky ",[883,32303,32305],{"className":32304},[886],[888,32306,32307],{"xmlns":890},[892,32308,32309,32317],{},[895,32310,32311],{},[2142,32312,32313,32315],{},[898,32314,6362],{},[2148,32316,2701],{},[902,32318,32319],{"encoding":904},"L_1"," je úměrný důchodu:",[724,32322,32323],{},[883,32324,32326],{"className":32325},[886],[888,32327,32328],{"xmlns":890},[892,32329,32330,32368],{},[895,32331,32332,32338,32340,32347,32349,32351,32353,32355,32357,32363,32365],{},[2142,32333,32334,32336],{},[898,32335,6362],{},[2148,32337,2701],{},[1706,32339,1708],{},[2142,32341,32342,32345],{},[898,32343,32344],{},"k",[2148,32346,2701],{},[898,32348,28247],{},[1706,32350,2505],{"separator":2504},[4898,32352],{"width":9524},[2148,32354,2150],{},[1706,32356,2539],{},[2142,32358,32359,32361],{},[898,32360,32344],{},[2148,32362,2701],{},[1706,32364,2539],{},[2148,32366,32367],{},"1.",[902,32369,32370],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,32372,32373,32374,32392,32393,1343,32406,32423],{},"Spekulační poptávka ",[883,32375,32377],{"className":32376},[886],[888,32378,32379],{"xmlns":890},[892,32380,32381,32389],{},[895,32382,32383],{},[2142,32384,32385,32387],{},[898,32386,6362],{},[2148,32388,2495],{},[902,32390,32391],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,32394,32396],{"className":32395},[886],[888,32397,32398],{"xmlns":890},[892,32399,32400,32404],{},[895,32401,32402],{},[898,32403,3950],{},[902,32405,3950],{"encoding":904},[883,32407,32409],{"className":32408},[886],[888,32410,32411],{"xmlns":890},[892,32412,32413,32421],{},[895,32414,32415],{},[2142,32416,32417,32419],{},[898,32418,6362],{},[2148,32420,2495],{},[902,32422,32391],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,32425,32426],{},[883,32427,32429],{"className":32428},[886],[888,32430,32431],{"xmlns":890},[892,32432,32433,32487],{},[895,32434,32435,32441,32443,32449,32451,32453,32459,32461,32463,32469,32471,32473,32475,32477,32483,32485],{},[2142,32436,32437,32439],{},[898,32438,6362],{},[2148,32440,2495],{},[1706,32442,1708],{},[2142,32444,32445,32447],{},[898,32446,32344],{},[2148,32448,2495],{},[898,32450,3950],{},[1706,32452,2447],{},[2142,32454,32455,32457],{},[898,32456,32344],{},[2148,32458,4284],{},[1706,32460,2505],{"separator":2504},[4898,32462],{"width":9524},[2142,32464,32465,32467],{},[898,32466,32344],{},[2148,32468,2495],{},[1706,32470,2539],{},[2148,32472,2150],{},[1706,32474,2505],{"separator":2504},[2415,32476,21505],{},[2142,32478,32479,32481],{},[898,32480,32344],{},[2148,32482,4284],{},[1706,32484,8922],{},[2148,32486,31567],{},[902,32488,32489],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,32491,32492],{},"Celková poptávka po penězích:",[724,32494,32495],{},[883,32496,32498],{"className":32497},[886],[888,32499,32500],{"xmlns":890},[892,32501,32502,32556],{},[895,32503,32504,32510,32512,32518,32520,32526,32528,32534,32536,32538,32544,32546,32548,32554],{},[2489,32505,32506,32508],{},[898,32507,1742],{},[898,32509,2334],{},[1706,32511,1708],{},[2142,32513,32514,32516],{},[898,32515,6362],{},[2148,32517,2701],{},[1706,32519,2447],{},[2142,32521,32522,32524],{},[898,32523,6362],{},[2148,32525,2495],{},[1706,32527,1708],{},[2142,32529,32530,32532],{},[898,32531,32344],{},[2148,32533,2701],{},[898,32535,28247],{},[1706,32537,2447],{},[2142,32539,32540,32542],{},[898,32541,32344],{},[2148,32543,2495],{},[898,32545,3950],{},[1706,32547,2447],{},[2142,32549,32550,32552],{},[898,32551,32344],{},[2148,32553,4284],{},[898,32555,1837],{"mathvariant":2409},[902,32557,32558],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,32560,32561,32562,4288],{},"Podmínka rovnováhy na trhu peněz ",[883,32563,32565],{"className":32564},[886],[888,32566,32567],{"xmlns":890},[892,32568,32569,32585],{},[895,32570,32571,32577,32579],{},[2489,32572,32573,32575],{},[898,32574,1742],{},[898,32576,2334],{},[1706,32578,1708],{},[2489,32580,32581,32583],{},[898,32582,1742],{},[1706,32584,3197],{},[902,32586,32587],{"encoding":904},"M^D = M^*",[724,32589,32590],{},[883,32591,32593],{"className":32592},[886],[888,32594,32595],{"xmlns":890},[892,32596,32597,32644],{},[895,32598,32599,32605,32607,32613,32615,32617,32623,32625,32627,32633,32635,32637,32639,32642],{},[2489,32600,32601,32603],{},[898,32602,1742],{},[1706,32604,3197],{},[1706,32606,1708],{},[2142,32608,32609,32611],{},[898,32610,32344],{},[2148,32612,2701],{},[898,32614,28247],{},[1706,32616,2447],{},[2142,32618,32619,32621],{},[898,32620,32344],{},[2148,32622,2495],{},[898,32624,3950],{},[1706,32626,2447],{},[2142,32628,32629,32631],{},[898,32630,32344],{},[2148,32632,4284],{},[1706,32634,2505],{"separator":2504},[4898,32636],{"width":9524},[1706,32638,2140],{"stretchy":2139},[2148,32640,32641],{},"7.15",[1706,32643,2153],{"stretchy":2139},[902,32645,32646],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,32648,32649,32650,5606],{},"po úpravě (vyjádření ",[883,32651,32653],{"className":32652},[886],[888,32654,32655],{"xmlns":890},[892,32656,32657,32661],{},[895,32658,32659],{},[898,32660,28247],{},[902,32662,28247],{"encoding":904},[724,32664,32665],{},[883,32666,32668],{"className":32667},[886],[888,32669,32670],{"xmlns":890},[892,32671,32672,32747],{},[895,32673,32674,32738,32740,32742,32745],{},[31939,32675,32676],{"notation":31941},[4745,32677,32678],{"scriptlevel":2150,"displaystyle":2139},[4745,32679,32680],{"scriptlevel":2150,"displaystyle":2139},[4745,32681,32682],{"scriptlevel":2150,"displaystyle":2504},[895,32683,32684,32686,32688,32690,32692,32706,32708,32710,32712,32736],{},[2415,32685,2799],{},[898,32687,28247],{},[1706,32689,1708],{},[1706,32691,1715],{},[2964,32693,32694,32700],{},[2142,32695,32696,32698],{},[898,32697,32344],{},[2148,32699,2495],{},[2142,32701,32702,32704],{},[898,32703,32344],{},[2148,32705,2701],{},[2415,32707,2799],{},[898,32709,3950],{},[1706,32711,2447],{},[2964,32713,32714,32730],{},[895,32715,32716,32722,32724],{},[2489,32717,32718,32720],{},[898,32719,1742],{},[1706,32721,3197],{},[1706,32723,1715],{},[2142,32725,32726,32728],{},[898,32727,32344],{},[2148,32729,4284],{},[2142,32731,32732,32734],{},[898,32733,32344],{},[2148,32735,2701],{},[2415,32737,2799],{},[4898,32739],{"width":9524},[1706,32741,2140],{"stretchy":2139},[2148,32743,32744],{},"7.16",[1706,32746,2153],{"stretchy":2139},[902,32748,32749],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,32751,32008,32752,2314,32755,32758,32759,32019,32762,32022,32765,32045,32786,32818,32819,32841,32842,32844,32845,32847],{},[38,32753,32754],{},"funkce LM",[614,32756,32757],{},"LM schedule","), její graf ",[38,32760,32761],{},"křivka LM",[38,32763,32764],{},"rostoucí",[883,32766,32768],{"className":32767},[886],[888,32769,32770],{"xmlns":890},[892,32771,32772,32784],{},[895,32773,32774,32776,32778,32780,32782],{},[1706,32775,2140],{"stretchy":2139},[898,32777,3950],{},[1706,32779,2505],{"separator":2504},[898,32781,28247],{},[1706,32783,2153],{"stretchy":2139},[902,32785,32044],{"encoding":904},[883,32787,32789],{"className":32788},[886],[888,32790,32791],{"xmlns":890},[892,32792,32793,32815],{},[895,32794,32795,32797,32811,32813],{},[1706,32796,1715],{},[2964,32798,32799,32805],{},[2142,32800,32801,32803],{},[898,32802,32344],{},[2148,32804,2495],{},[2142,32806,32807,32809],{},[898,32808,32344],{},[2148,32810,2701],{},[1706,32812,8922],{},[2148,32814,2150],{},[902,32816,32817],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,32820,32822],{"className":32821},[886],[888,32823,32824],{"xmlns":890},[892,32825,32826,32838],{},[895,32827,32828,32834,32836],{},[2142,32829,32830,32832],{},[898,32831,32344],{},[2148,32833,2495],{},[1706,32835,2539],{},[2148,32837,2150],{},[902,32839,32840],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,32843,6362],{},"iquidity of ",[38,32846,1742],{},"oney.",[1636,32849,32850],{},[724,32851,32852,32854,32855,32868,32869,32897,32898,32915,32916,32929,32930,32947,32948,1993,32961,32974,32975,32978],{},[883,32853,3174],{}," Intuice — proč LM roste\nVyšší důchod ",[883,32856,32858],{"className":32857},[886],[888,32859,32860],{"xmlns":890},[892,32861,32862,32866],{},[895,32863,32864],{},[898,32865,28247],{},[902,32867,28247],{"encoding":904}," → větší transakční poptávka po penězích ",[883,32870,32872],{"className":32871},[886],[888,32873,32874],{"xmlns":890},[892,32875,32876,32894],{},[895,32877,32878,32884,32886,32892],{},[2142,32879,32880,32882],{},[898,32881,6362],{},[2148,32883,2701],{},[1706,32885,1708],{},[2142,32887,32888,32890],{},[898,32889,32344],{},[2148,32891,2701],{},[898,32893,28247],{},[902,32895,32896],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,32899,32901],{"className":32900},[886],[888,32902,32903],{"xmlns":890},[892,32904,32905,32913],{},[895,32906,32907],{},[2489,32908,32909,32911],{},[898,32910,1742],{},[1706,32912,3197],{},[902,32914,31257],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,32917,32919],{"className":32918},[886],[888,32920,32921],{"xmlns":890},[892,32922,32923,32927],{},[895,32924,32925],{},[898,32926,3950],{},[902,32928,3950],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,32931,32933],{"className":32932},[886],[888,32934,32935],{"xmlns":890},[892,32936,32937,32945],{},[895,32938,32939],{},[2142,32940,32941,32943],{},[898,32942,6362],{},[2148,32944,2495],{},[902,32946,32391],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,32949,32951],{"className":32950},[886],[888,32952,32953],{"xmlns":890},[892,32954,32955,32959],{},[895,32956,32957],{},[898,32958,28247],{},[902,32960,28247],{"encoding":904},[883,32962,32964],{"className":32963},[886],[888,32965,32966],{"xmlns":890},[892,32967,32968,32972],{},[895,32969,32970],{},[898,32971,3950],{},[902,32973,3950],{"encoding":904}," na trhu peněz je proto ",[38,32976,32977],{},"přímý"," (rostoucí křivka).",[115,32980,32982],{"id":32981},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,32984,32985,32986,32989,32990,1647,32993,1993,33011,1647,33014,33032,33033,33051,33052,33070,33071,33087,33088,1993,33103,33118,33119,1837],{},"Řešením ",[38,32987,32988],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,32991,32992],{},"rovnovážný důchod",[883,32994,32996],{"className":32995},[886],[888,32997,32998],{"xmlns":890},[892,32999,33000,33008],{},[895,33001,33002],{},[2489,33003,33004,33006],{},[898,33005,28247],{},[898,33007,23410],{},[902,33009,33010],{"encoding":904},"Y^E",[38,33012,33013],{},"rovnovážnou úrokovou míru",[883,33015,33017],{"className":33016},[886],[888,33018,33019],{"xmlns":890},[892,33020,33021,33029],{},[895,33022,33023],{},[2489,33024,33025,33027],{},[898,33026,3950],{},[898,33028,23410],{},[902,33030,33031],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,33034,33036],{"className":33035},[886],[888,33037,33038],{"xmlns":890},[892,33039,33040,33048],{},[895,33041,33042],{},[2489,33043,33044,33046],{},[898,33045,31291],{},[898,33047,23410],{},[902,33049,33050],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,33053,33055],{"className":33054},[886],[888,33056,33057],{"xmlns":890},[892,33058,33059,33067],{},[895,33060,33061],{},[2489,33062,33063,33065],{},[898,33064,1683],{},[898,33066,23410],{},[902,33068,33069],{"encoding":904},"C^E",". Graficky jde o ",[38,33072,33073,33074],{},"průsečík ",[883,33075,33077],{"className":33076},[886],[888,33078,33079],{"xmlns":890},[892,33080,33081,33085],{},[895,33082,33083],{},[898,33084,23410],{},[902,33086,23410],{"encoding":904}," křivek ",[883,33089,33091],{"className":33090},[886],[888,33092,33093],{"xmlns":890},[892,33094,33095,33101],{},[895,33096,33097,33099],{},[898,33098,31291],{},[898,33100,14171],{},[902,33102,31159],{"encoding":904},[883,33104,33106],{"className":33105},[886],[888,33107,33108],{"xmlns":890},[892,33109,33110,33116],{},[895,33111,33112,33114],{},[898,33113,6362],{},[898,33115,1742],{},[902,33117,31166],{"encoding":904}," v rovině ",[883,33120,33122],{"className":33121},[886],[888,33123,33124],{"xmlns":890},[892,33125,33126,33138],{},[895,33127,33128,33130,33132,33134,33136],{},[1706,33129,2140],{"stretchy":2139},[898,33131,3950],{},[1706,33133,2505],{"separator":2504},[898,33135,28247],{},[1706,33137,2153],{"stretchy":2139},[902,33139,32044],{"encoding":904},[724,33141,33142],{},[614,33143,33144,33145,33166,33167,33182,33183,33198,33199,33212,33213,33230,33231,5354,33244,33230,33261,33274,33275,33288],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,33146,33148],{"className":33147},[886],[888,33149,33150],{"xmlns":890},[892,33151,33152,33164],{},[895,33153,33154,33156,33158,33160,33162],{},[1706,33155,2140],{"stretchy":2139},[898,33157,3950],{},[1706,33159,2505],{"separator":2504},[898,33161,28247],{},[1706,33163,2153],{"stretchy":2139},[902,33165,32044],{"encoding":904},". Rostoucí přímka ",[883,33168,33170],{"className":33169},[886],[888,33171,33172],{"xmlns":890},[892,33173,33174,33180],{},[895,33175,33176,33178],{},[898,33177,6362],{},[898,33179,1742],{},[902,33181,31166],{"encoding":904}," a klesající přímka ",[883,33184,33186],{"className":33185},[886],[888,33187,33188],{"xmlns":890},[892,33189,33190,33196],{},[895,33191,33192,33194],{},[898,33193,31291],{},[898,33195,14171],{},[902,33197,31159],{"encoding":904}," se protínají v bodě ",[883,33200,33202],{"className":33201},[886],[888,33203,33204],{"xmlns":890},[892,33205,33206,33210],{},[895,33207,33208],{},[898,33209,23410],{},[902,33211,23410],{"encoding":904}," se souřadnicemi ",[883,33214,33216],{"className":33215},[886],[888,33217,33218],{"xmlns":890},[892,33219,33220,33228],{},[895,33221,33222],{},[2489,33223,33224,33226],{},[898,33225,3950],{},[898,33227,23410],{},[902,33229,33031],{"encoding":904}," (na ose ",[883,33232,33234],{"className":33233},[886],[888,33235,33236],{"xmlns":890},[892,33237,33238,33242],{},[895,33239,33240],{},[898,33241,3950],{},[902,33243,3950],{"encoding":904},[883,33245,33247],{"className":33246},[886],[888,33248,33249],{"xmlns":890},[892,33250,33251,33259],{},[895,33252,33253],{},[2489,33254,33255,33257],{},[898,33256,28247],{},[898,33258,23410],{},[902,33260,33010],{"encoding":904},[883,33262,33264],{"className":33263},[886],[888,33265,33266],{"xmlns":890},[892,33267,33268,33272],{},[895,33269,33270],{},[898,33271,28247],{},[902,33273,28247],{"encoding":904},"); tečkované čáry z ",[883,33276,33278],{"className":33277},[886],[888,33279,33280],{"xmlns":890},[892,33281,33282,33286],{},[895,33283,33284],{},[898,33285,23410],{},[902,33287,23410],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[1636,33290,33291,33296],{},[724,33292,33293,33295],{},[883,33294,12314],{}," Postup — jak najít IS-LM rovnováhu",[152,33297,33298,33374,33442,33500,33573],{},[123,33299,33300,33303,33304,1993,33324,33344,33345,1993,33358,33371,33372,1837],{},[38,33301,33302],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,33305,33307],{"className":33306},[886],[888,33308,33309],{"xmlns":890},[892,33310,33311,33321],{},[895,33312,33313,33315,33317,33319],{},[898,33314,1683],{},[1706,33316,2140],{"stretchy":2139},[898,33318,28247],{},[1706,33320,2153],{"stretchy":2139},[902,33322,33323],{"encoding":904},"C(Y)",[883,33325,33327],{"className":33326},[886],[888,33328,33329],{"xmlns":890},[892,33330,33331,33341],{},[895,33332,33333,33335,33337,33339],{},[898,33334,31291],{},[1706,33336,2140],{"stretchy":2139},[898,33338,3950],{},[1706,33340,2153],{"stretchy":2139},[902,33342,33343],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,33346,33348],{"className":33347},[886],[888,33349,33350],{"xmlns":890},[892,33351,33352,33356],{},[895,33353,33354],{},[898,33355,28247],{},[902,33357,28247],{"encoding":904},[883,33359,33361],{"className":33360},[886],[888,33362,33363],{"xmlns":890},[892,33364,33365,33369],{},[895,33366,33367],{},[898,33368,3950],{},[902,33370,3950],{"encoding":904}," — dostaneš rovnici ",[38,33373,31159],{},[123,33375,33376,33379,33380,1993,33397,33414,33415,33371,33440,1837],{},[38,33377,33378],{},"Z trhu peněz (7.15)"," dosaď ",[883,33381,33383],{"className":33382},[886],[888,33384,33385],{"xmlns":890},[892,33386,33387,33395],{},[895,33388,33389],{},[2142,33390,33391,33393],{},[898,33392,6362],{},[2148,33394,2701],{},[902,33396,32319],{"encoding":904},[883,33398,33400],{"className":33399},[886],[888,33401,33402],{"xmlns":890},[892,33403,33404,33412],{},[895,33405,33406],{},[2142,33407,33408,33410],{},[898,33409,6362],{},[2148,33411,2495],{},[902,33413,32391],{"encoding":904}," a vztah ",[883,33416,33418],{"className":33417},[886],[888,33419,33420],{"xmlns":890},[892,33421,33422,33438],{},[895,33423,33424,33430,33432],{},[2489,33425,33426,33428],{},[898,33427,1742],{},[898,33429,2334],{},[1706,33431,1708],{},[2489,33433,33434,33436],{},[898,33435,1742],{},[1706,33437,3197],{},[902,33439,32587],{"encoding":904},[38,33441,31166],{},[123,33443,33444,33447,33448,1993,33461,33474,33475,33499],{},[38,33445,33446],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,33449,33451],{"className":33450},[886],[888,33452,33453],{"xmlns":890},[892,33454,33455,33459],{},[895,33456,33457],{},[898,33458,28247],{},[902,33460,28247],{"encoding":904},[883,33462,33464],{"className":33463},[886],[888,33465,33466],{"xmlns":890},[892,33467,33468,33472],{},[895,33469,33470],{},[898,33471,3950],{},[902,33473,3950],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,33476,33478],{"className":33477},[886],[888,33479,33480],{"xmlns":890},[892,33481,33482,33496],{},[895,33483,33484,33486,33488,33490,33492,33494],{},[898,33485,28247],{},[1706,33487,1708],{},[898,33489,21237],{},[1706,33491,2140],{"stretchy":2139},[898,33493,3950],{},[1706,33495,2153],{"stretchy":2139},[902,33497,33498],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,33501,33502,1647,33505,1993,33539,1837],{},[38,33503,33504],{},"Zpětně dopočítej",[883,33506,33508],{"className":33507},[886],[888,33509,33510],{"xmlns":890},[892,33511,33512,33536],{},[895,33513,33514,33520,33522,33524,33526,33532,33534],{},[2489,33515,33516,33518],{},[898,33517,1683],{},[898,33519,23410],{},[1706,33521,1708],{},[898,33523,207],{},[2415,33525,2799],{},[2489,33527,33528,33530],{},[898,33529,28247],{},[898,33531,23410],{},[1706,33533,2447],{},[898,33535,2450],{},[902,33537,33538],{"encoding":904},"C^E = a\\,Y^E + b",[883,33540,33542],{"className":33541},[886],[888,33543,33544],{"xmlns":890},[892,33545,33546,33570],{},[895,33547,33548,33554,33556,33558,33560,33566,33568],{},[2489,33549,33550,33552],{},[898,33551,31291],{},[898,33553,23410],{},[1706,33555,1708],{},[898,33557,20413],{},[2415,33559,2799],{},[2489,33561,33562,33564],{},[898,33563,3950],{},[898,33565,23410],{},[1706,33567,2447],{},[898,33569,3120],{},[902,33571,33572],{"encoding":904},"I^E = c\\,r^E + d",[123,33574,33575,33578,33579,33613,33614,33668],{},[38,33576,33577],{},"Ověř:"," musí platit ",[883,33580,33582],{"className":33581},[886],[888,33583,33584],{"xmlns":890},[892,33585,33586,33610],{},[895,33587,33588,33594,33596,33602,33604],{},[2489,33589,33590,33592],{},[898,33591,28247],{},[898,33593,23410],{},[1706,33595,1708],{},[2489,33597,33598,33600],{},[898,33599,1683],{},[898,33601,23410],{},[1706,33603,2447],{},[2489,33605,33606,33608],{},[898,33607,31291],{},[898,33609,23410],{},[902,33611,33612],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,33615,33617],{"className":33616},[886],[888,33618,33619],{"xmlns":890},[892,33620,33621,33665],{},[895,33622,33623,33629,33631,33637,33643,33645,33651,33657,33659],{},[2489,33624,33625,33627],{},[898,33626,1742],{},[1706,33628,3197],{},[1706,33630,1708],{},[2142,33632,33633,33635],{},[898,33634,32344],{},[2148,33636,2701],{},[2489,33638,33639,33641],{},[898,33640,28247],{},[898,33642,23410],{},[1706,33644,2447],{},[2142,33646,33647,33649],{},[898,33648,32344],{},[2148,33650,2495],{},[2489,33652,33653,33655],{},[898,33654,3950],{},[898,33656,23410],{},[1706,33658,2447],{},[2142,33660,33661,33663],{},[898,33662,32344],{},[2148,33664,4284],{},[902,33666,33667],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,33670,33672],{"id":33671},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,33674,33675],{},"Pro trh zboží jsou dány:",[120,33677,33678,33706],{},[123,33679,33680,33681,2505],{},"spotřeba ",[883,33682,33684],{"className":33683},[886],[888,33685,33686],{"xmlns":890},[892,33687,33688,33703],{},[895,33689,33690,33692,33694,33697,33699,33701],{},[898,33691,1683],{},[1706,33693,1708],{},[2148,33695,33696],{},"0,8",[898,33698,28247],{},[1706,33700,2447],{},[2148,33702,2590],{},[902,33704,33705],{"encoding":904},"C = 0{,}8Y + 100",[123,33707,33708,33709,1837],{},"investice ",[883,33710,33712],{"className":33711},[886],[888,33713,33714],{"xmlns":890},[892,33715,33716,33732],{},[895,33717,33718,33720,33722,33724,33726,33728,33730],{},[898,33719,31291],{},[1706,33721,1708],{},[1706,33723,1715],{},[2148,33725,3369],{},[898,33727,3950],{},[1706,33729,2447],{},[2148,33731,21978],{},[902,33733,33734],{"encoding":904},"I = -20r + 1000",[724,33736,33737],{},"Pro trh peněz:",[120,33739,33740,33766,33798],{},[123,33741,33742,2505],{},[883,33743,33745],{"className":33744},[886],[888,33746,33747],{"xmlns":890},[892,33748,33749,33763],{},[895,33750,33751,33757,33759,33761],{},[2142,33752,33753,33755],{},[898,33754,6362],{},[2148,33756,2701],{},[1706,33758,1708],{},[2148,33760,14840],{},[898,33762,28247],{},[902,33764,33765],{"encoding":904},"L_1 = 0{,}1Y",[123,33767,33768,2505],{},[883,33769,33771],{"className":33770},[886],[888,33772,33773],{"xmlns":890},[892,33774,33775,33795],{},[895,33776,33777,33783,33785,33787,33789,33791,33793],{},[2142,33778,33779,33781],{},[898,33780,6362],{},[2148,33782,2495],{},[1706,33784,1708],{},[1706,33786,1715],{},[2148,33788,2748],{},[898,33790,3950],{},[1706,33792,2447],{},[2148,33794,27726],{},[902,33796,33797],{"encoding":904},"L_2 = -25r + 2000",[123,33799,33800,33801,1837],{},"nabídka peněz ",[883,33802,33804],{"className":33803},[886],[888,33805,33806],{"xmlns":890},[892,33807,33808,33821],{},[895,33809,33810,33816,33818],{},[2489,33811,33812,33814],{},[898,33813,1742],{},[1706,33815,3197],{},[1706,33817,1708],{},[2148,33819,33820],{},"2375",[902,33822,33823],{"encoding":904},"M^* = 2375",[724,33825,33826,33829,33830,4288],{},[38,33827,33828],{},"Funkce IS"," — dosazením do (7.13) ",[883,33831,33833],{"className":33832},[886],[888,33834,33835],{"xmlns":890},[892,33836,33837,33849],{},[895,33838,33839,33841,33843,33845,33847],{},[898,33840,28247],{},[1706,33842,1708],{},[898,33844,1683],{},[1706,33846,2447],{},[898,33848,31291],{},[902,33850,33851],{"encoding":904},"Y = C + I",[724,33853,33854],{},[883,33855,33857],{"className":33856},[886],[888,33858,33859],{"xmlns":890},[892,33860,33861,33887],{},[895,33862,33863,33865,33867,33869,33871,33873,33875,33877,33879,33881,33883,33885],{},[898,33864,28247],{},[1706,33866,1708],{},[2148,33868,33696],{},[898,33870,28247],{},[1706,33872,2447],{},[2148,33874,2590],{},[1706,33876,1715],{},[2148,33878,3369],{},[898,33880,3950],{},[1706,33882,2447],{},[2148,33884,21978],{},[1706,33886,2505],{"separator":2504},[902,33888,33889],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,33891,33892],{},"tj.",[724,33894,33895],{},[883,33896,33898],{"className":33897},[886],[888,33899,33900],{"xmlns":890},[892,33901,33902,33927],{},[895,33903,33904,33906,33908,33910,33912,33914,33916,33919,33921,33923,33925],{},[2148,33905,15204],{},[898,33907,28247],{},[1706,33909,2447],{},[2148,33911,3369],{},[898,33913,3950],{},[1706,33915,1708],{},[2148,33917,33918],{},"1100.",[4898,33920],{"width":9524},[1706,33922,2140],{"stretchy":2139},[2415,33924,31159],{},[1706,33926,2153],{"stretchy":2139},[902,33928,33929],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,33931,33932,33935,33936,4288],{},[38,33933,33934],{},"Funkce LM"," — dosazením do (7.15) ",[883,33937,33939],{"className":33938},[886],[888,33940,33941],{"xmlns":890},[892,33942,33943,33967],{},[895,33944,33945,33951,33953,33959,33961],{},[2489,33946,33947,33949],{},[898,33948,1742],{},[1706,33950,3197],{},[1706,33952,1708],{},[2142,33954,33955,33957],{},[898,33956,6362],{},[2148,33958,2701],{},[1706,33960,2447],{},[2142,33962,33963,33965],{},[898,33964,6362],{},[2148,33966,2495],{},[902,33968,33969],{"encoding":904},"M^* = L_1 + L_2",[724,33971,33972],{},[883,33973,33975],{"className":33974},[886],[888,33976,33977],{"xmlns":890},[892,33978,33979,34001],{},[895,33980,33981,33983,33985,33987,33989,33991,33993,33995,33997,33999],{},[2148,33982,33820],{},[1706,33984,1708],{},[2148,33986,14840],{},[898,33988,28247],{},[1706,33990,1715],{},[2148,33992,2748],{},[898,33994,3950],{},[1706,33996,2447],{},[2148,33998,27726],{},[1706,34000,2505],{"separator":2504},[902,34002,34003],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,34005,33892],{},[724,34007,34008],{},[883,34009,34011],{"className":34010},[886],[888,34012,34013],{"xmlns":890},[892,34014,34015,34040],{},[895,34016,34017,34019,34021,34023,34025,34027,34029,34032,34034,34036,34038],{},[2148,34018,14840],{},[898,34020,28247],{},[1706,34022,1715],{},[2148,34024,2748],{},[898,34026,3950],{},[1706,34028,1708],{},[2148,34030,34031],{},"375.",[4898,34033],{"width":9524},[1706,34035,2140],{"stretchy":2139},[2415,34037,31166],{},[1706,34039,2153],{"stretchy":2139},[902,34041,34042],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,34044,34045,34048,34049,34074],{},[38,34046,34047],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,34050,34052],{"className":34051},[886],[888,34053,34054],{"xmlns":890},[892,34055,34056,34071],{},[895,34057,34058,34060,34062,34065,34067,34069],{},[898,34059,28247],{},[1706,34061,1708],{},[2148,34063,34064],{},"5500",[1706,34066,1715],{},[2148,34068,2590],{},[898,34070,3950],{},[902,34072,34073],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,34076,34077],{},[883,34078,34080],{"className":34079},[886],[888,34081,34082],{"xmlns":890},[892,34083,34084,34170],{},[895,34085,34086,34088,34090,34092,34094,34096,34098,34100,34102,34104,34106,34108,34111,34113,34116,34118,34121,34123,34125,34127,34129,34131,34133,34135,34137,34139,34141,34143,34146,34148,34150,34153,34155,34157,34159,34165,34167],{},[2148,34087,14840],{},[1706,34089,2140],{"stretchy":2139},[2148,34091,34064],{},[1706,34093,1715],{},[2148,34095,2590],{},[898,34097,3950],{},[1706,34099,2153],{"stretchy":2139},[1706,34101,1715],{},[2148,34103,2748],{},[898,34105,3950],{},[1706,34107,1708],{},[2148,34109,34110],{},"375",[2415,34112,3852],{},[1706,34114,34115],{},"⟹",[2415,34117,3852],{},[2148,34119,34120],{},"550",[1706,34122,1715],{},[2148,34124,7786],{},[898,34126,3950],{},[1706,34128,1715],{},[2148,34130,2748],{},[898,34132,3950],{},[1706,34134,1708],{},[2148,34136,34110],{},[2415,34138,3852],{},[1706,34140,34115],{},[2415,34142,3852],{},[2148,34144,34145],{},"35",[898,34147,3950],{},[1706,34149,1708],{},[2148,34151,34152],{},"175",[2415,34154,3852],{},[1706,34156,34115],{},[2415,34158,3852],{},[2489,34160,34161,34163],{},[898,34162,3950],{},[898,34164,23410],{},[1706,34166,1708],{},[2148,34168,34169],{},"5.",[902,34171,34172],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,34174,34175],{},[38,34176,34177],{},"Zpětné dosazení:",[120,34179,34180,34225,34262],{},[123,34181,34182,2505],{},[883,34183,34185],{"className":34184},[886],[888,34186,34187],{"xmlns":890},[892,34188,34189,34222],{},[895,34190,34191,34197,34199,34201,34203,34205,34207,34209,34211,34213,34215,34217,34219],{},[2489,34192,34193,34195],{},[898,34194,28247],{},[898,34196,23410],{},[1706,34198,1708],{},[2148,34200,34064],{},[1706,34202,1715],{},[2148,34204,2590],{},[1706,34206,2390],{},[2148,34208,7524],{},[1706,34210,1708],{},[2148,34212,34064],{},[1706,34214,1715],{},[2148,34216,17366],{},[1706,34218,1708],{},[2148,34220,34221],{},"5000",[902,34223,34224],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,34226,34227,2505],{},[883,34228,34230],{"className":34229},[886],[888,34231,34232],{"xmlns":890},[892,34233,34234,34259],{},[895,34235,34236,34242,34244,34246,34248,34250,34252,34254,34256],{},[2489,34237,34238,34240],{},[898,34239,1683],{},[898,34241,23410],{},[1706,34243,1708],{},[2148,34245,33696],{},[1706,34247,2390],{},[2148,34249,34221],{},[1706,34251,2447],{},[2148,34253,2590],{},[1706,34255,1708],{},[2148,34257,34258],{},"4100",[902,34260,34261],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,34263,34264,1837],{},[883,34265,34267],{"className":34266},[886],[888,34268,34269],{"xmlns":890},[892,34270,34271,34297],{},[895,34272,34273,34279,34281,34283,34285,34287,34289,34291,34293,34295],{},[2489,34274,34275,34277],{},[898,34276,31291],{},[898,34278,23410],{},[1706,34280,1708],{},[1706,34282,1715],{},[2148,34284,3369],{},[1706,34286,2390],{},[2148,34288,7524],{},[1706,34290,2447],{},[2148,34292,21978],{},[1706,34294,1708],{},[2148,34296,12956],{},[902,34298,34299],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,34301,34302,1647,34305,34351],{},[38,34303,34304],{},"Ověření:",[883,34306,34308],{"className":34307},[886],[888,34309,34310],{"xmlns":890},[892,34311,34312,34348],{},[895,34313,34314,34320,34322,34328,34330,34332,34334,34336,34338,34340,34342],{},[2489,34315,34316,34318],{},[898,34317,1683],{},[898,34319,23410],{},[1706,34321,2447],{},[2489,34323,34324,34326],{},[898,34325,31291],{},[898,34327,23410],{},[1706,34329,1708],{},[2148,34331,34258],{},[1706,34333,2447],{},[2148,34335,12956],{},[1706,34337,1708],{},[2148,34339,34221],{},[1706,34341,1708],{},[2489,34343,34344,34346],{},[898,34345,28247],{},[898,34347,23410],{},[902,34349,34350],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,34353,34354],{},[883,34355,34357],{"className":34356},[886],[888,34358,34359],{"xmlns":890},[892,34360,34361,34430],{},[895,34362,34363],{},[31939,34364,34365],{"notation":31941},[4745,34366,34367],{"scriptlevel":2150,"displaystyle":2139},[4745,34368,34369],{"scriptlevel":2150,"displaystyle":2139},[4745,34370,34371],{"scriptlevel":2150,"displaystyle":2504},[895,34372,34373,34375,34381,34383,34385,34387,34389,34395,34397,34399,34401,34403,34409,34411,34413,34415,34417,34423,34425,34428],{},[2415,34374,2799],{},[2489,34376,34377,34379],{},[898,34378,28247],{},[898,34380,23410],{},[1706,34382,1708],{},[2148,34384,34221],{},[1706,34386,2505],{"separator":2504},[4898,34388],{"width":4900},[2489,34390,34391,34393],{},[898,34392,3950],{},[898,34394,23410],{},[1706,34396,1708],{},[2148,34398,7524],{},[1706,34400,2505],{"separator":2504},[4898,34402],{"width":4900},[2489,34404,34405,34407],{},[898,34406,1683],{},[898,34408,23410],{},[1706,34410,1708],{},[2148,34412,34258],{},[1706,34414,2505],{"separator":2504},[4898,34416],{"width":4900},[2489,34418,34419,34421],{},[898,34420,31291],{},[898,34422,23410],{},[1706,34424,1708],{},[2148,34426,34427],{},"900.",[2415,34429,2799],{},[902,34431,34432],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,34434,34435],{},[614,34436,34437,34438,34451,34452,34465,34466,34481,34482,34495,34496,34511,34512,34525,34526,34539,34540,1837],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,34439,34441],{"className":34440},[886],[888,34442,34443],{"xmlns":890},[892,34444,34445,34449],{},[895,34446,34447],{},[898,34448,28247],{},[902,34450,28247],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,34453,34455],{"className":34454},[886],[888,34456,34457],{"xmlns":890},[892,34458,34459,34463],{},[895,34460,34461],{},[898,34462,3950],{},[902,34464,3950],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,34467,34469],{"className":34468},[886],[888,34470,34471],{"xmlns":890},[892,34472,34473,34479],{},[895,34474,34475,34477],{},[898,34476,6362],{},[898,34478,1742],{},[902,34480,31166],{"encoding":904}," stoupá z oblasti nízkých ",[883,34483,34485],{"className":34484},[886],[888,34486,34487],{"xmlns":890},[892,34488,34489,34493],{},[895,34490,34491],{},[898,34492,3950],{},[902,34494,3950],{"encoding":904},", přímka ",[883,34497,34499],{"className":34498},[886],[888,34500,34501],{"xmlns":890},[892,34502,34503,34509],{},[895,34504,34505,34507],{},[898,34506,31291],{},[898,34508,14171],{},[902,34510,31159],{"encoding":904}," klesá a protíná osu ",[883,34513,34515],{"className":34514},[886],[888,34516,34517],{"xmlns":890},[892,34518,34519,34523],{},[895,34520,34521],{},[898,34522,3950],{},[902,34524,3950],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,34527,34529],{"className":34528},[886],[888,34530,34531],{"xmlns":890},[892,34532,34533,34537],{},[895,34534,34535],{},[898,34536,23410],{},[902,34538,23410],{"encoding":904}," leží v bodě ",[883,34541,34543],{"className":34542},[886],[888,34544,34545],{"xmlns":890},[892,34546,34547,34569],{},[895,34548,34549,34551,34553,34555,34557,34559,34561,34563,34565,34567],{},[1706,34550,21693],{"stretchy":2139},[898,34552,3950],{},[1706,34554,1708],{},[2148,34556,7524],{},[1706,34558,2505],{"separator":2504},[2415,34560,21505],{},[898,34562,28247],{},[1706,34564,1708],{},[2148,34566,34221],{},[1706,34568,21708],{"stretchy":2139},[902,34570,34571],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,34573,34575],{"id":34574},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,34577,34578,34581,34582,34595,34596,21021,34609,34612,34613,34631,34632,34649,34650,34667,34668,34681,34682,34695],{},[38,34579,34580],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,34583,34585],{"className":34584},[886],[888,34586,34587],{"xmlns":890},[892,34588,34589,34593],{},[895,34590,34591],{},[898,34592,31220],{},[902,34594,31220],{"encoding":904}," nebo snížení daní ",[883,34597,34599],{"className":34598},[886],[888,34600,34601],{"xmlns":890},[892,34602,34603,34607],{},[895,34604,34605],{},[898,34606,1659],{},[902,34608,1659],{"encoding":904},[38,34610,34611],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,34614,34616],{"className":34615},[886],[888,34617,34618],{"xmlns":890},[892,34619,34620,34628],{},[895,34621,34622],{},[2489,34623,34624,34626],{},[898,34625,23410],{},[1706,34627,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,34629,34630],{"encoding":904},"E'"," má vyšší ",[883,34633,34635],{"className":34634},[886],[888,34636,34637],{"xmlns":890},[892,34638,34639,34647],{},[895,34640,34641],{},[2489,34642,34643,34645],{},[898,34644,28247],{},[898,34646,23410],{},[902,34648,33010],{"encoding":904}," i vyšší ",[883,34651,34653],{"className":34652},[886],[888,34654,34655],{"xmlns":890},[892,34656,34657,34665],{},[895,34658,34659],{},[2489,34660,34661,34663],{},[898,34662,3950],{},[898,34664,23410],{},[902,34666,33031],{"encoding":904}," (vyšší ",[883,34669,34671],{"className":34670},[886],[888,34672,34673],{"xmlns":890},[892,34674,34675,34679],{},[895,34676,34677],{},[898,34678,28247],{},[902,34680,28247],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,34683,34685],{"className":34684},[886],[888,34686,34687],{"xmlns":890},[892,34688,34689,34693],{},[895,34690,34691],{},[898,34692,3950],{},[902,34694,3950],{"encoding":904}," nahoru).",[724,34697,34698],{},[2286,34699],{"alt":34700,"className":34701,"src":34702},"imek-posun-is-lm-politiky",[210,2290],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,34704,34705,34708,34709,34726,34727,34730,34731,34748,34749,34766,34767,34780,34781,34800,34801,1936],{},[38,34706,34707],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,34710,34712],{"className":34711},[886],[888,34713,34714],{"xmlns":890},[892,34715,34716,34724],{},[895,34717,34718],{},[2489,34719,34720,34722],{},[898,34721,1742],{},[1706,34723,3197],{},[902,34725,31257],{"encoding":904}," národní bankou — ",[38,34728,34729],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,34732,34734],{"className":34733},[886],[888,34735,34736],{"xmlns":890},[892,34737,34738,34746],{},[895,34739,34740],{},[2489,34741,34742,34744],{},[898,34743,3950],{},[898,34745,23410],{},[902,34747,33031],{"encoding":904}," a vyšší ",[883,34750,34752],{"className":34751},[886],[888,34753,34754],{"xmlns":890},[892,34755,34756,34764],{},[895,34757,34758],{},[2489,34759,34760,34762],{},[898,34761,28247],{},[898,34763,23410],{},[902,34765,33010],{"encoding":904}," (nižší ",[883,34768,34770],{"className":34769},[886],[888,34771,34772],{"xmlns":890},[892,34773,34774,34778],{},[895,34775,34776],{},[898,34777,3950],{},[902,34779,3950],{"encoding":904}," povzbuzuje investice ",[883,34782,34784],{"className":34783},[886],[888,34785,34786],{"xmlns":890},[892,34787,34788,34798],{},[895,34789,34790,34792,34794,34796],{},[898,34791,31291],{},[1706,34793,2140],{"stretchy":2139},[898,34795,3950],{},[1706,34797,2153],{"stretchy":2139},[902,34799,33343],{"encoding":904},", ty zvedají ",[883,34802,34804],{"className":34803},[886],[888,34805,34806],{"xmlns":890},[892,34807,34808,34812],{},[895,34809,34810],{},[898,34811,28247],{},[902,34813,28247],{"encoding":904},[724,34815,34816,34817,34820],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,34818,34819],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,34822,19879],{"id":19878},[120,34824,34825,34897,34943,35025,35075,35142,35199,35240,35273],{},[123,34826,34827,21021,34860,1343,34877,7822,34894,34896],{},[38,34828,34829,34830],{},"Funkce investic ",[883,34831,34833],{"className":34832},[886],[888,34834,34835],{"xmlns":890},[892,34836,34837,34857],{},[895,34838,34839,34841,34843,34845,34847,34849,34851,34853,34855],{},[898,34840,31291],{},[1706,34842,2140],{"stretchy":2139},[898,34844,3950],{},[1706,34846,2153],{"stretchy":2139},[1706,34848,1708],{},[898,34850,20413],{},[898,34852,3950],{},[1706,34854,2447],{},[898,34856,3120],{},[902,34858,34859],{"encoding":904},"I(r) = cr + d",[883,34861,34863],{"className":34862},[886],[888,34864,34865],{"xmlns":890},[892,34866,34867,34875],{},[895,34868,34869,34871,34873],{},[898,34870,20413],{},[1706,34872,2539],{},[2148,34874,2150],{},[902,34876,31622],{"encoding":904},[883,34878,34880],{"className":34879},[886],[888,34881,34882],{"xmlns":890},[892,34883,34884,34892],{},[895,34885,34886,34888,34890],{},[898,34887,3120],{},[1706,34889,8922],{},[2148,34891,2150],{},[902,34893,31601],{"encoding":904},[38,34895,31626],{}," funkce úrokové míry.",[123,34898,34899,34902,34903,34924,34925,34942],{},[38,34900,34901],{},"Trh zboží"," — rovnováha ",[883,34904,34906],{"className":34905},[886],[888,34907,34908],{"xmlns":890},[892,34909,34910,34922],{},[895,34911,34912,34914,34916,34918,34920],{},[898,34913,28247],{},[1706,34915,1708],{},[898,34917,1683],{},[1706,34919,2447],{},[898,34921,31291],{},[902,34923,33851],{"encoding":904},", ekvivalentně ",[883,34926,34928],{"className":34927},[886],[888,34929,34930],{"xmlns":890},[892,34931,34932,34940],{},[895,34933,34934,34936,34938],{},[898,34935,31291],{},[1706,34937,1708],{},[898,34939,14171],{},[902,34941,31819],{"encoding":904}," (investice = úspory).",[123,34944,34945,2314,34948,34950,34951,35001,35002,32022,35004,1837],{},[38,34946,34947],{},"Křivka IS",[614,34949,31162],{},") — ",[883,34952,34954],{"className":34953},[886],[888,34955,34956],{"xmlns":890},[892,34957,34958,34998],{},[895,34959,34960,34962,34964,34976,34978,34980],{},[898,34961,28247],{},[1706,34963,1708],{},[2964,34965,34966,34968],{},[898,34967,20413],{},[895,34969,34970,34972,34974],{},[2148,34971,2701],{},[1706,34973,1715],{},[898,34975,207],{},[898,34977,3950],{},[1706,34979,2447],{},[2964,34981,34982,34990],{},[895,34983,34984,34986,34988],{},[898,34985,2450],{},[1706,34987,2447],{},[898,34989,3120],{},[895,34991,34992,34994,34996],{},[2148,34993,2701],{},[1706,34995,1715],{},[898,34997,207],{},[902,34999,35000],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,35003,31626],{},[883,35005,35007],{"className":35006},[886],[888,35008,35009],{"xmlns":890},[892,35010,35011,35023],{},[895,35012,35013,35015,35017,35019,35021],{},[1706,35014,2140],{"stretchy":2139},[898,35016,3950],{},[1706,35018,2505],{"separator":2504},[898,35020,28247],{},[1706,35022,2153],{"stretchy":2139},[902,35024,32044],{"encoding":904},[123,35026,35027,34902,35030,35056,35057,1837],{},[38,35028,35029],{},"Trh peněz",[883,35031,35033],{"className":35032},[886],[888,35034,35035],{"xmlns":890},[892,35036,35037,35053],{},[895,35038,35039,35045,35047],{},[2489,35040,35041,35043],{},[898,35042,1742],{},[898,35044,2334],{},[1706,35046,1708],{},[2489,35048,35049,35051],{},[898,35050,1742],{},[898,35052,14171],{},[902,35054,35055],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,35058,35060],{"className":35059},[886],[888,35061,35062],{"xmlns":890},[892,35063,35064,35072],{},[895,35065,35066],{},[2489,35067,35068,35070],{},[898,35069,1742],{},[1706,35071,3197],{},[902,35073,35074],{"encoding":904},"M^* ",[123,35076,35077,21021,35080,1837],{},[38,35078,35079],{},"Transakční, opatrnostní, spekulační poptávka",[883,35081,35083],{"className":35082},[886],[888,35084,35085],{"xmlns":890},[892,35086,35087,35139],{},[895,35088,35089,35095,35097,35103,35105,35111,35113,35119,35121,35123,35129,35131,35133],{},[2489,35090,35091,35093],{},[898,35092,1742],{},[898,35094,2334],{},[1706,35096,1708],{},[2142,35098,35099,35101],{},[898,35100,6362],{},[2148,35102,2701],{},[1706,35104,2447],{},[2142,35106,35107,35109],{},[898,35108,6362],{},[2148,35110,2495],{},[1706,35112,1708],{},[2142,35114,35115,35117],{},[898,35116,32344],{},[2148,35118,2701],{},[898,35120,28247],{},[1706,35122,2447],{},[2142,35124,35125,35127],{},[898,35126,32344],{},[2148,35128,2495],{},[898,35130,3950],{},[1706,35132,2447],{},[2142,35134,35135,35137],{},[898,35136,32344],{},[2148,35138,4284],{},[902,35140,35141],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,35143,35144,2314,35147,34950,35149,35195,35196,35198],{},[38,35145,35146],{},"Křivka LM",[614,35148,31169],{},[883,35150,35152],{"className":35151},[886],[888,35153,35154],{"xmlns":890},[892,35155,35156,35192],{},[895,35157,35158,35164,35166,35172,35174,35176,35182,35184,35186],{},[2489,35159,35160,35162],{},[898,35161,1742],{},[1706,35163,3197],{},[1706,35165,1708],{},[2142,35167,35168,35170],{},[898,35169,32344],{},[2148,35171,2701],{},[898,35173,28247],{},[1706,35175,2447],{},[2142,35177,35178,35180],{},[898,35179,32344],{},[2148,35181,2495],{},[898,35183,3950],{},[1706,35185,2447],{},[2142,35187,35188,35190],{},[898,35189,32344],{},[2148,35191,4284],{},[902,35193,35194],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,35197,32764],{}," přímka.",[123,35200,35201,35204,35205,35239],{},[38,35202,35203],{},"Simultánní rovnováha"," — průsečík ",[883,35206,35208],{"className":35207},[886],[888,35209,35210],{"xmlns":890},[892,35211,35212,35236],{},[895,35213,35214,35216,35218,35220,35226,35228,35234],{},[898,35215,23410],{},[1706,35217,1708],{},[1706,35219,2140],{"stretchy":2139},[2489,35221,35222,35224],{},[898,35223,3950],{},[898,35225,23410],{},[1706,35227,2505],{"separator":2504},[2489,35229,35230,35232],{},[898,35231,28247],{},[898,35233,23410],{},[1706,35235,2153],{"stretchy":2139},[902,35237,35238],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,35241,35242,35245,35246,1343,35259,35272],{},[38,35243,35244],{},"Fiskální politika"," — nástroje ",[883,35247,35249],{"className":35248},[886],[888,35250,35251],{"xmlns":890},[892,35252,35253,35257],{},[895,35254,35255],{},[898,35256,31220],{},[902,35258,31220],{"encoding":904},[883,35260,35262],{"className":35261},[886],[888,35263,35264],{"xmlns":890},[892,35265,35266,35270],{},[895,35267,35268],{},[898,35269,1659],{},[902,35271,1659],{"encoding":904}," posouvající křivku IS.",[123,35274,35275,35278,35279,35296],{},[38,35276,35277],{},"Monetární politika"," — nástroj ",[883,35280,35282],{"className":35281},[886],[888,35283,35284],{"xmlns":890},[892,35285,35286,35294],{},[895,35287,35288],{},[2489,35289,35290,35292],{},[898,35291,1742],{},[1706,35293,3197],{},[902,35295,31257],{"encoding":904}," posouvající křivku LM.",[115,35298,21083],{"id":21082},[120,35300,35301,35308,35317,35327],{},[123,35302,35303,1647,35305],{},[38,35304,21126],{},[207,35306,21132],{"className":35307,"dataFsResolvedFilePath":21130,"href":21131},[210],[123,35309,35310,1647,35313],{},[38,35311,35312],{},"Přednáška:",[207,35314,35316],{"className":35315,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,35318,35319,1647,35322,35326],{},[38,35320,35321],{},"Nadřazené téma:",[207,35323,35325],{"className":35324,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,35328,35329,35332],{},[38,35330,35331],{},"Související:",[120,35333,35334,35341,35347],{},[123,35335,35336,35340],{},[207,35337,35339],{"className":35338,"dataFsResolvedFilePath":800,"href":801},[210],"poptavka-nabidka"," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,35342,35343,35346],{},[207,35344,1145],{"className":35345,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,35348,35349,35353],{},[207,35350,35352],{"className":35351,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":35355},[35356,35357,35358,35359,35360,35361,35362,35363,35364,35365],{"id":31114,"depth":642,"text":31115},{"id":31267,"depth":642,"text":31268},{"id":31482,"depth":642,"text":31483},{"id":31775,"depth":642,"text":31776},{"id":32188,"depth":642,"text":32189},{"id":32981,"depth":642,"text":32982},{"id":33671,"depth":642,"text":33672},{"id":34574,"depth":642,"text":34575},{"id":19878,"depth":642,"text":19879},{"id":21082,"depth":642,"text":21083},{},"\u002Ftopics\u002Fis-lm",{"title":31106,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,35372,1143,35373,35374,35375,35376,35325],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":35379,"title":35380,"body":35381,"course":659,"courses":36971,"created":1129,"description":36972,"extension":661,"meta":36973,"navigation":664,"path":36974,"seo":36975,"sources":36976,"stem":36977,"tags":36978,"type":21181,"updated":677,"__hash__":36981},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":35382,"toc":36959},[35383,35386,35482,35489,35509,35511,35516,35579,35598,35600,35603,35739,35741,35951,35985,36122,36126,36190,36206,36234,36238,36336,36340,36344,36397,36503,36716,36720,36763,36869,36921,36923],[12,35384,35380],{"id":35385},"lagrangeova-metoda-vázané-extrémy",[724,35387,35388,35389,23078,35412,35444,35445,35448,35449,35476,35477,35481],{},"Hledáme extrém funkce ",[883,35390,35392],{"className":35391},[886],[888,35393,35394],{"xmlns":890},[892,35395,35396,35410],{},[895,35397,35398,35400,35402,35404,35406,35408],{},[898,35399,21237],{},[1706,35401,2140],{"stretchy":2139},[898,35403,18300],{},[1706,35405,2505],{"separator":2504},[898,35407,6930],{},[1706,35409,2153],{"stretchy":2139},[902,35411,28958],{"encoding":904},[883,35413,35415],{"className":35414},[886],[888,35416,35417],{"xmlns":890},[892,35418,35419,35441],{},[895,35420,35421,35423,35425,35431,35433,35439],{},[898,35422,900],{},[1706,35424,2140],{"stretchy":2139},[2142,35426,35427,35429],{},[898,35428,2146],{},[2148,35430,2701],{},[1706,35432,2505],{"separator":2504},[2142,35434,35435,35437],{},[898,35436,2146],{},[2148,35438,2495],{},[1706,35440,2153],{"stretchy":2139},[902,35442,35443],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,35446,35447],{},"podmíněný"," rovnicí ",[883,35450,35452],{"className":35451},[886],[888,35453,35454],{"xmlns":890},[892,35455,35456,35474],{},[895,35457,35458,35460,35462,35464,35466,35468,35470,35472],{},[898,35459,30152],{},[1706,35461,2140],{"stretchy":2139},[898,35463,18300],{},[1706,35465,2505],{"separator":2504},[898,35467,6930],{},[1706,35469,2153],{"stretchy":2139},[1706,35471,1708],{},[2148,35473,2150],{},[902,35475,30169],{"encoding":904},". V ",[207,35478,35480],{"className":35479,"dataFsResolvedFilePath":21130,"href":21131},[210],"matematické ekonomii"," se používá pro:",[724,35483,35484],{},[2286,35485],{"alt":35486,"className":35487,"src":35488},"imek-lagrange-tecnost",[210,2290],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,35490,35491,35500,35506],{},[123,35492,35493,35496,35497,2153],{},[38,35494,35495],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,35498,28889],{"className":35499,"dataFsResolvedFilePath":878,"href":879},[210],[123,35501,35502,35505],{},[38,35503,35504],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,35507,35508],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,35510,8604],{"id":8603},[724,35512,29818,35513,4288],{},[38,35514,35515],{},"Lagrangeovu funkci",[724,35517,35518],{},[883,35519,35521],{"className":35520},[886],[888,35522,35523],{"xmlns":890},[892,35524,35525,35576],{},[895,35526,35527,35529,35531,35533,35535,35537,35539,35542,35544,35546,35548,35550,35552,35554,35556,35558,35560,35562,35564,35566,35568,35570,35572,35574],{},[898,35528,6362],{},[1706,35530,2140],{"stretchy":2139},[898,35532,18300],{},[1706,35534,2505],{"separator":2504},[898,35536,6930],{},[1706,35538,2505],{"separator":2504},[898,35540,35541],{},"λ",[1706,35543,2153],{"stretchy":2139},[1706,35545,1708],{},[898,35547,21237],{},[1706,35549,2140],{"stretchy":2139},[898,35551,18300],{},[1706,35553,2505],{"separator":2504},[898,35555,6930],{},[1706,35557,2153],{"stretchy":2139},[1706,35559,2447],{},[898,35561,35541],{},[2415,35563,2799],{},[898,35565,30152],{},[1706,35567,2140],{"stretchy":2139},[898,35569,18300],{},[1706,35571,2505],{"separator":2504},[898,35573,6930],{},[1706,35575,2153],{"stretchy":2139},[902,35577,35578],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,35580,5331,35581,3484,35595,1837],{},[883,35582,35584],{"className":35583},[886],[888,35585,35586],{"xmlns":890},[892,35587,35588,35592],{},[895,35589,35590],{},[898,35591,35541],{},[902,35593,35594],{"encoding":904},"\\lambda",[38,35596,35597],{},"Lagrangeův multiplikátor",[115,35599,22432],{"id":22431},[724,35601,35602],{},"Řešíme soustavu:",[724,35604,35605,35653,35701],{},[883,35606,35608],{"className":35607},[886],[888,35609,35610],{"xmlns":890},[892,35611,35612,35650],{},[895,35613,35614,35622,35624,35632,35634,35636,35638,35646,35648],{},[28285,35615,35616,35618,35620],{},[898,35617,6362],{},[898,35619,18300],{},[1706,35621,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,35623,1708],{},[28285,35625,35626,35628,35630],{},[898,35627,21237],{},[898,35629,18300],{},[1706,35631,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,35633,2447],{},[898,35635,35541],{},[2415,35637,2799],{},[28285,35639,35640,35642,35644],{},[898,35641,30152],{},[898,35643,18300],{},[1706,35645,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,35647,1708],{},[2148,35649,2150],{},[902,35651,35652],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,35654,35656],{"className":35655},[886],[888,35657,35658],{"xmlns":890},[892,35659,35660,35698],{},[895,35661,35662,35670,35672,35680,35682,35684,35686,35694,35696],{},[28285,35663,35664,35666,35668],{},[898,35665,6362],{},[898,35667,6930],{},[1706,35669,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,35671,1708],{},[28285,35673,35674,35676,35678],{},[898,35675,21237],{},[898,35677,6930],{},[1706,35679,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,35681,2447],{},[898,35683,35541],{},[2415,35685,2799],{},[28285,35687,35688,35690,35692],{},[898,35689,30152],{},[898,35691,6930],{},[1706,35693,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,35695,1708],{},[2148,35697,2150],{},[902,35699,35700],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,35702,35704],{"className":35703},[886],[888,35705,35706],{"xmlns":890},[892,35707,35708,35736],{},[895,35709,35710,35718,35720,35722,35724,35726,35728,35730,35732,35734],{},[28285,35711,35712,35714,35716],{},[898,35713,6362],{},[898,35715,35541],{},[1706,35717,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,35719,1708],{},[898,35721,30152],{},[1706,35723,2140],{"stretchy":2139},[898,35725,18300],{},[1706,35727,2505],{"separator":2504},[898,35729,6930],{},[1706,35731,2153],{"stretchy":2139},[1706,35733,1708],{},[2148,35735,2150],{},[902,35737,35738],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,35740,22506],{"id":22505},[724,35742,35743],{},[883,35744,35746],{"className":35745},[886],[888,35747,35748],{"xmlns":890},[892,35749,35750,35948],{},[895,35751,35752,35754,35756,35758,35760,35762,35764,35766,35768,35770,35772,35788,35790,35792,35808,35810,35812,35820,35826,35828,35830,35846,35848,35850,35866,35868,35870,35878,35884,35886,35888,35890,35906,35908,35910,35926,35928,35930,35938,35940],{},[898,35753,2334],{},[1706,35755,2140],{"stretchy":2139},[898,35757,18300],{},[1706,35759,2505],{"separator":2504},[898,35761,6930],{},[1706,35763,2505],{"separator":2504},[898,35765,35541],{},[1706,35767,2153],{"stretchy":2139},[1706,35769,1708],{},[1706,35771,2140],{"stretchy":2139},[28285,35773,35774,35776,35782],{},[898,35775,21237],{},[895,35777,35778,35780],{},[898,35779,18300],{},[898,35781,18300],{},[895,35783,35784,35786],{},[1706,35785,3142],{"mathvariant":2409},[1706,35787,3142],{"mathvariant":2409},[1706,35789,2447],{},[898,35791,35541],{},[28285,35793,35794,35796,35802],{},[898,35795,30152],{},[895,35797,35798,35800],{},[898,35799,18300],{},[898,35801,18300],{},[895,35803,35804,35806],{},[1706,35805,3142],{"mathvariant":2409},[1706,35807,3142],{"mathvariant":2409},[1706,35809,2153],{"stretchy":2139},[1706,35811,2140],{"stretchy":2139},[28285,35813,35814,35816,35818],{},[898,35815,30152],{},[898,35817,6930],{},[1706,35819,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2489,35821,35822,35824],{},[1706,35823,2153],{"stretchy":2139},[2148,35825,2495],{},[1706,35827,2447],{},[1706,35829,2140],{"stretchy":2139},[28285,35831,35832,35834,35840],{},[898,35833,21237],{},[895,35835,35836,35838],{},[898,35837,6930],{},[898,35839,6930],{},[895,35841,35842,35844],{},[1706,35843,3142],{"mathvariant":2409},[1706,35845,3142],{"mathvariant":2409},[1706,35847,2447],{},[898,35849,35541],{},[28285,35851,35852,35854,35860],{},[898,35853,30152],{},[895,35855,35856,35858],{},[898,35857,6930],{},[898,35859,6930],{},[895,35861,35862,35864],{},[1706,35863,3142],{"mathvariant":2409},[1706,35865,3142],{"mathvariant":2409},[1706,35867,2153],{"stretchy":2139},[1706,35869,2140],{"stretchy":2139},[28285,35871,35872,35874,35876],{},[898,35873,30152],{},[898,35875,18300],{},[1706,35877,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2489,35879,35880,35882],{},[1706,35881,2153],{"stretchy":2139},[2148,35883,2495],{},[1706,35885,1715],{},[2148,35887,2495],{},[1706,35889,2140],{"stretchy":2139},[28285,35891,35892,35894,35900],{},[898,35893,21237],{},[895,35895,35896,35898],{},[898,35897,18300],{},[898,35899,6930],{},[895,35901,35902,35904],{},[1706,35903,3142],{"mathvariant":2409},[1706,35905,3142],{"mathvariant":2409},[1706,35907,2447],{},[898,35909,35541],{},[28285,35911,35912,35914,35920],{},[898,35913,30152],{},[895,35915,35916,35918],{},[898,35917,18300],{},[898,35919,6930],{},[895,35921,35922,35924],{},[1706,35923,3142],{"mathvariant":2409},[1706,35925,3142],{"mathvariant":2409},[1706,35927,2153],{"stretchy":2139},[2415,35929,2799],{},[28285,35931,35932,35934,35936],{},[898,35933,30152],{},[898,35935,18300],{},[1706,35937,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2415,35939,2799],{},[28285,35941,35942,35944,35946],{},[898,35943,30152],{},[898,35945,6930],{},[1706,35947,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,35949,35950],{"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",[724,35952,35953,35954,35984],{},"Je-li ",[883,35955,35957],{"className":35956},[886],[888,35958,35959],{"xmlns":890},[892,35960,35961,35981],{},[895,35962,35963,35965,35967,35969,35971,35973,35979],{},[1706,35964,21693],{"stretchy":2139},[898,35966,207],{},[1706,35968,2505],{"separator":2504},[898,35970,2450],{},[1706,35972,2505],{"separator":2504},[2142,35974,35975,35977],{},[898,35976,35541],{},[2148,35978,2150],{},[1706,35980,21708],{"stretchy":2139},[902,35982,35983],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,35986,35987,36055],{},[123,35988,35989,22593,36025,36027,36028],{},[883,35990,35992],{"className":35991},[886],[888,35993,35994],{"xmlns":890},[892,35995,35996,36022],{},[895,35997,35998,36000,36002,36004,36006,36008,36010,36016,36018,36020],{},[898,35999,2334],{},[1706,36001,2140],{"stretchy":2139},[898,36003,207],{},[1706,36005,2505],{"separator":2504},[898,36007,2450],{},[1706,36009,2505],{"separator":2504},[2142,36011,36012,36014],{},[898,36013,35541],{},[2148,36015,2150],{},[1706,36017,2153],{"stretchy":2139},[1706,36019,2539],{},[2148,36021,2150],{},[902,36023,36024],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,36026,13844],{}," vázané podmínkou ",[883,36029,36031],{"className":36030},[886],[888,36032,36033],{"xmlns":890},[892,36034,36035,36053],{},[895,36036,36037,36039,36041,36043,36045,36047,36049,36051],{},[898,36038,30152],{},[1706,36040,2140],{"stretchy":2139},[898,36042,18300],{},[1706,36044,2505],{"separator":2504},[898,36046,6930],{},[1706,36048,2153],{"stretchy":2139},[1706,36050,1708],{},[2148,36052,2150],{},[902,36054,30169],{"encoding":904},[123,36056,36057,22593,36093,36027,36095],{},[883,36058,36060],{"className":36059},[886],[888,36061,36062],{"xmlns":890},[892,36063,36064,36090],{},[895,36065,36066,36068,36070,36072,36074,36076,36078,36084,36086,36088],{},[898,36067,2334],{},[1706,36069,2140],{"stretchy":2139},[898,36071,207],{},[1706,36073,2505],{"separator":2504},[898,36075,2450],{},[1706,36077,2505],{"separator":2504},[2142,36079,36080,36082],{},[898,36081,35541],{},[2148,36083,2150],{},[1706,36085,2153],{"stretchy":2139},[1706,36087,8922],{},[2148,36089,2150],{},[902,36091,36092],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,36094,13792],{},[883,36096,36098],{"className":36097},[886],[888,36099,36100],{"xmlns":890},[892,36101,36102,36120],{},[895,36103,36104,36106,36108,36110,36112,36114,36116,36118],{},[898,36105,30152],{},[1706,36107,2140],{"stretchy":2139},[898,36109,18300],{},[1706,36111,2505],{"separator":2504},[898,36113,6930],{},[1706,36115,2153],{"stretchy":2139},[1706,36117,1708],{},[2148,36119,2150],{},[902,36121,30169],{"encoding":904},[115,36123,36125],{"id":36124},"význam-multiplikátoru","Význam multiplikátoru",[724,36127,36128],{},[883,36129,36131],{"className":36130},[886],[888,36132,36133],{"xmlns":890},[892,36134,36135,36187],{},[895,36136,36137,36139,36141,36163,36165],{},[898,36138,35541],{},[1706,36140,1708],{},[2964,36142,36143,36151],{},[28285,36144,36145,36147,36149],{},[898,36146,21237],{},[898,36148,18300],{},[1706,36150,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[895,36152,36153,36155],{},[1706,36154,1715],{},[28285,36156,36157,36159,36161],{},[898,36158,30152],{},[898,36160,18300],{},[1706,36162,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,36164,1708],{},[2964,36166,36167,36175],{},[28285,36168,36169,36171,36173],{},[898,36170,21237],{},[898,36172,6930],{},[1706,36174,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[895,36176,36177,36179],{},[1706,36178,1715],{},[28285,36180,36181,36183,36185],{},[898,36182,30152],{},[898,36184,6930],{},[1706,36186,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,36188,36189],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,36191,36192,36205],{},[883,36193,36195],{"className":36194},[886],[888,36196,36197],{"xmlns":890},[892,36198,36199,36203],{},[895,36200,36201],{},[898,36202,35541],{},[902,36204,35594],{"encoding":904}," udává:",[120,36207,36208,36214],{},[123,36209,36210,36211],{},"konstantní ",[38,36212,36213],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,36215,36216,36219,36220,36233],{},[38,36217,36218],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,36221,36223],{"className":36222},[886],[888,36224,36225],{"xmlns":890},[892,36226,36227,36231],{},[895,36228,36229],{},[898,36230,21237],{},[902,36232,21237],{"encoding":904},", uvolní-li se omezení o jednotku",[115,36235,36237],{"id":36236},"alternativní-postup","Alternativní postup",[724,36239,36240,36241,36268,36269,36293,36294,36318,36319,36332,36333,1837],{},"Lze-li z ",[883,36242,36244],{"className":36243},[886],[888,36245,36246],{"xmlns":890},[892,36247,36248,36266],{},[895,36249,36250,36252,36254,36256,36258,36260,36262,36264],{},[898,36251,30152],{},[1706,36253,2140],{"stretchy":2139},[898,36255,18300],{},[1706,36257,2505],{"separator":2504},[898,36259,6930],{},[1706,36261,2153],{"stretchy":2139},[1706,36263,1708],{},[2148,36265,2150],{},[902,36267,30169],{"encoding":904}," vyjádřit ",[883,36270,36272],{"className":36271},[886],[888,36273,36274],{"xmlns":890},[892,36275,36276,36290],{},[895,36277,36278,36280,36282,36284,36286,36288],{},[898,36279,6930],{},[1706,36281,1708],{},[898,36283,6930],{},[1706,36285,2140],{"stretchy":2139},[898,36287,18300],{},[1706,36289,2153],{"stretchy":2139},[902,36291,36292],{"encoding":904},"y = y(x)"," (nebo ",[883,36295,36297],{"className":36296},[886],[888,36298,36299],{"xmlns":890},[892,36300,36301,36315],{},[895,36302,36303,36305,36307,36309,36311,36313],{},[898,36304,18300],{},[1706,36306,1708],{},[898,36308,18300],{},[1706,36310,2140],{"stretchy":2139},[898,36312,6930],{},[1706,36314,2153],{"stretchy":2139},[902,36316,36317],{"encoding":904},"x = x(y)","), dosadíme do ",[883,36320,36322],{"className":36321},[886],[888,36323,36324],{"xmlns":890},[892,36325,36326,36330],{},[895,36327,36328],{},[898,36329,21237],{},[902,36331,21237],{"encoding":904}," a převedeme na ",[38,36334,36335],{},"extrém funkce jedné proměnné",[115,36337,36339],{"id":36338},"použití-v-imek","Použití v ImeK",[198,36341,36343],{"id":36342},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,36345,36346,36347,1837],{},"Rozpočtové omezení: ",[883,36348,36350],{"className":36349},[886],[888,36351,36352],{"xmlns":890},[892,36353,36354,36394],{},[895,36355,36356,36362,36364,36372,36378,36380,36388],{},[2489,36357,36358,36360],{},[898,36359,28247],{},[1706,36361,3197],{},[1706,36363,1708],{},[28285,36365,36366,36368,36370],{},[898,36367,1702],{},[2148,36369,2701],{},[1706,36371,3197],{},[2142,36373,36374,36376],{},[898,36375,2146],{},[2148,36377,2701],{},[1706,36379,2447],{},[28285,36381,36382,36384,36386],{},[898,36383,1702],{},[2148,36385,2495],{},[1706,36387,3197],{},[2142,36389,36390,36392],{},[898,36391,2146],{},[2148,36393,2495],{},[902,36395,36396],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,36398,36399],{},[883,36400,36402],{"className":36401},[886],[888,36403,36404],{"xmlns":890},[892,36405,36406,36500],{},[895,36407,36408,36410,36412,36418,36420,36426,36428,36430,36432,36434,36436,36438,36444,36446,36452,36454,36456,36458,36460,36466,36468,36476,36482,36484,36492,36498],{},[898,36409,6362],{},[1706,36411,2140],{"stretchy":2139},[2142,36413,36414,36416],{},[898,36415,2146],{},[2148,36417,2701],{},[1706,36419,2505],{"separator":2504},[2142,36421,36422,36424],{},[898,36423,2146],{},[2148,36425,2495],{},[1706,36427,2505],{"separator":2504},[898,36429,35541],{},[1706,36431,2153],{"stretchy":2139},[1706,36433,1708],{},[898,36435,900],{},[1706,36437,2140],{"stretchy":2139},[2142,36439,36440,36442],{},[898,36441,2146],{},[2148,36443,2701],{},[1706,36445,2505],{"separator":2504},[2142,36447,36448,36450],{},[898,36449,2146],{},[2148,36451,2495],{},[1706,36453,2153],{"stretchy":2139},[1706,36455,2447],{},[898,36457,35541],{},[1706,36459,2140],{"stretchy":2139},[2489,36461,36462,36464],{},[898,36463,28247],{},[1706,36465,3197],{},[1706,36467,1715],{},[28285,36469,36470,36472,36474],{},[898,36471,1702],{},[2148,36473,2701],{},[1706,36475,3197],{},[2142,36477,36478,36480],{},[898,36479,2146],{},[2148,36481,2701],{},[1706,36483,1715],{},[28285,36485,36486,36488,36490],{},[898,36487,1702],{},[2148,36489,2495],{},[1706,36491,3197],{},[2142,36493,36494,36496],{},[898,36495,2146],{},[2148,36497,2495],{},[1706,36499,2153],{"stretchy":2139},[902,36501,36502],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,36504,36505,36506,1343,36538,1343,36570,36619,36620,11019,36674,1837],{},"Soustava: ",[883,36507,36509],{"className":36508},[886],[888,36510,36511],{"xmlns":890},[892,36512,36513,36535],{},[895,36514,36515,36523,36525,36527],{},[28285,36516,36517,36519,36521],{},[898,36518,900],{},[2148,36520,2701],{},[1706,36522,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,36524,1708],{},[898,36526,35541],{},[28285,36528,36529,36531,36533],{},[898,36530,1702],{},[2148,36532,2701],{},[1706,36534,3197],{},[902,36536,36537],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,36539,36541],{"className":36540},[886],[888,36542,36543],{"xmlns":890},[892,36544,36545,36567],{},[895,36546,36547,36555,36557,36559],{},[28285,36548,36549,36551,36553],{},[898,36550,900],{},[2148,36552,2495],{},[1706,36554,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,36556,1708],{},[898,36558,35541],{},[28285,36560,36561,36563,36565],{},[898,36562,1702],{},[2148,36564,2495],{},[1706,36566,3197],{},[902,36568,36569],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,36571,36573],{"className":36572},[886],[888,36574,36575],{"xmlns":890},[892,36576,36577,36617],{},[895,36578,36579,36585,36587,36595,36601,36603,36611],{},[2489,36580,36581,36583],{},[898,36582,28247],{},[1706,36584,3197],{},[1706,36586,1708],{},[28285,36588,36589,36591,36593],{},[898,36590,1702],{},[2148,36592,2701],{},[1706,36594,3197],{},[2142,36596,36597,36599],{},[898,36598,2146],{},[2148,36600,2701],{},[1706,36602,2447],{},[28285,36604,36605,36607,36609],{},[898,36606,1702],{},[2148,36608,2495],{},[1706,36610,3197],{},[2142,36612,36613,36615],{},[898,36614,2146],{},[2148,36616,2495],{},[902,36618,36396],{"encoding":904},". Z prvních dvou: ",[883,36621,36623],{"className":36622},[886],[888,36624,36625],{"xmlns":890},[892,36626,36627,36671],{},[895,36628,36629,36649,36651],{},[4745,36630,36631],{"scriptlevel":2150,"displaystyle":2139},[2964,36632,36633,36641],{},[28285,36634,36635,36637,36639],{},[898,36636,900],{},[2148,36638,2701],{},[1706,36640,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[28285,36642,36643,36645,36647],{},[898,36644,900],{},[2148,36646,2495],{},[1706,36648,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,36650,1708],{},[4745,36652,36653],{"scriptlevel":2150,"displaystyle":2139},[2964,36654,36655,36663],{},[28285,36656,36657,36659,36661],{},[898,36658,1702],{},[2148,36660,2701],{},[1706,36662,3197],{},[28285,36664,36665,36667,36669],{},[898,36666,1702],{},[2148,36668,2495],{},[1706,36670,3197],{},[902,36672,36673],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",[883,36675,36677],{"className":36676},[886],[888,36678,36679],{"xmlns":890},[892,36680,36681,36713],{},[895,36682,36683,36685,36687,36689,36691,36693],{},[898,36684,1742],{},[898,36686,1662],{},[898,36688,1683],{},[898,36690,14171],{},[1706,36692,1708],{},[4745,36694,36695],{"scriptlevel":2150,"displaystyle":2139},[2964,36696,36697,36705],{},[28285,36698,36699,36701,36703],{},[898,36700,1702],{},[2148,36702,2701],{},[1706,36704,3197],{},[28285,36706,36707,36709,36711],{},[898,36708,1702],{},[2148,36710,2495],{},[1706,36712,3197],{},[902,36714,36715],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,36717,36719],{"id":36718},"minimalizace-výdajů","Minimalizace výdajů",[724,36721,36722,36723,1837],{},"Podmínka dané užitečnosti ",[883,36724,36726],{"className":36725},[886],[888,36727,36728],{"xmlns":890},[892,36729,36730,36760],{},[895,36731,36732,36738,36740,36742,36744,36750,36752,36758],{},[2489,36733,36734,36736],{},[898,36735,900],{},[1706,36737,3197],{},[1706,36739,1708],{},[898,36741,900],{},[1706,36743,2140],{"stretchy":2139},[2142,36745,36746,36748],{},[898,36747,2146],{},[2148,36749,2701],{},[1706,36751,2505],{"separator":2504},[2142,36753,36754,36756],{},[898,36755,2146],{},[2148,36757,2495],{},[1706,36759,2153],{"stretchy":2139},[902,36761,36762],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,36764,36765],{},[883,36766,36768],{"className":36767},[886],[888,36769,36770],{"xmlns":890},[892,36771,36772,36866],{},[895,36773,36774,36776,36778,36784,36786,36792,36794,36796,36798,36800,36808,36814,36816,36824,36830,36832,36834,36836,36842,36844,36846,36848,36854,36856,36862,36864],{},[898,36775,6362],{},[1706,36777,2140],{"stretchy":2139},[2142,36779,36780,36782],{},[898,36781,2146],{},[2148,36783,2701],{},[1706,36785,2505],{"separator":2504},[2142,36787,36788,36790],{},[898,36789,2146],{},[2148,36791,2495],{},[1706,36793,2505],{"separator":2504},[898,36795,35541],{},[1706,36797,2153],{"stretchy":2139},[1706,36799,1708],{},[28285,36801,36802,36804,36806],{},[898,36803,1702],{},[2148,36805,2701],{},[1706,36807,3197],{},[2142,36809,36810,36812],{},[898,36811,2146],{},[2148,36813,2701],{},[1706,36815,2447],{},[28285,36817,36818,36820,36822],{},[898,36819,1702],{},[2148,36821,2495],{},[1706,36823,3197],{},[2142,36825,36826,36828],{},[898,36827,2146],{},[2148,36829,2495],{},[1706,36831,2447],{},[898,36833,35541],{},[1706,36835,2140],{"stretchy":2139},[2489,36837,36838,36840],{},[898,36839,900],{},[1706,36841,3197],{},[1706,36843,1715],{},[898,36845,900],{},[1706,36847,2140],{"stretchy":2139},[2142,36849,36850,36852],{},[898,36851,2146],{},[2148,36853,2701],{},[1706,36855,2505],{"separator":2504},[2142,36857,36858,36860],{},[898,36859,2146],{},[2148,36861,2495],{},[1706,36863,2153],{"stretchy":2139},[1706,36865,2153],{"stretchy":2139},[902,36867,36868],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,36870,36871,36872,1837],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,36873,36875],{"className":36874},[886],[888,36876,36877],{"xmlns":890},[892,36878,36879,36918],{},[895,36880,36881,36888,36890,36896,36898,36904,36906,36912,36914,36916],{},[2142,36882,36883,36885],{},[898,36884,2146],{},[898,36886,36887],{},"i",[1706,36889,1708],{},[2142,36891,36892,36894],{},[898,36893,2334],{},[898,36895,36887],{},[1706,36897,2140],{"stretchy":2139},[2142,36899,36900,36902],{},[898,36901,1702],{},[2148,36903,2701],{},[1706,36905,2505],{"separator":2504},[2142,36907,36908,36910],{},[898,36909,1702],{},[2148,36911,2495],{},[1706,36913,2505],{"separator":2504},[898,36915,900],{},[1706,36917,2153],{"stretchy":2139},[902,36919,36920],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,36922,21083],{"id":21082},[120,36924,36925,36932,36939,36948],{},[123,36926,36927,1647,36929],{},[38,36928,22971],{},[207,36930,784],{"className":36931,"dataFsResolvedFilePath":782,"href":783},[210],[123,36933,36934,1647,36936],{},[38,36935,22979],{},[207,36937,21094],{"className":36938,"dataFsResolvedFilePath":800,"href":801},[210],[123,36940,36941,1647,36944,36947],{},[38,36942,36943],{},"Aplikace v kurzu:",[207,36945,880],{"className":36946,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,36949,36950,1647,36952,1343,36955,36958],{},[38,36951,22987],{},[207,36953,936],{"className":36954,"dataFsResolvedFilePath":934,"href":935},[210],[207,36956,1400],{"className":36957,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":36960},[36961,36962,36963,36964,36965,36966,36970],{"id":8603,"depth":642,"text":8604},{"id":22431,"depth":642,"text":22432},{"id":22505,"depth":642,"text":22506},{"id":36124,"depth":642,"text":36125},{"id":36236,"depth":642,"text":36237},{"id":36338,"depth":642,"text":36339,"children":36967},[36968,36969],{"id":36342,"depth":649,"text":36343},{"id":36718,"depth":649,"text":36719},{"id":21082,"depth":642,"text":21083},[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":35380,"description":36972},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,36979,36980],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":36983,"title":936,"body":36984,"course":1128,"courses":659,"created":21169,"description":641,"extension":661,"meta":46826,"navigation":664,"path":46827,"seo":46828,"sources":46829,"stem":46830,"tags":46831,"type":21181,"updated":677,"__hash__":46835},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":36985,"toc":46788},[36986,36989,36991,37114,37249,37253,37256,37369,37373,37401,37448,37451,37517,37562,37565,37591,37622,37626,37630,37674,37718,37780,37835,37838,37842,37845,37892,37988,38094,38100,38177,38206,38345,38349,38378,38426,38573,38663,38667,38693,38731,38758,38796,38858,38933,39011,39068,39134,39178,39182,39239,39288,39333,39545,39664,39670,39674,39697,39701,39708,39712,39743,39778,39782,39832,39915,39957,39978,40040,40100,40104,40175,40243,40314,40429,40477,40481,40484,40524,40563,40586,40699,40863,40871,40898,40928,40931,41008,41161,41245,41584,41588,41711,41847,41982,42034,42037,42287,42367,42371,42374,42432,42464,42467,42516,42519,42590,42786,42790,42939,43169,43207,43260,43305,43308,43364,43413,43617,43707,43711,43727,43734,43903,43907,43978,44058,44137,44216,44362,44450,44454,44637,44768,44813,44910,44914,45652,45654,46705,46707],[12,36987,936],{"id":36988},"národní-důchod",[115,36990,31115],{"id":31114},[724,36992,36993,36994,1647,36998,37001,37002,1647,37005,37018,37019,37022,37023,37026,37027,37030,37031,37033,37034,1647,37036,37053,37054,37071,37072,37075,37076,1936],{},"Kapitola 7 ",[207,36995,36997],{"className":36996,"dataFsResolvedFilePath":21130,"href":21131},[210],"Matematické ekonomie",[38,36999,37000],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,37003,37004],{},"národním důchodem",[883,37006,37008],{"className":37007},[886],[888,37009,37010],{"xmlns":890},[892,37011,37012,37016],{},[895,37013,37014],{},[898,37015,28247],{},[902,37017,28247],{"encoding":904},". Budují se postupně bohatší modely — ",[38,37020,37021],{},"C-I"," (jen spotřeba a investice) → ",[38,37024,37025],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,37028,37029],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,37032,31120],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,37035,32992],{},[883,37037,37039],{"className":37038},[886],[888,37040,37041],{"xmlns":890},[892,37042,37043,37051],{},[895,37044,37045],{},[2489,37046,37047,37049],{},[898,37048,28247],{},[898,37050,23410],{},[902,37052,33010],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,37055,37057],{"className":37056},[886],[888,37058,37059],{"xmlns":890},[892,37060,37061,37069],{},[895,37062,37063],{},[2489,37064,37065,37067],{},[898,37066,28247],{},[898,37068,23410],{},[902,37070,33010],{"encoding":904}," na exogenní veličiny popisují ",[38,37073,37074],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,37077,37079],{"className":37078},[886],[888,37080,37081],{"xmlns":890},[892,37082,37083,37111],{},[895,37084,37085,37087,37089,37091,37093,37095,37097,37099,37101,37103,37105,37107,37109],{},[2148,37086,2701],{},[898,37088,15493],{"mathvariant":2409},[1706,37090,2140],{"stretchy":2139},[2148,37092,2701],{},[1706,37094,1715],{},[898,37096,207],{},[1706,37098,2153],{"stretchy":2139},[1706,37100,1708],{},[2148,37102,2701],{},[898,37104,15493],{"mathvariant":2409},[898,37106,1742],{},[898,37108,1702],{},[898,37110,14171],{},[902,37112,37113],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[1636,37115,37116],{},[724,37117,37118,37120,37121,37124,37125,37143,37144,37174,37175,37222,37223,37225,37226,37248],{},[883,37119,3174],{}," Intuice\n",[38,37122,37123],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,37126,37128],{"className":37127},[886],[888,37129,37130],{"xmlns":890},[892,37131,37132,37140],{},[895,37133,37134,37136,37138],{},[898,37135,1742],{},[898,37137,1702],{},[898,37139,1683],{},[902,37141,37142],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,37145,37147],{"className":37146},[886],[888,37148,37149],{"xmlns":890},[892,37150,37151,37171],{},[895,37152,37153,37155,37157,37159,37161,37163,37165,37167,37169],{},[898,37154,1742],{},[898,37156,1702],{},[898,37158,14171],{},[1706,37160,1708],{},[2148,37162,2701],{},[1706,37164,1715],{},[898,37166,1742],{},[898,37168,1702],{},[898,37170,1683],{},[902,37172,37173],{"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 ",[883,37176,37178],{"className":37177},[886],[888,37179,37180],{"xmlns":890},[892,37181,37182,37219],{},[895,37183,37184,37186,37188,37190,37192,37198,37200,37203,37205,37207,37209,37211,37213,37215,37217],{},[2148,37185,2701],{},[1706,37187,2447],{},[898,37189,207],{},[1706,37191,2447],{},[2489,37193,37194,37196],{},[898,37195,207],{},[2148,37197,2495],{},[1706,37199,2447],{},[1706,37201,37202],{},"⋯",[1706,37204,1708],{},[2148,37206,2701],{},[898,37208,15493],{"mathvariant":2409},[1706,37210,2140],{"stretchy":2139},[2148,37212,2701],{},[1706,37214,1715],{},[898,37216,207],{},[1706,37218,2153],{"stretchy":2139},[902,37220,37221],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,37224,31120],{}," 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 ",[883,37227,37229],{"className":37228},[886],[888,37230,37231],{"xmlns":890},[892,37232,37233,37245],{},[895,37234,37235,37237,37239,37241,37243],{},[1706,37236,2140],{"stretchy":2139},[898,37238,28247],{},[1706,37240,2505],{"separator":2504},[898,37242,3950],{},[1706,37244,2153],{"stretchy":2139},[902,37246,37247],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,37250,37252],{"id":37251},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,37254,37255],{},"Po prostudování kapitoly by čtenář měl umět:",[120,37257,37258,37261,37264,37267,37270,37273,37276,37366],{},[123,37259,37260],{},"popsat zjednodušený model národní ekonomiky,",[123,37262,37263],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,37265,37266],{},"popsat lineární model spotřeby a úspor,",[123,37268,37269],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,37271,37272],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,37274,37275],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,37277,37278,37279,1343,37296,1343,37318,1993,37343,37365],{},"popsat modely ",[883,37280,37282],{"className":37281},[886],[888,37283,37284],{"xmlns":890},[892,37285,37286,37294],{},[895,37287,37288,37290,37292],{},[898,37289,1683],{},[2415,37291,31397],{},[898,37293,31291],{},[902,37295,31402],{"encoding":904},[883,37297,37299],{"className":37298},[886],[888,37300,37301],{"xmlns":890},[892,37302,37303,37315],{},[895,37304,37305,37307,37309,37311,37313],{},[898,37306,1683],{},[2415,37308,31397],{},[898,37310,31291],{},[2415,37312,31397],{},[898,37314,31220],{},[902,37316,37317],{"encoding":904},"C\\text{-}I\\text{-}G",[883,37319,37321],{"className":37320},[886],[888,37322,37323],{"xmlns":890},[892,37324,37325,37341],{},[895,37326,37327,37329,37331,37333,37335,37337,37339],{},[898,37328,1683],{},[2415,37330,31397],{},[898,37332,31291],{},[2415,37334,31397],{},[898,37336,31220],{},[2415,37338,31397],{},[898,37340,31427],{},[902,37342,31430],{"encoding":904},[883,37344,37346],{"className":37345},[886],[888,37347,37348],{"xmlns":890},[892,37349,37350,37362],{},[895,37351,37352,37354,37356,37358,37360],{},[898,37353,31291],{},[898,37355,14171],{},[2415,37357,31397],{},[898,37359,6362],{},[898,37361,1742],{},[902,37363,37364],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,37367,37368],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,37370,37372],{"id":37371},"gnp-a-národní-důchod","GNP a národní důchod",[724,37374,37375,1647,37378,2314,37397,37400],{},[38,37376,37377],{},"Hrubý národní produkt",[883,37379,37381],{"className":37380},[886],[888,37382,37383],{"xmlns":890},[892,37384,37385,37394],{},[895,37386,37387,37389,37392],{},[898,37388,31220],{},[898,37390,37391],{},"N",[898,37393,1702],{},[902,37395,37396],{"encoding":904},"GNP",[614,37398,37399],{},"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:",[724,37402,37403],{},[883,37404,37406],{"className":37405},[886],[888,37407,37408],{"xmlns":890},[892,37409,37410,37445],{},[895,37411,37412,37414,37416,37418,37420,37422,37424,37426,37428,37430,37432,37434,37436,37438,37440,37443],{},[898,37413,31220],{},[898,37415,37391],{},[898,37417,1702],{},[1706,37419,1708],{},[898,37421,1683],{},[1706,37423,2447],{},[898,37425,31291],{},[1706,37427,2447],{},[898,37429,31220],{},[1706,37431,2447],{},[898,37433,31427],{},[1706,37435,2505],{"separator":2504},[4898,37437],{"width":9524},[1706,37439,2140],{"stretchy":2139},[2148,37441,37442],{},"7.1",[1706,37444,2153],{"stretchy":2139},[902,37446,37447],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,37449,37450],{},"kde",[120,37452,37453,37469,37485,37501],{},[123,37454,37455,37468],{},[883,37456,37458],{"className":37457},[886],[888,37459,37460],{"xmlns":890},[892,37461,37462,37466],{},[895,37463,37464],{},[898,37465,1683],{},[902,37467,1683],{"encoding":904}," — výdaje domácností na spotřebu,",[123,37470,37471,37484],{},[883,37472,37474],{"className":37473},[886],[888,37475,37476],{"xmlns":890},[892,37477,37478,37482],{},[895,37479,37480],{},[898,37481,31291],{},[902,37483,31291],{"encoding":904}," — hrubé domácí investice,",[123,37486,37487,37500],{},[883,37488,37490],{"className":37489},[886],[888,37491,37492],{"xmlns":890},[892,37493,37494,37498],{},[895,37495,37496],{},[898,37497,31220],{},[902,37499,31220],{"encoding":904}," — vládní výdaje,",[123,37502,37503,37516],{},[883,37504,37506],{"className":37505},[886],[888,37507,37508],{"xmlns":890},[892,37509,37510,37514],{},[895,37511,37512],{},[898,37513,31427],{},[902,37515,31427],{"encoding":904}," — čistý export.",[724,37518,37519,37520,37537,37538,37541,37542,1647,37545,2314,37558,37561],{},"K měření ",[883,37521,37523],{"className":37522},[886],[888,37524,37525],{"xmlns":890},[892,37526,37527,37535],{},[895,37528,37529,37531,37533],{},[898,37530,31220],{},[898,37532,37391],{},[898,37534,1702],{},[902,37536,37396],{"encoding":904}," se užívá ",[38,37539,37540],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,37543,37544],{},"národní důchod",[883,37546,37548],{"className":37547},[886],[888,37549,37550],{"xmlns":890},[892,37551,37552,37556],{},[895,37553,37554],{},[898,37555,28247],{},[902,37557,28247],{"encoding":904},[614,37559,37560],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,37563,37564],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,37566,37567],{},[883,37568,37570],{"className":37569},[886],[888,37571,37572],{"xmlns":890},[892,37573,37574,37588],{},[895,37575,37576,37578,37580,37582,37584,37586],{},[898,37577,31220],{},[898,37579,37391],{},[898,37581,1702],{},[1706,37583,3248],{},[898,37585,28247],{},[1706,37587,2505],{"separator":2504},[902,37589,37590],{"encoding":904},"GNP \\approx Y,",[724,37592,37593,37594,2314,37597,37600,37601,37614,37615,37618,37619,1837],{},"a užívá se společného názvu ",[38,37595,37596],{},"důchod",[614,37598,37599],{},"income",") s označením ",[883,37602,37604],{"className":37603},[886],[888,37605,37606],{"xmlns":890},[892,37607,37608,37612],{},[895,37609,37610],{},[898,37611,28247],{},[902,37613,28247],{"encoding":904},". Domácnosti důchod použijí ke ",[38,37616,37617],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,37620,37621],{},"úspor",[115,37623,37625],{"id":37624},"spotřeba-a-úspory","Spotřeba a úspory",[198,37627,37629],{"id":37628},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,37631,37632,37633,37646,37647,37660,37661,4288],{},"Jak spotřeba ",[883,37634,37636],{"className":37635},[886],[888,37637,37638],{"xmlns":890},[892,37639,37640,37644],{},[895,37641,37642],{},[898,37643,1683],{},[902,37645,1683],{"encoding":904},", tak úspory ",[883,37648,37650],{"className":37649},[886],[888,37651,37652],{"xmlns":890},[892,37653,37654,37658],{},[895,37655,37656],{},[898,37657,14171],{},[902,37659,14171],{"encoding":904}," závisejí na důchodu ",[883,37662,37664],{"className":37663},[886],[888,37665,37666],{"xmlns":890},[892,37667,37668,37672],{},[895,37669,37670],{},[898,37671,28247],{},[902,37673,28247],{"encoding":904},[724,37675,37676],{},[883,37677,37679],{"className":37678},[886],[888,37680,37681],{"xmlns":890},[892,37682,37683,37715],{},[895,37684,37685,37687,37689,37691,37693,37695,37697,37699,37701,37703,37705,37707,37709,37711,37713],{},[898,37686,1683],{},[1706,37688,1708],{},[898,37690,1683],{},[1706,37692,2140],{"stretchy":2139},[898,37694,28247],{},[1706,37696,2153],{"stretchy":2139},[1706,37698,2505],{"separator":2504},[4898,37700],{"width":9524},[898,37702,14171],{},[1706,37704,1708],{},[898,37706,14171],{},[1706,37708,2140],{"stretchy":2139},[898,37710,28247],{},[1706,37712,2153],{"stretchy":2139},[898,37714,1837],{"mathvariant":2409},[902,37716,37717],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,37719,37720,3484,37739,2314,37742,37745,37746,3484,37766,2314,37769,37772,37773,1993,37776,37779],{},[883,37721,37723],{"className":37722},[886],[888,37724,37725],{"xmlns":890},[892,37726,37727,37737],{},[895,37728,37729,37731,37733,37735],{},[898,37730,1683],{},[1706,37732,2140],{"stretchy":2139},[898,37734,28247],{},[1706,37736,2153],{"stretchy":2139},[902,37738,33323],{"encoding":904},[38,37740,37741],{},"funkce spotřeby",[614,37743,37744],{},"consumption function","), ",[883,37747,37749],{"className":37748},[886],[888,37750,37751],{"xmlns":890},[892,37752,37753,37763],{},[895,37754,37755,37757,37759,37761],{},[898,37756,14171],{},[1706,37758,2140],{"stretchy":2139},[898,37760,28247],{},[1706,37762,2153],{"stretchy":2139},[902,37764,37765],{"encoding":904},"S(Y)",[38,37767,37768],{},"funkce úspor",[614,37770,37771],{},"savings function","); jejich grafy se nazývají ",[38,37774,37775],{},"křivka spotřeby",[38,37777,37778],{},"křivka úspor",". Platí základní identita",[724,37781,37782],{},[883,37783,37785],{"className":37784},[886],[888,37786,37787],{"xmlns":890},[892,37788,37789,37832],{},[895,37790,37791,37793,37795,37797,37799,37801,37803,37805,37807,37809,37811,37813,37815,37817,37819,37821,37823,37825,37827,37830],{},[898,37792,28247],{},[1706,37794,1708],{},[898,37796,1683],{},[1706,37798,2447],{},[898,37800,14171],{},[1706,37802,1708],{},[898,37804,1683],{},[1706,37806,2140],{"stretchy":2139},[898,37808,28247],{},[1706,37810,2153],{"stretchy":2139},[1706,37812,2447],{},[898,37814,14171],{},[1706,37816,2140],{"stretchy":2139},[898,37818,28247],{},[1706,37820,2153],{"stretchy":2139},[898,37822,1837],{"mathvariant":2409},[4898,37824],{"width":9524},[1706,37826,2140],{"stretchy":2139},[2148,37828,37829],{},"7.2",[1706,37831,2153],{"stretchy":2139},[902,37833,37834],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,37836,37837],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,37839,37841],{"id":37840},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,37843,37844],{},"Nejjednodušší model předpokládá lineární tvar",[724,37846,37847],{},[883,37848,37850],{"className":37849},[886],[888,37851,37852],{"xmlns":890},[892,37853,37854,37889],{},[895,37855,37856,37858,37860,37862,37864,37866,37868,37870,37872,37874,37876,37878,37880,37882,37884,37887],{},[898,37857,1683],{},[1706,37859,1708],{},[898,37861,1683],{},[1706,37863,2140],{"stretchy":2139},[898,37865,28247],{},[1706,37867,2153],{"stretchy":2139},[1706,37869,1708],{},[898,37871,207],{},[898,37873,28247],{},[1706,37875,2447],{},[898,37877,2450],{},[1706,37879,2505],{"separator":2504},[4898,37881],{"width":9524},[1706,37883,2140],{"stretchy":2139},[2148,37885,37886],{},"7.3",[1706,37888,2153],{"stretchy":2139},[902,37890,37891],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,37893,5331,37894,1993,37912,37934,37935,37974,37975,1837],{},[883,37895,37897],{"className":37896},[886],[888,37898,37899],{"xmlns":890},[892,37900,37901,37909],{},[895,37902,37903,37905,37907],{},[898,37904,2450],{},[1706,37906,8922],{},[2148,37908,2150],{},[902,37910,37911],{"encoding":904},"b > 0",[883,37913,37915],{"className":37914},[886],[888,37916,37917],{"xmlns":890},[892,37918,37919,37931],{},[895,37920,37921,37923,37925,37927,37929],{},[2148,37922,2150],{},[1706,37924,2539],{},[898,37926,207],{},[1706,37928,2539],{},[2148,37930,2701],{},[902,37932,37933],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,37936,37938],{"className":37937},[886],[888,37939,37940],{"xmlns":890},[892,37941,37942,37971],{},[895,37943,37944,37946,37948,37955,37957,37959,37961,37963,37965,37967,37969],{},[898,37945,207],{},[1706,37947,1708],{},[895,37949,37950,37953],{},[898,37951,37952],{"mathvariant":2409},"t",[898,37954,30152],{"mathvariant":2409},[2415,37956,2799],{},[898,37958,6307],{},[1706,37960,1708],{},[898,37962,3677],{"mathvariant":2409},[898,37964,1683],{},[898,37966,15493],{"mathvariant":2409},[898,37968,3677],{"mathvariant":2409},[898,37970,28247],{},[902,37972,37973],{"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 ",[883,37976,37978],{"className":37977},[886],[888,37979,37980],{"xmlns":890},[892,37981,37982,37986],{},[895,37983,37984],{},[898,37985,28247],{},[902,37987,28247],{"encoding":904},[724,37989,37990],{},[614,37991,37992,37993,38017,38018,38056,38057,38073,38074,1837],{},"Obrázek 7.1 — Přímka spotřeby ",[883,37994,37996],{"className":37995},[886],[888,37997,37998],{"xmlns":890},[892,37999,38000,38014],{},[895,38001,38002,38004,38006,38008,38010,38012],{},[898,38003,1683],{},[1706,38005,1708],{},[898,38007,207],{},[898,38009,28247],{},[1706,38011,2447],{},[898,38013,2450],{},[902,38015,38016],{"encoding":904},"C = aY + b"," se směrnicí ",[883,38019,38021],{"className":38020},[886],[888,38022,38023],{"xmlns":890},[892,38024,38025,38053],{},[895,38026,38027,38029,38031,38037,38039,38041,38043,38045,38047,38049,38051],{},[898,38028,207],{},[1706,38030,1708],{},[895,38032,38033,38035],{},[898,38034,37952],{"mathvariant":2409},[898,38036,30152],{"mathvariant":2409},[2415,38038,2799],{},[898,38040,6307],{},[1706,38042,1708],{},[898,38044,3677],{"mathvariant":2409},[898,38046,1683],{},[898,38048,15493],{"mathvariant":2409},[898,38050,3677],{"mathvariant":2409},[898,38052,28247],{},[902,38054,38055],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,38058,38060],{"className":38059},[886],[888,38061,38062],{"xmlns":890},[892,38063,38064,38070],{},[895,38065,38066,38068],{},[898,38067,3677],{"mathvariant":2409},[898,38069,1683],{},[902,38071,38072],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,38075,38077],{"className":38076},[886],[888,38078,38079],{"xmlns":890},[892,38080,38081,38091],{},[895,38082,38083,38085,38087,38089],{},[898,38084,3677],{"mathvariant":2409},[898,38086,28247],{},[1706,38088,1708],{},[2148,38090,2701],{},[902,38092,38093],{"encoding":904},"\\Delta Y = 1",[724,38095,38096,38097,4288],{},"Dosazením do (7.2) plyne ",[38,38098,38099],{},"lineární model úspor",[724,38101,38102],{},[883,38103,38105],{"className":38104},[886],[888,38106,38107],{"xmlns":890},[892,38108,38109,38174],{},[895,38110,38111,38113,38115,38117,38119,38121,38123,38125,38127,38129,38131,38133,38135,38137,38139,38141,38143,38145,38147,38149,38151,38153,38155,38157,38159,38161,38163,38165,38167,38169,38172],{},[898,38112,14171],{},[1706,38114,1708],{},[898,38116,28247],{},[1706,38118,1715],{},[898,38120,1683],{},[1706,38122,2140],{"stretchy":2139},[898,38124,28247],{},[1706,38126,2153],{"stretchy":2139},[1706,38128,1708],{},[898,38130,28247],{},[1706,38132,1715],{},[1706,38134,2140],{"stretchy":2139},[898,38136,207],{},[898,38138,28247],{},[1706,38140,2447],{},[898,38142,2450],{},[1706,38144,2153],{"stretchy":2139},[1706,38146,1708],{},[1706,38148,2140],{"stretchy":2139},[2148,38150,2701],{},[1706,38152,1715],{},[898,38154,207],{},[1706,38156,2153],{"stretchy":2139},[898,38158,28247],{},[1706,38160,1715],{},[898,38162,2450],{},[898,38164,1837],{"mathvariant":2409},[4898,38166],{"width":9524},[1706,38168,2140],{"stretchy":2139},[2148,38170,38171],{},"7.4",[1706,38173,2153],{"stretchy":2139},[902,38175,38176],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,38178,38179,38180,1936],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,38181,38183],{"className":38182},[886],[888,38184,38185],{"xmlns":890},[892,38186,38187,38203],{},[895,38188,38189,38191,38193,38195,38197,38199,38201],{},[2148,38190,2150],{},[1706,38192,2539],{},[2148,38194,2701],{},[1706,38196,1715],{},[898,38198,207],{},[1706,38200,2539],{},[2148,38202,2701],{},[902,38204,38205],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,38207,38208],{},[614,38209,38210,38211,1993,38234,38266,38267,2891,38280,38310,38311,2891,38329,1837],{},"Obrázek 7.2 — Přímky ",[883,38212,38214],{"className":38213},[886],[888,38215,38216],{"xmlns":890},[892,38217,38218,38232],{},[895,38219,38220,38222,38224,38226,38228,38230],{},[898,38221,1683],{},[1706,38223,1708],{},[898,38225,207],{},[898,38227,28247],{},[1706,38229,2447],{},[898,38231,2450],{},[902,38233,38016],{"encoding":904},[883,38235,38237],{"className":38236},[886],[888,38238,38239],{"xmlns":890},[892,38240,38241,38263],{},[895,38242,38243,38245,38247,38249,38251,38253,38255,38257,38259,38261],{},[898,38244,14171],{},[1706,38246,1708],{},[1706,38248,2140],{"stretchy":2139},[2148,38250,2701],{},[1706,38252,1715],{},[898,38254,207],{},[1706,38256,2153],{"stretchy":2139},[898,38258,28247],{},[1706,38260,1715],{},[898,38262,2450],{},[902,38264,38265],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,38268,38270],{"className":38269},[886],[888,38271,38272],{"xmlns":890},[892,38273,38274,38278],{},[895,38275,38276],{},[898,38277,28247],{},[902,38279,28247],{"encoding":904},[883,38281,38283],{"className":38282},[886],[888,38284,38285],{"xmlns":890},[892,38286,38287,38307],{},[895,38288,38289,38291,38293,38295,38297,38299,38301,38303,38305],{},[898,38290,28247],{},[1706,38292,1708],{},[898,38294,2450],{},[898,38296,15493],{"mathvariant":2409},[1706,38298,2140],{"stretchy":2139},[2148,38300,2701],{},[1706,38302,1715],{},[898,38304,207],{},[1706,38306,2153],{"stretchy":2139},[902,38308,38309],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,38312,38314],{"className":38313},[886],[888,38315,38316],{"xmlns":890},[892,38317,38318,38326],{},[895,38319,38320,38322,38324],{},[898,38321,1683],{},[1706,38323,2505],{"separator":2504},[898,38325,14171],{},[902,38327,38328],{"encoding":904},"C, S",[883,38330,38332],{"className":38331},[886],[888,38333,38334],{"xmlns":890},[892,38335,38336,38342],{},[895,38337,38338,38340],{},[1706,38339,1715],{},[898,38341,2450],{},[902,38343,38344],{"encoding":904},"-b",[198,38346,38348],{"id":38347},"příklad-71","Příklad 7.1",[724,38350,38351,38352,38377],{},"Pro spotřebu ",[883,38353,38355],{"className":38354},[886],[888,38356,38357],{"xmlns":890},[892,38358,38359,38374],{},[895,38360,38361,38363,38365,38368,38370,38372],{},[898,38362,1683],{},[1706,38364,1708],{},[2148,38366,38367],{},"0,4",[898,38369,28247],{},[1706,38371,2447],{},[2148,38373,7786],{},[902,38375,38376],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,38379,38380],{},[883,38381,38383],{"className":38382},[886],[888,38384,38385],{"xmlns":890},[892,38386,38387,38423],{},[895,38388,38389,38391,38393,38395,38397,38399,38401,38403,38405,38407,38409,38411,38413,38415,38417,38419,38421],{},[898,38390,14171],{},[1706,38392,1708],{},[898,38394,28247],{},[1706,38396,1715],{},[898,38398,1683],{},[1706,38400,1708],{},[898,38402,28247],{},[1706,38404,1715],{},[2148,38406,38367],{},[898,38408,28247],{},[1706,38410,1715],{},[2148,38412,7786],{},[1706,38414,1708],{},[2148,38416,13775],{},[898,38418,28247],{},[1706,38420,1715],{},[2148,38422,13684],{},[902,38424,38425],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,38427,38428],{},[614,38429,38430,38431,1993,38454,38478,38479,3484,38492,38516,38517,3484,38534,38550,38551,1837],{},"Obrázek 7.3 — Přímky ",[883,38432,38434],{"className":38433},[886],[888,38435,38436],{"xmlns":890},[892,38437,38438,38452],{},[895,38439,38440,38442,38444,38446,38448,38450],{},[898,38441,1683],{},[1706,38443,1708],{},[2148,38445,38367],{},[898,38447,28247],{},[1706,38449,2447],{},[2148,38451,7786],{},[902,38453,38376],{"encoding":904},[883,38455,38457],{"className":38456},[886],[888,38458,38459],{"xmlns":890},[892,38460,38461,38475],{},[895,38462,38463,38465,38467,38469,38471,38473],{},[898,38464,14171],{},[1706,38466,1708],{},[2148,38468,13775],{},[898,38470,28247],{},[1706,38472,1715],{},[2148,38474,7786],{},[902,38476,38477],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,38480,38482],{"className":38481},[886],[888,38483,38484],{"xmlns":890},[892,38485,38486,38490],{},[895,38487,38488],{},[898,38489,28247],{},[902,38491,28247],{"encoding":904},[883,38493,38495],{"className":38494},[886],[888,38496,38497],{"xmlns":890},[892,38498,38499,38513],{},[895,38500,38501,38503,38506],{},[1706,38502,3248],{},[2148,38504,38505],{},"16,",[3925,38507,38508,38510],{"accent":2504},[2148,38509,7044],{},[1706,38511,38512],{},"ˉ",[902,38514,38515],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,38518,38520],{"className":38519},[886],[888,38521,38522],{"xmlns":890},[892,38523,38524,38532],{},[895,38525,38526,38528,38530],{},[898,38527,1683],{},[1706,38529,2505],{"separator":2504},[898,38531,14171],{},[902,38533,38328],{"encoding":904},[883,38535,38537],{"className":38536},[886],[888,38538,38539],{"xmlns":890},[892,38540,38541,38547],{},[895,38542,38543,38545],{},[1706,38544,1715],{},[2148,38546,7786],{},[902,38548,38549],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,38552,38554],{"className":38553},[886],[888,38555,38556],{"xmlns":890},[892,38557,38558,38570],{},[895,38559,38560,38562,38564,38566,38568],{},[1706,38561,2140],{"stretchy":2139},[2148,38563,2150],{},[1706,38565,2505],{"separator":2504},[2148,38567,7786],{},[1706,38569,2153],{"stretchy":2139},[902,38571,38572],{"encoding":904},"(0, 10)",[724,38574,38575,38576,3484,38594,38624,38625,2314,38628,38631,38632,3484,38656,2314,38659,38662],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,38577,38579],{"className":38578},[886],[888,38580,38581],{"xmlns":890},[892,38582,38583,38591],{},[895,38584,38585,38587,38589],{},[898,38586,28247],{},[1706,38588,1708],{},[2148,38590,2150],{},[902,38592,38593],{"encoding":904},"Y = 0",[883,38595,38597],{"className":38596},[886],[888,38598,38599],{"xmlns":890},[892,38600,38601,38621],{},[895,38602,38603,38605,38607,38609,38611,38613,38615,38617,38619],{},[898,38604,14171],{},[1706,38606,2140],{"stretchy":2139},[2148,38608,2150],{},[1706,38610,2153],{"stretchy":2139},[1706,38612,1708],{},[1706,38614,1715],{},[898,38616,2450],{},[1706,38618,2539],{},[2148,38620,2150],{},[902,38622,38623],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,38626,38627],{},"autonomních úsporách",[614,38629,38630],{},"autonomous savings","). Analogicky ",[883,38633,38635],{"className":38634},[886],[888,38636,38637],{"xmlns":890},[892,38638,38639,38653],{},[895,38640,38641,38643,38645,38647,38649,38651],{},[898,38642,1683],{},[1706,38644,2140],{"stretchy":2139},[2148,38646,2150],{},[1706,38648,2153],{"stretchy":2139},[1706,38650,1708],{},[898,38652,2450],{},[902,38654,38655],{"encoding":904},"C(0) = b",[38,38657,38658],{},"autonomní spotřeba",[614,38660,38661],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,38664,38666],{"id":38665},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,38668,38669,1647,38672,2314,38689,38692],{},[38,38670,38671],{},"Mezní sklon ke spotřebě",[883,38673,38675],{"className":38674},[886],[888,38676,38677],{"xmlns":890},[892,38678,38679,38687],{},[895,38680,38681,38683,38685],{},[898,38682,1742],{},[898,38684,1702],{},[898,38686,1683],{},[902,38688,37142],{"encoding":904},[614,38690,38691],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,38694,38695],{},[883,38696,38698],{"className":38697},[886],[888,38699,38700],{"xmlns":890},[892,38701,38702,38728],{},[895,38703,38704,38706,38708,38710,38712,38726],{},[898,38705,1742],{},[898,38707,1702],{},[898,38709,1683],{},[1706,38711,1708],{},[2964,38713,38714,38720],{},[895,38715,38716,38718],{},[898,38717,3120],{"mathvariant":2409},[898,38719,1683],{},[895,38721,38722,38724],{},[898,38723,3120],{"mathvariant":2409},[898,38725,28247],{},[898,38727,1837],{"mathvariant":2409},[902,38729,38730],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,38732,38733,1647,38736,2314,38754,38757],{},[38,38734,38735],{},"Mezní sklon k úsporám",[883,38737,38739],{"className":38738},[886],[888,38740,38741],{"xmlns":890},[892,38742,38743,38751],{},[895,38744,38745,38747,38749],{},[898,38746,1742],{},[898,38748,1702],{},[898,38750,14171],{},[902,38752,38753],{"encoding":904},"MPS",[614,38755,38756],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,38759,38760],{},[883,38761,38763],{"className":38762},[886],[888,38764,38765],{"xmlns":890},[892,38766,38767,38793],{},[895,38768,38769,38771,38773,38775,38777,38791],{},[898,38770,1742],{},[898,38772,1702],{},[898,38774,14171],{},[1706,38776,1708],{},[2964,38778,38779,38785],{},[895,38780,38781,38783],{},[898,38782,3120],{"mathvariant":2409},[898,38784,14171],{},[895,38786,38787,38789],{},[898,38788,3120],{"mathvariant":2409},[898,38790,28247],{},[898,38792,1837],{"mathvariant":2409},[902,38794,38795],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,38797,38798,38799,38857],{},"Z (7.2) plyne ",[883,38800,38802],{"className":38801},[886],[888,38803,38804],{"xmlns":890},[892,38805,38806,38854],{},[895,38807,38808,38822,38824,38838,38840],{},[2964,38809,38810,38816],{},[895,38811,38812,38814],{},[898,38813,3120],{"mathvariant":2409},[898,38815,28247],{},[895,38817,38818,38820],{},[898,38819,3120],{"mathvariant":2409},[898,38821,28247],{},[1706,38823,1708],{},[2964,38825,38826,38832],{},[895,38827,38828,38830],{},[898,38829,3120],{"mathvariant":2409},[898,38831,1683],{},[895,38833,38834,38836],{},[898,38835,3120],{"mathvariant":2409},[898,38837,28247],{},[1706,38839,2447],{},[2964,38841,38842,38848],{},[895,38843,38844,38846],{},[898,38845,3120],{"mathvariant":2409},[898,38847,14171],{},[895,38849,38850,38852],{},[898,38851,3120],{"mathvariant":2409},[898,38853,28247],{},[902,38855,38856],{"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",[724,38859,38860],{},[883,38861,38863],{"className":38862},[886],[888,38864,38865],{"xmlns":890},[892,38866,38867,38930],{},[895,38868,38869,38921,38923,38925,38928],{},[31939,38870,38871],{"notation":31941},[4745,38872,38873],{"scriptlevel":2150,"displaystyle":2139},[4745,38874,38875],{"scriptlevel":2150,"displaystyle":2139},[4745,38876,38877],{"scriptlevel":2150,"displaystyle":2504},[895,38878,38879,38881,38883,38885,38887,38889,38891,38893,38895,38897,38899,38901,38903,38905,38907,38909,38911,38913,38915,38917,38919],{},[898,38880,1742],{},[898,38882,1702],{},[898,38884,1683],{},[1706,38886,2447],{},[898,38888,1742],{},[898,38890,1702],{},[898,38892,14171],{},[1706,38894,1708],{},[2148,38896,2701],{},[1706,38898,2505],{"separator":2504},[4898,38900],{"width":9524},[898,38902,1742],{},[898,38904,1702],{},[898,38906,14171],{},[1706,38908,1708],{},[2148,38910,2701],{},[1706,38912,1715],{},[898,38914,1742],{},[898,38916,1702],{},[898,38918,1683],{},[898,38920,1837],{"mathvariant":2409},[4898,38922],{"width":9524},[1706,38924,2140],{"stretchy":2139},[2148,38926,38927],{},"7.5",[1706,38929,2153],{"stretchy":2139},[902,38931,38932],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,38934,38935,1647,38938,38961,38962,1993,38984,39010],{},[38,38936,38937],{},"Pro lineární model",[883,38939,38941],{"className":38940},[886],[888,38942,38943],{"xmlns":890},[892,38944,38945,38959],{},[895,38946,38947,38949,38951,38953,38955,38957],{},[898,38948,1683],{},[1706,38950,1708],{},[898,38952,207],{},[898,38954,28247],{},[1706,38956,2447],{},[898,38958,2450],{},[902,38960,38016],{"encoding":904}," vychází ",[883,38963,38965],{"className":38964},[886],[888,38966,38967],{"xmlns":890},[892,38968,38969,38981],{},[895,38970,38971,38973,38975,38977,38979],{},[898,38972,1742],{},[898,38974,1702],{},[898,38976,1683],{},[1706,38978,1708],{},[898,38980,207],{},[902,38982,38983],{"encoding":904},"MPC = a",[883,38985,38987],{"className":38986},[886],[888,38988,38989],{"xmlns":890},[892,38990,38991,39007],{},[895,38992,38993,38995,38997,38999,39001,39003,39005],{},[898,38994,1742],{},[898,38996,1702],{},[898,38998,14171],{},[1706,39000,1708],{},[2148,39002,2701],{},[1706,39004,1715],{},[898,39006,207],{},[902,39008,39009],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,39012,39013,39016,39017,15532,39039,39067],{},[38,39014,39015],{},"Interpretace diferenciálem."," Pro pevné ",[883,39018,39020],{"className":39019},[886],[888,39021,39022],{"xmlns":890},[892,39023,39024,39036],{},[895,39025,39026,39028,39030],{},[898,39027,28247],{},[1706,39029,1708],{},[2489,39031,39032,39034],{},[898,39033,28247],{},[1706,39035,3197],{},[902,39037,39038],{"encoding":904},"Y = Y^*",[883,39040,39042],{"className":39041},[886],[888,39043,39044],{"xmlns":890},[892,39045,39046,39064],{},[895,39047,39048,39050,39052,39054,39056,39062],{},[898,39049,1742],{},[898,39051,1702],{},[898,39053,1683],{},[1706,39055,2140],{"stretchy":2139},[2489,39057,39058,39060],{},[898,39059,28247],{},[1706,39061,3197],{},[1706,39063,2153],{"stretchy":2139},[902,39065,39066],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,39069,39070],{},[883,39071,39073],{"className":39072},[886],[888,39074,39075],{"xmlns":890},[892,39076,39077,39131],{},[895,39078,39079,39081,39083,39085,39087,39089,39091,39097,39099,39101,39103,39105,39107,39109,39111,39113,39115,39117,39119,39121,39123,39125,39127,39129],{},[898,39080,3677],{"mathvariant":2409},[898,39082,1683],{},[1706,39084,3248],{},[898,39086,3120],{"mathvariant":2409},[898,39088,1683],{},[1706,39090,1708],{},[2489,39092,39093,39095],{},[898,39094,1683],{},[1706,39096,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,39098,2140],{"stretchy":2139},[898,39100,28247],{},[1706,39102,2153],{"stretchy":2139},[2415,39104,2799],{},[898,39106,3120],{"mathvariant":2409},[898,39108,28247],{},[1706,39110,1708],{},[898,39112,1742],{},[898,39114,1702],{},[898,39116,1683],{},[1706,39118,2140],{"stretchy":2139},[898,39120,28247],{},[1706,39122,2153],{"stretchy":2139},[2415,39124,2799],{},[898,39126,3120],{"mathvariant":2409},[898,39128,28247],{},[898,39130,1837],{"mathvariant":2409},[902,39132,39133],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,39135,39136,39137,39173,39174,39177],{},"Analogicky ",[883,39138,39140],{"className":39139},[886],[888,39141,39142],{"xmlns":890},[892,39143,39144,39170],{},[895,39145,39146,39148,39150,39152,39154,39156,39158,39160,39162,39164,39166,39168],{},[898,39147,3677],{"mathvariant":2409},[898,39149,14171],{},[1706,39151,3248],{},[898,39153,1742],{},[898,39155,1702],{},[898,39157,14171],{},[1706,39159,2140],{"stretchy":2139},[898,39161,28247],{},[1706,39163,2153],{"stretchy":2139},[2415,39165,2799],{},[898,39167,3120],{"mathvariant":2409},[898,39169,28247],{},[902,39171,39172],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,39175,1145],{"className":39176,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,39179,39181],{"id":39180},"příklad-72","Příklad 7.2",[724,39183,38351,39184,39219,39220,39238],{},[883,39185,39187],{"className":39186},[886],[888,39188,39189],{"xmlns":890},[892,39190,39191,39216],{},[895,39192,39193,39195,39197,39200,39206,39208,39210,39212,39214],{},[898,39194,1683],{},[1706,39196,1708],{},[2148,39198,39199],{},"0,001",[2489,39201,39202,39204],{},[898,39203,28247],{},[2148,39205,2495],{},[1706,39207,2447],{},[2148,39209,15204],{},[898,39211,28247],{},[1706,39213,2447],{},[2148,39215,2728],{},[902,39217,39218],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,39221,39223],{"className":39222},[886],[888,39224,39225],{"xmlns":890},[892,39226,39227,39235],{},[895,39228,39229,39231,39233],{},[898,39230,28247],{},[1706,39232,2539],{},[2148,39234,4361],{},[902,39236,39237],{"encoding":904},"Y \u003C 400",") platí",[724,39240,39241],{},[883,39242,39244],{"className":39243},[886],[888,39245,39246],{"xmlns":890},[892,39247,39248,39285],{},[895,39249,39250,39252,39254,39256,39258,39272,39274,39277,39279,39281,39283],{},[898,39251,1742],{},[898,39253,1702],{},[898,39255,1683],{},[1706,39257,1708],{},[2964,39259,39260,39266],{},[895,39261,39262,39264],{},[898,39263,3120],{"mathvariant":2409},[898,39265,1683],{},[895,39267,39268,39270],{},[898,39269,3120],{"mathvariant":2409},[898,39271,28247],{},[1706,39273,1708],{},[2148,39275,39276],{},"0,002",[898,39278,28247],{},[1706,39280,2447],{},[2148,39282,15204],{},[1706,39284,2505],{"separator":2504},[902,39286,39287],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,39289,39290],{},[883,39291,39293],{"className":39292},[886],[888,39294,39295],{"xmlns":890},[892,39296,39297,39330],{},[895,39298,39299,39301,39303,39305,39307,39309,39311,39313,39315,39317,39319,39321,39323,39325,39327],{},[898,39300,1742],{},[898,39302,1702],{},[898,39304,14171],{},[1706,39306,1708],{},[2148,39308,2701],{},[1706,39310,1715],{},[898,39312,1742],{},[898,39314,1702],{},[898,39316,1683],{},[1706,39318,1708],{},[1706,39320,1715],{},[2148,39322,39276],{},[898,39324,28247],{},[1706,39326,2447],{},[2148,39328,39329],{},"0,8.",[902,39331,39332],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,39334,39335,39414,39493],{},[123,39336,39337,1343,39365,20808,39393,3484,39411,1837],{},[883,39338,39340],{"className":39339},[886],[888,39341,39342],{"xmlns":890},[892,39343,39344,39362],{},[895,39345,39346,39348,39350,39352,39354,39356,39358,39360],{},[898,39347,1742],{},[898,39349,1702],{},[898,39351,1683],{},[1706,39353,2140],{"stretchy":2139},[2148,39355,2590],{},[1706,39357,2153],{"stretchy":2139},[1706,39359,1708],{},[2148,39361,38367],{},[902,39363,39364],{"encoding":904},"MPC(100) = 0{,}4",[883,39366,39368],{"className":39367},[886],[888,39369,39370],{"xmlns":890},[892,39371,39372,39390],{},[895,39373,39374,39376,39378,39380,39382,39384,39386,39388],{},[898,39375,1742],{},[898,39377,1702],{},[898,39379,14171],{},[1706,39381,2140],{"stretchy":2139},[2148,39383,2590],{},[1706,39385,2153],{"stretchy":2139},[1706,39387,1708],{},[2148,39389,13775],{},[902,39391,39392],{"encoding":904},"MPS(100) = 0{,}6",[883,39394,39396],{"className":39395},[886],[888,39397,39398],{"xmlns":890},[892,39399,39400,39408],{},[895,39401,39402,39404,39406],{},[898,39403,28247],{},[1706,39405,1708],{},[2148,39407,2590],{},[902,39409,39410],{"encoding":904},"Y = 100",[38,39412,39413],{},"větší sklon k úsporám",[123,39415,39416,1343,39444,20808,39472,3484,39490,1837],{},[883,39417,39419],{"className":39418},[886],[888,39420,39421],{"xmlns":890},[892,39422,39423,39441],{},[895,39424,39425,39427,39429,39431,39433,39435,39437,39439],{},[898,39426,1742],{},[898,39428,1702],{},[898,39430,1683],{},[1706,39432,2140],{"stretchy":2139},[2148,39434,7039],{},[1706,39436,2153],{"stretchy":2139},[1706,39438,1708],{},[2148,39440,13775],{},[902,39442,39443],{"encoding":904},"MPC(200) = 0{,}6",[883,39445,39447],{"className":39446},[886],[888,39448,39449],{"xmlns":890},[892,39450,39451,39469],{},[895,39452,39453,39455,39457,39459,39461,39463,39465,39467],{},[898,39454,1742],{},[898,39456,1702],{},[898,39458,14171],{},[1706,39460,2140],{"stretchy":2139},[2148,39462,7039],{},[1706,39464,2153],{"stretchy":2139},[1706,39466,1708],{},[2148,39468,38367],{},[902,39470,39471],{"encoding":904},"MPS(200) = 0{,}4",[883,39473,39475],{"className":39474},[886],[888,39476,39477],{"xmlns":890},[892,39478,39479,39487],{},[895,39480,39481,39483,39485],{},[898,39482,28247],{},[1706,39484,1708],{},[2148,39486,7039],{},[902,39488,39489],{"encoding":904},"Y = 200",[38,39491,39492],{},"větší sklon ke spotřebě",[123,39494,39495,39496,39514,39515,1936],{},"Přesně při ",[883,39497,39499],{"className":39498},[886],[888,39500,39501],{"xmlns":890},[892,39502,39503,39511],{},[895,39504,39505,39507,39509],{},[898,39506,28247],{},[1706,39508,1708],{},[2148,39510,27924],{},[902,39512,39513],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,39516,39518],{"className":39517},[886],[888,39519,39520],{"xmlns":890},[892,39521,39522,39542],{},[895,39523,39524,39526,39528,39530,39532,39534,39536,39538,39540],{},[898,39525,1742],{},[898,39527,1702],{},[898,39529,1683],{},[1706,39531,1708],{},[898,39533,1742],{},[898,39535,1702],{},[898,39537,14171],{},[1706,39539,1708],{},[2148,39541,11496],{},[902,39543,39544],{"encoding":904},"MPC = MPS = 0{,}5",[724,39546,39547,39548,39565,39566,39580,39581,4202,39594,39608,39609,7346,39622,39663],{},"Interpretace: při ",[883,39549,39551],{"className":39550},[886],[888,39552,39553],{"xmlns":890},[892,39554,39555,39563],{},[895,39556,39557,39559,39561],{},[898,39558,28247],{},[1706,39560,1708],{},[2148,39562,2590],{},[902,39564,39410],{"encoding":904}," se spotřeba mění ",[883,39567,39569],{"className":39568},[886],[888,39570,39571],{"xmlns":890},[892,39572,39573,39577],{},[895,39574,39575],{},[2148,39576,38367],{},[902,39578,39579],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,39582,39584],{"className":39583},[886],[888,39585,39586],{"xmlns":890},[892,39587,39588,39592],{},[895,39589,39590],{},[2148,39591,2590],{},[902,39593,2590],{"encoding":904},[883,39595,39597],{"className":39596},[886],[888,39598,39599],{"xmlns":890},[892,39600,39601,39606],{},[895,39602,39603],{},[2148,39604,39605],{},"101",[902,39607,39605],{"encoding":904},", změní se spotřeba přibližně o ",[883,39610,39612],{"className":39611},[886],[888,39613,39614],{"xmlns":890},[892,39615,39616,39620],{},[895,39617,39618],{},[2148,39619,38367],{},[902,39621,39579],{"encoding":904},[883,39623,39625],{"className":39624},[886],[888,39626,39627],{"xmlns":890},[892,39628,39629,39660],{},[895,39630,39631,39633,39635,39637,39639,39641,39643,39645,39647,39649,39651,39653,39655,39657],{},[898,39632,3677],{"mathvariant":2409},[898,39634,1683],{},[1706,39636,1708],{},[898,39638,1683],{},[1706,39640,2140],{"stretchy":2139},[2148,39642,39605],{},[1706,39644,2153],{"stretchy":2139},[1706,39646,1715],{},[898,39648,1683],{},[1706,39650,2140],{"stretchy":2139},[2148,39652,2590],{},[1706,39654,2153],{"stretchy":2139},[1706,39656,1708],{},[2148,39658,39659],{},"0,401",[902,39661,39662],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,39665,39666,39667],{},"Obecný trend: ",[38,39668,39669],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,39671,39673],{"id":39672},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,39675,39676,39677,2314,39680,39683,39684,2314,39687,5354,39690,2314,39693,39696],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,39678,39679],{},"makroekonomická rovnováha",[614,39681,39682],{},"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 ",[38,39685,39686],{},"agregátní poptávky",[614,39688,39689],{},"aggregate demand",[38,39691,39692],{},"agregátní nabídky",[614,39694,39695],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,39698,39700],{"id":39699},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,39702,39703],{},[2286,39704],{"alt":39705,"className":39706,"src":39707},"imek-keynesian-kriz",[210,2290],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,39709,39711],{"id":39710},"zadání-modelu","Zadání modelu",[724,39713,39714,39715,39728,39729,39742],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,39716,39718],{"className":39717},[886],[888,39719,39720],{"xmlns":890},[892,39721,39722,39726],{},[895,39723,39724],{},[898,39725,1683],{},[902,39727,1683],{"encoding":904}," a investice ",[883,39730,39732],{"className":39731},[886],[888,39733,39734],{"xmlns":890},[892,39735,39736,39740],{},[895,39737,39738],{},[898,39739,31291],{},[902,39741,31291],{"encoding":904},". Podmínka rovnováhy:",[724,39744,39745],{},[883,39746,39748],{"className":39747},[886],[888,39749,39750],{"xmlns":890},[892,39751,39752,39775],{},[895,39753,39754,39756,39758,39760,39762,39764,39766,39768,39770,39773],{},[898,39755,28247],{},[1706,39757,1708],{},[898,39759,1683],{},[1706,39761,2447],{},[898,39763,31291],{},[898,39765,1837],{"mathvariant":2409},[4898,39767],{"width":9524},[1706,39769,2140],{"stretchy":2139},[2148,39771,39772],{},"7.6",[1706,39774,2153],{"stretchy":2139},[902,39776,39777],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,39779,39781],{"id":39780},"soustava-rovnic","Soustava rovnic",[724,39783,39784,39785,39806,39807,39831],{},"Pro pevně zadané (plánované) investice ",[883,39786,39788],{"className":39787},[886],[888,39789,39790],{"xmlns":890},[892,39791,39792,39804],{},[895,39793,39794,39796,39798],{},[898,39795,31291],{},[1706,39797,1708],{},[2489,39799,39800,39802],{},[898,39801,31291],{},[1706,39803,3197],{},[902,39805,31302],{"encoding":904}," a funkci spotřeby ",[883,39808,39810],{"className":39809},[886],[888,39811,39812],{"xmlns":890},[892,39813,39814,39828],{},[895,39815,39816,39818,39820,39822,39824,39826],{},[898,39817,1683],{},[1706,39819,1708],{},[898,39821,1683],{},[1706,39823,2140],{"stretchy":2139},[898,39825,28247],{},[1706,39827,2153],{"stretchy":2139},[902,39829,39830],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,39833,39834],{},[883,39835,39837],{"className":39836},[886],[888,39838,39839],{"xmlns":890},[892,39840,39841,39912],{},[895,39842,39843,39903,39905,39907,39910],{},[2354,39844,39845,39875],{"rowspacing":7556,"columnalign":7557,"columnspacing":3141},[2358,39846,39847,39853],{},[2361,39848,39849],{},[4745,39850,39851],{"scriptlevel":2150,"displaystyle":2504},[898,39852,28247],{},[2361,39854,39855],{},[4745,39856,39857],{"scriptlevel":2150,"displaystyle":2504},[895,39858,39859,39861,39863,39865,39867,39873],{},[895,39860],{},[1706,39862,1708],{},[898,39864,1683],{},[1706,39866,2447],{},[2489,39868,39869,39871],{},[898,39870,31291],{},[1706,39872,3197],{},[1706,39874,2505],{"separator":2504},[2358,39876,39877,39883],{},[2361,39878,39879],{},[4745,39880,39881],{"scriptlevel":2150,"displaystyle":2504},[898,39882,1683],{},[2361,39884,39885],{},[4745,39886,39887],{"scriptlevel":2150,"displaystyle":2504},[895,39888,39889,39891,39893,39895,39897,39899,39901],{},[895,39890],{},[1706,39892,1708],{},[898,39894,1683],{},[1706,39896,2140],{"stretchy":2139},[898,39898,28247],{},[1706,39900,2153],{"stretchy":2139},[1706,39902,2505],{"separator":2504},[4898,39904],{"width":9524},[1706,39906,2140],{"stretchy":2139},[2148,39908,39909],{},"7.7",[1706,39911,2153],{"stretchy":2139},[902,39913,39914],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,39916,39917,39918,1647,39920,1993,39937,1647,39940,1837],{},"jejímž řešením jsou ",[38,39919,32992],{},[883,39921,39923],{"className":39922},[886],[888,39924,39925],{"xmlns":890},[892,39926,39927,39935],{},[895,39928,39929],{},[2489,39930,39931,39933],{},[898,39932,28247],{},[898,39934,23410],{},[902,39936,33010],{"encoding":904},[38,39938,39939],{},"rovnovážná spotřeba",[883,39941,39943],{"className":39942},[886],[888,39944,39945],{"xmlns":890},[892,39946,39947,39955],{},[895,39948,39949],{},[2489,39950,39951,39953],{},[898,39952,1683],{},[898,39954,23410],{},[902,39956,33069],{"encoding":904},[198,39958,39960,39961],{"id":39959},"výpočet-yeye","Výpočet ",[883,39962,39964],{"className":39963},[886],[888,39965,39966],{"xmlns":890},[892,39967,39968,39976],{},[895,39969,39970],{},[2489,39971,39972,39974],{},[898,39973,28247],{},[898,39975,23410],{},[902,39977,33010],{"encoding":904},[724,39979,39980,39981,40004,40005,11771,40037],{},"Pro lineární spotřebu ",[883,39982,39984],{"className":39983},[886],[888,39985,39986],{"xmlns":890},[892,39987,39988,40002],{},[895,39989,39990,39992,39994,39996,39998,40000],{},[898,39991,1683],{},[1706,39993,1708],{},[898,39995,207],{},[898,39997,28247],{},[1706,39999,2447],{},[898,40001,2450],{},[902,40003,38016],{"encoding":904}," plyne z (7.7) rovnice ",[883,40006,40008],{"className":40007},[886],[888,40009,40010],{"xmlns":890},[892,40011,40012,40034],{},[895,40013,40014,40016,40018,40020,40022,40024,40026,40028],{},[898,40015,28247],{},[1706,40017,1708],{},[898,40019,207],{},[898,40021,28247],{},[1706,40023,2447],{},[898,40025,2450],{},[1706,40027,2447],{},[2489,40029,40030,40032],{},[898,40031,31291],{},[1706,40033,3197],{},[902,40035,40036],{"encoding":904},"Y = aY + b + I^*",[38,40038,40039],{},"redukovaný tvar",[724,40041,40042],{},[883,40043,40045],{"className":40044},[886],[888,40046,40047],{"xmlns":890},[892,40048,40049,40097],{},[895,40050,40051],{},[31939,40052,40053],{"notation":31941},[4745,40054,40055],{"scriptlevel":2150,"displaystyle":2139},[4745,40056,40057],{"scriptlevel":2150,"displaystyle":2139},[4745,40058,40059],{"scriptlevel":2150,"displaystyle":2504},[895,40060,40061,40063,40069,40071,40093,40095],{},[2415,40062,2799],{},[2489,40064,40065,40067],{},[898,40066,28247],{},[898,40068,23410],{},[1706,40070,1708],{},[2964,40072,40073,40085],{},[895,40074,40075,40077,40079],{},[898,40076,2450],{},[1706,40078,2447],{},[2489,40080,40081,40083],{},[898,40082,31291],{},[1706,40084,3197],{},[895,40086,40087,40089,40091],{},[2148,40088,2701],{},[1706,40090,1715],{},[898,40092,207],{},[898,40094,1837],{"mathvariant":2409},[2415,40096,2799],{},[902,40098,40099],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,40101,40103],{"id":40102},"příklad-73","Příklad 7.3",[724,40105,40106,40107,3484,40124,1993,40148,40174],{},"V modelu ",[883,40108,40110],{"className":40109},[886],[888,40111,40112],{"xmlns":890},[892,40113,40114,40122],{},[895,40115,40116,40118,40120],{},[898,40117,1683],{},[2415,40119,31397],{},[898,40121,31291],{},[902,40123,31402],{"encoding":904},[883,40125,40127],{"className":40126},[886],[888,40128,40129],{"xmlns":890},[892,40130,40131,40145],{},[895,40132,40133,40135,40137,40139,40141,40143],{},[898,40134,1683],{},[1706,40136,1708],{},[2148,40138,13775],{},[898,40140,28247],{},[1706,40142,2447],{},[2148,40144,7786],{},[902,40146,40147],{"encoding":904},"C = 0{,}6Y + 10",[883,40149,40151],{"className":40150},[886],[888,40152,40153],{"xmlns":890},[892,40154,40155,40171],{},[895,40156,40157,40159,40161,40163,40165],{},[898,40158,31291],{},[1706,40160,1708],{},[2148,40162,7156],{},[1706,40164,1708],{},[2489,40166,40167,40169],{},[898,40168,31291],{},[1706,40170,3197],{},[902,40172,40173],{"encoding":904},"I = 12 = I^*",". Soustava",[724,40176,40177],{},[883,40178,40180],{"className":40179},[886],[888,40181,40182],{"xmlns":890},[892,40183,40184,40240],{},[2354,40185,40186,40212],{"rowspacing":7556,"columnalign":7557,"columnspacing":3141},[2358,40187,40188,40194],{},[2361,40189,40190],{},[4745,40191,40192],{"scriptlevel":2150,"displaystyle":2504},[898,40193,28247],{},[2361,40195,40196],{},[4745,40197,40198],{"scriptlevel":2150,"displaystyle":2504},[895,40199,40200,40202,40204,40206,40208,40210],{},[895,40201],{},[1706,40203,1708],{},[898,40205,1683],{},[1706,40207,2447],{},[2148,40209,7156],{},[1706,40211,2505],{"separator":2504},[2358,40213,40214,40220],{},[2361,40215,40216],{},[4745,40217,40218],{"scriptlevel":2150,"displaystyle":2504},[898,40219,1683],{},[2361,40221,40222],{},[4745,40223,40224],{"scriptlevel":2150,"displaystyle":2504},[895,40225,40226,40228,40230,40232,40234,40236,40238],{},[895,40227],{},[1706,40229,1708],{},[2148,40231,13775],{},[898,40233,28247],{},[1706,40235,2447],{},[2148,40237,7786],{},[1706,40239,2505],{"separator":2504},[902,40241,40242],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,40244,40245,40246,1343,40268,40291,40292,1936],{},"má řešení ",[883,40247,40249],{"className":40248},[886],[888,40250,40251],{"xmlns":890},[892,40252,40253,40265],{},[895,40254,40255,40261,40263],{},[2489,40256,40257,40259],{},[898,40258,28247],{},[898,40260,23410],{},[1706,40262,1708],{},[2148,40264,13913],{},[902,40266,40267],{"encoding":904},"Y^E = 55",[883,40269,40271],{"className":40270},[886],[888,40272,40273],{"xmlns":890},[892,40274,40275,40288],{},[895,40276,40277,40283,40285],{},[2489,40278,40279,40281],{},[898,40280,1683],{},[898,40282,23410],{},[1706,40284,1708],{},[2148,40286,40287],{},"43",[902,40289,40290],{"encoding":904},"C^E = 43"," (a ",[883,40293,40295],{"className":40294},[886],[888,40296,40297],{"xmlns":890},[892,40298,40299,40311],{},[895,40300,40301,40307,40309],{},[2489,40302,40303,40305],{},[898,40304,14171],{},[898,40306,23410],{},[1706,40308,1708],{},[2148,40310,7156],{},[902,40312,40313],{"encoding":904},"S^E = 12",[724,40315,40316],{},[614,40317,40318,40319,40341,40342,5354,40363,40386,40387,1837],{},"Obrázek 7.5 — Přímky ",[883,40320,40322],{"className":40321},[886],[888,40323,40324],{"xmlns":890},[892,40325,40326,40338],{},[895,40327,40328,40330,40332,40334,40336],{},[898,40329,1683],{},[1706,40331,1708],{},[898,40333,28247],{},[1706,40335,1715],{},[2148,40337,7156],{},[902,40339,40340],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,40343,40345],{"className":40344},[886],[888,40346,40347],{"xmlns":890},[892,40348,40349,40361],{},[895,40350,40351,40353,40355,40357,40359],{},[898,40352,28247],{},[1706,40354,1708],{},[898,40356,1683],{},[1706,40358,2447],{},[898,40360,31291],{},[902,40362,33851],{"encoding":904},[883,40364,40366],{"className":40365},[886],[888,40367,40368],{"xmlns":890},[892,40369,40370,40384],{},[895,40371,40372,40374,40376,40378,40380,40382],{},[898,40373,1683],{},[1706,40375,1708],{},[2148,40377,13775],{},[898,40379,28247],{},[1706,40381,2447],{},[2148,40383,7786],{},[902,40385,40147],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,40388,40390],{"className":40389},[886],[888,40391,40392],{"xmlns":890},[892,40393,40394,40426],{},[895,40395,40396,40398,40404,40406,40412,40414,40416,40418,40420,40422,40424],{},[1706,40397,21693],{"stretchy":2139},[2489,40399,40400,40402],{},[898,40401,28247],{},[898,40403,23410],{},[1706,40405,2505],{"separator":2504},[2489,40407,40408,40410],{},[898,40409,1683],{},[898,40411,23410],{},[1706,40413,21708],{"stretchy":2139},[1706,40415,1708],{},[1706,40417,21693],{"stretchy":2139},[2148,40419,13913],{},[1706,40421,2505],{"separator":2504},[2148,40423,40287],{},[1706,40425,21708],{"stretchy":2139},[902,40427,40428],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,40430,40431,40434,40435,40452,40453,1837],{},[38,40432,40433],{},"Komentář k přechodu."," Model ",[883,40436,40438],{"className":40437},[886],[888,40439,40440],{"xmlns":890},[892,40441,40442,40450],{},[895,40443,40444,40446,40448],{},[898,40445,1683],{},[2415,40447,31397],{},[898,40449,31291],{},[902,40451,31402],{"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 ",[38,40454,40455,40456],{},"model ",[883,40457,40459],{"className":40458},[886],[888,40460,40461],{"xmlns":890},[892,40462,40463,40475],{},[895,40464,40465,40467,40469,40471,40473],{},[898,40466,1683],{},[2415,40468,31397],{},[898,40470,31291],{},[2415,40472,31397],{},[898,40474,31220],{},[902,40476,37317],{"encoding":904},[115,40478,40480],{"id":40479},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,40482,39711],{"id":40483},"zadání-modelu-1",[724,40485,40486,40487,3570,40504,1647,40507,2314,40520,40523],{},"Rozšíření modelu ",[883,40488,40490],{"className":40489},[886],[888,40491,40492],{"xmlns":890},[892,40493,40494,40502],{},[895,40495,40496,40498,40500],{},[898,40497,1683],{},[2415,40499,31397],{},[898,40501,31291],{},[902,40503,31402],{"encoding":904},[38,40505,40506],{},"vládní výdaje",[883,40508,40510],{"className":40509},[886],[888,40511,40512],{"xmlns":890},[892,40513,40514,40518],{},[895,40515,40516],{},[898,40517,31220],{},[902,40519,31220],{"encoding":904},[614,40521,40522],{},"government expenditure","). Podmínka rovnováhy:",[724,40525,40526],{},[883,40527,40529],{"className":40528},[886],[888,40530,40531],{"xmlns":890},[892,40532,40533,40560],{},[895,40534,40535,40537,40539,40541,40543,40545,40547,40549,40551,40553,40555,40558],{},[898,40536,28247],{},[1706,40538,1708],{},[898,40540,1683],{},[1706,40542,2447],{},[898,40544,31291],{},[1706,40546,2447],{},[898,40548,31220],{},[898,40550,1837],{"mathvariant":2409},[4898,40552],{"width":9524},[1706,40554,2140],{"stretchy":2139},[2148,40556,40557],{},"7.8",[1706,40559,2153],{"stretchy":2139},[902,40561,40562],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,40564,40565,40566,1647,40569,2314,40582,40585],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,40567,40568],{},"zdaněním domácností",[883,40570,40572],{"className":40571},[886],[888,40573,40574],{"xmlns":890},[892,40575,40576,40580],{},[895,40577,40578],{},[898,40579,1659],{},[902,40581,1659],{"encoding":904},[614,40583,40584],{},"taxation","). Zdanění bývá:",[120,40587,40588,40621,40646],{},[123,40589,40590,40591,2505],{},"úměrné důchodu: ",[883,40592,40594],{"className":40593},[886],[888,40595,40596],{"xmlns":890},[892,40597,40598,40618],{},[895,40599,40600,40602,40604,40606,40608,40610,40612,40614,40616],{},[898,40601,1659],{},[1706,40603,1708],{},[898,40605,1659],{},[1706,40607,2140],{"stretchy":2139},[898,40609,28247],{},[1706,40611,2153],{"stretchy":2139},[1706,40613,1708],{},[898,40615,37952],{},[898,40617,28247],{},[902,40619,40620],{"encoding":904},"T = T(Y) = tY",[123,40622,40623,40624,2505],{},"fixní: ",[883,40625,40627],{"className":40626},[886],[888,40628,40629],{"xmlns":890},[892,40630,40631,40643],{},[895,40632,40633,40635,40637],{},[898,40634,1659],{},[1706,40636,1708],{},[2489,40638,40639,40641],{},[898,40640,1659],{},[1706,40642,3197],{},[902,40644,40645],{"encoding":904},"T = T^*",[123,40647,40648,40649,15842,40677,1837],{},"kombinované: ",[883,40650,40652],{"className":40651},[886],[888,40653,40654],{"xmlns":890},[892,40655,40656,40674],{},[895,40657,40658,40660,40662,40668,40670,40672],{},[898,40659,1659],{},[1706,40661,1708],{},[2489,40663,40664,40666],{},[898,40665,1659],{},[1706,40667,3197],{},[1706,40669,2447],{},[898,40671,37952],{},[898,40673,28247],{},[902,40675,40676],{"encoding":904},"T = T^* + tY",[883,40678,40680],{"className":40679},[886],[888,40681,40682],{"xmlns":890},[892,40683,40684,40696],{},[895,40685,40686,40688,40690,40692,40694],{},[2148,40687,2150],{},[1706,40689,26807],{},[898,40691,37952],{},[1706,40693,2539],{},[2148,40695,2701],{},[902,40697,40698],{"encoding":904},"0 \\le t \u003C 1",[1636,40700,40701],{},[724,40702,40703,40705,40706,40727,40728,40731,40732,40745,40746,5354,40772,1647,40775,40801,40802,40830,40831,1993,40844,40862],{},[883,40704,9276],{}," Pozor na disponibilní důchod\nV modelu ",[883,40707,40709],{"className":40708},[886],[888,40710,40711],{"xmlns":890},[892,40712,40713,40725],{},[895,40714,40715,40717,40719,40721,40723],{},[898,40716,1683],{},[2415,40718,31397],{},[898,40720,31291],{},[2415,40722,31397],{},[898,40724,31220],{},[902,40726,37317],{"encoding":904}," je nutné ",[38,40729,40730],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,40733,40735],{"className":40734},[886],[888,40736,40737],{"xmlns":890},[892,40738,40739,40743],{},[895,40740,40741],{},[898,40742,28247],{},[902,40744,28247],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,40747,40749],{"className":40748},[886],[888,40750,40751],{"xmlns":890},[892,40752,40753,40769],{},[895,40754,40755,40757,40759,40761,40763,40765,40767],{},[898,40756,28247],{},[1706,40758,1708],{},[898,40760,1683],{},[1706,40762,2447],{},[898,40764,31291],{},[1706,40766,2447],{},[898,40768,31220],{},[902,40770,40771],{"encoding":904},"Y = C + I + G",[38,40773,40774],{},"disponibilní důchod",[883,40776,40778],{"className":40777},[886],[888,40779,40780],{"xmlns":890},[892,40781,40782,40798],{},[895,40783,40784,40790,40792,40794,40796],{},[2142,40785,40786,40788],{},[898,40787,28247],{},[898,40789,2334],{},[1706,40791,1708],{},[898,40793,28247],{},[1706,40795,1715],{},[898,40797,1659],{},[902,40799,40800],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,40803,40805],{"className":40804},[886],[888,40806,40807],{"xmlns":890},[892,40808,40809,40827],{},[895,40810,40811,40813,40815,40817,40819,40825],{},[898,40812,1683],{},[1706,40814,1708],{},[898,40816,1683],{},[1706,40818,2140],{"stretchy":2139},[2142,40820,40821,40823],{},[898,40822,28247],{},[898,40824,2334],{},[1706,40826,2153],{"stretchy":2139},[902,40828,40829],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,40832,40834],{"className":40833},[886],[888,40835,40836],{"xmlns":890},[892,40837,40838,40842],{},[895,40839,40840],{},[898,40841,28247],{},[902,40843,28247],{"encoding":904},[883,40845,40847],{"className":40846},[886],[888,40848,40849],{"xmlns":890},[892,40850,40851,40859],{},[895,40852,40853],{},[2142,40854,40855,40857],{},[898,40856,28247],{},[898,40858,2334],{},[902,40860,40861],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,40864,40865,2314,40868,2153],{},[38,40866,40867],{},"Disponibilní důchod",[614,40869,40870],{},"disposable income",[724,40872,40873],{},[883,40874,40876],{"className":40875},[886],[888,40877,40878],{"xmlns":890},[892,40879,40880,40896],{},[895,40881,40882,40888,40890,40892,40894],{},[2142,40883,40884,40886],{},[898,40885,28247],{},[898,40887,2334],{},[1706,40889,1708],{},[898,40891,28247],{},[1706,40893,1715],{},[898,40895,1659],{},[902,40897,40800],{"encoding":904},[724,40899,40900,40901,1837],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,40902,40904],{"className":40903},[886],[888,40905,40906],{"xmlns":890},[892,40907,40908,40926],{},[895,40909,40910,40912,40914,40916,40918,40924],{},[898,40911,1683],{},[1706,40913,1708],{},[898,40915,1683],{},[1706,40917,2140],{"stretchy":2139},[2142,40919,40920,40922],{},[898,40921,28247],{},[898,40923,2334],{},[1706,40925,2153],{"stretchy":2139},[902,40927,40829],{"encoding":904},[198,40929,39781],{"id":40930},"soustava-rovnic-1",[724,40932,40933,40934,1343,40955,40977,40978,4288],{},"Pro pevně zadané ",[883,40935,40937],{"className":40936},[886],[888,40938,40939],{"xmlns":890},[892,40940,40941,40953],{},[895,40942,40943,40945,40947],{},[898,40944,31291],{},[1706,40946,1708],{},[2489,40948,40949,40951],{},[898,40950,31291],{},[1706,40952,3197],{},[902,40954,31302],{"encoding":904},[883,40956,40958],{"className":40957},[886],[888,40959,40960],{"xmlns":890},[892,40961,40962,40974],{},[895,40963,40964,40966,40968],{},[898,40965,31220],{},[1706,40967,1708],{},[2489,40969,40970,40972],{},[898,40971,31220],{},[1706,40973,3197],{},[902,40975,40976],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,40979,40981],{"className":40980},[886],[888,40982,40983],{"xmlns":890},[892,40984,40985,41005],{},[895,40986,40987,40989,40991,40993,40995,41001,41003],{},[898,40988,28247],{},[1706,40990,2505],{"separator":2504},[898,40992,1683],{},[1706,40994,2505],{"separator":2504},[2142,40996,40997,40999],{},[898,40998,28247],{},[898,41000,2334],{},[1706,41002,2505],{"separator":2504},[898,41004,1659],{},[902,41006,41007],{"encoding":904},"Y, C, Y_D, T",[724,41009,41010],{},[883,41011,41013],{"className":41012},[886],[888,41014,41015],{"xmlns":890},[892,41016,41017,41158],{},[895,41018,41019,41149,41151,41153,41156],{},[2354,41020,41021,41059,41087,41119],{"rowspacing":7556,"columnalign":7557,"columnspacing":3141},[2358,41022,41023,41029],{},[2361,41024,41025],{},[4745,41026,41027],{"scriptlevel":2150,"displaystyle":2504},[898,41028,28247],{},[2361,41030,41031],{},[4745,41032,41033],{"scriptlevel":2150,"displaystyle":2504},[895,41034,41035,41037,41039,41041,41043,41049,41051,41057],{},[895,41036],{},[1706,41038,1708],{},[898,41040,1683],{},[1706,41042,2447],{},[2489,41044,41045,41047],{},[898,41046,31291],{},[1706,41048,3197],{},[1706,41050,2447],{},[2489,41052,41053,41055],{},[898,41054,31220],{},[1706,41056,3197],{},[1706,41058,2505],{"separator":2504},[2358,41060,41061,41067],{},[2361,41062,41063],{},[4745,41064,41065],{"scriptlevel":2150,"displaystyle":2504},[898,41066,1659],{},[2361,41068,41069],{},[4745,41070,41071],{"scriptlevel":2150,"displaystyle":2504},[895,41072,41073,41075,41077,41079,41081,41083,41085],{},[895,41074],{},[1706,41076,1708],{},[898,41078,1659],{},[1706,41080,2140],{"stretchy":2139},[898,41082,28247],{},[1706,41084,2153],{"stretchy":2139},[1706,41086,2505],{"separator":2504},[2358,41088,41089,41095],{},[2361,41090,41091],{},[4745,41092,41093],{"scriptlevel":2150,"displaystyle":2504},[898,41094,1683],{},[2361,41096,41097],{},[4745,41098,41099],{"scriptlevel":2150,"displaystyle":2504},[895,41100,41101,41103,41105,41107,41109,41115,41117],{},[895,41102],{},[1706,41104,1708],{},[898,41106,1683],{},[1706,41108,2140],{"stretchy":2139},[2142,41110,41111,41113],{},[898,41112,28247],{},[898,41114,2334],{},[1706,41116,2153],{"stretchy":2139},[1706,41118,2505],{"separator":2504},[2358,41120,41121,41131],{},[2361,41122,41123],{},[4745,41124,41125],{"scriptlevel":2150,"displaystyle":2504},[2142,41126,41127,41129],{},[898,41128,28247],{},[898,41130,2334],{},[2361,41132,41133],{},[4745,41134,41135],{"scriptlevel":2150,"displaystyle":2504},[895,41136,41137,41139,41141,41143,41145,41147],{},[895,41138],{},[1706,41140,1708],{},[898,41142,28247],{},[1706,41144,1715],{},[898,41146,1659],{},[1706,41148,2505],{"separator":2504},[4898,41150],{"width":9524},[1706,41152,2140],{"stretchy":2139},[2148,41154,41155],{},"7.9",[1706,41157,2153],{"stretchy":2139},[902,41159,41160],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,41162,41163,41164,41208,41209,1837],{},"s řešeními ",[883,41165,41167],{"className":41166},[886],[888,41168,41169],{"xmlns":890},[892,41170,41171,41205],{},[895,41172,41173,41179,41181,41187,41189,41195,41197],{},[2489,41174,41175,41177],{},[898,41176,28247],{},[898,41178,23410],{},[1706,41180,2505],{"separator":2504},[2489,41182,41183,41185],{},[898,41184,1683],{},[898,41186,23410],{},[1706,41188,2505],{"separator":2504},[2489,41190,41191,41193],{},[898,41192,1659],{},[898,41194,23410],{},[1706,41196,2505],{"separator":2504},[28285,41198,41199,41201,41203],{},[898,41200,28247],{},[898,41202,2334],{},[898,41204,23410],{},[902,41206,41207],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,41210,41212],{"className":41211},[886],[888,41213,41214],{"xmlns":890},[892,41215,41216,41242],{},[895,41217,41218,41224,41226,41234,41236],{},[2489,41219,41220,41222],{},[898,41221,14171],{},[898,41223,23410],{},[1706,41225,1708],{},[28285,41227,41228,41230,41232],{},[898,41229,28247],{},[898,41231,2334],{},[898,41233,23410],{},[1706,41235,1715],{},[2489,41237,41238,41240],{},[898,41239,1683],{},[898,41241,23410],{},[902,41243,41244],{"encoding":904},"S^E = Y_D^E - C^E",[1636,41246,41247,41252],{},[724,41248,41249,41251],{},[883,41250,12314],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,41253,41254,41277,41360,41415,41505],{},[123,41255,41256,41259,41260,1837],{},[38,41257,41258],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,41261,41263],{"className":41262},[886],[888,41264,41265],{"xmlns":890},[892,41266,41267,41275],{},[895,41268,41269],{},[2142,41270,41271,41273],{},[898,41272,28247],{},[898,41274,2334],{},[902,41276,40861],{"encoding":904},[123,41278,41279,41328,41329,41346,41347,1837],{},[38,41280,41281,41282,41302,41303],{},"Dosaď ",[883,41283,41285],{"className":41284},[886],[888,41286,41287],{"xmlns":890},[892,41288,41289,41299],{},[895,41290,41291,41293,41295,41297],{},[898,41292,1659],{},[1706,41294,2140],{"stretchy":2139},[898,41296,28247],{},[1706,41298,2153],{"stretchy":2139},[902,41300,41301],{"encoding":904},"T(Y)"," do ",[883,41304,41306],{"className":41305},[886],[888,41307,41308],{"xmlns":890},[892,41309,41310,41326],{},[895,41311,41312,41318,41320,41322,41324],{},[2142,41313,41314,41316],{},[898,41315,28247],{},[898,41317,2334],{},[1706,41319,1708],{},[898,41321,28247],{},[1706,41323,1715],{},[898,41325,1659],{},[902,41327,40800],{"encoding":904}," — dostaneš ",[883,41330,41332],{"className":41331},[886],[888,41333,41334],{"xmlns":890},[892,41335,41336,41344],{},[895,41337,41338],{},[2142,41339,41340,41342],{},[898,41341,28247],{},[898,41343,2334],{},[902,41345,40861],{"encoding":904}," jako lineární funkci ",[883,41348,41350],{"className":41349},[886],[888,41351,41352],{"xmlns":890},[892,41353,41354,41358],{},[895,41355,41356],{},[898,41357,28247],{},[902,41359,28247],{"encoding":904},[123,41361,41362,41328,41389,41346,41402,1837],{},[38,41363,41281,41364,41388],{},[883,41365,41367],{"className":41366},[886],[888,41368,41369],{"xmlns":890},[892,41370,41371,41385],{},[895,41372,41373,41379,41381,41383],{},[2142,41374,41375,41377],{},[898,41376,28247],{},[898,41378,2334],{},[1706,41380,2140],{"stretchy":2139},[898,41382,28247],{},[1706,41384,2153],{"stretchy":2139},[902,41386,41387],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,41390,41392],{"className":41391},[886],[888,41393,41394],{"xmlns":890},[892,41395,41396,41400],{},[895,41397,41398],{},[898,41399,1683],{},[902,41401,1683],{"encoding":904},[883,41403,41405],{"className":41404},[886],[888,41406,41407],{"xmlns":890},[892,41408,41409,41413],{},[895,41410,41411],{},[898,41412,28247],{},[902,41414,28247],{"encoding":904},[123,41416,41417,1647,41439,41473,41474,41487,41488,1837],{},[38,41418,41281,41419,41438],{},[883,41420,41422],{"className":41421},[886],[888,41423,41424],{"xmlns":890},[892,41425,41426,41436],{},[895,41427,41428,41430,41432,41434],{},[898,41429,1683],{},[1706,41431,2140],{"stretchy":2139},[898,41433,28247],{},[1706,41435,2153],{"stretchy":2139},[902,41437,33323],{"encoding":904}," do podmínky rovnováhy",[883,41440,41442],{"className":41441},[886],[888,41443,41444],{"xmlns":890},[892,41445,41446,41470],{},[895,41447,41448,41450,41452,41454,41456,41462,41464],{},[898,41449,28247],{},[1706,41451,1708],{},[898,41453,1683],{},[1706,41455,2447],{},[2489,41457,41458,41460],{},[898,41459,31291],{},[1706,41461,3197],{},[1706,41463,2447],{},[2489,41465,41466,41468],{},[898,41467,31220],{},[1706,41469,3197],{},[902,41471,41472],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,41475,41477],{"className":41476},[886],[888,41478,41479],{"xmlns":890},[892,41480,41481,41485],{},[895,41482,41483],{},[898,41484,28247],{},[902,41486,28247],{"encoding":904},", odtud ",[883,41489,41491],{"className":41490},[886],[888,41492,41493],{"xmlns":890},[892,41494,41495,41503],{},[895,41496,41497],{},[2489,41498,41499,41501],{},[898,41500,28247],{},[898,41502,23410],{},[902,41504,33010],{"encoding":904},[123,41506,41507,41510,41511,1343,41529,1343,41549,1343,41566,1837],{},[38,41508,41509],{},"Zpětným dosazením"," dopočítej ",[883,41512,41514],{"className":41513},[886],[888,41515,41516],{"xmlns":890},[892,41517,41518,41526],{},[895,41519,41520],{},[2489,41521,41522,41524],{},[898,41523,1659],{},[898,41525,23410],{},[902,41527,41528],{"encoding":904},"T^E",[883,41530,41532],{"className":41531},[886],[888,41533,41534],{"xmlns":890},[892,41535,41536,41546],{},[895,41537,41538],{},[28285,41539,41540,41542,41544],{},[898,41541,28247],{},[898,41543,2334],{},[898,41545,23410],{},[902,41547,41548],{"encoding":904},"Y_D^E",[883,41550,41552],{"className":41551},[886],[888,41553,41554],{"xmlns":890},[892,41555,41556,41564],{},[895,41557,41558],{},[2489,41559,41560,41562],{},[898,41561,1683],{},[898,41563,23410],{},[902,41565,33069],{"encoding":904},[883,41567,41569],{"className":41568},[886],[888,41570,41571],{"xmlns":890},[892,41572,41573,41581],{},[895,41574,41575],{},[2489,41576,41577,41579],{},[898,41578,14171],{},[898,41580,23410],{},[902,41582,41583],{"encoding":904},"S^E",[198,41585,41587],{"id":41586},"příklad-74","Příklad 7.4",[724,41589,40106,41590,41611,41612,1343,41642,1343,41666,1343,41688,41710],{},[883,41591,41593],{"className":41592},[886],[888,41594,41595],{"xmlns":890},[892,41596,41597,41609],{},[895,41598,41599,41601,41603,41605,41607],{},[898,41600,1683],{},[2415,41602,31397],{},[898,41604,31291],{},[2415,41606,31397],{},[898,41608,31220],{},[902,41610,37317],{"encoding":904}," jsou dány ",[883,41613,41615],{"className":41614},[886],[888,41616,41617],{"xmlns":890},[892,41618,41619,41639],{},[895,41620,41621,41623,41625,41627,41629,41635,41637],{},[898,41622,1683],{},[1706,41624,1708],{},[2148,41626,13489],{},[2415,41628,2799],{},[2142,41630,41631,41633],{},[898,41632,28247],{},[898,41634,2334],{},[1706,41636,2447],{},[2148,41638,25033],{},[902,41640,41641],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,41643,41645],{"className":41644},[886],[888,41646,41647],{"xmlns":890},[892,41648,41649,41663],{},[895,41650,41651,41653,41655,41657,41659,41661],{},[898,41652,1659],{},[1706,41654,1708],{},[2148,41656,15204],{},[898,41658,28247],{},[1706,41660,2447],{},[2148,41662,2748],{},[902,41664,41665],{"encoding":904},"T = 0{,}2Y + 25",[883,41667,41669],{"className":41668},[886],[888,41670,41671],{"xmlns":890},[892,41672,41673,41685],{},[895,41674,41675,41681,41683],{},[2489,41676,41677,41679],{},[898,41678,31291],{},[1706,41680,3197],{},[1706,41682,1708],{},[2148,41684,34145],{},[902,41686,41687],{"encoding":904},"I^* = 35",[883,41689,41691],{"className":41690},[886],[888,41692,41693],{"xmlns":890},[892,41694,41695,41707],{},[895,41696,41697,41703,41705],{},[2489,41698,41699,41701],{},[898,41700,31220],{},[1706,41702,3197],{},[1706,41704,1708],{},[2148,41706,3369],{},[902,41708,41709],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,41712,41713],{},[883,41714,41716],{"className":41715},[886],[888,41717,41718],{"xmlns":890},[892,41719,41720,41844],{},[2354,41721,41722,41752,41780,41814],{"rowspacing":7556,"columnalign":7557,"columnspacing":3141},[2358,41723,41724,41730],{},[2361,41725,41726],{},[4745,41727,41728],{"scriptlevel":2150,"displaystyle":2504},[898,41729,28247],{},[2361,41731,41732],{},[4745,41733,41734],{"scriptlevel":2150,"displaystyle":2504},[895,41735,41736,41738,41740,41742,41744,41746,41748,41750],{},[895,41737],{},[1706,41739,1708],{},[898,41741,1683],{},[1706,41743,2447],{},[2148,41745,34145],{},[1706,41747,2447],{},[2148,41749,3369],{},[1706,41751,2505],{"separator":2504},[2358,41753,41754,41760],{},[2361,41755,41756],{},[4745,41757,41758],{"scriptlevel":2150,"displaystyle":2504},[898,41759,1659],{},[2361,41761,41762],{},[4745,41763,41764],{"scriptlevel":2150,"displaystyle":2504},[895,41765,41766,41768,41770,41772,41774,41776,41778],{},[895,41767],{},[1706,41769,1708],{},[2148,41771,15204],{},[898,41773,28247],{},[1706,41775,2447],{},[2148,41777,2748],{},[1706,41779,2505],{"separator":2504},[2358,41781,41782,41788],{},[2361,41783,41784],{},[4745,41785,41786],{"scriptlevel":2150,"displaystyle":2504},[898,41787,1683],{},[2361,41789,41790],{},[4745,41791,41792],{"scriptlevel":2150,"displaystyle":2504},[895,41793,41794,41796,41798,41800,41802,41808,41810,41812],{},[895,41795],{},[1706,41797,1708],{},[2148,41799,13489],{},[2415,41801,2799],{},[2142,41803,41804,41806],{},[898,41805,28247],{},[898,41807,2334],{},[1706,41809,2447],{},[2148,41811,25033],{},[1706,41813,2505],{"separator":2504},[2358,41815,41816,41826],{},[2361,41817,41818],{},[4745,41819,41820],{"scriptlevel":2150,"displaystyle":2504},[2142,41821,41822,41824],{},[898,41823,28247],{},[898,41825,2334],{},[2361,41827,41828],{},[4745,41829,41830],{"scriptlevel":2150,"displaystyle":2504},[895,41831,41832,41834,41836,41838,41840,41842],{},[895,41833],{},[1706,41835,1708],{},[898,41837,28247],{},[1706,41839,1715],{},[898,41841,1659],{},[898,41843,1837],{"mathvariant":2409},[902,41845,41846],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,41848,41849,41851,41852,41906,41907,41953,41954,4288],{},[38,41850,2615],{}," Z definice ",[883,41853,41855],{"className":41854},[886],[888,41856,41857],{"xmlns":890},[892,41858,41859,41903],{},[895,41860,41861,41867,41869,41871,41873,41875,41877,41879,41881,41883,41885,41887,41889,41891,41893,41895,41897,41899,41901],{},[2142,41862,41863,41865],{},[898,41864,28247],{},[898,41866,2334],{},[1706,41868,1708],{},[898,41870,28247],{},[1706,41872,1715],{},[898,41874,1659],{},[1706,41876,1708],{},[898,41878,28247],{},[1706,41880,1715],{},[1706,41882,2140],{"stretchy":2139},[2148,41884,15204],{},[898,41886,28247],{},[1706,41888,2447],{},[2148,41890,2748],{},[1706,41892,2153],{"stretchy":2139},[1706,41894,1708],{},[2148,41896,33696],{},[898,41898,28247],{},[1706,41900,1715],{},[2148,41902,2748],{},[902,41904,41905],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,41908,41910],{"className":41909},[886],[888,41911,41912],{"xmlns":890},[892,41913,41914,41950],{},[895,41915,41916,41918,41920,41922,41924,41926,41928,41930,41932,41934,41936,41938,41940,41943,41945,41947],{},[898,41917,1683],{},[1706,41919,1708],{},[2148,41921,13489],{},[1706,41923,2140],{"stretchy":2139},[2148,41925,33696],{},[898,41927,28247],{},[1706,41929,1715],{},[2148,41931,2748],{},[1706,41933,2153],{"stretchy":2139},[1706,41935,2447],{},[2148,41937,25033],{},[1706,41939,1708],{},[2148,41941,41942],{},"0,72",[898,41944,28247],{},[1706,41946,2447],{},[2148,41948,41949],{},"47,5",[902,41951,41952],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,41955,41957],{"className":41956},[886],[888,41958,41959],{"xmlns":890},[892,41960,41961,41979],{},[895,41962,41963,41965,41967,41969,41971,41973,41975,41977],{},[898,41964,28247],{},[1706,41966,1708],{},[2148,41968,41942],{},[898,41970,28247],{},[1706,41972,2447],{},[2148,41974,41949],{},[1706,41976,2447],{},[2148,41978,13913],{},[902,41980,41981],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,41983,41984],{},[883,41985,41987],{"className":41986},[886],[888,41988,41989],{"xmlns":890},[892,41990,41991,42031],{},[895,41992,41993,41996,41998,42000,42003,42005,42007,42009,42015,42017,42026,42028],{},[2148,41994,41995],{},"0,28",[898,41997,28247],{},[1706,41999,1708],{},[2148,42001,42002],{},"102,5",[2415,42004,3852],{},[1706,42006,34115],{},[2415,42008,3852],{},[2489,42010,42011,42013],{},[898,42012,28247],{},[898,42014,23410],{},[1706,42016,1708],{},[4745,42018,42019],{"scriptlevel":2150,"displaystyle":2139},[2964,42020,42021,42024],{},[2148,42022,42023],{},"5125",[2148,42025,12859],{},[1706,42027,7883],{},[2148,42029,42030],{},"366,071.",[902,42032,42033],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,42035,42036],{},"Rovnovážné veličiny:",[120,42038,42039,42074,42126,42180,42228],{},[123,42040,42041,2505],{},[883,42042,42044],{"className":42043},[886],[888,42045,42046],{"xmlns":890},[892,42047,42048,42071],{},[895,42049,42050,42056,42058,42066,42068],{},[2489,42051,42052,42054],{},[898,42053,28247],{},[898,42055,23410],{},[1706,42057,1708],{},[4745,42059,42060],{"scriptlevel":2150,"displaystyle":2139},[2964,42061,42062,42064],{},[2148,42063,42023],{},[2148,42065,12859],{},[1706,42067,7883],{},[2148,42069,42070],{},"366,071",[902,42072,42073],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,42075,42076,2505],{},[883,42077,42079],{"className":42078},[886],[888,42080,42081],{"xmlns":890},[892,42082,42083,42123],{},[895,42084,42085,42091,42093,42095,42097,42103,42105,42107,42109,42118,42120],{},[2489,42086,42087,42089],{},[898,42088,1659],{},[898,42090,23410],{},[1706,42092,1708],{},[2148,42094,15204],{},[2415,42096,2799],{},[2489,42098,42099,42101],{},[898,42100,28247],{},[898,42102,23410],{},[1706,42104,2447],{},[2148,42106,2748],{},[1706,42108,1708],{},[4745,42110,42111],{"scriptlevel":2150,"displaystyle":2139},[2964,42112,42113,42116],{},[2148,42114,42115],{},"1375",[2148,42117,12859],{},[1706,42119,7883],{},[2148,42121,42122],{},"98,214",[902,42124,42125],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,42127,42128,2505],{},[883,42129,42131],{"className":42130},[886],[888,42132,42133],{"xmlns":890},[892,42134,42135,42177],{},[895,42136,42137,42145,42147,42153,42155,42161,42163,42172,42174],{},[28285,42138,42139,42141,42143],{},[898,42140,28247],{},[898,42142,2334],{},[898,42144,23410],{},[1706,42146,1708],{},[2489,42148,42149,42151],{},[898,42150,28247],{},[898,42152,23410],{},[1706,42154,1715],{},[2489,42156,42157,42159],{},[898,42158,1659],{},[898,42160,23410],{},[1706,42162,1708],{},[4745,42164,42165],{"scriptlevel":2150,"displaystyle":2139},[2964,42166,42167,42170],{},[2148,42168,42169],{},"3750",[2148,42171,12859],{},[1706,42173,7883],{},[2148,42175,42176],{},"267,857",[902,42178,42179],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,42181,42182,2505],{},[883,42183,42185],{"className":42184},[886],[888,42186,42187],{"xmlns":890},[892,42188,42189,42225],{},[895,42190,42191,42197,42199,42205,42207,42209,42211,42220,42222],{},[2489,42192,42193,42195],{},[898,42194,1683],{},[898,42196,23410],{},[1706,42198,1708],{},[2489,42200,42201,42203],{},[898,42202,28247],{},[898,42204,23410],{},[1706,42206,1715],{},[2148,42208,13913],{},[1706,42210,1708],{},[4745,42212,42213],{"scriptlevel":2150,"displaystyle":2139},[2964,42214,42215,42218],{},[2148,42216,42217],{},"4355",[2148,42219,12859],{},[1706,42221,7883],{},[2148,42223,42224],{},"311,071",[902,42226,42227],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,42229,42230,42286],{},[883,42231,42233],{"className":42232},[886],[888,42234,42235],{"xmlns":890},[892,42236,42237,42283],{},[895,42238,42239,42245,42247,42255,42257,42263,42265,42267,42276,42278,42280],{},[2489,42240,42241,42243],{},[898,42242,14171],{},[898,42244,23410],{},[1706,42246,1708],{},[28285,42248,42249,42251,42253],{},[898,42250,28247],{},[898,42252,2334],{},[898,42254,23410],{},[1706,42256,1715],{},[2489,42258,42259,42261],{},[898,42260,1683],{},[898,42262,23410],{},[1706,42264,1708],{},[1706,42266,1715],{},[4745,42268,42269],{"scriptlevel":2150,"displaystyle":2139},[2964,42270,42271,42274],{},[2148,42272,42273],{},"605",[2148,42275,12859],{},[1706,42277,7883],{},[1706,42279,1715],{},[2148,42281,42282],{},"43,214",[902,42284,42285],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,42288,42289,40434,42291,42312,42313,42316,42317,42339,42340,1837],{},[38,42290,40433],{},[883,42292,42294],{"className":42293},[886],[888,42295,42296],{"xmlns":890},[892,42297,42298,42310],{},[895,42299,42300,42302,42304,42306,42308],{},[898,42301,1683],{},[2415,42303,31397],{},[898,42305,31291],{},[2415,42307,31397],{},[898,42309,31220],{},[902,42311,37317],{"encoding":904}," stále uvažuje ",[38,42314,42315],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,42318,42320],{"className":42319},[886],[888,42321,42322],{"xmlns":890},[892,42323,42324,42336],{},[895,42325,42326,42328,42330,42332,42334],{},[898,42327,31427],{},[1706,42329,1708],{},[898,42331,10315],{},[1706,42333,1715],{},[898,42335,1742],{},[902,42337,42338],{"encoding":904},"X = B - M"," dává ",[38,42341,40455,42342],{},[883,42343,42345],{"className":42344},[886],[888,42346,42347],{"xmlns":890},[892,42348,42349,42365],{},[895,42350,42351,42353,42355,42357,42359,42361,42363],{},[898,42352,1683],{},[2415,42354,31397],{},[898,42356,31291],{},[2415,42358,31397],{},[898,42360,31220],{},[2415,42362,31397],{},[898,42364,31427],{},[902,42366,31430],{"encoding":904},[115,42368,42370],{"id":42369},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,42372,39711],{"id":42373},"zadání-modelu-2",[724,42375,42376,42377,1647,42380,15842,42401,42414,42415,5354,42418,42431],{},"Rozšíření o ",[38,42378,42379],{},"čistý export",[883,42381,42383],{"className":42382},[886],[888,42384,42385],{"xmlns":890},[892,42386,42387,42399],{},[895,42388,42389,42391,42393,42395,42397],{},[898,42390,31427],{},[1706,42392,1708],{},[898,42394,10315],{},[1706,42396,1715],{},[898,42398,1742],{},[902,42400,42338],{"encoding":904},[883,42402,42404],{"className":42403},[886],[888,42405,42406],{"xmlns":890},[892,42407,42408,42412],{},[895,42409,42410],{},[898,42411,10315],{},[902,42413,10315],{"encoding":904}," je hrubý export (",[614,42416,42417],{},"brutto export",[883,42419,42421],{"className":42420},[886],[888,42422,42423],{"xmlns":890},[892,42424,42425,42429],{},[895,42426,42427],{},[898,42428,1742],{},[902,42430,1742],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,42433,42434],{},[883,42435,42437],{"className":42436},[886],[888,42438,42439],{"xmlns":890},[892,42440,42441,42461],{},[895,42442,42443,42445,42447,42449,42451,42457,42459],{},[898,42444,1742],{},[1706,42446,1708],{},[898,42448,1742],{},[1706,42450,2140],{"stretchy":2139},[2142,42452,42453,42455],{},[898,42454,28247],{},[898,42456,2334],{},[1706,42458,2153],{"stretchy":2139},[898,42460,1837],{"mathvariant":2409},[902,42462,42463],{"encoding":904},"M = M(Y_D).",[724,42465,42466],{},"Podmínka rovnováhy:",[724,42468,42469],{},[883,42470,42472],{"className":42471},[886],[888,42473,42474],{"xmlns":890},[892,42475,42476,42513],{},[895,42477,42478,42480,42482,42484,42486,42488,42490,42492,42494,42496,42498,42500,42502,42504,42506,42509,42511],{},[898,42479,28247],{},[1706,42481,1708],{},[898,42483,1683],{},[1706,42485,2447],{},[898,42487,31291],{},[1706,42489,2447],{},[898,42491,31220],{},[1706,42493,2447],{},[898,42495,10315],{},[1706,42497,1715],{},[898,42499,1742],{},[898,42501,1837],{"mathvariant":2409},[4898,42503],{"width":9524},[1706,42505,2140],{"stretchy":2139},[2148,42507,42508],{},"7.10",[2415,42510,207],{},[1706,42512,2153],{"stretchy":2139},[902,42514,42515],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,42517,39781],{"id":42518},"soustava-rovnic-2",[724,42520,40933,42521,42555,42556,4288],{},[883,42522,42524],{"className":42523},[886],[888,42525,42526],{"xmlns":890},[892,42527,42528,42552],{},[895,42529,42530,42536,42538,42544,42546],{},[2489,42531,42532,42534],{},[898,42533,31291],{},[1706,42535,3197],{},[1706,42537,2505],{"separator":2504},[2489,42539,42540,42542],{},[898,42541,31220],{},[1706,42543,3197],{},[1706,42545,2505],{"separator":2504},[2489,42547,42548,42550],{},[898,42549,10315],{},[1706,42551,3197],{},[902,42553,42554],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,42557,42559],{"className":42558},[886],[888,42560,42561],{"xmlns":890},[892,42562,42563,42587],{},[895,42564,42565,42567,42569,42571,42573,42575,42577,42583,42585],{},[898,42566,28247],{},[1706,42568,2505],{"separator":2504},[898,42570,1683],{},[1706,42572,2505],{"separator":2504},[898,42574,1659],{},[1706,42576,2505],{"separator":2504},[2142,42578,42579,42581],{},[898,42580,28247],{},[898,42582,2334],{},[1706,42584,2505],{"separator":2504},[898,42586,1742],{},[902,42588,42589],{"encoding":904},"Y, C, T, Y_D, M",[724,42591,42592],{},[883,42593,42595],{"className":42594},[886],[888,42596,42597],{"xmlns":890},[892,42598,42599,42783],{},[895,42600,42601,42775,42777,42779,42781],{},[2354,42602,42603,42635,42665,42693,42725],{"rowspacing":7556,"columnalign":7557,"columnspacing":3141},[2358,42604,42605,42611],{},[2361,42606,42607],{},[4745,42608,42609],{"scriptlevel":2150,"displaystyle":2504},[898,42610,1683],{},[2361,42612,42613],{},[4745,42614,42615],{"scriptlevel":2150,"displaystyle":2504},[895,42616,42617,42619,42621,42623,42625,42631,42633],{},[895,42618],{},[1706,42620,1708],{},[898,42622,1683],{},[1706,42624,2140],{"stretchy":2139},[2142,42626,42627,42629],{},[898,42628,28247],{},[898,42630,2334],{},[1706,42632,2153],{"stretchy":2139},[1706,42634,2505],{"separator":2504},[2358,42636,42637,42647],{},[2361,42638,42639],{},[4745,42640,42641],{"scriptlevel":2150,"displaystyle":2504},[2142,42642,42643,42645],{},[898,42644,28247],{},[898,42646,2334],{},[2361,42648,42649],{},[4745,42650,42651],{"scriptlevel":2150,"displaystyle":2504},[895,42652,42653,42655,42657,42659,42661,42663],{},[895,42654],{},[1706,42656,1708],{},[898,42658,28247],{},[1706,42660,1715],{},[898,42662,1659],{},[1706,42664,2505],{"separator":2504},[2358,42666,42667,42673],{},[2361,42668,42669],{},[4745,42670,42671],{"scriptlevel":2150,"displaystyle":2504},[898,42672,1659],{},[2361,42674,42675],{},[4745,42676,42677],{"scriptlevel":2150,"displaystyle":2504},[895,42678,42679,42681,42683,42685,42687,42689,42691],{},[895,42680],{},[1706,42682,1708],{},[898,42684,1659],{},[1706,42686,2140],{"stretchy":2139},[898,42688,28247],{},[1706,42690,2153],{"stretchy":2139},[1706,42692,2505],{"separator":2504},[2358,42694,42695,42701],{},[2361,42696,42697],{},[4745,42698,42699],{"scriptlevel":2150,"displaystyle":2504},[898,42700,1742],{},[2361,42702,42703],{},[4745,42704,42705],{"scriptlevel":2150,"displaystyle":2504},[895,42706,42707,42709,42711,42713,42715,42721,42723],{},[895,42708],{},[1706,42710,1708],{},[898,42712,1742],{},[1706,42714,2140],{"stretchy":2139},[2142,42716,42717,42719],{},[898,42718,28247],{},[898,42720,2334],{},[1706,42722,2153],{"stretchy":2139},[1706,42724,2505],{"separator":2504},[2358,42726,42727,42733],{},[2361,42728,42729],{},[4745,42730,42731],{"scriptlevel":2150,"displaystyle":2504},[898,42732,28247],{},[2361,42734,42735],{},[4745,42736,42737],{"scriptlevel":2150,"displaystyle":2504},[895,42738,42739,42741,42743,42745,42747,42753,42755,42761,42763,42769,42771,42773],{},[895,42740],{},[1706,42742,1708],{},[898,42744,1683],{},[1706,42746,2447],{},[2489,42748,42749,42751],{},[898,42750,31291],{},[1706,42752,3197],{},[1706,42754,2447],{},[2489,42756,42757,42759],{},[898,42758,31220],{},[1706,42760,3197],{},[1706,42762,2447],{},[2489,42764,42765,42767],{},[898,42766,10315],{},[1706,42768,3197],{},[1706,42770,1715],{},[898,42772,1742],{},[898,42774,1837],{"mathvariant":2409},[4898,42776],{"width":9524},[1706,42778,2140],{"stretchy":2139},[2148,42780,42508],{},[1706,42782,2153],{"stretchy":2139},[902,42784,42785],{"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)",[198,42787,42789],{"id":42788},"příklad-75","Příklad 7.5",[724,42791,42792,42793,1343,42824,1343,42851,1343,42871,1343,42893,1343,42915,42938],{},"Dáno: ",[883,42794,42796],{"className":42795},[886],[888,42797,42798],{"xmlns":890},[892,42799,42800,42821],{},[895,42801,42802,42804,42806,42809,42811,42817,42819],{},[898,42803,1683],{},[1706,42805,1708],{},[2148,42807,42808],{},"0,75",[2415,42810,2799],{},[2142,42812,42813,42815],{},[898,42814,28247],{},[898,42816,2334],{},[1706,42818,2447],{},[2148,42820,13287],{},[902,42822,42823],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,42825,42827],{"className":42826},[886],[888,42828,42829],{"xmlns":890},[892,42830,42831,42848],{},[895,42832,42833,42835,42837,42840,42842],{},[898,42834,1742],{},[1706,42836,1708],{},[2148,42838,42839],{},"0,15",[2415,42841,2799],{},[2142,42843,42844,42846],{},[898,42845,28247],{},[898,42847,2334],{},[902,42849,42850],{"encoding":904},"M = 0{,}15\\,Y_D",[883,42852,42854],{"className":42853},[886],[888,42855,42856],{"xmlns":890},[892,42857,42858,42868],{},[895,42859,42860,42862,42864,42866],{},[898,42861,1659],{},[1706,42863,1708],{},[2148,42865,19377],{},[898,42867,28247],{},[902,42869,42870],{"encoding":904},"T = 0{,}25Y",[883,42872,42874],{"className":42873},[886],[888,42875,42876],{"xmlns":890},[892,42877,42878,42890],{},[895,42879,42880,42886,42888],{},[2489,42881,42882,42884],{},[898,42883,31291],{},[1706,42885,3197],{},[1706,42887,1708],{},[2148,42889,17366],{},[902,42891,42892],{"encoding":904},"I^* = 500",[883,42894,42896],{"className":42895},[886],[888,42897,42898],{"xmlns":890},[892,42899,42900,42912],{},[895,42901,42902,42908,42910],{},[2489,42903,42904,42906],{},[898,42905,31220],{},[1706,42907,3197],{},[1706,42909,1708],{},[2148,42911,27924],{},[902,42913,42914],{"encoding":904},"G^* = 150",[883,42916,42918],{"className":42917},[886],[888,42919,42920],{"xmlns":890},[892,42921,42922,42935],{},[895,42923,42924,42930,42932],{},[2489,42925,42926,42928],{},[898,42927,10315],{},[1706,42929,3197],{},[1706,42931,1708],{},[2148,42933,42934],{},"800",[902,42936,42937],{"encoding":904},"B^* = 800",". Soustava:",[724,42940,42941],{},[883,42942,42944],{"className":42943},[886],[888,42945,42946],{"xmlns":890},[892,42947,42948,43166],{},[2354,42949,42950,42996,43038,43074,43116],{"rowspacing":7556,"columnalign":7557,"columnspacing":3141},[2358,42951,42952,42968],{},[2361,42953,42954],{},[4745,42955,42956],{"scriptlevel":2150,"displaystyle":2504},[895,42957,42958,42960,42962,42964,42966],{},[1706,42959,2140],{"stretchy":2139},[898,42961,3950],{},[2148,42963,2701],{},[1706,42965,2153],{"stretchy":2139},[2415,42967,21505],{},[2361,42969,42970],{},[4745,42971,42972],{"scriptlevel":2150,"displaystyle":2504},[895,42973,42974,42976,42978,42980,42982,42984,42990,42992,42994],{},[895,42975],{},[898,42977,1683],{},[1706,42979,1708],{},[2148,42981,42808],{},[2415,42983,2799],{},[2142,42985,42986,42988],{},[898,42987,28247],{},[898,42989,2334],{},[1706,42991,2447],{},[2148,42993,13287],{},[1706,42995,2505],{"separator":2504},[2358,42997,42998,43014],{},[2361,42999,43000],{},[4745,43001,43002],{"scriptlevel":2150,"displaystyle":2504},[895,43003,43004,43006,43008,43010,43012],{},[1706,43005,2140],{"stretchy":2139},[898,43007,3950],{},[2148,43009,2495],{},[1706,43011,2153],{"stretchy":2139},[2415,43013,21505],{},[2361,43015,43016],{},[4745,43017,43018],{"scriptlevel":2150,"displaystyle":2504},[895,43019,43020,43022,43028,43030,43032,43034,43036],{},[895,43021],{},[2142,43023,43024,43026],{},[898,43025,28247],{},[898,43027,2334],{},[1706,43029,1708],{},[898,43031,28247],{},[1706,43033,1715],{},[898,43035,1659],{},[1706,43037,2505],{"separator":2504},[2358,43039,43040,43056],{},[2361,43041,43042],{},[4745,43043,43044],{"scriptlevel":2150,"displaystyle":2504},[895,43045,43046,43048,43050,43052,43054],{},[1706,43047,2140],{"stretchy":2139},[898,43049,3950],{},[2148,43051,4284],{},[1706,43053,2153],{"stretchy":2139},[2415,43055,21505],{},[2361,43057,43058],{},[4745,43059,43060],{"scriptlevel":2150,"displaystyle":2504},[895,43061,43062,43064,43066,43068,43070,43072],{},[895,43063],{},[898,43065,1659],{},[1706,43067,1708],{},[2148,43069,19377],{},[898,43071,28247],{},[1706,43073,2505],{"separator":2504},[2358,43075,43076,43092],{},[2361,43077,43078],{},[4745,43079,43080],{"scriptlevel":2150,"displaystyle":2504},[895,43081,43082,43084,43086,43088,43090],{},[1706,43083,2140],{"stretchy":2139},[898,43085,3950],{},[2148,43087,3455],{},[1706,43089,2153],{"stretchy":2139},[2415,43091,21505],{},[2361,43093,43094],{},[4745,43095,43096],{"scriptlevel":2150,"displaystyle":2504},[895,43097,43098,43100,43102,43104,43106,43108,43114],{},[895,43099],{},[898,43101,1742],{},[1706,43103,1708],{},[2148,43105,42839],{},[2415,43107,2799],{},[2142,43109,43110,43112],{},[898,43111,28247],{},[898,43113,2334],{},[1706,43115,2505],{"separator":2504},[2358,43117,43118,43134],{},[2361,43119,43120],{},[4745,43121,43122],{"scriptlevel":2150,"displaystyle":2504},[895,43123,43124,43126,43128,43130,43132],{},[1706,43125,2140],{"stretchy":2139},[898,43127,3950],{},[2148,43129,7524],{},[1706,43131,2153],{"stretchy":2139},[2415,43133,21505],{},[2361,43135,43136],{},[4745,43137,43138],{"scriptlevel":2150,"displaystyle":2504},[895,43139,43140,43142,43144,43146,43148,43150,43152,43154,43156,43158,43160,43162,43164],{},[895,43141],{},[898,43143,28247],{},[1706,43145,1708],{},[898,43147,1683],{},[1706,43149,2447],{},[2148,43151,17366],{},[1706,43153,2447],{},[2148,43155,27924],{},[1706,43157,2447],{},[2148,43159,42934],{},[1706,43161,1715],{},[898,43163,1742],{},[898,43165,1837],{"mathvariant":2409},[902,43167,43168],{"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}",[724,43170,43171,43172,43206],{},"Postupná substituce — z (r3) do (r2): ",[883,43173,43175],{"className":43174},[886],[888,43176,43177],{"xmlns":890},[892,43178,43179,43203],{},[895,43180,43181,43187,43189,43191,43193,43195,43197,43199,43201],{},[2142,43182,43183,43185],{},[898,43184,28247],{},[898,43186,2334],{},[1706,43188,1708],{},[898,43190,28247],{},[1706,43192,1715],{},[2148,43194,19377],{},[898,43196,28247],{},[1706,43198,1708],{},[2148,43200,42808],{},[898,43202,28247],{},[902,43204,43205],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,43208,43209],{},[883,43210,43212],{"className":43211},[886],[888,43213,43214],{"xmlns":890},[892,43215,43216,43257],{},[895,43217,43218,43220,43222,43224,43226,43228,43230,43232,43234,43236,43238,43240,43242,43244,43246,43249,43251,43253,43255],{},[1706,43219,2140],{"stretchy":2139},[898,43221,3950],{},[2148,43223,7044],{},[1706,43225,2153],{"stretchy":2139},[2415,43227,21505],{},[898,43229,1683],{},[1706,43231,1708],{},[2148,43233,42808],{},[1706,43235,2390],{},[2148,43237,42808],{},[898,43239,28247],{},[1706,43241,2447],{},[2148,43243,13287],{},[1706,43245,1708],{},[2148,43247,43248],{},"0,5625",[898,43250,28247],{},[1706,43252,2447],{},[2148,43254,13287],{},[1706,43256,2505],{"separator":2504},[902,43258,43259],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,43261,43262],{},[883,43263,43265],{"className":43264},[886],[888,43266,43267],{"xmlns":890},[892,43268,43269,43302],{},[895,43270,43271,43273,43275,43277,43279,43281,43283,43285,43287,43289,43291,43293,43295,43298,43300],{},[1706,43272,2140],{"stretchy":2139},[898,43274,3950],{},[2148,43276,12597],{},[1706,43278,2153],{"stretchy":2139},[2415,43280,21505],{},[898,43282,1742],{},[1706,43284,1708],{},[2148,43286,42839],{},[1706,43288,2390],{},[2148,43290,42808],{},[898,43292,28247],{},[1706,43294,1708],{},[2148,43296,43297],{},"0,1125",[898,43299,28247],{},[898,43301,1837],{"mathvariant":2409},[902,43303,43304],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,43306,43307],{},"Dosazením do (r5):",[724,43309,43310],{},[883,43311,43313],{"className":43312},[886],[888,43314,43315],{"xmlns":890},[892,43316,43317,43361],{},[895,43318,43319,43321,43323,43325,43327,43329,43331,43333,43335,43337,43339,43341,43343,43345,43347,43349,43351,43354,43356,43358],{},[898,43320,28247],{},[1706,43322,1708],{},[2148,43324,43248],{},[898,43326,28247],{},[1706,43328,2447],{},[2148,43330,13287],{},[1706,43332,2447],{},[2148,43334,17366],{},[1706,43336,2447],{},[2148,43338,27924],{},[1706,43340,2447],{},[2148,43342,42934],{},[1706,43344,1715],{},[2148,43346,43297],{},[898,43348,28247],{},[1706,43350,1708],{},[2148,43352,43353],{},"0,45",[898,43355,28247],{},[1706,43357,2447],{},[2148,43359,43360],{},"2200.",[902,43362,43363],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,43365,43366,43367,24728,43389,43412],{},"Odtud ",[883,43368,43370],{"className":43369},[886],[888,43371,43372],{"xmlns":890},[892,43373,43374,43386],{},[895,43375,43376,43379,43381,43383],{},[2148,43377,43378],{},"0,55",[898,43380,28247],{},[1706,43382,1708],{},[2148,43384,43385],{},"2200",[902,43387,43388],{"encoding":904},"0{,}55Y = 2200",[883,43390,43392],{"className":43391},[886],[888,43393,43394],{"xmlns":890},[892,43395,43396,43409],{},[895,43397,43398,43404,43406],{},[2489,43399,43400,43402],{},[898,43401,28247],{},[898,43403,23410],{},[1706,43405,1708],{},[2148,43407,43408],{},"4000",[902,43410,43411],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,43414,43415,43438,43470,43505,43538,43574],{},[123,43416,43417,2505],{},[883,43418,43420],{"className":43419},[886],[888,43421,43422],{"xmlns":890},[892,43423,43424,43436],{},[895,43425,43426,43432,43434],{},[2489,43427,43428,43430],{},[898,43429,28247],{},[898,43431,23410],{},[1706,43433,1708],{},[2148,43435,43408],{},[902,43437,43411],{"encoding":904},[123,43439,43440,2505],{},[883,43441,43443],{"className":43442},[886],[888,43444,43445],{"xmlns":890},[892,43446,43447,43467],{},[895,43448,43449,43455,43457,43459,43461,43463,43465],{},[2489,43450,43451,43453],{},[898,43452,1659],{},[898,43454,23410],{},[1706,43456,1708],{},[2148,43458,19377],{},[1706,43460,2390],{},[2148,43462,43408],{},[1706,43464,1708],{},[2148,43466,21978],{},[902,43468,43469],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,43471,43472,2505],{},[883,43473,43475],{"className":43474},[886],[888,43476,43477],{"xmlns":890},[892,43478,43479,43502],{},[895,43480,43481,43489,43491,43493,43495,43497,43499],{},[28285,43482,43483,43485,43487],{},[898,43484,28247],{},[898,43486,2334],{},[898,43488,23410],{},[1706,43490,1708],{},[2148,43492,42808],{},[1706,43494,2390],{},[2148,43496,43408],{},[1706,43498,1708],{},[2148,43500,43501],{},"3000",[902,43503,43504],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,43506,43507,2505],{},[883,43508,43510],{"className":43509},[886],[888,43511,43512],{"xmlns":890},[892,43513,43514,43535],{},[895,43515,43516,43522,43524,43526,43528,43530,43532],{},[2489,43517,43518,43520],{},[898,43519,1742],{},[898,43521,23410],{},[1706,43523,1708],{},[2148,43525,42839],{},[1706,43527,2390],{},[2148,43529,43501],{},[1706,43531,1708],{},[2148,43533,43534],{},"450",[902,43536,43537],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,43539,43540,2505],{},[883,43541,43543],{"className":43542},[886],[888,43544,43545],{"xmlns":890},[892,43546,43547,43571],{},[895,43548,43549,43555,43557,43559,43561,43563,43565,43567,43569],{},[2489,43550,43551,43553],{},[898,43552,1683],{},[898,43554,23410],{},[1706,43556,1708],{},[2148,43558,42808],{},[1706,43560,2390],{},[2148,43562,43501],{},[1706,43564,2447],{},[2148,43566,13287],{},[1706,43568,1708],{},[2148,43570,43501],{},[902,43572,43573],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,43575,43576,43616],{},[883,43577,43579],{"className":43578},[886],[888,43580,43581],{"xmlns":890},[892,43582,43583,43613],{},[895,43584,43585,43591,43593,43601,43603,43609,43611],{},[2489,43586,43587,43589],{},[898,43588,14171],{},[898,43590,23410],{},[1706,43592,1708],{},[28285,43594,43595,43597,43599],{},[898,43596,28247],{},[898,43598,2334],{},[898,43600,23410],{},[1706,43602,1715],{},[2489,43604,43605,43607],{},[898,43606,1683],{},[898,43608,23410],{},[1706,43610,1708],{},[2148,43612,2150],{},[902,43614,43615],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,43618,43619,43621,43622,1343,43639,1993,43660,43685,43686,43689,43690,43703,43704,1837],{},[38,43620,40433],{}," Modely ",[883,43623,43625],{"className":43624},[886],[888,43626,43627],{"xmlns":890},[892,43628,43629,43637],{},[895,43630,43631,43633,43635],{},[898,43632,1683],{},[2415,43634,31397],{},[898,43636,31291],{},[902,43638,31402],{"encoding":904},[883,43640,43642],{"className":43641},[886],[888,43643,43644],{"xmlns":890},[892,43645,43646,43658],{},[895,43647,43648,43650,43652,43654,43656],{},[898,43649,1683],{},[2415,43651,31397],{},[898,43653,31291],{},[2415,43655,31397],{},[898,43657,31220],{},[902,43659,37317],{"encoding":904},[883,43661,43663],{"className":43662},[886],[888,43664,43665],{"xmlns":890},[892,43666,43667,43683],{},[895,43668,43669,43671,43673,43675,43677,43679,43681],{},[898,43670,1683],{},[2415,43672,31397],{},[898,43674,31291],{},[2415,43676,31397],{},[898,43678,31220],{},[2415,43680,31397],{},[898,43682,31427],{},[902,43684,31430],{"encoding":904}," pokládají investice za ",[38,43687,43688],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,43691,43693],{"className":43692},[886],[888,43694,43695],{"xmlns":890},[892,43696,43697,43701],{},[895,43698,43699],{},[898,43700,3950],{},[902,43702,3950],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,43705,43706],{},"model IS-LM",[115,43708,43710],{"id":43709},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,43712,43713,43714,43718,43719,43722,43723,43726],{},"V článku ",[207,43715,43717],{"className":43716,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,43720,43721],{},"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 ",[38,43724,43725],{},"výraznější"," než v mikroekonomických modelech.",[724,43728,43729],{},[2286,43730],{"alt":43731,"className":43732,"src":43733},"imek-multiplikatorovy-efekt-chain",[210,2290],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,43735,31271,43736,1343,43753,1343,43774,43799,43800,43803,43804,43822,43823,43841,43842,43860,43861,43864,43865,1343,43882,43899,43900,43902],{},[883,43737,43739],{"className":43738},[886],[888,43740,43741],{"xmlns":890},[892,43742,43743,43751],{},[895,43744,43745,43747,43749],{},[898,43746,1683],{},[2415,43748,31397],{},[898,43750,31291],{},[902,43752,31402],{"encoding":904},[883,43754,43756],{"className":43755},[886],[888,43757,43758],{"xmlns":890},[892,43759,43760,43772],{},[895,43761,43762,43764,43766,43768,43770],{},[898,43763,1683],{},[2415,43765,31397],{},[898,43767,31291],{},[2415,43769,31397],{},[898,43771,31220],{},[902,43773,37317],{"encoding":904},[883,43775,43777],{"className":43776},[886],[888,43778,43779],{"xmlns":890},[892,43780,43781,43797],{},[895,43782,43783,43785,43787,43789,43791,43793,43795],{},[898,43784,1683],{},[2415,43786,31397],{},[898,43788,31291],{},[2415,43790,31397],{},[898,43792,31220],{},[2415,43794,31397],{},[898,43796,31427],{},[902,43798,31430],{"encoding":904}," se vyšetřuje vliv změn ",[38,43801,43802],{},"exogenních"," veličin (plánovaných investic ",[883,43805,43807],{"className":43806},[886],[888,43808,43809],{"xmlns":890},[892,43810,43811,43819],{},[895,43812,43813],{},[2489,43814,43815,43817],{},[898,43816,31291],{},[1706,43818,3197],{},[902,43820,43821],{"encoding":904},"I^*",", vládních výdajů ",[883,43824,43826],{"className":43825},[886],[888,43827,43828],{"xmlns":890},[892,43829,43830,43838],{},[895,43831,43832],{},[2489,43833,43834,43836],{},[898,43835,31220],{},[1706,43837,3197],{},[902,43839,43840],{"encoding":904},"G^*",", exportu ",[883,43843,43845],{"className":43844},[886],[888,43846,43847],{"xmlns":890},[892,43848,43849,43857],{},[895,43850,43851],{},[2489,43852,43853,43855],{},[898,43854,10315],{},[1706,43856,3197],{},[902,43858,43859],{"encoding":904},"B^*",") na změny ",[38,43862,43863],{},"endogenních"," rovnovážných veličin (",[883,43866,43868],{"className":43867},[886],[888,43869,43870],{"xmlns":890},[892,43871,43872,43880],{},[895,43873,43874],{},[2489,43875,43876,43878],{},[898,43877,28247],{},[898,43879,23410],{},[902,43881,33010],{"encoding":904},[883,43883,43885],{"className":43884},[886],[888,43886,43887],{"xmlns":890},[892,43888,43889,43897],{},[895,43890,43891],{},[2489,43892,43893,43895],{},[898,43894,1683],{},[898,43896,23410],{},[902,43898,33069],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,43901,37074],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,43904,43906],{"id":43905},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,43908,39980,43909,43932,43933,43977],{},[883,43910,43912],{"className":43911},[886],[888,43913,43914],{"xmlns":890},[892,43915,43916,43930],{},[895,43917,43918,43920,43922,43924,43926,43928],{},[898,43919,1683],{},[1706,43921,1708],{},[898,43923,207],{},[898,43925,28247],{},[1706,43927,2447],{},[898,43929,2450],{},[902,43931,38016],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,43934,43936],{"className":43935},[886],[888,43937,43938],{"xmlns":890},[892,43939,43940,43974],{},[895,43941,43942,43948,43950],{},[2489,43943,43944,43946],{},[898,43945,28247],{},[898,43947,23410],{},[1706,43949,1708],{},[4745,43951,43952],{"scriptlevel":2150,"displaystyle":2504},[2964,43953,43954,43966],{},[895,43955,43956,43958,43960],{},[898,43957,2450],{},[1706,43959,2447],{},[2489,43961,43962,43964],{},[898,43963,31291],{},[1706,43965,3197],{},[895,43967,43968,43970,43972],{},[2148,43969,2701],{},[1706,43971,1715],{},[898,43973,207],{},[902,43975,43976],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,43979,43980],{},[883,43981,43983],{"className":43982},[886],[888,43984,43985],{"xmlns":890},[892,43986,43987,44055],{},[895,43988,43989,44007,44009,44039,44041],{},[2964,43990,43991,44001],{},[895,43992,43993,43995],{},[898,43994,28987],{"mathvariant":2409},[2489,43996,43997,43999],{},[898,43998,28247],{},[898,44000,23410],{},[895,44002,44003,44005],{},[898,44004,28987],{"mathvariant":2409},[898,44006,207],{},[1706,44008,1708],{},[2964,44010,44011,44023],{},[895,44012,44013,44015,44017],{},[898,44014,2450],{},[1706,44016,2447],{},[2489,44018,44019,44021],{},[898,44020,31291],{},[1706,44022,3197],{},[895,44024,44025,44027,44029,44031,44033],{},[1706,44026,2140],{"stretchy":2139},[2148,44028,2701],{},[1706,44030,1715],{},[898,44032,207],{},[2489,44034,44035,44037],{},[1706,44036,2153],{"stretchy":2139},[2148,44038,2495],{},[4898,44040],{"width":9524},[895,44042,44043,44046,44052],{},[2415,44044,44045],{},"(multiplik",[3925,44047,44048,44050],{"accent":2504},[2415,44049,207],{},[1706,44051,3942],{},[2415,44053,44054],{},"tor MPC)",[902,44056,44057],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,44059,44060],{},[883,44061,44063],{"className":44062},[886],[888,44064,44065],{"xmlns":890},[892,44066,44067,44134],{},[895,44068,44069,44087,44089,44101,44103],{},[2964,44070,44071,44081],{},[895,44072,44073,44075],{},[898,44074,28987],{"mathvariant":2409},[2489,44076,44077,44079],{},[898,44078,28247],{},[898,44080,23410],{},[895,44082,44083,44085],{},[898,44084,28987],{"mathvariant":2409},[898,44086,2450],{},[1706,44088,1708],{},[2964,44090,44091,44093],{},[2148,44092,2701],{},[895,44094,44095,44097,44099],{},[2148,44096,2701],{},[1706,44098,1715],{},[898,44100,207],{},[4898,44102],{"width":9524},[895,44104,44105,44107,44113,44116,44122,44125,44131],{},[2415,44106,44045],{},[3925,44108,44109,44111],{"accent":2504},[2415,44110,207],{},[1706,44112,3942],{},[2415,44114,44115],{},"tor autonomn",[3925,44117,44118,44120],{"accent":2504},[2415,44119,3957],{},[1706,44121,3942],{},[2415,44123,44124],{}," spot",[3925,44126,44127,44129],{"accent":2504},[2415,44128,3950],{},[1706,44130,3932],{},[2415,44132,44133],{},"eby)",[902,44135,44136],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,44138,44139],{},[883,44140,44142],{"className":44141},[886],[888,44143,44144],{"xmlns":890},[892,44145,44146,44213],{},[895,44147,44148,44170,44172,44184,44186,44198,44200],{},[2964,44149,44150,44160],{},[895,44151,44152,44154],{},[898,44153,28987],{"mathvariant":2409},[2489,44155,44156,44158],{},[898,44157,28247],{},[898,44159,23410],{},[895,44161,44162,44164],{},[898,44163,28987],{"mathvariant":2409},[2489,44165,44166,44168],{},[898,44167,31291],{},[1706,44169,3197],{},[1706,44171,1708],{},[2964,44173,44174,44176],{},[2148,44175,2701],{},[895,44177,44178,44180,44182],{},[2148,44179,2701],{},[1706,44181,1715],{},[898,44183,207],{},[1706,44185,1708],{},[2964,44187,44188,44190],{},[2148,44189,2701],{},[895,44191,44192,44194,44196],{},[898,44193,1742],{},[898,44195,1702],{},[898,44197,14171],{},[4898,44199],{"width":9524},[895,44201,44202,44204,44210],{},[2415,44203,44045],{},[3925,44205,44206,44208],{"accent":2504},[2415,44207,207],{},[1706,44209,3942],{},[2415,44211,44212],{},"tor investic)",[902,44214,44215],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[1636,44217,44218],{},[724,44219,44220,44222,44223,44226,44227,44240,44241,44258,44259,44277,44278,44322,44323,3570,44340,44343,44344,44361],{},[883,44221,3174],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,44224,44225],{},"důchodem","; z něj se utratí ",[883,44228,44230],{"className":44229},[886],[888,44231,44232],{"xmlns":890},[892,44233,44234,44238],{},[895,44235,44236],{},[898,44237,207],{},[902,44239,207],{"encoding":904}," Kč (= ",[883,44242,44244],{"className":44243},[886],[888,44245,44246],{"xmlns":890},[892,44247,44248,44256],{},[895,44249,44250,44252,44254],{},[898,44251,1742],{},[898,44253,1702],{},[898,44255,1683],{},[902,44257,37142],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,44260,44262],{"className":44261},[886],[888,44263,44264],{"xmlns":890},[892,44265,44266,44274],{},[895,44267,44268],{},[2489,44269,44270,44272],{},[898,44271,207],{},[2148,44273,2495],{},[902,44275,44276],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,44279,44281],{"className":44280},[886],[888,44282,44283],{"xmlns":890},[892,44284,44285,44319],{},[895,44286,44287,44289,44291,44293,44295,44301,44303,44305,44307],{},[2148,44288,2701],{},[1706,44290,2447],{},[898,44292,207],{},[1706,44294,2447],{},[2489,44296,44297,44299],{},[898,44298,207],{},[2148,44300,2495],{},[1706,44302,2447],{},[1706,44304,37202],{},[1706,44306,1708],{},[2964,44308,44309,44311],{},[2148,44310,2701],{},[895,44312,44313,44315,44317],{},[2148,44314,2701],{},[1706,44316,1715],{},[898,44318,207],{},[902,44320,44321],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,44324,44326],{"className":44325},[886],[888,44327,44328],{"xmlns":890},[892,44329,44330,44338],{},[895,44331,44332],{},[2489,44333,44334,44336],{},[898,44335,28247],{},[898,44337,23410],{},[902,44339,33010],{"encoding":904},[38,44341,44342],{},"více"," než korunu — čím vyšší ",[883,44345,44347],{"className":44346},[886],[888,44348,44349],{"xmlns":890},[892,44350,44351,44359],{},[895,44352,44353,44355,44357],{},[898,44354,1742],{},[898,44356,1702],{},[898,44358,1683],{},[902,44360,37142],{"encoding":904},", tím silnější multiplikační efekt.",[724,44363,44364,44367,44368,44394,44395,44398,44399,1993,44420,44445,44446,1837],{},[38,44365,44366],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,44369,44371],{"className":44370},[886],[888,44372,44373],{"xmlns":890},[892,44374,44375,44391],{},[895,44376,44377],{},[4745,44378,44379],{"scriptlevel":2150,"displaystyle":2139},[2964,44380,44381,44383],{},[2148,44382,2701],{},[895,44384,44385,44387,44389],{},[2148,44386,2701],{},[1706,44388,1715],{},[898,44390,207],{},[902,44392,44393],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,44396,44397],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,44400,44402],{"className":44401},[886],[888,44403,44404],{"xmlns":890},[892,44405,44406,44418],{},[895,44407,44408,44410,44412,44414,44416],{},[898,44409,1683],{},[2415,44411,31397],{},[898,44413,31291],{},[2415,44415,31397],{},[898,44417,31220],{},[902,44419,37317],{"encoding":904},[883,44421,44423],{"className":44422},[886],[888,44424,44425],{"xmlns":890},[892,44426,44427,44443],{},[895,44428,44429,44431,44433,44435,44437,44439,44441],{},[898,44430,1683],{},[2415,44432,31397],{},[898,44434,31291],{},[2415,44436,31397],{},[898,44438,31220],{},[2415,44440,31397],{},[898,44442,31427],{},[902,44444,31430],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,44447,44449],{"className":44448,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,44451,44453],{"id":44452},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,44455,31271,44456,1343,44473,1993,44494,31276,44519,2314,44522,44543,44544,1647,44547,44560,44561,24808,44590,44607,44608,44611,44612,44614,44615,44636],{},[883,44457,44459],{"className":44458},[886],[888,44460,44461],{"xmlns":890},[892,44462,44463,44471],{},[895,44464,44465,44467,44469],{},[898,44466,1683],{},[2415,44468,31397],{},[898,44470,31291],{},[902,44472,31402],{"encoding":904},[883,44474,44476],{"className":44475},[886],[888,44477,44478],{"xmlns":890},[892,44479,44480,44492],{},[895,44481,44482,44484,44486,44488,44490],{},[898,44483,1683],{},[2415,44485,31397],{},[898,44487,31291],{},[2415,44489,31397],{},[898,44491,31220],{},[902,44493,37317],{"encoding":904},[883,44495,44497],{"className":44496},[886],[888,44498,44499],{"xmlns":890},[892,44500,44501,44517],{},[895,44502,44503,44505,44507,44509,44511,44513,44515],{},[898,44504,1683],{},[2415,44506,31397],{},[898,44508,31291],{},[2415,44510,31397],{},[898,44512,31220],{},[2415,44514,31397],{},[898,44516,31427],{},[902,44518,31430],{"encoding":904},[38,44520,44521],{},"investice konstantní",[883,44523,44525],{"className":44524},[886],[888,44526,44527],{"xmlns":890},[892,44528,44529,44541],{},[895,44530,44531,44533,44535],{},[898,44532,31291],{},[1706,44534,1708],{},[2489,44536,44537,44539],{},[898,44538,31291],{},[1706,44540,3197],{},[902,44542,31302],{"encoding":904},"). Reálnější je předpoklad, že ",[38,44545,44546],{},"investice závisejí na úrokové míře",[883,44548,44550],{"className":44549},[886],[888,44551,44552],{"xmlns":890},[892,44553,44554,44558],{},[895,44555,44556],{},[898,44557,3950],{},[902,44559,3950],{"encoding":904}," — klesající funkce ",[883,44562,44564],{"className":44563},[886],[888,44565,44566],{"xmlns":890},[892,44567,44568,44588],{},[895,44569,44570,44572,44574,44576,44578,44580,44582,44584,44586],{},[898,44571,31291],{},[1706,44573,2140],{"stretchy":2139},[898,44575,3950],{},[1706,44577,2153],{"stretchy":2139},[1706,44579,1708],{},[898,44581,20413],{},[898,44583,3950],{},[1706,44585,2447],{},[898,44587,3120],{},[902,44589,34859],{"encoding":904},[883,44591,44593],{"className":44592},[886],[888,44594,44595],{"xmlns":890},[892,44596,44597,44605],{},[895,44598,44599,44601,44603],{},[898,44600,20413],{},[1706,44602,2539],{},[2148,44604,2150],{},[902,44606,31622],{"encoding":904},". Přidáním ",[38,44609,44610],{},"trhu peněz"," k trhu zboží vzniká model ",[38,44613,31120],{}," se dvěma neznámými ",[883,44616,44618],{"className":44617},[886],[888,44619,44620],{"xmlns":890},[892,44621,44622,44634],{},[895,44623,44624,44626,44628,44630,44632],{},[1706,44625,2140],{"stretchy":2139},[898,44627,28247],{},[1706,44629,2505],{"separator":2504},[898,44631,3950],{},[1706,44633,2153],{"stretchy":2139},[902,44635,37247],{"encoding":904}," a dvěma rovnicemi:",[120,44638,44639,44689],{},[123,44640,44641,2314,44643,44645,44646,44667,44668,1837],{},[38,44642,34947],{},[614,44644,31162],{},") — klesající přímka v rovině ",[883,44647,44649],{"className":44648},[886],[888,44650,44651],{"xmlns":890},[892,44652,44653,44665],{},[895,44654,44655,44657,44659,44661,44663],{},[1706,44656,2140],{"stretchy":2139},[898,44658,3950],{},[1706,44660,2505],{"separator":2504},[898,44662,28247],{},[1706,44664,2153],{"stretchy":2139},[902,44666,32044],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,44669,44671],{"className":44670},[886],[888,44672,44673],{"xmlns":890},[892,44674,44675,44687],{},[895,44676,44677,44679,44681,44683,44685],{},[898,44678,28247],{},[1706,44680,1708],{},[898,44682,1683],{},[1706,44684,2447],{},[898,44686,31291],{},[902,44688,33851],{"encoding":904},[123,44690,44691,2314,44693,44695,44696,15842,44721,44767],{},[38,44692,35146],{},[614,44694,31169],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,44697,44699],{"className":44698},[886],[888,44700,44701],{"xmlns":890},[892,44702,44703,44719],{},[895,44704,44705,44711,44713],{},[2489,44706,44707,44709],{},[898,44708,1742],{},[898,44710,2334],{},[1706,44712,1708],{},[2489,44714,44715,44717],{},[898,44716,1742],{},[1706,44718,3197],{},[902,44720,32587],{"encoding":904},[883,44722,44724],{"className":44723},[886],[888,44725,44726],{"xmlns":890},[892,44727,44728,44764],{},[895,44729,44730,44736,44738,44744,44746,44748,44754,44756,44758],{},[2489,44731,44732,44734],{},[898,44733,1742],{},[898,44735,2334],{},[1706,44737,1708],{},[2142,44739,44740,44742],{},[898,44741,32344],{},[2148,44743,2701],{},[898,44745,28247],{},[1706,44747,2447],{},[2142,44749,44750,44752],{},[898,44751,32344],{},[2148,44753,2495],{},[898,44755,3950],{},[1706,44757,2447],{},[2142,44759,44760,44762],{},[898,44761,32344],{},[2148,44763,4284],{},[902,44765,44766],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,44769,44770,1647,44773,44806,44807,44809,44810,44812],{},[38,44771,44772],{},"Simultánní rovnovážný bod",[883,44774,44776],{"className":44775},[886],[888,44777,44778],{"xmlns":890},[892,44779,44780,44804],{},[895,44781,44782,44784,44786,44788,44794,44796,44802],{},[898,44783,23410],{},[1706,44785,1708],{},[1706,44787,2140],{"stretchy":2139},[2489,44789,44790,44792],{},[898,44791,3950],{},[898,44793,23410],{},[1706,44795,2505],{"separator":2504},[2489,44797,44798,44800],{},[898,44799,28247],{},[898,44801,23410],{},[1706,44803,2153],{"stretchy":2139},[902,44805,35238],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,44808,31207],{}," (posun IS) a ",[38,44811,31238],{}," (posun LM).",[724,44814,44815],{},[38,44816,44817,44818,1343,44840,1343,44862,1343,44884,44906,44907,1837],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,44819,44821],{"className":44820},[886],[888,44822,44823],{"xmlns":890},[892,44824,44825,44837],{},[895,44826,44827,44833,44835],{},[2489,44828,44829,44831],{},[898,44830,28247],{},[898,44832,23410],{},[1706,44834,1708],{},[2148,44836,34221],{},[902,44838,44839],{"encoding":904},"Y^E = 5000",[883,44841,44843],{"className":44842},[886],[888,44844,44845],{"xmlns":890},[892,44846,44847,44859],{},[895,44848,44849,44855,44857],{},[2489,44850,44851,44853],{},[898,44852,3950],{},[898,44854,23410],{},[1706,44856,1708],{},[2148,44858,7524],{},[902,44860,44861],{"encoding":904},"r^E = 5",[883,44863,44865],{"className":44864},[886],[888,44866,44867],{"xmlns":890},[892,44868,44869,44881],{},[895,44870,44871,44877,44879],{},[2489,44872,44873,44875],{},[898,44874,1683],{},[898,44876,23410],{},[1706,44878,1708],{},[2148,44880,34258],{},[902,44882,44883],{"encoding":904},"C^E = 4100",[883,44885,44887],{"className":44886},[886],[888,44888,44889],{"xmlns":890},[892,44890,44891,44903],{},[895,44892,44893,44899,44901],{},[2489,44894,44895,44897],{},[898,44896,31291],{},[898,44898,23410],{},[1706,44900,1708],{},[2148,44902,12956],{},[902,44904,44905],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,44908,945],{"className":44909,"dataFsResolvedFilePath":943,"href":944},[210],[115,44911,44913],{"id":44912},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,44915,44916,44980,45091,45234,45475,45543],{},[123,44917,44918,44921,44922,44944,44945,44979],{},[38,44919,44920],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,44923,44925],{"className":44924},[886],[888,44926,44927],{"xmlns":890},[892,44928,44929,44941],{},[895,44930,44931,44933,44935,44937,44939],{},[898,44932,31220],{},[898,44934,37391],{},[898,44936,1702],{},[1706,44938,3248],{},[898,44940,28247],{},[902,44942,44943],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,44946,44948],{"className":44947},[886],[888,44949,44950],{"xmlns":890},[892,44951,44952,44976],{},[895,44953,44954,44956,44958,44960,44962,44964,44966,44968,44970,44972,44974],{},[898,44955,31220],{},[898,44957,37391],{},[898,44959,1702],{},[1706,44961,1708],{},[898,44963,1683],{},[1706,44965,2447],{},[898,44967,31291],{},[1706,44969,2447],{},[898,44971,31220],{},[1706,44973,2447],{},[898,44975,31427],{},[902,44977,44978],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,44981,44982,44984,44985,45006,45007,1343,45030,45061,45062,45075,45076,1837],{},[38,44983,37625],{}," splňují ",[883,44986,44988],{"className":44987},[886],[888,44989,44990],{"xmlns":890},[892,44991,44992,45004],{},[895,44993,44994,44996,44998,45000,45002],{},[898,44995,28247],{},[1706,44997,1708],{},[898,44999,1683],{},[1706,45001,2447],{},[898,45003,14171],{},[902,45005,31801],{"encoding":904}," (7.2); lineární model ",[883,45008,45010],{"className":45009},[886],[888,45011,45012],{"xmlns":890},[892,45013,45014,45028],{},[895,45015,45016,45018,45020,45022,45024,45026],{},[898,45017,1683],{},[1706,45019,1708],{},[898,45021,207],{},[898,45023,28247],{},[1706,45025,2447],{},[898,45027,2450],{},[902,45029,38016],{"encoding":904},[883,45031,45033],{"className":45032},[886],[888,45034,45035],{"xmlns":890},[892,45036,45037,45059],{},[895,45038,45039,45041,45043,45045,45047,45049,45051,45053,45055,45057],{},[898,45040,14171],{},[1706,45042,1708],{},[1706,45044,2140],{"stretchy":2139},[2148,45046,2701],{},[1706,45048,1715],{},[898,45050,207],{},[1706,45052,2153],{"stretchy":2139},[898,45054,28247],{},[1706,45056,1715],{},[898,45058,2450],{},[902,45060,38265],{"encoding":904}," s autonomní spotřebou ",[883,45063,45065],{"className":45064},[886],[888,45066,45067],{"xmlns":890},[892,45068,45069,45073],{},[895,45070,45071],{},[898,45072,2450],{},[902,45074,2450],{"encoding":904}," a autonomními úsporami ",[883,45077,45079],{"className":45078},[886],[888,45080,45081],{"xmlns":890},[892,45082,45083,45089],{},[895,45084,45085,45087],{},[1706,45086,1715],{},[898,45088,2450],{},[902,45090,38344],{"encoding":904},[123,45092,45093,1647,45096,1343,45126,45156,45157,45187,45188,1343,45209,1837],{},[38,45094,45095],{},"Mezní sklony",[883,45097,45099],{"className":45098},[886],[888,45100,45101],{"xmlns":890},[892,45102,45103,45123],{},[895,45104,45105,45107,45109,45111,45113,45115,45117,45119,45121],{},[898,45106,1742],{},[898,45108,1702],{},[898,45110,1683],{},[1706,45112,1708],{},[898,45114,3120],{"mathvariant":2409},[898,45116,1683],{},[898,45118,15493],{"mathvariant":2409},[898,45120,3120],{"mathvariant":2409},[898,45122,28247],{},[902,45124,45125],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,45127,45129],{"className":45128},[886],[888,45130,45131],{"xmlns":890},[892,45132,45133,45153],{},[895,45134,45135,45137,45139,45141,45143,45145,45147,45149,45151],{},[898,45136,1742],{},[898,45138,1702],{},[898,45140,14171],{},[1706,45142,1708],{},[898,45144,3120],{"mathvariant":2409},[898,45146,14171],{},[898,45148,15493],{"mathvariant":2409},[898,45150,3120],{"mathvariant":2409},[898,45152,28247],{},[902,45154,45155],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,45158,45160],{"className":45159},[886],[888,45161,45162],{"xmlns":890},[892,45163,45164,45184],{},[895,45165,45166,45168,45170,45172,45174,45176,45178,45180,45182],{},[898,45167,1742],{},[898,45169,1702],{},[898,45171,1683],{},[1706,45173,2447],{},[898,45175,1742],{},[898,45177,1702],{},[898,45179,14171],{},[1706,45181,1708],{},[2148,45183,2701],{},[902,45185,45186],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,45189,45191],{"className":45190},[886],[888,45192,45193],{"xmlns":890},[892,45194,45195,45207],{},[895,45196,45197,45199,45201,45203,45205],{},[898,45198,1742],{},[898,45200,1702],{},[898,45202,1683],{},[1706,45204,1708],{},[898,45206,207],{},[902,45208,38983],{"encoding":904},[883,45210,45212],{"className":45211},[886],[888,45213,45214],{"xmlns":890},[892,45215,45216,45232],{},[895,45217,45218,45220,45222,45224,45226,45228,45230],{},[898,45219,1742],{},[898,45221,1702],{},[898,45223,14171],{},[1706,45225,1708],{},[2148,45227,2701],{},[1706,45229,1715],{},[898,45231,207],{},[902,45233,39009],{"encoding":904},[123,45235,45236,45239,45240],{},[38,45237,45238],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,45241,45242,45329,45398],{},[123,45243,45244,8186,45261,45282,45283,2505],{},[883,45245,45247],{"className":45246},[886],[888,45248,45249],{"xmlns":890},[892,45250,45251,45259],{},[895,45252,45253,45255,45257],{},[898,45254,1683],{},[2415,45256,31397],{},[898,45258,31291],{},[902,45260,31402],{"encoding":904},[883,45262,45264],{"className":45263},[886],[888,45265,45266],{"xmlns":890},[892,45267,45268,45280],{},[895,45269,45270,45272,45274,45276,45278],{},[898,45271,28247],{},[1706,45273,1708],{},[898,45275,1683],{},[1706,45277,2447],{},[898,45279,31291],{},[902,45281,33851],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,45284,45286],{"className":45285},[886],[888,45287,45288],{"xmlns":890},[892,45289,45290,45326],{},[895,45291,45292,45298,45300,45302,45304,45306,45312,45314,45316,45318,45320,45322,45324],{},[2489,45293,45294,45296],{},[898,45295,28247],{},[898,45297,23410],{},[1706,45299,1708],{},[1706,45301,2140],{"stretchy":2139},[898,45303,2450],{},[1706,45305,2447],{},[2489,45307,45308,45310],{},[898,45309,31291],{},[1706,45311,3197],{},[1706,45313,2153],{"stretchy":2139},[898,45315,15493],{"mathvariant":2409},[1706,45317,2140],{"stretchy":2139},[2148,45319,2701],{},[1706,45321,1715],{},[898,45323,207],{},[1706,45325,2153],{"stretchy":2139},[902,45327,45328],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,45330,45331,45352,45353,45372,45373,2505],{},[883,45332,45334],{"className":45333},[886],[888,45335,45336],{"xmlns":890},[892,45337,45338,45350],{},[895,45339,45340,45342,45344,45346,45348],{},[898,45341,1683],{},[2415,45343,31397],{},[898,45345,31291],{},[2415,45347,31397],{},[898,45349,31220],{},[902,45351,37317],{"encoding":904},": přidává vládu, zdanění ",[883,45354,45356],{"className":45355},[886],[888,45357,45358],{"xmlns":890},[892,45359,45360,45370],{},[895,45361,45362,45364,45366,45368],{},[898,45363,1659],{},[1706,45365,2140],{"stretchy":2139},[898,45367,28247],{},[1706,45369,2153],{"stretchy":2139},[902,45371,41301],{"encoding":904}," a disponibilní důchod ",[883,45374,45376],{"className":45375},[886],[888,45377,45378],{"xmlns":890},[892,45379,45380,45396],{},[895,45381,45382,45388,45390,45392,45394],{},[2142,45383,45384,45386],{},[898,45385,28247],{},[898,45387,2334],{},[1706,45389,1708],{},[898,45391,28247],{},[1706,45393,1715],{},[898,45395,1659],{},[902,45397,40800],{"encoding":904},[123,45399,45400,45425,45426,15842,45447,1837],{},[883,45401,45403],{"className":45402},[886],[888,45404,45405],{"xmlns":890},[892,45406,45407,45423],{},[895,45408,45409,45411,45413,45415,45417,45419,45421],{},[898,45410,1683],{},[2415,45412,31397],{},[898,45414,31291],{},[2415,45416,31397],{},[898,45418,31220],{},[2415,45420,31397],{},[898,45422,31427],{},[902,45424,31430],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,45427,45429],{"className":45428},[886],[888,45430,45431],{"xmlns":890},[892,45432,45433,45445],{},[895,45434,45435,45437,45439,45441,45443],{},[898,45436,31427],{},[1706,45438,1708],{},[898,45440,10315],{},[1706,45442,1715],{},[898,45444,1742],{},[902,45446,42338],{"encoding":904},[883,45448,45450],{"className":45449},[886],[888,45451,45452],{"xmlns":890},[892,45453,45454,45472],{},[895,45455,45456,45458,45460,45462,45464,45470],{},[898,45457,1742],{},[1706,45459,1708],{},[898,45461,1742],{},[1706,45463,2140],{"stretchy":2139},[2142,45465,45466,45468],{},[898,45467,28247],{},[898,45469,2334],{},[1706,45471,2153],{"stretchy":2139},[902,45473,45474],{"encoding":904},"M = M(Y_D)",[123,45476,45477,45480,45481,1647,45484,45542],{},[38,45478,45479],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,45482,45483],{},"multiplikátor investic",[883,45485,45487],{"className":45486},[886],[888,45488,45489],{"xmlns":890},[892,45490,45491,45539],{},[895,45492,45493,45495,45501,45503,45505,45511,45513,45515,45517,45519,45521,45523,45525,45527,45529,45531,45533,45535,45537],{},[898,45494,28987],{"mathvariant":2409},[2489,45496,45497,45499],{},[898,45498,28247],{},[898,45500,23410],{},[898,45502,15493],{"mathvariant":2409},[898,45504,28987],{"mathvariant":2409},[2489,45506,45507,45509],{},[898,45508,31291],{},[1706,45510,3197],{},[1706,45512,1708],{},[2148,45514,2701],{},[898,45516,15493],{"mathvariant":2409},[1706,45518,2140],{"stretchy":2139},[2148,45520,2701],{},[1706,45522,1715],{},[898,45524,207],{},[1706,45526,2153],{"stretchy":2139},[1706,45528,1708],{},[2148,45530,2701],{},[898,45532,15493],{"mathvariant":2409},[898,45534,1742],{},[898,45536,1702],{},[898,45538,14171],{},[902,45540,45541],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,45544,45545,45547,45548,45563,45564,37745,45581,45596,45597,45622,45623,1837],{},[38,45546,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,45549,45551],{"className":45550},[886],[888,45552,45553],{"xmlns":890},[892,45554,45555,45561],{},[895,45556,45557,45559],{},[898,45558,31291],{},[898,45560,14171],{},[902,45562,31159],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,45565,45567],{"className":45566},[886],[888,45568,45569],{"xmlns":890},[892,45570,45571,45579],{},[895,45572,45573,45575,45577],{},[898,45574,31291],{},[1706,45576,1708],{},[898,45578,14171],{},[902,45580,31819],{"encoding":904},[883,45582,45584],{"className":45583},[886],[888,45585,45586],{"xmlns":890},[892,45587,45588,45594],{},[895,45589,45590,45592],{},[898,45591,6362],{},[898,45593,1742],{},[902,45595,31166],{"encoding":904}," rovnováhu trhu peněz (",[883,45598,45600],{"className":45599},[886],[888,45601,45602],{"xmlns":890},[892,45603,45604,45620],{},[895,45605,45606,45612,45614],{},[2489,45607,45608,45610],{},[898,45609,1742],{},[898,45611,2334],{},[1706,45613,1708],{},[2489,45615,45616,45618],{},[898,45617,1742],{},[1706,45619,3197],{},[902,45621,32587],{"encoding":904},"); průsečík dává ",[883,45624,45626],{"className":45625},[886],[888,45627,45628],{"xmlns":890},[892,45629,45630,45650],{},[895,45631,45632,45634,45640,45642,45648],{},[1706,45633,2140],{"stretchy":2139},[2489,45635,45636,45638],{},[898,45637,28247],{},[898,45639,23410],{},[1706,45641,2505],{"separator":2504},[2489,45643,45644,45646],{},[898,45645,3950],{},[898,45647,23410],{},[1706,45649,2153],{"stretchy":2139},[902,45651,31203],{"encoding":904},[115,45653,19879],{"id":19878},[120,45655,45656,45694,45734,45824,45906,45960,46016,46075,46110,46115,46187,46262,46348,46410,46478,46536,46589,46628],{},[123,45657,45658,21021,45661,44979],{},[38,45659,45660],{},"Hrubý národní produkt (GNP)",[883,45662,45664],{"className":45663},[886],[888,45665,45666],{"xmlns":890},[892,45667,45668,45692],{},[895,45669,45670,45672,45674,45676,45678,45680,45682,45684,45686,45688,45690],{},[898,45671,31220],{},[898,45673,37391],{},[898,45675,1702],{},[1706,45677,1708],{},[898,45679,1683],{},[1706,45681,2447],{},[898,45683,31291],{},[1706,45685,2447],{},[898,45687,31220],{},[1706,45689,2447],{},[898,45691,31427],{},[902,45693,44978],{"encoding":904},[123,45695,45696,45712,45713,1837],{},[38,45697,45698,45699],{},"Národní důchod ",[883,45700,45702],{"className":45701},[886],[888,45703,45704],{"xmlns":890},[892,45705,45706,45710],{},[895,45707,45708],{},[898,45709,28247],{},[902,45711,28247],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,45714,45716],{"className":45715},[886],[888,45717,45718],{"xmlns":890},[892,45719,45720,45732],{},[895,45721,45722,45724,45726,45728,45730],{},[898,45723,31220],{},[898,45725,37391],{},[898,45727,1702],{},[1706,45729,3248],{},[898,45731,28247],{},[902,45733,44943],{"encoding":904},[123,45735,45736,45762,45763,1343,45786,1343,45807,1837],{},[38,45737,45738,45739],{},"Funkce spotřeby ",[883,45740,45742],{"className":45741},[886],[888,45743,45744],{"xmlns":890},[892,45745,45746,45760],{},[895,45747,45748,45750,45752,45754,45756,45758],{},[898,45749,1683],{},[1706,45751,1708],{},[898,45753,1683],{},[1706,45755,2140],{"stretchy":2139},[898,45757,28247],{},[1706,45759,2153],{"stretchy":2139},[902,45761,39830],{"encoding":904}," — lineární model ",[883,45764,45766],{"className":45765},[886],[888,45767,45768],{"xmlns":890},[892,45769,45770,45784],{},[895,45771,45772,45774,45776,45778,45780,45782],{},[898,45773,1683],{},[1706,45775,1708],{},[898,45777,207],{},[898,45779,28247],{},[1706,45781,2447],{},[898,45783,2450],{},[902,45785,38016],{"encoding":904},[883,45787,45789],{"className":45788},[886],[888,45790,45791],{"xmlns":890},[892,45792,45793,45805],{},[895,45794,45795,45797,45799,45801,45803],{},[2148,45796,2150],{},[1706,45798,2539],{},[898,45800,207],{},[1706,45802,2539],{},[2148,45804,2701],{},[902,45806,37933],{"encoding":904},[883,45808,45810],{"className":45809},[886],[888,45811,45812],{"xmlns":890},[892,45813,45814,45822],{},[895,45815,45816,45818,45820],{},[898,45817,2450],{},[1706,45819,8922],{},[2148,45821,2150],{},[902,45823,37911],{"encoding":904},[123,45825,45826,21021,45853,45874,45875,1837],{},[38,45827,45828,45829],{},"Funkce úspor ",[883,45830,45832],{"className":45831},[886],[888,45833,45834],{"xmlns":890},[892,45835,45836,45850],{},[895,45837,45838,45840,45842,45844,45846,45848],{},[898,45839,14171],{},[1706,45841,1708],{},[898,45843,14171],{},[1706,45845,2140],{"stretchy":2139},[898,45847,28247],{},[1706,45849,2153],{"stretchy":2139},[902,45851,45852],{"encoding":904},"S = S(Y)",[883,45854,45856],{"className":45855},[886],[888,45857,45858],{"xmlns":890},[892,45859,45860,45872],{},[895,45861,45862,45864,45866,45868,45870],{},[898,45863,28247],{},[1706,45865,1708],{},[898,45867,1683],{},[1706,45869,2447],{},[898,45871,14171],{},[902,45873,31801],{"encoding":904},"; lineární ",[883,45876,45878],{"className":45877},[886],[888,45879,45880],{"xmlns":890},[892,45881,45882,45904],{},[895,45883,45884,45886,45888,45890,45892,45894,45896,45898,45900,45902],{},[898,45885,14171],{},[1706,45887,1708],{},[1706,45889,2140],{"stretchy":2139},[2148,45891,2701],{},[1706,45893,1715],{},[898,45895,207],{},[1706,45897,2153],{"stretchy":2139},[898,45899,28247],{},[1706,45901,1715],{},[898,45903,2450],{},[902,45905,38265],{"encoding":904},[123,45907,45908,21021,45911,1343,45934,1837],{},[38,45909,45910],{},"Autonomní spotřeba\u002Fúspory",[883,45912,45914],{"className":45913},[886],[888,45915,45916],{"xmlns":890},[892,45917,45918,45932],{},[895,45919,45920,45922,45924,45926,45928,45930],{},[898,45921,1683],{},[1706,45923,2140],{"stretchy":2139},[2148,45925,2150],{},[1706,45927,2153],{"stretchy":2139},[1706,45929,1708],{},[898,45931,2450],{},[902,45933,38655],{"encoding":904},[883,45935,45937],{"className":45936},[886],[888,45938,45939],{"xmlns":890},[892,45940,45941,45957],{},[895,45942,45943,45945,45947,45949,45951,45953,45955],{},[898,45944,14171],{},[1706,45946,2140],{"stretchy":2139},[2148,45948,2150],{},[1706,45950,2153],{"stretchy":2139},[1706,45952,1708],{},[1706,45954,1715],{},[898,45956,2450],{},[902,45958,45959],{"encoding":904},"S(0) = -b",[123,45961,45962,45994,45995,1936],{},[38,45963,45964,45965],{},"Mezní sklon ke spotřebě ",[883,45966,45968],{"className":45967},[886],[888,45969,45970],{"xmlns":890},[892,45971,45972,45992],{},[895,45973,45974,45976,45978,45980,45982,45984,45986,45988,45990],{},[898,45975,1742],{},[898,45977,1702],{},[898,45979,1683],{},[1706,45981,1708],{},[898,45983,3120],{"mathvariant":2409},[898,45985,1683],{},[898,45987,15493],{"mathvariant":2409},[898,45989,3120],{"mathvariant":2409},[898,45991,28247],{},[902,45993,45125],{"encoding":904}," (v lineárním modelu ",[883,45996,45998],{"className":45997},[886],[888,45999,46000],{"xmlns":890},[892,46001,46002,46014],{},[895,46003,46004,46006,46008,46010,46012],{},[898,46005,1742],{},[898,46007,1702],{},[898,46009,1683],{},[1706,46011,1708],{},[898,46013,207],{},[902,46015,38983],{"encoding":904},[123,46017,46018,45994,46050,1936],{},[38,46019,46020,46021],{},"Mezní sklon k úsporám ",[883,46022,46024],{"className":46023},[886],[888,46025,46026],{"xmlns":890},[892,46027,46028,46048],{},[895,46029,46030,46032,46034,46036,46038,46040,46042,46044,46046],{},[898,46031,1742],{},[898,46033,1702],{},[898,46035,14171],{},[1706,46037,1708],{},[898,46039,3120],{"mathvariant":2409},[898,46041,14171],{},[898,46043,15493],{"mathvariant":2409},[898,46045,3120],{"mathvariant":2409},[898,46047,28247],{},[902,46049,45155],{"encoding":904},[883,46051,46053],{"className":46052},[886],[888,46054,46055],{"xmlns":890},[892,46056,46057,46073],{},[895,46058,46059,46061,46063,46065,46067,46069,46071],{},[898,46060,1742],{},[898,46062,1702],{},[898,46064,14171],{},[1706,46066,1708],{},[2148,46068,2701],{},[1706,46070,1715],{},[898,46072,207],{},[902,46074,39009],{"encoding":904},[123,46076,46077,1647,46080,46109],{},[38,46078,46079],{},"Vztah",[883,46081,46083],{"className":46082},[886],[888,46084,46085],{"xmlns":890},[892,46086,46087,46107],{},[895,46088,46089,46091,46093,46095,46097,46099,46101,46103,46105],{},[898,46090,1742],{},[898,46092,1702],{},[898,46094,1683],{},[1706,46096,2447],{},[898,46098,1742],{},[898,46100,1702],{},[898,46102,14171],{},[1706,46104,1708],{},[2148,46106,2701],{},[902,46108,45186],{"encoding":904}," (7.5).",[123,46111,46112,46114],{},[38,46113,39673],{}," — rovnováha agregátní poptávky a nabídky.",[123,46116,46117,46120,46121,7822,46142,1837],{},[38,46118,46119],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,46122,46124],{"className":46123},[886],[888,46125,46126],{"xmlns":890},[892,46127,46128,46140],{},[895,46129,46130,46132,46134,46136,46138],{},[898,46131,28247],{},[1706,46133,1708],{},[898,46135,1683],{},[1706,46137,2447],{},[898,46139,31291],{},[902,46141,33851],{"encoding":904},[883,46143,46145],{"className":46144},[886],[888,46146,46147],{"xmlns":890},[892,46148,46149,46185],{},[895,46150,46151,46157,46159,46161,46163,46165,46171,46173,46175,46177,46179,46181,46183],{},[2489,46152,46153,46155],{},[898,46154,28247],{},[898,46156,23410],{},[1706,46158,1708],{},[1706,46160,2140],{"stretchy":2139},[898,46162,2450],{},[1706,46164,2447],{},[2489,46166,46167,46169],{},[898,46168,31291],{},[1706,46170,3197],{},[1706,46172,2153],{"stretchy":2139},[898,46174,15493],{"mathvariant":2409},[1706,46176,2140],{"stretchy":2139},[2148,46178,2701],{},[1706,46180,1715],{},[898,46182,207],{},[1706,46184,2153],{"stretchy":2139},[902,46186,45328],{"encoding":904},[123,46188,46189,46192,46193,1343,46212,7822,46237,1837],{},[38,46190,46191],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,46194,46196],{"className":46195},[886],[888,46197,46198],{"xmlns":890},[892,46199,46200,46210],{},[895,46201,46202,46204,46206,46208],{},[898,46203,1659],{},[1706,46205,2140],{"stretchy":2139},[898,46207,28247],{},[1706,46209,2153],{"stretchy":2139},[902,46211,41301],{"encoding":904},[883,46213,46215],{"className":46214},[886],[888,46216,46217],{"xmlns":890},[892,46218,46219,46235],{},[895,46220,46221,46227,46229,46231,46233],{},[2142,46222,46223,46225],{},[898,46224,28247],{},[898,46226,2334],{},[1706,46228,1708],{},[898,46230,28247],{},[1706,46232,1715],{},[898,46234,1659],{},[902,46236,40800],{"encoding":904},[883,46238,46240],{"className":46239},[886],[888,46241,46242],{"xmlns":890},[892,46243,46244,46260],{},[895,46245,46246,46248,46250,46252,46254,46256,46258],{},[898,46247,28247],{},[1706,46249,1708],{},[898,46251,1683],{},[1706,46253,2447],{},[898,46255,31291],{},[1706,46257,2447],{},[898,46259,31220],{},[902,46261,40771],{"encoding":904},[123,46263,46264,46267,46268,46289,46290,7822,46314,1837],{},[38,46265,46266],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,46269,46271],{"className":46270},[886],[888,46272,46273],{"xmlns":890},[892,46274,46275,46287],{},[895,46276,46277,46279,46281,46283,46285],{},[898,46278,31427],{},[1706,46280,1708],{},[898,46282,10315],{},[1706,46284,1715],{},[898,46286,1742],{},[902,46288,42338],{"encoding":904},", importem ",[883,46291,46293],{"className":46292},[886],[888,46294,46295],{"xmlns":890},[892,46296,46297,46311],{},[895,46298,46299,46301,46303,46309],{},[898,46300,1742],{},[1706,46302,2140],{"stretchy":2139},[2142,46304,46305,46307],{},[898,46306,28247],{},[898,46308,2334],{},[1706,46310,2153],{"stretchy":2139},[902,46312,46313],{"encoding":904},"M(Y_D)",[883,46315,46317],{"className":46316},[886],[888,46318,46319],{"xmlns":890},[892,46320,46321,46345],{},[895,46322,46323,46325,46327,46329,46331,46333,46335,46337,46339,46341,46343],{},[898,46324,28247],{},[1706,46326,1708],{},[898,46328,1683],{},[1706,46330,2447],{},[898,46332,31291],{},[1706,46334,2447],{},[898,46336,31220],{},[1706,46338,2447],{},[898,46340,10315],{},[1706,46342,1715],{},[898,46344,1742],{},[902,46346,46347],{"encoding":904},"Y = C + I + G + B - M",[123,46349,46350,21021,46353,45542],{},[38,46351,46352],{},"Multiplikátor investic",[883,46354,46356],{"className":46355},[886],[888,46357,46358],{"xmlns":890},[892,46359,46360,46408],{},[895,46361,46362,46364,46370,46372,46374,46380,46382,46384,46386,46388,46390,46392,46394,46396,46398,46400,46402,46404,46406],{},[898,46363,28987],{"mathvariant":2409},[2489,46365,46366,46368],{},[898,46367,28247],{},[898,46369,23410],{},[898,46371,15493],{"mathvariant":2409},[898,46373,28987],{"mathvariant":2409},[2489,46375,46376,46378],{},[898,46377,31291],{},[1706,46379,3197],{},[1706,46381,1708],{},[2148,46383,2701],{},[898,46385,15493],{"mathvariant":2409},[1706,46387,2140],{"stretchy":2139},[2148,46389,2701],{},[1706,46391,1715],{},[898,46393,207],{},[1706,46395,2153],{"stretchy":2139},[1706,46397,1708],{},[2148,46399,2701],{},[898,46401,15493],{"mathvariant":2409},[898,46403,1742],{},[898,46405,1702],{},[898,46407,14171],{},[902,46409,45541],{"encoding":904},[123,46411,46412,21021,46443,1343,46460,46477],{},[38,46413,34829,46414],{},[883,46415,46417],{"className":46416},[886],[888,46418,46419],{"xmlns":890},[892,46420,46421,46441],{},[895,46422,46423,46425,46427,46429,46431,46433,46435,46437,46439],{},[898,46424,31291],{},[1706,46426,2140],{"stretchy":2139},[898,46428,3950],{},[1706,46430,2153],{"stretchy":2139},[1706,46432,1708],{},[898,46434,20413],{},[898,46436,3950],{},[1706,46438,2447],{},[898,46440,3120],{},[902,46442,34859],{"encoding":904},[883,46444,46446],{"className":46445},[886],[888,46447,46448],{"xmlns":890},[892,46449,46450,46458],{},[895,46451,46452,46454,46456],{},[898,46453,20413],{},[1706,46455,2539],{},[2148,46457,2150],{},[902,46459,31622],{"encoding":904},[883,46461,46463],{"className":46462},[886],[888,46464,46465],{"xmlns":890},[892,46466,46467,46475],{},[895,46468,46469,46471,46473],{},[898,46470,3120],{},[1706,46472,8922],{},[2148,46474,2150],{},[902,46476,31601],{"encoding":904},"; klesající.",[123,46479,46480,46482,46483,46485,46486,46535],{},[38,46481,34947],{}," — rovnováha na trhu zboží (",[614,46484,31162],{},"); ",[883,46487,46489],{"className":46488},[886],[888,46490,46491],{"xmlns":890},[892,46492,46493,46533],{},[895,46494,46495,46497,46499,46511,46513,46515],{},[898,46496,28247],{},[1706,46498,1708],{},[2964,46500,46501,46503],{},[898,46502,20413],{},[895,46504,46505,46507,46509],{},[2148,46506,2701],{},[1706,46508,1715],{},[898,46510,207],{},[898,46512,3950],{},[1706,46514,2447],{},[2964,46516,46517,46525],{},[895,46518,46519,46521,46523],{},[898,46520,2450],{},[1706,46522,2447],{},[898,46524,3120],{},[895,46526,46527,46529,46531],{},[2148,46528,2701],{},[1706,46530,1715],{},[898,46532,207],{},[902,46534,35000],{"encoding":904}," (7.14); klesající.",[123,46537,46538,46540,46541,46485,46543,46588],{},[38,46539,35146],{}," — rovnováha na trhu peněz (",[614,46542,31169],{},[883,46544,46546],{"className":46545},[886],[888,46547,46548],{"xmlns":890},[892,46549,46550,46586],{},[895,46551,46552,46558,46560,46566,46568,46570,46576,46578,46580],{},[2489,46553,46554,46556],{},[898,46555,1742],{},[1706,46557,3197],{},[1706,46559,1708],{},[2142,46561,46562,46564],{},[898,46563,32344],{},[2148,46565,2701],{},[898,46567,28247],{},[1706,46569,2447],{},[2142,46571,46572,46574],{},[898,46573,32344],{},[2148,46575,2495],{},[898,46577,3950],{},[1706,46579,2447],{},[2142,46581,46582,46584],{},[898,46583,32344],{},[2148,46585,4284],{},[902,46587,35194],{"encoding":904}," (7.15); rostoucí.",[123,46590,46591,21021,46594,1837],{},[38,46592,46593],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,46595,46597],{"className":46596},[886],[888,46598,46599],{"xmlns":890},[892,46600,46601,46625],{},[895,46602,46603,46609,46611,46617,46619],{},[2489,46604,46605,46607],{},[898,46606,1742],{},[898,46608,2334],{},[1706,46610,1708],{},[2142,46612,46613,46615],{},[898,46614,6362],{},[2148,46616,2701],{},[1706,46618,2447],{},[2142,46620,46621,46623],{},[898,46622,6362],{},[2148,46624,2495],{},[902,46626,46627],{"encoding":904},"M^D = L_1 + L_2",[123,46629,46630,35204,46632,33087,46645,1993,46660,46675,46676,1837],{},[38,46631,945],{},[883,46633,46635],{"className":46634},[886],[888,46636,46637],{"xmlns":890},[892,46638,46639,46643],{},[895,46640,46641],{},[898,46642,23410],{},[902,46644,23410],{"encoding":904},[883,46646,46648],{"className":46647},[886],[888,46649,46650],{"xmlns":890},[892,46651,46652,46658],{},[895,46653,46654,46656],{},[898,46655,31291],{},[898,46657,14171],{},[902,46659,31159],{"encoding":904},[883,46661,46663],{"className":46662},[886],[888,46664,46665],{"xmlns":890},[892,46666,46667,46673],{},[895,46668,46669,46671],{},[898,46670,6362],{},[898,46672,1742],{},[902,46674,31166],{"encoding":904}," určuje ",[883,46677,46679],{"className":46678},[886],[888,46680,46681],{"xmlns":890},[892,46682,46683,46703],{},[895,46684,46685,46687,46693,46695,46701],{},[1706,46686,2140],{"stretchy":2139},[2489,46688,46689,46691],{},[898,46690,28247],{},[898,46692,23410],{},[1706,46694,2505],{"separator":2504},[2489,46696,46697,46699],{},[898,46698,3950],{},[898,46700,23410],{},[1706,46702,2153],{"stretchy":2139},[902,46704,31203],{"encoding":904},[115,46706,21083],{"id":21082},[120,46708,46709,46716,46723],{},[123,46710,46711,1647,46713],{},[38,46712,21126],{},[207,46714,21132],{"className":46715,"dataFsResolvedFilePath":21130,"href":21131},[210],[123,46717,46718,1647,46720],{},[38,46719,35312],{},[207,46721,35316],{"className":46722,"dataFsResolvedFilePath":868,"href":869},[210],[123,46724,46725,46727],{},[38,46726,35331],{},[120,46728,46729,46735,46741,46747],{},[123,46730,46731,46734],{},[207,46732,35372],{"className":46733,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,46736,46737,46740],{},[207,46738,35339],{"className":46739,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,46742,46743,46746],{},[207,46744,22138],{"className":46745,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,46748,46749,46752,46753,1343,46770,46787],{},[207,46750,1145],{"className":46751,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,46754,46756],{"className":46755},[886],[888,46757,46758],{"xmlns":890},[892,46759,46760,46768],{},[895,46761,46762,46764,46766],{},[898,46763,1742],{},[898,46765,1702],{},[898,46767,1683],{},[902,46769,37142],{"encoding":904},[883,46771,46773],{"className":46772},[886],[888,46774,46775],{"xmlns":890},[892,46776,46777,46785],{},[895,46778,46779,46781,46783],{},[898,46780,1742],{},[898,46782,1702],{},[898,46784,14171],{},[902,46786,38753],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":46789},[46790,46791,46792,46793,46798,46801,46802,46809,46814,46819,46822,46823,46824,46825],{"id":31114,"depth":642,"text":31115},{"id":37251,"depth":642,"text":37252},{"id":37371,"depth":642,"text":37372},{"id":37624,"depth":642,"text":37625,"children":46794},[46795,46796,46797],{"id":37628,"depth":649,"text":37629},{"id":37840,"depth":649,"text":37841},{"id":38347,"depth":649,"text":38348},{"id":38665,"depth":642,"text":38666,"children":46799},[46800],{"id":39180,"depth":649,"text":39181},{"id":39672,"depth":642,"text":39673},{"id":39699,"depth":642,"text":39700,"children":46803},[46804,46805,46806,46808],{"id":39710,"depth":649,"text":39711},{"id":39780,"depth":649,"text":39781},{"id":39959,"depth":649,"text":46807},"Výpočet YEY^E",{"id":40102,"depth":649,"text":40103},{"id":40479,"depth":642,"text":40480,"children":46810},[46811,46812,46813],{"id":40483,"depth":649,"text":39711},{"id":40930,"depth":649,"text":39781},{"id":41586,"depth":649,"text":41587},{"id":42369,"depth":642,"text":42370,"children":46815},[46816,46817,46818],{"id":42373,"depth":649,"text":39711},{"id":42518,"depth":649,"text":39781},{"id":42788,"depth":649,"text":42789},{"id":43709,"depth":642,"text":43710,"children":46820},[46821],{"id":43905,"depth":649,"text":43906},{"id":44452,"depth":642,"text":44453},{"id":44912,"depth":642,"text":44913},{"id":19878,"depth":642,"text":19879},{"id":21082,"depth":642,"text":21083},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,35325,1143,46832,46833,46834,35372,36980],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":46837,"title":46838,"body":46839,"course":1128,"courses":659,"created":21169,"description":641,"extension":661,"meta":55808,"navigation":664,"path":55809,"seo":55810,"sources":55811,"stem":55812,"tags":55813,"type":21181,"updated":677,"__hash__":55818},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":46840,"toc":55777},[46841,46844,46846,47075,47079,47132,47199,47311,47470,47474,47590,47594,47597,47719,47722,47915,47939,48007,48171,48189,48255,48632,48636,48643,48887,48942,48946,49010,49128,49259,49291,49411,49493,49496,49618,49810,50031,50035,50075,50180,50237,50337,50514,50643,50696,50699,50786,50790,50966,50970,50973,51058,51061,51118,51223,51227,51348,51351,51534,51537,51645,51854,52174,52222,52295,52369,52371,52595,52830,53098,53102,53105,53210,53267,53301,53348,53381,53465,53467,53699,53832,53909,54031,54186,54190,54331,54338,54562,54573,54577,54581,54686,54828,54938,55037,55041,55200,55309,55311,55704,55706],[12,46842,46838],{"id":46843},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,46845,31115],{"id":31114},[724,46847,46848,46850,46851,46885,46886,46889,46890,46921,46922,46968,46969,46972,46973,47015,47016,47034,47035,47039,47040,47070,47071,47074],{},[38,46849,913],{}," řeší, jaký svazek zboží ",[883,46852,46854],{"className":46853},[886],[888,46855,46856],{"xmlns":890},[892,46857,46858,46882],{},[895,46859,46860,46862,46870,46872,46880],{},[1706,46861,21693],{"stretchy":2139},[28285,46863,46864,46866,46868],{},[898,46865,2146],{},[2148,46867,2701],{},[1706,46869,3197],{},[1706,46871,2505],{"separator":2504},[28285,46873,46874,46876,46878],{},[898,46875,2146],{},[2148,46877,2495],{},[1706,46879,3197],{},[1706,46881,21708],{"stretchy":2139},[902,46883,46884],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,46887,46888],{},"primární úloha"," — maximalizace užitečnosti ",[883,46891,46893],{"className":46892},[886],[888,46894,46895],{"xmlns":890},[892,46896,46897,46919],{},[895,46898,46899,46901,46903,46909,46911,46917],{},[898,46900,900],{},[1706,46902,2140],{"stretchy":2139},[2142,46904,46905,46907],{},[898,46906,2146],{},[2148,46908,2701],{},[1706,46910,2505],{"separator":2504},[2142,46912,46913,46915],{},[898,46914,2146],{},[2148,46916,2495],{},[1706,46918,2153],{"stretchy":2139},[902,46920,35443],{"encoding":904}," při rozpočtovém omezení ",[883,46923,46925],{"className":46924},[886],[888,46926,46927],{"xmlns":890},[892,46928,46929,46965],{},[895,46930,46931,46937,46939,46945,46951,46953,46959],{},[2489,46932,46933,46935],{},[898,46934,28247],{},[1706,46936,3197],{},[1706,46938,1708],{},[2142,46940,46941,46943],{},[898,46942,1702],{},[2148,46944,2701],{},[2142,46946,46947,46949],{},[898,46948,2146],{},[2148,46950,2701],{},[1706,46952,2447],{},[2142,46954,46955,46957],{},[898,46956,1702],{},[2148,46958,2495],{},[2142,46960,46961,46963],{},[898,46962,2146],{},[2148,46964,2495],{},[902,46966,46967],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,46970,46971],{},"duální úloha"," — minimalizace výdajů ",[883,46974,46976],{"className":46975},[886],[888,46977,46978],{"xmlns":890},[892,46979,46980,47012],{},[895,46981,46982,46984,46986,46992,46998,47000,47006],{},[898,46983,23410],{},[1706,46985,1708],{},[2142,46987,46988,46990],{},[898,46989,1702],{},[2148,46991,2701],{},[2142,46993,46994,46996],{},[898,46995,2146],{},[2148,46997,2701],{},[1706,46999,2447],{},[2142,47001,47002,47004],{},[898,47003,1702],{},[2148,47005,2495],{},[2142,47007,47008,47010],{},[898,47009,2146],{},[2148,47011,2495],{},[902,47013,47014],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,47017,47019],{"className":47018},[886],[888,47020,47021],{"xmlns":890},[892,47022,47023,47031],{},[895,47024,47025],{},[2489,47026,47027,47029],{},[898,47028,900],{},[1706,47030,3197],{},[902,47032,47033],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,47036,47038],{"className":47037,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,47041,47043],{"className":47042},[886],[888,47044,47045],{"xmlns":890},[892,47046,47047,47067],{},[895,47048,47049,47051,47053,47059,47061],{},[2415,47050,29714],{},[1706,47052,1708],{},[2142,47054,47055,47057],{},[898,47056,1702],{},[2148,47058,2701],{},[898,47060,15493],{"mathvariant":2409},[2142,47062,47063,47065],{},[898,47064,1702],{},[2148,47066,2495],{},[902,47068,47069],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,47072,47073],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,47076,47078],{"id":47077},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,47080,47081,47082,47100,47101,47131],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,47083,47085],{"className":47084},[886],[888,47086,47087],{"xmlns":890},[892,47088,47089,47097],{},[895,47090,47091],{},[2489,47092,47093,47095],{},[898,47094,28247],{},[1706,47096,3197],{},[902,47098,47099],{"encoding":904},"Y^*"," a ceny ",[883,47102,47104],{"className":47103},[886],[888,47105,47106],{"xmlns":890},[892,47107,47108,47128],{},[895,47109,47110,47118,47120],{},[28285,47111,47112,47114,47116],{},[898,47113,1702],{},[2148,47115,2701],{},[1706,47117,3197],{},[1706,47119,2505],{"separator":2504},[28285,47121,47122,47124,47126],{},[898,47123,1702],{},[2148,47125,2495],{},[1706,47127,3197],{},[902,47129,47130],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,47133,47135],{"className":47134},[886],[888,47136,47137],{"xmlns":890,"display":2350},[892,47138,47139,47196],{},[2354,47140,47141],{"width":2356},[2358,47142,47143,47145,47189,47191],{},[2361,47144],{"width":2363},[2361,47146,47147],{},[895,47148,47149,47155,47157,47165,47171,47173,47181,47187],{},[2489,47150,47151,47153],{},[898,47152,28247],{},[1706,47154,3197],{},[1706,47156,1708],{},[28285,47158,47159,47161,47163],{},[898,47160,1702],{},[2148,47162,2701],{},[1706,47164,3197],{},[2142,47166,47167,47169],{},[898,47168,2146],{},[2148,47170,2701],{},[1706,47172,2447],{},[28285,47174,47175,47177,47179],{},[898,47176,1702],{},[2148,47178,2495],{},[1706,47180,3197],{},[2142,47182,47183,47185],{},[898,47184,2146],{},[2148,47186,2495],{},[1706,47188,2505],{"separator":2504},[2361,47190],{"width":2363},[2361,47192,47193],{},[2415,47194,47195],{},"(6.12)",[902,47197,47198],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,47200,47201,47202,47205,47206,1993,47242,47278,47279,47292,47293,47307,47308,1837],{},"geometricky ",[38,47203,47204],{},"rozpočtová přímka (budget line)"," procházející body ",[883,47207,47209],{"className":47208},[886],[888,47210,47211],{"xmlns":890},[892,47212,47213,47239],{},[895,47214,47215,47217,47223,47225,47233,47235,47237],{},[1706,47216,21693],{"stretchy":2139},[2489,47218,47219,47221],{},[898,47220,28247],{},[1706,47222,3197],{},[898,47224,15493],{"mathvariant":2409},[28285,47226,47227,47229,47231],{},[898,47228,1702],{},[2148,47230,2701],{},[1706,47232,3197],{},[1706,47234,2505],{"separator":2504},[2148,47236,2150],{},[1706,47238,21708],{"stretchy":2139},[902,47240,47241],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,47243,47245],{"className":47244},[886],[888,47246,47247],{"xmlns":890},[892,47248,47249,47275],{},[895,47250,47251,47253,47255,47257,47263,47265,47273],{},[1706,47252,21693],{"stretchy":2139},[2148,47254,2150],{},[1706,47256,2505],{"separator":2504},[2489,47258,47259,47261],{},[898,47260,28247],{},[1706,47262,3197],{},[898,47264,15493],{"mathvariant":2409},[28285,47266,47267,47269,47271],{},[898,47268,1702],{},[2148,47270,2495],{},[1706,47272,3197],{},[1706,47274,21708],{"stretchy":2139},[902,47276,47277],{"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 ",[883,47280,47282],{"className":47281},[886],[888,47283,47284],{"xmlns":890},[892,47285,47286,47290],{},[895,47287,47288],{},[898,47289,900],{},[902,47291,900],{"encoding":904},", indiferenční křivky a ",[883,47294,47296],{"className":47295},[886],[888,47297,47298],{"xmlns":890},[892,47299,47300,47304],{},[895,47301,47302],{},[2415,47303,29714],{},[902,47305,47306],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,47309,880],{"className":47310,"dataFsResolvedFilePath":878,"href":879},[210],[1636,47312,47313],{},[724,47314,47315,47317,47318,47321,47322,47335,47336,47338,47339,47352,47353,1647,47356,47396,47397,47414,47415,47432,47433,47450,47451,47469],{},[883,47316,9276],{}," Pozor — dvě úlohy, totéž řešení\n",[38,47319,47320],{},"Primární úloha"," (max ",[883,47323,47325],{"className":47324},[886],[888,47326,47327],{"xmlns":890},[892,47328,47329,47333],{},[895,47330,47331],{},[898,47332,900],{},[902,47334,900],{"encoding":904}," při pevném rozpočtu) a ",[38,47337,46971],{}," (min ",[883,47340,47342],{"className":47341},[886],[888,47343,47344],{"xmlns":890},[892,47345,47346,47350],{},[895,47347,47348],{},[898,47349,23410],{},[902,47351,23410],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,47354,47355],{},"tentýž bod",[883,47357,47359],{"className":47358},[886],[888,47360,47361],{"xmlns":890},[892,47362,47363,47393],{},[895,47364,47365,47371,47373,47381,47383,47391],{},[2489,47366,47367,47369],{},[898,47368,2146],{},[1706,47370,3197],{},[1706,47372,21693],{"stretchy":2139},[28285,47374,47375,47377,47379],{},[898,47376,2146],{},[2148,47378,2701],{},[1706,47380,3197],{},[1706,47382,2505],{"separator":2504},[28285,47384,47385,47387,47389],{},[898,47386,2146],{},[2148,47388,2495],{},[1706,47390,3197],{},[1706,47392,21708],{"stretchy":2139},[902,47394,47395],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,47398,47400],{"className":47399},[886],[888,47401,47402],{"xmlns":890},[892,47403,47404,47412],{},[895,47405,47406],{},[2489,47407,47408,47410],{},[898,47409,28247],{},[1706,47411,3197],{},[902,47413,47099],{"encoding":904}," a hledáme maximální ",[883,47416,47418],{"className":47417},[886],[888,47419,47420],{"xmlns":890},[892,47421,47422,47430],{},[895,47423,47424],{},[2489,47425,47426,47428],{},[898,47427,900],{},[1706,47429,3197],{},[902,47431,47033],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,47434,47436],{"className":47435},[886],[888,47437,47438],{"xmlns":890},[892,47439,47440,47448],{},[895,47441,47442],{},[2489,47443,47444,47446],{},[898,47445,900],{},[1706,47447,3197],{},[902,47449,47033],{"encoding":904}," a hledáme minimální ",[883,47452,47454],{"className":47453},[886],[888,47455,47456],{"xmlns":890},[892,47457,47458,47466],{},[895,47459,47460],{},[2489,47461,47462,47464],{},[898,47463,23410],{},[1706,47465,3197],{},[902,47467,47468],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,47471,47473],{"id":47472},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,47475,47476,47477,47508,47509,47585,47586,1837],{},"Úlohou je najít maximum ",[883,47478,47480],{"className":47479},[886],[888,47481,47482],{"xmlns":890},[892,47483,47484,47506],{},[895,47485,47486,47488,47490,47496,47498,47504],{},[898,47487,900],{},[1706,47489,2140],{"stretchy":2139},[2142,47491,47492,47494],{},[898,47493,2146],{},[2148,47495,2701],{},[1706,47497,2505],{"separator":2504},[2142,47499,47500,47502],{},[898,47501,2146],{},[2148,47503,2495],{},[1706,47505,2153],{"stretchy":2139},[902,47507,35443],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,47510,47512],{"className":47511},[886],[888,47513,47514],{"xmlns":890},[892,47515,47516,47582],{},[895,47517,47518,47520,47522,47528,47530,47536,47538,47540,47546,47548,47556,47562,47564,47572,47578,47580],{},[898,47519,30152],{},[1706,47521,2140],{"stretchy":2139},[2142,47523,47524,47526],{},[898,47525,2146],{},[2148,47527,2701],{},[1706,47529,2505],{"separator":2504},[2142,47531,47532,47534],{},[898,47533,2146],{},[2148,47535,2495],{},[1706,47537,2153],{"stretchy":2139},[1706,47539,1708],{},[2489,47541,47542,47544],{},[898,47543,28247],{},[1706,47545,3197],{},[1706,47547,1715],{},[28285,47549,47550,47552,47554],{},[898,47551,1702],{},[2148,47553,2701],{},[1706,47555,3197],{},[2142,47557,47558,47560],{},[898,47559,2146],{},[2148,47561,2701],{},[1706,47563,1715],{},[28285,47565,47566,47568,47570],{},[898,47567,1702],{},[2148,47569,2495],{},[1706,47571,3197],{},[2142,47573,47574,47576],{},[898,47575,2146],{},[2148,47577,2495],{},[1706,47579,1708],{},[2148,47581,2150],{},[902,47583,47584],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,47587,47589],{"className":47588,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,47591,47593],{"id":47592},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,47595,47596],{},"Sestavíme",[883,47598,47600],{"className":47599},[886],[888,47601,47602],{"xmlns":890,"display":2350},[892,47603,47604,47716],{},[2354,47605,47606],{"width":2356},[2358,47607,47608,47610,47709,47711],{},[2361,47609],{"width":2363},[2361,47611,47612],{},[895,47613,47614,47617,47619,47625,47627,47633,47635,47637,47639,47641,47643,47645,47651,47653,47659,47661,47663,47665,47667,47673,47675,47683,47689,47691,47699,47705,47707],{},[898,47615,6362],{"mathvariant":47616},"script",[1706,47618,2140],{"stretchy":2139},[2142,47620,47621,47623],{},[898,47622,2146],{},[2148,47624,2701],{},[1706,47626,2505],{"separator":2504},[2142,47628,47629,47631],{},[898,47630,2146],{},[2148,47632,2495],{},[1706,47634,2505],{"separator":2504},[898,47636,35541],{},[1706,47638,2153],{"stretchy":2139},[1706,47640,1708],{},[898,47642,900],{},[1706,47644,2140],{"stretchy":2139},[2142,47646,47647,47649],{},[898,47648,2146],{},[2148,47650,2701],{},[1706,47652,2505],{"separator":2504},[2142,47654,47655,47657],{},[898,47656,2146],{},[2148,47658,2495],{},[1706,47660,2153],{"stretchy":2139},[1706,47662,2447],{},[898,47664,35541],{},[1706,47666,2140],{"stretchy":2139},[2489,47668,47669,47671],{},[898,47670,28247],{},[1706,47672,3197],{},[1706,47674,1715],{},[28285,47676,47677,47679,47681],{},[898,47678,1702],{},[2148,47680,2701],{},[1706,47682,3197],{},[2142,47684,47685,47687],{},[898,47686,2146],{},[2148,47688,2701],{},[1706,47690,1715],{},[28285,47692,47693,47695,47697],{},[898,47694,1702],{},[2148,47696,2495],{},[1706,47698,3197],{},[2142,47700,47701,47703],{},[898,47702,2146],{},[2148,47704,2495],{},[1706,47706,2153],{"stretchy":2139},[898,47708,1837],{"mathvariant":2409},[2361,47710],{"width":2363},[2361,47712,47713],{},[2415,47714,47715],{},"(6.13)",[902,47717,47718],{"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}",[724,47720,47721],{},"Soustava prvního řádu:",[883,47723,47725],{"className":47724},[886],[888,47726,47727],{"xmlns":890,"display":2350},[892,47728,47729,47912],{},[2354,47730,47731],{"width":2356},[2358,47732,47733,47735,47905,47907],{},[2361,47734],{"width":2363},[2361,47736,47737],{},[2354,47738,47739,47789,47839],{"rowspacing":7556,"columnalign":7557,"columnspacing":3141},[2358,47740,47741,47753],{},[2361,47742,47743],{},[4745,47744,47745],{"scriptlevel":2150,"displaystyle":2504},[28285,47746,47747,47749,47751],{},[898,47748,6362],{"mathvariant":47616},[2148,47750,2701],{},[1706,47752,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2361,47754,47755],{},[4745,47756,47757],{"scriptlevel":2150,"displaystyle":2504},[895,47758,47759,47761,47763,47771,47773,47775,47783,47785,47787],{},[895,47760],{},[1706,47762,1708],{},[28285,47764,47765,47767,47769],{},[898,47766,900],{},[2148,47768,2701],{},[1706,47770,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,47772,1715],{},[898,47774,35541],{},[28285,47776,47777,47779,47781],{},[898,47778,1702],{},[2148,47780,2701],{},[1706,47782,3197],{},[1706,47784,1708],{},[2148,47786,2150],{},[1706,47788,2505],{"separator":2504},[2358,47790,47791,47803],{},[2361,47792,47793],{},[4745,47794,47795],{"scriptlevel":2150,"displaystyle":2504},[28285,47796,47797,47799,47801],{},[898,47798,6362],{"mathvariant":47616},[2148,47800,2495],{},[1706,47802,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2361,47804,47805],{},[4745,47806,47807],{"scriptlevel":2150,"displaystyle":2504},[895,47808,47809,47811,47813,47821,47823,47825,47833,47835,47837],{},[895,47810],{},[1706,47812,1708],{},[28285,47814,47815,47817,47819],{},[898,47816,900],{},[2148,47818,2495],{},[1706,47820,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,47822,1715],{},[898,47824,35541],{},[28285,47826,47827,47829,47831],{},[898,47828,1702],{},[2148,47830,2495],{},[1706,47832,3197],{},[1706,47834,1708],{},[2148,47836,2150],{},[1706,47838,2505],{"separator":2504},[2358,47840,47841,47853],{},[2361,47842,47843],{},[4745,47844,47845],{"scriptlevel":2150,"displaystyle":2504},[28285,47846,47847,47849,47851],{},[898,47848,6362],{"mathvariant":47616},[898,47850,35541],{},[1706,47852,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2361,47854,47855],{},[4745,47856,47857],{"scriptlevel":2150,"displaystyle":2504},[895,47858,47859,47861,47863,47869,47871,47879,47885,47887,47895,47901,47903],{},[895,47860],{},[1706,47862,1708],{},[2489,47864,47865,47867],{},[898,47866,28247],{},[1706,47868,3197],{},[1706,47870,1715],{},[28285,47872,47873,47875,47877],{},[898,47874,1702],{},[2148,47876,2701],{},[1706,47878,3197],{},[2142,47880,47881,47883],{},[898,47882,2146],{},[2148,47884,2701],{},[1706,47886,1715],{},[28285,47888,47889,47891,47893],{},[898,47890,1702],{},[2148,47892,2495],{},[1706,47894,3197],{},[2142,47896,47897,47899],{},[898,47898,2146],{},[2148,47900,2495],{},[1706,47902,1708],{},[2148,47904,31567],{},[2361,47906],{"width":2363},[2361,47908,47909],{},[2415,47910,47911],{},"(6.14)",[902,47913,47914],{"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}",[724,47916,47917,47918,47921,47922,47935,47936,4288],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,47919,47920],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,47923,47925],{"className":47924},[886],[888,47926,47927],{"xmlns":890},[892,47928,47929,47933],{},[895,47930,47931],{},[898,47932,35541],{},[902,47934,35594],{"encoding":904}," dostáváme ",[38,47937,47938],{},"podmínku optimality",[883,47940,47942],{"className":47941},[886],[888,47943,47944],{"xmlns":890,"display":2350},[892,47945,47946,48004],{},[895,47947,47948],{},[31939,47949,47950],{"notation":31941},[4745,47951,47952],{"scriptlevel":2150,"displaystyle":2139},[4745,47953,47954],{"scriptlevel":2150,"displaystyle":2139},[4745,47955,47956],{"scriptlevel":2150,"displaystyle":2504},[895,47957,47958,47960,47962,47964,47982,47984,48002],{},[2415,47959,3852],{},[2415,47961,29714],{},[1706,47963,1708],{},[2964,47965,47966,47974],{},[28285,47967,47968,47970,47972],{},[898,47969,900],{},[2148,47971,2701],{},[1706,47973,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[28285,47975,47976,47978,47980],{},[898,47977,900],{},[2148,47979,2495],{},[1706,47981,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,47983,1708],{},[2964,47985,47986,47994],{},[28285,47987,47988,47990,47992],{},[898,47989,1702],{},[2148,47991,2701],{},[1706,47993,3197],{},[28285,47995,47996,47998,48000],{},[898,47997,1702],{},[2148,47999,2495],{},[1706,48001,3197],{},[2415,48003,3852],{},[902,48005,48006],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[1636,48008,48009],{},[724,48010,48011,48013,48014,48048,48049,48052,48053,48071,48072,48090,48091,48121,48122,48139,48140,48170],{},[883,48012,3174],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,48015,48017],{"className":48016},[886],[888,48018,48019],{"xmlns":890},[892,48020,48021,48045],{},[895,48022,48023,48025,48027,48035,48037],{},[2415,48024,29714],{},[1706,48026,1708],{},[28285,48028,48029,48031,48033],{},[898,48030,1702],{},[2148,48032,2701],{},[1706,48034,3197],{},[898,48036,15493],{"mathvariant":2409},[28285,48038,48039,48041,48043],{},[898,48040,1702],{},[2148,48042,2495],{},[1706,48044,3197],{},[902,48046,48047],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,48050,48051],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,48054,48056],{"className":48055},[886],[888,48057,48058],{"xmlns":890},[892,48059,48060,48068],{},[895,48061,48062],{},[2142,48063,48064,48066],{},[898,48065,2146],{},[2148,48067,2701],{},[902,48069,48070],{"encoding":904},"Q_1"," za ",[883,48073,48075],{"className":48074},[886],[888,48076,48077],{"xmlns":890},[892,48078,48079,48087],{},[895,48080,48081],{},[2142,48082,48083,48085],{},[898,48084,2146],{},[2148,48086,2495],{},[902,48088,48089],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,48092,48094],{"className":48093},[886],[888,48095,48096],{"xmlns":890},[892,48097,48098,48118],{},[895,48099,48100,48102,48104,48110,48112],{},[2415,48101,29714],{},[1706,48103,8922],{},[2142,48105,48106,48108],{},[898,48107,1702],{},[2148,48109,2701],{},[898,48111,15493],{"mathvariant":2409},[2142,48113,48114,48116],{},[898,48115,1702],{},[2148,48117,2495],{},[902,48119,48120],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,48123,48125],{"className":48124},[886],[888,48126,48127],{"xmlns":890},[892,48128,48129,48137],{},[895,48130,48131],{},[2142,48132,48133,48135],{},[898,48134,2146],{},[2148,48136,2701],{},[902,48138,48070],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,48141,48143],{"className":48142},[886],[888,48144,48145],{"xmlns":890},[892,48146,48147,48167],{},[895,48148,48149,48151,48153,48159,48161],{},[2415,48150,29714],{},[1706,48152,2539],{},[2142,48154,48155,48157],{},[898,48156,1702],{},[2148,48158,2701],{},[898,48160,15493],{"mathvariant":2409},[2142,48162,48163,48165],{},[898,48164,1702],{},[2148,48166,2495],{},[902,48168,48169],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,48172,48174,48175,48188],{"id":48173},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,48176,48178],{"className":48177},[886],[888,48179,48180],{"xmlns":890},[892,48181,48182,48186],{},[895,48183,48184],{},[898,48185,35541],{},[902,48187,35594],{"encoding":904}," — mezní užitečnost důchodu",[724,48190,48191,48192,48210,48211,48214,48215,48232,48233,48250,48251,48254],{},"Lagrangeův multiplikátor ",[883,48193,48195],{"className":48194},[886],[888,48196,48197],{"xmlns":890},[892,48198,48199,48207],{},[895,48200,48201],{},[2489,48202,48203,48205],{},[898,48204,35541],{},[1706,48206,3197],{},[902,48208,48209],{"encoding":904},"\\lambda^*"," představuje ",[38,48212,48213],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,48216,48218],{"className":48217},[886],[888,48219,48220],{"xmlns":890},[892,48221,48222,48230],{},[895,48223,48224],{},[2489,48225,48226,48228],{},[898,48227,900],{},[1706,48229,3197],{},[902,48231,47033],{"encoding":904}," při jednotkové změně důchodu ",[883,48234,48236],{"className":48235},[886],[888,48237,48238],{"xmlns":890},[892,48239,48240,48248],{},[895,48241,48242],{},[2489,48243,48244,48246],{},[898,48245,28247],{},[1706,48247,3197],{},[902,48249,47099],{"encoding":904},". Je to ",[38,48252,48253],{},"stínová cena"," rozpočtového omezení.",[1636,48256,48257,48262],{},[724,48258,48259,48261],{},[883,48260,12314],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,48263,48264,48323,48410,48446,48533],{},[123,48265,48266,8091,48269,1837],{},[38,48267,48268],{},"Zapiš rozpočtové omezení",[883,48270,48272],{"className":48271},[886],[888,48273,48274],{"xmlns":890},[892,48275,48276,48320],{},[895,48277,48278,48284,48286,48294,48300,48302,48310,48316,48318],{},[2489,48279,48280,48282],{},[898,48281,28247],{},[1706,48283,3197],{},[1706,48285,1715],{},[28285,48287,48288,48290,48292],{},[898,48289,1702],{},[2148,48291,2701],{},[1706,48293,3197],{},[2142,48295,48296,48298],{},[898,48297,2146],{},[2148,48299,2701],{},[1706,48301,1715],{},[28285,48303,48304,48306,48308],{},[898,48305,1702],{},[2148,48307,2495],{},[1706,48309,3197],{},[2142,48311,48312,48314],{},[898,48313,2146],{},[2148,48315,2495],{},[1706,48317,1708],{},[2148,48319,2150],{},[902,48321,48322],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,48324,48325,1647,48328,1837],{},[38,48326,48327],{},"Sestav Lagrangeovu funkci",[883,48329,48331],{"className":48330},[886],[888,48332,48333],{"xmlns":890},[892,48334,48335,48407],{},[895,48336,48337,48339,48341,48343,48345,48351,48353,48359,48361,48363,48365,48367,48373,48375,48383,48389,48391,48399,48405],{},[898,48338,6362],{"mathvariant":47616},[1706,48340,1708],{},[898,48342,900],{},[1706,48344,2140],{"stretchy":2139},[2142,48346,48347,48349],{},[898,48348,2146],{},[2148,48350,2701],{},[1706,48352,2505],{"separator":2504},[2142,48354,48355,48357],{},[898,48356,2146],{},[2148,48358,2495],{},[1706,48360,2153],{"stretchy":2139},[1706,48362,2447],{},[898,48364,35541],{},[1706,48366,2140],{"stretchy":2139},[2489,48368,48369,48371],{},[898,48370,28247],{},[1706,48372,3197],{},[1706,48374,1715],{},[28285,48376,48377,48379,48381],{},[898,48378,1702],{},[2148,48380,2701],{},[1706,48382,3197],{},[2142,48384,48385,48387],{},[898,48386,2146],{},[2148,48388,2701],{},[1706,48390,1715],{},[28285,48392,48393,48395,48397],{},[898,48394,1702],{},[2148,48396,2495],{},[1706,48398,3197],{},[2142,48400,48401,48403],{},[898,48402,2146],{},[2148,48404,2495],{},[1706,48406,2153],{"stretchy":2139},[902,48408,48409],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,48411,48412,29579,48415,48445],{},[38,48413,48414],{},"Spočítej parciální derivace",[883,48416,48418],{"className":48417},[886],[888,48419,48420],{"xmlns":890},[892,48421,48422,48442],{},[895,48423,48424,48430,48432,48438,48440],{},[2142,48425,48426,48428],{},[898,48427,2146],{},[2148,48429,2701],{},[1706,48431,2505],{"separator":2504},[2142,48433,48434,48436],{},[898,48435,2146],{},[2148,48437,2495],{},[1706,48439,2505],{"separator":2504},[898,48441,35541],{},[902,48443,48444],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,48447,48448,48464,48465,48498,48499,1993,48516,1837],{},[38,48449,48450,48451],{},"Vyluč ",[883,48452,48454],{"className":48453},[886],[888,48455,48456],{"xmlns":890},[892,48457,48458,48462],{},[895,48459,48460],{},[898,48461,35541],{},[902,48463,35594],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,48466,48468],{"className":48467},[886],[888,48469,48470],{"xmlns":890},[892,48471,48472,48496],{},[895,48473,48474,48476,48478,48486,48488],{},[2415,48475,29714],{},[1706,48477,1708],{},[28285,48479,48480,48482,48484],{},[898,48481,1702],{},[2148,48483,2701],{},[1706,48485,3197],{},[898,48487,15493],{"mathvariant":2409},[28285,48489,48490,48492,48494],{},[898,48491,1702],{},[2148,48493,2495],{},[1706,48495,3197],{},[902,48497,48047],{"encoding":904},", která dá vztah mezi ",[883,48500,48502],{"className":48501},[886],[888,48503,48504],{"xmlns":890},[892,48505,48506,48514],{},[895,48507,48508],{},[2142,48509,48510,48512],{},[898,48511,2146],{},[2148,48513,2701],{},[902,48515,48070],{"encoding":904},[883,48517,48519],{"className":48518},[886],[888,48520,48521],{"xmlns":890},[892,48522,48523,48531],{},[895,48524,48525],{},[2142,48526,48527,48529],{},[898,48528,2146],{},[2148,48530,2495],{},[902,48532,48089],{"encoding":904},[123,48534,48535,48538,48539,48569,48570,48587,48588,1837],{},[38,48536,48537],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,48540,48542],{"className":48541},[886],[888,48543,48544],{"xmlns":890},[892,48545,48546,48566],{},[895,48547,48548,48556,48558],{},[28285,48549,48550,48552,48554],{},[898,48551,2146],{},[2148,48553,2701],{},[1706,48555,3197],{},[1706,48557,2505],{"separator":2504},[28285,48559,48560,48562,48564],{},[898,48561,2146],{},[2148,48563,2495],{},[1706,48565,3197],{},[902,48567,48568],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,48571,48573],{"className":48572},[886],[888,48574,48575],{"xmlns":890},[892,48576,48577,48585],{},[895,48578,48579],{},[2489,48580,48581,48583],{},[898,48582,35541],{},[1706,48584,3197],{},[902,48586,48209],{"encoding":904}," a maximální užitečnost ",[883,48589,48591],{"className":48590},[886],[888,48592,48593],{"xmlns":890},[892,48594,48595,48629],{},[895,48596,48597,48603,48605,48607,48609,48617,48619,48627],{},[2489,48598,48599,48601],{},[898,48600,900],{},[1706,48602,3197],{},[1706,48604,1708],{},[898,48606,900],{},[1706,48608,2140],{"stretchy":2139},[28285,48610,48611,48613,48615],{},[898,48612,2146],{},[2148,48614,2701],{},[1706,48616,3197],{},[1706,48618,2505],{"separator":2504},[28285,48620,48621,48623,48625],{},[898,48622,2146],{},[2148,48624,2495],{},[1706,48626,3197],{},[1706,48628,2153],{"stretchy":2139},[902,48630,48631],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,48633,48635],{"id":48634},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,48637,48638],{},[2286,48639],{"alt":48640,"className":48641,"src":48642},"imek-uzitecnost-optimum",[210,2290],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,48644,48645],{},[614,48646,48647,48648,48697,48698,1993,48726,48754,48755,48789,48790,48829,48830,48848,48849,48867,48868,48886],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,48649,48651],{"className":48650},[886],[888,48652,48653],{"xmlns":890},[892,48654,48655,48695],{},[895,48656,48657,48663,48665,48673,48679,48681,48689],{},[2489,48658,48659,48661],{},[898,48660,28247],{},[1706,48662,3197],{},[1706,48664,1708],{},[28285,48666,48667,48669,48671],{},[898,48668,1702],{},[2148,48670,2701],{},[1706,48672,3197],{},[2142,48674,48675,48677],{},[898,48676,2146],{},[2148,48678,2701],{},[1706,48680,2447],{},[28285,48682,48683,48685,48687],{},[898,48684,1702],{},[2148,48686,2495],{},[1706,48688,3197],{},[2142,48690,48691,48693],{},[898,48692,2146],{},[2148,48694,2495],{},[902,48696,36396],{"encoding":904}," protíná osy v ",[883,48699,48701],{"className":48700},[886],[888,48702,48703],{"xmlns":890},[892,48704,48705,48723],{},[895,48706,48707,48713,48715],{},[2489,48708,48709,48711],{},[898,48710,28247],{},[1706,48712,3197],{},[898,48714,15493],{"mathvariant":2409},[28285,48716,48717,48719,48721],{},[898,48718,1702],{},[2148,48720,2701],{},[1706,48722,3197],{},[902,48724,48725],{"encoding":904},"Y^*\u002FP_1^*",[883,48727,48729],{"className":48728},[886],[888,48730,48731],{"xmlns":890},[892,48732,48733,48751],{},[895,48734,48735,48741,48743],{},[2489,48736,48737,48739],{},[898,48738,28247],{},[1706,48740,3197],{},[898,48742,15493],{"mathvariant":2409},[28285,48744,48745,48747,48749],{},[898,48746,1702],{},[2148,48748,2495],{},[1706,48750,3197],{},[902,48752,48753],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,48756,48758],{"className":48757},[886],[888,48759,48760],{"xmlns":890},[892,48761,48762,48786],{},[895,48763,48764,48770,48772,48778,48780],{},[2142,48765,48766,48768],{},[898,48767,20413],{},[2148,48769,2701],{},[1706,48771,2539],{},[2489,48773,48774,48776],{},[898,48775,20413],{},[1706,48777,3197],{},[1706,48779,2539],{},[2142,48781,48782,48784],{},[898,48783,20413],{},[2148,48785,2495],{},[902,48787,48788],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,48791,48793],{"className":48792},[886],[888,48794,48795],{"xmlns":890},[892,48796,48797,48827],{},[895,48798,48799,48805,48807,48815,48817,48825],{},[2489,48800,48801,48803],{},[898,48802,2146],{},[1706,48804,3197],{},[1706,48806,21693],{"stretchy":2139},[28285,48808,48809,48811,48813],{},[898,48810,2146],{},[2148,48812,2701],{},[1706,48814,3197],{},[1706,48816,2505],{"separator":2504},[28285,48818,48819,48821,48823],{},[898,48820,2146],{},[2148,48822,2495],{},[1706,48824,3197],{},[1706,48826,21708],{"stretchy":2139},[902,48828,47395],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,48831,48833],{"className":48832},[886],[888,48834,48835],{"xmlns":890},[892,48836,48837,48845],{},[895,48838,48839],{},[2489,48840,48841,48843],{},[898,48842,20413],{},[1706,48844,3197],{},[902,48846,48847],{"encoding":904},"c^*",". Křivka ",[883,48850,48852],{"className":48851},[886],[888,48853,48854],{"xmlns":890},[892,48855,48856,48864],{},[895,48857,48858],{},[2142,48859,48860,48862],{},[898,48861,20413],{},[2148,48863,2701],{},[902,48865,48866],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,48869,48871],{"className":48870},[886],[888,48872,48873],{"xmlns":890},[892,48874,48875,48883],{},[895,48876,48877],{},[2142,48878,48879,48881],{},[898,48880,20413],{},[2148,48882,2495],{},[902,48884,48885],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,48888,48889,48890,48893,48894,48911,48912,48941],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,48891,48892],{},"dotýkají",", tj. mají v bodě ",[883,48895,48897],{"className":48896},[886],[888,48898,48899],{"xmlns":890},[892,48900,48901,48909],{},[895,48902,48903],{},[2489,48904,48905,48907],{},[898,48906,2146],{},[1706,48908,3197],{},[902,48910,3221],{"encoding":904}," společnou tečnu. To přímo převádí podmínku ",[883,48913,48915],{"className":48914},[886],[888,48916,48917],{"xmlns":890},[892,48918,48919,48939],{},[895,48920,48921,48923,48925,48931,48933],{},[2415,48922,29714],{},[1706,48924,1708],{},[2142,48926,48927,48929],{},[898,48928,1702],{},[2148,48930,2701],{},[898,48932,15493],{"mathvariant":2409},[2142,48934,48935,48937],{},[898,48936,1702],{},[2148,48938,2495],{},[902,48940,47069],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,48943,48945],{"id":48944},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,48947,3465,48948,2344],{},[883,48949,48951],{"className":48950},[886],[888,48952,48953],{"xmlns":890},[892,48954,48955,49007],{},[895,48956,48957,48959,48961,48967,48969,48975,48977,48979,48993],{},[898,48958,900],{},[1706,48960,2140],{"stretchy":2139},[2142,48962,48963,48965],{},[898,48964,2146],{},[2148,48966,2701],{},[1706,48968,2505],{"separator":2504},[2142,48970,48971,48973],{},[898,48972,2146],{},[2148,48974,2495],{},[1706,48976,2153],{"stretchy":2139},[1706,48978,1708],{},[28285,48980,48981,48983,48985],{},[898,48982,2146],{},[2148,48984,2701],{},[895,48986,48987,48989,48991],{},[2148,48988,2701],{},[898,48990,15493],{"mathvariant":2409},[2148,48992,2495],{},[28285,48994,48995,48997,48999],{},[898,48996,2146],{},[2148,48998,2495],{},[895,49000,49001,49003,49005],{},[2148,49002,2701],{},[898,49004,15493],{"mathvariant":2409},[2148,49006,2495],{},[902,49008,49009],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,49011,49012],{},[883,49013,49015],{"className":49014},[886],[888,49016,49017],{"xmlns":890},[892,49018,49019,49125],{},[895,49020,49021,49023,49025,49107,49109,49123],{},[2415,49022,29714],{},[1706,49024,1708],{},[2964,49026,49027,49067],{},[895,49028,49029,49037,49053],{},[4745,49030,49031],{"scriptlevel":2150,"displaystyle":2139},[2964,49032,49033,49035],{},[2148,49034,2701],{},[2148,49036,2495],{},[28285,49038,49039,49041,49043],{},[898,49040,2146],{},[2148,49042,2701],{},[895,49044,49045,49047,49049,49051],{},[1706,49046,1715],{},[2148,49048,2701],{},[898,49050,15493],{"mathvariant":2409},[2148,49052,2495],{},[28285,49054,49055,49057,49059],{},[898,49056,2146],{},[2148,49058,2495],{},[895,49060,49061,49063,49065],{},[2148,49062,2701],{},[898,49064,15493],{"mathvariant":2409},[2148,49066,2495],{},[895,49068,49069,49077,49091],{},[4745,49070,49071],{"scriptlevel":2150,"displaystyle":2139},[2964,49072,49073,49075],{},[2148,49074,2701],{},[2148,49076,2495],{},[28285,49078,49079,49081,49083],{},[898,49080,2146],{},[2148,49082,2701],{},[895,49084,49085,49087,49089],{},[2148,49086,2701],{},[898,49088,15493],{"mathvariant":2409},[2148,49090,2495],{},[28285,49092,49093,49095,49097],{},[898,49094,2146],{},[2148,49096,2495],{},[895,49098,49099,49101,49103,49105],{},[1706,49100,1715],{},[2148,49102,2701],{},[898,49104,15493],{"mathvariant":2409},[2148,49106,2495],{},[1706,49108,1708],{},[2964,49110,49111,49117],{},[2142,49112,49113,49115],{},[898,49114,2146],{},[2148,49116,2495],{},[2142,49118,49119,49121],{},[898,49120,2146],{},[2148,49122,2701],{},[898,49124,1837],{"mathvariant":2409},[902,49126,49127],{"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}.",[724,49129,49130,49131,3787,49175,49177,49178,49198,49199,49229,49230,1837],{},"Tedy ",[883,49132,49134],{"className":49133},[886],[888,49135,49136],{"xmlns":890},[892,49137,49138,49172],{},[895,49139,49140,49142,49144,49146,49148,49150,49152,49154,49162,49164],{},[2415,49141,29714],{},[1706,49143,2140],{"stretchy":2139},[2148,49145,19501],{},[1706,49147,2505],{"separator":2504},[2148,49149,17366],{},[1706,49151,2153],{"stretchy":2139},[1706,49153,1708],{},[4745,49155,49156],{"scriptlevel":2150,"displaystyle":2139},[2964,49157,49158,49160],{},[2148,49159,17366],{},[2148,49161,19501],{},[1706,49163,1708],{},[4745,49165,49166],{"scriptlevel":2150,"displaystyle":2139},[2964,49167,49168,49170],{},[2148,49169,7524],{},[2148,49171,4284],{},[902,49173,49174],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,49176,28335],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,49179,49181],{"className":49180},[886],[888,49182,49183],{"xmlns":890},[892,49184,49185,49195],{},[895,49186,49187],{},[4745,49188,49189],{"scriptlevel":2150,"displaystyle":2139},[2964,49190,49191,49193],{},[2148,49192,7524],{},[2148,49194,4284],{},[902,49196,49197],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,49200,49202],{"className":49201},[886],[888,49203,49204],{"xmlns":890},[892,49205,49206,49226],{},[895,49207,49208,49210,49212,49218,49220],{},[2415,49209,29714],{},[1706,49211,1708],{},[2142,49213,49214,49216],{},[898,49215,2146],{},[2148,49217,2495],{},[898,49219,15493],{"mathvariant":2409},[2142,49221,49222,49224],{},[898,49223,2146],{},[2148,49225,2701],{},[902,49227,49228],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,49231,49233],{"className":49232},[886],[888,49234,49235],{"xmlns":890},[892,49236,49237,49257],{},[895,49238,49239,49241,49243,49249,49251],{},[2415,49240,29714],{},[1706,49242,1708],{},[2142,49244,49245,49247],{},[898,49246,1702],{},[2148,49248,2701],{},[898,49250,15493],{"mathvariant":2409},[2142,49252,49253,49255],{},[898,49254,1702],{},[2148,49256,2495],{},[902,49258,47069],{"encoding":904},[115,49260,49262,49263],{"id":49261},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,49264,49266],{"className":49265},[886],[888,49267,49268],{"xmlns":890},[892,49269,49270,49288],{},[895,49271,49272,49274,49276,49282],{},[898,49273,900],{},[1706,49275,1708],{},[2142,49277,49278,49280],{},[898,49279,2146],{},[2148,49281,2701],{},[2142,49283,49284,49286],{},[898,49285,2146],{},[2148,49287,2495],{},[902,49289,49290],{"encoding":904},"U = Q_1 Q_2",[724,49292,49293,49294,1343,49340,1343,49364,1343,49388,49410],{},"Je dána ",[883,49295,49297],{"className":49296},[886],[888,49298,49299],{"xmlns":890},[892,49300,49301,49337],{},[895,49302,49303,49305,49307,49313,49315,49321,49323,49325,49331],{},[898,49304,900],{},[1706,49306,2140],{"stretchy":2139},[2142,49308,49309,49311],{},[898,49310,2146],{},[2148,49312,2701],{},[1706,49314,2505],{"separator":2504},[2142,49316,49317,49319],{},[898,49318,2146],{},[2148,49320,2495],{},[1706,49322,2153],{"stretchy":2139},[1706,49324,1708],{},[2142,49326,49327,49329],{},[898,49328,2146],{},[2148,49330,2701],{},[2142,49332,49333,49335],{},[898,49334,2146],{},[2148,49336,2495],{},[902,49338,49339],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,49341,49343],{"className":49342},[886],[888,49344,49345],{"xmlns":890},[892,49346,49347,49361],{},[895,49348,49349,49357,49359],{},[28285,49350,49351,49353,49355],{},[898,49352,1702],{},[2148,49354,2701],{},[1706,49356,3197],{},[1706,49358,1708],{},[2148,49360,2495],{},[902,49362,49363],{"encoding":904},"P_1^* = 2",[883,49365,49367],{"className":49366},[886],[888,49368,49369],{"xmlns":890},[892,49370,49371,49385],{},[895,49372,49373,49381,49383],{},[28285,49374,49375,49377,49379],{},[898,49376,1702],{},[2148,49378,2495],{},[1706,49380,3197],{},[1706,49382,1708],{},[2148,49384,7524],{},[902,49386,49387],{"encoding":904},"P_2^* = 5",[883,49389,49391],{"className":49390},[886],[888,49392,49393],{"xmlns":890},[892,49394,49395,49407],{},[895,49396,49397,49403,49405],{},[2489,49398,49399,49401],{},[898,49400,28247],{},[1706,49402,3197],{},[1706,49404,1708],{},[2148,49406,2590],{},[902,49408,49409],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,49412,49414],{"className":49413},[886],[888,49415,49416],{"xmlns":890,"display":2350},[892,49417,49418,49490],{},[895,49419,49420,49422,49424,49430,49432,49438,49440,49442,49444,49446,49452,49458,49460,49462,49464,49466,49468,49470,49476,49478,49480,49486,49488],{},[898,49421,6362],{"mathvariant":47616},[1706,49423,2140],{"stretchy":2139},[2142,49425,49426,49428],{},[898,49427,2146],{},[2148,49429,2701],{},[1706,49431,2505],{"separator":2504},[2142,49433,49434,49436],{},[898,49435,2146],{},[2148,49437,2495],{},[1706,49439,2505],{"separator":2504},[898,49441,35541],{},[1706,49443,2153],{"stretchy":2139},[1706,49445,1708],{},[2142,49447,49448,49450],{},[898,49449,2146],{},[2148,49451,2701],{},[2142,49453,49454,49456],{},[898,49455,2146],{},[2148,49457,2495],{},[1706,49459,2447],{},[898,49461,35541],{},[1706,49463,2140],{"stretchy":2139},[2148,49465,2590],{},[1706,49467,1715],{},[2148,49469,2495],{},[2142,49471,49472,49474],{},[898,49473,2146],{},[2148,49475,2701],{},[1706,49477,1715],{},[2148,49479,7524],{},[2142,49481,49482,49484],{},[898,49483,2146],{},[2148,49485,2495],{},[1706,49487,2153],{"stretchy":2139},[898,49489,1837],{"mathvariant":2409},[902,49491,49492],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,49494,49495],{},"Soustava:",[883,49497,49499],{"className":49498},[886],[888,49500,49501],{"xmlns":890,"display":2350},[892,49502,49503,49615],{},[2354,49504,49505,49539,49573],{"rowspacing":7556,"columnalign":7557,"columnspacing":3141},[2358,49506,49507,49525],{},[2361,49508,49509],{},[4745,49510,49511],{"scriptlevel":2150,"displaystyle":2504},[895,49512,49513,49519,49521,49523],{},[2142,49514,49515,49517],{},[898,49516,2146],{},[2148,49518,2495],{},[1706,49520,1715],{},[2148,49522,2495],{},[898,49524,35541],{},[2361,49526,49527],{},[4745,49528,49529],{"scriptlevel":2150,"displaystyle":2504},[895,49530,49531,49533,49535,49537],{},[895,49532],{},[1706,49534,1708],{},[2148,49536,2150],{},[1706,49538,2505],{"separator":2504},[2358,49540,49541,49559],{},[2361,49542,49543],{},[4745,49544,49545],{"scriptlevel":2150,"displaystyle":2504},[895,49546,49547,49553,49555,49557],{},[2142,49548,49549,49551],{},[898,49550,2146],{},[2148,49552,2701],{},[1706,49554,1715],{},[2148,49556,7524],{},[898,49558,35541],{},[2361,49560,49561],{},[4745,49562,49563],{"scriptlevel":2150,"displaystyle":2504},[895,49564,49565,49567,49569,49571],{},[895,49566],{},[1706,49568,1708],{},[2148,49570,2150],{},[1706,49572,2505],{"separator":2504},[2358,49574,49575,49603],{},[2361,49576,49577],{},[4745,49578,49579],{"scriptlevel":2150,"displaystyle":2504},[895,49580,49581,49583,49585,49587,49593,49595,49597],{},[2148,49582,2590],{},[1706,49584,1715],{},[2148,49586,2495],{},[2142,49588,49589,49591],{},[898,49590,2146],{},[2148,49592,2701],{},[1706,49594,1715],{},[2148,49596,7524],{},[2142,49598,49599,49601],{},[898,49600,2146],{},[2148,49602,2495],{},[2361,49604,49605],{},[4745,49606,49607],{"scriptlevel":2150,"displaystyle":2504},[895,49608,49609,49611,49613],{},[895,49610],{},[1706,49612,1708],{},[2148,49614,31567],{},[902,49616,49617],{"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}",[724,49619,49620,49621,1343,49645,49669,49670,24728,49710,49728,49729,49779,49780,1837],{},"Z prvních dvou rovnic ",[883,49622,49624],{"className":49623},[886],[888,49625,49626],{"xmlns":890},[892,49627,49628,49642],{},[895,49629,49630,49636,49638,49640],{},[2142,49631,49632,49634],{},[898,49633,2146],{},[2148,49635,2495],{},[1706,49637,1708],{},[2148,49639,2495],{},[898,49641,35541],{},[902,49643,49644],{"encoding":904},"Q_2 = 2\\lambda",[883,49646,49648],{"className":49647},[886],[888,49649,49650],{"xmlns":890},[892,49651,49652,49666],{},[895,49653,49654,49660,49662,49664],{},[2142,49655,49656,49658],{},[898,49657,2146],{},[2148,49659,2701],{},[1706,49661,1708],{},[2148,49663,7524],{},[898,49665,35541],{},[902,49667,49668],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,49671,49673],{"className":49672},[886],[888,49674,49675],{"xmlns":890},[892,49676,49677,49707],{},[895,49678,49679,49681,49683,49685,49687,49689,49691,49693,49695,49697,49699,49701,49703,49705],{},[2148,49680,2590],{},[1706,49682,1708],{},[2148,49684,2495],{},[1706,49686,2390],{},[2148,49688,7524],{},[898,49690,35541],{},[1706,49692,2447],{},[2148,49694,7524],{},[1706,49696,2390],{},[2148,49698,2495],{},[898,49700,35541],{},[1706,49702,1708],{},[2148,49704,3369],{},[898,49706,35541],{},[902,49708,49709],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,49711,49713],{"className":49712},[886],[888,49714,49715],{"xmlns":890},[892,49716,49717,49725],{},[895,49718,49719,49721,49723],{},[898,49720,35541],{},[1706,49722,1708],{},[2148,49724,7524],{},[902,49726,49727],{"encoding":904},"\\lambda = 5",". Odtud ",[38,49730,49731,1343,49755],{},[883,49732,49734],{"className":49733},[886],[888,49735,49736],{"xmlns":890},[892,49737,49738,49752],{},[895,49739,49740,49748,49750],{},[28285,49741,49742,49744,49746],{},[898,49743,2146],{},[2148,49745,2701],{},[1706,49747,3197],{},[1706,49749,1708],{},[2148,49751,2748],{},[902,49753,49754],{"encoding":904},"Q_1^* = 25",[883,49756,49758],{"className":49757},[886],[888,49759,49760],{"xmlns":890},[892,49761,49762,49776],{},[895,49763,49764,49772,49774],{},[28285,49765,49766,49768,49770],{},[898,49767,2146],{},[2148,49769,2495],{},[1706,49771,3197],{},[1706,49773,1708],{},[2148,49775,7786],{},[902,49777,49778],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,49781,49783],{"className":49782},[886],[888,49784,49785],{"xmlns":890},[892,49786,49787,49807],{},[895,49788,49789,49795,49797,49799,49801,49803,49805],{},[2489,49790,49791,49793],{},[898,49792,900],{},[1706,49794,3197],{},[1706,49796,1708],{},[2148,49798,2748],{},[1706,49800,2390],{},[2148,49802,7786],{},[1706,49804,1708],{},[2148,49806,2802],{},[902,49808,49809],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,49811,49812],{},[614,49813,49814,49815,47205,49853,1993,49877,49901,49902,49932,49933,49957,49958,49980,49981,1837],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,49816,49818],{"className":49817},[886],[888,49819,49820],{"xmlns":890},[892,49821,49822,49850],{},[895,49823,49824,49826,49828,49830,49836,49838,49840,49846,49848],{},[2148,49825,2590],{},[1706,49827,1715],{},[2148,49829,2495],{},[2142,49831,49832,49834],{},[898,49833,2146],{},[2148,49835,2701],{},[1706,49837,1715],{},[2148,49839,7524],{},[2142,49841,49842,49844],{},[898,49843,2146],{},[2148,49845,2495],{},[1706,49847,1708],{},[2148,49849,2150],{},[902,49851,49852],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,49854,49856],{"className":49855},[886],[888,49857,49858],{"xmlns":890},[892,49859,49860,49874],{},[895,49861,49862,49864,49866,49868,49870,49872],{},[898,49863,1735],{},[1706,49865,21693],{"stretchy":2139},[2148,49867,2150],{},[1706,49869,2505],{"separator":2504},[2148,49871,3369],{},[1706,49873,21708],{"stretchy":2139},[902,49875,49876],{"encoding":904},"A[0, 20]",[883,49878,49880],{"className":49879},[886],[888,49881,49882],{"xmlns":890},[892,49883,49884,49898],{},[895,49885,49886,49888,49890,49892,49894,49896],{},[898,49887,10315],{},[1706,49889,21693],{"stretchy":2139},[2148,49891,2728],{},[1706,49893,2505],{"separator":2504},[2148,49895,2150],{},[1706,49897,21708],{"stretchy":2139},[902,49899,49900],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,49903,49905],{"className":49904},[886],[888,49906,49907],{"xmlns":890},[892,49908,49909,49929],{},[895,49910,49911,49917,49919,49921,49923],{},[2142,49912,49913,49915],{},[898,49914,2146],{},[2148,49916,2495],{},[1706,49918,1708],{},[2148,49920,2802],{},[898,49922,15493],{"mathvariant":2409},[2142,49924,49925,49927],{},[898,49926,2146],{},[2148,49928,2701],{},[902,49930,49931],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,49934,49936],{"className":49935},[886],[888,49937,49938],{"xmlns":890},[892,49939,49940,49954],{},[895,49941,49942,49944,49946,49948,49950,49952],{},[898,49943,23410],{},[1706,49945,21693],{"stretchy":2139},[2148,49947,2748],{},[1706,49949,2505],{"separator":2504},[2148,49951,7786],{},[1706,49953,21708],{"stretchy":2139},[902,49955,49956],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,49959,49961],{"className":49960},[886],[888,49962,49963],{"xmlns":890},[892,49964,49965,49977],{},[895,49966,49967,49969],{},[1706,49968,1715],{},[4745,49970,49971],{"scriptlevel":2150,"displaystyle":2139},[2964,49972,49973,49975],{},[2148,49974,2495],{},[2148,49976,7524],{},[902,49978,49979],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,49982,49984],{"className":49983},[886],[888,49985,49986],{"xmlns":890},[892,49987,49988,50028],{},[895,49989,49990,49992,49994,49996,49998,50000,50002,50004,50006,50008,50016,50018,50020],{},[1706,49991,1715],{},[2415,49993,29714],{},[1706,49995,2140],{"stretchy":2139},[2148,49997,2748],{},[1706,49999,2505],{"separator":2504},[2148,50001,7786],{},[1706,50003,2153],{"stretchy":2139},[1706,50005,1708],{},[1706,50007,1715],{},[4745,50009,50010],{"scriptlevel":2150,"displaystyle":2139},[2964,50011,50012,50014],{},[2148,50013,7786],{},[2148,50015,2748],{},[1706,50017,1708],{},[1706,50019,1715],{},[4745,50021,50022],{"scriptlevel":2150,"displaystyle":2139},[2964,50023,50024,50026],{},[2148,50025,2495],{},[2148,50027,7524],{},[902,50029,50030],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,50032,50034],{"id":50033},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,50036,50037,50038,48071,50068,50071,50072,4288],{},"Považujeme-li v úloze ",[883,50039,50041],{"className":50040},[886],[888,50042,50043],{"xmlns":890},[892,50044,50045,50065],{},[895,50046,50047,50053,50055,50061,50063],{},[2142,50048,50049,50051],{},[898,50050,1702],{},[2148,50052,2701],{},[1706,50054,2505],{"separator":2504},[2142,50056,50057,50059],{},[898,50058,1702],{},[2148,50060,2495],{},[1706,50062,2505],{"separator":2504},[898,50064,28247],{},[902,50066,50067],{"encoding":904},"P_1, P_2, Y",[38,50069,50070],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,50073,50074],{},"Marshallovy poptávkové funkce",[883,50076,50078],{"className":50077},[886],[888,50079,50080],{"xmlns":890,"display":2350},[892,50081,50082,50177],{},[2354,50083,50084],{"width":2356},[2358,50085,50086,50088,50170,50172],{},[2361,50087],{"width":2363},[2361,50089,50090],{},[895,50091,50092,50098,50100,50106,50108,50114,50116,50122,50124,50126,50128,50130,50132,50138,50140,50146,50148,50154,50156,50162,50164,50166,50168],{},[2142,50093,50094,50096],{},[898,50095,2146],{},[2148,50097,2701],{},[1706,50099,1708],{},[2142,50101,50102,50104],{},[898,50103,2334],{},[2148,50105,2701],{},[1706,50107,2140],{"stretchy":2139},[2142,50109,50110,50112],{},[898,50111,1702],{},[2148,50113,2701],{},[1706,50115,2505],{"separator":2504},[2142,50117,50118,50120],{},[898,50119,1702],{},[2148,50121,2495],{},[1706,50123,2505],{"separator":2504},[898,50125,28247],{},[1706,50127,2153],{"stretchy":2139},[1706,50129,2505],{"separator":2504},[4898,50131],{"width":4900},[2142,50133,50134,50136],{},[898,50135,2146],{},[2148,50137,2495],{},[1706,50139,1708],{},[2142,50141,50142,50144],{},[898,50143,2334],{},[2148,50145,2495],{},[1706,50147,2140],{"stretchy":2139},[2142,50149,50150,50152],{},[898,50151,1702],{},[2148,50153,2701],{},[1706,50155,2505],{"separator":2504},[2142,50157,50158,50160],{},[898,50159,1702],{},[2148,50161,2495],{},[1706,50163,2505],{"separator":2504},[898,50165,28247],{},[1706,50167,2153],{"stretchy":2139},[1706,50169,2505],{"separator":2504},[2361,50171],{"width":2363},[2361,50173,50174],{},[2415,50175,50176],{},"(6.15)",[902,50178,50179],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,50181,50183],{"className":50182},[886],[888,50184,50185],{"xmlns":890,"display":2350},[892,50186,50187,50234],{},[2354,50188,50189],{"width":2356},[2358,50190,50191,50193,50227,50229],{},[2361,50192],{"width":2363},[2361,50194,50195],{},[895,50196,50197,50199,50201,50203,50205,50211,50213,50219,50221,50223,50225],{},[898,50198,35541],{},[1706,50200,1708],{},[898,50202,35541],{},[1706,50204,2140],{"stretchy":2139},[2142,50206,50207,50209],{},[898,50208,1702],{},[2148,50210,2701],{},[1706,50212,2505],{"separator":2504},[2142,50214,50215,50217],{},[898,50216,1702],{},[2148,50218,2495],{},[1706,50220,2505],{"separator":2504},[898,50222,28247],{},[1706,50224,2153],{"stretchy":2139},[898,50226,1837],{"mathvariant":2409},[2361,50228],{"width":2363},[2361,50230,50231],{},[2415,50232,50233],{},"(6.16)",[902,50235,50236],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,50238,50239,50269,50270,50336],{},[38,50240,50241,50242,1837],{},"Odvození pro ",[883,50243,50245],{"className":50244},[886],[888,50246,50247],{"xmlns":890},[892,50248,50249,50267],{},[895,50250,50251,50253,50255,50261],{},[898,50252,900],{},[1706,50254,1708],{},[2142,50256,50257,50259],{},[898,50258,2146],{},[2148,50260,2701],{},[2142,50262,50263,50265],{},[898,50264,2146],{},[2148,50266,2495],{},[902,50268,49290],{"encoding":904}," Lagrangeova funkce ",[883,50271,50273],{"className":50272},[886],[888,50274,50275],{"xmlns":890},[892,50276,50277,50333],{},[895,50278,50279,50281,50283,50289,50295,50297,50299,50301,50303,50305,50311,50317,50319,50325,50331],{},[898,50280,6362],{"mathvariant":47616},[1706,50282,1708],{},[2142,50284,50285,50287],{},[898,50286,2146],{},[2148,50288,2701],{},[2142,50290,50291,50293],{},[898,50292,2146],{},[2148,50294,2495],{},[1706,50296,2447],{},[898,50298,35541],{},[1706,50300,2140],{"stretchy":2139},[898,50302,28247],{},[1706,50304,1715],{},[2142,50306,50307,50309],{},[898,50308,1702],{},[2148,50310,2701],{},[2142,50312,50313,50315],{},[898,50314,2146],{},[2148,50316,2701],{},[1706,50318,1715],{},[2142,50320,50321,50323],{},[898,50322,1702],{},[2148,50324,2495],{},[2142,50326,50327,50329],{},[898,50328,2146],{},[2148,50330,2495],{},[1706,50332,2153],{"stretchy":2139},[902,50334,50335],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,50338,50340],{"className":50339},[886],[888,50341,50342],{"xmlns":890,"display":2350},[892,50343,50344,50511],{},[2354,50345,50346],{"width":2356},[2358,50347,50348,50350,50504,50506],{},[2361,50349],{"width":2363},[2361,50351,50352],{},[2354,50353,50354,50400,50446],{"rowspacing":7556,"columnalign":7557,"columnspacing":3141},[2358,50355,50356,50368],{},[2361,50357,50358],{},[4745,50359,50360],{"scriptlevel":2150,"displaystyle":2504},[28285,50361,50362,50364,50366],{},[898,50363,6362],{"mathvariant":47616},[2148,50365,2701],{},[1706,50367,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2361,50369,50370],{},[4745,50371,50372],{"scriptlevel":2150,"displaystyle":2504},[895,50373,50374,50376,50378,50384,50386,50388,50394,50396,50398],{},[895,50375],{},[1706,50377,1708],{},[2142,50379,50380,50382],{},[898,50381,2146],{},[2148,50383,2495],{},[1706,50385,1715],{},[898,50387,35541],{},[2142,50389,50390,50392],{},[898,50391,1702],{},[2148,50393,2701],{},[1706,50395,1708],{},[2148,50397,2150],{},[1706,50399,2505],{"separator":2504},[2358,50401,50402,50414],{},[2361,50403,50404],{},[4745,50405,50406],{"scriptlevel":2150,"displaystyle":2504},[28285,50407,50408,50410,50412],{},[898,50409,6362],{"mathvariant":47616},[2148,50411,2495],{},[1706,50413,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2361,50415,50416],{},[4745,50417,50418],{"scriptlevel":2150,"displaystyle":2504},[895,50419,50420,50422,50424,50430,50432,50434,50440,50442,50444],{},[895,50421],{},[1706,50423,1708],{},[2142,50425,50426,50428],{},[898,50427,2146],{},[2148,50429,2701],{},[1706,50431,1715],{},[898,50433,35541],{},[2142,50435,50436,50438],{},[898,50437,1702],{},[2148,50439,2495],{},[1706,50441,1708],{},[2148,50443,2150],{},[1706,50445,2505],{"separator":2504},[2358,50447,50448,50460],{},[2361,50449,50450],{},[4745,50451,50452],{"scriptlevel":2150,"displaystyle":2504},[28285,50453,50454,50456,50458],{},[898,50455,6362],{"mathvariant":47616},[898,50457,35541],{},[1706,50459,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2361,50461,50462],{},[4745,50463,50464],{"scriptlevel":2150,"displaystyle":2504},[895,50465,50466,50468,50470,50472,50474,50480,50486,50488,50494,50500,50502],{},[895,50467],{},[1706,50469,1708],{},[898,50471,28247],{},[1706,50473,1715],{},[2142,50475,50476,50478],{},[898,50477,1702],{},[2148,50479,2701],{},[2142,50481,50482,50484],{},[898,50483,2146],{},[2148,50485,2701],{},[1706,50487,1715],{},[2142,50489,50490,50492],{},[898,50491,1702],{},[2148,50493,2495],{},[2142,50495,50496,50498],{},[898,50497,2146],{},[2148,50499,2495],{},[1706,50501,1708],{},[2148,50503,31567],{},[2361,50505],{"width":2363},[2361,50507,50508],{},[2415,50509,50510],{},"(6.17)",[902,50512,50513],{"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}",[724,50515,50516,50517,50545,50546,50574,50575,4554],{},"Z prvních dvou: ",[883,50518,50520],{"className":50519},[886],[888,50521,50522],{"xmlns":890},[892,50523,50524,50542],{},[895,50525,50526,50532,50534,50540],{},[2142,50527,50528,50530],{},[898,50529,2146],{},[2148,50531,2495],{},[1706,50533,1708],{},[2142,50535,50536,50538],{},[898,50537,1702],{},[2148,50539,2701],{},[898,50541,35541],{},[902,50543,50544],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,50547,50549],{"className":50548},[886],[888,50550,50551],{"xmlns":890},[892,50552,50553,50571],{},[895,50554,50555,50561,50563,50569],{},[2142,50556,50557,50559],{},[898,50558,2146],{},[2148,50560,2701],{},[1706,50562,1708],{},[2142,50564,50565,50567],{},[898,50566,1702],{},[2148,50568,2495],{},[898,50570,35541],{},[902,50572,50573],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,50576,50578],{"className":50577},[886],[888,50579,50580],{"xmlns":890},[892,50581,50582,50640],{},[895,50583,50584,50586,50588,50594,50596,50602,50604,50606,50612,50614,50620,50622,50624,50626,50632,50638],{},[898,50585,28247],{},[1706,50587,1708],{},[2142,50589,50590,50592],{},[898,50591,1702],{},[2148,50593,2701],{},[1706,50595,2390],{},[2142,50597,50598,50600],{},[898,50599,1702],{},[2148,50601,2495],{},[898,50603,35541],{},[1706,50605,2447],{},[2142,50607,50608,50610],{},[898,50609,1702],{},[2148,50611,2495],{},[1706,50613,2390],{},[2142,50615,50616,50618],{},[898,50617,1702],{},[2148,50619,2701],{},[898,50621,35541],{},[1706,50623,1708],{},[2148,50625,2495],{},[2142,50627,50628,50630],{},[898,50629,1702],{},[2148,50631,2701],{},[2142,50633,50634,50636],{},[898,50635,1702],{},[2148,50637,2495],{},[898,50639,35541],{},[902,50641,50642],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",[883,50644,50646],{"className":50645},[886],[888,50647,50648],{"xmlns":890,"display":2350},[892,50649,50650,50693],{},[2354,50651,50652],{"width":2356},[2358,50653,50654,50656,50686,50688],{},[2361,50655],{"width":2363},[2361,50657,50658],{},[895,50659,50660,50662,50664,50684],{},[898,50661,35541],{},[1706,50663,1708],{},[2964,50665,50666,50668],{},[898,50667,28247],{},[895,50669,50670,50672,50678],{},[2148,50671,2495],{},[2142,50673,50674,50676],{},[898,50675,1702],{},[2148,50677,2701],{},[2142,50679,50680,50682],{},[898,50681,1702],{},[2148,50683,2495],{},[898,50685,1837],{"mathvariant":2409},[2361,50687],{"width":2363},[2361,50689,50690],{},[2415,50691,50692],{},"(6.20)",[902,50694,50695],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,50697,50698],{},"Zpětně:",[883,50700,50702],{"className":50701},[886],[888,50703,50704],{"xmlns":890,"display":2350},[892,50705,50706,50783],{},[2354,50707,50708],{"width":2356},[2358,50709,50710,50712,50776,50778],{},[2361,50711],{"width":2363},[2361,50713,50714],{},[31939,50715,50716],{"notation":31941},[4745,50717,50718],{"scriptlevel":2150,"displaystyle":2139},[4745,50719,50720],{"scriptlevel":2150,"displaystyle":2139},[4745,50721,50722],{"scriptlevel":2150,"displaystyle":2504},[895,50723,50724,50726,50732,50734,50748,50750,50752,50758,50760,50774],{},[2415,50725,3852],{},[2142,50727,50728,50730],{},[898,50729,2146],{},[2148,50731,2701],{},[1706,50733,1708],{},[2964,50735,50736,50738],{},[898,50737,28247],{},[895,50739,50740,50742],{},[2148,50741,2495],{},[2142,50743,50744,50746],{},[898,50745,1702],{},[2148,50747,2701],{},[1706,50749,2505],{"separator":2504},[4898,50751],{"width":4900},[2142,50753,50754,50756],{},[898,50755,2146],{},[2148,50757,2495],{},[1706,50759,1708],{},[2964,50761,50762,50764],{},[898,50763,28247],{},[895,50765,50766,50768],{},[2148,50767,2495],{},[2142,50769,50770,50772],{},[898,50771,1702],{},[2148,50773,2495],{},[2415,50775,3852],{},[2361,50777],{"width":2363},[2361,50779,50780],{},[2415,50781,50782],{},"(6.21)",[902,50784,50785],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,50787,50789],{"id":50788},"engelova-funkce","Engelova funkce",[724,50791,3465,50792,50795,50796,50799,50800,38961,50817,1343,50847,50877,50878,50912,50913,1343,50939,50965],{},[38,50793,50794],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,50797,50798],{},"Engelovou funkcí",": pro ",[883,50801,50803],{"className":50802},[886],[888,50804,50805],{"xmlns":890},[892,50806,50807,50815],{},[895,50808,50809,50811,50813],{},[898,50810,28247],{},[1706,50812,1708],{},[2148,50814,2590],{},[902,50816,39410],{"encoding":904},[883,50818,50820],{"className":50819},[886],[888,50821,50822],{"xmlns":890},[892,50823,50824,50844],{},[895,50825,50826,50832,50834,50836,50838],{},[2142,50827,50828,50830],{},[898,50829,2146],{},[2148,50831,2701],{},[1706,50833,1708],{},[2148,50835,2728],{},[898,50837,15493],{"mathvariant":2409},[2142,50839,50840,50842],{},[898,50841,1702],{},[2148,50843,2701],{},[902,50845,50846],{"encoding":904},"Q_1 = 50\u002FP_1",[883,50848,50850],{"className":50849},[886],[888,50851,50852],{"xmlns":890},[892,50853,50854,50874],{},[895,50855,50856,50862,50864,50866,50868],{},[2142,50857,50858,50860],{},[898,50859,2146],{},[2148,50861,2495],{},[1706,50863,1708],{},[2148,50865,2728],{},[898,50867,15493],{"mathvariant":2409},[2142,50869,50870,50872],{},[898,50871,1702],{},[2148,50873,2495],{},[902,50875,50876],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,50879,50881],{"className":50880},[886],[888,50882,50883],{"xmlns":890},[892,50884,50885,50909],{},[895,50886,50887,50893,50895,50897,50899,50905,50907],{},[2142,50888,50889,50891],{},[898,50890,1702],{},[2148,50892,2701],{},[1706,50894,1708],{},[2148,50896,7786],{},[1706,50898,2505],{"separator":2504},[2142,50900,50901,50903],{},[898,50902,1702],{},[2148,50904,2495],{},[1706,50906,1708],{},[2148,50908,3369],{},[902,50910,50911],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,50914,50916],{"className":50915},[886],[888,50917,50918],{"xmlns":890},[892,50919,50920,50936],{},[895,50921,50922,50928,50930,50932,50934],{},[2142,50923,50924,50926],{},[898,50925,2146],{},[2148,50927,2701],{},[1706,50929,1708],{},[898,50931,28247],{},[898,50933,15493],{"mathvariant":2409},[2148,50935,3369],{},[902,50937,50938],{"encoding":904},"Q_1 = Y\u002F20",[883,50940,50942],{"className":50941},[886],[888,50943,50944],{"xmlns":890},[892,50945,50946,50962],{},[895,50947,50948,50954,50956,50958,50960],{},[2142,50949,50950,50952],{},[898,50951,2146],{},[2148,50953,2495],{},[1706,50955,1708],{},[898,50957,28247],{},[898,50959,15493],{"mathvariant":2409},[2148,50961,3508],{},[902,50963,50964],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,50967,50969],{"id":50968},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,50971,50972],{},"Výdaje spotřebitele jsou",[883,50974,50976],{"className":50975},[886],[888,50977,50978],{"xmlns":890,"display":2350},[892,50979,50980,51055],{},[2354,50981,50982],{"width":2356},[2358,50983,50984,50986,51048,51050],{},[2361,50985],{"width":2363},[2361,50987,50988],{},[895,50989,50990,50992,50994,50996,50998,51004,51006,51012,51014,51016,51024,51030,51032,51040,51046],{},[898,50991,23410],{},[1706,50993,1708],{},[898,50995,23410],{},[1706,50997,2140],{"stretchy":2139},[2142,50999,51000,51002],{},[898,51001,2146],{},[2148,51003,2701],{},[1706,51005,2505],{"separator":2504},[2142,51007,51008,51010],{},[898,51009,2146],{},[2148,51011,2495],{},[1706,51013,2153],{"stretchy":2139},[1706,51015,1708],{},[28285,51017,51018,51020,51022],{},[898,51019,1702],{},[2148,51021,2701],{},[1706,51023,3197],{},[2142,51025,51026,51028],{},[898,51027,2146],{},[2148,51029,2701],{},[1706,51031,2447],{},[28285,51033,51034,51036,51038],{},[898,51035,1702],{},[2148,51037,2495],{},[1706,51039,3197],{},[2142,51041,51042,51044],{},[898,51043,2146],{},[2148,51045,2495],{},[1706,51047,2505],{"separator":2504},[2361,51049],{"width":2363},[2361,51051,51052],{},[2415,51053,51054],{},"(6.22)",[902,51056,51057],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,51059,51060],{},"a je pevně zadána hladina užitečnosti",[883,51062,51064],{"className":51063},[886],[888,51065,51066],{"xmlns":890,"display":2350},[892,51067,51068,51115],{},[2354,51069,51070],{"width":2356},[2358,51071,51072,51074,51108,51110],{},[2361,51073],{"width":2363},[2361,51075,51076],{},[895,51077,51078,51084,51086,51088,51090,51096,51098,51104,51106],{},[2489,51079,51080,51082],{},[898,51081,900],{},[1706,51083,3197],{},[1706,51085,1708],{},[898,51087,900],{},[1706,51089,2140],{"stretchy":2139},[2142,51091,51092,51094],{},[898,51093,2146],{},[2148,51095,2701],{},[1706,51097,2505],{"separator":2504},[2142,51099,51100,51102],{},[898,51101,2146],{},[2148,51103,2495],{},[1706,51105,2153],{"stretchy":2139},[898,51107,1837],{"mathvariant":2409},[2361,51109],{"width":2363},[2361,51111,51112],{},[2415,51113,51114],{},"(6.23)",[902,51116,51117],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,51119,51120,51123,51124,51156,51157,1837],{},[38,51121,51122],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,51125,51127],{"className":51126},[886],[888,51128,51129],{"xmlns":890},[892,51130,51131,51153],{},[895,51132,51133,51135,51137,51143,51145,51151],{},[898,51134,23410],{},[1706,51136,2140],{"stretchy":2139},[2142,51138,51139,51141],{},[898,51140,2146],{},[2148,51142,2701],{},[1706,51144,2505],{"separator":2504},[2142,51146,51147,51149],{},[898,51148,2146],{},[2148,51150,2495],{},[1706,51152,2153],{"stretchy":2139},[902,51154,51155],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,51158,51160],{"className":51159},[886],[888,51161,51162],{"xmlns":890},[892,51163,51164,51220],{},[895,51165,51166,51168,51170,51176,51178,51184,51186,51188,51194,51196,51198,51200,51206,51208,51214,51216,51218],{},[898,51167,30152],{},[1706,51169,2140],{"stretchy":2139},[2142,51171,51172,51174],{},[898,51173,2146],{},[2148,51175,2701],{},[1706,51177,2505],{"separator":2504},[2142,51179,51180,51182],{},[898,51181,2146],{},[2148,51183,2495],{},[1706,51185,2153],{"stretchy":2139},[1706,51187,1708],{},[2489,51189,51190,51192],{},[898,51191,900],{},[1706,51193,3197],{},[1706,51195,1715],{},[898,51197,900],{},[1706,51199,2140],{"stretchy":2139},[2142,51201,51202,51204],{},[898,51203,2146],{},[2148,51205,2701],{},[1706,51207,2505],{"separator":2504},[2142,51209,51210,51212],{},[898,51211,2146],{},[2148,51213,2495],{},[1706,51215,2153],{"stretchy":2139},[1706,51217,1708],{},[2148,51219,2150],{},[902,51221,51222],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,51224,51226],{"id":51225},"lagrangeova-funkce","Lagrangeova funkce",[883,51228,51230],{"className":51229},[886],[888,51231,51232],{"xmlns":890,"display":2350},[892,51233,51234,51345],{},[2354,51235,51236],{"width":2356},[2358,51237,51238,51240,51338,51340],{},[2361,51239],{"width":2363},[2361,51241,51242],{},[895,51243,51244,51246,51248,51254,51256,51262,51264,51266,51268,51270,51278,51284,51286,51294,51300,51302,51304,51306,51312,51314,51316,51318,51324,51326,51332,51334,51336],{},[898,51245,6362],{"mathvariant":47616},[1706,51247,2140],{"stretchy":2139},[2142,51249,51250,51252],{},[898,51251,2146],{},[2148,51253,2701],{},[1706,51255,2505],{"separator":2504},[2142,51257,51258,51260],{},[898,51259,2146],{},[2148,51261,2495],{},[1706,51263,2505],{"separator":2504},[898,51265,35541],{},[1706,51267,2153],{"stretchy":2139},[1706,51269,1708],{},[28285,51271,51272,51274,51276],{},[898,51273,1702],{},[2148,51275,2701],{},[1706,51277,3197],{},[2142,51279,51280,51282],{},[898,51281,2146],{},[2148,51283,2701],{},[1706,51285,2447],{},[28285,51287,51288,51290,51292],{},[898,51289,1702],{},[2148,51291,2495],{},[1706,51293,3197],{},[2142,51295,51296,51298],{},[898,51297,2146],{},[2148,51299,2495],{},[1706,51301,2447],{},[898,51303,35541],{},[1706,51305,2140],{"stretchy":2139},[2489,51307,51308,51310],{},[898,51309,900],{},[1706,51311,3197],{},[1706,51313,1715],{},[898,51315,900],{},[1706,51317,2140],{"stretchy":2139},[2142,51319,51320,51322],{},[898,51321,2146],{},[2148,51323,2701],{},[1706,51325,2505],{"separator":2504},[2142,51327,51328,51330],{},[898,51329,2146],{},[2148,51331,2495],{},[1706,51333,2153],{"stretchy":2139},[1706,51335,2153],{"stretchy":2139},[898,51337,1837],{"mathvariant":2409},[2361,51339],{"width":2363},[2361,51341,51342],{},[2415,51343,51344],{},"(6.24)",[902,51346,51347],{"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}",[724,51349,51350],{},"Soustava podmínek prvního řádu:",[883,51352,51354],{"className":51353},[886],[888,51355,51356],{"xmlns":890,"display":2350},[892,51357,51358,51531],{},[2354,51359,51360],{"width":2356},[2358,51361,51362,51364,51524,51526],{},[2361,51363],{"width":2363},[2361,51365,51366],{},[2354,51367,51368,51418,51468],{"rowspacing":7556,"columnalign":7557,"columnspacing":3141},[2358,51369,51370,51382],{},[2361,51371,51372],{},[4745,51373,51374],{"scriptlevel":2150,"displaystyle":2504},[28285,51375,51376,51378,51380],{},[898,51377,6362],{"mathvariant":47616},[2148,51379,2701],{},[1706,51381,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2361,51383,51384],{},[4745,51385,51386],{"scriptlevel":2150,"displaystyle":2504},[895,51387,51388,51390,51392,51400,51402,51404,51412,51414,51416],{},[895,51389],{},[1706,51391,1708],{},[28285,51393,51394,51396,51398],{},[898,51395,1702],{},[2148,51397,2701],{},[1706,51399,3197],{},[1706,51401,1715],{},[898,51403,35541],{},[28285,51405,51406,51408,51410],{},[898,51407,900],{},[2148,51409,2701],{},[1706,51411,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,51413,1708],{},[2148,51415,2150],{},[1706,51417,2505],{"separator":2504},[2358,51419,51420,51432],{},[2361,51421,51422],{},[4745,51423,51424],{"scriptlevel":2150,"displaystyle":2504},[28285,51425,51426,51428,51430],{},[898,51427,6362],{"mathvariant":47616},[2148,51429,2495],{},[1706,51431,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2361,51433,51434],{},[4745,51435,51436],{"scriptlevel":2150,"displaystyle":2504},[895,51437,51438,51440,51442,51450,51452,51454,51462,51464,51466],{},[895,51439],{},[1706,51441,1708],{},[28285,51443,51444,51446,51448],{},[898,51445,1702],{},[2148,51447,2495],{},[1706,51449,3197],{},[1706,51451,1715],{},[898,51453,35541],{},[28285,51455,51456,51458,51460],{},[898,51457,900],{},[2148,51459,2495],{},[1706,51461,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,51463,1708],{},[2148,51465,2150],{},[1706,51467,2505],{"separator":2504},[2358,51469,51470,51482],{},[2361,51471,51472],{},[4745,51473,51474],{"scriptlevel":2150,"displaystyle":2504},[28285,51475,51476,51478,51480],{},[898,51477,6362],{"mathvariant":47616},[898,51479,35541],{},[1706,51481,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2361,51483,51484],{},[4745,51485,51486],{"scriptlevel":2150,"displaystyle":2504},[895,51487,51488,51490,51492,51498,51500,51502,51504,51510,51512,51518,51520,51522],{},[895,51489],{},[1706,51491,1708],{},[2489,51493,51494,51496],{},[898,51495,900],{},[1706,51497,3197],{},[1706,51499,1715],{},[898,51501,900],{},[1706,51503,2140],{"stretchy":2139},[2142,51505,51506,51508],{},[898,51507,2146],{},[2148,51509,2701],{},[1706,51511,2505],{"separator":2504},[2142,51513,51514,51516],{},[898,51515,2146],{},[2148,51517,2495],{},[1706,51519,2153],{"stretchy":2139},[1706,51521,1708],{},[2148,51523,31567],{},[2361,51525],{"width":2363},[2361,51527,51528],{},[2415,51529,51530],{},"(6.25)",[902,51532,51533],{"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}",[724,51535,51536],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,51538,51540],{"className":51539},[886],[888,51541,51542],{"xmlns":890,"display":2350},[892,51543,51544,51642],{},[2354,51545,51546],{"width":2356},[2358,51547,51548,51550,51635,51637],{},[2361,51549],{"width":2363},[2361,51551,51552],{},[895,51553,51554,51556,51558,51564,51566,51572,51574,51576,51578,51580,51582,51584,51633],{},[898,51555,2334],{},[1706,51557,2140],{"stretchy":2139},[2142,51559,51560,51562],{},[898,51561,2146],{},[2148,51563,2701],{},[1706,51565,2505],{"separator":2504},[2142,51567,51568,51570],{},[898,51569,2146],{},[2148,51571,2495],{},[1706,51573,2505],{"separator":2504},[898,51575,35541],{},[1706,51577,2153],{"stretchy":2139},[1706,51579,1708],{},[1706,51581,1715],{},[898,51583,35541],{},[895,51585,51586,51588,51600,51602,51615,51617,51619,51631],{},[1706,51587,2140],{"fence":2504},[28285,51589,51590,51592,51594],{},[898,51591,900],{},[2148,51593,22094],{},[895,51595,51596,51598],{},[1706,51597,3142],{"mathvariant":2409},[1706,51599,3142],{"mathvariant":2409},[1706,51601,2447],{},[28285,51603,51604,51606,51609],{},[898,51605,900],{},[2148,51607,51608],{},"22",[895,51610,51611,51613],{},[1706,51612,3142],{"mathvariant":2409},[1706,51614,3142],{"mathvariant":2409},[1706,51616,2447],{},[2148,51618,2495],{},[28285,51620,51621,51623,51625],{},[898,51622,900],{},[2148,51624,7156],{},[895,51626,51627,51629],{},[1706,51628,3142],{"mathvariant":2409},[1706,51630,3142],{"mathvariant":2409},[1706,51632,2153],{"fence":2504},[898,51634,1837],{"mathvariant":2409},[2361,51636],{"width":2363},[2361,51638,51639],{},[2415,51640,51641],{},"(6.26)",[902,51643,51644],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,51646,51647,51650,51651,51690,51691,51730,51731,51781,51782,51808,51809,51826,51827,51853],{},[38,51648,51649],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,51652,51654],{"className":51653},[886],[888,51655,51656],{"xmlns":890},[892,51657,51658,51688],{},[895,51659,51660,51666,51668,51676,51678,51686],{},[2489,51661,51662,51664],{},[898,51663,2146],{},[1706,51665,3197],{},[1706,51667,21693],{"stretchy":2139},[28285,51669,51670,51672,51674],{},[898,51671,2146],{},[2148,51673,2701],{},[1706,51675,3197],{},[1706,51677,2505],{"separator":2504},[28285,51679,51680,51682,51684],{},[898,51681,2146],{},[2148,51683,2495],{},[1706,51685,3197],{},[1706,51687,21708],{"stretchy":2139},[902,51689,47395],{"encoding":904}," dotyku křivky užitečnosti ",[883,51692,51694],{"className":51693},[886],[888,51695,51696],{"xmlns":890},[892,51697,51698,51728],{},[895,51699,51700,51706,51708,51710,51712,51718,51720,51726],{},[2489,51701,51702,51704],{},[898,51703,900],{},[1706,51705,3197],{},[1706,51707,1708],{},[898,51709,900],{},[1706,51711,2140],{"stretchy":2139},[2142,51713,51714,51716],{},[898,51715,2146],{},[2148,51717,2701],{},[1706,51719,2505],{"separator":2504},[2142,51721,51722,51724],{},[898,51723,2146],{},[2148,51725,2495],{},[1706,51727,2153],{"stretchy":2139},[902,51729,36762],{"encoding":904}," s přímkou výdajů ",[883,51732,51734],{"className":51733},[886],[888,51735,51736],{"xmlns":890},[892,51737,51738,51778],{},[895,51739,51740,51746,51748,51756,51762,51764,51772],{},[2489,51741,51742,51744],{},[898,51743,23410],{},[1706,51745,3197],{},[1706,51747,1708],{},[28285,51749,51750,51752,51754],{},[898,51751,1702],{},[2148,51753,2701],{},[1706,51755,3197],{},[2142,51757,51758,51760],{},[898,51759,2146],{},[2148,51761,2701],{},[1706,51763,2447],{},[28285,51765,51766,51768,51770],{},[898,51767,1702],{},[2148,51769,2495],{},[1706,51771,3197],{},[2142,51773,51774,51776],{},[898,51775,2146],{},[2148,51777,2495],{},[902,51779,51780],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,51783,51785],{"className":51784},[886],[888,51786,51787],{"xmlns":890},[892,51788,51789,51805],{},[895,51790,51791,51797,51799],{},[2142,51792,51793,51795],{},[898,51794,23410],{},[2148,51796,2150],{},[1706,51798,2539],{},[2489,51800,51801,51803],{},[898,51802,23410],{},[1706,51804,3197],{},[902,51806,51807],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,51810,51812],{"className":51811},[886],[888,51813,51814],{"xmlns":890},[892,51815,51816,51824],{},[895,51817,51818],{},[2489,51819,51820,51822],{},[898,51821,900],{},[1706,51823,3197],{},[902,51825,47033],{"encoding":904},", hladina ",[883,51828,51830],{"className":51829},[886],[888,51831,51832],{"xmlns":890},[892,51833,51834,51850],{},[895,51835,51836,51842,51844],{},[2142,51837,51838,51840],{},[898,51839,23410],{},[2148,51841,2701],{},[1706,51843,8922],{},[2489,51845,51846,51848],{},[898,51847,23410],{},[1706,51849,3197],{},[902,51851,51852],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[1636,51855,51856,51861],{},[724,51857,51858,51860],{},[883,51859,12314],{}," Postup — duální úloha (minimalizace výdajů)",[152,51862,51863,51913,51999,52039,52114],{},[123,51864,51865,1647,51868,51912],{},[38,51866,51867],{},"Zapiš vazbu",[883,51869,51871],{"className":51870},[886],[888,51872,51873],{"xmlns":890},[892,51874,51875,51909],{},[895,51876,51877,51883,51885,51887,51889,51895,51897,51903,51905,51907],{},[2489,51878,51879,51881],{},[898,51880,900],{},[1706,51882,3197],{},[1706,51884,1715],{},[898,51886,900],{},[1706,51888,2140],{"stretchy":2139},[2142,51890,51891,51893],{},[898,51892,2146],{},[2148,51894,2701],{},[1706,51896,2505],{"separator":2504},[2142,51898,51899,51901],{},[898,51900,2146],{},[2148,51902,2495],{},[1706,51904,2153],{"stretchy":2139},[1706,51906,1708],{},[2148,51908,2150],{},[902,51910,51911],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,51914,51915,1647,51917,1837],{},[38,51916,48327],{},[883,51918,51920],{"className":51919},[886],[888,51921,51922],{"xmlns":890},[892,51923,51924,51996],{},[895,51925,51926,51928,51930,51938,51944,51946,51954,51960,51962,51964,51966,51972,51974,51976,51978,51984,51986,51992,51994],{},[898,51927,6362],{"mathvariant":47616},[1706,51929,1708],{},[28285,51931,51932,51934,51936],{},[898,51933,1702],{},[2148,51935,2701],{},[1706,51937,3197],{},[2142,51939,51940,51942],{},[898,51941,2146],{},[2148,51943,2701],{},[1706,51945,2447],{},[28285,51947,51948,51950,51952],{},[898,51949,1702],{},[2148,51951,2495],{},[1706,51953,3197],{},[2142,51955,51956,51958],{},[898,51957,2146],{},[2148,51959,2495],{},[1706,51961,2447],{},[898,51963,35541],{},[1706,51965,2140],{"stretchy":2139},[2489,51967,51968,51970],{},[898,51969,900],{},[1706,51971,3197],{},[1706,51973,1715],{},[898,51975,900],{},[1706,51977,2140],{"stretchy":2139},[2142,51979,51980,51982],{},[898,51981,2146],{},[2148,51983,2701],{},[1706,51985,2505],{"separator":2504},[2142,51987,51988,51990],{},[898,51989,2146],{},[2148,51991,2495],{},[1706,51993,2153],{"stretchy":2139},[1706,51995,2153],{"stretchy":2139},[902,51997,51998],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,52000,52001,52004,52005,52038],{},[38,52002,52003],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,52006,52008],{"className":52007},[886],[888,52009,52010],{"xmlns":890},[892,52011,52012,52036],{},[895,52013,52014,52016,52018,52026,52028],{},[2415,52015,29714],{},[1706,52017,1708],{},[28285,52019,52020,52022,52024],{},[898,52021,1702],{},[2148,52023,2701],{},[1706,52025,3197],{},[898,52027,15493],{"mathvariant":2409},[28285,52029,52030,52032,52034],{},[898,52031,1702],{},[2148,52033,2495],{},[1706,52035,3197],{},[902,52037,48047],{"encoding":904}," (stejná jako u maximalizace!).",[123,52040,52041,1647,52044,52084,52085,1837],{},[38,52042,52043],{},"Dosaď do vazby",[883,52045,52047],{"className":52046},[886],[888,52048,52049],{"xmlns":890},[892,52050,52051,52081],{},[895,52052,52053,52055,52057,52063,52065,52071,52073,52075],{},[898,52054,900],{},[1706,52056,2140],{"stretchy":2139},[2142,52058,52059,52061],{},[898,52060,2146],{},[2148,52062,2701],{},[1706,52064,2505],{"separator":2504},[2142,52066,52067,52069],{},[898,52068,2146],{},[2148,52070,2495],{},[1706,52072,2153],{"stretchy":2139},[1706,52074,1708],{},[2489,52076,52077,52079],{},[898,52078,900],{},[1706,52080,3197],{},[902,52082,52083],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,52086,52088],{"className":52087},[886],[888,52089,52090],{"xmlns":890},[892,52091,52092,52112],{},[895,52093,52094,52102,52104],{},[28285,52095,52096,52098,52100],{},[898,52097,2146],{},[2148,52099,2701],{},[1706,52101,3197],{},[1706,52103,2505],{"separator":2504},[28285,52105,52106,52108,52110],{},[898,52107,2146],{},[2148,52109,2495],{},[1706,52111,3197],{},[902,52113,48568],{"encoding":904},[123,52115,52116,1647,52119,52173],{},[38,52117,52118],{},"Vypočítej minimální výdaje",[883,52120,52122],{"className":52121},[886],[888,52123,52124],{"xmlns":890},[892,52125,52126,52170],{},[895,52127,52128,52134,52136,52144,52152,52154,52162],{},[2489,52129,52130,52132],{},[898,52131,23410],{},[1706,52133,3197],{},[1706,52135,1708],{},[28285,52137,52138,52140,52142],{},[898,52139,1702],{},[2148,52141,2701],{},[1706,52143,3197],{},[28285,52145,52146,52148,52150],{},[898,52147,2146],{},[2148,52149,2701],{},[1706,52151,3197],{},[1706,52153,2447],{},[28285,52155,52156,52158,52160],{},[898,52157,1702],{},[2148,52159,2495],{},[1706,52161,3197],{},[28285,52163,52164,52166,52168],{},[898,52165,2146],{},[2148,52167,2495],{},[1706,52169,3197],{},[902,52171,52172],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,52175,52177,52178],{"id":52176},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,52179,52181],{"className":52180},[886],[888,52182,52183],{"xmlns":890},[892,52184,52185,52219],{},[895,52186,52187,52189,52191,52205],{},[898,52188,900],{},[1706,52190,1708],{},[28285,52192,52193,52195,52197],{},[898,52194,2146],{},[2148,52196,2701],{},[895,52198,52199,52201,52203],{},[2148,52200,2701],{},[898,52202,15493],{"mathvariant":2409},[2148,52204,2495],{},[28285,52206,52207,52209,52211],{},[898,52208,2146],{},[2148,52210,2495],{},[895,52212,52213,52215,52217],{},[2148,52214,2701],{},[898,52216,15493],{"mathvariant":2409},[2148,52218,2495],{},[902,52220,52221],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,52223,52224,52225,1343,52247,1343,52271,49410],{},"Dáno ",[883,52226,52228],{"className":52227},[886],[888,52229,52230],{"xmlns":890},[892,52231,52232,52244],{},[895,52233,52234,52240,52242],{},[2489,52235,52236,52238],{},[898,52237,900],{},[1706,52239,3197],{},[1706,52241,1708],{},[2148,52243,2495],{},[902,52245,52246],{"encoding":904},"U^* = 2",[883,52248,52250],{"className":52249},[886],[888,52251,52252],{"xmlns":890},[892,52253,52254,52268],{},[895,52255,52256,52264,52266],{},[28285,52257,52258,52260,52262],{},[898,52259,1702],{},[2148,52261,2701],{},[1706,52263,3197],{},[1706,52265,1708],{},[2148,52267,19377],{},[902,52269,52270],{"encoding":904},"P_1^* = 0{,}25",[883,52272,52274],{"className":52273},[886],[888,52275,52276],{"xmlns":890},[892,52277,52278,52292],{},[895,52279,52280,52288,52290],{},[28285,52281,52282,52284,52286],{},[898,52283,1702],{},[2148,52285,2495],{},[1706,52287,3197],{},[1706,52289,1708],{},[2148,52291,2701],{},[902,52293,52294],{"encoding":904},"P_2^* = 1",[883,52296,52298],{"className":52297},[886],[888,52299,52300],{"xmlns":890,"display":2350},[892,52301,52302,52366],{},[895,52303,52304,52306,52308,52310,52316,52318,52324,52326,52328,52330,52332,52334,52348,52362,52364],{},[898,52305,6362],{"mathvariant":47616},[1706,52307,1708],{},[2148,52309,19377],{},[2142,52311,52312,52314],{},[898,52313,2146],{},[2148,52315,2701],{},[1706,52317,2447],{},[2142,52319,52320,52322],{},[898,52321,2146],{},[2148,52323,2495],{},[1706,52325,2447],{},[898,52327,35541],{},[1706,52329,2140],{"stretchy":2139},[2148,52331,2495],{},[1706,52333,1715],{},[28285,52335,52336,52338,52340],{},[898,52337,2146],{},[2148,52339,2701],{},[895,52341,52342,52344,52346],{},[2148,52343,2701],{},[898,52345,15493],{"mathvariant":2409},[2148,52347,2495],{},[28285,52349,52350,52352,52354],{},[898,52351,2146],{},[2148,52353,2495],{},[895,52355,52356,52358,52360],{},[2148,52357,2701],{},[898,52359,15493],{"mathvariant":2409},[2148,52361,2495],{},[1706,52363,2153],{"stretchy":2139},[898,52365,1837],{"mathvariant":2409},[902,52367,52368],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,52370,49495],{},[883,52372,52374],{"className":52373},[886],[888,52375,52376],{"xmlns":890,"display":2350},[892,52377,52378,52592],{},[2354,52379,52380,52456,52532],{"rowspacing":7556,"columnalign":7557,"columnspacing":3141},[2358,52381,52382,52394],{},[2361,52383,52384],{},[4745,52385,52386],{"scriptlevel":2150,"displaystyle":2504},[28285,52387,52388,52390,52392],{},[898,52389,6362],{"mathvariant":47616},[2148,52391,2701],{},[1706,52393,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2361,52395,52396],{},[4745,52397,52398],{"scriptlevel":2150,"displaystyle":2504},[895,52399,52400,52402,52404,52406,52408,52410,52412,52420,52436,52450,52452,52454],{},[895,52401],{},[1706,52403,1708],{},[2148,52405,19377],{},[1706,52407,1715],{},[898,52409,35541],{},[1706,52411,2390],{},[4745,52413,52414],{"scriptlevel":2150,"displaystyle":2139},[2964,52415,52416,52418],{},[2148,52417,2701],{},[2148,52419,2495],{},[28285,52421,52422,52424,52426],{},[898,52423,2146],{},[2148,52425,2701],{},[895,52427,52428,52430,52432,52434],{},[1706,52429,1715],{},[2148,52431,2701],{},[898,52433,15493],{"mathvariant":2409},[2148,52435,2495],{},[28285,52437,52438,52440,52442],{},[898,52439,2146],{},[2148,52441,2495],{},[895,52443,52444,52446,52448],{},[2148,52445,2701],{},[898,52447,15493],{"mathvariant":2409},[2148,52449,2495],{},[1706,52451,1708],{},[2148,52453,2150],{},[1706,52455,2505],{"separator":2504},[2358,52457,52458,52470],{},[2361,52459,52460],{},[4745,52461,52462],{"scriptlevel":2150,"displaystyle":2504},[28285,52463,52464,52466,52468],{},[898,52465,6362],{"mathvariant":47616},[2148,52467,2495],{},[1706,52469,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2361,52471,52472],{},[4745,52473,52474],{"scriptlevel":2150,"displaystyle":2504},[895,52475,52476,52478,52480,52482,52484,52486,52488,52496,52510,52526,52528,52530],{},[895,52477],{},[1706,52479,1708],{},[2148,52481,2701],{},[1706,52483,1715],{},[898,52485,35541],{},[1706,52487,2390],{},[4745,52489,52490],{"scriptlevel":2150,"displaystyle":2139},[2964,52491,52492,52494],{},[2148,52493,2701],{},[2148,52495,2495],{},[28285,52497,52498,52500,52502],{},[898,52499,2146],{},[2148,52501,2701],{},[895,52503,52504,52506,52508],{},[2148,52505,2701],{},[898,52507,15493],{"mathvariant":2409},[2148,52509,2495],{},[28285,52511,52512,52514,52516],{},[898,52513,2146],{},[2148,52515,2495],{},[895,52517,52518,52520,52522,52524],{},[1706,52519,1715],{},[2148,52521,2701],{},[898,52523,15493],{"mathvariant":2409},[2148,52525,2495],{},[1706,52527,1708],{},[2148,52529,2150],{},[1706,52531,2505],{"separator":2504},[2358,52533,52534,52546],{},[2361,52535,52536],{},[4745,52537,52538],{"scriptlevel":2150,"displaystyle":2504},[28285,52539,52540,52542,52544],{},[898,52541,6362],{"mathvariant":47616},[898,52543,35541],{},[1706,52545,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2361,52547,52548],{},[4745,52549,52550],{"scriptlevel":2150,"displaystyle":2504},[895,52551,52552,52554,52556,52558,52560,52574,52588,52590],{},[895,52553],{},[1706,52555,1708],{},[2148,52557,2495],{},[1706,52559,1715],{},[28285,52561,52562,52564,52566],{},[898,52563,2146],{},[2148,52565,2701],{},[895,52567,52568,52570,52572],{},[2148,52569,2701],{},[898,52571,15493],{"mathvariant":2409},[2148,52573,2495],{},[28285,52575,52576,52578,52580],{},[898,52577,2146],{},[2148,52579,2495],{},[895,52581,52582,52584,52586],{},[2148,52583,2701],{},[898,52585,15493],{"mathvariant":2409},[2148,52587,2495],{},[1706,52589,1708],{},[2148,52591,31567],{},[902,52593,52594],{"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}",[724,52596,52597,52598,11019,52628,52656,52657,24728,52719,1343,52769,52791,52792,1837],{},"Podílem prvních dvou rovnic: ",[883,52599,52601],{"className":52600},[886],[888,52602,52603],{"xmlns":890},[892,52604,52605,52625],{},[895,52606,52607,52609,52611,52617,52619],{},[2148,52608,19377],{},[1706,52610,1708],{},[2142,52612,52613,52615],{},[898,52614,2146],{},[2148,52616,2495],{},[898,52618,15493],{"mathvariant":2409},[2142,52620,52621,52623],{},[898,52622,2146],{},[2148,52624,2701],{},[902,52626,52627],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,52629,52631],{"className":52630},[886],[888,52632,52633],{"xmlns":890},[892,52634,52635,52653],{},[895,52636,52637,52643,52645,52647],{},[2142,52638,52639,52641],{},[898,52640,2146],{},[2148,52642,2495],{},[1706,52644,1708],{},[2148,52646,19377],{},[2142,52648,52649,52651],{},[898,52650,2146],{},[2148,52652,2701],{},[902,52654,52655],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,52658,52660],{"className":52659},[886],[888,52661,52662],{"xmlns":890},[892,52663,52664,52716],{},[895,52665,52666,52680,52682,52684,52690,52702,52704,52706,52712,52714],{},[28285,52667,52668,52670,52672],{},[898,52669,2146],{},[2148,52671,2701],{},[895,52673,52674,52676,52678],{},[2148,52675,2701],{},[898,52677,15493],{"mathvariant":2409},[2148,52679,2495],{},[1706,52681,2140],{"stretchy":2139},[2148,52683,19377],{},[2142,52685,52686,52688],{},[898,52687,2146],{},[2148,52689,2701],{},[2489,52691,52692,52694],{},[1706,52693,2153],{"stretchy":2139},[895,52695,52696,52698,52700],{},[2148,52697,2701],{},[898,52699,15493],{"mathvariant":2409},[2148,52701,2495],{},[1706,52703,1708],{},[2148,52705,11496],{},[2142,52707,52708,52710],{},[898,52709,2146],{},[2148,52711,2701],{},[1706,52713,1708],{},[2148,52715,2495],{},[902,52717,52718],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,52720,52721,1343,52745],{},[883,52722,52724],{"className":52723},[886],[888,52725,52726],{"xmlns":890},[892,52727,52728,52742],{},[895,52729,52730,52738,52740],{},[28285,52731,52732,52734,52736],{},[898,52733,2146],{},[2148,52735,2701],{},[1706,52737,3197],{},[1706,52739,1708],{},[2148,52741,3455],{},[902,52743,52744],{"encoding":904},"Q_1^* = 4",[883,52746,52748],{"className":52747},[886],[888,52749,52750],{"xmlns":890},[892,52751,52752,52766],{},[895,52753,52754,52762,52764],{},[28285,52755,52756,52758,52760],{},[898,52757,2146],{},[2148,52759,2495],{},[1706,52761,3197],{},[1706,52763,1708],{},[2148,52765,2701],{},[902,52767,52768],{"encoding":904},"Q_2^* = 1",[883,52770,52772],{"className":52771},[886],[888,52773,52774],{"xmlns":890},[892,52775,52776,52788],{},[895,52777,52778,52784,52786],{},[2489,52779,52780,52782],{},[898,52781,35541],{},[1706,52783,3197],{},[1706,52785,1708],{},[2148,52787,2701],{},[902,52789,52790],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,52793,52795],{"className":52794},[886],[888,52796,52797],{"xmlns":890},[892,52798,52799,52827],{},[895,52800,52801,52807,52809,52811,52813,52815,52817,52819,52821,52823,52825],{},[2489,52802,52803,52805],{},[898,52804,23410],{},[1706,52806,3197],{},[1706,52808,1708],{},[2148,52810,19377],{},[1706,52812,2390],{},[2148,52814,3455],{},[1706,52816,2447],{},[2148,52818,2701],{},[1706,52820,2390],{},[2148,52822,2701],{},[1706,52824,1708],{},[2148,52826,2495],{},[902,52828,52829],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,52831,52832,52835,52836,1343,52902,1343,52968,53034,53035,53072,53073,53095,53096,1837],{},[614,52833,52834],{},"Ověření postačující podmínky"," (6.26): ",[883,52837,52839],{"className":52838},[886],[888,52840,52841],{"xmlns":890},[892,52842,52843,52899],{},[895,52844,52845,52857,52859,52861,52869,52885],{},[28285,52846,52847,52849,52851],{},[898,52848,900],{},[2148,52850,22094],{},[895,52852,52853,52855],{},[1706,52854,3142],{"mathvariant":2409},[1706,52856,3142],{"mathvariant":2409},[1706,52858,1708],{},[1706,52860,1715],{},[4745,52862,52863],{"scriptlevel":2150,"displaystyle":2139},[2964,52864,52865,52867],{},[2148,52866,2701],{},[2148,52868,3455],{},[28285,52870,52871,52873,52875],{},[898,52872,2146],{},[2148,52874,2701],{},[895,52876,52877,52879,52881,52883],{},[1706,52878,1715],{},[2148,52880,4284],{},[898,52882,15493],{"mathvariant":2409},[2148,52884,2495],{},[28285,52886,52887,52889,52891],{},[898,52888,2146],{},[2148,52890,2495],{},[895,52892,52893,52895,52897],{},[2148,52894,2701],{},[898,52896,15493],{"mathvariant":2409},[2148,52898,2495],{},[902,52900,52901],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,52903,52905],{"className":52904},[886],[888,52906,52907],{"xmlns":890},[892,52908,52909,52965],{},[895,52910,52911,52923,52925,52927,52935,52949],{},[28285,52912,52913,52915,52917],{},[898,52914,900],{},[2148,52916,51608],{},[895,52918,52919,52921],{},[1706,52920,3142],{"mathvariant":2409},[1706,52922,3142],{"mathvariant":2409},[1706,52924,1708],{},[1706,52926,1715],{},[4745,52928,52929],{"scriptlevel":2150,"displaystyle":2139},[2964,52930,52931,52933],{},[2148,52932,2701],{},[2148,52934,3455],{},[28285,52936,52937,52939,52941],{},[898,52938,2146],{},[2148,52940,2701],{},[895,52942,52943,52945,52947],{},[2148,52944,2701],{},[898,52946,15493],{"mathvariant":2409},[2148,52948,2495],{},[28285,52950,52951,52953,52955],{},[898,52952,2146],{},[2148,52954,2495],{},[895,52956,52957,52959,52961,52963],{},[1706,52958,1715],{},[2148,52960,4284],{},[898,52962,15493],{"mathvariant":2409},[2148,52964,2495],{},[902,52966,52967],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,52969,52971],{"className":52970},[886],[888,52972,52973],{"xmlns":890},[892,52974,52975,53031],{},[895,52976,52977,52989,52991,52999,53015],{},[28285,52978,52979,52981,52983],{},[898,52980,900],{},[2148,52982,7156],{},[895,52984,52985,52987],{},[1706,52986,3142],{"mathvariant":2409},[1706,52988,3142],{"mathvariant":2409},[1706,52990,1708],{},[4745,52992,52993],{"scriptlevel":2150,"displaystyle":2139},[2964,52994,52995,52997],{},[2148,52996,2701],{},[2148,52998,3455],{},[28285,53000,53001,53003,53005],{},[898,53002,2146],{},[2148,53004,2701],{},[895,53006,53007,53009,53011,53013],{},[1706,53008,1715],{},[2148,53010,2701],{},[898,53012,15493],{"mathvariant":2409},[2148,53014,2495],{},[28285,53016,53017,53019,53021],{},[898,53018,2146],{},[2148,53020,2495],{},[895,53022,53023,53025,53027,53029],{},[1706,53024,1715],{},[2148,53026,2701],{},[898,53028,15493],{"mathvariant":2409},[2148,53030,2495],{},[902,53032,53033],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,53036,53038],{"className":53037},[886],[888,53039,53040],{"xmlns":890},[892,53041,53042,53069],{},[895,53043,53044,53046,53048,53050,53052,53054,53056,53058,53060,53062,53065,53067],{},[898,53045,2334],{},[1706,53047,2140],{"stretchy":2139},[2148,53049,3455],{},[1706,53051,2505],{"separator":2504},[2148,53053,2701],{},[1706,53055,2505],{"separator":2504},[2148,53057,2701],{},[1706,53059,2153],{"stretchy":2139},[1706,53061,1708],{},[2148,53063,53064],{},"0,28125",[1706,53066,8922],{},[2148,53068,2150],{},[902,53070,53071],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,53074,53076],{"className":53075},[886],[888,53077,53078],{"xmlns":890},[892,53079,53080,53092],{},[895,53081,53082,53084,53086,53088,53090],{},[1706,53083,21693],{"stretchy":2139},[2148,53085,3455],{},[1706,53087,2505],{"separator":2504},[2148,53089,2701],{},[1706,53091,21708],{"stretchy":2139},[902,53093,53094],{"encoding":904},"[4, 1]"," je vázané ",[38,53097,13792],{},[115,53099,53101],{"id":53100},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,53103,53104],{},"Obecně:",[883,53106,53108],{"className":53107},[886],[888,53109,53110],{"xmlns":890,"display":2350},[892,53111,53112,53207],{},[2354,53113,53114],{"width":2356},[2358,53115,53116,53118,53200,53202],{},[2361,53117],{"width":2363},[2361,53119,53120],{},[895,53121,53122,53128,53130,53136,53138,53144,53146,53152,53154,53156,53158,53160,53162,53168,53170,53176,53178,53184,53186,53192,53194,53196,53198],{},[2142,53123,53124,53126],{},[898,53125,2146],{},[2148,53127,2701],{},[1706,53129,1708],{},[2142,53131,53132,53134],{},[898,53133,2334],{},[2148,53135,2701],{},[1706,53137,2140],{"stretchy":2139},[2142,53139,53140,53142],{},[898,53141,1702],{},[2148,53143,2701],{},[1706,53145,2505],{"separator":2504},[2142,53147,53148,53150],{},[898,53149,1702],{},[2148,53151,2495],{},[1706,53153,2505],{"separator":2504},[898,53155,900],{},[1706,53157,2153],{"stretchy":2139},[1706,53159,2505],{"separator":2504},[4898,53161],{"width":4900},[2142,53163,53164,53166],{},[898,53165,2146],{},[2148,53167,2495],{},[1706,53169,1708],{},[2142,53171,53172,53174],{},[898,53173,2334],{},[2148,53175,2495],{},[1706,53177,2140],{"stretchy":2139},[2142,53179,53180,53182],{},[898,53181,1702],{},[2148,53183,2701],{},[1706,53185,2505],{"separator":2504},[2142,53187,53188,53190],{},[898,53189,1702],{},[2148,53191,2495],{},[1706,53193,2505],{"separator":2504},[898,53195,900],{},[1706,53197,2153],{"stretchy":2139},[1706,53199,2505],{"separator":2504},[2361,53201],{"width":2363},[2361,53203,53204],{},[2415,53205,53206],{},"(6.27)",[902,53208,53209],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,53211,53213],{"className":53212},[886],[888,53214,53215],{"xmlns":890,"display":2350},[892,53216,53217,53264],{},[2354,53218,53219],{"width":2356},[2358,53220,53221,53223,53257,53259],{},[2361,53222],{"width":2363},[2361,53224,53225],{},[895,53226,53227,53229,53231,53233,53235,53241,53243,53249,53251,53253,53255],{},[898,53228,35541],{},[1706,53230,1708],{},[898,53232,35541],{},[1706,53234,2140],{"stretchy":2139},[2142,53236,53237,53239],{},[898,53238,1702],{},[2148,53240,2701],{},[1706,53242,2505],{"separator":2504},[2142,53244,53245,53247],{},[898,53246,1702],{},[2148,53248,2495],{},[1706,53250,2505],{"separator":2504},[898,53252,900],{},[1706,53254,2153],{"stretchy":2139},[898,53256,1837],{"mathvariant":2409},[2361,53258],{"width":2363},[2361,53260,53261],{},[2415,53262,53263],{},"(6.28)",[902,53265,53266],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,53268,53269,53270,1647,53273,53286,53287,53300],{},"Hicksova poptávka závisí na ",[38,53271,53272],{},"hladině užitečnosti",[883,53274,53276],{"className":53275},[886],[888,53277,53278],{"xmlns":890},[892,53279,53280,53284],{},[895,53281,53282],{},[898,53283,900],{},[902,53285,900],{"encoding":904}," (nikoli na důchodu ",[883,53288,53290],{"className":53289},[886],[888,53291,53292],{"xmlns":890},[892,53293,53294,53298],{},[895,53295,53296],{},[898,53297,28247],{},[902,53299,28247],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,53302,53304,53305],{"id":53303},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,53306,53308],{"className":53307},[886],[888,53309,53310],{"xmlns":890},[892,53311,53312,53346],{},[895,53313,53314,53316,53318,53332],{},[898,53315,900],{},[1706,53317,1708],{},[28285,53319,53320,53322,53324],{},[898,53321,2146],{},[2148,53323,2701],{},[895,53325,53326,53328,53330],{},[2148,53327,2701],{},[898,53329,15493],{"mathvariant":2409},[2148,53331,2495],{},[28285,53333,53334,53336,53338],{},[898,53335,2146],{},[2148,53337,2495],{},[895,53339,53340,53342,53344],{},[2148,53341,2701],{},[898,53343,15493],{"mathvariant":2409},[2148,53345,2495],{},[902,53347,52221],{"encoding":904},[724,53349,53350,53380],{},[883,53351,53353],{"className":53352},[886],[888,53354,53355],{"xmlns":890},[892,53356,53357,53377],{},[895,53358,53359,53365,53367,53373,53375],{},[2142,53360,53361,53363],{},[898,53362,1702],{},[2148,53364,2701],{},[1706,53366,2505],{"separator":2504},[2142,53368,53369,53371],{},[898,53370,1702],{},[2148,53372,2495],{},[1706,53374,2505],{"separator":2504},[898,53376,900],{},[902,53378,53379],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,53382,53384],{"className":53383},[886],[888,53385,53386],{"xmlns":890,"display":2350},[892,53387,53388,53462],{},[895,53389,53390,53392,53394,53400,53406,53408,53414,53420,53422,53424,53426,53428,53430,53444,53458,53460],{},[898,53391,6362],{"mathvariant":47616},[1706,53393,1708],{},[2142,53395,53396,53398],{},[898,53397,1702],{},[2148,53399,2701],{},[2142,53401,53402,53404],{},[898,53403,2146],{},[2148,53405,2701],{},[1706,53407,2447],{},[2142,53409,53410,53412],{},[898,53411,1702],{},[2148,53413,2495],{},[2142,53415,53416,53418],{},[898,53417,2146],{},[2148,53419,2495],{},[1706,53421,2447],{},[898,53423,35541],{},[1706,53425,2140],{"stretchy":2139},[898,53427,900],{},[1706,53429,1715],{},[28285,53431,53432,53434,53436],{},[898,53433,2146],{},[2148,53435,2701],{},[895,53437,53438,53440,53442],{},[2148,53439,2701],{},[898,53441,15493],{"mathvariant":2409},[2148,53443,2495],{},[28285,53445,53446,53448,53450],{},[898,53447,2146],{},[2148,53449,2495],{},[895,53451,53452,53454,53456],{},[2148,53453,2701],{},[898,53455,15493],{"mathvariant":2409},[2148,53457,2495],{},[1706,53459,2153],{"stretchy":2139},[898,53461,1837],{"mathvariant":2409},[902,53463,53464],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,53466,49495],{},[883,53468,53470],{"className":53469},[886],[888,53471,53472],{"xmlns":890,"display":2350},[892,53473,53474,53696],{},[2354,53475,53476,53556,53636],{"rowspacing":7556,"columnalign":7557,"columnspacing":3141},[2358,53477,53478,53490],{},[2361,53479,53480],{},[4745,53481,53482],{"scriptlevel":2150,"displaystyle":2504},[28285,53483,53484,53486,53488],{},[898,53485,6362],{"mathvariant":47616},[2148,53487,2701],{},[1706,53489,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2361,53491,53492],{},[4745,53493,53494],{"scriptlevel":2150,"displaystyle":2504},[895,53495,53496,53498,53500,53506,53508,53510,53512,53520,53536,53550,53552,53554],{},[895,53497],{},[1706,53499,1708],{},[2142,53501,53502,53504],{},[898,53503,1702],{},[2148,53505,2701],{},[1706,53507,1715],{},[898,53509,35541],{},[1706,53511,2390],{},[4745,53513,53514],{"scriptlevel":2150,"displaystyle":2139},[2964,53515,53516,53518],{},[2148,53517,2701],{},[2148,53519,2495],{},[28285,53521,53522,53524,53526],{},[898,53523,2146],{},[2148,53525,2701],{},[895,53527,53528,53530,53532,53534],{},[1706,53529,1715],{},[2148,53531,2701],{},[898,53533,15493],{"mathvariant":2409},[2148,53535,2495],{},[28285,53537,53538,53540,53542],{},[898,53539,2146],{},[2148,53541,2495],{},[895,53543,53544,53546,53548],{},[2148,53545,2701],{},[898,53547,15493],{"mathvariant":2409},[2148,53549,2495],{},[1706,53551,1708],{},[2148,53553,2150],{},[1706,53555,2505],{"separator":2504},[2358,53557,53558,53570],{},[2361,53559,53560],{},[4745,53561,53562],{"scriptlevel":2150,"displaystyle":2504},[28285,53563,53564,53566,53568],{},[898,53565,6362],{"mathvariant":47616},[2148,53567,2495],{},[1706,53569,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2361,53571,53572],{},[4745,53573,53574],{"scriptlevel":2150,"displaystyle":2504},[895,53575,53576,53578,53580,53586,53588,53590,53592,53600,53614,53630,53632,53634],{},[895,53577],{},[1706,53579,1708],{},[2142,53581,53582,53584],{},[898,53583,1702],{},[2148,53585,2495],{},[1706,53587,1715],{},[898,53589,35541],{},[1706,53591,2390],{},[4745,53593,53594],{"scriptlevel":2150,"displaystyle":2139},[2964,53595,53596,53598],{},[2148,53597,2701],{},[2148,53599,2495],{},[28285,53601,53602,53604,53606],{},[898,53603,2146],{},[2148,53605,2701],{},[895,53607,53608,53610,53612],{},[2148,53609,2701],{},[898,53611,15493],{"mathvariant":2409},[2148,53613,2495],{},[28285,53615,53616,53618,53620],{},[898,53617,2146],{},[2148,53619,2495],{},[895,53621,53622,53624,53626,53628],{},[1706,53623,1715],{},[2148,53625,2701],{},[898,53627,15493],{"mathvariant":2409},[2148,53629,2495],{},[1706,53631,1708],{},[2148,53633,2150],{},[1706,53635,2505],{"separator":2504},[2358,53637,53638,53650],{},[2361,53639,53640],{},[4745,53641,53642],{"scriptlevel":2150,"displaystyle":2504},[28285,53643,53644,53646,53648],{},[898,53645,6362],{"mathvariant":47616},[898,53647,35541],{},[1706,53649,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2361,53651,53652],{},[4745,53653,53654],{"scriptlevel":2150,"displaystyle":2504},[895,53655,53656,53658,53660,53662,53664,53678,53692,53694],{},[895,53657],{},[1706,53659,1708],{},[898,53661,900],{},[1706,53663,1715],{},[28285,53665,53666,53668,53670],{},[898,53667,2146],{},[2148,53669,2701],{},[895,53671,53672,53674,53676],{},[2148,53673,2701],{},[898,53675,15493],{"mathvariant":2409},[2148,53677,2495],{},[28285,53679,53680,53682,53684],{},[898,53681,2146],{},[2148,53683,2495],{},[895,53685,53686,53688,53690],{},[2148,53687,2701],{},[898,53689,15493],{"mathvariant":2409},[2148,53691,2495],{},[1706,53693,1708],{},[2148,53695,31567],{},[902,53697,53698],{"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}",[724,53700,53701,53702,53772,53773,53831],{},"Podílem rovnic: ",[883,53703,53705],{"className":53704},[886],[888,53706,53707],{"xmlns":890},[892,53708,53709,53769],{},[895,53710,53711,53717,53719,53725,53727,53733,53735,53741,53743,53749,53755,53757,53763],{},[2142,53712,53713,53715],{},[898,53714,1702],{},[2148,53716,2701],{},[898,53718,15493],{"mathvariant":2409},[2142,53720,53721,53723],{},[898,53722,1702],{},[2148,53724,2495],{},[1706,53726,1708],{},[2142,53728,53729,53731],{},[898,53730,2146],{},[2148,53732,2495],{},[898,53734,15493],{"mathvariant":2409},[2142,53736,53737,53739],{},[898,53738,2146],{},[2148,53740,2701],{},[1706,53742,9609],{},[2142,53744,53745,53747],{},[898,53746,1702],{},[2148,53748,2701],{},[2142,53750,53751,53753],{},[898,53752,2146],{},[2148,53754,2701],{},[1706,53756,1708],{},[2142,53758,53759,53761],{},[898,53760,1702],{},[2148,53762,2495],{},[2142,53764,53765,53767],{},[898,53766,2146],{},[2148,53768,2495],{},[902,53770,53771],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,53774,53776],{"className":53775},[886],[888,53777,53778],{"xmlns":890},[892,53779,53780,53828],{},[895,53781,53782,53784,53786,53792,53798,53800,53806,53812,53814,53816,53822],{},[898,53783,23410],{},[1706,53785,1708],{},[2142,53787,53788,53790],{},[898,53789,1702],{},[2148,53791,2701],{},[2142,53793,53794,53796],{},[898,53795,2146],{},[2148,53797,2701],{},[1706,53799,2447],{},[2142,53801,53802,53804],{},[898,53803,1702],{},[2148,53805,2495],{},[2142,53807,53808,53810],{},[898,53809,2146],{},[2148,53811,2495],{},[1706,53813,1708],{},[2148,53815,2495],{},[2142,53817,53818,53820],{},[898,53819,1702],{},[2148,53821,2701],{},[2142,53823,53824,53826],{},[898,53825,2146],{},[2148,53827,2701],{},[902,53829,53830],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,53833,53835],{"className":53834},[886],[888,53836,53837],{"xmlns":890,"display":2350},[892,53838,53839,53906],{},[2354,53840,53841],{"width":2356},[2358,53842,53843,53845,53899,53901],{},[2361,53844],{"width":2363},[2361,53846,53847],{},[895,53848,53849,53855,53857,53871,53873,53875,53881,53883,53897],{},[2142,53850,53851,53853],{},[898,53852,2146],{},[2148,53854,2701],{},[1706,53856,1708],{},[2964,53858,53859,53861],{},[898,53860,23410],{},[895,53862,53863,53865],{},[2148,53864,2495],{},[2142,53866,53867,53869],{},[898,53868,1702],{},[2148,53870,2701],{},[1706,53872,2505],{"separator":2504},[4898,53874],{"width":4900},[2142,53876,53877,53879],{},[898,53878,2146],{},[2148,53880,2495],{},[1706,53882,1708],{},[2964,53884,53885,53887],{},[898,53886,23410],{},[895,53888,53889,53891],{},[2148,53890,2495],{},[2142,53892,53893,53895],{},[898,53894,1702],{},[2148,53896,2495],{},[898,53898,1837],{"mathvariant":2409},[2361,53900],{"width":2363},[2361,53902,53903],{},[2415,53904,53905],{},"(6.29)",[902,53907,53908],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,53910,53911,53912,11019,53994,54030],{},"Ze třetí rovnice ",[883,53913,53915],{"className":53914},[886],[888,53916,53917],{"xmlns":890},[892,53918,53919,53991],{},[895,53920,53921,53923,53925,53963,53965],{},[898,53922,900],{},[1706,53924,1708],{},[11087,53926,53927],{},[895,53928,53929,53945,53947],{},[4745,53930,53931],{"scriptlevel":2150,"displaystyle":2139},[2964,53932,53933,53935],{},[898,53934,23410],{},[895,53936,53937,53939],{},[2148,53938,2495],{},[2142,53940,53941,53943],{},[898,53942,1702],{},[2148,53944,2701],{},[1706,53946,2390],{},[4745,53948,53949],{"scriptlevel":2150,"displaystyle":2139},[2964,53950,53951,53953],{},[898,53952,23410],{},[895,53954,53955,53957],{},[2148,53956,2495],{},[2142,53958,53959,53961],{},[898,53960,1702],{},[2148,53962,2495],{},[1706,53964,1708],{},[4745,53966,53967],{"scriptlevel":2150,"displaystyle":2139},[2964,53968,53969,53971],{},[898,53970,23410],{},[895,53972,53973,53975],{},[2148,53974,2495],{},[11087,53976,53977],{},[895,53978,53979,53985],{},[2142,53980,53981,53983],{},[898,53982,1702],{},[2148,53984,2701],{},[2142,53986,53987,53989],{},[898,53988,1702],{},[2148,53990,2495],{},[902,53992,53993],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,53995,53997],{"className":53996},[886],[888,53998,53999],{"xmlns":890},[892,54000,54001,54027],{},[895,54002,54003,54005,54007,54009,54011],{},[898,54004,23410],{},[1706,54006,1708],{},[2148,54008,2495],{},[898,54010,900],{},[11087,54012,54013],{},[895,54014,54015,54021],{},[2142,54016,54017,54019],{},[898,54018,1702],{},[2148,54020,2701],{},[2142,54022,54023,54025],{},[898,54024,1702],{},[2148,54026,2495],{},[902,54028,54029],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,54032,54034],{"className":54033},[886],[888,54035,54036],{"xmlns":890,"display":2350},[892,54037,54038,54183],{},[2354,54039,54040],{"width":2356},[2358,54041,54042,54044,54176,54178],{},[2361,54043],{"width":2363},[2361,54045,54046],{},[31939,54047,54048],{"notation":31941},[4745,54049,54050],{"scriptlevel":2150,"displaystyle":2139},[4745,54051,54052],{"scriptlevel":2150,"displaystyle":2139},[4745,54053,54054],{"scriptlevel":2150,"displaystyle":2504},[895,54055,54056,54058,54064,54066,54068,54084,54086,54092,54094,54100,54102,54108,54110,54112,54114,54116,54118,54124,54126,54128,54144,54146,54152,54154,54160,54162,54168,54170,54172,54174],{},[2415,54057,3852],{},[2142,54059,54060,54062],{},[898,54061,2146],{},[2148,54063,2701],{},[1706,54065,1708],{},[898,54067,900],{},[11087,54069,54070],{},[2964,54071,54072,54078],{},[2142,54073,54074,54076],{},[898,54075,1702],{},[2148,54077,2495],{},[2142,54079,54080,54082],{},[898,54081,1702],{},[2148,54083,2701],{},[1706,54085,1708],{},[2142,54087,54088,54090],{},[898,54089,2334],{},[2148,54091,2701],{},[1706,54093,2140],{"stretchy":2139},[2142,54095,54096,54098],{},[898,54097,1702],{},[2148,54099,2701],{},[1706,54101,2505],{"separator":2504},[2142,54103,54104,54106],{},[898,54105,1702],{},[2148,54107,2495],{},[1706,54109,2505],{"separator":2504},[898,54111,900],{},[1706,54113,2153],{"stretchy":2139},[1706,54115,2505],{"separator":2504},[4898,54117],{"width":4900},[2142,54119,54120,54122],{},[898,54121,2146],{},[2148,54123,2495],{},[1706,54125,1708],{},[898,54127,900],{},[11087,54129,54130],{},[2964,54131,54132,54138],{},[2142,54133,54134,54136],{},[898,54135,1702],{},[2148,54137,2701],{},[2142,54139,54140,54142],{},[898,54141,1702],{},[2148,54143,2495],{},[1706,54145,1708],{},[2142,54147,54148,54150],{},[898,54149,2334],{},[2148,54151,2495],{},[1706,54153,2140],{"stretchy":2139},[2142,54155,54156,54158],{},[898,54157,1702],{},[2148,54159,2701],{},[1706,54161,2505],{"separator":2504},[2142,54163,54164,54166],{},[898,54165,1702],{},[2148,54167,2495],{},[1706,54169,2505],{"separator":2504},[898,54171,900],{},[1706,54173,2153],{"stretchy":2139},[2415,54175,3852],{},[2361,54177],{"width":2363},[2361,54179,54180],{},[2415,54181,54182],{},"(6.30)",[902,54184,54185],{"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}",[115,54187,54189],{"id":54188},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,54191,54192,54193,54206,54207,54224,54225,54238,54239,54256,54257,54260,54261,54300,54301,54330],{},"Primární (max ",[883,54194,54196],{"className":54195},[886],[888,54197,54198],{"xmlns":890},[892,54199,54200,54204],{},[895,54201,54202],{},[898,54203,900],{},[902,54205,900],{"encoding":904}," při rozpočtu ",[883,54208,54210],{"className":54209},[886],[888,54211,54212],{"xmlns":890},[892,54213,54214,54222],{},[895,54215,54216],{},[2489,54217,54218,54220],{},[898,54219,28247],{},[1706,54221,3197],{},[902,54223,47099],{"encoding":904},") a duální (min ",[883,54226,54228],{"className":54227},[886],[888,54229,54230],{"xmlns":890},[892,54231,54232,54236],{},[895,54233,54234],{},[898,54235,23410],{},[902,54237,23410],{"encoding":904}," při užitečnosti ",[883,54240,54242],{"className":54241},[886],[888,54243,54244],{"xmlns":890},[892,54245,54246,54254],{},[895,54247,54248],{},[2489,54249,54250,54252],{},[898,54251,900],{},[1706,54253,3197],{},[902,54255,47033],{"encoding":904},") úloha jsou ",[38,54258,54259],{},"ekvivalentní",": mají tentýž bod optima ",[883,54262,54264],{"className":54263},[886],[888,54265,54266],{"xmlns":890},[892,54267,54268,54298],{},[895,54269,54270,54276,54278,54286,54288,54296],{},[2489,54271,54272,54274],{},[898,54273,2146],{},[1706,54275,3197],{},[1706,54277,21693],{"stretchy":2139},[28285,54279,54280,54282,54284],{},[898,54281,2146],{},[2148,54283,2701],{},[1706,54285,3197],{},[1706,54287,2505],{"separator":2504},[28285,54289,54290,54292,54294],{},[898,54291,2146],{},[2148,54293,2495],{},[1706,54295,3197],{},[1706,54297,21708],{"stretchy":2139},[902,54299,47395],{"encoding":904}," a v obou platí ",[883,54302,54304],{"className":54303},[886],[888,54305,54306],{"xmlns":890},[892,54307,54308,54328],{},[895,54309,54310,54312,54314,54320,54322],{},[2415,54311,29714],{},[1706,54313,1708],{},[2142,54315,54316,54318],{},[898,54317,1702],{},[2148,54319,2701],{},[898,54321,15493],{"mathvariant":2409},[2142,54323,54324,54326],{},[898,54325,1702],{},[2148,54327,2495],{},[902,54329,47069],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,54332,54333],{},[2286,54334],{"alt":54335,"className":54336,"src":54337},"imek-primarni-vs-dualni",[210,2290],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,54339,54340,54451],{},[123,54341,54342,54345,54346,54359,54360,54400,54401,1837],{},[38,54343,54344],{},"Primární"," (Marshall): zadáno ",[883,54347,54349],{"className":54348},[886],[888,54350,54351],{"xmlns":890},[892,54352,54353,54357],{},[895,54354,54355],{},[898,54356,28247],{},[902,54358,28247],{"encoding":904},", hledáme maximální ",[883,54361,54363],{"className":54362},[886],[888,54364,54365],{"xmlns":890},[892,54366,54367,54397],{},[895,54368,54369,54375,54377,54383,54385,54391,54393,54395],{},[2489,54370,54371,54373],{},[898,54372,900],{},[1706,54374,3197],{},[1706,54376,2140],{"stretchy":2139},[2142,54378,54379,54381],{},[898,54380,1702],{},[2148,54382,2701],{},[1706,54384,2505],{"separator":2504},[2142,54386,54387,54389],{},[898,54388,1702],{},[2148,54390,2495],{},[1706,54392,2505],{"separator":2504},[898,54394,28247],{},[1706,54396,2153],{"stretchy":2139},[902,54398,54399],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,54402,54404],{"className":54403},[886],[888,54405,54406],{"xmlns":890},[892,54407,54408,54448],{},[895,54409,54410,54416,54418,54426,54428,54434,54436,54442,54444,54446],{},[2142,54411,54412,54414],{},[898,54413,2146],{},[898,54415,36887],{},[1706,54417,1708],{},[28285,54419,54420,54422,54424],{},[898,54421,2334],{},[898,54423,36887],{},[898,54425,1742],{},[1706,54427,2140],{"stretchy":2139},[2142,54429,54430,54432],{},[898,54431,1702],{},[2148,54433,2701],{},[1706,54435,2505],{"separator":2504},[2142,54437,54438,54440],{},[898,54439,1702],{},[2148,54441,2495],{},[1706,54443,2505],{"separator":2504},[898,54445,28247],{},[1706,54447,2153],{"stretchy":2139},[902,54449,54450],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,54452,54453,54456,54457,54470,54471,54400,54511,1837],{},[38,54454,54455],{},"Duální"," (Hicks): zadáno ",[883,54458,54460],{"className":54459},[886],[888,54461,54462],{"xmlns":890},[892,54463,54464,54468],{},[895,54465,54466],{},[898,54467,900],{},[902,54469,900],{"encoding":904},", hledáme minimální ",[883,54472,54474],{"className":54473},[886],[888,54475,54476],{"xmlns":890},[892,54477,54478,54508],{},[895,54479,54480,54486,54488,54494,54496,54502,54504,54506],{},[2489,54481,54482,54484],{},[898,54483,23410],{},[1706,54485,3197],{},[1706,54487,2140],{"stretchy":2139},[2142,54489,54490,54492],{},[898,54491,1702],{},[2148,54493,2701],{},[1706,54495,2505],{"separator":2504},[2142,54497,54498,54500],{},[898,54499,1702],{},[2148,54501,2495],{},[1706,54503,2505],{"separator":2504},[898,54505,900],{},[1706,54507,2153],{"stretchy":2139},[902,54509,54510],{"encoding":904},"E^*(P_1, P_2, U)",[883,54512,54514],{"className":54513},[886],[888,54515,54516],{"xmlns":890},[892,54517,54518,54559],{},[895,54519,54520,54526,54528,54537,54539,54545,54547,54553,54555,54557],{},[2142,54521,54522,54524],{},[898,54523,2146],{},[898,54525,36887],{},[1706,54527,1708],{},[28285,54529,54530,54532,54534],{},[898,54531,2334],{},[898,54533,36887],{},[898,54535,54536],{},"H",[1706,54538,2140],{"stretchy":2139},[2142,54540,54541,54543],{},[898,54542,1702],{},[2148,54544,2701],{},[1706,54546,2505],{"separator":2504},[2142,54548,54549,54551],{},[898,54550,1702],{},[2148,54552,2495],{},[1706,54554,2505],{"separator":2504},[898,54556,900],{},[1706,54558,2153],{"stretchy":2139},[902,54560,54561],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,54563,54564,54565,54568,54569,54572],{},"Proč se studují obě? Marshallova poptávka je ",[38,54566,54567],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,54570,54571],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,54574,54576],{"id":54575},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,54578,54580],{"id":54579},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,54582,54583,54586,54587,54619,54620,54658,54659,54685],{},[38,54584,54585],{},"6.8"," Jsou dány užitečnost ",[883,54588,54590],{"className":54589},[886],[888,54591,54592],{"xmlns":890},[892,54593,54594,54616],{},[895,54595,54596,54598,54600,54608],{},[898,54597,900],{},[1706,54599,1708],{},[28285,54601,54602,54604,54606],{},[898,54603,2146],{},[2148,54605,2701],{},[2148,54607,11496],{},[28285,54609,54610,54612,54614],{},[898,54611,2146],{},[2148,54613,2495],{},[2148,54615,11496],{},[902,54617,54618],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,54621,54623],{"className":54622},[886],[888,54624,54625],{"xmlns":890},[892,54626,54627,54655],{},[895,54628,54629,54637,54639,54641,54643,54651,54653],{},[28285,54630,54631,54633,54635],{},[898,54632,1702],{},[2148,54634,2701],{},[1706,54636,3197],{},[1706,54638,1708],{},[2148,54640,3455],{},[1706,54642,2505],{"separator":2504},[28285,54644,54645,54647,54649],{},[898,54646,1702],{},[2148,54648,2495],{},[1706,54650,3197],{},[1706,54652,1708],{},[2148,54654,7786],{},[902,54656,54657],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,54660,54662],{"className":54661},[886],[888,54663,54664],{"xmlns":890},[892,54665,54666,54682],{},[895,54667,54668,54674,54676],{},[2142,54669,54670,54672],{},[898,54671,2146],{},[2148,54673,2701],{},[1706,54675,2505],{"separator":2504},[2142,54677,54678,54680],{},[898,54679,2146],{},[2148,54681,2495],{},[902,54683,54684],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,54687,54688,54691,54692,54734,54735,54766,54767,54789,54790,1837],{},[38,54689,54690],{},"6.9"," Jsou dány rozpočtové omezení ",[883,54693,54695],{"className":54694},[886],[888,54696,54697],{"xmlns":890},[892,54698,54699,54731],{},[895,54700,54701,54703,54705,54711,54717,54719,54725],{},[898,54702,28247],{},[1706,54704,1708],{},[2142,54706,54707,54709],{},[898,54708,1702],{},[2148,54710,2701],{},[2142,54712,54713,54715],{},[898,54714,2146],{},[2148,54716,2701],{},[1706,54718,2447],{},[2142,54720,54721,54723],{},[898,54722,1702],{},[2148,54724,2495],{},[2142,54726,54727,54729],{},[898,54728,2146],{},[2148,54730,2495],{},[902,54732,54733],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,54736,54738],{"className":54737},[886],[888,54739,54740],{"xmlns":890},[892,54741,54742,54764],{},[895,54743,54744,54746,54748,54756],{},[898,54745,900],{},[1706,54747,1708],{},[28285,54749,54750,54752,54754],{},[898,54751,2146],{},[2148,54753,2701],{},[2148,54755,11496],{},[28285,54757,54758,54760,54762],{},[898,54759,2146],{},[2148,54761,2495],{},[2148,54763,11496],{},[902,54765,54618],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,54768,54770],{"className":54769},[886],[888,54771,54772],{"xmlns":890},[892,54773,54774,54786],{},[895,54775,54776,54782,54784],{},[2489,54777,54778,54780],{},[898,54779,28247],{},[1706,54781,3197],{},[1706,54783,1708],{},[2148,54785,17366],{},[902,54787,54788],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,54791,54793],{"className":54792},[886],[888,54794,54795],{"xmlns":890},[892,54796,54797,54825],{},[895,54798,54799,54807,54809,54811,54813,54821,54823],{},[28285,54800,54801,54803,54805],{},[898,54802,1702],{},[2148,54804,2701],{},[1706,54806,3197],{},[1706,54808,1708],{},[2148,54810,7524],{},[1706,54812,2505],{"separator":2504},[28285,54814,54815,54817,54819],{},[898,54816,1702],{},[2148,54818,2495],{},[1706,54820,3197],{},[1706,54822,1708],{},[2148,54824,7786],{},[902,54826,54827],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,54829,54830,54833,54834,15842,54866,54896,54897,1837],{},[38,54831,54832],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,54835,54837],{"className":54836},[886],[888,54838,54839],{"xmlns":890},[892,54840,54841,54863],{},[895,54842,54843,54845,54847,54855],{},[898,54844,900],{},[1706,54846,1708],{},[28285,54848,54849,54851,54853],{},[898,54850,2146],{},[2148,54852,2701],{},[898,54854,207],{},[28285,54856,54857,54859,54861],{},[898,54858,2146],{},[2148,54860,2495],{},[898,54862,2450],{},[902,54864,54865],{"encoding":904},"U = Q_1^a Q_2^b",[883,54867,54869],{"className":54868},[886],[888,54870,54871],{"xmlns":890},[892,54872,54873,54893],{},[895,54874,54875,54877,54879,54881,54883,54885,54887,54889,54891],{},[898,54876,207],{},[1706,54878,2505],{"separator":2504},[898,54880,2450],{},[1706,54882,25638],{},[1706,54884,24467],{"stretchy":2139},[2148,54886,2150],{},[1706,54888,2505],{"separator":2504},[2148,54890,2701],{},[1706,54892,24484],{"stretchy":2139},[902,54894,54895],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,54898,54900],{"className":54899},[886],[888,54901,54902],{"xmlns":890},[892,54903,54904,54936],{},[895,54905,54906,54908,54910,54916,54922,54924,54930],{},[898,54907,28247],{},[1706,54909,1708],{},[2142,54911,54912,54914],{},[898,54913,1702],{},[2148,54915,2701],{},[2142,54917,54918,54920],{},[898,54919,2146],{},[2148,54921,2701],{},[1706,54923,2447],{},[2142,54925,54926,54928],{},[898,54927,1702],{},[2148,54929,2495],{},[2142,54931,54932,54934],{},[898,54933,2146],{},[2148,54935,2495],{},[902,54937,54733],{"encoding":904},[724,54939,54940,54943,54944,15842,54978,54896,54996,1837],{},[38,54941,54942],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,54945,54947],{"className":54946},[886],[888,54948,54949],{"xmlns":890},[892,54950,54951,54975],{},[895,54952,54953,54955,54957,54965,54967],{},[898,54954,900],{},[1706,54956,1708],{},[28285,54958,54959,54961,54963],{},[898,54960,2146],{},[2148,54962,2701],{},[898,54964,207],{},[1706,54966,2447],{},[28285,54968,54969,54971,54973],{},[898,54970,2146],{},[2148,54972,2495],{},[898,54974,207],{},[902,54976,54977],{"encoding":904},"U = Q_1^a + Q_2^a",[883,54979,54981],{"className":54980},[886],[888,54982,54983],{"xmlns":890},[892,54984,54985,54993],{},[895,54986,54987,54989,54991],{},[898,54988,207],{},[1706,54990,22551],{"mathvariant":2409},[2148,54992,2150],{},[902,54994,54995],{"encoding":904},"a \\neq 0",[883,54997,54999],{"className":54998},[886],[888,55000,55001],{"xmlns":890},[892,55002,55003,55035],{},[895,55004,55005,55007,55009,55015,55021,55023,55029],{},[898,55006,28247],{},[1706,55008,1708],{},[2142,55010,55011,55013],{},[898,55012,1702],{},[2148,55014,2701],{},[2142,55016,55017,55019],{},[898,55018,2146],{},[2148,55020,2701],{},[1706,55022,2447],{},[2142,55024,55025,55027],{},[898,55026,1702],{},[2148,55028,2495],{},[2142,55030,55031,55033],{},[898,55032,2146],{},[2148,55034,2495],{},[902,55036,54733],{"encoding":904},[198,55038,55040],{"id":55039},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,55042,55043,54586,55046,1343,55073,55095,55096,1343,55119,55143,55144,55169,55170,1837],{},[38,55044,55045],{},"6.12",[883,55047,55049],{"className":55048},[886],[888,55050,55051],{"xmlns":890},[892,55052,55053,55071],{},[895,55054,55055,55057,55059,55065],{},[898,55056,900],{},[1706,55058,1708],{},[2142,55060,55061,55063],{},[898,55062,2146],{},[2148,55064,2701],{},[2142,55066,55067,55069],{},[898,55068,2146],{},[2148,55070,2495],{},[902,55072,49290],{"encoding":904},[883,55074,55076],{"className":55075},[886],[888,55077,55078],{"xmlns":890},[892,55079,55080,55092],{},[895,55081,55082,55088,55090],{},[2489,55083,55084,55086],{},[898,55085,900],{},[1706,55087,3197],{},[1706,55089,1708],{},[2148,55091,7786],{},[902,55093,55094],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,55097,55099],{"className":55098},[886],[888,55100,55101],{"xmlns":890},[892,55102,55103,55117],{},[895,55104,55105,55113,55115],{},[28285,55106,55107,55109,55111],{},[898,55108,1702],{},[2148,55110,2701],{},[1706,55112,3197],{},[1706,55114,1708],{},[2148,55116,2495],{},[902,55118,49363],{"encoding":904},[883,55120,55122],{"className":55121},[886],[888,55123,55124],{"xmlns":890},[892,55125,55126,55140],{},[895,55127,55128,55136,55138],{},[28285,55129,55130,55132,55134],{},[898,55131,1702],{},[2148,55133,2495],{},[1706,55135,3197],{},[1706,55137,1708],{},[2148,55139,3455],{},[902,55141,55142],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,55145,55147],{"className":55146},[886],[888,55148,55149],{"xmlns":890},[892,55150,55151,55167],{},[895,55152,55153,55159,55161],{},[2142,55154,55155,55157],{},[898,55156,2146],{},[2148,55158,2701],{},[1706,55160,2505],{"separator":2504},[2142,55162,55163,55165],{},[898,55164,2146],{},[2148,55166,2495],{},[902,55168,54684],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,55171,55173],{"className":55172},[886],[888,55174,55175],{"xmlns":890},[892,55176,55177,55197],{},[895,55178,55179,55181,55183,55189,55191],{},[898,55180,900],{},[1706,55182,1708],{},[2142,55184,55185,55187],{},[898,55186,2146],{},[2148,55188,2701],{},[1706,55190,2390],{},[2142,55192,55193,55195],{},[898,55194,2146],{},[2148,55196,2495],{},[902,55198,55199],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,55201,55202,55205,55206,55247,55248,55270,55271,1837],{},[38,55203,55204],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,55207,55209],{"className":55208},[886],[888,55210,55211],{"xmlns":890},[892,55212,55213,55245],{},[895,55214,55215,55217,55219,55225,55231,55233,55239],{},[898,55216,23410],{},[1706,55218,1708],{},[2142,55220,55221,55223],{},[898,55222,1702],{},[2148,55224,2701],{},[2142,55226,55227,55229],{},[898,55228,2146],{},[2148,55230,2701],{},[1706,55232,2447],{},[2142,55234,55235,55237],{},[898,55236,1702],{},[2148,55238,2495],{},[2142,55240,55241,55243],{},[898,55242,2146],{},[2148,55244,2495],{},[902,55246,47014],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,55249,55251],{"className":55250},[886],[888,55252,55253],{"xmlns":890},[892,55254,55255,55267],{},[895,55256,55257,55263,55265],{},[2489,55258,55259,55261],{},[898,55260,900],{},[1706,55262,3197],{},[1706,55264,1708],{},[2148,55266,2748],{},[902,55268,55269],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,55272,55274],{"className":55273},[886],[888,55275,55276],{"xmlns":890},[892,55277,55278,55306],{},[895,55279,55280,55288,55290,55292,55294,55302,55304],{},[28285,55281,55282,55284,55286],{},[898,55283,1702],{},[2148,55285,2701],{},[1706,55287,3197],{},[1706,55289,1708],{},[2148,55291,3369],{},[1706,55293,2505],{"separator":2504},[28285,55295,55296,55298,55300],{},[898,55297,1702],{},[2148,55299,2495],{},[1706,55301,3197],{},[1706,55303,1708],{},[2148,55305,3359],{},[902,55307,55308],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,55310,19879],{"id":19878},[120,55312,55313,55370,55409,55429,55464,55518,55523,55529,55625,55670],{},[123,55314,55315,1647,55318,55367,55368,1837],{},[38,55316,55317],{},"Rozpočtové omezení (budget constraint)",[883,55319,55321],{"className":55320},[886],[888,55322,55323],{"xmlns":890},[892,55324,55325,55365],{},[895,55326,55327,55333,55335,55343,55349,55351,55359],{},[2489,55328,55329,55331],{},[898,55330,28247],{},[1706,55332,3197],{},[1706,55334,1708],{},[28285,55336,55337,55339,55341],{},[898,55338,1702],{},[2148,55340,2701],{},[1706,55342,3197],{},[2142,55344,55345,55347],{},[898,55346,2146],{},[2148,55348,2701],{},[1706,55350,2447],{},[28285,55352,55353,55355,55357],{},[898,55354,1702],{},[2148,55356,2495],{},[1706,55358,3197],{},[2142,55360,55361,55363],{},[898,55362,2146],{},[2148,55364,2495],{},[902,55366,36396],{"encoding":904}," — (6.12); ",[38,55369,47204],{},[123,55371,55372,55375,55376,1837],{},[38,55373,55374],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,55377,55379],{"className":55378},[886],[888,55380,55381],{"xmlns":890},[892,55382,55383,55407],{},[895,55384,55385,55387,55389,55397,55399],{},[2415,55386,29714],{},[1706,55388,1708],{},[28285,55390,55391,55393,55395],{},[898,55392,1702],{},[2148,55394,2701],{},[1706,55396,3197],{},[898,55398,15493],{"mathvariant":2409},[28285,55400,55401,55403,55405],{},[898,55402,1702],{},[2148,55404,2495],{},[1706,55406,3197],{},[902,55408,48047],{"encoding":904},[123,55410,55411,55426,55427,1837],{},[38,55412,48191,55413],{},[883,55414,55416],{"className":55415},[886],[888,55417,55418],{"xmlns":890},[892,55419,55420,55424],{},[895,55421,55422],{},[898,55423,35541],{},[902,55425,35594],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,55428,48213],{},[123,55430,55431,55434,55435,1837],{},[38,55432,55433],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,55436,55438],{"className":55437},[886],[888,55439,55440],{"xmlns":890},[892,55441,55442,55462],{},[895,55443,55444,55446,55448,55454,55456],{},[2415,55445,29714],{},[1706,55447,1708],{},[2142,55449,55450,55452],{},[898,55451,1702],{},[2148,55453,2701],{},[898,55455,15493],{"mathvariant":2409},[2142,55457,55458,55460],{},[898,55459,1702],{},[2148,55461,2495],{},[902,55463,47069],{"encoding":904},[123,55465,55466,21021,55469,55517],{},[38,55467,55468],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,55470,55472],{"className":55471},[886],[888,55473,55474],{"xmlns":890},[892,55475,55476,55514],{},[895,55477,55478,55484,55486,55492,55494,55500,55502,55508,55510,55512],{},[2142,55479,55480,55482],{},[898,55481,2146],{},[898,55483,36887],{},[1706,55485,1708],{},[2142,55487,55488,55490],{},[898,55489,2334],{},[898,55491,36887],{},[1706,55493,2140],{"stretchy":2139},[2142,55495,55496,55498],{},[898,55497,1702],{},[2148,55499,2701],{},[1706,55501,2505],{"separator":2504},[2142,55503,55504,55506],{},[898,55505,1702],{},[2148,55507,2495],{},[1706,55509,2505],{"separator":2504},[898,55511,28247],{},[1706,55513,2153],{"stretchy":2139},[902,55515,55516],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,55519,55520,55522],{},[38,55521,50789],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,55524,55525,55528],{},[38,55526,55527],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,55530,55531,21021,55533,55580,55581,55624],{},[38,55532,53101],{},[883,55534,55536],{"className":55535},[886],[888,55537,55538],{"xmlns":890},[892,55539,55540,55578],{},[895,55541,55542,55548,55550,55556,55558,55564,55566,55572,55574,55576],{},[2142,55543,55544,55546],{},[898,55545,2146],{},[898,55547,36887],{},[1706,55549,1708],{},[2142,55551,55552,55554],{},[898,55553,2334],{},[898,55555,36887],{},[1706,55557,2140],{"stretchy":2139},[2142,55559,55560,55562],{},[898,55561,1702],{},[2148,55563,2701],{},[1706,55565,2505],{"separator":2504},[2142,55567,55568,55570],{},[898,55569,1702],{},[2148,55571,2495],{},[1706,55573,2505],{"separator":2504},[898,55575,900],{},[1706,55577,2153],{"stretchy":2139},[902,55579,36920],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,55582,55584],{"className":55583},[886],[888,55585,55586],{"xmlns":890},[892,55587,55588,55622],{},[895,55589,55590,55592,55594,55608],{},[898,55591,900],{},[1706,55593,1708],{},[28285,55595,55596,55598,55600],{},[898,55597,2146],{},[2148,55599,2701],{},[895,55601,55602,55604,55606],{},[2148,55603,2701],{},[898,55605,15493],{"mathvariant":2409},[2148,55607,2495],{},[28285,55609,55610,55612,55614],{},[898,55611,2146],{},[2148,55613,2495],{},[895,55615,55616,55618,55620],{},[2148,55617,2701],{},[898,55619,15493],{"mathvariant":2409},[2148,55621,2495],{},[902,55623,52221],{"encoding":904},": (6.30).",[123,55626,55627,55669],{},[38,55628,55629,55630],{},"Bod dotyku ",[883,55631,55633],{"className":55632},[886],[888,55634,55635],{"xmlns":890},[892,55636,55637,55667],{},[895,55638,55639,55645,55647,55655,55657,55665],{},[2489,55640,55641,55643],{},[898,55642,2146],{},[1706,55644,3197],{},[1706,55646,21693],{"stretchy":2139},[28285,55648,55649,55651,55653],{},[898,55650,2146],{},[2148,55652,2701],{},[1706,55654,3197],{},[1706,55656,2505],{"separator":2504},[28285,55658,55659,55661,55663],{},[898,55660,2146],{},[2148,55662,2495],{},[1706,55664,3197],{},[1706,55666,21708],{"stretchy":2139},[902,55668,47395],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,55671,55672,55675,55676,55689,55690,55703],{},[38,55673,55674],{},"Dualita"," — ekvivalence max ",[883,55677,55679],{"className":55678},[886],[888,55680,55681],{"xmlns":890},[892,55682,55683,55687],{},[895,55684,55685],{},[898,55686,900],{},[902,55688,900],{"encoding":904}," a min ",[883,55691,55693],{"className":55692},[886],[888,55694,55695],{"xmlns":890},[892,55696,55697,55701],{},[895,55698,55699],{},[898,55700,23410],{},[902,55702,23410],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,55705,21083],{"id":21082},[120,55707,55708,55731,55747,55760,55770],{},[123,55709,55710,1647,55713,55716,55717,55730],{},[38,55711,55712],{},"Teorie před optimalizací:",[207,55714,880],{"className":55715,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,55718,55720],{"className":55719},[886],[888,55721,55722],{"xmlns":890},[892,55723,55724,55728],{},[895,55725,55726],{},[898,55727,900],{},[902,55729,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,55732,55733,1647,55736,55739,55740,55743,55744,1837],{},[38,55734,55735],{},"Matematický aparát:",[207,55737,793],{"className":55738,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,55741,784],{"className":55742,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,55745,21102],{"className":55746,"dataFsResolvedFilePath":764,"href":765},[210],[123,55748,55749,1647,55752,55755,55756,55759],{},[38,55750,55751],{},"Paralely:",[207,55753,30199],{"className":55754,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,55757,21094],{"className":55758,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,55761,55762,1647,55764,1343,55767],{},[38,55763,21113],{},[207,55765,1094],{"className":55766,"dataFsResolvedFilePath":838,"href":839},[210],[207,55768,1101],{"className":55769,"dataFsResolvedFilePath":868,"href":869},[210],[123,55771,55772,1647,55774],{},[38,55773,21126],{},[207,55775,21132],{"className":55776,"dataFsResolvedFilePath":21130,"href":21131},[210],{"title":641,"searchDepth":642,"depth":642,"links":55778},[55779,55780,55781,55786,55787,55788,55790,55793,55796,55798,55799,55801,55802,55806,55807],{"id":31114,"depth":642,"text":31115},{"id":47077,"depth":642,"text":47078},{"id":47472,"depth":642,"text":47473,"children":55782},[55783,55784],{"id":47592,"depth":649,"text":47593},{"id":48173,"depth":649,"text":55785},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":48634,"depth":642,"text":48635},{"id":48944,"depth":642,"text":48945},{"id":49261,"depth":642,"text":55789},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":50033,"depth":642,"text":50034,"children":55791},[55792],{"id":50788,"depth":649,"text":50789},{"id":50968,"depth":642,"text":50969,"children":55794},[55795],{"id":51225,"depth":649,"text":51226},{"id":52176,"depth":642,"text":55797},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":53100,"depth":642,"text":53101},{"id":53303,"depth":642,"text":55800},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":54188,"depth":642,"text":54189},{"id":54575,"depth":642,"text":54576,"children":55803},[55804,55805],{"id":54579,"depth":649,"text":54580},{"id":55039,"depth":649,"text":55040},{"id":19878,"depth":642,"text":19879},{"id":21082,"depth":642,"text":21083},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":46838,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,55814,1144,28889,55815,55816,55817],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":55820,"title":802,"body":55821,"course":1128,"courses":659,"created":21169,"description":641,"extension":661,"meta":69852,"navigation":664,"path":69853,"seo":69854,"sources":69855,"stem":69856,"tags":69857,"type":21181,"updated":677,"__hash__":69863},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":55822,"toc":69808},[55823,55826,55852,55856,55863,56014,56028,56031,56033,56119,56123,56159,56232,56253,56378,56388,56401,56405,56409,56439,56501,56510,56514,56576,56583,56604,56722,56800,56804,56807,56866,56981,56986,57018,57079,57127,57182,57186,57207,57231,57279,57283,57295,57299,57408,57412,57428,57469,57480,57639,57649,57654,57658,57780,57790,57797,57801,57879,57890,57970,57976,57983,58122,58129,58132,58189,58193,58271,58317,58361,58367,58480,58484,58487,58682,58686,58923,58926,59079,59232,59234,59236,59316,59319,59423,59492,59501,59505,59508,59569,59578,59582,59615,59693,59732,59736,59785,59839,59843,59872,59901,59953,59960,60014,60092,60096,60139,60206,60250,60354,60373,60375,60379,60487,60491,60558,60607,60614,60699,60703,60775,60780,60828,61014,61018,61023,61199,61204,61263,61368,61372,61399,61403,61410,61574,61661,61666,61668,61671,61771,61921,61993,62067,62069,62073,62087,62091,62223,62278,62390,62466,62470,62527,62630,62688,62849,62853,62928,63000,63098,63156,63250,63303,63324,63378,63383,63461,63509,63596,63634,63722,63875,63911,63965,63968,63970,63972,64021,64028,64036,64123,64132,64219,64226,64228,64232,64457,64459,64463,64467,64535,64586,64788,64794,64805,64873,64879,65301,65305,65369,65393,65589,65595,65609,65677,65680,65720,65943,66011,66313,66722,66798,66964,66970,66973,67048,67501,67552,67958,68063,68726,68729,68806,68814,68888,68919,68921,68923,68967,68969,68971,68975,69204,69208,69299,69304,69398,69403,69576,69580,69698,69703,69752,69754,69756],[12,55824,802],{"id":55825},"poptávka-nabídka-a-tržní-rovnováha",[1636,55827,55828],{},[724,55829,55830,55832,55833,55836,55837,55840,55841,55844,55845,55847,55848,55851],{},[883,55831,3174],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,55834,55835],{},"poptávka",") a výrobce (",[38,55838,55839],{},"nabídka","), jejich interakci v ",[38,55842,55843],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,55846,37074],{},"). Uzavírá ji pojem ",[38,55849,55850],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,55853,55855],{"id":55854},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,55857,55858,55859,55862],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,55860,55861],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,55864,55865,55882,55923,55939],{},[123,55866,55867,55868,55881],{},"cena ",[883,55869,55871],{"className":55870},[886],[888,55872,55873],{"xmlns":890},[892,55874,55875,55879],{},[895,55876,55877],{},[898,55878,1702],{},[902,55880,1702],{"encoding":904}," zkoumaného zboží,",[123,55883,55884,55885,2505],{},"ceny alternativních zboží ",[883,55886,55888],{"className":55887},[886],[888,55889,55890],{"xmlns":890},[892,55891,55892,55920],{},[895,55893,55894,55900,55902,55908,55910,55912,55914],{},[2142,55895,55896,55898],{},[898,55897,1702],{},[2148,55899,2701],{},[1706,55901,2505],{"separator":2504},[2142,55903,55904,55906],{},[898,55905,1702],{},[2148,55907,2495],{},[1706,55909,2505],{"separator":2504},[1706,55911,28763],{},[1706,55913,2505],{"separator":2504},[2142,55915,55916,55918],{},[898,55917,1702],{},[898,55919,18465],{},[902,55921,55922],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,55924,55925,55926,2505],{},"důchod ",[883,55927,55929],{"className":55928},[886],[888,55930,55931],{"xmlns":890},[892,55932,55933,55937],{},[895,55934,55935],{},[898,55936,28247],{},[902,55938,28247],{"encoding":904},[123,55940,55941,55942,55955,55956,55969,55970,55983,55984,55998,55999,56013],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,55943,55945],{"className":55944},[886],[888,55946,55947],{"xmlns":890},[892,55948,55949,55953],{},[895,55950,55951],{},[898,55952,6362],{},[902,55954,6362],{"encoding":904},", kapitál ",[883,55957,55959],{"className":55958},[886],[888,55960,55961],{"xmlns":890},[892,55962,55963,55967],{},[895,55964,55965],{},[898,55966,28915],{},[902,55968,28915],{"encoding":904},", půda ",[883,55971,55973],{"className":55972},[886],[888,55974,55975],{"xmlns":890},[892,55976,55977,55981],{},[895,55978,55979],{},[898,55980,23410],{},[902,55982,23410],{"encoding":904},"), technologie, počet výrobců ",[883,55985,55987],{"className":55986},[886],[888,55988,55989],{"xmlns":890},[892,55990,55991,55996],{},[895,55992,55993],{},[898,55994,55995],{},"O",[902,55997,55995],{"encoding":904},", počasí ",[883,56000,56002],{"className":56001},[886],[888,56003,56004],{"xmlns":890},[892,56005,56006,56011],{},[895,56007,56008],{},[898,56009,56010],{},"W",[902,56012,56010],{"encoding":904}," atd.",[724,56015,56016,56017,56020,56021,56024,56025,1837],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,56018,56019],{},"ceteris paribus","), hovoříme o ",[38,56022,56023],{},"jednofaktorovém modelu","; jinak jde o model ",[38,56026,56027],{},"vícefaktorový",[56029,56030],"hr",{},[115,56032,32268],{"id":55835},[1636,56034,56035],{},[724,56036,56037,56039,56040,56053,56054,56067,56068,56071,56072,56095,56096,1837],{},[883,56038,3174],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,56041,56043],{"className":56042},[886],[888,56044,56045],{"xmlns":890},[892,56046,56047,56051],{},[895,56048,56049],{},[898,56050,2146],{},[902,56052,2146],{"encoding":904}," na ceně ",[883,56055,56057],{"className":56056},[886],[888,56058,56059],{"xmlns":890},[892,56060,56061,56065],{},[895,56062,56063],{},[898,56064,1702],{},[902,56066,1702],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,56069,56070],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,56073,56075],{"className":56074},[886],[888,56076,56077],{"xmlns":890},[892,56078,56079,56093],{},[895,56080,56081,56083,56085,56087,56089,56091],{},[898,56082,2146],{},[1706,56084,1708],{},[898,56086,2334],{},[1706,56088,2140],{"stretchy":2139},[898,56090,1702],{},[1706,56092,2153],{"stretchy":2139},[902,56094,23350],{"encoding":904}," a jeho lineární verzí ",[883,56097,56099],{"className":56098},[886],[888,56100,56101],{"xmlns":890},[892,56102,56103,56117],{},[895,56104,56105,56107,56109,56111,56113,56115],{},[898,56106,1702],{},[1706,56108,1708],{},[898,56110,207],{},[898,56112,2146],{},[1706,56114,2447],{},[898,56116,2450],{},[902,56118,2453],{"encoding":904},[198,56120,56122],{"id":56121},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,56124,56125,56126,56139,56140,56153,56154,2314,56156,5606],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,56127,56129],{"className":56128},[886],[888,56130,56131],{"xmlns":890},[892,56132,56133,56137],{},[895,56134,56135],{},[898,56136,2146],{},[902,56138,2146],{"encoding":904}," závisí na ceně ",[883,56141,56143],{"className":56142},[886],[888,56144,56145],{"xmlns":890},[892,56146,56147,56151],{},[895,56148,56149],{},[898,56150,1702],{},[902,56152,1702],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,56155,47073],{},[614,56157,56158],{},"demand function",[883,56160,56162],{"className":56161},[886],[888,56163,56164],{"xmlns":890,"display":2350},[892,56165,56166,56229],{},[2354,56167,56168],{"width":2356},[2358,56169,56170,56172,56222,56224],{},[2361,56171],{"width":2363},[2361,56173,56174],{},[895,56175,56176,56178,56180,56182,56184,56186,56188,56194,56196,56202,56204,56206,56208,56214,56216,56218,56220],{},[898,56177,2146],{},[1706,56179,1708],{},[898,56181,2334],{},[1706,56183,2140],{"stretchy":2139},[898,56185,1702],{},[1706,56187,2505],{"separator":2504},[2142,56189,56190,56192],{},[898,56191,1702],{},[2148,56193,2701],{},[1706,56195,2505],{"separator":2504},[2142,56197,56198,56200],{},[898,56199,1702],{},[2148,56201,2495],{},[1706,56203,2505],{"separator":2504},[1706,56205,28763],{},[1706,56207,2505],{"separator":2504},[2142,56209,56210,56212],{},[898,56211,1702],{},[898,56213,18465],{},[1706,56215,2505],{"separator":2504},[898,56217,28247],{},[1706,56219,2153],{"stretchy":2139},[898,56221,1837],{"mathvariant":2409},[2361,56223],{"width":2363},[2361,56225,56226],{},[2415,56227,56228],{},"(2.1)",[902,56230,56231],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,56233,56234,56235,56238,56239,56252],{},"Důležitou vlastností je ",[38,56236,56237],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,56240,56242],{"className":56241},[886],[888,56243,56244],{"xmlns":890},[892,56245,56246,56250],{},[895,56247,56248],{},[898,56249,3950],{},[902,56251,3950],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,56254,56256],{"className":56255},[886],[888,56257,56258],{"xmlns":890,"display":2350},[892,56259,56260,56375],{},[2354,56261,56262],{"width":2356},[2358,56263,56264,56266,56368,56370],{},[2361,56265],{"width":2363},[2361,56267,56268],{},[895,56269,56270,56272,56274,56276,56278,56280,56282,56284,56286,56292,56294,56296,56302,56304,56306,56308,56310,56316,56318,56320,56322,56324,56326,56328,56330,56332,56334,56340,56342,56348,56350,56352,56354,56360,56362,56364,56366],{},[898,56271,2146],{},[1706,56273,1708],{},[898,56275,2334],{},[1706,56277,2140],{"stretchy":2139},[898,56279,3950],{},[898,56281,1702],{},[1706,56283,2505],{"separator":2504},[898,56285,3950],{},[2142,56287,56288,56290],{},[898,56289,1702],{},[2148,56291,2701],{},[1706,56293,2505],{"separator":2504},[898,56295,3950],{},[2142,56297,56298,56300],{},[898,56299,1702],{},[2148,56301,2495],{},[1706,56303,2505],{"separator":2504},[1706,56305,28763],{},[1706,56307,2505],{"separator":2504},[898,56309,3950],{},[2142,56311,56312,56314],{},[898,56313,1702],{},[898,56315,18465],{},[1706,56317,2505],{"separator":2504},[898,56319,3950],{},[898,56321,28247],{},[1706,56323,2153],{"stretchy":2139},[1706,56325,1708],{},[898,56327,2334],{},[1706,56329,2140],{"stretchy":2139},[898,56331,1702],{},[1706,56333,2505],{"separator":2504},[2142,56335,56336,56338],{},[898,56337,1702],{},[2148,56339,2701],{},[1706,56341,2505],{"separator":2504},[2142,56343,56344,56346],{},[898,56345,1702],{},[2148,56347,2495],{},[1706,56349,2505],{"separator":2504},[1706,56351,28763],{},[1706,56353,2505],{"separator":2504},[2142,56355,56356,56358],{},[898,56357,1702],{},[898,56359,18465],{},[1706,56361,2505],{"separator":2504},[898,56363,28247],{},[1706,56365,2153],{"stretchy":2139},[898,56367,1837],{"mathvariant":2409},[2361,56369],{"width":2363},[2361,56371,56372],{},[2415,56373,56374],{},"(2.2)",[902,56376,56377],{"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}",[1636,56379,56380],{},[724,56381,56382,56384,56385,1837],{},[883,56383,9276],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,56386,56387],{},"v jednofaktorových modelech neplatí",[724,56389,56390,56391,1343,56394,1993,56397,56400],{},"Rozlišuje se poptávka ",[38,56392,56393],{},"individuální",[38,56395,56396],{},"tržní",[38,56398,56399],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,56402,56404],{"id":56403},"jednofaktorové-modely","Jednofaktorové modely",[2547,56406,56408],{"id":56407},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,56410,56411,56412,56425,56426,4288],{},"Poptávané množství ",[883,56413,56415],{"className":56414},[886],[888,56416,56417],{"xmlns":890},[892,56418,56419,56423],{},[895,56420,56421],{},[898,56422,2146],{},[902,56424,2146],{"encoding":904}," závisí pouze na ceně ",[883,56427,56429],{"className":56428},[886],[888,56430,56431],{"xmlns":890},[892,56432,56433,56437],{},[895,56434,56435],{},[898,56436,1702],{},[902,56438,1702],{"encoding":904},[883,56440,56442],{"className":56441},[886],[888,56443,56444],{"xmlns":890,"display":2350},[892,56445,56446,56498],{},[2354,56447,56448],{"width":2356},[2358,56449,56450,56452,56491,56493],{},[2361,56451],{"width":2363},[2361,56453,56454],{},[895,56455,56456,56458,56460,56462,56464,56466,56468,56470,56472,56475,56477,56479,56481,56483,56485,56487,56489],{},[898,56457,2146],{},[1706,56459,1708],{},[898,56461,2334],{},[1706,56463,2140],{"stretchy":2139},[898,56465,1702],{},[1706,56467,2153],{"stretchy":2139},[1706,56469,2505],{"separator":2504},[4898,56471],{"width":9524},[2415,56473,56474],{},"resp.",[4898,56476],{"width":9524},[898,56478,1702],{},[1706,56480,1708],{},[898,56482,2334],{},[1706,56484,2140],{"stretchy":2139},[898,56486,2146],{},[1706,56488,2153],{"stretchy":2139},[898,56490,1837],{"mathvariant":2409},[2361,56492],{"width":2363},[2361,56494,56495],{},[2415,56496,56497],{},"(2.3)",[902,56499,56500],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,56502,56503,56504,2314,56507,1936],{},"Graf této funkce se nazývá ",[38,56505,56506],{},"křivka poptávky",[614,56508,56509],{},"demand curve",[2547,56511,56513],{"id":56512},"zákon-klesající-poptávky","Zákon klesající poptávky",[1636,56515,56516],{},[724,56517,56518],{},[38,56519,56520,56521,56534,56535,56548,56549,56534,56562,56575],{},"Roste-li cena ",[883,56522,56524],{"className":56523},[886],[888,56525,56526],{"xmlns":890},[892,56527,56528,56532],{},[895,56529,56530],{},[898,56531,1702],{},[902,56533,1702],{"encoding":904},", pak množství ",[883,56536,56538],{"className":56537},[886],[888,56539,56540],{"xmlns":890},[892,56541,56542,56546],{},[895,56543,56544],{},[898,56545,2146],{},[902,56547,2146],{"encoding":904}," klesá; klesá-li cena ",[883,56550,56552],{"className":56551},[886],[888,56553,56554],{"xmlns":890},[892,56555,56556,56560],{},[895,56557,56558],{},[898,56559,1702],{},[902,56561,1702],{"encoding":904},[883,56563,56565],{"className":56564},[886],[888,56566,56567],{"xmlns":890},[892,56568,56569,56573],{},[895,56570,56571],{},[898,56572,2146],{},[902,56574,2146],{"encoding":904}," roste.",[724,56577,56578,56579,56582],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,56580,56581],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[1636,56584,56585,56590],{},[724,56586,56587,56589],{},[883,56588,3174],{}," Intuice — proč zákon platí",[120,56591,56592,56598],{},[123,56593,56594,56597],{},[38,56595,56596],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,56599,56600,56603],{},[38,56601,56602],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,56605,56606,56607,56620,56621,56634,56635,56661,56662,56688,56689,3484,56715,56718,56719,1837],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,56608,56610],{"className":56609},[886],[888,56611,56612],{"xmlns":890},[892,56613,56614,56618],{},[895,56615,56616],{},[898,56617,1702],{},[902,56619,1702],{"encoding":904}," se vynáší na svislou osu, množství ",[883,56622,56624],{"className":56623},[886],[888,56625,56626],{"xmlns":890},[892,56627,56628,56632],{},[895,56629,56630],{},[898,56631,2146],{},[902,56633,2146],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,56636,56638],{"className":56637},[886],[888,56639,56640],{"xmlns":890},[892,56641,56642,56658],{},[895,56643,56644,56646,56648,56650,56656],{},[1706,56645,21693],{"stretchy":2139},[2148,56647,2150],{},[1706,56649,2505],{"separator":2504},[2142,56651,56652,56654],{},[898,56653,1702],{},[2148,56655,2150],{},[1706,56657,21708],{"stretchy":2139},[902,56659,56660],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,56663,56665],{"className":56664},[886],[888,56666,56667],{"xmlns":890},[892,56668,56669,56685],{},[895,56670,56671,56673,56679,56681,56683],{},[1706,56672,21693],{"stretchy":2139},[2142,56674,56675,56677],{},[898,56676,2146],{},[2148,56678,2150],{},[1706,56680,2505],{"separator":2504},[2148,56682,2150],{},[1706,56684,21708],{"stretchy":2139},[902,56686,56687],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,56690,56692],{"className":56691},[886],[888,56693,56694],{"xmlns":890},[892,56695,56696,56712],{},[895,56697,56698,56700,56702,56704,56710],{},[1706,56699,2140],{"stretchy":2139},[2148,56701,2150],{},[1706,56703,2505],{"separator":2504},[2142,56705,56706,56708],{},[898,56707,1702],{},[2148,56709,2150],{},[1706,56711,2153],{"stretchy":2139},[902,56713,56714],{"encoding":904},"(0, P_0)",[38,56716,56717],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,56720,56721],{},"konvexní",[724,56723,56724],{},[614,56725,56726,56727,56749,56750,1993,56775,1837],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,56728,56730],{"className":56729},[886],[888,56731,56732],{"xmlns":890},[892,56733,56734,56746],{},[895,56735,56736,56738,56740,56742,56744],{},[1706,56737,2140],{"stretchy":2139},[898,56739,2146],{},[1706,56741,2505],{"separator":2504},[898,56743,1702],{},[1706,56745,2153],{"stretchy":2139},[902,56747,56748],{"encoding":904},"(Q, P)"," — klesající, konvexní, procházející body ",[883,56751,56753],{"className":56752},[886],[888,56754,56755],{"xmlns":890},[892,56756,56757,56773],{},[895,56758,56759,56761,56763,56765,56771],{},[1706,56760,21693],{"stretchy":2139},[2148,56762,2150],{},[1706,56764,2505],{"separator":2504},[2142,56766,56767,56769],{},[898,56768,1702],{},[2148,56770,2150],{},[1706,56772,21708],{"stretchy":2139},[902,56774,56660],{"encoding":904},[883,56776,56778],{"className":56777},[886],[888,56779,56780],{"xmlns":890},[892,56781,56782,56798],{},[895,56783,56784,56786,56792,56794,56796],{},[1706,56785,21693],{"stretchy":2139},[2142,56787,56788,56790],{},[898,56789,2146],{},[2148,56791,2150],{},[1706,56793,2505],{"separator":2504},[2148,56795,2150],{},[1706,56797,21708],{"stretchy":2139},[902,56799,56687],{"encoding":904},[2547,56801,56803],{"id":56802},"lineární-model-poptávky","Lineární model poptávky",[724,56805,56806],{},"Nejjednodušší závislostí je",[883,56808,56810],{"className":56809},[886],[888,56811,56812],{"xmlns":890,"display":2350},[892,56813,56814,56863],{},[2354,56815,56816],{"width":2356},[2358,56817,56818,56820,56856,56858],{},[2361,56819],{"width":2363},[2361,56821,56822],{},[895,56823,56824,56826,56828,56830,56832,56834,56836,56838,56840,56842,56844,56846,56848,56850,56852,56854],{},[898,56825,1702],{},[1706,56827,1708],{},[898,56829,207],{},[898,56831,2146],{},[1706,56833,2447],{},[898,56835,2450],{},[1706,56837,2505],{"separator":2504},[4898,56839],{"width":9524},[898,56841,207],{},[1706,56843,2539],{},[2148,56845,2150],{},[1706,56847,2505],{"separator":2504},[2415,56849,21505],{},[898,56851,2450],{},[1706,56853,8922],{},[2148,56855,31567],{},[2361,56857],{"width":2363},[2361,56859,56860],{},[2415,56861,56862],{},"(2.4)",[902,56864,56865],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,56867,56868,56869,15842,56905,1993,56929,27164,56955,56977,56978,1837],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,56870,56872],{"className":56871},[886],[888,56873,56874],{"xmlns":890},[892,56875,56876,56902],{},[895,56877,56878,56880,56882,56890,56892,56894],{},[898,56879,2146],{},[1706,56881,1708],{},[4745,56883,56884],{"scriptlevel":2150,"displaystyle":2139},[2964,56885,56886,56888],{},[2148,56887,2701],{},[898,56889,207],{},[898,56891,1702],{},[1706,56893,1715],{},[4745,56895,56896],{"scriptlevel":2150,"displaystyle":2139},[2964,56897,56898,56900],{},[898,56899,2450],{},[898,56901,207],{},[902,56903,56904],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,56906,56908],{"className":56907},[886],[888,56909,56910],{"xmlns":890},[892,56911,56912,56926],{},[895,56913,56914,56922,56924],{},[4745,56915,56916],{"scriptlevel":2150,"displaystyle":2139},[2964,56917,56918,56920],{},[2148,56919,2701],{},[898,56921,207],{},[1706,56923,2539],{},[2148,56925,2150],{},[902,56927,56928],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,56930,56932],{"className":56931},[886],[888,56933,56934],{"xmlns":890},[892,56935,56936,56952],{},[895,56937,56938,56940,56948,56950],{},[1706,56939,1715],{},[4745,56941,56942],{"scriptlevel":2150,"displaystyle":2139},[2964,56943,56944,56946],{},[898,56945,2450],{},[898,56947,207],{},[1706,56949,8922],{},[2148,56951,2150],{},[902,56953,56954],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,56956,56958],{"className":56957},[886],[888,56959,56960],{"xmlns":890},[892,56961,56962,56974],{},[895,56963,56964,56966,56968,56970,56972],{},[1706,56965,2140],{"stretchy":2139},[2148,56967,2150],{},[1706,56969,2505],{"separator":2504},[898,56971,2450],{},[1706,56973,2153],{"stretchy":2139},[902,56975,56976],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,56979,56980],{},"nedokonalé konkurenci",[56982,56983,56985],"h5",{"id":56984},"příklad-21","Příklad 2.1",[724,56987,56988,56991,56992,1837],{},[38,56989,56990],{},"Zadání:"," Lineární poptávka ",[883,56993,56995],{"className":56994},[886],[888,56996,56997],{"xmlns":890},[892,56998,56999,57015],{},[895,57000,57001,57003,57005,57007,57009,57011,57013],{},[898,57002,1702],{},[1706,57004,1708],{},[1706,57006,1715],{},[2148,57008,2495],{},[898,57010,2146],{},[1706,57012,2447],{},[2148,57014,4199],{},[902,57016,57017],{"encoding":904},"P = -2Q + 60",[724,57019,57020,57023,57024,57046,57047,1837],{},[38,57021,57022],{},"Řešení:"," Reálné cenové rozpětí je ",[883,57025,57027],{"className":57026},[886],[888,57028,57029],{"xmlns":890},[892,57030,57031,57043],{},[895,57032,57033,57035,57037,57039,57041],{},[1706,57034,2140],{"stretchy":2139},[2148,57036,2150],{},[1706,57038,2505],{"separator":2504},[2148,57040,4199],{},[1706,57042,2153],{"stretchy":2139},[902,57044,57045],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,57048,57050],{"className":57049},[886],[888,57051,57052],{"xmlns":890},[892,57053,57054,57076],{},[895,57055,57056,57058,57060,57062,57070,57072,57074],{},[898,57057,2146],{},[1706,57059,1708],{},[1706,57061,1715],{},[4745,57063,57064],{"scriptlevel":2150,"displaystyle":2139},[2964,57065,57066,57068],{},[2148,57067,2701],{},[2148,57069,2495],{},[898,57071,1702],{},[1706,57073,2447],{},[2148,57075,12556],{},[902,57077,57078],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,57080,57081,57104],{},[19,57082,57083],{},[22,57084,57085,57100,57102],{},[25,57086,57087],{},[883,57088,57090],{"className":57089},[886],[888,57091,57092],{"xmlns":890},[892,57093,57094,57098],{},[895,57095,57096],{},[898,57097,1702],{},[902,57099,1702],{"encoding":904},[25,57101,3508],{},[25,57103,3369],{},[30,57105,57106],{},[22,57107,57108,57123,57125],{},[35,57109,57110],{},[883,57111,57113],{"className":57112},[886],[888,57114,57115],{"xmlns":890},[892,57116,57117,57121],{},[895,57118,57119],{},[898,57120,2146],{},[902,57122,2146],{"encoding":904},[35,57124,7786],{},[35,57126,3369],{},[724,57128,57129],{},[614,57130,57131,57132,1993,57154,1837],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,57133,57135],{"className":57134},[886],[888,57136,57137],{"xmlns":890},[892,57138,57139,57151],{},[895,57140,57141,57143,57145,57147,57149],{},[1706,57142,21693],{"stretchy":2139},[2148,57144,2150],{},[1706,57146,2505],{"separator":2504},[898,57148,2450],{},[1706,57150,21708],{"stretchy":2139},[902,57152,57153],{"encoding":904},"[0, b]",[883,57155,57157],{"className":57156},[886],[888,57158,57159],{"xmlns":890},[892,57160,57161,57179],{},[895,57162,57163,57165,57167,57169,57171,57173,57175,57177],{},[1706,57164,21693],{"stretchy":2139},[1706,57166,1715],{},[898,57168,2450],{},[898,57170,15493],{"mathvariant":2409},[898,57172,207],{},[1706,57174,2505],{"separator":2504},[2148,57176,2150],{},[1706,57178,21708],{"stretchy":2139},[902,57180,57181],{"encoding":904},"[-b\u002Fa, 0]",[2547,57183,57185],{"id":57184},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,57187,57188,57189,57206],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,57190,57192],{"className":57191},[886],[888,57193,57194],{"xmlns":890},[892,57195,57196,57204],{},[895,57197,57198],{},[2489,57199,57200,57202],{},[898,57201,1702],{},[1706,57203,3197],{},[902,57205,14075],{"encoding":904},", je funkce poptávky konstantní:",[883,57208,57210],{"className":57209},[886],[888,57211,57212],{"xmlns":890,"display":2350},[892,57213,57214,57228],{},[895,57215,57216,57218,57220,57226],{},[898,57217,1702],{},[1706,57219,1708],{},[2489,57221,57222,57224],{},[898,57223,1702],{},[1706,57225,3197],{},[898,57227,1837],{"mathvariant":2409},[902,57229,57230],{"encoding":904},"P = P^*.",[724,57232,57233],{},[614,57234,57235,57236,57257,57258,1837],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,57237,57239],{"className":57238},[886],[888,57240,57241],{"xmlns":890},[892,57242,57243,57255],{},[895,57244,57245,57247,57249,57251,57253],{},[1706,57246,2140],{"stretchy":2139},[898,57248,2146],{},[1706,57250,2505],{"separator":2504},[898,57252,1702],{},[1706,57254,2153],{"stretchy":2139},[902,57256,56748],{"encoding":904}," na úrovni ",[883,57259,57261],{"className":57260},[886],[888,57262,57263],{"xmlns":890},[892,57264,57265,57277],{},[895,57266,57267,57269,57271],{},[898,57268,1702],{},[1706,57270,1708],{},[2489,57272,57273,57275],{},[898,57274,1702],{},[1706,57276,3197],{},[902,57278,21043],{"encoding":904},[2547,57280,57282],{"id":57281},"giffenův-statek","Giffenův statek",[724,57284,57285,57286,57288,57289,57291,57292,1837],{},"Existují zboží, u nichž je křivka poptávky ",[38,57287,32764],{}," — tzv. ",[38,57290,57282],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,57293,57294],{},"podřadnému zboží",[56982,57296,57298],{"id":57297},"příklad-22","Příklad 2.2",[724,57300,57301,57304,57305,57323,57324,57346,57347,57364,57365,57383,57384,57407],{},[38,57302,57303],{},"Zadání a popis:"," Křivka ",[883,57306,57308],{"className":57307},[886],[888,57309,57310],{"xmlns":890},[892,57311,57312,57320],{},[895,57313,57314],{},[2142,57315,57316,57318],{},[898,57317,2334],{},[2148,57319,2701],{},[902,57321,57322],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,57325,57327],{"className":57326},[886],[888,57328,57329],{"xmlns":890},[892,57330,57331,57343],{},[895,57332,57333,57335,57337,57339,57341],{},[1706,57334,2140],{"stretchy":2139},[2148,57336,2150],{},[1706,57338,2505],{"separator":2504},[2148,57340,3359],{},[1706,57342,2153],{"stretchy":2139},[902,57344,57345],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,57348,57350],{"className":57349},[886],[888,57351,57352],{"xmlns":890},[892,57353,57354,57362],{},[895,57355,57356],{},[2142,57357,57358,57360],{},[898,57359,2146],{},[2148,57361,2150],{},[902,57363,8625],{"encoding":904}," konkávní, se saturací kolem 17 liber. Křivka ",[883,57366,57368],{"className":57367},[886],[888,57369,57370],{"xmlns":890},[892,57371,57372,57380],{},[895,57373,57374],{},[2142,57375,57376,57378],{},[898,57377,2334],{},[2148,57379,2495],{},[902,57381,57382],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,57385,57387],{"className":57386},[886],[888,57388,57389],{"xmlns":890},[892,57390,57391,57404],{},[895,57392,57393,57395,57397,57399,57402],{},[1706,57394,21693],{"stretchy":2139},[2148,57396,2150],{},[1706,57398,2505],{"separator":2504},[2148,57400,57401],{},"21",[1706,57403,21708],{"stretchy":2139},[902,57405,57406],{"encoding":904},"[0, 21]"," centů.",[198,57409,57411],{"id":57410},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,57413,57414,57415,4288],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,57416,57418],{"className":57417},[886],[888,57419,57420],{"xmlns":890},[892,57421,57422,57426],{},[895,57423,57424],{},[898,57425,28247],{},[902,57427,28247],{"encoding":904},[883,57429,57431],{"className":57430},[886],[888,57432,57433],{"xmlns":890,"display":2350},[892,57434,57435,57466],{},[2354,57436,57437],{"width":2356},[2358,57438,57439,57441,57459,57461],{},[2361,57440],{"width":2363},[2361,57442,57443],{},[895,57444,57445,57447,57449,57451,57453,57455,57457],{},[898,57446,2146],{},[1706,57448,1708],{},[898,57450,23410],{},[1706,57452,2140],{"stretchy":2139},[898,57454,28247],{},[1706,57456,2153],{"stretchy":2139},[898,57458,1837],{"mathvariant":2409},[2361,57460],{"width":2363},[2361,57462,57463],{},[2415,57464,57465],{},"(2.5)",[902,57467,57468],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,57470,57471,57472,57475,57476,57479],{},"Funkce se nazývá ",[38,57473,57474],{},"Engelova",", její graf ",[38,57477,57478],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,57481,57482,57614],{},[123,57483,57484,21021,57487,57500,57501,57514,57515,57532,57533],{},[38,57485,57486],{},"Normální (superior) zboží",[883,57488,57490],{"className":57489},[886],[888,57491,57492],{"xmlns":890},[892,57493,57494,57498],{},[895,57495,57496],{},[898,57497,2146],{},[902,57499,2146],{"encoding":904}," roste s ",[883,57502,57504],{"className":57503},[886],[888,57505,57506],{"xmlns":890},[892,57507,57508,57512],{},[895,57509,57510],{},[898,57511,28247],{},[902,57513,28247],{"encoding":904},", nepřesáhne hodnotu ",[883,57516,57518],{"className":57517},[886],[888,57519,57520],{"xmlns":890},[892,57521,57522,57530],{},[895,57523,57524],{},[2142,57525,57526,57528],{},[898,57527,2146],{},[2148,57529,2150],{},[902,57531,8625],{"encoding":904},":\n",[120,57534,57535,57567],{},[123,57536,57537,57540,57541,57544,57545,1837],{},[38,57538,57539],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,57542,57543],{},"konkávní"," křivka, autonomní spotřeba ",[883,57546,57548],{"className":57547},[886],[888,57549,57550],{"xmlns":890},[892,57551,57552,57564],{},[895,57553,57554,57560,57562],{},[2142,57555,57556,57558],{},[898,57557,2146],{},[2148,57559,2701],{},[1706,57561,8922],{},[2148,57563,2150],{},[902,57565,57566],{"encoding":904},"Q_1 > 0",[123,57568,57569,57572,57573,57591,57592,57594,57595,1647,57612,1837],{},[38,57570,57571],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,57574,57576],{"className":57575},[886],[888,57577,57578],{"xmlns":890},[892,57579,57580,57588],{},[895,57581,57582],{},[2142,57583,57584,57586],{},[898,57585,28247],{},[2148,57587,2701],{},[902,57589,57590],{"encoding":904},"Y_1",", křivka je nejprve ",[38,57593,56721],{}," a od ",[883,57596,57598],{"className":57597},[886],[888,57599,57600],{"xmlns":890},[892,57601,57602,57610],{},[895,57603,57604],{},[2142,57605,57606,57608],{},[898,57607,28247],{},[2148,57609,2701],{},[902,57611,57590],{"encoding":904},[38,57613,57543],{},[123,57615,57616,57619,57620,57638],{},[38,57617,57618],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,57621,57623],{"className":57622},[886],[888,57624,57625],{"xmlns":890},[892,57626,57627,57635],{},[895,57628,57629],{},[2142,57630,57631,57633],{},[898,57632,28247],{},[2148,57634,2150],{},[902,57636,57637],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,57640,57641,57642,57645,57646,1936],{},"Mírou citlivosti je ",[614,57643,57644],{},"důchodová elasticita"," (viz ",[207,57647,23065],{"className":57648,"dataFsResolvedFilePath":848,"href":849},[210],[724,57650,57651],{},[614,57652,57653],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[2547,57655,57657],{"id":57656},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[1636,57659,57660,57731,57774],{},[724,57661,57662,57664,57665,1647,57668,1647,57681,24808,57683,57696,57697,57700,57701,1837],{},[883,57663,9276],{}," Pozor — nezbytné ≠ podřadné\n",[38,57666,57667],{},"Nezbytné zboží:",[883,57669,57671],{"className":57670},[886],[888,57672,57673],{"xmlns":890},[892,57674,57675,57679],{},[895,57676,57677],{},[898,57678,2146],{},[902,57680,2146],{"encoding":904},[38,57682,26451],{},[883,57684,57686],{"className":57685},[886],[888,57687,57688],{"xmlns":890},[892,57689,57690,57694],{},[895,57691,57692],{},[898,57693,28247],{},[902,57695,28247],{"encoding":904},", ale ",[38,57698,57699],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,57702,57704],{"className":57703},[886],[888,57705,57706],{"xmlns":890},[892,57707,57708,57728],{},[895,57709,57710,57716,57718,57720,57722,57724,57726],{},[2142,57711,57712,57714],{},[898,57713,23410],{},[898,57715,28247],{},[1706,57717,25638],{},[1706,57719,2140],{"stretchy":2139},[2148,57721,2150],{},[1706,57723,2505],{"separator":2504},[2148,57725,2701],{},[1706,57727,2153],{"stretchy":2139},[902,57729,57730],{"encoding":904},"E_Y \\in (0, 1)",[724,57732,57733,1647,57736,1647,57749,57751,57752,1837],{},[38,57734,57735],{},"Podřadné zboží:",[883,57737,57739],{"className":57738},[886],[888,57740,57741],{"xmlns":890},[892,57742,57743,57747],{},[895,57744,57745],{},[898,57746,2146],{},[902,57748,2146],{"encoding":904},[38,57750,26471],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,57753,57755],{"className":57754},[886],[888,57756,57757],{"xmlns":890},[892,57758,57759,57771],{},[895,57760,57761,57767,57769],{},[2142,57762,57763,57765],{},[898,57764,23410],{},[898,57766,28247],{},[1706,57768,2539],{},[2148,57770,2150],{},[902,57772,57773],{"encoding":904},"E_Y \u003C 0",[724,57775,57776,57777,1837],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,57778,57779],{},"méně kusů, ne jen proporčně méně",[724,57781,57782,57785,57786,57789],{},[38,57783,57784],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,57787,57788],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,57791,57792],{},[2286,57793],{"alt":57794,"className":57795,"src":57796},"imek-engelovy-krivky-3typy",[210,2290],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[56982,57798,57800],{"id":57799},"české-příklady","České příklady",[16,57802,57803,57813],{},[19,57804,57805],{},[22,57806,57807,57810],{},[25,57808,57809],{},"Podřadné",[25,57811,57812],{},"Nahradí se za",[30,57814,57815,57823,57831,57839,57847,57855,57863,57871],{},[22,57816,57817,57820],{},[35,57818,57819],{},"Instantní polévky, ramen",[35,57821,57822],{},"Čerstvé jídlo, restaurace",[22,57824,57825,57828],{},[35,57826,57827],{},"MHD (autobus, tramvaj)",[35,57829,57830],{},"Vlastní auto, Uber, taxi",[22,57832,57833,57836],{},[35,57834,57835],{},"Mražené polotovary, pizza z mrazáku",[35,57837,57838],{},"Čerstvé suroviny, hotovky",[22,57840,57841,57844],{},[35,57842,57843],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,57845,57846],{},"Značkové produkty",[22,57848,57849,57852],{},[35,57850,57851],{},"Paštika Májka, obyčejný měkký salám",[35,57853,57854],{},"Kvalitní uzeniny, šunka od kosti",[22,57856,57857,57860],{},[35,57858,57859],{},"Second hand oblečení",[35,57861,57862],{},"Nové oblečení, značky",[22,57864,57865,57868],{},[35,57866,57867],{},"Krabicové víno, nejlevnější pivo",[35,57869,57870],{},"Lahvové víno, řemeslná piva",[22,57872,57873,57876],{},[35,57874,57875],{},"Ojetá auta nižších tříd",[35,57877,57878],{},"Nová auta, prémiové značky",[1636,57880,57881],{},[724,57882,57883,57885,57886,57889],{},[883,57884,12314],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,57887,57888],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,57891,57892,57895,57896,2314,57899,57921,57922,2314,57925,57946,57947,57965,57966,57969],{},[38,57893,57894],{},"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 ",[38,57897,57898],{},"luxus",[883,57900,57902],{"className":57901},[886],[888,57903,57904],{"xmlns":890},[892,57905,57906,57918],{},[895,57907,57908,57914,57916],{},[2142,57909,57910,57912],{},[898,57911,23410],{},[898,57913,28247],{},[1706,57915,8922],{},[2148,57917,2701],{},[902,57919,57920],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,57923,57924],{},"podřadné",[883,57926,57928],{"className":57927},[886],[888,57929,57930],{"xmlns":890},[892,57931,57932,57944],{},[895,57933,57934,57940,57942],{},[2142,57935,57936,57938],{},[898,57937,23410],{},[898,57939,28247],{},[1706,57941,2539],{},[2148,57943,2150],{},[902,57945,57773],{"encoding":904},"). Proto je ",[883,57948,57950],{"className":57949},[886],[888,57951,57952],{"xmlns":890},[892,57953,57954,57962],{},[895,57955,57956],{},[2142,57957,57958,57960],{},[898,57959,23410],{},[898,57961,28247],{},[902,57963,57964],{"encoding":904},"E_Y"," vždy ",[38,57967,57968],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,57971,57972,57973,57975],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,57974,57282],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,57977,57979,57980,2153],{"id":57978},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,57981,57982],{},"shift of demand",[724,57984,57985,57986,58004,58005,58022,58023,58036,58037,4202,58050,58072,58073,58090,58091,58117,58118,58121],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,57987,57989],{"className":57988},[886],[888,57990,57991],{"xmlns":890},[892,57992,57993,58001],{},[895,57994,57995],{},[2142,57996,57997,57999],{},[898,57998,1702],{},[2148,58000,2150],{},[902,58002,58003],{"encoding":904},"P_0"," odpovídá množství ",[883,58006,58008],{"className":58007},[886],[888,58009,58010],{"xmlns":890},[892,58011,58012,58020],{},[895,58013,58014],{},[2142,58015,58016,58018],{},[898,58017,2146],{},[2148,58019,2150],{},[902,58021,8625],{"encoding":904}," na křivce ",[883,58024,58026],{"className":58025},[886],[888,58027,58028],{"xmlns":890},[892,58029,58030,58034],{},[895,58031,58032],{},[898,58033,2334],{},[902,58035,2334],{"encoding":904},"; vzroste-li důchod z ",[883,58038,58040],{"className":58039},[886],[888,58041,58042],{"xmlns":890},[892,58043,58044,58048],{},[895,58045,58046],{},[898,58047,28247],{},[902,58049,28247],{"encoding":904},[883,58051,58053],{"className":58052},[886],[888,58054,58055],{"xmlns":890},[892,58056,58057,58069],{},[895,58058,58059,58065,58067],{},[2142,58060,58061,58063],{},[898,58062,28247],{},[2148,58064,2701],{},[1706,58066,8922],{},[898,58068,28247],{},[902,58070,58071],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,58074,58076],{"className":58075},[886],[888,58077,58078],{"xmlns":890},[892,58079,58080,58088],{},[895,58081,58082],{},[2142,58083,58084,58086],{},[898,58085,1702],{},[2148,58087,2150],{},[902,58089,58003],{"encoding":904}," odpovídá vyšší ",[883,58092,58094],{"className":58093},[886],[888,58095,58096],{"xmlns":890},[892,58097,58098,58114],{},[895,58099,58100,58106,58108],{},[2142,58101,58102,58104],{},[898,58103,2146],{},[2148,58105,2701],{},[1706,58107,8922],{},[2142,58109,58110,58112],{},[898,58111,2146],{},[2148,58113,2150],{},[902,58115,58116],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,58119,58120],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,58123,58124],{},[2286,58125],{"alt":58126,"className":58127,"src":58128},"imek-posun-vs-pohyb-po-krivce",[210,2290],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,58130,58131],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,58133,58134],{},[614,58135,58136,58137,33118,58167,58188],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,58138,58140],{"className":58139},[886],[888,58141,58142],{"xmlns":890},[892,58143,58144,58164],{},[895,58145,58146,58152,58154,58156,58158],{},[2142,58147,58148,58150],{},[898,58149,2334],{},[2148,58151,2495],{},[1706,58153,2505],{"separator":2504},[898,58155,2334],{},[1706,58157,2505],{"separator":2504},[2142,58159,58160,58162],{},[898,58161,2334],{},[2148,58163,2701],{},[902,58165,58166],{"encoding":904},"D_2, D, D_1",[883,58168,58170],{"className":58169},[886],[888,58171,58172],{"xmlns":890},[892,58173,58174,58186],{},[895,58175,58176,58178,58180,58182,58184],{},[1706,58177,2140],{"stretchy":2139},[898,58179,2146],{},[1706,58181,2505],{"separator":2504},[898,58183,1702],{},[1706,58185,2153],{"stretchy":2139},[902,58187,56748],{"encoding":904},", šipky naznačují posuny.",[56982,58190,58192],{"id":58191},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,58194,58195,58197,58198,58221,58222,58239,58240,58257,58258,1837],{},[38,58196,56990],{}," Poptávce ",[883,58199,58201],{"className":58200},[886],[888,58202,58203],{"xmlns":890},[892,58204,58205,58219],{},[895,58206,58207,58209,58211,58213,58215,58217],{},[898,58208,1702],{},[1706,58210,1708],{},[898,58212,2334],{},[1706,58214,2140],{"stretchy":2139},[898,58216,2146],{},[1706,58218,2153],{"stretchy":2139},[902,58220,2343],{"encoding":904}," odpovídá ceně ",[883,58223,58225],{"className":58224},[886],[888,58226,58227],{"xmlns":890},[892,58228,58229,58237],{},[895,58230,58231],{},[2142,58232,58233,58235],{},[898,58234,1702],{},[2148,58236,2150],{},[902,58238,58003],{"encoding":904}," množství ",[883,58241,58243],{"className":58242},[886],[888,58244,58245],{"xmlns":890},[892,58246,58247,58255],{},[895,58248,58249],{},[2142,58250,58251,58253],{},[898,58252,2146],{},[2148,58254,2150],{},[902,58256,8625],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,58259,58261],{"className":58260},[886],[888,58262,58263],{"xmlns":890},[892,58264,58265,58269],{},[895,58266,58267],{},[898,58268,1659],{},[902,58270,1659],{"encoding":904},[724,58272,58273,58275,58276,58293,58294,58316],{},[38,58274,57022],{}," Kupující nakupuje množství ",[883,58277,58279],{"className":58278},[886],[888,58280,58281],{"xmlns":890},[892,58282,58283,58291],{},[895,58284,58285],{},[2142,58286,58287,58289],{},[898,58288,2146],{},[2148,58290,2701],{},[902,58292,48070],{"encoding":904},", které odpovídá ceně ",[883,58295,58297],{"className":58296},[886],[888,58298,58299],{"xmlns":890},[892,58300,58301,58313],{},[895,58302,58303,58309,58311],{},[2142,58304,58305,58307],{},[898,58306,1702],{},[2148,58308,2150],{},[1706,58310,2447],{},[898,58312,1659],{},[902,58314,58315],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,58318,58320],{"className":58319},[886],[888,58321,58322],{"xmlns":890,"display":2350},[892,58323,58324,58358],{},[895,58325,58326,58328,58330,58336,58338,58340,58342,58344,58346,58348,58350,58352,58354,58356],{},[898,58327,1702],{},[1706,58329,1708],{},[2142,58331,58332,58334],{},[898,58333,2334],{},[2148,58335,2701],{},[1706,58337,2140],{"stretchy":2139},[898,58339,2146],{},[1706,58341,2153],{"stretchy":2139},[1706,58343,1708],{},[898,58345,2334],{},[1706,58347,2140],{"stretchy":2139},[898,58349,2146],{},[1706,58351,2153],{"stretchy":2139},[1706,58353,1715],{},[898,58355,1659],{},[1706,58357,2505],{"separator":2504},[902,58359,58360],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,58362,58363,58364,1837],{},"tj. dojde k ",[38,58365,58366],{},"posunu poptávky doleva",[724,58368,58369],{},[614,58370,58371,58372,58393,58394,1343,58411,1343,58424,58445,58446,1993,58463,1837],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,58373,58375],{"className":58374},[886],[888,58376,58377],{"xmlns":890},[892,58378,58379,58391],{},[895,58380,58381,58383,58385,58387,58389],{},[1706,58382,2140],{"stretchy":2139},[898,58384,2146],{},[1706,58386,2505],{"separator":2504},[898,58388,1702],{},[1706,58390,2153],{"stretchy":2139},[902,58392,56748],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,58395,58397],{"className":58396},[886],[888,58398,58399],{"xmlns":890},[892,58400,58401,58409],{},[895,58402,58403],{},[2142,58404,58405,58407],{},[898,58406,1702],{},[2148,58408,2150],{},[902,58410,58003],{"encoding":904},[883,58412,58414],{"className":58413},[886],[888,58415,58416],{"xmlns":890},[892,58417,58418,58422],{},[895,58419,58420],{},[898,58421,1659],{},[902,58423,1659],{"encoding":904},[883,58425,58427],{"className":58426},[886],[888,58428,58429],{"xmlns":890},[892,58430,58431,58443],{},[895,58432,58433,58439,58441],{},[2142,58434,58435,58437],{},[898,58436,1702],{},[2148,58438,2150],{},[1706,58440,2447],{},[898,58442,1659],{},[902,58444,58315],{"encoding":904},"; na vodorovné ",[883,58447,58449],{"className":58448},[886],[888,58450,58451],{"xmlns":890},[892,58452,58453,58461],{},[895,58454,58455],{},[2142,58456,58457,58459],{},[898,58458,2146],{},[2148,58460,2701],{},[902,58462,48070],{"encoding":904},[883,58464,58466],{"className":58465},[886],[888,58467,58468],{"xmlns":890},[892,58469,58470,58478],{},[895,58471,58472],{},[2142,58473,58474,58476],{},[898,58475,2146],{},[2148,58477,2150],{},[902,58479,8625],{"encoding":904},[198,58481,58483],{"id":58482},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,58485,58486],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,58488,58490],{"className":58489},[886],[888,58491,58492],{"xmlns":890,"display":2350},[892,58493,58494,58679],{},[2354,58495,58496],{"width":2356},[2358,58497,58498,58500,58672,58674],{},[2361,58499],{"width":2363},[2361,58501,58502],{},[2354,58503,58504,58588],{"rowspacing":7556,"columnalign":7557,"columnspacing":3141},[2358,58505,58506,58516],{},[2361,58507,58508],{},[4745,58509,58510],{"scriptlevel":2150,"displaystyle":2504},[2142,58511,58512,58514],{},[898,58513,2146],{},[2148,58515,2701],{},[2361,58517,58518],{},[4745,58519,58520],{"scriptlevel":2150,"displaystyle":2504},[895,58521,58522,58524,58526,58532,58534,58540,58542,58548,58550,58552,58558,58560,58566,58572,58574,58580,58586],{},[895,58523],{},[1706,58525,1708],{},[2142,58527,58528,58530],{},[898,58529,2334],{},[2148,58531,2701],{},[1706,58533,2140],{"stretchy":2139},[2142,58535,58536,58538],{},[898,58537,1702],{},[2148,58539,2701],{},[1706,58541,2505],{"separator":2504},[2142,58543,58544,58546],{},[898,58545,1702],{},[2148,58547,2495],{},[1706,58549,2153],{"stretchy":2139},[1706,58551,1708],{},[2142,58553,58554,58556],{},[898,58555,207],{},[2148,58557,2701],{},[1706,58559,2447],{},[2142,58561,58562,58564],{},[898,58563,2450],{},[2148,58565,2701],{},[2142,58567,58568,58570],{},[898,58569,1702],{},[2148,58571,2701],{},[1706,58573,2447],{},[2142,58575,58576,58578],{},[898,58577,20413],{},[2148,58579,2701],{},[2142,58581,58582,58584],{},[898,58583,1702],{},[2148,58585,2495],{},[1706,58587,2505],{"separator":2504},[2358,58589,58590,58600],{},[2361,58591,58592],{},[4745,58593,58594],{"scriptlevel":2150,"displaystyle":2504},[2142,58595,58596,58598],{},[898,58597,2146],{},[2148,58599,2495],{},[2361,58601,58602],{},[4745,58603,58604],{"scriptlevel":2150,"displaystyle":2504},[895,58605,58606,58608,58610,58616,58618,58624,58626,58632,58634,58636,58642,58644,58650,58656,58658,58664,58670],{},[895,58607],{},[1706,58609,1708],{},[2142,58611,58612,58614],{},[898,58613,2334],{},[2148,58615,2495],{},[1706,58617,2140],{"stretchy":2139},[2142,58619,58620,58622],{},[898,58621,1702],{},[2148,58623,2701],{},[1706,58625,2505],{"separator":2504},[2142,58627,58628,58630],{},[898,58629,1702],{},[2148,58631,2495],{},[1706,58633,2153],{"stretchy":2139},[1706,58635,1708],{},[2142,58637,58638,58640],{},[898,58639,207],{},[2148,58641,2495],{},[1706,58643,2447],{},[2142,58645,58646,58648],{},[898,58647,2450],{},[2148,58649,2495],{},[2142,58651,58652,58654],{},[898,58653,1702],{},[2148,58655,2701],{},[1706,58657,2447],{},[2142,58659,58660,58662],{},[898,58661,20413],{},[2148,58663,2495],{},[2142,58665,58666,58668],{},[898,58667,1702],{},[2148,58669,2495],{},[898,58671,1837],{"mathvariant":2409},[2361,58673],{"width":2363},[2361,58675,58676],{},[2415,58677,58678],{},"(2.6)",[902,58680,58681],{"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}",[2547,58683,58685],{"id":58684},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,58687,58688,58735,58782],{},[123,58689,58690,1343,58712,58734],{},[883,58691,58693],{"className":58692},[886],[888,58694,58695],{"xmlns":890},[892,58696,58697,58709],{},[895,58698,58699,58705,58707],{},[2142,58700,58701,58703],{},[898,58702,207],{},[2148,58704,2701],{},[1706,58706,8922],{},[2148,58708,2150],{},[902,58710,58711],{"encoding":904},"a_1 > 0",[883,58713,58715],{"className":58714},[886],[888,58716,58717],{"xmlns":890},[892,58718,58719,58731],{},[895,58720,58721,58727,58729],{},[2142,58722,58723,58725],{},[898,58724,207],{},[2148,58726,2495],{},[1706,58728,8922],{},[2148,58730,2150],{},[902,58732,58733],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,58736,58737,1343,58759,58781],{},[883,58738,58740],{"className":58739},[886],[888,58741,58742],{"xmlns":890},[892,58743,58744,58756],{},[895,58745,58746,58752,58754],{},[2142,58747,58748,58750],{},[898,58749,2450],{},[2148,58751,2701],{},[1706,58753,2539],{},[2148,58755,2150],{},[902,58757,58758],{"encoding":904},"b_1 \u003C 0",[883,58760,58762],{"className":58761},[886],[888,58763,58764],{"xmlns":890},[892,58765,58766,58778],{},[895,58767,58768,58774,58776],{},[2142,58769,58770,58772],{},[898,58771,20413],{},[2148,58773,2495],{},[1706,58775,2539],{},[2148,58777,2150],{},[902,58779,58780],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,58783,58784,58785,1343,58802,58820,58821],{},"zkřížené koeficienty ",[883,58786,58788],{"className":58787},[886],[888,58789,58790],{"xmlns":890},[892,58791,58792,58800],{},[895,58793,58794],{},[2142,58795,58796,58798],{},[898,58797,20413],{},[2148,58799,2701],{},[902,58801,48866],{"encoding":904},[883,58803,58805],{"className":58804},[886],[888,58806,58807],{"xmlns":890},[892,58808,58809,58817],{},[895,58810,58811],{},[2142,58812,58813,58815],{},[898,58814,2450],{},[2148,58816,2495],{},[902,58818,58819],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,58822,58823,58873],{},[123,58824,58825,58828,58829,1343,58851,2505],{},[38,58826,58827],{},"substituty"," (máslo vs. margarín): ",[883,58830,58832],{"className":58831},[886],[888,58833,58834],{"xmlns":890},[892,58835,58836,58848],{},[895,58837,58838,58844,58846],{},[2142,58839,58840,58842],{},[898,58841,20413],{},[2148,58843,2701],{},[1706,58845,8922],{},[2148,58847,2150],{},[902,58849,58850],{"encoding":904},"c_1 > 0",[883,58852,58854],{"className":58853},[886],[888,58855,58856],{"xmlns":890},[892,58857,58858,58870],{},[895,58859,58860,58866,58868],{},[2142,58861,58862,58864],{},[898,58863,2450],{},[2148,58865,2495],{},[1706,58867,8922],{},[2148,58869,2150],{},[902,58871,58872],{"encoding":904},"b_2 > 0",[123,58874,58875,58878,58879,1343,58901,1837],{},[38,58876,58877],{},"komplementy"," (auto vs. benzín): ",[883,58880,58882],{"className":58881},[886],[888,58883,58884],{"xmlns":890},[892,58885,58886,58898],{},[895,58887,58888,58894,58896],{},[2142,58889,58890,58892],{},[898,58891,20413],{},[2148,58893,2701],{},[1706,58895,2539],{},[2148,58897,2150],{},[902,58899,58900],{"encoding":904},"c_1 \u003C 0",[883,58902,58904],{"className":58903},[886],[888,58905,58906],{"xmlns":890},[892,58907,58908,58920],{},[895,58909,58910,58916,58918],{},[2142,58911,58912,58914],{},[898,58913,2450],{},[2148,58915,2495],{},[1706,58917,2539],{},[2148,58919,2150],{},[902,58921,58922],{"encoding":904},"b_2 \u003C 0",[724,58924,58925],{},"Schematicky:",[724,58927,58928,58931],{},[38,58929,58930],{},"Substituty",[883,58932,58934],{"className":58933},[886],[888,58935,58936],{"xmlns":890},[892,58937,58938,59076],{},[895,58939,58940,58946,58948,58962,58964,58984,58986,59006,59008,59010,59016,59018,59032,59034,59054,59056],{},[2142,58941,58942,58944],{},[898,58943,2146],{},[2148,58945,2701],{},[1706,58947,1708],{},[898,58949,58950],{},[5900,58951,58952,58960],{},[1706,58953,58954],{},[2142,58955,58956,58958],{},[898,58957,207],{},[2148,58959,2701],{},[1706,58961,2447],{"lspace":3141,"rspace":3141},[1706,58963,2447],{},[898,58965,58966],{},[5900,58967,58968,58982],{},[1706,58969,58970,58976],{},[2142,58971,58972,58974],{},[898,58973,2450],{},[2148,58975,2701],{},[2142,58977,58978,58980],{},[898,58979,1702],{},[2148,58981,2701],{},[1706,58983,1715],{"lspace":3141,"rspace":3141},[1706,58985,2447],{},[898,58987,58988],{},[5900,58989,58990,59004],{},[1706,58991,58992,58998],{},[2142,58993,58994,58996],{},[898,58995,20413],{},[2148,58997,2701],{},[2142,58999,59000,59002],{},[898,59001,1702],{},[2148,59003,2495],{},[1706,59005,2447],{"lspace":3141,"rspace":3141},[1706,59007,2505],{"separator":2504},[4898,59009],{"width":9524},[2142,59011,59012,59014],{},[898,59013,2146],{},[2148,59015,2495],{},[1706,59017,1708],{},[898,59019,59020],{},[5900,59021,59022,59030],{},[1706,59023,59024],{},[2142,59025,59026,59028],{},[898,59027,207],{},[2148,59029,2495],{},[1706,59031,2447],{"lspace":3141,"rspace":3141},[1706,59033,2447],{},[898,59035,59036],{},[5900,59037,59038,59052],{},[1706,59039,59040,59046],{},[2142,59041,59042,59044],{},[898,59043,2450],{},[2148,59045,2495],{},[2142,59047,59048,59050],{},[898,59049,1702],{},[2148,59051,2701],{},[1706,59053,2447],{"lspace":3141,"rspace":3141},[1706,59055,2447],{},[898,59057,59058],{},[5900,59059,59060,59074],{},[1706,59061,59062,59068],{},[2142,59063,59064,59066],{},[898,59065,20413],{},[2148,59067,2495],{},[2142,59069,59070,59072],{},[898,59071,1702],{},[2148,59073,2495],{},[1706,59075,1715],{"lspace":3141,"rspace":3141},[902,59077,59078],{"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}",[724,59080,59081,59084],{},[38,59082,59083],{},"Komplementy",[883,59085,59087],{"className":59086},[886],[888,59088,59089],{"xmlns":890},[892,59090,59091,59229],{},[895,59092,59093,59099,59101,59115,59117,59137,59139,59159,59161,59163,59169,59171,59185,59187,59207,59209],{},[2142,59094,59095,59097],{},[898,59096,2146],{},[2148,59098,2701],{},[1706,59100,1708],{},[898,59102,59103],{},[5900,59104,59105,59113],{},[1706,59106,59107],{},[2142,59108,59109,59111],{},[898,59110,207],{},[2148,59112,2701],{},[1706,59114,2447],{"lspace":3141,"rspace":3141},[1706,59116,2447],{},[898,59118,59119],{},[5900,59120,59121,59135],{},[1706,59122,59123,59129],{},[2142,59124,59125,59127],{},[898,59126,2450],{},[2148,59128,2701],{},[2142,59130,59131,59133],{},[898,59132,1702],{},[2148,59134,2701],{},[1706,59136,1715],{"lspace":3141,"rspace":3141},[1706,59138,2447],{},[898,59140,59141],{},[5900,59142,59143,59157],{},[1706,59144,59145,59151],{},[2142,59146,59147,59149],{},[898,59148,20413],{},[2148,59150,2701],{},[2142,59152,59153,59155],{},[898,59154,1702],{},[2148,59156,2495],{},[1706,59158,1715],{"lspace":3141,"rspace":3141},[1706,59160,2505],{"separator":2504},[4898,59162],{"width":9524},[2142,59164,59165,59167],{},[898,59166,2146],{},[2148,59168,2495],{},[1706,59170,1708],{},[898,59172,59173],{},[5900,59174,59175,59183],{},[1706,59176,59177],{},[2142,59178,59179,59181],{},[898,59180,207],{},[2148,59182,2495],{},[1706,59184,2447],{"lspace":3141,"rspace":3141},[1706,59186,2447],{},[898,59188,59189],{},[5900,59190,59191,59205],{},[1706,59192,59193,59199],{},[2142,59194,59195,59197],{},[898,59196,2450],{},[2148,59198,2495],{},[2142,59200,59201,59203],{},[898,59202,1702],{},[2148,59204,2701],{},[1706,59206,1715],{"lspace":3141,"rspace":3141},[1706,59208,2447],{},[898,59210,59211],{},[5900,59212,59213,59227],{},[1706,59214,59215,59221],{},[2142,59216,59217,59219],{},[898,59218,20413],{},[2148,59220,2495],{},[2142,59222,59223,59225],{},[898,59224,1702],{},[2148,59226,2495],{},[1706,59228,1715],{"lspace":3141,"rspace":3141},[902,59230,59231],{"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}",[56029,59233],{},[115,59235,32232],{"id":55839},[1636,59237,59238],{},[724,59239,59240,59242,59243,56053,59256,56067,59269,59272,59273,24808,59297,59315],{},[883,59241,3174],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,59244,59246],{"className":59245},[886],[888,59247,59248],{"xmlns":890},[892,59249,59250,59254],{},[895,59251,59252],{},[898,59253,2146],{},[902,59255,2146],{"encoding":904},[883,59257,59259],{"className":59258},[886],[888,59260,59261],{"xmlns":890},[892,59262,59263,59267],{},[895,59264,59265],{},[898,59266,1702],{},[902,59268,1702],{"encoding":904},[38,59270,59271],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,59274,59276],{"className":59275},[886],[888,59277,59278],{"xmlns":890},[892,59279,59280,59294],{},[895,59281,59282,59284,59286,59288,59290,59292],{},[898,59283,1702],{},[1706,59285,1708],{},[898,59287,20413],{},[898,59289,2146],{},[1706,59291,2447],{},[898,59293,3120],{},[902,59295,59296],{"encoding":904},"P = cQ + d",[883,59298,59300],{"className":59299},[886],[888,59301,59302],{"xmlns":890},[892,59303,59304,59312],{},[895,59305,59306,59308,59310],{},[898,59307,20413],{},[1706,59309,8922],{},[2148,59311,2150],{},[902,59313,59314],{"encoding":904},"c > 0"," je standardní aproximací.",[198,59317,56122],{"id":59318},"obecný-vícefaktorový-model-1",[724,59320,59321,2314,59324,59327,59328,59341,59342,55955,59355,55969,59368,59381,59382,59395,59396,55998,59409,59422],{},[38,59322,59323],{},"Nabízené množství",[614,59325,59326],{},"quantity supplied",") závisí na ceně ",[883,59329,59331],{"className":59330},[886],[888,59332,59333],{"xmlns":890},[892,59334,59335,59339],{},[895,59336,59337],{},[898,59338,1702],{},[902,59340,1702],{"encoding":904},", cenách výrobních faktorů (práce ",[883,59343,59345],{"className":59344},[886],[888,59346,59347],{"xmlns":890},[892,59348,59349,59353],{},[895,59350,59351],{},[898,59352,6362],{},[902,59354,6362],{"encoding":904},[883,59356,59358],{"className":59357},[886],[888,59359,59360],{"xmlns":890},[892,59361,59362,59366],{},[895,59363,59364],{},[898,59365,28915],{},[902,59367,28915],{"encoding":904},[883,59369,59371],{"className":59370},[886],[888,59372,59373],{"xmlns":890},[892,59374,59375,59379],{},[895,59376,59377],{},[898,59378,23410],{},[902,59380,23410],{"encoding":904},"), očekávání ",[883,59383,59385],{"className":59384},[886],[888,59386,59387],{"xmlns":890},[892,59388,59389,59393],{},[895,59390,59391],{},[898,59392,1762],{},[902,59394,1762],{"encoding":904},", počtu výrobců ",[883,59397,59399],{"className":59398},[886],[888,59400,59401],{"xmlns":890},[892,59402,59403,59407],{},[895,59404,59405],{},[898,59406,55995],{},[902,59408,55995],{"encoding":904},[883,59410,59412],{"className":59411},[886],[888,59413,59414],{"xmlns":890},[892,59415,59416,59420],{},[895,59417,59418],{},[898,59419,56010],{},[902,59421,56010],{"encoding":904}," a dalších:",[883,59424,59426],{"className":59425},[886],[888,59427,59428],{"xmlns":890,"display":2350},[892,59429,59430,59489],{},[2354,59431,59432],{"width":2356},[2358,59433,59434,59436,59482,59484],{},[2361,59435],{"width":2363},[2361,59437,59438],{},[895,59439,59440,59442,59444,59446,59448,59450,59452,59454,59456,59458,59460,59462,59464,59466,59468,59470,59472,59474,59476,59478,59480],{},[898,59441,2146],{},[1706,59443,1708],{},[898,59445,14171],{},[1706,59447,2140],{"stretchy":2139},[898,59449,1702],{},[1706,59451,2505],{"separator":2504},[898,59453,6362],{},[1706,59455,2505],{"separator":2504},[898,59457,28915],{},[1706,59459,2505],{"separator":2504},[898,59461,23410],{},[1706,59463,2505],{"separator":2504},[898,59465,1762],{},[1706,59467,2505],{"separator":2504},[898,59469,55995],{},[1706,59471,2505],{"separator":2504},[898,59473,56010],{},[1706,59475,2505],{"separator":2504},[1706,59477,28763],{},[1706,59479,2153],{"stretchy":2139},[898,59481,1837],{"mathvariant":2409},[2361,59483],{"width":2363},[2361,59485,59486],{},[2415,59487,59488],{},"(2.7)",[902,59490,59491],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,59493,57471,59494,2314,59497,59500],{},[38,59495,59496],{},"funkce nabídky",[614,59498,59499],{},"supply function",") v širším slova smyslu.",[198,59502,59504],{"id":59503},"jednofaktorový-model","Jednofaktorový model",[724,59506,59507],{},"V nejpřirozenějším jednofaktorovém modelu",[883,59509,59511],{"className":59510},[886],[888,59512,59513],{"xmlns":890,"display":2350},[892,59514,59515,59566],{},[2354,59516,59517],{"width":2356},[2358,59518,59519,59521,59559,59561],{},[2361,59520],{"width":2363},[2361,59522,59523],{},[895,59524,59525,59527,59529,59531,59533,59535,59537,59539,59541,59543,59545,59547,59549,59551,59553,59555,59557],{},[898,59526,2146],{},[1706,59528,1708],{},[898,59530,14171],{},[1706,59532,2140],{"stretchy":2139},[898,59534,1702],{},[1706,59536,2153],{"stretchy":2139},[1706,59538,2505],{"separator":2504},[4898,59540],{"width":9524},[2415,59542,56474],{},[4898,59544],{"width":9524},[898,59546,1702],{},[1706,59548,1708],{},[898,59550,14171],{},[1706,59552,2140],{"stretchy":2139},[898,59554,2146],{},[1706,59556,2153],{"stretchy":2139},[898,59558,1837],{"mathvariant":2409},[2361,59560],{"width":2363},[2361,59562,59563],{},[2415,59564,59565],{},"(2.8)",[902,59567,59568],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,59570,59571,59572,2314,59575,1936],{},"Graf je ",[38,59573,59574],{},"křivka nabídky",[614,59576,59577],{},"supply curve",[2547,59579,59581],{"id":59580},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[1636,59583,59584],{},[724,59585,59586],{},[38,59587,56520,59588,59601,59602,56575],{},[883,59589,59591],{"className":59590},[886],[888,59592,59593],{"xmlns":890},[892,59594,59595,59599],{},[895,59596,59597],{},[898,59598,1702],{},[902,59600,1702],{"encoding":904},", pak nabízené množství ",[883,59603,59605],{"className":59604},[886],[888,59606,59607],{"xmlns":890},[892,59608,59609,59613],{},[895,59610,59611],{},[898,59612,2146],{},[902,59614,2146],{"encoding":904},[724,59616,59617,59618,59643,59644,59674,59675,59692],{},"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 ",[883,59619,59621],{"className":59620},[886],[888,59622,59623],{"xmlns":890},[892,59624,59625,59641],{},[895,59626,59627,59629,59631,59633,59639],{},[1706,59628,21693],{"stretchy":2139},[2148,59630,2150],{},[1706,59632,2505],{"separator":2504},[2142,59634,59635,59637],{},[898,59636,1702],{},[2148,59638,2150],{},[1706,59640,21708],{"stretchy":2139},[902,59642,56660],{"encoding":904}," na svislé ose (případně z ",[883,59645,59647],{"className":59646},[886],[888,59648,59649],{"xmlns":890},[892,59650,59651,59671],{},[895,59652,59653,59655,59661,59663,59669],{},[1706,59654,21693],{"stretchy":2139},[2142,59656,59657,59659],{},[898,59658,2146],{},[2148,59660,2701],{},[1706,59662,2505],{"separator":2504},[2142,59664,59665,59667],{},[898,59666,1702],{},[2148,59668,2701],{},[1706,59670,21708],{"stretchy":2139},[902,59672,59673],{"encoding":904},"[Q_1, P_1]","), kde ",[883,59676,59678],{"className":59677},[886],[888,59679,59680],{"xmlns":890},[892,59681,59682,59690],{},[895,59683,59684],{},[2142,59685,59686,59688],{},[898,59687,1702],{},[2148,59689,2150],{},[902,59691,58003],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,59694,59695],{},[614,59696,59697,59698,5027,59711,1837],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,59699,59701],{"className":59700},[886],[888,59702,59703],{"xmlns":890},[892,59704,59705,59709],{},[895,59706,59707],{},[898,59708,14171],{},[902,59710,14171],{"encoding":904},[883,59712,59714],{"className":59713},[886],[888,59715,59716],{"xmlns":890},[892,59717,59718,59730],{},[895,59719,59720,59722,59724,59726,59728],{},[1706,59721,2140],{"stretchy":2139},[898,59723,2146],{},[1706,59725,2505],{"separator":2504},[898,59727,1702],{},[1706,59729,2153],{"stretchy":2139},[902,59731,56748],{"encoding":904},[2547,59733,59735],{"id":59734},"lineární-model-nabídky","Lineární model nabídky",[883,59737,59739],{"className":59738},[886],[888,59740,59741],{"xmlns":890,"display":2350},[892,59742,59743,59782],{},[2354,59744,59745],{"width":2356},[2358,59746,59747,59749,59775,59777],{},[2361,59748],{"width":2363},[2361,59750,59751],{},[895,59752,59753,59755,59757,59759,59761,59763,59765,59767,59769,59771,59773],{},[898,59754,1702],{},[1706,59756,1708],{},[898,59758,20413],{},[898,59760,2146],{},[1706,59762,2447],{},[898,59764,3120],{},[1706,59766,2505],{"separator":2504},[4898,59768],{"width":9524},[898,59770,20413],{},[1706,59772,8922],{},[2148,59774,31567],{},[2361,59776],{"width":2363},[2361,59778,59779],{},[2415,59780,59781],{},"(2.9)",[902,59783,59784],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,59786,59787,59788,59824,59825,59838],{},"Alternativně ",[883,59789,59791],{"className":59790},[886],[888,59792,59793],{"xmlns":890},[892,59794,59795,59821],{},[895,59796,59797,59799,59801,59809,59811,59813],{},[898,59798,2146],{},[1706,59800,1708],{},[4745,59802,59803],{"scriptlevel":2150,"displaystyle":2139},[2964,59804,59805,59807],{},[2148,59806,2701],{},[898,59808,20413],{},[898,59810,1702],{},[1706,59812,1715],{},[4745,59814,59815],{"scriptlevel":2150,"displaystyle":2139},[2964,59816,59817,59819],{},[898,59818,3120],{},[898,59820,20413],{},[902,59822,59823],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,59826,59828],{"className":59827},[886],[888,59829,59830],{"xmlns":890},[892,59831,59832,59836],{},[895,59833,59834],{},[898,59835,1702],{},[902,59837,1702],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[56982,59840,59842],{"id":59841},"příklad-25","Příklad 2.5",[724,59844,59845,59847,59848,1837],{},[38,59846,56990],{}," Lineární nabídka ",[883,59849,59851],{"className":59850},[886],[888,59852,59853],{"xmlns":890},[892,59854,59855,59869],{},[895,59856,59857,59859,59861,59863,59865,59867],{},[898,59858,1702],{},[1706,59860,1708],{},[2148,59862,11496],{},[898,59864,2146],{},[1706,59866,2447],{},[2148,59868,2748],{},[902,59870,59871],{"encoding":904},"P = 0{,}5Q + 25",[724,59873,59874,59876,59877,1837],{},[38,59875,57022],{}," Alternativní tvar ",[883,59878,59880],{"className":59879},[886],[888,59881,59882],{"xmlns":890},[892,59883,59884,59898],{},[895,59885,59886,59888,59890,59892,59894,59896],{},[898,59887,2146],{},[1706,59889,1708],{},[2148,59891,2495],{},[898,59893,1702],{},[1706,59895,1715],{},[2148,59897,2728],{},[902,59899,59900],{"encoding":904},"Q = 2P - 50",[16,59902,59903,59928],{},[19,59904,59905],{},[22,59906,59907,59922,59924,59926],{},[25,59908,59909],{},[883,59910,59912],{"className":59911},[886],[888,59913,59914],{"xmlns":890},[892,59915,59916,59920],{},[895,59917,59918],{},[898,59919,1702],{},[902,59921,1702],{"encoding":904},[25,59923,12556],{},[25,59925,34145],{},[25,59927,3508],{},[30,59929,59930],{},[22,59931,59932,59947,59949,59951],{},[35,59933,59934],{},[883,59935,59937],{"className":59936},[886],[888,59938,59939],{"xmlns":890},[892,59940,59941,59945],{},[895,59942,59943],{},[898,59944,2146],{},[902,59946,2146],{"encoding":904},[35,59948,7786],{},[35,59950,3369],{},[35,59952,12556],{},[198,59954,59956,59957,2153],{"id":59955},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,59958,59959],{},"shift of supply",[724,59961,59962,59963,59966,59967,59984,59985,60010,60011,1837],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,59964,59965],{},"doprava",": při stejné ceně ",[883,59968,59970],{"className":59969},[886],[888,59971,59972],{"xmlns":890},[892,59973,59974,59982],{},[895,59975,59976],{},[2142,59977,59978,59980],{},[898,59979,1702],{},[2148,59981,2150],{},[902,59983,58003],{"encoding":904}," vyrobí výrobce větší ",[883,59986,59988],{"className":59987},[886],[888,59989,59990],{"xmlns":890},[892,59991,59992,60008],{},[895,59993,59994,60000,60002],{},[2142,59995,59996,59998],{},[898,59997,2146],{},[2148,59999,2701],{},[1706,60001,8922],{},[2142,60003,60004,60006],{},[898,60005,2146],{},[2148,60007,2150],{},[902,60009,58116],{"encoding":904},"); zdražení vstupů posune křivku ",[38,60012,60013],{},"doleva",[724,60015,60016],{},[614,60017,60018,60019,60032,60033,60051,60052,60070,60071,1837],{},"Obrázek 2.11: Původní ",[883,60020,60022],{"className":60021},[886],[888,60023,60024],{"xmlns":890},[892,60025,60026,60030],{},[895,60027,60028],{},[898,60029,14171],{},[902,60031,14171],{"encoding":904},", posunuté ",[883,60034,60036],{"className":60035},[886],[888,60037,60038],{"xmlns":890},[892,60039,60040,60048],{},[895,60041,60042],{},[2142,60043,60044,60046],{},[898,60045,14171],{},[2148,60047,2701],{},[902,60049,60050],{"encoding":904},"S_1"," (doprava) a ",[883,60053,60055],{"className":60054},[886],[888,60056,60057],{"xmlns":890},[892,60058,60059,60067],{},[895,60060,60061],{},[2142,60062,60063,60065],{},[898,60064,14171],{},[2148,60066,2495],{},[902,60068,60069],{"encoding":904},"S_2"," (doleva) v ",[883,60072,60074],{"className":60073},[886],[888,60075,60076],{"xmlns":890},[892,60077,60078,60090],{},[895,60079,60080,60082,60084,60086,60088],{},[1706,60081,2140],{"stretchy":2139},[898,60083,2146],{},[1706,60085,2505],{"separator":2504},[898,60087,1702],{},[1706,60089,2153],{"stretchy":2139},[902,60091,56748],{"encoding":904},[56982,60093,60095],{"id":60094},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,60097,60098,60100,60101,60125,60126,1837],{},[38,60099,56990],{}," Nabídka ",[883,60102,60104],{"className":60103},[886],[888,60105,60106],{"xmlns":890},[892,60107,60108,60122],{},[895,60109,60110,60112,60114,60116,60118,60120],{},[898,60111,1702],{},[1706,60113,1708],{},[898,60115,14171],{},[1706,60117,2140],{"stretchy":2139},[898,60119,2146],{},[1706,60121,2153],{"stretchy":2139},[902,60123,60124],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,60127,60129],{"className":60128},[886],[888,60130,60131],{"xmlns":890},[892,60132,60133,60137],{},[895,60134,60135],{},[898,60136,1659],{},[902,60138,1659],{"encoding":904},[724,60140,60141,60143,60144,60157,60158,60176,60177,60205],{},[38,60142,57022],{}," Spotřebitel zaplatí ",[883,60145,60147],{"className":60146},[886],[888,60148,60149],{"xmlns":890},[892,60150,60151,60155],{},[895,60152,60153],{},[898,60154,1702],{},[902,60156,1702],{"encoding":904},", výrobce obdrží ",[883,60159,60161],{"className":60160},[886],[888,60162,60163],{"xmlns":890},[892,60164,60165,60173],{},[895,60166,60167,60169,60171],{},[898,60168,1702],{},[1706,60170,1715],{},[898,60172,1659],{},[902,60174,60175],{"encoding":904},"P - T",". Z podmínky ",[883,60178,60180],{"className":60179},[886],[888,60181,60182],{"xmlns":890},[892,60183,60184,60202],{},[895,60185,60186,60188,60190,60192,60194,60196,60198,60200],{},[898,60187,1702],{},[1706,60189,1715],{},[898,60191,1659],{},[1706,60193,1708],{},[898,60195,14171],{},[1706,60197,2140],{"stretchy":2139},[898,60199,2146],{},[1706,60201,2153],{"stretchy":2139},[902,60203,60204],{"encoding":904},"P - T = S(Q)"," plyne",[883,60207,60209],{"className":60208},[886],[888,60210,60211],{"xmlns":890,"display":2350},[892,60212,60213,60247],{},[895,60214,60215,60217,60219,60225,60227,60229,60231,60233,60235,60237,60239,60241,60243,60245],{},[898,60216,1702],{},[1706,60218,1708],{},[2142,60220,60221,60223],{},[898,60222,14171],{},[2148,60224,2701],{},[1706,60226,2140],{"stretchy":2139},[898,60228,2146],{},[1706,60230,2153],{"stretchy":2139},[1706,60232,1708],{},[898,60234,14171],{},[1706,60236,2140],{"stretchy":2139},[898,60238,2146],{},[1706,60240,2153],{"stretchy":2139},[1706,60242,2447],{},[898,60244,1659],{},[898,60246,1837],{"mathvariant":2409},[902,60248,60249],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,60251,60252,60253,60266,60267,1647,60280,60283,60284,1993,60304,3484,60322,1837],{},"Křivka ",[883,60254,60256],{"className":60255},[886],[888,60257,60258],{"xmlns":890},[892,60259,60260,60264],{},[895,60261,60262],{},[898,60263,14171],{},[902,60265,14171],{"encoding":904}," se tedy posune o ",[883,60268,60270],{"className":60269},[886],[888,60271,60272],{"xmlns":890},[892,60273,60274,60278],{},[895,60275,60276],{},[898,60277,1659],{},[902,60279,1659],{"encoding":904},[38,60281,60282],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,60285,60287],{"className":60286},[886],[888,60288,60289],{"xmlns":890},[892,60290,60291,60301],{},[895,60292,60293,60295,60297,60299],{},[898,60294,1702],{},[1706,60296,1708],{},[2148,60298,2495],{},[898,60300,2146],{},[902,60302,60303],{"encoding":904},"P = 2Q",[883,60305,60307],{"className":60306},[886],[888,60308,60309],{"xmlns":890},[892,60310,60311,60319],{},[895,60312,60313,60315,60317],{},[898,60314,1659],{},[1706,60316,1708],{},[2148,60318,7044],{},[902,60320,60321],{"encoding":904},"T = 6",[883,60323,60325],{"className":60324},[886],[888,60326,60327],{"xmlns":890},[892,60328,60329,60351],{},[895,60330,60331,60337,60339,60341,60343,60345,60347,60349],{},[2142,60332,60333,60335],{},[898,60334,14171],{},[2148,60336,2701],{},[1706,60338,4288],{},[898,60340,1702],{},[1706,60342,1708],{},[2148,60344,2495],{},[898,60346,2146],{},[1706,60348,2447],{},[2148,60350,7044],{},[902,60352,60353],{"encoding":904},"S_1: P = 2Q + 6",[724,60355,60356],{},[614,60357,60358,60359,60372],{},"Obrázek 2.12: Posun nabídky o ",[883,60360,60362],{"className":60361},[886],[888,60363,60364],{"xmlns":890},[892,60365,60366,60370],{},[895,60367,60368],{},[898,60369,1659],{},[902,60371,1659],{"encoding":904}," svisle nahoru.",[56029,60374],{},[115,60376,60378],{"id":60377},"tržní-rovnováha","Tržní rovnováha",[1636,60380,60381],{},[724,60382,60383,60385,60386,1647,60389,60421,60422,1343,60445,60468,60469,60472,60473,60486],{},[883,60384,3174],{}," TL;DR\nV ",[38,60387,60388],{},"rovnovážném bodě",[883,60390,60392],{"className":60391},[886],[888,60393,60394],{"xmlns":890},[892,60395,60396,60418],{},[895,60397,60398,60400,60402,60408,60410,60416],{},[898,60399,23410],{},[1706,60401,21693],{"stretchy":2139},[2489,60403,60404,60406],{},[898,60405,2146],{},[898,60407,23410],{},[1706,60409,2505],{"separator":2504},[2489,60411,60412,60414],{},[898,60413,1702],{},[898,60415,23410],{},[1706,60417,21708],{"stretchy":2139},[902,60419,60420],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,60423,60425],{"className":60424},[886],[888,60426,60427],{"xmlns":890},[892,60428,60429,60443],{},[895,60430,60431,60433,60435,60437,60439,60441],{},[898,60432,1702],{},[1706,60434,1708],{},[898,60436,2334],{},[1706,60438,2140],{"stretchy":2139},[898,60440,2146],{},[1706,60442,2153],{"stretchy":2139},[902,60444,2343],{"encoding":904},[883,60446,60448],{"className":60447},[886],[888,60449,60450],{"xmlns":890},[892,60451,60452,60466],{},[895,60453,60454,60456,60458,60460,60462,60464],{},[898,60455,1702],{},[1706,60457,1708],{},[898,60459,14171],{},[1706,60461,2140],{"stretchy":2139},[898,60463,2146],{},[1706,60465,2153],{"stretchy":2139},[902,60467,60124],{"encoding":904},". Čtyři ",[38,60470,60471],{},"pravidla komparativní statiky"," popisují, jak se ",[883,60474,60476],{"className":60475},[886],[888,60477,60478],{"xmlns":890},[892,60479,60480,60484],{},[895,60481,60482],{},[898,60483,23410],{},[902,60485,23410],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,60488,60490],{"id":60489},"definice","Definice",[724,60492,60493,2314,60495,60498,60499,1647,60502,60520,60521,14335,60552,2314,60555,1936],{},[38,60494,60378],{},[614,60496,60497],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,60500,60501],{},"rovnovážné ceně",[883,60503,60505],{"className":60504},[886],[888,60506,60507],{"xmlns":890},[892,60508,60509,60517],{},[895,60510,60511],{},[2489,60512,60513,60515],{},[898,60514,1702],{},[898,60516,23410],{},[902,60518,60519],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,60522,60524],{"className":60523},[886],[888,60525,60526],{"xmlns":890},[892,60527,60528,60550],{},[895,60529,60530,60532,60534,60540,60542,60548],{},[898,60531,23410],{},[1706,60533,21693],{"stretchy":2139},[2489,60535,60536,60538],{},[898,60537,2146],{},[898,60539,23410],{},[1706,60541,2505],{"separator":2504},[2489,60543,60544,60546],{},[898,60545,1702],{},[898,60547,23410],{},[1706,60549,21708],{"stretchy":2139},[902,60551,60420],{"encoding":904},[38,60553,60554],{},"rovnovážný bod",[614,60556,60557],{},"equilibrium point",[724,60559,60560,60561,1343,60584,1837],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,60562,60564],{"className":60563},[886],[888,60565,60566],{"xmlns":890},[892,60567,60568,60582],{},[895,60569,60570,60572,60574,60576,60578,60580],{},[898,60571,1702],{},[1706,60573,1708],{},[898,60575,2334],{},[1706,60577,2140],{"stretchy":2139},[898,60579,2146],{},[1706,60581,2153],{"stretchy":2139},[902,60583,2343],{"encoding":904},[883,60585,60587],{"className":60586},[886],[888,60588,60589],{"xmlns":890},[892,60590,60591,60605],{},[895,60592,60593,60595,60597,60599,60601,60603],{},[898,60594,1702],{},[1706,60596,1708],{},[898,60598,14171],{},[1706,60600,2140],{"stretchy":2139},[898,60602,2146],{},[1706,60604,2153],{"stretchy":2139},[902,60606,60124],{"encoding":904},[724,60608,60609],{},[2286,60610],{"alt":60611,"className":60612,"src":60613},"imek-poptavka-nabidka-rovnovaha",[210,2290],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,60615,60616],{},[614,60617,60618,60619,60632,60633,33118,60646,60667,60668,1837],{},"Obrázek 2.13: Klesající ",[883,60620,60622],{"className":60621},[886],[888,60623,60624],{"xmlns":890},[892,60625,60626,60630],{},[895,60627,60628],{},[898,60629,2334],{},[902,60631,2334],{"encoding":904}," a rostoucí ",[883,60634,60636],{"className":60635},[886],[888,60637,60638],{"xmlns":890},[892,60639,60640,60644],{},[895,60641,60642],{},[898,60643,14171],{},[902,60645,14171],{"encoding":904},[883,60647,60649],{"className":60648},[886],[888,60650,60651],{"xmlns":890},[892,60652,60653,60665],{},[895,60654,60655,60657,60659,60661,60663],{},[1706,60656,2140],{"stretchy":2139},[898,60658,2146],{},[1706,60660,2505],{"separator":2504},[898,60662,1702],{},[1706,60664,2153],{"stretchy":2139},[902,60666,56748],{"encoding":904}," protínající se v ",[883,60669,60671],{"className":60670},[886],[888,60672,60673],{"xmlns":890},[892,60674,60675,60697],{},[895,60676,60677,60679,60681,60687,60689,60695],{},[898,60678,23410],{},[1706,60680,21693],{"stretchy":2139},[2489,60682,60683,60685],{},[898,60684,2146],{},[898,60686,23410],{},[1706,60688,2505],{"separator":2504},[2489,60690,60691,60693],{},[898,60692,1702],{},[898,60694,23410],{},[1706,60696,21708],{"stretchy":2139},[902,60698,60420],{"encoding":904},[198,60700,60702],{"id":60701},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,60704,60705,60707,60708,60742,60743,1837],{},[38,60706,56990],{}," Poptávka ",[883,60709,60711],{"className":60710},[886],[888,60712,60713],{"xmlns":890},[892,60714,60715,60739],{},[895,60716,60717,60719,60721,60723,60729,60731,60733,60735,60737],{},[898,60718,1702],{},[1706,60720,1708],{},[1706,60722,1715],{},[2489,60724,60725,60727],{},[898,60726,2146],{},[2148,60728,2495],{},[1706,60730,1715],{},[2148,60732,7786],{},[898,60734,2146],{},[1706,60736,2447],{},[2148,60738,27924],{},[902,60740,60741],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,60744,60746],{"className":60745},[886],[888,60747,60748],{"xmlns":890},[892,60749,60750,60772],{},[895,60751,60752,60754,60756,60762,60764,60766,60768,60770],{},[898,60753,1702],{},[1706,60755,1708],{},[2489,60757,60758,60760],{},[898,60759,2146],{},[2148,60761,2495],{},[1706,60763,2447],{},[2148,60765,12859],{},[898,60767,2146],{},[1706,60769,2447],{},[2148,60771,51608],{},[902,60773,60774],{"encoding":904},"P = Q^2 + 14Q + 22",[724,60776,60777,60779],{},[38,60778,57022],{}," Z rovnosti",[883,60781,60783],{"className":60782},[886],[888,60784,60785],{"xmlns":890,"display":2350},[892,60786,60787,60825],{},[895,60788,60789,60791,60797,60799,60801,60803,60805,60807,60809,60815,60817,60819,60821,60823],{},[1706,60790,1715],{},[2489,60792,60793,60795],{},[898,60794,2146],{},[2148,60796,2495],{},[1706,60798,1715],{},[2148,60800,7786],{},[898,60802,2146],{},[1706,60804,2447],{},[2148,60806,27924],{},[1706,60808,1708],{},[2489,60810,60811,60813],{},[898,60812,2146],{},[2148,60814,2495],{},[1706,60816,2447],{},[2148,60818,12859],{},[898,60820,2146],{},[1706,60822,2447],{},[2148,60824,51608],{},[902,60826,60827],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,60829,60830,60831,2173,60865,60898,60899,60915,60916,60929,60930,1343,60952,60989,60990,1837],{},"dostaneme ",[883,60832,60834],{"className":60833},[886],[888,60835,60836],{"xmlns":890},[892,60837,60838,60862],{},[895,60839,60840,60842,60848,60850,60852,60854,60856,60858,60860],{},[2148,60841,2495],{},[2489,60843,60844,60846],{},[898,60845,2146],{},[2148,60847,2495],{},[1706,60849,2447],{},[2148,60851,12665],{},[898,60853,2146],{},[1706,60855,1715],{},[2148,60857,24756],{},[1706,60859,1708],{},[2148,60861,2150],{},[902,60863,60864],{"encoding":904},"2Q^2 + 24Q - 128 = 0",[883,60866,60868],{"className":60867},[886],[888,60869,60870],{"xmlns":890},[892,60871,60872,60895],{},[895,60873,60874,60880,60882,60884,60886,60888,60891,60893],{},[2489,60875,60876,60878],{},[898,60877,2146],{},[2148,60879,2495],{},[1706,60881,2447],{},[2148,60883,7156],{},[898,60885,2146],{},[1706,60887,1715],{},[2148,60889,60890],{},"64",[1706,60892,1708],{},[2148,60894,2150],{},[902,60896,60897],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,60900,60902],{"className":60901},[886],[888,60903,60904],{"xmlns":890},[892,60905,60906,60912],{},[895,60907,60908,60910],{},[1706,60909,1715],{},[2148,60911,3364],{},[902,60913,60914],{"encoding":904},"-16"," (nevyhovuje) a ",[883,60917,60919],{"className":60918},[886],[888,60920,60921],{"xmlns":890},[892,60922,60923,60927],{},[895,60924,60925],{},[2148,60926,3455],{},[902,60928,3455],{"encoding":904},". Tedy ",[883,60931,60933],{"className":60932},[886],[888,60934,60935],{"xmlns":890},[892,60936,60937,60949],{},[895,60938,60939,60945,60947],{},[2489,60940,60941,60943],{},[898,60942,2146],{},[898,60944,23410],{},[1706,60946,1708],{},[2148,60948,3455],{},[902,60950,60951],{"encoding":904},"Q^E = 4",[883,60953,60955],{"className":60954},[886],[888,60956,60957],{"xmlns":890},[892,60958,60959,60986],{},[895,60960,60961,60967,60969,60971,60973,60975,60977,60979,60981,60983],{},[2489,60962,60963,60965],{},[898,60964,1702],{},[898,60966,23410],{},[1706,60968,1708],{},[1706,60970,1715],{},[2148,60972,3364],{},[1706,60974,1715],{},[2148,60976,3508],{},[1706,60978,2447],{},[2148,60980,27924],{},[1706,60982,1708],{},[2148,60984,60985],{},"94",[902,60987,60988],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,60991,60993],{"className":60992},[886],[888,60994,60995],{"xmlns":890},[892,60996,60997,61011],{},[895,60998,60999,61001,61003,61005,61007,61009],{},[898,61000,23410],{},[1706,61002,21693],{"stretchy":2139},[2148,61004,3455],{},[1706,61006,2505],{"separator":2504},[2148,61008,60985],{},[1706,61010,21708],{"stretchy":2139},[902,61012,61013],{"encoding":904},"E[4, 94]",[198,61015,61017],{"id":61016},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,61019,61020,61022],{},[38,61021,56990],{}," Poptávky a nabídky dvou zboží",[883,61024,61026],{"className":61025},[886],[888,61027,61028],{"xmlns":890,"display":2350},[892,61029,61030,61196],{},[2354,61031,61034,61122],{"rowspacing":7556,"columnalign":61032,"columnspacing":61033},"right left right left","0em 1em 0em",[2358,61035,61036,61046,61078,61088],{},[2361,61037,61038],{},[4745,61039,61040],{"scriptlevel":2150,"displaystyle":2504},[2142,61041,61042,61044],{},[898,61043,2146],{},[2148,61045,2701],{},[2361,61047,61048],{},[4745,61049,61050],{"scriptlevel":2150,"displaystyle":2504},[895,61051,61052,61054,61056,61058,61060,61062,61068,61070,61076],{},[895,61053],{},[1706,61055,1708],{},[2148,61057,3508],{},[1706,61059,1715],{},[2148,61061,7524],{},[2142,61063,61064,61066],{},[898,61065,1702],{},[2148,61067,2701],{},[1706,61069,1715],{},[2142,61071,61072,61074],{},[898,61073,1702],{},[2148,61075,2495],{},[1706,61077,2505],{"separator":2504},[2361,61079,61080],{},[4745,61081,61082],{"scriptlevel":2150,"displaystyle":2504},[2142,61083,61084,61086],{},[898,61085,2146],{},[2148,61087,2495],{},[2361,61089,61090],{},[4745,61091,61092],{"scriptlevel":2150,"displaystyle":2504},[895,61093,61094,61096,61098,61100,61102,61104,61110,61112,61114,61120],{},[895,61095],{},[1706,61097,1708],{},[2148,61099,2728],{},[1706,61101,1715],{},[2148,61103,2495],{},[2142,61105,61106,61108],{},[898,61107,1702],{},[2148,61109,2701],{},[1706,61111,1715],{},[2148,61113,3455],{},[2142,61115,61116,61118],{},[898,61117,1702],{},[2148,61119,2495],{},[1706,61121,2505],{"separator":2504},[2358,61123,61124,61134,61160,61170],{},[2361,61125,61126],{},[4745,61127,61128],{"scriptlevel":2150,"displaystyle":2504},[2142,61129,61130,61132],{},[898,61131,2146],{},[2148,61133,2701],{},[2361,61135,61136],{},[4745,61137,61138],{"scriptlevel":2150,"displaystyle":2504},[895,61139,61140,61142,61144,61146,61148,61150,61152,61158],{},[895,61141],{},[1706,61143,1708],{},[1706,61145,1715],{},[2148,61147,4284],{},[1706,61149,2447],{},[2148,61151,3455],{},[2142,61153,61154,61156],{},[898,61155,1702],{},[2148,61157,2701],{},[1706,61159,2505],{"separator":2504},[2361,61161,61162],{},[4745,61163,61164],{"scriptlevel":2150,"displaystyle":2504},[2142,61165,61166,61168],{},[898,61167,2146],{},[2148,61169,2495],{},[2361,61171,61172],{},[4745,61173,61174],{"scriptlevel":2150,"displaystyle":2504},[895,61175,61176,61178,61180,61182,61184,61186,61188,61194],{},[895,61177],{},[1706,61179,1708],{},[1706,61181,1715],{},[2148,61183,12597],{},[1706,61185,2447],{},[2148,61187,4284],{},[2142,61189,61190,61192],{},[898,61191,1702],{},[2148,61193,2495],{},[898,61195,1837],{"mathvariant":2409},[902,61197,61198],{"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}",[724,61200,61201,61203],{},[38,61202,57022],{}," Z rovností poptávek a nabídek dostaneme",[883,61205,61207],{"className":61206},[886],[888,61208,61209],{"xmlns":890,"display":2350},[892,61210,61211,61260],{},[895,61212,61213,61215,61221,61223,61229,61231,61233,61235,61237,61239,61245,61247,61249,61255,61257],{},[2148,61214,10800],{},[2142,61216,61217,61219],{},[898,61218,1702],{},[2148,61220,2701],{},[1706,61222,2447],{},[2142,61224,61225,61227],{},[898,61226,1702],{},[2148,61228,2495],{},[1706,61230,1708],{},[2148,61232,40287],{},[1706,61234,2505],{"separator":2504},[4898,61236],{"width":9524},[2148,61238,2495],{},[2142,61240,61241,61243],{},[898,61242,1702],{},[2148,61244,2701],{},[1706,61246,2447],{},[2148,61248,12597],{},[2142,61250,61251,61253],{},[898,61252,1702],{},[2148,61254,2495],{},[1706,61256,1708],{},[2148,61258,61259],{},"57.",[902,61261,61262],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,61264,61265,61266,1343,61290,61314,61315,1343,61340,61364,61365,61367],{},"Řešením je ",[883,61267,61269],{"className":61268},[886],[888,61270,61271],{"xmlns":890},[892,61272,61273,61287],{},[895,61274,61275,61283,61285],{},[28285,61276,61277,61279,61281],{},[898,61278,1702],{},[2148,61280,2701],{},[898,61282,23410],{},[1706,61284,1708],{},[2148,61286,3455],{},[902,61288,61289],{"encoding":904},"P_1^E = 4",[883,61291,61293],{"className":61292},[886],[888,61294,61295],{"xmlns":890},[892,61296,61297,61311],{},[895,61298,61299,61307,61309],{},[28285,61300,61301,61303,61305],{},[898,61302,1702],{},[2148,61304,2495],{},[898,61306,23410],{},[1706,61308,1708],{},[2148,61310,12597],{},[902,61312,61313],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,61316,61318],{"className":61317},[886],[888,61319,61320],{"xmlns":890},[892,61321,61322,61337],{},[895,61323,61324,61332,61334],{},[28285,61325,61326,61328,61330],{},[898,61327,2146],{},[2148,61329,2701],{},[898,61331,23410],{},[1706,61333,1708],{},[2148,61335,61336],{},"13",[902,61338,61339],{"encoding":904},"Q_1^E = 13",[883,61341,61343],{"className":61342},[886],[888,61344,61345],{"xmlns":890},[892,61346,61347,61361],{},[895,61348,61349,61357,61359],{},[28285,61350,61351,61353,61355],{},[898,61352,2146],{},[2148,61354,2495],{},[898,61356,23410],{},[1706,61358,1708],{},[2148,61360,12859],{},[902,61362,61363],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,61366,58877],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,61369,61371],{"id":61370},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,61373,61374,61375,61392,61393,2314,61396,1936],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,61376,61378],{"className":61377},[886],[888,61379,61380],{"xmlns":890},[892,61381,61382,61390],{},[895,61383,61384],{},[2489,61385,61386,61388],{},[898,61387,1702],{},[898,61389,23410],{},[902,61391,60519],{"encoding":904},"; mechanismus popisuje ",[38,61394,61395],{},"teorém pavučiny",[614,61397,61398],{},"cobweb model",[198,61400,61402],{"id":61401},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,61404,61405],{},[2286,61406],{"alt":61407,"className":61408,"src":61409},"imek-komparativni-statika-4pripady",[210,2290],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[1636,61411,61412,61453,61493,61533],{},[724,61413,61414,61417,61418,8156,61435,1837],{},[38,61415,61416],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,61419,61421],{"className":61420},[886],[888,61422,61423],{"xmlns":890},[892,61424,61425,61433],{},[895,61426,61427],{},[2489,61428,61429,61431],{},[898,61430,1702],{},[898,61432,23410],{},[902,61434,60519],{"encoding":904},[883,61436,61438],{"className":61437},[886],[888,61439,61440],{"xmlns":890},[892,61441,61442,61450],{},[895,61443,61444],{},[2489,61445,61446,61448],{},[898,61447,2146],{},[898,61449,23410],{},[902,61451,61452],{"encoding":904},"Q^E",[724,61454,61455,61458,61459,8156,61476,1837],{},[38,61456,61457],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,61460,61462],{"className":61461},[886],[888,61463,61464],{"xmlns":890},[892,61465,61466,61474],{},[895,61467,61468],{},[2489,61469,61470,61472],{},[898,61471,1702],{},[898,61473,23410],{},[902,61475,60519],{"encoding":904},[883,61477,61479],{"className":61478},[886],[888,61480,61481],{"xmlns":890},[892,61482,61483,61491],{},[895,61484,61485],{},[2489,61486,61487,61489],{},[898,61488,2146],{},[898,61490,23410],{},[902,61492,61452],{"encoding":904},[724,61494,61495,61498,61499,28474,61516,1837],{},[38,61496,61497],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,61500,61502],{"className":61501},[886],[888,61503,61504],{"xmlns":890},[892,61505,61506,61514],{},[895,61507,61508],{},[2489,61509,61510,61512],{},[898,61511,1702],{},[898,61513,23410],{},[902,61515,60519],{"encoding":904},[883,61517,61519],{"className":61518},[886],[888,61520,61521],{"xmlns":890},[892,61522,61523,61531],{},[895,61524,61525],{},[2489,61526,61527,61529],{},[898,61528,2146],{},[898,61530,23410],{},[902,61532,61452],{"encoding":904},[724,61534,61535,61538,61539,61556,61557,1837],{},[38,61536,61537],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,61540,61542],{"className":61541},[886],[888,61543,61544],{"xmlns":890},[892,61545,61546,61554],{},[895,61547,61548],{},[2489,61549,61550,61552],{},[898,61551,1702],{},[898,61553,23410],{},[902,61555,60519],{"encoding":904},", pokles ",[883,61558,61560],{"className":61559},[886],[888,61561,61562],{"xmlns":890},[892,61563,61564,61572],{},[895,61565,61566],{},[2489,61567,61568,61570],{},[898,61569,2146],{},[898,61571,23410],{},[902,61573,61452],{"encoding":904},[16,61575,61576,61621],{},[19,61577,61578],{},[22,61579,61580,61583,61602],{},[25,61581,61582],{},"Změna",[25,61584,61585],{},[883,61586,61588],{"className":61587},[886],[888,61589,61590],{"xmlns":890},[892,61591,61592,61600],{},[895,61593,61594],{},[2489,61595,61596,61598],{},[898,61597,1702],{},[898,61599,23410],{},[902,61601,60519],{"encoding":904},[25,61603,61604],{},[883,61605,61607],{"className":61606},[886],[888,61608,61609],{"xmlns":890},[892,61610,61611,61619],{},[895,61612,61613],{},[2489,61614,61615,61617],{},[898,61616,2146],{},[898,61618,23410],{},[902,61620,61452],{"encoding":904},[30,61622,61623,61633,61643,61652],{},[22,61624,61625,61628,61631],{},[35,61626,61627],{},"Růst poptávky",[35,61629,61630],{},"↑",[35,61632,61630],{},[22,61634,61635,61638,61641],{},[35,61636,61637],{},"Pokles poptávky",[35,61639,61640],{},"↓",[35,61642,61640],{},[22,61644,61645,61648,61650],{},[35,61646,61647],{},"Růst nabídky",[35,61649,61640],{},[35,61651,61630],{},[22,61653,61654,61657,61659],{},[35,61655,61656],{},"Pokles nabídky",[35,61658,61630],{},[35,61660,61640],{},[724,61662,61663],{},[614,61664,61665],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[56029,61667],{},[115,61669,811],{"id":61670},"zdanění-trhu",[1636,61672,61673,61762],{},[724,61674,61675,61677,61678,61691,61692,3787,61705,61708,61709,55836,61732,61757,61758,61761],{},[883,61676,3174],{}," TL;DR\nJednotková daň ",[883,61679,61681],{"className":61680},[886],[888,61682,61683],{"xmlns":890},[892,61684,61685,61689],{},[895,61686,61687],{},[898,61688,1659],{},[902,61690,1659],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,61693,61695],{"className":61694},[886],[888,61696,61697],{"xmlns":890},[892,61698,61699,61703],{},[895,61700,61701],{},[898,61702,1659],{},[902,61704,1659],{"encoding":904},[38,61706,61707],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,61710,61712],{"className":61711},[886],[888,61713,61714],{"xmlns":890},[892,61715,61716,61729],{},[895,61717,61718],{},[2142,61719,61720,61722],{},[898,61721,1659],{},[895,61723,61724,61727],{},[898,61725,61726],{},"s",[898,61728,724],{},[902,61730,61731],{"encoding":904},"T_{sp}",[883,61733,61735],{"className":61734},[886],[888,61736,61737],{"xmlns":890},[892,61738,61739,61754],{},[895,61740,61741],{},[2142,61742,61743,61745],{},[898,61744,1659],{},[895,61746,61747,61750,61752],{},[898,61748,61749],{},"v",[898,61751,6930],{},[898,61753,3950],{},[902,61755,61756],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,61759,61760],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,61763,61764],{},[614,61765,61766,61767,1837],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,61768,61770],{"className":61769,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,61772,61773,61774,61777,61778,61804,61805,61808,61809,61835,61836,61853,61854,61894,61895,1993,61908,1837],{},"Existují dvě formy zdanění — daň uložená ",[38,61775,61776],{},"výrobci"," (posun nabídky ",[883,61779,61781],{"className":61780},[886],[888,61782,61783],{"xmlns":890},[892,61784,61785,61801],{},[895,61786,61787,61793,61795,61797,61799],{},[2142,61788,61789,61791],{},[898,61790,14171],{},[2148,61792,2701],{},[1706,61794,1708],{},[898,61796,14171],{},[1706,61798,2447],{},[898,61800,1659],{},[902,61802,61803],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,61806,61807],{},"spotřebiteli"," (posun poptávky ",[883,61810,61812],{"className":61811},[886],[888,61813,61814],{"xmlns":890},[892,61815,61816,61832],{},[895,61817,61818,61824,61826,61828,61830],{},[2142,61819,61820,61822],{},[898,61821,2334],{},[2148,61823,2495],{},[1706,61825,1708],{},[898,61827,2334],{},[1706,61829,1715],{},[898,61831,1659],{},[902,61833,61834],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,61837,61839],{"className":61838},[886],[888,61840,61841],{"xmlns":890},[892,61842,61843,61851],{},[895,61844,61845],{},[2489,61846,61847,61849],{},[898,61848,2146],{},[898,61850,23410],{},[902,61852,61452],{"encoding":904}," klesá a vzniká rozklad daně ",[883,61855,61857],{"className":61856},[886],[888,61858,61859],{"xmlns":890},[892,61860,61861,61891],{},[895,61862,61863,61865,61867,61877,61879],{},[898,61864,1659],{},[1706,61866,1708],{},[2142,61868,61869,61871],{},[898,61870,1659],{},[895,61872,61873,61875],{},[898,61874,61726],{},[898,61876,724],{},[1706,61878,2447],{},[2142,61880,61881,61883],{},[898,61882,1659],{},[895,61884,61885,61887,61889],{},[898,61886,61749],{},[898,61888,6930],{},[898,61890,3950],{},[902,61892,61893],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,61896,61898],{"className":61897},[886],[888,61899,61900],{"xmlns":890},[892,61901,61902,61906],{},[895,61903,61904],{},[898,61905,2334],{},[902,61907,2334],{"encoding":904},[883,61909,61911],{"className":61910},[886],[888,61912,61913],{"xmlns":890},[892,61914,61915,61919],{},[895,61916,61917],{},[898,61918,14171],{},[902,61920,14171],{"encoding":904},[724,61922,61923,61924,61927,61928,1993,61958,61992],{},"Zásadním výsledkem kapitoly je ",[38,61925,61926],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,61929,61931],{"className":61930},[886],[888,61932,61933],{"xmlns":890},[892,61934,61935,61955],{},[895,61936,61937,61945,61947],{},[28285,61938,61939,61941,61943],{},[898,61940,2146],{},[2148,61942,2701],{},[898,61944,23410],{},[1706,61946,1708],{},[28285,61948,61949,61951,61953],{},[898,61950,2146],{},[2148,61952,2495],{},[898,61954,23410],{},[902,61956,61957],{"encoding":904},"Q_1^E = Q_2^E",[883,61959,61961],{"className":61960},[886],[888,61962,61963],{"xmlns":890},[892,61964,61965,61989],{},[895,61966,61967,61975,61977,61979,61981],{},[28285,61968,61969,61971,61973],{},[898,61970,1702],{},[2148,61972,2701],{},[898,61974,23410],{},[1706,61976,1715],{},[898,61978,1659],{},[1706,61980,1708],{},[28285,61982,61983,61985,61987],{},[898,61984,1702],{},[2148,61986,2495],{},[898,61988,23410],{},[902,61990,61991],{"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.",[724,61994,61995,61996,61999,62000,62026,62027,62055,62056,62059,62060,62063,62064,1837],{},"Podrobný výklad, Příklady ",[38,61997,61998],{},"2.9"," (daň výrobci, ",[883,62001,62003],{"className":62002},[886],[888,62004,62005],{"xmlns":890},[892,62006,62007,62023],{},[895,62008,62009,62019,62021],{},[2142,62010,62011,62013],{},[898,62012,1659],{},[895,62014,62015,62017],{},[898,62016,61726],{},[898,62018,724],{},[1706,62020,1708],{},[2148,62022,2495],{},[902,62024,62025],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,62028,62030],{"className":62029},[886],[888,62031,62032],{"xmlns":890},[892,62033,62034,62052],{},[895,62035,62036,62048,62050],{},[2142,62037,62038,62040],{},[898,62039,1659],{},[895,62041,62042,62044,62046],{},[898,62043,61749],{},[898,62045,6930],{},[898,62047,3950],{},[1706,62049,1708],{},[2148,62051,3455],{},[902,62053,62054],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,62057,62058],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,62061,62062],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,62065,61770],{"className":62066,"dataFsResolvedFilePath":809,"href":810},[210],[56029,62068],{},[115,62070,62072],{"id":62071},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[1636,62074,62075],{},[724,62076,62077,62079,62080,62083,62084,62086],{},[883,62078,3174],{}," TL;DR\nMultiplikátory jsou ",[38,62081,62082],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,62085,56019],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,62088,62090],{"id":62089},"redukovaný-tvar","Redukovaný tvar",[724,62092,62093,62094,2314,62117,1343,62134,5354,62151,2314,62174,62191,62192,62222],{},"Pro lineární model ",[883,62095,62097],{"className":62096},[886],[888,62098,62099],{"xmlns":890},[892,62100,62101,62115],{},[895,62102,62103,62105,62107,62109,62111,62113],{},[898,62104,1702],{},[1706,62106,1708],{},[898,62108,207],{},[898,62110,2146],{},[1706,62112,2447],{},[898,62114,2450],{},[902,62116,2453],{"encoding":904},[883,62118,62120],{"className":62119},[886],[888,62121,62122],{"xmlns":890},[892,62123,62124,62132],{},[895,62125,62126,62128,62130],{},[898,62127,207],{},[1706,62129,2539],{},[2148,62131,2150],{},[902,62133,2544],{"encoding":904},[883,62135,62137],{"className":62136},[886],[888,62138,62139],{"xmlns":890},[892,62140,62141,62149],{},[895,62142,62143,62145,62147],{},[898,62144,2450],{},[1706,62146,8922],{},[2148,62148,2150],{},[902,62150,37911],{"encoding":904},[883,62152,62154],{"className":62153},[886],[888,62155,62156],{"xmlns":890},[892,62157,62158,62172],{},[895,62159,62160,62162,62164,62166,62168,62170],{},[898,62161,1702],{},[1706,62163,1708],{},[898,62165,20413],{},[898,62167,2146],{},[1706,62169,2447],{},[898,62171,3120],{},[902,62173,59296],{"encoding":904},[883,62175,62177],{"className":62176},[886],[888,62178,62179],{"xmlns":890},[892,62180,62181,62189],{},[895,62182,62183,62185,62187],{},[898,62184,20413],{},[1706,62186,8922],{},[2148,62188,2150],{},[902,62190,59314],{"encoding":904},") dává podmínka rovnováhy ",[883,62193,62195],{"className":62194},[886],[888,62196,62197],{"xmlns":890},[892,62198,62199,62219],{},[895,62200,62201,62203,62205,62207,62209,62211,62213,62215,62217],{},[898,62202,207],{},[898,62204,2146],{},[1706,62206,2447],{},[898,62208,2450],{},[1706,62210,1708],{},[898,62212,20413],{},[898,62214,2146],{},[1706,62216,2447],{},[898,62218,3120],{},[902,62220,62221],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,62224,62226],{"className":62225},[886],[888,62227,62228],{"xmlns":890,"display":2350},[892,62229,62230,62275],{},[2354,62231,62232],{"width":2356},[2358,62233,62234,62236,62268,62270],{},[2361,62235],{"width":2363},[2361,62237,62238],{},[895,62239,62240,62246,62248,62266],{},[2489,62241,62242,62244],{},[898,62243,2146],{},[898,62245,23410],{},[1706,62247,1708],{},[2964,62249,62250,62258],{},[895,62251,62252,62254,62256],{},[898,62253,2450],{},[1706,62255,1715],{},[898,62257,3120],{},[895,62259,62260,62262,62264],{},[898,62261,20413],{},[1706,62263,1715],{},[898,62265,207],{},[898,62267,1837],{"mathvariant":2409},[2361,62269],{"width":2363},[2361,62271,62272],{},[2415,62273,62274],{},"(2.10)",[902,62276,62277],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,62279,62280,62281,2314,62283,62286,62287,62304,62305,1647,62308,62334,62335,62348,62349,62367,62368,1936],{},"Vztah (2.10) je ",[38,62282,40039],{},[614,62284,62285],{},"reduced form",") pro ",[883,62288,62290],{"className":62289},[886],[888,62291,62292],{"xmlns":890},[892,62293,62294,62302],{},[895,62295,62296],{},[2489,62297,62298,62300],{},[898,62299,2146],{},[898,62301,23410],{},[902,62303,61452],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,62306,62307],{},"parametrů",[883,62309,62311],{"className":62310},[886],[888,62312,62313],{"xmlns":890},[892,62314,62315,62331],{},[895,62316,62317,62319,62321,62323,62325,62327,62329],{},[898,62318,207],{},[1706,62320,2505],{"separator":2504},[898,62322,2450],{},[1706,62324,2505],{"separator":2504},[898,62326,20413],{},[1706,62328,2505],{"separator":2504},[898,62330,3120],{},[902,62332,62333],{"encoding":904},"a, b, c, d",". Aby ",[883,62336,62338],{"className":62337},[886],[888,62339,62340],{"xmlns":890},[892,62341,62342,62346],{},[895,62343,62344],{},[898,62345,23410],{},[902,62347,23410],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,62350,62352],{"className":62351},[886],[888,62353,62354],{"xmlns":890},[892,62355,62356,62364],{},[895,62357,62358,62360,62362],{},[898,62359,2450],{},[1706,62361,8922],{},[898,62363,3120],{},[902,62365,62366],{"encoding":904},"b > d"," (neboť ",[883,62369,62371],{"className":62370},[886],[888,62372,62373],{"xmlns":890},[892,62374,62375,62387],{},[895,62376,62377,62379,62381,62383,62385],{},[898,62378,20413],{},[1706,62380,1715],{},[898,62382,207],{},[1706,62384,8922],{},[2148,62386,2150],{},[902,62388,62389],{"encoding":904},"c - a > 0",[724,62391,62392],{},[614,62393,62394,62395,10590,62408,62421,62422,37745,62435,60989,62452,62465],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,62396,62398],{"className":62397},[886],[888,62399,62400],{"xmlns":890},[892,62401,62402,62406],{},[895,62403,62404],{},[898,62405,2450],{},[902,62407,2450],{"encoding":904},[883,62409,62411],{"className":62410},[886],[888,62412,62413],{"xmlns":890},[892,62414,62415,62419],{},[895,62416,62417],{},[898,62418,1702],{},[902,62420,1702],{"encoding":904},") a nabídka (úsek ",[883,62423,62425],{"className":62424},[886],[888,62426,62427],{"xmlns":890},[892,62428,62429,62433],{},[895,62430,62431],{},[898,62432,3120],{},[902,62434,3120],{"encoding":904},[883,62436,62438],{"className":62437},[886],[888,62439,62440],{"xmlns":890},[892,62441,62442,62450],{},[895,62443,62444,62446,62448],{},[898,62445,2450],{},[1706,62447,8922],{},[898,62449,3120],{},[902,62451,62366],{"encoding":904},[883,62453,62455],{"className":62454},[886],[888,62456,62457],{"xmlns":890},[892,62458,62459,62463],{},[895,62460,62461],{},[898,62462,23410],{},[902,62464,23410],{"encoding":904}," v 1. kvadrantu.",[198,62467,62469],{"id":62468},"definice-multiplikátorů","Definice multiplikátorů",[724,62471,62472,62473,62498,62499,62512,62513,62526],{},"V komparativní statice jsou ",[883,62474,62476],{"className":62475},[886],[888,62477,62478],{"xmlns":890},[892,62479,62480,62496],{},[895,62481,62482,62484,62486,62488,62490,62492,62494],{},[898,62483,207],{},[1706,62485,2505],{"separator":2504},[898,62487,2450],{},[1706,62489,2505],{"separator":2504},[898,62491,20413],{},[1706,62493,2505],{"separator":2504},[898,62495,3120],{},[902,62497,62333],{"encoding":904}," exogenní proměnné a ",[883,62500,62502],{"className":62501},[886],[888,62503,62504],{"xmlns":890},[892,62505,62506,62510],{},[895,62507,62508],{},[898,62509,2146],{},[902,62511,2146],{"encoding":904}," endogenní. Přibližná změna ",[883,62514,62516],{"className":62515},[886],[888,62517,62518],{"xmlns":890},[892,62519,62520,62524],{},[895,62521,62522],{},[898,62523,2146],{},[902,62525,2146],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,62528,62530],{"className":62529},[886],[888,62531,62532],{"xmlns":890,"display":2350},[892,62533,62534,62627],{},[2354,62535,62536],{"width":2356},[2358,62537,62538,62540,62620,62622],{},[2361,62539],{"width":2363},[2361,62541,62542],{},[895,62543,62544,62546,62548,62550,62552,62554,62556,62564,62566,62568,62570,62572,62580,62582,62584,62586,62588,62596,62598,62600,62602,62604,62612,62614,62616,62618],{},[898,62545,3677],{"mathvariant":2409},[898,62547,2146],{},[1706,62549,3248],{},[898,62551,3120],{},[898,62553,2146],{},[1706,62555,1708],{},[28285,62557,62558,62560,62562],{},[898,62559,2146],{},[898,62561,207],{},[1706,62563,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2415,62565,2799],{},[898,62567,3120],{},[898,62569,207],{},[1706,62571,2447],{},[28285,62573,62574,62576,62578],{},[898,62575,2146],{},[898,62577,2450],{},[1706,62579,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2415,62581,2799],{},[898,62583,3120],{},[898,62585,2450],{},[1706,62587,2447],{},[28285,62589,62590,62592,62594],{},[898,62591,2146],{},[898,62593,20413],{},[1706,62595,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2415,62597,2799],{},[898,62599,3120],{},[898,62601,20413],{},[1706,62603,2447],{},[28285,62605,62606,62608,62610],{},[898,62607,2146],{},[898,62609,3120],{},[1706,62611,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2415,62613,2799],{},[898,62615,3120],{},[898,62617,3120],{},[898,62619,1837],{"mathvariant":2409},[2361,62621],{"width":2363},[2361,62623,62624],{},[2415,62625,62626],{},"(2.11)",[902,62628,62629],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,62631,62632,62633,10234,62683,2314,62685,5606],{},"Parciální derivace ",[883,62634,62636],{"className":62635},[886],[888,62637,62638],{"xmlns":890},[892,62639,62640,62680],{},[895,62641,62642,62650,62652,62660,62662,62670,62672],{},[28285,62643,62644,62646,62648],{},[898,62645,2146],{},[898,62647,207],{},[1706,62649,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,62651,2505],{"separator":2504},[28285,62653,62654,62656,62658],{},[898,62655,2146],{},[898,62657,2450],{},[1706,62659,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,62661,2505],{"separator":2504},[28285,62663,62664,62666,62668],{},[898,62665,2146],{},[898,62667,20413],{},[1706,62669,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,62671,2505],{"separator":2504},[28285,62673,62674,62676,62678],{},[898,62675,2146],{},[898,62677,3120],{},[1706,62679,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,62681,62682],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d",[38,62684,37074],{},[614,62686,62687],{},"multipliers",[883,62689,62691],{"className":62690},[886],[888,62692,62693],{"xmlns":890,"display":2350},[892,62694,62695,62846],{},[2354,62696,62697],{"width":2356},[2358,62698,62699,62701,62839,62841],{},[2361,62700],{"width":2363},[2361,62702,62703],{},[895,62704,62705,62713,62715,62741,62743,62745,62753,62755,62767,62769,62771,62779,62781,62783,62809,62811,62813,62821,62823,62825,62837],{},[28285,62706,62707,62709,62711],{},[898,62708,2146],{},[898,62710,207],{},[1706,62712,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,62714,1708],{},[2964,62716,62717,62725],{},[895,62718,62719,62721,62723],{},[898,62720,2450],{},[1706,62722,1715],{},[898,62724,3120],{},[895,62726,62727,62729,62731,62733,62735],{},[1706,62728,2140],{"stretchy":2139},[898,62730,20413],{},[1706,62732,1715],{},[898,62734,207],{},[2489,62736,62737,62739],{},[1706,62738,2153],{"stretchy":2139},[2148,62740,2495],{},[1706,62742,2505],{"separator":2504},[4898,62744],{"width":4900},[28285,62746,62747,62749,62751],{},[898,62748,2146],{},[898,62750,2450],{},[1706,62752,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,62754,1708],{},[2964,62756,62757,62759],{},[2148,62758,2701],{},[895,62760,62761,62763,62765],{},[898,62762,20413],{},[1706,62764,1715],{},[898,62766,207],{},[1706,62768,2505],{"separator":2504},[4898,62770],{"width":4900},[28285,62772,62773,62775,62777],{},[898,62774,2146],{},[898,62776,20413],{},[1706,62778,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,62780,1708],{},[1706,62782,1715],{},[2964,62784,62785,62793],{},[895,62786,62787,62789,62791],{},[898,62788,2450],{},[1706,62790,1715],{},[898,62792,3120],{},[895,62794,62795,62797,62799,62801,62803],{},[1706,62796,2140],{"stretchy":2139},[898,62798,20413],{},[1706,62800,1715],{},[898,62802,207],{},[2489,62804,62805,62807],{},[1706,62806,2153],{"stretchy":2139},[2148,62808,2495],{},[1706,62810,2505],{"separator":2504},[4898,62812],{"width":4900},[28285,62814,62815,62817,62819],{},[898,62816,2146],{},[898,62818,3120],{},[1706,62820,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,62822,1708],{},[1706,62824,1715],{},[2964,62826,62827,62829],{},[2148,62828,2701],{},[895,62830,62831,62833,62835],{},[898,62832,20413],{},[1706,62834,1715],{},[898,62836,207],{},[898,62838,1837],{"mathvariant":2409},[2361,62840],{"width":2363},[2361,62842,62843],{},[2415,62844,62845],{},"(2.12)",[902,62847,62848],{"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}",[198,62850,62852],{"id":62851},"znaménka-a-interpretace","Znaménka a interpretace",[724,62854,62855,62856,1343,62873,1343,62890,1343,62907,62924,62925,5606],{},"Za podmínek ",[883,62857,62859],{"className":62858},[886],[888,62860,62861],{"xmlns":890},[892,62862,62863,62871],{},[895,62864,62865,62867,62869],{},[898,62866,207],{},[1706,62868,2539],{},[2148,62870,2150],{},[902,62872,2544],{"encoding":904},[883,62874,62876],{"className":62875},[886],[888,62877,62878],{"xmlns":890},[892,62879,62880,62888],{},[895,62881,62882,62884,62886],{},[898,62883,2450],{},[1706,62885,8922],{},[2148,62887,2150],{},[902,62889,37911],{"encoding":904},[883,62891,62893],{"className":62892},[886],[888,62894,62895],{"xmlns":890},[892,62896,62897,62905],{},[895,62898,62899,62901,62903],{},[898,62900,20413],{},[1706,62902,8922],{},[2148,62904,2150],{},[902,62906,59314],{"encoding":904},[883,62908,62910],{"className":62909},[886],[888,62911,62912],{"xmlns":890},[892,62913,62914,62922],{},[895,62915,62916,62918,62920],{},[898,62917,2450],{},[1706,62919,8922],{},[898,62921,3120],{},[902,62923,62366],{"encoding":904}," platí (znaménka se ",[38,62926,62927],{},"nemění",[883,62929,62931],{"className":62930},[886],[888,62932,62933],{"xmlns":890,"display":2350},[892,62934,62935,62997],{},[895,62936,62937,62945,62947,62949,62951,62953,62961,62963,62965,62967,62969,62977,62979,62981,62983,62985,62993,62995],{},[28285,62938,62939,62941,62943],{},[898,62940,2146],{},[898,62942,207],{},[1706,62944,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,62946,8922],{},[2148,62948,2150],{},[1706,62950,2505],{"separator":2504},[4898,62952],{"width":9524},[28285,62954,62955,62957,62959],{},[898,62956,2146],{},[898,62958,2450],{},[1706,62960,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,62962,8922],{},[2148,62964,2150],{},[1706,62966,2505],{"separator":2504},[4898,62968],{"width":9524},[28285,62970,62971,62973,62975],{},[898,62972,2146],{},[898,62974,20413],{},[1706,62976,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,62978,2539],{},[2148,62980,2150],{},[1706,62982,2505],{"separator":2504},[4898,62984],{"width":9524},[28285,62986,62987,62989,62991],{},[898,62988,2146],{},[898,62990,3120],{},[1706,62992,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,62994,2539],{},[2148,62996,31567],{},[902,62998,62999],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,63001,63002,63061],{},[123,63003,63004,1647,63007,63027,63028,63045,63046,1343,63059,1837],{},[38,63005,63006],{},"Kvantitativní smysl:",[883,63008,63010],{"className":63009},[886],[888,63011,63012],{"xmlns":890},[892,63013,63014,63024],{},[895,63015,63016],{},[28285,63017,63018,63020,63022],{},[898,63019,2146],{},[898,63021,18300],{},[1706,63023,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,63025,63026],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,63029,63031],{"className":63030},[886],[888,63032,63033],{"xmlns":890},[892,63034,63035,63043],{},[895,63036,63037],{},[2489,63038,63039,63041],{},[898,63040,2146],{},[898,63042,23410],{},[902,63044,61452],{"encoding":904}," při jednotkové změně parametru ",[883,63047,63049],{"className":63048},[886],[888,63050,63051],{"xmlns":890},[892,63052,63053,63057],{},[895,63054,63055],{},[898,63056,18300],{},[902,63058,18300],{"encoding":904},[614,63060,56019],{},[123,63062,63063,63066,63067,63084,63085,1837],{},[38,63064,63065],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,63068,63070],{"className":63069},[886],[888,63071,63072],{"xmlns":890},[892,63073,63074,63082],{},[895,63075,63076],{},[2489,63077,63078,63080],{},[898,63079,2146],{},[898,63081,23410],{},[902,63083,61452],{"encoding":904}," na růst ",[883,63086,63088],{"className":63087},[886],[888,63089,63090],{"xmlns":890},[892,63091,63092,63096],{},[895,63093,63094],{},[898,63095,18300],{},[902,63097,18300],{"encoding":904},[724,63099,63100,63101,63114,63115,62367,63132,1936],{},"Např. růst ",[883,63102,63104],{"className":63103},[886],[888,63105,63106],{"xmlns":890},[892,63107,63108,63112],{},[895,63109,63110],{},[898,63111,20413],{},[902,63113,20413],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,63116,63118],{"className":63117},[886],[888,63119,63120],{"xmlns":890},[892,63121,63122,63130],{},[895,63123,63124],{},[2489,63125,63126,63128],{},[898,63127,2146],{},[898,63129,23410],{},[902,63131,61452],{"encoding":904},[883,63133,63135],{"className":63134},[886],[888,63136,63137],{"xmlns":890},[892,63138,63139,63153],{},[895,63140,63141,63149,63151],{},[28285,63142,63143,63145,63147],{},[898,63144,2146],{},[898,63146,20413],{},[1706,63148,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,63150,2539],{},[2148,63152,2150],{},[902,63154,63155],{"encoding":904},"Q'_c \u003C 0",[724,63157,63158],{},[614,63159,63160,63161,63181,63182,63206,63207,63229,63230,1837],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,63162,63164],{"className":63163},[886],[888,63165,63166],{"xmlns":890},[892,63167,63168,63178],{},[895,63169,63170,63172,63174,63176],{},[898,63171,20413],{},[898,63173,2146],{},[1706,63175,2447],{},[898,63177,3120],{},[902,63179,63180],{"encoding":904},"cQ + d"," na strmější ",[883,63183,63185],{"className":63184},[886],[888,63186,63187],{"xmlns":890},[892,63188,63189,63203],{},[895,63190,63191,63197,63199,63201],{},[2142,63192,63193,63195],{},[898,63194,20413],{},[2148,63196,2701],{},[898,63198,2146],{},[1706,63200,2447],{},[898,63202,3120],{},[902,63204,63205],{"encoding":904},"c_1 Q + d"," (při ",[883,63208,63210],{"className":63209},[886],[888,63211,63212],{"xmlns":890},[892,63213,63214,63226],{},[895,63215,63216,63222,63224],{},[2142,63217,63218,63220],{},[898,63219,20413],{},[2148,63221,2701],{},[1706,63223,8922],{},[898,63225,20413],{},[902,63227,63228],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,63231,63233],{"className":63232},[886],[888,63234,63235],{"xmlns":890},[892,63236,63237,63247],{},[895,63238,63239,63245],{},[2489,63240,63241,63243],{},[898,63242,2146],{},[898,63244,23410],{},[1706,63246,61640],{},[902,63248,63249],{"encoding":904},"Q^E \\downarrow",[724,63251,63252,63253,63285,63286,1837],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,63254,63256],{"className":63255},[886],[888,63257,63258],{"xmlns":890},[892,63259,63260,63282],{},[895,63261,63262,63264,63266,63268,63276,63278,63280],{},[898,63263,3677],{"mathvariant":2409},[898,63265,2146],{},[1706,63267,3248],{},[28285,63269,63270,63272,63274],{},[898,63271,2146],{},[898,63273,2450],{},[1706,63275,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2415,63277,2799],{},[898,63279,3120],{},[898,63281,2450],{},[902,63283,63284],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,63287,63289],{"className":63288},[886],[888,63290,63291],{"xmlns":890},[892,63292,63293,63301],{},[895,63294,63295],{},[2489,63296,63297,63299],{},[898,63298,1702],{},[898,63300,23410],{},[902,63302,60519],{"encoding":904},[198,63304,63306,63307],{"id":63305},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,63308,63310],{"className":63309},[886],[888,63311,63312],{"xmlns":890},[892,63313,63314,63322],{},[895,63315,63316],{},[2489,63317,63318,63320],{},[898,63319,2146],{},[898,63321,23410],{},[902,63323,61452],{"encoding":904},[724,63325,63326,60707,63328,60742,63354,1837],{},[38,63327,56990],{},[883,63329,63331],{"className":63330},[886],[888,63332,63333],{"xmlns":890},[892,63334,63335,63351],{},[895,63336,63337,63339,63341,63343,63345,63347,63349],{},[898,63338,1702],{},[1706,63340,1708],{},[1706,63342,1715],{},[2148,63344,4284],{},[898,63346,2146],{},[1706,63348,2447],{},[2148,63350,3508],{},[902,63352,63353],{"encoding":904},"P = -3Q + 40",[883,63355,63357],{"className":63356},[886],[888,63358,63359],{"xmlns":890},[892,63360,63361,63375],{},[895,63362,63363,63365,63367,63369,63371,63373],{},[898,63364,1702],{},[1706,63366,1708],{},[2148,63368,11496],{},[898,63370,2146],{},[1706,63372,2447],{},[2148,63374,7786],{},[902,63376,63377],{"encoding":904},"P = 0{,}5Q + 10",[724,63379,63380,63382],{},[38,63381,57022],{}," Rovnovážné množství",[883,63384,63386],{"className":63385},[886],[888,63387,63388],{"xmlns":890,"display":2350},[892,63389,63390,63458],{},[895,63391,63392,63398,63400,63418,63420,63444,63446,63453,63455],{},[2489,63393,63394,63396],{},[898,63395,2146],{},[898,63397,23410],{},[1706,63399,1708],{},[2964,63401,63402,63410],{},[895,63403,63404,63406,63408],{},[898,63405,2450],{},[1706,63407,1715],{},[898,63409,3120],{},[895,63411,63412,63414,63416],{},[898,63413,20413],{},[1706,63415,1715],{},[898,63417,207],{},[1706,63419,1708],{},[2964,63421,63422,63430],{},[895,63423,63424,63426,63428],{},[2148,63425,3508],{},[1706,63427,1715],{},[2148,63429,7786],{},[895,63431,63432,63434,63436,63438,63440,63442],{},[2148,63433,11496],{},[1706,63435,1715],{},[1706,63437,2140],{"stretchy":2139},[1706,63439,1715],{},[2148,63441,4284],{},[1706,63443,2153],{"stretchy":2139},[1706,63445,1708],{},[2964,63447,63448,63450],{},[2148,63449,12556],{},[2148,63451,63452],{},"3,5",[1706,63454,3248],{},[2148,63456,63457],{},"8,571.",[902,63459,63460],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,63462,63463,63508],{},[38,63464,63465,63466,1889,63479,4202,63493,63507],{},"(a) Změna ",[883,63467,63469],{"className":63468},[886],[888,63470,63471],{"xmlns":890},[892,63472,63473,63477],{},[895,63474,63475],{},[898,63476,20413],{},[902,63478,20413],{"encoding":904},[883,63480,63482],{"className":63481},[886],[888,63483,63484],{"xmlns":890},[892,63485,63486,63490],{},[895,63487,63488],{},[2148,63489,11496],{},[902,63491,63492],{"encoding":904},"0{,}5",[883,63494,63496],{"className":63495},[886],[888,63497,63498],{"xmlns":890},[892,63499,63500,63504],{},[895,63501,63502],{},[2148,63503,13775],{},[902,63505,63506],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,63510,63512],{"className":63511},[886],[888,63513,63514],{"xmlns":890,"display":2350},[892,63515,63516,63593],{},[895,63517,63518,63526,63528,63530,63532,63534,63536,63562,63564,63566,63568,63570,63572,63582,63584,63586,63588,63590],{},[28285,63519,63520,63522,63524],{},[898,63521,2146],{},[898,63523,20413],{},[1706,63525,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2415,63527,2799],{},[898,63529,3120],{},[898,63531,20413],{},[1706,63533,1708],{},[1706,63535,1715],{},[2964,63537,63538,63546],{},[895,63539,63540,63542,63544],{},[898,63541,2450],{},[1706,63543,1715],{},[898,63545,3120],{},[895,63547,63548,63550,63552,63554,63556],{},[1706,63549,2140],{"stretchy":2139},[898,63551,20413],{},[1706,63553,1715],{},[898,63555,207],{},[2489,63557,63558,63560],{},[1706,63559,2153],{"stretchy":2139},[2148,63561,2495],{},[2415,63563,2799],{},[898,63565,3120],{},[898,63567,20413],{},[1706,63569,1708],{},[1706,63571,1715],{},[2964,63573,63574,63576],{},[2148,63575,12556],{},[2489,63577,63578,63580],{},[2148,63579,63452],{},[2148,63581,2495],{},[1706,63583,2390],{},[2148,63585,14840],{},[1706,63587,3248],{},[1706,63589,1715],{},[2148,63591,63592],{},"0,245.",[902,63594,63595],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,63597,63598,63599,1837],{},"Nové rovnovážné množství ",[883,63600,63602],{"className":63601},[886],[888,63603,63604],{"xmlns":890},[892,63605,63606,63631],{},[895,63607,63608,63616,63618,63621,63623,63626,63628],{},[28285,63609,63610,63612,63614],{},[898,63611,2146],{},[2148,63613,2701],{},[898,63615,23410],{},[1706,63617,3248],{},[2148,63619,63620],{},"8,571",[1706,63622,1715],{},[2148,63624,63625],{},"0,245",[1706,63627,1708],{},[2148,63629,63630],{},"8,326",[902,63632,63633],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,63635,63636,63721],{},[38,63637,63638,63639,1343,63659,1343,63681,1343,63701,1837],{},"(b) Současné změny ",[883,63640,63642],{"className":63641},[886],[888,63643,63644],{"xmlns":890},[892,63645,63646,63656],{},[895,63647,63648,63650,63652,63654],{},[898,63649,3120],{},[898,63651,207],{},[1706,63653,1708],{},[2148,63655,11496],{},[902,63657,63658],{"encoding":904},"da = 0{,}5",[883,63660,63662],{"className":63661},[886],[888,63663,63664],{"xmlns":890},[892,63665,63666,63678],{},[895,63667,63668,63670,63672,63674,63676],{},[898,63669,3120],{},[898,63671,2450],{},[1706,63673,1708],{},[1706,63675,1715],{},[2148,63677,7524],{},[902,63679,63680],{"encoding":904},"db = -5",[883,63682,63684],{"className":63683},[886],[888,63685,63686],{"xmlns":890},[892,63687,63688,63698],{},[895,63689,63690,63692,63694,63696],{},[898,63691,3120],{},[898,63693,20413],{},[1706,63695,1708],{},[2148,63697,14840],{},[902,63699,63700],{"encoding":904},"dc = 0{,}1",[883,63702,63704],{"className":63703},[886],[888,63705,63706],{"xmlns":890},[892,63707,63708,63718],{},[895,63709,63710,63712,63714,63716],{},[898,63711,3120],{},[898,63713,3120],{},[1706,63715,1708],{},[2148,63717,2701],{},[902,63719,63720],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,63723,63725],{"className":63724},[886],[888,63726,63727],{"xmlns":890,"display":2350},[892,63728,63729,63872],{},[2354,63730,63731,63813,63849],{"rowspacing":7556,"columnalign":7557,"columnspacing":3141},[2358,63732,63733,63743],{},[2361,63734,63735],{},[4745,63736,63737],{"scriptlevel":2150,"displaystyle":2504},[895,63738,63739,63741],{},[898,63740,3677],{"mathvariant":2409},[898,63742,2146],{},[2361,63744,63745],{},[4745,63746,63747],{"scriptlevel":2150,"displaystyle":2504},[895,63748,63749,63751,63753,63763,63765,63767,63769,63775,63777,63779,63781,63783,63785,63787,63797,63799,63801,63803,63809,63811],{},[895,63750],{},[1706,63752,3248],{},[2964,63754,63755,63757],{},[2148,63756,12556],{},[2489,63758,63759,63761],{},[2148,63760,63452],{},[2148,63762,2495],{},[1706,63764,2390],{},[2148,63766,11496],{},[1706,63768,2447],{},[2964,63770,63771,63773],{},[2148,63772,2701],{},[2148,63774,63452],{},[1706,63776,2390],{},[1706,63778,2140],{"stretchy":2139},[1706,63780,1715],{},[2148,63782,7524],{},[1706,63784,2153],{"stretchy":2139},[1706,63786,1715],{},[2964,63788,63789,63791],{},[2148,63790,12556],{},[2489,63792,63793,63795],{},[2148,63794,63452],{},[2148,63796,2495],{},[1706,63798,2390],{},[2148,63800,14840],{},[1706,63802,1715],{},[2964,63804,63805,63807],{},[2148,63806,2701],{},[2148,63808,63452],{},[1706,63810,2390],{},[2148,63812,2701],{},[2358,63814,63815,63821],{},[2361,63816,63817],{},[4745,63818,63819],{"scriptlevel":2150,"displaystyle":2504},[895,63820],{},[2361,63822,63823],{},[4745,63824,63825],{"scriptlevel":2150,"displaystyle":2504},[895,63826,63827,63829,63831,63834,63836,63839,63841,63844,63846],{},[895,63828],{},[1706,63830,1708],{},[2148,63832,63833],{},"1,2245",[1706,63835,1715],{},[2148,63837,63838],{},"1,4286",[1706,63840,1715],{},[2148,63842,63843],{},"0,2449",[1706,63845,1715],{},[2148,63847,63848],{},"0,2857",[2358,63850,63851,63857],{},[2361,63852,63853],{},[4745,63854,63855],{"scriptlevel":2150,"displaystyle":2504},[895,63856],{},[2361,63858,63859],{},[4745,63860,63861],{"scriptlevel":2150,"displaystyle":2504},[895,63862,63863,63865,63867,63869],{},[895,63864],{},[1706,63866,3248],{},[1706,63868,1715],{},[2148,63870,63871],{},"0,735.",[902,63873,63874],{"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}",[724,63876,49130,63877,1837],{},[883,63878,63880],{"className":63879},[886],[888,63881,63882],{"xmlns":890},[892,63883,63884,63908],{},[895,63885,63886,63894,63896,63898,63900,63903,63905],{},[28285,63887,63888,63890,63892],{},[898,63889,2146],{},[2148,63891,2701],{},[898,63893,23410],{},[1706,63895,3248],{},[2148,63897,63620],{},[1706,63899,1715],{},[2148,63901,63902],{},"0,735",[1706,63904,1708],{},[2148,63906,63907],{},"7,836",[902,63909,63910],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[1636,63912,63913],{},[724,63914,63915,63917,63918,63941,63942,63964],{},[883,63916,9276],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,63919,63921],{"className":63920},[886],[888,63922,63923],{"xmlns":890},[892,63924,63925,63938],{},[895,63926,63927,63929,63931,63933,63935],{},[898,63928,3677],{"mathvariant":2409},[898,63930,2146],{},[1706,63932,3248],{},[1706,63934,1715],{},[2148,63936,63937],{},"2,69",[902,63939,63940],{"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 ",[883,63943,63945],{"className":63944},[886],[888,63946,63947],{"xmlns":890},[892,63948,63949,63961],{},[895,63950,63951,63953,63955,63957,63959],{},[898,63952,3677],{"mathvariant":2409},[898,63954,2146],{},[1706,63956,3248],{},[1706,63958,1715],{},[2148,63960,63902],{},[902,63962,63963],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,63966,63967],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[56029,63969],{},[115,63971,820],{"id":30893},[1636,63973,63974],{},[724,63975,63976,1643,63978,2314,63981,5354,63997,2314,64000,64016,64017,1837],{},[883,63977,3174],{},[38,63979,63980],{},"Přebytek spotřebitele",[883,63982,63984],{"className":63983},[886],[888,63985,63986],{"xmlns":890},[892,63987,63988,63994],{},[895,63989,63990,63992],{},[898,63991,1683],{},[898,63993,14171],{},[902,63995,63996],{"encoding":904},"CS",[38,63998,63999],{},"přebytek výrobce",[883,64001,64003],{"className":64002},[886],[888,64004,64005],{"xmlns":890},[892,64006,64007,64013],{},[895,64008,64009,64011],{},[898,64010,1702],{},[898,64012,14171],{},[902,64014,64015],{"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 ",[207,64018,64020],{"className":64019,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,64022,64023],{},[2286,64024],{"alt":64025,"className":64026,"src":64027},"imek-prebytky-cs-ps",[210,2290],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,64029,64030,2314,64032,64035],{},[38,64031,63980],{},[614,64033,64034],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,64037,64039],{"className":64038},[886],[888,64040,64041],{"xmlns":890,"display":2350},[892,64042,64043,64120],{},[2354,64044,64045],{"width":2356},[2358,64046,64047,64049,64113,64115],{},[2361,64048],{"width":2363},[2361,64050,64051],{},[895,64052,64053,64055,64057,64059,64065,64067,64069,64081,64083,64085,64087,64089,64091,64093,64095,64097,64103,64105,64111],{},[898,64054,1683],{},[898,64056,14171],{},[1706,64058,2140],{"stretchy":2139},[2142,64060,64061,64063],{},[898,64062,2146],{},[2148,64064,2150],{},[1706,64066,2153],{"stretchy":2139},[1706,64068,1708],{},[28285,64070,64071,64073,64075],{},[1706,64072,30280],{},[2148,64074,2150],{},[2142,64076,64077,64079],{},[898,64078,2146],{},[2148,64080,2150],{},[898,64082,2334],{},[1706,64084,2140],{"stretchy":2139},[898,64086,2146],{},[1706,64088,2153],{"stretchy":2139},[2415,64090,2799],{},[898,64092,3120],{},[898,64094,2146],{},[1706,64096,1715],{},[2142,64098,64099,64101],{},[898,64100,1702],{},[2148,64102,2150],{},[2415,64104,2799],{},[2142,64106,64107,64109],{},[898,64108,2146],{},[2148,64110,2150],{},[898,64112,1837],{"mathvariant":2409},[2361,64114],{"width":2363},[2361,64116,64117],{},[2415,64118,64119],{},"(2.14)",[902,64121,64122],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,64124,64125,2314,64128,64131],{},[38,64126,64127],{},"Přebytek výrobce",[614,64129,64130],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,64133,64135],{"className":64134},[886],[888,64136,64137],{"xmlns":890,"display":2350},[892,64138,64139,64216],{},[2354,64140,64141],{"width":2356},[2358,64142,64143,64145,64209,64211],{},[2361,64144],{"width":2363},[2361,64146,64147],{},[895,64148,64149,64151,64153,64155,64161,64163,64165,64171,64173,64179,64181,64193,64195,64197,64199,64201,64203,64205,64207],{},[898,64150,1702],{},[898,64152,14171],{},[1706,64154,2140],{"stretchy":2139},[2142,64156,64157,64159],{},[898,64158,2146],{},[2148,64160,2150],{},[1706,64162,2153],{"stretchy":2139},[1706,64164,1708],{},[2142,64166,64167,64169],{},[898,64168,1702],{},[2148,64170,2150],{},[2415,64172,2799],{},[2142,64174,64175,64177],{},[898,64176,2146],{},[2148,64178,2150],{},[1706,64180,1715],{},[28285,64182,64183,64185,64187],{},[1706,64184,30280],{},[2148,64186,2150],{},[2142,64188,64189,64191],{},[898,64190,2146],{},[2148,64192,2150],{},[898,64194,14171],{},[1706,64196,2140],{"stretchy":2139},[898,64198,2146],{},[1706,64200,2153],{"stretchy":2139},[2415,64202,2799],{},[898,64204,3120],{},[898,64206,2146],{},[898,64208,1837],{"mathvariant":2409},[2361,64210],{"width":2363},[2361,64212,64213],{},[2415,64214,64215],{},"(2.15)",[902,64217,64218],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,64220,64221,64222,1837],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,64223,64225],{"className":64224,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[56029,64227],{},[115,64229,64231],{"id":64230},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,64233,64234,64265,64270,64276,64304,64310,64339,64345,64425,64451],{},[123,64235,64236,64238,64239,64264],{},[38,64237,56985],{}," — lineární poptávka ",[883,64240,64242],{"className":64241},[886],[888,64243,64244],{"xmlns":890},[892,64245,64246,64262],{},[895,64247,64248,64250,64252,64254,64256,64258,64260],{},[898,64249,1702],{},[1706,64251,1708],{},[1706,64253,1715],{},[2148,64255,2495],{},[898,64257,2146],{},[1706,64259,2447],{},[2148,64261,4199],{},[902,64263,57017],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,64266,64267,64269],{},[38,64268,57298],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,64271,64272,64275],{},[38,64273,64274],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,64277,64278,64280,64281,1837],{},[38,64279,59842],{}," — lineární nabídka ",[883,64282,64284],{"className":64283},[886],[888,64285,64286],{"xmlns":890},[892,64287,64288,64302],{},[895,64289,64290,64292,64294,64296,64298,64300],{},[898,64291,1702],{},[1706,64293,1708],{},[2148,64295,11496],{},[898,64297,2146],{},[1706,64299,2447],{},[2148,64301,2748],{},[902,64303,59871],{"encoding":904},[123,64305,64306,64309],{},[38,64307,64308],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,64311,64312,64315,64316,1837],{},[38,64313,64314],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,64317,64319],{"className":64318},[886],[888,64320,64321],{"xmlns":890},[892,64322,64323,64337],{},[895,64324,64325,64327,64329,64331,64333,64335],{},[898,64326,23410],{},[1706,64328,21693],{"stretchy":2139},[2148,64330,3455],{},[1706,64332,2505],{"separator":2504},[2148,64334,60985],{},[1706,64336,21708],{"stretchy":2139},[902,64338,61013],{"encoding":904},[123,64340,64341,64344],{},[38,64342,64343],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,64346,64347,64350,64351,64368,64369,1343,64394,64421,64422,22139],{},[38,64348,64349],{},"Příklad 2.9"," — daň ",[883,64352,64354],{"className":64353},[886],[888,64355,64356],{"xmlns":890},[892,64357,64358,64366],{},[895,64359,64360,64362,64364],{},[898,64361,1659],{},[1706,64363,1708],{},[2148,64365,7044],{},[902,64367,60321],{"encoding":904}," na výrobce; rozklad ",[883,64370,64372],{"className":64371},[886],[888,64373,64374],{"xmlns":890},[892,64375,64376,64392],{},[895,64377,64378,64388,64390],{},[2142,64379,64380,64382],{},[898,64381,1659],{},[895,64383,64384,64386],{},[898,64385,61726],{},[898,64387,724],{},[1706,64389,1708],{},[2148,64391,2495],{},[902,64393,62025],{"encoding":904},[883,64395,64397],{"className":64396},[886],[888,64398,64399],{"xmlns":890},[892,64400,64401,64419],{},[895,64402,64403,64415,64417],{},[2142,64404,64405,64407],{},[898,64406,1659],{},[895,64408,64409,64411,64413],{},[898,64410,61749],{},[898,64412,6930],{},[898,64414,3950],{},[1706,64416,1708],{},[2148,64418,3455],{},[902,64420,62054],{"encoding":904},". (Viz ",[207,64423,61770],{"className":64424,"dataFsResolvedFilePath":809,"href":810},[210],[123,64426,64427,64350,64430,64447,64448,22139],{},[38,64428,64429],{},"Příklad 2.10",[883,64431,64433],{"className":64432},[886],[888,64434,64435],{"xmlns":890},[892,64436,64437,64445],{},[895,64438,64439,64441,64443],{},[898,64440,1659],{},[1706,64442,1708],{},[2148,64444,7044],{},[902,64446,60321],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,64449,61770],{"className":64450,"dataFsResolvedFilePath":809,"href":810},[210],[123,64452,64453,64456],{},[38,64454,64455],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[56029,64458],{},[115,64460,64462],{"id":64461},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,64464,64466],{"id":64465},"základní-analýza-poptávky","Základní analýza poptávky",[724,64468,64469,15929,64472,64507,64508,64534],{},[38,64470,64471],{},"2.1",[883,64473,64475],{"className":64474},[886],[888,64476,64477],{"xmlns":890},[892,64478,64479,64504],{},[895,64480,64481,64483,64485,64487,64489,64491,64493,64495,64498,64500,64502],{},[898,64482,2146],{},[1706,64484,1708],{},[898,64486,2334],{},[1706,64488,2140],{"stretchy":2139},[898,64490,1702],{},[1706,64492,2153],{"stretchy":2139},[1706,64494,1708],{},[2148,64496,64497],{},"75",[1706,64499,1715],{},[2148,64501,7524],{},[898,64503,1702],{},[902,64505,64506],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,64509,64511],{"className":64510},[886],[888,64512,64513],{"xmlns":890},[892,64514,64515,64531],{},[895,64516,64517,64519,64521,64523,64525,64527,64529],{},[2148,64518,2150],{},[1706,64520,2505],{"separator":2504},[2148,64522,7524],{},[1706,64524,2505],{"separator":2504},[2148,64526,7786],{},[1706,64528,2505],{"separator":2504},[2148,64530,3359],{},[902,64532,64533],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,64536,64537,64540,64541,64559,64560,5606],{},[38,64538,64539],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,64542,64544],{"className":64543},[886],[888,64545,64546],{"xmlns":890},[892,64547,64548,64556],{},[895,64549,64550,64552,64554],{},[898,64551,1702],{},[1706,64553,2505],{"separator":2504},[898,64555,2146],{},[902,64557,64558],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,64561,64563],{"className":64562},[886],[888,64564,64565],{"xmlns":890},[892,64566,64567,64583],{},[895,64568,64569,64571,64573,64575,64577,64579,64581],{},[898,64570,207],{},[1706,64572,2505],{"separator":2504},[898,64574,2450],{},[1706,64576,2505],{"separator":2504},[898,64578,20413],{},[1706,64580,8922],{},[2148,64582,2150],{},[902,64584,64585],{"encoding":904},"a, b, c > 0",[120,64587,64588,64621,64652,64687,64718,64753],{},[123,64589,64590,64591],{},"(a) ",[883,64592,64594],{"className":64593},[886],[888,64595,64596],{"xmlns":890},[892,64597,64598,64618],{},[895,64599,64600,64602,64604],{},[898,64601,2146],{},[1706,64603,1708],{},[4745,64605,64606],{"scriptlevel":2150,"displaystyle":2504},[2964,64607,64608,64610],{},[898,64609,207],{},[895,64611,64612,64614,64616],{},[898,64613,1702],{},[1706,64615,2447],{},[898,64617,20413],{},[902,64619,64620],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,64622,64623,64624],{},"(b) ",[883,64625,64627],{"className":64626},[886],[888,64628,64629],{"xmlns":890},[892,64630,64631,64649],{},[895,64632,64633,64635,64637],{},[898,64634,2146],{},[1706,64636,1708],{},[11087,64638,64639],{},[895,64640,64641,64643,64645,64647],{},[898,64642,207],{},[1706,64644,1715],{},[898,64646,2450],{},[898,64648,2146],{},[902,64650,64651],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,64653,64654,64655],{},"(c) ",[883,64656,64658],{"className":64657},[886],[888,64659,64660],{"xmlns":890},[892,64661,64662,64684],{},[895,64663,64664,64666,64668],{},[898,64665,2146],{},[1706,64667,1708],{},[4745,64669,64670],{"scriptlevel":2150,"displaystyle":2504},[2964,64671,64672,64682],{},[895,64673,64674,64676,64678],{},[898,64675,207],{},[1706,64677,1715],{},[11087,64679,64680],{},[898,64681,1702],{},[898,64683,2450],{},[902,64685,64686],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,64688,64689,64690],{},"(d) ",[883,64691,64693],{"className":64692},[886],[888,64694,64695],{"xmlns":890},[892,64696,64697,64715],{},[895,64698,64699,64701,64703,64705,64707,64709],{},[898,64700,1702],{},[1706,64702,1708],{},[898,64704,207],{},[1706,64706,1715],{},[898,64708,2450],{},[2489,64710,64711,64713],{},[898,64712,2146],{},[2148,64714,2495],{},[902,64716,64717],{"encoding":904},"P = a - bQ^2",[123,64719,64720,64721],{},"(e) ",[883,64722,64724],{"className":64723},[886],[888,64725,64726],{"xmlns":890},[892,64727,64728,64750],{},[895,64729,64730,64732,64734,64736,64746,64748],{},[898,64731,2146],{},[1706,64733,1708],{},[898,64735,2450],{},[2489,64737,64738,64740],{},[898,64739,1702],{},[895,64741,64742,64744],{},[1706,64743,1715],{},[898,64745,207],{},[1706,64747,2447],{},[898,64749,20413],{},[902,64751,64752],{"encoding":904},"Q = bP^{-a} + c",[123,64754,64755,64756],{},"(f) ",[883,64757,64759],{"className":64758},[886],[888,64760,64761],{"xmlns":890},[892,64762,64763,64785],{},[895,64764,64765,64767,64769,64771,64773],{},[898,64766,2146],{},[1706,64768,1708],{},[898,64770,207],{},[1706,64772,2390],{},[2489,64774,64775,64777],{},[898,64776,3929],{},[895,64778,64779,64781,64783],{},[1706,64780,1715],{},[898,64782,2450],{},[898,64784,1702],{},[902,64786,64787],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,64789,64790,64793],{},[38,64791,64792],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,64795,64796,64799,64802],{},[123,64797,64798],{},"(a) Cena substitutu.",[123,64800,64801],{},"(b) Cena komplementu.",[123,64803,64804],{},"(c) Výdaje na reklamu.",[724,64806,64807,15929,64809,64843,64844,64872],{},[38,64808,43717],{},[883,64810,64812],{"className":64811},[886],[888,64813,64814],{"xmlns":890},[892,64815,64816,64840],{},[895,64817,64818,64820,64822,64824,64826,64828,64830,64832,64834,64836,64838],{},[898,64819,1702],{},[1706,64821,1708],{},[898,64823,2334],{},[1706,64825,2140],{"stretchy":2139},[898,64827,2146],{},[1706,64829,2153],{"stretchy":2139},[1706,64831,1708],{},[2148,64833,7156],{},[1706,64835,1715],{},[2148,64837,2495],{},[898,64839,2146],{},[902,64841,64842],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,64845,64847],{"className":64846},[886],[888,64848,64849],{"xmlns":890},[892,64850,64851,64869],{},[895,64852,64853,64855,64857,64863,64865,64867],{},[898,64854,1702],{},[1706,64856,1708],{},[2489,64858,64859,64861],{},[898,64860,2334],{},[1706,64862,3197],{},[1706,64864,2140],{"stretchy":2139},[898,64866,2146],{},[1706,64868,2153],{"stretchy":2139},[902,64870,64871],{"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.",[724,64874,64875,64878],{},[38,64876,64877],{},"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:",[120,64880,64881,64965,65041,65127,65215],{},[123,64882,64590,64883,1343,64923,1837],{},[883,64884,64886],{"className":64885},[886],[888,64887,64888],{"xmlns":890},[892,64889,64890,64920],{},[895,64891,64892,64898,64900,64902,64904,64906,64912,64914],{},[2142,64893,64894,64896],{},[898,64895,10315],{},[2148,64897,2701],{},[1706,64899,1708],{},[2148,64901,3369],{},[1706,64903,1715],{},[2148,64905,3455],{},[2142,64907,64908,64910],{},[898,64909,1735],{},[2148,64911,2701],{},[1706,64913,2447],{},[2142,64915,64916,64918],{},[898,64917,1735],{},[2148,64919,2495],{},[902,64921,64922],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,64924,64926],{"className":64925},[886],[888,64927,64928],{"xmlns":890},[892,64929,64930,64962],{},[895,64931,64932,64938,64940,64942,64944,64946,64952,64954,64956],{},[2142,64933,64934,64936],{},[898,64935,10315],{},[2148,64937,2495],{},[1706,64939,1708],{},[2148,64941,7786],{},[1706,64943,2447],{},[2148,64945,2495],{},[2142,64947,64948,64950],{},[898,64949,1735],{},[2148,64951,2701],{},[1706,64953,1715],{},[2148,64955,3455],{},[2142,64957,64958,64960],{},[898,64959,1735],{},[2148,64961,2495],{},[902,64963,64964],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,64966,64623,64967,1343,65009,1837],{},[883,64968,64970],{"className":64969},[886],[888,64971,64972],{"xmlns":890},[892,64973,64974,65006],{},[895,64975,64976,64982,64984,64986,64988,64990,64996,64998,65000],{},[2142,64977,64978,64980],{},[898,64979,10315],{},[2148,64981,2701],{},[1706,64983,1708],{},[2148,64985,2728],{},[1706,64987,1715],{},[2148,64989,7786],{},[2142,64991,64992,64994],{},[898,64993,1735],{},[2148,64995,2701],{},[1706,64997,1715],{},[2148,64999,7044],{},[2142,65001,65002,65004],{},[898,65003,1735],{},[2148,65005,2495],{},[902,65007,65008],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,65010,65012],{"className":65011},[886],[888,65013,65014],{"xmlns":890},[892,65015,65016,65038],{},[895,65017,65018,65024,65026,65028,65030,65032],{},[2142,65019,65020,65022],{},[898,65021,10315],{},[2148,65023,2495],{},[1706,65025,1708],{},[2148,65027,3359],{},[1706,65029,1715],{},[2148,65031,7786],{},[2142,65033,65034,65036],{},[898,65035,1735],{},[2148,65037,2495],{},[902,65039,65040],{"encoding":904},"B_2 = 15 - 10A_2",[123,65042,64654,65043,1343,65085,1837],{},[883,65044,65046],{"className":65045},[886],[888,65047,65048],{"xmlns":890},[892,65049,65050,65082],{},[895,65051,65052,65058,65060,65062,65064,65066,65072,65074,65076],{},[2142,65053,65054,65056],{},[898,65055,10315],{},[2148,65057,2701],{},[1706,65059,1708],{},[2148,65061,12556],{},[1706,65063,1715],{},[2148,65065,2495],{},[2142,65067,65068,65070],{},[898,65069,1735],{},[2148,65071,2701],{},[1706,65073,1715],{},[2148,65075,3455],{},[2142,65077,65078,65080],{},[898,65079,1735],{},[2148,65081,2495],{},[902,65083,65084],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,65086,65088],{"className":65087},[886],[888,65089,65090],{"xmlns":890},[892,65091,65092,65124],{},[895,65093,65094,65100,65102,65104,65106,65108,65114,65116,65118],{},[2142,65095,65096,65098],{},[898,65097,10315],{},[2148,65099,2495],{},[1706,65101,1708],{},[2148,65103,3359],{},[1706,65105,2447],{},[2148,65107,2495],{},[2142,65109,65110,65112],{},[898,65111,1735],{},[2148,65113,2701],{},[1706,65115,1715],{},[2148,65117,2495],{},[2142,65119,65120,65122],{},[898,65121,1735],{},[2148,65123,2495],{},[902,65125,65126],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,65128,64689,65129,1343,65173,1837],{},[883,65130,65132],{"className":65131},[886],[888,65133,65134],{"xmlns":890},[892,65135,65136,65170],{},[895,65137,65138,65144,65146,65148,65150,65152,65154,65160,65162,65164],{},[2142,65139,65140,65142],{},[898,65141,10315],{},[2148,65143,2701],{},[1706,65145,1708],{},[1706,65147,1715],{},[2148,65149,3369],{},[1706,65151,1715],{},[2148,65153,2495],{},[2142,65155,65156,65158],{},[898,65157,1735],{},[2148,65159,2701],{},[1706,65161,2447],{},[2148,65163,4284],{},[2142,65165,65166,65168],{},[898,65167,1735],{},[2148,65169,2495],{},[902,65171,65172],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,65174,65176],{"className":65175},[886],[888,65177,65178],{"xmlns":890},[892,65179,65180,65212],{},[895,65181,65182,65188,65190,65192,65194,65196,65202,65204,65206],{},[2142,65183,65184,65186],{},[898,65185,10315],{},[2148,65187,2495],{},[1706,65189,1708],{},[2148,65191,7786],{},[1706,65193,2447],{},[2148,65195,2495],{},[2142,65197,65198,65200],{},[898,65199,1735],{},[2148,65201,2701],{},[1706,65203,1715],{},[2148,65205,2495],{},[2142,65207,65208,65210],{},[898,65209,1735],{},[2148,65211,2495],{},[902,65213,65214],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,65216,64720,65217,1343,65259,1837],{},[883,65218,65220],{"className":65219},[886],[888,65221,65222],{"xmlns":890},[892,65223,65224,65256],{},[895,65225,65226,65232,65234,65236,65238,65240,65246,65248,65250],{},[2142,65227,65228,65230],{},[898,65229,10315],{},[2148,65231,2701],{},[1706,65233,1708],{},[2148,65235,3369],{},[1706,65237,2447],{},[2148,65239,2495],{},[2142,65241,65242,65244],{},[898,65243,1735],{},[2148,65245,2701],{},[1706,65247,2447],{},[2148,65249,3455],{},[2142,65251,65252,65254],{},[898,65253,1735],{},[2148,65255,2495],{},[902,65257,65258],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,65260,65262],{"className":65261},[886],[888,65263,65264],{"xmlns":890},[892,65265,65266,65298],{},[895,65267,65268,65274,65276,65278,65280,65282,65288,65290,65292],{},[2142,65269,65270,65272],{},[898,65271,10315],{},[2148,65273,2495],{},[1706,65275,1708],{},[2148,65277,3508],{},[1706,65279,1715],{},[2148,65281,4284],{},[2142,65283,65284,65286],{},[898,65285,1735],{},[2148,65287,2701],{},[1706,65289,2447],{},[2148,65291,7524],{},[2142,65293,65294,65296],{},[898,65295,1735],{},[2148,65297,2495],{},[902,65299,65300],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,65302,65304],{"id":65303},"základní-analýza-nabídky","Základní analýza nabídky",[724,65306,65307,65310,65311,65345,65346,65368],{},[38,65308,65309],{},"2.6"," Je dána nabídka ",[883,65312,65314],{"className":65313},[886],[888,65315,65316],{"xmlns":890},[892,65317,65318,65342],{},[895,65319,65320,65322,65324,65326,65328,65330,65332,65334,65336,65338,65340],{},[898,65321,1702],{},[1706,65323,1708],{},[898,65325,14171],{},[1706,65327,2140],{"stretchy":2139},[898,65329,2146],{},[1706,65331,2153],{"stretchy":2139},[1706,65333,1708],{},[2148,65335,3369],{},[1706,65337,2447],{},[2148,65339,15204],{},[898,65341,2146],{},[902,65343,65344],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,65347,65349],{"className":65348},[886],[888,65350,65351],{"xmlns":890},[892,65352,65353,65365],{},[895,65354,65355,65357,65359,65361,65363],{},[2148,65356,2748],{},[1706,65358,2505],{"separator":2504},[2148,65360,12556],{},[1706,65362,2505],{"separator":2504},[2148,65364,34145],{},[902,65366,65367],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,65370,65371,65374,65375,65392],{},[38,65372,65373],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,65376,65378],{"className":65377},[886],[888,65379,65380],{"xmlns":890},[892,65381,65382,65390],{},[895,65383,65384,65386,65388],{},[898,65385,1702],{},[1706,65387,2505],{"separator":2504},[898,65389,2146],{},[902,65391,64558],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,65394,65395,65421,65449,65482,65516,65552],{},[123,65396,64590,65397],{},[883,65398,65400],{"className":65399},[886],[888,65401,65402],{"xmlns":890},[892,65403,65404,65418],{},[895,65405,65406,65408,65410,65412,65414,65416],{},[898,65407,1702],{},[1706,65409,1708],{},[2148,65411,12556],{},[1706,65413,2447],{},[2148,65415,2495],{},[898,65417,2146],{},[902,65419,65420],{"encoding":904},"P = 30 + 2Q",[123,65422,64623,65423],{},[883,65424,65426],{"className":65425},[886],[888,65427,65428],{"xmlns":890},[892,65429,65430,65446],{},[895,65431,65432,65434,65436,65438,65440,65442,65444],{},[898,65433,2146],{},[1706,65435,1708],{},[1706,65437,1715],{},[2148,65439,4284],{},[1706,65441,2447],{},[2148,65443,7156],{},[898,65445,1702],{},[902,65447,65448],{"encoding":904},"Q = -3 + 12P",[123,65450,64654,65451],{},[883,65452,65454],{"className":65453},[886],[888,65455,65456],{"xmlns":890},[892,65457,65458,65480],{},[895,65459,65460,65462,65464,65470,65472,65474,65476,65478],{},[898,65461,1702],{},[1706,65463,1708],{},[2489,65465,65466,65468],{},[898,65467,2146],{},[2148,65469,2495],{},[1706,65471,2447],{},[2148,65473,12859],{},[898,65475,2146],{},[1706,65477,2447],{},[2148,65479,51608],{},[902,65481,60774],{"encoding":904},[123,65483,64689,65484],{},[883,65485,65487],{"className":65486},[886],[888,65488,65489],{"xmlns":890},[892,65490,65491,65513],{},[895,65492,65493,65495,65497,65503,65505,65507,65509,65511],{},[898,65494,1702],{},[1706,65496,1708],{},[2489,65498,65499,65501],{},[898,65500,2146],{},[2148,65502,2495],{},[1706,65504,2447],{},[2148,65506,2495],{},[898,65508,2146],{},[1706,65510,2447],{},[2148,65512,7156],{},[902,65514,65515],{"encoding":904},"P = Q^2 + 2Q + 12",[123,65517,64720,65518],{},[883,65519,65521],{"className":65520},[886],[888,65522,65523],{"xmlns":890},[892,65524,65525,65549],{},[895,65526,65527,65529,65531,65533,65535,65537,65539,65541,65543],{},[898,65528,2146],{},[1706,65530,1708],{},[2148,65532,27924],{},[1706,65534,2447],{},[2148,65536,7524],{},[898,65538,1702],{},[1706,65540,2447],{},[2148,65542,14840],{},[2489,65544,65545,65547],{},[898,65546,1702],{},[2148,65548,2495],{},[902,65550,65551],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,65553,64755,65554],{},[883,65555,65557],{"className":65556},[886],[888,65558,65559],{"xmlns":890},[892,65560,65561,65586],{},[895,65562,65563,65565,65567,65569,65571,65573,65575,65577,65580],{},[898,65564,2146],{},[1706,65566,1708],{},[2148,65568,12597],{},[1706,65570,2447],{},[2148,65572,14840],{},[898,65574,1702],{},[1706,65576,2447],{},[2148,65578,65579],{},"0,004",[2489,65581,65582,65584],{},[898,65583,1702],{},[2148,65585,2495],{},[902,65587,65588],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,65590,65591,65594],{},[38,65592,65593],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,65596,65597,65600,65603,65606],{},[123,65598,65599],{},"(a) Sníží ceny surovin — vstupů.",[123,65601,65602],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,65604,65605],{},"(c) Zvýší ceny všech energií.",[123,65607,65608],{},"(d) Sníží daňové odvody státu.",[724,65610,65611,65310,65613,65647,65648,65676],{},[38,65612,61998],{},[883,65614,65616],{"className":65615},[886],[888,65617,65618],{"xmlns":890},[892,65619,65620,65644],{},[895,65621,65622,65624,65626,65628,65630,65632,65634,65636,65638,65640,65642],{},[898,65623,1702],{},[1706,65625,1708],{},[898,65627,14171],{},[1706,65629,2140],{"stretchy":2139},[898,65631,2146],{},[1706,65633,2153],{"stretchy":2139},[1706,65635,1708],{},[2148,65637,11496],{},[898,65639,2146],{},[1706,65641,2447],{},[2148,65643,3359],{},[902,65645,65646],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,65649,65651],{"className":65650},[886],[888,65652,65653],{"xmlns":890},[892,65654,65655,65673],{},[895,65656,65657,65659,65661,65667,65669,65671],{},[898,65658,1702],{},[1706,65660,1708],{},[2489,65662,65663,65665],{},[898,65664,14171],{},[1706,65666,3197],{},[1706,65668,2140],{"stretchy":2139},[898,65670,2146],{},[1706,65672,2153],{"stretchy":2139},[902,65674,65675],{"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.",[198,65678,60378],{"id":65679},"tržní-rovnováha-1",[724,65681,65682,65684,65685,65702,65703,4288],{},[38,65683,62058],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,65686,65688],{"className":65687},[886],[888,65689,65690],{"xmlns":890},[892,65691,65692,65700],{},[895,65693,65694],{},[2489,65695,65696,65698],{},[898,65697,2146],{},[898,65699,23410],{},[902,65701,61452],{"encoding":904}," a rovnovážnou cenu ",[883,65704,65706],{"className":65705},[886],[888,65707,65708],{"xmlns":890},[892,65709,65710,65718],{},[895,65711,65712],{},[2489,65713,65714,65716],{},[898,65715,1702],{},[898,65717,23410],{},[902,65719,60519],{"encoding":904},[120,65721,65722,65774,65825,65884],{},[123,65723,64590,65724,1343,65750,1837],{},[883,65725,65727],{"className":65726},[886],[888,65728,65729],{"xmlns":890},[892,65730,65731,65747],{},[895,65732,65733,65735,65737,65739,65741,65743,65745],{},[898,65734,1702],{},[1706,65736,1708],{},[1706,65738,1715],{},[2148,65740,7524],{},[898,65742,2146],{},[1706,65744,2447],{},[2148,65746,17219],{},[902,65748,65749],{"encoding":904},"P = -5Q + 80",[883,65751,65753],{"className":65752},[886],[888,65754,65755],{"xmlns":890},[892,65756,65757,65771],{},[895,65758,65759,65761,65763,65765,65767,65769],{},[898,65760,1702],{},[1706,65762,1708],{},[2148,65764,2495],{},[898,65766,2146],{},[1706,65768,2447],{},[2148,65770,7786],{},[902,65772,65773],{"encoding":904},"P = 2Q + 10",[123,65775,64623,65776,1343,65802,1837],{},[883,65777,65779],{"className":65778},[886],[888,65780,65781],{"xmlns":890},[892,65782,65783,65799],{},[895,65784,65785,65787,65789,65791,65793,65795,65797],{},[898,65786,2146],{},[1706,65788,1708],{},[1706,65790,1715],{},[2148,65792,11496],{},[898,65794,1702],{},[1706,65796,2447],{},[2148,65798,2748],{},[902,65800,65801],{"encoding":904},"Q = -0{,}5P + 25",[883,65803,65805],{"className":65804},[886],[888,65806,65807],{"xmlns":890},[892,65808,65809,65823],{},[895,65810,65811,65813,65815,65817,65819,65821],{},[898,65812,2146],{},[1706,65814,1708],{},[2148,65816,2495],{},[898,65818,1702],{},[1706,65820,1715],{},[2148,65822,2728],{},[902,65824,59900],{"encoding":904},[123,65826,64654,65827,1343,65853,1837],{},[883,65828,65830],{"className":65829},[886],[888,65831,65832],{"xmlns":890},[892,65833,65834,65850],{},[895,65835,65836,65838,65840,65842,65844,65846,65848],{},[898,65837,1702],{},[1706,65839,1708],{},[1706,65841,1715],{},[2148,65843,3455],{},[898,65845,2146],{},[1706,65847,2447],{},[2148,65849,4314],{},[902,65851,65852],{"encoding":904},"P = -4Q + 120",[883,65854,65856],{"className":65855},[886],[888,65857,65858],{"xmlns":890},[892,65859,65860,65881],{},[895,65861,65862,65864,65866,65874,65876,65878],{},[898,65863,1702],{},[1706,65865,1708],{},[4745,65867,65868],{"scriptlevel":2150,"displaystyle":2139},[2964,65869,65870,65872],{},[2148,65871,2701],{},[2148,65873,4284],{},[898,65875,2146],{},[1706,65877,2447],{},[2148,65879,65880],{},"29",[902,65882,65883],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,65885,64689,65886,1343,65915,1837],{},[883,65887,65889],{"className":65888},[886],[888,65890,65891],{"xmlns":890},[892,65892,65893,65912],{},[895,65894,65895,65897,65899,65901,65907,65909],{},[898,65896,1702],{},[1706,65898,1708],{},[1706,65900,1715],{},[2489,65902,65903,65905],{},[898,65904,2146],{},[2148,65906,2495],{},[1706,65908,2447],{},[2148,65910,65911],{},"52",[902,65913,65914],{"encoding":904},"P = -Q^2 + 52",[883,65916,65918],{"className":65917},[886],[888,65919,65920],{"xmlns":890},[892,65921,65922,65940],{},[895,65923,65924,65926,65928,65930,65936,65938],{},[898,65925,1702],{},[1706,65927,1708],{},[2148,65929,2495],{},[2489,65931,65932,65934],{},[898,65933,2146],{},[2148,65935,2495],{},[1706,65937,2447],{},[2148,65939,7786],{},[902,65941,65942],{"encoding":904},"P = 2Q^2 + 10",[724,65944,65945,65948,65949,65979,65980,66010],{},[38,65946,65947],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,65950,65952],{"className":65951},[886],[888,65953,65954],{"xmlns":890},[892,65955,65956,65976],{},[895,65957,65958,65966,65968],{},[28285,65959,65960,65962,65964],{},[898,65961,2146],{},[2148,65963,2701],{},[898,65965,23410],{},[1706,65967,2505],{"separator":2504},[28285,65969,65970,65972,65974],{},[898,65971,2146],{},[2148,65973,2495],{},[898,65975,23410],{},[902,65977,65978],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,65981,65983],{"className":65982},[886],[888,65984,65985],{"xmlns":890},[892,65986,65987,66007],{},[895,65988,65989,65997,65999],{},[28285,65990,65991,65993,65995],{},[898,65992,1702],{},[2148,65994,2701],{},[898,65996,23410],{},[1706,65998,2505],{"separator":2504},[28285,66000,66001,66003,66005],{},[898,66002,1702],{},[2148,66004,2495],{},[898,66006,23410],{},[902,66008,66009],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,66012,66013,66165],{},[123,66014,64590,66015,1343,66055,1343,66097,1343,66131,1837],{},[883,66016,66018],{"className":66017},[886],[888,66019,66020],{"xmlns":890},[892,66021,66022,66052],{},[895,66023,66024,66030,66032,66034,66036,66038,66044,66046],{},[2142,66025,66026,66028],{},[898,66027,2146],{},[2148,66029,2701],{},[1706,66031,1708],{},[2148,66033,7786],{},[1706,66035,1715],{},[2148,66037,2495],{},[2142,66039,66040,66042],{},[898,66041,1702],{},[2148,66043,2701],{},[1706,66045,2447],{},[2142,66047,66048,66050],{},[898,66049,1702],{},[2148,66051,2495],{},[902,66053,66054],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,66056,66058],{"className":66057},[886],[888,66059,66060],{"xmlns":890},[892,66061,66062,66094],{},[895,66063,66064,66070,66072,66074,66076,66078,66084,66086,66088],{},[2142,66065,66066,66068],{},[898,66067,2146],{},[2148,66069,2495],{},[1706,66071,1708],{},[2148,66073,7524],{},[1706,66075,2447],{},[2148,66077,2495],{},[2142,66079,66080,66082],{},[898,66081,1702],{},[2148,66083,2701],{},[1706,66085,1715],{},[2148,66087,2495],{},[2142,66089,66090,66092],{},[898,66091,1702],{},[2148,66093,2495],{},[902,66095,66096],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,66098,66100],{"className":66099},[886],[888,66101,66102],{"xmlns":890},[892,66103,66104,66128],{},[895,66105,66106,66112,66114,66116,66118,66120,66122],{},[2142,66107,66108,66110],{},[898,66109,2146],{},[2148,66111,2701],{},[1706,66113,1708],{},[1706,66115,1715],{},[2148,66117,4284],{},[1706,66119,2447],{},[2148,66121,2495],{},[2142,66123,66124,66126],{},[898,66125,1702],{},[2148,66127,2701],{},[902,66129,66130],{"encoding":904},"Q_1 = -3 + 2P_1",[883,66132,66134],{"className":66133},[886],[888,66135,66136],{"xmlns":890},[892,66137,66138,66162],{},[895,66139,66140,66146,66148,66150,66152,66154,66156],{},[2142,66141,66142,66144],{},[898,66143,2146],{},[2148,66145,2495],{},[1706,66147,1708],{},[1706,66149,1715],{},[2148,66151,2495],{},[1706,66153,2447],{},[2148,66155,4284],{},[2142,66157,66158,66160],{},[898,66159,1702],{},[2148,66161,2495],{},[902,66163,66164],{"encoding":904},"Q_2 = -2 + 3P_2",[123,66166,64623,66167,1343,66207,1343,66249,1343,66281,1837],{},[883,66168,66170],{"className":66169},[886],[888,66171,66172],{"xmlns":890},[892,66173,66174,66204],{},[895,66175,66176,66182,66184,66186,66188,66190,66196,66198],{},[2142,66177,66178,66180],{},[898,66179,2146],{},[2148,66181,2701],{},[1706,66183,1708],{},[2148,66185,2590],{},[1706,66187,1715],{},[2148,66189,2495],{},[2142,66191,66192,66194],{},[898,66193,1702],{},[2148,66195,2701],{},[1706,66197,2447],{},[2142,66199,66200,66202],{},[898,66201,1702],{},[2148,66203,2495],{},[902,66205,66206],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,66208,66210],{"className":66209},[886],[888,66211,66212],{"xmlns":890},[892,66213,66214,66246],{},[895,66215,66216,66222,66224,66226,66228,66230,66236,66238,66240],{},[2142,66217,66218,66220],{},[898,66219,2146],{},[2148,66221,2495],{},[1706,66223,1708],{},[2148,66225,7524],{},[1706,66227,2447],{},[2148,66229,2495],{},[2142,66231,66232,66234],{},[898,66233,1702],{},[2148,66235,2701],{},[1706,66237,1715],{},[2148,66239,4284],{},[2142,66241,66242,66244],{},[898,66243,1702],{},[2148,66245,2495],{},[902,66247,66248],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,66250,66252],{"className":66251},[886],[888,66253,66254],{"xmlns":890},[892,66255,66256,66278],{},[895,66257,66258,66264,66266,66268,66270,66272],{},[2142,66259,66260,66262],{},[898,66261,2146],{},[2148,66263,2701],{},[1706,66265,1708],{},[1706,66267,1715],{},[2148,66269,7786],{},[1706,66271,2447],{},[2142,66273,66274,66276],{},[898,66275,1702],{},[2148,66277,2701],{},[902,66279,66280],{"encoding":904},"Q_1 = -10 + P_1",[883,66282,66284],{"className":66283},[886],[888,66285,66286],{"xmlns":890},[892,66287,66288,66310],{},[895,66289,66290,66296,66298,66300,66302,66304],{},[2142,66291,66292,66294],{},[898,66293,2146],{},[2148,66295,2495],{},[1706,66297,1708],{},[2148,66299,7524],{},[1706,66301,2447],{},[2148,66303,7044],{},[2142,66305,66306,66308],{},[898,66307,1702],{},[2148,66309,2495],{},[902,66311,66312],{"encoding":904},"Q_2 = 5 + 6P_2",[724,66314,66315,66318,66319,1343,66367,1343,66413,66463,66464,1343,66496,1343,66530,15842,66564,1993,66582,66600,66601,66614,66615,66641,66642,65979,66682,1837],{},[38,66316,66317],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,66320,66322],{"className":66321},[886],[888,66323,66324],{"xmlns":890},[892,66325,66326,66364],{},[895,66327,66328,66334,66336,66338,66340,66346,66348,66350,66356,66358],{},[2142,66329,66330,66332],{},[898,66331,2146],{},[2148,66333,2701],{},[1706,66335,1708],{},[2148,66337,3359],{},[1706,66339,1715],{},[2142,66341,66342,66344],{},[898,66343,1702],{},[2148,66345,2701],{},[1706,66347,2447],{},[2148,66349,2495],{},[2142,66351,66352,66354],{},[898,66353,1702],{},[2148,66355,2495],{},[1706,66357,2447],{},[2142,66359,66360,66362],{},[898,66361,1702],{},[2148,66363,4284],{},[902,66365,66366],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,66368,66370],{"className":66369},[886],[888,66371,66372],{"xmlns":890},[892,66373,66374,66410],{},[895,66375,66376,66382,66384,66386,66388,66394,66396,66402,66404],{},[2142,66377,66378,66380],{},[898,66379,2146],{},[2148,66381,2495],{},[1706,66383,1708],{},[2148,66385,10800],{},[1706,66387,2447],{},[2142,66389,66390,66392],{},[898,66391,1702],{},[2148,66393,2701],{},[1706,66395,1715],{},[2142,66397,66398,66400],{},[898,66399,1702],{},[2148,66401,2495],{},[1706,66403,1715],{},[2142,66405,66406,66408],{},[898,66407,1702],{},[2148,66409,4284],{},[902,66411,66412],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,66414,66416],{"className":66415},[886],[888,66417,66418],{"xmlns":890},[892,66419,66420,66460],{},[895,66421,66422,66428,66430,66432,66434,66436,66442,66444,66450,66452,66454],{},[2142,66423,66424,66426],{},[898,66425,2146],{},[2148,66427,4284],{},[1706,66429,1708],{},[2148,66431,12717],{},[1706,66433,2447],{},[2148,66435,2495],{},[2142,66437,66438,66440],{},[898,66439,1702],{},[2148,66441,2701],{},[1706,66443,1715],{},[2142,66445,66446,66448],{},[898,66447,1702],{},[2148,66449,2495],{},[1706,66451,1715],{},[2148,66453,3455],{},[2142,66455,66456,66458],{},[898,66457,1702],{},[2148,66459,4284],{},[902,66461,66462],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,66465,66467],{"className":66466},[886],[888,66468,66469],{"xmlns":890},[892,66470,66471,66493],{},[895,66472,66473,66479,66481,66483,66485,66487],{},[2142,66474,66475,66477],{},[898,66476,2146],{},[2148,66478,2701],{},[1706,66480,1708],{},[1706,66482,1715],{},[2148,66484,12597],{},[1706,66486,2447],{},[2142,66488,66489,66491],{},[898,66490,1702],{},[2148,66492,2701],{},[902,66494,66495],{"encoding":904},"Q_1 = -7 + P_1",[883,66497,66499],{"className":66498},[886],[888,66500,66501],{"xmlns":890},[892,66502,66503,66527],{},[895,66504,66505,66511,66513,66515,66517,66519,66521],{},[2142,66506,66507,66509],{},[898,66508,2146],{},[2148,66510,2495],{},[1706,66512,1708],{},[1706,66514,1715],{},[2148,66516,3455],{},[1706,66518,2447],{},[2148,66520,3455],{},[2142,66522,66523,66525],{},[898,66524,1702],{},[2148,66526,2495],{},[902,66528,66529],{"encoding":904},"Q_2 = -4 + 4P_2",[883,66531,66533],{"className":66532},[886],[888,66534,66535],{"xmlns":890},[892,66536,66537,66561],{},[895,66538,66539,66545,66547,66549,66551,66553,66555],{},[2142,66540,66541,66543],{},[898,66542,2146],{},[2148,66544,4284],{},[1706,66546,1708],{},[1706,66548,1715],{},[2148,66550,7524],{},[1706,66552,2447],{},[2148,66554,2495],{},[2142,66556,66557,66559],{},[898,66558,1702],{},[2148,66560,4284],{},[902,66562,66563],{"encoding":904},"Q_3 = -5 + 2P_3",[883,66565,66567],{"className":66566},[886],[888,66568,66569],{"xmlns":890},[892,66570,66571,66579],{},[895,66572,66573],{},[2142,66574,66575,66577],{},[898,66576,2146],{},[898,66578,36887],{},[902,66580,66581],{"encoding":904},"Q_i",[883,66583,66585],{"className":66584},[886],[888,66586,66587],{"xmlns":890},[892,66588,66589,66597],{},[895,66590,66591],{},[2142,66592,66593,66595],{},[898,66594,1702],{},[898,66596,36887],{},[902,66598,66599],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,66602,66604],{"className":66603},[886],[888,66605,66606],{"xmlns":890},[892,66607,66608,66612],{},[895,66609,66610],{},[898,66611,36887],{},[902,66613,36887],{"encoding":904},"-tého zboží, ",[883,66616,66618],{"className":66617},[886],[888,66619,66620],{"xmlns":890},[892,66621,66622,66638],{},[895,66623,66624,66626,66628,66630,66632,66634,66636],{},[898,66625,36887],{},[1706,66627,1708],{},[2148,66629,2701],{},[1706,66631,2505],{"separator":2504},[2148,66633,2495],{},[1706,66635,2505],{"separator":2504},[2148,66637,4284],{},[902,66639,66640],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,66643,66645],{"className":66644},[886],[888,66646,66647],{"xmlns":890},[892,66648,66649,66679],{},[895,66650,66651,66659,66661,66669,66671],{},[28285,66652,66653,66655,66657],{},[898,66654,2146],{},[2148,66656,2701],{},[898,66658,23410],{},[1706,66660,2505],{"separator":2504},[28285,66662,66663,66665,66667],{},[898,66664,2146],{},[2148,66666,2495],{},[898,66668,23410],{},[1706,66670,2505],{"separator":2504},[28285,66672,66673,66675,66677],{},[898,66674,2146],{},[2148,66676,4284],{},[898,66678,23410],{},[902,66680,66681],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,66683,66685],{"className":66684},[886],[888,66686,66687],{"xmlns":890},[892,66688,66689,66719],{},[895,66690,66691,66699,66701,66709,66711],{},[28285,66692,66693,66695,66697],{},[898,66694,1702],{},[2148,66696,2701],{},[898,66698,23410],{},[1706,66700,2505],{"separator":2504},[28285,66702,66703,66705,66707],{},[898,66704,1702],{},[2148,66706,2495],{},[898,66708,23410],{},[1706,66710,2505],{"separator":2504},[28285,66712,66713,66715,66717],{},[898,66714,1702],{},[2148,66716,4284],{},[898,66718,23410],{},[902,66720,66721],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,66723,66724,18688,66727,66763,66764,1837],{},[38,66725,66726],{},"2.13",[883,66728,66730],{"className":66729},[886],[888,66731,66732],{"xmlns":890},[892,66733,66734,66760],{},[895,66735,66736,66738,66740,66742,66744,66746,66748,66750,66752,66754,66756,66758],{},[898,66737,1702],{},[1706,66739,1708],{},[898,66741,2334],{},[1706,66743,2140],{"stretchy":2139},[898,66745,2146],{},[1706,66747,2153],{"stretchy":2139},[1706,66749,1708],{},[1706,66751,1715],{},[2148,66753,3455],{},[898,66755,2146],{},[1706,66757,2447],{},[2148,66759,17219],{},[902,66761,66762],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,66765,66767],{"className":66766},[886],[888,66768,66769],{"xmlns":890},[892,66770,66771,66795],{},[895,66772,66773,66775,66777,66779,66781,66783,66785,66787,66789,66791,66793],{},[898,66774,1702],{},[1706,66776,1708],{},[898,66778,14171],{},[1706,66780,2140],{"stretchy":2139},[898,66782,2146],{},[1706,66784,2153],{"stretchy":2139},[1706,66786,1708],{},[2148,66788,4284],{},[898,66790,2146],{},[1706,66792,2447],{},[2148,66794,7786],{},[902,66796,66797],{"encoding":904},"P = S(Q) = 3Q + 10",[120,66799,66800,66837,66901,66961],{},[123,66801,66802,66803,65702,66820,1837],{},"(a) Určete rovnovážné množství ",[883,66804,66806],{"className":66805},[886],[888,66807,66808],{"xmlns":890},[892,66809,66810,66818],{},[895,66811,66812],{},[2489,66813,66814,66816],{},[898,66815,2146],{},[898,66817,23410],{},[902,66819,61452],{"encoding":904},[883,66821,66823],{"className":66822},[886],[888,66824,66825],{"xmlns":890},[892,66826,66827,66835],{},[895,66828,66829],{},[2489,66830,66831,66833],{},[898,66832,1702],{},[898,66834,23410],{},[902,66836,60519],{"encoding":904},[123,66838,66839,66840,66858,66859,66879,66880,66900],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,66841,66843],{"className":66842},[886],[888,66844,66845],{"xmlns":890},[892,66846,66847,66855],{},[895,66848,66849,66851,66853],{},[898,66850,1659],{},[1706,66852,1708],{},[2148,66854,12597],{},[902,66856,66857],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,66860,66862],{"className":66861},[886],[888,66863,66864],{"xmlns":890},[892,66865,66866,66876],{},[895,66867,66868],{},[28285,66869,66870,66872,66874],{},[898,66871,2146],{},[2148,66873,2701],{},[898,66875,23410],{},[902,66877,66878],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,66881,66883],{"className":66882},[886],[888,66884,66885],{"xmlns":890},[892,66886,66887,66897],{},[895,66888,66889],{},[28285,66890,66891,66893,66895],{},[898,66892,1702],{},[2148,66894,2701],{},[898,66896,23410],{},[902,66898,66899],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,66902,66903,66904,66858,66921,66879,66941,66900],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,66905,66907],{"className":66906},[886],[888,66908,66909],{"xmlns":890},[892,66910,66911,66919],{},[895,66912,66913,66915,66917],{},[898,66914,1659],{},[1706,66916,1708],{},[2148,66918,12597],{},[902,66920,66857],{"encoding":904},[883,66922,66924],{"className":66923},[886],[888,66925,66926],{"xmlns":890},[892,66927,66928,66938],{},[895,66929,66930],{},[28285,66931,66932,66934,66936],{},[898,66933,2146],{},[2148,66935,2495],{},[898,66937,23410],{},[902,66939,66940],{"encoding":904},"Q_2^E",[883,66942,66944],{"className":66943},[886],[888,66945,66946],{"xmlns":890},[892,66947,66948,66958],{},[895,66949,66950],{},[28285,66951,66952,66954,66956],{},[898,66953,1702],{},[2148,66955,2495],{},[898,66957,23410],{},[902,66959,66960],{"encoding":904},"P_2^E",[123,66962,66963],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,66965,66966,66967,1837],{},"Viz též ",[207,66968,61770],{"className":66969,"dataFsResolvedFilePath":809,"href":810},[210],[198,66971,62072],{"id":66972},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,66974,66975,18688,66978,66763,67014,1837],{},[38,66976,66977],{},"2.14",[883,66979,66981],{"className":66980},[886],[888,66982,66983],{"xmlns":890},[892,66984,66985,67011],{},[895,66986,66987,66989,66991,66993,66995,66997,66999,67001,67003,67005,67007,67009],{},[898,66988,1702],{},[1706,66990,1708],{},[898,66992,207],{},[898,66994,2146],{},[1706,66996,2447],{},[898,66998,2450],{},[1706,67000,1708],{},[1706,67002,1715],{},[2148,67004,2495],{},[898,67006,2146],{},[1706,67008,2447],{},[2148,67010,2728],{},[902,67012,67013],{"encoding":904},"P = aQ + b = -2Q + 50",[883,67015,67017],{"className":67016},[886],[888,67018,67019],{"xmlns":890},[892,67020,67021,67045],{},[895,67022,67023,67025,67027,67029,67031,67033,67035,67037,67039,67041,67043],{},[898,67024,1702],{},[1706,67026,1708],{},[898,67028,20413],{},[898,67030,2146],{},[1706,67032,2447],{},[898,67034,3120],{},[1706,67036,1708],{},[2148,67038,13775],{},[898,67040,2146],{},[1706,67042,2447],{},[2148,67044,3369],{},[902,67046,67047],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,67049,67050,67086,67089,67175,67228,67308,67362],{},[123,67051,66802,67052,65702,67069,1837],{},[883,67053,67055],{"className":67054},[886],[888,67056,67057],{"xmlns":890},[892,67058,67059,67067],{},[895,67060,67061],{},[2489,67062,67063,67065],{},[898,67064,2146],{},[898,67066,23410],{},[902,67068,61452],{"encoding":904},[883,67070,67072],{"className":67071},[886],[888,67073,67074],{"xmlns":890},[892,67075,67076,67084],{},[895,67077,67078],{},[2489,67079,67080,67082],{},[898,67081,1702],{},[898,67083,23410],{},[902,67085,60519],{"encoding":904},[123,67087,67088],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,67090,67091,67092,67109,67110,1889,67123,4202,67139,67155,67156,1837],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,67093,67095],{"className":67094},[886],[888,67096,67097],{"xmlns":890},[892,67098,67099,67107],{},[895,67100,67101],{},[2489,67102,67103,67105],{},[898,67104,2146],{},[898,67106,23410],{},[902,67108,61452],{"encoding":904}," odpovídající změně ",[883,67111,67113],{"className":67112},[886],[888,67114,67115],{"xmlns":890},[892,67116,67117,67121],{},[895,67118,67119],{},[898,67120,207],{},[902,67122,207],{"encoding":904},[883,67124,67126],{"className":67125},[886],[888,67127,67128],{"xmlns":890},[892,67129,67130,67136],{},[895,67131,67132,67134],{},[1706,67133,1715],{},[2148,67135,2495],{},[902,67137,67138],{"encoding":904},"-2",[883,67140,67142],{"className":67141},[886],[888,67143,67144],{"xmlns":890},[892,67145,67146,67152],{},[895,67147,67148,67150],{},[1706,67149,1715],{},[2148,67151,4284],{},[902,67153,67154],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,67157,67159],{"className":67158},[886],[888,67160,67161],{"xmlns":890},[892,67162,67163,67173],{},[895,67164,67165],{},[28285,67166,67167,67169,67171],{},[898,67168,2146],{},[2148,67170,2701],{},[898,67172,23410],{},[902,67174,66878],{"encoding":904},[123,67176,67177,67178,67109,67195,67208,67209,1837],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,67179,67181],{"className":67180},[886],[888,67182,67183],{"xmlns":890},[892,67184,67185,67193],{},[895,67186,67187],{},[2489,67188,67189,67191],{},[898,67190,2146],{},[898,67192,23410],{},[902,67194,61452],{"encoding":904},[883,67196,67198],{"className":67197},[886],[888,67199,67200],{"xmlns":890},[892,67201,67202,67206],{},[895,67203,67204],{},[898,67205,2450],{},[902,67207,2450],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,67210,67212],{"className":67211},[886],[888,67213,67214],{"xmlns":890},[892,67215,67216,67226],{},[895,67217,67218],{},[28285,67219,67220,67222,67224],{},[898,67221,2146],{},[2148,67223,2495],{},[898,67225,23410],{},[902,67227,66940],{"encoding":904},[123,67229,67230,67231,67109,67248,1889,67261,4202,67274,67155,67288,1837],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,67232,67234],{"className":67233},[886],[888,67235,67236],{"xmlns":890},[892,67237,67238,67246],{},[895,67239,67240],{},[2489,67241,67242,67244],{},[898,67243,2146],{},[898,67245,23410],{},[902,67247,61452],{"encoding":904},[883,67249,67251],{"className":67250},[886],[888,67252,67253],{"xmlns":890},[892,67254,67255,67259],{},[895,67256,67257],{},[898,67258,20413],{},[902,67260,20413],{"encoding":904},[883,67262,67264],{"className":67263},[886],[888,67265,67266],{"xmlns":890},[892,67267,67268,67272],{},[895,67269,67270],{},[2148,67271,13775],{},[902,67273,63506],{"encoding":904},[883,67275,67277],{"className":67276},[886],[888,67278,67279],{"xmlns":890},[892,67280,67281,67285],{},[895,67282,67283],{},[2148,67284,33696],{},[902,67286,67287],{"encoding":904},"0{,}8",[883,67289,67291],{"className":67290},[886],[888,67292,67293],{"xmlns":890},[892,67294,67295,67305],{},[895,67296,67297],{},[28285,67298,67299,67301,67303],{},[898,67300,2146],{},[2148,67302,4284],{},[898,67304,23410],{},[902,67306,67307],{"encoding":904},"Q_3^E",[123,67309,67310,67311,67109,67328,67341,67342,1837],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,67312,67314],{"className":67313},[886],[888,67315,67316],{"xmlns":890},[892,67317,67318,67326],{},[895,67319,67320],{},[2489,67321,67322,67324],{},[898,67323,2146],{},[898,67325,23410],{},[902,67327,61452],{"encoding":904},[883,67329,67331],{"className":67330},[886],[888,67332,67333],{"xmlns":890},[892,67334,67335,67339],{},[895,67336,67337],{},[898,67338,3120],{},[902,67340,3120],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,67343,67345],{"className":67344},[886],[888,67346,67347],{"xmlns":890},[892,67348,67349,67359],{},[895,67350,67351],{},[28285,67352,67353,67355,67357],{},[898,67354,2146],{},[2148,67356,3455],{},[898,67358,23410],{},[902,67360,67361],{"encoding":904},"Q_4^E",[123,67363,67364,67365,67382,67383,67396,67397,3570,67410,1343,67425,3570,67438,1993,67452,3570,67465,67480,67481,1837],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,67366,67368],{"className":67367},[886],[888,67369,67370],{"xmlns":890},[892,67371,67372,67380],{},[895,67373,67374],{},[2489,67375,67376,67378],{},[898,67377,2146],{},[898,67379,23410],{},[902,67381,61452],{"encoding":904}," odpovídající změnám ",[883,67384,67386],{"className":67385},[886],[888,67387,67388],{"xmlns":890},[892,67389,67390,67394],{},[895,67391,67392],{},[898,67393,207],{},[902,67395,207],{"encoding":904}," o 1, ",[883,67398,67400],{"className":67399},[886],[888,67401,67402],{"xmlns":890},[892,67403,67404,67408],{},[895,67405,67406],{},[898,67407,2450],{},[902,67409,2450],{"encoding":904},[883,67411,67413],{"className":67412},[886],[888,67414,67415],{"xmlns":890},[892,67416,67417,67423],{},[895,67418,67419,67421],{},[1706,67420,1715],{},[2148,67422,7786],{},[902,67424,38549],{"encoding":904},[883,67426,67428],{"className":67427},[886],[888,67429,67430],{"xmlns":890},[892,67431,67432,67436],{},[895,67433,67434],{},[898,67435,20413],{},[902,67437,20413],{"encoding":904},[883,67439,67441],{"className":67440},[886],[888,67442,67443],{"xmlns":890},[892,67444,67445,67449],{},[895,67446,67447],{},[2148,67448,14840],{},[902,67450,67451],{"encoding":904},"0{,}1",[883,67453,67455],{"className":67454},[886],[888,67456,67457],{"xmlns":890},[892,67458,67459,67463],{},[895,67460,67461],{},[898,67462,3120],{},[902,67464,3120],{"encoding":904},[883,67466,67468],{"className":67467},[886],[888,67469,67470],{"xmlns":890},[892,67471,67472,67478],{},[895,67473,67474,67476],{},[1706,67475,1715],{},[2148,67477,7786],{},[902,67479,38549],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,67482,67484],{"className":67483},[886],[888,67485,67486],{"xmlns":890},[892,67487,67488,67498],{},[895,67489,67490],{},[28285,67491,67492,67494,67496],{},[898,67493,2146],{},[2148,67495,7524],{},[898,67497,23410],{},[902,67499,67500],{"encoding":904},"Q_5^E",[724,67502,67503,18688,67506,66763,67529,1837],{},[38,67504,67505],{},"2.15",[883,67507,67509],{"className":67508},[886],[888,67510,67511],{"xmlns":890},[892,67512,67513,67527],{},[895,67514,67515,67517,67519,67521,67523,67525],{},[898,67516,1702],{},[1706,67518,1708],{},[898,67520,207],{},[898,67522,2146],{},[1706,67524,2447],{},[898,67526,2450],{},[902,67528,2453],{"encoding":904},[883,67530,67532],{"className":67531},[886],[888,67533,67534],{"xmlns":890},[892,67535,67536,67550],{},[895,67537,67538,67540,67542,67544,67546,67548],{},[898,67539,1702],{},[1706,67541,1708],{},[898,67543,20413],{},[898,67545,2146],{},[1706,67547,2447],{},[898,67549,3120],{},[902,67551,59296],{"encoding":904},[120,67553,67554,67629,67646,67755,67808,67862],{},[123,67555,67556,67557,67570,67571,67596,67597,67628],{},"(a) Odvoďte redukovaný tvar pro ",[883,67558,67560],{"className":67559},[886],[888,67561,67562],{"xmlns":890},[892,67563,67564,67568],{},[895,67565,67566],{},[898,67567,1702],{},[902,67569,1702],{"encoding":904},". Stanovte podmínky pro ",[883,67572,67574],{"className":67573},[886],[888,67575,67576],{"xmlns":890},[892,67577,67578,67594],{},[895,67579,67580,67582,67584,67586,67588,67590,67592],{},[898,67581,207],{},[1706,67583,2505],{"separator":2504},[898,67585,2450],{},[1706,67587,2505],{"separator":2504},[898,67589,20413],{},[1706,67591,2505],{"separator":2504},[898,67593,3120],{},[902,67595,62333],{"encoding":904}," tak, aby rovnovážný bod ",[883,67598,67600],{"className":67599},[886],[888,67601,67602],{"xmlns":890},[892,67603,67604,67626],{},[895,67605,67606,67608,67610,67616,67618,67624],{},[898,67607,23410],{},[1706,67609,21693],{"stretchy":2139},[2489,67611,67612,67614],{},[898,67613,2146],{},[898,67615,23410],{},[1706,67617,2505],{"separator":2504},[2489,67619,67620,67622],{},[898,67621,1702],{},[898,67623,23410],{},[1706,67625,21708],{"stretchy":2139},[902,67627,60420],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,67630,67631,67632,67645],{},"(b) Vypočtěte multiplikátory pro ",[883,67633,67635],{"className":67634},[886],[888,67636,67637],{"xmlns":890},[892,67638,67639,67643],{},[895,67640,67641],{},[898,67642,1702],{},[902,67644,1702],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,67647,67648,67649,1343,67669,1343,67687,1343,67705,67723,67724,67741,67742,1837],{},"(c) Pro hodnoty parametrů ",[883,67650,67652],{"className":67651},[886],[888,67653,67654],{"xmlns":890},[892,67655,67656,67666],{},[895,67657,67658,67660,67662,67664],{},[898,67659,207],{},[1706,67661,1708],{},[1706,67663,1715],{},[2148,67665,2495],{},[902,67667,67668],{"encoding":904},"a = -2",[883,67670,67672],{"className":67671},[886],[888,67673,67674],{"xmlns":890},[892,67675,67676,67684],{},[895,67677,67678,67680,67682],{},[898,67679,2450],{},[1706,67681,1708],{},[2148,67683,3508],{},[902,67685,67686],{"encoding":904},"b = 40",[883,67688,67690],{"className":67689},[886],[888,67691,67692],{"xmlns":890},[892,67693,67694,67702],{},[895,67695,67696,67698,67700],{},[898,67697,20413],{},[1706,67699,1708],{},[2148,67701,11496],{},[902,67703,67704],{"encoding":904},"c = 0{,}5",[883,67706,67708],{"className":67707},[886],[888,67709,67710],{"xmlns":890},[892,67711,67712,67720],{},[895,67713,67714,67716,67718],{},[898,67715,3120],{},[1706,67717,1708],{},[2148,67719,7786],{},[902,67721,67722],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,67725,67727],{"className":67726},[886],[888,67728,67729],{"xmlns":890},[892,67730,67731,67739],{},[895,67732,67733],{},[2489,67734,67735,67737],{},[898,67736,1702],{},[898,67738,23410],{},[902,67740,60519],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,67743,67745],{"className":67744},[886],[888,67746,67747],{"xmlns":890},[892,67748,67749,67753],{},[895,67750,67751],{},[898,67752,1702],{},[902,67754,1702],{"encoding":904},[123,67756,67757,67758,67109,67775,67788,67789,1837],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,67759,67761],{"className":67760},[886],[888,67762,67763],{"xmlns":890},[892,67764,67765,67773],{},[895,67766,67767],{},[2489,67768,67769,67771],{},[898,67770,1702],{},[898,67772,23410],{},[902,67774,60519],{"encoding":904},[883,67776,67778],{"className":67777},[886],[888,67779,67780],{"xmlns":890},[892,67781,67782,67786],{},[895,67783,67784],{},[898,67785,207],{},[902,67787,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,67790,67792],{"className":67791},[886],[888,67793,67794],{"xmlns":890},[892,67795,67796,67806],{},[895,67797,67798],{},[28285,67799,67800,67802,67804],{},[898,67801,1702],{},[2148,67803,2701],{},[898,67805,23410],{},[902,67807,66899],{"encoding":904},[123,67809,67810,67811,67828,67829,67842,67843,1837],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,67812,67814],{"className":67813},[886],[888,67815,67816],{"xmlns":890},[892,67817,67818,67826],{},[895,67819,67820],{},[2489,67821,67822,67824],{},[898,67823,1702],{},[898,67825,23410],{},[902,67827,60519],{"encoding":904}," odpovídající poklesu ",[883,67830,67832],{"className":67831},[886],[888,67833,67834],{"xmlns":890},[892,67835,67836,67840],{},[895,67837,67838],{},[898,67839,207],{},[902,67841,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,67844,67846],{"className":67845},[886],[888,67847,67848],{"xmlns":890},[892,67849,67850,67860],{},[895,67851,67852],{},[28285,67853,67854,67856,67858],{},[898,67855,1702],{},[2148,67857,2495],{},[898,67859,23410],{},[902,67861,66960],{"encoding":904},[123,67863,67864,67865,67382,67882,67895,67896,4202,67909,1993,67924,67937,67938,1837],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,67866,67868],{"className":67867},[886],[888,67869,67870],{"xmlns":890},[892,67871,67872,67880],{},[895,67873,67874],{},[2489,67875,67876,67878],{},[898,67877,1702],{},[898,67879,23410],{},[902,67881,60519],{"encoding":904},[883,67883,67885],{"className":67884},[886],[888,67886,67887],{"xmlns":890},[892,67888,67889,67893],{},[895,67890,67891],{},[898,67892,207],{},[902,67894,207],{"encoding":904}," na 35, ",[883,67897,67899],{"className":67898},[886],[888,67900,67901],{"xmlns":890},[892,67902,67903,67907],{},[895,67904,67905],{},[898,67906,20413],{},[902,67908,20413],{"encoding":904},[883,67910,67912],{"className":67911},[886],[888,67913,67914],{"xmlns":890},[892,67915,67916,67921],{},[895,67917,67918],{},[2148,67919,67920],{},"0,7",[902,67922,67923],{"encoding":904},"0{,}7",[883,67925,67927],{"className":67926},[886],[888,67928,67929],{"xmlns":890},[892,67930,67931,67935],{},[895,67932,67933],{},[898,67934,3120],{},[902,67936,3120],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,67939,67941],{"className":67940},[886],[888,67942,67943],{"xmlns":890},[892,67944,67945,67955],{},[895,67946,67947],{},[28285,67948,67949,67951,67953],{},[898,67950,1702],{},[2148,67952,4284],{},[898,67954,23410],{},[902,67956,67957],{"encoding":904},"P_3^E",[724,67959,67960,18688,67963,66763,67991,15842,68019,1993,68045,1837],{},[38,67961,67962],{},"2.16",[883,67964,67966],{"className":67965},[886],[888,67967,67968],{"xmlns":890},[892,67969,67970,67988],{},[895,67971,67972,67974,67976,67978,67980,67982],{},[898,67973,1702],{},[1706,67975,1708],{},[898,67977,207],{},[1706,67979,2447],{},[898,67981,2450],{},[2489,67983,67984,67986],{},[898,67985,2146],{},[2148,67987,2495],{},[902,67989,67990],{"encoding":904},"P = a + bQ^2",[883,67992,67994],{"className":67993},[886],[888,67995,67996],{"xmlns":890},[892,67997,67998,68016],{},[895,67999,68000,68002,68004,68006,68008,68010],{},[898,68001,1702],{},[1706,68003,1708],{},[898,68005,20413],{},[1706,68007,2447],{},[898,68009,3120],{},[2489,68011,68012,68014],{},[898,68013,2146],{},[2148,68015,2495],{},[902,68017,68018],{"encoding":904},"P = c + dQ^2",[883,68020,68022],{"className":68021},[886],[888,68023,68024],{"xmlns":890},[892,68025,68026,68042],{},[895,68027,68028,68030,68032,68034,68036,68038,68040],{},[898,68029,207],{},[1706,68031,2505],{"separator":2504},[898,68033,20413],{},[1706,68035,2505],{"separator":2504},[898,68037,3120],{},[1706,68039,8922],{},[2148,68041,2150],{},[902,68043,68044],{"encoding":904},"a, c, d > 0",[883,68046,68048],{"className":68047},[886],[888,68049,68050],{"xmlns":890},[892,68051,68052,68060],{},[895,68053,68054,68056,68058],{},[898,68055,2450],{},[1706,68057,2539],{},[2148,68059,2150],{},[902,68061,68062],{"encoding":904},"b \u003C 0",[120,68064,68065,68113,68129,68236,68288,68340,68449,68465,68564,68617],{},[123,68066,67556,68067,68080,68081,68112],{},[883,68068,68070],{"className":68069},[886],[888,68071,68072],{"xmlns":890},[892,68073,68074,68078],{},[895,68075,68076],{},[898,68077,2146],{},[902,68079,2146],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,68082,68084],{"className":68083},[886],[888,68085,68086],{"xmlns":890},[892,68087,68088,68110],{},[895,68089,68090,68092,68094,68100,68102,68108],{},[898,68091,23410],{},[1706,68093,21693],{"stretchy":2139},[2489,68095,68096,68098],{},[898,68097,2146],{},[898,68099,23410],{},[1706,68101,2505],{"separator":2504},[2489,68103,68104,68106],{},[898,68105,1702],{},[898,68107,23410],{},[1706,68109,21708],{"stretchy":2139},[902,68111,60420],{"encoding":904}," patřil do 1. kvadrantu.",[123,68114,67631,68115,68128],{},[883,68116,68118],{"className":68117},[886],[888,68119,68120],{"xmlns":890},[892,68121,68122,68126],{},[895,68123,68124],{},[898,68125,2146],{},[902,68127,2146],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,68130,67648,68131,1343,68149,1343,68169,1343,68187,68205,68206,67741,68223,1837],{},[883,68132,68134],{"className":68133},[886],[888,68135,68136],{"xmlns":890},[892,68137,68138,68146],{},[895,68139,68140,68142,68144],{},[898,68141,207],{},[1706,68143,1708],{},[2148,68145,2590],{},[902,68147,68148],{"encoding":904},"a = 100",[883,68150,68152],{"className":68151},[886],[888,68153,68154],{"xmlns":890},[892,68155,68156,68166],{},[895,68157,68158,68160,68162,68164],{},[898,68159,2450],{},[1706,68161,1708],{},[1706,68163,1715],{},[2148,68165,2701],{},[902,68167,68168],{"encoding":904},"b = -1",[883,68170,68172],{"className":68171},[886],[888,68173,68174],{"xmlns":890},[892,68175,68176,68184],{},[895,68177,68178,68180,68182],{},[898,68179,20413],{},[1706,68181,1708],{},[2148,68183,3369],{},[902,68185,68186],{"encoding":904},"c = 20",[883,68188,68190],{"className":68189},[886],[888,68191,68192],{"xmlns":890},[892,68193,68194,68202],{},[895,68195,68196,68198,68200],{},[898,68197,3120],{},[1706,68199,1708],{},[2148,68201,2701],{},[902,68203,68204],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,68207,68209],{"className":68208},[886],[888,68210,68211],{"xmlns":890},[892,68212,68213,68221],{},[895,68214,68215],{},[2489,68216,68217,68219],{},[898,68218,2146],{},[898,68220,23410],{},[902,68222,61452],{"encoding":904},[883,68224,68226],{"className":68225},[886],[888,68227,68228],{"xmlns":890},[892,68229,68230,68234],{},[895,68231,68232],{},[898,68233,2146],{},[902,68235,2146],{"encoding":904},[123,68237,67177,68238,67109,68255,68268,68269,1837],{},[883,68239,68241],{"className":68240},[886],[888,68242,68243],{"xmlns":890},[892,68244,68245,68253],{},[895,68246,68247],{},[2489,68248,68249,68251],{},[898,68250,2146],{},[898,68252,23410],{},[902,68254,61452],{"encoding":904},[883,68256,68258],{"className":68257},[886],[888,68259,68260],{"xmlns":890},[892,68261,68262,68266],{},[895,68263,68264],{},[898,68265,207],{},[902,68267,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,68270,68272],{"className":68271},[886],[888,68273,68274],{"xmlns":890},[892,68275,68276,68286],{},[895,68277,68278],{},[28285,68279,68280,68282,68284],{},[898,68281,2146],{},[2148,68283,2701],{},[898,68285,23410],{},[902,68287,66878],{"encoding":904},[123,68289,67230,68290,67109,68307,68320,68321,1837],{},[883,68291,68293],{"className":68292},[886],[888,68294,68295],{"xmlns":890},[892,68296,68297,68305],{},[895,68298,68299],{},[2489,68300,68301,68303],{},[898,68302,2146],{},[898,68304,23410],{},[902,68306,61452],{"encoding":904},[883,68308,68310],{"className":68309},[886],[888,68311,68312],{"xmlns":890},[892,68313,68314,68318],{},[895,68315,68316],{},[898,68317,20413],{},[902,68319,20413],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,68322,68324],{"className":68323},[886],[888,68325,68326],{"xmlns":890},[892,68327,68328,68338],{},[895,68329,68330],{},[28285,68331,68332,68334,68336],{},[898,68333,2146],{},[2148,68335,2495],{},[898,68337,23410],{},[902,68339,66940],{"encoding":904},[123,68341,67310,68342,67382,68359,68372,68373,4202,68386,68401,68402,68415,68416,68429,68430,1837],{},[883,68343,68345],{"className":68344},[886],[888,68346,68347],{"xmlns":890},[892,68348,68349,68357],{},[895,68350,68351],{},[2489,68352,68353,68355],{},[898,68354,2146],{},[898,68356,23410],{},[902,68358,61452],{"encoding":904},[883,68360,68362],{"className":68361},[886],[888,68363,68364],{"xmlns":890},[892,68365,68366,68370],{},[895,68367,68368],{},[898,68369,207],{},[902,68371,207],{"encoding":904}," na 110, poklesu ",[883,68374,68376],{"className":68375},[886],[888,68377,68378],{"xmlns":890},[892,68379,68380,68384],{},[895,68381,68382],{},[898,68383,2450],{},[902,68385,2450],{"encoding":904},[883,68387,68389],{"className":68388},[886],[888,68390,68391],{"xmlns":890},[892,68392,68393,68399],{},[895,68394,68395,68397],{},[1706,68396,1715],{},[2148,68398,2495],{},[902,68400,67138],{"encoding":904},", růstu ",[883,68403,68405],{"className":68404},[886],[888,68406,68407],{"xmlns":890},[892,68408,68409,68413],{},[895,68410,68411],{},[898,68412,20413],{},[902,68414,20413],{"encoding":904}," na 25 a růstu ",[883,68417,68419],{"className":68418},[886],[888,68420,68421],{"xmlns":890},[892,68422,68423,68427],{},[895,68424,68425],{},[898,68426,3120],{},[902,68428,3120],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,68431,68433],{"className":68432},[886],[888,68434,68435],{"xmlns":890},[892,68436,68437,68447],{},[895,68438,68439],{},[28285,68440,68441,68443,68445],{},[898,68442,2146],{},[2148,68444,4284],{},[898,68446,23410],{},[902,68448,67307],{"encoding":904},[123,68450,68451,68452,68128],{},"(i) Vypočtěte multiplikátory pro ",[883,68453,68455],{"className":68454},[886],[888,68456,68457],{"xmlns":890},[892,68458,68459,68463],{},[895,68460,68461],{},[898,68462,1702],{},[902,68464,1702],{"encoding":904},[123,68466,68467,68468,67741,68485,68498,68499,67109,68516,4202,68529,68544,68545,1837],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,68469,68471],{"className":68470},[886],[888,68472,68473],{"xmlns":890},[892,68474,68475,68483],{},[895,68476,68477],{},[2489,68478,68479,68481],{},[898,68480,1702],{},[898,68482,23410],{},[902,68484,60519],{"encoding":904},[883,68486,68488],{"className":68487},[886],[888,68489,68490],{"xmlns":890},[892,68491,68492,68496],{},[895,68493,68494],{},[898,68495,1702],{},[902,68497,1702],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,68500,68502],{"className":68501},[886],[888,68503,68504],{"xmlns":890},[892,68505,68506,68514],{},[895,68507,68508],{},[2489,68509,68510,68512],{},[898,68511,1702],{},[898,68513,23410],{},[902,68515,60519],{"encoding":904},[883,68517,68519],{"className":68518},[886],[888,68520,68521],{"xmlns":890},[892,68522,68523,68527],{},[895,68524,68525],{},[898,68526,207],{},[902,68528,207],{"encoding":904},[883,68530,68532],{"className":68531},[886],[888,68533,68534],{"xmlns":890},[892,68535,68536,68542],{},[895,68537,68538,68540],{},[1706,68539,1715],{},[2148,68541,4284],{},[902,68543,67154],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,68546,68548],{"className":68547},[886],[888,68549,68550],{"xmlns":890},[892,68551,68552,68562],{},[895,68553,68554],{},[28285,68555,68556,68558,68560],{},[898,68557,1702],{},[2148,68559,2701],{},[898,68561,23410],{},[902,68563,66899],{"encoding":904},[123,68565,68566,68567,67109,68584,68597,68598,1837],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,68568,68570],{"className":68569},[886],[888,68571,68572],{"xmlns":890},[892,68573,68574,68582],{},[895,68575,68576],{},[2489,68577,68578,68580],{},[898,68579,1702],{},[898,68581,23410],{},[902,68583,60519],{"encoding":904},[883,68585,68587],{"className":68586},[886],[888,68588,68589],{"xmlns":890},[892,68590,68591,68595],{},[895,68592,68593],{},[898,68594,207],{},[902,68596,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,68599,68601],{"className":68600},[886],[888,68602,68603],{"xmlns":890},[892,68604,68605,68615],{},[895,68606,68607],{},[28285,68608,68609,68611,68613],{},[898,68610,1702],{},[2148,68612,2495],{},[898,68614,23410],{},[902,68616,66960],{"encoding":904},[123,68618,68619,68620,67828,68637,68650,68651,4202,68664,68401,68679,68692,68693,68706,68707,1837],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,68621,68623],{"className":68622},[886],[888,68624,68625],{"xmlns":890},[892,68626,68627,68635],{},[895,68628,68629],{},[2489,68630,68631,68633],{},[898,68632,1702],{},[898,68634,23410],{},[902,68636,60519],{"encoding":904},[883,68638,68640],{"className":68639},[886],[888,68641,68642],{"xmlns":890},[892,68643,68644,68648],{},[895,68645,68646],{},[898,68647,207],{},[902,68649,207],{"encoding":904}," na 90, poklesu ",[883,68652,68654],{"className":68653},[886],[888,68655,68656],{"xmlns":890},[892,68657,68658,68662],{},[895,68659,68660],{},[898,68661,2450],{},[902,68663,2450],{"encoding":904},[883,68665,68667],{"className":68666},[886],[888,68668,68669],{"xmlns":890},[892,68670,68671,68677],{},[895,68672,68673,68675],{},[1706,68674,1715],{},[2148,68676,4284],{},[902,68678,67154],{"encoding":904},[883,68680,68682],{"className":68681},[886],[888,68683,68684],{"xmlns":890},[892,68685,68686,68690],{},[895,68687,68688],{},[898,68689,20413],{},[902,68691,20413],{"encoding":904}," na 30 a růstu ",[883,68694,68696],{"className":68695},[886],[888,68697,68698],{"xmlns":890},[892,68699,68700,68704],{},[895,68701,68702],{},[898,68703,3120],{},[902,68705,3120],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,68708,68710],{"className":68709},[886],[888,68711,68712],{"xmlns":890},[892,68713,68714,68724],{},[895,68715,68716],{},[28285,68717,68718,68720,68722],{},[898,68719,1702],{},[2148,68721,4284],{},[898,68723,23410],{},[902,68725,67957],{"encoding":904},[198,68727,820],{"id":68728},"přebytek-spotřebitele-a-výrobce-1",[724,68730,68731,18688,68734,66763,68770,1837],{},[38,68732,68733],{},"2.17",[883,68735,68737],{"className":68736},[886],[888,68738,68739],{"xmlns":890},[892,68740,68741,68767],{},[895,68742,68743,68745,68747,68749,68751,68753,68755,68757,68759,68761],{},[898,68744,1702],{},[1706,68746,1708],{},[898,68748,2334],{},[1706,68750,2140],{"stretchy":2139},[898,68752,2146],{},[1706,68754,2153],{"stretchy":2139},[1706,68756,1708],{},[2148,68758,34145],{},[1706,68760,1715],{},[2489,68762,68763,68765],{},[898,68764,2146],{},[2148,68766,2495],{},[902,68768,68769],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,68771,68773],{"className":68772},[886],[888,68774,68775],{"xmlns":890},[892,68776,68777,68803],{},[895,68778,68779,68781,68783,68785,68787,68789,68791,68793,68795,68797],{},[898,68780,1702],{},[1706,68782,1708],{},[898,68784,14171],{},[1706,68786,2140],{"stretchy":2139},[898,68788,2146],{},[1706,68790,2153],{"stretchy":2139},[1706,68792,1708],{},[2148,68794,4284],{},[1706,68796,2447],{},[2489,68798,68799,68801],{},[898,68800,2146],{},[2148,68802,2495],{},[902,68804,68805],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,68807,68808,68811],{},[123,68809,68810],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,68812,68813],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,68815,68816,18688,68819,66763,68853,1837],{},[38,68817,68818],{},"2.18",[883,68820,68822],{"className":68821},[886],[888,68823,68824],{"xmlns":890},[892,68825,68826,68850],{},[895,68827,68828,68830,68832,68834,68836,68838,68840,68842,68844,68846,68848],{},[898,68829,1702],{},[1706,68831,1708],{},[898,68833,2334],{},[1706,68835,2140],{"stretchy":2139},[898,68837,2146],{},[1706,68839,2153],{"stretchy":2139},[1706,68841,1708],{},[2148,68843,22884],{},[1706,68845,1715],{},[2148,68847,2495],{},[898,68849,2146],{},[902,68851,68852],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,68854,68856],{"className":68855},[886],[888,68857,68858],{"xmlns":890},[892,68859,68860,68886],{},[895,68861,68862,68864,68866,68868,68870,68872,68874,68876,68878,68880],{},[898,68863,1702],{},[1706,68865,1708],{},[898,68867,14171],{},[1706,68869,2140],{"stretchy":2139},[898,68871,2146],{},[1706,68873,2153],{"stretchy":2139},[1706,68875,1708],{},[2148,68877,4284],{},[1706,68879,2447],{},[2489,68881,68882,68884],{},[898,68883,2146],{},[2148,68885,2495],{},[902,68887,68805],{"encoding":904},[120,68889,68890,68910,68913,68916],{},[123,68891,68892,68893,1837],{},"(a) Vypočtěte rovnovážné množství ",[883,68894,68896],{"className":68895},[886],[888,68897,68898],{"xmlns":890},[892,68899,68900,68908],{},[895,68901,68902],{},[2489,68903,68904,68906],{},[898,68905,2146],{},[898,68907,23410],{},[902,68909,61452],{"encoding":904},[123,68911,68912],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,68914,68915],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,68917,68918],{},"(c) Graficky interpretujte.",[56029,68920],{},[115,68922,15880],{"id":15879},[152,68924,68925,68928,68931,68934,68937,68940,68943,68946,68949,68952,68955,68958,68961,68964],{},[123,68926,68927],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,68929,68930],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,68932,68933],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,68935,68936],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,68938,68939],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,68941,68942],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,68944,68945],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,68947,68948],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,68950,68951],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,68953,68954],{},"K čemu slouží multiplikátory?",[123,68956,68957],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,68959,68960],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,68962,68963],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,68965,68966],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[56029,68968],{},[115,68970,19879],{"id":19878},[724,68972,68973],{},[38,68974,32268],{},[120,68976,68977,69012,69017,69047,69052,69115,69140,69145,69175,69184,69191,69197],{},[123,68978,68979,2314,68982,37745,68985,1647,68987,1343,69010],{},[38,68980,68981],{},"Poptávané množství",[614,68983,68984],{},"quantity demanded",[38,68986,47073],{},[883,68988,68990],{"className":68989},[886],[888,68991,68992],{"xmlns":890},[892,68993,68994,69008],{},[895,68995,68996,68998,69000,69002,69004,69006],{},[898,68997,2146],{},[1706,68999,1708],{},[898,69001,2334],{},[1706,69003,2140],{"stretchy":2139},[898,69005,1702],{},[1706,69007,2153],{"stretchy":2139},[902,69009,23350],{"encoding":904},[38,69011,56506],{},[123,69013,69014,69016],{},[38,69015,56513],{}," — substituční + důchodový efekt",[123,69018,69019,1647,69022],{},[38,69020,69021],{},"Reálné cenové rozpětí",[883,69023,69025],{"className":69024},[886],[888,69026,69027],{"xmlns":890},[892,69028,69029,69045],{},[895,69030,69031,69033,69035,69037,69043],{},[1706,69032,2140],{"stretchy":2139},[2148,69034,2150],{},[1706,69036,2505],{"separator":2504},[2142,69038,69039,69041],{},[898,69040,1702],{},[2148,69042,2150],{},[1706,69044,2153],{"stretchy":2139},[902,69046,56714],{"encoding":904},[123,69048,69049,30208],{},[38,69050,69051],{},"Homogenita poptávky",[123,69053,69054,1647,69057,1343,69080,1343,69097,69114],{},[38,69055,69056],{},"Lineární poptávka",[883,69058,69060],{"className":69059},[886],[888,69061,69062],{"xmlns":890},[892,69063,69064,69078],{},[895,69065,69066,69068,69070,69072,69074,69076],{},[898,69067,1702],{},[1706,69069,1708],{},[898,69071,207],{},[898,69073,2146],{},[1706,69075,2447],{},[898,69077,2450],{},[902,69079,2453],{"encoding":904},[883,69081,69083],{"className":69082},[886],[888,69084,69085],{"xmlns":890},[892,69086,69087,69095],{},[895,69088,69089,69091,69093],{},[898,69090,207],{},[1706,69092,2539],{},[2148,69094,2150],{},[902,69096,2544],{"encoding":904},[883,69098,69100],{"className":69099},[886],[888,69101,69102],{"xmlns":890},[892,69103,69104,69112],{},[895,69105,69106,69108,69110],{},[898,69107,2450],{},[1706,69109,8922],{},[2148,69111,2150],{},[902,69113,37911],{"encoding":904}," — nedokonalá konkurence",[123,69116,69117,21021,69119],{},[38,69118,21020],{},[883,69120,69122],{"className":69121},[886],[888,69123,69124],{"xmlns":890},[892,69125,69126,69138],{},[895,69127,69128,69130,69132],{},[898,69129,1702],{},[1706,69131,1708],{},[2489,69133,69134,69136],{},[898,69135,1702],{},[1706,69137,3197],{},[902,69139,21043],{"encoding":904},[123,69141,69142,69144],{},[38,69143,57282],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,69146,69147,1647,69149,1343,69173],{},[38,69148,50789],{},[883,69150,69152],{"className":69151},[886],[888,69153,69154],{"xmlns":890},[892,69155,69156,69170],{},[895,69157,69158,69160,69162,69164,69166,69168],{},[898,69159,2146],{},[1706,69161,1708],{},[898,69163,23410],{},[1706,69165,2140],{"stretchy":2139},[898,69167,28247],{},[1706,69169,2153],{"stretchy":2139},[902,69171,69172],{"encoding":904},"Q = E(Y)",[38,69174,57478],{},[123,69176,69177,69180,69181,69183],{},[38,69178,69179],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,69182,57924],{}," zboží",[123,69185,69186,1993,69188,69190],{},[38,69187,58930],{},[38,69189,58877],{}," — znaménka zkřížených koeficientů",[123,69192,69193,69196],{},[38,69194,69195],{},"Dvoukomoditní trh"," (2.6)",[123,69198,69199,2314,69202,2153],{},[38,69200,69201],{},"Posun poptávky",[614,69203,57982],{},[724,69205,69206],{},[38,69207,32232],{},[120,69209,69210,69243,69247,69292],{},[123,69211,69212,2314,69214,37745,69216,1647,69218,1343,69241],{},[38,69213,59323],{},[614,69215,59326],{},[38,69217,59496],{},[883,69219,69221],{"className":69220},[886],[888,69222,69223],{"xmlns":890},[892,69224,69225,69239],{},[895,69226,69227,69229,69231,69233,69235,69237],{},[898,69228,2146],{},[1706,69230,1708],{},[898,69232,14171],{},[1706,69234,2140],{"stretchy":2139},[898,69236,1702],{},[1706,69238,2153],{"stretchy":2139},[902,69240,27803],{"encoding":904},[38,69242,59574],{},[123,69244,69245],{},[38,69246,59581],{},[123,69248,69249,1647,69252,1343,69275],{},[38,69250,69251],{},"Lineární nabídka",[883,69253,69255],{"className":69254},[886],[888,69256,69257],{"xmlns":890},[892,69258,69259,69273],{},[895,69260,69261,69263,69265,69267,69269,69271],{},[898,69262,1702],{},[1706,69264,1708],{},[898,69266,20413],{},[898,69268,2146],{},[1706,69270,2447],{},[898,69272,3120],{},[902,69274,59296],{"encoding":904},[883,69276,69278],{"className":69277},[886],[888,69279,69280],{"xmlns":890},[892,69281,69282,69290],{},[895,69283,69284,69286,69288],{},[898,69285,20413],{},[1706,69287,8922],{},[2148,69289,2150],{},[902,69291,59314],{"encoding":904},[123,69293,69294,2314,69297,2153],{},[38,69295,69296],{},"Posun nabídky",[614,69298,59959],{},[724,69300,69301],{},[38,69302,69303],{},"Rovnováha a komparativní statika",[120,69305,69306,69385,69391],{},[123,69307,69308,2314,69310,37745,69312,1647,69315,1343,69332,1647,69335,1343,69352,1647,69354],{},[38,69309,60378],{},[614,69311,60497],{},[38,69313,69314],{},"rovnovážná cena",[883,69316,69318],{"className":69317},[886],[888,69319,69320],{"xmlns":890},[892,69321,69322,69330],{},[895,69323,69324],{},[2489,69325,69326,69328],{},[898,69327,1702],{},[898,69329,23410],{},[902,69331,60519],{"encoding":904},[38,69333,69334],{},"rovnovážné množství",[883,69336,69338],{"className":69337},[886],[888,69339,69340],{"xmlns":890},[892,69341,69342,69350],{},[895,69343,69344],{},[2489,69345,69346,69348],{},[898,69347,2146],{},[898,69349,23410],{},[902,69351,61452],{"encoding":904},[38,69353,60554],{},[883,69355,69357],{"className":69356},[886],[888,69358,69359],{"xmlns":890},[892,69360,69361,69383],{},[895,69362,69363,69365,69367,69373,69375,69381],{},[898,69364,23410],{},[1706,69366,21693],{"stretchy":2139},[2489,69368,69369,69371],{},[898,69370,2146],{},[898,69372,23410],{},[1706,69374,2505],{"separator":2504},[2489,69376,69377,69379],{},[898,69378,1702],{},[898,69380,23410],{},[1706,69382,21708],{"stretchy":2139},[902,69384,60420],{"encoding":904},[123,69386,69387,69390],{},[38,69388,69389],{},"Pravidla 1–4"," komparativní statiky",[123,69392,69393,2314,69396,2153],{},[38,69394,69395],{},"Teorém pavučiny",[614,69397,61398],{},[724,69399,69400],{},[38,69401,69402],{},"Zdanění",[120,69404,69405,69461,69509],{},[123,69406,69407,69409,69410,69435,69436,2153],{},[38,69408,69402],{}," — daň výrobci (",[883,69411,69413],{"className":69412},[886],[888,69414,69415],{"xmlns":890},[892,69416,69417,69433],{},[895,69418,69419,69425,69427,69429,69431],{},[2142,69420,69421,69423],{},[898,69422,14171],{},[2148,69424,2701],{},[1706,69426,1708],{},[898,69428,14171],{},[1706,69430,2447],{},[898,69432,1659],{},[902,69434,61803],{"encoding":904},") vs. daň spotřebiteli (",[883,69437,69439],{"className":69438},[886],[888,69440,69441],{"xmlns":890},[892,69442,69443,69459],{},[895,69444,69445,69451,69453,69455,69457],{},[2142,69446,69447,69449],{},[898,69448,2334],{},[2148,69450,2495],{},[1706,69452,1708],{},[898,69454,2334],{},[1706,69456,1715],{},[898,69458,1659],{},[902,69460,61834],{"encoding":904},[123,69462,69463,1647,69465,1343,69486],{},[38,69464,61707],{},[883,69466,69468],{"className":69467},[886],[888,69469,69470],{"xmlns":890},[892,69471,69472,69484],{},[895,69473,69474],{},[2142,69475,69476,69478],{},[898,69477,1659],{},[895,69479,69480,69482],{},[898,69481,61726],{},[898,69483,724],{},[902,69485,61731],{"encoding":904},[883,69487,69489],{"className":69488},[886],[888,69490,69491],{"xmlns":890},[892,69492,69493,69507],{},[895,69494,69495],{},[2142,69496,69497,69499],{},[898,69498,1659],{},[895,69500,69501,69503,69505],{},[898,69502,61749],{},[898,69504,6930],{},[898,69506,3950],{},[902,69508,61756],{"encoding":904},[123,69510,69511,1647,69514,1343,69543],{},[38,69512,69513],{},"Ekvivalence zdanění",[883,69515,69517],{"className":69516},[886],[888,69518,69519],{"xmlns":890},[892,69520,69521,69541],{},[895,69522,69523,69531,69533],{},[28285,69524,69525,69527,69529],{},[898,69526,2146],{},[2148,69528,2701],{},[898,69530,23410],{},[1706,69532,1708],{},[28285,69534,69535,69537,69539],{},[898,69536,2146],{},[2148,69538,2495],{},[898,69540,23410],{},[902,69542,61957],{"encoding":904},[883,69544,69546],{"className":69545},[886],[888,69547,69548],{"xmlns":890},[892,69549,69550,69574],{},[895,69551,69552,69560,69562,69564,69566],{},[28285,69553,69554,69556,69558],{},[898,69555,1702],{},[2148,69557,2701],{},[898,69559,23410],{},[1706,69561,1715],{},[898,69563,1659],{},[1706,69565,1708],{},[28285,69567,69568,69570,69572],{},[898,69569,1702],{},[2148,69571,2495],{},[898,69573,23410],{},[902,69575,61991],{"encoding":904},[724,69577,69578],{},[38,69579,45479],{},[120,69581,69582,69628,69659,69664,69670,69677],{},[123,69583,69584,1647,69586],{},[38,69585,62090],{},[883,69587,69589],{"className":69588},[886],[888,69590,69591],{"xmlns":890},[892,69592,69593,69625],{},[895,69594,69595,69601,69603,69605,69607,69609,69611,69613,69615,69617,69619,69621,69623],{},[2489,69596,69597,69599],{},[898,69598,2146],{},[898,69600,23410],{},[1706,69602,1708],{},[1706,69604,2140],{"stretchy":2139},[898,69606,2450],{},[1706,69608,1715],{},[898,69610,3120],{},[1706,69612,2153],{"stretchy":2139},[898,69614,15493],{"mathvariant":2409},[1706,69616,2140],{"stretchy":2139},[898,69618,20413],{},[1706,69620,1715],{},[898,69622,207],{},[1706,69624,2153],{"stretchy":2139},[902,69626,69627],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,69629,69630,1647,69633,69658],{},[38,69631,69632],{},"Parametry",[883,69634,69636],{"className":69635},[886],[888,69637,69638],{"xmlns":890},[892,69639,69640,69656],{},[895,69641,69642,69644,69646,69648,69650,69652,69654],{},[898,69643,207],{},[1706,69645,2505],{"separator":2504},[898,69647,2450],{},[1706,69649,2505],{"separator":2504},[898,69651,20413],{},[1706,69653,2505],{"separator":2504},[898,69655,3120],{},[902,69657,62333],{"encoding":904}," — exogenní proměnné",[123,69660,69661],{},[38,69662,69663],{},"Endogenní \u002F exogenní proměnná",[123,69665,69666,69669],{},[38,69667,69668],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,69671,69672,1343,69675],{},[38,69673,69674],{},"Komparativní statika",[38,69676,56019],{},[123,69678,69679,1647,69681,69697],{},[38,69680,22143],{},[883,69682,69684],{"className":69683},[886],[888,69685,69686],{"xmlns":890},[892,69687,69688,69694],{},[895,69689,69690,69692],{},[898,69691,3120],{},[898,69693,2146],{},[902,69695,69696],{"encoding":904},"dQ"," (2.11)",[724,69699,69700],{},[38,69701,69702],{},"Přebytky a ostatní",[120,69704,69705,69743],{},[123,69706,69707,1647,69709,69724,69725,1647,69727,69742],{},[38,69708,63980],{},[883,69710,69712],{"className":69711},[886],[888,69713,69714],{"xmlns":890},[892,69715,69716,69722],{},[895,69717,69718,69720],{},[898,69719,1683],{},[898,69721,14171],{},[902,69723,63996],{"encoding":904}," (2.14), ",[38,69726,63999],{},[883,69728,69730],{"className":69729},[886],[888,69731,69732],{"xmlns":890},[892,69733,69734,69740],{},[895,69735,69736,69738],{},[898,69737,1702],{},[898,69739,14171],{},[902,69741,64015],{"encoding":904}," (2.15)",[123,69744,69745,1343,69748,69751],{},[38,69746,69747],{},"Homo economicus",[38,69749,69750],{},"Marshallova formulace"," (1890)",[56029,69753],{},[115,69755,21083],{"id":21082},[120,69757,69758,69792,69801],{},[123,69759,69760,1647,69762,69765,69766,1343,69769,69772,69773,69776,69777,69780,69781,69784,69785,69788,69789],{},[38,69761,21090],{},[207,69763,811],{"className":69764,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,69767,820],{"className":69768,"dataFsResolvedFilePath":818,"href":819},[210],[207,69770,21102],{"className":69771,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,69774,775],{"className":69775,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,69778,784],{"className":69779,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,69782,793],{"className":69783,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,69786,21098],{"className":69787,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,69790,22995],{"className":69791,"dataFsResolvedFilePath":827,"href":828},[210],[123,69793,69794,1647,69797],{},[38,69795,69796],{},"Shrnutí přednášek:",[207,69798,69800],{"className":69799,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,69802,69803,1647,69805],{},[38,69804,21126],{},[207,69806,21132],{"className":69807,"dataFsResolvedFilePath":21130,"href":21131},[210],{"title":641,"searchDepth":642,"depth":642,"links":69809},[69810,69811,69819,69825,69832,69833,69840,69841,69842,69849,69850,69851],{"id":55854,"depth":642,"text":55855},{"id":55835,"depth":642,"text":32268,"children":69812},[69813,69814,69815,69816,69818],{"id":56121,"depth":649,"text":56122},{"id":56403,"depth":649,"text":56404},{"id":57410,"depth":649,"text":57411},{"id":57978,"depth":649,"text":69817},"Posun poptávky (shift of demand)",{"id":58482,"depth":649,"text":58483},{"id":55839,"depth":642,"text":32232,"children":69820},[69821,69822,69823],{"id":59318,"depth":649,"text":56122},{"id":59503,"depth":649,"text":59504},{"id":59955,"depth":649,"text":69824},"Posun nabídky (shift of supply)",{"id":60377,"depth":642,"text":60378,"children":69826},[69827,69828,69829,69830,69831],{"id":60489,"depth":649,"text":60490},{"id":60701,"depth":649,"text":60702},{"id":61016,"depth":649,"text":61017},{"id":61370,"depth":649,"text":61371},{"id":61401,"depth":649,"text":61402},{"id":61670,"depth":642,"text":811},{"id":62071,"depth":642,"text":62072,"children":69834},[69835,69836,69837,69838],{"id":62089,"depth":649,"text":62090},{"id":62468,"depth":649,"text":62469},{"id":62851,"depth":649,"text":62852},{"id":63305,"depth":649,"text":69839},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":30893,"depth":642,"text":820},{"id":64230,"depth":642,"text":64231},{"id":64461,"depth":642,"text":64462,"children":69843},[69844,69845,69846,69847,69848],{"id":64465,"depth":649,"text":64466},{"id":65303,"depth":649,"text":65304},{"id":65679,"depth":649,"text":60378},{"id":66972,"depth":649,"text":62072},{"id":68728,"depth":649,"text":820},{"id":15879,"depth":642,"text":15880},{"id":19878,"depth":642,"text":19879},{"id":21082,"depth":642,"text":21083},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,69858,69859,69860,36980,69861,69862],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":69865,"title":820,"body":69866,"course":1128,"courses":659,"created":21169,"description":641,"extension":661,"meta":74143,"navigation":664,"path":74144,"seo":74145,"sources":74146,"stem":74147,"tags":74148,"type":21181,"updated":677,"__hash__":74153},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":69867,"toc":74121},[69868,69870,69938,69988,69990,69992,70250,70326,70331,70333,70352,70356,70432,70517,70519,70833,70926,70928,70947,70951,71025,71110,71113,71289,71294,71296,71716,71718,71722,71726,71962,72006,72106,72172,72175,72208,72383,72445,72575,72653,72764,72798,72996,73015,73034,73099,73103,73106,73151,73154,73272,73318,73320,73324,73672,73674,73676,73954,73956,73960,73995,74002,74075,74077,74079],[12,69869,820],{"id":30893},[1636,69871,69872],{},[724,69873,69874,1643,69876,2314,69878,69893,69894,2314,69896,69911,69912,69934,69935,1837],{},[883,69875,1642],{},[38,69877,63980],{},[883,69879,69881],{"className":69880},[886],[888,69882,69883],{"xmlns":890},[892,69884,69885,69891],{},[895,69886,69887,69889],{},[898,69888,1683],{},[898,69890,14171],{},[902,69892,63996],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,69895,64127],{},[883,69897,69899],{"className":69898},[886],[888,69900,69901],{"xmlns":890},[892,69902,69903,69909],{},[895,69904,69905,69907],{},[898,69906,1702],{},[898,69908,14171],{},[902,69910,64015],{"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 ",[883,69913,69915],{"className":69914},[886],[888,69916,69917],{"xmlns":890},[892,69918,69919,69931],{},[895,69920,69921,69923,69925,69927,69929],{},[898,69922,1683],{},[898,69924,14171],{},[1706,69926,2447],{},[898,69928,1702],{},[898,69930,14171],{},[902,69932,69933],{"encoding":904},"CS + PS"," měří ",[38,69936,69937],{},"celkový blahobyt trhu",[724,69939,69940,2314,69942,1343,69944,5354,69959,2314,69961,1343,69963,69978,69979,69983,69984,1837],{},[38,69941,63980],{},[614,69943,64034],{},[883,69945,69947],{"className":69946},[886],[888,69948,69949],{"xmlns":890},[892,69950,69951,69957],{},[895,69952,69953,69955],{},[898,69954,1683],{},[898,69956,14171],{},[902,69958,63996],{"encoding":904},[38,69960,63999],{},[614,69962,64130],{},[883,69964,69966],{"className":69965},[886],[888,69967,69968],{"xmlns":890},[892,69969,69970,69976],{},[895,69971,69972,69974],{},[898,69973,1702],{},[898,69975,14171],{},[902,69977,64015],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,69980,69982],{"className":69981,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,69985,69987],{"className":69986,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[56029,69989],{},[115,69991,1241],{"id":1840},[724,69993,69994,69995,70018,70019,70042,70043,70060,70061,23078,70093,70125,70126,70152,70153,70156,70157,70160,70161,33118,70195,15842,70216,1837],{},"Je dána funkce poptávky ",[883,69996,69998],{"className":69997},[886],[888,69999,70000],{"xmlns":890},[892,70001,70002,70016],{},[895,70003,70004,70006,70008,70010,70012,70014],{},[898,70005,1702],{},[1706,70007,1708],{},[898,70009,2334],{},[1706,70011,2140],{"stretchy":2139},[898,70013,2146],{},[1706,70015,2153],{"stretchy":2139},[902,70017,2343],{"encoding":904},", resp. funkce nabídky ",[883,70020,70022],{"className":70021},[886],[888,70023,70024],{"xmlns":890},[892,70025,70026,70040],{},[895,70027,70028,70030,70032,70034,70036,70038],{},[898,70029,1702],{},[1706,70031,1708],{},[898,70033,14171],{},[1706,70035,2140],{"stretchy":2139},[898,70037,2146],{},[1706,70039,2153],{"stretchy":2139},[902,70041,60124],{"encoding":904},". Pro pevně zadané množství ",[883,70044,70046],{"className":70045},[886],[888,70047,70048],{"xmlns":890},[892,70049,70050,70058],{},[895,70051,70052],{},[2142,70053,70054,70056],{},[898,70055,2146],{},[2148,70057,2150],{},[902,70059,8625],{"encoding":904}," je odpovídající cena ",[883,70062,70064],{"className":70063},[886],[888,70065,70066],{"xmlns":890},[892,70067,70068,70090],{},[895,70069,70070,70076,70078,70080,70082,70088],{},[2142,70071,70072,70074],{},[898,70073,1702],{},[2148,70075,2150],{},[1706,70077,1708],{},[898,70079,2334],{},[1706,70081,2140],{"stretchy":2139},[2142,70083,70084,70086],{},[898,70085,2146],{},[2148,70087,2150],{},[1706,70089,2153],{"stretchy":2139},[902,70091,70092],{"encoding":904},"P_0 = D(Q_0)",[883,70094,70096],{"className":70095},[886],[888,70097,70098],{"xmlns":890},[892,70099,70100,70122],{},[895,70101,70102,70108,70110,70112,70114,70120],{},[2142,70103,70104,70106],{},[898,70105,1702],{},[2148,70107,2150],{},[1706,70109,1708],{},[898,70111,14171],{},[1706,70113,2140],{"stretchy":2139},[2142,70115,70116,70118],{},[898,70117,2146],{},[2148,70119,2150],{},[1706,70121,2153],{"stretchy":2139},[902,70123,70124],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,70127,70129],{"className":70128},[886],[888,70130,70131],{"xmlns":890},[892,70132,70133,70149],{},[895,70134,70135,70141,70143],{},[2142,70136,70137,70139],{},[898,70138,1702],{},[2148,70140,2150],{},[2415,70142,2799],{},[2142,70144,70145,70147],{},[898,70146,2146],{},[2148,70148,2150],{},[902,70150,70151],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,70154,70155],{},"výdaje spotřebitele",", nebo ",[38,70158,70159],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,70162,70164],{"className":70163},[886],[888,70165,70166],{"xmlns":890},[892,70167,70168,70192],{},[895,70169,70170,70172,70174,70180,70182,70184,70186],{},[2148,70171,2150],{},[2415,70173,2799],{},[2142,70175,70176,70178],{},[898,70177,2146],{},[2148,70179,2150],{},[2415,70181,2799],{},[898,70183,1735],{},[2415,70185,2799],{},[2142,70187,70188,70190],{},[898,70189,1702],{},[2148,70191,2150],{},[902,70193,70194],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,70196,70198],{"className":70197},[886],[888,70199,70200],{"xmlns":890},[892,70201,70202,70214],{},[895,70203,70204,70206,70208,70210,70212],{},[1706,70205,2140],{"stretchy":2139},[898,70207,2146],{},[1706,70209,2505],{"separator":2504},[898,70211,1702],{},[1706,70213,2153],{"stretchy":2139},[902,70215,56748],{"encoding":904},[883,70217,70219],{"className":70218},[886],[888,70220,70221],{"xmlns":890},[892,70222,70223,70247],{},[895,70224,70225,70227,70229,70231,70237,70239,70245],{},[898,70226,1735],{},[1706,70228,1708],{},[1706,70230,21693],{"stretchy":2139},[2142,70232,70233,70235],{},[898,70234,2146],{},[2148,70236,2150],{},[1706,70238,2505],{"separator":2504},[2142,70240,70241,70243],{},[898,70242,1702],{},[2148,70244,2150],{},[1706,70246,21708],{"stretchy":2139},[902,70248,70249],{"encoding":904},"A = [Q_0, P_0]",[1636,70251,70252,70257,70315],{},[724,70253,70254,70256],{},[883,70255,3174],{}," Intuice",[120,70258,70259,70287],{},[123,70260,70261,70262,70265,70266,70268,70269,70286],{},"Za jednotky zboží nakoupené ",[38,70263,70264],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,70267,44342],{}," než ",[883,70270,70272],{"className":70271},[886],[888,70273,70274],{"xmlns":890},[892,70275,70276,70284],{},[895,70277,70278],{},[2142,70279,70280,70282],{},[898,70281,1702],{},[2148,70283,2150],{},[902,70285,58003],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,70288,70289,70290,70292,70293,70296,70297,70314],{},"Za jednotky zboží prodané ",[38,70291,70264],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,70294,70295],{},"nižší"," cenu než ",[883,70298,70300],{"className":70299},[886],[888,70301,70302],{"xmlns":890},[892,70303,70304,70312],{},[895,70305,70306],{},[2142,70307,70308,70310],{},[898,70309,1702],{},[2148,70311,2150],{},[902,70313,58003],{"encoding":904}," — rozdíl je jeho přebytek.",[724,70316,70317,70318,70321,70322,70325],{},"Přebytek je tedy rozdíl mezi ",[614,70319,70320],{},"ochotou"," (platit \u002F prodávat) a ",[614,70323,70324],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,70327,70328],{},[2286,70329],{"alt":64025,"className":70330,"src":64027},[210,2290],[56029,70332],{},[115,70334,70336,70337,2153],{"id":70335},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,70338,70340],{"className":70339},[886],[888,70341,70342],{"xmlns":890},[892,70343,70344,70350],{},[895,70345,70346,70348],{},[898,70347,1683],{},[898,70349,14171],{},[902,70351,63996],{"encoding":904},[198,70353,70355],{"id":70354},"definice-vzorec-214","Definice (vzorec 2.14)",[724,70357,70358,70359,70382,70383,70400,70401,4288],{},"Pro poptávku ",[883,70360,70362],{"className":70361},[886],[888,70363,70364],{"xmlns":890},[892,70365,70366,70380],{},[895,70367,70368,70370,70372,70374,70376,70378],{},[898,70369,1702],{},[1706,70371,1708],{},[898,70373,2334],{},[1706,70375,2140],{"stretchy":2139},[898,70377,2146],{},[1706,70379,2153],{"stretchy":2139},[902,70381,2343],{"encoding":904}," a pevně zadané ",[883,70384,70386],{"className":70385},[886],[888,70387,70388],{"xmlns":890},[892,70389,70390,70398],{},[895,70391,70392],{},[2142,70393,70394,70396],{},[898,70395,2146],{},[2148,70397,2150],{},[902,70399,8625],{"encoding":904}," s cenou ",[883,70402,70404],{"className":70403},[886],[888,70405,70406],{"xmlns":890},[892,70407,70408,70430],{},[895,70409,70410,70416,70418,70420,70422,70428],{},[2142,70411,70412,70414],{},[898,70413,1702],{},[2148,70415,2150],{},[1706,70417,1708],{},[898,70419,2334],{},[1706,70421,2140],{"stretchy":2139},[2142,70423,70424,70426],{},[898,70425,2146],{},[2148,70427,2150],{},[1706,70429,2153],{"stretchy":2139},[902,70431,70092],{"encoding":904},[883,70433,70435],{"className":70434},[886],[888,70436,70437],{"xmlns":890,"display":2350},[892,70438,70439,70515],{},[2354,70440,70441],{"width":2356},[2358,70442,70443,70445,70509,70511],{},[2361,70444],{"width":2363},[2361,70446,70447],{},[895,70448,70449,70451,70453,70455,70461,70463,70465,70477,70479,70481,70483,70485,70487,70489,70491,70493,70499,70501,70507],{},[898,70450,1683],{},[898,70452,14171],{},[1706,70454,2140],{"stretchy":2139},[2142,70456,70457,70459],{},[898,70458,2146],{},[2148,70460,2150],{},[1706,70462,2153],{"stretchy":2139},[1706,70464,1708],{},[28285,70466,70467,70469,70471],{},[1706,70468,30280],{},[2148,70470,2150],{},[2142,70472,70473,70475],{},[898,70474,2146],{},[2148,70476,2150],{},[898,70478,2334],{},[1706,70480,2140],{"stretchy":2139},[898,70482,2146],{},[1706,70484,2153],{"stretchy":2139},[2415,70486,2799],{},[898,70488,3120],{},[898,70490,2146],{},[1706,70492,1715],{},[2142,70494,70495,70497],{},[898,70496,1702],{},[2148,70498,2150],{},[2415,70500,2799],{},[2142,70502,70503,70505],{},[898,70504,2146],{},[2148,70506,2150],{},[898,70508,1837],{"mathvariant":2409},[2361,70510],{"width":2363},[2361,70512,70513],{},[2415,70514,64119],{},[902,70516,64122],{"encoding":904},[198,70518,21651],{"id":21650},[120,70520,70521,70613,70675],{},[123,70522,70523,70563,70564,70590,70591,70594,70595,70612],{},[883,70524,70526],{"className":70525},[886],[888,70527,70528],{"xmlns":890},[892,70529,70530,70560],{},[895,70531,70532],{},[4745,70533,70534,70546,70548,70550,70552,70554,70556,70558],{"scriptlevel":2150,"displaystyle":2504},[28285,70535,70536,70538,70540],{},[1706,70537,30280],{},[2148,70539,2150],{},[2142,70541,70542,70544],{},[898,70543,2146],{},[2148,70545,2150],{},[898,70547,2334],{},[1706,70549,2140],{"stretchy":2139},[898,70551,2146],{},[1706,70553,2153],{"stretchy":2139},[2415,70555,2799],{},[898,70557,3120],{},[898,70559,2146],{},[902,70561,70562],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,70565,70567],{"className":70566},[886],[888,70568,70569],{"xmlns":890},[892,70570,70571,70587],{},[895,70572,70573,70575,70577,70579,70585],{},[1706,70574,21693],{"stretchy":2139},[2148,70576,2150],{},[1706,70578,2505],{"separator":2504},[2142,70580,70581,70583],{},[898,70582,2146],{},[2148,70584,2150],{},[1706,70586,21708],{"stretchy":2139},[902,70588,70589],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,70592,70593],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,70596,70598],{"className":70597},[886],[888,70599,70600],{"xmlns":890},[892,70601,70602,70610],{},[895,70603,70604],{},[2142,70605,70606,70608],{},[898,70607,2146],{},[2148,70609,2150],{},[902,70611,8625],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,70614,70615,70641,70642,1936],{},[883,70616,70618],{"className":70617},[886],[888,70619,70620],{"xmlns":890},[892,70621,70622,70638],{},[895,70623,70624,70630,70632],{},[2142,70625,70626,70628],{},[898,70627,1702],{},[2148,70629,2150],{},[2415,70631,2799],{},[2142,70633,70634,70636],{},[898,70635,2146],{},[2148,70637,2150],{},[902,70639,70640],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,70643,70645],{"className":70644},[886],[888,70646,70647],{"xmlns":890},[892,70648,70649,70673],{},[895,70650,70651,70653,70655,70661,70663,70665,70667],{},[2148,70652,2150],{},[2415,70654,2799],{},[2142,70656,70657,70659],{},[898,70658,2146],{},[2148,70660,2150],{},[2415,70662,2799],{},[898,70664,1735],{},[2415,70666,2799],{},[2142,70668,70669,70671],{},[898,70670,1702],{},[2148,70672,2150],{},[902,70674,70194],{"encoding":904},[123,70676,70677,70692,70693,70715,70716,70741,70742,15842,70768,1993,70800,1837],{},[883,70678,70680],{"className":70679},[886],[888,70681,70682],{"xmlns":890},[892,70683,70684,70690],{},[895,70685,70686,70688],{},[898,70687,1683],{},[898,70689,14171],{},[902,70691,63996],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,70694,70696],{"className":70695},[886],[888,70697,70698],{"xmlns":890},[892,70699,70700,70712],{},[895,70701,70702,70704,70706],{},[898,70703,1702],{},[1706,70705,1708],{},[2142,70707,70708,70710],{},[898,70709,1702],{},[2148,70711,2150],{},[902,70713,70714],{"encoding":904},"P = P_0"," v pásu ",[883,70717,70719],{"className":70718},[886],[888,70720,70721],{"xmlns":890},[892,70722,70723,70739],{},[895,70724,70725,70727,70729,70731,70737],{},[1706,70726,21693],{"stretchy":2139},[2148,70728,2150],{},[1706,70730,2505],{"separator":2504},[2142,70732,70733,70735],{},[898,70734,2146],{},[2148,70736,2150],{},[1706,70738,21708],{"stretchy":2139},[902,70740,70589],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,70743,70745],{"className":70744},[886],[888,70746,70747],{"xmlns":890},[892,70748,70749,70765],{},[895,70750,70751,70757,70759,70761,70763],{},[2142,70752,70753,70755],{},[898,70754,1702],{},[2148,70756,2150],{},[2415,70758,2799],{},[898,70760,10315],{},[2415,70762,2799],{},[898,70764,1735],{},[902,70766,70767],{"encoding":904},"P_0\\,B\\,A",[883,70769,70771],{"className":70770},[886],[888,70772,70773],{"xmlns":890},[892,70774,70775,70797],{},[895,70776,70777,70779,70781,70783,70785,70787,70789,70791,70793,70795],{},[898,70778,10315],{},[1706,70780,1708],{},[1706,70782,21693],{"stretchy":2139},[2148,70784,2150],{},[1706,70786,2505],{"separator":2504},[898,70788,2334],{},[1706,70790,2140],{"stretchy":2139},[2148,70792,2150],{},[1706,70794,2153],{"stretchy":2139},[1706,70796,21708],{"stretchy":2139},[902,70798,70799],{"encoding":904},"B = [0, D(0)]",[883,70801,70803],{"className":70802},[886],[888,70804,70805],{"xmlns":890},[892,70806,70807,70831],{},[895,70808,70809,70811,70813,70815,70821,70823,70829],{},[898,70810,1735],{},[1706,70812,1708],{},[1706,70814,21693],{"stretchy":2139},[2142,70816,70817,70819],{},[898,70818,2146],{},[2148,70820,2150],{},[1706,70822,2505],{"separator":2504},[2142,70824,70825,70827],{},[898,70826,1702],{},[2148,70828,2150],{},[1706,70830,21708],{"stretchy":2139},[902,70832,70249],{"encoding":904},[724,70834,70835],{},[614,70836,70837,70838,70851,70852,70885,70886,48210,70911,1837],{},"Obrázek 2.24: Křivka poptávky ",[883,70839,70841],{"className":70840},[886],[888,70842,70843],{"xmlns":890},[892,70844,70845,70849],{},[895,70846,70847],{},[898,70848,2334],{},[902,70850,2334],{"encoding":904},", bod ",[883,70853,70855],{"className":70854},[886],[888,70856,70857],{"xmlns":890},[892,70858,70859,70883],{},[895,70860,70861,70863,70865,70867,70873,70875,70881],{},[898,70862,1735],{},[1706,70864,1708],{},[1706,70866,21693],{"stretchy":2139},[2142,70868,70869,70871],{},[898,70870,2146],{},[2148,70872,2150],{},[1706,70874,2505],{"separator":2504},[2142,70876,70877,70879],{},[898,70878,1702],{},[2148,70880,2150],{},[1706,70882,21708],{"stretchy":2139},[902,70884,70249],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,70887,70889],{"className":70888},[886],[888,70890,70891],{"xmlns":890},[892,70892,70893,70909],{},[895,70894,70895,70901,70903,70905,70907],{},[2142,70896,70897,70899],{},[898,70898,1702],{},[2148,70900,2150],{},[2415,70902,2799],{},[898,70904,10315],{},[2415,70906,2799],{},[898,70908,1735],{},[902,70910,70767],{"encoding":904},[883,70912,70914],{"className":70913},[886],[888,70915,70916],{"xmlns":890},[892,70917,70918,70924],{},[895,70919,70920,70922],{},[898,70921,1683],{},[898,70923,14171],{},[902,70925,63996],{"encoding":904},[56029,70927],{},[115,70929,70931,70932,2153],{"id":70930},"přebytek-výrobce-psps","Přebytek výrobce (",[883,70933,70935],{"className":70934},[886],[888,70936,70937],{"xmlns":890},[892,70938,70939,70945],{},[895,70940,70941,70943],{},[898,70942,1702],{},[898,70944,14171],{},[902,70946,64015],{"encoding":904},[198,70948,70950],{"id":70949},"definice-vzorec-215","Definice (vzorec 2.15)",[724,70952,70953,70954,70382,70977,70400,70994,4288],{},"Analogicky — pro nabídku ",[883,70955,70957],{"className":70956},[886],[888,70958,70959],{"xmlns":890},[892,70960,70961,70975],{},[895,70962,70963,70965,70967,70969,70971,70973],{},[898,70964,1702],{},[1706,70966,1708],{},[898,70968,14171],{},[1706,70970,2140],{"stretchy":2139},[898,70972,2146],{},[1706,70974,2153],{"stretchy":2139},[902,70976,60124],{"encoding":904},[883,70978,70980],{"className":70979},[886],[888,70981,70982],{"xmlns":890},[892,70983,70984,70992],{},[895,70985,70986],{},[2142,70987,70988,70990],{},[898,70989,2146],{},[2148,70991,2150],{},[902,70993,8625],{"encoding":904},[883,70995,70997],{"className":70996},[886],[888,70998,70999],{"xmlns":890},[892,71000,71001,71023],{},[895,71002,71003,71009,71011,71013,71015,71021],{},[2142,71004,71005,71007],{},[898,71006,1702],{},[2148,71008,2150],{},[1706,71010,1708],{},[898,71012,14171],{},[1706,71014,2140],{"stretchy":2139},[2142,71016,71017,71019],{},[898,71018,2146],{},[2148,71020,2150],{},[1706,71022,2153],{"stretchy":2139},[902,71024,70124],{"encoding":904},[883,71026,71028],{"className":71027},[886],[888,71029,71030],{"xmlns":890,"display":2350},[892,71031,71032,71108],{},[2354,71033,71034],{"width":2356},[2358,71035,71036,71038,71102,71104],{},[2361,71037],{"width":2363},[2361,71039,71040],{},[895,71041,71042,71044,71046,71048,71054,71056,71058,71064,71066,71072,71074,71086,71088,71090,71092,71094,71096,71098,71100],{},[898,71043,1702],{},[898,71045,14171],{},[1706,71047,2140],{"stretchy":2139},[2142,71049,71050,71052],{},[898,71051,2146],{},[2148,71053,2150],{},[1706,71055,2153],{"stretchy":2139},[1706,71057,1708],{},[2142,71059,71060,71062],{},[898,71061,1702],{},[2148,71063,2150],{},[2415,71065,2799],{},[2142,71067,71068,71070],{},[898,71069,2146],{},[2148,71071,2150],{},[1706,71073,1715],{},[28285,71075,71076,71078,71080],{},[1706,71077,30280],{},[2148,71079,2150],{},[2142,71081,71082,71084],{},[898,71083,2146],{},[2148,71085,2150],{},[898,71087,14171],{},[1706,71089,2140],{"stretchy":2139},[898,71091,2146],{},[1706,71093,2153],{"stretchy":2139},[2415,71095,2799],{},[898,71097,3120],{},[898,71099,2146],{},[898,71101,1837],{"mathvariant":2409},[2361,71103],{"width":2363},[2361,71105,71106],{},[2415,71107,64215],{},[902,71109,64218],{"encoding":904},[198,71111,21651],{"id":71112},"geometrická-interpretace-1",[120,71114,71115,71163,71224],{},[123,71116,71117,21021,71142,71145,71146,1837],{},[883,71118,71120],{"className":71119},[886],[888,71121,71122],{"xmlns":890},[892,71123,71124,71140],{},[895,71125,71126,71132,71134],{},[2142,71127,71128,71130],{},[898,71129,1702],{},[2148,71131,2150],{},[2415,71133,2799],{},[2142,71135,71136,71138],{},[898,71137,2146],{},[2148,71139,2150],{},[902,71141,70640],{"encoding":904},[38,71143,71144],{},"tržba"," výrobce za prodané množství ",[883,71147,71149],{"className":71148},[886],[888,71150,71151],{"xmlns":890},[892,71152,71153,71161],{},[895,71154,71155],{},[2142,71156,71157,71159],{},[898,71158,2146],{},[2148,71160,2150],{},[902,71162,8625],{"encoding":904},[123,71164,71165,71205,71206,71223],{},[883,71166,71168],{"className":71167},[886],[888,71169,71170],{"xmlns":890},[892,71171,71172,71202],{},[895,71173,71174],{},[4745,71175,71176,71188,71190,71192,71194,71196,71198,71200],{"scriptlevel":2150,"displaystyle":2504},[28285,71177,71178,71180,71182],{},[1706,71179,30280],{},[2148,71181,2150],{},[2142,71183,71184,71186],{},[898,71185,2146],{},[2148,71187,2150],{},[898,71189,14171],{},[1706,71191,2140],{"stretchy":2139},[898,71193,2146],{},[1706,71195,2153],{"stretchy":2139},[2415,71197,2799],{},[898,71199,3120],{},[898,71201,2146],{},[902,71203,71204],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,71207,71209],{"className":71208},[886],[888,71210,71211],{"xmlns":890},[892,71212,71213,71221],{},[895,71214,71215],{},[2142,71216,71217,71219],{},[898,71218,2146],{},[2148,71220,2150],{},[902,71222,8625],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,71225,71226,71241,71242,71263,71264,1837],{},[883,71227,71229],{"className":71228},[886],[888,71230,71231],{"xmlns":890},[892,71232,71233,71239],{},[895,71234,71235,71237],{},[898,71236,1702],{},[898,71238,14171],{},[902,71240,64015],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,71243,71245],{"className":71244},[886],[888,71246,71247],{"xmlns":890},[892,71248,71249,71261],{},[895,71250,71251,71253,71255],{},[898,71252,1702],{},[1706,71254,1708],{},[2142,71256,71257,71259],{},[898,71258,1702],{},[2148,71260,2150],{},[902,71262,70714],{"encoding":904}," a křivkou nabídky v pásu ",[883,71265,71267],{"className":71266},[886],[888,71268,71269],{"xmlns":890},[892,71270,71271,71287],{},[895,71272,71273,71275,71277,71279,71285],{},[1706,71274,21693],{"stretchy":2139},[2148,71276,2150],{},[1706,71278,2505],{"separator":2504},[2142,71280,71281,71283],{},[898,71282,2146],{},[2148,71284,2150],{},[1706,71286,21708],{"stretchy":2139},[902,71288,70589],{"encoding":904},[724,71290,71291],{},[614,71292,71293],{},"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.",[56029,71295],{},[1636,71297,71298,71303],{},[724,71299,71300,71302],{},[883,71301,12314],{}," Postup výpočtu CS a PS",[152,71304,71305,71436,71546,71575,71709],{},[123,71306,71307,71308,71325,71326,71357,71358,71389,71390,1837],{},"Zjisti (nebo si zvol) množství ",[883,71309,71311],{"className":71310},[886],[888,71312,71313],{"xmlns":890},[892,71314,71315,71323],{},[895,71316,71317],{},[2142,71318,71319,71321],{},[898,71320,2146],{},[2148,71322,2150],{},[902,71324,8625],{"encoding":904}," a odpovídající cenu ",[883,71327,71329],{"className":71328},[886],[888,71330,71331],{"xmlns":890},[892,71332,71333,71355],{},[895,71334,71335,71341,71343,71345,71347,71353],{},[2142,71336,71337,71339],{},[898,71338,1702],{},[2148,71340,2150],{},[1706,71342,1708],{},[898,71344,2334],{},[1706,71346,2140],{"stretchy":2139},[2142,71348,71349,71351],{},[898,71350,2146],{},[2148,71352,2150],{},[1706,71354,2153],{"stretchy":2139},[902,71356,70092],{"encoding":904}," resp. ",[883,71359,71361],{"className":71360},[886],[888,71362,71363],{"xmlns":890},[892,71364,71365,71387],{},[895,71366,71367,71373,71375,71377,71379,71385],{},[2142,71368,71369,71371],{},[898,71370,1702],{},[2148,71372,2150],{},[1706,71374,1708],{},[898,71376,14171],{},[1706,71378,2140],{"stretchy":2139},[2142,71380,71381,71383],{},[898,71382,2146],{},[2148,71384,2150],{},[1706,71386,2153],{"stretchy":2139},[902,71388,70124],{"encoding":904},". V rovnováze platí ",[883,71391,71393],{"className":71392},[886],[888,71394,71395],{"xmlns":890},[892,71396,71397,71433],{},[895,71398,71399,71401,71403,71409,71411,71413,71415,71417,71423,71425,71427],{},[898,71400,2334],{},[1706,71402,2140],{"stretchy":2139},[2489,71404,71405,71407],{},[898,71406,2146],{},[898,71408,23410],{},[1706,71410,2153],{"stretchy":2139},[1706,71412,1708],{},[898,71414,14171],{},[1706,71416,2140],{"stretchy":2139},[2489,71418,71419,71421],{},[898,71420,2146],{},[898,71422,23410],{},[1706,71424,2153],{"stretchy":2139},[1706,71426,1708],{},[2489,71428,71429,71431],{},[898,71430,1702],{},[898,71432,23410],{},[902,71434,71435],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,71437,71438,71439,39219,71477,71492,71493,39219,71531,1936],{},"Spočti určitý integrál ",[883,71440,71442],{"className":71441},[886],[888,71443,71444],{"xmlns":890},[892,71445,71446,71474],{},[895,71447,71448,71460,71462,71464,71466,71468,71470,71472],{},[28285,71449,71450,71452,71454],{},[1706,71451,30280],{},[2148,71453,2150],{},[2142,71455,71456,71458],{},[898,71457,2146],{},[2148,71459,2150],{},[898,71461,2334],{},[1706,71463,2140],{"stretchy":2139},[898,71465,2146],{},[1706,71467,2153],{"stretchy":2139},[2415,71469,2799],{},[898,71471,3120],{},[898,71473,2146],{},[902,71475,71476],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,71478,71480],{"className":71479},[886],[888,71481,71482],{"xmlns":890},[892,71483,71484,71490],{},[895,71485,71486,71488],{},[898,71487,1683],{},[898,71489,14171],{},[902,71491,63996],{"encoding":904},") nebo ",[883,71494,71496],{"className":71495},[886],[888,71497,71498],{"xmlns":890},[892,71499,71500,71528],{},[895,71501,71502,71514,71516,71518,71520,71522,71524,71526],{},[28285,71503,71504,71506,71508],{},[1706,71505,30280],{},[2148,71507,2150],{},[2142,71509,71510,71512],{},[898,71511,2146],{},[2148,71513,2150],{},[898,71515,14171],{},[1706,71517,2140],{"stretchy":2139},[898,71519,2146],{},[1706,71521,2153],{"stretchy":2139},[2415,71523,2799],{},[898,71525,3120],{},[898,71527,2146],{},[902,71529,71530],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,71532,71534],{"className":71533},[886],[888,71535,71536],{"xmlns":890},[892,71537,71538,71544],{},[895,71539,71540,71542],{},[898,71541,1702],{},[898,71543,14171],{},[902,71545,64015],{"encoding":904},[123,71547,71548,71549,1837],{},"Sestav obdélník ",[883,71550,71552],{"className":71551},[886],[888,71553,71554],{"xmlns":890},[892,71555,71556,71572],{},[895,71557,71558,71564,71566],{},[2142,71559,71560,71562],{},[898,71561,1702],{},[2148,71563,2150],{},[1706,71565,2390],{},[2142,71567,71568,71570],{},[898,71569,2146],{},[2148,71571,2150],{},[902,71573,71574],{"encoding":904},"P_0 \\cdot Q_0",[123,71576,71577,71578],{},"Dosaď:\n",[120,71579,71580,71645],{},[123,71581,71582,71640,71641,71644],{},[883,71583,71585],{"className":71584},[886],[888,71586,71587],{"xmlns":890},[892,71588,71589,71637],{},[895,71590,71591,71593,71595,71597,71609,71611,71613,71615,71617,71619,71621,71623,71625,71631],{},[898,71592,1683],{},[898,71594,14171],{},[1706,71596,1708],{},[28285,71598,71599,71601,71603],{},[1706,71600,30280],{},[2148,71602,2150],{},[2142,71604,71605,71607],{},[898,71606,2146],{},[2148,71608,2150],{},[898,71610,2334],{},[1706,71612,2140],{"stretchy":2139},[898,71614,2146],{},[1706,71616,2153],{"stretchy":2139},[2415,71618,2799],{},[898,71620,3120],{},[898,71622,2146],{},[1706,71624,1715],{},[2142,71626,71627,71629],{},[898,71628,1702],{},[2148,71630,2150],{},[2142,71632,71633,71635],{},[898,71634,2146],{},[2148,71636,2150],{},[902,71638,71639],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,71642,71643],{},"mínus"," obdélník)",[123,71646,71647,71705,71706,71708],{},[883,71648,71650],{"className":71649},[886],[888,71651,71652],{"xmlns":890},[892,71653,71654,71702],{},[895,71655,71656,71658,71660,71662,71668,71674,71676,71688,71690,71692,71694,71696,71698,71700],{},[898,71657,1702],{},[898,71659,14171],{},[1706,71661,1708],{},[2142,71663,71664,71666],{},[898,71665,1702],{},[2148,71667,2150],{},[2142,71669,71670,71672],{},[898,71671,2146],{},[2148,71673,2150],{},[1706,71675,1715],{},[28285,71677,71678,71680,71682],{},[1706,71679,30280],{},[2148,71681,2150],{},[2142,71683,71684,71686],{},[898,71685,2146],{},[2148,71687,2150],{},[898,71689,14171],{},[1706,71691,2140],{"stretchy":2139},[898,71693,2146],{},[1706,71695,2153],{"stretchy":2139},[2415,71697,2799],{},[898,71699,3120],{},[898,71701,2146],{},[902,71703,71704],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,71707,71643],{}," integrál)",[123,71710,71711,71712,71715],{},"Kontrola znaménka: obě hodnoty musí být ",[38,71713,71714],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[56029,71717],{},[115,71719,71721],{"id":71720},"příklady","Příklady",[198,71723,71725],{"id":71724},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[1636,71727,71728],{},[724,71729,71730,71733,71734,66763,71757,71780,71781,1343,71801,1343,71818,1343,71835,71852,71853,71929,71930,71947,71948,71961],{},[883,71731,71732],{},"!example"," Zadání\nJsou dány poptávka ",[883,71735,71737],{"className":71736},[886],[888,71738,71739],{"xmlns":890},[892,71740,71741,71755],{},[895,71742,71743,71745,71747,71749,71751,71753],{},[898,71744,1702],{},[1706,71746,1708],{},[898,71748,207],{},[898,71750,2146],{},[1706,71752,2447],{},[898,71754,2450],{},[902,71756,2453],{"encoding":904},[883,71758,71760],{"className":71759},[886],[888,71761,71762],{"xmlns":890},[892,71763,71764,71778],{},[895,71765,71766,71768,71770,71772,71774,71776],{},[898,71767,1702],{},[1706,71769,1708],{},[898,71771,20413],{},[898,71773,2146],{},[1706,71775,2447],{},[898,71777,3120],{},[902,71779,59296],{"encoding":904}," s hodnotami ",[883,71782,71784],{"className":71783},[886],[888,71785,71786],{"xmlns":890},[892,71787,71788,71798],{},[895,71789,71790,71792,71794,71796],{},[898,71791,207],{},[1706,71793,1708],{},[1706,71795,1715],{},[2148,71797,4284],{},[902,71799,71800],{"encoding":904},"a = -3",[883,71802,71804],{"className":71803},[886],[888,71805,71806],{"xmlns":890},[892,71807,71808,71816],{},[895,71809,71810,71812,71814],{},[898,71811,2450],{},[1706,71813,1708],{},[2148,71815,3508],{},[902,71817,67686],{"encoding":904},[883,71819,71821],{"className":71820},[886],[888,71822,71823],{"xmlns":890},[892,71824,71825,71833],{},[895,71826,71827,71829,71831],{},[898,71828,20413],{},[1706,71830,1708],{},[2148,71832,11496],{},[902,71834,67704],{"encoding":904},[883,71836,71838],{"className":71837},[886],[888,71839,71840],{"xmlns":890},[892,71841,71842,71850],{},[895,71843,71844,71846,71848],{},[898,71845,3120],{},[1706,71847,1708],{},[2148,71849,7786],{},[902,71851,67722],{"encoding":904},".\nRovnovážné množství:\n",[883,71854,71856],{"className":71855},[886],[888,71857,71858],{"xmlns":890},[892,71859,71860,71926],{},[895,71861,71862,71868,71870,71888,71890,71914,71916,71922,71924],{},[2489,71863,71864,71866],{},[898,71865,2146],{},[898,71867,23410],{},[1706,71869,1708],{},[2964,71871,71872,71880],{},[895,71873,71874,71876,71878],{},[898,71875,2450],{},[1706,71877,1715],{},[898,71879,3120],{},[895,71881,71882,71884,71886],{},[898,71883,20413],{},[1706,71885,1715],{},[898,71887,207],{},[1706,71889,1708],{},[2964,71891,71892,71900],{},[895,71893,71894,71896,71898],{},[2148,71895,3508],{},[1706,71897,1715],{},[2148,71899,7786],{},[895,71901,71902,71904,71906,71908,71910,71912],{},[2148,71903,11496],{},[1706,71905,1715],{},[1706,71907,2140],{"stretchy":2139},[1706,71909,1715],{},[2148,71911,4284],{},[1706,71913,2153],{"stretchy":2139},[1706,71915,1708],{},[2964,71917,71918,71920],{},[2148,71919,12556],{},[2148,71921,63452],{},[1706,71923,7883],{},[2148,71925,63457],{},[902,71927,71928],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,71931,71933],{"className":71932},[886],[888,71934,71935],{"xmlns":890},[892,71936,71937,71945],{},[895,71938,71939],{},[2489,71940,71941,71943],{},[898,71942,2146],{},[898,71944,23410],{},[902,71946,61452],{"encoding":904}," (a) při změně samotného parametru ",[883,71949,71951],{"className":71950},[886],[888,71952,71953],{"xmlns":890},[892,71954,71955,71959],{},[895,71956,71957],{},[898,71958,20413],{},[902,71960,20413],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,71963,71964],{},[38,71965,71966,71967,1889,71980,4202,71993,28414],{},"Řešení (a) — změna ",[883,71968,71970],{"className":71969},[886],[888,71971,71972],{"xmlns":890},[892,71973,71974,71978],{},[895,71975,71976],{},[898,71977,20413],{},[902,71979,20413],{"encoding":904},[883,71981,71983],{"className":71982},[886],[888,71984,71985],{"xmlns":890},[892,71986,71987,71991],{},[895,71988,71989],{},[2148,71990,11496],{},[902,71992,63492],{"encoding":904},[883,71994,71996],{"className":71995},[886],[888,71997,71998],{"xmlns":890},[892,71999,72000,72004],{},[895,72001,72002],{},[2148,72003,13775],{},[902,72005,63506],{"encoding":904},[724,72007,72008,72009,72073,72074,4288],{},"Pomocí vzorce (2.13) pro ",[883,72010,72012],{"className":72011},[886],[888,72013,72014],{"xmlns":890},[892,72015,72016,72070],{},[895,72017,72018,72038,72040,72042],{},[4745,72019,72020],{"scriptlevel":2150,"displaystyle":2504},[2964,72021,72022,72032],{},[895,72023,72024,72026],{},[898,72025,28987],{"mathvariant":2409},[2489,72027,72028,72030],{},[898,72029,2146],{},[898,72031,23410],{},[895,72033,72034,72036],{},[898,72035,28987],{"mathvariant":2409},[898,72037,20413],{},[1706,72039,1708],{},[1706,72041,1715],{},[4745,72043,72044],{"scriptlevel":2150,"displaystyle":2504},[2964,72045,72046,72054],{},[895,72047,72048,72050,72052],{},[898,72049,2450],{},[1706,72051,1715],{},[898,72053,3120],{},[895,72055,72056,72058,72060,72062,72064],{},[1706,72057,2140],{"stretchy":2139},[898,72059,20413],{},[1706,72061,1715],{},[898,72063,207],{},[2489,72065,72066,72068],{},[1706,72067,2153],{"stretchy":2139},[2148,72069,2495],{},[902,72071,72072],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,72075,72077],{"className":72076},[886],[888,72078,72079],{"xmlns":890},[892,72080,72081,72103],{},[895,72082,72083,72085],{},[1706,72084,1715],{},[4745,72086,72087],{"scriptlevel":2150,"displaystyle":2504},[2964,72088,72089,72095],{},[2489,72090,72091,72093],{},[898,72092,2146],{},[898,72094,23410],{},[895,72096,72097,72099,72101],{},[898,72098,20413],{},[1706,72100,1715],{},[898,72102,207],{},[902,72104,72105],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,72107,72109],{"className":72108},[886],[888,72110,72111],{"xmlns":890,"display":2350},[892,72112,72113,72169],{},[895,72114,72115,72117,72123,72125,72127,72143,72145,72147,72149,72151,72153,72159,72161,72163,72165,72167],{},[898,72116,3120],{},[2489,72118,72119,72121],{},[898,72120,2146],{},[898,72122,23410],{},[1706,72124,1708],{},[1706,72126,1715],{},[2964,72128,72129,72135],{},[2489,72130,72131,72133],{},[898,72132,2146],{},[898,72134,23410],{},[895,72136,72137,72139,72141],{},[898,72138,20413],{},[1706,72140,1715],{},[898,72142,207],{},[2415,72144,2799],{},[898,72146,3120],{},[898,72148,20413],{},[1706,72150,1708],{},[1706,72152,1715],{},[2964,72154,72155,72157],{},[2148,72156,63620],{},[2148,72158,63452],{},[1706,72160,2390],{},[2148,72162,14840],{},[1706,72164,7883],{},[1706,72166,1715],{},[2148,72168,63592],{},[902,72170,72171],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,72173,72174],{},"Nové rovnovážné množství:",[883,72176,72178],{"className":72177},[886],[888,72179,72180],{"xmlns":890,"display":2350},[892,72181,72182,72205],{},[895,72183,72184,72192,72194,72196,72198,72200,72202],{},[28285,72185,72186,72188,72190],{},[898,72187,2146],{},[2148,72189,2701],{},[898,72191,23410],{},[1706,72193,3248],{},[2148,72195,63620],{},[1706,72197,1715],{},[2148,72199,63625],{},[1706,72201,1708],{},[2148,72203,72204],{},"8,326.",[902,72206,72207],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,72209,72210,1647,72213,1343,72239,1343,72261,1343,72283,24728,72305,1343,72324,1343,72345,1343,72364,1837],{},[38,72211,72212],{},"Řešení (b) — současná změna všech parametrů:",[883,72214,72216],{"className":72215},[886],[888,72217,72218],{"xmlns":890},[892,72219,72220,72236],{},[895,72221,72222,72224,72226,72228,72230,72232,72234],{},[898,72223,207],{},[1706,72225,4288],{},[1706,72227,1715],{},[2148,72229,4284],{},[1706,72231,5915],{},[1706,72233,1715],{},[2148,72235,10065],{},[902,72237,72238],{"encoding":904},"a: -3 \\to -2{,}5",[883,72240,72242],{"className":72241},[886],[888,72243,72244],{"xmlns":890},[892,72245,72246,72258],{},[895,72247,72248,72250,72252,72254,72256],{},[898,72249,2450],{},[1706,72251,4288],{},[2148,72253,3508],{},[1706,72255,5915],{},[2148,72257,34145],{},[902,72259,72260],{"encoding":904},"b: 40 \\to 35",[883,72262,72264],{"className":72263},[886],[888,72265,72266],{"xmlns":890},[892,72267,72268,72280],{},[895,72269,72270,72272,72274,72276,72278],{},[898,72271,20413],{},[1706,72273,4288],{},[2148,72275,11496],{},[1706,72277,5915],{},[2148,72279,13775],{},[902,72281,72282],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,72284,72286],{"className":72285},[886],[888,72287,72288],{"xmlns":890},[892,72289,72290,72302],{},[895,72291,72292,72294,72296,72298,72300],{},[898,72293,3120],{},[1706,72295,4288],{},[2148,72297,7786],{},[1706,72299,5915],{},[2148,72301,22094],{},[902,72303,72304],{"encoding":904},"d: 10 \\to 11",[883,72306,72308],{"className":72307},[886],[888,72309,72310],{"xmlns":890},[892,72311,72312,72322],{},[895,72313,72314,72316,72318,72320],{},[898,72315,3120],{},[898,72317,207],{},[1706,72319,1708],{},[2148,72321,11496],{},[902,72323,63658],{"encoding":904},[883,72325,72327],{"className":72326},[886],[888,72328,72329],{"xmlns":890},[892,72330,72331,72343],{},[895,72332,72333,72335,72337,72339,72341],{},[898,72334,3120],{},[898,72336,2450],{},[1706,72338,1708],{},[1706,72340,1715],{},[2148,72342,7524],{},[902,72344,63680],{"encoding":904},[883,72346,72348],{"className":72347},[886],[888,72349,72350],{"xmlns":890},[892,72351,72352,72362],{},[895,72353,72354,72356,72358,72360],{},[898,72355,3120],{},[898,72357,20413],{},[1706,72359,1708],{},[2148,72361,14840],{},[902,72363,63700],{"encoding":904},[883,72365,72367],{"className":72366},[886],[888,72368,72369],{"xmlns":890},[892,72370,72371,72381],{},[895,72372,72373,72375,72377,72379],{},[898,72374,3120],{},[898,72376,3120],{},[1706,72378,1708],{},[2148,72380,2701],{},[902,72382,63720],{"encoding":904},[724,72384,72385,72386,72444],{},"Totální diferenciál ",[883,72387,72389],{"className":72388},[886],[888,72390,72391],{"xmlns":890},[892,72392,72393,72441],{},[895,72394,72395,72401,72403,72405,72407,72409,72411,72413,72415,72417,72419,72421],{},[2489,72396,72397,72399],{},[898,72398,2146],{},[898,72400,23410],{},[1706,72402,2140],{"stretchy":2139},[898,72404,207],{},[1706,72406,2505],{"separator":2504},[898,72408,2450],{},[1706,72410,2505],{"separator":2504},[898,72412,20413],{},[1706,72414,2505],{"separator":2504},[898,72416,3120],{},[1706,72418,2153],{"stretchy":2139},[1706,72420,1708],{},[4745,72422,72423],{"scriptlevel":2150,"displaystyle":2504},[2964,72424,72425,72433],{},[895,72426,72427,72429,72431],{},[898,72428,2450],{},[1706,72430,1715],{},[898,72432,3120],{},[895,72434,72435,72437,72439],{},[898,72436,20413],{},[1706,72438,1715],{},[898,72440,207],{},[902,72442,72443],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,72446,72448],{"className":72447},[886],[888,72449,72450],{"xmlns":890,"display":2350},[892,72451,72452,72572],{},[895,72453,72454,72456,72462,72464,72490,72492,72494,72496,72498,72510,72512,72514,72516,72518,72544,72546,72548,72550,72552,72564,72566,72568,72570],{},[898,72455,3120],{},[2489,72457,72458,72460],{},[898,72459,2146],{},[898,72461,23410],{},[1706,72463,1708],{},[2964,72465,72466,72474],{},[895,72467,72468,72470,72472],{},[898,72469,2450],{},[1706,72471,1715],{},[898,72473,3120],{},[895,72475,72476,72478,72480,72482,72484],{},[1706,72477,2140],{"stretchy":2139},[898,72479,20413],{},[1706,72481,1715],{},[898,72483,207],{},[2489,72485,72486,72488],{},[1706,72487,2153],{"stretchy":2139},[2148,72489,2495],{},[2415,72491,2799],{},[898,72493,3120],{},[898,72495,207],{},[1706,72497,2447],{},[2964,72499,72500,72502],{},[2148,72501,2701],{},[895,72503,72504,72506,72508],{},[898,72505,20413],{},[1706,72507,1715],{},[898,72509,207],{},[2415,72511,2799],{},[898,72513,3120],{},[898,72515,2450],{},[1706,72517,1715],{},[2964,72519,72520,72528],{},[895,72521,72522,72524,72526],{},[898,72523,2450],{},[1706,72525,1715],{},[898,72527,3120],{},[895,72529,72530,72532,72534,72536,72538],{},[1706,72531,2140],{"stretchy":2139},[898,72533,20413],{},[1706,72535,1715],{},[898,72537,207],{},[2489,72539,72540,72542],{},[1706,72541,2153],{"stretchy":2139},[2148,72543,2495],{},[2415,72545,2799],{},[898,72547,3120],{},[898,72549,20413],{},[1706,72551,1715],{},[2964,72553,72554,72556],{},[2148,72555,2701],{},[895,72557,72558,72560,72562],{},[898,72559,20413],{},[1706,72561,1715],{},[898,72563,207],{},[2415,72565,2799],{},[898,72567,3120],{},[898,72569,3120],{},[898,72571,1837],{"mathvariant":2409},[902,72573,72574],{"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.",[724,72576,72577,72578,1343,72600,1343,72631,5606],{},"Dosazením číselných hodnot (",[883,72579,72581],{"className":72580},[886],[888,72582,72583],{"xmlns":890},[892,72584,72585,72597],{},[895,72586,72587,72589,72591,72593,72595],{},[898,72588,20413],{},[1706,72590,1715],{},[898,72592,207],{},[1706,72594,1708],{},[2148,72596,63452],{},[902,72598,72599],{"encoding":904},"c - a = 3{,}5",[883,72601,72603],{"className":72602},[886],[888,72604,72605],{"xmlns":890},[892,72606,72607,72628],{},[895,72608,72609,72611,72613,72615,72617,72623,72625],{},[1706,72610,2140],{"stretchy":2139},[898,72612,20413],{},[1706,72614,1715],{},[898,72616,207],{},[2489,72618,72619,72621],{},[1706,72620,2153],{"stretchy":2139},[2148,72622,2495],{},[1706,72624,1708],{},[2148,72626,72627],{},"12,25",[902,72629,72630],{"encoding":904},"(c-a)^2 = 12{,}25",[883,72632,72634],{"className":72633},[886],[888,72635,72636],{"xmlns":890},[892,72637,72638,72650],{},[895,72639,72640,72642,72644,72646,72648],{},[898,72641,2450],{},[1706,72643,1715],{},[898,72645,3120],{},[1706,72647,1708],{},[2148,72649,12556],{},[902,72651,72652],{"encoding":904},"b - d = 30",[883,72654,72656],{"className":72655},[886],[888,72657,72658],{"xmlns":890,"display":2350},[892,72659,72660,72761],{},[895,72661,72662,72664,72670,72672,72680,72682,72684,72686,72688,72696,72698,72700,72702,72704,72706,72714,72716,72718,72720,72722,72730,72732,72734,72736,72738,72741,72743,72746,72748,72750,72752,72755,72757,72759],{},[898,72663,3120],{},[2489,72665,72666,72668],{},[898,72667,2146],{},[898,72669,23410],{},[1706,72671,3248],{},[4745,72673,72674],{"scriptlevel":2150,"displaystyle":2139},[2964,72675,72676,72678],{},[2148,72677,12556],{},[2148,72679,72627],{},[1706,72681,2140],{"stretchy":2139},[2148,72683,11496],{},[1706,72685,2153],{"stretchy":2139},[1706,72687,2447],{},[4745,72689,72690],{"scriptlevel":2150,"displaystyle":2139},[2964,72691,72692,72694],{},[2148,72693,2701],{},[2148,72695,63452],{},[1706,72697,2140],{"stretchy":2139},[1706,72699,1715],{},[2148,72701,7524],{},[1706,72703,2153],{"stretchy":2139},[1706,72705,1715],{},[4745,72707,72708],{"scriptlevel":2150,"displaystyle":2139},[2964,72709,72710,72712],{},[2148,72711,12556],{},[2148,72713,72627],{},[1706,72715,2140],{"stretchy":2139},[2148,72717,14840],{},[1706,72719,2153],{"stretchy":2139},[1706,72721,1715],{},[4745,72723,72724],{"scriptlevel":2150,"displaystyle":2139},[2964,72725,72726,72728],{},[2148,72727,2701],{},[2148,72729,63452],{},[1706,72731,2140],{"stretchy":2139},[2148,72733,2701],{},[1706,72735,2153],{"stretchy":2139},[1706,72737,7883],{},[2148,72739,72740],{},"1,224",[1706,72742,1715],{},[2148,72744,72745],{},"1,429",[1706,72747,1715],{},[2148,72749,63625],{},[1706,72751,1715],{},[2148,72753,72754],{},"0,286",[1706,72756,7883],{},[1706,72758,1715],{},[2148,72760,63871],{},[902,72762,72763],{"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.",[724,72765,49130,72766,1837],{},[883,72767,72769],{"className":72768},[886],[888,72770,72771],{"xmlns":890},[892,72772,72773,72795],{},[895,72774,72775,72783,72785,72787,72789,72791,72793],{},[28285,72776,72777,72779,72781],{},[898,72778,2146],{},[2148,72780,2701],{},[898,72782,23410],{},[1706,72784,3248],{},[2148,72786,63620],{},[1706,72788,1715],{},[2148,72790,63902],{},[1706,72792,7883],{},[2148,72794,63907],{},[902,72796,72797],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[1636,72799,72800],{},[724,72801,72802,72804,72805,72826,72827,72853,72854,72857,72858,72954,72955,72978,72979,72995],{},[883,72803,9276],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,72806,72808],{"className":72807},[886],[888,72809,72810],{"xmlns":890},[892,72811,72812,72824],{},[895,72813,72814,72816,72818,72820,72822],{},[898,72815,3677],{"mathvariant":2409},[898,72817,2146],{},[1706,72819,3248],{},[1706,72821,1715],{},[2148,72823,63937],{},[902,72825,63940],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,72828,72830],{"className":72829},[886],[888,72831,72832],{"xmlns":890},[892,72833,72834,72850],{},[895,72835,72836,72838,72844,72846,72848],{},[898,72837,3120],{},[2489,72839,72840,72842],{},[898,72841,2146],{},[898,72843,23410],{},[1706,72845,7883],{},[1706,72847,1715],{},[2148,72849,63902],{},[902,72851,72852],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,72855,72856],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,72859,72861],{"className":72860},[886],[888,72862,72863],{"xmlns":890},[892,72864,72865,72951],{},[895,72866,72867,72875,72877,72911,72913,72937,72939,72946,72948],{},[28285,72868,72869,72871,72873],{},[898,72870,2146],{},[2148,72872,2701],{},[898,72874,23410],{},[1706,72876,1708],{},[2964,72878,72879,72895],{},[895,72880,72881,72887,72889],{},[2489,72882,72883,72885],{},[898,72884,2450],{},[1706,72886,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,72888,1715],{},[2489,72890,72891,72893],{},[898,72892,3120],{},[1706,72894,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[895,72896,72897,72903,72905],{},[2489,72898,72899,72901],{},[898,72900,20413],{},[1706,72902,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,72904,1715],{},[2489,72906,72907,72909],{},[898,72908,207],{},[1706,72910,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,72912,1708],{},[2964,72914,72915,72923],{},[895,72916,72917,72919,72921],{},[2148,72918,34145],{},[1706,72920,1715],{},[2148,72922,22094],{},[895,72924,72925,72927,72929,72931,72933,72935],{},[2148,72926,13775],{},[1706,72928,1715],{},[1706,72930,2140],{"stretchy":2139},[1706,72932,1715],{},[2148,72934,10065],{},[1706,72936,2153],{"stretchy":2139},[1706,72938,1708],{},[2964,72940,72941,72943],{},[2148,72942,12665],{},[2148,72944,72945],{},"3,1",[1706,72947,7883],{},[2148,72949,72950],{},"7,742",[902,72952,72953],{"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 ",[883,72956,72958],{"className":72957},[886],[888,72959,72960],{"xmlns":890},[892,72961,72962,72975],{},[895,72963,72964,72966,72968,72970,72972],{},[898,72965,3677],{"mathvariant":2409},[898,72967,2146],{},[1706,72969,7883],{},[1706,72971,1715],{},[2148,72973,72974],{},"0,829",[902,72976,72977],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,72980,72982],{"className":72981},[886],[888,72983,72984],{"xmlns":890},[892,72985,72986,72992],{},[895,72987,72988,72990],{},[1706,72989,1715],{},[2148,72991,63937],{},[902,72993,72994],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,72997,72998],{},[614,72999,73000,73001,73014],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,73002,73004],{"className":73003},[886],[888,73005,73006],{"xmlns":890},[892,73007,73008,73012],{},[895,73009,73010],{},[898,73011,2146],{},[902,73013,2146],{"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.",[198,73016,73018,73019],{"id":73017},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,73020,73022],{"className":73021},[886],[888,73023,73024],{"xmlns":890},[892,73025,73026,73032],{},[895,73027,73028,73030],{},[898,73029,1702],{},[898,73031,14171],{},[902,73033,64015],{"encoding":904},[1636,73035,73036],{},[724,73037,73038,73040,73041,73075,73076,73098],{},[883,73039,71732],{}," Zadání\nPro nabídku ",[883,73042,73044],{"className":73043},[886],[888,73045,73046],{"xmlns":890},[892,73047,73048,73072],{},[895,73049,73050,73052,73054,73056,73058,73060,73062,73064,73066,73068,73070],{},[898,73051,1702],{},[1706,73053,1708],{},[898,73055,14171],{},[1706,73057,2140],{"stretchy":2139},[898,73059,2146],{},[1706,73061,2153],{"stretchy":2139},[1706,73063,1708],{},[2148,73065,7786],{},[1706,73067,2447],{},[2148,73069,2495],{},[898,73071,2146],{},[902,73073,73074],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,73077,73079],{"className":73078},[886],[888,73080,73081],{"xmlns":890},[892,73082,73083,73095],{},[895,73084,73085,73091,73093],{},[2142,73086,73087,73089],{},[898,73088,2146],{},[2148,73090,2150],{},[1706,73092,1708],{},[2148,73094,7786],{},[902,73096,73097],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,73100,73101],{},[38,73102,2615],{},[724,73104,73105],{},"Odpovídající cena:",[883,73107,73109],{"className":73108},[886],[888,73110,73111],{"xmlns":890,"display":2350},[892,73112,73113,73148],{},[895,73114,73115,73121,73123,73125,73127,73129,73131,73133,73135,73137,73139,73141,73143,73145],{},[2142,73116,73117,73119],{},[898,73118,1702],{},[2148,73120,2150],{},[1706,73122,1708],{},[898,73124,14171],{},[1706,73126,2140],{"stretchy":2139},[2148,73128,7786],{},[1706,73130,2153],{"stretchy":2139},[1706,73132,1708],{},[2148,73134,7786],{},[1706,73136,2447],{},[2148,73138,2495],{},[1706,73140,2390],{},[2148,73142,7786],{},[1706,73144,1708],{},[2148,73146,73147],{},"30.",[902,73149,73150],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,73152,73153],{},"Dle vzorce (2.15):",[883,73155,73157],{"className":73156},[886],[888,73158,73159],{"xmlns":890,"display":2350},[892,73160,73161,73269],{},[895,73162,73163,73165,73167,73169,73171,73173,73175,73181,73187,73189,73197,73199,73201,73203,73205,73207,73209,73211,73213,73215,73217,73219,73221,73223,73225,73228,73230,73232,73234,73240,73248,73250,73252,73254,73256,73258,73260,73262,73264,73266],{},[898,73164,1702],{},[898,73166,14171],{},[1706,73168,2140],{"stretchy":2139},[2148,73170,7786],{},[1706,73172,2153],{"stretchy":2139},[1706,73174,1708],{},[2142,73176,73177,73179],{},[898,73178,1702],{},[2148,73180,2150],{},[2142,73182,73183,73185],{},[898,73184,2146],{},[2148,73186,2150],{},[1706,73188,1715],{},[28285,73190,73191,73193,73195],{},[1706,73192,30280],{},[2148,73194,2150],{},[2148,73196,7786],{},[1706,73198,2140],{"stretchy":2139},[2148,73200,7786],{},[1706,73202,2447],{},[2148,73204,2495],{},[898,73206,2146],{},[1706,73208,2153],{"stretchy":2139},[2415,73210,2799],{},[898,73212,3120],{},[898,73214,2146],{},[1706,73216,1708],{},[2148,73218,7786],{},[1706,73220,2390],{},[2148,73222,12556],{},[1706,73224,1715],{},[1706,73226,21693],{"fence":2139,"stretchy":2504,"minsize":73227,"maxsize":73227},"1.8em",[2148,73229,7786],{},[898,73231,2146],{},[1706,73233,2447],{},[2489,73235,73236,73238],{},[898,73237,2146],{},[2148,73239,2495],{},[28285,73241,73242,73244,73246],{},[1706,73243,21708],{"fence":2139,"stretchy":2504,"minsize":73227,"maxsize":73227},[2148,73245,2150],{},[2148,73247,7786],{},[1706,73249,1708],{},[2148,73251,19501],{},[1706,73253,1715],{},[1706,73255,2140],{"stretchy":2139},[2148,73257,2590],{},[1706,73259,2447],{},[2148,73261,2590],{},[1706,73263,2153],{"stretchy":2139},[1706,73265,1708],{},[2148,73267,73268],{},"100.",[902,73270,73271],{"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.",[724,73273,73274,73275,73296,73297,73317],{},"Přebytek výrobce při množství ",[883,73276,73278],{"className":73277},[886],[888,73279,73280],{"xmlns":890},[892,73281,73282,73294],{},[895,73283,73284,73290,73292],{},[2142,73285,73286,73288],{},[898,73287,2146],{},[2148,73289,2150],{},[1706,73291,1708],{},[2148,73293,7786],{},[902,73295,73097],{"encoding":904}," je tedy ",[883,73298,73300],{"className":73299},[886],[888,73301,73302],{"xmlns":890},[892,73303,73304,73314],{},[895,73305,73306,73308,73310,73312],{},[898,73307,1702],{},[898,73309,14171],{},[1706,73311,1708],{},[2148,73313,2590],{},[902,73315,73316],{"encoding":904},"PS = 100"," (peněžních jednotek).",[56029,73319],{},[115,73321,73323],{"id":73322},"cheat-sheet","Cheat sheet",[16,73325,73326,73339],{},[19,73327,73328],{},[22,73329,73330,73333,73336],{},[25,73331,73332],{},"Veličina",[25,73334,73335],{},"Vzorec",[25,73337,73338],{},"Geometrie",[30,73340,73341,73459,73573,73641],{},[22,73342,73343,73371,73427],{},[35,73344,73345],{},[883,73346,73348],{"className":73347},[886],[888,73349,73350],{"xmlns":890},[892,73351,73352,73368],{},[895,73353,73354,73356,73358,73360,73366],{},[898,73355,1683],{},[898,73357,14171],{},[1706,73359,2140],{"stretchy":2139},[2142,73361,73362,73364],{},[898,73363,2146],{},[2148,73365,2150],{},[1706,73367,2153],{"stretchy":2139},[902,73369,73370],{"encoding":904},"CS(Q_0)",[35,73372,73373],{},[883,73374,73376],{"className":73375},[886],[888,73377,73378],{"xmlns":890},[892,73379,73380,73424],{},[895,73381,73382],{},[4745,73383,73384,73396,73398,73400,73402,73404,73406,73408,73410,73412,73418],{"scriptlevel":2150,"displaystyle":2504},[28285,73385,73386,73388,73390],{},[1706,73387,30280],{},[2148,73389,2150],{},[2142,73391,73392,73394],{},[898,73393,2146],{},[2148,73395,2150],{},[898,73397,2334],{},[1706,73399,2140],{"stretchy":2139},[898,73401,2146],{},[1706,73403,2153],{"stretchy":2139},[2415,73405,2799],{},[898,73407,3120],{},[898,73409,2146],{},[1706,73411,1715],{},[2142,73413,73414,73416],{},[898,73415,1702],{},[2148,73417,2150],{},[2142,73419,73420,73422],{},[898,73421,2146],{},[2148,73423,2150],{},[902,73425,73426],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,73428,73429,73430,73433,73434,73437,73438],{},"plocha ",[38,73431,73432],{},"pod"," křivkou poptávky, ",[38,73435,73436],{},"nad"," čárou ",[883,73439,73441],{"className":73440},[886],[888,73442,73443],{"xmlns":890},[892,73444,73445,73457],{},[895,73446,73447,73449,73451],{},[898,73448,1702],{},[1706,73450,1708],{},[2142,73452,73453,73455],{},[898,73454,1702],{},[2148,73456,2150],{},[902,73458,70714],{"encoding":904},[22,73460,73461,73489,73545],{},[35,73462,73463],{},[883,73464,73466],{"className":73465},[886],[888,73467,73468],{"xmlns":890},[892,73469,73470,73486],{},[895,73471,73472,73474,73476,73478,73484],{},[898,73473,1702],{},[898,73475,14171],{},[1706,73477,2140],{"stretchy":2139},[2142,73479,73480,73482],{},[898,73481,2146],{},[2148,73483,2150],{},[1706,73485,2153],{"stretchy":2139},[902,73487,73488],{"encoding":904},"PS(Q_0)",[35,73490,73491],{},[883,73492,73494],{"className":73493},[886],[888,73495,73496],{"xmlns":890},[892,73497,73498,73542],{},[895,73499,73500],{},[4745,73501,73502,73508,73514,73516,73528,73530,73532,73534,73536,73538,73540],{"scriptlevel":2150,"displaystyle":2504},[2142,73503,73504,73506],{},[898,73505,1702],{},[2148,73507,2150],{},[2142,73509,73510,73512],{},[898,73511,2146],{},[2148,73513,2150],{},[1706,73515,1715],{},[28285,73517,73518,73520,73522],{},[1706,73519,30280],{},[2148,73521,2150],{},[2142,73523,73524,73526],{},[898,73525,2146],{},[2148,73527,2150],{},[898,73529,14171],{},[1706,73531,2140],{"stretchy":2139},[898,73533,2146],{},[1706,73535,2153],{"stretchy":2139},[2415,73537,2799],{},[898,73539,3120],{},[898,73541,2146],{},[902,73543,73544],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,73546,73429,73547,73549,73550,73437,73552],{},[38,73548,73436],{}," křivkou nabídky, ",[38,73551,73432],{},[883,73553,73555],{"className":73554},[886],[888,73556,73557],{"xmlns":890},[892,73558,73559,73571],{},[895,73560,73561,73563,73565],{},[898,73562,1702],{},[1706,73564,1708],{},[2142,73566,73567,73569],{},[898,73568,1702],{},[2148,73570,2150],{},[902,73572,70714],{"encoding":904},[22,73574,73575,73578,73605],{},[35,73576,73577],{},"Výdaje \u002F tržby",[35,73579,73580],{},[883,73581,73583],{"className":73582},[886],[888,73584,73585],{"xmlns":890},[892,73586,73587,73603],{},[895,73588,73589,73595,73597],{},[2142,73590,73591,73593],{},[898,73592,1702],{},[2148,73594,2150],{},[1706,73596,2390],{},[2142,73598,73599,73601],{},[898,73600,2146],{},[2148,73602,2150],{},[902,73604,71574],{"encoding":904},[35,73606,73607,73608],{},"obdélník ",[883,73609,73611],{"className":73610},[886],[888,73612,73613],{"xmlns":890},[892,73614,73615,73639],{},[895,73616,73617,73619,73621,73627,73629,73631,73633],{},[2148,73618,2150],{},[2415,73620,2799],{},[2142,73622,73623,73625],{},[898,73624,2146],{},[2148,73626,2150],{},[2415,73628,2799],{},[898,73630,1735],{},[2415,73632,2799],{},[2142,73634,73635,73637],{},[898,73636,1702],{},[2148,73638,2150],{},[902,73640,70194],{"encoding":904},[22,73642,73643,73646,73669],{},[35,73644,73645],{},"Celkový přebytek",[35,73647,73648],{},[883,73649,73651],{"className":73650},[886],[888,73652,73653],{"xmlns":890},[892,73654,73655,73667],{},[895,73656,73657,73659,73661,73663,73665],{},[898,73658,1683],{},[898,73660,14171],{},[1706,73662,2447],{},[898,73664,1702],{},[898,73666,14171],{},[902,73668,69933],{"encoding":904},[35,73670,73671],{},"součet obou ploch v rovnováze",[56029,73673],{},[115,73675,19879],{"id":19878},[120,73677,73678,73700,73722,73766,73810,73873,73901],{},[123,73679,73680,2314,73682,1343,73697,73699],{},[38,73681,63980],{},[883,73683,73685],{"className":73684},[886],[888,73686,73687],{"xmlns":890},[892,73688,73689,73695],{},[895,73690,73691,73693],{},[898,73692,1683],{},[898,73694,14171],{},[902,73696,63996],{"encoding":904},[614,73698,64034],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,73701,73702,2314,73704,1343,73719,73721],{},[38,73703,64127],{},[883,73705,73707],{"className":73706},[886],[888,73708,73709],{"xmlns":890},[892,73710,73711,73717],{},[895,73712,73713,73715],{},[898,73714,1702],{},[898,73716,14171],{},[902,73718,64015],{"encoding":904},[614,73720,64130],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,73723,73724,21021,73727,1837],{},[38,73725,73726],{},"Ochota platit",[883,73728,73730],{"className":73729},[886],[888,73731,73732],{"xmlns":890},[892,73733,73734,73764],{},[895,73735,73736],{},[4745,73737,73738,73750,73752,73754,73756,73758,73760,73762],{"scriptlevel":2150,"displaystyle":2504},[28285,73739,73740,73742,73744],{},[1706,73741,30280],{},[2148,73743,2150],{},[2142,73745,73746,73748],{},[898,73747,2146],{},[2148,73749,2150],{},[898,73751,2334],{},[1706,73753,2140],{"stretchy":2139},[898,73755,2146],{},[1706,73757,2153],{"stretchy":2139},[2415,73759,2799],{},[898,73761,3120],{},[898,73763,2146],{},[902,73765,70562],{"encoding":904},[123,73767,73768,21021,73771,1837],{},[38,73769,73770],{},"Minimální cena výrobce",[883,73772,73774],{"className":73773},[886],[888,73775,73776],{"xmlns":890},[892,73777,73778,73808],{},[895,73779,73780],{},[4745,73781,73782,73794,73796,73798,73800,73802,73804,73806],{"scriptlevel":2150,"displaystyle":2504},[28285,73783,73784,73786,73788],{},[1706,73785,30280],{},[2148,73787,2150],{},[2142,73789,73790,73792],{},[898,73791,2146],{},[2148,73793,2150],{},[898,73795,14171],{},[1706,73797,2140],{"stretchy":2139},[898,73799,2146],{},[1706,73801,2153],{"stretchy":2139},[2415,73803,2799],{},[898,73805,3120],{},[898,73807,2146],{},[902,73809,71204],{"encoding":904},[123,73811,73812,21021,73815,71705,73840,1936],{},[38,73813,73814],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,73816,73818],{"className":73817},[886],[888,73819,73820],{"xmlns":890},[892,73821,73822,73838],{},[895,73823,73824,73830,73832],{},[2142,73825,73826,73828],{},[898,73827,1702],{},[2148,73829,2150],{},[2415,73831,2799],{},[2142,73833,73834,73836],{},[898,73835,2146],{},[2148,73837,2150],{},[902,73839,70640],{"encoding":904},[883,73841,73843],{"className":73842},[886],[888,73844,73845],{"xmlns":890},[892,73846,73847,73871],{},[895,73848,73849,73851,73853,73859,73861,73863,73865],{},[2148,73850,2150],{},[2415,73852,2799],{},[2142,73854,73855,73857],{},[898,73856,2146],{},[2148,73858,2150],{},[2415,73860,2799],{},[898,73862,1735],{},[2415,73864,2799],{},[2142,73866,73867,73869],{},[898,73868,1702],{},[2148,73870,2150],{},[902,73872,70194],{"encoding":904},[123,73874,73875,73878,73879,73900],{},[38,73876,73877],{},"Celkový přebytek trhu"," — součet ",[883,73880,73882],{"className":73881},[886],[888,73883,73884],{"xmlns":890},[892,73885,73886,73898],{},[895,73887,73888,73890,73892,73894,73896],{},[898,73889,1683],{},[898,73891,14171],{},[1706,73893,2447],{},[898,73895,1702],{},[898,73897,14171],{},[902,73899,69933],{"encoding":904}," v rovnovážném bodě.",[123,73902,73903,73905,73906,1343,73919,73932,73933,1837],{},[38,73904,21651],{}," — plochy ohraničené křivkami ",[883,73907,73909],{"className":73908},[886],[888,73910,73911],{"xmlns":890},[892,73912,73913,73917],{},[895,73914,73915],{},[898,73916,2334],{},[902,73918,2334],{"encoding":904},[883,73920,73922],{"className":73921},[886],[888,73923,73924],{"xmlns":890},[892,73925,73926,73930],{},[895,73927,73928],{},[898,73929,14171],{},[902,73931,14171],{"encoding":904}," a přímkou ",[883,73934,73936],{"className":73935},[886],[888,73937,73938],{"xmlns":890},[892,73939,73940,73952],{},[895,73941,73942,73944,73946],{},[898,73943,1702],{},[1706,73945,1708],{},[2142,73947,73948,73950],{},[898,73949,1702],{},[2148,73951,2150],{},[902,73953,70714],{"encoding":904},[56029,73955],{},[115,73957,73959],{"id":73958},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,73961,73962,73963,73976,73977,73994],{},"Uvalení jednotkové daně ",[883,73964,73966],{"className":73965},[886],[888,73967,73968],{"xmlns":890},[892,73969,73970,73974],{},[895,73971,73972],{},[898,73973,1659],{},[902,73975,1659],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,73978,73980],{"className":73979},[886],[888,73981,73982],{"xmlns":890},[892,73983,73984,73992],{},[895,73985,73986],{},[2489,73987,73988,73990],{},[898,73989,2146],{},[898,73991,23410],{},[902,73993,61452],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,73996,73997],{},[2286,73998],{"alt":73999,"className":74000,"src":74001},"imek-prebytky-s-dani-deadweight",[210,2290],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,74003,74004,74005,74020,74021,74036,74037,71705,74040,74064,74065,2314,74068,74071,74072,1837],{},"Přebytek spotřebitele ",[883,74006,74008],{"className":74007},[886],[888,74009,74010],{"xmlns":890},[892,74011,74012,74018],{},[895,74013,74014,74016],{},[898,74015,1683],{},[898,74017,14171],{},[902,74019,63996],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,74022,74024],{"className":74023},[886],[888,74025,74026],{"xmlns":890},[892,74027,74028,74034],{},[895,74029,74030,74032],{},[898,74031,1702],{},[898,74033,14171],{},[902,74035,64015],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,74038,74039],{},"daňový příjem",[883,74041,74043],{"className":74042},[886],[888,74044,74045],{"xmlns":890},[892,74046,74047,74061],{},[895,74048,74049,74051,74053],{},[898,74050,1659],{},[1706,74052,2390],{},[28285,74054,74055,74057,74059],{},[898,74056,2146],{},[2148,74058,2701],{},[898,74060,23410],{},[902,74062,74063],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,74066,74067],{},"mrtvá ztráta",[614,74069,74070],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,74073,811],{"className":74074,"dataFsResolvedFilePath":809,"href":810},[210],[56029,74076],{},[115,74078,21083],{"id":21082},[120,74080,74081,74088,74100,74107,74114],{},[123,74082,74083,1647,74085],{},[38,74084,35321],{},[207,74086,802],{"className":74087,"dataFsResolvedFilePath":800,"href":801},[210],[123,74089,74090,1647,74092,74095,74096,74099],{},[38,74091,55735],{},[207,74093,775],{"className":74094,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,74097,21102],{"className":74098,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,74101,74102,1647,74104],{},[38,74103,35331],{},[207,74105,22995],{"className":74106,"dataFsResolvedFilePath":827,"href":828},[210],[123,74108,74109,1647,74111],{},[38,74110,69796],{},[207,74112,69800],{"className":74113,"dataFsResolvedFilePath":745,"href":746},[210],[123,74115,74116,1647,74118],{},[38,74117,21126],{},[207,74119,21132],{"className":74120,"dataFsResolvedFilePath":21130,"href":21131},[210],{"title":641,"searchDepth":642,"depth":642,"links":74122},[74123,74124,74129,74134,74139,74140,74141,74142],{"id":1840,"depth":642,"text":1241},{"id":70335,"depth":642,"text":74125,"children":74126},"Přebytek spotřebitele (CSCS)",[74127,74128],{"id":70354,"depth":649,"text":70355},{"id":21650,"depth":649,"text":21651},{"id":70930,"depth":642,"text":74130,"children":74131},"Přebytek výrobce (PSPS)",[74132,74133],{"id":70949,"depth":649,"text":70950},{"id":71112,"depth":649,"text":21651},{"id":71720,"depth":642,"text":71721,"children":74135},[74136,74137],{"id":71724,"depth":649,"text":71725},{"id":73017,"depth":649,"text":74138},"Příklad 2.13 — numerický výpočet 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— produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":92425,"toc":104478},[92426,92429,92785,92789,92792,92860,92912,92922,92926,92960,93001,93025,93048,93077,93144,93251,93294,93351,93426,93471,93475,93483,93491,93494,93759,93810,93890,93960,93983,94011,94056,94078,94082,94089,94138,94164,94315,94318,94355,94518,94626,94630,94667,94742,94811,94930,95052,95133,95139,95180,95253,95346,95350,95386,95474,95588,95693,95778,95918,95922,95970,96015,96021,96025,96028,96079,96129,96136,96202,96335,96380,96384,96405,96784,96879,96896,96950,96954,97036,97120,97290,97293,97336,97403,97477,97481,97486,97555,97563,97572,97650,97716,97721,97816,97859,97864,97912,97917,97965,98083,98166,98204,98307,98366,98507,98511,98554,98627,98651,98705,98712,98714,98759,98804,98815,98820,98856,98918,98941,98950,99051,99118,99191,99198,99289,99351,99387,99444,99503,99688,99784,99788,99792,99871,99876,100000,100086,100092,100202,100239,100330,100428,100431,100435,100501,100538,100660,100712,100716,100744,100796,100870,100975,100999,101058,101062,101080,101223,101371,101373,101408,101412,101414,101504,101634,101760,101852,101927,101931,102047,102151,102341,102377,102471,102477,102590,102893,102899,103017,103116,103192,103194,104356,104358],[12,92427,92423],{"id":92428},"produkce-produkční-funkce-cobb-douglas-mrts",[1636,92430,92431],{},[724,92432,92433,1643,92435,92437,92438,55955,92451,92464,92465,35476,92478,2314,92480,92504,92505,1647,92507,1993,92541,1647,92544,92572,92573,4521,92593,92623,92624,2314,92627,92655,92656,92659,92660,92690,92691,92721,92722,1647,92725,92765,92766,92784],{},[883,92434,1642],{},[38,92436,859],{}," popisuje vztah mezi vstupy (práce ",[883,92439,92441],{"className":92440},[886],[888,92442,92443],{"xmlns":890},[892,92444,92445,92449],{},[895,92446,92447],{},[898,92448,6362],{},[902,92450,6362],{"encoding":904},[883,92452,92454],{"className":92453},[886],[888,92455,92456],{"xmlns":890},[892,92457,92458,92462],{},[895,92459,92460],{},[898,92461,28915],{},[902,92463,28915],{"encoding":904},") a výstupem ",[883,92466,92468],{"className":92467},[886],[888,92469,92470],{"xmlns":890},[892,92471,92472,92476],{},[895,92473,92474],{},[898,92475,2146],{},[902,92477,2146],{"encoding":904},[38,92479,56023],{},[883,92481,92483],{"className":92482},[886],[888,92484,92485],{"xmlns":890},[892,92486,92487,92501],{},[895,92488,92489,92491,92493,92495,92497,92499],{},[898,92490,2146],{},[1706,92492,1708],{},[898,92494,2146],{},[1706,92496,2140],{"stretchy":2139},[898,92498,6362],{},[1706,92500,2153],{"stretchy":2139},[902,92502,92503],{"encoding":904},"Q = Q(L)",") studujeme ",[614,92506,29139],{},[883,92508,92510],{"className":92509},[886],[888,92511,92512],{"xmlns":890},[892,92513,92514,92538],{},[895,92515,92516,92518,92524,92526,92532,92534,92536],{},[898,92517,1742],{},[2142,92519,92520,92522],{},[898,92521,1702],{},[898,92523,6362],{},[1706,92525,1708],{},[2489,92527,92528,92530],{},[898,92529,2146],{},[1706,92531,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,92533,2140],{"stretchy":2139},[898,92535,6362],{},[1706,92537,2153],{"stretchy":2139},[902,92539,92540],{"encoding":904},"MP_L = Q'(L)",[614,92542,92543],{},"průměrný produkt",[883,92545,92547],{"className":92546},[886],[888,92548,92549],{"xmlns":890},[892,92550,92551,92569],{},[895,92552,92553,92555,92561,92563,92565,92567],{},[898,92554,1735],{},[2142,92556,92557,92559],{},[898,92558,1702],{},[898,92560,6362],{},[1706,92562,1708],{},[898,92564,2146],{},[898,92566,15493],{"mathvariant":2409},[898,92568,6362],{},[902,92570,92571],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,92574,92576],{"className":92575},[886],[888,92577,92578],{"xmlns":890},[892,92579,92580,92590],{},[895,92581,92582,92584],{},[898,92583,1735],{},[2142,92585,92586,92588],{},[898,92587,1702],{},[898,92589,6362],{},[902,92591,92592],{"encoding":904},"AP_L",[883,92594,92596],{"className":92595},[886],[888,92597,92598],{"xmlns":890},[892,92599,92600,92620],{},[895,92601,92602,92604,92610,92612,92614],{},[898,92603,1742],{},[2142,92605,92606,92608],{},[898,92607,1702],{},[898,92609,6362],{},[1706,92611,1708],{},[898,92613,1735],{},[2142,92615,92616,92618],{},[898,92617,1702],{},[898,92619,6362],{},[902,92621,92622],{"encoding":904},"MP_L = AP_L",". Ve ",[38,92625,92626],{},"dvoufaktorovém modelu",[883,92628,92630],{"className":92629},[886],[888,92631,92632],{"xmlns":890},[892,92633,92634,92652],{},[895,92635,92636,92638,92640,92642,92644,92646,92648,92650],{},[898,92637,2146],{},[1706,92639,1708],{},[898,92641,2146],{},[1706,92643,2140],{"stretchy":2139},[898,92645,6362],{},[1706,92647,2505],{"separator":2504},[898,92649,28915],{},[1706,92651,2153],{"stretchy":2139},[902,92653,92654],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,92657,92658],{},"Cobb-Douglasovy"," funkce ",[883,92661,92663],{"className":92662},[886],[888,92664,92665],{"xmlns":890},[892,92666,92667,92687],{},[895,92668,92669,92671,92673,92675,92681],{},[898,92670,2146],{},[1706,92672,1708],{},[898,92674,1735],{},[2489,92676,92677,92679],{},[898,92678,6362],{},[898,92680,207],{},[2489,92682,92683,92685],{},[898,92684,28915],{},[898,92686,2450],{},[902,92688,92689],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,92692,92694],{"className":92693},[886],[888,92695,92696],{"xmlns":890},[892,92697,92698,92718],{},[895,92699,92700,92702,92708,92710,92712],{},[898,92701,1742],{},[2142,92703,92704,92706],{},[898,92705,1702],{},[898,92707,6362],{},[1706,92709,2505],{"separator":2504},[898,92711,1742],{},[2142,92713,92714,92716],{},[898,92715,1702],{},[898,92717,28915],{},[902,92719,92720],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,92723,92724],{},"mezní míru technické substituce",[883,92726,92728],{"className":92727},[886],[888,92729,92730],{"xmlns":890},[892,92731,92732,92762],{},[895,92733,92734,92736,92738,92740,92742,92744,92746,92752,92754,92756],{},[898,92735,1742],{},[898,92737,1662],{},[898,92739,1659],{},[898,92741,14171],{},[1706,92743,1708],{},[898,92745,1742],{},[2142,92747,92748,92750],{},[898,92749,1702],{},[898,92751,6362],{},[898,92753,15493],{"mathvariant":2409},[898,92755,1742],{},[2142,92757,92758,92760],{},[898,92759,1702],{},[898,92761,28915],{},[902,92763,92764],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,92767,92769],{"className":92768},[886],[888,92770,92771],{"xmlns":890},[892,92772,92773,92781],{},[895,92774,92775,92777,92779],{},[898,92776,207],{},[1706,92778,2447],{},[898,92780,2450],{},[902,92782,92783],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,92786,92788],{"id":92787},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,92790,92791],{},"Po prostudování kapitoly 5 student umí:",[120,92793,92794,92800,92810,92816,92822,92827,92833,92843,92848,92854],{},[123,92795,92796,92797,2505],{},"popsat ",[38,92798,92799],{},"jednofaktorový model produkce",[123,92801,92802,92803,1993,92806,92809],{},"vypočítat ",[38,92804,92805],{},"mezní",[38,92807,92808],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,92811,92812,92813,2505],{},"charakterizovat průběh ",[38,92814,92815],{},"křivky produkce",[123,92817,92818,92819,2505],{},"formulovat ",[38,92820,92821],{},"princip maximalizace průměrného produktu práce",[123,92823,92796,92824,2505],{},[38,92825,92826],{},"dvoufaktorový model produkce",[123,92828,92829,92830,2505],{},"uvést tvar ",[38,92831,92832],{},"Cobb–Douglasových produkčních funkcí",[123,92834,92835,92836,1343,92838,1343,92840,2505],{},"vyložit, co jsou ",[38,92837,43688],{},[38,92839,32764],{},[38,92841,92842],{},"klesající výnosy z rozsahu",[123,92844,92802,92845,92809],{},[38,92846,92847],{},"mezní produkty práce a kapitálu",[123,92849,92850,92851,2505],{},"najít ",[38,92852,92853],{},"izokvanty",[123,92855,92802,92856,92859],{},[38,92857,92858],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,92861,92862,92863,92866,92867,92870,92871,1647,92874,1343,92887,1647,92890,1993,92903,92906,92907,92909,92910,1837],{},"Každý proces produkce je určován ",[38,92864,92865],{},"faktory"," (též ",[38,92868,92869],{},"vstupy",") produkce. K hlavním patří ",[38,92872,92873],{},"práce",[883,92875,92877],{"className":92876},[886],[888,92878,92879],{"xmlns":890},[892,92880,92881,92885],{},[895,92882,92883],{},[898,92884,6362],{},[902,92886,6362],{"encoding":904},[38,92888,92889],{},"kapitál",[883,92891,92893],{"className":92892},[886],[888,92894,92895],{"xmlns":890},[892,92896,92897,92901],{},[895,92898,92899],{},[898,92900,28915],{},[902,92902,28915],{"encoding":904},[38,92904,92905],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,92908,56023],{}," (produkce závisí jen na práci); v opačném případě o ",[38,92911,92626],{},[724,92913,92914,92915,1343,92918,92921],{},"Související matematický aparát: ",[207,92916,21102],{"className":92917,"dataFsResolvedFilePath":764,"href":765},[210],[207,92919,784],{"className":92920,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,92923,92925],{"id":92924},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,92927,92928,92929,92942,92943,92956,92957],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,92930,92932],{"className":92931},[886],[888,92933,92934],{"xmlns":890},[892,92935,92936,92940],{},[895,92937,92938],{},[898,92939,2146],{},[902,92941,2146],{"encoding":904}," na práci ",[883,92944,92946],{"className":92945},[886],[888,92947,92948],{"xmlns":890},[892,92949,92950,92954],{},[895,92951,92952],{},[898,92953,6362],{},[902,92955,6362],{"encoding":904}," vyjadřuje ",[38,92958,92959],{},"produkční funkce",[883,92961,92963],{"className":92962},[886],[888,92964,92965],{"xmlns":890,"display":2350},[892,92966,92967,92998],{},[2354,92968,92969],{"width":2356},[2358,92970,92971,92973,92991,92993],{},[2361,92972],{"width":2363},[2361,92974,92975],{},[895,92976,92977,92979,92981,92983,92985,92987,92989],{},[898,92978,2146],{},[1706,92980,1708],{},[898,92982,2146],{},[1706,92984,2140],{"stretchy":2139},[898,92986,6362],{},[1706,92988,2153],{"stretchy":2139},[1706,92990,2505],{"separator":2504},[2361,92992],{"width":2363},[2361,92994,92995],{},[2415,92996,92997],{},"(5.1)",[902,92999,93000],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,93002,93003,93004,2314,93007,93010,93011,93024],{},"jejíž graf se nazývá ",[38,93005,93006],{},"křivka produkce",[614,93008,93009],{},"production curve","). Práce ",[883,93012,93014],{"className":93013},[886],[888,93015,93016],{"xmlns":890},[892,93017,93018,93022],{},[895,93019,93020],{},[898,93021,6362],{},[902,93023,6362],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,93026,93028,93029,2153],{"id":93027},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,93030,93032],{"className":93031},[886],[888,93033,93034],{"xmlns":890},[892,93035,93036,93046],{},[895,93037,93038,93040],{},[898,93039,1742],{},[2142,93041,93042,93044],{},[898,93043,1702],{},[898,93045,6362],{},[902,93047,29159],{"encoding":904},[724,93049,93050,2314,93053,93056,93057,93076],{},[38,93051,93052],{},"Mezní produkt práce",[614,93054,93055],{},"marginal product of labour",") ",[883,93058,93060],{"className":93059},[886],[888,93061,93062],{"xmlns":890},[892,93063,93064,93074],{},[895,93065,93066,93068],{},[898,93067,1742],{},[2142,93069,93070,93072],{},[898,93071,1702],{},[898,93073,6362],{},[902,93075,29159],{"encoding":904}," je derivace produkce podle práce:",[883,93078,93080],{"className":93079},[886],[888,93081,93082],{"xmlns":890,"display":2350},[892,93083,93084,93141],{},[2354,93085,93086],{"width":2356},[2358,93087,93088,93090,93134,93136],{},[2361,93089],{"width":2363},[2361,93091,93092],{},[895,93093,93094,93096,93102,93104,93118,93120,93126,93128,93130,93132],{},[898,93095,1742],{},[2142,93097,93098,93100],{},[898,93099,1702],{},[898,93101,6362],{},[1706,93103,1708],{},[2964,93105,93106,93112],{},[895,93107,93108,93110],{},[898,93109,3120],{},[898,93111,2146],{},[895,93113,93114,93116],{},[898,93115,3120],{},[898,93117,6362],{},[1706,93119,1708],{},[2489,93121,93122,93124],{},[898,93123,2146],{},[1706,93125,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,93127,2140],{"stretchy":2139},[898,93129,6362],{},[1706,93131,2153],{"stretchy":2139},[898,93133,1837],{"mathvariant":2409},[2361,93135],{"width":2363},[2361,93137,93138],{},[2415,93139,93140],{},"(5.2)",[902,93142,93143],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,93145,93146,93147,15532,93165,93193,93194,93211,93212,4202,93229,1936],{},"Pro pevnou hodnotu ",[883,93148,93150],{"className":93149},[886],[888,93151,93152],{"xmlns":890},[892,93153,93154,93162],{},[895,93155,93156],{},[2489,93157,93158,93160],{},[898,93159,6362],{},[1706,93161,3197],{},[902,93163,93164],{"encoding":904},"L^*",[883,93166,93168],{"className":93167},[886],[888,93169,93170],{"xmlns":890},[892,93171,93172,93190],{},[895,93173,93174,93180,93182,93188],{},[2489,93175,93176,93178],{},[898,93177,2146],{},[1706,93179,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,93181,2140],{"stretchy":2139},[2489,93183,93184,93186],{},[898,93185,6362],{},[1706,93187,3197],{},[1706,93189,2153],{"stretchy":2139},[902,93191,93192],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,93195,93197],{"className":93196},[886],[888,93198,93199],{"xmlns":890},[892,93200,93201,93209],{},[895,93202,93203],{},[2489,93204,93205,93207],{},[898,93206,6362],{},[1706,93208,3197],{},[902,93210,93164],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,93213,93215],{"className":93214},[886],[888,93216,93217],{"xmlns":890},[892,93218,93219,93227],{},[895,93220,93221],{},[2489,93222,93223,93225],{},[898,93224,6362],{},[1706,93226,3197],{},[902,93228,93164],{"encoding":904},[883,93230,93232],{"className":93231},[886],[888,93233,93234],{"xmlns":890},[892,93235,93236,93248],{},[895,93237,93238,93244,93246],{},[2489,93239,93240,93242],{},[898,93241,6362],{},[1706,93243,3197],{},[1706,93245,2447],{},[2148,93247,2701],{},[902,93249,93250],{"encoding":904},"L^*+1",[1636,93252,93253],{},[724,93254,93255,37120,93257,93276,93277,93280,93281,1837],{},[883,93256,3174],{},[883,93258,93260],{"className":93259},[886],[888,93261,93262],{"xmlns":890},[892,93263,93264,93274],{},[895,93265,93266,93268],{},[898,93267,1742],{},[2142,93269,93270,93272],{},[898,93271,1702],{},[898,93273,6362],{},[902,93275,29159],{"encoding":904}," odpovídá na otázku „",[38,93278,93279],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,93282,93284],{"className":93283},[886],[888,93285,93286],{"xmlns":890},[892,93287,93288,93292],{},[895,93289,93290],{},[898,93291,6362],{},[902,93293,6362],{"encoding":904},[724,93295,93296,93299,93300,93316,93317,4202,93330,93350],{},[38,93297,93298],{},"Přibližná změna produkce"," pro změnu práce o ",[883,93301,93303],{"className":93302},[886],[888,93304,93305],{"xmlns":890},[892,93306,93307,93313],{},[895,93308,93309,93311],{},[898,93310,3120],{},[898,93312,6362],{},[902,93314,93315],{"encoding":904},"dL"," (z ",[883,93318,93320],{"className":93319},[886],[888,93321,93322],{"xmlns":890},[892,93323,93324,93328],{},[895,93325,93326],{},[898,93327,6362],{},[902,93329,6362],{"encoding":904},[883,93331,93333],{"className":93332},[886],[888,93334,93335],{"xmlns":890},[892,93336,93337,93347],{},[895,93338,93339,93341,93343,93345],{},[898,93340,6362],{},[1706,93342,2447],{},[898,93344,3120],{},[898,93346,6362],{},[902,93348,93349],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,93352,93354],{"className":93353},[886],[888,93355,93356],{"xmlns":890,"display":2350},[892,93357,93358,93423],{},[2354,93359,93360],{"width":2356},[2358,93361,93362,93364,93416,93418],{},[2361,93363],{"width":2363},[2361,93365,93366],{},[895,93367,93368,93370,93372,93374,93376,93378,93380,93386,93388,93390,93392,93394,93396,93398,93400,93402,93408,93410,93412,93414],{},[898,93369,3677],{"mathvariant":2409},[898,93371,2146],{},[1706,93373,3248],{},[898,93375,3120],{},[898,93377,2146],{},[1706,93379,1708],{},[2489,93381,93382,93384],{},[898,93383,2146],{},[1706,93385,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,93387,2140],{"stretchy":2139},[898,93389,6362],{},[1706,93391,2153],{"stretchy":2139},[2415,93393,2799],{},[898,93395,3120],{},[898,93397,6362],{},[1706,93399,1708],{},[898,93401,1742],{},[2142,93403,93404,93406],{},[898,93405,1702],{},[898,93407,6362],{},[2415,93409,2799],{},[898,93411,3120],{},[898,93413,6362],{},[898,93415,1837],{"mathvariant":2409},[2361,93417],{"width":2363},[2361,93419,93420],{},[2415,93421,93422],{},"(5.3)",[902,93424,93425],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,93427,93428,93429,1837],{},"Skutečná změna je ",[883,93430,93432],{"className":93431},[886],[888,93433,93434],{"xmlns":890},[892,93435,93436,93468],{},[895,93437,93438,93440,93442,93444,93446,93448,93450,93452,93454,93456,93458,93460,93462,93464,93466],{},[898,93439,3677],{"mathvariant":2409},[898,93441,2146],{},[1706,93443,1708],{},[898,93445,2146],{},[1706,93447,2140],{"stretchy":2139},[898,93449,6362],{},[1706,93451,2447],{},[898,93453,3120],{},[898,93455,6362],{},[1706,93457,2153],{"stretchy":2139},[1706,93459,1715],{},[898,93461,2146],{},[1706,93463,2140],{"stretchy":2139},[898,93465,6362],{},[1706,93467,2153],{"stretchy":2139},[902,93469,93470],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,93472,93474],{"id":93473},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,93476,93477,2314,93480,5606],{},[38,93478,93479],{},"Zákon klesajících výnosů",[614,93481,93482],{},"law of diminishing marginal productivity",[1636,93484,93485],{},[724,93486,93487,93488,93490],{},"Roste-li postupně některý ze vstupů (",[614,93489,56019],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,93492,93493],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,93495,93496,93497,1647,93518,93537,93538,93588,93589,93591,93592,1647,93612,93631,93632,93588,93664,3787,93666,93685,93686,15842,93703,93737,93738,3484,93755,93758],{},"1° ",[38,93498,93499,93500,4288],{},"Do bodu ",[883,93501,93503],{"className":93502},[886],[888,93504,93505],{"xmlns":890},[892,93506,93507,93515],{},[895,93508,93509],{},[2142,93510,93511,93513],{},[898,93512,6362],{},[2148,93514,2150],{},[902,93516,93517],{"encoding":904},"L_0",[883,93519,93521],{"className":93520},[886],[888,93522,93523],{"xmlns":890},[892,93524,93525,93535],{},[895,93526,93527,93529],{},[898,93528,1742],{},[2142,93530,93531,93533],{},[898,93532,1702],{},[898,93534,6362],{},[902,93536,29159],{"encoding":904}," roste, tj. ",[883,93539,93541],{"className":93540},[886],[888,93542,93543],{"xmlns":890},[892,93544,93545,93585],{},[895,93546,93547,93549,93551,93557,93563,93565,93575,93577,93579,93581,93583],{},[1706,93548,2140],{"stretchy":2139},[898,93550,1742],{},[2142,93552,93553,93555],{},[898,93554,1702],{},[898,93556,6362],{},[2489,93558,93559,93561],{},[1706,93560,2153],{"stretchy":2139},[1706,93562,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,93564,1708],{},[2489,93566,93567,93569],{},[898,93568,2146],{},[895,93570,93571,93573],{},[1706,93572,3142],{"mathvariant":2409},[1706,93574,3142],{"mathvariant":2409},[1706,93576,2140],{"stretchy":2139},[898,93578,6362],{},[1706,93580,2153],{"stretchy":2139},[1706,93582,8922],{},[2148,93584,2150],{},[902,93586,93587],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,93590,56721],{},".\n2° ",[38,93593,93594,93595,4288],{},"Od bodu ",[883,93596,93598],{"className":93597},[886],[888,93599,93600],{"xmlns":890},[892,93601,93602,93610],{},[895,93603,93604],{},[2142,93605,93606,93608],{},[898,93607,6362],{},[2148,93609,2150],{},[902,93611,93517],{"encoding":904},[883,93613,93615],{"className":93614},[886],[888,93616,93617],{"xmlns":890},[892,93618,93619,93629],{},[895,93620,93621,93623],{},[898,93622,1742],{},[2142,93624,93625,93627],{},[898,93626,1702],{},[898,93628,6362],{},[902,93630,29159],{"encoding":904}," klesá, ",[883,93633,93635],{"className":93634},[886],[888,93636,93637],{"xmlns":890},[892,93638,93639,93661],{},[895,93640,93641,93651,93653,93655,93657,93659],{},[2489,93642,93643,93645],{},[898,93644,2146],{},[895,93646,93647,93649],{},[1706,93648,3142],{"mathvariant":2409},[1706,93650,3142],{"mathvariant":2409},[1706,93652,2140],{"stretchy":2139},[898,93654,6362],{},[1706,93656,2153],{"stretchy":2139},[1706,93658,2539],{},[2148,93660,2150],{},[902,93662,93663],{"encoding":904},"Q''(L) \u003C 0",[38,93665,57543],{},[883,93667,93669],{"className":93668},[886],[888,93670,93671],{"xmlns":890},[892,93672,93673,93683],{},[895,93674,93675,93677],{},[898,93676,1742],{},[2142,93678,93679,93681],{},[898,93680,1702],{},[898,93682,6362],{},[902,93684,29159],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,93687,93689],{"className":93688},[886],[888,93690,93691],{"xmlns":890},[892,93692,93693,93701],{},[895,93694,93695],{},[2142,93696,93697,93699],{},[898,93698,6362],{},[2148,93700,2701],{},[902,93702,32319],{"encoding":904},[883,93704,93706],{"className":93705},[886],[888,93707,93708],{"xmlns":890},[892,93709,93710,93734],{},[895,93711,93712,93714,93720,93722,93728,93730,93732],{},[898,93713,1742],{},[2142,93715,93716,93718],{},[898,93717,1702],{},[898,93719,6362],{},[1706,93721,2140],{"stretchy":2139},[2142,93723,93724,93726],{},[898,93725,6362],{},[2148,93727,2701],{},[1706,93729,2153],{"stretchy":2139},[1706,93731,1708],{},[2148,93733,2150],{},[902,93735,93736],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,93739,93741],{"className":93740},[886],[888,93742,93743],{"xmlns":890},[892,93744,93745,93753],{},[895,93746,93747],{},[2142,93748,93749,93751],{},[898,93750,6362],{},[2148,93752,2150],{},[902,93754,93517],{"encoding":904},[38,93756,93757],{},"inflexním bodem"," produkční funkce.",[724,93760,93761,93762,4521,93779,1837],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,93763,93765],{"className":93764},[886],[888,93766,93767],{"xmlns":890},[892,93768,93769,93777],{},[895,93770,93771],{},[2142,93772,93773,93775],{},[898,93774,6362],{},[2148,93776,2150],{},[902,93778,93517],{"encoding":904},[883,93780,93782],{"className":93781},[886],[888,93783,93784],{"xmlns":890},[892,93785,93786,93808],{},[895,93787,93788,93798,93800,93802,93804,93806],{},[2489,93789,93790,93792],{},[898,93791,2146],{},[895,93793,93794,93796],{},[1706,93795,3142],{"mathvariant":2409},[1706,93797,3142],{"mathvariant":2409},[1706,93799,2140],{"stretchy":2139},[898,93801,6362],{},[1706,93803,2153],{"stretchy":2139},[1706,93805,2539],{},[2148,93807,2150],{},[902,93809,93663],{"encoding":904},[724,93811,93812,1647,93815,24808,93855,1343,93872,93889],{},[38,93813,93814],{},"Typický polynom třetího stupně:",[883,93816,93818],{"className":93817},[886],[888,93819,93820],{"xmlns":890},[892,93821,93822,93852],{},[895,93823,93824,93826,93828,93830,93832,93834,93836,93842,93844,93846],{},[898,93825,2146],{},[1706,93827,2140],{"stretchy":2139},[898,93829,6362],{},[1706,93831,2153],{"stretchy":2139},[1706,93833,1708],{},[898,93835,207],{},[2489,93837,93838,93840],{},[898,93839,6362],{},[2148,93841,4284],{},[1706,93843,2447],{},[898,93845,2450],{},[2489,93847,93848,93850],{},[898,93849,6362],{},[2148,93851,2495],{},[902,93853,93854],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,93856,93858],{"className":93857},[886],[888,93859,93860],{"xmlns":890},[892,93861,93862,93870],{},[895,93863,93864,93866,93868],{},[898,93865,207],{},[1706,93867,2539],{},[2148,93869,2150],{},[902,93871,2544],{"encoding":904},[883,93873,93875],{"className":93874},[886],[888,93876,93877],{"xmlns":890},[892,93878,93879,93887],{},[895,93880,93881,93883,93885],{},[898,93882,2450],{},[1706,93884,8922],{},[2148,93886,2150],{},[902,93888,37911],{"encoding":904},". Pak",[883,93891,93893],{"className":93892},[886],[888,93894,93895],{"xmlns":890,"display":2350},[892,93896,93897,93957],{},[895,93898,93899,93905,93907,93909,93917,93925,93927,93929,93935,93937,93939,93947,93955],{},[2142,93900,93901,93903],{},[898,93902,6362],{},[2148,93904,2150],{},[1706,93906,1708],{},[1706,93908,1715],{},[4745,93910,93911],{"scriptlevel":2150,"displaystyle":2139},[2964,93912,93913,93915],{},[2148,93914,2701],{},[2148,93916,4284],{},[4745,93918,93919],{"scriptlevel":2150,"displaystyle":2139},[2964,93920,93921,93923],{},[898,93922,2450],{},[898,93924,207],{},[1706,93926,2505],{"separator":2504},[4898,93928],{"width":9524},[2142,93930,93931,93933],{},[898,93932,6362],{},[2148,93934,2701],{},[1706,93936,1708],{},[1706,93938,1715],{},[4745,93940,93941],{"scriptlevel":2150,"displaystyle":2139},[2964,93942,93943,93945],{},[2148,93944,2495],{},[2148,93946,4284],{},[4745,93948,93949],{"scriptlevel":2150,"displaystyle":2139},[2964,93950,93951,93953],{},[898,93952,2450],{},[898,93954,207],{},[898,93956,1837],{"mathvariant":2409},[902,93958,93959],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,93961,93963,93964,2153],{"id":93962},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,93965,93967],{"className":93966},[886],[888,93968,93969],{"xmlns":890},[892,93970,93971,93981],{},[895,93972,93973,93975],{},[898,93974,1735],{},[2142,93976,93977,93979],{},[898,93978,1702],{},[898,93980,6362],{},[902,93982,92592],{"encoding":904},[724,93984,93985,2314,93988,93056,93991,94010],{},[38,93986,93987],{},"Průměrný produkt práce",[614,93989,93990],{},"average product of labour",[883,93992,93994],{"className":93993},[886],[888,93995,93996],{"xmlns":890},[892,93997,93998,94008],{},[895,93999,94000,94002],{},[898,94001,1735],{},[2142,94003,94004,94006],{},[898,94005,1702],{},[898,94007,6362],{},[902,94009,92592],{"encoding":904}," je podíl produkce a práce:",[883,94012,94014],{"className":94013},[886],[888,94015,94016],{"xmlns":890,"display":2350},[892,94017,94018,94053],{},[2354,94019,94020],{"width":2356},[2358,94021,94022,94024,94046,94048],{},[2361,94023],{"width":2363},[2361,94025,94026],{},[895,94027,94028,94030,94036,94038,94044],{},[898,94029,1735],{},[2142,94031,94032,94034],{},[898,94033,1702],{},[898,94035,6362],{},[1706,94037,1708],{},[2964,94039,94040,94042],{},[898,94041,2146],{},[898,94043,6362],{},[898,94045,1837],{"mathvariant":2409},[2361,94047],{"width":2363},[2361,94049,94050],{},[2415,94051,94052],{},"(5.4)",[902,94054,94055],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,94057,94058,94059,1837],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,94060,94062],{"className":94061},[886],[888,94063,94064],{"xmlns":890},[892,94065,94066,94076],{},[895,94067,94068,94070],{},[898,94069,1735],{},[2142,94071,94072,94074],{},[898,94073,1702],{},[898,94075,6362],{},[902,94077,92592],{"encoding":904},[115,94079,94081],{"id":94080},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,94083,94084],{},[2286,94085],{"alt":94086,"className":94087,"src":94088},"imek-q-mpl-apl-tripanel",[210,2290],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[1636,94090,94091],{},[724,94092,94093,94096,94097,2891,94116,94133,94134],{},[38,94094,94095],{},"Princip:"," Má-li ",[883,94098,94100],{"className":94099},[886],[888,94101,94102],{"xmlns":890},[892,94103,94104,94114],{},[895,94105,94106,94108],{},[898,94107,1735],{},[2142,94109,94110,94112],{},[898,94111,1702],{},[898,94113,6362],{},[902,94115,92592],{"encoding":904},[883,94117,94119],{"className":94118},[886],[888,94120,94121],{"xmlns":890},[892,94122,94123,94131],{},[895,94124,94125],{},[2142,94126,94127,94129],{},[898,94128,6362],{},[2148,94130,2150],{},[902,94132,93517],{"encoding":904}," maximum, pak platí\n",[883,94135,94137],{"className":94136,"title":23358,"style":23359},[23357],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,94139,94140,94141,94144,94145,1647,94149,1837],{},"Slovně: ",[38,94142,94143],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,94146,94148],{"className":94147,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,94150,94152],{"className":94151},[886],[888,94153,94154],{"xmlns":890},[892,94155,94156,94162],{},[895,94157,94158,94160],{},[898,94159,1735],{},[898,94161,1683],{},[902,94163,2094],{"encoding":904},[1636,94165,94166,94190],{},[724,94167,94168,94170,94171],{},[883,94169,12314],{}," Postup — jak najít max ",[883,94172,94174],{"className":94173},[886],[888,94175,94176],{"xmlns":890},[892,94177,94178,94188],{},[895,94179,94180,94182],{},[898,94181,1735],{},[2142,94183,94184,94186],{},[898,94185,1702],{},[898,94187,6362],{},[902,94189,92592],{"encoding":904},[152,94191,94192,94230,94312],{},[123,94193,94194,94195,94229],{},"Napište ",[883,94196,94198],{"className":94197},[886],[888,94199,94200],{"xmlns":890},[892,94201,94202,94226],{},[895,94203,94204,94206,94212,94214,94216,94218,94220,94222,94224],{},[898,94205,1735],{},[2142,94207,94208,94210],{},[898,94209,1702],{},[898,94211,6362],{},[1706,94213,1708],{},[898,94215,2146],{},[1706,94217,2140],{"stretchy":2139},[898,94219,6362],{},[1706,94221,2153],{"stretchy":2139},[898,94223,15493],{"mathvariant":2409},[898,94225,6362],{},[902,94227,94228],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,94231,94232,94233,94265,94266,94269,94270,1837],{},"Položte ",[883,94234,94236],{"className":94235},[886],[888,94237,94238],{"xmlns":890},[892,94239,94240,94262],{},[895,94241,94242,94244,94246,94252,94258,94260],{},[1706,94243,2140],{"stretchy":2139},[898,94245,1735],{},[2142,94247,94248,94250],{},[898,94249,1702],{},[898,94251,6362],{},[2489,94253,94254,94256],{},[1706,94255,2153],{"stretchy":2139},[1706,94257,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,94259,1708],{},[2148,94261,2150],{},[902,94263,94264],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,94267,94268],{},"Zkratka:"," můžete rovnou řešit ",[883,94271,94273],{"className":94272},[886],[888,94274,94275],{"xmlns":890},[892,94276,94277,94309],{},[895,94278,94279,94281,94287,94289,94291,94293,94295,94297,94303,94305,94307],{},[898,94280,1742],{},[2142,94282,94283,94285],{},[898,94284,1702],{},[898,94286,6362],{},[1706,94288,2140],{"stretchy":2139},[898,94290,6362],{},[1706,94292,2153],{"stretchy":2139},[1706,94294,1708],{},[898,94296,1735],{},[2142,94298,94299,94301],{},[898,94300,1702],{},[898,94302,6362],{},[1706,94304,2140],{"stretchy":2139},[898,94306,6362],{},[1706,94308,2153],{"stretchy":2139},[902,94310,94311],{"encoding":904},"MP_L(L) = AP_L(L)",[123,94313,94314],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,94316,12163],{"id":94317},"odvození",[724,94319,94320,94321,94354],{},"Z ",[883,94322,94324],{"className":94323},[886],[888,94325,94326],{"xmlns":890},[892,94327,94328,94352],{},[895,94329,94330,94332,94338,94340,94342,94344,94346,94348,94350],{},[898,94331,1735],{},[2142,94333,94334,94336],{},[898,94335,1702],{},[898,94337,6362],{},[1706,94339,1708],{},[898,94341,2146],{},[1706,94343,2140],{"stretchy":2139},[898,94345,6362],{},[1706,94347,2153],{"stretchy":2139},[898,94349,15493],{"mathvariant":2409},[898,94351,6362],{},[902,94353,94228],{"encoding":904}," a derivace podílu:",[883,94356,94358],{"className":94357},[886],[888,94359,94360],{"xmlns":890,"display":2350},[892,94361,94362,94515],{},[895,94363,94364,94366,94368,94374,94380,94382,94384,94386,94388,94428,94430,94436,94470,94472,94478,94481,94483,94489,94491,94493,94495,94497,94499,94505,94507,94509,94511,94513],{},[1706,94365,2140],{"stretchy":2139},[898,94367,1735],{},[2142,94369,94370,94372],{},[898,94371,1702],{},[898,94373,6362],{},[2489,94375,94376,94378],{},[1706,94377,2153],{"stretchy":2139},[1706,94379,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,94381,2140],{"stretchy":2139},[898,94383,6362],{},[1706,94385,2153],{"stretchy":2139},[1706,94387,1708],{},[2964,94389,94390,94422],{},[895,94391,94392,94398,94400,94402,94404,94406,94408,94410,94412,94414,94416,94418,94420],{},[2489,94393,94394,94396],{},[898,94395,2146],{},[1706,94397,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,94399,2140],{"stretchy":2139},[898,94401,6362],{},[1706,94403,2153],{"stretchy":2139},[1706,94405,2390],{},[898,94407,6362],{},[1706,94409,1715],{},[898,94411,2146],{},[1706,94413,2140],{"stretchy":2139},[898,94415,6362],{},[1706,94417,2153],{"stretchy":2139},[1706,94419,2390],{},[2148,94421,2701],{},[2489,94423,94424,94426],{},[898,94425,6362],{},[2148,94427,2495],{},[1706,94429,1708],{},[2964,94431,94432,94434],{},[2148,94433,2701],{},[898,94435,6362],{},[895,94437,94438,94440,94446,94448,94450,94452,94454,94468],{},[1706,94439,2140],{"fence":2504},[2489,94441,94442,94444],{},[898,94443,2146],{},[1706,94445,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,94447,2140],{"stretchy":2139},[898,94449,6362],{},[1706,94451,2153],{"stretchy":2139},[1706,94453,1715],{},[2964,94455,94456,94466],{},[895,94457,94458,94460,94462,94464],{},[898,94459,2146],{},[1706,94461,2140],{"stretchy":2139},[898,94463,6362],{},[1706,94465,2153],{"stretchy":2139},[898,94467,6362],{},[1706,94469,2153],{"fence":2504},[1706,94471,1708],{},[2964,94473,94474,94476],{},[2148,94475,2701],{},[898,94477,6362],{},[1706,94479,2140],{"fence":2504,"stretchy":2504,"minsize":94480,"maxsize":94480},"1.2em",[898,94482,1742],{},[2142,94484,94485,94487],{},[898,94486,1702],{},[898,94488,6362],{},[1706,94490,2140],{"stretchy":2139},[898,94492,6362],{},[1706,94494,2153],{"stretchy":2139},[1706,94496,1715],{},[898,94498,1735],{},[2142,94500,94501,94503],{},[898,94502,1702],{},[898,94504,6362],{},[1706,94506,2140],{"stretchy":2139},[898,94508,6362],{},[1706,94510,2153],{"stretchy":2139},[1706,94512,2153],{"fence":2504,"stretchy":2504,"minsize":94480,"maxsize":94480},[898,94514,1837],{"mathvariant":2409},[902,94516,94517],{"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).",[724,94519,3465,94520,3484,94542,94625],{},[883,94521,94523],{"className":94522},[886],[888,94524,94525],{"xmlns":890},[892,94526,94527,94539],{},[895,94528,94529,94535,94537],{},[2142,94530,94531,94533],{},[898,94532,6362],{},[2148,94534,2150],{},[1706,94536,8922],{},[2148,94538,2150],{},[902,94540,94541],{"encoding":904},"L_0 > 0",[883,94543,94545],{"className":94544},[886],[888,94546,94547],{"xmlns":890},[892,94548,94549,94622],{},[895,94550,94551,94553,94555,94561,94567,94569,94575,94577,94579,94581,94584,94586,94592,94594,94600,94602,94604,94606,94612,94614,94620],{},[1706,94552,2140],{"stretchy":2139},[898,94554,1735],{},[2142,94556,94557,94559],{},[898,94558,1702],{},[898,94560,6362],{},[2489,94562,94563,94565],{},[1706,94564,2153],{"stretchy":2139},[1706,94566,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,94568,2140],{"stretchy":2139},[2142,94570,94571,94573],{},[898,94572,6362],{},[2148,94574,2150],{},[1706,94576,2153],{"stretchy":2139},[1706,94578,1708],{},[2148,94580,2150],{},[1706,94582,94583],{},"⇔",[898,94585,1742],{},[2142,94587,94588,94590],{},[898,94589,1702],{},[898,94591,6362],{},[1706,94593,2140],{"stretchy":2139},[2142,94595,94596,94598],{},[898,94597,6362],{},[2148,94599,2150],{},[1706,94601,2153],{"stretchy":2139},[1706,94603,1708],{},[898,94605,1735],{},[2142,94607,94608,94610],{},[898,94609,1702],{},[898,94611,6362],{},[1706,94613,2140],{"stretchy":2139},[2142,94615,94616,94618],{},[898,94617,6362],{},[2148,94619,2150],{},[1706,94621,2153],{"stretchy":2139},[902,94623,94624],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,94627,94629],{"id":94628},"příklad-51","Příklad 5.1",[724,94631,94632,94633,1837],{},"Je dána produkce ",[883,94634,94636],{"className":94635},[886],[888,94637,94638],{"xmlns":890},[892,94639,94640,94664],{},[895,94641,94642,94644,94646,94648,94654,94656,94658],{},[898,94643,2146],{},[1706,94645,1708],{},[2148,94647,7044],{},[2489,94649,94650,94652],{},[898,94651,6362],{},[2148,94653,2495],{},[1706,94655,1715],{},[2148,94657,15204],{},[2489,94659,94660,94662],{},[898,94661,6362],{},[2148,94663,4284],{},[902,94665,94666],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,94668,94669,4127,94672,94722,94723,1837],{},[38,94670,94671],{},"(a)",[883,94673,94675],{"className":94674},[886],[888,94676,94677],{"xmlns":890},[892,94678,94679,94719],{},[895,94680,94681,94683,94685,94687,94689,94691,94693,94695,94697,94699,94701,94703,94705,94707,94709,94711,94713,94715,94717],{},[898,94682,6362],{},[1706,94684,1708],{},[2148,94686,2495],{},[1706,94688,2505],{"separator":2504},[2148,94690,7524],{},[1706,94692,2505],{"separator":2504},[2148,94694,12717],{},[1706,94696,2505],{"separator":2504},[2148,94698,7786],{},[1706,94700,2505],{"separator":2504},[2148,94702,12859],{},[1706,94704,2505],{"separator":2504},[2148,94706,22884],{},[1706,94708,2505],{"separator":2504},[2148,94710,3369],{},[1706,94712,2505],{"separator":2504},[2148,94714,57401],{},[1706,94716,2505],{"separator":2504},[2148,94718,2748],{},[902,94720,94721],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,94724,94726],{"className":94725},[886],[888,94727,94728],{"xmlns":890},[892,94729,94730,94740],{},[895,94731,94732,94734],{},[898,94733,1742],{},[2142,94735,94736,94738],{},[898,94737,1702],{},[898,94739,6362],{},[902,94741,29159],{"encoding":904},[724,94743,94744,94745,54030],{},"Podle (5.2): ",[883,94746,94748],{"className":94747},[886],[888,94749,94750],{"xmlns":890},[892,94751,94752,94808],{},[895,94753,94754,94756,94762,94764,94770,94772,94774,94776,94778,94780,94782,94784,94786,94792,94794,94796,94798,94800,94802,94804,94806],{},[898,94755,1742],{},[2142,94757,94758,94760],{},[898,94759,1702],{},[898,94761,6362],{},[1706,94763,1708],{},[2489,94765,94766,94768],{},[898,94767,2146],{},[1706,94769,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,94771,2140],{"stretchy":2139},[898,94773,6362],{},[1706,94775,2153],{"stretchy":2139},[1706,94777,1708],{},[2148,94779,7156],{},[898,94781,6362],{},[1706,94783,1715],{},[2148,94785,13775],{},[2489,94787,94788,94790],{},[898,94789,6362],{},[2148,94791,2495],{},[1706,94793,1708],{},[898,94795,6362],{},[1706,94797,2140],{"stretchy":2139},[2148,94799,7156],{},[1706,94801,1715],{},[2148,94803,13775],{},[898,94805,6362],{},[1706,94807,2153],{"stretchy":2139},[902,94809,94810],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,94812,94813,94850],{},[19,94814,94815],{},[22,94816,94817,94832,94834,94836,94838,94840,94842,94844,94846,94848],{},[25,94818,94819],{},[883,94820,94822],{"className":94821},[886],[888,94823,94824],{"xmlns":890},[892,94825,94826,94830],{},[895,94827,94828],{},[898,94829,6362],{},[902,94831,6362],{"encoding":904},[25,94833,2495],{},[25,94835,7524],{},[25,94837,12717],{},[25,94839,7786],{},[25,94841,12859],{},[25,94843,22884],{},[25,94845,3369],{},[25,94847,57401],{},[25,94849,2748],{},[30,94851,94852],{},[22,94853,94854,94875,94878,94881,94884,94886,94889,94891,94893,94912],{},[35,94855,94856],{},[883,94857,94859],{"className":94858},[886],[888,94860,94861],{"xmlns":890},[892,94862,94863,94873],{},[895,94864,94865,94867],{},[898,94866,1742],{},[2142,94868,94869,94871],{},[898,94870,1702],{},[898,94872,6362],{},[902,94874,29159],{"encoding":904},[35,94876,94877],{},"21,6",[35,94879,94880],{},"45",[35,94882,94883],{},"57,6",[35,94885,4199],{},[35,94887,94888],{},"50,4",[35,94890,94877],{},[35,94892,2150],{},[35,94894,94895],{},[883,94896,94898],{"className":94897},[886],[888,94899,94900],{"xmlns":890},[892,94901,94902,94909],{},[895,94903,94904,94906],{},[1706,94905,1715],{},[2148,94907,94908],{},"12,6",[902,94910,94911],{"encoding":904},"-12{,}6",[35,94913,94914],{},[883,94915,94917],{"className":94916},[886],[888,94918,94919],{"xmlns":890},[892,94920,94921,94927],{},[895,94922,94923,94925],{},[1706,94924,1715],{},[2148,94926,64497],{},[902,94928,94929],{"encoding":904},"-75",[724,94931,94932,94951,94952,94970,94971,94988,94989,95007,95008,95032,95033,95051],{},[883,94933,94935],{"className":94934},[886],[888,94936,94937],{"xmlns":890},[892,94938,94939,94949],{},[895,94940,94941,94943],{},[898,94942,1742],{},[2142,94944,94945,94947],{},[898,94946,1702],{},[898,94948,6362],{},[902,94950,29159],{"encoding":904}," nabývá maxima pro ",[883,94953,94955],{"className":94954},[886],[888,94956,94957],{"xmlns":890},[892,94958,94959,94967],{},[895,94960,94961,94963,94965],{},[898,94962,6362],{},[1706,94964,1708],{},[2148,94966,7786],{},[902,94968,94969],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,94972,94974],{"className":94973},[886],[888,94975,94976],{"xmlns":890},[892,94977,94978,94986],{},[895,94979,94980,94982,94984],{},[898,94981,6362],{},[1706,94983,1708],{},[2148,94985,7786],{},[902,94987,94969],{"encoding":904}," přírůstky klesají, v ",[883,94990,94992],{"className":94991},[886],[888,94993,94994],{"xmlns":890},[892,94995,94996,95004],{},[895,94997,94998,95000,95002],{},[898,94999,6362],{},[1706,95001,1708],{},[2148,95003,3369],{},[902,95005,95006],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,95009,95011],{"className":95010},[886],[888,95012,95013],{"xmlns":890},[892,95014,95015,95029],{},[895,95016,95017,95019,95021,95023,95025,95027],{},[898,95018,2146],{},[1706,95020,2140],{"stretchy":2139},[2148,95022,3369],{},[1706,95024,2153],{"stretchy":2139},[1706,95026,1708],{},[2148,95028,42934],{},[902,95030,95031],{"encoding":904},"Q(20) = 800","), od ",[883,95034,95036],{"className":95035},[886],[888,95037,95038],{"xmlns":890},[892,95039,95040,95048],{},[895,95041,95042,95044,95046],{},[898,95043,6362],{},[1706,95045,8922],{},[2148,95047,3369],{},[902,95049,95050],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,95053,95054],{},[614,95055,95056,95057,95097,95098,2891,95116,1837],{},"Obrázek 5.1 — graf produkce ",[883,95058,95060],{"className":95059},[886],[888,95061,95062],{"xmlns":890},[892,95063,95064,95094],{},[895,95065,95066,95068,95070,95072,95074,95076,95078,95084,95086,95088],{},[898,95067,2146],{},[1706,95069,2140],{"stretchy":2139},[898,95071,6362],{},[1706,95073,2153],{"stretchy":2139},[1706,95075,1708],{},[2148,95077,7044],{},[2489,95079,95080,95082],{},[898,95081,6362],{},[2148,95083,2495],{},[1706,95085,1715],{},[2148,95087,15204],{},[2489,95089,95090,95092],{},[898,95091,6362],{},[2148,95093,4284],{},[902,95095,95096],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,95099,95101],{"className":95100},[886],[888,95102,95103],{"xmlns":890},[892,95104,95105,95113],{},[895,95106,95107,95109,95111],{},[898,95108,2146],{},[1706,95110,1708],{},[2148,95112,42934],{},[902,95114,95115],{"encoding":904},"Q = 800",[883,95117,95119],{"className":95118},[886],[888,95120,95121],{"xmlns":890},[892,95122,95123,95131],{},[895,95124,95125,95127,95129],{},[898,95126,6362],{},[1706,95128,1708],{},[2148,95130,3369],{},[902,95132,95006],{"encoding":904},[724,95134,95135,95138],{},[38,95136,95137],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,95140,95141,95142,1343,95160,4288],{},"Podle (5.3) s ",[883,95143,95145],{"className":95144},[886],[888,95146,95147],{"xmlns":890},[892,95148,95149,95157],{},[895,95150,95151,95153,95155],{},[898,95152,6362],{},[1706,95154,1708],{},[2148,95156,7044],{},[902,95158,95159],{"encoding":904},"L = 6",[883,95161,95163],{"className":95162},[886],[888,95164,95165],{"xmlns":890},[892,95166,95167,95177],{},[895,95168,95169,95171,95173,95175],{},[898,95170,3120],{},[898,95172,6362],{},[1706,95174,1708],{},[2148,95176,4284],{},[902,95178,95179],{"encoding":904},"dL = 3",[883,95181,95183],{"className":95182},[886],[888,95184,95185],{"xmlns":890,"display":2350},[892,95186,95187,95250],{},[895,95188,95189,95191,95193,95195,95197,95203,95205,95207,95209,95211,95213,95215,95217,95219,95221,95223,95225,95227,95229,95231,95233,95235,95237,95239,95241,95243,95245,95247],{},[898,95190,3120],{},[898,95192,2146],{},[1706,95194,1708],{},[898,95196,1742],{},[2142,95198,95199,95201],{},[898,95200,1702],{},[898,95202,6362],{},[1706,95204,2140],{"stretchy":2139},[2148,95206,7044],{},[1706,95208,2153],{"stretchy":2139},[1706,95210,2390],{},[2148,95212,4284],{},[1706,95214,1708],{},[1706,95216,2140],{"stretchy":2139},[2148,95218,7156],{},[1706,95220,2390],{},[2148,95222,7044],{},[1706,95224,1715],{},[2148,95226,13775],{},[1706,95228,2390],{},[2148,95230,3757],{},[1706,95232,2153],{"stretchy":2139},[1706,95234,2390],{},[2148,95236,4284],{},[1706,95238,1708],{},[2148,95240,94888],{},[1706,95242,2390],{},[2148,95244,4284],{},[1706,95246,1708],{},[2148,95248,95249],{},"151,2.",[902,95251,95252],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,95254,95255,95256,4365,95281,95295,95296,1837],{},"Produkce vzroste z ",[883,95257,95259],{"className":95258},[886],[888,95260,95261],{"xmlns":890},[892,95262,95263,95278],{},[895,95264,95265,95267,95269,95271,95273,95275],{},[898,95266,2146],{},[1706,95268,2140],{"stretchy":2139},[2148,95270,7044],{},[1706,95272,2153],{"stretchy":2139},[1706,95274,1708],{},[2148,95276,95277],{},"172,8",[902,95279,95280],{"encoding":904},"Q(6) = 172{,}8",[883,95282,95284],{"className":95283},[886],[888,95285,95286],{"xmlns":890},[892,95287,95288,95293],{},[895,95289,95290],{},[2148,95291,95292],{},"324",[902,95294,95292],{"encoding":904},". Skutečná hodnota: ",[883,95297,95299],{"className":95298},[886],[888,95300,95301],{"xmlns":890},[892,95302,95303,95343],{},[895,95304,95305,95307,95309,95311,95313,95315,95317,95319,95321,95323,95325,95327,95329,95331,95334,95336,95338,95340],{},[898,95306,3677],{"mathvariant":2409},[898,95308,2146],{},[1706,95310,1708],{},[898,95312,2146],{},[1706,95314,2140],{"stretchy":2139},[2148,95316,10800],{},[1706,95318,2153],{"stretchy":2139},[1706,95320,1715],{},[898,95322,2146],{},[1706,95324,2140],{"stretchy":2139},[2148,95326,7044],{},[1706,95328,2153],{"stretchy":2139},[1706,95330,1708],{},[2148,95332,95333],{},"340,2",[1706,95335,1715],{},[2148,95337,95277],{},[1706,95339,1708],{},[2148,95341,95342],{},"167,4",[902,95344,95345],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,95347,95349],{"id":95348},"příklad-52","Příklad 5.2",[724,95351,95352,95353,1837],{},"Ověříme princip (5.5) pro ",[883,95354,95356],{"className":95355},[886],[888,95357,95358],{"xmlns":890},[892,95359,95360,95384],{},[895,95361,95362,95364,95366,95368,95374,95376,95378],{},[898,95363,2146],{},[1706,95365,1708],{},[2148,95367,7044],{},[2489,95369,95370,95372],{},[898,95371,6362],{},[2148,95373,2495],{},[1706,95375,1715],{},[2148,95377,15204],{},[2489,95379,95380,95382],{},[898,95381,6362],{},[2148,95383,4284],{},[902,95385,94666],{"encoding":904},[883,95387,95389],{"className":95388},[886],[888,95390,95391],{"xmlns":890,"display":2350},[892,95392,95393,95471],{},[895,95394,95395,95397,95403,95405,95411,95413,95415,95417,95419,95421,95427,95429,95431,95433,95441,95443,95445,95447,95449,95451,95453,95455,95457,95459,95461,95467,95469],{},[898,95396,1735],{},[2142,95398,95399,95401],{},[898,95400,1702],{},[898,95402,6362],{},[1706,95404,1708],{},[2964,95406,95407,95409],{},[898,95408,2146],{},[898,95410,6362],{},[1706,95412,1708],{},[2148,95414,7044],{},[898,95416,6362],{},[1706,95418,1715],{},[2148,95420,15204],{},[2489,95422,95423,95425],{},[898,95424,6362],{},[2148,95426,2495],{},[1706,95428,2505],{"separator":2504},[4898,95430],{"width":4900},[898,95432,1735],{},[28285,95434,95435,95437,95439],{},[898,95436,1702],{},[898,95438,6362],{},[1706,95440,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,95442,1708],{},[2148,95444,7044],{},[1706,95446,1715],{},[2148,95448,38367],{},[898,95450,6362],{},[1706,95452,1708],{},[2148,95454,2150],{},[2415,95456,3852],{},[1706,95458,9609],{},[2415,95460,3852],{},[2142,95462,95463,95465],{},[898,95464,6362],{},[2148,95466,2150],{},[1706,95468,1708],{},[2148,95470,14964],{},[902,95472,95473],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,95475,95476,95512,95513,95531,95532,1837],{},[883,95477,95479],{"className":95478},[886],[888,95480,95481],{"xmlns":890},[892,95482,95483,95509],{},[895,95484,95485,95487,95499,95501,95503,95505,95507],{},[898,95486,1735],{},[28285,95488,95489,95491,95493],{},[898,95490,1702],{},[898,95492,6362],{},[895,95494,95495,95497],{},[1706,95496,3142],{"mathvariant":2409},[1706,95498,3142],{"mathvariant":2409},[1706,95500,1708],{},[1706,95502,1715],{},[2148,95504,38367],{},[1706,95506,2539],{},[2148,95508,2150],{},[902,95510,95511],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,95514,95516],{"className":95515},[886],[888,95517,95518],{"xmlns":890},[892,95519,95520,95528],{},[895,95521,95522,95524,95526],{},[898,95523,6362],{},[1706,95525,1708],{},[2148,95527,3359],{},[902,95529,95530],{"encoding":904},"L = 15"," je maximum, ",[883,95533,95535],{"className":95534},[886],[888,95536,95537],{"xmlns":890},[892,95538,95539,95585],{},[895,95540,95541,95543,95549,95551,95553,95555,95557,95559,95561,95563,95565,95567,95569,95572,95574,95577,95579,95581,95583],{},[898,95542,1735],{},[2142,95544,95545,95547],{},[898,95546,1702],{},[898,95548,6362],{},[1706,95550,2140],{"stretchy":2139},[2148,95552,3359],{},[1706,95554,2153],{"stretchy":2139},[1706,95556,1708],{},[2148,95558,7044],{},[1706,95560,2390],{},[2148,95562,3359],{},[1706,95564,1715],{},[2148,95566,15204],{},[1706,95568,2390],{},[2148,95570,95571],{},"225",[1706,95573,1708],{},[2148,95575,95576],{},"90",[1706,95578,1715],{},[2148,95580,94880],{},[1706,95582,1708],{},[2148,95584,94880],{},[902,95586,95587],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,95589,95590,60929,95646,95692],{},[883,95591,95593],{"className":95592},[886],[888,95594,95595],{"xmlns":890},[892,95596,95597,95643],{},[895,95598,95599,95601,95607,95609,95611,95613,95615,95617,95619,95621,95623,95625,95627,95629,95631,95634,95636,95639,95641],{},[898,95600,1742],{},[2142,95602,95603,95605],{},[898,95604,1702],{},[898,95606,6362],{},[1706,95608,2140],{"stretchy":2139},[2148,95610,3359],{},[1706,95612,2153],{"stretchy":2139},[1706,95614,1708],{},[2148,95616,7156],{},[1706,95618,2390],{},[2148,95620,3359],{},[1706,95622,1715],{},[2148,95624,13775],{},[1706,95626,2390],{},[2148,95628,95571],{},[1706,95630,1708],{},[2148,95632,95633],{},"180",[1706,95635,1715],{},[2148,95637,95638],{},"135",[1706,95640,1708],{},[2148,95642,94880],{},[902,95644,95645],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,95647,95649],{"className":95648},[886],[888,95650,95651],{"xmlns":890},[892,95652,95653,95689],{},[895,95654,95655,95657,95663,95665,95667,95669,95671,95673,95679,95681,95683,95685,95687],{},[898,95656,1742],{},[2142,95658,95659,95661],{},[898,95660,1702],{},[898,95662,6362],{},[1706,95664,2140],{"stretchy":2139},[2148,95666,3359],{},[1706,95668,2153],{"stretchy":2139},[1706,95670,1708],{},[898,95672,1735],{},[2142,95674,95675,95677],{},[898,95676,1702],{},[898,95678,6362],{},[1706,95680,2140],{"stretchy":2139},[2148,95682,3359],{},[1706,95684,2153],{"stretchy":2139},[1706,95686,1708],{},[2148,95688,94880],{},[902,95690,95691],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,95694,95695,95698,95699,11019,95728,1837],{},[38,95696,95697],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,95700,95702],{"className":95701},[886],[888,95703,95704],{"xmlns":890},[892,95705,95706,95726],{},[895,95707,95708,95710,95716,95718,95720],{},[898,95709,1742],{},[2142,95711,95712,95714],{},[898,95713,1702],{},[898,95715,6362],{},[1706,95717,1708],{},[898,95719,1735],{},[2142,95721,95722,95724],{},[898,95723,1702],{},[898,95725,6362],{},[902,95727,92622],{"encoding":904},[883,95729,95731],{"className":95730},[886],[888,95732,95733],{"xmlns":890},[892,95734,95735,95775],{},[895,95736,95737,95739,95741,95743,95745,95751,95753,95755,95757,95759,95761,95767,95769,95771,95773],{},[2148,95738,7156],{},[898,95740,6362],{},[1706,95742,1715],{},[2148,95744,13775],{},[2489,95746,95747,95749],{},[898,95748,6362],{},[2148,95750,2495],{},[1706,95752,1708],{},[2148,95754,7044],{},[898,95756,6362],{},[1706,95758,1715],{},[2148,95760,15204],{},[2489,95762,95763,95765],{},[898,95764,6362],{},[2148,95766,2495],{},[1706,95768,9609],{},[898,95770,6362],{},[1706,95772,1708],{},[2148,95774,3359],{},[902,95776,95777],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,95779,95780],{},[614,95781,95782,95783,95802,95803,5354,95821,95840,95841,95859,95860,95877,95878,95897,95898,95917],{},"Obrázek 5.3 — křivky ",[883,95784,95786],{"className":95785},[886],[888,95787,95788],{"xmlns":890},[892,95789,95790,95800],{},[895,95791,95792,95794],{},[898,95793,1742],{},[2142,95795,95796,95798],{},[898,95797,1702],{},[898,95799,6362],{},[902,95801,29159],{"encoding":904}," (max 60 při ",[883,95804,95806],{"className":95805},[886],[888,95807,95808],{"xmlns":890},[892,95809,95810,95818],{},[895,95811,95812,95814,95816],{},[898,95813,6362],{},[1706,95815,1708],{},[2148,95817,7786],{},[902,95819,95820],{"encoding":904},"L=10",[883,95822,95824],{"className":95823},[886],[888,95825,95826],{"xmlns":890},[892,95827,95828,95838],{},[895,95829,95830,95832],{},[898,95831,1735],{},[2142,95833,95834,95836],{},[898,95835,1702],{},[898,95837,6362],{},[902,95839,92592],{"encoding":904}," (max 45 při ",[883,95842,95844],{"className":95843},[886],[888,95845,95846],{"xmlns":890},[892,95847,95848,95856],{},[895,95849,95850,95852,95854],{},[898,95851,6362],{},[1706,95853,1708],{},[2148,95855,3359],{},[902,95857,95858],{"encoding":904},"L=15","), průsečík v ",[883,95861,95863],{"className":95862},[886],[888,95864,95865],{"xmlns":890},[892,95866,95867,95875],{},[895,95868,95869,95871,95873],{},[898,95870,6362],{},[1706,95872,1708],{},[2148,95874,3359],{},[902,95876,95530],{"encoding":904},". Nalevo od 15 leží ",[883,95879,95881],{"className":95880},[886],[888,95882,95883],{"xmlns":890},[892,95884,95885,95895],{},[895,95886,95887,95889],{},[898,95888,1742],{},[2142,95890,95891,95893],{},[898,95892,1702],{},[898,95894,6362],{},[902,95896,29159],{"encoding":904}," nad ",[883,95899,95901],{"className":95900},[886],[888,95902,95903],{"xmlns":890},[892,95904,95905,95915],{},[895,95906,95907,95909],{},[898,95908,1735],{},[2142,95910,95911,95913],{},[898,95912,1702],{},[898,95914,6362],{},[902,95916,92592],{"encoding":904},", napravo pod ní.",[115,95919,95921],{"id":95920},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,95923,95924,95925,4202,95938,1647,95941,8156,95954,1647,95957,4288],{},"V dvoufaktorovém modelu závisí produkce ",[883,95926,95928],{"className":95927},[886],[888,95929,95930],{"xmlns":890},[892,95931,95932,95936],{},[895,95933,95934],{},[898,95935,2146],{},[902,95937,2146],{"encoding":904},[38,95939,95940],{},"práci",[883,95942,95944],{"className":95943},[886],[888,95945,95946],{"xmlns":890},[892,95947,95948,95952],{},[895,95949,95950],{},[898,95951,6362],{},[902,95953,6362],{"encoding":904},[38,95955,95956],{},"kapitálu",[883,95958,95960],{"className":95959},[886],[888,95961,95962],{"xmlns":890},[892,95963,95964,95968],{},[895,95965,95966],{},[898,95967,28915],{},[902,95969,28915],{"encoding":904},[883,95971,95973],{"className":95972},[886],[888,95974,95975],{"xmlns":890,"display":2350},[892,95976,95977,96012],{},[2354,95978,95979],{"width":2356},[2358,95980,95981,95983,96005,96007],{},[2361,95982],{"width":2363},[2361,95984,95985],{},[895,95986,95987,95989,95991,95993,95995,95997,95999,96001,96003],{},[898,95988,2146],{},[1706,95990,1708],{},[898,95992,2146],{},[1706,95994,2140],{"stretchy":2139},[898,95996,6362],{},[1706,95998,2505],{"separator":2504},[898,96000,28915],{},[1706,96002,2153],{"stretchy":2139},[898,96004,1837],{"mathvariant":2409},[2361,96006],{"width":2363},[2361,96008,96009],{},[2415,96010,96011],{},"(5.6)",[902,96013,96014],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,96016,96017,96018,96020],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,96019,92959],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,96022,96024],{"id":96023},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,96026,96027],{},"Široce používané produkční funkce mají tvar",[883,96029,96031],{"className":96030},[886],[888,96032,96033],{"xmlns":890,"display":2350},[892,96034,96035,96076],{},[2354,96036,96037],{"width":2356},[2358,96038,96039,96041,96069,96071],{},[2361,96040],{"width":2363},[2361,96042,96043],{},[895,96044,96045,96047,96049,96051,96053,96059,96061,96067],{},[898,96046,2146],{},[1706,96048,1708],{},[898,96050,1735],{},[2415,96052,2799],{},[2489,96054,96055,96057],{},[898,96056,6362],{},[898,96058,207],{},[2415,96060,2799],{},[2489,96062,96063,96065],{},[898,96064,28915],{},[898,96066,2450],{},[1706,96068,2505],{"separator":2504},[2361,96070],{"width":2363},[2361,96072,96073],{},[2415,96074,96075],{},"(5.7)",[902,96077,96078],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,96080,5331,96081,96103,96104,96106,96107,1837],{},[883,96082,96084],{"className":96083},[886],[888,96085,96086],{"xmlns":890},[892,96087,96088,96100],{},[895,96089,96090,96092,96094,96096,96098],{},[898,96091,1735],{},[1706,96093,2505],{"separator":2504},[898,96095,207],{},[1706,96097,2505],{"separator":2504},[898,96099,2450],{},[902,96101,96102],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,96105,92658],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,96108,96110],{"className":96109},[886],[888,96111,96112],{"xmlns":890},[892,96113,96114,96126],{},[895,96115,96116,96118,96120,96122,96124],{},[898,96117,207],{},[1706,96119,2505],{"separator":2504},[898,96121,2450],{},[1706,96123,2539],{},[2148,96125,2701],{},[902,96127,96128],{"encoding":904},"a, b \u003C 1",[724,96130,96131],{},[2286,96132],{"alt":96133,"className":96134,"src":96135},"imek-vynosy-z-rozsahu-3typy",[210,2290],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,96137,96138,96139,96142,96143,4202,96156,96172,96173,4202,96186,4288],{},"Reflektují ekonomickou zákonitost, že ",[38,96140,96141],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,96144,96146],{"className":96145},[886],[888,96147,96148],{"xmlns":890},[892,96149,96150,96154],{},[895,96151,96152],{},[898,96153,6362],{},[902,96155,6362],{"encoding":904},[883,96157,96159],{"className":96158},[886],[888,96160,96161],{"xmlns":890},[892,96162,96163,96169],{},[895,96164,96165,96167],{},[898,96166,3950],{},[898,96168,6362],{},[902,96170,96171],{"encoding":904},"rL"," a kapitál z ",[883,96174,96176],{"className":96175},[886],[888,96177,96178],{"xmlns":890},[892,96179,96180,96184],{},[895,96181,96182],{},[898,96183,28915],{},[902,96185,28915],{"encoding":904},[883,96187,96189],{"className":96188},[886],[888,96190,96191],{"xmlns":890},[892,96192,96193,96199],{},[895,96194,96195,96197],{},[898,96196,3950],{},[898,96198,28915],{},[902,96200,96201],{"encoding":904},"rK",[883,96203,96205],{"className":96204},[886],[888,96206,96207],{"xmlns":890,"display":2350},[892,96208,96209,96332],{},[2354,96210,96211],{"width":2356},[2358,96212,96213,96215,96325,96327],{},[2361,96214],{"width":2363},[2361,96216,96217],{},[895,96218,96219,96221,96223,96225,96227,96229,96231,96233,96235,96237,96239,96241,96243,96245,96251,96253,96255,96257,96263,96265,96267,96269,96281,96283,96289,96295,96297,96309,96311,96313,96315,96317,96319,96321,96323],{},[898,96220,2146],{},[1706,96222,2140],{"stretchy":2139},[898,96224,3950],{},[898,96226,6362],{},[1706,96228,2505],{"separator":2504},[898,96230,3950],{},[898,96232,28915],{},[1706,96234,2153],{"stretchy":2139},[1706,96236,1708],{},[898,96238,1735],{},[1706,96240,2140],{"stretchy":2139},[898,96242,3950],{},[898,96244,6362],{},[2489,96246,96247,96249],{},[1706,96248,2153],{"stretchy":2139},[898,96250,207],{},[1706,96252,2140],{"stretchy":2139},[898,96254,3950],{},[898,96256,28915],{},[2489,96258,96259,96261],{},[1706,96260,2153],{"stretchy":2139},[898,96262,2450],{},[1706,96264,1708],{},[898,96266,1735],{},[2415,96268,2799],{},[2489,96270,96271,96273],{},[898,96272,3950],{},[895,96274,96275,96277,96279],{},[898,96276,207],{},[1706,96278,2447],{},[898,96280,2450],{},[2415,96282,2799],{},[2489,96284,96285,96287],{},[898,96286,6362],{},[898,96288,207],{},[2489,96290,96291,96293],{},[898,96292,28915],{},[898,96294,2450],{},[1706,96296,1708],{},[2489,96298,96299,96301],{},[898,96300,3950],{},[895,96302,96303,96305,96307],{},[898,96304,207],{},[1706,96306,2447],{},[898,96308,2450],{},[2415,96310,2799],{},[898,96312,2146],{},[1706,96314,2140],{"stretchy":2139},[898,96316,6362],{},[1706,96318,2505],{"separator":2504},[898,96320,28915],{},[1706,96322,2153],{"stretchy":2139},[898,96324,1837],{"mathvariant":2409},[2361,96326],{"width":2363},[2361,96328,96329],{},[2415,96330,96331],{},"(5.8)",[902,96333,96334],{"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}",[724,96336,96337,96338],{},"Volně: ",[38,96339,96340,96341,96354,96355,96379],{},"změní-li se vstupy ",[883,96342,96344],{"className":96343},[886],[888,96345,96346],{"xmlns":890},[892,96347,96348,96352],{},[895,96349,96350],{},[898,96351,3950],{},[902,96353,3950],{"encoding":904},"-krát, změní se výstup ",[883,96356,96358],{"className":96357},[886],[888,96359,96360],{"xmlns":890},[892,96361,96362,96376],{},[895,96363,96364],{},[2489,96365,96366,96368],{},[898,96367,3950],{},[895,96369,96370,96372,96374],{},[898,96371,207],{},[1706,96373,2447],{},[898,96375,2450],{},[902,96377,96378],{"encoding":904},"r^{a+b}","-krát.",[198,96381,96383],{"id":96382},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,96385,96386,96387,96404],{},"Součet exponentů ",[883,96388,96390],{"className":96389},[886],[888,96391,96392],{"xmlns":890},[892,96393,96394,96402],{},[895,96395,96396,96398,96400],{},[898,96397,207],{},[1706,96399,2447],{},[898,96401,2450],{},[902,96403,92783],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,96406,96407,96436],{},[19,96408,96409],{},[22,96410,96411,96414,96417,96434],{},[25,96412,96413],{},"Typ",[25,96415,96416],{},"Podmínka",[25,96418,96419,96420,96433],{},"Chování produkce při ",[883,96421,96423],{"className":96422},[886],[888,96424,96425],{"xmlns":890},[892,96426,96427,96431],{},[895,96428,96429],{},[898,96430,3950],{},[902,96432,3950],{"encoding":904},"-násobném zvýšení vstupů",[25,96435,22257],{},[30,96437,96438,96549,96664],{},[22,96439,96440,96448,96472,96505],{},[35,96441,93496,96442,2314,96445,2153],{},[38,96443,96444],{},"Konstantní",[614,96446,96447],{},"constant returns",[35,96449,96450],{},[883,96451,96453],{"className":96452},[886],[888,96454,96455],{"xmlns":890},[892,96456,96457,96469],{},[895,96458,96459,96461,96463,96465,96467],{},[898,96460,207],{},[1706,96462,2447],{},[898,96464,2450],{},[1706,96466,1708],{},[2148,96468,2701],{},[902,96470,96471],{"encoding":904},"a+b = 1",[35,96473,96474,96487,96488,1647,96491,96504],{},[883,96475,96477],{"className":96476},[886],[888,96478,96479],{"xmlns":890},[892,96480,96481,96485],{},[895,96482,96483],{},[898,96484,2146],{},[902,96486,2146],{"encoding":904}," vzroste ",[38,96489,96490],{},"přesně",[883,96492,96494],{"className":96493},[886],[888,96495,96496],{"xmlns":890},[892,96497,96498,96502],{},[895,96499,96500],{},[898,96501,3950],{},[902,96503,3950],{"encoding":904},"-krát",[35,96506,96507],{},[883,96508,96510],{"className":96509},[886],[888,96511,96512],{"xmlns":890},[892,96513,96514,96546],{},[895,96515,96516,96518,96520,96522,96534],{},[898,96517,2146],{},[1706,96519,1708],{},[2148,96521,2495],{},[2489,96523,96524,96526],{},[898,96525,6362],{},[895,96527,96528,96530,96532],{},[2148,96529,2701],{},[898,96531,15493],{"mathvariant":2409},[2148,96533,3455],{},[2489,96535,96536,96538],{},[898,96537,28915],{},[895,96539,96540,96542,96544],{},[2148,96541,4284],{},[898,96543,15493],{"mathvariant":2409},[2148,96545,3455],{},[902,96547,96548],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,96550,96551,96560,96584,96614],{},[35,96552,96553,96554,2314,96557,2153],{},"2° ",[38,96555,96556],{},"Rostoucí",[614,96558,96559],{},"increasing returns",[35,96561,96562],{},[883,96563,96565],{"className":96564},[886],[888,96566,96567],{"xmlns":890},[892,96568,96569,96581],{},[895,96570,96571,96573,96575,96577,96579],{},[898,96572,207],{},[1706,96574,2447],{},[898,96576,2450],{},[1706,96578,8922],{},[2148,96580,2701],{},[902,96582,96583],{"encoding":904},"a+b > 1",[35,96585,96586,96487,96599,70268,96601,96504],{},[883,96587,96589],{"className":96588},[886],[888,96590,96591],{"xmlns":890},[892,96592,96593,96597],{},[895,96594,96595],{},[898,96596,2146],{},[902,96598,2146],{"encoding":904},[38,96600,44342],{},[883,96602,96604],{"className":96603},[886],[888,96605,96606],{"xmlns":890},[892,96607,96608,96612],{},[895,96609,96610],{},[898,96611,3950],{},[902,96613,3950],{"encoding":904},[35,96615,96616,2314,96642,2153],{},[883,96617,96619],{"className":96618},[886],[888,96620,96621],{"xmlns":890},[892,96622,96623,96639],{},[895,96624,96625,96627,96629,96631,96633],{},[898,96626,2146],{},[1706,96628,1708],{},[2148,96630,12597],{},[898,96632,6362],{},[2489,96634,96635,96637],{},[898,96636,28915],{},[2148,96638,2495],{},[902,96640,96641],{"encoding":904},"Q = 7LK^2",[883,96643,96645],{"className":96644},[886],[888,96646,96647],{"xmlns":890},[892,96648,96649,96661],{},[895,96650,96651,96653,96655,96657,96659],{},[898,96652,207],{},[1706,96654,2447],{},[898,96656,2450],{},[1706,96658,1708],{},[2148,96660,4284],{},[902,96662,96663],{"encoding":904},"a+b = 3",[22,96665,96666,96675,96699,96730],{},[35,96667,96668,96669,2314,96672,2153],{},"3° ",[38,96670,96671],{},"Klesající",[614,96673,96674],{},"decreasing returns",[35,96676,96677],{},[883,96678,96680],{"className":96679},[886],[888,96681,96682],{"xmlns":890},[892,96683,96684,96696],{},[895,96685,96686,96688,96690,96692,96694],{},[898,96687,207],{},[1706,96689,2447],{},[898,96691,2450],{},[1706,96693,2539],{},[2148,96695,2701],{},[902,96697,96698],{"encoding":904},"a+b \u003C 1",[35,96700,96701,96487,96714,70268,96717,96504],{},[883,96702,96704],{"className":96703},[886],[888,96705,96706],{"xmlns":890},[892,96707,96708,96712],{},[895,96709,96710],{},[898,96711,2146],{},[902,96713,2146],{"encoding":904},[38,96715,96716],{},"méně",[883,96718,96720],{"className":96719},[886],[888,96721,96722],{"xmlns":890},[892,96723,96724,96728],{},[895,96725,96726],{},[898,96727,3950],{},[902,96729,3950],{"encoding":904},[35,96731,96732,2314,96762,2153],{},[883,96733,96735],{"className":96734},[886],[888,96736,96737],{"xmlns":890},[892,96738,96739,96759],{},[895,96740,96741,96743,96745,96747,96753],{},[898,96742,2146],{},[1706,96744,1708],{},[2148,96746,7786],{},[2489,96748,96749,96751],{},[898,96750,6362],{},[2148,96752,14892],{},[2489,96754,96755,96757],{},[898,96756,28915],{},[2148,96758,11496],{},[902,96760,96761],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,96763,96765],{"className":96764},[886],[888,96766,96767],{"xmlns":890},[892,96768,96769,96781],{},[895,96770,96771,96773,96775,96777,96779],{},[898,96772,207],{},[1706,96774,2447],{},[898,96776,2450],{},[1706,96778,1708],{},[2148,96780,33696],{},[902,96782,96783],{"encoding":904},"a+b = 0{,}8",[1636,96785,96786],{},[724,96787,96788,96790,96791,96808,96809,96812,96813,1647,96816,96852,96853,96875,96876,1837],{},[883,96789,9276],{}," Pozor\nSoučet ",[883,96792,96794],{"className":96793},[886],[888,96795,96796],{"xmlns":890},[892,96797,96798,96806],{},[895,96799,96800,96802,96804],{},[898,96801,207],{},[1706,96803,2447],{},[898,96805,2450],{},[902,96807,92783],{"encoding":904}," neudává velikost produkce, ale ",[38,96810,96811],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,96814,96815],{},"ryzí Cobb-Douglas",[883,96817,96819],{"className":96818},[886],[888,96820,96821],{"xmlns":890},[892,96822,96823,96849],{},[895,96824,96825,96827,96829,96831,96837],{},[898,96826,2146],{},[1706,96828,1708],{},[898,96830,1735],{},[2489,96832,96833,96835],{},[898,96834,6362],{},[898,96836,207],{},[2489,96838,96839,96841],{},[898,96840,28915],{},[895,96842,96843,96845,96847],{},[2148,96844,2701],{},[1706,96846,1715],{},[898,96848,207],{},[902,96850,96851],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,96854,96856],{"className":96855},[886],[888,96857,96858],{"xmlns":890},[892,96859,96860,96872],{},[895,96861,96862,96864,96866,96868,96870],{},[898,96863,2450],{},[1706,96865,1708],{},[2148,96867,2701],{},[1706,96869,1715],{},[898,96871,207],{},[902,96873,96874],{"encoding":904},"b = 1-a",", tedy vždy ",[38,96877,96878],{},"konstantní výnosy z rozsahu",[198,96880,96882,96883],{"id":96881},"parametr-efektivity-aa","Parametr efektivity ",[883,96884,96886],{"className":96885},[886],[888,96887,96888],{"xmlns":890},[892,96889,96890,96894],{},[895,96891,96892],{},[898,96893,1735],{},[902,96895,1735],{"encoding":904},[724,96897,96898,96899,96912,96913,96926,96927,96945,96946,96949],{},"Konstanta ",[883,96900,96902],{"className":96901},[886],[888,96903,96904],{"xmlns":890},[892,96905,96906,96910],{},[895,96907,96908],{},[898,96909,1735],{},[902,96911,1735],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,96914,96916],{"className":96915},[886],[888,96917,96918],{"xmlns":890},[892,96919,96920,96924],{},[895,96921,96922],{},[898,96923,2146],{},[902,96925,2146],{"encoding":904}," při pevně zadaných ",[883,96928,96930],{"className":96929},[886],[888,96931,96932],{"xmlns":890},[892,96933,96934,96942],{},[895,96935,96936,96938,96940],{},[898,96937,6362],{},[1706,96939,2505],{"separator":2504},[898,96941,28915],{},[902,96943,96944],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,96947,96948],{},"parametr efektivity"," — indikátor stavu technologie.",[198,96951,96953],{"id":96952},"příklad-53","Příklad 5.3",[724,96955,96956,96957,96852,96999,97001,97002,1837],{},"Produkční funkce ",[883,96958,96960],{"className":96959},[886],[888,96961,96962],{"xmlns":890},[892,96963,96964,96996],{},[895,96965,96966,96968,96970,96972,96984],{},[898,96967,2146],{},[1706,96969,1708],{},[2148,96971,2495],{},[2489,96973,96974,96976],{},[898,96975,6362],{},[895,96977,96978,96980,96982],{},[2148,96979,2701],{},[898,96981,15493],{"mathvariant":2409},[2148,96983,3455],{},[2489,96985,96986,96988],{},[898,96987,28915],{},[895,96989,96990,96992,96994],{},[2148,96991,4284],{},[898,96993,15493],{"mathvariant":2409},[2148,96995,3455],{},[902,96997,96998],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,97000,43688],{}," výnosy z rozsahu, neboť ",[883,97003,97005],{"className":97004},[886],[888,97006,97007],{"xmlns":890},[892,97008,97009,97033],{},[895,97010,97011,97019,97021,97029,97031],{},[4745,97012,97013],{"scriptlevel":2150,"displaystyle":2139},[2964,97014,97015,97017],{},[2148,97016,2701],{},[2148,97018,3455],{},[1706,97020,2447],{},[4745,97022,97023],{"scriptlevel":2150,"displaystyle":2139},[2964,97024,97025,97027],{},[2148,97026,4284],{},[2148,97028,3455],{},[1706,97030,1708],{},[2148,97032,2701],{},[902,97034,97035],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,97037,97038,97039,8156,97052,97065,97066,1647,97079,97119],{},"Změní-li se ",[883,97040,97042],{"className":97041},[886],[888,97043,97044],{"xmlns":890},[892,97045,97046,97050],{},[895,97047,97048],{},[898,97049,6362],{},[902,97051,6362],{"encoding":904},[883,97053,97055],{"className":97054},[886],[888,97056,97057],{"xmlns":890},[892,97058,97059,97063],{},[895,97060,97061],{},[898,97062,28915],{},[902,97064,28915],{"encoding":904}," čtyřnásobně, změní se ",[883,97067,97069],{"className":97068},[886],[888,97070,97071],{"xmlns":890},[892,97072,97073,97077],{},[895,97074,97075],{},[898,97076,2146],{},[902,97078,2146],{"encoding":904},[883,97080,97082],{"className":97081},[886],[888,97083,97084],{"xmlns":890},[892,97085,97086,97116],{},[895,97087,97088,97108,97110],{},[2489,97089,97090,97092],{},[2148,97091,3455],{},[895,97093,97094,97096,97098,97100,97102,97104,97106],{},[2148,97095,2701],{},[898,97097,15493],{"mathvariant":2409},[2148,97099,3455],{},[1706,97101,2447],{},[2148,97103,4284],{},[898,97105,15493],{"mathvariant":2409},[2148,97107,3455],{},[1706,97109,1708],{},[2489,97111,97112,97114],{},[2148,97113,3455],{},[2148,97115,2701],{},[902,97117,97118],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,97121,97123],{"className":97122},[886],[888,97124,97125],{"xmlns":890,"display":2350},[892,97126,97127,97287],{},[895,97128,97129,97131,97133,97135,97137,97139,97141,97143,97145,97147,97149,97151,97153,97155,97167,97169,97171,97173,97185,97187,97189,97191,97211,97223,97235,97237,97239,97241,97243,97255,97267,97269,97271,97273,97275,97277,97279,97281,97283,97285],{},[898,97130,2146],{},[1706,97132,2140],{"stretchy":2139},[2148,97134,3455],{},[898,97136,6362],{},[1706,97138,2505],{"separator":2504},[2148,97140,3455],{},[898,97142,28915],{},[1706,97144,2153],{"stretchy":2139},[1706,97146,1708],{},[2148,97148,2495],{},[1706,97150,2140],{"stretchy":2139},[2148,97152,3455],{},[898,97154,6362],{},[2489,97156,97157,97159],{},[1706,97158,2153],{"stretchy":2139},[895,97160,97161,97163,97165],{},[2148,97162,2701],{},[898,97164,15493],{"mathvariant":2409},[2148,97166,3455],{},[1706,97168,2140],{"stretchy":2139},[2148,97170,3455],{},[898,97172,28915],{},[2489,97174,97175,97177],{},[1706,97176,2153],{"stretchy":2139},[895,97178,97179,97181,97183],{},[2148,97180,4284],{},[898,97182,15493],{"mathvariant":2409},[2148,97184,3455],{},[1706,97186,1708],{},[2148,97188,2495],{},[1706,97190,2390],{},[2489,97192,97193,97195],{},[2148,97194,3455],{},[895,97196,97197,97199,97201,97203,97205,97207,97209],{},[2148,97198,2701],{},[898,97200,15493],{"mathvariant":2409},[2148,97202,3455],{},[1706,97204,2447],{},[2148,97206,4284],{},[898,97208,15493],{"mathvariant":2409},[2148,97210,3455],{},[2489,97212,97213,97215],{},[898,97214,6362],{},[895,97216,97217,97219,97221],{},[2148,97218,2701],{},[898,97220,15493],{"mathvariant":2409},[2148,97222,3455],{},[2489,97224,97225,97227],{},[898,97226,28915],{},[895,97228,97229,97231,97233],{},[2148,97230,4284],{},[898,97232,15493],{"mathvariant":2409},[2148,97234,3455],{},[1706,97236,1708],{},[2148,97238,3455],{},[1706,97240,2390],{},[2148,97242,2495],{},[2489,97244,97245,97247],{},[898,97246,6362],{},[895,97248,97249,97251,97253],{},[2148,97250,2701],{},[898,97252,15493],{"mathvariant":2409},[2148,97254,3455],{},[2489,97256,97257,97259],{},[898,97258,28915],{},[895,97260,97261,97263,97265],{},[2148,97262,4284],{},[898,97264,15493],{"mathvariant":2409},[2148,97266,3455],{},[1706,97268,1708],{},[2148,97270,3455],{},[2415,97272,2799],{},[898,97274,2146],{},[1706,97276,2140],{"stretchy":2139},[898,97278,6362],{},[1706,97280,2505],{"separator":2504},[898,97282,28915],{},[1706,97284,2153],{"stretchy":2139},[898,97286,1837],{"mathvariant":2409},[902,97288,97289],{"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).",[198,97291,97292],{"id":56237},"Homogenita",[724,97294,97295,97296,3484,97319,97335],{},"Funkce ",[883,97297,97299],{"className":97298},[886],[888,97300,97301],{"xmlns":890},[892,97302,97303,97317],{},[895,97304,97305,97307,97309,97311,97313,97315],{},[898,97306,2146],{},[1706,97308,2140],{"stretchy":2139},[898,97310,6362],{},[1706,97312,2505],{"separator":2504},[898,97314,28915],{},[1706,97316,2153],{"stretchy":2139},[902,97318,29112],{"encoding":904},[38,97320,97321,97322],{},"homogenní stupně ",[883,97323,97325],{"className":97324},[886],[888,97326,97327],{"xmlns":890},[892,97328,97329,97333],{},[895,97330,97331],{},[898,97332,18465],{},[902,97334,18465],{"encoding":904},", jestliže",[883,97337,97339],{"className":97338},[886],[888,97340,97341],{"xmlns":890,"display":2350},[892,97342,97343,97400],{},[2354,97344,97345],{"width":2356},[2358,97346,97347,97349,97393,97395],{},[2361,97348],{"width":2363},[2361,97350,97351],{},[895,97352,97353,97355,97357,97359,97361,97363,97365,97367,97369,97371,97377,97379,97381,97383,97385,97387,97389,97391],{},[898,97354,2146],{},[1706,97356,2140],{"stretchy":2139},[898,97358,3950],{},[898,97360,6362],{},[1706,97362,2505],{"separator":2504},[898,97364,3950],{},[898,97366,28915],{},[1706,97368,2153],{"stretchy":2139},[1706,97370,1708],{},[2489,97372,97373,97375],{},[898,97374,3950],{},[898,97376,18465],{},[2415,97378,2799],{},[898,97380,2146],{},[1706,97382,2140],{"stretchy":2139},[898,97384,6362],{},[1706,97386,2505],{"separator":2504},[898,97388,28915],{},[1706,97390,2153],{"stretchy":2139},[1706,97392,2505],{"separator":2504},[2361,97394],{"width":2363},[2361,97396,97397],{},[2415,97398,97399],{},"(5.10)",[902,97401,97402],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,97404,5331,97405,97423,97424,97442,97443,10234,97456,97459,97460,1837],{},[883,97406,97408],{"className":97407},[886],[888,97409,97410],{"xmlns":890},[892,97411,97412,97420],{},[895,97413,97414,97416,97418],{},[898,97415,18465],{},[1706,97417,14220],{},[2148,97419,2150],{},[902,97421,97422],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,97425,97427],{"className":97426},[886],[888,97428,97429],{"xmlns":890},[892,97430,97431,97439],{},[895,97432,97433,97435,97437],{},[898,97434,3950],{},[1706,97436,8922],{},[2148,97438,2150],{},[902,97440,97441],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,97444,97446],{"className":97445},[886],[888,97447,97448],{"xmlns":890},[892,97449,97450,97454],{},[895,97451,97452],{},[2148,97453,2701],{},[902,97455,2701],{"encoding":904},[38,97457,97458],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,97461,97463],{"className":97462},[886],[888,97464,97465],{"xmlns":890},[892,97466,97467,97475],{},[895,97468,97469,97471,97473],{},[898,97470,207],{},[1706,97472,2447],{},[898,97474,2450],{},[902,97476,92783],{"encoding":904},[115,97478,97480],{"id":97479},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,97482,97483],{},[38,97484,97485],{},"Ryzí Cobb-Douglasovy funkce:",[883,97487,97489],{"className":97488},[886],[888,97490,97491],{"xmlns":890,"display":2350},[892,97492,97493,97552],{},[2354,97494,97495],{"width":2356},[2358,97496,97497,97499,97545,97547],{},[2361,97498],{"width":2363},[2361,97500,97501],{},[895,97502,97503,97505,97507,97509,97511,97517,97519,97531,97533,97535,97537,97539,97541,97543],{},[898,97504,2146],{},[1706,97506,1708],{},[898,97508,1735],{},[2415,97510,2799],{},[2489,97512,97513,97515],{},[898,97514,6362],{},[898,97516,207],{},[2415,97518,2799],{},[2489,97520,97521,97523],{},[898,97522,28915],{},[895,97524,97525,97527,97529],{},[2148,97526,2701],{},[1706,97528,1715],{},[898,97530,207],{},[1706,97532,2505],{"separator":2504},[4898,97534],{"width":4900},[2148,97536,2150],{},[1706,97538,2539],{},[898,97540,207],{},[1706,97542,2539],{},[2148,97544,32367],{},[2361,97546],{"width":2363},[2361,97548,97549],{},[2415,97550,97551],{},"(5.9)",[902,97553,97554],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,97556,97557,97558,97560,97561,1837],{},"Mají vždy ",[38,97559,96878],{}," a jsou ",[38,97562,97458],{},[724,97564,97565,2314,97568,97571],{},[38,97566,97567],{},"CES produkční funkce",[614,97569,97570],{},"Constant Elasticity of Substitution",", 1961):",[883,97573,97575],{"className":97574},[886],[888,97576,97577],{"xmlns":890,"display":2350},[892,97578,97579,97647],{},[895,97580,97581,97583,97585,97587,97645],{},[898,97582,2146],{},[1706,97584,1708],{},[898,97586,1735],{},[2489,97588,97589,97633],{},[895,97590,97591,97593,97595,97597,97599,97601,97603,97605,97615,97617,97619,97621,97631],{},[1706,97592,21693],{"fence":2504},[1706,97594,2140],{"stretchy":2139},[2148,97596,2701],{},[1706,97598,1715],{},[898,97600,207],{},[1706,97602,2153],{"stretchy":2139},[2415,97604,2799],{},[2489,97606,97607,97609],{},[898,97608,6362],{},[895,97610,97611,97613],{},[1706,97612,1715],{},[898,97614,2450],{},[1706,97616,2447],{},[898,97618,207],{},[2415,97620,2799],{},[2489,97622,97623,97625],{},[898,97624,28915],{},[895,97626,97627,97629],{},[1706,97628,1715],{},[898,97630,2450],{},[1706,97632,21708],{"fence":2504},[895,97634,97635,97637],{},[1706,97636,1715],{},[4745,97638,97639],{"scriptlevel":2150,"displaystyle":2139},[2964,97640,97641,97643],{},[2148,97642,2701],{},[898,97644,2450],{},[1706,97646,2505],{"separator":2504},[902,97648,97649],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,97651,5331,97652,1343,97670,1343,97691,97715],{},[883,97653,97655],{"className":97654},[886],[888,97656,97657],{"xmlns":890},[892,97658,97659,97667],{},[895,97660,97661,97663,97665],{},[898,97662,1735],{},[1706,97664,8922],{},[2148,97666,2150],{},[902,97668,97669],{"encoding":904},"A > 0",[883,97671,97673],{"className":97672},[886],[888,97674,97675],{"xmlns":890},[892,97676,97677,97689],{},[895,97678,97679,97681,97683,97685,97687],{},[2148,97680,2150],{},[1706,97682,2539],{},[898,97684,207],{},[1706,97686,2539],{},[2148,97688,2701],{},[902,97690,37933],{"encoding":904},[883,97692,97694],{"className":97693},[886],[888,97695,97696],{"xmlns":890},[892,97697,97698,97712],{},[895,97699,97700,97702,97704,97706,97708,97710],{},[1706,97701,1715],{},[2148,97703,2701],{},[1706,97705,2539],{},[898,97707,2450],{},[1706,97709,22551],{"mathvariant":2409},[2148,97711,2150],{},[902,97713,97714],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,97717,97718],{},[38,97719,97720],{},"Další typy:",[120,97722,97723,97765],{},[123,97724,97725,1647,97728,97764],{},[38,97726,97727],{},"Lineární:",[883,97729,97731],{"className":97730},[886],[888,97732,97733],{"xmlns":890},[892,97734,97735,97761],{},[895,97736,97737,97739,97741,97743,97745,97747,97749,97751,97753,97755,97757,97759],{},[898,97738,2146],{},[1706,97740,2140],{"stretchy":2139},[898,97742,6362],{},[1706,97744,2505],{"separator":2504},[898,97746,28915],{},[1706,97748,2153],{"stretchy":2139},[1706,97750,1708],{},[898,97752,207],{},[898,97754,6362],{},[1706,97756,2447],{},[898,97758,2450],{},[898,97760,28915],{},[902,97762,97763],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,97766,97767,1647,97770,97815],{},[38,97768,97769],{},"Leontiefova:",[883,97771,97773],{"className":97772},[886],[888,97774,97775],{"xmlns":890},[892,97776,97777,97812],{},[895,97778,97779,97781,97783,97785,97787,97789,97791,97793,97796,97798,97800,97802,97804,97806,97808,97810],{},[898,97780,2146],{},[1706,97782,2140],{"stretchy":2139},[898,97784,6362],{},[1706,97786,2505],{"separator":2504},[898,97788,28915],{},[1706,97790,2153],{"stretchy":2139},[1706,97792,1708],{},[898,97794,97795],{},"min",[1706,97797,2773],{},[1706,97799,2140],{"stretchy":2139},[898,97801,207],{},[898,97803,6362],{},[1706,97805,2505],{"separator":2504},[898,97807,2450],{},[898,97809,28915],{},[1706,97811,2153],{"stretchy":2139},[902,97813,97814],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,97817,97819,97820,1343,97839,97858],{"id":97818},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,97821,97823],{"className":97822},[886],[888,97824,97825],{"xmlns":890},[892,97826,97827,97837],{},[895,97828,97829,97831],{},[898,97830,1742],{},[2142,97832,97833,97835],{},[898,97834,1702],{},[898,97836,6362],{},[902,97838,29159],{"encoding":904},[883,97840,97842],{"className":97841},[886],[888,97843,97844],{"xmlns":890},[892,97845,97846,97856],{},[895,97847,97848,97850],{},[898,97849,1742],{},[2142,97851,97852,97854],{},[898,97853,1702],{},[898,97855,28915],{},[902,97857,29204],{"encoding":904}," a totální diferenciál",[724,97860,97861],{},[38,97862,97863],{},"Mezní produkt práce:",[883,97865,97867],{"className":97866},[886],[888,97868,97869],{"xmlns":890,"display":2350},[892,97870,97871,97909],{},[895,97872,97873,97875,97881,97883,97891,97893,97907],{},[898,97874,1742],{},[2142,97876,97877,97879],{},[898,97878,1702],{},[898,97880,6362],{},[1706,97882,1708],{},[28285,97884,97885,97887,97889],{},[898,97886,2146],{},[898,97888,6362],{},[1706,97890,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,97892,1708],{},[2964,97894,97895,97901],{},[895,97896,97897,97899],{},[898,97898,28987],{"mathvariant":2409},[898,97900,2146],{},[895,97902,97903,97905],{},[898,97904,28987],{"mathvariant":2409},[898,97906,6362],{},[898,97908,1837],{"mathvariant":2409},[902,97910,97911],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,97913,97914],{},[38,97915,97916],{},"Mezní produkt kapitálu:",[883,97918,97920],{"className":97919},[886],[888,97921,97922],{"xmlns":890,"display":2350},[892,97923,97924,97962],{},[895,97925,97926,97928,97934,97936,97944,97946,97960],{},[898,97927,1742],{},[2142,97929,97930,97932],{},[898,97931,1702],{},[898,97933,28915],{},[1706,97935,1708],{},[28285,97937,97938,97940,97942],{},[898,97939,2146],{},[898,97941,28915],{},[1706,97943,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,97945,1708],{},[2964,97947,97948,97954],{},[895,97949,97950,97952],{},[898,97951,28987],{"mathvariant":2409},[898,97953,2146],{},[895,97955,97956,97958],{},[898,97957,28987],{"mathvariant":2409},[898,97959,28915],{},[898,97961,1837],{"mathvariant":2409},[902,97963,97964],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,97966,97967,97997,97998,98019,98020,98038,98039,98052,98053,1837],{},[883,97968,97970],{"className":97969},[886],[888,97971,97972],{"xmlns":890},[892,97973,97974,97994],{},[895,97975,97976,97978,97984,97986,97988,97990,97992],{},[898,97977,1742],{},[2142,97979,97980,97982],{},[898,97981,1702],{},[898,97983,6362],{},[1706,97985,2140],{"stretchy":2139},[898,97987,207],{},[1706,97989,2505],{"separator":2504},[898,97991,2450],{},[1706,97993,2153],{"stretchy":2139},[902,97995,97996],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,97999,98001],{"className":98000},[886],[888,98002,98003],{"xmlns":890},[892,98004,98005,98017],{},[895,98006,98007,98009,98011,98013,98015],{},[1706,98008,21693],{"stretchy":2139},[898,98010,207],{},[1706,98012,2505],{"separator":2504},[898,98014,2450],{},[1706,98016,21708],{"stretchy":2139},[902,98018,29935],{"encoding":904}," (na hladině ",[883,98021,98023],{"className":98022},[886],[888,98024,98025],{"xmlns":890},[892,98026,98027,98035],{},[895,98028,98029,98031,98033],{},[898,98030,28915],{},[1706,98032,1708],{},[898,98034,2450],{},[902,98036,98037],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,98040,98042],{"className":98041},[886],[888,98043,98044],{"xmlns":890},[892,98045,98046,98050],{},[895,98047,98048],{},[898,98049,6362],{},[902,98051,6362],{"encoding":904},". Analogicky ",[883,98054,98056],{"className":98055},[886],[888,98057,98058],{"xmlns":890},[892,98059,98060,98080],{},[895,98061,98062,98064,98070,98072,98074,98076,98078],{},[898,98063,1742],{},[2142,98065,98066,98068],{},[898,98067,1702],{},[898,98069,28915],{},[1706,98071,2140],{"stretchy":2139},[898,98073,207],{},[1706,98075,2505],{"separator":2504},[898,98077,2450],{},[1706,98079,2153],{"stretchy":2139},[902,98081,98082],{"encoding":904},"MP_K(a, b)",[1636,98084,98085,98089],{},[724,98086,98087,70256],{},[883,98088,3174],{},[120,98090,98091,98129],{},[123,98092,98093,8186,98112],{},[883,98094,98096],{"className":98095},[886],[888,98097,98098],{"xmlns":890},[892,98099,98100,98110],{},[895,98101,98102,98104],{},[898,98103,1742],{},[2142,98105,98106,98108],{},[898,98107,1702],{},[898,98109,6362],{},[902,98111,29159],{"encoding":904},[614,98113,98114,98115,98128],{},"„o kolik vzroste ",[883,98116,98118],{"className":98117},[886],[888,98119,98120],{"xmlns":890},[892,98121,98122,98126],{},[895,98123,98124],{},[898,98125,2146],{},[902,98127,2146],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,98130,98131,8186,98150],{},[883,98132,98134],{"className":98133},[886],[888,98135,98136],{"xmlns":890},[892,98137,98138,98148],{},[895,98139,98140,98142],{},[898,98141,1742],{},[2142,98143,98144,98146],{},[898,98145,1702],{},[898,98147,28915],{},[902,98149,29204],{"encoding":904},[614,98151,98114,98152,98165],{},[883,98153,98155],{"className":98154},[886],[888,98156,98157],{"xmlns":890},[892,98158,98159,98163],{},[895,98160,98161],{},[898,98162,2146],{},[902,98164,2146],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,98167,98168,98171,98172,98187,98188,4288],{},[38,98169,98170],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,98173,98175],{"className":98174},[886],[888,98176,98177],{"xmlns":890},[892,98178,98179,98185],{},[895,98180,98181,98183],{},[898,98182,3120],{},[898,98184,6362],{},[902,98186,93315],{"encoding":904}," a kapitálu o ",[883,98189,98191],{"className":98190},[886],[888,98192,98193],{"xmlns":890},[892,98194,98195,98201],{},[895,98196,98197,98199],{},[898,98198,3120],{},[898,98200,28915],{},[902,98202,98203],{"encoding":904},"dK",[883,98205,98207],{"className":98206},[886],[888,98208,98209],{"xmlns":890,"display":2350},[892,98210,98211,98304],{},[2354,98212,98213],{"width":2356},[2358,98214,98215,98217,98297,98299],{},[2361,98216],{"width":2363},[2361,98218,98219],{},[895,98220,98221,98223,98225,98227,98229,98231,98233,98241,98243,98245,98247,98249,98257,98259,98261,98263,98265,98267,98273,98275,98277,98279,98281,98283,98289,98291,98293,98295],{},[898,98222,3677],{"mathvariant":2409},[898,98224,2146],{},[1706,98226,3248],{},[898,98228,3120],{},[898,98230,2146],{},[1706,98232,1708],{},[28285,98234,98235,98237,98239],{},[898,98236,2146],{},[898,98238,6362],{},[1706,98240,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2415,98242,2799],{},[898,98244,3120],{},[898,98246,6362],{},[1706,98248,2447],{},[28285,98250,98251,98253,98255],{},[898,98252,2146],{},[898,98254,28915],{},[1706,98256,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[2415,98258,2799],{},[898,98260,3120],{},[898,98262,28915],{},[1706,98264,1708],{},[898,98266,1742],{},[2142,98268,98269,98271],{},[898,98270,1702],{},[898,98272,6362],{},[2415,98274,2799],{},[898,98276,3120],{},[898,98278,6362],{},[1706,98280,2447],{},[898,98282,1742],{},[2142,98284,98285,98287],{},[898,98286,1702],{},[898,98288,28915],{},[2415,98290,2799],{},[898,98292,3120],{},[898,98294,28915],{},[898,98296,1837],{"mathvariant":2409},[2361,98298],{"width":2363},[2361,98300,98301],{},[2415,98302,98303],{},"(5.11)",[902,98305,98306],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,98308,98309,98310,1837],{},"Skutečná změna: ",[883,98311,98313],{"className":98312},[886],[888,98314,98315],{"xmlns":890},[892,98316,98317,98363],{},[895,98318,98319,98321,98323,98325,98327,98329,98331,98333,98335,98337,98339,98341,98343,98345,98347,98349,98351,98353,98355,98357,98359,98361],{},[898,98320,3677],{"mathvariant":2409},[898,98322,2146],{},[1706,98324,1708],{},[898,98326,2146],{},[1706,98328,2140],{"stretchy":2139},[898,98330,6362],{},[1706,98332,2447],{},[898,98334,3120],{},[898,98336,6362],{},[1706,98338,2505],{"separator":2504},[898,98340,28915],{},[1706,98342,2447],{},[898,98344,3120],{},[898,98346,28915],{},[1706,98348,2153],{"stretchy":2139},[1706,98350,1715],{},[898,98352,2146],{},[1706,98354,2140],{"stretchy":2139},[898,98356,6362],{},[1706,98358,2505],{"separator":2504},[898,98360,28915],{},[1706,98362,2153],{"stretchy":2139},[902,98364,98365],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,98367,98368,98370,98371,98389,98390,98403,98404,98423,98424,98456,98457,98489,98490,1837],{},[38,98369,93479],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,98372,98374],{"className":98373},[886],[888,98375,98376],{"xmlns":890},[892,98377,98378,98386],{},[895,98379,98380],{},[2142,98381,98382,98384],{},[898,98383,28915],{},[2148,98385,2150],{},[902,98387,98388],{"encoding":904},"K_0"," se od jistého ",[883,98391,98393],{"className":98392},[886],[888,98394,98395],{"xmlns":890},[892,98396,98397,98401],{},[895,98398,98399],{},[898,98400,6362],{},[902,98402,6362],{"encoding":904}," stane ",[883,98405,98407],{"className":98406},[886],[888,98408,98409],{"xmlns":890},[892,98410,98411,98421],{},[895,98412,98413,98415],{},[898,98414,1742],{},[2142,98416,98417,98419],{},[898,98418,1702],{},[898,98420,6362],{},[902,98422,29159],{"encoding":904}," klesající (",[883,98425,98427],{"className":98426},[886],[888,98428,98429],{"xmlns":890},[892,98430,98431,98453],{},[895,98432,98433,98449,98451],{},[28285,98434,98435,98437,98443],{},[898,98436,2146],{},[895,98438,98439,98441],{},[898,98440,6362],{},[898,98442,6362],{},[895,98444,98445,98447],{},[1706,98446,3142],{"mathvariant":2409},[1706,98448,3142],{"mathvariant":2409},[1706,98450,2539],{},[2148,98452,2150],{},[902,98454,98455],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,98458,98460],{"className":98459},[886],[888,98461,98462],{"xmlns":890},[892,98463,98464,98486],{},[895,98465,98466,98482,98484],{},[28285,98467,98468,98470,98476],{},[898,98469,2146],{},[895,98471,98472,98474],{},[898,98473,28915],{},[898,98475,28915],{},[895,98477,98478,98480],{},[1706,98479,3142],{"mathvariant":2409},[1706,98481,3142],{"mathvariant":2409},[1706,98483,2539],{},[2148,98485,2150],{},[902,98487,98488],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,98491,98493],{"className":98492},[886],[888,98494,98495],{"xmlns":890},[892,98496,98497,98505],{},[895,98498,98499],{},[2142,98500,98501,98503],{},[898,98502,6362],{},[2148,98504,2150],{},[902,98506,93517],{"encoding":904},[115,98508,98510],{"id":98509},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,98512,98513,98516,98517,98540,98541,2344],{},[38,98514,98515],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,98518,98520],{"className":98519},[886],[888,98521,98522],{"xmlns":890},[892,98523,98524,98538],{},[895,98525,98526,98528,98530,98532,98534,98536],{},[898,98527,2146],{},[1706,98529,2140],{"stretchy":2139},[898,98531,6362],{},[1706,98533,2505],{"separator":2504},[898,98535,28915],{},[1706,98537,2153],{"stretchy":2139},[902,98539,29112],{"encoding":904}," stupně ",[883,98542,98544],{"className":98543},[886],[888,98545,98546],{"xmlns":890},[892,98547,98548,98552],{},[895,98549,98550],{},[898,98551,18465],{},[902,98553,18465],{"encoding":904},[883,98555,98557],{"className":98556},[886],[888,98558,98559],{"xmlns":890,"display":2350},[892,98560,98561,98624],{},[2354,98562,98563],{"width":2356},[2358,98564,98565,98567,98617,98619],{},[2361,98566],{"width":2363},[2361,98568,98569],{},[895,98570,98571,98573,98575,98583,98585,98587,98589,98597,98599,98601,98603,98605,98607,98609,98611,98613,98615],{},[898,98572,6362],{},[2415,98574,2799],{},[28285,98576,98577,98579,98581],{},[898,98578,2146],{},[898,98580,6362],{},[1706,98582,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,98584,2447],{},[898,98586,28915],{},[2415,98588,2799],{},[28285,98590,98591,98593,98595],{},[898,98592,2146],{},[898,98594,28915],{},[1706,98596,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,98598,1708],{},[898,98600,18465],{},[2415,98602,2799],{},[898,98604,2146],{},[1706,98606,2140],{"stretchy":2139},[898,98608,6362],{},[1706,98610,2505],{"separator":2504},[898,98612,28915],{},[1706,98614,2153],{"stretchy":2139},[898,98616,1837],{"mathvariant":2409},[2361,98618],{"width":2363},[2361,98620,98621],{},[2415,98622,98623],{},"(5.12)",[902,98625,98626],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,98628,98629,98650],{},[38,98630,98631,98632],{},"Speciální případ ",[883,98633,98635],{"className":98634},[886],[888,98636,98637],{"xmlns":890},[892,98638,98639,98647],{},[895,98640,98641,98643,98645],{},[898,98642,18465],{},[1706,98644,1708],{},[2148,98646,2701],{},[902,98648,98649],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,98652,98654],{"className":98653},[886],[888,98655,98656],{"xmlns":890,"display":2350},[892,98657,98658,98702],{},[895,98659,98660,98662,98664,98666,98672,98674,98676,98678,98680,98686,98688,98690,98692,98694,98696,98698,98700],{},[898,98661,6362],{},[1706,98663,2390],{},[898,98665,1742],{},[2142,98667,98668,98670],{},[898,98669,1702],{},[898,98671,6362],{},[1706,98673,2447],{},[898,98675,28915],{},[1706,98677,2390],{},[898,98679,1742],{},[2142,98681,98682,98684],{},[898,98683,1702],{},[898,98685,28915],{},[1706,98687,1708],{},[898,98689,2146],{},[1706,98691,2140],{"stretchy":2139},[898,98693,6362],{},[1706,98695,2505],{"separator":2504},[898,98697,28915],{},[1706,98699,2153],{"stretchy":2139},[898,98701,1837],{"mathvariant":2409},[902,98703,98704],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,98706,98707,98708,98711],{},"Slovně — ",[38,98709,98710],{},"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).",[115,98713,28894],{"id":92853},[724,98715,98716,2314,98718,98721,98722,98744,98745,4288],{},[38,98717,28894],{},[614,98719,98720],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,98723,98725],{"className":98724},[886],[888,98726,98727],{"xmlns":890},[892,98728,98729,98741],{},[895,98730,98731,98733,98735,98737,98739],{},[1706,98732,21693],{"stretchy":2139},[898,98734,6362],{},[1706,98736,2505],{"separator":2504},[898,98738,28915],{},[1706,98740,21708],{"stretchy":2139},[902,98742,98743],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,98746,98748],{"className":98747},[886],[888,98749,98750],{"xmlns":890},[892,98751,98752,98757],{},[895,98753,98754],{},[898,98755,98756],{},"q",[902,98758,98756],{"encoding":904},[883,98760,98762],{"className":98761},[886],[888,98763,98764],{"xmlns":890,"display":2350},[892,98765,98766,98801],{},[2354,98767,98768],{"width":2356},[2358,98769,98770,98772,98794,98796],{},[2361,98771],{"width":2363},[2361,98773,98774],{},[895,98775,98776,98778,98780,98782,98784,98786,98788,98790,98792],{},[898,98777,2146],{},[1706,98779,2140],{"stretchy":2139},[898,98781,6362],{},[1706,98783,2505],{"separator":2504},[898,98785,28915],{},[1706,98787,2153],{"stretchy":2139},[1706,98789,1708],{},[898,98791,98756],{},[898,98793,1837],{"mathvariant":2409},[2361,98795],{"width":2363},[2361,98797,98798],{},[2415,98799,98800],{},"(5.13)",[902,98802,98803],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,98805,98806,98807,98810,98811,1936],{},"Jsou to ",[38,98808,98809],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,98812,98814],{"className":98813,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,98816,98817],{},[38,98818,98819],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,98821,98822,98827,98832,98837],{},[123,98823,98824,98826],{},[38,98825,31626],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,98828,98829,98831],{},[38,98830,56721],{}," (úloha 5.14);",[123,98833,98834,2110],{},[38,98835,98836],{},"neprotínají se",[123,98838,98839,98840,3526,98853,1837],{},"s rostoucím ",[883,98841,98843],{"className":98842},[886],[888,98844,98845],{"xmlns":890},[892,98846,98847,98851],{},[895,98848,98849],{},[898,98850,98756],{},[902,98852,98756],{"encoding":904},[38,98854,98855],{},"vzdalují od počátku",[724,98857,98858],{},[614,98859,98860,98861,98883,98884,1837],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,98862,98864],{"className":98863},[886],[888,98865,98866],{"xmlns":890},[892,98867,98868,98880],{},[895,98869,98870,98872,98874,98876,98878],{},[1706,98871,2140],{"stretchy":2139},[898,98873,6362],{},[1706,98875,2505],{"separator":2504},[898,98877,28915],{},[1706,98879,2153],{"stretchy":2139},[902,98881,98882],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,98885,98887],{"className":98886},[886],[888,98888,98889],{"xmlns":890},[892,98890,98891,98915],{},[895,98892,98893,98899,98901,98907,98909],{},[2142,98894,98895,98897],{},[898,98896,98756],{},[2148,98898,2701],{},[1706,98900,2539],{},[2142,98902,98903,98905],{},[898,98904,98756],{},[2148,98906,2150],{},[1706,98908,2539],{},[2142,98910,98911,98913],{},[898,98912,98756],{},[2148,98914,2495],{},[902,98916,98917],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,98919,98921,98922,2153],{"id":98920},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,98923,98925],{"className":98924},[886],[888,98926,98927],{"xmlns":890},[892,98928,98929,98939],{},[895,98930,98931,98933,98935,98937],{},[898,98932,1742],{},[898,98934,1662],{},[898,98936,1659],{},[898,98938,14171],{},[902,98940,29710],{"encoding":904},[724,98942,98943,2314,98946,98949],{},[38,98944,98945],{},"Mezní míra technické substituce",[614,98947,98948],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,98951,98953],{"className":98952},[886],[888,98954,98955],{"xmlns":890,"display":2350},[892,98956,98957,99048],{},[2354,98958,98959],{"width":2356},[2358,98960,98961,98963,99041,99043],{},[2361,98962],{"width":2363},[2361,98964,98965],{},[895,98966,98967,98969,98971,98973,98975,98977,98979,98981,98983,98985,98987,98989,98991,98993,98995,98997,99019,99021,99039],{},[898,98968,1742],{},[898,98970,1662],{},[898,98972,1659],{},[898,98974,14171],{},[1706,98976,1708],{},[898,98978,1742],{},[898,98980,1662],{},[898,98982,1659],{},[898,98984,14171],{},[1706,98986,2140],{"stretchy":2139},[898,98988,6362],{},[1706,98990,2505],{"separator":2504},[898,98992,28915],{},[1706,98994,2153],{"stretchy":2139},[1706,98996,1708],{},[2964,98998,98999,99009],{},[895,99000,99001,99003],{},[898,99002,1742],{},[2142,99004,99005,99007],{},[898,99006,1702],{},[898,99008,6362],{},[895,99010,99011,99013],{},[898,99012,1742],{},[2142,99014,99015,99017],{},[898,99016,1702],{},[898,99018,28915],{},[1706,99020,1708],{},[2964,99022,99023,99031],{},[28285,99024,99025,99027,99029],{},[898,99026,2146],{},[898,99028,6362],{},[1706,99030,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[28285,99032,99033,99035,99037],{},[898,99034,2146],{},[898,99036,28915],{},[1706,99038,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[898,99040,1837],{"mathvariant":2409},[2361,99042],{"width":2363},[2361,99044,99045],{},[2415,99046,99047],{},"(5.14)",[902,99049,99050],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,99052,99053,1647,99055,99085,99086,99117],{},[38,99054,28335],{},[883,99056,99058],{"className":99057},[886],[888,99059,99060],{"xmlns":890},[892,99061,99062,99082],{},[895,99063,99064,99066,99068,99070,99072,99074,99076,99078,99080],{},[898,99065,1742],{},[898,99067,1662],{},[898,99069,1659],{},[898,99071,14171],{},[1706,99073,2140],{"stretchy":2139},[898,99075,6362],{},[1706,99077,2505],{"separator":2504},[898,99079,28915],{},[1706,99081,2153],{"stretchy":2139},[902,99083,99084],{"encoding":904},"MRTS(L, K)"," udává, ",[38,99087,99088,99089,99102,99103,99116],{},"o kolik se musí přibližně změnit kapitál ",[883,99090,99092],{"className":99091},[886],[888,99093,99094],{"xmlns":890},[892,99095,99096,99100],{},[895,99097,99098],{},[898,99099,28915],{},[902,99101,28915],{"encoding":904},", jestliže se práce ",[883,99104,99106],{"className":99105},[886],[888,99107,99108],{"xmlns":890},[892,99109,99110,99114],{},[895,99111,99112],{},[898,99113,6362],{},[902,99115,6362],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[1636,99119,99120],{},[724,99121,99122,37120,99124,99143,99144,99181,99182,99185,99186,99190],{},[883,99123,3174],{},[883,99125,99127],{"className":99126},[886],[888,99128,99129],{"xmlns":890},[892,99130,99131,99141],{},[895,99132,99133,99135,99137,99139],{},[898,99134,1742],{},[898,99136,1662],{},[898,99138,1659],{},[898,99140,14171],{},[902,99142,29710],{"encoding":904}," říká: ",[614,99145,99146,99147,99166,99167,99180],{},"„jednu jednotku práce musím nahradit přibližně ",[883,99148,99150],{"className":99149},[886],[888,99151,99152],{"xmlns":890},[892,99153,99154,99164],{},[895,99155,99156,99158,99160,99162],{},[898,99157,1742],{},[898,99159,1662],{},[898,99161,1659],{},[898,99163,14171],{},[902,99165,29710],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,99168,99170],{"className":99169},[886],[888,99171,99172],{"xmlns":890},[892,99173,99174,99178],{},[895,99175,99176],{},[898,99177,2146],{},[902,99179,2146],{"encoding":904}," zůstala stejná.\""," Je to ",[38,99183,99184],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,99187,99189],{"className":99188,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,99192,99193],{},[2286,99194],{"alt":99195,"className":99196,"src":99197},"imek-izokvanty-mrts",[210,2290],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,99199,99200,99203,99204,3484,99234,99256,99257,5606],{},[38,99201,99202],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,99205,99207],{"className":99206},[886],[888,99208,99209],{"xmlns":890},[892,99210,99211,99231],{},[895,99212,99213,99215,99221,99223,99229],{},[1706,99214,21693],{"stretchy":2139},[2142,99216,99217,99219],{},[898,99218,6362],{},[2148,99220,2150],{},[1706,99222,2505],{"separator":2504},[2142,99224,99225,99227],{},[898,99226,28915],{},[2148,99228,2150],{},[1706,99230,21708],{"stretchy":2139},[902,99232,99233],{"encoding":904},"[L_0, K_0]",[883,99235,99237],{"className":99236},[886],[888,99238,99239],{"xmlns":890},[892,99240,99241,99253],{},[895,99242,99243,99245,99247,99249,99251],{},[1706,99244,1715],{},[898,99246,1742],{},[898,99248,1662],{},[898,99250,1659],{},[898,99252,14171],{},[902,99254,99255],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,99258,99260],{"className":99259},[886],[888,99261,99262],{"xmlns":890},[892,99263,99264,99286],{},[895,99265,99266,99268,99270,99272,99274,99276,99278,99280],{},[898,99267,2146],{},[1706,99269,2140],{"stretchy":2139},[898,99271,6362],{},[1706,99273,2505],{"separator":2504},[898,99275,28915],{},[1706,99277,2153],{"stretchy":2139},[1706,99279,1708],{},[2142,99281,99282,99284],{},[898,99283,98756],{},[2148,99285,2150],{},[902,99287,99288],{"encoding":904},"Q(L,K) = q_0",[883,99290,99292],{"className":99291},[886],[888,99293,99294],{"xmlns":890,"display":2350},[892,99295,99296,99348],{},[895,99297,99298,99312,99314,99316,99334,99336,99338,99340,99342,99344,99346],{},[2964,99299,99300,99306],{},[895,99301,99302,99304],{},[898,99303,3120],{},[898,99305,28915],{},[895,99307,99308,99310],{},[898,99309,3120],{},[898,99311,6362],{},[1706,99313,1708],{},[1706,99315,1715],{},[2964,99317,99318,99326],{},[28285,99319,99320,99322,99324],{},[898,99321,2146],{},[898,99323,6362],{},[1706,99325,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[28285,99327,99328,99330,99332],{},[898,99329,2146],{},[898,99331,28915],{},[1706,99333,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,99335,1708],{},[1706,99337,1715],{},[898,99339,1742],{},[898,99341,1662],{},[898,99343,1659],{},[898,99345,14171],{},[898,99347,1837],{"mathvariant":2409},[902,99349,99350],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,99352,99353,99354,99369,99370,99386],{},"Změní-li se práce o ",[883,99355,99357],{"className":99356},[886],[888,99358,99359],{"xmlns":890},[892,99360,99361,99367],{},[895,99362,99363,99365],{},[898,99364,3120],{},[898,99366,6362],{},[902,99368,93315],{"encoding":904},", lze pro odhad změny kapitálu ",[883,99371,99373],{"className":99372},[886],[888,99374,99375],{"xmlns":890},[892,99376,99377,99383],{},[895,99378,99379,99381],{},[898,99380,3677],{"mathvariant":2409},[898,99382,28915],{},[902,99384,99385],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,99388,99390],{"className":99389},[886],[888,99391,99392],{"xmlns":890,"display":2350},[892,99393,99394,99441],{},[2354,99395,99396],{"width":2356},[2358,99397,99398,99400,99434,99436],{},[2361,99399],{"width":2363},[2361,99401,99402],{},[895,99403,99404,99406,99408,99410,99412,99414,99416,99418,99420,99422,99424,99426,99428,99430,99432],{},[898,99405,3677],{"mathvariant":2409},[898,99407,28915],{},[1706,99409,3248],{},[898,99411,3120],{},[898,99413,28915],{},[1706,99415,1708],{},[1706,99417,1715],{},[898,99419,1742],{},[898,99421,1662],{},[898,99423,1659],{},[898,99425,14171],{},[2415,99427,2799],{},[898,99429,3120],{},[898,99431,6362],{},[1706,99433,2505],{"separator":2504},[2361,99435],{"width":2363},[2361,99437,99438],{},[2415,99439,99440],{},"(5.15)",[902,99442,99443],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,99445,99447],{"className":99446},[886],[888,99448,99449],{"xmlns":890,"display":2350},[892,99450,99451,99500],{},[2354,99452,99453],{"width":2356},[2358,99454,99455,99457,99493,99495],{},[2361,99456],{"width":2363},[2361,99458,99459],{},[895,99460,99461,99463,99465,99467,99485,99487,99489,99491],{},[898,99462,3120],{},[898,99464,6362],{},[1706,99466,1708],{},[2964,99468,99469,99475],{},[895,99470,99471,99473],{},[1706,99472,1715],{},[2148,99474,2701],{},[895,99476,99477,99479,99481,99483],{},[898,99478,1742],{},[898,99480,1662],{},[898,99482,1659],{},[898,99484,14171],{},[2415,99486,2799],{},[898,99488,3120],{},[898,99490,28915],{},[898,99492,1837],{"mathvariant":2409},[2361,99494],{"width":2363},[2361,99496,99497],{},[2415,99498,99499],{},"(5.16)",[902,99501,99502],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[1636,99504,99505,99529],{},[724,99506,99507,99509,99510],{},[883,99508,12314],{}," Postup — jak spočítat ",[883,99511,99513],{"className":99512},[886],[888,99514,99515],{"xmlns":890},[892,99516,99517,99527],{},[895,99518,99519,99521,99523,99525],{},[898,99520,1742],{},[898,99522,1662],{},[898,99524,1659],{},[898,99526,14171],{},[902,99528,29710],{"encoding":904},[152,99530,99531,99572,99615,99647],{},[123,99532,99533,99534,1993,99553,1837],{},"Vypočtěte parciální derivace ",[883,99535,99537],{"className":99536},[886],[888,99538,99539],{"xmlns":890},[892,99540,99541,99551],{},[895,99542,99543],{},[28285,99544,99545,99547,99549],{},[898,99546,2146],{},[898,99548,6362],{},[1706,99550,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,99552,29136],{"encoding":904},[883,99554,99556],{"className":99555},[886],[888,99557,99558],{"xmlns":890},[892,99559,99560,99570],{},[895,99561,99562],{},[28285,99563,99564,99566,99568],{},[898,99565,2146],{},[898,99567,28915],{},[1706,99569,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,99571,29181],{"encoding":904},[123,99573,12504,99574,99614],{},[883,99575,99577],{"className":99576},[886],[888,99578,99579],{"xmlns":890},[892,99580,99581,99611],{},[895,99582,99583,99585,99587,99589,99591,99593,99601,99603],{},[898,99584,1742],{},[898,99586,1662],{},[898,99588,1659],{},[898,99590,14171],{},[1706,99592,1708],{},[28285,99594,99595,99597,99599],{},[898,99596,2146],{},[898,99598,6362],{},[1706,99600,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[898,99602,15493],{"mathvariant":2409},[28285,99604,99605,99607,99609],{},[898,99606,2146],{},[898,99608,28915],{},[1706,99610,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,99612,99613],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,99616,99617,99618,1837],{},"Případně dosaďte konkrétní ",[883,99619,99621],{"className":99620},[886],[888,99622,99623],{"xmlns":890},[892,99624,99625,99645],{},[895,99626,99627,99629,99635,99637,99643],{},[1706,99628,21693],{"stretchy":2139},[2142,99630,99631,99633],{},[898,99632,6362],{},[2148,99634,2150],{},[1706,99636,2505],{"separator":2504},[2142,99638,99639,99641],{},[898,99640,28915],{},[2148,99642,2150],{},[1706,99644,21708],{"stretchy":2139},[902,99646,99233],{"encoding":904},[123,99648,99649,99650,99684,99685,99687],{},"Pro odhad substituce použijte ",[883,99651,99653],{"className":99652},[886],[888,99654,99655],{"xmlns":890},[892,99656,99657,99681],{},[895,99658,99659,99661,99663,99665,99667,99669,99671,99673,99675,99677,99679],{},[898,99660,3677],{"mathvariant":2409},[898,99662,28915],{},[1706,99664,3248],{},[1706,99666,1715],{},[898,99668,1742],{},[898,99670,1662],{},[898,99672,1659],{},[898,99674,14171],{},[1706,99676,2390],{},[898,99678,3677],{"mathvariant":2409},[898,99680,6362],{},[902,99682,99683],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,99686,71643],{}," — substituce, ne doplnění).",[724,99689,99690],{},[614,99691,99692,99693,99725,99726,2891,99739,7822,99768,99783],{},"Obrázek 5.7 — izokvanta ",[883,99694,99696],{"className":99695},[886],[888,99697,99698],{"xmlns":890},[892,99699,99700,99722],{},[895,99701,99702,99708,99710,99712,99714,99716,99718,99720],{},[2142,99703,99704,99706],{},[898,99705,98756],{},[2148,99707,2150],{},[1706,99709,1708],{},[898,99711,2146],{},[1706,99713,2140],{"stretchy":2139},[898,99715,6362],{},[1706,99717,2505],{"separator":2504},[898,99719,28915],{},[1706,99721,2153],{"stretchy":2139},[902,99723,99724],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,99727,99729],{"className":99728},[886],[888,99730,99731],{"xmlns":890},[892,99732,99733,99737],{},[895,99734,99735],{},[898,99736,37952],{},[902,99738,37952],{"encoding":904},[883,99740,99742],{"className":99741},[886],[888,99743,99744],{"xmlns":890},[892,99745,99746,99766],{},[895,99747,99748,99750,99756,99758,99764],{},[1706,99749,21693],{"stretchy":2139},[2142,99751,99752,99754],{},[898,99753,6362],{},[2148,99755,2150],{},[1706,99757,2505],{"separator":2504},[2142,99759,99760,99762],{},[898,99761,28915],{},[2148,99763,2150],{},[1706,99765,21708],{"stretchy":2139},[902,99767,99233],{"encoding":904},[883,99769,99771],{"className":99770},[886],[888,99772,99773],{"xmlns":890},[892,99774,99775,99781],{},[895,99776,99777,99779],{},[898,99778,3677],{"mathvariant":2409},[898,99780,28915],{},[902,99782,99385],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,99785,99787],{"id":99786},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,99789,99791],{"id":99790},"příklad-54","Příklad 5.4",[724,99793,94632,99794,1343,99836,1343,99853,1837],{},[883,99795,99797],{"className":99796},[886],[888,99798,99799],{"xmlns":890},[892,99800,99801,99833],{},[895,99802,99803,99805,99807,99809,99821],{},[898,99804,2146],{},[1706,99806,1708],{},[2148,99808,3359],{},[2489,99810,99811,99813],{},[898,99812,6362],{},[895,99814,99815,99817,99819],{},[2148,99816,2701],{},[898,99818,15493],{"mathvariant":2409},[2148,99820,2495],{},[2489,99822,99823,99825],{},[898,99824,28915],{},[895,99826,99827,99829,99831],{},[2148,99828,2701],{},[898,99830,15493],{"mathvariant":2409},[2148,99832,4284],{},[902,99834,99835],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,99837,99839],{"className":99838},[886],[888,99840,99841],{"xmlns":890},[892,99842,99843,99851],{},[895,99844,99845,99847,99849],{},[898,99846,6362],{},[1706,99848,1708],{},[2148,99850,3369],{},[902,99852,95006],{"encoding":904},[883,99854,99856],{"className":99855},[886],[888,99857,99858],{"xmlns":890},[892,99859,99860,99868],{},[895,99861,99862,99864,99866],{},[898,99863,28915],{},[1706,99865,1708],{},[2148,99867,2590],{},[902,99869,99870],{"encoding":904},"K = 100",[724,99872,99873],{},[38,99874,99875],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,99877,99879],{"className":99878},[886],[888,99880,99881],{"xmlns":890,"display":2350},[892,99882,99883,99997],{},[895,99884,99885,99887,99893,99895,99903,99905,99913,99927,99939,99941,99943,99945,99951,99953,99955,99957,99959,99961,99963,99971,99973,99983,99985,99992,99994],{},[898,99886,1742],{},[2142,99888,99889,99891],{},[898,99890,1702],{},[898,99892,6362],{},[1706,99894,1708],{},[28285,99896,99897,99899,99901],{},[898,99898,2146],{},[898,99900,6362],{},[1706,99902,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,99904,1708],{},[4745,99906,99907],{"scriptlevel":2150,"displaystyle":2139},[2964,99908,99909,99911],{},[2148,99910,3359],{},[2148,99912,2495],{},[2489,99914,99915,99917],{},[898,99916,6362],{},[895,99918,99919,99921,99923,99925],{},[1706,99920,1715],{},[2148,99922,2701],{},[898,99924,15493],{"mathvariant":2409},[2148,99926,2495],{},[2489,99928,99929,99931],{},[898,99930,28915],{},[895,99932,99933,99935,99937],{},[2148,99934,2701],{},[898,99936,15493],{"mathvariant":2409},[2148,99938,4284],{},[1706,99940,2505],{"separator":2504},[4898,99942],{"width":4900},[898,99944,1742],{},[2142,99946,99947,99949],{},[898,99948,1702],{},[898,99950,6362],{},[1706,99952,2140],{"stretchy":2139},[2148,99954,3369],{},[1706,99956,2505],{"separator":2504},[2148,99958,2590],{},[1706,99960,2153],{"stretchy":2139},[1706,99962,1708],{},[4745,99964,99965],{"scriptlevel":2150,"displaystyle":2139},[2964,99966,99967,99969],{},[2148,99968,3359],{},[2148,99970,2495],{},[1706,99972,2390],{},[4745,99974,99975],{"scriptlevel":2150,"displaystyle":2139},[2964,99976,99977,99979],{},[2148,99978,2701],{},[11087,99980,99981],{},[2148,99982,3369],{},[1706,99984,2390],{},[99986,99987,99988,99990],"mroot",{},[2148,99989,2590],{},[2148,99991,4284],{},[1706,99993,3248],{},[2148,99995,99996],{},"7,153.",[902,99998,99999],{"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.",[724,100001,100002,100003,63206,100025,29346,100042,100063,100064,100085],{},"Přibližná změna při ",[883,100004,100006],{"className":100005},[886],[888,100007,100008],{"xmlns":890},[892,100009,100010,100022],{},[895,100011,100012,100014,100016,100018,100020],{},[898,100013,6362],{},[1706,100015,4288],{},[2148,100017,3369],{},[1706,100019,5915],{},[2148,100021,57401],{},[902,100023,100024],{"encoding":904},"L: 20 \\to 21",[883,100026,100028],{"className":100027},[886],[888,100029,100030],{"xmlns":890},[892,100031,100032,100040],{},[895,100033,100034,100036,100038],{},[898,100035,28915],{},[1706,100037,1708],{},[2148,100039,2590],{},[902,100041,99870],{"encoding":904},[883,100043,100045],{"className":100044},[886],[888,100046,100047],{"xmlns":890},[892,100048,100049,100060],{},[895,100050,100051,100053,100055,100057],{},[898,100052,3677],{"mathvariant":2409},[898,100054,2146],{},[1706,100056,3248],{},[2148,100058,100059],{},"7,153",[902,100061,100062],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,100065,100067],{"className":100066},[886],[888,100068,100069],{"xmlns":890},[892,100070,100071,100082],{},[895,100072,100073,100075,100077,100079],{},[898,100074,3677],{"mathvariant":2409},[898,100076,2146],{},[1706,100078,3248],{},[2148,100080,100081],{},"26,888",[902,100083,100084],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,100087,100088,100091],{},[38,100089,100090],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,100093,100095],{"className":100094},[886],[888,100096,100097],{"xmlns":890,"display":2350},[892,100098,100099,100199],{},[895,100100,100101,100103,100109,100111,100119,100121,100123,100135,100149,100151,100153,100155,100161,100163,100165,100167,100169,100171,100173,100175,100179,100181,100194,100196],{},[898,100102,1742],{},[2142,100104,100105,100107],{},[898,100106,1702],{},[898,100108,28915],{},[1706,100110,1708],{},[28285,100112,100113,100115,100117],{},[898,100114,2146],{},[898,100116,28915],{},[1706,100118,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,100120,1708],{},[2148,100122,7524],{},[2489,100124,100125,100127],{},[898,100126,6362],{},[895,100128,100129,100131,100133],{},[2148,100130,2701],{},[898,100132,15493],{"mathvariant":2409},[2148,100134,2495],{},[2489,100136,100137,100139],{},[898,100138,28915],{},[895,100140,100141,100143,100145,100147],{},[1706,100142,1715],{},[2148,100144,2495],{},[898,100146,15493],{"mathvariant":2409},[2148,100148,4284],{},[1706,100150,2505],{"separator":2504},[4898,100152],{"width":4900},[898,100154,1742],{},[2142,100156,100157,100159],{},[898,100158,1702],{},[898,100160,28915],{},[1706,100162,2140],{"stretchy":2139},[2148,100164,3369],{},[1706,100166,2505],{"separator":2504},[2148,100168,2590],{},[1706,100170,2153],{"stretchy":2139},[1706,100172,1708],{},[2148,100174,7524],{},[11087,100176,100177],{},[2148,100178,3369],{},[1706,100180,2390],{},[4745,100182,100183],{"scriptlevel":2150,"displaystyle":2139},[2964,100184,100185,100187],{},[2148,100186,2701],{},[99986,100188,100189,100192],{},[2148,100190,100191],{},"10000",[2148,100193,4284],{},[1706,100195,3248],{},[2148,100197,100198],{},"4,525.",[902,100200,100201],{"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.",[724,100203,100204,100205,4202,100222,1936],{},"Produkce poklesne přibližně o 4,525 (z ",[883,100206,100208],{"className":100207},[886],[888,100209,100210],{"xmlns":890},[892,100211,100212,100219],{},[895,100213,100214,100216],{},[1706,100215,3248],{},[2148,100217,100218],{},"905,126",[902,100220,100221],{"encoding":904},"\\approx 905{,}126",[883,100223,100225],{"className":100224},[886],[888,100226,100227],{"xmlns":890},[892,100228,100229,100236],{},[895,100230,100231,100233],{},[1706,100232,3248],{},[2148,100234,100235],{},"900,601",[902,100237,100238],{"encoding":904},"\\approx 900{,}601",[724,100240,100241,22313,100288,1343,100310,1936],{},[38,100242,100243,100244,1993,100266],{},"(c) Změna ",[883,100245,100247],{"className":100246},[886],[888,100248,100249],{"xmlns":890},[892,100250,100251,100263],{},[895,100252,100253,100255,100257,100259,100261],{},[898,100254,6362],{},[1706,100256,4288],{},[2148,100258,3369],{},[1706,100260,5915],{},[2148,100262,3359],{},[902,100264,100265],{"encoding":904},"L: 20 \\to 15",[883,100267,100269],{"className":100268},[886],[888,100270,100271],{"xmlns":890},[892,100272,100273,100285],{},[895,100274,100275,100277,100279,100281,100283],{},[898,100276,28915],{},[1706,100278,4288],{},[2148,100280,2590],{},[1706,100282,5915],{},[2148,100284,27924],{},[902,100286,100287],{"encoding":904},"K: 100 \\to 150",[883,100289,100291],{"className":100290},[886],[888,100292,100293],{"xmlns":890},[892,100294,100295,100307],{},[895,100296,100297,100299,100301,100303,100305],{},[898,100298,3120],{},[898,100300,6362],{},[1706,100302,1708],{},[1706,100304,1715],{},[2148,100306,7524],{},[902,100308,100309],{"encoding":904},"dL = -5",[883,100311,100313],{"className":100312},[886],[888,100314,100315],{"xmlns":890},[892,100316,100317,100327],{},[895,100318,100319,100321,100323,100325],{},[898,100320,3120],{},[898,100322,28915],{},[1706,100324,1708],{},[2148,100326,2728],{},[902,100328,100329],{"encoding":904},"dK = 50",[883,100331,100333],{"className":100332},[886],[888,100334,100335],{"xmlns":890,"display":2350},[892,100336,100337,100425],{},[895,100338,100339,100341,100343,100345,100347,100353,100355,100357,100359,100361,100363,100365,100367,100369,100371,100373,100375,100377,100383,100385,100387,100389,100391,100393,100395,100397,100399,100401,100403,100405,100407,100409,100411,100413,100416,100418,100420,100422],{},[898,100340,3120],{},[898,100342,2146],{},[1706,100344,1708],{},[898,100346,1742],{},[2142,100348,100349,100351],{},[898,100350,1702],{},[898,100352,6362],{},[1706,100354,2140],{"stretchy":2139},[2148,100356,3369],{},[1706,100358,2505],{"separator":2504},[2148,100360,2590],{},[1706,100362,2153],{"stretchy":2139},[1706,100364,2390],{},[1706,100366,2140],{"stretchy":2139},[1706,100368,1715],{},[2148,100370,7524],{},[1706,100372,2153],{"stretchy":2139},[1706,100374,2447],{},[898,100376,1742],{},[2142,100378,100379,100381],{},[898,100380,1702],{},[898,100382,28915],{},[1706,100384,2140],{"stretchy":2139},[2148,100386,3369],{},[1706,100388,2505],{"separator":2504},[2148,100390,2590],{},[1706,100392,2153],{"stretchy":2139},[1706,100394,2390],{},[2148,100396,2728],{},[1706,100398,1708],{},[2148,100400,100059],{},[1706,100402,2390],{},[1706,100404,2140],{"stretchy":2139},[1706,100406,1715],{},[2148,100408,7524],{},[1706,100410,2153],{"stretchy":2139},[1706,100412,2447],{},[2148,100414,100415],{},"4,525",[1706,100417,2390],{},[2148,100419,2728],{},[1706,100421,3248],{},[2148,100423,100424],{},"190,485.",[902,100426,100427],{"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.",[724,100429,100430],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,100432,100434],{"id":100433},"příklad-55","Příklad 5.5",[724,100436,100437,100438,100474,100475,1837],{},"Pro produkci ",[883,100439,100441],{"className":100440},[886],[888,100442,100443],{"xmlns":890},[892,100444,100445,100471],{},[895,100446,100447,100449,100451,100453,100455,100457,100459,100461,100467],{},[898,100448,2146],{},[1706,100450,2140],{"stretchy":2139},[898,100452,6362],{},[1706,100454,2505],{"separator":2504},[898,100456,28915],{},[1706,100458,2153],{"stretchy":2139},[1706,100460,1708],{},[99986,100462,100463,100465],{},[898,100464,6362],{},[2148,100466,4284],{},[11087,100468,100469],{},[898,100470,28915],{},[902,100472,100473],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,100476,100478],{"className":100477},[886],[888,100479,100480],{"xmlns":890},[892,100481,100482,100498],{},[895,100483,100484,100490,100494,100496],{},[99986,100485,100486,100488],{},[898,100487,6362],{},[2148,100489,4284],{},[11087,100491,100492],{},[898,100493,28915],{},[1706,100495,1708],{},[898,100497,98756],{},[902,100499,100500],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,100502,100503,100504,1837],{},"Umocněním na druhou: ",[883,100505,100507],{"className":100506},[886],[888,100508,100509],{"xmlns":890},[892,100510,100511,100535],{},[895,100512,100513,100515,100517,100523,100525],{},[898,100514,28915],{},[1706,100516,1708],{},[2489,100518,100519,100521],{},[898,100520,98756],{},[2148,100522,2495],{},[898,100524,15493],{"mathvariant":2409},[99986,100526,100527,100533],{},[2489,100528,100529,100531],{},[898,100530,6362],{},[2148,100532,2495],{},[2148,100534,4284],{},[902,100536,100537],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,100539,100540,100580,100620],{},[123,100541,100542],{},[883,100543,100545],{"className":100544},[886],[888,100546,100547],{"xmlns":890},[892,100548,100549,100577],{},[895,100550,100551,100553,100555,100557,100559,100561,100563,100565,100567],{},[898,100552,98756],{},[1706,100554,1708],{},[2148,100556,2701],{},[1706,100558,9609],{},[898,100560,28915],{},[1706,100562,1708],{},[2148,100564,2701],{},[898,100566,15493],{"mathvariant":2409},[99986,100568,100569,100575],{},[2489,100570,100571,100573],{},[898,100572,6362],{},[2148,100574,2495],{},[2148,100576,4284],{},[902,100578,100579],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,100581,100582],{},[883,100583,100585],{"className":100584},[886],[888,100586,100587],{"xmlns":890},[892,100588,100589,100617],{},[895,100590,100591,100593,100595,100597,100599,100601,100603,100605,100607],{},[898,100592,98756],{},[1706,100594,1708],{},[2148,100596,2495],{},[1706,100598,9609],{},[898,100600,28915],{},[1706,100602,1708],{},[2148,100604,3455],{},[898,100606,15493],{"mathvariant":2409},[99986,100608,100609,100615],{},[2489,100610,100611,100613],{},[898,100612,6362],{},[2148,100614,2495],{},[2148,100616,4284],{},[902,100618,100619],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,100621,100622],{},[883,100623,100625],{"className":100624},[886],[888,100626,100627],{"xmlns":890},[892,100628,100629,100657],{},[895,100630,100631,100633,100635,100637,100639,100641,100643,100645,100647],{},[898,100632,98756],{},[1706,100634,1708],{},[2148,100636,4284],{},[1706,100638,9609],{},[898,100640,28915],{},[1706,100642,1708],{},[2148,100644,10800],{},[898,100646,15493],{"mathvariant":2409},[99986,100648,100649,100655],{},[2489,100650,100651,100653],{},[898,100652,6362],{},[2148,100654,2495],{},[2148,100656,4284],{},[902,100658,100659],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,100661,100662],{},[614,100663,100664,100665,10691,100686,1837],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,100666,100668],{"className":100667},[886],[888,100669,100670],{"xmlns":890},[892,100671,100672,100684],{},[895,100673,100674,100676,100678,100680,100682],{},[1706,100675,2140],{"stretchy":2139},[898,100677,6362],{},[1706,100679,2505],{"separator":2504},[898,100681,28915],{},[1706,100683,2153],{"stretchy":2139},[902,100685,98882],{"encoding":904},[883,100687,100689],{"className":100688},[886],[888,100690,100691],{"xmlns":890},[892,100692,100693,100709],{},[895,100694,100695,100697,100699,100701,100703,100705,100707],{},[898,100696,98756],{},[1706,100698,1708],{},[2148,100700,2701],{},[1706,100702,2505],{"separator":2504},[2148,100704,2495],{},[1706,100706,2505],{"separator":2504},[2148,100708,4284],{},[902,100710,100711],{"encoding":904},"q = 1, 2, 3",[198,100713,100715],{"id":100714},"příklad-56","Příklad 5.6",[724,100717,94632,100718,1837],{},[883,100719,100721],{"className":100720},[886],[888,100722,100723],{"xmlns":890},[892,100724,100725,100741],{},[895,100726,100727,100729,100731,100733,100735,100737],{},[898,100728,2146],{},[1706,100730,1708],{},[2148,100732,2495],{},[898,100734,6362],{},[1706,100736,2447],{},[11087,100738,100739],{},[898,100740,28915],{},[902,100742,100743],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,100745,100747],{"className":100746},[886],[888,100748,100749],{"xmlns":890,"display":2350},[892,100750,100751,100793],{},[895,100752,100753,100755,100761,100763,100765,100767,100769,100771,100777,100779,100791],{},[898,100754,1742],{},[2142,100756,100757,100759],{},[898,100758,1702],{},[898,100760,6362],{},[1706,100762,1708],{},[2148,100764,2495],{},[1706,100766,2505],{"separator":2504},[4898,100768],{"width":9524},[898,100770,1742],{},[2142,100772,100773,100775],{},[898,100774,1702],{},[898,100776,28915],{},[1706,100778,1708],{},[2964,100780,100781,100783],{},[2148,100782,2701],{},[895,100784,100785,100787],{},[2148,100786,2495],{},[11087,100788,100789],{},[898,100790,28915],{},[898,100792,1837],{"mathvariant":2409},[902,100794,100795],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,100797,100799],{"className":100798},[886],[888,100800,100801],{"xmlns":890,"display":2350},[892,100802,100803,100867],{},[895,100804,100805,100807,100809,100811,100813,100815,100837,100839,100857,100859,100861,100865],{},[898,100806,1742],{},[898,100808,1662],{},[898,100810,1659],{},[898,100812,14171],{},[1706,100814,1708],{},[2964,100816,100817,100827],{},[895,100818,100819,100821],{},[898,100820,1742],{},[2142,100822,100823,100825],{},[898,100824,1702],{},[898,100826,6362],{},[895,100828,100829,100831],{},[898,100830,1742],{},[2142,100832,100833,100835],{},[898,100834,1702],{},[898,100836,28915],{},[1706,100838,1708],{},[2964,100840,100841,100843],{},[2148,100842,2495],{},[4745,100844,100845],{"scriptlevel":2150,"displaystyle":2139},[2964,100846,100847,100849],{},[2148,100848,2701],{},[895,100850,100851,100853],{},[2148,100852,2495],{},[11087,100854,100855],{},[898,100856,28915],{},[1706,100858,1708],{},[2148,100860,3455],{},[11087,100862,100863],{},[898,100864,28915],{},[898,100866,1837],{"mathvariant":2409},[902,100868,100869],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,100871,100872,100873,100916,100917,100956,100957,1837],{},"Například ",[883,100874,100876],{"className":100875},[886],[888,100877,100878],{"xmlns":890},[892,100879,100880,100913],{},[895,100881,100882,100884,100886,100888,100890,100892,100894,100896,100898,100900,100902,100904,100908,100910],{},[898,100883,1742],{},[898,100885,1662],{},[898,100887,1659],{},[898,100889,14171],{},[1706,100891,2140],{"stretchy":2139},[2148,100893,3455],{},[1706,100895,2505],{"separator":2504},[2148,100897,12597],{},[1706,100899,2153],{"stretchy":2139},[1706,100901,1708],{},[2148,100903,3455],{},[11087,100905,100906],{},[2148,100907,12597],{},[1706,100909,3248],{},[2148,100911,100912],{},"10,58",[902,100914,100915],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,100918,100920],{"className":100919},[886],[888,100921,100922],{"xmlns":890},[892,100923,100924,100953],{},[895,100925,100926,100928,100930,100932,100934,100936,100938,100940,100942,100944,100948,100950],{},[898,100927,2146],{},[1706,100929,2140],{"stretchy":2139},[2148,100931,3455],{},[1706,100933,2505],{"separator":2504},[2148,100935,12597],{},[1706,100937,2153],{"stretchy":2139},[1706,100939,1708],{},[2148,100941,12717],{},[1706,100943,2447],{},[11087,100945,100946],{},[2148,100947,12597],{},[1706,100949,3248],{},[2148,100951,100952],{},"10,646",[902,100954,100955],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,100958,100960],{"className":100959},[886],[888,100961,100962],{"xmlns":890},[892,100963,100964,100972],{},[895,100965,100966,100968],{},[2148,100967,3455],{},[11087,100969,100970],{},[2148,100971,12597],{},[902,100973,100974],{"encoding":904},"4\\sqrt{7}",[724,100976,100977,100978,100998],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,100979,100981],{"className":100980},[886],[888,100982,100983],{"xmlns":890},[892,100984,100985,100995],{},[895,100986,100987,100989,100991,100993],{},[898,100988,3120],{},[898,100990,6362],{},[1706,100992,1708],{},[2148,100994,2495],{},[902,100996,100997],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,101000,101002],{"className":101001},[886],[888,101003,101004],{"xmlns":890,"display":2350},[892,101005,101006,101055],{},[895,101007,101008,101010,101012,101014,101016,101018,101020,101022,101024,101026,101028,101030,101032,101034,101036,101038,101040,101042,101044,101048,101050,101052],{},[898,101009,3120],{},[898,101011,28915],{},[1706,101013,1708],{},[1706,101015,1715],{},[898,101017,1742],{},[898,101019,1662],{},[898,101021,1659],{},[898,101023,14171],{},[1706,101025,2140],{"stretchy":2139},[2148,101027,3455],{},[1706,101029,2505],{"separator":2504},[2148,101031,12597],{},[1706,101033,2153],{"stretchy":2139},[1706,101035,2390],{},[2148,101037,2495],{},[1706,101039,1708],{},[1706,101041,1715],{},[2148,101043,12717],{},[11087,101045,101046],{},[2148,101047,12597],{},[1706,101049,3248],{},[1706,101051,1715],{},[2148,101053,101054],{},"21,17.",[902,101056,101057],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,101059,101061],{"id":101060},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,101063,101064,101065,1343,101067,1993,101069,101071,101072,101075,101076,101079],{},"Hlavními faktory produkce jsou ",[38,101066,92873],{},[38,101068,92889],{},[38,101070,92905],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,101073,101074],{},"jednofaktorový"," (pouze práce) a ",[38,101077,101078],{},"dvoufaktorový"," (práce + kapitál) model.",[724,101081,101082,101083,101086,101087,101089,101090,101092,101093,8186,101096,101115,101116,101133,101134,101151,101152,101174,101175,3526,101194,1837],{},"V ",[38,101084,101085],{},"1F modelu"," se definuje ",[38,101088,29139],{}," (derivace produkce podle práce) a ",[38,101091,92808],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,101094,101095],{},"zákonu klesajících výnosů",[883,101097,101099],{"className":101098},[886],[888,101100,101101],{"xmlns":890},[892,101102,101103,101113],{},[895,101104,101105,101107],{},[898,101106,1742],{},[2142,101108,101109,101111],{},[898,101110,1702],{},[898,101112,6362],{},[902,101114,29159],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,101117,101119],{"className":101118},[886],[888,101120,101121],{"xmlns":890},[892,101122,101123,101131],{},[895,101124,101125],{},[2142,101126,101127,101129],{},[898,101128,6362],{},[2148,101130,2150],{},[902,101132,93517],{"encoding":904}," klesá a v bodě ",[883,101135,101137],{"className":101136},[886],[888,101138,101139],{"xmlns":890},[892,101140,101141,101149],{},[895,101142,101143],{},[2142,101144,101145,101147],{},[898,101146,6362],{},[2148,101148,2701],{},[902,101150,32319],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,101153,101154,101155],{},"princip maximalizace ",[883,101156,101158],{"className":101157},[886],[888,101159,101160],{"xmlns":890},[892,101161,101162,101172],{},[895,101163,101164,101166],{},[898,101165,1735],{},[2142,101167,101168,101170],{},[898,101169,1702],{},[898,101171,6362],{},[902,101173,92592],{"encoding":904},": v bodě maxima ",[883,101176,101178],{"className":101177},[886],[888,101179,101180],{"xmlns":890},[892,101181,101182,101192],{},[895,101183,101184,101186],{},[898,101185,1735],{},[2142,101187,101188,101190],{},[898,101189,1702],{},[898,101191,6362],{},[902,101193,92592],{"encoding":904},[883,101195,101197],{"className":101196},[886],[888,101198,101199],{"xmlns":890},[892,101200,101201,101221],{},[895,101202,101203,101205,101211,101213,101215],{},[898,101204,1742],{},[2142,101206,101207,101209],{},[898,101208,1702],{},[898,101210,6362],{},[1706,101212,1708],{},[898,101214,1735],{},[2142,101216,101217,101219],{},[898,101218,1702],{},[898,101220,6362],{},[902,101222,92622],{"encoding":904},[724,101224,101225,101226,101229,101230,1647,101233,101262,101263,101280,101281,101284,101285,101314,101315,101317,101318,3484,101348,101370],{},"Ve ",[38,101227,101228],{},"2F modelu"," se obvykle používají ",[38,101231,101232],{},"Cobb-Douglasovy funkce",[883,101234,101236],{"className":101235},[886],[888,101237,101238],{"xmlns":890},[892,101239,101240,101260],{},[895,101241,101242,101244,101246,101248,101254],{},[898,101243,2146],{},[1706,101245,1708],{},[898,101247,1735],{},[2489,101249,101250,101252],{},[898,101251,6362],{},[898,101253,207],{},[2489,101255,101256,101258],{},[898,101257,28915],{},[898,101259,2450],{},[902,101261,92689],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,101264,101266],{"className":101265},[886],[888,101267,101268],{"xmlns":890},[892,101269,101270,101278],{},[895,101271,101272,101274,101276],{},[898,101273,207],{},[1706,101275,2447],{},[898,101277,2450],{},[902,101279,92783],{"encoding":904}," rozlišujeme ",[38,101282,101283],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,101286,101288],{"className":101287},[886],[888,101289,101290],{"xmlns":890},[892,101291,101292,101312],{},[895,101293,101294,101296,101302,101304,101306],{},[898,101295,1742],{},[2142,101297,101298,101300],{},[898,101299,1702],{},[898,101301,6362],{},[1706,101303,2505],{"separator":2504},[898,101305,1742],{},[2142,101307,101308,101310],{},[898,101309,1702],{},[898,101311,28915],{},[902,101313,92720],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,101316,28894],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,101319,101321],{"className":101320},[886],[888,101322,101323],{"xmlns":890},[892,101324,101325,101345],{},[895,101326,101327,101329,101335,101337,101339],{},[898,101328,1742],{},[2142,101330,101331,101333],{},[898,101332,1702],{},[898,101334,6362],{},[898,101336,15493],{"mathvariant":2409},[898,101338,1742],{},[2142,101340,101341,101343],{},[898,101342,1702],{},[898,101344,28915],{},[902,101346,101347],{"encoding":904},"MP_L\u002FMP_K",[38,101349,101350,101351,2153],{},"mezní míra technické substituce (",[883,101352,101354],{"className":101353},[886],[888,101355,101356],{"xmlns":890},[892,101357,101358,101368],{},[895,101359,101360,101362,101364,101366],{},[898,101361,1742],{},[898,101363,1662],{},[898,101365,1659],{},[898,101367,14171],{},[902,101369,29710],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,101372,15880],{"id":15879},[152,101374,101375,101378,101381,101384,101387,101390,101393,101396,101399,101402,101405],{},[123,101376,101377],{},"Jaké jsou faktory produkce?",[123,101379,101380],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,101382,101383],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,101385,101386],{},"Co udává mezní produkt práce?",[123,101388,101389],{},"Co musí respektovat průběh křivky produkce?",[123,101391,101392],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,101394,101395],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,101397,101398],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,101400,101401],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,101403,101404],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,101406,101407],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,101409,101411],{"id":101410},"úlohy-51517","Úlohy 5.1–5.17",[198,101413,59504],{"id":59503},[724,101415,101416,101419,101420,101442,101443,1343,101463,1343,101483,101503],{},[38,101417,101418],{},"5.1"," Je dána produkce ",[883,101421,101423],{"className":101422},[886],[888,101424,101425],{"xmlns":890},[892,101426,101427,101439],{},[895,101428,101429,101431,101433,101435],{},[898,101430,2146],{},[1706,101432,1708],{},[2148,101434,7786],{},[11087,101436,101437],{},[898,101438,6362],{},[902,101440,101441],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,101444,101446],{"className":101445},[886],[888,101447,101448],{"xmlns":890},[892,101449,101450,101460],{},[895,101451,101452,101454,101456,101458],{},[898,101453,2146],{},[1706,101455,2140],{"stretchy":2139},[2148,101457,2701],{},[1706,101459,2153],{"stretchy":2139},[902,101461,101462],{"encoding":904},"Q(1)",[883,101464,101466],{"className":101465},[886],[888,101467,101468],{"xmlns":890},[892,101469,101470,101480],{},[895,101471,101472,101474,101476,101478],{},[898,101473,2146],{},[1706,101475,2140],{"stretchy":2139},[2148,101477,3455],{},[1706,101479,2153],{"stretchy":2139},[902,101481,101482],{"encoding":904},"Q(4)",[883,101484,101486],{"className":101485},[886],[888,101487,101488],{"xmlns":890},[892,101489,101490,101500],{},[895,101491,101492,101494,101496,101498],{},[898,101493,2146],{},[1706,101495,2140],{"stretchy":2139},[2148,101497,10800],{},[1706,101499,2153],{"stretchy":2139},[902,101501,101502],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,101505,101506,101419,101509,101545,101546,101559,101560,101579,101580,101606,101607,4202,101620,101633],{},[38,101507,101508],{},"5.2",[883,101510,101512],{"className":101511},[886],[888,101513,101514],{"xmlns":890},[892,101515,101516,101542],{},[895,101517,101518,101520,101522,101524,101526,101532,101534,101536],{},[898,101519,2146],{},[1706,101521,1708],{},[1706,101523,1715],{},[2148,101525,14840],{},[2489,101527,101528,101530],{},[898,101529,6362],{},[2148,101531,4284],{},[1706,101533,2447],{},[2148,101535,10800],{},[2489,101537,101538,101540],{},[898,101539,6362],{},[2148,101541,2495],{},[902,101543,101544],{"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 ",[883,101547,101549],{"className":101548},[886],[888,101550,101551],{"xmlns":890},[892,101552,101553,101557],{},[895,101554,101555],{},[898,101556,6362],{},[902,101558,6362],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,101561,101563],{"className":101562},[886],[888,101564,101565],{"xmlns":890},[892,101566,101567,101577],{},[895,101568,101569,101571],{},[898,101570,1742],{},[2142,101572,101573,101575],{},[898,101574,1702],{},[898,101576,6362],{},[902,101578,29159],{"encoding":904},". (f) Vypočtěte ",[883,101581,101583],{"className":101582},[886],[888,101584,101585],{"xmlns":890},[892,101586,101587,101603],{},[895,101588,101589,101591,101597,101599,101601],{},[898,101590,1742],{},[2142,101592,101593,101595],{},[898,101594,1702],{},[898,101596,6362],{},[1706,101598,2140],{"stretchy":2139},[2148,101600,7786],{},[1706,101602,2153],{"stretchy":2139},[902,101604,101605],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,101608,101610],{"className":101609},[886],[888,101611,101612],{"xmlns":890},[892,101613,101614,101618],{},[895,101615,101616],{},[2148,101617,7786],{},[902,101619,7786],{"encoding":904},[883,101621,101623],{"className":101622},[886],[888,101624,101625],{"xmlns":890},[892,101626,101627,101631],{},[895,101628,101629],{},[2148,101630,61336],{},[902,101632,61336],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,101635,101636,101639,101640,101662,101663,101691,101692,101723,101724,1837],{},[38,101637,101638],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,101641,101643],{"className":101642},[886],[888,101644,101645],{"xmlns":890},[892,101646,101647,101659],{},[895,101648,101649,101651,101653,101655],{},[898,101650,2146],{},[1706,101652,1708],{},[2148,101654,17366],{},[11087,101656,101657],{},[898,101658,6362],{},[902,101660,101661],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,101664,101666],{"className":101665},[886],[888,101667,101668],{"xmlns":890},[892,101669,101670,101688],{},[895,101671,101672,101674,101676,101678,101682,101684,101686],{},[898,101673,2146],{},[1706,101675,1708],{},[2148,101677,19501],{},[11087,101679,101680],{},[898,101681,6362],{},[1706,101683,1715],{},[2148,101685,3455],{},[898,101687,6362],{},[902,101689,101690],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,101693,101695],{"className":101694},[886],[888,101696,101697],{"xmlns":890},[892,101698,101699,101720],{},[895,101700,101701,101703,101705,101707,101709,101711,101714],{},[898,101702,2146],{},[1706,101704,1708],{},[2148,101706,2728],{},[898,101708,6362],{},[1706,101710,1715],{},[2148,101712,101713],{},"0,01",[2489,101715,101716,101718],{},[898,101717,6362],{},[2148,101719,2495],{},[902,101721,101722],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,101725,101727],{"className":101726},[886],[888,101728,101729],{"xmlns":890},[892,101730,101731,101757],{},[895,101732,101733,101735,101737,101739,101741,101747,101749,101751],{},[898,101734,2146],{},[1706,101736,1708],{},[1706,101738,1715],{},[2148,101740,14892],{},[2489,101742,101743,101745],{},[898,101744,6362],{},[2148,101746,4284],{},[1706,101748,2447],{},[2148,101750,10800],{},[2489,101752,101753,101755],{},[898,101754,6362],{},[2148,101756,2495],{},[902,101758,101759],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,101761,101762,101765,101766,2891,101785,18895,101802,1837],{},[38,101763,101764],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,101767,101769],{"className":101768},[886],[888,101770,101771],{"xmlns":890},[892,101772,101773,101783],{},[895,101774,101775,101777],{},[898,101776,1735],{},[2142,101778,101779,101781],{},[898,101780,1702],{},[898,101782,6362],{},[902,101784,92592],{"encoding":904},[883,101786,101788],{"className":101787},[886],[888,101789,101790],{"xmlns":890},[892,101791,101792,101800],{},[895,101793,101794],{},[2142,101795,101796,101798],{},[898,101797,6362],{},[2148,101799,2150],{},[902,101801,93517],{"encoding":904},[883,101803,101805],{"className":101804},[886],[888,101806,101807],{"xmlns":890},[892,101808,101809,101849],{},[895,101810,101811,101813,101819,101821,101827,101829,101831,101833,101839,101841,101847],{},[898,101812,1735],{},[2142,101814,101815,101817],{},[898,101816,1702],{},[898,101818,6362],{},[1706,101820,2140],{"stretchy":2139},[2142,101822,101823,101825],{},[898,101824,6362],{},[2148,101826,2150],{},[1706,101828,2153],{"stretchy":2139},[1706,101830,1708],{},[898,101832,1742],{},[2142,101834,101835,101837],{},[898,101836,1702],{},[898,101838,6362],{},[1706,101840,2140],{"stretchy":2139},[2142,101842,101843,101845],{},[898,101844,6362],{},[2148,101846,2150],{},[1706,101848,2153],{"stretchy":2139},[902,101850,101851],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,101853,101854,101419,101857,15842,101893,101906,101907,101926],{},[38,101855,101856],{},"5.5",[883,101858,101860],{"className":101859},[886],[888,101861,101862],{"xmlns":890},[892,101863,101864,101890],{},[895,101865,101866,101868,101870,101872,101874,101880,101882,101884],{},[898,101867,2146],{},[1706,101869,1708],{},[1706,101871,1715],{},[2148,101873,15204],{},[2489,101875,101876,101878],{},[898,101877,6362],{},[2148,101879,4284],{},[1706,101881,2447],{},[2148,101883,7156],{},[2489,101885,101886,101888],{},[898,101887,6362],{},[2148,101889,2495],{},[902,101891,101892],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,101894,101896],{"className":101895},[886],[888,101897,101898],{"xmlns":890},[892,101899,101900,101904],{},[895,101901,101902],{},[898,101903,6362],{},[902,101905,6362],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,101908,101910],{"className":101909},[886],[888,101911,101912],{"xmlns":890},[892,101913,101914,101924],{},[895,101915,101916,101918],{},[898,101917,1735],{},[2142,101919,101920,101922],{},[898,101921,1702],{},[898,101923,6362],{},[902,101925,92592],{"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.",[198,101928,101930],{"id":101929},"dvoufaktorový-model","Dvoufaktorový model",[724,101932,101933,101936,101937,101662,101963,101691,102005,1837],{},[38,101934,101935],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,101938,101940],{"className":101939},[886],[888,101941,101942],{"xmlns":890},[892,101943,101944,101960],{},[895,101945,101946,101948,101950,101952,101954],{},[898,101947,2146],{},[1706,101949,1708],{},[2148,101951,12597],{},[898,101953,6362],{},[2489,101955,101956,101958],{},[898,101957,28915],{},[2148,101959,2495],{},[902,101961,101962],{"encoding":904},"Q = 7 L K^{2}",[883,101964,101966],{"className":101965},[886],[888,101967,101968],{"xmlns":890},[892,101969,101970,102002],{},[895,101971,101972,101974,101976,101978,101990],{},[898,101973,2146],{},[1706,101975,1708],{},[2148,101977,2728],{},[2489,101979,101980,101982],{},[898,101981,6362],{},[895,101983,101984,101986,101988],{},[2148,101985,2495],{},[898,101987,15493],{"mathvariant":2409},[2148,101989,4284],{},[2489,101991,101992,101994],{},[898,101993,28915],{},[895,101995,101996,101998,102000],{},[2148,101997,2701],{},[898,101999,15493],{"mathvariant":2409},[2148,102001,4284],{},[902,102003,102004],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,102006,102008],{"className":102007},[886],[888,102009,102010],{"xmlns":890},[892,102011,102012,102044],{},[895,102013,102014,102016,102018,102020,102032],{},[898,102015,2146],{},[1706,102017,1708],{},[2148,102019,22884],{},[2489,102021,102022,102024],{},[898,102023,6362],{},[895,102025,102026,102028,102030],{},[2148,102027,4284],{},[898,102029,15493],{"mathvariant":2409},[2148,102031,7524],{},[2489,102033,102034,102036],{},[898,102035,28915],{},[895,102037,102038,102040,102042],{},[2148,102039,2495],{},[898,102041,15493],{"mathvariant":2409},[2148,102043,7524],{},[902,102045,102046],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,102048,102049,101419,102052,102094,102095,1343,102113,102132,102133,102150],{},[38,102050,102051],{},"5.7",[883,102053,102055],{"className":102054},[886],[888,102056,102057],{"xmlns":890},[892,102058,102059,102091],{},[895,102060,102061,102063,102065,102067,102079],{},[898,102062,2146],{},[1706,102064,1708],{},[2148,102066,7786],{},[2489,102068,102069,102071],{},[898,102070,6362],{},[895,102072,102073,102075,102077],{},[2148,102074,2701],{},[898,102076,15493],{"mathvariant":2409},[2148,102078,2495],{},[2489,102080,102081,102083],{},[898,102082,28915],{},[895,102084,102085,102087,102089],{},[2148,102086,2701],{},[898,102088,15493],{"mathvariant":2409},[2148,102090,2495],{},[902,102092,102093],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,102096,102098],{"className":102097},[886],[888,102099,102100],{"xmlns":890},[892,102101,102102,102110],{},[895,102103,102104,102106,102108],{},[898,102105,6362],{},[1706,102107,1708],{},[2148,102109,4361],{},[902,102111,102112],{"encoding":904},"L = 400",[883,102114,102116],{"className":102115},[886],[888,102117,102118],{"xmlns":890},[892,102119,102120,102129],{},[895,102121,102122,102124,102126],{},[898,102123,28915],{},[1706,102125,1708],{},[2148,102127,102128],{},"17576",[902,102130,102131],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,102134,102136],{"className":102135},[886],[888,102137,102138],{"xmlns":890},[892,102139,102140,102148],{},[895,102141,102142,102144,102146],{},[898,102143,6362],{},[1706,102145,2505],{"separator":2504},[898,102147,28915],{},[902,102149,96944],{"encoding":904}," zdvojnásobí.",[724,102152,102153,102156,102157,102094,102188,1343,102206,16273,102224,102254,102255,102285,102286,4202,102299,102313,102314,4202,102327,102340],{},[38,102154,102155],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,102158,102160],{"className":102159},[886],[888,102161,102162],{"xmlns":890},[892,102163,102164,102185],{},[895,102165,102166,102168,102170,102173,102179],{},[898,102167,2146],{},[1706,102169,1708],{},[2148,102171,102172],{},"1,01",[2489,102174,102175,102177],{},[898,102176,6362],{},[2148,102178,42808],{},[2489,102180,102181,102183],{},[898,102182,28915],{},[2148,102184,19377],{},[902,102186,102187],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,102189,102191],{"className":102190},[886],[888,102192,102193],{"xmlns":890},[892,102194,102195,102203],{},[895,102196,102197,102199,102201],{},[898,102198,6362],{},[1706,102200,1708],{},[2148,102202,2802],{},[902,102204,102205],{"encoding":904},"L = 250",[883,102207,102209],{"className":102208},[886],[888,102210,102211],{"xmlns":890},[892,102212,102213,102221],{},[895,102214,102215,102217,102219],{},[898,102216,28915],{},[1706,102218,1708],{},[2148,102220,21978],{},[902,102222,102223],{"encoding":904},"K = 1000",[883,102225,102227],{"className":102226},[886],[888,102228,102229],{"xmlns":890},[892,102230,102231,102251],{},[895,102232,102233,102235,102241,102243,102245,102247,102249],{},[898,102234,1742],{},[2142,102236,102237,102239],{},[898,102238,1702],{},[898,102240,6362],{},[1706,102242,2140],{"stretchy":2139},[2148,102244,2802],{},[1706,102246,2505],{"separator":2504},[2148,102248,21978],{},[1706,102250,2153],{"stretchy":2139},[902,102252,102253],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,102256,102258],{"className":102257},[886],[888,102259,102260],{"xmlns":890},[892,102261,102262,102282],{},[895,102263,102264,102266,102272,102274,102276,102278,102280],{},[898,102265,1742],{},[2142,102267,102268,102270],{},[898,102269,1702],{},[898,102271,28915],{},[1706,102273,2140],{"stretchy":2139},[2148,102275,2802],{},[1706,102277,2505],{"separator":2504},[2148,102279,21978],{},[1706,102281,2153],{"stretchy":2139},[902,102283,102284],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,102287,102289],{"className":102288},[886],[888,102290,102291],{"xmlns":890},[892,102292,102293,102297],{},[895,102294,102295],{},[898,102296,6362],{},[902,102298,6362],{"encoding":904},[883,102300,102302],{"className":102301},[886],[888,102303,102304],{"xmlns":890},[892,102305,102306,102311],{},[895,102307,102308],{},[2148,102309,102310],{},"260",[902,102312,102310],{"encoding":904}," a současném poklesu ",[883,102315,102317],{"className":102316},[886],[888,102318,102319],{"xmlns":890},[892,102320,102321,102325],{},[895,102322,102323],{},[898,102324,28915],{},[902,102326,28915],{"encoding":904},[883,102328,102330],{"className":102329},[886],[888,102331,102332],{"xmlns":890},[892,102333,102334,102338],{},[895,102335,102336],{},[2148,102337,12956],{},[902,102339,12956],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,102342,102343,102346,102347,1837],{},[38,102344,102345],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,102348,102350],{"className":102349},[886],[888,102351,102352],{"xmlns":890},[892,102353,102354,102374],{},[895,102355,102356,102358,102360,102362,102368],{},[898,102357,2146],{},[1706,102359,1708],{},[2148,102361,7786],{},[2489,102363,102364,102366],{},[898,102365,6362],{},[2148,102367,14892],{},[2489,102369,102370,102372],{},[898,102371,28915],{},[2148,102373,11496],{},[902,102375,102376],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,102378,102379,102382,102383,98540,102406,4521,102419,2314,102469,1936],{},[38,102380,102381],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,102384,102386],{"className":102385},[886],[888,102387,102388],{"xmlns":890},[892,102389,102390,102404],{},[895,102391,102392,102394,102396,102398,102400,102402],{},[898,102393,2146],{},[1706,102395,2140],{"stretchy":2139},[898,102397,6362],{},[1706,102399,2505],{"separator":2504},[898,102401,28915],{},[1706,102403,2153],{"stretchy":2139},[902,102405,29112],{"encoding":904},[883,102407,102409],{"className":102408},[886],[888,102410,102411],{"xmlns":890},[892,102412,102413,102417],{},[895,102414,102415],{},[898,102416,18465],{},[902,102418,18465],{"encoding":904},[883,102420,102422],{"className":102421},[886],[888,102423,102424],{"xmlns":890},[892,102425,102426,102466],{},[895,102427,102428,102430,102438,102440,102442,102450,102452,102454,102456,102458,102460,102462,102464],{},[898,102429,6362],{},[28285,102431,102432,102434,102436],{},[898,102433,2146],{},[898,102435,6362],{},[1706,102437,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,102439,2447],{},[898,102441,28915],{},[28285,102443,102444,102446,102448],{},[898,102445,2146],{},[898,102447,28915],{},[1706,102449,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,102451,1708],{},[898,102453,18465],{},[898,102455,2146],{},[1706,102457,2140],{"stretchy":2139},[898,102459,6362],{},[1706,102461,2505],{"separator":2504},[898,102463,28915],{},[1706,102465,2153],{"stretchy":2139},[902,102467,102468],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,102470,98515],{},[724,102472,102473,102476],{},[38,102474,102475],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,102478,102479,101419,102482,102522,102523,1343,102545,1343,102567,102589],{},[38,102480,102481],{},"5.12",[883,102483,102485],{"className":102484},[886],[888,102486,102487],{"xmlns":890},[892,102488,102489,102519],{},[895,102490,102491,102493,102495,102507],{},[898,102492,2146],{},[1706,102494,1708],{},[2489,102496,102497,102499],{},[898,102498,6362],{},[895,102500,102501,102503,102505],{},[2148,102502,2701],{},[898,102504,15493],{"mathvariant":2409},[2148,102506,4284],{},[2489,102508,102509,102511],{},[898,102510,28915],{},[895,102512,102513,102515,102517],{},[2148,102514,2701],{},[898,102516,15493],{"mathvariant":2409},[2148,102518,3455],{},[902,102520,102521],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,102524,102526],{"className":102525},[886],[888,102527,102528],{"xmlns":890},[892,102529,102530,102542],{},[895,102531,102532,102538,102540],{},[2142,102533,102534,102536],{},[898,102535,98756],{},[2148,102537,2150],{},[1706,102539,1708],{},[2148,102541,2701],{},[902,102543,102544],{"encoding":904},"q_0 = 1",[883,102546,102548],{"className":102547},[886],[888,102549,102550],{"xmlns":890},[892,102551,102552,102564],{},[895,102553,102554,102560,102562],{},[2142,102555,102556,102558],{},[898,102557,98756],{},[2148,102559,2701],{},[1706,102561,1708],{},[2148,102563,2495],{},[902,102565,102566],{"encoding":904},"q_1 = 2",[883,102568,102570],{"className":102569},[886],[888,102571,102572],{"xmlns":890},[892,102573,102574,102586],{},[895,102575,102576,102582,102584],{},[2142,102577,102578,102580],{},[898,102579,98756],{},[2148,102581,2495],{},[1706,102583,1708],{},[2148,102585,4284],{},[902,102587,102588],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,102591,102592,101419,102595,102635,102636,1343,102664,1343,102692,1343,102720,1343,102749,1343,102778,1343,102807,1343,102836,1343,102865,1837],{},[38,102593,102594],{},"5.13",[883,102596,102598],{"className":102597},[886],[888,102599,102600],{"xmlns":890},[892,102601,102602,102632],{},[895,102603,102604,102606,102608,102620],{},[898,102605,2146],{},[1706,102607,1708],{},[2489,102609,102610,102612],{},[898,102611,6362],{},[895,102613,102614,102616,102618],{},[2148,102615,2701],{},[898,102617,15493],{"mathvariant":2409},[2148,102619,4284],{},[2489,102621,102622,102624],{},[898,102623,28915],{},[895,102625,102626,102628,102630],{},[2148,102627,2701],{},[898,102629,15493],{"mathvariant":2409},[2148,102631,2495],{},[902,102633,102634],{"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): ",[883,102637,102639],{"className":102638},[886],[888,102640,102641],{"xmlns":890},[892,102642,102643,102661],{},[895,102644,102645,102651,102653,102655,102657,102659],{},[2142,102646,102647,102649],{},[898,102648,1735],{},[2148,102650,2701],{},[1706,102652,21693],{"stretchy":2139},[2148,102654,2701],{},[1706,102656,2110],{"separator":2504},[2148,102658,2701],{},[1706,102660,21708],{"stretchy":2139},[902,102662,102663],{"encoding":904},"A_1[1; 1]",[883,102665,102667],{"className":102666},[886],[888,102668,102669],{"xmlns":890},[892,102670,102671,102689],{},[895,102672,102673,102679,102681,102683,102685,102687],{},[2142,102674,102675,102677],{},[898,102676,1735],{},[2148,102678,2495],{},[1706,102680,21693],{"stretchy":2139},[2148,102682,2701],{},[1706,102684,2110],{"separator":2504},[2148,102686,12717],{},[1706,102688,21708],{"stretchy":2139},[902,102690,102691],{"encoding":904},"A_2[1; 8]",[883,102693,102695],{"className":102694},[886],[888,102696,102697],{"xmlns":890},[892,102698,102699,102717],{},[895,102700,102701,102707,102709,102711,102713,102715],{},[2142,102702,102703,102705],{},[898,102704,1735],{},[2148,102706,4284],{},[1706,102708,21693],{"stretchy":2139},[2148,102710,2701],{},[1706,102712,2110],{"separator":2504},[2148,102714,13266],{},[1706,102716,21708],{"stretchy":2139},[902,102718,102719],{"encoding":904},"A_3[1; 27]",[883,102721,102723],{"className":102722},[886],[888,102724,102725],{"xmlns":890},[892,102726,102727,102746],{},[895,102728,102729,102735,102737,102739,102741,102744],{},[2142,102730,102731,102733],{},[898,102732,1735],{},[2148,102734,3455],{},[1706,102736,21693],{"stretchy":2139},[2148,102738,2495],{},[1706,102740,2110],{"separator":2504},[2148,102742,102743],{},"0,353",[1706,102745,21708],{"stretchy":2139},[902,102747,102748],{"encoding":904},"A_4[2; 0{,}353]",[883,102750,102752],{"className":102751},[886],[888,102753,102754],{"xmlns":890},[892,102755,102756,102775],{},[895,102757,102758,102764,102766,102768,102770,102773],{},[2142,102759,102760,102762],{},[898,102761,1735],{},[2148,102763,7524],{},[1706,102765,21693],{"stretchy":2139},[2148,102767,2495],{},[1706,102769,2110],{"separator":2504},[2148,102771,102772],{},"2,828",[1706,102774,21708],{"stretchy":2139},[902,102776,102777],{"encoding":904},"A_5[2; 2{,}828]",[883,102779,102781],{"className":102780},[886],[888,102782,102783],{"xmlns":890},[892,102784,102785,102804],{},[895,102786,102787,102793,102795,102797,102799,102802],{},[2142,102788,102789,102791],{},[898,102790,1735],{},[2148,102792,7044],{},[1706,102794,21693],{"stretchy":2139},[2148,102796,2495],{},[1706,102798,2110],{"separator":2504},[2148,102800,102801],{},"9,545",[1706,102803,21708],{"stretchy":2139},[902,102805,102806],{"encoding":904},"A_6[2; 9{,}545]",[883,102808,102810],{"className":102809},[886],[888,102811,102812],{"xmlns":890},[892,102813,102814,102833],{},[895,102815,102816,102822,102824,102826,102828,102831],{},[2142,102817,102818,102820],{},[898,102819,1735],{},[2148,102821,12597],{},[1706,102823,21693],{"stretchy":2139},[2148,102825,11218],{},[1706,102827,2110],{"separator":2504},[2148,102829,102830],{},"0,544",[1706,102832,21708],{"stretchy":2139},[902,102834,102835],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,102837,102839],{"className":102838},[886],[888,102840,102841],{"xmlns":890},[892,102842,102843,102862],{},[895,102844,102845,102851,102853,102855,102857,102860],{},[2142,102846,102847,102849],{},[898,102848,1735],{},[2148,102850,12717],{},[1706,102852,21693],{"stretchy":2139},[2148,102854,11218],{},[1706,102856,2110],{"separator":2504},[2148,102858,102859],{},"14,696",[1706,102861,21708],{"stretchy":2139},[902,102863,102864],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,102866,102868],{"className":102867},[886],[888,102869,102870],{"xmlns":890},[892,102871,102872,102890],{},[895,102873,102874,102880,102882,102884,102886,102888],{},[2142,102875,102876,102878],{},[898,102877,1735],{},[2148,102879,10800],{},[1706,102881,21693],{"stretchy":2139},[2148,102883,2495],{},[1706,102885,2110],{"separator":2504},[2148,102887,7524],{},[1706,102889,21708],{"stretchy":2139},[902,102891,102892],{"encoding":904},"A_9[2; 5]",[724,102894,102895,102898],{},[38,102896,102897],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,102900,102901,102904,102905,102935,102936,102949,102950,102963,102964,16006,102983,103002,103003,1837],{},[38,102902,102903],{},"5.15"," Produkce firmy je dána vztahem ",[883,102906,102908],{"className":102907},[886],[888,102909,102910],{"xmlns":890},[892,102911,102912,102932],{},[895,102913,102914,102916,102918,102920,102926],{},[898,102915,2146],{},[1706,102917,1708],{},[2148,102919,2495],{},[2489,102921,102922,102924],{},[898,102923,6362],{},[2148,102925,11496],{},[2489,102927,102928,102930],{},[898,102929,28915],{},[2148,102931,19377],{},[902,102933,102934],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,102937,102939],{"className":102938},[886],[888,102940,102941],{"xmlns":890},[892,102942,102943,102947],{},[895,102944,102945],{},[2148,102946,2590],{},[902,102948,2590],{"encoding":904}," pracovníků a disponuje-li ",[883,102951,102953],{"className":102952},[886],[888,102954,102955],{"xmlns":890},[892,102956,102957,102961],{},[895,102958,102959],{},[2148,102960,11093],{},[902,102962,11093],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,102965,102967],{"className":102966},[886],[888,102968,102969],{"xmlns":890},[892,102970,102971,102981],{},[895,102972,102973,102975,102977,102979],{},[898,102974,1742],{},[898,102976,1662],{},[898,102978,1659],{},[898,102980,14171],{},[902,102982,29710],{"encoding":904},[883,102984,102986],{"className":102985},[886],[888,102987,102988],{"xmlns":890},[892,102989,102990,103000],{},[895,102991,102992,102994,102996,102998],{},[898,102993,1742],{},[898,102995,1662],{},[898,102997,1659],{},[898,102999,14171],{},[902,103001,29710],{"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 ",[883,103004,103006],{"className":103005},[886],[888,103007,103008],{"xmlns":890},[892,103009,103010,103015],{},[895,103011,103012],{},[2148,103013,103014],{},"95",[902,103016,103014],{"encoding":904},[724,103018,103019,101419,103022,17684,103054,103073,103074,103087,103088,103101,103102,103115],{},[38,103020,103021],{},"5.16",[883,103023,103025],{"className":103024},[886],[888,103026,103027],{"xmlns":890},[892,103028,103029,103051],{},[895,103030,103031,103033,103035,103041,103043,103045],{},[898,103032,2146],{},[1706,103034,1708],{},[2489,103036,103037,103039],{},[898,103038,28915],{},[2148,103040,2495],{},[1706,103042,2447],{},[2148,103044,2495],{},[2489,103046,103047,103049],{},[898,103048,6362],{},[2148,103050,2495],{},[902,103052,103053],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,103055,103057],{"className":103056},[886],[888,103058,103059],{"xmlns":890},[892,103060,103061,103071],{},[895,103062,103063,103065,103067,103069],{},[898,103064,1742],{},[898,103066,1662],{},[898,103068,1659],{},[898,103070,14171],{},[902,103072,29710],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,103075,103077],{"className":103076},[886],[888,103078,103079],{"xmlns":890},[892,103080,103081,103085],{},[895,103082,103083],{},[2148,103084,2728],{},[902,103086,2728],{"encoding":904}," pracovníky a ",[883,103089,103091],{"className":103090},[886],[888,103092,103093],{"xmlns":890},[892,103094,103095,103099],{},[895,103096,103097],{},[2148,103098,95576],{},[902,103100,95576],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,103103,103105],{"className":103104},[886],[888,103106,103107],{"xmlns":890},[892,103108,103109,103113],{},[895,103110,103111],{},[2148,103112,17219],{},[902,103114,17219],{"encoding":904}," jednotek.",[724,103117,103118,103121,103122,4521,103152,1837],{},[38,103119,103120],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,103123,103125],{"className":103124},[886],[888,103126,103127],{"xmlns":890},[892,103128,103129,103149],{},[895,103130,103131,103133,103135,103137,103143],{},[898,103132,2146],{},[1706,103134,1708],{},[898,103136,1735],{},[2489,103138,103139,103141],{},[898,103140,6362],{},[898,103142,207],{},[2489,103144,103145,103147],{},[898,103146,28915],{},[898,103148,2450],{},[902,103150,103151],{"encoding":904},"Q = A L^{a} K^{b}",[883,103153,103155],{"className":103154},[886],[888,103156,103157],{"xmlns":890},[892,103158,103159,103189],{},[895,103160,103161,103163,103165,103167,103169,103171,103179,103181],{},[898,103162,1742],{},[898,103164,1662],{},[898,103166,1659],{},[898,103168,14171],{},[1706,103170,1708],{},[4745,103172,103173],{"scriptlevel":2150,"displaystyle":2139},[2964,103174,103175,103177],{},[898,103176,207],{},[898,103178,2450],{},[1706,103180,2390],{},[4745,103182,103183],{"scriptlevel":2150,"displaystyle":2139},[2964,103184,103185,103187],{},[898,103186,28915],{},[898,103188,6362],{},[902,103190,103191],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,103193,19879],{"id":19878},[120,103195,103196,103229,103256,103265,103315,103346,103399,103422,103477,103550,103628,103671,103703,103736,103777,103849,103910,103976,103993,104066,104132,104184,104240,104274,104317],{},[123,103197,103198,103201,103202,55955,103215,103228],{},[38,103199,103200],{},"Faktory (vstupy) produkce:"," práce ",[883,103203,103205],{"className":103204},[886],[888,103206,103207],{"xmlns":890},[892,103208,103209,103213],{},[895,103210,103211],{},[898,103212,6362],{},[902,103214,6362],{"encoding":904},[883,103216,103218],{"className":103217},[886],[888,103219,103220],{"xmlns":890},[892,103221,103222,103226],{},[895,103223,103224],{},[898,103225,28915],{},[902,103227,28915],{"encoding":904},", půda.",[123,103230,103231,21021,103233,1837],{},[38,103232,59504],{},[883,103234,103236],{"className":103235},[886],[888,103237,103238],{"xmlns":890},[892,103239,103240,103254],{},[895,103241,103242,103244,103246,103248,103250,103252],{},[898,103243,2146],{},[1706,103245,1708],{},[898,103247,2146],{},[1706,103249,2140],{"stretchy":2139},[898,103251,6362],{},[1706,103253,2153],{"stretchy":2139},[902,103255,92503],{"encoding":904},[123,103257,103258,2314,103260,5354,103263,1837],{},[38,103259,859],{},[614,103261,103262],{},"production function",[38,103264,93006],{},[123,103266,103267,1647,103269,1837],{},[38,103268,93052],{},[883,103270,103272],{"className":103271},[886],[888,103273,103274],{"xmlns":890},[892,103275,103276,103312],{},[895,103277,103278,103280,103286,103288,103290,103292,103294,103296,103298,103300,103306,103308,103310],{},[898,103279,1742],{},[2142,103281,103282,103284],{},[898,103283,1702],{},[898,103285,6362],{},[1706,103287,1708],{},[898,103289,3120],{},[898,103291,2146],{},[898,103293,15493],{"mathvariant":2409},[898,103295,3120],{},[898,103297,6362],{},[1706,103299,1708],{},[2489,103301,103302,103304],{},[898,103303,2146],{},[1706,103305,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,103307,2140],{"stretchy":2139},[898,103309,6362],{},[1706,103311,2153],{"stretchy":2139},[902,103313,103314],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,103316,103317,1647,103319,1837],{},[38,103318,93987],{},[883,103320,103322],{"className":103321},[886],[888,103323,103324],{"xmlns":890},[892,103325,103326,103344],{},[895,103327,103328,103330,103336,103338,103340,103342],{},[898,103329,1735],{},[2142,103331,103332,103334],{},[898,103333,1702],{},[898,103335,6362],{},[1706,103337,1708],{},[898,103339,2146],{},[898,103341,15493],{"mathvariant":2409},[898,103343,6362],{},[902,103345,92571],{"encoding":904},[123,103347,103348,103350,103351,4521,103368,1837],{},[38,103349,93474],{}," — od určitého ",[883,103352,103354],{"className":103353},[886],[888,103355,103356],{"xmlns":890},[892,103357,103358,103366],{},[895,103359,103360],{},[2142,103361,103362,103364],{},[898,103363,6362],{},[2148,103365,2150],{},[902,103367,93517],{"encoding":904},[883,103369,103371],{"className":103370},[886],[888,103372,103373],{"xmlns":890},[892,103374,103375,103397],{},[895,103376,103377,103387,103389,103391,103393,103395],{},[2489,103378,103379,103381],{},[898,103380,2146],{},[895,103382,103383,103385],{},[1706,103384,3142],{"mathvariant":2409},[1706,103386,3142],{"mathvariant":2409},[1706,103388,2140],{"stretchy":2139},[898,103390,6362],{},[1706,103392,2153],{"stretchy":2139},[1706,103394,2539],{},[2148,103396,2150],{},[902,103398,93663],{"encoding":904},[123,103400,103401,1647,103404,103421],{},[38,103402,103403],{},"Inflexní bod",[883,103405,103407],{"className":103406},[886],[888,103408,103409],{"xmlns":890},[892,103410,103411,103419],{},[895,103412,103413],{},[2142,103414,103415,103417],{},[898,103416,6362],{},[2148,103418,2150],{},[902,103420,93517],{"encoding":904}," — přechod z konvexity do konkavity.",[123,103423,103424,1647,103427,21021,103444,1837],{},[38,103425,103426],{},"Bod maxima produkce",[883,103428,103430],{"className":103429},[886],[888,103431,103432],{"xmlns":890},[892,103433,103434,103442],{},[895,103435,103436],{},[2142,103437,103438,103440],{},[898,103439,6362],{},[2148,103441,2701],{},[902,103443,32319],{"encoding":904},[883,103445,103447],{"className":103446},[886],[888,103448,103449],{"xmlns":890},[892,103450,103451,103475],{},[895,103452,103453,103455,103461,103463,103469,103471,103473],{},[898,103454,1742],{},[2142,103456,103457,103459],{},[898,103458,1702],{},[898,103460,6362],{},[1706,103462,2140],{"stretchy":2139},[2142,103464,103465,103467],{},[898,103466,6362],{},[2148,103468,2701],{},[1706,103470,2153],{"stretchy":2139},[1706,103472,1708],{},[2148,103474,2150],{},[902,103476,93736],{"encoding":904},[123,103478,103479,103501,103502,4521,103521,1837],{},[38,103480,103481,103482],{},"Princip maximalizace ",[883,103483,103485],{"className":103484},[886],[888,103486,103487],{"xmlns":890},[892,103488,103489,103499],{},[895,103490,103491,103493],{},[898,103492,1735],{},[2142,103494,103495,103497],{},[898,103496,1702],{},[898,103498,6362],{},[902,103500,92592],{"encoding":904}," — v bodě maxima ",[883,103503,103505],{"className":103504},[886],[888,103506,103507],{"xmlns":890},[892,103508,103509,103519],{},[895,103510,103511,103513],{},[898,103512,1735],{},[2142,103514,103515,103517],{},[898,103516,1702],{},[898,103518,6362],{},[902,103520,92592],{"encoding":904},[883,103522,103524],{"className":103523},[886],[888,103525,103526],{"xmlns":890},[892,103527,103528,103548],{},[895,103529,103530,103532,103538,103540,103542],{},[898,103531,1742],{},[2142,103533,103534,103536],{},[898,103535,1702],{},[898,103537,6362],{},[1706,103539,1708],{},[898,103541,1735],{},[2142,103543,103544,103546],{},[898,103545,1702],{},[898,103547,6362],{},[902,103549,92622],{"encoding":904},[123,103551,103552,1647,103555,1343,103594,1343,103611,1837],{},[38,103553,103554],{},"Polynomiální produkční funkce",[883,103556,103558],{"className":103557},[886],[888,103559,103560],{"xmlns":890},[892,103561,103562,103592],{},[895,103563,103564,103566,103568,103570,103572,103574,103576,103582,103584,103586],{},[898,103565,2146],{},[1706,103567,2140],{"stretchy":2139},[898,103569,6362],{},[1706,103571,2153],{"stretchy":2139},[1706,103573,1708],{},[898,103575,207],{},[2489,103577,103578,103580],{},[898,103579,6362],{},[2148,103581,4284],{},[1706,103583,2447],{},[898,103585,2450],{},[2489,103587,103588,103590],{},[898,103589,6362],{},[2148,103591,2495],{},[902,103593,93854],{"encoding":904},[883,103595,103597],{"className":103596},[886],[888,103598,103599],{"xmlns":890},[892,103600,103601,103609],{},[895,103602,103603,103605,103607],{},[898,103604,207],{},[1706,103606,2539],{},[2148,103608,2150],{},[902,103610,2544],{"encoding":904},[883,103612,103614],{"className":103613},[886],[888,103615,103616],{"xmlns":890},[892,103617,103618,103626],{},[895,103619,103620,103622,103624],{},[898,103621,2450],{},[1706,103623,8922],{},[2148,103625,2150],{},[902,103627,37911],{"encoding":904},[123,103629,103630,1647,103633,1837],{},[38,103631,103632],{},"Diferenciál produkce",[883,103634,103636],{"className":103635},[886],[888,103637,103638],{"xmlns":890},[892,103639,103640,103668],{},[895,103641,103642,103644,103646,103648,103650,103652,103654,103656,103662,103664,103666],{},[898,103643,3677],{"mathvariant":2409},[898,103645,2146],{},[1706,103647,3248],{},[898,103649,3120],{},[898,103651,2146],{},[1706,103653,1708],{},[898,103655,1742],{},[2142,103657,103658,103660],{},[898,103659,1702],{},[898,103661,6362],{},[2415,103663,2799],{},[898,103665,3120],{},[898,103667,6362],{},[902,103669,103670],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,103672,103673,21021,103675,1837],{},[38,103674,101930],{},[883,103676,103678],{"className":103677},[886],[888,103679,103680],{"xmlns":890},[892,103681,103682,103700],{},[895,103683,103684,103686,103688,103690,103692,103694,103696,103698],{},[898,103685,2146],{},[1706,103687,1708],{},[898,103689,2146],{},[1706,103691,2140],{"stretchy":2139},[898,103693,6362],{},[1706,103695,2505],{"separator":2504},[898,103697,28915],{},[1706,103699,2153],{"stretchy":2139},[902,103701,103702],{"encoding":904},"Q = Q(L, K)",[123,103704,103705,21021,103707,1837],{},[38,103706,96024],{},[883,103708,103710],{"className":103709},[886],[888,103711,103712],{"xmlns":890},[892,103713,103714,103734],{},[895,103715,103716,103718,103720,103722,103728],{},[898,103717,2146],{},[1706,103719,1708],{},[898,103721,1735],{},[2489,103723,103724,103726],{},[898,103725,6362],{},[898,103727,207],{},[2489,103729,103730,103732],{},[898,103731,28915],{},[898,103733,2450],{},[902,103735,92689],{"encoding":904},[123,103737,103738,21021,103741,103776],{},[38,103739,103740],{},"Ryzí Cobb-Douglas",[883,103742,103744],{"className":103743},[886],[888,103745,103746],{"xmlns":890},[892,103747,103748,103774],{},[895,103749,103750,103752,103754,103756,103762],{},[898,103751,2146],{},[1706,103753,1708],{},[898,103755,1735],{},[2489,103757,103758,103760],{},[898,103759,6362],{},[898,103761,207],{},[2489,103763,103764,103766],{},[898,103765,28915],{},[895,103767,103768,103770,103772],{},[2148,103769,2701],{},[1706,103771,1715],{},[898,103773,207],{},[902,103775,96851],{"encoding":904}," (konstantní výnosy).",[123,103778,103779,21021,103781,1837],{},[38,103780,97567],{},[883,103782,103784],{"className":103783},[886],[888,103785,103786],{"xmlns":890},[892,103787,103788,103846],{},[895,103789,103790,103792,103794,103796,103798,103800,103802,103804,103806,103808,103818,103820,103822,103832],{},[898,103791,2146],{},[1706,103793,1708],{},[898,103795,1735],{},[1706,103797,21693],{"stretchy":2139},[1706,103799,2140],{"stretchy":2139},[2148,103801,2701],{},[1706,103803,1715],{},[898,103805,207],{},[1706,103807,2153],{"stretchy":2139},[2489,103809,103810,103812],{},[898,103811,6362],{},[895,103813,103814,103816],{},[1706,103815,1715],{},[898,103817,2450],{},[1706,103819,2447],{},[898,103821,207],{},[2489,103823,103824,103826],{},[898,103825,28915],{},[895,103827,103828,103830],{},[1706,103829,1715],{},[898,103831,2450],{},[2489,103833,103834,103836],{},[1706,103835,21708],{"stretchy":2139},[895,103837,103838,103840,103842,103844],{},[1706,103839,1715],{},[2148,103841,2701],{},[898,103843,15493],{"mathvariant":2409},[898,103845,2450],{},[902,103847,103848],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,103850,103851,2314,103854,5354,103876,2314,103879,103909],{},[38,103852,103853],{},"Lineární",[883,103855,103857],{"className":103856},[886],[888,103858,103859],{"xmlns":890},[892,103860,103861,103873],{},[895,103862,103863,103865,103867,103869,103871],{},[898,103864,207],{},[898,103866,6362],{},[1706,103868,2447],{},[898,103870,2450],{},[898,103872,28915],{},[902,103874,103875],{"encoding":904},"aL + bK",[38,103877,103878],{},"Leontiefova",[883,103880,103882],{"className":103881},[886],[888,103883,103884],{"xmlns":890},[892,103885,103886,103906],{},[895,103887,103888,103890,103892,103894,103896,103898,103900,103902,103904],{},[898,103889,97795],{},[1706,103891,2773],{},[1706,103893,2140],{"stretchy":2139},[898,103895,207],{},[898,103897,6362],{},[1706,103899,2505],{"separator":2504},[898,103901,2450],{},[898,103903,28915],{},[1706,103905,2153],{"stretchy":2139},[902,103907,103908],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,103911,103912,21021,103928,1837],{},[38,103913,103914,103915],{},"Homogenita stupně ",[883,103916,103918],{"className":103917},[886],[888,103919,103920],{"xmlns":890},[892,103921,103922,103926],{},[895,103923,103924],{},[898,103925,18465],{},[902,103927,18465],{"encoding":904},[883,103929,103931],{"className":103930},[886],[888,103932,103933],{"xmlns":890},[892,103934,103935,103973],{},[895,103936,103937,103939,103941,103943,103945,103947,103949,103951,103953,103955,103961,103963,103965,103967,103969,103971],{},[898,103938,2146],{},[1706,103940,2140],{"stretchy":2139},[898,103942,3950],{},[898,103944,6362],{},[1706,103946,2505],{"separator":2504},[898,103948,3950],{},[898,103950,28915],{},[1706,103952,2153],{"stretchy":2139},[1706,103954,1708],{},[2489,103956,103957,103959],{},[898,103958,3950],{},[898,103960,18465],{},[898,103962,2146],{},[1706,103964,2140],{"stretchy":2139},[898,103966,6362],{},[1706,103968,2505],{"separator":2504},[898,103970,28915],{},[1706,103972,2153],{"stretchy":2139},[902,103974,103975],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,103977,103978,96949],{},[38,103979,96882,103980],{},[883,103981,103983],{"className":103982},[886],[888,103984,103985],{"xmlns":890},[892,103986,103987,103991],{},[895,103988,103989],{},[898,103990,1735],{},[902,103992,1735],{"encoding":904},[123,103994,103995,103997,103998,104020,104021,104043,104044,1936],{},[38,103996,96383],{}," — konstantní (",[883,103999,104001],{"className":104000},[886],[888,104002,104003],{"xmlns":890},[892,104004,104005,104017],{},[895,104006,104007,104009,104011,104013,104015],{},[898,104008,207],{},[1706,104010,2447],{},[898,104012,2450],{},[1706,104014,1708],{},[2148,104016,2701],{},[902,104018,104019],{"encoding":904},"a+b=1","), rostoucí (",[883,104022,104024],{"className":104023},[886],[888,104025,104026],{"xmlns":890},[892,104027,104028,104040],{},[895,104029,104030,104032,104034,104036,104038],{},[898,104031,207],{},[1706,104033,2447],{},[898,104035,2450],{},[1706,104037,8922],{},[2148,104039,2701],{},[902,104041,104042],{"encoding":904},"a+b>1","), klesající (",[883,104045,104047],{"className":104046},[886],[888,104048,104049],{"xmlns":890},[892,104050,104051,104063],{},[895,104052,104053,104055,104057,104059,104061],{},[898,104054,207],{},[1706,104056,2447],{},[898,104058,2450],{},[1706,104060,2539],{},[2148,104062,2701],{},[902,104064,104065],{"encoding":904},"a+b\u003C1",[123,104067,104068,1647,104070,1343,104100,1647,104102,1837],{},[38,104069,93052],{},[883,104071,104073],{"className":104072},[886],[888,104074,104075],{"xmlns":890},[892,104076,104077,104097],{},[895,104078,104079,104081,104087,104089],{},[898,104080,1742],{},[2142,104082,104083,104085],{},[898,104084,1702],{},[898,104086,6362],{},[1706,104088,1708],{},[28285,104090,104091,104093,104095],{},[898,104092,2146],{},[898,104094,6362],{},[1706,104096,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,104098,104099],{"encoding":904},"MP_L = Q'_L",[38,104101,95956],{},[883,104103,104105],{"className":104104},[886],[888,104106,104107],{"xmlns":890},[892,104108,104109,104129],{},[895,104110,104111,104113,104119,104121],{},[898,104112,1742],{},[2142,104114,104115,104117],{},[898,104116,1702],{},[898,104118,28915],{},[1706,104120,1708],{},[28285,104122,104123,104125,104127],{},[898,104124,2146],{},[898,104126,28915],{},[1706,104128,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,104130,104131],{"encoding":904},"MP_K = Q'_K",[123,104133,104134,1647,104136,1837],{},[38,104135,98170],{},[883,104137,104139],{"className":104138},[886],[888,104140,104141],{"xmlns":890},[892,104142,104143,104181],{},[895,104144,104145,104147,104149,104151,104153,104159,104161,104163,104165,104167,104169,104175,104177,104179],{},[898,104146,3120],{},[898,104148,2146],{},[1706,104150,1708],{},[898,104152,1742],{},[2142,104154,104155,104157],{},[898,104156,1702],{},[898,104158,6362],{},[2415,104160,2799],{},[898,104162,3120],{},[898,104164,6362],{},[1706,104166,2447],{},[898,104168,1742],{},[2142,104170,104171,104173],{},[898,104172,1702],{},[898,104174,28915],{},[2415,104176,2799],{},[898,104178,3120],{},[898,104180,28915],{},[902,104182,104183],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,104185,104186,21021,104188,1837],{},[38,104187,98515],{},[883,104189,104191],{"className":104190},[886],[888,104192,104193],{"xmlns":890},[892,104194,104195,104237],{},[895,104196,104197,104199,104207,104209,104211,104219,104221,104223,104225,104227,104229,104231,104233,104235],{},[898,104198,6362],{},[28285,104200,104201,104203,104205],{},[898,104202,2146],{},[898,104204,6362],{},[1706,104206,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,104208,2447],{},[898,104210,28915],{},[28285,104212,104213,104215,104217],{},[898,104214,2146],{},[898,104216,28915],{},[1706,104218,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,104220,1708],{},[898,104222,18465],{},[2415,104224,2799],{},[898,104226,2146],{},[1706,104228,2140],{"stretchy":2139},[898,104230,6362],{},[1706,104232,2505],{"separator":2504},[898,104234,28915],{},[1706,104236,2153],{"stretchy":2139},[902,104238,104239],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,104241,104242,104245,104246,1837],{},[38,104243,104244],{},"Izokvanta"," — křivka ",[883,104247,104249],{"className":104248},[886],[888,104250,104251],{"xmlns":890},[892,104252,104253,104271],{},[895,104254,104255,104257,104259,104261,104263,104265,104267,104269],{},[898,104256,2146],{},[1706,104258,2140],{"stretchy":2139},[898,104260,6362],{},[1706,104262,2505],{"separator":2504},[898,104264,28915],{},[1706,104266,2153],{"stretchy":2139},[1706,104268,1708],{},[898,104270,98756],{},[902,104272,104273],{"encoding":904},"Q(L, K) = q",[123,104275,104276,1647,104278,1837],{},[38,104277,98945],{},[883,104279,104281],{"className":104280},[886],[888,104282,104283],{"xmlns":890},[892,104284,104285,104315],{},[895,104286,104287,104289,104291,104293,104295,104297,104299,104305,104307,104309],{},[898,104288,1742],{},[898,104290,1662],{},[898,104292,1659],{},[898,104294,14171],{},[1706,104296,1708],{},[898,104298,1742],{},[2142,104300,104301,104303],{},[898,104302,1702],{},[898,104304,6362],{},[898,104306,15493],{"mathvariant":2409},[898,104308,1742],{},[2142,104310,104311,104313],{},[898,104312,1702],{},[898,104314,28915],{},[902,104316,92764],{"encoding":904},[123,104318,104319,1647,104322,1837],{},[38,104320,104321],{},"Substituční vztah",[883,104323,104325],{"className":104324},[886],[888,104326,104327],{"xmlns":890},[892,104328,104329,104353],{},[895,104330,104331,104333,104335,104337,104339,104341,104343,104345,104347,104349,104351],{},[898,104332,3677],{"mathvariant":2409},[898,104334,28915],{},[1706,104336,3248],{},[1706,104338,1715],{},[898,104340,1742],{},[898,104342,1662],{},[898,104344,1659],{},[898,104346,14171],{},[2415,104348,2799],{},[898,104350,3120],{},[898,104352,6362],{},[902,104354,104355],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,104357,21083],{"id":21082},[120,104359,104360,104457,104464,104471],{},[123,104361,104362,1647,104364,104367,104368,1343,104371,104374,104375,104378,104379,104398,104399,37745,104418,104421,104422,104441,104442,1936],{},[38,104363,21090],{},[207,104365,784],{"className":104366,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,104369,21102],{"className":104370,"dataFsResolvedFilePath":764,"href":765},[210],[207,104372,793],{"className":104373,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,104376,880],{"className":104377,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,104380,104382],{"className":104381},[886],[888,104383,104384],{"xmlns":890},[892,104385,104386,104396],{},[895,104387,104388,104390,104392,104394],{},[898,104389,1742],{},[898,104391,1662],{},[898,104393,1659],{},[898,104395,14171],{},[902,104397,29710],{"encoding":904}," ↔ ",[883,104400,104402],{"className":104401},[886],[888,104403,104404],{"xmlns":890},[892,104405,104406,104416],{},[895,104407,104408,104410,104412,104414],{},[898,104409,1742],{},[898,104411,1662],{},[898,104413,1683],{},[898,104415,14171],{},[902,104417,29714],{"encoding":904},[207,104419,22995],{"className":104420,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,104423,104425],{"className":104424},[886],[888,104426,104427],{"xmlns":890},[892,104428,104429,104439],{},[895,104430,104431,104433],{},[898,104432,1735],{},[2142,104434,104435,104437],{},[898,104436,1702],{},[898,104438,6362],{},[902,104440,92592],{"encoding":904}," ↔ min ",[883,104443,104445],{"className":104444},[886],[888,104446,104447],{"xmlns":890},[892,104448,104449,104455],{},[895,104450,104451,104453],{},[898,104452,1735],{},[898,104454,1683],{},[902,104456,2094],{"encoding":904},[123,104458,104459,1647,104461,1837],{},[38,104460,22971],{},[207,104462,21098],{"className":104463,"dataFsResolvedFilePath":848,"href":849},[210],[123,104465,104466,1647,104468,1837],{},[38,104467,35312],{},[207,104469,1094],{"className":104470,"dataFsResolvedFilePath":838,"href":839},[210],[123,104472,104473,1647,104475,1837],{},[38,104474,21126],{},[207,104476,21132],{"className":104477,"dataFsResolvedFilePath":21130,"href":21131},[210],{"title":641,"searchDepth":642,"depth":642,"links":104479},[104480,104481,104482,104486,104488,104493,104494,104501,104502,104504,104505,104506,104508,104513,104514,104515,104519,104520],{"id":92787,"depth":642,"text":92788},{"id":92924,"depth":642,"text":92925},{"id":93027,"depth":642,"text":104483,"children":104484},"Mezní produkt práce (MPLMP_L)",[104485],{"id":93473,"depth":649,"text":93474},{"id":93962,"depth":642,"text":104487},"Průměrný produkt práce (APLAP_L)",{"id":94080,"depth":642,"text":94081,"children":104489},[104490,104491,104492],{"id":94317,"depth":649,"text":12163},{"id":94628,"depth":649,"text":94629},{"id":95348,"depth":649,"text":95349},{"id":95920,"depth":642,"text":95921},{"id":96023,"depth":642,"text":96024,"children":104495},[104496,104497,104499,104500],{"id":96382,"depth":649,"text":96383},{"id":96881,"depth":649,"text":104498},"Parametr efektivity AA",{"id":96952,"depth":649,"text":96953},{"id":56237,"depth":649,"text":97292},{"id":97479,"depth":642,"text":97480},{"id":97818,"depth":642,"text":104503},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":98509,"depth":642,"text":98510},{"id":92853,"depth":642,"text":28894},{"id":98920,"depth":642,"text":104507},"Mezní míra technické substituce (MRTSMRTS)",{"id":99786,"depth":642,"text":99787,"children":104509},[104510,104511,104512],{"id":99790,"depth":649,"text":99791},{"id":100433,"depth":649,"text":100434},{"id":100714,"depth":649,"text":100715},{"id":101060,"depth":642,"text":101061},{"id":15879,"depth":642,"text":15880},{"id":101410,"depth":642,"text":101411,"children":104516},[104517,104518],{"id":59503,"depth":649,"text":59504},{"id":101929,"depth":649,"text":101930},{"id":19878,"depth":642,"text":19879},{"id":21082,"depth":642,"text":21083},{},"\u002Ftopics\u002Fprodukce",{"title":92423,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,28928,104527,104528,104529,92853,104530,104531],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":104534,"title":104535,"body":104536,"course":1128,"courses":659,"created":21169,"description":641,"extension":661,"meta":113483,"navigation":664,"path":113484,"seo":113485,"sources":113486,"stem":113487,"tags":113488,"type":21181,"updated":677,"__hash__":113491},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":104537,"toc":113457},[104538,104541,104543,104740,104749,104753,104756,104809,104813,104825,104829,104832,104849,104972,104978,105122,105132,105136,105171,105209,105257,105314,105374,105416,105992,105996,106079,106188,106281,106539,106542,106595,106706,106788,106792,106803,107036,107091,107097,107137,107200,107211,107402,107508,107661,107709,107714,107828,107866,107992,108038,108065,108142,108217,108297,108427,108488,108576,108580,108583,108652,108735,108742,108802,109112,109116,109122,109175,109191,109242,109380,109456,109569,109886,109890,109897,110057,110116,110120,110142,110239,110360,110474,110497,110560,110617,110869,110877,110881,110888,111142,111192,111248,111251,111415,111419,111517,111519,111551,111555,111688,111930,112114,112282,112589,112722,112909,112921,112923,113358,113360],[12,104539,104535],{"id":104540},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,104542,31115],{"id":31114},[724,104544,104545,1647,104547,104578,104579,104582,104583,104613,104614,104632,104633,104673,104674,104677,104678,104691,104692,47321,104695,104708,104709,104722,104723,104736,104737,1837],{},[38,104546,880],{},[883,104548,104550],{"className":104549},[886],[888,104551,104552],{"xmlns":890},[892,104553,104554,104576],{},[895,104555,104556,104558,104560,104566,104568,104574],{},[898,104557,900],{},[1706,104559,2140],{"stretchy":2139},[2142,104561,104562,104564],{},[898,104563,2146],{},[2148,104565,2701],{},[1706,104567,2505],{"separator":2504},[2142,104569,104570,104572],{},[898,104571,2146],{},[2148,104573,2495],{},[1706,104575,2153],{"stretchy":2139},[902,104577,35443],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,104580,104581],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,104584,104586],{"className":104585},[886],[888,104587,104588],{"xmlns":890},[892,104589,104590,104610],{},[895,104591,104592,104594,104600,104602],{},[898,104593,1742],{},[2142,104595,104596,104598],{},[898,104597,900],{},[898,104599,36887],{},[1706,104601,1708],{},[28285,104603,104604,104606,104608],{},[898,104605,900],{},[898,104607,36887],{},[1706,104609,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,104611,104612],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,104615,104617],{"className":104616},[886],[888,104618,104619],{"xmlns":890},[892,104620,104621,104629],{},[895,104622,104623,104625,104627],{},[898,104624,900],{},[1706,104626,1708],{},[898,104628,20413],{},[902,104630,104631],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,104634,104636],{"className":104635},[886],[888,104637,104638],{"xmlns":890},[892,104639,104640,104670],{},[895,104641,104642,104644,104646,104648,104650,104652,104654,104660,104662,104664],{},[898,104643,1742],{},[898,104645,1662],{},[898,104647,1683],{},[898,104649,14171],{},[1706,104651,1708],{},[898,104653,1742],{},[2142,104655,104656,104658],{},[898,104657,900],{},[2148,104659,2701],{},[898,104661,15493],{"mathvariant":2409},[898,104663,1742],{},[2142,104665,104666,104668],{},[898,104667,900],{},[2148,104669,2495],{},[902,104671,104672],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,104675,104676],{},"teorii užitečnosti"," — funkce ",[883,104679,104681],{"className":104680},[886],[888,104682,104683],{"xmlns":890},[892,104684,104685,104689],{},[895,104686,104687],{},[898,104688,900],{},[902,104690,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,104693,104694],{},"Optimalizaci spotřebitele",[883,104696,104698],{"className":104697},[886],[888,104699,104700],{"xmlns":890},[892,104701,104702,104706],{},[895,104703,104704],{},[898,104705,900],{},[902,104707,900],{"encoding":904}," při rozpočtu, min ",[883,104710,104712],{"className":104711},[886],[888,104713,104714],{"xmlns":890},[892,104715,104716,104720],{},[895,104717,104718],{},[898,104719,23410],{},[902,104721,23410],{"encoding":904}," při dané ",[883,104724,104726],{"className":104725},[886],[888,104727,104728],{"xmlns":890},[892,104729,104730,104734],{},[895,104731,104732],{},[898,104733,900],{},[902,104735,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,104738,913],{"className":104739,"dataFsResolvedFilePath":911,"href":912},[210],[724,104741,104742,104743,104745,104746,1837],{},"Kapitola 6 knihy ",[614,104744,21132],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,104747,55814],{"className":104748,"dataFsResolvedFilePath":911,"href":912},[210],[115,104750,104752],{"id":104751},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,104754,104755],{},"Po prostudování této kapitoly byste měli umět:",[120,104757,104758,104764,104773,104778,104781,104787,104793,104796,104802],{},[123,104759,104760,104761,2505],{},"vyložit, co se rozumí termínem ",[38,104762,104763],{},"užitečnost",[123,104765,104766,104767,1993,104770,2505],{},"definovat pojmy ",[38,104768,104769],{},"svazek zboží",[38,104771,104772],{},"funkce užitečnosti",[123,104774,92802,104775,92809],{},[38,104776,104777],{},"mezní užitečnosti",[123,104779,104780],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,104782,92829,104783,104786],{},[38,104784,104785],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,104788,92850,104789,104792],{},[38,104790,104791],{},"křivky užitečnosti"," (indiferenční křivky),",[123,104794,104795],{},"vyjmenovat jejich základní vlastnosti,",[123,104797,92802,104798,104801],{},[38,104799,104800],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,104803,104804,104805,104808],{},"řešit ",[38,104806,104807],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,104810,104812],{"id":104811},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,104814,104815,104816,104820,104821,104824],{},"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 ",[207,104817,104819],{"className":104818,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,104822,104823],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,104826,104828],{"id":104827},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,104830,104831],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,104833,104834,104840],{},[123,104835,104836,104839],{},[38,104837,104838],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,104841,104842,104845,104846,104848],{},[38,104843,104844],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,104847,104581],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[1636,104850,104851],{},[724,104852,104853,104855,104856,104859,104860,1647,104873,104876,104877,1993,104890,104909,104910,1343,104936,104963,104964,104967,104968,104971],{},[883,104854,9276],{}," Pozor — ordinalisté užitečnost ",[38,104857,104858],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,104861,104863],{"className":104862},[886],[888,104864,104865],{"xmlns":890},[892,104866,104867,104871],{},[895,104868,104869],{},[898,104870,900],{},[902,104872,900],{"encoding":904},[38,104874,104875],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,104878,104880],{"className":104879},[886],[888,104881,104882],{"xmlns":890},[892,104883,104884,104888],{},[895,104885,104886],{},[898,104887,900],{},[902,104889,900],{"encoding":904},[883,104891,104893],{"className":104892},[886],[888,104894,104895],{"xmlns":890},[892,104896,104897,104906],{},[895,104898,104899],{},[3925,104900,104901,104903],{"accent":2504},[898,104902,900],{},[1706,104904,104905],{},"~",[902,104907,104908],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,104911,104913],{"className":104912},[886],[888,104914,104915],{"xmlns":890},[892,104916,104917,104933],{},[895,104918,104919,104925,104927],{},[3925,104920,104921,104923],{"accent":2504},[898,104922,900],{},[1706,104924,104905],{},[1706,104926,1708],{},[2489,104928,104929,104931],{},[898,104930,900],{},[2148,104932,2495],{},[902,104934,104935],{"encoding":904},"\\tilde U = U^2",[883,104937,104939],{"className":104938},[886],[888,104940,104941],{"xmlns":890},[892,104942,104943,104960],{},[895,104944,104945,104951,104953,104956,104958],{},[3925,104946,104947,104949],{"accent":2504},[898,104948,900],{},[1706,104950,104905],{},[1706,104952,1708],{},[898,104954,104955],{},"ln",[1706,104957,2773],{},[898,104959,900],{},[902,104961,104962],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,104965,104966],{},"porovnání"," mezi svazky a ",[38,104969,104970],{},"poměry"," mezních veličin.",[724,104973,104974,104975,4288],{},"Ordinalistický přístup vychází z ",[38,104976,104977],{},"pěti hlavních předpokladů",[152,104979,104980,104986,104992,105110,105116],{},[123,104981,104982,104985],{},[38,104983,104984],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,104987,104988,104991],{},[38,104989,104990],{},"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.",[123,104993,104994,104997,104998,8384,105011,105024,105025,8384,105038,3787,105051,105054,105055,1993,105074,9217,105092,1837],{},[38,104995,104996],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,104999,105001],{"className":105000},[886],[888,105002,105003],{"xmlns":890},[892,105004,105005,105009],{},[895,105006,105007],{},[898,105008,1735],{},[902,105010,1735],{"encoding":904},[883,105012,105014],{"className":105013},[886],[888,105015,105016],{"xmlns":890},[892,105017,105018,105022],{},[895,105019,105020],{},[898,105021,10315],{},[902,105023,10315],{"encoding":904},", nebude jindy preferovat ",[883,105026,105028],{"className":105027},[886],[888,105029,105030],{"xmlns":890},[892,105031,105032,105036],{},[895,105033,105034],{},[898,105035,10315],{},[902,105037,10315],{"encoding":904},[883,105039,105041],{"className":105040},[886],[888,105042,105043],{"xmlns":890},[892,105044,105045,105049],{},[895,105046,105047],{},[898,105048,1735],{},[902,105050,1735],{"encoding":904},[38,105052,105053],{},"Tranzitivita",": pokud ",[883,105056,105058],{"className":105057},[886],[888,105059,105060],{"xmlns":890},[892,105061,105062,105071],{},[895,105063,105064,105066,105069],{},[898,105065,1735],{},[1706,105067,105068],{},"≻",[898,105070,10315],{},[902,105072,105073],{"encoding":904},"A \\succ B",[883,105075,105077],{"className":105076},[886],[888,105078,105079],{"xmlns":890},[892,105080,105081,105089],{},[895,105082,105083,105085,105087],{},[898,105084,10315],{},[1706,105086,105068],{},[898,105088,1683],{},[902,105090,105091],{"encoding":904},"B \\succ C",[883,105093,105095],{"className":105094},[886],[888,105096,105097],{"xmlns":890},[892,105098,105099,105107],{},[895,105100,105101,105103,105105],{},[898,105102,1735],{},[1706,105104,105068],{},[898,105106,1683],{},[902,105108,105109],{"encoding":904},"A \\succ C",[123,105111,105112,105115],{},[38,105113,105114],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,105117,105118,105121],{},[38,105119,105120],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,105123,105124,105125,105128,105129,1837],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,105126,105127],{},"preference"," a na příbuzné ",[614,105130,105131],{},"funkci užitečnosti",[115,105133,105135],{"id":105134},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,105137,105138,105139,105152,105153,105156,105157,105170],{},"Uvažujme ",[883,105140,105142],{"className":105141},[886],[888,105143,105144],{"xmlns":890},[892,105145,105146,105150],{},[895,105147,105148],{},[898,105149,18465],{},[902,105151,18465],{"encoding":904}," různých zboží. ",[38,105154,105155],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,105158,105160],{"className":105159},[886],[888,105161,105162],{"xmlns":890},[892,105163,105164,105168],{},[895,105165,105166],{},[898,105167,18465],{},[902,105169,18465],{"encoding":904},"-tice",[724,105172,105173],{},[883,105174,105176],{"className":105175},[886],[888,105177,105178],{"xmlns":890},[892,105179,105180,105206],{},[895,105181,105182,105184,105190,105192,105194,105196,105202,105204],{},[1706,105183,2140],{"stretchy":2139},[2142,105185,105186,105188],{},[898,105187,2146],{},[2148,105189,2701],{},[1706,105191,2505],{"separator":2504},[1706,105193,28763],{},[1706,105195,2505],{"separator":2504},[2142,105197,105198,105200],{},[898,105199,2146],{},[898,105201,18465],{},[1706,105203,2153],{"stretchy":2139},[1706,105205,2505],{"separator":2504},[902,105207,105208],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,105210,5331,105211,105228,105229,105242,105243,105246,105247,105250,105251,105254,105255,4288],{},[883,105212,105214],{"className":105213},[886],[888,105215,105216],{"xmlns":890},[892,105217,105218,105226],{},[895,105219,105220],{},[2142,105221,105222,105224],{},[898,105223,2146],{},[898,105225,36887],{},[902,105227,66581],{"encoding":904}," značí množství ",[883,105230,105232],{"className":105231},[886],[888,105233,105234],{"xmlns":890},[892,105235,105236,105240],{},[895,105237,105238],{},[898,105239,36887],{},[902,105241,36887],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,105244,105245],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,105248,105249],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,105252,105253],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,105256,105131],{},[883,105258,105260],{"className":105259},[886],[888,105261,105262],{"xmlns":890,"display":2350},[892,105263,105264,105311],{},[2354,105265,105266],{"width":2356},[2358,105267,105268,105270,105304,105306],{},[2361,105269],{"width":2363},[2361,105271,105272],{},[895,105273,105274,105276,105278,105280,105282,105288,105290,105292,105294,105300,105302],{},[898,105275,900],{},[1706,105277,1708],{},[898,105279,900],{},[1706,105281,2140],{"stretchy":2139},[2142,105283,105284,105286],{},[898,105285,2146],{},[2148,105287,2701],{},[1706,105289,2505],{"separator":2504},[1706,105291,28763],{},[1706,105293,2505],{"separator":2504},[2142,105295,105296,105298],{},[898,105297,2146],{},[898,105299,18465],{},[1706,105301,2153],{"stretchy":2139},[1706,105303,2505],{"separator":2504},[2361,105305],{"width":2363},[2361,105307,105308],{},[2415,105309,105310],{},"(6.1)",[902,105312,105313],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,105315,5331,105316,105346,105347,105369,105370,105373],{},[883,105317,105319],{"className":105318},[886],[888,105320,105321],{"xmlns":890},[892,105322,105323,105343],{},[895,105324,105325,105331,105333,105335,105337],{},[2142,105326,105327,105329],{},[898,105328,2146],{},[2148,105330,2701],{},[1706,105332,2505],{"separator":2504},[1706,105334,28763],{},[1706,105336,2505],{"separator":2504},[2142,105338,105339,105341],{},[898,105340,2146],{},[898,105342,18465],{},[902,105344,105345],{"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 ",[883,105348,105350],{"className":105349},[886],[888,105351,105352],{"xmlns":890},[892,105353,105354,105366],{},[895,105355,105356,105358,105360],{},[898,105357,900],{},[1706,105359,2505],{"separator":2504},[3925,105361,105362,105364],{"accent":2504},[898,105363,900],{},[1706,105365,104905],{},[902,105367,105368],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,105371,105372],{},"monotónní transformace"," zachovávající pořadí.",[724,105375,105376,105377,21021,105380,1837],{},"Dále se omezíme na funkce pro ",[38,105378,105379],{},"dvě zboží",[883,105381,105383],{"className":105382},[886],[888,105384,105385],{"xmlns":890},[892,105386,105387,105413],{},[895,105388,105389,105391,105393,105395,105397,105403,105405,105411],{},[898,105390,900],{},[1706,105392,1708],{},[898,105394,900],{},[1706,105396,2140],{"stretchy":2139},[2142,105398,105399,105401],{},[898,105400,2146],{},[2148,105402,2701],{},[1706,105404,2505],{"separator":2504},[2142,105406,105407,105409],{},[898,105408,2146],{},[2148,105410,2495],{},[1706,105412,2153],{"stretchy":2139},[902,105414,105415],{"encoding":904},"U = U(Q_1, Q_2)",[1636,105417,105418,105493],{},[724,105419,105420,105422,105423,4288],{},[883,105421,71732],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,105424,105426],{"className":105425},[886],[888,105427,105428],{"xmlns":890},[892,105429,105430,105490],{},[895,105431,105432,105434,105436,105438,105440,105446,105448,105454,105456,105462,105464,105466,105468],{},[898,105433,900],{},[1706,105435,1708],{},[898,105437,900],{},[1706,105439,2140],{"stretchy":2139},[2142,105441,105442,105444],{},[898,105443,2146],{},[2148,105445,2701],{},[1706,105447,2505],{"separator":2504},[2142,105449,105450,105452],{},[898,105451,2146],{},[2148,105453,2495],{},[1706,105455,2505],{"separator":2504},[2142,105457,105458,105460],{},[898,105459,2146],{},[2148,105461,4284],{},[1706,105463,2153],{"stretchy":2139},[1706,105465,1708],{},[2148,105467,2495],{},[11087,105469,105470],{},[895,105471,105472,105478,105484],{},[2142,105473,105474,105476],{},[898,105475,2146],{},[2148,105477,2701],{},[2142,105479,105480,105482],{},[898,105481,2146],{},[2148,105483,2495],{},[2142,105485,105486,105488],{},[898,105487,2146],{},[2148,105489,4284],{},[902,105491,105492],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,105494,105495,105688],{},[123,105496,105497,105498,105524,105525,32045,105551,1993,105610,24728,105670,2110],{},"svazek ",[883,105499,105501],{"className":105500},[886],[888,105502,105503],{"xmlns":890},[892,105504,105505,105521],{},[895,105506,105507,105509,105511,105513,105515,105517,105519],{},[1706,105508,2140],{"stretchy":2139},[2148,105510,3364],{},[1706,105512,2505],{"separator":2504},[2148,105514,3455],{},[1706,105516,2505],{"separator":2504},[2148,105518,60890],{},[1706,105520,2153],{"stretchy":2139},[902,105522,105523],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,105526,105528],{"className":105527},[886],[888,105529,105530],{"xmlns":890},[892,105531,105532,105548],{},[895,105533,105534,105536,105538,105540,105542,105544,105546],{},[1706,105535,2140],{"stretchy":2139},[2148,105537,10800],{},[1706,105539,2505],{"separator":2504},[2148,105541,10800],{},[1706,105543,2505],{"separator":2504},[2148,105545,13266],{},[1706,105547,2153],{"stretchy":2139},[902,105549,105550],{"encoding":904},"(9, 9, 27)",[883,105552,105554],{"className":105553},[886],[888,105555,105556],{"xmlns":890},[892,105557,105558,105607],{},[895,105559,105560,105562,105564,105566,105568,105570,105572,105574,105576,105578,105580,105594,105596,105598,105603,105605],{},[898,105561,900],{},[1706,105563,2140],{"stretchy":2139},[2148,105565,3364],{},[1706,105567,2505],{"separator":2504},[2148,105569,3455],{},[1706,105571,2505],{"separator":2504},[2148,105573,60890],{},[1706,105575,2153],{"stretchy":2139},[1706,105577,1708],{},[2148,105579,2495],{},[11087,105581,105582],{},[895,105583,105584,105586,105588,105590,105592],{},[2148,105585,3364],{},[1706,105587,2390],{},[2148,105589,3455],{},[1706,105591,2390],{},[2148,105593,60890],{},[1706,105595,1708],{},[2148,105597,2495],{},[11087,105599,105600],{},[2148,105601,105602],{},"4096",[1706,105604,1708],{},[2148,105606,24756],{},[902,105608,105609],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,105611,105613],{"className":105612},[886],[888,105614,105615],{"xmlns":890},[892,105616,105617,105667],{},[895,105618,105619,105621,105623,105625,105627,105629,105631,105633,105635,105637,105639,105653,105655,105657,105662,105664],{},[898,105620,900],{},[1706,105622,2140],{"stretchy":2139},[2148,105624,10800],{},[1706,105626,2505],{"separator":2504},[2148,105628,10800],{},[1706,105630,2505],{"separator":2504},[2148,105632,13266],{},[1706,105634,2153],{"stretchy":2139},[1706,105636,1708],{},[2148,105638,2495],{},[11087,105640,105641],{},[895,105642,105643,105645,105647,105649,105651],{},[2148,105644,10800],{},[1706,105646,2390],{},[2148,105648,10800],{},[1706,105650,2390],{},[2148,105652,13266],{},[1706,105654,1708],{},[2148,105656,2495],{},[11087,105658,105659],{},[2148,105660,105661],{},"2187",[1706,105663,7883],{},[2148,105665,105666],{},"93,53",[902,105668,105669],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,105671,105673],{"className":105672},[886],[888,105674,105675],{"xmlns":890},[892,105676,105677,105685],{},[895,105678,105679,105681,105683],{},[2148,105680,24756],{},[1706,105682,8922],{},[2148,105684,105666],{},[902,105686,105687],{"encoding":904},"128 > 93{,}53",[123,105689,105690,105691,1993,105717,105743,105744,1993,105784,105825,105826,105872,105873,1993,105899,22037,105925,1993,105943,105961,105962,1837],{},"svazky ",[883,105692,105694],{"className":105693},[886],[888,105695,105696],{"xmlns":890},[892,105697,105698,105714],{},[895,105699,105700,105702,105704,105706,105708,105710,105712],{},[1706,105701,2140],{"stretchy":2139},[2148,105703,3455],{},[1706,105705,2505],{"separator":2504},[2148,105707,12717],{},[1706,105709,2505],{"separator":2504},[2148,105711,2495],{},[1706,105713,2153],{"stretchy":2139},[902,105715,105716],{"encoding":904},"(4, 8, 2)",[883,105718,105720],{"className":105719},[886],[888,105721,105722],{"xmlns":890},[892,105723,105724,105740],{},[895,105725,105726,105728,105730,105732,105734,105736,105738],{},[1706,105727,2140],{"stretchy":2139},[2148,105729,60890],{},[1706,105731,2505],{"separator":2504},[2148,105733,2701],{},[1706,105735,2505],{"separator":2504},[2148,105737,3455],{},[1706,105739,2153],{"stretchy":2139},[902,105741,105742],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,105745,105747],{"className":105746},[886],[888,105748,105749],{"xmlns":890},[892,105750,105751,105781],{},[895,105752,105753,105755,105757,105759,105761,105763,105765,105767,105769,105771,105773,105777,105779],{},[898,105754,900],{},[1706,105756,2140],{"stretchy":2139},[2148,105758,3455],{},[1706,105760,2505],{"separator":2504},[2148,105762,12717],{},[1706,105764,2505],{"separator":2504},[2148,105766,2495],{},[1706,105768,2153],{"stretchy":2139},[1706,105770,1708],{},[2148,105772,2495],{},[11087,105774,105775],{},[2148,105776,60890],{},[1706,105778,1708],{},[2148,105780,3364],{},[902,105782,105783],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,105785,105787],{"className":105786},[886],[888,105788,105789],{"xmlns":890},[892,105790,105791,105822],{},[895,105792,105793,105795,105797,105799,105801,105803,105805,105807,105809,105811,105813,105818,105820],{},[898,105794,900],{},[1706,105796,2140],{"stretchy":2139},[2148,105798,60890],{},[1706,105800,2505],{"separator":2504},[2148,105802,2701],{},[1706,105804,2505],{"separator":2504},[2148,105806,3455],{},[1706,105808,2153],{"stretchy":2139},[1706,105810,1708],{},[2148,105812,2495],{},[11087,105814,105815],{},[2148,105816,105817],{},"256",[1706,105819,1708],{},[2148,105821,19056],{},[902,105823,105824],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,105827,105829],{"className":105828},[886],[888,105830,105831],{"xmlns":890},[892,105832,105833,105869],{},[895,105834,105835,105837,105839,105841,105843,105845,105847,105849,105851,105853,105855,105857,105859,105861,105863,105865,105867],{},[898,105836,900],{},[1706,105838,2140],{"stretchy":2139},[2148,105840,3455],{},[1706,105842,2505],{"separator":2504},[2148,105844,12717],{},[1706,105846,2505],{"separator":2504},[2148,105848,2495],{},[1706,105850,2153],{"stretchy":2139},[1706,105852,1708],{},[898,105854,900],{},[1706,105856,2140],{"stretchy":2139},[2148,105858,60890],{},[1706,105860,2505],{"separator":2504},[2148,105862,2701],{},[1706,105864,2505],{"separator":2504},[2148,105866,3455],{},[1706,105868,2153],{"stretchy":2139},[902,105870,105871],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,105874,105876],{"className":105875},[886],[888,105877,105878],{"xmlns":890},[892,105879,105880,105896],{},[895,105881,105882,105884,105886,105888,105890,105892,105894],{},[2148,105883,3455],{},[1706,105885,2390],{},[2148,105887,12717],{},[1706,105889,2390],{},[2148,105891,2495],{},[1706,105893,1708],{},[2148,105895,60890],{},[902,105897,105898],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,105900,105902],{"className":105901},[886],[888,105903,105904],{"xmlns":890},[892,105905,105906,105922],{},[895,105907,105908,105910,105912,105914,105916,105918,105920],{},[2148,105909,60890],{},[1706,105911,2390],{},[2148,105913,2701],{},[1706,105915,2390],{},[2148,105917,3455],{},[1706,105919,1708],{},[2148,105921,105817],{},[902,105923,105924],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,105926,105928],{"className":105927},[886],[888,105929,105930],{"xmlns":890},[892,105931,105932,105940],{},[895,105933,105934,105936,105938],{},[898,105935,900],{},[1706,105937,1708],{},[2148,105939,3364],{},[902,105941,105942],{"encoding":904},"U = 16",[883,105944,105946],{"className":105945},[886],[888,105947,105948],{"xmlns":890},[892,105949,105950,105958],{},[895,105951,105952,105954,105956],{},[898,105953,900],{},[1706,105955,1708],{},[2148,105957,19056],{},[902,105959,105960],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,105963,105965],{"className":105964},[886],[888,105966,105967],{"xmlns":890},[892,105968,105969,105989],{},[895,105970,105971,105977,105983],{},[2142,105972,105973,105975],{},[898,105974,2146],{},[2148,105976,2701],{},[2142,105978,105979,105981],{},[898,105980,2146],{},[2148,105982,2495],{},[2142,105984,105985,105987],{},[898,105986,2146],{},[2148,105988,4284],{},[902,105990,105991],{"encoding":904},"Q_1 Q_2 Q_3",[115,105993,105995],{"id":105994},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,105997,105998,105999,3484,106034,1647,106037,2173,106054,2314,106071,106074,106075,106078],{},"Pro funkci užitečnosti ",[883,106000,106002],{"className":106001},[886],[888,106003,106004],{"xmlns":890},[892,106005,106006,106032],{},[895,106007,106008,106010,106012,106014,106016,106022,106024,106030],{},[898,106009,900],{},[1706,106011,1708],{},[898,106013,900],{},[1706,106015,2140],{"stretchy":2139},[2142,106017,106018,106020],{},[898,106019,2146],{},[2148,106021,2701],{},[1706,106023,2505],{"separator":2504},[2142,106025,106026,106028],{},[898,106027,2146],{},[2148,106029,2495],{},[1706,106031,2153],{"stretchy":2139},[902,106033,105415],{"encoding":904},[38,106035,106036],{},"mezní užitečnost",[883,106038,106040],{"className":106039},[886],[888,106041,106042],{"xmlns":890},[892,106043,106044,106052],{},[895,106045,106046],{},[2142,106047,106048,106050],{},[898,106049,2146],{},[2148,106051,2701],{},[902,106053,48070],{"encoding":904},[883,106055,106057],{"className":106056},[886],[888,106058,106059],{"xmlns":890},[892,106060,106061,106069],{},[895,106062,106063],{},[2142,106064,106065,106067],{},[898,106066,2146],{},[2148,106068,2495],{},[902,106070,48089],{"encoding":904},[38,106072,106073],{},"marginal utility",") parciální ",[207,106076,1145],{"className":106077,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,106080,106082],{"className":106081},[886],[888,106083,106084],{"xmlns":890,"display":2350},[892,106085,106086,106185],{},[2354,106087,106088],{"width":2356},[2358,106089,106090,106092,106178,106180],{},[2361,106091],{"width":2363},[2361,106093,106094],{},[895,106095,106096,106098,106104,106106,106114,106116,106134,106136,106138,106140,106146,106148,106156,106158,106176],{},[898,106097,1742],{},[2142,106099,106100,106102],{},[898,106101,900],{},[2148,106103,2701],{},[1706,106105,1708],{},[28285,106107,106108,106110,106112],{},[898,106109,900],{},[2148,106111,2701],{},[1706,106113,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,106115,1708],{},[2964,106117,106118,106124],{},[895,106119,106120,106122],{},[898,106121,28987],{"mathvariant":2409},[898,106123,900],{},[895,106125,106126,106128],{},[898,106127,28987],{"mathvariant":2409},[2142,106129,106130,106132],{},[898,106131,2146],{},[2148,106133,2701],{},[1706,106135,2505],{"separator":2504},[4898,106137],{"width":4900},[898,106139,1742],{},[2142,106141,106142,106144],{},[898,106143,900],{},[2148,106145,2495],{},[1706,106147,1708],{},[28285,106149,106150,106152,106154],{},[898,106151,900],{},[2148,106153,2495],{},[1706,106155,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,106157,1708],{},[2964,106159,106160,106166],{},[895,106161,106162,106164],{},[898,106163,28987],{"mathvariant":2409},[898,106165,900],{},[895,106167,106168,106170],{},[898,106169,28987],{"mathvariant":2409},[2142,106171,106172,106174],{},[898,106173,2146],{},[2148,106175,2495],{},[898,106177,1837],{"mathvariant":2409},[2361,106179],{"width":2363},[2361,106181,106182],{},[2415,106183,106184],{},"(6.2)",[902,106186,106187],{"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}",[724,106189,106190,106191,106225,106226,106256,106257,1647,106260,1837],{},"Pro pevné ",[883,106192,106194],{"className":106193},[886],[888,106195,106196],{"xmlns":890},[892,106197,106198,106222],{},[895,106199,106200,106206,106208,106210,106212,106218,106220],{},[2142,106201,106202,106204],{},[898,106203,2146],{},[2148,106205,2701],{},[1706,106207,1708],{},[898,106209,207],{},[1706,106211,2505],{"separator":2504},[2142,106213,106214,106216],{},[898,106215,2146],{},[2148,106217,2495],{},[1706,106219,1708],{},[898,106221,2450],{},[902,106223,106224],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,106227,106229],{"className":106228},[886],[888,106230,106231],{"xmlns":890},[892,106232,106233,106253],{},[895,106234,106235,106237,106243,106245,106247,106249,106251],{},[898,106236,1742],{},[2142,106238,106239,106241],{},[898,106240,900],{},[2148,106242,2701],{},[1706,106244,2140],{"stretchy":2139},[898,106246,207],{},[1706,106248,2505],{"separator":2504},[898,106250,2450],{},[1706,106252,2153],{"stretchy":2139},[902,106254,106255],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,106258,106259],{},"v bodě (na hladině)",[883,106261,106263],{"className":106262},[886],[888,106264,106265],{"xmlns":890},[892,106266,106267,106279],{},[895,106268,106269,106271,106273,106275,106277],{},[1706,106270,21693],{"stretchy":2139},[898,106272,207],{},[1706,106274,2505],{"separator":2504},[898,106276,2450],{},[1706,106278,21708],{"stretchy":2139},[902,106280,29935],{"encoding":904},[1636,106282,106283],{},[724,106284,106285,106287,106288,106318,106347,106348,21814,106361,2891,106378,106399,106400,1889,106417,4202,106430,106447,106448,106470,106471,106500,106501,10691,106521,106538],{},[883,106286,3174],{}," Intuice — co říká ",[883,106289,106291],{"className":106290},[886],[888,106292,106293],{"xmlns":890},[892,106294,106295,106315],{},[895,106296,106297,106299,106305,106307,106309,106311,106313],{},[898,106298,1742],{},[2142,106300,106301,106303],{},[898,106302,900],{},[2148,106304,2701],{},[1706,106306,2140],{"stretchy":2139},[898,106308,207],{},[1706,106310,2505],{"separator":2504},[898,106312,2450],{},[1706,106314,2153],{"stretchy":2139},[902,106316,106317],{"encoding":904},"MU_1(a,b)",[883,106319,106321],{"className":106320},[886],[888,106322,106323],{"xmlns":890},[892,106324,106325,106345],{},[895,106326,106327,106329,106335,106337,106339,106341,106343],{},[898,106328,1742],{},[2142,106330,106331,106333],{},[898,106332,900],{},[2148,106334,2701],{},[1706,106336,2140],{"stretchy":2139},[898,106338,207],{},[1706,106340,2505],{"separator":2504},[898,106342,2450],{},[1706,106344,2153],{"stretchy":2139},[902,106346,106255],{"encoding":904}," je rychlost změny ",[883,106349,106351],{"className":106350},[886],[888,106352,106353],{"xmlns":890},[892,106354,106355,106359],{},[895,106356,106357],{},[898,106358,900],{},[902,106360,900],{"encoding":904},[883,106362,106364],{"className":106363},[886],[888,106365,106366],{"xmlns":890},[892,106367,106368,106376],{},[895,106369,106370],{},[2142,106371,106372,106374],{},[898,106373,2146],{},[2148,106375,2701],{},[902,106377,48070],{"encoding":904},[883,106379,106381],{"className":106380},[886],[888,106382,106383],{"xmlns":890},[892,106384,106385,106397],{},[895,106386,106387,106389,106391,106393,106395],{},[1706,106388,21693],{"stretchy":2139},[898,106390,207],{},[1706,106392,2505],{"separator":2504},[898,106394,2450],{},[1706,106396,21708],{"stretchy":2139},[902,106398,29935],{"encoding":904},". Přibližně: změní-li se ",[883,106401,106403],{"className":106402},[886],[888,106404,106405],{"xmlns":890},[892,106406,106407,106415],{},[895,106408,106409],{},[2142,106410,106411,106413],{},[898,106412,2146],{},[2148,106414,2701],{},[902,106416,48070],{"encoding":904},[883,106418,106420],{"className":106419},[886],[888,106421,106422],{"xmlns":890},[892,106423,106424,106428],{},[895,106425,106426],{},[898,106427,207],{},[902,106429,207],{"encoding":904},[883,106431,106433],{"className":106432},[886],[888,106434,106435],{"xmlns":890},[892,106436,106437,106445],{},[895,106438,106439,106441,106443],{},[898,106440,207],{},[1706,106442,2447],{},[2148,106444,2701],{},[902,106446,21903],{"encoding":904}," při pevném ",[883,106449,106451],{"className":106450},[886],[888,106452,106453],{"xmlns":890},[892,106454,106455,106467],{},[895,106456,106457,106463,106465],{},[2142,106458,106459,106461],{},[898,106460,2146],{},[2148,106462,2495],{},[1706,106464,1708],{},[898,106466,2450],{},[902,106468,106469],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,106472,106474],{"className":106473},[886],[888,106475,106476],{"xmlns":890},[892,106477,106478,106498],{},[895,106479,106480,106482,106488,106490,106492,106494,106496],{},[898,106481,1742],{},[2142,106483,106484,106486],{},[898,106485,900],{},[2148,106487,2701],{},[1706,106489,2140],{"stretchy":2139},[898,106491,207],{},[1706,106493,2505],{"separator":2504},[898,106495,2450],{},[1706,106497,2153],{"stretchy":2139},[902,106499,106255],{"encoding":904},". Stejně tak ",[883,106502,106504],{"className":106503},[886],[888,106505,106506],{"xmlns":890},[892,106507,106508,106518],{},[895,106509,106510,106512],{},[898,106511,1742],{},[2142,106513,106514,106516],{},[898,106515,900],{},[2148,106517,2495],{},[902,106519,106520],{"encoding":904},"MU_2",[883,106522,106524],{"className":106523},[886],[888,106525,106526],{"xmlns":890},[892,106527,106528,106536],{},[895,106529,106530],{},[2142,106531,106532,106534],{},[898,106533,2146],{},[2148,106535,2495],{},[902,106537,48089],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,106540,98170],{"id":106541},"totální-diferenciál",[724,106543,106544,106545,67382,106561,106591,106592,4288],{},"Přibližnou změnu užitečnosti ",[883,106546,106548],{"className":106547},[886],[888,106549,106550],{"xmlns":890},[892,106551,106552,106558],{},[895,106553,106554,106556],{},[898,106555,3677],{"mathvariant":2409},[898,106557,900],{},[902,106559,106560],{"encoding":904},"\\Delta U",[883,106562,106564],{"className":106563},[886],[888,106565,106566],{"xmlns":890},[892,106567,106568,106588],{},[895,106569,106570,106572,106578,106580,106582],{},[898,106571,3120],{"mathvariant":2409},[2142,106573,106574,106576],{},[898,106575,2146],{},[2148,106577,2701],{},[1706,106579,2505],{"separator":2504},[898,106581,3120],{"mathvariant":2409},[2142,106583,106584,106586],{},[898,106585,2146],{},[2148,106587,2495],{},[902,106589,106590],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,106593,106594],{},"totálního diferenciálu",[883,106596,106598],{"className":106597},[886],[888,106599,106600],{"xmlns":890,"display":2350},[892,106601,106602,106703],{},[2354,106603,106604],{"width":2356},[2358,106605,106606,106608,106696,106698],{},[2361,106607],{"width":2363},[2361,106609,106610],{},[895,106611,106612,106614,106616,106618,106620,106622,106624,106632,106634,106640,106642,106650,106652,106658,106660,106662,106668,106670,106676,106678,106680,106686,106688,106694],{},[898,106613,3677],{"mathvariant":2409},[898,106615,900],{},[1706,106617,3248],{},[898,106619,3120],{"mathvariant":2409},[898,106621,900],{},[1706,106623,1708],{},[28285,106625,106626,106628,106630],{},[898,106627,900],{},[2148,106629,2701],{},[1706,106631,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[898,106633,3120],{"mathvariant":2409},[2142,106635,106636,106638],{},[898,106637,2146],{},[2148,106639,2701],{},[1706,106641,2447],{},[28285,106643,106644,106646,106648],{},[898,106645,900],{},[2148,106647,2495],{},[1706,106649,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[898,106651,3120],{"mathvariant":2409},[2142,106653,106654,106656],{},[898,106655,2146],{},[2148,106657,2495],{},[1706,106659,1708],{},[898,106661,1742],{},[2142,106663,106664,106666],{},[898,106665,900],{},[2148,106667,2701],{},[898,106669,3120],{"mathvariant":2409},[2142,106671,106672,106674],{},[898,106673,2146],{},[2148,106675,2701],{},[1706,106677,2447],{},[898,106679,1742],{},[2142,106681,106682,106684],{},[898,106683,900],{},[2148,106685,2495],{},[898,106687,3120],{"mathvariant":2409},[2142,106689,106690,106692],{},[898,106691,2146],{},[2148,106693,2495],{},[898,106695,1837],{"mathvariant":2409},[2361,106697],{"width":2363},[2361,106699,106700],{},[2415,106701,106702],{},"(6.3)",[902,106704,106705],{"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}",[724,106707,93428,106708,1837],{},[883,106709,106711],{"className":106710},[886],[888,106712,106713],{"xmlns":890},[892,106714,106715,106785],{},[895,106716,106717,106719,106721,106723,106725,106727,106733,106735,106737,106743,106745,106751,106753,106755,106761,106763,106765,106767,106769,106775,106777,106783],{},[898,106718,3677],{"mathvariant":2409},[898,106720,900],{},[1706,106722,1708],{},[898,106724,900],{},[1706,106726,2140],{"stretchy":2139},[2142,106728,106729,106731],{},[898,106730,2146],{},[2148,106732,2701],{},[1706,106734,2447],{},[898,106736,3120],{"mathvariant":2409},[2142,106738,106739,106741],{},[898,106740,2146],{},[2148,106742,2701],{},[1706,106744,2505],{"separator":2504},[2142,106746,106747,106749],{},[898,106748,2146],{},[2148,106750,2495],{},[1706,106752,2447],{},[898,106754,3120],{"mathvariant":2409},[2142,106756,106757,106759],{},[898,106758,2146],{},[2148,106760,2495],{},[1706,106762,2153],{"stretchy":2139},[1706,106764,1715],{},[898,106766,900],{},[1706,106768,2140],{"stretchy":2139},[2142,106770,106771,106773],{},[898,106772,2146],{},[2148,106774,2701],{},[1706,106776,2505],{"separator":2504},[2142,106778,106779,106781],{},[898,106780,2146],{},[2148,106782,2495],{},[1706,106784,2153],{"stretchy":2139},[902,106786,106787],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,106789,106791],{"id":106790},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,106793,106794,106795,106798,106799,106802],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,106796,106797],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,106800,106801],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,106804,106805,106808,106809,2173,106835,106861,106862,1343,106894,106926,106927,1993,106981,107035],{},[38,106806,106807],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,106810,106812],{"className":106811},[886],[888,106813,106814],{"xmlns":890},[892,106815,106816,106832],{},[895,106817,106818,106824,106826],{},[2142,106819,106820,106822],{},[898,106821,2146],{},[2148,106823,2495],{},[1706,106825,1708],{},[2142,106827,106828,106830],{},[898,106829,207],{},[2148,106831,2150],{},[902,106833,106834],{"encoding":904},"Q_2 = a_0",[883,106836,106838],{"className":106837},[886],[888,106839,106840],{"xmlns":890},[892,106841,106842,106858],{},[895,106843,106844,106850,106852],{},[2142,106845,106846,106848],{},[898,106847,2146],{},[2148,106849,2701],{},[1706,106851,1708],{},[2142,106853,106854,106856],{},[898,106855,2450],{},[2148,106857,2150],{},[902,106859,106860],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,106863,106865],{"className":106864},[886],[888,106866,106867],{"xmlns":890},[892,106868,106869,106891],{},[895,106870,106871,106873,106875,106881,106883,106889],{},[898,106872,900],{},[1706,106874,2140],{"stretchy":2139},[2142,106876,106877,106879],{},[898,106878,2146],{},[2148,106880,2701],{},[1706,106882,2505],{"separator":2504},[2142,106884,106885,106887],{},[898,106886,207],{},[2148,106888,2150],{},[1706,106890,2153],{"stretchy":2139},[902,106892,106893],{"encoding":904},"U(Q_1, a_0)",[883,106895,106897],{"className":106896},[886],[888,106898,106899],{"xmlns":890},[892,106900,106901,106923],{},[895,106902,106903,106905,106907,106913,106915,106921],{},[898,106904,900],{},[1706,106906,2140],{"stretchy":2139},[2142,106908,106909,106911],{},[898,106910,2450],{},[2148,106912,2150],{},[1706,106914,2505],{"separator":2504},[2142,106916,106917,106919],{},[898,106918,2146],{},[2148,106920,2495],{},[1706,106922,2153],{"stretchy":2139},[902,106924,106925],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,106928,106930],{"className":106929},[886],[888,106931,106932],{"xmlns":890},[892,106933,106934,106978],{},[895,106935,106936,106974,106976],{},[4745,106937,106938],{"scriptlevel":2150,"displaystyle":2504},[2964,106939,106940,106964],{},[895,106941,106942,106944,106946,106948,106954,106956,106962],{},[898,106943,3120],{"mathvariant":2409},[898,106945,900],{},[1706,106947,2140],{"stretchy":2139},[2142,106949,106950,106952],{},[898,106951,2146],{},[2148,106953,2701],{},[1706,106955,2505],{"separator":2504},[2142,106957,106958,106960],{},[898,106959,207],{},[2148,106961,2150],{},[1706,106963,2153],{"stretchy":2139},[895,106965,106966,106968],{},[898,106967,3120],{"mathvariant":2409},[2142,106969,106970,106972],{},[898,106971,2146],{},[2148,106973,2701],{},[1706,106975,8922],{},[2148,106977,2150],{},[902,106979,106980],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,106982,106984],{"className":106983},[886],[888,106985,106986],{"xmlns":890},[892,106987,106988,107032],{},[895,106989,106990,107028,107030],{},[4745,106991,106992],{"scriptlevel":2150,"displaystyle":2504},[2964,106993,106994,107018],{},[895,106995,106996,106998,107000,107002,107008,107010,107016],{},[898,106997,3120],{"mathvariant":2409},[898,106999,900],{},[1706,107001,2140],{"stretchy":2139},[2142,107003,107004,107006],{},[898,107005,2450],{},[2148,107007,2150],{},[1706,107009,2505],{"separator":2504},[2142,107011,107012,107014],{},[898,107013,2146],{},[2148,107015,2495],{},[1706,107017,2153],{"stretchy":2139},[895,107019,107020,107022],{},[898,107021,3120],{"mathvariant":2409},[2142,107023,107024,107026],{},[898,107025,2146],{},[2148,107027,2495],{},[1706,107029,8922],{},[2148,107031,2150],{},[902,107033,107034],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,107037,107039],{"className":107038},[886],[888,107040,107041],{"xmlns":890,"display":2350},[892,107042,107043,107088],{},[2354,107044,107045],{"width":2356},[2358,107046,107047,107049,107081,107083],{},[2361,107048],{"width":2363},[2361,107050,107051],{},[895,107052,107053,107061,107063,107065,107067,107069,107077,107079],{},[28285,107054,107055,107057,107059],{},[898,107056,900],{},[2148,107058,2701],{},[1706,107060,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,107062,8922],{},[2148,107064,2150],{},[1706,107066,2505],{"separator":2504},[4898,107068],{"width":4900},[28285,107070,107071,107073,107075],{},[898,107072,900],{},[2148,107074,2495],{},[1706,107076,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,107078,8922],{},[2148,107080,31567],{},[2361,107082],{"width":2363},[2361,107084,107085],{},[2415,107086,107087],{},"(6.4)",[902,107089,107090],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,107092,107093,107094,107096],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,107095,71714],{}," — užitečnost roste s množstvím každého zboží.",[724,107098,107099,107102,107103,107133,107134,4288],{},[38,107100,107101],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,107104,107106],{"className":107105},[886],[888,107107,107108],{"xmlns":890},[892,107109,107110,107130],{},[895,107111,107112,107120,107122],{},[28285,107113,107114,107116,107118],{},[898,107115,900],{},[2148,107117,2701],{},[1706,107119,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,107121,2505],{"separator":2504},[28285,107123,107124,107126,107128],{},[898,107125,900],{},[2148,107127,2495],{},[1706,107129,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,107131,107132],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,107135,107136],{},"záporné",[883,107138,107140],{"className":107139},[886],[888,107141,107142],{"xmlns":890,"display":2350},[892,107143,107144,107197],{},[2354,107145,107146],{"width":2356},[2358,107147,107148,107150,107190,107192],{},[2361,107149],{"width":2363},[2361,107151,107152],{},[895,107153,107154,107166,107168,107170,107172,107174,107186,107188],{},[28285,107155,107156,107158,107160],{},[898,107157,900],{},[2148,107159,22094],{},[895,107161,107162,107164],{},[1706,107163,3142],{"mathvariant":2409},[1706,107165,3142],{"mathvariant":2409},[1706,107167,2539],{},[2148,107169,2150],{},[1706,107171,2505],{"separator":2504},[4898,107173],{"width":4900},[28285,107175,107176,107178,107180],{},[898,107177,900],{},[2148,107179,51608],{},[895,107181,107182,107184],{},[1706,107183,3142],{"mathvariant":2409},[1706,107185,3142],{"mathvariant":2409},[1706,107187,2539],{},[2148,107189,31567],{},[2361,107191],{"width":2363},[2361,107193,107194],{},[2415,107195,107196],{},"(6.5)",[902,107198,107199],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,107201,107202,107203,107206,107207,1837],{},"Podmínka (6.5) je známa jako ",[38,107204,107205],{},"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 ",[207,107208,107210],{"className":107209,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,107212,107213,107214,1993,107246,107278,107279,1993,107305,107331,107332,107360,107361,1993,107363,107365,107366,107401],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,107215,107217],{"className":107216},[886],[888,107218,107219],{"xmlns":890},[892,107220,107221,107243],{},[895,107222,107223,107225,107227,107233,107235,107241],{},[898,107224,900],{},[1706,107226,2140],{"stretchy":2139},[2142,107228,107229,107231],{},[898,107230,2146],{},[2148,107232,2701],{},[1706,107234,2505],{"separator":2504},[2142,107236,107237,107239],{},[898,107238,2450],{},[2148,107240,2150],{},[1706,107242,2153],{"stretchy":2139},[902,107244,107245],{"encoding":904},"U(Q_1, b_0)",[883,107247,107249],{"className":107248},[886],[888,107250,107251],{"xmlns":890},[892,107252,107253,107275],{},[895,107254,107255,107257,107259,107265,107267,107273],{},[898,107256,900],{},[1706,107258,2140],{"stretchy":2139},[2142,107260,107261,107263],{},[898,107262,207],{},[2148,107264,2150],{},[1706,107266,2505],{"separator":2504},[2142,107268,107269,107271],{},[898,107270,2146],{},[2148,107272,2495],{},[1706,107274,2153],{"stretchy":2139},[902,107276,107277],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,107280,107282],{"className":107281},[886],[888,107283,107284],{"xmlns":890},[892,107285,107286,107302],{},[895,107287,107288,107290,107292,107294,107300],{},[1706,107289,2140],{"stretchy":2139},[898,107291,900],{},[1706,107293,2505],{"separator":2504},[2142,107295,107296,107298],{},[898,107297,2146],{},[2148,107299,2701],{},[1706,107301,2153],{"stretchy":2139},[902,107303,107304],{"encoding":904},"(U, Q_1)",[883,107306,107308],{"className":107307},[886],[888,107309,107310],{"xmlns":890},[892,107311,107312,107328],{},[895,107313,107314,107316,107318,107320,107326],{},[1706,107315,2140],{"stretchy":2139},[898,107317,900],{},[1706,107319,2505],{"separator":2504},[2142,107321,107322,107324],{},[898,107323,2146],{},[2148,107325,2495],{},[1706,107327,2153],{"stretchy":2139},[902,107329,107330],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,107333,107335],{"className":107334},[886],[888,107336,107337],{"xmlns":890},[892,107338,107339,107357],{},[895,107340,107341,107343,107345,107347,107349,107351,107353,107355],{},[898,107342,900],{},[1706,107344,2140],{"stretchy":2139},[2148,107346,2150],{},[1706,107348,2505],{"separator":2504},[2148,107350,2150],{},[1706,107352,2153],{"stretchy":2139},[1706,107354,1708],{},[2148,107356,2150],{},[902,107358,107359],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,107362,32764],{},[38,107364,57543],{},". Typický tvar grafu ",[883,107367,107369],{"className":107368},[886],[888,107370,107371],{"xmlns":890},[892,107372,107373,107399],{},[895,107374,107375,107377,107379,107381,107383,107389,107391,107397],{},[898,107376,900],{},[1706,107378,1708],{},[898,107380,900],{},[1706,107382,2140],{"stretchy":2139},[2142,107384,107385,107387],{},[898,107386,2146],{},[2148,107388,2701],{},[1706,107390,2505],{"separator":2504},[2142,107392,107393,107395],{},[898,107394,2146],{},[2148,107396,2495],{},[1706,107398,2153],{"stretchy":2139},[902,107400,105415],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,107403,107404],{},[614,107405,107406,107407,106447,107435,107456,107457,106447,107485,107507],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,107408,107410],{"className":107409},[886],[888,107411,107412],{"xmlns":890},[892,107413,107414,107432],{},[895,107415,107416,107418,107420,107426,107428,107430],{},[898,107417,900],{},[1706,107419,2140],{"stretchy":2139},[2142,107421,107422,107424],{},[898,107423,2146],{},[2148,107425,2701],{},[1706,107427,2505],{"separator":2504},[898,107429,2450],{},[1706,107431,2153],{"stretchy":2139},[902,107433,107434],{"encoding":904},"U(Q_1, b)",[883,107436,107438],{"className":107437},[886],[888,107439,107440],{"xmlns":890},[892,107441,107442,107454],{},[895,107443,107444,107450,107452],{},[2142,107445,107446,107448],{},[898,107447,2146],{},[2148,107449,2495],{},[1706,107451,1708],{},[898,107453,2450],{},[902,107455,106469],{"encoding":904}," (vlevo) a ",[883,107458,107460],{"className":107459},[886],[888,107461,107462],{"xmlns":890},[892,107463,107464,107482],{},[895,107465,107466,107468,107470,107472,107474,107480],{},[898,107467,900],{},[1706,107469,2140],{"stretchy":2139},[898,107471,207],{},[1706,107473,2505],{"separator":2504},[2142,107475,107476,107478],{},[898,107477,2146],{},[2148,107479,2495],{},[1706,107481,2153],{"stretchy":2139},[902,107483,107484],{"encoding":904},"U(a, Q_2)",[883,107486,107488],{"className":107487},[886],[888,107489,107490],{"xmlns":890},[892,107491,107492,107504],{},[895,107493,107494,107500,107502],{},[2142,107495,107496,107498],{},[898,107497,2146],{},[2148,107499,2701],{},[1706,107501,1708],{},[898,107503,207],{},[902,107505,107506],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,107509,107510],{},[614,107511,107512,107513,107548,107549,107579,107580,1993,107603,107625,107626,1837],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,107514,107516],{"className":107515},[886],[888,107517,107518],{"xmlns":890},[892,107519,107520,107546],{},[895,107521,107522,107524,107526,107528,107530,107536,107538,107544],{},[898,107523,900],{},[1706,107525,1708],{},[898,107527,900],{},[1706,107529,2140],{"stretchy":2139},[2142,107531,107532,107534],{},[898,107533,2146],{},[2148,107535,2701],{},[1706,107537,2505],{"separator":2504},[2142,107539,107540,107542],{},[898,107541,2146],{},[2148,107543,2495],{},[1706,107545,2153],{"stretchy":2139},[902,107547,105415],{"encoding":904}," nad rovinou ",[883,107550,107552],{"className":107551},[886],[888,107553,107554],{"xmlns":890},[892,107555,107556,107576],{},[895,107557,107558,107560,107566,107568,107574],{},[1706,107559,2140],{"stretchy":2139},[2142,107561,107562,107564],{},[898,107563,2146],{},[2148,107565,2701],{},[1706,107567,2505],{"separator":2504},[2142,107569,107570,107572],{},[898,107571,2146],{},[2148,107573,2495],{},[1706,107575,2153],{"stretchy":2139},[902,107577,107578],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,107581,107583],{"className":107582},[886],[888,107584,107585],{"xmlns":890},[892,107586,107587,107600],{},[895,107588,107589,107595,107597],{},[2142,107590,107591,107593],{},[898,107592,2146],{},[2148,107594,2701],{},[1706,107596,1708],{},[2415,107598,107599],{},"const",[902,107601,107602],{"encoding":904},"Q_1 = \\text{const}",[883,107604,107606],{"className":107605},[886],[888,107607,107608],{"xmlns":890},[892,107609,107610,107622],{},[895,107611,107612,107618,107620],{},[2142,107613,107614,107616],{},[898,107615,2146],{},[2148,107617,2495],{},[1706,107619,1708],{},[2415,107621,107599],{},[902,107623,107624],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,107627,107629],{"className":107628},[886],[888,107630,107631],{"xmlns":890},[892,107632,107633,107659],{},[895,107634,107635,107637,107639,107645,107647,107653,107655,107657],{},[898,107636,900],{},[1706,107638,2140],{"stretchy":2139},[2142,107640,107641,107643],{},[898,107642,2146],{},[2148,107644,2701],{},[1706,107646,2505],{"separator":2504},[2142,107648,107649,107651],{},[898,107650,2146],{},[2148,107652,2495],{},[1706,107654,2153],{"stretchy":2139},[1706,107656,1708],{},[898,107658,20413],{},[902,107660,28884],{"encoding":904},[198,107662,107664,107665],{"id":107663},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,107666,107668],{"className":107667},[886],[888,107669,107670],{"xmlns":890},[892,107671,107672,107706],{},[895,107673,107674,107676,107678,107692],{},[898,107675,900],{},[1706,107677,1708],{},[28285,107679,107680,107682,107684],{},[898,107681,2146],{},[2148,107683,2701],{},[895,107685,107686,107688,107690],{},[2148,107687,2701],{},[898,107689,15493],{"mathvariant":2409},[2148,107691,2495],{},[28285,107693,107694,107696,107698],{},[898,107695,2146],{},[2148,107697,2495],{},[895,107699,107700,107702,107704],{},[2148,107701,2701],{},[898,107703,15493],{"mathvariant":2409},[2148,107705,4284],{},[902,107707,107708],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,107710,107711],{},[38,107712,107713],{},"Ověření (6.4) a (6.5).",[883,107715,107717],{"className":107716},[886],[888,107718,107719],{"xmlns":890,"display":2350},[892,107720,107721,107825],{},[895,107722,107723,107731,107733,107741,107757,107771,107773,107775,107783,107785,107793,107807,107823],{},[28285,107724,107725,107727,107729],{},[898,107726,900],{},[2148,107728,2701],{},[1706,107730,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,107732,1708],{},[4745,107734,107735],{"scriptlevel":2150,"displaystyle":2139},[2964,107736,107737,107739],{},[2148,107738,2701],{},[2148,107740,2495],{},[28285,107742,107743,107745,107747],{},[898,107744,2146],{},[2148,107746,2701],{},[895,107748,107749,107751,107753,107755],{},[1706,107750,1715],{},[2148,107752,2701],{},[898,107754,15493],{"mathvariant":2409},[2148,107756,2495],{},[28285,107758,107759,107761,107763],{},[898,107760,2146],{},[2148,107762,2495],{},[895,107764,107765,107767,107769],{},[2148,107766,2701],{},[898,107768,15493],{"mathvariant":2409},[2148,107770,4284],{},[1706,107772,2505],{"separator":2504},[4898,107774],{"width":4900},[28285,107776,107777,107779,107781],{},[898,107778,900],{},[2148,107780,2495],{},[1706,107782,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,107784,1708],{},[4745,107786,107787],{"scriptlevel":2150,"displaystyle":2139},[2964,107788,107789,107791],{},[2148,107790,2701],{},[2148,107792,4284],{},[28285,107794,107795,107797,107799],{},[898,107796,2146],{},[2148,107798,2701],{},[895,107800,107801,107803,107805],{},[2148,107802,2701],{},[898,107804,15493],{"mathvariant":2409},[2148,107806,2495],{},[28285,107808,107809,107811,107813],{},[898,107810,2146],{},[2148,107812,2495],{},[895,107814,107815,107817,107819,107821],{},[1706,107816,1715],{},[2148,107818,2495],{},[898,107820,15493],{"mathvariant":2409},[2148,107822,4284],{},[1706,107824,2505],{"separator":2504},[902,107826,107827],{"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},",[724,107829,107830,107831,107865],{},"zřejmě ",[883,107832,107834],{"className":107833},[886],[888,107835,107836],{"xmlns":890},[892,107837,107838,107862],{},[895,107839,107840,107848,107850,107858,107860],{},[28285,107841,107842,107844,107846],{},[898,107843,900],{},[2148,107845,2701],{},[1706,107847,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,107849,2505],{"separator":2504},[28285,107851,107852,107854,107856],{},[898,107853,900],{},[2148,107855,2495],{},[1706,107857,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,107859,8922],{},[2148,107861,2150],{},[902,107863,107864],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,107867,107869],{"className":107868},[886],[888,107870,107871],{"xmlns":890,"display":2350},[892,107872,107873,107989],{},[895,107874,107875,107887,107889,107891,107899,107915,107929,107931,107933,107945,107947,107949,107957,107971,107987],{},[28285,107876,107877,107879,107881],{},[898,107878,900],{},[2148,107880,22094],{},[895,107882,107883,107885],{},[1706,107884,3142],{"mathvariant":2409},[1706,107886,3142],{"mathvariant":2409},[1706,107888,1708],{},[1706,107890,1715],{},[4745,107892,107893],{"scriptlevel":2150,"displaystyle":2139},[2964,107894,107895,107897],{},[2148,107896,2701],{},[2148,107898,3455],{},[28285,107900,107901,107903,107905],{},[898,107902,2146],{},[2148,107904,2701],{},[895,107906,107907,107909,107911,107913],{},[1706,107908,1715],{},[2148,107910,4284],{},[898,107912,15493],{"mathvariant":2409},[2148,107914,2495],{},[28285,107916,107917,107919,107921],{},[898,107918,2146],{},[2148,107920,2495],{},[895,107922,107923,107925,107927],{},[2148,107924,2701],{},[898,107926,15493],{"mathvariant":2409},[2148,107928,4284],{},[1706,107930,2505],{"separator":2504},[4898,107932],{"width":4900},[28285,107934,107935,107937,107939],{},[898,107936,900],{},[2148,107938,51608],{},[895,107940,107941,107943],{},[1706,107942,3142],{"mathvariant":2409},[1706,107944,3142],{"mathvariant":2409},[1706,107946,1708],{},[1706,107948,1715],{},[4745,107950,107951],{"scriptlevel":2150,"displaystyle":2139},[2964,107952,107953,107955],{},[2148,107954,2495],{},[2148,107956,10800],{},[28285,107958,107959,107961,107963],{},[898,107960,2146],{},[2148,107962,2701],{},[895,107964,107965,107967,107969],{},[2148,107966,2701],{},[898,107968,15493],{"mathvariant":2409},[2148,107970,2495],{},[28285,107972,107973,107975,107977],{},[898,107974,2146],{},[2148,107976,2495],{},[895,107978,107979,107981,107983,107985],{},[1706,107980,1715],{},[2148,107982,7524],{},[898,107984,15493],{"mathvariant":2409},[2148,107986,4284],{},[1706,107988,2505],{"separator":2504},[902,107990,107991],{"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},",[724,107993,107994,107995,108037],{},"opět ",[883,107996,107998],{"className":107997},[886],[888,107999,108000],{"xmlns":890},[892,108001,108002,108034],{},[895,108003,108004,108016,108018,108030,108032],{},[28285,108005,108006,108008,108010],{},[898,108007,900],{},[2148,108009,22094],{},[895,108011,108012,108014],{},[1706,108013,3142],{"mathvariant":2409},[1706,108015,3142],{"mathvariant":2409},[1706,108017,2505],{"separator":2504},[28285,108019,108020,108022,108024],{},[898,108021,900],{},[2148,108023,51608],{},[895,108025,108026,108028],{},[1706,108027,3142],{"mathvariant":2409},[1706,108029,3142],{"mathvariant":2409},[1706,108031,2539],{},[2148,108033,2150],{},[902,108035,108036],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,108039,108040],{},[38,108041,108042,108043,1837],{},"(a) Mezní užitečnosti v bodě ",[883,108044,108046],{"className":108045},[886],[888,108047,108048],{"xmlns":890},[892,108049,108050,108062],{},[895,108051,108052,108054,108056,108058,108060],{},[1706,108053,21693],{"stretchy":2139},[2148,108055,2590],{},[1706,108057,2505],{"separator":2504},[2148,108059,7039],{},[1706,108061,21708],{"stretchy":2139},[902,108063,108064],{"encoding":904},"[100, 200]",[883,108066,108068],{"className":108067},[886],[888,108069,108070],{"xmlns":890,"display":2350},[892,108071,108072,108139],{},[895,108073,108074,108076,108082,108084,108086,108088,108090,108092,108094,108102,108104,108118,108120,108132,108134,108137],{},[898,108075,1742],{},[2142,108077,108078,108080],{},[898,108079,900],{},[2148,108081,2701],{},[1706,108083,2140],{"stretchy":2139},[2148,108085,2590],{},[1706,108087,2505],{"separator":2504},[2148,108089,7039],{},[1706,108091,2153],{"stretchy":2139},[1706,108093,1708],{},[4745,108095,108096],{"scriptlevel":2150,"displaystyle":2139},[2964,108097,108098,108100],{},[2148,108099,2701],{},[2148,108101,2495],{},[1706,108103,2390],{},[2489,108105,108106,108108],{},[2148,108107,2590],{},[895,108109,108110,108112,108114,108116],{},[1706,108111,1715],{},[2148,108113,2701],{},[898,108115,15493],{"mathvariant":2409},[2148,108117,2495],{},[1706,108119,2390],{},[2489,108121,108122,108124],{},[2148,108123,7039],{},[895,108125,108126,108128,108130],{},[2148,108127,2701],{},[898,108129,15493],{"mathvariant":2409},[2148,108131,4284],{},[1706,108133,7883],{},[2148,108135,108136],{},"0,4204",[1706,108138,2505],{"separator":2504},[902,108140,108141],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,108143,108145],{"className":108144},[886],[888,108146,108147],{"xmlns":890,"display":2350},[892,108148,108149,108214],{},[895,108150,108151,108153,108159,108161,108163,108165,108167,108169,108171,108179,108181,108193,108195,108209,108211],{},[898,108152,1742],{},[2142,108154,108155,108157],{},[898,108156,900],{},[2148,108158,2495],{},[1706,108160,2140],{"stretchy":2139},[2148,108162,2590],{},[1706,108164,2505],{"separator":2504},[2148,108166,7039],{},[1706,108168,2153],{"stretchy":2139},[1706,108170,1708],{},[4745,108172,108173],{"scriptlevel":2150,"displaystyle":2139},[2964,108174,108175,108177],{},[2148,108176,2701],{},[2148,108178,4284],{},[1706,108180,2390],{},[2489,108182,108183,108185],{},[2148,108184,2590],{},[895,108186,108187,108189,108191],{},[2148,108188,2701],{},[898,108190,15493],{"mathvariant":2409},[2148,108192,2495],{},[1706,108194,2390],{},[2489,108196,108197,108199],{},[2148,108198,7039],{},[895,108200,108201,108203,108205,108207],{},[1706,108202,1715],{},[2148,108204,2495],{},[898,108206,15493],{"mathvariant":2409},[2148,108208,4284],{},[1706,108210,7883],{},[2148,108212,108213],{},"0,63067.",[902,108215,108216],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,108218,108219,1647,108221,108256,108257,108278,108279,108296],{},[614,108220,28335],{},[883,108222,108224],{"className":108223},[886],[888,108225,108226],{"xmlns":890},[892,108227,108228,108253],{},[895,108229,108230,108232,108238,108240,108242,108244,108246,108248,108250],{},[898,108231,1742],{},[2142,108233,108234,108236],{},[898,108235,900],{},[2148,108237,2495],{},[1706,108239,2140],{"stretchy":2139},[2148,108241,2590],{},[1706,108243,2505],{"separator":2504},[2148,108245,7039],{},[1706,108247,2153],{"stretchy":2139},[1706,108249,7883],{},[2148,108251,108252],{},"0,63067",[902,108254,108255],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,108258,108260],{"className":108259},[886],[888,108261,108262],{"xmlns":890},[892,108263,108264,108276],{},[895,108265,108266,108268,108270,108272,108274],{},[1706,108267,21693],{"stretchy":2139},[2148,108269,2590],{},[1706,108271,2505],{"separator":2504},[2148,108273,7039],{},[1706,108275,21708],{"stretchy":2139},[902,108277,108064],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,108280,108282],{"className":108281},[886],[888,108283,108284],{"xmlns":890},[892,108285,108286,108294],{},[895,108287,108288],{},[2142,108289,108290,108292],{},[898,108291,2146],{},[2148,108293,2495],{},[902,108295,48089],{"encoding":904}," přibližně o 0,63067.",[724,108298,108299,108318,108319,58239,108340,108357,108358,108384,108385,108402,108403,5606],{},[38,108300,108301,108302,108317],{},"(b) Odhad změny ",[883,108303,108305],{"className":108304},[886],[888,108306,108307],{"xmlns":890},[892,108308,108309,108315],{},[895,108310,108311,108313],{},[898,108312,3677],{"mathvariant":2409},[898,108314,900],{},[902,108316,106560],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,108320,108322],{"className":108321},[886],[888,108323,108324],{"xmlns":890},[892,108325,108326,108338],{},[895,108327,108328,108330,108332,108334,108336],{},[1706,108329,21693],{"stretchy":2139},[2148,108331,2590],{},[1706,108333,2505],{"separator":2504},[2148,108335,7039],{},[1706,108337,21708],{"stretchy":2139},[902,108339,108064],{"encoding":904},[883,108341,108343],{"className":108342},[886],[888,108344,108345],{"xmlns":890},[892,108346,108347,108355],{},[895,108348,108349],{},[2142,108350,108351,108353],{},[898,108352,2146],{},[2148,108354,2701],{},[902,108356,48070],{"encoding":904}," na 98 (tj. ",[883,108359,108361],{"className":108360},[886],[888,108362,108363],{"xmlns":890},[892,108364,108365,108381],{},[895,108366,108367,108369,108375,108377,108379],{},[898,108368,3120],{"mathvariant":2409},[2142,108370,108371,108373],{},[898,108372,2146],{},[2148,108374,2701],{},[1706,108376,1708],{},[1706,108378,1715],{},[2148,108380,2495],{},[902,108382,108383],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,108386,108388],{"className":108387},[886],[888,108389,108390],{"xmlns":890},[892,108391,108392,108400],{},[895,108393,108394],{},[2142,108395,108396,108398],{},[898,108397,2146],{},[2148,108399,2495],{},[902,108401,48089],{"encoding":904}," o 3 (tj. ",[883,108404,108406],{"className":108405},[886],[888,108407,108408],{"xmlns":890},[892,108409,108410,108424],{},[895,108411,108412,108414,108420,108422],{},[898,108413,3120],{"mathvariant":2409},[2142,108415,108416,108418],{},[898,108417,2146],{},[2148,108419,2495],{},[1706,108421,1708],{},[2148,108423,4284],{},[902,108425,108426],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,108428,108430],{"className":108429},[886],[888,108431,108432],{"xmlns":890,"display":2350},[892,108433,108434,108485],{},[895,108435,108436,108438,108440,108442,108444,108446,108448,108450,108452,108454,108456,108458,108460,108462,108464,108466,108468,108470,108472,108475,108477,108480,108482],{},[898,108437,3677],{"mathvariant":2409},[898,108439,900],{},[1706,108441,3248],{},[898,108443,3120],{"mathvariant":2409},[898,108445,900],{},[1706,108447,1708],{},[2148,108449,108136],{},[1706,108451,2390],{},[1706,108453,2140],{"stretchy":2139},[1706,108455,1715],{},[2148,108457,2495],{},[1706,108459,2153],{"stretchy":2139},[1706,108461,2447],{},[2148,108463,108252],{},[1706,108465,2390],{},[2148,108467,4284],{},[1706,108469,1708],{},[1706,108471,1715],{},[2148,108473,108474],{},"0,8408",[1706,108476,2447],{},[2148,108478,108479],{},"1,89201",[1706,108481,7883],{},[2148,108483,108484],{},"1,05.",[902,108486,108487],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,108489,108490,108491,108494,108495,108546,108547,1837],{},"Užitečnost se tedy zvýší přibližně o ",[38,108492,108493],{},"1,05",". Skutečná změna je ",[883,108496,108498],{"className":108497},[886],[888,108499,108500],{"xmlns":890},[892,108501,108502,108543],{},[895,108503,108504,108506,108508,108510,108512,108514,108517,108519,108522,108524,108526,108528,108530,108532,108534,108536,108538,108540],{},[898,108505,3677],{"mathvariant":2409},[898,108507,900],{},[1706,108509,1708],{},[898,108511,900],{},[1706,108513,2140],{"stretchy":2139},[2148,108515,108516],{},"98",[1706,108518,2505],{"separator":2504},[2148,108520,108521],{},"203",[1706,108523,2153],{"stretchy":2139},[1706,108525,1715],{},[898,108527,900],{},[1706,108529,2140],{"stretchy":2139},[2148,108531,2590],{},[1706,108533,2505],{"separator":2504},[2148,108535,7039],{},[1706,108537,2153],{"stretchy":2139},[1706,108539,7883],{},[2148,108541,108542],{},"1,031",[902,108544,108545],{"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 ",[883,108548,108550],{"className":108549},[886],[888,108551,108552],{"xmlns":890},[892,108553,108554,108574],{},[895,108555,108556,108558,108564,108566,108568],{},[898,108557,3120],{"mathvariant":2409},[2142,108559,108560,108562],{},[898,108561,2146],{},[2148,108563,2701],{},[1706,108565,2505],{"separator":2504},[898,108567,3120],{"mathvariant":2409},[2142,108569,108570,108572],{},[898,108571,2146],{},[2148,108573,2495],{},[902,108575,106590],{"encoding":904},[115,108577,108579],{"id":108578},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,108581,108582],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,108584,108586],{"className":108585},[886],[888,108587,108588],{"xmlns":890,"display":2350},[892,108589,108590,108649],{},[2354,108591,108592],{"width":2356},[2358,108593,108594,108596,108642,108644],{},[2361,108595],{"width":2363},[2361,108597,108598],{},[895,108599,108600,108602,108604,108610,108612,108618,108620,108622,108630,108632,108640],{},[898,108601,900],{},[1706,108603,2140],{"stretchy":2139},[2142,108605,108606,108608],{},[898,108607,2146],{},[2148,108609,2701],{},[1706,108611,2505],{"separator":2504},[2142,108613,108614,108616],{},[898,108615,2146],{},[2148,108617,2495],{},[1706,108619,2153],{"stretchy":2139},[1706,108621,1708],{},[28285,108623,108624,108626,108628],{},[898,108625,2146],{},[2148,108627,2701],{},[898,108629,207],{},[1706,108631,2390],{},[28285,108633,108634,108636,108638],{},[898,108635,2146],{},[2148,108637,2495],{},[898,108639,2450],{},[1706,108641,2505],{"separator":2504},[2361,108643],{"width":2363},[2361,108645,108646],{},[2415,108647,108648],{},"(6.6)",[902,108650,108651],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,108653,5331,108654,108672,108673,108675,108676,108680,108681,108711,108712,108734],{},[883,108655,108657],{"className":108656},[886],[888,108658,108659],{"xmlns":890},[892,108660,108661,108669],{},[895,108662,108663,108665,108667],{},[898,108664,207],{},[1706,108666,2505],{"separator":2504},[898,108668,2450],{},[902,108670,108671],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,108674,92658],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,108677,108679],{"className":108678,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,108682,108684],{"className":108683},[886],[888,108685,108686],{"xmlns":890},[892,108687,108688,108708],{},[895,108689,108690,108692,108694,108696,108698,108700,108702,108704,108706],{},[898,108691,207],{},[1706,108693,2505],{"separator":2504},[898,108695,2450],{},[1706,108697,25638],{},[1706,108699,2140],{"stretchy":2139},[2148,108701,2150],{},[1706,108703,2505],{"separator":2504},[2148,108705,2701],{},[1706,108707,2153],{"stretchy":2139},[902,108709,108710],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,108713,108715],{"className":108714},[886],[888,108716,108717],{"xmlns":890},[892,108718,108719,108731],{},[895,108720,108721,108723,108725,108727,108729],{},[898,108722,2450],{},[1706,108724,1708],{},[2148,108726,2701],{},[1706,108728,1715],{},[898,108730,207],{},[902,108732,108733],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,108736,108737],{},[2286,108738],{"alt":108739,"className":108740,"src":108741},"imek-cobb-douglas-3d-plus-ic",[210,2290],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,108743,108745],{"className":108744},[886],[888,108746,108747],{"xmlns":890,"display":2350},[892,108748,108749,108799],{},[895,108750,108751,108753,108755,108761,108763,108769,108771,108773,108781,108783,108797],{},[898,108752,900],{},[1706,108754,2140],{"stretchy":2139},[2142,108756,108757,108759],{},[898,108758,2146],{},[2148,108760,2701],{},[1706,108762,2505],{"separator":2504},[2142,108764,108765,108767],{},[898,108766,2146],{},[2148,108768,2495],{},[1706,108770,2153],{"stretchy":2139},[1706,108772,1708],{},[28285,108774,108775,108777,108779],{},[898,108776,2146],{},[2148,108778,2701],{},[898,108780,207],{},[1706,108782,2390],{},[28285,108784,108785,108787,108789],{},[898,108786,2146],{},[2148,108788,2495],{},[895,108790,108791,108793,108795],{},[2148,108792,2701],{},[1706,108794,1715],{},[898,108796,207],{},[898,108798,1837],{"mathvariant":2409},[902,108800,108801],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[1636,108803,108804,108853,108975,109109],{},[724,108805,108806,108808,108809],{},[883,108807,71732],{}," Příklad 6.3 — ověření vlastností pro ",[883,108810,108812],{"className":108811},[886],[888,108813,108814],{"xmlns":890},[892,108815,108816,108850],{},[895,108817,108818,108820,108822,108836],{},[898,108819,900],{},[1706,108821,1708],{},[28285,108823,108824,108826,108828],{},[898,108825,2146],{},[2148,108827,2701],{},[895,108829,108830,108832,108834],{},[2148,108831,2701],{},[898,108833,15493],{"mathvariant":2409},[2148,108835,3455],{},[28285,108837,108838,108840,108842],{},[898,108839,2146],{},[2148,108841,2495],{},[895,108843,108844,108846,108848],{},[2148,108845,4284],{},[898,108847,15493],{"mathvariant":2409},[2148,108849,3455],{},[902,108851,108852],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,108854,108856],{"className":108855},[886],[888,108857,108858],{"xmlns":890,"display":2350},[892,108859,108860,108972],{},[895,108861,108862,108870,108872,108880,108896,108910,108912,108914,108916,108918,108926,108928,108936,108950,108966,108968,108970],{},[28285,108863,108864,108866,108868],{},[898,108865,900],{},[2148,108867,2701],{},[1706,108869,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,108871,1708],{},[4745,108873,108874],{"scriptlevel":2150,"displaystyle":2139},[2964,108875,108876,108878],{},[2148,108877,2701],{},[2148,108879,3455],{},[28285,108881,108882,108884,108886],{},[898,108883,2146],{},[2148,108885,2701],{},[895,108887,108888,108890,108892,108894],{},[1706,108889,1715],{},[2148,108891,4284],{},[898,108893,15493],{"mathvariant":2409},[2148,108895,3455],{},[28285,108897,108898,108900,108902],{},[898,108899,2146],{},[2148,108901,2495],{},[895,108903,108904,108906,108908],{},[2148,108905,4284],{},[898,108907,15493],{"mathvariant":2409},[2148,108909,3455],{},[1706,108911,8922],{},[2148,108913,2150],{},[1706,108915,2505],{"separator":2504},[4898,108917],{"width":4900},[28285,108919,108920,108922,108924],{},[898,108921,900],{},[2148,108923,2495],{},[1706,108925,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,108927,1708],{},[4745,108929,108930],{"scriptlevel":2150,"displaystyle":2139},[2964,108931,108932,108934],{},[2148,108933,4284],{},[2148,108935,3455],{},[28285,108937,108938,108940,108942],{},[898,108939,2146],{},[2148,108941,2701],{},[895,108943,108944,108946,108948],{},[2148,108945,2701],{},[898,108947,15493],{"mathvariant":2409},[2148,108949,3455],{},[28285,108951,108952,108954,108956],{},[898,108953,2146],{},[2148,108955,2495],{},[895,108957,108958,108960,108962,108964],{},[1706,108959,1715],{},[2148,108961,2701],{},[898,108963,15493],{"mathvariant":2409},[2148,108965,3455],{},[1706,108967,8922],{},[2148,108969,2150],{},[1706,108971,2505],{"separator":2504},[902,108973,108974],{"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,",[883,108976,108978],{"className":108977},[886],[888,108979,108980],{"xmlns":890,"display":2350},[892,108981,108982,109106],{},[895,108983,108984,108996,108998,109000,109008,109024,109038,109040,109042,109044,109046,109058,109060,109062,109070,109084,109100,109102,109104],{},[28285,108985,108986,108988,108990],{},[898,108987,900],{},[2148,108989,22094],{},[895,108991,108992,108994],{},[1706,108993,3142],{"mathvariant":2409},[1706,108995,3142],{"mathvariant":2409},[1706,108997,1708],{},[1706,108999,1715],{},[4745,109001,109002],{"scriptlevel":2150,"displaystyle":2139},[2964,109003,109004,109006],{},[2148,109005,4284],{},[2148,109007,3364],{},[28285,109009,109010,109012,109014],{},[898,109011,2146],{},[2148,109013,2701],{},[895,109015,109016,109018,109020,109022],{},[1706,109017,1715],{},[2148,109019,12597],{},[898,109021,15493],{"mathvariant":2409},[2148,109023,3455],{},[28285,109025,109026,109028,109030],{},[898,109027,2146],{},[2148,109029,2495],{},[895,109031,109032,109034,109036],{},[2148,109033,4284],{},[898,109035,15493],{"mathvariant":2409},[2148,109037,3455],{},[1706,109039,2539],{},[2148,109041,2150],{},[1706,109043,2505],{"separator":2504},[4898,109045],{"width":4900},[28285,109047,109048,109050,109052],{},[898,109049,900],{},[2148,109051,51608],{},[895,109053,109054,109056],{},[1706,109055,3142],{"mathvariant":2409},[1706,109057,3142],{"mathvariant":2409},[1706,109059,1708],{},[1706,109061,1715],{},[4745,109063,109064],{"scriptlevel":2150,"displaystyle":2139},[2964,109065,109066,109068],{},[2148,109067,4284],{},[2148,109069,3364],{},[28285,109071,109072,109074,109076],{},[898,109073,2146],{},[2148,109075,2701],{},[895,109077,109078,109080,109082],{},[2148,109079,2701],{},[898,109081,15493],{"mathvariant":2409},[2148,109083,3455],{},[28285,109085,109086,109088,109090],{},[898,109087,2146],{},[2148,109089,2495],{},[895,109091,109092,109094,109096,109098],{},[1706,109093,1715],{},[2148,109095,7524],{},[898,109097,15493],{"mathvariant":2409},[2148,109099,3455],{},[1706,109101,2539],{},[2148,109103,2150],{},[1706,109105,2505],{"separator":2504},[902,109107,109108],{"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,",[724,109110,109111],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,109113,109115],{"id":109114},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,109117,109118,109121],{},[38,109119,109120],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,109123,109125],{"className":109124},[886],[888,109126,109127],{"xmlns":890,"display":2350},[892,109128,109129,109172],{},[2354,109130,109131],{"width":2356},[2358,109132,109133,109135,109165,109167],{},[2361,109134],{"width":2363},[2361,109136,109137],{},[895,109138,109139,109141,109143,109149,109151,109157,109159,109161,109163],{},[898,109140,900],{},[1706,109142,2140],{"stretchy":2139},[2142,109144,109145,109147],{},[898,109146,2146],{},[2148,109148,2701],{},[1706,109150,2505],{"separator":2504},[2142,109152,109153,109155],{},[898,109154,2146],{},[2148,109156,2495],{},[1706,109158,2153],{"stretchy":2139},[1706,109160,1708],{},[898,109162,20413],{},[1706,109164,2505],{"separator":2504},[2361,109166],{"width":2363},[2361,109168,109169],{},[2415,109170,109171],{},"(6.7)",[902,109173,109174],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,109176,5331,109177,109190],{},[883,109178,109180],{"className":109179},[886],[888,109181,109182],{"xmlns":890},[892,109183,109184,109188],{},[895,109185,109186],{},[898,109187,20413],{},[902,109189,20413],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,109192,109194],{"className":109193},[886],[888,109195,109196],{"xmlns":890,"display":2350},[892,109197,109198,109239],{},[2354,109199,109200],{"width":2356},[2358,109201,109202,109204,109232,109234],{},[2361,109203],{"width":2363},[2361,109205,109206],{},[895,109207,109208,109216,109218,109226,109228,109230],{},[28285,109209,109210,109212,109214],{},[898,109211,2146],{},[2148,109213,2701],{},[898,109215,207],{},[1706,109217,2390],{},[28285,109219,109220,109222,109224],{},[898,109221,2146],{},[2148,109223,2495],{},[898,109225,2450],{},[1706,109227,1708],{},[898,109229,20413],{},[898,109231,1837],{"mathvariant":2409},[2361,109233],{"width":2363},[2361,109235,109236],{},[2415,109237,109238],{},"(6.8)",[902,109240,109241],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,109243,109244,109245,3526,109275,1647,109278,109291,109292,109327,109328,109345,109346,109375,109376,109379],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,109246,109248],{"className":109247},[886],[888,109249,109250],{"xmlns":890},[892,109251,109252,109272],{},[895,109253,109254,109256,109262,109264,109270],{},[1706,109255,21693],{"stretchy":2139},[2142,109257,109258,109260],{},[898,109259,2146],{},[2148,109261,2701],{},[1706,109263,2505],{"separator":2504},[2142,109265,109266,109268],{},[898,109267,2146],{},[2148,109269,2495],{},[1706,109271,21708],{"stretchy":2139},[902,109273,109274],{"encoding":904},"[Q_1, Q_2]",[38,109276,109277],{},"stejnou úrovní uspokojení",[883,109279,109281],{"className":109280},[886],[888,109282,109283],{"xmlns":890},[892,109284,109285,109289],{},[895,109286,109287],{},[898,109288,20413],{},[902,109290,20413],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,109293,109295],{"className":109294},[886],[888,109296,109297],{"xmlns":890},[892,109298,109299,109325],{},[895,109300,109301,109303,109305,109307,109309,109315,109317,109323],{},[898,109302,900],{},[1706,109304,1708],{},[898,109306,900],{},[1706,109308,2140],{"stretchy":2139},[2142,109310,109311,109313],{},[898,109312,2146],{},[2148,109314,2701],{},[1706,109316,2505],{"separator":2504},[2142,109318,109319,109321],{},[898,109320,2146],{},[2148,109322,2495],{},[1706,109324,2153],{"stretchy":2139},[902,109326,105415],{"encoding":904}," s rovinami ",[883,109329,109331],{"className":109330},[886],[888,109332,109333],{"xmlns":890},[892,109334,109335,109343],{},[895,109336,109337,109339,109341],{},[898,109338,900],{},[1706,109340,1708],{},[898,109342,20413],{},[902,109344,104631],{"encoding":904}," rovnoběžnými s rovinou ",[883,109347,109349],{"className":109348},[886],[888,109350,109351],{"xmlns":890},[892,109352,109353,109373],{},[895,109354,109355,109357,109363,109365,109371],{},[1706,109356,2140],{"stretchy":2139},[2142,109358,109359,109361],{},[898,109360,2146],{},[2148,109362,2701],{},[1706,109364,2505],{"separator":2504},[2142,109366,109367,109369],{},[898,109368,2146],{},[2148,109370,2495],{},[1706,109372,2153],{"stretchy":2139},[902,109374,107578],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,109377,109378],{},"izokvantami"," produkčních funkcí.",[724,109381,109382],{},[614,109383,109384,109385,107456,109403,109421,109422,1837],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,109386,109388],{"className":109387},[886],[888,109389,109390],{"xmlns":890},[892,109391,109392,109400],{},[895,109393,109394,109396,109398],{},[898,109395,207],{},[1706,109397,2539],{},[898,109399,2450],{},[902,109401,109402],{"encoding":904},"a \u003C b",[883,109404,109406],{"className":109405},[886],[888,109407,109408],{"xmlns":890},[892,109409,109410,109418],{},[895,109411,109412,109414,109416],{},[898,109413,207],{},[1706,109415,8922],{},[898,109417,2450],{},[902,109419,109420],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,109423,109425],{"className":109424},[886],[888,109426,109427],{"xmlns":890},[892,109428,109429,109453],{},[895,109430,109431,109437,109439,109445,109447],{},[2142,109432,109433,109435],{},[898,109434,20413],{},[2148,109436,2150],{},[1706,109438,2539],{},[2142,109440,109441,109443],{},[898,109442,20413],{},[2148,109444,2701],{},[1706,109446,2539],{},[2142,109448,109449,109451],{},[898,109450,20413],{},[2148,109452,2495],{},[902,109454,109455],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,109457,109458],{},[614,109459,109460,109461,109490,109491,109549,109550,109568],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,109462,109464],{"className":109463},[886],[888,109465,109466],{"xmlns":890},[892,109467,109468,109488],{},[895,109469,109470,109472,109478,109480,109486],{},[1706,109471,2140],{"stretchy":2139},[2142,109473,109474,109476],{},[898,109475,2146],{},[2148,109477,2701],{},[1706,109479,2505],{"separator":2504},[2142,109481,109482,109484],{},[898,109483,2146],{},[2148,109485,2495],{},[1706,109487,2153],{"stretchy":2139},[902,109489,107578],{"encoding":904},"; body ",[883,109492,109494],{"className":109493},[886],[888,109495,109496],{"xmlns":890},[892,109497,109498,109546],{},[895,109499,109500,109502,109504,109506,109512,109514,109520,109522,109524,109526,109528,109530,109536,109538,109544],{},[898,109501,1735],{},[1706,109503,1708],{},[1706,109505,21693],{"stretchy":2139},[2142,109507,109508,109510],{},[898,109509,207],{},[2148,109511,2701],{},[1706,109513,2505],{"separator":2504},[2142,109515,109516,109518],{},[898,109517,207],{},[2148,109519,2495],{},[1706,109521,21708],{"stretchy":2139},[1706,109523,2505],{"separator":2504},[898,109525,10315],{},[1706,109527,1708],{},[1706,109529,21693],{"stretchy":2139},[2142,109531,109532,109534],{},[898,109533,2450],{},[2148,109535,2701],{},[1706,109537,2505],{"separator":2504},[2142,109539,109540,109542],{},[898,109541,2450],{},[2148,109543,2495],{},[1706,109545,21708],{"stretchy":2139},[902,109547,109548],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,109551,109553],{"className":109552},[886],[888,109554,109555],{"xmlns":890},[892,109556,109557,109565],{},[895,109558,109559,109561,109563],{},[898,109560,1683],{},[1706,109562,2505],{"separator":2504},[898,109564,2334],{},[902,109566,109567],{"encoding":904},"C, D"," na vyšší hladině.",[1636,109570,109571],{},[724,109572,109573,109575,109576,109638,109639,109683,109684,109718,109719,8186,109737,109718,109791,8186,109809,109885],{},[883,109574,71732],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,109577,109579],{"className":109578},[886],[888,109580,109581],{"xmlns":890},[892,109582,109583,109635],{},[895,109584,109585,109587,109589,109595,109597,109603,109605,109607,109621],{},[898,109586,900],{},[1706,109588,2140],{"stretchy":2139},[2142,109590,109591,109593],{},[898,109592,2146],{},[2148,109594,2701],{},[1706,109596,2505],{"separator":2504},[2142,109598,109599,109601],{},[898,109600,2146],{},[2148,109602,2495],{},[1706,109604,2153],{"stretchy":2139},[1706,109606,1708],{},[28285,109608,109609,109611,109613],{},[898,109610,2146],{},[2148,109612,2701],{},[895,109614,109615,109617,109619],{},[2148,109616,2701],{},[898,109618,15493],{"mathvariant":2409},[2148,109620,3455],{},[28285,109622,109623,109625,109627],{},[898,109624,2146],{},[2148,109626,2495],{},[895,109628,109629,109631,109633],{},[2148,109630,4284],{},[898,109632,15493],{"mathvariant":2409},[2148,109634,3455],{},[902,109636,109637],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,109640,109642],{"className":109641},[886],[888,109643,109644],{"xmlns":890},[892,109645,109646,109680],{},[895,109647,109648,109662,109676,109678],{},[28285,109649,109650,109652,109654],{},[898,109651,2146],{},[2148,109653,2701],{},[895,109655,109656,109658,109660],{},[2148,109657,2701],{},[898,109659,15493],{"mathvariant":2409},[2148,109661,3455],{},[28285,109663,109664,109666,109668],{},[898,109665,2146],{},[2148,109667,2495],{},[895,109669,109670,109672,109674],{},[2148,109671,4284],{},[898,109673,15493],{"mathvariant":2409},[2148,109675,3455],{},[1706,109677,1708],{},[898,109679,20413],{},[902,109681,109682],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,109685,109687],{"className":109686},[886],[888,109688,109689],{"xmlns":890},[892,109690,109691,109715],{},[895,109692,109693,109699,109707,109709],{},[2142,109694,109695,109697],{},[898,109696,2146],{},[2148,109698,2701],{},[28285,109700,109701,109703,109705],{},[898,109702,2146],{},[2148,109704,2495],{},[2148,109706,4284],{},[1706,109708,1708],{},[2489,109710,109711,109713],{},[898,109712,20413],{},[2148,109714,3455],{},[902,109716,109717],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,109720,109722],{"className":109721},[886],[888,109723,109724],{"xmlns":890},[892,109725,109726,109734],{},[895,109727,109728,109730,109732],{},[898,109729,20413],{},[1706,109731,1708],{},[2148,109733,2701],{},[902,109735,109736],{"encoding":904},"c = 1",[883,109738,109740],{"className":109739},[886],[888,109741,109742],{"xmlns":890},[892,109743,109744,109788],{},[895,109745,109746,109752,109754,109770,109772],{},[2142,109747,109748,109750],{},[898,109749,2146],{},[2148,109751,2495],{},[1706,109753,1708],{},[28285,109755,109756,109758,109760],{},[898,109757,2146],{},[2148,109759,2701],{},[895,109761,109762,109764,109766,109768],{},[1706,109763,1715],{},[2148,109765,2701],{},[898,109767,15493],{"mathvariant":2409},[2148,109769,4284],{},[1706,109771,1708],{},[4745,109773,109774],{"scriptlevel":2150,"displaystyle":2504},[2964,109775,109776,109778],{},[2148,109777,2701],{},[99986,109779,109780,109786],{},[2142,109781,109782,109784],{},[898,109783,2146],{},[2148,109785,2701],{},[2148,109787,4284],{},[902,109789,109790],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,109792,109794],{"className":109793},[886],[888,109795,109796],{"xmlns":890},[892,109797,109798,109806],{},[895,109799,109800,109802,109804],{},[898,109801,20413],{},[1706,109803,1708],{},[2148,109805,2495],{},[902,109807,109808],{"encoding":904},"c = 2",[883,109810,109812],{"className":109811},[886],[888,109813,109814],{"xmlns":890},[892,109815,109816,109882],{},[895,109817,109818,109824,109826,109838,109840,109856,109858],{},[2142,109819,109820,109822],{},[898,109821,2146],{},[2148,109823,2495],{},[1706,109825,1708],{},[2489,109827,109828,109830],{},[2148,109829,2495],{},[895,109831,109832,109834,109836],{},[2148,109833,3455],{},[898,109835,15493],{"mathvariant":2409},[2148,109837,4284],{},[1706,109839,2390],{},[28285,109841,109842,109844,109846],{},[898,109843,2146],{},[2148,109845,2701],{},[895,109847,109848,109850,109852,109854],{},[1706,109849,1715],{},[2148,109851,2701],{},[898,109853,15493],{"mathvariant":2409},[2148,109855,4284],{},[1706,109857,1708],{},[4745,109859,109860],{"scriptlevel":2150,"displaystyle":2504},[2964,109861,109862,109872],{},[895,109863,109864,109866],{},[2148,109865,2495],{},[99986,109867,109868,109870],{},[2148,109869,2495],{},[2148,109871,4284],{},[99986,109873,109874,109880],{},[2142,109875,109876,109878],{},[898,109877,2146],{},[2148,109879,2701],{},[2148,109881,4284],{},[902,109883,109884],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,109887,109889],{"id":109888},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,109891,109892],{},[2286,109893],{"alt":109894,"className":109895,"src":109896},"imek-ic-4vlastnosti-anotovane",[210,2290],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[1636,109898,109899,109908,109955,109999,110005,110011],{},[724,109900,109901,109903,109904,109907],{},[883,109902,9276],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,109905,109906],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,109909,109910],{},[883,109911,109913],{"className":109912},[886],[888,109914,109915],{"xmlns":890},[892,109916,109917,109952],{},[895,109918,109919,109922,109924,109926,109928,109930,109948,109950],{},[898,109920,109921],{"mathvariant":2409},"tg",[1706,109923,2773],{},[898,109925,6307],{},[1706,109927,1708],{},[1706,109929,1715],{},[2964,109931,109932,109940],{},[28285,109933,109934,109936,109938],{},[898,109935,900],{},[2148,109937,2701],{},[1706,109939,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[28285,109941,109942,109944,109946],{},[898,109943,900],{},[2148,109945,2495],{},[1706,109947,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,109949,2539],{},[2148,109951,2150],{},[902,109953,109954],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,109956,109957,109958,109998],{},"(derivace implicitně zadané funkce ",[883,109959,109961],{"className":109960},[886],[888,109962,109963],{"xmlns":890},[892,109964,109965,109995],{},[895,109966,109967,109969,109971,109977,109979,109985,109987,109989,109991,109993],{},[898,109968,900],{},[1706,109970,2140],{"stretchy":2139},[2142,109972,109973,109975],{},[898,109974,2146],{},[2148,109976,2701],{},[1706,109978,2505],{"separator":2504},[2142,109980,109981,109983],{},[898,109982,2146],{},[2148,109984,2495],{},[1706,109986,2153],{"stretchy":2139},[1706,109988,1715],{},[898,109990,20413],{},[1706,109992,1708],{},[2148,109994,2150],{},[902,109996,109997],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,110000,110001,110004],{},[38,110002,110003],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,110006,110007,110010],{},[38,110008,110009],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,110012,110013,110016,110017,110035,110036,110052,110053,110056],{},[38,110014,110015],{},"4° Konvexní."," Pro každé dva body ",[883,110018,110020],{"className":110019},[886],[888,110021,110022],{"xmlns":890},[892,110023,110024,110032],{},[895,110025,110026,110028,110030],{},[898,110027,1735],{},[1706,110029,2505],{"separator":2504},[898,110031,10315],{},[902,110033,110034],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,110037,110039],{"className":110038},[886],[888,110040,110041],{"xmlns":890},[892,110042,110043,110049],{},[895,110044,110045,110047],{},[898,110046,1735],{},[898,110048,10315],{},[902,110050,110051],{"encoding":904},"AB"," ve ",[38,110054,110055],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,110058,110059],{},[614,110060,110061,110062,110097,110098,1837],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,110063,110065],{"className":110064},[886],[888,110066,110067],{"xmlns":890},[892,110068,110069,110095],{},[895,110070,110071,110073,110075,110081,110083,110089,110091,110093],{},[898,110072,900],{},[1706,110074,2140],{"stretchy":2139},[2142,110076,110077,110079],{},[898,110078,2146],{},[2148,110080,2701],{},[1706,110082,2505],{"separator":2504},[2142,110084,110085,110087],{},[898,110086,2146],{},[2148,110088,2495],{},[1706,110090,2153],{"stretchy":2139},[1706,110092,1708],{},[898,110094,20413],{},[902,110096,28884],{"encoding":904}," s tečnou se sklonem ",[883,110099,110101],{"className":110100},[886],[888,110102,110103],{"xmlns":890},[892,110104,110105,110113],{},[895,110106,110107,110109,110111],{},[898,110108,109921],{"mathvariant":2409},[1706,110110,2773],{},[898,110112,6307],{},[902,110114,110115],{"encoding":904},"\\operatorname{tg}\\alpha",[115,110117,110119],{"id":110118},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,110121,110122,1647,110125,2314,110138,110141],{},[38,110123,110124],{},"Mezní míra komoditní substituce",[883,110126,110128],{"className":110127},[886],[888,110129,110130],{"xmlns":890},[892,110131,110132,110136],{},[895,110133,110134],{},[2415,110135,29714],{},[902,110137,47306],{"encoding":904},[38,110139,110140],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,110143,110145],{"className":110144},[886],[888,110146,110147],{"xmlns":890,"display":2350},[892,110148,110149,110236],{},[2354,110150,110151],{"width":2356},[2358,110152,110153,110155,110229,110231],{},[2361,110154],{"width":2363},[2361,110156,110157],{},[895,110158,110159,110161,110163,110165,110167,110173,110175,110181,110183,110185,110207,110209,110227],{},[2415,110160,29714],{},[1706,110162,1708],{},[2415,110164,29714],{},[1706,110166,2140],{"stretchy":2139},[2142,110168,110169,110171],{},[898,110170,2146],{},[2148,110172,2701],{},[1706,110174,2505],{"separator":2504},[2142,110176,110177,110179],{},[898,110178,2146],{},[2148,110180,2495],{},[1706,110182,2153],{"stretchy":2139},[1706,110184,1708],{},[2964,110186,110187,110197],{},[895,110188,110189,110191],{},[898,110190,1742],{},[2142,110192,110193,110195],{},[898,110194,900],{},[2148,110196,2701],{},[895,110198,110199,110201],{},[898,110200,1742],{},[2142,110202,110203,110205],{},[898,110204,900],{},[2148,110206,2495],{},[1706,110208,1708],{},[2964,110210,110211,110219],{},[28285,110212,110213,110215,110217],{},[898,110214,900],{},[2148,110216,2701],{},[1706,110218,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[28285,110220,110221,110223,110225],{},[898,110222,900],{},[2148,110224,2495],{},[1706,110226,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[898,110228,1837],{"mathvariant":2409},[2361,110230],{"width":2363},[2361,110232,110233],{},[2415,110234,110235],{},"(6.9)",[902,110237,110238],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,110240,110241,110242,110276,110277,110309,110310,110345,110346,110359],{},"Geometricky: ",[883,110243,110245],{"className":110244},[886],[888,110246,110247],{"xmlns":890},[892,110248,110249,110273],{},[895,110250,110251,110253],{},[1706,110252,1715],{},[4745,110254,110255],{"scriptlevel":2150,"displaystyle":2139},[2964,110256,110257,110265],{},[28285,110258,110259,110261,110263],{},[898,110260,900],{},[2148,110262,2701],{},[1706,110264,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[28285,110266,110267,110269,110271],{},[898,110268,900],{},[2148,110270,2495],{},[1706,110272,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,110274,110275],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,110278,110280],{"className":110279},[886],[888,110281,110282],{"xmlns":890},[892,110283,110284,110306],{},[895,110285,110286,110292,110294,110296,110298,110304],{},[2142,110287,110288,110290],{},[898,110289,2146],{},[2148,110291,2495],{},[1706,110293,1708],{},[898,110295,21237],{},[1706,110297,2140],{"stretchy":2139},[2142,110299,110300,110302],{},[898,110301,2146],{},[2148,110303,2701],{},[1706,110305,2153],{"stretchy":2139},[902,110307,110308],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,110311,110313],{"className":110312},[886],[888,110314,110315],{"xmlns":890},[892,110316,110317,110343],{},[895,110318,110319,110321,110323,110329,110331,110337,110339,110341],{},[898,110320,900],{},[1706,110322,2140],{"stretchy":2139},[2142,110324,110325,110327],{},[898,110326,2146],{},[2148,110328,2701],{},[1706,110330,2505],{"separator":2504},[2142,110332,110333,110335],{},[898,110334,2146],{},[2148,110336,2495],{},[1706,110338,2153],{"stretchy":2139},[1706,110340,1708],{},[898,110342,20413],{},[902,110344,28884],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,110347,110349],{"className":110348},[886],[888,110350,110351],{"xmlns":890},[892,110352,110353,110357],{},[895,110354,110355],{},[2415,110356,29714],{},[902,110358,47306],{"encoding":904}," chápeme jako velikost kompenzace.",[1636,110361,110362],{},[724,110363,110364,110366,110367,3484,110399,110437,110438,110455,110456,110473],{},[883,110365,3174],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,110368,110370],{"className":110369},[886],[888,110371,110372],{"xmlns":890},[892,110373,110374,110396],{},[895,110375,110376,110378,110380,110386,110388,110394],{},[2415,110377,29714],{},[1706,110379,2140],{"stretchy":2139},[2142,110381,110382,110384],{},[898,110383,2146],{},[2148,110385,2701],{},[1706,110387,2505],{"separator":2504},[2142,110389,110390,110392],{},[898,110391,2146],{},[2148,110393,2495],{},[1706,110395,2153],{"stretchy":2139},[902,110397,110398],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,110400,110401,110402,48071,110419,110436],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,110403,110405],{"className":110404},[886],[888,110406,110407],{"xmlns":890},[892,110408,110409,110417],{},[895,110410,110411],{},[2142,110412,110413,110415],{},[898,110414,2146],{},[2148,110416,2701],{},[902,110418,48070],{"encoding":904},[883,110420,110422],{"className":110421},[886],[888,110423,110424],{"xmlns":890},[892,110425,110426,110434],{},[895,110427,110428],{},[2142,110429,110430,110432],{},[898,110431,2146],{},[2148,110433,2495],{},[902,110435,48089],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,110439,110441],{"className":110440},[886],[888,110442,110443],{"xmlns":890},[892,110444,110445,110453],{},[895,110446,110447],{},[2142,110448,110449,110451],{},[898,110450,2146],{},[2148,110452,2495],{},[902,110454,48089],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,110457,110459],{"className":110458},[886],[888,110460,110461],{"xmlns":890},[892,110462,110463,110471],{},[895,110464,110465],{},[2142,110466,110467,110469],{},[898,110468,2146],{},[2148,110470,2701],{},[902,110472,48070],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,110475,110476,110477,2344],{},"Pro obecnou změnu ",[883,110478,110480],{"className":110479},[886],[888,110481,110482],{"xmlns":890},[892,110483,110484,110494],{},[895,110485,110486,110488],{},[898,110487,3120],{"mathvariant":2409},[2142,110489,110490,110492],{},[898,110491,2146],{},[2148,110493,2701],{},[902,110495,110496],{"encoding":904},"\\mathrm{d} Q_1",[883,110498,110500],{"className":110499},[886],[888,110501,110502],{"xmlns":890,"display":2350},[892,110503,110504,110557],{},[2354,110505,110506],{"width":2356},[2358,110507,110508,110510,110550,110552],{},[2361,110509],{"width":2363},[2361,110511,110512],{},[895,110513,110514,110516,110522,110524,110526,110532,110534,110536,110538,110540,110542,110548],{},[898,110515,3677],{"mathvariant":2409},[2142,110517,110518,110520],{},[898,110519,2146],{},[2148,110521,2495],{},[1706,110523,3248],{},[898,110525,3120],{"mathvariant":2409},[2142,110527,110528,110530],{},[898,110529,2146],{},[2148,110531,2495],{},[1706,110533,1708],{},[1706,110535,1715],{},[2415,110537,29714],{},[1706,110539,2390],{},[898,110541,3120],{"mathvariant":2409},[2142,110543,110544,110546],{},[898,110545,2146],{},[2148,110547,2701],{},[1706,110549,2505],{"separator":2504},[2361,110551],{"width":2363},[2361,110553,110554],{},[2415,110555,110556],{},"(6.10)",[902,110558,110559],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,110561,110563],{"className":110562},[886],[888,110564,110565],{"xmlns":890,"display":2350},[892,110566,110567,110614],{},[2354,110568,110569],{"width":2356},[2358,110570,110571,110573,110607,110609],{},[2361,110572],{"width":2363},[2361,110574,110575],{},[895,110576,110577,110579,110585,110587,110589,110595,110597,110599,110605],{},[898,110578,3120],{"mathvariant":2409},[2142,110580,110581,110583],{},[898,110582,2146],{},[2148,110584,2701],{},[1706,110586,1708],{},[1706,110588,1715],{},[2964,110590,110591,110593],{},[2148,110592,2701],{},[2415,110594,29714],{},[2415,110596,2799],{},[898,110598,3120],{"mathvariant":2409},[2142,110600,110601,110603],{},[898,110602,2146],{},[2148,110604,2495],{},[898,110606,1837],{"mathvariant":2409},[2361,110608],{"width":2363},[2361,110610,110611],{},[2415,110612,110613],{},"(6.11)",[902,110615,110616],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[1636,110618,110619,110685,110802],{},[724,110620,110621,110623,110624,2344],{},[883,110622,71732],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,110625,110627],{"className":110626},[886],[888,110628,110629],{"xmlns":890},[892,110630,110631,110683],{},[895,110632,110633,110635,110637,110643,110645,110651,110653,110655,110669],{},[898,110634,900],{},[1706,110636,2140],{"stretchy":2139},[2142,110638,110639,110641],{},[898,110640,2146],{},[2148,110642,2701],{},[1706,110644,2505],{"separator":2504},[2142,110646,110647,110649],{},[898,110648,2146],{},[2148,110650,2495],{},[1706,110652,2153],{"stretchy":2139},[1706,110654,1708],{},[28285,110656,110657,110659,110661],{},[898,110658,2146],{},[2148,110660,2701],{},[895,110662,110663,110665,110667],{},[2148,110664,2701],{},[898,110666,15493],{"mathvariant":2409},[2148,110668,2495],{},[28285,110670,110671,110673,110675],{},[898,110672,2146],{},[2148,110674,2495],{},[895,110676,110677,110679,110681],{},[2148,110678,2701],{},[898,110680,15493],{"mathvariant":2409},[2148,110682,2495],{},[902,110684,49009],{"encoding":904},[724,110686,110687],{},[883,110688,110690],{"className":110689},[886],[888,110691,110692],{"xmlns":890},[892,110693,110694,110800],{},[895,110695,110696,110698,110700,110782,110784,110798],{},[2415,110697,29714],{},[1706,110699,1708],{},[2964,110701,110702,110742],{},[895,110703,110704,110712,110728],{},[4745,110705,110706],{"scriptlevel":2150,"displaystyle":2139},[2964,110707,110708,110710],{},[2148,110709,2701],{},[2148,110711,2495],{},[28285,110713,110714,110716,110718],{},[898,110715,2146],{},[2148,110717,2701],{},[895,110719,110720,110722,110724,110726],{},[1706,110721,1715],{},[2148,110723,2701],{},[898,110725,15493],{"mathvariant":2409},[2148,110727,2495],{},[28285,110729,110730,110732,110734],{},[898,110731,2146],{},[2148,110733,2495],{},[895,110735,110736,110738,110740],{},[2148,110737,2701],{},[898,110739,15493],{"mathvariant":2409},[2148,110741,2495],{},[895,110743,110744,110752,110766],{},[4745,110745,110746],{"scriptlevel":2150,"displaystyle":2139},[2964,110747,110748,110750],{},[2148,110749,2701],{},[2148,110751,2495],{},[28285,110753,110754,110756,110758],{},[898,110755,2146],{},[2148,110757,2701],{},[895,110759,110760,110762,110764],{},[2148,110761,2701],{},[898,110763,15493],{"mathvariant":2409},[2148,110765,2495],{},[28285,110767,110768,110770,110772],{},[898,110769,2146],{},[2148,110771,2495],{},[895,110773,110774,110776,110778,110780],{},[1706,110775,1715],{},[2148,110777,2701],{},[898,110779,15493],{"mathvariant":2409},[2148,110781,2495],{},[1706,110783,1708],{},[2964,110785,110786,110792],{},[2142,110787,110788,110790],{},[898,110789,2146],{},[2148,110791,2495],{},[2142,110793,110794,110796],{},[898,110795,2146],{},[2148,110797,2701],{},[898,110799,1837],{"mathvariant":2409},[902,110801,49127],{"encoding":904},[724,110803,49130,110804,3787,110847,49177,110849,110868],{},[883,110805,110807],{"className":110806},[886],[888,110808,110809],{"xmlns":890},[892,110810,110811,110845],{},[895,110812,110813,110815,110817,110819,110821,110823,110825,110827,110835,110837],{},[2415,110814,29714],{},[1706,110816,2140],{"stretchy":2139},[2148,110818,19501],{},[1706,110820,2505],{"separator":2504},[2148,110822,17366],{},[1706,110824,2153],{"stretchy":2139},[1706,110826,1708],{},[4745,110828,110829],{"scriptlevel":2150,"displaystyle":2139},[2964,110830,110831,110833],{},[2148,110832,17366],{},[2148,110834,19501],{},[1706,110836,1708],{},[4745,110838,110839],{"scriptlevel":2150,"displaystyle":2139},[2964,110840,110841,110843],{},[2148,110842,7524],{},[2148,110844,4284],{},[902,110846,49174],{"encoding":904},[614,110848,28335],{},[883,110850,110852],{"className":110851},[886],[888,110853,110854],{"xmlns":890},[892,110855,110856,110866],{},[895,110857,110858],{},[4745,110859,110860],{"scriptlevel":2150,"displaystyle":2139},[2964,110861,110862,110864],{},[2148,110863,7524],{},[2148,110865,4284],{},[902,110867,49197],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,110870,110871,110872,110876],{},"(Paralelou je ",[207,110873,110875],{"className":110874,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,110878,110880],{"id":110879},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,110882,110883,110884,110887],{},"Rámcově se v kapitole 6 studují ",[38,110885,110886],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,110889,110890,111026],{},[123,110891,110892,110894,110895,16573,110926,1647,110929,110978,110979,1837],{},[38,110893,47320],{}," — maximalizace ",[883,110896,110898],{"className":110897},[886],[888,110899,110900],{"xmlns":890},[892,110901,110902,110924],{},[895,110903,110904,110906,110908,110914,110916,110922],{},[898,110905,900],{},[1706,110907,2140],{"stretchy":2139},[2142,110909,110910,110912],{},[898,110911,2146],{},[2148,110913,2701],{},[1706,110915,2505],{"separator":2504},[2142,110917,110918,110920],{},[898,110919,2146],{},[2148,110921,2495],{},[1706,110923,2153],{"stretchy":2139},[902,110925,35443],{"encoding":904},[38,110927,110928],{},"rozpočtovém omezení",[883,110930,110932],{"className":110931},[886],[888,110933,110934],{"xmlns":890},[892,110935,110936,110976],{},[895,110937,110938,110944,110946,110954,110960,110962,110970],{},[2489,110939,110940,110942],{},[898,110941,28247],{},[1706,110943,3197],{},[1706,110945,1708],{},[28285,110947,110948,110950,110952],{},[898,110949,1702],{},[2148,110951,2701],{},[1706,110953,3197],{},[2142,110955,110956,110958],{},[898,110957,2146],{},[2148,110959,2701],{},[1706,110961,2447],{},[28285,110963,110964,110966,110968],{},[898,110965,1702],{},[2148,110967,2495],{},[1706,110969,3197],{},[2142,110971,110972,110974],{},[898,110973,2146],{},[2148,110975,2495],{},[902,110977,36396],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,110980,110982],{"className":110981},[886],[888,110983,110984],{"xmlns":890},[892,110985,110986,111024],{},[895,110987,110988,110994,110996,111002,111004,111010,111012,111018,111020,111022],{},[2142,110989,110990,110992],{},[898,110991,2146],{},[898,110993,36887],{},[1706,110995,1708],{},[2142,110997,110998,111000],{},[898,110999,2334],{},[898,111001,36887],{},[1706,111003,2140],{"stretchy":2139},[2142,111005,111006,111008],{},[898,111007,1702],{},[2148,111009,2701],{},[1706,111011,2505],{"separator":2504},[2142,111013,111014,111016],{},[898,111015,1702],{},[2148,111017,2495],{},[1706,111019,2505],{"separator":2504},[898,111021,28247],{},[1706,111023,2153],{"stretchy":2139},[902,111025,55516],{"encoding":904},[123,111027,111028,46972,111031,47015,111077,111094,111095,1837],{},[38,111029,111030],{},"Duální úloha",[883,111032,111034],{"className":111033},[886],[888,111035,111036],{"xmlns":890},[892,111037,111038,111074],{},[895,111039,111040,111042,111044,111052,111058,111060,111068],{},[898,111041,23410],{},[1706,111043,1708],{},[28285,111045,111046,111048,111050],{},[898,111047,1702],{},[2148,111049,2701],{},[1706,111051,3197],{},[2142,111053,111054,111056],{},[898,111055,2146],{},[2148,111057,2701],{},[1706,111059,2447],{},[28285,111061,111062,111064,111066],{},[898,111063,1702],{},[2148,111065,2495],{},[1706,111067,3197],{},[2142,111069,111070,111072],{},[898,111071,2146],{},[2148,111073,2495],{},[902,111075,111076],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,111078,111080],{"className":111079},[886],[888,111081,111082],{"xmlns":890},[892,111083,111084,111092],{},[895,111085,111086],{},[2489,111087,111088,111090],{},[898,111089,900],{},[1706,111091,3197],{},[902,111093,47033],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,111096,111098],{"className":111097},[886],[888,111099,111100],{"xmlns":890},[892,111101,111102,111140],{},[895,111103,111104,111110,111112,111118,111120,111126,111128,111134,111136,111138],{},[2142,111105,111106,111108],{},[898,111107,2146],{},[898,111109,36887],{},[1706,111111,1708],{},[2142,111113,111114,111116],{},[898,111115,2334],{},[898,111117,36887],{},[1706,111119,2140],{"stretchy":2139},[2142,111121,111122,111124],{},[898,111123,1702],{},[2148,111125,2701],{},[1706,111127,2505],{"separator":2504},[2142,111129,111130,111132],{},[898,111131,1702],{},[2148,111133,2495],{},[1706,111135,2505],{"separator":2504},[898,111137,900],{},[1706,111139,2153],{"stretchy":2139},[902,111141,36920],{"encoding":904},[724,111143,111144,111145,111148,111149,1647,111152,111191],{},"Obě úlohy se řeší ",[207,111146,47038],{"className":111147,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,111150,111151],{},"tentýž bod dotyku",[883,111153,111155],{"className":111154},[886],[888,111156,111157],{"xmlns":890},[892,111158,111159,111189],{},[895,111160,111161,111167,111169,111177,111179,111187],{},[2489,111162,111163,111165],{},[898,111164,2146],{},[1706,111166,3197],{},[1706,111168,21693],{"stretchy":2139},[28285,111170,111171,111173,111175],{},[898,111172,2146],{},[2148,111174,2701],{},[1706,111176,3197],{},[1706,111178,2505],{"separator":2504},[28285,111180,111181,111183,111185],{},[898,111182,2146],{},[2148,111184,2495],{},[1706,111186,3197],{},[1706,111188,21708],{"stretchy":2139},[902,111190,47395],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,111193,111195],{"className":111194},[886],[888,111196,111197],{"xmlns":890,"display":2350},[892,111198,111199,111245],{},[895,111200,111201,111203,111205,111223,111225,111243],{},[2415,111202,29714],{},[1706,111204,1708],{},[2964,111206,111207,111215],{},[28285,111208,111209,111211,111213],{},[898,111210,900],{},[2148,111212,2701],{},[1706,111214,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[28285,111216,111217,111219,111221],{},[898,111218,900],{},[2148,111220,2495],{},[1706,111222,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,111224,1708],{},[2964,111226,111227,111235],{},[28285,111228,111229,111231,111233],{},[898,111230,1702],{},[2148,111232,2701],{},[1706,111234,3197],{},[28285,111236,111237,111239,111241],{},[898,111238,1702],{},[2148,111240,2495],{},[1706,111242,3197],{},[898,111244,1837],{"mathvariant":2409},[902,111246,111247],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,111249,111250],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[1636,111252,111253],{},[724,111254,111255,111257,111258,111261,111262,111265,111266,111293,111294,111328,111329,111363,111364,111407,111408,111411,111412,1837],{},[883,111256,3174],{}," Pro detailní postup viz ",[207,111259,55814],{"className":111260,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,111263,111264],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,111267,111269],{"className":111268},[886],[888,111270,111271],{"xmlns":890},[892,111272,111273,111291],{},[895,111274,111275,111277,111279,111285],{},[898,111276,900],{},[1706,111278,1708],{},[2142,111280,111281,111283],{},[898,111282,2146],{},[2148,111284,2701],{},[2142,111286,111287,111289],{},[898,111288,2146],{},[2148,111290,2495],{},[902,111292,49290],{"encoding":904}," s výsledkem ",[883,111295,111297],{"className":111296},[886],[888,111298,111299],{"xmlns":890},[892,111300,111301,111325],{},[895,111302,111303,111309,111311,111313,111315,111321,111323],{},[2142,111304,111305,111307],{},[898,111306,2146],{},[2148,111308,2701],{},[1706,111310,1708],{},[2148,111312,2748],{},[1706,111314,2505],{"separator":2504},[2142,111316,111317,111319],{},[898,111318,2146],{},[2148,111320,2495],{},[1706,111322,1708],{},[2148,111324,7786],{},[902,111326,111327],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,111330,111332],{"className":111331},[886],[888,111333,111334],{"xmlns":890},[892,111335,111336,111360],{},[895,111337,111338,111344,111346,111348,111350,111356,111358],{},[2142,111339,111340,111342],{},[898,111341,2146],{},[2148,111343,2701],{},[1706,111345,1708],{},[2148,111347,3455],{},[1706,111349,2505],{"separator":2504},[2142,111351,111352,111354],{},[898,111353,2146],{},[2148,111355,2495],{},[1706,111357,1708],{},[2148,111359,2701],{},[902,111361,111362],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,111365,111367],{"className":111366},[886],[888,111368,111369],{"xmlns":890},[892,111370,111371,111405],{},[895,111372,111373,111375,111377,111391],{},[898,111374,900],{},[1706,111376,1708],{},[28285,111378,111379,111381,111383],{},[898,111380,2146],{},[2148,111382,2701],{},[895,111384,111385,111387,111389],{},[2148,111386,2701],{},[898,111388,15493],{"mathvariant":2409},[2148,111390,2495],{},[28285,111392,111393,111395,111397],{},[898,111394,2146],{},[2148,111396,2495],{},[895,111398,111399,111401,111403],{},[2148,111400,2701],{},[898,111402,15493],{"mathvariant":2409},[2148,111404,2495],{},[902,111406,52221],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,111409,111410],{},"6.8–6.13"," jsou na stránce ",[207,111413,46838],{"className":111414,"dataFsResolvedFilePath":911,"href":912},[210],[115,111416,111418],{"id":111417},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,111420,111421,111422,111435,111436,111438,111439,111441,111442,111444,111445,111447,111448,111450,111451,111453,111454,1647,111456,111491,111492,111505,111506,111509,111510,111513,111514,1837],{},"Každá ",[883,111423,111425],{"className":111424},[886],[888,111426,111427],{"xmlns":890},[892,111428,111429,111433],{},[895,111430,111431],{},[898,111432,18465],{},[902,111434,18465],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,111437,104769],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,111440,105253],{}," a současně ",[38,111443,104772],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,111446,104777],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,111449,71714],{}," (6.4) a druhé parciální derivace ",[38,111452,107136],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,111455,28847],{},[883,111457,111459],{"className":111458},[886],[888,111460,111461],{"xmlns":890},[892,111462,111463,111489],{},[895,111464,111465,111467,111469,111475,111477,111483,111485,111487],{},[898,111466,900],{},[1706,111468,2140],{"stretchy":2139},[2142,111470,111471,111473],{},[898,111472,2146],{},[2148,111474,2701],{},[1706,111476,2505],{"separator":2504},[2142,111478,111479,111481],{},[898,111480,2146],{},[2148,111482,2495],{},[1706,111484,2153],{"stretchy":2139},[1706,111486,1708],{},[898,111488,20413],{},[902,111490,28884],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,111493,111495],{"className":111494},[886],[888,111496,111497],{"xmlns":890},[892,111498,111499,111503],{},[895,111500,111501],{},[2415,111502,29714],{},[902,111504,47306],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,111507,111508],{},"maximalizace užitečnosti"," a duální ",[38,111511,111512],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,111515,55814],{"className":111516,"dataFsResolvedFilePath":911,"href":912},[210],[115,111518,15880],{"id":15879},[152,111520,111521,111524,111527,111530,111533,111536,111539,111542,111545,111548],{},[123,111522,111523],{},"Co se zahrnuje pod termín užitečnost?",[123,111525,111526],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,111528,111529],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,111531,111532],{},"Jak se vypočítá mezní užitečnost?",[123,111534,111535],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,111537,111538],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,111540,111541],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,111543,111544],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,111546,111547],{},"Proč mají křivky užitečnosti záporný sklon?",[123,111549,111550],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,111552,111554],{"id":111553},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,111556,111557,111560,111561,101442,111603,1343,111631,1343,111659,111687],{},[38,111558,111559],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,111562,111564],{"className":111563},[886],[888,111565,111566],{"xmlns":890},[892,111567,111568,111600],{},[895,111569,111570,111572,111574,111580,111582,111584,111590,111592,111594],{},[898,111571,900],{},[1706,111573,1708],{},[2142,111575,111576,111578],{},[898,111577,2146],{},[2148,111579,2701],{},[1706,111581,2447],{},[2148,111583,11218],{},[2142,111585,111586,111588],{},[898,111587,2146],{},[2148,111589,2495],{},[1706,111591,2447],{},[2148,111593,2495],{},[2142,111595,111596,111598],{},[898,111597,2146],{},[2148,111599,4284],{},[902,111601,111602],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,111604,111606],{"className":111605},[886],[888,111607,111608],{"xmlns":890},[892,111609,111610,111628],{},[895,111611,111612,111614,111616,111618,111620,111622,111624,111626],{},[898,111613,900],{},[1706,111615,2140],{"stretchy":2139},[2148,111617,3455],{},[1706,111619,2505],{"separator":2504},[2148,111621,2495],{},[1706,111623,2505],{"separator":2504},[2148,111625,2495],{},[1706,111627,2153],{"stretchy":2139},[902,111629,111630],{"encoding":904},"U(4, 2, 2)",[883,111632,111634],{"className":111633},[886],[888,111635,111636],{"xmlns":890},[892,111637,111638,111656],{},[895,111639,111640,111642,111644,111646,111648,111650,111652,111654],{},[898,111641,900],{},[1706,111643,2140],{"stretchy":2139},[2148,111645,2701],{},[1706,111647,2505],{"separator":2504},[2148,111649,3455],{},[1706,111651,2505],{"separator":2504},[2148,111653,2495],{},[1706,111655,2153],{"stretchy":2139},[902,111657,111658],{"encoding":904},"U(1, 4, 2)",[883,111660,111662],{"className":111661},[886],[888,111663,111664],{"xmlns":890},[892,111665,111666,111684],{},[895,111667,111668,111670,111672,111674,111676,111678,111680,111682],{},[898,111669,900],{},[1706,111671,2140],{"stretchy":2139},[2148,111673,2495],{},[1706,111675,2505],{"separator":2504},[2148,111677,4284],{},[1706,111679,2505],{"separator":2504},[2148,111681,2701],{},[1706,111683,2153],{"stretchy":2139},[902,111685,111686],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,111689,111690,111693,111694,111746,111747,1343,111773,1343,111799,1343,111825,1343,111851,1343,111877,1343,111903,111929],{},[38,111691,111692],{},"6.2"," Je dána užitečnost ",[883,111695,111697],{"className":111696},[886],[888,111698,111699],{"xmlns":890},[892,111700,111701,111743],{},[895,111702,111703,111705,111707,111709,111723,111737],{},[898,111704,900],{},[1706,111706,1708],{},[2148,111708,2495],{},[28285,111710,111711,111713,111715],{},[898,111712,2146],{},[2148,111714,2701],{},[895,111716,111717,111719,111721],{},[2148,111718,2701],{},[898,111720,15493],{"mathvariant":2409},[2148,111722,4284],{},[28285,111724,111725,111727,111729],{},[898,111726,2146],{},[2148,111728,2495],{},[895,111730,111731,111733,111735],{},[2148,111732,2701],{},[898,111734,15493],{"mathvariant":2409},[2148,111736,2495],{},[2142,111738,111739,111741],{},[898,111740,2146],{},[2148,111742,4284],{},[902,111744,111745],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,111748,111750],{"className":111749},[886],[888,111751,111752],{"xmlns":890},[892,111753,111754,111770],{},[895,111755,111756,111758,111760,111762,111764,111766,111768],{},[1706,111757,2140],{"stretchy":2139},[2148,111759,3757],{},[1706,111761,2505],{"separator":2504},[2148,111763,13266],{},[1706,111765,2505],{"separator":2504},[2148,111767,7786],{},[1706,111769,2153],{"stretchy":2139},[902,111771,111772],{"encoding":904},"(36, 27, 10)",[883,111774,111776],{"className":111775},[886],[888,111777,111778],{"xmlns":890},[892,111779,111780,111796],{},[895,111781,111782,111784,111786,111788,111790,111792,111794],{},[1706,111783,2140],{"stretchy":2139},[2148,111785,60890],{},[1706,111787,2505],{"separator":2504},[2148,111789,12717],{},[1706,111791,2505],{"separator":2504},[2148,111793,3369],{},[1706,111795,2153],{"stretchy":2139},[902,111797,111798],{"encoding":904},"(64, 8, 20)",[883,111800,111802],{"className":111801},[886],[888,111803,111804],{"xmlns":890},[892,111805,111806,111822],{},[895,111807,111808,111810,111812,111814,111816,111818,111820],{},[1706,111809,2140],{"stretchy":2139},[2148,111811,2748],{},[1706,111813,2505],{"separator":2504},[2148,111815,60890],{},[1706,111817,2505],{"separator":2504},[2148,111819,12717],{},[1706,111821,2153],{"stretchy":2139},[902,111823,111824],{"encoding":904},"(25, 64, 8)",[883,111826,111828],{"className":111827},[886],[888,111829,111830],{"xmlns":890},[892,111831,111832,111848],{},[895,111833,111834,111836,111838,111840,111842,111844,111846],{},[1706,111835,2140],{"stretchy":2139},[2148,111837,3455],{},[1706,111839,2505],{"separator":2504},[2148,111841,19227],{},[1706,111843,2505],{"separator":2504},[2148,111845,7044],{},[1706,111847,2153],{"stretchy":2139},[902,111849,111850],{"encoding":904},"(4, 125, 6)",[883,111852,111854],{"className":111853},[886],[888,111855,111856],{"xmlns":890},[892,111857,111858,111874],{},[895,111859,111860,111862,111864,111866,111868,111870,111872],{},[1706,111861,2140],{"stretchy":2139},[2148,111863,10800],{},[1706,111865,2505],{"separator":2504},[2148,111867,3508],{},[1706,111869,2505],{"separator":2504},[2148,111871,7156],{},[1706,111873,2153],{"stretchy":2139},[902,111875,111876],{"encoding":904},"(9, 40, 12)",[883,111878,111880],{"className":111879},[886],[888,111881,111882],{"xmlns":890},[892,111883,111884,111900],{},[895,111885,111886,111888,111890,111892,111894,111896,111898],{},[1706,111887,2140],{"stretchy":2139},[2148,111889,10800],{},[1706,111891,2505],{"separator":2504},[2148,111893,60890],{},[1706,111895,2505],{"separator":2504},[2148,111897,7524],{},[1706,111899,2153],{"stretchy":2139},[902,111901,111902],{"encoding":904},"(9, 64, 5)",[883,111904,111906],{"className":111905},[886],[888,111907,111908],{"xmlns":890},[892,111909,111910,111926],{},[895,111911,111912,111914,111916,111918,111920,111922,111924],{},[1706,111913,2140],{"stretchy":2139},[2148,111915,60890],{},[1706,111917,2505],{"separator":2504},[2148,111919,12717],{},[1706,111921,2505],{"separator":2504},[2148,111923,7786],{},[1706,111925,2153],{"stretchy":2139},[902,111927,111928],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,111931,111932,111693,111935,111978,111979,112013,112014,10691,112044,112077,112078,112095,112096,112113],{},[38,111933,111934],{},"6.3",[883,111936,111938],{"className":111937},[886],[888,111939,111940],{"xmlns":890},[892,111941,111942,111976],{},[895,111943,111944,111946,111948,111962],{},[898,111945,900],{},[1706,111947,1708],{},[28285,111949,111950,111952,111954],{},[898,111951,2146],{},[2148,111953,2701],{},[895,111955,111956,111958,111960],{},[2148,111957,2701],{},[898,111959,15493],{"mathvariant":2409},[2148,111961,2495],{},[28285,111963,111964,111966,111968],{},[898,111965,2146],{},[2148,111967,2495],{},[895,111969,111970,111972,111974],{},[2148,111971,2701],{},[898,111973,15493],{"mathvariant":2409},[2148,111975,2495],{},[902,111977,52221],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,111980,111982],{"className":111981},[886],[888,111983,111984],{"xmlns":890},[892,111985,111986,112010],{},[895,111987,111988,111994,111996,111998,112000,112006,112008],{},[2142,111989,111990,111992],{},[898,111991,2146],{},[2148,111993,2701],{},[1706,111995,1708],{},[2148,111997,2728],{},[1706,111999,2505],{"separator":2504},[2142,112001,112002,112004],{},[898,112003,2146],{},[2148,112005,2495],{},[1706,112007,1708],{},[2148,112009,17219],{},[902,112011,112012],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,112015,112017],{"className":112016},[886],[888,112018,112019],{"xmlns":890},[892,112020,112021,112041],{},[895,112022,112023,112025,112031,112033,112035],{},[898,112024,1742],{},[2142,112026,112027,112029],{},[898,112028,900],{},[2148,112030,2701],{},[1706,112032,2505],{"separator":2504},[898,112034,1742],{},[2142,112036,112037,112039],{},[898,112038,900],{},[2148,112040,2495],{},[902,112042,112043],{"encoding":904},"MU_1, MU_2",[883,112045,112047],{"className":112046},[886],[888,112048,112049],{"xmlns":890},[892,112050,112051,112075],{},[895,112052,112053,112059,112061,112063,112065,112071,112073],{},[2142,112054,112055,112057],{},[898,112056,2146],{},[2148,112058,2701],{},[1706,112060,1708],{},[2148,112062,2728],{},[1706,112064,2505],{"separator":2504},[2142,112066,112067,112069],{},[898,112068,2146],{},[2148,112070,2495],{},[1706,112072,1708],{},[2148,112074,17219],{},[902,112076,112012],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,112079,112081],{"className":112080},[886],[888,112082,112083],{"xmlns":890},[892,112084,112085,112093],{},[895,112086,112087],{},[2142,112088,112089,112091],{},[898,112090,2146],{},[2148,112092,2701],{},[902,112094,48070],{"encoding":904}," na 60 a poklesu ",[883,112097,112099],{"className":112098},[886],[888,112100,112101],{"xmlns":890},[892,112102,112103,112111],{},[895,112104,112105],{},[2142,112106,112107,112109],{},[898,112108,2146],{},[2148,112110,2495],{},[902,112112,48089],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,112115,112116,112119,112120,112181,112182,1837],{},[38,112117,112118],{},"6.4"," Je dána funkce ",[883,112121,112123],{"className":112122},[886],[888,112124,112125],{"xmlns":890},[892,112126,112127,112179],{},[895,112128,112129,112131,112133,112139,112141,112147,112149,112151,112165],{},[898,112130,900],{},[1706,112132,2140],{"stretchy":2139},[2142,112134,112135,112137],{},[898,112136,2146],{},[2148,112138,2701],{},[1706,112140,2505],{"separator":2504},[2142,112142,112143,112145],{},[898,112144,2146],{},[2148,112146,2495],{},[1706,112148,2153],{"stretchy":2139},[1706,112150,1708],{},[28285,112152,112153,112155,112157],{},[898,112154,2146],{},[2148,112156,2701],{},[895,112158,112159,112161,112163],{},[2148,112160,2701],{},[898,112162,15493],{"mathvariant":2409},[2148,112164,2495],{},[28285,112166,112167,112169,112171],{},[898,112168,2146],{},[2148,112170,2495],{},[895,112172,112173,112175,112177],{},[2148,112174,2701],{},[898,112176,15493],{"mathvariant":2409},[2148,112178,2495],{},[902,112180,49009],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,112183,112185],{"className":112184},[886],[888,112186,112187],{"xmlns":890},[892,112188,112189,112279],{},[895,112190,112191,112193,112195,112201,112203,112205,112207,112209,112211,112213,112219,112221,112223,112225,112227,112229,112231,112233,112235,112241,112243,112245,112247,112249,112251,112253,112259,112261,112263,112265,112267,112269,112271,112277],{},[898,112192,900],{},[1706,112194,2140],{"stretchy":2139},[2142,112196,112197,112199],{},[898,112198,2146],{},[2148,112200,2701],{},[1706,112202,2505],{"separator":2504},[2148,112204,2701],{},[1706,112206,2153],{"stretchy":2139},[1706,112208,2505],{"separator":2504},[898,112210,900],{},[1706,112212,2140],{"stretchy":2139},[2142,112214,112215,112217],{},[898,112216,2146],{},[2148,112218,2701],{},[1706,112220,2505],{"separator":2504},[2148,112222,2495],{},[1706,112224,2153],{"stretchy":2139},[1706,112226,2505],{"separator":2504},[898,112228,900],{},[1706,112230,2140],{"stretchy":2139},[2148,112232,2701],{},[1706,112234,2505],{"separator":2504},[2142,112236,112237,112239],{},[898,112238,2146],{},[2148,112240,2495],{},[1706,112242,2153],{"stretchy":2139},[1706,112244,2505],{"separator":2504},[898,112246,900],{},[1706,112248,2140],{"stretchy":2139},[2148,112250,2495],{},[1706,112252,2505],{"separator":2504},[2142,112254,112255,112257],{},[898,112256,2146],{},[2148,112258,2495],{},[1706,112260,2153],{"stretchy":2139},[1706,112262,2505],{"separator":2504},[898,112264,900],{},[1706,112266,2140],{"stretchy":2139},[2148,112268,4284],{},[1706,112270,2505],{"separator":2504},[2142,112272,112273,112275],{},[898,112274,2146],{},[2148,112276,2495],{},[1706,112278,2153],{"stretchy":2139},[902,112280,112281],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,112283,112284,111693,112287,112331,112332,112440,112441,1343,112466,1343,112491,112533,112534,1343,112563,112588],{},[38,112285,112286],{},"6.5",[883,112288,112290],{"className":112289},[886],[888,112291,112292],{"xmlns":890},[892,112293,112294,112328],{},[895,112295,112296,112298,112300,112314],{},[898,112297,900],{},[1706,112299,1708],{},[28285,112301,112302,112304,112306],{},[898,112303,2146],{},[2148,112305,2701],{},[895,112307,112308,112310,112312],{},[2148,112309,2495],{},[898,112311,15493],{"mathvariant":2409},[2148,112313,4284],{},[28285,112315,112316,112318,112320],{},[898,112317,2146],{},[2148,112319,2495],{},[895,112321,112322,112324,112326],{},[2148,112323,2701],{},[898,112325,15493],{"mathvariant":2409},[2148,112327,4284],{},[902,112329,112330],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,112333,112335],{"className":112334},[886],[888,112336,112337],{"xmlns":890},[892,112338,112339,112437],{},[895,112340,112341,112343,112345,112351,112353,112359,112361,112363,112365,112367,112369,112371,112377,112379,112381,112383,112385,112387,112389,112395,112397,112399,112401,112403,112405,112407,112409,112411,112417,112419,112421,112423,112425,112427,112429,112435],{},[898,112342,900],{},[1706,112344,2140],{"stretchy":2139},[2142,112346,112347,112349],{},[898,112348,2146],{},[2148,112350,2701],{},[1706,112352,2505],{"separator":2504},[2142,112354,112355,112357],{},[898,112356,2146],{},[2148,112358,2495],{},[1706,112360,2153],{"stretchy":2139},[1706,112362,1708],{},[2148,112364,2495],{},[1706,112366,2505],{"separator":2504},[898,112368,900],{},[1706,112370,2140],{"stretchy":2139},[2142,112372,112373,112375],{},[898,112374,2146],{},[2148,112376,2701],{},[1706,112378,2505],{"separator":2504},[2148,112380,4284],{},[1706,112382,2153],{"stretchy":2139},[1706,112384,2505],{"separator":2504},[898,112386,900],{},[1706,112388,2140],{"stretchy":2139},[2142,112390,112391,112393],{},[898,112392,2146],{},[2148,112394,2701],{},[1706,112396,2505],{"separator":2504},[2148,112398,2495],{},[1706,112400,2153],{"stretchy":2139},[1706,112402,2505],{"separator":2504},[898,112404,900],{},[1706,112406,2140],{"stretchy":2139},[2148,112408,2495],{},[1706,112410,2505],{"separator":2504},[2142,112412,112413,112415],{},[898,112414,2146],{},[2148,112416,2495],{},[1706,112418,2153],{"stretchy":2139},[1706,112420,2505],{"separator":2504},[898,112422,900],{},[1706,112424,2140],{"stretchy":2139},[2148,112426,4284],{},[1706,112428,2505],{"separator":2504},[2142,112430,112431,112433],{},[898,112432,2146],{},[2148,112434,2495],{},[1706,112436,2153],{"stretchy":2139},[902,112438,112439],{"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 ",[883,112442,112444],{"className":112443},[886],[888,112445,112446],{"xmlns":890},[892,112447,112448,112463],{},[895,112449,112450,112452,112454,112456,112458,112461],{},[898,112451,1735],{},[1706,112453,21693],{"stretchy":2139},[2148,112455,11218],{},[1706,112457,2110],{"separator":2504},[2148,112459,112460],{},"3,555",[1706,112462,21708],{"stretchy":2139},[902,112464,112465],{"encoding":904},"A[1{,}5; 3{,}555]",[883,112467,112469],{"className":112468},[886],[888,112470,112471],{"xmlns":890},[892,112472,112473,112488],{},[895,112474,112475,112477,112479,112481,112483,112486],{},[898,112476,10315],{},[1706,112478,21693],{"stretchy":2139},[2148,112480,10065],{},[1706,112482,2110],{"separator":2504},[2148,112484,112485],{},"1,28",[1706,112487,21708],{"stretchy":2139},[902,112489,112490],{"encoding":904},"B[2{,}5; 1{,}28]",[883,112492,112494],{"className":112493},[886],[888,112495,112496],{"xmlns":890},[892,112497,112498,112530],{},[895,112499,112500,112502,112504,112506,112508,112510,112512,112518,112520,112522,112524,112526,112528],{},[898,112501,1683],{},[1706,112503,21693],{"stretchy":2139},[2148,112505,2495],{},[1706,112507,2110],{"separator":2504},[898,112509,900],{},[1706,112511,2140],{"stretchy":2139},[2142,112513,112514,112516],{},[898,112515,2146],{},[2148,112517,2701],{},[1706,112519,2505],{"separator":2504},[2148,112521,4284],{},[1706,112523,2153],{"stretchy":2139},[1706,112525,1708],{},[2148,112527,4284],{},[1706,112529,21708],{"stretchy":2139},[902,112531,112532],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,112535,112537],{"className":112536},[886],[888,112538,112539],{"xmlns":890},[892,112540,112541,112560],{},[895,112542,112543,112545,112547,112549,112551,112553,112555,112558],{},[898,112544,2334],{},[1706,112546,21693],{"stretchy":2139},[2148,112548,4284],{},[1706,112550,2110],{"separator":2504},[2148,112552,2701],{},[1706,112554,2110],{"separator":2504},[2148,112556,112557],{},"0,832",[1706,112559,21708],{"stretchy":2139},[902,112561,112562],{"encoding":904},"D[3; 1; 0{,}832]",[883,112564,112566],{"className":112565},[886],[888,112567,112568],{"xmlns":890},[892,112569,112570,112585],{},[895,112571,112572,112574,112576,112578,112580,112583],{},[898,112573,23410],{},[1706,112575,21693],{"stretchy":2139},[2148,112577,10065],{},[1706,112579,2110],{"separator":2504},[2148,112581,112582],{},"4,32",[1706,112584,21708],{"stretchy":2139},[902,112586,112587],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,112590,112591,111693,112594,112637,112638,10691,112651,112685,112686,112703,112704,112721],{},[38,112592,112593],{},"6.6",[883,112595,112597],{"className":112596},[886],[888,112598,112599],{"xmlns":890},[892,112600,112601,112635],{},[895,112602,112603,112605,112607,112621],{},[898,112604,900],{},[1706,112606,1708],{},[28285,112608,112609,112611,112613],{},[898,112610,2146],{},[2148,112612,2701],{},[895,112614,112615,112617,112619],{},[2148,112616,2495],{},[898,112618,15493],{"mathvariant":2409},[2148,112620,4284],{},[28285,112622,112623,112625,112627],{},[898,112624,2146],{},[2148,112626,2495],{},[895,112628,112629,112631,112633],{},[2148,112630,2701],{},[898,112632,15493],{"mathvariant":2409},[2148,112634,4284],{},[902,112636,112330],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,112639,112641],{"className":112640},[886],[888,112642,112643],{"xmlns":890},[892,112644,112645,112649],{},[895,112646,112647],{},[2415,112648,29714],{},[902,112650,47306],{"encoding":904},[883,112652,112654],{"className":112653},[886],[888,112655,112656],{"xmlns":890},[892,112657,112658,112682],{},[895,112659,112660,112666,112668,112670,112672,112678,112680],{},[2142,112661,112662,112664],{},[898,112663,2146],{},[2148,112665,2701],{},[1706,112667,1708],{},[2148,112669,2590],{},[1706,112671,2505],{"separator":2504},[2142,112673,112674,112676],{},[898,112675,2146],{},[2148,112677,2495],{},[1706,112679,1708],{},[2148,112681,7039],{},[902,112683,112684],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,112687,112689],{"className":112688},[886],[888,112690,112691],{"xmlns":890},[892,112692,112693,112701],{},[895,112694,112695],{},[2142,112696,112697,112699],{},[898,112698,2146],{},[2148,112700,2701],{},[902,112702,48070],{"encoding":904},", poklesne-li ",[883,112705,112707],{"className":112706},[886],[888,112708,112709],{"xmlns":890},[892,112710,112711,112719],{},[895,112712,112713],{},[2142,112714,112715,112717],{},[898,112716,2146],{},[2148,112718,2495],{},[902,112720,48089],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,112723,112724,112727,112728,112745,112746,112763,112764,112796,112797,112822,112823,112836,112837,1343,112861,1343,112885,1837],{},[38,112725,112726],{},"6.7"," Míra uspokojení z nákupu množství ",[883,112729,112731],{"className":112730},[886],[888,112732,112733],{"xmlns":890},[892,112734,112735,112743],{},[895,112736,112737],{},[2142,112738,112739,112741],{},[898,112740,2146],{},[2148,112742,2701],{},[902,112744,48070],{"encoding":904}," nealko nápojů a množství ",[883,112747,112749],{"className":112748},[886],[888,112750,112751],{"xmlns":890},[892,112752,112753,112761],{},[895,112754,112755],{},[2142,112756,112757,112759],{},[898,112758,2146],{},[2148,112760,2495],{},[902,112762,48089],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,112765,112767],{"className":112766},[886],[888,112768,112769],{"xmlns":890},[892,112770,112771,112793],{},[895,112772,112773,112775,112777],{},[898,112774,900],{},[1706,112776,1708],{},[11087,112778,112779],{},[895,112780,112781,112787],{},[2142,112782,112783,112785],{},[898,112784,2146],{},[2148,112786,2701],{},[2142,112788,112789,112791],{},[898,112790,2146],{},[2148,112792,2495],{},[902,112794,112795],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,112798,112800],{"className":112799},[886],[888,112801,112802],{"xmlns":890},[892,112803,112804,112820],{},[895,112805,112806,112812,112814],{},[2142,112807,112808,112810],{},[898,112809,2146],{},[2148,112811,2701],{},[1706,112813,2505],{"separator":2504},[2142,112815,112816,112818],{},[898,112817,2146],{},[2148,112819,2495],{},[902,112821,54684],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,112824,112826],{"className":112825},[886],[888,112827,112828],{"xmlns":890},[892,112829,112830,112834],{},[895,112831,112832],{},[2415,112833,29714],{},[902,112835,47306],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,112838,112840],{"className":112839},[886],[888,112841,112842],{"xmlns":890},[892,112843,112844,112858],{},[895,112845,112846,112848,112850,112852,112854,112856],{},[2415,112847,29714],{},[1706,112849,2140],{"stretchy":2139},[2148,112851,7524],{},[1706,112853,2505],{"separator":2504},[2148,112855,3369],{},[1706,112857,2153],{"stretchy":2139},[902,112859,112860],{"encoding":904},"\\text{MRCS}(5, 20)",[883,112862,112864],{"className":112863},[886],[888,112865,112866],{"xmlns":890},[892,112867,112868,112882],{},[895,112869,112870,112872,112874,112876,112878,112880],{},[2415,112871,29714],{},[1706,112873,2140],{"stretchy":2139},[2148,112875,3369],{},[1706,112877,2505],{"separator":2504},[2148,112879,7524],{},[1706,112881,2153],{"stretchy":2139},[902,112883,112884],{"encoding":904},"\\text{MRCS}(20, 5)",[883,112886,112888],{"className":112887},[886],[888,112889,112890],{"xmlns":890},[892,112891,112892,112906],{},[895,112893,112894,112896,112898,112900,112902,112904],{},[2415,112895,29714],{},[1706,112897,2140],{"stretchy":2139},[2148,112899,2495],{},[1706,112901,2505],{"separator":2504},[2148,112903,2728],{},[1706,112905,2153],{"stretchy":2139},[902,112907,112908],{"encoding":904},"\\text{MRCS}(2, 50)",[1636,112910,112911],{},[724,112912,112913,112915,112916,1837],{},[883,112914,12314],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,112917,112920],{"className":112918,"dataFsResolvedFilePath":911,"href":112919},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,112922,19879],{"id":19878},[120,112924,112925,112931,112936,112942,112995,113005,113051,113106,113169,113226,113281,113320],{},[123,112926,112927,112930],{},[38,112928,112929],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,112932,112933,112935],{},[38,112934,104828],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,112937,112938,112941],{},[38,112939,112940],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,112943,112944,112946,112947,112960,112961,1837],{},[38,112945,105155],{}," — uspořádaná ",[883,112948,112950],{"className":112949},[886],[888,112951,112952],{"xmlns":890},[892,112953,112954,112958],{},[895,112955,112956],{},[898,112957,18465],{},[902,112959,18465],{"encoding":904},"-tice ",[883,112962,112964],{"className":112963},[886],[888,112965,112966],{"xmlns":890},[892,112967,112968,112992],{},[895,112969,112970,112972,112978,112980,112982,112984,112990],{},[1706,112971,2140],{"stretchy":2139},[2142,112973,112974,112976],{},[898,112975,2146],{},[2148,112977,2701],{},[1706,112979,2505],{"separator":2504},[1706,112981,28763],{},[1706,112983,2505],{"separator":2504},[2142,112985,112986,112988],{},[898,112987,2146],{},[898,112989,18465],{},[1706,112991,2153],{"stretchy":2139},[902,112993,112994],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,112996,112997,113000,113001,113004],{},[38,112998,112999],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,113002,113003],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,113006,113007,1647,113010,113050],{},[38,113008,113009],{},"Funkce užitečnosti",[883,113011,113013],{"className":113012},[886],[888,113014,113015],{"xmlns":890},[892,113016,113017,113047],{},[895,113018,113019,113021,113023,113025,113027,113033,113035,113037,113039,113045],{},[898,113020,900],{},[1706,113022,1708],{},[898,113024,900],{},[1706,113026,2140],{"stretchy":2139},[2142,113028,113029,113031],{},[898,113030,2146],{},[2148,113032,2701],{},[1706,113034,2505],{"separator":2504},[1706,113036,28763],{},[1706,113038,2505],{"separator":2504},[2142,113040,113041,113043],{},[898,113042,2146],{},[898,113044,18465],{},[1706,113046,2153],{"stretchy":2139},[902,113048,113049],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,113052,113053,1647,113056,113085,113086,1647,113089,113105],{},[38,113054,113055],{},"Mezní užitečnost",[883,113057,113059],{"className":113058},[886],[888,113060,113061],{"xmlns":890},[892,113062,113063,113083],{},[895,113064,113065,113067,113073,113075],{},[898,113066,1742],{},[2142,113068,113069,113071],{},[898,113070,900],{},[898,113072,36887],{},[1706,113074,1708],{},[28285,113076,113077,113079,113081],{},[898,113078,900],{},[898,113080,36887],{},[1706,113082,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[902,113084,104612],{"encoding":904}," — vzorec (6.2); ",[38,113087,113088],{},"totální diferenciál",[883,113090,113092],{"className":113091},[886],[888,113093,113094],{"xmlns":890},[892,113095,113096,113102],{},[895,113097,113098,113100],{},[898,113099,3120],{"mathvariant":2409},[898,113101,900],{},[902,113103,113104],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,113107,113108,113110,113111,113135,113136,113168],{},[38,113109,106791],{}," — (6.4) ",[883,113112,113114],{"className":113113},[886],[888,113115,113116],{"xmlns":890},[892,113117,113118,113132],{},[895,113119,113120,113128,113130],{},[28285,113121,113122,113124,113126],{},[898,113123,900],{},[898,113125,36887],{},[1706,113127,3142],{"mathvariant":2409,"lspace":3141,"rspace":3141},[1706,113129,8922],{},[2148,113131,2150],{},[902,113133,113134],{"encoding":904},"U'_i > 0",", (6.5) ",[883,113137,113139],{"className":113138},[886],[888,113140,113141],{"xmlns":890},[892,113142,113143,113165],{},[895,113144,113145,113161,113163],{},[28285,113146,113147,113149,113155],{},[898,113148,900],{},[895,113150,113151,113153],{},[898,113152,36887],{},[898,113154,36887],{},[895,113156,113157,113159],{},[1706,113158,3142],{"mathvariant":2409},[1706,113160,3142],{"mathvariant":2409},[1706,113162,2539],{},[2148,113164,2150],{},[902,113166,113167],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,113170,113171,1647,113173,113204,113205,1837],{},[38,113172,108579],{},[883,113174,113176],{"className":113175},[886],[888,113177,113178],{"xmlns":890},[892,113179,113180,113202],{},[895,113181,113182,113184,113186,113194],{},[898,113183,900],{},[1706,113185,1708],{},[28285,113187,113188,113190,113192],{},[898,113189,2146],{},[2148,113191,2701],{},[898,113193,207],{},[28285,113195,113196,113198,113200],{},[898,113197,2146],{},[2148,113199,2495],{},[898,113201,2450],{},[902,113203,54865],{"encoding":904}," — (6.6), speciálně ",[883,113206,113208],{"className":113207},[886],[888,113209,113210],{"xmlns":890},[892,113211,113212,113224],{},[895,113213,113214,113216,113218,113220,113222],{},[898,113215,2450],{},[1706,113217,1708],{},[2148,113219,2701],{},[1706,113221,1715],{},[898,113223,207],{},[902,113225,108733],{"encoding":904},[123,113227,113228,1647,113231,113266,113267,113280],{},[38,113229,113230],{},"Křivky užitečnosti (indiferenční)",[883,113232,113234],{"className":113233},[886],[888,113235,113236],{"xmlns":890},[892,113237,113238,113264],{},[895,113239,113240,113242,113244,113250,113252,113258,113260,113262],{},[898,113241,900],{},[1706,113243,2140],{"stretchy":2139},[2142,113245,113246,113248],{},[898,113247,2146],{},[2148,113249,2701],{},[1706,113251,2505],{"separator":2504},[2142,113253,113254,113256],{},[898,113255,2146],{},[2148,113257,2495],{},[1706,113259,2153],{"stretchy":2139},[1706,113261,1708],{},[898,113263,20413],{},[902,113265,28884],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,113268,113270],{"className":113269},[886],[888,113271,113272],{"xmlns":890},[892,113273,113274,113278],{},[895,113275,113276],{},[898,113277,900],{},[902,113279,900],{"encoding":904},", konvexní.",[123,113282,113283,1647,113285,113319],{},[38,113284,110124],{},[883,113286,113288],{"className":113287},[886],[888,113289,113290],{"xmlns":890},[892,113291,113292,113316],{},[895,113293,113294,113296,113298,113300,113306,113308,113310],{},[2415,113295,29714],{},[1706,113297,1708],{},[898,113299,1742],{},[2142,113301,113302,113304],{},[898,113303,900],{},[2148,113305,2701],{},[898,113307,15493],{"mathvariant":2409},[898,113309,1742],{},[2142,113311,113312,113314],{},[898,113313,900],{},[2148,113315,2495],{},[902,113317,113318],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,113321,113322,1647,113325,28885,113354,113357],{},[38,113323,113324],{},"Podmínka optimality",[883,113326,113328],{"className":113327},[886],[888,113329,113330],{"xmlns":890},[892,113331,113332,113352],{},[895,113333,113334,113336,113338,113344,113346],{},[2415,113335,29714],{},[1706,113337,1708],{},[2142,113339,113340,113342],{},[898,113341,1702],{},[2148,113343,2701],{},[898,113345,15493],{"mathvariant":2409},[2142,113347,113348,113350],{},[898,113349,1702],{},[2148,113351,2495],{},[902,113353,47069],{"encoding":904},[207,113355,55814],{"className":113356,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,113359,21083],{"id":21082},[120,113361,113362,113399,113440,113450],{},[123,113363,113364,1647,113367,113370,113371,113384,113385,113398],{},[38,113365,113366],{},"Navazující téma:",[207,113368,913],{"className":113369,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,113372,113374],{"className":113373},[886],[888,113375,113376],{"xmlns":890},[892,113377,113378,113382],{},[895,113379,113380],{},[898,113381,900],{},[902,113383,900],{"encoding":904},", min ",[883,113386,113388],{"className":113387},[886],[888,113389,113390],{"xmlns":890},[892,113391,113392,113396],{},[895,113393,113394],{},[898,113395,23410],{},[902,113397,23410],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,113400,113401,1647,113404,30204,113407,104367,113410,113413,113414,113417,113418,37745,113436,113439],{},[38,113402,113403],{},"Související pojmy:",[207,113405,784],{"className":113406,"dataFsResolvedFilePath":782,"href":783},[210],[207,113408,21102],{"className":113409,"dataFsResolvedFilePath":764,"href":765},[210],[207,113411,30199],{"className":113412,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,113415,21094],{"className":113416,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,113419,113421],{"className":113420},[886],[888,113422,113423],{"xmlns":890},[892,113424,113425,113433],{},[895,113426,113427],{},[2142,113428,113429,113431],{},[898,113430,2334],{},[898,113432,36887],{},[902,113434,113435],{"encoding":904},"D_i",[207,113437,793],{"className":113438,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,113441,113442,1647,113444,1343,113447],{},[38,113443,21113],{},[207,113445,1094],{"className":113446,"dataFsResolvedFilePath":838,"href":839},[210],[207,113448,1101],{"className":113449,"dataFsResolvedFilePath":868,"href":869},[210],[123,113451,113452,1647,113454],{},[38,113453,21126],{},[207,113455,21132],{"className":113456,"dataFsResolvedFilePath":21130,"href":21131},[210],{"title":641,"searchDepth":642,"depth":642,"links":113458},[113459,113460,113461,113464,113465,113468,113472,113473,113476,113477,113478,113479,113480,113481,113482],{"id":31114,"depth":642,"text":31115},{"id":104751,"depth":642,"text":104752},{"id":104811,"depth":642,"text":104812,"children":113462},[113463],{"id":104827,"depth":649,"text":104828},{"id":105134,"depth":642,"text":105135},{"id":105994,"depth":642,"text":105995,"children":113466},[113467],{"id":106541,"depth":649,"text":98170},{"id":106790,"depth":642,"text":106791,"children":113469},[113470],{"id":107663,"depth":649,"text":113471},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":108578,"depth":642,"text":108579},{"id":109114,"depth":642,"text":109115,"children":113474},[113475],{"id":109888,"depth":649,"text":109889},{"id":110118,"depth":642,"text":110119},{"id":110879,"depth":642,"text":110880},{"id":111417,"depth":642,"text":111418},{"id":15879,"depth":642,"text":15880},{"id":111553,"depth":642,"text":111554},{"id":19878,"depth":642,"text":19879},{"id":21082,"depth":642,"text":21083},{},"\u002Ftopics\u002Fuzitecnost",{"title":104535,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,28889,113489,104529,30234,113490],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":113493,"title":757,"body":113494,"course":1128,"courses":659,"created":1129,"description":113767,"extension":661,"meta":113768,"navigation":664,"path":113769,"seo":113770,"sources":113771,"stem":113772,"tags":113773,"type":21181,"updated":677,"__hash__":113779},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":113495,"toc":113759},[113496,113499,113506,113513,113517,113527,113529,113563,113567,113610,113613,113671,113675,113705,113709,113730,113732],[12,113497,757],{"id":113498},"základy-matematické-ekonomie",[724,113500,113501,113502,113505],{},"Úvodní pojmy a princip modelování v ",[207,113503,35480],{"className":113504,"dataFsResolvedFilePath":21130,"href":21131},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,113507,113508],{},[2286,113509],{"alt":113510,"className":113511,"src":113512},"imek-model-promenne",[210,2290],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,113514,113516],{"id":113515},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,113518,113519,113522,113523,113526],{},[38,113520,113521],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,113524,113525],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,113528,19879],{"id":19878},[120,113530,113531,113537,113543,113549,113558],{},[123,113532,113533,113536],{},[38,113534,113535],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,113538,113539,113542],{},[38,113540,113541],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,113544,113545,113548],{},[38,113546,113547],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,113550,113551,21021,113554,113557],{},[38,113552,113553],{},"Ceteris paribus",[614,113555,113556],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,113559,113560,113562],{},[38,113561,69674],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,113564,113566],{"id":113565},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,113568,113569,113609],{},[883,113570,113572],{"className":113571},[886],[888,113573,113574],{"xmlns":890},[892,113575,113576,113606],{},[895,113577,113578,113580,113582,113584,113586,113588,113590,113592,113594,113596,113598,113600,113602,113604],{},[898,113579,2146],{},[1706,113581,1708],{},[898,113583,2334],{},[1706,113585,2140],{"stretchy":2139},[898,113587,1702],{},[1706,113589,2505],{"separator":2504},[898,113591,28247],{},[1706,113593,2505],{"separator":2504},[898,113595,37391],{},[1706,113597,2505],{"separator":2504},[898,113599,900],{},[1706,113601,2505],{"separator":2504},[1706,113603,28763],{},[1706,113605,2153],{"stretchy":2139},[902,113607,113608],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,113611,113612],{},"Zjednodušení:",[120,113614,113615,113643],{},[123,113616,113617,1647,113620],{},[38,113618,113619],{},"Jednofaktorový model:",[883,113621,113623],{"className":113622},[886],[888,113624,113625],{"xmlns":890},[892,113626,113627,113641],{},[895,113628,113629,113631,113633,113635,113637,113639],{},[898,113630,2146],{},[1706,113632,1708],{},[898,113634,2334],{},[1706,113636,2140],{"stretchy":2139},[898,113638,1702],{},[1706,113640,2153],{"stretchy":2139},[902,113642,23350],{"encoding":904},[123,113644,113645,1647,113648],{},[38,113646,113647],{},"Inverzní zápis:",[883,113649,113651],{"className":113650},[886],[888,113652,113653],{"xmlns":890},[892,113654,113655,113669],{},[895,113656,113657,113659,113661,113663,113665,113667],{},[898,113658,1702],{},[1706,113660,1708],{},[898,113662,2334],{},[1706,113664,2140],{"stretchy":2139},[898,113666,2146],{},[1706,113668,2153],{"stretchy":2139},[902,113670,2343],{"encoding":904},[115,113672,113674],{"id":113673},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,113676,113677,113686],{},[123,113678,113679,113682,113683,1936],{},[38,113680,113681],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,113684,35339],{"className":113685,"dataFsResolvedFilePath":800,"href":801},[210],[123,113687,113688,113691,113692,113695,113696,113699,113700,113704],{},[38,113689,113690],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,113693,1145],{"className":113694,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,113697,35352],{"className":113698,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,113701,113703],{"className":113702,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,113706,113708],{"id":113707},"konvence-z-přednášek","Konvence z přednášek",[120,113710,113711,113718,113724],{},[123,113712,113713,113714,113717],{},"Symbol ",[113715,113716,3248],"code",{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,113719,113720,113721,1837],{},"Numerické výsledky ",[38,113722,113723],{},"na 3 desetinná místa",[123,113725,23062,113726,113729],{},[614,113727,113728],{},"jednotková změna"," má standardní význam (změna o 1).",[115,113731,21083],{"id":21082},[120,113733,113734,113739,113747],{},[123,113735,113736,113738],{},[38,113737,22971],{}," —",[123,113740,113741,1647,113743],{},[38,113742,22979],{},[207,113744,113746],{"className":113745,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,113748,113749,1647,113751,1343,113755],{},[38,113750,22987],{},[207,113752,113754],{"className":113753,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,113756,113758],{"className":113757,"dataFsResolvedFilePath":21130,"href":21131},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":113760},[113761,113762,113763,113764,113765,113766],{"id":113515,"depth":642,"text":113516},{"id":19878,"depth":642,"text":19879},{"id":113565,"depth":642,"text":113566},{"id":113673,"depth":642,"text":113674},{"id":113707,"depth":642,"text":113708},{"id":21082,"depth":642,"text":21083},"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":113767},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,113774,113775,113776,113777,113778],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":113781,"title":113782,"body":113783,"course":1128,"courses":659,"created":21169,"description":641,"extension":661,"meta":118055,"navigation":664,"path":118056,"seo":118057,"sources":118058,"stem":118059,"tags":118060,"type":21181,"updated":677,"__hash__":118064},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":113784,"toc":118038},[113785,113788,113882,113886,113908,113922,113974,113976,113980,114043,114086,114105,114268,114367,114370,114437,114441,114570,114609,114639,114751,114796,114862,114915,114991,115047,115049,115053,115117,115161,115181,115342,115345,115429,115526,115529,115595,115599,115648,115674,115779,115843,115848,115944,115991,115993,115996,116018,116060,116067,116100,116102,116173,116227,116336,116340,116429,116505,116769,116807,116809,116813,116816,116823,117134,117137,117195,117375,117404,117406,117410,117416,117554,117563,117565,117567,117992,117994,117996],[12,113786,113782],{"id":113787},"zdanění-trhu-dopady-daně-na-rovnováhu",[1636,113789,113790],{},[724,113791,113792,61677,113794,113807,113808,113811,113812,113814,113815,113818,113819,113840,113841,113864,113865,113868,113869,1837],{},[883,113793,3174],{},[883,113795,113797],{"className":113796},[886],[888,113798,113799],{"xmlns":890},[892,113800,113801,113805],{},[895,113802,113803],{},[898,113804,1659],{},[902,113806,1659],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,113809,113810],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,113813,104819],{}," (je-li uložena spotřebiteli). Výsledné ",[38,113816,113817],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,113820,113822],{"className":113821},[886],[888,113823,113824],{"xmlns":890},[892,113825,113826,113838],{},[895,113827,113828],{},[2142,113829,113830,113832],{},[898,113831,1659],{},[895,113833,113834,113836],{},[898,113835,61726],{},[898,113837,724],{},[902,113839,61731],{"encoding":904}," (spotřebitel) a ",[883,113842,113844],{"className":113843},[886],[888,113845,113846],{"xmlns":890},[892,113847,113848,113862],{},[895,113849,113850],{},[2142,113851,113852,113854],{},[898,113853,1659],{},[895,113855,113856,113858,113860],{},[898,113857,61749],{},[898,113859,6930],{},[898,113861,3950],{},[902,113863,61756],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,113866,113867],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,113870,113872],{"className":113871},[886],[888,113873,113874],{"xmlns":890},[892,113875,113876,113880],{},[895,113877,113878],{},[898,113879,1659],{},[902,113881,1659],{"encoding":904},[115,113883,113885],{"id":113884},"dvě-formy-zdanění","Dvě formy zdanění",[724,113887,113888,113889,113907],{},"Uvažujme jednotkovou daň ",[883,113890,113892],{"className":113891},[886],[888,113893,113894],{"xmlns":890},[892,113895,113896,113904],{},[895,113897,113898,113900,113902],{},[898,113899,1659],{},[1706,113901,8922],{},[2148,113903,2150],{},[902,113905,113906],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,113909,113910,113916],{},[123,113911,113912,113915],{},[38,113913,113914],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,113917,113918,113921],{},[38,113919,113920],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,113923,113924,113925,113938,113939,113942,113943,1837],{},"V obou případech dochází k posunu jedné z křivek o ",[883,113926,113928],{"className":113927},[886],[888,113929,113930],{"xmlns":890},[892,113931,113932,113936],{},[895,113933,113934],{},[898,113935,1659],{},[902,113937,1659],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,113940,113941],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,113944,113946],{"className":113945},[886],[888,113947,113948],{"xmlns":890},[892,113949,113950,113972],{},[895,113951,113952,113954,113956,113962,113964,113970],{},[898,113953,23410],{},[1706,113955,21693],{"stretchy":2139},[2489,113957,113958,113960],{},[898,113959,2146],{},[898,113961,23410],{},[1706,113963,2505],{"separator":2504},[2489,113965,113966,113968],{},[898,113967,1702],{},[898,113969,23410],{},[1706,113971,21708],{"stretchy":2139},[902,113973,60420],{"encoding":904},[56029,113975],{},[115,113977,113979],{"id":113978},"daň-uložená-výrobci","Daň uložená výrobci",[724,113981,113982,113983,113996,113997,114014,114015,114042],{},"Je-li daň ",[883,113984,113986],{"className":113985},[886],[888,113987,113988],{"xmlns":890},[892,113989,113990,113994],{},[895,113991,113992],{},[898,113993,1659],{},[902,113995,1659],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,113998,114000],{"className":113999},[886],[888,114001,114002],{"xmlns":890},[892,114003,114004,114012],{},[895,114005,114006,114008,114010],{},[898,114007,1702],{},[1706,114009,1715],{},[898,114011,1659],{},[902,114013,60175],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,114016,114018],{"className":114017},[886],[888,114019,114020],{"xmlns":890},[892,114021,114022,114040],{},[895,114023,114024,114026,114028,114030,114032,114034,114036,114038],{},[898,114025,1702],{},[1706,114027,1715],{},[898,114029,1659],{},[1706,114031,1708],{},[898,114033,14171],{},[1706,114035,2140],{"stretchy":2139},[898,114037,2146],{},[1706,114039,2153],{"stretchy":2139},[902,114041,60204],{"encoding":904}," nová funkce nabídky:",[883,114044,114046],{"className":114045},[886],[888,114047,114048],{"xmlns":890,"display":2350},[892,114049,114050,114084],{},[895,114051,114052,114054,114056,114062,114064,114066,114068,114070,114072,114074,114076,114078,114080,114082],{},[898,114053,1702],{},[1706,114055,1708],{},[2142,114057,114058,114060],{},[898,114059,14171],{},[2148,114061,2701],{},[1706,114063,2140],{"stretchy":2139},[898,114065,2146],{},[1706,114067,2153],{"stretchy":2139},[1706,114069,1708],{},[898,114071,14171],{},[1706,114073,2140],{"stretchy":2139},[898,114075,2146],{},[1706,114077,2153],{"stretchy":2139},[1706,114079,2447],{},[898,114081,1659],{},[898,114083,1837],{"mathvariant":2409},[902,114085,60249],{"encoding":904},[724,114087,114088,114089,1647,114102,114104],{},"Nabídka se tedy posouvá o ",[883,114090,114092],{"className":114091},[886],[888,114093,114094],{"xmlns":890},[892,114095,114096,114100],{},[895,114097,114098],{},[898,114099,1659],{},[902,114101,1659],{"encoding":904},[38,114103,60282],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,114106,114107,114108,114148,114149,1993,114177,114205,114206,114225,114226,114250,114251,1936],{},"Nový rovnovážný bod ",[883,114109,114111],{"className":114110},[886],[888,114112,114113],{"xmlns":890},[892,114114,114115,114145],{},[895,114116,114117,114123,114125,114133,114135,114143],{},[2142,114118,114119,114121],{},[898,114120,23410],{},[2148,114122,2701],{},[1706,114124,21693],{"stretchy":2139},[28285,114126,114127,114129,114131],{},[898,114128,2146],{},[2148,114130,2701],{},[898,114132,23410],{},[1706,114134,2505],{"separator":2504},[28285,114136,114137,114139,114141],{},[898,114138,1702],{},[2148,114140,2701],{},[898,114142,23410],{},[1706,114144,21708],{"stretchy":2139},[902,114146,114147],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,114150,114152],{"className":114151},[886],[888,114153,114154],{"xmlns":890},[892,114155,114156,114174],{},[895,114157,114158,114166,114168],{},[28285,114159,114160,114162,114164],{},[898,114161,2146],{},[2148,114163,2701],{},[898,114165,23410],{},[1706,114167,2539],{},[2489,114169,114170,114172],{},[898,114171,2146],{},[898,114173,23410],{},[902,114175,114176],{"encoding":904},"Q_1^E \u003C Q^E",[883,114178,114180],{"className":114179},[886],[888,114181,114182],{"xmlns":890},[892,114183,114184,114202],{},[895,114185,114186,114194,114196],{},[28285,114187,114188,114190,114192],{},[898,114189,1702],{},[2148,114191,2701],{},[898,114193,23410],{},[1706,114195,8922],{},[2489,114197,114198,114200],{},[898,114199,1702],{},[898,114201,23410],{},[902,114203,114204],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,114207,114209],{"className":114208},[886],[888,114210,114211],{"xmlns":890},[892,114212,114213,114223],{},[895,114214,114215],{},[28285,114216,114217,114219,114221],{},[898,114218,1702],{},[2148,114220,2701],{},[898,114222,23410],{},[902,114224,66899],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,114227,114229],{"className":114228},[886],[888,114230,114231],{"xmlns":890},[892,114232,114233,114247],{},[895,114234,114235,114243,114245],{},[28285,114236,114237,114239,114241],{},[898,114238,1702],{},[2148,114240,2701],{},[898,114242,23410],{},[1706,114244,1715],{},[898,114246,1659],{},[902,114248,114249],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,114252,114254],{"className":114253},[886],[888,114255,114256],{"xmlns":890},[892,114257,114258,114266],{},[895,114259,114260],{},[2489,114261,114262,114264],{},[898,114263,1702],{},[898,114265,23410],{},[902,114267,60519],{"encoding":904},[724,114269,114270],{},[614,114271,114272,114273,114303,114304,114317,114318,24808,114335,114348,114349,1837],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,114274,114276],{"className":114275},[886],[888,114277,114278],{"xmlns":890},[892,114279,114280,114300],{},[895,114281,114282,114284,114286,114292,114294,114296,114298],{},[898,114283,14171],{},[1706,114285,5915],{},[2142,114287,114288,114290],{},[898,114289,14171],{},[2148,114291,2701],{},[1706,114293,1708],{},[898,114295,14171],{},[1706,114297,2447],{},[898,114299,1659],{},[902,114301,114302],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,114305,114307],{"className":114306},[886],[888,114308,114309],{"xmlns":890},[892,114310,114311,114315],{},[895,114312,114313],{},[898,114314,1659],{},[902,114316,1659],{"encoding":904},". Průsečík ",[883,114319,114321],{"className":114320},[886],[888,114322,114323],{"xmlns":890},[892,114324,114325,114333],{},[895,114326,114327],{},[2142,114328,114329,114331],{},[898,114330,14171],{},[2148,114332,2701],{},[902,114334,60050],{"encoding":904},[883,114336,114338],{"className":114337},[886],[888,114339,114340],{"xmlns":890},[892,114341,114342,114346],{},[895,114343,114344],{},[898,114345,2334],{},[902,114347,2334],{"encoding":904}," je nový rovnovážný bod ",[883,114350,114352],{"className":114351},[886],[888,114353,114354],{"xmlns":890},[892,114355,114356,114364],{},[895,114357,114358],{},[2142,114359,114360,114362],{},[898,114361,23410],{},[2148,114363,2701],{},[902,114365,114366],{"encoding":904},"E_1",[198,114368,64349],{"id":114369},"příklad-29",[724,114371,114372,60707,114374,60742,114398,114418,114419,114436],{},[38,114373,56990],{},[883,114375,114377],{"className":114376},[886],[888,114378,114379],{"xmlns":890},[892,114380,114381,114395],{},[895,114382,114383,114385,114387,114389,114391,114393],{},[898,114384,1702],{},[1706,114386,1708],{},[2148,114388,7156],{},[1706,114390,1715],{},[2148,114392,2495],{},[898,114394,2146],{},[902,114396,114397],{"encoding":904},"P = 12 - 2Q",[883,114399,114401],{"className":114400},[886],[888,114402,114403],{"xmlns":890},[892,114404,114405,114415],{},[895,114406,114407,114409,114411,114413],{},[898,114408,1702],{},[1706,114410,1708],{},[2148,114412,3455],{},[898,114414,2146],{},[902,114416,114417],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,114420,114422],{"className":114421},[886],[888,114423,114424],{"xmlns":890},[892,114425,114426,114434],{},[895,114427,114428,114430,114432],{},[898,114429,1659],{},[1706,114431,1708],{},[2148,114433,7044],{},[902,114435,60321],{"encoding":904}," Kč.",[724,114438,114439],{},[38,114440,57022],{},[724,114442,114443,114446,114447,24710,114473,24728,114493,1343,114515,114545,114546,1837],{},[614,114444,114445],{},"Bez daně."," Z rovnosti ",[883,114448,114450],{"className":114449},[886],[888,114451,114452],{"xmlns":890},[892,114453,114454,114470],{},[895,114455,114456,114458,114460,114462,114464,114466,114468],{},[2148,114457,7156],{},[1706,114459,1715],{},[2148,114461,2495],{},[898,114463,2146],{},[1706,114465,1708],{},[2148,114467,3455],{},[898,114469,2146],{},[902,114471,114472],{"encoding":904},"12 - 2Q = 4Q",[883,114474,114476],{"className":114475},[886],[888,114477,114478],{"xmlns":890},[892,114479,114480,114490],{},[895,114481,114482,114484,114486,114488],{},[2148,114483,7044],{},[898,114485,2146],{},[1706,114487,1708],{},[2148,114489,7156],{},[902,114491,114492],{"encoding":904},"6Q = 12",[883,114494,114496],{"className":114495},[886],[888,114497,114498],{"xmlns":890},[892,114499,114500,114512],{},[895,114501,114502,114508,114510],{},[2489,114503,114504,114506],{},[898,114505,2146],{},[898,114507,23410],{},[1706,114509,1708],{},[2148,114511,2495],{},[902,114513,114514],{"encoding":904},"Q^E = 2",[883,114516,114518],{"className":114517},[886],[888,114519,114520],{"xmlns":890},[892,114521,114522,114542],{},[895,114523,114524,114530,114532,114534,114536,114538,114540],{},[2489,114525,114526,114528],{},[898,114527,1702],{},[898,114529,23410],{},[1706,114531,1708],{},[2148,114533,3455],{},[1706,114535,2390],{},[2148,114537,2495],{},[1706,114539,1708],{},[2148,114541,12717],{},[902,114543,114544],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,114547,114549],{"className":114548},[886],[888,114550,114551],{"xmlns":890},[892,114552,114553,114567],{},[895,114554,114555,114557,114559,114561,114563,114565],{},[898,114556,23410],{},[1706,114558,21693],{"stretchy":2139},[2148,114560,2495],{},[1706,114562,2505],{"separator":2504},[2148,114564,12717],{},[1706,114566,21708],{"stretchy":2139},[902,114568,114569],{"encoding":904},"E[2, 8]",[724,114571,114572,114575,114576,114608],{},[614,114573,114574],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,114577,114579],{"className":114578},[886],[888,114580,114581],{"xmlns":890},[892,114582,114583,114605],{},[895,114584,114585,114591,114593,114595,114597,114599,114601,114603],{},[2142,114586,114587,114589],{},[898,114588,14171],{},[2148,114590,2701],{},[1706,114592,4288],{},[898,114594,1702],{},[1706,114596,1708],{},[2148,114598,3455],{},[898,114600,2146],{},[1706,114602,2447],{},[2148,114604,7044],{},[902,114606,114607],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,114610,114612],{"className":114611},[886],[888,114613,114614],{"xmlns":890,"display":2350},[892,114615,114616,114636],{},[895,114617,114618,114620,114622,114624,114626,114628,114630,114632,114634],{},[2148,114619,7156],{},[1706,114621,1715],{},[2148,114623,2495],{},[898,114625,2146],{},[1706,114627,1708],{},[2148,114629,3455],{},[898,114631,2146],{},[1706,114633,2447],{},[2148,114635,7044],{},[902,114637,114638],{"encoding":904},"12 - 2Q = 4Q + 6",[724,114640,114641,114642,24728,114662,1343,114686,114722,114723,1837],{},"plyne ",[883,114643,114645],{"className":114644},[886],[888,114646,114647],{"xmlns":890},[892,114648,114649,114659],{},[895,114650,114651,114653,114655,114657],{},[2148,114652,7044],{},[898,114654,2146],{},[1706,114656,1708],{},[2148,114658,7044],{},[902,114660,114661],{"encoding":904},"6Q = 6",[883,114663,114665],{"className":114664},[886],[888,114666,114667],{"xmlns":890},[892,114668,114669,114683],{},[895,114670,114671,114679,114681],{},[28285,114672,114673,114675,114677],{},[898,114674,2146],{},[2148,114676,2701],{},[898,114678,23410],{},[1706,114680,1708],{},[2148,114682,2701],{},[902,114684,114685],{"encoding":904},"Q_1^E = 1",[883,114687,114689],{"className":114688},[886],[888,114690,114691],{"xmlns":890},[892,114692,114693,114719],{},[895,114694,114695,114703,114705,114707,114709,114711,114713,114715,114717],{},[28285,114696,114697,114699,114701],{},[898,114698,1702],{},[2148,114700,2701],{},[898,114702,23410],{},[1706,114704,1708],{},[2148,114706,3455],{},[1706,114708,2390],{},[2148,114710,2701],{},[1706,114712,2447],{},[2148,114714,7044],{},[1706,114716,1708],{},[2148,114718,7786],{},[902,114720,114721],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,114724,114726],{"className":114725},[886],[888,114727,114728],{"xmlns":890},[892,114729,114730,114748],{},[895,114731,114732,114738,114740,114742,114744,114746],{},[2142,114733,114734,114736],{},[898,114735,23410],{},[2148,114737,2701],{},[1706,114739,21693],{"stretchy":2139},[2148,114741,2701],{},[1706,114743,2505],{"separator":2504},[2148,114745,7786],{},[1706,114747,21708],{"stretchy":2139},[902,114749,114750],{"encoding":904},"E_1[1, 10]",[724,114752,114753,114756,114757,114781,114782,114795],{},[614,114754,114755],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,114758,114760],{"className":114759},[886],[888,114761,114762],{"xmlns":890},[892,114763,114764,114778],{},[895,114765,114766,114774,114776],{},[28285,114767,114768,114770,114772],{},[898,114769,1702],{},[2148,114771,2701],{},[898,114773,23410],{},[1706,114775,1708],{},[2148,114777,7786],{},[902,114779,114780],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,114783,114785],{"className":114784},[886],[888,114786,114787],{"xmlns":890},[892,114788,114789,114793],{},[895,114790,114791],{},[2148,114792,12717],{},[902,114794,12717],{"encoding":904},", navýšení je",[883,114797,114799],{"className":114798},[886],[888,114800,114801],{"xmlns":890,"display":2350},[892,114802,114803,114859],{},[895,114804,114805,114815,114817,114825,114827,114833,114835,114837,114839,114841,114843,114845,114847,114857],{},[2142,114806,114807,114809],{},[898,114808,1659],{},[895,114810,114811,114813],{},[898,114812,61726],{},[898,114814,724],{},[1706,114816,1708],{},[28285,114818,114819,114821,114823],{},[898,114820,1702],{},[2148,114822,2701],{},[898,114824,23410],{},[1706,114826,1715],{},[2489,114828,114829,114831],{},[898,114830,1702],{},[898,114832,23410],{},[1706,114834,1708],{},[2148,114836,7786],{},[1706,114838,1715],{},[2148,114840,12717],{},[1706,114842,1708],{},[2148,114844,2495],{},[2415,114846,21505],{},[895,114848,114849,114851],{},[2415,114850,28915],{},[3925,114852,114853,114855],{"accent":2504},[2415,114854,20413],{},[1706,114856,3932],{},[898,114858,1837],{"mathvariant":2409},[902,114860,114861],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,114863,114864,114865,114781,114901,114914],{},"Výrobci zůstává čistá cena ",[883,114866,114868],{"className":114867},[886],[888,114869,114870],{"xmlns":890},[892,114871,114872,114898],{},[895,114873,114874,114882,114884,114886,114888,114890,114892,114894,114896],{},[28285,114875,114876,114878,114880],{},[898,114877,1702],{},[2148,114879,2701],{},[898,114881,23410],{},[1706,114883,1715],{},[898,114885,1659],{},[1706,114887,1708],{},[2148,114889,7786],{},[1706,114891,1715],{},[2148,114893,7044],{},[1706,114895,1708],{},[2148,114897,3455],{},[902,114899,114900],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,114902,114904],{"className":114903},[886],[888,114905,114906],{"xmlns":890},[892,114907,114908,114912],{},[895,114909,114910],{},[2148,114911,12717],{},[902,114913,12717],{"encoding":904},", pokles je",[883,114916,114918],{"className":114917},[886],[888,114919,114920],{"xmlns":890,"display":2350},[892,114921,114922,114988],{},[895,114923,114924,114936,114938,114944,114946,114948,114956,114958,114960,114962,114964,114966,114968,114970,114972,114974,114976,114986],{},[2142,114925,114926,114928],{},[898,114927,1659],{},[895,114929,114930,114932,114934],{},[898,114931,61749],{},[898,114933,6930],{},[898,114935,3950],{},[1706,114937,1708],{},[2489,114939,114940,114942],{},[898,114941,1702],{},[898,114943,23410],{},[1706,114945,1715],{},[1706,114947,2140],{"stretchy":2139},[28285,114949,114950,114952,114954],{},[898,114951,1702],{},[2148,114953,2701],{},[898,114955,23410],{},[1706,114957,1715],{},[898,114959,1659],{},[1706,114961,2153],{"stretchy":2139},[1706,114963,1708],{},[2148,114965,12717],{},[1706,114967,1715],{},[2148,114969,3455],{},[1706,114971,1708],{},[2148,114973,3455],{},[2415,114975,21505],{},[895,114977,114978,114980],{},[2415,114979,28915],{},[3925,114981,114982,114984],{"accent":2504},[2415,114983,20413],{},[1706,114985,3932],{},[898,114987,1837],{"mathvariant":2409},[902,114989,114990],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,114992,114993,114994,115046],{},"Kontrola: ",[883,114995,114997],{"className":114996},[886],[888,114998,114999],{"xmlns":890},[892,115000,115001,115043],{},[895,115002,115003,115013,115015,115027,115029,115031,115033,115035,115037,115039,115041],{},[2142,115004,115005,115007],{},[898,115006,1659],{},[895,115008,115009,115011],{},[898,115010,61726],{},[898,115012,724],{},[1706,115014,2447],{},[2142,115016,115017,115019],{},[898,115018,1659],{},[895,115020,115021,115023,115025],{},[898,115022,61749],{},[898,115024,6930],{},[898,115026,3950],{},[1706,115028,1708],{},[2148,115030,2495],{},[1706,115032,2447],{},[2148,115034,3455],{},[1706,115036,1708],{},[2148,115038,7044],{},[1706,115040,1708],{},[898,115042,1659],{},[902,115044,115045],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[56029,115048],{},[115,115050,115052],{"id":115051},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,115054,113982,115055,115068,115069,115087,115088,115116],{},[883,115056,115058],{"className":115057},[886],[888,115059,115060],{"xmlns":890},[892,115061,115062,115066],{},[895,115063,115064],{},[898,115065,1659],{},[902,115067,1659],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,115070,115072],{"className":115071},[886],[888,115073,115074],{"xmlns":890},[892,115075,115076,115084],{},[895,115077,115078,115080,115082],{},[898,115079,1702],{},[1706,115081,2447],{},[898,115083,1659],{},[902,115085,115086],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,115089,115091],{"className":115090},[886],[888,115092,115093],{"xmlns":890},[892,115094,115095,115113],{},[895,115096,115097,115099,115101,115103,115105,115107,115109,115111],{},[898,115098,1702],{},[1706,115100,2447],{},[898,115102,1659],{},[1706,115104,1708],{},[898,115106,2334],{},[1706,115108,2140],{"stretchy":2139},[898,115110,2146],{},[1706,115112,2153],{"stretchy":2139},[902,115114,115115],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,115118,115120],{"className":115119},[886],[888,115121,115122],{"xmlns":890,"display":2350},[892,115123,115124,115158],{},[895,115125,115126,115128,115130,115136,115138,115140,115142,115144,115146,115148,115150,115152,115154,115156],{},[898,115127,1702],{},[1706,115129,1708],{},[2142,115131,115132,115134],{},[898,115133,2334],{},[2148,115135,2495],{},[1706,115137,2140],{"stretchy":2139},[898,115139,2146],{},[1706,115141,2153],{"stretchy":2139},[1706,115143,1708],{},[898,115145,2334],{},[1706,115147,2140],{"stretchy":2139},[898,115149,2146],{},[1706,115151,2153],{"stretchy":2139},[1706,115153,1715],{},[898,115155,1659],{},[898,115157,1837],{"mathvariant":2409},[902,115159,115160],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,115162,115163,115164,1647,115177,115180],{},"Poptávka se tedy posouvá o ",[883,115165,115167],{"className":115166},[886],[888,115168,115169],{"xmlns":890},[892,115170,115171,115175],{},[895,115172,115173],{},[898,115174,1659],{},[902,115176,1659],{"encoding":904},[38,115178,115179],{},"svisle dolů",". Nabídka se nemění.",[724,115182,114107,115183,114148,115223,1993,115251,115279,115280,115299,115300,115324,115325,1936],{},[883,115184,115186],{"className":115185},[886],[888,115187,115188],{"xmlns":890},[892,115189,115190,115220],{},[895,115191,115192,115198,115200,115208,115210,115218],{},[2142,115193,115194,115196],{},[898,115195,23410],{},[2148,115197,2495],{},[1706,115199,21693],{"stretchy":2139},[28285,115201,115202,115204,115206],{},[898,115203,2146],{},[2148,115205,2495],{},[898,115207,23410],{},[1706,115209,2505],{"separator":2504},[28285,115211,115212,115214,115216],{},[898,115213,1702],{},[2148,115215,2495],{},[898,115217,23410],{},[1706,115219,21708],{"stretchy":2139},[902,115221,115222],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,115224,115226],{"className":115225},[886],[888,115227,115228],{"xmlns":890},[892,115229,115230,115248],{},[895,115231,115232,115240,115242],{},[28285,115233,115234,115236,115238],{},[898,115235,2146],{},[2148,115237,2495],{},[898,115239,23410],{},[1706,115241,2539],{},[2489,115243,115244,115246],{},[898,115245,2146],{},[898,115247,23410],{},[902,115249,115250],{"encoding":904},"Q_2^E \u003C Q^E",[883,115252,115254],{"className":115253},[886],[888,115255,115256],{"xmlns":890},[892,115257,115258,115276],{},[895,115259,115260,115268,115270],{},[28285,115261,115262,115264,115266],{},[898,115263,1702],{},[2148,115265,2495],{},[898,115267,23410],{},[1706,115269,2539],{},[2489,115271,115272,115274],{},[898,115273,1702],{},[898,115275,23410],{},[902,115277,115278],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,115281,115283],{"className":115282},[886],[888,115284,115285],{"xmlns":890},[892,115286,115287,115297],{},[895,115288,115289],{},[28285,115290,115291,115293,115295],{},[898,115292,1702],{},[2148,115294,2495],{},[898,115296,23410],{},[902,115298,66960],{"encoding":904},", spotřebitel platí celkem ",[883,115301,115303],{"className":115302},[886],[888,115304,115305],{"xmlns":890},[892,115306,115307,115321],{},[895,115308,115309,115317,115319],{},[28285,115310,115311,115313,115315],{},[898,115312,1702],{},[2148,115314,2495],{},[898,115316,23410],{},[1706,115318,2447],{},[898,115320,1659],{},[902,115322,115323],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,115326,115328],{"className":115327},[886],[888,115329,115330],{"xmlns":890},[892,115331,115332,115340],{},[895,115333,115334],{},[2489,115335,115336,115338],{},[898,115337,1702],{},[898,115339,23410],{},[902,115341,60519],{"encoding":904},[724,115343,115344],{},"Daňové břemeno:",[883,115346,115348],{"className":115347},[886],[888,115349,115350],{"xmlns":890,"display":2350},[892,115351,115352,115426],{},[895,115353,115354,115364,115366,115368,115376,115378,115380,115382,115384,115390,115392,115394,115406,115408,115414,115416,115424],{},[2142,115355,115356,115358],{},[898,115357,1659],{},[895,115359,115360,115362],{},[898,115361,61726],{},[898,115363,724],{},[1706,115365,1708],{},[1706,115367,2140],{"stretchy":2139},[28285,115369,115370,115372,115374],{},[898,115371,1702],{},[2148,115373,2495],{},[898,115375,23410],{},[1706,115377,2447],{},[898,115379,1659],{},[1706,115381,2153],{"stretchy":2139},[1706,115383,1715],{},[2489,115385,115386,115388],{},[898,115387,1702],{},[898,115389,23410],{},[1706,115391,2505],{"separator":2504},[4898,115393],{"width":9524},[2142,115395,115396,115398],{},[898,115397,1659],{},[895,115399,115400,115402,115404],{},[898,115401,61749],{},[898,115403,6930],{},[898,115405,3950],{},[1706,115407,1708],{},[2489,115409,115410,115412],{},[898,115411,1702],{},[898,115413,23410],{},[1706,115415,1715],{},[28285,115417,115418,115420,115422],{},[898,115419,1702],{},[2148,115421,2495],{},[898,115423,23410],{},[898,115425,1837],{"mathvariant":2409},[902,115427,115428],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,115430,115431],{},[614,115432,115433,115434,115464,115465,114317,115478,24808,115495,114348,115508,1837],{},"Obrázek 2.19: Posun ",[883,115435,115437],{"className":115436},[886],[888,115438,115439],{"xmlns":890},[892,115440,115441,115461],{},[895,115442,115443,115445,115447,115453,115455,115457,115459],{},[898,115444,2334],{},[1706,115446,5915],{},[2142,115448,115449,115451],{},[898,115450,2334],{},[2148,115452,2495],{},[1706,115454,1708],{},[898,115456,2334],{},[1706,115458,1715],{},[898,115460,1659],{},[902,115462,115463],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,115466,115468],{"className":115467},[886],[888,115469,115470],{"xmlns":890},[892,115471,115472,115476],{},[895,115473,115474],{},[898,115475,1659],{},[902,115477,1659],{"encoding":904},[883,115479,115481],{"className":115480},[886],[888,115482,115483],{"xmlns":890},[892,115484,115485,115493],{},[895,115486,115487],{},[2142,115488,115489,115491],{},[898,115490,2334],{},[2148,115492,2495],{},[902,115494,57382],{"encoding":904},[883,115496,115498],{"className":115497},[886],[888,115499,115500],{"xmlns":890},[892,115501,115502,115506],{},[895,115503,115504],{},[898,115505,14171],{},[902,115507,14171],{"encoding":904},[883,115509,115511],{"className":115510},[886],[888,115512,115513],{"xmlns":890},[892,115514,115515,115523],{},[895,115516,115517],{},[2142,115518,115519,115521],{},[898,115520,23410],{},[2148,115522,2495],{},[902,115524,115525],{"encoding":904},"E_2",[198,115527,64429],{"id":115528},"příklad-210",[724,115530,115531,115533,115534,60742,115557,115576,115577,115594],{},[38,115532,56990],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,115535,115537],{"className":115536},[886],[888,115538,115539],{"xmlns":890},[892,115540,115541,115555],{},[895,115542,115543,115545,115547,115549,115551,115553],{},[898,115544,1702],{},[1706,115546,1708],{},[2148,115548,7156],{},[1706,115550,1715],{},[2148,115552,2495],{},[898,115554,2146],{},[902,115556,114397],{"encoding":904},[883,115558,115560],{"className":115559},[886],[888,115561,115562],{"xmlns":890},[892,115563,115564,115574],{},[895,115565,115566,115568,115570,115572],{},[898,115567,1702],{},[1706,115569,1708],{},[2148,115571,3455],{},[898,115573,2146],{},[902,115575,114417],{"encoding":904},". Daň ",[883,115578,115580],{"className":115579},[886],[888,115581,115582],{"xmlns":890},[892,115583,115584,115592],{},[895,115585,115586,115588,115590],{},[898,115587,1659],{},[1706,115589,1708],{},[2148,115591,7044],{},[902,115593,60321],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,115596,115597],{},[38,115598,57022],{},[724,115600,115601,115602,114608],{},"Nová poptávka je ",[883,115603,115605],{"className":115604},[886],[888,115606,115607],{"xmlns":890},[892,115608,115609,115645],{},[895,115610,115611,115617,115619,115621,115623,115625,115627,115629,115631,115633,115635,115637,115639,115641,115643],{},[2142,115612,115613,115615],{},[898,115614,2334],{},[2148,115616,2495],{},[1706,115618,4288],{},[898,115620,1702],{},[1706,115622,1708],{},[2148,115624,7156],{},[1706,115626,1715],{},[2148,115628,2495],{},[898,115630,2146],{},[1706,115632,1715],{},[2148,115634,7044],{},[1706,115636,1708],{},[2148,115638,7044],{},[1706,115640,1715],{},[2148,115642,2495],{},[898,115644,2146],{},[902,115646,115647],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,115649,115651],{"className":115650},[886],[888,115652,115653],{"xmlns":890,"display":2350},[892,115654,115655,115671],{},[895,115656,115657,115659,115661,115663,115665,115667,115669],{},[2148,115658,7044],{},[1706,115660,1715],{},[2148,115662,2495],{},[898,115664,2146],{},[1706,115666,1708],{},[2148,115668,3455],{},[898,115670,2146],{},[902,115672,115673],{"encoding":904},"6 - 2Q = 4Q",[724,115675,114641,115676,24728,115695,1343,115719,114722,115751,1837],{},[883,115677,115679],{"className":115678},[886],[888,115680,115681],{"xmlns":890},[892,115682,115683,115693],{},[895,115684,115685,115687,115689,115691],{},[2148,115686,7044],{},[898,115688,2146],{},[1706,115690,1708],{},[2148,115692,7044],{},[902,115694,114661],{"encoding":904},[883,115696,115698],{"className":115697},[886],[888,115699,115700],{"xmlns":890},[892,115701,115702,115716],{},[895,115703,115704,115712,115714],{},[28285,115705,115706,115708,115710],{},[898,115707,2146],{},[2148,115709,2495],{},[898,115711,23410],{},[1706,115713,1708],{},[2148,115715,2701],{},[902,115717,115718],{"encoding":904},"Q_2^E = 1",[883,115720,115722],{"className":115721},[886],[888,115723,115724],{"xmlns":890},[892,115725,115726,115748],{},[895,115727,115728,115736,115738,115740,115742,115744,115746],{},[28285,115729,115730,115732,115734],{},[898,115731,1702],{},[2148,115733,2495],{},[898,115735,23410],{},[1706,115737,1708],{},[2148,115739,3455],{},[1706,115741,2390],{},[2148,115743,2701],{},[1706,115745,1708],{},[2148,115747,3455],{},[902,115749,115750],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,115752,115754],{"className":115753},[886],[888,115755,115756],{"xmlns":890},[892,115757,115758,115776],{},[895,115759,115760,115766,115768,115770,115772,115774],{},[2142,115761,115762,115764],{},[898,115763,23410],{},[2148,115765,2495],{},[1706,115767,21693],{"stretchy":2139},[2148,115769,2701],{},[1706,115771,2505],{"separator":2504},[2148,115773,3455],{},[1706,115775,21708],{"stretchy":2139},[902,115777,115778],{"encoding":904},"E_2[1, 4]",[724,115780,115781,115782,115818,115819,114436],{},"Spotřebitel platí celkem ",[883,115783,115785],{"className":115784},[886],[888,115786,115787],{"xmlns":890},[892,115788,115789,115815],{},[895,115790,115791,115799,115801,115803,115805,115807,115809,115811,115813],{},[28285,115792,115793,115795,115797],{},[898,115794,1702],{},[2148,115796,2495],{},[898,115798,23410],{},[1706,115800,2447],{},[898,115802,1659],{},[1706,115804,1708],{},[2148,115806,3455],{},[1706,115808,2447],{},[2148,115810,7044],{},[1706,115812,1708],{},[2148,115814,7786],{},[902,115816,115817],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,115820,115822],{"className":115821},[886],[888,115823,115824],{"xmlns":890},[892,115825,115826,115840],{},[895,115827,115828,115836,115838],{},[28285,115829,115830,115832,115834],{},[898,115831,1702],{},[2148,115833,2495],{},[898,115835,23410],{},[1706,115837,1708],{},[2148,115839,3455],{},[902,115841,115842],{"encoding":904},"P_2^E = 4",[724,115844,115845],{},[614,115846,115847],{},"Rozklad daňového břemene:",[883,115849,115851],{"className":115850},[886],[888,115852,115853],{"xmlns":890,"display":2350},[892,115854,115855,115941],{},[895,115856,115857,115867,115869,115871,115873,115875,115877,115879,115881,115883,115885,115887,115889,115899,115901,115903,115915,115917,115919,115921,115923,115925,115927,115929,115939],{},[2142,115858,115859,115861],{},[898,115860,1659],{},[895,115862,115863,115865],{},[898,115864,61726],{},[898,115866,724],{},[1706,115868,1708],{},[1706,115870,2140],{"stretchy":2139},[2148,115872,3455],{},[1706,115874,2447],{},[2148,115876,7044],{},[1706,115878,2153],{"stretchy":2139},[1706,115880,1715],{},[2148,115882,12717],{},[1706,115884,1708],{},[2148,115886,2495],{},[2415,115888,21505],{},[895,115890,115891,115893],{},[2415,115892,28915],{},[3925,115894,115895,115897],{"accent":2504},[2415,115896,20413],{},[1706,115898,3932],{},[1706,115900,2505],{"separator":2504},[4898,115902],{"width":9524},[2142,115904,115905,115907],{},[898,115906,1659],{},[895,115908,115909,115911,115913],{},[898,115910,61749],{},[898,115912,6930],{},[898,115914,3950],{},[1706,115916,1708],{},[2148,115918,12717],{},[1706,115920,1715],{},[2148,115922,3455],{},[1706,115924,1708],{},[2148,115926,3455],{},[2415,115928,21505],{},[895,115930,115931,115933],{},[2415,115932,28915],{},[3925,115934,115935,115937],{"accent":2504},[2415,115936,20413],{},[1706,115938,3932],{},[898,115940,1837],{"mathvariant":2409},[902,115942,115943],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,115945,115946,115947,1837],{},"Opět ",[883,115948,115950],{"className":115949},[886],[888,115951,115952],{"xmlns":890},[892,115953,115954,115988],{},[895,115955,115956,115966,115968,115980,115982,115984,115986],{},[2142,115957,115958,115960],{},[898,115959,1659],{},[895,115961,115962,115964],{},[898,115963,61726],{},[898,115965,724],{},[1706,115967,2447],{},[2142,115969,115970,115972],{},[898,115971,1659],{},[895,115973,115974,115976,115978],{},[898,115975,61749],{},[898,115977,6930],{},[898,115979,3950],{},[1706,115981,1708],{},[2148,115983,7044],{},[1706,115985,1708],{},[898,115987,1659],{},[902,115989,115990],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[56029,115992],{},[115,115994,61707],{"id":115995},"daňové-břemeno",[724,115997,115998,2314,116000,116003,116004,116017],{},[38,115999,61707],{},[614,116001,116002],{},"tax burden",") je rozdělení zaplacené daně ",[883,116005,116007],{"className":116006},[886],[888,116008,116009],{"xmlns":890},[892,116010,116011,116015],{},[895,116012,116013],{},[898,116014,1659],{},[902,116016,1659],{"encoding":904}," mezi spotřebitele a výrobce:",[883,116019,116021],{"className":116020},[886],[888,116022,116023],{"xmlns":890,"display":2350},[892,116024,116025,116057],{},[895,116026,116027,116029,116031,116041,116043,116055],{},[898,116028,1659],{},[1706,116030,1708],{},[2142,116032,116033,116035],{},[898,116034,1659],{},[895,116036,116037,116039],{},[898,116038,61726],{},[898,116040,724],{},[1706,116042,2447],{},[2142,116044,116045,116047],{},[898,116046,1659],{},[895,116048,116049,116051,116053],{},[898,116050,61749],{},[898,116052,6930],{},[898,116054,3950],{},[898,116056,1837],{"mathvariant":2409},[902,116058,116059],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,116061,116062],{},[2286,116063],{"alt":116064,"className":116065,"src":116066},"imek-dan-rozklad-bremene-sklony",[210,2290],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[1636,116068,116069],{},[724,116070,116071,116073,116074,1993,116087,1837],{},[883,116072,3174],{}," 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 ",[883,116075,116077],{"className":116076},[886],[888,116078,116079],{"xmlns":890},[892,116080,116081,116085],{},[895,116082,116083],{},[898,116084,2334],{},[902,116086,2334],{"encoding":904},[883,116088,116090],{"className":116089},[886],[888,116091,116092],{"xmlns":890},[892,116093,116094,116098],{},[895,116095,116096],{},[898,116097,14171],{},[902,116099,14171],{"encoding":904},[198,116101,21651],{"id":21650},[724,116103,116104,116105,116126,116127,116140,116141,116158,116159,116172],{},"V grafu ",[883,116106,116108],{"className":116107},[886],[888,116109,116110],{"xmlns":890},[892,116111,116112,116124],{},[895,116113,116114,116116,116118,116120,116122],{},[1706,116115,2140],{"stretchy":2139},[898,116117,2146],{},[1706,116119,2505],{"separator":2504},[898,116121,1702],{},[1706,116123,2153],{"stretchy":2139},[902,116125,56748],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,116128,116130],{"className":116129},[886],[888,116131,116132],{"xmlns":890},[892,116133,116134,116138],{},[895,116135,116136],{},[898,116137,1659],{},[902,116139,1659],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,116142,116144],{"className":116143},[886],[888,116145,116146],{"xmlns":890},[892,116147,116148,116156],{},[895,116149,116150],{},[2489,116151,116152,116154],{},[898,116153,1702],{},[898,116155,23410],{},[902,116157,60519],{"encoding":904},", rozdělí se úsečka ",[883,116160,116162],{"className":116161},[886],[888,116163,116164],{"xmlns":890},[892,116165,116166,116170],{},[895,116167,116168],{},[898,116169,1659],{},[902,116171,1659],{"encoding":904}," na dvě části:",[120,116174,116175,116200],{},[123,116176,116177,116178,116199],{},"horní část odpovídá ",[883,116179,116181],{"className":116180},[886],[888,116182,116183],{"xmlns":890},[892,116184,116185,116197],{},[895,116186,116187],{},[2142,116188,116189,116191],{},[898,116190,1659],{},[895,116192,116193,116195],{},[898,116194,61726],{},[898,116196,724],{},[902,116198,61731],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,116201,116202,116203,116226],{},"dolní část odpovídá ",[883,116204,116206],{"className":116205},[886],[888,116207,116208],{"xmlns":890},[892,116209,116210,116224],{},[895,116211,116212],{},[2142,116213,116214,116216],{},[898,116215,1659],{},[895,116217,116218,116220,116222],{},[898,116219,61749],{},[898,116221,6930],{},[898,116223,3950],{},[902,116225,61756],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,116228,116229],{},[614,116230,116231,116232,4202,116245,116266,116267,116290,116291,1993,116312,116335],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,116233,116235],{"className":116234},[886],[888,116236,116237],{"xmlns":890},[892,116238,116239,116243],{},[895,116240,116241],{},[898,116242,1659],{},[902,116244,1659],{"encoding":904},[883,116246,116248],{"className":116247},[886],[888,116249,116250],{"xmlns":890},[892,116251,116252,116264],{},[895,116253,116254],{},[2142,116255,116256,116258],{},[898,116257,1659],{},[895,116259,116260,116262],{},[898,116261,61726],{},[898,116263,724],{},[902,116265,61731],{"encoding":904}," (nahoře) a ",[883,116268,116270],{"className":116269},[886],[888,116271,116272],{"xmlns":890},[892,116273,116274,116288],{},[895,116275,116276],{},[2142,116277,116278,116280],{},[898,116279,1659],{},[895,116281,116282,116284,116286],{},[898,116283,61749],{},[898,116285,6930],{},[898,116287,3950],{},[902,116289,61756],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,116292,116294],{"className":116293},[886],[888,116295,116296],{"xmlns":890},[892,116297,116298,116310],{},[895,116299,116300],{},[2142,116301,116302,116304],{},[898,116303,1659],{},[895,116305,116306,116308],{},[898,116307,61726],{},[898,116309,724],{},[902,116311,61731],{"encoding":904},[883,116313,116315],{"className":116314},[886],[888,116316,116317],{"xmlns":890},[892,116318,116319,116333],{},[895,116320,116321],{},[2142,116322,116323,116325],{},[898,116324,1659],{},[895,116326,116327,116329,116331],{},[898,116328,61749],{},[898,116330,6930],{},[898,116332,3950],{},[902,116334,61756],{"encoding":904}," je v obou případech stejná.",[198,116337,116339],{"id":116338},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,116341,116342,116343,116346,116347,2314,116370,116387,116388,2314,116411,116428],{},"Platí obecně: ",[38,116344,116345],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,116348,116350],{"className":116349},[886],[888,116351,116352],{"xmlns":890},[892,116353,116354,116368],{},[895,116355,116356,116358,116360,116362,116364,116366],{},[898,116357,1702],{},[1706,116359,1708],{},[898,116361,207],{},[898,116363,2146],{},[1706,116365,2447],{},[898,116367,2450],{},[902,116369,2453],{"encoding":904},[883,116371,116373],{"className":116372},[886],[888,116374,116375],{"xmlns":890},[892,116376,116377,116385],{},[895,116378,116379,116381,116383],{},[898,116380,207],{},[1706,116382,2539],{},[2148,116384,2150],{},[902,116386,2544],{"encoding":904},") a lineární nabídku ",[883,116389,116391],{"className":116390},[886],[888,116392,116393],{"xmlns":890},[892,116394,116395,116409],{},[895,116396,116397,116399,116401,116403,116405,116407],{},[898,116398,1702],{},[1706,116400,1708],{},[898,116402,20413],{},[898,116404,2146],{},[1706,116406,2447],{},[898,116408,3120],{},[902,116410,59296],{"encoding":904},[883,116412,116414],{"className":116413},[886],[888,116415,116416],{"xmlns":890},[892,116417,116418,116426],{},[895,116419,116420,116422,116424],{},[898,116421,20413],{},[1706,116423,8922],{},[2148,116425,2150],{},[902,116427,59314],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,116430,116432],{"className":116431},[886],[888,116433,116434],{"xmlns":890,"display":2350},[892,116435,116436,116502],{},[895,116437,116438,116462,116464,116474,116476,116500],{},[2964,116439,116440,116450],{},[2142,116441,116442,116444],{},[898,116443,1659],{},[895,116445,116446,116448],{},[898,116447,61726],{},[898,116449,724],{},[2142,116451,116452,116454],{},[898,116453,1659],{},[895,116455,116456,116458,116460],{},[898,116457,61749],{},[898,116459,6930],{},[898,116461,3950],{},[1706,116463,1708],{},[2964,116465,116466,116468],{},[898,116467,20413],{},[895,116469,116470,116472],{},[1706,116471,1715],{},[898,116473,207],{},[1706,116475,1708],{},[2964,116477,116478,116490],{},[895,116479,116480,116483,116486,116488],{},[898,116481,116482],{"mathvariant":2409},"∣",[2415,116484,116485],{},"sklon ",[898,116487,14171],{},[898,116489,116482],{"mathvariant":2409},[895,116491,116492,116494,116496,116498],{},[898,116493,116482],{"mathvariant":2409},[2415,116495,116485],{},[898,116497,2334],{},[898,116499,116482],{"mathvariant":2409},[898,116501,1837],{"mathvariant":2409},[902,116503,116504],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[1636,116506,116507,116512],{},[724,116508,116509,116511],{},[883,116510,12314],{}," Postup výpočtu rozkladu",[152,116513,116514,116549,116602,116681],{},[123,116515,116516,116517,116548],{},"Spočti rovnovážný bod ",[883,116518,116520],{"className":116519},[886],[888,116521,116522],{"xmlns":890},[892,116523,116524,116546],{},[895,116525,116526,116528,116530,116536,116538,116544],{},[898,116527,23410],{},[1706,116529,21693],{"stretchy":2139},[2489,116531,116532,116534],{},[898,116533,2146],{},[898,116535,23410],{},[1706,116537,2505],{"separator":2504},[2489,116539,116540,116542],{},[898,116541,1702],{},[898,116543,23410],{},[1706,116545,21708],{"stretchy":2139},[902,116547,60420],{"encoding":904}," bez daně.",[123,116550,116551,116552,1348,116577,1936],{},"Urči posunutou křivku (",[883,116553,116555],{"className":116554},[886],[888,116556,116557],{"xmlns":890},[892,116558,116559,116575],{},[895,116560,116561,116567,116569,116571,116573],{},[2142,116562,116563,116565],{},[898,116564,14171],{},[2148,116566,2701],{},[1706,116568,1708],{},[898,116570,14171],{},[1706,116572,2447],{},[898,116574,1659],{},[902,116576,61803],{"encoding":904},[883,116578,116580],{"className":116579},[886],[888,116581,116582],{"xmlns":890},[892,116583,116584,116600],{},[895,116585,116586,116592,116594,116596,116598],{},[2142,116587,116588,116590],{},[898,116589,2334],{},[2148,116591,2495],{},[1706,116593,1708],{},[898,116595,2334],{},[1706,116597,1715],{},[898,116599,1659],{},[902,116601,61834],{"encoding":904},[123,116603,116604,116605,23078,116624,5354,116643,23078,116662,1936],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,116606,116608],{"className":116607},[886],[888,116609,116610],{"xmlns":890},[892,116611,116612,116622],{},[895,116613,116614],{},[28285,116615,116616,116618,116620],{},[898,116617,2146],{},[2148,116619,2701],{},[898,116621,23410],{},[902,116623,66878],{"encoding":904},[883,116625,116627],{"className":116626},[886],[888,116628,116629],{"xmlns":890},[892,116630,116631,116641],{},[895,116632,116633],{},[28285,116634,116635,116637,116639],{},[898,116636,2146],{},[2148,116638,2495],{},[898,116640,23410],{},[902,116642,66940],{"encoding":904},[883,116644,116646],{"className":116645},[886],[888,116647,116648],{"xmlns":890},[892,116649,116650,116660],{},[895,116651,116652],{},[28285,116653,116654,116656,116658],{},[898,116655,1702],{},[2148,116657,2701],{},[898,116659,23410],{},[902,116661,66899],{"encoding":904},[883,116663,116665],{"className":116664},[886],[888,116666,116667],{"xmlns":890},[892,116668,116669,116679],{},[895,116670,116671],{},[28285,116672,116673,116675,116677],{},[898,116674,1702],{},[2148,116676,2495],{},[898,116678,23410],{},[902,116680,66960],{"encoding":904},[123,116682,116683,116684,1993,116705,116728,116729,1837],{},"Dopočítej ",[883,116685,116687],{"className":116686},[886],[888,116688,116689],{"xmlns":890},[892,116690,116691,116703],{},[895,116692,116693],{},[2142,116694,116695,116697],{},[898,116696,1659],{},[895,116698,116699,116701],{},[898,116700,61726],{},[898,116702,724],{},[902,116704,61731],{"encoding":904},[883,116706,116708],{"className":116707},[886],[888,116709,116710],{"xmlns":890},[892,116711,116712,116726],{},[895,116713,116714],{},[2142,116715,116716,116718],{},[898,116717,1659],{},[895,116719,116720,116722,116724],{},[898,116721,61749],{},[898,116723,6930],{},[898,116725,3950],{},[902,116727,61756],{"encoding":904}," z definice, vždy ověř ",[883,116730,116732],{"className":116731},[886],[888,116733,116734],{"xmlns":890},[892,116735,116736,116766],{},[895,116737,116738,116748,116750,116762,116764],{},[2142,116739,116740,116742],{},[898,116741,1659],{},[895,116743,116744,116746],{},[898,116745,61726],{},[898,116747,724],{},[1706,116749,2447],{},[2142,116751,116752,116754],{},[898,116753,1659],{},[895,116755,116756,116758,116760],{},[898,116757,61749],{},[898,116759,6930],{},[898,116761,3950],{},[1706,116763,1708],{},[898,116765,1659],{},[902,116767,116768],{"encoding":904},"T_{sp} + T_{vyr} = T",[1636,116770,116771],{},[724,116772,116773,116775,116776,116779,116780,1993,116793,116806],{},[883,116774,9276],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,116777,116778],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,116781,116783],{"className":116782},[886],[888,116784,116785],{"xmlns":890},[892,116786,116787,116791],{},[895,116788,116789],{},[898,116790,2334],{},[902,116792,2334],{"encoding":904},[883,116794,116796],{"className":116795},[886],[888,116797,116798],{"xmlns":890},[892,116799,116800,116804],{},[895,116801,116802],{},[898,116803,14171],{},[902,116805,14171],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[56029,116808],{},[115,116810,116812],{"id":116811},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,116814,116815],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,116817,116818],{},[2286,116819],{"alt":116820,"className":116821,"src":116822},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,2290],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,116824,116825,116837],{},[19,116826,116827],{},[22,116828,116829,116831,116834],{},[25,116830,73332],{},[25,116832,116833],{},"(a) daň výrobci",[25,116835,116836],{},"(b) daň spotřebiteli",[30,116838,116839,116894,116961,117021],{},[22,116840,116841,116844,116869],{},[35,116842,116843],{},"Rovnovážné množství",[35,116845,116846],{},[883,116847,116849],{"className":116848},[886],[888,116850,116851],{"xmlns":890},[892,116852,116853,116867],{},[895,116854,116855,116863,116865],{},[28285,116856,116857,116859,116861],{},[898,116858,2146],{},[2148,116860,2701],{},[898,116862,23410],{},[1706,116864,1708],{},[2148,116866,2701],{},[902,116868,114685],{"encoding":904},[35,116870,116871],{},[883,116872,116874],{"className":116873},[886],[888,116875,116876],{"xmlns":890},[892,116877,116878,116892],{},[895,116879,116880,116888,116890],{},[28285,116881,116882,116884,116886],{},[898,116883,2146],{},[2148,116885,2495],{},[898,116887,23410],{},[1706,116889,1708],{},[2148,116891,2701],{},[902,116893,115718],{"encoding":904},[22,116895,116896,116899,116924],{},[35,116897,116898],{},"Cena placená spotřebitelem",[35,116900,116901],{},[883,116902,116904],{"className":116903},[886],[888,116905,116906],{"xmlns":890},[892,116907,116908,116922],{},[895,116909,116910,116918,116920],{},[28285,116911,116912,116914,116916],{},[898,116913,1702],{},[2148,116915,2701],{},[898,116917,23410],{},[1706,116919,1708],{},[2148,116921,7786],{},[902,116923,114780],{"encoding":904},[35,116925,116926],{},[883,116927,116929],{"className":116928},[886],[888,116930,116931],{"xmlns":890},[892,116932,116933,116959],{},[895,116934,116935,116943,116945,116947,116949,116951,116953,116955,116957],{},[28285,116936,116937,116939,116941],{},[898,116938,1702],{},[2148,116940,2495],{},[898,116942,23410],{},[1706,116944,2447],{},[898,116946,1659],{},[1706,116948,1708],{},[2148,116950,3455],{},[1706,116952,2447],{},[2148,116954,7044],{},[1706,116956,1708],{},[2148,116958,7786],{},[902,116960,115817],{"encoding":904},[22,116962,116963,116966,116996],{},[35,116964,116965],{},"Cena přijímaná výrobcem",[35,116967,116968],{},[883,116969,116971],{"className":116970},[886],[888,116972,116973],{"xmlns":890},[892,116974,116975,116993],{},[895,116976,116977,116985,116987,116989,116991],{},[28285,116978,116979,116981,116983],{},[898,116980,1702],{},[2148,116982,2701],{},[898,116984,23410],{},[1706,116986,1715],{},[898,116988,1659],{},[1706,116990,1708],{},[2148,116992,3455],{},[902,116994,116995],{"encoding":904},"P_1^E - T = 4",[35,116997,116998],{},[883,116999,117001],{"className":117000},[886],[888,117002,117003],{"xmlns":890},[892,117004,117005,117019],{},[895,117006,117007,117015,117017],{},[28285,117008,117009,117011,117013],{},[898,117010,1702],{},[2148,117012,2495],{},[898,117014,23410],{},[1706,117016,1708],{},[2148,117018,3455],{},[902,117020,115842],{"encoding":904},[22,117022,117023,117026,117080],{},[35,117024,117025],{},"Rozklad břemene",[35,117027,117028,1343,117053],{},[883,117029,117031],{"className":117030},[886],[888,117032,117033],{"xmlns":890},[892,117034,117035,117051],{},[895,117036,117037,117047,117049],{},[2142,117038,117039,117041],{},[898,117040,1659],{},[895,117042,117043,117045],{},[898,117044,61726],{},[898,117046,724],{},[1706,117048,1708],{},[2148,117050,2495],{},[902,117052,62025],{"encoding":904},[883,117054,117056],{"className":117055},[886],[888,117057,117058],{"xmlns":890},[892,117059,117060,117078],{},[895,117061,117062,117074,117076],{},[2142,117063,117064,117066],{},[898,117065,1659],{},[895,117067,117068,117070,117072],{},[898,117069,61749],{},[898,117071,6930],{},[898,117073,3950],{},[1706,117075,1708],{},[2148,117077,3455],{},[902,117079,62054],{"encoding":904},[35,117081,117082,1343,117107],{},[883,117083,117085],{"className":117084},[886],[888,117086,117087],{"xmlns":890},[892,117088,117089,117105],{},[895,117090,117091,117101,117103],{},[2142,117092,117093,117095],{},[898,117094,1659],{},[895,117096,117097,117099],{},[898,117098,61726],{},[898,117100,724],{},[1706,117102,1708],{},[2148,117104,2495],{},[902,117106,62025],{"encoding":904},[883,117108,117110],{"className":117109},[886],[888,117111,117112],{"xmlns":890},[892,117113,117114,117132],{},[895,117115,117116,117128,117130],{},[2142,117117,117118,117120],{},[898,117119,1659],{},[895,117121,117122,117124,117126],{},[898,117123,61749],{},[898,117125,6930],{},[898,117127,3950],{},[1706,117129,1708],{},[2148,117131,3455],{},[902,117133,62054],{"encoding":904},[724,117135,117136],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,117138,117140],{"className":117139},[886],[888,117141,117142],{"xmlns":890,"display":2350},[892,117143,117144,117192],{},[895,117145,117146,117154,117156,117164,117166,117168,117176,117178,117180,117182,117190],{},[28285,117147,117148,117150,117152],{},[898,117149,2146],{},[2148,117151,2701],{},[898,117153,23410],{},[1706,117155,1708],{},[28285,117157,117158,117160,117162],{},[898,117159,2146],{},[2148,117161,2495],{},[898,117163,23410],{},[1706,117165,2505],{"separator":2504},[4898,117167],{"width":9524},[28285,117169,117170,117172,117174],{},[898,117171,1702],{},[2148,117173,2701],{},[898,117175,23410],{},[1706,117177,1715],{},[898,117179,1659],{},[1706,117181,1708],{},[28285,117183,117184,117186,117188],{},[898,117185,1702],{},[2148,117187,2495],{},[898,117189,23410],{},[898,117191,1837],{"mathvariant":2409},[902,117193,117194],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[1636,117196,117197,117216,117370],{},[724,117198,117199,117201,117202,117215],{},[883,117200,12314],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,117203,117205],{"className":117204},[886],[888,117206,117207],{"xmlns":890},[892,117208,117209,117213],{},[895,117210,117211],{},[898,117212,1659],{},[902,117214,1659],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,117217,117218,117250,117286,117323],{},[123,117219,117220,117221,2505],{},"rovnovážná množství obou režimů, ",[883,117222,117224],{"className":117223},[886],[888,117225,117226],{"xmlns":890},[892,117227,117228,117248],{},[895,117229,117230,117238,117240],{},[28285,117231,117232,117234,117236],{},[898,117233,2146],{},[2148,117235,2701],{},[898,117237,23410],{},[1706,117239,1708],{},[28285,117241,117242,117244,117246],{},[898,117243,2146],{},[2148,117245,2495],{},[898,117247,23410],{},[902,117249,61957],{"encoding":904},[123,117251,117252,117253,2505],{},"čistá cena přijímaná výrobcem, ",[883,117254,117256],{"className":117255},[886],[888,117257,117258],{"xmlns":890},[892,117259,117260,117284],{},[895,117261,117262,117270,117272,117274,117276],{},[28285,117263,117264,117266,117268],{},[898,117265,1702],{},[2148,117267,2701],{},[898,117269,23410],{},[1706,117271,1715],{},[898,117273,1659],{},[1706,117275,1708],{},[28285,117277,117278,117280,117282],{},[898,117279,1702],{},[2148,117281,2495],{},[898,117283,23410],{},[902,117285,61991],{"encoding":904},[123,117287,117288,117289,2505],{},"celková cena placená spotřebitelem, ",[883,117290,117292],{"className":117291},[886],[888,117293,117294],{"xmlns":890},[892,117295,117296,117320],{},[895,117297,117298,117306,117308,117316,117318],{},[28285,117299,117300,117302,117304],{},[898,117301,1702],{},[2148,117303,2701],{},[898,117305,23410],{},[1706,117307,1708],{},[28285,117309,117310,117312,117314],{},[898,117311,1702],{},[2148,117313,2495],{},[898,117315,23410],{},[1706,117317,2447],{},[898,117319,1659],{},[902,117321,117322],{"encoding":904},"P_1^E = P_2^E + T",[123,117324,117325,117326,1993,117347,1837],{},"rozklad daňového břemene ",[883,117327,117329],{"className":117328},[886],[888,117330,117331],{"xmlns":890},[892,117332,117333,117345],{},[895,117334,117335],{},[2142,117336,117337,117339],{},[898,117338,1659],{},[895,117340,117341,117343],{},[898,117342,61726],{},[898,117344,724],{},[902,117346,61731],{"encoding":904},[883,117348,117350],{"className":117349},[886],[888,117351,117352],{"xmlns":890},[892,117353,117354,117368],{},[895,117355,117356],{},[2142,117357,117358,117360],{},[898,117359,1659],{},[895,117361,117362,117364,117366],{},[898,117363,61749],{},[898,117365,6930],{},[898,117367,3950],{},[902,117369,61756],{"encoding":904},[724,117371,117372,117373,1837],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,117374,54259],{},[724,117376,117377,117378,1993,117391,1936],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,117379,117381],{"className":117380},[886],[888,117382,117383],{"xmlns":890},[892,117384,117385,117389],{},[895,117386,117387],{},[898,117388,2334],{},[902,117390,2334],{"encoding":904},[883,117392,117394],{"className":117393},[886],[888,117395,117396],{"xmlns":890},[892,117397,117398,117402],{},[895,117399,117400],{},[898,117401,14171],{},[902,117403,14171],{"encoding":904},[56029,117405],{},[115,117407,117409],{"id":117408},"úlohy","Úlohy",[724,117411,117412,117413,5606],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,117414,35339],{"className":117415,"dataFsResolvedFilePath":800,"href":801},[210],[120,117417,117418,117448,117479],{},[123,117419,117420,117423,117424,117447],{},[38,117421,117422],{},"Úloha 2.4"," — Poptávka ",[883,117425,117427],{"className":117426},[886],[888,117428,117429],{"xmlns":890},[892,117430,117431,117445],{},[895,117432,117433,117435,117437,117439,117441,117443],{},[898,117434,1702],{},[1706,117436,1708],{},[2148,117438,7156],{},[1706,117440,1715],{},[2148,117442,2495],{},[898,117444,2146],{},[902,117446,114397],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,117449,117450,117453,117454,117478],{},[38,117451,117452],{},"Úloha 2.9"," — Nabídka ",[883,117455,117457],{"className":117456},[886],[888,117458,117459],{"xmlns":890},[892,117460,117461,117475],{},[895,117462,117463,117465,117467,117469,117471,117473],{},[898,117464,1702],{},[1706,117466,1708],{},[2148,117468,11496],{},[898,117470,2146],{},[1706,117472,2447],{},[2148,117474,3359],{},[902,117476,117477],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,117480,117481,117484,117485,1993,117511,117535,117536,117553],{},[38,117482,117483],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,117486,117488],{"className":117487},[886],[888,117489,117490],{"xmlns":890},[892,117491,117492,117508],{},[895,117493,117494,117496,117498,117500,117502,117504,117506],{},[898,117495,1702],{},[1706,117497,1708],{},[1706,117499,1715],{},[2148,117501,3455],{},[898,117503,2146],{},[1706,117505,2447],{},[2148,117507,17219],{},[902,117509,117510],{"encoding":904},"P = -4Q + 80",[883,117512,117514],{"className":117513},[886],[888,117515,117516],{"xmlns":890},[892,117517,117518,117532],{},[895,117519,117520,117522,117524,117526,117528,117530],{},[898,117521,1702],{},[1706,117523,1708],{},[2148,117525,4284],{},[898,117527,2146],{},[1706,117529,2447],{},[2148,117531,7786],{},[902,117533,117534],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,117537,117539],{"className":117538},[886],[888,117540,117541],{"xmlns":890},[892,117542,117543,117551],{},[895,117544,117545,117547,117549],{},[898,117546,1659],{},[1706,117548,1708],{},[2148,117550,12597],{},[902,117552,66857],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,117555,117556,117557,117559,117560,117562],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,117558,64274],{}," (posun poptávky při zdanění kupujícího) a ",[38,117561,64308],{}," (posun nabídky při zdanění výrobce).",[56029,117564],{},[115,117566,19879],{"id":19878},[120,117568,117569,117588,117646,117703,117786,117832,117875,117920,117986],{},[123,117570,117571,1647,117574,117587],{},[38,117572,117573],{},"Jednotková daň",[883,117575,117577],{"className":117576},[886],[888,117578,117579],{"xmlns":890},[892,117580,117581,117585],{},[895,117582,117583],{},[898,117584,1659],{},[902,117586,1659],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,117589,117590,117592,117593,117631,117632,117645],{},[38,117591,113979],{}," — posun nabídky ",[883,117594,117596],{"className":117595},[886],[888,117597,117598],{"xmlns":890},[892,117599,117600,117628],{},[895,117601,117602,117608,117610,117612,117614,117616,117618,117620,117622,117624,117626],{},[2142,117603,117604,117606],{},[898,117605,14171],{},[2148,117607,2701],{},[1706,117609,2140],{"stretchy":2139},[898,117611,2146],{},[1706,117613,2153],{"stretchy":2139},[1706,117615,1708],{},[898,117617,14171],{},[1706,117619,2140],{"stretchy":2139},[898,117621,2146],{},[1706,117623,2153],{"stretchy":2139},[1706,117625,2447],{},[898,117627,1659],{},[902,117629,117630],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,117633,117635],{"className":117634},[886],[888,117636,117637],{"xmlns":890},[892,117638,117639,117643],{},[895,117640,117641],{},[898,117642,1659],{},[902,117644,1659],{"encoding":904}," svisle nahoru)",[123,117647,117648,117650,117651,117631,117689,117702],{},[38,117649,115052],{}," — posun poptávky ",[883,117652,117654],{"className":117653},[886],[888,117655,117656],{"xmlns":890},[892,117657,117658,117686],{},[895,117659,117660,117666,117668,117670,117672,117674,117676,117678,117680,117682,117684],{},[2142,117661,117662,117664],{},[898,117663,2334],{},[2148,117665,2495],{},[1706,117667,2140],{"stretchy":2139},[898,117669,2146],{},[1706,117671,2153],{"stretchy":2139},[1706,117673,1708],{},[898,117675,2334],{},[1706,117677,2140],{"stretchy":2139},[898,117679,2146],{},[1706,117681,2153],{"stretchy":2139},[1706,117683,1715],{},[898,117685,1659],{},[902,117687,117688],{"encoding":904},"D_2(Q) = D(Q) - T",[883,117690,117692],{"className":117691},[886],[888,117693,117694],{"xmlns":890},[892,117695,117696,117700],{},[895,117697,117698],{},[898,117699,1659],{},[902,117701,1659],{"encoding":904}," svisle dolů)",[123,117704,117705,21021,117708,2173,117747],{},[38,117706,117707],{},"Rovnovážný bod s daní",[883,117709,117711],{"className":117710},[886],[888,117712,117713],{"xmlns":890},[892,117714,117715,117745],{},[895,117716,117717,117723,117725,117733,117735,117743],{},[2142,117718,117719,117721],{},[898,117720,23410],{},[2148,117722,2701],{},[1706,117724,21693],{"stretchy":2139},[28285,117726,117727,117729,117731],{},[898,117728,2146],{},[2148,117730,2701],{},[898,117732,23410],{},[1706,117734,2505],{"separator":2504},[28285,117736,117737,117739,117741],{},[898,117738,1702],{},[2148,117740,2701],{},[898,117742,23410],{},[1706,117744,21708],{"stretchy":2139},[902,117746,114147],{"encoding":904},[883,117748,117750],{"className":117749},[886],[888,117751,117752],{"xmlns":890},[892,117753,117754,117784],{},[895,117755,117756,117762,117764,117772,117774,117782],{},[2142,117757,117758,117760],{},[898,117759,23410],{},[2148,117761,2495],{},[1706,117763,21693],{"stretchy":2139},[28285,117765,117766,117768,117770],{},[898,117767,2146],{},[2148,117769,2495],{},[898,117771,23410],{},[1706,117773,2505],{"separator":2504},[28285,117775,117776,117778,117780],{},[898,117777,1702],{},[2148,117779,2495],{},[898,117781,23410],{},[1706,117783,21708],{"stretchy":2139},[902,117785,115222],{"encoding":904},[123,117787,117788,2314,117790,117792,117793],{},[38,117789,61707],{},[614,117791,116002],{},") — rozklad ",[883,117794,117796],{"className":117795},[886],[888,117797,117798],{"xmlns":890},[892,117799,117800,117830],{},[895,117801,117802,117804,117806,117816,117818],{},[898,117803,1659],{},[1706,117805,1708],{},[2142,117807,117808,117810],{},[898,117809,1659],{},[895,117811,117812,117814],{},[898,117813,61726],{},[898,117815,724],{},[1706,117817,2447],{},[2142,117819,117820,117822],{},[898,117821,1659],{},[895,117823,117824,117826,117828],{},[898,117825,61749],{},[898,117827,6930],{},[898,117829,3950],{},[902,117831,61893],{"encoding":904},[123,117833,117834,117857,117858,2153],{},[38,117835,117836],{},[883,117837,117839],{"className":117838},[886],[888,117840,117841],{"xmlns":890},[892,117842,117843,117855],{},[895,117844,117845],{},[2142,117846,117847,117849],{},[898,117848,1659],{},[895,117850,117851,117853],{},[898,117852,61726],{},[898,117854,724],{},[902,117856,61731],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,117859,117861],{"className":117860},[886],[888,117862,117863],{"xmlns":890},[892,117864,117865,117873],{},[895,117866,117867],{},[2489,117868,117869,117871],{},[898,117870,1702],{},[898,117872,23410],{},[902,117874,60519],{"encoding":904},[123,117876,117877,117902,117903,2153],{},[38,117878,117879],{},[883,117880,117882],{"className":117881},[886],[888,117883,117884],{"xmlns":890},[892,117885,117886,117900],{},[895,117887,117888],{},[2142,117889,117890,117892],{},[898,117891,1659],{},[895,117893,117894,117896,117898],{},[898,117895,61749],{},[898,117897,6930],{},[898,117899,3950],{},[902,117901,61756],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,117904,117906],{"className":117905},[886],[888,117907,117908],{"xmlns":890},[892,117909,117910,117918],{},[895,117911,117912],{},[2489,117913,117914,117916],{},[898,117915,1702],{},[898,117917,23410],{},[902,117919,60519],{"encoding":904},[123,117921,117922,21021,117924,1343,117953],{},[38,117923,69513],{},[883,117925,117927],{"className":117926},[886],[888,117928,117929],{"xmlns":890},[892,117930,117931,117951],{},[895,117932,117933,117941,117943],{},[28285,117934,117935,117937,117939],{},[898,117936,2146],{},[2148,117938,2701],{},[898,117940,23410],{},[1706,117942,1708],{},[28285,117944,117945,117947,117949],{},[898,117946,2146],{},[2148,117948,2495],{},[898,117950,23410],{},[902,117952,61957],{"encoding":904},[883,117954,117956],{"className":117955},[886],[888,117957,117958],{"xmlns":890},[892,117959,117960,117984],{},[895,117961,117962,117970,117972,117974,117976],{},[28285,117963,117964,117966,117968],{},[898,117965,1702],{},[2148,117967,2701],{},[898,117969,23410],{},[1706,117971,1715],{},[898,117973,1659],{},[1706,117975,1708],{},[28285,117977,117978,117980,117982],{},[898,117979,1702],{},[2148,117981,2495],{},[898,117983,23410],{},[902,117985,61991],{"encoding":904},[123,117987,117988,117991],{},[38,117989,117990],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[56029,117993],{},[115,117995,21083],{"id":21082},[120,117997,117998,118006,118024,118031],{},[123,117999,118000,1647,118003],{},[38,118001,118002],{},"Kontext (hub):",[207,118004,802],{"className":118005,"dataFsResolvedFilePath":800,"href":801},[210],[123,118007,118008,1647,118010,118013,118014,37745,118016,118019,118020,118023],{},[38,118009,21090],{},[207,118011,820],{"className":118012,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,118015,74070],{},[207,118017,21102],{"className":118018,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,118021,21098],{"className":118022,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[123,118025,118026,1647,118028],{},[38,118027,69796],{},[207,118029,69800],{"className":118030,"dataFsResolvedFilePath":745,"href":746},[210],[123,118032,118033,1647,118035],{},[38,118034,21126],{},[207,118036,21132],{"className":118037,"dataFsResolvedFilePath":21130,"href":21131},[210],{"title":641,"searchDepth":642,"depth":642,"links":118039},[118040,118041,118044,118047,118051,118052,118053,118054],{"id":113884,"depth":642,"text":113885},{"id":113978,"depth":642,"text":113979,"children":118042},[118043],{"id":114369,"depth":649,"text":64349},{"id":115051,"depth":642,"text":115052,"children":118045},[118046],{"id":115528,"depth":649,"text":64429},{"id":115995,"depth":642,"text":61707,"children":118048},[118049,118050],{"id":21650,"depth":649,"text":21651},{"id":116338,"depth":649,"text":116339},{"id":116811,"depth":642,"text":116812},{"id":117408,"depth":642,"text":117409},{"id":19878,"depth":642,"text":19879},{"id":21082,"depth":642,"text":21083},{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":113782,"description":641},[1138,1135],"topics\u002Fzdaneni-trhu",[1128,69861,118061,118062,118063,35339],"dane","danove-bremeno","posun-krivek","cFuKqHgzIrqvY-l4jNdqjFEM7_ixjw33HOL0So8cPn0",[118066,118068,118070,118072,118076,118080,118084,118086],{"slug":1145,"path":765,"title":21191,"snippet":118067},"… ** $\\Delta TC = TC(11) - TC(10) = 4{,}2$. **Přibližný (lineární):** $4$. (Viz aplikace v \u003C\u003Cprijem-naklady-zisk>>.) ## Diferenciál $$df = f'(x)\\, dx$$ Pro malá $dx$ platí: $\\Delta f = f(x + dx) - f(x) …",{"slug":23065,"path":849,"title":23031,"snippet":118069},"… astická) $\\Rightarrow$ $MR \u003C 0$ — $TR$ klesá s množstvím, tj. roste s cenou. > > Viz také \u003C\u003Cprijem-naklady-zisk>>. ### Pravidla 1–3 (odvození z (4.12)) **(a) Poptávka elastická ($E > 1$).** Z (4.12) pl …",{"slug":1128,"path":21131,"title":681,"snippet":118071},"… potrebitele-vyrobce|Přebytek spotřebitele a výrobce]] — CS, PS, plochy pod\u002Fnad křivkami - \u003C\u003Cprijem-naklady-zisk>> — TR, AR, MR, TC, AC, MC, body zvratu, konstrukce nabídky firmy ### Blok 2 — [[imek-blok …",{"slug":118073,"path":746,"title":118074,"snippet":118075},"imek-blok-01","KS 1. blok — Kalkul a mikroekonomie","… Poptávka a nabídka]] — modely D, S, tržní rovnováha, multiplikátory, přebytky, zdanění 7. \u003C\u003Cprijem-naklady-zisk>> — TR\u002FAR\u002FMR, TC\u002FAC\u002FMC\u002FAVC\u002FAFC, body zvratu, maximalizace zisku, konstrukce nabídky firmy …",{"slug":118077,"path":1109,"title":118078,"snippet":118079},"imek-kniha","Kniha — *Úvod do matematické ekonomie pro ekonomy*","… ídky firmy ($P = MC$ nad minimem AVC). **Příklady 3.1–3.12**, **Úlohy 3.1–3.28**. Topic: \u003C\u003Cprijem-naklady-zisk>>. ### Kapitola 4 — Elasticita *(str. 83–96)* Pojem elasticity jako míry citlivosti na pr …",{"slug":118081,"path":959,"title":118082,"snippet":118083},"imek-vzorce-prehled","ImeK — kompletní přehled vzorců se zdroji a intuicí","… jí stálá: u $a, b$ kladná, u $c, d$ záporná. --- ## 3. Příjem firmy **Základní téma:** \u003C\u003Cprijem-naklady-zisk>> ### Celkový příjem $$TR = P \\cdot Q$$ **Původ:** definice (3.1) — tržba jako cena krát …",{"slug":31097,"path":774,"title":775,"snippet":118085},"… ]] - **Navazující:** Funkce více proměnných - **Souvislosti:** \u003C\u003Cprijem-naklady-zisk>> (TR\u002FTC), Poptávka a nabídka (přebytky CS\u002FPS)",{"slug":35325,"path":935,"title":936,"snippet":118087},"… íry vzniká **model IS-LM**. ## 7.4 Multiplikátory pro makroekonomické proměnné V článku \u003C\u003Cprijem-naklady-zisk>> (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. **Analogické ú …",[],1777154971401]